LMFDB - Embedded newform 637.2.q.j.491.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(491,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("637.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.q (of order $6$, 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:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			491.12
Character	$\chi$	$=$	637.491
Dual form			637.2.q.j.589.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900699 - 0.520019i) q^{2} +(0.384681 + 0.666288i) q^{3} +(-0.459161 + 0.795291i) q^{4} +1.67669i q^{5} +(0.692964 + 0.400083i) q^{6} +3.03516i q^{8} +(1.20404 - 2.08546i) q^{9} +O(q^{10})$	\(q+(0.900699 - 0.520019i) q^{2} +(0.384681 + 0.666288i) q^{3} +(-0.459161 + 0.795291i) q^{4} +1.67669i q^{5} +(0.692964 + 0.400083i) q^{6} +3.03516i q^{8} +(1.20404 - 2.08546i) q^{9} +(0.871910 + 1.51019i) q^{10} +(-0.465414 + 0.268707i) q^{11} -0.706523 q^{12} +(-1.96370 + 3.02389i) q^{13} +(-1.11716 + 0.644991i) q^{15} +(0.660019 + 1.14319i) q^{16} +(-2.81443 + 4.87473i) q^{17} -2.50449i q^{18} +(1.74449 + 1.00718i) q^{19} +(-1.33346 - 0.769871i) q^{20} +(-0.279465 + 0.484048i) q^{22} +(-3.33781 - 5.78125i) q^{23} +(-2.02229 + 1.16757i) q^{24} +2.18871 q^{25} +(-0.196223 + 3.74477i) q^{26} +4.16078 q^{27} +(2.43711 + 4.22119i) q^{29} +(-0.670815 + 1.16189i) q^{30} +3.78899i q^{31} +(-4.06810 - 2.34872i) q^{32} +(-0.358072 - 0.206733i) q^{33} +5.85422i q^{34} +(1.10570 + 1.91512i) q^{36} +(-1.19678 + 0.690961i) q^{37} +2.09501 q^{38} +(-2.77018 - 0.145155i) q^{39} -5.08903 q^{40} +(-1.07523 + 0.620782i) q^{41} +(-1.63377 + 2.82976i) q^{43} -0.493519i q^{44} +(3.49667 + 2.01880i) q^{45} +(-6.01271 - 3.47144i) q^{46} -3.79963i q^{47} +(-0.507794 + 0.879525i) q^{48} +(1.97137 - 1.13817i) q^{50} -4.33063 q^{51} +(-1.50322 - 2.95016i) q^{52} +13.4665 q^{53} +(3.74760 - 2.16368i) q^{54} +(-0.450538 - 0.780355i) q^{55} +1.54978i q^{57} +(4.39020 + 2.53468i) q^{58} +(6.99419 + 4.03810i) q^{59} -1.18462i q^{60} +(1.88912 - 3.27205i) q^{61} +(1.97034 + 3.41274i) q^{62} -7.52559 q^{64} +(-5.07012 - 3.29251i) q^{65} -0.430020 q^{66} +(8.31170 - 4.79876i) q^{67} +(-2.58455 - 4.47658i) q^{68} +(2.56798 - 4.44788i) q^{69} +(1.31706 + 0.760403i) q^{71} +(6.32971 + 3.65446i) q^{72} -15.6451i q^{73} +(-0.718625 + 1.24470i) q^{74} +(0.841957 + 1.45831i) q^{75} +(-1.60200 + 0.924918i) q^{76} +(-2.57058 + 1.30980i) q^{78} +8.26567 q^{79} +(-1.91677 + 1.10665i) q^{80} +(-2.01155 - 3.48410i) q^{81} +(-0.645636 + 1.11827i) q^{82} -9.42392i q^{83} +(-8.17341 - 4.71892i) q^{85} +3.39835i q^{86} +(-1.87502 + 3.24763i) q^{87} +(-0.815570 - 1.41261i) q^{88} +(-1.85300 + 1.06983i) q^{89} +4.19926 q^{90} +6.13037 q^{92} +(-2.52456 + 1.45755i) q^{93} +(-1.97588 - 3.42232i) q^{94} +(-1.68873 + 2.92497i) q^{95} -3.61403i q^{96} +(-5.58111 - 3.22225i) q^{97} +1.29414i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) $ 32 * q + 20 * q^4 - 28 * q^9	$ 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) $ 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.900699	−	0.520019i	0.636890	−	0.367709i	−0.146525	−	0.989207i	$-0.546809\pi$
