LMFDB - Embedded newform 560.2.cq.a.171.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(131,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cq (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:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			171.12
Character	$\chi$	$=$	560.171
Dual form			560.2.cq.a.131.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.17180 - 0.791760i) q^{2} +(0.282699 + 1.05505i) q^{3} +(0.746231 + 1.85557i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.504077 - 1.46013i) q^{6} +(2.60058 - 0.486822i) q^{7} +(0.594732 - 2.76519i) q^{8} +(1.56487 - 0.903479i) q^{9} +(-0.926949 - 1.06807i) q^{10} +(-1.45253 - 5.42093i) q^{11} +(-1.74675 + 1.31188i) q^{12} +(-0.831055 - 0.831055i) q^{13} +(-3.43280 - 1.48858i) q^{14} +1.09226i q^{15} +(-2.88628 + 2.76937i) q^{16} +(-2.08371 - 1.20303i) q^{17} +(-2.54906 - 0.180306i) q^{18} +(4.60400 + 1.23364i) q^{19} +(0.240547 + 1.98548i) q^{20} +(1.24880 + 2.60611i) q^{21} +(-2.59000 + 7.50231i) q^{22} +(-1.18177 - 2.04689i) q^{23} +(3.08554 - 0.154247i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.315834 + 1.63183i) q^{26} +(3.71264 + 3.71264i) q^{27} +(2.84396 + 4.46227i) q^{28} +(-1.13087 + 1.13087i) q^{29} +(0.864812 - 1.27992i) q^{30} +(4.50402 - 7.80119i) q^{31} +(5.57482 - 0.959907i) q^{32} +(5.30871 - 3.06498i) q^{33} +(1.48918 + 3.05951i) q^{34} +(2.63796 + 0.202845i) q^{35} +(2.84422 + 2.22952i) q^{36} +(-0.616460 + 2.30066i) q^{37} +(-4.41822 - 5.09084i) q^{38} +(0.641863 - 1.11174i) q^{39} +(1.29015 - 2.51704i) q^{40} -6.99689 q^{41} +(0.600067 - 4.04259i) q^{42} +(-2.42804 + 2.42804i) q^{43} +(8.97499 - 6.74055i) q^{44} +(1.74539 - 0.467675i) q^{45} +(-0.235845 + 3.33423i) q^{46} +(5.17110 + 8.95662i) q^{47} +(-3.73776 - 2.26226i) q^{48} +(6.52601 - 2.53204i) q^{49} +(-0.618929 - 1.27158i) q^{50} +(0.680192 - 2.53851i) q^{51} +(0.921921 - 2.16224i) q^{52} +(-2.43697 + 0.652983i) q^{53} +(-1.41095 - 7.29000i) q^{54} -5.61216i q^{55} +(0.200491 - 7.48063i) q^{56} +5.20618i q^{57} +(2.22053 - 0.429776i) q^{58} +(8.66890 - 2.32282i) q^{59} +(-2.02677 + 0.815082i) q^{60} +(-1.52811 + 5.70300i) q^{61} +(-11.4545 + 5.57533i) q^{62} +(3.62974 - 3.11138i) q^{63} +(-7.29259 - 3.28910i) q^{64} +(-0.587645 - 1.01783i) q^{65} +(-8.64748 - 0.611675i) q^{66} +(-15.4938 + 4.15156i) q^{67} +(0.677378 - 4.76421i) q^{68} +(1.82548 - 1.82548i) q^{69} +(-2.93056 - 2.32633i) q^{70} +9.12096 q^{71} +(-1.56761 - 4.86450i) q^{72} +(-3.70123 + 6.41071i) q^{73} +(2.54394 - 2.20782i) q^{74} +(-0.282699 + 1.05505i) q^{75} +(1.14655 + 9.46361i) q^{76} +(-6.41646 - 13.3904i) q^{77} +(-1.63237 + 0.794535i) q^{78} +(13.5743 - 7.83715i) q^{79} +(-3.50470 + 1.92798i) q^{80} +(-0.157015 + 0.271957i) q^{81} +(8.19895 + 5.53986i) q^{82} +(-0.287441 + 0.287441i) q^{83} +(-3.90392 + 4.26199i) q^{84} +(-1.70134 - 1.70134i) q^{85} +(4.76760 - 0.922752i) q^{86} +(-1.51282 - 0.873424i) q^{87} +(-15.8538 + 0.792535i) q^{88} +(-0.657205 - 1.13831i) q^{89} +(-2.41553 - 0.833907i) q^{90} +(-2.56580 - 1.75665i) q^{91} +(2.91628 - 3.72032i) q^{92} +(9.50390 + 2.54656i) q^{93} +(1.03199 - 14.5896i) q^{94} +(4.12783 + 2.38320i) q^{95} +(2.58874 + 5.61033i) q^{96} +13.9928i q^{97} +(-9.65194 - 2.19999i) q^{98} +(-7.17073 - 7.17073i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) $ 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.17180	−	0.791760i	−0.828588	−	0.559859i
$2$	−1.17180	−	0.791760i	−0.828588	−	0.559859i
$3$	0.282699	+	1.05505i	0.163216	+	0.609131i	0.998261	+	0.0589493i	$0.0187750\pi$
$3$	0.282699	+	1.05505i	0.163216	+	0.609131i	−0.835045	+	0.550182i	$0.814558\pi$
$4$	0.746231	+	1.85557i	0.373116	+	0.927785i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$5$	0.965926	+	0.258819i	0.431975	+	0.115747i
$6$	0.504077	−	1.46013i	0.205789	−	0.596097i
$7$	2.60058	−	0.486822i	0.982926	−	0.184001i
$7$	2.60058	−	0.486822i	0.982926	−	0.184001i
$8$	0.594732	−	2.76519i	0.210270	−	0.977643i
$9$	1.56487	−	0.903479i	0.521624	−	0.301160i
$10$	−0.926949	−	1.06807i	−0.293127	−	0.337752i
$11$	−1.45253	−	5.42093i	−0.437956	−	1.63447i	−0.733893	−	0.679265i	$-0.762299\pi$
$11$	−1.45253	−	5.42093i	−0.437956	−	1.63447i	0.295937	−	0.955207i	$-0.404368\pi$
$12$	−1.74675	+	1.31188i	−0.504244	+	0.378706i
$13$	−0.831055	−	0.831055i	−0.230493	−	0.230493i	0.582405	−	0.812899i	$-0.302112\pi$
$13$	−0.831055	−	0.831055i	−0.230493	−	0.230493i	−0.812899	+	0.582405i	$0.802112\pi$
$14$	−3.43280	−	1.48858i	−0.917455	−	0.397839i
$15$			1.09226i			0.282022i
$16$	−2.88628	+	2.76937i	−0.721569	+	0.692342i
$17$	−2.08371	−	1.20303i	−0.505375	−	0.291778i	0.225556	−	0.974230i	$-0.427580\pi$
$17$	−2.08371	−	1.20303i	−0.505375	−	0.291778i	−0.730930	+	0.682452i	$0.760914\pi$
$18$	−2.54906	−	0.180306i	−0.600818	−	0.0424986i
$19$	4.60400	+	1.23364i	1.05623	+	0.283016i	0.744824	−	0.667261i	$-0.232534\pi$
$19$	4.60400	+	1.23364i	1.05623	+	0.283016i	0.311405	+	0.950277i	$0.399200\pi$
$20$	0.240547	+	1.98548i	0.0537880	+	0.443967i
$21$	1.24880	+	2.60611i	0.272511	+	0.568699i
$22$	−2.59000	+	7.50231i	−0.552190	+	1.59950i
$23$	−1.18177	−	2.04689i	−0.246417	−	0.426807i	0.716112	−	0.697985i	$-0.245920\pi$
$23$	−1.18177	−	2.04689i	−0.246417	−	0.426807i	−0.962529	+	0.271178i	$0.912587\pi$
$24$	3.08554	−	0.154247i	0.629833	−	0.0314855i
$25$	0.866025	+	0.500000i	0.173205	+	0.100000i
$26$	0.315834	+	1.63183i	0.0619402	+	0.320028i
$27$	3.71264	+	3.71264i	0.714498	+	0.714498i
$28$	2.84396	+	4.46227i	0.537459	+	0.843290i
$29$	−1.13087	+	1.13087i	−0.209997	+	0.209997i	−0.804266	−	0.594269i	$-0.797441\pi$
$29$	−1.13087	+	1.13087i	−0.209997	+	0.209997i	0.594269	+	0.804266i	$0.297441\pi$
$30$	0.864812	−	1.27992i	0.157892	−	0.233680i
$31$	4.50402	−	7.80119i	0.808946	−	1.40114i	−0.104649	−	0.994509i	$-0.533372\pi$
$31$	4.50402	−	7.80119i	0.808946	−	1.40114i	0.913595	−	0.406626i	$-0.133295\pi$
$32$	5.57482	−	0.959907i	0.985498	−	0.169689i
$33$	5.30871	−	3.06498i	0.924127	−	0.533545i
$34$	1.48918	+	3.05951i	0.255393	+	0.524702i
$35$	2.63796	+	0.202845i	0.445897	+	0.0342871i
$36$	2.84422	+	2.22952i	0.474037	+	0.371587i
$37$	−0.616460	+	2.30066i	−0.101345	+	0.378226i	−0.997905	−	0.0646971i	$-0.979392\pi$
$37$	−0.616460	+	2.30066i	−0.101345	+	0.378226i	0.896560	+	0.442923i	$0.146059\pi$
$38$	−4.41822	−	5.09084i	−0.716730	−	0.825843i
$39$	0.641863	−	1.11174i	0.102780	−	0.178021i
$40$	1.29015	−	2.51704i	0.203991	−	0.397980i
$41$	−6.99689			−1.09273			−0.546365	−	0.837547i	$-0.683989\pi$
$41$	−6.99689			−1.09273			−0.546365	+	0.837547i	$0.683989\pi$
$42$	0.600067	−	4.04259i	0.0925924	−	0.623785i
$43$	−2.42804	+	2.42804i	−0.370273	+	0.370273i	−0.867576	−	0.497304i	$-0.834323\pi$
$43$	−2.42804	+	2.42804i	−0.370273	+	0.370273i	0.497304	+	0.867576i	$0.334323\pi$
$44$	8.97499	−	6.74055i	1.35303	−	1.01618i
$45$	1.74539	−	0.467675i	0.260187	−	0.0697169i
$46$	−0.235845	+	3.33423i	−0.0347735	+	0.491606i
$47$	5.17110	+	8.95662i	0.754283	+	1.30646i	0.945730	+	0.324954i	$0.105349\pi$
$47$	5.17110	+	8.95662i	0.754283	+	1.30646i	−0.191447	+	0.981503i	$0.561318\pi$
$48$	−3.73776	−	2.26226i	−0.539499	−	0.326529i
$49$	6.52601	−	2.53204i	0.932287	−	0.361719i
$50$	−0.618929	−	1.27158i	−0.0875297	−	0.179829i
$51$	0.680192	−	2.53851i	0.0952459	−	0.355462i
$52$	0.921921	−	2.16224i	0.127847	−	0.299849i
$53$	−2.43697	+	0.652983i	−0.334743	+	0.0896941i	−0.422275	−	0.906468i	$-0.638769\pi$
$53$	−2.43697	+	0.652983i	−0.334743	+	0.0896941i	0.0875325	+	0.996162i	$0.472102\pi$
$54$	−1.41095	−	7.29000i	−0.192006	−	0.992043i
$55$		−	5.61216i		−	0.756744i
$56$	0.200491	−	7.48063i	0.0267917	−	0.999641i
$57$			5.20618i			0.689575i
$58$	2.22053	−	0.429776i	0.291570	−	0.0564323i
$59$	8.66890	−	2.32282i	1.12859	−	0.302406i	0.354238	−	0.935155i	$-0.384740\pi$
$59$	8.66890	−	2.32282i	1.12859	−	0.302406i	0.774357	+	0.632749i	$0.218074\pi$
$60$	−2.02677	+	0.815082i	−0.261655	+	0.105227i
$61$	−1.52811	+	5.70300i	−0.195655	+	0.730194i	0.796441	+	0.604716i	$0.206713\pi$
$61$	−1.52811	+	5.70300i	−0.195655	+	0.730194i	−0.992096	+	0.125478i	$0.959953\pi$
$62$	−11.4545	+	5.57533i	−1.45472	+	0.708068i
$63$	3.62974	−	3.11138i	0.457304	−	0.391997i
$64$	−7.29259	−	3.28910i	−0.911573	−	0.411137i
$65$	−0.587645	−	1.01783i	−0.0728883	−	0.126246i
$66$	−8.64748	−	0.611675i	−1.06443	−	0.0752920i
$67$	−15.4938	+	4.15156i	−1.89287	+	0.507194i	−0.894707	+	0.446653i	$0.852616\pi$
$67$	−15.4938	+	4.15156i	−1.89287	+	0.507194i	−0.998166	+	0.0605411i	$0.980717\pi$
$68$	0.677378	−	4.76421i	0.0821442	−	0.577746i
$69$	1.82548	−	1.82548i	0.219762	−	0.219762i
$70$	−2.93056	−	2.32633i	−0.350269	−	0.278050i
$71$	9.12096			1.08246			0.541229	−	0.840875i	$-0.317959\pi$
$71$	9.12096			1.08246			0.541229	+	0.840875i	$0.317959\pi$
$72$	−1.56761	−	4.86450i	−0.184745	−	0.573287i
$73$	−3.70123	+	6.41071i	−0.433196	+	0.750317i	−0.997146	−	0.0754914i	$-0.975947\pi$
$73$	−3.70123	+	6.41071i	−0.433196	+	0.750317i	0.563951	+	0.825808i	$0.309281\pi$
$74$	2.54394	−	2.20782i	0.295727	−	0.256654i
$75$	−0.282699	+	1.05505i	−0.0326433	+	0.121826i
$76$	1.14655	+	9.46361i	0.131518	+	1.08555i
$77$	−6.41646	−	13.3904i	−0.731223	−	1.52598i
$78$	−1.63237	+	0.794535i	−0.184829	+	0.0899634i
$79$	13.5743	−	7.83715i	1.52723	−	0.881748i	0.527756	−	0.849396i	$-0.323033\pi$
