LMFDB - Embedded newform 213.2.n.a.11.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [213,2,Mod(11,213)] 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("213.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(213, base_ring=CyclotomicField(70)) chi = DirichletCharacter(H, H._module([35, 31])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 213 = 3 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	213.n (of order $70$, degree $24$, 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:	$1.70081356305$
Analytic rank:	$0$
Dimension:	$528$
Relative dimension:	$22$ over $\Q(\zeta_{70})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{70}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	213.11
Dual form			213.2.n.a.155.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.237517 + 0.127813i) q^{2} +(-0.762824 - 1.55502i) q^{3} +(-1.06172 - 1.60843i) q^{4} +(-3.20904 + 1.04268i) q^{5} +(0.0175691 - 0.466844i) q^{6} +(0.617551 + 3.40299i) q^{7} +(-0.0949523 - 1.05501i) q^{8} +(-1.83620 + 2.37242i) q^{9} +(-0.895472 - 0.162504i) q^{10} +(-0.642974 - 0.561749i) q^{11} +(-1.69125 + 2.87794i) q^{12} +(-2.67276 - 3.05922i) q^{13} +(-0.288269 + 0.887200i) q^{14} +(4.06933 + 4.19476i) q^{15} +(-1.40262 + 3.28160i) q^{16} +(0.807312 + 0.586547i) q^{17} +(-0.739356 + 0.328800i) q^{18} +(-3.32712 - 0.918227i) q^{19} +(5.08417 + 4.05449i) q^{20} +(4.82065 - 3.55619i) q^{21} +(-0.0809182 - 0.215606i) q^{22} +(-7.91961 - 3.81388i) q^{23} +(-1.56813 + 0.952438i) q^{24} +(5.16570 - 3.75310i) q^{25} +(-0.243817 - 1.06823i) q^{26} +(5.08987 + 1.04559i) q^{27} +(4.81781 - 4.60630i) q^{28} +(3.59128 - 9.56893i) q^{29} +(0.430390 + 1.51644i) q^{30} +(0.266286 - 0.113816i) q^{31} +(-2.40892 + 1.92105i) q^{32} +(-0.383058 + 1.42836i) q^{33} +(0.116782 + 0.242500i) q^{34} +(-5.52998 - 10.2764i) q^{35} +(5.76539 + 0.434561i) q^{36} +(-1.81830 + 0.875648i) q^{37} +(-0.672887 - 0.643346i) q^{38} +(-2.71831 + 6.48985i) q^{39} +(1.40474 + 3.28656i) q^{40} +(-1.40947 + 6.17531i) q^{41} +(1.59951 - 0.228513i) q^{42} +(1.14473 + 1.19729i) q^{43} +(-0.220879 + 1.63060i) q^{44} +(3.41876 - 9.52777i) q^{45} +(-1.39358 - 1.91810i) q^{46} +(-0.0943551 - 2.10098i) q^{47} +(6.17292 - 0.322172i) q^{48} +(-4.64532 + 1.74342i) q^{49} +(1.70664 - 0.231180i) q^{50} +(0.296257 - 1.70282i) q^{51} +(-2.08283 + 7.54697i) q^{52} +(-1.47068 + 2.22799i) q^{53} +(1.07529 + 0.898899i) q^{54} +(2.64906 + 1.13226i) q^{55} +(3.53154 - 0.974642i) q^{56} +(1.11014 + 5.87420i) q^{57} +(2.07603 - 1.81377i) q^{58} +(-1.59456 + 0.952707i) q^{59} +(2.42650 - 10.9989i) q^{60} +(-1.18187 + 6.51262i) q^{61} +(0.0777947 + 0.00700165i) q^{62} +(-9.20727 - 4.78347i) q^{63} +(6.20518 - 1.12607i) q^{64} +(11.7668 + 7.03034i) q^{65} +(-0.273546 + 0.290299i) q^{66} +(11.3834 - 7.51410i) q^{67} +(0.0862835 - 1.92125i) q^{68} +(0.110592 + 15.2245i) q^{69} -3.14764i q^{70} +(-3.15624 - 7.81269i) q^{71} +(2.67727 + 1.71193i) q^{72} +(-6.91141 + 12.8435i) q^{73} +(-0.543797 - 0.0244220i) q^{74} +(-9.77668 - 5.16983i) q^{75} +(2.05555 + 6.32634i) q^{76} +(1.51456 - 2.53494i) q^{77} +(-1.47514 + 1.19401i) q^{78} +(-0.996812 + 0.0897147i) q^{79} +(1.07942 - 11.9933i) q^{80} +(-2.25675 - 8.71247i) q^{81} +(-1.12406 + 1.28659i) q^{82} +(1.09620 + 1.83473i) q^{83} +(-10.8380 - 3.97801i) q^{84} +(-3.20228 - 1.04048i) q^{85} +(0.118863 + 0.430689i) q^{86} +(-17.6194 + 1.71489i) q^{87} +(-0.531597 + 0.731681i) q^{88} +(9.07471 + 5.99017i) q^{89} +(2.02979 - 1.82605i) q^{90} +(8.75993 - 10.9846i) q^{91} +(2.27401 + 16.7874i) q^{92} +(-0.380116 - 0.327259i) q^{93} +(0.246123 - 0.511079i) q^{94} +(11.6343 - 0.522497i) q^{95} +(4.82487 + 2.28051i) q^{96} +(-12.6196 + 2.88034i) q^{97} +(-1.32618 - 0.179643i) q^{98} +(2.51333 - 0.493921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) $ 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/213\mathbb{Z}\right)^\times$.

$n$	$7$	$143$
$\chi(n)$	$e\left(\frac{31}{70}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (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 $

$2$	0.237517	+	0.127813i	0.167950	+	0.0903778i	0.555684	−	0.831394i	$-0.312456\pi$
$2$	0.237517	+	0.127813i	0.167950	+	0.0903778i	−0.387734	+	0.921771i	$0.626742\pi$
$3$	−0.762824	−	1.55502i	−0.440417	−	0.897793i
$3$	−0.762824	−	1.55502i	−0.440417	−	0.897793i
$4$	−1.06172	−	1.60843i	−0.530858	−	0.804215i
$5$	−3.20904	+	1.04268i	−1.43513	+	0.466301i	−0.920375	−	0.391037i	$-0.872116\pi$
$5$	−3.20904	+	1.04268i	−1.43513	+	0.466301i	−0.514753	+	0.857338i	$0.672116\pi$
$6$	0.0175691	−	0.466844i	0.00717254	−	0.190588i
$7$	0.617551	+	3.40299i	0.233412	+	1.28621i	0.861377	+	0.507967i	$0.169603\pi$
$7$	0.617551	+	3.40299i	0.233412	+	1.28621i	−0.627964	+	0.778242i	$0.716112\pi$
$8$	−0.0949523	−	1.05501i	−0.0335707	−	0.373001i
$9$	−1.83620	+	2.37242i	−0.612066	+	0.790807i
$10$	−0.895472	−	0.162504i	−0.283173	−	0.0513883i
$11$	−0.642974	−	0.561749i	−0.193864	−	0.169374i	0.555534	−	0.831494i	$-0.312514\pi$
$11$	−0.642974	−	0.561749i	−0.193864	−	0.169374i	−0.749398	+	0.662120i	$0.769657\pi$
$12$	−1.69125	+	2.87794i	−0.488220	+	0.830791i
$13$	−2.67276	−	3.05922i	−0.741290	−	0.848475i	0.251560	−	0.967842i	$-0.419056\pi$
$13$	−2.67276	−	3.05922i	−0.741290	−	0.848475i	−0.992850	+	0.119367i	$0.961914\pi$
$14$	−0.288269	+	0.887200i	−0.0770430	+	0.237114i
$15$	4.06933	+	4.19476i	1.05070	+	1.08308i
$16$	−1.40262	+	3.28160i	−0.350656	+	0.820400i
$17$	0.807312	+	0.586547i	0.195802	+	0.142259i	0.681367	−	0.731942i	$-0.261386\pi$
$17$	0.807312	+	0.586547i	0.195802	+	0.142259i	−0.485565	+	0.874201i	$0.661386\pi$
$18$	−0.739356	+	0.328800i	−0.174268	+	0.0774988i
$19$	−3.32712	−	0.918227i	−0.763294	−	0.210656i	−0.137349	−	0.990523i	$-0.543858\pi$
$19$	−3.32712	−	0.918227i	−0.763294	−	0.210656i	−0.625945	+	0.779867i	$0.715287\pi$
$20$	5.08417	+	4.05449i	1.13686	+	0.906612i
$21$	4.82065	−	3.55619i	1.05195	−	0.776024i
$22$	−0.0809182	−	0.215606i	−0.0172518	−	0.0459673i
$23$	−7.91961	−	3.81388i	−1.65135	−	0.795250i	−0.999313	−	0.0370656i	$-0.988199\pi$
$23$	−7.91961	−	3.81388i	−1.65135	−	0.795250i	−0.652040	−	0.758184i	$-0.726087\pi$
$24$	−1.56813	+	0.952438i	−0.320093	+	0.194416i
$25$	5.16570	−	3.75310i	1.03314	−	0.750620i
$26$	−0.243817	−	1.06823i	−0.0478165	−	0.209498i
$27$	5.08987	+	1.04559i	0.979545	+	0.201224i
$28$	4.81781	−	4.60630i	0.910480	−	0.870508i
$29$	3.59128	−	9.56893i	0.666884	−	1.77691i	0.0381666	−	0.999271i	$-0.487848\pi$
$29$	3.59128	−	9.56893i	0.666884	−	1.77691i	0.628717	−	0.777634i	$-0.283580\pi$
$30$	0.430390	+	1.51644i	0.0785781	+	0.276863i
$31$	0.266286	−	0.113816i	0.0478263	−	0.0204420i	−0.368979	−	0.929438i	$-0.620293\pi$
$31$	0.266286	−	0.113816i	0.0478263	−	0.0204420i	0.416805	+	0.908996i	$0.363150\pi$
$32$	−2.40892	+	1.92105i	−0.425841	+	0.339597i
$33$	−0.383058	+	1.42836i	−0.0666818	+	0.248645i
$34$	0.116782	+	0.242500i	0.0200279	+	0.0415885i
$35$	−5.52998	−	10.2764i	−0.934738	−	1.73703i
$36$	5.76539	+	0.434561i	0.960899	+	0.0724269i
$37$	−1.81830	+	0.875648i	−0.298927	+	0.143956i	−0.577335	−	0.816507i	$-0.695907\pi$
$37$	−1.81830	+	0.875648i	−0.298927	+	0.143956i	0.278408	+	0.960463i	$0.410193\pi$
$38$	−0.672887	−	0.643346i	−0.109157	−	0.104364i
$39$	−2.71831	+	6.48985i	−0.435279	+	1.03921i
$40$	1.40474	+	3.28656i	0.222109	+	0.519650i
$41$	−1.40947	+	6.17531i	−0.220123	+	0.964422i	0.737262	+	0.675607i	$0.236118\pi$
$41$	−1.40947	+	6.17531i	−0.220123	+	0.964422i	−0.957385	+	0.288815i	$0.906739\pi$
$42$	1.59951	−	0.228513i	0.246811	−	0.0352603i
$43$	1.14473	+	1.19729i	0.174569	+	0.182585i	0.804291	−	0.594236i	$-0.202545\pi$
$43$	1.14473	+	1.19729i	0.174569	+	0.182585i	−0.629722	+	0.776821i	$0.716831\pi$
$44$	−0.220879	+	1.63060i	−0.0332988	+	0.245822i
$45$	3.41876	−	9.52777i	0.509639	−	1.42032i
$46$	−1.39358	−	1.91810i	−0.205472	−	0.282808i
$47$	−0.0943551	−	2.10098i	−0.0137631	−	0.306459i	−0.994053	−	0.108896i	$-0.965269\pi$
$47$	−0.0943551	−	2.10098i	−0.0137631	−	0.306459i	0.980290	−	0.197564i	$-0.0633029\pi$
$48$	6.17292	−	0.322172i	0.890984	−	0.0465015i
$49$	−4.64532	+	1.74342i	−0.663617	+	0.249060i
$50$	1.70664	−	0.231180i	0.241355	−	0.0326938i
$51$	0.296257	−	1.70282i	0.0414842	−	0.238443i
$52$	−2.08283	+	7.54697i	−0.288837	+	1.04658i
$53$	−1.47068	+	2.22799i	−0.202014	+	0.306038i	−0.921432	−	0.388539i	$-0.872980\pi$
$53$	−1.47068	+	2.22799i	−0.202014	+	0.306038i	0.719419	+	0.694577i	$0.244408\pi$
$54$	1.07529	+	0.898899i	0.146328	+	0.122325i
$55$	2.64906	+	1.13226i	0.357199	+	0.152674i
$56$	3.53154	−	0.974642i	0.471922	−	0.130242i
$57$	1.11014	+	5.87420i	0.147042	+	0.778057i
$58$	2.07603	−	1.81377i	0.272596	−	0.238160i
$59$	−1.59456	+	0.952707i	−0.207594	+	0.124032i	−0.612933	−	0.790135i	$-0.710011\pi$
$59$	−1.59456	+	0.952707i	−0.207594	+	0.124032i	0.405339	+	0.914166i	$0.367153\pi$
$60$	2.42650	−	10.9989i	0.313260	−	1.41995i
$61$	−1.18187	+	6.51262i	−0.151323	+	0.833856i	0.815567	+	0.578662i	$0.196425\pi$
$61$	−1.18187	+	6.51262i	−0.151323	+	0.833856i	−0.966890	+	0.255194i	$0.917861\pi$
$62$	0.0777947	+	0.00700165i	0.00987993	+	0.000889210i
$63$	−9.20727	−	4.78347i	−1.16001	−	0.602661i
$64$	6.20518	−	1.12607i	0.775647	−	0.140759i
$65$	11.7668	+	7.03034i	1.45949	+	0.872006i
$66$	−0.273546	+	0.290299i	−0.0336712	+	0.0357334i
$67$	11.3834	−	7.51410i	1.39070	−	0.917994i	0.390704	−	0.920516i	$-0.372231\pi$
$67$	11.3834	−	7.51410i	1.39070	−	0.917994i	0.999997	+	0.00252234i	$0.000802886\pi$
$68$	0.0862835	−	1.92125i	0.0104634	−	0.232986i
$69$	0.110592	+	15.2245i	0.0133138	+	1.83282i
$70$		−	3.14764i		−	0.376214i
$71$	−3.15624	−	7.81269i	−0.374577	−	0.927196i
