# Properties

 Label 2575.1.c.b.2574.3 Level 2575 Weight 1 Character 2575.2574 Analytic conductor 1.285 Analytic rank 0 Dimension 4 Projective image $$D_{5}$$ CM discriminant -103 Inner twists 4

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2575 = 5^{2} \cdot 103$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2575.c (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.28509240753$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3 x^{2} + 1$$ Coefficient ring: $$\Z[a_1, a_2]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 103) Projective image $$D_{5}$$ Projective field Galois closure of 5.1.10609.1 Artin image $C_4\times D_5$ Artin field Galois closure of $$\mathbb{Q}[x]/(x^{20} - \cdots)$$

## Embedding invariants

 Embedding label 2574.3 Root $$1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 2575.2574 Dual form 2575.1.c.b.2574.2

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+0.618034i q^{2} +0.618034 q^{4} -1.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q+0.618034i q^{2} +0.618034 q^{4} -1.61803i q^{7} +1.00000i q^{8} -1.00000 q^{9} -0.618034i q^{13} +1.00000 q^{14} -1.61803i q^{17} -0.618034i q^{18} -0.618034 q^{19} -0.618034i q^{23} +0.381966 q^{26} -1.00000i q^{28} +1.61803 q^{29} +1.00000i q^{32} +1.00000 q^{34} -0.618034 q^{36} -0.381966i q^{38} +0.618034 q^{41} +0.381966 q^{46} -1.61803 q^{49} -0.381966i q^{52} +1.61803 q^{56} +1.00000i q^{58} +1.61803 q^{59} -1.61803 q^{61} +1.61803i q^{63} -0.618034 q^{64} -1.00000i q^{68} -1.00000i q^{72} -0.381966 q^{76} -0.618034 q^{79} +1.00000 q^{81} +0.381966i q^{82} +1.61803i q^{83} -1.00000 q^{91} -0.381966i q^{92} -1.61803i q^{97} -1.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q - 2q^{4} - 4q^{9} + O(q^{10})$$ $$4q - 2q^{4} - 4q^{9} + 4q^{14} + 2q^{19} + 6q^{26} + 2q^{29} + 4q^{34} + 2q^{36} - 2q^{41} + 6q^{46} - 2q^{49} + 2q^{56} + 2q^{59} - 2q^{61} + 2q^{64} - 6q^{76} + 2q^{79} + 4q^{81} - 4q^{91} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2575\mathbb{Z}\right)^\times$$.