$79$	13.5743	−	7.83715i	1.52723	−	0.881748i	0.999477	−	0.0323524i	$-0.0102999\pi$
$80$	−3.50470	+	1.92798i	−0.391837	+	0.215555i
$81$	−0.157015	+	0.271957i	−0.0174461	+	0.0302175i
$82$	8.19895	+	5.53986i	0.905423	+	0.611775i
$83$	−0.287441	+	0.287441i	−0.0315507	+	0.0315507i	−0.722706	−	0.691155i	$-0.757102\pi$
$83$	−0.287441	+	0.287441i	−0.0315507	+	0.0315507i	0.691155	+	0.722706i	$0.257102\pi$
$84$	−3.90392	+	4.26199i	−0.425952	+	0.465022i
$85$	−1.70134	−	1.70134i	−0.184537	−	0.184537i
$86$	4.76760	−	0.922752i	0.514104	−	0.0995029i
$87$	−1.51282	−	0.873424i	−0.162191	−	0.0936409i
$88$	−15.8538	+	0.792535i	−1.69002	+	0.0844845i
$89$	−0.657205	−	1.13831i	−0.0696636	−	0.120661i	0.829090	−	0.559116i	$-0.188859\pi$
$89$	−0.657205	−	1.13831i	−0.0696636	−	0.120661i	−0.898753	+	0.438455i	$0.855526\pi$
$90$	−2.41553	−	0.833907i	−0.254619	−	0.0879015i
$91$	−2.56580	−	1.75665i	−0.268969	−	0.184147i
$92$	2.91628	−	3.72032i	0.304043	−	0.387870i
$93$	9.50390	+	2.54656i	0.985509	+	0.264066i
$94$	1.03199	−	14.5896i	0.106442	−	1.50481i
$95$	4.12783	+	2.38320i	0.423506	+	0.244512i
$96$	2.58874	+	5.61033i	0.264212	+	0.572602i
$97$			13.9928i			1.42076i	0.703820	+	0.710378i	$0.251476\pi$
$97$			13.9928i			1.42076i	−0.703820	+	0.710378i	$0.748524\pi$
$98$	−9.65194	−	2.19999i	−0.974994	−	0.222233i
$99$	−7.17073	−	7.17073i	−0.720685	−	0.720685i
$100$	−0.281530	+	1.98009i	−0.0281530	+	0.198009i
$101$	0.346007	+	1.29132i	0.0344290	+	0.128491i	0.981001	−	0.194001i	$-0.0621464\pi$
$101$	0.346007	+	1.29132i	0.0344290	+	0.128491i	−0.946572	+	0.322491i	$0.895480\pi$
$102$	−2.80694	+	2.43608i	−0.277928	+	0.241208i
$103$	5.45584	−	3.14993i	0.537580	−	0.310372i	−0.206517	−	0.978443i	$-0.566213\pi$
$103$	5.45584	−	3.14993i	0.537580	−	0.310372i	0.744098	+	0.668071i	$0.232880\pi$
$104$	−2.79228	+	1.80377i	−0.273806	+	0.176874i
$105$	0.531738	+	2.84052i	0.0518924	+	0.277206i
$106$	3.37264	+	1.16433i	0.327580	+	0.113089i
$107$	−6.07660	−	1.62822i	−0.587448	−	0.157406i	−0.0471612	−	0.998887i	$-0.515017\pi$
$107$	−6.07660	−	1.62822i	−0.587448	−	0.157406i	−0.540286	+	0.841481i	$0.681684\pi$
$108$	−4.11858	+	9.65956i	−0.396310	+	0.929491i
$109$	3.57974	+	13.3598i	0.342877	+	1.27963i	0.895073	+	0.445919i	$0.147123\pi$
$109$	3.57974	+	13.3598i	0.342877	+	1.27963i	−0.552197	+	0.833714i	$0.686210\pi$
$110$	−4.44349	+	6.57633i	−0.423670	+	0.627029i
$111$	−2.60158			−0.246931
$112$	−6.15780	+	8.60706i	−0.581857	+	0.813291i
$113$	5.07602			0.477512			0.238756	−	0.971080i	$-0.423260\pi$
$113$	5.07602			0.477512			0.238756	+	0.971080i	$0.423260\pi$
$114$	4.12204	−	6.10060i	0.386065	−	0.571374i
$115$	−0.611732	−	2.28301i	−0.0570443	−	0.212892i
$116$	−2.94230	−	1.25452i	−0.273185	−	0.116479i
$117$	−2.05134	−	0.549654i	−0.189646	−	0.0508155i
$118$	−11.9973	−	4.14180i	−1.10444	−	0.381284i
$119$	−6.00452	−	2.11418i	−0.550433	−	0.193807i
$120$	3.02032	+	0.649605i	0.275716	+	0.0593006i
$121$	−17.7504	+	10.2482i	−1.61367	+	0.931653i
$122$	6.30605	−	5.47288i	0.570923	−	0.495491i
$123$	−1.97801	−	7.38204i	−0.178351	−	0.665616i
$124$	17.8367	+	2.53603i	1.60178	+	0.227742i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−6.71679	+	0.772036i	−0.598380	+	0.0687784i
$127$			1.69822i			0.150692i	0.997157	+	0.0753462i	$0.0240062\pi$
$127$			1.69822i			0.150692i	−0.997157	+	0.0753462i	$0.975994\pi$
$128$	5.94128	+	9.62815i	0.525140	+	0.851016i
$129$	−3.24810	−	1.87529i	−0.285979	−	0.165110i
$130$	−0.117276	+	1.65797i	−0.0102857	+	0.145413i
$131$	−10.9869	−	2.94394i	−0.959931	−	0.257213i	−0.255360	−	0.966846i	$-0.582194\pi$
$131$	−10.9869	−	2.94394i	−0.959931	−	0.257213i	−0.704571	+	0.709633i	$0.748861\pi$
$132$	9.64881	+	7.56349i	0.839821	+	0.658317i
$133$	12.5736	+	0.966843i	1.09027	+	0.0838359i
$134$	21.4427	+	7.40260i	1.85237	+	0.639488i
$135$	2.62524	+	4.54704i	0.225944	+	0.391347i
$136$	−4.56587	+	5.04639i	−0.391520	+	0.432724i
$137$	−10.2600	−	5.92359i	−0.876568	−	0.506087i	−0.00704259	−	0.999975i	$-0.502242\pi$
$137$	−10.2600	−	5.92359i	−0.876568	−	0.506087i	−0.869525	+	0.493889i	$0.835575\pi$
$138$	−3.58445	+	0.693756i	−0.305128	+	0.0590564i
$139$	2.12982	+	2.12982i	0.180649	+	0.180649i	0.791638	−	0.610990i	$-0.209228\pi$
$139$	2.12982	+	2.12982i	0.180649	+	0.180649i	−0.610990	+	0.791638i	$0.709228\pi$
$140$	1.59214	+	5.04630i	0.134560	+	0.426490i
$141$	−7.98778	+	7.98778i	−0.672693	+	0.672693i
$142$	−10.6879	−	7.22161i	−0.896912	−	0.606024i
$143$	−3.29796	+	5.71223i	−0.275789	+	0.477681i
$144$	−2.01459	+	6.94140i	−0.167882	+	0.578450i
$145$	−1.38503	+	0.799645i	−0.115020	+	0.0664069i
$146$	9.41284	−	4.58159i	0.779013	−	0.379175i
$147$	4.51631	+	6.16944i	0.372499	+	0.508847i
$148$	−4.72906	+	0.572940i	−0.388726	+	0.0470954i
$149$	−5.97330	+	22.2926i	−0.489351	+	1.82628i	0.0702593	+	0.997529i	$0.477617\pi$
$149$	−5.97330	+	22.2926i	−0.489351	+	1.82628i	−0.559611	+	0.828756i	$0.689049\pi$
$150$	1.16661	−	1.01247i	0.0952534	−	0.0826682i
$151$	−10.5722	+	18.3115i	−0.860351	+	1.49017i	0.0112395	+	0.999937i	$0.496422\pi$
$151$	−10.5722	+	18.3115i	−0.860351	+	1.49017i	−0.871590	+	0.490235i	$0.836911\pi$
$152$	6.14939	−	11.9973i	0.498781	−	0.973106i
$153$	−4.34766			−0.351487
$154$	−3.08320	+	20.7712i	−0.248452	+	1.67379i
$155$	6.36965	−	6.36965i	0.511622	−	0.511622i
$156$	2.54189	+	0.361407i	0.203514	+	0.0289357i
$157$	0.289664	−	0.0776151i	0.0231177	−	0.00619436i	−0.247242	−	0.968954i	$-0.579524\pi$
$157$	0.289664	−	0.0776151i	0.0231177	−	0.00619436i	0.270359	+	0.962759i	$0.412857\pi$
$158$	−22.1116	−	1.56405i	−1.75910	−	0.124429i
$159$	−1.37786	−	2.38651i	−0.109271	−	0.189263i
$160$	5.63330	+	0.515670i	0.445352	+	0.0407673i
$161$	−4.06977	−	4.74779i	−0.320743	−	0.374179i
$162$	0.399315	−	0.194362i	0.0313731	−	0.0152705i
$163$	−3.17086	+	11.8338i	−0.248361	+	0.926896i	0.723303	+	0.690531i	$0.242623\pi$
$163$	−3.17086	+	11.8338i	−0.248361	+	0.926896i	−0.971664	+	0.236366i	$0.924044\pi$
$164$	−5.22130	−	12.9832i	−0.407715	−	1.01382i
$165$	5.92109	−	1.58655i	0.460956	−	0.123513i
$166$	0.564408	−	0.109239i	0.0438065	−	0.00847859i
$167$		−	20.9553i		−	1.62157i	−0.585343	−	0.810786i	$-0.699040\pi$
$167$		−	20.9553i		−	1.62157i	0.585343	−	0.810786i	$-0.300960\pi$
$168$	7.94909	−	1.90324i	0.613286	−	0.146838i
$169$		−	11.6187i		−	0.893746i
$170$	0.646579	+	3.34069i	0.0495903	+	0.256219i
$171$	8.31923	−	2.22913i	0.636187	−	0.170466i
$172$	−6.31728	−	2.69352i	−0.481688	−	0.205379i
$173$	−2.55497	+	9.53526i	−0.194250	+	0.724952i	0.798209	+	0.602380i	$0.205781\pi$
$173$	−2.55497	+	9.53526i	−0.194250	+	0.724952i	−0.992460	+	0.122572i	$0.960886\pi$
$174$	1.08117	+	2.22127i	0.0819636	+	0.168394i
$175$	2.49558	+	0.878689i	0.188648	+	0.0664226i
$176$	19.2050	+	11.6237i	1.44763	+	0.876170i
$177$	4.90138	+	8.48943i	0.368410	+	0.638105i
$178$	−0.131158	+	1.85422i	−0.00983069	+	0.138980i
$179$	−14.6637	+	3.92912i	−1.09601	+	0.293676i	−0.761140	−	0.648587i	$-0.775360\pi$
$179$	−14.6637	+	3.92912i	−1.09601	+	0.293676i	−0.334873	+	0.942263i	$0.608693\pi$
$180$	2.17027	+	2.88969i	0.161762	+	0.215385i
$181$	2.75846	−	2.75846i	0.205034	−	0.205034i	−0.597119	−	0.802153i	$-0.703688\pi$
$181$	2.75846	−	2.75846i	0.205034	−	0.205034i	0.802153	+	0.597119i	$0.203688\pi$
$182$	1.61576	+	4.08994i	0.119768	+	0.303166i
$183$	−6.44893			−0.476718
$184$	−6.36290	+	2.05048i	−0.469079	+	0.151164i
$185$	−1.19091	+	2.06271i	−0.0875574	+	0.151654i
$186$	−9.12041	−	10.5089i	−0.668741	−	0.770548i
$187$	−3.49489	+	13.0431i	−0.255572	+	0.953807i
$188$	−12.7608	+	16.2791i	−0.930676	+	1.18727i
$189$	11.4624	+	7.84762i	0.833768	+	0.570830i
$190$	−2.95007	−	6.06089i	−0.214020	−	0.439703i
$191$	12.9489	−	7.47603i	0.936947	−	0.540947i	0.0479449	−	0.998850i	$-0.484733\pi$
$191$	12.9489	−	7.47603i	0.936947	−	0.540947i	0.889002	+	0.457903i	$0.151399\pi$
$192$	1.40855	−	8.62384i	0.101653	−	0.622372i
$193$	2.86835	−	4.96813i	0.206468	−	0.357614i	−0.744131	−	0.668033i	$-0.767136\pi$
$193$	2.86835	−	4.96813i	0.206468	−	0.357614i	0.950600	+	0.310420i	$0.100470\pi$
$194$	11.0790	−	16.3968i	0.795423	−	1.17722i
$195$	0.907732	−	0.907732i	0.0650040	−	0.0650040i
$196$	9.56828	+	10.2200i	0.683449	+	0.729999i
$197$	−11.0743	−	11.0743i	−0.789010	−	0.789010i	0.192322	−	0.981332i	$-0.438398\pi$
$197$	−11.0743	−	11.0743i	−0.789010	−	0.789010i	−0.981332	+	0.192322i	$0.938398\pi$
$198$	2.72516	+	14.0802i	0.193669	+	1.00063i
$199$	−14.1302	−	8.15810i	−1.00167	−	0.578312i	−0.0929255	−	0.995673i	$-0.529622\pi$
$199$	−14.1302	−	8.15810i	−1.00167	−	0.578312i	−0.908741	+	0.417361i	$0.862955\pi$
$200$	1.89765	−	2.09736i	0.134184	−	0.148306i
$201$	−8.76018	−	15.1731i	−0.617895	−	1.07023i
$202$	0.616962	−	1.78712i	0.0434093	−	0.125741i
$203$	−2.39038	+	3.49145i	−0.167772	+	0.245051i
$204$	5.21796	−	0.632173i	0.365330	−	0.0442609i
$205$	−6.75847	−	1.81093i	−0.472032	−	0.126481i
$206$	−8.88715	−	0.628628i	−0.619197	−	0.0437986i
$207$	−3.69865	−	2.13542i	−0.257074	−	0.148422i
$208$	4.70015	+	0.0971579i	0.325897	+	0.00673669i
$209$		−	26.7498i		−	1.85033i
$210$	1.62592	−	3.74953i	0.112199	−	0.258742i
$211$	−10.4097	−	10.4097i	−0.716632	−	0.716632i	0.251282	−	0.967914i	$-0.419148\pi$
$211$	−10.4097	−	10.4097i	−0.716632	−	0.716632i	−0.967914	+	0.251282i	$0.919148\pi$
