LMFDB - Embedded newform 832.2.br.a.529.4

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			529.4
Character	$\chi$	$=$	832.529
Dual form			832.2.br.a.497.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.32767 + 0.623697i) q^{3} +(-2.33843 + 2.33843i) q^{5} +(-3.16277 + 1.82602i) q^{7} +(2.43097 - 1.40352i) q^{9} +O(q^{10})$	\(q+(-2.32767 + 0.623697i) q^{3} +(-2.33843 + 2.33843i) q^{5} +(-3.16277 + 1.82602i) q^{7} +(2.43097 - 1.40352i) q^{9} +(0.965741 + 3.60420i) q^{11} +(-3.49203 + 0.897619i) q^{13} +(3.98462 - 6.90156i) q^{15} +(1.39318 + 2.41306i) q^{17} +(-1.77673 + 6.63086i) q^{19} +(6.22299 - 6.22299i) q^{21} +(-5.70507 - 3.29383i) q^{23} -5.93649i q^{25} +(0.328797 - 0.328797i) q^{27} +(1.17296 - 0.314295i) q^{29} +4.09157 q^{31} +(-4.49585 - 7.78705i) q^{33} +(3.12588 - 11.6659i) q^{35} +(-0.988774 - 3.69016i) q^{37} +(7.56845 - 4.26733i) q^{39} +(0.123461 + 0.0712802i) q^{41} +(2.88183 + 0.772184i) q^{43} +(-2.40261 + 8.96668i) q^{45} +7.34533 q^{47} +(3.16873 - 5.48840i) q^{49} +(-4.74789 - 4.74789i) q^{51} +(-6.32639 + 6.32639i) q^{53} +(-10.6865 - 6.16984i) q^{55} -16.5426i q^{57} +(-1.44649 - 0.387585i) q^{59} +(0.646240 - 2.41180i) q^{61} +(-5.12572 + 8.87801i) q^{63} +(6.06685 - 10.2649i) q^{65} +(-2.33535 + 0.625756i) q^{67} +(15.3339 + 4.10870i) q^{69} +(7.89833 - 4.56010i) q^{71} +10.8639i q^{73} +(3.70257 + 13.8182i) q^{75} +(-9.63576 - 9.63576i) q^{77} -10.7847 q^{79} +(-4.77082 + 8.26331i) q^{81} +(-0.331076 - 0.331076i) q^{83} +(-8.90063 - 2.38492i) q^{85} +(-2.53425 + 1.46315i) q^{87} +(6.75424 + 3.89956i) q^{89} +(9.40541 - 9.21549i) q^{91} +(-9.52382 + 2.55190i) q^{93} +(-11.3510 - 19.6606i) q^{95} +(5.70247 + 9.87697i) q^{97} +(7.40625 + 7.40625i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/832\mathbb{Z}\right)^\times$.

$n$	$261$	$703$	$769$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−2.32767	+	0.623697i	−1.34388	+	0.360092i	−0.857872	−	0.513863i	$-0.828214\pi$
$3$	−2.32767	+	0.623697i	−1.34388	+	0.360092i	−0.486008	+	0.873954i	$0.661547\pi$
$4$		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	$-0.909132\pi$
$7$	−3.16277	+	1.82602i	−1.19541	+	0.690172i	−0.235884	+	0.971781i	$0.575799\pi$
$8$		0			0
$9$	2.43097	−	1.40352i	0.810323	−	0.467840i
$10$		0			0
$11$	0.965741	+	3.60420i	0.291182	+	1.08671i	0.944202	+	0.329366i	$0.106835\pi$
$11$	0.965741	+	3.60420i	0.291182	+	1.08671i	−0.653020	+	0.757340i	$0.726498\pi$
$12$		0			0
$13$	−3.49203	+	0.897619i	−0.968515	+	0.248955i
$13$	−3.49203	+	0.897619i	−0.968515	+	0.248955i
$14$		0			0
$15$	3.98462	−	6.90156i	1.02882	−	1.78197i
$16$		0			0
$17$	1.39318	+	2.41306i	0.337896	+	0.585254i	0.984037	−	0.177965i	$-0.0569513\pi$
$17$	1.39318	+	2.41306i	0.337896	+	0.585254i	−0.646140	+	0.763219i	$0.723618\pi$
$18$		0			0
$19$	−1.77673	+	6.63086i	−0.407611	+	1.52122i	0.391578	+	0.920145i	$0.371929\pi$
$19$	−1.77673	+	6.63086i	−0.407611	+	1.52122i	−0.799189	+	0.601080i	$0.794737\pi$
$20$		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	$-0.574323\pi$
$23$	−5.70507	−	3.29383i	−1.18959	−	0.686810i	−0.958213	+	0.286054i	$0.907656\pi$
$24$		0			0
$25$		−	5.93649i		−	1.18730i
$26$		0			0
$27$	0.328797	−	0.328797i	0.0632770	−	0.0632770i
$28$		0			0
$29$	1.17296	−	0.314295i	0.217814	−	0.0583631i	−0.148262	−	0.988948i	$-0.547368\pi$
$29$	1.17296	−	0.314295i	0.217814	−	0.0583631i	0.366076	+	0.930585i	$0.380701\pi$
$30$		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
$35$	3.12588	−	11.6659i	0.528369	−	1.97190i
$36$		0			0
$37$	−0.988774	−	3.69016i	−0.162553	−	0.606658i	−0.998340	−	0.0576027i	$-0.981654\pi$
$37$	−0.988774	−	3.69016i	−0.162553	−	0.606658i	0.835786	−	0.549055i	$-0.185012\pi$
$38$		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	$-0.329790\pi$
$41$	0.123461	+	0.0712802i	0.0192814	+	0.0111321i	−0.490328	+	0.871538i	$0.663123\pi$
$42$		0			0
$43$	2.88183	+	0.772184i	0.439475	+	0.117757i	0.471770	−	0.881721i	$-0.343615\pi$
$43$	2.88183	+	0.772184i	0.439475	+	0.117757i	−0.0322955	+	0.999478i	$0.510282\pi$
$44$		0			0
$45$	−2.40261	+	8.96668i	−0.358161	+	1.33667i
$46$		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
$59$	−1.44649	−	0.387585i	−0.188317	−	0.0504593i	0.163428	−	0.986555i	$-0.447745\pi$
$59$	−1.44649	−	0.387585i	−0.188317	−	0.0504593i	−0.351745	+	0.936096i	$0.614411\pi$
$60$		0			0
$61$	0.646240	−	2.41180i	0.0827425	−	0.308799i	−0.912135	−	0.409891i	$-0.865567\pi$
$61$	0.646240	−	2.41180i	0.0827425	−	0.308799i	0.994877	+	0.101091i	$0.0322335\pi$
$62$		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
