LMFDB - Embedded newform 112.2.v.a.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(3,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.v (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	112.19
Dual form			112.2.v.a.59.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29274 + 0.573436i) q^{2} +(-0.388227 + 1.44888i) q^{3} +(1.34234 - 1.48261i) q^{4} +(2.81809 - 0.755106i) q^{5} +(-0.328966 - 2.09565i) q^{6} +(-1.47726 + 2.19493i) q^{7} +(-0.885116 + 2.68637i) q^{8} +(0.649537 + 0.375010i) q^{9} +(-3.21005 + 2.59215i) q^{10} +(0.0165920 - 0.0619222i) q^{11} +(1.62699 + 2.52048i) q^{12} +(-3.62997 + 3.62997i) q^{13} +(0.651060 - 3.68458i) q^{14} +4.37624i q^{15} +(-0.396237 - 3.98033i) q^{16} +(3.26044 - 1.88242i) q^{17} +(-1.05473 - 0.112322i) q^{18} +(2.13834 - 0.572967i) q^{19} +(2.66332 - 5.19173i) q^{20} +(-2.60668 - 2.99251i) q^{21} +(0.0140593 + 0.0895636i) q^{22} +(3.80570 - 6.59167i) q^{23} +(-3.54860 - 2.32535i) q^{24} +(3.04134 - 1.75592i) q^{25} +(2.61104 - 6.77415i) q^{26} +(-3.97748 + 3.97748i) q^{27} +(1.27122 + 5.13654i) q^{28} +(-4.74233 - 4.74233i) q^{29} +(-2.50949 - 5.65733i) q^{30} +(-0.329500 - 0.570711i) q^{31} +(2.79469 + 4.91830i) q^{32} +(0.0832764 + 0.0480797i) q^{33} +(-3.13545 + 4.30313i) q^{34} +(-2.50566 + 7.30100i) q^{35} +(1.42789 - 0.459615i) q^{36} +(-1.08717 - 4.05737i) q^{37} +(-2.43575 + 1.96690i) q^{38} +(-3.85014 - 6.66865i) q^{39} +(-0.465849 + 8.23879i) q^{40} +7.67610 q^{41} +(5.08576 + 2.37376i) q^{42} +(-2.54426 - 2.54426i) q^{43} +(-0.0695340 - 0.107720i) q^{44} +(2.11363 + 0.566345i) q^{45} +(-1.13987 + 10.7036i) q^{46} +(2.62703 - 4.55014i) q^{47} +(5.92085 + 0.971168i) q^{48} +(-2.63540 - 6.48496i) q^{49} +(-2.92475 + 4.01396i) q^{50} +(1.46161 + 5.45480i) q^{51} +(0.509152 + 10.2545i) q^{52} +(-10.1607 - 2.72255i) q^{53} +(2.86101 - 7.42267i) q^{54} -0.187031i q^{55} +(-4.58883 - 5.91123i) q^{56} +3.32064i q^{57} +(8.85000 + 3.41116i) q^{58} +(2.43435 + 0.652282i) q^{59} +(6.48824 + 5.87441i) q^{60} +(1.84853 + 6.89881i) q^{61} +(0.753224 + 0.548832i) q^{62} +(-1.78266 + 0.871698i) q^{63} +(-6.43314 - 4.75549i) q^{64} +(-7.48858 + 12.9706i) q^{65} +(-0.135225 - 0.0144007i) q^{66} +(5.98832 + 1.60456i) q^{67} +(1.58575 - 7.36080i) q^{68} +(8.07307 + 8.07307i) q^{69} +(-0.947500 - 10.8751i) q^{70} +1.08883 q^{71} +(-1.58233 + 1.41297i) q^{72} +(-0.0232448 - 0.0402613i) q^{73} +(3.73207 + 4.62169i) q^{74} +(1.36339 + 5.08824i) q^{75} +(2.02090 - 3.93943i) q^{76} +(0.111404 + 0.127893i) q^{77} +(8.80127 + 6.41300i) q^{78} +(-15.2466 - 8.80264i) q^{79} +(-4.12220 - 10.9177i) q^{80} +(-3.09370 - 5.35845i) q^{81} +(-9.92319 + 4.40176i) q^{82} +(-5.07720 - 5.07720i) q^{83} +(-7.93576 - 0.152291i) q^{84} +(7.76681 - 7.76681i) q^{85} +(4.74802 + 1.83009i) q^{86} +(8.71217 - 5.02997i) q^{87} +(0.151660 + 0.0993805i) q^{88} +(-4.47814 + 7.75636i) q^{89} +(-3.05713 + 0.479896i) q^{90} +(-2.60510 - 13.3299i) q^{91} +(-4.66429 - 14.4906i) q^{92} +(0.954814 - 0.255842i) q^{93} +(-0.786839 + 7.38857i) q^{94} +(5.59340 - 3.22935i) q^{95} +(-8.21101 + 2.13977i) q^{96} +1.85612i q^{97} +(7.12559 + 6.87211i) q^{98} +(0.0339986 - 0.0339986i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) $ 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.29274	+	0.573436i	−0.914104	+	0.405481i
$2$	−1.29274	+	0.573436i	−0.914104	+	0.405481i
$3$	−0.388227	+	1.44888i	−0.224143	+	0.836512i	0.758603	+	0.651553i	$0.225882\pi$
$3$	−0.388227	+	1.44888i	−0.224143	+	0.836512i	−0.982746	+	0.184960i	$0.940785\pi$
$4$	1.34234	−	1.48261i	0.671171	−	0.741303i
$5$	2.81809	−	0.755106i	1.26029	−	0.337694i	0.433987	−	0.900919i	$-0.357106\pi$
$5$	2.81809	−	0.755106i	1.26029	−	0.337694i	0.826303	+	0.563225i	$0.190440\pi$
$6$	−0.328966	−	2.09565i	−0.134300	−	0.855545i
$7$	−1.47726	+	2.19493i	−0.558352	+	0.829604i
$7$	−1.47726	+	2.19493i	−0.558352	+	0.829604i
$8$	−0.885116	+	2.68637i	−0.312936	+	0.949774i
$9$	0.649537	+	0.375010i	0.216512	+	0.125003i
$10$	−3.21005	+	2.59215i	−1.01511	+	0.819710i
$11$	0.0165920	−	0.0619222i	0.00500267	−	0.0186702i	−0.963379	−	0.268142i	$-0.913590\pi$
$11$	0.0165920	−	0.0619222i	0.00500267	−	0.0186702i	0.968382	+	0.249472i	$0.0802570\pi$
$12$	1.62699	+	2.52048i	0.469671	+	0.727600i
$13$	−3.62997	+	3.62997i	−1.00677	+	1.00677i	−0.00679491	+	0.999977i	$0.502163\pi$
$13$	−3.62997	+	3.62997i	−1.00677	+	1.00677i	−0.999977	+	0.00679491i	$0.997837\pi$
$14$	0.651060	−	3.68458i	0.174003	−	0.984745i
$15$			4.37624i			1.12994i
$16$	−0.396237	−	3.98033i	−0.0990593	−	0.995082i
$17$	3.26044	−	1.88242i	0.790773	−	0.456553i	−0.0494614	−	0.998776i	$-0.515750\pi$
$17$	3.26044	−	1.88242i	0.790773	−	0.456553i	0.840235	+	0.542223i	$0.182417\pi$
$18$	−1.05473	−	0.112322i	−0.248601	−	0.0264746i
$19$	2.13834	−	0.572967i	0.490569	−	0.131448i	−0.00505063	−	0.999987i	$-0.501608\pi$
$19$	2.13834	−	0.572967i	0.490569	−	0.131448i	0.495620	+	0.868540i	$0.334941\pi$
$20$	2.66332	−	5.19173i	0.595537	−	1.16091i
$21$	−2.60668	−	2.99251i	−0.568824	−	0.653018i
$22$	0.0140593	+	0.0895636i	0.00299746	+	0.0190950i
$23$	3.80570	−	6.59167i	0.793543	−	1.37446i	−0.130217	−	0.991486i	$-0.541567\pi$
$23$	3.80570	−	6.59167i	0.793543	−	1.37446i	0.923760	−	0.382972i	$-0.125099\pi$
$24$	−3.54860	−	2.32535i	−0.724356	−	0.474660i
$25$	3.04134	−	1.75592i	0.608269	−	0.351184i
$26$	2.61104	−	6.77415i	0.512067	−	1.32852i
$27$	−3.97748	+	3.97748i	−0.765466	+	0.765466i
$28$	1.27122	+	5.13654i	0.240238	+	0.970714i
$29$	−4.74233	−	4.74233i	−0.880628	−	0.880628i	0.112971	−	0.993598i	$-0.463963\pi$
$29$	−4.74233	−	4.74233i	−0.880628	−	0.880628i	−0.993598	+	0.112971i	$0.963963\pi$
$30$	−2.50949	−	5.65733i	−0.458169	−	1.03288i
$31$	−0.329500	−	0.570711i	−0.0591800	−	0.102503i	0.834918	−	0.550375i	$-0.185515\pi$
$31$	−0.329500	−	0.570711i	−0.0591800	−	0.102503i	−0.894098	+	0.447872i	$0.852182\pi$
$32$	2.79469	+	4.91830i	0.494037	+	0.869441i
$33$	0.0832764	+	0.0480797i	0.0144966	+	0.00836960i
$34$	−3.13545	+	4.30313i	−0.537725	+	0.737980i
$35$	−2.50566	+	7.30100i	−0.423533	+	1.23409i
$36$	1.42789	−	0.459615i	0.237982	−	0.0766025i
$37$	−1.08717	−	4.05737i	−0.178729	−	0.667027i	−0.995886	−	0.0906119i	$-0.971118\pi$
$37$	−1.08717	−	4.05737i	−0.178729	−	0.667027i	0.817157	−	0.576415i	$-0.195549\pi$
$38$	−2.43575	+	1.96690i	−0.395131	+	0.319073i
$39$	−3.85014	−	6.66865i	−0.616516	−	1.06784i
$40$	−0.465849	+	8.23879i	−0.0736571	+	1.30267i
$41$	7.67610			1.19881			0.599403	−	0.800447i	$-0.295405\pi$
$41$	7.67610			1.19881			0.599403	+	0.800447i	$0.295405\pi$
$42$	5.08576	+	2.37376i	0.784750	+	0.366279i
$43$	−2.54426	−	2.54426i	−0.387995	−	0.387995i	0.485976	−	0.873972i	$-0.338464\pi$
$43$	−2.54426	−	2.54426i	−0.387995	−	0.387995i	−0.873972	+	0.485976i	$0.838464\pi$
$44$	−0.0695340	−	0.107720i	−0.0104826	−	0.0162394i
$45$	2.11363	+	0.566345i	0.315081	+	0.0844258i
$46$	−1.13987	+	10.7036i	−0.168065	+	1.57816i
$47$	2.62703	−	4.55014i	0.383191	−	0.663707i	−0.608325	−	0.793688i	$-0.708158\pi$
$47$	2.62703	−	4.55014i	0.383191	−	0.663707i	0.991516	+	0.129981i	$0.0414917\pi$
$48$	5.92085	+	0.971168i	0.854602	+	0.140176i
$49$	−2.63540	−	6.48496i	−0.376486	−	0.926422i
$50$	−2.92475	+	4.01396i	−0.413622	+	0.567660i
$51$	1.46161	+	5.45480i	0.204666	+	0.763825i
$52$	0.509152	+	10.2545i	0.0706067	+	1.42204i
$53$	−10.1607	−	2.72255i	−1.39568	−	0.373970i	−0.518886	−	0.854843i	$-0.673653\pi$
$53$	−10.1607	−	2.72255i	−1.39568	−	0.373970i	−0.876790	+	0.480873i	$0.840320\pi$
$54$	2.86101	−	7.42267i	0.389334	−	1.01010i
$55$		−	0.187031i		−	0.0252193i
$56$	−4.58883	−	5.91123i	−0.613208	−	0.789921i
$57$			3.32064i			0.439830i
$58$	8.85000	+	3.41116i	1.16206	+	0.447908i
$59$	2.43435	+	0.652282i	0.316925	+	0.0849199i	0.413775	−	0.910379i	$-0.364210\pi$
$59$	2.43435	+	0.652282i	0.316925	+	0.0849199i	−0.0968497	+	0.995299i	$0.530877\pi$
$60$	6.48824	+	5.87441i	0.837628	+	0.758383i
$61$	1.84853	+	6.89881i	0.236680	+	0.883302i	0.977384	+	0.211471i	$0.0678253\pi$
$61$	1.84853	+	6.89881i	0.236680	+	0.883302i	−0.740704	+	0.671831i	$0.765508\pi$
$62$	0.753224	+	0.548832i	0.0956595	+	0.0697018i
$63$	−1.78266	+	0.871698i	−0.224594	+	0.109824i
$64$	−6.43314	−	4.75549i	−0.804142	−	0.594437i
$65$	−7.48858	+	12.9706i	−0.928844	+	1.60881i
$66$	−0.135225	−	0.0144007i	−0.0166451	−	0.00177260i
$67$	5.98832	+	1.60456i	0.731589	+	0.196029i	0.605337	−	0.795969i	$-0.293038\pi$
$67$	5.98832	+	1.60456i	0.731589	+	0.196029i	0.126252	+	0.991998i	$0.459705\pi$
$68$	1.58575	−	7.36080i	0.192300	−	0.892628i
$69$	8.07307	+	8.07307i	0.971884	+	0.971884i
$70$	−0.947500	−	10.8751i	−0.113248	−	1.29982i
$71$	1.08883			0.129221			0.0646104	−	0.997911i	$-0.479420\pi$
$71$	1.08883			0.129221			0.0646104	+	0.997911i	$0.479420\pi$
$72$	−1.58233	+	1.41297i	−0.186480	+	0.166520i
$73$	−0.0232448	−	0.0402613i	−0.00272060	−	0.00471222i	0.864662	−	0.502354i	$-0.167533\pi$
$73$	−0.0232448	−	0.0402613i	−0.00272060	−	0.00471222i	−0.867383	+	0.497642i	$0.834199\pi$
$74$	3.73207	+	4.62169i	0.433844	+	0.537261i
$75$	1.36339	+	5.08824i	0.157431	+	0.587540i
$76$	2.02090	−	3.93943i	0.231813	−	0.451884i
$77$	0.111404	+	0.127893i	0.0126957	+	0.0145748i
$78$	8.80127	+	6.41300i	0.996548	+	0.726129i
$79$	−15.2466	−	8.80264i	−1.71538	−	0.990374i	−0.926897	−	0.375316i	$-0.877534\pi$
$79$	−15.2466	−	8.80264i	−1.71538	−	0.990374i	−0.788482	−	0.615058i	$-0.789133\pi$
$80$	−4.12220	−	10.9177i	−0.460876	−	1.22064i
$81$	−3.09370	−	5.35845i	−0.343745	−	0.595383i
