LMFDB - Embedded newform 832.2.br.a.81.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [832,2,Mod(81,832)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(832, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 4]))

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

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

chi := DirichletCharacter("832.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 832 = 2^{6} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	832.br (of order $12$, degree $4$, not 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:	$6.64355344817$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 208)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			81.23
Character	$\chi$	$=$	832.81
Dual form			832.2.br.a.113.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.623697 - 2.32767i) q^{3} +(-2.33843 + 2.33843i) q^{5} +(3.16277 + 1.82602i) q^{7} +(-2.43097 - 1.40352i) q^{9} +O(q^{10})$	\(q+(0.623697 - 2.32767i) q^{3} +(-2.33843 + 2.33843i) q^{5} +(3.16277 + 1.82602i) q^{7} +(-2.43097 - 1.40352i) q^{9} +(-3.60420 - 0.965741i) q^{11} +(0.897619 - 3.49203i) q^{13} +(3.98462 + 6.90156i) q^{15} +(1.39318 - 2.41306i) q^{17} +(6.63086 - 1.77673i) q^{19} +(6.22299 - 6.22299i) q^{21} +(5.70507 - 3.29383i) q^{23} -5.93649i q^{25} +(0.328797 - 0.328797i) q^{27} +(-0.314295 + 1.17296i) q^{29} +4.09157 q^{31} +(-4.49585 + 7.78705i) q^{33} +(-11.6659 + 3.12588i) q^{35} +(3.69016 + 0.988774i) q^{37} +(-7.56845 - 4.26733i) q^{39} +(-0.123461 + 0.0712802i) q^{41} +(-0.772184 - 2.88183i) q^{43} +(8.96668 - 2.40261i) q^{45} +7.34533 q^{47} +(3.16873 + 5.48840i) q^{49} +(-4.74789 - 4.74789i) q^{51} +(-6.32639 + 6.32639i) q^{53} +(10.6865 - 6.16984i) q^{55} -16.5426i q^{57} +(0.387585 + 1.44649i) q^{59} +(-2.41180 + 0.646240i) q^{61} +(-5.12572 - 8.87801i) q^{63} +(6.06685 + 10.2649i) q^{65} +(0.625756 - 2.33535i) q^{67} +(-4.10870 - 15.3339i) q^{69} +(-7.89833 - 4.56010i) q^{71} +10.8639i q^{73} +(-13.8182 - 3.70257i) q^{75} +(-9.63576 - 9.63576i) q^{77} -10.7847 q^{79} +(-4.77082 - 8.26331i) q^{81} +(-0.331076 - 0.331076i) q^{83} +(2.38492 + 8.90063i) q^{85} +(2.53425 + 1.46315i) q^{87} +(-6.75424 + 3.89956i) q^{89} +(9.21549 - 9.40541i) q^{91} +(2.55190 - 9.52382i) q^{93} +(-11.3510 + 19.6606i) q^{95} +(5.70247 - 9.87697i) q^{97} +(7.40625 + 7.40625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q + 2 q^{3} - 8 q^{5}+O(q^{10}) $ 104 * q + 2 * q^3 - 8 * q^5	$ 104 q + 2 q^{3} - 8 q^{5} + 2 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 2 q^{19} - 20 q^{21} - 4 q^{27} - 2 q^{29} + 16 q^{31} - 4 q^{33} - 8 q^{35} - 2 q^{37} + 18 q^{43} + 20 q^{45} + 16 q^{47} + 24 q^{49} - 4 q^{51} - 8 q^{53} + 42 q^{59} - 2 q^{61} + 60 q^{63} - 16 q^{65} + 2 q^{67} - 14 q^{69} - 10 q^{75} - 36 q^{77} - 64 q^{79} + 16 q^{81} + 48 q^{83} - 12 q^{85} - 38 q^{91} - 56 q^{93} - 60 q^{95} - 4 q^{97} + 160 q^{99}+O(q^{100}) $ 104 * q + 2 * q^3 - 8 * q^5 + 2 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 2 * q^19 - 20 * q^21 - 4 * q^27 - 2 * q^29 + 16 * q^31 - 4 * q^33 - 8 * q^35 - 2 * q^37 + 18 * q^43 + 20 * q^45 + 16 * q^47 + 24 * q^49 - 4 * q^51 - 8 * q^53 + 42 * q^59 - 2 * q^61 + 60 * q^63 - 16 * q^65 + 2 * q^67 - 14 * q^69 - 10 * q^75 - 36 * q^77 - 64 * q^79 + 16 * q^81 + 48 * q^83 - 12 * q^85 - 38 * q^91 - 56 * q^93 - 60 * q^95 - 4 * q^97 + 160 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	0.623697	−	2.32767i	0.360092	−	1.34388i	−0.513863	−	0.857872i	$-0.671786\pi$
$3$	0.623697	−	2.32767i	0.360092	−	1.34388i	0.873954	−	0.486008i	$-0.161547\pi$
$4$		0			0
$5$	−2.33843	+	2.33843i	−1.04578	+	1.04578i	−0.0468761	+	0.998901i	$0.514927\pi$
$5$	−2.33843	+	2.33843i	−1.04578	+	1.04578i	−0.998901	+	0.0468761i	$0.985073\pi$
$6$		0			0
$7$	3.16277	+	1.82602i	1.19541	+	0.690172i	0.959529	−	0.281609i	$-0.0908681\pi$
$7$	3.16277	+	1.82602i	1.19541	+	0.690172i	0.235884	+	0.971781i	$0.424201\pi$
$8$		0			0
$9$	−2.43097	−	1.40352i	−0.810323	−	0.467840i
$10$		0			0
$11$	−3.60420	−	0.965741i	−1.08671	−	0.291182i	−0.329366	−	0.944202i	$-0.606835\pi$
$11$	−3.60420	−	0.965741i	−1.08671	−	0.291182i	−0.757340	+	0.653020i	$0.773502\pi$
$12$		0			0
$13$	0.897619	−	3.49203i	0.248955	−	0.968515i
$13$	0.897619	−	3.49203i	0.248955	−	0.968515i
$14$		0			0
$15$	3.98462	+	6.90156i	1.02882	+	1.78197i
$16$		0			0
$17$	1.39318	−	2.41306i	0.337896	−	0.585254i	−0.646140	−	0.763219i	$-0.723618\pi$
$17$	1.39318	−	2.41306i	0.337896	−	0.585254i	0.984037	+	0.177965i	$0.0569513\pi$
$18$		0			0
$19$	6.63086	−	1.77673i	1.52122	−	0.407611i	0.601080	−	0.799189i	$-0.294737\pi$
$19$	6.63086	−	1.77673i	1.52122	−	0.407611i	0.920145	+	0.391578i	$0.128071\pi$
$20$		0			0
$21$	6.22299	−	6.22299i	1.35797	−	1.35797i
$22$		0			0
$23$	5.70507	−	3.29383i	1.18959	−	0.686810i	0.231377	−	0.972864i	$-0.425677\pi$
$23$	5.70507	−	3.29383i	1.18959	−	0.686810i	0.958213	+	0.286054i	$0.0923437\pi$
$24$		0			0
$25$		−	5.93649i		−	1.18730i
$26$		0			0
$27$	0.328797	−	0.328797i	0.0632770	−	0.0632770i
$28$		0			0
$29$	−0.314295	+	1.17296i	−0.0583631	+	0.217814i	−0.988948	−	0.148262i	$-0.952632\pi$
$29$	−0.314295	+	1.17296i	−0.0583631	+	0.217814i	0.930585	+	0.366076i	$0.119299\pi$
$30$		0			0
$31$	4.09157			0.734867			0.367434	−	0.930050i	$-0.380236\pi$
$31$	4.09157			0.734867			0.367434	+	0.930050i	$0.380236\pi$
$32$		0			0
$33$	−4.49585	+	7.78705i	−0.782627	+	1.35555i
$34$		0			0
$35$	−11.6659	+	3.12588i	−1.97190	+	0.528369i
$36$		0			0
$37$	3.69016	+	0.988774i	0.606658	+	0.162553i	0.549055	−	0.835786i	$-0.314988\pi$
$37$	3.69016	+	0.988774i	0.606658	+	0.162553i	0.0576027	+	0.998340i	$0.481654\pi$
$38$		0			0
$39$	−7.56845	−	4.26733i	−1.21192	−	0.683319i
$40$		0			0
$41$	−0.123461	+	0.0712802i	−0.0192814	+	0.0111321i	−0.509610	−	0.860406i	$-0.670210\pi$
$41$	−0.123461	+	0.0712802i	−0.0192814	+	0.0111321i	0.490328	+	0.871538i	$0.336877\pi$
$42$		0			0
$43$	−0.772184	−	2.88183i	−0.117757	−	0.439475i	0.881721	−	0.471770i	$-0.156385\pi$
$43$	−0.772184	−	2.88183i	−0.117757	−	0.439475i	−0.999478	+	0.0322955i	$0.989718\pi$
$44$		0			0
$45$	8.96668	−	2.40261i	1.33667	−	0.358161i
$46$		0			0
$47$	7.34533			1.07143			0.535713	−	0.844400i	$-0.320043\pi$
$47$	7.34533			1.07143			0.535713	+	0.844400i	$0.320043\pi$
$48$		0			0
$49$	3.16873	+	5.48840i	0.452675	+	0.784057i
$50$		0			0
$51$	−4.74789	−	4.74789i	−0.664837	−	0.664837i
$52$		0			0
$53$	−6.32639	+	6.32639i	−0.868997	+	0.868997i	−0.992361	−	0.123365i	$-0.960631\pi$
$53$	−6.32639	+	6.32639i	−0.868997	+	0.868997i	0.123365	+	0.992361i	$0.460631\pi$
$54$		0			0
$55$	10.6865	−	6.16984i	1.44096	−	0.831940i
$56$		0			0
$57$		−	16.5426i		−	2.19112i
$58$		0			0
$59$	0.387585	+	1.44649i	0.0504593	+	0.188317i	0.986555	−	0.163428i	$-0.0522552\pi$
$59$	0.387585	+	1.44649i	0.0504593	+	0.188317i	−0.936096	+	0.351745i	$0.885589\pi$
$60$		0			0
$61$	−2.41180	+	0.646240i	−0.308799	+	0.0827425i	−0.409891	−	0.912135i	$-0.634433\pi$