$67$	−2.33535	+	0.625756i	−0.285309	+	0.0764483i	−0.398635	−	0.917110i	$-0.630516\pi$
$67$	−2.33535	+	0.625756i	−0.285309	+	0.0764483i	0.113326	+	0.993558i	$0.463849\pi$
$68$		0			0
$69$	15.3339	+	4.10870i	1.84598	+	0.494629i
$70$		0			0
$71$	7.89833	−	4.56010i	0.937359	−	0.541185i	0.0482279	−	0.998836i	$-0.484643\pi$
$71$	7.89833	−	4.56010i	0.937359	−	0.541185i	0.889132	+	0.457652i	$0.151309\pi$
$72$		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
$75$	3.70257	+	13.8182i	0.427536	+	1.59559i
$76$		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
$85$	−8.90063	−	2.38492i	−0.965409	−	0.258681i
$86$		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	$-0.197691\pi$
$89$	6.75424	+	3.89956i	0.715948	+	0.413353i	−0.0973116	+	0.995254i	$0.531024\pi$
$90$		0			0
$91$	9.40541	−	9.21549i	0.985954	−	0.966046i
$92$		0			0
$93$	−9.52382	+	2.55190i	−0.987574	+	0.264620i
$94$		0			0
$95$	−11.3510	−	19.6606i	−1.16459	−	2.01713i
$96$		0			0
$97$	5.70247	+	9.87697i	0.578998	+	1.00285i	0.995595	+	0.0937630i	$0.0298896\pi$
$97$	5.70247	+	9.87697i	0.578998	+	1.00285i	−0.416596	+	0.909092i	$0.636777\pi$
$98$		0			0
$99$	7.40625	+	7.40625i	0.744356	+	0.744356i
$100$		0			0
$101$	0.599616	+	2.23780i	0.0596640	+	0.222669i	0.989320	−	0.145759i	$-0.0465626\pi$
$101$	0.599616	+	2.23780i	0.0596640	+	0.222669i	−0.929656	+	0.368429i	$0.879896\pi$
$102$		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
$107$	−2.93513	−	10.9540i	−0.283749	−	1.05897i	−0.949748	−	0.313014i	$-0.898661\pi$
$107$	−2.93513	−	10.9540i	−0.283749	−	1.05897i	0.665999	−	0.745953i	$-0.268005\pi$
$108$		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	0.555066	−	0.831806i	$-0.312693\pi$
$113$	−4.70737	−	8.15341i	−0.442833	−	0.767008i	−0.997898	+	0.0647979i	$0.979360\pi$
$114$		0			0
$115$	21.0433	−	5.63853i	1.96230	−	0.525796i
$116$		0			0
$117$	−7.22919	+	7.08322i	−0.668339	+	0.654844i
$118$		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
$123$	−0.331833	−	0.0889145i	−0.0299204	−	0.00801715i
$124$		0			0
$125$	2.18992	+	2.18992i	0.195872	+	0.195872i
$126$		0			0
$127$	−2.35499	+	4.07897i	−0.208972	+	0.361950i	−0.951391	−	0.307986i	$-0.900345\pi$
$127$	−2.35499	+	4.07897i	−0.208972	+	0.361950i	0.742419	+	0.669936i	$0.233678\pi$
$128$		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
$133$	−6.48872	−	24.2162i	−0.562643	−	2.09981i
$134$		0			0
$135$			1.53774i			0.132347i
$136$		0			0
$137$	−6.48097	+	3.74179i	−0.553707	+	0.319683i	−0.750616	−	0.660739i	$-0.770243\pi$
$137$	−6.48097	+	3.74179i	−0.553707	+	0.319683i	0.196909	+	0.980422i	$0.436910\pi$
$138$		0			0
$139$	14.8539	+	3.98009i	1.25989	+	0.337587i	0.826150	−	0.563451i	$-0.190527\pi$
$139$	14.8539	+	3.98009i	1.25989	+	0.337587i	0.433741	+	0.901037i	$0.357193\pi$
$140$		0			0
$141$	−17.0975	+	4.58126i	−1.43987	+	0.385812i
$142$		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
$147$	−3.95265	+	14.7515i	−0.326009	+	1.21668i
$148$		0			0
$149$	3.22484	+	0.864092i	0.264189	+	0.0707892i	0.388482	−	0.921456i	$-0.373000\pi$
$149$	3.22484	+	0.864092i	0.264189	+	0.0707892i	−0.124293	+	0.992246i	$0.539666\pi$
$150$		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
$163$	1.57092	−	5.86275i	0.123044	−	0.459206i	−0.876719	−	0.481004i	$-0.840272\pi$
$163$	1.57092	−	5.86275i	0.123044	−	0.459206i	0.999762	+	0.0217979i	$0.00693903\pi$
$164$		0			0
$165$	28.7227	+	7.69622i	2.23606	+	0.599150i
$166$		0			0
$167$	−5.53339	−	3.19470i	−0.428186	−	0.247214i	0.270387	−	0.962752i	$-0.412848\pi$
$167$	−5.53339	−	3.19470i	−0.428186	−	0.247214i	−0.698574	+	0.715538i	$0.746182\pi$
$168$		0			0
$169$	11.3886	−	6.26902i	0.876043	−	0.482233i
$170$		0			0
$171$	4.98737	+	18.6131i	0.381393	+	1.42338i
$172$		0			0
$173$	0.627768	−	2.34286i	0.0477283	−	0.178125i	−0.937947	−	0.346779i	$-0.887275\pi$
$173$	0.627768	−	2.34286i	0.0477283	−	0.178125i	0.985675	+	0.168654i	$0.0539421\pi$
$174$		0			0
$175$	10.8402	+	18.7757i	0.819440	+	1.41931i
$176$		0			0
$177$	3.60868			0.271245
$178$		0			0
$179$	−18.4114	+	4.93333i	−1.37614	+	0.368734i	−0.869716	−	0.493553i	$-0.835698\pi$
$179$	−18.4114	+	4.93333i	−1.37614	+	0.368734i	−0.506419	+	0.862287i	$0.669031\pi$
$180$		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
$189$	−0.439517	+	1.64030i	−0.0319701	+	0.119314i
$190$		0			0
$191$	6.30968	+	10.9287i	0.456552	+	0.790772i	0.998776	−	0.0494625i	$-0.0157508\pi$
$191$	6.30968	+	10.9287i	0.456552	+	0.790772i	−0.542224	+	0.840234i	$0.682418\pi$
$192$		0			0