$212$	−3.03020	−	4.03468i	−0.208115	−	0.277103i
$213$	2.57848	+	9.62303i	0.176675	+	0.659359i
$214$	5.83141	+	6.71916i	0.398627	+	0.459313i
$215$	−2.97373	+	1.71688i	−0.202807	+	0.117090i
$216$	12.4742	−	8.05815i	0.848762	−	0.548287i
$217$	7.91526	−	22.4803i	0.537323	−	1.52606i
$218$	6.38299	−	18.4893i	0.432311	−	1.25225i
$219$	−7.80993	−	2.09267i	−0.527746	−	0.141409i
$220$	10.4138	−	4.18797i	0.702095	−	0.282353i
$221$	0.731894	+	2.73147i	0.0492325	+	0.183738i
$222$	3.04853	+	2.05982i	0.204604	+	0.138246i
$223$	28.1296			1.88370			0.941850	−	0.336034i	$-0.109086\pi$
$223$	28.1296			1.88370			0.941850	+	0.336034i	$0.109086\pi$
$224$	14.0304	−	5.21025i	0.937448	−	0.348125i
$225$	1.80696			0.120464
$226$	−5.94808	−	4.01899i	−0.395661	−	0.267339i
$227$	−3.58153	−	13.3665i	−0.237715	−	0.887164i	−0.976906	−	0.213668i	$-0.931459\pi$
$227$	−3.58153	−	13.3665i	−0.237715	−	0.887164i	0.739191	−	0.673495i	$-0.235208\pi$
$228$	−9.66043	+	3.88501i	−0.639777	+	0.257291i
$229$	−5.76272	−	1.54412i	−0.380812	−	0.102038i	0.0633350	−	0.997992i	$-0.479826\pi$
$229$	−5.76272	−	1.54412i	−0.380812	−	0.102038i	−0.444146	+	0.895954i	$0.646493\pi$
$230$	−1.09077	+	3.15958i	−0.0719234	+	0.208337i
$231$	12.3136	−	10.5551i	0.810176	−	0.694476i
$232$	2.45451	+	3.79964i	0.161146	+	0.249458i
$233$	−15.0446	+	8.68603i	−0.985607	+	0.569041i	−0.903958	−	0.427620i	$-0.859352\pi$
$233$	−15.0446	+	8.68603i	−0.985607	+	0.569041i	−0.0816490	+	0.996661i	$0.526019\pi$
$234$	1.96856	+	2.26825i	0.128689	+	0.148280i
$235$	2.67676	+	9.98981i	0.174613	+	0.651663i
$236$	10.7792	+	14.3524i	0.701664	+	0.934260i
$237$	12.1060	+	12.1060i	0.786370	+	0.786370i
$238$	5.36217	+	7.23154i	0.347578	+	0.468751i
$239$			8.14315i			0.526737i	0.964695	+	0.263368i	$0.0848335\pi$
$239$			8.14315i			0.526737i	−0.964695	+	0.263368i	$0.915167\pi$
$240$	−3.02488	−	3.15258i	−0.195255	−	0.203498i
$241$	−14.8958	−	8.60009i	−0.959523	−	0.553981i	−0.0634966	−	0.997982i	$-0.520225\pi$
$241$	−14.8958	−	8.60009i	−0.959523	−	0.553981i	−0.896026	+	0.444001i	$0.853559\pi$
$242$	28.9140	+	2.04522i	1.85866	+	0.131472i
$243$	14.8834	+	3.98799i	0.954769	+	0.255830i
$244$	−11.7226	+	1.42023i	−0.750465	+	0.0909212i
$245$	6.95898	−	0.756704i	0.444593	−	0.0483440i
$246$	−3.52697	+	10.2164i	−0.224872	+	0.651373i
$247$	−2.80095	−	4.85139i	−0.178220	−	0.308687i
$248$	−18.8931	−	17.0941i	−1.19971	−	1.08548i
$249$	−0.384523	−	0.222004i	−0.0243681	−	0.0140690i
$250$	−0.268729	−	1.38845i	−0.0169959	−	0.0878131i
$251$	−3.55797	−	3.55797i	−0.224577	−	0.224577i	0.585846	−	0.810423i	$-0.300762\pi$
$251$	−3.55797	−	3.55797i	−0.224577	−	0.224577i	−0.810423	+	0.585846i	$0.800762\pi$
$252$	8.48201	+	4.41342i	0.534316	+	0.278019i
$253$	−9.37951	+	9.37951i	−0.589685	+	0.589685i
$254$	1.34458	−	1.98997i	0.0843665	−	0.124862i
$255$	1.31403	−	2.27597i	0.0822877	−	0.142526i
$256$	0.661197	−	15.9863i	0.0413248	−	0.999146i
$257$	11.1204	−	6.42036i	0.693671	−	0.400491i	−0.111315	−	0.993785i	$-0.535506\pi$
$257$	11.1204	−	6.42036i	0.693671	−	0.400491i	0.804986	+	0.593294i	$0.202173\pi$
$258$	2.32134	+	4.76918i	0.144520	+	0.296916i
$259$	−0.483140	+	6.28315i	−0.0300209	+	0.390416i
$260$	1.45014	−	1.84995i	0.0899336	−	0.114729i
$261$	−0.747949	+	2.79138i	−0.0462969	+	0.172782i
$262$	10.5436	+	12.1487i	0.651384	+	0.750550i
$263$	0.965165	−	1.67172i	0.0595147	−	0.103082i	−0.834733	−	0.550655i	$-0.814378\pi$
$263$	0.965165	−	1.67172i	0.0595147	−	0.103082i	0.894248	+	0.447573i	$0.147711\pi$
$264$	−5.31801	−	16.5024i	−0.327301	−	1.01566i
$265$	−2.52293			−0.154983
$266$	−13.9683	−	11.0882i	−0.856448	−	0.679863i
$267$	1.01518	−	1.01518i	0.0621281	−	0.0621281i
$268$	−19.2655	−	25.6519i	−1.17683	−	1.56694i
$269$	13.4667	−	3.60839i	0.821079	−	0.220007i	0.176261	−	0.984344i	$-0.443600\pi$
$269$	13.4667	−	3.60839i	0.821079	−	0.220007i	0.644818	+	0.764336i	$0.276933\pi$
$270$	0.523915	−	7.40678i	0.0318845	−	0.450762i
$271$	−7.00278	−	12.1292i	−0.425389	−	0.736795i	0.571068	−	0.820903i	$-0.306529\pi$
$271$	−7.00278	−	12.1292i	−0.425389	−	0.736795i	−0.996457	+	0.0841077i	$0.973196\pi$
$272$	9.34581	−	2.29828i	0.566673	−	0.139354i
$273$	1.12800	−	3.20364i	0.0682694	−	0.193893i
$274$	7.33256	+	15.0647i	0.442976	+	0.910092i
$275$	1.45253	−	5.42093i	0.0875911	−	0.326895i
$276$	4.74954	+	2.02508i	0.285889	+	0.121895i
$277$	−6.14529	+	1.64663i	−0.369235	+	0.0989362i	−0.438665	−	0.898651i	$-0.644549\pi$
$277$	−6.14529	+	1.64663i	−0.369235	+	0.0989362i	0.0694303	+	0.997587i	$0.477882\pi$
$278$	−0.809415	−	4.18202i	−0.0485455	−	0.250821i
$279$		−	16.2772i		−	0.974488i
$280$	2.12979	−	7.17384i	0.127279	−	0.428719i
$281$			17.9147i			1.06870i	0.845264	+	0.534349i	$0.179443\pi$
$281$			17.9147i			1.06870i	−0.845264	+	0.534349i	$0.820557\pi$
$282$	15.6845	−	3.03568i	0.933998	−	0.180772i
$283$	−11.5666	+	3.09927i	−0.687565	+	0.184233i	−0.585654	−	0.810561i	$-0.699162\pi$
$283$	−11.5666	+	3.09927i	−0.687565	+	0.184233i	−0.101911	+	0.994794i	$0.532496\pi$
$284$	6.80634	+	16.9246i	0.403882	+	1.00429i
$285$	−1.34746	+	5.02878i	−0.0798165	+	0.297879i
$286$	8.38726	−	4.08240i	0.495949	−	0.241397i
$287$	−18.1960	+	3.40624i	−1.07407	+	0.201064i
$288$	7.85662	−	6.53886i	0.462956	−	0.385306i
$289$	−5.60543	−	9.70889i	−0.329731	−	0.571111i
$290$	2.25610	+	0.159584i	0.132483	+	0.00937111i
$291$	−14.7631	+	3.95576i	−0.865427	+	0.231891i
$292$	−14.6575	−	2.08401i	−0.857765	−	0.121957i
$293$	−0.254030	+	0.254030i	−0.0148406	+	0.0148406i	−0.714488	−	0.699648i	$-0.753340\pi$
$293$	−0.254030	+	0.254030i	−0.0148406	+	0.0148406i	0.699648	+	0.714488i	$0.253340\pi$
$294$	−0.407498	−	10.8052i	−0.0237658	−	0.630171i
$295$	8.97470			0.522527
$296$	5.99514	+	3.07291i	0.348460	+	0.178609i
$297$	14.7332	−	25.5187i	0.854910	−	1.48075i
$298$	24.6499	−	21.3931i	1.42793	−	1.23927i
$299$	−0.718962	+	2.68320i	−0.0415786	+	0.155174i
$300$	−2.16867	+	0.262741i	−0.125208	+	0.0151694i
$301$	−5.13228	+	7.49633i	−0.295820	+	0.432081i
$302$	26.8868	−	13.0868i	1.54716	−	0.753063i
$303$	−1.26458	+	0.730107i	−0.0726484	+	0.0419436i
$304$	−16.7048	+	9.18954i	−0.958086	+	0.527056i
$305$	−2.95209	+	5.11317i	−0.169036	+	0.292779i
$306$	5.09458	+	3.44230i	0.291238	+	0.196783i
$307$	8.50094	−	8.50094i	0.485174	−	0.485174i	−0.421605	−	0.906780i	$-0.638533\pi$
$307$	8.50094	−	8.50094i	0.485174	−	0.485174i	0.906780	+	0.421605i	$0.138533\pi$
$308$	20.0587	−	21.8985i	1.14295	−	1.24779i
$309$	4.86569	+	4.86569i	0.276799	+	0.276799i
$310$	−12.5072	+	2.42072i	−0.710360	+	0.137488i
$311$	0.819111	+	0.472914i	0.0464476	+	0.0268165i	0.523044	−	0.852306i	$-0.324796\pi$
$311$	0.819111	+	0.472914i	0.0464476	+	0.0268165i	−0.476596	+	0.879122i	$0.658130\pi$
$312$	−2.69244	−	2.43606i	−0.152429	−	0.137915i
$313$	10.6372	+	18.4241i	0.601247	+	1.04139i	0.992633	+	0.121164i	$0.0386627\pi$
$313$	10.6372	+	18.4241i	0.601247	+	1.04139i	−0.391385	+	0.920227i	$0.628004\pi$
$314$	−0.400880	−	0.138395i	−0.0226230	−	0.00781006i
$315$	4.31134	−	2.06592i	0.242917	−	0.116401i
$316$	24.6720	+	19.3398i	1.38791	+	1.08795i
$317$	15.2072	+	4.07477i	0.854124	+	0.228862i	0.659210	−	0.751959i	$-0.270891\pi$
$317$	15.2072	+	4.07477i	0.854124	+	0.228862i	0.194914	+	0.980820i	$0.437557\pi$
$318$	−0.274977	+	3.88745i	−0.0154199	+	0.217997i
$319$	7.77299	+	4.48774i	0.435204	+	0.251265i
$320$	−6.19282	−	5.06449i	−0.346189	−	0.283113i
$321$		−	6.87140i		−	0.383524i
$322$	1.00984	+	8.78575i	0.0562764	+	0.489611i
$323$	−8.10930	−	8.10930i	−0.451213	−	0.451213i
$324$	−0.621805	−	0.0884085i	−0.0345447	−	0.00491158i
$325$	−0.304187	−	1.13524i	−0.0168733	−	0.0629719i
$326$	13.0852	−	11.3563i	0.724720	−	0.628968i
$327$	−13.0832	+	7.55358i	−0.723501	+	0.417714i
$328$	−4.16128	+	19.3477i	−0.229768	+	1.06830i
$329$	17.8081	+	20.7750i	0.981794	+	1.14536i
$330$	−8.19451	−	2.82896i	−0.451093	−	0.155729i
$331$	23.0964	+	6.18865i	1.26949	+	0.340159i	0.829836	−	0.558008i	$-0.188434\pi$
$331$	23.0964	+	6.18865i	1.26949	+	0.340159i	0.439655	+	0.898167i	$0.355101\pi$
$332$	−0.747864	−	0.318869i	−0.0410444	−	0.0175002i
$333$	1.11392	+	4.15719i	0.0610423	+	0.227813i
$334$	−16.5916	+	24.5555i	−0.907852	+	1.34362i
$335$	−16.0404			−0.876381
$336$	−10.8217	−	4.06356i	−0.590370	−	0.221685i
$337$	−3.03271			−0.165202			−0.0826011	−	0.996583i	$-0.526323\pi$
$337$	−3.03271			−0.165202			−0.0826011	+	0.996583i	$0.526323\pi$
$338$	−9.19922	+	13.6148i	−0.500372	+	0.740547i
$339$	1.43499	+	5.35544i	0.0779377	+	0.290867i
$340$	1.88737	−	4.42656i	0.102357	−	0.240064i
$341$	−48.8320	−	13.0845i	−2.64440	−	0.708565i
$342$	−11.5134	−	3.97474i	−0.622574	−	0.214929i
$343$	15.7387	−	9.76176i	0.849812	−	0.527086i
$344$	5.26996	+	8.15803i	0.284137	+	0.439852i
$345$	2.23575	−	1.29081i	0.120369	−	0.0694949i
$346$	10.5435	−	9.15050i	0.566825	−	0.491934i
$347$	3.07715	+	11.4841i	0.165190	+	0.616497i	0.998016	+	0.0629623i	$0.0200548\pi$
$347$	3.07715	+	11.4841i	0.165190	+	0.616497i	−0.832826	+	0.553535i	$0.813279\pi$
$348$	0.491790	−	3.45891i	0.0263627	−	0.185417i
$349$	−2.92259	−	2.92259i	−0.156442	−	0.156442i	0.624546	−	0.780988i	$-0.285284\pi$
$349$	−2.92259	−	2.92259i	−0.156442	−	0.156442i	−0.780988	+	0.624546i	$0.785284\pi$
$350$	−2.22861	−	3.00555i	−0.119124	−	0.160653i