$71$	−3.15624	−	7.81269i	−0.374577	−	0.927196i
$72$	2.67727	+	1.71193i	0.315519	+	0.201753i
$73$	−6.91141	+	12.8435i	−0.808919	+	1.50322i	0.0543745	+	0.998521i	$0.482684\pi$
$73$	−6.91141	+	12.8435i	−0.808919	+	1.50322i	−0.863293	+	0.504702i	$0.831602\pi$
$74$	−0.543797	−	0.0244220i	−0.0632152	−	0.00283900i
$75$	−9.77668	−	5.16983i	−1.12891	−	0.596960i
$76$	2.05555	+	6.32634i	0.235788	+	0.725681i
$77$	1.51456	−	2.53494i	0.172600	−	0.288884i
$78$	−1.47514	+	1.19401i	−0.167026	+	0.135196i
$79$	−0.996812	+	0.0897147i	−0.112150	+	0.0100937i	−0.145572	−	0.989348i	$-0.546502\pi$
$79$	−0.996812	+	0.0897147i	−0.112150	+	0.0100937i	0.0334221	+	0.999441i	$0.489359\pi$
$80$	1.07942	−	11.9933i	0.120682	−	1.34089i
$81$	−2.25675	−	8.71247i	−0.250750	−	0.968052i
$82$	−1.12406	+	1.28659i	−0.124132	+	0.142080i
$83$	1.09620	+	1.83473i	0.120323	+	0.201387i	0.912684	−	0.408665i	$-0.134006\pi$
$83$	1.09620	+	1.83473i	0.120323	+	0.201387i	−0.792361	+	0.610052i	$0.791148\pi$
$84$	−10.8380	−	3.97801i	−1.18253	−	0.434037i
$85$	−3.20228	−	1.04048i	−0.347336	−	0.112856i
$86$	0.118863	+	0.430689i	0.0128173	+	0.0464424i
$87$	−17.6194	+	1.71489i	−1.88900	+	0.183855i
$88$	−0.531597	+	0.731681i	−0.0566685	+	0.0779975i
$89$	9.07471	+	5.99017i	0.961918	+	0.634956i	0.931176	−	0.364571i	$-0.118784\pi$
$89$	9.07471	+	5.99017i	0.961918	+	0.634956i	0.0307421	+	0.999527i	$0.490213\pi$
$90$	2.02979	−	1.82605i	0.213959	−	0.192482i
$91$	8.75993	−	10.9846i	0.918290	−	1.15150i
$92$	2.27401	+	16.7874i	0.237082	+	1.75021i
$93$	−0.380116	−	0.327259i	−0.0394162	−	0.0339352i
$94$	0.246123	−	0.511079i	0.0253856	−	0.0527137i
$95$	11.6343	−	0.522497i	1.19365	−	0.0536071i
$96$	4.82487	+	2.28051i	0.492436	+	0.232753i
$97$	−12.6196	+	2.88034i	−1.28132	+	0.292454i	−0.808392	−	0.588645i	$-0.799662\pi$
$97$	−12.6196	+	2.88034i	−1.28132	+	0.292454i	−0.472932	+	0.881099i	$0.656804\pi$
$98$	−1.32618	−	0.179643i	−0.133964	−	0.0181466i
$99$	2.51333	−	0.493921i	0.252599	−	0.0496409i
$100$	−11.5211	−	4.32394i	−1.15211	−	0.432394i
$101$	−10.3387	−	2.35975i	−1.02874	−	0.234803i	−0.325341	−	0.945597i	$-0.605479\pi$
$101$	−10.3387	−	2.35975i	−1.02874	−	0.234803i	−0.703401	+	0.710793i	$0.748336\pi$
$102$	0.288010	−	0.366584i	0.0285172	−	0.0362972i
$103$	−9.48599	−	11.8950i	−0.934682	−	1.17205i	−0.984867	−	0.173314i	$-0.944552\pi$
$103$	−9.48599	−	11.8950i	−0.934682	−	1.17205i	0.0501847	−	0.998740i	$-0.484019\pi$
$104$	−2.97371	+	3.11026i	−0.291597	+	0.304986i
$105$	−11.7617	+	16.4384i	−1.14782	+	1.60422i
$106$	−0.634079	+	0.341212i	−0.0615872	+	0.0331415i
$107$	−12.9677	+	6.97821i	−1.25363	+	0.674609i	−0.959649	−	0.281201i	$-0.909267\pi$
$107$	−12.9677	+	6.97821i	−1.25363	+	0.674609i	−0.293985	+	0.955810i	$0.594982\pi$
$108$	−3.72223	−	9.29682i	−0.358172	−	0.894587i
$109$	7.52369	−	7.86917i	0.720639	−	0.753729i	−0.256451	−	0.966557i	$-0.582553\pi$
$109$	7.52369	−	7.86917i	0.720639	−	0.753729i	0.977090	+	0.212828i	$0.0682674\pi$
$110$	0.484479	+	0.607517i	0.0461932	+	0.0579245i
$111$	2.74870	+	2.15954i	0.260895	+	0.204974i
$112$	−12.0334	−	2.74655i	−1.13705	−	0.259525i
$113$	10.4847	+	3.93499i	0.986321	+	0.370173i	0.791837	−	0.610733i	$-0.209125\pi$
$113$	10.4847	+	3.93499i	0.986321	+	0.370173i	0.194485	+	0.980906i	$0.437697\pi$
$114$	−0.487123	+	1.53711i	−0.0456233	+	0.143964i
$115$	29.3911	+	3.98129i	2.74073	+	0.371257i
$116$	−19.2039	+	4.38316i	−1.78304	+	0.406966i
$117$	12.1655	−	0.723576i	1.12470	−	0.0668946i
$118$	−0.500505	+	0.0224777i	−0.0460752	+	0.00206924i
$119$	−1.49746	+	3.10950i	−0.137272	+	0.285047i
$120$	4.03910	−	4.69147i	0.368718	−	0.428271i
$121$	−1.37871	−	10.1781i	−0.125338	−	0.925279i
$122$	−1.11311	+	1.39580i	−0.100777	+	0.126370i
$123$	10.6779	−	2.51891i	0.962797	−	0.227123i
$124$	−0.465785	−	0.307462i	−0.0418287	−	0.0276109i
$125$	−2.74717	+	3.78116i	−0.245714	+	0.338197i
$126$	−1.57549	−	2.31297i	−0.140356	−	0.206056i
$127$	−1.07201	−	3.88434i	−0.0951254	−	0.344679i	0.900869	−	0.434090i	$-0.142930\pi$
$127$	−1.07201	−	3.88434i	−0.0951254	−	0.344679i	−0.995995	+	0.0894110i	$0.971502\pi$
$128$	7.47842	+	2.42988i	0.661005	+	0.214773i
$129$	0.988590	−	2.69340i	0.0870405	−	0.237141i
$130$	1.89625	+	3.17378i	0.166312	+	0.278359i
$131$	8.18886	−	9.37290i	0.715464	−	0.818914i	−0.274298	−	0.961645i	$-0.588445\pi$
$131$	8.18886	−	9.37290i	0.715464	−	0.818914i	0.989762	+	0.142731i	$0.0455882\pi$
$132$	2.70411	−	0.900387i	0.235363	−	0.0783686i
$133$	1.07005	−	11.8892i	0.0927850	−	1.03093i
$134$	3.66415	−	0.329780i	0.316535	−	0.0284886i
$135$	−17.4238	+	1.95176i	−1.49960	+	0.167981i
$136$	0.542155	−	0.907414i	0.0464894	−	0.0778101i
$137$	3.59279	+	11.0575i	0.306953	+	0.944704i	0.978941	+	0.204142i	$0.0654405\pi$
$137$	3.59279	+	11.0575i	0.306953	+	0.944704i	−0.671988	+	0.740562i	$0.734560\pi$
$138$	−1.91963	+	3.63022i	−0.163410	+	0.309025i
$139$	−12.0616	−	0.541687i	−1.02305	−	0.0459453i	−0.472989	−	0.881068i	$-0.656825\pi$
$139$	−12.0616	−	0.541687i	−1.02305	−	0.0459453i	−0.550063	+	0.835123i	$0.685396\pi$
$140$	−10.6577	+	19.8052i	−0.900737	+	1.67385i
$141$	−3.19510	+	1.74940i	−0.269076	+	0.147326i
$142$	0.248906	−	2.25906i	0.0208878	−	0.189576i
$143$			3.46842i			0.290044i
$144$	−5.20984	−	9.35328i	−0.434153	−	0.779440i
$145$	−1.54723	+	34.4517i	−0.128490	+	2.86106i
$146$	−3.28316	+	2.16719i	−0.271716	+	0.179358i
$147$	6.25462	+	5.89366i	0.515872	+	0.486101i
$148$	3.33894	+	1.99492i	0.274459	+	0.163982i
$149$	2.28669	−	0.414973i	0.187333	−	0.0339959i	−0.0840795	−	0.996459i	$-0.526795\pi$
$149$	2.28669	−	0.414973i	0.187333	−	0.0339959i	0.271413	+	0.962463i	$0.412509\pi$
$150$	−1.66136	−	2.47751i	−0.135649	−	0.202288i
$151$	−3.95490	−	0.355947i	−0.321845	−	0.0289666i	−0.0724609	−	0.997371i	$-0.523085\pi$
$151$	−3.95490	−	0.355947i	−0.321845	−	0.0289666i	−0.249384	+	0.968405i	$0.580228\pi$
$152$	−0.652818	+	3.59732i	−0.0529505	+	0.291781i
$153$	−2.87392	+	0.838268i	−0.232343	+	0.0677700i
$154$	0.683733	−	0.408512i	0.0550968	−	0.0329188i
$155$	−0.735849	+	0.642892i	−0.0591048	+	0.0516383i
$156$	13.3246	−	2.51816i	1.06682	−	0.201614i
$157$	−13.1605	+	3.63208i	−1.05033	+	0.289871i	−0.748253	−	0.663414i	$-0.769107\pi$
$157$	−13.1605	+	3.63208i	−1.05033	+	0.289871i	−0.302072	+	0.953285i	$0.597678\pi$
$158$	−0.248227	−	0.106097i	−0.0197479	−	0.00844064i
$159$	4.58644	+	0.587382i	0.363729	+	0.0465824i
$160$	5.72729	−	8.67648i	0.452782	−	0.685936i
$161$	8.08784	−	29.3056i	0.637411	−	2.30961i
$162$	0.577552	−	2.35780i	0.0453768	−	0.185247i
$163$	−16.8251	+	2.27912i	−1.31785	+	0.178514i	−0.759181	−	0.650880i	$-0.774400\pi$
$163$	−16.8251	+	2.27912i	−1.31785	+	0.178514i	−0.558664	+	0.829394i	$0.688686\pi$
$164$	11.4290	−	4.28938i	0.892457	−	0.334945i
$165$	−0.260072	−	4.98307i	−0.0202466	−	0.387931i
$166$	0.0258632	+	0.575888i	0.00200737	+	0.0446976i
$167$	−0.516059	−	0.710294i	−0.0399338	−	0.0549642i	0.788583	−	0.614928i	$-0.210815\pi$
$167$	−0.516059	−	0.710294i	−0.0399338	−	0.0549642i	−0.828517	+	0.559964i	$0.810815\pi$
$168$	−4.20954	−	4.74814i	−0.324773	−	0.366327i
$169$	−0.470150	+	3.47078i	−0.0361654	+	0.266983i
$170$	−0.627609	−	0.656428i	−0.0481354	−	0.0503457i
$171$	8.28768	−	6.20728i	0.633774	−	0.474683i
$172$	0.710384	−	3.11240i	0.0541663	−	0.237318i
$173$	2.17524	+	5.08923i	0.165380	+	0.386927i	0.981636	−	0.190764i	$-0.0610966\pi$
$173$	2.17524	+	5.08923i	0.165380	+	0.386927i	−0.816255	+	0.577691i	$0.803954\pi$
$174$	−4.40410	−	1.84468i	−0.333874	−	0.139845i
$175$	15.9618	+	15.2611i	1.20660	+	1.15363i
$176$	2.74529	−	1.32206i	0.206934	−	0.0996541i
$177$	2.69785	+	1.75284i	0.202783	+	0.131751i
$178$	1.38978	+	2.58264i	0.104168	+	0.193577i
$179$	−6.35025	−	13.1864i	−0.474640	−	0.985600i	−0.991570	−	0.129572i	$-0.958640\pi$
$179$	−6.35025	−	13.1864i	−0.474640	−	0.985600i	0.516930	−	0.856028i	$-0.327075\pi$
$180$	−18.9545	+	4.61694i	−1.41279	+	0.344127i
$181$	5.39714	−	4.30408i	0.401167	−	0.319920i	−0.402038	−	0.915623i	$-0.631698\pi$
$181$	5.39714	−	4.30408i	0.401167	−	0.319920i	0.803205	+	0.595703i	$0.203127\pi$
$182$	3.48461	−	1.48940i	0.258297	−	0.110401i
$183$	11.0288	−	3.13016i	0.815275	−	0.231388i
$184$	−3.27169	+	8.71738i	−0.241192	+	0.642654i
$185$	4.92199	−	4.70590i	0.361872	−	0.345985i
$186$	−0.0484560	−	0.126314i	−0.00355296	−	0.00926176i
$187$	−0.189589	−	0.830642i	−0.0138641	−	0.0607425i
$188$	−3.27910	+	2.38241i	−0.239153	+	0.173755i
$189$	−0.414883	+	17.9665i	−0.0301783	+	1.30687i
$190$	2.83013	+	1.36292i	0.205319	+	0.0988765i
$191$	0.775981	+	2.06759i	0.0561480	+	0.149606i	0.961316	−	0.275449i	$-0.0888264\pi$
$191$	0.775981	+	2.06759i	0.0561480	+	0.149606i	−0.905168	+	0.425054i	$0.860255\pi$
$192$	−6.48453	−	8.79020i	−0.467981	−	0.634378i
$193$	15.3260	+	12.2221i	1.10319	+	0.879764i	0.993458	−	0.114197i	$-0.0364295\pi$
$193$	15.3260	+	12.2221i	1.10319	+	0.879764i	0.109731	+	0.993961i	$0.465001\pi$
$194$	−3.36551	−	0.928822i	−0.241630	−	0.0666856i
$195$	1.95634	−	23.6606i	0.140096	−	1.69437i
$196$	7.73617	+	5.62066i	0.552584	+	0.401476i
$197$	−3.05835	+	7.15537i	−0.217899	+	0.509799i	−0.992441	−	0.122723i	$-0.960837\pi$
$197$	−3.05835	+	7.15537i	−0.217899	+	0.509799i	0.774542	+	0.632522i	$0.217980\pi$
$198$	0.660090	+	0.203923i	0.0469105	+	0.0144922i
$199$	1.62494	−	5.00106i	0.115189	−	0.354516i	−0.876797	−	0.480860i	$-0.840324\pi$
$199$	1.62494	−	5.00106i	0.115189	−	0.354516i	0.991986	+	0.126344i	$0.0403245\pi$
$200$	−4.45004	−	5.09348i	−0.314665	−	0.360163i
$201$	−20.3681	−	11.9695i	−1.43666	−	0.844262i
$202$	−2.15402	−	1.88191i	−0.151556	−	0.132411i
$203$	34.7808	+	6.31178i	2.44113	+	0.443000i
$204$	−3.05341	+	1.33141i	−0.213782	+	0.0932170i
