LMFDB - Embedded newform 560.2.cq.a.131.12

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			131.12
Character	$\chi$	$=$	560.131
Dual form			560.2.cq.a.171.12

$q$-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 $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.17180	+	0.791760i	−0.828588	+	0.559859i
$2$	−1.17180	+	0.791760i	−0.828588	+	0.559859i
$3$	0.282699	−	1.05505i	0.163216	−	0.609131i	−0.835045	−	0.550182i	$-0.814558\pi$
$3$	0.282699	−	1.05505i	0.163216	−	0.609131i	0.998261	−	0.0589493i	$-0.0187750\pi$
$4$	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	0.295937	+	0.955207i	$0.404368\pi$
$11$	−1.45253	+	5.42093i	−0.437956	+	1.63447i	−0.733893	+	0.679265i	$0.762299\pi$
$12$	−1.74675	−	1.31188i	−0.504244	−	0.378706i
$13$	−0.831055	+	0.831055i	−0.230493	+	0.230493i	−0.812899	−	0.582405i	$-0.802112\pi$
$13$	−0.831055	+	0.831055i	−0.230493	+	0.230493i	0.582405	+	0.812899i	$0.302112\pi$
$14$	−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	−0.730930	−	0.682452i	$-0.760914\pi$
$17$	−2.08371	+	1.20303i	−0.505375	+	0.291778i	0.225556	+	0.974230i	$0.427580\pi$
$18$	−2.54906	+	0.180306i	−0.600818	+	0.0424986i
$19$	4.60400	−	1.23364i	1.05623	−	0.283016i	0.311405	−	0.950277i	$-0.399200\pi$
$19$	4.60400	−	1.23364i	1.05623	−	0.283016i	0.744824	+	0.667261i	$0.232534\pi$
$20$	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	−0.962529	−	0.271178i	$-0.912587\pi$
$23$	−1.18177	+	2.04689i	−0.246417	+	0.426807i	0.716112	+	0.697985i	$0.245920\pi$
$24$	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	0.594269	−	0.804266i	$-0.297441\pi$
$29$	−1.13087	−	1.13087i	−0.209997	−	0.209997i	−0.804266	+	0.594269i	$0.797441\pi$
$30$	0.864812	+	1.27992i	0.157892	+	0.233680i
$31$	4.50402	+	7.80119i	0.808946	+	1.40114i	0.913595	+	0.406626i	$0.133295\pi$
$31$	4.50402	+	7.80119i	0.808946	+	1.40114i	−0.104649	+	0.994509i	$0.533372\pi$
$32$	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	0.896560	−	0.442923i	$-0.146059\pi$
$37$	−0.616460	−	2.30066i	−0.101345	−	0.378226i	−0.997905	+	0.0646971i	$0.979392\pi$
$38$	−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	0.497304	−	0.867576i	$-0.334323\pi$
$43$	−2.42804	−	2.42804i	−0.370273	−	0.370273i	−0.867576	+	0.497304i	$0.834323\pi$
$44$	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	−0.191447	−	0.981503i	$-0.561318\pi$
$47$	5.17110	−	8.95662i	0.754283	−	1.30646i	0.945730	−	0.324954i	$-0.105349\pi$
$48$	−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	0.0875325	−	0.996162i	$-0.472102\pi$
$53$	−2.43697	−	0.652983i	−0.334743	−	0.0896941i	−0.422275	+	0.906468i	$0.638769\pi$
$54$	−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	0.774357	−	0.632749i	$-0.218074\pi$
$59$	8.66890	+	2.32282i	1.12859	+	0.302406i	0.354238	+	0.935155i	$0.384740\pi$
$60$	−2.02677	−	0.815082i	−0.261655	−	0.105227i
$61$	−1.52811	−	5.70300i	−0.195655	−	0.730194i	−0.992096	−	0.125478i	$-0.959953\pi$
$61$	−1.52811	−	5.70300i	−0.195655	−	0.730194i	0.796441	−	0.604716i	$-0.206713\pi$
$62$	−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	−0.998166	−	0.0605411i	$-0.980717\pi$
$67$	−15.4938	−	4.15156i	−1.89287	−	0.507194i	−0.894707	−	0.446653i	$-0.852616\pi$
$68$	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	0.563951	−	0.825808i	$-0.309281\pi$
$73$	−3.70123	−	6.41071i	−0.433196	−	0.750317i	−0.997146	+	0.0754914i	$0.975947\pi$
$74$	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	0.999477	+	0.0323524i	$0.0102999\pi$
$79$	13.5743	+	7.83715i	1.52723	+	0.881748i	0.527756	+	0.849396i	$0.323033\pi$
$80$	−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	0.691155	−	0.722706i	$-0.257102\pi$
