LMFDB - Embedded newform 460.2.x.a.217.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [460,2,Mod(17,460)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("460.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(460, base_ring=CyclotomicField(44)) chi = DirichletCharacter(H, H._module([0, 11, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.x (of order $44$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			217.3
Character	$\chi$	$=$	460.217
Dual form			460.2.x.a.53.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.88091 + 0.409167i) q^{3} +(1.87492 + 1.21847i) q^{5} +(2.30981 - 1.26125i) q^{7} +(0.641504 - 0.292965i) q^{9} +(-1.17609 - 1.01909i) q^{11} +(0.559823 - 1.02524i) q^{13} +(-4.02511 - 1.52469i) q^{15} +(4.73973 + 3.54811i) q^{17} +(-0.0509022 + 0.354033i) q^{19} +(-3.82848 + 3.31740i) q^{21} +(1.64018 + 4.50664i) q^{23} +(2.03064 + 4.56908i) q^{25} +(3.53614 - 2.64712i) q^{27} +(3.90544 - 0.561517i) q^{29} +(-2.13262 + 1.37055i) q^{31} +(2.62910 + 1.43559i) q^{33} +(5.86751 + 0.449701i) q^{35} +(8.38679 + 3.12811i) q^{37} +(-0.633482 + 2.15744i) q^{39} +(-2.24922 + 4.92510i) q^{41} +(-1.22867 - 5.64811i) q^{43} +(1.55974 + 0.232371i) q^{45} +(5.03561 + 5.03561i) q^{47} +(-0.0400207 + 0.0622734i) q^{49} +(-10.3668 - 4.73434i) q^{51} +(1.91822 + 3.51295i) q^{53} +(-0.963341 - 3.34374i) q^{55} +(-0.0491159 - 0.686731i) q^{57} +(-3.29147 - 11.2097i) q^{59} +(-1.61423 - 2.51179i) q^{61} +(1.11225 - 1.48579i) q^{63} +(2.29885 - 1.24011i) q^{65} +(-11.7254 - 0.838615i) q^{67} +(-4.92899 - 7.80548i) q^{69} +(1.27528 + 1.47175i) q^{71} +(-0.0365712 - 0.0488535i) q^{73} +(-5.68896 - 7.76315i) q^{75} +(-4.00187 - 0.870554i) q^{77} +(-4.71121 + 1.38334i) q^{79} +(-6.95354 + 8.02481i) q^{81} +(5.17177 - 13.8661i) q^{83} +(4.56331 + 12.4277i) q^{85} +(-7.11601 + 2.65414i) q^{87} +(-12.6908 - 8.15588i) q^{89} -3.07419i q^{91} +(3.45048 - 3.45048i) q^{93} +(-0.526817 + 0.601759i) q^{95} +(-3.09580 - 8.30017i) q^{97} +(-1.05302 - 0.309196i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) $ 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.88091	+	0.409167i	−1.08594	+	0.236232i	−0.719699	−	0.694286i	$-0.755720\pi$
$3$	−1.88091	+	0.409167i	−1.08594	+	0.236232i	−0.366244	+	0.930519i	$0.619357\pi$
$4$		0			0
$5$	1.87492	+	1.21847i	0.838489	+	0.544918i
$5$	1.87492	+	1.21847i	0.838489	+	0.544918i
$6$		0			0
$7$	2.30981	−	1.26125i	0.873026	−	0.476708i	0.0207403	−	0.999785i	$-0.493398\pi$
$7$	2.30981	−	1.26125i	0.873026	−	0.476708i	0.852286	+	0.523077i	$0.175216\pi$
$8$		0			0
$9$	0.641504	−	0.292965i	0.213835	−	0.0976550i
$10$		0			0
$11$	−1.17609	−	1.01909i	−0.354605	−	0.307267i	0.459282	−	0.888291i	$-0.348107\pi$
$11$	−1.17609	−	1.01909i	−0.354605	−	0.307267i	−0.813886	+	0.581024i	$0.802652\pi$
$12$		0			0
$13$	0.559823	−	1.02524i	0.155267	−	0.284350i	−0.788453	−	0.615094i	$-0.789118\pi$
$13$	0.559823	−	1.02524i	0.155267	−	0.284350i	0.943720	+	0.330744i	$0.107300\pi$
$14$		0			0
$15$	−4.02511	−	1.52469i	−1.03928	−	0.393672i
$16$		0			0
$17$	4.73973	+	3.54811i	1.14955	+	0.860544i	0.991909	−	0.126952i	$-0.0405194\pi$
$17$	4.73973	+	3.54811i	1.14955	+	0.860544i	0.157644	+	0.987496i	$0.449610\pi$
$18$		0			0
$19$	−0.0509022	+	0.354033i	−0.0116778	+	0.0812207i	−0.994827	−	0.101585i	$-0.967609\pi$
$19$	−0.0509022	+	0.354033i	−0.0116778	+	0.0812207i	0.983149	+	0.182805i	$0.0585178\pi$
$20$		0			0
$21$	−3.82848	+	3.31740i	−0.835443	+	0.723915i
$22$		0			0
$23$	1.64018	+	4.50664i	0.342001	+	0.939700i
$23$	1.64018	+	4.50664i	0.342001	+	0.939700i
$24$		0			0
$25$	2.03064	+	4.56908i	0.406128	+	0.913816i
$26$		0			0
$27$	3.53614	−	2.64712i	0.680531	−	0.509439i
$28$		0			0
$29$	3.90544	−	0.561517i	0.725221	−	0.104271i	0.230189	−	0.973146i	$-0.426065\pi$
$29$	3.90544	−	0.561517i	0.725221	−	0.104271i	0.495032	+	0.868875i	$0.335156\pi$
$30$		0			0
$31$	−2.13262	+	1.37055i	−0.383030	+	0.246158i	−0.717960	−	0.696085i	$-0.754924\pi$
$31$	−2.13262	+	1.37055i	−0.383030	+	0.246158i	0.334930	+	0.942243i	$0.391287\pi$
$32$		0			0
$33$	2.62910	+	1.43559i	0.457667	+	0.249905i
$34$		0			0
$35$	5.86751	+	0.449701i	0.991790	+	0.0760133i
$36$		0			0
$37$	8.38679	+	3.12811i	1.37878	+	0.514258i	0.926054	−	0.377391i	$-0.123179\pi$
$37$	8.38679	+	3.12811i	1.37878	+	0.514258i	0.452726	+	0.891650i	$0.350452\pi$
$38$		0			0
$39$	−0.633482	+	2.15744i	−0.101438	+	0.345467i
$40$		0			0
$41$	−2.24922	+	4.92510i	−0.351269	+	0.769172i	0.648698	+	0.761046i	$0.275314\pi$
$41$	−2.24922	+	4.92510i	−0.351269	+	0.769172i	−0.999967	+	0.00812570i	$0.997413\pi$
$42$		0			0
$43$	−1.22867	−	5.64811i	−0.187371	−	0.861328i	−0.970808	−	0.239858i	$-0.922899\pi$
$43$	−1.22867	−	5.64811i	−0.187371	−	0.861328i	0.783438	−	0.621471i	$-0.213464\pi$
$44$		0			0
$45$	1.55974	+	0.232371i	0.232512	+	0.0346398i
$46$		0			0
$47$	5.03561	+	5.03561i	0.734519	+	0.734519i	0.971511	−	0.236993i	$-0.0761617\pi$
$47$	5.03561	+	5.03561i	0.734519	+	0.734519i	−0.236993	+	0.971511i	$0.576162\pi$
$48$		0			0
$49$	−0.0400207	+	0.0622734i	−0.00571724	+	0.00889621i
$50$		0			0
$51$	−10.3668	−	4.73434i	−1.45164	−	0.662940i
$52$		0			0
$53$	1.91822	+	3.51295i	0.263487	+	0.482541i	0.975609	−	0.219515i	$-0.0704474\pi$
$53$	1.91822	+	3.51295i	0.263487	+	0.482541i	−0.712122	+	0.702056i	$0.752266\pi$
$54$		0			0
$55$	−0.963341	−	3.34374i	−0.129897	−	0.450870i
$56$		0			0
$57$	−0.0491159	−	0.686731i	−0.00650557	−	0.0909597i
$58$		0			0
$59$	−3.29147	−	11.2097i	−0.428513	−	1.45938i	−0.837297	−	0.546749i	$-0.815865\pi$
$59$	−3.29147	−	11.2097i	−0.428513	−	1.45938i	0.408784	−	0.912631i	$-0.365953\pi$
$60$		0			0
$61$	−1.61423	−	2.51179i	−0.206681	−	0.321602i	0.722402	−	0.691473i	$-0.243038\pi$
$61$	−1.61423	−	2.51179i	−0.206681	−	0.321602i	−0.929083	+	0.369871i	$0.879402\pi$
$62$		0			0
$63$	1.11225	−	1.48579i	0.140130	−	0.187192i
$64$		0			0
$65$	2.29885	−	1.24011i	0.285137	−	0.153817i
$66$		0			0
$67$	−11.7254	−	0.838615i	−1.43248	−	0.102453i	−0.666591	−	0.745423i	$-0.732247\pi$
$67$	−11.7254	−	0.838615i	−1.43248	−	0.102453i	−0.765891	+	0.642970i	$0.777702\pi$
$68$		0			0
$69$	−4.92899	−	7.80548i	−0.593381	−	0.939669i
$70$		0			0
$71$	1.27528	+	1.47175i	0.151348	+	0.174665i	0.826361	−	0.563141i	$-0.190407\pi$
$71$	1.27528	+	1.47175i	0.151348	+	0.174665i	−0.675013	+	0.737806i	$0.735862\pi$
$72$		0			0
$73$	−0.0365712	−	0.0488535i	−0.00428034	−	0.00571787i	0.798396	−	0.602133i	$-0.205682\pi$
$73$	−0.0365712	−	0.0488535i	−0.00428034	−	0.00571787i	−0.802676	+	0.596415i	$0.796591\pi$
$74$		0			0
$75$	−5.68896	−	7.76315i	−0.656905	−	0.896412i
$76$		0			0
$77$	−4.00187	−	0.870554i	−0.456055	−	0.0992088i
$78$		0			0
$79$	−4.71121	+	1.38334i	−0.530052	+	0.155637i	−0.535798	−	0.844346i	$-0.679989\pi$
$79$	−4.71121	+	1.38334i	−0.530052	+	0.155637i	0.00574580	+	0.999983i	$0.498171\pi$
$80$		0			0
$81$	−6.95354	+	8.02481i	−0.772615	+	0.891646i
