LMFDB - Embedded newform 637.2.cc.a.304.2

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			304.2
Character	$\chi$	$=$	637.304
Dual form			637.2.cc.a.593.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.17285 + 1.60364i) q^{2} +(-1.54581 - 2.26729i) q^{3} +(1.56013 - 5.05780i) q^{4} +(1.33812 - 1.55493i) q^{5} +(6.99474 + 2.44757i) q^{6} +(1.46828 + 2.20094i) q^{7} +(2.93710 + 8.39375i) q^{8} +(-1.65505 + 4.21700i) q^{9} +(-0.414004 + 5.52450i) q^{10} +(0.710645 - 1.62882i) q^{11} +(-13.8792 + 4.28116i) q^{12} +(0.347431 + 3.58877i) q^{13} +(-6.71988 - 2.42773i) q^{14} +(-5.59397 - 0.630289i) q^{15} +(-11.0959 - 7.56509i) q^{16} +(1.91962 + 1.78115i) q^{17} +(-3.16636 - 11.8170i) q^{18} +(-0.822980 + 3.07140i) q^{19} +(-5.77688 - 9.19386i) q^{20} +(2.72049 - 6.73127i) q^{21} +(1.06791 + 4.67880i) q^{22} +(0.397623 + 0.428536i) q^{23} +(14.4909 - 19.6344i) q^{24} +(0.117985 + 0.782779i) q^{25} +(-6.51002 - 7.24073i) q^{26} +(4.09362 - 0.934343i) q^{27} +(13.4226 - 3.99254i) q^{28} +(-2.25436 + 9.87698i) q^{29} +(13.1656 - 7.60118i) q^{30} +(-9.63818 + 2.58254i) q^{31} +(18.4684 - 0.691040i) q^{32} +(-4.79152 + 0.906605i) q^{33} +(-7.02737 - 0.791794i) q^{34} +(5.38705 + 0.662058i) q^{35} +(18.7467 + 14.9500i) q^{36} +(8.43479 + 4.45792i) q^{37} +(-3.13721 - 7.99347i) q^{38} +(7.59973 - 6.33530i) q^{39} +(16.9819 + 6.66490i) q^{40} +(-2.58757 - 7.39484i) q^{41} +(4.88331 + 18.9887i) q^{42} +(4.50742 + 9.35975i) q^{43} +(-7.12954 - 6.13546i) q^{44} +(4.34247 + 8.21635i) q^{45} +(-1.55119 - 0.293502i) q^{46} +(2.92881 - 2.16156i) q^{47} +36.8520i q^{48} +(-2.68829 + 6.46321i) q^{49} +(-1.51166 - 1.51166i) q^{50} +(1.07100 - 7.10565i) q^{51} +(18.6933 + 3.84170i) q^{52} +(-7.89106 - 2.43407i) q^{53} +(-7.39650 + 8.59489i) q^{54} +(-1.58176 - 3.28456i) q^{55} +(-14.1617 + 18.7888i) q^{56} +(8.23594 - 2.88188i) q^{57} +(-10.9407 - 25.0764i) q^{58} +(-1.08310 - 1.25859i) q^{59} +(-11.9152 + 27.3099i) q^{60} +(2.11663 + 6.86195i) q^{61} +(16.8009 - 21.0676i) q^{62} +(-11.7114 + 2.54908i) q^{63} +(-18.0219 + 14.3720i) q^{64} +(6.04519 + 4.26199i) q^{65} +(8.95742 - 9.65380i) q^{66} +(-0.937267 - 3.49793i) q^{67} +(12.0035 - 6.93024i) q^{68} +(0.356965 - 1.56396i) q^{69} +(-12.7670 + 7.20033i) q^{70} +(3.72804 + 2.34248i) q^{71} +(-40.2575 - 1.50633i) q^{72} +(-0.409985 + 0.555509i) q^{73} +(-25.4765 + 3.83996i) q^{74} +(1.59240 - 1.47754i) q^{75} +(14.2506 + 8.95425i) q^{76} +(4.62836 - 0.827474i) q^{77} +(-6.35357 + 25.9529i) q^{78} +(-0.441303 - 0.764359i) q^{79} +(-26.6109 + 7.13038i) q^{80} +(1.51610 + 1.40673i) q^{81} +(17.4811 + 11.9184i) q^{82} +(0.276126 - 2.45069i) q^{83} +(-29.8012 - 24.2613i) q^{84} +(5.33824 - 0.601475i) q^{85} +(-24.8036 - 13.1091i) q^{86} +(25.8788 - 10.1567i) q^{87} +(15.7591 + 1.18098i) q^{88} +(-1.35655 - 3.10925i) q^{89} +(-22.6116 - 10.8892i) q^{90} +(-7.38855 + 6.03401i) q^{91} +(2.78779 - 1.34253i) q^{92} +(20.7542 + 17.8604i) q^{93} +(-2.89751 + 9.39351i) q^{94} +(3.67456 + 5.38959i) q^{95} +(-30.1155 - 40.8051i) q^{96} +(9.67543 + 9.67543i) q^{97} +(-4.52340 - 18.3547i) 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 $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{13}{42}\right)$

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 $

$2$	−2.17285	+	1.60364i	−1.53644	+	1.13394i	−0.591684	+	0.806170i	$0.701537\pi$
$2$	−2.17285	+	1.60364i	−1.53644	+	1.13394i	−0.944756	+	0.327774i	$0.893701\pi$
$3$	−1.54581	−	2.26729i	−0.892476	−	1.30902i	−0.950506	−	0.310706i	$-0.899434\pi$
$3$	−1.54581	−	2.26729i	−0.892476	−	1.30902i	0.0580303	−	0.998315i	$-0.481518\pi$
$4$	1.56013	−	5.05780i	0.780063	−	2.52890i
$5$	1.33812	−	1.55493i	0.598427	−	0.695385i	−0.374308	−	0.927305i	$-0.622120\pi$
$5$	1.33812	−	1.55493i	0.598427	−	0.695385i	0.972735	+	0.231919i	$0.0745006\pi$
$6$	6.99474	+	2.44757i	2.85559	+	0.999215i
$7$	1.46828	+	2.20094i	0.554959	+	0.831878i
$7$	1.46828	+	2.20094i	0.554959	+	0.831878i
$8$	2.93710	+	8.39375i	1.03842	+	2.96764i
$9$	−1.65505	+	4.21700i	−0.551683	+	1.40567i
$10$	−0.414004	+	5.52450i	−0.130920	+	1.74700i
$11$	0.710645	−	1.62882i	0.214268	−	0.491106i	−0.775923	−	0.630827i	$-0.782716\pi$
$11$	0.710645	−	1.62882i	0.214268	−	0.491106i	0.990191	+	0.139721i	$0.0446205\pi$
$12$	−13.8792	+	4.28116i	−4.00657	+	1.23586i
$13$	0.347431	+	3.58877i	0.0963601	+	0.995347i
$13$	0.347431	+	3.58877i	0.0963601	+	0.995347i
$14$	−6.71988	−	2.42773i	−1.79596	−	0.648838i
$15$	−5.59397	−	0.630289i	−1.44436	−	0.162740i
$16$	−11.0959	−	7.56509i	−2.77399	−	1.89127i
$17$	1.91962	+	1.78115i	0.465576	+	0.431991i	0.877754	−	0.479112i	$-0.159041\pi$
$17$	1.91962	+	1.78115i	0.465576	+	0.431991i	−0.412178	+	0.911103i	$0.635232\pi$
$18$	−3.16636	−	11.8170i	−0.746318	−	2.78530i
$19$	−0.822980	+	3.07140i	−0.188804	+	0.704628i	0.804980	+	0.593303i	$0.202176\pi$
$19$	−0.822980	+	3.07140i	−0.188804	+	0.704628i	−0.993784	+	0.111325i	$0.964490\pi$
$20$	−5.77688	−	9.19386i	−1.29175	−	2.05581i
$21$	2.72049	−	6.73127i	0.593659	−	1.46888i
$22$	1.06791	+	4.67880i	0.227678	+	0.997523i
$23$	0.397623	+	0.428536i	0.0829102	+	0.0893559i	0.773144	−	0.634230i	$-0.218683\pi$
$23$	0.397623	+	0.428536i	0.0829102	+	0.0893559i	−0.690234	+	0.723586i	$0.742492\pi$
$24$	14.4909	−	19.6344i	2.95794	−	4.00786i
$25$	0.117985	+	0.782779i	0.0235970	+	0.156556i
$26$	−6.51002	−	7.24073i	−1.27672	−	1.42002i
$27$	4.09362	−	0.934343i	0.787818	−	0.179814i
$28$	13.4226	−	3.99254i	2.53664	−	0.754520i
$29$	−2.25436	+	9.87698i	−0.418623	+	1.83411i	0.121589	+	0.992580i	$0.461201\pi$
$29$	−2.25436	+	9.87698i	−0.418623	+	1.83411i	−0.540213	+	0.841528i	$0.681656\pi$
$30$	13.1656	−	7.60118i	2.40370	−	1.38778i
$31$	−9.63818	+	2.58254i	−1.73107	+	0.463838i	−0.980429	−	0.196874i	$-0.936921\pi$
$31$	−9.63818	+	2.58254i	−1.73107	+	0.463838i	−0.750639	+	0.660713i	$0.770254\pi$
$32$	18.4684	−	0.691040i	3.26479	−	0.122160i
$33$	−4.79152	+	0.906605i	−0.834097	+	0.157820i
$34$	−7.02737	−	0.791794i	−1.20518	−	0.135792i
$35$	5.38705	+	0.662058i	0.910578	+	0.111908i
$36$	18.7467	+	14.9500i	3.12444	+	2.49166i
$37$	8.43479	+	4.45792i	1.38667	+	0.732877i	0.983271	−	0.182147i	$-0.0583045\pi$
$37$	8.43479	+	4.45792i	1.38667	+	0.732877i	0.403400	+	0.915024i	$0.367828\pi$
$38$	−3.13721	−	7.99347i	−0.508922	−	1.29671i
$39$	7.59973	−	6.33530i	1.21693	−	1.01446i
$40$	16.9819	+	6.66490i	2.68507	+	1.05381i
$41$	−2.58757	−	7.39484i	−0.404110	−	1.15488i	−0.948700	−	0.316177i	$-0.897601\pi$
$41$	−2.58757	−	7.39484i	−0.404110	−	1.15488i	0.544590	−	0.838702i	$-0.316685\pi$
$42$	4.88331	+	18.9887i	0.753512	+	2.93003i
$43$	4.50742	+	9.35975i	0.687375	+	1.42735i	0.893609	+	0.448845i	$0.148165\pi$
$43$	4.50742	+	9.35975i	0.687375	+	1.42735i	−0.206235	+	0.978503i	$0.566121\pi$
$44$	−7.12954	−	6.13546i	−1.07482	−	0.924956i
$45$	4.34247	+	8.21635i	0.647337	+	1.22482i
$46$	−1.55119	−	0.293502i	−0.228711	−	0.0432745i
$47$	2.92881	−	2.16156i	0.427211	−	0.315296i	−0.358906	−	0.933374i	$-0.616850\pi$
$47$	2.92881	−	2.16156i	0.427211	−	0.315296i	0.786117	+	0.618078i	$0.212088\pi$
$48$			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
$52$	18.6933	+	3.84170i	2.59230	+	0.532748i
$53$	−7.89106	−	2.43407i	−1.08392	−	0.334345i	−0.299197	−	0.954191i	$-0.596719\pi$
$53$	−7.89106	−	2.43407i	−1.08392	−	0.334345i	−0.784723	+	0.619846i	$0.787195\pi$
$54$	−7.39650	+	8.59489i	−1.00654	+	1.16962i
$55$	−1.58176	−	3.28456i	−0.213285	−	0.442890i
$56$	−14.1617	+	18.7888i	−1.89243	+	2.51076i
$57$	8.23594	−	2.88188i	1.09088	−	0.381714i
$58$	−10.9407	−	25.0764i	−1.43659	−	3.29269i
$59$	−1.08310	−	1.25859i	−0.141008	−	0.163854i	0.683027	−	0.730393i	$-0.260663\pi$
$59$	−1.08310	−	1.25859i	−0.141008	−	0.163854i	−0.824035	+	0.566539i	$0.808282\pi$
$60$	−11.9152	+	27.3099i	−1.53824	+	3.52569i
$61$	2.11663	+	6.86195i	0.271007	+	0.878582i	0.984116	+	0.177529i	$0.0568104\pi$
$61$	2.11663	+	6.86195i	0.271007	+	0.878582i	−0.713109	+	0.701053i	$0.752713\pi$
$62$	16.8009	−	21.0676i	2.13371	−	2.67559i
$63$	−11.7114	+	2.54908i	−1.47550	+	0.321154i
$64$	−18.0219	+	14.3720i	−2.25273	+	1.79649i
$65$	6.04519	+	4.26199i	0.749814	+	0.528635i
$66$	8.95742	−	9.65380i	1.10258	−	1.18830i
$67$	−0.937267	−	3.49793i	−0.114505	−	0.427340i	0.884744	−	0.466077i	$-0.154333\pi$
$67$	−0.937267	−	3.49793i	−0.114505	−	0.427340i	−0.999249	+	0.0387373i	$0.987666\pi$
$68$	12.0035	−	6.93024i	1.45564	−	0.840415i
$69$	0.356965	−	1.56396i	0.0429735	−	0.188279i
$70$	−12.7670	+	7.20033i	−1.52595	+	0.860605i
$71$	3.72804	+	2.34248i	0.442437	+	0.278002i	0.734772	−	0.678314i	$-0.237289\pi$
$71$	3.72804	+	2.34248i	0.442437	+	0.278002i	−0.292335	+	0.956316i	$0.594432\pi$
$72$	−40.2575	−	1.50633i	−4.74439	−	0.177522i
$73$	−0.409985	+	0.555509i	−0.0479851	+	0.0650175i	−0.827933	−	0.560827i	$-0.810483\pi$
$73$	−0.409985	+	0.555509i	−0.0479851	+	0.0650175i	0.779948	+	0.625844i	$0.215245\pi$
$74$	−25.4765	+	3.83996i	−2.96158	+	0.446386i
$75$	1.59240	−	1.47754i	0.183875	−	0.170611i
$76$	14.2506	+	8.95425i	1.63466	+	1.02712i
$77$	4.62836	−	0.827474i	0.527450	−	0.0942994i