$83$	−0.287441	−	0.287441i	−0.0315507	−	0.0315507i	−0.722706	+	0.691155i	$0.757102\pi$
$84$	−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	−0.898753	−	0.438455i	$-0.855526\pi$
$89$	−0.657205	+	1.13831i	−0.0696636	+	0.120661i	0.829090	+	0.559116i	$0.188859\pi$
$90$	−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	$-0.748524\pi$
$97$		−	13.9928i		−	1.42076i	0.703820	−	0.710378i	$-0.251476\pi$
$98$	−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	−0.946572	−	0.322491i	$-0.895480\pi$
$101$	0.346007	−	1.29132i	0.0344290	−	0.128491i	0.981001	+	0.194001i	$0.0621464\pi$
$102$	−2.80694	−	2.43608i	−0.277928	−	0.241208i
$103$	5.45584	+	3.14993i	0.537580	+	0.310372i	0.744098	−	0.668071i	$-0.232880\pi$
$103$	5.45584	+	3.14993i	0.537580	+	0.310372i	−0.206517	+	0.978443i	$0.566213\pi$
$104$	−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	−0.540286	−	0.841481i	$-0.681684\pi$
$107$	−6.07660	+	1.62822i	−0.587448	+	0.157406i	−0.0471612	+	0.998887i	$0.515017\pi$
$108$	−4.11858	−	9.65956i	−0.396310	−	0.929491i
$109$	3.57974	−	13.3598i	0.342877	−	1.27963i	−0.552197	−	0.833714i	$-0.686210\pi$
$109$	3.57974	−	13.3598i	0.342877	−	1.27963i	0.895073	−	0.445919i	$-0.147123\pi$
$110$	−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	$-0.975994\pi$
$127$		−	1.69822i		−	0.150692i	0.997157	−	0.0753462i	$-0.0240062\pi$
$128$	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	−0.704571	−	0.709633i	$-0.748861\pi$
$131$	−10.9869	+	2.94394i	−0.959931	+	0.257213i	−0.255360	+	0.966846i	$0.582194\pi$
$132$	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	−0.869525	−	0.493889i	$-0.835575\pi$
$137$	−10.2600	+	5.92359i	−0.876568	+	0.506087i	−0.00704259	+	0.999975i	$0.502242\pi$
$138$	−3.58445	−	0.693756i	−0.305128	−	0.0590564i
$139$	2.12982	−	2.12982i	0.180649	−	0.180649i	−0.610990	−	0.791638i	$-0.709228\pi$
$139$	2.12982	−	2.12982i	0.180649	−	0.180649i	0.791638	+	0.610990i	$0.209228\pi$
$140$	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	−0.559611	−	0.828756i	$-0.689049\pi$
$149$	−5.97330	−	22.2926i	−0.489351	−	1.82628i	0.0702593	−	0.997529i	$-0.477617\pi$
$150$	1.16661	+	1.01247i	0.0952534	+	0.0826682i
$151$	−10.5722	−	18.3115i	−0.860351	−	1.49017i	−0.871590	−	0.490235i	$-0.836911\pi$
$151$	−10.5722	−	18.3115i	−0.860351	−	1.49017i	0.0112395	−	0.999937i	$-0.496422\pi$
$152$	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	0.270359	−	0.962759i	$-0.412857\pi$
$157$	0.289664	+	0.0776151i	0.0231177	+	0.00619436i	−0.247242	+	0.968954i	$0.579524\pi$
$158$	−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	−0.971664	−	0.236366i	$-0.924044\pi$
$163$	−3.17086	−	11.8338i	−0.248361	−	0.926896i	0.723303	−	0.690531i	$-0.242623\pi$
$164$	−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	$0.300960\pi$
$167$			20.9553i			1.62157i	−0.585343	+	0.810786i	$0.699040\pi$
$168$	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	−0.992460	−	0.122572i	$-0.960886\pi$
$173$	−2.55497	−	9.53526i	−0.194250	−	0.724952i	0.798209	−	0.602380i	$-0.205781\pi$
$174$	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	−0.334873	−	0.942263i	$-0.608693\pi$
$179$	−14.6637	−	3.92912i	−1.09601	−	0.293676i	−0.761140	+	0.648587i	$0.775360\pi$
$180$	2.17027	−	2.88969i	0.161762	−	0.215385i
$181$	2.75846	+	2.75846i	0.205034	+	0.205034i	0.802153	−	0.597119i	$-0.203688\pi$
$181$	2.75846	+	2.75846i	0.205034	+	0.205034i	−0.597119	+	0.802153i	$0.703688\pi$
$182$	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	0.889002	−	0.457903i	$-0.151399\pi$
$191$	12.9489	+	7.47603i	0.936947	+	0.540947i	0.0479449	+	0.998850i	$0.484733\pi$
$192$	1.40855	+	8.62384i	0.101653	+	0.622372i
