LMFDB - Embedded newform 820.2.bo.b.21.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(21,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([0, 0, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.21"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bo (of order $20$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			21.5
Character	$\chi$	$=$	820.21
Dual form			820.2.bo.b.781.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.335549 + 0.335549i) q^{3} +(0.587785 - 0.809017i) q^{5} +(-1.60673 + 3.15338i) q^{7} -2.77481i q^{9} +(-2.50592 - 0.396899i) q^{11} +(-5.67658 + 2.89236i) q^{13} +(0.468696 - 0.0742341i) q^{15} +(-1.22640 + 7.74315i) q^{17} +(6.40838 + 3.26523i) q^{19} +(-1.59725 + 0.518977i) q^{21} +(-1.77180 + 5.45303i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(1.93773 - 1.93773i) q^{27} +(-0.175572 - 1.10852i) q^{29} +(1.92551 - 1.39897i) q^{31} +(-0.707681 - 0.974039i) q^{33} +(1.60673 + 3.15338i) q^{35} +(-9.02710 - 6.55857i) q^{37} +(-2.87530 - 0.934242i) q^{39} +(-2.64208 + 5.83261i) q^{41} +(9.56664 + 3.10839i) q^{43} +(-2.24487 - 1.63099i) q^{45} +(-4.33116 - 8.50037i) q^{47} +(-3.24772 - 4.47011i) q^{49} +(-3.00972 + 2.18669i) q^{51} +(0.794447 + 5.01594i) q^{53} +(-1.79404 + 1.79404i) q^{55} +(1.05468 + 3.24597i) q^{57} +(-2.65621 + 8.17497i) q^{59} +(4.00604 - 1.30164i) q^{61} +(8.75003 + 4.45836i) q^{63} +(-0.996641 + 6.29254i) q^{65} +(2.69023 - 0.426091i) q^{67} +(-2.42428 + 1.23523i) q^{69} +(3.25817 + 0.516043i) q^{71} +5.65957i q^{73} +(0.215436 - 0.422816i) q^{75} +(5.27790 - 7.26441i) q^{77} +(-3.23457 - 3.23457i) q^{79} -7.02403 q^{81} -6.85729 q^{83} +(5.54349 + 5.54349i) q^{85} +(0.313049 - 0.430875i) q^{87} +(-3.16286 + 6.20747i) q^{89} -22.5476i q^{91} +(1.11553 + 0.176682i) q^{93} +(6.40838 - 3.26523i) q^{95} +(-0.669208 + 0.105992i) q^{97} +(-1.10132 + 6.95347i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) $ 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.335549	+	0.335549i	0.193729	+	0.193729i	0.797305	−	0.603576i	$-0.206258\pi$
$3$	0.335549	+	0.335549i	0.193729	+	0.193729i	−0.603576	+	0.797305i	$0.706258\pi$
$4$		0			0
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$5$	0.587785	−	0.809017i	0.262866	−	0.361803i
$6$		0			0
$7$	−1.60673	+	3.15338i	−0.607285	+	1.19186i	0.358745	+	0.933436i	$0.383205\pi$
$7$	−1.60673	+	3.15338i	−0.607285	+	1.19186i	−0.966030	+	0.258429i	$0.916795\pi$
$8$		0			0
$9$		−	2.77481i		−	0.924938i
$10$		0			0
$11$	−2.50592	−	0.396899i	−0.755564	−	0.119670i	−0.233243	−	0.972418i	$-0.574934\pi$
$11$	−2.50592	−	0.396899i	−0.755564	−	0.119670i	−0.522321	+	0.852749i	$0.674934\pi$
$12$		0			0
$13$	−5.67658	+	2.89236i	−1.57440	+	0.802197i	−0.999867	−	0.0162837i	$-0.994817\pi$
$13$	−5.67658	+	2.89236i	−1.57440	+	0.802197i	−0.574534	+	0.818481i	$0.694817\pi$
$14$		0			0
$15$	0.468696	−	0.0742341i	0.121017	−	0.0191672i
$16$		0			0
$17$	−1.22640	+	7.74315i	−0.297445	+	1.87799i	0.157571	+	0.987508i	$0.449634\pi$
$17$	−1.22640	+	7.74315i	−0.297445	+	1.87799i	−0.455016	+	0.890483i	$0.650366\pi$
$18$		0			0
$19$	6.40838	+	3.26523i	1.47018	+	0.749096i	0.991648	−	0.128972i	$-0.0411677\pi$
$19$	6.40838	+	3.26523i	1.47018	+	0.749096i	0.478536	+	0.878068i	$0.341168\pi$
$20$		0			0
$21$	−1.59725	+	0.518977i	−0.348548	+	0.113250i
$22$		0			0
$23$	−1.77180	+	5.45303i	−0.369445	+	1.13704i	0.577705	+	0.816246i	$0.303948\pi$
$23$	−1.77180	+	5.45303i	−0.369445	+	1.13704i	−0.947150	+	0.320790i	$0.896052\pi$
$24$		0			0
$25$	−0.309017	−	0.951057i	−0.0618034	−	0.190211i
$26$		0			0
$27$	1.93773	−	1.93773i	0.372917	−	0.372917i
$28$		0			0
$29$	−0.175572	−	1.10852i	−0.0326029	−	0.205846i	0.966010	−	0.258506i	$-0.0832302\pi$
$29$	−0.175572	−	1.10852i	−0.0326029	−	0.205846i	−0.998613	+	0.0526596i	$0.983230\pi$
$30$		0			0
$31$	1.92551	−	1.39897i	0.345832	−	0.251262i	−0.401286	−	0.915953i	$-0.631437\pi$
$31$	1.92551	−	1.39897i	0.345832	−	0.251262i	0.747119	+	0.664691i	$0.231437\pi$
$32$		0			0
$33$	−0.707681	−	0.974039i	−0.123191	−	0.169558i
$34$		0			0
$35$	1.60673	+	3.15338i	0.271586	+	0.533018i
$36$		0			0
$37$	−9.02710	−	6.55857i	−1.48405	−	1.07822i	−0.976225	−	0.216759i	$-0.930451\pi$
$37$	−9.02710	−	6.55857i	−1.48405	−	1.07822i	−0.507820	−	0.861463i	$-0.669549\pi$
$38$		0			0
$39$	−2.87530	−	0.934242i	−0.460417	−	0.149598i
$40$		0			0
$41$	−2.64208	+	5.83261i	−0.412624	+	0.910901i
$41$	−2.64208	+	5.83261i	−0.412624	+	0.910901i
$42$		0			0
$43$	9.56664	+	3.10839i	1.45890	+	0.474025i	0.927734	−	0.373243i	$-0.121754\pi$
$43$	9.56664	+	3.10839i	1.45890	+	0.474025i	0.531165	+	0.847268i	$0.321754\pi$
$44$		0			0
$45$	−2.24487	−	1.63099i	−0.334646	−	0.243134i
$46$		0			0
$47$	−4.33116	−	8.50037i	−0.631764	−	1.23991i	−0.955843	−	0.293877i	$-0.905054\pi$
$47$	−4.33116	−	8.50037i	−0.631764	−	1.23991i	0.324079	−	0.946030i	$-0.394946\pi$
$48$		0			0
$49$	−3.24772	−	4.47011i	−0.463960	−	0.638586i
$50$		0			0
$51$	−3.00972	+	2.18669i	−0.421446	+	0.306198i
$52$		0			0
$53$	0.794447	+	5.01594i	0.109126	+	0.688992i	0.980225	+	0.197886i	$0.0634075\pi$
$53$	0.794447	+	5.01594i	0.109126	+	0.688992i	−0.871099	+	0.491107i	$0.836593\pi$
$54$		0			0
$55$	−1.79404	+	1.79404i	−0.241909	+	0.241909i
$56$		0			0
$57$	1.05468	+	3.24597i	0.139696	+	0.429940i
$58$		0			0
$59$	−2.65621	+	8.17497i	−0.345809	+	1.06429i	0.615340	+	0.788262i	$0.289019\pi$
$59$	−2.65621	+	8.17497i	−0.345809	+	1.06429i	−0.961149	+	0.276029i	$0.910981\pi$
$60$		0			0
$61$	4.00604	−	1.30164i	0.512921	−	0.166658i	−0.0411093	−	0.999155i	$-0.513089\pi$
$61$	4.00604	−	1.30164i	0.512921	−	0.166658i	0.554030	+	0.832497i	$0.313089\pi$
$62$		0			0
$63$	8.75003	+	4.45836i	1.10240	+	0.561701i
$64$		0			0
$65$	−0.996641	+	6.29254i	−0.123618	+	0.780494i
$66$		0			0
$67$	2.69023	−	0.426091i	0.328664	−	0.0520553i	0.0100781	−	0.999949i	$-0.496792\pi$
$67$	2.69023	−	0.426091i	0.328664	−	0.0520553i	0.318586	+	0.947894i	$0.396792\pi$
$68$		0			0
$69$	−2.42428	+	1.23523i	−0.291849	+	0.148705i
$70$		0			0
$71$	3.25817	+	0.516043i	0.386673	+	0.0612430i	0.346745	−	0.937959i	$-0.387287\pi$
$71$	3.25817	+	0.516043i	0.386673	+	0.0612430i	0.0399285	+	0.999203i	$0.487287\pi$
$72$		0			0
$73$			5.65957i			0.662403i	0.943560	+	0.331201i	$0.107454\pi$
$73$			5.65957i			0.662403i	−0.943560	+	0.331201i	$0.892546\pi$
$74$		0			0
$75$	0.215436	−	0.422816i	0.0248764	−	0.0488226i
$76$		0			0
$77$	5.27790	−	7.26441i	0.601473	−	0.827856i
$78$		0			0
$79$	−3.23457	−	3.23457i	−0.363918	−	0.363918i	0.501335	−	0.865253i	$-0.332842\pi$
$79$	−3.23457	−	3.23457i	−0.363918	−	0.363918i	−0.865253	+	0.501335i	$0.832842\pi$
$80$		0			0
$81$	−7.02403			−0.780448
$82$		0			0
$83$	−6.85729			−0.752685			−0.376343	−	0.926481i	$-0.622818\pi$
