# Properties

 Label 500.1.d.a.499.2 Level $500$ Weight $1$ Character 500.499 Self dual yes Analytic conductor $0.250$ Analytic rank $0$ Dimension $2$ Projective image $D_{5}$ CM discriminant -20 Inner twists $2$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$500 = 2^{2} \cdot 5^{3}$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 500.d (of order $$2$$, degree $$1$$, not minimal)

## Newform invariants

 Self dual: yes Analytic conductor: $$0.249532506317$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\zeta_{10})^+$$ Defining polynomial: $$x^{2} - x - 1$$ x^2 - x - 1 Coefficient ring: $$\Z[a_1, a_2, a_3]$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image: $$D_{5}$$ Projective field: Galois closure of 5.1.250000.1

## Embedding invariants

 Embedding label 499.2 Root $$-0.618034$$ of defining polynomial Character $$\chi$$ $$=$$ 500.499

## $q$-expansion

 $$f(q)$$ $$=$$ $$q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -0.618034 q^{7} -1.00000 q^{8} +1.61803 q^{9} +O(q^{10})$$ $$q-1.00000 q^{2} +1.61803 q^{3} +1.00000 q^{4} -1.61803 q^{6} -0.618034 q^{7} -1.00000 q^{8} +1.61803 q^{9} +1.61803 q^{12} +0.618034 q^{14} +1.00000 q^{16} -1.61803 q^{18} -1.00000 q^{21} -0.618034 q^{23} -1.61803 q^{24} +1.00000 q^{27} -0.618034 q^{28} -1.61803 q^{29} -1.00000 q^{32} +1.61803 q^{36} -1.61803 q^{41} +1.00000 q^{42} +1.61803 q^{43} +0.618034 q^{46} +1.61803 q^{47} +1.61803 q^{48} -0.618034 q^{49} -1.00000 q^{54} +0.618034 q^{56} +1.61803 q^{58} +0.618034 q^{61} -1.00000 q^{63} +1.00000 q^{64} -2.00000 q^{67} -1.00000 q^{69} -1.61803 q^{72} +1.61803 q^{82} -0.618034 q^{83} -1.00000 q^{84} -1.61803 q^{86} -2.61803 q^{87} +0.618034 q^{89} -0.618034 q^{92} -1.61803 q^{94} -1.61803 q^{96} +0.618034 q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + q^{7} - 2 q^{8} + q^{9}+O(q^{10})$$ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + q^7 - 2 * q^8 + q^9 $$2 q - 2 q^{2} + q^{3} + 2 q^{4} - q^{6} + q^{7} - 2 q^{8} + q^{9} + q^{12} - q^{14} + 2 q^{16} - q^{18} - 2 q^{21} + q^{23} - q^{24} + 2 q^{27} + q^{28} - q^{29} - 2 q^{32} + q^{36} - q^{41} + 2 q^{42} + q^{43} - q^{46} + q^{47} + q^{48} + q^{49} - 2 q^{54} - q^{56} + q^{58} - q^{61} - 2 q^{63} + 2 q^{64} - 4 q^{67} - 2 q^{69} - q^{72} + q^{82} + q^{83} - 2 q^{84} - q^{86} - 3 q^{87} - q^{89} + q^{92} - q^{94} - q^{96} - q^{98}+O(q^{100})$$ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - q^6 + q^7 - 2 * q^8 + q^9 + q^12 - q^14 + 2 * q^16 - q^18 - 2 * q^21 + q^23 - q^24 + 2 * q^27 + q^28 - q^29 - 2 * q^32 + q^36 - q^41 + 2 * q^42 + q^43 - q^46 + q^47 + q^48 + q^49 - 2 * q^54 - q^56 + q^58 - q^61 - 2 * q^63 + 2 * q^64 - 4 * q^67 - 2 * q^69 - q^72 + q^82 + q^83 - 2 * q^84 - q^86 - 3 * q^87 - q^89 + q^92 - q^94 - q^96 - q^98

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$$.

