LMFDB - Embedded newform 276.2.k.a.5.4

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			5.4
Character	$\chi$	$=$	276.5
Dual form			276.2.k.a.221.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00876 + 1.40798i) q^{3} +(0.395237 - 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(-0.964814 - 2.84062i) q^{9} +O(q^{10})$	\(q+(-1.00876 + 1.40798i) q^{3} +(0.395237 - 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(-0.964814 - 2.84062i) q^{9} +(5.12676 - 1.50535i) q^{11} +(-0.356468 + 0.780556i) q^{13} +(3.47175 + 3.32950i) q^{15} +(2.26084 - 1.45295i) q^{17} +(-1.15710 + 1.80049i) q^{19} +(-0.261437 + 1.33570i) q^{21} +(4.59687 + 1.36703i) q^{23} +(-2.60298 - 0.764303i) q^{25} +(4.97280 + 1.50706i) q^{27} +(-3.91782 - 6.09624i) q^{29} +(1.14624 + 1.32283i) q^{31} +(-3.05216 + 8.73692i) q^{33} +(-0.614830 - 2.09392i) q^{35} +(5.85758 - 0.842193i) q^{37} +(-0.739417 - 1.28929i) q^{39} +(-7.95761 - 1.14413i) q^{41} +(-6.40757 - 5.55219i) q^{43} +(-8.19002 + 1.52949i) q^{45} +3.23252i q^{47} +(-4.17966 + 4.82359i) q^{49} +(-0.234911 + 4.64889i) q^{51} +(-0.151808 - 0.332413i) q^{53} +(-2.11183 - 14.6881i) q^{55} +(-1.36781 - 3.44543i) q^{57} +(-11.4354 - 5.22236i) q^{59} +(0.851709 - 0.738010i) q^{61} +(-1.61691 - 1.71549i) q^{63} +(2.00481 + 1.28841i) q^{65} +(-3.75708 + 12.7954i) q^{67} +(-6.56188 + 5.09331i) q^{69} +(0.390072 - 1.32846i) q^{71} +(11.4103 + 7.33298i) q^{73} +(3.70190 - 2.89394i) q^{75} +(3.17314 - 2.74954i) q^{77} +(11.8032 + 5.39034i) q^{79} +(-7.13827 + 5.48134i) q^{81} +(1.22527 + 8.52192i) q^{83} +(-3.10051 - 6.78917i) q^{85} +(12.5355 + 0.633426i) q^{87} +(-7.91446 + 9.13377i) q^{89} +0.674293i q^{91} +(-3.01879 + 0.279465i) q^{93} +(4.49210 + 3.89242i) q^{95} +(-7.08845 - 1.01917i) q^{97} +(-9.22251 - 13.1108i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.00876	+	1.40798i	−0.582407	+	0.812898i
$3$	−1.00876	+	1.40798i	−0.582407	+	0.812898i
$4$		0			0
$5$	0.395237	−	2.74894i	0.176756	−	1.22936i	−0.687453	−	0.726229i	$-0.741271\pi$
$5$	0.395237	−	2.74894i	0.176756	−	1.22936i	0.864209	−	0.503133i	$-0.167820\pi$
$6$		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
$9$	−0.964814	−	2.84062i	−0.321605	−	0.946874i
$10$		0			0
$11$	5.12676	−	1.50535i	1.54578	−	0.453881i	0.605942	−	0.795509i	$-0.292796\pi$
$11$	5.12676	−	1.50535i	1.54578	−	0.453881i	0.939835	+	0.341628i	$0.110978\pi$
$12$		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
$15$	3.47175	+	3.32950i	0.896402	+	0.859673i
$16$		0			0
$17$	2.26084	−	1.45295i	0.548334	−	0.352393i	−0.236957	−	0.971520i	$-0.576150\pi$
$17$	2.26084	−	1.45295i	0.548334	−	0.352393i	0.785291	+	0.619127i	$0.212514\pi$
$18$		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
$21$	−0.261437	+	1.33570i	−0.0570502	+	0.291473i
$22$		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
$27$	4.97280	+	1.50706i	0.957016	+	0.290034i
$28$		0			0
$29$	−3.91782	−	6.09624i	−0.727520	−	1.13204i	−0.986116	−	0.166058i	$-0.946896\pi$
$29$	−3.91782	−	6.09624i	−0.727520	−	1.13204i	0.258596	−	0.965986i	$-0.416740\pi$
$30$		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
$33$	−3.05216	+	8.73692i	−0.531312	+	1.52090i
$34$		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
$39$	−0.739417	−	1.28929i	−0.118401	−	0.206452i
$40$		0			0
$41$	−7.95761	−	1.14413i	−1.24277	−	0.178683i	−0.510608	−	0.859814i	$-0.670580\pi$
$41$	−7.95761	−	1.14413i	−1.24277	−	0.178683i	−0.732162	+	0.681130i	$0.761489\pi$
$42$		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	$0.0757566\pi$
$47$			3.23252i			0.471512i	−0.971812	+	0.235756i	$0.924243\pi$
$48$		0			0
$49$	−4.17966	+	4.82359i	−0.597095	+	0.689084i
$50$		0			0
$51$	−0.234911	+	4.64889i	−0.0328941	+	0.650975i
$52$		0			0
$53$	−0.151808	−	0.332413i	−0.0208524	−	0.0456604i	0.898919	−	0.438114i	$-0.144354\pi$
$53$	−0.151808	−	0.332413i	−0.0208524	−	0.0456604i	−0.919772	+	0.392454i	$0.871626\pi$
$54$		0			0
$55$	−2.11183	−	14.6881i	−0.284760	−	1.98055i
$56$		0			0
$57$	−1.36781	−	3.44543i	−0.181171	−	0.456359i
$58$		0			0
$59$	−11.4354	−	5.22236i	−1.48876	−	0.679894i	−0.505621	−	0.862756i	$-0.668737\pi$
$59$	−11.4354	−	5.22236i	−1.48876	−	0.679894i	−0.983139	+	0.182862i	$0.941464\pi$
$60$		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
$63$	−1.61691	−	1.71549i	−0.203711	−	0.216132i
$64$		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
$69$	−6.56188	+	5.09331i	−0.789957	+	0.613162i
$70$		0			0
$71$	0.390072	−	1.32846i	0.0462930	−	0.157659i	−0.933103	−	0.359610i	$-0.882910\pi$