$2$	0.900699	−	0.520019i	0.636890	−	0.367709i	0.783416	+	0.621498i	$0.213476\pi$
$3$	0.384681	+	0.666288i	0.222096	+	0.384681i	0.955444	−	0.295172i	$-0.0953769\pi$
$3$	0.384681	+	0.666288i	0.222096	+	0.384681i	−0.733348	+	0.679853i	$0.762044\pi$
$4$	−0.459161	+	0.795291i	−0.229581	+	0.397645i
$5$			1.67669i			0.749838i	0.927057	+	0.374919i	$0.122330\pi$
$5$			1.67669i			0.749838i	−0.927057	+	0.374919i	$0.877670\pi$
$6$	0.692964	+	0.400083i	0.282901	+	0.163333i
$7$		0			0
$7$		0			0
$8$			3.03516i			1.07309i
$9$	1.20404	−	2.08546i	0.401347	−	0.695153i
$10$	0.871910	+	1.51019i	0.275722	+	0.477565i
$11$	−0.465414	+	0.268707i	−0.140328	+	0.0810182i	−0.568520	−	0.822669i	$-0.692484\pi$
$11$	−0.465414	+	0.268707i	−0.140328	+	0.0810182i	0.428193	+	0.903688i	$0.359151\pi$
$12$	−0.706523			−0.203956
$13$	−1.96370	+	3.02389i	−0.544632	+	0.838675i
$13$	−1.96370	+	3.02389i	−0.544632	+	0.838675i
$14$		0			0
$15$	−1.11716	+	0.644991i	−0.288449	+	0.166536i
$16$	0.660019	+	1.14319i	0.165005	+	0.285797i
$17$	−2.81443	+	4.87473i	−0.682599	+	1.18230i	0.291586	+	0.956545i	$0.405817\pi$
$17$	−2.81443	+	4.87473i	−0.682599	+	1.18230i	−0.974185	+	0.225751i	$0.927516\pi$
$18$		−	2.50449i		−	0.590315i
$19$	1.74449	+	1.00718i	0.400213	+	0.231063i	0.686576	−	0.727058i	$-0.259113\pi$
$19$	1.74449	+	1.00718i	0.400213	+	0.231063i	−0.286363	+	0.958121i	$0.592446\pi$
$20$	−1.33346	−	0.769871i	−0.298170	−	0.172148i
$21$		0			0
$22$	−0.279465	+	0.484048i	−0.0595822	+	0.103199i
$23$	−3.33781	−	5.78125i	−0.695981	−	1.20547i	−0.969849	−	0.243707i	$-0.921637\pi$
$23$	−3.33781	−	5.78125i	−0.695981	−	1.20547i	0.273868	−	0.961767i	$-0.411697\pi$
$24$	−2.02229	+	1.16757i	−0.412799	+	0.238329i
$25$	2.18871			0.437742
$26$	−0.196223	+	3.74477i	−0.0384824	+	0.734410i
$27$	4.16078			0.800742
$28$		0			0
$29$	2.43711	+	4.22119i	0.452559	+	0.783856i	0.998544	−	0.0539391i	$-0.0171777\pi$
$29$	2.43711	+	4.22119i	0.452559	+	0.783856i	−0.545985	+	0.837795i	$0.683844\pi$
$30$	−0.670815	+	1.16189i	−0.122473	+	0.212130i
$31$			3.78899i			0.680523i	0.940331	+	0.340261i	$0.110516\pi$
$31$			3.78899i			0.680523i	−0.940331	+	0.340261i	$0.889484\pi$
$32$	−4.06810	−	2.34872i	−0.719146	−	0.415199i
$33$	−0.358072	−	0.206733i	−0.0623324	−	0.0359876i
$34$			5.85422i			1.00399i
$35$		0			0
$36$	1.10570	+	1.91512i	0.184283	+	0.319187i
$37$	−1.19678	+	0.690961i	−0.196749	+	0.113593i	−0.595138	−	0.803623i	$-0.702903\pi$