$82$		0			0
$83$	5.17177	−	13.8661i	0.567676	−	1.52200i	−0.262747	−	0.964865i	$-0.584628\pi$
$83$	5.17177	−	13.8661i	0.567676	−	1.52200i	0.830423	−	0.557133i	$-0.188099\pi$
$84$		0			0
$85$	4.56331	+	12.4277i	0.494961	+	1.34797i
$86$		0			0
$87$	−7.11601	+	2.65414i	−0.762917	+	0.284553i
$88$		0			0
$89$	−12.6908	−	8.15588i	−1.34522	−	0.864522i	−0.347891	−	0.937535i	$-0.613102\pi$
$89$	−12.6908	−	8.15588i	−1.34522	−	0.864522i	−0.997331	+	0.0730132i	$0.976738\pi$
$90$		0			0
$91$		−	3.07419i		−	0.322262i
$92$		0			0
$93$	3.45048	−	3.45048i	0.357798	−	0.357798i
$94$		0			0
$95$	−0.526817	+	0.601759i	−0.0540503	+	0.0617392i
$96$		0			0
$97$	−3.09580	−	8.30017i	−0.314331	−	0.842754i	−0.994014	−	0.109249i	$-0.965156\pi$
$97$	−3.09580	−	8.30017i	−0.314331	−	0.842754i	0.679683	−	0.733506i	$-0.262117\pi$
$98$		0			0
$99$	−1.05302	−	0.309196i	−0.105833	−	0.0310753i
$100$		0			0
$101$	0.238700	+	0.522680i	0.0237515	+	0.0520086i	0.921136	−	0.389241i	$-0.127263\pi$
$101$	0.238700	+	0.522680i	0.0237515	+	0.0520086i	−0.897384	+	0.441250i	$0.854535\pi$
$102$		0			0
$103$	8.31918	−	0.595000i	0.819714	−	0.0586271i	0.344818	−	0.938669i	$-0.387940\pi$
$103$	8.31918	−	0.595000i	0.819714	−	0.0586271i	0.474895	+	0.880042i	$0.342486\pi$
$104$		0			0
$105$	−11.2202	+	1.55494i	−1.09498	+	0.151747i
$106$		0			0
$107$	−3.20725	+	14.7435i	−0.310056	+	1.42531i	0.513508	+	0.858085i	$0.328346\pi$
$107$	−3.20725	+	14.7435i	−0.310056	+	1.42531i	−0.823565	+	0.567222i	$0.808018\pi$
$108$		0			0
$109$	−2.10349	−	14.6301i	−0.201477	−	1.40131i	−0.799904	−	0.600128i	$-0.795116\pi$
$109$	−2.10349	−	14.6301i	−0.201477	−	1.40131i	0.598426	−	0.801178i	$-0.295793\pi$
$110$		0			0
$111$	−17.0547	−	2.45210i	−1.61876	−	0.232743i
$112$		0			0
$113$	0.223352	−	3.12287i	0.0210112	−	0.293775i	−0.976072	−	0.217449i	$-0.930226\pi$
$113$	0.223352	−	3.12287i	0.0210112	−	0.293775i	0.997083	−	0.0763262i	$-0.0243190\pi$
$114$		0			0
$115$	−2.41603	+	10.4481i	−0.225296	+	0.974290i
$116$		0			0
$117$	0.0587694	−	0.821704i	0.00543323	−	0.0759665i
$118$		0			0
$119$	15.4229	+	2.21748i	1.41382	+	0.203276i
$120$		0			0
$121$	−1.22082	−	8.49096i	−0.110983	−	0.771905i
$122$		0			0
$123$	2.21539	−	10.1840i	0.199755	−	0.918258i
$124$		0			0
$125$	−1.76003	+	11.0409i	−0.157422	+	0.987531i
$126$		0			0
$127$	2.81933	−	0.201642i	0.250175	−	0.0178929i	0.0543115	−	0.998524i	$-0.482704\pi$
$127$	2.81933	−	0.201642i	0.250175	−	0.0178929i	0.195864	+	0.980631i	$0.437249\pi$
$128$		0			0
$129$	4.62203	+	10.1208i	0.406947	+	0.891091i
$130$		0			0
$131$	15.5619	+	4.56939i	1.35965	+	0.399229i	0.878639	−	0.477486i	$-0.158452\pi$
$131$	15.5619	+	4.56939i	1.35965	+	0.399229i	0.481010	+	0.876715i	$0.340270\pi$
$132$		0			0
$133$	0.328950	+	0.881949i	0.0285236	+	0.0764746i
$134$		0			0
$135$	9.85543	−	0.654440i	0.848221	−	0.0563253i
$136$		0			0
$137$	7.74973	−	7.74973i	0.662104	−	0.662104i	−0.293771	−	0.955876i	$-0.594910\pi$
$137$	7.74973	−	7.74973i	0.662104	−	0.662104i	0.955876	+	0.293771i	$0.0949105\pi$
$138$		0			0
$139$			10.2759i			0.871589i	0.900046	+	0.435795i	$0.143533\pi$
$139$			10.2759i			0.871589i	−0.900046	+	0.435795i	$0.856467\pi$
$140$		0			0
$141$	−11.5319	−	7.41111i	−0.971163	−	0.624128i
$142$		0			0
$143$	−1.70321	+	0.635265i	−0.142430	+	0.0531235i
$144$		0			0
$145$	8.00657	+	3.70588i	0.664909	+	0.307756i
$146$		0			0
$147$	0.0497951	−	0.133506i	0.00410703	−	0.0110114i
$148$		0			0
$149$	9.72439	−	11.2225i	0.796653	−	0.919387i	−0.201539	−	0.979480i	$-0.564594\pi$
$149$	9.72439	−	11.2225i	0.796653	−	0.919387i	0.998193	+	0.0600935i	$0.0191399\pi$
$150$		0			0
$151$	−8.94743	+	2.62720i	−0.728131	+	0.213799i	−0.624730	−	0.780841i	$-0.714791\pi$
$151$	−8.94743	+	2.62720i	−0.728131	+	0.213799i	−0.103402	+	0.994640i	$0.532973\pi$
$152$		0			0
$153$	4.08003	+	0.887555i	0.329851	+	0.0717546i
$154$		0			0
$155$	−5.66847	−	0.0288707i	−0.455302	−	0.00231895i
$156$		0			0
$157$	−9.93978	−	13.2780i	−0.793280	−	1.05970i	−0.996745	−	0.0806163i	$-0.974311\pi$
$157$	−9.93978	−	13.2780i	−0.793280	−	1.05970i	0.203465	−	0.979082i	$-0.434780\pi$
$158$		0			0
$159$	−5.04538	−	5.82267i	−0.400124	−	0.461768i
$160$		0			0
$161$	9.47250	+	8.34081i	0.746538	+	0.657348i
$162$		0			0
$163$	−13.5539	−	0.969392i	−1.06162	−	0.0759287i	−0.470412	−	0.882447i	$-0.655895\pi$
$163$	−13.5539	−	0.969392i	−1.06162	−	0.0759287i	−0.591209	+	0.806518i	$0.701349\pi$
$164$		0			0
$165$	3.18010	+	5.89511i	0.247571	+	0.458934i
$166$		0			0
$167$	−3.33326	+	4.45272i	−0.257936	+	0.344561i	−0.910751	−	0.412955i	$-0.864497\pi$
$167$	−3.33326	+	4.45272i	−0.257936	+	0.344561i	0.652816	+	0.757517i	$0.273588\pi$
$168$		0			0
$169$	6.29062	+	9.78839i	0.483894	+	0.752953i
$170$		0			0
$171$	0.0710652	+	0.242026i	0.00543449	+	0.0185082i
$172$		0			0
$173$	−0.603219	−	8.43410i	−0.0458619	−	0.641233i	−0.967450	−	0.253063i	$-0.918562\pi$
$173$	−0.603219	−	8.43410i	−0.0458619	−	0.641233i	0.921588	−	0.388170i	$-0.126893\pi$
$174$		0			0
$175$	10.4532	+	7.99256i	0.790184	+	0.604181i
$176$		0			0
$177$	10.7776	+	19.7377i	0.810093	+	1.48358i
$178$		0			0
$179$	3.20259	+	1.46257i	0.239373	+	0.109318i	0.531490	−	0.847065i	$-0.321632\pi$
$179$	3.20259	+	1.46257i	0.239373	+	0.109318i	−0.292117	+	0.956383i	$0.594360\pi$
$180$		0			0
$181$	−6.12224	+	9.52639i	−0.455063	+	0.708091i	−0.990656	−	0.136385i	$-0.956452\pi$
$181$	−6.12224	+	9.52639i	−0.455063	+	0.708091i	0.535593	+	0.844476i	$0.320088\pi$
$182$		0			0
$183$	4.06396	+	4.06396i	0.300417	+	0.300417i
$184$		0			0
$185$	11.9130	+	16.0840i	0.875863	+	1.18252i
$186$		0			0
$187$	−1.95850	−	9.00310i	−0.143220	−	0.658372i
$188$		0			0
$189$	4.82913	−	10.5743i	0.351267	−	0.769168i
$190$		0			0
$191$	0.728922	−	2.48248i	0.0527429	−	0.179626i	−0.928909	−	0.370309i	$-0.879252\pi$
$191$	0.728922	−	2.48248i	0.0527429	−	0.179626i	0.981652	+	0.190683i	$0.0610701\pi$
$192$		0			0
$193$	−12.5776	−	4.69120i	−0.905355	−	0.337680i	−0.146706	−	0.989180i	$-0.546867\pi$
$193$	−12.5776	−	4.69120i	−0.905355	−	0.337680i	−0.758649	+	0.651500i	$0.774140\pi$
$194$		0			0
$195$	−3.81652	+	3.27315i	−0.273306	+	0.234395i
$196$		0			0
$197$	−8.62214	−	4.70804i	−0.614302	−	0.335434i	0.141793	−	0.989896i	$-0.454713\pi$
$197$	−8.62214	−	4.70804i	−0.614302	−	0.335434i	−0.756095	+	0.654462i	$0.772895\pi$
$198$		0			0
$199$	−8.56989	+	5.50754i	−0.607504	+	0.390419i	−0.807920	−	0.589292i	$-0.799407\pi$
$199$	−8.56989	+	5.50754i	−0.607504	+	0.390419i	0.200417	+	0.979711i	$0.435770\pi$
$200$		0			0
$201$	22.3975	−	3.22027i	1.57980	−	0.227141i
$202$		0			0
$203$	8.31260	−	6.22273i	0.583430	−	0.436750i
$204$		0			0
$205$	−10.2182	+	6.49355i	−0.713671	+	0.453529i
$206$		0			0
$207$	2.37247	+	2.41051i	0.164898	+	0.167542i
$208$		0			0
$209$	0.420656	−	0.364501i	0.0290974	−	0.0252130i
$210$		0			0
$211$	1.09617	−	7.62404i	0.0754636	−	0.524861i	−0.916667	−	0.399652i	$-0.869131\pi$