$193$	1.86581	−	3.23168i	0.134304	−	0.232621i	−0.791027	−	0.611781i	$-0.790454\pi$
$193$	1.86581	−	3.23168i	0.134304	−	0.232621i	0.925331	+	0.379160i	$0.123787\pi$
$194$		0			0
$195$	−7.71944	+	27.6771i	−0.552800	+	1.98200i
$196$		0			0
$197$	−6.95047	−	25.9395i	−0.495201	−	1.84811i	−0.528904	−	0.848682i	$-0.677397\pi$
$197$	−6.95047	−	25.9395i	−0.495201	−	1.84811i	0.0337033	−	0.999432i	$-0.489270\pi$
$198$		0			0
$199$	0.729619	−	0.421246i	0.0517213	−	0.0298613i	−0.473916	−	0.880570i	$-0.657160\pi$
$199$	0.729619	−	0.421246i	0.0517213	−	0.0298613i	0.525638	+	0.850709i	$0.323827\pi$
$200$		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
$205$	−0.455388	+	0.122021i	−0.0318057	+	0.00852231i
$206$		0			0
$207$	−18.4918			−1.28527
$208$		0			0
$209$	−25.6148			−1.77181
$210$		0			0
$211$	1.07131	−	0.287056i	0.0737518	−	0.0197617i	−0.221754	−	0.975103i	$-0.571178\pi$
$211$	1.07131	−	0.287056i	0.0737518	−	0.0197617i	0.295506	+	0.955341i	$0.404512\pi$
$212$		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
$219$	−6.77579	−	25.2876i	−0.457865	−	1.70878i
$220$		0			0
$221$	−7.03105	−	7.17594i	−0.472959	−	0.482706i
$222$		0			0
$223$	−6.94501	+	12.0291i	−0.465072	+	0.805528i	−0.999205	−	0.0398723i	$-0.987305\pi$
$223$	−6.94501	+	12.0291i	−0.465072	+	0.805528i	0.534133	+	0.845401i	$0.320638\pi$
$224$		0			0
$225$	−8.33199	−	14.4314i	−0.555466	−	0.962095i
$226$		0			0
$227$	3.14174	−	11.7251i	0.208524	−	0.778224i	−0.779822	−	0.626002i	$-0.784690\pi$
$227$	3.14174	−	11.7251i	0.208524	−	0.778224i	0.988346	−	0.152222i	$-0.0486430\pi$
$228$		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
$237$	25.1032	−	6.72638i	1.63063	−	0.436925i
$238$		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	0.771353	−	0.636407i	$-0.219580\pi$
$241$	−2.56875	−	4.44921i	−0.165468	−	0.286599i	−0.936821	+	0.349808i	$0.886247\pi$
$242$		0			0
$243$	5.59005	−	20.8624i	0.358602	−	1.33832i
$244$		0			0
$245$	5.42438	+	20.2441i	0.346551	+	1.29335i
$246$		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
$251$	−9.06141	−	2.42800i	−0.571951	−	0.153254i	−0.0387600	−	0.999249i	$-0.512341\pi$
$251$	−9.06141	−	2.42800i	−0.571951	−	0.153254i	−0.533191	+	0.845995i	$0.679007\pi$
$252$		0			0
$253$	6.36197	−	23.7432i	0.399973	−	1.49272i
$254$		0			0
$255$	22.2052			1.39054
$256$		0			0
$257$	−2.52088	+	4.36629i	−0.157248	+	0.272362i	−0.933875	−	0.357599i	$-0.883596\pi$
$257$	−2.52088	+	4.36629i	−0.157248	+	0.272362i	0.776627	+	0.629960i	$0.216929\pi$
$258$		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	$-0.149976\pi$
$263$	15.3002	+	8.83358i	0.943451	+	0.544702i	0.0524109	+	0.998626i	$0.483309\pi$
$264$		0			0
$265$		−	29.5876i		−	1.81755i
$266$		0			0
$267$	−18.1538	−	4.86429i	−1.11099	−	0.297690i
$268$		0			0
$269$	5.80158	−	21.6518i	0.353729	−	1.32013i	−0.528348	−	0.849028i	$-0.677188\pi$
$269$	5.80158	−	21.6518i	0.353729	−	1.32013i	0.882077	−	0.471106i	$-0.156145\pi$
$270$		0			0
$271$	3.22911	−	5.59299i	0.196155	−	0.339750i	−0.751124	−	0.660161i	$-0.770488\pi$
$271$	3.22911	−	5.59299i	0.196155	−	0.339750i	0.947278	+	0.320412i	$0.103821\pi$
$272$		0			0
$273$	−16.1450	+	27.3167i	−0.977140	+	1.65328i
$274$		0			0
$275$	21.3963	−	5.73311i	1.29024	−	0.345720i
$276$		0			0
$277$	29.9418	+	8.02289i	1.79903	+	0.482048i	0.993826	−	0.110950i	$-0.0353894\pi$
$277$	29.9418	+	8.02289i	1.79903	+	0.482048i	0.805204	+	0.592999i	$0.202056\pi$
$278$		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
$283$	−1.67193	−	6.23971i	−0.0993857	−	0.370912i	0.898262	−	0.439460i	$-0.144830\pi$
$283$	−1.67193	−	6.23971i	−0.0993857	−	0.370912i	−0.997648	+	0.0685476i	$0.978164\pi$
$284$		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
$293$	−26.5510	−	7.11431i	−1.55112	−	0.415622i	−0.621284	−	0.783586i	$-0.713389\pi$
$293$	−26.5510	−	7.11431i	−1.55112	−	0.415622i	−0.929840	+	0.367963i	$0.880055\pi$
$294$		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
$299$	22.8789	+	6.38116i	1.32312	+	0.369032i
$300$		0			0
$301$	−10.5246	+	2.82005i	−0.606627	+	0.162545i
$302$		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
$309$	−5.41700	−	20.2165i	−0.308163	−	1.15008i
$310$		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
$315$	−8.77446	−	32.7467i	−0.494385	−	1.84507i
$316$		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
$323$	−18.4760	+	4.95063i	−1.02803	+	0.275460i
$324$		0			0
$325$	5.32870	+	20.7304i	0.295583	+	1.14992i
$326$		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
$331$	7.86485	+	2.10738i	0.432291	+	0.115832i	0.468401	−	0.883516i	$-0.344830\pi$