$71$	0.390072	−	1.32846i	0.0462930	−	0.157659i	0.979396	+	0.201950i	$0.0647280\pi$
$72$		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
$75$	3.70190	−	2.89394i	0.427458	−	0.334164i
$76$		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
$81$	−7.13827	+	5.48134i	−0.793141	+	0.609038i
$82$		0			0
$83$	1.22527	+	8.52192i	0.134491	+	0.935403i	0.939600	+	0.342276i	$0.111198\pi$
$83$	1.22527	+	8.52192i	0.134491	+	0.935403i	−0.805109	+	0.593127i	$0.797893\pi$
$84$		0			0
$85$	−3.10051	−	6.78917i	−0.336297	−	0.736388i
$86$		0			0
$87$	12.5355	+	0.633426i	1.34395	+	0.0679104i
$88$		0			0
$89$	−7.91446	+	9.13377i	−0.838931	+	0.968178i	−0.999823	−	0.0187942i	$-0.994017\pi$
$89$	−7.91446	+	9.13377i	−0.838931	+	0.968178i	0.160893	+	0.986972i	$0.448563\pi$
$90$		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
$99$	−9.22251	−	13.1108i	−0.926898	−	1.31769i
$100$		0			0
$101$	17.3230	−	2.49067i	1.72370	−	0.247831i	0.791862	−	0.610700i	$-0.209112\pi$
$101$	17.3230	−	2.49067i	1.72370	−	0.247831i	0.931840	+	0.362869i	$0.118203\pi$
$102$		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
$105$	3.56841	+	1.24659i	0.348241	+	0.121655i
$106$		0			0
$107$	−4.53943	−	5.23878i	−0.438843	−	0.506452i	0.492642	−	0.870232i	$-0.336031\pi$
$107$	−4.53943	−	5.23878i	−0.438843	−	0.506452i	−0.931485	+	0.363780i	$0.881486\pi$
$108$		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
$111$	−4.72309	+	9.09692i	−0.448296	+	0.863442i
$112$		0			0
$113$	−2.67490	−	0.785421i	−0.251633	−	0.0738862i	0.153483	−	0.988151i	$-0.450951\pi$
$113$	−2.67490	−	0.785421i	−0.251633	−	0.0738862i	−0.405116	+	0.914265i	$0.632769\pi$
$114$		0			0
$115$	5.57472	−	12.0962i	0.519846	−	1.12798i
$116$		0			0
$117$	2.56119	+	0.259499i	0.236782	+	0.0239907i
$118$		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
$123$	9.63822	−	10.0500i	0.869049	−	0.906178i
$124$		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
$129$	14.2811	−	3.42091i	1.25738	−	0.301194i
$130$		0			0
$131$	−12.7065	+	5.80287i	−1.11017	+	0.506999i	−0.884188	−	0.467132i	$-0.845287\pi$
$131$	−12.7065	+	5.80287i	−1.11017	+	0.506999i	−0.225985	+	0.974131i	$0.572560\pi$
$132$		0			0
$133$	−0.239345	+	1.66468i	−0.0207538	+	0.144346i
$134$		0			0
$135$	6.10826	−	13.0743i	0.525715	−	1.12525i
$136$		0			0
$137$	15.7968			1.34961			0.674804	−	0.737997i	$-0.264228\pi$
$137$	15.7968			1.34961			0.674804	+	0.737997i	$0.264228\pi$
$138$		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
$141$	−4.55133	−	3.26083i	−0.383291	−	0.274612i
$142$		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
$147$	−2.57525	−	10.7507i	−0.212403	−	0.886704i
$148$		0			0
$149$	−5.10967	+	1.50034i	−0.418601	+	0.122912i	−0.484248	−	0.874931i	$-0.660907\pi$
$149$	−5.10967	+	1.50034i	−0.418601	+	0.122912i	0.0656476	+	0.997843i	$0.479089\pi$
$150$		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
$153$	−6.30858	−	5.02036i	−0.510018	−	0.405872i
$154$		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
$159$	0.621168	+	0.121582i	0.0492619	+	0.00964207i
$160$		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
$165$	22.8109	+	11.8433i	1.77583	+	0.922003i
$166$		0			0
$167$	10.5810	+	16.4644i	0.818786	+	1.27406i	0.958850	+	0.283913i	$0.0916326\pi$
$167$	10.5810	+	16.4644i	0.818786	+	1.27406i	−0.140065	+	0.990142i	$0.544731\pi$
$168$		0			0
$169$	8.03099	+	9.26826i	0.617769	+	0.712943i
$170$		0			0
$171$	6.23089	+	1.54976i	0.476488	+	0.118513i
$172$		0			0
$173$	−0.0418712	−	0.142600i	−0.00318341	−	0.0108417i	0.957886	−	0.287149i	$-0.0927075\pi$
$173$	−0.0418712	−	0.142600i	−0.00318341	−	0.0108417i	−0.961069	+	0.276307i	$0.910889\pi$
$174$		0			0
$175$	−2.11007	+	0.303382i	−0.159506	+	0.0229335i
$176$		0			0
$177$	18.8885	−	10.8327i	1.41975	−	0.814234i
$178$		0			0
$179$	−12.5727	−	1.80768i	−0.939729	−	0.135113i	−0.344606	−	0.938747i	$-0.611987\pi$
$179$	−12.5727	−	1.80768i	−0.939729	−	0.135113i	−0.595123	+	0.803635i	$0.702897\pi$
$180$		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
$189$	4.04644	−	0.546055i	0.294335	−	0.0397196i
$190$		0			0
$191$	9.13854	+	20.0106i	0.661242	+	1.44792i	0.881360	+	0.472445i	$0.156628\pi$
$191$	9.13854	+	20.0106i	0.661242	+	1.44792i	−0.220119	+	0.975473i	$0.570644\pi$
$192$		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
$195$	−3.83643	+	1.52303i	−0.274732	+	0.109067i
$196$		0			0
$197$	16.0655	+	7.33688i	1.14462	+	0.522731i	0.895200	−	0.445664i	$-0.147032\pi$
$197$	16.0655	+	7.33688i	1.14462	+	0.522731i	0.249421	+	0.968395i	$0.419760\pi$