 $$n$$ $$251$$ $$377$$ $$\chi(n)$$ $$-1$$ $$-1$$

## 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
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ −1.00000 −1.00000
$$3$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$4$$ 1.00000 1.00000
$$5$$ 0 0
$$6$$ −1.61803 −1.61803
$$7$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$8$$ −1.00000 −1.00000
$$9$$ 1.61803 1.61803
$$10$$ 0 0
$$11$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$12$$ 1.61803 1.61803
$$13$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$14$$ 0.618034 0.618034
$$15$$ 0 0
$$16$$ 1.00000 1.00000
$$17$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$18$$ −1.61803 −1.61803
$$19$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$20$$ 0 0
$$21$$ −1.00000 −1.00000
$$22$$ 0 0
$$23$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$24$$ −1.61803 −1.61803
$$25$$ 0 0
$$26$$ 0 0
$$27$$ 1.00000 1.00000
$$28$$ −0.618034 −0.618034
$$29$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$30$$ 0 0
$$31$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$32$$ −1.00000 −1.00000
$$33$$ 0 0
$$34$$ 0 0
$$35$$ 0 0
$$36$$ 1.61803 1.61803
$$37$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$38$$ 0 0
$$39$$ 0 0
$$40$$ 0 0
$$41$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$42$$ 1.00000 1.00000
$$43$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$44$$ 0 0
$$45$$ 0 0
$$46$$ 0.618034 0.618034
$$47$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$48$$ 1.61803 1.61803
$$49$$ −0.618034 −0.618034
$$50$$ 0 0
$$51$$ 0 0
$$52$$ 0 0
$$53$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$54$$ −1.00000 −1.00000
$$55$$ 0 0
$$56$$ 0.618034 0.618034
$$57$$ 0 0
$$58$$ 1.61803 1.61803
$$59$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$60$$ 0 0
$$61$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$62$$ 0 0
$$63$$ −1.00000 −1.00000
$$64$$ 1.00000 1.00000
$$65$$ 0 0
$$66$$ 0 0
$$67$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$68$$ 0 0
$$69$$ −1.00000 −1.00000
$$70$$ 0 0
$$71$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$72$$ −1.61803 −1.61803
$$73$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$74$$ 0 0
$$75$$ 0 0
$$76$$ 0 0
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$80$$ 0 0
$$81$$ 0 0
$$82$$ 1.61803 1.61803
$$83$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$84$$ −1.00000 −1.00000
$$85$$ 0 0
$$86$$ −1.61803 −1.61803
$$87$$ −2.61803 −2.61803
$$88$$ 0 0
$$89$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −0.618034 −0.618034
$$93$$ 0 0
$$94$$ −1.61803 −1.61803
$$95$$ 0 0
$$96$$ −1.61803 −1.61803
$$97$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$98$$ 0.618034 0.618034
$$99$$ 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
$$103$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$104$$ 0 0
$$105$$ 0 0
$$106$$ 0 0
$$107$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$108$$ 1.00000 1.00000
$$109$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$110$$ 0 0
$$111$$ 0 0
$$112$$ −0.618034 −0.618034
$$113$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$114$$ 0 0
$$115$$ 0 0
$$116$$ −1.61803 −1.61803
$$117$$ 0 0
$$118$$ 0 0
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 1.00000 1.00000
$$122$$ −0.618034 −0.618034
$$123$$ −2.61803 −2.61803
$$124$$ 0 0
$$125$$ 0 0
$$126$$ 1.00000 1.00000
$$127$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$128$$ −1.00000 −1.00000
$$129$$ 2.61803 2.61803
$$130$$ 0 0
$$131$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ 2.00000 2.00000
$$135$$ 0 0
$$136$$ 0 0
$$137$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$138$$ 1.00000 1.00000