$83$	−6.85729			−0.752685			−0.376343	+	0.926481i	$0.622818\pi$
$84$		0			0
$85$	5.54349	+	5.54349i	0.601276	+	0.601276i
$86$		0			0
$87$	0.313049	−	0.430875i	0.0335623	−	0.0461946i
$88$		0			0
$89$	−3.16286	+	6.20747i	−0.335263	+	0.657990i	−0.995674	−	0.0929136i	$-0.970382\pi$
$89$	−3.16286	+	6.20747i	−0.335263	+	0.657990i	0.660411	+	0.750904i	$0.270382\pi$
$90$		0			0
$91$		−	22.5476i		−	2.36364i
$92$		0			0
$93$	1.11553	+	0.176682i	0.115675	+	0.0183211i
$94$		0			0
$95$	6.40838	−	3.26523i	0.657486	−	0.335006i
$96$		0			0
$97$	−0.669208	+	0.105992i	−0.0679477	+	0.0107619i	−0.190316	−	0.981723i	$-0.560951\pi$
$97$	−0.669208	+	0.105992i	−0.0679477	+	0.0107619i	0.122368	+	0.992485i	$0.460951\pi$
$98$		0			0
$99$	−1.10132	+	6.95347i	−0.110687	+	0.698850i
$100$		0			0
$101$	−1.55392	−	0.791759i	−0.154620	−	0.0787830i	0.374968	−	0.927038i	$-0.377654\pi$
$101$	−1.55392	−	0.791759i	−0.154620	−	0.0787830i	−0.529588	+	0.848255i	$0.677654\pi$
$102$		0			0
$103$	−3.09793	+	1.00658i	−0.305248	+	0.0991810i	−0.457636	−	0.889140i	$-0.651304\pi$
$103$	−3.09793	+	1.00658i	−0.305248	+	0.0991810i	0.152388	+	0.988321i	$0.451304\pi$
$104$		0			0
$105$	−0.518977	+	1.59725i	−0.0506470	+	0.155875i
$106$		0			0
$107$	−4.37269	−	13.4577i	−0.422724	−	1.30101i	−0.905157	−	0.425077i	$-0.860247\pi$
$107$	−4.37269	−	13.4577i	−0.422724	−	1.30101i	0.482434	−	0.875932i	$-0.339753\pi$
$108$		0			0
$109$	11.7506	−	11.7506i	1.12550	−	1.12550i	0.134603	−	0.990900i	$-0.457024\pi$
$109$	11.7506	−	11.7506i	1.12550	−	1.12550i	0.990900	−	0.134603i	$-0.0429760\pi$
$110$		0			0
$111$	−0.828312	−	5.22975i	−0.0786199	−	0.496386i
$112$		0			0
$113$	7.11657	−	5.17049i	0.669470	−	0.486399i	−0.200378	−	0.979719i	$-0.564217\pi$
$113$	7.11657	−	5.17049i	0.669470	−	0.486399i	0.869848	+	0.493320i	$0.164217\pi$
$114$		0			0
$115$	3.37016	+	4.63862i	0.314269	+	0.432554i
$116$		0			0
$117$	8.02577	+	15.7515i	0.741983	+	1.45622i
$118$		0			0
$119$	−22.4466	−	16.3084i	−2.05768	−	1.49499i
$120$		0			0
$121$	−4.33950	−	1.40999i	−0.394500	−	0.128181i
$122$		0			0
$123$	−2.84368	+	1.07058i	−0.256406	+	0.0965309i
$124$		0			0
$125$	−0.951057	−	0.309017i	−0.0850651	−	0.0276393i
$126$		0			0
$127$	−2.40858	−	1.74994i	−0.213727	−	0.155282i	0.475771	−	0.879569i	$-0.342169\pi$
$127$	−2.40858	−	1.74994i	−0.213727	−	0.155282i	−0.689498	+	0.724287i	$0.742169\pi$
$128$		0			0
$129$	2.16706	+	4.25309i	0.190799	+	0.374464i
$130$		0			0
$131$	1.89615	+	2.60982i	0.165667	+	0.228021i	0.883777	−	0.467909i	$-0.154992\pi$
$131$	1.89615	+	2.60982i	0.165667	+	0.228021i	−0.718110	+	0.695930i	$0.754992\pi$
$132$		0			0
$133$	−20.5930	+	14.9617i	−1.78564	+	1.29734i
$134$		0			0
$135$	−0.428688	−	2.70663i	−0.0368956	−	0.232950i
$136$		0			0
$137$	4.26084	−	4.26084i	0.364028	−	0.364028i	−0.501265	−	0.865294i	$-0.667132\pi$
$137$	4.26084	−	4.26084i	0.364028	−	0.364028i	0.865294	+	0.501265i	$0.167132\pi$
$138$		0			0
$139$	5.47195	+	16.8409i	0.464125	+	1.42843i	0.860080	+	0.510159i	$0.170414\pi$
$139$	5.47195	+	16.8409i	0.464125	+	1.42843i	−0.395955	+	0.918270i	$0.629586\pi$
$140$		0			0
$141$	1.39898	−	4.30561i	0.117815	−	0.362598i
$142$		0			0
$143$	15.3731	−	4.99501i	1.28556	−	0.417704i
$144$		0			0
$145$	−1.00001	−	0.509529i	−0.0830461	−	0.0423141i
$146$		0			0
$147$	0.410170	−	2.58971i	0.0338302	−	0.213596i
$148$		0			0
$149$	−8.90861	+	1.41099i	−0.729822	+	0.115592i	−0.510277	−	0.860010i	$-0.670457\pi$
$149$	−8.90861	+	1.41099i	−0.729822	+	0.115592i	−0.219545	+	0.975602i	$0.570457\pi$
$150$		0			0
$151$	7.20210	−	3.66966i	0.586099	−	0.298632i	−0.135684	−	0.990752i	$-0.543323\pi$
$151$	7.20210	−	3.66966i	0.586099	−	0.298632i	0.721783	+	0.692120i	$0.243323\pi$
$152$		0			0
$153$	21.4858	+	3.40302i	1.73703	+	0.275118i
$154$		0			0
$155$		−	2.38006i		−	0.191171i
$156$		0			0
$157$	−0.641644	+	1.25930i	−0.0512088	+	0.100503i	−0.915193	−	0.403016i	$-0.867962\pi$
$157$	−0.641644	+	1.25930i	−0.0512088	+	0.100503i	0.863984	+	0.503519i	$0.167962\pi$
$158$		0			0
$159$	−1.41652	+	1.94967i	−0.112337	+	0.154619i
$160$		0			0
$161$	−14.3487	−	14.3487i	−1.13083	−	1.13083i
$162$		0			0
$163$	17.6003			1.37856			0.689280	−	0.724495i	$-0.257927\pi$
$163$	17.6003			1.37856			0.689280	+	0.724495i	$0.257927\pi$
$164$		0			0
$165$	−1.20398			−0.0937296
$166$		0			0
$167$	5.00032	+	5.00032i	0.386936	+	0.386936i	0.873593	−	0.486657i	$-0.161784\pi$
$167$	5.00032	+	5.00032i	0.386936	+	0.386936i	−0.486657	+	0.873593i	$0.661784\pi$
$168$		0			0
$169$	16.2166	−	22.3203i	1.24743	−	1.71694i
$170$		0			0
$171$	9.06042	−	17.7821i	0.692867	−	1.35983i
$172$		0			0
$173$		−	9.02118i		−	0.685867i	−0.939360	−	0.342934i	$-0.888579\pi$
$173$		−	9.02118i		−	0.685867i	0.939360	−	0.342934i	$-0.111421\pi$
$174$		0			0
$175$	3.49555	+	0.553640i	0.264238	+	0.0418512i
$176$		0			0
$177$	−3.63439	+	1.85181i	−0.273178	+	0.139191i
$178$		0			0
$179$	17.7104	−	2.80505i	1.32373	−	0.209659i	0.545753	−	0.837946i	$-0.316244\pi$
$179$	17.7104	−	2.80505i	1.32373	−	0.209659i	0.777982	+	0.628287i	$0.216244\pi$
$180$		0			0
$181$	−0.699509	+	4.41652i	−0.0519941	+	0.328278i	0.947957	+	0.318398i	$0.103145\pi$
$181$	−0.699509	+	4.41652i	−0.0519941	+	0.328278i	−0.999951	+	0.00987963i	$0.996855\pi$
$182$		0			0
$183$	1.78099	+	0.907458i	0.131654	+	0.0670812i
$184$		0			0
$185$	−10.6120	+	3.44804i	−0.780209	+	0.253505i
$186$		0			0
$187$	6.14650	−	18.9170i	0.449477	−	1.38335i
$188$		0			0
$189$	2.99700	+	9.22381i	0.217999	+	0.670933i
$190$		0			0
$191$	8.76921	−	8.76921i	0.634518	−	0.634518i	−0.314680	−	0.949198i	$-0.601897\pi$
$191$	8.76921	−	8.76921i	0.634518	−	0.634518i	0.949198	+	0.314680i	$0.101897\pi$
$192$		0			0
$193$	2.68951	+	16.9809i	0.193595	+	1.22231i	0.872695	+	0.488266i	$0.162371\pi$
$193$	2.68951	+	16.9809i	0.193595	+	1.22231i	−0.679099	+	0.734046i	$0.737629\pi$
$194$		0			0
$195$	−2.44588	+	1.77703i	−0.175153	+	0.127256i
$196$		0			0
$197$	−13.0478	−	17.9587i	−0.929617	−	1.27951i	−0.960009	−	0.279969i	$-0.909676\pi$
$197$	−13.0478	−	17.9587i	−0.929617	−	1.27951i	0.0303923	−	0.999538i	$-0.490324\pi$
$198$		0			0
$199$	6.61439	+	12.9815i	0.468881	+	0.920232i	0.997452	+	0.0713421i	$0.0227282\pi$
$199$	6.61439	+	12.9815i	0.468881	+	0.920232i	−0.528571	+	0.848889i	$0.677272\pi$
$200$		0			0
$201$	1.04568	+	0.759730i	0.0737565	+	0.0535873i
$202$		0			0
$203$	3.77767	+	1.22744i	0.265140	+	0.0861493i
$204$		0			0
$205$	3.16571	+	5.56582i	0.221103	+	0.388733i
$206$		0			0
$207$	15.1311	+	4.91641i	1.05169	+	0.341714i
$208$		0			0
$209$	−14.7629	−	10.7259i	−1.02117	−	0.741926i
$210$		0			0
$211$	5.15430	+	10.1159i	0.354837	+	0.696406i	0.997569	−	0.0696844i	$-0.0221992\pi$
$211$	5.15430	+	10.1159i	0.354837	+	0.696406i	−0.642732	+	0.766091i	$0.722199\pi$
$212$		0			0
$213$	0.920117	+	1.26643i	0.0630454	+	0.0867745i
