LMFDB - Embedded newform 630.2.bv.d.73.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(73,630)] 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([0, 9, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.73"); 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.bv (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,4] 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			73.3
Character	$\chi$	$=$	630.73
Dual form			630.2.bv.d.397.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.316731 - 2.21352i) q^{5} +(1.51871 + 2.16646i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.878841 + 2.05612i) q^{10} +(-3.20142 + 5.54503i) q^{11} +(-4.52364 + 4.52364i) q^{13} +(-0.906239 - 2.48571i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.161291 - 0.0432177i) q^{17} +(1.04950 + 1.81778i) q^{19} +(1.38106 - 1.75860i) q^{20} +(4.52750 - 4.52750i) q^{22} +(1.39635 - 5.21124i) q^{23} +(-4.79936 - 1.40218i) q^{25} +(5.54030 - 3.19870i) q^{26} +(0.232012 + 2.63556i) q^{28} +3.74448i q^{29} +(6.20971 + 3.58518i) q^{31} +(-0.258819 - 0.965926i) q^{32} -0.166980 q^{34} +(5.27652 - 2.67551i) q^{35} +(-0.703938 - 0.188620i) q^{37} +(-0.543260 - 2.02747i) q^{38} +(-1.78916 + 1.34123i) q^{40} +2.33142i q^{41} +(1.92479 + 1.92479i) q^{43} +(-5.54503 + 3.20142i) q^{44} +(-2.69753 + 4.67227i) q^{46} +(-1.98829 + 7.42041i) q^{47} +(-2.38705 + 6.58042i) q^{49} +(4.27292 + 2.59657i) q^{50} +(-6.17941 + 1.65577i) q^{52} +(-10.2832 + 2.75538i) q^{53} +(11.2601 + 8.84271i) q^{55} +(0.458027 - 2.60580i) q^{56} +(0.969143 - 3.61689i) q^{58} +(-2.22826 + 3.85946i) q^{59} +(9.91039 - 5.72176i) q^{61} +(-5.07021 - 5.07021i) q^{62} +1.00000i q^{64} +(8.58040 + 11.4460i) q^{65} +(-3.18097 - 11.8715i) q^{67} +(0.161291 + 0.0432177i) q^{68} +(-5.78920 + 1.21868i) q^{70} +9.94282 q^{71} +(-2.18599 - 8.15822i) q^{73} +(0.631133 + 0.364385i) q^{74} +2.09900i q^{76} +(-16.8751 + 1.48554i) q^{77} +(-4.16589 + 2.40518i) q^{79} +(2.07533 - 0.832464i) q^{80} +(0.603415 - 2.25198i) q^{82} +(3.88443 - 3.88443i) q^{83} +(-0.0445775 - 0.370709i) q^{85} +(-1.36103 - 2.35737i) q^{86} +(6.18468 - 1.65718i) q^{88} +(5.84862 + 10.1301i) q^{89} +(-16.6703 - 2.93018i) q^{91} +(3.81489 - 3.81489i) q^{92} +(3.84109 - 6.65296i) q^{94} +(4.35611 - 1.74734i) q^{95} +(8.73441 + 8.73441i) q^{97} +(4.00886 - 5.73839i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{7} + 12 q^{10} + 16 q^{16} + 8 q^{22} + 20 q^{28} + 48 q^{31} + 32 q^{37} + 80 q^{43} + 8 q^{46} - 28 q^{58} + 48 q^{61} + 16 q^{67} - 60 q^{70} - 24 q^{73} + 48 q^{82} - 144 q^{85} + 4 q^{88}+ \cdots - 32 q^{91}+O(q^{100}) $ 32 * q + 4 * q^7 + 12 * q^10 + 16 * q^16 + 8 * q^22 + 20 * q^28 + 48 * q^31 + 32 * q^37 + 80 * q^43 + 8 * q^46 - 28 * q^58 + 48 * q^61 + 16 * q^67 - 60 * q^70 - 24 * q^73 + 48 * q^82 - 144 * q^85 + 4 * q^88 - 32 * q^91

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$		0			0
$3$		0			0
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.316731	−	2.21352i	0.141647	−	0.989917i
$5$	0.316731	−	2.21352i	0.141647	−	0.989917i
$6$		0			0
$7$	1.51871	+	2.16646i	0.574017	+	0.818843i
$7$	1.51871	+	2.16646i	0.574017	+	0.818843i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	−0.878841	+	2.05612i	−0.277914	+	0.650203i
$11$	−3.20142	+	5.54503i	−0.965266	+	1.67189i	−0.256367	+	0.966580i	$0.582525\pi$
$11$	−3.20142	+	5.54503i	−0.965266	+	1.67189i	−0.708899	+	0.705310i	$0.750808\pi$
$12$		0			0
$13$	−4.52364	+	4.52364i	−1.25463	+	1.25463i	−0.301011	+	0.953621i	$0.597324\pi$
$13$	−4.52364	+	4.52364i	−1.25463	+	1.25463i	−0.953621	+	0.301011i	$0.902676\pi$
$14$	−0.906239	−	2.48571i	−0.242203	−	0.664333i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.161291	−	0.0432177i	0.0391187	−	0.0104818i	−0.239207	−	0.970969i	$-0.576887\pi$
$17$	0.161291	−	0.0432177i	0.0391187	−	0.0104818i	0.278325	+	0.960487i	$0.410221\pi$
$18$		0			0
$19$	1.04950	+	1.81778i	0.240771	+	0.417028i	0.960934	−	0.276777i	$-0.0892663\pi$
$19$	1.04950	+	1.81778i	0.240771	+	0.417028i	−0.720163	+	0.693805i	$0.755933\pi$
$20$	1.38106	−	1.75860i	0.308814	−	0.393235i
$21$		0			0
$22$	4.52750	−	4.52750i	0.965266	−	0.965266i
$23$	1.39635	−	5.21124i	0.291158	−	1.08662i	−0.653062	−	0.757304i	$-0.726516\pi$
$23$	1.39635	−	5.21124i	0.291158	−	1.08662i	0.944221	−	0.329314i	$-0.106817\pi$
$24$		0			0
$25$	−4.79936	−	1.40218i	−0.959873	−	0.280437i
$26$	5.54030	−	3.19870i	1.08654	−	0.627316i
$27$		0			0
$28$	0.232012	+	2.63556i	0.0438461	+	0.498074i
$29$			3.74448i			0.695333i	0.937618	+	0.347666i	$0.113026\pi$
$29$			3.74448i			0.695333i	−0.937618	+	0.347666i	$0.886974\pi$
$30$		0			0
$31$	6.20971	+	3.58518i	1.11530	+	0.643917i	0.940196	−	0.340633i	$-0.110641\pi$
$31$	6.20971	+	3.58518i	1.11530	+	0.643917i	0.175101	+	0.984550i	$0.443975\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$		0			0
$34$	−0.166980			−0.0286369
$35$	5.27652	−	2.67551i	0.891894	−	0.452244i
$36$		0			0
$37$	−0.703938	−	0.188620i	−0.115727	−	0.0310089i	0.200491	−	0.979696i	$-0.435746\pi$
$37$	−0.703938	−	0.188620i	−0.115727	−	0.0310089i	−0.316218	+	0.948687i	$0.602413\pi$
$38$	−0.543260	−	2.02747i	−0.0881284	−	0.328900i
$39$		0			0
$40$	−1.78916	+	1.34123i	−0.282891	+	0.212068i
$41$			2.33142i			0.364106i	0.983289	+	0.182053i	$0.0582743\pi$
$41$			2.33142i			0.364106i	−0.983289	+	0.182053i	$0.941726\pi$
$42$		0			0
$43$	1.92479	+	1.92479i	0.293527	+	0.293527i	0.838472	−	0.544945i	$-0.183449\pi$
$43$	1.92479	+	1.92479i	0.293527	+	0.293527i	−0.544945	+	0.838472i	$0.683449\pi$
$44$	−5.54503	+	3.20142i	−0.835945	+	0.482633i
$45$		0			0
$46$	−2.69753	+	4.67227i	−0.397730	+	0.688888i
$47$	−1.98829	+	7.42041i	−0.290022	+	1.08238i	0.655068	+	0.755570i	$0.272640\pi$
$47$	−1.98829	+	7.42041i	−0.290022	+	1.08238i	−0.945091	+	0.326808i	$0.894027\pi$
$48$		0			0
$49$	−2.38705	+	6.58042i	−0.341008	+	0.940060i
$50$	4.27292	+	2.59657i	0.604282	+	0.367211i
$51$		0			0
$52$	−6.17941	+	1.65577i	−0.856929	+	0.229614i
$53$	−10.2832	+	2.75538i	−1.41251	+	0.378481i	−0.882821	−	0.469710i	$-0.844358\pi$
$53$	−10.2832	+	2.75538i	−1.41251	+	0.378481i	−0.529690	+	0.848191i	$0.677692\pi$
$54$		0			0
$55$	11.2601	+	8.84271i	1.51831	+	1.19235i
$56$	0.458027	−	2.60580i	0.0612064	−	0.348215i
$57$		0			0
$58$	0.969143	−	3.61689i	0.127255	−	0.474921i
$59$	−2.22826	+	3.85946i	−0.290095	+	0.502459i	−0.973832	−	0.227269i	$-0.927020\pi$
$59$	−2.22826	+	3.85946i	−0.290095	+	0.502459i	0.683737	+	0.729728i	$0.260354\pi$
$60$		0			0
$61$	9.91039	−	5.72176i	1.26890	−	0.732597i	0.294116	−	0.955770i	$-0.404975\pi$
$61$	9.91039	−	5.72176i	1.26890	−	0.732597i	0.974779	+	0.223173i	$0.0716414\pi$
$62$	−5.07021	−	5.07021i	−0.643917	−	0.643917i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	8.58040	+	11.4460i	1.06427	+	1.41970i
$66$		0			0
$67$	−3.18097	−	11.8715i	−0.388617	−	1.45034i	−0.832386	−	0.554197i	$-0.813025\pi$
$67$	−3.18097	−	11.8715i	−0.388617	−	1.45034i	0.443769	−	0.896141i	$-0.353641\pi$
$68$	0.161291	+	0.0432177i	0.0195594	+	0.00524092i
$69$		0			0
$70$	−5.78920	+	1.21868i	−0.691942	+	0.145660i
$71$	9.94282			1.18000			0.589998	−	0.807405i	$-0.299129\pi$
$71$	9.94282			1.18000			0.589998	+	0.807405i	$0.299129\pi$
$72$		0			0
$73$	−2.18599	−	8.15822i	−0.255851	−	0.954848i	−0.967615	−	0.252430i	$-0.918770\pi$
$73$	−2.18599	−	8.15822i	−0.255851	−	0.954848i	0.711764	−	0.702418i	$-0.247896\pi$
$74$	0.631133	+	0.364385i	0.0733678	+	0.0423589i
$75$		0			0
$76$			2.09900i			0.240771i
$77$	−16.8751	+	1.48554i	−1.92309	+	0.169293i
$78$		0			0
$79$	−4.16589	+	2.40518i	−0.468699	+	0.270604i	−0.715695	−	0.698413i	$-0.753890\pi$
