LMFDB - Embedded newform 630.2.bt.a.317.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(317,630)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 3, 4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("630.317");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bt (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.22
Character	$\chi$	$=$	630.317
Dual form			630.2.bt.a.473.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(1.59237 - 0.681437i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.93677 - 1.11755i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(1.44802 + 2.21433i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07129 - 2.17020i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(1.59237 - 0.681437i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.93677 - 1.11755i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(1.44802 + 2.21433i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07129 - 2.17020i) q^{9} +(-2.16002 + 0.578198i) q^{10} -5.61811i q^{11} +(1.71975 + 0.206043i) q^{12} +(-5.23268 - 1.40209i) q^{13} +(-0.825566 - 2.51365i) q^{14} +(2.32252 - 3.09934i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.42422 + 0.917516i) q^{17} +(-2.56240 + 1.56016i) q^{18} +(-2.96649 - 1.71270i) q^{19} +(2.23607 + 0.000558109i) q^{20} +(3.81470 + 2.53930i) q^{21} +(-1.45407 + 5.42668i) q^{22} +(4.84782 + 4.84782i) q^{23} +(-1.60782 - 0.644127i) q^{24} +(2.50216 - 4.32888i) q^{25} +(4.69149 + 2.70864i) q^{26} +(1.81940 - 4.86721i) q^{27} +(0.146855 + 2.64167i) q^{28} +(-3.11239 + 5.39082i) q^{29} +(-3.04555 + 2.39262i) q^{30} +(-2.92080 + 5.05898i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.82839 - 8.94612i) q^{33} +(-3.07007 - 1.77250i) q^{34} +(5.27910 + 2.67041i) q^{35} +(2.87889 - 0.843805i) q^{36} +(6.67262 - 1.78792i) q^{37} +(2.42213 + 2.42213i) q^{38} +(-9.28781 + 1.33309i) q^{39} +(-2.15973 - 0.579276i) q^{40} +(-0.460590 + 0.265922i) q^{41} +(-3.02750 - 3.44009i) q^{42} +(-1.05122 - 3.92322i) q^{43} +(2.80906 - 4.86543i) q^{44} +(1.58630 - 6.51795i) q^{45} +(-3.42793 - 5.93734i) q^{46} +(0.112364 + 0.0301078i) q^{47} +(1.38633 + 1.03831i) q^{48} +(-2.80650 + 6.41277i) q^{49} +(-3.53730 + 3.53377i) q^{50} +(6.07785 - 0.872363i) q^{51} +(-3.83059 - 3.83059i) q^{52} +(-0.378116 + 1.41115i) q^{53} +(-3.01713 + 4.23047i) q^{54} +(-6.27853 - 10.8810i) q^{55} +(0.541864 - 2.58967i) q^{56} +(-5.89085 - 0.705782i) q^{57} +(4.40159 - 4.40159i) q^{58} +(-1.40284 + 2.42978i) q^{59} +(3.56103 - 1.52285i) q^{60} +(4.53736 + 7.85893i) q^{61} +(4.13064 - 4.13064i) q^{62} +(7.80479 + 1.44402i) q^{63} +1.00000i q^{64} +(-11.7014 + 3.13225i) q^{65} +(1.38252 + 9.63215i) q^{66} +(-2.47728 + 0.663784i) q^{67} +(2.50670 + 2.50670i) q^{68} +(11.0230 + 4.41604i) q^{69} +(-4.40806 - 3.94575i) q^{70} -9.18544i q^{71} +(-2.99918 + 0.0699423i) q^{72} +(5.01109 + 1.34272i) q^{73} -6.90801 q^{74} +(1.03451 - 8.59824i) q^{75} +(-1.71270 - 2.96649i) q^{76} +(12.4403 - 8.13512i) q^{77} +(9.31636 + 1.11619i) q^{78} +(-13.3443 + 7.70434i) q^{79} +(1.93621 + 1.11852i) q^{80} +(-0.419540 - 8.99022i) q^{81} +(0.513722 - 0.137651i) q^{82} +(14.0608 - 3.76758i) q^{83} +(2.03398 + 4.10645i) q^{84} +(7.65729 - 2.04972i) q^{85} +4.06161i q^{86} +(-1.28258 + 10.7051i) q^{87} +(-3.97261 + 3.97261i) q^{88} +(2.54650 - 4.41067i) q^{89} +(-3.21922 + 5.88529i) q^{90} +(-4.47232 - 13.6171i) q^{91} +(1.77443 + 6.62225i) q^{92} +(-1.20362 + 10.0461i) q^{93} +(-0.100743 - 0.0581638i) q^{94} +(-7.65944 - 0.00191175i) q^{95} +(-1.07035 - 1.36174i) q^{96} +(-1.96921 + 0.527648i) q^{97} +(4.37061 - 5.46788i) q^{98} +(-12.1924 - 11.6367i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	1.59237	−	0.681437i	0.919355	−	0.393428i
$3$	1.59237	−	0.681437i	0.919355	−	0.393428i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	1.93677	−	1.11755i	0.866150	−	0.499784i
$5$	1.93677	−	1.11755i	0.866150	−	0.499784i
$6$	−1.71448	+	0.246082i	−0.699934	+	0.100463i
$7$	1.44802	+	2.21433i	0.547299	+	0.836937i
$7$	1.44802	+	2.21433i	0.547299	+	0.836937i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.07129	−	2.17020i	0.690429	−	0.723400i
$10$	−2.16002	+	0.578198i	−0.683058	+	0.182842i
$11$		−	5.61811i		−	1.69392i	−0.531653	−	0.846962i	$-0.678429\pi$
$11$		−	5.61811i		−	1.69392i	0.531653	−	0.846962i	$-0.321571\pi$
$12$	1.71975	+	0.206043i	0.496450	+	0.0594796i
$13$	−5.23268	−	1.40209i	−1.45128	−	0.388871i	−0.554814	−	0.831974i	$-0.687211\pi$
$13$	−5.23268	−	1.40209i	−1.45128	−	0.388871i	−0.896470	+	0.443104i	$0.853877\pi$
$14$	−0.825566	−	2.51365i	−0.220642	−	0.671801i
$15$	2.32252	−	3.09934i	0.599671	−	0.800247i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.42422	+	0.917516i	0.830494	+	0.222530i	0.648929	−	0.760849i	$-0.275217\pi$
$17$	3.42422	+	0.917516i	0.830494	+	0.222530i	0.181565	+	0.983379i	$0.441884\pi$
$18$	−2.56240	+	1.56016i	−0.603963	+	0.367734i
$19$	−2.96649	−	1.71270i	−0.680559	−	0.392921i	0.119506	−	0.992833i	$-0.461869\pi$
$19$	−2.96649	−	1.71270i	−0.680559	−	0.392921i	−0.800066	+	0.599912i	$0.795202\pi$
$20$	2.23607		0.000558109i	0.500000		0.000124797i
$21$	3.81470	+	2.53930i	0.832437	+	0.554120i
$22$	−1.45407	+	5.42668i	−0.310010	+	1.15697i
$23$	4.84782	+	4.84782i	1.01084	+	1.01084i	0.999941	+	0.0108999i	$0.00346961\pi$
$23$	4.84782	+	4.84782i	1.01084	+	1.01084i	0.0108999	+	0.999941i	$0.496530\pi$
$24$	−1.60782	−	0.644127i	−0.328196	−	0.131482i
$25$	2.50216	−	4.32888i	0.500432	−	0.865776i
$26$	4.69149	+	2.70864i	0.920078	+	0.531207i
$27$	1.81940	−	4.86721i	0.350144	−	0.936696i
$28$	0.146855	+	2.64167i	0.0277530	+	0.499229i
$29$	−3.11239	+	5.39082i	−0.577957	+	1.00105i	0.417756	+	0.908559i	$0.362817\pi$
$29$	−3.11239	+	5.39082i	−0.577957	+	1.00105i	−0.995713	+	0.0924919i	$0.970517\pi$
$30$	−3.04555	+	2.39262i	−0.556038	+	0.436831i
$31$	−2.92080	+	5.05898i	−0.524592	+	0.908620i	0.474998	+	0.879987i	$0.342449\pi$
$31$	−2.92080	+	5.05898i	−0.524592	+	0.908620i	−0.999590	+	0.0286329i	$0.990885\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−3.82839	−	8.94612i	−0.666437	−	1.55732i
$34$	−3.07007	−	1.77250i	−0.526512	−	0.303982i
$35$	5.27910	+	2.67041i	0.892331	+	0.451382i
$36$	2.87889	−	0.843805i	0.479815	−	0.140634i
$37$	6.67262	−	1.78792i	1.09697	−	0.293933i	0.335441	−	0.942061i	$-0.391115\pi$
$37$	6.67262	−	1.78792i	1.09697	−	0.293933i	0.761531	+	0.648128i	$0.224448\pi$
$38$	2.42213	+	2.42213i	0.392921	+	0.392921i
$39$	−9.28781	+	1.33309i	−1.48724	+	0.213466i
$40$	−2.15973	−	0.579276i	−0.341484	−	0.0915916i
$41$	−0.460590	+	0.265922i	−0.0719321	+	0.0415300i	−0.535535	−	0.844513i	$-0.679890\pi$
$41$	−0.460590	+	0.265922i	−0.0719321	+	0.0415300i	0.463603	+	0.886043i	$0.346557\pi$
$42$	−3.02750	−	3.44009i	−0.467154	−	0.530818i
$43$	−1.05122	−	3.92322i	−0.160310	−	0.598285i	−0.998592	−	0.0530480i	$-0.983106\pi$
$43$	−1.05122	−	3.92322i	−0.160310	−	0.598285i	0.838282	−	0.545237i	$-0.183560\pi$
$44$	2.80906	−	4.86543i	0.423481	−	0.733491i
$45$	1.58630	−	6.51795i	0.236472	−	0.971638i
$46$	−3.42793	−	5.93734i	−0.505420	−	0.875414i
$47$	0.112364	+	0.0301078i	0.0163899	+	0.00439167i	0.267005	−	0.963695i	$-0.413966\pi$
$47$	0.112364	+	0.0301078i	0.0163899	+	0.00439167i	−0.250615	+	0.968087i	$0.580633\pi$
$48$	1.38633	+	1.03831i	0.200099	+	0.149868i
$49$	−2.80650	+	6.41277i	−0.400928	+	0.916110i
$50$	−3.53730	+	3.53377i	−0.500250	+	0.499750i
$51$	6.07785	−	0.872363i	0.851069	−	0.122155i
$52$	−3.83059	−	3.83059i	−0.531207	−	0.531207i
$53$	−0.378116	+	1.41115i	−0.0519382	+	0.193836i	−0.987020	−	0.160595i	$-0.948659\pi$
$53$	−0.378116	+	1.41115i	−0.0519382	+	0.193836i	0.935082	+	0.354431i	$0.115325\pi$
$54$	−3.01713	+	4.23047i	−0.410580	+	0.575694i
$55$	−6.27853	−	10.8810i	−0.846596	−	1.46719i
$56$	0.541864	−	2.58967i	0.0724096	−	0.346059i
$57$	−5.89085	−	0.705782i	−0.780262	−	0.0934832i
$58$	4.40159	−	4.40159i	0.577957	−	0.577957i
$59$	−1.40284	+	2.42978i	−0.182634	+	0.316331i	−0.942777	−	0.333425i	$-0.891796\pi$
$59$	−1.40284	+	2.42978i	−0.182634	+	0.316331i	0.760143	+	0.649756i	$0.225129\pi$
$60$	3.56103	−	1.52285i	0.459727	−	0.196599i
$61$	4.53736	+	7.85893i	0.580949	+	1.00623i	0.995367	+	0.0961464i	$0.0306517\pi$
$61$	4.53736	+	7.85893i	0.580949	+	1.00623i	−0.414418	+	0.910086i	$0.636015\pi$
$62$	4.13064	−	4.13064i	0.524592	−	0.524592i
$63$	7.80479	+	1.44402i	0.983312	+	0.181930i
$64$			1.00000i			0.125000i
$65$	−11.7014	+	3.13225i	−1.45138	+	0.388508i
$66$	1.38252	+	9.63215i	0.170176	+	1.18564i
$67$	−2.47728	+	0.663784i	−0.302647	+	0.0810941i	−0.406947	−	0.913452i	$-0.633407\pi$
$67$	−2.47728	+	0.663784i	−0.302647	+	0.0810941i	0.104299	+	0.994546i	$0.466740\pi$
$68$	2.50670	+	2.50670i	0.303982	+	0.303982i
$69$	11.0230	+	4.41604i	1.32701	+	0.531629i
$70$	−4.40806	−	3.94575i	−0.526865	−	0.471608i
$71$		−	9.18544i		−	1.09011i	−0.838400	−	0.545056i	$-0.816508\pi$
$71$		−	9.18544i		−	1.09011i	0.838400	−	0.545056i	$-0.183492\pi$
$72$	−2.99918	+	0.0699423i	−0.353457	+	0.00824278i
$73$	5.01109	+	1.34272i	0.586504	+	0.157153i	0.539855	−	0.841758i	$-0.318479\pi$
$73$	5.01109	+	1.34272i	0.586504	+	0.157153i	0.0466491	+	0.998911i	$0.485146\pi$
$74$	−6.90801			−0.803040
$75$	1.03451	−	8.59824i	0.119455	−	0.992840i