$78$	−6.35357	+	25.9529i	−0.719400	+	2.93859i
$79$	−0.441303	−	0.764359i	−0.0496504	−	0.0859971i	0.840132	−	0.542382i	$-0.182477\pi$
$79$	−0.441303	−	0.764359i	−0.0496504	−	0.0859971i	−0.889783	+	0.456385i	$0.849144\pi$
$80$	−26.6109	+	7.13038i	−2.97519	+	0.797201i
$81$	1.51610	+	1.40673i	0.168455	+	0.156304i
$82$	17.4811	+	11.9184i	1.93046	+	1.31617i
$83$	0.276126	−	2.45069i	0.0303088	−	0.268998i	−0.969414	−	0.245433i	$-0.921070\pi$
$83$	0.276126	−	2.45069i	0.0303088	−	0.268998i	0.999722	−	0.0235647i	$-0.00750158\pi$
$84$	−29.8012	−	24.2613i	−3.25157	−	2.64713i
$85$	5.33824	−	0.601475i	0.579014	−	0.0652392i
$86$	−24.8036	−	13.1091i	−2.67464	−	1.41359i
$87$	25.8788	−	10.1567i	2.77450	−	1.08891i
$88$	15.7591	+	1.18098i	1.67993	+	0.125893i
$89$	−1.35655	−	3.10925i	−0.143794	−	0.329580i	0.829729	−	0.558166i	$-0.188495\pi$
$89$	−1.35655	−	3.10925i	−0.143794	−	0.329580i	−0.973524	+	0.228586i	$0.926590\pi$
$90$	−22.6116	−	10.8892i	−2.38347	−	1.14782i
$91$	−7.38855	+	6.03401i	−0.774531	+	0.632536i
$92$	2.78779	−	1.34253i	0.290648	−	0.139968i
$93$	20.7542	+	17.8604i	2.15211	+	1.85204i
$94$	−2.89751	+	9.39351i	−0.298856	+	0.968867i
$95$	3.67456	+	5.38959i	0.377002	+	0.552961i
$96$	−30.1155	−	40.8051i	−3.07365	−	4.16465i
$97$	9.67543	+	9.67543i	0.982391	+	0.982391i	0.999848	−	0.0174565i	$-0.00555687\pi$
$97$	9.67543	+	9.67543i	0.982391	+	0.982391i	−0.0174565	+	0.999848i	$0.505557\pi$
$98$	−4.52340	−	18.3547i	−0.456932	−	1.85410i
$99$	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	$-0.728866\pi$
$101$	−1.99807	+	1.36226i	−0.198815	+	0.135550i	0.459820	+	0.888012i	$0.347914\pi$
$102$	9.06777	+	17.1571i	0.897843	+	1.69880i
$103$	−0.262686	−	3.50530i	−0.0258832	−	0.345388i	−0.995078	−	0.0990928i	$-0.968406\pi$
$103$	−0.262686	−	3.50530i	−0.0258832	−	0.345388i	0.969195	−	0.246295i	$-0.0792131\pi$
$104$	−29.1028	+	13.4568i	−2.85377	+	1.31955i
$105$	−6.82630	−	13.2374i	−0.666178	−	1.29184i
$106$	21.0495	−	7.36554i	2.04451	−	0.715404i
$107$	−3.05492	+	7.78382i	−0.295331	+	0.752490i	0.703784	+	0.710414i	$0.251492\pi$
$107$	−3.05492	+	7.78382i	−0.295331	+	0.752490i	−0.999114	+	0.0420760i	$0.986603\pi$
$108$	1.66084	−	22.1624i	0.159815	−	2.13258i
$109$	3.04838	+	1.32999i	0.291982	+	0.127390i	0.540777	−	0.841166i	$-0.318130\pi$
$109$	3.04838	+	1.32999i	0.291982	+	0.127390i	−0.248796	+	0.968556i	$0.580035\pi$
$110$	8.70419	+	4.60030i	0.829912	+	0.438621i
$111$	−2.93121	−	26.0152i	−0.278218	−	2.46926i
$112$	0.358328	−	35.5292i	0.0338588	−	3.35720i
$113$	−8.15707	−	10.2286i	−0.767353	−	0.962230i	0.232594	−	0.972574i	$-0.425279\pi$
$113$	−8.15707	−	10.2286i	−0.767353	−	0.962230i	−0.999946	+	0.0103443i	$0.996707\pi$
$114$	−13.2740	+	19.4694i	−1.24322	+	1.82347i
$115$	1.19841	−	0.0448414i	0.111752	−	0.00418148i
$116$	46.4388	+	26.8114i	4.31173	+	2.48938i
$117$	−15.7089	−	4.47448i	−1.45228	−	0.413666i
$118$	4.37174	+	0.997821i	0.402451	+	0.0918569i
$119$	−1.10165	+	6.84019i	−0.100989	+	0.627040i
$120$	−11.1396	−	48.8056i	−1.01690	−	4.45532i
$121$	5.33388	+	5.74855i	0.484898	+	0.522596i
$122$	−15.6032	−	11.5157i	−1.41265	−	1.04258i
$123$	−12.7664	+	17.2978i	−1.15110	+	1.55969i
$124$	−1.97478	+	52.7771i	−0.177340	+	4.73952i
$125$	10.0600	+	6.32114i	0.899797	+	0.565380i
$126$	21.3595	−	24.3197i	1.90285	−	2.16657i
$127$	−9.20188	−	2.10027i	−0.816535	−	0.186369i	−0.206198	−	0.978510i	$-0.566109\pi$
$127$	−9.20188	−	2.10027i	−0.816535	−	0.186369i	−0.610337	+	0.792142i	$0.708966\pi$
$128$	6.54480	−	24.4255i	0.578484	−	2.15893i
$129$	14.2536	−	24.6880i	1.25496	−	2.17366i
$130$	−19.9700	+	0.433617i	−1.75149	+	0.0380307i
$131$	7.27838	−	10.6754i	0.635915	−	0.932717i	−0.364084	−	0.931366i	$-0.618618\pi$
$131$	7.27838	−	10.6754i	0.635915	−	0.932717i	0.999999	−	0.00135029i	$-0.000429809\pi$
$132$	−2.88995	+	25.6490i	−0.251538	+	2.23246i
$133$	−7.96834	+	2.69836i	−0.690943	+	0.233977i
$134$	7.64596	+	6.09745i	0.660510	+	0.526739i
$135$	4.02494	−	7.61556i	0.346412	−	0.655443i
$136$	−9.31238	+	21.3442i	−0.798530	+	1.83025i
$137$	10.2846	−	8.85057i	0.878669	−	0.756156i	−0.0922069	−	0.995740i	$-0.529392\pi$
$137$	10.2846	−	8.85057i	0.878669	−	0.756156i	0.970876	+	0.239584i	$0.0770112\pi$
$138$	1.73240	+	3.97071i	0.147472	+	0.338009i
$139$	6.78128	−	14.0815i	0.575181	−	1.19438i	−0.387029	−	0.922068i	$-0.626499\pi$
$139$	6.78128	−	14.0815i	0.575181	−	1.19438i	0.962210	−	0.272308i	$-0.0877870\pi$
$140$	11.7530	−	26.2138i	0.993313	−	2.21547i
$141$	−9.42828	−	3.29910i	−0.794004	−	0.277834i
$142$	−11.8570	+	0.888559i	−0.995017	+	0.0745662i
$143$	6.09235	+	1.98444i	0.509468	+	0.165947i
$144$	50.2663	−	34.2710i	4.18886	−	2.85592i
$145$	12.3414	+	16.7220i	1.02490	+	1.38869i
$146$		−	1.86451i		−	0.154308i
$147$	18.8096	−	3.89578i	1.55139	−	0.321319i
$148$	35.7066	−	35.7066i	2.93507	−	2.93507i
$149$	4.54492	−	3.35431i	0.372335	−	0.274795i	−0.391539	−	0.920162i	$-0.628057\pi$
$149$	4.54492	−	3.35431i	0.372335	−	0.274795i	0.763873	+	0.645366i	$0.223295\pi$
$150$	−1.09063	+	5.76411i	−0.0890495	+	0.470638i
$151$	−4.01235	−	7.59174i	−0.326521	−	0.617807i	0.665135	−	0.746723i	$-0.268374\pi$
$151$	−4.01235	−	7.59174i	−0.326521	−	0.617807i	−0.991656	+	0.128916i	$0.958850\pi$
$152$	−28.1978	+	2.11313i	−2.28714	+	0.171397i
$153$	−10.6881	+	5.14714i	−0.864085	+	0.416122i
$154$	−8.72977	+	9.22020i	−0.703465	+	0.742985i
$155$	−8.88141	+	18.4424i	−0.713372	+	1.48133i
$156$	−20.1862	−	48.3218i	−1.61619	−	3.86884i
$157$	1.73472	+	0.129999i	0.138446	+	0.0103751i	0.143773	−	0.989611i	$-0.454077\pi$
$157$	1.73472	+	0.129999i	0.138446	+	0.0103751i	−0.00532691	+	0.999986i	$0.501696\pi$
$158$	2.18464	+	0.953150i	0.173801	+	0.0758285i
$159$	6.67936	+	21.6539i	0.529708	+	1.71727i
$160$	23.6385	−	29.6418i	1.86879	−	2.34339i
$161$	−0.359359	+	1.50436i	−0.0283215	+	0.118560i
$162$	−5.55016	−	0.625352i	−0.436061	−	0.0491323i
$163$	1.04367	+	5.51592i	0.0817465	+	0.432041i	0.999399	+	0.0346574i	$0.0110340\pi$
$163$	1.04367	+	5.51592i	0.0817465	+	0.432041i	−0.917653	+	0.397383i	$0.869918\pi$
$164$	−41.4386	+	1.55052i	−3.23581	+	0.121075i
$165$	−5.00195	+	8.66363i	−0.389401	+	0.674463i
$166$	3.33004	+	5.76779i	0.258461	+	0.447667i
$167$	−6.85502	−	10.9097i	−0.530458	−	0.844218i	0.468778	−	0.883316i	$-0.344695\pi$
$167$	−6.85502	−	10.9097i	−0.530458	−	0.844218i	−0.999235	+	0.0390977i	$0.987552\pi$
$168$	64.4909	+	3.06466i	4.97558	+	0.236443i
$169$	−12.7586	+	2.49370i	−0.981429	+	0.191823i
$170$	−10.6347	+	9.86753i	−0.815642	+	0.756805i
$171$	−11.5900	−	8.55382i	−0.886311	−	0.654127i
$172$	54.3719	−	8.19525i	4.14582	−	0.624882i
$173$	−0.317118	+	0.294243i	−0.0241101	+	0.0223709i	−0.692136	−	0.721767i	$-0.743330\pi$
$173$	−0.317118	+	0.294243i	−0.0241101	+	0.0223709i	0.668026	+	0.744138i	$0.267140\pi$
$174$	−39.9432	+	63.5693i	−3.02809	+	4.81917i
$175$	−1.54962	+	1.40902i	−0.117140	+	0.106512i
$176$	−20.2074	+	12.6972i	−1.52319	+	0.957085i
$177$	−1.17931	+	4.40124i	−0.0886424	+	0.330818i
$178$	7.93371	+	4.58053i	0.594657	+	0.343325i
$179$	0.362720	−	0.390919i	0.0271110	−	0.0292187i	−0.719351	−	0.694647i	$-0.755561\pi$
$179$	0.362720	−	0.390919i	0.0271110	−	0.0292187i	0.746462	+	0.665428i	$0.231751\pi$
$180$	48.3315	−	9.14481i	3.60242	−	0.681614i
$181$	−7.30816	−	9.16414i	−0.543211	−	0.681165i	0.432145	−	0.901804i	$-0.357757\pi$
$181$	−7.30816	−	9.16414i	−0.543211	−	0.681165i	−0.975355	+	0.220639i	$0.929186\pi$
$182$	6.37787	−	24.9596i	0.472759	−	1.85013i
$183$	12.2861	−	15.4063i	0.908216	−	1.13887i
$184$	−2.42916	+	4.59620i	−0.179080	+	0.338837i
$185$	18.2185	−	7.15025i	1.33945	−	0.525697i
$186$	−73.7375	−	5.52586i	−5.40670	−	0.405176i
$187$	4.26533	−	1.86094i	0.311911	−	0.136086i
$188$	−6.36344	−	18.1857i	−0.464101	−	1.32633i
$189$	8.06703	+	7.63795i	0.586790	+	0.555579i
$190$	−16.6273	−	5.81813i	−1.20627	−	0.422091i
$191$	−0.324282	−	4.32724i	−0.0234642	−	0.313108i	−0.996570	−	0.0827505i	$-0.973630\pi$
$191$	−0.324282	−	4.32724i	−0.0234642	−	0.313108i	0.973106	−	0.230357i	$-0.0739895\pi$
$192$	60.4439	+	18.6445i	4.36216	+	1.34555i
$193$	7.21502	+	1.36516i	0.519348	+	0.0982660i	0.438976	−	0.898499i	$-0.355341\pi$
$193$	7.21502	+	1.36516i	0.519348	+	0.0982660i	0.0803726	+	0.996765i	$0.474389\pi$
$194$	−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	$-0.676331\pi$
$199$	1.03556	−	0.706033i	0.0734089	−	0.0500494i	0.599468	+	0.800398i	$0.295379\pi$
$200$	−6.22392	+	3.28944i	−0.440097	+	0.232598i
$201$	−6.48198	+	7.53220i	−0.457204	+	0.531280i
$202$	2.15694	−	6.16418i	0.151762	−	0.433710i
$203$	−25.0487	+	9.54050i	−1.75807	+	0.669611i
$204$	−34.2681	−	16.5026i	−2.39925	−	1.15542i
$205$	−14.9609	−	5.87173i	−1.04492	−	0.410100i
$206$	6.19202	+	7.19525i	0.431418	+	0.501317i
$207$	−2.46522	+	0.967528i	−0.171345	+	0.0672478i
$208$	23.2943	−	42.4492i	1.61517	−	2.94332i
$209$	4.41790	+	3.52316i	0.305593	+	0.243702i
$210$	36.0606	+	17.8161i	2.48842	+	1.22943i
$211$	−11.5115	−	14.4350i	−0.792485	−	0.993745i	−0.999880	−	0.0154877i	$-0.995070\pi$
$211$	−11.5115	−	14.4350i	−0.792485	−	0.993745i	0.207395	−	0.978257i	$-0.433502\pi$