$79$	−4.16589	+	2.40518i	−0.468699	+	0.270604i	0.246996	+	0.969017i	$0.420557\pi$
$80$	2.07533	−	0.832464i	0.232029	−	0.0930723i
$81$		0			0
$82$	0.603415	−	2.25198i	0.0666360	−	0.248689i
$83$	3.88443	−	3.88443i	0.426371	−	0.426371i	−0.461019	−	0.887390i	$-0.652516\pi$
$83$	3.88443	−	3.88443i	0.426371	−	0.426371i	0.887390	+	0.461019i	$0.152516\pi$
$84$		0			0
$85$	−0.0445775	−	0.370709i	−0.00483511	−	0.0402090i
$86$	−1.36103	−	2.35737i	−0.146764	−	0.254202i
$87$		0			0
$88$	6.18468	−	1.65718i	0.659289	−	0.176656i
$89$	5.84862	+	10.1301i	0.619952	+	1.07379i	0.989494	+	0.144575i	$0.0461814\pi$
$89$	5.84862	+	10.1301i	0.619952	+	1.07379i	−0.369542	+	0.929214i	$0.620485\pi$
$90$		0			0
$91$	−16.6703	−	2.93018i	−1.74753	−	0.307166i
$92$	3.81489	−	3.81489i	0.397730	−	0.397730i
$93$		0			0
$94$	3.84109	−	6.65296i	0.396178	−	0.686200i
$95$	4.35611	−	1.74734i	0.446928	−	0.179273i
$96$		0			0
$97$	8.73441	+	8.73441i	0.886845	+	0.886845i	0.994219	−	0.107373i	$-0.0342440\pi$
$97$	8.73441	+	8.73441i	0.886845	+	0.886845i	−0.107373	+	0.994219i	$0.534244\pi$
$98$	4.00886	−	5.73839i	0.404956	−	0.579664i
$99$		0			0
$100$	−3.45528	−	3.61401i	−0.345528	−	0.361401i
$101$	3.04723	+	1.75932i	0.303211	+	0.175059i	0.643884	−	0.765123i	$-0.277322\pi$
$101$	3.04723	+	1.75932i	0.303211	+	0.175059i	−0.340674	+	0.940182i	$0.610655\pi$
$102$		0			0
$103$	−8.73475	−	2.34047i	−0.860660	−	0.230613i	−0.198615	−	0.980078i	$-0.563644\pi$
$103$	−8.73475	−	2.34047i	−0.860660	−	0.230613i	−0.662045	+	0.749464i	$0.730311\pi$
$104$	6.39739			0.627316
$105$		0			0
$106$	10.6460			1.03403
$107$	8.95923	+	2.40062i	0.866121	+	0.232077i	0.664410	−	0.747368i	$-0.268683\pi$
$107$	8.95923	+	2.40062i	0.866121	+	0.232077i	0.201712	+	0.979445i	$0.435350\pi$
$108$		0			0
$109$	10.9463	+	6.31985i	1.04847	+	0.605332i	0.922220	−	0.386667i	$-0.126374\pi$
$109$	10.9463	+	6.31985i	1.04847	+	0.605332i	0.126247	+	0.991999i	$0.459707\pi$
$110$	−8.58772	−	11.4557i	−0.818807	−	1.09226i
$111$		0			0
$112$	−1.11685	+	2.39847i	−0.105533	+	0.226634i
$113$	−4.76690	−	4.76690i	−0.448432	−	0.448432i	0.446401	−	0.894833i	$-0.352706\pi$
$113$	−4.76690	−	4.76690i	−0.448432	−	0.448432i	−0.894833	+	0.446401i	$0.852706\pi$
$114$		0			0
$115$	−11.0929	−	4.74141i	−1.03442	−	0.442138i
$116$	−1.87224	+	3.24282i	−0.173833	+	0.301088i
$117$		0			0
$118$	3.15124	−	3.15124i	0.290095	−	0.290095i
$119$	0.338583	+	0.283794i	0.0310378	+	0.0260153i
$120$		0			0
$121$	−14.9982	−	25.9777i	−1.36348	−	2.36161i
$122$	−11.0536	+	2.96180i	−1.00075	+	0.268149i
$123$		0			0
$124$	3.58518	+	6.20971i	0.321959	+	0.557649i
$125$	−4.62387	+	10.1794i	−0.413572	+	0.910471i
$126$		0			0
$127$	8.53377	−	8.53377i	0.757250	−	0.757250i	−0.218571	−	0.975821i	$-0.570140\pi$
$127$	8.53377	−	8.53377i	0.757250	−	0.757250i	0.975821	+	0.218571i	$0.0701395\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$		0			0
$130$	−5.32560	−	13.2767i	−0.467086	−	1.16444i
$131$	−3.62474	+	2.09274i	−0.316695	+	0.182844i	−0.649918	−	0.760004i	$-0.725197\pi$
$131$	−3.62474	+	2.09274i	−0.316695	+	0.182844i	0.333224	+	0.942848i	$0.391864\pi$
$132$		0			0
$133$	−2.34427	+	5.03437i	−0.203274	+	0.436535i
$134$			12.2903i			1.06172i
$135$		0			0
$136$	−0.144609	−	0.0834902i	−0.0124001	−	0.00715923i
$137$	−0.934097	−	3.48610i	−0.0798053	−	0.297837i	0.914475	−	0.404643i	$-0.132604\pi$
$137$	−0.934097	−	3.48610i	−0.0798053	−	0.297837i	−0.994280	+	0.106806i	$0.965938\pi$
$138$		0			0
$139$	−2.57986			−0.218821			−0.109410	−	0.993997i	$-0.534896\pi$
$139$	−2.57986			−0.218821			−0.109410	+	0.993997i	$0.534896\pi$
$140$	5.90735	+	0.321201i	0.499263	+	0.0271464i
$141$		0			0
$142$	−9.60403	−	2.57339i	−0.805952	−	0.215954i
$143$	−10.6016	−	39.5658i	−0.886552	−	3.30866i
$144$		0			0
$145$	8.28849	+	1.18599i	0.688322	+	0.0984915i
$146$			8.44602i			0.698997i
$147$		0			0
$148$	−0.515318	−	0.515318i	−0.0423589	−	0.0423589i
$149$	−8.57321	+	4.94975i	−0.702345	+	0.405499i	−0.808220	−	0.588880i	$-0.799569\pi$
$149$	−8.57321	+	4.94975i	−0.702345	+	0.405499i	0.105875	+	0.994379i	$0.466236\pi$
$150$		0			0
$151$	5.49303	−	9.51421i	0.447016	−	0.774255i	−0.551174	−	0.834390i	$-0.685820\pi$
$151$	5.49303	−	9.51421i	0.447016	−	0.774255i	0.998190	+	0.0601353i	$0.0191532\pi$
$152$	0.543260	−	2.02747i	0.0440642	−	0.164450i
$153$		0			0
$154$	16.6846	+	2.93268i	1.34448	+	0.236322i
$155$	9.90269	−	12.6098i	0.795403	−	1.01284i
$156$		0			0
$157$	−8.84880	+	2.37103i	−0.706211	+	0.189229i	−0.594011	−	0.804457i	$-0.702456\pi$
$157$	−8.84880	+	2.37103i	−0.706211	+	0.189229i	−0.112200	+	0.993686i	$0.535790\pi$
$158$	4.64645	−	1.24501i	0.369651	−	0.0990478i
$159$		0			0
$160$	−2.22007	+	0.266963i	−0.175512	+	0.0211053i
$161$	13.4106	−	4.88922i	1.05690	−	0.385325i
$162$		0			0
$163$	0.202806	−	0.756884i	0.0158850	−	0.0592837i	−0.957528	−	0.288339i	$-0.906897\pi$
$163$	0.202806	−	0.756884i	0.0158850	−	0.0592837i	0.973413	+	0.229055i	$0.0735637\pi$
$164$	−1.16571	+	2.01907i	−0.0910265	+	0.157663i
$165$		0			0
$166$	−4.75743	+	2.74670i	−0.369248	+	0.213186i
$167$	0.0141982	+	0.0141982i	0.00109869	+	0.00109869i	0.707656	−	0.706557i	$-0.249753\pi$
$167$	0.0141982	+	0.0141982i	0.00109869	+	0.00109869i	−0.706557	+	0.707656i	$0.749753\pi$
$168$		0			0
$169$		−	27.9266i		−	2.14820i
$170$	−0.0528879	+	0.369615i	−0.00405632	+	0.0283482i
$171$		0			0
$172$	0.704521	+	2.62931i	0.0537192	+	0.200483i
$173$	6.27037	+	1.68014i	0.476728	+	0.127739i	0.489178	−	0.872184i	$-0.337297\pi$
$173$	6.27037	+	1.68014i	0.476728	+	0.127739i	−0.0124509	+	0.999922i	$0.503963\pi$
$174$		0			0
$175$	−4.25106	−	12.5271i	−0.321350	−	0.946961i
$176$	−6.40285			−0.482633
$177$		0			0
$178$	−3.02747	−	11.2987i	−0.226918	−	0.846871i
$179$	−12.1002	−	6.98604i	−0.904409	−	0.522161i	−0.0257813	−	0.999668i	$-0.508207\pi$
$179$	−12.1002	−	6.98604i	−0.904409	−	0.522161i	−0.878628	+	0.477507i	$0.841541\pi$
$180$		0			0
$181$			8.45277i			0.628289i	0.949375	+	0.314145i	$0.101718\pi$
$181$			8.45277i			0.628289i	−0.949375	+	0.314145i	$0.898282\pi$
$182$	15.3439	+	7.14494i	1.13737	+	0.529618i
$183$		0			0
$184$	−4.67227	+	2.69753i	−0.344444	+	0.198865i
$185$	−0.640473	+	1.49844i	−0.0470885	+	0.110168i
$186$		0			0
$187$	−0.276716	+	1.03272i	−0.0202355	+	0.0755200i
$188$	−5.43212	+	5.43212i	−0.396178	+	0.396178i
$189$		0			0
$190$	−4.65993	+	0.560354i	−0.338067	+	0.0406523i
$191$	−5.71004	−	9.89008i	−0.413164	−	0.715621i	0.582070	−	0.813139i	$-0.302243\pi$
$191$	−5.71004	−	9.89008i	−0.413164	−	0.715621i	−0.995234	+	0.0975179i	$0.968910\pi$
$192$		0			0
$193$	−2.41450	+	0.646964i	−0.173800	+	0.0465695i	−0.344669	−	0.938724i	$-0.612009\pi$
$193$	−2.41450	+	0.646964i	−0.173800	+	0.0465695i	0.170870	+	0.985294i	$0.445342\pi$
$194$	−6.17616	−	10.6974i	−0.443423	−	0.768031i
$195$		0			0
$196$	−5.35746	+	4.50529i	−0.382676	+	0.321806i
$197$	−11.6147	+	11.6147i	−0.827515	+	0.827515i	−0.987172	−	0.159657i	$-0.948961\pi$
$197$	−11.6147	+	11.6147i	−0.827515	+	0.827515i	0.159657	+	0.987172i	$0.448961\pi$
$198$		0			0
$199$	−8.79681	+	15.2365i	−0.623589	+	1.08009i	0.365223	+	0.930920i	$0.380993\pi$
$199$	−8.79681	+	15.2365i	−0.623589	+	1.08009i	−0.988812	+	0.149168i	$0.952340\pi$
$200$	2.40217	+	4.38516i	0.169859	+	0.310077i
$201$		0			0
$202$	−2.48805	−	2.48805i	−0.175059	−	0.175059i
$203$	−8.11225	+	5.68677i	−0.569368	+	0.399133i
$204$		0			0
$205$	5.16064	+	0.738433i	0.360435	+	0.0515744i
$206$	7.83136	+	4.52144i	0.545637	+	0.315023i
$207$		0			0
$208$	−6.17941	−	1.65577i	−0.428465	−	0.114807i
$209$	−13.4396			−0.929633
$210$		0			0