$211$	1.09617	−	7.62404i	0.0754636	−	0.524861i	0.992130	−	0.125209i	$-0.0399600\pi$
$212$		0			0
$213$	−3.00088	−	2.24643i	−0.205617	−	0.153923i
$214$		0			0
$215$	4.57842	−	12.0868i	0.312246	−	0.824316i
$216$		0			0
$217$	−3.19733	+	5.85548i	−0.217049	+	0.397496i
$218$		0			0
$219$	0.0887764	+	0.0769252i	0.00599895	+	0.00519812i
$220$		0			0
$221$	6.29108	−	2.87304i	0.423184	−	0.193261i
$222$		0			0
$223$	−16.5099	+	9.01510i	−1.10559	+	0.603696i	−0.925040	−	0.379871i	$-0.875968\pi$
$223$	−16.5099	+	9.01510i	−1.10559	+	0.603696i	−0.180547	+	0.983566i	$0.557787\pi$
$224$		0			0
$225$	2.64124	+	2.33618i	0.176083	+	0.155745i
$226$		0			0
$227$	−9.79983	+	2.13182i	−0.650438	+	0.141494i	−0.525666	−	0.850691i	$-0.676184\pi$
$227$	−9.79983	+	2.13182i	−0.650438	+	0.141494i	−0.124772	+	0.992185i	$0.539820\pi$
$228$		0			0
$229$	−14.4598			−0.955528			−0.477764	−	0.878488i	$-0.658553\pi$
$229$	−14.4598			−0.955528			−0.477764	+	0.878488i	$0.658553\pi$
$230$		0			0
$231$	7.88335			0.518687
$232$		0			0
$233$	8.59987	−	1.87079i	0.563396	−	0.122559i	0.0781574	−	0.996941i	$-0.475096\pi$
$233$	8.59987	−	1.87079i	0.563396	−	0.122559i	0.485239	+	0.874382i	$0.338733\pi$
$234$		0			0
$235$	3.30559	+	15.5771i	0.215633	+	1.01614i
$236$		0			0
$237$	8.29534	−	4.52960i	0.538840	−	0.294229i
$238$		0			0
$239$	8.55142	−	3.90530i	0.553146	−	0.252613i	−0.119175	−	0.992873i	$-0.538025\pi$
$239$	8.55142	−	3.90530i	0.553146	−	0.252613i	0.672321	+	0.740260i	$0.265298\pi$
$240$		0			0
$241$	−21.1872	−	18.3588i	−1.36479	−	1.18259i	−0.963837	−	0.266494i	$-0.914135\pi$
$241$	−21.1872	−	18.3588i	−1.36479	−	1.18259i	−0.400950	−	0.916100i	$-0.631320\pi$
$242$		0			0
$243$	3.44468	−	6.30847i	0.220977	−	0.404688i
$244$		0			0
$245$	−0.150914	+	0.0679934i	−0.00964155	+	0.00434394i
$246$		0			0
$247$	0.334472	+	0.250383i	0.0212819	+	0.0159315i
$248$		0			0
$249$	−4.05410	+	28.1969i	−0.256918	+	1.78691i
$250$		0			0
$251$	−16.5575	+	14.3471i	−1.04510	+	0.905582i	−0.995648	−	0.0931945i	$-0.970292\pi$
$251$	−16.5575	+	14.3471i	−1.04510	+	0.905582i	−0.0494496	+	0.998777i	$0.515747\pi$
$252$		0			0
$253$	2.66367	−	6.97170i	0.167463	−	0.438307i
$254$		0			0
$255$	−13.6682	−	21.5081i	−0.855933	−	1.34689i
$256$		0			0
$257$	19.7393	−	14.7766i	1.23130	−	0.921741i	0.232595	−	0.972574i	$-0.425278\pi$
$257$	19.7393	−	14.7766i	1.23130	−	0.921741i	0.998707	+	0.0508324i	$0.0161874\pi$
$258$		0			0
$259$	23.3172	−	3.35251i	1.44886	−	0.208315i
$260$		0			0
$261$	2.34085	−	1.50437i	0.144895	−	0.0931183i
$262$		0			0
$263$	16.0432	+	8.76022i	0.989263	+	0.540179i	0.890525	−	0.454935i	$-0.150337\pi$
$263$	16.0432	+	8.76022i	0.989263	+	0.540179i	0.0987384	+	0.995113i	$0.468519\pi$
$264$		0			0
$265$	−0.683943	+	8.92380i	−0.0420143	+	0.548185i
$266$		0			0
$267$	27.2074	+	10.1478i	1.66506	+	0.621036i
$268$		0			0
$269$	−1.41085	+	4.80491i	−0.0860210	+	0.292961i	−0.991256	−	0.131950i	$-0.957876\pi$
$269$	−1.41085	+	4.80491i	−0.0860210	+	0.292961i	0.905235	+	0.424910i	$0.139694\pi$
$270$		0			0
$271$	11.3991	−	24.9605i	0.692444	−	1.51624i	−0.156454	−	0.987685i	$-0.550006\pi$
$271$	11.3991	−	24.9605i	0.692444	−	1.51624i	0.848898	−	0.528557i	$-0.177267\pi$
$272$		0			0
$273$	1.25785	+	5.78226i	0.0761288	+	0.349958i
$274$		0			0
$275$	2.26808	−	7.44305i	0.136770	−	0.448833i
$276$		0			0
$277$	−0.712183	−	0.712183i	−0.0427909	−	0.0427909i	0.685388	−	0.728178i	$-0.259633\pi$
$277$	−0.712183	−	0.712183i	−0.0427909	−	0.0427909i	−0.728178	+	0.685388i	$0.759633\pi$
$278$		0			0
$279$	−0.966560	+	1.50400i	−0.0578664	+	0.0900419i
$280$		0			0
$281$	27.8579	+	12.7223i	1.66186	+	0.758947i	0.999956	+	0.00935886i	$0.00297906\pi$
$281$	27.8579	+	12.7223i	1.66186	+	0.758947i	0.661905	+	0.749588i	$0.269748\pi$
$282$		0			0
$283$	3.71375	+	6.80122i	0.220760	+	0.404291i	0.964463	−	0.264219i	$-0.0851142\pi$
$283$	3.71375	+	6.80122i	0.220760	+	0.404291i	−0.743703	+	0.668510i	$0.766932\pi$
$284$		0			0
$285$	0.744675	−	1.34741i	0.0441108	−	0.0798137i
$286$		0			0
$287$	1.01652	+	14.2129i	0.0600036	+	0.838959i
$288$		0			0
$289$	5.08643	+	17.3228i	0.299202	+	1.01899i
$290$		0			0
$291$	9.21907	+	14.3452i	0.540432	+	0.840928i
$292$		0			0
$293$	−12.3290	+	16.4696i	−0.720267	+	0.962164i	0.279731	+	0.960078i	$0.409755\pi$
$293$	−12.3290	+	16.4696i	−0.720267	+	0.962164i	−0.999998	+	0.00208527i	$0.999336\pi$
$294$		0			0
$295$	7.48752	−	25.0279i	0.435940	−	1.45718i
$296$		0			0
$297$	−6.85648	−	0.490385i	−0.397853	−	0.0284550i
$298$		0			0
$299$	5.53860	+	0.841348i	0.320305	+	0.0486564i
$300$		0			0
$301$	−9.96168	−	11.4964i	−0.574182	−	0.662641i
$302$		0			0
$303$	−0.662836	−	0.885445i	−0.0380789	−	0.0508675i
$304$		0			0
$305$	0.0340038	−	6.67630i	0.00194705	−	0.382284i
$306$		0			0
$307$	−18.3874	−	3.99993i	−1.04942	−	0.228288i	−0.345393	−	0.938458i	$-0.612254\pi$
$307$	−18.3874	−	3.99993i	−1.04942	−	0.228288i	−0.704030	+	0.710170i	$0.748618\pi$
$308$		0			0
$309$	−15.4042	+	4.52307i	−0.876313	+	0.257309i
$310$		0			0
$311$	−21.1298	+	24.3851i	−1.19816	+	1.38275i	−0.293864	+	0.955847i	$0.594941\pi$
$311$	−21.1298	+	24.3851i	−1.19816	+	1.38275i	−0.904297	+	0.426904i	$0.859604\pi$
$312$		0			0
$313$	0.305893	−	0.820131i	0.0172901	−	0.0463566i	−0.928018	−	0.372536i	$-0.878488\pi$
$313$	0.305893	−	0.820131i	0.0172901	−	0.0463566i	0.945308	+	0.326179i	$0.105761\pi$
$314$		0			0
$315$	3.89578	−	1.43049i	0.219502	−	0.0805990i
$316$		0			0
$317$	6.43401	−	2.39976i	0.361370	−	0.134784i	−0.162220	−	0.986755i	$-0.551865\pi$
$317$	6.43401	−	2.39976i	0.361370	−	0.134784i	0.523590	+	0.851971i	$0.324593\pi$
$318$		0			0
$319$	−5.16538	−	3.31959i	−0.289206	−	0.185861i
$320$		0			0
$321$		−	29.0434i		−	1.62105i
$322$		0			0
$323$	−1.49741	+	1.49741i	−0.0833182	+	0.0833182i
$324$		0			0
$325$	5.82120	+	0.475986i	0.322902	+	0.0264030i
$326$		0			0
$327$	9.94260	+	26.6571i	0.549827	+	1.47414i
$328$		0			0
$329$	17.9825	+	5.28013i	0.991405	+	0.291103i
$330$		0			0
$331$	6.12855	+	13.4197i	0.336856	+	0.737611i	0.999940	−	0.0109334i	$-0.00348028\pi$
$331$	6.12855	+	13.4197i	0.336856	+	0.737611i	−0.663085	+	0.748545i	$0.730753\pi$
$332$		0			0
$333$	6.29659	−	0.450341i	0.345051	−	0.0246785i
$334$		0			0
$335$	−20.9623	−	15.8594i	−1.14529	−	0.866492i
$336$		0			0
$337$	−3.12054	+	14.3449i	−0.169986	+	0.781415i	0.810643	+	0.585541i	$0.199118\pi$
$337$	−3.12054	+	14.3449i	−0.169986	+	0.781415i	−0.980629	+	0.195874i	$0.937246\pi$
$338$		0			0
$339$	0.857670	+	5.96523i	0.0465823	+	0.323987i
$340$		0			0
$341$	3.90486	+	0.561435i	0.211460	+	0.0304034i
$342$		0			0
$343$	−1.32811	+	18.5695i	−0.0717114	+	1.00266i
$344$		0			0
$345$	0.269319	−	20.6405i	0.0144996	−	1.11125i
$346$		0			0
$347$	1.45352	−	20.3228i	0.0780290	−	1.09099i	−0.796059	−	0.605219i	$-0.793085\pi$
$347$	1.45352	−	20.3228i	0.0780290	−	1.09099i	0.874088	−	0.485768i	$-0.161460\pi$
$348$		0			0