$$139$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$140$$ 0 0
$$141$$ 2.61803 2.61803
$$142$$ 0 0
$$143$$ 0 0
$$144$$ 1.61803 1.61803
$$145$$ 0 0
$$146$$ 0 0
$$147$$ −1.00000 −1.00000
$$148$$ 0 0
$$149$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$150$$ 0 0
$$151$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$152$$ 0 0
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 0 0
$$156$$ 0 0
$$157$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$158$$ 0 0
$$159$$ 0 0
$$160$$ 0 0
$$161$$ 0.381966 0.381966
$$162$$ 0 0
$$163$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$164$$ −1.61803 −1.61803
$$165$$ 0 0
$$166$$ 0.618034 0.618034
$$167$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$168$$ 1.00000 1.00000
$$169$$ 1.00000 1.00000
$$170$$ 0 0
$$171$$ 0 0
$$172$$ 1.61803 1.61803
$$173$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$174$$ 2.61803 2.61803
$$175$$ 0 0
$$176$$ 0 0
$$177$$ 0 0
$$178$$ −0.618034 −0.618034
$$179$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$180$$ 0 0
$$181$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$182$$ 0 0
$$183$$ 1.00000 1.00000
$$184$$ 0.618034 0.618034
$$185$$ 0 0
$$186$$ 0 0
$$187$$ 0 0
$$188$$ 1.61803 1.61803
$$189$$ −0.618034 −0.618034
$$190$$ 0 0
$$191$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$192$$ 1.61803 1.61803
$$193$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$194$$ 0 0
$$195$$ 0 0
$$196$$ −0.618034 −0.618034
$$197$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$198$$ 0 0
$$199$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$200$$ 0 0
$$201$$ −3.23607 −3.23607
$$202$$ −0.618034 −0.618034
$$203$$ 1.00000 1.00000
$$204$$ 0 0
$$205$$ 0 0
$$206$$ 2.00000 2.00000
$$207$$ −1.00000 −1.00000
$$208$$ 0 0
$$209$$ 0 0
$$210$$ 0 0
$$211$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$212$$ 0 0
$$213$$ 0 0
$$214$$ −1.61803 −1.61803
$$215$$ 0 0
$$216$$ −1.00000 −1.00000
$$217$$ 0 0
$$218$$ 1.61803 1.61803
$$219$$ 0 0
$$220$$ 0 0
$$221$$ 0 0
$$222$$ 0 0
$$223$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$224$$ 0.618034 0.618034
$$225$$ 0 0
$$226$$ 0 0
$$227$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$228$$ 0 0
$$229$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$230$$ 0 0
$$231$$ 0 0
$$232$$ 1.61803 1.61803
$$233$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$234$$ 0 0
$$235$$ 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 $$0.400000\pi$$
$$242$$ −1.00000 −1.00000
$$243$$ −1.00000 −1.00000
$$244$$ 0.618034 0.618034
$$245$$ 0 0
$$246$$ 2.61803 2.61803
$$247$$ 0 0
$$248$$ 0 0
$$249$$ −1.00000 −1.00000
$$250$$ 0 0
$$251$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$252$$ −1.00000 −1.00000
$$253$$ 0 0
$$254$$ −1.61803 −1.61803
$$255$$ 0 0
$$256$$ 1.00000 1.00000
$$257$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$258$$ −2.61803 −2.61803
$$259$$ 0 0
$$260$$ 0 0
$$261$$ −2.61803 −2.61803
$$262$$ 0 0
$$263$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$264$$ 0 0
$$265$$ 0 0
$$266$$ 0 0
$$267$$ 1.00000 1.00000
$$268$$ −2.00000 −2.00000
$$269$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$270$$ 0 0
$$271$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$272$$ 0 0
$$273$$ 0 0
$$274$$ 0 0
$$275$$ 0 0
$$276$$ −1.00000 −1.00000
$$277$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$278$$ 0 0
$$279$$ 0 0
$$280$$ 0 0
$$281$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$282$$ −2.61803 −2.61803
$$283$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$284$$ 0 0
$$285$$ 0 0
$$286$$ 0 0
$$287$$ 1.00000 1.00000