$331$	7.86485	+	2.10738i	0.432291	+	0.115832i	−0.0361104	+	0.999348i	$0.511497\pi$
$332$		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
$341$	3.95140	+	14.7468i	0.213980	+	0.798585i
$342$		0			0
$343$		−	2.41965i		−	0.130649i
$344$		0			0
$345$	−45.4651	+	26.2493i	−2.44776	+	1.41321i
$346$		0			0
$347$	−12.0427	−	3.22684i	−0.646488	−	0.173226i	−0.0793476	−	0.996847i	$-0.525284\pi$
$347$	−12.0427	−	3.22684i	−0.646488	−	0.173226i	−0.567141	+	0.823621i	$0.691950\pi$
$348$		0			0
$349$	26.5282	−	7.10822i	1.42002	−	0.380494i	0.534532	−	0.845148i	$-0.320488\pi$
$349$	26.5282	−	7.10822i	1.42002	−	0.380494i	0.885492	+	0.464654i	$0.153821\pi$
$350$		0			0
$351$	−0.853035	+	1.44330i	−0.0455316	+	0.0770378i
$352$		0			0
$353$	−17.4243	+	30.1797i	−0.927401	+	1.60631i	−0.139748	+	0.990187i	$0.544629\pi$
$353$	−17.4243	+	30.1797i	−0.927401	+	1.60631i	−0.787653	+	0.616119i	$0.788704\pi$
$354$		0			0
$355$	−7.80620	+	29.1332i	−0.414310	+	1.54623i
$356$		0			0
$357$	23.6862	+	6.34670i	1.25361	+	0.335903i
$358$		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	−0.999852	−	0.0172172i	$-0.994519\pi$
$367$	−9.29156	+	16.0935i	−0.485015	+	0.840071i	0.514836	+	0.857288i	$0.327853\pi$
$368$		0			0
$369$	0.400173			0.0208322
$370$		0			0
$371$	8.45675	−	31.5610i	0.439053	−	1.63857i
$372$		0			0
$373$	−15.6005	−	4.18014i	−0.807762	−	0.216439i	−0.168773	−	0.985655i	$-0.553980\pi$
$373$	−15.6005	−	4.18014i	−0.807762	−	0.216439i	−0.638989	+	0.769216i	$0.720647\pi$
$374$		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
$379$	−6.21090	−	23.1794i	−0.319033	−	1.19065i	−0.920176	−	0.391505i	$-0.871955\pi$
$379$	−6.21090	−	23.1794i	−0.319033	−	1.19065i	0.601143	−	0.799141i	$-0.294712\pi$
$380$		0			0
$381$	2.93761	−	10.9633i	0.150498	−	0.561667i
$382$		0			0
$383$	−2.67972	−	4.64141i	−0.136927	−	0.237165i	0.789405	−	0.613873i	$-0.210389\pi$
$383$	−2.67972	−	4.64141i	−0.136927	−	0.237165i	−0.926332	+	0.376708i	$0.877056\pi$
$384$		0			0
$385$	45.0651			2.29673
$386$		0			0
$387$	8.08942	−	2.16755i	0.411208	−	0.110183i
$388$		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
$397$	1.13461	−	4.23444i	0.0569447	−	0.212520i	−0.931591	−	0.363508i	$-0.881579\pi$
$397$	1.13461	−	4.23444i	0.0569447	−	0.212520i	0.988536	+	0.150988i	$0.0482455\pi$
$398$		0			0
$399$	30.2072	+	52.3204i	1.51225	+	2.61930i
$400$		0			0
$401$	9.11661	−	15.7904i	0.455262	−	0.788536i	−0.543441	−	0.839447i	$-0.682879\pi$
$401$	9.11661	−	15.7904i	0.455262	−	0.788536i	0.998703	+	0.0509106i	$0.0162123\pi$
$402$		0			0
$403$	−14.2879	+	3.67267i	−0.711730	+	0.182949i
$404$		0			0
$405$	−8.16692	−	30.4794i	−0.405818	−	1.51453i
$406$		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	$-0.845193\pi$
$409$	−18.6321	+	10.7572i	−0.921297	+	0.531911i	−0.0372483	+	0.999306i	$0.511859\pi$
$410$		0			0
$411$	12.7518	−	12.7518i	0.629001	−	0.629001i
$412$		0			0
$413$	5.28264	−	1.41548i	0.259942	−	0.0696512i
$414$		0			0
$415$	1.54840			0.0760077
$416$		0			0
$417$	−37.0573			−1.81470
$418$		0			0
$419$	12.0599	−	3.23143i	0.589163	−	0.157866i	0.0480925	−	0.998843i	$-0.484686\pi$
$419$	12.0599	−	3.23143i	0.589163	−	0.157866i	0.541071	+	0.840977i	$0.318019\pi$
$420$		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
$427$	2.36010	+	8.80801i	0.114213	+	0.426249i
$428$		0			0
$429$	22.6895	+	23.1570i	1.09546	+	1.11803i
$430$		0			0
$431$	−3.47069	+	6.01142i	−0.167177	+	0.289560i	−0.937426	−	0.348184i	$-0.886799\pi$
$431$	−3.47069	+	6.01142i	−0.167177	+	0.289560i	0.770249	+	0.637743i	$0.220132\pi$
$432$		0			0
$433$	−6.31803	−	10.9431i	−0.303625	−	0.525894i	0.673329	−	0.739343i	$-0.264864\pi$
$433$	−6.31803	−	10.9431i	−0.303625	−	0.525894i	−0.976954	+	0.213449i	$0.931530\pi$
$434$		0			0
$435$	2.50469	−	9.34762i	0.120091	−	0.448184i
$436$		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	$-0.334461\pi$
$439$	−0.128570	−	0.0742300i	−0.00613632	−	0.00354280i	−0.503065	+	0.864249i	$0.667794\pi$
$440$		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
$445$	−24.9131	+	6.67546i	−1.18100	+	0.316447i
$446$		0			0
$447$	−8.04528			−0.380529
$448$		0			0
$449$	−4.95110	−	8.57556i	−0.233657	−	0.404706i	0.725225	−	0.688512i	$-0.241736\pi$
$449$	−4.95110	−	8.57556i	−0.233657	−	0.404706i	−0.958882	+	0.283807i	$0.908403\pi$
$450$		0			0
$451$	−0.137676	+	0.513816i	−0.00648293	+	0.0241946i
$452$		0			0
$453$	−13.0265	−	48.6155i	−0.612038	−	2.28416i
$454$		0			0
$455$	−0.444103	+	43.5436i	−0.0208199	+	2.04136i
$456$		0			0
$457$	34.6636	+	20.0130i	1.62149	+	0.936170i	0.986521	+	0.163637i	$0.0523224\pi$
