LMFDB - Embedded newform 637.2.cc.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(5,637)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(84))

chi = DirichletCharacter(H, H._module([58, 63]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("637.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.cc (of order $84$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$1536$
Relative dimension:	$64$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	637.5
Dual form			637.2.cc.a.255.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.60364 + 2.17285i) q^{2} +(-1.54581 + 2.26729i) q^{3} +(-1.56013 - 5.05780i) q^{4} +(1.55493 - 1.33812i) q^{5} +(-2.44757 - 6.99474i) q^{6} +(2.20094 + 1.46828i) q^{7} +(8.39375 + 2.93710i) q^{8} +(-1.65505 - 4.21700i) q^{9} +(0.414004 + 5.52450i) q^{10} +(-1.62882 + 0.710645i) q^{11} +(13.8792 + 4.28116i) q^{12} +(3.57611 + 0.459857i) q^{13} +(-6.71988 + 2.42773i) q^{14} +(0.630289 + 5.59397i) q^{15} +(-11.0959 + 7.56509i) q^{16} +(-1.91962 + 1.78115i) q^{17} +(11.8170 + 3.16636i) q^{18} +(-3.07140 + 0.822980i) q^{19} +(-9.19386 - 5.77688i) q^{20} +(-6.73127 + 2.72049i) q^{21} +(1.06791 - 4.67880i) q^{22} +(-0.397623 + 0.428536i) q^{23} +(-19.6344 + 14.4909i) q^{24} +(-0.117985 + 0.782779i) q^{25} +(-6.73399 + 7.03291i) q^{26} +(4.09362 + 0.934343i) q^{27} +(3.99254 - 13.4226i) q^{28} +(-2.25436 - 9.87698i) q^{29} +(-13.1656 - 7.60118i) q^{30} +(-2.58254 + 9.63818i) q^{31} +(0.691040 - 18.4684i) q^{32} +(0.906605 - 4.79152i) q^{33} +(-0.791794 - 7.02737i) q^{34} +(5.38705 - 0.662058i) q^{35} +(-18.7467 + 14.9500i) q^{36} +(4.45792 + 8.43479i) q^{37} +(3.13721 - 7.99347i) q^{38} +(-6.57062 + 7.39722i) q^{39} +(16.9819 - 6.66490i) q^{40} +(7.39484 + 2.58757i) q^{41} +(4.88331 - 18.9887i) q^{42} +(-4.50742 + 9.35975i) q^{43} +(6.13546 + 7.12954i) q^{44} +(-8.21635 - 4.34247i) q^{45} +(-0.293502 - 1.55119i) q^{46} +(-2.16156 + 2.92881i) q^{47} -36.8520i q^{48} +(2.68829 + 6.46321i) q^{49} +(-1.51166 - 1.51166i) q^{50} +(-1.07100 - 7.10565i) q^{51} +(-3.25331 - 18.8047i) q^{52} +(-7.89106 + 2.43407i) q^{53} +(-8.59489 + 7.39650i) q^{54} +(-1.58176 + 3.28456i) q^{55} +(14.1617 + 18.7888i) q^{56} +(2.88188 - 8.23594i) q^{57} +(25.0764 + 10.9407i) q^{58} +(-1.25859 - 1.08310i) q^{59} +(27.3099 - 11.9152i) q^{60} +(2.11663 - 6.86195i) q^{61} +(-16.8009 - 21.0676i) q^{62} +(2.54908 - 11.7114i) q^{63} +(18.0219 + 14.3720i) q^{64} +(6.17593 - 4.07023i) q^{65} +(8.95742 + 9.65380i) q^{66} +(3.49793 + 0.937267i) q^{67} +(12.0035 + 6.93024i) q^{68} +(-0.356965 - 1.56396i) q^{69} +(-7.20033 + 12.7670i) q^{70} +(-2.34248 - 3.72804i) q^{71} +(-1.50633 - 40.2575i) q^{72} +(0.555509 - 0.409985i) q^{73} +(-25.4765 - 3.83996i) q^{74} +(-1.59240 - 1.47754i) q^{75} +(8.95425 + 14.2506i) q^{76} +(-4.62836 - 0.827474i) q^{77} +(-5.53618 - 26.1395i) q^{78} +(-0.441303 + 0.764359i) q^{79} +(-7.13038 + 26.6109i) q^{80} +(1.51610 - 1.40673i) q^{81} +(-17.4811 + 11.9184i) q^{82} +(2.45069 - 0.276126i) q^{83} +(24.2613 + 29.8012i) q^{84} +(-0.601475 + 5.33824i) q^{85} +(-13.1091 - 24.8036i) q^{86} +(25.8788 + 10.1567i) q^{87} +(-15.7591 + 1.18098i) q^{88} +(-3.10925 - 1.35655i) q^{89} +(22.6116 - 10.8892i) q^{90} +(7.19560 + 6.26285i) q^{91} +(2.78779 + 1.34253i) q^{92} +(-17.8604 - 20.7542i) q^{93} +(-2.89751 - 9.39351i) q^{94} +(-3.67456 + 5.38959i) q^{95} +(40.8051 + 30.1155i) q^{96} +(-9.67543 - 9.67543i) q^{97} +(-18.3547 - 4.52340i) q^{98} +(5.69256 + 5.69256i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1536 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 28 q^{6} - 22 q^{7} - 12 q^{8} - 176 q^{9} - 22 q^{11} - 28 q^{13} - 84 q^{14} - 8 q^{15} - 180 q^{16} - 18 q^{18} - 54 q^{19} - 28 q^{20} - 2 q^{21} - 48 q^{22}+ \cdots - 32 q^{99}+O(q^{100}) $ 1536 * q - 26 * q^2 - 44 * q^3 - 22 * q^5 - 28 * q^6 - 22 * q^7 - 12 * q^8 - 176 * q^9 - 22 * q^11 - 28 * q^13 - 84 * q^14 - 8 * q^15 - 180 * q^16 - 18 * q^18 - 54 * q^19 - 28 * q^20 - 2 * q^21 - 48 * q^22 + 68 * q^24 - 52 * q^26 - 56 * q^27 + 62 * q^28 - 48 * q^29 - 66 * q^31 - 32 * q^32 - 76 * q^33 + 28 * q^34 - 140 * q^35 - 62 * q^37 - 16 * q^39 + 76 * q^40 - 28 * q^41 + 128 * q^42 - 226 * q^44 + 66 * q^45 - 32 * q^46 + 68 * q^47 + 156 * q^50 + 48 * q^52 - 48 * q^53 - 64 * q^54 + 28 * q^55 - 62 * q^57 - 22 * q^58 + 54 * q^59 - 88 * q^60 - 8 * q^61 - 150 * q^63 - 12 * q^65 + 72 * q^66 - 30 * q^67 - 36 * q^68 + 62 * q^70 + 104 * q^71 - 54 * q^72 - 136 * q^73 + 12 * q^74 + 28 * q^76 + 68 * q^78 - 16 * q^79 - 180 * q^80 + 64 * q^81 + 70 * q^83 + 30 * q^84 - 96 * q^85 + 30 * q^86 + 416 * q^87 - 38 * q^89 - 196 * q^91 - 180 * q^92 + 38 * q^93 - 264 * q^94 - 350 * q^96 - 390 * q^98 - 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{29}{42}\right)$

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 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.60364	+	2.17285i	−1.13394	+	1.53644i	−0.327774	+	0.944756i	$0.606299\pi$
$2$	−1.60364	+	2.17285i	−1.13394	+	1.53644i	−0.806170	+	0.591684i	$0.798463\pi$
$3$	−1.54581	+	2.26729i	−0.892476	+	1.30902i	0.0580303	+	0.998315i	$0.481518\pi$
$3$	−1.54581	+	2.26729i	−0.892476	+	1.30902i	−0.950506	+	0.310706i	$0.899434\pi$
$4$	−1.56013	−	5.05780i	−0.780063	−	2.52890i
$5$	1.55493	−	1.33812i	0.695385	−	0.598427i	−0.231919	−	0.972735i	$-0.574501\pi$
$5$	1.55493	−	1.33812i	0.695385	−	0.598427i	0.927305	+	0.374308i	$0.122120\pi$
$6$	−2.44757	−	6.99474i	−0.999215	−	2.85559i
$7$	2.20094	+	1.46828i	0.831878	+	0.554959i
$7$	2.20094	+	1.46828i	0.831878	+	0.554959i
$8$	8.39375	+	2.93710i	2.96764	+	1.03842i
$9$	−1.65505	−	4.21700i	−0.551683	−	1.40567i
$10$	0.414004	+	5.52450i	0.130920	+	1.74700i
$11$	−1.62882	+	0.710645i	−0.491106	+	0.214268i	−0.630827	−	0.775923i	$-0.717284\pi$
$11$	−1.62882	+	0.710645i	−0.491106	+	0.214268i	0.139721	+	0.990191i	$0.455380\pi$
$12$	13.8792	+	4.28116i	4.00657	+	1.23586i
$13$	3.57611	+	0.459857i	0.991833	+	0.127541i
$13$	3.57611	+	0.459857i	0.991833	+	0.127541i
$14$	−6.71988	+	2.42773i	−1.79596	+	0.648838i
$15$	0.630289	+	5.59397i	0.162740	+	1.44436i
$16$	−11.0959	+	7.56509i	−2.77399	+	1.89127i
$17$	−1.91962	+	1.78115i	−0.465576	+	0.431991i	−0.877754	−	0.479112i	$-0.840959\pi$
$17$	−1.91962	+	1.78115i	−0.465576	+	0.431991i	0.412178	+	0.911103i	$0.364768\pi$
$18$	11.8170	+	3.16636i	2.78530	+	0.746318i
$19$	−3.07140	+	0.822980i	−0.704628	+	0.188804i	−0.593303	−	0.804980i	$-0.702176\pi$
$19$	−3.07140	+	0.822980i	−0.704628	+	0.188804i	−0.111325	+	0.993784i	$0.535510\pi$
$20$	−9.19386	−	5.77688i	−2.05581	−	1.29175i
$21$	−6.73127	+	2.72049i	−1.46888	+	0.593659i
$22$	1.06791	−	4.67880i	0.227678	−	0.997523i
$23$	−0.397623	+	0.428536i	−0.0829102	+	0.0893559i	−0.773144	−	0.634230i	$-0.781317\pi$
$23$	−0.397623	+	0.428536i	−0.0829102	+	0.0893559i	0.690234	+	0.723586i	$0.257508\pi$
$24$	−19.6344	+	14.4909i	−4.00786	+	2.95794i
$25$	−0.117985	+	0.782779i	−0.0235970	+	0.156556i
$26$	−6.73399	+	7.03291i	−1.32064	+	1.37927i
$27$	4.09362	+	0.934343i	0.787818	+	0.179814i
$28$	3.99254	−	13.4226i	0.754520	−	2.53664i
$29$	−2.25436	−	9.87698i	−0.418623	−	1.83411i	−0.540213	−	0.841528i	$-0.681656\pi$
$29$	−2.25436	−	9.87698i	−0.418623	−	1.83411i	0.121589	−	0.992580i	$-0.461201\pi$
$30$	−13.1656	−	7.60118i	−2.40370	−	1.38778i
$31$	−2.58254	+	9.63818i	−0.463838	+	1.73107i	0.196874	+	0.980429i	$0.436921\pi$
$31$	−2.58254	+	9.63818i	−0.463838	+	1.73107i	−0.660713	+	0.750639i	$0.729746\pi$
$32$	0.691040	−	18.4684i	0.122160	−	3.26479i
$33$	0.906605	−	4.79152i	0.157820	−	0.834097i
$34$	−0.791794	−	7.02737i	−0.135792	−	1.20518i
$35$	5.38705	−	0.662058i	0.910578	−	0.111908i
$36$	−18.7467	+	14.9500i	−3.12444	+	2.49166i
$37$	4.45792	+	8.43479i	0.732877	+	1.38667i	0.915024	+	0.403400i	$0.132172\pi$
$37$	4.45792	+	8.43479i	0.732877	+	1.38667i	−0.182147	+	0.983271i	$0.558305\pi$
$38$	3.13721	−	7.99347i	0.508922	−	1.29671i
$39$	−6.57062	+	7.39722i	−1.05214	+	1.18450i
$40$	16.9819	−	6.66490i	2.68507	−	1.05381i
$41$	7.39484	+	2.58757i	1.15488	+	0.404110i	0.838702	−	0.544590i	$-0.183315\pi$
$41$	7.39484	+	2.58757i	1.15488	+	0.404110i	0.316177	+	0.948700i	$0.397601\pi$
$42$	4.88331	−	18.9887i	0.753512	−	2.93003i
$43$	−4.50742	+	9.35975i	−0.687375	+	1.42735i	0.206235	+	0.978503i	$0.433879\pi$
$43$	−4.50742	+	9.35975i	−0.687375	+	1.42735i	−0.893609	+	0.448845i	$0.851835\pi$
$44$	6.13546	+	7.12954i	0.924956	+	1.07482i
$45$	−8.21635	−	4.34247i	−1.22482	−	0.647337i
$46$	−0.293502	−	1.55119i	−0.0432745	−	0.228711i
$47$	−2.16156	+	2.92881i	−0.315296	+	0.427211i	−0.933374	−	0.358906i	$-0.883150\pi$
$47$	−2.16156	+	2.92881i	−0.315296	+	0.427211i	0.618078	+	0.786117i	$0.287912\pi$
$48$		−	36.8520i		−	5.31912i
$49$	2.68829	+	6.46321i	0.384041	+	0.923316i
$50$	−1.51166	−	1.51166i	−0.213781	−	0.213781i
$51$	−1.07100	−	7.10565i	−0.149971	−	0.994990i
$52$	−3.25331	−	18.8047i	−0.451153	−	2.60774i
$53$	−7.89106	+	2.43407i	−1.08392	+	0.334345i	−0.784723	−	0.619846i	$-0.787195\pi$
$53$	−7.89106	+	2.43407i	−1.08392	+	0.334345i	−0.299197	+	0.954191i	$0.596719\pi$
$54$	−8.59489	+	7.39650i	−1.16962	+	1.00654i
$55$	−1.58176	+	3.28456i	−0.213285	+	0.442890i
$56$	14.1617	+	18.7888i	1.89243	+	2.51076i
$57$	2.88188	−	8.23594i	0.381714	−	1.09088i
$58$	25.0764	+	10.9407i	3.29269	+	1.43659i
$59$	−1.25859	−	1.08310i	−0.163854	−	0.141008i	0.566539	−	0.824035i	$-0.308282\pi$
$59$	−1.25859	−	1.08310i	−0.163854	−	0.141008i	−0.730393	+	0.683027i	$0.760663\pi$
$60$	27.3099	−	11.9152i	3.52569	−	1.53824i
$61$	2.11663	−	6.86195i	0.271007	−	0.878582i	−0.713109	−	0.701053i	$-0.752713\pi$
