LMFDB - Embedded newform 637.2.bc.c.31.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(31,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("637.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bc (of order $12$, degree $4$, not 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:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.19
Character	$\chi$	$=$	637.31
Dual form			637.2.bc.c.411.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.43251 + 0.383841i) q^{2} +(-0.765995 - 0.442247i) q^{3} +(0.172712 + 0.0997153i) q^{4} +(-1.01546 + 3.78973i) q^{5} +(-0.927546 - 0.927546i) q^{6} +(-1.88821 - 1.88821i) q^{8} +(-1.10883 - 1.92056i) q^{9} +(-2.90931 + 5.03907i) q^{10} +(-2.51265 + 0.673262i) q^{11} +(-0.0881976 - 0.152763i) q^{12} +(-3.36514 - 1.29454i) q^{13} +(2.45383 - 2.45383i) q^{15} +(-2.17954 - 3.77508i) q^{16} +(-0.680066 + 1.17791i) q^{17} +(-0.851232 - 3.17684i) q^{18} +(0.828597 - 3.09237i) q^{19} +(-0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +(-1.39284 + 0.804158i) q^{23} +(0.611303 + 2.28141i) q^{24} +(-9.00081 - 5.19662i) q^{25} +(-4.32371 - 3.14612i) q^{26} +4.61500i q^{27} +9.34669 q^{29} +(4.45703 - 2.57327i) q^{30} +(-8.22399 + 2.20361i) q^{31} +(-0.290932 - 1.08577i) q^{32} +(2.22242 + 0.595497i) q^{33} +(-1.42633 + 1.42633i) q^{34} -0.442271i q^{36} +(-1.24632 + 4.65133i) q^{37} +(2.37395 - 4.11181i) q^{38} +(2.00517 + 2.47983i) q^{39} +(9.07320 - 5.23842i) q^{40} +(-2.14628 - 2.14628i) q^{41} +11.5495i q^{43} +(-0.501099 - 0.134269i) q^{44} +(8.40438 - 2.25195i) q^{45} +(-2.30394 + 0.617338i) q^{46} +(-9.58391 - 2.56800i) q^{47} +3.85559i q^{48} +(-10.8991 - 10.8991i) q^{50} +(1.04185 - 0.601515i) q^{51} +(-0.452114 - 0.559138i) q^{52} +(1.51173 - 2.61840i) q^{53} +(-1.77143 + 6.61105i) q^{54} -10.2059i q^{55} +(-2.00229 + 2.00229i) q^{57} +(13.3893 + 3.58764i) q^{58} +(0.0670618 + 0.250278i) q^{59} +(0.668491 - 0.179122i) q^{60} +(-0.288679 + 0.166669i) q^{61} -12.6268 q^{62} +7.05112i q^{64} +(8.32311 - 11.4384i) q^{65} +(2.95508 + 1.70611i) q^{66} +(0.272292 + 1.01621i) q^{67} +(-0.234911 + 0.135626i) q^{68} +1.42255 q^{69} +(-0.333748 + 0.333748i) q^{71} +(-1.53270 + 5.72013i) q^{72} +(2.17380 + 8.11275i) q^{73} +(-3.57074 + 6.18470i) q^{74} +(4.59638 + 7.96117i) q^{75} +(0.451465 - 0.451465i) q^{76} +(1.92058 + 4.32207i) q^{78} +(-1.45162 - 2.51428i) q^{79} +(16.5198 - 4.42646i) q^{80} +(-1.28553 + 2.22661i) q^{81} +(-2.25074 - 3.89840i) q^{82} +(3.84570 + 3.84570i) q^{83} +(-3.77338 - 3.77338i) q^{85} +(-4.43317 + 16.5448i) q^{86} +(-7.15951 - 4.13355i) q^{87} +(6.01566 + 3.47314i) q^{88} +(7.14176 + 1.91363i) q^{89} +12.9038 q^{90} -0.320747 q^{92} +(7.27408 + 1.94908i) q^{93} +(-12.7434 - 7.35740i) q^{94} +(10.8778 + 6.28033i) q^{95} +(-0.257328 + 0.960361i) q^{96} +(7.45885 + 7.45885i) q^{97} +(4.07915 + 4.07915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 56 q^{9} + 16 q^{11} + 96 q^{15} + 56 q^{16} + 32 q^{18} - 96 q^{29} + 32 q^{39} + 64 q^{44} - 32 q^{46} - 80 q^{50} + 16 q^{53} - 192 q^{57} - 72 q^{58} + 64 q^{60} - 32 q^{65} + 64 q^{71} - 208 q^{72}+ \cdots - 64 q^{93}+O(q^{100}) $ 112 * q + 56 * q^9 + 16 * q^11 + 96 * q^15 + 56 * q^16 + 32 * q^18 - 96 * q^29 + 32 * q^39 + 64 * q^44 - 32 * q^46 - 80 * q^50 + 16 * q^53 - 192 * q^57 - 72 * q^58 + 64 * q^60 - 32 * q^65 + 64 * q^71 - 208 * q^72 - 208 * q^74 + 320 * q^78 + 80 * q^79 - 152 * q^81 + 48 * q^85 - 64 * q^86 - 256 * q^92 - 64 * q^93

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.43251	+	0.383841i	1.01294	+	0.271417i	0.726858	−	0.686788i	$-0.240980\pi$
$2$	1.43251	+	0.383841i	1.01294	+	0.271417i	0.286083	+	0.958205i	$0.407647\pi$
$3$	−0.765995	−	0.442247i	−0.442247	−	0.255332i	0.262303	−	0.964986i	$-0.415518\pi$
$3$	−0.765995	−	0.442247i	−0.442247	−	0.255332i	−0.704550	+	0.709654i	$0.748851\pi$
$4$	0.172712	+	0.0997153i	0.0863560	+	0.0498576i
$5$	−1.01546	+	3.78973i	−0.454126	+	1.69482i	0.236519	+	0.971627i	$0.423993\pi$
$5$	−1.01546	+	3.78973i	−0.454126	+	1.69482i	−0.690645	+	0.723194i	$0.742673\pi$
$6$	−0.927546	−	0.927546i	−0.378669	−	0.378669i
$7$		0			0
$7$		0			0
$8$	−1.88821	−	1.88821i	−0.667583	−	0.667583i
$9$	−1.10883	−	1.92056i	−0.369612	−	0.640186i
$10$	−2.90931	+	5.03907i	−0.920005	+	1.59350i
$11$	−2.51265	+	0.673262i	−0.757592	+	0.202996i	−0.616883	−	0.787055i	$-0.711605\pi$
$11$	−2.51265	+	0.673262i	−0.757592	+	0.202996i	−0.140709	+	0.990051i	$0.544938\pi$
$12$	−0.0881976	−	0.152763i	−0.0254605	−	0.0440988i
$13$	−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
$16$	−2.17954	−	3.77508i	−0.544886	−	0.943770i
$17$	−0.680066	+	1.17791i	−0.164940	+	0.285685i	−0.936634	−	0.350309i	$-0.886076\pi$
$17$	−0.680066	+	1.17791i	−0.164940	+	0.285685i	0.771694	+	0.635994i	$0.219410\pi$
$18$	−0.851232	−	3.17684i	−0.200637	−	0.748789i
$19$	0.828597	−	3.09237i	0.190093	−	0.709437i	−0.803389	−	0.595454i	$-0.796972\pi$
$19$	0.828597	−	3.09237i	0.190093	−	0.709437i	0.993483	−	0.113984i	$-0.0363611\pi$
$20$	−0.553276	+	0.553276i	−0.123716	+	0.123716i
$21$		0			0
$22$	−3.85783			−0.822492
$23$	−1.39284	+	0.804158i	−0.290428	+	0.167679i	−0.638135	−	0.769925i	$-0.720294\pi$
$23$	−1.39284	+	0.804158i	−0.290428	+	0.167679i	0.347707	+	0.937603i	$0.386960\pi$
$24$	0.611303	+	2.28141i	0.124782	+	0.465692i
$25$	−9.00081	−	5.19662i	−1.80016	−	1.03932i
$26$	−4.32371	−	3.14612i	−0.847950	−	0.617006i
$27$			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	$0.165522\pi$
$30$	4.45703	−	2.57327i	0.813739	−	0.469813i
$31$	−8.22399	+	2.20361i	−1.47707	+	0.395781i	−0.905350	−	0.424666i	$-0.860391\pi$
$31$	−8.22399	+	2.20361i	−1.47707	+	0.395781i	−0.571723	+	0.820447i	$0.693725\pi$
$32$	−0.290932	−	1.08577i	−0.0514300	−	0.191939i
$33$	2.22242	+	0.595497i	0.386874	+	0.103663i
$34$	−1.42633	+	1.42633i	−0.244614	+	0.244614i
$35$		0			0
$36$		−	0.442271i		−	0.0737118i
$37$	−1.24632	+	4.65133i	−0.204894	+	0.764673i	0.784588	+	0.620017i	$0.212874\pi$
$37$	−1.24632	+	4.65133i	−0.204894	+	0.764673i	−0.989482	+	0.144656i	$0.953792\pi$
$38$	2.37395	−	4.11181i	0.385106	−	0.667023i
$39$	2.00517	+	2.47983i	0.321085	+	0.397091i
$40$	9.07320	−	5.23842i	1.43460	−	0.828266i
$41$	−2.14628	−	2.14628i	−0.335192	−	0.335192i	0.519362	−	0.854554i	$-0.326170\pi$
$41$	−2.14628	−	2.14628i	−0.335192	−	0.335192i	−0.854554	+	0.519362i	$0.826170\pi$
$42$		0			0
$43$			11.5495i			1.76128i	0.473786	+	0.880640i	$0.342887\pi$
$43$			11.5495i			1.76128i	−0.473786	+	0.880640i	$0.657113\pi$
$44$	−0.501099	−	0.134269i	−0.0755435	−	0.0202418i
$45$	8.40438	−	2.25195i	1.25285	−	0.335700i
$46$	−2.30394	+	0.617338i	−0.339697	+	0.0910215i
$47$	−9.58391	−	2.56800i	−1.39796	−	0.374582i	−0.520347	−	0.853955i	$-0.674197\pi$
$47$	−9.58391	−	2.56800i	−1.39796	−	0.374582i	−0.877611	+	0.479374i	$0.840864\pi$
$48$			3.85559i			0.556507i
$49$		0			0
$50$	−10.8991	−	10.8991i	−1.54137	−	1.54137i
$51$	1.04185	−	0.601515i	0.145889	−	0.0842289i
$52$	−0.452114	−	0.559138i	−0.0626970	−	0.0775385i
$53$	1.51173	−	2.61840i	0.207652	−	0.359665i	−0.743322	−	0.668934i	$-0.766751\pi$
$53$	1.51173	−	2.61840i	0.207652	−	0.359665i	0.950975	+	0.309269i	$0.100084\pi$
$54$	−1.77143	+	6.61105i	−0.241061	+	0.899650i
$55$		−	10.2059i		−	1.37617i
$56$		0			0
$57$	−2.00229	+	2.00229i	−0.265210	+	0.265210i
$58$	13.3893	+	3.58764i	1.75810	+	0.471080i
$59$	0.0670618	+	0.250278i	0.00873071	+	0.0325834i	0.970154	−	0.242491i	$-0.0779643\pi$
$59$	0.0670618	+	0.250278i	0.00873071	+	0.0325834i	−0.961423	+	0.275074i	$0.911298\pi$
$60$	0.668491	−	0.179122i	0.0863018	−	0.0231245i
$61$	−0.288679	+	0.166669i	−0.0369616	+	0.0213398i	−0.518367	−	0.855158i	$-0.673460\pi$
$61$	−0.288679	+	0.166669i	−0.0369616	+	0.0213398i	0.481405	+	0.876498i	$0.340127\pi$
$62$	−12.6268			−1.60361
$63$		0			0
$64$			7.05112i			0.881390i
$65$	8.32311	−	11.4384i	1.03236	−	1.41876i
$66$	2.95508	+	1.70611i	0.363745	+	0.210008i
$67$	0.272292	+	1.01621i	0.0332658	+	0.124150i	0.980562	−	0.196209i	$-0.0628632\pi$
$67$	0.272292	+	1.01621i	0.0332658	+	0.124150i	−0.947296	+	0.320359i	$0.896196\pi$
$68$	−0.234911	+	0.135626i	−0.0284871	+	0.0164471i
$69$	1.42255			0.171255
$70$		0			0
$71$	−0.333748	+	0.333748i	−0.0396086	+	0.0396086i	−0.726634	−	0.687025i	$-0.758916\pi$