$205$	−1.91582	−	21.2865i	−0.133807	−	1.48671i
$206$	−0.732737	−	4.03772i	−0.0510522	−	0.281321i
$207$	23.5901	−	11.7856i	1.63963	−	0.819156i
$208$	13.7880	−	4.48000i	0.956027	−	0.310632i
$209$	1.62344	+	2.45941i	0.112296	+	0.170121i
$210$	−4.89465	+	2.40109i	−0.337763	+	0.165691i
$211$	17.3787	+	9.35187i	1.19640	+	0.643809i	0.945947	−	0.324320i	$-0.105135\pi$
$211$	17.3787	+	9.35187i	1.19640	+	0.643809i	0.250451	+	0.968129i	$0.419421\pi$
$212$	5.14501			0.353361
$213$	−9.74127	+	10.8677i	−0.667461	+	0.744645i
$214$	−3.97196			−0.271517
$215$	−4.92187	−	2.64857i	−0.335669	−	0.180631i
$216$	0.619811	−	5.46912i	0.0421728	−	0.372127i
$217$	0.551760	+	0.835880i	0.0374559	+	0.0567433i
$218$	2.79279	−	0.907433i	0.189152	−	0.0614591i
$219$	25.2442	+	0.950032i	1.70585	+	0.0641972i
$220$	−0.991382	−	5.46297i	−0.0668390	−	0.368313i
$221$	−0.363377	−	4.03745i	−0.0244434	−	0.271588i
$222$	0.376845	+	0.864248i	0.0252922	+	0.0580045i
$223$	−23.4340	−	4.25265i	−1.56926	−	0.284778i	−0.676890	−	0.736085i	$-0.736673\pi$
$223$	−23.4340	−	4.25265i	−1.56926	−	0.284778i	−0.892369	+	0.451306i	$0.850958\pi$
$224$	−8.02495	−	7.01119i	−0.536190	−	0.468455i
$225$	−0.581316	+	19.1466i	−0.0387544	+	1.27644i
$226$	1.98736	+	2.27472i	0.132197	+	0.151312i
$227$	−1.39219	+	4.28473i	−0.0924031	+	0.284387i	−0.986568	−	0.163350i	$-0.947770\pi$
$227$	−1.39219	+	4.28473i	−0.0924031	+	0.284387i	0.894165	+	0.447737i	$0.147770\pi$
$228$	8.26959	−	8.02232i	0.547667	−	0.531291i
$229$	1.41694	−	3.31510i	0.0936342	−	0.219068i	−0.866164	−	0.499761i	$-0.833421\pi$
$229$	1.41694	−	3.31510i	0.0936342	−	0.219068i	0.959798	+	0.280693i	$0.0905641\pi$
$230$	6.47202	+	4.70220i	0.426752	+	0.310054i
$231$	−5.09724	−	0.421457i	−0.335374	−	0.0277298i
$232$	−10.4363	−	2.88023i	−0.685176	−	0.189096i
$233$	20.5128	+	16.3584i	1.34384	+	1.07168i	0.990694	+	0.136107i	$0.0434591\pi$
$233$	20.5128	+	16.3584i	1.34384	+	1.07168i	0.353145	+	0.935569i	$0.385112\pi$
$234$	2.98199	+	1.38305i	0.194939	+	0.0904128i
$235$	2.49344	+	6.64376i	0.162654	+	0.433391i
$236$	3.22534	+	1.55324i	0.209952	+	0.101107i
$237$	0.899901	+	1.48163i	0.0584549	+	0.0962422i
$238$	−0.753107	+	0.547164i	−0.0488167	+	0.0354674i
$239$	−5.27789	−	23.1239i	−0.341398	−	1.49576i	−0.796125	−	0.605132i	$-0.793120\pi$
$239$	−5.27789	−	23.1239i	−0.341398	−	1.49576i	0.454727	−	0.890631i	$-0.349737\pi$
$240$	−19.4733	+	7.47026i	−1.25699	+	0.482203i
$241$	0.415914	−	0.397655i	0.0267914	−	0.0256152i	−0.677548	−	0.735478i	$-0.736958\pi$
$241$	0.415914	−	0.397655i	0.0267914	−	0.0256152i	0.704340	+	0.709863i	$0.251243\pi$
$242$	0.973426	−	2.59368i	0.0625742	−	0.166728i
$243$	−11.8266	+	10.1554i	−0.758676	+	0.651468i
$244$	11.7299	−	5.01360i	0.750931	−	0.320963i
$245$	13.0892	−	10.4383i	0.836239	−	0.666878i
$246$	2.85814	+	0.766499i	0.182229	+	0.0488702i
$247$	6.08354	+	12.6326i	0.387086	+	0.803793i
$248$	−0.145361	−	0.270126i	−0.00923044	−	0.0171530i
$249$	2.01684	−	3.10419i	0.127812	−	0.196720i
$250$	−1.13578	+	0.546964i	−0.0718332	+	0.0345930i
$251$	−10.9038	−	10.4251i	−0.688244	−	0.658028i	0.263593	−	0.964634i	$-0.415092\pi$
$251$	−10.9038	−	10.4251i	−0.688244	−	0.658028i	−0.951837	+	0.306606i	$0.900807\pi$
$252$	2.08162	+	19.8879i	0.131130	+	1.25282i
$253$	2.94966	+	6.90107i	0.185443	+	0.433866i
$254$	0.241850	−	1.05961i	0.0151750	−	0.0664861i
$255$	0.824801	+	5.77333i	0.0516510	+	0.361540i
$256$	−7.25073	−	7.58367i	−0.453170	−	0.473979i
$257$	−2.13680	+	15.7745i	−0.133290	+	0.983984i	0.793544	+	0.608513i	$0.208234\pi$
$257$	−2.13680	+	15.7745i	−0.133290	+	0.983984i	−0.926834	+	0.375472i	$0.877481\pi$
$258$	0.579060	−	0.513374i	0.0360507	−	0.0319613i
$259$	−4.10271	−	5.64690i	−0.254930	−	0.350881i
$260$	−1.18519	−	26.3903i	−0.0735024	−	1.63666i
$261$	16.1072	+	26.0905i	0.997012	+	1.61496i
$262$	3.14298	−	1.17958i	0.194174	−	0.0728746i
$263$	−15.9156	+	2.15591i	−0.981396	+	0.132939i	−0.607318	−	0.794459i	$-0.707755\pi$
$263$	−15.9156	+	2.15591i	−0.981396	+	0.132939i	−0.374077	+	0.927398i	$0.622040\pi$
$264$	1.54330	+	0.268503i	0.0949834	+	0.0165252i
$265$	2.39640	−	8.68316i	0.147210	−	0.533402i
$266$	1.77376	−	2.68713i	0.108756	−	0.164758i
$267$	2.39244	−	18.6808i	0.146415	−	1.14325i
$268$	−24.1718	−	10.3315i	−1.47653	−	0.631099i
$269$	−20.4017	+	5.63051i	−1.24391	+	0.343298i	−0.825211	−	0.564825i	$-0.808944\pi$
$269$	−20.4017	+	5.63051i	−1.24391	+	0.343298i	−0.418703	+	0.908123i	$0.637515\pi$
$270$	−4.38792	−	1.76342i	−0.267040	−	0.107318i
$271$	−10.4215	+	9.10495i	−0.633059	+	0.553087i	−0.913528	−	0.406776i	$-0.866653\pi$
$271$	−10.4215	+	9.10495i	−0.633059	+	0.553087i	0.280469	+	0.959863i	$0.409510\pi$
$272$	−3.05717	+	1.82657i	−0.185368	+	0.110752i
$273$	−23.7636	−	5.24257i	−1.43824	−	0.317295i
$274$	−0.559944	+	3.08555i	−0.0338275	+	0.186405i
$275$	−5.42971	−	0.488683i	−0.327424	−	0.0294687i
$276$	24.3701	−	16.3420i	1.46691	−	0.983672i
$277$	−9.13351	+	1.65749i	−0.548780	+	0.0995888i	−0.445863	−	0.895101i	$-0.647103\pi$
$277$	−9.13351	+	1.65749i	−0.548780	+	0.0995888i	−0.102917	+	0.994690i	$0.532817\pi$
$278$	−2.79560	−	1.67029i	−0.167669	−	0.100178i
$279$	−0.218934	+	0.840731i	−0.0131072	+	0.0503332i
$280$	−10.3166	+	6.80994i	−0.616536	+	0.406972i
$281$	0.569145	−	12.6730i	0.0339523	−	0.756007i	−0.907740	−	0.419533i	$-0.862194\pi$
$281$	0.569145	−	12.6730i	0.0339523	−	0.756007i	0.941693	−	0.336475i	$-0.109235\pi$
$282$	−0.982488	+	0.00713690i	−0.0585063	+	0.000424996i
$283$		−	2.92816i		−	0.174061i	−0.996206	−	0.0870307i	$-0.972262\pi$
$283$		−	2.92816i		−	0.174061i	0.996206	−	0.0870307i	$-0.0277378\pi$
$284$	−9.21515	+	13.3714i	−0.546818	+	0.793450i
$285$	−9.68742	−	17.6930i	−0.573834	−	1.04805i
$286$	−0.443311	+	0.823810i	−0.0262135	+	0.0487129i
$287$	−21.8849	−	0.982854i	−1.29183	−	0.0580160i
$288$	−0.134283	−	9.24241i	−0.00791269	−	0.544614i
$289$	−4.94557	−	15.2209i	−0.290916	−	0.895348i
$290$	−4.77088	+	7.98511i	−0.280156	+	0.468902i
$291$	14.1055	+	17.4266i	0.826880	+	1.02156i
$292$	27.9959	−	2.51968i	1.63834	−	0.147453i
$293$	−0.824306	+	9.15879i	−0.0481565	+	0.535062i	0.935292	+	0.353876i	$0.115137\pi$
$293$	−0.824306	+	9.15879i	−0.0481565	+	0.535062i	−0.983449	+	0.181186i	$0.942006\pi$
$294$	0.732290	+	2.19927i	0.0427080	+	0.128264i
$295$	4.12365	−	4.71990i	0.240088	−	0.274803i
$296$	1.09647	+	1.83518i	0.0637308	+	0.106667i
$297$	−2.68529	−	3.53152i	−0.155816	−	0.204919i
$298$	0.596168	+	0.193707i	0.0345351	+	0.0112211i
$299$	9.49971	+	34.4214i	0.549383	+	1.99064i
$300$	2.06474	+	21.2140i	0.119208	+	1.22479i
$301$	−3.36744	+	4.63488i	−0.194096	+	0.267150i
$302$	−0.893861	−	0.590032i	−0.0514359	−	0.0339525i
$303$	4.21717	+	17.8770i	0.242270	+	1.02701i
$304$	7.67995	−	9.63036i	0.440476	−	0.552339i
$305$	−2.99793	−	22.1316i	−0.171661	−	1.26725i
$306$	−0.789748	−	0.168223i	−0.0451469	−	0.00961665i
$307$	−1.92761	+	4.00273i	−0.110015	+	0.228448i	−0.948706	−	0.316159i	$-0.897607\pi$
$307$	−1.92761	+	4.00273i	−0.110015	+	0.228448i	0.838692	+	0.544607i	$0.183321\pi$
$308$	−5.68531	+	0.255328i	−0.323951	+	0.0145486i
$309$	−11.2609	+	23.8248i	−0.640613	+	1.35534i
$310$	−0.256947	+	0.0586465i	−0.0145936	+	0.00333090i
$311$	20.4313	+	2.76761i	1.15855	+	0.156937i	0.688187	−	0.725534i	$-0.258407\pi$
$311$	20.4313	+	2.76761i	1.15855	+	0.156937i	0.470368	+	0.882470i	$0.344121\pi$
$312$	7.10495	+	2.25161i	0.402239	+	0.127472i
$313$	7.90651	+	2.96736i	0.446903	+	0.167725i	0.564672	−	0.825316i	$-0.309003\pi$
$313$	7.90651	+	2.96736i	0.446903	+	0.167725i	−0.117769	+	0.993041i	$0.537574\pi$
$314$	−3.59008	−	0.819413i	−0.202600	−	0.0462421i
$315$	34.5342	+	5.75012i	1.94578	+	0.323983i
$316$	1.20263	+	1.50805i	0.0676533	+	0.0848345i
$317$	−10.9800	+	11.4842i	−0.616699	+	0.645017i	−0.955204	−	0.295948i	$-0.904365\pi$
$317$	−10.9800	+	11.4842i	−0.616699	+	0.645017i	0.338505	+	0.940965i	$0.390079\pi$
$318$	1.01428	+	0.725722i	0.0568782	+	0.0406965i
$319$	−7.68444	+	4.13517i	−0.430246	+	0.231525i
$320$	−18.7386	+	10.0836i	−1.04752	+	0.563693i
$321$	20.7434	+	14.8419i	1.15778	+	0.828395i
$322$	5.66665	−	5.92685i	0.315790	−	0.330291i
$323$	−2.14744	−	2.69281i	−0.119487	−	0.149832i
$324$	−11.6174	+	12.8800i	−0.645409	+	0.715555i
$325$	−25.2882	−	5.77187i	−1.40274	−	0.320166i
$326$	−4.28756	−	1.60915i	−0.237466	−	0.0891224i
$327$	−17.9760	−	5.69673i	−0.994075	−	0.315030i
$328$	6.64883	+	0.900645i	0.367120	+	0.0497298i
$329$	7.09134	−	1.61855i	0.390958	−	0.0892337i
$330$	0.575131	−	1.21680i	0.0316599	−	0.0669829i
$331$	6.55348	−	0.294317i	0.360212	−	0.0161771i	0.135976	−	0.990712i	$-0.456583\pi$
$331$	6.55348	−	0.294317i	0.360212	−	0.0161771i	0.224236	+	0.974535i	$0.428011\pi$
$332$	1.78718	−	3.71112i	0.0980843	−	0.203674i
$333$	1.26136	−	5.92164i	0.0691219	−	0.324504i
$334$	−0.0317877	−	0.234666i	−0.00173935	−	0.0128404i
$335$	−28.6950	+	35.9823i	−1.56777	+	1.96593i
$336$	4.90844	+	20.8074i	0.267778	+	1.13514i
$337$	−21.9636	−	14.4981i	−1.19643	−	0.789759i	−0.214085	−	0.976815i	$-0.568677\pi$
$337$	−21.9636	−	14.4981i	−1.19643	−	0.789759i	−0.982349	+	0.187056i	$0.940106\pi$
$338$	−0.555282	+	0.764280i	−0.0302033	+	0.0415713i
$339$	−1.87901	−	19.3057i	−0.102054	−	1.04854i
$340$	1.72637	+	6.25535i	0.0936254	+	0.339244i
$341$	−0.235151	−	0.0764052i	−0.0127341	−	0.00413757i
$342$	2.76184	−	0.415060i	0.149343	−	0.0224439i
$343$	3.61573	+	6.05172i	0.195231	+	0.326762i
$344$	1.15446	−	1.32138i	0.0622441	−	0.0712441i
$345$	−16.2292	−	48.7408i	−0.873752	−	2.62412i
$346$	−0.133815	+	1.48680i	−0.00719393	+	0.0799311i
$347$	−26.0275	+	2.34251i	−1.39723	+	0.125753i	−0.762503	−	0.646985i	$-0.776030\pi$