$61$	2.11663	−	6.86195i	0.271007	−	0.878582i	0.984116	−	0.177529i	$-0.0568104\pi$
$62$	−16.8009	−	21.0676i	−2.13371	−	2.67559i
$63$	2.54908	−	11.7114i	0.321154	−	1.47550i
$64$	18.0219	+	14.3720i	2.25273	+	1.79649i
$65$	6.17593	−	4.07023i	0.766030	−	0.504850i
$66$	8.95742	+	9.65380i	1.10258	+	1.18830i
$67$	3.49793	+	0.937267i	0.427340	+	0.114505i	0.466077	−	0.884744i	$-0.345667\pi$
$67$	3.49793	+	0.937267i	0.427340	+	0.114505i	−0.0387373	+	0.999249i	$0.512334\pi$
$68$	12.0035	+	6.93024i	1.45564	+	0.840415i
$69$	−0.356965	−	1.56396i	−0.0429735	−	0.188279i
$70$	−7.20033	+	12.7670i	−0.860605	+	1.52595i
$71$	−2.34248	−	3.72804i	−0.278002	−	0.442437i	0.678314	−	0.734772i	$-0.262711\pi$
$71$	−2.34248	−	3.72804i	−0.278002	−	0.442437i	−0.956316	+	0.292335i	$0.905568\pi$
$72$	−1.50633	−	40.2575i	−0.177522	−	4.74439i
$73$	0.555509	−	0.409985i	0.0650175	−	0.0479851i	−0.560827	−	0.827933i	$-0.689517\pi$
$73$	0.555509	−	0.409985i	0.0650175	−	0.0479851i	0.625844	+	0.779948i	$0.284755\pi$
$74$	−25.4765	−	3.83996i	−2.96158	−	0.446386i
$75$	−1.59240	−	1.47754i	−0.183875	−	0.170611i
$76$	8.95425	+	14.2506i	1.02712	+	1.63466i
$77$	−4.62836	−	0.827474i	−0.527450	−	0.0942994i
$78$	−5.53618	−	26.1395i	−0.626849	−	2.95971i
$79$	−0.441303	+	0.764359i	−0.0496504	+	0.0859971i	−0.889783	−	0.456385i	$-0.849144\pi$
$79$	−0.441303	+	0.764359i	−0.0496504	+	0.0859971i	0.840132	+	0.542382i	$0.182477\pi$
$80$	−7.13038	+	26.6109i	−0.797201	+	2.97519i
$81$	1.51610	−	1.40673i	0.168455	−	0.156304i
$82$	−17.4811	+	11.9184i	−1.93046	+	1.31617i
$83$	2.45069	−	0.276126i	0.268998	−	0.0303088i	0.0235647	−	0.999722i	$-0.492498\pi$
$83$	2.45069	−	0.276126i	0.268998	−	0.0303088i	0.245433	+	0.969414i	$0.421070\pi$
$84$	24.2613	+	29.8012i	2.64713	+	3.25157i
$85$	−0.601475	+	5.33824i	−0.0652392	+	0.579014i
$86$	−13.1091	−	24.8036i	−1.41359	−	2.67464i
$87$	25.8788	+	10.1567i	2.77450	+	1.08891i
$88$	−15.7591	+	1.18098i	−1.67993	+	0.125893i
$89$	−3.10925	−	1.35655i	−0.329580	−	0.143794i	0.228586	−	0.973524i	$-0.426590\pi$
$89$	−3.10925	−	1.35655i	−0.329580	−	0.143794i	−0.558166	+	0.829729i	$0.688495\pi$
$90$	22.6116	−	10.8892i	2.38347	−	1.14782i
$91$	7.19560	+	6.26285i	0.754304	+	0.656525i
$92$	2.78779	+	1.34253i	0.290648	+	0.139968i
$93$	−17.8604	−	20.7542i	−1.85204	−	2.15211i
$94$	−2.89751	−	9.39351i	−0.298856	−	0.968867i
$95$	−3.67456	+	5.38959i	−0.377002	+	0.552961i
$96$	40.8051	+	30.1155i	4.16465	+	3.07365i
$97$	−9.67543	−	9.67543i	−0.982391	−	0.982391i	0.0174565	−	0.999848i	$-0.494443\pi$
$97$	−9.67543	−	9.67543i	−0.982391	−	0.982391i	−0.999848	+	0.0174565i	$0.994443\pi$
$98$	−18.3547	−	4.52340i	−1.85410	−	0.456932i
$99$	5.69256	+	5.69256i	0.572124	+	0.572124i
$100$	4.14321	−	0.624489i	0.414321	−	0.0624489i
$101$	1.99807	+	1.36226i	0.198815	+	0.135550i	0.658636	−	0.752462i	$-0.271134\pi$
$101$	1.99807	+	1.36226i	0.198815	+	0.135550i	−0.459820	+	0.888012i	$0.652086\pi$
$102$	17.1571	+	9.06777i	1.69880	+	0.897843i
$103$	0.262686	−	3.50530i	0.0258832	−	0.345388i	−0.969195	−	0.246295i	$-0.920787\pi$
$103$	0.262686	−	3.50530i	0.0258832	−	0.345388i	0.995078	−	0.0990928i	$-0.0315941\pi$
$104$	28.6663	+	14.3633i	2.81096	+	1.40844i
$105$	−6.82630	+	13.2374i	−0.666178	+	1.29184i
$106$	7.36554	−	21.0495i	0.715404	−	2.04451i
$107$	−3.05492	−	7.78382i	−0.295331	−	0.752490i	−0.999114	−	0.0420760i	$-0.986603\pi$
$107$	−3.05492	−	7.78382i	−0.295331	−	0.752490i	0.703784	−	0.710414i	$-0.251492\pi$
$108$	−1.66084	−	22.1624i	−0.159815	−	2.13258i
$109$	−1.32999	−	3.04838i	−0.127390	−	0.291982i	0.841166	−	0.540777i	$-0.181870\pi$
$109$	−1.32999	−	3.04838i	−0.127390	−	0.291982i	−0.968556	+	0.248796i	$0.919965\pi$
$110$	−4.60030	−	8.70419i	−0.438621	−	0.829912i
$111$	−26.0152	−	2.93121i	−2.46926	−	0.278218i
$112$	−35.5292	+	0.358328i	−3.35720	+	0.0338588i
$113$	−8.15707	+	10.2286i	−0.767353	+	0.962230i	−0.999946	−	0.0103443i	$-0.996707\pi$
$113$	−8.15707	+	10.2286i	−0.767353	+	0.962230i	0.232594	+	0.972574i	$0.425279\pi$
$114$	13.2740	+	19.4694i	1.24322	+	1.82347i
$115$	−0.0448414	+	1.19841i	−0.00418148	+	0.111752i
$116$	−46.4388	+	26.8114i	−4.31173	+	2.48938i
$117$	−3.97942	−	15.8415i	−0.367897	−	1.46455i
$118$	4.37174	−	0.997821i	0.402451	−	0.0918569i
$119$	−6.84019	+	1.10165i	−0.627040	+	0.100989i
$120$	−11.1396	+	48.8056i	−1.01690	+	4.45532i
$121$	−5.33388	+	5.74855i	−0.484898	+	0.522596i
$122$	11.5157	+	15.6032i	1.04258	+	1.41265i
$123$	−17.2978	+	12.7664i	−1.55969	+	1.15110i
$124$	52.7771	−	1.97478i	4.73952	−	0.177340i
$125$	6.32114	+	10.0600i	0.565380	+	0.899797i
$126$	21.3595	+	24.3197i	1.90285	+	2.16657i
$127$	9.20188	−	2.10027i	0.816535	−	0.186369i	0.206198	−	0.978510i	$-0.433891\pi$
$127$	9.20188	−	2.10027i	0.816535	−	0.186369i	0.610337	+	0.792142i	$0.291034\pi$
$128$	−24.4255	+	6.54480i	−2.15893	+	0.578484i
$129$	−14.2536	−	24.6880i	−1.25496	−	2.17366i
$130$	−1.05996	+	19.9466i	−0.0929644	+	1.74943i
$131$	7.27838	+	10.6754i	0.635915	+	0.932717i	0.999999	+	0.00135029i	$0.000429809\pi$
$131$	7.27838	+	10.6754i	0.635915	+	0.932717i	−0.364084	+	0.931366i	$0.618618\pi$
$132$	−25.6490	+	2.88995i	−2.23246	+	0.251538i
$133$	−7.96834	−	2.69836i	−0.690943	−	0.233977i
$134$	−7.64596	+	6.09745i	−0.660510	+	0.526739i
$135$	7.61556	−	4.02494i	0.655443	−	0.346412i
$136$	−21.3442	+	9.31238i	−1.83025	+	0.798530i
$137$	−8.85057	+	10.2846i	−0.756156	+	0.878669i	−0.995740	−	0.0922069i	$-0.970608\pi$
$137$	−8.85057	+	10.2846i	−0.756156	+	0.878669i	0.239584	+	0.970876i	$0.422989\pi$
$138$	3.97071	+	1.73240i	0.338009	+	0.147472i
$139$	6.78128	+	14.0815i	0.575181	+	1.19438i	0.962210	+	0.272308i	$0.0877870\pi$
$139$	6.78128	+	14.0815i	0.575181	+	1.19438i	−0.387029	+	0.922068i	$0.626499\pi$
$140$	−11.7530	−	26.2138i	−0.993313	−	2.21547i
$141$	−3.29910	−	9.42828i	−0.277834	−	0.794004i
$142$	11.8570	+	0.888559i	0.995017	+	0.0745662i
$143$	−6.15161	+	1.79232i	−0.514424	+	0.149881i
$144$	50.2663	+	34.2710i	4.18886	+	2.85592i
$145$	−16.7220	−	12.3414i	−1.38869	−	1.02490i
$146$			1.86451i			0.154308i
$147$	−18.8096	−	3.89578i	−1.55139	−	0.321319i
$148$	35.7066	−	35.7066i	2.93507	−	2.93507i
$149$	3.35431	−	4.54492i	0.274795	−	0.372335i	−0.645366	−	0.763873i	$-0.723295\pi$
$149$	3.35431	−	4.54492i	0.274795	−	0.372335i	0.920162	+	0.391539i	$0.128057\pi$
$150$	5.76411	−	1.09063i	0.470638	−	0.0890495i
$151$	−7.59174	−	4.01235i	−0.617807	−	0.326521i	0.128916	−	0.991656i	$-0.458850\pi$
$151$	−7.59174	−	4.01235i	−0.617807	−	0.326521i	−0.746723	+	0.665135i	$0.768374\pi$
$152$	−28.1978	−	2.11313i	−2.28714	−	0.171397i
$153$	10.6881	+	5.14714i	0.864085	+	0.416122i
$154$	9.22020	−	8.72977i	0.742985	−	0.703465i
$155$	8.88141	+	18.4424i	0.713372	+	1.48133i
$156$	47.6647	+	21.6923i	3.81623	+	1.73678i
$157$	1.73472	−	0.129999i	0.138446	−	0.0103751i	−0.00532691	−	0.999986i	$-0.501696\pi$
$157$	1.73472	−	0.129999i	0.138446	−	0.0103751i	0.143773	+	0.989611i	$0.454077\pi$
$158$	−0.953150	−	2.18464i	−0.0758285	−	0.173801i
$159$	6.67936	−	21.6539i	0.529708	−	1.71727i
$160$	−23.6385	−	29.6418i	−1.86879	−	2.34339i
$161$	−1.50436	+	0.359359i	−0.118560	+	0.0283215i
$162$	0.625352	+	5.55016i	0.0491323	+	0.436061i
$163$	5.51592	+	1.04367i	0.432041	+	0.0817465i	0.397383	−	0.917653i	$-0.369918\pi$
$163$	5.51592	+	1.04367i	0.432041	+	0.0817465i	0.0346574	+	0.999399i	$0.488966\pi$
$164$	1.55052	−	41.4386i	0.121075	−	3.23581i
$165$	−5.00195	−	8.66363i	−0.389401	−	0.674463i
$166$	−3.33004	+	5.76779i	−0.258461	+	0.447667i
$167$	−10.9097	−	6.85502i	−0.844218	−	0.530458i	0.0390977	−	0.999235i	$-0.487552\pi$
$167$	−10.9097	−	6.85502i	−0.844218	−	0.530458i	−0.883316	+	0.468778i	$0.844695\pi$
$168$	−64.4909	+	3.06466i	−4.97558	+	0.236443i
$169$	12.5771	+	3.28899i	0.967466	+	0.252999i
$170$	−10.6347	−	9.86753i	−0.815642	−	0.756805i
$171$	8.55382	+	11.5900i	0.654127	+	0.886311i
$172$	54.3719	+	8.19525i	4.14582	+	0.624882i
$173$	0.317118	+	0.294243i	0.0241101	+	0.0223709i	0.692136	−	0.721767i	$-0.256670\pi$
$173$	0.317118	+	0.294243i	0.0241101	+	0.0223709i	−0.668026	+	0.744138i	$0.732860\pi$
$174$	−63.5693	+	39.9432i	−4.81917	+	3.02809i
$175$	−1.40902	+	1.54962i	−0.106512	+	0.117140i
$176$	12.6972	−	20.2074i	0.957085	−	1.52319i
$177$	4.40124	−	1.17931i	0.330818	−	0.0886424i
$178$	7.93371	−	4.58053i	0.594657	−	0.343325i
$179$	−0.362720	−	0.390919i	−0.0271110	−	0.0292187i	0.719351	−	0.694647i	$-0.244439\pi$
$179$	−0.362720	−	0.390919i	−0.0271110	−	0.0292187i	−0.746462	+	0.665428i	$0.768249\pi$
$180$	−9.14481	+	48.3315i	−0.681614	+	3.60242i
$181$	7.30816	−	9.16414i	0.543211	−	0.681165i	−0.432145	−	0.901804i	$-0.642243\pi$
$181$	7.30816	−	9.16414i	0.543211	−	0.681165i	0.975355	+	0.220639i	$0.0708144\pi$
$182$	−25.1474	+	5.59163i	−1.86405	+	0.414479i
$183$	12.2861	+	15.4063i	0.908216	+	1.13887i
$184$	−4.59620	+	2.42916i	−0.338837	+	0.179080i
$185$	18.2185	+	7.15025i	1.33945	+	0.525697i
$186$	73.7375	−	5.52586i	5.40670	−	0.405176i
$187$	1.86094	−	4.26533i	0.136086	−	0.311911i
$188$	18.1857	+	6.36344i	1.32633	+	0.464101i
$189$	7.63795	+	8.06703i	0.555579	+	0.586790i
$190$	−5.81813	−	16.6273i	−0.422091	−	1.20627i
$191$	−0.324282	+	4.32724i	−0.0234642	+	0.313108i	0.973106	+	0.230357i	$0.0739895\pi$
$191$	−0.324282	+	4.32724i	−0.0234642	+	0.313108i	−0.996570	+	0.0827505i	$0.973630\pi$
$192$	−60.4439	+	18.6445i	−4.36216	+	1.34555i
$193$	1.36516	+	7.21502i	0.0982660	+	0.519348i	0.996765	+	0.0803726i	$0.0256110\pi$
$193$	1.36516	+	7.21502i	0.0982660	+	0.519348i	−0.898499	+	0.438976i	$0.855341\pi$
$194$	36.5392	−	5.50740i	2.62336	−	0.395408i
$195$	−0.318445	+	20.2945i	−0.0228043	+	1.45332i
$196$	28.4956	−	23.6803i	2.03540	−	1.69145i