$212$	−24.6221	+	36.1140i	−1.69105	+	2.48032i
$213$	−0.451762	−	12.0736i	−0.0309542	−	0.827269i
$214$	−5.84454	−	21.8121i	−0.399524	−	1.49104i
$215$	20.5852	+	5.51579i	1.40390	+	0.376174i
$216$	19.8660	+	31.6166i	1.35171	+	2.15124i
$217$	−19.8356	−	17.4212i	−1.34653	−	1.18263i
$218$	−8.75651	+	1.99862i	−0.593066	+	0.135363i
$219$	1.89326	+	0.0708408i	0.127935	+	0.00478698i
$220$	−19.0804	+	2.87591i	−1.28640	+	0.193894i
$221$	−5.72519	+	7.50790i	−0.385118	+	0.505036i
$222$	48.0882	+	51.8267i	3.22747	+	3.47838i
$223$	14.5951	−	23.2279i	0.977357	−	1.55546i	0.153893	−	0.988087i	$-0.450819\pi$
$223$	14.5951	−	23.2279i	0.977357	−	1.55546i	0.823464	−	0.567368i	$-0.192038\pi$
$224$	28.6378	+	39.6333i	1.91345	+	2.64811i
$225$	−3.49625	−	0.797995i	−0.233083	−	0.0531997i
$226$	34.1272	+	9.14435i	2.27011	+	0.608273i
$227$	13.7370	−	3.68083i	0.911759	−	0.244305i	0.227700	−	0.973731i	$-0.426879\pi$
$227$	13.7370	−	3.68083i	0.911759	−	0.244305i	0.684060	+	0.729426i	$0.260213\pi$
$228$	−1.72688	−	46.1519i	−0.114365	−	3.05648i
$229$	−27.3858	+	5.18168i	−1.80971	+	0.342415i	−0.977318	−	0.211777i	$-0.932075\pi$
$229$	−27.3858	+	5.18168i	−1.80971	+	0.342415i	−0.832389	+	0.554192i	$0.813027\pi$
$230$	−2.53207	+	2.01925i	−0.166959	+	0.133146i
$231$	−9.03070	−	9.21471i	−0.594176	−	0.606284i
$232$	−89.5262	+	10.0872i	−5.87768	+	0.662256i
$233$	8.16314	+	26.4643i	0.534785	+	1.73373i	0.669466	+	0.742843i	$0.266523\pi$
$233$	8.16314	+	26.4643i	0.534785	+	1.73373i	−0.134681	+	0.990889i	$0.543001\pi$
$234$	41.3085	−	15.4690i	2.70042	−	1.01124i
$235$	0.558040	−	7.44653i	0.0364025	−	0.485758i
$236$	−8.05546	+	3.51456i	−0.524366	+	0.228778i
$237$	−1.05085	+	2.18212i	−0.0682602	+	0.141744i
$238$	−8.57547	−	16.6294i	−0.555865	−	1.07792i
$239$	5.15430	−	14.7301i	0.333404	−	0.952814i	−0.648130	−	0.761529i	$-0.724449\pi$
$239$	5.15430	−	14.7301i	0.333404	−	0.952814i	0.981535	−	0.191285i	$-0.0612654\pi$
$240$	57.3022	+	49.3125i	3.69884	+	3.18311i
$241$	−1.10002	+	0.581376i	−0.0708584	+	0.0374497i	−0.502322	−	0.864680i	$-0.667521\pi$
$241$	−1.10002	+	0.581376i	−0.0708584	+	0.0374497i	0.431464	+	0.902130i	$0.357997\pi$
$242$	−20.8083	−	3.93715i	−1.33761	−	0.253090i
$243$	2.72331	−	18.0680i	0.174700	−	1.15906i
$244$	38.0086			2.43325
$245$	6.45257	+	12.8287i	0.412239	+	0.819594i
$246$		−	58.0582i		−	3.70166i
$247$	−11.3085	−	1.88639i	−0.719542	−	0.120028i
$248$	−49.9855	−	73.3153i	−3.17408	−	4.65552i
$249$	−5.98326	+	3.16225i	−0.379174	+	0.200399i
$250$	−31.9958	+	2.39776i	−2.02359	+	0.151647i
$251$	−11.3341	+	5.45822i	−0.715402	+	0.344520i	−0.755924	−	0.654659i	$-0.772812\pi$
$251$	−11.3341	+	5.45822i	−0.715402	+	0.344520i	0.0405220	+	0.999179i	$0.487098\pi$
$252$	−5.37859	+	63.2111i	−0.338819	+	3.98192i
$253$	0.980575	−	0.343118i	0.0616482	−	0.0215716i
$254$	23.3624	−	10.1929i	1.46589	−	0.639561i
$255$	−9.61564	−	11.1736i	−0.602155	−	0.699717i
$256$	8.10600	+	20.6538i	0.506625	+	1.29086i
$257$	−0.422044	+	0.130183i	−0.0263264	+	0.00812062i	−0.307890	−	0.951422i	$-0.599623\pi$
$257$	−0.422044	+	0.130183i	−0.0263264	+	0.00812062i	0.281564	+	0.959542i	$0.409147\pi$
$258$	8.61962	+	76.5012i	0.536634	+	4.76276i
$259$	2.57305	+	25.1100i	0.159881	+	1.56026i
$260$	30.9876	−	23.9262i	1.92177	−	1.48384i
$261$	−37.9201	−	25.8535i	−2.34720	−	1.60029i
$262$	1.30467	+	34.8681i	0.0806028	+	2.15416i
$263$	−14.8057	+	25.6443i	−0.912961	+	1.58130i	−0.103102	+	0.994671i	$0.532877\pi$
$263$	−14.8057	+	25.6443i	−0.912961	+	1.58130i	−0.809859	+	0.586625i	$0.800456\pi$
$264$	−21.6830	−	37.5561i	−1.33450	−	2.31142i
$265$	−14.3440	+	9.01295i	−0.881146	+	0.553661i
$266$	12.9869	−	18.6415i	0.796275	−	1.14298i
$267$	−4.95260	+	7.88202i	−0.303094	+	0.482372i
$268$	−19.1541	−	0.716695i	−1.17002	−	0.0437791i
$269$	2.28196	+	15.1398i	0.139133	+	0.923090i	0.944074	+	0.329734i	$0.106959\pi$
$269$	2.28196	+	15.1398i	0.139133	+	0.923090i	−0.804940	+	0.593356i	$0.797803\pi$
$270$	3.46700	+	23.0020i	0.210995	+	1.39986i
$271$	0.747079	−	19.9661i	0.0453818	−	1.21285i	−0.771568	−	0.636146i	$-0.780527\pi$
$271$	0.747079	−	19.9661i	0.0453818	−	1.21285i	0.816950	−	0.576708i	$-0.195663\pi$
$272$	−7.82546	−	34.2856i	−0.474488	−	2.07887i
$273$	25.1022	+	7.42455i	1.51925	+	0.449354i
$274$	−8.15371	+	35.7237i	−0.492583	+	2.15815i
$275$	1.35885	+	0.364102i	0.0819416	+	0.0219562i
$276$	−7.35331	−	4.24544i	−0.442618	−	0.255545i
$277$	−16.3914	+	17.6657i	−0.984861	+	1.06143i	0.0132452	+	0.999912i	$0.495784\pi$
$277$	−16.3914	+	17.6657i	−0.984861	+	1.06143i	−0.998106	+	0.0615153i	$0.980407\pi$
$278$	7.84688	+	41.4717i	0.470624	+	2.48731i
$279$	5.06109	−	44.9184i	0.302999	−	2.68919i
$280$	10.2652	+	47.1621i	0.613461	+	2.81847i
$281$	16.9818	−	1.91339i	1.01305	−	0.114143i	0.410198	−	0.911996i	$-0.365460\pi$
$281$	16.9818	−	1.91339i	1.01305	−	0.114143i	0.602852	+	0.797853i	$0.294031\pi$
$282$	25.7768	−	7.95110i	1.53499	−	0.473481i
$283$	−4.82250	−	12.2875i	−0.286668	−	0.730418i	−0.999575	−	0.0291593i	$-0.990717\pi$
$283$	−4.82250	−	12.2875i	−0.286668	−	0.730418i	0.712907	−	0.701259i	$-0.247378\pi$
$284$	17.6640	−	15.2011i	1.04817	−	0.902022i
$285$	6.53959	−	16.6626i	0.387372	−	0.987008i
$286$	−16.4201	+	5.45803i	−0.970942	+	0.322740i
$287$	12.4763	−	16.5528i	0.736454	−	0.977081i
$288$	−27.6520	+	79.0250i	−1.62941	+	4.65659i
$289$	−0.757956	−	10.1142i	−0.0445857	−	0.594954i
$290$	−53.6321	−	16.5433i	−3.14938	−	0.971456i
$291$	6.98061	−	36.8934i	0.409211	−	2.16273i
$292$	2.17003	+	2.94029i	0.126991	+	0.172067i
$293$	−21.9466	+	21.9466i	−1.28213	+	1.28213i	−0.342682	+	0.939452i	$0.611335\pi$
$293$	−21.9466	+	21.9466i	−1.28213	+	1.28213i	−0.939452	+	0.342682i	$0.888665\pi$
$294$	−34.6230	+	38.6287i	−2.01926	+	2.25287i
$295$	−3.40634			−0.198324
$296$	−12.6448	+	83.8929i	−0.734965	+	4.87618i
$297$	1.38724	−	7.33174i	0.0804959	−	0.425431i
$298$	−4.49636	+	14.5768i	−0.260467	+	0.844414i
$299$	−1.39977	+	1.57587i	−0.0809509	+	0.0911347i
$300$	−4.98873	−	10.3592i	−0.288025	−	0.598090i
$301$	−13.9821	+	23.6633i	−0.805914	+	1.36393i
$302$	20.8927	+	10.0614i	1.20224	+	0.578967i
$303$	6.17728	+	2.42440i	0.354876	+	0.139278i
$304$	32.3672	−	27.8542i	1.85638	−	1.59755i
$305$	13.5022	+	5.89093i	0.773131	+	0.337314i
$306$	14.9696	−	28.3239i	0.855757	−	1.61917i
$307$	2.75860	+	24.4832i	0.157441	+	1.39733i	0.785354	+	0.619047i	$0.212481\pi$
$307$	2.75860	+	24.4832i	0.157441	+	1.39733i	−0.627912	+	0.778284i	$0.716090\pi$
$308$	3.03562	−	24.7003i	0.172970	−	1.40743i
$309$	−7.54147	+	6.01413i	−0.429020	+	0.342132i
$310$	−10.2770	−	54.3153i	−0.583695	−	3.08490i
$311$	12.2403	+	11.3573i	0.694083	+	0.644015i	0.946163	−	0.323692i	$-0.104924\pi$
$311$	12.2403	+	11.3573i	0.694083	+	0.644015i	−0.252080	+	0.967707i	$0.581114\pi$
$312$	75.4981	+	45.1828i	4.27424	+	2.55797i
$313$	22.4311	−	12.9506i	1.26788	−	0.732011i	0.293293	−	0.956023i	$-0.405249\pi$
$313$	22.4311	−	12.9506i	1.26788	−	0.732011i	0.974586	+	0.224012i	$0.0719155\pi$
$314$	−3.97777	+	2.49940i	−0.224478	+	0.141049i
$315$	−11.7077	+	21.6214i	−0.659656	+	1.21823i
$316$	−4.55446	+	1.03953i	−0.256209	+	0.0584780i
$317$	−0.0310927	+	0.830970i	−0.00174634	+	0.0466719i	−0.999901	−	0.0140450i	$-0.995529\pi$
$317$	−0.0310927	+	0.830970i	−0.00174634	+	0.0466719i	0.998155	+	0.0607170i	$0.0193387\pi$
$318$	−49.2384	−	36.3396i	−2.76115	−	2.03782i
$319$	14.4857	+	10.6910i	0.811045	+	0.598579i
$320$	−1.76813	+	47.2542i	−0.0988413	+	2.64159i
$321$	22.3705	−	5.10593i	1.24860	−	0.284985i
$322$	−1.63161	−	3.84503i	−0.0909262	−	0.214275i
$323$	−7.05042	+	4.43007i	−0.392296	+	0.246496i
$324$	9.48029	−	5.47345i	0.526683	−	0.304081i
$325$	−2.76822	+	0.695383i	−0.153553	+	0.0385729i
$326$	−11.1133	−	10.3116i	−0.615509	−	0.571108i
$327$	−1.69674	−	8.96748i	−0.0938299	−	0.495903i
$328$	54.4705	−	43.4388i	3.00763	−	2.39850i
$329$	9.05779	+	3.27236i	0.499372	+	0.180411i
$330$	−3.02483	−	26.8461i	−0.166512	−	1.47783i
$331$	−7.64710	+	14.4690i	−0.420323	+	0.795290i	−0.999806	−	0.0196946i	$-0.993731\pi$
$331$	−7.64710	+	14.4690i	−0.420323	+	0.795290i	0.579483	+	0.814984i	$0.303254\pi$
$332$	−11.9643	−	5.21997i	−0.656626	−	0.286483i
$333$	−32.7590	+	28.1914i	−1.79518	+	1.54488i
$334$	32.3902	+	12.7122i	1.77231	+	0.695582i
$335$	−6.69321	−	3.22328i	−0.365689	−	0.176107i
$336$	−81.1090	+	54.1091i	−4.42486	+	2.95189i
$337$	12.6672	+	26.3036i	0.690024	+	1.43285i	0.891345	+	0.453325i	$0.149762\pi$
$337$	12.6672	+	26.3036i	0.690024	+	1.43285i	−0.201321	+	0.979525i	$0.564524\pi$
$338$	23.7235	−	25.8786i	1.29039	−	1.40761i
$339$	−10.5820	+	34.3060i	−0.574736	+	1.86325i
$340$	5.28619	−	27.9382i	0.286684	−	1.51516i
$341$	−2.64284	+	17.5341i	−0.143118	+	0.949524i
$342$	38.9007			2.10351
$343$	−18.1723	+	3.57305i	−0.981213	+	0.192927i
$344$	−65.3246	+	65.3246i	−3.52207	+	3.52207i
$345$	−1.95419	−	2.64783i	−0.105210	−	0.142555i
$346$	0.217193	−	1.14789i	0.0116763	−	0.0617110i
$347$	19.2941	+	5.95145i	1.03576	+	0.319491i	0.765595	−	0.643322i	$-0.222444\pi$
$347$	19.2941	+	5.95145i	1.03576	+	0.319491i	0.270168	+	0.962813i	$0.412921\pi$