$37$	−1.19678	+	0.690961i	−0.196749	+	0.113593i	0.398389	+	0.917217i	$0.369569\pi$
$38$	2.09501			0.339856
$39$	−2.77018	−	0.145155i	−0.443583	−	0.0232434i
$40$	−5.08903			−0.804646
$41$	−1.07523	+	0.620782i	−0.167922	+	0.0969498i	−0.581606	−	0.813471i	$-0.697575\pi$
$41$	−1.07523	+	0.620782i	−0.167922	+	0.0969498i	0.413684	+	0.910421i	$0.364242\pi$
$42$		0			0
$43$	−1.63377	+	2.82976i	−0.249147	+	0.431535i	−0.963289	−	0.268465i	$-0.913484\pi$
$43$	−1.63377	+	2.82976i	−0.249147	+	0.431535i	0.714142	+	0.700000i	$0.246817\pi$
$44$		−	0.493519i		−	0.0744008i
$45$	3.49667	+	2.01880i	0.521253	+	0.300945i
$46$	−6.01271	−	3.47144i	−0.886526	−	0.511836i
$47$		−	3.79963i		−	0.554232i	−0.960836	−	0.277116i	$-0.910621\pi$
$47$		−	3.79963i		−	0.554232i	0.960836	−	0.277116i	$-0.0893787\pi$
$48$	−0.507794	+	0.879525i	−0.0732937	+	0.126948i
$49$		0			0
$50$	1.97137	−	1.13817i	0.278794	−	0.160962i
$51$	−4.33063			−0.606409
$52$	−1.50322	−	2.95016i	−0.208458	−	0.409114i
$53$	13.4665			1.84977			0.924886	−	0.380246i	$-0.124161\pi$
$53$	13.4665			1.84977			0.924886	+	0.380246i	$0.124161\pi$
$54$	3.74760	−	2.16368i	0.509984	−	0.294440i
$55$	−0.450538	−	0.780355i	−0.0607505	−	0.105223i
$56$		0			0
$57$			1.54978i			0.205273i
$58$	4.39020	+	2.53468i	0.576461	+	0.332820i
$59$	6.99419	+	4.03810i	0.910566	+	0.525715i	0.880613	−	0.473836i	$-0.157131\pi$
$59$	6.99419	+	4.03810i	0.910566	+	0.525715i	0.0299525	+	0.999551i	$0.490464\pi$
$60$		−	1.18462i		−	0.152934i
$61$	1.88912	−	3.27205i	0.241877	−	0.418944i	−0.719372	−	0.694625i	$-0.755570\pi$
$61$	1.88912	−	3.27205i	0.241877	−	0.418944i	0.961249	+	0.275682i	$0.0889036\pi$
$62$	1.97034	+	3.41274i	0.250234	+	0.433418i
$63$		0			0
$64$	−7.52559			−0.940698
$65$	−5.07012	−	3.29251i	−0.628871	−	0.408386i
$66$	−0.430020			−0.0529318
$67$	8.31170	−	4.79876i	1.01544	−	0.586262i	0.102657	−	0.994717i	$-0.467266\pi$
$67$	8.31170	−	4.79876i	1.01544	−	0.586262i	0.912779	+	0.408455i	$0.133932\pi$
$68$	−2.58455	−	4.47658i	−0.313423	−	0.542865i
$69$	2.56798	−	4.44788i	0.309149	−	0.535462i
$70$		0			0
$71$	1.31706	+	0.760403i	0.156306	+	0.0902433i	0.576113	−	0.817370i	$-0.304569\pi$
$71$	1.31706	+	0.760403i	0.156306	+	0.0902433i	−0.419807	+	0.907613i	$0.637902\pi$
$72$	6.32971	+	3.65446i	0.745964	+	0.430682i
$73$		−	15.6451i		−	1.83112i	−0.402181	−	0.915560i	$-0.631748\pi$
$73$		−	15.6451i		−	1.83112i	0.402181	−	0.915560i	$-0.368252\pi$
$74$	−0.718625	+	1.24470i	−0.0835385	+	0.144693i
$75$	0.841957	+	1.45831i	0.0972208	+	0.168391i
$76$	−1.60200	+	0.924918i	−0.183763	+	0.106095i
$77$		0			0
$78$	−2.57058	+	1.30980i	−0.291061	+	0.148306i
$79$	8.26567			0.929961			0.464980	−	0.885321i	$-0.346061\pi$
$79$	8.26567			0.929961			0.464980	+	0.885321i	$0.346061\pi$