$61$	−2.41180	+	0.646240i	−0.308799	+	0.0827425i	0.101091	+	0.994877i	$0.467767\pi$
$62$		0			0
$63$	−5.12572	−	8.87801i	−0.645781	−	1.11852i
$64$		0			0
$65$	6.06685	+	10.2649i	0.752500	+	1.27320i
$66$		0			0
$67$	0.625756	−	2.33535i	0.0764483	−	0.285309i	−0.917110	−	0.398635i	$-0.869484\pi$
$67$	0.625756	−	2.33535i	0.0764483	−	0.285309i	0.993558	+	0.113326i	$0.0361506\pi$
$68$		0			0
$69$	−4.10870	−	15.3339i	−0.494629	−	1.84598i
$70$		0			0
$71$	−7.89833	−	4.56010i	−0.937359	−	0.541185i	−0.0482279	−	0.998836i	$-0.515357\pi$
$71$	−7.89833	−	4.56010i	−0.937359	−	0.541185i	−0.889132	+	0.457652i	$0.848691\pi$
$72$		0			0
$73$			10.8639i			1.27152i	0.771885	+	0.635762i	$0.219314\pi$
$73$			10.8639i			1.27152i	−0.771885	+	0.635762i	$0.780686\pi$
$74$		0			0
$75$	−13.8182	−	3.70257i	−1.59559	−	0.427536i
$76$		0			0
$77$	−9.63576	−	9.63576i	−1.09810	−	1.09810i
$78$		0			0
$79$	−10.7847			−1.21337			−0.606686	−	0.794941i	$-0.707502\pi$
$79$	−10.7847			−1.21337			−0.606686	+	0.794941i	$0.707502\pi$
$80$		0			0
$81$	−4.77082	−	8.26331i	−0.530091	−	0.918145i
$82$		0			0
$83$	−0.331076	−	0.331076i	−0.0363403	−	0.0363403i	0.688703	−	0.725043i	$-0.258180\pi$
$83$	−0.331076	−	0.331076i	−0.0363403	−	0.0363403i	−0.725043	+	0.688703i	$0.758180\pi$
$84$		0			0
$85$	2.38492	+	8.90063i	0.258681	+	0.965409i
$86$		0			0
$87$	2.53425	+	1.46315i	0.271700	+	0.156866i
$88$		0			0
$89$	−6.75424	+	3.89956i	−0.715948	+	0.413353i	−0.813259	−	0.581901i	$-0.802309\pi$
$89$	−6.75424	+	3.89956i	−0.715948	+	0.413353i	0.0973116	+	0.995254i	$0.468976\pi$
$90$		0			0
$91$	9.21549	−	9.40541i	0.966046	−	0.985954i
$92$		0			0
$93$	2.55190	−	9.52382i	0.264620	−	0.987574i
$94$		0			0
$95$	−11.3510	+	19.6606i	−1.16459	+	2.01713i
$96$		0			0
$97$	5.70247	−	9.87697i	0.578998	−	1.00285i	−0.416596	−	0.909092i	$-0.636777\pi$
$97$	5.70247	−	9.87697i	0.578998	−	1.00285i	0.995595	−	0.0937630i	$-0.0298896\pi$
$98$		0			0
$99$	7.40625	+	7.40625i	0.744356	+	0.744356i
$100$		0			0
$101$	−2.23780	−	0.599616i	−0.222669	−	0.0596640i	0.145759	−	0.989320i	$-0.453437\pi$
$101$	−2.23780	−	0.599616i	−0.222669	−	0.0596640i	−0.368429	+	0.929656i	$0.620104\pi$
$102$		0			0
$103$			8.68531i			0.855789i	0.903829	+	0.427895i	$0.140745\pi$
$103$			8.68531i			0.855789i	−0.903829	+	0.427895i	$0.859255\pi$
$104$		0			0
$105$			29.1040i			2.84026i
$106$		0			0
$107$	10.9540	+	2.93513i	1.05897	+	0.283749i	0.745953	−	0.665999i	$-0.231995\pi$
$107$	10.9540	+	2.93513i	1.05897	+	0.283749i	0.313014	+	0.949748i	$0.398661\pi$
$108$		0			0
$109$	5.96844	+	5.96844i	0.571672	+	0.571672i	0.932596	−	0.360923i	$-0.117538\pi$
$109$	5.96844	+	5.96844i	0.571672	+	0.571672i	−0.360923	+	0.932596i	$0.617538\pi$
$110$		0			0
$111$	4.60308	−	7.97277i	0.436905	−	0.756741i
$112$		0			0
$113$	−4.70737	+	8.15341i	−0.442833	+	0.767008i	−0.997898	−	0.0647979i	$-0.979360\pi$
$113$	−4.70737	+	8.15341i	−0.442833	+	0.767008i	0.555066	+	0.831806i	$0.312693\pi$
$114$		0			0
$115$	−5.63853	+	21.0433i	−0.525796	+	1.96230i
$116$		0			0
$117$	−7.08322	+	7.22919i	−0.654844	+	0.668339i
$118$		0			0
$119$	8.81262	−	5.08797i	0.807852	−	0.466413i
$120$		0			0
$121$	2.53129	+	1.46144i	0.230117	+	0.132858i
$122$		0			0
$123$	0.0889145	+	0.331833i	0.00801715	+	0.0299204i
$124$		0			0
$125$	2.18992	+	2.18992i	0.195872	+	0.195872i
$126$		0			0
$127$	−2.35499	−	4.07897i	−0.208972	−	0.361950i	0.742419	−	0.669936i	$-0.233678\pi$
$127$	−2.35499	−	4.07897i	−0.208972	−	0.361950i	−0.951391	+	0.307986i	$0.900345\pi$
$128$		0			0
$129$	−7.18956			−0.633005
$130$		0			0
$131$	0.104732	+	0.104732i	0.00915046	+	0.00915046i	0.711667	−	0.702517i	$-0.247940\pi$
$131$	0.104732	+	0.104732i	0.00915046	+	0.00915046i	−0.702517	+	0.711667i	$0.747940\pi$
$132$		0			0
$133$	24.2162	+	6.48872i	2.09981	+	0.562643i
$134$		0			0
$135$			1.53774i			0.132347i
$136$		0			0
$137$	6.48097	+	3.74179i	0.553707	+	0.319683i	0.750616	−	0.660739i	$-0.229757\pi$
$137$	6.48097	+	3.74179i	0.553707	+	0.319683i	−0.196909	+	0.980422i	$0.563090\pi$
$138$		0			0
$139$	−3.98009	−	14.8539i	−0.337587	−	1.25989i	−0.901037	−	0.433741i	$-0.857193\pi$
$139$	−3.98009	−	14.8539i	−0.337587	−	1.25989i	0.563451	−	0.826150i	$-0.309473\pi$
$140$		0			0
$141$	4.58126	−	17.0975i	0.385812	−	1.43987i
$142$		0			0
$143$	−6.60759	+	11.7191i	−0.552555	+	0.980000i
$144$		0			0
$145$	−2.00794	−	3.47785i	−0.166750	−	0.288820i
$146$		0			0
$147$	14.7515	−	3.95265i	1.21668	−	0.326009i
$148$		0			0
$149$	−0.864092	−	3.22484i	−0.0707892	−	0.264189i	0.921456	−	0.388482i	$-0.127000\pi$
$149$	−0.864092	−	3.22484i	−0.0707892	−	0.264189i	−0.992246	+	0.124293i	$0.960334\pi$
$150$		0			0
$151$			20.8859i			1.69967i	0.527047	+	0.849836i	$0.323299\pi$
$151$			20.8859i			1.69967i	−0.527047	+	0.849836i	$0.676701\pi$
$152$		0			0
$153$	−6.77357	+	3.91072i	−0.547610	+	0.316163i
$154$		0			0
$155$	−9.56784	+	9.56784i	−0.768507	+	0.768507i
$156$		0			0
$157$	8.48001	+	8.48001i	0.676778	+	0.676778i	0.959270	−	0.282491i	$-0.0911609\pi$
$157$	8.48001	+	8.48001i	0.676778	+	0.676778i	−0.282491	+	0.959270i	$0.591161\pi$
$158$		0			0
$159$	10.7800	+	18.6715i	0.854909	+	1.48075i
$160$		0			0
$161$	24.0584			1.89607
$162$		0			0
$163$	−5.86275	+	1.57092i	−0.459206	+	0.123044i	−0.481004	−	0.876719i	$-0.659728\pi$
$163$	−5.86275	+	1.57092i	−0.459206	+	0.123044i	0.0217979	+	0.999762i	$0.493061\pi$
$164$		0			0
$165$	−7.69622	−	28.7227i	−0.599150	−	2.23606i
$166$		0			0
$167$	5.53339	−	3.19470i	0.428186	−	0.247214i	−0.270387	−	0.962752i	$-0.587152\pi$
$167$	5.53339	−	3.19470i	0.428186	−	0.247214i	0.698574	+	0.715538i	$0.253818\pi$
$168$		0			0
$169$	−11.3886	−	6.26902i	−0.876043	−	0.482233i
$170$		0			0
$171$	−18.6131	−	4.98737i	−1.42338	−	0.381393i
$172$		0			0
$173$	−2.34286	+	0.627768i	−0.178125	+	0.0477283i	−0.346779	−	0.937947i	$-0.612725\pi$
$173$	−2.34286	+	0.627768i	−0.178125	+	0.0477283i	0.168654	+	0.985675i	$0.446058\pi$
$174$		0			0
$175$	10.8402	−	18.7757i	0.819440	−	1.41931i
$176$		0			0
$177$	3.60868			0.271245
$178$		0			0
$179$	4.93333	−	18.4114i	0.368734	−	1.37614i	−0.493553	−	0.869716i	$-0.664302\pi$
$179$	4.93333	−	18.4114i	0.368734	−	1.37614i	0.862287	−	0.506419i	$-0.169031\pi$
$180$		0			0
$181$	−12.6523	+	12.6523i	−0.940441	+	0.940441i	−0.998323	−	0.0578822i	$-0.981565\pi$
$181$	−12.6523	+	12.6523i	−0.940441	+	0.940441i	0.0578822	+	0.998323i	$0.481565\pi$
$182$		0			0
$183$			6.01693i			0.444784i
$184$		0			0
$185$	−10.9413	+	6.31699i	−0.804423	+	0.464434i
$186$		0			0
$187$	−7.35170	+	7.35170i	−0.537609	+	0.537609i
$188$		0			0
$189$	1.64030	−	0.439517i	0.119314	−	0.0319701i
$190$		0			0
$191$	6.30968	−	10.9287i	0.456552	−	0.790772i	−0.542224	−	0.840234i	$-0.682418\pi$
$191$	6.30968	−	10.9287i	0.456552	−	0.790772i	0.998776	+	0.0494625i	$0.0157508\pi$
$192$		0			0
$193$	1.86581	+	3.23168i	0.134304	+	0.232621i	0.925331	−	0.379160i	$-0.123787\pi$