$71$	−0.333748	+	0.333748i	−0.0396086	+	0.0396086i	0.687025	+	0.726634i	$0.258916\pi$
$72$	−1.53270	+	5.72013i	−0.180631	+	0.674123i
$73$	2.17380	+	8.11275i	0.254425	+	0.949525i	0.968410	+	0.249365i	$0.0802217\pi$
$73$	2.17380	+	8.11275i	0.254425	+	0.949525i	−0.713985	+	0.700161i	$0.753112\pi$
$74$	−3.57074	+	6.18470i	−0.415090	+	0.718957i
$75$	4.59638	+	7.96117i	0.530744	+	0.919276i
$76$	0.451465	−	0.451465i	0.0517866	−	0.0517866i
$77$		0			0
$78$	1.92058	+	4.32207i	0.217462	+	0.489378i
$79$	−1.45162	−	2.51428i	−0.163320	−	0.282878i	0.772738	−	0.634726i	$-0.218887\pi$
$79$	−1.45162	−	2.51428i	−0.163320	−	0.282878i	−0.936057	+	0.351847i	$0.885554\pi$
$80$	16.5198	−	4.42646i	1.84697	−	0.494894i
$81$	−1.28553	+	2.22661i	−0.142837	+	0.247401i
$82$	−2.25074	−	3.89840i	−0.248553	−	0.430506i
$83$	3.84570	+	3.84570i	0.422120	+	0.422120i	0.885933	−	0.463813i	$-0.153519\pi$
$83$	3.84570	+	3.84570i	0.422120	+	0.422120i	−0.463813	+	0.885933i	$0.653519\pi$
$84$		0			0
$85$	−3.77338	−	3.77338i	−0.409281	−	0.409281i
$86$	−4.43317	+	16.5448i	−0.478041	+	1.78407i
$87$	−7.15951	−	4.13355i	−0.767580	−	0.443163i
$88$	6.01566	+	3.47314i	0.641272	+	0.370238i
$89$	7.14176	+	1.91363i	0.757025	+	0.202844i	0.616632	−	0.787251i	$-0.288497\pi$
$89$	7.14176	+	1.91363i	0.757025	+	0.202844i	0.140393	+	0.990096i	$0.455163\pi$
$90$	12.9038			1.36018
$91$		0			0
$92$	−0.320747			−0.0334402
$93$	7.27408	+	1.94908i	0.754287	+	0.202111i
$94$	−12.7434	−	7.35740i	−1.31438	−	0.758858i
$95$	10.8778	+	6.28033i	1.11604	+	0.644348i
$96$	−0.257328	+	0.960361i	−0.0262634	+	0.0980164i
$97$	7.45885	+	7.45885i	0.757332	+	0.757332i	0.975836	−	0.218504i	$-0.0701178\pi$
$97$	7.45885	+	7.45885i	0.757332	+	0.757332i	−0.218504	+	0.975836i	$0.570118\pi$
$98$		0			0
$99$	4.07915	+	4.07915i	0.409970	+	0.409970i
$100$	−1.03636	−	1.79504i	−0.103636	−	0.179504i
$101$	0.104651	−	0.181261i	0.0104132	−	0.0180362i	−0.860772	−	0.508991i	$-0.830019\pi$
$101$	0.104651	−	0.181261i	0.0104132	−	0.0180362i	0.871185	+	0.490955i	$0.163352\pi$
$102$	1.72336	−	0.461772i	0.170638	−	0.0457222i
$103$	−8.17798	−	14.1647i	−0.805800	−	1.39569i	−0.915749	−	0.401750i	$-0.868402\pi$
$103$	−8.17798	−	14.1647i	−0.805800	−	1.39569i	0.109949	−	0.993937i	$-0.464931\pi$
$104$	3.90973	+	8.79845i	0.383380	+	0.862759i
$105$		0			0
$106$	3.17063	−	3.17063i	0.307958	−	0.307958i
$107$	−8.52958	−	14.7737i	−0.824585	−	1.42822i	−0.902236	−	0.431243i	$-0.858075\pi$
$107$	−8.52958	−	14.7737i	−0.824585	−	1.42822i	0.0776502	−	0.996981i	$-0.475258\pi$
$108$	−0.460186	+	0.797066i	−0.0442814	+	0.0766977i
$109$	−1.81493	−	6.77341i	−0.173839	−	0.648775i	−0.996747	−	0.0806001i	$-0.974316\pi$
$109$	−1.81493	−	6.77341i	−0.173839	−	0.648775i	0.822908	−	0.568175i	$-0.192350\pi$
$110$	3.91746	−	14.6201i	0.373515	−	1.39398i
$111$	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	$0.431042\pi$
$114$	−3.63687	+	2.09975i	−0.340624	+	0.196660i
$115$	−1.63318	−	6.09509i	−0.152294	−	0.568370i
$116$	1.61428	+	0.932007i	0.149883	+	0.0865347i
$117$	1.24515	+	7.89838i	0.115114	+	0.730205i
$118$			0.384268i			0.0353747i
$119$		0			0
$120$	−9.26670			−0.845930
$121$	−3.66616	+	2.11666i	−0.333287	+	0.192424i
$122$	−0.477511	+	0.127949i	−0.0432318	+	0.0115839i
$123$	0.694851	+	2.59322i	0.0626526	+	0.233823i
$124$	−1.64012	−	0.439468i	−0.147287	−	0.0394654i
$125$	14.9623	−	14.9623i	1.33827	−	1.33827i
$126$		0			0
$127$		−	10.4126i		−	0.923968i	−0.886888	−	0.461984i	$-0.847138\pi$
$127$		−	10.4126i		−	0.923968i	0.886888	−	0.461984i	$-0.152862\pi$
$128$	−3.28837	+	12.2724i	−0.290654	+	1.08473i
$129$	5.10773	−	8.84684i	0.449710	−	0.778921i
$130$	16.3135	−	13.1910i	1.43079	−	1.15692i
$131$	15.1481	−	8.74577i	1.32350	−	0.764121i	0.339212	−	0.940710i	$-0.389840\pi$
$131$	15.1481	−	8.74577i	1.32350	−	0.764121i	0.984285	+	0.176589i	$0.0565063\pi$
$132$	0.324459	+	0.324459i	0.0282405	+	0.0282405i
$133$		0			0
$134$			1.56025i			0.134785i
$135$	−17.4896	−	4.68633i	−1.50527	−	0.403335i
$136$	3.50824	−	0.940031i	0.300829	−	0.0806070i
$137$	19.4448	−	5.21021i	1.66128	−	0.445138i	0.698540	−	0.715571i	$-0.253833\pi$
$137$	19.4448	−	5.21021i	1.66128	−	0.445138i	0.962739	+	0.270433i	$0.0871668\pi$
$138$	2.03782	+	0.546032i	0.173471	+	0.0464813i
$139$		−	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
$142$	−0.606204	+	0.349992i	−0.0508715	+	0.0293707i
$143$	9.32698	+	0.987101i	0.779961	+	0.0825455i
$144$	−4.83351	+	8.37188i	−0.402792	+	0.697657i
$145$	−9.49115	+	35.4215i	−0.788197	+	2.94159i
$146$			12.4560i			1.03087i
$147$		0			0
$148$	−0.679062	+	0.679062i	−0.0558186	+	0.0558186i
$149$	−21.1240	−	5.66017i	−1.73055	−	0.463699i	−0.750239	−	0.661166i	$-0.770062\pi$
$149$	−21.1240	−	5.66017i	−1.73055	−	0.463699i	−0.980310	+	0.197467i	$0.936728\pi$
$150$	3.52856	+	13.1688i	0.288106	+	1.07523i
$151$	−13.0689	+	3.50181i	−1.06353	+	0.284973i	−0.747834	−	0.663886i	$-0.768906\pi$
$151$	−13.0689	+	3.50181i	−1.06353	+	0.284973i	−0.315700	+	0.948859i	$0.602239\pi$
$152$	−7.40360	+	4.27447i	−0.600511	+	0.346705i
$153$	3.01632			0.243855
$154$		0			0
$155$		−	33.4044i		−	2.68311i
$156$	0.0990399	+	0.628243i	0.00792954	+	0.0502997i
$157$	−11.1379	−	6.43044i	−0.888897	−	0.513205i	−0.0153156	−	0.999883i	$-0.504875\pi$
$157$	−11.1379	−	6.43044i	−0.888897	−	0.513205i	−0.873582	+	0.486678i	$0.838209\pi$
$158$	−1.11438	−	4.15893i	−0.0886554	−	0.330867i
$159$	−2.31596	+	1.33712i	−0.183667	+	0.106040i
$160$	4.41022			0.348659
$161$		0			0
$162$	−2.69621	+	2.69621i	−0.211834	+	0.211834i
$163$	−2.77257	+	10.3474i	−0.217164	+	0.810468i	0.768229	+	0.640175i	$0.221138\pi$
$163$	−2.77257	+	10.3474i	−0.217164	+	0.810468i	−0.985393	+	0.170293i	$0.945529\pi$
$164$	−0.156671	−	0.584704i	−0.0122339	−	0.0456577i
$165$	−4.51355	+	7.81769i	−0.351379	+	0.608607i
$166$	4.03288	+	6.98516i	0.313012	+	0.542153i
$167$	−6.07140	+	6.07140i	−0.469819	+	0.469819i	−0.901856	−	0.432037i	$-0.857795\pi$
$167$	−6.07140	+	6.07140i	−0.469819	+	0.469819i	0.432037	+	0.901856i	$0.357795\pi$
$168$		0			0
$169$	9.64834	+	8.71261i	0.742180	+	0.670201i
$170$	−3.95705	−	6.85380i	−0.303492	−	0.525663i
$171$	−6.85785	+	1.83755i	−0.524433	+	0.140521i
$172$	−1.15166	+	1.99473i	−0.0878132	+	0.152097i
$173$	1.77614	+	3.07637i	0.135037	+	0.233892i	0.925612	−	0.378474i	$-0.123551\pi$
$173$	1.77614	+	3.07637i	0.135037	+	0.233892i	−0.790574	+	0.612366i	$0.790218\pi$
$174$	−8.66948	−	8.66948i	−0.657232	−	0.657232i
$175$		0			0
$176$	8.01805	+	8.01805i	0.604383	+	0.604383i
$177$	0.0593158	−	0.221370i	0.00445845	−	0.0166392i
$178$	9.49615	+	5.48260i	0.711766	+	0.410938i
$179$	14.9201	+	8.61412i	1.11518	+	0.643850i	0.940166	−	0.340716i	$-0.110670\pi$
$179$	14.9201	+	8.61412i	1.11518	+	0.643850i	0.175014	+	0.984566i	$0.444003\pi$
$180$	1.67609	+	0.449107i	0.124928	+	0.0334744i
$181$	−6.21868			−0.462231			−0.231115	−	0.972926i	$-0.574238\pi$
$181$	−6.21868			−0.462231			−0.231115	+	0.972926i	$0.574238\pi$
$182$		0			0
$183$	0.294836			0.0217949
$184$	4.14840	+	1.11156i	0.305824	+	0.0819453i
$185$	−16.3617	−	9.44644i	−1.20294	−	0.694516i
$186$	9.67208	+	5.58418i	0.709192	+	0.409452i
$187$	0.915725	−	3.41753i	0.0669644	−	0.249915i
$188$	−1.39919	−	1.39919i	−0.102046	−	0.102046i
$189$		0			0
$190$	13.1720	+	13.1720i	0.955599	+	0.955599i
$191$	6.15368	+	10.6585i	0.445264	+	0.771221i	0.998071	−	0.0620893i	$-0.0197763\pi$
$191$	6.15368	+	10.6585i	0.445264	+	0.771221i	−0.552806	+	0.833310i	$0.686443\pi$
$192$	3.11834	−	5.40112i	0.225047	−	0.389792i
$193$	−20.7241	+	5.55301i	−1.49176	+	0.399715i	−0.910329	−	0.413885i	$-0.864172\pi$
$193$	−20.7241	+	5.55301i	−1.49176	+	0.399715i	−0.581426	+	0.813599i	$0.697505\pi$
$194$	7.82190	+	13.5479i	0.561579	+	0.972684i
$195$	−11.4341	+	5.08091i	−0.818812	+	0.363852i
$196$		0			0
$197$	−1.42501	+	1.42501i	−0.101528	+	0.101528i	−0.756046	−	0.654518i	$-0.772872\pi$
$197$	−1.42501	+	1.42501i	−0.101528	+	0.101528i	0.654518	+	0.756046i	$0.272872\pi$
$198$	4.27769	+	7.40918i	0.304002	+	0.526548i
$199$	−3.33814	+	5.78184i	−0.236635	+	0.409863i	−0.959747	−	0.280868i	$-0.909378\pi$
$199$	−3.33814	+	5.78184i	−0.236635	+	0.409863i	0.723112	+	0.690731i	$0.242711\pi$
$200$	7.18310	+	26.8077i	0.507922	+	1.89559i
$201$	0.240841	−	0.898832i	0.0169876	−	0.0633987i
$202$	0.219490	−	0.219490i	0.0154432	−	0.0154432i