$76$	−1.71270	−	2.96649i	−0.196461	−	0.340280i
$77$	12.4403	−	8.13512i	1.41771	−	0.927083i
$78$	9.31636	+	1.11619i	1.05487	+	0.126384i
$79$	−13.3443	+	7.70434i	−1.50135	+	0.866806i	−0.501353	+	0.865243i	$0.667164\pi$
$79$	−13.3443	+	7.70434i	−1.50135	+	0.866806i	−0.999999	+	0.00156257i	$0.999503\pi$
$80$	1.93621	+	1.11852i	0.216475	+	0.125054i
$81$	−0.419540	−	8.99022i	−0.0466155	−	0.998913i
$82$	0.513722	−	0.137651i	0.0567311	−	0.0152010i
$83$	14.0608	−	3.76758i	1.54337	−	0.413546i	0.616020	−	0.787730i	$-0.288744\pi$
$83$	14.0608	−	3.76758i	1.54337	−	0.413546i	0.927354	+	0.374184i	$0.122077\pi$
$84$	2.03398	+	4.10645i	0.221926	+	0.448050i
$85$	7.65729	−	2.04972i	0.830550	−	0.222323i
$86$			4.06161i			0.437975i
$87$	−1.28258	+	10.7051i	−0.137507	+	1.14771i
$88$	−3.97261	+	3.97261i	−0.423481	+	0.423481i
$89$	2.54650	−	4.41067i	0.269929	−	0.467530i	−0.698915	−	0.715205i	$-0.746333\pi$
$89$	2.54650	−	4.41067i	0.269929	−	0.467530i	0.968843	+	0.247675i	$0.0796666\pi$
$90$	−3.21922	+	5.88529i	−0.339335	+	0.620364i
$91$	−4.47232	−	13.6171i	−0.468826	−	1.42746i
$92$	1.77443	+	6.62225i	0.184997	+	0.690417i
$93$	−1.20362	+	10.0461i	−0.124810	+	1.04173i
$94$	−0.100743	−	0.0581638i	−0.0103908	−	0.00599914i
$95$	−7.65944	−	0.00191175i	−0.785842	−	0.000196142i
$96$	−1.07035	−	1.36174i	−0.109242	−	0.138982i
$97$	−1.96921	+	0.527648i	−0.199943	+	0.0535745i	−0.357401	−	0.933951i	$-0.616337\pi$
$97$	−1.96921	+	0.527648i	−0.199943	+	0.0535745i	0.157458	+	0.987526i	$0.449670\pi$
$98$	4.37061	−	5.46788i	0.441499	−	0.552340i
$99$	−12.1924	−	11.6367i	−1.22539	−	1.16953i
$100$	4.33137	−	2.49784i	0.433137	−	0.249784i
$101$		−	2.52122i		−	0.250871i	−0.992102	−	0.125435i	$-0.959967\pi$
$101$		−	2.52122i		−	0.250871i	0.992102	−	0.125435i	$-0.0400327\pi$
$102$	−6.09654	−	0.730426i	−0.603647	−	0.0723229i
$103$	−10.5625	+	10.5625i	−1.04076	+	1.04076i	−0.0416245	+	0.999133i	$0.513253\pi$
$103$	−10.5625	+	10.5625i	−1.04076	+	1.04076i	−0.999133	+	0.0416245i	$0.986747\pi$
$104$	2.70864	+	4.69149i	0.265604	+	0.460039i
$105$	10.2260	+	0.654913i	0.997955	+	0.0639130i
$106$	0.730463	−	1.26520i	0.0709489	−	0.122887i
$107$	−0.268125	−	1.00066i	−0.0259206	−	0.0967371i	0.951754	−	0.306863i	$-0.0992793\pi$
$107$	−0.268125	−	1.00066i	−0.0259206	−	0.0967371i	−0.977674	+	0.210126i	$0.932613\pi$
$108$	4.00926	−	3.30543i	0.385791	−	0.318065i
$109$	1.13812	−	0.657095i	0.109012	−	0.0629382i	−0.444503	−	0.895778i	$-0.646620\pi$
$109$	1.13812	−	0.657095i	0.109012	−	0.0629382i	0.553515	+	0.832839i	$0.313286\pi$
$110$	3.24838	+	12.1352i	0.309721	+	1.15705i
$111$	9.40693	−	7.39401i	0.892866	−	0.701808i
$112$	−1.19366	+	2.36118i	−0.112790	+	0.223111i
$113$	−0.125136	+	0.467015i	−0.0117718	+	0.0439331i	−0.971562	−	0.236786i	$-0.923906\pi$
$113$	−0.125136	+	0.467015i	−0.0117718	+	0.0439331i	0.959790	+	0.280719i	$0.0905728\pi$
$114$	5.50745	+	2.20640i	0.515820	+	0.206648i
$115$	14.8068	+	3.97143i	1.38074	+	0.370338i
$116$	−5.39082	+	3.11239i	−0.500525	+	0.288979i
$117$	−13.8812	+	8.45183i	−1.28332	+	0.781372i
$118$	1.98391	−	1.98391i	0.182634	−	0.182634i
$119$	2.92664	+	8.91092i	0.268285	+	0.816862i
$120$	−3.83383	+	0.549299i	−0.349979	+	0.0501439i
$121$	−20.5632			−1.86938
$122$	−2.34871	−	8.76550i	−0.212642	−	0.793591i
$123$	−0.552221	+	0.737310i	−0.0497921	+	0.0664810i
$124$	−5.05898	+	2.92080i	−0.454310	+	0.262296i
$125$	0.00837164	−	11.1803i	0.000748782	−	1.00000i
$126$	−7.16511	−	3.41485i	−0.638319	−	0.304219i
$127$	11.5953	+	11.5953i	1.02892	+	1.02892i	0.999569	+	0.0293496i	$0.00934362\pi$
$127$	11.5953	+	11.5953i	1.02892	+	1.02892i	0.0293496	+	0.999569i	$0.490656\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−4.34736	−	5.53087i	−0.382764	−	0.486966i
$130$	12.1134	+	0.00302343i	1.06241	+	0.000265172i
$131$			11.1985i			0.978419i	0.872166	+	0.489210i	$0.162715\pi$
$131$			11.1985i			0.978419i	−0.872166	+	0.489210i	$0.837285\pi$
$132$	1.15758	−	9.66176i	0.100754	−	0.840948i
$133$	−0.503039	−	9.04880i	−0.0436190	−	0.784631i
$134$	2.56467			0.221553
$135$	−1.91560	−	11.4600i	−0.164868	−	0.986316i
$136$	−1.77250	−	3.07007i	−0.151991	−	0.263256i
$137$	0.828557	−	0.828557i	0.0707884	−	0.0707884i	−0.670826	−	0.741615i	$-0.734060\pi$
$137$	0.828557	−	0.828557i	0.0707884	−	0.0707884i	0.741615	+	0.670826i	$0.234060\pi$
$138$	−9.50446	−	7.11853i	−0.809073	−	0.605970i
$139$	−16.4430	+	9.49334i	−1.39467	+	0.805215i	−0.993828	−	0.110931i	$-0.964617\pi$
$139$	−16.4430	+	9.49334i	−1.39467	+	0.805215i	−0.400845	+	0.916146i	$0.631283\pi$
$140$	3.23663	+	4.95220i	0.273545	+	0.418537i
$141$	0.199441	−	0.0286261i	0.0167960	−	0.00241075i
$142$	−2.37737	+	8.87246i	−0.199504	+	0.744560i
$143$	−7.87712	+	29.3978i	−0.658718	+	2.45837i
$144$	2.91509	+	0.708687i	0.242924	+	0.0590573i
$145$	−0.00347411	+	13.9190i	−0.000288509	+	1.15591i
$146$	−4.49282	−	2.59393i	−0.371829	−	0.214675i
$147$	−0.0990839	+	12.1240i	−0.00817230	+	0.999967i
$148$	6.67262	+	1.78792i	0.548486	+	0.146966i
$149$	−1.46287			−0.119843			−0.0599216	−	0.998203i	$-0.519085\pi$
$149$	−1.46287			−0.119843			−0.0599216	+	0.998203i	$0.519085\pi$
$150$	−3.22465	+	8.03751i	−0.263291	+	0.656260i
$151$	−5.61091			−0.456610			−0.228305	−	0.973590i	$-0.573318\pi$
$151$	−5.61091			−0.456610			−0.228305	+	0.973590i	$0.573318\pi$
$152$	0.886560	+	3.30869i	0.0719095	+	0.268370i
$153$	9.08373	−	5.53080i	0.734376	−	0.447138i
$154$	−14.1220	+	4.63813i	−1.13798	+	0.373751i
$155$	−0.00326026	+	13.0622i	−0.000261870	+	1.04918i
$156$	−8.71002	−	3.48941i	−0.697360	−	0.279377i
$157$	1.55168	−	0.415770i	0.123837	−	0.0331821i	−0.196368	−	0.980530i	$-0.562915\pi$
$157$	1.55168	−	0.415770i	0.123837	−	0.0331821i	0.320205	+	0.947348i	$0.396248\pi$
$158$	14.8836	−	3.98806i	1.18408	−	0.317273i
$159$	0.359508	+	2.50473i	0.0285108	+	0.198638i
$160$	−1.58074	−	1.58153i	−0.124969	−	0.125031i
$161$	−3.71494	+	17.7544i	−0.292778	+	1.39924i
$162$	−1.92159	+	8.79247i	−0.150975	+	0.690801i
$163$	5.18921	+	19.3664i	0.406450	+	1.51689i	0.801366	+	0.598175i	$0.204107\pi$
$163$	5.18921	+	19.3664i	0.406450	+	1.51689i	−0.394916	+	0.918717i	$0.629226\pi$
$164$	−0.531844			−0.0415300
$165$	−17.4125	−	13.0482i	−1.35556	−	1.01580i
$166$	−14.5568			−1.12983
$167$	−21.3810	−	5.72901i	−1.65451	−	0.443324i	−0.693639	−	0.720323i	$-0.743994\pi$
$167$	−21.3810	−	5.72901i	−1.65451	−	0.443324i	−0.960870	+	0.276999i	$0.910660\pi$
$168$	−0.901848	−	4.49296i	−0.0695791	−	0.346639i
$169$	14.1568	+	8.17341i	1.08898	+	0.628724i
$170$	−7.92688	−	0.00197850i	−0.607964	−	0.000151744i
$171$	−9.86136	+	2.89038i	−0.754117	+	0.221033i
$172$	1.05122	−	3.92322i	0.0801550	−	0.299142i
$173$	−2.48486	+	9.27362i	−0.188920	+	0.705060i	0.804837	+	0.593496i	$0.202253\pi$
$173$	−2.48486	+	9.27362i	−0.188920	+	0.705060i	−0.993757	+	0.111564i	$0.964414\pi$
$174$	4.00955	−	10.0084i	0.303964	−	0.758732i
$175$	13.2087	−	0.727683i	0.998486	−	0.0550076i
$176$	4.86543	−	2.80906i	0.366746	−	0.211741i
$177$	−0.578090	+	4.82506i	−0.0434519	+	0.362674i
$178$	−3.60130	+	3.60130i	−0.269929	+	0.269929i
$179$	−4.15894	−	7.20350i	−0.310854	−	0.538415i	0.667693	−	0.744436i	$-0.267282\pi$
$179$	−4.15894	−	7.20350i	−0.310854	−	0.538415i	−0.978548	+	0.206021i	$0.933948\pi$
$180$	4.63275	−	4.85156i	0.345305	−	0.361614i
$181$	12.9851			0.965173			0.482587	−	0.875848i	$-0.339697\pi$
$181$	12.9851			0.965173			0.482587	+	0.875848i	$0.339697\pi$
$182$	0.795555	+	14.3107i	0.0589704	+	1.06078i
$183$	12.5805	+	9.42241i	0.929979	+	0.696524i
$184$		−	6.85585i		−	0.505420i
$185$	10.9252	−	10.9198i	0.803240	−	0.802839i
$186$	3.76274	−	9.39228i	0.275897	−	0.688675i
$187$	5.15471	−	19.2376i	0.376950	−	1.40680i
$188$	0.0822560	+	0.0822560i	0.00599914	+	0.00599914i
$189$	13.4121	−	3.01906i	0.975589	−	0.219604i
$190$	7.39796	+	1.98426i	0.536704	+	0.143953i
$191$	10.5354	−	6.08260i	0.762312	−	0.440121i	−0.0678130	−	0.997698i	$-0.521602\pi$
$191$	10.5354	−	6.08260i	0.762312	−	0.440121i	0.830125	+	0.557577i	$0.188269\pi$
$192$	0.681437	+	1.59237i	0.0491785	+	0.114919i
$193$	3.96701	+	14.8051i	0.285552	+	1.06569i	0.948435	+	0.316971i	$0.102666\pi$
$193$	3.96701	+	14.8051i	0.285552	+	1.06569i	−0.662883	+	0.748723i	$0.730667\pi$
$194$	2.03868			0.146368
$195$	−16.4986	+	12.9615i	−1.18149	+	0.928191i
$196$	−5.63688	+	4.15037i	−0.402634	+	0.296455i
$197$	5.54709	−	5.54709i	0.395214	−	0.395214i	−0.481327	−	0.876541i	$-0.659845\pi$
$197$	5.54709	−	5.54709i	0.395214	−	0.395214i	0.876541	+	0.481327i	$0.159845\pi$
$198$	8.76518	+	14.3958i	0.622914	+	1.02307i
$199$	−4.63242	+	2.67453i	−0.328384	+	0.189592i	−0.655123	−	0.755522i	$-0.727383\pi$
$199$	−4.63242	+	2.67453i	−0.328384	+	0.189592i	0.326740	+	0.945114i	$0.394050\pi$
$200$	−4.83027	+	1.29168i	−0.341552	+	0.0913359i
$201$	−3.49241	+	2.74510i	−0.246336	+	0.193624i
$202$	−0.652539	+	2.43531i	−0.0459125	+	0.171348i
$203$	−16.4439	+	0.914143i	−1.15413	+	0.0641602i
$204$	5.69975	+	2.28344i	0.399063	+	0.159873i
$205$	−0.594877	+	1.02976i	−0.0415480	+	0.0719218i
$206$	12.9364	−	7.46884i	0.901323	−	0.520379i
$207$	20.5620	−	0.479514i	1.42916	−	0.0333285i
$208$	−1.40209	−	5.23268i	−0.0972177	−	0.362821i
$209$	−9.62216	+	16.6661i	−0.665579	+	1.15282i
$210$	−9.70805	−	3.27928i	−0.669919	−	0.226292i