$$288$$ −1.61803 −1.61803
$$289$$ 1.00000 1.00000
$$290$$ 0 0
$$291$$ 0 0
$$292$$ 0 0
$$293$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$294$$ 1.00000 1.00000
$$295$$ 0 0
$$296$$ 0 0
$$297$$ 0 0
$$298$$ −0.618034 −0.618034
$$299$$ 0 0
$$300$$ 0 0
$$301$$ −1.00000 −1.00000
$$302$$ 0 0
$$303$$ 1.00000 1.00000
$$304$$ 0 0
$$305$$ 0 0
$$306$$ 0 0
$$307$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$308$$ 0 0
$$309$$ −3.23607 −3.23607
$$310$$ 0 0
$$311$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$312$$ 0 0
$$313$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$314$$ 0 0
$$315$$ 0 0
$$316$$ 0 0
$$317$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$318$$ 0 0
$$319$$ 0 0
$$320$$ 0 0
$$321$$ 2.61803 2.61803
$$322$$ −0.381966 −0.381966
$$323$$ 0 0
$$324$$ 0 0
$$325$$ 0 0
$$326$$ 0.618034 0.618034
$$327$$ −2.61803 −2.61803
$$328$$ 1.61803 1.61803
$$329$$ −1.00000 −1.00000
$$330$$ 0 0
$$331$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$332$$ −0.618034 −0.618034
$$333$$ 0 0
$$334$$ −1.61803 −1.61803
$$335$$ 0 0
$$336$$ −1.00000 −1.00000
$$337$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$338$$ −1.00000 −1.00000
$$339$$ 0 0
$$340$$ 0 0
$$341$$ 0 0
$$342$$ 0 0
$$343$$ 1.00000 1.00000
$$344$$ −1.61803 −1.61803
$$345$$ 0 0
$$346$$ 0 0
$$347$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$348$$ −2.61803 −2.61803
$$349$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ 0 0
$$353$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$354$$ 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
$$362$$ 1.61803 1.61803
$$363$$ 1.61803 1.61803
$$364$$ 0 0
$$365$$ 0 0
$$366$$ −1.00000 −1.00000
$$367$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$368$$ −0.618034 −0.618034
$$369$$ −2.61803 −2.61803
$$370$$ 0 0
$$371$$ 0 0
$$372$$ 0 0
$$373$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$374$$ 0 0
$$375$$ 0 0
$$376$$ −1.61803 −1.61803
$$377$$ 0 0
$$378$$ 0.618034 0.618034
$$379$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$380$$ 0 0
$$381$$ 2.61803 2.61803
$$382$$ 0 0
$$383$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$384$$ −1.61803 −1.61803
$$385$$ 0 0
$$386$$ 0 0
$$387$$ 2.61803 2.61803
$$388$$ 0 0
$$389$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$390$$ 0 0
$$391$$ 0 0
$$392$$ 0.618034 0.618034
$$393$$ 0 0
$$394$$ 0 0
$$395$$ 0 0
$$396$$ 0 0
$$397$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$398$$ 0 0
$$399$$ 0 0
$$400$$ 0 0
$$401$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$402$$ 3.23607 3.23607
$$403$$ 0 0
$$404$$ 0.618034 0.618034
$$405$$ 0 0
$$406$$ −1.00000 −1.00000
$$407$$ 0 0
$$408$$ 0 0
$$409$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$410$$ 0 0
$$411$$ 0 0
$$412$$ −2.00000 −2.00000
$$413$$ 0 0
$$414$$ 1.00000 1.00000
$$415$$ 0 0
$$416$$ 0 0
$$417$$ 0 0
$$418$$ 0 0
$$419$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$420$$ 0 0
$$421$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$422$$ 0 0
$$423$$ 2.61803 2.61803
$$424$$ 0 0
$$425$$ 0 0
$$426$$ 0 0
$$427$$ −0.381966 −0.381966
$$428$$ 1.61803 1.61803
$$429$$ 0 0
$$430$$ 0 0
$$431$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$432$$ 1.00000 1.00000
$$433$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$434$$ 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
$$442$$ 0 0
$$443$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$444$$ 0 0
$$445$$ 0 0
$$446$$ −1.61803 −1.61803
$$447$$ 1.00000 1.00000
$$448$$ −0.618034 −0.618034
$$449$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$450$$ 0 0
$$451$$ 0 0
$$452$$ 0 0
$$453$$ 0 0
