LMFDB - Embedded newform 630.2.ce.c.53.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(53,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.ce (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	630.53
Dual form			630.2.ce.c.107.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.923861 + 2.03629i) q^{5} +(-2.56861 - 0.634242i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.20602 + 0.365351i) q^{10} +(-4.28438 - 2.47359i) q^{11} +(-4.34735 - 4.34735i) q^{13} +(1.27744 - 2.31693i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.25035 - 1.13888i) q^{17} +(-3.22874 + 1.86412i) q^{19} +(0.218058 - 2.22541i) q^{20} +(3.49819 - 3.49819i) q^{22} +(-1.87844 - 0.503327i) q^{23} +(-3.29296 + 3.76250i) q^{25} +(5.32440 - 3.07404i) q^{26} +(1.90736 + 1.83357i) q^{28} +3.56555 q^{29} +(-0.272207 + 0.471476i) q^{31} +(-0.965926 + 0.258819i) q^{32} +4.40029i q^{34} +(-1.08153 - 5.81638i) q^{35} +(-1.62530 - 0.435499i) q^{37} +(-0.964938 - 3.60120i) q^{38} +(2.09314 + 0.786607i) q^{40} -0.268424i q^{41} +(-8.39666 - 8.39666i) q^{43} +(2.47359 + 4.28438i) q^{44} +(0.972352 - 1.68416i) q^{46} +(-0.240094 + 0.896043i) q^{47} +(6.19547 + 3.25824i) q^{49} +(-2.78202 - 4.15456i) q^{50} +(1.59124 + 5.93859i) q^{52} +(-2.06426 - 7.70392i) q^{53} +(1.07877 - 11.0095i) q^{55} +(-2.26476 + 1.36780i) q^{56} +(-0.922831 + 3.44405i) q^{58} +(-4.90077 + 8.48838i) q^{59} +(-5.71103 - 9.89179i) q^{61} +(-0.384959 - 0.384959i) q^{62} -1.00000i q^{64} +(4.83612 - 12.8688i) q^{65} +(-0.0109452 - 0.0408482i) q^{67} +(-4.25035 - 1.13888i) q^{68} +(5.89811 + 0.460709i) q^{70} +16.3109i q^{71} +(8.42396 - 2.25719i) q^{73} +(0.841319 - 1.45721i) q^{74} +3.72823 q^{76} +(9.43604 + 9.07102i) q^{77} +(-6.93305 + 4.00280i) q^{79} +(-1.30155 + 1.81823i) q^{80} +(0.259278 + 0.0694733i) q^{82} +(1.30281 - 1.30281i) q^{83} +(6.24583 + 7.60279i) q^{85} +(10.2838 - 5.93734i) q^{86} +(-4.77861 + 1.28042i) q^{88} +(0.229324 + 0.397201i) q^{89} +(8.40936 + 13.9239i) q^{91} +(1.37511 + 1.37511i) q^{92} +(-0.803371 - 0.463826i) q^{94} +(-6.77880 - 4.85248i) q^{95} +(-10.6198 + 10.6198i) q^{97} +(-4.75072 + 5.14107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85}+ \cdots - 40 q^{97}+O(q^{100}) $ 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$		0			0
$3$		0			0
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	0.923861	+	2.03629i	0.413163	+	0.910657i
$5$	0.923861	+	2.03629i	0.413163	+	0.910657i
$6$		0			0
$7$	−2.56861	−	0.634242i	−0.970842	−	0.239721i
$7$	−2.56861	−	0.634242i	−0.970842	−	0.239721i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		0			0
$10$	−2.20602	+	0.365351i	−0.697604	+	0.115534i
$11$	−4.28438	−	2.47359i	−1.29179	−	0.745816i	−0.312819	−	0.949813i	$-0.601273\pi$
$11$	−4.28438	−	2.47359i	−1.29179	−	0.745816i	−0.978971	+	0.203997i	$0.934607\pi$
$12$		0			0
$13$	−4.34735	−	4.34735i	−1.20574	−	1.20574i	−0.972394	−	0.233344i	$-0.925033\pi$
$13$	−4.34735	−	4.34735i	−1.20574	−	1.20574i	−0.233344	−	0.972394i	$-0.574967\pi$
$14$	1.27744	−	2.31693i	0.341409	−	0.619225i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	4.25035	−	1.13888i	1.03086	−	0.276219i	0.296541	−	0.955020i	$-0.404167\pi$
$17$	4.25035	−	1.13888i	1.03086	−	0.276219i	0.734322	+	0.678802i	$0.237500\pi$
$18$		0			0
$19$	−3.22874	+	1.86412i	−0.740725	+	0.427658i	−0.822333	−	0.569007i	$-0.807328\pi$
$19$	−3.22874	+	1.86412i	−0.740725	+	0.427658i	0.0816079	+	0.996665i	$0.473994\pi$
$20$	0.218058	−	2.22541i	0.0487593	−	0.497617i
$21$		0			0
$22$	3.49819	−	3.49819i	0.745816	−	0.745816i
$23$	−1.87844	−	0.503327i	−0.391682	−	0.104951i	0.0576026	−	0.998340i	$-0.481654\pi$
$23$	−1.87844	−	0.503327i	−0.391682	−	0.104951i	−0.449284	+	0.893389i	$0.648321\pi$
$24$		0			0
$25$	−3.29296	+	3.76250i	−0.658592	+	0.752500i
$26$	5.32440	−	3.07404i	1.04420	−	0.602869i
$27$		0			0
$28$	1.90736	+	1.83357i	0.360457	+	0.346513i
$29$	3.56555			0.662105			0.331053	−	0.943612i	$-0.392596\pi$
$29$	3.56555			0.662105			0.331053	+	0.943612i	$0.392596\pi$
$30$		0			0
$31$	−0.272207	+	0.471476i	−0.0488898	+	0.0846796i	−0.889435	−	0.457062i	$-0.848902\pi$
$31$	−0.272207	+	0.471476i	−0.0488898	+	0.0846796i	0.840545	+	0.541742i	$0.182235\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$		0			0
$34$			4.40029i			0.754644i
$35$	−1.08153	−	5.81638i	−0.182813	−	0.983148i
$36$		0			0
$37$	−1.62530	−	0.435499i	−0.267198	−	0.0715955i	0.122732	−	0.992440i	$-0.460834\pi$
$37$	−1.62530	−	0.435499i	−0.267198	−	0.0715955i	−0.389931	+	0.920844i	$0.627501\pi$
$38$	−0.964938	−	3.60120i	−0.156534	−	0.584191i
$39$		0			0
$40$	2.09314	+	0.786607i	0.330955	+	0.124373i
$41$		−	0.268424i		−	0.0419208i	−0.999780	−	0.0209604i	$-0.993328\pi$
$41$		−	0.268424i		−	0.0419208i	0.999780	−	0.0209604i	$-0.00667239\pi$
$42$		0			0
$43$	−8.39666	−	8.39666i	−1.28048	−	1.28048i	−0.940395	−	0.340084i	$-0.889545\pi$
$43$	−8.39666	−	8.39666i	−1.28048	−	1.28048i	−0.340084	−	0.940395i	$-0.610455\pi$
$44$	2.47359	+	4.28438i	0.372908	+	0.645895i
$45$		0			0
$46$	0.972352	−	1.68416i	0.143366	−	0.248316i
$47$	−0.240094	+	0.896043i	−0.0350213	+	0.130701i	−0.981223	−	0.192875i	$-0.938219\pi$
$47$	−0.240094	+	0.896043i	−0.0350213	+	0.130701i	0.946202	+	0.323577i	$0.104885\pi$
$48$		0			0
$49$	6.19547	+	3.25824i	0.885068	+	0.465462i
$50$	−2.78202	−	4.15456i	−0.393436	−	0.587544i
$51$		0			0
$52$	1.59124	+	5.93859i	0.220665	+	0.823534i
$53$	−2.06426	−	7.70392i	−0.283548	−	1.05822i	−0.949894	−	0.312573i	$-0.898809\pi$
$53$	−2.06426	−	7.70392i	−0.283548	−	1.05822i	0.666346	−	0.745643i	$-0.267857\pi$
$54$		0			0
$55$	1.07877	−	11.0095i	0.145462	−	1.48452i
$56$	−2.26476	+	1.36780i	−0.302641	+	0.182780i
$57$		0			0
$58$	−0.922831	+	3.44405i	−0.121174	+	0.452226i
$59$	−4.90077	+	8.48838i	−0.638026	+	1.10509i	0.347840	+	0.937554i	$0.386915\pi$
$59$	−4.90077	+	8.48838i	−0.638026	+	1.10509i	−0.985865	+	0.167539i	$0.946418\pi$
$60$		0			0
$61$	−5.71103	−	9.89179i	−0.731222	−	1.26651i	−0.956361	−	0.292187i	$-0.905617\pi$
$61$	−5.71103	−	9.89179i	−0.731222	−	1.26651i	0.225139	−	0.974327i	$-0.427716\pi$
$62$	−0.384959	−	0.384959i	−0.0488898	−	0.0488898i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	4.83612	−	12.8688i	0.599847	−	1.59618i
$66$		0			0
$67$	−0.0109452	−	0.0408482i	−0.00133717	−	0.00499040i	0.965254	−	0.261313i	$-0.0841556\pi$
$67$	−0.0109452	−	0.0408482i	−0.00133717	−	0.00499040i	−0.966591	+	0.256323i	$0.917489\pi$
$68$	−4.25035	−	1.13888i	−0.515431	−	0.138109i
$69$		0			0
$70$	5.89811	+	0.460709i	0.704959	+	0.0550652i
$71$			16.3109i			1.93574i	0.251443	+	0.967872i	$0.419095\pi$
$71$			16.3109i			1.93574i	−0.251443	+	0.967872i	$0.580905\pi$
$72$		0			0
$73$	8.42396	−	2.25719i	0.985950	−	0.264185i	0.270402	−	0.962748i	$-0.412844\pi$
$73$	8.42396	−	2.25719i	0.985950	−	0.264185i	0.715548	+	0.698563i	$0.246177\pi$
$74$	0.841319	−	1.45721i	0.0978013	−	0.169397i
$75$		0			0
$76$	3.72823			0.427658
$77$	9.43604	+	9.07102i	1.07534	+	1.03374i
$78$		0			0
$79$	−6.93305	+	4.00280i	−0.780029	+	0.450350i	−0.836440	−	0.548058i	$-0.815367\pi$
$79$	−6.93305	+	4.00280i	−0.780029	+	0.450350i	0.0564118	+	0.998408i	$0.482034\pi$
$80$	−1.30155	+	1.81823i	−0.145518	+	0.203285i
$81$		0			0
$82$	0.259278	+	0.0694733i	0.0286324	+	0.00767204i
$83$	1.30281	−	1.30281i	0.143002	−	0.143002i	−0.631981	−	0.774984i	$-0.717758\pi$
$83$	1.30281	−	1.30281i	0.143002	−	0.143002i	0.774984	+	0.631981i	$0.217758\pi$
$84$		0			0
$85$	6.24583	+	7.60279i	0.677455	+	0.824639i
$86$	10.2838	−	5.93734i	1.10893	−	0.640239i
$87$		0			0
