# Properties

 Label 127.1.b.a.126.1 Level 127 Weight 1 Character 127.126 Self dual yes Analytic conductor 0.063 Analytic rank 0 Dimension 2 Projective image $$D_{5}$$ CM discriminant -127 Inner twists 2

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$127$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 127.b (of order $$2$$, degree $$1$$, minimal)

## Newform invariants

 Self dual: yes Analytic conductor: $$0.0633812566044$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ Defining polynomial: $$x^{2} - x - 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image $$D_{5}$$ Projective field Galois closure of 5.1.16129.1 Artin image $D_5$ Artin field Galois closure of 5.1.16129.1

## Embedding invariants

 Embedding label 126.1 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 127.126

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.61803 q^{2} +1.61803 q^{4} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$$ $$q-1.61803 q^{2} +1.61803 q^{4} -1.00000 q^{8} +1.00000 q^{9} +0.618034 q^{11} +0.618034 q^{13} -1.61803 q^{17} -1.61803 q^{18} -1.61803 q^{19} -1.00000 q^{22} +1.00000 q^{25} -1.00000 q^{26} -1.61803 q^{31} +1.00000 q^{32} +2.61803 q^{34} +1.61803 q^{36} -1.61803 q^{37} +2.61803 q^{38} +0.618034 q^{41} +1.00000 q^{44} +0.618034 q^{47} +1.00000 q^{49} -1.61803 q^{50} +1.00000 q^{52} -1.61803 q^{61} +2.61803 q^{62} -1.61803 q^{64} -2.61803 q^{68} -1.61803 q^{71} -1.00000 q^{72} +0.618034 q^{73} +2.61803 q^{74} -2.61803 q^{76} +0.618034 q^{79} +1.00000 q^{81} -1.00000 q^{82} -0.618034 q^{88} -1.00000 q^{94} -1.61803 q^{98} +0.618034 q^{99} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q - q^{2} + q^{4} - 2q^{8} + 2q^{9} + O(q^{10})$$ $$2q - q^{2} + q^{4} - 2q^{8} + 2q^{9} - q^{11} - q^{13} - q^{17} - q^{18} - q^{19} - 2q^{22} + 2q^{25} - 2q^{26} - q^{31} + 2q^{32} + 3q^{34} + q^{36} - q^{37} + 3q^{38} - q^{41} + 2q^{44} - q^{47} + 2q^{49} - q^{50} + 2q^{52} - q^{61} + 3q^{62} - q^{64} - 3q^{68} - q^{71} - 2q^{72} - q^{73} + 3q^{74} - 3q^{76} - q^{79} + 2q^{81} - 2q^{82} + q^{88} - 2q^{94} - q^{98} - q^{99} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/127\mathbb{Z}\right)^\times$$.