$214$		0			0
$215$	8.13787	−	5.91251i	0.554998	−	0.403230i
$216$		0			0
$217$	1.31770	+	8.31962i	0.0894512	+	0.564773i
$218$		0			0
$219$	−1.89906	+	1.89906i	−0.128327	+	0.128327i
$220$		0			0
$221$	−15.4343	−	47.5018i	−1.03822	−	3.19532i
$222$		0			0
$223$	−0.374285	+	1.15193i	−0.0250639	+	0.0771389i	−0.962806	−	0.270193i	$-0.912912\pi$
$223$	−0.374285	+	1.15193i	−0.0250639	+	0.0771389i	0.937742	+	0.347332i	$0.112912\pi$
$224$		0			0
$225$	−2.63900	+	0.857465i	−0.175934	+	0.0571643i
$226$		0			0
$227$	1.44758	+	0.737581i	0.0960795	+	0.0489550i	0.501370	−	0.865233i	$-0.332830\pi$
$227$	1.44758	+	0.737581i	0.0960795	+	0.0489550i	−0.405290	+	0.914188i	$0.632830\pi$
$228$		0			0
$229$	−1.45104	+	9.16149i	−0.0958872	+	0.605408i	0.892215	+	0.451611i	$0.149150\pi$
$229$	−1.45104	+	9.16149i	−0.0958872	+	0.605408i	−0.988102	+	0.153798i	$0.950850\pi$
$230$		0			0
$231$	4.20856	−	0.666570i	0.276903	−	0.0438571i
$232$		0			0
$233$	−4.82792	+	2.45995i	−0.316287	+	0.161156i	−0.604926	−	0.796282i	$-0.706797\pi$
$233$	−4.82792	+	2.45995i	−0.316287	+	0.161156i	0.288639	+	0.957438i	$0.406797\pi$
$234$		0			0
$235$	−9.42274	−	1.49242i	−0.614672	−	0.0973544i
$236$		0			0
$237$		−	2.17071i		−	0.141003i
$238$		0			0
$239$	0.110990	−	0.217830i	0.00717935	−	0.0140903i	−0.887389	−	0.461021i	$-0.847483\pi$
$239$	0.110990	−	0.217830i	0.00717935	−	0.0140903i	0.894568	+	0.446931i	$0.147483\pi$
$240$		0			0
$241$	1.02694	−	1.41346i	0.0661507	−	0.0910487i	−0.774660	−	0.632378i	$-0.782079\pi$
$241$	1.02694	−	1.41346i	0.0661507	−	0.0910487i	0.840810	+	0.541330i	$0.182079\pi$
$242$		0			0
$243$	−8.17010	−	8.17010i	−0.524112	−	0.524112i
$244$		0			0
$245$	−5.52535			−0.353002
$246$		0			0
$247$	−45.8220			−2.91558
$248$		0			0
$249$	−2.30096	−	2.30096i	−0.145817	−	0.145817i
$250$		0			0
$251$	−13.1716	+	18.1291i	−0.831382	+	1.14430i	0.156282	+	0.987713i	$0.450049\pi$
$251$	−13.1716	+	18.1291i	−0.831382	+	1.14430i	−0.987664	+	0.156587i	$0.949951\pi$
$252$		0			0
$253$	6.60429	−	12.9616i	0.415208	−	0.814892i
$254$		0			0
$255$			3.72022i			0.232969i
$256$		0			0
$257$	−1.60838	−	0.254742i	−0.100328	−	0.0158904i	0.106069	−	0.994359i	$-0.466174\pi$
$257$	−1.60838	−	0.254742i	−0.100328	−	0.0158904i	−0.206397	+	0.978468i	$0.566174\pi$
$258$		0			0
$259$	35.1857	−	17.9280i	2.18633	−	1.11399i
$260$		0			0
$261$	−3.07593	+	0.487179i	−0.190395	+	0.0301556i
$262$		0			0
$263$	−2.67291	+	16.8761i	−0.164818	+	1.04062i	0.757117	+	0.653279i	$0.226607\pi$
$263$	−2.67291	+	16.8761i	−0.164818	+	1.04062i	−0.921936	+	0.387343i	$0.873393\pi$
$264$		0			0
$265$	4.52494	+	2.30557i	0.277965	+	0.141630i
$266$		0			0
$267$	−3.14421	+	1.02161i	−0.192422	+	0.0625218i
$268$		0			0
$269$	−3.07834	+	9.47417i	−0.187690	+	0.577650i	−0.999984	−	0.00559748i	$-0.998218\pi$
$269$	−3.07834	+	9.47417i	−0.187690	+	0.577650i	0.812294	+	0.583248i	$0.198218\pi$
$270$		0			0
$271$	4.22824	+	13.0132i	0.256847	+	0.790494i	0.993460	+	0.114180i	$0.0364240\pi$
$271$	4.22824	+	13.0132i	0.256847	+	0.790494i	−0.736613	+	0.676315i	$0.763576\pi$
$272$		0			0
$273$	7.56584	−	7.56584i	0.457905	−	0.457905i
$274$		0			0
$275$	0.396899	+	2.50592i	0.0239339	+	0.151113i
$276$		0			0
$277$	−1.26424	+	0.918523i	−0.0759607	+	0.0551887i	−0.625118	−	0.780531i	$-0.714949\pi$
$277$	−1.26424	+	0.918523i	−0.0759607	+	0.0551887i	0.549157	+	0.835719i	$0.314949\pi$
$278$		0			0
$279$	−3.88187	−	5.34294i	−0.232402	−	0.319873i
$280$		0			0
$281$	0.0890693	+	0.174808i	0.00531343	+	0.0104282i	0.893648	−	0.448769i	$-0.148137\pi$
$281$	0.0890693	+	0.174808i	0.00531343	+	0.0104282i	−0.888335	+	0.459197i	$0.848137\pi$
$282$		0			0
$283$	−2.20437	−	1.60157i	−0.131036	−	0.0952035i	0.520336	−	0.853961i	$-0.325807\pi$
$283$	−2.20437	−	1.60157i	−0.131036	−	0.0952035i	−0.651373	+	0.758758i	$0.725807\pi$
$284$		0			0
$285$	3.24597	+	1.05468i	0.192275	+	0.0624739i
$286$		0			0
$287$	−14.1473	−	17.7029i	−0.835090	−	1.04497i
$288$		0			0
$289$	−42.2844	−	13.7390i	−2.48732	−	0.808179i
$290$		0			0
$291$	−0.260117	−	0.188986i	−0.0152484	−	0.0110786i
$292$		0			0
$293$	5.84808	+	11.4775i	0.341649	+	0.670523i	0.996350	−	0.0853646i	$-0.0272055\pi$
$293$	5.84808	+	11.4775i	0.341649	+	0.670523i	−0.654701	+	0.755888i	$0.727206\pi$
$294$		0			0
$295$	5.05241	+	6.95405i	0.294163	+	0.404880i
$296$		0			0
$297$	−5.62489	+	4.08672i	−0.326389	+	0.237136i
$298$		0			0
$299$	−5.71439	−	36.0793i	−0.330472	−	2.08652i
$300$		0			0
$301$	−25.1729	+	25.1729i	−1.45094	+	1.45094i
$302$		0			0
$303$	−0.255741	−	0.787089i	−0.0146919	−	0.0452171i
$304$		0			0
$305$	1.30164	−	4.00604i	0.0745318	−	0.229385i
$306$		0			0
$307$	26.4900	−	8.60713i	1.51187	−	0.491235i	0.568413	−	0.822743i	$-0.307558\pi$
$307$	26.4900	−	8.60713i	1.51187	−	0.491235i	0.943452	+	0.331508i	$0.107558\pi$
$308$		0			0
$309$	−1.37726	−	0.701750i	−0.0783497	−	0.0399211i
$310$		0			0
$311$	1.79605	−	11.3398i	0.101845	−	0.643022i	−0.882972	−	0.469425i	$-0.844461\pi$
$311$	1.79605	−	11.3398i	0.101845	−	0.643022i	0.984817	−	0.173596i	$-0.0555388\pi$
$312$		0			0
$313$	18.0866	−	2.86464i	1.02232	−	0.161919i	0.377302	−	0.926090i	$-0.376852\pi$
$313$	18.0866	−	2.86464i	1.02232	−	0.161919i	0.645013	+	0.764171i	$0.276852\pi$
$314$		0			0
$315$	8.75003	−	4.45836i	0.493009	−	0.251200i
$316$		0			0
$317$	23.3600	+	3.69986i	1.31203	+	0.207805i	0.772959	−	0.634456i	$-0.218776\pi$
$317$	23.3600	+	3.69986i	1.31203	+	0.207805i	0.539070	+	0.842261i	$0.318776\pi$
$318$		0			0
$319$			2.84754i			0.159432i
$320$		0			0
$321$	3.04848	−	5.98298i	0.170150	−	0.333938i
$322$		0			0
$323$	−33.1424	+	45.6166i	−1.84409	+	2.53818i
$324$		0			0
$325$	4.50496	+	4.50496i	0.249890	+	0.249890i
$326$		0			0
$327$	7.88580			0.436086
$328$		0			0
$329$	33.7639			1.86146
$330$		0			0
$331$	−0.482730	−	0.482730i	−0.0265332	−	0.0265332i	0.693716	−	0.720249i	$-0.255972\pi$
$331$	−0.482730	−	0.482730i	−0.0265332	−	0.0265332i	−0.720249	+	0.693716i	$0.755972\pi$
$332$		0			0
$333$	−18.1988	+	25.0485i	−0.997289	+	1.37265i
$334$		0			0
$335$	1.23656	−	2.42689i	0.0675607	−	0.132595i
$336$		0			0
$337$			14.7211i			0.801910i	0.916098	+	0.400955i	$0.131322\pi$
$337$			14.7211i			0.801910i	−0.916098	+	0.400955i	$0.868678\pi$
$338$		0			0
$339$	4.12291	+	0.653004i	0.223926	+	0.0354663i
$340$		0			0
$341$	−5.38043	+	2.74147i	−0.291367	+	0.148459i
$342$		0			0
$343$	−5.15469	+	0.816423i	−0.278327	+	0.0440827i
$344$		0			0
$345$	−0.425633	+	2.68734i	−0.0229153	+	0.144681i
$346$		0			0
$347$	21.3176	+	10.8619i	1.14439	+	0.583095i	0.920199	−	0.391450i	$-0.128026\pi$
$347$	21.3176	+	10.8619i	1.14439	+	0.583095i	0.224190	+	0.974546i	$0.428026\pi$
$348$		0			0
$349$	31.6268	−	10.2762i	1.69295	−	0.550071i	0.705594	−	0.708616i	$-0.250680\pi$