$347$	−26.0275	+	2.34251i	−1.39723	+	0.125753i	−0.634725	+	0.772738i	$0.718887\pi$
$348$	21.4651	+	26.5189i	1.15065	+	1.42156i
$349$	−2.04426	+	3.42151i	−0.109427	+	0.183149i	−0.908264	−	0.418398i	$-0.862592\pi$
$349$	−2.04426	+	3.42151i	−0.109427	+	0.183149i	0.798837	+	0.601547i	$0.205449\pi$
$350$	1.84064	+	5.66490i	0.0983863	+	0.302802i
$351$	−10.4053	−	18.3656i	−0.555394	−	0.980285i
$352$	2.62802	+	0.118025i	0.140074	+	0.00629074i
$353$	12.5180	−	23.2624i	0.666268	−	1.23813i	−0.293129	−	0.956073i	$-0.594696\pi$
$353$	12.5180	−	23.2624i	0.666268	−	1.23813i	0.959397	−	0.282060i	$-0.0910178\pi$
$354$	0.416751	+	0.761151i	0.0221501	+	0.0404547i
$355$	18.2747	+	21.7803i	0.969918	+	1.15598i
$356$		−	20.9559i		−	1.11066i
$357$	5.97764	−	0.0434222i	0.316370	−	0.00229815i
$358$	0.177109	−	3.94365i	0.00936053	−	0.208428i
$359$	13.1516	−	8.68127i	0.694113	−	0.458180i	−0.153948	−	0.988079i	$-0.549199\pi$
$359$	13.1516	−	8.68127i	0.694113	−	0.458180i	0.848061	+	0.529899i	$0.177770\pi$
$360$	−10.3765	−	2.70213i	−0.546889	−	0.142415i
$361$	−6.08393	−	3.63498i	−0.320207	−	0.191315i
$362$	1.83203	−	0.332465i	0.0962896	−	0.0174740i
$363$	−14.7754	+	9.90801i	−0.775508	+	0.520036i
$364$	−26.9685	−	2.42721i	−1.41353	−	0.127220i
$365$	8.78728	−	48.4219i	0.459947	−	2.53452i
$366$	3.01962	+	0.666168i	0.157838	+	0.0348212i
$367$	15.4381	−	9.22385i	0.805864	−	0.481481i	−0.0499586	−	0.998751i	$-0.515909\pi$
$367$	15.4381	−	9.22385i	0.805864	−	0.481481i	0.855822	+	0.517270i	$0.173052\pi$
$368$	23.6239	−	20.6396i	1.23148	−	1.07591i
$369$	−12.0624	−	14.6830i	−0.627941	−	0.764364i
$370$	1.77053	−	0.488636i	0.0920457	−	0.0254030i
$371$	−8.49003	−	3.62882i	−0.440781	−	0.188399i
$372$	−0.122799	+	0.958846i	−0.00636681	+	0.0497139i
$373$	10.3433	−	15.6694i	0.535556	−	0.811332i	−0.461569	−	0.887104i	$-0.652713\pi$
$373$	10.3433	−	15.6694i	0.535556	−	0.811332i	0.997125	+	0.0757718i	$0.0241421\pi$
$374$	0.0611366	−	0.221524i	0.00316130	−	0.0114547i
$375$	7.97539	+	1.38756i	0.411848	+	0.0716532i
$376$	−2.20759	+	0.299038i	−0.113848	+	0.0154217i
$377$	−38.8721	+	14.5889i	−2.00201	+	0.751369i
$378$	−2.39490	+	4.21432i	−0.123180	+	0.216761i
$379$	0.328240	+	7.30883i	0.0168605	+	0.375429i	0.989629	+	0.143649i	$0.0458836\pi$
$379$	0.328240	+	7.30883i	0.0168605	+	0.375429i	−0.972768	+	0.231780i	$0.925545\pi$
$380$	−13.1927	−	18.1582i	−0.676772	−	0.931497i
$381$	−5.22248	+	4.63007i	−0.267556	+	0.237206i
$382$	−0.0799575	+	0.590270i	−0.00409098	+	0.0302008i
$383$	1.07258	+	1.12183i	0.0548065	+	0.0573231i	0.749630	−	0.661858i	$-0.230232\pi$
$383$	1.07258	+	1.12183i	0.0548065	+	0.0573231i	−0.694823	+	0.719181i	$0.744517\pi$
$384$	−1.92619	−	13.4827i	−0.0982954	−	0.688036i
$385$	−2.21714	+	9.71394i	−0.112996	+	0.495068i
$386$	2.07804	+	4.86182i	0.105770	+	0.247460i
$387$	−4.94242	+	0.517311i	−0.251237	+	0.0262964i
$388$	18.0312	+	17.2396i	0.915397	+	0.875209i
$389$	−5.14089	+	2.47572i	−0.260654	+	0.125524i	−0.559647	−	0.828731i	$-0.689063\pi$
$389$	−5.14089	+	2.47572i	−0.260654	+	0.125524i	0.298994	+	0.954255i	$0.403349\pi$
$390$	3.48880	−	5.36975i	0.176662	−	0.271908i
$391$	−4.15658	−	7.72422i	−0.210207	−	0.390631i
$392$	2.28040	+	4.73530i	0.115178	+	0.239169i
$393$	−20.8217	−	5.58399i	−1.05032	−	0.281675i
$394$	−1.64096	+	1.30862i	−0.0826705	+	0.0659276i
$395$	3.10527	−	1.32726i	0.156243	−	0.0667815i
$396$	−3.46288	−	3.51812i	−0.174016	−	0.176792i
$397$	11.0344	−	29.4010i	0.553800	−	1.47559i	−0.299460	−	0.954109i	$-0.596806\pi$
$397$	11.0344	−	29.4010i	0.553800	−	1.47559i	0.853260	−	0.521486i	$-0.174622\pi$
$398$	1.02515	−	0.980148i	0.0513863	−	0.0491304i
$399$	−19.3043	+	7.40543i	−0.966422	+	0.370735i
$400$	5.07064	+	22.2159i	0.253532	+	1.11080i
$401$	−15.0023	+	10.8998i	−0.749178	+	0.544310i	−0.895572	−	0.444917i	$-0.853233\pi$
$401$	−15.0023	+	10.8998i	−0.749178	+	0.544310i	0.146394	+	0.989226i	$0.453233\pi$
$402$	−3.30792	−	5.44628i	−0.164984	−	0.271636i
$403$	−1.05991	−	0.510424i	−0.0527977	−	0.0254260i
$404$	7.18130	+	19.1345i	0.357283	+	0.951977i
$405$	16.3264	+	25.6056i	0.811263	+	1.27235i
$406$	7.45430	+	5.94460i	0.369951	+	0.295026i
$407$	1.66102	+	0.458411i	0.0823335	+	0.0227226i
$408$	−1.82462	−	0.150866i	−0.0903321	−	0.00746897i
$409$	18.2997	+	13.2955i	0.904863	+	0.657421i	0.939710	−	0.341971i	$-0.111095\pi$
$409$	18.2997	+	13.2955i	0.904863	+	0.657421i	−0.0348474	+	0.999393i	$0.511095\pi$
$410$	2.26566	−	5.30077i	0.111893	−	0.261787i
$411$	14.4540	−	14.0218i	0.712962	−	0.691644i
$412$	−9.06094	+	27.8867i	−0.446401	+	1.37388i
$413$	−4.22678	−	4.83794i	−0.207986	−	0.238059i
$414$	7.10941	+	0.215851i	0.349409	+	0.0106085i
$415$	−5.43079	−	4.74473i	−0.266587	−	0.232910i
$416$	12.3154	+	2.23491i	0.603812	+	0.109576i
$417$	8.35855	+	19.1693i	0.409320	+	0.938724i
$418$	0.0712496	+	0.791648i	0.00348493	+	0.0387208i
$419$	−2.45196	−	13.5114i	−0.119786	−	0.660075i	−0.986819	−	0.161825i	$-0.948262\pi$
$419$	−2.45196	−	13.5114i	−0.119786	−	0.660075i	0.867034	−	0.498250i	$-0.166024\pi$
$420$	38.9276	+	1.46499i	1.89947	+	0.0714840i
$421$	34.3379	−	11.1571i	1.67353	−	0.543762i	0.689889	−	0.723915i	$-0.257659\pi$
$421$	34.3379	−	11.1571i	1.67353	−	0.543762i	0.983638	+	0.180154i	$0.0576595\pi$
$422$	2.93244	+	4.44246i	0.142749	+	0.216256i
$423$	5.15766	+	3.63397i	0.250774	+	0.176689i
$424$	2.49019	+	1.34003i	0.120934	+	0.0650774i
$425$	6.37170			0.309073
$426$	−3.70276	+	1.33621i	−0.179399	+	0.0647396i
$427$	−22.8922			−1.10783
$428$	24.9920	+	13.4488i	1.20803	+	0.650070i
$429$	5.39348	−	2.64580i	0.260400	−	0.127740i
$430$	−0.830506	−	1.25816i	−0.0400506	−	0.0606740i
$431$	23.1525	−	7.52270i	1.11522	−	0.362356i	0.307277	−	0.951620i	$-0.400582\pi$
$431$	23.1525	−	7.52270i	1.11522	−	0.362356i	0.807940	+	0.589264i	$0.200582\pi$
$432$	−10.5704	+	15.2363i	−0.508568	+	0.733058i
$433$	1.85740	+	10.2351i	0.0892607	+	0.491867i	0.997329	+	0.0730443i	$0.0232715\pi$
$433$	1.85740	+	10.2351i	0.0892607	+	0.491867i	−0.908068	+	0.418823i	$0.862443\pi$
$434$	0.0242157	+	0.269058i	0.00116239	+	0.0129152i
$435$	54.7534	−	23.8746i	2.62523	−	1.14470i
$436$	−20.6450	−	3.74652i	−0.988718	−	0.179426i
$437$	22.8475	+	19.9613i	1.09294	+	0.954877i
$438$	5.87451	+	3.45220i	0.280695	+	0.164952i
$439$	−2.08356	−	2.38483i	−0.0994430	−	0.113822i	0.701196	−	0.712968i	$-0.252650\pi$
$439$	−2.08356	−	2.38483i	−0.0994430	−	0.113822i	−0.800639	+	0.599146i	$0.795507\pi$
$440$	0.943009	−	2.90228i	0.0449562	−	0.138361i
$441$	4.39361	−	14.2219i	0.209219	−	0.677234i
$442$	0.429732	−	1.00541i	0.0204403	−	0.0478224i
$443$	−24.6101	−	17.8803i	−1.16926	−	0.849518i	−0.178341	−	0.983969i	$-0.557073\pi$
$443$	−24.6101	−	17.8803i	−1.16926	−	0.849518i	−0.990920	+	0.134450i	$0.957073\pi$
$444$	0.555129	−	6.71390i	0.0263452	−	0.318628i
$445$	−35.3670	−	9.76067i	−1.67656	−	0.462700i
$446$	−5.02244	−	4.00526i	−0.237819	−	0.189655i
$447$	−2.38964	−	3.23931i	−0.113026	−	0.153214i
$448$	7.66403	+	20.4207i	0.362091	+	0.964789i
$449$	0.160624	+	0.0773524i	0.00758031	+	0.00365048i	0.437670	−	0.899136i	$-0.355804\pi$
$449$	0.160624	+	0.0773524i	0.00758031	+	0.00365048i	−0.430090	+	0.902786i	$0.641518\pi$
$450$	−2.58527	+	4.47335i	−0.121871	+	0.210876i
$451$	4.37523	−	3.17879i	0.206022	−	0.149684i
$452$	−4.80266	−	21.0418i	−0.225898	−	0.989724i
$453$	2.46338	+	6.42148i	0.115740	+	0.301707i
$454$	−0.878316	+	0.839756i	−0.0412214	+	0.0394117i
$455$	−16.6576	+	44.3839i	−0.780918	+	2.08075i
$456$	6.09191	−	1.72898i	0.285280	−	0.0809668i
$457$	17.8401	−	7.62524i	0.834526	−	0.356693i	0.0670329	−	0.997751i	$-0.478647\pi$
$457$	17.8401	−	7.62524i	0.834526	−	0.356693i	0.767493	+	0.641057i	$0.221504\pi$
$458$	0.760263	−	0.606290i	0.0355248	−	0.0283301i
$459$	3.49582	+	3.82956i	0.163171	+	0.178749i
$460$	−24.8013	−	51.5005i	−1.15637	−	2.40122i
$461$	5.79243	+	10.7641i	0.269780	+	0.501336i	0.979055	−	0.203597i	$-0.0652631\pi$
$461$	5.79243	+	10.7641i	0.269780	+	0.501336i	−0.709275	+	0.704932i	$0.750977\pi$
$462$	−1.15681	−	0.751599i	−0.0538198	−	0.0349675i
$463$	−7.05691	+	3.39843i	−0.327962	+	0.157938i	−0.590618	−	0.806951i	$-0.701116\pi$
$463$	−7.05691	+	3.39843i	−0.327962	+	0.157938i	0.262656	+	0.964890i	$0.415402\pi$
$464$	26.3642	+	25.2067i	1.22393	+	1.17019i
$465$	1.56104	+	0.653849i	0.0723913	+	0.0303215i
$466$	2.78132	+	6.50722i	0.128842	+	0.301441i
$467$	5.56419	−	24.3783i	0.257480	−	1.12809i	−0.666456	−	0.745545i	$-0.732189\pi$
$467$	5.56419	−	24.3783i	0.257480	−	1.12809i	0.923936	−	0.382548i	$-0.124953\pi$
$468$	−14.0801	−	18.7991i	−0.650853	−	0.868988i
$469$	32.6002	+	34.0972i	1.50534	+	1.57446i
$470$	−0.256926	+	1.89670i	−0.0118511	+	0.0874883i
$471$	15.6871	+	17.6943i	0.722826	+	0.815311i
$472$	1.15652	+	1.59181i	0.0532331	+	0.0732691i
$473$	−0.0634524	−	1.41288i	−0.00291754	−	0.0649641i
$474$	0.0243697	+	0.466932i	0.00111934	+	0.0214469i
$475$	−20.6331	+	7.74373i	−0.946712	+	0.355307i
$476$	6.59128	−	0.892850i	0.302111	−	0.0409237i
$477$	−2.58526	−	7.58010i	−0.118371	−	0.347069i
$478$	1.70196	−	6.16692i	0.0778459	−	0.282068i
$479$	2.72193	−	4.12354i	0.124368	−	0.188409i	−0.767055	−	0.641581i	$-0.778279\pi$
$479$	2.72193	−	4.12354i	0.124368	−	0.188409i	0.891423	+	0.453171i	$0.149707\pi$
$480$	−17.8611	−	2.28745i	−0.815242	−	0.104407i
$481$	7.53868	+	3.22219i	0.343734	+	0.146919i
$482$	0.149612	−	0.0412904i	0.00681466	−	0.00188073i
$483$	−51.7405	+	9.77826i	−2.35428	+	0.444926i
$484$	−14.9069	+	13.0238i	−0.677587	+	0.591990i
$485$	37.4935	−	22.4013i	1.70249	−	1.01719i
$486$	−4.10701	+	0.900483i	−0.186298	+	0.0408467i
$487$	3.10676	−	17.1197i	0.140781	−	0.775767i	−0.833857	−	0.551980i	$-0.813872\pi$