$349$	−27.6833	−	3.98026i	−1.48185	−	0.213058i	−0.646561	−	0.762863i	$-0.723793\pi$
$349$	−27.6833	−	3.98026i	−1.48185	−	0.213058i	−0.835294	+	0.549804i	$0.814702\pi$
$350$		0			0
$351$	−0.734321	−	5.10732i	−0.0391952	−	0.272608i
$352$		0			0
$353$	−7.40364	+	34.0340i	−0.394056	+	1.81145i	0.169689	+	0.985498i	$0.445724\pi$
$353$	−7.40364	+	34.0340i	−0.394056	+	1.81145i	−0.563745	+	0.825949i	$0.690640\pi$
$354$		0			0
$355$	0.597755	+	4.31332i	0.0317256	+	0.228927i
$356$		0			0
$357$	−29.9164	+	2.13967i	−1.58335	+	0.113243i
$358$		0			0
$359$	−1.05297	−	2.30568i	−0.0555735	−	0.121689i	0.879808	−	0.475329i	$-0.157671\pi$
$359$	−1.05297	−	2.30568i	−0.0555735	−	0.121689i	−0.935382	+	0.353640i	$0.884944\pi$
$360$		0			0
$361$	18.1076	+	5.31688i	0.953033	+	0.279836i
$362$		0			0
$363$	5.77046	+	15.4712i	0.302871	+	0.812027i
$364$		0			0
$365$	−0.00904140	−	0.136157i	−0.000473248	−	0.00712680i
$366$		0			0
$367$	12.6125	−	12.6125i	0.658370	−	0.658370i	−0.296624	−	0.954994i	$-0.595861\pi$
$367$	12.6125	−	12.6125i	0.658370	−	0.658370i	0.954994	+	0.296624i	$0.0958610\pi$
$368$		0			0
$369$			3.81841i			0.198779i
$370$		0			0
$371$	8.86144	+	5.69490i	0.460063	+	0.295664i
$372$		0			0
$373$	24.6084	−	9.17845i	1.27417	−	0.475242i	0.380842	−	0.924640i	$-0.375634\pi$
$373$	24.6084	−	9.17845i	1.27417	−	0.475242i	0.893332	+	0.449398i	$0.148361\pi$
$374$		0			0
$375$	−1.20713	−	21.4871i	−0.0623361	−	1.10959i
$376$		0			0
$377$	1.61066	−	4.31836i	0.0829534	−	0.222407i
$378$		0			0
$379$	10.6338	−	12.2720i	0.546221	−	0.630372i	−0.413778	−	0.910378i	$-0.635791\pi$
$379$	10.6338	−	12.2720i	0.546221	−	0.630372i	0.959998	+	0.280006i	$0.0903364\pi$
$380$		0			0
$381$	−5.22040	+	1.53285i	−0.267449	+	0.0785301i
$382$		0			0
$383$	1.07132	+	0.233051i	0.0547418	+	0.0119083i	0.239853	−	0.970809i	$-0.422901\pi$
$383$	1.07132	+	0.233051i	0.0547418	+	0.0119083i	−0.185111	+	0.982718i	$0.559264\pi$
$384$		0			0
$385$	−6.44243	−	6.50840i	−0.328337	−	0.331699i
$386$		0			0
$387$	−2.44289	−	3.26333i	−0.124179	−	0.165884i
$388$		0			0
$389$	−16.8606	−	19.4582i	−0.854867	−	0.986569i	0.145129	−	0.989413i	$-0.453640\pi$
$389$	−16.8606	−	19.4582i	−0.854867	−	0.986569i	−0.999996	+	0.00284364i	$0.999095\pi$
$390$		0			0
$391$	−8.21609	+	27.1798i	−0.415506	+	1.37454i
$392$		0			0
$393$	−31.1402	−	2.22719i	−1.57081	−	0.112347i
$394$		0			0
$395$	−10.5187	−	3.14685i	−0.529253	−	0.158335i
$396$		0			0
$397$	14.9583	−	19.9819i	0.750735	−	1.00286i	−0.248677	−	0.968586i	$-0.579996\pi$
$397$	14.9583	−	19.9819i	0.750735	−	1.00286i	0.999412	−	0.0342782i	$-0.0109132\pi$
$398$		0			0
$399$	−0.979588	−	1.52427i	−0.0490408	−	0.0763089i
$400$		0			0
$401$	−5.96453	−	20.3133i	−0.297855	−	1.01440i	−0.963406	−	0.268047i	$-0.913622\pi$
$401$	−5.96453	−	20.3133i	−0.297855	−	1.01440i	0.665551	−	0.746352i	$-0.268197\pi$
$402$		0			0
$403$	0.211254	+	2.95371i	0.0105233	+	0.147135i
$404$		0			0
$405$	−22.8153	+	6.57316i	−1.13370	+	0.326623i
$406$		0			0
$407$	−6.67580	−	12.2258i	−0.330907	−	0.606011i
$408$		0			0
$409$	−33.9101	−	15.4862i	−1.67675	−	0.765744i	−0.999552	−	0.0299397i	$-0.990468\pi$
$409$	−33.9101	−	15.4862i	−1.67675	−	0.765744i	−0.677194	−	0.735804i	$-0.736804\pi$
$410$		0			0
$411$	−11.4056	+	17.7475i	−0.562597	+	0.875418i
$412$		0			0
$413$	−21.7409	−	21.7409i	−1.06980	−	1.06980i
$414$		0			0
$415$	26.5921	−	19.6961i	1.30536	−	0.966842i
$416$		0			0
$417$	−4.20455	−	19.3280i	−0.205898	−	0.946496i
$418$		0			0
$419$	−4.09093	+	8.95790i	−0.199855	+	0.437622i	−0.982850	−	0.184406i	$-0.940964\pi$
$419$	−4.09093	+	8.95790i	−0.199855	+	0.437622i	0.782995	+	0.622028i	$0.213691\pi$
$420$		0			0
$421$	3.43392	−	11.6949i	0.167359	−	0.569973i	−0.832513	−	0.554005i	$-0.813099\pi$
$421$	3.43392	−	11.6949i	0.167359	−	0.569973i	0.999873	−	0.0159679i	$-0.00508297\pi$
$422$		0			0
$423$	4.70562	+	1.75511i	0.228795	+	0.0853361i
$424$		0			0
$425$	−6.58695	+	28.8611i	−0.319514	+	1.39997i
$426$		0			0
$427$	−6.89657	−	3.76581i	−0.333748	−	0.182240i
$428$		0			0
$429$	2.94366	−	1.89177i	0.142121	−	0.0913357i
$430$		0			0
$431$	13.0320	−	1.87372i	0.627729	−	0.0902537i	0.178894	−	0.983868i	$-0.442748\pi$
$431$	13.0320	−	1.87372i	0.627729	−	0.0902537i	0.448835	+	0.893615i	$0.351839\pi$
$432$		0			0
$433$	−15.1615	+	11.3497i	−0.728613	+	0.545433i	−0.897935	−	0.440128i	$-0.854933\pi$
$433$	−15.1615	+	11.3497i	−0.728613	+	0.545433i	0.169322	+	0.985561i	$0.445842\pi$
$434$		0			0
$435$	−16.5759	−	3.69439i	−0.794756	−	0.177133i
$436$		0			0
$437$	−1.67899	+	0.351278i	−0.0803168	+	0.0168039i
$438$		0			0
$439$	25.2078	−	21.8427i	1.20310	−	1.04249i	0.205138	−	0.978733i	$-0.434236\pi$
$439$	25.2078	−	21.8427i	1.20310	−	1.04249i	0.997965	−	0.0637618i	$-0.0203098\pi$
$440$		0			0
$441$	−0.00742950	+	0.0516733i	−0.000353786	+	0.00246063i
$442$		0			0
$443$	−12.4702	−	9.33511i	−0.592479	−	0.443524i	0.260497	−	0.965475i	$-0.416114\pi$
$443$	−12.4702	−	9.33511i	−0.592479	−	0.443524i	−0.852976	+	0.521950i	$0.825205\pi$
$444$		0			0
$445$	−13.8565	−	30.7550i	−0.656860	−	1.45793i
$446$		0			0
$447$	−13.6988	+	25.0875i	−0.647931	+	1.18660i
$448$		0			0
$449$	−15.3549	−	13.3051i	−0.724643	−	0.627907i	0.212374	−	0.977188i	$-0.431880\pi$
$449$	−15.3549	−	13.3051i	−0.724643	−	0.627907i	−0.937018	+	0.349281i	$0.886426\pi$
$450$		0			0
$451$	7.66439	−	3.50021i	0.360902	−	0.164819i
$452$		0			0
$453$	15.7543	−	8.60252i	0.740203	−	0.404181i
$454$		0			0
$455$	3.74582	−	5.76385i	0.175607	−	0.270213i
$456$		0			0
$457$	30.4010	−	6.61334i	1.42210	−	0.309359i	0.565248	−	0.824921i	$-0.308780\pi$
$457$	30.4010	−	6.61334i	1.42210	−	0.309359i	0.856852	+	0.515562i	$0.172417\pi$
$458$		0			0
$459$	26.1527			1.22070
$460$		0			0
$461$	−23.6814			−1.10295			−0.551476	−	0.834191i	$-0.685935\pi$
$461$	−23.6814			−1.10295			−0.551476	+	0.834191i	$0.685935\pi$
$462$		0			0
$463$	−18.5028	+	4.02504i	−0.859899	+	0.187060i	−0.620832	−	0.783943i	$-0.713205\pi$
$463$	−18.5028	+	4.02504i	−0.859899	+	0.187060i	−0.239067	+	0.971003i	$0.576842\pi$
$464$		0			0
$465$	10.6737	−	2.26504i	0.494980	−	0.105039i
$466$		0			0
$467$	−25.3723	+	13.8543i	−1.17409	+	0.641102i	−0.943313	−	0.331905i	$-0.892309\pi$
$467$	−25.3723	+	13.8543i	−1.17409	+	0.641102i	−0.230777	+	0.973007i	$0.574127\pi$
$468$		0			0
$469$	−28.1411	+	12.8516i	−1.29943	+	0.593432i
$470$		0			0
$471$	24.1287	+	20.9077i	1.11179	+	0.963374i
$472$		0			0
$473$	−4.31089	+	7.89481i	−0.198215	+	0.363004i
$474$		0			0
$475$	−1.72097	+	0.486336i	−0.0789634	+	0.0223146i
$476$		0			0
$477$	2.25972	+	1.69160i	0.103465	+	0.0774532i
$478$		0			0
$479$	0.353763	−	2.46048i	0.0161639	−	0.112422i	−0.980142	−	0.198296i	$-0.936459\pi$
$479$	0.353763	−	2.46048i	0.0161639	−	0.112422i	0.996306	+	0.0858741i	$0.0273683\pi$
$480$		0			0
$481$	7.90218	−	6.84728i	0.360309	−	0.312209i
$482$		0			0
$483$	−21.2297	−	11.8125i	−0.965985	−	0.537486i
$484$		0			0