$457$	34.6636	+	20.0130i	1.62149	+	0.936170i	0.634974	+	0.772534i	$0.281011\pi$
$458$		0			0
$459$	1.25148	+	0.335333i	0.0584141	+	0.0156520i
$460$		0			0
$461$	−2.18388	+	8.15036i	−0.101714	+	0.379600i	−0.997952	−	0.0639733i	$-0.979623\pi$
$461$	−2.18388	+	8.15036i	−0.101714	+	0.379600i	0.896238	+	0.443573i	$0.146289\pi$
$462$		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
$475$	39.3641	+	10.5476i	1.80615	+	0.483956i
$476$		0			0
$477$	−6.50004	+	24.2585i	−0.297616	+	1.11072i
$478$		0			0
$479$	16.2487	−	28.1436i	0.742423	−	1.28591i	−0.208966	−	0.977923i	$-0.567010\pi$
$479$	16.2487	−	28.1436i	0.742423	−	1.28591i	0.951389	−	0.307991i	$-0.0996568\pi$
$480$		0			0
$481$	6.76518	+	11.9986i	0.308466	+	0.547089i
$482$		0			0
$483$	−56.0000	+	15.0052i	−2.54809	+	0.682759i
$484$		0			0
$485$	−36.4314	−	9.76177i	−1.65427	−	0.443259i
$486$		0			0
$487$	23.9015	−	13.7995i	1.08308	−	0.625316i	0.151354	−	0.988480i	$-0.451637\pi$
$487$	23.9015	−	13.7995i	1.08308	−	0.625316i	0.931725	+	0.363163i	$0.118303\pi$
$488$		0			0
$489$			14.6263i			0.661425i
$490$		0			0
$491$	−10.7861	−	40.2542i	−0.486768	−	1.81664i	−0.571962	−	0.820280i	$-0.693817\pi$
$491$	−10.7861	−	40.2542i	−0.486768	−	1.81664i	0.0851933	−	0.996364i	$-0.472849\pi$
$492$		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
$501$	14.8724	+	3.98505i	0.664451	+	0.178039i
$502$		0			0
$503$	−0.355066	+	0.204998i	−0.0158316	+	0.00914039i	−0.507895	−	0.861419i	$-0.669576\pi$
$503$	−0.355066	+	0.204998i	−0.0158316	+	0.00914039i	0.492063	+	0.870559i	$0.336243\pi$
$504$		0			0
$505$	−6.63509	−	3.83077i	−0.295258	−	0.170467i
$506$		0			0
$507$	−22.5988	+	21.6952i	−1.00365	+	0.963519i
$508$		0			0
$509$	−13.1574	+	3.52551i	−0.583190	+	0.156265i	−0.538339	−	0.842728i	$-0.680948\pi$
$509$	−13.1574	+	3.52551i	−0.583190	+	0.156265i	−0.0448510	+	0.998994i	$0.514281\pi$
$510$		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
$517$	7.09369	+	26.4740i	0.311980	+	1.16433i
$518$		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
$523$	−8.53256	−	31.8439i	−0.373103	−	1.39244i	−0.856097	−	0.516815i	$-0.827118\pi$
$523$	−8.53256	−	31.8439i	−0.373103	−	1.39244i	0.482994	−	0.875623i	$-0.339549\pi$
$524$		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
$531$	−4.06035	+	1.08797i	−0.176204	+	0.0472138i
$532$		0			0
$533$	−0.495112	−	0.138092i	−0.0214457	−	0.00598142i
$534$		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
$539$	22.8414	+	6.12034i	0.983850	+	0.263622i
$540$		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
$549$	−1.81402	−	6.77002i	−0.0774205	−	0.288937i
$550$		0			0
$551$			8.33619i			0.355133i
$552$		0			0
$553$	34.1095	−	19.6931i	1.45048	−	0.837436i
$554$		0			0
$555$	−29.4077	−	7.87977i	−1.24829	−	0.334478i
$556$		0			0
$557$	27.0526	−	7.24872i	1.14626	−	0.307138i	0.364792	−	0.931089i	$-0.381140\pi$
$557$	27.0526	−	7.24872i	1.14626	−	0.307138i	0.781464	+	0.623951i	$0.214473\pi$
$558$		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
$563$	5.19950	−	19.4048i	0.219133	−	0.817815i	−0.765538	−	0.643391i	$-0.777527\pi$
$563$	5.19950	−	19.4048i	0.219133	−	0.817815i	0.984671	−	0.174424i	$-0.0558064\pi$
$564$		0			0
$565$	30.0740	+	8.05831i	1.26522	+	0.339016i
$566$		0			0
$567$		−	34.8465i		−	1.46342i
$568$		0			0
$569$	2.23116	+	1.28816i	0.0935352	+	0.0540026i	0.546038	−	0.837760i	$-0.316135\pi$
$569$	2.23116	+	1.28816i	0.0935352	+	0.0540026i	−0.452503	+	0.891763i	$0.649469\pi$
$570$		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
$579$	−2.32740	+	8.68597i	−0.0967234	+	0.360977i
$580$		0			0
$581$	1.65167	+	0.442563i	0.0685228	+	0.0183606i
$582$		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
$587$	11.7823	+	43.9722i	0.486309	+	1.81493i	0.574094	+	0.818789i	$0.305354\pi$
$587$	11.7823	+	43.9722i	0.486309	+	1.81493i	−0.0877856	+	0.996139i	$0.527979\pi$
$588$		0			0
$589$	−7.26963	+	27.1306i	−0.299540	+	1.11790i
$590$		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
$595$	32.5055	−	8.70983i	1.33260	−	0.357068i
$596$		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	−0.998601	−	0.0528759i	$-0.983161\pi$
$601$	−37.8441	−	21.8493i	−1.54369	−	0.891252i	−0.545092	−	0.838376i	$-0.683505\pi$
$602$		0			0
$603$	−4.79891	+	4.79891i	−0.195427	+	0.195427i
$604$		0			0
$605$	2.50177	−	9.33672i	0.101711	−	0.379592i
$606$		0			0
$607$	−10.8339	−	18.7648i	−0.439734	−	0.761641i	0.557935	−	0.829885i	$-0.311594\pi$
$607$	−10.8339	−	18.7648i	−0.439734	−	0.761641i	−0.997669	+	0.0682435i	$0.978261\pi$
$608$		0			0