$487$	3.10676	−	17.1197i	0.140781	−	0.775767i	0.974638	−	0.223787i	$-0.0718419\pi$
$488$	6.98308	+	0.628489i	0.316109	+	0.0284503i
$489$	16.3787	+	24.4249i	0.740670	+	1.10453i
$490$	4.44307	−	0.806297i	0.200717	−	0.0364248i
$491$	−30.1764	−	18.0295i	−1.36184	−	0.813662i	−0.368584	−	0.929595i	$-0.620157\pi$
$491$	−30.1764	−	18.0295i	−1.36184	−	0.813662i	−0.993257	+	0.115933i	$0.963014\pi$
$492$	−15.3884	−	14.5004i	−0.693764	−	0.653726i
$493$	8.51191	−	5.61866i	0.383357	−	0.253052i
$494$	−0.169671	+	3.77802i	−0.00763386	+	0.169981i
$495$	−7.55040	+	4.20562i	−0.339365	+	0.189029i
$496$			1.03348i			0.0464048i
$497$	24.6374	−	15.5654i	1.10514	−	0.698203i
$498$	0.875791	−	0.479519i	0.0392451	−	0.0214878i
$499$	10.0918	−	18.7537i	0.451770	−	0.839530i	−0.548225	−	0.836331i	$-0.684696\pi$
$499$	10.0918	−	18.7537i	0.451770	−	0.839530i	0.999995	−	0.00319850i	$-0.00101812\pi$
$500$	8.99844	+	0.404120i	0.402422	+	0.0180728i
$501$	−0.710862	+	1.34431i	−0.0317590	+	0.0600595i
$502$	−1.25738	−	3.86980i	−0.0561194	−	0.172718i
$503$	−5.31933	+	8.90305i	−0.237177	+	0.396967i	−0.953776	−	0.300518i	$-0.902841\pi$
$503$	−5.31933	+	8.90305i	−0.237177	+	0.396967i	0.716599	+	0.697485i	$0.245698\pi$
$504$	−4.17234	+	10.1679i	−0.185851	+	0.452915i
$505$	35.6379	−	3.20747i	1.58587	−	0.142730i
$506$	−0.181455	+	2.01613i	−0.00806665	+	0.0896278i
$507$	5.75579	−	1.91651i	0.255624	−	0.0851150i
$508$	−5.10952	+	5.84832i	−0.226698	+	0.259477i
$509$	−7.36480	−	12.3266i	−0.326439	−	0.546367i	0.650602	−	0.759419i	$-0.274517\pi$
$509$	−7.36480	−	12.3266i	−0.326439	−	0.546367i	−0.977041	+	0.213052i	$0.931660\pi$
$510$	−0.542005	+	1.47669i	−0.0240004	+	0.0653888i
$511$	−47.9746	−	15.5879i	−2.12227	−	0.689568i
$512$	−4.93672	−	17.8878i	−0.218174	−	0.790536i
$513$	−15.9745	−	8.15247i	−0.705292	−	0.359940i
$514$	−2.52371	+	3.47360i	−0.111316	+	0.153214i
$515$	42.8437	+	28.2809i	1.88792	+	1.24620i
$516$	−5.38175	+	1.26955i	−0.236918	+	0.0558887i
$517$	−1.11956	+	1.40388i	−0.0492380	+	0.0617425i
$518$	−0.252715	−	1.86562i	−0.0111037	−	0.0819706i
$519$	6.25455	−	7.26474i	0.274544	−	0.318887i
$520$	6.29977	−	13.0816i	0.276263	−	0.573666i
$521$	−13.0992	+	0.588285i	−0.573885	+	0.0257732i	−0.329917	−	0.944010i	$-0.607021\pi$
$521$	−13.0992	+	0.588285i	−0.573885	+	0.0257732i	−0.243968	+	0.969783i	$0.578449\pi$
$522$	0.491029	+	8.25565i	0.0214917	+	0.361340i
$523$	−34.9827	+	7.98457i	−1.52969	+	0.349141i	−0.902831	−	0.429995i	$-0.858515\pi$
$523$	−34.9827	+	7.98457i	−1.52969	+	0.349141i	−0.626855	+	0.779136i	$0.715658\pi$
$524$	−23.7699	−	3.21985i	−1.03839	−	0.140660i
$525$	11.5553	−	36.4626i	0.504313	−	1.59136i
$526$	−4.05577	−	1.52216i	−0.176840	−	0.0663692i
$527$	0.281734	+	0.0643040i	0.0122725	+	0.00280113i
$528$	−4.15001	−	3.26049i	−0.180606	−	0.141894i
$529$	33.8343	+	42.4268i	1.47106	+	1.84465i
$530$	1.67901	−	1.75611i	0.0729316	−	0.0762804i
$531$	0.667712	−	5.53233i	0.0289762	−	0.240083i
$532$	−20.2591	+	10.9019i	−0.878342	+	0.472656i
$533$	22.6588	−	12.1932i	0.981463	−	0.528148i
$534$	2.95591	−	4.13123i	0.127915	−	0.178776i
$535$	34.3378	−	35.9146i	1.48455	−	1.55272i
$536$	−9.00831	−	11.2961i	−0.389100	−	0.487915i
$537$	−15.6611	+	19.9337i	−0.675825	+	0.860203i
$538$	−5.56541	−	1.27027i	−0.239942	−	0.0547652i
$539$	3.96618	+	1.48853i	0.170836	+	0.0641157i
$540$	21.6384	+	25.9528i	0.931170	+	1.11683i
$541$	−0.0726019	−	0.00983460i	−0.00312140	−	0.000422822i	0.132672	−	0.991160i	$-0.457644\pi$
$541$	−0.0726019	−	0.00983460i	−0.00312140	−	0.000422822i	−0.135794	+	0.990737i	$0.543358\pi$
$542$	−3.63901	+	0.830581i	−0.156309	+	0.0356765i
$543$	−10.8100	−	5.10943i	−0.463902	−	0.219267i
$544$	−3.07154	+	0.137943i	−0.131691	+	0.00591426i
$545$	−15.9388	+	33.0973i	−0.682744	+	1.41773i
$546$	−4.97419	−	4.28251i	−0.212876	−	0.183274i
$547$	−0.677786	−	5.00362i	−0.0289800	−	0.213939i	0.970669	−	0.240419i	$-0.0772847\pi$
$547$	−0.677786	−	5.00362i	−0.0289800	−	0.213939i	−0.999649	+	0.0264793i	$0.991570\pi$
$548$	13.9707	−	17.5187i	0.596797	−	0.748360i
$549$	−13.2805	−	14.7624i	−0.566800	−	0.630042i
$550$	−1.22719	−	0.810060i	−0.0523275	−	0.0345411i
$551$	−20.7351	+	28.5394i	−0.883344	+	1.21582i
$552$	16.0515	−	1.56228i	0.683195	−	0.0664950i
$553$	−0.920881	−	3.33674i	−0.0391598	−	0.141892i
$554$	−2.38122	−	0.773704i	−0.101168	−	0.0328715i
$555$	−11.0724	−	4.06403i	−0.469997	−	0.172509i
$556$	11.9347	+	19.9754i	0.506145	+	0.847144i
$557$	−11.2061	+	12.8264i	−0.474817	+	0.543471i	−0.939745	−	0.341877i	$-0.888937\pi$
$557$	−11.2061	+	12.8264i	−0.474817	+	0.543471i	0.464928	+	0.885348i	$0.346080\pi$
$558$	−0.159457	+	0.171705i	−0.00675037	+	0.00726886i
$559$	0.603195	−	6.70205i	0.0255124	−	0.283466i
$560$	41.4796	−	3.73323i	1.75283	−	0.157758i
$561$	−1.14704	+	0.928448i	−0.0484283	+	0.0391991i
$562$	1.75496	−	2.93731i	0.0740285	−	0.123903i
$563$	2.63797	+	8.11885i	0.111177	+	0.342169i	0.991131	−	0.132892i	$-0.0424262\pi$
$563$	2.63797	+	8.11885i	0.111177	+	0.342169i	−0.879953	+	0.475060i	$0.842426\pi$
$564$	6.20608	+	3.28172i	0.261323	+	0.138186i
$565$	−37.7489	−	1.69531i	−1.58811	−	0.0713221i
$566$	0.374259	−	0.695489i	0.0157313	−	0.0292336i
$567$	28.2548	−	13.0601i	1.18659	−	0.548473i
$568$	−7.94275	+	4.07168i	−0.333270	+	0.170844i
$569$		−	4.53341i		−	0.190051i	−0.995475	−	0.0950253i	$-0.969707\pi$
$569$		−	4.53341i		−	0.190051i	0.995475	−	0.0950253i	$-0.0302932\pi$
$570$	−0.0395210	−	5.44058i	−0.00165535	−	0.227881i
$571$	−0.453499	+	10.0979i	−0.0189783	+	0.422585i	0.966903	+	0.255143i	$0.0821224\pi$
$571$	−0.453499	+	10.0979i	−0.0189783	+	0.422585i	−0.985882	+	0.167443i	$0.946449\pi$
$572$	5.57872	−	3.68248i	0.233258	−	0.153972i
$573$	2.62322	−	2.78388i	0.109587	−	0.116298i
$574$	−5.07243	−	3.03063i	−0.211719	−	0.126496i
$575$	−55.2242	+	10.0217i	−2.30301	+	0.417934i
$576$	−8.72241	+	16.7890i	−0.363434	+	0.699541i
$577$	−14.3118	−	1.28808i	−0.595807	−	0.0536236i	−0.212368	−	0.977190i	$-0.568118\pi$
$577$	−14.3118	−	1.28808i	−0.595807	−	0.0536236i	−0.383439	+	0.923566i	$0.625260\pi$
$578$	0.770778	−	4.24734i	0.0320601	−	0.176666i
$579$	7.31457	−	33.1556i	0.303983	−	1.37790i
$580$	57.0559	−	34.0893i	2.36912	−	1.41548i
$581$	−5.56660	+	4.86339i	−0.230941	+	0.201767i
$582$	1.12295	+	5.94198i	0.0465479	+	0.246303i
$583$	2.19718	−	0.606383i	0.0909979	−	0.0251138i
$584$	14.2063	+	6.07205i	0.587860	+	0.251263i
$585$	−38.2851	+	15.0067i	−1.58289	+	0.620451i
$586$	−1.36640	+	2.07001i	−0.0564456	+	0.0855114i
$587$	2.96848	−	10.7561i	0.122522	−	0.443950i	−0.876796	−	0.480862i	$-0.840324\pi$
$587$	2.96848	−	10.7561i	0.122522	−	0.443950i	0.999319	+	0.0369125i	$0.0117523\pi$
$588$	2.83892	−	16.3175i	0.117075	−	0.672923i
$589$	−0.990475	+	0.134169i	−0.0408118	+	0.00552833i
$590$	1.58271	−	0.593999i	0.0651590	−	0.0244546i
$591$	13.4598	−	0.702480i	0.553660	−	0.0288962i
$592$	−0.323134	−	7.19514i	−0.0132807	−	0.295719i
$593$	4.67575	+	6.43562i	0.192010	+	0.264279i	0.894158	−	0.447752i	$-0.147775\pi$
$593$	4.67575	+	6.43562i	0.192010	+	0.264279i	−0.702148	+	0.712031i	$0.747775\pi$
$594$	−0.186427	−	1.18201i	−0.00764920	−	0.0484986i
$595$	1.56318	−	11.5399i	0.0640843	−	0.473089i
$596$	−3.09527	−	3.23740i	−0.126787	−	0.132609i
$597$	−9.01631	+	1.28811i	−0.369013	+	0.0527186i
$598$	−2.14318	+	9.38988i	−0.0876411	+	0.383981i
$599$	13.8388	+	32.3775i	0.565438	+	1.32291i	0.921475	+	0.388437i	$0.126985\pi$
$599$	13.8388	+	32.3775i	0.565438	+	1.32291i	−0.356037	+	0.934472i	$0.615872\pi$
$600$	−4.52588	+	10.8053i	−0.184768	+	0.441126i
$601$	5.35147	+	5.11653i	0.218291	+	0.208708i	0.792284	−	0.610153i	$-0.208892\pi$
$601$	5.35147	+	5.11653i	0.218291	+	0.208708i	−0.573993	+	0.818860i	$0.694606\pi$
$602$	−1.39223	+	0.670460i	−0.0567429	+	0.0273259i
$603$	−3.07553	+	40.8035i	−0.125245	+	1.66165i
$604$	3.62646	+	6.73909i	0.147559	+	0.274210i
$605$	15.0368	+	31.2243i	0.611334	+	1.26945i
$606$	−1.28327	+	4.78511i	−0.0521295	+	0.194382i
$607$	9.93019	−	7.91907i	0.403054	−	0.321425i	−0.400894	−	0.916124i	$-0.631300\pi$
$607$	9.93019	−	7.91907i	0.403054	−	0.321425i	0.803948	+	0.594700i	$0.202729\pi$
$608$	9.77874	−	4.17963i	0.396580	−	0.169507i
$609$	−16.7166	−	58.8997i	−0.677393	−	2.38674i
$610$	2.11666	−	5.63981i	0.0857010	−	0.228349i
$611$	−6.17517	+	5.90407i	−0.249821	+	0.238853i
$612$	4.39958	+	3.73250i	0.177843	+	0.150877i
$613$	−3.06867	−	13.4447i	−0.123943	−	0.543028i	−0.998328	−	0.0577966i	$-0.981593\pi$
$613$	−3.06867	−	13.4447i	−0.123943	−	0.543028i	0.874386	−	0.485231i	$-0.161265\pi$
$614$	−0.969443	+	0.704342i	−0.0391235	+	0.0284249i
$615$	−31.6396	+	19.2170i	−1.27583	+	0.774904i
$616$	−2.81819	−	1.35717i	−0.113548	−	0.0546819i
$617$	−4.72473	−	12.5890i	−0.190211	−	0.506814i	0.806183	−	0.591666i	$-0.201530\pi$
$617$	−4.72473	−	12.5890i	−0.190211	−	0.506814i	−0.996394	+	0.0848520i	$0.972958\pi$
$618$	−5.71979	+	4.21949i	−0.230084	+	0.169733i
$619$	7.85932	+	6.26760i	0.315893	+	0.251916i	0.768580	−	0.639753i	$-0.220963\pi$
$619$	7.85932	+	6.26760i	0.315893	+	0.251916i	−0.452688	+	0.891669i	$0.649535\pi$
$620$	1.81531	+	0.500994i	0.0729046	+	0.0201204i
$621$	−36.3220	−	27.6928i	−1.45755	−	1.11128i
$622$	4.49905	+	3.26875i	0.180396	+	0.131065i
$623$	−14.7804	+	34.5804i	−0.592163	+	1.38543i
$624$	−17.4843	−	18.0232i	−0.699934	−	0.721507i
$625$	−4.99235	+	15.3649i	−0.199694	+	0.614595i
$626$	1.49866	+	1.71536i	0.0598987	+	0.0685595i
$627$	2.58603	−	4.40058i	0.103276	−	0.175742i
$628$	19.8147	+	17.3116i	0.790693	+	0.690807i
$629$	−1.98155	−	0.359598i	−0.0790094	−	0.0143381i
$630$	7.46751	+	5.77968i	0.297513	+	0.230268i
$631$	0.270192	+	3.00208i	0.0107562	+	0.119511i	0.999558	−	0.0297224i	$-0.00946234\pi$