$485$	4.30917	−	19.3343i	0.195669	−	0.877925i
$486$		0			0
$487$	−5.55928	+	4.16163i	−0.251915	+	0.188581i	−0.717771	−	0.696279i	$-0.754837\pi$
$487$	−5.55928	+	4.16163i	−0.251915	+	0.188581i	0.465856	+	0.884861i	$0.345747\pi$
$488$		0			0
$489$	25.8902	−	3.72246i	1.17080	−	0.168335i
$490$		0			0
$491$	24.3880	−	15.6732i	1.10061	−	0.707322i	0.141386	−	0.989954i	$-0.454844\pi$
$491$	24.3880	−	15.6732i	1.10061	−	0.707322i	0.959228	+	0.282632i	$0.0912076\pi$
$492$		0			0
$493$	20.5030	+	11.1955i	0.923410	+	0.504220i
$494$		0			0
$495$	−1.59759	−	1.86280i	−0.0718062	−	0.0837266i
$496$		0			0
$497$	4.80191	+	1.79102i	0.215395	+	0.0803383i
$498$		0			0
$499$	−8.31261	+	28.3101i	−0.372124	+	1.26734i	0.534418	+	0.845220i	$0.320531\pi$
$499$	−8.31261	+	28.3101i	−0.372124	+	1.26734i	−0.906542	+	0.422116i	$0.861287\pi$
$500$		0			0
$501$	4.44766	−	9.73901i	0.198707	−	0.435107i
$502$		0			0
$503$	−2.19806	−	10.1043i	−0.0980067	−	0.450530i	−0.999830	−	0.0184250i	$-0.994135\pi$
$503$	−2.19806	−	10.1043i	−0.0980067	−	0.450530i	0.901824	−	0.432104i	$-0.142229\pi$
$504$		0			0
$505$	−0.189329	+	1.27083i	−0.00842504	+	0.0565513i
$506$		0			0
$507$	−15.8372	−	15.8372i	−0.703353	−	0.703353i
$508$		0			0
$509$	6.33041	−	9.85031i	0.280590	−	0.436607i	−0.672140	−	0.740424i	$-0.734625\pi$
$509$	6.33041	−	9.85031i	0.280590	−	0.436607i	0.952730	+	0.303817i	$0.0982611\pi$
$510$		0			0
$511$	−0.146089	−	0.0667167i	−0.00646260	−	0.00295137i
$512$		0			0
$513$	0.757171	+	1.38665i	0.0334299	+	0.0612223i
$514$		0			0
$515$	16.3228	+	9.02114i	0.719268	+	0.397519i
$516$		0			0
$517$	−0.790602	−	11.0541i	−0.0347706	−	0.486157i
$518$		0			0
$519$	4.58555	+	15.6170i	0.201283	+	0.685508i
$520$		0			0
$521$	12.9691	+	20.1803i	0.568187	+	0.884117i	0.999839	−	0.0179234i	$-0.00570549\pi$
$521$	12.9691	+	20.1803i	0.568187	+	0.884117i	−0.431652	+	0.902040i	$0.642069\pi$
$522$		0			0
$523$	−3.90592	+	5.21770i	−0.170794	+	0.228154i	−0.877769	−	0.479085i	$-0.840969\pi$
$523$	−3.90592	+	5.21770i	−0.170794	+	0.228154i	0.706975	+	0.707239i	$0.250060\pi$
$524$		0			0
$525$	−22.9317	−	10.7562i	−1.00082	−	0.469439i
$526$		0			0
$527$	−14.9709	−	1.07074i	−0.652143	−	0.0466422i
$528$		0			0
$529$	−17.6196	+	14.7834i	−0.766071	+	0.642756i
$530$		0			0
$531$	−5.39554	−	6.22679i	−0.234147	−	0.270220i
$532$		0			0
$533$	3.79024	+	5.06317i	0.164174	+	0.219310i
$534$		0			0
$535$	−23.9779	+	23.7349i	−1.03665	+	1.02615i
$536$		0			0
$537$	−6.62222	−	1.44058i	−0.285770	−	0.0621654i
$538$		0			0
$539$	0.110530	−	0.0324546i	0.00476087	−	0.00139792i
$540$		0			0
$541$	−20.0793	+	23.1727i	−0.863275	+	0.996272i	0.136709	+	0.990611i	$0.456347\pi$
$541$	−20.0793	+	23.1727i	−0.863275	+	0.996272i	−0.999984	+	0.00566075i	$0.998198\pi$
$542$		0			0
$543$	7.61749	−	20.4233i	0.326898	−	0.876447i
$544$		0			0
$545$	13.8825	−	29.9932i	0.594661	−	1.28477i
$546$		0			0
$547$	17.9052	−	6.67831i	0.765573	−	0.285544i	0.0638173	−	0.997962i	$-0.479672\pi$
$547$	17.9052	−	6.67831i	0.765573	−	0.285544i	0.701756	+	0.712418i	$0.252400\pi$
$548$		0			0
$549$	−1.77140	−	1.13841i	−0.0756016	−	0.0485862i
$550$		0			0
$551$			1.41123i			0.0601206i
$552$		0			0
$553$	−9.13726	+	9.13726i	−0.388556	+	0.388556i
$554$		0			0
$555$	−28.9884	−	25.3782i	−1.23049	−	1.07725i
$556$		0			0
$557$	7.38513	+	19.8003i	0.312918	+	0.838966i	0.994259	+	0.107000i	$0.0341244\pi$
$557$	7.38513	+	19.8003i	0.312918	+	0.838966i	−0.681341	+	0.731966i	$0.738603\pi$
$558$		0			0
$559$	−6.47850	−	1.90226i	−0.274011	−	0.0804570i
$560$		0			0
$561$	7.36754	+	16.1327i	0.311058	+	0.681121i
$562$		0			0
$563$	−18.2807	+	1.30746i	−0.770438	+	0.0551028i	−0.451023	−	0.892512i	$-0.648941\pi$
$563$	−18.2807	+	1.30746i	−0.770438	+	0.0551028i	−0.319415	+	0.947615i	$0.603486\pi$
$564$		0			0
$565$	4.22391	−	5.58298i	0.177701	−	0.234878i
$566$		0			0
$567$	−5.94005	+	27.3059i	−0.249458	+	1.14674i
$568$		0			0
$569$	3.63710	+	25.2966i	0.152475	+	1.06049i	0.912053	+	0.410073i	$0.134497\pi$
$569$	3.63710	+	25.2966i	0.152475	+	1.06049i	−0.759578	+	0.650417i	$0.774594\pi$
$570$		0			0
$571$	39.6417	+	5.69962i	1.65895	+	0.238522i	0.907133	−	0.420844i	$-0.138266\pi$
$571$	39.6417	+	5.69962i	1.65895	+	0.238522i	0.751822	+	0.659366i	$0.229175\pi$
$572$		0			0
$573$	−0.355288	+	4.96757i	−0.0148423	+	0.207523i
$574$		0			0
$575$	−17.2606	+	16.6455i	−0.719817	+	0.694164i
$576$		0			0
$577$	2.88544	−	40.3438i	0.120123	−	1.67953i	−0.478180	−	0.878262i	$-0.658703\pi$
$577$	2.88544	−	40.3438i	0.120123	−	1.67953i	0.598302	−	0.801271i	$-0.295842\pi$
$578$		0			0
$579$	25.5768	+	3.67739i	1.06294	+	0.152827i
$580$		0			0
$581$	−5.54278	−	38.5509i	−0.229953	−	1.59936i
$582$		0			0
$583$	1.32401	−	6.08638i	0.0548350	−	0.252072i
$584$		0			0
$585$	1.11141	−	1.46902i	0.0459513	−	0.0607364i
$586$		0			0
$587$	−36.0265	+	2.57667i	−1.48697	+	0.106351i	−0.791044	−	0.611759i	$-0.790462\pi$
$587$	−36.0265	+	2.57667i	−1.48697	+	0.106351i	−0.695930	+	0.718109i	$0.745008\pi$
$588$		0			0
$589$	−0.376665	−	0.824781i	−0.0155202	−	0.0339845i
$590$		0			0
$591$	18.1438	+	5.32751i	0.746337	+	0.219144i
$592$		0			0
$593$	12.8818	+	34.5373i	0.528990	+	1.41828i	0.876865	+	0.480737i	$0.159631\pi$
$593$	12.8818	+	34.5373i	0.528990	+	1.41828i	−0.347875	+	0.937541i	$0.613097\pi$
$594$		0			0
$595$	26.2148	+	22.9500i	1.07470	+	0.940860i
$596$		0			0
$597$	13.8657	−	13.8657i	0.567485	−	0.567485i
$598$		0			0
$599$		−	12.2761i		−	0.501586i	−0.968041	−	0.250793i	$-0.919309\pi$
$599$		−	12.2761i		−	0.501586i	0.968041	−	0.250793i	$-0.0806914\pi$
$600$		0			0
$601$	−19.6215	−	12.6100i	−0.800378	−	0.514372i	0.0753612	−	0.997156i	$-0.475989\pi$
$601$	−19.6215	−	12.6100i	−0.800378	−	0.514372i	−0.875739	+	0.482785i	$0.839625\pi$
$602$		0			0
$603$	−7.76756	+	2.89715i	−0.316319	+	0.117981i
$604$		0			0
$605$	8.05709	−	17.4074i	0.327567	−	0.707711i
$606$		0			0
$607$	11.5961	−	31.0903i	0.470670	−	1.26191i	−0.457318	−	0.889303i	$-0.651190\pi$
$607$	11.5961	−	31.0903i	0.470670	−	1.26191i	0.927987	−	0.372611i	$-0.121538\pi$
$608$		0			0
$609$	−13.0891	+	15.1056i	−0.530397	+	0.612111i
$610$		0			0
$611$	7.98175	−	2.34365i	0.322907	−	0.0948141i
$612$		0			0
$613$	45.5207	+	9.90243i	1.83856	+	0.399955i	0.991344	−	0.131287i	$-0.0419109\pi$
$613$	45.5207	+	9.90243i	1.83856	+	0.399955i	0.847220	+	0.531242i	$0.178275\pi$
$614$		0			0
$615$	16.5626	−	16.3947i	0.667868	−	0.661099i
$616$		0			0
$617$	9.86505	+	13.1782i	0.397152	+	0.530533i	0.953890	−	0.300155i	$-0.0970384\pi$
$617$	9.86505	+	13.1782i	0.397152	+	0.530533i	−0.556739	+	0.830688i	$0.687947\pi$
$618$		0			0
$619$	30.9344	+	35.7002i	1.24336	+	1.43491i	0.859196	+	0.511647i	$0.170964\pi$
$619$	30.9344	+	35.7002i	1.24336	+	1.43491i	0.384162	+	0.923266i	$0.374490\pi$
$620$		0			0
$621$	17.7295	+	11.5944i	0.711462	+	0.465266i
$622$		0			0
$623$	−39.5999	−	2.83224i	−1.58654	−	0.113471i
$624$		0			0