$609$	5.34349	−	9.25520i	0.216529	−	0.375039i
$610$		0			0
$611$	−25.6501	+	6.59330i	−1.03769	+	0.266737i
$612$		0			0
$613$	5.96673	+	22.2681i	0.240994	+	0.899402i	0.975355	+	0.220642i	$0.0708154\pi$
$613$	5.96673	+	22.2681i	0.240994	+	0.899402i	−0.734361	+	0.678759i	$0.762518\pi$
$614$		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	$-0.740392\pi$
$617$	−9.87594	+	5.70188i	−0.397590	+	0.229549i	0.287853	+	0.957674i	$0.407058\pi$
$618$		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
$621$	−2.95881	+	0.792811i	−0.118733	+	0.0318144i
$622$		0			0
$623$	−28.4828			−1.14114
$624$		0			0
$625$	19.4405			0.777621
$626$		0			0
$627$	59.6228	−	15.9759i	2.38110	−	0.638015i
$628$		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	$-0.866451\pi$
$631$	−25.5498	+	14.7512i	−1.01712	+	0.587236i	−0.103854	+	0.994593i	$0.533117\pi$
$632$		0			0
$633$	−2.31461	+	1.33634i	−0.0919975	+	0.0531148i
$634$		0			0
$635$	−4.03139	−	15.0454i	−0.159981	−	0.597057i
$636$		0			0
$637$	−6.13881	+	22.0100i	−0.243228	+	0.872066i
$638$		0			0
$639$	12.8004	−	22.1709i	0.506376	−	0.877069i
$640$		0			0
$641$	−4.47481	−	7.75060i	−0.176744	−	0.306130i	0.764019	−	0.645194i	$-0.223223\pi$
$641$	−4.47481	−	7.75060i	−0.176744	−	0.306130i	−0.940764	+	0.339063i	$0.889890\pi$
$642$		0			0
$643$	−7.25463	+	27.0746i	−0.286095	+	1.06772i	0.661941	+	0.749556i	$0.269733\pi$
$643$	−7.25463	+	27.0746i	−0.286095	+	1.06772i	−0.948036	+	0.318164i	$0.896934\pi$
$644$		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	$-0.244619\pi$
$647$	12.1204	+	6.99773i	0.476503	+	0.275109i	−0.242455	+	0.970163i	$0.577953\pi$
$648$		0			0
$649$		−	5.58773i		−	0.219338i
$650$		0			0
$651$	25.4618	−	25.4618i	0.997926	−	0.997926i
$652$		0			0
$653$	32.9642	−	8.83272i	1.28999	−	0.345651i	0.452332	−	0.891850i	$-0.350592\pi$
$653$	32.9642	−	8.83272i	1.28999	−	0.345651i	0.837656	+	0.546198i	$0.183926\pi$
$654$		0			0
$655$	−0.489816			−0.0191387
$656$		0			0
$657$	15.2477	+	26.4098i	0.594870	+	1.03035i
$658$		0			0
$659$	−5.31180	+	19.8239i	−0.206918	+	0.772230i	0.781938	+	0.623356i	$0.214231\pi$
$659$	−5.31180	+	19.8239i	−0.206918	+	0.772230i	−0.988856	+	0.148874i	$0.952435\pi$
$660$		0			0
$661$	1.40218	+	5.23300i	0.0545384	+	0.203540i	0.987819	−	0.155609i	$-0.0497338\pi$
$661$	1.40218	+	5.23300i	0.0545384	+	0.203540i	−0.933280	+	0.359148i	$0.883067\pi$
$662$		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
$667$	−7.72708	−	2.07047i	−0.299194	−	0.0801687i
$668$		0			0
$669$	8.66316	−	32.3313i	0.334937	−	1.25000i
$670$		0			0
$671$	9.31670			0.359667
$672$		0			0
$673$	−20.3005	+	35.1615i	−0.782527	+	1.35538i	0.147938	+	0.988997i	$0.452736\pi$
$673$	−20.3005	+	35.1615i	−0.782527	+	1.35538i	−0.930465	+	0.366380i	$0.880597\pi$
$674$		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
$683$	−13.1491	−	3.52328i	−0.503135	−	0.134815i	−0.00168044	−	0.999999i	$-0.500535\pi$
$683$	−13.1491	−	3.52328i	−0.503135	−	0.134815i	−0.501455	+	0.865184i	$0.667202\pi$
$684$		0			0
$685$	6.40538	−	23.9052i	0.244737	−	0.913371i
$686$		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
$691$	24.5096	−	6.56734i	0.932391	−	0.249833i	0.239517	−	0.970892i	$-0.423011\pi$
$691$	24.5096	−	6.56734i	0.932391	−	0.249833i	0.692874	+	0.721059i	$0.256344\pi$
$692$		0			0
$693$	−36.9482	−	9.90025i	−1.40355	−	0.376079i
$694$		0			0
$695$	−44.0419	+	25.4276i	−1.67061	+	0.964524i
$696$		0			0
$697$			0.397225i			0.0150460i
$698$		0			0
$699$	5.29873	+	19.7751i	0.200416	+	0.747964i
$700$		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
$709$	10.5047	+	2.81472i	0.394511	+	0.105709i	0.450620	−	0.892716i	$-0.351203\pi$
$709$	10.5047	+	2.81472i	0.394511	+	0.105709i	−0.0561091	+	0.998425i	$0.517869\pi$
$710$		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
$715$	42.8556	+	11.9529i	1.60271	+	0.447013i
$716$		0			0
$717$	8.17780	−	2.19124i	0.305406	−	0.0818332i
$718$		0			0
$719$	8.88267	+	15.3852i	0.331268	+	0.573772i	0.982761	−	0.184882i	$-0.0591903\pi$
$719$	8.88267	+	15.3852i	0.331268	+	0.573772i	−0.651493	+	0.758655i	$0.725857\pi$
$720$		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
$725$	−1.86581	−	6.96329i	−0.0692944	−	0.258610i
$726$		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
$731$	2.15159	+	8.02983i	0.0795793	+	0.296994i
$732$		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
$739$	6.76247	−	1.81200i	0.248761	−	0.0666554i	−0.132284	−	0.991212i	$-0.542231\pi$
$739$	6.76247	−	1.81200i	0.248761	−	0.0666554i	0.381045	+	0.924556i	$0.375564\pi$
$740$		0			0