$197$	−6.46692	+	6.46692i	−0.460749	+	0.460749i	−0.898901	−	0.438152i	$-0.855633\pi$
$197$	−6.46692	+	6.46692i	−0.460749	+	0.460749i	0.438152	+	0.898901i	$0.355633\pi$
$198$	−21.4979	+	3.24029i	−1.52779	+	0.230277i
$199$	−1.03556	−	0.706033i	−0.0734089	−	0.0500494i	0.526059	−	0.850448i	$-0.323669\pi$
$199$	−1.03556	−	0.706033i	−0.0734089	−	0.0500494i	−0.599468	+	0.800398i	$0.704621\pi$
$200$	−3.28944	+	6.22392i	−0.232598	+	0.440097i
$201$	−7.53220	+	6.48198i	−0.531280	+	0.457204i
$202$	−6.16418	+	2.15694i	−0.433710	+	0.151762i
$203$	9.54050	−	25.0487i	0.669611	−	1.75807i
$204$	−34.2681	+	16.5026i	−2.39925	+	1.15542i
$205$	14.9609	−	5.87173i	1.04492	−	0.410100i
$206$	7.19525	+	6.19202i	0.501317	+	0.431418i
$207$	2.46522	+	0.967528i	0.171345	+	0.0672478i
$208$	−43.1591	+	21.9510i	−2.99255	+	1.52203i
$209$	4.41790	−	3.52316i	0.305593	−	0.243702i
$210$	−17.8161	−	36.0606i	−1.22943	−	2.48842i
$211$	−11.5115	+	14.4350i	−0.792485	+	0.993745i	0.207395	+	0.978257i	$0.433502\pi$
$211$	−11.5115	+	14.4350i	−0.792485	+	0.993745i	−0.999880	+	0.0154877i	$0.995070\pi$
$212$	24.6221	+	36.1140i	1.69105	+	2.48032i
$213$	12.0736	+	0.451762i	0.827269	+	0.0309542i
$214$	21.8121	+	5.84454i	1.49104	+	0.399524i
$215$	5.51579	+	20.5852i	0.376174	+	1.40390i
$216$	31.6166	+	19.8660i	2.15124	+	1.35171i
$217$	−19.8356	+	17.4212i	−1.34653	+	1.18263i
$218$	8.75651	+	1.99862i	0.593066	+	0.135363i
$219$	0.0708408	+	1.89326i	0.00478698	+	0.127935i
$220$	19.0804	+	2.87591i	1.28640	+	0.193894i
$221$	−7.68383	+	5.48682i	−0.516870	+	0.369083i
$222$	48.0882	−	51.8267i	3.22747	−	3.47838i
$223$	23.2279	−	14.5951i	1.55546	−	0.977357i	0.567368	−	0.823464i	$-0.307962\pi$
$223$	23.2279	−	14.5951i	1.55546	−	0.977357i	0.988087	−	0.153893i	$-0.0491812\pi$
$224$	28.6378	−	39.6333i	1.91345	−	2.64811i
$225$	3.49625	−	0.797995i	0.233083	−	0.0531997i
$226$	−9.14435	−	34.1272i	−0.608273	−	2.27011i
$227$	3.68083	−	13.7370i	0.244305	−	0.911759i	−0.729426	−	0.684060i	$-0.760213\pi$
$227$	3.68083	−	13.7370i	0.244305	−	0.911759i	0.973731	−	0.227700i	$-0.0731205\pi$
$228$	−46.1519	−	1.72688i	−3.05648	−	0.114365i
$229$	5.18168	−	27.3858i	0.342415	−	1.80971i	−0.211777	−	0.977318i	$-0.567925\pi$
$229$	5.18168	−	27.3858i	0.342415	−	1.80971i	0.554192	−	0.832389i	$-0.313027\pi$
$230$	−2.53207	−	2.01925i	−0.166959	−	0.133146i
$231$	9.03070	−	9.21471i	0.594176	−	0.606284i
$232$	10.0872	−	89.5262i	0.662256	−	5.87768i
$233$	−8.16314	+	26.4643i	−0.534785	+	1.73373i	0.134681	+	0.990889i	$0.456999\pi$
$233$	−8.16314	+	26.4643i	−0.534785	+	1.73373i	−0.669466	+	0.742843i	$0.733477\pi$
$234$	40.8028	+	16.7574i	2.66737	+	1.09546i
$235$	0.558040	+	7.44653i	0.0364025	+	0.485758i
$236$	−3.51456	+	8.05546i	−0.228778	+	0.524366i
$237$	−1.05085	−	2.18212i	−0.0682602	−	0.141744i
$238$	8.57547	−	16.6294i	0.555865	−	1.07792i
$239$	14.7301	−	5.15430i	0.952814	−	0.333404i	0.191285	−	0.981535i	$-0.438735\pi$
$239$	14.7301	−	5.15430i	0.952814	−	0.333404i	0.761529	+	0.648130i	$0.224449\pi$
$240$	−49.3125	−	57.3022i	−3.18311	−	3.69884i
$241$	0.581376	−	1.10002i	0.0374497	−	0.0708584i	−0.864680	−	0.502322i	$-0.832479\pi$
$241$	0.581376	−	1.10002i	0.0374497	−	0.0708584i	0.902130	+	0.431464i	$0.142003\pi$
$242$	−3.93715	−	20.8083i	−0.253090	−	1.33761i
$243$	2.72331	+	18.0680i	0.174700	+	1.15906i
$244$	−38.0086			−2.43325
$245$	12.8287	+	6.45257i	0.819594	+	0.412239i
$246$		−	58.0582i		−	3.70166i
$247$	−11.3621	+	1.53066i	−0.722954	+	0.0973934i
$248$	−49.9855	+	73.3153i	−3.17408	+	4.65552i
$249$	−3.16225	+	5.98326i	−0.200399	+	0.379174i
$250$	−31.9958	−	2.39776i	−2.02359	−	0.151647i
$251$	11.3341	+	5.45822i	0.715402	+	0.344520i	0.755924	−	0.654659i	$-0.227188\pi$
$251$	11.3341	+	5.45822i	0.715402	+	0.344520i	−0.0405220	+	0.999179i	$0.512902\pi$
$252$	−63.2111	+	5.37859i	−3.98192	+	0.338819i
$253$	0.343118	−	0.980575i	0.0215716	−	0.0616482i
$254$	−10.1929	+	23.3624i	−0.639561	+	1.46589i
$255$	−11.1736	−	9.61564i	−0.699717	−	0.602155i
$256$	8.10600	−	20.6538i	0.506625	−	1.29086i
$257$	0.422044	+	0.130183i	0.0263264	+	0.00812062i	0.307890	−	0.951422i	$-0.400377\pi$
$257$	0.422044	+	0.130183i	0.0263264	+	0.00812062i	−0.281564	+	0.959542i	$0.590853\pi$
$258$	76.5012	+	8.61962i	4.76276	+	0.536634i
$259$	−2.57305	+	25.1100i	−0.159881	+	1.56026i
$260$	−30.2217	−	24.8866i	−1.87427	−	1.54340i
$261$	−37.9201	+	25.8535i	−2.34720	+	1.60029i
$262$	−34.8681	−	1.30467i	−2.15416	−	0.0806028i
$263$	−14.8057	−	25.6443i	−0.912961	−	1.58130i	−0.809859	−	0.586625i	$-0.800456\pi$
$263$	−14.8057	−	25.6443i	−0.912961	−	1.58130i	−0.103102	−	0.994671i	$-0.532877\pi$
$264$	21.6830	−	37.5561i	1.33450	−	2.31142i
$265$	−9.01295	+	14.3440i	−0.553661	+	0.881146i
$266$	18.6415	−	12.9869i	1.14298	−	0.796275i
$267$	7.88202	−	4.95260i	0.482372	−	0.303094i
$268$	−0.716695	−	19.1541i	−0.0437791	−	1.17002i
$269$	2.28196	−	15.1398i	0.139133	−	0.923090i	−0.804940	−	0.593356i	$-0.797803\pi$
$269$	2.28196	−	15.1398i	0.139133	−	0.923090i	0.944074	−	0.329734i	$-0.106959\pi$
$270$	−3.46700	+	23.0020i	−0.210995	+	1.39986i
$271$	−19.9661	+	0.747079i	−1.21285	+	0.0453818i	−0.636146	−	0.771568i	$-0.719473\pi$
$271$	−19.9661	+	0.747079i	−1.21285	+	0.0453818i	−0.576708	+	0.816950i	$0.695663\pi$
$272$	7.82546	−	34.2856i	0.474488	−	2.07887i
$273$	−25.3228	+	6.63332i	−1.53260	+	0.401467i
$274$	−8.15371	−	35.7237i	−0.492583	−	2.15815i
$275$	−0.364102	−	1.35885i	−0.0219562	−	0.0819416i
$276$	−7.35331	+	4.24544i	−0.442618	+	0.255545i
$277$	16.3914	+	17.6657i	0.984861	+	1.06143i	0.998106	+	0.0615153i	$0.0195933\pi$
$277$	16.3914	+	17.6657i	0.984861	+	1.06143i	−0.0132452	+	0.999912i	$0.504216\pi$
$278$	−41.4717	−	7.84688i	−2.48731	−	0.470624i
$279$	44.9184	−	5.06109i	2.68919	−	0.302999i
$280$	47.1621	+	10.2652i	2.81847	+	0.613461i
$281$	−1.91339	+	16.9818i	−0.114143	+	1.01305i	0.797853	+	0.602852i	$0.205969\pi$
$281$	−1.91339	+	16.9818i	−0.114143	+	1.01305i	−0.911996	+	0.410198i	$0.865460\pi$
$282$	25.7768	+	7.95110i	1.53499	+	0.473481i
$283$	4.82250	−	12.2875i	0.286668	−	0.730418i	−0.712907	−	0.701259i	$-0.752622\pi$
$283$	4.82250	−	12.2875i	0.286668	−	0.730418i	0.999575	−	0.0291593i	$-0.00928301\pi$
$284$	−15.2011	+	17.6640i	−0.902022	+	1.04817i
$285$	−6.53959	−	16.6626i	−0.387372	−	0.987008i
$286$	5.97052	−	16.2408i	0.353044	−	0.960338i
$287$	12.4763	+	16.5528i	0.736454	+	0.977081i
$288$	−79.0250	+	27.6520i	−4.65659	+	1.62941i
$289$	−0.757956	+	10.1142i	−0.0445857	+	0.594954i
$290$	53.6321	−	16.5433i	3.14938	−	0.971456i
$291$	36.8934	−	6.98061i	2.16273	−	0.409211i
$292$	−2.94029	−	2.17003i	−0.172067	−	0.126991i
$293$	21.9466	−	21.9466i	1.28213	−	1.28213i	0.342682	−	0.939452i	$-0.388665\pi$
$293$	21.9466	−	21.9466i	1.28213	−	1.28213i	0.939452	−	0.342682i	$-0.111335\pi$
$294$	38.6287	−	34.6230i	2.25287	−	2.01926i
$295$	−3.40634			−0.198324
$296$	12.6448	+	83.8929i	0.734965	+	4.87618i
$297$	−7.33174	+	1.38724i	−0.425431	+	0.0804959i
$298$	4.49636	+	14.5768i	0.260467	+	0.844414i
$299$	−1.61901	+	1.34964i	−0.0936296	+	0.0780517i
$300$	−4.98873	+	10.3592i	−0.288025	+	0.598090i
$301$	−23.6633	+	13.9821i	−1.36393	+	0.805914i
$302$	20.8927	−	10.0614i	1.20224	−	0.578967i
$303$	−6.17728	+	2.42440i	−0.354876	+	0.139278i
$304$	27.8542	−	32.3672i	1.59755	−	1.85638i
$305$	−5.89093	−	13.5022i	−0.337314	−	0.773131i
$306$	−28.3239	+	14.9696i	−1.61917	+	0.855757i
$307$	24.4832	+	2.75860i	1.39733	+	0.157441i	0.778284	−	0.627912i	$-0.216090\pi$
$307$	24.4832	+	2.75860i	1.39733	+	0.157441i	0.619047	+	0.785354i	$0.287519\pi$
$308$	3.03562	+	24.7003i	0.172970	+	1.40743i
$309$	7.54147	+	6.01413i	0.429020	+	0.342132i
$310$	−54.3153	−	10.2770i	−3.08490	−	0.583695i
$311$	−12.2403	+	11.3573i	−0.694083	+	0.644015i	−0.946163	−	0.323692i	$-0.895076\pi$
$311$	−12.2403	+	11.3573i	−0.694083	+	0.644015i	0.252080	+	0.967707i	$0.418886\pi$
$312$	−76.8785	+	42.7919i	−4.35239	+	2.42261i
$313$	22.4311	+	12.9506i	1.26788	+	0.732011i	0.974586	−	0.224012i	$-0.0719155\pi$
$313$	22.4311	+	12.9506i	1.26788	+	0.732011i	0.293293	+	0.956023i	$0.405249\pi$
$314$	−2.49940	+	3.97777i	−0.141049	+	0.224478i
$315$	−11.7077	−	21.6214i	−0.659656	−	1.21823i
$316$	4.55446	+	1.03953i	0.256209	+	0.0584780i
$317$	−0.830970	+	0.0310927i	−0.0466719	+	0.00174634i	−0.0607170	−	0.998155i	$-0.519339\pi$
$317$	−0.830970	+	0.0310927i	−0.0466719	+	0.00174634i	0.0140450	+	0.999901i	$0.495529\pi$
$318$	36.3396	+	49.2384i	2.03782	+	2.76115i
$319$	10.6910	+	14.4857i	0.598579	+	0.811045i
$320$	47.2542	−	1.76813i	2.64159	−	0.0988413i
$321$	22.3705	+	5.10593i	1.24860	+	0.284985i
$322$	1.63161	−	3.84503i	0.0909262	−	0.214275i
$323$	4.43007	−	7.05042i	0.246496	−	0.392296i
$324$	−9.48029	−	5.47345i	−0.526683	−	0.304081i
$325$	−0.781893	+	2.74504i	−0.0433716	+	0.152268i
$326$	−11.1133	+	10.3116i	−0.615509	+	0.571108i
$327$	8.96748	+	1.69674i	0.495903	+	0.0938299i
$328$	54.4705	+	43.4388i	3.00763	+	2.39850i
$329$	−9.05779	+	3.27236i	−0.499372	+	0.180411i
$330$	26.8461	+	3.02483i	1.47783	+	0.166512i
$331$	−14.4690	+	7.64710i	−0.795290	+	0.420323i	−0.814984	−	0.579483i	$-0.803254\pi$
$331$	−14.4690	+	7.64710i	−0.795290	+	0.420323i	0.0196946	+	0.999806i	$0.493731\pi$
$332$	−5.21997	−	11.9643i	−0.286483	−	0.656626i
$333$	28.1914	−	32.7590i	1.54488	−	1.79518i
$334$	32.3902	−	12.7122i	1.77231	−	0.695582i
$335$	6.69321	−	3.22328i	0.365689	−	0.176107i
$336$	54.1091	−	81.1090i	2.95189	−	4.42486i
$337$	−12.6672	+	26.3036i	−0.690024	+	1.43285i	0.201321	+	0.979525i	$0.435476\pi$
$337$	−12.6672	+	26.3036i	−0.690024	+	1.43285i	−0.891345	+	0.453325i	$0.850238\pi$
$338$	−27.3156	+	22.0538i	−1.48577	+	1.19957i