$625$	−16.7530	+	18.5563i	−0.670120	+	0.742252i
$626$		0			0
$627$	−0.642074	+	0.857711i	−0.0256420	+	0.0342537i
$628$		0			0
$629$	28.6522	+	44.5837i	1.14244	+	1.77767i
$630$		0			0
$631$	1.66744	+	5.67878i	0.0663798	+	0.226069i	0.986002	−	0.166736i	$-0.0533229\pi$
$631$	1.66744	+	5.67878i	0.0663798	+	0.226069i	−0.919622	+	0.392805i	$0.871505\pi$
$632$		0			0
$633$	1.05770	+	14.7886i	0.0420400	+	0.587796i
$634$		0			0
$635$	5.53171	+	3.05722i	0.219519	+	0.121322i
$636$		0			0
$637$	0.0414407	+	0.0758929i	0.00164194	+	0.00300699i
$638$		0			0
$639$	1.24927	+	0.570523i	0.0494204	+	0.0225695i
$640$		0			0
$641$	21.6896	−	33.7497i	0.856689	−	1.33303i	−0.0849412	−	0.996386i	$-0.527070\pi$
$641$	21.6896	−	33.7497i	0.856689	−	1.33303i	0.941630	−	0.336648i	$-0.109293\pi$
$642$		0			0
$643$	24.7767	+	24.7767i	0.977098	+	0.977098i	0.999744	−	0.0226457i	$-0.00720897\pi$
$643$	24.7767	+	24.7767i	0.977098	+	0.977098i	−0.0226457	+	0.999744i	$0.507209\pi$
$644$		0			0
$645$	−3.66605	+	24.6076i	−0.144351	+	0.968923i
$646$		0			0
$647$	−4.06500	−	18.6865i	−0.159812	−	0.734643i	−0.985384	−	0.170347i	$-0.945511\pi$
$647$	−4.06500	−	18.6865i	−0.159812	−	0.734643i	0.825573	−	0.564296i	$-0.190852\pi$
$648$		0			0
$649$	−7.55262	+	16.5379i	−0.296466	+	0.649171i
$650$		0			0
$651$	3.61803	−	12.3219i	0.141802	−	0.482932i
$652$		0			0
$653$	−28.0274	−	10.4537i	−1.09680	−	0.409085i	−0.265049	−	0.964235i	$-0.585388\pi$
$653$	−28.0274	−	10.4537i	−1.09680	−	0.409085i	−0.831750	+	0.555150i	$0.812661\pi$
$654$		0			0
$655$	23.6096	+	27.5290i	0.922504	+	1.07565i
$656$		0			0
$657$	−0.0377729	−	0.0206256i	−0.00147366	−	0.000804681i
$658$		0			0
$659$	21.4131	−	13.7614i	0.834136	−	0.536067i	−0.0524538	−	0.998623i	$-0.516704\pi$
$659$	21.4131	−	13.7614i	0.834136	−	0.536067i	0.886590	+	0.462557i	$0.153068\pi$
$660$		0			0
$661$	−0.246259	+	0.0354067i	−0.00957836	+	0.00137716i	−0.147102	−	0.989121i	$-0.546995\pi$
$661$	−0.246259	+	0.0354067i	−0.00957836	+	0.00137716i	0.137524	+	0.990498i	$0.456086\pi$
$662$		0			0
$663$	−10.6574	+	7.97802i	−0.413899	+	0.309841i
$664$		0			0
$665$	−0.457878	+	2.05440i	−0.0177557	+	0.0796662i
$666$		0			0
$667$	8.93616	+	16.6794i	0.346010	+	0.645829i
$668$		0			0
$669$	27.3650	−	23.7119i	1.05799	−	0.916755i
$670$		0			0
$671$	−0.661256	+	4.59914i	−0.0255275	+	0.177548i
$672$		0			0
$673$	1.62327	+	1.21516i	0.0625725	+	0.0468412i	0.630106	−	0.776509i	$-0.283011\pi$
$673$	1.62327	+	1.21516i	0.0625725	+	0.0468412i	−0.567534	+	0.823350i	$0.692102\pi$
$674$		0			0
$675$	19.2756	+	10.7816i	0.741916	+	0.414983i
$676$		0			0
$677$	−22.8011	+	41.7572i	−0.876319	+	1.60486i	−0.0825932	+	0.996583i	$0.526320\pi$
$677$	−22.8011	+	41.7572i	−0.876319	+	1.60486i	−0.793726	+	0.608275i	$0.791862\pi$
$678$		0			0
$679$	−17.6193	−	15.2672i	−0.676167	−	0.585902i
$680$		0			0
$681$	17.5603	−	8.01953i	0.672913	−	0.307309i
$682$		0			0
$683$	0.618416	−	0.337681i	0.0236630	−	0.0129210i	−0.467374	−	0.884060i	$-0.654800\pi$
$683$	0.618416	−	0.337681i	0.0236630	−	0.0129210i	0.491037	+	0.871139i	$0.336618\pi$
$684$		0			0
$685$	23.9730	−	5.08726i	0.915960	−	0.194374i
$686$		0			0
$687$	27.1975	−	5.91645i	1.03765	−	0.225727i
$688$		0			0
$689$	4.67548			0.178122
$690$		0			0
$691$	23.7061			0.901824			0.450912	−	0.892569i	$-0.351099\pi$
$691$	23.7061			0.901824			0.450912	+	0.892569i	$0.351099\pi$
$692$		0			0
$693$	−2.82226	+	0.613945i	−0.107209	+	0.0233218i
$694$		0			0
$695$	−12.5209	+	19.2664i	−0.474945	+	0.730818i
$696$		0			0
$697$	−28.1355	+	15.3631i	−1.06571	+	0.581921i
$698$		0			0
$699$	−15.4101	+	7.03756i	−0.582864	+	0.266185i
$700$		0			0
$701$	−25.3805	−	21.9923i	−0.958607	−	0.830638i	0.0270093	−	0.999635i	$-0.491402\pi$
$701$	−25.3805	−	21.9923i	−0.958607	−	0.830638i	−0.985617	+	0.168997i	$0.945947\pi$
$702$		0			0
$703$	−1.53436	+	2.80997i	−0.0578695	+	0.105980i
$704$		0			0
$705$	−12.5912	−	27.9466i	−0.474210	−	1.05253i
$706$		0			0
$707$	1.21058	+	0.906230i	0.0455286	+	0.0340823i
$708$		0			0
$709$	0.397071	−	2.76169i	0.0149123	−	0.103717i	−0.981006	−	0.193978i	$-0.937861\pi$
$709$	0.397071	−	2.76169i	0.0149123	−	0.103717i	0.995918	+	0.0902607i	$0.0287700\pi$
$710$		0			0
$711$	−2.61699	+	2.26763i	−0.0981448	+	0.0850429i
$712$		0			0
$713$	−9.67445	−	7.36300i	−0.362311	−	0.275747i
$714$		0			0
$715$	−3.96744	−	0.884250i	−0.148374	−	0.0330691i
$716$		0			0
$717$	−14.4865	+	10.8445i	−0.541009	+	0.404994i
$718$		0			0
$719$	−7.74420	+	1.11345i	−0.288810	+	0.0415246i	−0.285197	−	0.958469i	$-0.592059\pi$
$719$	−7.74420	+	1.11345i	−0.288810	+	0.0415246i	−0.00361274	+	0.999993i	$0.501150\pi$
$720$		0			0
$721$	18.4653	−	11.8669i	0.687683	−	0.441947i
$722$		0			0
$723$	47.3630	+	25.8621i	1.76145	+	0.961823i
$724$		0			0
$725$	10.4961	+	16.7040i	0.389817	+	0.620372i
$726$		0			0
$727$	28.8369	+	10.7556i	1.06950	+	0.398903i	0.821708	−	0.569909i	$-0.193022\pi$
$727$	28.8369	+	10.7556i	1.06950	+	0.398903i	0.247794	+	0.968813i	$0.420294\pi$
$728$		0			0
$729$	5.07668	−	17.2896i	0.188025	−	0.640355i
$730$		0			0
$731$	14.2166	−	31.1299i	0.525819	−	1.15138i
$732$		0			0
$733$	−3.73712	−	17.1793i	−0.138034	−	0.634531i	−0.993224	−	0.116217i	$-0.962923\pi$
$733$	−3.73712	−	17.1793i	−0.138034	−	0.634531i	0.855190	−	0.518314i	$-0.173440\pi$
$734$		0			0
$735$	0.256035	−	0.189638i	0.00944400	−	0.00699492i
$736$		0			0
$737$	12.9355	+	12.9355i	0.476484	+	0.476484i
$738$		0			0
$739$	−9.61508	+	14.9613i	−0.353696	+	0.550362i	−0.971822	−	0.235717i	$-0.924256\pi$
$739$	−9.61508	+	14.9613i	−0.353696	+	0.550362i	0.618125	+	0.786080i	$0.287892\pi$
$740$		0			0
$741$	−0.731560	−	0.334092i	−0.0268745	−	0.0122732i
$742$		0			0
$743$	−5.38505	−	9.86199i	−0.197558	−	0.361801i	0.760055	−	0.649859i	$-0.225172\pi$
$743$	−5.38505	−	9.86199i	−0.197558	−	0.361801i	−0.957613	+	0.288058i	$0.906990\pi$
$744$		0			0
$745$	31.9068	−	9.19244i	1.16898	−	0.336785i
$746$		0			0
$747$	−0.744558	−	10.4103i	−0.0272420	−	0.380892i
$748$		0			0
$749$	11.1871	+	38.0998i	0.408768	+	1.39214i
$750$		0			0
$751$	−13.3203	−	20.7268i	−0.486066	−	0.756333i	0.508431	−	0.861103i	$-0.330226\pi$
$751$	−13.3203	−	20.7268i	−0.486066	−	0.756333i	−0.994497	+	0.104770i	$0.966589\pi$
$752$		0			0
$753$	25.2727	−	33.7604i	0.920989	−	1.23030i
$754$		0			0
$755$	−19.9769	−	5.97642i	−0.727033	−	0.217504i
$756$		0			0
$757$	−0.498568	−	0.0356583i	−0.0181208	−	0.00129602i	0.0622759	−	0.998059i	$-0.480164\pi$
$757$	−0.498568	−	0.0356583i	−0.0181208	−	0.00129602i	−0.0803966	+	0.996763i	$0.525619\pi$
$758$		0			0
$759$	−2.15753	+	14.2030i	−0.0783133	+	0.515537i
$760$		0			0
$761$	23.5616	+	27.1916i	0.854108	+	0.985693i	0.999993	−	0.00360849i	$-0.00114862\pi$
$761$	23.5616	+	27.1916i	0.854108	+	0.985693i	−0.145886	+	0.989301i	$0.546603\pi$
$762$		0			0
$763$	−23.3108	−	31.1396i	−0.843909	−	1.12733i
$764$		0			0
$765$	6.56825	+	6.63550i	0.237476	+	0.239907i