$203$		0			0
$204$	0.239921			0.0167978
$205$	10.3133	−	5.95437i	0.720310	−	0.415871i
$206$	−6.27809	−	23.4301i	−0.437415	−	1.63246i
$207$	3.08886	+	1.78336i	0.214691	+	0.123952i
$208$	2.44748	+	15.5252i	0.169702	+	1.07648i
$209$			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	$0.726762\pi$
$212$	0.522188	−	0.301486i	0.0358640	−	0.0207061i
$213$	0.403248	−	0.108050i	0.0276301	−	0.00740346i
$214$	−6.54800	−	24.4375i	−0.447612	−	1.67051i
$215$	−43.7695	−	11.7280i	−2.98505	−	0.799843i
$216$	8.71408	−	8.71408i	0.592918	−	0.592918i
$217$		0			0
$218$		−	10.3996i		−	0.704353i
$219$	1.92272	−	7.17568i	0.129925	−	0.484888i
$220$	1.01769	−	1.76269i	0.0686125	−	0.118840i
$221$	3.81337	−	3.08346i	0.256515	−	0.207416i
$222$	5.47034	−	3.15830i	0.367145	−	0.211971i
$223$	−2.04467	−	2.04467i	−0.136921	−	0.136921i	0.635324	−	0.772245i	$-0.280866\pi$
$223$	−2.04467	−	2.04467i	−0.136921	−	0.136921i	−0.772245	+	0.635324i	$0.780866\pi$
$224$		0			0
$225$			23.0488i			1.53658i
$226$	6.54633	+	1.75408i	0.435455	+	0.116680i
$227$	−6.34006	+	1.69881i	−0.420805	+	0.112754i	−0.463007	−	0.886355i	$-0.653229\pi$
$227$	−6.34006	+	1.69881i	−0.420805	+	0.112754i	0.0422019	+	0.999109i	$0.486563\pi$
$228$	−0.545479	+	0.146161i	−0.0361252	+	0.00967972i
$229$	1.37763	+	0.369136i	0.0910366	+	0.0243932i	0.304050	−	0.952656i	$-0.401661\pi$
$229$	1.37763	+	0.369136i	0.0910366	+	0.0243932i	−0.213013	+	0.977049i	$0.568328\pi$
$230$		−	9.35819i		−	0.617060i
$231$		0			0
$232$	−17.6485	−	17.6485i	−1.15868	−	1.15868i
$233$	−7.35621	+	4.24711i	−0.481921	+	0.278237i	−0.721217	−	0.692709i	$-0.756417\pi$
$233$	−7.35621	+	4.24711i	−0.481921	+	0.278237i	0.239295	+	0.970947i	$0.423084\pi$
$234$	−1.24803	+	11.7925i	−0.0815864	+	0.770898i
$235$	19.4641	−	33.7128i	1.26970	−	2.19918i
$236$	−0.0133742	+	0.0499131i	−0.000870585	+	0.00324907i
$237$			2.56790i			0.166803i
$238$		0			0
$239$	−4.64810	+	4.64810i	−0.300661	+	0.300661i	−0.841272	−	0.540612i	$-0.818193\pi$
$239$	−4.64810	+	4.64810i	−0.300661	+	0.300661i	0.540612	+	0.841272i	$0.318193\pi$
$240$	−14.6117	−	3.91518i	−0.943179	−	0.252724i
$241$	2.79130	+	10.4173i	0.179803	+	0.671034i	0.995683	+	0.0928137i	$0.0295861\pi$
$241$	2.79130	+	10.4173i	0.179803	+	0.671034i	−0.815880	+	0.578221i	$0.803747\pi$
$242$	−6.06429	+	1.62492i	−0.389827	+	0.104454i
$243$	13.9595	−	8.05955i	0.895505	−	0.517020i
$244$	−0.0664778			−0.00425580
$245$		0			0
$246$			3.98154i			0.253854i
$247$	−6.79154	+	9.33359i	−0.432135	+	0.593882i
$248$	19.6895	+	11.3677i	1.25028	+	0.721852i
$249$	−1.24504	−	4.64654i	−0.0789009	−	0.294462i
$250$	27.1769	−	15.6906i	1.71882	−	0.992361i
$251$	−28.0524			−1.77065			−0.885327	−	0.464968i	$-0.846066\pi$
$251$	−28.0524			−1.77065			−0.885327	+	0.464968i	$0.846066\pi$
$252$		0			0
$253$	2.95831	−	2.95831i	0.185988	−	0.185988i
$254$	3.99678	−	14.9162i	0.250780	−	0.935925i
$255$	1.22162	+	4.55916i	0.0765010	+	0.285506i
$256$	−2.37016	+	4.10524i	−0.148135	+	0.256578i
$257$	−7.06032	−	12.2288i	−0.440411	−	0.762813i	0.557309	−	0.830305i	$-0.311834\pi$
$257$	−7.06032	−	12.2288i	−0.440411	−	0.762813i	−0.997720	+	0.0674915i	$0.978500\pi$
$258$	10.7127	−	10.7127i	0.666942	−	0.666942i
$259$		0			0
$260$	2.57809	−	1.14561i	0.159886	−	0.0710479i
$261$	−10.3639	−	17.9509i	−0.641511	−	1.11113i
$262$	25.0569	−	6.71397i	1.54802	−	0.414790i
$263$	−11.1615	+	19.3323i	−0.688248	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$263$	−11.1615	+	19.3323i	−0.688248	+	1.19208i	−0.972404	+	0.233302i	$0.925047\pi$
$264$	−3.07198	−	5.32082i	−0.189067	−	0.327474i
$265$	8.38793	+	8.38793i	0.515267	+	0.515267i
$266$		0			0
$267$	−4.62426	−	4.62426i	−0.283000	−	0.283000i
$268$	−0.0543034	+	0.202663i	−0.00331711	+	0.0123796i
$269$	−10.2451	−	5.91503i	−0.624656	−	0.360645i	0.154023	−	0.988067i	$-0.450777\pi$
$269$	−10.2451	−	5.91503i	−0.624656	−	0.360645i	−0.778680	+	0.627422i	$0.784110\pi$
$270$	−23.2553	−	13.4265i	−1.41527	−	0.817109i
$271$	−4.77450	−	1.27932i	−0.290030	−	0.0777134i	0.110870	−	0.993835i	$-0.464636\pi$
$271$	−4.77450	−	1.27932i	−0.290030	−	0.0777134i	−0.400901	+	0.916121i	$0.631303\pi$
$272$	5.92893			0.359494
$273$		0			0
$274$	29.8548			1.80359
$275$	26.1145	+	6.99737i	1.57477	+	0.421957i
$276$	0.245691	+	0.141850i	0.0147889	+	0.00853835i
$277$	0.730512	+	0.421761i	0.0438922	+	0.0253412i	0.521786	−	0.853077i	$-0.325266\pi$
$277$	0.730512	+	0.421761i	0.0438922	+	0.0253412i	−0.477893	+	0.878418i	$0.658599\pi$
$278$	5.62628	−	20.9976i	0.337442	−	1.25935i
$279$	13.3512	+	13.3512i	0.799316	+	0.799316i
$280$		0			0
$281$	−6.80029	−	6.80029i	−0.405671	−	0.405671i	0.474555	−	0.880226i	$-0.342609\pi$
$281$	−6.80029	−	6.80029i	−0.405671	−	0.405671i	−0.880226	+	0.474555i	$0.842609\pi$
$282$	6.50758	+	11.2715i	0.387521	+	0.671206i
$283$	9.91175	−	17.1677i	0.589192	−	1.02051i	−0.405146	−	0.914252i	$-0.632779\pi$
$283$	9.91175	−	17.1677i	0.589192	−	1.02051i	0.994338	−	0.106259i	$-0.0338873\pi$
$284$	−0.0909219	+	0.0243625i	−0.00539522	+	0.00144565i
$285$	−5.55491	−	9.62139i	−0.329045	−	0.569922i
$286$	12.9821	+	4.99411i	0.767650	+	0.295308i
$287$		0			0
$288$	−1.76270	+	1.76270i	−0.103868	+	0.103868i
$289$	7.57502	+	13.1203i	0.445589	+	0.771784i
$290$	−27.1924	+	47.0987i	−1.59679	+	2.76573i
$291$	−2.41478	−	9.01210i	−0.141557	−	0.528299i
$292$	−0.433523	+	1.61793i	−0.0253700	+	0.0946822i
$293$	−6.47711	+	6.47711i	−0.378397	+	0.378397i	−0.870524	−	0.492127i	$-0.836220\pi$
$293$	−6.47711	+	6.47711i	−0.378397	+	0.378397i	0.492127	+	0.870524i	$0.336220\pi$
$294$		0			0
$295$	−1.01659			−0.0591879
$296$	11.1360	−	6.42936i	0.647266	−	0.373699i
$297$	−3.10710	−	11.5959i	−0.180292	−	0.672861i
$298$	−28.0879	−	16.2165i	−1.62709	−	0.939399i
$299$	5.72813	−	0.903015i	0.331266	−	0.0522227i
$300$			1.83332i			0.105847i
$301$		0			0
$302$	−20.0656			−1.15464
$303$	−0.160325	+	0.0925634i	−0.00921040	+	0.00531763i
$304$	−13.4799	+	3.61193i	−0.773125	+	0.207158i
$305$	−0.338490	−	1.26326i	−0.0193819	−	0.0723342i
$306$	4.32092	+	1.15779i	0.247011	+	0.0661863i
$307$	−17.9487	+	17.9487i	−1.02438	+	1.02438i	−0.0246898	+	0.999695i	$0.507860\pi$
$307$	−17.9487	+	17.9487i	−1.02438	+	1.02438i	−0.999695	+	0.0246898i	$0.992140\pi$
$308$		0			0
$309$			14.4668i			0.822985i
$310$	12.8220	−	47.8523i	0.728240	−	2.71783i
$311$	6.73937	−	11.6729i	0.382155	−	0.661912i	−0.609215	−	0.793005i	$-0.708515\pi$
$311$	6.73937	−	11.6729i	0.382155	−	0.661912i	0.991370	+	0.131093i	$0.0418488\pi$
$312$	0.896260	−	8.46863i	0.0507407	−	0.479442i
$313$	5.61548	−	3.24210i	0.317406	−	0.183254i	−0.332830	−	0.942987i	$-0.608003\pi$
$313$	5.61548	−	3.24210i	0.317406	−	0.183254i	0.650236	+	0.759733i	$0.274670\pi$
$314$	−13.4869	−	13.4869i	−0.761108	−	0.761108i
$315$		0			0
$316$		−	0.578994i		−	0.0325710i
$317$	30.2378	+	8.10220i	1.69833	+	0.455065i	0.972517	−	0.232832i	$-0.0747992\pi$
$317$	30.2378	+	8.10220i	1.69833	+	0.455065i	0.725808	+	0.687897i	$0.241466\pi$
$318$	−3.83088	+	1.02648i	−0.214825	+	0.0575623i
$319$	−23.4849	+	6.29277i	−1.31490	+	0.352327i
$320$	−26.7219	−	7.16010i	−1.49380	−	0.400262i
$321$			15.0887i			0.842171i
$322$		0			0
$323$	3.07902	+	3.07902i	0.171322	+	0.171322i
$324$	−0.444054	+	0.256374i	−0.0246696	+	0.0142430i
$325$	23.5618	+	29.1393i	1.30697	+	1.61636i
$326$	−7.94348	+	13.7585i	−0.439949	+	0.762013i
$327$	−1.60530	+	5.99104i	−0.0887730	+	0.331306i
$328$			8.10523i			0.447537i
$329$		0			0
$330$	−9.46647	+	9.46647i	−0.521112	+	0.521112i
$331$	12.0897	+	3.23943i	0.664512	+	0.178055i	0.575281	−	0.817956i	$-0.304893\pi$
$331$	12.0897	+	3.23943i	0.664512	+	0.178055i	0.0892305	+	0.996011i	$0.471559\pi$
$332$	0.280723	+	1.04767i	0.0154067	+	0.0574985i
$333$	10.3151	−	2.76392i	0.565264	−	0.151462i
$334$	−11.0278	+	6.36691i	−0.603415	+	0.348382i
$335$	−4.12767			−0.225518
$336$		0			0
$337$		−	4.54349i		−	0.247500i	−0.992313	−	0.123750i	$-0.960508\pi$
$337$		−	4.54349i		−	0.247500i	0.992313	−	0.123750i	$-0.0394920\pi$
$338$	10.4771	+	16.1844i	0.569880	+	0.880314i
$339$	−3.50046	−	2.02099i	−0.190119	−	0.109765i
$340$	−0.275444	−	1.02797i	−0.0149381	−	0.0557496i
$341$	19.1804	−	11.0738i	1.03868	−	0.599680i
$342$	−10.5293			−0.569359
$343$		0			0
$344$	21.8078	−	21.8078i	1.17580	−	1.17580i
$345$	−1.44453	+	5.39108i	−0.0777711	+	0.290246i