$211$	19.0654			1.31252			0.656259	−	0.754536i	$-0.272138\pi$
$211$	19.0654			1.31252			0.656259	+	0.754536i	$0.272138\pi$
$212$	−10.2832	−	2.75538i	−0.706255	−	0.189241i
$213$		0			0
$214$	−8.03263	−	4.63764i	−0.549099	−	0.317022i
$215$	4.87020	−	3.65092i	0.332145	−	0.248990i
$216$		0			0
$217$	1.66361	+	18.8979i	0.112933	+	1.28287i
$218$	−8.93762	−	8.93762i	−0.605332	−	0.605332i
$219$		0			0
$220$	5.33014	+	13.2880i	0.359358	+	0.895879i
$221$	−0.534119	+	0.925122i	−0.0359288	+	0.0622304i
$222$		0			0
$223$	4.73842	−	4.73842i	0.317308	−	0.317308i	−0.530424	−	0.847732i	$-0.677967\pi$
$223$	4.73842	−	4.73842i	0.317308	−	0.317308i	0.847732	+	0.530424i	$0.177967\pi$
$224$	1.69956	−	2.02768i	0.113557	−	0.135480i
$225$		0			0
$226$	3.37071	+	5.83824i	0.224216	+	0.388354i
$227$	−6.05586	+	1.62266i	−0.401942	+	0.107700i	−0.454126	−	0.890938i	$-0.650048\pi$
$227$	−6.05586	+	1.62266i	−0.401942	+	0.107700i	0.0521842	+	0.998637i	$0.483382\pi$
$228$		0			0
$229$	−8.42986	−	14.6010i	−0.557061	−	0.964858i	−0.997740	−	0.0671932i	$-0.978596\pi$
$229$	−8.42986	−	14.6010i	−0.557061	−	0.964858i	0.440679	−	0.897665i	$-0.354738\pi$
$230$	9.48777	+	7.45091i	0.625605	+	0.491298i
$231$		0			0
$232$	2.64775	−	2.64775i	0.173833	−	0.173833i
$233$	−2.10647	+	7.86147i	−0.138000	+	0.515022i	0.861968	+	0.506963i	$0.169232\pi$
$233$	−2.10647	+	7.86147i	−0.138000	+	0.515022i	−0.999968	+	0.00805892i	$0.997435\pi$
$234$		0			0
$235$	15.7955	+	6.75141i	1.03038	+	0.440413i
$236$	−3.85946	+	2.22826i	−0.251230	+	0.145047i
$237$		0			0
$238$	−0.253594	−	0.361756i	−0.0164381	−	0.0234491i
$239$		−	7.59533i		−	0.491301i	−0.969358	−	0.245651i	$-0.920998\pi$
$239$		−	7.59533i		−	0.491301i	0.969358	−	0.245651i	$-0.0790016\pi$
$240$		0			0
$241$	−7.49824	−	4.32911i	−0.483004	−	0.278862i	0.238664	−	0.971102i	$-0.423291\pi$
$241$	−7.49824	−	4.32911i	−0.483004	−	0.278862i	−0.721668	+	0.692240i	$0.756624\pi$
$242$	7.76366	+	28.9744i	0.499067	+	1.86254i
$243$		0			0
$244$	11.4435			0.732597
$245$	13.8099	+	7.36803i	0.882280	+	0.470726i
$246$		0			0
$247$	−12.9705	−	3.47545i	−0.825296	−	0.221137i
$248$	−1.85583	−	6.92604i	−0.117845	−	0.439804i
$249$		0			0
$250$	7.10094	−	8.63578i	0.449103	−	0.546175i
$251$		−	7.35879i		−	0.464483i	−0.972658	−	0.232241i	$-0.925394\pi$
$251$		−	7.35879i		−	0.464483i	0.972658	−	0.232241i	$-0.0746059\pi$
$252$		0			0
$253$	24.4262	+	24.4262i	1.53566	+	1.53566i
$254$	−10.4517	+	6.03429i	−0.655798	+	0.378625i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.27164	−	19.6740i	0.328836	−	1.22723i	−0.581563	−	0.813501i	$-0.697559\pi$
$257$	5.27164	−	19.6740i	0.328836	−	1.22723i	0.910399	−	0.413731i	$-0.135775\pi$
$258$		0			0
$259$	−0.660440	−	1.81151i	−0.0410377	−	0.112562i
$260$	1.70787	+	14.2027i	0.105917	+	0.880813i
$261$		0			0
$262$	4.04287	−	1.08328i	0.249769	−	0.0669255i
$263$	25.0750	−	6.71883i	1.54619	−	0.414301i	0.617931	−	0.786232i	$-0.287971\pi$
$263$	25.0750	−	6.71883i	1.54619	−	0.414301i	0.928260	+	0.371931i	$0.121304\pi$
$264$		0			0
$265$	2.84208	+	23.6349i	0.174588	+	1.45188i
$266$	3.56738	−	4.25609i	0.218730	−	0.260958i
$267$		0			0
$268$	3.18097	−	11.8715i	0.194308	−	0.725169i
$269$	−4.32616	+	7.49314i	−0.263771	+	0.456865i	−0.967241	−	0.253860i	$-0.918300\pi$
$269$	−4.32616	+	7.49314i	−0.263771	+	0.456865i	0.703470	+	0.710725i	$0.251633\pi$
$270$		0			0
$271$	−5.91873	+	3.41718i	−0.359538	+	0.207579i	−0.668878	−	0.743372i	$-0.733225\pi$
$271$	−5.91873	+	3.41718i	−0.359538	+	0.207579i	0.309340	+	0.950951i	$0.399892\pi$
$272$	0.118073	+	0.118073i	0.00715923	+	0.00715923i
$273$		0			0
$274$			3.60907i			0.218032i
$275$	23.1399	−	22.1236i	1.39539	−	1.33410i
$276$		0			0
$277$	−0.105861	−	0.395080i	−0.00636059	−	0.0237380i	0.962673	−	0.270669i	$-0.0872447\pi$
$277$	−0.105861	−	0.395080i	−0.00636059	−	0.0237380i	−0.969033	+	0.246930i	$0.920578\pi$
$278$	2.49195	+	0.667716i	0.149457	+	0.0400470i
$279$		0			0
$280$	−5.62293	−	1.83919i	−0.336035	−	0.109913i
$281$	20.0813			1.19795			0.598974	−	0.800768i	$-0.295575\pi$
$281$	20.0813			1.19795			0.598974	+	0.800768i	$0.295575\pi$
$282$		0			0
$283$	4.31086	+	16.0884i	0.256254	+	0.956353i	0.967389	+	0.253297i	$0.0815150\pi$
$283$	4.31086	+	16.0884i	0.256254	+	0.956353i	−0.711134	+	0.703056i	$0.751818\pi$
$284$	8.61074	+	4.97141i	0.510953	+	0.294999i
$285$		0			0
$286$			40.9615i			2.42211i
$287$	−5.05091	+	3.54074i	−0.298146	+	0.209003i
$288$		0			0
$289$	−14.6983	+	8.48606i	−0.864605	+	0.499180i
$290$	−7.69911	−	3.29080i	−0.452107	−	0.193243i
$291$		0			0
$292$	2.18599	−	8.15822i	0.127925	−	0.477424i
$293$	10.6204	−	10.6204i	0.620450	−	0.620450i	−0.325196	−	0.945647i	$-0.605430\pi$
$293$	10.6204	−	10.6204i	0.620450	−	0.620450i	0.945647	+	0.325196i	$0.105430\pi$
$294$		0			0
$295$	7.83724	+	6.15472i	0.456302	+	0.358342i
$296$	0.364385	+	0.631133i	0.0211794	+	0.0366839i
$297$		0			0
$298$	9.56218	−	2.56218i	0.553922	−	0.148423i
$299$	17.2572	+	29.8903i	0.998009	+	1.72860i
$300$		0			0
$301$	−1.24678	+	7.09315i	−0.0718629	+	0.408842i
$302$	−7.76832	+	7.76832i	−0.447016	+	0.447016i
$303$		0			0
$304$	−1.04950	+	1.81778i	−0.0601928	+	0.104257i
$305$	−9.52632	−	23.7491i	−0.545476	−	1.35987i
$306$		0			0
$307$	18.1826	+	18.1826i	1.03774	+	1.03774i	0.999259	+	0.0384786i	$0.0122511\pi$
$307$	18.1826	+	18.1826i	1.03774	+	1.03774i	0.0384786	+	0.999259i	$0.487749\pi$
$308$	−15.3570	−	7.15103i	−0.875047	−	0.407468i
$309$		0			0
$310$	−12.8289	+	9.61713i	−0.728634	+	0.546216i
$311$	21.9321	+	12.6625i	1.24366	+	0.718025i	0.969837	−	0.243756i	$-0.0783796\pi$
$311$	21.9321	+	12.6625i	1.24366	+	0.718025i	0.273820	+	0.961781i	$0.411713\pi$
$312$		0			0
$313$	−6.39754	−	1.71422i	−0.361610	−	0.0968932i	0.0734393	−	0.997300i	$-0.476602\pi$
$313$	−6.39754	−	1.71422i	−0.361610	−	0.0968932i	−0.435050	+	0.900407i	$0.643269\pi$
$314$	9.16095			0.516982
$315$		0			0
$316$	−4.81036			−0.270604
$317$	8.06195	+	2.16019i	0.452804	+	0.121329i	0.478011	−	0.878354i	$-0.341358\pi$
$317$	8.06195	+	2.16019i	0.452804	+	0.121329i	−0.0252069	+	0.999682i	$0.508024\pi$
$318$		0			0
$319$	−20.7633	−	11.9877i	−1.16252	−	0.671181i
$320$	2.21352	+	0.316731i	0.123740	+	0.0177058i
$321$		0			0
$322$	−14.2190	+	1.25172i	−0.792395	+	0.0697556i
$323$	0.247835	+	0.247835i	0.0137899	+	0.0137899i
$324$		0			0
$325$	28.0536	−	15.3676i	1.55613	−	0.852442i
$326$	−0.391792	+	0.678603i	−0.0216993	+	0.0375844i
$327$		0			0
$328$	1.64856	−	1.64856i	0.0910265	−	0.0910265i
$329$	−19.0956	+	6.96188i	−1.05278	+	0.383821i
$330$		0			0
$331$	6.84214	+	11.8509i	0.376078	+	0.651387i	0.990488	−	0.137601i	$-0.0439391\pi$
$331$	6.84214	+	11.8509i	0.376078	+	0.651387i	−0.614410	+	0.788987i	$0.710606\pi$
$332$	5.30622	−	1.42180i	0.291217	−	0.0780313i
$333$		0			0
$334$	−0.0100397	−	0.0173892i	−0.000549345	−	0.000951494i
$335$	−27.2854	+	3.28106i	−1.49076	+	0.179263i
$336$		0			0
$337$	12.7271	−	12.7271i	0.693290	−	0.693290i	−0.269665	−	0.962954i	$-0.586913\pi$
$337$	12.7271	−	12.7271i	0.693290	−	0.693290i	0.962954	+	0.269665i	$0.0869129\pi$
$338$	−7.22794	+	26.9750i	−0.393148	+	1.46725i
$339$		0			0
$340$	0.146749	−	0.343332i	0.00795859	−	0.0186198i
$341$	−39.7599	+	22.9554i	−2.15312	+	1.24310i
$342$		0			0
$343$	−17.8814	+	4.82229i	−0.965506	+	0.260379i
$344$		−	2.72206i		−	0.146764i
$345$		0			0
$346$	−5.62186	−	3.24578i	−0.302233	−	0.174494i
$347$	−5.49792	−	20.5185i	−0.295144	−	1.10149i	−0.941103	−	0.338120i	$-0.890209\pi$
$347$	−5.49792	−	20.5185i	−0.295144	−	1.10149i	0.645959	−	0.763372i	$-0.276458\pi$
$348$		0			0
$349$	−17.9442			−0.960531			−0.480266	−	0.877123i	$-0.659460\pi$