$82$	−9.92319	+	4.40176i	−1.09583	+	0.486093i
$83$	−5.07720	−	5.07720i	−0.557295	−	0.557295i	0.371241	−	0.928536i	$-0.378932\pi$
$83$	−5.07720	−	5.07720i	−0.557295	−	0.557295i	−0.928536	+	0.371241i	$0.878932\pi$
$84$	−7.93576	−	0.152291i	−0.865862	−	0.0166163i
$85$	7.76681	−	7.76681i	0.842429	−	0.842429i
$86$	4.74802	+	1.83009i	0.511993	+	0.197343i
$87$	8.71217	−	5.02997i	0.934042	−	0.539270i
$88$	0.151660	+	0.0993805i	0.0161670	+	0.0105940i
$89$	−4.47814	+	7.75636i	−0.474681	+	0.822172i	−0.999580	−	0.0289926i	$-0.990770\pi$
$89$	−4.47814	+	7.75636i	−0.474681	+	0.822172i	0.524898	+	0.851165i	$0.324103\pi$
$90$	−3.05713	+	0.479896i	−0.322250	+	0.0505855i
$91$	−2.60510	−	13.3299i	−0.273089	−	1.39736i
$92$	−4.66429	−	14.4906i	−0.486286	−	1.51075i
$93$	0.954814	−	0.255842i	0.0990096	−	0.0265295i
$94$	−0.786839	+	7.38857i	−0.0811563	+	0.762073i
$95$	5.59340	−	3.22935i	0.573870	−	0.331324i
$96$	−8.21101	+	2.13977i	−0.838033	+	0.218389i
$97$			1.85612i			0.188460i	0.995550	+	0.0942302i	$0.0300390\pi$
$97$			1.85612i			0.188460i	−0.995550	+	0.0942302i	$0.969961\pi$
$98$	7.12559	+	6.87211i	0.719794	+	0.694188i
$99$	0.0339986	−	0.0339986i	0.00341698	−	0.00341698i
$100$	1.47919	−	6.86616i	0.147919	−	0.686616i
$101$	−4.53028	+	16.9072i	−0.450780	+	1.68233i	0.249427	+	0.968393i	$0.419758\pi$
$101$	−4.53028	+	16.9072i	−0.450780	+	1.68233i	−0.700207	+	0.713940i	$0.746909\pi$
$102$	−5.01746	−	6.21349i	−0.496802	−	0.615227i
$103$	6.82381	+	3.93973i	0.672370	+	0.388193i	0.796974	−	0.604014i	$-0.206433\pi$
$103$	6.82381	+	3.93973i	0.672370	+	0.388193i	−0.124604	+	0.992207i	$0.539766\pi$
$104$	−6.53848	−	12.9644i	−0.641151	−	1.27126i
$105$	−9.60552	−	6.46484i	−0.937403	−	0.630904i
$106$	14.6963	−	2.30696i	1.42743	−	0.224072i
$107$	8.07325	−	2.16322i	0.780470	−	0.209126i	0.153478	−	0.988152i	$-0.450952\pi$
$107$	8.07325	−	2.16322i	0.780470	−	0.209126i	0.626992	+	0.779026i	$0.284286\pi$
$108$	0.557896	+	11.2362i	0.0536835	+	1.08120i
$109$	2.09025	−	7.80091i	0.200210	−	0.747192i	−0.790647	−	0.612272i	$-0.790256\pi$
$109$	2.09025	−	7.80091i	0.200210	−	0.747192i	0.990857	−	0.134920i	$-0.0430777\pi$
$110$	0.107250	+	0.241782i	0.0102259	+	0.0230530i
$111$	6.30072			0.598037
$112$	9.32187	+	5.01027i	0.880834	+	0.473426i
$113$	12.8566			1.20945			0.604725	−	0.796434i	$-0.293283\pi$
$113$	12.8566			1.20945			0.604725	+	0.796434i	$0.293283\pi$
$114$	−1.90418	−	4.29272i	−0.178343	−	0.402050i
$115$	5.74741	−	21.4496i	0.535949	−	2.00019i
$116$	−13.3968	+	0.665176i	−1.24386	+	0.0617600i
$117$	−3.71907	+	0.996523i	−0.343829	+	0.0921286i
$118$	−3.52102	+	0.552715i	−0.324136	+	0.0508815i
$119$	−0.684755	+	9.93725i	−0.0627714	+	0.910946i
$120$	−11.7562	−	3.87348i	−1.07319	−	0.353599i
$121$	9.52272	+	5.49795i	0.865702	+	0.499813i
$122$	−6.34569	−	7.85834i	−0.574512	−	0.711460i
$123$	−2.98007	+	11.1218i	−0.268704	+	1.00282i
$124$	−1.28844	−	0.277570i	−0.115705	−	0.0249266i
$125$	−3.07005	+	3.07005i	−0.274594	+	0.274594i
$126$	1.80464	−	2.14912i	0.160770	−	0.191459i
$127$			15.3580i			1.36280i	0.731912	+	0.681399i	$0.238628\pi$
$127$			15.3580i			1.36280i	−0.731912	+	0.681399i	$0.761372\pi$
$128$	11.0433	+	2.45861i	0.976102	+	0.217313i
$129$	4.67408	−	2.69858i	0.411529	−	0.237597i
$130$	2.24296	−	21.0618i	0.196720	−	1.84724i
$131$	−0.328184	+	0.0879366i	−0.0286736	+	0.00768306i	−0.273127	−	0.961978i	$-0.588058\pi$
$131$	−0.328184	+	0.0879366i	−0.0286736	+	0.00768306i	0.244454	+	0.969661i	$0.421391\pi$
$132$	0.183069	−	0.0589267i	0.0159341	−	0.00512891i
$133$	−1.90127	+	5.53992i	−0.164861	+	0.480372i
$134$	−8.66144	+	1.35964i	−0.748234	+	0.117455i
$135$	−8.20549	+	14.2123i	−0.706216	+	1.22320i
$136$	2.17099	+	10.4249i	0.186161	+	0.893928i
$137$	−7.82357	+	4.51694i	−0.668412	+	0.385908i	−0.795475	−	0.605987i	$-0.792778\pi$
$137$	−7.82357	+	4.51694i	−0.668412	+	0.385908i	0.127062	+	0.991895i	$0.459445\pi$
$138$	−15.0658	−	5.80697i	−1.28248	−	0.494322i
$139$	−3.85776	+	3.85776i	−0.327211	+	0.327211i	−0.851525	−	0.524314i	$-0.824322\pi$
$139$	−3.85776	+	3.85776i	−0.327211	+	0.327211i	0.524314	+	0.851525i	$0.324322\pi$
$140$	7.46105	+	13.5153i	0.630574	+	1.14225i
$141$	5.57274	+	5.57274i	0.469309	+	0.469309i
$142$	−1.40758	+	0.624377i	−0.118121	+	0.0523965i
$143$	0.164547	+	0.285004i	0.0137601	+	0.0238332i
$144$	1.23529	−	2.73396i	0.102941	−	0.227830i
$145$	−16.9453	−	9.78336i	−1.40723	−	0.812464i
$146$	0.0531367	+	0.0387178i	0.00439763	+	0.00320431i
$147$	10.4191	−	1.30076i	0.859350	−	0.107284i
$148$	−7.47483	−	3.83453i	−0.614427	−	0.315197i
$149$	−1.65112	−	6.16207i	−0.135265	−	0.504816i	−0.999997	−	0.00258197i	$-0.999178\pi$
$149$	−1.65112	−	6.16207i	−0.135265	−	0.504816i	0.864732	−	0.502234i	$-0.167489\pi$
$150$	−4.68029	−	5.79595i	−0.382144	−	0.473237i
$151$	1.70746	+	2.95741i	0.138951	+	0.240671i	0.927100	−	0.374814i	$-0.122293\pi$
$151$	1.70746	+	2.95741i	0.138951	+	0.240671i	−0.788149	+	0.615485i	$0.788960\pi$
$152$	−0.353481	+	6.25151i	−0.0286711	+	0.507064i
$153$	2.82370			0.228283
$154$	−0.217355	−	0.101450i	−0.0175149	−	0.00817504i
$155$	−1.35951	−	1.35951i	−0.109198	−	0.109198i
$156$	−15.0552	−	3.24336i	−1.20538	−	0.259676i
$157$	−4.54025	−	1.21656i	−0.362352	−	0.0970918i	0.0730497	−	0.997328i	$-0.476727\pi$
$157$	−4.54025	−	1.21656i	−0.362352	−	0.0970918i	−0.435401	+	0.900236i	$0.643394\pi$
$158$	24.7576	+	2.63654i	1.96961	+	0.209752i
$159$	7.88930	−	13.6647i	0.625662	−	1.08368i
$160$	11.5896	+	11.7499i	0.916234	+	0.928915i
$161$	8.84621	+	18.0908i	0.697179	+	1.42576i
$162$	7.07208	+	5.15303i	0.555635	+	0.404860i
$163$	0.420383	+	1.56889i	0.0329269	+	0.122885i	0.980433	−	0.196852i	$-0.0630720\pi$
$163$	0.420383	+	1.56889i	0.0329269	+	0.122885i	−0.947506	+	0.319737i	$0.896405\pi$
$164$	10.3040	−	11.3806i	0.804604	−	0.888678i
$165$	0.270986	+	0.0726105i	0.0210962	+	0.00565272i
$166$	9.47494	+	3.65204i	0.735398	+	0.283453i
$167$		−	7.81760i		−	0.604944i	−0.953158	−	0.302472i	$-0.902188\pi$
$167$		−	7.81760i		−	0.604944i	0.953158	−	0.302472i	$-0.0978118\pi$
$168$	10.3462	−	4.35378i	0.798225	−	0.335901i
$169$		−	13.3533i		−	1.02718i
$170$	−5.58668	+	14.4942i	−0.428479	+	1.11166i
$171$	1.60380	+	0.429737i	0.122646	+	0.0328628i
$172$	−7.18739	+	0.356867i	−0.548033	+	0.0272108i
$173$	−1.07228	−	4.00179i	−0.0815237	−	0.304251i	0.913110	−	0.407714i	$-0.133674\pi$
$173$	−1.07228	−	4.00179i	−0.0815237	−	0.304251i	−0.994633	+	0.103464i	$0.967007\pi$
$174$	−8.37818	+	11.4983i	−0.635148	+	0.871685i
$175$	−0.638740	+	9.26948i	−0.0482842	+	0.700707i
$176$	−0.253045	−	0.0415057i	−0.0190740	−	0.00312861i
$177$	−1.89016	+	3.27385i	−0.142073	+	0.246078i
$178$	1.34128	−	12.5949i	0.100533	−	0.944025i
$179$	−10.7595	−	2.88301i	−0.804205	−	0.215486i	−0.166776	−	0.985995i	$-0.553336\pi$
$179$	−10.7595	−	2.88301i	−0.804205	−	0.215486i	−0.637429	+	0.770509i	$0.720002\pi$
$180$	3.67688	−	2.37345i	0.274058	−	0.176906i
$181$	4.50721	+	4.50721i	0.335018	+	0.335018i	0.854489	−	0.519470i	$-0.173871\pi$
$181$	4.50721	+	4.50721i	0.335018	+	0.335018i	−0.519470	+	0.854489i	$0.673871\pi$
$182$	11.0116	+	15.7382i	0.816232	+	1.16660i
$183$	−10.7132			−0.791943
$184$	14.3391	+	16.0579i	1.05710	+	1.18380i
$185$	−6.12749	−	10.6131i	−0.450502	−	0.780292i
$186$	−1.08761	+	0.878261i	−0.0797478	+	0.0643972i
$187$	−0.0624661	−	0.233127i	−0.00456797	−	0.0170479i
$188$	−3.21970	−	10.0027i	−0.234821	−	0.729521i
$189$	−2.85450	−	14.6060i	−0.207634	−	1.06243i
$190$	−5.37897	+	7.38216i	−0.390231	+	0.535558i
$191$	14.4515	+	8.34360i	1.04568	+	0.603722i	0.921436	−	0.388530i	$-0.127017\pi$
$191$	14.4515	+	8.34360i	1.04568	+	0.603722i	0.124241	+	0.992252i	$0.460350\pi$
$192$	9.38767	−	7.47465i	0.677497	−	0.539436i
$193$	−1.36382	−	2.36220i	−0.0981697	−	0.170035i	0.812757	−	0.582602i	$-0.197965\pi$
$193$	−1.36382	−	2.36220i	−0.0981697	−	0.170035i	−0.910927	+	0.412567i	$0.864632\pi$
$194$	−1.06437	−	2.39948i	−0.0764171	−	0.172272i
$195$	−15.8856	−	15.8856i	−1.13759	−	1.13759i
$196$	−13.1522	−	4.79776i	−0.939446	−	0.342697i
$197$	3.88713	−	3.88713i	0.276947	−	0.276947i	−0.554942	−	0.831889i	$-0.687260\pi$
$197$	3.88713	−	3.88713i	0.276947	−	0.276947i	0.831889	+	0.554942i	$0.187260\pi$
$198$	−0.0244552	+	0.0634472i	−0.00173796	+	0.00450900i
$199$	−12.5878	+	7.26759i	−0.892329	+	0.515186i	−0.874703	−	0.484659i	$-0.838944\pi$
$199$	−12.5878	+	7.26759i	−0.892329	+	0.515186i	−0.0176251	+	0.999845i	$0.505611\pi$
$200$	2.02511	+	9.72436i	0.143197	+	0.687616i
$201$	−4.64965	+	8.05343i	−0.327961	+	0.568045i
$202$	−3.83876	−	24.4545i	−0.270094	−	1.72061i
$203$	17.4147	−	3.40341i	1.22227	−	0.238872i
$204$	10.0493	+	5.15522i	0.703591	+	0.360937i
$205$	21.6320	−	5.79627i	1.51084	−	0.404829i
$206$	−11.0806	−	1.18002i	−0.772021	−	0.0822156i
$207$	4.94389	−	2.85435i	0.343624	−	0.198391i
$208$	15.8868	+	13.0101i	1.10155	+	0.902090i
$209$		−	0.141917i		−	0.00981663i
$210$	16.1246	+	2.84919i	1.11270	+	0.196613i
$211$	−18.5514	+	18.5514i	−1.27713	+	1.27713i	−0.334867	+	0.942265i	$0.608692\pi$
$211$	−18.5514	+	18.5514i	−1.27713	+	1.27713i	−0.942265	+	0.334867i	$0.891308\pi$
$212$	−17.6756	+	11.4097i	−1.21396	+	0.783621i
$213$	−0.422714	+	1.57759i	−0.0289639	+	0.108095i
$214$	−9.19612	+	7.42597i	−0.628634	+	0.507629i
$215$	−9.09114	−	5.24877i	−0.620010	−	0.357963i
$216$	−7.16444	−	14.2055i	−0.487478	−	0.966562i
$217$	1.73943	+	0.119860i	0.118080	+	0.00813664i
$218$	1.77118	+	11.2832i	0.119960	+	0.764192i
$219$	0.0673581	−	0.0180485i	0.00455164	−	0.00121961i