$349$	31.6268	−	10.2762i	1.69295	−	0.550071i	0.987352	+	0.158545i	$0.0506803\pi$
$350$		0			0
$351$	−5.39507	+	16.6043i	−0.287968	+	0.886273i
$352$		0			0
$353$	3.34190	+	10.2853i	0.177871	+	0.547432i	0.999753	−	0.0222267i	$-0.00707557\pi$
$353$	3.34190	+	10.2853i	0.177871	+	0.547432i	−0.821882	+	0.569658i	$0.807076\pi$
$354$		0			0
$355$	2.33259	−	2.33259i	0.123801	−	0.123801i
$356$		0			0
$357$	−2.05966	−	13.0042i	−0.109009	−	0.688256i
$358$		0			0
$359$	−0.598706	+	0.434986i	−0.0315985	+	0.0229577i	−0.603472	−	0.797384i	$-0.706217\pi$
$359$	−0.598706	+	0.434986i	−0.0315985	+	0.0229577i	0.571874	+	0.820342i	$0.306217\pi$
$360$		0			0
$361$	19.2377	+	26.4784i	1.01251	+	1.39360i
$362$		0			0
$363$	−0.982995	−	1.92924i	−0.0515939	−	0.101259i
$364$		0			0
$365$	4.57869	+	3.32661i	0.239660	+	0.174123i
$366$		0			0
$367$	2.52952	+	0.821891i	0.132040	+	0.0429023i	0.374291	−	0.927311i	$-0.377886\pi$
$367$	2.52952	+	0.821891i	0.132040	+	0.0429023i	−0.242252	+	0.970213i	$0.577886\pi$
$368$		0			0
$369$	16.1844	+	7.33129i	0.842527	+	0.381652i
$370$		0			0
$371$	−17.0936	−	5.55405i	−0.887456	−	0.288352i
$372$		0			0
$373$	17.8654	+	12.9800i	0.925037	+	0.672079i	0.944773	−	0.327727i	$-0.106282\pi$
$373$	17.8654	+	12.9800i	0.925037	+	0.672079i	−0.0197358	+	0.999805i	$0.506282\pi$
$374$		0			0
$375$	−0.215436	−	0.422816i	−0.0111251	−	0.0218341i
$376$		0			0
$377$	4.20288	+	5.78477i	0.216459	+	0.297931i
$378$		0			0
$379$	8.73942	−	6.34956i	0.448914	−	0.326155i	−0.340253	−	0.940334i	$-0.610513\pi$
$379$	8.73942	−	6.34956i	0.448914	−	0.326155i	0.789167	+	0.614179i	$0.210513\pi$
$380$		0			0
$381$	−0.221008	−	1.39539i	−0.0113226	−	0.0714878i
$382$		0			0
$383$	5.66501	−	5.66501i	0.289469	−	0.289469i	−0.547401	−	0.836870i	$-0.684383\pi$
$383$	5.66501	−	5.66501i	0.289469	−	0.289469i	0.836870	+	0.547401i	$0.184383\pi$
$384$		0			0
$385$	−2.77476	−	8.53983i	−0.141415	−	0.435230i
$386$		0			0
$387$	8.62520	−	26.5456i	0.438444	−	1.34939i
$388$		0			0
$389$	−19.3396	+	6.28382i	−0.980557	+	0.318602i	−0.755070	−	0.655644i	$-0.772397\pi$
$389$	−19.3396	+	6.28382i	−0.980557	+	0.318602i	−0.225487	+	0.974246i	$0.572397\pi$
$390$		0			0
$391$	−40.0507	−	20.4069i	−2.02545	−	1.03202i
$392$		0			0
$393$	−0.239473	+	1.51197i	−0.0120798	+	0.0762690i
$394$		0			0
$395$	−4.51806	+	0.715590i	−0.227328	+	0.0360052i
$396$		0			0
$397$	−32.4282	+	16.5230i	−1.62752	+	0.829265i	−0.628864	+	0.777515i	$0.716480\pi$
$397$	−32.4282	+	16.5230i	−1.62752	+	0.829265i	−0.998660	+	0.0517502i	$0.983520\pi$
$398$		0			0
$399$	−11.9304	−	1.88958i	−0.597265	−	0.0945975i
$400$		0			0
$401$		−	28.1565i		−	1.40607i	−0.711157	−	0.703033i	$-0.751828\pi$
$401$		−	28.1565i		−	1.40607i	0.711157	−	0.703033i	$-0.248172\pi$
$402$		0			0
$403$	−6.88401	+	13.5106i	−0.342917	+	0.673013i
$404$		0			0
$405$	−4.12862	+	5.68256i	−0.205153	+	0.282369i
$406$		0			0
$407$	20.0181	+	20.0181i	0.992261	+	0.992261i
$408$		0			0
$409$	−28.7390			−1.42105			−0.710525	−	0.703672i	$-0.751543\pi$
$409$	−28.7390			−1.42105			−0.710525	+	0.703672i	$0.751543\pi$
$410$		0			0
$411$	2.85944			0.141046
$412$		0			0
$413$	−21.5110	−	21.5110i	−1.05849	−	1.05849i
$414$		0			0
$415$	−4.03061	+	5.54766i	−0.197855	+	0.272324i
$416$		0			0
$417$	−3.81485	+	7.48706i	−0.186814	+	0.366643i
$418$		0			0
$419$			37.9928i			1.85607i	0.372492	+	0.928035i	$0.378503\pi$
$419$			37.9928i			1.85607i	−0.372492	+	0.928035i	$0.621497\pi$
$420$		0			0
$421$	27.3024	+	4.32427i	1.33064	+	0.210752i	0.780936	−	0.624611i	$-0.214742\pi$
$421$	27.3024	+	4.32427i	1.33064	+	0.210752i	0.549699	+	0.835363i	$0.314742\pi$
$422$		0			0
$423$	−23.5870	+	12.0182i	−1.14684	+	0.584343i
$424$		0			0
$425$	7.74315	−	1.22640i	0.375598	−	0.0594889i
$426$		0			0
$427$	−2.33204	+	14.7239i	−0.112855	+	0.712541i
$428$		0			0
$429$	6.83448	+	3.48234i	0.329972	+	0.168129i
$430$		0			0
$431$	−37.9237	+	12.3222i	−1.82672	+	0.593537i	−0.827222	+	0.561876i	$0.810080\pi$
$431$	−37.9237	+	12.3222i	−1.82672	+	0.593537i	−0.999499	+	0.0316619i	$0.989920\pi$
$432$		0			0
$433$	4.67501	−	14.3882i	0.224666	−	0.691452i	−0.773659	−	0.633602i	$-0.781576\pi$
$433$	4.67501	−	14.3882i	0.224666	−	0.691452i	0.998325	−	0.0578499i	$-0.0184245\pi$
$434$		0			0
$435$	−0.164579	−	0.506523i	−0.00789098	−	0.0242859i
$436$		0			0
$437$	−29.1598	+	29.1598i	−1.39490	+	1.39490i
$438$		0			0
$439$	4.49217	+	28.3625i	0.214400	+	1.35367i	0.826522	+	0.562904i	$0.190316\pi$
$439$	4.49217	+	28.3625i	0.214400	+	1.35367i	−0.612123	+	0.790763i	$0.709684\pi$
$440$		0			0
$441$	−12.4037	+	9.01182i	−0.590653	+	0.429134i
$442$		0			0
$443$	20.3231	+	27.9724i	0.965581	+	1.32901i	0.944248	+	0.329236i	$0.106791\pi$
$443$	20.3231	+	27.9724i	0.965581	+	1.32901i	0.0213338	+	0.999772i	$0.493209\pi$
$444$		0			0
$445$	3.16286	+	6.20747i	0.149934	+	0.294262i
$446$		0			0
$447$	−3.46273	−	2.51582i	−0.163782	−	0.118994i
$448$		0			0
$449$	−34.1623	−	11.1000i	−1.61222	−	0.523841i	−0.642130	−	0.766596i	$-0.721949\pi$
$449$	−34.1623	−	11.1000i	−1.61222	−	0.523841i	−0.970088	+	0.242754i	$0.921949\pi$
$450$		0			0
$451$	8.93582	−	13.5674i	0.420771	−	0.638866i
$452$		0			0
$453$	3.64801	+	1.18531i	0.171398	+	0.0556907i
$454$		0			0
$455$	−18.2414	−	13.2532i	−0.855171	−	0.621318i
$456$		0			0
$457$	−18.7725	−	36.8430i	−0.878139	−	1.72345i	−0.665624	−	0.746287i	$-0.731834\pi$
$457$	−18.7725	−	36.8430i	−0.878139	−	1.72345i	−0.212515	−	0.977158i	$-0.568166\pi$
$458$		0			0
$459$	12.6277	+	17.3806i	0.589412	+	0.811256i
$460$		0			0
$461$	2.72541	−	1.98013i	0.126935	−	0.0922237i	−0.522506	−	0.852635i	$-0.675003\pi$
$461$	2.72541	−	1.98013i	0.126935	−	0.0922237i	0.649441	+	0.760412i	$0.275003\pi$
$462$		0			0
$463$	−1.83854	−	11.6081i	−0.0854443	−	0.539474i	−0.992864	−	0.119249i	$-0.961951\pi$
$463$	−1.83854	−	11.6081i	−0.0854443	−	0.539474i	0.907420	−	0.420225i	$-0.138049\pi$
$464$		0			0
$465$	0.798628	−	0.798628i	0.0370355	−	0.0370355i
$466$		0			0
$467$	−9.45061	−	29.0860i	−0.437322	−	1.34594i	−0.890688	−	0.454615i	$-0.849777\pi$
$467$	−9.45061	−	29.0860i	−0.437322	−	1.34594i	0.453366	−	0.891325i	$-0.350223\pi$
$468$		0			0
$469$	−2.97884	+	9.16793i	−0.137550	+	0.423336i
$470$		0			0
$471$	−0.637859	+	0.207253i	−0.0293910	+	0.00954971i
$472$		0			0
$473$	−22.7395	−	11.5864i	−1.04557	−	0.532742i
$474$		0			0
$475$	1.12512	−	7.10375i	0.0516242	−	0.325942i
$476$		0			0
$477$	13.9183	−	2.20444i	0.637275	−	0.100934i
$478$		0			0
$479$	−25.7590	+	13.1249i	−1.17696	+	0.599691i	−0.929361	−	0.369171i	$-0.879642\pi$
$479$	−25.7590	+	13.1249i	−1.17696	+	0.599691i	−0.247599	+	0.968863i	$0.579642\pi$
$480$		0			0
$481$	70.2128	+	11.1206i	3.20143	+	0.507057i
$482$		0			0
$483$		−	9.62936i		−	0.438151i
$484$		0			0
$485$	−0.307601	+	0.603701i	−0.0139674	+	0.0274126i
$486$		0			0