$198$		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
$201$	−14.2257	−	18.1974i	−1.00340	−	1.28354i
$202$		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
$207$	−0.551926	−	14.3769i	−0.0383615	−	0.999264i
$208$		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
$213$	1.47696	+	1.88931i	0.101200	+	0.129453i
$214$		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
$219$	−21.8350	+	8.66832i	−1.47547	+	0.585751i
$220$		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
$225$	0.340293	+	8.13149i	0.0226862	+	0.542099i
$226$		0			0
$227$	2.42774	−	2.80177i	0.161135	−	0.185960i	−0.669441	−	0.742866i	$-0.733466\pi$
$227$	2.42774	−	2.80177i	0.161135	−	0.185960i	0.830576	+	0.556906i	$0.188012\pi$
$228$		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	0.451663	−	0.892189i	$-0.350831\pi$
$233$	−5.60455	−	4.85637i	−0.367166	−	0.318151i	−0.818829	+	0.574037i	$0.805376\pi$
$234$		0			0
$235$	8.88600	+	1.27761i	0.579659	+	0.0833423i
$236$		0			0
$237$	−19.4961	+	11.1811i	−1.26641	+	0.726291i
$238$		0			0
$239$	−25.7844	+	3.70724i	−1.66786	+	0.239802i	−0.910592	−	0.413307i	$-0.864374\pi$
$239$	−25.7844	+	3.70724i	−1.66786	+	0.239802i	−0.757265	+	0.653108i	$0.773465\pi$
$240$		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
$243$	−0.516838	−	15.5799i	−0.0331552	−	0.999450i
$244$		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
$249$	−13.2347	−	6.87141i	−0.838715	−	0.435458i
$250$		0			0
$251$	−23.2475	−	6.82607i	−1.46737	−	0.430858i	−0.552125	−	0.833762i	$-0.686183\pi$
$251$	−23.2475	−	6.82607i	−1.46737	−	0.430858i	−0.915242	+	0.402904i	$0.868001\pi$
$252$		0			0
$253$	25.6249	+	0.0884960i	1.61103	+	0.00556370i
$254$		0			0
$255$	12.6867	+	2.48317i	0.794470	+	0.155502i
$256$		0			0
$257$	−11.1549	+	17.3573i	−0.695823	+	1.08272i	0.296011	+	0.955184i	$0.404343\pi$
$257$	−11.1549	+	17.3573i	−0.695823	+	1.08272i	−0.991834	+	0.127537i	$0.959293\pi$
$258$		0			0
$259$	3.91200	−	2.51409i	0.243080	−	0.156218i
$260$		0			0
$261$	−13.5372	+	17.0108i	−0.837929	+	1.05294i
$262$		0			0
$263$	3.41652	−	7.48114i	0.210672	−	0.461307i	−0.774567	−	0.632492i	$-0.782032\pi$
$263$	3.41652	−	7.48114i	0.210672	−	0.461307i	0.985239	+	0.171185i	$0.0547596\pi$
$264$		0			0
$265$	−0.973783	+	0.285928i	−0.0598190	+	0.0175644i
$266$		0			0
$267$	−4.87639	−	20.3572i	−0.298430	−	1.24584i
$268$		0			0
$269$	−0.755924	+	0.345219i	−0.0460895	+	0.0210484i	−0.438326	−	0.898816i	$-0.644429\pi$
$269$	−0.755924	+	0.345219i	−0.0460895	+	0.0210484i	0.392237	+	0.919864i	$0.371701\pi$
$270$		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
$273$	−0.949390	−	0.680198i	−0.0574597	−	0.0411675i
$274$		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
$279$	2.65175	−	4.53231i	0.158756	−	0.271342i
$280$		0			0
$281$	3.34042	−	23.2331i	0.199273	−	1.38597i	−0.607128	−	0.794604i	$-0.707678\pi$
$281$	3.34042	−	23.2331i	0.199273	−	1.38597i	0.806401	−	0.591369i	$-0.201412\pi$
$282$		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
$285$	−10.0119	+	2.39827i	−0.593053	+	0.142061i
$286$		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
$291$	8.58550	−	8.95231i	0.503291	−	0.524793i
$292$		0			0
$293$	−14.5168	+	9.32939i	−0.848081	+	0.545029i	−0.890976	−	0.454051i	$-0.849978\pi$
$293$	−14.5168	+	9.32939i	−0.848081	+	0.545029i	0.0428947	+	0.999080i	$0.486342\pi$
$294$		0			0
$295$	−18.8756	+	29.3711i	−1.09898	+	1.71005i
$296$		0			0
$297$	27.7630	+	0.240522i	1.61098	+	0.0139565i
$298$		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
$303$	−13.9679	+	26.9029i	−0.802435	+	1.54553i
$304$		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
$309$	−22.3619	−	7.81190i	−1.27212	−	0.444403i
$310$		0			0
$311$	−6.96854	−	23.7327i	−0.395150	−	1.34576i	−0.881579	−	0.472036i	$-0.843519\pi$
$311$	−6.96854	−	23.7327i	−0.395150	−	1.34576i	0.486429	−	0.873720i	$-0.338299\pi$
$312$		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
$315$	−5.35484	+	3.76674i	−0.301711	+	0.212232i
$316$		0			0
$317$	22.7023	+	3.26410i	1.27509	+	0.183330i	0.746407	−	0.665489i	$-0.231777\pi$
$317$	22.7023	+	3.26410i	1.27509	+	0.183330i	0.528683	+	0.848820i	$0.322686\pi$
$318$		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
$327$	28.0392	+	1.41684i	1.55057	+	0.0783513i
$328$		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
$333$	−8.04383	−	15.8266i	−0.440799	−	0.867293i
$334$		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
$339$	3.80418	−	2.97390i	0.206615	−	0.161520i
$340$		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
