# Properties

 Label 2500.1.d.a.2499.1 Level $2500$ Weight $1$ Character 2500.2499 Analytic conductor $1.248$ Analytic rank $0$ Dimension $4$ Projective image $D_{5}$ CM discriminant -4 Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2500 = 2^{2} \cdot 5^{4}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 2500.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$1.24766253158$$ Analytic rank: $$0$$ Dimension: $$4$$ Coefficient field: $$\Q(i, \sqrt{5})$$ Defining polynomial: $$x^{4} + 3x^{2} + 1$$ x^4 + 3*x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 100) Projective image: $$D_{5}$$ Projective field: Galois closure of 5.1.6250000.1

## Embedding invariants

 Embedding label 2499.1 Root $$1.61803i$$ of defining polynomial Character $$\chi$$ $$=$$ 2500.2499 Dual form 2500.1.d.a.2499.4

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000i q^{2} -1.00000 q^{4} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$$ $$q-1.00000i q^{2} -1.00000 q^{4} +1.00000i q^{8} -1.00000 q^{9} -1.61803i q^{13} +1.00000 q^{16} -0.618034i q^{17} +1.00000i q^{18} -1.61803 q^{26} -0.618034 q^{29} -1.00000i q^{32} -0.618034 q^{34} +1.00000 q^{36} -0.618034i q^{37} -1.61803 q^{41} -1.00000 q^{49} +1.61803i q^{52} -1.61803i q^{53} +0.618034i q^{58} -1.61803 q^{61} -1.00000 q^{64} +0.618034i q^{68} -1.00000i q^{72} -1.61803i q^{73} -0.618034 q^{74} +1.00000 q^{81} +1.61803i q^{82} -0.618034 q^{89} -0.618034i q^{97} +1.00000i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4 q - 4 q^{4} - 4 q^{9}+O(q^{10})$$ 4 * q - 4 * q^4 - 4 * q^9 $$4 q - 4 q^{4} - 4 q^{9} + 4 q^{16} - 2 q^{26} + 2 q^{29} + 2 q^{34} + 4 q^{36} - 2 q^{41} - 4 q^{49} - 2 q^{61} - 4 q^{64} + 2 q^{74} + 4 q^{81} + 2 q^{89}+O(q^{100})$$ 4 * q - 4 * q^4 - 4 * q^9 + 4 * q^16 - 2 * q^26 + 2 * q^29 + 2 * q^34 + 4 * q^36 - 2 * q^41 - 4 * q^49 - 2 * q^61 - 4 * q^64 + 2 * q^74 + 4 * q^81 + 2 * q^89

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2500\mathbb{Z}\right)^\times$$.

 $$n$$ $$1251$$ $$1877$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ − 1.00000i − 1.00000i
$$3$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$4$$ −1.00000 −1.00000
$$5$$ 0 0
$$6$$ 0 0
$$7$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$8$$ 1.00000i 1.00000i
$$9$$ −1.00000 −1.00000
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 0 0
$$13$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$18$$ 1.00000i 1.00000i
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ 0 0
$$22$$ 0 0
$$23$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$24$$ 0 0
$$25$$ 0 0
$$26$$ −1.61803 −1.61803
$$27$$ 0 0
$$28$$ 0 0
$$29$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ − 1.00000i − 1.00000i
$$33$$ 0 0
$$34$$ −0.618034 −0.618034
$$35$$ 0 0
$$36$$ 1.00000 1.00000
$$37$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$42$$ 0 0
$$43$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0 0
$$47$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$48$$ 0 0
$$49$$ −1.00000 −1.00000
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 1.61803i 1.61803i
$$53$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$54$$ 0 0
$$55$$ 0 0
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 0.618034i 0.618034i
$$59$$ 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 $$0.800000\pi$$
$$62$$ 0 0
$$63$$ 0 0
$$64$$ −1.00000 −1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$68$$ 0.618034i 0.618034i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ − 1.00000i − 1.00000i
$$73$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$74$$ −0.618034 −0.618034
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 1.00000 1.00000
$$82$$ 1.61803i 1.61803i
$$83$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$84$$ 0 0
$$85$$ 0 0
$$86$$ 0 0
$$87$$ 0 0
$$88$$ 0 0
$$89$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ 0 0