$88$	−4.77861	+	1.28042i	−0.509402	+	0.136494i
$89$	0.229324	+	0.397201i	0.0243083	+	0.0421033i	0.877924	−	0.478801i	$-0.158928\pi$
$89$	0.229324	+	0.397201i	0.0243083	+	0.0421033i	−0.853615	+	0.520904i	$0.825595\pi$
$90$		0			0
$91$	8.40936	+	13.9239i	0.881540	+	1.45962i
$92$	1.37511	+	1.37511i	0.143366	+	0.143366i
$93$		0			0
$94$	−0.803371	−	0.463826i	−0.0828613	−	0.0478400i
$95$	−6.77880	−	4.85248i	−0.695490	−	0.497854i
$96$		0			0
$97$	−10.6198	+	10.6198i	−1.07828	+	1.07828i	−0.0816181	+	0.996664i	$0.526009\pi$
$97$	−10.6198	+	10.6198i	−1.07828	+	1.07828i	−0.996664	+	0.0816181i	$0.973991\pi$
$98$	−4.75072	+	5.14107i	−0.479895	+	0.519327i
$99$		0			0
$100$	4.73304	−	1.61194i	0.473304	−	0.161194i
$101$	−4.33656	−	2.50371i	−0.431504	−	0.249129i	0.268483	−	0.963284i	$-0.413478\pi$
$101$	−4.33656	−	2.50371i	−0.431504	−	0.249129i	−0.699987	+	0.714156i	$0.746811\pi$
$102$		0			0
$103$	4.73881	−	17.6855i	0.466929	−	1.74260i	−0.183486	−	0.983022i	$-0.558738\pi$
$103$	4.73881	−	17.6855i	0.466929	−	1.74260i	0.650415	−	0.759579i	$-0.274595\pi$
$104$	−6.14808			−0.602869
$105$		0			0
$106$	7.97569			0.774667
$107$	−1.00810	+	3.76228i	−0.0974568	+	0.363714i	−0.997380	−	0.0723338i	$-0.976955\pi$
$107$	−1.00810	+	3.76228i	−0.0974568	+	0.363714i	0.899924	+	0.436047i	$0.143622\pi$
$108$		0			0
$109$	7.47396	+	4.31509i	0.715875	+	0.413311i	0.813233	−	0.581939i	$-0.197706\pi$
$109$	7.47396	+	4.31509i	0.715875	+	0.413311i	−0.0973573	+	0.995249i	$0.531039\pi$
$110$	10.3552	+	3.89148i	0.987326	+	0.371039i
$111$		0			0
$112$	−0.735033	−	2.54160i	−0.0694541	−	0.240159i
$113$	−13.9091	+	13.9091i	−1.30845	+	1.30845i	−0.385925	+	0.922530i	$0.626118\pi$
$113$	−13.9091	+	13.9091i	−1.30845	+	1.30845i	−0.922530	+	0.385925i	$0.873882\pi$
$114$		0			0
$115$	−0.710499	−	4.29005i	−0.0662544	−	0.400050i
$116$	−3.08785	−	1.78277i	−0.286700	−	0.165526i
$117$		0			0
$118$	−6.93073	−	6.93073i	−0.638026	−	0.638026i
$119$	−11.6398	+	0.229577i	−1.06702	+	0.0210453i
$120$		0			0
$121$	6.73730	+	11.6693i	0.612482	+	1.06085i
$122$	11.0329	−	2.95625i	0.998868	−	0.267646i
$123$		0			0
$124$	0.471476	−	0.272207i	0.0423398	−	0.0244449i
$125$	−10.7038	−	3.22940i	−0.957376	−	0.288846i
$126$		0			0
$127$	−0.200145	+	0.200145i	−0.0177600	+	0.0177600i	−0.715931	−	0.698171i	$-0.753998\pi$
$127$	−0.200145	+	0.200145i	−0.0177600	+	0.0177600i	0.698171	+	0.715931i	$0.253998\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$		0			0
$130$	11.1786	+	8.00203i	0.980432	+	0.701824i
$131$	13.5876	−	7.84483i	1.18716	−	0.685406i	0.229498	−	0.973309i	$-0.426291\pi$
$131$	13.5876	−	7.84483i	1.18716	−	0.685406i	0.957660	+	0.287903i	$0.0929581\pi$
$132$		0			0
$133$	9.47568	−	2.74038i	0.821645	−	0.237621i
$134$	0.0422892			0.00365323
$135$		0			0
$136$	2.20015	−	3.81076i	0.188661	−	0.326770i
$137$	−2.44530	+	0.655217i	−0.208916	+	0.0559789i	−0.361759	−	0.932272i	$-0.617824\pi$
$137$	−2.44530	+	0.655217i	−0.208916	+	0.0559789i	0.152843	+	0.988250i	$0.451157\pi$
$138$		0			0
$139$			2.80784i			0.238158i	0.992885	+	0.119079i	$0.0379942\pi$
$139$			2.80784i			0.238158i	−0.992885	+	0.119079i	$0.962006\pi$
$140$	−1.97155	+	5.57790i	−0.166627	+	0.471419i
$141$		0			0
$142$	−15.7551	−	4.22156i	−1.32214	−	0.354266i
$143$	7.87216	+	29.3793i	0.658303	+	2.45682i
$144$		0			0
$145$	3.29407	+	7.26049i	0.273558	+	0.602951i
$146$			8.72113i			0.721766i
$147$		0			0
$148$	1.18980	+	1.18980i	0.0978013	+	0.0978013i
$149$	9.80410	+	16.9812i	0.803184	+	1.39115i	0.917510	+	0.397712i	$0.130196\pi$
$149$	9.80410	+	16.9812i	0.803184	+	1.39115i	−0.114327	+	0.993443i	$0.536471\pi$
$150$		0			0
$151$	1.25264	−	2.16964i	0.101939	−	0.176563i	−0.810545	−	0.585677i	$-0.800829\pi$
$151$	1.25264	−	2.16964i	0.101939	−	0.176563i	0.912483	+	0.409114i	$0.134162\pi$
$152$	−0.964938	+	3.60120i	−0.0782668	+	0.292096i
$153$		0			0
$154$	−11.2042	+	6.76676i	−0.902857	+	0.545281i
$155$	−1.21154	−	0.118714i	−0.0973136	−	0.00953533i
$156$		0			0
$157$	−5.05560	−	18.8678i	−0.403481	−	1.50581i	−0.806840	−	0.590770i	$-0.798824\pi$
$157$	−5.05560	−	18.8678i	−0.403481	−	1.50581i	0.403360	−	0.915042i	$-0.367842\pi$
$158$	−2.07200	−	7.73281i	−0.164839	−	0.615189i
$159$		0			0
$160$	−1.41941	−	1.72779i	−0.112214	−	0.136594i
$161$	4.50574	+	2.48423i	0.355102	+	0.195785i
$162$		0			0
$163$	0.00961679	−	0.0358904i	0.000753245	−	0.00281115i	−0.965548	−	0.260224i	$-0.916203\pi$
$163$	0.00961679	−	0.0358904i	0.000753245	−	0.00281115i	0.966301	+	0.257413i	$0.0828701\pi$
$164$	−0.134212	+	0.232462i	−0.0104802	+	0.0181522i
$165$		0			0
$166$	0.921227	+	1.59561i	0.0715011	+	0.123844i
$167$	−9.26150	−	9.26150i	−0.716676	−	0.716676i	0.251247	−	0.967923i	$-0.419159\pi$
$167$	−9.26150	−	9.26150i	−0.716676	−	0.716676i	−0.967923	+	0.251247i	$0.919159\pi$
$168$		0			0
$169$			24.7989i			1.90761i
$170$	−8.96027	+	4.06526i	−0.687221	+	0.311791i
$171$		0			0
$172$	3.07339	+	11.4701i	0.234344	+	0.874583i
$173$	−0.706925	−	0.189420i	−0.0537465	−	0.0144013i	0.231846	−	0.972753i	$-0.425524\pi$
$173$	−0.706925	−	0.189420i	−0.0537465	−	0.0144013i	−0.285592	+	0.958351i	$0.592190\pi$
$174$		0			0
$175$	10.8447	−	7.57585i	0.819779	−	0.572680i
$176$		−	4.94718i		−	0.372908i
$177$		0			0
$178$	−0.443021	+	0.118707i	−0.0332058	+	0.00889747i
$179$	−3.20263	+	5.54712i	−0.239376	+	0.414611i	−0.960535	−	0.278158i	$-0.910276\pi$
$179$	−3.20263	+	5.54712i	−0.239376	+	0.414611i	0.721159	+	0.692769i	$0.243610\pi$
$180$		0			0
$181$	−8.70196			−0.646812			−0.323406	−	0.946260i	$-0.604828\pi$
$181$	−8.70196			−0.646812			−0.323406	+	0.946260i	$0.604828\pi$
$182$	−15.6260	+	4.51904i	−1.15827	+	0.334974i
$183$		0			0
$184$	−1.68416	+	0.972352i	−0.124158	+	0.0716828i
$185$	−0.614753	−	3.71193i	−0.0451975	−	0.272907i
$186$		0			0
$187$	−21.0273	−	5.63424i	−1.53767	−	0.412016i
$188$	0.655949	−	0.655949i	0.0478400	−	0.0478400i
$189$		0			0
$190$	6.44162	−	5.29190i	0.467324	−	0.383915i
$191$	−6.91128	+	3.99023i	−0.500083	+	0.288723i	−0.728748	−	0.684782i	$-0.759897\pi$
$191$	−6.91128	+	3.99023i	−0.500083	+	0.288723i	0.228665	+	0.973505i	$0.426564\pi$
$192$		0			0
$193$	−18.8317	+	5.04593i	−1.35553	+	0.363214i	−0.862174	−	0.506612i	$-0.830898\pi$
$193$	−18.8317	+	5.04593i	−1.35553	+	0.363214i	−0.493358	+	0.869826i	$0.664231\pi$
$194$	−7.50936	−	13.0066i	−0.539141	−	0.933819i
$195$		0			0
$196$	−3.73632	−	5.91945i	−0.266880	−	0.422818i
$197$	10.0960	+	10.0960i	0.719312	+	0.719312i	0.968464	−	0.249153i	$-0.0801520\pi$
$197$	10.0960	+	10.0960i	0.719312	+	0.719312i	−0.249153	+	0.968464i	$0.580152\pi$
$198$		0			0
$199$	−11.0002	−	6.35098i	−0.779785	−	0.450209i	0.0565691	−	0.998399i	$-0.481984\pi$
$199$	−11.0002	−	6.35098i	−0.779785	−	0.450209i	−0.836354	+	0.548190i	$0.815317\pi$
$200$	0.332015	+	4.98896i	0.0234770	+	0.352773i
$201$		0			0
$202$	3.54078	−	3.54078i	0.249129	−	0.249129i
$203$	−9.15848	−	2.26142i	−0.642800	−	0.158721i
$204$		0			0
$205$	0.546590	−	0.247987i	0.0381755	−	0.0173201i
$206$	15.8564	+	9.15468i	1.10477	+	0.637837i
$207$		0			0
$208$	1.59124	−	5.93859i	0.110333	−	0.411767i
$209$	18.4442			1.27582
$210$		0			0
$211$	18.8900			1.30044			0.650220	−	0.759746i	$-0.274677\pi$
$211$	18.8900			1.30044			0.650220	+	0.759746i	$0.274677\pi$
$212$	−2.06426	+	7.70392i	−0.141774	+	0.529108i
$213$		0			0
$214$	−3.37317	−	1.94750i	−0.230585	−	0.133128i
$215$	9.34069	−	24.8554i	0.637030	−	1.69512i
$216$		0			0
$217$	0.998223	−	1.03839i	0.0677638	−	0.0704906i
$218$	−6.10246	+	6.10246i	−0.413311	+	0.413311i
$219$		0			0
$220$	−6.43900	+	8.99513i	−0.434117	+	0.606451i