$348$	−10.9963	−	146.736i	−0.589464	−	7.86586i
$349$	8.27299	−	23.6428i	0.442843	−	1.26557i	−0.478934	−	0.877851i	$-0.658977\pi$
$349$	8.27299	−	23.6428i	0.442843	−	1.26557i	0.921777	−	0.387721i	$-0.126738\pi$
$350$	1.10753	−	5.54662i	0.0592000	−	0.296479i
$351$	4.77540	+	14.3665i	0.254892	+	0.766825i
$352$	11.9989	−	30.5728i	0.639545	−	1.62953i
$353$	15.8230	−	13.6168i	0.842172	−	0.724748i	−0.121283	−	0.992618i	$-0.538701\pi$
$353$	15.8230	−	13.6168i	0.842172	−	0.724748i	0.963455	+	0.267870i	$0.0863198\pi$
$354$	−4.49554	−	11.4545i	−0.238935	−	0.608797i
$355$	8.63098	−	2.66230i	0.458085	−	0.141300i
$356$	−17.8424	+	2.01035i	−0.945645	+	0.106549i
$357$	17.2117	−	8.07589i	0.910938	−	0.427421i
$358$	−0.161244	+	1.43108i	−0.00852203	+	0.0756351i
$359$	−0.474543	−	2.50802i	−0.0250454	−	0.132368i	0.967812	−	0.251673i	$-0.0809809\pi$
$359$	−0.474543	−	2.50802i	−0.0250454	−	0.132368i	−0.992858	+	0.119305i	$0.961933\pi$
$360$	−56.2117	+	60.5818i	−2.96262	+	3.19294i
$361$	7.69827	+	4.44460i	0.405172	+	0.233926i
$362$	30.5755	+	8.19269i	1.60701	+	0.430598i
$363$	4.78846	−	20.9796i	0.251329	−	1.10115i
$364$	18.9918	+	46.7837i	0.995439	+	2.45213i
$365$	0.315167	+	1.38084i	0.0164966	+	0.0722763i
$366$	−1.98979	+	53.1782i	−0.104008	+	2.77967i
$367$	3.99739	+	26.5210i	0.208662	+	1.38438i	0.810488	+	0.585755i	$0.199202\pi$
$367$	3.99739	+	26.5210i	0.208662	+	1.38438i	−0.601826	+	0.798627i	$0.705560\pi$
$368$	−1.17009	−	7.76307i	−0.0609954	−	0.404678i
$369$	35.4665	+	1.32706i	1.84631	+	0.0690842i
$370$	−28.1198	+	44.7524i	−1.46188	+	2.32657i
$371$	−6.22906	−	20.9417i	−0.323397	−	1.08724i
$372$	122.714	−	77.1061i	6.36241	−	3.99777i
$373$	11.9499	+	20.6978i	0.618742	+	1.07169i	0.989716	+	0.143049i	$0.0456906\pi$
$373$	11.9499	+	20.6978i	0.618742	+	1.07169i	−0.370974	+	0.928643i	$0.620976\pi$
$374$	−6.28365	+	10.8836i	−0.324920	+	0.562778i
$375$	−1.21907	−	32.5803i	−0.0629525	−	1.68244i
$376$	26.7458	+	18.2350i	1.37931	+	0.940397i
$377$	−36.2295	−	4.65880i	−1.86591	−	0.239940i
$378$	−29.7770	−	3.65953i	−1.53156	−	0.188226i
$379$	−2.30815	−	20.4854i	−0.118562	−	1.05227i	−0.902280	−	0.431150i	$-0.858108\pi$
$379$	−2.30815	−	20.4854i	−0.118562	−	1.05227i	0.783719	−	0.621116i	$-0.213320\pi$
$380$	32.9923	−	10.1768i	1.69247	−	0.522057i
$381$	9.46247	+	24.1100i	0.484777	+	1.23519i
$382$	7.64394	+	8.88242i	0.391098	+	0.454464i
$383$	4.09142	−	1.78507i	0.209062	−	0.0912128i	−0.292752	−	0.956188i	$-0.594571\pi$
$383$	4.09142	−	1.78507i	0.209062	−	0.0912128i	0.501814	+	0.864976i	$0.332666\pi$
$384$	−65.4968	+	22.9183i	−3.34237	+	1.16955i
$385$	4.90665	−	8.30403i	0.250066	−	0.423212i
$386$	−17.8664	+	8.60401i	−0.909376	+	0.437932i
$387$	−46.9300	+	3.51692i	−2.38559	+	0.178775i
$388$	64.0313	−	33.8415i	3.25070	−	1.71804i
$389$	−12.5628	−	18.4263i	−0.636960	−	0.934249i	−0.999997	−	0.00247452i	$-0.999212\pi$
$389$	−12.5628	−	18.4263i	−0.636960	−	0.934249i	0.363036	−	0.931775i	$-0.381740\pi$
$390$	31.8531	+	44.6076i	1.61294	+	2.25879i
$391$			1.53085i			0.0774184i
$392$	−62.1464	−	3.58173i	−3.13886	−	0.180905i
$393$	−35.4553			−1.78848
$394$	3.68107	−	24.4223i	0.185450	−	1.23038i
$395$	−1.77904	−	0.336613i	−0.0895133	−	0.0169368i
$396$	37.6730	−	19.9107i	1.89314	−	1.00055i
$397$	−2.51784	−	2.16678i	−0.126367	−	0.108747i	0.586834	−	0.809707i	$-0.300374\pi$
$397$	−2.51784	−	2.16678i	−0.126367	−	0.108747i	−0.713201	+	0.700960i	$0.752755\pi$
$398$	−1.11790	+	3.19477i	−0.0560352	+	0.160139i
$399$	18.4355	+	13.8954i	0.922931	+	0.695640i
$400$	4.61264	−	9.57824i	0.230632	−	0.478912i
$401$	8.96443	−	3.91114i	0.447662	−	0.195313i	−0.163953	−	0.986468i	$-0.552425\pi$
$401$	8.96443	−	3.91114i	0.447662	−	0.195313i	0.611616	+	0.791155i	$0.290520\pi$
$402$	2.00547	−	26.7611i	0.100024	−	1.33472i
$403$	−12.6168	−	33.6920i	−0.628486	−	1.67832i
$404$	3.77281	+	12.2311i	0.187704	+	0.608522i
$405$	4.21610	−	0.475040i	0.209500	−	0.0236049i
$406$	39.1276	−	60.8992i	1.94187	−	3.02238i
$407$	13.2553	−	10.5707i	0.657039	−	0.523971i
$408$	62.7887	−	11.8803i	3.10850	−	0.588161i
$409$	−0.272680	−	7.28752i	−0.0134831	−	0.360344i	−0.989666	−	0.143394i	$-0.954198\pi$
$409$	−0.272680	−	7.28752i	−0.0134831	−	0.360344i	0.976183	−	0.216951i	$-0.0696111\pi$
$410$	41.9241	−	11.2335i	2.07048	−	0.554784i
$411$	−35.9648	−	9.63675i	−1.77401	−	0.475346i
$412$	−18.1390	−	4.14010i	−0.893642	−	0.203968i
$413$	1.17978	−	4.23180i	0.0580530	−	0.208233i
$414$	3.80500	−	6.05562i	0.187005	−	0.297618i
$415$	−3.44115	−	3.70868i	−0.168919	−	0.182052i
$416$	8.89649	+	66.0389i	0.436187	+	3.23782i
$417$	−42.4094	+	6.39219i	−2.07680	+	0.313027i
$418$	−15.2493	−	0.570590i	−0.745869	−	0.0279085i
$419$	16.3520	−	3.73224i	0.798849	−	0.182332i	0.196436	−	0.980517i	$-0.437063\pi$
$419$	16.3520	−	3.73224i	0.798849	−	0.182332i	0.602413	+	0.798185i	$0.294206\pi$
$420$	−77.6023	+	13.8740i	−3.78660	+	0.676982i
$421$	4.46649	+	7.10838i	0.217683	+	0.346441i	0.937658	−	0.347559i	$-0.112989\pi$
$421$	4.46649	+	7.10838i	0.217683	+	0.346441i	−0.719975	+	0.694000i	$0.755847\pi$
$422$	48.1613	+	12.9048i	2.34446	+	0.628196i
$423$	4.26797	+	15.9283i	0.207516	+	0.774459i
$424$	−2.74586	−	73.3847i	−0.133351	−	3.56388i
$425$	−1.16776	+	1.71278i	−0.0566445	+	0.0830823i
$426$	20.3433	+	25.5097i	0.985637	+	1.23595i
$427$	−11.9949	+	14.7339i	−0.580476	+	0.713022i
$428$	34.6030	+	27.5950i	1.67260	+	1.33385i
$429$	−4.91833	−	16.8807i	−0.237459	−	0.815008i
$430$	−53.5740	+	21.0263i	−2.58357	+	1.01398i
$431$	−15.7252	−	18.2730i	−0.757457	−	0.880181i	0.238395	−	0.971168i	$-0.423379\pi$
$431$	−15.7252	−	18.2730i	−0.757457	−	0.880181i	−0.995852	+	0.0909873i	$0.970998\pi$
$432$	−52.4910	−	20.6012i	−2.52548	−	0.991176i
$433$	5.68432	+	2.73743i	0.273171	+	0.131552i	0.565455	−	0.824779i	$-0.308701\pi$
$433$	5.68432	+	2.73743i	0.273171	+	0.131552i	−0.292283	+	0.956332i	$0.594415\pi$
$434$	71.0371	+	6.04451i	3.40989	+	0.290146i
$435$	18.8361	−	53.8306i	0.903124	−	2.58098i
$436$	11.4827	−	13.3431i	0.549921	−	0.639020i
$437$	−1.64344	+	0.868584i	−0.0786165	+	0.0415500i
$438$	−4.22738	+	2.88218i	−0.201992	+	0.137716i
$439$	−9.72055	−	1.46514i	−0.463936	−	0.0699272i	−0.0870850	−	0.996201i	$-0.527755\pi$
$439$	−9.72055	−	1.46514i	−0.463936	−	0.0699272i	−0.376851	+	0.926274i	$0.622993\pi$
$440$	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	−0.138706	−	0.990334i	$-0.544294\pi$
$443$	−11.8530	−	1.78656i	−0.563155	−	0.0848820i	−0.424449	+	0.905452i	$0.639532\pi$
$444$	−136.153	−	25.7615i	−6.46154	−	1.22259i
$445$	−6.64990	−	2.05122i	−0.315236	−	0.0972373i
$446$	5.53625	+	73.8761i	0.262149	+	3.49813i
$447$	−14.6308	−	5.11954i	−0.692013	−	0.242146i
$448$	−58.0930	−	18.5630i	−2.74464	−	0.877018i
$449$	−0.279993	−	0.800174i	−0.0132137	−	0.0377625i	0.937088	−	0.349094i	$-0.113511\pi$
$449$	−0.279993	−	0.800174i	−0.0132137	−	0.0377625i	−0.950301	+	0.311332i	$0.899225\pi$
$450$	8.87653	−	3.87279i	0.418444	−	0.182565i
$451$	−13.8837	−	1.04044i	−0.653756	−	0.0489923i
$452$	−64.4605	+	25.2989i	−3.03197	+	1.18996i
$453$	−11.0103	+	20.8326i	−0.517311	+	0.978800i
$454$	−23.9459	+	30.0272i	−1.12384	+	1.40924i
$455$	−0.504347	+	19.5629i	−0.0236441	+	0.917124i
$456$	48.3795	+	60.6660i	2.26558	+	2.84095i
$457$	5.97740	−	1.13099i	0.279611	−	0.0529053i	−0.0442145	−	0.999022i	$-0.514078\pi$
$457$	5.97740	−	1.13099i	0.279611	−	0.0529053i	0.323826	+	0.946117i	$0.395031\pi$
$458$	51.1959	−	55.1760i	2.39223	−	2.57821i
$459$	9.52239	+	5.49776i	0.444467	+	0.256613i
$460$	1.64287	−	6.13129i	0.0765994	−	0.285873i
$461$	−12.6885	+	7.97274i	−0.590965	+	0.371328i	−0.794067	−	0.607830i	$-0.792040\pi$
$461$	−12.6885	+	7.97274i	−0.590965	+	0.371328i	0.203103	+	0.979157i	$0.434897\pi$
$462$	34.3995	+	5.54024i	1.60041	+	0.257755i
$463$	−11.0969	+	17.6606i	−0.515716	+	0.820757i	−0.998487	−	0.0549897i	$-0.982487\pi$
$463$	−11.0969	+	17.6606i	−0.515716	+	0.820757i	0.482771	+	0.875746i	$0.339630\pi$
$464$	99.7345	−	92.5401i	4.63006	−	4.29606i
$465$	55.5434	−	8.37182i	2.57576	−	0.388234i
$466$	−60.1765	−	44.4123i	−2.78762	−	2.05736i
$467$	−23.2343	+	21.5583i	−1.07515	+	0.997597i	−0.0751540	+	0.997172i	$0.523945\pi$
$467$	−23.2343	+	21.5583i	−1.07515	+	0.997597i	−1.00000		0.000425134i	$0.999865\pi$
$468$	−47.1388	+	72.4716i	−2.17899	+	3.35000i
$469$	6.32256	−	7.19882i	0.291949	−	0.332411i
$470$	10.7290	+	17.0751i	0.494892	+	0.787616i
$471$	−2.38681	−	4.13407i	−0.109978	−	0.190488i
$472$	7.38308	−	12.7879i	0.339834	−	0.588610i
$473$	18.4485	−	0.690293i	0.848262	−	0.0317397i
$474$	−1.21598	−	6.42661i	−0.0558518	−	0.295184i
$475$	−2.50133	−	0.281832i	−0.114769	−	0.0129313i
$476$	32.8776	+	16.2435i	1.50694	+	0.744521i
$477$	23.3246	−	29.2481i	1.06796	−	1.33918i
$478$	12.4223	+	40.2721i	0.568183	+	1.84200i
$479$	−9.90070	−	4.31963i	−0.452374	−	0.197369i	0.161337	−	0.986899i	$-0.448419\pi$
$479$	−9.90070	−	4.31963i	−0.452374	−	0.197369i	−0.613711	+	0.789530i	$0.710324\pi$
$480$	−103.747	−	7.77479i	−4.73540	−	0.354869i
$481$	−13.0679	+	31.8194i	−0.595847	+	1.45084i
$482$	1.45786	−	3.02728i	0.0664037	−	0.137889i