$487$	0.0890756	−	0.122602i	0.00403640	−	0.00555563i	−0.806994	−	0.590560i	$-0.798907\pi$
$487$	0.0890756	−	0.122602i	0.00403640	−	0.00555563i	0.811030	+	0.585004i	$0.198907\pi$
$488$		0			0
$489$	5.90575	+	5.90575i	0.267067	+	0.267067i
$490$		0			0
$491$	−9.24647			−0.417287			−0.208644	−	0.977992i	$-0.566905\pi$
$491$	−9.24647			−0.417287			−0.208644	+	0.977992i	$0.566905\pi$
$492$		0			0
$493$	8.79874			0.396275
$494$		0			0
$495$	4.97813	+	4.97813i	0.223750	+	0.223750i
$496$		0			0
$497$	−6.86226	+	9.44509i	−0.307814	+	0.423670i
$498$		0			0
$499$	−11.9027	+	23.3604i	−0.532838	+	1.04575i	0.455032	+	0.890475i	$0.349628\pi$
$499$	−11.9027	+	23.3604i	−0.532838	+	1.04575i	−0.987871	+	0.155279i	$0.950372\pi$
$500$		0			0
$501$			3.35570i			0.149922i
$502$		0			0
$503$	−9.68788	−	1.53441i	−0.431961	−	0.0684159i	−0.0633321	−	0.997993i	$-0.520173\pi$
$503$	−9.68788	−	1.53441i	−0.431961	−	0.0684159i	−0.368629	+	0.929577i	$0.620173\pi$
$504$		0			0
$505$	−1.55392	+	0.791759i	−0.0691483	+	0.0352328i
$506$		0			0
$507$	12.9310	−	2.04807i	0.574286	−	0.0909580i
$508$		0			0
$509$	−1.40367	+	8.86240i	−0.0622164	+	0.392819i	0.936854	+	0.349720i	$0.113723\pi$
$509$	−1.40367	+	8.86240i	−0.0622164	+	0.392819i	−0.999071	+	0.0430992i	$0.986277\pi$
$510$		0			0
$511$	−17.8468	−	9.09338i	−0.789494	−	0.402267i
$512$		0			0
$513$	18.7449	−	6.09058i	0.827607	−	0.268906i
$514$		0			0
$515$	−1.00658	+	3.09793i	−0.0443551	+	0.136511i
$516$		0			0
$517$	7.47975	+	23.0203i	0.328959	+	1.01243i
$518$		0			0
$519$	3.02705	−	3.02705i	0.132873	−	0.132873i
$520$		0			0
$521$	−0.0797642	−	0.503611i	−0.00349453	−	0.0220636i	0.985879	−	0.167457i	$-0.0535554\pi$
$521$	−0.0797642	−	0.503611i	−0.00349453	−	0.0220636i	−0.989374	+	0.145393i	$0.953555\pi$
$522$		0			0
$523$	31.5807	−	22.9447i	1.38093	−	1.00330i	0.384136	−	0.923277i	$-0.374500\pi$
$523$	31.5807	−	22.9447i	1.38093	−	1.00330i	0.996793	−	0.0800264i	$-0.0255005\pi$
$524$		0			0
$525$	0.987153	+	1.35870i	0.0430829	+	0.0592985i
$526$		0			0
$527$	8.47098	+	16.6252i	0.369002	+	0.724206i
$528$		0			0
$529$	−7.98889	−	5.80427i	−0.347343	−	0.252359i
$530$		0			0
$531$	22.6840	+	7.37049i	0.984403	+	0.319852i
$532$		0			0
$533$	−1.87203	−	40.7512i	−0.0810868	−	1.76513i
$534$		0			0
$535$	−13.4577	−	4.37269i	−0.581829	−	0.189048i
$536$		0			0
$537$	6.88392	+	5.00146i	0.297063	+	0.215829i
$538$		0			0
$539$	6.36436	+	12.4908i	0.274132	+	0.538015i
$540$		0			0
$541$	7.01748	+	9.65873i	0.301705	+	0.415261i	0.932772	−	0.360467i	$-0.117383\pi$
$541$	7.01748	+	9.65873i	0.301705	+	0.415261i	−0.631067	+	0.775728i	$0.717383\pi$
$542$		0			0
$543$	−1.71668	+	1.24724i	−0.0736698	+	0.0535242i
$544$		0			0
$545$	−2.59960	−	16.4133i	−0.111355	−	0.703067i
$546$		0			0
$547$	−24.2547	+	24.2547i	−1.03706	+	1.03706i	−0.0377695	+	0.999286i	$0.512025\pi$
$547$	−24.2547	+	24.2547i	−1.03706	+	1.03706i	−0.999286	+	0.0377695i	$0.987975\pi$
$548$		0			0
$549$	−3.61181	−	11.1160i	−0.154148	−	0.474420i
$550$		0			0
$551$	2.49444	−	7.67708i	0.106267	−	0.327055i
$552$		0			0
$553$	15.3969	−	5.00275i	0.654742	−	0.212739i
$554$		0			0
$555$	−4.71783	−	2.40385i	−0.200261	−	0.102038i
$556$		0			0
$557$	−4.84057	+	30.5621i	−0.205101	+	1.29496i	0.643304	+	0.765611i	$0.277563\pi$
$557$	−4.84057	+	30.5621i	−0.205101	+	1.29496i	−0.848405	+	0.529348i	$0.822437\pi$
$558$		0			0
$559$	−63.2964	+	10.0252i	−2.67715	+	0.424019i
$560$		0			0
$561$	8.41003	−	4.28512i	0.355072	−	0.180918i
$562$		0			0
$563$	0.681580	+	0.107952i	0.0287252	+	0.00454962i	0.170781	−	0.985309i	$-0.445371\pi$
$563$	0.681580	+	0.107952i	0.0287252	+	0.00454962i	−0.142055	+	0.989859i	$0.545371\pi$
$564$		0			0
$565$		−	8.79656i		−	0.370074i
$566$		0			0
$567$	11.2857	−	22.1494i	0.473955	−	0.930188i
$568$		0			0
$569$	−5.04658	+	6.94602i	−0.211563	+	0.291192i	−0.901590	−	0.432592i	$-0.857599\pi$
$569$	−5.04658	+	6.94602i	−0.211563	+	0.291192i	0.690026	+	0.723784i	$0.257599\pi$
$570$		0			0
$571$	−0.468988	−	0.468988i	−0.0196265	−	0.0196265i	0.697225	−	0.716852i	$-0.254418\pi$
$571$	−0.468988	−	0.468988i	−0.0196265	−	0.0196265i	−0.716852	+	0.697225i	$0.754418\pi$
$572$		0			0
$573$	5.88500			0.245849
$574$		0			0
$575$	5.73366			0.239110
$576$		0			0
$577$	3.09424	+	3.09424i	0.128815	+	0.128815i	0.768575	−	0.639760i	$-0.220966\pi$
$577$	3.09424	+	3.09424i	0.128815	+	0.128815i	−0.639760	+	0.768575i	$0.720966\pi$
$578$		0			0
$579$	−4.79546	+	6.60039i	−0.199293	+	0.274303i
$580$		0			0
$581$	11.0178	−	21.6236i	0.457095	−	0.897099i
$582$		0			0
$583$		−	12.8849i		−	0.533637i
$584$		0			0
$585$	17.4606	+	2.76549i	0.721908	+	0.114339i
$586$		0			0
$587$	24.1321	−	12.2959i	0.996038	−	0.507507i	0.121566	−	0.992583i	$-0.461208\pi$
$587$	24.1321	−	12.2959i	0.996038	−	0.507507i	0.874472	+	0.485077i	$0.161208\pi$
$588$		0			0
$589$	16.9074	−	2.67787i	0.696656	−	0.110340i
$590$		0			0
$591$	1.64786	−	10.4042i	0.0677841	−	0.427972i
$592$		0			0
$593$	−37.9592	−	19.3412i	−1.55880	−	0.794248i	−0.559400	−	0.828898i	$-0.688968\pi$
$593$	−37.9592	−	19.3412i	−1.55880	−	0.794248i	−0.999400	+	0.0346500i	$0.988968\pi$
$594$		0			0
$595$	−26.3876	+	8.57384i	−1.08178	+	0.351493i
$596$		0			0
$597$	−2.13647	+	6.57537i	−0.0874397	+	0.269112i
$598$		0			0
$599$	0.342022	+	1.05264i	0.0139746	+	0.0430095i	0.957801	−	0.287433i	$-0.0928019\pi$
$599$	0.342022	+	1.05264i	0.0139746	+	0.0430095i	−0.943826	+	0.330443i	$0.892802\pi$
$600$		0			0
$601$	−18.6896	+	18.6896i	−0.762364	+	0.762364i	−0.976749	−	0.214385i	$-0.931225\pi$
$601$	−18.6896	+	18.6896i	−0.762364	+	0.762364i	0.214385	+	0.976749i	$0.431225\pi$
$602$		0			0
$603$	−1.18232	−	7.46490i	−0.0481479	−	0.303994i
$604$		0			0
$605$	−3.69140	+	2.68196i	−0.150077	+	0.109037i
$606$		0			0
$607$	−8.96114	−	12.3339i	−0.363721	−	0.500620i	0.587459	−	0.809254i	$-0.300128\pi$
$607$	−8.96114	−	12.3339i	−0.363721	−	0.500620i	−0.951181	+	0.308634i	$0.900128\pi$
$608$		0			0
$609$	0.855726	+	1.67946i	0.0346758	+	0.0680551i
$610$		0			0
$611$	49.1724	+	35.7258i	1.98930	+	1.44531i
$612$		0			0
$613$	20.5900	+	6.69010i	0.831623	+	0.270211i	0.693729	−	0.720236i	$-0.255967\pi$
$613$	20.5900	+	6.69010i	0.831623	+	0.270211i	0.137894	+	0.990447i	$0.455967\pi$
$614$		0			0
$615$	−0.805354	+	2.92985i	−0.0324750	+	0.118143i
$616$		0			0
$617$	−15.2876	−	4.96725i	−0.615457	−	0.199974i	−0.0153346	−	0.999882i	$-0.504881\pi$
$617$	−15.2876	−	4.96725i	−0.615457	−	0.199974i	−0.600122	+	0.799908i	$0.704881\pi$
$618$		0			0
$619$	17.3954	+	12.6385i	0.699182	+	0.507985i	0.879666	−	0.475593i	$-0.157766\pi$
$619$	17.3954	+	12.6385i	0.699182	+	0.507985i	−0.180484	+	0.983578i	$0.557766\pi$
$620$		0			0
$621$	7.13325	+	13.9998i	0.286247	+	0.561792i
$622$		0			0