 $$n$$ $$726$$ $$1752$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ 0.618034 0.618034
$$5$$ 0 0
$$6$$ 0 0
$$7$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$8$$ 1.00000i 1.00000i
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$14$$ 1.00000 1.00000
$$15$$ 0 0
$$16$$ 0 0
$$17$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$18$$ − 0.618034i − 0.618034i
$$19$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ 0.381966 0.381966
$$27$$ 0 0
$$28$$ − 1.00000i − 1.00000i
$$29$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ 1.00000i 1.00000i
$$33$$ 0 0
$$34$$ 1.00000 1.00000
$$35$$ 0 0
$$36$$ −0.618034 −0.618034
$$37$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$38$$ − 0.381966i − 0.381966i
$$39$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0.381966 0.381966
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −1.61803 −1.61803
$$50$$ 0 0
$$51$$ 0 0
$$52$$ − 0.381966i − 0.381966i
$$53$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 1.61803 1.61803
$$57$$ 0 0
$$58$$ 1.00000i 1.00000i
$$59$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$60$$ 0 0
$$61$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$62$$ 0 0
$$63$$ 1.61803i 1.61803i
$$64$$ −0.618034 −0.618034
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ − 1.00000i − 1.00000i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ − 1.00000i − 1.00000i
$$73$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ −0.381966 −0.381966
$$77$$ 0 0
$$78$$ 0 0
$$79$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ 0.381966i 0.381966i
$$83$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$90$$ 0 0
$$91$$ −1.00000 −1.00000
$$92$$ − 0.381966i − 0.381966i
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$98$$ − 1.00000i − 1.00000i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$102$$ 0 0
$$103$$ − 1.00000i − 1.00000i
$$104$$ 0.618034 0.618034
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 1.00000 1.00000
$$117$$ 0.618034i 0.618034i
$$118$$ 1.00000i 1.00000i
$$119$$ −2.61803 −2.61803
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ − 1.00000i − 1.00000i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ −1.00000 −1.00000
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 0.618034i 0.618034i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$132$$ 0 0
$$133$$ 1.00000i 1.00000i
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 1.61803 1.61803
$$137$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$138$$ 0 0
$$139$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 0 0
$$145$$ 0 0
$$146$$ 0 0
$$147$$ 0 0
$$148$$ 0 0
$$149$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ − 0.618034i − 0.618034i
$$153$$ 1.61803i 1.61803i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$158$$ − 0.381966i − 0.381966i
$$159$$ 0 0
$$160$$ 0 0
$$161$$ −1.00000 −1.00000
$$162$$ 0.618034i 0.618034i
$$163$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$164$$ 0.381966 0.381966
$$165$$ 0 0
$$166$$ −1.00000 −1.00000
$$167$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ 0.618034 0.618034
$$170$$ 0 0
$$171$$ 0.618034 0.618034
$$172$$ 0 0
$$173$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0 0
$$179$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$180$$ 0 0
$$181$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$182$$ − 0.618034i − 0.618034i
$$183$$ 0 0
$$184$$ 0.618034 0.618034
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 0 0
$$189$$ 0 0
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 0 0
$$193$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$194$$ 1.00000 1.00000
$$195$$ 0 0
$$196$$ −1.00000 −1.00000
$$197$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ 0 0
$$203$$ − 2.61803i − 2.61803i
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0.618034 0.618034
$$207$$ 0.618034i 0.618034i
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −1.23607 −1.23607
$$215$$ 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
$$223$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$224$$ 1.61803 1.61803
$$225$$ 0 0
$$226$$ 0 0
$$227$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$228$$ 0 0
$$229$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1.61803i 1.61803i
$$233$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$234$$ −0.381966 −0.381966
$$235$$ 0 0
$$236$$ 1.00000 1.00000
$$237$$ 0 0
$$238$$ − 1.61803i − 1.61803i
$$239$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$240$$ 0 0
$$241$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$242$$ 0.618034i 0.618034i
$$243$$ 0 0
$$244$$ −1.00000 −1.00000
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0.381966i 0.381966i
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 1.00000i 1.00000i
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ −1.00000 −1.00000
$$257$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −1.61803 −1.61803
$$262$$ 0.381966i 0.381966i
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ −0.618034 −0.618034
$$267$$ 0 0
$$268$$ 0 0
$$269$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ −0.381966 −0.381966
$$275$$ 0 0
$$276$$ 0 0
$$277$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$278$$ − 1.23607i − 1.23607i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ − 1.00000i − 1.00000i
$$288$$ − 1.00000i − 1.00000i
$$289$$ −1.61803 −1.61803
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ − 0.381966i − 0.381966i
$$299$$ −0.381966 −0.381966
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ −1.00000 −1.00000
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$312$$ 0 0
$$313$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ −0.381966 −0.381966
$$317$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ − 0.618034i − 0.618034i
$$323$$ 1.00000i 1.00000i
$$324$$ 0.618034 0.618034
$$325$$ 0 0
$$326$$ −1.00000 −1.00000
$$327$$ 0 0