$483$	3.96632	−	1.51068i	0.180474	−	0.0687385i
$484$	37.3966	−	18.0092i	1.69984	−	0.818602i
$485$	27.9915	−	2.09768i	1.27103	−	0.0952505i
$486$	23.0572	+	43.6263i	1.04589	+	1.97893i
$487$	−2.04794	+	10.8236i	−0.0928011	+	0.490466i	0.905071	+	0.425261i	$0.139818\pi$
$487$	−2.04794	+	10.8236i	−0.0928011	+	0.490466i	−0.997872	+	0.0652047i	$0.979230\pi$
$488$	−51.3807	+	37.9207i	−2.32590	+	1.71659i
$489$	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	$-0.0131104\pi$
$492$	67.5718	+	91.5565i	3.04637	+	4.12769i
$493$	−21.9198	+	14.9447i	−0.987220	+	0.673075i
$494$	27.5968	−	14.0359i	1.24164	−	0.631505i
$495$	16.4689	−	1.23417i	0.740221	−	0.0554719i
$496$	126.482	+	44.2579i	5.67920	+	1.98724i
$497$	0.318150	+	11.6446i	0.0142710	+	0.522333i
$498$	7.92965	−	16.4661i	0.355336	−	0.737863i
$499$	12.6645	+	29.0274i	0.566943	+	1.29945i	0.929959	+	0.367664i	$0.119842\pi$
$499$	12.6645	+	29.0274i	0.566943	+	1.29945i	−0.363016	+	0.931783i	$0.618253\pi$
$500$	47.6660	−	41.0199i	2.13169	−	1.83447i
$501$	−14.1389	+	32.4067i	−0.631679	+	1.44782i
$502$	15.8743	−	30.0357i	0.708507	−	1.34056i
$503$	−28.9898	−	23.1186i	−1.29259	−	1.03081i	−0.997150	−	0.0754475i	$-0.975961\pi$
$503$	−28.9898	−	23.1186i	−1.29259	−	1.03081i	−0.295443	−	0.955361i	$-0.595467\pi$
$504$	−55.7940	−	90.8160i	−2.48526	−	4.04527i
$505$	−0.555447	+	4.92973i	−0.0247171	+	0.219370i
$506$	−1.58041	+	2.31803i	−0.0702577	+	0.103049i
$507$	25.3763	+	25.0726i	1.12700	+	1.11351i
$508$	−24.9789	+	43.2646i	−1.10826	+	1.91956i
$509$	3.03273	−	11.3183i	0.134423	−	0.501675i	−0.865576	−	0.500777i	$-0.833048\pi$
$509$	3.03273	−	11.3183i	0.134423	−	0.501675i	1.00000		0.000897769i	$-0.000285769\pi$
$510$	38.8118	+	8.85854i	1.71862	+	0.392263i
$511$	−1.82462	−	0.0867072i	−0.0807163	−	0.00383570i
$512$	−7.91185	−	4.97135i	−0.349658	−	0.219705i
$513$	−0.499226	+	13.3421i	−0.0220414	+	0.589068i
$514$	0.708273	−	0.959676i	0.0312406	−	0.0423295i
$515$	−5.80200	−	4.28207i	−0.255667	−	0.188691i
$516$	−102.630	−	110.609i	−4.51803	−	4.86927i
$517$	−1.43944	−	6.30659i	−0.0633065	−	0.277364i
$518$	−45.8582	−	50.4341i	−2.01489	−	2.21595i
$519$	1.15734	+	0.264155i	0.0508016	+	0.0115951i
$520$	−18.0188	+	63.2597i	−0.790176	+	2.77412i
$521$	30.6630	+	17.7033i	1.34337	+	0.775595i	0.987300	−	0.158865i	$-0.0507834\pi$
$521$	30.6630	+	17.7033i	1.34337	+	0.775595i	0.356069	+	0.934460i	$0.384117\pi$
$522$	123.855	−	4.63431i	5.42097	−	0.202838i
$523$	16.0253	−	23.5049i	0.700739	−	1.02780i	−0.296607	−	0.955000i	$-0.595855\pi$
$523$	16.0253	−	23.5049i	0.700739	−	1.02780i	0.997347	−	0.0727965i	$-0.0231923\pi$
$524$	−42.6390	−	53.4677i	−1.86269	−	2.33575i
$525$	5.59007	+	1.33535i	0.243971	+	0.0582794i
$526$	−8.95349	−	79.4644i	−0.390391	−	3.46481i
$527$	−23.1015	−	12.2095i	−1.00632	−	0.531854i
$528$	60.0251	+	26.1887i	2.61226	+	1.13972i
$529$	1.69325	−	22.5949i	0.0736197	−	0.982387i
$530$	16.7140	−	42.5865i	0.726008	−	1.84984i
$531$	7.10004	−	2.48441i	0.308115	−	0.107814i
$532$	1.21614	+	44.5121i	0.0527264	+	1.92984i
$533$	25.6394	−	11.8554i	1.11057	−	0.513514i
$534$	−1.87864	−	25.0687i	−0.0812966	−	1.08483i
$535$	8.01542	+	15.1659i	0.346537	+	0.655679i
$536$	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
$539$	8.61696	+	8.97178i	0.371159	+	0.386442i
$540$	−32.2386	−	32.2386i	−1.38733	−	1.38733i
$541$	11.1266	+	15.0760i	0.478370	+	0.648168i	0.975627	−	0.219435i	$-0.0704214\pi$
$541$	11.1266	+	15.0760i	0.478370	+	0.648168i	−0.497257	+	0.867603i	$0.665660\pi$
$542$	30.3951	+	44.5815i	1.30558	+	1.91494i
$543$	−9.48073	+	30.7358i	−0.406857	+	1.31900i
$544$	36.6832	+	31.5684i	1.57278	+	1.35349i
$545$	6.14715	−	2.96031i	0.263315	−	0.126806i
$546$	−66.4497	+	24.1224i	−2.84378	+	1.03234i
$547$	4.60885	+	2.21951i	0.197060	+	0.0948992i	0.529811	−	0.848115i	$-0.322263\pi$
$547$	4.60885	+	2.21951i	0.197060	+	0.0948992i	−0.332751	+	0.943015i	$0.607977\pi$
$548$	−28.7193	−	65.8253i	−1.22683	−	2.81192i
$549$	−32.4399	−	2.43104i	−1.38450	−	0.103754i
$550$	−3.53647	+	1.38796i	−0.150795	+	0.0591829i
$551$	−28.4809	−	15.0526i	−1.21333	−	0.641262i
$552$	14.1760	−	1.59725i	0.603369	−	0.0679834i
$553$	1.03435	−	2.09358i	0.0439851	−	0.0890279i
$554$	7.28664	−	64.6708i	0.309580	−	2.74760i
$555$	−44.3742	−	30.2538i	−1.88358	−	1.28420i
$556$	−60.6417	−	56.2673i	−2.57178	−	2.38627i
$557$	9.74913	−	2.61227i	0.413084	−	0.110686i	−0.0462909	−	0.998928i	$-0.514740\pi$
$557$	9.74913	−	2.61227i	0.413084	−	0.110686i	0.459375	+	0.888242i	$0.348073\pi$
$558$	61.0359	+	105.717i	2.58386	+	4.47537i
$559$	−32.0240	+	19.4280i	−1.35447	+	0.821715i
$560$	−54.7659	−	48.0997i	−2.31428	−	2.03258i
$561$	−10.8127	−	6.79407i	−0.456512	−	0.286846i
$562$	−33.8306	+	31.3902i	−1.42706	+	1.32412i
$563$	19.3841	−	2.92168i	0.816942	−	0.123134i	0.272739	−	0.962088i	$-0.412070\pi$
$563$	19.3841	−	2.92168i	0.816942	−	0.123134i	0.544203	+	0.838954i	$0.316832\pi$
$564$	−31.3955	+	42.5394i	−1.32199	+	1.79123i
$565$	−26.8200	−	1.00353i	−1.12833	−	0.0422189i
$566$	30.1834	+	18.9655i	1.26870	+	0.797178i
$567$	−0.870078	+	5.40233i	−0.0365398	+	0.226877i
$568$	−8.71259	+	38.1724i	−0.365572	+	1.60168i
$569$	−24.1531	+	13.9448i	−1.01255	+	0.584597i	−0.911938	−	0.410329i	$-0.865414\pi$
$569$	−24.1531	+	13.9448i	−1.01255	+	0.584597i	−0.100614	+	0.994926i	$0.532081\pi$
$570$	12.5112	+	46.6926i	0.524038	+	1.95574i
$571$	4.54638	−	4.89983i	0.190260	−	0.205051i	−0.630717	−	0.776013i	$-0.717239\pi$
$571$	4.54638	−	4.89983i	0.190260	−	0.205051i	0.820977	+	0.570962i	$0.193430\pi$
$572$	19.5418	−	27.7179i	0.817082	−	1.15895i
$573$	−9.30983	+	7.42434i	−0.388924	+	0.310156i
$574$	−0.564527	+	55.9743i	−0.0235629	+	2.33632i
$575$	−0.288535	+	0.361812i	−0.0120328	+	0.0150886i
$576$	−30.7794	−	99.7844i	−1.28248	−	4.15769i
$577$	13.1455	−	30.1298i	0.547254	−	1.25432i	−0.394771	−	0.918780i	$-0.629176\pi$
$577$	13.1455	−	30.1298i	0.547254	−	1.25432i	0.942026	−	0.335541i	$-0.108919\pi$
$578$	17.8665	+	20.7612i	0.743148	+	0.863554i
$579$	−8.05787	−	18.4688i	−0.334873	−	0.767538i
$580$	103.831	−	36.3319i	4.31133	−	1.50860i
$581$	5.79925	−	2.99056i	0.240593	−	0.124070i
$582$	43.9959	+	91.3584i	1.82369	+	3.78693i
$583$	−9.57239	+	11.1233i	−0.396448	+	0.460681i
$584$	−5.86697	−	1.80972i	−0.242777	−	0.0748868i
$585$	−27.9779	+	18.4387i	−1.15674	+	0.762348i
$586$	12.4923	−	82.8812i	0.516053	−	3.42379i
$587$	3.55145	+	3.55145i	0.146584	+	0.146584i	0.776590	−	0.630006i	$-0.216948\pi$
$587$	3.55145	+	3.55145i	0.146584	+	0.146584i	−0.630006	+	0.776590i	$0.716948\pi$
$588$	9.64121	−	101.213i	0.397597	−	4.17396i
$589$		−	31.7281i		−	1.30733i
$590$	7.40147	−	5.46253i	0.304714	−	0.224889i
$591$	24.6590	+	4.66574i	1.01434	+	0.191923i
$592$	−59.8675	−	113.275i	−2.46054	−	4.65557i
$593$	13.0924	+	11.2669i	0.537641	+	0.462678i	0.878707	−	0.477362i	$-0.158407\pi$
$593$	13.0924	+	11.2669i	0.537641	+	0.462678i	−0.341066	+	0.940039i	$0.610788\pi$
$594$	8.74320	+	18.1554i	0.358738	+	0.744927i
$595$	9.16186	+	10.8660i	0.375600	+	0.445464i
$596$	−9.87477	−	28.2205i	−0.404486	−	1.15596i
$597$	−3.20157	−	1.25652i	−0.131031	−	0.0514260i
$598$	0.514378	−	5.66886i	0.0210345	−	0.231817i
$599$	12.0439	+	30.6873i	0.492100	+	1.25385i	0.934157	+	0.356863i	$0.116154\pi$
$599$	12.0439	+	30.6873i	0.492100	+	1.25385i	−0.442057	+	0.896987i	$0.645751\pi$
$600$	17.0791	+	9.02658i	0.697252	+	0.368508i
$601$	7.59102	+	6.05364i	0.309644	+	0.246933i	0.765965	−	0.642882i	$-0.222262\pi$
$601$	7.59102	+	6.05364i	0.309644	+	0.246933i	−0.456321	+	0.889815i	$0.650833\pi$
$602$	−7.56638	−	73.8392i	−0.308383	−	3.00946i
$603$	16.3020	+	1.83679i	0.663868	+	0.0747999i
$604$	−44.6573	+	8.44962i	−1.81708	+	0.343810i
$605$	16.0760	−	0.601521i	0.653581	−	0.0244553i
$606$	−17.3102	+	4.63826i	−0.703179	+	0.188416i
$607$	−6.61851	+	3.82120i	−0.268637	+	0.155098i	−0.628268	−	0.777997i	$-0.716236\pi$
$607$	−6.61851	+	3.82120i	−0.268637	+	0.155098i	0.359631	+	0.933095i	$0.382903\pi$
$608$	−13.0767	+	57.2927i	−0.530330	+	2.32353i
$609$	60.3517	+	42.0449i	2.44557	+	1.70374i
$610$	−38.7851	+	8.85246i	−1.57036	+	0.358425i
$611$	8.77491	+	9.75984i	0.354995	+	0.394841i
$612$	9.35837	+	62.0887i	0.378290	+	2.50979i
$613$	17.8492	−	24.1849i	0.720924	−	0.976818i	−0.278939	−	0.960309i	$-0.589983\pi$
$613$	17.8492	−	24.1849i	0.720924	−	0.976818i	0.999864	−	0.0165091i	$-0.00525523\pi$
$614$	−45.2563	−	48.7747i	−1.82640	−	1.96839i
$615$	9.81387	+	42.9974i	0.395734	+	1.73382i
$616$	20.5396	+	36.4189i	0.827562	+	1.46736i
$617$	−16.0690	−	25.5737i	−0.646914	−	1.02956i	−0.995725	−	0.0923645i	$-0.970557\pi$
$617$	−16.0690	−	25.5737i	−0.646914	−	1.02956i	0.348811	−	0.937193i	$-0.386585\pi$
$618$	6.74204	−	25.1616i	0.271205	−	1.01215i
$619$	2.31041	+	8.62258i	0.0928633	+	0.346571i	0.996687	−	0.0813348i	$-0.0259183\pi$
$619$	2.31041	+	8.62258i	0.0928633	+	0.346571i	−0.903824	+	0.427905i	$0.859252\pi$
$620$	79.4221	+	73.6930i	3.18967	+	2.95958i
$621$	2.02812	+	1.38275i	0.0813856	+	0.0554878i
$622$	−44.8094	−	5.04881i	−1.79669	−	0.202439i
$623$	4.85148	−	7.55096i	0.194370	−	0.302523i