$345$	11.4077	+	20.0513i	0.614169	+	1.07952i
$346$		0			0
$347$	4.42257	−	15.0619i	0.237416	−	0.808565i	−0.751454	−	0.659785i	$-0.770647\pi$
$347$	4.42257	−	15.0619i	0.237416	−	0.808565i	0.988870	−	0.148780i	$-0.0475345\pi$
$348$		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
$351$	−2.94899	+	3.34433i	−0.157405	+	0.178507i
$352$		0			0
$353$	−3.50780	+	3.03953i	−0.186702	+	0.161778i	−0.743197	−	0.669073i	$-0.766691\pi$
$353$	−3.50780	+	3.03953i	−0.186702	+	0.161778i	0.556495	+	0.830851i	$0.312146\pi$
$354$		0			0
$355$	−3.49769	−	1.59734i	−0.185638	−	0.0847780i
$356$		0			0
$357$	1.34964	+	3.39965i	0.0714303	+	0.179928i
$358$		0			0
$359$	−2.53840	−	17.6549i	−0.133972	−	0.931793i	−0.940305	−	0.340332i	$-0.889461\pi$
$359$	−2.53840	−	17.6549i	−0.133972	−	0.931793i	0.806334	−	0.591461i	$-0.201449\pi$
$360$		0			0
$361$	5.99002	+	13.1163i	0.315264	+	0.690332i
$362$		0			0
$363$	−1.53403	+	30.3584i	−0.0805155	+	1.59340i
$364$		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
$375$	5.47331	+	9.54360i	0.282641	+	0.492829i
$376$		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
$381$	6.31501	−	18.0769i	0.323528	−	0.926110i
$382$		0			0
$383$	−0.824211	−	0.951190i	−0.0421152	−	0.0486035i	0.734301	−	0.678824i	$-0.237510\pi$
$383$	−0.824211	−	0.951190i	−0.0421152	−	0.0486035i	−0.776416	+	0.630220i	$0.782965\pi$
$384$		0			0
$385$	−6.30418	−	9.80949i	−0.321291	−	0.499938i
$386$		0			0
$387$	−9.58956	+	23.5583i	−0.487465	+	1.19754i
$388$		0			0
$389$	11.8422	+	3.47719i	0.600425	+	0.176301i	0.567799	−	0.823167i	$-0.307795\pi$
$389$	11.8422	+	3.47719i	0.600425	+	0.176301i	0.0326257	+	0.999468i	$0.489613\pi$
$390$		0			0
$391$	12.3790	−	3.58842i	0.626034	−	0.181474i
$392$		0			0
$393$	4.64747	−	23.7442i	0.234434	−	1.19774i
$394$		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
$399$	−2.10239	−	2.01625i	−0.105251	−	0.100939i
$400$		0			0
$401$	9.72149	−	21.2871i	0.485468	−	1.06303i	−0.495455	−	0.868633i	$-0.664999\pi$
$401$	9.72149	−	21.2871i	0.485468	−	1.06303i	0.980924	−	0.194394i	$-0.0622740\pi$
$402$		0			0
$403$	−1.44114	+	0.423156i	−0.0717882	+	0.0210789i
$404$		0			0
$405$	12.2466	+	21.7891i	0.608537	+	1.08271i
$406$		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
$411$	−15.9351	+	22.2415i	−0.786021	+	1.09709i
$412$		0			0
$413$	−9.87860			−0.486094
$414$		0			0
$415$	23.9105			1.17372
$416$		0			0
$417$	−6.93169	+	9.67495i	−0.339447	+	0.473784i
$418$		0			0
$419$	−3.62089	+	25.1839i	−0.176892	+	1.23031i	0.687008	+	0.726650i	$0.258924\pi$
$419$	−3.62089	+	25.1839i	−0.176892	+	1.23031i	−0.863900	+	0.503663i	$0.831985\pi$
$420$		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
$423$	9.18237	−	3.11878i	0.446462	−	0.151640i
$424$		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
$429$	−5.73165	−	5.49681i	−0.276727	−	0.265388i
$430$		0			0
$431$	15.4252	−	9.91319i	0.743007	−	0.477502i	−0.113564	−	0.993531i	$-0.536227\pi$
$431$	15.4252	−	9.91319i	0.743007	−	0.477502i	0.856571	+	0.516029i	$0.172590\pi$
$432$		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
$435$	6.69575	−	34.2090i	0.321037	−	1.64020i
$436$		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
$441$	17.7346	+	7.21898i	0.844504	+	0.343761i
$442$		0			0
$443$	−2.09130	−	3.25413i	−0.0993606	−	0.154608i	0.788014	−	0.615657i	$-0.211109\pi$
$443$	−2.09130	−	3.25413i	−0.0993606	−	0.154608i	−0.887375	+	0.461049i	$0.847473\pi$
$444$		0			0
$445$	21.9801	+	25.3664i	1.04196	+	1.20248i
$446$		0			0
$447$	3.04198	−	8.70779i	0.143881	−	0.411864i
$448$		0			0
$449$	0.327701	+	1.11605i	0.0154652	+	0.0526695i	0.966864	−	0.255292i	$-0.0821715\pi$
$449$	0.327701	+	1.11605i	0.0154652	+	0.0526695i	−0.951399	+	0.307961i	$0.900353\pi$
$450$		0			0
$451$	−42.5191	+	6.11333i	−2.00215	+	0.287865i
$452$		0			0
$453$	−6.67110	−	11.6321i	−0.313436	−	0.546525i
$454$		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	$-0.741403\pi$
$461$		−	31.1734i		−	1.45189i	0.687754	−	0.725944i	$-0.258597\pi$
$462$		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
$465$	−0.424908	+	8.40893i	−0.0197046	+	0.389955i
$466$		0			0
$467$	−9.80267	−	21.4649i	−0.453614	−	0.993275i	−0.988897	−	0.148603i	$-0.952522\pi$
$467$	−9.80267	−	21.4649i	−0.453614	−	0.993275i	0.535283	−	0.844672i	$-0.320205\pi$
$468$		0			0
$469$	1.49133	+	10.3724i	0.0688632	+	0.478954i
$470$		0			0
$471$	−6.31210	−	15.8998i	−0.290846	−	0.732624i
$472$		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
$477$	−0.797793	+	0.751946i	−0.0365285	+	0.0344292i