$193$	2.86835	+	4.96813i	0.206468	+	0.357614i	0.950600	−	0.310420i	$-0.100470\pi$
$193$	2.86835	+	4.96813i	0.206468	+	0.357614i	−0.744131	+	0.668033i	$0.767136\pi$
$194$	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	−0.981332	−	0.192322i	$-0.938398\pi$
$197$	−11.0743	+	11.0743i	−0.789010	+	0.789010i	0.192322	+	0.981332i	$0.438398\pi$
$198$	2.72516	−	14.0802i	0.193669	−	1.00063i
$199$	−14.1302	+	8.15810i	−1.00167	+	0.578312i	−0.908741	−	0.417361i	$-0.862955\pi$
$199$	−14.1302	+	8.15810i	−1.00167	+	0.578312i	−0.0929255	+	0.995673i	$0.529622\pi$
$200$	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	−0.967914	−	0.251282i	$-0.919148\pi$
$211$	−10.4097	+	10.4097i	−0.716632	+	0.716632i	0.251282	+	0.967914i	$0.419148\pi$
$212$	−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	0.739191	+	0.673495i	$0.235208\pi$
$227$	−3.58153	+	13.3665i	−0.237715	+	0.887164i	−0.976906	+	0.213668i	$0.931459\pi$
$228$	−9.66043	−	3.88501i	−0.639777	−	0.257291i
$229$	−5.76272	+	1.54412i	−0.380812	+	0.102038i	−0.444146	−	0.895954i	$-0.646493\pi$
$229$	−5.76272	+	1.54412i	−0.380812	+	0.102038i	0.0633350	+	0.997992i	$0.479826\pi$
$230$	−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	−0.0816490	−	0.996661i	$-0.526019\pi$
$233$	−15.0446	−	8.68603i	−0.985607	−	0.569041i	−0.903958	+	0.427620i	$0.859352\pi$
$234$	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	$-0.915167\pi$
$239$		−	8.14315i		−	0.526737i	0.964695	−	0.263368i	$-0.0848335\pi$
$240$	−3.02488	+	3.15258i	−0.195255	+	0.203498i
$241$	−14.8958	+	8.60009i	−0.959523	+	0.553981i	−0.896026	−	0.444001i	$-0.853559\pi$
$241$	−14.8958	+	8.60009i	−0.959523	+	0.553981i	−0.0634966	+	0.997982i	$0.520225\pi$
$242$	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	−0.810423	−	0.585846i	$-0.800762\pi$
$251$	−3.55797	+	3.55797i	−0.224577	+	0.224577i	0.585846	+	0.810423i	$0.300762\pi$
$252$	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	0.804986	−	0.593294i	$-0.202173\pi$
$257$	11.1204	+	6.42036i	0.693671	+	0.400491i	−0.111315	+	0.993785i	$0.535506\pi$
$258$	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	0.894248	−	0.447573i	$-0.147711\pi$
$263$	0.965165	+	1.67172i	0.0595147	+	0.103082i	−0.834733	+	0.550655i	$0.814378\pi$
$264$	−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	0.644818	−	0.764336i	$-0.276933\pi$
$269$	13.4667	+	3.60839i	0.821079	+	0.220007i	0.176261	+	0.984344i	$0.443600\pi$
$270$	0.523915	+	7.40678i	0.0318845	+	0.450762i
$271$	−7.00278	+	12.1292i	−0.425389	+	0.736795i	−0.996457	−	0.0841077i	$-0.973196\pi$
$271$	−7.00278	+	12.1292i	−0.425389	+	0.736795i	0.571068	+	0.820903i	$0.306529\pi$
$272$	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	0.0694303	−	0.997587i	$-0.477882\pi$
$277$	−6.14529	−	1.64663i	−0.369235	−	0.0989362i	−0.438665	+	0.898651i	$0.644549\pi$
$278$	−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	$-0.820557\pi$
$281$		−	17.9147i		−	1.06870i	0.845264	−	0.534349i	$-0.179443\pi$
$282$	15.6845	+	3.03568i	0.933998	+	0.180772i
$283$	−11.5666	−	3.09927i	−0.687565	−	0.184233i	−0.101911	−	0.994794i	$-0.532496\pi$
$283$	−11.5666	−	3.09927i	−0.687565	−	0.184233i	−0.585654	+	0.810561i	$0.699162\pi$
$284$	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	0.699648	−	0.714488i	$-0.253340\pi$
$293$	−0.254030	−	0.254030i	−0.0148406	−	0.0148406i	−0.714488	+	0.699648i	$0.753340\pi$
$294$	−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	0.906780	−	0.421605i	$-0.138533\pi$
$307$	8.50094	+	8.50094i	0.485174	+	0.485174i	−0.421605	+	0.906780i	$0.638533\pi$
$308$	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	−0.476596	−	0.879122i	$-0.658130\pi$