$349$	−17.9442			−0.960531			−0.480266	+	0.877123i	$0.659460\pi$
$350$	0.863954	+	13.2005i	0.0461803	+	0.705597i
$351$		0			0
$352$	6.18468	+	1.65718i	0.329644	+	0.0883280i
$353$	7.10696	+	26.5235i	0.378265	+	1.41170i	0.848515	+	0.529171i	$0.177497\pi$
$353$	7.10696	+	26.5235i	0.378265	+	1.41170i	−0.470250	+	0.882533i	$0.655836\pi$
$354$		0			0
$355$	3.14920	−	22.0087i	0.167142	−	1.16810i
$356$			11.6972i			0.619952i
$357$		0			0
$358$	9.87975	+	9.87975i	0.522161	+	0.522161i
$359$	22.0411	−	12.7254i	1.16328	−	0.671623i	0.211195	−	0.977444i	$-0.432264\pi$
$359$	22.0411	−	12.7254i	1.16328	−	0.671623i	0.952089	+	0.305821i	$0.0989310\pi$
$360$		0			0
$361$	7.29711	−	12.6390i	0.384058	−	0.665209i
$362$	2.18774	−	8.16475i	0.114985	−	0.429130i
$363$		0			0
$364$	−12.9719	−	10.8728i	−0.679910	−	0.569889i
$365$	−18.7508	+	2.25477i	−0.981461	+	0.118020i
$366$		0			0
$367$	−1.72190	+	0.461382i	−0.0898825	+	0.0240839i	−0.303480	−	0.952838i	$-0.598149\pi$
$367$	−1.72190	+	0.461382i	−0.0898825	+	0.0240839i	0.213597	+	0.976922i	$0.431482\pi$
$368$	5.21124	−	1.39635i	0.271654	−	0.0727896i
$369$		0			0
$370$	1.00647	−	1.28162i	0.0523241	−	0.0666280i
$371$	−21.5866	−	18.0935i	−1.12072	−	0.939370i
$372$		0			0
$373$	−3.94946	+	14.7396i	−0.204496	+	0.763188i	0.785107	+	0.619360i	$0.212608\pi$
$373$	−3.94946	+	14.7396i	−0.204496	+	0.763188i	−0.989603	+	0.143828i	$0.954059\pi$
$374$	0.534575	−	0.925911i	0.0276422	−	0.0478777i
$375$		0			0
$376$	6.65296	−	3.84109i	0.343100	−	0.198089i
$377$	−16.9387	−	16.9387i	−0.872386	−	0.872386i
$378$		0			0
$379$		−	0.453587i		−	0.0232992i	−0.999932	−	0.0116496i	$-0.996292\pi$
$379$		−	0.453587i		−	0.0232992i	0.999932	−	0.0116496i	$-0.00370827\pi$
$380$	4.64617	+	0.664818i	0.238344	+	0.0341044i
$381$		0			0
$382$	2.95573	+	11.0309i	0.151228	+	0.564392i
$383$	−2.97916	−	0.798263i	−0.152228	−	0.0407893i	0.181900	−	0.983317i	$-0.441775\pi$
$383$	−2.97916	−	0.798263i	−0.152228	−	0.0407893i	−0.334128	+	0.942528i	$0.608442\pi$
$384$		0			0
$385$	−2.05660	+	37.8239i	−0.104814	+	1.92768i
$386$	2.49968			0.127230
$387$		0			0
$388$	3.19702	+	11.9314i	0.162304	+	0.605727i
$389$	−10.6514	−	6.14959i	−0.540048	−	0.311797i	0.205050	−	0.978751i	$-0.434264\pi$
$389$	−10.6514	−	6.14959i	−0.540048	−	0.311797i	−0.745098	+	0.666955i	$0.767597\pi$
$390$		0			0
$391$		−	0.900871i		−	0.0455590i
$392$	6.34096	−	2.96516i	0.320267	−	0.149763i
$393$		0			0
$394$	14.2251	−	8.21285i	0.716649	−	0.413758i
$395$	4.00445	+	9.98309i	0.201486	+	0.502304i
$396$		0			0
$397$	−6.72452	+	25.0963i	−0.337494	+	1.25954i	0.563646	+	0.826017i	$0.309398\pi$
$397$	−6.72452	+	25.0963i	−0.337494	+	1.25954i	−0.901140	+	0.433528i	$0.857268\pi$
$398$	12.4406	−	12.4406i	0.623589	−	0.623589i
$399$		0			0
$400$	−1.18535	−	4.85746i	−0.0592677	−	0.242873i
$401$	0.371752	+	0.643893i	0.0185644	+	0.0321545i	0.875158	−	0.483837i	$-0.160757\pi$
$401$	0.371752	+	0.643893i	0.0185644	+	0.0321545i	−0.856594	+	0.515991i	$0.827424\pi$
$402$		0			0
$403$	−44.3086	+	11.8724i	−2.20717	+	0.591409i
$404$	1.75932	+	3.04723i	0.0875294	+	0.151605i
$405$		0			0
$406$	9.30767	−	3.39339i	0.461932	−	0.168411i
$407$	3.29950	−	3.29950i	0.163550	−	0.163550i
$408$		0			0
$409$	3.41820	−	5.92050i	0.169019	−	0.292750i	−0.769056	−	0.639181i	$-0.779273\pi$
$409$	3.41820	−	5.92050i	0.169019	−	0.292750i	0.938075	+	0.346432i	$0.112607\pi$
$410$	−4.79368	−	2.04894i	−0.236743	−	0.101190i
$411$		0			0
$412$	−6.39428	−	6.39428i	−0.315023	−	0.315023i
$413$	−11.7454	+	1.03397i	−0.577955	+	0.0508781i
$414$		0			0
$415$	−7.36794	−	9.82858i	−0.361678	−	0.482466i
$416$	5.54030	+	3.19870i	0.271636	+	0.156829i
$417$		0			0
$418$	12.9816	+	3.47841i	0.634951	+	0.170135i
$419$	36.1102			1.76410			0.882050	−	0.471156i	$-0.156163\pi$
$419$	36.1102			1.76410			0.882050	+	0.471156i	$0.156163\pi$
$420$		0			0
$421$	−27.1406			−1.32275			−0.661377	−	0.750054i	$-0.730027\pi$
$421$	−27.1406			−1.32275			−0.661377	+	0.750054i	$0.730027\pi$
$422$	−18.4158	−	4.93449i	−0.896466	−	0.240207i
$423$		0			0
$424$	9.21969	+	5.32299i	0.447748	+	0.258507i
$425$	−0.834692	−	0.0187417i	−0.0404885	−	0.000909108i
$426$		0			0
$427$	27.4469	+	12.7807i	1.32825	+	0.618502i
$428$	6.55861	+	6.55861i	0.317022	+	0.317022i
$429$		0			0
$430$	−5.64918	+	2.26602i	−0.272427	+	0.109277i
$431$	7.78998	−	13.4926i	0.375230	−	0.649918i	−0.615131	−	0.788425i	$-0.710897\pi$
$431$	7.78998	−	13.4926i	0.375230	−	0.649918i	0.990361	+	0.138507i	$0.0442304\pi$
$432$		0			0
$433$	14.8325	−	14.8325i	0.712802	−	0.712802i	−0.254318	−	0.967121i	$-0.581851\pi$
$433$	14.8325	−	14.8325i	0.712802	−	0.712802i	0.967121	+	0.254318i	$0.0818511\pi$
$434$	3.28422	−	18.6845i	0.157647	−	0.896887i
$435$		0			0
$436$	6.31985	+	10.9463i	0.302666	+	0.524233i
$437$	10.9384	−	2.93093i	0.523253	−	0.140205i
$438$		0			0
$439$	20.0936	+	34.8031i	0.959014	+	1.66106i	0.724903	+	0.688851i	$0.241884\pi$
$439$	20.0936	+	34.8031i	0.959014	+	1.66106i	0.234110	+	0.972210i	$0.424782\pi$
$440$	−1.70932	−	14.2148i	−0.0814887	−	0.677664i
$441$		0			0
$442$	0.755359	−	0.755359i	0.0359288	−	0.0359288i
$443$	−1.02465	+	3.82405i	−0.0486826	+	0.181686i	−0.985986	−	0.166829i	$-0.946647\pi$
$443$	−1.02465	+	3.82405i	−0.0486826	+	0.181686i	0.937303	+	0.348515i	$0.113314\pi$
$444$		0			0
$445$	24.2757	−	9.73753i	1.15078	−	0.461603i
$446$	−5.80336	+	3.35057i	−0.274797	+	0.158654i
$447$		0			0
$448$	−2.16646	+	1.51871i	−0.102355	+	0.0717522i
$449$		−	34.5063i		−	1.62845i	−0.580546	−	0.814227i	$-0.697161\pi$
$449$		−	34.5063i		−	1.62845i	0.580546	−	0.814227i	$-0.302839\pi$
$450$		0			0
$451$	−12.9278	−	7.46385i	−0.608745	−	0.351459i
$452$	−1.74481	−	6.51171i	−0.0820688	−	0.306285i
$453$		0			0
$454$	6.26949			0.294242
$455$	−11.7660	+	35.9721i	−0.551600	+	1.68640i
$456$		0			0
$457$	−3.91655	−	1.04944i	−0.183208	−	0.0490905i	0.166048	−	0.986118i	$-0.446899\pi$
$457$	−3.91655	−	1.04944i	−0.183208	−	0.0490905i	−0.349257	+	0.937027i	$0.613566\pi$
$458$	4.36362	+	16.2852i	0.203898	+	0.760959i
$459$		0			0
$460$	−7.23605	−	9.65264i	−0.337382	−	0.450057i
$461$		−	19.0506i		−	0.887274i	−0.896206	−	0.443637i	$-0.853688\pi$
$461$		−	19.0506i		−	0.887274i	0.896206	−	0.443637i	$-0.146312\pi$
$462$		0			0
$463$	−0.835173	−	0.835173i	−0.0388138	−	0.0388138i	0.687434	−	0.726247i	$-0.258737\pi$
$463$	−0.835173	−	0.835173i	−0.0388138	−	0.0388138i	−0.726247	+	0.687434i	$0.758737\pi$
$464$	−3.24282	+	1.87224i	−0.150544	+	0.0869166i
$465$		0			0
$466$	4.06940	−	7.04840i	0.188511	−	0.326511i
$467$	2.92289	−	10.9084i	0.135255	−	0.504779i	−0.864742	−	0.502217i	$-0.832518\pi$
$467$	2.92289	−	10.9084i	0.135255	−	0.504779i	0.999997	−	0.00256202i	$-0.000815518\pi$
$468$		0			0
$469$	20.8882	−	24.9208i	0.964526	−	1.15074i
$470$	−13.5099	−	10.6095i	−0.623164	−	0.489381i
$471$		0			0
$472$	4.30467	−	1.15343i	0.198138	−	0.0530910i
$473$	−16.8351	+	4.51094i	−0.774077	+	0.207413i
$474$		0			0
$475$	−2.48805	−	10.1958i	−0.114160	−	0.467815i
$476$	0.151324	+	0.415064i	0.00693593	+	0.0190244i
$477$		0			0
$478$	−1.96582	+	7.33652i	−0.0899143	+	0.335565i
$479$	13.9561	−	24.1726i	0.637668	−	1.10447i	−0.348275	−	0.937392i	$-0.613232\pi$
$479$	13.9561	−	24.1726i	0.637668	−	1.10447i	0.985943	−	0.167081i	$-0.0534343\pi$
$480$		0			0
$481$	4.03761	−	2.33111i	0.184099	−	0.106290i
$482$	6.12229	+	6.12229i	0.278862	+	0.278862i
$483$		0			0
$484$		−	29.9965i		−	1.36348i
$485$	22.1003	−	16.5674i	1.00352	−	0.752285i
$486$		0			0
$487$	4.53397	+	16.9210i	0.205454	+	0.766764i	0.989311	+	0.145822i	$0.0465828\pi$
$487$	4.53397	+	16.9210i	0.205454	+	0.766764i	−0.783857	+	0.620941i	$0.786751\pi$