 $$n$$ $$3$$ $$\chi(n)$$ $$-1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
 Significant digits: Refresh table
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$3$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$4$$ 1.61803 1.61803
$$5$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$6$$ 0 0
$$7$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ 1.00000 1.00000
$$10$$ 0 0
$$11$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$12$$ 0 0
$$13$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 0 0
$$17$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$18$$ −1.61803 −1.61803
$$19$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ −1.00000 −1.00000
$$23$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$24$$ 0 0
$$25$$ 1.00000 1.00000
$$26$$ −1.00000 −1.00000
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$30$$ 0 0
$$31$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$32$$ 1.00000 1.00000
$$33$$ 0 0
$$34$$ 2.61803 2.61803
$$35$$ 0 0
$$36$$ 1.61803 1.61803
$$37$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$38$$ 2.61803 2.61803
$$39$$ 0 0
$$40$$ 0 0
$$41$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$44$$ 1.00000 1.00000
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$48$$ 0 0
$$49$$ 1.00000 1.00000
$$50$$ −1.61803 −1.61803
$$51$$ 0 0
$$52$$ 1.00000 1.00000
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0 0
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$62$$ 2.61803 2.61803
$$63$$ 0 0
$$64$$ −1.61803 −1.61803
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$68$$ −2.61803 −2.61803
$$69$$ 0 0
$$70$$ 0 0
$$71$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$72$$ −1.00000 −1.00000
$$73$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$74$$ 2.61803 2.61803
$$75$$ 0 0
$$76$$ −2.61803 −2.61803
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ −1.00000 −1.00000
$$83$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ −0.618034 −0.618034
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ −1.00000 −1.00000
$$95$$ 0 0
$$96$$ 0 0
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ −1.61803 −1.61803
$$99$$ 0.618034 0.618034
$$100$$ 1.61803 1.61803
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$104$$ −0.618034 −0.618034
$$105$$ 0 0
$$106$$ 0 0
$$107$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0 0
$$117$$ 0.618034 0.618034
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ −0.618034 −0.618034
$$122$$ 2.61803 2.61803
$$123$$ 0 0
$$124$$ −2.61803 −2.61803
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 1.00000 1.00000
$$128$$ 1.61803 1.61803
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 1.61803 1.61803
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 2.61803 2.61803
$$143$$ 0.381966 0.381966
$$144$$ 0 0
$$145$$ 0 0
$$146$$ −1.00000 −1.00000
$$147$$ 0 0
$$148$$ −2.61803 −2.61803
$$149$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 1.61803 1.61803
$$153$$ −1.61803 −1.61803
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$158$$ −1.00000 −1.00000
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ −1.61803 −1.61803
$$163$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$164$$ 1.00000 1.00000
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$168$$ 0 0
$$169$$ −0.618034 −0.618034
$$170$$ 0 0
$$171$$ −1.61803 −1.61803
$$172$$ 0 0
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 0 0
$$186$$ 0 0
$$187$$ −1.00000 −1.00000
$$188$$ 1.00000 1.00000
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$192$$ 0 0
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ 1.61803 1.61803
$$197$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$198$$ −1.00000 −1.00000
$$199$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$200$$ −1.00000 −1.00000
$$201$$ 0 0
$$202$$ 0 0
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ −1.00000 −1.00000
$$207$$ 0 0
$$208$$ 0 0
$$209$$ −1.00000 −1.00000
$$210$$ 0 0
$$211$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ 2.61803 2.61803
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ 0 0
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.00000 −1.00000
$$222$$ 0 0
$$223$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$224$$ 0 0
$$225$$ 1.00000 1.00000
$$226$$ −1.00000 −1.00000
$$227$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$228$$ 0 0
$$229$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 0 0
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ −1.00000 −1.00000
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 1.00000 1.00000
$$243$$ 0 0
$$244$$ −2.61803 −2.61803
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −1.00000 −1.00000
$$248$$ 1.61803 1.61803
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ −1.61803 −1.61803
$$255$$ 0 0
$$256$$ −1.00000 −1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0 0
$$262$$ −3.23607 −3.23607
$$263$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$270$$ 0 0
$$271$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0.618034 0.618034
$$276$$ 0 0
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ −1.61803 −1.61803
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$284$$ −2.61803 −2.61803
$$285$$ 0 0
$$286$$ −0.618034 −0.618034
$$287$$ 0 0
$$288$$ 1.00000 1.00000
$$289$$ 1.61803 1.61803
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.00000 1.00000
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 1.61803 1.61803
$$297$$ 0 0
$$298$$ 2.61803 2.61803
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 2.61803 2.61803
$$307$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ −1.00000 −1.00000
$$315$$ 0 0
$$316$$ 1.00000 1.00000
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 2.61803 2.61803
$$324$$ 1.61803 1.61803
$$325$$ 0.618034 0.618034
$$326$$ −3.23607 −3.23607
$$327$$ 0 0
$$328$$ −0.618034 −0.618034
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ −1.61803 −1.61803
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ 1.00000 1.00000
$$339$$ 0 0
$$340$$ 0 0
$$341$$ −1.00000 −1.00000
$$342$$ 2.61803 2.61803
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0.618034 0.618034
$$353$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 2.61803 2.61803
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.61803 1.61803
$$362$$ 0 0
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$368$$ 0 0
$$369$$ 0.618034 0.618034
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 1.61803 1.61803
$$375$$ 0 0
$$376$$ −0.618034 −0.618034
$$377$$ 0 0
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ −3.23607 −3.23607
$$383$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ 0 0
$$389$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ −1.00000 −1.00000
$$393$$ 0 0
$$394$$ −1.00000 −1.00000
$$395$$ 0 0
$$396$$ 1.00000 1.00000
$$397$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$398$$ −1.00000 −1.00000
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$402$$ 0 0
$$403$$ −1.00000 −1.00000
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 0 0
$$407$$ −1.00000 −1.00000
$$408$$ 0 0
$$409$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 1.00000 1.00000
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ 0.618034 0.618034
$$417$$ 0 0
$$418$$ 1.61803 1.61803
$$419$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$420$$ 0 0
$$421$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$422$$ −1.00000 −1.00000
$$423$$ 0.618034 0.618034
$$424$$ 0 0
$$425$$ −1.61803 −1.61803
$$426$$ 0 0
$$427$$ 0 0
$$428$$ −2.61803 −2.61803
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$432$$ 0 0
$$433$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 1.00000 1.00000
$$442$$ 1.61803 1.61803
$$443$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$450$$ −1.61803 −1.61803
$$451$$ 0.381966 0.381966
$$452$$ 1.00000 1.00000
$$453$$ 0 0
$$454$$ −3.23607 −3.23607
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$458$$ 0 0
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$462$$ 0 0
$$463$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$468$$ 1.00000 1.00000
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ −1.61803 −1.61803