$311$	0.819111	−	0.472914i	0.0464476	−	0.0268165i	0.523044	+	0.852306i	$0.324796\pi$
$312$	−2.69244	+	2.43606i	−0.152429	+	0.137915i
$313$	10.6372	−	18.4241i	0.601247	−	1.04139i	−0.391385	−	0.920227i	$-0.628004\pi$
$313$	10.6372	−	18.4241i	0.601247	−	1.04139i	0.992633	−	0.121164i	$-0.0386627\pi$
$314$	−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	0.194914	−	0.980820i	$-0.437557\pi$
$317$	15.2072	−	4.07477i	0.854124	−	0.228862i	0.659210	+	0.751959i	$0.270891\pi$
$318$	−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	0.439655	−	0.898167i	$-0.355101\pi$
$331$	23.0964	−	6.18865i	1.26949	−	0.340159i	0.829836	+	0.558008i	$0.188434\pi$
$332$	−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	−0.832826	−	0.553535i	$-0.813279\pi$
$347$	3.07715	−	11.4841i	0.165190	−	0.616497i	0.998016	−	0.0629623i	$-0.0200548\pi$
$348$	0.491790	+	3.45891i	0.0263627	+	0.185417i
$349$	−2.92259	+	2.92259i	−0.156442	+	0.156442i	−0.780988	−	0.624546i	$-0.785284\pi$
$349$	−2.92259	+	2.92259i	−0.156442	+	0.156442i	0.624546	+	0.780988i	$0.285284\pi$
$350$	−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	−0.770285	−	0.637700i	$-0.779886\pi$
$353$	−11.3324	+	6.54278i	−0.603164	+	0.348237i	0.167121	+	0.985936i	$0.446553\pi$
$354$	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	−0.679264	−	0.733894i	$-0.737701\pi$
$359$	5.60724	−	9.71202i	0.295939	−	0.512581i	0.975203	+	0.221313i	$0.0710342\pi$
$360$	−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	−0.976685	−	0.214678i	$-0.931130\pi$
$367$	−12.9169	−	22.3728i	−0.674259	−	1.16785i	0.302426	−	0.953173i	$-0.402204\pi$
$368$	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	0.903664	+	0.428242i	$0.140867\pi$
$373$	6.47358	+	24.1597i	0.335189	+	1.25094i	−0.568475	+	0.822701i	$0.692466\pi$
$374$	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	−0.998619	−	0.0525306i	$-0.983271\pi$
$379$	−20.4637	−	20.4637i	−1.05115	−	1.05115i	−0.0525306	−	0.998619i	$-0.516729\pi$
$380$	−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	0.0495970	−	0.998769i	$-0.484206\pi$
$383$	17.4129	−	30.1600i	0.889758	−	1.54111i	0.840161	−	0.542337i	$-0.182460\pi$
$384$	−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	0.704367	−	0.709836i	$-0.251231\pi$
$389$	18.9233	+	5.07048i	0.959449	+	0.257084i	0.255082	+	0.966919i	$0.417898\pi$
$390$	−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	0.938127	+	0.346290i	$0.112559\pi$
$397$	5.95415	+	22.2212i	0.298830	+	1.11525i	−0.639297	+	0.768960i	$0.720775\pi$
$398$	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	−0.542778	−	0.839876i	$-0.682627\pi$
$401$	9.13070	−	15.8148i	0.455966	−	0.789755i	0.998743	+	0.0501210i	$0.0159607\pi$
$402$	−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	0.987137	+	0.159879i	$0.0511105\pi$
$409$	12.7820	+	22.1390i	0.632028	+	1.09470i	−0.355109	+	0.934825i	$0.615556\pi$
$410$	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	−0.978129	−	0.207999i	$-0.933305\pi$
$419$	−24.2794	−	24.2794i	−1.18613	−	1.18613i	−0.207999	−	0.978129i	$-0.566695\pi$
$420$	−4.87398	−	3.10636i	−0.237826	−	0.151575i
$421$	6.95860	−	6.95860i	0.339142	−	0.339142i	−0.516903	−	0.856044i	$-0.672915\pi$
$421$	6.95860	−	6.95860i	0.339142	−	0.339142i	0.856044	+	0.516903i	$0.172915\pi$
$422$	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	−0.804368	−	0.594132i	$-0.797496\pi$
$431$	−14.3667	+	8.29461i	−0.692019	+	0.399537i	0.112349	+	0.993669i	$0.464162\pi$
$432$	−20.9974	+	0.434042i	−1.01024	+	0.0208828i
$433$			27.4467i			1.31900i	0.751703	+	0.659502i	$0.229233\pi$
$433$			27.4467i			1.31900i	−0.751703	+	0.659502i	$0.770767\pi$
