LMFDB - Embedded newform 637.2.i.b.489.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(489,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("637.489");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.i (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			489.10
Character	$\chi$	$=$	637.489
Dual form			637.2.i.b.538.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.04867 - 1.04867i) q^{2} +0.884495i q^{3} +0.199431i q^{4} +(2.77428 - 2.77428i) q^{5} +(0.927546 - 0.927546i) q^{6} +(-1.88821 + 1.88821i) q^{8} +2.21767 q^{9} -5.81862 q^{10} +(1.83939 - 1.83939i) q^{11} -0.176395 q^{12} +(3.36514 - 1.29454i) q^{13} +(2.45383 + 2.45383i) q^{15} +4.35909 q^{16} -1.36013 q^{17} +(-2.32561 - 2.32561i) q^{18} +(-2.26377 + 2.26377i) q^{19} +(0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +1.60832i q^{23} +(-1.67011 - 1.67011i) q^{24} -10.3932i q^{25} +(-4.88648 - 2.17138i) q^{26} +4.61500i q^{27} +9.34669 q^{29} -5.14654i q^{30} +(-6.02038 + 6.02038i) q^{31} +(-0.794841 - 0.794841i) q^{32} +(1.62693 + 1.62693i) q^{33} +(1.42633 + 1.42633i) q^{34} +0.442271i q^{36} +(-3.40501 + 3.40501i) q^{37} +4.74791 q^{38} +(1.14501 + 2.97645i) q^{39} +10.4768i q^{40} +(2.14628 - 2.14628i) q^{41} -11.5495i q^{43} +(0.366830 + 0.366830i) q^{44} +(6.15243 - 6.15243i) q^{45} +(1.68660 - 1.68660i) q^{46} +(-7.01591 - 7.01591i) q^{47} +3.85559i q^{48} +(-10.8991 + 10.8991i) q^{50} -1.20303i q^{51} +(0.258171 + 0.671112i) q^{52} -3.02346 q^{53} +(4.83963 - 4.83963i) q^{54} -10.2059i q^{55} +(-2.00229 - 2.00229i) q^{57} +(-9.80162 - 9.80162i) q^{58} +(-0.183216 - 0.183216i) q^{59} +(-0.489369 + 0.489369i) q^{60} -0.333338i q^{61} +12.6268 q^{62} -7.05112i q^{64} +(5.74442 - 12.9272i) q^{65} -3.41223i q^{66} +(0.743917 + 0.743917i) q^{67} -0.271252i q^{68} -1.42255 q^{69} +(-0.333748 - 0.333748i) q^{71} +(-4.18742 + 4.18742i) q^{72} +(-5.93894 - 5.93894i) q^{73} +7.14148 q^{74} +9.19276 q^{75} +(-0.451465 - 0.451465i) q^{76} +(1.92058 - 4.32207i) q^{78} +2.90324 q^{79} +(12.0933 - 12.0933i) q^{80} +2.57106 q^{81} -4.50148 q^{82} +(-3.84570 + 3.84570i) q^{83} +(-3.77338 + 3.77338i) q^{85} +(-12.1116 + 12.1116i) q^{86} +8.26709i q^{87} +6.94629i q^{88} +(5.22813 + 5.22813i) q^{89} -12.9038 q^{90} -0.320747 q^{92} +(-5.32500 - 5.32500i) q^{93} +14.7148i q^{94} +12.5607i q^{95} +(0.703033 - 0.703033i) q^{96} +(-7.45885 + 7.45885i) q^{97} +(4.07915 - 4.07915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{9} - 16 q^{11} + 48 q^{15} - 56 q^{16} - 32 q^{18} - 48 q^{29} - 32 q^{39} - 64 q^{44} + 32 q^{46} - 40 q^{50} - 16 q^{53} - 96 q^{57} + 72 q^{58} - 64 q^{60} + 32 q^{65} + 32 q^{71} + 208 q^{72}+ \cdots + 64 q^{93}+O(q^{100}) $ 56 * q - 56 * q^9 - 16 * q^11 + 48 * q^15 - 56 * q^16 - 32 * q^18 - 48 * q^29 - 32 * q^39 - 64 * q^44 + 32 * q^46 - 40 * q^50 - 16 * q^53 - 96 * q^57 + 72 * q^58 - 64 * q^60 + 32 * q^65 + 32 * q^71 + 208 * q^72 + 208 * q^74 + 160 * q^78 - 80 * q^79 + 152 * q^81 + 24 * q^85 + 64 * q^86 - 128 * q^92 + 64 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.04867	−	1.04867i	−0.741524	−	0.741524i	0.231347	−	0.972871i	$-0.425687\pi$
$2$	−1.04867	−	1.04867i	−0.741524	−	0.741524i	−0.972871	+	0.231347i	$0.925687\pi$
$3$			0.884495i			0.510663i	0.966854	+	0.255332i	$0.0821846\pi$
$3$			0.884495i			0.510663i	−0.966854	+	0.255332i	$0.917815\pi$
$4$			0.199431i			0.0997153i
$5$	2.77428	−	2.77428i	1.24069	−	1.24069i	0.280982	−	0.959713i	$-0.409340\pi$
$5$	2.77428	−	2.77428i	1.24069	−	1.24069i	0.959713	−	0.280982i	$-0.0906601\pi$
$6$	0.927546	−	0.927546i	0.378669	−	0.378669i
$7$		0			0
$7$		0			0
$8$	−1.88821	+	1.88821i	−0.667583	+	0.667583i
$9$	2.21767			0.739223
$10$	−5.81862			−1.84001
$11$	1.83939	−	1.83939i	0.554596	−	0.554596i	−0.373168	−	0.927764i	$-0.621729\pi$
$11$	1.83939	−	1.83939i	0.554596	−	0.554596i	0.927764	+	0.373168i	$0.121729\pi$
$12$	−0.176395			−0.0509209
$13$	3.36514	−	1.29454i	0.933322	−	0.359041i
$13$	3.36514	−	1.29454i	0.933322	−	0.359041i
$14$		0			0
$15$	2.45383	+	2.45383i	0.633577	+	0.633577i
$16$	4.35909			1.08977
$17$	−1.36013			−0.329880			−0.164940	−	0.986304i	$-0.552743\pi$
$17$	−1.36013			−0.329880			−0.164940	+	0.986304i	$0.552743\pi$
$18$	−2.32561	−	2.32561i	−0.548152	−	0.548152i
$19$	−2.26377	+	2.26377i	−0.519344	+	0.519344i	−0.917373	−	0.398029i	$-0.869694\pi$
$19$	−2.26377	+	2.26377i	−0.519344	+	0.519344i	0.398029	+	0.917373i	$0.369694\pi$
$20$	0.553276	+	0.553276i	0.123716	+	0.123716i
$21$		0			0
$22$	−3.85783			−0.822492
$23$			1.60832i			0.335357i	0.985842	+	0.167679i	$0.0536271\pi$
$23$			1.60832i			0.335357i	−0.985842	+	0.167679i	$0.946373\pi$
$24$	−1.67011	−	1.67011i	−0.340910	−	0.340910i
$25$		−	10.3932i		−	2.07865i
$26$	−4.88648	−	2.17138i	−0.958318	−	0.425843i
$27$			4.61500i			0.888157i
$28$		0			0
$29$	9.34669			1.73564			0.867818	−	0.496882i	$-0.165522\pi$
$29$	9.34669			1.73564			0.867818	+	0.496882i	$0.165522\pi$
$30$		−	5.14654i		−	0.939625i
$31$	−6.02038	+	6.02038i	−1.08129	+	1.08129i	−0.0849034	+	0.996389i	$0.527058\pi$
$31$	−6.02038	+	6.02038i	−1.08129	+	1.08129i	−0.996389	+	0.0849034i	$0.972942\pi$
$32$	−0.794841	−	0.794841i	−0.140509	−	0.140509i
$33$	1.62693	+	1.62693i	0.283212	+	0.283212i
$34$	1.42633	+	1.42633i	0.244614	+	0.244614i
$35$		0			0
$36$			0.442271i			0.0737118i
$37$	−3.40501	+	3.40501i	−0.559780	+	0.559780i	−0.929245	−	0.369465i	$-0.879541\pi$
$37$	−3.40501	+	3.40501i	−0.559780	+	0.559780i	0.369465	+	0.929245i	$0.379541\pi$
$38$	4.74791			0.770212
$39$	1.14501	+	2.97645i	0.183349	+	0.476613i
$40$			10.4768i			1.65653i
$41$	2.14628	−	2.14628i	0.335192	−	0.335192i	−0.519362	−	0.854554i	$-0.673830\pi$
$41$	2.14628	−	2.14628i	0.335192	−	0.335192i	0.854554	+	0.519362i	$0.173830\pi$
$42$		0			0
$43$		−	11.5495i		−	1.76128i	−0.473786	−	0.880640i	$-0.657113\pi$
$43$		−	11.5495i		−	1.76128i	0.473786	−	0.880640i	$-0.342887\pi$
$44$	0.366830	+	0.366830i	0.0553017	+	0.0553017i
$45$	6.15243	−	6.15243i	0.917150	−	0.917150i
$46$	1.68660	−	1.68660i	0.248675	−	0.248675i
$47$	−7.01591	−	7.01591i	−1.02338	−	1.02338i	−0.999720	−	0.0236558i	$-0.992469\pi$
$47$	−7.01591	−	7.01591i	−1.02338	−	1.02338i	−0.0236558	−	0.999720i	$-0.507531\pi$
$48$			3.85559i			0.556507i
$49$		0			0
$50$	−10.8991	+	10.8991i	−1.54137	+	1.54137i
$51$		−	1.20303i		−	0.168458i
$52$	0.258171	+	0.671112i	0.0358018	+	0.0930664i
$53$	−3.02346			−0.415305			−0.207652	−	0.978203i	$-0.566582\pi$
$53$	−3.02346			−0.415305			−0.207652	+	0.978203i	$0.566582\pi$
$54$	4.83963	−	4.83963i	0.658590	−	0.658590i
$55$		−	10.2059i		−	1.37617i
$56$		0			0
$57$	−2.00229	−	2.00229i	−0.265210	−	0.265210i
$58$	−9.80162	−	9.80162i	−1.28702	−	1.28702i
$59$	−0.183216	−	0.183216i	−0.0238527	−	0.0238527i	0.695080	−	0.718933i	$-0.255369\pi$
$59$	−0.183216	−	0.183216i	−0.0238527	−	0.0238527i	−0.718933	+	0.695080i	$0.755369\pi$
$60$	−0.489369	+	0.489369i	−0.0631773	+	0.0631773i
$61$		−	0.333338i		−	0.0426796i	−0.999772	−	0.0213398i	$-0.993207\pi$
$61$		−	0.333338i		−	0.0426796i	0.999772	−	0.0213398i	$-0.00679318\pi$
$62$	12.6268			1.60361
$63$		0			0
$64$		−	7.05112i		−	0.881390i
$65$	5.74442	−	12.9272i	0.712508	−	1.60343i
$66$		−	3.41223i		−	0.420016i
$67$	0.743917	+	0.743917i	0.0908839	+	0.0908839i	0.751087	−	0.660203i	$-0.229530\pi$
$67$	0.743917	+	0.743917i	0.0908839	+	0.0908839i	−0.660203	+	0.751087i	$0.729530\pi$
$68$		−	0.271252i		−	0.0328941i
$69$	−1.42255			−0.171255
$70$		0			0
$71$	−0.333748	−	0.333748i	−0.0396086	−	0.0396086i	0.687025	−	0.726634i	$-0.258916\pi$
$71$	−0.333748	−	0.333748i	−0.0396086	−	0.0396086i	−0.726634	+	0.687025i	$0.758916\pi$