$488$	−11.0536	−	2.96180i	−0.500373	−	0.134075i
$489$		0			0
$490$	−11.4323	−	10.6912i	−0.516459	−	0.482980i
$491$	−6.03651			−0.272424			−0.136212	−	0.990680i	$-0.543493\pi$
$491$	−6.03651			−0.272424			−0.136212	+	0.990680i	$0.543493\pi$
$492$		0			0
$493$	0.161828	+	0.603950i	0.00728836	+	0.0272005i
$494$	11.6291	+	6.71405i	0.523217	+	0.302079i
$495$		0			0
$496$			7.17036i			0.321959i
$497$	15.1002	+	21.5407i	0.677338	+	0.966231i
$498$		0			0
$499$	−0.0350182	+	0.0202177i	−0.00156763	+	0.000905071i	−0.500784	−	0.865573i	$-0.666955\pi$
$499$	−0.0350182	+	0.0202177i	−0.00156763	+	0.000905071i	0.499216	+	0.866478i	$0.333621\pi$
$500$	−9.09408	+	6.50367i	−0.406700	+	0.290853i
$501$		0			0
$502$	−1.90459	+	7.10804i	−0.0850062	+	0.317248i
$503$	−21.1889	+	21.1889i	−0.944766	+	0.944766i	−0.998552	−	0.0537866i	$-0.982871\pi$
$503$	−21.1889	+	21.1889i	−0.944766	+	0.944766i	0.0537866	+	0.998552i	$0.482871\pi$
$504$		0			0
$505$	4.85945	−	6.18788i	0.216243	−	0.275357i
$506$	−17.2719	−	29.9158i	−0.767830	−	1.32992i
$507$		0			0
$508$	11.6574	−	3.12358i	0.517211	−	0.138586i
$509$	13.8919	+	24.0614i	0.615746	+	1.06650i	0.990253	+	0.139279i	$0.0444785\pi$
$509$	13.8919	+	24.0614i	0.615746	+	1.06650i	−0.374507	+	0.927224i	$0.622188\pi$
$510$		0			0
$511$	14.3545	−	17.1258i	0.635008	−	0.757601i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$	−10.1840	+	17.6393i	−0.449198	+	0.778034i
$515$	−7.94725	+	18.5933i	−0.350198	+	0.819317i
$516$		0			0
$517$	−34.7810	−	34.7810i	−1.52967	−	1.52967i
$518$	0.169083	+	1.92072i	0.00742909	+	0.0843914i
$519$		0			0
$520$	2.02625	−	14.1608i	0.0888571	−	0.620991i
$521$	27.1354	+	15.6667i	1.18883	+	0.686369i	0.958040	−	0.286636i	$-0.0925370\pi$
$521$	27.1354	+	15.6667i	1.18883	+	0.686369i	0.230786	+	0.973005i	$0.425870\pi$
$522$		0			0
$523$	10.3236	+	2.76619i	0.451419	+	0.120957i	0.477363	−	0.878706i	$-0.341593\pi$
$523$	10.3236	+	2.76619i	0.451419	+	0.120957i	−0.0259445	+	0.999663i	$0.508259\pi$
$524$	−4.18549			−0.182844
$525$		0			0
$526$	−25.9596			−1.13189
$527$	1.15651	+	0.309887i	0.0503785	+	0.0134989i
$528$		0			0
$529$	−5.28861	−	3.05338i	−0.229940	−	0.132756i
$530$	3.37192	−	23.5651i	0.146467	−	1.02360i
$531$		0			0
$532$	−4.54738	+	3.18776i	−0.197154	+	0.138207i
$533$	−10.5465	−	10.5465i	−0.456819	−	0.456819i
$534$		0			0
$535$	8.15149	−	19.0711i	0.352420	−	0.824516i
$536$	−6.14516	+	10.6437i	−0.265430	+	0.459739i
$537$		0			0
$538$	6.11812	−	6.11812i	0.263771	−	0.263771i
$539$	−28.8467	−	34.3030i	−1.24251	−	1.47754i
$540$		0			0
$541$	−5.21982	−	9.04100i	−0.224418	−	0.388703i	0.731727	−	0.681598i	$-0.238715\pi$
$541$	−5.21982	−	9.04100i	−0.224418	−	0.388703i	−0.956145	+	0.292895i	$0.905381\pi$
$542$	6.60149	−	1.76886i	0.283558	−	0.0759792i
$543$		0			0
$544$	−0.0834902	−	0.144609i	−0.00357961	−	0.00620007i
$545$	17.4562	−	22.2282i	0.747741	−	0.952152i
$546$		0			0
$547$	11.2203	−	11.2203i	0.479745	−	0.479745i	−0.425305	−	0.905050i	$-0.639833\pi$
$547$	11.2203	−	11.2203i	0.479745	−	0.479745i	0.905050	+	0.425305i	$0.139833\pi$
$548$	0.934097	−	3.48610i	0.0399026	−	0.148919i
$549$		0			0
$550$	−28.0775	+	15.3807i	−1.19723	+	0.655836i
$551$	−6.80666	+	3.92982i	−0.289973	+	0.167416i
$552$		0			0
$553$	−11.5375	−	5.37245i	−0.490623	−	0.228460i
$554$			0.409017i			0.0173775i
$555$		0			0
$556$	−2.23422	−	1.28993i	−0.0947521	−	0.0547052i
$557$	7.65431	+	28.5663i	0.324324	+	1.21039i	0.914990	+	0.403477i	$0.132198\pi$
$557$	7.65431	+	28.5663i	0.324324	+	1.21039i	−0.590666	+	0.806916i	$0.701135\pi$
$558$		0			0
$559$	−17.4141			−0.736537
$560$	4.95532	+	3.23185i	0.209400	+	0.136570i
$561$		0			0
$562$	−19.3970	−	5.19742i	−0.818214	−	0.219240i
$563$	4.95291	+	18.4845i	0.208740	+	0.779029i	0.988277	+	0.152673i	$0.0487880\pi$
$563$	4.95291	+	18.4845i	0.208740	+	0.779029i	−0.779537	+	0.626357i	$0.784545\pi$
$564$		0			0
$565$	−12.0615	+	9.04182i	−0.507430	+	0.380392i
$566$		−	16.6559i		−	0.700099i
$567$		0			0
$568$	−7.03064	−	7.03064i	−0.294999	−	0.294999i
$569$	−17.2067	+	9.93427i	−0.721341	+	0.416466i	−0.815246	−	0.579115i	$-0.803398\pi$
$569$	−17.2067	+	9.93427i	−0.721341	+	0.416466i	0.0939053	+	0.995581i	$0.470065\pi$
$570$		0			0
$571$	4.69056	−	8.12429i	0.196294	−	0.339991i	−0.751030	−	0.660268i	$-0.770443\pi$
$571$	4.69056	−	8.12429i	0.196294	−	0.339991i	0.947324	+	0.320277i	$0.103776\pi$
$572$	10.6016	−	39.5658i	0.443276	−	1.65433i
$573$		0			0
$574$	5.79522	−	2.11282i	0.241888	−	0.0881874i
$575$	−14.0087	+	23.0527i	−0.584203	+	0.961363i
$576$		0			0
$577$	−20.8218	+	5.57918i	−0.866822	+	0.232264i	−0.664713	−	0.747099i	$-0.731446\pi$
$577$	−20.8218	+	5.57918i	−0.866822	+	0.232264i	−0.202109	+	0.979363i	$0.564780\pi$
$578$	16.3938	−	4.39271i	0.681892	−	0.182713i
$579$		0			0
$580$	6.58505	+	5.17135i	0.273429	+	0.214728i
$581$	14.3147	+	2.51613i	0.593875	+	0.104387i
$582$		0			0
$583$	17.6423	−	65.8420i	0.730670	−	2.72690i
$584$	−4.22301	+	7.31446i	−0.174749	+	0.302675i
$585$		0			0
$586$	−13.0073	+	7.50976i	−0.537326	+	0.310225i
$587$	19.7138	+	19.7138i	0.813676	+	0.813676i	0.985183	−	0.171507i	$-0.0548637\pi$
$587$	19.7138	+	19.7138i	0.813676	+	0.813676i	−0.171507	+	0.985183i	$0.554864\pi$
$588$		0			0
$589$			15.0506i			0.620147i
$590$	−5.97724	−	7.97343i	−0.246079	−	0.328261i
$591$		0			0
$592$	−0.188620	−	0.703938i	−0.00775222	−	0.0289317i
$593$	44.6168	+	11.9550i	1.83219	+	0.490934i	0.998152	−	0.0607712i	$-0.0193560\pi$
$593$	44.6168	+	11.9550i	1.83219	+	0.490934i	0.834039	+	0.551705i	$0.186023\pi$
$594$		0			0
$595$	0.735424	−	0.659574i	0.0301494	−	0.0270399i
$596$	−9.89949			−0.405499
$597$		0			0
$598$	−8.93298	−	33.3383i	−0.365297	−	1.36331i
$599$	−4.26297	−	2.46123i	−0.174180	−	0.100563i	0.410375	−	0.911917i	$-0.365398\pi$
$599$	−4.26297	−	2.46123i	−0.174180	−	0.100563i	−0.584555	+	0.811354i	$0.698731\pi$
$600$		0			0
$601$		−	3.06956i		−	0.125210i	−0.998038	−	0.0626049i	$-0.980059\pi$
$601$		−	3.06956i		−	0.125210i	0.998038	−	0.0626049i	$-0.0199408\pi$
$602$	3.04013	−	6.52877i	0.123907	−	0.266093i
$603$		0			0
$604$	9.51421	−	5.49303i	0.387128	−	0.223508i
$605$	−62.2527	+	24.9710i	−2.53093	+	1.01521i
$606$		0			0
$607$	−2.32572	+	8.67972i	−0.0943982	+	0.352299i	−0.996928	−	0.0783295i	$-0.975041\pi$
$607$	−2.32572	+	8.67972i	−0.0943982	+	0.352299i	0.902529	+	0.430628i	$0.141708\pi$
$608$	1.48421	−	1.48421i	0.0601928	−	0.0601928i
$609$		0			0
$610$	3.05500	+	25.4055i	0.123693	+	1.02864i
$611$	−24.5729	−	42.5616i	−0.994115	−	1.72186i
$612$		0			0
$613$	10.7867	−	2.89030i	0.435673	−	0.116738i	−0.0343152	−	0.999411i	$-0.510925\pi$
$613$	10.7867	−	2.89030i	0.435673	−	0.116738i	0.469988	+	0.882673i	$0.344258\pi$
$614$	−12.8571	−	22.2691i	−0.518869	−	0.898707i
$615$		0			0
$616$	12.9829	+	10.8821i	0.523097	+	0.438450i
$617$	17.1120	−	17.1120i	0.688904	−	0.688904i	−0.273085	−	0.961990i	$-0.588044\pi$
$617$	17.1120	−	17.1120i	0.688904	−	0.688904i	0.961990	+	0.273085i	$0.0880442\pi$
$618$		0			0
$619$	−3.24578	+	5.62186i	−0.130459	+	0.225962i	−0.923854	−	0.382746i	$-0.874978\pi$
$619$	−3.24578	+	5.62186i	−0.130459	+	0.225962i	0.793395	+	0.608708i	$0.208312\pi$
$620$	14.8809	−	5.96907i	0.597631	−	0.239723i
$621$		0			0
$622$	−17.9075	−	17.9075i	−0.718025	−	0.718025i
$623$	−13.0641	+	28.0554i	−0.523401	+	1.12402i
$624$		0			0
$625$	21.0678	+	13.4592i	0.842710	+	0.538367i
$626$	5.73588	+	3.31161i	0.229252	+	0.132359i
$627$		0			0
$628$	−8.84880	−	2.37103i	−0.353105	−	0.0946143i
$629$	−0.121690			−0.00485211
$630$		0			0
$631$	−10.2203			−0.406863			−0.203431	−	0.979089i	$-0.565209\pi$