$346$	1.36351	+	5.08869i	0.0733028	+	0.273570i
$347$	5.56642	−	9.64133i	0.298821	−	0.517574i	−0.677045	−	0.735941i	$-0.736740\pi$
$347$	5.56642	−	9.64133i	0.298821	−	0.517574i	0.975867	+	0.218368i	$0.0700732\pi$
$348$	−0.824356	−	1.42783i	−0.0441901	−	0.0765395i
$349$	16.7058	−	16.7058i	0.894240	−	0.894240i	−0.100679	−	0.994919i	$-0.532101\pi$
$349$	16.7058	−	16.7058i	0.894240	−	0.894240i	0.994919	+	0.100679i	$0.0321014\pi$
$350$		0			0
$351$	5.97430	−	15.5301i	0.318885	−	0.828937i
$352$	1.46202	+	2.53229i	0.0779259	+	0.134972i
$353$	5.91578	−	1.58513i	0.314865	−	0.0843678i	−0.0979257	−	0.995194i	$-0.531221\pi$
$353$	5.91578	−	1.58513i	0.314865	−	0.0843678i	0.412791	+	0.910826i	$0.364554\pi$
$354$	0.169942	−	0.294347i	0.00903229	−	0.0156444i
$355$	−0.925909	−	1.60372i	−0.0491421	−	0.0851167i
$356$	1.04265	+	1.04265i	0.0552603	+	0.0552603i
$357$		0			0
$358$	18.0668	+	18.0668i	0.954860	+	0.954860i
$359$	5.62963	−	21.0100i	0.297120	−	1.10887i	−0.642399	−	0.766371i	$-0.722061\pi$
$359$	5.62963	−	21.0100i	0.297120	−	1.10887i	0.939519	−	0.342497i	$-0.111273\pi$
$360$	−20.1214	−	11.6171i	−1.06049	−	0.612274i
$361$	7.57833	+	4.37535i	0.398859	+	0.230282i
$362$	−8.90835	−	2.38698i	−0.468212	−	0.125457i
$363$	3.74435			0.196527
$364$		0			0
$365$	−32.9526			−1.72482
$366$	0.422356	+	0.113170i	0.0220769	+	0.00591549i
$367$	14.0740	+	8.12564i	0.734658	+	0.424155i	0.820124	−	0.572186i	$-0.193905\pi$
$367$	14.0740	+	8.12564i	0.734658	+	0.424155i	−0.0854660	+	0.996341i	$0.527238\pi$
$368$	6.07153	+	3.50540i	0.316500	+	0.182731i
$369$	−1.74218	+	6.50191i	−0.0906944	+	0.338476i
$370$	−19.8124	−	19.8124i	−1.03000	−	1.03000i
$371$		0			0
$372$	1.06197	+	1.06197i	0.0550604	+	0.0550604i
$373$	−2.10783	−	3.65087i	−0.109139	−	0.189035i	0.806283	−	0.591531i	$-0.201476\pi$
$373$	−2.10783	−	3.65087i	−0.109139	−	0.189035i	−0.915422	+	0.402496i	$0.868143\pi$
$374$	2.62358	−	4.54417i	0.135662	−	0.234973i
$375$	−18.0781	+	4.84402i	−0.933551	+	0.250144i
$376$	13.2475	+	22.9454i	0.683188	+	1.18332i
$377$	−31.4529	−	12.0997i	−1.61991	−	0.623164i
$378$		0			0
$379$	18.1305	−	18.1305i	0.931303	−	0.931303i	−0.0664849	−	0.997787i	$-0.521178\pi$
$379$	18.1305	−	18.1305i	0.931303	−	0.931303i	0.997787	+	0.0664849i	$0.0211784\pi$
$380$	1.25249	+	2.16937i	0.0642513	+	0.111287i
$381$	−4.60494	+	7.97599i	−0.235918	+	0.408623i
$382$	4.72407	+	17.6305i	0.241704	+	0.902053i
$383$	−6.07450	+	22.6703i	−0.310392	+	1.15840i	0.617811	+	0.786327i	$0.288020\pi$
$383$	−6.07450	+	22.6703i	−0.310392	+	1.15840i	−0.928203	+	0.372073i	$0.878647\pi$
$384$	7.94630	−	7.94630i	0.405508	−	0.405508i
$385$		0			0
$386$	−31.8191			−1.61955
$387$	22.1815	−	12.8065i	1.12755	−	0.650989i
$388$	0.544471	+	2.03199i	0.0276413	+	0.103159i
$389$	−16.8646	−	9.73676i	−0.855067	−	0.493673i	0.00729024	−	0.999973i	$-0.497679\pi$
$389$	−16.8646	−	9.73676i	−0.855067	−	0.493673i	−0.862357	+	0.506300i	$0.831013\pi$
$390$	−18.3297	+	2.88961i	−0.928163	+	0.146321i
$391$		−	2.18752i		−	0.110628i
$392$		0			0
$393$	−15.4712			−0.780417
$394$	−2.58833	+	1.49437i	−0.130398	+	0.0752855i
$395$	11.0025	−	2.94811i	0.553596	−	0.148336i
$396$	0.297764	+	1.11127i	0.0149632	+	0.0558435i
$397$	11.5515	+	3.09522i	0.579755	+	0.155345i	0.536767	−	0.843731i	$-0.319646\pi$
$397$	11.5515	+	3.09522i	0.579755	+	0.155345i	0.0429883	+	0.999076i	$0.486312\pi$
$398$	−7.00124	+	7.00124i	−0.350941	+	0.350941i
$399$		0			0
$400$			45.3051i			2.26525i
$401$	−2.43214	+	9.07687i	−0.121455	+	0.453277i	−0.999689	−	0.0249551i	$-0.992056\pi$
$401$	−2.43214	+	9.07687i	−0.121455	+	0.453277i	0.878233	+	0.478233i	$0.158722\pi$
$402$	0.690017	−	1.19514i	0.0344149	−	0.0596084i
$403$	30.5276	+	3.23082i	1.52069	+	0.160939i
$404$	0.0361490	−	0.0208706i	0.00179848	−	0.00103835i
$405$	−7.13285	−	7.13285i	−0.354434	−	0.354434i
$406$		0			0
$407$		−	12.5262i		−	0.620903i
$408$	−3.10302	−	0.831452i	−0.153623	−	0.0411630i
$409$	−18.6466	+	4.99635i	−0.922017	+	0.247054i	−0.688447	−	0.725286i	$-0.741707\pi$
$409$	−18.6466	+	4.99635i	−0.922017	+	0.247054i	−0.233570	+	0.972340i	$0.575041\pi$
$410$	17.0594	−	4.57106i	0.842505	−	0.225749i
$411$	−17.1988	−	4.60840i	−0.848354	−	0.227316i
$412$		−	3.26188i		−	0.160701i
$413$		0			0
$414$	3.74032	+	3.74032i	0.183827	+	0.183827i
$415$	−18.4793	+	10.6690i	−0.907114	+	0.523723i
$416$	−0.426549	+	4.03040i	−0.0209133	+	0.197607i
$417$	−6.48239	+	11.2278i	−0.317444	+	0.549829i
$418$	−3.19659	+	11.9298i	−0.156350	+	0.583507i
$419$		−	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	−0.987227	−	0.159321i	$-0.949070\pi$
$421$	−16.9872	+	16.9872i	−0.827906	+	0.827906i	0.159321	+	0.987227i	$0.449070\pi$
$422$	−27.2028	−	7.28898i	−1.32421	−	0.354822i
$423$	5.69498	+	21.2540i	0.276899	+	1.03340i
$424$	−7.79855	+	2.08961i	−0.378731	+	0.101481i
$425$	12.2423	−	7.06809i	0.593838	−	0.342853i
$426$	0.619132			0.0299971
$427$		0			0
$428$		−	3.40212i		−	0.164448i
$429$	−6.70787	−	4.88094i	−0.323859	−	0.235654i
$430$	−58.1987	−	33.6010i	−2.80659	−	1.62039i
$431$	−7.10522	−	26.5171i	−0.342247	−	1.27728i	−0.895796	−	0.444465i	$-0.853394\pi$
$431$	−7.10522	−	26.5171i	−0.342247	−	1.27728i	0.553549	−	0.832816i	$-0.313273\pi$
$432$	17.4220	−	10.0586i	0.838216	−	0.483945i
$433$	26.0271			1.25078			0.625391	−	0.780312i	$-0.284940\pi$
$433$	26.0271			1.25078			0.625391	+	0.780312i	$0.284940\pi$
$434$		0			0
$435$	22.9352	−	22.9352i	1.09966	−	1.09966i
$436$	0.361952	−	1.35082i	0.0173344	−	0.0646928i
$437$	1.33265	+	4.97350i	0.0637491	+	0.237915i
$438$	5.50864	−	9.54125i	0.263213	−	0.455899i
$439$	1.85272	+	3.20901i	0.0884257	+	0.153158i	0.906846	−	0.421463i	$-0.138483\pi$
$439$	1.85272	+	3.20901i	0.0884257	+	0.153158i	−0.818420	+	0.574620i	$0.805150\pi$
$440$	−19.2709	+	19.2709i	−0.918706	+	0.918706i
$441$		0			0
$442$	6.64626	−	2.95337i	0.316130	−	0.140477i
$443$	−1.34404	−	2.32795i	−0.0638573	−	0.110604i	0.832329	−	0.554282i	$-0.187007\pi$
$443$	−1.34404	−	2.32795i	−0.0638573	−	0.110604i	−0.896187	+	0.443678i	$0.853674\pi$
$444$	0.820472	−	0.219845i	0.0389379	−	0.0104334i
$445$	−14.5043	+	25.1222i	−0.687570	+	1.19091i
$446$	−2.14419	−	3.71384i	−0.101530	−	0.175855i
$447$	13.6777	+	13.6777i	0.646934	+	0.646934i
$448$		0			0
$449$	24.6366	+	24.6366i	1.16267	+	1.16267i	0.983888	+	0.178784i	$0.0572164\pi$
$449$	24.6366	+	24.6366i	1.16267	+	1.16267i	0.178784	+	0.983888i	$0.442784\pi$
$450$	−8.84706	+	33.0177i	−0.417054	+	1.55647i
$451$	6.83784	+	3.94783i	0.321981	+	0.185896i
$452$	0.789262	+	0.455681i	0.0371238	+	0.0214334i
$453$	11.5594	+	3.09733i	0.543108	+	0.145525i
$454$	−9.73430			−0.456854
$455$		0			0
$456$	7.56149			0.354099
$457$	−6.58491	−	1.76442i	−0.308029	−	0.0825361i	0.101493	−	0.994836i	$-0.467638\pi$
$457$	−6.58491	−	1.76442i	−0.308029	−	0.0825361i	−0.409522	+	0.912300i	$0.634305\pi$
$458$	1.83179	+	1.05758i	0.0855939	+	0.0494177i
$459$	−5.43605	−	3.13850i	−0.253733	−	0.146493i
$460$	0.325705	−	1.21555i	0.0151861	−	0.0566752i
$461$	−5.06375	−	5.06375i	−0.235842	−	0.235842i	0.579284	−	0.815126i	$-0.303332\pi$
$461$	−5.06375	−	5.06375i	−0.235842	−	0.235842i	−0.815126	+	0.579284i	$0.803332\pi$
$462$		0			0
$463$	−14.8196	−	14.8196i	−0.688725	−	0.688725i	0.273226	−	0.961950i	$-0.411909\pi$
$463$	−14.8196	−	14.8196i	−0.688725	−	0.688725i	−0.961950	+	0.273226i	$0.911909\pi$
$464$	−20.3715	−	35.2845i	−0.945724	−	1.63804i
$465$	−14.7730	+	25.5876i	−0.685082	+	1.18660i
$466$	−12.1681	+	3.26043i	−0.563676	+	0.151036i
$467$	0.228257	+	0.395352i	0.0105625	+	0.0182947i	0.871258	−	0.490825i	$-0.163304\pi$
$467$	0.228257	+	0.395352i	0.0105625	+	0.0182947i	−0.860696	+	0.509119i	$0.829971\pi$
$468$	−0.572537	+	1.48830i	−0.0264655	+	0.0687969i
$469$		0			0
$470$	40.8229	−	40.8229i	1.88302	−	1.88302i
$471$	5.68769	+	9.85137i	0.262075	+	0.453927i
$472$	0.345951	−	0.599204i	0.0159237	−	0.0275806i
$473$	−7.77583	−	29.0198i	−0.357533	−	1.33433i
$474$	−0.985664	+	3.67855i	−0.0452731	+	0.168961i
$475$	−23.5279	+	23.5279i	−1.07953	+	1.07953i
$476$		0			0
$477$	−6.70504			−0.307003
$478$	−8.44260	+	4.87434i	−0.386155	+	0.222947i
$479$	−8.50540	−	31.7426i	−0.388622	−	1.45036i	−0.832378	−	0.554209i	$-0.813021\pi$
$479$	−8.50540	−	31.7426i	−0.388622	−	1.45036i	0.443756	−	0.896148i	$-0.353646\pi$
$480$	−3.37821	−	1.95041i	−0.154193	−	0.0890236i