$623$	−14.4926	−	19.9474i	−0.580635	−	0.799176i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$	−1.35462	−	8.55276i	−0.0540985	−	0.341564i
$628$		0			0
$629$	61.8548	−	61.8548i	2.46631	−	2.46631i
$630$		0			0
$631$	9.66665	+	29.7509i	0.384823	+	1.18436i	0.936608	+	0.350378i	$0.113947\pi$
$631$	9.66665	+	29.7509i	0.384823	+	1.18436i	−0.551785	+	0.833986i	$0.686053\pi$
$632$		0			0
$633$	−1.66485	+	5.12390i	−0.0661720	+	0.203657i
$634$		0			0
$635$	−2.83146	+	0.919997i	−0.112363	+	0.0365090i
$636$		0			0
$637$	31.3651	+	15.9813i	1.24273	+	0.633203i
$638$		0			0
$639$	1.43192	−	9.04081i	0.0566460	−	0.357649i
$640$		0			0
$641$	−24.5736	+	3.89208i	−0.970600	+	0.153728i	−0.621548	−	0.783376i	$-0.713496\pi$
$641$	−24.5736	+	3.89208i	−0.970600	+	0.153728i	−0.349051	+	0.937104i	$0.613496\pi$
$642$		0			0
$643$	0.837111	−	0.426530i	0.0330124	−	0.0168207i	−0.437406	−	0.899264i	$-0.644103\pi$
$643$	0.837111	−	0.426530i	0.0330124	−	0.0168207i	0.470419	+	0.882443i	$0.344103\pi$
$644$		0			0
$645$	4.71459	+	0.746718i	0.185637	+	0.0294020i
$646$		0			0
$647$		−	17.1658i		−	0.674857i	−0.941351	−	0.337428i	$-0.890443\pi$
$647$		−	17.1658i		−	0.674857i	0.941351	−	0.337428i	$-0.109557\pi$
$648$		0			0
$649$	9.90089	−	19.4316i	0.388644	−	0.762757i
$650$		0			0
$651$	−2.34949	+	3.23379i	−0.0920837	+	0.126742i
$652$		0			0
$653$	1.58410	+	1.58410i	0.0619908	+	0.0619908i	0.737423	−	0.675432i	$-0.236043\pi$
$653$	1.58410	+	1.58410i	0.0619908	+	0.0619908i	−0.675432	+	0.737423i	$0.736043\pi$
$654$		0			0
$655$	3.22592			0.126047
$656$		0			0
$657$	15.7043			0.612681
$658$		0			0
$659$	−1.99195	−	1.99195i	−0.0775955	−	0.0775955i	0.667244	−	0.744839i	$-0.267474\pi$
$659$	−1.99195	−	1.99195i	−0.0775955	−	0.0775955i	−0.744839	+	0.667244i	$0.767474\pi$
$660$		0			0
$661$	15.4192	−	21.2227i	0.599738	−	0.825469i	−0.395946	−	0.918274i	$-0.629583\pi$
$661$	15.4192	−	21.2227i	0.599738	−	0.825469i	0.995684	+	0.0928051i	$0.0295834\pi$
$662$		0			0
$663$	10.7602	−	21.1182i	0.417893	−	0.820161i
$664$		0			0
$665$			25.4544i			0.987079i
$666$		0			0
$667$	6.35585	+	1.00667i	0.246100	+	0.0389783i
$668$		0			0
$669$	−0.512119	+	0.260938i	−0.0197997	+	0.0100884i
$670$		0			0
$671$	−10.5554	+	1.67182i	−0.407489	+	0.0645398i
$672$		0			0
$673$	3.07047	−	19.3862i	0.118358	−	0.747282i	−0.855108	−	0.518450i	$-0.826509\pi$
$673$	3.07047	−	19.3862i	0.118358	−	0.747282i	0.973466	−	0.228832i	$-0.0734907\pi$
$674$		0			0
$675$	−2.44169	−	1.24410i	−0.0939805	−	0.0478855i
$676$		0			0
$677$	26.5814	−	8.63681i	1.02160	−	0.331939i	0.250139	−	0.968210i	$-0.419524\pi$
$677$	26.5814	−	8.63681i	1.02160	−	0.331939i	0.771466	+	0.636271i	$0.219524\pi$
$678$		0			0
$679$	0.741000	−	2.28056i	0.0284370	−	0.0875200i
$680$		0			0
$681$	0.238241	+	0.733230i	0.00912941	+	0.0280974i
$682$		0			0
$683$	−7.67050	+	7.67050i	−0.293503	+	0.293503i	−0.838463	−	0.544959i	$-0.816545\pi$
$683$	−7.67050	+	7.67050i	−0.293503	+	0.293503i	0.544959	+	0.838463i	$0.316545\pi$
$684$		0			0
$685$	−0.942634	−	5.95156i	−0.0360162	−	0.227397i
$686$		0			0
$687$	−3.56102	+	2.58723i	−0.135861	+	0.0987091i
$688$		0			0
$689$	−19.0177	−	26.1756i	−0.724515	−	0.997210i
$690$		0			0
$691$	9.38526	+	18.4196i	0.357032	+	0.700715i	0.997749	−	0.0670624i	$-0.0213626\pi$
$691$	9.38526	+	18.4196i	0.357032	+	0.700715i	−0.640717	+	0.767777i	$0.721363\pi$
$692$		0			0
$693$	−20.1574	−	14.6452i	−0.765716	−	0.556325i
$694$		0			0
$695$	16.8409	+	5.47195i	0.638813	+	0.207563i
$696$		0			0
$697$	−41.9226	−	27.6112i	−1.58793	−	1.04585i
$698$		0			0
$699$	−2.44543	−	0.794570i	−0.0924948	−	0.0300534i
$700$		0			0
$701$	8.64786	+	6.28304i	0.326625	+	0.237307i	0.738997	−	0.673708i	$-0.235300\pi$
$701$	8.64786	+	6.28304i	0.326625	+	0.237307i	−0.412372	+	0.911015i	$0.635300\pi$
$702$		0			0
$703$	−36.4338	−	71.5054i	−1.37413	−	2.69688i
$704$		0			0
$705$	−2.66101	−	3.66257i	−0.100219	−	0.137940i
$706$		0			0
$707$	4.99343	−	3.62794i	0.187797	−	0.136443i
$708$		0			0
$709$	−7.53314	−	47.5624i	−0.282913	−	1.78624i	−0.563194	−	0.826325i	$-0.690427\pi$
$709$	−7.53314	−	47.5624i	−0.282913	−	1.78624i	0.280280	−	0.959918i	$-0.409573\pi$
$710$		0			0
$711$	−8.97533	+	8.97533i	−0.336601	+	0.336601i
$712$		0			0
$713$	4.21699	+	12.9786i	0.157928	+	0.486051i
$714$		0			0
$715$	4.99501	−	15.3731i	0.186803	−	0.574920i
$716$		0			0
$717$	0.110335	−	0.0358501i	0.00412055	−	0.00133885i
$718$		0			0
$719$	14.8995	+	7.59166i	0.555657	+	0.283121i	0.709184	−	0.705023i	$-0.249063\pi$
$719$	14.8995	+	7.59166i	0.555657	+	0.283121i	−0.153528	+	0.988144i	$0.549063\pi$
$720$		0			0
$721$	1.80340	−	11.3862i	0.0671621	−	0.424045i
$722$		0			0
$723$	0.818870	−	0.129696i	0.0304541	−	0.00482346i
$724$		0			0
$725$	−1.00001	+	0.509529i	−0.0371393	+	0.0189234i
$726$		0			0
$727$	−23.1291	−	3.66330i	−0.857813	−	0.135864i	−0.287992	−	0.957633i	$-0.592988\pi$
$727$	−23.1291	−	3.66330i	−0.857813	−	0.135864i	−0.569821	+	0.821769i	$0.692988\pi$
$728$		0			0
$729$			15.5892i			0.577376i
$730$		0			0
$731$	−35.8012	+	70.2639i	−1.32416	+	2.59880i
$732$		0			0
$733$	−3.34579	+	4.60508i	−0.123579	+	0.170092i	−0.866324	−	0.499482i	$-0.833524\pi$
$733$	−3.34579	+	4.60508i	−0.123579	+	0.170092i	0.742745	+	0.669575i	$0.233524\pi$
$734$		0			0
$735$	−1.85403	−	1.85403i	−0.0683868	−	0.0683868i
$736$		0			0
$737$	−6.91063			−0.254556
$738$		0			0
$739$	−7.71404			−0.283766			−0.141883	−	0.989883i	$-0.545316\pi$
$739$	−7.71404			−0.283766			−0.141883	+	0.989883i	$0.545316\pi$
$740$		0			0
$741$	−15.3755	−	15.3755i	−0.564834	−	0.564834i
$742$		0			0
$743$	−4.56618	+	6.28480i	−0.167517	+	0.230567i	−0.884519	−	0.466503i	$-0.845514\pi$
$743$	−4.56618	+	6.28480i	−0.167517	+	0.230567i	0.717003	+	0.697070i	$0.245514\pi$
$744$		0			0
$745$	−4.09484	+	8.03658i	−0.150023	+	0.294437i
$746$		0			0
$747$			19.0277i			0.696187i
$748$		0			0
$749$	49.4631	+	7.83418i	1.80734	+	0.286255i
$750$		0			0
$751$	2.10530	−	1.07270i	0.0768234	−	0.0391435i	−0.415157	−	0.909750i	$-0.636273\pi$
$751$	2.10530	−	1.07270i	0.0768234	−	0.0391435i	0.491980	+	0.870606i	$0.336273\pi$
$752$		0			0
$753$	−10.5029	+	1.66350i	−0.382747	+	0.0606212i
$754$		0			0
$755$	1.26448	−	7.98359i	0.0460190	−	0.290553i
$756$		0			0
$757$	−33.5116	−	17.0750i	−1.21800	−	0.620602i	−0.277608	−	0.960695i	$-0.589542\pi$
$757$	−33.5116	−	17.0750i	−1.21800	−	0.620602i	−0.940392	+	0.340093i	$0.889542\pi$
$758$		0			0
$759$	6.56533	−	2.13320i	0.238306	−	0.0774304i
$760$		0			0
$761$	−4.02663	+	12.3927i	−0.145965	+	0.449235i	−0.997134	−	0.0756573i	$-0.975894\pi$
$761$	−4.02663	+	12.3927i	−0.145965	+	0.449235i	0.851169	+	0.524893i	$0.175894\pi$
$762$		0			0
$763$	18.1741	+	55.9340i	0.657946	+	2.02495i
$764$		0			0
$765$	15.3821	−	15.3821i	0.556143	−	0.556143i
$766$		0			0
$767$	−8.56680	−	54.0886i	−0.309329	−	1.95303i
