LMFDB - Embedded newform 276.2.k.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			5.2
Character	$\chi$	$=$	276.5
Dual form			276.2.k.a.221.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.25009 + 1.19887i) q^{3} +(-0.395237 + 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(0.125437 - 2.99738i) q^{9} +O(q^{10})$	\(q+(-1.25009 + 1.19887i) q^{3} +(-0.395237 + 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(0.125437 - 2.99738i) q^{9} +(-5.12676 + 1.50535i) q^{11} +(-0.356468 + 0.780556i) q^{13} +(-2.80153 - 3.91025i) q^{15} +(-2.26084 + 1.45295i) q^{17} +(-1.15710 + 1.80049i) q^{19} +(-0.502197 + 1.26500i) q^{21} +(-4.59687 - 1.36703i) q^{23} +(-2.60298 - 0.764303i) q^{25} +(3.43665 + 3.89736i) q^{27} +(3.91782 + 6.09624i) q^{29} +(1.14624 + 1.32283i) q^{31} +(4.60418 - 8.02813i) q^{33} +(0.614830 + 2.09392i) q^{35} +(5.85758 - 0.842193i) q^{37} +(-0.490166 - 1.40312i) q^{39} +(7.95761 + 1.14413i) q^{41} +(-6.40757 - 5.55219i) q^{43} +(8.19002 + 1.52949i) q^{45} -3.23252i q^{47} +(-4.17966 + 4.82359i) q^{49} +(1.08435 - 4.52676i) q^{51} +(0.151808 + 0.332413i) q^{53} +(-2.11183 - 14.6881i) q^{55} +(-0.712065 - 3.63798i) q^{57} +(11.4354 + 5.22236i) q^{59} +(0.851709 - 0.738010i) q^{61} +(-0.888779 - 2.18343i) q^{63} +(-2.00481 - 1.28841i) q^{65} +(-3.75708 + 12.7954i) q^{67} +(7.38537 - 3.80214i) q^{69} +(-0.390072 + 1.32846i) q^{71} +(11.4103 + 7.33298i) q^{73} +(4.17025 - 2.16518i) q^{75} +(-3.17314 + 2.74954i) q^{77} +(11.8032 + 5.39034i) q^{79} +(-8.96853 - 0.751962i) q^{81} +(-1.22527 - 8.52192i) q^{83} +(-3.10051 - 6.78917i) q^{85} +(-12.2062 - 2.92389i) q^{87} +(7.91446 - 9.13377i) q^{89} +0.674293i q^{91} +(-3.01879 - 0.279465i) q^{93} +(-4.49210 - 3.89242i) q^{95} +(-7.08845 - 1.01917i) q^{97} +(3.86903 + 15.5557i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{1}{22}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.25009	+	1.19887i	−0.721738	+	0.692166i
$3$	−1.25009	+	1.19887i	−0.721738	+	0.692166i
$4$		0			0
$5$	−0.395237	+	2.74894i	−0.176756	+	1.22936i	0.687453	+	0.726229i	$0.258729\pi$
$5$	−0.395237	+	2.74894i	−0.176756	+	1.22936i	−0.864209	+	0.503133i	$0.832180\pi$
$6$		0			0
$7$	0.714786	−	0.326432i	0.270164	−	0.123380i	−0.275727	−	0.961236i	$-0.588919\pi$
$7$	0.714786	−	0.326432i	0.270164	−	0.123380i	0.545891	+	0.837856i	$0.316191\pi$
$8$		0			0
$9$	0.125437	−	2.99738i	0.0418122	−	0.999125i
$10$		0			0
$11$	−5.12676	+	1.50535i	−1.54578	+	0.453881i	−0.939835	−	0.341628i	$-0.889022\pi$
$11$	−5.12676	+	1.50535i	−1.54578	+	0.453881i	−0.605942	+	0.795509i	$0.707204\pi$
$12$		0			0
$13$	−0.356468	+	0.780556i	−0.0988664	+	0.216487i	−0.952602	−	0.304220i	$-0.901604\pi$
$13$	−0.356468	+	0.780556i	−0.0988664	+	0.216487i	0.853736	+	0.520707i	$0.174332\pi$
$14$		0			0
$15$	−2.80153	−	3.91025i	−0.723351	−	1.00962i
$16$		0			0
$17$	−2.26084	+	1.45295i	−0.548334	+	0.352393i	−0.785291	−	0.619127i	$-0.787486\pi$
$17$	−2.26084	+	1.45295i	−0.548334	+	0.352393i	0.236957	+	0.971520i	$0.423850\pi$
$18$		0			0
$19$	−1.15710	+	1.80049i	−0.265458	+	0.413060i	−0.948237	−	0.317565i	$-0.897135\pi$
$19$	−1.15710	+	1.80049i	−0.265458	+	0.413060i	0.682779	+	0.730625i	$0.260771\pi$
$20$		0			0
$21$	−0.502197	+	1.26500i	−0.109588	+	0.276046i
$22$		0			0
$23$	−4.59687	−	1.36703i	−0.958514	−	0.285044i
$23$	−4.59687	−	1.36703i	−0.958514	−	0.285044i
$24$		0			0
$25$	−2.60298	−	0.764303i	−0.520596	−	0.152861i
$26$		0			0
$27$	3.43665	+	3.89736i	0.661383	+	0.750048i
$28$		0			0
$29$	3.91782	+	6.09624i	0.727520	+	1.13204i	0.986116	+	0.166058i	$0.0531038\pi$
$29$	3.91782	+	6.09624i	0.727520	+	1.13204i	−0.258596	+	0.965986i	$0.583260\pi$
$30$		0			0
$31$	1.14624	+	1.32283i	0.205870	+	0.237587i	0.849290	−	0.527927i	$-0.177030\pi$
$31$	1.14624	+	1.32283i	0.205870	+	0.237587i	−0.643420	+	0.765514i	$0.722485\pi$
$32$		0			0
$33$	4.60418	−	8.02813i	0.801485	−	1.39752i
$34$		0			0
$35$	0.614830	+	2.09392i	0.103925	+	0.353937i
$36$		0			0
$37$	5.85758	−	0.842193i	0.962980	−	0.138456i	0.357148	−	0.934048i	$-0.383749\pi$
$37$	5.85758	−	0.842193i	0.962980	−	0.138456i	0.605833	+	0.795592i	$0.292840\pi$
$38$		0			0
$39$	−0.490166	−	1.40312i	−0.0784894	−	0.224679i
$40$		0			0
$41$	7.95761	+	1.14413i	1.24277	+	0.178683i	0.732162	−	0.681130i	$-0.238511\pi$
$41$	7.95761	+	1.14413i	1.24277	+	0.178683i	0.510608	+	0.859814i	$0.329420\pi$
$42$		0			0
$43$	−6.40757	−	5.55219i	−0.977145	−	0.846701i	0.0110441	−	0.999939i	$-0.496484\pi$
$43$	−6.40757	−	5.55219i	−0.977145	−	0.846701i	−0.988189	+	0.153238i	$0.951030\pi$
$44$		0			0
$45$	8.19002	+	1.52949i	1.22090	+	0.228003i
$46$		0			0
$47$		−	3.23252i		−	0.471512i	−0.971812	−	0.235756i	$-0.924243\pi$
$47$		−	3.23252i		−	0.471512i	0.971812	−	0.235756i	$-0.0757566\pi$
$48$		0			0
$49$	−4.17966	+	4.82359i	−0.597095	+	0.689084i
$50$		0			0
$51$	1.08435	−	4.52676i	0.151839	−	0.633874i
$52$		0			0
$53$	0.151808	+	0.332413i	0.0208524	+	0.0456604i	0.919772	−	0.392454i	$-0.128374\pi$
$53$	0.151808	+	0.332413i	0.0208524	+	0.0456604i	−0.898919	+	0.438114i	$0.855646\pi$
$54$		0			0
$55$	−2.11183	−	14.6881i	−0.284760	−	1.98055i
$56$		0			0
$57$	−0.712065	−	3.63798i	−0.0943153	−	0.481862i
$58$		0			0
$59$	11.4354	+	5.22236i	1.48876	+	0.679894i	0.983139	−	0.182862i	$-0.0585361\pi$
$59$	11.4354	+	5.22236i	1.48876	+	0.679894i	0.505621	+	0.862756i	$0.331263\pi$
$60$		0			0
$61$	0.851709	−	0.738010i	0.109050	−	0.0944926i	−0.598629	−	0.801026i	$-0.704288\pi$
$61$	0.851709	−	0.738010i	0.109050	−	0.0944926i	0.707679	+	0.706534i	$0.249742\pi$
$62$		0			0
$63$	−0.888779	−	2.18343i	−0.111976	−	0.275086i
$64$		0			0
$65$	−2.00481	−	1.28841i	−0.248666	−	0.159808i
$66$		0			0
$67$	−3.75708	+	12.7954i	−0.459000	+	1.56321i	0.327026	+	0.945015i	$0.393954\pi$
$67$	−3.75708	+	12.7954i	−0.459000	+	1.56321i	−0.786025	+	0.618194i	$0.787865\pi$
$68$		0			0
$69$	7.38537	−	3.80214i	0.889095	−	0.457724i
$70$		0			0
$71$	−0.390072	+	1.32846i	−0.0462930	+	0.157659i	−0.979396	−	0.201950i	$-0.935272\pi$
$71$	−0.390072	+	1.32846i	−0.0462930	+	0.157659i	0.933103	+	0.359610i	$0.117090\pi$
$72$		0			0
$73$	11.4103	+	7.33298i	1.33548	+	0.858260i	0.996586	−	0.0825643i	$-0.0263110\pi$
$73$	11.4103	+	7.33298i	1.33548	+	0.858260i	0.338894	+	0.940825i	$0.389947\pi$
$74$		0			0
$75$	4.17025	−	2.16518i	0.481539	−	0.250013i
$76$		0			0
$77$	−3.17314	+	2.74954i	−0.361613	+	0.313340i
$78$		0			0
$79$	11.8032	+	5.39034i	1.32796	+	0.606460i	0.947920	−	0.318508i	$-0.103182\pi$
$79$	11.8032	+	5.39034i	1.32796	+	0.606460i	0.380043	+	0.924969i	$0.375909\pi$
$80$		0			0
$81$	−8.96853	−	0.751962i	−0.996503	−	0.0835514i
$82$		0			0
$83$	−1.22527	−	8.52192i	−0.134491	−	0.935403i	−0.939600	−	0.342276i	$-0.888802\pi$