$339$	−10.5820	−	34.3060i	−0.574736	−	1.86325i
$340$	27.9382	−	5.28619i	1.51516	−	0.286684i
$341$	−2.64284	−	17.5341i	−0.143118	−	0.949524i
$342$	−38.9007			−2.10351
$343$	−3.57305	+	18.1723i	−0.192927	+	0.981213i
$344$	−65.3246	+	65.3246i	−3.52207	+	3.52207i
$345$	−2.64783	−	1.95419i	−0.142555	−	0.105210i
$346$	−1.14789	+	0.217193i	−0.0617110	+	0.0116763i
$347$	19.2941	−	5.95145i	1.03576	−	0.319491i	0.270168	−	0.962813i	$-0.412921\pi$
$347$	19.2941	−	5.95145i	1.03576	−	0.319491i	0.765595	+	0.643322i	$0.222444\pi$
$348$	10.9963	−	146.736i	0.589464	−	7.86586i
$349$	−23.6428	+	8.27299i	−1.26557	+	0.442843i	−0.877851	−	0.478934i	$-0.841023\pi$
$349$	−23.6428	+	8.27299i	−1.26557	+	0.442843i	−0.387721	+	0.921777i	$0.626738\pi$
$350$	−1.10753	−	5.54662i	−0.0592000	−	0.296479i
$351$	14.2096	+	5.22379i	0.758450	+	0.278825i
$352$	11.9989	+	30.5728i	0.639545	+	1.62953i
$353$	13.6168	−	15.8230i	0.724748	−	0.842172i	−0.267870	−	0.963455i	$-0.586320\pi$
$353$	13.6168	−	15.8230i	0.724748	−	0.842172i	0.992618	+	0.121283i	$0.0387008\pi$
$354$	−4.49554	+	11.4545i	−0.238935	+	0.608797i
$355$	−8.63098	−	2.66230i	−0.458085	−	0.141300i
$356$	−2.01035	+	17.8424i	−0.106549	+	0.945645i
$357$	8.07589	−	17.2117i	0.427421	−	0.910938i
$358$	1.43108	−	0.161244i	0.0756351	−	0.00852203i
$359$	−2.50802	−	0.474543i	−0.132368	−	0.0250454i	0.119305	−	0.992858i	$-0.461933\pi$
$359$	−2.50802	−	0.474543i	−0.132368	−	0.0250454i	−0.251673	+	0.967812i	$0.580981\pi$
$360$	−56.2117	−	60.5818i	−2.96262	−	3.19294i
$361$	−7.69827	+	4.44460i	−0.405172	+	0.233926i
$362$	8.19269	+	30.5755i	0.430598	+	1.60701i
$363$	−4.78846	−	20.9796i	−0.251329	−	1.10115i
$364$	20.4502	−	46.1648i	1.07188	−	2.41969i
$365$	0.315167	−	1.38084i	0.0164966	−	0.0722763i
$366$	−53.1782	+	1.98979i	−2.77967	+	0.104008i
$367$	3.99739	−	26.5210i	0.208662	−	1.38438i	−0.601826	−	0.798627i	$-0.705560\pi$
$367$	3.99739	−	26.5210i	0.208662	−	1.38438i	0.810488	−	0.585755i	$-0.199202\pi$
$368$	1.17009	−	7.76307i	0.0609954	−	0.404678i
$369$	−1.32706	−	35.4665i	−0.0690842	−	1.84631i
$370$	−44.7524	+	28.1198i	−2.32657	+	1.46188i
$371$	−20.9417	−	6.22906i	−1.08724	−	0.323397i
$372$	−77.1061	+	122.714i	−3.99777	+	6.36241i
$373$	11.9499	−	20.6978i	0.618742	−	1.07169i	−0.370974	−	0.928643i	$-0.620976\pi$
$373$	11.9499	−	20.6978i	0.618742	−	1.07169i	0.989716	−	0.143049i	$-0.0456906\pi$
$374$	6.28365	+	10.8836i	0.324920	+	0.562778i
$375$	−32.5803	−	1.21907i	−1.68244	−	0.0629525i
$376$	−26.7458	+	18.2350i	−1.37931	+	0.940397i
$377$	−3.51982	−	36.3578i	−0.181280	−	1.87252i
$378$	−29.7770	+	3.65953i	−1.53156	+	0.188226i
$379$	20.4854	+	2.30815i	1.05227	+	0.118562i	0.621116	−	0.783719i	$-0.286680\pi$
$379$	20.4854	+	2.30815i	1.05227	+	0.118562i	0.431150	+	0.902280i	$0.358108\pi$
$380$	32.9923	+	10.1768i	1.69247	+	0.522057i
$381$	−9.46247	+	24.1100i	−0.484777	+	1.23519i
$382$	−8.88242	−	7.64394i	−0.454464	−	0.391098i
$383$	1.78507	−	4.09142i	0.0912128	−	0.209062i	−0.864976	−	0.501814i	$-0.832666\pi$
$383$	1.78507	−	4.09142i	0.0912128	−	0.209062i	0.956188	+	0.292752i	$0.0945710\pi$
$384$	22.9183	−	65.4968i	1.16955	−	3.34237i
$385$	−8.30403	+	4.90665i	−0.423212	+	0.250066i
$386$	−17.8664	−	8.60401i	−0.909376	−	0.437932i
$387$	46.9300	+	3.51692i	2.38559	+	0.178775i
$388$	−33.8415	+	64.0313i	−1.71804	+	3.25070i
$389$	12.5628	−	18.4263i	0.636960	−	0.934249i	−0.363036	−	0.931775i	$-0.618260\pi$
$389$	12.5628	−	18.4263i	0.636960	−	0.934249i	0.999997	−	0.00247452i	$-0.000787664\pi$
$390$	−43.5862	−	33.2369i	−2.20707	−	1.68302i
$391$		−	1.53085i		−	0.0774184i
$392$	3.58173	+	62.1464i	0.180905	+	3.13886i
$393$	−35.4553			−1.78848
$394$	−3.68107	−	24.4223i	−0.185450	−	1.23038i
$395$	0.336613	+	1.77904i	0.0169368	+	0.0895133i
$396$	19.9107	−	37.6730i	1.00055	−	1.89314i
$397$	−2.16678	−	2.51784i	−0.108747	−	0.126367i	0.700960	−	0.713201i	$-0.252755\pi$
$397$	−2.16678	−	2.51784i	−0.108747	−	0.126367i	−0.809707	+	0.586834i	$0.800374\pi$
$398$	3.19477	−	1.11790i	0.160139	−	0.0560352i
$399$	18.4355	−	13.8954i	0.922931	−	0.695640i
$400$	−4.61264	−	9.57824i	−0.230632	−	0.478912i
$401$	−3.91114	+	8.96443i	−0.195313	+	0.447662i	−0.986468	−	0.163953i	$-0.947575\pi$
$401$	−3.91114	+	8.96443i	−0.195313	+	0.447662i	0.791155	+	0.611616i	$0.209480\pi$
$402$	−2.00547	−	26.7611i	−0.100024	−	1.33472i
$403$	−13.6676	+	33.2795i	−0.680833	+	1.65777i
$404$	3.77281	−	12.2311i	0.187704	−	0.608522i
$405$	0.475040	−	4.21610i	0.0236049	−	0.209500i
$406$	39.1276	+	60.8992i	1.94187	+	3.02238i
$407$	−13.2553	−	10.5707i	−0.657039	−	0.523971i
$408$	11.8803	−	62.7887i	0.588161	−	3.10850i
$409$	7.28752	+	0.272680i	0.360344	+	0.0134831i	0.216951	−	0.976183i	$-0.430389\pi$
$409$	7.28752	+	0.272680i	0.360344	+	0.0134831i	0.143394	+	0.989666i	$0.454198\pi$
$410$	−11.2335	+	41.9241i	−0.554784	+	2.07048i
$411$	−9.63675	−	35.9648i	−0.475346	−	1.77401i
$412$	−18.1390	+	4.14010i	−0.893642	+	0.203968i
$413$	−1.17978	−	4.23180i	−0.0580530	−	0.208233i
$414$	−6.05562	+	3.80500i	−0.297618	+	0.187005i
$415$	3.44115	−	3.70868i	0.168919	−	0.182052i
$416$	10.9641	−	65.7273i	0.537558	−	3.22255i
$417$	−42.4094	−	6.39219i	−2.07680	−	0.313027i
$418$	0.570590	+	15.2493i	0.0279085	+	0.745869i
$419$	16.3520	+	3.73224i	0.798849	+	0.182332i	0.602413	−	0.798185i	$-0.294206\pi$
$419$	16.3520	+	3.73224i	0.798849	+	0.182332i	0.196436	+	0.980517i	$0.437063\pi$
$420$	77.6023	+	13.8740i	3.78660	+	0.676982i
$421$	−7.10838	−	4.46649i	−0.346441	−	0.217683i	0.347559	−	0.937658i	$-0.387011\pi$
$421$	−7.10838	−	4.46649i	−0.346441	−	0.217683i	−0.694000	+	0.719975i	$0.744153\pi$
$422$	−12.9048	−	48.1613i	−0.628196	−	2.34446i
$423$	15.9283	+	4.26797i	0.774459	+	0.207516i
$424$	−73.3847	−	2.74586i	−3.56388	−	0.133351i
$425$	−1.16776	−	1.71278i	−0.0566445	−	0.0830823i
$426$	−20.3433	+	25.5097i	−0.985637	+	1.23595i
$427$	14.7339	−	11.9949i	0.713022	−	0.580476i
$428$	−34.6030	+	27.5950i	−1.67260	+	1.33385i
$429$	5.44553	−	16.7181i	0.262913	−	0.807157i
$430$	−53.5740	−	21.0263i	−2.58357	−	1.01398i
$431$	18.2730	+	15.7252i	0.880181	+	0.757457i	0.971168	−	0.238395i	$-0.0766213\pi$
$431$	18.2730	+	15.7252i	0.880181	+	0.757457i	−0.0909873	+	0.995852i	$0.529002\pi$
$432$	−52.4910	+	20.6012i	−2.52548	+	0.991176i
$433$	−5.68432	+	2.73743i	−0.273171	+	0.131552i	−0.565455	−	0.824779i	$-0.691299\pi$
$433$	−5.68432	+	2.73743i	−0.273171	+	0.131552i	0.292283	+	0.956332i	$0.405585\pi$
$434$	−6.04451	−	71.0371i	−0.290146	−	3.40989i
$435$	53.8306	−	18.8361i	2.58098	−	0.903124i
$436$	−13.3431	+	11.4827i	−0.639020	+	0.549921i
$437$	0.868584	−	1.64344i	0.0415500	−	0.0786165i
$438$	−4.22738	−	2.88218i	−0.201992	−	0.137716i
$439$	9.72055	−	1.46514i	0.463936	−	0.0699272i	0.0870850	−	0.996201i	$-0.472245\pi$
$439$	9.72055	−	1.46514i	0.463936	−	0.0699272i	0.376851	+	0.926274i	$0.377007\pi$
$440$	−22.9240	+	22.9240i	−1.09286	+	1.09286i
$441$	22.8061	−	22.0334i	1.08600	−	1.04921i
$442$	0.400043	−	25.4947i	0.0190281	−	1.21266i
$443$	−11.8530	+	1.78656i	−0.563155	+	0.0848820i	−0.424449	−	0.905452i	$-0.639532\pi$
$443$	−11.8530	+	1.78656i	−0.563155	+	0.0848820i	−0.138706	+	0.990334i	$0.544294\pi$
$444$	25.7615	+	136.153i	1.22259	+	6.46154i
$445$	−6.64990	+	2.05122i	−0.315236	+	0.0972373i
$446$	−5.53625	+	73.8761i	−0.262149	+	3.49813i
$447$	5.11954	+	14.6308i	0.242146	+	0.692013i
$448$	18.5630	+	58.0930i	0.877018	+	2.74464i
$449$	−0.800174	−	0.279993i	−0.0377625	−	0.0132137i	0.311332	−	0.950301i	$-0.399225\pi$
$449$	−0.800174	−	0.279993i	−0.0377625	−	0.0132137i	−0.349094	+	0.937088i	$0.613511\pi$
$450$	−3.87279	+	8.87653i	−0.182565	+	0.418444i
$451$	−13.8837	+	1.04044i	−0.653756	+	0.0489923i
$452$	64.4605	+	25.2989i	3.03197	+	1.18996i
$453$	20.8326	−	11.0103i	0.978800	−	0.517311i
$454$	23.9459	+	30.0272i	1.12384	+	1.40924i
$455$	19.5691	+	0.109682i	0.917415	+	0.00514199i
$456$	48.3795	−	60.6660i	2.26558	−	2.84095i
$457$	1.13099	−	5.97740i	0.0529053	−	0.279611i	−0.946117	−	0.323826i	$-0.895031\pi$
$457$	1.13099	−	5.97740i	0.0529053	−	0.279611i	0.999022	+	0.0442145i	$0.0140785\pi$
$458$	51.1959	+	55.1760i	2.39223	+	2.57821i
$459$	−9.52239	+	5.49776i	−0.444467	+	0.256613i
$460$	6.13129	−	1.64287i	0.285873	−	0.0765994i
$461$	−7.97274	+	12.6885i	−0.371328	+	0.590965i	−0.979157	−	0.203103i	$-0.934897\pi$
$461$	−7.97274	+	12.6885i	−0.371328	+	0.590965i	0.607830	+	0.794067i	$0.292040\pi$
$462$	5.54024	+	34.3995i	0.257755	+	1.60041i
$463$	17.6606	−	11.0969i	0.820757	−	0.515716i	−0.0549897	−	0.998487i	$-0.517513\pi$
$463$	17.6606	−	11.0969i	0.820757	−	0.515716i	0.875746	+	0.482771i	$0.160370\pi$
$464$	99.7345	+	92.5401i	4.63006	+	4.29606i
$465$	−55.5434	−	8.37182i	−2.57576	−	0.388234i
$466$	−44.4123	−	60.1765i	−2.05736	−	2.78762i
$467$	23.2343	+	21.5583i	1.07515	+	0.997597i	1.00000		0.000425134i	$0.000135324\pi$
$467$	23.2343	+	21.5583i	1.07515	+	0.997597i	0.0751540	+	0.997172i	$0.476055\pi$
$468$	−73.9149	+	44.8419i	−3.41672	+	2.07282i
$469$	6.32256	+	7.19882i	0.291949	+	0.332411i
$470$	−17.0751	−	10.7290i	−0.787616	−	0.494892i
$471$	−2.38681	+	4.13407i	−0.109978	+	0.190488i
$472$	−7.38308	−	12.7879i	−0.339834	−	0.588610i
$473$	0.690293	−	18.4485i	0.0317397	−	0.848262i
$474$	6.42661	+	1.21598i	0.295184	+	0.0558518i
$475$	−0.281832	−	2.50133i	−0.0129313	−	0.114769i
$476$	16.2435	+	32.8776i	0.744521	+	1.50694i
$477$	23.3246	+	29.2481i	1.06796	+	1.33918i
$478$	−12.4223	+	40.2721i	−0.568183	+	1.84200i
$479$	−4.31963	−	9.90070i	−0.197369	−	0.452374i	0.789530	−	0.613711i	$-0.210324\pi$
$479$	−4.31963	−	9.90070i	−0.197369	−	0.452374i	−0.986899	+	0.161337i	$0.948419\pi$
$480$	103.747	−	7.77479i	4.73540	−	0.354869i