$193$	1.86581	+	3.23168i	0.134304	+	0.232621i	−0.791027	+	0.611781i	$0.790454\pi$
$194$		0			0
$195$	27.6771	−	7.71944i	1.98200	−	0.552800i
$196$		0			0
$197$	25.9395	+	6.95047i	1.84811	+	0.495201i	0.999432	−	0.0337033i	$-0.0107301\pi$
$197$	25.9395	+	6.95047i	1.84811	+	0.495201i	0.848682	+	0.528904i	$0.177397\pi$
$198$		0			0
$199$	−0.729619	−	0.421246i	−0.0517213	−	0.0298613i	0.473916	−	0.880570i	$-0.342840\pi$
$199$	−0.729619	−	0.421246i	−0.0517213	−	0.0298613i	−0.525638	+	0.850709i	$0.676173\pi$
$200$		0			0
$201$	−5.04565	−	2.91311i	−0.355893	−	0.205475i
$202$		0			0
$203$	−3.13590	+	3.13590i	−0.220097	+	0.220097i
$204$		0			0
$205$	0.122021	−	0.455388i	0.00852231	−	0.0318057i
$206$		0			0
$207$	−18.4918			−1.28527
$208$		0			0
$209$	−25.6148			−1.77181
$210$		0			0
$211$	−0.287056	+	1.07131i	−0.0197617	+	0.0737518i	−0.975103	−	0.221754i	$-0.928822\pi$
$211$	−0.287056	+	1.07131i	−0.0197617	+	0.0737518i	0.955341	+	0.295506i	$0.0954883\pi$
$212$		0			0
$213$	−15.5406	+	15.5406i	−1.06482	+	1.06482i
$214$		0			0
$215$	8.54465	+	4.93326i	0.582740	+	0.336445i
$216$		0			0
$217$	12.9407	+	7.47130i	0.878470	+	0.507185i
$218$		0			0
$219$	25.2876	+	6.77579i	1.70878	+	0.457865i
$220$		0			0
$221$	−7.17594	−	7.03105i	−0.482706	−	0.472959i
$222$		0			0
$223$	−6.94501	−	12.0291i	−0.465072	−	0.805528i	0.534133	−	0.845401i	$-0.320638\pi$
$223$	−6.94501	−	12.0291i	−0.465072	−	0.805528i	−0.999205	+	0.0398723i	$0.987305\pi$
$224$		0			0
$225$	−8.33199	+	14.4314i	−0.555466	+	0.962095i
$226$		0			0
$227$	−11.7251	+	3.14174i	−0.778224	+	0.208524i	−0.626002	−	0.779822i	$-0.715310\pi$
$227$	−11.7251	+	3.14174i	−0.778224	+	0.208524i	−0.152222	+	0.988346i	$0.548643\pi$
$228$		0			0
$229$	−7.51976	+	7.51976i	−0.496920	+	0.496920i	−0.910478	−	0.413558i	$-0.864286\pi$
$229$	−7.51976	+	7.51976i	−0.496920	+	0.496920i	0.413558	+	0.910478i	$0.364286\pi$
$230$		0			0
$231$	−28.4387	+	16.4191i	−1.87113	+	1.08030i
$232$		0			0
$233$		−	8.49568i		−	0.556570i	−0.960498	−	0.278285i	$-0.910234\pi$
$233$		−	8.49568i		−	0.556570i	0.960498	−	0.278285i	$-0.0897660\pi$
$234$		0			0
$235$	−17.1765	+	17.1765i	−1.12047	+	1.12047i
$236$		0			0
$237$	−6.72638	+	25.1032i	−0.436925	+	1.63063i
$238$		0			0
$239$	−3.51330			−0.227257			−0.113628	−	0.993523i	$-0.536247\pi$
$239$	−3.51330			−0.227257			−0.113628	+	0.993523i	$0.536247\pi$
$240$		0			0
$241$	−2.56875	+	4.44921i	−0.165468	+	0.286599i	−0.936821	−	0.349808i	$-0.886247\pi$
$241$	−2.56875	+	4.44921i	−0.165468	+	0.286599i	0.771353	+	0.636407i	$0.219580\pi$
$242$		0			0
$243$	−20.8624	+	5.59005i	−1.33832	+	0.358602i
$244$		0			0
$245$	−20.2441	−	5.42438i	−1.29335	−	0.346551i
$246$		0			0
$247$	−0.252426	−	24.7500i	−0.0160615	−	1.57481i
$248$		0			0
$249$	−0.977127	+	0.564144i	−0.0619229	+	0.0357512i
$250$		0			0
$251$	2.42800	+	9.06141i	0.153254	+	0.571951i	0.999249	+	0.0387600i	$0.0123408\pi$
$251$	2.42800	+	9.06141i	0.153254	+	0.571951i	−0.845995	+	0.533191i	$0.820993\pi$
$252$		0			0
$253$	−23.7432	+	6.36197i	−1.49272	+	0.399973i
$254$		0			0
$255$	22.2052			1.39054
$256$		0			0
$257$	−2.52088	−	4.36629i	−0.157248	−	0.272362i	0.776627	−	0.629960i	$-0.216929\pi$
$257$	−2.52088	−	4.36629i	−0.157248	−	0.272362i	−0.933875	+	0.357599i	$0.883596\pi$
$258$		0			0
$259$	9.86557	+	9.86557i	0.613017	+	0.613017i
$260$		0			0
$261$	2.41032	−	2.41032i	0.149195	−	0.149195i
$262$		0			0
$263$	−15.3002	+	8.83358i	−0.943451	+	0.544702i	−0.891041	−	0.453924i	$-0.850024\pi$
$263$	−15.3002	+	8.83358i	−0.943451	+	0.544702i	−0.0524109	+	0.998626i	$0.516691\pi$
$264$		0			0
$265$		−	29.5876i		−	1.81755i
$266$		0			0
$267$	4.86429	+	18.1538i	0.297690	+	1.11099i
$268$		0			0
$269$	−21.6518	+	5.80158i	−1.32013	+	0.353729i	−0.849028	−	0.528348i	$-0.822812\pi$
$269$	−21.6518	+	5.80158i	−1.32013	+	0.353729i	−0.471106	+	0.882077i	$0.656145\pi$
$270$		0			0
$271$	3.22911	+	5.59299i	0.196155	+	0.339750i	0.947278	−	0.320412i	$-0.103821\pi$
$271$	3.22911	+	5.59299i	0.196155	+	0.339750i	−0.751124	+	0.660161i	$0.770488\pi$
$272$		0			0
$273$	−16.1450	−	27.3167i	−0.977140	−	1.65328i
$274$		0			0
$275$	−5.73311	+	21.3963i	−0.345720	+	1.29024i
$276$		0			0
$277$	−8.02289	−	29.9418i	−0.482048	−	1.79903i	−0.592999	−	0.805204i	$-0.702056\pi$
$277$	−8.02289	−	29.9418i	−0.482048	−	1.79903i	0.110950	−	0.993826i	$-0.464611\pi$
$278$		0			0
$279$	−9.94647	−	5.74260i	−0.595480	−	0.343800i
$280$		0			0
$281$		−	32.1422i		−	1.91744i	−0.284347	−	0.958721i	$-0.591777\pi$
$281$		−	32.1422i		−	1.91744i	0.284347	−	0.958721i	$-0.408223\pi$
$282$		0			0
$283$	6.23971	+	1.67193i	0.370912	+	0.0993857i	0.439460	−	0.898262i	$-0.355170\pi$
$283$	6.23971	+	1.67193i	0.370912	+	0.0993857i	−0.0685476	+	0.997648i	$0.521836\pi$
$284$		0			0
$285$	38.6837	+	38.6837i	2.29142	+	2.29142i
$286$		0			0
$287$	−0.520637			−0.0307323
$288$		0			0
$289$	4.61809	+	7.99876i	0.271652	+	0.470515i
$290$		0			0
$291$	−19.4337	−	19.4337i	−1.13922	−	1.13922i
$292$		0			0
$293$	7.11431	+	26.5510i	0.415622	+	1.55112i	0.783586	+	0.621284i	$0.213389\pi$
$293$	7.11431	+	26.5510i	0.415622	+	1.55112i	−0.367963	+	0.929840i	$0.619945\pi$
$294$		0			0
$295$	−4.28885	−	2.47617i	−0.249706	−	0.144168i
$296$		0			0
$297$	−1.50258	+	0.867515i	−0.0871886	+	0.0503384i
$298$		0			0
$299$	−6.38116	−	22.8789i	−0.369032	−	1.32312i
$300$		0			0
$301$	2.82005	−	10.5246i	0.162545	−	0.606627i
$302$		0			0
$303$	−2.79142	+	4.83487i	−0.160363	+	0.277756i
$304$		0			0
$305$	4.12863	−	7.15100i	0.236405	−	0.409465i
$306$		0			0
$307$	−19.3492	−	19.3492i	−1.10432	−	1.10432i	−0.993884	−	0.110433i	$-0.964776\pi$
$307$	−19.3492	−	19.3492i	−1.10432	−	1.10432i	−0.110433	−	0.993884i	$-0.535224\pi$
$308$		0			0
$309$	20.2165	+	5.41700i	1.15008	+	0.308163i
$310$		0			0
$311$			6.83310i			0.387469i	0.981054	+	0.193735i	$0.0620601\pi$
$311$			6.83310i			0.387469i	−0.981054	+	0.193735i	$0.937940\pi$
$312$		0			0
$313$		−	14.4698i		−	0.817879i	−0.912562	−	0.408939i	$-0.865899\pi$
$313$		−	14.4698i		−	0.817879i	0.912562	−	0.408939i	$-0.134101\pi$
$314$		0			0
$315$	32.7467	+	8.77446i	1.84507	+	0.494385i
$316$		0			0
$317$	9.83293	+	9.83293i	0.552272	+	0.552272i	0.927096	−	0.374824i	$-0.122297\pi$
$317$	9.83293	+	9.83293i	0.552272	+	0.552272i	−0.374824	+	0.927096i	$0.622297\pi$
$318$		0			0
$319$	2.26556	−	3.92407i	0.126847	−	0.219706i
$320$		0			0
$321$	13.6640	−	23.6667i	0.762650	−	1.32095i
$322$		0			0
$323$	4.95063	−	18.4760i	0.275460	−	1.02803i
$324$		0			0
$325$	−20.7304	−	5.32870i	−1.14992	−	0.295583i
$326$		0			0
$327$	17.6150	−	10.1700i	0.974114	−	0.562405i
$328$		0			0
$329$	23.2316	+	13.4127i	1.28080	+	0.739469i
$330$		0			0
$331$	−2.10738	−	7.86485i	−0.115832	−	0.432291i	0.883516	−	0.468401i	$-0.155170\pi$
$331$	−2.10738	−	7.86485i	−0.115832	−	0.432291i	−0.999348	+	0.0361104i	$0.988503\pi$
$332$		0			0
$333$	−7.58289	−	7.58289i	−0.415540	−	0.415540i
$334$		0			0
$335$	3.99777	+	6.92434i	0.218422	+	0.378317i
$336$		0			0