$766$		0			0
$767$	−13.3353	−	2.90091i	−0.481509	−	0.104746i
$768$		0			0
$769$	−38.7314	+	11.3726i	−1.39669	+	0.410105i	−0.891546	−	0.452931i	$-0.850379\pi$
$769$	−38.7314	+	11.3726i	−1.39669	+	0.410105i	−0.505143	+	0.863036i	$0.668560\pi$
$770$		0			0
$771$	−31.0817	+	35.8702i	−1.11938	+	1.29183i
$772$		0			0
$773$	8.23901	−	22.0896i	0.296337	−	0.794509i	−0.700397	−	0.713753i	$-0.746994\pi$
$773$	8.23901	−	22.0896i	0.296337	−	0.794509i	0.996734	−	0.0807560i	$-0.0257334\pi$
$774$		0			0
$775$	−10.5927	−	6.96101i	−0.380502	−	0.250047i
$776$		0			0
$777$	−42.4858	+	15.8464i	−1.52417	+	0.568486i
$778$		0			0
$779$	−1.62916	−	1.04700i	−0.0583706	−	0.0375125i
$780$		0			0
$781$		−	3.03054i		−	0.108441i
$782$		0			0
$783$	12.3238	−	12.3238i	0.440416	−	0.440416i
$784$		0			0
$785$	−2.45738	−	37.0065i	−0.0877077	−	1.32082i
$786$		0			0
$787$	−1.01669	−	2.72586i	−0.0362412	−	0.0971665i	0.917569	−	0.397577i	$-0.130149\pi$
$787$	−1.01669	−	2.72586i	−0.0362412	−	0.0971665i	−0.953810	+	0.300411i	$0.902876\pi$
$788$		0			0
$789$	−33.7601	−	9.91286i	−1.20189	−	0.352907i
$790$		0			0
$791$	−3.42283	−	7.49495i	−0.121702	−	0.266490i
$792$		0			0
$793$	−3.47887	+	0.248814i	−0.123538	+	0.00883564i
$794$		0			0
$795$	−2.36489	−	17.0647i	−0.0838739	−	0.605223i
$796$		0			0
$797$	6.19429	−	28.4747i	0.219413	−	1.00863i	−0.727243	−	0.686380i	$-0.759199\pi$
$797$	6.19429	−	28.4747i	0.219413	−	1.00863i	0.946656	−	0.322246i	$-0.104438\pi$
$798$		0			0
$799$	6.00049	+	41.7343i	0.212282	+	1.47645i
$800$		0			0
$801$	−10.5306	−	1.51407i	−0.372080	−	0.0534970i
$802$		0			0
$803$	−0.00677489	+	0.0947254i	−0.000239081	+	0.00334279i
$804$		0			0
$805$	7.59711	+	27.1803i	0.267763	+	0.957981i
$806$		0			0
$807$	0.687669	−	9.61487i	0.0242071	−	0.338459i
$808$		0			0
$809$	−3.06094	−	0.440096i	−0.107617	−	0.0154730i	0.0882960	−	0.996094i	$-0.471858\pi$
$809$	−3.06094	−	0.440096i	−0.107617	−	0.0154730i	−0.195913	+	0.980621i	$0.562767\pi$
$810$		0			0
$811$	−6.65768	−	46.3052i	−0.233783	−	1.62599i	−0.681499	−	0.731819i	$-0.738672\pi$
$811$	−6.65768	−	46.3052i	−0.233783	−	1.62599i	0.447716	−	0.894176i	$-0.352237\pi$
$812$		0			0
$813$	−11.2276	+	51.6125i	−0.393770	+	1.81013i
$814$		0			0
$815$	−24.2312	−	18.3326i	−0.848783	−	0.642162i
$816$		0			0
$817$	2.06216	−	0.147488i	0.0721457	−	0.00515996i
$818$		0			0
$819$	−0.900629	−	1.97210i	−0.0314705	−	0.0689108i
$820$		0			0
$821$	18.1031	+	5.31554i	0.631802	+	0.185514i	0.581926	−	0.813242i	$-0.302299\pi$
$821$	18.1031	+	5.31554i	0.631802	+	0.185514i	0.0498756	+	0.998755i	$0.484117\pi$
$822$		0			0
$823$	−4.12328	−	11.0549i	−0.143728	−	0.385351i	0.845060	−	0.534671i	$-0.179564\pi$
$823$	−4.12328	−	11.0549i	−0.143728	−	0.385351i	−0.988789	+	0.149320i	$0.952292\pi$
$824$		0			0
$825$	−1.22060	+	14.9277i	−0.0424960	+	0.519717i
$826$		0			0
$827$	−9.12302	+	9.12302i	−0.317239	+	0.317239i	−0.847706	−	0.530467i	$-0.822017\pi$
$827$	−9.12302	+	9.12302i	−0.317239	+	0.317239i	0.530467	+	0.847706i	$0.322017\pi$
$828$		0			0
$829$		−	39.3056i		−	1.36514i	−0.730819	−	0.682571i	$-0.760862\pi$
$829$		−	39.3056i		−	1.36514i	0.730819	−	0.682571i	$-0.239138\pi$
$830$		0			0
$831$	1.63095	+	1.04815i	0.0565771	+	0.0363599i
$832$		0			0
$833$	−0.410641	+	0.153161i	−0.0142279	+	0.00530671i
$834$		0			0
$835$	−11.6751	+	4.28699i	−0.404034	+	0.148357i
$836$		0			0
$837$	−3.91323	+	10.4918i	−0.135261	+	0.362649i
$838$		0			0
$839$	15.4138	−	17.7885i	0.532145	−	0.614128i	−0.424485	−	0.905435i	$-0.639545\pi$
$839$	15.4138	−	17.7885i	0.532145	−	0.614128i	0.956629	+	0.291307i	$0.0940902\pi$
$840$		0			0
$841$	−12.8882	+	3.78431i	−0.444420	+	0.130493i
$842$		0			0
$843$	−57.6036	−	12.5309i	−1.98397	−	0.431587i
$844$		0			0
$845$	−0.132512	+	26.0174i	−0.00455855	+	0.895025i
$846$		0			0
$847$	−13.5291	−	18.0727i	−0.464865	−	0.620987i
$848$		0			0
$849$	−9.76806	−	11.2729i	−0.335239	−	0.386886i
$850$		0			0
$851$	−0.341455	+	42.9269i	−0.0117049	+	1.47152i
$852$		0			0
$853$	57.4908	+	4.11183i	1.96845	+	0.140786i	0.995804	−	0.0915120i	$-0.0291700\pi$
$853$	57.4908	+	4.11183i	1.96845	+	0.140786i	0.972645	+	0.232298i	$0.0746245\pi$
$854$		0			0
$855$	−0.161661	+	0.540370i	−0.00552869	+	0.0184803i
$856$		0			0
$857$	14.9160	−	19.9255i	0.509522	−	0.680641i	−0.469841	−	0.882751i	$-0.655689\pi$
$857$	14.9160	−	19.9255i	0.509522	−	0.680641i	0.979363	+	0.202110i	$0.0647797\pi$
$858$		0			0
$859$	−5.68526	−	8.84643i	−0.193978	−	0.301836i	0.730616	−	0.682788i	$-0.239233\pi$
$859$	−5.68526	−	8.84643i	−0.193978	−	0.301836i	−0.924595	+	0.380952i	$0.875596\pi$
$860$		0			0
$861$	−7.72742	−	26.3172i	−0.263350	−	0.896887i
$862$		0			0
$863$	−3.60308	−	50.3776i	−0.122650	−	1.71487i	−0.570945	−	0.820989i	$-0.693423\pi$
$863$	−3.60308	−	50.3776i	−0.122650	−	1.71487i	0.448294	−	0.893886i	$-0.352032\pi$
$864$		0			0
$865$	9.14575	−	16.5483i	0.310965	−	0.562658i
$866$		0			0
$867$	−16.6550	−	30.5014i	−0.565635	−	1.03588i
$868$		0			0
$869$	6.95055	+	3.17421i	0.235781	+	0.107678i
$870$		0			0
$871$	−7.42392	+	11.5518i	−0.251550	+	0.391419i
$872$		0			0
$873$	−4.41763	−	4.41763i	−0.149514	−	0.149514i
$874$		0			0
$875$	9.86007	+	27.7223i	0.333331	+	0.937185i
$876$		0			0
$877$	10.7326	+	49.3369i	0.362414	+	1.66599i	0.692026	+	0.721872i	$0.256718\pi$
$877$	10.7326	+	49.3369i	0.362414	+	1.66599i	−0.329613	+	0.944116i	$0.606918\pi$
$878$		0			0
$879$	16.4509	−	36.0224i	0.554874	−	1.21501i
$880$		0			0
$881$	−7.94512	+	27.0586i	−0.267678	+	0.911628i	0.710472	+	0.703726i	$0.248482\pi$
$881$	−7.94512	+	27.0586i	−0.267678	+	0.911628i	−0.978150	+	0.207902i	$0.933337\pi$
$882$		0			0
$883$	23.4149	+	8.73329i	0.787973	+	0.293899i	0.711053	−	0.703138i	$-0.248219\pi$
$883$	23.4149	+	8.73329i	0.787973	+	0.293899i	0.0769202	+	0.997037i	$0.475491\pi$
$884$		0			0
$885$	−3.84276	+	50.1388i	−0.129173	+	1.68540i
$886$		0			0
$887$	15.8019	+	8.62850i	0.530577	+	0.289717i	0.722120	−	0.691767i	$-0.243168\pi$
$887$	15.8019	+	8.62850i	0.530577	+	0.289717i	−0.191544	+	0.981484i	$0.561349\pi$
$888$		0			0
$889$	6.25779	−	4.02164i	0.209880	−	0.134881i
$890$		0			0
$891$	16.3560	−	2.35163i	0.547946	−	0.0787827i
$892$		0			0
$893$	−2.03909	+	1.52645i	−0.0682357	+	0.0510806i
$894$		0			0
$895$	4.22249	+	6.64448i	0.141142	+	0.222101i
$896$		0			0
$897$	−10.7618	+	0.683710i	−0.359328	+	0.0228284i
$898$		0			0
$899$	−7.55922	+	6.55010i	−0.252114	+	0.218458i
$900$		0			0
$901$	−3.37253	+	23.4565i	−0.112355	+	0.781449i
$902$		0			0
$903$	23.4409	+	17.5477i	0.780066	+	0.583950i
$904$		0			0
$905$	−23.0864	+	10.4014i	−0.767417	+	0.345755i
$906$		0			0
$907$	12.0912	−	22.1434i	0.401481	−	0.735258i	−0.596234	−	0.802810i	$-0.703337\pi$
$907$	12.0912	−	22.1434i	0.401481	−	0.735258i	0.997716	+	0.0675523i	$0.0215190\pi$
$908$		0			0
$909$	0.306254	+	0.265370i	0.0101578	+	0.00880178i
$910$		0			0
$911$	−40.3342	+	18.4200i	−1.33633	+	0.610282i	−0.950050	−	0.312099i	$-0.898968\pi$