$220$	−0.277293	−	0.251060i	−0.0186951	−	0.0169264i
$221$	−5.00219	+	18.6684i	−0.336483	+	1.25577i
$222$	−8.14517	+	3.61306i	−0.546668	+	0.242493i
$223$	−22.7321			−1.52225			−0.761126	−	0.648604i	$-0.775353\pi$
$223$	−22.7321			−1.52225			−0.761126	+	0.648604i	$0.775353\pi$
$224$	−14.9238	−	1.13146i	−0.997138	−	0.0755991i
$225$	2.63395			0.175597
$226$	−16.6203	+	7.37246i	−1.10556	+	0.490409i
$227$	0.466286	−	1.74020i	0.0309485	−	0.115501i	−0.948724	−	0.316107i	$-0.897624\pi$
$227$	0.466286	−	1.74020i	0.0309485	−	0.115501i	0.979672	+	0.200605i	$0.0642909\pi$
$228$	4.92321	+	4.45744i	0.326047	+	0.295201i
$229$	14.3174	−	3.83633i	0.946119	−	0.253512i	0.247404	−	0.968912i	$-0.420422\pi$
$229$	14.3174	−	3.83633i	0.946119	−	0.253512i	0.698715	+	0.715400i	$0.253756\pi$
$230$	4.87010	+	31.0245i	0.321125	+	2.04570i
$231$	−0.228552	+	0.111759i	−0.0150376	+	0.00735323i
$232$	16.9371	−	8.54212i	1.11198	−	0.560818i
$233$	−18.4936	−	10.6773i	−1.21156	−	0.699493i	−0.248460	−	0.968642i	$-0.579924\pi$
$233$	−18.4936	−	10.6773i	−1.21156	−	0.699493i	−0.963099	+	0.269149i	$0.913258\pi$
$234$	4.23635	−	3.42089i	0.276939	−	0.223631i
$235$	3.96737	−	14.8064i	0.258802	−	0.965864i
$236$	4.23481	−	2.73360i	0.275662	−	0.177942i
$237$	18.6731	−	18.6731i	1.21295	−	1.21295i
$238$	−4.81317	−	13.2389i	−0.311992	−	0.858152i
$239$		−	0.632980i		−	0.0409441i	−0.999790	−	0.0204720i	$-0.993483\pi$
$239$		−	0.632980i		−	0.0409441i	0.999790	−	0.0204720i	$-0.00651691\pi$
$240$	17.4189	−	1.73403i	1.12438	−	0.111931i
$241$	16.2105	−	9.35914i	1.04421	−	0.602875i	0.123188	−	0.992383i	$-0.460688\pi$
$241$	16.2105	−	9.35914i	1.04421	−	0.602875i	0.921023	+	0.389508i	$0.127355\pi$
$242$	−15.4631	−	1.64673i	−0.994006	−	0.105856i
$243$	−7.33519	+	1.96546i	−0.470553	+	0.126084i
$244$	12.7096	+	6.51992i	0.813647	+	0.417395i
$245$	−12.3236	−	16.2852i	−0.787329	−	1.04042i
$246$	−2.52518	−	16.0864i	−0.160999	−	1.02563i
$247$	−5.68226	+	9.84196i	−0.361553	+	0.626229i
$248$	1.82479	−	0.380013i	0.115874	−	0.0241308i
$249$	9.32737	−	5.38516i	0.591098	−	0.341271i
$250$	2.20829	−	5.72925i	0.139665	−	0.362350i
$251$	11.0434	−	11.0434i	0.697054	−	0.697054i	−0.266720	−	0.963774i	$-0.585940\pi$
$251$	11.0434	−	11.0434i	0.697054	−	0.697054i	0.963774	+	0.266720i	$0.0859400\pi$
$252$	−1.10055	+	3.81309i	−0.0693281	+	0.240202i
$253$	−0.345026	−	0.345026i	−0.0216916	−	0.0216916i
$254$	−8.80681	−	19.8538i	−0.552588	−	1.24574i
$255$	8.23791	+	14.2685i	0.515878	+	0.893526i
$256$	−15.6860	+	3.15431i	−0.980375	+	0.197144i
$257$	−26.9179	−	15.5411i	−1.67909	−	0.969425i	−0.962240	−	0.272201i	$-0.912248\pi$
$257$	−26.9179	−	15.5411i	−1.67909	−	0.969425i	−0.716853	−	0.697224i	$-0.754418\pi$
$258$	−4.49489	+	6.16884i	−0.279840	+	0.384055i
$259$	10.5117	+	3.60753i	0.653162	+	0.224161i
$260$	9.17805	+	28.5136i	0.569198	+	1.76834i
$261$	−1.30189	−	4.85874i	−0.0805853	−	0.300748i
$262$	0.373830	−	0.301872i	0.0230953	−	0.0186497i
$263$	6.47429	+	11.2138i	0.399222	+	0.691473i	0.993630	−	0.112691i	$-0.0359469\pi$
$263$	6.47429	+	11.2138i	0.399222	+	0.691473i	−0.594408	+	0.804164i	$0.702614\pi$
$264$	−0.202869	+	0.181155i	−0.0124857	+	0.0111493i
$265$	−30.6896			−1.88525
$266$	−0.718953	−	8.25192i	−0.0440818	−	0.505958i
$267$	−9.49952	−	9.49952i	−0.581361	−	0.581361i
$268$	10.4173	−	6.72444i	0.636338	−	0.410760i
$269$	−1.48882	−	0.398929i	−0.0907751	−	0.0243231i	0.213146	−	0.977020i	$-0.431629\pi$
$269$	−1.48882	−	0.398929i	−0.0907751	−	0.0243231i	−0.303921	+	0.952697i	$0.598296\pi$
$270$	2.45769	−	23.0781i	0.149570	−	1.40449i
$271$	5.33475	−	9.24005i	0.324063	−	0.561293i	−0.657259	−	0.753664i	$-0.728284\pi$
$271$	5.33475	−	9.24005i	0.324063	−	0.561293i	0.981322	+	0.192371i	$0.0616177\pi$
$272$	−8.78454	−	12.2317i	−0.532641	−	0.741658i
$273$	20.3249	+	1.40054i	1.23012	+	0.0847647i
$274$	7.52364	−	10.3255i	0.454520	−	0.623788i
$275$	−0.0582685	−	0.217461i	−0.00351372	−	0.0131134i
$276$	22.8060	−	1.13236i	1.37276	−	0.0681599i
$277$	24.0573	+	6.44615i	1.44547	+	0.387311i	0.894444	−	0.447180i	$-0.147572\pi$
$277$	24.0573	+	6.44615i	1.44547	+	0.387311i	0.551022	+	0.834491i	$0.314238\pi$
$278$	2.77489	−	7.19924i	0.166427	−	0.431782i
$279$		−	0.494264i		−	0.0295908i
$280$	−17.3954	−	13.1933i	−1.03957	−	0.788453i
$281$		−	15.2176i		−	0.907808i	−0.891051	−	0.453904i	$-0.850031\pi$
$281$		−	15.2176i		−	0.907808i	0.891051	−	0.453904i	$-0.149969\pi$
$282$	−10.3997	−	4.00848i	−0.619293	−	0.238701i
$283$	−21.6985	−	5.81408i	−1.28984	−	0.345611i	−0.452240	−	0.891896i	$-0.649375\pi$
$283$	−21.6985	−	5.81408i	−1.28984	−	0.345611i	−0.837599	+	0.546285i	$0.816042\pi$
$284$	1.46159	−	1.61431i	0.0867292	−	0.0957917i
$285$	2.50744	+	9.35789i	0.148528	+	0.554314i
$286$	−0.376148	−	0.274078i	−0.0222421	−	0.0162066i
$287$	−11.3396	+	16.8485i	−0.669356	+	0.994534i
$288$	−0.0291567	+	4.24266i	−0.00171807	+	0.250001i
$289$	−1.41301	+	2.44741i	−0.0831184	+	0.143965i
$290$	27.5159	+	2.93028i	1.61579	+	0.172072i
$291$	−2.68930	−	0.720595i	−0.157649	−	0.0422421i
$292$	−0.0908941	−	0.0195814i	−0.00531917	−	0.00114592i
$293$	6.75242	+	6.75242i	0.394480	+	0.394480i	0.876281	−	0.481800i	$-0.160017\pi$
$293$	6.75242	+	6.75242i	0.394480	+	0.394480i	−0.481800	+	0.876281i	$0.660017\pi$
$294$	−12.7232	+	7.65621i	−0.742034	+	0.446519i
$295$	7.35277			0.428095
$296$	11.8619	+	0.670708i	0.689456	+	0.0389841i
$297$	0.180300	+	0.312288i	0.0104621	+	0.0181208i
$298$	5.66802	+	7.01913i	0.328340	+	0.406607i
$299$	10.1130	+	37.7421i	0.584848	+	2.18268i
$300$	9.37400	+	4.80879i	0.541208	+	0.277636i
$301$	9.34298	−	1.82593i	0.538521	−	0.105245i
$302$	−3.90319	−	2.84404i	−0.224603	−	0.163656i
$303$	−22.7378	−	13.1277i	−1.30625	−	0.754166i
$304$	−3.12788	−	8.28426i	−0.179396	−	0.475135i
$305$	10.4187	+	18.0457i	0.596571	+	1.03329i
$306$	−3.65031	+	1.61921i	−0.208674	+	0.0925643i
$307$	13.0278	+	13.0278i	0.743535	+	0.743535i	0.973257	−	0.229721i	$-0.0737814\pi$
$307$	13.0278	+	13.0278i	0.743535	+	0.743535i	−0.229721	+	0.973257i	$0.573781\pi$
$308$	0.339157	+	0.00650860i	0.0193253	+	0.000370862i
$309$	−8.35739	+	8.35739i	−0.475435	+	0.475435i
$310$	2.53708	+	0.977897i	0.144097	+	0.0555408i
$311$	−0.115702	+	0.0668004i	−0.00656084	+	0.00378790i	−0.503277	−	0.864125i	$-0.667872\pi$
$311$	−0.115702	+	0.0668004i	−0.00656084	+	0.00378790i	0.496716	+	0.867913i	$0.334539\pi$
$312$	21.3223	−	4.44038i	1.20713	−	0.251387i
$313$	0.970543	−	1.68103i	0.0548583	−	0.0950174i	−0.837292	−	0.546756i	$-0.815863\pi$
$313$	0.970543	−	1.68103i	0.0548583	−	0.0950174i	0.892150	+	0.451738i	$0.149196\pi$
$314$	6.56697	−	1.03086i	0.370596	−	0.0581746i
$315$	−4.36547	+	3.80262i	−0.245966	+	0.214253i
$316$	−33.5170	+	10.7886i	−1.88548	+	0.606904i
$317$	−10.7114	+	2.87011i	−0.601613	+	0.161202i	−0.546755	−	0.837293i	$-0.684137\pi$
$317$	−10.7114	+	2.87011i	−0.601613	+	0.161202i	−0.0548575	+	0.998494i	$0.517470\pi$
$318$	−2.36298	+	22.1888i	−0.132509	+	1.24429i
$319$	−0.372340	+	0.214970i	−0.0208470	+	0.0120360i
$320$	−21.7201	−	8.54373i	−1.21419	−	0.477609i
$321$			12.5370i			0.699747i
$322$	−21.8098	−	18.3140i	−1.21541	−	1.02060i
$323$	5.89337	−	5.89337i	0.327916	−	0.327916i
$324$	−12.0973	−	2.60613i	−0.672071	−	0.144785i
$325$	−4.66604	+	17.4139i	−0.258826	+	0.965950i
$326$	−1.44310	−	1.78710i	−0.0799261	−	0.0989783i
$327$	10.4911	+	6.05705i	0.580160	+	0.334956i
$328$	−6.79424	+	20.6208i	−0.375149	+	1.13859i
$329$	6.10643	+	12.4879i	0.336658	+	0.688479i
$330$	−0.391952	+	0.0615269i	−0.0215762	+	0.00338695i
$331$	24.2423	−	6.49571i	1.33248	−	0.357037i	0.478840	−	0.877902i	$-0.341057\pi$
$331$	24.2423	−	6.49571i	1.33248	−	0.357037i	0.853639	+	0.520865i	$0.174391\pi$
$332$	−14.3428	+	0.712146i	−0.787165	+	0.0390841i
$333$	0.815399	−	3.04311i	0.0446836	−	0.166761i
$334$	4.48289	+	10.1061i	0.245293	+	0.552981i
$335$	18.0873			0.988212
$336$	−10.8783	+	11.5612i	−0.593459	+	0.630713i
$337$	−21.4362			−1.16770			−0.583851	−	0.811861i	$-0.698455\pi$
$337$	−21.4362			−1.16770			−0.583851	+	0.811861i	$0.698455\pi$
$338$	7.65728	+	17.2623i	0.416501	+	0.938948i
$339$	−4.99129	+	18.6278i	−0.271090	+	1.01172i
$340$	−1.08940	−	21.9408i	−0.0590810	−	1.18991i
$341$	−0.0408067	+	0.0109341i	−0.00220981	+	0.000592116i
$342$	−2.31972	+	0.364140i	−0.125436	+	0.0196904i
$343$	18.1272	+	3.79545i	0.978776	+	0.204935i
$344$	9.08677	−	4.58284i	0.489926	−	0.247090i
$345$	28.8467	+	16.6547i	1.55305	+	0.896656i
$346$	3.68095	+	4.55839i	0.197889	+	0.245060i
$347$	−1.16752	+	4.35725i	−0.0626758	+	0.233909i	−0.990157	−	0.139960i	$-0.955303\pi$
$347$	−1.16752	+	4.35725i	−0.0626758	+	0.233909i	0.927481	+	0.373870i	$0.121969\pi$
$348$	4.23724	−	19.6686i	0.227140	−	1.05435i
$349$	−13.4710	+	13.4710i	−0.721087	+	0.721087i	−0.968827	−	0.247739i	$-0.920312\pi$
$349$	−13.4710	+	13.4710i	−0.721087	+	0.721087i	0.247739	+	0.968827i	$0.420312\pi$
$350$	−4.48973	−	12.3493i	−0.239986	−	0.660097i
$351$		−	28.8762i		−	1.54130i
$352$	0.350921	−	0.0914491i	0.0187042	−	0.00487425i
$353$	−14.8316	+	8.56303i	−0.789407	+	0.455764i	−0.839754	−	0.542968i	$-0.817301\pi$
$353$	−14.8316	+	8.56303i	−0.789407	+	0.455764i	0.0503468	+	0.998732i	$0.483967\pi$
$354$	0.566135	−	5.31612i	0.0300897	−	0.282549i
$355$	3.06844	−	0.822185i	0.162856	−	0.0436371i
$356$	5.48843	+	17.0510i	0.290886	+	0.903701i
$357$	−14.1321	−	4.85004i	−0.747948	−	0.256691i
$358$	15.5625	−	2.44293i	0.822502	−	0.129113i
$359$	9.24447	−	16.0119i	0.487904	−	0.845075i	−0.511999	−	0.858986i	$-0.671095\pi$