$337$	11.9397			0.650399			0.325199	−	0.945646i	$-0.394569\pi$
$337$	11.9397			0.650399			0.325199	+	0.945646i	$0.394569\pi$
$338$		0			0
$339$	16.0425	+	16.0425i	0.871307	+	0.871307i
$340$		0			0
$341$	−14.7468	−	3.95140i	−0.798585	−	0.213980i
$342$		0			0
$343$		−	2.41965i		−	0.130649i
$344$		0			0
$345$	45.4651	+	26.2493i	2.44776	+	1.41321i
$346$		0			0
$347$	3.22684	+	12.0427i	0.173226	+	0.646488i	0.996847	+	0.0793476i	$0.0252837\pi$
$347$	3.22684	+	12.0427i	0.173226	+	0.646488i	−0.823621	+	0.567141i	$0.808050\pi$
$348$		0			0
$349$	−7.10822	+	26.5282i	−0.380494	+	1.42002i	0.464654	+	0.885492i	$0.346179\pi$
$349$	−7.10822	+	26.5282i	−0.380494	+	1.42002i	−0.845148	+	0.534532i	$0.820488\pi$
$350$		0			0
$351$	−0.853035	−	1.44330i	−0.0455316	−	0.0770378i
$352$		0			0
$353$	−17.4243	−	30.1797i	−0.927401	−	1.60631i	−0.787653	−	0.616119i	$-0.788704\pi$
$353$	−17.4243	−	30.1797i	−0.927401	−	1.60631i	−0.139748	−	0.990187i	$-0.544629\pi$
$354$		0			0
$355$	29.1332	−	7.80620i	1.54623	−	0.414310i
$356$		0			0
$357$	−6.34670	−	23.6862i	−0.335903	−	1.25361i
$358$		0			0
$359$			4.13815i			0.218403i	0.994020	+	0.109202i	$0.0348294\pi$
$359$			4.13815i			0.218403i	−0.994020	+	0.109202i	$0.965171\pi$
$360$		0			0
$361$	24.3571	−	14.0626i	1.28195	−	0.740135i
$362$		0			0
$363$	4.98051	−	4.98051i	0.261409	−	0.261409i
$364$		0			0
$365$	−25.4045	−	25.4045i	−1.32973	−	1.32973i
$366$		0			0
$367$	−9.29156	−	16.0935i	−0.485015	−	0.840071i	0.514836	−	0.857288i	$-0.327853\pi$
$367$	−9.29156	−	16.0935i	−0.485015	−	0.840071i	−0.999852	+	0.0172172i	$0.994519\pi$
$368$		0			0
$369$	0.400173			0.0208322
$370$		0			0
$371$	−31.5610	+	8.45675i	−1.63857	+	0.439053i
$372$		0			0
$373$	4.18014	+	15.6005i	0.216439	+	0.807762i	0.985655	+	0.168773i	$0.0539805\pi$
$373$	4.18014	+	15.6005i	0.216439	+	0.807762i	−0.769216	+	0.638989i	$0.779353\pi$
$374$		0			0
$375$	6.46324	−	3.73155i	0.333760	−	0.192697i
$376$		0			0
$377$	3.81391	+	2.15040i	0.196426	+	0.110751i
$378$		0			0
$379$	23.1794	+	6.21090i	1.19065	+	0.319033i	0.799141	−	0.601143i	$-0.205288\pi$
$379$	23.1794	+	6.21090i	1.19065	+	0.319033i	0.391505	+	0.920176i	$0.371955\pi$
$380$		0			0
$381$	−10.9633	+	2.93761i	−0.561667	+	0.150498i
$382$		0			0
$383$	−2.67972	+	4.64141i	−0.136927	+	0.237165i	−0.926332	−	0.376708i	$-0.877056\pi$
$383$	−2.67972	+	4.64141i	−0.136927	+	0.237165i	0.789405	+	0.613873i	$0.210389\pi$
$384$		0			0
$385$	45.0651			2.29673
$386$		0			0
$387$	−2.16755	+	8.08942i	−0.110183	+	0.411208i
$388$		0			0
$389$	11.0330	−	11.0330i	0.559397	−	0.559397i	−0.369738	−	0.929136i	$-0.620553\pi$
$389$	11.0330	−	11.0330i	0.559397	−	0.559397i	0.929136	+	0.369738i	$0.120553\pi$
$390$		0			0
$391$		−	18.3556i		−	0.928283i
$392$		0			0
$393$	0.309102	−	0.178460i	0.0155921	−	0.00900212i
$394$		0			0
$395$	25.2192	−	25.2192i	1.26892	−	1.26892i
$396$		0			0
$397$	−4.23444	+	1.13461i	−0.212520	+	0.0569447i	−0.363508	−	0.931591i	$-0.618421\pi$
$397$	−4.23444	+	1.13461i	−0.212520	+	0.0569447i	0.150988	+	0.988536i	$0.451755\pi$
$398$		0			0
$399$	30.2072	−	52.3204i	1.51225	−	2.61930i
$400$		0			0
$401$	9.11661	+	15.7904i	0.455262	+	0.788536i	0.998703	−	0.0509106i	$-0.0162123\pi$
$401$	9.11661	+	15.7904i	0.455262	+	0.788536i	−0.543441	+	0.839447i	$0.682879\pi$
$402$		0			0
$403$	3.67267	−	14.2879i	0.182949	−	0.711730i
$404$		0			0
$405$	30.4794	+	8.16692i	1.51453	+	0.405818i
$406$		0			0
$407$	−12.3451	−	7.12747i	−0.611926	−	0.353296i
$408$		0			0
$409$	18.6321	+	10.7572i	0.921297	+	0.531911i	0.884049	−	0.467395i	$-0.154807\pi$
$409$	18.6321	+	10.7572i	0.921297	+	0.531911i	0.0372483	+	0.999306i	$0.488141\pi$
$410$		0			0
$411$	12.7518	−	12.7518i	0.629001	−	0.629001i
$412$		0			0
$413$	−1.41548	+	5.28264i	−0.0696512	+	0.259942i
$414$		0			0
$415$	1.54840			0.0760077
$416$		0			0
$417$	−37.0573			−1.81470
$418$		0			0
$419$	−3.23143	+	12.0599i	−0.157866	+	0.589163i	0.840977	+	0.541071i	$0.181981\pi$
$419$	−3.23143	+	12.0599i	−0.157866	+	0.589163i	−0.998843	+	0.0480925i	$0.984686\pi$
$420$		0			0
$421$	−26.0539	+	26.0539i	−1.26979	+	1.26979i	−0.323592	+	0.946197i	$0.604891\pi$
$421$	−26.0539	+	26.0539i	−1.26979	+	1.26979i	−0.946197	+	0.323592i	$0.895109\pi$
$422$		0			0
$423$	−17.8563	−	10.3093i	−0.868201	−	0.501256i
$424$		0			0
$425$	−14.3251	−	8.27061i	−0.694871	−	0.401184i
$426$		0			0
$427$	−8.80801	−	2.36010i	−0.426249	−	0.114213i
$428$		0			0
$429$	23.1570	+	22.6895i	1.11803	+	1.09546i
$430$		0			0
$431$	−3.47069	−	6.01142i	−0.167177	−	0.289560i	0.770249	−	0.637743i	$-0.220132\pi$
$431$	−3.47069	−	6.01142i	−0.167177	−	0.289560i	−0.937426	+	0.348184i	$0.886799\pi$
$432$		0			0
$433$	−6.31803	+	10.9431i	−0.303625	+	0.525894i	−0.976954	−	0.213449i	$-0.931530\pi$
$433$	−6.31803	+	10.9431i	−0.303625	+	0.525894i	0.673329	+	0.739343i	$0.264864\pi$
$434$		0			0
$435$	−9.34762	+	2.50469i	−0.448184	+	0.120091i
$436$		0			0
$437$	31.9773	−	31.9773i	1.52968	−	1.52968i
$438$		0			0
$439$	0.128570	−	0.0742300i	0.00613632	−	0.00354280i	−0.496929	−	0.867791i	$-0.665539\pi$
$439$	0.128570	−	0.0742300i	0.00613632	−	0.00354280i	0.503065	+	0.864249i	$0.332206\pi$
$440$		0			0
$441$		−	17.7895i		−	0.847119i
$442$		0			0
$443$	−27.4219	+	27.4219i	−1.30285	+	1.30285i	−0.376392	+	0.926461i	$0.622835\pi$
$443$	−27.4219	+	27.4219i	−1.30285	+	1.30285i	−0.926461	+	0.376392i	$0.877165\pi$
$444$		0			0
$445$	6.67546	−	24.9131i	0.316447	−	1.18100i
$446$		0			0
$447$	−8.04528			−0.380529
$448$		0			0
$449$	−4.95110	+	8.57556i	−0.233657	+	0.404706i	−0.958882	−	0.283807i	$-0.908403\pi$
$449$	−4.95110	+	8.57556i	−0.233657	+	0.404706i	0.725225	+	0.688512i	$0.241736\pi$
$450$		0			0
$451$	0.513816	−	0.137676i	0.0241946	−	0.00648293i
$452$		0			0
$453$	48.6155	+	13.0265i	2.28416	+	0.612038i
$454$		0			0
$455$	0.444103	+	43.5436i	0.0208199	+	2.04136i
$456$		0			0
$457$	−34.6636	+	20.0130i	−1.62149	+	0.936170i	−0.634974	+	0.772534i	$0.718989\pi$
$457$	−34.6636	+	20.0130i	−1.62149	+	0.936170i	−0.986521	+	0.163637i	$0.947678\pi$
$458$		0			0
$459$	−0.335333	−	1.25148i	−0.0156520	−	0.0584141i
$460$		0			0
$461$	8.15036	−	2.18388i	0.379600	−	0.101714i	−0.0639733	−	0.997952i	$-0.520377\pi$
$461$	8.15036	−	2.18388i	0.379600	−	0.101714i	0.443573	+	0.896238i	$0.353711\pi$
$462$		0			0
$463$	−21.0993			−0.980570			−0.490285	−	0.871562i	$-0.663107\pi$
$463$	−21.0993			−0.980570			−0.490285	+	0.871562i	$0.663107\pi$
$464$		0			0
$465$	16.3033	+	28.2382i	0.756049	+	1.30951i
$466$		0			0
$467$	13.9906	+	13.9906i	0.647408	+	0.647408i	0.952366	−	0.304958i	$-0.0986424\pi$
$467$	13.9906	+	13.9906i	0.647408	+	0.647408i	−0.304958	+	0.952366i	$0.598642\pi$
$468$		0			0
$469$	6.24353	−	6.24353i	0.288300	−	0.288300i
$470$		0			0
$471$	25.0276	−	14.4497i	1.15321	−	0.665807i
$472$		0			0
$473$			11.1324i			0.511869i
$474$		0			0
$475$	−10.5476	−	39.3641i	−0.483956	−	1.80615i
$476$		0			0
$477$	24.2585	−	6.50004i	1.11072	−	0.297616i
$478$		0			0