$351$		−	6.17082i		−	0.329374i
$352$	−13.3012	−	28.8264i	−0.708956	−	1.53645i
$353$	−11.3324	−	6.54278i	−0.603164	−	0.348237i	0.167121	−	0.985936i	$-0.446553\pi$
$353$	−11.3324	−	6.54278i	−0.603164	−	0.348237i	−0.770285	+	0.637700i	$0.779886\pi$
$354$	0.978162	−	13.8286i	0.0519887	−	0.734983i
$355$	8.81017	+	2.36068i	0.467595	+	0.125292i
$356$	1.62179	−	2.06894i	0.0859548	−	0.109653i
$357$	0.533089	−	6.93272i	0.0282141	−	0.366919i
$358$	20.2938	+	7.00596i	1.07256	+	0.370277i
$359$	5.60724	+	9.71202i	0.295939	+	0.512581i	0.975203	−	0.221313i	$-0.0710342\pi$
$359$	5.60724	+	9.71202i	0.295939	+	0.512581i	−0.679264	+	0.733894i	$0.737701\pi$
$360$	−0.255174	−	5.10447i	−0.0134488	−	0.269029i
$361$	3.22043	+	1.85932i	0.169496	+	0.0978588i
$362$	−5.41639	+	1.04832i	−0.284679	+	0.0550986i
$363$	−15.8303	−	15.8303i	−0.830876	−	0.830876i
$364$	1.34490	−	6.07188i	0.0704920	−	0.318253i
$365$	−5.23432	+	5.23432i	−0.273977	+	0.273977i
$366$	7.55685	+	5.10600i	0.395003	+	0.266895i
$367$	−12.9169	+	22.3728i	−0.674259	+	1.16785i	0.302426	+	0.953173i	$0.402204\pi$
$367$	−12.9169	+	22.3728i	−0.674259	+	1.16785i	−0.976685	+	0.214678i	$0.931130\pi$
$368$	9.07954	+	2.63513i	0.473303	+	0.137366i
$369$	−10.9492	+	6.32154i	−0.569994	+	0.329086i
$370$	3.02868	−	1.47418i	0.157454	−	0.0766387i
$371$	−6.01963	+	2.88450i	−0.312524	+	0.149756i
$372$	2.36679	+	19.5355i	0.122712	+	1.01287i
$373$	6.47358	−	24.1597i	0.335189	−	1.25094i	−0.568475	−	0.822701i	$-0.692466\pi$
$373$	6.47358	−	24.1597i	0.335189	−	1.25094i	0.903664	−	0.428242i	$-0.140867\pi$
$374$	14.4223	−	12.5168i	0.745761	−	0.647229i
$375$	−0.546132	+	0.945929i	−0.0282022	+	0.0488476i
$376$	27.8422	−	8.97231i	1.43585	−	0.462712i
$377$	1.87963			0.0968058
$378$	−7.21822	−	18.2713i	−0.371265	−	0.939776i
$379$	−20.4637	+	20.4637i	−1.05115	+	1.05115i	−0.0525306	+	0.998619i	$0.516729\pi$
$379$	−20.4637	+	20.4637i	−1.05115	+	1.05115i	−0.998619	+	0.0525306i	$0.983271\pi$
$380$	−1.34188	+	9.43790i	−0.0688372	+	0.484154i
$381$	−1.79170	+	0.480084i	−0.0917915	+	0.0245955i
$382$	−21.0927	−	1.49198i	−1.07920	−	0.0763365i
$383$	17.4129	+	30.1600i	0.889758	+	1.54111i	0.840161	+	0.542337i	$0.182460\pi$
$383$	17.4129	+	30.1600i	0.889758	+	1.54111i	0.0495970	+	0.998769i	$0.484206\pi$
$384$	−8.47855	+	8.99019i	−0.432669	+	0.458779i
$385$	−2.73212	−	14.5949i	−0.139242	−	0.743823i
$386$	−7.29470	+	3.55061i	−0.371290	+	0.180721i
$387$	−1.60589	+	5.99325i	−0.0816318	+	0.304654i
$388$	−25.9647	+	10.4419i	−1.31816	+	0.530106i
$389$	18.9233	−	5.07048i	0.959449	−	0.257084i	0.255082	−	0.966919i	$-0.417898\pi$
$389$	18.9233	−	5.07048i	0.959449	−	0.257084i	0.704367	+	0.709836i	$0.251231\pi$
$390$	−1.78239	+	0.344974i	−0.0902547	+	0.0174685i
$391$			5.68685i			0.287597i
$392$	−3.12034	−	19.5516i	−0.157601	−	0.987503i
$393$		−	12.4240i		−	0.626706i
$394$	4.20867	+	21.7450i	0.212030	+	1.09550i
$395$	15.1402	−	4.05681i	0.761787	−	0.204120i
$396$	7.95476	−	18.6568i	0.399742	−	0.937540i
$397$	5.95415	−	22.2212i	0.298830	−	1.11525i	−0.639297	−	0.768960i	$-0.720775\pi$
$397$	5.95415	−	22.2212i	0.298830	−	1.11525i	0.938127	−	0.346290i	$-0.112559\pi$
$398$	10.0986	+	20.7474i	0.506195	+	1.03997i
$399$	2.53448	+	13.5391i	0.126883	+	0.677801i
$400$	−3.88427	+	0.955205i	−0.194214	+	0.0477602i
$401$	9.13070	+	15.8148i	0.455966	+	0.789755i	0.998743	−	0.0501210i	$-0.0159607\pi$
$401$	9.13070	+	15.8148i	0.455966	+	0.789755i	−0.542778	+	0.839876i	$0.682627\pi$
$402$	−1.74826	+	24.7158i	−0.0871952	+	1.23271i
$403$	−10.2263	+	2.74013i	−0.509409	+	0.136496i
$404$	−2.13793	+	1.60566i	−0.106366	+	0.0798846i
$405$	−0.222052	+	0.222052i	−0.0110339	+	0.0110339i
$406$	5.56544	−	2.19867i	0.276208	−	0.109118i
$407$	13.3671			0.662585
$408$	−6.61494	−	3.39060i	−0.327488	−	0.167859i
$409$	12.7820	−	22.1390i	0.632028	−	1.09470i	−0.355109	−	0.934825i	$-0.615556\pi$
$409$	12.7820	−	22.1390i	0.632028	−	1.09470i	0.987137	−	0.159879i	$-0.0511105\pi$
$410$	6.48576	+	7.47314i	0.320309	+	0.369072i
$411$	3.34919	−	12.4993i	0.165203	−	0.616547i
$412$	9.91624	+	7.77312i	0.488538	+	0.382954i
$413$	21.4133	−	10.2609i	1.05368	−	0.504906i
$414$	2.64334	+	5.43073i	0.129913	+	0.266906i
$415$	−0.352042	+	0.203251i	−0.0172810	+	0.00997722i
$416$	−5.43071	−	3.83524i	−0.266263	−	0.188038i
$417$	−1.64496	+	2.84915i	−0.0805540	+	0.139524i
$418$	−21.1795	+	31.3455i	−1.03592	+	1.53316i
$419$	−24.2794	+	24.2794i	−1.18613	+	1.18613i	−0.207999	+	0.978129i	$0.566695\pi$
$419$	−24.2794	+	24.2794i	−1.18613	+	1.18613i	−0.978129	+	0.207999i	$0.933305\pi$
$420$	−4.87398	+	3.10636i	−0.237826	+	0.151575i
$421$	6.95860	+	6.95860i	0.339142	+	0.339142i	0.856044	−	0.516903i	$-0.172915\pi$
$421$	6.95860	+	6.95860i	0.339142	+	0.339142i	−0.516903	+	0.856044i	$0.672915\pi$
$422$	3.95609	+	20.4400i	0.192580	+	0.995005i
$423$	16.1842	+	9.34397i	0.786904	+	0.454319i
$424$	0.356282	+	7.12703i	0.0173026	+	0.346119i
$425$	−1.20303	−	2.08371i	−0.0583556	−	0.101075i
$426$	4.59767	−	13.3178i	0.222758	−	0.645250i
$427$	−1.19763	+	15.5750i	−0.0579576	+	0.753728i
$428$	−1.51327	−	12.4906i	−0.0731469	−	0.603756i
$429$	−6.95900	−	1.86466i	−0.335984	−	0.0900265i
$430$	4.84398	+	0.342636i	0.233597	+	0.0165234i
$431$	−14.3667	−	8.29461i	−0.692019	−	0.399537i	0.112349	−	0.993669i	$-0.464162\pi$
$431$	−14.3667	−	8.29461i	−0.692019	−	0.399537i	−0.804368	+	0.594132i	$0.797496\pi$
$432$	−20.9974	−	0.434042i	−1.01024	−	0.0208828i
$433$		−	27.4467i		−	1.31900i	−0.751703	−	0.659502i	$-0.770767\pi$
$433$		−	27.4467i		−	1.31900i	0.751703	−	0.659502i	$-0.229233\pi$
$434$	−27.0741	+	20.0754i	−1.29960	+	0.963649i
$435$	−1.23521	−	1.23521i	−0.0592237	−	0.0592237i
$436$	−22.1186	+	16.6119i	−1.05929	+	0.795567i
$437$	−2.91576	−	10.8818i	−0.139480	−	0.520546i
$438$	7.49479	+	8.63578i	0.358115	+	0.412634i
$439$	20.1578	−	11.6381i	0.962080	−	0.555457i	0.0652671	−	0.997868i	$-0.479210\pi$
$439$	20.1578	−	11.6381i	0.962080	−	0.555457i	0.896812	+	0.442411i	$0.145877\pi$
$440$	−15.5187	−	3.33773i	−0.739826	−	0.159120i
$441$	7.92472	−	9.85842i	0.377368	−	0.469449i
$442$	1.30503	−	3.78022i	0.0620741	−	0.179807i
$443$	18.5867	+	4.98028i	0.883079	+	0.236620i	0.671735	−	0.740791i	$-0.265549\pi$
$443$	18.5867	+	4.98028i	0.883079	+	0.236620i	0.211344	+	0.977412i	$0.432216\pi$
$444$	−1.94138	−	4.82740i	−0.0921337	−	0.229098i
$445$	−0.340195	−	1.26962i	−0.0161268	−	0.0601859i
$446$	−32.9623	−	22.2719i	−1.56081	−	1.05461i
$447$	−25.2084			−1.19232
$448$	−20.5661	−	5.00337i	−0.971659	−	0.236387i
$449$	−8.59985			−0.405852			−0.202926	−	0.979194i	$-0.565045\pi$
$449$	−8.59985			−0.405852			−0.202926	+	0.979194i	$0.565045\pi$
$450$	−2.11739	−	1.43068i	−0.0998149	−	0.0674428i
$451$	10.1632	+	37.9297i	0.478567	+	1.78604i
$452$	3.78789	+	9.41891i	0.178167	+	0.443028i
$453$	−22.3083	−	5.97748i	−1.04813	−	0.280847i
$454$	−6.38620	+	18.4985i	−0.299719	+	0.868180i
$455$	−2.02372	−	2.36087i	−0.0948733	−	0.110679i
$456$	14.3961	+	3.09628i	0.674159	+	0.144997i
$457$	−28.7392	+	16.5926i	−1.34436	+	0.776169i	−0.987445	−	0.157966i	$-0.949506\pi$
$457$	−28.7392	+	16.5926i	−1.34436	+	0.776169i	−0.356920	+	0.934135i	$0.616173\pi$
$458$	5.53019	+	6.37209i	0.258409	+	0.297748i
$459$	−3.26965	−	12.2025i	−0.152614	−	0.569564i
$460$	3.77980	−	2.83877i	0.176234	−	0.132358i
$461$	8.20665	+	8.20665i	0.382222	+	0.382222i	0.871902	−	0.489680i	$-0.162887\pi$
$461$	8.20665	+	8.20665i	0.382222	+	0.382222i	−0.489680	+	0.871902i	$0.662887\pi$
$462$	−22.7862	+	2.61907i	−1.06011	+	0.121850i
$463$		−	30.1052i		−	1.39911i	−0.714579	−	0.699555i	$-0.753382\pi$
$463$		−	30.1052i		−	1.39911i	0.714579	−	0.699555i	$-0.246618\pi$
$464$	0.132209	−	6.39580i	0.00613765	−	0.296917i
$465$	8.52097	+	4.91958i	0.395150	+	0.228140i
$466$	24.5066	+	1.73346i	1.13524	+	0.0803010i
$467$	31.3313	+	8.39519i	1.44984	+	0.388483i	0.895968	−	0.444119i	$-0.146483\pi$
$467$	31.3313	+	8.39519i	1.44984	+	0.388483i	0.553871	+	0.832602i	$0.313150\pi$
$468$	−0.510850	−	4.21656i	−0.0236140	−	0.194911i
$469$	−38.2718	+	18.3392i	−1.76723	+	0.846825i
$470$	4.77290	−	13.8254i	0.220158	−	0.637719i
$471$	0.163775	+	0.283667i	0.00754636	+	0.0130707i
$472$	−1.26738	−	25.3526i	−0.0583361	−	1.16695i
$473$	16.6890	+	9.63543i	0.767363	+	0.443037i
$474$	−4.60077	−	23.7709i	−0.211320	−	1.09183i
$475$	3.37036	+	3.37036i	0.154643	+	0.154643i
$476$	−0.557749	−	12.7195i	−0.0255644	−	0.582996i
$477$	−3.22358	+	3.22358i	−0.147598	+	0.147598i
$478$	6.44743	−	9.54215i	0.294898	−	0.436448i
$479$	−13.3559	+	23.1330i	−0.610245	+	1.05698i	0.380954	+	0.924594i	$0.375596\pi$
$479$	−13.3559	+	23.1330i	−0.610245	+	1.05698i	−0.991199	+	0.132381i	$0.957738\pi$
$480$	1.04847	+	6.08918i	0.0478560	+	0.277932i
$481$	2.42429	−	1.39966i	0.110538	−	0.0638191i
$482$	10.6457	+	21.8715i	0.484898	+	0.996219i
$483$	3.85862	−	5.63599i	0.175573	−	0.256447i
$484$	−32.2621	−	25.2895i	−1.46646	−	1.14952i
$485$	−3.62161	+	13.5160i	−0.164449	+	0.613731i
$486$	−14.2828	−	16.4572i	−0.647882	−	0.746514i
$487$	−20.3228	+	35.2000i	−0.920912	+	1.59507i	−0.122904	+	0.992419i	$0.539221\pi$
$487$	−20.3228	+	35.2000i	−0.920912	+	1.59507i	−0.798008	+	0.602648i	$0.794113\pi$
$488$	14.8611	+	7.61729i	0.672729	+	0.344818i
$489$	−13.3816			−0.605138
$490$	−8.75366	−	4.62314i	−0.395450	−	0.208852i