$478$		0			0
$479$	2.05997	+	1.32386i	0.0941223	+	0.0604888i	0.586855	−	0.809692i	$-0.300366\pi$
$479$	2.05997	+	1.32386i	0.0941223	+	0.0604888i	−0.492733	+	0.870181i	$0.664002\pi$
$480$		0			0
$481$	−1.43066	+	4.87238i	−0.0652325	+	0.222161i
$482$		0			0
$483$	−3.02772	+	5.78263i	−0.137766	+	0.263119i
$484$		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
$489$	3.26378	−	2.55145i	0.147593	−	0.115381i
$490$		0			0
$491$	16.6711	−	14.4456i	0.752357	−	0.651921i	−0.191793	−	0.981435i	$-0.561430\pi$
$491$	16.6711	−	14.4456i	0.752357	−	0.651921i	0.944151	+	0.329514i	$0.106885\pi$
$492$		0			0
$493$	−17.7151	−	8.09022i	−0.797848	−	0.364365i
$494$		0			0
$495$	−39.6859	+	20.1702i	−1.78375	+	0.906584i
$496$		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
$501$	−33.8553	−	1.71073i	−1.51254	−	0.0764296i
$502$		0			0
$503$	−3.90821	+	4.51031i	−0.174258	+	0.201105i	−0.836160	−	0.548486i	$-0.815204\pi$
$503$	−3.90821	+	4.51031i	−0.174258	+	0.201105i	0.661901	+	0.749591i	$0.269750\pi$
$504$		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	0.743311	−	0.668946i	$-0.233254\pi$
$509$	4.21797	+	3.65489i	0.186958	+	0.162000i	−0.556353	+	0.830946i	$0.687800\pi$
$510$		0			0
$511$	10.5497	+	1.51681i	0.466690	+	0.0670999i
$512$		0			0
$513$	−8.46749	+	7.20964i	−0.373849	+	0.318314i
$514$		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
$519$	0.243016	+	0.0848953i	0.0106672	+	0.00372649i
$520$		0			0
$521$	−0.887232	−	1.02392i	−0.0388703	−	0.0448587i	0.735982	−	0.677002i	$-0.236721\pi$
$521$	−0.887232	−	1.02392i	−0.0388703	−	0.0448587i	−0.774852	+	0.632143i	$0.782176\pi$
$522$		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
$525$	1.70139	−	3.27697i	0.0742548	−	0.143019i
$526$		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
$531$	−3.80174	+	37.5222i	−0.164982	+	1.62832i
$532$		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
$537$	15.2280	−	15.8786i	0.657137	−	0.685213i
$538$		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
$543$	10.8094	−	2.58929i	0.463874	−	0.111117i
$544$		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
$549$	−2.91815	−	1.70734i	−0.124544	−	0.0728676i
$550$		0			0
$551$	15.5095			0.660728
$552$		0			0
$553$	10.1963			0.433592
$554$		0			0
$555$	23.1401	+	16.5789i	0.982244	+	0.703736i
$556$		0			0
$557$	−2.15976	+	15.0215i	−0.0915120	+	0.636480i	0.891511	+	0.452999i	$0.149646\pi$
$557$	−2.15976	+	15.0215i	−0.0915120	+	0.636480i	−0.983023	+	0.183481i	$0.941263\pi$
$558$		0			0
$559$	6.61789	−	3.02229i	0.279907	−	0.127829i
$560$		0			0
$561$	5.79389	+	24.1874i	0.244618	+	1.02119i
$562$		0			0
$563$	18.5176	−	5.43725i	0.780422	−	0.229153i	0.132829	−	0.991139i	$-0.457594\pi$
$563$	18.5176	−	5.43725i	0.780422	−	0.229153i	0.647593	+	0.761986i	$0.275776\pi$
$564$		0			0
$565$	−3.21629	+	7.04270i	−0.135310	+	0.296288i
$566$		0			0
$567$	−3.31305	+	6.24815i	−0.139135	+	0.262397i
$568$		0			0
$569$	−16.4254	+	10.5559i	−0.688587	+	0.442528i	−0.837583	−	0.546310i	$-0.816032\pi$
$569$	−16.4254	+	10.5559i	−0.688587	+	0.442528i	0.148996	+	0.988838i	$0.452396\pi$
$570$		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
$573$	−37.3931	−	7.31899i	−1.56212	−	0.305755i
$574$		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
$579$	20.5628	+	10.6762i	0.854563	+	0.443686i
$580$		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
$585$	1.72562	−	6.93798i	0.0713458	−	0.286850i
$586$		0			0
$587$	7.44298	+	25.3485i	0.307205	+	1.04624i	0.957947	+	0.286945i	$0.0926397\pi$
$587$	7.44298	+	25.3485i	0.307205	+	1.04624i	−0.650742	+	0.759299i	$0.725542\pi$
$588$		0			0
$589$	−3.70805	+	0.533138i	−0.152788	+	0.0219675i
$590$		0			0
$591$	−26.5364	+	15.2188i	−1.09156	+	0.626018i
$592$		0			0
$593$	−9.01479	−	1.29613i	−0.370193	−	0.0532257i	−0.0452921	−	0.998974i	$-0.514422\pi$
$593$	−9.01479	−	1.29613i	−0.370193	−	0.0532257i	−0.324901	+	0.945748i	$0.605331\pi$
$594$		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	$0.133499\pi$
$599$			19.9326i			0.814422i	−0.913334	+	0.407211i	$0.866501\pi$
$600$		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
$603$	39.9718	−	1.67278i	1.62778	−	0.0681207i
$604$		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
$609$	9.16698	−	3.63923i	0.371465	−	0.147469i
$610$		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
$615$	−23.8174	−	30.4670i	−0.960412	−	1.22855i
$616$		0			0
$617$	−22.7706	−	14.6338i	−0.916710	−	0.589133i	−0.00500838	−	0.999987i	$-0.501594\pi$
$617$	−22.7706	−	14.6338i	−0.916710	−	0.589133i	−0.911701	+	0.410854i	$0.865231\pi$