$83$	−1.22527	−	8.52192i	−0.134491	−	0.935403i	0.805109	−	0.593127i	$-0.202107\pi$
$84$		0			0
$85$	−3.10051	−	6.78917i	−0.336297	−	0.736388i
$86$		0			0
$87$	−12.2062	−	2.92389i	−1.30864	−	0.313474i
$88$		0			0
$89$	7.91446	−	9.13377i	0.838931	−	0.968178i	−0.160893	−	0.986972i	$-0.551437\pi$
$89$	7.91446	−	9.13377i	0.838931	−	0.968178i	0.999823	+	0.0187942i	$0.00598272\pi$
$90$		0			0
$91$			0.674293i			0.0706851i
$92$		0			0
$93$	−3.01879	−	0.279465i	−0.313034	−	0.0289792i
$94$		0			0
$95$	−4.49210	−	3.89242i	−0.460879	−	0.399354i
$96$		0			0
$97$	−7.08845	−	1.01917i	−0.719723	−	0.103481i	−0.227285	−	0.973828i	$-0.572985\pi$
$97$	−7.08845	−	1.01917i	−0.719723	−	0.103481i	−0.492438	+	0.870348i	$0.663894\pi$
$98$		0			0
$99$	3.86903	+	15.5557i	0.388852	+	1.56340i
$100$		0			0
$101$	−17.3230	+	2.49067i	−1.72370	+	0.247831i	−0.931840	−	0.362869i	$-0.881797\pi$
$101$	−17.3230	+	2.49067i	−1.72370	+	0.247831i	−0.791862	+	0.610700i	$0.790888\pi$
$102$		0			0
$103$	3.85290	+	13.1218i	0.379638	+	1.29293i	0.898840	+	0.438277i	$0.144411\pi$
$103$	3.85290	+	13.1218i	0.379638	+	1.29293i	−0.519202	+	0.854651i	$0.673771\pi$
$104$		0			0
$105$	−3.27892	−	1.88048i	−0.319990	−	0.183516i
$106$		0			0
$107$	4.53943	+	5.23878i	0.438843	+	0.506452i	0.931485	−	0.363780i	$-0.118514\pi$
$107$	4.53943	+	5.23878i	0.438843	+	0.506452i	−0.492642	+	0.870232i	$0.663969\pi$
$108$		0			0
$109$	−8.76331	−	13.6360i	−0.839373	−	1.30609i	−0.950007	−	0.312229i	$-0.898925\pi$
$109$	−8.76331	−	13.6360i	−0.839373	−	1.30609i	0.110634	−	0.993861i	$-0.464712\pi$
$110$		0			0
$111$	−6.31281	+	8.07527i	−0.599185	+	0.766471i
$112$		0			0
$113$	2.67490	+	0.785421i	0.251633	+	0.0738862i	0.405116	−	0.914265i	$-0.367231\pi$
$113$	2.67490	+	0.785421i	0.251633	+	0.0738862i	−0.153483	+	0.988151i	$0.549049\pi$
$114$		0			0
$115$	5.57472	−	12.0962i	0.519846	−	1.12798i
$116$		0			0
$117$	2.29490	+	1.16638i	0.212164	+	0.107832i
$118$		0			0
$119$	−1.14173	+	1.77656i	−0.104662	+	0.162857i
$120$		0			0
$121$	14.7638	−	9.48813i	1.34217	−	0.862557i
$122$		0			0
$123$	−11.3194	+	8.10985i	−1.02063	+	0.731241i
$124$		0			0
$125$	−2.63865	+	5.77783i	−0.236008	+	0.516785i
$126$		0			0
$127$	−10.6074	+	3.11462i	−0.941257	+	0.276378i	−0.716142	−	0.697954i	$-0.754094\pi$
$127$	−10.6074	+	3.11462i	−0.941257	+	0.276378i	−0.225115	+	0.974332i	$0.572276\pi$
$128$		0			0
$129$	14.6664	−	0.741099i	1.29130	−	0.0652502i
$130$		0			0
$131$	12.7065	−	5.80287i	1.11017	−	0.506999i	0.225985	−	0.974131i	$-0.427440\pi$
$131$	12.7065	−	5.80287i	1.11017	−	0.506999i	0.884188	+	0.467132i	$0.154713\pi$
$132$		0			0
$133$	−0.239345	+	1.66468i	−0.0207538	+	0.144346i
$134$		0			0
$135$	−12.0719	+	7.90675i	−1.03898	+	0.680504i
$136$		0			0
$137$	−15.7968			−1.34961			−0.674804	−	0.737997i	$-0.735772\pi$
$137$	−15.7968			−1.34961			−0.674804	+	0.737997i	$0.735772\pi$
$138$		0			0
$139$	6.87151			0.582834			0.291417	−	0.956596i	$-0.405873\pi$
$139$	6.87151			0.582834			0.291417	+	0.956596i	$0.405873\pi$
$140$		0			0
$141$	3.87536	+	4.04093i	0.326364	+	0.340308i
$142$		0			0
$143$	0.652514	−	4.53833i	0.0545659	−	0.379514i
$144$		0			0
$145$	−18.3066	+	8.36037i	−1.52028	+	0.694291i
$146$		0			0
$147$	−0.557896	−	11.0408i	−0.0460145	−	0.910627i
$148$		0			0
$149$	5.10967	−	1.50034i	0.418601	−	0.122912i	−0.0656476	−	0.997843i	$-0.520911\pi$
$149$	5.10967	−	1.50034i	0.418601	−	0.122912i	0.484248	+	0.874931i	$0.339093\pi$
$150$		0			0
$151$	−3.21609	+	7.04226i	−0.261722	+	0.573091i	−0.994181	−	0.107720i	$-0.965645\pi$
$151$	−3.21609	+	7.04226i	−0.261722	+	0.573091i	0.732459	+	0.680811i	$0.238372\pi$
$152$		0			0
$153$	4.07146	+	6.95884i	0.329158	+	0.562589i
$154$		0			0
$155$	−4.08941	+	2.62810i	−0.328469	+	0.211094i
$156$		0			0
$157$	−5.33973	+	8.30878i	−0.426157	+	0.663113i	−0.986239	−	0.165324i	$-0.947133\pi$
$157$	−5.33973	+	8.30878i	−0.426157	+	0.663113i	0.560082	+	0.828437i	$0.310769\pi$
$158$		0			0
$159$	−0.588292	−	0.233548i	−0.0466546	−	0.0185215i
$160$		0			0
$161$	−3.73202	+	0.523435i	−0.294124	+	0.0412525i
$162$		0			0
$163$	−2.29492	−	0.673849i	−0.179752	−	0.0527799i	0.190618	−	0.981664i	$-0.438951\pi$
$163$	−2.29492	−	0.673849i	−0.179752	−	0.0527799i	−0.370370	+	0.928884i	$0.620769\pi$
$164$		0			0
$165$	20.2491	+	15.8296i	1.57639	+	1.23233i
$166$		0			0
$167$	−10.5810	−	16.4644i	−0.818786	−	1.27406i	−0.958850	−	0.283913i	$-0.908367\pi$
$167$	−10.5810	−	16.4644i	−0.818786	−	1.27406i	0.140065	−	0.990142i	$-0.455269\pi$
$168$		0			0
$169$	8.03099	+	9.26826i	0.617769	+	0.712943i
$170$		0			0
$171$	5.25160	+	3.69412i	0.401600	+	0.282496i
$172$		0			0
$173$	0.0418712	+	0.142600i	0.00318341	+	0.0108417i	0.961069	−	0.276307i	$-0.0891107\pi$
$173$	0.0418712	+	0.142600i	0.00318341	+	0.0108417i	−0.957886	+	0.287149i	$0.907293\pi$
$174$		0			0
$175$	−2.11007	+	0.303382i	−0.159506	+	0.0229335i
$176$		0			0
$177$	−20.5561	+	7.18109i	−1.54509	+	0.539764i
$178$		0			0
$179$	12.5727	+	1.80768i	0.939729	+	0.135113i	0.595123	−	0.803635i	$-0.297103\pi$
$179$	12.5727	+	1.80768i	0.939729	+	0.135113i	0.344606	+	0.938747i	$0.388013\pi$
$180$		0			0
$181$	−4.84990	−	4.20246i	−0.360490	−	0.312367i	0.455718	−	0.890124i	$-0.349382\pi$
$181$	−4.84990	−	4.20246i	−0.360490	−	0.312367i	−0.816208	+	0.577758i	$0.803928\pi$
$182$		0			0
$183$	−0.179935	+	1.94366i	−0.0133012	+	0.143680i
$184$		0			0
$185$			16.4350i			1.20832i
$186$		0			0
$187$	9.40358	−	10.8523i	0.687658	−	0.793599i
$188$		0			0
$189$	3.72869	+	1.66395i	0.271222	+	0.121035i
$190$		0			0
$191$	−9.13854	−	20.0106i	−0.661242	−	1.44792i	−0.881360	−	0.472445i	$-0.843372\pi$
$191$	−9.13854	−	20.0106i	−0.661242	−	1.44792i	0.220119	−	0.975473i	$-0.429356\pi$
$192$		0			0
$193$	−1.90371	−	13.2406i	−0.137032	−	0.953078i	−0.936074	−	0.351803i	$-0.885569\pi$
$193$	−1.90371	−	13.2406i	−0.137032	−	0.953078i	0.799042	−	0.601275i	$-0.205340\pi$
$194$		0			0
$195$	4.05082	−	0.792871i	0.290085	−	0.0567786i
$196$		0			0
$197$	−16.0655	−	7.33688i	−1.14462	−	0.522731i	−0.249421	−	0.968395i	$-0.580240\pi$
$197$	−16.0655	−	7.33688i	−1.14462	−	0.522731i	−0.895200	+	0.445664i	$0.852968\pi$
$198$		0			0
$199$	2.19084	−	1.89837i	0.155304	−	0.134572i	−0.573743	−	0.819036i	$-0.694509\pi$
$199$	2.19084	−	1.89837i	0.155304	−	0.134572i	0.729047	+	0.684464i	$0.239964\pi$
$200$		0			0
$201$	−10.6433	−	20.4996i	−0.750723	−	1.44593i
$202$		0			0
$203$	4.79041	+	3.07861i	0.336221	+	0.216076i
$204$		0			0
$205$	−6.29029	+	21.4228i	−0.439333	+	1.49623i
$206$		0			0
$207$	−4.67411	+	13.6071i	−0.324873	+	0.945758i
$208$		0			0
$209$	3.22182	−	10.9725i	0.222858	−	0.758985i
$210$		0			0
$211$	3.94007	+	2.53213i	0.271245	+	0.174319i	0.669192	−	0.743090i	$-0.266641\pi$