$481$	10.2154	−	14.0390i	0.465780	−	0.640121i
$482$			15.9943i			0.728519i
$483$		0			0
$484$	−0.844253			−0.0383751
$485$	−35.8412	+	20.6929i	−1.62747	+	0.939617i
$486$	23.0908	−	6.18717i	1.04742	−	0.280656i
$487$	2.99178	+	11.1655i	0.135571	+	0.505956i	0.999995	+	0.00319321i	$0.00101643\pi$
$487$	2.99178	+	11.1655i	0.135571	+	0.505956i	−0.864424	+	0.502763i	$0.832317\pi$
$488$	0.859792	+	0.230381i	0.0389210	+	0.0104288i
$489$	6.69986	−	6.69986i	0.302978	−	0.302978i
$490$		0			0
$491$		−	0.946627i		−	0.0427207i	−0.999772	−	0.0213603i	$-0.993200\pi$
$491$		−	0.946627i		−	0.0427207i	0.999772	−	0.0213603i	$-0.00679973\pi$
$492$	−0.138575	+	0.517167i	−0.00624743	+	0.0233157i
$493$	−6.35636	+	11.0095i	−0.286276	+	0.495845i
$494$	−13.3116	+	10.7636i	−0.598917	+	0.484279i
$495$	−19.6011	+	11.3167i	−0.881004	+	0.508648i
$496$	26.2434	+	26.2434i	1.17836	+	1.17836i
$497$		0			0
$498$		−	7.13412i		−	0.319688i
$499$	−21.2427	−	5.69198i	−0.950956	−	0.254808i	−0.250188	−	0.968197i	$-0.580492\pi$
$499$	−21.2427	−	5.69198i	−0.950956	−	0.254808i	−0.700768	+	0.713389i	$0.747159\pi$
$500$	4.07615	−	1.09220i	0.182291	−	0.0488447i
$501$	7.33572	−	1.96560i	0.327736	−	0.0878165i
$502$	−40.1855	−	10.7677i	−1.79357	−	0.480585i
$503$			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
$506$	5.37335	−	3.10230i	0.238875	−	0.137914i
$507$	−3.53744	−	10.9408i	−0.157103	−	0.485897i
$508$	1.03829	−	1.79838i	0.0460669	−	0.0797902i
$509$	−4.97409	+	18.5635i	−0.220473	+	0.822815i	0.763695	+	0.645577i	$0.223383\pi$
$509$	−4.97409	+	18.5635i	−0.220473	+	0.822815i	−0.984168	+	0.177238i	$0.943284\pi$
$510$			6.99997i			0.309964i
$511$		0			0
$512$	12.9970	−	12.9970i	0.574390	−	0.574390i
$513$	14.2713	+	3.82398i	0.630092	+	0.168833i
$514$	−5.42008	−	20.2280i	−0.239069	−	0.892219i
$515$	61.9848	−	16.6088i	2.73137	−	0.731870i
$516$	1.76433	−	1.01864i	0.0776703	−	0.0448430i
$517$	25.8099			1.13512
$518$		0			0
$519$		−	3.14197i		−	0.137917i
$520$	−37.3139	+	5.88238i	−1.63632	+	0.257960i
$521$	19.3198	+	11.1543i	0.846416	+	0.488678i	0.859440	−	0.511237i	$-0.170813\pi$
$521$	19.3198	+	11.1543i	0.846416	+	0.488678i	−0.0130243	+	0.999915i	$0.504146\pi$
$522$	−7.95620	−	29.6930i	−0.348234	−	1.29963i
$523$	15.3793	−	8.87924i	0.672489	−	0.388262i	−0.124530	−	0.992216i	$-0.539742\pi$
$523$	15.3793	−	8.87924i	0.672489	−	0.388262i	0.797019	+	0.603954i	$0.206409\pi$
$524$	3.48835			0.152389
$525$		0			0
$526$	−23.4095	+	23.4095i	−1.02070	+	1.02070i
$527$	2.99720	−	11.1857i	0.130560	−	0.487257i
$528$	−2.59582	−	9.68774i	−0.112969	−	0.421605i
$529$	−10.2067	+	17.6785i	−0.443768	+	0.768628i
$530$	8.79620	+	15.2355i	0.382082	+	0.661786i
$531$	0.406313	−	0.406313i	0.0176325	−	0.0176325i
$532$		0			0
$533$	4.44408	+	10.0010i	0.192494	+	0.433190i
$534$	−4.84933	−	8.39929i	−0.209851	−	0.363473i
$535$	64.6497	−	17.3228i	2.79505	−	0.748931i
$536$	1.40467	−	2.43296i	0.0606725	−	0.105088i
$537$	−7.61914	−	13.1967i	−0.328790	−	0.569482i
$538$	−12.4059	−	12.4059i	−0.534854	−	0.534854i
$539$		0			0
$540$	−2.55337	−	2.55337i	−0.109879	−	0.109879i
$541$	3.43267	−	12.8109i	0.147582	−	0.550783i	−0.852045	−	0.523468i	$-0.824638\pi$
$541$	3.43267	−	12.8109i	0.147582	−	0.550783i	0.999627	−	0.0273145i	$-0.00869555\pi$
$542$	−6.34848	−	3.66530i	−0.272691	−	0.157438i
$543$	4.76348	+	2.75019i	0.204420	+	0.118022i
$544$	1.47680	+	0.395706i	0.0633171	+	0.0169658i
$545$	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	$0.597239\pi$
$548$	3.87788	+	1.03908i	0.165655	+	0.0443871i
$549$	0.640195	+	0.369617i	0.0273229	+	0.0157749i
$550$	34.7236	+	20.0477i	1.48062	+	0.854835i
$551$	7.74464	−	28.9034i	0.329933	−	1.23133i
$552$	−2.68607	−	2.68607i	−0.114327	−	0.114327i
$553$		0			0
$554$	0.884579	+	0.884579i	0.0375822	+	0.0375822i
$555$	8.35532	+	14.4718i	0.354664	+	0.614295i
$556$	1.46161	−	2.53158i	0.0619861	−	0.107363i
$557$	16.4161	−	4.39869i	0.695574	−	0.186379i	0.106327	−	0.994331i	$-0.466091\pi$
$557$	16.4161	−	4.39869i	0.695574	−	0.186379i	0.589247	+	0.807953i	$0.299424\pi$
$558$	14.0011	+	24.2505i	0.592712	+	1.02661i
$559$	14.9513	−	38.8656i	0.632371	−	1.64384i
$560$		0			0
$561$	−2.21283	+	2.21283i	−0.0934260	+	0.0934260i
$562$	−7.13128	−	12.3517i	−0.300815	−	0.521026i
$563$	−8.62337	+	14.9361i	−0.363432	+	0.629482i	−0.988523	−	0.151069i	$-0.951728\pi$
$563$	−8.62337	+	14.9361i	−0.363432	+	0.629482i	0.625091	+	0.780552i	$0.285062\pi$
$564$	0.452983	+	1.69056i	0.0190740	+	0.0711853i
$565$	−4.64045	+	17.3184i	−0.195225	+	0.728590i
$566$	20.7884	−	20.7884i	0.873800	−	0.873800i
$567$		0			0
$568$	1.26037			0.0528840
$569$	−13.5496	+	7.82285i	−0.568028	+	0.327951i	−0.756361	−	0.654154i	$-0.773025\pi$
$569$	−13.5496	+	7.82285i	−0.568028	+	0.327951i	0.188333	+	0.982105i	$0.439691\pi$
$570$	−4.26441	−	15.9150i	−0.178616	−	0.666605i
$571$	10.5267	+	6.07757i	0.440527	+	0.254338i	0.703821	−	0.710377i	$-0.251476\pi$
$571$	10.5267	+	6.07757i	0.440527	+	0.254338i	−0.263294	+	0.964716i	$0.584809\pi$
$572$	1.51245	+	1.10053i	0.0632387	+	0.0460153i
$573$		−	10.8858i		−	0.454760i
$574$		0			0
$575$	16.7156			0.697089
$576$	13.5421	−	7.81853i	0.564253	−	0.325772i
$577$	−37.7804	+	10.1232i	−1.57282	+	0.421435i	−0.936693	−	0.350151i	$-0.886130\pi$
$577$	−37.7804	+	10.1232i	−1.57282	+	0.421435i	−0.636125	+	0.771586i	$0.719464\pi$
$578$	5.81521	+	21.7026i	0.241881	+	0.902711i
$579$	18.3304	+	4.91161i	0.761785	+	0.204120i
$580$	−5.17130	+	5.17130i	−0.214726	+	0.214726i
$581$		0			0
$582$		−	13.8369i		−	0.573556i
$583$	−2.03558	+	7.59690i	−0.0843053	+	0.314632i
$584$	11.2140	−	19.4232i	0.464037	−	0.803736i
$585$	−31.1971	−	3.30168i	−1.28984	−	0.136508i
$586$	−11.7647	+	6.79237i	−0.485996	+	0.280590i
$587$	6.17868	+	6.17868i	0.255021	+	0.255021i	0.823026	−	0.568004i	$-0.192284\pi$
$587$	6.17868	+	6.17868i	0.255021	+	0.255021i	−0.568004	+	0.823026i	$0.692284\pi$
$588$		0			0
$589$			27.2575i			1.12313i
$590$	−1.45627	−	0.390207i	−0.0599538	−	0.0160646i
$591$	1.72176	−	0.461345i	0.0708239	−	0.0189772i
$592$	20.2755	−	5.43281i	0.833320	−	0.223287i
$593$	32.6629	+	8.75200i	1.34130	+	0.359402i	0.856918	−	0.515453i	$-0.172376\pi$
$593$	32.6629	+	8.75200i	1.34130	+	0.359402i	0.484387	+	0.874854i	$0.339043\pi$
$594$		−	17.8039i		−	0.730502i
$595$		0			0
$596$	−3.08397	−	3.08397i	−0.126324	−	0.126324i
$597$	5.11400	−	2.95257i	0.209302	−	0.120841i
$598$	8.55224	+	0.905108i	0.349727	+	0.0370126i
$599$	−5.13357	+	8.89161i	−0.209752	+	0.363301i	−0.951636	−	0.307227i	$-0.900599\pi$
$599$	−5.13357	+	8.89161i	−0.209752	+	0.363301i	0.741884	+	0.670528i	$0.233932\pi$
$600$	6.35342	−	23.7113i	0.259377	−	0.968009i
$601$		−	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
$604$	−2.60634	−	0.698368i	−0.106051	−	0.0284162i
$605$	−4.29875	−	16.0432i	−0.174769	−	0.652247i
$606$	−0.265197	+	0.0710593i	−0.0107729	+	0.00288658i
$607$	−6.28556	+	3.62897i	−0.255123	+	0.147295i	−0.622108	−	0.782932i	$-0.713723\pi$
$607$	−6.28556	+	3.62897i	−0.255123	+	0.147295i	0.366985	+	0.930227i	$0.380390\pi$
$608$	−3.59867			−0.145946
$609$		0			0
$610$		−	1.93957i		−	0.0785308i
$611$	28.9268	+	21.0484i	1.17025	+	0.851529i
$612$	0.520955	+	0.300773i	0.0210583	+	0.0121580i
$613$	5.57436	+	20.8038i	0.225146	+	0.840257i	0.982346	+	0.187073i	$0.0599002\pi$
$613$	5.57436	+	20.8038i	0.225146	+	0.840257i	−0.757200	+	0.653183i	$0.773433\pi$
$614$	−32.6012	+	18.8223i	−1.31568	+	0.759606i
$615$	−10.5332			−0.424740
$616$		0			0
$617$	−28.5301	+	28.5301i	−1.14858	+	1.14858i	−0.161748	+	0.986832i	$0.551713\pi$
$617$	−28.5301	+	28.5301i	−1.14858	+	1.14858i	−0.986832	+	0.161748i	$0.948287\pi$
$618$	−5.55294	+	20.7238i	−0.223372	+	0.833635i
$619$	8.91786	+	33.2819i	0.358439	+	1.33771i	0.876101	+	0.482128i	$0.160136\pi$
$619$	8.91786	+	33.2819i	0.358439	+	1.33771i	−0.517662	+	0.855585i	$0.673197\pi$
$620$	3.33093	−	5.76934i	0.133773	−	0.231702i
$621$	−3.71119	−	6.42797i	−0.148925	−	0.257946i
$622$	14.1348	−	14.1348i	0.566754	−	0.566754i
$623$		0			0
$624$	4.99121	−	12.9746i	0.199808	−	0.519400i
$625$	15.5266	+	26.8929i	0.621065	+	1.07572i
$626$	9.28871	−	2.48890i	0.371252	−	0.0994766i
$627$	3.68299	−	6.37912i	0.147084	−	0.254758i
$628$	−1.28243	−	2.22123i	−0.0511744	−	0.0886366i
$629$	−4.63126	−	4.63126i	−0.184660	−	0.184660i