$80$	−1.91677	+	1.10665i	−0.214301	+	0.123727i
$81$	−2.01155	−	3.48410i	−0.223505	−	0.387123i
$82$	−0.645636	+	1.11827i	−0.0712986	+	0.123493i
$83$		−	9.42392i		−	1.03441i	−0.855862	−	0.517205i	$-0.826973\pi$
$83$		−	9.42392i		−	1.03441i	0.855862	−	0.517205i	$-0.173027\pi$
$84$		0			0
$85$	−8.17341	−	4.71892i	−0.886531	−	0.511839i
$86$			3.39835i			0.366454i
$87$	−1.87502	+	3.24763i	−0.201023	+	0.348182i
$88$	−0.815570	−	1.41261i	−0.0869400	−	0.150585i
$89$	−1.85300	+	1.06983i	−0.196418	+	0.113402i	−0.594984	−	0.803738i	$-0.702841\pi$
$89$	−1.85300	+	1.06983i	−0.196418	+	0.113402i	0.398566	+	0.917140i	$0.369508\pi$
$90$	4.19926			0.442641
$91$		0			0
$92$	6.13037			0.639135
$93$	−2.52456	+	1.45755i	−0.261784	+	0.151141i
$94$	−1.97588	−	3.42232i	−0.203796	−	0.352985i
$95$	−1.68873	+	2.92497i	−0.173260	+	0.300095i
$96$		−	3.61403i		−	0.368856i
$97$	−5.58111	−	3.22225i	−0.566676	−	0.327170i	0.189145	−	0.981949i	$-0.439428\pi$
$97$	−5.58111	−	3.22225i	−0.566676	−	0.327170i	−0.755821	+	0.654779i	$0.772762\pi$
$98$		0			0
$99$			1.29414i			0.130066i
$100$	−1.00497	+	1.74066i	−0.100497	+	0.174066i
$101$	−3.69473	−	6.39945i	−0.367639	−	0.636770i	0.621557	−	0.783369i	$-0.286500\pi$
$101$	−3.69473	−	6.39945i	−0.367639	−	0.636770i	−0.989196	+	0.146599i	$0.953167\pi$
$102$	−3.90059	+	2.25201i	−0.386216	+	0.222982i
$103$	17.5253			1.72682			0.863411	−	0.504502i	$-0.168324\pi$
$103$	17.5253			1.72682			0.863411	+	0.504502i	$0.168324\pi$
$104$	−9.17799	−	5.96015i	−0.899976	−	0.584440i
$105$		0			0
$106$	12.1293	−	7.00285i	1.17810	−	0.680177i
$107$	−2.51154	−	4.35012i	−0.242800	−	0.420542i	0.718711	−	0.695309i	$-0.244733\pi$
$107$	−2.51154	−	4.35012i	−0.242800	−	0.420542i	−0.961511	+	0.274767i	$0.911399\pi$
$108$	−1.91047	+	3.30903i	−0.183835	+	0.318411i
$109$			17.8660i			1.71125i	0.517595	+	0.855626i	$0.326827\pi$
$109$			17.8660i			1.71125i	−0.517595	+	0.855626i	$0.673173\pi$
$110$	−0.811598	−	0.468576i	−0.0773828	−	0.0446770i
$111$	−0.920758	−	0.531600i	−0.0873945	−	0.0504572i
$112$		0			0
$113$	3.78753	−	6.56020i	0.356301	−	0.617131i	−0.631039	−	0.775751i	$-0.717371\pi$
$113$	3.78753	−	6.56020i	0.356301	−	0.617131i	0.987340	+	0.158620i	$0.0507044\pi$
$114$	0.805912	+	1.39588i	0.0754806	+	0.130736i
$115$	9.69336	−	5.59646i	0.903911	−	0.521873i
$116$	−4.47610			−0.415596
$117$	3.94182	+	7.73609i	0.364421	+	0.715202i
$118$	8.39954			0.773240
$119$		0			0
$120$	−1.95765	−	3.39076i	−0.178709	−	0.309532i
$121$	−5.35559	+	9.27616i	−0.486872	+	0.843287i
$122$		−	3.92951i		−	0.355761i
$123$	−0.827238	−	0.477606i	−0.0745896	−	0.0430643i
$124$	−3.01335	−	1.73976i	−0.270607	−	0.156235i
$125$			12.0532i			1.07807i
$126$		0			0
$127$	−5.33604	−	9.24230i	−0.473497	−	0.820121i	0.526042	−	0.850458i	$-0.323675\pi$