$72$	−4.18742	+	4.18742i	−0.493492	+	0.493492i
$73$	−5.93894	−	5.93894i	−0.695101	−	0.695101i	0.268249	−	0.963350i	$-0.413555\pi$
$73$	−5.93894	−	5.93894i	−0.695101	−	0.695101i	−0.963350	+	0.268249i	$0.913555\pi$
$74$	7.14148			0.830180
$75$	9.19276			1.06149
$76$	−0.451465	−	0.451465i	−0.0517866	−	0.0517866i
$77$		0			0
$78$	1.92058	−	4.32207i	0.217462	−	0.489378i
$79$	2.90324			0.326640			0.163320	−	0.986573i	$-0.447780\pi$
$79$	2.90324			0.326640			0.163320	+	0.986573i	$0.447780\pi$
$80$	12.0933	−	12.0933i	1.35207	−	1.35207i
$81$	2.57106			0.285674
$82$	−4.50148			−0.497106
$83$	−3.84570	+	3.84570i	−0.422120	+	0.422120i	−0.885933	−	0.463813i	$-0.846481\pi$
$83$	−3.84570	+	3.84570i	−0.422120	+	0.422120i	0.463813	+	0.885933i	$0.346481\pi$
$84$		0			0
$85$	−3.77338	+	3.77338i	−0.409281	+	0.409281i
$86$	−12.1116	+	12.1116i	−1.30603	+	1.30603i
$87$			8.26709i			0.886326i
$88$			6.94629i			0.740477i
$89$	5.22813	+	5.22813i	0.554181	+	0.554181i	0.927645	−	0.373464i	$-0.121830\pi$
$89$	5.22813	+	5.22813i	0.554181	+	0.554181i	−0.373464	+	0.927645i	$0.621830\pi$
$90$	−12.9038			−1.36018
$91$		0			0
$92$	−0.320747			−0.0334402
$93$	−5.32500	−	5.32500i	−0.552176	−	0.552176i
$94$			14.7148i			1.51772i
$95$			12.5607i			1.28870i
$96$	0.703033	−	0.703033i	0.0717530	−	0.0717530i
$97$	−7.45885	+	7.45885i	−0.757332	+	0.757332i	−0.975836	−	0.218504i	$-0.929882\pi$
$97$	−7.45885	+	7.45885i	−0.757332	+	0.757332i	0.218504	+	0.975836i	$0.429882\pi$
$98$		0			0
$99$	4.07915	−	4.07915i	0.409970	−	0.409970i
$100$	2.07273			0.207273
$101$	0.209302			0.0208264			0.0104132	−	0.999946i	$-0.496685\pi$
$101$	0.209302			0.0208264			0.0104132	+	0.999946i	$0.496685\pi$
$102$	−1.26158	+	1.26158i	−0.124915	+	0.124915i
$103$	−16.3560			−1.61160			−0.805800	−	0.592187i	$-0.798265\pi$
$103$	−16.3560			−1.61160			−0.805800	+	0.592187i	$0.798265\pi$
$104$	−3.90973	+	8.79845i	−0.383380	+	0.862759i
$105$		0			0
$106$	3.17063	+	3.17063i	0.307958	+	0.307958i
$107$	17.0592			1.64917			0.824585	−	0.565737i	$-0.191408\pi$
$107$	17.0592			1.64917			0.824585	+	0.565737i	$0.191408\pi$
$108$	−0.920372			−0.0885628
$109$	−4.95848	−	4.95848i	−0.474936	−	0.474936i	0.428572	−	0.903508i	$-0.359017\pi$
$109$	−4.95848	−	4.95848i	−0.474936	−	0.474936i	−0.903508	+	0.428572i	$0.859017\pi$
$110$	−10.7027	+	10.7027i	−1.02046	+	1.02046i
$111$	−3.01171	−	3.01171i	−0.285859	−	0.285859i
$112$		0			0
$113$	4.56982			0.429892			0.214946	−	0.976626i	$-0.431042\pi$
$113$	4.56982			0.429892			0.214946	+	0.976626i	$0.431042\pi$
$114$			4.19950i			0.393319i
$115$	4.46192	+	4.46192i	0.416076	+	0.416076i
$116$			1.86401i			0.173069i
$117$	7.46277	−	2.87086i	0.689933	−	0.265411i
$118$			0.384268i			0.0353747i
$119$		0			0
$120$	−9.26670			−0.845930
$121$			4.23332i			0.384847i
$122$	−0.349563	+	0.349563i	−0.0316479	+	0.0316479i
$123$	1.89837	+	1.89837i	0.171170	+	0.171170i
$124$	−1.20065	−	1.20065i	−0.107821	−	0.107821i
$125$	−14.9623	−	14.9623i	−1.33827	−	1.33827i
$126$		0			0
$127$			10.4126i			0.923968i	0.886888	+	0.461984i	$0.152862\pi$
$127$			10.4126i			0.923968i	−0.886888	+	0.461984i	$0.847138\pi$
$128$	−8.98400	+	8.98400i	−0.794081	+	0.794081i
$129$	10.2155			0.899421
$130$	−19.5805	+	7.53244i	−1.71732	+	0.660638i
$131$			17.4915i			1.52824i	0.645073	+	0.764121i	$0.276827\pi$
$131$			17.4915i			1.52824i	−0.645073	+	0.764121i	$0.723173\pi$
$132$	−0.324459	+	0.324459i	−0.0282405	+	0.0282405i
$133$		0			0
$134$		−	1.56025i		−	0.134785i
$135$	12.8033	+	12.8033i	1.10193	+	1.10193i
$136$	2.56821	−	2.56821i	0.220222	−	0.220222i
$137$	−14.2346	+	14.2346i	−1.21614	+	1.21614i	−0.247168	+	0.968973i	$0.579500\pi$
$137$	−14.2346	+	14.2346i	−1.21614	+	1.21614i	−0.968973	+	0.247168i	$0.920500\pi$
$138$	1.49179	+	1.49179i	0.126989	+	0.126989i
$139$		−	14.6578i		−	1.24326i	−0.783310	−	0.621631i	$-0.786470\pi$
$139$		−	14.6578i		−	1.24326i	0.783310	−	0.621631i	$-0.213530\pi$
$140$		0			0
$141$	6.20554	−	6.20554i	0.522600	−	0.522600i
$142$			0.699984i			0.0587414i
$143$	3.80863	−	8.57095i	0.318494	−	0.716739i
$144$	9.66702			0.805585
$145$	25.9303	−	25.9303i	2.15340	−	2.15340i
$146$			12.4560i			1.03087i
$147$		0			0
$148$	−0.679062	−	0.679062i	−0.0558186	−	0.0558186i
$149$	15.4639	+	15.4639i	1.26685	+	1.26685i	0.947706	+	0.319143i	$0.103395\pi$
$149$	15.4639	+	15.4639i	1.26685	+	1.26685i	0.319143	+	0.947706i	$0.396605\pi$
$150$	−9.64020	−	9.64020i	−0.787119	−	0.787119i
$151$	9.56712	−	9.56712i	0.778561	−	0.778561i	−0.201025	−	0.979586i	$-0.564427\pi$
$151$	9.56712	−	9.56712i	0.778561	−	0.778561i	0.979586	+	0.201025i	$0.0644272\pi$
$152$		−	8.54894i		−	0.693410i
$153$	−3.01632			−0.243855
$154$		0			0
$155$			33.4044i			2.68311i
$156$	−0.593595	+	0.228351i	−0.0475256	+	0.0182827i
$157$			12.8609i			1.02641i	0.858266	+	0.513205i	$0.171542\pi$
$157$			12.8609i			1.02641i	−0.858266	+	0.513205i	$0.828458\pi$
$158$	−3.04455	−	3.04455i	−0.242211	−	0.242211i
$159$		−	2.67424i		−	0.212081i
$160$	−4.41022			−0.348659
$161$		0			0
$162$	−2.69621	−	2.69621i	−0.211834	−	0.211834i
$163$	−7.57479	+	7.57479i	−0.593303	+	0.593303i	−0.938522	−	0.345219i	$-0.887805\pi$
$163$	−7.57479	+	7.57479i	−0.593303	+	0.593303i	0.345219	+	0.938522i	$0.387805\pi$
$164$	0.428033	+	0.428033i	0.0334238	+	0.0334238i
$165$	9.02710			0.702758
$166$	8.06576			0.626025
$167$	6.07140	+	6.07140i	0.469819	+	0.469819i	0.901856	−	0.432037i	$-0.142205\pi$
$167$	6.07140	+	6.07140i	0.469819	+	0.469819i	−0.432037	+	0.901856i	$0.642205\pi$
$168$		0			0
$169$	9.64834	−	8.71261i	0.742180	−	0.670201i
$170$	7.91409			0.606983
$171$	−5.02029	+	5.02029i	−0.383911	+	0.383911i
$172$	2.30332			0.175626
$173$	3.55228			0.270075			0.135037	−	0.990840i	$-0.456885\pi$
$173$	3.55228			0.270075			0.135037	+	0.990840i	$0.456885\pi$
$174$	8.66948	−	8.66948i	0.657232	−	0.657232i
$175$		0			0
$176$	8.01805	−	8.01805i	0.604383	−	0.604383i
$177$	0.162054	−	0.162054i	0.0121807	−	0.0121807i
$178$		−	10.9652i		−	0.821877i
$179$			17.2282i			1.28770i	0.765152	+	0.643850i	$0.222664\pi$
$179$			17.2282i			1.28770i	−0.765152	+	0.643850i	$0.777336\pi$
$180$	1.22698	+	1.22698i	0.0914539	+	0.0914539i
$181$	6.21868			0.462231			0.231115	−	0.972926i	$-0.425762\pi$
$181$	6.21868			0.462231			0.231115	+	0.972926i	$0.425762\pi$
$182$		0			0
$183$	0.294836			0.0217949
$184$	−3.03684	−	3.03684i	−0.223879	−	0.223879i
$185$			18.8929i			1.38903i
$186$			11.1684i			0.818904i
$187$	−2.50181	+	2.50181i	−0.182950	+	0.182950i
$188$	1.39919	−	1.39919i	0.102046	−	0.102046i
$189$		0			0
$190$	13.1720	−	13.1720i	0.955599	−	0.955599i
$191$	−12.3074			−0.890529			−0.445264	−	0.895399i	$-0.646890\pi$
$191$	−12.3074			−0.890529			−0.445264	+	0.895399i	$0.646890\pi$
$192$	6.23668			0.450093
$193$	15.1711	−	15.1711i	1.09204	−	1.09204i	0.0967300	−	0.995311i	$-0.469162\pi$
$193$	15.1711	−	15.1711i	1.09204	−	1.09204i	0.995311	−	0.0967300i	$-0.0308383\pi$
$194$	15.6438			1.12316
$195$	11.4341	+	5.08091i	0.818812	+	0.363852i
$196$		0			0
$197$	−1.42501	−	1.42501i	−0.101528	−	0.101528i	0.654518	−	0.756046i	$-0.272872\pi$
$197$	−1.42501	−	1.42501i	−0.101528	−	0.101528i	−0.756046	+	0.654518i	$0.772872\pi$
$198$	−8.55539			−0.608005
$199$	−6.67629			−0.473270			−0.236635	−	0.971599i	$-0.576044\pi$
$199$	−6.67629			−0.473270			−0.236635	+	0.971599i	$0.576044\pi$
$200$	19.6246	+	19.6246i	1.38767	+	1.38767i
$201$	−0.657991	+	0.657991i	−0.0464111	+	0.0464111i
$202$	−0.219490	−	0.219490i	−0.0154432	−	0.0154432i
$203$		0			0
$204$	0.239921			0.0167978
$205$		−	11.9087i		−	0.831742i
$206$	17.1521	+	17.1521i	1.19504	+	1.19504i