$631$	0.270192	+	3.00208i	0.0107562	+	0.119511i	−0.988802	+	0.149233i	$0.952319\pi$
$632$	0.189299	+	1.04312i	0.00752992	+	0.0414933i
$633$	1.28549	−	34.1581i	0.0510938	−	1.35766i
$634$	−4.07578	+	1.32430i	−0.161870	+	0.0525947i
$635$	7.49025	+	11.3472i	0.297242	+	0.450302i
$636$	−3.92474	−	8.00061i	−0.155626	−	0.317245i
$637$	17.7493	+	9.55132i	0.703254	+	0.378437i
$638$	−2.35372			−0.0931846
$639$	24.3305	+	6.85773i	0.962498	+	0.271287i
$640$	−26.5322			−1.04878
$641$	−19.0103	−	10.2299i	−0.750861	−	0.404056i	0.0532141	−	0.998583i	$-0.483053\pi$
$641$	−19.0103	−	10.2299i	−0.750861	−	0.404056i	−0.804075	+	0.594527i	$0.797339\pi$
$642$	3.02991	+	6.17649i	0.119581	+	0.243767i
$643$	−18.2982	−	27.7205i	−0.721609	−	1.09319i	−0.991476	−	0.130293i	$-0.958408\pi$
$643$	−18.2982	−	27.7205i	−0.721609	−	1.09319i	0.269867	−	0.962898i	$-0.413020\pi$
$644$	−55.7230	+	18.1055i	−2.19580	+	0.713457i
$645$	−0.364069	+	9.67403i	−0.0143352	+	0.380914i
$646$	−0.165878	−	0.914061i	−0.00652637	−	0.0359632i
$647$	2.06300	+	22.9218i	0.0811050	+	0.901150i	0.928779	+	0.370633i	$0.120859\pi$
$647$	2.06300	+	22.9218i	0.0811050	+	0.901150i	−0.847674	+	0.530517i	$0.821998\pi$
$648$	−8.97742	+	3.20816i	−0.352667	+	0.126028i
$649$	1.56045	+	0.283179i	0.0612528	+	0.0111158i
$650$	−5.26867	−	4.60309i	−0.206654	−	0.180548i
$651$	0.878918	−	1.49563i	0.0344475	−	0.0586184i
$652$	21.5293	+	24.6423i	0.843153	+	0.965066i
$653$	2.83122	−	8.71360i	0.110794	−	0.340990i	−0.880252	−	0.474506i	$-0.842627\pi$
$653$	2.83122	−	8.71360i	0.110794	−	0.340990i	0.991047	+	0.133516i	$0.0426268\pi$
$654$	−3.54149	−	3.65065i	−0.138483	−	0.142752i
$655$	−16.5055	+	38.6164i	−0.644922	+	1.50887i
$656$	−18.2879	−	13.2870i	−0.714024	−	0.518769i
$657$	−17.7796	−	39.9800i	−0.693647	−	1.55977i
$658$	1.89119	+	0.521935i	0.0737262	+	0.0203471i
$659$	17.4712	+	13.9329i	0.680583	+	0.542747i	0.901626	−	0.432517i	$-0.142375\pi$
$659$	17.4712	+	13.9329i	0.680583	+	0.542747i	−0.221043	+	0.975264i	$0.570946\pi$
$660$	−7.73879	+	5.70891i	−0.301232	+	0.222219i
$661$	7.12493	+	18.9843i	0.277128	+	0.738404i	0.998927	+	0.0463024i	$0.0147438\pi$
$661$	7.12493	+	18.9843i	0.277128	+	0.738404i	−0.721800	+	0.692102i	$0.756685\pi$
$662$	1.59418	+	0.767718i	0.0619597	+	0.0298382i
$663$	−6.00113	+	3.64492i	−0.233065	+	0.141557i
$664$	1.83156	−	1.33071i	0.0710784	−	0.0516415i
$665$	8.96283	+	39.2687i	0.347564	+	1.52278i
$666$	1.05646	−	1.24527i	0.0409369	−	0.0482533i
$667$	−64.9363	+	62.0855i	−2.51434	+	2.40396i
$668$	−0.594551	+	1.58417i	−0.0230039	+	0.0612936i
$669$	11.2631	+	39.6845i	0.435456	+	1.53429i
$670$	−11.4146	+	4.87882i	−0.440983	+	0.188485i
$671$	4.41837	−	3.52353i	0.170569	−	0.136025i
$672$	−4.78094	+	17.8273i	−0.184429	+	0.687703i
$673$	1.60950	+	3.34215i	0.0620415	+	0.128830i	0.929684	−	0.368358i	$-0.120080\pi$
$673$	1.60950	+	3.34215i	0.0620415	+	0.128830i	−0.867642	+	0.497189i	$0.834366\pi$
$674$	−3.36369	−	6.25078i	−0.129564	−	0.240771i
$675$	30.2169	−	13.7016i	1.16305	−	0.527373i
$676$	6.08168	−	2.92878i	0.233911	−	0.112646i
$677$	37.5266	+	35.8791i	1.44226	+	1.37895i	0.767981	+	0.640473i	$0.221262\pi$
$677$	37.5266	+	35.8791i	1.44226	+	1.37895i	0.674283	+	0.738473i	$0.264453\pi$
$678$	2.02123	−	4.82560i	0.0776250	−	0.185326i
$679$	−17.5950	−	41.1655i	−0.675234	−	1.57979i
$680$	−0.793654	+	3.47723i	−0.0304353	+	0.133346i
$681$	7.72485	−	1.10360i	0.296017	−	0.0422901i
$682$	−0.0460868	−	0.0482030i	−0.00176475	−	0.00184579i
$683$	−1.28871	+	9.51364i	−0.0493111	+	0.364029i	0.949435	+	0.313964i	$0.101657\pi$
$683$	−1.28871	+	9.51364i	−0.0493111	+	0.364029i	−0.998746	+	0.0500651i	$0.984057\pi$
$684$	−18.7831	−	6.73978i	−0.718191	−	0.257702i
$685$	−23.0589	−	31.7378i	−0.881034	−	1.21264i
$686$	0.0853078	+	1.89953i	0.00325707	+	0.0725242i
$687$	−6.23594	+	0.325461i	−0.237916	+	0.0124171i
$688$	−5.53465	+	2.07719i	−0.211007	+	0.0791921i
$689$	10.7467	−	1.45574i	0.409416	−	0.0554592i
$690$	2.37501	−	13.6511i	0.0904152	−	0.519688i
$691$	3.55650	−	12.8867i	0.135296	−	0.490233i	−0.864630	−	0.502409i	$-0.832447\pi$
$691$	3.55650	−	12.8867i	0.135296	−	0.490233i	0.999926	+	0.0121759i	$0.00387580\pi$
$692$	5.87618	−	8.90204i	0.223379	−	0.338405i
$693$	3.23292	+	8.24782i	0.122809	+	0.313309i
$694$	−6.48138	−	2.77027i	−0.246030	−	0.105158i
$695$	39.2710	−	10.8381i	1.48963	−	0.411113i
$696$	3.48222	+	18.4258i	0.131993	+	0.698427i
$697$	−4.76000	+	4.15868i	−0.180298	+	0.157521i
$698$	−0.922862	+	0.551385i	−0.0349309	+	0.0208702i
$699$	9.79006	−	44.3765i	0.370294	−	1.67847i
$700$	7.59945	−	41.8764i	0.287232	−	1.58278i
$701$	−35.9127	−	3.23220i	−1.35640	−	0.122079i	−0.612556	−	0.790427i	$-0.709859\pi$
$701$	−35.9127	−	3.23220i	−1.35640	−	0.122079i	−0.743848	+	0.668349i	$0.767001\pi$
$702$	−0.124061	−	5.69209i	−0.00468240	−	0.214834i
$703$	6.85375	−	1.24377i	0.258494	−	0.0469098i
$704$	−4.62234	−	2.76172i	−0.174211	−	0.104086i
$705$	8.42914	−	8.94538i	0.317460	−	0.336903i
$706$	5.94650	−	3.92525i	0.223799	−	0.147729i
$707$	1.64550	−	36.6398i	0.0618853	−	1.37798i
$708$	−0.0450398	−	6.20032i	−0.00169270	−	0.233022i
$709$			38.4410i			1.44368i	0.692059	+	0.721841i	$0.256704\pi$
$709$			38.4410i			1.44368i	−0.692059	+	0.721841i	$0.743296\pi$
$710$	1.55673	+	7.50895i	0.0584229	+	0.281806i
$711$	1.61750	−	2.52959i	0.0606611	−	0.0948671i
$712$	5.45800	−	10.1427i	0.204547	−	0.380112i
$713$	−2.54296	−	0.114205i	−0.0952347	−	0.00427699i
$714$	1.42534	+	0.753709i	0.0533421	+	0.0282069i
$715$	−3.61646	−	11.1303i	−0.135248	−	0.416250i
$716$	−14.4673	+	24.2142i	−0.540668	+	0.904926i
$717$	−31.9322	+	25.8467i	−1.19253	+	0.965264i
$718$	4.23331	−	0.381004i	0.157986	−	0.0142190i
$719$	−3.37720	+	37.5237i	−0.125948	+	1.39940i	0.645817	+	0.763492i	$0.276517\pi$
$719$	−3.37720	+	37.5237i	−0.125948	+	1.39940i	−0.771765	+	0.635907i	$0.780626\pi$
$720$	26.4711	+	24.5829i	0.986520	+	0.916150i
$721$	34.6206	−	39.6265i	1.28934	−	1.47577i
$722$	−0.980438	−	1.64098i	−0.0364881	−	0.0610708i
$723$	−0.935633	−	0.343416i	−0.0347966	−	0.0127718i
$724$	−12.6530	−	4.11122i	−0.470247	−	0.152792i
$725$	−17.3617	−	62.9086i	−0.644796	−	2.33637i
$726$	−4.77579	+	0.464825i	−0.177246	+	0.0172513i
$727$	−6.22743	+	8.57133i	−0.230963	+	0.317893i	−0.908731	−	0.417383i	$-0.862947\pi$
$727$	−6.22743	+	8.57133i	−0.230963	+	0.317893i	0.677768	+	0.735276i	$0.262947\pi$
$728$	−12.4206	−	8.19877i	−0.460338	−	0.303867i
$729$	24.8135	+	10.6438i	0.919018	+	0.394216i
$730$	8.27610	−	10.3779i	0.306312	−	0.384103i
$731$	0.221885	+	1.63802i	0.00820673	+	0.0605845i
$732$	−16.7441	−	14.4158i	−0.618881	−	0.532823i
$733$	0.548133	−	1.13821i	0.0202458	−	0.0420408i	−0.890601	−	0.454786i	$-0.849716\pi$
$733$	0.548133	−	1.13821i	0.0202458	−	0.0420408i	0.910847	+	0.412745i	$0.135430\pi$
$734$	4.84575	−	0.217623i	0.178860	−	0.00803261i
$735$	−26.2166	−	12.3914i	−0.967012	−	0.457065i
$736$	26.4044	−	6.02663i	0.973279	−	0.222145i
$737$	−11.5403	−	1.56323i	−0.425091	−	0.0575825i
$738$	−0.988338	−	5.02919i	−0.0363812	−	0.185127i
$739$	12.5620	+	4.71460i	0.462101	+	0.173429i	0.571557	−	0.820562i	$-0.306340\pi$
$739$	12.5620	+	4.71460i	0.462101	+	0.173429i	−0.109456	+	0.993992i	$0.534911\pi$
$740$	−12.7949	−	2.92035i	−0.470349	−	0.107354i
$741$	15.0033	−	19.0965i	0.551161	−	0.701528i
$742$	−1.55272	−	1.94705i	−0.0570021	−	0.0714783i
$743$	11.0073	−	11.5127i	0.403818	−	0.422361i	−0.489347	−	0.872089i	$-0.662765\pi$
$743$	11.0073	−	11.5127i	0.403818	−	0.422361i	0.893165	+	0.449728i	$0.148479\pi$
$744$	−0.309168	+	0.432099i	−0.0113346	+	0.0158415i
$745$	−6.90541	+	3.71596i	−0.252995	+	0.136142i
$746$	4.45948	−	2.39975i	0.163273	−	0.0878609i
$747$	−6.36558	−	0.768279i	−0.232904	−	0.0281099i
$748$	−1.13474	+	1.18685i	−0.0414902	+	0.0433954i
$749$	−31.7550	−	39.8195i	−1.16030	−	1.45497i
$750$	1.71694	+	1.34893i	0.0626940	+	0.0492560i
$751$	39.2447	+	8.95735i	1.43206	+	0.326858i	0.867048	−	0.498224i	$-0.166014\pi$
$751$	39.2447	+	8.95735i	1.43206	+	0.326858i	0.565012	+	0.825083i	$0.308871\pi$
$752$	7.02692	+	2.63725i	0.256245	+	0.0961705i
$753$	−7.89362	+	24.9083i	−0.287659	+	0.907708i
$754$	−11.0975	−	1.50325i	−0.404145	−	0.0547452i
$755$	13.0626	−	2.98145i	0.475396	−	0.108506i
$756$	29.3383	−	18.4080i	1.06702	−	0.669491i
$757$	29.3389	−	1.31761i	1.06634	−	0.0478895i	0.495230	−	0.868762i	$-0.335084\pi$
$757$	29.3389	−	1.31761i	1.06634	−	0.0478895i	0.571112	+	0.820872i	$0.306512\pi$
$758$	−0.856204	+	1.77793i	−0.0310987	+	0.0645772i
$759$	8.48125	−	9.85109i	0.307850	−	0.357572i
$760$	−1.65594	−	12.2247i	−0.0600673	−	0.443435i
$761$	20.5236	−	25.7358i	0.743979	−	0.932920i	−0.255446	−	0.966823i	$-0.582222\pi$
$761$	20.5236	−	25.7358i	0.743979	−	0.932920i	0.999425	+	0.0339030i	$0.0107937\pi$
$762$	−1.83221	+	0.432217i	−0.0663741	+	0.0156576i
$763$	31.4250	+	20.7434i	1.13766	+	0.750963i
$764$	2.50171	−	3.44331i	0.0905087	−	0.124575i
$765$	8.34849	−	5.68663i	0.301840	−	0.205600i
$766$	0.111371	+	0.403545i	0.00402402	+	0.0145807i
$767$	7.17643	+	2.33176i	0.259126	+	0.0841951i
$768$	−6.26175	+	17.0601i	−0.225951	+	0.615602i
$769$	−20.8390	−	34.8787i	−0.751475	−	1.25776i	−0.960071	−	0.279755i	$-0.909747\pi$
$769$	−20.8390	−	34.8787i	−0.751475	−	1.25776i	0.208597	−	0.978002i	$-0.433110\pi$
$770$	−1.76818	+	2.02385i	−0.0637209	+	0.0729344i
$771$	26.1597	−	8.71038i	0.942118	−	0.313697i
$772$	3.38651	−	37.6272i	0.121883	−	1.35423i
$773$	21.3256	−	1.91934i	0.767027	−	0.0690337i	0.300786	−	0.953692i	$-0.402751\pi$
$773$	21.3256	−	1.91934i	0.767027	−	0.0690337i	0.466241	+	0.884658i	$0.345608\pi$
$774$	−1.24003	−	0.508838i	−0.0445719	−	0.0182898i
$775$	0.948389	−	1.58734i	0.0340671	−	0.0570188i