$359$	9.24447	−	16.0119i	0.487904	−	0.845075i	0.999903	+	0.0139109i	$0.00442811\pi$
$360$	−3.39222	+	5.17670i	−0.178786	+	0.272836i
$361$	−12.2103	+	7.04960i	−0.642646	+	0.371032i
$362$	−8.41124	−	3.24204i	−0.442085	−	0.170398i
$363$	−11.6628	+	11.6628i	−0.612141	+	0.612141i
$364$	−23.2599	−	14.0310i	−1.21915	−	0.735422i
$365$	−0.0959077	−	0.0959077i	−0.00502004	−	0.00502004i
$366$	13.8494	−	6.14334i	0.723918	−	0.321118i
$367$	12.2336	+	21.1892i	0.638587	+	1.10607i	0.985743	+	0.168258i	$0.0538142\pi$
$367$	12.2336	+	21.1892i	0.638587	+	1.10607i	−0.347156	+	0.937807i	$0.612852\pi$
$368$	−27.7449	−	12.5361i	−1.44630	−	0.653487i
$369$	4.98591	+	2.87862i	0.259556	+	0.149855i
$370$	14.0072	+	10.2063i	0.728199	+	0.530598i
$371$	20.9858	−	18.2800i	1.08953	−	0.949052i
$372$	0.902374	−	1.75904i	0.0467859	−	0.0912019i
$373$	−5.27316	−	19.6797i	−0.273034	−	1.01898i	−0.957147	−	0.289601i	$-0.906477\pi$
$373$	−5.27316	−	19.6797i	−0.273034	−	1.01898i	0.684114	−	0.729376i	$-0.260189\pi$
$374$	0.214436	+	0.265551i	0.0110882	+	0.0137313i
$375$	−3.25627	−	5.64002i	−0.168153	−	0.291249i
$376$	9.89813	+	11.0846i	0.510457	+	0.571643i
$377$	34.4290			1.77318
$378$	12.0658	+	17.2449i	0.620596	+	0.886983i
$379$	24.7561	+	24.7561i	1.27163	+	1.27163i	0.945230	+	0.326404i	$0.105837\pi$
$379$	24.7561	+	24.7561i	1.27163	+	1.27163i	0.326404	+	0.945230i	$0.394163\pi$
$380$	2.72040	−	12.6277i	0.139554	−	0.647787i
$381$	−22.2519	−	5.96237i	−1.14000	−	0.305462i
$382$	−23.4666	−	2.49905i	−1.20065	−	0.127863i
$383$	9.84997	−	17.0606i	0.503310	−	0.871758i	−0.496683	−	0.867932i	$-0.665449\pi$
$383$	9.84997	−	17.0606i	0.503310	−	0.871758i	0.999993	−	0.00382628i	$-0.00121794\pi$
$384$	−7.84956	+	15.0460i	−0.400571	+	0.767812i
$385$	0.410520	+	0.276294i	0.0209220	+	0.0140812i
$386$	3.11763	+	2.27164i	0.158683	+	0.115624i
$387$	−0.698466	−	2.60671i	−0.0355050	−	0.132507i
$388$	2.75189	+	2.49155i	0.139706	+	0.126489i
$389$	2.83524	+	0.759700i	0.143752	+	0.0385183i	0.329978	−	0.943989i	$-0.392959\pi$
$389$	2.83524	+	0.759700i	0.143752	+	0.0385183i	−0.186225	+	0.982507i	$0.559625\pi$
$390$	29.6453	+	11.4265i	1.50115	+	0.578605i
$391$		−	28.6557i		−	1.44918i
$392$	19.7536	−	1.33972i	0.997708	−	0.0676662i
$393$		−	0.509639i		−	0.0257079i
$394$	−2.79602	+	7.25407i	−0.140862	+	0.365455i
$395$	−49.6133	−	13.2939i	−2.49632	−	0.668886i
$396$	−0.00476876	−	0.0960442i	−0.000239639	−	0.00482640i
$397$	2.96194	+	11.0541i	0.148656	+	0.554791i	0.999565	+	0.0294787i	$0.00938472\pi$
$397$	2.96194	+	11.0541i	0.148656	+	0.554791i	−0.850910	+	0.525312i	$0.823949\pi$
$398$	12.1053	−	16.6134i	0.606783	−	0.832755i
$399$	−7.28857	−	4.90546i	−0.364885	−	0.245580i
$400$	−8.19423	−	11.4098i	−0.409712	−	0.570489i
$401$	2.80472	−	4.85792i	0.140061	−	0.242593i	−0.787458	−	0.616368i	$-0.788603\pi$
$401$	2.80472	−	4.85792i	0.140061	−	0.242593i	0.927519	+	0.373775i	$0.121937\pi$
$402$	1.39265	−	13.0772i	0.0694590	−	0.652234i
$403$	3.26774	+	0.875587i	0.162778	+	0.0436161i
$404$	18.9856	+	29.4119i	0.944568	+	1.46330i
$405$	−12.7645	−	12.7645i	−0.634275	−	0.634275i
$406$	−20.5610	+	14.3859i	−1.02043	+	0.713962i
$407$	−0.269279			−0.0133477
$408$	−15.9473	−	0.901713i	−0.789509	−	0.0446414i
$409$	16.8193	+	29.1319i	0.831662	+	1.44048i	0.896719	+	0.442600i	$0.145944\pi$
$409$	16.8193	+	29.1319i	0.831662	+	1.44048i	−0.0650570	+	0.997882i	$0.520723\pi$
$410$	−24.6407	+	19.8976i	−1.21692	+	0.982674i
$411$	−3.50719	−	13.0890i	−0.172997	−	0.645634i
$412$	15.0009	−	4.82856i	0.739044	−	0.237886i
$413$	−5.02788	+	4.37963i	−0.247406	+	0.215507i
$414$	−4.75436	+	6.52494i	−0.233664	+	0.320683i
$415$	−18.1419	−	10.4742i	−0.890549	−	0.514158i
$416$	−27.9979	−	7.70862i	−1.37271	−	0.377946i
$417$	−4.09175	−	7.08712i	−0.200374	−	0.347058i
$418$	0.0813805	+	0.183462i	0.00398045	+	0.00897341i
$419$	7.47278	+	7.47278i	0.365069	+	0.365069i	0.865675	−	0.500606i	$-0.166889\pi$
$419$	7.47278	+	7.47278i	0.365069	+	0.365069i	−0.500606	+	0.865675i	$0.666889\pi$
$420$	−22.4787	+	5.56317i	−1.09685	+	0.271455i
$421$	−10.0923	+	10.0923i	−0.491866	+	0.491866i	−0.908894	−	0.417028i	$-0.863072\pi$
$421$	−10.0923	+	10.0923i	−0.491866	+	0.491866i	0.417028	+	0.908894i	$0.363072\pi$
$422$	13.3441	−	34.6202i	0.649579	−	1.68528i
$423$	3.41270	−	1.97032i	0.165931	−	0.0958004i
$424$	16.3071	−	24.8856i	0.791945	−	1.20855i
$425$	6.61075	−	11.4502i	0.320669	−	0.555414i
$426$	−0.358189	−	2.28181i	−0.0173543	−	0.110554i
$427$	−17.8731	−	6.13395i	−0.864942	−	0.296843i
$428$	7.62986	−	14.8732i	0.368803	−	0.718924i
$429$	−0.476818	+	0.127763i	−0.0230210	+	0.00616846i
$430$	14.7623	+	1.57210i	0.711901	+	0.0758132i
$431$	−6.09461	+	3.51872i	−0.293567	+	0.169491i	−0.639549	−	0.768750i	$-0.720879\pi$
$431$	−6.09461	+	3.51872i	−0.293567	+	0.169491i	0.345982	+	0.938241i	$0.387546\pi$
$432$	17.4077	+	14.2556i	0.837528	+	0.685875i
$433$		−	38.5837i		−	1.85422i	−0.374795	−	0.927108i	$-0.622287\pi$
$433$		−	38.5837i		−	1.85422i	0.374795	−	0.927108i	$-0.377713\pi$
$434$	−2.31735	+	0.842502i	−0.111237	+	0.0404414i
$435$	20.7536	−	20.7536i	0.995057	−	0.995057i
$436$	−8.75985	−	13.5705i	−0.419521	−	0.649909i
$437$	4.36108	−	16.2758i	0.208619	−	0.778576i
$438$	−0.0767266	+	0.0619576i	−0.00366614	+	0.00296045i
$439$	−15.4436	−	8.91638i	−0.737084	−	0.425555i	0.0839243	−	0.996472i	$-0.473255\pi$
$439$	−15.4436	−	8.91638i	−0.737084	−	0.425555i	−0.821008	+	0.570917i	$0.806588\pi$
$440$	0.502435	+	0.165544i	0.0239526	+	0.00789202i
$441$	0.720134	−	5.20052i	0.0342921	−	0.247644i
$442$	−4.23863	−	27.0018i	−0.201611	−	1.28434i
$443$	8.51469	−	2.28150i	0.404545	−	0.108397i	−0.0508081	−	0.998708i	$-0.516180\pi$
$443$	8.51469	−	2.28150i	0.404545	−	0.108397i	0.455353	+	0.890311i	$0.349513\pi$
$444$	8.45771	−	9.34147i	0.401385	−	0.443327i
$445$	−6.76294	+	25.2396i	−0.320594	+	1.19647i
$446$	29.3866	−	13.0354i	1.39150	−	0.617244i
$447$	9.56912			0.452604
$448$	19.9414	−	7.09516i	0.942142	−	0.335215i
$449$	14.4915			0.683898			0.341949	−	0.939718i	$-0.388913\pi$
$449$	14.4915			0.683898			0.341949	+	0.939718i	$0.388913\pi$
$450$	−3.40501	+	1.51041i	−0.160514	+	0.0712012i
$451$	0.127362	−	0.475321i	0.00599723	−	0.0223820i
$452$	17.2580	−	19.0613i	0.811748	−	0.896569i
$453$	−4.94783	+	1.32577i	−0.232469	+	0.0622899i
$454$	0.395110	+	2.51701i	0.0185434	+	0.118129i
$455$	−17.4069	−	35.5978i	−0.816050	−	1.66885i
$456$	−8.92047	−	2.93916i	−0.417739	−	0.137639i
$457$	−2.59164	−	1.49628i	−0.121232	−	0.0699932i	0.438158	−	0.898898i	$-0.355631\pi$
$457$	−2.59164	−	1.49628i	−0.121232	−	0.0699932i	−0.559390	+	0.828905i	$0.688964\pi$
$458$	−16.3087	+	13.1695i	−0.762057	+	0.615369i
$459$	−5.48107	+	20.4556i	−0.255834	+	0.954786i
$460$	−24.0864	−	37.3139i	−1.12303	−	1.73977i
$461$	6.89015	−	6.89015i	0.320906	−	0.320906i	−0.528209	−	0.849115i	$-0.677136\pi$
$461$	6.89015	−	6.89015i	0.320906	−	0.320906i	0.849115	+	0.528209i	$0.177136\pi$
$462$	0.231371	−	0.275536i	0.0107644	−	0.0128191i
$463$			28.9432i			1.34511i	0.740049	+	0.672553i	$0.234802\pi$
$463$			28.9432i			1.34511i	−0.740049	+	0.672553i	$0.765198\pi$
$464$	−16.9969	+	20.7551i	−0.789062	+	0.963531i
$465$	2.49757	−	1.44197i	0.115822	−	0.0668698i
$466$	30.0302	+	3.19803i	1.39112	+	0.148146i
$467$	−23.9512	+	6.41771i	−1.10833	+	0.296976i	−0.766152	−	0.642659i	$-0.777831\pi$
$467$	−23.9512	+	6.41771i	−1.10833	+	0.296976i	−0.342177	+	0.939635i	$0.611164\pi$
$468$	−3.51482	+	6.85159i	−0.162473	+	0.316715i
$469$	−12.3682	+	10.7736i	−0.571111	+	0.497476i
$470$	3.36177	+	21.4158i	0.155067	+	0.987839i
$471$	3.52530	−	6.10599i	0.162437	−	0.281349i
$472$	−3.90695	+	5.96221i	−0.179832	+	0.274433i
$473$	−0.199760	+	0.115332i	−0.00918498	+	0.00530295i
$474$	−13.4316	+	34.8473i	−0.616934	+	1.60059i
$475$	5.49735	−	5.49735i	0.252236	−	0.252236i
$476$	13.8138	+	14.3544i	0.633157	+	0.657933i
$477$	−5.57876	−	5.57876i	−0.255434	−	0.255434i
$478$	0.362974	+	0.818278i	0.0166020	+	0.0374271i
$479$	−5.53947	−	9.59464i	−0.253105	−	0.438390i	0.711274	−	0.702915i	$-0.248118\pi$
$479$	−5.53947	−	9.59464i	−0.253105	−	0.438390i	−0.964379	+	0.264524i	$0.914785\pi$
$480$	−21.5237	+	12.2302i	−0.982416	+	0.558232i
$481$	18.6745	+	10.7817i	0.851484	+	0.491604i
$482$	−15.5891	+	21.3946i	−0.710063	+	0.974498i
$483$	−29.6458	+	5.79377i	−1.34893	+	0.263626i
$484$	20.9340	−	6.73831i	0.951547	−	0.306287i
$485$	1.40157	+	5.23072i	0.0636419	+	0.237515i
$486$	8.35541	−	6.74709i	0.379009	−	0.306054i
$487$	11.0071	+	19.0648i	0.498779	+	0.863910i	0.999999	−	0.00140957i	$-0.000448679\pi$
$487$	11.0071	+	19.0648i	0.498779	+	0.863910i	−0.501220	+	0.865320i	$0.667115\pi$
$488$	−20.1689	−	1.14042i	−0.913003	−	0.0516242i
$489$	−2.43634			−0.110175
$490$	25.2698	+	13.9857i	1.14157	+	0.631809i
$491$	−18.0641	−	18.0641i	−0.815221	−	0.815221i	0.170191	−	0.985411i	$-0.445562\pi$
$491$	−18.0641	−	18.0641i	−0.815221	−	0.815221i	−0.985411	+	0.170191i	$0.945562\pi$
$492$	12.4889	+	19.3475i	0.563044	+	0.872252i
$493$	−24.3891	−	6.53504i	−1.09843	−	0.294324i
$494$	1.70193	−	15.9815i	0.0765736	−	0.719041i
$495$	0.0701387	−	0.121484i	0.00315250	−	0.00546029i
$496$	−2.14106	+	1.53765i	−0.0961362	+	0.0690427i
$497$	−1.60849	+	2.38991i	−0.0721507	+	0.107202i
$498$	−8.96980	+	12.3102i	−0.401946	+	0.551635i
$499$	0.618516	+	2.30833i	0.0276886	+	0.103335i	0.978387	−	0.206781i	$-0.0662987\pi$
$499$	0.618516	+	2.30833i	0.0276886	+	0.103335i	−0.950699	+	0.310116i	$0.899632\pi$
$500$	0.430617	+	8.67274i	0.0192578	+	0.387857i
$501$	11.3268	+	3.03500i	0.506043	+	0.135594i