$211$	1.97854	+	3.42694i	0.136209	+	0.235920i	0.926059	−	0.377380i	$-0.123175\pi$
$211$	1.97854	+	3.42694i	0.136209	+	0.235920i	−0.789850	+	0.613300i	$0.789842\pi$
$212$	−1.03303	+	1.03303i	−0.0709489	+	0.0709489i
$213$	−6.25930	−	14.6266i	−0.428880	−	1.00220i
$214$			1.03596i			0.0708165i
$215$	−6.42037	−	6.42358i	−0.437866	−	0.438084i
$216$	−4.72815	+	2.15513i	−0.321710	+	0.146638i
$217$	−15.4316	+	0.857871i	−1.04757	+	0.0582360i
$218$	−1.26941	+	0.340137i	−0.0859752	+	0.0230370i
$219$	8.89450	−	1.27664i	0.601034	−	0.0862673i
$220$	0.00313552	−	12.5625i	0.000211397	−	0.846962i
$221$	−16.6314	−	9.60214i	−1.11875	−	0.645910i
$222$	−11.0001	+	4.70737i	−0.738279	+	0.315938i
$223$	3.27990	+	12.2407i	0.219638	+	0.819701i	0.984482	+	0.175485i	$0.0561494\pi$
$223$	3.27990	+	12.2407i	0.219638	+	0.819701i	−0.764844	+	0.644216i	$0.777184\pi$
$224$	1.76410	−	1.97179i	0.117869	−	0.131746i
$225$	−4.21184	−	14.3965i	−0.280789	−	0.959769i
$226$	0.241745	−	0.418714i	0.0160806	−	0.0278525i
$227$	−17.7838	+	17.7838i	−1.18035	+	1.18035i	−0.200697	+	0.979653i	$0.564321\pi$
$227$	−17.7838	+	17.7838i	−1.18035	+	1.18035i	−0.979653	+	0.200697i	$0.935679\pi$
$228$	−4.74873	−	3.55665i	−0.314493	−	0.235545i
$229$		−	14.8765i		−	0.983065i	−0.870859	−	0.491532i	$-0.836437\pi$
$229$		−	14.8765i		−	0.983065i	0.870859	−	0.491532i	$-0.163563\pi$
$230$	−13.2744	−	7.66839i	−0.875287	−	0.505639i
$231$	14.2661	−	21.4314i	0.938638	−	1.41009i
$232$	6.01268	−	1.61109i	0.394752	−	0.105773i
$233$	9.72889	−	2.60685i	0.637361	−	0.170780i	0.0743532	−	0.997232i	$-0.476311\pi$
$233$	9.72889	−	2.60685i	0.637361	−	0.170780i	0.563008	+	0.826452i	$0.309644\pi$
$234$	15.5957	−	4.57112i	1.01952	−	0.298824i
$235$	0.251270	−	0.0672604i	0.0163910	−	0.00438758i
$236$	−2.42978	+	1.40284i	−0.158165	+	0.0913168i
$237$	−15.9991	+	21.3615i	−1.03925	+	1.38758i
$238$	−0.520603	−	9.36475i	−0.0337457	−	0.607027i
$239$	−6.41530	−	11.1116i	−0.414971	−	0.718752i	0.580454	−	0.814293i	$-0.302875\pi$
$239$	−6.41530	−	11.1116i	−0.414971	−	0.718752i	−0.995425	+	0.0955414i	$0.969542\pi$
$240$	3.84537	+	0.461687i	0.248217	+	0.0298018i
$241$	1.67741			0.108051			0.0540257	−	0.998540i	$-0.482795\pi$
$241$	1.67741			0.108051			0.0540257	+	0.998540i	$0.482795\pi$
$242$	19.8625	+	5.32215i	1.27681	+	0.342121i
$243$	−6.79433	−	14.0299i	−0.435856	−	0.900016i
$244$			9.07471i			0.580949i
$245$	1.73105	+	15.5565i	0.110593	+	0.993866i
$246$	0.724235	−	0.569261i	0.0461755	−	0.0362948i
$247$	13.1213	+	13.1213i	0.834890	+	0.834890i
$248$	5.64256	−	1.51192i	0.358303	−	0.0960070i
$249$	19.8226	−	15.5809i	1.25621	−	0.987402i
$250$	−2.90177	+	10.7972i	−0.183524	+	0.682875i
$251$			0.581820i			0.0367242i	0.999831	+	0.0183621i	$0.00584516\pi$
$251$			0.581820i			0.0367242i	−0.999831	+	0.0183621i	$0.994155\pi$
$252$	6.03714	+	5.15296i	0.380304	+	0.324606i
$253$	27.2356	−	27.2356i	1.71229	−	1.71229i
$254$	−8.19913	−	14.2013i	−0.514459	−	0.891070i
$255$	10.7965	−	8.48187i	0.676103	−	0.531155i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.50253	+	1.50253i	−0.0937253	+	0.0937253i	−0.752415	−	0.658690i	$-0.771111\pi$
$257$	−1.50253	+	1.50253i	−0.0937253	+	0.0937253i	0.658690	+	0.752415i	$0.271111\pi$
$258$	2.76773	+	6.46759i	0.172312	+	0.402655i
$259$	13.6211	+	12.1864i	0.846375	+	0.757228i
$260$	−11.6998	−	3.13810i	−0.725594	−	0.194616i
$261$	5.25251	+	17.9205i	0.325122	+	1.10925i
$262$	2.89839	−	10.8169i	0.179063	−	0.668273i
$263$	−20.1102	−	20.1102i	−1.24005	−	1.24005i	−0.959981	−	0.280066i	$-0.909644\pi$
$263$	−20.1102	−	20.1102i	−1.24005	−	1.24005i	−0.280066	−	0.959981i	$-0.590356\pi$
$264$	−3.61878	+	9.03294i	−0.222720	+	0.555939i
$265$	0.844705	+	3.15563i	0.0518898	+	0.193849i
$266$	−1.85610	+	8.87067i	−0.113805	+	0.543896i
$267$	1.04938	−	8.75870i	0.0642210	−	0.536024i
$268$	−2.47728	−	0.663784i	−0.151324	−	0.0405471i
$269$	−6.07208	−	10.5171i	−0.370221	−	0.641242i	0.619378	−	0.785093i	$-0.287385\pi$
$269$	−6.07208	−	10.5171i	−0.370221	−	0.641242i	−0.989599	+	0.143851i	$0.954051\pi$
$270$	−1.11573	+	11.5653i	−0.0679012	+	0.703839i
$271$	−8.51049	+	14.7406i	−0.516975	+	0.895427i	0.482830	+	0.875714i	$0.339609\pi$
$271$	−8.51049	+	14.7406i	−0.516975	+	0.895427i	−0.999806	+	0.0197135i	$0.993725\pi$
$272$	0.917516	+	3.42422i	0.0556326	+	0.207624i
$273$	−16.4008	−	18.6359i	−0.992622	−	1.12790i
$274$	−1.01477	+	0.585878i	−0.0613046	+	0.0353942i
$275$	−24.3201	−	14.0574i	−1.46656	−	0.847695i
$276$	7.33819	+	9.33591i	0.441707	+	0.561956i
$277$	−12.6187	−	12.6187i	−0.758187	−	0.758187i	0.217805	−	0.975992i	$-0.430110\pi$
$277$	−12.6187	−	12.6187i	−0.758187	−	0.758187i	−0.975992	+	0.217805i	$0.930110\pi$
$278$	18.3397	−	4.91412i	1.09994	−	0.294729i
$279$	4.92918	+	16.8173i	0.295102	+	1.00683i
$280$	−1.84462	−	5.62115i	−0.110237	−	0.335928i
$281$	7.96344	+	4.59770i	0.475059	+	0.274276i	0.718355	−	0.695677i	$-0.244895\pi$
$281$	7.96344	+	4.59770i	0.475059	+	0.274276i	−0.243296	+	0.969952i	$0.578229\pi$
$282$	−0.200055	−	0.0239685i	−0.0119131	−	0.00142731i
$283$	−6.56925	−	24.5168i	−0.390501	−	1.45737i	−0.829309	−	0.558790i	$-0.811266\pi$
$283$	−6.56925	−	24.5168i	−0.390501	−	1.45737i	0.438808	−	0.898581i	$-0.355401\pi$
$284$	4.59272	−	7.95483i	0.272528	−	0.472032i
$285$	−12.1980	+	5.21638i	−0.722545	+	0.308992i
$286$	15.2174	−	26.3573i	0.899825	−	1.55854i
$287$	−1.25578	−	0.634839i	−0.0741264	−	0.0374733i
$288$	−2.63234	−	1.43902i	−0.155112	−	0.0847951i
$289$	−3.83901	−	2.21645i	−0.225824	−	0.130380i
$290$	3.60587	−	13.4439i	0.211744	−	0.789451i
$291$	−2.77615	+	2.18210i	−0.162741	+	0.127917i
$292$	3.66838	+	3.66838i	0.214675	+	0.214675i
$293$	1.99307	−	7.43825i	0.116437	−	0.434547i	−0.882954	−	0.469460i	$-0.844449\pi$
$293$	1.99307	−	7.43825i	0.116437	−	0.434547i	0.999390	+	0.0349126i	$0.0111153\pi$
$294$	3.23362	−	11.6852i	0.188588	−	0.681494i
$295$	−0.00156587	+	6.27367i	−9.11686e−5	+	0.365267i
$296$	−5.98251	−	3.45400i	−0.347726	−	0.200760i
$297$	−27.3446	−	10.2216i	−1.58669	−	0.593118i
$298$	1.41303	+	0.378619i	0.0818545	+	0.0219328i
$299$	−18.5700	−	32.1642i	−1.07393	−	1.86010i
$300$	5.19503	−	6.92904i	0.299935	−	0.400048i
$301$	7.16510	−	8.00863i	0.412990	−	0.461610i
$302$	5.41972	+	1.45221i	0.311870	+	0.0835653i
$303$	−1.71805	−	4.01471i	−0.0986995	−	0.230639i
$304$		−	3.42541i		−	0.196461i
$305$	17.5706	+	10.1502i	1.00609	+	0.581200i
$306$	−10.2057	+	2.99130i	−0.583420	+	0.171001i
$307$	−7.93485	−	7.93485i	−0.452866	−	0.452866i	0.443439	−	0.896305i	$-0.353758\pi$
$307$	−7.93485	−	7.93485i	−0.452866	−	0.452866i	−0.896305	+	0.443439i	$0.853758\pi$
$308$	14.8412	−	0.825049i	0.845657	−	0.0470115i
$309$	−9.62177	+	24.0172i	−0.547363	+	1.36629i
$310$	3.38390	−	12.6163i	0.192193	−	0.716558i
$311$	5.51809	+	3.18587i	0.312902	+	0.180654i	0.648225	−	0.761449i	$-0.275512\pi$
$311$	5.51809	+	3.18587i	0.312902	+	0.180654i	−0.335322	+	0.942104i	$0.608845\pi$
$312$	7.51011	+	5.62483i	0.425176	+	0.318443i
$313$	28.0028	+	7.50333i	1.58281	+	0.424113i	0.939795	−	0.341738i	$-0.111016\pi$
$313$	28.0028	+	7.50333i	1.58281	+	0.424113i	0.643017	+	0.765852i	$0.277682\pi$
$314$	−1.60641			−0.0906551
$315$	16.7299	−	5.92551i	0.942621	−	0.333865i
$316$	−15.4087			−0.866806
$317$	27.3368	+	7.32488i	1.53539	+	0.411406i	0.924773	−	0.380520i	$-0.124255\pi$
$317$	27.3368	+	7.32488i	1.53539	+	0.411406i	0.610617	+	0.791926i	$0.290922\pi$
$318$	0.301014	−	2.51243i	0.0168800	−	0.140890i
$319$	30.2863	+	17.4858i	1.69571	+	0.979016i
$320$	1.11755	+	1.93677i	0.0624730	+	0.108269i
$321$	−1.10884	−	1.41070i	−0.0618893	−	0.0787379i
$322$	8.18353	−	16.1879i	0.456050	−	0.902118i
$323$	−8.58647	−	8.58647i	−0.477764	−	0.477764i
$324$	4.13178	−	7.99553i	0.229543	−	0.444196i
$325$	−19.1625	+	19.1434i	−1.06294	+	1.06188i
$326$		−	20.0496i		−	1.11044i
$327$	1.36454	−	1.82190i	0.0754593	−	0.100751i
$328$	0.513722	+	0.137651i	0.0283655	+	0.00760052i
$329$	0.0960362	+	0.292407i	0.00529464	+	0.0161209i
$330$	13.4420	+	17.1102i	0.739959	+	0.941887i
$331$	−2.01667	−	3.49298i	−0.110846	−	0.191991i	0.805265	−	0.592914i	$-0.202023\pi$
$331$	−2.01667	−	3.49298i	−0.110846	−	0.191991i	−0.916112	+	0.400923i	$0.868689\pi$
$332$	14.0608	+	3.76758i	0.771687	+	0.206773i
$333$	9.94076	−	18.1842i	0.544751	−	0.996490i
$334$	19.1697	+	11.0676i	1.04892	+	0.605592i
$335$	−4.05610	+	4.05408i	−0.221609	+	0.221498i
$336$	−0.291745	+	4.57328i	−0.0159160	+	0.249493i
$337$	3.57510	−	13.3424i	0.194748	−	0.726809i	−0.797584	−	0.603208i	$-0.793889\pi$
$337$	3.57510	−	13.3424i	0.194748	−	0.726809i	0.992332	−	0.123601i	$-0.0394444\pi$
$338$	−11.5590	−	11.5590i	−0.628724	−	0.628724i
$339$	0.118978	+	0.828934i	0.00646200	+	0.0450215i
$340$	7.65627	+	2.05354i	0.415219	+	0.111369i
$341$	28.4219	+	16.4094i	1.53913	+	0.888619i
$342$	10.2734	−	0.239581i	0.555523	−	0.0129550i
$343$	−18.2638	+	3.07129i	−0.986154	+	0.165834i
$344$	−2.03081	+	3.51746i	−0.109494	+	0.189649i
$345$	26.2842	−	3.76591i	1.41509	−	0.202750i
$346$	4.80038	−	8.31450i	0.258070	−	0.446990i
$347$	4.29931	+	16.0452i	0.230799	+	0.861353i	0.979998	+	0.199008i	$0.0637720\pi$
$347$	4.29931	+	16.0452i	0.230799	+	0.861353i	−0.749199	+	0.662345i	$0.769561\pi$
$348$	−6.46329	+	8.62959i	−0.346469	+	0.462595i
$349$	4.32988	+	2.49986i	0.231773	+	0.133814i	0.611390	−	0.791329i	$-0.290611\pi$