$479$	16.2487	+	28.1436i	0.742423	+	1.28591i	0.951389	+	0.307991i	$0.0996568\pi$
$479$	16.2487	+	28.1436i	0.742423	+	1.28591i	−0.208966	+	0.977923i	$0.567010\pi$
$480$		0			0
$481$	6.76518	−	11.9986i	0.308466	−	0.547089i
$482$		0			0
$483$	15.0052	−	56.0000i	0.682759	−	2.54809i
$484$		0			0
$485$	9.76177	+	36.4314i	0.443259	+	1.65427i
$486$		0			0
$487$	−23.9015	−	13.7995i	−1.08308	−	0.625316i	−0.151354	−	0.988480i	$-0.548363\pi$
$487$	−23.9015	−	13.7995i	−1.08308	−	0.625316i	−0.931725	+	0.363163i	$0.881697\pi$
$488$		0			0
$489$			14.6263i			0.661425i
$490$		0			0
$491$	40.2542	+	10.7861i	1.81664	+	0.486768i	0.996364	−	0.0851933i	$-0.0271508\pi$
$491$	40.2542	+	10.7861i	1.81664	+	0.486768i	0.820280	+	0.571962i	$0.193817\pi$
$492$		0			0
$493$	2.39257	+	2.39257i	0.107756	+	0.107756i
$494$		0			0
$495$	−34.6380			−1.55686
$496$		0			0
$497$	−16.6537	−	28.8451i	−0.747021	−	1.29388i
$498$		0			0
$499$	23.5197	+	23.5197i	1.05288	+	1.05288i	0.998521	+	0.0543635i	$0.0173130\pi$
$499$	23.5197	+	23.5197i	1.05288	+	1.05288i	0.0543635	+	0.998521i	$0.482687\pi$
$500$		0			0
$501$	−3.98505	−	14.8724i	−0.178039	−	0.664451i
$502$		0			0
$503$	0.355066	+	0.204998i	0.0158316	+	0.00914039i	0.507895	−	0.861419i	$-0.330424\pi$
$503$	0.355066	+	0.204998i	0.0158316	+	0.00914039i	−0.492063	+	0.870559i	$0.663757\pi$
$504$		0			0
$505$	6.63509	−	3.83077i	0.295258	−	0.170467i
$506$		0			0
$507$	−21.6952	+	22.5988i	−0.963519	+	1.00365i
$508$		0			0
$509$	3.52551	−	13.1574i	0.156265	−	0.583190i	−0.842728	−	0.538339i	$-0.819052\pi$
$509$	3.52551	−	13.1574i	0.156265	−	0.583190i	0.998994	−	0.0448510i	$-0.0142813\pi$
$510$		0			0
$511$	−19.8378	+	34.3600i	−0.877571	+	1.52000i
$512$		0			0
$513$	1.59602	−	2.76439i	0.0704661	−	0.122051i
$514$		0			0
$515$	−20.3100	−	20.3100i	−0.894964	−	0.894964i
$516$		0			0
$517$	−26.4740	−	7.09369i	−1.16433	−	0.311980i
$518$		0			0
$519$			5.84495i			0.256565i
$520$		0			0
$521$			36.1745i			1.58483i	0.609979	+	0.792417i	$0.291178\pi$
$521$			36.1745i			1.58483i	−0.609979	+	0.792417i	$0.708822\pi$
$522$		0			0
$523$	31.8439	+	8.53256i	1.39244	+	0.373103i	0.875623	−	0.482994i	$-0.160451\pi$
$523$	31.8439	+	8.53256i	1.39244	+	0.373103i	0.516815	+	0.856097i	$0.327118\pi$
$524$		0			0
$525$	−36.9427	−	36.9427i	−1.61231	−	1.61231i
$526$		0			0
$527$	5.70030	−	9.87321i	0.248309	−	0.430084i
$528$		0			0
$529$	10.1986	−	17.6645i	0.443416	−	0.768020i
$530$		0			0
$531$	1.08797	−	4.06035i	0.0472138	−	0.176204i
$532$		0			0
$533$	0.138092	+	0.495112i	0.00598142	+	0.0214457i
$534$		0			0
$535$	−32.4788	+	18.7516i	−1.40418	+	0.810704i
$536$		0			0
$537$	−39.7788	−	22.9663i	−1.71658	−	0.991070i
$538$		0			0
$539$	−6.12034	−	22.8414i	−0.263622	−	0.983850i
$540$		0			0
$541$	−13.1581	−	13.1581i	−0.565709	−	0.565709i	0.365214	−	0.930923i	$-0.380996\pi$
$541$	−13.1581	−	13.1581i	−0.565709	−	0.565709i	−0.930923	+	0.365214i	$0.880996\pi$
$542$		0			0
$543$	21.5592	+	37.3417i	0.925195	+	1.60249i
$544$		0			0
$545$	−27.9135			−1.19568
$546$		0			0
$547$	10.3233	+	10.3233i	0.441392	+	0.441392i	0.892480	−	0.451087i	$-0.148964\pi$
$547$	10.3233	+	10.3233i	0.441392	+	0.441392i	−0.451087	+	0.892480i	$0.648964\pi$
$548$		0			0
$549$	6.77002	+	1.81402i	0.288937	+	0.0774205i
$550$		0			0
$551$			8.33619i			0.355133i
$552$		0			0
$553$	−34.1095	−	19.6931i	−1.45048	−	0.837436i
$554$		0			0
$555$	7.87977	+	29.4077i	0.334478	+	1.24829i
$556$		0			0
$557$	−7.24872	+	27.0526i	−0.307138	+	1.14626i	0.623951	+	0.781464i	$0.285527\pi$
$557$	−7.24872	+	27.0526i	−0.307138	+	1.14626i	−0.931089	+	0.364792i	$0.881140\pi$
$558$		0			0
$559$	−10.7566	+	0.109707i	−0.454954	+	0.00464010i
$560$		0			0
$561$	12.5271	+	21.6975i	0.528894	+	0.916071i
$562$		0			0
$563$	−19.4048	+	5.19950i	−0.817815	+	0.219133i	−0.643391	−	0.765538i	$-0.722473\pi$
$563$	−19.4048	+	5.19950i	−0.817815	+	0.219133i	−0.174424	+	0.984671i	$0.555806\pi$
$564$		0			0
$565$	−8.05831	−	30.0740i	−0.339016	−	1.26522i
$566$		0			0
$567$		−	34.8465i		−	1.46342i
$568$		0			0
$569$	−2.23116	+	1.28816i	−0.0935352	+	0.0540026i	−0.546038	−	0.837760i	$-0.683865\pi$
$569$	−2.23116	+	1.28816i	−0.0935352	+	0.0540026i	0.452503	+	0.891763i	$0.350531\pi$
$570$		0			0
$571$	24.9092	−	24.9092i	1.04242	−	1.04242i	0.0433595	−	0.999060i	$-0.486194\pi$
$571$	24.9092	−	24.9092i	1.04242	−	1.04242i	0.999060	−	0.0433595i	$-0.0138061\pi$
$572$		0			0
$573$	−21.5030	−	21.5030i	−0.898302	−	0.898302i
$574$		0			0
$575$	−19.5538	−	33.8681i	−0.815448	−	1.41240i
$576$		0			0
$577$	11.3178			0.471166			0.235583	−	0.971854i	$-0.424300\pi$
$577$	11.3178			0.471166			0.235583	+	0.971854i	$0.424300\pi$
$578$		0			0
$579$	8.68597	−	2.32740i	0.360977	−	0.0967234i
$580$		0			0
$581$	−0.442563	−	1.65167i	−0.0183606	−	0.0685228i
$582$		0			0
$583$	28.9112	−	16.6919i	1.19738	−	0.691308i
$584$		0			0
$585$	−0.341347	−	33.4685i	−0.0141130	−	1.38375i
$586$		0			0
$587$	−43.9722	−	11.7823i	−1.81493	−	0.486309i	−0.818789	−	0.574094i	$-0.805354\pi$
$587$	−43.9722	−	11.7823i	−1.81493	−	0.486309i	−0.996139	+	0.0877856i	$0.972021\pi$
$588$		0			0
$589$	27.1306	−	7.26963i	1.11790	−	0.299540i
$590$		0			0
$591$	32.3568	−	56.0436i	1.33098	−	2.30533i
$592$		0			0
$593$	−43.9585			−1.80516			−0.902580	−	0.430522i	$-0.858329\pi$
$593$	−43.9585			−1.80516			−0.902580	+	0.430522i	$0.858329\pi$
$594$		0			0
$595$	−8.70983	+	32.5055i	−0.357068	+	1.33260i
$596$		0			0
$597$	−1.43558	+	1.43558i	−0.0587545	+	0.0587545i
$598$		0			0
$599$		−	19.5769i		−	0.799891i	−0.916539	−	0.399946i	$-0.869029\pi$
$599$		−	19.5769i		−	0.799891i	0.916539	−	0.399946i	$-0.130971\pi$
$600$		0			0
$601$	37.8441	−	21.8493i	1.54369	−	0.891252i	0.545092	−	0.838376i	$-0.316495\pi$
$601$	37.8441	−	21.8493i	1.54369	−	0.891252i	0.998601	−	0.0528759i	$-0.0168388\pi$
$602$		0			0
$603$	−4.79891	+	4.79891i	−0.195427	+	0.195427i
$604$		0			0
$605$	−9.33672	+	2.50177i	−0.379592	+	0.101711i
$606$		0			0
$607$	−10.8339	+	18.7648i	−0.439734	+	0.761641i	−0.997669	−	0.0682435i	$-0.978261\pi$
$607$	−10.8339	+	18.7648i	−0.439734	+	0.761641i	0.557935	+	0.829885i	$0.311594\pi$
$608$		0			0
$609$	5.34349	+	9.25520i	0.216529	+	0.375039i
$610$		0			0
$611$	6.59330	−	25.6501i	0.266737	−	1.03769i
$612$		0			0
$613$	−22.2681	−	5.96673i	−0.899402	−	0.240994i	−0.220642	−	0.975355i	$-0.570815\pi$
$613$	−22.2681	−	5.96673i	−0.899402	−	0.240994i	−0.678759	+	0.734361i	$0.737482\pi$
$614$		0			0
$615$	−0.983889	−	0.568048i	−0.0396742	−	0.0229059i
$616$		0			0
$617$	9.87594	+	5.70188i	0.397590	+	0.229549i	0.685444	−	0.728126i	$-0.259608\pi$
$617$	9.87594	+	5.70188i	0.397590	+	0.229549i	−0.287853	+	0.957674i	$0.592942\pi$
$618$		0			0
$619$	−30.6367	+	30.6367i	−1.23139	+	1.23139i	−0.267964	+	0.963429i	$0.586351\pi$
$619$	−30.6367	+	30.6367i	−1.23139	+	1.23139i	−0.963429	+	0.267964i	$0.913649\pi$
$620$		0			0
$621$	0.792811	−	2.95881i	0.0318144	−	0.118733i
$622$		0			0
$623$	−28.4828			−1.14114
$624$		0			0
$625$	19.4405			0.777621