$$93$$ 0 0
$$94$$ 0 0
$$95$$ 0 0
$$96$$ 0 0
$$97$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$98$$ 1.00000i 1.00000i
$$99$$ 0 0
$$100$$ 0 0
$$101$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$102$$ 0 0
$$103$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$104$$ 1.61803 1.61803
$$105$$ 0 0
$$106$$ −1.61803 −1.61803
$$107$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$108$$ 0 0
$$109$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ 0.618034 0.618034
$$117$$ 1.61803i 1.61803i
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ 1.61803i 1.61803i
$$123$$ 0 0
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 0 0
$$127$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$128$$ 1.00000i 1.00000i
$$129$$ 0 0
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 0 0
$$135$$ 0 0
$$136$$ 0.618034 0.618034
$$137$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$138$$ 0 0
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 0 0
$$143$$ 0 0
$$144$$ −1.00000 −1.00000
$$145$$ 0 0
$$146$$ −1.61803 −1.61803
$$147$$ 0 0
$$148$$ 0.618034i 0.618034i
$$149$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0.618034i 0.618034i
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0 0
$$162$$ − 1.00000i − 1.00000i
$$163$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$164$$ 1.61803 1.61803
$$165$$ 0 0
$$166$$ 0 0
$$167$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$168$$ 0 0
$$169$$ −1.61803 −1.61803
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 0 0
$$173$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ 0.618034i 0.618034i
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ 0 0
$$185$$ 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
$$193$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$194$$ −0.618034 −0.618034
$$195$$ 0 0
$$196$$ 1.00000 1.00000
$$197$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ 0 0
$$202$$ − 0.618034i − 0.618034i
$$203$$ 0 0
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 0 0
$$207$$ 0 0
$$208$$ − 1.61803i − 1.61803i
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 1.61803i 1.61803i
$$213$$ 0 0
$$214$$ 0 0
$$215$$ 0 0
$$216$$ 0 0
$$217$$ 0 0
$$218$$ − 1.61803i − 1.61803i
$$219$$ 0 0
$$220$$ 0 0
$$221$$ −1.00000 −1.00000
$$222$$ 0 0
$$223$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 0.618034 0.618034
$$227$$ 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
$$232$$ − 0.618034i − 0.618034i
$$233$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$234$$ 1.61803 1.61803
$$235$$ 0 0
$$236$$ 0 0
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$240$$ 0 0
$$241$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$242$$ − 1.00000i − 1.00000i
$$243$$ 0 0
$$244$$ 1.61803 1.61803
$$245$$ 0 0
$$246$$ 0 0
$$247$$ 0 0
$$248$$ 0 0
$$249$$ 0 0
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ 0 0
$$253$$ 0 0
$$254$$ 0 0
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ 0 0
$$261$$ 0.618034 0.618034
$$262$$ 0 0
$$263$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 0 0
$$268$$ 0 0
$$269$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ − 0.618034i − 0.618034i
$$273$$ 0 0
$$274$$ 1.61803 1.61803
$$275$$ 0 0
$$276$$ 0 0
$$277$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$282$$ 0 0
$$283$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 0 0
$$288$$ 1.00000i 1.00000i
$$289$$ 0.618034 0.618034
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 1.61803i 1.61803i
$$293$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$294$$ 0 0
$$295$$ 0 0
$$296$$ 0.618034 0.618034
$$297$$ 0 0
$$298$$ − 1.61803i − 1.61803i
$$299$$ 0 0
$$300$$ 0 0
$$301$$ 0 0
$$302$$ 0 0
$$303$$ 0 0
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0.618034 0.618034
$$307$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$314$$ −0.618034 −0.618034