$221$	−23.4289	−	13.5267i	−1.57600	−	0.909903i
$222$		0			0
$223$	2.93799	+	2.93799i	0.196743	+	0.196743i	0.798602	−	0.601859i	$-0.205573\pi$
$223$	2.93799	+	2.93799i	0.196743	+	0.196743i	−0.601859	+	0.798602i	$0.705573\pi$
$224$	2.64524	−	0.0521732i	0.176742	−	0.00348597i
$225$		0			0
$226$	−9.83520	−	17.0351i	−0.654227	−	1.13316i
$227$	0.861758	−	0.230907i	0.0571969	−	0.0153259i	−0.230107	−	0.973165i	$-0.573908\pi$
$227$	0.861758	−	0.230907i	0.0571969	−	0.0153259i	0.287304	+	0.957839i	$0.407241\pi$
$228$		0			0
$229$	17.8423	−	10.3013i	1.17905	−	0.680728i	0.223259	−	0.974759i	$-0.428330\pi$
$229$	17.8423	−	10.3013i	1.17905	−	0.680728i	0.955796	+	0.294032i	$0.0949971\pi$
$230$	4.32777	+	0.424059i	0.285364	+	0.0279616i
$231$		0			0
$232$	2.52122	−	2.52122i	0.165526	−	0.165526i
$233$	4.65452	+	1.24718i	0.304928	+	0.0817052i	0.408038	−	0.912965i	$-0.366213\pi$
$233$	4.65452	+	1.24718i	0.304928	+	0.0817052i	−0.103111	+	0.994670i	$0.532880\pi$
$234$		0			0
$235$	−2.04642	+	0.338918i	−0.133494	+	0.0221086i
$236$	8.48838	−	4.90077i	0.552547	−	0.319013i
$237$		0			0
$238$	2.79085	−	11.3026i	0.180904	−	0.732640i
$239$	15.7251			1.01717			0.508585	−	0.861012i	$-0.330169\pi$
$239$	15.7251			1.01717			0.508585	+	0.861012i	$0.330169\pi$
$240$		0			0
$241$	−3.64485	+	6.31306i	−0.234785	+	0.406660i	−0.959210	−	0.282693i	$-0.908772\pi$
$241$	−3.64485	+	6.31306i	−0.234785	+	0.406660i	0.724425	+	0.689354i	$0.242105\pi$
$242$	−13.0155	+	3.48748i	−0.836666	+	0.224184i
$243$		0			0
$244$			11.4221i			0.731222i
$245$	−0.910960	+	15.6259i	−0.0581991	+	0.998305i
$246$		0			0
$247$	22.1405	+	5.93252i	1.40876	+	0.377477i
$248$	0.140905	+	0.525863i	0.00894746	+	0.0333924i
$249$		0			0
$250$	5.88970	−	9.50323i	0.372497	−	0.601037i
$251$		−	8.22912i		−	0.519418i	−0.965687	−	0.259709i	$-0.916373\pi$
$251$		−	8.22912i		−	0.519418i	0.965687	−	0.259709i	$-0.0836266\pi$
$252$		0			0
$253$	6.80294	+	6.80294i	0.427697	+	0.427697i
$254$	−0.141524	−	0.245127i	−0.00888001	−	0.0153806i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.337836	+	1.26082i	−0.0210736	+	0.0786479i	−0.975662	−	0.219281i	$-0.929629\pi$
$257$	−0.337836	+	1.26082i	−0.0210736	+	0.0786479i	0.954588	+	0.297928i	$0.0962957\pi$
$258$		0			0
$259$	3.89855	+	2.14946i	0.242244	+	0.133561i
$260$	−10.6226	+	8.72666i	−0.658787	+	0.541205i
$261$		0			0
$262$	4.06078	+	15.1550i	0.250876	+	0.936282i
$263$	−3.82344	−	14.2693i	−0.235763	−	0.879881i	−0.977803	−	0.209525i	$-0.932808\pi$
$263$	−3.82344	−	14.2693i	−0.235763	−	0.879881i	0.742040	−	0.670356i	$-0.233859\pi$
$264$		0			0
$265$	13.7803	−	11.3208i	0.846520	−	0.695431i
$266$	0.194514	+	9.86206i	0.0119264	+	0.604682i
$267$		0			0
$268$	−0.0109452	+	0.0408482i	−0.000668587	+	0.00249520i
$269$	10.5069	−	18.1984i	0.640615	−	1.10958i	−0.344680	−	0.938720i	$-0.612013\pi$
$269$	10.5069	−	18.1984i	0.640615	−	1.10958i	0.985296	−	0.170858i	$-0.0546539\pi$
$270$		0			0
$271$	4.95098	+	8.57534i	0.300750	+	0.520915i	0.976306	−	0.216394i	$-0.0694296\pi$
$271$	4.95098	+	8.57534i	0.300750	+	0.520915i	−0.675556	+	0.737309i	$0.736096\pi$
$272$	3.11148	+	3.11148i	0.188661	+	0.188661i
$273$		0			0
$274$		−	2.53156i		−	0.152937i
$275$	23.4152	−	7.97456i	1.41199	−	0.480884i
$276$		0			0
$277$	5.36596	+	20.0261i	0.322410	+	1.20325i	0.916890	+	0.399139i	$0.130691\pi$
$277$	5.36596	+	20.0261i	0.322410	+	1.20325i	−0.594481	+	0.804110i	$0.702642\pi$
$278$	−2.71217	−	0.726722i	−0.162665	−	0.0435859i
$279$		0			0
$280$	−4.87756	−	3.34804i	−0.291490	−	0.200084i
$281$		−	24.6495i		−	1.47046i	−0.677816	−	0.735232i	$-0.737073\pi$
$281$		−	24.6495i		−	1.47046i	0.677816	−	0.735232i	$-0.262927\pi$
$282$		0			0
$283$	−5.33016	+	1.42821i	−0.316845	+	0.0848985i	−0.413737	−	0.910396i	$-0.635777\pi$
$283$	−5.33016	+	1.42821i	−0.316845	+	0.0848985i	0.0968916	+	0.995295i	$0.469110\pi$
$284$	8.15543	−	14.1256i	0.483936	−	0.838202i
$285$		0			0
$286$	−30.4157			−1.79852
$287$	−0.170246	+	0.689476i	−0.0100493	+	0.0406985i
$288$		0			0
$289$	2.04603	−	1.18128i	0.120355	−	0.0694870i
$290$	−7.86566	+	1.30267i	−0.461888	+	0.0764957i
$291$		0			0
$292$	−8.42396	−	2.25719i	−0.492975	−	0.132092i
$293$	13.1648	−	13.1648i	0.769096	−	0.769096i	−0.208851	−	0.977947i	$-0.566972\pi$
$293$	13.1648	−	13.1648i	0.769096	−	0.769096i	0.977947	+	0.208851i	$0.0669725\pi$
$294$		0			0
$295$	−21.8124	−	2.13731i	−1.26997	−	0.124439i
$296$	−1.45721	+	0.841319i	−0.0846984	+	0.0489007i
$297$		0			0
$298$	−18.9401	+	5.07498i	−1.09717	+	0.293986i
$299$	5.97810	+	10.3544i	0.345723	+	0.598809i
$300$		0			0
$301$	16.2422	+	26.8932i	0.936185	+	1.55010i
$302$	1.77151	+	1.77151i	0.101939	+	0.101939i
$303$		0			0
$304$	−3.22874	−	1.86412i	−0.185181	−	0.106914i
$305$	14.8664	−	20.7680i	0.851245	−	1.18917i
$306$		0			0
$307$	16.9282	−	16.9282i	0.966145	−	0.966145i	−0.0333006	−	0.999445i	$-0.510602\pi$
$307$	16.9282	−	16.9282i	0.966145	−	0.966145i	0.999445	+	0.0333006i	$0.0106019\pi$
$308$	−3.63634	−	12.5738i	−0.207200	−	0.716456i
$309$		0			0
$310$	0.428240	−	1.13954i	0.0243224	−	0.0647213i
$311$	−23.6318	−	13.6438i	−1.34004	−	0.773671i	−0.353225	−	0.935539i	$-0.614915\pi$
$311$	−23.6318	−	13.6438i	−1.34004	−	0.773671i	−0.986812	+	0.161868i	$0.948248\pi$
$312$		0			0
$313$	1.92449	−	7.18228i	0.108778	−	0.405967i	−0.889968	−	0.456023i	$-0.849273\pi$
$313$	1.92449	−	7.18228i	0.108778	−	0.405967i	0.998746	+	0.0500564i	$0.0159401\pi$
$314$	19.5333			1.10233
$315$		0			0
$316$	8.00559			0.450350
$317$	8.08855	−	30.1869i	0.454298	−	1.69546i	−0.235845	−	0.971791i	$-0.575786\pi$
$317$	8.08855	−	30.1869i	0.454298	−	1.69546i	0.690143	−	0.723673i	$-0.257548\pi$
$318$		0			0
$319$	−15.2762	−	8.81970i	−0.855302	−	0.493809i
$320$	2.03629	−	0.923861i	0.113832	−	0.0516454i
$321$		0			0
$322$	−3.56576	+	3.70925i	−0.198712	+	0.206708i
$323$	−11.6003	+	11.6003i	−0.645458	+	0.645458i
$324$		0			0
$325$	30.6726	−	2.04125i	1.70141	−	0.113228i
$326$	0.0321784	+	0.0185782i	0.00178220	+	0.00102895i
$327$		0			0
$328$	−0.189805	−	0.189805i	−0.0104802	−	0.0104802i
$329$	1.18502	−	2.14930i	0.0653320	−	0.118495i
$330$		0			0
$331$	−5.38534	−	9.32768i	−0.296005	−	0.512696i	0.679213	−	0.733941i	$-0.262321\pi$
$331$	−5.38534	−	9.32768i	−0.296005	−	0.512696i	−0.975218	+	0.221245i	$0.928988\pi$
$332$	−1.77967	+	0.476862i	−0.0976723	+	0.0261712i
$333$		0			0
$334$	11.3430	−	6.54887i	0.620660	−	0.358338i
$335$	0.0730669	−	0.0600258i	0.00399207	−	0.00327956i
$336$		0			0
$337$	−21.8140	+	21.8140i	−1.18828	+	1.18828i	−0.210740	+	0.977542i	$0.567587\pi$
$337$	−21.8140	+	21.8140i	−1.18828	+	1.18828i	−0.977542	+	0.210740i	$0.932413\pi$
$338$	−23.9539	−	6.41843i	−1.30292	−	0.349117i
$339$		0			0
$340$	−1.60765	−	9.70712i	−0.0871870	−	0.526443i
$341$	2.33248	−	1.34666i	0.126311	−	0.0729256i
$342$		0			0
$343$	−13.8472	−	12.2986i	−0.747680	−	0.664060i
$344$	−11.8747			−0.640239
$345$		0			0
$346$	0.365931	−	0.633812i	0.0196726	−	0.0340739i
$347$	−5.94688	+	1.59346i	−0.319245	+	0.0855415i	−0.414883	−	0.909875i	$-0.636178\pi$
$347$	−5.94688	+	1.59346i	−0.319245	+	0.0855415i	0.0956379	+	0.995416i	$0.469511\pi$
$348$		0			0
$349$		−	0.197242i		−	0.0105581i	−0.999986	−	0.00527907i	$-0.998320\pi$
$349$		−	0.197242i		−	0.0105581i	0.999986	−	0.00527907i	$-0.00168039\pi$
$350$	4.51090	+	12.4359i	0.241118	+	0.664727i
$351$		0			0
$352$	4.77861	+	1.28042i	0.254701	+	0.0682469i
$353$	−2.64401	−	9.86759i	−0.140727	−	0.525199i	−0.999908	−	0.0135287i	$-0.995694\pi$
$353$	−2.64401	−	9.86759i	−0.140727	−	0.525199i	0.859182	−	0.511670i	$-0.170973\pi$