$434$	−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	0.896812	−	0.442411i	$-0.145877\pi$
$439$	20.1578	+	11.6381i	0.962080	+	0.555457i	0.0652671	+	0.997868i	$0.479210\pi$
$440$	−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	0.211344	−	0.977412i	$-0.432216\pi$
$443$	18.5867	−	4.98028i	0.883079	−	0.236620i	0.671735	+	0.740791i	$0.265549\pi$
$444$	−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	−0.356920	−	0.934135i	$-0.616173\pi$
$457$	−28.7392	−	16.5926i	−1.34436	−	0.776169i	−0.987445	+	0.157966i	$0.949506\pi$
$458$	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	−0.489680	−	0.871902i	$-0.662887\pi$
$461$	8.20665	−	8.20665i	0.382222	−	0.382222i	0.871902	+	0.489680i	$0.162887\pi$
$462$	−22.7862	−	2.61907i	−1.06011	−	0.121850i
$463$			30.1052i			1.39911i	0.714579	+	0.699555i	$0.246618\pi$
$463$			30.1052i			1.39911i	−0.714579	+	0.699555i	$0.753382\pi$
$464$	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	0.553871	−	0.832602i	$-0.313150\pi$
$467$	31.3313	−	8.39519i	1.44984	−	0.388483i	0.895968	+	0.444119i	$0.146483\pi$
$468$	−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	−0.991199	−	0.132381i	$-0.957738\pi$
$479$	−13.3559	−	23.1330i	−0.610245	−	1.05698i	0.380954	−	0.924594i	$-0.375596\pi$
$480$	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	−0.798008	−	0.602648i	$-0.794113\pi$
$487$	−20.3228	−	35.2000i	−0.920912	−	1.59507i	−0.122904	−	0.992419i	$-0.539221\pi$
$488$	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	0.295998	−	0.955189i	$-0.404348\pi$
$491$	−14.6067	−	14.6067i	−0.659190	−	0.659190i	−0.955189	+	0.295998i	$0.904348\pi$
$492$	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	−0.992161	−	0.124969i	$-0.960117\pi$
$499$	−4.36510	−	16.2908i	−0.195409	−	0.729275i	0.796752	−	0.604306i	$-0.206550\pi$
$500$	−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	$0.000634307\pi$
$503$			0.0893847i			0.00398547i	−0.999998	+	0.00199273i	$0.999366\pi$
$504$	−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	0.995437	+	0.0954234i	$0.0304205\pi$
$509$	4.08524	+	15.2463i	0.181075	+	0.675781i	−0.814362	+	0.580357i	$0.802913\pi$
$510$	−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	−0.993821	−	0.110999i	$-0.964595\pi$
$521$	−13.5363	−	23.4456i	−0.593038	−	1.02717i	0.400782	−	0.916173i	$-0.368738\pi$
$522$	3.08655	+	2.67875i	0.135095	+	0.117246i
$523$	−1.63096	−	6.08681i	−0.0713168	−	0.266158i	0.921056	−	0.389430i	$-0.127328\pi$
$523$	−1.63096	−	6.08681i	−0.0713168	−	0.266158i	−0.992373	+	0.123272i	$0.960661\pi$
$524$	−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	−0.219613	−	0.975587i	$-0.570479\pi$
$541$	1.81400	−	0.486060i	0.0779901	−	0.0208974i	0.297603	+	0.954690i	$0.403813\pi$
$542$	−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	−0.619362	−	0.785106i	$-0.712609\pi$
$547$	3.87642	−	3.87642i	0.165744	−	0.165744i	0.785106	+	0.619362i	$0.212609\pi$
$548$	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	−0.991951	−	0.126624i	$-0.959586\pi$
$557$	−1.64225	+	6.12895i	−0.0695842	+	0.259692i	0.922367	+	0.386316i	$0.126253\pi$
$558$	−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	−0.891025	−	0.453954i	$-0.850013\pi$
$563$	2.55315	−	9.52847i	0.107602	−	0.401577i	0.998627	+	0.0523768i	$0.0166797\pi$
$564$	−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	0.601696	−	0.798725i	$-0.294492\pi$
$569$	5.02901	+	2.90350i	0.210827	+	0.121721i	−0.390869	+	0.920447i	$0.627825\pi$
$570$	5.56054	+	4.82586i	0.232905	+	0.202133i
$571$	−11.9120	+	44.4562i	−0.498502	+	1.86043i	0.0109578	+	0.999940i	$0.496512\pi$
$571$	−11.9120	+	44.4562i	−0.498502	+	1.86043i	−0.509460	+	0.860494i	$0.670155\pi$