$$315$$ 0 0
$$316$$ 0 0
$$317$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 0 0
$$322$$ 0 0
$$323$$ 0 0
$$324$$ −1.00000 −1.00000
$$325$$ 0 0
$$326$$ 0 0
$$327$$ 0 0
$$328$$ − 1.61803i − 1.61803i
$$329$$ 0 0
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ 0 0
$$333$$ 0.618034i 0.618034i
$$334$$ 0 0
$$335$$ 0 0
$$336$$ 0 0
$$337$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$338$$ 1.61803i 1.61803i
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 0 0
$$344$$ 0 0
$$345$$ 0 0
$$346$$ 0.618034 0.618034
$$347$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$348$$ 0 0
$$349$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$354$$ 0 0
$$355$$ 0 0
$$356$$ 0.618034 0.618034
$$357$$ 0 0
$$358$$ 0 0
$$359$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$360$$ 0 0
$$361$$ 1.00000 1.00000
$$362$$ − 0.618034i − 0.618034i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 0 0
$$366$$ 0 0
$$367$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$368$$ 0 0
$$369$$ 1.61803 1.61803
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$374$$ 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
$$386$$ −1.61803 −1.61803
$$387$$ 0 0
$$388$$ 0.618034i 0.618034i
$$389$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ − 1.00000i − 1.00000i
$$393$$ 0 0
$$394$$ 1.61803 1.61803
$$395$$ 0 0
$$396$$ 0 0
$$397$$ − 2.00000i − 2.00000i 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
$$404$$ −0.618034 −0.618034
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 0 0
$$408$$ 0 0
$$409$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ 0 0
$$413$$ 0 0
$$414$$ 0 0
$$415$$ 0 0
$$416$$ −1.61803 −1.61803
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$422$$ 0 0
$$423$$ 0 0
$$424$$ 1.61803 1.61803
$$425$$ 0 0
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 0 0
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 0 0
$$433$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −1.61803 −1.61803
$$437$$ 0 0
$$438$$ 0 0
$$439$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$440$$ 0 0
$$441$$ 1.00000 1.00000
$$442$$ 1.00000i 1.00000i
$$443$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ 0 0
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ − 0.618034i − 0.618034i
$$453$$ 0 0
$$454$$ 0 0
$$455$$ 0 0
$$456$$ 0 0
$$457$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$458$$ − 1.61803i − 1.61803i
$$459$$ 0 0
$$460$$ 0 0
$$461$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$462$$ 0 0
$$463$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$464$$ −0.618034 −0.618034
$$465$$ 0 0
$$466$$ −1.61803 −1.61803
$$467$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$468$$ − 1.61803i − 1.61803i
$$469$$ 0 0
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 1.61803i 1.61803i
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ −1.00000 −1.00000
$$482$$ − 0.618034i − 0.618034i
$$483$$ 0 0
$$484$$ −1.00000 −1.00000
$$485$$ 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
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ 0 0
$$493$$ 0.381966i 0.381966i
$$494$$ 0 0
$$495$$ 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
$$503$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$504$$ 0 0
$$505$$ 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
$$512$$ − 1.00000i − 1.00000i
$$513$$ 0 0
$$514$$ 1.61803 1.61803
$$515$$ 0 0
$$516$$ 0 0
$$517$$ 0 0
$$518$$ 0 0
$$519$$ 0 0
$$520$$ 0 0
$$521$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$522$$ − 0.618034i − 0.618034i
$$523$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ 0 0
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −1.00000 −1.00000
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 2.61803i 2.61803i
$$534$$ 0 0
$$535$$ 0 0
$$536$$ 0 0
$$537$$ 0 0
$$538$$ − 1.61803i − 1.61803i
$$539$$ 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