$354$		0			0
$355$	−33.2137	+	15.0690i	−1.76280	+	0.799778i
$356$		−	0.458649i		−	0.0243083i
$357$		0			0
$358$	−4.52921	−	4.52921i	−0.239376	−	0.239376i
$359$	−7.63203	−	13.2191i	−0.402803	−	0.697676i	0.591260	−	0.806481i	$-0.298631\pi$
$359$	−7.63203	−	13.2191i	−0.402803	−	0.697676i	−0.994063	+	0.108805i	$0.965297\pi$
$360$		0			0
$361$	−2.55014	+	4.41697i	−0.134218	+	0.232472i
$362$	2.25223	−	8.40545i	0.118375	−	0.441781i
$363$		0			0
$364$	−0.320765	−	16.2631i	−0.0168127	−	0.852420i
$365$	12.3789	+	15.0683i	0.647940	+	0.788711i
$366$		0			0
$367$	−6.14181	−	22.9216i	−0.320600	−	1.19650i	−0.918662	−	0.395045i	$-0.870729\pi$
$367$	−6.14181	−	22.9216i	−0.320600	−	1.19650i	0.598062	−	0.801450i	$-0.295938\pi$
$368$	−0.503327	−	1.87844i	−0.0262377	−	0.0979205i
$369$		0			0
$370$	3.74456	+	0.366913i	0.194670	+	0.0190749i
$371$	0.416117	+	21.0976i	0.0216037	+	1.09533i
$372$		0			0
$373$	4.81825	−	17.9820i	0.249480	−	0.931071i	−0.721599	−	0.692311i	$-0.756593\pi$
$373$	4.81825	−	17.9820i	0.249480	−	0.931071i	0.971079	−	0.238760i	$-0.0767408\pi$
$374$	10.8845	−	18.8525i	0.562825	−	0.974841i
$375$		0			0
$376$	0.463826	+	0.803371i	0.0239200	+	0.0414307i
$377$	−15.5007	−	15.5007i	−0.798326	−	0.798326i
$378$		0			0
$379$		−	34.8805i		−	1.79169i	−0.444367	−	0.895845i	$-0.646571\pi$
$379$		−	34.8805i		−	1.79169i	0.444367	−	0.895845i	$-0.353429\pi$
$380$	3.44437	+	7.59177i	0.176692	+	0.389449i
$381$		0			0
$382$	−2.06549	−	7.70853i	−0.105680	−	0.394403i
$383$	30.0303	+	8.04661i	1.53448	+	0.411162i	0.924477	−	0.381238i	$-0.124502\pi$
$383$	30.0303	+	8.04661i	1.53448	+	0.411162i	0.610002	+	0.792400i	$0.291169\pi$
$384$		0			0
$385$	−9.75364	+	27.5949i	−0.497091	+	1.40637i
$386$		−	19.4960i		−	0.992319i
$387$		0			0
$388$	14.5070	−	3.88713i	0.736480	−	0.197339i
$389$	−9.96369	+	17.2576i	−0.505179	+	0.874996i	0.494803	+	0.869005i	$0.335240\pi$
$389$	−9.96369	+	17.2576i	−0.505179	+	0.874996i	−0.999982	+	0.00599092i	$0.998093\pi$
$390$		0			0
$391$	−8.55726			−0.432759
$392$	6.68478	−	2.07694i	0.337633	−	0.104901i
$393$		0			0
$394$	−12.3651	+	7.13897i	−0.622942	+	0.359656i
$395$	−14.5560	−	10.4197i	−0.732393	−	0.524271i
$396$		0			0
$397$	−12.5094	−	3.35189i	−0.627831	−	0.168227i	−0.0691456	−	0.997607i	$-0.522027\pi$
$397$	−12.5094	−	3.35189i	−0.627831	−	0.168227i	−0.558685	+	0.829380i	$0.688694\pi$
$398$	8.98164	−	8.98164i	0.450209	−	0.450209i
$399$		0			0
$400$	−4.90490	−	0.970538i	−0.245245	−	0.0485269i
$401$	1.57729	−	0.910650i	0.0787662	−	0.0454757i	−0.460100	−	0.887867i	$-0.652186\pi$
$401$	1.57729	−	0.910650i	0.0787662	−	0.0454757i	0.538866	+	0.842392i	$0.318853\pi$
$402$		0			0
$403$	3.23305	−	0.866294i	0.161050	−	0.0431532i
$404$	2.50371	+	4.33656i	0.124564	+	0.215752i
$405$		0			0
$406$	4.55475	−	8.26112i	0.226049	−	0.409992i
$407$	5.88618	+	5.88618i	0.291767	+	0.291767i
$408$		0			0
$409$	−17.8771	−	10.3214i	−0.883967	−	0.510359i	−0.0120026	−	0.999928i	$-0.503821\pi$
$409$	−17.8771	−	10.3214i	−0.883967	−	0.510359i	−0.871964	+	0.489569i	$0.837154\pi$
$410$	0.0980689	+	0.592149i	0.00484328	+	0.0292441i
$411$		0			0
$412$	−12.9467	+	12.9467i	−0.637837	+	0.637837i
$413$	17.9718	−	18.6950i	0.884336	−	0.919922i
$414$		0			0
$415$	3.85652	+	1.44929i	0.189309	+	0.0711427i
$416$	5.32440	+	3.07404i	0.261050	+	0.150717i
$417$		0			0
$418$	−4.77372	+	17.8158i	−0.233490	+	0.871398i
$419$	−12.8948			−0.629954			−0.314977	−	0.949099i	$-0.601997\pi$
$419$	−12.8948			−0.629954			−0.314977	+	0.949099i	$0.601997\pi$
$420$		0			0
$421$	−16.9311			−0.825170			−0.412585	−	0.910919i	$-0.635374\pi$
$421$	−16.9311			−0.825170			−0.412585	+	0.910919i	$0.635374\pi$
$422$	−4.88909	+	18.2463i	−0.237997	+	0.888217i
$423$		0			0
$424$	−6.90715	−	3.98784i	−0.335441	−	0.193667i
$425$	−9.71122	+	19.7422i	−0.471063	+	0.957639i
$426$		0			0
$427$	8.39559	+	29.0303i	0.406291	+	1.40487i
$428$	2.75418	−	2.75418i	0.133128	−	0.133128i
$429$		0			0
$430$	21.5909	+	15.4555i	1.04121	+	0.745329i
$431$	−25.7429	−	14.8627i	−1.23999	−	0.715910i	−0.270901	−	0.962607i	$-0.587321\pi$
$431$	−25.7429	−	14.8627i	−1.23999	−	0.715910i	−0.969093	+	0.246697i	$0.920655\pi$
$432$		0			0
$433$	20.0190	+	20.0190i	0.962052	+	0.962052i	0.999306	−	0.0372534i	$-0.0118609\pi$
$433$	20.0190	+	20.0190i	0.962052	+	0.962052i	−0.0372534	+	0.999306i	$0.511861\pi$
$434$	0.744650	+	1.23296i	0.0357444	+	0.0591842i
$435$		0			0
$436$	−4.31509	−	7.47396i	−0.206655	−	0.357938i
$437$	7.00326	−	1.87652i	0.335012	−	0.0897661i
$438$		0			0
$439$	−5.54137	+	3.19931i	−0.264475	+	0.152695i	−0.626374	−	0.779522i	$-0.715462\pi$
$439$	−5.54137	+	3.19931i	−0.264475	+	0.152695i	0.361899	+	0.932217i	$0.382128\pi$
$440$	−7.02209	−	8.54771i	−0.334765	−	0.407496i
$441$		0			0
$442$	19.1296	−	19.1296i	0.909903	−	0.909903i
$443$	−0.328032	−	0.0878959i	−0.0155853	−	0.00417606i	0.251018	−	0.967982i	$-0.419235\pi$
$443$	−0.328032	−	0.0878959i	−0.0155853	−	0.00417606i	−0.266603	+	0.963806i	$0.585901\pi$
$444$		0			0
$445$	−0.596954	+	0.833930i	−0.0282983	+	0.0395321i
$446$	−3.59829	+	2.07747i	−0.170384	+	0.0983713i
$447$		0			0
$448$	−0.634242	+	2.56861i	−0.0299651	+	0.121355i
$449$	11.8831			0.560800			0.280400	−	0.959883i	$-0.409533\pi$
$449$	11.8831			0.560800			0.280400	+	0.959883i	$0.409533\pi$
$450$		0			0
$451$	−0.663971	+	1.15003i	−0.0312652	+	0.0541529i
$452$	19.0001	−	5.09107i	0.893691	−	0.239464i
$453$		0			0
$454$			0.892157i			0.0418710i
$455$	−20.5840	+	29.9877i	−0.964995	+	1.40584i
$456$		0			0
$457$	19.4777	+	5.21904i	0.911129	+	0.244136i	0.683790	−	0.729679i	$-0.260331\pi$
$457$	19.4777	+	5.21904i	0.911129	+	0.244136i	0.227340	+	0.973816i	$0.426997\pi$
$458$	5.33233	+	19.9005i	0.249164	+	0.929891i
$459$		0			0
$460$	−1.52972	+	4.07055i	−0.0713234	+	0.189790i
$461$			19.5952i			0.912638i	0.889816	+	0.456319i	$0.150832\pi$
$461$			19.5952i			0.912638i	−0.889816	+	0.456319i	$0.849168\pi$
$462$		0			0
$463$	19.2239	+	19.2239i	0.893411	+	0.893411i	0.994843	−	0.101432i	$-0.0323423\pi$
$463$	19.2239	+	19.2239i	0.893411	+	0.893411i	−0.101432	+	0.994843i	$0.532342\pi$
$464$	1.78277	+	3.08785i	0.0827632	+	0.143350i
$465$		0			0
$466$	−2.40936	+	4.17313i	−0.111611	+	0.193316i
$467$	−7.83232	+	29.2306i	−0.362437	+	1.35263i	0.508426	+	0.861105i	$0.330227\pi$
$467$	−7.83232	+	29.2306i	−0.362437	+	1.35263i	−0.870863	+	0.491526i	$0.836439\pi$
$468$		0			0
$469$	0.00220636	+	0.111865i	0.000101880	+	0.00516544i
$470$	0.202282	−	2.06441i	0.00933058	−	0.0952240i
$471$		0			0
$472$	2.53682	+	9.46756i	0.116767	+	0.435780i
$473$	15.2046	+	56.7444i	0.699109	+	2.60911i
$474$		0			0
$475$	3.61839	−	18.2866i	0.166023	−	0.839048i
$476$	10.1952	+	5.62109i	0.467294	+	0.257642i
$477$		0			0
$478$	−4.06995	+	15.1892i	−0.186155	+	0.694740i
$479$	0.818104	−	1.41700i	0.0373801	−	0.0647443i	−0.846730	−	0.532023i	$-0.821432\pi$
$479$	0.818104	−	1.41700i	0.0373801	−	0.0647443i	0.884110	+	0.467278i	$0.154765\pi$
$480$		0			0
$481$	5.17250	+	8.95903i	0.235846	+	0.408497i
$482$	−5.15460	−	5.15460i	−0.234785	−	0.234785i
$483$		0			0
$484$		−	13.4746i		−	0.612482i
$485$	−31.4364	−	11.8138i	−1.42745	−	0.536438i
$486$		0			0
$487$	−1.86735	−	6.96906i	−0.0846178	−	0.315798i	0.910624	−	0.413237i	$-0.135602\pi$
$487$	−1.86735	−	6.96906i	−0.0846178	−	0.315798i	−0.995242	+	0.0974385i	$0.968935\pi$
$488$	−11.0329	−	2.95625i	−0.499434	−	0.133823i
$489$		0			0
$490$	−14.8577	−	4.92421i	−0.671204	−	0.222453i
$491$			23.4235i			1.05709i	0.848907	+	0.528543i	$0.177261\pi$
$491$			23.4235i			1.05709i	−0.848907	+	0.528543i	$0.822739\pi$