$481$	12.0632	+	32.2137i	0.550034	+	1.46882i
$482$	1.45786	+	3.02728i	0.0664037	+	0.137889i
$483$	1.51068	−	3.96632i	0.0687385	−	0.180474i
$484$	37.3966	+	18.0092i	1.69984	+	0.818602i
$485$	−27.9915	−	2.09768i	−1.27103	−	0.0952505i
$486$	−43.6263	−	23.0572i	−1.97893	−	1.04589i
$487$	−10.8236	+	2.04794i	−0.490466	+	0.0928011i	−0.425261	−	0.905071i	$-0.639818\pi$
$487$	−10.8236	+	2.04794i	−0.490466	+	0.0928011i	−0.0652047	+	0.997872i	$0.520770\pi$
$488$	37.9207	−	51.3807i	1.71659	−	2.32590i
$489$	−10.8929	+	10.8929i	−0.492594	+	0.492594i
$490$	−34.5931	+	17.5273i	−1.56276	+	0.791801i
$491$		−	1.82479i		−	0.0823515i	−0.999152	−	0.0411758i	$-0.986890\pi$
$491$		−	1.82479i		−	0.0823515i	0.999152	−	0.0411758i	$-0.0131104\pi$
$492$	91.5565	+	67.5718i	4.12769	+	3.04637i
$493$	21.9198	+	14.9447i	0.987220	+	0.673075i
$494$	14.8948	−	27.1428i	0.670150	−	1.22121i
$495$	16.4689	+	1.23417i	0.740221	+	0.0554719i
$496$	−44.2579	−	126.482i	−1.98724	−	5.67920i
$497$	0.318150	−	11.6446i	0.0142710	−	0.522333i
$498$	−7.92965	−	16.4661i	−0.355336	−	0.737863i
$499$	−29.0274	−	12.6645i	−1.29945	−	0.566943i	−0.367664	−	0.929959i	$-0.619842\pi$
$499$	−29.0274	−	12.6645i	−1.29945	−	0.566943i	−0.931783	+	0.363016i	$0.881747\pi$
$500$	41.0199	−	47.6660i	1.83447	−	2.13169i
$501$	32.4067	−	14.1389i	1.44782	−	0.631679i
$502$	−30.0357	+	15.8743i	−1.34056	+	0.708507i
$503$	−28.9898	+	23.1186i	−1.29259	+	1.03081i	−0.295443	+	0.955361i	$0.595467\pi$
$503$	−28.9898	+	23.1186i	−1.29259	+	1.03081i	−0.997150	+	0.0754475i	$0.975961\pi$
$504$	55.7940	−	90.8160i	2.48526	−	4.04527i
$505$	4.92973	−	0.555447i	0.219370	−	0.0247171i
$506$	1.58041	+	2.31803i	0.0702577	+	0.103049i
$507$	−26.8989	+	23.4317i	−1.19462	+	1.04064i
$508$	−24.9789	−	43.2646i	−1.10826	−	1.91956i
$509$	11.3183	−	3.03273i	0.501675	−	0.134423i	0.000897769	−	1.00000i	$-0.499714\pi$
$509$	11.3183	−	3.03273i	0.501675	−	0.134423i	0.500777	+	0.865576i	$0.333048\pi$
$510$	38.8118	−	8.85854i	1.71862	−	0.392263i
$511$	1.82462	−	0.0867072i	0.0807163	−	0.00383570i
$512$	4.97135	+	7.91185i	0.219705	+	0.349658i
$513$	−13.3421	+	0.499226i	−0.589068	+	0.0220414i
$514$	−0.959676	+	0.708273i	−0.0423295	+	0.0312406i
$515$	−4.28207	−	5.80200i	−0.188691	−	0.255667i
$516$	−102.630	+	110.609i	−4.51803	+	4.86927i
$517$	1.43944	−	6.30659i	0.0633065	−	0.277364i
$518$	−50.4341	−	45.8582i	−2.21595	−	2.01489i
$519$	−1.15734	+	0.264155i	−0.0508016	+	0.0115951i
$520$	63.7939	−	16.0251i	2.79755	−	0.702749i
$521$	30.6630	−	17.7033i	1.34337	−	0.775595i	0.356069	−	0.934460i	$-0.384117\pi$
$521$	30.6630	−	17.7033i	1.34337	−	0.775595i	0.987300	+	0.158865i	$0.0507834\pi$
$522$	4.63431	−	123.855i	0.202838	−	5.42097i
$523$	16.0253	+	23.5049i	0.700739	+	1.02780i	0.997347	+	0.0727965i	$0.0231923\pi$
$523$	16.0253	+	23.5049i	0.700739	+	1.02780i	−0.296607	+	0.955000i	$0.595855\pi$
$524$	42.6390	−	53.4677i	1.86269	−	2.33575i
$525$	−1.33535	−	5.59007i	−0.0582794	−	0.243971i
$526$	79.4644	+	8.95349i	3.46481	+	0.390391i
$527$	−12.2095	−	23.1015i	−0.531854	−	1.00632i
$528$	26.1887	+	60.0251i	1.13972	+	2.61226i
$529$	1.69325	+	22.5949i	0.0736197	+	0.982387i
$530$	−16.7140	−	42.5865i	−0.726008	−	1.84984i
$531$	−2.48441	+	7.10004i	−0.107814	+	0.308115i
$532$	−1.21614	+	44.5121i	−0.0527264	+	1.92984i
$533$	25.2548	+	12.6540i	1.09391	+	0.548104i
$534$	−1.87864	+	25.0687i	−0.0812966	+	1.08483i
$535$	−15.1659	−	8.01542i	−0.655679	−	0.346537i
$536$	26.6079	+	18.1409i	1.14929	+	0.783570i
$537$	1.44703	−	0.218104i	0.0624438	−	0.00941189i
$538$	29.2372	+	29.2372i	1.26050	+	1.26050i
$539$	−8.97178	−	8.61696i	−0.386442	−	0.371159i
$540$	−32.2386	−	32.2386i	−1.38733	−	1.38733i
$541$	15.0760	+	11.1266i	0.648168	+	0.478370i	0.867603	−	0.497257i	$-0.165660\pi$
$541$	15.0760	+	11.1266i	0.648168	+	0.478370i	−0.219435	+	0.975627i	$0.570421\pi$
$542$	30.3951	−	44.5815i	1.30558	−	1.91494i
$543$	9.48073	+	30.7358i	0.406857	+	1.31900i
$544$	31.5684	+	36.6832i	1.35349	+	1.57278i
$545$	−6.14715	−	2.96031i	−0.263315	−	0.126806i
$546$	26.1953	−	65.6601i	1.12106	−	2.80999i
$547$	4.60885	−	2.21951i	0.197060	−	0.0948992i	−0.332751	−	0.943015i	$-0.607977\pi$
$547$	4.60885	−	2.21951i	0.197060	−	0.0948992i	0.529811	+	0.848115i	$0.322263\pi$
$548$	65.8253	+	28.7193i	2.81192	+	1.22683i
$549$	−32.4399	+	2.43104i	−1.38450	+	0.103754i
$550$	3.53647	+	1.38796i	0.150795	+	0.0591829i
$551$	15.0526	+	28.4809i	0.641262	+	1.21333i
$552$	1.59725	−	14.1760i	0.0679834	−	0.603369i
$553$	−2.09358	+	1.03435i	−0.0890279	+	0.0439851i
$554$	−64.6708	+	7.28664i	−2.74760	+	0.309580i
$555$	−44.3742	+	30.2538i	−1.88358	+	1.28420i
$556$	60.6417	−	56.2673i	2.57178	−	2.38627i
$557$	−2.61227	+	9.74913i	−0.110686	+	0.413084i	−0.998928	−	0.0462909i	$-0.985260\pi$
$557$	−2.61227	+	9.74913i	−0.110686	+	0.413084i	0.888242	+	0.459375i	$0.151927\pi$
$558$	−61.0359	+	105.717i	−2.58386	+	4.47537i
$559$	−20.4231	+	31.3987i	−0.863807	+	1.32802i
$560$	−54.7659	+	48.0997i	−2.31428	+	2.03258i
$561$	6.79407	+	10.8127i	0.286846	+	0.456512i
$562$	−33.8306	−	31.3902i	−1.42706	−	1.32412i
$563$	−19.3841	−	2.92168i	−0.816942	−	0.123134i	−0.272739	−	0.962088i	$-0.587930\pi$
$563$	−19.3841	−	2.92168i	−0.816942	−	0.123134i	−0.544203	+	0.838954i	$0.683168\pi$
$564$	−42.5394	+	31.3955i	−1.79123	+	1.32199i
$565$	1.00353	+	26.8200i	0.0422189	+	1.12833i
$566$	18.9655	+	30.1834i	0.797178	+	1.26870i
$567$	5.40233	−	0.870078i	0.226877	−	0.0365398i
$568$	−8.71259	−	38.1724i	−0.365572	−	1.60168i
$569$	24.1531	+	13.9448i	1.01255	+	0.584597i	0.911938	−	0.410329i	$-0.134586\pi$
$569$	24.1531	+	13.9448i	1.01255	+	0.584597i	0.100614	+	0.994926i	$0.467919\pi$
$570$	46.6926	+	12.5112i	1.95574	+	0.524038i
$571$	−4.54638	−	4.89983i	−0.190260	−	0.205051i	0.630717	−	0.776013i	$-0.282761\pi$
$571$	−4.54638	−	4.89983i	−0.190260	−	0.205051i	−0.820977	+	0.570962i	$0.806570\pi$
$572$	18.6625	+	28.3174i	0.780318	+	1.18401i
$573$	−9.30983	−	7.42434i	−0.388924	−	0.310156i
$574$	−55.9743	+	0.564527i	−2.33632	+	0.0235629i
$575$	−0.288535	−	0.361812i	−0.0120328	−	0.0150886i
$576$	30.7794	−	99.7844i	1.28248	−	4.15769i
$577$	30.1298	−	13.1455i	1.25432	−	0.547254i	0.335541	−	0.942026i	$-0.391081\pi$
$577$	30.1298	−	13.1455i	1.25432	−	0.547254i	0.918780	+	0.394771i	$0.129176\pi$
$578$	−20.7612	−	17.8665i	−0.863554	−	0.743148i
$579$	−18.4688	−	8.05787i	−0.767538	−	0.334873i
$580$	−36.3319	+	103.831i	−1.50860	+	4.31133i
$581$	5.79925	+	2.99056i	0.240593	+	0.124070i
$582$	−43.9959	+	91.3584i	−1.82369	+	3.78693i
$583$	11.1233	−	9.57239i	0.460681	−	0.396448i
$584$	5.86697	−	1.80972i	0.242777	−	0.0748868i
$585$	−27.3856	−	19.3075i	−1.13226	−	0.798265i
$586$	12.4923	+	82.8812i	0.516053	+	3.42379i
$587$	−3.55145	−	3.55145i	−0.146584	−	0.146584i	0.630006	−	0.776590i	$-0.283052\pi$
$587$	−3.55145	−	3.55145i	−0.146584	−	0.146584i	−0.776590	+	0.630006i	$0.783052\pi$
$588$	9.64121	+	101.213i	0.397597	+	4.17396i
$589$		−	31.7281i		−	1.30733i
$590$	5.46253	−	7.40147i	0.224889	−	0.304714i
$591$	−4.66574	−	24.6590i	−0.191923	−	1.01434i
$592$	−113.275	−	59.8675i	−4.65557	−	2.46054i
$593$	11.2669	+	13.0924i	0.462678	+	0.537641i	0.940039	−	0.341066i	$-0.110788\pi$
$593$	11.2669	+	13.0924i	0.462678	+	0.537641i	−0.477362	+	0.878707i	$0.658407\pi$
$594$	8.74320	−	18.1554i	0.358738	−	0.744927i
$595$	−9.16186	+	10.8660i	−0.375600	+	0.445464i
$596$	−28.2205	−	9.87477i	−1.15596	−	0.404486i
$597$	3.20157	−	1.25652i	0.131031	−	0.0514260i
$598$	−0.336266	−	5.68220i	−0.0137509	−	0.232363i
$599$	12.0439	−	30.6873i	0.492100	−	1.25385i	−0.442057	−	0.896987i	$-0.645751\pi$
$599$	12.0439	−	30.6873i	0.492100	−	1.25385i	0.934157	−	0.356863i	$-0.116154\pi$
$600$	−9.02658	−	17.0791i	−0.368508	−	0.697252i
$601$	7.59102	−	6.05364i	0.309644	−	0.246933i	−0.456321	−	0.889815i	$-0.650833\pi$
$601$	7.59102	−	6.05364i	0.309644	−	0.246933i	0.765965	+	0.642882i	$0.222262\pi$
$602$	7.56638	−	73.8392i	0.308383	−	3.00946i
$603$	−1.83679	−	16.3020i	−0.0747999	−	0.663868i
$604$	−8.44962	+	44.6573i	−0.343810	+	1.81708i
$605$	−0.601521	+	16.0760i	−0.0244553	+	0.653581i
$606$	4.63826	−	17.3102i	0.188416	−	0.703179i
$607$	−6.61851	−	3.82120i	−0.268637	−	0.155098i	0.359631	−	0.933095i	$-0.382903\pi$
$607$	−6.61851	−	3.82120i	−0.268637	−	0.155098i	−0.628268	+	0.777997i	$0.716236\pi$
$608$	13.0767	+	57.2927i	0.530330	+	2.32353i
$609$	42.0449	+	60.3517i	1.70374	+	2.44557i
$610$	38.7851	+	8.85246i	1.57036	+	0.358425i
$611$	−9.07680	+	9.47973i	−0.367208	+	0.383509i
$612$	9.35837	−	62.0887i	0.378290	−	2.50979i
$613$	24.1849	−	17.8492i	0.976818	−	0.720924i	0.0165091	−	0.999864i	$-0.494745\pi$
$613$	24.1849	−	17.8492i	0.976818	−	0.720924i	0.960309	+	0.278939i	$0.0899829\pi$
$614$	−45.2563	+	48.7747i	−1.82640	+	1.96839i
$615$	−9.81387	+	42.9974i	−0.395734	+	1.73382i
$616$	−36.4189	−	20.5396i	−1.46736	−	0.827562i
$617$	25.5737	+	16.0690i	1.02956	+	0.646914i	0.937193	−	0.348811i	$-0.113415\pi$
$617$	25.5737	+	16.0690i	1.02956	+	0.646914i	0.0923645	+	0.995725i	$0.470557\pi$
$618$	−25.1616	+	6.74204i	−1.01215	+	0.271205i
$619$	8.62258	+	2.31041i	0.346571	+	0.0928633i	0.427905	−	0.903824i	$-0.359252\pi$
$619$	8.62258	+	2.31041i	0.346571	+	0.0928633i	−0.0813348	+	0.996687i	$0.525918\pi$
$620$	79.4221	−	73.6930i	3.18967	−	2.95958i
$621$	−2.02812	+	1.38275i	−0.0813856	+	0.0554878i
$622$	−5.04881	−	44.8094i	−0.202439	−	1.79669i
$623$	−4.85148	−	7.55096i	−0.194370	−	0.302523i
$624$	16.9466	−	131.787i	0.678408	−	5.27568i
$625$	19.5082	+	6.01750i	0.780330	+	0.240700i
$626$	−64.1111	+	27.9714i	−2.56240	+	1.11796i
$627$	1.15878	+	15.4628i	0.0462771	+	0.617525i
$628$	−3.36390	−	8.57107i	−0.134234	−	0.342023i