$776$	4.23703	+	13.0402i	0.152101	+	0.468117i
$777$	−5.65142	+	10.6874i	−0.202743	+	0.383409i
$778$	−1.53748	−	0.0690483i	−0.0551214	−	0.00247550i
$779$	10.3598	−	19.2518i	0.371180	−	0.689767i
$780$	−40.1335	+	21.9742i	−1.43701	+	0.786801i
$781$	−2.35940	+	6.79637i	−0.0844259	+	0.243193i
$782$		−	2.36590i		−	0.0846045i
$783$	28.2843	−	44.9496i	1.01080	−	1.60637i
$784$	0.794433	−	17.6894i	0.0283726	−	0.631766i
$785$	38.4457	−	25.3778i	1.37218	−	0.905771i
$786$	−4.23181	−	3.98759i	−0.150944	−	0.142233i
$787$	14.9968	+	8.96020i	0.534580	+	0.319397i	0.754693	−	0.656078i	$-0.227786\pi$
$787$	14.9968	+	8.96020i	0.534580	+	0.319397i	−0.220114	+	0.975474i	$0.570643\pi$
$788$	14.7560	−	2.67782i	0.525661	−	0.0953935i
$789$	15.4933	+	23.1045i	0.551575	+	0.822542i
$790$	0.907196	+	0.0816492i	0.0322766	+	0.00290495i
$791$	−6.91586	+	38.1095i	−0.245900	+	1.35502i
$792$	−0.759737	−	2.60468i	−0.0269961	−	0.0925534i
$793$	23.0824	−	13.7911i	0.819680	−	0.489736i
$794$	6.37870	−	5.57290i	0.226372	−	0.197775i
$795$	−15.3306	+	2.89727i	−0.543719	+	0.102755i
$796$	−9.76908	+	2.69610i	−0.346256	+	0.0955606i
$797$	−19.2393	−	8.22328i	−0.681492	−	0.291284i	0.0242981	−	0.999705i	$-0.492265\pi$
$797$	−19.2393	−	8.22328i	−0.681492	−	0.291284i	−0.705790	+	0.708421i	$0.749408\pi$
$798$	−5.53161	−	0.708428i	−0.195817	−	0.0250781i
$799$	1.15615	−	1.75149i	0.0409016	−	0.0619633i
$800$	−5.23387	+	18.9645i	−0.185045	+	0.670496i
$801$	−30.8742	+	10.5299i	−1.09088	+	0.372056i
$802$	−4.95644	+	0.671395i	−0.175018	+	0.0237078i
$803$	11.6587	−	4.37559i	0.411427	−	0.154411i
$804$	2.37308	+	45.4689i	0.0836920	+	1.60357i
$805$	4.60221	+	102.476i	0.162206	+	3.61181i
$806$	−0.186507	−	0.256705i	−0.00656943	−	0.00904204i
$807$	24.3185	+	27.4300i	0.856052	+	0.965583i
$808$	−1.50786	+	11.1315i	−0.0530464	+	0.391604i
$809$	30.1619	+	31.5468i	1.06043	+	1.10913i	0.993781	+	0.111351i	$0.0355178\pi$
$809$	30.1619	+	31.5468i	1.06043	+	1.10913i	0.0666531	+	0.997776i	$0.478768\pi$
$810$	0.605048	+	8.16850i	0.0212592	+	0.287012i
$811$	−6.44170	+	28.2229i	−0.226199	+	0.991041i	0.726510	+	0.687156i	$0.241141\pi$
$811$	−6.44170	+	28.2229i	−0.226199	+	0.991041i	−0.952709	+	0.303885i	$0.901716\pi$
$812$	−26.7752	−	62.6438i	−0.939626	−	2.19836i
$813$	22.1082	+	9.26014i	0.775367	+	0.324767i
$814$	0.335929	+	0.321181i	0.0117743	+	0.0112574i
$815$	51.6162	−	24.8570i	1.80804	−	0.870704i
$816$	5.17245	+	3.36061i	0.181072	+	0.117645i
$817$	−2.70926	−	5.03465i	−0.0947851	−	0.176140i
$818$	2.64715	+	5.49687i	0.0925555	+	0.192193i
$819$	9.97513	+	40.9521i	0.348559	+	1.43098i
$820$	−32.2038	+	25.6817i	−1.12460	+	0.896842i
$821$	−23.5542	+	10.0675i	−0.822047	+	0.351360i	−0.762599	−	0.646872i	$-0.776077\pi$
$821$	−23.5542	+	10.0675i	−0.822047	+	0.351360i	−0.0594480	+	0.998231i	$0.518934\pi$
$822$	5.22524	−	1.48300i	0.182251	−	0.0517257i
$823$	−10.9201	+	29.0965i	−0.380651	+	1.01424i	0.596672	+	0.802485i	$0.296489\pi$
$823$	−10.9201	+	29.0965i	−0.380651	+	1.01424i	−0.977323	+	0.211755i	$0.932082\pi$
$824$	−11.6486	+	11.1372i	−0.405800	+	0.387984i
$825$	3.38200	+	8.81611i	0.117746	+	0.306937i
$826$	−0.385579	−	1.68933i	−0.0134160	−	0.0587794i
$827$	11.2786	−	8.19441i	0.392197	−	0.284948i	−0.374158	−	0.927365i	$-0.622068\pi$
$827$	11.2786	−	8.19441i	0.392197	−	0.284948i	0.766355	+	0.642417i	$0.222068\pi$
$828$	−44.0023	−	25.4301i	−1.52919	−	0.883757i
$829$	−10.1417	−	4.88399i	−0.352236	−	0.169628i	0.249395	−	0.968402i	$-0.419768\pi$
$829$	−10.1417	−	4.88399i	−0.352236	−	0.169628i	−0.601632	+	0.798774i	$0.705482\pi$
$830$	−0.683464	−	1.82108i	−0.0237234	−	0.0632107i
$831$	9.54470	+	12.9385i	0.331102	+	0.448830i
$832$	−20.0299	−	15.9733i	−0.694410	−	0.553774i
$833$	−4.77282	−	1.31721i	−0.165368	−	0.0456388i
$834$	−0.464794	+	5.62137i	−0.0160945	+	0.194652i
$835$	2.39667	+	1.74128i	0.0829400	+	0.0602595i
$836$	2.23215	−	5.22238i	0.0772006	−	0.180620i
$837$	1.47436	−	0.300882i	0.0509615	−	0.0104000i
$838$	1.14456	−	3.52258i	0.0395380	−	0.121686i
$839$	−15.6217	−	17.8805i	−0.539322	−	0.617304i	0.417253	−	0.908790i	$-0.362993\pi$
$839$	−15.6217	−	17.8805i	−0.539322	−	0.617304i	−0.956575	+	0.291487i	$0.905850\pi$
$840$	18.4594	+	10.8478i	0.636909	+	0.374285i
$841$	−56.8280	−	49.6492i	−1.95959	−	1.71204i
$842$	9.58187	+	1.73885i	0.330213	+	0.0599248i
$843$	−20.1410	+	8.78223i	−0.693691	+	0.302476i
$844$	−3.40939	−	37.8814i	−0.117356	−	1.30393i
$845$	−2.11019	−	11.6281i	−0.0725928	−	0.400019i
$846$	0.760564	+	1.52235i	0.0261487	+	0.0523394i
$847$	33.7844	−	10.9772i	1.16085	−	0.377182i
$848$	−5.24855	−	7.95121i	−0.180236	−	0.273046i
$849$	−4.55337	+	2.23368i	−0.156271	+	0.0766595i
$850$	1.51339	+	0.814389i	0.0519088	+	0.0279333i
$851$	17.7399			0.608115
$852$	27.8225	+	4.12970i	0.953182	+	0.141481i
$853$	−21.0838			−0.721895			−0.360947	−	0.932586i	$-0.617547\pi$
$853$	−21.0838			−0.721895			−0.360947	+	0.932586i	$0.617547\pi$
$854$	−5.43730	−	2.92594i	−0.186061	−	0.100124i
$855$	−20.1233	+	28.5609i	−0.688202	+	0.976761i
$856$	8.59337	+	13.0184i	0.293715	+	0.444960i
$857$	45.0679	−	14.6434i	1.53949	−	0.500211i	0.588254	−	0.808676i	$-0.299815\pi$
$857$	45.0679	−	14.6434i	1.53949	−	0.500211i	0.951236	+	0.308465i	$0.0998153\pi$
$858$	1.61921	+	0.0609369i	0.0552790	+	0.00208035i
$859$	3.67503	+	20.2511i	0.125391	+	0.690959i	0.983978	+	0.178291i	$0.0570569\pi$
$859$	3.67503	+	20.2511i	0.125391	+	0.690959i	−0.858587	+	0.512667i	$0.828657\pi$
$860$	0.965585	+	10.7285i	0.0329262	+	0.365840i
$861$	15.1660	+	34.7813i	0.516856	+	1.18535i
$862$	6.46062	+	1.17243i	0.220050	+	0.0399331i
$863$	14.8516	+	12.9755i	0.505555	+	0.441690i	0.872544	−	0.488535i	$-0.162469\pi$
$863$	14.8516	+	12.9755i	0.505555	+	0.441690i	−0.366989	+	0.930225i	$0.619611\pi$
$864$	−14.2697	+	7.25915i	−0.485466	+	0.246961i
$865$	−12.2869	−	14.0635i	−0.417767	−	0.478173i
$866$	−0.867019	+	2.66841i	−0.0294625	+	0.0906763i
$867$	−19.8963	+	19.3014i	−0.675713	+	0.655509i
$868$	0.758644	−	1.77494i	0.0257500	−	0.0602452i
$869$	0.691321	+	0.502274i	0.0234515	+	0.0170385i
$870$	16.0564	+	1.32760i	0.544362	+	0.0450098i
$871$	−53.4124	−	14.7409i	−1.80981	−	0.499475i
$872$	−9.01641	−	7.19035i	−0.305334	−	0.243496i
$873$	16.3387	−	35.2278i	0.552980	−	1.19228i
$874$	2.87536	+	7.66136i	0.0972604	+	0.259149i
$875$	−14.5637	−	7.01353i	−0.492345	−	0.237101i
$876$	−25.2741	−	41.6122i	−0.853933	−	1.40595i
$877$	−20.0811	+	14.5898i	−0.678091	+	0.492662i	−0.872724	−	0.488214i	$-0.837649\pi$
$877$	−20.0811	+	14.5898i	−0.678091	+	0.492662i	0.194633	+	0.980876i	$0.437649\pi$
$878$	−0.190069	−	0.832745i	−0.00641451	−	0.0281038i
$879$	14.8709	−	5.70473i	0.501584	−	0.192416i
$880$	−7.43126	+	7.10501i	−0.250508	+	0.239510i
$881$	0.106120	−	0.282757i	0.00357529	−	0.00952631i	−0.934435	−	0.356133i	$-0.884095\pi$
$881$	0.106120	−	0.282757i	0.00357529	−	0.00952631i	0.938010	+	0.346607i	$0.112666\pi$
$882$	2.86131	−	2.81639i	0.0963452	−	0.0948326i
$883$	15.8856	−	6.78985i	0.534595	−	0.228497i	−0.108756	−	0.994068i	$-0.534687\pi$
$883$	15.8856	−	6.78985i	0.534595	−	0.228497i	0.643350	+	0.765572i	$0.277544\pi$
$884$	−6.10815	+	4.87109i	−0.205439	+	0.163832i
$885$	−10.4852	−	2.81192i	−0.352456	−	0.0945218i
$886$	−3.55998	−	7.39238i	−0.119600	−	0.248352i
$887$	−27.1923	−	50.5317i	−0.913026	−	1.69669i	−0.692652	−	0.721272i	$-0.743558\pi$
$887$	−27.1923	−	50.5317i	−0.913026	−	1.69669i	−0.220375	−	0.975415i	$-0.570728\pi$
$888$	2.01733	−	3.10495i	0.0676972	−	0.104195i
$889$	12.5563	−	6.04681i	0.421126	−	0.202804i
$890$	−7.15272	−	6.83870i	−0.239760	−	0.229234i
$891$	−3.44319	+	6.86962i	−0.115351	+	0.230141i
$892$	18.0402	+	42.2071i	0.604030	+	1.41320i
$893$	−1.61525	+	7.07686i	−0.0540522	+	0.236818i
$894$	−0.153553	−	1.07482i	−0.00513557	−	0.0359473i
$895$	34.1275	+	35.6945i	1.14076	+	1.19314i
$896$	−3.65056	+	26.9495i	−0.121957	+	0.900321i
$897$	46.2795	−	41.0298i	1.54523	−	1.36995i
$898$	0.0282643	+	0.0389024i	0.000943190	+	0.00129819i
$899$	−0.132791	−	2.95682i	−0.00442882	−	0.0986153i
$900$	31.4132	−	19.3933i	1.04711	−	0.646443i
$901$	−2.49412	+	0.936058i	−0.0830911	+	0.0311846i
$902$	1.44549	−	0.195804i	0.0481294	−	0.00651957i
$903$	9.77612	+	1.70085i	0.325329	+	0.0566006i
$904$	3.15589	−	11.4351i	0.104963	−	0.380326i
$905$	−12.8319	+	19.4395i	−0.426547	+	0.646190i
$906$	−0.235656	+	1.84007i	−0.00782913	+	0.0611321i
$907$	35.4748	+	15.1627i	1.17792	+	0.503468i	0.890787	−	0.454422i	$-0.150154\pi$
$907$	35.4748	+	15.1627i	1.17792	+	0.503468i	0.287135	+	0.957890i	$0.407297\pi$
$908$	8.36980	−	2.30992i	0.277762	−	0.0766574i
$909$	24.5822	−	20.1948i	0.815342	−	0.669820i
$910$	−9.62931	+	8.41288i	−0.319209	+	0.278884i
$911$	−24.4564	+	14.6120i	−0.810278	+	0.484118i	−0.857326	−	0.514774i	$-0.827876\pi$
$911$	−24.4564	+	14.6120i	−0.810278	+	0.484118i	0.0470480	+	0.998893i	$0.485019\pi$
$912$	−20.8339	−	4.59624i	−0.689879	−	0.152197i
$913$	0.325830	−	1.79547i	0.0107834	−	0.0594214i
$914$	5.21194	+	0.469083i	0.172396	+	0.0155159i
$915$	−32.1283	+	21.5444i	−1.06213	+	0.712235i
$916$	−6.83650	+	1.24064i	−0.225884	+	0.0409920i
$917$	36.9529	+	22.0783i	1.22029	+	0.729091i
$918$	0.340848	+	1.35640i	0.0112497	+	0.0447679i
$919$	−12.7016	+	8.38427i	−0.418988	+	0.276572i	−0.742752	−	0.669566i	$-0.766480\pi$
$919$	−12.7016	+	8.38427i	−0.418988	+	0.276572i	0.323764	+	0.946138i	$0.395052\pi$
$920$	1.40954	−	31.3858i	0.0464711	−	1.03476i
$921$	7.69477	−	0.0558956i	0.253551	−	0.00184182i
$922$			3.29702i			0.108581i
$923$	−15.4649	+	30.5371i	−0.509033	+	1.00514i
$924$	4.73393	+	8.64602i	0.155735	+	0.284433i
$925$	−6.10640	+	11.3476i	−0.200777	+	0.373107i
$926$	−2.11050	−	0.0947828i	−0.0693554	−	0.00311476i