$491$	−14.6067	+	14.6067i	−0.659190	+	0.659190i	−0.955189	−	0.295998i	$-0.904348\pi$
$491$	−14.6067	+	14.6067i	−0.659190	+	0.659190i	0.295998	+	0.955189i	$0.404348\pi$
$492$	12.2218	−	9.17905i	0.551003	−	0.413824i
$493$	3.71688	−	0.995935i	0.167400	−	0.0448546i
$494$	−0.558983	+	7.90255i	−0.0251498	+	0.355552i
$495$	−5.07047	−	8.78231i	−0.227901	−	0.394736i
$496$	8.60452	+	34.9897i	0.386354	+	1.57108i
$497$	23.7198	−	4.44028i	1.06398	−	0.199174i
$498$	0.274810	+	0.564595i	0.0123145	+	0.0253001i
$499$	−4.36510	+	16.2908i	−0.195409	+	0.729275i	0.796752	+	0.604306i	$0.206550\pi$
$499$	−4.36510	+	16.2908i	−0.195409	+	0.729275i	−0.992161	+	0.124969i	$0.960117\pi$
$500$	−0.784421	+	1.83975i	−0.0350804	+	0.0822762i
$501$	22.1089	−	5.92405i	0.987751	−	0.264667i
$502$	1.35217	+	6.98628i	0.0603503	+	0.311813i
$503$		−	0.0893847i		−	0.00398547i	−0.999998	−	0.00199273i	$-0.999366\pi$
$503$		−	0.0893847i		−	0.00398547i	0.999998	−	0.00199273i	$-0.000634307\pi$
$504$	−6.44485	−	11.8874i	−0.287076	−	0.529505i
$505$			1.33687i			0.0594899i
$506$	18.4172	−	3.56459i	0.818746	−	0.158465i
$507$	12.2583	−	3.28459i	0.544409	−	0.145874i
$508$	−3.15116	+	1.26726i	−0.139810	+	0.0562257i
$509$	4.08524	−	15.2463i	0.181075	−	0.675781i	−0.814362	−	0.580357i	$-0.802913\pi$
$509$	4.08524	−	15.2463i	0.181075	−	0.675781i	0.995437	−	0.0954234i	$-0.0304205\pi$
$510$	−3.34180	+	1.62658i	−0.147977	+	0.0720262i
$511$	−6.50445	+	18.4734i	−0.287740	+	0.817215i
$512$	−13.4321	+	18.2093i	−0.593622	+	0.804744i
$513$	12.5129	+	21.6730i	0.552460	+	0.956888i
$514$	−18.1143	−	1.28130i	−0.798986	−	0.0565159i
$515$	6.08520	−	1.63052i	0.268146	−	0.0718495i
$516$	1.05590	−	7.42647i	0.0464834	−	0.326932i
$517$	41.0420	−	41.0420i	1.80503	−	1.80503i
$518$	5.54089	−	6.98006i	0.243453	−	0.306686i
$519$	−10.7824			−0.473296
$520$	−3.16399	+	1.01961i	−0.138750	+	0.0447130i
$521$	−13.5363	+	23.4456i	−0.593038	+	1.02717i	0.400782	+	0.916173i	$0.368738\pi$
$521$	−13.5363	+	23.4456i	−0.593038	+	1.02717i	−0.993821	+	0.110999i	$0.964595\pi$
$522$	3.08655	−	2.67875i	0.135095	−	0.117246i
$523$	−1.63096	+	6.08681i	−0.0713168	+	0.266158i	−0.992373	−	0.123272i	$-0.960661\pi$
$523$	−1.63096	+	6.08681i	−0.0713168	+	0.266158i	0.921056	+	0.389430i	$0.127328\pi$
$524$	−2.73610	−	22.5838i	−0.119527	−	0.986580i
$525$	−0.221561	+	2.88135i	−0.00966970	+	0.125753i
$526$	−2.45458	+	1.19474i	−0.107025	+	0.0520930i
$527$	−18.7702	+	10.8370i	−0.817641	+	0.472065i
$528$	−6.83433	+	23.5482i	−0.297426	+	1.02480i
$529$	8.70682	−	15.0806i	0.378557	−	0.655680i
$530$	2.95637	+	1.99756i	0.128417	+	0.0867684i
$531$	11.4671	−	11.4671i	0.497629	−	0.497629i
$532$	7.58878	+	24.0527i	0.329015	+	1.04282i
$533$	5.81480	+	5.81480i	0.251867	+	0.251867i
$534$	−1.99337	+	0.385810i	−0.0862616	+	0.0166956i
$535$	−5.44813	−	3.14548i	−0.235543	−	0.135991i
$536$	2.26518	+	45.3125i	0.0978410	+	1.95720i
$537$	−8.29080	−	14.3601i	−0.357774	−	0.619684i
$538$	−18.6372	−	6.43408i	−0.803509	−	0.277393i
$539$	−23.2053	−	31.6992i	−0.999521	−	1.36538i
$540$	−6.47832	+	8.26445i	−0.278782	+	0.355645i
$541$	1.81400	+	0.486060i	0.0779901	+	0.0208974i	0.297603	−	0.954690i	$-0.403813\pi$
$541$	1.81400	+	0.486060i	0.0779901	+	0.0208974i	−0.219613	+	0.975587i	$0.570479\pi$
$542$	−1.39754	+	19.7575i	−0.0600294	+	0.848657i
$543$	3.69011	+	2.13049i	0.158358	+	0.0914279i
$544$	−12.7711	−	4.70651i	−0.547557	−	0.201790i
$545$			13.8310i			0.592457i
$546$	−3.85830	+	2.86092i	−0.165120	+	0.122436i
$547$	3.87642	+	3.87642i	0.165744	+	0.165744i	0.785106	−	0.619362i	$-0.212609\pi$
$547$	3.87642	+	3.87642i	0.165744	+	0.165744i	−0.619362	+	0.785106i	$0.712609\pi$
$548$	3.33533	−	23.4584i	0.142478	−	1.00210i
$549$	2.76124	+	10.3051i	0.117847	+	0.439810i
$550$	−5.99416	+	5.20219i	−0.255592	+	0.221822i
$551$	−6.60160	+	3.81144i	−0.281238	+	0.162373i
$552$	−3.96214	−	6.13349i	−0.168640	−	0.261058i
$553$	31.4858	−	26.9894i	1.33891	−	1.14771i
$554$	8.50479	+	2.93608i	0.361334	+	0.124742i
$555$	−2.51293	−	0.673337i	−0.106668	−	0.0285816i
$556$	−2.36269	+	5.54136i	−0.100200	+	0.235006i
$557$	−1.64225	−	6.12895i	−0.0695842	−	0.259692i	0.922367	−	0.386316i	$-0.126253\pi$
$557$	−1.64225	−	6.12895i	−0.0695842	−	0.259692i	−0.991951	+	0.126624i	$0.959586\pi$
$558$	−12.8876	+	19.0736i	−0.545576	+	0.807449i
$559$	4.03567			0.170691
$560$	−8.17565	+	6.72003i	−0.345484	+	0.283973i
$561$	−14.7491			−0.622707
$562$	14.1841	−	20.9924i	0.598321	−	0.885511i
$563$	2.55315	+	9.52847i	0.107602	+	0.401577i	0.998627	−	0.0523768i	$-0.0166797\pi$
$563$	2.55315	+	9.52847i	0.107602	+	0.401577i	−0.891025	+	0.453954i	$0.850013\pi$
$564$	−20.7826	−	8.86115i	−0.875106	−	0.373122i
$565$	4.90306	+	1.31377i	0.206273	+	0.0552708i
$566$	16.0077	+	5.52628i	0.672853	+	0.232287i
$567$	−0.275934	+	0.783684i	−0.0115881	+	0.0329116i
$568$	5.42453	−	25.2212i	0.227608	−	1.05826i
$569$	5.02901	−	2.90350i	0.210827	−	0.121721i	−0.390869	−	0.920447i	$-0.627825\pi$
$569$	5.02901	−	2.90350i	0.210827	−	0.121721i	0.601696	+	0.798725i	$0.294492\pi$
$570$	5.56054	−	4.82586i	0.232905	−	0.202133i
$571$	−11.9120	−	44.4562i	−0.498502	−	1.86043i	−0.509460	−	0.860494i	$-0.670155\pi$
$571$	−11.9120	−	44.4562i	−0.498502	−	1.86043i	0.0109578	−	0.999940i	$-0.496512\pi$
$572$	−13.0605	−	1.85694i	−0.546086	−	0.0776428i
$573$	11.5482	+	11.5482i	0.482433	+	0.482433i
$574$	24.0189	+	10.4154i	1.00253	+	0.434730i
$575$		−	2.36355i		−	0.0985668i
$576$	−14.3836	+	1.44168i	−0.599316	+	0.0600700i
$577$	2.95732	+	1.70741i	0.123115	+	0.0710803i	0.560293	−	0.828295i	$-0.310689\pi$
$577$	2.95732	+	1.70741i	0.123115	+	0.0710803i	−0.437178	+	0.899375i	$0.644022\pi$
$578$	−1.11867	+	15.8150i	−0.0465305	+	0.657818i
$579$	6.05249	+	1.62176i	0.251533	+	0.0673980i
$580$	−2.51735	−	1.97329i	−0.104527	−	0.0819365i
$581$	−0.607580	+	0.887445i	−0.0252067	+	0.0368174i
$582$	20.4314	+	7.05347i	0.846909	+	0.292376i
$583$	7.07955	+	12.2621i	0.293205	+	0.507846i
$584$	15.5256	+	14.0473i	0.642455	+	0.581280i
$585$	−1.83918	−	1.06185i	−0.0760406	−	0.0439021i
$586$	0.498804	−	0.0965417i	0.0206054	−	0.00398810i
$587$	−18.0249	−	18.0249i	−0.743965	−	0.743965i	0.229373	−	0.973339i	$-0.426332\pi$
$587$	−18.0249	−	18.0249i	−0.743965	−	0.743965i	−0.973339	+	0.229373i	$0.926332\pi$
$588$	−8.07761	+	12.9842i	−0.333115	+	0.535458i
$589$	30.3603	−	30.3603i	1.25098	−	1.25098i
$590$	−10.5166	−	7.10581i	−0.432960	−	0.292542i
$591$	8.55320	−	14.8146i	0.351832	−	0.609390i
$592$	−4.59210	−	8.34755i	−0.188734	−	0.343082i
$593$	−1.08068	+	0.623933i	−0.0443783	+	0.0256218i	−0.522025	−	0.852930i	$-0.674823\pi$
$593$	−1.08068	+	0.623933i	−0.0443783	+	0.0256218i	0.477647	+	0.878552i	$0.341490\pi$
$594$	−37.4691	+	18.2377i	−1.53738	+	0.748300i
$595$	−5.25273	−	3.59623i	−0.215341	−	0.147431i
$596$	−45.8230	+	5.55160i	−1.87698	+	0.227402i
$597$	4.61257	−	17.2144i	0.188780	−	0.704537i
$598$	2.96693	−	2.57493i	0.121327	−	0.105297i
$599$	−2.57744	+	4.46426i	−0.105311	+	0.182405i	−0.913865	−	0.406017i	$-0.866917\pi$
$599$	−2.57744	+	4.46426i	−0.105311	+	0.182405i	0.808554	+	0.588422i	$0.200251\pi$
$600$	2.74928	+	1.40919i	0.112239	+	0.0575298i
$601$	20.1340			0.821283			0.410641	−	0.911797i	$-0.365305\pi$
$601$	20.1340			0.821283			0.410641	+	0.911797i	$0.365305\pi$
$602$	11.9493	−	4.72066i	0.487017	−	0.192400i
$603$	−20.4950	+	20.4950i	−0.834621	+	0.834621i
$604$	−41.8676	−	5.95276i	−1.70357	−	0.242214i
$605$	−19.7980	+	5.30485i	−0.804902	+	0.215673i
$606$	2.05991	+	0.145707i	0.0836781	+	0.00591893i
$607$	−4.26889	−	7.39393i	−0.173269	−	0.300110i	0.766292	−	0.642493i	$-0.222100\pi$
$607$	−4.26889	−	7.39393i	−0.173269	−	0.300110i	−0.939561	+	0.342382i	$0.888766\pi$
$608$	26.8506	+	2.45789i	1.08894	+	0.0996808i
$609$	−4.35940	−	1.53494i	−0.176652	−	0.0621988i
$610$	7.50766	−	3.65427i	0.303976	−	0.147957i
$611$	3.14597	−	11.7409i	0.127272	−	0.474987i
$612$	−3.24436	−	8.06738i	−0.131145	−	0.326104i
$613$	38.2393	−	10.2462i	1.54447	−	0.413839i	0.616763	−	0.787149i	$-0.288444\pi$
$613$	38.2393	−	10.2462i	1.54447	−	0.413839i	0.927707	+	0.373310i	$0.121777\pi$
$614$	−16.6921	+	3.23070i	−0.673639	+	0.130380i
$615$		−	7.64245i		−	0.308173i
$616$	−40.8432	+	9.77902i	−1.64562	+	0.394008i
$617$		−	5.40222i		−	0.217485i	−0.994070	−	0.108743i	$-0.965318\pi$
$617$		−	5.40222i		−	0.217485i	0.994070	−	0.108743i	$-0.0346824\pi$
$618$	−1.84915	−	9.55407i	−0.0743839	−	0.384321i
$619$	37.7735	−	10.1214i	1.51825	−	0.406813i	0.599082	−	0.800688i	$-0.295532\pi$
$619$	37.7735	−	10.1214i	1.51825	−	0.406813i	0.919164	+	0.393875i	$0.128866\pi$
$620$	16.5726	+	7.06609i	0.665570	+	0.283781i
$621$	3.21188	−	11.9869i	0.128888	−	0.481018i
$622$	−0.585400	−	1.20270i	−0.0234724	−	0.0482239i
$623$	−2.26327	−	2.64033i	−0.0906760	−	0.105783i
$624$	1.22622	+	4.98635i	0.0490882	+	0.199614i
$625$	0.500000	+	0.866025i	0.0200000	+	0.0346410i
$626$	2.12284	−	30.0114i	0.0848459	−	1.19950i
$627$	28.2223	−	7.56215i	1.12709	−	0.302003i
$628$	0.360176	+	0.479572i	0.0143726	+	0.0191370i
$629$	4.05229	−	4.05229i	0.161575	−	0.161575i
$630$	−6.68774	−	0.992705i	−0.266446	−	0.0395503i
$631$	−0.277063			−0.0110297			−0.00551485	−	0.999985i	$-0.501755\pi$
$631$	−0.277063			−0.0110297			−0.00551485	+	0.999985i	$0.501755\pi$
$632$	−13.5981	−	42.1967i	−0.540905	−	1.67849i