$207$			3.56671i			0.247904i
$208$	14.6689	−	5.64301i	1.01711	−	0.391272i
$209$			8.32789i			0.576052i
$210$		0			0
$211$	−18.9896			−1.30730			−0.653648	−	0.756798i	$-0.726762\pi$
$211$	−18.9896			−1.30730			−0.653648	+	0.756798i	$0.726762\pi$
$212$		−	0.602971i		−	0.0414122i
$213$	0.295198	−	0.295198i	0.0202266	−	0.0202266i
$214$	−17.8895	−	17.8895i	−1.22290	−	1.22290i
$215$	−32.0415	−	32.0415i	−2.18521	−	2.18521i
$216$	−8.71408	−	8.71408i	−0.592918	−	0.592918i
$217$		0			0
$218$			10.3996i			0.704353i
$219$	5.25296	−	5.25296i	0.354962	−	0.354962i
$220$	2.03538			0.137225
$221$	−4.57703	+	1.76074i	−0.307885	+	0.118440i
$222$			6.31660i			0.423942i
$223$	2.04467	−	2.04467i	0.136921	−	0.136921i	−0.635324	−	0.772245i	$-0.719134\pi$
$223$	2.04467	−	2.04467i	0.136921	−	0.136921i	0.772245	+	0.635324i	$0.219134\pi$
$224$		0			0
$225$		−	23.0488i		−	1.53658i
$226$	−4.79224	−	4.79224i	−0.318775	−	0.318775i
$227$	−4.64125	+	4.64125i	−0.308050	+	0.308050i	−0.844153	−	0.536102i	$-0.819896\pi$
$227$	−4.64125	+	4.64125i	−0.308050	+	0.308050i	0.536102	+	0.844153i	$0.319896\pi$
$228$	0.399318	−	0.399318i	0.0264455	−	0.0264455i
$229$	1.00850	+	1.00850i	0.0666434	+	0.0666434i	0.739643	−	0.673000i	$-0.234994\pi$
$229$	1.00850	+	1.00850i	0.0666434	+	0.0666434i	−0.673000	+	0.739643i	$0.734994\pi$
$230$		−	9.35819i		−	0.617060i
$231$		0			0
$232$	−17.6485	+	17.6485i	−1.15868	+	1.15868i
$233$			8.49422i			0.556475i	0.960512	+	0.278237i	$0.0897502\pi$
$233$			8.49422i			0.556475i	−0.960512	+	0.278237i	$0.910250\pi$
$234$	−10.8366	−	4.81541i	−0.708411	−	0.314793i
$235$	−38.9282			−2.53939
$236$	0.0365389	−	0.0365389i	0.00237848	−	0.00237848i
$237$			2.56790i			0.166803i
$238$		0			0
$239$	−4.64810	−	4.64810i	−0.300661	−	0.300661i	0.540612	−	0.841272i	$-0.318193\pi$
$239$	−4.64810	−	4.64810i	−0.300661	−	0.300661i	−0.841272	+	0.540612i	$0.818193\pi$
$240$	10.6965	+	10.6965i	0.690455	+	0.690455i
$241$	−7.62596	−	7.62596i	−0.491231	−	0.491231i	0.417463	−	0.908694i	$-0.362919\pi$
$241$	−7.62596	−	7.62596i	−0.491231	−	0.491231i	−0.908694	+	0.417463i	$0.862919\pi$
$242$	4.43937	−	4.43937i	0.285373	−	0.285373i
$243$			16.1191i			1.03404i
$244$	0.0664778			0.00425580
$245$		0			0
$246$		−	3.98154i		−	0.253854i
$247$	−4.68736	+	10.5484i	−0.298250	+	0.671181i
$248$		−	22.7355i		−	1.44370i
$249$	−3.40150	−	3.40150i	−0.215561	−	0.215561i
$250$			31.3812i			1.98472i
$251$	28.0524			1.77065			0.885327	−	0.464968i	$-0.153934\pi$
$251$	28.0524			1.77065			0.885327	+	0.464968i	$0.153934\pi$
$252$		0			0
$253$	2.95831	+	2.95831i	0.185988	+	0.185988i
$254$	10.9194	−	10.9194i	0.685145	−	0.685145i
$255$	−3.33754	−	3.33754i	−0.209005	−	0.209005i
$256$	4.74032			0.296270
$257$	−14.1206			−0.880821			−0.440411	−	0.897797i	$-0.645167\pi$
$257$	−14.1206			−0.880821			−0.440411	+	0.897797i	$0.645167\pi$
$258$	−10.7127	−	10.7127i	−0.666942	−	0.666942i
$259$		0			0
$260$	2.57809	+	1.14561i	0.159886	+	0.0710479i
$261$	20.7279			1.28302
$262$	18.3429	−	18.3429i	1.13323	−	1.13323i
$263$	22.3230			1.37650			0.688248	−	0.725476i	$-0.258380\pi$
$263$	22.3230			1.37650			0.688248	+	0.725476i	$0.258380\pi$
$264$	−6.14395			−0.378134
$265$	−8.38793	+	8.38793i	−0.515267	+	0.515267i
$266$		0			0
$267$	−4.62426	+	4.62426i	−0.283000	+	0.283000i
$268$	−0.148360	+	0.148360i	−0.00906251	+	0.00906251i
$269$			11.8301i			0.721291i	0.932703	+	0.360645i	$0.117444\pi$
$269$			11.8301i			0.721291i	−0.932703	+	0.360645i	$0.882556\pi$
$270$		−	26.8529i		−	1.63422i
$271$	−3.49518	−	3.49518i	−0.212317	−	0.212317i	0.592934	−	0.805251i	$-0.297969\pi$
$271$	−3.49518	−	3.49518i	−0.212317	−	0.212317i	−0.805251	+	0.592934i	$0.797969\pi$
$272$	−5.92893			−0.359494
$273$		0			0
$274$	29.8548			1.80359
$275$	−19.1172	−	19.1172i	−1.15281	−	1.15281i
$276$		−	0.283699i		−	0.0170767i
$277$			0.843523i			0.0506824i	0.999679	+	0.0253412i	$0.00806721\pi$
$277$			0.843523i			0.0506824i	−0.999679	+	0.0253412i	$0.991933\pi$
$278$	−15.3713	+	15.3713i	−0.921909	+	0.921909i
$279$	−13.3512	+	13.3512i	−0.799316	+	0.799316i
$280$		0			0
$281$	−6.80029	+	6.80029i	−0.405671	+	0.405671i	−0.880226	−	0.474555i	$-0.842609\pi$
$281$	−6.80029	+	6.80029i	−0.405671	+	0.405671i	0.474555	+	0.880226i	$0.342609\pi$
$282$	−13.0152			−0.775041
$283$	19.8235			1.17838			0.589192	−	0.807993i	$-0.299446\pi$
$283$	19.8235			1.17838			0.589192	+	0.807993i	$0.299446\pi$
$284$	0.0665595	−	0.0665595i	0.00394958	−	0.00394958i
$285$	−11.1098			−0.658089
$286$	−12.9821	+	4.99411i	−0.767650	+	0.295308i
$287$		0			0
$288$	−1.76270	−	1.76270i	−0.103868	−	0.103868i
$289$	−15.1500			−0.891179
$290$	−54.3848			−3.19359
$291$	−6.59731	−	6.59731i	−0.386741	−	0.386741i
$292$	1.18441	−	1.18441i	0.0693122	−	0.0693122i
$293$	6.47711	+	6.47711i	0.378397	+	0.378397i	0.870524	−	0.492127i	$-0.163780\pi$
$293$	6.47711	+	6.47711i	0.378397	+	0.378397i	−0.492127	+	0.870524i	$0.663780\pi$
$294$		0			0
$295$	−1.01659			−0.0591879
$296$		−	12.8587i		−	0.747398i
$297$	8.48877	+	8.48877i	0.492568	+	0.492568i
$298$		−	32.4331i		−	1.87880i
$299$	2.08203	+	5.41221i	0.120407	+	0.312996i
$300$			1.83332i			0.105847i
$301$		0			0
$302$	−20.0656			−1.15464
$303$			0.185127i			0.0106353i
$304$	−9.86797	+	9.86797i	−0.565967	+	0.565967i
$305$	−0.924772	−	0.924772i	−0.0529523	−	0.0529523i
$306$	3.16314	+	3.16314i	0.180824	+	0.180824i
$307$	17.9487	+	17.9487i	1.02438	+	1.02438i	0.999695	+	0.0246898i	$0.00785980\pi$
$307$	17.9487	+	17.9487i	1.02438	+	1.02438i	0.0246898	+	0.999695i	$0.492140\pi$
$308$		0			0
$309$		−	14.4668i		−	0.822985i
$310$	35.0303	−	35.0303i	1.98959	−	1.98959i
$311$	13.4787			0.764310			0.382155	−	0.924098i	$-0.375182\pi$
$311$	13.4787			0.764310			0.382155	+	0.924098i	$0.375182\pi$
$312$	−7.78218	−	3.45813i	−0.440579	−	0.195778i
$313$			6.48420i			0.366509i	0.983066	+	0.183254i	$0.0586632\pi$
$313$			6.48420i			0.366509i	−0.983066	+	0.183254i	$0.941337\pi$
$314$	13.4869	−	13.4869i	0.761108	−	0.761108i
$315$		0			0
$316$			0.578994i			0.0325710i
$317$	−22.1356	−	22.1356i	−1.24326	−	1.24326i	−0.958640	−	0.284620i	$-0.908133\pi$
$317$	−22.1356	−	22.1356i	−1.24326	−	1.24326i	−0.284620	−	0.958640i	$-0.591867\pi$
$318$	−2.80440	+	2.80440i	−0.157263	+	0.157263i
$319$	17.1922	−	17.1922i	0.962576	−	0.962576i
$320$	−19.5618	−	19.5618i	−1.09354	−	1.09354i
$321$			15.0887i			0.842171i
$322$		0			0
$323$	3.07902	−	3.07902i	0.171322	−	0.171322i
$324$			0.512749i			0.0284860i
$325$	−13.4545	−	34.9747i	−0.746319	−	1.94005i
$326$	15.8870			0.879897
$327$	4.38575	−	4.38575i	0.242532	−	0.242532i
$328$			8.10523i			0.447537i
$329$		0			0
$330$	−9.46647	−	9.46647i	−0.521112	−	0.521112i
$331$	−8.85030	−	8.85030i	−0.486456	−	0.486456i	0.420730	−	0.907186i	$-0.361774\pi$
$331$	−8.85030	−	8.85030i	−0.486456	−	0.486456i	−0.907186	+	0.420730i	$0.861774\pi$
$332$	−0.766950	−	0.766950i	−0.0420918	−	0.0420918i
$333$	−7.55118	+	7.55118i	−0.413802	+	0.413802i
$334$		−	12.7338i		−	0.696764i
$335$	4.12767			0.225518
$336$		0			0
$337$			4.54349i			0.247500i	0.992313	+	0.123750i	$0.0394920\pi$
$337$			4.54349i			0.247500i	−0.992313	+	0.123750i	$0.960508\pi$
$338$	−19.2546	−	0.981266i	−1.04731	−	0.0533739i
$339$			4.04198i			0.219530i
$340$	−0.752528	−	0.752528i	−0.0408116	−	0.0408116i
$341$			22.1476i			1.19936i
$342$	10.5293			0.569359
$343$		0			0
$344$	21.8078	+	21.8078i	1.17580	+	1.17580i
$345$	−3.94654	+	3.94654i	−0.212475	+	0.212475i
$346$	−3.72518	−	3.72518i	−0.200267	−	0.200267i
$347$	−11.1328			−0.597643			−0.298821	−	0.954309i	$-0.596593\pi$
$347$	−11.1328			−0.597643			−0.298821	+	0.954309i	$0.596593\pi$