$741$	14.8489	+	57.7673i	0.545490	+	2.12213i
$742$		0			0
$743$	26.4580	+	15.2755i	0.970649	+	0.560404i	0.899434	−	0.437057i	$-0.143979\pi$
$743$	26.4580	+	15.2755i	0.970649	+	0.560404i	0.0712146	+	0.997461i	$0.477312\pi$
$744$		0			0
$745$	−9.56166	+	5.52043i	−0.350312	+	0.202253i
$746$		0			0
$747$	−1.26951	−	0.340164i	−0.0464489	−	0.0124459i
$748$		0			0
$749$	29.2855	+	29.2855i	1.07007	+	1.07007i
$750$		0			0
$751$	−14.1774	+	24.5560i	−0.517341	+	0.896061i	0.482456	+	0.875920i	$0.339745\pi$
$751$	−14.1774	+	24.5560i	−0.517341	+	0.896061i	−0.999797	+	0.0201407i	$0.993589\pi$
$752$		0			0
$753$	22.6063			0.823820
$754$		0			0
$755$	−48.8402	−	48.8402i	−1.77748	−	1.77748i
$756$		0			0
$757$	3.38255	+	12.6239i	0.122941	+	0.458822i	0.999758	−	0.0220023i	$-0.00700412\pi$
$757$	3.38255	+	12.6239i	0.122941	+	0.458822i	−0.876817	+	0.480824i	$0.840337\pi$
$758$		0			0
$759$			59.2342i			2.15007i
$760$		0			0
$761$	23.2880	−	13.4453i	0.844189	−	0.487393i	−0.0144972	−	0.999895i	$-0.504615\pi$
$761$	23.2880	−	13.4453i	0.844189	−	0.487393i	0.858686	+	0.512502i	$0.171281\pi$
$762$		0			0
$763$	−29.7753	−	7.97826i	−1.07794	−	0.288832i
$764$		0			0
$765$	−24.9844	+	6.69456i	−0.903314	+	0.242042i
$766$		0			0
$767$	5.39908	+	0.0550655i	0.194950	+	0.00198830i
$768$		0			0
$769$	0.556208	−	0.963381i	0.0200574	−	0.0347404i	−0.855822	−	0.517270i	$-0.826948\pi$
$769$	0.556208	−	0.963381i	0.0200574	−	0.0347404i	0.875880	+	0.482529i	$0.160282\pi$
$770$		0			0
$771$	3.14453	−	11.7355i	0.113247	−	0.422645i
$772$		0			0
$773$	42.4985	+	11.3874i	1.52857	+	0.409578i	0.922551	−	0.385875i	$-0.126100\pi$
$773$	42.4985	+	11.3874i	1.52857	+	0.409578i	0.606015	+	0.795453i	$0.292767\pi$
$774$		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
$787$	−3.01478	+	11.2513i	−0.107465	+	0.401067i	−0.998613	−	0.0526467i	$-0.983234\pi$
$787$	−3.01478	+	11.2513i	−0.107465	+	0.401067i	0.891148	+	0.453713i	$0.149901\pi$
$788$		0			0
$789$	−41.1233	−	11.0190i	−1.46403	−	0.392285i
$790$		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
$795$	18.4537	+	68.8702i	0.654486	+	2.44257i
$796$		0			0
$797$	−2.67051	+	9.96647i	−0.0945942	+	0.353030i	−0.996958	−	0.0779455i	$-0.975164\pi$
$797$	−2.67051	+	9.96647i	−0.0945942	+	0.353030i	0.902363	+	0.430976i	$0.141831\pi$
$798$		0			0
$799$	10.2334	+	17.7247i	0.362031	+	0.627056i
$800$		0			0
$801$	21.8925			0.773532
$802$		0			0
$803$	−39.1557	+	10.4917i	−1.38177	+	0.370245i
$804$		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	$-0.515380\pi$
$809$	−26.6642	−	15.3946i	−0.937463	−	0.541245i	−0.889164	+	0.457588i	$0.848713\pi$
$810$		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
$813$	−4.02798	+	15.0326i	−0.141267	+	0.527217i
$814$		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
$819$	9.93012	−	35.6032i	0.346986	−	1.24408i
$820$		0			0
$821$	3.55391	+	13.2634i	0.124032	+	0.462894i	0.999803	−	0.0198321i	$-0.00631316\pi$
$821$	3.55391	+	13.2634i	0.124032	+	0.462894i	−0.875771	+	0.482727i	$0.839646\pi$
$822$		0			0
$823$	−24.3305	+	14.0472i	−0.848107	+	0.489655i	−0.860012	−	0.510274i	$-0.829544\pi$
$823$	−24.3305	+	14.0472i	−0.848107	+	0.489655i	0.0119046	+	0.999929i	$0.496211\pi$
$824$		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
$829$	−15.1799	+	4.06744i	−0.527220	+	0.141268i	−0.512604	−	0.858625i	$-0.671319\pi$
$829$	−15.1799	+	4.06744i	−0.527220	+	0.141268i	−0.0146157	+	0.999893i	$0.504652\pi$
$830$		0			0
$831$	−74.6985			−2.59126
$832$		0			0
$833$	17.6585			0.611829
$834$		0			0
$835$	20.4100	−	5.46885i	0.706318	−	0.189257i
$836$		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	$-0.373960\pi$
$839$	39.9019	−	23.0374i	1.37757	−	0.795338i	0.991866	+	0.127286i	$0.0406265\pi$
$840$		0			0
$841$	−23.8377	+	13.7627i	−0.821989	+	0.474575i
$842$		0			0
$843$	20.0470	+	74.8164i	0.690455	+	2.57681i
$844$		0			0
$845$	−11.9717	+	41.2910i	−0.411838	+	1.42045i
$846$		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
$851$	−6.51370	+	24.3095i	−0.223287	+	0.833318i
$852$		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
$861$	1.21187	−	0.324720i	0.0413005	−	0.0110664i
$862$		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
$867$	−5.76057	+	21.4987i	−0.195639	+	0.730136i
$868$		0			0
$869$	−10.4152	−	38.8701i	−0.353312	−	1.31858i
$870$		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
$875$	−10.9250	−	2.92735i	−0.369333	−	0.0989626i
$876$		0			0
$877$	−10.8981	+	40.6721i	−0.368001	+	1.37340i	0.495305	+	0.868719i	$0.335056\pi$
$877$	−10.8981	+	40.6721i	−0.368001	+	1.37340i	−0.863306	+	0.504681i	$0.831610\pi$