$633$	8.03989	−	13.9255i	0.319557	−	0.553489i
$634$	−14.5936	−	16.8153i	−0.579586	−	0.667821i
$635$	−0.439531	+	1.64035i	−0.0174423	+	0.0650954i
$636$	3.40015	−	4.33760i	0.134825	−	0.171997i
$637$	−7.52773	−	3.31921i	−0.298260	−	0.131512i
$638$	−5.55518	−	11.4131i	−0.219932	−	0.451848i
$639$	14.2731	−	8.24059i	0.564636	−	0.325993i
$640$	3.24688	+	10.8378i	0.128344	+	0.428401i
$641$	−21.5892	+	37.3935i	−0.852721	+	1.47696i	0.0260219	+	0.999661i	$0.491716\pi$
$641$	−21.5892	+	37.3935i	−0.852721	+	1.47696i	−0.878743	+	0.477295i	$0.841617\pi$
$642$	−5.44050	+	8.05191i	−0.214719	+	0.317783i
$643$	−3.65839	+	3.65839i	−0.144273	+	0.144273i	−0.775554	−	0.631281i	$-0.782529\pi$
$643$	−3.65839	+	3.65839i	−0.144273	+	0.144273i	0.631281	+	0.775554i	$0.282529\pi$
$644$	5.77287	−	11.0947i	0.227483	−	0.437192i
$645$	−2.65206	−	2.65206i	−0.104425	−	0.104425i
$646$	3.08186	+	15.9231i	0.121254	+	0.626486i
$647$	−24.8943	−	14.3727i	−0.978697	−	0.565051i	−0.0768202	−	0.997045i	$-0.524477\pi$
$647$	−24.8943	−	14.3727i	−0.978697	−	0.565051i	−0.901876	+	0.431994i	$0.857810\pi$
$648$	0.658633	+	0.595917i	0.0258735	+	0.0234099i
$649$	−25.1837	−	43.6195i	−0.988548	−	1.71222i
$650$	−0.542393	+	1.57112i	−0.0212744	+	0.0616244i
$651$	25.9554	+	1.99583i	1.01727	+	0.0782226i
$652$	−24.3247	+	2.94701i	−0.952628	+	0.115414i
$653$	−23.0516	−	6.17664i	−0.902077	−	0.241711i	−0.222169	−	0.975008i	$-0.571314\pi$
$653$	−23.0516	−	6.17664i	−0.902077	−	0.241711i	−0.679908	+	0.733297i	$0.737980\pi$
$654$	21.3115	+	1.50746i	0.833345	+	0.0589463i
$655$	−9.85060	−	5.68725i	−0.384895	−	0.222219i
$656$	20.1950	−	19.3770i	0.788481	−	0.756543i
$657$			13.3759i			0.521844i
$658$	−4.41878	−	38.4439i	−0.172262	−	1.49870i
$659$	3.24232	+	3.24232i	0.126303	+	0.126303i	0.767433	−	0.641130i	$-0.221534\pi$
$659$	3.24232	+	3.24232i	0.126303	+	0.126303i	−0.641130	+	0.767433i	$0.721534\pi$
$660$	7.36246	+	9.80307i	0.286583	+	0.381584i
$661$	9.91238	+	36.9935i	0.385547	+	1.43888i	0.837303	+	0.546739i	$0.184131\pi$
$661$	9.91238	+	36.9935i	0.385547	+	1.43888i	−0.451756	+	0.892141i	$0.649202\pi$
$662$	−22.1644	−	25.5386i	−0.861444	−	0.992588i
$663$	−2.67492	+	1.54436i	−0.103885	+	0.0599782i
$664$	0.623879	+	0.965780i	0.0242112	+	0.0374795i
$665$	11.8949	+	4.18819i	0.461266	+	0.162411i
$666$	1.98621	−	5.75336i	0.0769642	−	0.222938i
$667$	3.65120	+	0.978337i	0.141375	+	0.0378814i
$668$	38.8841	−	15.6375i	1.50447	−	0.605034i
$669$	7.95222	+	29.6781i	0.307450	+	1.14742i
$670$	18.7961	+	12.7001i	0.726158	+	0.490650i
$671$	33.1352			1.27917
$672$	9.46345	+	13.3298i	0.365061	+	0.514210i
$673$	5.11238			0.197068			0.0985339	−	0.995134i	$-0.468585\pi$
$673$	5.11238			0.197068			0.0985339	+	0.995134i	$0.468585\pi$
$674$	3.55373	+	2.40118i	0.136885	+	0.0924900i
$675$	1.35892	+	5.07156i	0.0523049	+	0.195205i
$676$	21.5593	−	8.67023i	0.829204	−	0.333471i
$677$	12.0060	+	3.21701i	0.461429	+	0.123640i	0.482042	−	0.876148i	$-0.339895\pi$
$677$	12.0060	+	3.21701i	0.461429	+	0.123640i	−0.0206131	+	0.999788i	$0.506562\pi$
$678$	2.55871	−	7.41167i	0.0982666	−	0.284643i
$679$	6.81201	+	36.3894i	0.261421	+	1.39650i
$680$	−5.71639	+	3.69270i	−0.219214	+	0.141609i
$681$	13.0898	−	7.55737i	0.501600	−	0.289599i
$682$	46.8615	+	53.9956i	1.79442	+	2.06760i
$683$	−10.3135	−	38.4907i	−0.394637	−	1.47281i	−0.822398	−	0.568913i	$-0.807364\pi$
$683$	−10.3135	−	38.4907i	−0.394637	−	1.47281i	0.427761	−	0.903892i	$-0.359303\pi$
$684$	10.3444	+	13.7735i	0.395527	+	0.526641i
$685$	−8.37722	−	8.37722i	−0.320077	−	0.320077i
$686$	−26.1716	−	1.02248i	−0.999238	−	0.0390383i
$687$		−	6.51646i		−	0.248619i
$688$	0.283860	−	13.7321i	0.0108221	−	0.523533i
$689$	2.56792	+	1.48259i	0.0978299	+	0.0564821i
$690$	−3.64187	−	0.257606i	−0.138643	−	0.00980688i
$691$	−27.6033	−	7.39628i	−1.05008	−	0.281368i	−0.307794	−	0.951453i	$-0.599591\pi$
$691$	−27.6033	−	7.39628i	−1.05008	−	0.281368i	−0.742284	+	0.670085i	$0.766258\pi$
$692$	−19.5999	+	2.37459i	−0.745078	+	0.0902685i
$693$	−22.1389	−	15.1572i	−0.840987	−	0.575773i
$694$	5.48683	−	15.8934i	0.208277	−	0.603305i
$695$	1.50601	+	2.60848i	0.0571261	+	0.0989453i
$696$	−3.31491	+	3.66377i	−0.125651	+	0.138875i
$697$	14.5795	+	8.41748i	0.552238	+	0.318835i
$698$	1.11070	+	5.73867i	0.0420406	+	0.217212i
$699$	−13.4173	−	13.4173i	−0.507488	−	0.507488i
$700$	0.231810	+	5.28642i	0.00876159	+	0.199808i
$701$	−26.4939	+	26.4939i	−1.00066	+	1.00066i	−0.000661237		1.00000i	$0.500210\pi$
$701$	−26.4939	+	26.4939i	−1.00066	+	1.00066i	−1.00000		0.000661237i	$0.999790\pi$
$702$	−4.88581	+	7.23097i	−0.184403	+	0.272915i
$703$	−5.67636	+	9.83174i	−0.214088	+	0.370811i
$704$	−7.23725	+	44.3102i	−0.272764	+	1.67000i
$705$	−9.78300	+	5.64821i	−0.368449	+	0.212724i
$706$	8.09902	+	16.6394i	0.304811	+	0.626232i
$707$	1.52846	+	3.18972i	0.0574836	+	0.119962i
$708$	−12.0952	+	15.4299i	−0.454564	+	0.579892i
$709$	−10.2629	+	38.3017i	−0.385432	+	1.43845i	0.452053	+	0.891991i	$0.350692\pi$
$709$	−10.2629	+	38.3017i	−0.385432	+	1.43845i	−0.837485	+	0.546460i	$0.815975\pi$
$710$	−8.45466	−	9.74178i	−0.317298	−	0.365603i
$711$	14.1614	−	24.5283i	0.531094	−	0.919882i
$712$	−3.53852	+	1.14031i	−0.132612	+	0.0427349i
$713$	−21.2910			−0.797353
$714$	−6.11373	+	7.70169i	−0.228801	+	0.288228i
$715$	−4.66402	+	4.66402i	−0.174424	+	0.174424i
$716$	−18.2332	−	24.2774i	−0.681408	−	0.907290i
$717$	−8.59141	+	2.30206i	−0.320852	+	0.0859720i
$718$	1.11903	−	15.8201i	0.0417618	−	0.590402i
$719$	11.6815	+	20.2330i	0.435647	+	0.754562i	0.997348	−	0.0727776i	$-0.0231863\pi$
$719$	11.6815	+	20.2330i	0.435647	+	0.754562i	−0.561701	+	0.827340i	$0.689853\pi$
$720$	−3.74251	+	6.18346i	−0.139475	+	0.230444i
$721$	12.6549	−	10.8477i	0.471293	−	0.403988i
$722$	−2.30157	−	4.72856i	−0.0856556	−	0.175979i
$723$	4.86247	−	18.1470i	0.180837	−	0.674894i
$724$	7.17695	+	3.06006i	0.266729	+	0.113726i
$725$	−1.54480	+	0.413927i	−0.0573723	+	0.0153729i
$726$	6.01615	+	31.0838i	0.223280	+	1.15363i
$727$			10.8399i			0.402028i	0.979588	+	0.201014i	$0.0644237\pi$
$727$			10.8399i			0.402028i	−0.979588	+	0.201014i	$0.935576\pi$
$728$	−6.38343	+	6.05019i	−0.236586	+	0.224235i
$729$			17.7721i			0.658228i
$730$	10.2779	−	1.98925i	0.380403	−	0.0736255i
$731$	7.98035	−	2.13833i	0.295164	−	0.0790889i
$732$	−4.81239	−	11.9664i	−0.177871	−	0.442292i
$733$	11.0445	−	41.2186i	0.407937	−	1.52244i	−0.390636	−	0.920545i	$-0.627745\pi$
$733$	11.0445	−	41.2186i	0.407937	−	1.52244i	0.798573	−	0.601898i	$-0.205589\pi$
$734$	32.8500	−	15.9893i	1.21252	−	0.590177i
$735$	2.76565	+	7.12813i	0.102013	+	0.262925i
$736$	−8.55301	−	10.2767i	−0.315268	−	0.378803i
$737$	45.0107	+	77.9607i	1.65799	+	2.87172i
$738$	17.8355	+	1.26158i	0.656532	+	0.0464395i
$739$	28.7089	−	7.69252i	1.05607	−	0.282974i	0.311314	−	0.950307i	$-0.399231\pi$
$739$	28.7089	−	7.69252i	1.05607	−	0.282974i	0.744759	+	0.667333i	$0.232564\pi$
$740$	−4.71620	−	0.670552i	−0.173371	−	0.0246500i
$741$	4.32662	−	4.32662i	0.158942	−	0.158942i
$742$	9.33764	+	1.38605i	0.342796	+	0.0508834i
$743$	−5.68941			−0.208724			−0.104362	−	0.994539i	$-0.533280\pi$
$743$	−5.68941			−0.208724			−0.104362	+	0.994539i	$0.533280\pi$
$744$	12.6940	−	24.7656i	0.465385	−	0.907951i
$745$	−11.5395	+	19.9870i	−0.422775	+	0.732268i
$746$	−26.7144	+	23.1848i	−0.978085	+	0.848857i
$747$	−0.190111	+	0.709505i	−0.00695581	+	0.0259594i
$748$	−26.8104	+	3.24816i	−0.980285	+	0.118765i
$749$	−16.5953	−	1.27609i	−0.606380	−	0.0466274i
$750$	1.38891	−	0.676034i	0.0507157	−	0.0246853i
$751$	35.9303	−	20.7443i	1.31111	−	0.756972i	0.328833	−	0.944388i	$-0.393345\pi$
$751$	35.9303	−	20.7443i	1.31111	−	0.756972i	0.982281	+	0.187416i	$0.0600114\pi$
$752$	−39.7294	−	11.5306i	−1.44878	−	0.420477i
$753$	2.74799	−	4.75965i	0.100142	−	0.173451i
$754$	−2.20255	−	1.48822i	−0.0802121	−	0.0541976i
$755$	−14.9513	+	14.9513i	−0.544134	+	0.544134i
$756$	−6.00820	+	27.1254i	−0.218516	+	0.986543i
$757$	8.11771	+	8.11771i	0.295043	+	0.295043i	0.839069	−	0.544025i	$-0.183100\pi$
$757$	8.11771	+	8.11771i	0.295043	+	0.295043i	−0.544025	+	0.839069i	$0.683100\pi$
$758$	40.1817	−	7.77702i	1.45947	−	0.282474i
$759$	−12.5474	−	7.24424i	−0.455442	−	0.262949i
$760$	9.04497	−	9.99688i	0.328096	−	0.362625i
$761$	16.4975	+	28.5745i	0.598034	+	1.03583i	0.993111	+	0.117178i	$0.0373847\pi$
$761$	16.4975	+	28.5745i	0.598034	+	1.03583i	−0.395077	+	0.918648i	$0.629282\pi$
$762$	2.47962	+	0.856033i	0.0898273	+	0.0310108i
$763$	15.8132	+	33.0004i	0.572476	+	1.19469i
$764$	23.5351	+	18.4487i	0.851472	+	0.667449i
$765$	−4.19951	−	1.12526i	−0.151834	−	0.0406837i
$766$	3.47507	−	49.1284i	0.125560	−	1.77508i
$767$	−9.13472	−	5.27394i	−0.329836	−	0.190431i
$768$	17.0532	−	3.82173i	0.615356	−	0.137905i
$769$		−	10.6222i		−	0.383046i	−0.981488	−	0.191523i	$-0.938657\pi$
$769$		−	10.6222i		−	0.383046i	0.981488	−	0.191523i	$-0.0613427\pi$
$770$	−8.35413	+	19.2655i	−0.301062	+	0.694279i
$771$	9.91750	+	9.91750i	0.357170	+	0.357170i
$772$	11.3592	+	1.61505i	0.408825	+	0.0581269i
$773$	10.1756	+	37.9759i	0.365991	+	1.36590i	0.866072	+	0.499919i	$0.166637\pi$
$773$	10.1756	+	37.9759i	0.365991	+	1.36590i	−0.500081	+	0.865979i	$0.666696\pi$
$774$	6.62700	−	5.75142i	0.238203	−	0.206730i