$348$	−1.64871			−0.0883802
$349$	−16.7058	−	16.7058i	−0.894240	−	0.894240i	0.100679	−	0.994919i	$-0.467899\pi$
$349$	−16.7058	−	16.7058i	−0.894240	−	0.894240i	−0.994919	+	0.100679i	$0.967899\pi$
$350$		0			0
$351$	5.97430	+	15.5301i	0.318885	+	0.828937i
$352$	−2.92404			−0.155852
$353$	4.33065	−	4.33065i	0.230497	−	0.230497i	−0.582403	−	0.812900i	$-0.697887\pi$
$353$	4.33065	−	4.33065i	0.230497	−	0.230497i	0.812900	+	0.582403i	$0.197887\pi$
$354$	−0.339883			−0.0180646
$355$	−1.85182			−0.0982843
$356$	−1.04265	+	1.04265i	−0.0552603	+	0.0552603i
$357$		0			0
$358$	18.0668	−	18.0668i	0.954860	−	0.954860i
$359$	15.3804	−	15.3804i	0.811748	−	0.811748i	−0.173148	−	0.984896i	$-0.555394\pi$
$359$	15.3804	−	15.3804i	0.811748	−	0.811748i	0.984896	+	0.173148i	$0.0553939\pi$
$360$			23.2342i			1.22455i
$361$			8.75070i			0.460563i
$362$	−6.52136	−	6.52136i	−0.342755	−	0.342755i
$363$	−3.74435			−0.196527
$364$		0			0
$365$	−32.9526			−1.72482
$366$	−0.309186	−	0.309186i	−0.0161614	−	0.0161614i
$367$		−	16.2513i		−	0.848310i	−0.905590	−	0.424155i	$-0.860571\pi$
$367$		−	16.2513i		−	0.848310i	0.905590	−	0.424155i	$-0.139429\pi$
$368$			7.01079i			0.365463i
$369$	4.75973	−	4.75973i	0.247782	−	0.247782i
$370$	19.8124	−	19.8124i	1.03000	−	1.03000i
$371$		0			0
$372$	1.06197	−	1.06197i	0.0550604	−	0.0550604i
$373$	4.21566			0.218279			0.109139	−	0.994026i	$-0.465191\pi$
$373$	4.21566			0.218279			0.109139	+	0.994026i	$0.465191\pi$
$374$	5.24716			0.271324
$375$	13.2341	−	13.2341i	0.683407	−	0.683407i
$376$	26.4950			1.36638
$377$	31.4529	−	12.0997i	1.61991	−	0.623164i
$378$		0			0
$379$	18.1305	+	18.1305i	0.931303	+	0.931303i	0.997787	−	0.0664849i	$-0.0211784\pi$
$379$	18.1305	+	18.1305i	0.931303	+	0.931303i	−0.0664849	+	0.997787i	$0.521178\pi$
$380$	−2.50498			−0.128503
$381$	−9.20988			−0.471837
$382$	12.9064	+	12.9064i	0.660348	+	0.660348i
$383$	16.5958	−	16.5958i	0.848007	−	0.848007i	−0.141877	−	0.989884i	$-0.545314\pi$
$383$	16.5958	−	16.5958i	0.848007	−	0.848007i	0.989884	+	0.141877i	$0.0453137\pi$
$384$	−7.94630	−	7.94630i	−0.405508	−	0.405508i
$385$		0			0
$386$	−31.8191			−1.61955
$387$		−	25.6129i		−	1.30198i
$388$	−1.48752	−	1.48752i	−0.0755175	−	0.0755175i
$389$		−	19.4735i		−	0.987346i	−0.869648	−	0.493673i	$-0.835654\pi$
$389$		−	19.4735i		−	0.987346i	0.869648	−	0.493673i	$-0.164346\pi$
$390$	−6.66240	−	17.3188i	−0.337364	−	0.876973i
$391$		−	2.18752i		−	0.110628i
$392$		0			0
$393$	−15.4712			−0.780417
$394$			2.98875i			0.150571i
$395$	8.05439	−	8.05439i	0.405260	−	0.405260i
$396$	0.813507	+	0.813507i	0.0408803	+	0.0408803i
$397$	8.45631	+	8.45631i	0.424410	+	0.424410i	0.886719	−	0.462309i	$-0.152979\pi$
$397$	8.45631	+	8.45631i	0.424410	+	0.424410i	−0.462309	+	0.886719i	$0.652979\pi$
$398$	7.00124	+	7.00124i	0.350941	+	0.350941i
$399$		0			0
$400$		−	45.3051i		−	2.26525i
$401$	−6.64473	+	6.64473i	−0.331822	+	0.331822i	−0.853278	−	0.521456i	$-0.825389\pi$
$401$	−6.64473	+	6.64473i	−0.331822	+	0.331822i	0.521456	+	0.853278i	$0.325389\pi$
$402$	1.38003			0.0688298
$403$	−12.4658	+	28.0531i	−0.620966	+	1.39742i
$404$			0.0417413i			0.00207671i
$405$	7.13285	−	7.13285i	0.354434	−	0.354434i
$406$		0			0
$407$			12.5262i			0.620903i
$408$	2.27157	+	2.27157i	0.112459	+	0.112459i
$409$	−13.6503	+	13.6503i	−0.674963	+	0.674963i	−0.958856	−	0.283893i	$-0.908374\pi$
$409$	−13.6503	+	13.6503i	−0.674963	+	0.674963i	0.283893	+	0.958856i	$0.408374\pi$
$410$	−12.4884	+	12.4884i	−0.616757	+	0.616757i
$411$	−12.5904	−	12.5904i	−0.621038	−	0.621038i
$412$		−	3.26188i		−	0.160701i
$413$		0			0
$414$	3.74032	−	3.74032i	0.183827	−	0.183827i
$415$			21.3381i			1.04745i
$416$	−3.70371	−	1.64580i	−0.181589	−	0.0806919i
$417$	12.9648			0.634888
$418$	8.73323	−	8.73323i	0.427156	−	0.427156i
$419$		−	24.1967i		−	1.18208i	−0.806641	−	0.591042i	$-0.798717\pi$
$419$		−	24.1967i		−	1.18208i	0.806641	−	0.591042i	$-0.201283\pi$
$420$		0			0
$421$	−16.9872	−	16.9872i	−0.827906	−	0.827906i	0.159321	−	0.987227i	$-0.449070\pi$
$421$	−16.9872	−	16.9872i	−0.827906	−	0.827906i	−0.987227	+	0.159321i	$0.949070\pi$
$422$	19.9139	+	19.9139i	0.969392	+	0.969392i
$423$	−15.5590	−	15.5590i	−0.756503	−	0.756503i
$424$	5.70893	−	5.70893i	0.277250	−	0.277250i
$425$			14.1362i			0.685705i
$426$	−0.619132			−0.0299971
$427$		0			0
$428$			3.40212i			0.164448i
$429$	7.58096	+	3.36872i	0.366012	+	0.162643i
$430$			67.2021i			3.24077i
$431$	−19.4118	−	19.4118i	−0.935035	−	0.935035i	0.0629797	−	0.998015i	$-0.479940\pi$
$431$	−19.4118	−	19.4118i	−0.935035	−	0.935035i	−0.998015	+	0.0629797i	$0.979940\pi$
$432$			20.1172i			0.967889i
$433$	−26.0271			−1.25078			−0.625391	−	0.780312i	$-0.715060\pi$
$433$	−26.0271			−1.25078			−0.625391	+	0.780312i	$0.715060\pi$
$434$		0			0
$435$	22.9352	+	22.9352i	1.09966	+	1.09966i
$436$	0.988872	−	0.988872i	0.0473584	−	0.0473584i
$437$	−3.64086	−	3.64086i	−0.174166	−	0.174166i
$438$	−11.0173			−0.526426
$439$	3.70545			0.176851			0.0884257	−	0.996083i	$-0.471816\pi$
$439$	3.70545			0.176851			0.0884257	+	0.996083i	$0.471816\pi$
$440$	19.2709	+	19.2709i	0.918706	+	0.918706i
$441$		0			0
$442$	6.64626	+	2.95337i	0.316130	+	0.140477i
$443$	2.68808			0.127715			0.0638573	−	0.997959i	$-0.479660\pi$
$443$	2.68808			0.127715			0.0638573	+	0.997959i	$0.479660\pi$
$444$	0.600627	−	0.600627i	0.0285045	−	0.0285045i
$445$	29.0086			1.37514
$446$	−4.28837			−0.203060
$447$	−13.6777	+	13.6777i	−0.646934	+	0.646934i
$448$		0			0
$449$	24.6366	−	24.6366i	1.16267	−	1.16267i	0.178784	−	0.983888i	$-0.442784\pi$
$449$	24.6366	−	24.6366i	1.16267	−	1.16267i	0.983888	−	0.178784i	$-0.0572164\pi$
$450$	−24.1706	+	24.1706i	−1.13941	+	1.13941i
$451$		−	7.89566i		−	0.371792i
$452$			0.911361i			0.0428668i
$453$	8.46207	+	8.46207i	0.397583	+	0.397583i
$454$	9.73430			0.456854
$455$		0			0
$456$	7.56149			0.354099
$457$	4.82049	+	4.82049i	0.225493	+	0.225493i	0.810807	−	0.585314i	$-0.199029\pi$
$457$	4.82049	+	4.82049i	0.225493	+	0.225493i	−0.585314	+	0.810807i	$0.699029\pi$
$458$		−	2.11517i		−	0.0988353i
$459$		−	6.27701i		−	0.292986i
$460$	−0.889843	+	0.889843i	−0.0414891	+	0.0414891i
$461$	5.06375	−	5.06375i	0.235842	−	0.235842i	−0.579284	−	0.815126i	$-0.696668\pi$
$461$	5.06375	−	5.06375i	0.235842	−	0.235842i	0.815126	+	0.579284i	$0.196668\pi$
$462$		0			0
$463$	−14.8196	+	14.8196i	−0.688725	+	0.688725i	−0.961950	−	0.273226i	$-0.911909\pi$
$463$	−14.8196	+	14.8196i	−0.688725	+	0.688725i	0.273226	+	0.961950i	$0.411909\pi$
$464$	40.7430			1.89145
$465$	−29.5460			−1.37016
$466$	8.90766	−	8.90766i	0.412639	−	0.412639i
$467$	0.456514			0.0211249			0.0105625	−	0.999944i	$-0.496638\pi$
$467$	0.456514			0.0211249			0.0105625	+	0.999944i	$0.496638\pi$
$468$	0.572537	+	1.48830i	0.0264655	+	0.0687969i
$469$		0			0
$470$	40.8229	+	40.8229i	1.88302	+	1.88302i
$471$	−11.3754			−0.524150
$472$	0.691901			0.0318473
$473$	−21.2440	−	21.2440i	−0.976798	−	0.976798i
$474$	2.69289	−	2.69289i	0.123688	−	0.123688i
$475$	23.5279	+	23.5279i	1.07953	+	1.07953i
$476$		0			0
$477$	−6.70504			−0.307003
$478$			9.74867i			0.445894i
$479$	23.2372	+	23.2372i	1.06173	+	1.06173i	0.997965	+	0.0637700i	$0.0203124\pi$
$479$	23.2372	+	23.2372i	1.06173	+	1.06173i	0.0637700	+	0.997965i	$0.479688\pi$
$480$		−	3.90082i		−	0.178047i
$481$	−7.05041	+	15.8662i	−0.321471	+	0.723438i
$482$			15.9943i			0.728519i
$483$		0			0
$484$	−0.844253			−0.0383751
$485$			41.3859i			1.87923i
$486$	16.9037	−	16.9037i	0.766766	−	0.766766i
$487$	8.17370	+	8.17370i	0.370386	+	0.370386i	0.867618	−	0.497232i	$-0.165650\pi$