$502$	−7.94354	+	20.6089i	−0.354538	+	0.919821i
$503$			15.2639i			0.680582i	0.940320	+	0.340291i	$0.110526\pi$
$503$			15.2639i			0.680582i	−0.940320	+	0.340291i	$0.889474\pi$
$504$	−0.763844	−	5.56042i	−0.0340243	−	0.247681i
$505$			51.0670i			2.27245i
$506$	0.643879	+	0.248178i	0.0286239	+	0.0110328i
$507$	19.3474	+	5.18412i	0.859248	+	0.230235i
$508$	22.7698	+	20.6156i	1.01025	+	0.914671i
$509$	−4.48980	−	16.7561i	−0.199007	−	0.742703i	−0.991193	−	0.132424i	$-0.957724\pi$
$509$	−4.48980	−	16.7561i	−0.199007	−	0.742703i	0.792186	−	0.610279i	$-0.208943\pi$
$510$	−18.8315	−	13.7215i	−0.833873	−	0.607597i
$511$	0.122709	+	0.00845563i	0.00542833	+	0.000374055i
$512$	18.4691	−	13.0726i	0.816226	−	0.577733i
$513$	−6.22624	+	10.7842i	−0.274895	+	0.476133i
$514$	43.7096	+	4.65481i	1.92795	+	0.205315i
$515$	22.2051	+	5.94983i	0.978472	+	0.262181i
$516$	2.27328	−	10.5522i	0.100076	−	0.464536i
$517$	−0.238167	−	0.238167i	−0.0104746	−	0.0104746i
$518$	−15.6575	+	1.36417i	−0.687951	+	0.0599381i
$519$	6.21441			0.272782
$520$	−28.2155	−	31.5976i	−1.23733	−	1.38565i
$521$	3.31388	+	5.73981i	0.145184	+	0.251466i	0.929441	−	0.368970i	$-0.120289\pi$
$521$	3.31388	+	5.73981i	0.145184	+	0.251466i	−0.784258	+	0.620435i	$0.786956\pi$
$522$	4.46919	+	5.53452i	0.195611	+	0.242239i
$523$	−6.67146	−	24.8982i	−0.291723	−	1.08872i	−0.943785	−	0.330559i	$-0.892763\pi$
$523$	−6.67146	−	24.8982i	−0.291723	−	1.08872i	0.652063	−	0.758165i	$-0.273904\pi$
$524$	−0.310160	+	0.604608i	−0.0135494	+	0.0264124i
$525$	−13.1824	−	4.52412i	−0.575327	−	0.197449i
$526$	−14.8000	−	10.7839i	−0.645309	−	0.470201i
$527$	−2.14863	−	1.24051i	−0.0935959	−	0.0540376i
$528$	0.158376	−	0.350518i	0.00689241	−	0.0152544i
$529$	−17.4667	−	30.2532i	−0.759422	−	1.31536i
$530$	39.6736	−	17.5985i	1.72331	−	0.764430i
$531$	1.33659	+	1.33659i	0.0580030	+	0.0580030i
$532$	5.66137	+	10.2553i	0.245451	+	0.444623i
$533$	−27.8640	+	27.8640i	−1.20692	+	1.20692i
$534$	17.7278	+	6.83302i	0.767155	+	0.295694i
$535$	21.1177	−	12.1923i	0.912999	−	0.527120i
$536$	−9.61080	+	14.6666i	−0.415124	+	0.633500i
$537$	8.35428	−	14.4700i	0.360514	−	0.624428i
$538$	2.15342	−	0.338034i	0.0928404	−	0.0145737i
$539$	−0.445289	+	0.0555915i	−0.0191800	+	0.00239450i
$540$	10.0567	+	31.2433i	0.432772	+	1.34450i
$541$	−6.62484	+	1.77512i	−0.284824	+	0.0763184i	−0.398403	−	0.917211i	$-0.630435\pi$
$541$	−6.62484	+	1.77512i	−0.284824	+	0.0763184i	0.113579	+	0.993529i	$0.463769\pi$
$542$	−1.59785	+	15.0041i	−0.0686334	+	0.644481i
$543$	−8.28024	+	4.78060i	−0.355339	+	0.205155i
$544$	18.3702	+	10.7751i	0.787617	+	0.461977i
$545$		−	23.5621i		−	1.00929i
$546$	−27.0778	+	9.84447i	−1.15882	+	0.421304i
$547$	8.23199	−	8.23199i	0.351974	−	0.351974i	−0.508869	−	0.860844i	$-0.669936\pi$
$547$	8.23199	−	8.23199i	0.351974	−	0.351974i	0.860844	+	0.508869i	$0.169936\pi$
$548$	−3.80506	+	17.6625i	−0.162544	+	0.754506i
$549$	−1.38644	+	5.17425i	−0.0591716	+	0.220832i
$550$	0.200026	+	0.247707i	0.00852913	+	0.0105622i
$551$	−12.8579	−	7.42351i	−0.547765	−	0.316252i
$552$	−28.8328	+	14.5416i	−1.22721	+	0.618933i
$553$	41.8444	−	20.4614i	1.77940	−	0.870108i
$554$	−34.7963	+	5.46218i	−1.47835	+	0.232066i
$555$	17.7560	−	4.75771i	0.753701	−	0.201953i
$556$	0.541103	+	10.8980i	0.0229479	+	0.462176i
$557$	7.05595	−	26.3332i	0.298970	−	1.11577i	−0.639043	−	0.769171i	$-0.720669\pi$
$557$	7.05595	−	26.3332i	0.298970	−	1.11577i	0.938013	−	0.346600i	$-0.112664\pi$
$558$	0.283429	+	0.638954i	0.0119985	+	0.0270491i
$559$	18.4711			0.781246
$560$	30.0532	+	7.08040i	1.26998	+	0.299202i
$561$	0.362024			0.0152847
$562$	8.72634	+	19.6724i	0.368098	+	0.829830i
$563$	−0.167327	+	0.624473i	−0.00705199	+	0.0263184i	−0.969362	−	0.245636i	$-0.921003\pi$
$563$	−0.167327	+	0.624473i	−0.00705199	+	0.0263184i	0.962310	+	0.271954i	$0.0876699\pi$
$564$	15.7427	−	0.781652i	0.662887	−	0.0329135i
$565$	36.2312	−	9.70813i	1.52426	−	0.408424i
$566$	31.3844	−	4.92659i	1.31919	−	0.207080i
$567$	16.3316	+	1.12538i	0.685863	+	0.0472614i
$568$	−0.963745	+	2.92501i	−0.0404378	+	0.122731i
$569$	−17.1431	−	9.89757i	−0.718676	−	0.414928i	0.0955892	−	0.995421i	$-0.469526\pi$
$569$	−17.1431	−	9.89757i	−0.718676	−	0.414928i	−0.814265	+	0.580493i	$0.802860\pi$
$570$	−8.60761	−	10.6594i	−0.360533	−	0.446475i
$571$	2.77408	−	10.3530i	0.116092	−	0.433260i	−0.883275	−	0.468856i	$-0.844666\pi$
$571$	2.77408	−	10.3530i	0.116092	−	0.433260i	0.999366	+	0.0355961i	$0.0113330\pi$
$572$	0.643427	+	0.138614i	0.0269030	+	0.00579575i
$573$	−17.6994	+	17.6994i	−0.739402	+	0.739402i
$574$	4.99760	−	28.2832i	0.208596	−	1.18052i
$575$		−	26.7300i		−	1.11472i
$576$	−2.39520	−	5.50136i	−0.0998001	−	0.229224i
$577$	−20.6057	+	11.8967i	−0.857828	+	0.495267i	−0.863284	−	0.504718i	$-0.831597\pi$
$577$	−20.6057	+	11.8967i	−0.857828	+	0.495267i	0.00545613	+	0.999985i	$0.498263\pi$
$578$	0.423221	−	3.97413i	0.0176037	−	0.165302i
$579$	3.95202	−	1.05894i	0.164240	−	0.0440081i
$580$	−37.2512	+	11.9905i	−1.54677	+	0.497880i
$581$	18.6444	−	3.64373i	0.773501	−	0.151168i
$582$	3.88977	−	0.610600i	0.161236	−	0.0253102i
$583$	−0.337172	+	0.583999i	−0.0139642	+	0.0241868i
$584$	0.128731	−	0.0268083i	0.00532692	−	0.00110934i
$585$	−9.72822	+	5.61659i	−0.402212	+	0.232217i
$586$	−12.6012	−	4.85702i	−0.520550	−	0.200642i
$587$	−18.9775	+	18.9775i	−0.783286	+	0.783286i	−0.980384	−	0.197098i	$-0.936848\pi$
$587$	−18.9775	+	18.9775i	−0.783286	+	0.783286i	0.197098	+	0.980384i	$0.436848\pi$
$588$	12.0574	−	17.1934i	0.497241	−	0.709045i
$589$	−1.03158	−	1.03158i	−0.0425056	−	0.0425056i
$590$	−9.50521	+	4.21635i	−0.391323	+	0.173584i
$591$	4.12291	+	7.14109i	0.169594	+	0.293745i
$592$	−15.7189	+	5.93497i	−0.646042	+	0.243926i
$593$	0.728860	+	0.420807i	0.0299307	+	0.0172805i	0.514891	−	0.857256i	$-0.327833\pi$
$593$	0.728860	+	0.420807i	0.0299307	+	0.0172805i	−0.484960	+	0.874536i	$0.661166\pi$
$594$	−0.412158	−	0.300317i	−0.0169110	−	0.0123221i
$595$	5.57397	+	28.5212i	0.228511	+	1.16925i
$596$	−11.3523	−	5.82364i	−0.465008	−	0.238546i
$597$	−5.64295	−	21.0598i	−0.230951	−	0.861919i
$598$	−34.7161	−	42.9915i	−1.41965	−	1.75805i
$599$	−0.848110	−	1.46897i	−0.0346529	−	0.0600205i	0.848179	−	0.529710i	$-0.177699\pi$
$599$	−0.848110	−	1.46897i	−0.0346529	−	0.0600205i	−0.882832	+	0.469689i	$0.844366\pi$
$600$	−14.8757	−	0.841119i	−0.607296	−	0.0343385i
$601$	−28.0938			−1.14597			−0.572984	−	0.819566i	$-0.694214\pi$
$601$	−28.0938			−1.14597			−0.572984	+	0.819566i	$0.694214\pi$
$602$	−11.0310	+	7.71805i	−0.449589	+	0.314564i
$603$	3.28790	+	3.28790i	0.133894	+	0.133894i
$604$	6.67668	+	1.43837i	0.271670	+	0.0585263i
$605$	30.9875	+	8.30306i	1.25982	+	0.337568i
$606$	36.9219	+	3.93197i	1.49985	+	0.159725i
$607$	−19.5443	+	33.8517i	−0.793277	+	1.37400i	0.130650	+	0.991428i	$0.458293\pi$
$607$	−19.5443	+	33.8517i	−0.793277	+	1.37400i	−0.923927	+	0.382568i	$0.875040\pi$
$608$	8.79403	+	8.91574i	0.356645	+	0.361581i
$609$	−1.82972	+	26.5531i	−0.0741441	+	1.07599i
$610$	−23.8166	−	17.3539i	−0.964307	−	0.702637i
$611$	6.98085	+	26.0529i	0.282415	+	1.05399i
$612$	3.79038	−	4.18644i	0.153217	−	0.169227i
$613$	−7.15084	−	1.91606i	−0.288820	−	0.0773891i	0.111500	−	0.993764i	$-0.464434\pi$
$613$	−7.15084	−	1.91606i	−0.288820	−	0.0773891i	−0.400320	+	0.916375i	$0.631101\pi$
$614$	−24.3121	−	9.37091i	−0.981158	−	0.378179i
$615$			33.5925i			1.35458i
$616$	−0.442174	+	0.186071i	−0.0178157	+	0.00749703i
$617$		−	11.3503i		−	0.456945i	−0.973550	−	0.228472i	$-0.926627\pi$
$617$		−	11.3503i		−	0.456945i	0.973550	−	0.228472i	$-0.0733731\pi$
$618$	6.01148	−	15.5963i	0.241817	−	0.627377i
$619$	29.8682	+	8.00317i	1.20051	+	0.321675i	0.803030	−	0.595938i	$-0.203220\pi$
$619$	29.8682	+	8.00317i	1.20051	+	0.321675i	0.397476	+	0.917613i	$0.369886\pi$
$620$	−3.84054	+	0.190690i	−0.154240	+	0.00765828i
$621$	11.0811	+	41.3553i	0.444670	+	1.65953i
$622$	0.111266	−	0.152703i	0.00446136	−	0.00612283i
$623$	−10.4093	−	21.2873i	−0.417038	−	0.852859i
$624$	−25.0178	+	17.9672i	−1.00151	+	0.719263i
$625$	−15.1131	+	26.1766i	−0.604524	+	1.04707i
$626$	−0.290694	+	2.72968i	−0.0116185	+	0.109100i
$627$	0.205621	+	0.0550961i	0.00821173	+	0.00220033i
$628$	−7.89824	+	5.09837i	−0.315174	+	0.203447i
$629$	−11.1823	−	11.1823i	−0.445868	−	0.445868i
$630$	3.46284	−	7.41911i	0.137963	−	0.295584i
$631$	−11.1640			−0.444430			−0.222215	−	0.974998i	$-0.571329\pi$
$631$	−11.1640			−0.444430			−0.222215	+	0.974998i	$0.571329\pi$
$632$	37.1422	−	33.1667i	1.47744	−	1.31930i
$633$	−19.6767	−	34.0810i	−0.782077	−	1.35460i
$634$	12.2012	−	9.85261i	0.484572	−	0.391297i
$635$	11.5969	+	43.2802i	0.460209	+	1.71752i
$636$	−9.66917	−	30.0394i	−0.383408	−	1.19114i
$637$	33.1066	+	13.9737i	1.31173	+	0.553660i
$638$	0.358066	−	0.491413i	0.0141760	−	0.0194552i
$639$	0.707238	+	0.408324i	0.0279779	+	0.0161531i
$640$	32.9777	−	1.41029i	1.30356	−	0.0557465i
$641$	3.95262	+	6.84614i	0.156119	+	0.270406i	0.933466	−	0.358666i	$-0.116768\pi$
$641$	3.95262	+	6.84614i	0.156119	+	0.270406i	−0.777347	+	0.629072i	$0.783435\pi$
$642$	−7.18917	−	16.2071i	−0.283734	−	0.639642i
$643$	−1.49041	−	1.49041i	−0.0587758	−	0.0587758i	0.677108	−	0.735884i	$-0.263233\pi$
$643$	−1.49041	−	1.49041i	−0.0587758	−	0.0587758i	−0.735884	+	0.677108i	$0.763233\pi$
$644$	38.6962	+	11.1686i	1.52484	+	0.440106i
$645$	11.1343	−	11.1343i	0.438412	−	0.438412i
$646$	−4.23911	+	10.9981i	−0.166786	+	0.432713i