$626$		0			0
$627$	−15.9759	+	59.6228i	−0.638015	+	2.38110i
$628$		0			0
$629$	7.52703	−	7.52703i	0.300123	−	0.300123i
$630$		0			0
$631$	25.5498	+	14.7512i	1.01712	+	0.587236i	0.913269	−	0.407356i	$-0.133549\pi$
$631$	25.5498	+	14.7512i	1.01712	+	0.587236i	0.103854	+	0.994593i	$0.466883\pi$
$632$		0			0
$633$	2.31461	+	1.33634i	0.0919975	+	0.0531148i
$634$		0			0
$635$	15.0454	+	4.03139i	0.597057	+	0.159981i
$636$		0			0
$637$	22.0100	−	6.13881i	0.872066	−	0.243228i
$638$		0			0
$639$	12.8004	+	22.1709i	0.506376	+	0.877069i
$640$		0			0
$641$	−4.47481	+	7.75060i	−0.176744	+	0.306130i	−0.940764	−	0.339063i	$-0.889890\pi$
$641$	−4.47481	+	7.75060i	−0.176744	+	0.306130i	0.764019	+	0.645194i	$0.223223\pi$
$642$		0			0
$643$	27.0746	−	7.25463i	1.06772	−	0.286095i	0.318164	−	0.948036i	$-0.396934\pi$
$643$	27.0746	−	7.25463i	1.06772	−	0.286095i	0.749556	+	0.661941i	$0.230267\pi$
$644$		0			0
$645$	16.8123	−	16.8123i	0.661982	−	0.661982i
$646$		0			0
$647$	−12.1204	+	6.99773i	−0.476503	+	0.275109i	−0.718958	−	0.695054i	$-0.755381\pi$
$647$	−12.1204	+	6.99773i	−0.476503	+	0.275109i	0.242455	+	0.970163i	$0.422047\pi$
$648$		0			0
$649$		−	5.58773i		−	0.219338i
$650$		0			0
$651$	25.4618	−	25.4618i	0.997926	−	0.997926i
$652$		0			0
$653$	−8.83272	+	32.9642i	−0.345651	+	1.28999i	0.546198	+	0.837656i	$0.316074\pi$
$653$	−8.83272	+	32.9642i	−0.345651	+	1.28999i	−0.891850	+	0.452332i	$0.850592\pi$
$654$		0			0
$655$	−0.489816			−0.0191387
$656$		0			0
$657$	15.2477	−	26.4098i	0.594870	−	1.03035i
$658$		0			0
$659$	19.8239	−	5.31180i	0.772230	−	0.206918i	0.148874	−	0.988856i	$-0.452435\pi$
$659$	19.8239	−	5.31180i	0.772230	−	0.206918i	0.623356	+	0.781938i	$0.285769\pi$
$660$		0			0
$661$	−5.23300	−	1.40218i	−0.203540	−	0.0545384i	0.155609	−	0.987819i	$-0.450266\pi$
$661$	−5.23300	−	1.40218i	−0.203540	−	0.0545384i	−0.359148	+	0.933280i	$0.616933\pi$
$662$		0			0
$663$	−20.8416	+	12.3180i	−0.809419	+	0.478391i
$664$		0			0
$665$	−71.8013	+	41.4545i	−2.78434	+	1.60754i
$666$		0			0
$667$	2.07047	+	7.72708i	0.0801687	+	0.299194i
$668$		0			0
$669$	−32.3313	+	8.66316i	−1.25000	+	0.334937i
$670$		0			0
$671$	9.31670			0.359667
$672$		0			0
$673$	−20.3005	−	35.1615i	−0.782527	−	1.35538i	−0.930465	−	0.366380i	$-0.880597\pi$
$673$	−20.3005	−	35.1615i	−0.782527	−	1.35538i	0.147938	−	0.988997i	$-0.452736\pi$
$674$		0			0
$675$	−1.95190	−	1.95190i	−0.0751286	−	0.0751286i
$676$		0			0
$677$	−0.547336	+	0.547336i	−0.0210358	+	0.0210358i	−0.717546	−	0.696511i	$-0.754735\pi$
$677$	−0.547336	+	0.547336i	−0.0210358	+	0.0210358i	0.696511	+	0.717546i	$0.254735\pi$
$678$		0			0
$679$	36.0712	−	20.8257i	1.38428	−	0.799217i
$680$		0			0
$681$			29.2517i			1.12093i
$682$		0			0
$683$	3.52328	+	13.1491i	0.134815	+	0.503135i	0.999999	+	0.00168044i	$0.000534901\pi$
$683$	3.52328	+	13.1491i	0.134815	+	0.503135i	−0.865184	+	0.501455i	$0.832798\pi$
$684$		0			0
$685$	−23.9052	+	6.40538i	−0.913371	+	0.244737i
$686$		0			0
$687$	12.8135	+	22.1936i	0.488864	+	0.846737i
$688$		0			0
$689$	16.4133	+	27.7706i	0.625296	+	1.05798i
$690$		0			0
$691$	−6.56734	+	24.5096i	−0.249833	+	0.932391i	0.721059	+	0.692874i	$0.243656\pi$
$691$	−6.56734	+	24.5096i	−0.249833	+	0.932391i	−0.970892	+	0.239517i	$0.923011\pi$
$692$		0			0
$693$	9.90025	+	36.9482i	0.376079	+	1.40355i
$694$		0			0
$695$	44.0419	+	25.4276i	1.67061	+	0.964524i
$696$		0			0
$697$			0.397225i			0.0150460i
$698$		0			0
$699$	−19.7751	−	5.29873i	−0.747964	−	0.200416i
$700$		0			0
$701$	−17.3322	−	17.3322i	−0.654629	−	0.654629i	0.299475	−	0.954104i	$-0.403189\pi$
$701$	−17.3322	−	17.3322i	−0.654629	−	0.654629i	−0.954104	+	0.299475i	$0.903189\pi$
$702$		0			0
$703$	26.2257			0.989121
$704$		0			0
$705$	29.2683	+	50.6942i	1.10231	+	1.90925i
$706$		0			0
$707$	−5.98272	−	5.98272i	−0.225003	−	0.225003i
$708$		0			0
$709$	−2.81472	−	10.5047i	−0.105709	−	0.394511i	0.892716	−	0.450620i	$-0.148797\pi$
$709$	−2.81472	−	10.5047i	−0.105709	−	0.394511i	−0.998425	+	0.0561091i	$0.982131\pi$
$710$		0			0
$711$	26.2172	+	15.1365i	0.983223	+	0.567664i
$712$		0			0
$713$	23.3427	−	13.4769i	0.874191	−	0.504714i
$714$		0			0
$715$	−11.9529	−	42.8556i	−0.447013	−	1.60271i
$716$		0			0
$717$	−2.19124	+	8.17780i	−0.0818332	+	0.305406i
$718$		0			0
$719$	8.88267	−	15.3852i	0.331268	−	0.573772i	−0.651493	−	0.758655i	$-0.725857\pi$
$719$	8.88267	−	15.3852i	0.331268	−	0.573772i	0.982761	+	0.184882i	$0.0591903\pi$
$720$		0			0
$721$	−15.8596	+	27.4696i	−0.590642	+	1.02302i
$722$		0			0
$723$	8.75416	+	8.75416i	0.325571	+	0.325571i
$724$		0			0
$725$	6.96329	+	1.86581i	0.258610	+	0.0692944i
$726$		0			0
$727$		−	5.81246i		−	0.215572i	−0.994174	−	0.107786i	$-0.965624\pi$
$727$		−	5.81246i		−	0.215572i	0.994174	−	0.107786i	$-0.0343762\pi$
$728$		0			0
$729$			23.4222i			0.867490i
$730$		0			0
$731$	−8.02983	−	2.15159i	−0.296994	−	0.0795793i
$732$		0			0
$733$	10.6617	+	10.6617i	0.393797	+	0.393797i	0.876038	−	0.482241i	$-0.160177\pi$
$733$	10.6617	+	10.6617i	0.393797	+	0.393797i	−0.482241	+	0.876038i	$0.660177\pi$
$734$		0			0
$735$	−25.2523	+	43.7383i	−0.931446	+	1.61331i
$736$		0			0
$737$	−4.51070	+	7.81275i	−0.166154	+	0.287787i
$738$		0			0
$739$	−1.81200	+	6.76247i	−0.0666554	+	0.248761i	−0.991212	−	0.132284i	$-0.957769\pi$
$739$	−1.81200	+	6.76247i	−0.0666554	+	0.248761i	0.924556	+	0.381045i	$0.124436\pi$
$740$		0			0
$741$	−57.7673	−	14.8489i	−2.12213	−	0.545490i
$742$		0			0
$743$	−26.4580	+	15.2755i	−0.970649	+	0.560404i	−0.899434	−	0.437057i	$-0.856021\pi$
$743$	−26.4580	+	15.2755i	−0.970649	+	0.560404i	−0.0712146	+	0.997461i	$0.522688\pi$
$744$		0			0
$745$	9.56166	+	5.52043i	0.350312	+	0.202253i
$746$		0			0
$747$	0.340164	+	1.26951i	0.0124459	+	0.0464489i
$748$		0			0
$749$	29.2855	+	29.2855i	1.07007	+	1.07007i
$750$		0			0
$751$	−14.1774	−	24.5560i	−0.517341	−	0.896061i	−0.999797	−	0.0201407i	$-0.993589\pi$
$751$	−14.1774	−	24.5560i	−0.517341	−	0.896061i	0.482456	−	0.875920i	$-0.339745\pi$
$752$		0			0
$753$	22.6063			0.823820
$754$		0			0
$755$	−48.8402	−	48.8402i	−1.77748	−	1.77748i
$756$		0			0
$757$	−12.6239	−	3.38255i	−0.458822	−	0.122941i	0.0220023	−	0.999758i	$-0.492996\pi$
$757$	−12.6239	−	3.38255i	−0.458822	−	0.122941i	−0.480824	+	0.876817i	$0.659663\pi$
$758$		0			0
$759$			59.2342i			2.15007i
$760$		0			0
$761$	−23.2880	−	13.4453i	−0.844189	−	0.487393i	0.0144972	−	0.999895i	$-0.495385\pi$
$761$	−23.2880	−	13.4453i	−0.844189	−	0.487393i	−0.858686	+	0.512502i	$0.828719\pi$
$762$		0			0
$763$	7.97826	+	29.7753i	0.288832	+	1.07794i
$764$		0			0
$765$	6.69456	−	24.9844i	0.242042	−	0.903314i
$766$		0			0
$767$	5.39908	−	0.0550655i	0.194950	−	0.00198830i
$768$		0			0
$769$	0.556208	+	0.963381i	0.0200574	+	0.0347404i	0.875880	−	0.482529i	$-0.160282\pi$
$769$	0.556208	+	0.963381i	0.0200574	+	0.0347404i	−0.855822	+	0.517270i	$0.826948\pi$
$770$		0			0
$771$	−11.7355	+	3.14453i	−0.422645	+	0.113247i
$772$		0			0