$211$	3.94007	+	2.53213i	0.271245	+	0.174319i	−0.397946	+	0.917409i	$0.630277\pi$
$212$		0			0
$213$	−1.10503	−	2.12834i	−0.0757151	−	0.145831i
$214$		0			0
$215$	17.7951	−	15.4196i	1.21362	−	1.05161i
$216$		0			0
$217$	1.25113	+	0.571371i	0.0849321	+	0.0387872i
$218$		0			0
$219$	−23.0552	+	4.51261i	−1.55793	+	0.304934i
$220$		0			0
$221$	−0.328194	−	2.28264i	−0.0220767	−	0.153547i
$222$		0			0
$223$	−6.36318	−	13.9334i	−0.426110	−	0.933050i	−0.993942	−	0.109906i	$-0.964945\pi$
$223$	−6.36318	−	13.9334i	−0.426110	−	0.933050i	0.567832	−	0.823144i	$-0.307782\pi$
$224$		0			0
$225$	−2.61741	+	7.70623i	−0.174494	+	0.513749i
$226$		0			0
$227$	−2.42774	+	2.80177i	−0.161135	+	0.185960i	−0.830576	−	0.556906i	$-0.811988\pi$
$227$	−2.42774	+	2.80177i	−0.161135	+	0.185960i	0.669441	+	0.742866i	$0.266534\pi$
$228$		0			0
$229$		−	19.7518i		−	1.30524i	−0.757687	−	0.652618i	$-0.773671\pi$
$229$		−	19.7518i		−	1.30524i	0.757687	−	0.652618i	$-0.226329\pi$
$230$		0			0
$231$	0.670369	−	7.24135i	0.0441070	−	0.476446i
$232$		0			0
$233$	5.60455	+	4.85637i	0.367166	+	0.318151i	0.818829	−	0.574037i	$-0.194624\pi$
$233$	5.60455	+	4.85637i	0.367166	+	0.318151i	−0.451663	+	0.892189i	$0.649169\pi$
$234$		0			0
$235$	8.88600	+	1.27761i	0.579659	+	0.0833423i
$236$		0			0
$237$	−21.2173	+	7.41207i	−1.37821	+	0.481465i
$238$		0			0
$239$	25.7844	−	3.70724i	1.66786	−	0.239802i	0.757265	−	0.653108i	$-0.226535\pi$
$239$	25.7844	−	3.70724i	1.66786	−	0.239802i	0.910592	+	0.413307i	$0.135626\pi$
$240$		0			0
$241$	2.22864	+	7.59004i	0.143559	+	0.488917i	0.999609	−	0.0279765i	$-0.00890635\pi$
$241$	2.22864	+	7.59004i	0.143559	+	0.488917i	−0.856049	+	0.516894i	$0.827088\pi$
$242$		0			0
$243$	12.1129	−	9.81206i	0.777046	−	0.629444i
$244$		0			0
$245$	−11.6078	−	13.3961i	−0.741594	−	0.855845i
$246$		0			0
$247$	−0.992911	−	1.54500i	−0.0631774	−	0.0983059i
$248$		0			0
$249$	11.7483	+	9.18422i	0.744521	+	0.582026i
$250$		0			0
$251$	23.2475	+	6.82607i	1.46737	+	0.430858i	0.915242	−	0.402904i	$-0.131999\pi$
$251$	23.2475	+	6.82607i	1.46737	+	0.430858i	0.552125	+	0.833762i	$0.313817\pi$
$252$		0			0
$253$	25.6249	+	0.0884960i	1.61103	+	0.00556370i
$254$		0			0
$255$	12.0152	+	4.76995i	0.752422	+	0.298706i
$256$		0			0
$257$	11.1549	−	17.3573i	0.695823	−	1.08272i	−0.296011	−	0.955184i	$-0.595657\pi$
$257$	11.1549	−	17.3573i	0.695823	−	1.08272i	0.991834	−	0.127537i	$-0.0407070\pi$
$258$		0			0
$259$	3.91200	−	2.51409i	0.243080	−	0.156218i
$260$		0			0
$261$	18.7642	−	10.9785i	1.16147	−	0.679551i
$262$		0			0
$263$	−3.41652	+	7.48114i	−0.210672	+	0.461307i	−0.985239	−	0.171185i	$-0.945240\pi$
$263$	−3.41652	+	7.48114i	−0.210672	+	0.461307i	0.774567	+	0.632492i	$0.217968\pi$
$264$		0			0
$265$	−0.973783	+	0.285928i	−0.0598190	+	0.0175644i
$266$		0			0
$267$	1.05641	+	20.9064i	0.0646513	+	1.27945i
$268$		0			0
$269$	0.755924	−	0.345219i	0.0460895	−	0.0210484i	−0.392237	−	0.919864i	$-0.628299\pi$
$269$	0.755924	−	0.345219i	0.0460895	−	0.0210484i	0.438326	+	0.898816i	$0.355571\pi$
$270$		0			0
$271$	−0.555157	+	3.86120i	−0.0337234	+	0.234551i	−0.999711	−	0.0240368i	$-0.992348\pi$
$271$	−0.555157	+	3.86120i	−0.0337234	+	0.234551i	0.965988	+	0.258588i	$0.0832572\pi$
$272$		0			0
$273$	−0.808387	−	0.842925i	−0.0489258	−	0.0510161i
$274$		0			0
$275$	14.4954			0.874105
$276$		0			0
$277$	18.1904			1.09295			0.546477	−	0.837474i	$-0.315969\pi$
$277$	18.1904			1.09295			0.546477	+	0.837474i	$0.315969\pi$
$278$		0			0
$279$	4.10880	−	3.26978i	0.245987	−	0.195756i
$280$		0			0
$281$	−3.34042	+	23.2331i	−0.199273	+	1.38597i	0.607128	+	0.794604i	$0.292322\pi$
$281$	−3.34042	+	23.2331i	−0.199273	+	1.38597i	−0.806401	+	0.591369i	$0.798588\pi$
$282$		0			0
$283$	−9.10857	+	4.15974i	−0.541448	+	0.247271i	−0.667314	−	0.744776i	$-0.732556\pi$
$283$	−9.10857	+	4.15974i	−0.541448	+	0.247271i	0.125866	+	0.992047i	$0.459829\pi$
$284$		0			0
$285$	10.2820	−	0.519556i	0.609054	−	0.0307758i
$286$		0			0
$287$	6.06147	−	1.77981i	0.357797	−	0.105059i
$288$		0			0
$289$	−4.06173	+	8.89396i	−0.238926	+	0.523174i
$290$		0			0
$291$	10.0830	−	7.22406i	0.591078	−	0.423482i
$292$		0			0
$293$	14.5168	−	9.32939i	0.848081	−	0.545029i	−0.0428947	−	0.999080i	$-0.513658\pi$
$293$	14.5168	−	9.32939i	0.848081	−	0.545029i	0.890976	+	0.454051i	$0.150022\pi$
$294$		0			0
$295$	−18.8756	+	29.3711i	−1.09898	+	1.71005i
$296$		0			0
$297$	−23.4858	−	14.8075i	−1.36278	−	0.859218i
$298$		0			0
$299$	2.70568	−	3.10081i	0.156473	−	0.179325i
$300$		0			0
$301$	−6.39245	−	1.87699i	−0.368455	−	0.108188i
$302$		0			0
$303$	18.6693	−	23.8815i	1.07252	−	1.37196i
$304$		0			0
$305$	1.69212	+	2.63299i	0.0968903	+	0.150764i
$306$		0			0
$307$	11.1132	+	12.8253i	0.634262	+	0.731977i	0.978349	−	0.206961i	$-0.0663572\pi$
$307$	11.1132	+	12.8253i	0.634262	+	0.731977i	−0.344088	+	0.938938i	$0.611812\pi$
$308$		0			0
$309$	−20.5477	−	11.7843i	−1.16892	−	0.670383i
$310$		0			0
$311$	6.96854	+	23.7327i	0.395150	+	1.34576i	0.881579	+	0.472036i	$0.156481\pi$
$311$	6.96854	+	23.7327i	0.395150	+	1.34576i	−0.486429	+	0.873720i	$0.661701\pi$
$312$		0			0
$313$	−14.2795	+	2.05309i	−0.807126	+	0.116047i	−0.533512	−	0.845792i	$-0.679128\pi$
$313$	−14.2795	+	2.05309i	−0.807126	+	0.116047i	−0.273614	+	0.961840i	$0.588219\pi$
$314$		0			0
$315$	6.35339	−	1.58022i	0.357973	−	0.0890355i
$316$		0			0
$317$	−22.7023	−	3.26410i	−1.27509	−	0.183330i	−0.528683	−	0.848820i	$-0.677314\pi$
$317$	−22.7023	−	3.26410i	−1.27509	−	0.183330i	−0.746407	+	0.665489i	$0.768223\pi$
$318$		0			0
$319$	−29.2627	−	25.3563i	−1.63840	−	1.41968i
$320$		0			0
$321$	−11.9553	−	1.10676i	−0.667279	−	0.0617734i
$322$		0			0
$323$		−	5.75183i		−	0.320040i
$324$		0			0
$325$	1.52446	−	1.75932i	0.0845618	−	0.0975895i
$326$		0			0
$327$	27.3026	+	6.54012i	1.50984	+	0.361669i
$328$		0			0
$329$	−1.05520	−	2.31056i	−0.0581750	−	0.127385i
$330$		0			0
$331$	−3.63995	−	25.3164i	−0.200069	−	1.39151i	−0.804072	−	0.594532i	$-0.797337\pi$
$331$	−3.63995	−	25.3164i	−0.200069	−	1.39151i	0.604003	−	0.796982i	$-0.293572\pi$
$332$		0			0
$333$	−1.78961	−	17.6630i	−0.0980702	−	0.967927i
$334$		0			0
$335$	−33.6889	−	15.3852i	−1.84062	−	0.840583i
$336$		0			0
$337$	25.1727	−	21.8123i	1.37124	−	1.18819i	0.410133	−	0.912026i	$-0.365482\pi$
$337$	25.1727	−	21.8123i	1.37124	−	1.18819i	0.961111	−	0.276163i	$-0.0890631\pi$
$338$		0			0
$339$	−4.28547	+	2.22500i	−0.232755	+	0.120845i
$340$		0			0
$341$	−7.86782	−	5.05634i	−0.426066	−	0.273816i
$342$		0			0
$343$	−2.96268	+	10.0900i	−0.159970	+	0.544807i
$344$		0			0
$345$	7.53286	+	21.8047i	0.405556	+	1.17392i
$346$		0			0
$347$	−4.42257	+	15.0619i	−0.237416	+	0.808565i	0.751454	+	0.659785i	$0.229353\pi$
$347$	−4.42257	+	15.0619i	−0.237416	+	0.808565i	−0.988870	+	0.148780i	$0.952466\pi$