$631$	−10.2203			−0.406863			−0.203431	+	0.979089i	$0.565209\pi$
$632$	4.64645	+	1.24501i	0.184826	+	0.0495239i
$633$		0			0
$634$	−7.22815	−	4.17317i	−0.287067	−	0.165738i
$635$	−16.1868	−	21.5926i	−0.642353	−	0.856877i
$636$		0			0
$637$	−18.9693	−	40.5656i	−0.751590	−	1.60727i
$638$	16.9531	+	16.9531i	0.671181	+	0.671181i
$639$		0			0
$640$	−2.05612	−	0.878841i	−0.0812754	−	0.0347392i
$641$	−1.75152	+	3.03371i	−0.0691807	+	0.119825i	−0.898541	−	0.438890i	$-0.855372\pi$
$641$	−1.75152	+	3.03371i	−0.0691807	+	0.119825i	0.829360	+	0.558714i	$0.188705\pi$
$642$		0			0
$643$	20.0653	−	20.0653i	0.791299	−	0.791299i	−0.190407	−	0.981705i	$-0.560981\pi$
$643$	20.0653	−	20.0653i	0.791299	−	0.791299i	0.981705	+	0.190407i	$0.0609806\pi$
$644$	14.0585	+	2.47109i	0.553982	+	0.0973744i
$645$		0			0
$646$	−0.175246	−	0.303534i	−0.00689495	−	0.0119424i
$647$	−3.40818	+	0.913219i	−0.133989	+	0.0359023i	−0.325190	−	0.945649i	$-0.605428\pi$
$647$	−3.40818	+	0.913219i	−0.133989	+	0.0359023i	0.191201	+	0.981551i	$0.438762\pi$
$648$		0			0
$649$	−14.2672	−	24.7115i	−0.560037	−	0.970013i
$650$	−31.0751	+	7.58318i	−1.21887	+	0.297437i
$651$		0			0
$652$	0.554077	−	0.554077i	0.0216993	−	0.0216993i
$653$	−11.0702	+	41.3146i	−0.433211	+	1.61677i	0.312100	+	0.950049i	$0.398968\pi$
$653$	−11.0702	+	41.3146i	−0.433211	+	1.61677i	−0.745311	+	0.666717i	$0.767699\pi$
$654$		0			0
$655$	3.48427	+	8.68627i	0.136142	+	0.339401i
$656$	−2.01907	+	1.16571i	−0.0788313	+	0.0455133i
$657$		0			0
$658$	20.2468	−	1.78235i	0.789303	−	0.0694834i
$659$			16.7292i			0.651678i	0.945425	+	0.325839i	$0.105647\pi$
$659$			16.7292i			0.651678i	−0.945425	+	0.325839i	$0.894353\pi$
$660$		0			0
$661$	−7.82077	−	4.51533i	−0.304193	−	0.175626i	0.340132	−	0.940378i	$-0.389528\pi$
$661$	−7.82077	−	4.51533i	−0.304193	−	0.175626i	−0.644325	+	0.764752i	$0.722862\pi$
$662$	−3.54175	−	13.2180i	−0.137654	−	0.513732i
$663$		0			0
$664$	−5.49341			−0.213186
$665$	10.4012	+	6.78363i	0.403341	+	0.263058i
$666$		0			0
$667$	19.5134	+	5.22859i	0.755561	+	0.202452i
$668$	0.00519691	+	0.0193951i	0.000201074	+	0.000750420i
$669$		0			0
$670$	27.2049	+	3.89273i	1.05102	+	0.150389i
$671$			73.2712i			2.82860i
$672$		0			0
$673$	−5.23874	−	5.23874i	−0.201938	−	0.201938i	0.598892	−	0.800830i	$-0.295608\pi$
$673$	−5.23874	−	5.23874i	−0.201938	−	0.201938i	−0.800830	+	0.598892i	$0.795608\pi$
$674$	−15.5875	+	8.99942i	−0.600406	+	0.346645i
$675$		0			0
$676$	13.9633	−	24.1852i	0.537050	−	0.930199i
$677$	−10.5285	+	39.2929i	−0.404643	+	1.51015i	0.400071	+	0.916484i	$0.368986\pi$
$677$	−10.5285	+	39.2929i	−0.404643	+	1.51015i	−0.804713	+	0.593663i	$0.797681\pi$
$678$		0			0
$679$	−5.65769	+	32.1877i	−0.217122	+	1.23525i
$680$	−0.230610	+	0.293652i	−0.00884348	+	0.0112610i
$681$		0			0
$682$	44.3464	−	11.8826i	1.69811	−	0.455007i
$683$	21.0342	−	5.63609i	0.804851	−	0.215659i	0.167138	−	0.985933i	$-0.446547\pi$
$683$	21.0342	−	5.63609i	0.804851	−	0.215659i	0.637713	+	0.770274i	$0.279881\pi$
$684$		0			0
$685$	−8.01241	+	0.963488i	−0.306139	+	0.0368130i
$686$	18.5202	−	0.0299210i	0.707106	−	0.00114239i
$687$		0			0
$688$	−0.704521	+	2.62931i	−0.0268596	+	0.100241i
$689$	34.0533	−	58.9820i	1.29733	−	2.24704i
$690$		0			0
$691$	32.0081	−	18.4799i	1.21765	−	0.703008i	0.253232	−	0.967406i	$-0.418506\pi$
$691$	32.0081	−	18.4799i	1.21765	−	0.703008i	0.964414	+	0.264397i	$0.0851730\pi$
$692$	4.59023	+	4.59023i	0.174494	+	0.174494i
$693$		0			0
$694$			21.2423i			0.806348i
$695$	−0.817122	+	5.71057i	−0.0309952	+	0.216614i
$696$		0			0
$697$	0.100758	+	0.376036i	0.00381650	+	0.0142434i
$698$	17.3328	+	4.64430i	0.656055	+	0.175789i
$699$		0			0
$700$	2.58203	−	12.9743i	0.0975915	−	0.490383i
$701$	−50.0832			−1.89161			−0.945807	−	0.324728i	$-0.894727\pi$
$701$	−50.0832			−1.89161			−0.945807	+	0.324728i	$0.894727\pi$
$702$		0			0
$703$	−0.395912	−	1.47756i	−0.0149321	−	0.0557273i
$704$	−5.54503	−	3.20142i	−0.208986	−	0.120658i
$705$		0			0
$706$		−	27.4592i		−	1.03344i
$707$	0.816366	+	9.27358i	0.0307026	+	0.348769i
$708$		0			0
$709$	31.9251	−	18.4320i	1.19897	−	0.692228i	0.238647	−	0.971106i	$-0.423296\pi$
$709$	31.9251	−	18.4320i	1.19897	−	0.692228i	0.960326	+	0.278879i	$0.0899628\pi$
$710$	−8.73816	+	20.4437i	−0.327937	+	0.767237i
$711$		0			0
$712$	3.02747	−	11.2987i	0.113459	−	0.423435i
$713$	27.3541	−	27.3541i	1.02442	−	1.02442i
$714$		0			0
$715$	−90.9377	+	10.9352i	−3.40088	+	0.408953i
$716$	−6.98604	−	12.1002i	−0.261081	−	0.452205i
$717$		0			0
$718$	−24.5836	+	6.58717i	−0.917453	+	0.245831i
$719$	0.638450	+	1.10583i	0.0238102	+	0.0412404i	0.877685	−	0.479238i	$-0.159087\pi$
$719$	0.638450	+	1.10583i	0.0238102	+	0.0412404i	−0.853875	+	0.520478i	$0.825754\pi$
$720$		0			0
$721$	−8.19501	−	22.4779i	−0.305198	−	0.837122i
$722$	−10.3197	+	10.3197i	−0.384058	+	0.384058i
$723$		0			0
$724$	−4.22638	+	7.32031i	−0.157072	+	0.272057i
$725$	5.25045	−	17.9711i	0.194997	−	0.667431i
$726$		0			0
$727$	5.37795	+	5.37795i	0.199457	+	0.199457i	0.799767	−	0.600310i	$-0.204956\pi$
$727$	5.37795	+	5.37795i	0.199457	+	0.199457i	−0.600310	+	0.799767i	$0.704956\pi$
$728$	9.71577	+	13.8597i	0.360090	+	0.513673i
$729$		0			0
$730$	18.6954	+	2.67512i	0.691949	+	0.0990106i
$731$	0.393635	+	0.227265i	0.0145591	+	0.00840571i
$732$		0			0
$733$	−19.5984	−	5.25137i	−0.723882	−	0.193964i	−0.121979	−	0.992533i	$-0.538924\pi$
$733$	−19.5984	−	5.25137i	−0.723882	−	0.193964i	−0.601903	+	0.798569i	$0.705591\pi$
$734$	1.78264			0.0657986
$735$		0			0
$736$	−5.39507			−0.198865
$737$	76.0116	+	20.3673i	2.79992	+	0.750237i
$738$		0			0
$739$	14.6947	+	8.48399i	0.540553	+	0.312089i	0.745303	−	0.666726i	$-0.232305\pi$
$739$	14.6947	+	8.48399i	0.540553	+	0.312089i	−0.204750	+	0.978814i	$0.565638\pi$
$740$	−1.30389	+	0.977451i	−0.0479318	+	0.0359318i
$741$		0			0
$742$	16.1681	+	23.0641i	0.593551	+	0.846708i
$743$	12.6206	+	12.6206i	0.463004	+	0.463004i	0.899639	−	0.436635i	$-0.143830\pi$
$743$	12.6206	+	12.6206i	0.463004	+	0.463004i	−0.436635	+	0.899639i	$0.643830\pi$
$744$		0			0
$745$	8.24097	+	20.5447i	0.301926	+	0.752701i
$746$	7.62978	−	13.2152i	0.279346	−	0.483842i
$747$		0			0
$748$	−0.756003	+	0.756003i	−0.0276422	+	0.0276422i
$749$	8.40562	+	23.0556i	0.307135	+	0.842434i
$750$		0			0
$751$	14.3912	+	24.9264i	0.525144	+	0.909576i	0.999571	+	0.0292810i	$0.00932175\pi$
$751$	14.3912	+	24.9264i	0.525144	+	0.909576i	−0.474428	+	0.880295i	$0.657345\pi$
$752$	−7.42041	+	1.98829i	−0.270594	+	0.0725056i
$753$		0			0
$754$	11.9775	+	20.7456i	0.436193	+	0.755509i
$755$	−19.3201	−	15.1724i	−0.703130	−	0.552180i
$756$		0			0
$757$	−27.7316	+	27.7316i	−1.00792	+	1.00792i	−0.00795446	+	0.999968i	$0.502532\pi$
$757$	−27.7316	+	27.7316i	−1.00792	+	1.00792i	−0.999968	+	0.00795446i	$0.997468\pi$
$758$	−0.117397	+	0.438132i	−0.00426405	+	0.0159137i
$759$		0			0
$760$	−4.31579	−	1.84468i	−0.156550	−	0.0669137i
$761$	−30.2569	+	17.4688i	−1.09681	+	0.633244i	−0.935381	−	0.353640i	$-0.884944\pi$
$761$	−30.2569	+	17.4688i	−1.09681	+	0.633244i	−0.161429	+	0.986884i	$0.551610\pi$
$762$		0			0
$763$	2.93256	+	33.3127i	0.106166	+	1.20600i
$764$		−	11.4201i		−	0.413164i
$765$		0			0
$766$	2.67104	+	1.54213i	0.0965086	+	0.0557193i
$767$	−7.37896	−	27.5387i	−0.266439	−	0.994363i
$768$		0			0
$769$	20.1606			0.727009			0.363504	−	0.931593i	$-0.381580\pi$
$769$	20.1606			0.727009			0.363504	+	0.931593i	$0.381580\pi$
$770$	11.7761	−	36.0028i	0.424380	−	1.29745i
$771$		0			0
$772$	−2.41450	−	0.646964i	−0.0868999	−	0.0232847i
$773$	−5.12297	−	19.1192i	−0.184260	−	0.687669i	−0.994788	−	0.101968i	$-0.967486\pi$