$487$	8.17370	+	8.17370i	0.370386	+	0.370386i	−0.497232	+	0.867618i	$0.665650\pi$
$488$	0.629412	+	0.629412i	0.0284921	+	0.0284921i
$489$	−6.69986	−	6.69986i	−0.302978	−	0.302978i
$490$		0			0
$491$			0.946627i			0.0427207i	0.999772	+	0.0213603i	$0.00679973\pi$
$491$			0.946627i			0.0427207i	−0.999772	+	0.0213603i	$0.993200\pi$
$492$	−0.378593	+	0.378593i	−0.0170683	+	0.0170683i
$493$	−12.7127			−0.572552
$494$	15.9774	−	6.14635i	0.718856	−	0.276538i
$495$		−	22.6334i		−	1.01730i
$496$	−26.2434	+	26.2434i	−1.17836	+	1.17836i
$497$		0			0
$498$			7.13412i			0.319688i
$499$	15.5508	+	15.5508i	0.696148	+	0.696148i	0.963577	−	0.267430i	$-0.0861743\pi$
$499$	15.5508	+	15.5508i	0.696148	+	0.696148i	−0.267430	+	0.963577i	$0.586174\pi$
$500$	2.98395	−	2.98395i	0.133446	−	0.133446i
$501$	−5.37012	+	5.37012i	−0.239919	+	0.239919i
$502$	−29.4178	−	29.4178i	−1.31298	−	1.31298i
$503$			1.12263i			0.0500556i	0.999687	+	0.0250278i	$0.00796742\pi$
$503$			1.12263i			0.0500556i	−0.999687	+	0.0250278i	$0.992033\pi$
$504$		0			0
$505$	0.580663	−	0.580663i	0.0258392	−	0.0258392i
$506$		−	6.20461i		−	0.275829i
$507$	7.70626	+	8.53390i	0.342247	+	0.379004i
$508$	−2.07659			−0.0921338
$509$	13.5895	−	13.5895i	0.602342	−	0.602342i	−0.338591	−	0.940934i	$-0.609950\pi$
$509$	13.5895	−	13.5895i	0.602342	−	0.602342i	0.940934	+	0.338591i	$0.109950\pi$
$510$			6.99997i			0.309964i
$511$		0			0
$512$	12.9970	+	12.9970i	0.574390	+	0.574390i
$513$	−10.4473	−	10.4473i	−0.461259	−	0.461259i
$514$	14.8079	+	14.8079i	0.653150	+	0.653150i
$515$	−45.3760	+	45.3760i	−1.99950	+	1.99950i
$516$			2.03727i			0.0896860i
$517$	−25.8099			−1.13512
$518$		0			0
$519$			3.14197i			0.137917i
$520$	13.5627	+	35.2560i	0.594763	+	1.54608i
$521$		−	22.3086i		−	0.977356i	−0.872464	−	0.488678i	$-0.837479\pi$
$521$		−	22.3086i		−	0.977356i	0.872464	−	0.488678i	$-0.162521\pi$
$522$	−21.7368	−	21.7368i	−0.951392	−	0.951392i
$523$			17.7585i			0.776524i	0.921549	+	0.388262i	$0.126924\pi$
$523$			17.7585i			0.776524i	−0.921549	+	0.388262i	$0.873076\pi$
$524$	−3.48835			−0.152389
$525$		0			0
$526$	−23.4095	−	23.4095i	−1.02070	−	1.02070i
$527$	8.18851	−	8.18851i	0.356697	−	0.356697i
$528$	7.09192	+	7.09192i	0.308636	+	0.308636i
$529$	20.4133			0.887536
$530$	17.5924			0.764165
$531$	−0.406313	−	0.406313i	−0.0176325	−	0.0176325i
$532$		0			0
$533$	4.44408	−	10.0010i	0.192494	−	0.433190i
$534$	9.69867			0.419702
$535$	47.3268	−	47.3268i	2.04612	−	2.04612i
$536$	−2.80934			−0.121345
$537$	−15.2383			−0.657581
$538$	12.4059	−	12.4059i	0.534854	−	0.534854i
$539$		0			0
$540$	−2.55337	+	2.55337i	−0.109879	+	0.109879i
$541$	9.37822	−	9.37822i	0.403201	−	0.403201i	−0.476158	−	0.879360i	$-0.657971\pi$
$541$	9.37822	−	9.37822i	0.403201	−	0.403201i	0.879360	+	0.476158i	$0.157971\pi$
$542$			7.33060i			0.314876i
$543$			5.50039i			0.236044i
$544$	1.08109	+	1.08109i	0.0463513	+	0.0463513i
$545$	−27.5124			−1.17850
$546$		0			0
$547$	−14.0683			−0.601515			−0.300757	−	0.953701i	$-0.597239\pi$
$547$	−14.0683			−0.601515			−0.300757	+	0.953701i	$0.597239\pi$
$548$	−2.83881	−	2.83881i	−0.121268	−	0.121268i
$549$		−	0.739233i		−	0.0315497i
$550$			40.0953i			1.70967i
$551$	−21.1587	+	21.1587i	−0.901393	+	0.901393i
$552$	2.68607	−	2.68607i	0.114327	−	0.114327i
$553$		0			0
$554$	0.884579	−	0.884579i	0.0375822	−	0.0375822i
$555$	−16.7106			−0.709327
$556$	2.92322			0.123972
$557$	−12.0175	+	12.0175i	−0.509196	+	0.509196i	−0.914280	−	0.405084i	$-0.867242\pi$
$557$	−12.0175	+	12.0175i	−0.509196	+	0.509196i	0.405084	+	0.914280i	$0.367242\pi$
$558$	28.0021			1.18542
$559$	−14.9513	−	38.8656i	−0.632371	−	1.64384i
$560$		0			0
$561$	−2.21283	−	2.21283i	−0.0934260	−	0.0934260i
$562$	14.2626			0.601630
$563$	−17.2467			−0.726864			−0.363432	−	0.931621i	$-0.618395\pi$
$563$	−17.2467			−0.726864			−0.363432	+	0.931621i	$0.618395\pi$
$564$	1.23757	+	1.23757i	0.0521112	+	0.0521112i
$565$	12.6779	−	12.6779i	0.533365	−	0.533365i
$566$	−20.7884	−	20.7884i	−0.873800	−	0.873800i
$567$		0			0
$568$	1.26037			0.0528840
$569$			15.6457i			0.655902i	0.944695	+	0.327951i	$0.106358\pi$
$569$			15.6457i			0.655902i	−0.944695	+	0.327951i	$0.893642\pi$
$570$	11.6506	+	11.6506i	0.487989	+	0.487989i
$571$			12.1551i			0.508676i	0.967115	+	0.254338i	$0.0818576\pi$
$571$			12.1551i			0.508676i	−0.967115	+	0.254338i	$0.918142\pi$
$572$	1.70931	+	0.759558i	0.0714698	+	0.0317587i
$573$		−	10.8858i		−	0.454760i
$574$		0			0
$575$	16.7156			0.697089
$576$		−	15.6371i		−	0.651544i
$577$	−27.6572	+	27.6572i	−1.15138	+	1.15138i	−0.165107	+	0.986276i	$0.552797\pi$
$577$	−27.6572	+	27.6572i	−1.15138	+	1.15138i	−0.986276	+	0.165107i	$0.947203\pi$
$578$	15.8874	+	15.8874i	0.660830	+	0.660830i
$579$	13.4188	+	13.4188i	0.557665	+	0.557665i
$580$	5.17130	+	5.17130i	0.214726	+	0.214726i
$581$		0			0
$582$			13.8369i			0.573556i
$583$	−5.56132	+	5.56132i	−0.230326	+	0.230326i
$584$	22.4279			0.928075
$585$	12.7392	−	28.6684i	0.526702	−	1.18529i
$586$		−	13.5847i		−	0.561180i
$587$	−6.17868	+	6.17868i	−0.255021	+	0.255021i	−0.823026	−	0.568004i	$-0.807716\pi$
$587$	−6.17868	+	6.17868i	−0.255021	+	0.255021i	0.568004	+	0.823026i	$0.307716\pi$
$588$		0			0
$589$		−	27.2575i		−	1.12313i
$590$	1.06607	+	1.06607i	0.0438893	+	0.0438893i
$591$	1.26042	−	1.26042i	0.0518467	−	0.0518467i
$592$	−14.8427	+	14.8427i	−0.610032	+	0.610032i
$593$	23.9109	+	23.9109i	0.981903	+	0.981903i	0.999839	−	0.0179360i	$-0.00570950\pi$
$593$	23.9109	+	23.9109i	0.981903	+	0.981903i	−0.0179360	+	0.999839i	$0.505710\pi$
$594$		−	17.8039i		−	0.730502i
$595$		0			0
$596$	−3.08397	+	3.08397i	−0.126324	+	0.126324i
$597$		−	5.90514i		−	0.241681i
$598$	3.49227	−	7.85901i	0.142810	−	0.321379i
$599$	10.2671			0.419504			0.209752	−	0.977755i	$-0.432734\pi$
$599$	10.2671			0.419504			0.209752	+	0.977755i	$0.432734\pi$
$600$	−17.3579	+	17.3579i	−0.708632	+	0.708632i
$601$		−	4.09959i		−	0.167226i	−0.996498	−	0.0836128i	$-0.973354\pi$
$601$		−	4.09959i		−	0.167226i	0.996498	−	0.0836128i	$-0.0266459\pi$
$602$		0			0
$603$	1.64976	+	1.64976i	0.0671835	+	0.0671835i
$604$	1.90798	+	1.90798i	0.0776344	+	0.0776344i
$605$	11.7444	+	11.7444i	0.477478	+	0.477478i
$606$	0.194137	−	0.194137i	0.00788630	−	0.00788630i
$607$		−	7.25794i		−	0.294591i	−0.989093	−	0.147295i	$-0.952943\pi$
$607$		−	7.25794i		−	0.294591i	0.989093	−	0.147295i	$-0.0470568\pi$
$608$	3.59867			0.145946
$609$		0			0
$610$			1.93957i			0.0785308i
$611$	−32.6919	−	14.5272i	−1.32257	−	0.587706i
$612$		−	0.601547i		−	0.0243161i
$613$	15.2294	+	15.2294i	0.615111	+	0.615111i	0.944273	−	0.329163i	$-0.106766\pi$
$613$	15.2294	+	15.2294i	0.615111	+	0.615111i	−0.329163	+	0.944273i	$0.606766\pi$
$614$		−	37.6446i		−	1.51921i
$615$	10.5332			0.424740
$616$		0			0
$617$	−28.5301	−	28.5301i	−1.14858	−	1.14858i	−0.986832	−	0.161748i	$-0.948287\pi$
$617$	−28.5301	−	28.5301i	−1.14858	−	1.14858i	−0.161748	−	0.986832i	$-0.551713\pi$
$618$	−15.1709	+	15.1709i	−0.610263	+	0.610263i
$619$	−24.3640	−	24.3640i	−0.979274	−	0.979274i	0.0205158	−	0.999790i	$-0.493469\pi$
$619$	−24.3640	−	24.3640i	−0.979274	−	0.979274i	−0.999790	+	0.0205158i	$0.993469\pi$
$620$	−6.66186			−0.267547
$621$	−7.42238			−0.297850
$622$	−14.1348	−	14.1348i	−0.566754	−	0.566754i
$623$		0			0
$624$	4.99121	+	12.9746i	0.199808	+	0.519400i
$625$	−31.0532			−1.24213
$626$	6.79981	−	6.79981i	0.271775	−	0.271775i
$627$	−7.36597			−0.294169
$628$	−2.56485			−0.102349
$629$	4.63126	−	4.63126i	0.184660	−	0.184660i
$630$		0			0
$631$	−26.1762	+	26.1762i	−1.04206	+	1.04206i	−0.0429839	+	0.999076i	$0.513686\pi$