$348$		0			0
$349$	−2.65233	−	1.70455i	−0.141976	−	0.0912424i	0.467725	−	0.883874i	$-0.345074\pi$
$349$	−2.65233	−	1.70455i	−0.141976	−	0.0912424i	−0.609701	+	0.792632i	$0.708710\pi$
$350$		0			0
$351$	−4.26716	+	1.29321i	−0.227764	+	0.0690264i
$352$		0			0
$353$	3.50780	−	3.03953i	0.186702	−	0.161778i	−0.556495	−	0.830851i	$-0.687854\pi$
$353$	3.50780	−	3.03953i	0.186702	−	0.161778i	0.743197	+	0.669073i	$0.233309\pi$
$354$		0			0
$355$	−3.49769	−	1.59734i	−0.185638	−	0.0847780i
$356$		0			0
$357$	−0.702602	−	3.58963i	−0.0371856	−	0.189984i
$358$		0			0
$359$	2.53840	+	17.6549i	0.133972	+	0.931793i	0.940305	+	0.340332i	$0.110539\pi$
$359$	2.53840	+	17.6549i	0.133972	+	0.931793i	−0.806334	+	0.591461i	$0.798551\pi$
$360$		0			0
$361$	5.99002	+	13.1163i	0.315264	+	0.690332i
$362$		0			0
$363$	−7.08106	+	29.5608i	−0.371659	+	1.55154i
$364$		0			0
$365$	−24.6677	+	28.4680i	−1.29117	+	1.49009i
$366$		0			0
$367$		−	14.3888i		−	0.751090i	−0.926804	−	0.375545i	$-0.877456\pi$
$367$		−	14.3888i		−	0.751090i	0.926804	−	0.375545i	$-0.122544\pi$
$368$		0			0
$369$	4.42757	−	23.7084i	0.230490	−	1.23421i
$370$		0			0
$371$	0.217020	+	0.188049i	0.0112671	+	0.00976303i
$372$		0			0
$373$	−15.2680	−	2.19521i	−0.790549	−	0.113664i	−0.264800	−	0.964303i	$-0.585306\pi$
$373$	−15.2680	−	2.19521i	−0.790549	−	0.113664i	−0.525749	+	0.850640i	$0.676215\pi$
$374$		0			0
$375$	−3.62831	−	10.3862i	−0.187365	−	0.536340i
$376$		0			0
$377$	−6.15503	+	0.884960i	−0.317000	+	0.0455777i
$378$		0			0
$379$	5.95806	+	20.2913i	0.306045	+	1.04229i	0.958648	+	0.284593i	$0.0918586\pi$
$379$	5.95806	+	20.2913i	0.306045	+	1.04229i	−0.652604	+	0.757700i	$0.726323\pi$
$380$		0			0
$381$	9.52620	−	16.6104i	0.488042	−	0.850979i
$382$		0			0
$383$	0.824211	+	0.951190i	0.0421152	+	0.0486035i	0.776416	−	0.630220i	$-0.217035\pi$
$383$	0.824211	+	0.951190i	0.0421152	+	0.0486035i	−0.734301	+	0.678824i	$0.762490\pi$
$384$		0			0
$385$	−6.30418	−	9.80949i	−0.321291	−	0.499938i
$386$		0			0
$387$	−17.4458	+	18.5094i	−0.886817	+	0.940888i
$388$		0			0
$389$	−11.8422	−	3.47719i	−0.600425	−	0.176301i	−0.0326257	−	0.999468i	$-0.510387\pi$
$389$	−11.8422	−	3.47719i	−0.600425	−	0.176301i	−0.567799	+	0.823167i	$0.692205\pi$
$390$		0			0
$391$	12.3790	−	3.58842i	0.626034	−	0.181474i
$392$		0			0
$393$	−8.92738	+	22.4875i	−0.450327	+	1.13434i
$394$		0			0
$395$	−19.4828	+	30.3158i	−0.980284	+	1.52535i
$396$		0			0
$397$	−3.83135	+	2.46226i	−0.192290	+	0.123577i	−0.633243	−	0.773953i	$-0.718277\pi$
$397$	−3.83135	+	2.46226i	−0.192290	+	0.123577i	0.440953	+	0.897530i	$0.354640\pi$
$398$		0			0
$399$	−1.69653	−	2.36794i	−0.0849325	−	0.118545i
$400$		0			0
$401$	−9.72149	+	21.2871i	−0.485468	+	1.06303i	0.495455	+	0.868633i	$0.335001\pi$
$401$	−9.72149	+	21.2871i	−0.485468	+	1.06303i	−0.980924	+	0.194394i	$0.937726\pi$
$402$		0			0
$403$	−1.44114	+	0.423156i	−0.0717882	+	0.0210789i
$404$		0			0
$405$	5.61180	−	24.3567i	0.278852	−	1.21030i
$406$		0			0
$407$	−28.7626	+	13.1355i	−1.42571	+	0.651100i
$408$		0			0
$409$	−1.64059	+	11.4106i	−0.0811220	+	0.564216i	0.908208	+	0.418520i	$0.137451\pi$
$409$	−1.64059	+	11.4106i	−0.0811220	+	0.564216i	−0.989329	+	0.145695i	$0.953458\pi$
$410$		0			0
$411$	19.7473	−	18.9382i	0.974064	−	0.934153i
$412$		0			0
$413$	9.87860			0.486094
$414$		0			0
$415$	23.9105			1.17372
$416$		0			0
$417$	−8.58999	+	8.23803i	−0.420654	+	0.403418i
$418$		0			0
$419$	3.62089	−	25.1839i	0.176892	−	1.23031i	−0.687008	−	0.726650i	$-0.741076\pi$
$419$	3.62089	−	25.1839i	0.176892	−	1.23031i	0.863900	−	0.503663i	$-0.168015\pi$
$420$		0			0
$421$	−28.1389	+	12.8506i	−1.37141	+	0.626301i	−0.958662	−	0.284546i	$-0.908157\pi$
$421$	−28.1389	+	12.8506i	−1.37141	+	0.626301i	−0.412745	+	0.910847i	$0.635430\pi$
$422$		0			0
$423$	−9.68909	−	0.405477i	−0.471099	−	0.0197150i
$424$		0			0
$425$	6.99541	−	2.05404i	0.339327	−	0.0996355i
$426$		0			0
$427$	0.367880	−	0.805545i	0.0178030	−	0.0389830i
$428$		0			0
$429$	4.62516	+	6.45559i	0.223305	+	0.311679i
$430$		0			0
$431$	−15.4252	+	9.91319i	−0.743007	+	0.477502i	−0.856571	−	0.516029i	$-0.827410\pi$
$431$	−15.4252	+	9.91319i	−0.743007	+	0.477502i	0.113564	+	0.993531i	$0.463773\pi$
$432$		0			0
$433$	0.274130	−	0.426555i	0.0131738	−	0.0204989i	−0.834604	−	0.550850i	$-0.814304\pi$
$433$	0.274130	−	0.426555i	0.0131738	−	0.0204989i	0.847778	+	0.530351i	$0.177940\pi$
$434$		0			0
$435$	12.8619	−	32.3984i	0.616683	−	1.55339i
$436$		0			0
$437$	7.78037	−	6.69482i	0.372185	−	0.320257i
$438$		0			0
$439$	28.3204	+	8.31561i	1.35166	+	0.396882i	0.875814	−	0.482648i	$-0.160325\pi$
$439$	28.3204	+	8.31561i	1.35166	+	0.396882i	0.475843	+	0.879530i	$0.342143\pi$
$440$		0			0
$441$	13.9338	+	13.1331i	0.663516	+	0.625385i
$442$		0			0
$443$	2.09130	+	3.25413i	0.0993606	+	0.154608i	0.887375	−	0.461049i	$-0.152527\pi$
$443$	2.09130	+	3.25413i	0.0993606	+	0.154608i	−0.788014	+	0.615657i	$0.788891\pi$
$444$		0			0
$445$	21.9801	+	25.3664i	1.04196	+	1.20248i
$446$		0			0
$447$	−4.58883	+	8.00137i	−0.217044	+	0.378452i
$448$		0			0
$449$	−0.327701	−	1.11605i	−0.0154652	−	0.0526695i	0.951399	−	0.307961i	$-0.0996467\pi$
$449$	−0.327701	−	1.11605i	−0.0154652	−	0.0526695i	−0.966864	+	0.255292i	$0.917829\pi$
$450$		0			0
$451$	−42.5191	+	6.11333i	−2.00215	+	0.287865i
$452$		0			0
$453$	−4.42234	−	12.6591i	−0.207779	−	0.594777i
$454$		0			0
$455$	−1.85359	−	0.266506i	−0.0868975	−	0.0124940i
$456$		0			0
$457$	−0.894314	−	0.774928i	−0.0418343	−	0.0362496i	0.633693	−	0.773585i	$-0.281538\pi$
$457$	−0.894314	−	0.774928i	−0.0418343	−	0.0362496i	−0.675527	+	0.737335i	$0.736084\pi$
$458$		0			0
$459$	−13.4324	−	3.81803i	−0.626971	−	0.178210i
$460$		0			0
$461$			31.1734i			1.45189i	0.687754	+	0.725944i	$0.258597\pi$
$461$			31.1734i			1.45189i	−0.687754	+	0.725944i	$0.741403\pi$
$462$		0			0
$463$	26.6950	−	30.8076i	1.24062	−	1.43175i	0.378074	−	0.925775i	$-0.376586\pi$
$463$	26.6950	−	30.8076i	1.24062	−	1.43175i	0.862547	−	0.505978i	$-0.168868\pi$
$464$		0			0
$465$	1.96137	−	8.18802i	0.0909565	−	0.379710i
$466$		0			0
$467$	9.80267	+	21.4649i	0.453614	+	0.993275i	0.988897	+	0.148603i	$0.0474775\pi$
$467$	9.80267	+	21.4649i	0.453614	+	0.993275i	−0.535283	+	0.844672i	$0.679795\pi$
$468$		0			0
$469$	1.49133	+	10.3724i	0.0688632	+	0.478954i
$470$		0			0
$471$	−3.28600	−	16.7883i	−0.151411	−	0.773566i
$472$		0			0
$473$	41.2081	+	18.8191i	1.89475	+	0.865304i
$474$		0			0
$475$	4.38803	−	3.80225i	0.201337	−	0.174459i
$476$		0			0
$477$	1.01541	−	0.413329i	0.0464924	−	0.0189250i
$478$		0			0
$479$	−2.05997	−	1.32386i	−0.0941223	−	0.0604888i	0.492733	−	0.870181i	$-0.335998\pi$
$479$	−2.05997	−	1.32386i	−0.0941223	−	0.0604888i	−0.586855	+	0.809692i	$0.699634\pi$