$629$	−23.5811	−	8.25138i	−0.940240	−	0.329004i
$630$	65.7552	+	9.23380i	2.61975	+	0.367883i
$631$	−1.28540	−	3.67347i	−0.0511711	−	0.146239i	0.915461	−	0.402406i	$-0.131826\pi$
$631$	−1.28540	−	3.67347i	−0.0511711	−	0.146239i	−0.966632	+	0.256167i	$0.917540\pi$
$632$	−5.94918	+	5.11969i	−0.236646	+	0.203650i
$633$	−14.9337	−	48.4137i	−0.593560	−	1.92427i
$634$	1.26502	−	1.85544i	0.0502402	−	0.0736889i
$635$	11.4978	−	15.5790i	0.456278	−	0.618235i
$636$	−119.942			−4.75601
$637$	6.64146	+	24.3494i	0.263144	+	0.964757i
$638$	−48.6198			−1.92488
$639$	−11.8442	+	16.0483i	−0.468550	+	0.634862i
$640$	−29.2222	+	42.8611i	−1.15511	+	1.69423i
$641$	−8.35667	−	27.0917i	−0.330069	−	1.07006i	−0.956782	−	0.290806i	$-0.906076\pi$
$641$	−8.35667	−	27.0917i	−0.330069	−	1.07006i	0.626713	−	0.779250i	$-0.284400\pi$
$642$	−46.9687	+	40.4198i	−1.85371	+	1.59524i
$643$	−9.49932	−	27.1475i	−0.374617	−	1.07059i	−0.964723	−	0.263267i	$-0.915200\pi$
$643$	−9.49932	−	27.1475i	−0.374617	−	1.07059i	0.590106	−	0.807326i	$-0.299086\pi$
$644$	4.16456	+	7.04810i	0.164106	+	0.277734i
$645$	−55.1991	−	19.3150i	−2.17346	−	0.760527i
$646$	8.21530	+	20.9322i	0.323227	+	0.823568i
$647$	0.0926362	+	1.23614i	0.00364190	+	0.0485978i	0.998729	−	0.0504090i	$-0.0160525\pi$
$647$	0.0926362	+	1.23614i	0.00364190	+	0.0485978i	−0.995087	+	0.0990068i	$0.968433\pi$
$648$	16.8575	−	7.35484i	0.662224	−	0.288925i
$649$	2.81971	+	0.869764i	0.110683	+	0.0341412i
$650$	−4.71071	−	6.10100i	−0.184769	−	0.239301i
$651$	−8.83673	−	71.9029i	−0.346339	−	2.81810i
$652$	−3.32686	−	29.5267i	−0.130290	−	1.15636i
$653$	−5.53030	+	3.77050i	−0.216417	+	0.147551i	−0.666677	−	0.745347i	$-0.732284\pi$
$653$	−5.53030	+	3.77050i	−0.216417	+	0.147551i	0.450259	+	0.892898i	$0.351331\pi$
$654$	−18.0674	+	16.7641i	−0.706490	+	0.655527i
$655$	25.6024	+	6.86015i	1.00037	+	0.268048i
$656$	−101.628	+	27.2311i	−3.96790	+	1.06320i
$657$	−2.64830	−	1.66404i	−0.103320	−	0.0649202i
$658$	7.41507	−	24.9289i	0.289070	−	0.971831i
$659$	9.21020	−	40.3525i	0.358779	−	1.57191i	−0.397462	−	0.917618i	$-0.630109\pi$
$659$	9.21020	−	40.3525i	0.358779	−	1.57191i	0.756241	−	0.654293i	$-0.227034\pi$
$660$	−36.0153	+	38.8152i	−1.40189	+	1.51088i
$661$	−16.1881	+	11.9473i	−0.629643	+	0.464697i	−0.861298	−	0.508101i	$-0.830348\pi$
$661$	−16.1881	+	11.9473i	−0.629643	+	0.464697i	0.231655	+	0.972798i	$0.425586\pi$
$662$	6.58706	−	43.7023i	0.256013	−	1.69854i
$663$	−0.562444	−	25.9031i	−0.0218435	−	1.00599i
$664$	21.3815	+	4.88018i	0.829762	+	0.189388i
$665$	−16.0009	+	6.46688i	−0.620490	+	0.250775i
$666$	25.9717	+	113.789i	1.00638	+	4.40925i
$667$	5.12902	+	2.96124i	0.198597	+	0.114660i
$668$	−17.6509	+	65.8739i	−0.682932	+	2.54874i
$669$	−2.81475	+	75.2257i	−0.108824	+	2.90839i
$670$	−3.72978	+	19.7123i	−0.144094	+	0.761554i
$671$	1.42881	+	12.6810i	0.0551585	+	0.489545i
$672$	45.5915	+	126.196i	1.75873	+	4.86812i
$673$	−0.562031	+	0.448204i	−0.0216647	+	0.0172770i	−0.634262	−	0.773118i	$-0.718696\pi$
$673$	−0.562031	+	0.448204i	−0.0216647	+	0.0172770i	0.612598	+	0.790395i	$0.290125\pi$
$674$	−36.8404	−	69.7054i	−1.41904	−	2.68495i
$675$	−1.21437	+	3.09416i	−0.0467411	+	0.119094i
$676$	−2.98672	−	68.7436i	−0.114874	−	2.64398i
$677$	−5.82194	+	2.28494i	−0.223755	+	0.0878175i	−0.474571	−	0.880217i	$-0.657397\pi$
$677$	−5.82194	+	2.28494i	−0.223755	+	0.0878175i	0.250815	+	0.968035i	$0.419301\pi$
$678$	91.5117	+	32.0213i	3.51449	+	1.22977i
$679$	−7.08879	−	35.5013i	−0.272043	−	1.36242i
$680$	−20.7276	+	43.0413i	−0.794867	+	1.65056i
$681$	25.4560	+	29.5804i	0.975476	+	1.13352i
$682$	42.3372	+	22.3758i	1.62117	+	0.856816i
$683$	0.984594	+	5.20370i	0.0376744	+	0.199114i	0.996347	−	0.0853977i	$-0.0272161\pi$
$683$	0.984594	+	5.20370i	0.0376744	+	0.199114i	−0.958673	+	0.284512i	$0.908168\pi$
$684$	45.2750	−	61.3455i	1.73113	−	2.34560i
$685$			27.8349i			1.06352i
$686$	−33.7559	−	36.9056i	−1.28881	−	1.40906i
$687$	54.0818	+	54.0818i	2.06335	+	2.06335i
$688$	−20.7933	−	137.954i	−0.792736	−	5.25946i
$689$	−29.3386	+	5.07573i	−1.11771	+	0.193370i
$690$	8.49234	−	2.61954i	0.323298	−	0.0997242i
$691$	29.5234	−	25.4070i	1.12312	−	0.966526i	0.123457	−	0.992350i	$-0.460602\pi$
$691$	29.5234	−	25.4070i	1.12312	−	0.966526i	0.999667	+	0.0258238i	$0.00822088\pi$
$692$	0.993479	−	2.06298i	0.0377664	−	0.0784227i
$693$	4.17070	+	20.8873i	0.158432	+	0.793442i
$694$	−18.0092	+	51.4673i	−0.683620	+	1.95367i
$695$	29.3872	+	12.8215i	1.11472	+	0.486347i
$696$	187.389	+	161.261i	7.10296	+	6.11259i
$697$	−18.8041	+	8.20414i	−0.712256	+	0.310754i
$698$	19.9386	−	64.6394i	0.754687	−	2.44664i
$699$	−47.3835	−	59.4170i	−1.79221	−	2.24736i
$700$	10.0359	+	4.70895i	0.379321	+	0.177981i
$701$	−13.3954	−	10.6825i	−0.505939	−	0.403473i	0.336981	−	0.941511i	$-0.390594\pi$
$701$	−13.3954	−	10.6825i	−0.505939	−	0.403473i	−0.842920	+	0.538039i	$0.819165\pi$
$702$	−34.1375	+	22.4982i	−1.28844	+	0.849141i
$703$	−20.6337	−	22.2379i	−0.778216	−	0.838717i
$704$	−39.5677	−	10.6021i	−1.49126	−	0.399583i
$705$	−17.7461	−	10.2457i	−0.668356	−	0.385875i
$706$	12.5446	+	54.9616i	0.472124	+	2.06851i
$707$	2.39745	+	5.93199i	0.0901654	+	0.223095i
$708$	−12.8312	−	20.4208i	−0.482227	−	0.767459i
$709$	−1.31998	−	35.2771i	−0.0495727	−	1.32486i	−0.772977	−	0.634434i	$-0.781233\pi$
$709$	−1.31998	−	35.2771i	−0.0495727	−	1.32486i	0.723404	−	0.690425i	$-0.242576\pi$
$710$	19.6258	−	14.4845i	0.736542	−	0.543593i
$711$	3.95368	+	0.595921i	0.148274	+	0.0223488i
$712$	−22.1140	−	20.5188i	−0.828756	−	0.768973i
$713$	−3.10343	−	4.93907i	−0.116224	−	0.184970i
$714$	24.4476	+	45.1490i	0.914929	+	1.68966i
$715$	−7.16697	+	11.0186i	−0.268030	+	0.412070i
$716$	−1.41131	+	2.44445i	−0.0527429	+	0.0913535i
$717$	−11.0838	+	41.3651i	−0.413930	+	1.54481i
$718$	5.05307	−	4.68856i	0.188579	−	0.174976i
$719$	−10.4472	+	7.12281i	−0.389617	+	0.265636i	−0.742247	−	0.670127i	$-0.766240\pi$
$719$	−10.4472	+	7.12281i	−0.389617	+	0.265636i	0.352630	+	0.935763i	$0.385287\pi$
$720$	124.019	−	13.9736i	4.62193	−	0.520766i
$721$	5.72493	−	7.32927i	0.213208	−	0.272956i
$722$	2.68778	−	23.8547i	0.100029	−	0.887782i
$723$	1.59536	+	3.01857i	0.0593321	+	0.112262i
$724$	−57.7521	−	22.6660i	−2.14634	−	0.842376i
$725$	7.99747	−	0.599327i	0.297019	−	0.0222585i
$726$	53.2647	+	23.2391i	1.97684	+	0.862485i
$727$	11.9059	−	5.73356i	0.441564	−	0.212646i	−0.199873	−	0.979822i	$-0.564053\pi$
$727$	11.9059	−	5.73356i	0.441564	−	0.212646i	0.641437	+	0.767176i	$0.278339\pi$
$728$	42.0034	+	73.7030i	1.55675	+	2.73162i
$729$	−39.5850	−	19.0631i	−1.46611	−	0.706041i
$730$	2.49494	+	2.89918i	0.0923420	+	0.107303i
$731$	−8.01855	−	25.9955i	−0.296577	−	0.961479i
$732$	58.7542	−	86.1766i	2.17162	−	3.18518i
$733$	−5.91943	−	4.36874i	−0.218639	−	0.161363i	0.478994	−	0.877818i	$-0.341002\pi$
$733$	−5.91943	−	4.36874i	−0.218639	−	0.161363i	−0.697633	+	0.716455i	$0.745763\pi$
$734$	51.2158	+	51.2158i	1.89041	+	1.89041i
$735$	−34.4606	+	19.1119i	−1.27110	+	0.704953i
$736$	7.63961	+	7.63961i	0.281600	+	0.281600i
$737$	−6.36354	+	0.959150i	−0.234404	+	0.0353307i
$738$	79.1918	+	53.9920i	2.91509	+	1.98747i
$739$	29.9625	+	15.8356i	1.10219	+	0.582523i	0.916479	−	0.400082i	$-0.131018\pi$
$739$	29.9625	+	15.8356i	1.10219	+	0.582523i	0.185708	+	0.982605i	$0.440542\pi$
$740$	7.74135	−	103.301i	0.284578	−	3.79743i
$741$	14.0933	−	28.1273i	0.517729	−	1.03328i
$742$	47.1177	−	35.5140i	1.72975	−	1.30376i
$743$	−0.919691	+	2.62832i	−0.0337402	+	0.0964239i	−0.959521	−	0.281636i	$-0.909123\pi$
$743$	−0.919691	+	2.62832i	−0.0337402	+	0.0964239i	0.925781	+	0.378060i	$0.123409\pi$
$744$	−88.9588	−	226.663i	−3.26139	−	8.30988i
$745$	−0.865966	−	11.5555i	−0.0317265	−	0.423361i
$746$	25.8100	+	59.1572i	0.944972	+	2.16590i
$747$	−5.22043	−	9.87753i	−0.191006	−	0.361400i
$748$	−24.4765	−	2.75784i	−0.894949	−	0.100837i
$749$	4.70514	−	21.6172i	0.171922	−	0.789876i
$750$	54.8960	−	68.8374i	2.00452	−	2.51359i
$751$	−23.2201	−	34.0577i	−0.847314	−	1.24278i	−0.968216	−	0.250117i	$-0.919531\pi$
$751$	−23.2201	−	34.0577i	−0.847314	−	1.24278i	0.120901	−	0.992665i	$-0.461422\pi$
$752$	1.82785	−	48.8503i	0.0666548	−	1.78139i
$753$	−29.8958	+	17.2603i	−1.08946	+	0.629001i
$754$	84.6447	+	50.6568i	3.08258	+	1.84481i
$755$	−17.1736	+	3.91977i	−0.625013	+	0.142655i
$756$	28.8853	−	51.2168i	1.05055	−	1.86274i
$757$	2.11007	−	9.24484i	0.0766920	−	0.336009i	−0.921997	−	0.387197i	$-0.873443\pi$
$757$	2.11007	−	9.24484i	0.0766920	−	0.336009i	0.998689	+	0.0511873i	$0.0163006\pi$
$758$	−37.8665	+	40.8104i	−1.37537	+	1.48230i
$759$	1.69285	+	2.29373i	0.0614467	+	0.0832573i
$760$	−46.6731	+	34.4463i	−1.69301	+	1.24950i
$761$	−24.0144	+	0.898556i	−0.870522	+	0.0325726i	−0.468919	−	0.883241i	$-0.655356\pi$
$761$	−24.0144	+	0.898556i	−0.870522	+	0.0325726i	−0.401603	+	0.915814i	$0.631547\pi$
$762$	−37.2131	−	59.2243i	−1.34809	−	2.14547i
$763$	1.54864	−	8.66211i	0.0560646	−	0.313589i
$764$	22.3922	−	5.11088i	0.810123	−	0.184905i
$765$	23.5068	−	6.29863i	0.849891	−	0.227728i
$766$	6.02746	+	10.4399i	0.217781	+	0.377208i
$767$	−4.00277	−	4.45205i	−0.144531	−	0.160754i
$768$	34.2977	+	50.3055i	1.23761	+	1.81524i
$769$	−10.9916	+	1.23845i	−0.396366	+	0.0446597i	−0.307898	−	0.951419i	$-0.599626\pi$
$769$	−10.9916	+	1.23845i	−0.396366	+	0.0446597i	−0.0884676	+	0.996079i	$0.528197\pi$
$770$	2.65522	−	25.9119i	0.0956876	−	0.933802i
$771$	−0.947565	+	0.755658i	−0.0341257	+	0.0272144i
$772$	34.3623	−	18.1610i	1.23673	−	0.653630i
$773$	13.2944	−	5.80030i	0.478168	−	0.208622i	−0.146964	−	0.989142i	$-0.546950\pi$