$631$	−26.1762	+	26.1762i	−1.04206	+	1.04206i	−0.999076	+	0.0429839i	$0.986314\pi$
$632$	−5.48192	+	5.48192i	−0.218059	+	0.218059i
$633$		−	16.7962i		−	0.667588i
$634$			46.4261i			1.84381i
$635$	28.8874	+	28.8874i	1.14636	+	1.14636i
$636$	0.533325			0.0211477
$637$		0			0
$638$	−36.0579			−1.42755
$639$	−0.740142	−	0.740142i	−0.0292796	−	0.0292796i
$640$			49.8482i			1.97042i
$641$			11.6779i			0.461250i	0.973043	+	0.230625i	$0.0740770\pi$
$641$			11.6779i			0.461250i	−0.973043	+	0.230625i	$0.925923\pi$
$642$	15.8231	−	15.8231i	0.624490	−	0.624490i
$643$	−12.8214	+	12.8214i	−0.505627	+	0.505627i	−0.913181	−	0.407554i	$-0.866382\pi$
$643$	−12.8214	+	12.8214i	−0.505627	+	0.505627i	0.407554	+	0.913181i	$0.366382\pi$
$644$		0			0
$645$	28.3405	−	28.3405i	1.11591	−	1.11591i
$646$	−6.45778			−0.254078
$647$	11.4697			0.450920			0.225460	−	0.974252i	$-0.427612\pi$
$647$	11.4697			0.450920			0.225460	+	0.974252i	$0.427612\pi$
$648$	−4.85471	+	4.85471i	−0.190711	+	0.190711i
$649$	−0.674011			−0.0264572
$650$	−22.5677	+	50.7864i	−0.885178	+	1.99200i
$651$		0			0
$652$	−1.51064	−	1.51064i	−0.0591614	−	0.0591614i
$653$	−8.95381			−0.350390			−0.175195	−	0.984534i	$-0.556056\pi$
$653$	−8.95381			−0.350390			−0.175195	+	0.984534i	$0.556056\pi$
$654$	−9.19843			−0.359687
$655$	48.5264	+	48.5264i	1.89608	+	1.89608i
$656$	9.35581	−	9.35581i	0.365283	−	0.365283i
$657$	−13.1706	−	13.1706i	−0.513835	−	0.513835i
$658$		0			0
$659$	22.2313			0.866009			0.433005	−	0.901392i	$-0.357453\pi$
$659$	22.2313			0.866009			0.433005	+	0.901392i	$0.357453\pi$
$660$			1.80028i			0.0700757i
$661$	−1.73878	−	1.73878i	−0.0676305	−	0.0676305i	0.672482	−	0.740113i	$-0.265228\pi$
$661$	−1.73878	−	1.73878i	−0.0676305	−	0.0676305i	−0.740113	+	0.672482i	$0.765228\pi$
$662$			18.5621i			0.721438i
$663$	−1.55737	−	4.04836i	−0.0604832	−	0.157225i
$664$		−	14.5230i		−	0.563600i
$665$		0			0
$666$	15.8374			0.613688
$667$			15.0324i			0.582058i
$668$	−1.21082	+	1.21082i	−0.0468481	+	0.0468481i
$669$	1.80850	+	1.80850i	0.0699205	+	0.0699205i
$670$	−4.32857	−	4.32857i	−0.167227	−	0.167227i
$671$	−0.613137	−	0.613137i	−0.0236699	−	0.0236699i
$672$		0			0
$673$			6.44000i			0.248244i	0.992267	+	0.124122i	$0.0396114\pi$
$673$			6.44000i			0.248244i	−0.992267	+	0.124122i	$0.960389\pi$
$674$	4.76463	−	4.76463i	0.183527	−	0.183527i
$675$	47.9648			1.84617
$676$	1.73756	+	1.92417i	0.0668293	+	0.0740066i
$677$			4.62885i			0.177901i	0.996036	+	0.0889507i	$0.0283513\pi$
$677$			4.62885i			0.177901i	−0.996036	+	0.0889507i	$0.971649\pi$
$678$	4.23871	−	4.23871i	0.162787	−	0.162787i
$679$		0			0
$680$		−	14.2499i		−	0.546458i
$681$	−4.10516	−	4.10516i	−0.157310	−	0.157310i
$682$	23.2256	−	23.2256i	0.889354	−	0.889354i
$683$	12.8234	−	12.8234i	0.490673	−	0.490673i	−0.417845	−	0.908518i	$-0.637215\pi$
$683$	12.8234	−	12.8234i	0.490673	−	0.490673i	0.908518	+	0.417845i	$0.137215\pi$
$684$	−1.00120	−	1.00120i	−0.0382818	−	0.0382818i
$685$			78.9813i			3.01772i
$686$		0			0
$687$	−0.892011	+	0.892011i	−0.0340323	+	0.0340323i
$688$		−	50.3452i		−	1.91939i
$689$	−10.1744	+	3.91399i	−0.387613	+	0.149111i
$690$	8.27726			0.315110
$691$	−0.436821	+	0.436821i	−0.0166174	+	0.0166174i	−0.715367	−	0.698749i	$-0.753740\pi$
$691$	−0.436821	+	0.436821i	−0.0166174	+	0.0166174i	0.698749	+	0.715367i	$0.253740\pi$
$692$			0.708433i			0.0269306i
$693$		0			0
$694$	11.6747	+	11.6747i	0.443166	+	0.443166i
$695$	−40.6649	−	40.6649i	−1.54251	−	1.54251i
$696$	−15.6100	−	15.6100i	−0.591696	−	0.591696i
$697$	−2.91922	+	2.91922i	−0.110573	+	0.110573i
$698$			35.0378i			1.32620i
$699$	−7.51309			−0.284171
$700$		0			0
$701$			14.4452i			0.545586i	0.962073	+	0.272793i	$0.0879474\pi$
$701$			14.4452i			0.545586i	−0.962073	+	0.272793i	$0.912053\pi$
$702$	10.0209	−	22.5511i	0.378216	−	0.851137i
$703$		−	15.4163i		−	0.581437i
$704$	−12.9697	−	12.9697i	−0.488815	−	0.488815i
$705$		−	34.4318i		−	1.29678i
$706$	−9.08287			−0.341838
$707$		0			0
$708$	0.0323185	+	0.0323185i	0.00121460	+	0.00121460i
$709$	2.32721	−	2.32721i	0.0874003	−	0.0874003i	−0.662055	−	0.749455i	$-0.730315\pi$
$709$	2.32721	−	2.32721i	0.0874003	−	0.0874003i	0.749455	+	0.662055i	$0.230315\pi$
$710$	1.94195	+	1.94195i	0.0728801	+	0.0728801i
$711$	6.43842			0.241460
$712$	−19.7436			−0.739923
$713$	−9.68268	−	9.68268i	−0.362619	−	0.362619i
$714$		0			0
$715$	−13.2120	−	34.3444i	−0.494100	−	1.28441i
$716$	−3.43584			−0.128403
$717$	4.11122	−	4.11122i	0.153536	−	0.153536i
$718$	−32.2581			−1.20386
$719$	−49.2353			−1.83617			−0.918083	−	0.396387i	$-0.870264\pi$
$719$	−49.2353			−1.83617			−0.918083	+	0.396387i	$0.870264\pi$
$720$	26.8190	−	26.8190i	0.999485	−	0.999485i
$721$		0			0
$722$	9.17662	−	9.17662i	0.341518	−	0.341518i
$723$	6.74512	−	6.74512i	0.250854	−	0.250854i
$724$			1.24019i			0.0460915i
$725$		−	97.1424i		−	3.60778i
$726$	3.92660	+	3.92660i	0.145730	+	0.145730i
$727$	34.0096			1.26135			0.630674	−	0.776048i	$-0.282779\pi$
$727$	34.0096			1.26135			0.630674	+	0.776048i	$0.282779\pi$
$728$		0			0
$729$	−6.54406			−0.242372
$730$	34.5565	+	34.5565i	1.27899	+	1.27899i
$731$			15.7088i			0.581012i
$732$			0.0587992i			0.00217328i
$733$	−26.5120	+	26.5120i	−0.979242	+	0.979242i	−0.999789	−	0.0205464i	$-0.993459\pi$
$733$	−26.5120	+	26.5120i	−0.979242	+	0.979242i	0.0205464	+	0.999789i	$0.493459\pi$
$734$	−17.0423	+	17.0423i	−0.629042	+	0.629042i
$735$		0			0
$736$	1.27836	−	1.27836i	0.0471208	−	0.0471208i
$737$	2.73670			0.100808
$738$	−9.98280			−0.367472
$739$	3.02847	−	3.02847i	0.111404	−	0.111404i	−0.649207	−	0.760611i	$-0.724899\pi$
$739$	3.02847	−	3.02847i	0.111404	−	0.111404i	0.760611	+	0.649207i	$0.224899\pi$
$740$	−3.76782			−0.138508
$741$	−9.33004	−	4.14595i	−0.342748	−	0.152305i
$742$		0			0
$743$	−25.3436	−	25.3436i	−0.929767	−	0.929767i	0.0679234	−	0.997691i	$-0.478363\pi$
$743$	−25.3436	−	25.3436i	−0.929767	−	0.929767i	−0.997691	+	0.0679234i	$0.978363\pi$
$744$	20.1094			0.737247
$745$	85.8022			3.14355
$746$	−4.42085	−	4.42085i	−0.161859	−	0.161859i
$747$	−8.52849	+	8.52849i	−0.312041	+	0.312041i
$748$	−0.498937	−	0.498937i	−0.0182429	−	0.0182429i
$749$		0			0
$750$	−27.7565			−1.01352
$751$			46.1245i			1.68311i	0.540174	+	0.841554i	$0.318359\pi$
$751$			46.1245i			1.68311i	−0.540174	+	0.841554i	$0.681641\pi$
$752$	−30.5830	−	30.5830i	−1.11525	−	1.11525i
$753$			24.8122i			0.904208i
$754$	−45.6724	−	20.2952i	−1.66329	−	0.739109i
$755$		−	53.0837i		−	1.93191i
$756$		0			0
$757$	−38.5756			−1.40205			−0.701027	−	0.713135i	$-0.747275\pi$
$757$	−38.5756			−1.40205			−0.701027	+	0.713135i	$0.747275\pi$
$758$		−	38.0260i		−	1.38117i
$759$	−2.61661	+	2.61661i	−0.0949770	+	0.0949770i
$760$	−23.7171	−	23.7171i	−0.860311	−	0.860311i
$761$	−7.03057	−	7.03057i	−0.254858	−	0.254858i	0.568101	−	0.822959i	$-0.307678\pi$
$761$	−7.03057	−	7.03057i	−0.254858	−	0.254858i	−0.822959	+	0.568101i	$0.807678\pi$
$762$	9.65816	+	9.65816i	0.349878	+	0.349878i
$763$		0			0
$764$		−	2.45446i		−	0.0887993i
$765$	−8.36812	+	8.36812i	−0.302550	+	0.302550i
$766$	−34.8072			−1.25764
$767$	−0.853729	−	0.379368i	−0.0308264	−	0.0136982i
$768$			4.19279i			0.151294i
$769$	−28.4649	+	28.4649i	−1.02647	+	1.02647i	−0.0268295	+	0.999640i	$0.508541\pi$
$769$	−28.4649	+	28.4649i	−1.02647	+	1.02647i	−0.999640	+	0.0268295i	$0.991459\pi$
$770$		0			0
$771$		−	12.4896i		−	0.449803i
$772$	3.02558	+	3.02558i	0.108893	+	0.108893i
$773$	18.0777	−	18.0777i	0.650210	−	0.650210i	−0.302834	−	0.953043i	$-0.597933\pi$
$773$	18.0777	−	18.0777i	0.650210	−	0.650210i	0.953043	+	0.302834i	$0.0979326\pi$
$774$	−26.8596	+	26.8596i	−0.965448	+	0.965448i