$$328$$ 0.618034i 0.618034i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 1.00000i 1.00000i
$$333$$ 0 0
$$334$$ −1.23607 −1.23607
$$335$$ 0 0
$$336$$ 0 0
$$337$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$338$$ 0.381966i 0.381966i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0.381966i 0.381966i
$$343$$ 1.00000i 1.00000i
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0 0
$$347$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$348$$ 0 0
$$349$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0 0
$$357$$ 0 0
$$358$$ 1.00000i 1.00000i
$$359$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ −0.618034 −0.618034
$$362$$ 0 0
$$363$$ 0 0
$$364$$ −0.618034 −0.618034
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$368$$ 0 0
$$369$$ −0.618034 −0.618034
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ 0 0
$$377$$ − 1.00000i − 1.00000i
$$378$$ 0 0
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 0 0
$$382$$ 0 0
$$383$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 0 0
$$388$$ − 1.00000i − 1.00000i
$$389$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$390$$ 0 0
$$391$$ −1.00000 −1.00000
$$392$$ − 1.61803i − 1.61803i
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$402$$ 0 0
$$403$$ 0 0
$$404$$ 0 0
$$405$$ 0 0
$$406$$ 1.61803 1.61803
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ − 0.618034i − 0.618034i
$$413$$ − 2.61803i − 2.61803i
$$414$$ −0.381966 −0.381966
$$415$$ 0 0
$$416$$ 0.618034 0.618034
$$417$$ 0 0
$$418$$ 0 0
$$419$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$420$$ 0 0
$$421$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 2.61803i 2.61803i
$$428$$ 1.23607i 1.23607i
$$429$$ 0 0
$$430$$ 0 0
$$431$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$432$$ 0 0
$$433$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ 0 0
$$437$$ 0.381966i 0.381966i
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 1.61803 1.61803
$$442$$ − 0.618034i − 0.618034i
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0.381966 0.381966
$$447$$ 0 0
$$448$$ 1.00000i 1.00000i
$$449$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$458$$ 1.00000i 1.00000i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ 0 0
$$465$$ 0 0
$$466$$ 0 0
$$467$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$468$$ 0.381966i 0.381966i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 1.61803i 1.61803i
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ −1.61803 −1.61803
$$477$$ 0 0
$$478$$ 1.00000i 1.00000i
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ 0 0
$$483$$ 0 0
$$484$$ 0.618034 0.618034
$$485$$ 0 0
$$486$$ 0 0
$$487$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$488$$ − 1.61803i − 1.61803i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$492$$ 0 0
$$493$$ − 2.61803i − 2.61803i
$$494$$ −0.236068 −0.236068
$$495$$ 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
$$502$$ 0 0
$$503$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$504$$ −1.61803 −1.61803
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 0 0
$$508$$ 0 0
$$509$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ 0 0
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$522$$ − 1.00000i − 1.00000i
$$523$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$524$$ 0.381966 0.381966
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ 0.618034 0.618034
$$530$$ 0 0
$$531$$ −1.61803 −1.61803
$$532$$ 0.618034i 0.618034i
$$533$$ − 0.381966i − 0.381966i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ − 0.381966i − 0.381966i
$$539$$ 0 0
$$540$$ 0 0
$$541$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$542$$ 0 0
$$543$$ 0 0
$$544$$ 1.61803 1.61803
$$545$$ 0 0
$$546$$ 0 0
$$547$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$548$$ 0.381966i 0.381966i
$$549$$ 1.61803 1.61803
$$550$$ 0 0
$$551$$ −1.00000 −1.00000
$$552$$ 0 0
$$553$$ 1.00000i 1.00000i
$$554$$ 0 0
$$555$$ 0 0
$$556$$ −1.23607 −1.23607
$$557$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 0 0
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ − 1.61803i − 1.61803i
$$568$$ 0 0
$$569$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$570$$ 0 0
$$571$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0.618034 0.618034
$$575$$ 0 0
$$576$$ 0.618034 0.618034
$$577$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$578$$ − 1.00000i − 1.00000i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 2.61803 2.61803
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −0.381966 −0.381966
$$597$$ 0 0
$$598$$ − 0.236068i − 0.236068i
$$599$$ 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
$$607$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$608$$ − 0.618034i − 0.618034i
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 1.00000i 1.00000i
$$613$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$618$$ 0 0
$$619$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$620$$ 0 0
$$621$$ 0 0
$$622$$ − 1.00000i − 1.00000i
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0.381966 0.381966
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$632$$ − 0.618034i − 0.618034i
$$633$$ 0 0
$$634$$ 1.00000 1.00000
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.00000i 1.00000i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$642$$ 0 0
$$643$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$644$$ −0.618034 −0.618034
$$645$$ 0 0
$$646$$ −0.618034 −0.618034
$$647$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$648$$ 1.00000i 1.00000i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 1.00000i 1.00000i
$$653$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ 0 0
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$660$$ 0 0
$$661$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ −1.61803 −1.61803
$$665$$ 0 0
$$666$$ 0 0
$$667$$ − 1.00000i − 1.00000i
$$668$$ 1.23607i 1.23607i