$$454$$ 0.618034 0.618034
$$455$$ 0 0
$$456$$ 0 0
$$457$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$458$$ −0.618034 −0.618034
$$459$$ 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
$$463$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$464$$ −1.61803 −1.61803
$$465$$ 0 0
$$466$$ 0 0
$$467$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$468$$ 0 0
$$469$$ 1.23607 1.23607
$$470$$ 0 0
$$471$$ 0 0
$$472$$ 0 0
$$473$$ 0 0
$$474$$ 0 0
$$475$$ 0 0
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 0 0
$$479$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$480$$ 0 0
$$481$$ 0 0
$$482$$ −0.618034 −0.618034
$$483$$ 0.618034 0.618034
$$484$$ 1.00000 1.00000
$$485$$ 0 0
$$486$$ 1.00000 1.00000
$$487$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$488$$ −0.618034 −0.618034
$$489$$ −1.00000 −1.00000
$$490$$ 0 0
$$491$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$492$$ −2.61803 −2.61803
$$493$$ 0 0
$$494$$ 0 0
$$495$$ 0 0
$$496$$ 0 0
$$497$$ 0 0
$$498$$ 1.00000 1.00000
$$499$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$500$$ 0 0
$$501$$ 2.61803 2.61803
$$502$$ 0 0
$$503$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$504$$ 1.00000 1.00000
$$505$$ 0 0
$$506$$ 0 0
$$507$$ 1.61803 1.61803
$$508$$ 1.61803 1.61803
$$509$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −1.00000 −1.00000
$$513$$ 0 0
$$514$$ 0 0
$$515$$ 0 0
$$516$$ 2.61803 2.61803
$$517$$ 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 $$0.800000\pi$$
$$522$$ 2.61803 2.61803
$$523$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$524$$ 0 0
$$525$$ 0 0
$$526$$ −1.61803 −1.61803
$$527$$ 0 0
$$528$$ 0 0
$$529$$ −0.618034 −0.618034
$$530$$ 0 0
$$531$$ 0 0
$$532$$ 0 0
$$533$$ 0 0
$$534$$ −1.00000 −1.00000
$$535$$ 0 0
$$536$$ 2.00000 2.00000
$$537$$ 0 0
$$538$$ −2.00000 −2.00000
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$542$$ 0 0
$$543$$ −2.61803 −2.61803
$$544$$ 0 0
$$545$$ 0 0
$$546$$ 0 0
$$547$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$548$$ 0 0
$$549$$ 1.00000 1.00000
$$550$$ 0 0
$$551$$ 0 0
$$552$$ 1.00000 1.00000
$$553$$ 0 0
$$554$$ 0 0
$$555$$ 0 0
$$556$$ 0 0
$$557$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$558$$ 0 0
$$559$$ 0 0
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −0.618034 −0.618034
$$563$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$564$$ 2.61803 2.61803
$$565$$ 0 0
$$566$$ 2.00000 2.00000
$$567$$ 0 0
$$568$$ 0 0
$$569$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$570$$ 0 0
$$571$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$572$$ 0 0
$$573$$ 0 0
$$574$$ −1.00000 −1.00000
$$575$$ 0 0
$$576$$ 1.61803 1.61803
$$577$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$578$$ −1.00000 −1.00000
$$579$$ 0 0
$$580$$ 0 0
$$581$$ 0.381966 0.381966
$$582$$ 0 0
$$583$$ 0 0
$$584$$ 0 0
$$585$$ 0 0
$$586$$ 0 0
$$587$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$588$$ −1.00000 −1.00000
$$589$$ 0 0
$$590$$ 0 0
$$591$$ 0 0
$$592$$ 0 0
$$593$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 0.618034 0.618034
$$597$$ 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 $$0.800000\pi$$
$$602$$ 1.00000 1.00000
$$603$$ −3.23607 −3.23607
$$604$$ 0 0
$$605$$ 0 0
$$606$$ −1.00000 −1.00000
$$607$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$608$$ 0 0
$$609$$ 1.61803 1.61803
$$610$$ 0 0
$$611$$ 0 0
$$612$$ 0 0
$$613$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$614$$ 0.618034 0.618034
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$618$$ 3.23607 3.23607
$$619$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$620$$ 0 0