$775$	7.80119	−	4.50402i	0.280227	−	0.161789i
$776$	38.6929	+	8.32199i	1.38899	+	0.298742i
$777$	−6.76560	+	1.26650i	−0.242715	+	0.0454356i
$778$	−26.1889	−	9.04112i	−0.938918	−	0.324140i
$779$	−32.2136	−	8.63162i	−1.15417	−	0.309260i
$780$	2.36174	+	1.00698i	0.0845638	+	0.0360557i
$781$	−13.2485	−	49.4441i	−0.474069	−	1.76925i
$782$	4.50262	−	6.66386i	0.161014	−	0.238299i
$783$	−8.39703			−0.300085
$784$	−11.8237	+	25.3811i	−0.422276	+	0.906467i
$785$	0.299882			0.0107032
$786$	−9.83679	+	14.5584i	−0.350867	+	0.519281i
$787$	−11.8037	−	44.0520i	−0.420757	−	1.57029i	−0.773018	−	0.634384i	$-0.781254\pi$
$787$	−11.8037	−	44.0520i	−0.420757	−	1.57029i	0.352262	−	0.935902i	$-0.385413\pi$
$788$	12.2851	−	28.8131i	0.437640	−	1.02642i
$789$	2.03659	+	0.545702i	0.0725045	+	0.0194275i
$790$	−20.9533	−	7.23365i	−0.745486	−	0.257362i
$791$	13.2006	−	2.47112i	0.469359	−	0.0878628i
$792$	−24.0931	+	15.5638i	−0.856111	+	0.553035i
$793$	6.00945	−	3.46956i	0.213402	−	0.123208i
$794$	−24.5709	+	21.3245i	−0.871990	+	0.756780i
$795$	−0.713230	−	2.66181i	−0.0252957	−	0.0944047i
$796$	4.59349	−	32.3075i	0.162812	−	1.14511i
$797$	−13.4689	−	13.4689i	−0.477094	−	0.477094i	0.427107	−	0.904201i	$-0.359533\pi$
$797$	−13.4689	−	13.4689i	−0.477094	−	0.477094i	−0.904201	+	0.427107i	$0.859533\pi$
$798$	7.74979	−	17.8718i	0.274340	−	0.632654i
$799$		−	24.8840i		−	0.880333i
$800$	5.30789	+	1.95610i	0.187662	+	0.0691587i
$801$	−2.05688	−	1.18754i	−0.0726764	−	0.0419597i
$802$	1.82220	−	25.7612i	0.0643442	−	0.909658i
$803$	40.1282	+	10.7523i	1.41609	+	0.379441i
$804$	21.6176	−	27.5777i	0.762393	−	0.972592i
$805$	−2.70228	−	5.63935i	−0.0952428	−	0.198761i
$806$	14.1527	+	4.88590i	0.498508	+	0.172098i
$807$	7.61404	+	13.1879i	0.268027	+	0.464236i
$808$	3.77652	−	0.188789i	0.132858	−	0.00664158i
$809$	0.334837	+	0.193318i	0.0117722	+	0.00679670i	0.505875	−	0.862607i	$-0.331170\pi$
$809$	0.334837	+	0.193318i	0.0117722	+	0.00679670i	−0.494102	+	0.869404i	$0.664503\pi$
$810$	0.436013	−	0.0843887i	0.0153199	−	0.00296512i
$811$	33.2147	+	33.2147i	1.16633	+	1.16633i	0.983064	+	0.183261i	$0.0586654\pi$
$811$	33.2147	+	33.2147i	1.16633	+	1.16633i	0.183261	+	0.983064i	$0.441335\pi$
$812$	−8.26240	−	1.83009i	−0.289953	−	0.0642237i
$813$	10.8172	−	10.8172i	0.379375	−	0.379375i
$814$	−15.6636	−	10.5836i	−0.549010	−	0.370954i
$815$	−6.12564	+	10.6099i	−0.214572	+	0.371649i
$816$	5.06685	+	9.21055i	0.177375	+	0.322434i
$817$	−14.1740	+	8.18336i	−0.495886	+	0.286300i
$818$	−32.5067	+	15.8223i	−1.13657	+	0.553212i
$819$	−5.60224	−	0.430782i	−0.195758	−	0.0150527i
$820$	−1.68308	−	13.8922i	−0.0587758	−	0.485136i
$821$	9.96871	−	37.2037i	0.347910	−	1.29842i	−0.541265	−	0.840852i	$-0.682054\pi$
$821$	9.96871	−	37.2037i	0.347910	−	1.29842i	0.889175	−	0.457567i	$-0.151279\pi$
$822$	−13.8211	+	11.9950i	−0.482065	+	0.418373i
$823$	−5.03157	+	8.71493i	−0.175389	+	0.303784i	−0.940296	−	0.340358i	$-0.889452\pi$
$823$	−5.03157	+	8.71493i	−0.175389	+	0.303784i	0.764907	+	0.644141i	$0.222785\pi$
$824$	−5.46541	−	16.9598i	−0.190396	−	0.590824i
$825$	6.12997			0.213418
$826$	−33.2163	−	4.93051i	−1.15574	−	0.171555i
$827$	−14.5966	+	14.5966i	−0.507575	+	0.507575i	−0.913781	−	0.406207i	$-0.866851\pi$
$827$	−14.5966	+	14.5966i	−0.507575	+	0.507575i	0.406207	+	0.913781i	$0.366851\pi$
$828$	1.20237	−	8.45662i	0.0417851	−	0.293888i
$829$	26.6457	−	7.13970i	0.925444	−	0.247972i	0.235533	−	0.971866i	$-0.424316\pi$
$829$	26.6457	−	7.13970i	0.925444	−	0.247972i	0.689911	+	0.723894i	$0.257650\pi$
$830$	0.573449	+	0.0405626i	0.0199047	+	0.00140795i
$831$	−3.47453	−	6.01807i	−0.120530	−	0.208765i
$832$	3.32712	+	8.79396i	0.115347	+	0.304876i
$833$	−16.6444	−	2.57496i	−0.576696	−	0.0892171i
$834$	4.18341	−	2.03622i	0.144860	−	0.0705087i
$835$	5.42364	−	20.2413i	0.187693	−	0.700479i
$836$	49.6362	−	19.9616i	1.71670	−	0.690386i
$837$	45.6849	−	12.2412i	1.57910	−	0.423119i
$838$	47.6742	−	9.22716i	1.64688	−	0.318747i
$839$			9.19001i			0.317274i	0.987337	+	0.158637i	$0.0507100\pi$
$839$			9.19001i			0.317274i	−0.987337	+	0.158637i	$0.949290\pi$
$840$	8.17083	+	0.218989i	0.281920	+	0.00755585i
$841$			26.4423i			0.911802i
$842$	−2.64455	−	13.6636i	−0.0911371	−	0.470880i
$843$	−18.9008	+	5.06445i	−0.650978	+	0.174429i
$844$	11.5479	−	27.0839i	0.397494	−	0.932267i
$845$	3.00714	−	11.2228i	0.103449	−	0.386076i
$846$	−11.5665	−	23.7633i	−0.397664	−	0.816999i
$847$	−41.1722	+	35.2925i	−1.41469	+	1.21266i
$848$	5.22541	−	8.63355i	0.179441	−	0.296477i
$849$	−6.53975	−	11.3272i	−0.224444	−	0.388748i
$850$	−0.240088	+	3.39421i	−0.00823494	+	0.116420i
$851$	5.43772	−	1.45703i	0.186403	−	0.0499465i
$852$	−15.9321	+	11.9656i	−0.545823	+	0.409934i
$853$	−17.7978	+	17.7978i	−0.609385	+	0.609385i	−0.942785	−	0.333401i	$-0.891804\pi$
$853$	−17.7978	+	17.7978i	−0.609385	+	0.609385i	0.333401	+	0.942785i	$0.391804\pi$
$854$	13.7351	−	17.3026i	0.470004	−	0.592081i
$855$	8.61270			0.294548
$856$	−8.11630	+	15.8346i	−0.277409	+	0.541217i
$857$	−16.8156	+	29.1255i	−0.574410	+	0.994907i	0.421696	+	0.906737i	$0.361435\pi$
$857$	−16.8156	+	29.1255i	−0.574410	+	0.994907i	−0.996106	+	0.0881693i	$0.971898\pi$
$858$	6.67819	+	7.69486i	0.227990	+	0.262698i
$859$	−11.9682	+	44.6659i	−0.408349	+	1.52398i	0.389444	+	0.921050i	$0.372667\pi$
$859$	−11.9682	+	44.6659i	−0.408349	+	1.52398i	−0.797794	+	0.602931i	$0.794000\pi$
$860$	−5.40489	−	4.23677i	−0.184305	−	0.144473i
$861$	−8.73772	−	18.2346i	−0.297781	−	0.621435i
$862$	10.2675	+	21.0946i	0.349714	+	0.718485i
$863$	5.73957	−	3.31374i	0.195377	−	0.112801i	−0.399120	−	0.916899i	$-0.630684\pi$
$863$	5.73957	−	3.31374i	0.195377	−	0.112801i	0.594497	+	0.804097i	$0.297351\pi$
$864$	24.2611	+	17.1335i	0.825379	+	0.582894i
$865$	−4.93581	+	8.54908i	−0.167823	+	0.290677i
$866$	−21.7312	+	32.1620i	−0.738456	+	1.09291i
$867$	8.65868	−	8.65868i	0.294064	−	0.294064i
$868$	47.6203	−	2.08815i	1.61634	−	0.0708765i
$869$	−62.2019	−	62.2019i	−2.11005	−	2.11005i
$870$	0.469429	+	2.42541i	0.0159151	+	0.0822290i
$871$	16.3264	+	9.42605i	0.553199	+	0.319390i
$872$	39.0713	−	1.95318i	1.32312	−	0.0661431i
$873$	12.6422	+	21.8970i	0.427874	+	0.741100i
$874$	−5.19907	+	15.0598i	−0.175861	+	0.509407i
$875$	2.18312	+	1.49465i	0.0738030	+	0.0505284i
$876$	−1.94493	−	16.0535i	−0.0657131	−	0.542397i
$877$	−30.7754	−	8.24624i	−1.03921	−	0.278456i	−0.301425	−	0.953490i	$-0.597462\pi$
$877$	−30.7754	−	8.24624i	−1.03921	−	0.278456i	−0.737786	+	0.675034i	$0.764129\pi$
$878$	−32.8355	−	2.32261i	−1.10815	−	0.0783841i
$879$	−0.339828	−	0.196200i	−0.0114621	−	0.00661766i
$880$	15.5421	+	16.1983i	0.523926	+	0.546043i
$881$		−	36.0913i		−	1.21595i	−0.793957	−	0.607973i	$-0.791983\pi$
$881$		−	36.0913i		−	1.21595i	0.793957	−	0.607973i	$-0.208017\pi$
$882$	−17.0917	+	5.27762i	−0.575507	+	0.177707i
$883$	−26.9446	−	26.9446i	−0.906757	−	0.906757i	0.0892517	−	0.996009i	$-0.471552\pi$
$883$	−26.9446	−	26.9446i	−0.906757	−	0.906757i	−0.996009	+	0.0892517i	$0.971552\pi$
$884$	−4.52226	+	3.39639i	−0.152100	+	0.114233i
$885$	2.53714	+	9.46873i	0.0852850	+	0.318288i
$886$	−17.8367	−	20.5521i	−0.599234	−	0.690460i
$887$	30.5917	−	17.6621i	1.02717	−	0.593035i	0.110995	−	0.993821i	$-0.464596\pi$
$887$	30.5917	−	17.6621i	1.02717	−	0.593035i	0.916172	+	0.400786i	$0.131263\pi$
$888$	−1.54724	+	7.19386i	−0.0519220	+	0.241410i
$889$	0.826729	+	4.41635i	0.0277276	+	0.148119i
$890$	−0.606597	+	1.75710i	−0.0203332	+	0.0588980i
$891$	1.70233	+	0.456138i	0.0570302	+	0.0152812i
$892$	20.9912	+	52.1965i	0.702838	+	1.74767i
$893$	12.7585	+	47.6155i	0.426948	+	1.59339i
$894$	29.5392	+	19.9590i	0.987940	+	0.667530i
$895$	−15.1809			−0.507443
$896$	20.1379	+	22.1464i	0.672761	+	0.739859i
$897$	−3.03415			−0.101307
$898$	10.0773	+	6.80902i	0.336284	+	0.227220i
$899$	3.72867	+	13.9156i	0.124358	+	0.464111i
$900$	1.34841	+	3.35294i	0.0449470	+	0.111765i
$901$	5.86350	+	1.57112i	0.195341	+	0.0523416i
$902$	18.1219	−	52.4928i	0.603394	−	1.74782i
$903$	−9.35987	−	3.29559i	−0.311477	−	0.109670i
$904$	3.01887	−	14.0362i	0.100406	−	0.466836i
$905$	3.37840	−	1.95052i	0.112302	−	0.0648376i
$906$	21.4081	+	24.6672i	0.711236	+	0.819513i
$907$	6.79681	+	25.3661i	0.225684	+	0.842266i	0.982129	+	0.188208i	$0.0602680\pi$
$907$	6.79681	+	25.3661i	0.225684	+	0.842266i	−0.756445	+	0.654058i	$0.773065\pi$
$908$	22.1298	−	16.6203i	0.734402	−	0.551563i
$909$	1.70813	+	1.70813i	0.0566552	+	0.0566552i
$910$	0.502151	+	4.36877i	0.0166461	+	0.144823i
$911$		−	27.7822i		−	0.920465i	−0.887799	−	0.460232i	$-0.847766\pi$
$911$		−	27.7822i		−	0.920465i	0.887799	−	0.460232i	$-0.152234\pi$
$912$	−14.4178	−	15.0265i	−0.477422	−	0.497576i
$913$	1.97572	+	1.14068i	0.0653866	+	0.0377510i
$914$	46.8140	+	3.31137i	1.54847	+	0.109530i
$915$	−6.22918	−	1.66910i	−0.205930	−	0.0551789i
$916$	−1.43511	−	11.8454i	−0.0474173	−	0.391383i
$917$	−30.0055	−	2.30726i	−0.990869	−	0.0761925i
$918$	−5.83008	+	16.8877i	−0.192421	+	0.557377i
$919$	−3.80310	−	6.58717i	−0.125453	−	0.217291i	0.796457	−	0.604695i	$-0.206705\pi$
$919$	−3.80310	−	6.58717i	−0.125453	−	0.217291i	−0.921910	+	0.387404i	$0.873372\pi$
$920$	−6.67679	+	0.333774i	−0.220127	+	0.0110042i
$921$	11.3721	+	6.56568i	0.374723	+	0.216347i
$922$	−3.11885	−	16.1142i	−0.102714	−	0.530695i