$127$	−5.33604	−	9.24230i	−0.473497	−	0.820121i	−0.999540	+	0.0303370i	$0.990342\pi$
$128$	1.35792	−	0.783994i	0.120024	−	0.0692960i
$129$	−2.51392			−0.221338
$130$	−6.27882	−	0.329005i	−0.550689	−	0.0288556i
$131$	−9.01437			−0.787589			−0.393794	−	0.919199i	$-0.628838\pi$
$131$	−9.01437			−0.787589			−0.393794	+	0.919199i	$0.628838\pi$
$132$	0.328826	−	0.189848i	0.0286206	−	0.0165241i
$133$		0			0
$134$	4.99089	−	8.64448i	0.431147	−	0.746769i
$135$			6.97633i			0.600427i
$136$	−14.7956	−	8.54225i	−1.26871	−	0.732492i
$137$	3.57625	+	2.06475i	0.305540	+	0.176404i	0.644929	−	0.764243i	$-0.276887\pi$
$137$	3.57625	+	2.06475i	0.305540	+	0.176404i	−0.339389	+	0.940646i	$0.610220\pi$
$138$		−	5.34160i		−	0.454707i
$139$	9.85576	−	17.0707i	0.835955	−	1.44792i	−0.0572961	−	0.998357i	$-0.518248\pi$
$139$	9.85576	−	17.0707i	0.835955	−	1.44792i	0.893251	−	0.449559i	$-0.148419\pi$
$140$		0			0
$141$	2.53164	−	1.46164i	0.213203	−	0.123093i
$142$	1.58170			0.132733
$143$	0.101393	−	1.93502i	0.00847893	−	0.161814i
$144$	3.17876			0.264897
$145$	−7.07763	+	4.08627i	−0.587765	+	0.339346i
$146$	−8.13574	−	14.0915i	−0.673319	−	1.16622i
$147$		0			0
$148$		−	1.26905i		−	0.104315i
$149$	−12.8068	−	7.39400i	−1.04917	−	0.605740i	−0.126755	−	0.991934i	$-0.540456\pi$
$149$	−12.8068	−	7.39400i	−1.04917	−	0.605740i	−0.922418	+	0.386194i	$0.873789\pi$
$150$	1.51670	+	0.875666i	0.123838	+	0.0714978i
$151$			16.1538i			1.31458i	0.753639	+	0.657289i	$0.228297\pi$
$151$			16.1538i			1.31458i	−0.753639	+	0.657289i	$0.771703\pi$
$152$	−3.05696	+	5.29481i	−0.247952	+	0.429466i
$153$	6.77737	+	11.7387i	0.547918	+	0.949021i
$154$		0			0
$155$	−6.35296			−0.510282
$156$	1.38740	−	2.13645i	0.111081	−	0.171053i
$157$	2.91745			0.232838			0.116419	−	0.993200i	$-0.462859\pi$
$157$	2.91745			0.232838			0.116419	+	0.993200i	$0.462859\pi$
$158$	7.44488	−	4.29830i	0.592283	−	0.341955i
$159$	5.18033	+	8.97259i	0.410827	+	0.711572i
$160$	3.93807	−	6.82094i	0.311332	−	0.539243i
$161$		0			0
$162$	−3.62360	−	2.09209i	−0.284697	−	0.164370i
$163$	14.5833	+	8.41966i	1.14225	+	0.659479i	0.946987	−	0.321272i	$-0.104110\pi$
$163$	14.5833	+	8.41966i	1.14225	+	0.659479i	0.195264	+	0.980751i	$0.437444\pi$
$164$		−	1.14016i		−	0.0890312i
$165$	0.346627	−	0.600376i	0.0269849	−	0.0467392i
$166$	−4.90061	−	8.48811i	−0.380361	−	0.658805i
$167$	−21.5414	+	12.4369i	−1.66692	+	0.962399i	−0.697643	+	0.716446i	$0.745768\pi$
$167$	−21.5414	+	12.4369i	−1.66692	+	0.962399i	−0.969282	+	0.245953i	$0.920899\pi$
$168$		0			0
$169$	−5.28778	−	11.8760i	−0.406752	−	0.913538i
$170$	−9.81571			−0.752830
$171$	4.20087	−	2.42537i	0.321249	−	0.185473i
$172$	−1.50032	−	2.59864i	−0.114399	−	0.198144i
$173$	0.0777653	−	0.134694i	0.00591239	−	0.0102406i	−0.863054	−	0.505112i	$-0.831451\pi$