$349$	4.32988	+	2.49986i	0.231773	+	0.133814i	−0.379616	+	0.925144i	$0.623944\pi$
$350$	−12.9470	−	2.71578i	−0.692046	−	0.145165i
$351$	−16.3446	+	22.9176i	−0.872412	+	1.22325i
$352$	−5.42668	+	1.45407i	−0.289243	+	0.0775024i
$353$	16.9205	+	16.9205i	0.900585	+	0.900585i	0.995487	−	0.0949019i	$-0.0302538\pi$
$353$	16.9205	+	16.9205i	0.900585	+	0.900585i	−0.0949019	+	0.995487i	$0.530254\pi$
$354$	1.80721	−	4.51103i	0.0960521	−	0.239758i
$355$	−10.2652	−	17.7901i	−0.544820	−	0.944200i
$356$	4.41067	−	2.54650i	0.233765	−	0.134964i
$357$	10.7325	+	12.1952i	0.568025	+	0.645436i
$358$	2.15283	+	8.03446i	0.113781	+	0.424635i
$359$	−5.48263	+	9.49619i	−0.289362	+	0.501190i	−0.973658	−	0.228015i	$-0.926776\pi$
$359$	−5.48263	+	9.49619i	−0.289362	+	0.501190i	0.684296	+	0.729205i	$0.260110\pi$
$360$	−5.73057	+	3.48720i	−0.302027	+	0.183792i
$361$	−3.63330	−	6.29305i	−0.191226	−	0.331213i
$362$	−12.5426	−	3.36079i	−0.659226	−	0.176639i
$363$	−32.7442	+	14.0125i	−1.71863	+	0.735467i
$364$	2.93542	−	14.0289i	0.153858	−	0.735316i
$365$	11.2059	−	2.99961i	0.586543	−	0.157007i
$366$	−9.71315	−	12.3574i	−0.507714	−	0.645933i
$367$	−8.32095	−	8.32095i	−0.434350	−	0.434350i	0.455755	−	0.890105i	$-0.349369\pi$
$367$	−8.32095	−	8.32095i	−0.434350	−	0.434350i	−0.890105	+	0.455755i	$0.849369\pi$
$368$	−1.77443	+	6.62225i	−0.0924983	+	0.345208i
$369$	−0.376911	+	1.55037i	−0.0196212	+	0.0807093i
$370$	−13.3792	+	7.72005i	−0.695553	+	0.401346i
$371$	−3.67226	+	1.20609i	−0.190654	+	0.0626172i
$372$	−6.06543	+	8.09838i	−0.314478	+	0.419881i
$373$	13.3333	−	13.3333i	0.690373	−	0.690373i	−0.271941	−	0.962314i	$-0.587666\pi$
$373$	13.3333	−	13.3333i	0.690373	−	0.690373i	0.962314	+	0.271941i	$0.0876656\pi$
$374$	−9.95813	+	17.2480i	−0.514923	+	0.891873i
$375$	−7.60537	−	17.8089i	−0.392739	−	0.919650i
$376$	−0.0581638	−	0.100743i	−0.00299957	−	0.00519541i
$377$	23.8446	−	23.8446i	1.22806	−	1.22806i
$378$	−13.7365	−	0.555130i	−0.706530	−	0.0285528i
$379$		−	29.2781i		−	1.50392i	−0.659211	−	0.751958i	$-0.729109\pi$
$379$		−	29.2781i		−	1.50392i	0.659211	−	0.751958i	$-0.270891\pi$
$380$	−6.63231	−	3.83138i	−0.340231	−	0.196545i
$381$	26.3655	+	10.5626i	1.35075	+	0.541137i
$382$	−11.7507	+	3.14858i	−0.601217	+	0.161096i
$383$	14.2552	+	14.2552i	0.728409	+	0.728409i	0.970303	−	0.241894i	$-0.0777686\pi$
$383$	14.2552	+	14.2552i	0.728409	+	0.728409i	−0.241894	+	0.970303i	$0.577769\pi$
$384$	−0.246082	−	1.71448i	−0.0125578	−	0.0874917i
$385$	15.0027	−	29.6586i	0.764608	−	1.51154i
$386$		−	15.3274i		−	0.780142i
$387$	−10.6916	−	5.84474i	−0.543482	−	0.297105i
$388$	−1.96921	−	0.527648i	−0.0999715	−	0.0267873i
$389$	6.96909			0.353347			0.176673	−	0.984270i	$-0.443466\pi$
$389$	6.96909			0.353347			0.176673	+	0.984270i	$0.443466\pi$
$390$	19.2911	−	8.24970i	0.976841	−	0.417740i
$391$	12.1520	+	21.0479i	0.614555	+	1.06444i
$392$	6.51900	−	2.55002i	0.329259	−	0.128795i
$393$	7.63109	+	17.8322i	0.384937	+	0.899515i
$394$	−6.79377	+	3.92239i	−0.342265	+	0.197607i
$395$	−17.2349	+	29.8345i	−0.867180	+	1.50113i
$396$	−4.74059	−	16.1739i	−0.238224	−	0.812770i
$397$	−12.8233	+	3.43599i	−0.643583	+	0.172448i	−0.565826	−	0.824525i	$-0.691443\pi$
$397$	−12.8233	+	3.43599i	−0.643583	+	0.172448i	−0.0777571	+	0.996972i	$0.524776\pi$
$398$	5.16679	−	1.38444i	0.258988	−	0.0693956i
$399$	−6.96721	−	14.0663i	−0.348797	−	0.704194i
$400$	5.00000	+	0.00249594i	0.250000	+	0.000124797i
$401$		−	23.5031i		−	1.17369i	−0.809699	−	0.586845i	$-0.800370\pi$
$401$		−	23.5031i		−	1.17369i	0.809699	−	0.586845i	$-0.199630\pi$
$402$	4.08390	−	1.74766i	0.203686	−	0.0871653i
$403$	22.3768	−	22.3768i	1.11467	−	1.11467i
$404$	1.26061	−	2.18344i	0.0627177	−	0.108630i
$405$	−10.8596	−	16.9431i	−0.539617	−	0.841911i
$406$	16.1201	+	3.37299i	0.800029	+	0.167399i
$407$	−10.0448	−	37.4876i	−0.497900	−	1.85819i
$408$	−4.91454	−	3.68084i	−0.243306	−	0.182229i
$409$	14.5601	+	8.40628i	0.719951	+	0.415664i	0.814735	−	0.579834i	$-0.196883\pi$
$409$	14.5601	+	8.40628i	0.719951	+	0.415664i	−0.0947838	+	0.995498i	$0.530216\pi$
$410$	0.841129	−	0.840709i	0.0415404	−	0.0415197i
$411$	0.754760	−	1.88398i	0.0372296	−	0.0929298i
$412$	−14.4287	+	3.86616i	−0.710851	+	0.190472i
$413$	−7.41167	+	0.412028i	−0.364704	+	0.0202745i
$414$	−19.9854	−	4.85865i	−0.982231	−	0.238790i
$415$	23.0221	−	23.0106i	1.13011	−	1.12955i
$416$			5.41727i			0.265604i
$417$	−19.7142	+	26.3218i	−0.965406	+	1.28898i
$418$	13.6078	−	13.6078i	0.665579	−	0.665579i
$419$	−17.4144	−	30.1626i	−0.850748	−	1.47354i	−0.880534	−	0.473983i	$-0.842816\pi$
$419$	−17.4144	−	30.1626i	−0.850748	−	1.47354i	0.0297862	−	0.999556i	$-0.490517\pi$
$420$	8.52852	+	5.68017i	0.416149	+	0.277164i
$421$	−14.0377	+	24.3140i	−0.684155	+	1.18499i	0.289546	+	0.957164i	$0.406496\pi$
$421$	−14.0377	+	24.3140i	−0.684155	+	1.18499i	−0.973701	+	0.227828i	$0.926838\pi$
$422$	−1.02417	−	3.82225i	−0.0498558	−	0.186064i
$423$	0.298078	−	0.181490i	0.0144930	−	0.00882435i
$424$	1.26520	−	0.730463i	0.0614435	−	0.0354744i
$425$	12.5398	−	12.5272i	0.608268	−	0.607661i
$426$	2.26037	+	15.7483i	0.109515	+	0.763006i
$427$	−10.8321	+	21.4271i	−0.524201	+	1.03693i
$428$	0.268125	−	1.00066i	0.0129603	−	0.0483685i
$429$	7.48946	+	52.1800i	0.361595	+	2.51927i
$430$	4.53906	+	7.86641i	0.218893	+	0.379352i
$431$	29.0585	−	16.7770i	1.39970	−	0.808117i	0.405339	−	0.914166i	$-0.367153\pi$
$431$	29.0585	−	16.7770i	1.39970	−	0.808117i	0.994361	+	0.106049i	$0.0338200\pi$
$432$	5.12483	−	0.857960i	0.246569	−	0.0412786i
$433$	−11.1429	+	11.1429i	−0.535495	+	0.535495i	−0.922202	−	0.386707i	$-0.873612\pi$
$433$	−11.1429	+	11.1429i	−0.535495	+	0.535495i	0.386707	+	0.922202i	$0.373612\pi$
$434$	15.1278	+	3.16536i	0.726159	+	0.151942i
$435$	9.47942	+	22.1666i	0.454504	+	1.06281i
$436$	1.31419			0.0629382
$437$	−6.07813	−	22.6839i	−0.290756	−	1.08512i
$438$	−8.92184	−	1.06893i	−0.426302	−	0.0510752i
$439$	−27.2847	+	15.7528i	−1.30223	+	0.751841i	−0.980786	−	0.195089i	$-0.937500\pi$
$439$	−27.2847	+	15.7528i	−1.30223	+	0.751841i	−0.321441	+	0.946930i	$0.604167\pi$
$440$	−3.25444	+	12.1336i	−0.155149	+	0.578447i
$441$	8.10393	+	19.3733i	0.385901	+	0.922540i
$442$	13.5795	+	13.5795i	0.645910	+	0.645910i
$443$	−8.36708	+	31.2264i	−0.397532	+	1.48361i	0.419893	+	0.907574i	$0.362068\pi$
$443$	−8.36708	+	31.2264i	−0.397532	+	1.48361i	−0.817425	+	0.576036i	$0.804599\pi$
$444$	11.8436	−	1.69994i	0.562075	−	0.0806754i
$445$	0.00284245	−	11.3883i	0.000134745	−	0.539857i
$446$		−	12.6726i		−	0.600063i
$447$	−2.32944	+	0.996856i	−0.110179	+	0.0471497i
$448$	−2.21433	+	1.44802i	−0.104617	+	0.0684124i
$449$	−34.0514			−1.60699			−0.803493	−	0.595315i	$-0.797027\pi$
$449$	−34.0514			−1.60699			−0.803493	+	0.595315i	$0.797027\pi$
$450$	0.342226	+	14.9961i	0.0161327	+	0.706923i
$451$	1.49398	+	2.58765i	0.0703488	+	0.121848i
$452$	−0.341879	+	0.341879i	−0.0160806	+	0.0160806i
$453$	−8.93465	+	3.82348i	−0.419786	+	0.179643i
$454$	21.7806	−	12.5750i	1.02221	−	0.590175i
$455$	−23.8797	−	21.3752i	−1.11950	−	1.00209i
$456$	3.66640	+	4.66452i	0.171695	+	0.218436i
$457$	7.25595	−	27.0796i	0.339419	−	1.26673i	−0.559579	−	0.828777i	$-0.689037\pi$
$457$	7.25595	−	27.0796i	0.339419	−	1.26673i	0.898998	−	0.437952i	$-0.144296\pi$
$458$	−3.85031	+	14.3696i	−0.179913	+	0.671446i
$459$	10.6958	−	14.9971i	0.499236	−	0.700003i
$460$	10.8374	+	10.8428i	0.505294	+	0.505546i
$461$	5.23792	+	3.02411i	0.243954	+	0.140847i	0.616993	−	0.786969i	$-0.288351\pi$
$461$	5.23792	+	3.02411i	0.243954	+	0.140847i	−0.373039	+	0.927816i	$0.621684\pi$
$462$	−19.3268	+	17.0089i	−0.899165	+	0.791323i
$463$	−11.4243	−	3.06112i	−0.530931	−	0.142263i	−0.0166128	−	0.999862i	$-0.505288\pi$
$463$	−11.4243	−	3.06112i	−0.530931	−	0.142263i	−0.514318	+	0.857599i	$0.671955\pi$
$464$	−6.22479			−0.288979
$465$	8.89590	+	20.8021i	0.412537	+	0.964676i
$466$	−10.0721			−0.466581
$467$	3.63120	+	13.5518i	0.168032	+	0.627104i	0.997634	+	0.0687487i	$0.0219007\pi$
$467$	3.63120	+	13.5518i	0.168032	+	0.627104i	−0.829602	+	0.558355i	$0.811433\pi$
$468$	−16.2474	+	0.378896i	−0.751036	+	0.0175145i
$469$	−5.05697	−	4.52433i	−0.233509	−	0.208914i
$470$	−0.260116		6.49235e-5i	−0.0119983		2.99470e-6i
$471$	2.18752	−	1.71943i	0.100796	−	0.0792271i
$472$	2.71007	−	0.726161i	0.124741	−	0.0334243i
$473$	−22.0411	+	5.90589i	−1.01345	+	0.271553i
$474$	20.9827	−	16.4927i	0.963765	−	0.757536i
$475$	−14.8367	+	8.55611i	−0.680755	+	0.392581i
$476$	−1.92091	+	9.18040i	−0.0880449	+	0.420783i
$477$	2.27929	+	3.74348i	0.104361	+	0.171402i
$478$	3.32081	+	12.3934i	0.151890	+	0.566862i
$479$	−41.8093			−1.91032			−0.955158	−	0.296096i	$-0.904315\pi$
$479$	−41.8093			−1.91032			−0.955158	+	0.296096i	$0.904315\pi$
$480$	−3.59485	−	1.44121i	−0.164082	−	0.0657819i
$481$	−37.4225			−1.70632
$482$	−1.62025	−	0.434146i	−0.0738005	−	0.0197748i
$483$	6.18294	+	30.8031i	0.281333	+	1.40159i
$484$	−17.8083	−	10.2816i	−0.809466	−	0.467345i
$485$	−3.22423	+	3.22262i	−0.146405	+	0.146332i
$486$	2.93162	+	15.3103i	0.132981	+	0.694490i
$487$	−0.371900	+	1.38795i	−0.0168524	+	0.0628940i	−0.973840	−	0.227235i	$-0.927031\pi$
$487$	−0.371900	+	1.38795i	−0.0168524	+	0.0628940i	0.956988	+	0.290129i	$0.0936982\pi$