$480$		0			0
$481$	−1.43066	+	4.87238i	−0.0652325	+	0.222161i
$482$		0			0
$483$	4.03782	−	5.12854i	0.183727	−	0.233356i
$484$		0			0
$485$	5.60324	−	19.0829i	0.254430	−	0.866510i
$486$		0			0
$487$	−12.4416	−	7.99573i	−0.563783	−	0.362321i	0.227494	−	0.973780i	$-0.426947\pi$
$487$	−12.4416	−	7.99573i	−0.563783	−	0.362321i	−0.791277	+	0.611458i	$0.790583\pi$
$488$		0			0
$489$	3.67670	−	1.90893i	0.166266	−	0.0863249i
$490$		0			0
$491$	−16.6711	+	14.4456i	−0.752357	+	0.651921i	−0.944151	−	0.329514i	$-0.893115\pi$
$491$	−16.6711	+	14.4456i	−0.752357	+	0.651921i	0.191793	+	0.981435i	$0.438570\pi$
$492$		0			0
$493$	−17.7151	−	8.09022i	−0.797848	−	0.364365i
$494$		0			0
$495$	−44.2907	+	4.48753i	−1.99072	+	0.201699i
$496$		0			0
$497$	0.154834	+	1.07690i	0.00694528	+	0.0483055i
$498$		0			0
$499$	−6.36070	−	13.9280i	−0.284744	−	0.623502i	0.712170	−	0.702007i	$-0.247713\pi$
$499$	−6.36070	−	13.9280i	−0.284744	−	0.623502i	−0.996914	+	0.0785052i	$0.974985\pi$
$500$		0			0
$501$	32.9659	+	7.89671i	1.47281	+	0.352799i
$502$		0			0
$503$	3.90821	−	4.51031i	0.174258	−	0.201105i	−0.661901	−	0.749591i	$-0.730250\pi$
$503$	3.90821	−	4.51031i	0.174258	−	0.201105i	0.836160	+	0.548486i	$0.184796\pi$
$504$		0			0
$505$		−	48.6042i		−	2.16286i
$506$		0			0
$507$	−21.1508	−	1.95804i	−0.939342	−	0.0869598i
$508$		0			0
$509$	−4.21797	−	3.65489i	−0.186958	−	0.162000i	0.556353	−	0.830946i	$-0.312200\pi$
$509$	−4.21797	−	3.65489i	−0.186958	−	0.162000i	−0.743311	+	0.668946i	$0.766746\pi$
$510$		0			0
$511$	10.5497	+	1.51681i	0.466690	+	0.0670999i
$512$		0			0
$513$	−10.9937	+	1.67799i	−0.485384	+	0.0740851i
$514$		0			0
$515$	−37.5938	+	5.40517i	−1.65658	+	0.238180i
$516$		0			0
$517$	4.86609	+	16.5724i	0.214010	+	0.728852i
$518$		0			0
$519$	−0.223301	−	0.128065i	−0.00980183	−	0.00562141i
$520$		0			0
$521$	0.887232	+	1.02392i	0.0388703	+	0.0448587i	0.774852	−	0.632143i	$-0.217824\pi$
$521$	0.887232	+	1.02392i	0.0388703	+	0.0448587i	−0.735982	+	0.677002i	$0.763279\pi$
$522$		0			0
$523$	11.3517	+	17.6637i	0.496377	+	0.772378i	0.995561	−	0.0941182i	$-0.0300032\pi$
$523$	11.3517	+	17.6637i	0.496377	+	0.772378i	−0.499184	+	0.866496i	$0.666367\pi$
$524$		0			0
$525$	2.27405	−	2.90894i	0.0992477	−	0.126957i
$526$		0			0
$527$	−4.51347	−	1.32527i	−0.196610	−	0.0577298i
$528$		0			0
$529$	19.2625	+	12.5681i	0.837499	+	0.546438i
$530$		0			0
$531$	17.0878	−	33.6211i	0.741548	−	1.45903i
$532$		0			0
$533$	−3.72969	+	5.80351i	−0.161551	+	0.251378i
$534$		0			0
$535$	−16.1952	+	10.4080i	−0.700181	+	0.449979i
$536$		0			0
$537$	−17.8842	+	12.8132i	−0.771759	+	0.552932i
$538$		0			0
$539$	14.1669	−	31.0213i	0.610213	−	1.33618i
$540$		0			0
$541$	35.4504	−	10.4092i	1.52413	−	0.447526i	0.590884	−	0.806757i	$-0.298779\pi$
$541$	35.4504	−	10.4092i	1.52413	−	0.447526i	0.933249	+	0.359231i	$0.116961\pi$
$542$		0			0
$543$	11.1010	−	0.560939i	0.476389	−	0.0240722i
$544$		0			0
$545$	40.9480	−	18.7003i	1.75402	−	0.801035i
$546$		0			0
$547$	−1.63184	+	11.3497i	−0.0697724	+	0.485278i	0.924735	+	0.380612i	$0.124286\pi$
$547$	−1.63184	+	11.3497i	−0.0697724	+	0.485278i	−0.994507	+	0.104666i	$0.966623\pi$
$548$		0			0
$549$	−2.10526	−	2.64547i	−0.0898503	−	0.112906i
$550$		0			0
$551$	−15.5095			−0.660728
$552$		0			0
$553$	10.1963			0.433592
$554$		0			0
$555$	−19.7034	−	20.5452i	−0.836361	−	0.872094i
$556$		0			0
$557$	2.15976	−	15.0215i	0.0915120	−	0.636480i	−0.891511	−	0.452999i	$-0.850354\pi$
$557$	2.15976	−	15.0215i	0.0915120	−	0.636480i	0.983023	−	0.183481i	$-0.0587367\pi$
$558$		0			0
$559$	6.61789	−	3.02229i	0.279907	−	0.127829i
$560$		0			0
$561$	1.25518	+	24.8400i	0.0529936	+	1.04874i
$562$		0			0
$563$	−18.5176	+	5.43725i	−0.780422	+	0.229153i	−0.647593	−	0.761986i	$-0.724224\pi$
$563$	−18.5176	+	5.43725i	−0.780422	+	0.229153i	−0.132829	+	0.991139i	$0.542406\pi$
$564$		0			0
$565$	−3.21629	+	7.04270i	−0.135310	+	0.296288i
$566$		0			0
$567$	−6.65605	+	2.39012i	−0.279528	+	0.100376i
$568$		0			0
$569$	16.4254	−	10.5559i	0.688587	−	0.442528i	−0.148996	−	0.988838i	$-0.547604\pi$
$569$	16.4254	−	10.5559i	0.688587	−	0.442528i	0.837583	+	0.546310i	$0.183968\pi$
$570$		0			0
$571$	−9.07190	+	14.1162i	−0.379647	+	0.590743i	−0.977519	−	0.210850i	$-0.932377\pi$
$571$	−9.07190	+	14.1162i	−0.379647	+	0.590743i	0.597871	+	0.801592i	$0.296013\pi$
$572$		0			0
$573$	35.4140	+	14.0591i	1.47944	+	0.587328i
$574$		0			0
$575$	10.9207	+	7.07174i	0.455426	+	0.294912i
$576$		0			0
$577$	−29.5574	−	8.67882i	−1.23049	−	0.361304i	−0.399054	−	0.916927i	$-0.630662\pi$
$577$	−29.5574	−	8.67882i	−1.23049	−	0.361304i	−0.831434	+	0.555623i	$0.812480\pi$
$578$		0			0
$579$	18.2535	+	14.2696i	0.758589	+	0.593024i
$580$		0			0
$581$	−3.65763	−	5.69139i	−0.151744	−	0.236118i
$582$		0			0
$583$	−1.27868	−	1.47568i	−0.0529576	−	0.0611164i
$584$		0			0
$585$	−4.11333	+	5.84755i	−0.170065	+	0.241767i
$586$		0			0
$587$	−7.44298	−	25.3485i	−0.307205	−	1.04624i	−0.957947	−	0.286945i	$-0.907360\pi$
$587$	−7.44298	−	25.3485i	−0.307205	−	1.04624i	0.650742	−	0.759299i	$-0.274458\pi$
$588$		0			0
$589$	−3.70805	+	0.533138i	−0.152788	+	0.0219675i
$590$		0			0
$591$	28.8793	−	10.0887i	1.18793	−	0.414993i
$592$		0			0
$593$	9.01479	+	1.29613i	0.370193	+	0.0532257i	0.324901	−	0.945748i	$-0.394669\pi$
$593$	9.01479	+	1.29613i	0.370193	+	0.0532257i	0.0452921	+	0.998974i	$0.485578\pi$
$594$		0			0
$595$	−4.43240	−	3.84070i	−0.181711	−	0.157453i
$596$		0			0
$597$	−0.462844	+	4.99965i	−0.0189429	+	0.204622i
$598$		0			0
$599$		−	19.9326i		−	0.814422i	−0.913334	−	0.407211i	$-0.866501\pi$
$599$		−	19.9326i		−	0.814422i	0.913334	−	0.407211i	$-0.133499\pi$
$600$		0			0
$601$	11.2610	−	12.9959i	0.459348	−	0.530116i	−0.478070	−	0.878322i	$-0.658664\pi$
$601$	11.2610	−	12.9959i	0.459348	−	0.530116i	0.937418	+	0.348206i	$0.113209\pi$
$602$		0			0
$603$	37.8814	+	12.8664i	1.54265	+	0.523960i
$604$		0			0
$605$	20.2471	+	44.3349i	0.823160	+	1.80247i
$606$		0			0
$607$	0.149097	+	1.03700i	0.00605168	+	0.0420904i	0.992624	−	0.121237i	$-0.0386863\pi$
$607$	0.149097	+	1.03700i	0.00605168	+	0.0420904i	−0.986572	+	0.163328i	$0.947777\pi$
$608$		0			0
$609$	−9.67927	+	1.89453i	−0.392224	+	0.0767703i
$610$		0			0
$611$	2.52316	+	1.15229i	0.102076	+	0.0466167i
$612$		0			0
$613$	2.73228	−	2.36753i	0.110356	−	0.0956238i	−0.597935	−	0.801545i	$-0.704012\pi$
$613$	2.73228	−	2.36753i	0.110356	−	0.0956238i	0.708291	+	0.705921i	$0.249467\pi$
$614$		0			0
$615$	−17.8196	−	34.3216i	−0.718557	−	1.38398i
$616$		0			0
$617$	22.7706	+	14.6338i	0.916710	+	0.589133i	0.911701	−	0.410854i	$-0.134769\pi$
$617$	22.7706	+	14.6338i	0.916710	+	0.589133i	0.00500838	+	0.999987i	$0.498406\pi$