$923$	−7.58002	−	7.58002i	−0.249499	−	0.249499i
$924$	28.7746	+	14.9722i	0.946614	+	0.492549i
$925$	−1.68420	+	1.68420i	−0.0553761	+	0.0553761i
$926$	−23.8361	+	35.2773i	−0.783304	+	1.15929i
$927$	5.69180	−	9.85848i	0.186943	−	0.323795i
$928$	−5.21886	+	7.38992i	−0.171317	+	0.242586i
$929$	3.03299	−	1.75110i	0.0995092	−	0.0574516i	−0.449420	−	0.893321i	$-0.648369\pi$
$929$	3.03299	−	1.75110i	0.0995092	−	0.0574516i	0.548929	+	0.835869i	$0.315036\pi$
$930$	−6.08974	−	12.5113i	−0.199690	−	0.410263i
$931$	33.1693	−	3.60676i	1.08708	−	0.118207i
$932$	−27.3443	−	21.4346i	−0.895693	−	0.702114i
$933$	−0.267385	+	0.997893i	−0.00875378	+	0.0326696i
$934$	−30.0670	−	34.6444i	−0.983823	−	1.13360i
$935$	−6.75161	+	11.6941i	−0.220801	+	0.382439i
$936$	−2.73989	+	5.34544i	−0.0895562	+	0.174721i
$937$	51.4098			1.67949			0.839743	−	0.542984i	$-0.182706\pi$
$937$	51.4098			1.67949			0.839743	+	0.542984i	$0.182706\pi$
$938$	59.3672	+	8.81226i	1.93841	+	0.287730i
$939$	−16.4312	+	16.4312i	−0.536211	+	0.536211i
$940$	−16.5393	+	12.4216i	−0.539453	+	0.405149i
$941$	−42.0767	+	11.2744i	−1.37166	+	0.367535i	−0.868085	−	0.496415i	$-0.834649\pi$
$941$	−42.0767	+	11.2744i	−1.37166	+	0.367535i	−0.503576	+	0.863951i	$0.667983\pi$
$942$	0.0326844	−	0.462071i	0.00106492	−	0.0150551i
$943$	8.26875	+	14.3219i	0.269267	+	0.466385i
$944$	−18.5881	+	30.7117i	−0.604991	+	0.999580i
$945$	9.04073	+	10.5469i	0.294095	+	0.343091i
$946$	−11.9273	−	24.5045i	−0.387789	−	0.796711i
$947$	9.25737	−	34.5490i	0.300824	−	1.12269i	−0.635656	−	0.771972i	$-0.719270\pi$
$947$	9.25737	−	34.5490i	0.300824	−	1.12269i	0.936481	−	0.350719i	$-0.114063\pi$
$948$	−13.4297	+	31.4974i	−0.436175	+	1.02299i
$949$	8.40358	−	2.25173i	0.272792	−	0.0730943i
$950$	−1.28087	−	6.61790i	−0.0415569	−	0.214713i
$951$			17.1963i			0.557628i
$952$	−9.41720	+	15.3463i	−0.305213	+	0.497376i
$953$		−	22.5096i		−	0.729157i	−0.931173	−	0.364578i	$-0.881213\pi$
$953$		−	22.5096i		−	0.729157i	0.931173	−	0.364578i	$-0.118787\pi$
$954$	6.32970	−	1.22509i	0.204932	−	0.0396637i
$955$	14.4426	−	3.86988i	0.467351	−	0.125226i
$956$	−15.1102	+	6.07668i	−0.488699	+	0.196534i
$957$	−2.53736	+	9.46955i	−0.0820211	+	0.306107i
$958$	33.9662	−	16.5326i	1.09740	−	0.534146i
$959$	−29.5656	−	10.4100i	−0.954722	−	0.336156i
$960$	3.59257	−	7.96543i	0.115950	−	0.257083i
$961$	−25.0724	−	43.4267i	−0.808787	−	1.40086i
$962$	−3.94898	−	0.279329i	−0.127320	−	0.00900593i
$963$	−10.9802	+	2.94213i	−0.353831	+	0.0948087i
$964$	4.84236	−	34.0578i	0.155962	−	1.09693i
$965$	4.05646	−	4.05646i	0.130582	−	0.130582i
$966$	−8.98389	+	3.54915i	−0.289052	+	0.114192i
$967$	−9.37295			−0.301414			−0.150707	−	0.988579i	$-0.548155\pi$
$967$	−9.37295			−0.301414			−0.150707	+	0.988579i	$0.548155\pi$
$968$	17.7815	+	55.1781i	0.571518	+	1.77349i
$969$	6.26320	−	10.8482i	0.201203	−	0.348494i
$970$	14.9453	−	12.9706i	0.479863	−	0.416462i
$971$	−2.40683	+	8.98240i	−0.0772388	+	0.288259i	−0.993732	−	0.111792i	$-0.964341\pi$
$971$	−2.40683	+	8.98240i	−0.0772388	+	0.288259i	0.916493	+	0.400051i	$0.131008\pi$
$972$	3.70645	+	30.5931i	0.118884	+	0.981274i
$973$	6.57559	+	4.50191i	0.210804	+	0.144325i
$974$	51.6842	−	25.1567i	1.65607	−	0.806072i
$975$	1.11174	−	0.641863i	0.0356042	−	0.0205561i
$976$	−11.3831	−	20.6923i	−0.364366	−	0.662346i
$977$	−15.8619	+	27.4736i	−0.507466	+	0.878958i	0.492496	+	0.870315i	$0.336085\pi$
$977$	−15.8619	+	27.4736i	−0.507466	+	0.878958i	−0.999963	+	0.00864313i	$0.997249\pi$
$978$	15.6806	+	10.5950i	0.501410	+	0.338792i
$979$	−5.21610	+	5.21610i	−0.166707	+	0.166707i
$980$	6.59713	+	12.3482i	0.210737	+	0.394449i
$981$	17.6721	+	17.6721i	0.564226	+	0.564226i
$982$	28.6811	−	5.55112i	0.915251	−	0.177143i
$983$	−34.7187	−	20.0448i	−1.10735	−	0.639331i	−0.169211	−	0.985580i	$-0.554122\pi$
$983$	−34.7187	−	20.0448i	−1.10735	−	0.639331i	−0.938143	+	0.346249i	$0.887455\pi$
$984$	−21.5892	+	1.07925i	−0.688237	+	0.0344051i
$985$	−7.83070	−	13.5632i	−0.249507	−	0.432159i
$986$	−5.14398	−	1.77584i	−0.163818	−	0.0565543i
$987$	−16.8842	+	24.6615i	−0.537431	+	0.784983i
$988$	6.91194	−	8.81763i	0.219898	−	0.280526i
$989$	7.83934	+	2.10054i	0.249276	+	0.0667934i
$990$	−1.01191	+	14.3057i	−0.0321605	+	0.454665i
$991$	−5.49072	−	3.17007i	−0.174419	−	0.100701i	0.410249	−	0.911973i	$-0.365442\pi$
$991$	−5.49072	−	3.17007i	−0.174419	−	0.100701i	−0.584668	+	0.811273i	$0.698775\pi$
$992$	17.6207	−	47.8137i	0.559457	−	1.51809i
$993$			26.1173i			0.828806i
$994$	−31.3104	−	13.5772i	−0.993107	−	0.430644i
$995$	−11.5373	−	11.5373i	−0.365757	−	0.365757i
$996$	0.125002	−	0.879175i	0.00396083	−	0.0278577i
$997$	0.251144	+	0.937281i	0.00795380	+	0.0296840i	0.969789	−	0.243946i	$-0.0784421\pi$
$997$	0.251144	+	0.937281i	0.00795380	+	0.0296840i	−0.961835	+	0.273630i	$0.911775\pi$
$998$	18.0134	−	15.6334i	0.570204	−	0.494867i
$999$	−10.8302	+	6.25283i	−0.342653	+	0.197831i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cq.a.171.12	yes	256
7.5	odd	6	inner	560.2.cq.a.411.30	yes	256
16.3	odd	4	inner	560.2.cq.a.451.30	yes	256
112.19	even	12	inner	560.2.cq.a.131.12	✓	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cq.a.131.12	✓	256	112.19	even	12	inner
560.2.cq.a.171.12	yes	256	1.1	even	1	trivial
560.2.cq.a.411.30	yes	256	7.5	odd	6	inner
560.2.cq.a.451.30	yes	256	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cq (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.17180 - 0.791760i) q^{2} +(0.282699 + 1.05505i) q^{3} +(0.746231 + 1.85557i) q^{4} +(0.965926 + 0.258819i) q^{5} +(0.504077 - 1.46013i) q^{6} +(2.60058 - 0.486822i) q^{7} +(0.594732 - 2.76519i) q^{8} +(1.56487 - 0.903479i) q^{9} +(-0.926949 - 1.06807i) q^{10} +(-1.45253 - 5.42093i) q^{11} +(-1.74675 + 1.31188i) q^{12} +(-0.831055 - 0.831055i) q^{13} +(-3.43280 - 1.48858i) q^{14} +1.09226i q^{15} +(-2.88628 + 2.76937i) q^{16} +(-2.08371 - 1.20303i) q^{17} +(-2.54906 - 0.180306i) q^{18} +(4.60400 + 1.23364i) q^{19} +(0.240547 + 1.98548i) q^{20} +(1.24880 + 2.60611i) q^{21} +(-2.59000 + 7.50231i) q^{22} +(-1.18177 - 2.04689i) q^{23} +(3.08554 - 0.154247i) q^{24} +(0.866025 + 0.500000i) q^{25} +(0.315834 + 1.63183i) q^{26} +(3.71264 + 3.71264i) q^{27} +(2.84396 + 4.46227i) q^{28} +(-1.13087 + 1.13087i) q^{29} +(0.864812 - 1.27992i) q^{30} +(4.50402 - 7.80119i) q^{31} +(5.57482 - 0.959907i) q^{32} +(5.30871 - 3.06498i) q^{33} +(1.48918 + 3.05951i) q^{34} +(2.63796 + 0.202845i) q^{35} +(2.84422 + 2.22952i) q^{36} +(-0.616460 + 2.30066i) q^{37} +(-4.41822 - 5.09084i) q^{38} +(0.641863 - 1.11174i) q^{39} +(1.29015 - 2.51704i) q^{40} -6.99689 q^{41} +(0.600067 - 4.04259i) q^{42} +(-2.42804 + 2.42804i) q^{43} +(8.97499 - 6.74055i) q^{44} +(1.74539 - 0.467675i) q^{45} +(-0.235845 + 3.33423i) q^{46} +(5.17110 + 8.95662i) q^{47} +(-3.73776 - 2.26226i) q^{48} +(6.52601 - 2.53204i) q^{49} +(-0.618929 - 1.27158i) q^{50} +(0.680192 - 2.53851i) q^{51} +(0.921921 - 2.16224i) q^{52} +(-2.43697 + 0.652983i) q^{53} +(-1.41095 - 7.29000i) q^{54} -5.61216i q^{55} +(0.200491 - 7.48063i) q^{56} +5.20618i q^{57} +(2.22053 - 0.429776i) q^{58} +(8.66890 - 2.32282i) q^{59} +(-2.02677 + 0.815082i) q^{60} +(-1.52811 + 5.70300i) q^{61} +(-11.4545 + 5.57533i) q^{62} +(3.62974 - 3.11138i) q^{63} +(-7.29259 - 3.28910i) q^{64} +(-0.587645 - 1.01783i) q^{65} +(-8.64748 - 0.611675i) q^{66} +(-15.4938 + 4.15156i) q^{67} +(0.677378 - 4.76421i) q^{68} +(1.82548 - 1.82548i) q^{69} +(-2.93056 - 2.32633i) q^{70} +9.12096 q^{71} +(-1.56761 - 4.86450i) q^{72} +(-3.70123 + 6.41071i) q^{73} +(2.54394 - 2.20782i) q^{74} +(-0.282699 + 1.05505i) q^{75} +(1.14655 + 9.46361i) q^{76} +(-6.41646 - 13.3904i) q^{77} +(-1.63237 + 0.794535i) q^{78} +(13.5743 - 7.83715i) q^{79} +(-3.50470 + 1.92798i) q^{80} +(-0.157015 + 0.271957i) q^{81} +(8.19895 + 5.53986i) q^{82} +(-0.287441 + 0.287441i) q^{83} +(-3.90392 + 4.26199i) q^{84} +(-1.70134 - 1.70134i) q^{85} +(4.76760 - 0.922752i) q^{86} +(-1.51282 - 0.873424i) q^{87} +(-15.8538 + 0.792535i) q^{88} +(-0.657205 - 1.13831i) q^{89} +(-2.41553 - 0.833907i) q^{90} +(-2.56580 - 1.75665i) q^{91} +(2.91628 - 3.72032i) q^{92} +(9.50390 + 2.54656i) q^{93} +(1.03199 - 14.5896i) q^{94} +(4.12783 + 2.38320i) q^{95} +(2.58874 + 5.61033i) q^{96} +13.9928i q^{97} +(-9.65194 - 2.19999i) q^{98} +(-7.17073 - 7.17073i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 4 q^{4} - 8 q^{11} - 16 q^{14} - 20 q^{16} + 40 q^{18} + 40 q^{22} + 16 q^{23} - 44 q^{28} + 32 q^{29} + 20 q^{32} - 16 q^{37} - 60 q^{42} - 16 q^{43} - 48 q^{44} - 20 q^{46} - 8 q^{50} + 40 q^{51}+ \cdots - 80 q^{99}+O(q^{100}) \) 256 * q + 4 * q^4 - 8 * q^11 - 16 * q^14 - 20 * q^16 + 40 * q^18 + 40 * q^22 + 16 * q^23 - 44 * q^28 + 32 * q^29 + 20 * q^32 - 16 * q^37 - 60 * q^42 - 16 * q^43 - 48 * q^44 - 20 * q^46 - 8 * q^50 + 40 * q^51 - 72 * q^52 - 16 * q^53 - 84 * q^54 - 96 * q^56 - 8 * q^58 - 48 * q^59 - 28 * q^60 + 40 * q^64 - 192 * q^66 - 40 * q^67 - 60 * q^68 - 16 * q^70 + 64 * q^71 + 36 * q^72 - 60 * q^74 + 48 * q^78 + 128 * q^81 + 164 * q^84 - 52 * q^86 - 20 * q^88 + 32 * q^91 + 128 * q^92 + 72 * q^94 - 204 * q^96 + 160 * q^98 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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