$$621$$ −0.618034 −0.618034
$$622$$ 0 0
$$623$$ −0.381966 −0.381966
$$624$$ 0 0
$$625$$ 0 0
$$626$$ 0 0
$$627$$ 0 0
$$628$$ 0 0
$$629$$ 0 0
$$630$$ 0 0
$$631$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$632$$ 0 0
$$633$$ 0 0
$$634$$ 0 0
$$635$$ 0 0
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 0 0
$$639$$ 0 0
$$640$$ 0 0
$$641$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$642$$ −2.61803 −2.61803
$$643$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$644$$ 0.381966 0.381966
$$645$$ 0 0
$$646$$ 0 0
$$647$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$648$$ 0 0
$$649$$ 0 0
$$650$$ 0 0
$$651$$ 0 0
$$652$$ −0.618034 −0.618034
$$653$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$654$$ 2.61803 2.61803
$$655$$ 0 0
$$656$$ −1.61803 −1.61803
$$657$$ 0 0
$$658$$ 1.00000 1.00000
$$659$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$660$$ 0 0
$$661$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$662$$ 0 0
$$663$$ 0 0
$$664$$ 0.618034 0.618034
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 1.00000 1.00000
$$668$$ 1.61803 1.61803
$$669$$ 2.61803 2.61803
$$670$$ 0 0
$$671$$ 0 0
$$672$$ 1.00000 1.00000
$$673$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$674$$ 0 0
$$675$$ 0 0
$$676$$ 1.00000 1.00000
$$677$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ 0 0
$$681$$ −1.00000 −1.00000
$$682$$ 0 0
$$683$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$684$$ 0 0
$$685$$ 0 0
$$686$$ −1.00000 −1.00000
$$687$$ 1.00000 1.00000
$$688$$ 1.61803 1.61803
$$689$$ 0 0
$$690$$ 0 0
$$691$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$692$$ 0 0
$$693$$ 0 0
$$694$$ 0.618034 0.618034
$$695$$ 0 0
$$696$$ 2.61803 2.61803
$$697$$ 0 0
$$698$$ −0.618034 −0.618034
$$699$$ 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
$$707$$ −0.381966 −0.381966
$$708$$ 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 0
$$712$$ −0.618034 −0.618034
$$713$$ 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
$$721$$ 1.23607 1.23607
$$722$$ −1.00000 −1.00000
$$723$$ 1.00000 1.00000
$$724$$ −1.61803 −1.61803
$$725$$ 0 0
$$726$$ −1.61803 −1.61803
$$727$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$728$$ 0 0
$$729$$ −1.61803 −1.61803
$$730$$ 0 0
$$731$$ 0 0
$$732$$ 1.00000 1.00000
$$733$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$734$$ 0.618034 0.618034
$$735$$ 0 0
$$736$$ 0.618034 0.618034
$$737$$ 0 0
$$738$$ 2.61803 2.61803
$$739$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$740$$ 0 0
$$741$$ 0 0
$$742$$ 0 0
$$743$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$744$$ 0 0
$$745$$ 0 0
$$746$$ 0 0
$$747$$ −1.00000 −1.00000
$$748$$ 0 0
$$749$$ −1.00000 −1.00000
$$750$$ 0 0
$$751$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$752$$ 1.61803 1.61803
$$753$$ 0 0
$$754$$ 0 0
$$755$$ 0 0
$$756$$ −0.618034 −0.618034
$$757$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$758$$ 0 0
$$759$$ 0 0
$$760$$ 0 0
$$761$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$762$$ −2.61803 −2.61803
$$763$$ 1.00000 1.00000
$$764$$ 0 0
$$765$$ 0 0
$$766$$ −1.61803 −1.61803
$$767$$ 0 0
$$768$$ 1.61803 1.61803
$$769$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ 0 0
$$773$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$774$$ −2.61803 −2.61803
$$775$$ 0 0
$$776$$ 0 0
$$777$$ 0 0
$$778$$ 1.61803 1.61803
$$779$$ 0 0
$$780$$ 0 0
$$781$$ 0 0
$$782$$ 0 0
$$783$$ −1.61803 −1.61803
$$784$$ −0.618034 −0.618034
$$785$$ 0 0
$$786$$ 0 0
$$787$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$788$$ 0 0
$$789$$ 2.61803 2.61803
$$790$$ 0 0
$$791$$ 0 0
$$792$$ 0 0
$$793$$ 0 0