$775$	62.5713	+	62.5713i	2.24763	+	2.24763i
$776$		−	28.1677i		−	1.01116i
$777$		0			0
$778$	−20.4214	+	20.4214i	−0.732141	+	0.732141i
$779$			9.71735i			0.348160i
$780$	−1.01329	+	2.28030i	−0.0362816	+	0.0816480i
$781$	−1.22778			−0.0439335
$782$	−2.29400	+	2.29400i	−0.0820331	+	0.0820331i
$783$			43.1350i			1.54152i
$784$		0			0
$785$	35.6797	+	35.6797i	1.27346	+	1.27346i
$786$	16.2242	+	16.2242i	0.578698	+	0.578698i
$787$	−12.8291	−	12.8291i	−0.457307	−	0.457307i	0.440464	−	0.897770i	$-0.354814\pi$
$787$	−12.8291	−	12.8291i	−0.457307	−	0.457307i	−0.897770	+	0.440464i	$0.854814\pi$
$788$	0.284191	−	0.284191i	0.0101239	−	0.0101239i
$789$			19.7446i			0.702925i
$790$	−16.8928			−0.601020
$791$		0			0
$792$			15.4046i			0.547378i
$793$	−0.431519	−	1.12173i	−0.0153237	−	0.0398338i
$794$		−	17.7358i		−	0.629420i
$795$	−7.41908	−	7.41908i	−0.263128	−	0.263128i
$796$		−	1.33146i		−	0.0471922i
$797$	−6.98547			−0.247438			−0.123719	−	0.992317i	$-0.539482\pi$
$797$	−6.98547			−0.247438			−0.123719	+	0.992317i	$0.539482\pi$
$798$		0			0
$799$	9.54256	+	9.54256i	0.337592	+	0.337592i
$800$	−8.26098	+	8.26098i	−0.292070	+	0.292070i
$801$	11.5943	+	11.5943i	0.409663	+	0.409663i
$802$	13.9363			0.492108
$803$	−21.8480			−0.771000
$804$	−0.131223	−	0.131223i	−0.00462789	−	0.00462789i
$805$		0			0
$806$	42.4910	−	16.3459i	1.49668	−	0.575761i
$807$	−10.4636			−0.368337
$808$	−0.395207	+	0.395207i	−0.0139033	+	0.0139033i
$809$	2.01320			0.0707804			0.0353902	−	0.999374i	$-0.488733\pi$
$809$	2.01320			0.0707804			0.0353902	+	0.999374i	$0.488733\pi$
$810$	−14.9601			−0.525643
$811$	19.2255	−	19.2255i	0.675097	−	0.675097i	−0.283790	−	0.958887i	$-0.591592\pi$
$811$	19.2255	−	19.2255i	0.675097	−	0.675097i	0.958887	+	0.283790i	$0.0915917\pi$
$812$		0			0
$813$	3.09147	−	3.09147i	0.108422	−	0.108422i
$814$	13.1359	−	13.1359i	0.460414	−	0.460414i
$815$			42.0292i			1.47222i
$816$		−	5.24411i		−	0.183581i
$817$	26.1454	+	26.1454i	0.914711	+	0.914711i
$818$	28.6294			1.00100
$819$		0			0
$820$	2.37497			0.0829374
$821$	6.81744	+	6.81744i	0.237930	+	0.237930i	0.815993	−	0.578062i	$-0.196191\pi$
$821$	6.81744	+	6.81744i	0.237930	+	0.237930i	−0.578062	+	0.815993i	$0.696191\pi$
$822$			26.4064i			0.921029i
$823$		−	18.0834i		−	0.630348i	−0.949034	−	0.315174i	$-0.897937\pi$
$823$		−	18.0834i		−	0.630348i	0.949034	−	0.315174i	$-0.102063\pi$
$824$	30.8835	−	30.8835i	1.07588	−	1.07588i
$825$	16.9090	−	16.9090i	0.588697	−	0.588697i
$826$		0			0
$827$	12.8291	−	12.8291i	0.446111	−	0.446111i	−0.447949	−	0.894059i	$-0.647845\pi$
$827$	12.8291	−	12.8291i	0.446111	−	0.446111i	0.894059	+	0.447949i	$0.147845\pi$
$828$	−0.711312			−0.0247198
$829$	−28.2067			−0.979658			−0.489829	−	0.871818i	$-0.662941\pi$
$829$	−28.2067			−0.979658			−0.489829	+	0.871818i	$0.662941\pi$
$830$	22.3767	−	22.3767i	0.776706	−	0.776706i
$831$	−0.746091			−0.0258816
$832$	−9.12795	−	23.7280i	−0.316455	−	0.822621i
$833$		0			0
$834$	−13.5958	−	13.5958i	−0.470785	−	0.470785i
$835$	33.6875			1.16580
$836$	−1.66084			−0.0574412
$837$	−27.7841	−	27.7841i	−0.960358	−	0.960358i
$838$	−25.3744	+	25.3744i	−0.876543	+	0.876543i
$839$	7.67294	+	7.67294i	0.264899	+	0.264899i	0.827041	−	0.562142i	$-0.190022\pi$
$839$	7.67294	+	7.67294i	0.264899	+	0.264899i	−0.562142	+	0.827041i	$0.690022\pi$
$840$		0			0
$841$	58.3606			2.01243
$842$			35.6281i			1.22782i
$843$	−6.01482	−	6.01482i	−0.207161	−	0.207161i
$844$		−	3.78710i		−	0.130357i
$845$	2.59595	−	50.9384i	0.0893035	−	1.75233i
$846$			32.6326i			1.12193i
$847$		0			0
$848$	−13.1796			−0.452588
$849$			17.5338i			0.601758i
$850$	14.8242	−	14.8242i	0.508467	−	0.508467i
$851$	−5.47633	−	5.47633i	−0.187726	−	0.187726i
$852$	0.0588715	+	0.0588715i	0.00201690	+	0.00201690i
$853$	10.4908	+	10.4908i	0.359198	+	0.359198i	0.863517	−	0.504319i	$-0.168256\pi$
$853$	10.4908	+	10.4908i	0.359198	+	0.359198i	−0.504319	+	0.863517i	$0.668256\pi$
$854$		0			0
$855$			27.8554i			0.952634i
$856$	−32.2112	+	32.2112i	−1.10096	+	1.10096i
$857$	−17.2345			−0.588721			−0.294360	−	0.955695i	$-0.595107\pi$
$857$	−17.2345			−0.588721			−0.294360	+	0.955695i	$0.595107\pi$
$858$	−4.41726	−	11.4826i	−0.150803	−	0.392010i
$859$		−	37.5784i		−	1.28216i	−0.767475	−	0.641079i	$-0.778487\pi$
$859$		−	37.5784i		−	1.28216i	0.767475	−	0.641079i	$-0.221513\pi$
$860$	6.39005	−	6.39005i	0.217899	−	0.217899i
$861$		0			0
$862$			40.7133i			1.38670i
$863$	0.873318	+	0.873318i	0.0297281	+	0.0297281i	0.721815	−	0.692086i	$-0.243308\pi$
$863$	0.873318	+	0.873318i	0.0297281	+	0.0297281i	−0.692086	+	0.721815i	$0.743308\pi$
$864$	3.66819	−	3.66819i	0.124794	−	0.124794i
$865$	9.85502	−	9.85502i	0.335081	−	0.335081i
$866$	27.2939	+	27.2939i	0.927484	+	0.927484i
$867$		−	13.4001i		−	0.455092i
$868$		0			0
$869$	5.34017	−	5.34017i	0.181153	−	0.181153i
$870$		−	48.1031i		−	1.63085i
$871$	3.46641	+	1.54035i	0.117455	+	0.0521929i
$872$	18.7253			0.634118
$873$	−16.5413	+	16.5413i	−0.559837	+	0.559837i
$874$			7.63614i			0.258296i
$875$		0			0
$876$	1.04760	+	1.04760i	0.0353952	+	0.0353952i
$877$	−33.4786	−	33.4786i	−1.13049	−	1.13049i	−0.990095	−	0.140398i	$-0.955162\pi$
$877$	−33.4786	−	33.4786i	−1.13049	−	1.13049i	−0.140398	−	0.990095i	$-0.544838\pi$
$878$	−3.88580	−	3.88580i	−0.131139	−	0.131139i
$879$	−5.72897	+	5.72897i	−0.193233	+	0.193233i
$880$		−	44.4886i		−	1.49971i
$881$	25.5041			0.859255			0.429627	−	0.903006i	$-0.358645\pi$
$881$	25.5041			0.859255			0.429627	+	0.903006i	$0.358645\pi$
$882$		0			0
$883$		−	34.7968i		−	1.17101i	−0.810670	−	0.585503i	$-0.800897\pi$
$883$		−	34.7968i		−	1.17101i	0.810670	−	0.585503i	$-0.199103\pi$
$884$	−0.351146	−	0.912800i	−0.0118103	−	0.0307008i
$885$		−	0.899165i		−	0.0302251i
$886$	−2.81892	−	2.81892i	−0.0947034	−	0.0947034i
$887$		−	45.4015i		−	1.52443i	−0.647321	−	0.762217i	$-0.724111\pi$
$887$		−	45.4015i		−	1.52443i	0.647321	−	0.762217i	$-0.275889\pi$
$888$	11.3735			0.381669
$889$		0			0
$890$	−30.4205	−	30.4205i	−1.01970	−	1.01970i
$891$	4.72918	−	4.72918i	0.158433	−	0.158433i
$892$	0.407769	+	0.407769i	0.0136531	+	0.0136531i
$893$	31.7648			1.06297
$894$	28.6869			0.959433
$895$	47.7959	+	47.7959i	1.59764	+	1.59764i
$896$		0			0
$897$	−4.78707	+	1.84154i	−0.159836	+	0.0614873i
$898$	−51.6715			−1.72430
$899$	−56.2706	+	56.2706i	−1.87673	+	1.87673i
$900$	4.59663			0.153221
$901$	4.11231			0.137001
$902$	−8.27996	+	8.27996i	−0.275693	+	0.275693i
$903$		0			0
$904$	−8.62877	+	8.62877i	−0.286989	+	0.286989i
$905$	17.2523	−	17.2523i	0.573487	−	0.573487i
$906$		−	17.7479i		−	0.589634i
$907$		−	0.112787i		−	0.00374503i	−0.999998	−	0.00187251i	$-0.999404\pi$
$907$		−	0.112787i		−	0.00374503i	0.999998	−	0.00187251i	$-0.000596040\pi$
$908$	−0.925607	−	0.925607i	−0.0307173	−	0.0307173i
$909$	0.464163			0.0153953
$910$		0			0
$911$	−0.606928			−0.0201084			−0.0100542	−	0.999949i	$-0.503200\pi$
$911$	−0.606928			−0.0201084			−0.0100542	+	0.999949i	$0.503200\pi$
$912$	−8.72817	−	8.72817i	−0.289018	−	0.289018i
$913$			14.1474i			0.468212i
$914$		−	10.1102i		−	0.334417i
$915$	0.817956	−	0.817956i	0.0270408	−	0.0270408i
$916$	−0.201125	+	0.201125i	−0.00664536	+	0.00664536i
$917$		0			0
$918$	−6.58253	+	6.58253i	−0.217256	+	0.217256i
$919$	48.9648			1.61520			0.807600	−	0.589731i	$-0.200766\pi$
$919$	48.9648			1.61520			0.807600	+	0.589731i	$0.200766\pi$
$920$	−16.8501			−0.555530
$921$	−15.8755	+	15.8755i	−0.523116	+	0.523116i
$922$	−10.6204			−0.349766
$923$	−1.55516	−	0.691058i	−0.0511886	−	0.0227465i
$924$		0			0
$925$	35.3890	+	35.3890i	1.16358	+	1.16358i
$926$	31.0818			1.02141