$618$		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
$621$	20.7992	+	13.7257i	0.834641	+	0.550794i
$622$		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
$627$	−12.1990	−	15.6049i	−0.487183	−	0.623199i
$628$		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
$633$	−7.53976	+	2.99323i	−0.299678	+	0.118970i
$634$		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
$639$	−4.15000	+	0.173673i	−0.164172	+	0.00687039i
$640$		0			0
$641$	−29.5141	+	34.0611i	−1.16574	+	1.34533i	−0.238372	+	0.971174i	$0.576614\pi$
$641$	−29.5141	+	34.0611i	−1.16574	+	1.34533i	−0.927365	+	0.374158i	$0.877932\pi$
$642$		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	0.413992	−	0.910280i	$-0.364134\pi$
$647$	−10.8894	−	9.43570i	−0.428106	−	0.370956i	−0.842098	+	0.539325i	$0.818680\pi$
$648$		0			0
$649$	−66.4880	−	9.55953i	−2.60988	−	0.375244i
$650$		0			0
$651$	−2.06657	+	1.18519i	−0.0809951	+	0.0464512i
$652$		0			0
$653$	−44.1640	+	6.34982i	−1.72827	+	0.248488i	−0.933539	−	0.358475i	$-0.883297\pi$
$653$	−44.1640	+	6.34982i	−1.72827	+	0.248488i	−0.794730	+	0.606963i	$0.792388\pi$
$654$		0			0
$655$	10.9296	+	37.2229i	0.427056	+	1.45442i
$656$		0			0
$657$	9.82137	−	39.4874i	0.383168	−	1.54055i
$658$		0			0
$659$	−2.60744	−	3.00914i	−0.101571	−	0.117219i	0.702688	−	0.711498i	$-0.251983\pi$
$659$	−2.60744	−	3.00914i	−0.101571	−	0.117219i	−0.804259	+	0.594279i	$0.797438\pi$
$660$		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
$663$	−3.54498	−	1.84054i	−0.137676	−	0.0714807i
$664$		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
$669$	26.0369	+	5.09622i	1.00664	+	0.197031i
$670$		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
$675$	−11.7922	−	7.72358i	−0.453884	−	0.297281i
$676$		0			0
$677$	−21.1490	+	46.3098i	−0.812822	+	1.77983i	−0.218050	+	0.975938i	$0.569970\pi$
$677$	−21.1490	+	46.3098i	−0.812822	+	1.77983i	−0.594772	+	0.803894i	$0.702758\pi$
$678$		0			0
$679$	−5.39941	+	1.58541i	−0.207211	+	0.0608425i
$680$		0			0
$681$	1.49582	+	6.24452i	0.0573201	+	0.239291i
$682$		0			0
$683$	17.9742	−	8.20854i	0.687764	−	0.314091i	−0.0407040	−	0.999171i	$-0.512960\pi$
$683$	17.9742	−	8.20854i	0.687764	−	0.314091i	0.728468	+	0.685080i	$0.240233\pi$
$684$		0			0
$685$	6.24347	−	43.4243i	0.238551	−	1.65916i
$686$		0			0
$687$	27.8102	+	19.9248i	1.06102	+	0.760179i
$688$		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
$693$	−10.8719	−	6.36090i	−0.412990	−	0.241631i
$694$		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
$699$	12.4913	−	2.99219i	0.472464	−	0.113175i
$700$		0			0
$701$	17.4985	−	5.13803i	0.660910	−	0.194061i	0.0659588	−	0.997822i	$-0.478989\pi$
$701$	17.4985	−	5.13803i	0.660910	−	0.194061i	0.594952	+	0.803762i	$0.297171\pi$
$702$		0			0
$703$	−5.26147	+	11.5210i	−0.198440	+	0.434523i
$704$		0			0
$705$	−10.7627	+	11.2225i	−0.405346	+	0.422664i
$706$		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
$711$	3.92402	−	38.7291i	0.147162	−	1.45245i
$712$		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
$717$	20.7905	−	40.0437i	0.776437	−	1.49546i
$718$		0			0
$719$	−9.22714	−	14.3577i	−0.344114	−	0.535452i	0.625458	−	0.780258i	$-0.284912\pi$
$719$	−9.22714	−	14.3577i	−0.344114	−	0.535452i	−0.969572	+	0.244806i	$0.921276\pi$
$720$		0			0
$721$	7.03737	+	8.12156i	0.262085	+	0.302463i
$722$		0			0
$723$	−12.9348	−	4.51864i	−0.481050	−	0.168050i
$724$		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
$729$	22.4575	+	14.9886i	0.831760	+	0.555135i
$730$		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
$741$	3.17693	+	0.160532i	0.116708	+	0.00589730i
$742$		0			0
$743$	−4.65598	−	10.1952i	−0.170811	−	0.374024i	0.804795	−	0.593553i	$-0.202275\pi$
$743$	−4.65598	−	10.1952i	−0.170811	−	0.374024i	−0.975606	+	0.219529i	$0.929548\pi$
$744$		0			0
$745$	2.10479	+	14.6392i	0.0771136	+	0.536337i
$746$		0			0
$747$	23.0254	−	11.7026i	0.842456	−	0.428176i
$748$		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
$753$	33.0620	−	25.8461i	1.20485	−	0.941884i
$754$		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
$759$	−25.9740	+	35.9901i	−0.942795	+	1.30636i
$760$		0			0
$761$	9.10415	−	31.0059i	0.330025	−	1.12396i	−0.612679	−	0.790332i	$-0.709908\pi$
$761$	9.10415	−	31.0059i	0.330025	−	1.12396i	0.942704	−	0.333631i	$-0.108274\pi$
$762$		0			0
$763$	−10.7151	−	6.88618i	−0.387913	−	0.249297i
$764$		0			0
$765$	−16.2940	+	15.3577i	−0.589112	+	0.555257i
$766$		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
$771$	−13.1862	−	33.2152i	−0.474889	−	1.19622i