$647$	8.79347	−	5.07691i	0.345707	−	0.199594i	−0.317086	−	0.948397i	$-0.602704\pi$
$647$	8.79347	−	5.07691i	0.345707	−	0.199594i	0.662793	+	0.748803i	$0.269371\pi$
$648$	17.1331	−	3.56797i	0.673050	−	0.140163i
$649$	0.0807815	−	0.139918i	0.00317095	−	0.00549225i
$650$	−3.95380	−	25.1873i	−0.155081	−	0.987927i
$651$	−0.848955	+	2.47369i	−0.0332732	+	0.0969516i
$652$	2.89034	+	1.48272i	0.113194	+	0.0580680i
$653$	20.3975	−	5.46551i	0.798218	−	0.213882i	0.163416	−	0.986557i	$-0.447749\pi$
$653$	20.3975	−	5.46551i	0.798218	−	0.213882i	0.634801	+	0.772675i	$0.281082\pi$
$654$	−17.0356	−	1.81419i	−0.666144	−	0.0709404i
$655$	−0.858452	+	0.495627i	−0.0335425	+	0.0193658i
$656$	−3.04156	−	30.5534i	−0.118753	−	1.19291i
$657$		−	0.0348682i		−	0.00136034i
$658$	−15.0550	−	12.6419i	−0.586905	−	0.492833i
$659$	−12.2016	+	12.2016i	−0.475308	+	0.475308i	−0.903627	−	0.428319i	$-0.859106\pi$
$659$	−12.2016	+	12.2016i	−0.475308	+	0.475308i	0.428319	+	0.903627i	$0.359106\pi$
$660$	0.471409	−	0.304297i	0.0183496	−	0.0118448i
$661$	10.8248	−	40.3987i	0.421036	−	1.57133i	−0.351393	−	0.936228i	$-0.614292\pi$
$661$	10.8248	−	40.3987i	0.421036	−	1.57133i	0.772429	−	0.635101i	$-0.219041\pi$
$662$	−27.6141	+	22.2987i	−1.07325	+	0.866663i
$663$	−25.1063	−	14.4952i	−0.975049	−	0.562945i
$664$	18.1331	−	9.14531i	0.703702	−	0.354907i
$665$	−1.17472	+	17.0477i	−0.0455537	+	0.661081i
$666$	0.690933	+	4.40152i	0.0267731	+	0.170556i
$667$	−49.3077	+	13.2120i	−1.90920	+	0.511569i
$668$	−11.5904	−	10.4939i	−0.448446	−	0.406021i
$669$	8.82520	−	32.9361i	0.341202	−	1.27338i
$670$	−23.3821	+	10.3719i	−0.903329	+	0.400701i
$671$	0.457860			0.0176755
$672$	7.43318	−	21.1836i	0.286741	−	0.817174i
$673$	28.4793			1.09780			0.548899	−	0.835889i	$-0.315047\pi$
$673$	28.4793			1.09780			0.548899	+	0.835889i	$0.315047\pi$
$674$	27.7113	−	12.2923i	1.06740	−	0.473481i
$675$	−5.11274	+	19.0810i	−0.196790	+	0.734429i
$676$	−19.7977	−	17.9247i	−0.761451	−	0.689413i
$677$	30.3235	−	8.12515i	1.16543	−	0.312275i	0.376295	−	0.926500i	$-0.377198\pi$
$677$	30.3235	−	8.12515i	1.16543	−	0.312275i	0.789131	+	0.614225i	$0.210531\pi$
$678$	−4.22940	−	26.9430i	−0.162429	−	1.03474i
$679$	−4.07405	−	2.74197i	−0.156348	−	0.105227i
$680$	13.9900	+	27.7390i	0.536491	+	1.06374i
$681$	2.34033	+	1.35119i	0.0896815	+	0.0517776i
$682$	0.0464824	−	0.0375350i	0.00177990	−	0.00143729i
$683$	0.723851	−	2.70145i	0.0276974	−	0.103368i	−0.950693	−	0.310132i	$-0.899627\pi$
$683$	0.723851	−	2.70145i	0.0276974	−	0.103368i	0.978391	+	0.206764i	$0.0662933\pi$
$684$	2.78998	−	1.80095i	0.106677	−	0.0688610i
$685$	−18.6368	+	18.6368i	−0.712075	+	0.712075i
$686$	−25.6101	+	5.48826i	−0.977800	+	0.209543i
$687$			22.2336i			0.848263i
$688$	−9.11884	+	11.1351i	−0.347653	+	0.424522i
$689$	46.7657	−	27.0002i	1.78163	−	1.02863i
$690$	−46.8416	−	4.98835i	−1.78323	−	0.189903i
$691$	−18.0563	+	4.83818i	−0.686895	+	0.184053i	−0.585353	−	0.810778i	$-0.699044\pi$
$691$	−18.0563	+	4.83818i	−0.686895	+	0.184053i	−0.101542	+	0.994831i	$0.532377\pi$
$692$	−7.37244	−	3.78201i	−0.280258	−	0.143770i
$693$	0.0243996	+	0.124849i	0.000926865	+	0.00474263i
$694$	−0.989305	−	6.30228i	−0.0375535	−	0.239231i
$695$	−7.95850	+	13.7845i	−0.301883	+	0.522877i
$696$	5.80107	+	27.8562i	0.219889	+	1.05589i
$697$	25.0275	−	14.4496i	0.947984	−	0.547319i
$698$	9.68973	−	25.1393i	0.366762	−	0.951536i
$699$	22.6499	−	22.6499i	0.856697	−	0.856697i
$700$	12.8856	+	13.3898i	0.487029	+	0.506087i
$701$	−8.68328	−	8.68328i	−0.327963	−	0.327963i	0.523848	−	0.851811i	$-0.324496\pi$
$701$	−8.68328	−	8.68328i	−0.327963	−	0.327963i	−0.851811	+	0.523848i	$0.824496\pi$
$702$	16.5587	+	37.3294i	0.624967	+	1.40891i
$703$	−4.64947	−	8.05312i	−0.175358	−	0.303729i
$704$	−0.401209	+	0.319451i	−0.0151211	+	0.0120398i
$705$	19.9125	+	11.4965i	0.749949	+	0.432983i
$706$	14.2630	−	19.5747i	0.536796	−	0.736705i
$707$	−30.4177	−	34.9200i	−1.14398	−	1.31330i
$708$	2.31659	+	7.19699i	0.0870628	+	0.270479i
$709$	5.08085	+	18.9620i	0.190815	+	0.712132i	0.993311	+	0.115474i	$0.0368385\pi$
$709$	5.08085	+	18.9620i	0.190815	+	0.712132i	−0.802495	+	0.596658i	$0.796495\pi$
$710$	−3.49521	+	2.82242i	−0.131173	+	0.105924i
$711$	−6.60216	−	11.4353i	−0.247600	−	0.428857i
$712$	−16.8728	−	18.8952i	−0.632333	−	0.708127i
$713$	−5.01591			−0.187847
$714$	21.0502	−	1.83401i	0.787785	−	0.0686362i
$715$	0.678917	+	0.678917i	0.0253901	+	0.0253901i
$716$	−18.7173	+	12.0822i	−0.699499	+	0.451531i
$717$	0.917114	+	0.245740i	0.0342502	+	0.00917733i
$718$	−2.76888	+	26.0003i	−0.103334	+	0.970322i
$719$	−0.995256	+	1.72383i	−0.0371168	+	0.0642882i	−0.883987	−	0.467511i	$-0.845151\pi$
$719$	−0.995256	+	1.72383i	−0.0371168	+	0.0642882i	0.846870	+	0.531800i	$0.178484\pi$
$720$	1.41674	−	8.63734i	0.0527988	−	0.321895i
$721$	−18.7280	+	9.15776i	−0.697466	+	0.341053i
$722$	11.7422	−	16.1151i	0.436999	−	0.599742i
$723$	7.26694	+	27.1206i	0.270260	+	1.00863i
$724$	12.7326	−	0.632198i	0.473205	−	0.0234954i
$725$	−22.7502	−	6.09590i	−0.844921	−	0.226396i
$726$	8.38910	−	21.7649i	0.311349	−	0.807771i
$727$			24.4403i			0.906440i	0.891399	+	0.453220i	$0.149725\pi$
$727$			24.4403i			0.906440i	−0.891399	+	0.453220i	$0.850275\pi$
$728$	38.1149	+	4.80026i	1.41263	+	0.177909i
$729$		−	29.9531i		−	1.10937i
$730$	0.178980	+	0.0689865i	0.00662436	+	0.00255331i
$731$	−13.0848	−	3.50605i	−0.483957	−	0.129676i
$732$	−14.3808	+	15.8835i	−0.531529	+	0.587070i
$733$	−6.67020	−	24.8935i	−0.246369	−	0.919463i	−0.972690	−	0.232107i	$-0.925438\pi$
$733$	−6.67020	−	24.8935i	−0.246369	−	0.919463i	0.726321	−	0.687356i	$-0.241229\pi$
$734$	−27.9654	−	20.3769i	−1.03222	−	0.752124i
$735$	28.3797	−	11.5332i	1.04680	−	0.425407i
$736$	43.0556	+	0.295889i	1.58705	+	0.0109066i
$737$	0.198716	−	0.344187i	0.00731980	−	0.0126783i
$738$	−8.09618	−	0.862195i	−0.298025	−	0.0317378i
$739$	−30.3564	−	8.13399i	−1.11668	−	0.299214i	−0.347141	−	0.937813i	$-0.612847\pi$
$739$	−30.3564	−	8.13399i	−1.11668	−	0.299214i	−0.769539	+	0.638600i	$0.779514\pi$
$740$	−23.9602	−	5.16179i	−0.880796	−	0.189751i
$741$	−12.0538	−	12.0538i	−0.442809	−	0.442809i
$742$	−16.6466	+	35.6653i	−0.611118	+	1.30931i
$743$	12.7380			0.467313			0.233656	−	0.972319i	$-0.424931\pi$
$743$	12.7380			0.467313			0.233656	+	0.972319i	$0.424931\pi$
$744$	−0.157837	+	2.79143i	−0.00578657	+	0.102339i
$745$	−9.30603	−	16.1185i	−0.340947	−	0.590537i
$746$	18.1019	+	22.4169i	0.662757	+	0.820740i
$747$	−1.39383	−	5.20183i	−0.0509975	−	0.190325i
$748$	−0.429486	−	0.220323i	−0.0157036	−	0.00805581i
$749$	−7.17818	+	20.9158i	−0.262285	+	0.764248i
$750$	7.44369	+	5.42381i	0.271805	+	0.198049i
$751$	12.0504	+	6.95728i	0.439724	+	0.253875i	0.703481	−	0.710715i	$-0.251628\pi$
$751$	12.0504	+	6.95728i	0.439724	+	0.253875i	−0.263757	+	0.964589i	$0.584962\pi$
$752$	−19.1520	−	8.65348i	−0.698401	−	0.315560i
$753$	11.7132	+	20.2879i	0.426854	+	0.739334i
$754$	−44.5076	+	19.7428i	−1.62087	+	0.718991i
$755$	7.04496	+	7.04496i	0.256392	+	0.256392i
$756$	−25.4867	−	15.3742i	−0.926943	−	0.559155i
$757$	−6.51961	+	6.51961i	−0.236959	+	0.236959i	−0.815590	−	0.578631i	$-0.803587\pi$
$757$	−6.51961	+	6.51961i	−0.236959	+	0.236959i	0.578631	+	0.815590i	$0.303587\pi$
$758$	−46.1992	−	17.8071i	−1.67803	−	0.646782i
$759$	0.633850	−	0.365954i	0.0230073	−	0.0132833i
$760$	3.72441	+	17.8843i	0.135099	+	0.648730i
$761$	−10.3566	+	17.9382i	−0.375428	+	0.650260i	−0.990391	−	0.138296i	$-0.955838\pi$
$761$	−10.3566	+	17.9382i	−0.375428	+	0.650260i	0.614963	+	0.788556i	$0.289171\pi$
$762$	32.1849	−	5.05225i	1.16594	−	0.183024i
$763$	14.0346	+	16.1119i	0.508086	+	0.583291i
$764$	31.7692	−	10.2260i	1.14937	−	0.369963i
$765$	7.95746	−	2.13220i	0.287703	−	0.0770897i
$766$	−2.95023	+	27.7033i	−0.106596	+	1.00096i
$767$	−11.2044	+	6.46885i	−0.404567	+	0.233577i
$768$	1.51950	−	23.9517i	0.0548304	−	0.864284i
$769$			2.25846i			0.0814421i	0.999171	+	0.0407210i	$0.0129655\pi$
$769$			2.25846i			0.0814421i	−0.999171	+	0.0407210i	$0.987035\pi$
$770$	−0.689131	−	0.121769i	−0.0248346	−	0.00438823i
$771$	32.9674	−	32.9674i	1.18729	−	1.18729i
$772$	−5.33292	−	1.14888i	−0.191936	−	0.0413490i
$773$	−0.149388	+	0.557523i	−0.00537311	+	0.0200527i	−0.968560	−	0.248779i	$-0.919971\pi$
$773$	−0.149388	+	0.557523i	−0.00537311	+	0.0200527i	0.963187	+	0.268831i	$0.0866375\pi$
$774$	2.39772	+	2.96927i	0.0861841	+	0.106728i
$775$	−2.00425	−	1.15715i	−0.0719947	−	0.0415661i
$776$	−4.98622	−	1.64288i	−0.178995	−	0.0589760i
$777$	−9.30780	+	13.8296i	−0.333915	+	0.496134i
$778$	−4.10086	+	0.643736i	−0.147023	+	0.0230791i
$779$	16.4141	−	4.39815i	0.588097	−	0.157580i
$780$	−44.8760	+	2.22817i	−1.60682	+	0.0797814i
$781$	0.0180659	−	0.0674229i	0.000646450	−	0.00241258i
$782$	16.4322	+	37.0442i	0.587614	+	1.32470i
$783$	37.7250			1.34818
$784$	−24.7680	+	13.0593i	−0.884571	+	0.466405i
$785$	−13.7135			−0.489455
$786$	0.292246	+	0.658830i	0.0104241	+	0.0234997i
$787$	8.19123	−	30.5701i	0.291986	−	1.08971i	−0.651596	−	0.758566i	$-0.725900\pi$
$787$	8.19123	−	30.5701i	0.291986	−	1.08971i	0.943582	−	0.331140i	$-0.107433\pi$
$788$	−0.545223	−	10.9809i	−0.0194228	−	0.391180i
$789$	−18.7610	+	5.02699i	−0.667909	+	0.178966i
$790$	71.7602	−	11.2646i	2.55311	−	0.400777i
$791$	−18.9926	+	28.2194i	−0.675299	+	1.00337i
$792$	0.0612400	+	0.121425i	0.00217607	+	0.00431466i
$793$	−31.7526	−	18.3323i	−1.12757	−	0.651001i
$794$	−10.1679	−	12.5916i	−0.360844	−	0.446859i
$795$	11.9145	−	44.4656i	0.422564	−	1.57703i