$911$	−40.3342	+	18.4200i	−1.33633	+	0.610282i	−0.386281	+	0.922381i	$0.626241\pi$
$912$		0			0
$913$	−20.2132	+	11.0372i	−0.668960	+	0.365280i
$914$		0			0
$915$	2.66776	+	12.5714i	0.0881935	+	0.415599i
$916$		0			0
$917$	41.7082	−	9.07306i	1.37733	−	0.299619i
$918$		0			0
$919$	17.3396			0.571980			0.285990	−	0.958233i	$-0.407678\pi$
$919$	17.3396			0.571980			0.285990	+	0.958233i	$0.407678\pi$
$920$		0			0
$921$	36.2216			1.19354
$922$		0			0
$923$	2.22283	−	0.483548i	0.0731655	−	0.0159162i
$924$		0			0
$925$	2.73795	+	44.6720i	0.0900233	+	1.46881i
$926$		0			0
$927$	5.16248	−	2.81892i	0.169558	−	0.0925856i
$928$		0			0
$929$	16.7168	−	7.63431i	0.548461	−	0.250474i	−0.121857	−	0.992548i	$-0.538885\pi$
$929$	16.7168	−	7.63431i	0.548461	−	0.250474i	0.670318	+	0.742074i	$0.266158\pi$
$930$		0			0
$931$	−0.0200097	−	0.0173385i	−0.000655791	−	0.000568246i
$932$		0			0
$933$	29.7656	−	54.5117i	0.974484	−	1.78463i
$934$		0			0
$935$	7.29801	−	19.2665i	0.238671	−	0.630081i
$936$		0			0
$937$	−8.56260	−	6.40989i	−0.279728	−	0.209402i	0.450196	−	0.892930i	$-0.351354\pi$
$937$	−8.56260	−	6.40989i	−0.279728	−	0.209402i	−0.729925	+	0.683528i	$0.760445\pi$
$938$		0			0
$939$	−0.239787	+	1.66775i	−0.00782515	+	0.0544251i
$940$		0			0
$941$	−22.6831	+	19.6550i	−0.739449	+	0.640736i	−0.940870	−	0.338769i	$-0.889990\pi$
$941$	−22.6831	+	19.6550i	−0.739449	+	0.640736i	0.201421	+	0.979505i	$0.435444\pi$
$942$		0			0
$943$	−25.8848	−	2.05838i	−0.842924	−	0.0670302i
$944$		0			0
$945$	21.9388	−	13.9418i	0.713668	−	0.453527i
$946$		0			0
$947$	−17.7699	+	13.3024i	−0.577444	+	0.432269i	−0.847667	−	0.530529i	$-0.821993\pi$
$947$	−17.7699	+	13.3024i	−0.577444	+	0.432269i	0.270223	+	0.962798i	$0.412902\pi$
$948$		0			0
$949$	−0.0705599	+	0.0101450i	−0.00229047	+	0.000329320i
$950$		0			0
$951$	−11.1199	+	7.14632i	−0.360587	+	0.231735i
$952$		0			0
$953$	30.6433	+	16.7325i	0.992633	+	0.542018i	0.891580	−	0.452863i	$-0.149597\pi$
$953$	30.6433	+	16.7325i	0.992633	+	0.542018i	0.101052	+	0.994881i	$0.467779\pi$
$954$		0			0
$955$	4.39151	−	3.76627i	0.142106	−	0.121874i
$956$		0			0
$957$	11.0739	+	4.13034i	0.357967	+	0.133515i
$958$		0			0
$959$	8.12604	−	27.6748i	0.262404	−	0.893665i
$960$		0			0
$961$	−10.2082	+	22.3529i	−0.329297	+	0.721060i
$962$		0			0
$963$	2.26186	+	10.3976i	0.0728875	+	0.335058i
$964$		0			0
$965$	−17.8659	−	24.1211i	−0.575122	−	0.776486i
$966$		0			0
$967$	−18.6580	−	18.6580i	−0.600000	−	0.600000i	0.340313	−	0.940312i	$-0.389467\pi$
$967$	−18.6580	−	18.6580i	−0.600000	−	0.600000i	−0.940312	+	0.340313i	$0.889467\pi$
$968$		0			0
$969$	2.20380	−	3.42918i	0.0707963	−	0.110161i
$970$		0			0
$971$	−46.7620	−	21.3555i	−1.50066	−	0.685330i	−0.515491	−	0.856895i	$-0.672391\pi$
$971$	−46.7620	−	21.3555i	−1.50066	−	0.685330i	−0.985173	+	0.171564i	$0.945118\pi$
$972$		0			0
$973$	12.9605	+	23.7353i	0.415494	+	0.760920i
$974$		0			0
$975$	−11.1439	+	1.48656i	−0.356891	+	0.0476079i
$976$		0			0
$977$	1.53638	+	21.4814i	0.0491532	+	0.687252i	0.960970	+	0.276654i	$0.0892255\pi$
$977$	1.53638	+	21.4814i	0.0491532	+	0.687252i	−0.911816	+	0.410598i	$0.865320\pi$
$978$		0			0
$979$	6.61396	+	22.5251i	0.211383	+	0.719905i
$980$		0			0
$981$	−5.63549	−	8.76900i	−0.179927	−	0.279973i
$982$		0			0
$983$	−32.5679	+	43.5057i	−1.03876	+	1.38762i	−0.120007	+	0.992773i	$0.538292\pi$
$983$	−32.5679	+	43.5057i	−1.03876	+	1.38762i	−0.918749	+	0.394842i	$0.870799\pi$
$984$		0			0
$985$	−10.4292	−	19.3331i	−0.332301	−	0.616002i
$986$		0			0
$987$	−35.9838	−	2.57361i	−1.14538	−	0.0819190i
$988$		0			0
$989$	23.4388	−	14.8011i	0.745309	−	0.470647i
$990$		0			0
$991$	−22.8572	−	26.3786i	−0.726082	−	0.837943i	0.265942	−	0.963989i	$-0.414317\pi$
$991$	−22.8572	−	26.3786i	−0.726082	−	0.837943i	−0.992024	+	0.126045i	$0.959771\pi$
$992$		0			0
$993$	−17.0181	−	22.7336i	−0.540054	−	0.721427i
$994$		0			0
$995$	−22.7786	−	0.116016i	−0.722132	−	0.00367796i
$996$		0			0
$997$	7.26012	+	1.57934i	0.229930	+	0.0500183i	0.326054	−	0.945351i	$-0.394281\pi$
$997$	7.26012	+	1.57934i	0.229930	+	0.0500183i	−0.0961238	+	0.995369i	$0.530644\pi$
$998$		0			0
$999$	37.9374	−	11.1394i	1.20029	−	0.352436i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.x.a.217.3	yes	240
5.3	odd	4	inner	460.2.x.a.33.3	✓	240
23.7	odd	22	inner	460.2.x.a.237.3	yes	240
115.53	even	44	inner	460.2.x.a.53.3	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.x.a.33.3	✓	240	5.3	odd	4	inner
460.2.x.a.53.3	yes	240	115.53	even	44	inner
460.2.x.a.217.3	yes	240	1.1	even	1	trivial
460.2.x.a.237.3	yes	240	23.7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.x (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.88091 + 0.409167i) q^{3} +(1.87492 + 1.21847i) q^{5} +(2.30981 - 1.26125i) q^{7} +(0.641504 - 0.292965i) q^{9} +(-1.17609 - 1.01909i) q^{11} +(0.559823 - 1.02524i) q^{13} +(-4.02511 - 1.52469i) q^{15} +(4.73973 + 3.54811i) q^{17} +(-0.0509022 + 0.354033i) q^{19} +(-3.82848 + 3.31740i) q^{21} +(1.64018 + 4.50664i) q^{23} +(2.03064 + 4.56908i) q^{25} +(3.53614 - 2.64712i) q^{27} +(3.90544 - 0.561517i) q^{29} +(-2.13262 + 1.37055i) q^{31} +(2.62910 + 1.43559i) q^{33} +(5.86751 + 0.449701i) q^{35} +(8.38679 + 3.12811i) q^{37} +(-0.633482 + 2.15744i) q^{39} +(-2.24922 + 4.92510i) q^{41} +(-1.22867 - 5.64811i) q^{43} +(1.55974 + 0.232371i) q^{45} +(5.03561 + 5.03561i) q^{47} +(-0.0400207 + 0.0622734i) q^{49} +(-10.3668 - 4.73434i) q^{51} +(1.91822 + 3.51295i) q^{53} +(-0.963341 - 3.34374i) q^{55} +(-0.0491159 - 0.686731i) q^{57} +(-3.29147 - 11.2097i) q^{59} +(-1.61423 - 2.51179i) q^{61} +(1.11225 - 1.48579i) q^{63} +(2.29885 - 1.24011i) q^{65} +(-11.7254 - 0.838615i) q^{67} +(-4.92899 - 7.80548i) q^{69} +(1.27528 + 1.47175i) q^{71} +(-0.0365712 - 0.0488535i) q^{73} +(-5.68896 - 7.76315i) q^{75} +(-4.00187 - 0.870554i) q^{77} +(-4.71121 + 1.38334i) q^{79} +(-6.95354 + 8.02481i) q^{81} +(5.17177 - 13.8661i) q^{83} +(4.56331 + 12.4277i) q^{85} +(-7.11601 + 2.65414i) q^{87} +(-12.6908 - 8.15588i) q^{89} -3.07419i q^{91} +(3.45048 - 3.45048i) q^{93} +(-0.526817 + 0.601759i) q^{95} +(-3.09580 - 8.30017i) q^{97} +(-1.05302 - 0.309196i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 4 q^{3} - 8 q^{13} + 46 q^{23} - 24 q^{25} - 20 q^{27} + 12 q^{31} + 22 q^{33} + 4 q^{35} - 88 q^{37} + 12 q^{41} - 92 q^{47} - 36 q^{55} - 88 q^{57} + 88 q^{61} + 168 q^{71} + 20 q^{73} + 12 q^{75}+ \cdots - 66 q^{97}+O(q^{100}) \) 240 * q + 4 * q^3 - 8 * q^13 + 46 * q^23 - 24 * q^25 - 20 * q^27 + 12 * q^31 + 22 * q^33 + 4 * q^35 - 88 * q^37 + 12 * q^41 - 92 * q^47 - 36 * q^55 - 88 * q^57 + 88 * q^61 + 168 * q^71 + 20 * q^73 + 12 * q^75 + 36 * q^77 + 200 * q^81 - 28 * q^85 + 16 * q^87 - 88 * q^93 - 86 * q^95 - 66 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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