$773$	−11.3874	−	42.4985i	−0.409578	−	1.52857i	−0.795453	−	0.606015i	$-0.792767\pi$
$773$	−11.3874	−	42.4985i	−0.409578	−	1.52857i	0.385875	−	0.922551i	$-0.373900\pi$
$774$		0			0
$775$		−	24.2896i		−	0.872507i
$776$		0			0
$777$	29.1169	−	16.8107i	1.04456	−	0.603079i
$778$		0			0
$779$	−0.692007	+	0.692007i	−0.0247937	+	0.0247937i
$780$		0			0
$781$	24.0633	+	24.0633i	0.861051	+	0.861051i
$782$		0			0
$783$	0.282328	+	0.489006i	0.0100896	+	0.0174757i
$784$		0			0
$785$	−39.6598			−1.41552
$786$		0			0
$787$	11.2513	−	3.01478i	0.401067	−	0.107465i	−0.0526467	−	0.998613i	$-0.516766\pi$
$787$	11.2513	−	3.01478i	0.401067	−	0.107465i	0.453713	+	0.891148i	$0.350099\pi$
$788$		0			0
$789$	11.0190	+	41.1233i	0.392285	+	1.46403i
$790$		0			0
$791$	−29.7767	+	17.1916i	−1.05874	+	0.611261i
$792$		0			0
$793$	0.0918133	+	9.00216i	0.00326039	+	0.319676i
$794$		0			0
$795$	−68.8702	−	18.4537i	−2.44257	−	0.654486i
$796$		0			0
$797$	9.96647	−	2.67051i	0.353030	−	0.0945942i	−0.0779455	−	0.996958i	$-0.524836\pi$
$797$	9.96647	−	2.67051i	0.353030	−	0.0945942i	0.430976	+	0.902363i	$0.358169\pi$
$798$		0			0
$799$	10.2334	−	17.7247i	0.362031	−	0.627056i
$800$		0			0
$801$	21.8925			0.773532
$802$		0			0
$803$	10.4917	−	39.1557i	0.370245	−	1.38177i
$804$		0			0
$805$	−56.2589	+	56.2589i	−1.98287	+	1.98287i
$806$		0			0
$807$			54.0166i			1.90148i
$808$		0			0
$809$	26.6642	−	15.3946i	0.937463	−	0.541245i	0.0482991	−	0.998833i	$-0.484620\pi$
$809$	26.6642	−	15.3946i	0.937463	−	0.541245i	0.889164	+	0.457588i	$0.151287\pi$
$810$		0			0
$811$	−34.8062	+	34.8062i	−1.22221	+	1.22221i	−0.255369	+	0.966844i	$0.582197\pi$
$811$	−34.8062	+	34.8062i	−1.22221	+	1.22221i	−0.966844	+	0.255369i	$0.917803\pi$
$812$		0			0
$813$	15.0326	−	4.02798i	0.527217	−	0.141267i
$814$		0			0
$815$	10.0361	−	17.3831i	0.351550	−	0.608903i
$816$		0			0
$817$	−10.2405	−	17.7371i	−0.358270	−	0.620541i
$818$		0			0
$819$	−35.6032	+	9.93012i	−1.24408	+	0.346986i
$820$		0			0
$821$	−13.2634	−	3.55391i	−0.462894	−	0.124032i	0.0198321	−	0.999803i	$-0.493687\pi$
$821$	−13.2634	−	3.55391i	−0.462894	−	0.124032i	−0.482727	+	0.875771i	$0.660354\pi$
$822$		0			0
$823$	24.3305	+	14.0472i	0.848107	+	0.489655i	0.860012	−	0.510274i	$-0.170456\pi$
$823$	24.3305	+	14.0472i	0.848107	+	0.489655i	−0.0119046	+	0.999929i	$0.503789\pi$
$824$		0			0
$825$	46.2277	+	26.6896i	1.60944	+	0.929212i
$826$		0			0
$827$	8.95549	−	8.95549i	0.311413	−	0.311413i	−0.534044	−	0.845457i	$-0.679328\pi$
$827$	8.95549	−	8.95549i	0.311413	−	0.311413i	0.845457	+	0.534044i	$0.179328\pi$
$828$		0			0
$829$	4.06744	−	15.1799i	0.141268	−	0.527220i	−0.858625	−	0.512604i	$-0.828681\pi$
$829$	4.06744	−	15.1799i	0.141268	−	0.527220i	0.999893	−	0.0146157i	$-0.00465249\pi$
$830$		0			0
$831$	−74.6985			−2.59126
$832$		0			0
$833$	17.6585			0.611829
$834$		0			0
$835$	−5.46885	+	20.4100i	−0.189257	+	0.706318i
$836$		0			0
$837$	1.34529	−	1.34529i	0.0465002	−	0.0465002i
$838$		0			0
$839$	−39.9019	−	23.0374i	−1.37757	−	0.795338i	−0.385700	−	0.922624i	$-0.626040\pi$
$839$	−39.9019	−	23.0374i	−1.37757	−	0.795338i	−0.991866	+	0.127286i	$0.959374\pi$
$840$		0			0
$841$	23.8377	+	13.7627i	0.821989	+	0.474575i
$842$		0			0
$843$	−74.8164	−	20.0470i	−2.57681	−	0.690455i
$844$		0			0
$845$	41.2910	−	11.9717i	1.42045	−	0.411838i
$846$		0			0
$847$	5.33726	+	9.24440i	0.183390	+	0.317641i
$848$		0			0
$849$	7.78338	−	13.4812i	0.267125	−	0.462674i
$850$		0			0
$851$	24.3095	−	6.51370i	0.833318	−	0.223287i
$852$		0			0
$853$	−37.7165	+	37.7165i	−1.29139	+	1.29139i	−0.357458	+	0.933929i	$0.616356\pi$
$853$	−37.7165	+	37.7165i	−1.29139	+	1.29139i	−0.933929	+	0.357458i	$0.883644\pi$
$854$		0			0
$855$	55.1880	−	31.8628i	1.88739	−	1.08969i
$856$		0			0
$857$			9.46712i			0.323391i	0.986841	+	0.161695i	$0.0516962\pi$
$857$			9.46712i			0.323391i	−0.986841	+	0.161695i	$0.948304\pi$
$858$		0			0
$859$	8.81388	−	8.81388i	0.300726	−	0.300726i	−0.540572	−	0.841298i	$-0.681792\pi$
$859$	8.81388	−	8.81388i	0.300726	−	0.300726i	0.841298	+	0.540572i	$0.181792\pi$
$860$		0			0
$861$	−0.324720	+	1.21187i	−0.0110664	+	0.0413005i
$862$		0			0
$863$	36.6455			1.24743			0.623714	−	0.781653i	$-0.285623\pi$
$863$	36.6455			1.24743			0.623714	+	0.781653i	$0.285623\pi$
$864$		0			0
$865$	4.01062	−	6.94661i	0.136365	−	0.236192i
$866$		0			0
$867$	21.4987	−	5.76057i	0.730136	−	0.195639i
$868$		0			0
$869$	38.8701	+	10.4152i	1.31858	+	0.353312i
$870$		0			0
$871$	−7.59344	−	4.28142i	−0.257294	−	0.145070i
$872$		0			0
$873$	−27.7251	+	16.0071i	−0.938351	+	0.541757i
$874$		0			0
$875$	2.92735	+	10.9250i	0.0989626	+	0.369333i
$876$		0			0
$877$	40.6721	−	10.8981i	1.37340	−	0.368001i	0.504681	−	0.863306i	$-0.331610\pi$
$877$	40.6721	−	10.8981i	1.37340	−	0.368001i	0.868719	+	0.495305i	$0.164944\pi$
$878$		0			0
$879$	66.2390			2.23419
$880$		0			0
$881$	2.72997	+	4.72845i	0.0919750	+	0.159305i	0.908342	−	0.418228i	$-0.137349\pi$
$881$	2.72997	+	4.72845i	0.0919750	+	0.159305i	−0.816367	+	0.577533i	$0.804015\pi$
$882$		0			0
$883$	17.0761	+	17.0761i	0.574657	+	0.574657i	0.933426	−	0.358769i	$-0.116803\pi$
$883$	17.0761	+	17.0761i	0.574657	+	0.574657i	−0.358769	+	0.933426i	$0.616803\pi$
$884$		0			0
$885$	−8.43864	+	8.43864i	−0.283662	+	0.283662i
$886$		0			0
$887$	5.61724	−	3.24312i	0.188609	−	0.108893i	−0.402722	−	0.915322i	$-0.631936\pi$
$887$	5.61724	−	3.24312i	0.188609	−	0.108893i	0.591331	+	0.806429i	$0.298603\pi$
$888$		0			0
$889$		−	17.2011i		−	0.576907i
$890$		0			0
$891$	9.21476	+	34.3900i	0.308706	+	1.15211i
$892$		0			0
$893$	48.7059	−	13.0507i	1.62988	−	0.436725i
$894$		0			0
$895$	31.5176	+	54.5900i	1.05352	+	1.82474i
$896$		0			0
$897$	−57.2344	+	0.583736i	−1.91100	+	0.0194904i
$898$		0			0
$899$	−1.28596	+	4.79926i	−0.0428891	+	0.160064i
$900$		0			0
$901$	6.45216	+	24.0798i	0.214953	+	0.802214i
$902$		0			0
$903$	−22.7389	−	13.1283i	−0.756703	−	0.436883i
$904$		0			0
$905$		−	59.1732i		−	1.96698i
$906$		0			0
$907$	−40.4610	−	10.8415i	−1.34349	−	0.359986i	−0.485760	−	0.874092i	$-0.661457\pi$
$907$	−40.4610	−	10.8415i	−1.34349	−	0.359986i	−0.857727	+	0.514106i	$0.828124\pi$
$908$		0			0
$909$	4.59844	+	4.59844i	0.152521	+	0.152521i
$910$		0			0
$911$	27.7840			0.920525			0.460263	−	0.887783i	$-0.347755\pi$
$911$	27.7840			0.920525			0.460263	+	0.887783i	$0.347755\pi$
$912$		0			0
$913$	0.873529	+	1.51300i	0.0289096	+	0.0500729i
$914$		0			0
$915$	−14.0702	−	14.0702i	−0.465145	−	0.465145i
$916$		0			0
$917$	0.139999	+	0.522485i	0.00462319	+	0.0172540i
$918$		0			0
$919$	−32.2776	−	18.6355i	−1.06474	−	0.614729i	−0.138001	−	0.990432i	$-0.544068\pi$
$919$	−32.2776	−	18.6355i	−1.06474	−	0.614729i	−0.926740	+	0.375703i	$0.877401\pi$
$920$		0			0
$921$	−57.1065	+	32.9705i	−1.88172	+	1.08641i
$922$		0			0
$923$	−23.0137	+	23.4880i	−0.757506	+	0.773116i
$924$		0			0
$925$	5.86985	−	21.9066i	0.192999	−	0.720284i
$926$		0			0