$618$		0			0
$619$	1.13022	−	3.84916i	0.0454272	−	0.154711i	−0.933656	−	0.358171i	$-0.883401\pi$
$619$	1.13022	−	3.84916i	0.0454272	−	0.154711i	0.979083	+	0.203460i	$0.0652187\pi$
$620$		0			0
$621$	−10.4700	−	22.6137i	−0.420148	−	0.907455i
$622$		0			0
$623$	2.67559	−	9.11222i	0.107195	−	0.365073i
$624$		0			0
$625$	−26.2511	−	16.8705i	−1.05004	−	0.674821i
$626$		0			0
$627$	9.12703	+	17.5791i	0.364499	+	0.702044i
$628$		0			0
$629$	−12.0194	+	10.4149i	−0.479244	+	0.415267i
$630$		0			0
$631$	0.484123	+	0.221091i	0.0192726	+	0.00880151i	0.425028	−	0.905180i	$-0.360264\pi$
$631$	0.484123	+	0.221091i	0.0192726	+	0.00880151i	−0.405755	+	0.913982i	$0.632992\pi$
$632$		0			0
$633$	−7.96111	+	1.55823i	−0.316426	+	0.0619343i
$634$		0			0
$635$	−4.36945	−	30.3902i	−0.173396	−	1.20600i
$636$		0			0
$637$	−2.27516	−	4.98191i	−0.0901453	−	0.197391i
$638$		0			0
$639$	3.93297	+	1.33583i	0.155586	+	0.0528446i
$640$		0			0
$641$	29.5141	−	34.0611i	1.16574	−	1.34533i	0.238372	−	0.971174i	$-0.423386\pi$
$641$	29.5141	−	34.0611i	1.16574	−	1.34533i	0.927365	−	0.374158i	$-0.122068\pi$
$642$		0			0
$643$			35.3040i			1.39225i	0.717919	+	0.696126i	$0.245095\pi$
$643$			35.3040i			1.39225i	−0.717919	+	0.696126i	$0.754905\pi$
$644$		0			0
$645$	−3.75946	+	40.6098i	−0.148029	+	1.59901i
$646$		0			0
$647$	10.8894	+	9.43570i	0.428106	+	0.370956i	0.842098	−	0.539325i	$-0.181320\pi$
$647$	10.8894	+	9.43570i	0.428106	+	0.370956i	−0.413992	+	0.910280i	$0.635866\pi$
$648$		0			0
$649$	−66.4880	−	9.55953i	−2.60988	−	0.375244i
$650$		0			0
$651$	−2.24902	+	0.785672i	−0.0881460	+	0.0307929i
$652$		0			0
$653$	44.1640	−	6.34982i	1.72827	−	0.248488i	0.794730	−	0.606963i	$-0.207612\pi$
$653$	44.1640	−	6.34982i	1.72827	−	0.248488i	0.933539	+	0.358475i	$0.116703\pi$
$654$		0			0
$655$	10.9296	+	37.2229i	0.427056	+	1.45442i
$656$		0			0
$657$	23.4110	−	33.2813i	0.913349	−	1.29843i
$658$		0			0
$659$	2.60744	+	3.00914i	0.101571	+	0.117219i	0.804259	−	0.594279i	$-0.202562\pi$
$659$	2.60744	+	3.00914i	0.101571	+	0.117219i	−0.702688	+	0.711498i	$0.748017\pi$
$660$		0			0
$661$	7.57406	+	11.7855i	0.294597	+	0.458401i	0.956727	−	0.290987i	$-0.0939838\pi$
$661$	7.57406	+	11.7855i	0.294597	+	0.458401i	−0.662130	+	0.749389i	$0.730347\pi$
$662$		0			0
$663$	3.14685	+	2.46004i	0.122214	+	0.0955400i
$664$		0			0
$665$	−4.48150	−	1.31589i	−0.173785	−	0.0510279i
$666$		0			0
$667$	−9.67599	−	33.3794i	−0.374656	−	1.29246i
$668$		0			0
$669$	24.6588	+	9.78938i	0.953365	+	0.378479i
$670$		0			0
$671$	−3.25555	+	5.06573i	−0.125679	+	0.195560i
$672$		0			0
$673$	31.6137	−	20.3169i	1.21862	−	0.783158i	0.236538	−	0.971622i	$-0.423987\pi$
$673$	31.6137	−	20.3169i	1.21862	−	0.783158i	0.982080	+	0.188464i	$0.0603508\pi$
$674$		0			0
$675$	−5.96675	−	12.7714i	−0.229660	−	0.491571i
$676$		0			0
$677$	21.1490	−	46.3098i	0.812822	−	1.77983i	0.218050	−	0.975938i	$-0.430030\pi$
$677$	21.1490	−	46.3098i	0.812822	−	1.77983i	0.594772	−	0.803894i	$-0.297242\pi$
$678$		0			0
$679$	−5.39941	+	1.58541i	−0.207211	+	0.0608425i
$680$		0			0
$681$	−0.324052	−	6.41300i	−0.0124177	−	0.245747i
$682$		0			0
$683$	−17.9742	+	8.20854i	−0.687764	+	0.314091i	−0.728468	−	0.685080i	$-0.759767\pi$
$683$	−17.9742	+	8.20854i	−0.687764	+	0.314091i	0.0407040	+	0.999171i	$0.487040\pi$
$684$		0			0
$685$	6.24347	−	43.4243i	0.238551	−	1.65916i
$686$		0			0
$687$	23.6798	+	24.6915i	0.903440	+	0.942039i
$688$		0			0
$689$	−0.313582			−0.0119465
$690$		0			0
$691$	−22.3943			−0.851920			−0.425960	−	0.904742i	$-0.640064\pi$
$691$	−22.3943			−0.851920			−0.425960	+	0.904742i	$0.640064\pi$
$692$		0			0
$693$	7.84339	+	9.85600i	0.297946	+	0.374398i
$694$		0			0
$695$	−2.71588	+	18.8894i	−0.103019	+	0.716514i
$696$		0			0
$697$	−19.6533	+	8.97534i	−0.744420	+	0.339965i
$698$		0			0
$699$	−12.8283	+	0.648222i	−0.485211	+	0.0245180i
$700$		0			0
$701$	−17.4985	+	5.13803i	−0.660910	+	0.194061i	−0.594952	−	0.803762i	$-0.702829\pi$
$701$	−17.4985	+	5.13803i	−0.660910	+	0.194061i	−0.0659588	+	0.997822i	$0.521011\pi$
$702$		0			0
$703$	−5.26147	+	11.5210i	−0.198440	+	0.434523i
$704$		0			0
$705$	−12.6400	+	9.05600i	−0.476049	+	0.341069i
$706$		0			0
$707$	−11.5692	+	7.43507i	−0.435105	+	0.279625i
$708$		0			0
$709$	10.6179	−	16.5217i	0.398762	−	0.620486i	−0.582576	−	0.812776i	$-0.697955\pi$
$709$	10.6179	−	16.5217i	0.398762	−	0.620486i	0.981338	+	0.192290i	$0.0615915\pi$
$710$		0			0
$711$	17.6374	−	34.7025i	0.661455	−	1.30144i
$712$		0			0
$713$	−3.46077	−	7.64781i	−0.129607	−	0.286413i
$714$		0			0
$715$	12.2177	+	3.58744i	0.456916	+	0.134163i
$716$		0			0
$717$	−27.7883	+	35.5465i	−1.03777	+	1.32751i
$718$		0			0
$719$	9.22714	+	14.3577i	0.344114	+	0.535452i	0.969572	−	0.244806i	$-0.0787242\pi$
$719$	9.22714	+	14.3577i	0.344114	+	0.535452i	−0.625458	+	0.780258i	$0.715088\pi$
$720$		0			0
$721$	7.03737	+	8.12156i	0.262085	+	0.302463i
$722$		0			0
$723$	−11.8854	−	6.81637i	−0.442024	−	0.253504i
$724$		0			0
$725$	−5.53861	−	18.8628i	−0.205699	−	0.700546i
$726$		0			0
$727$	5.99528	−	0.861991i	0.222352	−	0.0319695i	−0.0302381	−	0.999543i	$-0.509627\pi$
$727$	5.99528	−	0.861991i	0.222352	−	0.0319695i	0.252591	+	0.967573i	$0.418717\pi$
$728$		0			0
$729$	−3.37890	+	26.7877i	−0.125144	+	0.992139i
$730$		0			0
$731$	22.5536	+	3.24271i	0.834173	+	0.119936i
$732$		0			0
$733$	16.1245	+	13.9720i	0.595573	+	0.516067i	0.899668	−	0.436575i	$-0.143809\pi$
$733$	16.1245	+	13.9720i	0.595573	+	0.516067i	−0.304095	+	0.952642i	$0.598354\pi$
$734$		0			0
$735$	30.5709	+	2.83010i	1.12762	+	0.104390i
$736$		0			0
$737$		−	71.2548i		−	2.62471i
$738$		0			0
$739$	8.74099	−	10.0876i	0.321542	−	0.371080i	−0.571849	−	0.820359i	$-0.693774\pi$
$739$	8.74099	−	10.0876i	0.321542	−	0.371080i	0.893391	+	0.449279i	$0.148319\pi$
$740$		0			0
$741$	3.09347	+	0.741016i	0.113642	+	0.0272219i
$742$		0			0
$743$	4.65598	+	10.1952i	0.170811	+	0.374024i	0.975606	−	0.219529i	$-0.0704520\pi$
$743$	4.65598	+	10.1952i	0.170811	+	0.374024i	−0.804795	+	0.593553i	$0.797725\pi$
$744$		0			0
$745$	2.10479	+	14.6392i	0.0771136	+	0.536337i
$746$		0			0
$747$	−25.6971	+	2.60363i	−0.940208	+	0.0952617i
$748$		0			0
$749$	4.95482	+	2.26279i	0.181045	+	0.0826806i
$750$		0			0
$751$	−4.01202	+	3.47643i	−0.146401	+	0.126857i	−0.724982	−	0.688768i	$-0.758152\pi$
$751$	−4.01202	+	3.47643i	−0.146401	+	0.126857i	0.578581	+	0.815625i	$0.303606\pi$
$752$		0			0
$753$	−37.2449	+	19.3374i	−1.35728	+	0.704695i
$754$		0			0
$755$	−18.0876	−	11.6242i	−0.658276	−	0.423048i
$756$		0			0
$757$	−12.9303	+	44.0367i	−0.469961	+	1.60054i	0.294354	+	0.955697i	$0.404896\pi$
$757$	−12.9303	+	44.0367i	−0.469961	+	1.60054i	−0.764315	+	0.644844i	$0.776923\pi$
$758$		0			0