$492$		0			0
$493$	15.1548	−	4.06073i	0.682540	−	0.182886i
$494$	−11.4607	+	19.8506i	−0.515643	+	0.893120i
$495$		0			0
$496$	−0.544414			−0.0244449
$497$	10.3450	−	41.8962i	0.464039	−	1.87930i
$498$		0			0
$499$	25.5933	−	14.7763i	1.14571	−	0.661477i	0.197873	−	0.980228i	$-0.436597\pi$
$499$	25.5933	−	14.7763i	1.14571	−	0.661477i	0.947838	+	0.318751i	$0.103263\pi$
$500$	7.65505	+	8.14863i	0.342344	+	0.364418i
$501$		0			0
$502$	7.94872	+	2.12985i	0.354769	+	0.0950600i
$503$	16.6368	−	16.6368i	0.741797	−	0.741797i	−0.231127	−	0.972924i	$-0.574241\pi$
$503$	16.6368	−	16.6368i	0.741797	−	0.741797i	0.972924	+	0.231127i	$0.0742413\pi$
$504$		0			0
$505$	1.09191	−	11.1436i	0.0485893	−	0.495883i
$506$	−8.33186	+	4.81040i	−0.370396	+	0.213848i
$507$		0			0
$508$	0.273404	−	0.0732583i	0.0121303	−	0.00325031i
$509$	−4.84247	−	8.38740i	−0.214639	−	0.371765i	0.738522	−	0.674229i	$-0.235524\pi$
$509$	−4.84247	−	8.38740i	−0.214639	−	0.371765i	−0.953161	+	0.302464i	$0.902191\pi$
$510$		0			0
$511$	−23.0694	+	0.455009i	−1.02053	+	0.0201284i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$		0			0
$514$	−1.13042	−	0.652649i	−0.0498608	−	0.0287871i
$515$	40.3908	−	6.68933i	1.77983	−	0.294767i
$516$		0			0
$517$	3.24510	−	3.24510i	0.142719	−	0.142719i
$518$	−3.08524	+	3.20939i	−0.135558	+	0.141013i
$519$		0			0
$520$	−5.67997	−	12.5193i	−0.249083	−	0.549007i
$521$	18.3916	+	10.6184i	0.805750	+	0.465200i	0.845478	−	0.534011i	$-0.179316\pi$
$521$	18.3916	+	10.6184i	0.805750	+	0.465200i	−0.0397281	+	0.999211i	$0.512649\pi$
$522$		0			0
$523$	0.0569475	−	0.212531i	0.00249014	−	0.00929332i	−0.964670	−	0.263463i	$-0.915135\pi$
$523$	0.0569475	−	0.212531i	0.00249014	−	0.00929332i	0.967160	+	0.254169i	$0.0818021\pi$
$524$	−15.6897			−0.685406
$525$		0			0
$526$	14.7726			0.644118
$527$	−0.620022	+	2.31395i	−0.0270086	+	0.100797i
$528$		0			0
$529$	−16.6434	−	9.60906i	−0.723625	−	0.417785i
$530$	7.36843	+	16.2408i	0.320064	+	0.705456i
$531$		0			0
$532$	−9.57636	−	2.36460i	−0.415188	−	0.102519i
$533$	−1.16693	+	1.16693i	−0.0505455	+	0.0505455i
$534$		0			0
$535$	−8.59245	+	1.42304i	−0.371484	+	0.0615234i
$536$	−0.0366235	−	0.0211446i	−0.00158189	−	0.000913307i
$537$		0			0
$538$	14.8590	+	14.8590i	0.640615	+	0.640615i
$539$	−18.4842	−	29.2846i	−0.796173	−	1.26138i
$540$		0			0
$541$	−21.0652	−	36.4861i	−0.905666	−	1.56866i	−0.820021	−	0.572333i	$-0.806038\pi$
$541$	−21.0652	−	36.4861i	−0.905666	−	1.56866i	−0.0856442	−	0.996326i	$-0.527295\pi$
$542$	−9.56455	+	2.56281i	−0.410833	+	0.110082i
$543$		0			0
$544$	−3.81076	+	2.20015i	−0.163385	+	0.0943305i
$545$	−1.88188	+	19.2057i	−0.0806110	+	0.822682i
$546$		0			0
$547$	10.6450	−	10.6450i	0.455147	−	0.455147i	−0.441911	−	0.897059i	$-0.645699\pi$
$547$	10.6450	−	10.6450i	0.455147	−	0.455147i	0.897059	+	0.441911i	$0.145699\pi$
$548$	2.44530	+	0.655217i	0.104458	+	0.0279895i
$549$		0			0
$550$	1.64254	+	24.6813i	0.0700380	+	1.05241i
$551$	−11.5122	+	6.64660i	−0.490438	+	0.283154i
$552$		0			0
$553$	20.3470	−	5.88438i	0.865243	−	0.250229i
$554$	−20.7325			−0.880839
$555$		0			0
$556$	1.40392	−	2.43166i	0.0595395	−	0.103125i
$557$	−30.4049	+	8.14696i	−1.28830	+	0.345198i	−0.837013	−	0.547183i	$-0.815700\pi$
$557$	−30.4049	+	8.14696i	−1.28830	+	0.345198i	−0.451283	+	0.892381i	$0.649033\pi$
$558$		0			0
$559$			73.0065i			3.08784i
$560$	4.49637	−	3.84483i	0.190006	−	0.162474i
$561$		0			0
$562$	23.8096	+	6.37975i	1.00435	+	0.269114i
$563$	−0.0168462	−	0.0628710i	−0.000709984	−	0.00264969i	0.965570	−	0.260144i	$-0.0837699\pi$
$563$	−0.0168462	−	0.0628710i	−0.000709984	−	0.00264969i	−0.966280	+	0.257494i	$0.917103\pi$
$564$		0			0
$565$	−41.1730	−	15.4729i	−1.73216	−	0.650948i
$566$		−	5.51819i		−	0.231947i
$567$		0			0
$568$	11.5335	+	11.5335i	0.483936	+	0.483936i
$569$	13.5754	+	23.5133i	0.569110	+	0.985728i	0.996654	+	0.0817335i	$0.0260456\pi$
$569$	13.5754	+	23.5133i	0.569110	+	0.985728i	−0.427544	+	0.903995i	$0.640621\pi$
$570$		0			0
$571$	13.3600	−	23.1403i	0.559101	−	0.968391i	−0.438471	−	0.898745i	$-0.644480\pi$
$571$	13.3600	−	23.1403i	0.559101	−	0.968391i	0.997572	−	0.0696454i	$-0.0221868\pi$
$572$	7.87216	−	29.3793i	0.329151	−	1.22841i
$573$		0			0
$574$	−0.621920	−	0.342894i	−0.0259584	−	0.0143121i
$575$	8.07940	−	5.41020i	0.336934	−	0.225621i
$576$		0			0
$577$	3.91412	+	14.6077i	0.162947	+	0.608127i	0.998293	+	0.0584023i	$0.0186006\pi$
$577$	3.91412	+	14.6077i	0.162947	+	0.608127i	−0.835346	+	0.549724i	$0.814733\pi$
$578$	0.611475	+	2.28205i	0.0254340	+	0.0949210i
$579$		0			0
$580$	0.777496	−	7.93480i	0.0322838	−	0.329475i
$581$	−4.17271	+	2.52011i	−0.173113	+	0.104552i
$582$		0			0
$583$	−10.2123	+	38.1127i	−0.422949	+	1.57847i
$584$	4.36056	−	7.55272i	0.180441	−	0.312534i
$585$		0			0
$586$	9.30892	+	16.1235i	0.384548	+	0.666057i
$587$	0.814359	+	0.814359i	0.0336122	+	0.0336122i	0.723713	−	0.690101i	$-0.242434\pi$
$587$	0.814359	+	0.814359i	0.0336122	+	0.0336122i	−0.690101	+	0.723713i	$0.742434\pi$
$588$		0			0
$589$		−	2.02970i		−	0.0836324i
$590$	7.70995	−	20.5160i	0.317414	−	0.844631i
$591$		0			0
$592$	−0.435499	−	1.62530i	−0.0178989	−	0.0667996i
$593$	0.591195	+	0.158410i	0.0242775	+	0.00650513i	0.270937	−	0.962597i	$-0.412666\pi$
$593$	0.591195	+	0.158410i	0.0242775	+	0.00650513i	−0.246660	+	0.969102i	$0.579333\pi$
$594$		0			0
$595$	−11.2211	−	23.4899i	−0.460018	−	0.962994i
$596$		−	19.6082i		−	0.803184i
$597$		0			0
$598$	−11.5488	+	3.09449i	−0.472266	+	0.126543i
$599$	−6.50281	+	11.2632i	−0.265698	+	0.460202i	−0.967746	−	0.251927i	$-0.918936\pi$
$599$	−6.50281	+	11.2632i	−0.265698	+	0.460202i	0.702049	+	0.712129i	$0.252269\pi$
$600$		0			0
$601$	−12.4846			−0.509258			−0.254629	−	0.967039i	$-0.581953\pi$
$601$	−12.4846			−0.509258			−0.254629	+	0.967039i	$0.581953\pi$
$602$	−30.1807	+	8.72828i	−1.23007	+	0.355738i
$603$		0			0
$604$	−2.16964	+	1.25264i	−0.0882816	+	0.0509694i
$605$	−17.5379	+	24.5000i	−0.713015	+	0.996065i
$606$		0			0
$607$	8.60280	+	2.30511i	0.349177	+	0.0935616i	0.429145	−	0.903236i	$-0.358815\pi$
$607$	8.60280	+	2.30511i	0.349177	+	0.0935616i	−0.0799678	+	0.996797i	$0.525482\pi$
$608$	2.63626	−	2.63626i	0.106914	−	0.106914i
$609$		0			0
$610$	16.2126	+	19.7349i	0.656429	+	0.799045i
$611$	4.93919	−	2.85164i	0.199818	−	0.115365i
$612$		0			0
$613$	−27.7729	+	7.44173i	−1.12174	+	0.300569i	−0.771586	−	0.636125i	$-0.780536\pi$
$613$	−27.7729	+	7.44173i	−1.12174	+	0.300569i	−0.350151	+	0.936693i	$0.613870\pi$
$614$	11.9701	+	20.7328i	0.483072	+	0.836706i
$615$		0			0
$616$	13.0865	−	0.258110i	0.527269	−	0.0103996i
$617$	−3.97067	−	3.97067i	−0.159853	−	0.159853i	0.622649	−	0.782502i	$-0.286057\pi$
$617$	−3.97067	−	3.97067i	−0.159853	−	0.159853i	−0.782502	+	0.622649i	$0.786057\pi$
$618$		0			0
$619$	29.1348	+	16.8210i	1.17103	+	0.676092i	0.953921	−	0.300057i	$-0.0970056\pi$
$619$	29.1348	+	16.8210i	1.17103	+	0.676092i	0.217104	+	0.976148i	$0.430339\pi$
$620$	0.989871	+	0.708581i	0.0397542	+	0.0284573i
$621$		0			0
$622$	19.2953	−	19.2953i	0.773671	−	0.773671i
$623$	−0.337122	−	1.16570i	−0.0135065	−	0.0467028i
$624$		0			0
$625$	−3.31282	−	24.7795i	−0.132513	−	0.991181i
$626$	6.43946	+	3.71782i	0.257373	+	0.148594i
$627$		0			0
$628$	−5.05560	+	18.8678i	−0.201740	+	0.752906i
$629$	−7.40409			−0.295221
$630$		0			0
$631$	−15.9081			−0.633292			−0.316646	−	0.948544i	$-0.602557\pi$
$631$	−15.9081			−0.633292			−0.316646	+	0.948544i	$0.602557\pi$
$632$	−2.07200	+	7.73281i	−0.0824197	+	0.307595i
$633$		0			0