$927$	45.6382	−	0.663077i	1.49896	−	0.0217783i
$928$	9.73129	+	29.9498i	0.319445	+	0.983152i
$929$	4.94202	−	8.27154i	0.162142	−	0.271380i	−0.766586	−	0.642142i	$-0.778046\pi$
$929$	4.94202	−	8.27154i	0.162142	−	0.271380i	0.928728	+	0.370761i	$0.120903\pi$
$930$	0.287202	+	0.354822i	0.00941773	+	0.0116351i
$931$	17.0564	−	1.53510i	0.559001	−	0.0503110i
$932$	4.53261	−	50.3614i	0.148471	−	1.64964i
$933$	−11.2818	−	33.8824i	−0.369350	−	1.10926i
$934$	4.43746	−	5.07908i	0.145198	−	0.166193i
$935$	1.47449	+	2.46789i	0.0482211	+	0.0807085i
$936$	−1.91852	−	12.7660i	−0.0627087	−	0.417268i
$937$	35.3923	+	11.4997i	1.15622	+	0.375677i	0.823482	−	0.567343i	$-0.192029\pi$
$937$	35.3923	+	11.4997i	1.15622	+	0.375677i	0.332735	+	0.943021i	$0.392029\pi$
$938$	3.38504	+	12.2654i	0.110525	+	0.400480i
$939$	−1.41696	−	14.5584i	−0.0462407	−	0.475095i
$940$	8.03869	−	11.0643i	0.262193	−	0.360878i
$941$	−24.8486	−	16.4024i	−0.810040	−	0.534703i	0.0766548	−	0.997058i	$-0.475576\pi$
$941$	−24.8486	−	16.4024i	−0.810040	−	0.534703i	−0.886695	+	0.462355i	$0.847005\pi$
$942$	1.46440	+	6.20773i	0.0477126	+	0.202259i
$943$	34.7144	−	43.5305i	1.13046	−	1.41755i
$944$	−0.889833	−	6.56901i	−0.0289616	−	0.213803i
$945$	−17.4019	−	58.0878i	−0.566085	−	1.88960i
$946$	0.165514	−	0.343693i	0.00538131	−	0.0111744i
$947$	−34.7676	+	1.56141i	−1.12979	+	0.0507391i	−0.601901	−	0.798571i	$-0.705590\pi$
$947$	−34.7676	+	1.56141i	−1.12979	+	0.0507391i	−0.527894	+	0.849310i	$0.677018\pi$
$948$	1.42766	−	3.02050i	0.0463682	−	0.0981012i
$949$	57.7638	−	13.1842i	1.87509	−	0.427977i
$950$	−5.89047	−	0.797918i	−0.191112	−	0.0258879i
$951$	26.2340	+	8.31377i	0.850697	+	0.269592i
$952$	3.42273	+	1.28457i	0.110931	+	0.0416332i
$953$	−10.1084	−	2.30717i	−0.327442	−	0.0747365i	0.0556397	−	0.998451i	$-0.482280\pi$
$953$	−10.1084	−	2.30717i	−0.327442	−	0.0747365i	−0.383082	+	0.923714i	$0.625137\pi$
$954$	0.354795	−	2.13083i	0.0114869	−	0.0689883i
$955$	−4.64600	−	5.82590i	−0.150341	−	0.188522i
$956$	−31.5896	+	33.0402i	−1.02168	+	1.06860i
$957$	12.2922	+	8.79508i	0.397349	+	0.284304i
$958$	1.17355	−	0.631513i	0.0379156	−	0.0204033i
$959$	−35.4097	+	19.0548i	−1.14344	+	0.615311i
$960$	29.9745	+	21.4468i	0.967424	+	0.692194i
$961$	−21.3650	+	22.3460i	−0.689193	+	0.720840i
$962$	1.37873	+	1.72887i	0.0444520	+	0.0557410i
$963$	7.25600	−	43.5782i	0.233821	−	1.40429i
$964$	−1.08118	−	0.246773i	−0.0348226	−	0.00794803i
$965$	−61.9255	−	23.2410i	−1.99345	−	0.748156i
$966$	−13.5391	−	4.29063i	−0.435612	−	0.138049i
$967$	18.9630	+	2.56872i	0.609810	+	0.0826044i	0.432626	−	0.901573i	$-0.357587\pi$
$967$	18.9630	+	2.56872i	0.609810	+	0.0826044i	0.177184	+	0.984178i	$0.443301\pi$
$968$	−10.6070	+	2.42098i	−0.340922	+	0.0778133i
$969$	−2.54926	+	5.39347i	−0.0818940	+	0.173263i
$970$	11.7685	−	0.528526i	0.377865	−	0.0169699i
$971$	9.13618	−	18.9715i	0.293194	−	0.608824i	−0.701388	−	0.712780i	$-0.747436\pi$
$971$	9.13618	−	18.9715i	0.293194	−	0.608824i	0.994582	+	0.103956i	$0.0331502\pi$
$972$	28.8907	+	8.24011i	0.926670	+	0.264302i
$973$	−5.60530	−	41.3800i	−0.179698	−	1.32658i
$974$	2.92604	−	3.66913i	0.0937562	−	0.117567i
$975$	10.3151	+	43.7267i	0.330347	+	1.40038i
$976$	−19.7141	−	13.0132i	−0.631033	−	0.416542i
$977$	4.98257	−	6.85792i	0.159406	−	0.219404i	−0.721841	−	0.692058i	$-0.756704\pi$
$977$	4.98257	−	6.85792i	0.159406	−	0.219404i	0.881248	+	0.472654i	$0.156704\pi$
$978$	0.768391	+	7.89475i	0.0245704	+	0.252446i
$979$	−2.46983	−	8.94924i	−0.0789362	−	0.286019i
$980$	−30.6863	−	9.97058i	−0.980237	−	0.318498i
$981$	4.85398	+	32.2987i	0.154976	+	1.03122i
$982$	−4.86299	−	8.13927i	−0.155184	−	0.259735i
$983$	−6.38517	+	7.30842i	−0.203655	+	0.233102i	−0.845825	−	0.533460i	$-0.820892\pi$
$983$	−6.38517	+	7.30842i	−0.203655	+	0.233102i	0.642170	+	0.766562i	$0.278034\pi$
$984$	−3.67136	−	11.0261i	−0.117039	−	0.351500i
$985$	2.35361	−	26.1508i	0.0749923	−	0.833233i
$986$	2.73987	−	0.246592i	0.0872551	−	0.00785310i
$987$	−7.92634	−	9.79253i	−0.252298	−	0.311700i
$988$	13.8597	−	23.1972i	0.440935	−	0.738001i
$989$	−4.49947	−	13.8479i	−0.143075	−	0.440339i
$990$	−2.33088	+	0.0338654i	−0.0740803	+	0.00107631i
$991$	−30.1733	−	1.35508i	−0.958487	−	0.0430457i	−0.439878	−	0.898058i	$-0.644978\pi$
$991$	−30.1733	−	1.35508i	−0.958487	−	0.0430457i	−0.518608	+	0.855012i	$0.673550\pi$
$992$	−0.422815	+	0.785723i	−0.0134244	+	0.0249467i
$993$	−5.45683	−	9.96631i	−0.173167	−	0.316271i
$994$	7.84126	−	0.548059i	0.248710	−	0.0173834i
$995$			17.7429i			0.562488i
$996$	−7.13418	+	0.0518235i	−0.226055	+	0.00164209i
$997$	1.08857	−	24.2389i	0.0344753	−	0.767653i	−0.905077	−	0.425248i	$-0.860187\pi$
$997$	1.08857	−	24.2389i	0.0344753	−	0.767653i	0.939552	−	0.342405i	$-0.111242\pi$
$998$	4.79394	−	3.16445i	0.151750	−	0.100169i
$999$	−10.1705	+	2.55573i	−0.321780	+	0.0808597i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	213.2.n.a.11.12	yes	528
3.2	odd	2	inner	213.2.n.a.11.11	✓	528
71.13	odd	70	inner	213.2.n.a.155.11	yes	528
213.155	even	70	inner	213.2.n.a.155.12	yes	528

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
213.2.n.a.11.11	✓	528	3.2	odd	2	inner
213.2.n.a.11.12	yes	528	1.1	even	1	trivial
213.2.n.a.155.11	yes	528	71.13	odd	70	inner
213.2.n.a.155.12	yes	528	213.155	even	70	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 213 = 3 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	213.n (of order \(70\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.237517 + 0.127813i) q^{2} +(-0.762824 - 1.55502i) q^{3} +(-1.06172 - 1.60843i) q^{4} +(-3.20904 + 1.04268i) q^{5} +(0.0175691 - 0.466844i) q^{6} +(0.617551 + 3.40299i) q^{7} +(-0.0949523 - 1.05501i) q^{8} +(-1.83620 + 2.37242i) q^{9} +(-0.895472 - 0.162504i) q^{10} +(-0.642974 - 0.561749i) q^{11} +(-1.69125 + 2.87794i) q^{12} +(-2.67276 - 3.05922i) q^{13} +(-0.288269 + 0.887200i) q^{14} +(4.06933 + 4.19476i) q^{15} +(-1.40262 + 3.28160i) q^{16} +(0.807312 + 0.586547i) q^{17} +(-0.739356 + 0.328800i) q^{18} +(-3.32712 - 0.918227i) q^{19} +(5.08417 + 4.05449i) q^{20} +(4.82065 - 3.55619i) q^{21} +(-0.0809182 - 0.215606i) q^{22} +(-7.91961 - 3.81388i) q^{23} +(-1.56813 + 0.952438i) q^{24} +(5.16570 - 3.75310i) q^{25} +(-0.243817 - 1.06823i) q^{26} +(5.08987 + 1.04559i) q^{27} +(4.81781 - 4.60630i) q^{28} +(3.59128 - 9.56893i) q^{29} +(0.430390 + 1.51644i) q^{30} +(0.266286 - 0.113816i) q^{31} +(-2.40892 + 1.92105i) q^{32} +(-0.383058 + 1.42836i) q^{33} +(0.116782 + 0.242500i) q^{34} +(-5.52998 - 10.2764i) q^{35} +(5.76539 + 0.434561i) q^{36} +(-1.81830 + 0.875648i) q^{37} +(-0.672887 - 0.643346i) q^{38} +(-2.71831 + 6.48985i) q^{39} +(1.40474 + 3.28656i) q^{40} +(-1.40947 + 6.17531i) q^{41} +(1.59951 - 0.228513i) q^{42} +(1.14473 + 1.19729i) q^{43} +(-0.220879 + 1.63060i) q^{44} +(3.41876 - 9.52777i) q^{45} +(-1.39358 - 1.91810i) q^{46} +(-0.0943551 - 2.10098i) q^{47} +(6.17292 - 0.322172i) q^{48} +(-4.64532 + 1.74342i) q^{49} +(1.70664 - 0.231180i) q^{50} +(0.296257 - 1.70282i) q^{51} +(-2.08283 + 7.54697i) q^{52} +(-1.47068 + 2.22799i) q^{53} +(1.07529 + 0.898899i) q^{54} +(2.64906 + 1.13226i) q^{55} +(3.53154 - 0.974642i) q^{56} +(1.11014 + 5.87420i) q^{57} +(2.07603 - 1.81377i) q^{58} +(-1.59456 + 0.952707i) q^{59} +(2.42650 - 10.9989i) q^{60} +(-1.18187 + 6.51262i) q^{61} +(0.0777947 + 0.00700165i) q^{62} +(-9.20727 - 4.78347i) q^{63} +(6.20518 - 1.12607i) q^{64} +(11.7668 + 7.03034i) q^{65} +(-0.273546 + 0.290299i) q^{66} +(11.3834 - 7.51410i) q^{67} +(0.0862835 - 1.92125i) q^{68} +(0.110592 + 15.2245i) q^{69} -3.14764i q^{70} +(-3.15624 - 7.81269i) q^{71} +(2.67727 + 1.71193i) q^{72} +(-6.91141 + 12.8435i) q^{73} +(-0.543797 - 0.0244220i) q^{74} +(-9.77668 - 5.16983i) q^{75} +(2.05555 + 6.32634i) q^{76} +(1.51456 - 2.53494i) q^{77} +(-1.47514 + 1.19401i) q^{78} +(-0.996812 + 0.0897147i) q^{79} +(1.07942 - 11.9933i) q^{80} +(-2.25675 - 8.71247i) q^{81} +(-1.12406 + 1.28659i) q^{82} +(1.09620 + 1.83473i) q^{83} +(-10.8380 - 3.97801i) q^{84} +(-3.20228 - 1.04048i) q^{85} +(0.118863 + 0.430689i) q^{86} +(-17.6194 + 1.71489i) q^{87} +(-0.531597 + 0.731681i) q^{88} +(9.07471 + 5.99017i) q^{89} +(2.02979 - 1.82605i) q^{90} +(8.75993 - 10.9846i) q^{91} +(2.27401 + 16.7874i) q^{92} +(-0.380116 - 0.327259i) q^{93} +(0.246123 - 0.511079i) q^{94} +(11.6343 - 0.522497i) q^{95} +(4.82487 + 2.28051i) q^{96} +(-12.6196 + 2.88034i) q^{97} +(-1.32618 - 0.179643i) q^{98} +(2.51333 - 0.493921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 528 q - 20 q^{3} - 70 q^{4} - 30 q^{6} - 46 q^{7} - 26 q^{9} - 62 q^{10} - 55 q^{12} - 46 q^{13} - 22 q^{15} - 70 q^{16} - 18 q^{18} - 46 q^{19} - 2 q^{21} - 86 q^{22} - 13 q^{24} + 24 q^{25} + 7 q^{27}+ \cdots - 94 q^{99}+O(q^{100}) \) 528 * q - 20 * q^3 - 70 * q^4 - 30 * q^6 - 46 * q^7 - 26 * q^9 - 62 * q^10 - 55 * q^12 - 46 * q^13 - 22 * q^15 - 70 * q^16 - 18 * q^18 - 46 * q^19 - 2 * q^21 - 86 * q^22 - 13 * q^24 + 24 * q^25 + 7 * q^27 + 22 * q^28 - 55 * q^30 - 44 * q^31 - 28 * q^33 - 28 * q^34 + 8 * q^36 - 72 * q^37 - 144 * q^40 - 2 * q^42 - 76 * q^43 - 55 * q^45 - 30 * q^46 + 55 * q^48 - 72 * q^49 + 63 * q^51 + 78 * q^52 - 47 * q^54 - 70 * q^55 + 102 * q^57 - 166 * q^58 - 66 * q^60 - 74 * q^61 - 85 * q^63 + 58 * q^64 + 135 * q^66 + 52 * q^67 + 173 * q^69 + 154 * q^72 - 28 * q^73 + 127 * q^75 + 160 * q^76 + 184 * q^78 - 166 * q^79 + 102 * q^81 + 162 * q^82 + 168 * q^84 - 90 * q^85 + 87 * q^87 - 20 * q^88 + 60 * q^90 - 148 * q^91 + 5 * q^93 - 84 * q^94 + 120 * q^96 - 28 * q^97 - 94 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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