$796$	−6.12221	+	28.4184i	−0.216996	+	1.00726i
$797$	17.1473	−	17.1473i	0.607387	−	0.607387i	−0.334875	−	0.942263i	$-0.608694\pi$
$797$	17.1473	−	17.1473i	0.607387	−	0.607387i	0.942263	+	0.334875i	$0.108694\pi$
$798$	12.2352	+	2.16194i	0.433121	+	0.0765318i
$799$		−	19.7806i		−	0.699789i
$800$	17.1358	+	10.0510i	0.605841	+	0.355356i
$801$	−5.81743	+	3.35870i	−0.205549	+	0.118674i
$802$	−0.840062	+	7.88835i	−0.0296636	+	0.278547i
$803$	−0.00287874		0.000771357i	−0.000101589		2.72206e-5i
$804$	5.69864	+	17.7040i	0.200975	+	0.624374i
$805$	38.5900	+	44.3019i	1.36012	+	1.56144i
$806$	−4.72642	+	0.741934i	−0.166481	+	0.0261335i
$807$	1.15600	−	2.00225i	0.0406932	−	0.0704826i
$808$	−41.4092	−	27.1349i	−1.45677	−	0.954601i
$809$	−5.51003	+	3.18122i	−0.193722	+	0.111846i	−0.593724	−	0.804669i	$-0.702343\pi$
$809$	−5.51003	+	3.18122i	−0.193722	+	0.111846i	0.400002	+	0.916514i	$0.369010\pi$
$810$	23.8209	+	9.18156i	0.836980	+	0.322607i
$811$	−9.98197	+	9.98197i	−0.350514	+	0.350514i	−0.860301	−	0.509787i	$-0.829724\pi$
$811$	−9.98197	+	9.98197i	−0.350514	+	0.350514i	0.509787	+	0.860301i	$0.329724\pi$
$812$	18.3306	−	30.3877i	0.643277	−	1.06640i
$813$	11.3167	+	11.3167i	0.396892	+	0.396892i
$814$	0.348107	−	0.154414i	0.0122012	−	0.00541223i
$815$	2.36936	+	4.10385i	0.0829949	+	0.143751i
$816$	21.1327	−	7.97908i	0.739794	−	0.279324i
$817$	−6.89826	−	3.98271i	−0.241340	−	0.139337i
$818$	−38.4483	−	28.0151i	−1.34431	−	0.979526i
$819$	3.30675	−	9.63522i	0.115547	−	0.336682i
$820$	20.4439	−	39.8523i	0.713933	−	1.39170i
$821$	12.1404	+	45.3088i	0.423704	+	1.58129i	0.766736	+	0.641963i	$0.221880\pi$
$821$	12.1404	+	45.3088i	0.423704	+	1.58129i	−0.343031	+	0.939324i	$0.611454\pi$
$822$	12.0396	+	14.9095i	0.419929	+	0.520029i
$823$	−18.5100	−	32.0602i	−0.645218	−	1.11755i	−0.984251	−	0.176775i	$-0.943433\pi$
$823$	−18.5100	−	32.0602i	−0.645218	−	1.11755i	0.339034	−	0.940774i	$-0.389900\pi$
$824$	−16.6234	+	14.8441i	−0.579104	+	0.517120i
$825$	0.337696			0.0117571
$826$	3.98829	−	8.54488i	0.138770	−	0.297314i
$827$	−2.13977	−	2.13977i	−0.0744071	−	0.0744071i	0.668924	−	0.743331i	$-0.266755\pi$
$827$	−2.13977	−	2.13977i	−0.0744071	−	0.0744071i	−0.743331	+	0.668924i	$0.766755\pi$
$828$	2.40450	−	11.1614i	0.0835623	−	0.387884i
$829$	27.5450	+	7.38067i	0.956678	+	0.256341i	0.703194	−	0.710998i	$-0.251757\pi$
$829$	27.5450	+	7.38067i	0.956678	+	0.256341i	0.253485	+	0.967339i	$0.418423\pi$
$830$	29.4589	+	3.13720i	1.02253	+	0.108894i
$831$	−18.6794	+	32.3537i	−0.647982	+	1.12234i
$832$	40.6144	−	6.08979i	1.40805	−	0.211126i
$833$	−20.8000	−	16.1829i	−0.720676	−	0.560704i
$834$	9.35357	+	6.81543i	0.323888	+	0.235999i
$835$	−5.90311	−	22.0307i	−0.204286	−	0.762405i
$836$	−0.210407	−	0.190502i	−0.00727709	−	0.00658863i
$837$	3.58057	+	0.959411i	0.123763	+	0.0331621i
$838$	−13.9455	−	5.37518i	−0.481740	−	0.185683i
$839$			39.5103i			1.36405i	0.731330	+	0.682023i	$0.238900\pi$
$839$			39.5103i			1.36405i	−0.731330	+	0.682023i	$0.761100\pi$
$840$	25.8689	−	20.0818i	0.892564	−	0.692889i
$841$			15.9793i			0.551011i
$842$	7.25937	−	18.8339i	0.250174	−	0.649059i
$843$	22.0486	+	5.90789i	0.759392	+	0.203479i
$844$	2.60209	+	52.4068i	0.0895676	+	1.80392i
$845$	−10.0832	−	37.6309i	−0.346872	−	1.29454i
$846$	−3.28187	+	4.50408i	−0.112833	+	0.154853i
$847$	−26.1351	+	12.7798i	−0.898013	+	0.439118i
$848$	−6.81058	+	41.5216i	−0.233876	+	1.42586i
$849$	16.8478	−	29.1813i	0.578216	−	1.00150i
$850$	−1.98003	+	18.5929i	−0.0679146	+	0.637731i
$851$	−30.8822	−	8.27487i	−1.05863	−	0.283659i
$852$	1.77152	+	2.74439i	0.0606912	+	0.0940211i
$853$	13.2644	+	13.2644i	0.454165	+	0.454165i	0.896734	−	0.442570i	$-0.145933\pi$
$853$	13.2644	+	13.2644i	0.454165	+	0.454165i	−0.442570	+	0.896734i	$0.645933\pi$
$854$	26.6227	−	2.31952i	0.911010	−	0.0793722i
$855$	4.84416			0.165667
$856$	−1.33456	+	23.6024i	−0.0456143	+	0.806714i
$857$	3.96984	+	6.87597i	0.135607	+	0.234879i	0.925829	−	0.377942i	$-0.123368\pi$
$857$	3.96984	+	6.87597i	0.135607	+	0.234879i	−0.790222	+	0.612821i	$0.790035\pi$
$858$	0.543137	−	0.438589i	0.0185424	−	0.0149732i
$859$	−9.90335	−	36.9598i	−0.337898	−	1.26105i	−0.900693	−	0.434456i	$-0.856941\pi$
$859$	−9.90335	−	36.9598i	−0.337898	−	1.26105i	0.562795	−	0.826596i	$-0.309726\pi$
$860$	−19.9853	+	6.43293i	−0.681492	+	0.219361i
$861$	−20.0091	−	22.9708i	−0.681909	−	0.782842i
$862$	5.86096	−	8.04365i	0.199625	−	0.273968i
$863$	43.1275	+	24.8997i	1.46808	+	0.847595i	0.999361	−	0.0357536i	$-0.0113832\pi$
$863$	43.1275	+	24.8997i	1.46808	+	0.847595i	0.468717	+	0.883349i	$0.344716\pi$
$864$	−30.6783	−	8.44660i	−1.04370	−	0.287359i
$865$	−6.04356	−	10.4677i	−0.205487	−	0.355914i
$866$	22.1253	+	49.8786i	0.751848	+	1.69494i
$867$	−2.99744	−	2.99744i	−0.101798	−	0.101798i
$868$	2.51261	−	2.41799i	0.0852835	−	0.0820719i
$869$	−0.798050	+	0.798050i	−0.0270720	+	0.0270720i
$870$	−14.9281	+	38.7297i	−0.506109	+	1.31306i
$871$	−27.5619	+	15.9129i	−0.933900	+	0.539187i
$872$	19.1060	+	12.5199i	0.647011	+	0.423977i
$873$	−0.696064	+	1.20562i	−0.0235582	+	0.0408040i
$874$	3.69538	+	23.5411i	0.124998	+	0.796290i
$875$	−2.20327	−	11.2738i	−0.0744842	−	0.381124i
$876$	0.0636587	−	0.124093i	0.00215083	−	0.00419271i
$877$	7.34403	−	1.96783i	0.247990	−	0.0664488i	−0.132682	−	0.991159i	$-0.542359\pi$
$877$	7.34403	−	1.96783i	0.247990	−	0.0664488i	0.380673	+	0.924710i	$0.375692\pi$
$878$	25.0775	+	2.67061i	0.846325	+	0.0901286i
$879$	−12.4049	+	7.16199i	−0.418408	+	0.241568i
$880$	−0.744445	+	0.0741087i	−0.0250952	+	0.00249820i
$881$			15.5915i			0.525291i	0.964892	+	0.262645i	$0.0845949\pi$
$881$			15.5915i			0.525291i	−0.964892	+	0.262645i	$0.915405\pi$
$882$	2.05122	+	7.13586i	0.0690683	+	0.240277i
$883$	38.0811	−	38.0811i	1.28153	−	1.28153i	0.341736	−	0.939796i	$-0.388985\pi$
$883$	38.0811	−	38.0811i	1.28153	−	1.28153i	0.939796	−	0.341736i	$-0.111015\pi$
$884$	20.9632	+	32.4757i	0.705070	+	1.09227i
$885$	−2.85454	+	10.6533i	−0.0959544	+	0.358107i
$886$	−9.69896	+	7.83202i	−0.325843	+	0.263122i
$887$	42.5365	+	24.5585i	1.42824	+	0.824593i	0.996982	−	0.0776375i	$-0.0247377\pi$
$887$	42.5365	+	24.5585i	1.42824	+	0.824593i	0.431255	+	0.902230i	$0.358071\pi$
$888$	−5.57687	+	16.9260i	−0.187147	+	0.568001i
$889$	−33.7096	−	22.6877i	−1.13058	−	0.760921i
$890$	−5.73061	−	36.5063i	−0.192091	−	1.22369i
$891$	−0.383138	+	0.102661i	−0.0128356	+	0.00343929i
$892$	−30.5142	+	33.7027i	−1.02169	+	1.12845i
$893$	3.01040	−	11.2350i	0.100739	−	0.375963i
$894$	−12.3704	+	5.48728i	−0.413727	+	0.183522i
$895$	−32.4983			−1.08630
$896$	−21.7104	+	20.6073i	−0.725292	+	0.688441i
$897$	−58.6100			−1.95693
$898$	−18.7338	+	8.30998i	−0.625154	+	0.277307i
$899$	−1.14390	+	4.26909i	−0.0381512	+	0.142382i
$900$	3.53567	−	3.90512i	0.117856	−	0.130171i
$901$	−38.2533	+	10.2499i	−1.27440	+	0.341475i
$902$	0.107921	+	0.687499i	0.00359337	+	0.0228912i
$903$	−0.981645	+	14.2458i	−0.0326671	+	0.474069i
$904$	−11.3796	+	34.5377i	−0.378480	+	1.14871i
$905$	16.1052	+	9.29833i	0.535354	+	0.309087i
$906$	5.63600	−	4.55113i	0.187244	−	0.151201i
$907$	3.61344	−	13.4855i	0.119982	−	0.447780i	−0.879629	−	0.475660i	$-0.842209\pi$
$907$	3.61344	−	13.4855i	0.119982	−	0.447780i	0.999611	+	0.0278807i	$0.00887586\pi$
$908$	−1.95412	−	3.02727i	−0.0648498	−	0.100463i
$909$	−9.28298	+	9.28298i	−0.307897	+	0.307897i
$910$	42.9157	+	36.0369i	1.42264	+	1.19461i
$911$		−	22.9755i		−	0.761211i	−0.924737	−	0.380606i	$-0.875716\pi$
$911$		−	22.9755i		−	0.761211i	0.924737	−	0.380606i	$-0.124284\pi$
$912$	13.2172	−	1.31576i	0.437667	−	0.0435693i
$913$	−0.398632	+	0.230150i	−0.0131928	+	0.00761686i
$914$	4.20833	+	0.448162i	0.139199	+	0.0148239i
$915$	−30.1908	+	8.08961i	−0.998078	+	0.267434i
$916$	13.5311	−	26.3767i	0.447079	−	0.871511i
$917$	0.291799	−	0.850245i	0.00963604	−	0.0280776i
$918$	−4.64441	−	29.5868i	−0.153288	−	0.976509i
$919$	−18.7608	+	32.4947i	−0.618862	+	1.07190i	0.370832	+	0.928700i	$0.379073\pi$
$919$	−18.7608	+	32.4947i	−0.618862	+	1.07190i	−0.989694	+	0.143200i	$0.954261\pi$
$920$	52.5345	+	34.4251i	1.73201	+	1.13496i
$921$	−23.9335	+	13.8180i	−0.788635	+	0.455319i
$922$	−4.95609	+	12.8582i	−0.163220	+	0.423463i
$923$	−3.95243	+	3.95243i	−0.130096	+	0.130096i
$924$	−0.141100	+	0.488872i	−0.00464186	+	0.0160827i
$925$	−10.4309	−	10.4309i	−0.342965	−	0.342965i
$926$	−16.5971	−	37.4160i	−0.545414	−	1.22957i
$927$	2.95488	+	5.11800i	0.0970510	+	0.168097i
$928$	10.0708	−	36.5775i	0.330591	−	1.20072i
$929$	11.3306	+	6.54174i	0.371746	+	0.214627i	0.674221	−	0.738530i	$-0.264480\pi$
$929$	11.3306	+	6.54174i	0.371746	+	0.214627i	−0.302475	+	0.953157i	$0.597813\pi$
$930$	−2.40182	+	3.29629i	−0.0787588	+	0.108089i
$931$	−9.35105	−	12.3570i	−0.306468	−	0.404986i
$932$	−40.6550	+	13.0862i	−1.33170	+	0.428652i
$933$	−0.0518674	−	0.193572i	−0.00169806	−	0.00633725i
$934$	27.2825	−	22.0309i	0.892710	−	0.720873i
$935$	−0.352071	−	0.609804i	−0.0115139	−	0.0199427i
$936$	0.614786	−	10.8728i	0.0200949	−	0.355390i
$937$	−12.8178			−0.418739			−0.209370	−	0.977837i	$-0.567141\pi$
$937$	−12.8178			−0.418739			−0.209370	+	0.977837i	$0.567141\pi$
$938$	9.81090	−	21.0198i	0.320337	−	0.686319i
$939$	2.05882	+	2.05882i	0.0671871	+	0.0671871i
$940$	−16.6265	−	25.7573i	−0.542297	−	0.840111i
$941$	31.0245	+	8.31298i	1.01137	+	0.270995i	0.726201	−	0.687482i	$-0.241284\pi$
$941$	31.0245	+	8.31298i	1.01137	+	0.270995i	0.285167	+	0.958478i	$0.407951\pi$
$942$	−1.05589	+	9.91498i	−0.0344026	+	0.323047i