$773$	−5.12297	−	19.1192i	−0.184260	−	0.687669i	0.810527	−	0.585701i	$-0.199181\pi$
$774$		0			0
$775$	−24.7756	−	25.9137i	−0.889965	−	0.930849i
$776$		−	12.3523i		−	0.443423i
$777$		0			0
$778$	8.69684	+	8.69684i	0.311797	+	0.311797i
$779$	−4.23801	+	2.44682i	−0.151843	+	0.0876663i
$780$		0			0
$781$	−31.8312	+	55.1332i	−1.13901	+	1.97282i
$782$	−0.233162	+	0.870174i	−0.00833787	+	0.0311174i
$783$		0			0
$784$	−6.89234	+	1.22296i	−0.246155	+	0.0436772i
$785$	2.44563	+	20.3380i	0.0872883	+	0.725894i
$786$		0			0
$787$	−3.14552	+	0.842840i	−0.112126	+	0.0300440i	−0.314446	−	0.949275i	$-0.601819\pi$
$787$	−3.14552	+	0.842840i	−0.112126	+	0.0300440i	0.202320	+	0.979319i	$0.435152\pi$
$788$	−15.8660	+	4.25129i	−0.565203	+	0.151446i
$789$		0			0
$790$	−1.28419	−	10.6793i	−0.0456893	−	0.379954i
$791$	3.08775	−	17.5668i	0.109788	−	0.624604i
$792$		0			0
$793$	−18.9478	+	70.7142i	−0.672857	+	2.51114i
$794$	12.9908	−	22.5007i	0.461025	−	0.798519i
$795$		0			0
$796$	−15.2365	+	8.79681i	−0.540044	+	0.311795i
$797$	−24.9240	−	24.9240i	−0.882852	−	0.882852i	0.110971	−	0.993824i	$-0.464604\pi$
$797$	−24.9240	−	24.9240i	−0.882852	−	0.882852i	−0.993824	+	0.110971i	$0.964604\pi$
$798$		0			0
$799$			1.28277i			0.0453812i
$800$	−0.112239	+	4.99874i	−0.00396825	+	0.176732i
$801$		0			0
$802$	−0.192433	−	0.718170i	−0.00679505	−	0.0253595i
$803$	52.2359	+	13.9966i	1.84336	+	0.493928i
$804$		0			0
$805$	−6.57486	−	31.2331i	−0.231733	−	1.10082i
$806$	45.8716			1.61576
$807$		0			0
$808$	−0.910691	−	3.39875i	−0.0320380	−	0.119567i
$809$	40.1547	+	23.1833i	1.41176	+	0.815082i	0.995555	−	0.0941872i	$-0.0300252\pi$
$809$	40.1547	+	23.1833i	1.41176	+	0.815082i	0.416209	+	0.909269i	$0.363359\pi$
$810$		0			0
$811$		−	29.8077i		−	1.04669i	−0.852120	−	0.523346i	$-0.824684\pi$
$811$		−	29.8077i		−	1.04669i	0.852120	−	0.523346i	$-0.175316\pi$
$812$	−9.86880	+	0.868764i	−0.346327	+	0.0304876i
$813$		0			0
$814$	−4.04105	+	2.33310i	−0.141639	+	0.0817752i
$815$	−1.61114	−	0.688645i	−0.0564359	−	0.0241222i
$816$		0			0
$817$	−1.47879	+	5.51890i	−0.0517362	+	0.193082i
$818$	−4.83406	+	4.83406i	−0.169019	+	0.169019i
$819$		0			0
$820$	4.10003	+	3.21982i	0.143179	+	0.112441i
$821$	−15.5650	−	26.9593i	−0.543221	−	0.940886i	−0.998717	−	0.0506482i	$-0.983871\pi$
$821$	−15.5650	−	26.9593i	−0.543221	−	0.940886i	0.455496	−	0.890238i	$-0.349462\pi$
$822$		0			0
$823$	−6.48862	+	1.73862i	−0.226179	+	0.0606045i	−0.370129	−	0.928981i	$-0.620686\pi$
$823$	−6.48862	+	1.73862i	−0.226179	+	0.0606045i	0.143950	+	0.989585i	$0.454020\pi$
$824$	4.52144	+	7.83136i	0.157512	+	0.272818i
$825$		0			0
$826$	11.6128	+	2.04121i	0.404062	+	0.0710226i
$827$	23.1948	−	23.1948i	0.806562	−	0.806562i	−0.177550	−	0.984112i	$-0.556817\pi$
$827$	23.1948	−	23.1948i	0.806562	−	0.806562i	0.984112	+	0.177550i	$0.0568171\pi$
$828$		0			0
$829$	14.6772	−	25.4217i	0.509762	−	0.882933i	−0.490174	−	0.871624i	$-0.663067\pi$
$829$	14.6772	−	25.4217i	0.509762	−	0.882933i	0.999936	−	0.0113086i	$-0.00359973\pi$
$830$	4.57306	+	11.4006i	0.158733	+	0.395722i
$831$		0			0
$832$	−4.52364	−	4.52364i	−0.156829	−	0.156829i
$833$	−0.100619	+	1.16452i	−0.00348624	+	0.0403484i
$834$		0			0
$835$	0.0359251	−	0.0269310i	0.00124324	−	0.000931987i
$836$	−11.6390	−	6.71978i	−0.402543	−	0.232408i
$837$		0			0
$838$	−34.8798	−	9.34601i	−1.20490	−	0.322853i
$839$	−11.9227			−0.411619			−0.205809	−	0.978592i	$-0.565983\pi$
$839$	−11.9227			−0.411619			−0.205809	+	0.978592i	$0.565983\pi$
$840$		0			0
$841$	14.9789			0.516513
$842$	26.2158	+	7.02451i	0.903457	+	0.242081i
$843$		0			0
$844$	16.5111	+	9.53271i	0.568337	+	0.328129i
$845$	−61.8162	−	8.84524i	−2.12654	−	0.304285i
$846$		0			0
$847$	33.5016	−	71.9456i	1.15113	−	2.47208i
$848$	−7.52785	−	7.52785i	−0.258507	−	0.258507i
$849$		0			0
$850$	0.801399	+	0.234137i	0.0274878	+	0.00803084i
$851$	−1.96588	+	3.40501i	−0.0673896	+	0.116722i
$852$		0			0
$853$	9.07222	−	9.07222i	0.310627	−	0.310627i	−0.534525	−	0.845152i	$-0.679510\pi$
$853$	9.07222	−	9.07222i	0.310627	−	0.310627i	0.845152	+	0.534525i	$0.179510\pi$
$854$	−23.2038	−	19.4490i	−0.794018	−	0.665532i
$855$		0			0
$856$	−4.63764	−	8.03263i	−0.158511	−	0.274549i
$857$	10.4366	−	2.79649i	0.356508	−	0.0955262i	−0.0761195	−	0.997099i	$-0.524253\pi$
$857$	10.4366	−	2.79649i	0.356508	−	0.0955262i	0.432628	+	0.901573i	$0.357586\pi$
$858$		0			0
$859$	13.3334	+	23.0940i	0.454928	+	0.787959i	0.998684	−	0.0512848i	$-0.0163316\pi$
$859$	13.3334	+	23.0940i	0.454928	+	0.787959i	−0.543756	+	0.839243i	$0.682998\pi$
$860$	6.04317	−	0.726688i	0.206070	−	0.0247799i
$861$		0			0
$862$	−11.0167	+	11.0167i	−0.375230	+	0.375230i
$863$	−10.7780	+	40.2240i	−0.366887	+	1.36924i	0.497958	+	0.867201i	$0.334083\pi$
$863$	−10.7780	+	40.2240i	−0.366887	+	1.36924i	−0.864845	+	0.502039i	$0.832583\pi$
$864$		0			0
$865$	5.70505	−	13.3475i	0.193978	−	0.453827i
$866$	−18.1660	+	10.4881i	−0.617305	+	0.356401i
$867$		0			0
$868$	−8.00823	+	17.1979i	−0.271817	+	0.583734i
$869$		−	30.8000i		−	1.04482i
$870$		0			0
$871$	68.0921	+	39.3130i	2.30721	+	1.33207i
$872$	−3.27140	−	12.2090i	−0.110784	−	0.413450i
$873$		0			0
$874$	−11.3242			−0.383048
$875$	−29.0755	+	5.44209i	−0.982931	+	0.183976i
$876$		0			0
$877$	56.5413	+	15.1502i	1.90926	+	0.511586i	0.994095	+	0.108514i	$0.0346091\pi$
$877$	56.5413	+	15.1502i	1.90926	+	0.511586i	0.915168	+	0.403072i	$0.132058\pi$
$878$	−10.4012	−	38.8178i	−0.351023	−	1.31004i
$879$		0			0
$880$	−2.02798	+	14.1728i	−0.0683633	+	0.477767i
$881$			5.21431i			0.175675i	0.996135	+	0.0878373i	$0.0279956\pi$
$881$			5.21431i			0.175675i	−0.996135	+	0.0878373i	$0.972004\pi$
$882$		0			0
$883$	−1.39598	−	1.39598i	−0.0469786	−	0.0469786i	0.683227	−	0.730206i	$-0.260576\pi$
$883$	−1.39598	−	1.39598i	−0.0469786	−	0.0469786i	−0.730206	+	0.683227i	$0.760576\pi$
$884$	−0.925122	+	0.534119i	−0.0311152	+	0.0179644i
$885$		0			0
$886$	1.97947	−	3.42855i	0.0665017	−	0.115184i
$887$	−4.65470	+	17.3716i	−0.156289	+	0.583280i	0.842702	+	0.538380i	$0.180964\pi$
$887$	−4.65470	+	17.3716i	−0.156289	+	0.583280i	−0.998991	+	0.0448998i	$0.985703\pi$
$888$		0			0
$889$	31.4483	+	5.52773i	1.05474	+	0.185394i
$890$	−25.9687	+	3.12273i	−0.870474	+	0.104674i
$891$		0			0
$892$	6.47280	−	1.73438i	0.216725	−	0.0580714i
$893$	−15.5754	+	4.17342i	−0.521211	+	0.139658i
$894$		0			0
$895$	−19.2963	+	24.5713i	−0.645003	+	0.821328i
$896$	2.48571	−	0.906239i	0.0830416	−	0.0302753i
$897$		0			0
$898$	−8.93090	+	33.3306i	−0.298028	+	1.11226i
$899$	−13.4246	+	23.2522i	−0.447737	+	0.775503i
$900$		0			0
$901$	−1.53951	+	0.888835i	−0.0512885	+	0.0296114i
$902$	10.5555	+	10.5555i	0.351459	+	0.351459i
$903$		0			0
$904$			6.74142i			0.224216i
$905$	18.7104	+	2.67726i	0.621955	+	0.0889950i
$906$		0			0
$907$	−4.21277	−	15.7223i	−0.139883	−	0.522049i	−0.999930	−	0.0118350i	$-0.996233\pi$
$907$	−4.21277	−	15.7223i	−0.139883	−	0.522049i	0.860047	−	0.510214i	$-0.170434\pi$
$908$	−6.05586	−	1.62266i	−0.200971	−	0.0538500i
$909$		0			0
$910$	20.6754	−	31.7011i	0.685382	−	1.05088i
$911$	30.1101			0.997592			0.498796	−	0.866719i	$-0.333776\pi$
$911$	30.1101			0.997592			0.498796	+	0.866719i	$0.333776\pi$
$912$		0			0
$913$	9.10356	+	33.9750i	0.301284	+	1.12441i
$914$	3.51148	+	2.02735i	0.116149	+	0.0670589i
$915$		0			0
$916$		−	16.8597i		−	0.557061i
$917$	−10.0387	−	4.67457i	−0.331509	−	0.154368i
$918$		0			0
$919$	−49.5704	+	28.6195i	−1.63518	+	0.944070i	−0.652716	+	0.757603i	$0.726370\pi$
$919$	−49.5704	+	28.6195i	−1.63518	+	0.944070i	−0.982461	+	0.186467i	$0.940296\pi$