$$544$$ −0.618034 −0.618034
$$545$$ 0 0
$$546$$ 0 0
$$547$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$548$$ − 1.61803i − 1.61803i
$$549$$ 1.61803 1.61803
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 0 0
$$553$$ 0 0
$$554$$ −0.618034 −0.618034
$$555$$ 0 0
$$556$$ 0 0
$$557$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ 1.61803i 1.61803i
$$563$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$564$$ 0 0
$$565$$ 0 0
$$566$$ 0 0
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 0 0
$$576$$ 1.00000 1.00000
$$577$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$578$$ − 0.618034i − 0.618034i
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0 0
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 1.61803 1.61803
$$585$$ 0 0
$$586$$ 0.618034 0.618034
$$587$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$588$$ 0 0
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ − 0.618034i − 0.618034i
$$593$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ −1.61803 −1.61803
$$597$$ 0 0
$$598$$ 0 0
$$599$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$600$$ 0 0
$$601$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ 0 0
$$605$$ 0 0
$$606$$ 0 0
$$607$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$608$$ 0 0
$$609$$ 0 0
$$610$$ 0 0
$$611$$ 0 0
$$612$$ − 0.618034i − 0.618034i
$$613$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$614$$ 0 0
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$618$$ 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
$$625$$ 0 0
$$626$$ 2.00000 2.00000
$$627$$ 0 0
$$628$$ 0.618034i 0.618034i
$$629$$ −0.381966 −0.381966
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ −2.00000 −2.00000
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 1.61803i 1.61803i
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$642$$ 0 0
$$643$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ 0 0
$$647$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$648$$ 1.00000i 1.00000i
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ 0 0
$$653$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$654$$ 0 0
$$655$$ 0 0
$$656$$ −1.61803 −1.61803
$$657$$ 1.61803i 1.61803i
$$658$$ 0 0
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0 0
$$665$$ 0 0
$$666$$ 0.618034 0.618034
$$667$$ 0 0
$$668$$ 0 0
$$669$$ 0 0
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 0 0
$$673$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$674$$ −2.00000 −2.00000
$$675$$ 0 0
$$676$$ 1.61803 1.61803
$$677$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ 0 0
$$682$$ 0 0
$$683$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ 0 0
$$687$$ 0 0
$$688$$ 0 0
$$689$$ −2.61803 −2.61803
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ − 0.618034i − 0.618034i
$$693$$ 0 0
$$694$$ 0 0
$$695$$ 0 0
$$696$$ 0 0
$$697$$ 1.00000i 1.00000i
$$698$$ 0.618034i 0.618034i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$702$$ 0 0
$$703$$ 0 0
$$704$$ 0 0
$$705$$ 0 0
$$706$$ 2.00000 2.00000
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$710$$ 0 0
$$711$$ 0 0
$$712$$ − 0.618034i − 0.618034i
$$713$$ 0 0
$$714$$ 0 0
$$715$$ 0 0
$$716$$ 0 0
$$717$$ 0 0
$$718$$ 0 0
$$719$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ − 1.00000i − 1.00000i
$$723$$ 0 0
$$724$$ −0.618034 −0.618034
$$725$$ 0 0
$$726$$ 0 0
$$727$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$728$$ 0 0
$$729$$ −1.00000 −1.00000
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 0 0
$$733$$ 2.00000i 2.00000i 1.00000i $$0.5\pi$$
1.00000i $$0.5\pi$$
$$734$$ 0 0
$$735$$ 0 0
$$736$$ 0 0
$$737$$ 0 0
$$738$$ − 1.61803i − 1.61803i
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 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
$$746$$ 2.00000 2.00000
$$747$$ 0 0
$$748$$ 0 0
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 0 0