$$794$$ 0 0
$$795$$ 0 0
$$796$$ 0 0
$$797$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$798$$ 0 0
$$799$$ 0 0
$$800$$ 0 0
$$801$$ 1.00000 1.00000
$$802$$ −0.618034 −0.618034
$$803$$ 0 0
$$804$$ −3.23607 −3.23607
$$805$$ 0 0
$$806$$ 0 0
$$807$$ 3.23607 3.23607
$$808$$ −0.618034 −0.618034
$$809$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$810$$ 0 0
$$811$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$812$$ 1.00000 1.00000
$$813$$ 0 0
$$814$$ 0 0
$$815$$ 0 0
$$816$$ 0 0
$$817$$ 0 0
$$818$$ −0.618034 −0.618034
$$819$$ 0 0
$$820$$ 0 0
$$821$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$822$$ 0 0
$$823$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$824$$ 2.00000 2.00000
$$825$$ 0 0
$$826$$ 0 0
$$827$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$828$$ −1.00000 −1.00000
$$829$$ −1.61803 −1.61803 −0.809017 0.587785i $$-0.800000\pi$$
−0.809017 + 0.587785i $$0.800000\pi$$
$$830$$ 0 0
$$831$$ 0 0
$$832$$ 0 0
$$833$$ 0 0
$$834$$ 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
$$841$$ 1.61803 1.61803
$$842$$ 1.61803 1.61803
$$843$$ 1.00000 1.00000
$$844$$ 0 0
$$845$$ 0 0
$$846$$ −2.61803 −2.61803
$$847$$ −0.618034 −0.618034
$$848$$ 0 0
$$849$$ −3.23607 −3.23607
$$850$$ 0 0
$$851$$ 0 0
$$852$$ 0 0
$$853$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$854$$ 0.381966 0.381966
$$855$$ 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
$$861$$ 1.61803 1.61803
$$862$$ 0 0
$$863$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$864$$ −1.00000 −1.00000
$$865$$ 0 0
$$866$$ 0 0
$$867$$ 1.61803 1.61803
$$868$$ 0 0
$$869$$ 0 0
$$870$$ 0 0
$$871$$ 0 0
$$872$$ 1.61803 1.61803
$$873$$ 0 0
$$874$$ 0 0
$$875$$ 0 0
$$876$$ 0 0
$$877$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$878$$ 0 0
$$879$$ 0 0
$$880$$ 0 0
$$881$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$882$$ 1.00000 1.00000
$$883$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$884$$ 0 0
$$885$$ 0 0
$$886$$ 0.618034 0.618034
$$887$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$888$$ 0 0
$$889$$ −1.00000 −1.00000
$$890$$ 0 0
$$891$$ 0 0
$$892$$ 1.61803 1.61803
$$893$$ 0 0
$$894$$ −1.00000 −1.00000
$$895$$ 0 0
$$896$$ 0.618034 0.618034
$$897$$ 0 0
$$898$$ −2.00000 −2.00000
$$899$$ 0 0
$$900$$ 0 0
$$901$$ 0 0
$$902$$ 0 0
$$903$$ −1.61803 −1.61803
$$904$$ 0 0
$$905$$ 0 0
$$906$$ 0 0
$$907$$ −0.618034 −0.618034 −0.309017 0.951057i $$-0.600000\pi$$
−0.309017 + 0.951057i $$0.600000\pi$$
$$908$$ −0.618034 −0.618034
$$909$$ 1.00000 1.00000
$$910$$ 0 0
$$911$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$912$$ 0 0
$$913$$ 0 0
$$914$$ 0 0
$$915$$ 0 0
$$916$$ 0.618034 0.618034
$$917$$ 0 0
$$918$$ 0 0
$$919$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$920$$ 0 0
$$921$$ −1.00000 −1.00000
$$922$$ −0.618034 −0.618034
$$923$$ 0 0
$$924$$ 0 0
$$925$$ 0 0
$$926$$ 0.618034 0.618034
$$927$$ −3.23607 −3.23607
$$928$$ 1.61803 1.61803
$$929$$ 0.618034 0.618034 0.309017 0.951057i $$-0.400000\pi$$
0.309017 + 0.951057i $$0.400000\pi$$
$$930$$ 0 0
$$931$$ 0 0
$$932$$ 0 0
$$933$$ 0 0
$$934$$ 0.618034 0.618034
$$935$$ 0 0
$$936$$ 0 0
$$937$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$938$$ −1.23607 −1.23607
$$939$$ 0 0
$$940$$ 0 0
$$941$$ 2.00000 2.00000 1.00000 $$0$$
1.00000 $$0$$
$$942$$ 0 0
$$943$$ 1.00000 1.00000
$$944$$ 0 0
$$945$$ 0 0
$$946$$ 0 0
$$947$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$948$$ 0 0
$$949$$ 0 0
$$950$$ 0 0
$$951$$ 0 0
$$952$$ 0 0
$$953$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$954$$ 0 0
$$955$$ 0 0
$$956$$ 0 0
$$957$$ 0 0
$$958$$ 0 0
$$959$$ 0 0
$$960$$ 0 0