$768$		0			0
$769$	36.2840	−	26.3619i	1.30844	−	0.950634i	0.308436	−	0.951245i	$-0.400194\pi$
$769$	36.2840	−	26.3619i	1.30844	−	0.950634i	1.00000		0.000610690i	$0.000194389\pi$
$770$		0			0
$771$	−0.454211	−	0.625168i	−0.0163580	−	0.0225149i
$772$		0			0
$773$	−17.3879	−	34.1258i	−0.625401	−	1.22742i	−0.958652	−	0.284580i	$-0.908146\pi$
$773$	−17.3879	−	34.1258i	−0.625401	−	1.22742i	0.333251	−	0.942838i	$-0.391854\pi$
$774$		0			0
$775$	−1.92551	−	1.39897i	−0.0691665	−	0.0502524i
$776$		0			0
$777$	17.8223	+	5.79080i	0.639370	+	0.207744i
$778$		0			0
$779$	−35.9763	+	28.7506i	−1.28899	+	1.03010i
$780$		0			0
$781$	−7.95990	−	2.58633i	−0.284828	−	0.0925461i
$782$		0			0
$783$	−2.48822	−	1.80780i	−0.0889217	−	0.0646054i
$784$		0			0
$785$	0.641644	+	1.25930i	0.0229013	+	0.0449462i
$786$		0			0
$787$	−10.4093	−	14.3272i	−0.371051	−	0.510709i	0.582135	−	0.813092i	$-0.302218\pi$
$787$	−10.4093	−	14.3272i	−0.371051	−	0.510709i	−0.953186	+	0.302384i	$0.902218\pi$
$788$		0			0
$789$	−6.55964	+	4.76585i	−0.233529	+	0.169669i
$790$		0			0
$791$	4.87013	+	30.7488i	0.173162	+	1.09330i
$792$		0			0
$793$	−18.9758	+	18.9758i	−0.673851	+	0.673851i
$794$		0			0
$795$	0.744707	+	2.29197i	0.0264120	+	0.0812879i
$796$		0			0
$797$	−7.99686	+	24.6118i	−0.283263	+	0.871795i	0.703651	+	0.710546i	$0.251552\pi$
$797$	−7.99686	+	24.6118i	−0.283263	+	0.871795i	−0.986914	+	0.161248i	$0.948448\pi$
$798$		0			0
$799$	71.1314	−	23.1120i	2.51645	−	0.817644i
$800$		0			0
$801$	17.2246	+	8.77636i	0.608600	+	0.310097i
$802$		0			0
$803$	2.24628	−	14.1824i	0.0792695	−	0.500488i
$804$		0			0
$805$	−20.0423	+	3.17438i	−0.706397	+	0.111882i
$806$		0			0
$807$	−4.21198	+	2.14611i	−0.148269	+	0.0755467i
$808$		0			0
$809$	40.3836	+	6.39614i	1.41981	+	0.224876i	0.818670	−	0.574265i	$-0.194712\pi$
$809$	40.3836	+	6.39614i	1.41981	+	0.224876i	0.601144	+	0.799141i	$0.294712\pi$
$810$		0			0
$811$		−	45.9950i		−	1.61510i	−0.589797	−	0.807551i	$-0.700792\pi$
$811$		−	45.9950i		−	1.61510i	0.589797	−	0.807551i	$-0.299208\pi$
$812$		0			0
$813$	−2.94778	+	5.78534i	−0.103383	+	0.202901i
$814$		0			0
$815$	10.3452	−	14.2389i	0.362376	−	0.498768i
$816$		0			0
$817$	51.1571	+	51.1571i	1.78976	+	1.78976i
$818$		0			0
$819$	−62.5655			−2.18622
$820$		0			0
$821$	50.8054			1.77312			0.886561	−	0.462612i	$-0.153088\pi$
$821$	50.8054			1.77312			0.886561	+	0.462612i	$0.153088\pi$
$822$		0			0
$823$	−9.70145	−	9.70145i	−0.338171	−	0.338171i	0.517507	−	0.855679i	$-0.326860\pi$
$823$	−9.70145	−	9.70145i	−0.338171	−	0.338171i	−0.855679	+	0.517507i	$0.826860\pi$
$824$		0			0
$825$	−0.707681	+	0.974039i	−0.0246383	+	0.0339117i
$826$		0			0
$827$	−8.84085	+	17.3511i	−0.307426	+	0.603358i	−0.992094	−	0.125497i	$-0.959947\pi$
$827$	−8.84085	+	17.3511i	−0.307426	+	0.603358i	0.684668	+	0.728855i	$0.259947\pi$
$828$		0			0
$829$		−	19.9544i		−	0.693045i	−0.938042	−	0.346522i	$-0.887362\pi$
$829$		−	19.9544i		−	0.693045i	0.938042	−	0.346522i	$-0.112638\pi$
$830$		0			0
$831$	−0.732423	−	0.116004i	−0.0254075	−	0.00402415i
$832$		0			0
$833$	38.5957	−	19.6655i	1.33726	−	0.681369i
$834$		0			0
$835$	6.98446	−	1.10623i	0.241707	−	0.0382826i
$836$		0			0
$837$	1.02031	−	6.44195i	0.0352669	−	0.222666i
$838$		0			0
$839$	−5.60143	−	2.85407i	−0.193383	−	0.0985335i	0.354618	−	0.935011i	$-0.384611\pi$
$839$	−5.60143	−	2.85407i	−0.193383	−	0.0985335i	−0.548001	+	0.836478i	$0.684611\pi$
$840$		0			0
$841$	26.3827	−	8.57224i	0.909747	−	0.295595i
$842$		0			0
$843$	−0.0287696	+	0.0885438i	−0.000990879	+	0.00304961i
$844$		0			0
$845$	−8.52558	−	26.2390i	−0.293289	−	0.902651i
$846$		0			0
$847$	11.4186	−	11.4186i	0.392348	−	0.392348i
$848$		0			0
$849$	−0.202270	−	1.27708i	−0.00694188	−	0.0438293i
$850$		0			0
$851$	51.7583	−	37.6046i	1.77425	−	1.28907i
$852$		0			0
$853$	5.60410	+	7.71338i	0.191881	+	0.264101i	0.894108	−	0.447852i	$-0.147811\pi$
$853$	5.60410	+	7.71338i	0.191881	+	0.264101i	−0.702227	+	0.711953i	$0.747811\pi$
$854$		0			0
$855$	−9.06042	−	17.7821i	−0.309860	−	0.608134i
$856$		0			0
$857$	3.57785	+	2.59946i	0.122217	+	0.0887960i	0.647215	−	0.762308i	$-0.275934\pi$
$857$	3.57785	+	2.59946i	0.122217	+	0.0887960i	−0.524997	+	0.851104i	$0.675934\pi$
$858$		0			0
$859$	−3.63997	−	1.18270i	−0.124194	−	0.0403531i	0.246261	−	0.969204i	$-0.420798\pi$
$859$	−3.63997	−	1.18270i	−0.124194	−	0.0403531i	−0.370455	+	0.928851i	$0.620798\pi$
$860$		0			0
$861$	1.19307	−	10.6873i	0.0406596	−	0.364223i
$862$		0			0
$863$	33.8488	+	10.9981i	1.15223	+	0.374381i	0.821981	−	0.569515i	$-0.192869\pi$
$863$	33.8488	+	10.9981i	1.15223	+	0.374381i	0.330244	+	0.943896i	$0.392869\pi$
$864$		0			0
$865$	−7.29829	−	5.30251i	−0.248149	−	0.180291i
$866$		0			0
$867$	−9.57838	−	18.7986i	−0.325299	−	0.638435i
$868$		0			0
$869$	6.82178	+	9.38938i	0.231413	+	0.318513i
$870$		0			0
$871$	−14.0389	+	10.1999i	−0.475691	+	0.345610i
$872$		0			0
$873$	0.294108	+	1.85693i	0.00995406	+	0.0628474i
$874$		0			0
$875$	2.50253	−	2.50253i	0.0846011	−	0.0846011i
$876$		0			0
$877$	17.4909	+	53.8313i	0.590625	+	1.81776i	0.575401	+	0.817871i	$0.304846\pi$
$877$	17.4909	+	53.8313i	0.590625	+	1.81776i	0.0152235	+	0.999884i	$0.495154\pi$
$878$		0			0
$879$	−1.88895	+	5.81358i	−0.0637126	+	0.196087i
$880$		0			0
$881$	−14.9454	+	4.85606i	−0.503523	+	0.163605i	−0.549755	−	0.835326i	$-0.685279\pi$
$881$	−14.9454	+	4.85606i	−0.503523	+	0.163605i	0.0462314	+	0.998931i	$0.485279\pi$
$882$		0			0
$883$	42.7509	+	21.7827i	1.43868	+	0.733046i	0.987238	−	0.159253i	$-0.0509085\pi$
$883$	42.7509	+	21.7827i	1.43868	+	0.733046i	0.451446	+	0.892299i	$0.350909\pi$
$884$		0			0
$885$	−0.638092	+	4.02875i	−0.0214492	+	0.135425i
$886$		0			0
$887$	−18.6619	+	2.95575i	−0.626604	+	0.0992444i	−0.461658	−	0.887058i	$-0.652745\pi$
$887$	−18.6619	+	2.95575i	−0.626604	+	0.0992444i	−0.164947	+	0.986303i	$0.552745\pi$
$888$		0			0
$889$	9.38814	−	4.78350i	0.314868	−	0.160433i
$890$		0			0
$891$	17.6017	+	2.78783i	0.589679	+	0.0933959i
$892$		0			0
$893$		−	68.6159i		−	2.29614i
$894$		0			0
$895$	8.14056	−	15.9767i	0.272109	−	0.534044i
$896$		0			0
$897$	10.1889	−	14.0238i	0.340197	−	0.468242i
$898$		0			0
$899$	−1.88884	−	1.88884i	−0.0629965	−	0.0629965i
$900$		0			0
$901$	−39.8135			−1.32638
$902$		0			0
$903$	−16.8935			−0.562180
$904$		0			0
$905$	3.16188	+	3.16188i	0.105105	+	0.105105i
$906$		0			0
$907$	13.0203	−	17.9209i	0.432332	−	0.595053i	−0.536155	−	0.844120i	$-0.680124\pi$
$907$	13.0203	−	17.9209i	0.432332	−	0.595053i	0.968486	+	0.249066i	$0.0801237\pi$
$908$		0			0
$909$	−2.19698	+	4.31183i	−0.0728694	+	0.143014i
$910$		0			0
$911$			18.0734i			0.598799i	0.954128	+	0.299400i	$0.0967864\pi$
$911$			18.0734i			0.598799i	−0.954128	+	0.299400i	$0.903214\pi$
$912$		0			0