$572$	−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	−0.437178	−	0.899375i	$-0.644022\pi$
$577$	2.95732	−	1.70741i	0.123115	−	0.0710803i	0.560293	+	0.828295i	$0.310689\pi$
$578$	−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	−0.973339	−	0.229373i	$-0.926332\pi$
$587$	−18.0249	+	18.0249i	−0.743965	+	0.743965i	0.229373	+	0.973339i	$0.426332\pi$
$588$	−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	0.477647	−	0.878552i	$-0.341490\pi$
$593$	−1.08068	−	0.623933i	−0.0443783	−	0.0256218i	−0.522025	+	0.852930i	$0.674823\pi$
$594$	−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	0.808554	−	0.588422i	$-0.200251\pi$
$599$	−2.57744	−	4.46426i	−0.105311	−	0.182405i	−0.913865	+	0.406017i	$0.866917\pi$
$600$	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	−0.939561	−	0.342382i	$-0.888766\pi$
$607$	−4.26889	+	7.39393i	−0.173269	+	0.300110i	0.766292	+	0.642493i	$0.222100\pi$
$608$	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	0.927707	−	0.373310i	$-0.121777\pi$
$613$	38.2393	+	10.2462i	1.54447	+	0.413839i	0.616763	+	0.787149i	$0.288444\pi$
$614$	−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	$0.0346824\pi$
$617$			5.40222i			0.217485i	−0.994070	+	0.108743i	$0.965318\pi$
$618$	−1.84915	+	9.55407i	−0.0743839	+	0.384321i
$619$	37.7735	+	10.1214i	1.51825	+	0.406813i	0.919164	−	0.393875i	$-0.128866\pi$
$619$	37.7735	+	10.1214i	1.51825	+	0.406813i	0.599082	+	0.800688i	$0.295532\pi$
$620$	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	−0.878743	−	0.477295i	$-0.841617\pi$
$641$	−21.5892	−	37.3935i	−0.852721	−	1.47696i	0.0260219	−	0.999661i	$-0.491716\pi$
$642$	−5.44050	−	8.05191i	−0.214719	−	0.317783i
$643$	−3.65839	−	3.65839i	−0.144273	−	0.144273i	0.631281	−	0.775554i	$-0.282529\pi$
$643$	−3.65839	−	3.65839i	−0.144273	−	0.144273i	−0.775554	+	0.631281i	$0.782529\pi$
$644$	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	−0.901876	−	0.431994i	$-0.857810\pi$
$647$	−24.8943	+	14.3727i	−0.978697	+	0.565051i	−0.0768202	+	0.997045i	$0.524477\pi$
$648$	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	−0.679908	−	0.733297i	$-0.737980\pi$
$653$	−23.0516	+	6.17664i	−0.902077	+	0.241711i	−0.222169	+	0.975008i	$0.571314\pi$
$654$	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	−0.641130	−	0.767433i	$-0.721534\pi$
$659$	3.24232	−	3.24232i	0.126303	−	0.126303i	0.767433	+	0.641130i	$0.221534\pi$
$660$	7.36246	−	9.80307i	0.286583	−	0.381584i
$661$	9.91238	−	36.9935i	0.385547	−	1.43888i	−0.451756	−	0.892141i	$-0.649202\pi$
$661$	9.91238	−	36.9935i	0.385547	−	1.43888i	0.837303	−	0.546739i	$-0.184131\pi$
$662$	−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	−0.0206131	−	0.999788i	$-0.506562\pi$
$677$	12.0060	−	3.21701i	0.461429	−	0.123640i	0.482042	+	0.876148i	$0.339895\pi$
$678$	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	0.427761	+	0.903892i	$0.359303\pi$
$683$	−10.3135	+	38.4907i	−0.394637	+	1.47281i	−0.822398	+	0.568913i	$0.807364\pi$
$684$	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	−0.742284	−	0.670085i	$-0.766258\pi$
$691$	−27.6033	+	7.39628i	−1.05008	+	0.281368i	−0.307794	+	0.951453i	$0.599591\pi$
$692$	−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	−1.00000		0.000661237i	$-0.999790\pi$
$701$	−26.4939	−	26.4939i	−1.00066	−	1.00066i	−0.000661237	−	1.00000i	$-0.500210\pi$
$702$	−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	−0.837485	−	0.546460i	$-0.815975\pi$
$709$	−10.2629	−	38.3017i	−0.385432	−	1.43845i	0.452053	−	0.891991i	$-0.350692\pi$
$710$	−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	−0.561701	−	0.827340i	$-0.689853\pi$