$630$		0			0
$631$	−26.1762	−	26.1762i	−1.04206	−	1.04206i	−0.999076	−	0.0429839i	$-0.986314\pi$
$631$	−26.1762	−	26.1762i	−1.04206	−	1.04206i	−0.0429839	−	0.999076i	$-0.513686\pi$
$632$	−2.00652	+	7.48844i	−0.0798151	+	0.297874i
$633$	14.5459	+	8.39809i	0.578148	+	0.333794i
$634$	40.2062	+	23.2130i	1.59679	+	0.921907i
$635$	39.4610	+	10.5735i	1.56596	+	0.419598i
$636$	−0.533325			−0.0211477
$637$		0			0
$638$	−36.0579			−1.42755
$639$	1.01105	+	0.270911i	0.0399966	+	0.0107171i
$640$	−43.1698	−	24.9241i	−1.70644	−	0.985212i
$641$	10.1134	+	5.83896i	0.399454	+	0.230625i	0.686248	−	0.727367i	$-0.259256\pi$
$641$	10.1134	+	5.83896i	0.399454	+	0.230625i	−0.286794	+	0.957992i	$0.592590\pi$
$642$	−5.79167	+	21.6148i	−0.228579	+	0.853069i
$643$	12.8214	+	12.8214i	0.505627	+	0.505627i	0.913181	−	0.407554i	$-0.133618\pi$
$643$	12.8214	+	12.8214i	0.505627	+	0.505627i	−0.407554	+	0.913181i	$0.633618\pi$
$644$		0			0
$645$	28.3405	+	28.3405i	1.11591	+	1.11591i
$646$	3.22889	+	5.59260i	0.127039	+	0.220038i
$647$	5.73484	−	9.93304i	0.225460	−	0.390508i	−0.730997	−	0.682380i	$-0.760945\pi$
$647$	5.73484	−	9.93304i	0.225460	−	0.390508i	0.956457	+	0.291872i	$0.0942782\pi$
$648$	6.63165	−	1.77695i	0.260516	−	0.0698050i
$649$	−0.337005	−	0.583711i	−0.0132286	−	0.0229126i
$650$	22.5677	+	50.7864i	0.885178	+	1.99200i
$651$		0			0
$652$	−1.51064	+	1.51064i	−0.0591614	+	0.0591614i
$653$	4.47691	+	7.75423i	0.175195	+	0.303446i	0.940229	−	0.340544i	$-0.110611\pi$
$653$	4.47691	+	7.75423i	0.175195	+	0.303446i	−0.765034	+	0.643990i	$0.777278\pi$
$654$	−4.59922	+	7.96608i	−0.179844	+	0.311498i
$655$	17.7619	+	66.2883i	0.694014	+	2.59010i
$656$	−3.42446	+	12.7803i	−0.133703	+	0.498986i
$657$	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	$0.357453\pi$
$660$	−1.55909	+	0.900139i	−0.0606874	+	0.0350379i
$661$	0.636436	+	2.37521i	0.0247545	+	0.0923850i	0.977198	−	0.212330i	$-0.0681053\pi$
$661$	0.636436	+	2.37521i	0.0247545	+	0.0923850i	−0.952443	+	0.304715i	$0.901439\pi$
$662$	16.0753	+	9.28107i	0.624784	+	0.360719i
$663$	−4.28467	+	0.675460i	−0.166403	+	0.0262327i
$664$		−	14.5230i		−	0.563600i
$665$		0			0
$666$	15.8374			0.613688
$667$	−13.0185	+	7.51622i	−0.504077	+	0.291029i
$668$	−1.65401	+	0.443192i	−0.0639957	+	0.0171476i
$669$	0.661955	+	2.47045i	0.0255927	+	0.0955132i
$670$	−5.91294	−	1.58437i	−0.228437	−	0.0612094i
$671$	0.613137	−	0.613137i	0.0236699	−	0.0236699i
$672$		0			0
$673$		−	6.44000i		−	0.248244i	−0.992267	−	0.124122i	$-0.960389\pi$
$673$		−	6.44000i		−	0.248244i	0.992267	−	0.124122i	$-0.0396114\pi$
$674$	1.74398	−	6.50861i	0.0671755	−	0.250702i
$675$	23.9824	−	41.5387i	0.923083	−	1.59883i
$676$	0.797602	+	2.46686i	0.0306770	+	0.0948792i
$677$	4.00871	−	2.31443i	0.154067	−	0.0889507i	−0.420984	−	0.907068i	$-0.638315\pi$
$677$	4.00871	−	2.31443i	0.154067	−	0.0889507i	0.575052	+	0.818117i	$0.304982\pi$
$678$	−4.23871	−	4.23871i	−0.162787	−	0.162787i
$679$		0			0
$680$			14.2499i			0.546458i
$681$	5.60775	+	1.50259i	0.214889	+	0.0575795i
$682$	31.7268	−	8.50116i	1.21488	−	0.325526i
$683$	−17.5171	+	4.69368i	−0.670272	+	0.179599i	−0.577877	−	0.816124i	$-0.696119\pi$
$683$	−17.5171	+	4.69368i	−0.670272	+	0.179599i	−0.0923945	+	0.995722i	$0.529452\pi$
$684$	−1.36766	−	0.366464i	−0.0522939	−	0.0140121i
$685$			78.9813i			3.01772i
$686$		0			0
$687$	−0.892011	−	0.892011i	−0.0340323	−	0.0340323i
$688$	43.6002	−	25.1726i	1.66224	−	0.959697i
$689$	−8.47681	+	6.85428i	−0.322941	+	0.261127i
$690$	−4.13863	+	7.16832i	−0.157555	+	0.272893i
$691$	0.159887	−	0.596708i	0.00608240	−	0.0226998i	−0.962818	−	0.270151i	$-0.912926\pi$
$691$	0.159887	−	0.596708i	0.00608240	−	0.0226998i	0.968900	+	0.247451i	$0.0795930\pi$
$692$			0.708433i			0.0269306i
$693$		0			0
$694$	11.6747	−	11.6747i	0.443166	−	0.443166i
$695$	55.5493	+	14.8844i	2.10711	+	0.564597i
$696$	5.71366	+	21.3237i	0.216576	+	0.808271i
$697$	3.98773	−	1.06851i	0.151046	−	0.0404726i
$698$	30.3436	−	17.5189i	1.14852	−	0.663101i
$699$	7.51309			0.284171
$700$		0			0
$701$		−	14.4452i		−	0.545586i	−0.962073	−	0.272793i	$-0.912053\pi$
$701$		−	14.4452i		−	0.545586i	0.962073	−	0.272793i	$-0.0879474\pi$
$702$	14.5194	−	19.9539i	0.547998	−	0.753113i
$703$	13.3509	+	7.70815i	0.503539	+	0.290718i
$704$	−4.74725	−	17.7170i	−0.178919	−	0.667734i
$705$	−29.8188	+	17.2159i	−1.12304	+	0.648388i
$706$	9.08287			0.341838
$707$		0			0
$708$	0.0323185	−	0.0323185i	0.00121460	−	0.00121460i
$709$	0.851819	−	3.17903i	0.0319907	−	0.119391i	−0.948084	−	0.318020i	$-0.896982\pi$
$709$	0.851819	−	3.17903i	0.0319907	−	0.119391i	0.980075	+	0.198629i	$0.0636488\pi$
$710$	−0.710803	−	2.65275i	−0.0266760	−	0.0995561i
$711$	−3.21921	+	5.57583i	−0.120730	+	0.209110i
$712$	−9.87181	−	17.0985i	−0.369962	−	0.640792i
$713$	9.68268	−	9.68268i	0.362619	−	0.362619i
$714$		0			0
$715$	−13.2120	+	34.3444i	−0.494100	+	1.28441i
$716$	1.71792	+	2.97552i	0.0642016	+	0.111201i
$717$	5.61603	−	1.50481i	0.209734	−	0.0561982i
$718$	16.1290	−	27.9363i	0.601930	−	1.04257i
$719$	−24.6176	−	42.6390i	−0.918083	−	1.59017i	−0.802323	−	0.596890i	$-0.796403\pi$
$719$	−24.6176	−	42.6390i	−0.918083	−	1.59017i	−0.115760	−	0.993277i	$-0.536930\pi$
$720$	−26.8190	−	26.8190i	−0.999485	−	0.999485i
$721$		0			0
$722$	9.17662	+	9.17662i	0.341518	+	0.341518i
$723$	2.46889	−	9.21401i	0.0918188	−	0.342673i
$724$	−1.07404	−	0.620097i	−0.0399164	−	0.0230457i
$725$	−84.1277	−	48.5712i	−3.12443	−	1.80389i
$726$	5.36383	+	1.43723i	0.199070	+	0.0533408i
$727$	−34.0096			−1.26135			−0.630674	−	0.776048i	$-0.717221\pi$
$727$	−34.0096			−1.26135			−0.630674	+	0.776048i	$0.717221\pi$
$728$		0			0
$729$	−6.54406			−0.242372
$730$	−47.2050	−	12.6485i	−1.74714	−	0.468144i
$731$	−13.6042	−	7.85441i	−0.503171	−	0.290506i
$732$	0.0509216	+	0.0293996i	0.00188212	+	0.00108664i
$733$	9.70406	−	36.2160i	0.358428	−	1.33767i	−0.517688	−	0.855569i	$-0.673207\pi$
$733$	9.70406	−	36.2160i	0.358428	−	1.33767i	0.876116	−	0.482101i	$-0.160126\pi$
$734$	17.0423	+	17.0423i	0.629042	+	0.629042i
$735$		0			0
$736$	1.27836	+	1.27836i	0.0471208	+	0.0471208i
$737$	−1.36835	−	2.37005i	−0.0504038	−	0.0873020i
$738$	−4.99140	+	8.64536i	−0.183736	+	0.318240i
$739$	−4.13697	+	1.10850i	−0.152181	+	0.0407767i	−0.334105	−	0.942536i	$-0.608434\pi$
$739$	−4.13697	+	1.10850i	−0.152181	+	0.0407767i	0.181924	+	0.983313i	$0.441767\pi$
$740$	−1.88391	−	3.26302i	−0.0692538	−	0.119951i
$741$	9.33004	−	4.14595i	0.342748	−	0.152305i
$742$		0			0
$743$	−25.3436	+	25.3436i	−0.929767	+	0.929767i	−0.997691	−	0.0679234i	$-0.978363\pi$
$743$	−25.3436	+	25.3436i	−0.929767	+	0.929767i	0.0679234	+	0.997691i	$0.478363\pi$
$744$	−10.0547	−	17.4153i	−0.368623	−	0.638474i
$745$	42.9011	−	74.3069i	1.57177	−	2.72239i
$746$	−1.61814	−	6.03899i	−0.0592444	−	0.221103i
$747$	3.12164	−	11.6501i	0.114215	−	0.426256i
$748$	0.498937	−	0.498937i	0.0182429	−	0.0182429i
$749$		0			0
$750$	−27.7565			−1.01352
$751$	−39.9450	+	23.0623i	−1.45761	+	0.841554i	−0.998894	−	0.0470273i	$-0.985025\pi$
$751$	−39.9450	+	23.0623i	−1.45761	+	0.841554i	−0.458720	+	0.888581i	$0.651692\pi$
$752$	11.1941	+	41.7771i	0.408209	+	1.52346i
$753$	21.4880	+	12.4061i	0.783067	+	0.452104i
$754$	−40.4124	−	29.4058i	−1.47173	−	1.07090i
$755$		−	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	$0.747275\pi$
$758$	32.9315	−	19.0130i	1.19612	−	0.690583i
$759$	−3.57436	+	0.957747i	−0.129741	+	0.0347640i
$760$	−8.68107	−	32.3982i	−0.314896	−	1.17521i
$761$	−9.60394	−	2.57337i	−0.348142	−	0.0932845i	0.0805104	−	0.996754i	$-0.474345\pi$
$761$	−9.60394	−	2.57337i	−0.348142	−	0.0932845i	−0.428653	+	0.903469i	$0.641012\pi$
$762$	−9.65816	+	9.65816i	−0.349878	+	0.349878i
$763$		0			0
$764$			2.45446i			0.0887993i
$765$	−3.06294	+	11.4311i	−0.110741	+	0.413291i
$766$	−17.4036	+	30.1439i	−0.628818	+	1.08914i
$767$	0.0983225	−	0.929035i	0.00355022	−	0.0335455i
$768$	3.63106	−	2.09640i	0.131025	−	0.0756472i
$769$	28.4649	+	28.4649i	1.02647	+	1.02647i	0.999640	+	0.0268295i	$0.00854111\pi$
$769$	28.4649	+	28.4649i	1.02647	+	1.02647i	0.0268295	+	0.999640i	$0.491459\pi$
$770$		0			0
$771$			12.4896i			0.449803i
$772$	−4.13302	−	1.10744i	−0.148751	−	0.0398577i
$773$	24.6946	−	6.61690i	0.888203	−	0.237993i	0.214260	−	0.976777i	$-0.431266\pi$