$773$	13.2944	−	5.80030i	0.478168	−	0.208622i	0.625132	+	0.780519i	$0.285045\pi$
$774$	−82.9006	+	96.3322i	−2.97980	+	3.46259i
$775$	−7.23986	−	3.15872i	−0.260063	−	0.113464i
$776$	−52.7954	−	109.631i	−1.89525	−	3.93552i
$777$	−52.9542	−	44.6492i	−1.89972	−	1.60178i
$778$	19.8914	+	56.8463i	0.713141	+	2.03804i
$779$	−24.8420	−	1.86165i	−0.890058	−	0.0667006i
$780$	103.142	−	30.0513i	3.69308	−	1.07601i
$781$	6.46479	+	4.40762i	0.231328	+	0.157717i
$782$	3.32631	+	2.45493i	0.118949	+	0.0877882i
$783$		−	42.5390i		−	1.52022i
$784$	−78.7239	−	51.3783i	−2.81157	−	1.83494i
$785$	2.52341	−	2.52341i	0.0900645	−	0.0900645i
$786$	56.8576	−	77.0393i	2.02804	−	2.74790i
$787$	13.8736	−	2.62503i	0.494541	−	0.0935721i	0.0673420	−	0.997730i	$-0.478548\pi$
$787$	13.8736	−	2.62503i	0.494541	−	0.0935721i	0.427199	+	0.904158i	$0.359501\pi$
$788$	42.7976	+	22.6192i	1.52460	+	0.805776i
$789$	81.0300	+	6.07236i	2.88474	+	0.216182i
$790$	−4.40540	−	2.12153i	−0.156737	−	0.0754807i
$791$	−32.9718	+	10.5358i	−1.17234	+	0.374608i
$792$	31.0623	+	64.5015i	1.10375	+	2.29196i
$793$	10.7248	−	23.5657i	0.380849	−	0.836843i
$794$	8.94563	−	0.670382i	0.317469	−	0.0237910i
$795$	−18.5897	−	42.6082i	−0.659310	−	1.51116i
$796$	−1.95537	+	6.33916i	−0.0693063	+	0.224686i
$797$	23.2140	+	29.1094i	0.822282	+	1.03111i	0.998903	+	0.0468301i	$0.0149119\pi$
$797$	23.2140	+	29.1094i	0.822282	+	1.03111i	−0.176621	+	0.984279i	$0.556517\pi$
$798$	0.628737	+	62.3409i	0.0222570	+	2.20685i
$799$	−1.06727	−	9.47225i	−0.0377572	−	0.335104i
$800$	14.3752	+	2.71993i	0.508239	+	0.0961640i
$801$	−0.574613	+	15.3569i	−0.0203030	+	0.542608i
$802$	−13.2063	−	22.8741i	−0.466332	−	0.807711i
$803$	−0.613469	+	1.06256i	−0.0216488	+	0.0374969i
$804$	44.5358	+	27.9837i	1.57066	+	0.986908i
$805$	−1.85830	+	2.57179i	−0.0654965	+	0.0906439i
$806$	−50.3937	−	83.0661i	−1.77504	−	2.92588i
$807$	30.7989	+	28.5772i	1.08417	+	1.00596i
$808$	12.7702	+	17.3030i	0.449254	+	0.608718i
$809$	32.7543	+	4.93692i	1.15158	+	0.173573i	0.696958	−	0.717112i	$-0.254536\pi$
$809$	32.7543	+	4.93692i	1.15158	+	0.173573i	0.454622	+	0.890684i	$0.349774\pi$
$810$	8.39918	+	7.79330i	0.295117	+	0.273829i
$811$	−22.4533	+	14.1084i	−0.788443	+	0.495412i	−0.865072	−	0.501648i	$-0.832727\pi$
$811$	−22.4533	+	14.1084i	−0.788443	+	0.495412i	0.0766286	+	0.997060i	$0.475584\pi$
$812$	−141.576	−	9.17485i	−4.96834	−	0.321974i
$813$	29.1700	−	46.4238i	1.02304	−	1.62815i
$814$	44.2253	−	11.8501i	1.55010	−	0.415347i
$815$	9.97343	−	5.75816i	0.349354	−	0.201700i
$816$	65.6387	+	70.7417i	2.29781	+	2.47646i
$817$	6.14121	−	32.4571i	0.214854	−	1.13553i
$818$	−12.2790	+	15.3974i	−0.429327	+	0.538359i
$819$	14.5014	−	40.7091i	0.506718	−	1.42249i
$820$	−53.0390	−	66.5088i	−1.85220	−	2.32259i
$821$	−9.77918	+	5.16845i	−0.341296	+	0.180380i	−0.629130	−	0.777300i	$-0.716589\pi$
$821$	−9.77918	+	5.16845i	−0.341296	+	0.180380i	0.287834	+	0.957680i	$0.407065\pi$
$822$	93.6002	+	36.7354i	3.26468	+	1.28129i
$823$	−23.5452	+	1.76447i	−0.820733	+	0.0615054i	−0.478476	−	0.878101i	$-0.658811\pi$
$823$	−23.5452	+	1.76447i	−0.820733	+	0.0615054i	−0.342257	+	0.939606i	$0.611191\pi$
$824$	12.5003	−	28.6511i	0.435470	−	0.998108i
$825$	3.64374	+	1.27500i	0.126859	+	0.0443898i
$826$	11.0870	+	4.22280i	0.385767	+	0.146930i
$827$	9.92884	+	28.3750i	0.345260	+	0.986695i	0.977318	+	0.211775i	$0.0679244\pi$
$827$	9.92884	+	28.3750i	0.345260	+	0.986695i	−0.632059	+	0.774920i	$0.717790\pi$
$828$	1.04751	−	13.9781i	0.0364035	−	0.485771i
$829$	−10.3602	+	3.19569i	−0.359824	+	0.110991i	−0.469396	−	0.882988i	$-0.655528\pi$
$829$	−10.3602	+	3.19569i	−0.359824	+	0.110991i	0.109572	+	0.993979i	$0.465052\pi$
$830$	2.54005	+	13.4245i	0.0881666	+	0.465971i
$831$	−65.3912	+	9.85614i	−2.26840	+	0.341906i
$832$	57.8391	+	59.6831i	2.00521	+	2.06914i
$833$	−16.6724	−	7.61866i	−0.577665	−	0.263971i
$834$	81.8987	−	81.8987i	2.83592	−	2.83592i
$835$	−26.1367	+	3.93947i	−0.904497	+	0.136331i
$836$	−24.7119	−	16.8483i	−0.854680	−	0.582711i
$837$	−19.5773	+	37.0421i	−0.676691	+	1.28036i
$838$	−34.3324	+	29.5454i	−1.18599	+	1.02063i
$839$	−7.99604	+	2.79794i	−0.276054	+	0.0965954i	−0.464756	−	0.885439i	$-0.653858\pi$
$839$	−7.99604	+	2.79794i	−0.276054	+	0.0965954i	0.188702	+	0.982034i	$0.439572\pi$
$840$	−96.1779	+	91.0622i	−3.31845	+	3.14194i
$841$	−66.3445	+	31.9498i	−2.28774	+	1.10172i
$842$	21.1043	−	8.28283i	0.727303	−	0.285445i
$843$	−35.5450	−	30.5889i	−1.22423	−	1.05354i
$844$	90.9687	+	35.7026i	3.13127	+	1.22893i
$845$	23.9575	−	11.7155i	0.824164	−	0.403026i
$846$	−34.8169	+	27.7655i	−1.19703	+	0.954599i
$847$	−20.1801	+	4.82059i	−0.693395	+	0.165637i
$848$	69.1448	−	86.7049i	2.37444	−	2.97746i
$849$	20.4047	+	29.9282i	0.700289	+	1.02713i
$850$	5.59429	+	0.209324i	0.191883	+	0.00717974i
$851$	−5.38718	−	1.44349i	−0.184670	−	0.0494822i
$852$	−16.5514	−	61.7707i	−0.567042	−	2.11623i
$853$	15.6605	+	9.84017i	0.536207	+	0.336921i	0.772761	−	0.634697i	$-0.218875\pi$
$853$	15.6605	+	9.84017i	0.536207	+	0.336921i	−0.236554	+	0.971618i	$0.576018\pi$
$854$	2.43544	+	51.2501i	0.0833391	+	1.75374i
$855$	28.8095	+	6.57557i	0.985263	+	0.224880i
$856$	−2.78041	−	74.3081i	−0.0950325	−	2.53980i
$857$	−2.73412	−	0.412102i	−0.0933956	−	0.0140771i	0.102178	−	0.994766i	$-0.467419\pi$
$857$	−2.73412	−	0.412102i	−0.0933956	−	0.0140771i	−0.195574	+	0.980689i	$0.562657\pi$
$858$	27.5933	+	38.6421i	0.942020	+	1.31922i
$859$	−0.0848854	+	0.0914847i	−0.00289625	+	0.00312142i	−0.734498	−	0.678610i	$-0.762582\pi$
$859$	−0.0848854	+	0.0914847i	−0.00289625	+	0.00312142i	0.731602	+	0.681732i	$0.238773\pi$
$860$	95.5107	−	60.0133i	3.25689	−	2.04644i
$861$	−56.8161	+	2.69994i	−1.93629	+	0.0920138i
$862$	−63.4720	+	14.4871i	−2.16186	+	0.493431i
$863$	9.67148	+	36.0944i	0.329221	+	1.22867i	0.910000	+	0.414608i	$0.136081\pi$
$863$	9.67148	+	36.0944i	0.329221	+	1.22867i	−0.580779	+	0.814061i	$0.697252\pi$
$864$	20.0847	−	74.9571i	0.683295	−	2.55009i
$865$	0.886830	+	0.0331828i	0.0301531	+	0.00112825i
$866$	3.16758	−	16.7411i	0.107639	−	0.568884i
$867$	−21.7602	−	17.3532i	−0.739016	−	0.589346i
$868$	119.059	+	73.1454i	4.04112	+	2.48272i
$869$	0.175613	−	1.55861i	0.00595727	−	0.0528722i
$870$	−45.3967	+	147.172i	−1.53909	+	4.98961i
$871$	12.0780	+	4.96031i	0.409246	+	0.168074i
$872$	−2.21024	−	29.4936i	−0.0748483	−	0.998781i
$873$	−24.7879	+	56.8146i	−0.838945	+	1.92288i
$874$	2.17806	+	4.52280i	0.0736741	+	0.152986i
$875$	−0.858520	+	31.4228i	−0.0290233	+	1.06228i
$876$	9.46522	−	3.31203i	0.319800	−	0.111903i
$877$	−18.2350	−	21.1895i	−0.615753	−	0.715518i	0.360352	−	0.932816i	$-0.382657\pi$
$877$	−18.2350	−	21.1895i	−0.615753	−	0.715518i	−0.976105	+	0.217298i	$0.930276\pi$
$878$	−12.4047	+	23.4709i	−0.418639	+	0.792104i
$879$	15.8340	+	83.6846i	0.534067	+	2.82261i
$880$	−7.29686	−	48.4115i	−0.245977	−	1.63195i
$881$	21.0350			0.708687			0.354344	−	0.935115i	$-0.384704\pi$
$881$	21.0350			0.708687			0.354344	+	0.935115i	$0.384704\pi$
$882$	11.3027	+	84.8880i	0.380582	+	2.85833i
$883$			27.0503i			0.910316i	0.890411	+	0.455158i	$0.150417\pi$
$883$			27.0503i			0.910316i	−0.890411	+	0.455158i	$0.849583\pi$
$884$	39.7390	+	30.3032i	1.33657	+	1.01921i
$885$	5.26556	−	7.72315i	0.177000	−	0.259611i
$886$	15.1261	−	28.6199i	0.508170	−	0.961505i
$887$	−13.2728	−	0.994657i	−0.445656	−	0.0333973i	−0.149988	−	0.988688i	$-0.547923\pi$
$887$	−13.2728	−	0.994657i	−0.445656	−	0.0333973i	−0.295669	+	0.955291i	$0.595542\pi$
$888$	−209.756	−	101.013i	−7.03896	−	3.38978i
$889$	23.3366	+	8.88840i	0.782684	+	0.298107i
$890$	6.20704	−	17.7387i	0.208060	−	0.594602i
$891$	−1.46976	+	3.36872i	−0.0492387	+	0.112856i
$892$	−110.057	−	94.7121i	−3.68500	−	3.17119i
$893$	4.22867	−	10.7745i	0.141507	−	0.360554i
$894$	−40.0005	−	12.3385i	−1.33782	−	0.412662i
$895$	−1.08710	−	0.122487i	−0.0363378	−	0.00409429i
$896$	−63.3688	−	21.4589i	−2.11700	−	0.716890i
$897$	−0.557344	−	5.75705i	−0.0186092	−	0.192222i
$898$	1.89157	−	1.28965i	0.0631227	−	0.0430363i
$899$	101.018	+	3.77983i	3.36914	+	0.126064i
$900$	−9.49069	−	16.4384i	−0.316356	−	0.547945i
$901$	10.8124	−	18.7276i	0.360213	−	0.623907i
$902$	20.0037	−	31.8357i	0.666050	−	1.06001i
$903$	4.87759	−	75.2653i	0.162316	−	2.50467i
$904$	−98.5109	+	61.8985i	−3.27643	+	2.05871i
$905$	−0.899094	−	24.0288i	−0.0298869	−	0.798744i
$906$	−9.48409	+	62.9228i	−0.315088	+	2.09047i
$907$	3.27571	−	21.7329i	0.108768	−	0.721629i	−0.866268	−	0.499580i	$-0.833488\pi$
$907$	3.27571	−	21.7329i	0.108768	−	0.721629i	0.975036	−	0.222048i	$-0.0712743\pi$
$908$	−75.2218	+	2.81460i	−2.49632	+	0.0934059i
$909$	2.43774	−	10.6805i	0.0808549	−	0.354248i
$910$	−31.6201	+	42.3450i	−1.04820	+	1.40372i
$911$	−1.02200	−	4.47769i	−0.0338605	−	0.148353i	0.955172	−	0.296052i	$-0.0956702\pi$
$911$	−1.02200	−	4.47769i	−0.0338605	−	0.148353i	−0.989032	+	0.147700i	$0.952813\pi$
$912$	30.3284	+	113.187i	1.00427	+	3.74800i
$913$	−3.79549	+	2.19133i	−0.125612	+	0.0725223i
$914$	11.1743	+	12.0431i	0.369614	+	0.398349i
$915$	39.7196	+	7.51535i	1.31309	+	0.248450i
$916$	−146.596	+	16.5174i	−4.84368	+	0.545751i
$917$	0.344748	+	34.1827i	0.0113846	+	1.12881i
$918$	3.32466	−	29.5072i	0.109730	−	0.973883i
$919$	44.7507	+	13.8038i	1.47619	+	0.455344i	0.925301	−	0.379234i	$-0.123812\pi$
$919$	44.7507	+	13.8038i	1.47619	+	0.455344i	0.550889	+	0.834578i	$0.314289\pi$
$920$	−3.89624	+	9.92747i	−0.128455	+	0.327299i
$921$	−44.1010	+	51.2463i	−1.45318	+	1.68862i
$922$	−14.7850	−	37.6715i	−0.486917	−	1.24064i
$923$	−6.66261	−	14.4091i	−0.219302	−	0.474281i
$924$	−60.6952	−	31.2994i	−1.99673	−	1.02967i