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$674$$ −0.381966 −0.381966
$$675$$ 0 0
$$676$$ 0.381966 0.381966
$$677$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$678$$ 0 0
$$679$$ −2.61803 −2.61803
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0.381966 0.381966
$$685$$ 0 0
$$686$$ −0.618034 −0.618034
$$687$$ 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
$$694$$ −0.381966 −0.381966
$$695$$ 0 0
$$696$$ 0 0
$$697$$ − 1.00000i − 1.00000i
$$698$$ 0 0
$$699$$ 0 0
$$700$$ 0 0
$$701$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 0 0
$$707$$ 0 0
$$708$$ 0 0
$$709$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$710$$ 0 0
$$711$$ 0.618034 0.618034
$$712$$ 0 0
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 1.00000 1.00000
$$717$$ 0 0
$$718$$ − 1.23607i − 1.23607i
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ −1.61803 −1.61803
$$722$$ − 0.381966i − 0.381966i
$$723$$ 0 0
$$724$$ 0 0
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ − 1.00000i − 1.00000i
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ −0.381966 −0.381966
$$735$$ 0 0
$$736$$ 0.618034 0.618034
$$737$$ 0 0
$$738$$ − 0.381966i − 0.381966i
$$739$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ −1.00000 −1.00000
$$747$$ − 1.61803i − 1.61803i
$$748$$ 0 0
$$749$$ 3.23607 3.23607
$$750$$ 0 0
$$751$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 0.618034 0.618034
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ − 1.00000i − 1.00000i
$$768$$ 0 0
$$769$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 1.61803 1.61803
$$777$$ 0 0
$$778$$ 0 0
$$779$$ −0.381966 −0.381966
$$780$$ 0 0
$$781$$ 0 0
$$782$$ − 0.618034i − 0.618034i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$788$$ 0 0
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 1.00000i 1.00000i
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0 0
$$802$$ − 1.00000i − 1.00000i
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0 0
$$809$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ − 1.61803i − 1.61803i
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 1.00000i 1.00000i
$$819$$ 1.00000 1.00000
$$820$$ 0 0
$$821$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 1.00000 1.00000
$$825$$ 0 0
$$826$$ 1.61803 1.61803
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0.381966i 0.381966i
$$829$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0.381966i 0.381966i
$$833$$ 2.61803i 2.61803i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ − 0.381966i − 0.381966i
$$839$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$840$$ 0 0
$$841$$ 1.61803 1.61803
$$842$$ 1.23607i 1.23607i
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ − 1.61803i − 1.61803i
$$848$$ 0 0
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$854$$ −1.61803 −1.61803
$$855$$ 0 0
$$856$$ −2.00000 −2.00000
$$857$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ − 1.00000i − 1.00000i
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 0 0
$$873$$ 1.61803i 1.61803i
$$874$$ −0.236068 −0.236068
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$882$$ 1.00000i 1.00000i
$$883$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$884$$ −0.618034 −0.618034
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ − 0.381966i − 0.381966i
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 1.00000 1.00000
$$897$$ 0 0
$$898$$ 0 0
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ 0 0
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$908$$ 0 0
$$909$$ 0 0
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 1.00000 1.00000
$$917$$ − 1.00000i − 1.00000i
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ 1.23607i 1.23607i
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 1.00000i 1.00000i
$$928$$ 1.61803i 1.61803i
$$929$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$930$$ 0 0
$$931$$ 1.00000 1.00000
$$932$$ 0 0
$$933$$ 0 0
$$934$$ −0.381966 −0.381966
$$935$$ 0 0
$$936$$ −0.618034 −0.618034
$$937$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$938$$ 0 0
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$942$$ 0 0
$$943$$ − 0.381966i − 0.381966i
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ − 2.61803i − 2.61803i
$$953$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 1.00000 1.00000
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 1.00000 1.00000
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ 0 0
$$963$$ − 2.00000i − 2.00000i
$$964$$ 0 0
$$965$$ 0 0
$$966$$ 0 0
$$967$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$968$$ 1.00000i 1.00000i
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ 0 0
$$973$$ 3.23607i 3.23607i
$$974$$ 0 0
$$975$$ 0 0
$$976$$ 0 0
$$977$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ 0 0
$$982$$ − 1.00000i − 1.00000i
$$983$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 1.61803 1.61803
$$987$$ 0 0
$$988$$ 0.236068i 0.236068i
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$998$$ 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 2575.1.c.b.2574.3 4
5.2 odd 4 2575.1.d.d.926.1 2
5.3 odd 4 103.1.b.a.102.2 2
5.4 even 2 inner 2575.1.c.b.2574.2 4
15.8 even 4 927.1.d.b.514.1 2
20.3 even 4 1648.1.c.a.1441.2 2
103.102 odd 2 CM 2575.1.c.b.2574.3 4
515.102 even 4 2575.1.d.d.926.1 2
515.308 even 4 103.1.b.a.102.2 2
515.514 odd 2 inner 2575.1.c.b.2574.2 4
1545.308 odd 4 927.1.d.b.514.1 2
2060.823 odd 4 1648.1.c.a.1441.2 2

By twisted newform
Twist Min Dim Char Parity Ord Type
103.1.b.a.102.2 2 5.3 odd 4
103.1.b.a.102.2 2 515.308 even 4
927.1.d.b.514.1 2 15.8 even 4
927.1.d.b.514.1 2 1545.308 odd 4
1648.1.c.a.1441.2 2 20.3 even 4
1648.1.c.a.1441.2 2 2060.823 odd 4
2575.1.c.b.2574.2 4 5.4 even 2 inner
2575.1.c.b.2574.2 4 515.514 odd 2 inner
2575.1.c.b.2574.3 4 1.1 even 1 trivial
2575.1.c.b.2574.3 4 103.102 odd 2 CM
2575.1.d.d.926.1 2 5.2 odd 4
2575.1.d.d.926.1 2 515.102 even 4