$$753$$ 0 0
$$754$$ 1.00000 1.00000
$$755$$ 0 0
$$756$$ 0 0
$$757$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 0 0
$$765$$ 0 0
$$766$$ 0 0
$$767$$ 0 0
$$768$$ 0 0
$$769$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 1.61803i 1.61803i
$$773$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$774$$ 0 0
$$775$$ 0 0
$$776$$ 0.618034 0.618034
$$777$$ 0 0
$$778$$ − 1.61803i − 1.61803i
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ 0 0
$$784$$ −1.00000 −1.00000
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$788$$ − 1.61803i − 1.61803i
$$789$$ 0 0
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 2.61803i 2.61803i
$$794$$ −2.00000 −2.00000
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 0.618034 0.618034
$$802$$ 1.61803i 1.61803i
$$803$$ 0 0
$$804$$ 0 0
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 0 0
$$808$$ 0.618034i 0.618034i
$$809$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 0 0
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ 0.618034i 0.618034i
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$822$$ 0 0
$$823$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$824$$ 0 0
$$825$$ 0 0
$$826$$ 0 0
$$827$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$828$$ 0 0
$$829$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 1.61803i 1.61803i
$$833$$ 0.618034i 0.618034i
$$834$$ 0 0
$$835$$ 0 0
$$836$$ 0 0
$$837$$ 0 0
$$838$$ 0 0
$$839$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$840$$ 0 0
$$841$$ −0.618034 −0.618034
$$842$$ − 0.618034i − 0.618034i
$$843$$ 0 0
$$844$$ 0 0
$$845$$ 0 0
$$846$$ 0 0
$$847$$ 0 0
$$848$$ − 1.61803i − 1.61803i
$$849$$ 0 0
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ − 1.61803i − 1.61803i −0.587785 0.809017i $$-0.700000\pi$$
0.587785 0.809017i $$-0.300000\pi$$
$$854$$ 0 0
$$855$$ 0 0
$$856$$ 0 0
$$857$$ − 2.00000i − 2.00000i 1.00000i $$-0.5\pi$$
1.00000i $$-0.5\pi$$
$$858$$ 0 0
$$859$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$860$$ 0 0
$$861$$ 0 0
$$862$$ 0 0
$$863$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$864$$ 0 0
$$865$$ 0 0
$$866$$ −1.61803 −1.61803
$$867$$ 0 0
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 1.61803i 1.61803i
$$873$$ 0.618034i 0.618034i
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$882$$ − 1.00000i − 1.00000i
$$883$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$884$$ 1.00000 1.00000
$$885$$ 0 0
$$886$$ 0 0
$$887$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$888$$ 0 0
$$889$$ 0 0
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 0 0
$$893$$ 0 0
$$894$$ 0 0
$$895$$ 0 0
$$896$$ 0 0
$$897$$ 0 0
$$898$$ 0.618034i 0.618034i
$$899$$ 0 0
$$900$$ 0 0
$$901$$ −1.00000 −1.00000
$$902$$ 0 0
$$903$$ 0 0
$$904$$ −0.618034 −0.618034
$$905$$ 0 0
$$906$$ 0 0
$$907$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$908$$ 0 0
$$909$$ −0.618034 −0.618034
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ −2.00000 −2.00000
$$915$$ 0 0
$$916$$ −1.61803 −1.61803
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ 0 0
$$922$$ − 0.618034i − 0.618034i
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0 0
$$927$$ 0 0
$$928$$ 0.618034i 0.618034i
$$929$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 1.61803i 1.61803i
$$933$$ 0 0
$$934$$ 0 0
$$935$$ 0 0
$$936$$ −1.61803 −1.61803
$$937$$ − 0.618034i − 0.618034i −0.951057 0.309017i $$-0.900000\pi$$
0.951057 0.309017i $$-0.100000\pi$$
$$938$$ 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 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$948$$ 0 0
$$949$$ −2.61803 −2.61803
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0.618034i 0.618034i 0.951057 + 0.309017i $$0.100000\pi$$
−0.951057 + 0.309017i $$0.900000\pi$$
$$954$$ 1.61803 1.61803
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ 1.00000i 1.00000i