$925$	−7.12854	+	2.49438i	−0.234385	+	0.0820149i
$926$	−4.20930	+	56.1693i	−0.138326	+	1.84584i
$927$	−15.2166	+	4.69370i	−0.499779	+	0.154161i
$928$	−183.970	+	34.8090i	−6.03912	+	1.14266i
$929$	22.5910	+	16.6729i	0.741187	+	0.547021i	0.897675	−	0.440659i	$-0.145255\pi$
$929$	22.5910	+	16.6729i	0.741187	+	0.547021i	−0.156487	+	0.987680i	$0.550017\pi$
$930$	107.262	−	107.262i	3.51727	−	3.51727i
$931$	−13.5759	−	17.6387i	−0.444932	−	0.578085i
$932$	146.587			4.80160
$933$	−6.82917	−	45.3086i	−0.223577	−	1.48334i
$934$	−84.1023	+	15.9130i	−2.75191	+	0.520690i
$935$	−2.81390	−	9.12245i	−0.0920245	−	0.298336i
$936$	13.1259	−	144.658i	0.429033	−	4.72828i
$937$	−19.1278	+	39.7194i	−0.624879	+	1.29758i	0.312716	+	0.949847i	$0.398761\pi$
$937$	−19.1278	+	39.7194i	−0.624879	+	1.29758i	−0.937595	+	0.347729i	$0.886953\pi$
$938$	−25.7811	+	2.19370i	−0.841783	+	0.0716268i
$939$	−64.0370	+	30.8386i	−2.08977	+	1.00638i
$940$	36.7925	−	14.4400i	1.20004	−	0.470980i
$941$	15.6455	−	18.1804i	0.510028	−	0.592664i	−0.442631	−	0.896704i	$-0.645955\pi$
$941$	15.6455	−	18.1804i	0.510028	−	0.592664i	0.952659	+	0.304040i	$0.0983357\pi$
$942$	−5.15516	−	11.8158i	−0.167964	−	0.384978i
$943$	−4.04922	+	2.14008i	−0.131861	+	0.0696905i
$944$	22.1590	+	2.49672i	0.721213	+	0.0812612i
$945$	22.6711	+	2.32314i	0.737493	+	0.0755716i
$946$	38.9789	+	31.0846i	1.26731	+	1.01065i
$947$	−22.9970	−	4.35127i	−0.747302	−	0.141397i	−0.201707	−	0.979446i	$-0.564649\pi$
$947$	−22.9970	−	4.35127i	−0.747302	−	0.141397i	−0.545595	+	0.838049i	$0.683696\pi$
$948$	−9.39726	+	8.71938i	−0.305209	+	0.283192i
$949$	2.17509	−	1.21069i	0.0706066	−	0.0393008i
$950$	5.88698	+	3.39885i	0.190999	+	0.110273i
$951$	1.21403	−	1.93211i	0.0393676	−	0.0626531i
$952$	−60.6506	−	10.8433i	−1.96570	−	0.351434i
$953$	−33.2547	−	7.59017i	−1.07723	−	0.245870i	−0.353133	−	0.935573i	$-0.614884\pi$
$953$	−33.2547	−	7.59017i	−1.07723	−	0.245870i	−0.724092	+	0.689703i	$0.757741\pi$
$954$	−100.956	+	3.77751i	−3.26857	+	0.122301i
$955$	5.28615	+	7.16247i	0.171056	+	0.231772i
$956$	−49.0503	−	66.4609i	−1.58640	−	2.14950i
$957$	−49.3696	+	1.84728i	−1.59589	+	0.0597141i
$958$	28.4399	+	6.49122i	0.918852	+	0.209722i
$959$	−34.5802	+	9.64056i	−1.11665	+	0.311310i
$960$	−69.0373	+	109.872i	−2.22817	+	3.54611i
$961$	−59.3781	−	34.2820i	−1.91542	−	1.10587i
$962$	−89.3407	−	25.4476i	−2.88046	−	0.820464i
$963$	−27.7683	+	25.7652i	−0.894821	+	0.830272i
$964$	−6.47070	−	1.22432i	−0.208407	−	0.0394327i
$965$	11.7773	+	9.39209i	0.379125	+	0.302342i
$966$	6.19564	+	9.64304i	0.199341	+	0.310260i
$967$	45.8751	+	5.16889i	1.47524	+	0.166220i	0.812647	−	0.582756i	$-0.198025\pi$
$967$	45.8751	+	5.16889i	1.47524	+	0.166220i	0.662597	+	0.748976i	$0.269454\pi$
$968$	−61.6553	+	32.5858i	−1.98168	+	1.04735i
$969$	9.13729	+	20.9429i	0.293532	+	0.672783i
$970$	49.4463	−	57.4576i	1.58762	−	1.84485i
$971$	−6.86444	+	2.69410i	−0.220290	+	0.0864576i	−0.472920	−	0.881106i	$-0.656800\pi$
$971$	−6.86444	+	2.69410i	−0.220290	+	0.0864576i	0.252629	+	0.967563i	$0.418705\pi$
$972$	87.1356	−	41.9623i	2.79488	−	1.34594i
$973$	−5.75039	+	40.9494i	−0.184349	+	1.31278i
$974$	12.9073	−	26.8023i	0.413577	−	0.858802i
$975$	−5.01515	−	6.01610i	−0.160613	−	0.192669i
$976$	28.4252	+	92.1523i	0.909870	+	2.94972i
$977$	9.54595	−	1.80619i	0.305402	−	0.0577852i	−0.0309518	−	0.999521i	$-0.509854\pi$
$977$	9.54595	−	1.80619i	0.305402	−	0.0577852i	0.336354	+	0.941736i	$0.390806\pi$
$978$	−6.20040	−	41.1369i	−0.198267	−	1.31541i
$979$	6.02843			0.192669
$980$	12.6215	−	74.9518i	0.403178	−	2.39425i
$981$	−10.6538	+	10.6538i	−0.340149	+	0.340149i
$982$	3.96500	+	2.92630i	0.126528	+	0.0933821i
$983$	−5.52033	+	1.04450i	−0.176071	+	0.0333145i	−0.273199	−	0.961957i	$-0.588082\pi$
$983$	−5.52033	+	1.04450i	−0.176071	+	0.0333145i	0.0971283	+	0.995272i	$0.469034\pi$
$984$	−182.689	+	56.3522i	−5.82393	+	1.79644i
$985$	−1.40206	+	18.7091i	−0.0446732	+	0.596123i
$986$	−67.6242	+	23.6627i	−2.15359	+	0.753575i
$987$	6.58226	−	25.5951i	0.209516	−	0.814701i
$988$	25.4681	+	55.0793i	0.810248	+	1.75231i
$989$	−2.21873	−	5.65324i	−0.0705516	−	0.179763i
$990$	−29.0918	+	33.8053i	−0.924598	+	1.07440i
$991$	2.83204	−	7.21592i	0.0899627	−	0.229221i	−0.878810	−	0.477172i	$-0.841662\pi$
$991$	2.83204	−	7.21592i	0.0899627	−	0.229221i	0.968773	+	0.247951i	$0.0797571\pi$
$992$	176.217	+	54.3559i	5.59491	+	1.72580i
$993$	5.02820	−	44.6265i	0.159565	−	1.41618i
$994$	24.7919	+	19.3651i	0.786351	+	0.614223i
$995$	−2.55498	+	0.287877i	−0.0809984	+	0.00912633i
$996$	35.1957	+	6.65938i	1.11522	+	0.211010i
$997$	10.3499	+	11.1545i	0.327784	+	0.353267i	0.875345	−	0.483499i	$-0.160634\pi$
$997$	10.3499	+	11.1545i	0.327784	+	0.353267i	−0.547561	+	0.836766i	$0.684444\pi$
$998$	74.0678	−	42.7630i	2.34457	−	1.35364i
$999$	10.3680	+	38.6941i	0.328030	+	1.22423i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.cc.a.5.2	✓	1536
13.8	odd	4	inner	637.2.cc.a.593.2	yes	1536
49.10	odd	42	inner	637.2.cc.a.304.2	yes	1536
637.255	even	84	inner	637.2.cc.a.255.2	yes	1536

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.cc.a.5.2	✓	1536	1.1	even	1	trivial
637.2.cc.a.255.2	yes	1536	637.255	even	84	inner
637.2.cc.a.304.2	yes	1536	49.10	odd	42	inner
637.2.cc.a.593.2	yes	1536	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.cc (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.60364 + 2.17285i) q^{2} +(-1.54581 + 2.26729i) q^{3} +(-1.56013 - 5.05780i) q^{4} +(1.55493 - 1.33812i) q^{5} +(-2.44757 - 6.99474i) q^{6} +(2.20094 + 1.46828i) q^{7} +(8.39375 + 2.93710i) q^{8} +(-1.65505 - 4.21700i) q^{9} +(0.414004 + 5.52450i) q^{10} +(-1.62882 + 0.710645i) q^{11} +(13.8792 + 4.28116i) q^{12} +(3.57611 + 0.459857i) q^{13} +(-6.71988 + 2.42773i) q^{14} +(0.630289 + 5.59397i) q^{15} +(-11.0959 + 7.56509i) q^{16} +(-1.91962 + 1.78115i) q^{17} +(11.8170 + 3.16636i) q^{18} +(-3.07140 + 0.822980i) q^{19} +(-9.19386 - 5.77688i) q^{20} +(-6.73127 + 2.72049i) q^{21} +(1.06791 - 4.67880i) q^{22} +(-0.397623 + 0.428536i) q^{23} +(-19.6344 + 14.4909i) q^{24} +(-0.117985 + 0.782779i) q^{25} +(-6.73399 + 7.03291i) q^{26} +(4.09362 + 0.934343i) q^{27} +(3.99254 - 13.4226i) q^{28} +(-2.25436 - 9.87698i) q^{29} +(-13.1656 - 7.60118i) q^{30} +(-2.58254 + 9.63818i) q^{31} +(0.691040 - 18.4684i) q^{32} +(0.906605 - 4.79152i) q^{33} +(-0.791794 - 7.02737i) q^{34} +(5.38705 - 0.662058i) q^{35} +(-18.7467 + 14.9500i) q^{36} +(4.45792 + 8.43479i) q^{37} +(3.13721 - 7.99347i) q^{38} +(-6.57062 + 7.39722i) q^{39} +(16.9819 - 6.66490i) q^{40} +(7.39484 + 2.58757i) q^{41} +(4.88331 - 18.9887i) q^{42} +(-4.50742 + 9.35975i) q^{43} +(6.13546 + 7.12954i) q^{44} +(-8.21635 - 4.34247i) q^{45} +(-0.293502 - 1.55119i) q^{46} +(-2.16156 + 2.92881i) q^{47} -36.8520i q^{48} +(2.68829 + 6.46321i) q^{49} +(-1.51166 - 1.51166i) q^{50} +(-1.07100 - 7.10565i) q^{51} +(-3.25331 - 18.8047i) q^{52} +(-7.89106 + 2.43407i) q^{53} +(-8.59489 + 7.39650i) q^{54} +(-1.58176 + 3.28456i) q^{55} +(14.1617 + 18.7888i) q^{56} +(2.88188 - 8.23594i) q^{57} +(25.0764 + 10.9407i) q^{58} +(-1.25859 - 1.08310i) q^{59} +(27.3099 - 11.9152i) q^{60} +(2.11663 - 6.86195i) q^{61} +(-16.8009 - 21.0676i) q^{62} +(2.54908 - 11.7114i) q^{63} +(18.0219 + 14.3720i) q^{64} +(6.17593 - 4.07023i) q^{65} +(8.95742 + 9.65380i) q^{66} +(3.49793 + 0.937267i) q^{67} +(12.0035 + 6.93024i) q^{68} +(-0.356965 - 1.56396i) q^{69} +(-7.20033 + 12.7670i) q^{70} +(-2.34248 - 3.72804i) q^{71} +(-1.50633 - 40.2575i) q^{72} +(0.555509 - 0.409985i) q^{73} +(-25.4765 - 3.83996i) q^{74} +(-1.59240 - 1.47754i) q^{75} +(8.95425 + 14.2506i) q^{76} +(-4.62836 - 0.827474i) q^{77} +(-5.53618 - 26.1395i) q^{78} +(-0.441303 + 0.764359i) q^{79} +(-7.13038 + 26.6109i) q^{80} +(1.51610 - 1.40673i) q^{81} +(-17.4811 + 11.9184i) q^{82} +(2.45069 - 0.276126i) q^{83} +(24.2613 + 29.8012i) q^{84} +(-0.601475 + 5.33824i) q^{85} +(-13.1091 - 24.8036i) q^{86} +(25.8788 + 10.1567i) q^{87} +(-15.7591 + 1.18098i) q^{88} +(-3.10925 - 1.35655i) q^{89} +(22.6116 - 10.8892i) q^{90} +(7.19560 + 6.26285i) q^{91} +(2.78779 + 1.34253i) q^{92} +(-17.8604 - 20.7542i) q^{93} +(-2.89751 - 9.39351i) q^{94} +(-3.67456 + 5.38959i) q^{95} +(40.8051 + 30.1155i) q^{96} +(-9.67543 - 9.67543i) q^{97} +(-18.3547 - 4.52340i) q^{98} +(5.69256 + 5.69256i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1536 q - 26 q^{2} - 44 q^{3} - 22 q^{5} - 28 q^{6} - 22 q^{7} - 12 q^{8} - 176 q^{9} - 22 q^{11} - 28 q^{13} - 84 q^{14} - 8 q^{15} - 180 q^{16} - 18 q^{18} - 54 q^{19} - 28 q^{20} - 2 q^{21} - 48 q^{22}+ \cdots - 32 q^{99}+O(q^{100}) \) 1536 * q - 26 * q^2 - 44 * q^3 - 22 * q^5 - 28 * q^6 - 22 * q^7 - 12 * q^8 - 176 * q^9 - 22 * q^11 - 28 * q^13 - 84 * q^14 - 8 * q^15 - 180 * q^16 - 18 * q^18 - 54 * q^19 - 28 * q^20 - 2 * q^21 - 48 * q^22 + 68 * q^24 - 52 * q^26 - 56 * q^27 + 62 * q^28 - 48 * q^29 - 66 * q^31 - 32 * q^32 - 76 * q^33 + 28 * q^34 - 140 * q^35 - 62 * q^37 - 16 * q^39 + 76 * q^40 - 28 * q^41 + 128 * q^42 - 226 * q^44 + 66 * q^45 - 32 * q^46 + 68 * q^47 + 156 * q^50 + 48 * q^52 - 48 * q^53 - 64 * q^54 + 28 * q^55 - 62 * q^57 - 22 * q^58 + 54 * q^59 - 88 * q^60 - 8 * q^61 - 150 * q^63 - 12 * q^65 + 72 * q^66 - 30 * q^67 - 36 * q^68 + 62 * q^70 + 104 * q^71 - 54 * q^72 - 136 * q^73 + 12 * q^74 + 28 * q^76 + 68 * q^78 - 16 * q^79 - 180 * q^80 + 64 * q^81 + 70 * q^83 + 30 * q^84 - 96 * q^85 + 30 * q^86 + 416 * q^87 - 38 * q^89 - 196 * q^91 - 180 * q^92 + 38 * q^93 - 264 * q^94 - 350 * q^96 - 390 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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