$634$	27.0648	+	15.6259i	1.07488	+	0.620583i
$635$	−0.592460	−	0.222648i	−0.0235111	−	0.00883550i
$636$		0			0
$637$	−12.7692	−	41.0986i	−0.505934	−	1.62839i
$638$	12.4729	−	12.4729i	0.493809	−	0.493809i
$639$		0			0
$640$	0.365351	+	2.20602i	0.0144417	+	0.0872005i
$641$	31.4224	+	18.1417i	1.24111	+	0.716555i	0.969320	−	0.245802i	$-0.0790513\pi$
$641$	31.4224	+	18.1417i	1.24111	+	0.716555i	0.271789	+	0.962357i	$0.412385\pi$
$642$		0			0
$643$	2.60079	+	2.60079i	0.102565	+	0.102565i	0.756527	−	0.653962i	$-0.226894\pi$
$643$	2.60079	+	2.60079i	0.102565	+	0.102565i	−0.653962	+	0.756527i	$0.726894\pi$
$644$	−2.65997	−	4.40428i	−0.104818	−	0.173553i
$645$		0			0
$646$	−8.20266	−	14.2074i	−0.322729	−	0.558983i
$647$	7.66073	−	2.05269i	0.301174	−	0.0806994i	−0.105067	−	0.994465i	$-0.533506\pi$
$647$	7.66073	−	2.05269i	0.301174	−	0.0806994i	0.406242	+	0.913766i	$0.366839\pi$
$648$		0			0
$649$	41.9936	−	24.2450i	1.64839	−	0.951699i
$650$	−5.96694	+	30.1557i	−0.234043	+	1.18281i
$651$		0			0
$652$	−0.0262736	+	0.0262736i	−0.00102895	+	0.00102895i
$653$	−45.9484	−	12.3118i	−1.79810	−	0.481799i	−0.804421	−	0.594060i	$-0.797524\pi$
$653$	−45.9484	−	12.3118i	−1.79810	−	0.481799i	−0.993679	+	0.112260i	$0.964191\pi$
$654$		0			0
$655$	28.5275	+	20.4209i	1.11466	+	0.797909i
$656$	0.232462	−	0.134212i	0.00907612	−	0.00524010i
$657$		0			0
$658$	1.76936	+	1.70092i	0.0689770	+	0.0663087i
$659$	−40.4379			−1.57524			−0.787618	−	0.616164i	$-0.788686\pi$
$659$	−40.4379			−1.57524			−0.787618	+	0.616164i	$0.788686\pi$
$660$		0			0
$661$	15.3620	−	26.6078i	0.597513	−	1.03492i	−0.395674	−	0.918391i	$-0.629489\pi$
$661$	15.3620	−	26.6078i	0.597513	−	1.03492i	0.993187	−	0.116532i	$-0.0371777\pi$
$662$	10.4037	−	2.78766i	0.404350	−	0.108345i
$663$		0			0
$664$		−	1.84245i		−	0.0715011i
$665$	14.3344	+	16.7635i	0.555865	+	0.650061i
$666$		0			0
$667$	−6.69767	−	1.79463i	−0.259335	−	0.0694885i
$668$	3.38994	+	12.6514i	0.131161	+	0.489499i
$669$		0			0
$670$	0.0390693	+	0.0861130i	0.00150938	+	0.00332684i
$671$			56.5070i			2.18143i
$672$		0			0
$673$	2.13524	+	2.13524i	0.0823073	+	0.0823073i	0.747062	−	0.664755i	$-0.231464\pi$
$673$	2.13524	+	2.13524i	0.0823073	+	0.0823073i	−0.664755	+	0.747062i	$0.731464\pi$
$674$	−15.4248	−	26.7165i	−0.594141	−	1.02908i
$675$		0			0
$676$	12.3995	−	21.4765i	0.476902	−	0.826019i
$677$	−0.625198	+	2.33327i	−0.0240283	+	0.0896749i	−0.976899	−	0.213703i	$-0.931448\pi$
$677$	−0.625198	+	2.33327i	−0.0240283	+	0.0896749i	0.952870	+	0.303378i	$0.0981143\pi$
$678$		0			0
$679$	34.0137	−	20.5426i	1.30533	−	0.788354i
$680$	9.79245	+	0.959519i	0.375523	+	0.0367959i
$681$		0			0
$682$	0.697081	+	2.60154i	0.0266926	+	0.0996182i
$683$	5.33754	+	19.9200i	0.204235	+	0.762216i	0.989681	+	0.143286i	$0.0457669\pi$
$683$	5.33754	+	19.9200i	0.204235	+	0.762216i	−0.785446	+	0.618930i	$0.787566\pi$
$684$		0			0
$685$	−3.59333	−	4.37402i	−0.137294	−	0.167123i
$686$	15.4634	−	10.1923i	0.590396	−	0.389143i
$687$		0			0
$688$	3.07339	−	11.4701i	0.117172	−	0.437292i
$689$	−24.5176	+	42.4657i	−0.934046	+	1.61782i
$690$		0			0
$691$	20.3078	+	35.1742i	0.772546	+	1.33809i	0.936163	+	0.351566i	$0.114351\pi$
$691$	20.3078	+	35.1742i	0.772546	+	1.33809i	−0.163617	+	0.986524i	$0.552316\pi$
$692$	0.517505	+	0.517505i	0.0196726	+	0.0196726i
$693$		0			0
$694$		−	6.15667i		−	0.233704i
$695$	−5.71758	+	2.59405i	−0.216880	+	0.0983981i
$696$		0			0
$697$	−0.305703	−	1.14090i	−0.0115793	−	0.0432146i
$698$	0.190521	+	0.0510501i	0.00721134	+	0.00193227i
$699$		0			0
$700$	−13.1797	+	1.13855i	−0.498145	+	0.0430330i
$701$		−	16.4455i		−	0.621140i	−0.950551	−	0.310570i	$-0.899480\pi$
$701$		−	16.4455i		−	0.621140i	0.950551	−	0.310570i	$-0.100520\pi$
$702$		0			0
$703$	6.05951	−	1.62364i	0.228539	−	0.0612368i
$704$	−2.47359	+	4.28438i	−0.0932270	+	0.161474i
$705$		0			0
$706$	10.2157			0.384472
$707$	9.55095	+	9.18148i	0.359200	+	0.345305i
$708$		0			0
$709$	17.3375	−	10.0098i	0.651122	−	0.375926i	−0.137764	−	0.990465i	$-0.543991\pi$
$709$	17.3375	−	10.0098i	0.651122	−	0.375926i	0.788886	+	0.614539i	$0.210658\pi$
$710$	−5.95919	−	35.9821i	−0.223644	−	1.35038i
$711$		0			0
$712$	0.443021	+	0.118707i	0.0166029	+	0.00444873i
$713$	0.748631	−	0.748631i	0.0280365	−	0.0280365i
$714$		0			0
$715$	−52.5520	+	43.1724i	−1.96533	+	1.61456i
$716$	5.54712	−	3.20263i	0.207306	−	0.119688i
$717$		0			0
$718$	14.7440	−	3.95063i	0.550239	−	0.147436i
$719$	−20.2948	−	35.1516i	−0.756868	−	1.31093i	−0.944440	−	0.328683i	$-0.893395\pi$
$719$	−20.2948	−	35.1516i	−0.756868	−	1.31093i	0.187572	−	0.982251i	$-0.439938\pi$
$720$		0			0
$721$	−23.3890	+	42.4215i	−0.871052	+	1.57986i
$722$	−3.60644	−	3.60644i	−0.134218	−	0.134218i
$723$		0			0
$724$	7.53612	+	4.35098i	0.280078	+	0.161703i
$725$	−11.7412	+	13.4154i	−0.436057	+	0.498234i
$726$		0			0
$727$	17.5089	−	17.5089i	0.649368	−	0.649368i	−0.303473	−	0.952840i	$-0.598146\pi$
$727$	17.5089	−	17.5089i	0.649368	−	0.649368i	0.952840	+	0.303473i	$0.0981461\pi$
$728$	15.7920	+	3.89937i	0.585290	+	0.144520i
$729$		0			0
$730$	−17.7587	+	8.05711i	−0.657281	+	0.298207i
$731$	−45.2516	−	26.1260i	−1.67369	−	0.966305i
$732$		0			0
$733$	1.36477	−	5.09340i	0.0504090	−	0.188129i	−0.936130	−	0.351653i	$-0.885620\pi$
$733$	1.36477	−	5.09340i	0.0504090	−	0.188129i	0.986539	+	0.163524i	$0.0522862\pi$
$734$	23.7301			0.875896
$735$		0			0
$736$	1.94470			0.0716828
$737$	−0.0541481	+	0.202083i	−0.00199457	+	0.00744384i
$738$		0			0
$739$	3.95782	+	2.28505i	0.145591	+	0.0840570i	0.571026	−	0.820932i	$-0.306546\pi$
$739$	3.95782	+	2.28505i	0.145591	+	0.0840570i	−0.425435	+	0.904989i	$0.639879\pi$
$740$	−1.32357	+	3.52200i	−0.0486555	+	0.129471i
$741$		0			0
$742$	−20.4864	−	5.05852i	−0.752080	−	0.185704i
$743$	12.0060	−	12.0060i	0.440459	−	0.440459i	−0.451707	−	0.892166i	$-0.649185\pi$
$743$	12.0060	−	12.0060i	0.440459	−	0.440459i	0.892166	+	0.451707i	$0.149185\pi$
$744$		0			0
$745$	−25.5210	+	35.6523i	−0.935019	+	1.30620i
$746$	16.1222	+	9.30815i	0.590275	+	0.340796i
$747$		0			0
$748$	15.3930	+	15.3930i	0.562825	+	0.562825i
$749$	4.97561	−	9.02444i	0.181805	−	0.329746i
$750$		0			0
$751$	7.40868	+	12.8322i	0.270347	+	0.468254i	0.968951	−	0.247255i	$-0.0795284\pi$
$751$	7.40868	+	12.8322i	0.270347	+	0.468254i	−0.698604	+	0.715509i	$0.746195\pi$
$752$	−0.896043	+	0.240094i	−0.0326753	+	0.00875533i
$753$		0			0
$754$	18.9844	−	10.9606i	0.691370	−	0.399163i
$755$	5.57530	+	0.546299i	0.202906	+	0.0198818i
$756$		0			0
$757$	−15.0073	+	15.0073i	−0.545448	+	0.545448i	−0.925121	−	0.379673i	$-0.876037\pi$
$757$	−15.0073	+	15.0073i	−0.545448	+	0.545448i	0.379673	+	0.925121i	$0.376037\pi$
$758$	33.6920	+	9.02773i	1.22375	+	0.327902i
$759$		0			0
$760$	−8.22455	+	1.36211i	−0.298336	+	0.0494090i
$761$	−2.48525	+	1.43486i	−0.0900904	+	0.0520137i	−0.544368	−	0.838846i	$-0.683231\pi$
$761$	−2.48525	+	1.43486i	−0.0900904	+	0.0520137i	0.454278	+	0.890860i	$0.349897\pi$
$762$		0			0
$763$	−16.4608	−	15.8241i	−0.595922	−	0.572870i
$764$	7.98046			0.288723
$765$		0			0
$766$	−15.5448	+	26.9245i	−0.561658	+	0.972821i
$767$	58.2073	−	15.5966i	2.10174	−	0.563161i
$768$		0			0
$769$		−	35.3321i		−	1.27411i	−0.770819	−	0.637055i	$-0.780153\pi$
$769$		−	35.3321i		−	1.27411i	0.770819	−	0.637055i	$-0.219847\pi$
$770$	−24.1302	−	16.5634i	−0.869591	−	0.596902i
$771$		0			0
$772$	18.8317	+	5.04593i	0.677766	+	0.181607i
$773$	−3.63582	−	13.5691i	−0.130771	−	0.488045i	0.869208	−	0.494446i	$-0.164629\pi$
$773$	−3.63582	−	13.5691i	−0.130771	−	0.488045i	−0.999980	+	0.00640103i	$0.997962\pi$