$624$	−132.253	+	12.8035i	−5.29437	+	0.512551i
$625$	19.5082	−	6.01750i	0.780330	−	0.240700i
$626$	−27.9714	+	64.1111i	−1.11796	+	2.56240i
$627$	1.15878	−	15.4628i	0.0462771	−	0.617525i
$628$	3.36390	−	8.57107i	0.134234	−	0.342023i
$629$	8.25138	+	23.5811i	0.329004	+	0.940240i
$630$	−9.23380	−	65.7552i	−0.367883	−	2.61975i
$631$	−3.67347	−	1.28540i	−0.146239	−	0.0511711i	0.256167	−	0.966632i	$-0.417540\pi$
$631$	−3.67347	−	1.28540i	−0.146239	−	0.0511711i	−0.402406	+	0.915461i	$0.631826\pi$
$632$	5.11969	−	5.94918i	0.203650	−	0.236646i
$633$	−14.9337	+	48.4137i	−0.593560	+	1.92427i
$634$	−1.26502	−	1.85544i	−0.0502402	−	0.0736889i
$635$	−15.5790	+	11.4978i	−0.618235	+	0.456278i
$636$	119.942			4.75601
$637$	−24.1290	−	7.40214i	−0.956026	−	0.293283i
$638$	−48.6198			−1.92488
$639$	−16.0483	+	11.8442i	−0.634862	+	0.468550i
$640$	−29.2222	−	42.8611i	−1.15511	−	1.69423i
$641$	8.35667	−	27.0917i	0.330069	−	1.07006i	−0.626713	−	0.779250i	$-0.715600\pi$
$641$	8.35667	−	27.0917i	0.330069	−	1.07006i	0.956782	−	0.290806i	$-0.0939236\pi$
$642$	−40.4198	+	46.9687i	−1.59524	+	1.85371i
$643$	27.1475	+	9.49932i	1.07059	+	0.374617i	0.807326	−	0.590106i	$-0.200914\pi$
$643$	27.1475	+	9.49932i	1.07059	+	0.374617i	0.263267	+	0.964723i	$0.415200\pi$
$644$	7.04810	+	4.16456i	0.277734	+	0.164106i
$645$	−19.3150	−	55.1991i	−0.760527	−	2.17346i
$646$	8.21530	−	20.9322i	0.323227	−	0.823568i
$647$	−0.0926362	+	1.23614i	−0.00364190	+	0.0485978i	−0.998729	−	0.0504090i	$-0.983948\pi$
$647$	−0.0926362	+	1.23614i	−0.00364190	+	0.0485978i	0.995087	+	0.0990068i	$0.0315666\pi$
$648$	−7.35484	+	16.8575i	−0.288925	+	0.662224i
$649$	−2.81971	+	0.869764i	−0.110683	+	0.0341412i
$650$	4.89980	−	5.95020i	0.192186	−	0.233386i
$651$	−8.83673	+	71.9029i	−0.346339	+	2.81810i
$652$	29.5267	+	3.32686i	1.15636	+	0.130290i
$653$	−5.53030	−	3.77050i	−0.216417	−	0.147551i	0.450259	−	0.892898i	$-0.351331\pi$
$653$	−5.53030	−	3.77050i	−0.216417	−	0.147551i	−0.666677	+	0.745347i	$0.732284\pi$
$654$	18.0674	+	16.7641i	0.706490	+	0.655527i
$655$	−6.86015	−	25.6024i	−0.268048	−	1.00037i
$656$	−27.2311	+	101.628i	−1.06320	+	3.96790i
$657$	−1.66404	−	2.64830i	−0.0649202	−	0.103320i
$658$	−24.9289	+	7.41507i	−0.971831	+	0.289070i
$659$	9.21020	+	40.3525i	0.358779	+	1.57191i	0.756241	+	0.654293i	$0.227034\pi$
$659$	9.21020	+	40.3525i	0.358779	+	1.57191i	−0.397462	+	0.917618i	$0.630109\pi$
$660$	36.0153	+	38.8152i	1.40189	+	1.51088i
$661$	11.9473	−	16.1881i	0.464697	−	0.629643i	−0.508101	−	0.861298i	$-0.669652\pi$
$661$	11.9473	−	16.1881i	0.464697	−	0.629643i	0.972798	+	0.231655i	$0.0744141\pi$
$662$	−6.58706	−	43.7023i	−0.256013	−	1.69854i
$663$	25.8727	+	1.37487i	1.00481	+	0.0533954i
$664$	21.3815	−	4.88018i	0.829762	−	0.189388i
$665$	−6.46688	+	16.0009i	−0.250775	+	0.620490i
$666$	25.9717	−	113.789i	1.00638	−	4.40925i
$667$	−5.12902	+	2.96124i	−0.198597	+	0.114660i
$668$	−65.8739	+	17.6509i	−2.54874	+	0.682932i
$669$	−75.2257	+	2.81475i	−2.90839	+	0.108824i
$670$	19.7123	−	3.72978i	0.761554	−	0.144094i
$671$	12.6810	+	1.42881i	0.489545	+	0.0551585i
$672$	45.5915	−	126.196i	1.75873	−	4.86812i
$673$	0.562031	+	0.448204i	0.0216647	+	0.0172770i	0.634262	−	0.773118i	$-0.281304\pi$
$673$	0.562031	+	0.448204i	0.0216647	+	0.0172770i	−0.612598	+	0.790395i	$0.709875\pi$
$674$	−69.7054	−	36.8404i	−2.68495	−	1.41904i
$675$	1.21437	+	3.09416i	0.0467411	+	0.119094i
$676$	−7.29234	+	68.4209i	−0.280474	+	2.63157i
$677$	−5.82194	−	2.28494i	−0.223755	−	0.0878175i	0.250815	−	0.968035i	$-0.419301\pi$
$677$	−5.82194	−	2.28494i	−0.223755	−	0.0878175i	−0.474571	+	0.880217i	$0.657397\pi$
$678$	−32.0213	−	91.5117i	−1.22977	−	3.51449i
$679$	−7.08879	+	35.5013i	−0.272043	+	1.36242i
$680$	20.7276	+	43.0413i	0.794867	+	1.65056i
$681$	−29.5804	−	25.4560i	−1.13352	−	0.975476i
$682$	−22.3758	−	42.3372i	−0.856816	−	1.62117i
$683$	5.20370	+	0.984594i	0.199114	+	0.0376744i	0.284512	−	0.958673i	$-0.408168\pi$
$683$	5.20370	+	0.984594i	0.199114	+	0.0376744i	−0.0853977	+	0.996347i	$0.527216\pi$
$684$	−61.3455	+	45.2750i	−2.34560	+	1.73113i
$685$		−	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
$689$	5.99372	−	29.1649i	0.228343	−	1.11109i
$690$	8.49234	+	2.61954i	0.323298	+	0.0997242i
$691$	25.4070	−	29.5234i	0.966526	−	1.12312i	−0.0258238	−	0.999667i	$-0.508221\pi$
$691$	25.4070	−	29.5234i	0.966526	−	1.12312i	0.992350	−	0.123457i	$-0.0393982\pi$
$692$	0.993479	+	2.06298i	0.0377664	+	0.0784227i
$693$	−4.17070	+	20.8873i	−0.158432	+	0.793442i
$694$	−51.4673	+	18.0092i	−1.95367	+	0.683620i
$695$	−12.8215	−	29.3872i	−0.486347	−	1.11472i
$696$	161.261	+	187.389i	6.11259	+	7.10296i
$697$	8.20414	−	18.8041i	0.310754	−	0.712256i
$698$	19.9386	+	64.6394i	0.754687	+	2.44664i
$699$	47.3835	−	59.4170i	1.79221	−	2.24736i
$700$	4.70895	+	10.0359i	0.177981	+	0.379321i
$701$	13.3954	−	10.6825i	0.505939	−	0.403473i	−0.336981	−	0.941511i	$-0.609406\pi$
$701$	13.3954	−	10.6825i	0.505939	−	0.403473i	0.842920	+	0.538039i	$0.180835\pi$
$702$	−33.4149	−	23.5582i	−1.26116	−	0.889148i
$703$	−20.6337	+	22.2379i	−0.778216	+	0.838717i
$704$	10.6021	+	39.5677i	0.399583	+	1.49126i
$705$	−17.7461	+	10.2457i	−0.668356	+	0.385875i
$706$	−12.5446	+	54.9616i	−0.472124	+	2.06851i
$707$	−5.93199	−	2.39745i	−0.223095	−	0.0901654i
$708$	20.4208	+	12.8312i	0.767459	+	0.482227i
$709$	−35.2771	−	1.31998i	−1.32486	−	0.0495727i	−0.634434	−	0.772977i	$-0.718767\pi$
$709$	−35.2771	−	1.31998i	−1.32486	−	0.0495727i	−0.690425	+	0.723404i	$0.742576\pi$
$710$	−14.4845	+	19.6258i	−0.543593	+	0.736542i
$711$	3.95368	−	0.595921i	0.148274	−	0.0223488i
$712$	22.1140	−	20.5188i	0.828756	−	0.768973i
$713$	−4.93907	−	3.10343i	−0.184970	−	0.116224i
$714$	−24.4476	+	45.1490i	−0.914929	+	1.68966i
$715$	11.2380	−	6.81774i	0.420277	−	0.254969i
$716$	−1.41131	−	2.44445i	−0.0527429	−	0.0913535i
$717$	−41.3651	+	11.0838i	−1.54481	+	0.413930i
$718$	5.05307	+	4.68856i	0.188579	+	0.174976i
$719$	10.4472	+	7.12281i	0.389617	+	0.265636i	0.742247	−	0.670127i	$-0.233760\pi$
$719$	10.4472	+	7.12281i	0.389617	+	0.265636i	−0.352630	+	0.935763i	$0.614713\pi$
$720$	13.9736	−	124.019i	0.520766	−	4.62193i
$721$	7.32927	−	5.72493i	0.272956	−	0.213208i
$722$	−23.8547	+	2.68778i	−0.887782	+	0.100029i
$723$	3.01857	+	1.59536i	0.112262	+	0.0593321i
$724$	−57.7521	+	22.6660i	−2.14634	+	0.842376i
$725$	−7.99747	−	0.599327i	−0.297019	−	0.0222585i
$726$	23.2391	+	53.2647i	0.862485	+	1.97684i
$727$	−11.9059	−	5.73356i	−0.441564	−	0.212646i	0.199873	−	0.979822i	$-0.435947\pi$
$727$	−11.9059	−	5.73356i	−0.441564	−	0.212646i	−0.641437	+	0.767176i	$0.721661\pi$
$728$	−72.3489	−	44.2952i	−2.68143	−	1.64169i
$729$	−39.5850	+	19.0631i	−1.46611	+	0.706041i
$730$	−2.89918	−	2.49494i	−0.107303	−	0.0923420i
$731$	−8.01855	+	25.9955i	−0.296577	+	0.961479i
$732$	−58.7542	−	86.1766i	−2.17162	−	3.18518i
$733$	4.36874	+	5.91943i	0.161363	+	0.218639i	0.877818	−	0.478994i	$-0.158998\pi$
$733$	4.36874	+	5.91943i	0.161363	+	0.218639i	−0.716455	+	0.697633i	$0.754237\pi$
$734$	−51.2158	−	51.2158i	−1.89041	−	1.89041i
$735$	19.1119	−	34.4606i	0.704953	−	1.27110i
$736$	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
$739$	15.8356	+	29.9625i	0.582523	+	1.10219i	0.982605	+	0.185708i	$0.0594579\pi$
$739$	15.8356	+	29.9625i	0.582523	+	1.10219i	−0.400082	+	0.916479i	$0.631018\pi$
$740$	−7.74135	−	103.301i	−0.284578	−	3.79743i
$741$	13.2038	+	28.5557i	0.485055	+	1.04902i
$742$	47.1177	+	35.5140i	1.72975	+	1.30376i
$743$	−2.62832	+	0.919691i	−0.0964239	+	0.0337402i	−0.378060	−	0.925781i	$-0.623409\pi$
$743$	−2.62832	+	0.919691i	−0.0964239	+	0.0337402i	0.281636	+	0.959521i	$0.409123\pi$
$744$	−88.9588	+	226.663i	−3.26139	+	8.30988i
$745$	0.865966	−	11.5555i	0.0317265	−	0.423361i
$746$	−59.1572	−	25.8100i	−2.16590	−	0.944972i
$747$	9.87753	+	5.22043i	0.361400	+	0.191006i
$748$	−2.75784	−	24.4765i	−0.100837	−	0.894949i
$749$	−21.6172	+	4.70514i	−0.789876	+	0.171922i
$750$	54.8960	+	68.8374i	2.00452	+	2.51359i
$751$	23.2201	−	34.0577i	0.847314	−	1.24278i	−0.120901	−	0.992665i	$-0.538578\pi$
$751$	23.2201	−	34.0577i	0.847314	−	1.24278i	0.968216	−	0.250117i	$-0.0804692\pi$
$752$	−48.8503	+	1.82785i	−1.78139	+	0.0666548i
$753$	29.8958	+	17.2603i	1.08946	+	0.629001i
$754$	86.1924	−	47.9761i	3.13894	−	1.74719i
$755$	−17.1736	−	3.91977i	−0.625013	−	0.142655i
$756$	51.2168	−	28.8853i	1.86274	−	1.05055i
$757$	2.11007	+	9.24484i	0.0766920	+	0.336009i	0.998689	−	0.0511873i	$-0.0163006\pi$
$757$	2.11007	+	9.24484i	0.0766920	+	0.336009i	−0.921997	+	0.387197i	$0.873443\pi$
$758$	37.8665	+	40.8104i	1.37537	+	1.48230i
$759$	−2.29373	−	1.69285i	−0.0832573	−	0.0614467i
$760$	−34.4463	+	46.6731i	−1.24950	+	1.69301i
$761$	0.898556	−	24.0144i	0.0325726	−	0.870522i	−0.883241	−	0.468919i	$-0.844644\pi$
$761$	0.898556	−	24.0144i	0.0325726	−	0.870522i	0.915814	−	0.401603i	$-0.131547\pi$
$762$	−59.2243	−	37.2131i	−2.14547	−	1.34809i
$763$	1.54864	+	8.66211i	0.0560646	+	0.313589i
$764$	−22.3922	−	5.11088i	−0.810123	−	0.184905i