$927$	−36.2721			−1.19133
$928$	−7.42913	−	7.42913i	−0.243873	−	0.243873i
$929$	11.1212	−	11.1212i	0.364873	−	0.364873i	−0.500730	−	0.865603i	$-0.666935\pi$
$929$	11.1212	−	11.1212i	0.364873	−	0.364873i	0.865603	+	0.500730i	$0.166935\pi$
$930$	30.9841	+	30.9841i	1.01601	+	1.01601i
$931$		0			0
$932$	−1.69401			−0.0554890
$933$			11.9219i			0.390305i
$934$	−0.478734	−	0.478734i	−0.0156646	−	0.0156646i
$935$			13.8814i			0.453971i
$936$	−8.67048	+	19.5120i	−0.283403	+	0.637771i
$937$			2.27169i			0.0742129i	0.999311	+	0.0371065i	$0.0118141\pi$
$937$			2.27169i			0.0742129i	−0.999311	+	0.0371065i	$0.988186\pi$
$938$		0			0
$939$	−5.73524			−0.187163
$940$		−	7.76347i		−	0.253216i
$941$	−20.1996	+	20.1996i	−0.658488	+	0.658488i	−0.955022	−	0.296534i	$-0.904169\pi$
$941$	−20.1996	+	20.1996i	−0.658488	+	0.658488i	0.296534	+	0.955022i	$0.404169\pi$
$942$	11.9291	+	11.9291i	0.388670	+	0.388670i
$943$	3.45189	+	3.45189i	0.112409	+	0.112409i
$944$	−0.798656	−	0.798656i	−0.0259940	−	0.0259940i
$945$		0			0
$946$			44.5559i			1.44864i
$947$	−0.538186	+	0.538186i	−0.0174887	+	0.0174887i	−0.715797	−	0.698308i	$-0.753936\pi$
$947$	−0.538186	+	0.538186i	−0.0174887	+	0.0174887i	0.698308	+	0.715797i	$0.253936\pi$
$948$	−0.512117			−0.0166328
$949$	−27.6736	−	12.2972i	−0.898322	−	0.399183i
$950$		−	49.3461i		−	1.60100i
$951$	19.5788	−	19.5788i	0.634887	−	0.634887i
$952$		0			0
$953$		−	7.93535i		−	0.257051i	−0.991706	−	0.128526i	$-0.958976\pi$
$953$		−	7.93535i		−	0.257051i	0.991706	−	0.128526i	$-0.0410244\pi$
$954$	7.03140	+	7.03140i	0.227650	+	0.227650i
$955$	−34.1440	+	34.1440i	−1.10487	+	1.10487i
$956$	0.926973	−	0.926973i	0.0299804	−	0.0299804i
$957$	15.2064	+	15.2064i	0.491552	+	0.491552i
$958$		−	48.7364i		−	1.57460i
$959$		0			0
$960$	17.3023	−	17.3023i	0.558429	−	0.558429i
$961$		−	41.4900i		−	1.33839i
$962$	24.0321	−	9.24493i	0.774825	−	0.298068i
$963$	37.8316			1.21911
$964$	1.52085	−	1.52085i	0.0489833	−	0.0489833i
$965$		−	84.1778i		−	2.70978i
$966$		0			0
$967$	−1.26298	−	1.26298i	−0.0406147	−	0.0406147i	0.686508	−	0.727122i	$-0.259143\pi$
$967$	−1.26298	−	1.26298i	−0.0406147	−	0.0406147i	−0.727122	+	0.686508i	$0.759143\pi$
$968$	−7.99339	−	7.99339i	−0.256917	−	0.256917i
$969$	2.72338	+	2.72338i	0.0874876	+	0.0874876i
$970$	43.4002	−	43.4002i	1.39350	−	1.39350i
$971$			0.347211i			0.0111425i	0.999984	+	0.00557126i	$0.00177340\pi$
$971$			0.347211i			0.0111425i	−0.999984	+	0.00557126i	$0.998227\pi$
$972$	−3.21464			−0.103110
$973$		0			0
$974$		−	17.1431i		−	0.549299i
$975$	30.9349	−	11.9004i	0.990711	−	0.381118i
$976$		−	1.45305i		−	0.0465110i
$977$	−7.87884	−	7.87884i	−0.252066	−	0.252066i	0.569751	−	0.821817i	$-0.307040\pi$
$977$	−7.87884	−	7.87884i	−0.252066	−	0.252066i	−0.821817	+	0.569751i	$0.807040\pi$
$978$			14.0519i			0.449331i
$979$	19.2331			0.614693
$980$		0			0
$981$	−10.9963	−	10.9963i	−0.351084	−	0.351084i
$982$	0.992703	−	0.992703i	0.0316784	−	0.0316784i
$983$	−23.7035	−	23.7035i	−0.756024	−	0.756024i	0.219572	−	0.975596i	$-0.429534\pi$
$983$	−23.7035	−	23.7035i	−0.756024	−	0.756024i	−0.975596	+	0.219572i	$0.929534\pi$
$984$	−7.16904			−0.228541
$985$	−7.90678			−0.251931
$986$	13.3315	+	13.3315i	0.424561	+	0.424561i
$987$		0			0
$988$	−2.10368	−	0.934803i	−0.0669270	−	0.0297400i
$989$	18.5752			0.590658
$990$	−23.7350	+	23.7350i	−0.754349	+	0.754349i
$991$	35.7997			1.13722			0.568608	−	0.822609i	$-0.307482\pi$
$991$	35.7997			1.13722			0.568608	+	0.822609i	$0.307482\pi$
$992$	9.57050			0.303864
$993$	7.82804	−	7.82804i	0.248415	−	0.248415i
$994$		0			0
$995$	−18.5219	+	18.5219i	−0.587183	+	0.587183i
$996$	0.678363	−	0.678363i	0.0214948	−	0.0214948i
$997$		−	62.3262i		−	1.97389i	−0.161054	−	0.986946i	$-0.551489\pi$
$997$		−	62.3262i		−	1.97389i	0.161054	−	0.986946i	$-0.448511\pi$
$998$		−	32.6153i		−	1.03242i
$999$	−15.7141	−	15.7141i	−0.497172	−	0.497172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.i.b.489.10	yes	56
7.2	even	3		637.2.bc.c.619.9		112
7.3	odd	6		637.2.bc.c.411.19		112
7.4	even	3		637.2.bc.c.411.20		112
7.5	odd	6		637.2.bc.c.619.10		112
7.6	odd	2	inner	637.2.i.b.489.9	✓	56
13.5	odd	4	inner	637.2.i.b.538.10	yes	56
91.5	even	12		637.2.bc.c.31.20		112
91.18	odd	12		637.2.bc.c.460.10		112
91.31	even	12		637.2.bc.c.460.9		112
91.44	odd	12		637.2.bc.c.31.19		112
91.83	even	4	inner	637.2.i.b.538.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.i.b.489.9	✓	56	7.6	odd	2	inner
637.2.i.b.489.10	yes	56	1.1	even	1	trivial
637.2.i.b.538.9	yes	56	91.83	even	4	inner
637.2.i.b.538.10	yes	56	13.5	odd	4	inner
637.2.bc.c.31.19		112	91.44	odd	12
637.2.bc.c.31.20		112	91.5	even	12
637.2.bc.c.411.19		112	7.3	odd	6
637.2.bc.c.411.20		112	7.4	even	3
637.2.bc.c.460.9		112	91.31	even	12
637.2.bc.c.460.10		112	91.18	odd	12
637.2.bc.c.619.9		112	7.2	even	3
637.2.bc.c.619.10		112	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04867 - 1.04867i) q^{2} +0.884495i q^{3} +0.199431i q^{4} +(2.77428 - 2.77428i) q^{5} +(0.927546 - 0.927546i) q^{6} +(-1.88821 + 1.88821i) q^{8} +2.21767 q^{9} -5.81862 q^{10} +(1.83939 - 1.83939i) q^{11} -0.176395 q^{12} +(3.36514 - 1.29454i) q^{13} +(2.45383 + 2.45383i) q^{15} +4.35909 q^{16} -1.36013 q^{17} +(-2.32561 - 2.32561i) q^{18} +(-2.26377 + 2.26377i) q^{19} +(0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +1.60832i q^{23} +(-1.67011 - 1.67011i) q^{24} -10.3932i q^{25} +(-4.88648 - 2.17138i) q^{26} +4.61500i q^{27} +9.34669 q^{29} -5.14654i q^{30} +(-6.02038 + 6.02038i) q^{31} +(-0.794841 - 0.794841i) q^{32} +(1.62693 + 1.62693i) q^{33} +(1.42633 + 1.42633i) q^{34} +0.442271i q^{36} +(-3.40501 + 3.40501i) q^{37} +4.74791 q^{38} +(1.14501 + 2.97645i) q^{39} +10.4768i q^{40} +(2.14628 - 2.14628i) q^{41} -11.5495i q^{43} +(0.366830 + 0.366830i) q^{44} +(6.15243 - 6.15243i) q^{45} +(1.68660 - 1.68660i) q^{46} +(-7.01591 - 7.01591i) q^{47} +3.85559i q^{48} +(-10.8991 + 10.8991i) q^{50} -1.20303i q^{51} +(0.258171 + 0.671112i) q^{52} -3.02346 q^{53} +(4.83963 - 4.83963i) q^{54} -10.2059i q^{55} +(-2.00229 - 2.00229i) q^{57} +(-9.80162 - 9.80162i) q^{58} +(-0.183216 - 0.183216i) q^{59} +(-0.489369 + 0.489369i) q^{60} -0.333338i q^{61} +12.6268 q^{62} -7.05112i q^{64} +(5.74442 - 12.9272i) q^{65} -3.41223i q^{66} +(0.743917 + 0.743917i) q^{67} -0.271252i q^{68} -1.42255 q^{69} +(-0.333748 - 0.333748i) q^{71} +(-4.18742 + 4.18742i) q^{72} +(-5.93894 - 5.93894i) q^{73} +7.14148 q^{74} +9.19276 q^{75} +(-0.451465 - 0.451465i) q^{76} +(1.92058 - 4.32207i) q^{78} +2.90324 q^{79} +(12.0933 - 12.0933i) q^{80} +2.57106 q^{81} -4.50148 q^{82} +(-3.84570 + 3.84570i) q^{83} +(-3.77338 + 3.77338i) q^{85} +(-12.1116 + 12.1116i) q^{86} +8.26709i q^{87} +6.94629i q^{88} +(5.22813 + 5.22813i) q^{89} -12.9038 q^{90} -0.320747 q^{92} +(-5.32500 - 5.32500i) q^{93} +14.7148i q^{94} +12.5607i q^{95} +(0.703033 - 0.703033i) q^{96} +(-7.45885 + 7.45885i) q^{97} +(4.07915 - 4.07915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{9} - 16 q^{11} + 48 q^{15} - 56 q^{16} - 32 q^{18} - 48 q^{29} - 32 q^{39} - 64 q^{44} + 32 q^{46} - 40 q^{50} - 16 q^{53} - 96 q^{57} + 72 q^{58} - 64 q^{60} + 32 q^{65} + 32 q^{71} + 208 q^{72}+ \cdots + 64 q^{93}+O(q^{100}) \) 56 * q - 56 * q^9 - 16 * q^11 + 48 * q^15 - 56 * q^16 - 32 * q^18 - 48 * q^29 - 32 * q^39 - 64 * q^44 + 32 * q^46 - 40 * q^50 - 16 * q^53 - 96 * q^57 + 72 * q^58 - 64 * q^60 + 32 * q^65 + 32 * q^71 + 208 * q^72 + 208 * q^74 + 160 * q^78 - 80 * q^79 + 152 * q^81 + 24 * q^85 + 64 * q^86 - 128 * q^92 + 64 * q^93

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