$$961$$ 1.00000 1.00000
$$962$$ 0 0
$$963$$ 2.61803 2.61803
$$964$$ 0.618034 0.618034
$$965$$ 0 0
$$966$$ −0.618034 −0.618034
$$967$$ 1.61803 1.61803 0.809017 0.587785i $$-0.200000\pi$$
0.809017 + 0.587785i $$0.200000\pi$$
$$968$$ −1.00000 −1.00000
$$969$$ 0 0
$$970$$ 0 0
$$971$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$972$$ −1.00000 −1.00000
$$973$$ 0 0
$$974$$ −1.61803 −1.61803
$$975$$ 0 0
$$976$$ 0.618034 0.618034
$$977$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$978$$ 1.00000 1.00000
$$979$$ 0 0
$$980$$ 0 0
$$981$$ −2.61803 −2.61803
$$982$$ 0 0
$$983$$ −2.00000 −2.00000 −1.00000 $$\pi$$
−1.00000 $$\pi$$
$$984$$ 2.61803 2.61803
$$985$$ 0 0
$$986$$ 0 0
$$987$$ −1.61803 −1.61803
$$988$$ 0 0
$$989$$ −1.00000 −1.00000
$$990$$ 0 0
$$991$$ 0 0 1.00000 $$0$$
−1.00000 $$\pi$$
$$992$$ 0 0
$$993$$ 0 0
$$994$$ 0 0
$$995$$ 0 0
$$996$$ −1.00000 −1.00000
$$997$$ 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 500.1.d.a.499.2 2
4.3 odd 2 500.1.d.b.499.1 2
5.2 odd 4 500.1.b.a.251.1 4
5.3 odd 4 500.1.b.a.251.4 yes 4
5.4 even 2 500.1.d.b.499.1 2
20.3 even 4 500.1.b.a.251.1 4
20.7 even 4 500.1.b.a.251.4 yes 4
20.19 odd 2 CM 500.1.d.a.499.2 2
25.2 odd 20 2500.1.j.d.1751.1 8
25.3 odd 20 2500.1.j.c.2251.2 8
25.4 even 10 2500.1.h.a.1499.1 4
25.6 even 5 2500.1.h.d.999.1 4
25.8 odd 20 2500.1.j.c.251.1 8
25.9 even 10 2500.1.h.b.499.1 4
25.11 even 5 2500.1.h.c.1999.1 4
25.12 odd 20 2500.1.j.d.751.2 8
25.13 odd 20 2500.1.j.d.751.1 8
25.14 even 10 2500.1.h.b.1999.1 4
25.16 even 5 2500.1.h.c.499.1 4
25.17 odd 20 2500.1.j.c.251.2 8
25.19 even 10 2500.1.h.a.999.1 4
25.21 even 5 2500.1.h.d.1499.1 4
25.22 odd 20 2500.1.j.c.2251.1 8
25.23 odd 20 2500.1.j.d.1751.2 8
100.3 even 20 2500.1.j.c.2251.1 8
100.11 odd 10 2500.1.h.b.1999.1 4
100.19 odd 10 2500.1.h.d.999.1 4
100.23 even 20 2500.1.j.d.1751.1 8
100.27 even 20 2500.1.j.d.1751.2 8
100.31 odd 10 2500.1.h.a.999.1 4
100.39 odd 10 2500.1.h.c.1999.1 4
100.47 even 20 2500.1.j.c.2251.2 8
100.59 odd 10 2500.1.h.c.499.1 4
100.63 even 20 2500.1.j.d.751.2 8
100.67 even 20 2500.1.j.c.251.1 8
100.71 odd 10 2500.1.h.a.1499.1 4
100.79 odd 10 2500.1.h.d.1499.1 4
100.83 even 20 2500.1.j.c.251.2 8
100.87 even 20 2500.1.j.d.751.1 8
100.91 odd 10 2500.1.h.b.499.1 4

By twisted newform
Twist Min Dim Char Parity Ord Type
500.1.b.a.251.1 4 5.2 odd 4
500.1.b.a.251.1 4 20.3 even 4
500.1.b.a.251.4 yes 4 5.3 odd 4
500.1.b.a.251.4 yes 4 20.7 even 4
500.1.d.a.499.2 2 1.1 even 1 trivial
500.1.d.a.499.2 2 20.19 odd 2 CM
500.1.d.b.499.1 2 4.3 odd 2
500.1.d.b.499.1 2 5.4 even 2
2500.1.h.a.999.1 4 25.19 even 10
2500.1.h.a.999.1 4 100.31 odd 10
2500.1.h.a.1499.1 4 25.4 even 10
2500.1.h.a.1499.1 4 100.71 odd 10
2500.1.h.b.499.1 4 25.9 even 10
2500.1.h.b.499.1 4 100.91 odd 10
2500.1.h.b.1999.1 4 25.14 even 10
2500.1.h.b.1999.1 4 100.11 odd 10
2500.1.h.c.499.1 4 25.16 even 5
2500.1.h.c.499.1 4 100.59 odd 10
2500.1.h.c.1999.1 4 25.11 even 5
2500.1.h.c.1999.1 4 100.39 odd 10
2500.1.h.d.999.1 4 25.6 even 5
2500.1.h.d.999.1 4 100.19 odd 10
2500.1.h.d.1499.1 4 25.21 even 5
2500.1.h.d.1499.1 4 100.79 odd 10
2500.1.j.c.251.1 8 25.8 odd 20
2500.1.j.c.251.1 8 100.67 even 20
2500.1.j.c.251.2 8 25.17 odd 20
2500.1.j.c.251.2 8 100.83 even 20
2500.1.j.c.2251.1 8 25.22 odd 20
2500.1.j.c.2251.1 8 100.3 even 20
2500.1.j.c.2251.2 8 25.3 odd 20
2500.1.j.c.2251.2 8 100.47 even 20
2500.1.j.d.751.1 8 25.13 odd 20
2500.1.j.d.751.1 8 100.87 even 20
2500.1.j.d.751.2 8 25.12 odd 20
2500.1.j.d.751.2 8 100.63 even 20
2500.1.j.d.1751.1 8 25.2 odd 20
2500.1.j.d.1751.1 8 100.23 even 20
2500.1.j.d.1751.2 8 25.23 odd 20
2500.1.j.d.1751.2 8 100.27 even 20