$$963$$ 0 0
$$964$$ −0.618034 −0.618034
$$965$$ 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
$$973$$ 0 0
$$974$$ 0 0
$$975$$ 0 0
$$976$$ −1.61803 −1.61803
$$977$$ 1.61803i 1.61803i 0.587785 + 0.809017i $$0.300000\pi$$
−0.587785 + 0.809017i $$0.700000\pi$$
$$978$$ 0 0
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −1.61803 −1.61803
$$982$$ 0 0
$$983$$ 0 0 1.00000i $$-0.5\pi$$
1.00000i $$0.5\pi$$
$$984$$ 0 0
$$985$$ 0 0
$$986$$ 0.381966 0.381966
$$987$$ 0 0
$$988$$ 0 0
$$989$$ 0 0
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ 0 0
$$997$$ − 2.00000i − 2.00000i 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 2500.1.d.a.2499.1 4
4.3 odd 2 CM 2500.1.d.a.2499.1 4
5.2 odd 4 2500.1.b.b.1251.1 2
5.3 odd 4 2500.1.b.a.1251.2 2
5.4 even 2 inner 2500.1.d.a.2499.4 4
20.3 even 4 2500.1.b.a.1251.2 2
20.7 even 4 2500.1.b.b.1251.1 2
20.19 odd 2 inner 2500.1.d.a.2499.4 4
25.2 odd 20 100.1.j.a.71.1 yes 4
25.3 odd 20 2500.1.j.b.2251.1 4
25.4 even 10 2500.1.h.e.1499.2 8
25.6 even 5 2500.1.h.e.999.2 8
25.8 odd 20 2500.1.j.b.251.1 4
25.9 even 10 500.1.h.a.99.1 8
25.11 even 5 500.1.h.a.399.1 8
25.12 odd 20 100.1.j.a.31.1 4
25.13 odd 20 500.1.j.a.151.1 4
25.14 even 10 500.1.h.a.399.2 8
25.16 even 5 500.1.h.a.99.2 8
25.17 odd 20 2500.1.j.a.251.1 4
25.19 even 10 2500.1.h.e.999.1 8
25.21 even 5 2500.1.h.e.1499.1 8
25.22 odd 20 2500.1.j.a.2251.1 4
25.23 odd 20 500.1.j.a.351.1 4
75.2 even 20 900.1.x.a.271.1 4
75.62 even 20 900.1.x.a.631.1 4
100.3 even 20 2500.1.j.b.2251.1 4
100.11 odd 10 500.1.h.a.399.1 8
100.19 odd 10 2500.1.h.e.999.1 8
100.23 even 20 500.1.j.a.351.1 4
100.27 even 20 100.1.j.a.71.1 yes 4
100.31 odd 10 2500.1.h.e.999.2 8
100.39 odd 10 500.1.h.a.399.2 8
100.47 even 20 2500.1.j.a.2251.1 4
100.59 odd 10 500.1.h.a.99.1 8
100.63 even 20 500.1.j.a.151.1 4
100.67 even 20 2500.1.j.a.251.1 4
100.71 odd 10 2500.1.h.e.1499.1 8
100.79 odd 10 2500.1.h.e.1499.2 8
100.83 even 20 2500.1.j.b.251.1 4
100.87 even 20 100.1.j.a.31.1 4
100.91 odd 10 500.1.h.a.99.2 8
200.27 even 20 1600.1.bh.a.1471.1 4
200.37 odd 20 1600.1.bh.a.831.1 4
200.77 odd 20 1600.1.bh.a.1471.1 4
200.187 even 20 1600.1.bh.a.831.1 4
300.227 odd 20 900.1.x.a.271.1 4
300.287 odd 20 900.1.x.a.631.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
100.1.j.a.31.1 4 25.12 odd 20
100.1.j.a.31.1 4 100.87 even 20
100.1.j.a.71.1 yes 4 25.2 odd 20
100.1.j.a.71.1 yes 4 100.27 even 20
500.1.h.a.99.1 8 25.9 even 10
500.1.h.a.99.1 8 100.59 odd 10
500.1.h.a.99.2 8 25.16 even 5
500.1.h.a.99.2 8 100.91 odd 10
500.1.h.a.399.1 8 25.11 even 5
500.1.h.a.399.1 8 100.11 odd 10
500.1.h.a.399.2 8 25.14 even 10
500.1.h.a.399.2 8 100.39 odd 10
500.1.j.a.151.1 4 25.13 odd 20
500.1.j.a.151.1 4 100.63 even 20
500.1.j.a.351.1 4 25.23 odd 20
500.1.j.a.351.1 4 100.23 even 20
900.1.x.a.271.1 4 75.2 even 20
900.1.x.a.271.1 4 300.227 odd 20
900.1.x.a.631.1 4 75.62 even 20
900.1.x.a.631.1 4 300.287 odd 20
1600.1.bh.a.831.1 4 200.37 odd 20
1600.1.bh.a.831.1 4 200.187 even 20
1600.1.bh.a.1471.1 4 200.27 even 20
1600.1.bh.a.1471.1 4 200.77 odd 20
2500.1.b.a.1251.2 2 5.3 odd 4
2500.1.b.a.1251.2 2 20.3 even 4
2500.1.b.b.1251.1 2 5.2 odd 4
2500.1.b.b.1251.1 2 20.7 even 4
2500.1.d.a.2499.1 4 1.1 even 1 trivial
2500.1.d.a.2499.1 4 4.3 odd 2 CM
2500.1.d.a.2499.4 4 5.4 even 2 inner
2500.1.d.a.2499.4 4 20.19 odd 2 inner
2500.1.h.e.999.1 8 25.19 even 10
2500.1.h.e.999.1 8 100.19 odd 10
2500.1.h.e.999.2 8 25.6 even 5
2500.1.h.e.999.2 8 100.31 odd 10
2500.1.h.e.1499.1 8 25.21 even 5
2500.1.h.e.1499.1 8 100.71 odd 10
2500.1.h.e.1499.2 8 25.4 even 10
2500.1.h.e.1499.2 8 100.79 odd 10
2500.1.j.a.251.1 4 25.17 odd 20
2500.1.j.a.251.1 4 100.67 even 20
2500.1.j.a.2251.1 4 25.22 odd 20
2500.1.j.a.2251.1 4 100.47 even 20
2500.1.j.b.251.1 4 25.8 odd 20
2500.1.j.b.251.1 4 100.83 even 20
2500.1.j.b.2251.1 4 25.3 odd 20
2500.1.j.b.2251.1 4 100.3 even 20