$173$	0.0777653	−	0.134694i	0.00591239	−	0.0102406i	0.868966	+	0.494871i	$0.164785\pi$
$174$			3.90018i			0.295672i
$175$		0			0
$176$	−0.614364	−	0.354703i	−0.0463094	−	0.0267368i
$177$			6.21352i			0.467037i
$178$	−1.11267	+	1.92719i	−0.0833978	+	0.144449i
$179$	10.2123	+	17.6882i	0.763302	+	1.32208i	0.941140	+	0.338018i	$0.109757\pi$
$179$	10.2123	+	17.6882i	0.763302	+	1.32208i	−0.177837	+	0.984060i	$0.556910\pi$
$180$	−3.21107	+	1.85391i	−0.239339	+	0.138182i
$181$	−5.78777			−0.430202			−0.215101	−	0.976592i	$-0.569008\pi$
$181$	−5.78777			−0.430202			−0.215101	+	0.976592i	$0.569008\pi$
$182$		0			0
$183$	2.90684			0.214880
$184$	17.5470	−	10.1308i	1.29358	−	0.746852i
$185$	−1.15853	−	2.00663i	−0.0851767	−	0.147530i
$186$	−1.51591	+	2.62563i	−0.111152	+	0.192521i
$187$		−	3.02502i		−	0.221212i
$188$	3.02181	+	1.74464i	0.220388	+	0.127241i
$189$		0			0
$190$			3.51269i			0.254837i
$191$	4.22925	−	7.32528i	0.306018	−	0.530038i	−0.671470	−	0.741032i	$-0.734337\pi$
$191$	4.22925	−	7.32528i	0.306018	−	0.530038i	0.977487	+	0.210994i	$0.0676699\pi$
$192$	−2.89495	−	5.01421i	−0.208925	−	0.361869i
$193$	−1.16622	+	0.673316i	−0.0839461	+	0.0484663i	−0.541385	−	0.840775i	$-0.682100\pi$
$193$	−1.16622	+	0.673316i	−0.0839461	+	0.0484663i	0.457439	+	0.889241i	$0.348767\pi$
$194$	−6.70253			−0.481214
$195$	0.243380	−	4.64473i	0.0174288	−	0.332616i
$196$		0			0
$197$	5.53882	−	3.19784i	0.394625	−	0.227837i	−0.289537	−	0.957167i	$-0.593501\pi$
$197$	5.53882	−	3.19784i	0.394625	−	0.227837i	0.684162	+	0.729330i	$0.260168\pi$
$198$	0.672975	+	1.16563i	0.0478262	+	0.0828375i
$199$	−8.77149	+	15.1927i	−0.621794	+	1.07698i	0.367357	+	0.930080i	$0.380263\pi$
$199$	−8.77149	+	15.1927i	−0.621794	+	1.07698i	−0.989151	+	0.146900i	$0.953071\pi$
$200$			6.64310i			0.469738i
$201$	6.39471	+	3.69199i	0.451048	+	0.260413i
$202$	−6.65567	−	3.84265i	−0.468291	−	0.270368i
$203$		0			0
$204$	1.98846	−	3.44411i	0.139220	−	0.241136i
$205$	−1.04086	−	1.80282i	−0.0726967	−	0.125914i
$206$	15.7850	−	9.11349i	1.09980	−	0.634967i
$207$	−16.0754			−1.11732
$208$	−4.75294	−	0.249050i	−0.329557	−	0.0172685i
$209$	−1.08255			−0.0748813
$210$		0			0
$211$	−9.89766	−	17.1432i	−0.681383	−	1.18019i	−0.974559	−	0.224131i	$-0.928046\pi$
$211$	−9.89766	−	17.1432i	−0.681383	−	1.18019i	0.293176	−	0.956058i	$-0.405288\pi$
$212$	−6.18331	+	10.7098i	−0.424672	+	0.735553i
$213$			1.17005i			0.0801706i
$214$	−4.52429	−	2.61210i	−0.309274	−	0.178559i
$215$	−4.74464	−	2.73932i	−0.323582	−	0.186820i
$216$			12.6286i			0.859270i
$217$		0			0
$218$	9.29064	+	16.0919i	0.629242	+	1.08988i
$219$	10.4241	−	6.01838i	0.704398	−	0.406684i
$220$	0.827479			0.0557886
$221$	−9.21395	−	18.0830i	−0.619797	−	1.21639i
$222$	−1.10577			−0.0742142