$719$	11.6815	−	20.2330i	0.435647	−	0.754562i	0.997348	+	0.0727776i	$0.0231863\pi$
$720$	−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	$-0.935576\pi$
$727$		−	10.8399i		−	0.402028i	0.979588	−	0.201014i	$-0.0644237\pi$
$728$	−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	0.798573	+	0.601898i	$0.205589\pi$
$733$	11.0445	+	41.2186i	0.407937	+	1.52244i	−0.390636	+	0.920545i	$0.627745\pi$
$734$	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	0.744759	−	0.667333i	$-0.232564\pi$
$739$	28.7089	+	7.69252i	1.05607	+	0.282974i	0.311314	+	0.950307i	$0.399231\pi$
$740$	−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	0.982281	−	0.187416i	$-0.0600114\pi$
$751$	35.9303	+	20.7443i	1.31111	+	0.756972i	0.328833	+	0.944388i	$0.393345\pi$
$752$	−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	−0.544025	−	0.839069i	$-0.683100\pi$
$757$	8.11771	−	8.11771i	0.295043	−	0.295043i	0.839069	+	0.544025i	$0.183100\pi$
$758$	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	−0.395077	−	0.918648i	$-0.629282\pi$
$761$	16.4975	−	28.5745i	0.598034	−	1.03583i	0.993111	−	0.117178i	$-0.0373847\pi$
$762$	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	$0.0613427\pi$
$769$			10.6222i			0.383046i	−0.981488	+	0.191523i	$0.938657\pi$
$770$	−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	−0.500081	−	0.865979i	$-0.666696\pi$
$773$	10.1756	−	37.9759i	0.365991	−	1.36590i	0.866072	−	0.499919i	$-0.166637\pi$
$774$	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	0.352262	+	0.935902i	$0.385413\pi$
$787$	−11.8037	+	44.0520i	−0.420757	+	1.57029i	−0.773018	+	0.634384i	$0.781254\pi$
$788$	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	−0.904201	−	0.427107i	$-0.859533\pi$
$797$	−13.4689	+	13.4689i	−0.477094	+	0.477094i	0.427107	+	0.904201i	$0.359533\pi$
$798$	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	−0.494102	−	0.869404i	$-0.664503\pi$
$809$	0.334837	−	0.193318i	0.0117722	−	0.00679670i	0.505875	+	0.862607i	$0.331170\pi$
$810$	0.436013	+	0.0843887i	0.0153199	+	0.00296512i
$811$	33.2147	−	33.2147i	1.16633	−	1.16633i	0.183261	−	0.983064i	$-0.441335\pi$
$811$	33.2147	−	33.2147i	1.16633	−	1.16633i	0.983064	−	0.183261i	$-0.0586654\pi$
$812$	−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	0.889175	+	0.457567i	$0.151279\pi$
$821$	9.96871	+	37.2037i	0.347910	+	1.29842i	−0.541265	+	0.840852i	$0.682054\pi$
$822$	−13.8211	−	11.9950i	−0.482065	−	0.418373i
$823$	−5.03157	−	8.71493i	−0.175389	−	0.303784i	0.764907	−	0.644141i	$-0.222785\pi$
$823$	−5.03157	−	8.71493i	−0.175389	−	0.303784i	−0.940296	+	0.340358i	$0.889452\pi$
$824$	−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	0.406207	−	0.913781i	$-0.366851\pi$
$827$	−14.5966	−	14.5966i	−0.507575	−	0.507575i	−0.913781	+	0.406207i	$0.866851\pi$
$828$	1.20237	+	8.45662i	0.0417851	+	0.293888i
$829$	26.6457	+	7.13970i	0.925444	+	0.247972i	0.689911	−	0.723894i	$-0.257650\pi$
$829$	26.6457	+	7.13970i	0.925444	+	0.247972i	0.235533	+	0.971866i	$0.424316\pi$
$830$	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	$-0.949290\pi$
$839$		−	9.19001i		−	0.317274i	0.987337	−	0.158637i	$-0.0507100\pi$
$840$	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	0.333401	−	0.942785i	$-0.391804\pi$
$853$	−17.7978	−	17.7978i	−0.609385	−	0.609385i	−0.942785	+	0.333401i	$0.891804\pi$
$854$	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	−0.996106	−	0.0881693i	$-0.971898\pi$
$857$	−16.8156	−	29.1255i	−0.574410	−	0.994907i	0.421696	−	0.906737i	$-0.361435\pi$
$858$	6.67819	−	7.69486i	0.227990	−	0.262698i
$859$	−11.9682	−	44.6659i	−0.408349	−	1.52398i	−0.797794	−	0.602931i	$-0.794000\pi$