$488$	2.34871	−	8.76550i	0.106321	−	0.396795i
$489$	21.4601	+	27.3023i	0.970460	+	1.23465i
$490$	2.35424	−	15.4744i	0.106354	−	0.699063i
$491$	2.09234	−	1.20802i	0.0944262	−	0.0545170i	−0.452043	−	0.891996i	$-0.649305\pi$
$491$	2.09234	−	1.20802i	0.0944262	−	0.0545170i	0.546470	+	0.837479i	$0.315971\pi$
$492$	−0.846893	+	0.362418i	−0.0381809	+	0.0163391i
$493$	−15.6037	+	15.6037i	−0.702754	+	0.702754i
$494$	−9.27818	−	16.0703i	−0.417445	−	0.723036i
$495$	−36.6186	−	8.91201i	−1.64588	−	0.400565i
$496$	−5.84161			−0.262296
$497$	20.3396	−	13.3007i	0.912355	−	0.596617i
$498$	−23.1799	+	9.91956i	−1.03871	+	0.444506i
$499$			6.82796i			0.305662i	0.988252	+	0.152831i	$0.0488389\pi$
$499$			6.82796i			0.305662i	−0.988252	+	0.152831i	$0.951161\pi$
$500$	5.59742	−	9.67827i	0.250324	−	0.432825i
$501$	−37.9504	+	5.44707i	−1.69550	+	0.243357i
$502$	0.150586	−	0.561995i	0.00672099	−	0.0250831i
$503$	−10.6908	−	10.6908i	−0.476680	−	0.476680i	0.427389	−	0.904068i	$-0.359434\pi$
$503$	−10.6908	−	10.6908i	−0.476680	−	0.476680i	−0.904068	+	0.427389i	$0.859434\pi$
$504$	−4.49774	−	6.53990i	−0.200345	−	0.291310i
$505$	−2.81759	−	4.88302i	−0.125381	−	0.217292i
$506$	−33.3567	+	19.2585i	−1.48288	+	0.856144i
$507$	28.1125	+	3.36816i	1.24852	+	0.149585i
$508$	4.24418	+	15.8395i	0.188305	+	0.702765i
$509$	3.09171			0.137038			0.0685189	−	0.997650i	$-0.478173\pi$
$509$	3.09171			0.137038			0.0685189	+	0.997650i	$0.478173\pi$
$510$	−12.6239	+	5.39852i	−0.558995	+	0.239051i
$511$	4.28293	+	13.0405i	0.189466	+	0.576877i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−13.7333	+	11.3224i	−0.606341	+	0.499898i
$514$	1.84022	−	1.06245i	0.0811685	−	0.0468626i
$515$	−8.65304	+	32.2614i	−0.381299	+	1.42161i
$516$	−0.999489	−	6.96356i	−0.0440001	−	0.306553i
$517$	0.169149	−	0.631273i	0.00743917	−	0.0277633i
$518$	−10.0029	−	15.2966i	−0.439503	−	0.672094i
$519$	2.36257	+	16.4603i	0.103705	+	0.722527i
$520$	10.4890	+	6.05931i	0.459973	+	0.265718i
$521$	−11.7621	+	6.79086i	−0.515307	+	0.297513i	−0.735013	−	0.678053i	$-0.762824\pi$
$521$	−11.7621	+	6.79086i	−0.515307	+	0.297513i	0.219705	+	0.975566i	$0.429490\pi$
$522$	−0.435376	−	18.6693i	−0.0190559	−	0.817133i
$523$	−3.83312	−	14.3054i	−0.167611	−	0.625532i	−0.997693	−	0.0678906i	$-0.978373\pi$
$523$	−3.83312	−	14.3054i	−0.167611	−	0.625532i	0.830082	−	0.557641i	$-0.188294\pi$
$524$	−5.59926	+	9.69820i	−0.244605	+	0.423668i
$525$	20.5373	−	10.1597i	0.896322	−	0.443404i
$526$	14.2200	+	24.6298i	0.620023	+	1.07391i
$527$	−14.6432	+	14.6432i	−0.637866	+	0.637866i
$528$	5.83337	−	7.78854i	0.253865	−	0.338953i
$529$			24.0027i			1.04360i
$530$	0.000815357	−	3.26673i	3.54168e−5	−	0.141898i
$531$	2.36744	+	8.07721i	0.102738	+	0.350521i
$532$	4.08876	−	8.08801i	0.177270	−	0.350660i
$533$	2.78297	−	0.745695i	0.120544	−	0.0322996i
$534$	−3.28054	+	8.18865i	−0.141963	+	0.354358i
$535$	−1.63758	−	1.63840i	−0.0707988	−	0.0708341i
$536$	2.22107	+	1.28233i	0.0959354	+	0.0553883i
$537$	−11.5313	−	8.63659i	−0.497613	−	0.372696i
$538$	3.14314	+	11.7304i	0.135510	+	0.505731i
$539$	36.0277	+	15.7672i	1.55182	+	0.679142i
$540$	4.07102	−	10.8824i	0.175189	−	0.468304i
$541$	20.8408	−	36.0974i	0.896017	−	1.55195i	0.0634772	−	0.997983i	$-0.479781\pi$
$541$	20.8408	−	36.0974i	0.896017	−	1.55195i	0.832540	−	0.553965i	$-0.186886\pi$
$542$	12.0356	−	12.0356i	0.516975	−	0.516975i
$543$	20.6771	−	8.84851i	0.887337	−	0.379726i
$544$		−	3.54501i		−	0.151991i
$545$	1.46994	−	2.54455i	0.0629655	−	0.108997i
$546$	11.0186	+	22.2457i	0.471554	+	0.952030i
$547$	26.7205	−	7.15975i	1.14249	−	0.306129i	0.362537	−	0.931969i	$-0.381911\pi$
$547$	26.7205	−	7.15975i	1.14249	−	0.306129i	0.779951	+	0.625841i	$0.215244\pi$
$548$	1.13183	−	0.303273i	0.0483494	−	0.0129552i
$549$	26.4536	+	6.43113i	1.12901	+	0.274474i
$550$	19.8531	+	19.8729i	0.846540	+	0.847385i
$551$	18.4658	−	10.6612i	0.786668	−	0.454183i
$552$	−4.67183	−	10.9171i	−0.198846	−	0.464661i
$553$	−36.3827	−	18.3927i	−1.54715	−	0.782135i
$554$	8.92280	+	15.4547i	0.379093	+	0.656609i
$555$	9.95589	−	24.8332i	0.422604	−	1.05411i
$556$	−18.9867			−0.805215
$557$	−19.8166	−	5.30984i	−0.839655	−	0.224985i	−0.186734	−	0.982411i	$-0.559790\pi$
$557$	−19.8166	−	5.30984i	−0.839655	−	0.224985i	−0.652922	+	0.757426i	$0.726457\pi$
$558$	−0.408575	−	17.5201i	−0.0172964	−	0.741683i
$559$			22.0029i			0.930622i
$560$	0.326904	+	5.90704i	0.0138142	+	0.249618i
$561$	−4.90103	−	34.1461i	−0.206922	−	1.44165i
$562$	−6.50213	−	6.50213i	−0.274276	−	0.274276i
$563$	−31.4813	+	8.43539i	−1.32678	+	0.355509i	−0.851513	−	0.524333i	$-0.824315\pi$
$563$	−31.4813	+	8.43539i	−1.32678	+	0.355509i	−0.475266	+	0.879842i	$0.657648\pi$
$564$	0.187034	+	0.0749298i	0.00787557	+	0.00315511i
$565$	0.279553	+	1.04435i	0.0117609	+	0.0439360i
$566$			25.3816i			1.06687i
$567$	19.2998	−	13.9470i	0.810515	−	0.585718i
$568$	−6.49509	+	6.49509i	−0.272528	+	0.272528i
$569$	−8.27990	−	14.3412i	−0.347111	−	0.601215i	0.638624	−	0.769519i	$-0.279504\pi$
$569$	−8.27990	−	14.3412i	−0.347111	−	0.601215i	−0.985735	+	0.168305i	$0.946171\pi$
$570$	13.1324	−	1.88157i	0.550057	−	0.0788104i
$571$	1.23597	−	2.14076i	0.0517236	−	0.0895879i	−0.839004	−	0.544125i	$-0.816862\pi$
$571$	1.23597	−	2.14076i	0.0517236	−	0.0895879i	0.890728	+	0.454537i	$0.150195\pi$
$572$	−21.5207	+	21.5207i	−0.899825	+	0.899825i
$573$	12.6313	−	16.8649i	0.527680	−	0.704543i
$574$	1.04868	+	0.938227i	0.0437712	+	0.0391608i
$575$	33.1157	−	8.85560i	1.38102	−	0.369304i
$576$	2.17020	+	2.07129i	0.0904250	+	0.0863036i
$577$	2.09826	−	7.83081i	0.0873516	−	0.326001i	−0.908398	−	0.418108i	$-0.862693\pi$
$577$	2.09826	−	7.83081i	0.0873516	−	0.326001i	0.995749	+	0.0921069i	$0.0293602\pi$
$578$	3.13454	+	3.13454i	0.130380	+	0.130380i
$579$	16.4057	+	20.8719i	0.681798	+	0.867408i
$580$	−6.96253	+	12.0525i	−0.289103	+	0.500453i
$581$	28.7030	+	25.6797i	1.19080	+	1.06537i
$582$	3.24633	−	1.38923i	0.134565	−	0.0575854i
$583$	7.92798	+	2.12430i	0.328343	+	0.0879794i
$584$	−2.59393	−	4.49282i	−0.107338	−	0.185914i
$585$	−17.4394	+	31.8822i	−0.721029	+	1.31817i
$586$	−3.85032	+	6.66895i	−0.159055	+	0.275492i
$587$	−5.28778	−	19.7343i	−0.218250	−	0.814521i	−0.984997	−	0.172571i	$-0.944792\pi$
$587$	−5.28778	−	19.7343i	−0.218250	−	0.814521i	0.766747	−	0.641950i	$-0.221874\pi$
$588$	−6.14778	+	10.4501i	−0.253530	+	0.430955i
$589$	17.3291	−	10.0049i	0.714032	−	0.412246i
$590$	1.62526	−	6.05950i	0.0669108	−	0.249466i
$591$	5.05303	−	12.6130i	0.207854	−	0.518830i
$592$	4.88470	+	4.88470i	0.200760	+	0.200760i
$593$	−10.5168	+	2.81796i	−0.431872	+	0.115720i	−0.468205	−	0.883620i	$-0.655099\pi$
$593$	−10.5168	+	2.81796i	−0.431872	+	0.115720i	0.0363328	+	0.999340i	$0.488432\pi$
$594$	23.7673	+	16.9506i	0.975183	+	0.695492i
$595$	15.6266	+	13.9877i	0.640629	+	0.573441i
$596$	−1.26689	−	0.731437i	−0.0518937	−	0.0299608i
$597$	−5.55401	+	7.41555i	−0.227310	+	0.303498i
$598$	9.61254	+	35.8745i	0.393086	+	1.46702i
$599$	18.9139	−	32.7599i	0.772802	−	1.33853i	−0.163220	−	0.986590i	$-0.552188\pi$
$599$	18.9139	−	32.7599i	0.772802	−	1.33853i	0.936022	−	0.351942i	$-0.114479\pi$
$600$	−6.81138	+	5.34837i	−0.278074	+	0.218346i
$601$	−5.75054	+	9.96023i	−0.234569	+	0.406286i	−0.959147	−	0.282907i	$-0.908701\pi$
$601$	−5.75054	+	9.96023i	−0.234569	+	0.406286i	0.724578	+	0.689193i	$0.242035\pi$
$602$	−8.99374	+	5.88128i	−0.366558	+	0.239703i
$603$	−3.69061	+	6.75107i	−0.150293	+	0.274925i
$604$	−4.85919	−	2.80546i	−0.197718	−	0.114152i
$605$	−39.8262	+	22.9804i	−1.61917	+	0.934287i
$606$	0.620426	+	4.32258i	0.0252031	+	0.175593i
$607$	8.52682	+	8.52682i	0.346093	+	0.346093i	0.858652	−	0.512559i	$-0.171302\pi$
$607$	8.52682	+	8.52682i	0.346093	+	0.346093i	−0.512559	+	0.858652i	$0.671302\pi$
$608$	−0.886560	+	3.30869i	−0.0359548	+	0.134185i
$609$	−25.5618	+	12.6611i	−1.03582	+	0.513054i
$610$	−14.3448	−	14.3520i	−0.580804	−	0.581094i
$611$	−0.545750	−	0.315089i	−0.0220787	−	0.0127471i
$612$	10.6321	−	0.247946i	0.429779	−	0.0100226i
$613$	34.3116	+	9.19377i	1.38583	+	0.371333i	0.873236	−	0.487297i	$-0.162017\pi$
$613$	34.3116	+	9.19377i	1.38583	+	0.371333i	0.512597	+	0.858630i	$0.328684\pi$
$614$	5.61079	+	9.71817i	0.226433	+	0.392193i
$615$	−0.245545	+	2.04513i	−0.00990134	+	0.0824678i
$616$	−14.5491	−	3.04425i	−0.586198	−	0.122656i
$617$	−10.7313	−	2.87544i	−0.432025	−	0.115761i	0.0362515	−	0.999343i	$-0.488458\pi$
$617$	−10.7313	−	2.87544i	−0.432025	−	0.115761i	−0.468277	+	0.883582i	$0.655125\pi$
$618$	15.5100	−	20.7085i	0.623904	−	0.833019i
$619$		−	12.5527i		−	0.504537i	−0.967657	−	0.252269i	$-0.918823\pi$
$619$		−	12.5527i		−	0.504537i	0.967657	−	0.252269i	$-0.0811766\pi$
$620$	−6.53394	+	11.3106i	−0.262409	+	0.454244i
$621$	32.4155	−	14.7753i	1.30079	−	0.592910i
$622$	−4.50550	−	4.50550i	−0.180654	−	0.180654i
$623$	13.4540	−	0.747934i	0.539025	−	0.0299653i
$624$	−5.79839	−	7.37693i	−0.232122	−	0.295314i
$625$	−12.4784	−	21.6631i	−0.499135	−	0.866524i
$626$	−25.1066	−	14.4953i	−1.00346	−	0.579350i
$627$	−3.96517	+	33.0955i	−0.158353	+	1.32171i
$628$	1.55168	+	0.415770i	0.0619186	+	0.0165910i
$629$	24.4890			0.976439
$630$	−17.6934	+	1.39360i	−0.704924	+	0.0555222i
$631$	26.3199			1.04778			0.523889	−	0.851786i	$-0.324480\pi$