$773$	24.6946	−	6.61690i	0.888203	−	0.237993i	0.673943	+	0.738783i	$0.264599\pi$
$774$	36.6909	−	9.83129i	1.31883	−	0.353379i
$775$	85.4739	+	22.9027i	3.07031	+	0.822688i
$776$		−	28.1677i		−	1.01116i
$777$		0			0
$778$	−20.4214	−	20.4214i	−0.732141	−	0.732141i
$779$	−8.41547	+	4.85867i	−0.301515	+	0.174080i
$780$	−2.48145	−	0.262619i	−0.0888500	−	0.00940326i
$781$	0.613891	−	1.06329i	0.0219667	−	0.0380475i
$782$	0.839661	−	3.13366i	0.0300262	−	0.112059i
$783$			43.1350i			1.54152i
$784$		0			0
$785$	35.6797	−	35.6797i	1.27346	−	1.27346i
$786$	−22.1627	−	5.93847i	−0.790516	−	0.211818i
$787$	4.69577	+	17.5248i	0.167386	+	0.624693i	0.997724	+	0.0674326i	$0.0214808\pi$
$787$	4.69577	+	17.5248i	0.167386	+	0.624693i	−0.830338	+	0.557260i	$0.811853\pi$
$788$	−0.388213	+	0.104021i	−0.0138295	+	0.00370561i
$789$	17.0993	−	9.87229i	0.608751	−	0.351463i
$790$	16.8928			0.601020
$791$		0			0
$792$		−	15.4046i		−	0.547378i
$793$	1.18721	−	0.187158i	0.0421589	−	0.00664617i
$794$	15.3597	+	8.86791i	0.545094	+	0.314710i
$795$	−2.71557	−	10.1347i	−0.0963114	−	0.359439i
$796$	−1.15307	+	0.665728i	−0.0408696	+	0.0235961i
$797$	6.98547			0.247438			0.123719	−	0.992317i	$-0.460518\pi$
$797$	6.98547			0.247438			0.123719	+	0.992317i	$0.460518\pi$
$798$		0			0
$799$	9.54256	−	9.54256i	0.337592	−	0.337592i
$800$	−3.02373	+	11.2847i	−0.106905	+	0.398975i
$801$	−4.24380	−	15.8381i	−0.149947	−	0.559611i
$802$	−6.96815	+	12.0692i	−0.246054	+	0.426178i
$803$	−10.9240	−	18.9209i	−0.385500	−	0.667706i
$804$	0.131223	−	0.131223i	0.00462789	−	0.00462789i
$805$		0			0
$806$	42.4910	+	16.3459i	1.49668	+	0.575761i
$807$	5.23181	+	9.06176i	0.184168	+	0.318989i
$808$	−0.539862	+	0.144656i	−0.0189923	+	0.00508897i
$809$	−1.00660	+	1.74348i	−0.0353902	+	0.0612976i	−0.883178	−	0.469038i	$-0.844601\pi$
$809$	−1.00660	+	1.74348i	−0.0353902	+	0.0612976i	0.847788	+	0.530336i	$0.177934\pi$
$810$	−7.48003	−	12.9558i	−0.262821	−	0.455220i
$811$	−19.2255	−	19.2255i	−0.675097	−	0.675097i	0.283790	−	0.958887i	$-0.408408\pi$
$811$	−19.2255	−	19.2255i	−0.675097	−	0.675097i	−0.958887	+	0.283790i	$0.908408\pi$
$812$		0			0
$813$	3.09147	+	3.09147i	0.108422	+	0.108422i
$814$	4.80809	−	17.9440i	0.168523	−	0.628938i
$815$	−36.3983	−	21.0146i	−1.27498	−	0.736109i
$816$	−4.54153	−	2.62206i	−0.158985	−	0.0917903i
$817$	35.7152	+	9.56987i	1.24952	+	0.334807i
$818$	−28.6294			−1.00100
$819$		0			0
$820$	2.37497			0.0829374
$821$	−9.31280	−	2.49536i	−0.325019	−	0.0870885i	0.0926203	−	0.995702i	$-0.470476\pi$
$821$	−9.31280	−	2.49536i	−0.325019	−	0.0870885i	−0.417639	+	0.908613i	$0.637142\pi$
$822$	−22.8686	−	13.2032i	−0.797635	−	0.460515i
$823$	−15.6607	−	9.04171i	−0.545898	−	0.315174i	0.201568	−	0.979475i	$-0.435396\pi$
$823$	−15.6607	−	9.04171i	−0.545898	−	0.315174i	−0.747466	+	0.664300i	$0.768730\pi$
$824$	−11.3041	+	42.1876i	−0.393798	+	1.46967i
$825$	−16.9090	−	16.9090i	−0.588697	−	0.588697i
$826$		0			0
$827$	12.8291	+	12.8291i	0.446111	+	0.446111i	0.894059	−	0.447949i	$-0.147845\pi$
$827$	12.8291	+	12.8291i	0.446111	+	0.446111i	−0.447949	+	0.894059i	$0.647845\pi$
$828$	0.355656	+	0.616014i	0.0123599	+	0.0214080i
$829$	−14.1033	+	24.4277i	−0.489829	+	0.848409i	−0.999931	−	0.0117047i	$-0.996274\pi$
$829$	−14.1033	+	24.4277i	−0.489829	+	0.848409i	0.510102	+	0.860114i	$0.329608\pi$
$830$	−30.5671	+	8.19043i	−1.06100	+	0.284294i
$831$	−0.373046	−	0.646134i	−0.0129408	−	0.0224141i
$832$	9.12795	−	23.7280i	0.316455	−	0.822621i
$833$		0			0
$834$	−13.5958	+	13.5958i	−0.470785	+	0.470785i
$835$	−16.8438	−	29.1742i	−0.582902	−	1.00962i
$836$	−0.830418	+	1.43833i	−0.0287206	+	0.0497455i
$837$	−10.1697	−	37.9537i	−0.351515	−	1.31187i
$838$	9.28767	−	34.6620i	0.320837	−	1.19738i
$839$	−7.67294	+	7.67294i	−0.264899	+	0.264899i	−0.827041	−	0.562142i	$-0.809978\pi$
$839$	−7.67294	+	7.67294i	−0.264899	+	0.264899i	0.562142	+	0.827041i	$0.309978\pi$
$840$		0			0
$841$	58.3606			2.01243
$842$	−30.8548	+	17.8140i	−1.06333	+	0.613912i
$843$	2.20158	+	8.21639i	0.0758263	+	0.282988i
$844$	−3.27973	−	1.89355i	−0.112893	−	0.0651787i
$845$	−42.8160	+	27.7174i	−1.47291	+	0.953506i
$846$			32.6326i			1.12193i
$847$		0			0
$848$	−13.1796			−0.452588
$849$	−15.1847	+	8.76689i	−0.521137	+	0.300879i
$850$	20.2503	−	5.42604i	0.694579	−	0.186112i
$851$	−2.00448	−	7.48080i	−0.0687125	−	0.256439i
$852$	0.0804200	+	0.0215485i	0.00275514	+	0.000738238i
$853$	−10.4908	+	10.4908i	−0.359198	+	0.359198i	−0.863517	−	0.504319i	$-0.831744\pi$
$853$	−10.4908	+	10.4908i	−0.359198	+	0.359198i	0.504319	+	0.863517i	$0.331744\pi$
$854$		0			0
$855$		−	27.8554i		−	0.952634i
$856$	−11.7901	+	44.0014i	−0.402979	+	1.50394i
$857$	−8.61727	+	14.9255i	−0.294360	+	0.509847i	−0.974836	−	0.222924i	$-0.928440\pi$
$857$	−8.61727	+	14.9255i	−0.294360	+	0.509847i	0.680476	+	0.732771i	$0.261773\pi$
$858$	−7.73561	−	9.56678i	−0.264090	−	0.326604i
$859$	−32.5438	+	18.7892i	−1.11038	+	0.641079i	−0.938928	−	0.344113i	$-0.888180\pi$
$859$	−32.5438	+	18.7892i	−1.11038	+	0.641079i	−0.171453	+	0.985192i	$0.554846\pi$
$860$	−6.39005	−	6.39005i	−0.217899	−	0.217899i
$861$		0			0
$862$		−	40.7133i		−	1.38670i
$863$	−1.19297	−	0.319657i	−0.0406093	−	0.0108812i	0.238457	−	0.971153i	$-0.423358\pi$
$863$	−1.19297	−	0.319657i	−0.0406093	−	0.0108812i	−0.279067	+	0.960272i	$0.590025\pi$
$864$	5.01085	−	1.34265i	0.170472	−	0.0456779i
$865$	−13.4622	+	3.60719i	−0.457729	+	0.122648i
$866$	37.2842	+	9.99026i	1.26697	+	0.339483i
$867$		−	13.4001i		−	0.455092i
$868$		0			0
$869$	5.34017	+	5.34017i	0.181153	+	0.181153i
$870$	41.6585	−	24.0515i	1.41236	−	0.815424i
$871$	0.399221	−	3.77218i	0.0135271	−	0.127815i
$872$	−9.36265	+	16.2166i	−0.317059	+	0.549163i
$873$	6.05452	−	22.5958i	0.204915	−	0.764752i
$874$			7.63614i			0.258296i
$875$		0			0
$876$	1.04760	−	1.04760i	0.0353952	−	0.0353952i
$877$	45.7327	+	12.2540i	1.54428	+	0.413789i	0.927646	−	0.373460i	$-0.121829\pi$
$877$	45.7327	+	12.2540i	1.54428	+	0.413789i	0.616636	+	0.787249i	$0.288495\pi$
$878$	1.42230	+	5.30810i	0.0480004	+	0.179140i
$879$	7.82591	−	2.09695i	0.263962	−	0.0707283i
$880$	−38.5282	+	22.2443i	−1.29879	+	0.749855i
$881$	−25.5041			−0.859255			−0.429627	−	0.903006i	$-0.641355\pi$
$881$	−25.5041			−0.859255			−0.429627	+	0.903006i	$0.641355\pi$
$882$		0			0
$883$			34.7968i			1.17101i	0.810670	+	0.585503i	$0.199103\pi$
$883$			34.7968i			1.17101i	−0.810670	+	0.585503i	$0.800897\pi$
$884$	0.966081	−	0.152299i	0.0324928	−	0.00512236i
$885$	0.778700	+	0.449582i	0.0261757	+	0.0151125i
$886$	−1.03180	−	3.85071i	−0.0346638	−	0.129367i
$887$	−39.3189	+	22.7008i	−1.32020	+	0.762217i	−0.983760	−	0.179488i	$-0.942556\pi$
$887$	−39.3189	+	22.7008i	−1.32020	+	0.762217i	−0.336439	+	0.941705i	$0.609223\pi$
$888$	−11.3735			−0.381669
$889$		0			0
$890$	−30.4205	+	30.4205i	−1.01970	+	1.01970i
$891$	1.73100	−	6.46018i	0.0579907	−	0.216424i
$892$	−0.149254	−	0.557023i	−0.00499739	−	0.0186505i
$893$	−15.8824	+	27.5091i	−0.531484	+	0.920558i
$894$	14.3434	+	24.8436i	0.479717	+	0.830894i
$895$	−47.7959	+	47.7959i	−1.59764	+	1.59764i
$896$		0			0
$897$	−4.78707	−	1.84154i	−0.159836	−	0.0614873i
$898$	25.8357	+	44.7488i	0.862149	+	1.49329i
$899$	−76.8671	+	20.5965i	−2.56366	+	0.686931i
$900$	−2.29831	+	3.98080i	−0.0766105	+	0.132693i
$901$	2.05616	+	3.56137i	0.0685005	+	0.118646i
$902$	8.27996	+	8.27996i	0.275693	+	0.275693i
$903$		0			0
$904$	−8.62877	−	8.62877i	−0.286989	−	0.286989i
$905$	6.31480	−	23.5671i	0.209911	−	0.783398i
$906$	15.3701	+	8.87394i	0.510638	+	0.294817i
$907$	−0.0976763	−	0.0563935i	−0.00324329	−	0.00187251i	0.498377	−	0.866960i	$-0.333929\pi$
$907$	−0.0976763	−	0.0563935i	−0.00324329	−	0.00187251i	−0.501621	+	0.865088i	$0.667263\pi$
$908$	−1.26440	−	0.338796i	−0.0419607	−	0.0112433i
$909$	−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	$0.503200\pi$
$912$	11.9229	+	3.19473i	0.394807	+	0.105788i
$913$	−12.2521	−	7.07372i	−0.405484	−	0.234106i
$914$	−8.75571	−	5.05511i	−0.289613	−	0.167208i
$915$	−0.299393	+	1.11735i	−0.00989762	+	0.0369384i
$916$	0.201125	+	0.201125i	0.00664536	+	0.00664536i
$917$		0			0
$918$	−6.58253	−	6.58253i	−0.217256	−	0.217256i
$919$	−24.4824	−	42.4048i	−0.807600	−	1.39880i	−0.914522	−	0.404536i	$-0.867433\pi$