$759$	−32.1395	+	30.6103i	−1.16659	+	1.11108i
$760$		0			0
$761$	−9.10415	+	31.0059i	−0.330025	+	1.12396i	0.612679	+	0.790332i	$0.290092\pi$
$761$	−9.10415	+	31.0059i	−0.330025	+	1.12396i	−0.942704	+	0.333631i	$0.891726\pi$
$762$		0			0
$763$	−10.7151	−	6.88618i	−0.387913	−	0.249297i
$764$		0			0
$765$	−20.7386	+	8.44178i	−0.749806	+	0.305213i
$766$		0			0
$767$	−8.15269	+	7.06435i	−0.294377	+	0.255079i
$768$		0			0
$769$	31.4826	+	14.3776i	1.13529	+	0.518470i	0.892248	−	0.451545i	$-0.149127\pi$
$769$	31.4826	+	14.3776i	1.13529	+	0.518470i	0.243044	+	0.970015i	$0.421854\pi$
$770$		0			0
$771$	6.86456	+	35.0714i	0.247221	+	1.26307i
$772$		0			0
$773$	3.57910	+	24.8932i	0.128731	+	0.895345i	0.947166	+	0.320745i	$0.103933\pi$
$773$	3.57910	+	24.8932i	0.128731	+	0.895345i	−0.818434	+	0.574600i	$0.805158\pi$
$774$		0			0
$775$	−1.97259	−	4.31937i	−0.0708575	−	0.155156i
$776$		0			0
$777$	−1.87628	+	7.83280i	−0.0673112	+	0.281000i
$778$		0			0
$779$	−11.2678	+	13.0037i	−0.403710	+	0.465906i
$780$		0			0
$781$		−	7.39790i		−	0.264718i
$782$		0			0
$783$	−10.2951	+	36.2198i	−0.367917	+	1.29439i
$784$		0			0
$785$	−20.7299	−	17.9625i	−0.739881	−	0.641110i
$786$		0			0
$787$	26.7774	+	3.85000i	0.954510	+	0.137238i	0.601934	−	0.798546i	$-0.294397\pi$
$787$	26.7774	+	3.85000i	0.954510	+	0.137238i	0.352575	+	0.935783i	$0.385306\pi$
$788$		0			0
$789$	−4.69794	−	13.4480i	−0.167251	−	0.478762i
$790$		0			0
$791$	2.16837	−	0.311764i	0.0770982	−	0.0110850i
$792$		0			0
$793$	0.272451	+	0.927884i	0.00967503	+	0.0329501i
$794$		0			0
$795$	0.874523	−	1.52487i	0.0310162	−	0.0540816i
$796$		0			0
$797$	−17.1896	−	19.8379i	−0.608888	−	0.702694i	0.364669	−	0.931137i	$-0.381182\pi$
$797$	−17.1896	−	19.8379i	−0.608888	−	0.702694i	−0.973557	+	0.228443i	$0.926637\pi$
$798$		0			0
$799$	4.69670	+	7.30821i	0.166157	+	0.258546i
$800$		0			0
$801$	−26.3846	−	24.8683i	−0.932253	−	0.878679i
$802$		0			0
$803$	−69.5368	−	20.4179i	−2.45390	−	0.720531i
$804$		0			0
$805$	0.0361444	−	10.4660i	0.00127392	−	0.368877i
$806$		0			0
$807$	−0.531100	+	1.33781i	−0.0186956	+	0.0470930i
$808$		0			0
$809$	23.1680	−	36.0501i	0.814543	−	1.26745i	−0.145990	−	0.989286i	$-0.546637\pi$
$809$	23.1680	−	36.0501i	0.814543	−	1.26745i	0.960533	−	0.278167i	$-0.0897269\pi$
$810$		0			0
$811$	8.94234	−	5.74689i	0.314008	−	0.201801i	−0.374138	−	0.927373i	$-0.622061\pi$
$811$	8.94234	−	5.74689i	0.314008	−	0.201801i	0.688146	+	0.725572i	$0.258425\pi$
$812$		0			0
$813$	−3.93507	−	5.49240i	−0.138009	−	0.192627i
$814$		0			0
$815$	2.75941	−	6.04226i	0.0966578	−	0.211651i
$816$		0			0
$817$	17.4109	−	5.11229i	0.609129	−	0.178856i
$818$		0			0
$819$	2.02111	+	0.0845811i	0.0706233	+	0.00295550i
$820$		0			0
$821$	−37.5501	+	17.1486i	−1.31051	+	0.598489i	−0.943390	−	0.331685i	$-0.892383\pi$
$821$	−37.5501	+	17.1486i	−1.31051	+	0.598489i	−0.367119	+	0.930174i	$0.619656\pi$
$822$		0			0
$823$	1.63340	−	11.3605i	0.0569366	−	0.396003i	−0.941347	−	0.337440i	$-0.890439\pi$
$823$	1.63340	−	11.3605i	0.0569366	−	0.396003i	0.998284	−	0.0585631i	$-0.0186519\pi$
$824$		0			0
$825$	−18.1205	+	17.3780i	−0.630875	+	0.605026i
$826$		0			0
$827$	22.0014			0.765063			0.382531	−	0.923943i	$-0.375052\pi$
$827$	22.0014			0.765063			0.382531	+	0.923943i	$0.375052\pi$
$828$		0			0
$829$	20.3391			0.706405			0.353202	−	0.935547i	$-0.385093\pi$
$829$	20.3391			0.706405			0.353202	+	0.935547i	$0.385093\pi$
$830$		0			0
$831$	−22.7396	+	21.8078i	−0.788827	+	0.756505i
$832$		0			0
$833$	2.44110	−	16.9782i	0.0845791	−	0.588260i
$834$		0			0
$835$	49.4417	−	22.5793i	1.71100	−	0.781388i
$836$		0			0
$837$	−1.21633	+	9.01341i	−0.0420425	+	0.311549i
$838$		0			0
$839$	23.9999	−	7.04700i	0.828568	−	0.243290i	0.160166	−	0.987090i	$-0.448797\pi$
$839$	23.9999	−	7.04700i	0.828568	−	0.243290i	0.668402	+	0.743800i	$0.266979\pi$
$840$		0			0
$841$	−9.76783	+	21.3886i	−0.336822	+	0.737537i
$842$		0			0
$843$	−23.6776	−	33.0482i	−0.815501	−	1.13824i
$844$		0			0
$845$	−28.6520	+	18.4135i	−0.985659	+	0.633445i
$846$		0			0
$847$	7.45574	−	11.6014i	0.256182	−	0.398628i
$848$		0			0
$849$	6.39953	−	16.1200i	0.219631	−	0.553237i
$850$		0			0
$851$	−28.0779	−	4.13601i	−0.962496	−	0.141780i
$852$		0			0
$853$	−47.0473	−	13.8143i	−1.61087	−	0.472994i	−0.652326	−	0.757938i	$-0.726207\pi$
$853$	−47.0473	−	13.8143i	−1.61087	−	0.472994i	−0.958544	+	0.284944i	$0.908025\pi$
$854$		0			0
$855$	−12.2305	+	12.9763i	−0.418275	+	0.443778i
$856$		0			0
$857$	21.2242	+	33.0255i	0.725004	+	1.12813i	0.986633	+	0.162960i	$0.0521041\pi$
$857$	21.2242	+	33.0255i	0.725004	+	1.12813i	−0.261628	+	0.965169i	$0.584259\pi$
$858$		0			0
$859$	−23.9018	−	27.5842i	−0.815520	−	0.941160i	0.183604	−	0.983000i	$-0.441224\pi$
$859$	−23.9018	−	27.5842i	−0.815520	−	0.941160i	−0.999124	+	0.0418398i	$0.986678\pi$
$860$		0			0
$861$	−5.44361	+	9.49181i	−0.185518	+	0.323480i
$862$		0			0
$863$	−0.0917261	−	0.312390i	−0.00312239	−	0.0106339i	0.957917	−	0.287045i	$-0.0926730\pi$
$863$	−0.0917261	−	0.312390i	−0.00312239	−	0.0106339i	−0.961039	+	0.276411i	$0.910855\pi$
$864$		0			0
$865$	−0.408548	+	0.0587403i	−0.0138910	+	0.00199723i
$866$		0			0
$867$	−5.58515	−	15.9877i	−0.189682	−	0.542971i
$868$		0			0
$869$	−68.6266	−	9.86701i	−2.32800	−	0.334715i
$870$		0			0
$871$	−8.64826	−	7.49376i	−0.293035	−	0.253916i
$872$		0			0
$873$	−3.94398	+	21.1189i	−0.133483	+	0.714767i
$874$		0			0
$875$			4.99125i			0.168735i
$876$		0			0
$877$	−27.0282	+	31.1923i	−0.912679	+	1.05329i	0.0856972	+	0.996321i	$0.472688\pi$
$877$	−27.0282	+	31.1923i	−0.912679	+	1.05329i	−0.998376	+	0.0569663i	$0.981857\pi$
$878$		0			0
$879$	−6.96259	+	29.0663i	−0.234842	+	0.980381i
$880$		0			0
$881$	−16.1237	−	35.3059i	−0.543220	−	1.18949i	−0.959877	−	0.280422i	$-0.909526\pi$
$881$	−16.1237	−	35.3059i	−0.543220	−	1.18949i	0.416657	−	0.909064i	$-0.363202\pi$
$882$		0			0
$883$	−0.728403	−	5.06615i	−0.0245127	−	0.170490i	0.973888	−	0.227031i	$-0.0729018\pi$
$883$	−0.728403	−	5.06615i	−0.0245127	−	0.170490i	−0.998400	+	0.0565413i	$0.981993\pi$
$884$		0			0
$885$	−11.6158	−	59.3458i	−0.390461	−	1.99489i
$886$		0			0
$887$	36.9814	+	16.8888i	1.24171	+	0.567072i	0.924464	−	0.381270i	$-0.124513\pi$
$887$	36.9814	+	16.8888i	1.24171	+	0.567072i	0.317250	+	0.948342i	$0.397240\pi$
$888$		0			0
$889$	−6.56533	+	5.68889i	−0.220194	+	0.190799i
$890$		0			0
$891$	47.1115	−	9.64568i	1.57829	−	0.323142i
$892$		0			0
$893$	5.82012	+	3.74036i	0.194763	+	0.125166i
$894$		0			0
$895$	−9.93842	+	33.8471i	−0.332205	+	1.13139i
$896$		0			0
$897$	0.335132	+	7.12003i	0.0111897	+	0.237731i
$898$		0			0
$899$	−3.57354	+	12.1703i	−0.119184	+	0.405904i
$900$		0			0
$901$	−0.826194	−	0.530963i	−0.0275245	−	0.0176889i