$631$	26.3199			1.04778			0.523889	+	0.851786i	$0.324480\pi$
$632$	14.8836	+	3.98806i	0.592039	+	0.158636i
$633$	5.48582	+	4.10870i	0.218042	+	0.163306i
$634$	−24.5095	−	14.1506i	−0.973398	−	0.561992i
$635$	35.4159	+	9.49912i	1.40544	+	0.376961i
$636$	−0.941022	+	2.34891i	−0.0373140	+	0.0931405i
$637$	23.6768	−	29.6210i	0.938109	−	1.17363i
$638$	−24.7286	−	24.7286i	−0.979016	−	0.979016i
$639$	−19.9343	−	19.0257i	−0.788587	−	0.752645i
$640$	−0.578198	−	2.16002i	−0.0228553	−	0.0853823i
$641$			7.06289i			0.278968i	0.990224	+	0.139484i	$0.0445443\pi$
$641$			7.06289i			0.278968i	−0.990224	+	0.139484i	$0.955456\pi$
$642$	0.705938	+	1.64962i	0.0278612	+	0.0651055i
$643$	−18.3812	−	4.92522i	−0.724882	−	0.194232i	−0.122533	−	0.992464i	$-0.539102\pi$
$643$	−18.3812	−	4.92522i	−0.724882	−	0.194232i	−0.602349	+	0.798233i	$0.705768\pi$
$644$	−12.0944	+	13.5183i	−0.476587	+	0.532695i
$645$	−14.6009	−	5.85363i	−0.574909	−	0.230487i
$646$	6.07155	+	10.5162i	0.238882	+	0.413756i
$647$	8.72870	+	2.33885i	0.343161	+	0.0919496i	0.426283	−	0.904590i	$-0.359823\pi$
$647$	8.72870	+	2.33885i	0.343161	+	0.0919496i	−0.0831226	+	0.996539i	$0.526489\pi$
$648$	−6.06038	+	6.65370i	−0.238074	+	0.261382i
$649$	13.6508	+	7.88129i	0.535841	+	0.309368i
$650$	23.4642	−	13.5315i	0.920343	−	0.530748i
$651$	−23.9883	+	11.8817i	−0.940174	+	0.465681i
$652$	−5.18921	+	19.3664i	−0.203225	+	0.758446i
$653$	0.743687	+	0.743687i	0.0291027	+	0.0291027i	0.721508	−	0.692406i	$-0.243449\pi$
$653$	0.743687	+	0.743687i	0.0291027	+	0.0291027i	−0.692406	+	0.721508i	$0.743449\pi$
$654$	−1.78959	+	1.40665i	−0.0699784	+	0.0550042i
$655$	12.5149	+	21.6890i	0.488998	+	0.847458i
$656$	−0.460590	−	0.265922i	−0.0179830	−	0.0103825i
$657$	13.2934	−	8.09392i	0.518624	−	0.315774i
$658$	−0.0170833	−	0.307299i	−0.000665977	−	0.0119798i
$659$	21.3289	−	36.9428i	0.830857	−	1.43909i	−0.0665027	−	0.997786i	$-0.521184\pi$
$659$	21.3289	−	36.9428i	0.830857	−	1.43909i	0.897360	−	0.441300i	$-0.145483\pi$
$660$	−8.55555	−	20.0063i	−0.333024	−	0.778743i
$661$	8.82790	−	15.2904i	0.343366	−	0.594727i	−0.641690	−	0.766964i	$-0.721766\pi$
$661$	8.82790	−	15.2904i	0.343366	−	0.594727i	0.985055	+	0.172238i	$0.0550997\pi$
$662$	1.04391	+	3.89591i	0.0405725	+	0.151419i
$663$	−33.0266	−	3.95691i	−1.28265	−	0.153674i
$664$	−12.6066	−	7.27841i	−0.489230	−	0.282457i
$665$	−11.0868	−	16.9633i	−0.429926	−	0.657808i
$666$	−14.3085	+	14.9918i	−0.554442	+	0.580919i
$667$	−41.2221	+	11.0454i	−1.59613	+	0.427680i
$668$	−15.6520	−	15.6520i	−0.605592	−	0.605592i
$669$	13.5641	+	17.2568i	0.524419	+	0.667185i
$670$	4.96717	−	2.86614i	0.191898	−	0.110729i
$671$	44.1524	−	25.4914i	1.70448	−	0.984084i
$672$	1.46546	−	4.34194i	0.0565312	−	0.167494i
$673$	−4.42470	−	16.5132i	−0.170560	−	0.636537i	−0.997265	−	0.0739027i	$-0.976455\pi$
$673$	−4.42470	−	16.5132i	−0.170560	−	0.636537i	0.826706	−	0.562634i	$-0.190212\pi$
$674$	−6.90656	+	11.9625i	−0.266031	+	0.460779i
$675$	−16.5171	−	20.0545i	−0.635745	−	0.771899i
$676$	8.17341	+	14.1568i	0.314362	+	0.544491i
$677$	40.0923	+	10.7427i	1.54087	+	0.412876i	0.926548	−	0.376177i	$-0.122761\pi$
$677$	40.0923	+	10.7427i	1.54087	+	0.412876i	0.614326	+	0.789053i	$0.289428\pi$
$678$	0.0996199	−	0.831482i	0.00382588	−	0.0319329i
$679$	−4.01983	−	3.59643i	−0.154267	−	0.138018i
$680$	−6.86389	−	3.96515i	−0.263218	−	0.152057i
$681$	−16.1998	+	40.4369i	−0.620779	+	1.54954i
$682$	−23.2064	−	23.2064i	−0.888619	−	0.888619i
$683$	7.83441	−	29.2384i	0.299775	−	1.11878i	−0.637575	−	0.770389i	$-0.720062\pi$
$683$	7.83441	−	29.2384i	0.299775	−	1.11878i	0.937350	−	0.348389i	$-0.113271\pi$
$684$	−9.98538	−	2.42754i	−0.381800	−	0.0928193i
$685$	0.678771	−	2.53068i	0.0259345	−	0.0966923i
$686$	18.4364	+	1.76039i	0.703905	+	0.0672118i
$687$	−10.1374	−	23.6889i	−0.386765	−	0.903786i
$688$	2.87199	−	2.87199i	0.109494	−	0.109494i
$689$	3.95712	−	6.85393i	0.150754	−	0.261114i
$690$	−26.3633	−	3.16526i	−1.00363	−	0.120499i
$691$	−6.49143	−	11.2435i	−0.246946	−	0.427722i	0.715731	−	0.698376i	$-0.246094\pi$
$691$	−6.49143	−	11.2435i	−0.246946	−	0.427722i	−0.962677	+	0.270654i	$0.912760\pi$
$692$	−6.78876	+	6.78876i	−0.258070	+	0.258070i
$693$	8.11268	−	43.8482i	0.308175	−	1.66566i
$694$		−	16.6112i		−	0.630554i
$695$	−21.2369	+	36.7623i	−0.805563	+	1.39447i
$696$	8.47656	−	6.66272i	0.321303	−	0.252550i
$697$	−1.82115	+	0.487975i	−0.0689809	+	0.0184834i
$698$	−3.53534	−	3.53534i	−0.133814	−	0.133814i
$699$	13.7156	−	10.7807i	0.518772	−	0.407763i
$700$	11.8029	+	5.97417i	0.446109	+	0.225802i
$701$		−	24.9232i		−	0.941337i	−0.882310	−	0.470669i	$-0.844013\pi$
$701$		−	24.9232i		−	0.941337i	0.882310	−	0.470669i	$-0.155987\pi$
$702$	21.7192	−	17.9064i	0.819739	−	0.675834i
$703$	−22.8564	−	6.12437i	−0.862047	−	0.230985i
$704$	5.61811			0.211741
$705$	0.354281	−	0.278328i	0.0133430	−	0.0104824i
$706$	−11.9646	−	20.7232i	−0.450292	−	0.779929i
$707$	5.58280	−	3.65077i	0.209963	−	0.137301i
$708$	−2.91317	+	3.88958i	−0.109484	+	0.146179i
$709$	32.6768	−	18.8660i	1.22720	−	0.708526i	0.260759	−	0.965404i	$-0.416027\pi$
$709$	32.6768	−	18.8660i	1.22720	−	0.708526i	0.966444	+	0.256878i	$0.0826938\pi$
$710$	5.31100	+	19.8407i	0.199318	+	0.744610i
$711$	−10.9199	+	44.9177i	−0.409529	+	1.68455i
$712$	−4.91946	+	1.31817i	−0.184365	+	0.0494004i
$713$	−38.6846	+	10.3655i	−1.44875	+	0.388191i
$714$	−7.21048	−	14.5574i	−0.269846	−	0.544797i
$715$	17.5974	+	65.7399i	0.658104	+	2.45853i
$716$		−	8.31789i		−	0.310854i
$717$	−17.7874	−	13.3222i	−0.664283	−	0.497527i
$718$	7.75361	−	7.75361i	0.289362	−	0.289362i
$719$	0.510343	−	0.883941i	0.0190326	−	0.0329654i	−0.856352	−	0.516392i	$-0.827275\pi$
$719$	0.510343	−	0.883941i	0.0190326	−	0.0329654i	0.875385	+	0.483427i	$0.160608\pi$
$720$	6.43786	−	1.88520i	0.239925	−	0.0702572i
$721$	−38.6837	−	8.09419i	−1.44065	−	0.301443i
$722$	1.88073	+	7.01899i	0.0699936	+	0.261220i
$723$	2.67106	−	1.14305i	0.0993377	−	0.0425104i
$724$	11.2454	+	6.49254i	0.417932	+	0.241293i
$725$	15.5485	+	26.9619i	0.577457	+	1.00134i
$726$	35.2552	−	5.06023i	1.30844	−	0.187803i
$727$	25.9622	−	6.95656i	0.962886	−	0.258005i	0.257065	−	0.966394i	$-0.417245\pi$
$727$	25.9622	−	6.95656i	0.962886	−	0.258005i	0.705822	+	0.708390i	$0.250578\pi$
$728$	−6.46636	+	12.7912i	−0.239659	+	0.474072i
$729$	−20.3796	−	17.7108i	−0.754798	−	0.655957i
$730$	−11.6004	−	0.00289540i	−0.429351	−	0.000107163i
$731$		−	14.3985i		−	0.532546i
$732$	6.18384	+	14.4503i	0.228561	+	0.534099i
$733$	−24.5734	+	24.5734i	−0.907638	+	0.907638i	−0.996081	−	0.0884431i	$-0.971811\pi$
$733$	−24.5734	+	24.5734i	−0.907638	+	0.907638i	0.0884431	+	0.996081i	$0.471811\pi$
$734$	5.88380	+	10.1910i	0.217175	+	0.376158i
$735$	13.3572	+	23.5920i	0.492689	+	0.870206i
$736$	3.42793	−	5.93734i	0.126355	−	0.218853i
$737$	3.72921	+	13.9176i	0.137367	+	0.512662i
$738$	0.765334	−	1.39999i	0.0281723	−	0.0515345i
$739$	−31.7659	+	18.3401i	−1.16853	+	0.674650i	−0.953333	−	0.301921i	$-0.902372\pi$
$739$	−31.7659	+	18.3401i	−1.16853	+	0.674650i	−0.215195	+	0.976571i	$0.569039\pi$
$740$	14.9214	−	3.99420i	0.548523	−	0.146830i
$741$	29.8354	+	11.9527i	1.09603	+	0.439092i
$742$	3.85929	−	0.214545i	0.141679	−	0.00787618i
$743$	−2.13351	+	7.96238i	−0.0782710	+	0.292111i	−0.993955	−	0.109787i	$-0.964983\pi$
$743$	−2.13351	+	7.96238i	−0.0782710	+	0.292111i	0.915684	+	0.401899i	$0.131650\pi$
$744$	7.95477	−	6.25258i	0.291636	−	0.229231i
$745$	−2.83325	+	1.63484i	−0.103802	+	0.0598957i
$746$	−16.3299	+	9.42808i	−0.597880	+	0.345186i
$747$	20.9476	−	38.3185i	0.766431	−	1.40200i
$748$	14.0829	−	14.0829i	0.514923	−	0.514923i
$749$	1.82753	−	2.04268i	0.0667765	−	0.0746380i
$750$	2.73693	+	19.1705i	0.0999384	+	0.700009i
$751$	10.0825			0.367915			0.183957	−	0.982934i	$-0.441109\pi$
$751$	10.0825			0.367915			0.183957	+	0.982934i	$0.441109\pi$
$752$	0.0301078	+	0.112364i	0.00109792	+	0.00409749i
$753$	0.396474	+	0.926473i	0.0144483	+	0.0337626i
$754$	−29.2036	+	16.8607i	−1.06353	+	0.614030i
$755$	−10.8670	+	6.27048i	−0.395492	+	0.228206i
$756$	13.1248	+	4.09149i	0.477343	+	0.148806i
$757$	−33.3785	−	33.3785i	−1.21316	−	1.21316i	−0.969981	−	0.243180i	$-0.921810\pi$
$757$	−33.3785	−	33.3785i	−1.21316	−	1.21316i	−0.243180	−	0.969981i	$-0.578190\pi$
$758$	−7.57774	+	28.2805i	−0.275236	+	1.02719i
$759$	24.8098	−	61.9285i	0.900540	−	2.24786i
$760$	5.41469	+	5.41739i	0.196411	+	0.196510i
$761$			41.8161i			1.51583i	0.652351	+	0.757917i	$0.273783\pi$
$761$			41.8161i			1.51583i	−0.652351	+	0.757917i	$0.726217\pi$
$762$	−22.7334	−	17.0266i	−0.823543	−	0.616807i
$763$	3.10304	+	1.56869i	0.112338	+	0.0567904i
$764$	12.1652			0.440121
$765$	11.4122	−	20.8634i	0.412607	−	0.754318i
$766$	−10.0800	−	17.4590i	−0.364204	−	0.630820i
$767$	10.7474	−	10.7474i	0.388065	−	0.388065i
$768$	−0.206043	+	1.71975i	−0.00743495	+	0.0620562i
$769$	41.6771	−	24.0623i	1.50292	−	0.867709i	0.502922	−	0.864332i	$-0.332258\pi$
$769$	41.6771	−	24.0623i	1.50292	−	0.867709i	0.999994	−	0.00337699i	$-0.00107493\pi$
$770$	−22.1677	+	24.7650i	−0.798868	+	0.892469i
$771$	−1.36871	+	3.41647i	−0.0492927	+	0.123041i
$772$	−3.96701	+	14.8051i	−0.142776	+	0.532847i
$773$	4.00832	−	14.9592i	0.144169	−	0.538046i	−0.855622	−	0.517601i	$-0.826825\pi$