$772$		0			0
$773$	−3.57910	−	24.8932i	−0.128731	−	0.895345i	−0.947166	−	0.320745i	$-0.896067\pi$
$773$	−3.57910	−	24.8932i	−0.128731	−	0.895345i	0.818434	−	0.574600i	$-0.194842\pi$
$774$		0			0
$775$	−1.97259	−	4.31937i	−0.0708575	−	0.155156i
$776$		0			0
$777$	−0.406474	+	8.04412i	−0.0145822	+	0.288581i
$778$		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
$789$	7.08684	+	12.3570i	0.252298	+	0.439923i
$790$		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
$795$	0.579730	−	1.65950i	0.0205609	−	0.0588564i
$796$		0			0
$797$	17.1896	+	19.8379i	0.608888	+	0.702694i	0.973557	−	0.228443i	$-0.0733634\pi$
$797$	17.1896	+	19.8379i	0.608888	+	0.702694i	−0.364669	+	0.931137i	$0.618818\pi$
$798$		0			0
$799$	4.69670	+	7.30821i	0.166157	+	0.258546i
$800$		0			0
$801$	33.5816	+	13.6696i	1.18655	+	0.482991i
$802$		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
$807$	0.276483	−	1.41257i	0.00973267	−	0.0497248i
$808$		0			0
$809$	−23.1680	+	36.0501i	−0.814543	+	1.26745i	0.145990	+	0.989286i	$0.453363\pi$
$809$	−23.1680	+	36.0501i	−0.814543	+	1.26745i	−0.960533	+	0.278167i	$0.910273\pi$
$810$		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
$813$	−4.87647	−	4.67667i	−0.171025	−	0.164018i
$814$		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
$819$	1.91541	−	0.650567i	0.0669299	−	0.0227327i
$820$		0			0
$821$	37.5501	−	17.1486i	1.31051	−	0.598489i	0.367119	−	0.930174i	$-0.380344\pi$
$821$	37.5501	−	17.1486i	1.31051	−	0.598489i	0.943390	+	0.331685i	$0.107617\pi$
$822$		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
$825$	14.6223	−	20.4092i	0.509085	−	0.710558i
$826$		0			0
$827$	−22.0014			−0.765063			−0.382531	−	0.923943i	$-0.624948\pi$
$827$	−22.0014			−0.765063			−0.382531	+	0.923943i	$0.624948\pi$
$828$		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
$831$	−18.3497	+	25.6117i	−0.636544	+	0.888459i
$832$		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
$837$	3.70643	+	8.30562i	0.128113	+	0.287084i
$838$		0			0
$839$	−23.9999	+	7.04700i	−0.828568	+	0.243290i	−0.668402	−	0.743800i	$-0.733021\pi$
$839$	−23.9999	+	7.04700i	−0.828568	+	0.243290i	−0.160166	+	0.987090i	$0.551203\pi$
$840$		0			0
$841$	−9.76783	+	21.3886i	−0.336822	+	0.737537i
$842$		0			0
$843$	29.3421	+	28.1399i	1.01060	+	0.969189i
$844$		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
$849$	3.33151	−	17.0208i	0.114337	−	0.584154i
$850$		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
$855$	6.72287	−	16.5158i	0.229917	−	0.564829i
$856$		0			0
$857$	−21.2242	−	33.0255i	−0.725004	−	1.12813i	−0.986633	−	0.162960i	$-0.947896\pi$
$857$	−21.2242	−	33.0255i	−0.725004	−	1.12813i	0.261628	−	0.965169i	$-0.415741\pi$
$858$		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
$861$	3.60862	−	10.3298i	0.122982	−	0.352039i
$862$		0			0
$863$	0.0917261	+	0.312390i	0.00312239	+	0.0106339i	0.961039	−	0.276411i	$-0.0891452\pi$
$863$	0.0917261	+	0.312390i	0.00312239	+	0.0106339i	−0.957917	+	0.287045i	$0.907327\pi$
$864$		0			0
$865$	−0.408548	+	0.0587403i	−0.0138910	+	0.00199723i
$866$		0			0
$867$	−8.42520	−	14.6907i	−0.286135	−	0.498922i
$868$		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
$879$	1.50836	−	29.8505i	0.0508757	−	1.00683i
$880$		0			0
$881$	16.1237	+	35.3059i	0.543220	+	1.18949i	0.959877	+	0.280422i	$0.0904743\pi$
$881$	16.1237	+	35.3059i	0.543220	+	1.18949i	−0.416657	+	0.909064i	$0.636798\pi$
$882$		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
$885$	−22.3129	−	56.2048i	−0.750040	−	1.88930i
$886$		0			0
$887$	−36.9814	−	16.8888i	−1.24171	−	0.567072i	−0.317250	−	0.948342i	$-0.602760\pi$
$887$	−36.9814	−	16.8888i	−1.24171	−	0.567072i	−0.924464	+	0.381270i	$0.875487\pi$
$888$		0			0
$889$	−6.56533	+	5.68889i	−0.220194	+	0.190799i
$890$		0			0
$891$	−28.3448	+	38.8472i	−0.949588	+	1.30143i
$892$		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
$897$	−1.63651	−	6.93751i	−0.0546415	−	0.231637i
$898$		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
$903$	9.09121	−	7.10701i	0.302536	−	0.236507i
$904$		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
$909$	−23.7885	−	46.8050i	−0.789016	−	1.55243i
$910$		0			0
$911$	−2.87572	−	20.0010i	−0.0952767	−	0.662664i	−0.980358	−	0.197227i	$-0.936806\pi$
$911$	−2.87572	−	20.0010i	−0.0952767	−	0.662664i	0.885081	−	0.465437i	$-0.154103\pi$
$912$		0			0
$913$	19.1102	+	41.8454i	0.632454	+	1.38488i
$914$		0			0
$915$	5.41413	+	0.273579i	0.178986	+	0.00904424i
$916$		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