$765$	−6.29863	+	23.5068i	−0.227728	+	0.849891i
$766$	−6.02746	+	10.4399i	−0.217781	+	0.377208i
$767$	4.14048	−	4.32428i	0.149504	−	0.156141i
$768$	34.2977	−	50.3055i	1.23761	−	1.81524i
$769$	−1.23845	+	10.9916i	−0.0446597	+	0.396366i	0.951419	+	0.307898i	$0.0996256\pi$
$769$	−1.23845	+	10.9916i	−0.0446597	+	0.396366i	−0.996079	+	0.0884676i	$0.971803\pi$
$770$	2.65522	+	25.9119i	0.0956876	+	0.933802i
$771$	0.947565	+	0.755658i	0.0341257	+	0.0272144i
$772$	18.1610	−	34.3623i	0.653630	−	1.23673i
$773$	5.80030	−	13.2944i	0.208622	−	0.478168i	−0.780519	−	0.625132i	$-0.785045\pi$
$773$	5.80030	−	13.2944i	0.208622	−	0.478168i	0.989142	+	0.146964i	$0.0469501\pi$
$774$	96.3322	−	82.9006i	3.46259	−	2.97980i
$775$	−3.15872	−	7.23986i	−0.113464	−	0.260063i
$776$	−52.7954	+	109.631i	−1.89525	+	3.93552i
$777$	52.9542	−	44.6492i	1.89972	−	1.60178i
$778$	56.8463	+	19.8914i	2.03804	+	0.713141i
$779$	24.8420	−	1.86165i	0.890058	−	0.0667006i
$780$	−102.149	−	33.2725i	−3.65751	−	1.19135i
$781$	6.46479	−	4.40762i	0.231328	−	0.157717i
$782$	−2.45493	−	3.32631i	−0.0877882	−	0.118949i
$783$			42.5390i			1.52022i
$784$	78.7239	−	51.3783i	2.81157	−	1.83494i
$785$	2.52341	−	2.52341i	0.0900645	−	0.0900645i
$786$	77.0393	−	56.8576i	2.74790	−	2.02804i
$787$	−2.62503	+	13.8736i	−0.0935721	+	0.494541i	0.904158	+	0.427199i	$0.140499\pi$
$787$	−2.62503	+	13.8736i	−0.0935721	+	0.494541i	−0.997730	+	0.0673420i	$0.978548\pi$
$788$	22.6192	+	42.7976i	0.805776	+	1.52460i
$789$	81.0300	−	6.07236i	2.88474	−	0.216182i
$790$	4.40540	−	2.12153i	0.156737	−	0.0754807i
$791$	10.5358	−	32.9718i	0.374608	−	1.17234i
$792$	−31.0623	+	64.5015i	−1.10375	+	2.29196i
$793$	−23.8906	+	9.98016i	−0.848380	+	0.354406i
$794$	8.94563	+	0.670382i	0.317469	+	0.0237910i
$795$	42.6082	+	18.5897i	1.51116	+	0.659310i
$796$	−1.95537	−	6.33916i	−0.0693063	−	0.224686i
$797$	−23.2140	+	29.1094i	−0.822282	+	1.03111i	0.176621	+	0.984279i	$0.443483\pi$
$797$	−23.2140	+	29.1094i	−0.822282	+	1.03111i	−0.998903	+	0.0468301i	$0.985088\pi$
$798$	−62.3409	−	0.628737i	−2.20685	−	0.0222570i
$799$	9.47225	+	1.06727i	0.335104	+	0.0377572i
$800$	2.71993	+	14.3752i	0.0961640	+	0.508239i
$801$	15.3569	−	0.574613i	0.542608	−	0.0203030i
$802$	−13.2063	+	22.8741i	−0.466332	+	0.807711i
$803$	0.613469	+	1.06256i	0.0216488	+	0.0374969i
$804$	27.9837	+	44.5358i	0.986908	+	1.57066i
$805$	1.85830	+	2.57179i	0.0654965	+	0.0906439i
$806$	81.4442	+	52.9750i	2.86875	+	1.86597i
$807$	30.7989	−	28.5772i	1.08417	−	1.00596i
$808$	−17.3030	−	12.7702i	−0.608718	−	0.449254i
$809$	32.7543	−	4.93692i	1.15158	−	0.173573i	0.454622	−	0.890684i	$-0.349774\pi$
$809$	32.7543	−	4.93692i	1.15158	−	0.173573i	0.696958	+	0.717112i	$0.254536\pi$
$810$	−8.39918	+	7.79330i	−0.295117	+	0.273829i
$811$	−14.1084	+	22.4533i	−0.495412	+	0.788443i	−0.997060	−	0.0766286i	$-0.975584\pi$
$811$	−14.1084	+	22.4533i	−0.495412	+	0.788443i	0.501648	+	0.865072i	$0.332727\pi$
$812$	9.17485	+	141.576i	0.321974	+	4.96834i
$813$	−46.4238	+	29.1700i	−1.62815	+	1.02304i
$814$	−11.8501	+	44.2253i	−0.415347	+	1.55010i
$815$	9.97343	+	5.75816i	0.349354	+	0.201700i
$816$	−65.6387	+	70.7417i	−2.29781	+	2.47646i
$817$	−32.4571	+	6.14121i	−1.13553	+	0.214854i
$818$	12.2790	+	15.3974i	0.429327	+	0.538359i
$819$	−13.2170	−	41.1441i	−0.461839	−	1.43769i
$820$	−53.0390	+	66.5088i	−1.85220	+	2.32259i
$821$	−5.16845	+	9.77918i	−0.180380	+	0.341296i	−0.957680	−	0.287834i	$-0.907065\pi$
$821$	−5.16845	+	9.77918i	−0.180380	+	0.341296i	0.777300	+	0.629130i	$0.216589\pi$
$822$	93.6002	−	36.7354i	3.26468	−	1.28129i
$823$	23.5452	+	1.76447i	0.820733	+	0.0615054i	0.478476	−	0.878101i	$-0.341189\pi$
$823$	23.5452	+	1.76447i	0.820733	+	0.0615054i	0.342257	+	0.939606i	$0.388809\pi$
$824$	28.6511	−	12.5003i	0.998108	−	0.435470i
$825$	−1.27500	−	3.64374i	−0.0443898	−	0.126859i
$826$	4.22280	+	11.0870i	0.146930	+	0.385767i
$827$	28.3750	+	9.92884i	0.986695	+	0.345260i	0.774920	−	0.632059i	$-0.217790\pi$
$827$	28.3750	+	9.92884i	0.986695	+	0.345260i	0.211775	+	0.977318i	$0.432076\pi$
$828$	1.04751	+	13.9781i	0.0364035	+	0.485771i
$829$	10.3602	+	3.19569i	0.359824	+	0.110991i	0.469396	−	0.882988i	$-0.344472\pi$
$829$	10.3602	+	3.19569i	0.359824	+	0.110991i	−0.109572	+	0.993979i	$0.534948\pi$
$830$	13.4245	+	2.54005i	0.465971	+	0.0881666i
$831$	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
$837$	−37.0421	+	19.5773i	−1.28036	+	0.676691i
$838$	−29.5454	+	34.3324i	−1.02063	+	1.18599i
$839$	2.79794	−	7.99604i	0.0965954	−	0.276054i	−0.885439	−	0.464756i	$-0.846142\pi$
$839$	2.79794	−	7.99604i	0.0965954	−	0.276054i	0.982034	+	0.188702i	$0.0604279\pi$
$840$	91.0622	−	96.1779i	3.14194	−	3.31845i
$841$	−66.3445	−	31.9498i	−2.28774	−	1.10172i
$842$	−21.1043	−	8.28283i	−0.727303	−	0.285445i
$843$	−30.5889	−	35.5450i	−1.05354	−	1.22423i
$844$	−90.9687	+	35.7026i	−3.13127	+	1.22893i
$845$	−13.1950	+	23.1756i	−0.453923	+	0.797264i
$846$	−34.8169	−	27.7655i	−1.19703	−	0.954599i
$847$	−4.82059	+	20.1801i	−0.165637	+	0.693395i
$848$	69.1448	+	86.7049i	2.37444	+	2.97746i
$849$	−20.4047	+	29.9282i	−0.700289	+	1.02713i
$850$	−0.209324	−	5.59429i	−0.00717974	−	0.191883i
$851$	1.44349	+	5.38718i	0.0494822	+	0.184670i
$852$	−61.7707	−	16.5514i	−2.11623	−	0.567042i
$853$	9.84017	+	15.6605i	0.336921	+	0.536207i	0.971618	−	0.236554i	$-0.0760180\pi$
$853$	9.84017	+	15.6605i	0.336921	+	0.536207i	−0.634697	+	0.772761i	$0.718875\pi$
$854$	2.43544	−	51.2501i	0.0833391	−	1.75374i
$855$	−28.8095	+	6.57557i	−0.985263	+	0.224880i
$856$	−74.3081	−	2.78041i	−2.53980	−	0.0950325i
$857$	2.73412	−	0.412102i	0.0933956	−	0.0140771i	−0.102178	−	0.994766i	$-0.532581\pi$
$857$	2.73412	−	0.412102i	0.0933956	−	0.0140771i	0.195574	+	0.980689i	$0.437343\pi$
$858$	37.7574	+	28.7921i	1.28902	+	0.982946i
$859$	−0.0848854	−	0.0914847i	−0.00289625	−	0.00312142i	0.731602	−	0.681732i	$-0.238773\pi$
$859$	−0.0848854	−	0.0914847i	−0.00289625	−	0.00312142i	−0.734498	+	0.678610i	$0.762582\pi$
$860$	60.0133	−	95.5107i	2.04644	−	3.25689i
$861$	−56.8161	−	2.69994i	−1.93629	−	0.0920138i
$862$	63.4720	+	14.4871i	2.16186	+	0.493431i
$863$	−36.0944	−	9.67148i	−1.22867	−	0.329221i	−0.414608	−	0.910000i	$-0.636081\pi$
$863$	−36.0944	−	9.67148i	−1.22867	−	0.329221i	−0.814061	+	0.580779i	$0.802748\pi$
$864$	74.9571	−	20.0847i	2.55009	−	0.683295i
$865$	0.0331828	+	0.886830i	0.00112825	+	0.0301531i
$866$	−16.7411	+	3.16758i	−0.568884	+	0.107639i
$867$	−21.7602	+	17.3532i	−0.739016	+	0.589346i
$868$	−119.059	+	73.1454i	−4.04112	+	2.48272i
$869$	−1.55861	+	0.175613i	−0.0528722	+	0.00595727i
$870$	45.3967	+	147.172i	1.53909	+	4.98961i
$871$	12.2276	−	4.57893i	0.414318	−	0.155151i
$872$	−2.21024	+	29.4936i	−0.0748483	+	0.998781i
$873$	−56.8146	+	24.7879i	−1.92288	+	0.838945i
$874$	2.17806	−	4.52280i	0.0736741	−	0.152986i
$875$	0.858520	+	31.4228i	0.0290233	+	1.06228i
$876$	3.31203	−	9.46522i	0.111903	−	0.319800i
$877$	21.1895	+	18.2350i	0.715518	+	0.615753i	0.932816	−	0.360352i	$-0.117343\pi$
$877$	21.1895	+	18.2350i	0.715518	+	0.615753i	−0.217298	+	0.976105i	$0.569724\pi$
$878$	23.4709	−	12.4047i	0.792104	−	0.418639i
$879$	83.6846	+	15.8340i	2.82261	+	0.534067i
$880$	−7.29686	+	48.4115i	−0.245977	+	1.63195i
$881$	−21.0350			−0.708687			−0.354344	−	0.935115i	$-0.615296\pi$
$881$	−21.0350			−0.708687			−0.354344	+	0.935115i	$0.615296\pi$
$882$	84.8880	+	11.3027i	2.85833	+	0.380582i
$883$			27.0503i			0.910316i	0.890411	+	0.455158i	$0.150417\pi$
$883$			27.0503i			0.910316i	−0.890411	+	0.455158i	$0.849583\pi$
$884$	29.0415	+	40.6702i	0.976770	+	1.36789i
$885$	5.26556	+	7.72315i	0.177000	+	0.259611i
$886$	28.6199	−	15.1261i	0.961505	−	0.508170i
$887$	−13.2728	+	0.994657i	−0.445656	+	0.0333973i	−0.295669	−	0.955291i	$-0.595542\pi$
$887$	−13.2728	+	0.994657i	−0.445656	+	0.0333973i	−0.149988	+	0.988688i	$0.547923\pi$
$888$	209.756	−	101.013i	7.03896	−	3.38978i
$889$	−8.88840	−	23.3366i	−0.298107	−	0.782684i
$890$	17.7387	−	6.20704i	0.594602	−	0.208060i
$891$	3.36872	−	1.46976i	0.112856	−	0.0492387i
$892$	−94.7121	−	110.057i	−3.17119	−	3.68500i
$893$	4.22867	+	10.7745i	0.141507	+	0.360554i
$894$	40.0005	−	12.3385i	1.33782	−	0.412662i
$895$	−0.122487	−	1.08710i	−0.00409429	−	0.0363378i
$896$	63.3688	−	21.4589i	2.11700	−	0.716890i
$897$	5.73673	+	0.737695i	0.191544	+	0.0246309i
$898$	1.89157	+	1.28965i	0.0631227	+	0.0430363i
$899$	−3.77983	−	101.018i	−0.126064	−	3.36914i
$900$	−9.49069	+	16.4384i	−0.316356	+	0.547945i
$901$	−10.8124	−	18.7276i	−0.360213	−	0.623907i
$902$	31.8357	−	20.0037i	1.06001	−	0.666050i
$903$	75.2653	−	4.87759i	2.50467	−	0.162316i
$904$	61.8985	−	98.5109i	2.05871	−	3.27643i
$905$	−24.0288	−	0.899094i	−0.798744	−	0.0298869i
$906$	−9.48409	−	62.9228i	−0.315088	−	2.09047i
$907$	−3.27571	−	21.7329i	−0.108768	−	0.721629i	−0.975036	−	0.222048i	$-0.928726\pi$
$907$	−3.27571	−	21.7329i	−0.108768	−	0.721629i	0.866268	−	0.499580i	$-0.166512\pi$
$908$	2.81460	−	75.2218i	0.0934059	−	2.49632i
$909$	−2.43774	−	10.6805i	−0.0808549	−	0.354248i
$910$	−30.2760	−	43.3162i	−1.00364	−	1.43592i