$859$	−11.9682	−	44.6659i	−0.408349	−	1.52398i	0.389444	−	0.921050i	$-0.372667\pi$
$860$	−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	0.594497	−	0.804097i	$-0.297351\pi$
$863$	5.73957	+	3.31374i	0.195377	+	0.112801i	−0.399120	+	0.916899i	$0.630684\pi$
$864$	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	−0.737786	−	0.675034i	$-0.764129\pi$
$877$	−30.7754	+	8.24624i	−1.03921	+	0.278456i	−0.301425	+	0.953490i	$0.597462\pi$
$878$	−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	$0.208017\pi$
$881$			36.0913i			1.21595i	−0.793957	+	0.607973i	$0.791983\pi$
$882$	−17.0917	−	5.27762i	−0.575507	−	0.177707i
$883$	−26.9446	+	26.9446i	−0.906757	+	0.906757i	−0.996009	−	0.0892517i	$-0.971552\pi$
$883$	−26.9446	+	26.9446i	−0.906757	+	0.906757i	0.0892517	+	0.996009i	$0.471552\pi$
$884$	−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	0.916172	−	0.400786i	$-0.131263\pi$
$887$	30.5917	+	17.6621i	1.02717	+	0.593035i	0.110995	+	0.993821i	$0.464596\pi$
$888$	−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	−0.756445	−	0.654058i	$-0.773065\pi$
$907$	6.79681	−	25.3661i	0.225684	−	0.842266i	0.982129	−	0.188208i	$-0.0602680\pi$
$908$	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	$0.152234\pi$
$911$			27.7822i			0.920465i	−0.887799	+	0.460232i	$0.847766\pi$
$912$	−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	−0.921910	−	0.387404i	$-0.873372\pi$
$919$	−3.80310	+	6.58717i	−0.125453	+	0.217291i	0.796457	+	0.604695i	$0.206705\pi$
$920$	−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	0.548929	−	0.835869i	$-0.315036\pi$
$929$	3.03299	+	1.75110i	0.0995092	+	0.0574516i	−0.449420	+	0.893321i	$0.648369\pi$
$930$	−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	−0.503576	−	0.863951i	$-0.667983\pi$
$941$	−42.0767	−	11.2744i	−1.37166	−	0.367535i	−0.868085	+	0.496415i	$0.834649\pi$
$942$	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	0.936481	+	0.350719i	$0.114063\pi$
$947$	9.25737	+	34.5490i	0.300824	+	1.12269i	−0.635656	+	0.771972i	$0.719270\pi$
$948$	−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	$0.118787\pi$
$953$			22.5096i			0.729157i	−0.931173	+	0.364578i	$0.881213\pi$
$954$	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	0.916493	−	0.400051i	$-0.131008\pi$
$971$	−2.40683	−	8.98240i	−0.0772388	−	0.288259i	−0.993732	+	0.111792i	$0.964341\pi$
$972$	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	−0.999963	−	0.00864313i	$-0.997249\pi$
$977$	−15.8619	−	27.4736i	−0.507466	−	0.878958i	0.492496	−	0.870315i	$-0.336085\pi$
$978$	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	−0.938143	−	0.346249i	$-0.887455\pi$
$983$	−34.7187	+	20.0448i	−1.10735	+	0.639331i	−0.169211	+	0.985580i	$0.554122\pi$
$984$	−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	−0.584668	−	0.811273i	$-0.698775\pi$
$991$	−5.49072	+	3.17007i	−0.174419	+	0.100701i	0.410249	+	0.911973i	$0.365442\pi$
$992$	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	−0.961835	−	0.273630i	$-0.911775\pi$
$997$	0.251144	−	0.937281i	0.00795380	−	0.0296840i	0.969789	+	0.243946i	$0.0784421\pi$
$998$	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.131.12	✓	256
7.3	odd	6	inner	560.2.cq.a.451.30	yes	256
16.11	odd	4	inner	560.2.cq.a.411.30	yes	256
112.59	even	12	inner	560.2.cq.a.171.12	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cq.a.131.12	✓	256	1.1	even	1	trivial
560.2.cq.a.171.12	yes	256	112.59	even	12	inner
560.2.cq.a.411.30	yes	256	16.11	odd	4	inner
560.2.cq.a.451.30	yes	256	7.3	odd	6	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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