$913$	17.1838	+	2.72165i	0.568702	+	0.0900735i
$914$		0			0
$915$	1.78099	−	0.907458i	0.0588776	−	0.0299996i
$916$		0			0
$917$	−11.2764	+	1.78600i	−0.372378	+	0.0589789i
$918$		0			0
$919$	−5.54008	+	34.9787i	−0.182750	+	1.15384i	0.710305	+	0.703894i	$0.248557\pi$
$919$	−5.54008	+	34.9787i	−0.182750	+	1.15384i	−0.893055	+	0.449947i	$0.851443\pi$
$920$		0			0
$921$	11.7768	+	6.00059i	0.388059	+	0.197726i
$922$		0			0
$923$	−19.9878	+	6.49444i	−0.657908	+	0.213767i
$924$		0			0
$925$	−3.44804	+	10.6120i	−0.113371	+	0.348920i
$926$		0			0
$927$	2.79306	+	8.59617i	0.0917362	+	0.282335i
$928$		0			0
$929$	−6.39497	+	6.39497i	−0.209812	+	0.209812i	−0.804188	−	0.594375i	$-0.797399\pi$
$929$	−6.39497	+	6.39497i	−0.209812	+	0.209812i	0.594375	+	0.804188i	$0.297399\pi$
$930$		0			0
$931$	−6.21670	−	39.2507i	−0.203744	−	1.28639i
$932$		0			0
$933$	4.40772	−	3.20240i	0.144302	−	0.104842i
$934$		0			0
$935$	−11.6913	−	16.0918i	−0.382348	−	0.526257i
$936$		0			0
$937$	8.02099	+	15.7421i	0.262034	+	0.514271i	0.984114	−	0.177539i	$-0.0568135\pi$
$937$	8.02099	+	15.7421i	0.262034	+	0.514271i	−0.722079	+	0.691810i	$0.756814\pi$
$938$		0			0
$939$	7.03017	+	5.10772i	0.229421	+	0.166684i
$940$		0			0
$941$	30.7087	+	9.97786i	1.00108	+	0.325269i	0.763295	−	0.646050i	$-0.223580\pi$
$941$	30.7087	+	9.97786i	1.00108	+	0.325269i	0.237780	+	0.971319i	$0.423580\pi$
$942$		0			0
$943$	−27.1242	−	24.7416i	−0.883285	−	0.805696i
$944$		0			0
$945$	9.22381	+	2.99700i	0.300050	+	0.0974923i
$946$		0			0
$947$	−4.82434	−	3.50509i	−0.156770	−	0.113900i	0.506635	−	0.862161i	$-0.330889\pi$
$947$	−4.82434	−	3.50509i	−0.156770	−	0.113900i	−0.663405	+	0.748261i	$0.730889\pi$
$948$		0			0
$949$	−16.3695	−	32.1270i	−0.531378	−	1.04289i
$950$		0			0
$951$	6.59694	+	9.07991i	0.213920	+	0.294436i
$952$		0			0
$953$	−22.7060	+	16.4968i	−0.735518	+	0.534385i	−0.891304	−	0.453406i	$-0.850209\pi$
$953$	−22.7060	+	16.4968i	−0.735518	+	0.534385i	0.155786	+	0.987791i	$0.450209\pi$
$954$		0			0
$955$	−1.94003	−	12.2489i	−0.0627778	−	0.396364i
$956$		0			0
$957$	−0.955489	+	0.955489i	−0.0308866	+	0.0308866i
$958$		0			0
$959$	6.59004	+	20.2821i	0.212803	+	0.654942i
$960$		0			0
$961$	−7.82904	+	24.0953i	−0.252550	+	0.777268i
$962$		0			0
$963$	−37.3427	+	12.1334i	−1.20335	+	0.390993i
$964$		0			0
$965$	15.3187	+	7.80527i	0.493126	+	0.251261i
$966$		0			0
$967$	−3.30788	+	20.8851i	−0.106374	+	0.671620i	0.875662	+	0.482925i	$0.160426\pi$
$967$	−3.30788	+	20.8851i	−0.106374	+	0.671620i	−0.982036	+	0.188695i	$0.939574\pi$
$968$		0			0
$969$	−26.4275	+	4.18571i	−0.848974	+	0.134464i
$970$		0			0
$971$	49.3087	−	25.1240i	1.58239	−	0.806268i	0.582413	−	0.812893i	$-0.302109\pi$
$971$	49.3087	−	25.1240i	1.58239	−	0.806268i	0.999978	+	0.00662465i	$0.00210871\pi$
$972$		0			0
$973$	−61.8977	−	9.80364i	−1.98435	−	0.314290i
$974$		0			0
$975$			3.02327i			0.0968221i
$976$		0			0
$977$	14.2936	−	28.0528i	0.457294	−	0.897489i	−0.541107	−	0.840954i	$-0.681995\pi$
$977$	14.2936	−	28.0528i	0.457294	−	0.897489i	0.998401	−	0.0565354i	$-0.0180054\pi$
$978$		0			0
$979$	10.3896	−	14.3001i	0.332054	−	0.457033i
$980$		0			0
$981$	−32.6057	−	32.6057i	−1.04102	−	1.04102i
$982$		0			0
$983$	27.6275			0.881181			0.440591	−	0.897708i	$-0.354769\pi$
$983$	27.6275			0.881181			0.440591	+	0.897708i	$0.354769\pi$
$984$		0			0
$985$	−22.1982			−0.707294
$986$		0			0
$987$	11.3294	+	11.3294i	0.360620	+	0.360620i
$988$		0			0
$989$	−33.9003	+	46.6597i	−1.07797	+	1.48369i
$990$		0			0
$991$	−24.9742	+	49.0146i	−0.793330	+	1.55700i	0.0367299	+	0.999325i	$0.488306\pi$
$991$	−24.9742	+	49.0146i	−0.793330	+	1.55700i	−0.830060	+	0.557674i	$0.811694\pi$
$992$		0			0
$993$		−	0.323959i		−	0.0102805i
$994$		0			0
$995$	14.3901	+	2.27916i	0.456196	+	0.0722543i
$996$		0			0
$997$	15.7532	−	8.02665i	0.498908	−	0.254207i	−0.186381	−	0.982478i	$-0.559676\pi$
$997$	15.7532	−	8.02665i	0.498908	−	0.254207i	0.685289	+	0.728271i	$0.259676\pi$
$998$		0			0
$999$	−30.2009	+	4.78335i	−0.955513	+	0.151338i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bo.b.21.5	✓	64
41.2	even	20	inner	820.2.bo.b.781.5	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bo.b.21.5	✓	64	1.1	even	1	trivial
820.2.bo.b.781.5	yes	64	41.2	even	20	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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bo (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.335549 + 0.335549i) q^{3} +(0.587785 - 0.809017i) q^{5} +(-1.60673 + 3.15338i) q^{7} -2.77481i q^{9} +(-2.50592 - 0.396899i) q^{11} +(-5.67658 + 2.89236i) q^{13} +(0.468696 - 0.0742341i) q^{15} +(-1.22640 + 7.74315i) q^{17} +(6.40838 + 3.26523i) q^{19} +(-1.59725 + 0.518977i) q^{21} +(-1.77180 + 5.45303i) q^{23} +(-0.309017 - 0.951057i) q^{25} +(1.93773 - 1.93773i) q^{27} +(-0.175572 - 1.10852i) q^{29} +(1.92551 - 1.39897i) q^{31} +(-0.707681 - 0.974039i) q^{33} +(1.60673 + 3.15338i) q^{35} +(-9.02710 - 6.55857i) q^{37} +(-2.87530 - 0.934242i) q^{39} +(-2.64208 + 5.83261i) q^{41} +(9.56664 + 3.10839i) q^{43} +(-2.24487 - 1.63099i) q^{45} +(-4.33116 - 8.50037i) q^{47} +(-3.24772 - 4.47011i) q^{49} +(-3.00972 + 2.18669i) q^{51} +(0.794447 + 5.01594i) q^{53} +(-1.79404 + 1.79404i) q^{55} +(1.05468 + 3.24597i) q^{57} +(-2.65621 + 8.17497i) q^{59} +(4.00604 - 1.30164i) q^{61} +(8.75003 + 4.45836i) q^{63} +(-0.996641 + 6.29254i) q^{65} +(2.69023 - 0.426091i) q^{67} +(-2.42428 + 1.23523i) q^{69} +(3.25817 + 0.516043i) q^{71} +5.65957i q^{73} +(0.215436 - 0.422816i) q^{75} +(5.27790 - 7.26441i) q^{77} +(-3.23457 - 3.23457i) q^{79} -7.02403 q^{81} -6.85729 q^{83} +(5.54349 + 5.54349i) q^{85} +(0.313049 - 0.430875i) q^{87} +(-3.16286 + 6.20747i) q^{89} -22.5476i q^{91} +(1.11553 + 0.176682i) q^{93} +(6.40838 - 3.26523i) q^{95} +(-0.669208 + 0.105992i) q^{97} +(-1.10132 + 6.95347i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 2 q^{3} - 10 q^{7} + 2 q^{11} + 6 q^{13} - 2 q^{15} + 2 q^{17} + 10 q^{19} - 22 q^{23} + 16 q^{25} + 20 q^{27} - 12 q^{29} + 22 q^{31} + 30 q^{33} + 10 q^{35} + 12 q^{37} + 20 q^{39} - 10 q^{41}+ \cdots - 54 q^{99}+O(q^{100}) \) 64 * q + 2 * q^3 - 10 * q^7 + 2 * q^11 + 6 * q^13 - 2 * q^15 + 2 * q^17 + 10 * q^19 - 22 * q^23 + 16 * q^25 + 20 * q^27 - 12 * q^29 + 22 * q^31 + 30 * q^33 + 10 * q^35 + 12 * q^37 + 20 * q^39 - 10 * q^41 + 10 * q^43 + 32 * q^45 + 28 * q^47 + 10 * q^49 - 22 * q^51 + 4 * q^53 - 12 * q^55 - 30 * q^57 + 18 * q^59 - 20 * q^61 + 52 * q^63 - 6 * q^65 - 6 * q^67 - 50 * q^69 + 34 * q^71 + 8 * q^75 - 110 * q^77 - 14 * q^79 - 108 * q^81 + 32 * q^83 - 8 * q^85 - 80 * q^87 - 122 * q^89 + 42 * q^93 + 10 * q^95 - 64 * q^97 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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