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$480$$ 0 0
$$481$$ −1.00000 −1.00000
$$482$$ 0 0
$$483$$ 0 0
$$484$$ −1.00000 −1.00000
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$488$$ 1.61803 1.61803
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0 0
$$494$$ 1.61803 1.61803
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 0 0
$$502$$ −1.00000 −1.00000
$$503$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$504$$ 0 0
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 1.61803 1.61803
$$509$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0.381966 0.381966
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$522$$ 0 0
$$523$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$524$$ 3.23607 3.23607
$$525$$ 0 0
$$526$$ 2.61803 2.61803
$$527$$ 2.61803 2.61803
$$528$$ 0 0
$$529$$ 1.00000 1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0.381966 0.381966
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ 2.61803 2.61803
$$539$$ 0.618034 0.618034
$$540$$ 0 0
$$541$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$542$$ −3.23607 −3.23607
$$543$$ 0 0
$$544$$ −1.61803 −1.61803
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$548$$ 0 0
$$549$$ −1.61803 −1.61803
$$550$$ −1.00000 −1.00000
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$558$$ 2.61803 2.61803
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 1.61803 1.61803
$$569$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0.618034 0.618034
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ −1.61803 −1.61803
$$577$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$578$$ −2.61803 −2.61803
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ −0.618034 −0.618034
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$588$$ 0 0
$$589$$ 2.61803 2.61803
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −2.61803 −2.61803
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$608$$ −1.61803 −1.61803
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0.381966 0.381966
$$612$$ −2.61803 −2.61803
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 0 0
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ 0 0
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 1.00000 1.00000
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 1.00000 1.00000
$$629$$ 2.61803 2.61803
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ −0.618034 −0.618034
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0.618034 0.618034
$$638$$ 0 0
$$639$$ −1.61803 −1.61803
$$640$$ 0 0
$$641$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$642$$ 0 0
$$643$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −4.23607 −4.23607
$$647$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$648$$ −1.00000 −1.00000
$$649$$ 0 0
$$650$$ −1.00000 −1.00000
$$651$$ 0 0
$$652$$ 3.23607 3.23607
$$653$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0.618034 0.618034
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 2.61803 2.61803
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ −1.00000 −1.00000
$$672$$ 0 0
$$673$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ −1.00000 −1.00000
$$677$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 1.61803 1.61803
$$683$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$684$$ −2.61803 −2.61803
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ −1.00000 −1.00000
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$702$$ 0 0
$$703$$ 2.61803 2.61803
$$704$$ −1.00000 −1.00000
$$705$$ 0 0
$$706$$ 2.61803 2.61803
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$710$$ 0 0
$$711$$ 0.618034 0.618034
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ −2.61803 −2.61803
$$717$$ 0 0
$$718$$ 0 0
$$719$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ −2.61803 −2.61803
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$728$$ 0 0
$$729$$ 1.00000 1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$734$$ 2.61803 2.61803
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ −1.00000 −1.00000
$$739$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ 0 0
$$748$$ −1.61803 −1.61803
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ 0 0
$$757$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 3.23607 3.23607
$$765$$ 0 0
$$766$$ −3.23607 −3.23607
$$767$$ 0 0
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$774$$ 0 0
$$775$$ −1.61803 −1.61803
$$776$$ 0 0
$$777$$ 0 0
$$778$$ −1.00000 −1.00000
$$779$$ −1.00000 −1.00000
$$780$$ 0 0
$$781$$ −1.00000 −1.00000
$$782$$ 0 0
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$788$$ 1.00000 1.00000
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ −0.618034 −0.618034
$$793$$ −1.00000 −1.00000
$$794$$ 2.61803 2.61803
$$795$$ 0 0
$$796$$ 1.00000 1.00000
$$797$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$798$$ 0 0
$$799$$ −1.00000 −1.00000
$$800$$ 1.00000 1.00000
$$801$$ 0 0
$$802$$ 0 0
$$803$$ 0.381966 0.381966
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 1.61803 1.61803
$$807$$ 0 0
$$808$$ 0 0
$$809$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$810$$ 0 0
$$811$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 1.61803 1.61803
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0 0
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$822$$ 0 0
$$823$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$824$$ −0.618034 −0.618034
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$828$$ 0 0
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ −1.00000 −1.00000
$$833$$ −1.61803 −1.61803
$$834$$ 0 0
$$835$$ 0 0
$$836$$ −1.61803 −1.61803
$$837$$ 0 0
$$838$$ 2.61803 2.61803
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ 1.00000 1.00000
$$842$$ 0 0
$$843$$ 0 0
$$844$$ 1.00000 1.00000
$$845$$ 0 0
$$846$$ −1.00000 −1.00000
$$847$$ 0 0
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 2.61803 2.61803
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 1.61803 1.61803
$$857$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ −1.00000 −1.00000
$$863$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 2.61803 2.61803
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0.381966 0.381966
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ −1.61803 −1.61803
$$883$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$884$$ −1.61803 −1.61803
$$885$$ 0 0
$$886$$ 2.61803 2.61803
$$887$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0.618034 0.618034
$$892$$ 0 0
$$893$$ −1.00000 −1.00000
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ −1.00000 −1.00000
$$899$$ 0 0
$$900$$ 1.61803 1.61803
$$901$$ 0 0
$$902$$ −0.618034 −0.618034
$$903$$ 0 0
$$904$$ −0.618034 −0.618034
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$908$$ 3.23607 3.23607
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −1.00000 −1.00000
$$915$$ 0 0
$$916$$ 0 0
$$917$$ 0 0
$$918$$ 0 0
$$919$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 0 0
$$923$$ −1.00000 −1.00000
$$924$$ 0 0
$$925$$ −1.61803 −1.61803
$$926$$ 2.61803 2.61803
$$927$$ 0.618034 0.618034
$$928$$ 0 0
$$929$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$930$$ 0 0
$$931$$ −1.61803 −1.61803
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ −0.618034 −0.618034
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$942$$ 0 0
$$943$$ 0 0
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$948$$ 0 0
$$949$$ 0.381966 0.381966
$$950$$ 2.61803 2.61803
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ −1.00000 −1.00000
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.61803 1.61803
$$962$$ 1.61803 1.61803
$$963$$ −1.61803 −1.61803
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$968$$ 0.618034 0.618034
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$972$$ 0 0
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ 0 0
$$983$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0 0
$$987$$ 0 0
$$988$$ −1.61803 −1.61803
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ −1.61803 −1.61803
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$998$$ 0 0
$$999$$ 0 0
Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000