$902$		0			0
$903$	10.2414	−	5.31729i	0.340812	−	0.176948i
$904$		0			0
$905$	13.4692	−	11.6711i	0.447730	−	0.387960i
$906$		0			0
$907$	−6.28991	−	2.87251i	−0.208853	−	0.0953800i	0.308242	−	0.951308i	$-0.400259\pi$
$907$	−6.28991	−	2.87251i	−0.208853	−	0.0953800i	−0.517095	+	0.855928i	$0.672987\pi$
$908$		0			0
$909$	5.29254	+	52.2360i	0.175542	+	1.73256i
$910$		0			0
$911$	2.87572	+	20.0010i	0.0952767	+	0.662664i	0.980358	+	0.197227i	$0.0631937\pi$
$911$	2.87572	+	20.0010i	0.0952767	+	0.662664i	−0.885081	+	0.465437i	$0.845897\pi$
$912$		0			0
$913$	19.1102	+	41.8454i	0.632454	+	1.38488i
$914$		0			0
$915$	−5.27189	−	1.26284i	−0.174283	−	0.0417482i
$916$		0			0
$917$	7.18820	−	8.29562i	0.237375	−	0.273945i
$918$		0			0
$919$		−	6.14592i		−	0.202735i	−0.994849	−	0.101368i	$-0.967678\pi$
$919$		−	6.14592i		−	0.202735i	0.994849	−	0.101368i	$-0.0323218\pi$
$920$		0			0
$921$	−29.2682	−	2.70951i	−0.964421	−	0.0892814i
$922$		0			0
$923$	−0.897890	−	0.778026i	−0.0295544	−	0.0256090i
$924$		0			0
$925$	−15.8908	−	2.28476i	−0.522488	−	0.0751224i
$926$		0			0
$927$	39.8142	−	9.90265i	1.30767	−	0.325246i
$928$		0			0
$929$	−8.68968	+	1.24939i	−0.285099	+	0.0409911i	−0.283381	−	0.959007i	$-0.591456\pi$
$929$	−8.68968	+	1.24939i	−0.285099	+	0.0409911i	−0.00171833	+	0.999999i	$0.500547\pi$
$930$		0			0
$931$	−3.84851	−	13.1068i	−0.126130	−	0.429559i
$932$		0			0
$933$	−37.1636	−	21.3136i	−1.21668	−	0.697775i
$934$		0			0
$935$	26.1157	+	30.1391i	0.854074	+	0.985653i
$936$		0			0
$937$	18.3123	+	28.4945i	0.598236	+	0.930873i	0.999886	+	0.0150801i	$0.00480032\pi$
$937$	18.3123	+	28.4945i	0.598236	+	0.930873i	−0.401650	+	0.915793i	$0.631563\pi$
$938$		0			0
$939$	15.3893	−	19.6858i	0.502210	−	0.642421i
$940$		0			0
$941$	30.3669	+	8.91652i	0.989932	+	0.290670i	0.736318	−	0.676635i	$-0.236563\pi$
$941$	30.3669	+	8.91652i	0.989932	+	0.290670i	0.253614	+	0.967306i	$0.418381\pi$
$942$		0			0
$943$	−35.0161	−	16.1377i	−1.14028	−	0.525515i
$944$		0			0
$945$	−6.04781	+	9.59228i	−0.196735	+	0.312037i
$946$		0			0
$947$	29.8192	−	46.3996i	0.968995	−	1.50779i	0.111197	−	0.993798i	$-0.464532\pi$
$947$	29.8192	−	46.3996i	0.968995	−	1.50779i	0.857798	−	0.513987i	$-0.171832\pi$
$948$		0			0
$949$	−9.79122	+	6.29243i	−0.317836	+	0.204261i
$950$		0			0
$951$	32.2931	−	23.1367i	1.04718	−	0.750258i
$952$		0			0
$953$	−7.14919	+	15.6545i	−0.231585	+	0.507100i	−0.989373	−	0.145401i	$-0.953553\pi$
$953$	−7.14919	+	15.6545i	−0.231585	+	0.507100i	0.757788	+	0.652501i	$0.226280\pi$
$954$		0			0
$955$	58.6198	−	17.2123i	1.89689	−	0.556978i
$956$		0			0
$957$	66.9797	−	3.38452i	2.16515	−	0.109406i
$958$		0			0
$959$	−11.2913	+	5.15657i	−0.364615	+	0.166514i
$960$		0			0
$961$	3.97574	−	27.6519i	0.128250	−	0.891997i
$962$		0			0
$963$	16.2720	−	12.9492i	0.524358	−	0.417283i
$964$		0			0
$965$	37.1499			1.19590
$966$		0			0
$967$	11.6132			0.373456			0.186728	−	0.982412i	$-0.440212\pi$
$967$	11.6132			0.373456			0.186728	+	0.982412i	$0.440212\pi$
$968$		0			0
$969$	6.89568	+	7.19029i	0.221521	+	0.230985i
$970$		0			0
$971$	−0.754590	+	5.24829i	−0.0242160	+	0.168426i	−0.998341	−	0.0575860i	$-0.981660\pi$
$971$	−0.754590	+	5.24829i	−0.0242160	+	0.168426i	0.974125	+	0.226012i	$0.0725687\pi$
$972$		0			0
$973$	4.91166	−	2.24308i	0.157461	−	0.0719099i
$974$		0			0
$975$	0.203483	+	4.02693i	0.00651666	+	0.128965i
$976$		0			0
$977$	−16.0508	+	4.71293i	−0.513509	+	0.150780i	−0.528213	−	0.849112i	$-0.677138\pi$
$977$	−16.0508	+	4.71293i	−0.513509	+	0.150780i	0.0147037	+	0.999892i	$0.495320\pi$
$978$		0			0
$979$	−26.8260	+	58.7407i	−0.857362	+	1.87736i
$980$		0			0
$981$	−41.9714	+	24.5565i	−1.34004	+	0.784028i
$982$		0			0
$983$	46.2932	−	29.7508i	1.47652	−	0.948904i	0.479056	−	0.877784i	$-0.340979\pi$
$983$	46.2932	−	29.7508i	1.47652	−	0.948904i	0.997468	−	0.0711198i	$-0.0226573\pi$
$984$		0			0
$985$	26.5183	−	41.2633i	0.844944	−	1.31476i
$986$		0			0
$987$	4.08915	+	1.62336i	0.130159	+	0.0516722i
$988$		0			0
$989$	21.8648	+	34.2820i	0.695260	+	1.09010i
$990$		0			0
$991$	12.3127	+	3.61533i	0.391126	+	0.114845i	0.471381	−	0.881929i	$-0.343756\pi$
$991$	12.3127	+	3.61533i	0.391126	+	0.114845i	−0.0802558	+	0.996774i	$0.525574\pi$
$992$		0			0
$993$	34.9012	+	27.2839i	1.10756	+	0.865828i
$994$		0			0
$995$	4.35260	+	6.77278i	0.137987	+	0.214712i
$996$		0			0
$997$	−1.32335	−	1.52723i	−0.0419110	−	0.0483679i	0.734407	−	0.678709i	$-0.237460\pi$
$997$	−1.32335	−	1.52723i	−0.0419110	−	0.0483679i	−0.776318	+	0.630341i	$0.782915\pi$
$998$		0			0
$999$	23.4128	+	19.9348i	0.740747	+	0.630709i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.5.2	✓	80
3.2	odd	2	inner	276.2.k.a.5.4	yes	80
23.14	odd	22	inner	276.2.k.a.221.4	yes	80
69.14	even	22	inner	276.2.k.a.221.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.5.2	✓	80	1.1	even	1	trivial
276.2.k.a.5.4	yes	80	3.2	odd	2	inner
276.2.k.a.221.2	yes	80	69.14	even	22	inner
276.2.k.a.221.4	yes	80	23.14	odd	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.25009 + 1.19887i) q^{3} +(-0.395237 + 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(0.125437 - 2.99738i) q^{9} +O(q^{10})\)	\(q+(-1.25009 + 1.19887i) q^{3} +(-0.395237 + 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(0.125437 - 2.99738i) q^{9} +(-5.12676 + 1.50535i) q^{11} +(-0.356468 + 0.780556i) q^{13} +(-2.80153 - 3.91025i) q^{15} +(-2.26084 + 1.45295i) q^{17} +(-1.15710 + 1.80049i) q^{19} +(-0.502197 + 1.26500i) q^{21} +(-4.59687 - 1.36703i) q^{23} +(-2.60298 - 0.764303i) q^{25} +(3.43665 + 3.89736i) q^{27} +(3.91782 + 6.09624i) q^{29} +(1.14624 + 1.32283i) q^{31} +(4.60418 - 8.02813i) q^{33} +(0.614830 + 2.09392i) q^{35} +(5.85758 - 0.842193i) q^{37} +(-0.490166 - 1.40312i) q^{39} +(7.95761 + 1.14413i) q^{41} +(-6.40757 - 5.55219i) q^{43} +(8.19002 + 1.52949i) q^{45} -3.23252i q^{47} +(-4.17966 + 4.82359i) q^{49} +(1.08435 - 4.52676i) q^{51} +(0.151808 + 0.332413i) q^{53} +(-2.11183 - 14.6881i) q^{55} +(-0.712065 - 3.63798i) q^{57} +(11.4354 + 5.22236i) q^{59} +(0.851709 - 0.738010i) q^{61} +(-0.888779 - 2.18343i) q^{63} +(-2.00481 - 1.28841i) q^{65} +(-3.75708 + 12.7954i) q^{67} +(7.38537 - 3.80214i) q^{69} +(-0.390072 + 1.32846i) q^{71} +(11.4103 + 7.33298i) q^{73} +(4.17025 - 2.16518i) q^{75} +(-3.17314 + 2.74954i) q^{77} +(11.8032 + 5.39034i) q^{79} +(-8.96853 - 0.751962i) q^{81} +(-1.22527 - 8.52192i) q^{83} +(-3.10051 - 6.78917i) q^{85} +(-12.2062 - 2.92389i) q^{87} +(7.91446 - 9.13377i) q^{89} +0.674293i q^{91} +(-3.01879 - 0.279465i) q^{93} +(-4.49210 - 3.89242i) q^{95} +(-7.08845 - 1.01917i) q^{97} +(3.86903 + 15.5557i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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