$774$		0			0
$775$	−0.877563	−	2.57673i	−0.0315230	−	0.0925589i
$776$			15.0187i			0.539141i
$777$		0			0
$778$	−14.0908	−	14.0908i	−0.505179	−	0.505179i
$779$	0.500374	+	0.866673i	0.0179278	+	0.0310518i
$780$		0			0
$781$	40.3464	−	69.8820i	1.44371	−	2.50058i
$782$	2.21478	−	8.26568i	0.0792005	−	0.295580i
$783$		0			0
$784$	0.276021	+	6.99456i	0.00985789	+	0.249806i
$785$	33.7496	−	27.7259i	1.20457	−	0.989579i
$786$		0			0
$787$	−3.81054	−	14.2211i	−0.135831	−	0.506929i	−0.999993	−	0.00371495i	$-0.998817\pi$
$787$	−3.81054	−	14.2211i	−0.135831	−	0.506929i	0.864162	−	0.503214i	$-0.167849\pi$
$788$	−3.69540	−	13.7914i	−0.131643	−	0.491299i
$789$		0			0
$790$	13.8320	−	11.3632i	0.492121	−	0.404286i
$791$	44.5486	−	26.9052i	1.58397	−	0.956639i
$792$		0			0
$793$	−18.1752	+	67.8309i	−0.645422	+	2.40875i
$794$	6.47536	−	11.2157i	0.229802	−	0.398029i
$795$		0			0
$796$	6.35098	+	11.0002i	0.225105	+	0.389892i
$797$	−17.8544	−	17.8544i	−0.632437	−	0.632437i	0.316242	−	0.948679i	$-0.397579\pi$
$797$	−17.8544	−	17.8544i	−0.632437	−	0.632437i	−0.948679	+	0.316242i	$0.897579\pi$
$798$		0			0
$799$			4.08194i			0.144409i
$800$	2.20695	−	4.48658i	0.0780274	−	0.158624i
$801$		0			0
$802$	0.471387	+	1.75924i	0.0166453	+	0.0621210i
$803$	−41.6749	−	11.1667i	−1.47067	−	0.394066i
$804$		0			0
$805$	−0.895942	+	11.4701i	−0.0315778	+	0.404268i
$806$			3.34710i			0.117897i
$807$		0			0
$808$	−4.83680	+	1.29602i	−0.170158	+	0.0455937i
$809$	8.23813	−	14.2689i	0.289637	−	0.501666i	−0.684086	−	0.729401i	$-0.739799\pi$
$809$	8.23813	−	14.2689i	0.289637	−	0.501666i	0.973723	+	0.227735i	$0.0731320\pi$
$810$		0			0
$811$	−24.1358			−0.847522			−0.423761	−	0.905774i	$-0.639290\pi$
$811$	−24.1358			−0.847522			−0.423761	+	0.905774i	$0.639290\pi$
$812$	6.80077	+	6.53769i	0.238660	+	0.229428i
$813$		0			0
$814$	−7.20907	+	4.16216i	−0.252678	+	0.145884i
$815$	0.0819678	−	0.0135751i	0.00287121	−	0.000475516i
$816$		0			0
$817$	42.7630	+	11.4583i	1.49609	+	0.400876i
$818$	14.5966	−	14.5966i	0.510359	−	0.510359i
$819$		0			0
$820$	−0.597354	−	0.0585321i	−0.0208605	−	0.00204403i
$821$	−22.7639	+	13.1427i	−0.794464	+	0.458684i	−0.841532	−	0.540207i	$-0.818346\pi$
$821$	−22.7639	+	13.1427i	−0.794464	+	0.458684i	0.0470674	+	0.998892i	$0.485012\pi$
$822$		0			0
$823$	22.4829	−	6.02428i	0.783705	−	0.209993i	0.155287	−	0.987869i	$-0.450370\pi$
$823$	22.4829	−	6.02428i	0.783705	−	0.209993i	0.628417	+	0.777876i	$0.283703\pi$
$824$	−9.15468	−	15.8564i	−0.318918	−	0.552383i
$825$		0			0
$826$	13.4066	+	22.1981i	0.466474	+	0.772370i
$827$	−3.56023	−	3.56023i	−0.123801	−	0.123801i	0.642492	−	0.766293i	$-0.277901\pi$
$827$	−3.56023	−	3.56023i	−0.123801	−	0.123801i	−0.766293	+	0.642492i	$0.777901\pi$
$828$		0			0
$829$	−25.5490	−	14.7507i	−0.887354	−	0.512314i	−0.0142776	−	0.999898i	$-0.504545\pi$
$829$	−25.5490	−	14.7507i	−0.887354	−	0.512314i	−0.873076	+	0.487584i	$0.837878\pi$
$830$	−2.39804	+	3.35001i	−0.0832373	+	0.116281i
$831$		0			0
$832$	−4.34735	+	4.34735i	−0.150717	+	0.150717i
$833$	30.0437	+	6.79277i	1.04095	+	0.235355i
$834$		0			0
$835$	10.3028	−	27.4155i	0.356542	−	0.948751i
$836$	−15.9732	−	9.22212i	−0.552444	−	0.318954i
$837$		0			0
$838$	3.33743	−	12.4555i	0.115290	−	0.430267i
$839$	−18.9600			−0.654573			−0.327286	−	0.944925i	$-0.606134\pi$
$839$	−18.9600			−0.654573			−0.327286	+	0.944925i	$0.606134\pi$
$840$		0			0
$841$	−16.2869			−0.561616
$842$	4.38208	−	16.3542i	0.151017	−	0.563601i
$843$		0			0
$844$	−16.3592	−	9.44499i	−0.563107	−	0.325110i
$845$	−50.4978	+	22.9108i	−1.73718	+	0.788154i
$846$		0			0
$847$	−9.90428	−	34.2470i	−0.340315	−	1.17674i
$848$	5.63966	−	5.63966i	0.193667	−	0.193667i
$849$		0			0
$850$	−16.5561	−	14.4900i	−0.567869	−	0.497002i
$851$	2.83384	+	1.63612i	0.0971427	+	0.0560854i
$852$		0			0
$853$	14.2865	+	14.2865i	0.489159	+	0.489159i	0.908041	−	0.418882i	$-0.137578\pi$
$853$	14.2865	+	14.2865i	0.489159	+	0.489159i	−0.418882	+	0.908041i	$0.637578\pi$
$854$	−30.2140	+	0.595925i	−1.03390	+	0.0203921i
$855$		0			0
$856$	1.94750	+	3.37317i	0.0665642	+	0.115293i
$857$	14.9651	−	4.00989i	0.511199	−	0.136975i	0.00600644	−	0.999982i	$-0.498088\pi$
$857$	14.9651	−	4.00989i	0.511199	−	0.136975i	0.505193	+	0.863007i	$0.331421\pi$
$858$		0			0
$859$	−42.4333	+	24.4989i	−1.44781	+	0.835891i	−0.998351	−	0.0574123i	$-0.981715\pi$
$859$	−42.4333	+	24.4989i	−1.44781	+	0.835891i	−0.449455	+	0.893303i	$0.648382\pi$
$860$	−20.5170	+	16.8551i	−0.699623	+	0.574753i
$861$		0			0
$862$	21.0190	−	21.0190i	0.715910	−	0.715910i
$863$	50.5379	+	13.5416i	1.72033	+	0.460961i	0.977919	−	0.208984i	$-0.0670157\pi$
$863$	50.5379	+	13.5416i	1.72033	+	0.460961i	0.742411	+	0.669945i	$0.233682\pi$
$864$		0			0
$865$	−0.267387	−	1.61450i	−0.00909142	−	0.0548948i
$866$	−24.5182	+	14.1556i	−0.833162	+	0.481026i
$867$		0			0
$868$	−1.38368	+	0.400162i	−0.0469652	+	0.0135824i
$869$	39.6051			1.34351
$870$		0			0
$871$	−0.129999	+	0.225164i	−0.00440484	+	0.00762940i
$872$	8.33612	−	2.23366i	0.282297	−	0.0756411i
$873$		0			0
$874$			7.25031i			0.245245i
$875$	25.4456	+	15.0838i	0.860218	+	0.509927i
$876$		0			0
$877$	−19.1533	−	5.13210i	−0.646760	−	0.173299i	−0.0794965	−	0.996835i	$-0.525331\pi$
$877$	−19.1533	−	5.13210i	−0.646760	−	0.173299i	−0.567264	+	0.823536i	$0.691998\pi$
$878$	−1.65609	−	6.18060i	−0.0558902	−	0.208585i
$879$		0			0
$880$	10.0739	−	4.57051i	0.339591	−	0.154072i
$881$			22.4079i			0.754943i	0.926021	+	0.377471i	$0.123206\pi$
$881$			22.4079i			0.754943i	−0.926021	+	0.377471i	$0.876794\pi$
$882$		0			0
$883$	−24.7816	−	24.7816i	−0.833966	−	0.833966i	0.154091	−	0.988057i	$-0.450755\pi$
$883$	−24.7816	−	24.7816i	−0.833966	−	0.833966i	−0.988057	+	0.154091i	$0.950755\pi$
$884$	13.5267	+	23.4289i	0.454951	+	0.787999i
$885$		0			0
$886$	0.169802	−	0.294105i	0.00570460	−	0.00988066i
$887$	−9.95542	+	37.1542i	−0.334270	+	1.24751i	0.570387	+	0.821376i	$0.306793\pi$
$887$	−9.95542	+	37.1542i	−0.334270	+	1.24751i	−0.904658	+	0.426139i	$0.859874\pi$
$888$		0			0
$889$	0.641035	−	0.387154i	0.0214996	−	0.0129847i
$890$	−0.651012	−	0.792450i	−0.0218220	−	0.0265630i
$891$		0			0
$892$	−1.07538	−	4.01337i	−0.0360064	−	0.134378i
$893$	−0.895127	−	3.34066i	−0.0299543	−	0.111791i
$894$		0			0
$895$	−14.2543	−	1.39672i	−0.476470	−	0.0466872i
$896$	−2.31693	−	1.27744i	−0.0774032	−	0.0426761i
$897$		0			0
$898$	−3.07558	+	11.4782i	−0.102633	+	0.383033i
$899$	−0.970567	+	1.68107i	−0.0323702	+	0.0560668i
$900$		0			0
$901$	−17.5477	−	30.3935i	−0.584598	−	1.01255i
$902$	−0.938997	−	0.938997i	−0.0312652	−	0.0312652i
$903$		0			0
$904$			19.6704i			0.654227i
$905$	−8.03940	−	17.7197i	−0.267239	−	0.589023i
$906$		0			0
$907$	8.21125	+	30.6448i	0.272650	+	1.01754i	0.957400	+	0.288766i	$0.0932448\pi$
$907$	8.21125	+	30.6448i	0.272650	+	1.01754i	−0.684750	+	0.728778i	$0.740089\pi$
$908$	−0.861758	−	0.230907i	−0.0285984	−	0.00766293i
$909$		0			0
$910$	−23.6383	−	27.6440i	−0.783602	−	0.916391i
$911$			38.5994i			1.27886i	0.768851	+	0.639428i	$0.220829\pi$
$911$			38.5994i			1.27886i	−0.768851	+	0.639428i	$0.779171\pi$
$912$		0			0
$913$	−8.80437	+	2.35912i	−0.291382	+	0.0780756i
$914$	−10.0824	+	17.4632i	−0.333496	+	0.577633i
$915$		0			0
$916$	−20.6026			−0.680728
$917$	−39.8768	+	11.5324i	−1.31685	+	0.380834i
$918$		0			0
$919$	−3.71713	+	2.14609i	−0.122617	+	0.0707928i	−0.560054	−	0.828456i	$-0.689220\pi$
$919$	−3.71713	+	2.14609i	−0.122617	+	0.0707928i	0.437437	+	0.899249i	$0.355886\pi$