$943$	29.2129	−	50.5983i	0.951304	−	1.64771i
$944$	1.63172	−	9.94797i	0.0531078	−	0.323779i
$945$	−19.0734	−	39.0058i	−0.620457	−	1.26886i
$946$	0.192102	−	0.263643i	0.00624578	−	0.00857178i
$947$	−10.3703	−	38.7026i	−0.336991	−	1.25767i	−0.901695	−	0.432373i	$-0.857676\pi$
$947$	−10.3703	−	38.7026i	−0.336991	−	1.25767i	0.564704	−	0.825293i	$-0.308990\pi$
$948$	−2.61916	−	52.7506i	−0.0850664	−	1.71326i
$949$	0.230525	+	0.0617690i	0.00748316	+	0.00200511i
$950$	−3.95425	+	10.2590i	−0.128293	+	0.332846i
$951$		−	16.6338i		−	0.539389i
$952$	−26.0890	−	10.6351i	−0.845550	−	0.344686i
$953$			53.3527i			1.72826i	0.503266	+	0.864132i	$0.332132\pi$
$953$			53.3527i			1.72826i	−0.503266	+	0.864132i	$0.667868\pi$
$954$	10.4109	+	4.01281i	0.337066	+	0.129919i
$955$	47.0261	+	12.6006i	1.52173	+	0.407746i
$956$	−0.938460	−	0.849676i	−0.0303520	−	0.0274805i
$957$	−0.166915	−	0.622934i	−0.00539558	−	0.0201366i
$958$	12.6630	+	9.22682i	0.409123	+	0.298105i
$959$	1.64310	−	23.8448i	0.0530584	−	0.769990i
$960$	20.8112	−	28.1530i	0.671678	−	0.908633i
$961$	15.2829	−	26.4707i	0.492995	−	0.853893i
$962$	−30.3239	−	3.22931i	−0.977681	−	0.104117i
$963$	6.05511	+	1.62246i	0.195123	+	0.0522831i
$964$	7.88413	−	36.5970i	0.253931	−	1.17871i
$965$	−5.62708	−	5.62708i	−0.181142	−	0.181142i
$966$	35.0019	−	24.4898i	1.12617	−	0.787947i
$967$	13.7500			0.442169			0.221085	−	0.975255i	$-0.429040\pi$
$967$	13.7500			0.442169			0.221085	+	0.975255i	$0.429040\pi$
$968$	−23.1982	+	20.7152i	−0.745619	+	0.665812i
$969$	6.25084	+	10.8268i	0.200806	+	0.347806i
$970$	−4.81134	−	5.95824i	−0.154483	−	0.191308i
$971$	3.00563	+	11.2172i	0.0964554	+	0.359976i	0.997236	−	0.0742978i	$-0.0236715\pi$
$971$	3.00563	+	11.2172i	0.0964554	+	0.359976i	−0.900781	+	0.434274i	$0.857005\pi$
$972$	−6.93233	+	13.5135i	−0.222355	+	0.433446i
$973$	−2.76858	−	14.1664i	−0.0887566	−	0.454154i
$974$	−25.1617	−	18.3340i	−0.806234	−	0.587458i
$975$	−23.4192	−	13.5211i	−0.750016	−	0.433022i
$976$	26.7270	−	10.0913i	0.855512	−	0.323015i
$977$	9.47758	+	16.4156i	0.303215	+	0.525183i	0.976862	−	0.213870i	$-0.0686068\pi$
$977$	9.47758	+	16.4156i	0.303215	+	0.525183i	−0.673648	+	0.739053i	$0.735273\pi$
$978$	3.14955	−	1.39709i	0.100711	−	0.0446739i
$979$	0.405989	+	0.405989i	0.0129755	+	0.0129755i
$980$	−40.6871	−	3.58921i	−1.29970	−	0.114653i
$981$	4.28312	−	4.28312i	0.136749	−	0.136749i
$982$	33.7107	+	12.9935i	1.07575	+	0.414640i
$983$	−29.7964	+	17.2029i	−0.950357	+	0.548689i	−0.893192	−	0.449676i	$-0.851539\pi$
$983$	−29.7964	+	17.2029i	−0.950357	+	0.548689i	−0.0571649	+	0.998365i	$0.518206\pi$
$984$	−27.2394	−	17.8496i	−0.868362	−	0.569025i
$985$	8.01911	−	13.8895i	0.255510	−	0.442557i
$986$	35.2762	−	5.53750i	1.12342	−	0.176350i
$987$	−20.4641	+	3.99936i	−0.651381	+	0.127301i
$988$	6.96421	+	21.6358i	0.221561	+	0.688327i
$989$	−26.4536	+	7.08821i	−0.841174	+	0.225392i
$990$	−0.0210077	+	0.197267i	−0.000667669	+	0.00626954i
$991$	49.1173	−	28.3579i	1.56026	−	0.900817i	0.563032	−	0.826435i	$-0.309635\pi$
$991$	49.1173	−	28.3579i	1.56026	−	0.900817i	0.997230	−	0.0743822i	$-0.0236985\pi$
$992$	1.88608	−	3.21554i	0.0598830	−	0.102094i
$993$			37.6461i			1.19466i
$994$	0.708896	−	4.01189i	0.0224848	−	0.127250i
$995$	−29.9859	+	29.9859i	−0.950618	+	0.950618i
$996$	4.53645	−	21.0575i	0.143743	−	0.667233i
$997$	9.18819	−	34.2908i	0.290993	−	1.08600i	−0.653355	−	0.757052i	$-0.726639\pi$
$997$	9.18819	−	34.2908i	0.290993	−	1.08600i	0.944348	−	0.328949i	$-0.106694\pi$
$998$	−2.12326	−	2.62939i	−0.0672107	−	0.0832319i
$999$	20.4623	+	11.8139i	0.647398	+	0.373775i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.v.a.19.3	yes	56
4.3	odd	2		448.2.z.a.47.11		56
7.2	even	3		784.2.j.a.195.21		56
7.3	odd	6	inner	112.2.v.a.3.8	✓	56
7.4	even	3		784.2.w.f.227.8		56
7.5	odd	6		784.2.j.a.195.22		56
7.6	odd	2		784.2.w.f.19.3		56
8.3	odd	2		896.2.z.a.607.4		56
8.5	even	2		896.2.z.b.607.11		56
16.3	odd	4		896.2.z.b.159.11		56
16.5	even	4		448.2.z.a.271.11		56
16.11	odd	4	inner	112.2.v.a.75.8	yes	56
16.13	even	4		896.2.z.a.159.4		56
28.3	even	6		448.2.z.a.367.11		56
56.3	even	6		896.2.z.a.479.4		56
56.45	odd	6		896.2.z.b.479.11		56
112.3	even	12		896.2.z.b.31.11		56
112.11	odd	12		784.2.w.f.619.3		56
112.27	even	4		784.2.w.f.411.8		56
112.45	odd	12		896.2.z.a.31.4		56
112.59	even	12	inner	112.2.v.a.59.3	yes	56
112.75	even	12		784.2.j.a.587.21		56
112.101	odd	12		448.2.z.a.143.11		56
112.107	odd	12		784.2.j.a.587.22		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.v.a.3.8	✓	56	7.3	odd	6	inner
112.2.v.a.19.3	yes	56	1.1	even	1	trivial
112.2.v.a.59.3	yes	56	112.59	even	12	inner
112.2.v.a.75.8	yes	56	16.11	odd	4	inner
448.2.z.a.47.11		56	4.3	odd	2
448.2.z.a.143.11		56	112.101	odd	12
448.2.z.a.271.11		56	16.5	even	4
448.2.z.a.367.11		56	28.3	even	6
784.2.j.a.195.21		56	7.2	even	3
784.2.j.a.195.22		56	7.5	odd	6
784.2.j.a.587.21		56	112.75	even	12
784.2.j.a.587.22		56	112.107	odd	12
784.2.w.f.19.3		56	7.6	odd	2
784.2.w.f.227.8		56	7.4	even	3
784.2.w.f.411.8		56	112.27	even	4
784.2.w.f.619.3		56	112.11	odd	12
896.2.z.a.31.4		56	112.45	odd	12
896.2.z.a.159.4		56	16.13	even	4
896.2.z.a.479.4		56	56.3	even	6
896.2.z.a.607.4		56	8.3	odd	2
896.2.z.b.31.11		56	112.3	even	12
896.2.z.b.159.11		56	16.3	odd	4
896.2.z.b.479.11		56	56.45	odd	6
896.2.z.b.607.11		56	8.5	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29274 + 0.573436i) q^{2} +(-0.388227 + 1.44888i) q^{3} +(1.34234 - 1.48261i) q^{4} +(2.81809 - 0.755106i) q^{5} +(-0.328966 - 2.09565i) q^{6} +(-1.47726 + 2.19493i) q^{7} +(-0.885116 + 2.68637i) q^{8} +(0.649537 + 0.375010i) q^{9} +(-3.21005 + 2.59215i) q^{10} +(0.0165920 - 0.0619222i) q^{11} +(1.62699 + 2.52048i) q^{12} +(-3.62997 + 3.62997i) q^{13} +(0.651060 - 3.68458i) q^{14} +4.37624i q^{15} +(-0.396237 - 3.98033i) q^{16} +(3.26044 - 1.88242i) q^{17} +(-1.05473 - 0.112322i) q^{18} +(2.13834 - 0.572967i) q^{19} +(2.66332 - 5.19173i) q^{20} +(-2.60668 - 2.99251i) q^{21} +(0.0140593 + 0.0895636i) q^{22} +(3.80570 - 6.59167i) q^{23} +(-3.54860 - 2.32535i) q^{24} +(3.04134 - 1.75592i) q^{25} +(2.61104 - 6.77415i) q^{26} +(-3.97748 + 3.97748i) q^{27} +(1.27122 + 5.13654i) q^{28} +(-4.74233 - 4.74233i) q^{29} +(-2.50949 - 5.65733i) q^{30} +(-0.329500 - 0.570711i) q^{31} +(2.79469 + 4.91830i) q^{32} +(0.0832764 + 0.0480797i) q^{33} +(-3.13545 + 4.30313i) q^{34} +(-2.50566 + 7.30100i) q^{35} +(1.42789 - 0.459615i) q^{36} +(-1.08717 - 4.05737i) q^{37} +(-2.43575 + 1.96690i) q^{38} +(-3.85014 - 6.66865i) q^{39} +(-0.465849 + 8.23879i) q^{40} +7.67610 q^{41} +(5.08576 + 2.37376i) q^{42} +(-2.54426 - 2.54426i) q^{43} +(-0.0695340 - 0.107720i) q^{44} +(2.11363 + 0.566345i) q^{45} +(-1.13987 + 10.7036i) q^{46} +(2.62703 - 4.55014i) q^{47} +(5.92085 + 0.971168i) q^{48} +(-2.63540 - 6.48496i) q^{49} +(-2.92475 + 4.01396i) q^{50} +(1.46161 + 5.45480i) q^{51} +(0.509152 + 10.2545i) q^{52} +(-10.1607 - 2.72255i) q^{53} +(2.86101 - 7.42267i) q^{54} -0.187031i q^{55} +(-4.58883 - 5.91123i) q^{56} +3.32064i q^{57} +(8.85000 + 3.41116i) q^{58} +(2.43435 + 0.652282i) q^{59} +(6.48824 + 5.87441i) q^{60} +(1.84853 + 6.89881i) q^{61} +(0.753224 + 0.548832i) q^{62} +(-1.78266 + 0.871698i) q^{63} +(-6.43314 - 4.75549i) q^{64} +(-7.48858 + 12.9706i) q^{65} +(-0.135225 - 0.0144007i) q^{66} +(5.98832 + 1.60456i) q^{67} +(1.58575 - 7.36080i) q^{68} +(8.07307 + 8.07307i) q^{69} +(-0.947500 - 10.8751i) q^{70} +1.08883 q^{71} +(-1.58233 + 1.41297i) q^{72} +(-0.0232448 - 0.0402613i) q^{73} +(3.73207 + 4.62169i) q^{74} +(1.36339 + 5.08824i) q^{75} +(2.02090 - 3.93943i) q^{76} +(0.111404 + 0.127893i) q^{77} +(8.80127 + 6.41300i) q^{78} +(-15.2466 - 8.80264i) q^{79} +(-4.12220 - 10.9177i) q^{80} +(-3.09370 - 5.35845i) q^{81} +(-9.92319 + 4.40176i) q^{82} +(-5.07720 - 5.07720i) q^{83} +(-7.93576 - 0.152291i) q^{84} +(7.76681 - 7.76681i) q^{85} +(4.74802 + 1.83009i) q^{86} +(8.71217 - 5.02997i) q^{87} +(0.151660 + 0.0993805i) q^{88} +(-4.47814 + 7.75636i) q^{89} +(-3.05713 + 0.479896i) q^{90} +(-2.60510 - 13.3299i) q^{91} +(-4.66429 - 14.4906i) q^{92} +(0.954814 - 0.255842i) q^{93} +(-0.786839 + 7.38857i) q^{94} +(5.59340 - 3.22935i) q^{95} +(-8.21101 + 2.13977i) q^{96} +1.85612i q^{97} +(7.12559 + 6.87211i) q^{98} +(0.0339986 - 0.0339986i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 8 q^{7} + 4 q^{8} - 24 q^{10} + 2 q^{11} - 6 q^{12} + 16 q^{14} + 8 q^{16} - 12 q^{17} - 30 q^{18} - 6 q^{19} - 10 q^{21} - 28 q^{22} - 12 q^{23} - 6 q^{24}+ \cdots - 16 q^{99}+O(q^{100}) \) 56 * q - 2 * q^2 - 6 * q^3 - 4 * q^4 - 6 * q^5 - 8 * q^7 + 4 * q^8 - 24 * q^10 + 2 * q^11 - 6 * q^12 + 16 * q^14 + 8 * q^16 - 12 * q^17 - 30 * q^18 - 6 * q^19 - 10 * q^21 - 28 * q^22 - 12 * q^23 - 6 * q^24 - 6 * q^26 + 26 * q^28 - 24 * q^29 - 18 * q^30 - 12 * q^32 - 12 * q^33 - 2 * q^35 + 16 * q^36 + 6 * q^37 - 6 * q^38 - 4 * q^39 - 66 * q^40 + 70 * q^42 + 26 * q^44 + 12 * q^45 + 16 * q^46 - 8 * q^49 - 34 * q^51 + 84 * q^52 + 6 * q^53 + 42 * q^54 + 16 * q^56 + 18 * q^58 + 42 * q^59 + 78 * q^60 - 6 * q^61 - 16 * q^64 - 4 * q^65 + 126 * q^66 + 6 * q^67 + 24 * q^68 - 80 * q^70 - 80 * q^71 - 4 * q^72 + 62 * q^74 + 24 * q^75 + 10 * q^77 + 4 * q^78 + 12 * q^80 - 8 * q^81 + 42 * q^82 - 152 * q^84 - 28 * q^85 - 12 * q^87 + 30 * q^88 + 16 * q^91 - 20 * q^92 + 10 * q^93 - 42 * q^94 + 36 * q^96 - 108 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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