$911$	−1.02200	+	4.47769i	−0.0338605	+	0.148353i	−0.989032	−	0.147700i	$-0.952813\pi$
$911$	−1.02200	+	4.47769i	−0.0338605	+	0.148353i	0.955172	+	0.296052i	$0.0956702\pi$
$912$	−113.187	−	30.3284i	−3.74800	−	1.00427i
$913$	−3.79549	−	2.19133i	−0.125612	−	0.0725223i
$914$	−11.1743	+	12.0431i	−0.369614	+	0.398349i
$915$	−7.51535	−	39.7196i	−0.248450	−	1.31309i
$916$	−16.5174	+	146.596i	−0.545751	+	4.84368i
$917$	34.1827	+	0.344748i	1.12881	+	0.0113846i
$918$	−29.5072	+	3.32466i	−0.973883	+	0.109730i
$919$	44.7507	−	13.8038i	1.47619	−	0.455344i	0.550889	−	0.834578i	$-0.314289\pi$
$919$	44.7507	−	13.8038i	1.47619	−	0.455344i	0.925301	+	0.379234i	$0.123812\pi$
$920$	3.89624	+	9.92747i	0.128455	+	0.327299i
$921$	51.2463	−	44.1010i	1.68862	−	1.45318i
$922$	14.7850	−	37.6715i	0.486917	−	1.24064i
$923$	−7.11141	+	14.1929i	−0.234075	+	0.467167i
$924$	−60.6952	+	31.2994i	−1.99673	+	1.02967i
$925$	−2.49438	+	7.12854i	−0.0820149	+	0.234385i
$926$	−4.20930	−	56.1693i	−0.138326	−	1.84584i
$927$	15.2166	+	4.69370i	0.499779	+	0.154161i
$928$	−34.8090	+	183.970i	−1.14266	+	6.03912i
$929$	−16.6729	−	22.5910i	−0.547021	−	0.741187i	0.440659	−	0.897675i	$-0.354745\pi$
$929$	−16.6729	−	22.5910i	−0.547021	−	0.741187i	−0.987680	+	0.156487i	$0.949983\pi$
$930$	−107.262	+	107.262i	−3.51727	+	3.51727i
$931$	−17.6387	−	13.5759i	−0.578085	−	0.444932i
$932$	146.587			4.80160
$933$	6.82917	−	45.3086i	0.223577	−	1.48334i
$934$	15.9130	−	84.1023i	0.520690	−	2.75191i
$935$	2.81390	−	9.12245i	0.0920245	−	0.298336i
$936$	−8.58083	−	144.998i	−0.280473	−	4.73942i
$937$	−19.1278	−	39.7194i	−0.624879	−	1.29758i	−0.937595	−	0.347729i	$-0.886953\pi$
$937$	−19.1278	−	39.7194i	−0.624879	−	1.29758i	0.312716	−	0.949847i	$-0.398761\pi$
$938$	−2.19370	+	25.7811i	−0.0716268	+	0.841783i
$939$	−64.0370	−	30.8386i	−2.08977	−	1.00638i
$940$	−36.7925	−	14.4400i	−1.20004	−	0.470980i
$941$	18.1804	−	15.6455i	0.592664	−	0.510028i	−0.304040	−	0.952659i	$-0.598336\pi$
$941$	18.1804	−	15.6455i	0.592664	−	0.510028i	0.896704	+	0.442631i	$0.145955\pi$
$942$	11.8158	+	5.15516i	0.384978	+	0.167964i
$943$	2.14008	−	4.04922i	0.0696905	−	0.131861i
$944$	2.49672	+	22.1590i	0.0812612	+	0.721213i
$945$	22.6711	−	2.32314i	0.737493	−	0.0755716i
$946$	−38.9789	+	31.0846i	−1.26731	+	1.01065i
$947$	−4.35127	−	22.9970i	−0.141397	−	0.747302i	−0.979446	−	0.201707i	$-0.935351\pi$
$947$	−4.35127	−	22.9970i	−0.141397	−	0.747302i	0.838049	−	0.545595i	$-0.183696\pi$
$948$	9.39726	+	8.71938i	0.305209	+	0.283192i
$949$	−2.13604	−	1.27834i	−0.0693387	−	0.0414967i
$950$	5.88698	−	3.39885i	0.190999	−	0.110273i
$951$	1.93211	−	1.21403i	0.0626531	−	0.0393676i
$952$	−60.6506	+	10.8433i	−1.96570	+	0.351434i
$953$	33.2547	−	7.59017i	1.07723	−	0.245870i	0.353133	−	0.935573i	$-0.385116\pi$
$953$	33.2547	−	7.59017i	1.07723	−	0.245870i	0.724092	+	0.689703i	$0.242259\pi$
$954$	−3.77751	+	100.956i	−0.122301	+	3.26857i
$955$	−7.16247	−	5.28615i	−0.231772	−	0.171056i
$956$	−66.4609	−	49.0503i	−2.14950	−	1.58640i
$957$	1.84728	−	49.3696i	0.0597141	−	1.59589i
$958$	28.4399	−	6.49122i	0.918852	−	0.209722i
$959$	34.5802	+	9.64056i	1.11665	+	0.311310i
$960$	109.872	−	69.0373i	3.54611	−	2.22817i
$961$	59.3781	−	34.2820i	1.91542	−	1.10587i
$962$	−22.6321	−	90.0951i	−0.729687	−	2.90478i
$963$	−27.7683	−	25.7652i	−0.894821	−	0.830272i
$964$	1.22432	+	6.47070i	0.0394327	+	0.208407i
$965$	11.7773	−	9.39209i	0.379125	−	0.302342i
$966$	−6.19564	+	9.64304i	−0.199341	+	0.310260i
$967$	−5.16889	−	45.8751i	−0.166220	−	1.47524i	−0.748976	−	0.662597i	$-0.769454\pi$
$967$	−5.16889	−	45.8751i	−0.166220	−	1.47524i	0.582756	−	0.812647i	$-0.301975\pi$
$968$	−32.5858	+	61.6553i	−1.04735	+	1.98168i
$969$	20.9429	+	9.13729i	0.672783	+	0.293532i
$970$	−57.4576	+	49.4463i	−1.84485	+	1.58762i
$971$	−6.86444	−	2.69410i	−0.220290	−	0.0864576i	0.252629	−	0.967563i	$-0.418705\pi$
$971$	−6.86444	−	2.69410i	−0.220290	−	0.0864576i	−0.472920	+	0.881106i	$0.656800\pi$
$972$	−87.1356	−	41.9623i	−2.79488	−	1.34594i
$973$	40.9494	−	5.75039i	1.31278	−	0.184349i
$974$	−12.9073	−	26.8023i	−0.413577	−	0.858802i
$975$	5.85579	+	5.20144i	0.187535	+	0.166579i
$976$	28.4252	−	92.1523i	0.909870	−	2.94972i
$977$	1.80619	−	9.54595i	0.0577852	−	0.305402i	−0.941736	−	0.336354i	$-0.890806\pi$
$977$	1.80619	−	9.54595i	0.0577852	−	0.305402i	0.999521	+	0.0309518i	$0.00985385\pi$
$978$	−6.20040	+	41.1369i	−0.198267	+	1.31541i
$979$	−6.02843			−0.192669
$980$	74.9518	−	12.6215i	2.39425	−	0.403178i
$981$	−10.6538	+	10.6538i	−0.340149	+	0.340149i
$982$	2.92630	+	3.96500i	0.0933821	+	0.126528i
$983$	1.04450	−	5.52033i	0.0333145	−	0.176071i	−0.961957	−	0.273199i	$-0.911918\pi$
$983$	1.04450	−	5.52033i	0.0333145	−	0.176071i	0.995272	+	0.0971283i	$0.0309657\pi$
$984$	−182.689	−	56.3522i	−5.82393	−	1.79644i
$985$	1.40206	+	18.7091i	0.0446732	+	0.596123i
$986$	23.6627	−	67.6242i	0.753575	−	2.15359i
$987$	−6.58226	−	25.5951i	−0.209516	−	0.814701i
$988$	−27.1837	+	54.2532i	−0.864827	+	1.72602i
$989$	−2.21873	+	5.65324i	−0.0705516	+	0.179763i
$990$	−33.8053	+	29.0918i	−1.07440	+	0.924598i
$991$	2.83204	+	7.21592i	0.0899627	+	0.229221i	0.968773	−	0.247951i	$-0.0797571\pi$
$991$	2.83204	+	7.21592i	0.0899627	+	0.229221i	−0.878810	+	0.477172i	$0.841662\pi$
$992$	−176.217	+	54.3559i	−5.59491	+	1.72580i
$993$	44.6265	−	5.02820i	1.41618	−	0.159565i
$994$	−19.3651	−	24.7919i	−0.614223	−	0.786351i
$995$	0.287877	−	2.55498i	0.00912633	−	0.0809984i
$996$	6.65938	+	35.1957i	0.211010	+	1.11522i
$997$	10.3499	−	11.1545i	0.327784	−	0.353267i	−0.547561	−	0.836766i	$-0.684444\pi$
$997$	10.3499	−	11.1545i	0.327784	−	0.353267i	0.875345	+	0.483499i	$0.160634\pi$
$998$	−74.0678	−	42.7630i	−2.34457	−	1.35364i
$999$	38.6941	+	10.3680i	1.22423	+	0.328030i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.cc.a.5.2	✓	1536	49.5	odd	42	inner
637.2.cc.a.255.2	yes	1536	13.8	odd	4	inner
637.2.cc.a.304.2	yes	1536	1.1	even	1	trivial
637.2.cc.a.593.2	yes	1536	637.593	even	84	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+(-2.17285 + 1.60364i) q^{2} +(-1.54581 - 2.26729i) q^{3} +(1.56013 - 5.05780i) q^{4} +(1.33812 - 1.55493i) q^{5} +(6.99474 + 2.44757i) q^{6} +(1.46828 + 2.20094i) q^{7} +(2.93710 + 8.39375i) q^{8} +(-1.65505 + 4.21700i) q^{9} +(-0.414004 + 5.52450i) q^{10} +(0.710645 - 1.62882i) q^{11} +(-13.8792 + 4.28116i) q^{12} +(0.347431 + 3.58877i) q^{13} +(-6.71988 - 2.42773i) q^{14} +(-5.59397 - 0.630289i) q^{15} +(-11.0959 - 7.56509i) q^{16} +(1.91962 + 1.78115i) q^{17} +(-3.16636 - 11.8170i) q^{18} +(-0.822980 + 3.07140i) q^{19} +(-5.77688 - 9.19386i) q^{20} +(2.72049 - 6.73127i) q^{21} +(1.06791 + 4.67880i) q^{22} +(0.397623 + 0.428536i) q^{23} +(14.4909 - 19.6344i) q^{24} +(0.117985 + 0.782779i) q^{25} +(-6.51002 - 7.24073i) q^{26} +(4.09362 - 0.934343i) q^{27} +(13.4226 - 3.99254i) q^{28} +(-2.25436 + 9.87698i) q^{29} +(13.1656 - 7.60118i) q^{30} +(-9.63818 + 2.58254i) q^{31} +(18.4684 - 0.691040i) q^{32} +(-4.79152 + 0.906605i) q^{33} +(-7.02737 - 0.791794i) q^{34} +(5.38705 + 0.662058i) q^{35} +(18.7467 + 14.9500i) q^{36} +(8.43479 + 4.45792i) q^{37} +(-3.13721 - 7.99347i) q^{38} +(7.59973 - 6.33530i) q^{39} +(16.9819 + 6.66490i) q^{40} +(-2.58757 - 7.39484i) q^{41} +(4.88331 + 18.9887i) q^{42} +(4.50742 + 9.35975i) q^{43} +(-7.12954 - 6.13546i) q^{44} +(4.34247 + 8.21635i) q^{45} +(-1.55119 - 0.293502i) q^{46} +(2.92881 - 2.16156i) q^{47} +36.8520i q^{48} +(-2.68829 + 6.46321i) q^{49} +(-1.51166 - 1.51166i) q^{50} +(1.07100 - 7.10565i) q^{51} +(18.6933 + 3.84170i) q^{52} +(-7.89106 - 2.43407i) q^{53} +(-7.39650 + 8.59489i) q^{54} +(-1.58176 - 3.28456i) q^{55} +(-14.1617 + 18.7888i) q^{56} +(8.23594 - 2.88188i) q^{57} +(-10.9407 - 25.0764i) q^{58} +(-1.08310 - 1.25859i) q^{59} +(-11.9152 + 27.3099i) q^{60} +(2.11663 + 6.86195i) q^{61} +(16.8009 - 21.0676i) q^{62} +(-11.7114 + 2.54908i) q^{63} +(-18.0219 + 14.3720i) q^{64} +(6.04519 + 4.26199i) q^{65} +(8.95742 - 9.65380i) q^{66} +(-0.937267 - 3.49793i) q^{67} +(12.0035 - 6.93024i) q^{68} +(0.356965 - 1.56396i) q^{69} +(-12.7670 + 7.20033i) q^{70} +(3.72804 + 2.34248i) q^{71} +(-40.2575 - 1.50633i) q^{72} +(-0.409985 + 0.555509i) q^{73} +(-25.4765 + 3.83996i) q^{74} +(1.59240 - 1.47754i) q^{75} +(14.2506 + 8.95425i) q^{76} +(4.62836 - 0.827474i) q^{77} +(-6.35357 + 25.9529i) q^{78} +(-0.441303 - 0.764359i) q^{79} +(-26.6109 + 7.13038i) q^{80} +(1.51610 + 1.40673i) q^{81} +(17.4811 + 11.9184i) q^{82} +(0.276126 - 2.45069i) q^{83} +(-29.8012 - 24.2613i) q^{84} +(5.33824 - 0.601475i) q^{85} +(-24.8036 - 13.1091i) q^{86} +(25.8788 - 10.1567i) q^{87} +(15.7591 + 1.18098i) q^{88} +(-1.35655 - 3.10925i) q^{89} +(-22.6116 - 10.8892i) q^{90} +(-7.38855 + 6.03401i) q^{91} +(2.78779 - 1.34253i) q^{92} +(20.7542 + 17.8604i) q^{93} +(-2.89751 + 9.39351i) q^{94} +(3.67456 + 5.38959i) q^{95} +(-30.1155 - 40.8051i) q^{96} +(9.67543 + 9.67543i) q^{97} +(-4.52340 - 18.3547i) 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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