$927$	12.1900	−	21.1137i	0.400373	−	0.693466i
$928$		0			0
$929$	−2.54306	+	4.40470i	−0.0834350	+	0.144514i	−0.904723	−	0.426000i	$-0.859922\pi$
$929$	−2.54306	+	4.40470i	−0.0834350	+	0.144514i	0.821288	+	0.570513i	$0.193256\pi$
$930$		0			0
$931$	30.7628	+	30.7628i	1.00821	+	1.00821i
$932$		0			0
$933$	15.9052	+	4.26178i	0.520712	+	0.139524i
$934$		0			0
$935$		−	34.3828i		−	1.12444i
$936$		0			0
$937$			8.61858i			0.281557i	0.990041	+	0.140778i	$0.0449605\pi$
$937$			8.61858i			0.281557i	−0.990041	+	0.140778i	$0.955040\pi$
$938$		0			0
$939$	−33.6808	−	9.02474i	−1.09913	−	0.294511i
$940$		0			0
$941$	26.1193	+	26.1193i	0.851464	+	0.851464i	0.990313	−	0.138850i	$-0.0443405\pi$
$941$	26.1193	+	26.1193i	0.851464	+	0.851464i	−0.138850	+	0.990313i	$0.544340\pi$
$942$		0			0
$943$	−0.469569	+	0.813318i	−0.0152913	+	0.0264853i
$944$		0			0
$945$	−2.80794	+	4.86350i	−0.0913424	+	0.158210i
$946$		0			0
$947$	0.844658	−	3.15231i	0.0274477	−	0.102436i	−0.950843	−	0.309673i	$-0.899780\pi$
$947$	0.844658	−	3.15231i	0.0274477	−	0.102436i	0.978291	+	0.207237i	$0.0664471\pi$
$948$		0			0
$949$	37.9371	+	9.75165i	1.23149	+	0.316552i
$950$		0			0
$951$	29.0206	−	16.7550i	0.941056	−	0.543319i
$952$		0			0
$953$	−26.3291	−	15.2011i	−0.852883	−	0.492412i	0.00873957	−	0.999962i	$-0.497218\pi$
$953$	−26.3291	−	15.2011i	−0.852883	−	0.492412i	−0.861623	+	0.507550i	$0.830551\pi$
$954$		0			0
$955$	10.8012	+	40.3107i	0.349519	+	1.30442i
$956$		0			0
$957$	−7.72090	−	7.72090i	−0.249581	−	0.249581i
$958$		0			0
$959$	13.6652	+	23.6688i	0.441272	+	0.764306i
$960$		0			0
$961$	−14.2591			−0.459970
$962$		0			0
$963$	−22.5094	−	22.5094i	−0.725356	−	0.725356i
$964$		0			0
$965$	−11.9201	−	3.19398i	−0.383722	−	0.102818i
$966$		0			0
$967$		−	15.2093i		−	0.489098i	−0.969637	−	0.244549i	$-0.921360\pi$
$967$		−	15.2093i		−	0.489098i	0.969637	−	0.244549i	$-0.0786399\pi$
$968$		0			0
$969$	−39.9183	−	23.0469i	−1.28236	−	0.740372i
$970$		0			0
$971$	−11.3040	−	42.1871i	−0.362763	−	1.35385i	−0.870428	−	0.492295i	$-0.836158\pi$
$971$	−11.3040	−	42.1871i	−0.362763	−	1.35385i	0.507666	−	0.861554i	$-0.330508\pi$
$972$		0			0
$973$	14.5355	−	54.2471i	0.465986	−	1.73908i
$974$		0			0
$975$	−25.3330	+	44.9300i	−0.811304	+	1.43891i
$976$		0			0
$977$	22.9985	+	39.8345i	0.735786	+	1.27442i	0.954377	+	0.298603i	$0.0965206\pi$
$977$	22.9985	+	39.8345i	0.735786	+	1.27442i	−0.218591	+	0.975817i	$0.570146\pi$
$978$		0			0
$979$	28.1096	−	7.53194i	0.898386	−	0.240722i
$980$		0			0
$981$	−6.13226	−	22.8859i	−0.195788	−	0.730691i
$982$		0			0
$983$		−	35.1499i		−	1.12111i	−0.828118	−	0.560553i	$-0.810588\pi$
$983$		−	35.1499i		−	1.12111i	0.828118	−	0.560553i	$-0.189412\pi$
$984$		0			0
$985$	−76.9109	+	44.4045i	−2.45058	+	1.41485i
$986$		0			0
$987$	45.7099	−	45.7099i	1.45496	−	1.45496i
$988$		0			0
$989$	−13.8976	−	13.8976i	−0.441918	−	0.441918i
$990$		0			0
$991$	−11.4614	−	19.8518i	−0.364085	−	0.630613i	0.624544	−	0.780990i	$-0.285285\pi$
$991$	−11.4614	−	19.8518i	−0.364085	−	0.630613i	−0.988629	+	0.150376i	$0.951951\pi$
$992$		0			0
$993$	−19.6211			−0.622658
$994$		0			0
$995$	2.69121	−	0.721109i	0.0853172	−	0.0228607i
$996$		0			0
$997$	−3.17660	−	11.8552i	−0.100604	−	0.375459i	0.897205	−	0.441613i	$-0.145594\pi$
$997$	−3.17660	−	11.8552i	−0.100604	−	0.375459i	−0.997809	+	0.0661544i	$0.978927\pi$
$998$		0			0
$999$	1.53842	−	0.888206i	0.0486734	−	0.0281016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	832.2.br.a.81.23		104
4.3	odd	2		208.2.bj.a.29.1	✓	104
13.9	even	3	inner	832.2.br.a.529.4		104
16.5	even	4	inner	832.2.br.a.497.4		104
16.11	odd	4		208.2.bj.a.133.18	yes	104
52.35	odd	6		208.2.bj.a.61.18	yes	104
208.139	odd	12		208.2.bj.a.165.1	yes	104
208.165	even	12	inner	832.2.br.a.113.23		104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.bj.a.29.1	✓	104	4.3	odd	2
208.2.bj.a.61.18	yes	104	52.35	odd	6
208.2.bj.a.133.18	yes	104	16.11	odd	4
208.2.bj.a.165.1	yes	104	208.139	odd	12
832.2.br.a.81.23		104	1.1	even	1	trivial
832.2.br.a.113.23		104	208.165	even	12	inner
832.2.br.a.497.4		104	16.5	even	4	inner
832.2.br.a.529.4		104	13.9	even	3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 832 = 2^{6} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	832.br (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.623697 - 2.32767i) q^{3} +(-2.33843 + 2.33843i) q^{5} +(3.16277 + 1.82602i) q^{7} +(-2.43097 - 1.40352i) q^{9} +O(q^{10})\)	\(q+(0.623697 - 2.32767i) q^{3} +(-2.33843 + 2.33843i) q^{5} +(3.16277 + 1.82602i) q^{7} +(-2.43097 - 1.40352i) q^{9} +(-3.60420 - 0.965741i) q^{11} +(0.897619 - 3.49203i) q^{13} +(3.98462 + 6.90156i) q^{15} +(1.39318 - 2.41306i) q^{17} +(6.63086 - 1.77673i) q^{19} +(6.22299 - 6.22299i) q^{21} +(5.70507 - 3.29383i) q^{23} -5.93649i q^{25} +(0.328797 - 0.328797i) q^{27} +(-0.314295 + 1.17296i) q^{29} +4.09157 q^{31} +(-4.49585 + 7.78705i) q^{33} +(-11.6659 + 3.12588i) q^{35} +(3.69016 + 0.988774i) q^{37} +(-7.56845 - 4.26733i) q^{39} +(-0.123461 + 0.0712802i) q^{41} +(-0.772184 - 2.88183i) q^{43} +(8.96668 - 2.40261i) q^{45} +7.34533 q^{47} +(3.16873 + 5.48840i) q^{49} +(-4.74789 - 4.74789i) q^{51} +(-6.32639 + 6.32639i) q^{53} +(10.6865 - 6.16984i) q^{55} -16.5426i q^{57} +(0.387585 + 1.44649i) q^{59} +(-2.41180 + 0.646240i) q^{61} +(-5.12572 - 8.87801i) q^{63} +(6.06685 + 10.2649i) q^{65} +(0.625756 - 2.33535i) q^{67} +(-4.10870 - 15.3339i) q^{69} +(-7.89833 - 4.56010i) q^{71} +10.8639i q^{73} +(-13.8182 - 3.70257i) q^{75} +(-9.63576 - 9.63576i) q^{77} -10.7847 q^{79} +(-4.77082 - 8.26331i) q^{81} +(-0.331076 - 0.331076i) q^{83} +(2.38492 + 8.90063i) q^{85} +(2.53425 + 1.46315i) q^{87} +(-6.75424 + 3.89956i) q^{89} +(9.21549 - 9.40541i) q^{91} +(2.55190 - 9.52382i) q^{93} +(-11.3510 + 19.6606i) q^{95} +(5.70247 - 9.87697i) q^{97} +(7.40625 + 7.40625i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q + 2 q^{3} - 8 q^{5}+O(q^{10}) \) 104 * q + 2 * q^3 - 8 * q^5	\( 104 q + 2 q^{3} - 8 q^{5} + 2 q^{11} - 4 q^{13} + 4 q^{15} - 4 q^{17} + 2 q^{19} - 20 q^{21} - 4 q^{27} - 2 q^{29} + 16 q^{31} - 4 q^{33} - 8 q^{35} - 2 q^{37} + 18 q^{43} + 20 q^{45} + 16 q^{47} + 24 q^{49} - 4 q^{51} - 8 q^{53} + 42 q^{59} - 2 q^{61} + 60 q^{63} - 16 q^{65} + 2 q^{67} - 14 q^{69} - 10 q^{75} - 36 q^{77} - 64 q^{79} + 16 q^{81} + 48 q^{83} - 12 q^{85} - 38 q^{91} - 56 q^{93} - 60 q^{95} - 4 q^{97} + 160 q^{99}+O(q^{100}) \) 104 * q + 2 * q^3 - 8 * q^5 + 2 * q^11 - 4 * q^13 + 4 * q^15 - 4 * q^17 + 2 * q^19 - 20 * q^21 - 4 * q^27 - 2 * q^29 + 16 * q^31 - 4 * q^33 - 8 * q^35 - 2 * q^37 + 18 * q^43 + 20 * q^45 + 16 * q^47 + 24 * q^49 - 4 * q^51 - 8 * q^53 + 42 * q^59 - 2 * q^61 + 60 * q^63 - 16 * q^65 + 2 * q^67 - 14 * q^69 - 10 * q^75 - 36 * q^77 - 64 * q^79 + 16 * q^81 + 48 * q^83 - 12 * q^85 - 38 * q^91 - 56 * q^93 - 60 * q^95 - 4 * q^97 + 160 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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