$920$	−3.53593	−	2.53113i	−0.116576	−	0.0834488i
$921$		0			0
$922$	−18.9275	−	5.07160i	−0.623343	−	0.167024i
$923$	70.9091	−	70.9091i	2.33400	−	2.33400i
$924$		0			0
$925$	6.99062	−	4.68112i	0.229850	−	0.153914i
$926$	−23.5444	+	13.5934i	−0.773716	+	0.446705i
$927$		0			0
$928$	−3.44405	+	0.922831i	−0.113057	+	0.0302934i
$929$	−8.99774	−	15.5845i	−0.295206	−	0.511312i	0.679827	−	0.733373i	$-0.262055\pi$
$929$	−8.99774	−	15.5845i	−0.295206	−	0.511312i	−0.975033	+	0.222061i	$0.928722\pi$
$930$		0			0
$931$	−26.0773	+	1.02907i	−0.854650	+	0.0337264i
$932$	−3.40735	−	3.40735i	−0.111611	−	0.111611i
$933$		0			0
$934$	−26.2075	−	15.1309i	−0.857534	−	0.495098i
$935$	−7.95333	−	48.0229i	−0.260102	−	1.57052i
$936$		0			0
$937$	25.1463	−	25.1463i	0.821495	−	0.821495i	−0.164828	−	0.986322i	$-0.552707\pi$
$937$	25.1463	−	25.1463i	0.821495	−	0.821495i	0.986322	+	0.164828i	$0.0527068\pi$
$938$	−0.108624	−	0.0268216i	−0.00354671	−	0.000875756i
$939$		0			0
$940$	1.94171	+	0.729697i	0.0633316	+	0.0238001i
$941$	−19.8371	−	11.4529i	−0.646670	−	0.373355i	0.140509	−	0.990079i	$-0.455126\pi$
$941$	−19.8371	−	11.4529i	−0.646670	−	0.373355i	−0.787179	+	0.616724i	$0.788459\pi$
$942$		0			0
$943$	−0.135105	+	0.504219i	−0.00439962	+	0.0164196i
$944$	−9.80154			−0.319013
$945$		0			0
$946$	−58.7462			−1.91000
$947$	−5.17572	+	19.3161i	−0.168188	+	0.627687i	0.829424	+	0.558620i	$0.188669\pi$
$947$	−5.17572	+	19.3161i	−0.168188	+	0.627687i	−0.997612	+	0.0690674i	$0.977998\pi$
$948$		0			0
$949$	−46.4347	−	26.8091i	−1.50733	−	0.870260i
$950$	16.7270	+	8.22802i	0.542696	+	0.266952i
$951$		0			0
$952$	−8.06825	+	8.39292i	−0.261494	+	0.272016i
$953$	−5.12950	+	5.12950i	−0.166161	+	0.166161i	−0.785289	−	0.619129i	$-0.787486\pi$
$953$	−5.12950	+	5.12950i	−0.166161	+	0.166161i	0.619129	+	0.785289i	$0.287486\pi$
$954$		0			0
$955$	−14.5103	−	10.3870i	−0.469543	−	0.336114i
$956$	−13.6183	−	7.86253i	−0.440448	−	0.254293i
$957$		0			0
$958$	1.15697	+	1.15697i	0.0373801	+	0.0373801i
$959$	6.69658	−	0.132080i	0.216244	−	0.00426508i
$960$		0			0
$961$	15.3518	+	26.5901i	0.495220	+	0.857745i
$962$	−9.99250	+	2.67748i	−0.322171	+	0.0863255i
$963$		0			0
$964$	6.31306	−	3.64485i	0.203330	−	0.117393i
$965$	−27.6728	−	33.6850i	−0.890819	−	1.08436i
$966$		0			0
$967$	−19.0930	+	19.0930i	−0.613989	+	0.613989i	−0.943983	−	0.329994i	$-0.892953\pi$
$967$	−19.0930	+	19.0930i	−0.613989	+	0.613989i	0.329994	+	0.943983i	$0.392953\pi$
$968$	13.0155	+	3.48748i	0.418333	+	0.112092i
$969$		0			0
$970$	19.5476	−	27.3075i	0.627636	−	0.876792i
$971$	38.4438	−	22.1955i	1.23372	−	0.712289i	0.265917	−	0.963996i	$-0.414325\pi$
$971$	38.4438	−	22.1955i	1.23372	−	0.712289i	0.967804	+	0.251707i	$0.0809918\pi$
$972$		0			0
$973$	1.78085	−	7.21223i	0.0570915	−	0.231214i
$974$	7.21490			0.231180
$975$		0			0
$976$	5.71103	−	9.89179i	0.182806	−	0.316628i
$977$	8.10250	−	2.17106i	0.259222	−	0.0694583i	−0.126868	−	0.991920i	$-0.540492\pi$
$977$	8.10250	−	2.17106i	0.259222	−	0.0694583i	0.386089	+	0.922461i	$0.373826\pi$
$978$		0			0
$979$		−	2.26902i		−	0.0725181i
$980$	8.60189	−	13.0770i	0.274777	−	0.417729i
$981$		0			0
$982$	−22.6253	−	6.06244i	−0.722003	−	0.193460i
$983$	0.734462	+	2.74105i	0.0234257	+	0.0874259i	0.976649	−	0.214841i	$-0.0689233\pi$
$983$	0.734462	+	2.74105i	0.0234257	+	0.0874259i	−0.953223	+	0.302267i	$0.902257\pi$
$984$		0			0
$985$	−11.2311	+	29.8858i	−0.357853	+	0.952239i
$986$			15.6894i			0.499654i
$987$		0			0
$988$	−16.2079	−	16.2079i	−0.515643	−	0.515643i
$989$	11.5464	+	19.9989i	0.367153	+	0.635928i
$990$		0			0
$991$	17.4678	−	30.2552i	0.554884	−	0.961088i	−0.443028	−	0.896508i	$-0.646096\pi$
$991$	17.4678	−	30.2552i	0.554884	−	0.961088i	0.997913	−	0.0645801i	$-0.0205708\pi$
$992$	0.140905	−	0.525863i	0.00447373	−	0.0166962i
$993$		0			0
$994$	37.7911	+	20.8361i	1.19866	+	0.660880i
$995$	2.76977	−	28.2671i	0.0878075	−	0.896126i
$996$		0			0
$997$	−0.417054	−	1.55647i	−0.0132082	−	0.0492938i	0.959007	−	0.283382i	$-0.0914563\pi$
$997$	−0.417054	−	1.55647i	−0.0132082	−	0.0492938i	−0.972215	+	0.234088i	$0.924790\pi$
$998$	7.64876	+	28.5456i	0.242117	+	0.903594i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.ce.c.53.3	✓	32
3.2	odd	2	inner	630.2.ce.c.53.6	yes	32
5.2	odd	4	inner	630.2.ce.c.557.2	yes	32
7.2	even	3	inner	630.2.ce.c.233.7	yes	32
15.2	even	4	inner	630.2.ce.c.557.7	yes	32
21.2	odd	6	inner	630.2.ce.c.233.2	yes	32
35.2	odd	12	inner	630.2.ce.c.107.6	yes	32
105.2	even	12	inner	630.2.ce.c.107.3	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.ce.c.53.3	✓	32	1.1	even	1	trivial
630.2.ce.c.53.6	yes	32	3.2	odd	2	inner
630.2.ce.c.107.3	yes	32	105.2	even	12	inner
630.2.ce.c.107.6	yes	32	35.2	odd	12	inner
630.2.ce.c.233.2	yes	32	21.2	odd	6	inner
630.2.ce.c.233.7	yes	32	7.2	even	3	inner
630.2.ce.c.557.2	yes	32	5.2	odd	4	inner
630.2.ce.c.557.7	yes	32	15.2	even	4	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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.ce (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-0.866025 - 0.500000i) q^{4} +(0.923861 + 2.03629i) q^{5} +(-2.56861 - 0.634242i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.20602 + 0.365351i) q^{10} +(-4.28438 - 2.47359i) q^{11} +(-4.34735 - 4.34735i) q^{13} +(1.27744 - 2.31693i) q^{14} +(0.500000 + 0.866025i) q^{16} +(4.25035 - 1.13888i) q^{17} +(-3.22874 + 1.86412i) q^{19} +(0.218058 - 2.22541i) q^{20} +(3.49819 - 3.49819i) q^{22} +(-1.87844 - 0.503327i) q^{23} +(-3.29296 + 3.76250i) q^{25} +(5.32440 - 3.07404i) q^{26} +(1.90736 + 1.83357i) q^{28} +3.56555 q^{29} +(-0.272207 + 0.471476i) q^{31} +(-0.965926 + 0.258819i) q^{32} +4.40029i q^{34} +(-1.08153 - 5.81638i) q^{35} +(-1.62530 - 0.435499i) q^{37} +(-0.964938 - 3.60120i) q^{38} +(2.09314 + 0.786607i) q^{40} -0.268424i q^{41} +(-8.39666 - 8.39666i) q^{43} +(2.47359 + 4.28438i) q^{44} +(0.972352 - 1.68416i) q^{46} +(-0.240094 + 0.896043i) q^{47} +(6.19547 + 3.25824i) q^{49} +(-2.78202 - 4.15456i) q^{50} +(1.59124 + 5.93859i) q^{52} +(-2.06426 - 7.70392i) q^{53} +(1.07877 - 11.0095i) q^{55} +(-2.26476 + 1.36780i) q^{56} +(-0.922831 + 3.44405i) q^{58} +(-4.90077 + 8.48838i) q^{59} +(-5.71103 - 9.89179i) q^{61} +(-0.384959 - 0.384959i) q^{62} -1.00000i q^{64} +(4.83612 - 12.8688i) q^{65} +(-0.0109452 - 0.0408482i) q^{67} +(-4.25035 - 1.13888i) q^{68} +(5.89811 + 0.460709i) q^{70} +16.3109i q^{71} +(8.42396 - 2.25719i) q^{73} +(0.841319 - 1.45721i) q^{74} +3.72823 q^{76} +(9.43604 + 9.07102i) q^{77} +(-6.93305 + 4.00280i) q^{79} +(-1.30155 + 1.81823i) q^{80} +(0.259278 + 0.0694733i) q^{82} +(1.30281 - 1.30281i) q^{83} +(6.24583 + 7.60279i) q^{85} +(10.2838 - 5.93734i) q^{86} +(-4.77861 + 1.28042i) q^{88} +(0.229324 + 0.397201i) q^{89} +(8.40936 + 13.9239i) q^{91} +(1.37511 + 1.37511i) q^{92} +(-0.803371 - 0.463826i) q^{94} +(-6.77880 - 4.85248i) q^{95} +(-10.6198 + 10.6198i) q^{97} +(-4.75072 + 5.14107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 12 q^{7} + 8 q^{13} + 16 q^{16} + 32 q^{22} - 16 q^{25} - 56 q^{31} + 20 q^{37} + 4 q^{40} + 24 q^{46} + 4 q^{52} + 12 q^{58} - 48 q^{61} + 8 q^{67} + 24 q^{70} + 48 q^{73} - 36 q^{82} - 136 q^{85}+ \cdots - 40 q^{97}+O(q^{100}) \) 32 * q - 12 * q^7 + 8 * q^13 + 16 * q^16 + 32 * q^22 - 16 * q^25 - 56 * q^31 + 20 * q^37 + 4 * q^40 + 24 * q^46 + 4 * q^52 + 12 * q^58 - 48 * q^61 + 8 * q^67 + 24 * q^70 + 48 * q^73 - 36 * q^82 - 136 * q^85 - 16 * q^88 - 40 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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