$223$	23.2560	−	13.4268i	1.55734	−	0.899128i	0.559825	−	0.828611i	$-0.310868\pi$
$223$	23.2560	−	13.4268i	1.55734	−	0.899128i	0.997511	−	0.0705174i	$-0.0224650\pi$
$224$		0			0
$225$	2.63530	−	4.56447i	0.175686	−	0.304298i
$226$		−	7.87835i		−	0.524060i
$227$	−1.42128	−	0.820574i	−0.0943334	−	0.0544634i	0.452091	−	0.891972i	$-0.350678\pi$
$227$	−1.42128	−	0.820574i	−0.0943334	−	0.0544634i	−0.546425	+	0.837508i	$0.684011\pi$
$228$	−1.23252	−	0.711597i	−0.0816258	−	0.0471267i
$229$			6.98091i			0.461311i	0.973035	+	0.230656i	$0.0740871\pi$
$229$			6.98091i			0.461311i	−0.973035	+	0.230656i	$0.925913\pi$
$230$	5.82053	−	10.0815i	0.383794	−	0.664751i
$231$		0			0
$232$	−12.8120	+	7.39702i	−0.841150	+	0.485638i
$233$	−14.3619			−0.940882			−0.470441	−	0.882431i	$-0.655905\pi$
$233$	−14.3619			−0.940882			−0.470441	+	0.882431i	$0.655905\pi$
$234$	7.57331	+	4.91807i	0.495082	+	0.321504i
$235$	6.37079			0.415585
$236$	−6.42292	+	3.70827i	−0.418097	+	0.241388i
$237$	3.17965	+	5.50732i	0.206541	+	0.357739i
$238$		0			0
$239$			19.9962i			1.29345i	0.762724	+	0.646724i	$0.223861\pi$
$239$			19.9962i			1.29345i	−0.762724	+	0.646724i	$0.776139\pi$
$240$	−1.47469	−	0.851413i	−0.0951909	−	0.0549585i
$241$	23.9904	+	13.8509i	1.54536	+	0.892214i	0.998486	+	0.0549987i	$0.0175155\pi$
$241$	23.9904	+	13.8509i	1.54536	+	0.892214i	0.546873	+	0.837215i	$0.315818\pi$
$242$			11.1400i			0.716108i
$243$	7.78877	−	13.4906i	0.499650	−	0.865419i
$244$	1.73482	+	3.00480i	0.111061	+	0.192363i
$245$		0			0
$246$	−0.993456			−0.0633405
$247$	−6.47125	+	3.29734i	−0.411756	+	0.209805i
$248$	−11.5002			−0.730264
$249$	6.27904	−	3.62520i	0.397918	−	0.229738i
$250$	6.26791	+	10.8563i	0.396417	+	0.686615i
$251$	4.79782	−	8.31007i	0.302836	−	0.524527i	−0.673941	−	0.738785i	$-0.735400\pi$
$251$	4.79782	−	8.31007i	0.302836	−	0.524527i	0.976777	+	0.214258i	$0.0687334\pi$
$252$		0			0
$253$	3.10692	+	1.79378i	0.195331	+	0.112774i
$254$	−9.61233	−	5.54968i	−0.603131	−	0.348218i
$255$		−	7.26112i		−	0.454709i
$256$	8.34097	−	14.4470i	0.521311	−	0.902937i
$257$	−2.45632	−	4.25448i	−0.153221	−	0.265387i	0.779189	−	0.626789i	$-0.215631\pi$
$257$	−2.45632	−	4.25448i	−0.153221	−	0.265387i	−0.932410	+	0.361403i	$0.882298\pi$
$258$	−2.26428	+	1.30728i	−0.140968	+	0.0813879i
$259$		0			0
$260$	4.94651	−	2.52043i	0.306769	−	0.156310i
$261$	11.7375			0.726533
$262$	−8.11923	+	4.68764i	−0.501607	+	0.289603i
$263$	−9.26860	−	16.0537i	−0.571526	−	0.989913i	−0.996410	−	0.0846645i	$-0.973018\pi$
$263$	−9.26860	−	16.0537i	−0.571526	−	0.989913i	0.424883	−	0.905248i	$-0.360315\pi$
$264$	0.627469	−	1.08681i	0.0386180	−	0.0668884i
$265$			22.5792i			1.38703i
$266$		0			0
$267$	−1.42563	−	0.823089i	−0.0872473	−	0.0503723i
$268$			8.81362i			0.538378i