## Twists

By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 127.1.b.a.126.1 2
3.2 odd 2 1143.1.d.b.253.2 2
4.3 odd 2 2032.1.b.a.1777.1 2
5.2 odd 4 3175.1.c.b.3174.1 4
5.3 odd 4 3175.1.c.b.3174.4 4
5.4 even 2 3175.1.d.d.126.2 2
127.126 odd 2 CM 127.1.b.a.126.1 2
381.380 even 2 1143.1.d.b.253.2 2
508.507 even 2 2032.1.b.a.1777.1 2
635.253 even 4 3175.1.c.b.3174.4 4
635.507 even 4 3175.1.c.b.3174.1 4
635.634 odd 2 3175.1.d.d.126.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
127.1.b.a.126.1 2 1.1 even 1 trivial
127.1.b.a.126.1 2 127.126 odd 2 CM
1143.1.d.b.253.2 2 3.2 odd 2
1143.1.d.b.253.2 2 381.380 even 2
2032.1.b.a.1777.1 2 4.3 odd 2
2032.1.b.a.1777.1 2 508.507 even 2
3175.1.c.b.3174.1 4 5.2 odd 4
3175.1.c.b.3174.1 4 635.507 even 4
3175.1.c.b.3174.4 4 5.3 odd 4
3175.1.c.b.3174.4 4 635.253 even 4
3175.1.d.d.126.2 2 5.4 even 2
3175.1.d.d.126.2 2 635.634 odd 2
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