$773$	4.00832	−	14.9592i	0.144169	−	0.538046i	0.999791	−	0.0204450i	$-0.00650830\pi$
$774$	8.81451	+	8.41277i	0.316831	+	0.302391i
$775$	14.5914	+	25.3022i	0.524138	+	0.908881i
$776$	1.76554	+	1.01934i	0.0633794	+	0.0365921i
$777$	29.9942	+	10.1234i	1.07603	+	0.363174i
$778$	−6.73162	−	1.80373i	−0.241340	−	0.0646670i
$779$	1.82178			0.0652721
$780$	−20.7689	+	2.97570i	−0.743646	+	0.106547i
$781$	−51.6049			−1.84657
$782$	−6.29036	−	23.4759i	−0.224943	−	0.839497i
$783$	20.5756	+	24.9568i	0.735312	+	0.891882i
$784$	−6.95687	+	0.775887i	−0.248460	+	0.0277102i
$785$	2.54060	−	2.53933i	0.0906777	−	0.0906325i
$786$	−2.75575	−	19.1996i	−0.0982945	−	0.684829i
$787$	28.4051	−	7.61113i	1.01253	−	0.271307i	0.285846	−	0.958276i	$-0.407726\pi$
$787$	28.4051	−	7.61113i	1.01253	−	0.271307i	0.726687	+	0.686968i	$0.241059\pi$
$788$	7.57747	−	2.03038i	0.269936	−	0.0723292i
$789$	−45.7267	−	18.3190i	−1.62791	−	0.652175i
$790$	24.3693	−	24.3572i	0.867022	−	0.866589i
$791$	−1.21532	+	0.399153i	−0.0432120	+	0.0141922i
$792$	0.392944	+	16.8498i	0.0139627	+	0.598730i
$793$	−12.7236	−	47.4851i	−0.451828	−	1.68624i
$794$	13.2757			0.471135
$795$	3.49545	+	4.44932i	0.123971	+	0.157801i
$796$	−5.34906			−0.189592
$797$	−21.6608	−	5.80399i	−0.767265	−	0.205588i	−0.146102	−	0.989270i	$-0.546673\pi$
$797$	−21.6608	−	5.80399i	−0.767265	−	0.205588i	−0.621163	+	0.783681i	$0.713339\pi$
$798$	3.08920	+	15.3902i	0.109356	+	0.544807i
$799$	0.357134	+	0.206191i	0.0126345	+	0.00729452i
$800$	−4.82898	−	1.29651i	−0.170730	−	0.0458384i
$801$	−4.29750	−	14.6622i	−0.151845	−	0.518063i
$802$	−6.08306	+	22.7023i	−0.214800	+	0.801645i
$803$	7.54355	−	28.1529i	0.266206	−	0.993494i
$804$	−4.39707	+	0.631118i	−0.155073	+	0.0222578i
$805$	12.6464	+	38.5378i	0.445729	+	1.35828i
$806$	−27.4059	+	15.8228i	−0.965331	+	0.557334i
$807$	−16.8358	−	12.6095i	−0.592647	−	0.443874i
$808$	−1.78277	+	1.78277i	−0.0627177	+	0.0627177i
$809$	0.895949	+	1.55183i	0.0314999	+	0.0545594i	0.881346	−	0.472472i	$-0.156638\pi$
$809$	0.895949	+	1.55183i	0.0314999	+	0.0545594i	−0.849846	+	0.527032i	$0.823305\pi$
$810$	6.10434	+	19.1765i	0.214485	+	0.673793i
$811$	44.6319			1.56724			0.783619	−	0.621242i	$-0.213371\pi$
$811$	44.6319			1.56724			0.783619	+	0.621242i	$0.213371\pi$
$812$	−14.6979	−	7.43025i	−0.515794	−	0.260751i
$813$	−3.50706	+	29.2718i	−0.122998	+	1.02661i
$814$			38.8100i			1.36029i
$815$	31.6932	+	31.7090i	1.11016	+	1.11072i
$816$	3.79441	+	4.82739i	0.132831	+	0.168993i
$817$	−3.60087	+	13.4386i	−0.125978	+	0.470158i
$818$	−11.8883	−	11.8883i	−0.415664	−	0.415664i
$819$	−38.8153	−	18.4992i	−1.35632	−	0.646413i
$820$	−1.03006	+	0.594363i	−0.0359712	+	0.0207560i
$821$	48.6014	−	28.0600i	1.69620	−	0.979301i	0.746896	−	0.664940i	$-0.231543\pi$
$821$	48.6014	−	28.0600i	1.69620	−	0.979301i	0.949303	−	0.314361i	$-0.101790\pi$
$822$	−1.21665	+	1.62444i	−0.0424356	+	0.0566588i
$823$	6.79204	+	25.3482i	0.236756	+	0.883584i	0.977350	+	0.211631i	$0.0678776\pi$
$823$	6.79204	+	25.3482i	0.236756	+	0.883584i	−0.740594	+	0.671953i	$0.765456\pi$
$824$	14.9377			0.520379
$825$	−48.3059	−	5.81199i	−1.68180	−	0.202348i
$826$	7.26576	+	1.52029i	0.252808	+	0.0528977i
$827$	−31.1516	+	31.1516i	−1.08325	+	1.08325i	−0.0870414	+	0.996205i	$0.527741\pi$
$827$	−31.1516	+	31.1516i	−1.08325	+	1.08325i	−0.996205	+	0.0870414i	$0.972259\pi$
$828$	18.0469	+	9.86571i	0.627175	+	0.342857i
$829$	−28.9067	+	16.6893i	−1.00397	+	0.579642i	−0.909421	−	0.415878i	$-0.863474\pi$
$829$	−28.9067	+	16.6893i	−1.00397	+	0.579642i	−0.0945496	+	0.995520i	$0.530141\pi$
$830$	−28.1932	+	16.2680i	−0.978601	+	0.564670i
$831$	−28.6926	−	11.4948i	−0.995335	−	0.398751i
$832$	1.40209	−	5.23268i	0.0486088	−	0.181411i
$833$	−15.4939	+	19.3837i	−0.536831	+	0.671605i
$834$	25.8550	−	20.3225i	0.895285	−	0.703709i
$835$	−47.8125	+	12.7985i	−1.65462	+	0.442911i
$836$	−16.6661	+	9.62216i	−0.576408	+	0.332789i
$837$	19.3090	+	23.4205i	0.667418	+	0.809531i
$838$	9.01435	+	33.6420i	0.311395	+	1.16214i
$839$	−3.20025	+	5.54299i	−0.110485	+	0.191365i	−0.915966	−	0.401256i	$-0.868574\pi$
$839$	−3.20025	+	5.54299i	−0.110485	+	0.191365i	0.805481	+	0.592622i	$0.201907\pi$
$840$	−6.76778	−	7.69397i	−0.233511	−	0.265467i
$841$	−4.87399	−	8.44200i	−0.168069	−	0.291103i
$842$	19.8523	−	19.8523i	0.684155	−	0.684155i
$843$	15.8138	+	1.89465i	0.544656	+	0.0652552i
$844$			3.95709i			0.136209i
$845$	36.5526	+	0.00912332i	1.25745	+	0.000313852i
$846$	−0.334894	+	0.0981578i	−0.0115139	+	0.00337474i
$847$	−29.7759	−	45.5337i	−1.02311	−	1.56456i
$848$	−1.41115	+	0.378116i	−0.0484590	+	0.0129845i
$849$	−27.1673	−	34.5633i	−0.932380	−	1.18621i
$850$	−15.3548	+	8.85486i	−0.526664	+	0.303719i
$851$	41.0152	+	23.6801i	1.40598	+	0.811745i
$852$	1.89260	−	15.7967i	0.0648394	−	0.541185i
$853$	0.597276	+	2.22906i	0.0204503	+	0.0763217i	0.975397	−	0.220456i	$-0.0707546\pi$
$853$	0.597276	+	2.22906i	0.0204503	+	0.0763217i	−0.954947	+	0.296778i	$0.904088\pi$
$854$	16.0087	−	17.8934i	0.547807	−	0.612299i
$855$	−15.8691	+	16.6186i	−0.542710	+	0.568343i
$856$	−0.517978	+	0.897164i	−0.0177041	+	0.0306644i
$857$	−4.82860	+	4.82860i	−0.164942	+	0.164942i	−0.784752	−	0.619810i	$-0.787210\pi$
$857$	−4.82860	+	4.82860i	−0.164942	+	0.164942i	0.619810	+	0.784752i	$0.287210\pi$
$858$	6.27090	−	52.3404i	0.214085	−	1.78687i
$859$			41.1543i			1.40417i	0.712094	+	0.702084i	$0.247747\pi$
$859$			41.1543i			1.40417i	−0.712094	+	0.702084i	$0.752253\pi$
$860$	−2.34842	−	8.77317i	−0.0800803	−	0.299162i
$861$	−2.43227	−	0.155163i	−0.0828916	−	0.00528793i
$862$	−32.4106	+	8.68439i	−1.10391	+	0.295791i
$863$	39.2484	−	10.5166i	1.33603	−	0.357989i	0.481071	−	0.876682i	$-0.340248\pi$
$863$	39.2484	−	10.5166i	1.33603	−	0.357989i	0.854961	+	0.518693i	$0.173581\pi$
$864$	−5.17226	−	0.497679i	−0.175964	−	0.0169314i
$865$	5.55114	+	20.7378i	0.188744	+	0.705107i
$866$	13.6472	−	7.87924i	0.463752	−	0.267747i
$867$	−7.62350	−	0.913371i	−0.258908	−	0.0310197i
$868$	−13.7931	−	6.97287i	−0.468168	−	0.236675i
$869$	43.2838	+	74.9698i	1.46830	+	2.54318i
$870$	−3.41927	−	23.8648i	−0.115924	−	0.809092i
$871$	13.8935			0.470763
$872$	−1.26941	−	0.340137i	−0.0429876	−	0.0115185i
$873$	−2.93370	+	5.36649i	−0.0992906	+	0.181628i
$874$			23.4841i			0.794361i
$875$	24.7691	−	16.1708i	0.837347	−	0.546672i
$876$	8.34118	+	3.34165i	0.281822	+	0.112904i
$877$	9.32872	+	9.32872i	0.315009	+	0.315009i	0.846846	−	0.531838i	$-0.178498\pi$
$877$	9.32872	+	9.32872i	0.315009	+	0.315009i	−0.531838	+	0.846846i	$0.678498\pi$
$878$	30.4321	−	8.15426i	1.02703	−	0.275193i
$879$	−1.89499	−	13.2026i	−0.0639164	−	0.445313i
$880$	6.28396	−	10.8779i	0.211832	−	0.366693i
$881$		−	9.10886i		−	0.306885i	−0.988158	−	0.153443i	$-0.950964\pi$
$881$		−	9.10886i		−	0.306885i	0.988158	−	0.153443i	$-0.0490360\pi$
$882$	−2.81361	−	20.8107i	−0.0947391	−	0.700731i
$883$	−12.5456	+	12.5456i	−0.422195	+	0.422195i	−0.885959	−	0.463764i	$-0.846499\pi$
$883$	−12.5456	+	12.5456i	−0.422195	+	0.422195i	0.463764	+	0.885959i	$0.346499\pi$
$884$	−9.60214	−	16.6314i	−0.322955	−	0.559374i
$885$	4.27262	+	9.99108i	0.143623	+	0.335846i
$886$	16.1640	−	27.9968i	0.543039	−	0.940571i
$887$	9.19655	−	9.19655i	0.308790	−	0.308790i	−0.535650	−	0.844440i	$-0.679933\pi$
$887$	9.19655	−	9.19655i	0.308790	−	0.308790i	0.844440	+	0.535650i	$0.179933\pi$
$888$	−11.8801	−	1.42335i	−0.398669	−	0.0477645i
$889$	−8.88563	+	42.4661i	−0.298014	+	1.42427i
$890$	−2.95025	+	10.9995i	−0.0988927	+	0.368705i
$891$	−50.5081	+	2.35702i	−1.69208	+	0.0789632i
$892$	−3.27990	+	12.2407i	−0.109819	+	0.409850i
$893$	−0.281760	−	0.281760i	−0.00942875	−	0.00942875i
$894$	2.50807	−	0.359987i	0.0838823	−	0.0120398i
$895$	−16.1052	−	9.30370i	−0.538338	−	0.310989i
$896$	2.51365	−	0.825566i	0.0839752	−	0.0275802i
$897$	−51.4882	−	38.5630i	−1.71914	−	1.28758i
$898$	32.8911	+	8.81315i	1.09759	+	0.294099i
$899$	−18.1814	−	31.4911i	−0.606383	−	1.05029i
$900$	3.55071	−	14.5737i	0.118357	−	0.485790i
$901$	−2.58950	+	4.48514i	−0.0862687	+	0.149422i
$902$	−0.773341	−	2.88615i	−0.0257494	−	0.0960982i
$903$	5.95211	−	17.6353i	0.198074	−	0.586865i
$904$	0.418714	−	0.241745i	0.0139262	−	0.00804031i
$905$	25.1491	−	14.5115i	0.835985	−	0.482378i
$906$	9.61980	−	1.38074i	0.319596	−	0.0458721i
$907$	−20.2838	−	20.2838i	−0.673513	−	0.673513i	0.285011	−	0.958524i	$-0.408003\pi$
$907$	−20.2838	−	20.2838i	−0.673513	−	0.673513i	−0.958524	+	0.285011i	$0.908003\pi$
$908$	−24.2931	+	6.50931i	−0.806194	+	0.216019i
$909$	−5.47155	−	5.22217i	−0.181480	−	0.173208i
$910$	17.5337	+	26.8274i	0.581236	+	0.889319i
$911$	−28.5182	−	16.4650i	−0.944850	−	0.545509i	−0.0533726	−	0.998575i	$-0.516997\pi$
$911$	−28.5182	−	16.4650i	−0.944850	−	0.545509i	−0.891477	+	0.453065i	$0.850330\pi$
$912$	−2.33420	−	5.45452i	−0.0772930	−	0.180617i
$913$	−21.1667	−	78.9952i	−0.700516	−	2.61436i
$914$	−14.0174	+	24.2789i	−0.463655	+	0.803074i
$915$	34.8956	+	4.18967i	1.15361	+	0.138506i
$916$	7.43824	−	12.8834i	0.245766	−	0.425680i
$917$	−24.7972	+	16.2156i	−0.818876	+	0.535488i
$918$	−14.2128	+	11.7178i	−0.469094	+	0.386745i
$919$	20.3805	+	11.7667i	0.672292	+	0.388148i	0.796944	−	0.604053i	$-0.206448\pi$
$919$	20.3805	+	11.7667i	0.672292	+	0.388148i	−0.124653	+	0.992200i	$0.539782\pi$