$878$		0			0
$879$	66.2390			2.23419
$880$		0			0
$881$	2.72997	−	4.72845i	0.0919750	−	0.159305i	−0.816367	−	0.577533i	$-0.804015\pi$
$881$	2.72997	−	4.72845i	0.0919750	−	0.159305i	0.908342	+	0.418228i	$0.137349\pi$
$882$		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	$-0.368064\pi$
$887$	−5.61724	−	3.24312i	−0.188609	−	0.108893i	−0.591331	+	0.806429i	$0.701397\pi$
$888$		0			0
$889$		−	17.2011i		−	0.576907i
$890$		0			0
$891$	−34.3900	−	9.21476i	−1.15211	−	0.308706i
$892$		0			0
$893$	−13.0507	+	48.7059i	−0.436725	+	1.62988i
$894$		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
$899$	4.79926	−	1.28596i	0.160064	−	0.0428891i
$900$		0			0
$901$	−24.0798	−	6.45216i	−0.802214	−	0.214953i
$902$		0			0
$903$	22.7389	−	13.1283i	0.756703	−	0.436883i
$904$		0			0
$905$		−	59.1732i		−	1.96698i
$906$		0			0
$907$	10.8415	+	40.4610i	0.359986	+	1.34349i	0.874092	+	0.485760i	$0.161457\pi$
$907$	10.8415	+	40.4610i	0.359986	+	1.34349i	−0.514106	+	0.857727i	$0.671876\pi$
$908$		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
$917$	−0.522485	−	0.139999i	−0.0172540	−	0.00462319i
$918$		0			0
$919$	32.2776	−	18.6355i	1.06474	−	0.614729i	0.138001	−	0.990432i	$-0.455932\pi$
$919$	32.2776	−	18.6355i	1.06474	−	0.614729i	0.926740	+	0.375703i	$0.122599\pi$
$920$		0			0
$921$	57.1065	+	32.9705i	1.88172	+	1.08641i
$922$		0			0
$923$	−23.4880	+	23.0137i	−0.773116	+	0.757506i
$924$		0			0
$925$	−21.9066	+	5.86985i	−0.720284	+	0.192999i
$926$		0			0
$927$	12.1900	+	21.1137i	0.400373	+	0.693466i
$928$		0			0
$929$	−2.54306	−	4.40470i	−0.0834350	−	0.144514i	0.821288	−	0.570513i	$-0.193256\pi$
$929$	−2.54306	−	4.40470i	−0.0834350	−	0.144514i	−0.904723	+	0.426000i	$0.859922\pi$
$930$		0			0
$931$	30.7628	+	30.7628i	1.00821	+	1.00821i
$932$		0			0
$933$	−4.26178	−	15.9052i	−0.139524	−	0.520712i
$934$		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
$939$	9.02474	+	33.6808i	0.294511	+	1.09913i
$940$		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
$947$	−3.15231	+	0.844658i	−0.102436	+	0.0274477i	−0.309673	−	0.950843i	$-0.600220\pi$
$947$	−3.15231	+	0.844658i	−0.102436	+	0.0274477i	0.207237	+	0.978291i	$0.433553\pi$
$948$		0			0
$949$	−9.75165	−	37.9371i	−0.316552	−	1.23149i
$950$		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	$-0.502782\pi$
$953$	26.3291	−	15.2011i	0.852883	−	0.492412i	0.861623	+	0.507550i	$0.169449\pi$
$954$		0			0
$955$	−40.3107	−	10.8012i	−1.30442	−	0.349519i
$956$		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
$965$	3.19398	+	11.9201i	0.102818	+	0.383722i
$966$		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
$971$	42.1871	+	11.3040i	1.35385	+	0.362763i	0.861554	−	0.507666i	$-0.169492\pi$
$971$	42.1871	+	11.3040i	1.35385	+	0.362763i	0.492295	+	0.870428i	$0.336158\pi$
$972$		0			0
$973$	−54.2471	+	14.5355i	−1.73908	+	0.465986i
$974$		0			0
$975$	−25.3330	−	44.9300i	−0.811304	−	1.43891i
$976$		0			0
$977$	22.9985	−	39.8345i	0.735786	−	1.27442i	−0.218591	−	0.975817i	$-0.570146\pi$
$977$	22.9985	−	39.8345i	0.735786	−	1.27442i	0.954377	−	0.298603i	$-0.0965206\pi$
$978$		0			0
$979$	−7.53194	+	28.1096i	−0.240722	+	0.898386i
$980$		0			0
$981$	22.8859	+	6.13226i	0.730691	+	0.195788i
$982$		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	−0.988629	−	0.150376i	$-0.951951\pi$
$991$	−11.4614	+	19.8518i	−0.364085	+	0.630613i	0.624544	+	0.780990i	$0.285285\pi$
$992$		0			0
$993$	−19.6211			−0.622658
$994$		0			0
$995$	−0.721109	+	2.69121i	−0.0228607	+	0.0853172i
$996$		0			0
$997$	11.8552	+	3.17660i	0.375459	+	0.100604i	0.441613	−	0.897205i	$-0.354406\pi$
$997$	11.8552	+	3.17660i	0.375459	+	0.100604i	−0.0661544	+	0.997809i	$0.521073\pi$
$998$		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.529.4		104
4.3	odd	2		208.2.bj.a.61.18	yes	104
13.3	even	3	inner	832.2.br.a.81.23		104
16.5	even	4	inner	832.2.br.a.113.23		104
16.11	odd	4		208.2.bj.a.165.1	yes	104
52.3	odd	6		208.2.bj.a.29.1	✓	104
208.107	odd	12		208.2.bj.a.133.18	yes	104
208.133	even	12	inner	832.2.br.a.497.4		104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.bj.a.29.1	✓	104	52.3	odd	6
208.2.bj.a.61.18	yes	104	4.3	odd	2
208.2.bj.a.133.18	yes	104	208.107	odd	12
208.2.bj.a.165.1	yes	104	16.11	odd	4
832.2.br.a.81.23		104	13.3	even	3	inner
832.2.br.a.113.23		104	16.5	even	4	inner
832.2.br.a.497.4		104	208.133	even	12	inner
832.2.br.a.529.4		104	1.1	even	1	trivial

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)

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