$920$	4.49120	+	11.1966i	0.148070	+	0.369140i
$921$		0			0
$922$	−4.93066	+	18.4015i	−0.162382	+	0.606020i
$923$	−44.9777	+	44.9777i	−1.48046	+	1.48046i
$924$		0			0
$925$	3.11397	+	1.89230i	0.102387	+	0.0622186i
$926$	0.590556	+	1.02287i	0.0194069	+	0.0336137i
$927$		0			0
$928$	3.61689	−	0.969143i	0.118730	−	0.0318137i
$929$	−23.2278	−	40.2317i	−0.762078	−	1.31996i	−0.941778	−	0.336236i	$-0.890846\pi$
$929$	−23.2278	−	40.2317i	−0.762078	−	1.31996i	0.179700	−	0.983722i	$-0.442487\pi$
$930$		0			0
$931$	−14.4670	+	2.56699i	−0.474137	+	0.0841297i
$932$	−5.75499	+	5.75499i	−0.188511	+	0.188511i
$933$		0			0
$934$	−5.64659	+	9.78018i	−0.184762	+	0.320017i
$935$	2.19830	+	0.939613i	0.0718922	+	0.0307286i
$936$		0			0
$937$	−2.59520	−	2.59520i	−0.0847814	−	0.0847814i	0.663444	−	0.748226i	$-0.269094\pi$
$937$	−2.59520	−	2.59520i	−0.0847814	−	0.0847814i	−0.748226	+	0.663444i	$0.769094\pi$
$938$	−26.6264	+	18.6654i	−0.869383	+	0.609447i
$939$		0			0
$940$	10.3036	+	13.7446i	0.336066	+	0.448300i
$941$	−13.6189	−	7.86288i	−0.443964	−	0.256323i	0.261314	−	0.965254i	$-0.415844\pi$
$941$	−13.6189	−	7.86288i	−0.443964	−	0.256323i	−0.705278	+	0.708931i	$0.749178\pi$
$942$		0			0
$943$	12.1496	+	3.25547i	0.395644	+	0.106013i
$944$	−4.45652			−0.145047
$945$		0			0
$946$	17.4289			0.566663
$947$	39.5464	+	10.5964i	1.28509	+	0.344338i	0.835792	−	0.549046i	$-0.185009\pi$
$947$	39.5464	+	10.5964i	1.28509	+	0.344338i	0.449294	+	0.893384i	$0.351675\pi$
$948$		0			0
$949$	46.7935	+	27.0162i	1.51898	+	0.876984i
$950$	−0.235589	+	10.4923i	−0.00764353	+	0.340416i
$951$		0			0
$952$	−0.0387414	−	0.440087i	−0.00125562	−	0.0142633i
$953$	−14.5512	−	14.5512i	−0.471358	−	0.471358i	0.430996	−	0.902354i	$-0.358162\pi$
$953$	−14.5512	−	14.5512i	−0.471358	−	0.471358i	−0.902354	+	0.430996i	$0.858162\pi$
$954$		0			0
$955$	−23.7005	+	9.50680i	−0.766929	+	0.307633i
$956$	3.79766	−	6.57775i	0.122825	−	0.212740i
$957$		0			0
$958$	−19.7368	+	19.7368i	−0.637668	+	0.637668i
$959$	6.13385	−	7.31804i	0.198072	−	0.236312i
$960$		0			0
$961$	10.2070	+	17.6791i	0.329259	+	0.570294i
$962$	−4.50337	+	1.20667i	−0.145194	+	0.0389047i
$963$		0			0
$964$	−4.32911	−	7.49824i	−0.139431	−	0.241502i
$965$	0.667321	+	5.54947i	0.0214818	+	0.178644i
$966$		0			0
$967$	−15.3042	+	15.3042i	−0.492148	+	0.492148i	−0.908983	−	0.416834i	$-0.863140\pi$
$967$	−15.3042	+	15.3042i	−0.492148	+	0.492148i	0.416834	+	0.908983i	$0.363140\pi$
$968$	−7.76366	+	28.9744i	−0.249533	+	0.931272i
$969$		0			0
$970$	−25.6352	+	10.2829i	−0.823096	+	0.330163i
$971$	−13.0517	+	7.53542i	−0.418850	+	0.241823i	−0.694585	−	0.719410i	$-0.744412\pi$
$971$	−13.0517	+	7.53542i	−0.418850	+	0.241823i	0.275735	+	0.961234i	$0.411079\pi$
$972$		0			0
$973$	−3.91805	−	5.58915i	−0.125607	−	0.179180i
$974$		−	17.5179i		−	0.561310i
$975$		0			0
$976$	9.91039	+	5.72176i	0.317224	+	0.183149i
$977$	−11.2120	−	41.8438i	−0.358704	−	1.33870i	−0.875759	−	0.482749i	$-0.839638\pi$
$977$	−11.2120	−	41.8438i	−0.358704	−	1.33870i	0.517055	−	0.855952i	$-0.327028\pi$
$978$		0			0
$979$	−74.8956			−2.39368
$980$	8.27568	+	13.2858i	0.264357	+	0.424400i
$981$		0			0
$982$	5.83082	+	1.56236i	0.186069	+	0.0498570i
$983$	−11.4868	−	42.8692i	−0.366371	−	1.36731i	−0.865553	−	0.500817i	$-0.833033\pi$
$983$	−11.4868	−	42.8692i	−0.366371	−	1.36731i	0.499183	−	0.866497i	$-0.333634\pi$
$984$		0			0
$985$	22.0307	+	29.3882i	0.701957	+	0.936386i
$986$		−	0.625255i		−	0.0199122i
$987$		0			0
$988$	−9.49510	−	9.49510i	−0.302079	−	0.302079i
$989$	12.7182	−	7.34285i	0.404415	−	0.233489i
$990$		0			0
$991$	−26.0327	+	45.0900i	−0.826956	+	1.43233i	0.0734588	+	0.997298i	$0.476596\pi$
$991$	−26.0327	+	45.0900i	−0.826956	+	1.43233i	−0.900415	+	0.435032i	$0.856737\pi$
$992$	1.85583	−	6.92604i	0.0589225	−	0.219902i
$993$		0			0
$994$	−9.01057	−	24.7149i	−0.285798	−	0.783910i
$995$	30.9401	+	24.2978i	0.980869	+	0.770292i
$996$		0			0
$997$	−22.5397	+	6.03949i	−0.713839	+	0.191273i	−0.597421	−	0.801928i	$-0.703808\pi$
$997$	−22.5397	+	6.03949i	−0.713839	+	0.191273i	−0.116418	+	0.993200i	$0.537141\pi$
$998$	0.0390577	−	0.0104655i	0.00123635	−	0.000331279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bv.d.73.3	✓	32
3.2	odd	2	inner	630.2.bv.d.73.6	yes	32
5.2	odd	4	inner	630.2.bv.d.577.8	yes	32
7.5	odd	6	inner	630.2.bv.d.523.8	yes	32
15.2	even	4	inner	630.2.bv.d.577.1	yes	32
21.5	even	6	inner	630.2.bv.d.523.1	yes	32
35.12	even	12	inner	630.2.bv.d.397.3	yes	32
105.47	odd	12	inner	630.2.bv.d.397.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bv.d.73.3	✓	32	1.1	even	1	trivial
630.2.bv.d.73.6	yes	32	3.2	odd	2	inner
630.2.bv.d.397.3	yes	32	35.12	even	12	inner
630.2.bv.d.397.6	yes	32	105.47	odd	12	inner
630.2.bv.d.523.1	yes	32	21.5	even	6	inner
630.2.bv.d.523.8	yes	32	7.5	odd	6	inner
630.2.bv.d.577.1	yes	32	15.2	even	4	inner
630.2.bv.d.577.8	yes	32	5.2	odd	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.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(0.866025 + 0.500000i) q^{4} +(0.316731 - 2.21352i) q^{5} +(1.51871 + 2.16646i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.878841 + 2.05612i) q^{10} +(-3.20142 + 5.54503i) q^{11} +(-4.52364 + 4.52364i) q^{13} +(-0.906239 - 2.48571i) q^{14} +(0.500000 + 0.866025i) q^{16} +(0.161291 - 0.0432177i) q^{17} +(1.04950 + 1.81778i) q^{19} +(1.38106 - 1.75860i) q^{20} +(4.52750 - 4.52750i) q^{22} +(1.39635 - 5.21124i) q^{23} +(-4.79936 - 1.40218i) q^{25} +(5.54030 - 3.19870i) q^{26} +(0.232012 + 2.63556i) q^{28} +3.74448i q^{29} +(6.20971 + 3.58518i) q^{31} +(-0.258819 - 0.965926i) q^{32} -0.166980 q^{34} +(5.27652 - 2.67551i) q^{35} +(-0.703938 - 0.188620i) q^{37} +(-0.543260 - 2.02747i) q^{38} +(-1.78916 + 1.34123i) q^{40} +2.33142i q^{41} +(1.92479 + 1.92479i) q^{43} +(-5.54503 + 3.20142i) q^{44} +(-2.69753 + 4.67227i) q^{46} +(-1.98829 + 7.42041i) q^{47} +(-2.38705 + 6.58042i) q^{49} +(4.27292 + 2.59657i) q^{50} +(-6.17941 + 1.65577i) q^{52} +(-10.2832 + 2.75538i) q^{53} +(11.2601 + 8.84271i) q^{55} +(0.458027 - 2.60580i) q^{56} +(0.969143 - 3.61689i) q^{58} +(-2.22826 + 3.85946i) q^{59} +(9.91039 - 5.72176i) q^{61} +(-5.07021 - 5.07021i) q^{62} +1.00000i q^{64} +(8.58040 + 11.4460i) q^{65} +(-3.18097 - 11.8715i) q^{67} +(0.161291 + 0.0432177i) q^{68} +(-5.78920 + 1.21868i) q^{70} +9.94282 q^{71} +(-2.18599 - 8.15822i) q^{73} +(0.631133 + 0.364385i) q^{74} +2.09900i q^{76} +(-16.8751 + 1.48554i) q^{77} +(-4.16589 + 2.40518i) q^{79} +(2.07533 - 0.832464i) q^{80} +(0.603415 - 2.25198i) q^{82} +(3.88443 - 3.88443i) q^{83} +(-0.0445775 - 0.370709i) q^{85} +(-1.36103 - 2.35737i) q^{86} +(6.18468 - 1.65718i) q^{88} +(5.84862 + 10.1301i) q^{89} +(-16.6703 - 2.93018i) q^{91} +(3.81489 - 3.81489i) q^{92} +(3.84109 - 6.65296i) q^{94} +(4.35611 - 1.74734i) q^{95} +(8.73441 + 8.73441i) q^{97} +(4.00886 - 5.73839i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{7} + 12 q^{10} + 16 q^{16} + 8 q^{22} + 20 q^{28} + 48 q^{31} + 32 q^{37} + 80 q^{43} + 8 q^{46} - 28 q^{58} + 48 q^{61} + 16 q^{67} - 60 q^{70} - 24 q^{73} + 48 q^{82} - 144 q^{85} + 4 q^{88}+ \cdots - 32 q^{91}+O(q^{100}) \) 32 * q + 4 * q^7 + 12 * q^10 + 16 * q^16 + 8 * q^22 + 20 * q^28 + 48 * q^31 + 32 * q^37 + 80 * q^43 + 8 * q^46 - 28 * q^58 + 48 * q^61 + 16 * q^67 - 60 * q^70 - 24 * q^73 + 48 * q^82 - 144 * q^85 + 4 * q^88 - 32 * q^91

Introduction

L-functions

Modular forms

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Fields

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Database

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