$920$	−7.66176	−	13.2782i	−0.252601	−	0.437770i
$921$	−18.0423	−	7.22812i	−0.594515	−	0.238175i
$922$	−4.27674	−	4.27674i	−0.140847	−	0.140847i
$923$	−12.8788	+	48.0645i	−0.423912	+	1.58206i
$924$	23.0705	−	11.4271i	0.758964	−	0.375925i
$925$	8.95627	−	33.3586i	0.294480	−	1.09683i
$926$	10.2427	+	5.91364i	0.336597	+	0.194334i
$927$	1.04478	+	44.8009i	0.0343150	+	1.47145i
$928$	6.01268	+	1.61109i	0.197376	+	0.0528867i
$929$	−14.8040	−	25.6412i	−0.485702	−	0.841261i	0.514163	−	0.857693i	$-0.328103\pi$
$929$	−14.8040	−	25.6412i	−0.485702	−	0.841261i	−0.999865	+	0.0164317i	$0.994769\pi$
$930$	−3.20879	−	22.3957i	−0.105220	−	0.734385i
$931$	19.3086	−	14.2167i	0.632814	−	0.465934i
$932$	9.72889	+	2.60685i	0.318680	+	0.0853902i
$933$	10.9578	+	1.31286i	0.358743	+	0.0429810i
$934$		−	14.0299i		−	0.459072i
$935$	−11.5155	−	43.0195i	−0.376599	−	1.40689i
$936$	15.7918	+	3.83915i	0.516173	+	0.125487i
$937$	9.71004	+	9.71004i	0.317213	+	0.317213i	0.847696	−	0.530483i	$-0.177989\pi$
$937$	9.71004	+	9.71004i	0.317213	+	0.317213i	−0.530483	+	0.847696i	$0.677989\pi$
$938$	3.71368	+	5.67901i	0.121256	+	0.185426i
$939$	49.7039	−	7.13407i	1.62203	−	0.232812i
$940$	0.251236	+	0.0673858i	0.00819443	+	0.00219788i
$941$	−32.5111	−	18.7703i	−1.05983	−	0.611894i	−0.134446	−	0.990921i	$-0.542925\pi$
$941$	−32.5111	−	18.7703i	−1.05983	−	0.611894i	−0.925386	+	0.379027i	$0.876259\pi$
$942$	−2.55800	+	1.09467i	−0.0833443	+	0.0356662i
$943$	−3.52200	−	0.943717i	−0.114692	−	0.0307317i
$944$	−2.80567			−0.0913168
$945$	22.6023	−	20.8360i	0.735252	−	0.677794i
$946$	22.8186			0.741897
$947$	37.2481	+	9.98059i	1.21040	+	0.324325i	0.806919	−	0.590663i	$-0.201134\pi$
$947$	37.2481	+	9.98059i	1.21040	+	0.324325i	0.403481	+	0.914988i	$0.367800\pi$
$948$	−24.5363	+	10.5000i	−0.796903	+	0.341025i
$949$	−24.3388	−	14.0520i	−0.790072	−	0.456148i
$950$	16.5457	−	4.42454i	0.536812	−	0.143551i
$951$	48.5218	−	6.96441i	1.57343	−	0.225836i
$952$	4.23152	−	8.37042i	0.137144	−	0.271287i
$953$	−26.9503	−	26.9503i	−0.873007	−	0.873007i	0.119792	−	0.992799i	$-0.461777\pi$
$953$	−26.9503	−	26.9503i	−0.873007	−	0.873007i	−0.992799	+	0.119792i	$0.961777\pi$
$954$	−1.23274	−	4.20584i	−0.0399113	−	0.136169i
$955$	13.6070	−	23.5544i	0.440311	−	0.762202i
$956$		−	12.8306i		−	0.414971i
$957$	60.1424	+	7.20566i	1.94413	+	0.232926i
$958$	40.3847	+	10.8210i	1.30477	+	0.349612i
$959$	3.03446	+	0.634933i	0.0979879	+	0.0205030i
$960$	3.09934	+	2.32252i	0.100031	+	0.0749589i
$961$	−1.56219	−	2.70579i	−0.0503932	−	0.0872836i
$962$	36.1474	+	9.68567i	1.16544	+	0.312278i
$963$	−2.72699	−	1.49076i	−0.0878760	−	0.0480391i
$964$	1.45268	+	0.838705i	0.0467876	+	0.0270129i
$965$	24.2286	+	24.2407i	0.779948	+	0.780337i
$966$	2.00016	−	31.3537i	0.0643541	−	1.00879i
$967$	4.13435	−	15.4296i	0.132952	−	0.496183i	−0.867046	−	0.498228i	$-0.833984\pi$
$967$	4.13435	−	15.4296i	0.132952	−	0.496183i	0.999998	+	0.00204486i	$0.000650900\pi$
$968$	14.5404	+	14.5404i	0.467345	+	0.467345i
$969$	−19.5240	−	7.82170i	−0.627200	−	0.251269i
$970$	3.94845	−	2.27832i	0.126777	−	0.0731525i
$971$	−18.9731	−	10.9541i	−0.608876	−	0.351535i	0.163649	−	0.986519i	$-0.447673\pi$
$971$	−18.9731	−	10.9541i	−0.608876	−	0.351535i	−0.772526	+	0.634984i	$0.781007\pi$
$972$	1.13087	−	15.5474i	0.0362727	−	0.498683i
$973$	−44.8310	−	22.6636i	−1.43722	−	0.726561i
$974$	0.718455	−	1.24440i	0.0230208	−	0.0398732i
$975$	−17.4688	+	43.5414i	−0.559449	+	1.39444i
$976$	−4.53736	+	7.85893i	−0.145237	+	0.251558i
$977$	2.74473	+	10.2435i	0.0878117	+	0.327718i	0.995832	−	0.0912089i	$-0.0290731\pi$
$977$	2.74473	+	10.2435i	0.0878117	+	0.327718i	−0.908020	+	0.418927i	$0.862406\pi$
$978$	−13.6625	−	31.9263i	−0.436879	−	1.02089i
$979$	−24.7796	−	14.3065i	−0.791961	−	0.457239i
$980$	−6.27909	+	14.3378i	−0.200578	+	0.458005i
$981$	0.931349	−	3.83098i	0.0297357	−	0.122314i
$982$	−2.33371	+	0.625315i	−0.0744716	+	0.0199546i
$983$	18.2248	+	18.2248i	0.581280	+	0.581280i	0.935255	−	0.353975i	$-0.115170\pi$
$983$	18.2248	+	18.2248i	0.581280	+	0.581280i	−0.353975	+	0.935255i	$0.615170\pi$
$984$	0.911836	−	0.130877i	0.0290683	−	0.00417221i
$985$	4.54429	−	16.9426i	0.144793	−	0.539836i
$986$	19.1105	−	11.0335i	0.608603	−	0.351377i
$987$	0.352182	+	0.400178i	0.0112101	+	0.0127378i
$988$	4.80274	+	17.9241i	0.152795	+	0.570240i
$989$	13.9229	−	24.1152i	0.442723	−	0.766818i
$990$	33.0642	+	18.0859i	1.05085	+	0.574808i
$991$	−0.122795	−	0.212687i	−0.00390070	−	0.00675621i	0.864068	−	0.503374i	$-0.167908\pi$
$991$	−0.122795	−	0.212687i	−0.00390070	−	0.00675621i	−0.867969	+	0.496618i	$0.834575\pi$
$992$	5.64256	+	1.51192i	0.179151	+	0.0480035i
$993$	−5.59153	−	4.18788i	−0.177442	−	0.132898i
$994$	−23.0890	+	7.58319i	−0.732339	+	0.240524i
$995$	−5.98302	+	10.3569i	−0.189674	+	0.328336i
$996$	24.9574	−	3.58217i	0.790805	−	0.113505i
$997$	37.7285	+	37.7285i	1.19487	+	1.19487i	0.975682	+	0.219192i	$0.0703419\pi$
$997$	37.7285	+	37.7285i	1.19487	+	1.19487i	0.219192	+	0.975682i	$0.429658\pi$
$998$	1.76721	−	6.59530i	0.0559399	−	0.208771i
$999$	3.43797	−	35.7300i	0.108773	−	1.13045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bt.a.317.22	✓	192
5.3	odd	4	inner	630.2.bt.a.443.15	yes	192
7.4	even	3		630.2.cd.a.137.30	yes	192
9.5	odd	6		630.2.cd.a.527.17	yes	192
35.18	odd	12		630.2.cd.a.263.17	yes	192
45.23	even	12		630.2.cd.a.23.30	yes	192
63.32	odd	6	inner	630.2.bt.a.347.15	yes	192
315.158	even	12	inner	630.2.bt.a.473.22	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.22	✓	192	1.1	even	1	trivial
630.2.bt.a.347.15	yes	192	63.32	odd	6	inner
630.2.bt.a.443.15	yes	192	5.3	odd	4	inner
630.2.bt.a.473.22	yes	192	315.158	even	12	inner
630.2.cd.a.23.30	yes	192	45.23	even	12
630.2.cd.a.137.30	yes	192	7.4	even	3
630.2.cd.a.263.17	yes	192	35.18	odd	12
630.2.cd.a.527.17	yes	192	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bt (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.59237 - 0.681437i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.93677 - 1.11755i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(1.44802 + 2.21433i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07129 - 2.17020i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(1.59237 - 0.681437i) q^{3} +(0.866025 + 0.500000i) q^{4} +(1.93677 - 1.11755i) q^{5} +(-1.71448 + 0.246082i) q^{6} +(1.44802 + 2.21433i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.07129 - 2.17020i) q^{9} +(-2.16002 + 0.578198i) q^{10} -5.61811i q^{11} +(1.71975 + 0.206043i) q^{12} +(-5.23268 - 1.40209i) q^{13} +(-0.825566 - 2.51365i) q^{14} +(2.32252 - 3.09934i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.42422 + 0.917516i) q^{17} +(-2.56240 + 1.56016i) q^{18} +(-2.96649 - 1.71270i) q^{19} +(2.23607 + 0.000558109i) q^{20} +(3.81470 + 2.53930i) q^{21} +(-1.45407 + 5.42668i) q^{22} +(4.84782 + 4.84782i) q^{23} +(-1.60782 - 0.644127i) q^{24} +(2.50216 - 4.32888i) q^{25} +(4.69149 + 2.70864i) q^{26} +(1.81940 - 4.86721i) q^{27} +(0.146855 + 2.64167i) q^{28} +(-3.11239 + 5.39082i) q^{29} +(-3.04555 + 2.39262i) q^{30} +(-2.92080 + 5.05898i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(-3.82839 - 8.94612i) q^{33} +(-3.07007 - 1.77250i) q^{34} +(5.27910 + 2.67041i) q^{35} +(2.87889 - 0.843805i) q^{36} +(6.67262 - 1.78792i) q^{37} +(2.42213 + 2.42213i) q^{38} +(-9.28781 + 1.33309i) q^{39} +(-2.15973 - 0.579276i) q^{40} +(-0.460590 + 0.265922i) q^{41} +(-3.02750 - 3.44009i) q^{42} +(-1.05122 - 3.92322i) q^{43} +(2.80906 - 4.86543i) q^{44} +(1.58630 - 6.51795i) q^{45} +(-3.42793 - 5.93734i) q^{46} +(0.112364 + 0.0301078i) q^{47} +(1.38633 + 1.03831i) q^{48} +(-2.80650 + 6.41277i) q^{49} +(-3.53730 + 3.53377i) q^{50} +(6.07785 - 0.872363i) q^{51} +(-3.83059 - 3.83059i) q^{52} +(-0.378116 + 1.41115i) q^{53} +(-3.01713 + 4.23047i) q^{54} +(-6.27853 - 10.8810i) q^{55} +(0.541864 - 2.58967i) q^{56} +(-5.89085 - 0.705782i) q^{57} +(4.40159 - 4.40159i) q^{58} +(-1.40284 + 2.42978i) q^{59} +(3.56103 - 1.52285i) q^{60} +(4.53736 + 7.85893i) q^{61} +(4.13064 - 4.13064i) q^{62} +(7.80479 + 1.44402i) q^{63} +1.00000i q^{64} +(-11.7014 + 3.13225i) q^{65} +(1.38252 + 9.63215i) q^{66} +(-2.47728 + 0.663784i) q^{67} +(2.50670 + 2.50670i) q^{68} +(11.0230 + 4.41604i) q^{69} +(-4.40806 - 3.94575i) q^{70} -9.18544i q^{71} +(-2.99918 + 0.0699423i) q^{72} +(5.01109 + 1.34272i) q^{73} -6.90801 q^{74} +(1.03451 - 8.59824i) q^{75} +(-1.71270 - 2.96649i) q^{76} +(12.4403 - 8.13512i) q^{77} +(9.31636 + 1.11619i) q^{78} +(-13.3443 + 7.70434i) q^{79} +(1.93621 + 1.11852i) q^{80} +(-0.419540 - 8.99022i) q^{81} +(0.513722 - 0.137651i) q^{82} +(14.0608 - 3.76758i) q^{83} +(2.03398 + 4.10645i) q^{84} +(7.65729 - 2.04972i) q^{85} +4.06161i q^{86} +(-1.28258 + 10.7051i) q^{87} +(-3.97261 + 3.97261i) q^{88} +(2.54650 - 4.41067i) q^{89} +(-3.21922 + 5.88529i) q^{90} +(-4.47232 - 13.6171i) q^{91} +(1.77443 + 6.62225i) q^{92} +(-1.20362 + 10.0461i) q^{93} +(-0.100743 - 0.0581638i) q^{94} +(-7.65944 - 0.00191175i) q^{95} +(-1.07035 - 1.36174i) q^{96} +(-1.96921 + 0.527648i) q^{97} +(4.37061 - 5.46788i) q^{98} +(-12.1924 - 11.6367i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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