$927$	33.5567	−	23.6047i	1.10215	−	0.775281i
$928$		0			0
$929$	8.68968	−	1.24939i	0.285099	−	0.0409911i	0.00171833	−	0.999999i	$-0.499453\pi$
$929$	8.68968	−	1.24939i	0.285099	−	0.0409911i	0.283381	+	0.959007i	$0.408544\pi$
$930$		0			0
$931$	−3.84851	−	13.1068i	−0.126130	−	0.429559i
$932$		0			0
$933$	40.4447	+	14.1290i	1.32410	+	0.462561i
$934$		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
$939$	11.5139	−	22.1763i	0.375741	−	0.723698i
$940$		0			0
$941$	−30.3669	−	8.91652i	−0.989932	−	0.290670i	−0.253614	−	0.967306i	$-0.581619\pi$
$941$	−30.3669	−	8.91652i	−0.989932	−	0.290670i	−0.736318	+	0.676635i	$0.763437\pi$
$942$		0			0
$943$	−35.0161	−	16.1377i	−1.14028	−	0.525515i
$944$		0			0
$945$	0.0982363	−	11.3392i	0.00319563	−	0.368865i
$946$		0			0
$947$	−29.8192	+	46.3996i	−0.968995	+	1.50779i	−0.111197	+	0.993798i	$0.535468\pi$
$947$	−29.8192	+	46.3996i	−0.968995	+	1.50779i	−0.857798	+	0.513987i	$0.828168\pi$
$948$		0			0
$949$	−9.79122	+	6.29243i	−0.317836	+	0.204261i
$950$		0			0
$951$	−27.4969	+	28.6717i	−0.891650	+	0.929745i
$952$		0			0
$953$	7.14919	−	15.6545i	0.231585	−	0.507100i	−0.757788	−	0.652501i	$-0.773720\pi$
$953$	7.14919	−	15.6545i	0.231585	−	0.507100i	0.989373	+	0.145401i	$0.0464471\pi$
$954$		0			0
$955$	58.6198	−	17.2123i	1.89689	−	0.556978i
$956$		0			0
$957$	65.2201	−	15.6229i	2.10827	−	0.505018i
$958$		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
$963$	−10.5017	+	17.9492i	−0.338412	+	0.578406i
$964$		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
$969$	−8.09846	−	5.80220i	−0.260160	−	0.186394i
$970$		0			0
$971$	0.754590	−	5.24829i	0.0242160	−	0.168426i	−0.974125	−	0.226012i	$-0.927431\pi$
$971$	0.754590	−	5.24829i	0.0242160	−	0.168426i	0.998341	+	0.0575860i	$0.0183403\pi$
$972$		0			0
$973$	4.91166	−	2.24308i	0.157461	−	0.0719099i
$974$		0			0
$975$	0.939276	+	3.92113i	0.0300809	+	0.125577i
$976$		0			0
$977$	16.0508	−	4.71293i	0.513509	−	0.150780i	−0.0147037	−	0.999892i	$-0.504680\pi$
$977$	16.0508	−	4.71293i	0.513509	−	0.150780i	0.528213	+	0.849112i	$0.322862\pi$
$978$		0			0
$979$	−26.8260	+	58.7407i	−0.857362	+	1.87736i
$980$		0			0
$981$	−30.2797	+	38.0494i	−0.966756	+	1.21483i
$982$		0			0
$983$	−46.2932	+	29.7508i	−1.47652	+	0.948904i	−0.479056	+	0.877784i	$0.659021\pi$
$983$	−46.2932	+	29.7508i	−1.47652	+	0.948904i	−0.997468	+	0.0711198i	$0.977343\pi$
$984$		0			0
$985$	26.5183	−	41.2633i	0.844944	−	1.31476i
$986$		0			0
$987$	−4.31766	−	0.845100i	−0.137433	−	0.0268998i
$988$		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
$993$	39.3168	+	20.4131i	1.24768	+	0.647791i
$994$		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
$999$	30.3978	+	4.63968i	0.961745	+	0.146793i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.00876 + 1.40798i) q^{3} +(0.395237 - 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(-0.964814 - 2.84062i) q^{9} +O(q^{10})\)	\(q+(-1.00876 + 1.40798i) q^{3} +(0.395237 - 2.74894i) q^{5} +(0.714786 - 0.326432i) q^{7} +(-0.964814 - 2.84062i) q^{9} +(5.12676 - 1.50535i) q^{11} +(-0.356468 + 0.780556i) q^{13} +(3.47175 + 3.32950i) q^{15} +(2.26084 - 1.45295i) q^{17} +(-1.15710 + 1.80049i) q^{19} +(-0.261437 + 1.33570i) q^{21} +(4.59687 + 1.36703i) q^{23} +(-2.60298 - 0.764303i) q^{25} +(4.97280 + 1.50706i) q^{27} +(-3.91782 - 6.09624i) q^{29} +(1.14624 + 1.32283i) q^{31} +(-3.05216 + 8.73692i) q^{33} +(-0.614830 - 2.09392i) q^{35} +(5.85758 - 0.842193i) q^{37} +(-0.739417 - 1.28929i) q^{39} +(-7.95761 - 1.14413i) q^{41} +(-6.40757 - 5.55219i) q^{43} +(-8.19002 + 1.52949i) q^{45} +3.23252i q^{47} +(-4.17966 + 4.82359i) q^{49} +(-0.234911 + 4.64889i) q^{51} +(-0.151808 - 0.332413i) q^{53} +(-2.11183 - 14.6881i) q^{55} +(-1.36781 - 3.44543i) q^{57} +(-11.4354 - 5.22236i) q^{59} +(0.851709 - 0.738010i) q^{61} +(-1.61691 - 1.71549i) q^{63} +(2.00481 + 1.28841i) q^{65} +(-3.75708 + 12.7954i) q^{67} +(-6.56188 + 5.09331i) q^{69} +(0.390072 - 1.32846i) q^{71} +(11.4103 + 7.33298i) q^{73} +(3.70190 - 2.89394i) q^{75} +(3.17314 - 2.74954i) q^{77} +(11.8032 + 5.39034i) q^{79} +(-7.13827 + 5.48134i) q^{81} +(1.22527 + 8.52192i) q^{83} +(-3.10051 - 6.78917i) q^{85} +(12.5355 + 0.633426i) q^{87} +(-7.91446 + 9.13377i) q^{89} +0.674293i q^{91} +(-3.01879 + 0.279465i) q^{93} +(4.49210 + 3.89242i) q^{95} +(-7.08845 - 1.01917i) q^{97} +(-9.22251 - 13.1108i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 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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