$919$	−24.4824	−	42.4048i	−0.807600	−	1.39880i	0.106922	−	0.994267i	$-0.465900\pi$
$920$	−8.42503	+	14.5926i	−0.277765	+	0.481103i
$921$	21.6863	−	5.81084i	0.714589	−	0.191474i
$922$	−5.31022	−	9.19757i	−0.174883	−	0.302906i
$923$	1.55516	−	0.691058i	0.0511886	−	0.0227465i
$924$		0			0
$925$	35.3890	−	35.3890i	1.16358	−	1.16358i
$926$	−15.5409	−	26.9176i	−0.510706	−	0.884568i
$927$	−18.1361	+	31.4126i	−0.595666	+	1.03172i
$928$	−2.71925	−	10.1484i	−0.0892638	−	0.333137i
$929$	−4.07062	+	15.1918i	−0.133553	+	0.498426i	−1.00000		0.000843401i	$-0.999732\pi$
$929$	−4.07062	+	15.1918i	−0.133553	+	0.498426i	0.866447	+	0.499269i	$0.166398\pi$
$930$	−30.9841	+	30.9841i	−1.01601	+	1.01601i
$931$		0			0
$932$	−1.69401			−0.0554890
$933$	−10.3247	+	5.96094i	−0.338014	+	0.195152i
$934$	0.175229	+	0.653962i	0.00573366	+	0.0213983i
$935$	12.0217	+	6.94071i	0.393150	+	0.226985i
$936$	12.5627	−	17.2649i	0.410624	−	0.564320i
$937$			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
$940$	6.72336	−	3.88173i	0.219292	−	0.126608i
$941$	−27.5932	+	7.39357i	−0.899512	+	0.241023i	−0.678807	−	0.734317i	$-0.737502\pi$
$941$	−27.5932	+	7.39357i	−0.899512	+	0.241023i	−0.220705	+	0.975341i	$0.570836\pi$
$942$	4.36634	+	16.2954i	0.142263	+	0.530933i
$943$	4.71537	+	1.26348i	0.153554	+	0.0411446i
$944$	0.798656	−	0.798656i	0.0259940	−	0.0259940i
$945$		0			0
$946$		−	44.5559i		−	1.44864i
$947$	−0.196990	+	0.735176i	−0.00640131	+	0.0238900i	−0.969053	−	0.246854i	$-0.920603\pi$
$947$	−0.196990	+	0.735176i	−0.00640131	+	0.0238900i	0.962651	+	0.270744i	$0.0872698\pi$
$948$	−0.256059	+	0.443506i	−0.00831640	+	0.0144044i
$949$	3.18712	−	30.1146i	0.103458	−	0.977562i
$950$	−42.7350	+	24.6731i	−1.38651	+	0.800500i
$951$	−19.5788	−	19.5788i	−0.634887	−	0.634887i
$952$		0			0
$953$			7.93535i			0.257051i	0.991706	+	0.128526i	$0.0410244\pi$
$953$			7.93535i			0.257051i	−0.991706	+	0.128526i	$0.958976\pi$
$954$	−9.60507	−	2.57367i	−0.310976	−	0.0833257i
$955$	−46.6416	+	12.4976i	−1.50929	+	0.404412i
$956$	−1.26627	+	0.339296i	−0.0409540	+	0.0109736i
$957$	20.7723	+	5.56592i	0.671473	+	0.179921i
$958$		−	48.7364i		−	1.57460i
$959$		0			0
$960$	17.3023	+	17.3023i	0.558429	+	0.558429i
$961$	35.9314	−	20.7450i	1.15908	−	0.669194i
$962$	20.0224	−	16.1899i	0.645547	−	0.521984i
$963$	−18.9158	+	32.7631i	−0.609553	+	1.05578i
$964$	−0.556670	+	2.07752i	−0.0179291	+	0.0669124i
$965$		−	84.1778i		−	2.70978i
$966$		0			0
$967$	−1.26298	+	1.26298i	−0.0406147	+	0.0406147i	−0.727122	−	0.686508i	$-0.759143\pi$
$967$	−1.26298	+	1.26298i	−0.0406147	+	0.0406147i	0.686508	+	0.727122i	$0.259143\pi$
$968$	10.9192	+	2.92578i	0.350956	+	0.0940383i
$969$	−0.996826	−	3.72021i	−0.0320227	−	0.119510i
$970$	−59.2858	+	15.8856i	−1.90355	+	0.510055i
$971$	0.300693	−	0.173605i	0.00964970	−	0.00557126i	−0.495167	−	0.868798i	$-0.664893\pi$
$971$	0.300693	−	0.173605i	0.00964970	−	0.00557126i	0.504817	+	0.863226i	$0.331560\pi$
$972$	3.21464			0.103110
$973$		0			0
$974$			17.1431i			0.549299i
$975$	−5.16142	−	32.7406i	−0.165298	−	1.04854i
$976$	1.25838	+	0.726525i	0.0402797	+	0.0232555i
$977$	−2.88386	−	10.7627i	−0.0922627	−	0.344329i	0.904328	−	0.426839i	$-0.140373\pi$
$977$	−2.88386	−	10.7627i	−0.0922627	−	0.344329i	−0.996590	+	0.0825101i	$0.973706\pi$
$978$	12.1693	−	7.02596i	0.389132	−	0.224666i
$979$	−19.2331			−0.614693
$980$		0			0
$981$	−10.9963	+	10.9963i	−0.351084	+	0.351084i
$982$	0.363354	−	1.35606i	0.0115951	−	0.0432735i
$983$	8.67608	+	32.3796i	0.276724	+	1.03275i	0.954677	+	0.297643i	$0.0962006\pi$
$983$	8.67608	+	32.3796i	0.276724	+	1.03275i	−0.677953	+	0.735105i	$0.737133\pi$
$984$	3.58452	−	6.20857i	0.114270	−	0.197922i
$985$	−3.95339	−	6.84747i	−0.125965	−	0.218178i
$986$	−13.3315	+	13.3315i	−0.424561	+	0.424561i
$987$		0			0
$988$	−2.10368	+	0.934803i	−0.0669270	+	0.0297400i
$989$	−9.28761	−	16.0866i	−0.295329	−	0.511525i
$990$	−32.4227	+	8.68762i	−1.03046	+	0.276111i
$991$	−17.8999	+	31.0035i	−0.568608	+	0.984858i	0.428096	+	0.903733i	$0.359184\pi$
$991$	−17.8999	+	31.0035i	−0.568608	+	0.984858i	−0.996704	+	0.0811244i	$0.974149\pi$
$992$	4.78525	+	8.28829i	0.151932	+	0.263154i
$993$	−7.82804	−	7.82804i	−0.248415	−	0.248415i
$994$		0			0
$995$	−18.5219	−	18.5219i	−0.587183	−	0.587183i
$996$	0.248298	−	0.926661i	0.00786763	−	0.0293624i
$997$	53.9761	+	31.1631i	1.70944	+	0.986946i	0.935247	+	0.353996i	$0.115177\pi$
$997$	53.9761	+	31.1631i	1.70944	+	0.986946i	0.774193	+	0.632949i	$0.218156\pi$
$998$	−28.2457	−	16.3077i	−0.894102	−	0.516210i
$999$	−21.4659	−	5.75176i	−0.679150	−	0.181978i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.i.b.489.9	✓	56	91.73	even	12
637.2.i.b.489.10	yes	56	91.60	odd	12
637.2.i.b.538.9	yes	56	7.3	odd	6
637.2.i.b.538.10	yes	56	7.4	even	3
637.2.bc.c.31.19		112	1.1	even	1	trivial
637.2.bc.c.31.20		112	7.6	odd	2	inner
637.2.bc.c.411.19		112	91.47	even	12	inner
637.2.bc.c.411.20		112	91.86	odd	12	inner
637.2.bc.c.460.9		112	7.5	odd	6	inner
637.2.bc.c.460.10		112	7.2	even	3	inner
637.2.bc.c.619.9		112	13.8	odd	4	inner
637.2.bc.c.619.10		112	91.34	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bc (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.43251 + 0.383841i) q^{2} +(-0.765995 - 0.442247i) q^{3} +(0.172712 + 0.0997153i) q^{4} +(-1.01546 + 3.78973i) q^{5} +(-0.927546 - 0.927546i) q^{6} +(-1.88821 - 1.88821i) q^{8} +(-1.10883 - 1.92056i) q^{9} +(-2.90931 + 5.03907i) q^{10} +(-2.51265 + 0.673262i) q^{11} +(-0.0881976 - 0.152763i) q^{12} +(-3.36514 - 1.29454i) q^{13} +(2.45383 - 2.45383i) q^{15} +(-2.17954 - 3.77508i) q^{16} +(-0.680066 + 1.17791i) q^{17} +(-0.851232 - 3.17684i) q^{18} +(0.828597 - 3.09237i) q^{19} +(-0.553276 + 0.553276i) q^{20} -3.85783 q^{22} +(-1.39284 + 0.804158i) q^{23} +(0.611303 + 2.28141i) q^{24} +(-9.00081 - 5.19662i) q^{25} +(-4.32371 - 3.14612i) q^{26} +4.61500i q^{27} +9.34669 q^{29} +(4.45703 - 2.57327i) q^{30} +(-8.22399 + 2.20361i) q^{31} +(-0.290932 - 1.08577i) q^{32} +(2.22242 + 0.595497i) q^{33} +(-1.42633 + 1.42633i) q^{34} -0.442271i q^{36} +(-1.24632 + 4.65133i) q^{37} +(2.37395 - 4.11181i) q^{38} +(2.00517 + 2.47983i) q^{39} +(9.07320 - 5.23842i) q^{40} +(-2.14628 - 2.14628i) q^{41} +11.5495i q^{43} +(-0.501099 - 0.134269i) q^{44} +(8.40438 - 2.25195i) q^{45} +(-2.30394 + 0.617338i) q^{46} +(-9.58391 - 2.56800i) q^{47} +3.85559i q^{48} +(-10.8991 - 10.8991i) q^{50} +(1.04185 - 0.601515i) q^{51} +(-0.452114 - 0.559138i) q^{52} +(1.51173 - 2.61840i) q^{53} +(-1.77143 + 6.61105i) q^{54} -10.2059i q^{55} +(-2.00229 + 2.00229i) q^{57} +(13.3893 + 3.58764i) q^{58} +(0.0670618 + 0.250278i) q^{59} +(0.668491 - 0.179122i) q^{60} +(-0.288679 + 0.166669i) q^{61} -12.6268 q^{62} +7.05112i q^{64} +(8.32311 - 11.4384i) q^{65} +(2.95508 + 1.70611i) q^{66} +(0.272292 + 1.01621i) q^{67} +(-0.234911 + 0.135626i) q^{68} +1.42255 q^{69} +(-0.333748 + 0.333748i) q^{71} +(-1.53270 + 5.72013i) q^{72} +(2.17380 + 8.11275i) q^{73} +(-3.57074 + 6.18470i) q^{74} +(4.59638 + 7.96117i) q^{75} +(0.451465 - 0.451465i) q^{76} +(1.92058 + 4.32207i) q^{78} +(-1.45162 - 2.51428i) q^{79} +(16.5198 - 4.42646i) q^{80} +(-1.28553 + 2.22661i) q^{81} +(-2.25074 - 3.89840i) q^{82} +(3.84570 + 3.84570i) q^{83} +(-3.77338 - 3.77338i) q^{85} +(-4.43317 + 16.5448i) q^{86} +(-7.15951 - 4.13355i) q^{87} +(6.01566 + 3.47314i) q^{88} +(7.14176 + 1.91363i) q^{89} +12.9038 q^{90} -0.320747 q^{92} +(7.27408 + 1.94908i) q^{93} +(-12.7434 - 7.35740i) q^{94} +(10.8778 + 6.28033i) q^{95} +(-0.257328 + 0.960361i) q^{96} +(7.45885 + 7.45885i) q^{97} +(4.07915 + 4.07915i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 56 q^{9} + 16 q^{11} + 96 q^{15} + 56 q^{16} + 32 q^{18} - 96 q^{29} + 32 q^{39} + 64 q^{44} - 32 q^{46} - 80 q^{50} + 16 q^{53} - 192 q^{57} - 72 q^{58} + 64 q^{60} - 32 q^{65} + 64 q^{71} - 208 q^{72}+ \cdots - 64 q^{93}+O(q^{100}) \) 112 * q + 56 * q^9 + 16 * q^11 + 96 * q^15 + 56 * q^16 + 32 * q^18 - 96 * q^29 + 32 * q^39 + 64 * q^44 - 32 * q^46 - 80 * q^50 + 16 * q^53 - 192 * q^57 - 72 * q^58 + 64 * q^60 - 32 * q^65 + 64 * q^71 - 208 * q^72 - 208 * q^74 + 320 * q^78 + 80 * q^79 - 152 * q^81 + 48 * q^85 - 64 * q^86 - 256 * q^92 - 64 * q^93

Introduction

L-functions

Modular forms

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