$269$	−6.89201	+	11.9373i	−0.420213	+	0.727831i	−0.995960	−	0.0897971i	$-0.971378\pi$
$269$	−6.89201	+	11.9373i	−0.420213	+	0.727831i	0.575747	+	0.817628i	$0.304711\pi$
$270$	3.62782	+	6.28357i	0.220782	+	0.382406i
$271$	17.3173	−	9.99813i	1.05195	−	0.607343i	0.128755	−	0.991676i	$-0.458902\pi$
$271$	17.3173	−	9.99813i	1.05195	−	0.607343i	0.923195	+	0.384333i	$0.125569\pi$
$272$	−7.43030			−0.450528
$273$		0			0
$274$	4.29484			0.259461
$275$	−1.01866	+	0.588122i	−0.0614273	+	0.0354651i
$276$	2.35824	+	4.08459i	0.141949	+	0.245863i
$277$	12.9409	−	22.4142i	0.777540	−	1.34674i	−0.155815	−	0.987786i	$-0.549800\pi$
$277$	12.9409	−	22.4142i	0.777540	−	1.34674i	0.933356	−	0.358953i	$-0.116866\pi$
$278$		−	20.5007i		−	1.22955i
$279$	7.90178	+	4.56210i	0.473067	+	0.273126i
$280$		0			0
$281$			20.2430i			1.20760i	0.797138	+	0.603798i	$0.206347\pi$
$281$			20.2430i			1.20760i	−0.797138	+	0.603798i	$0.793653\pi$
$282$	1.52016	−	2.63300i	0.0905245	−	0.156793i
$283$	−11.1977	−	19.3950i	−0.665635	−	1.15291i	−0.979113	−	0.203318i	$-0.934827\pi$
$283$	−11.1977	−	19.3950i	−0.665635	−	1.15291i	0.313478	−	0.949596i	$-0.398506\pi$
$284$	−1.20948	+	0.698296i	−0.0717696	+	0.0414362i
$285$	−2.59849			−0.153921
$286$	−0.914921	−	1.79559i	−0.0541004	−	0.106176i
$287$		0			0
$288$	−9.79632	+	5.65591i	−0.577254	+	0.333278i
$289$	−7.34200	−	12.7167i	−0.431882	−	0.748042i
$290$	−4.24988	+	7.36100i	−0.249561	+	0.432253i
$291$		−	4.95817i		−	0.290653i
$292$	12.4424	+	7.18363i	0.728137	+	0.420390i
$293$	−19.8513	−	11.4611i	−1.15972	−	0.669568i	−0.208487	−	0.978025i	$-0.566854\pi$
$293$	−19.8513	−	11.4611i	−1.15972	−	0.669568i	−0.951238	+	0.308458i	$0.900187\pi$
$294$		0			0
$295$	−6.77063	+	11.7271i	−0.394202	+	0.682777i
$296$	−2.09718	−	3.63242i	−0.121896	−	0.211130i
$297$	−1.93648	+	1.11803i	−0.112366	+	0.0648746i
$298$	−15.3801			−0.890943
$299$	24.0363	+	1.25948i	1.39005	+	0.0728377i
$300$	−1.54638			−0.0892800
$301$		0			0
$302$	8.40028	+	14.5497i	0.483382	+	0.837242i
$303$	2.84259	−	4.92350i	0.163302	−	0.282848i
$304$			2.65904i			0.152506i
$305$	5.48622	+	3.16747i	0.314140	+	0.181369i
$306$	12.2087	+	7.04871i	0.697927	+	0.402948i
$307$			28.9163i			1.65034i	0.564884	+	0.825170i	$0.308921\pi$
$307$			28.9163i			1.65034i	−0.564884	+	0.825170i	$0.691079\pi$
$308$		0			0
$309$	6.74166	+	11.6769i	0.383520	+	0.664276i
$310$	−5.72210	+	3.30366i	−0.324994	+	0.187635i
$311$	−5.23639			−0.296928			−0.148464	−	0.988918i	$-0.547433\pi$
$311$	−5.23639			−0.296928			−0.148464	+	0.988918i	$0.547433\pi$
$312$	0.440569	−	8.40794i	0.0249423	−	0.476006i
$313$	−15.7163			−0.888338			−0.444169	−	0.895943i	$-0.646501\pi$
$313$	−15.7163			−0.888338			−0.444169	+	0.895943i	$0.646501\pi$
$314$	2.62774	−	1.51713i	0.148292	−	0.0856164i
$315$		0			0
$316$	−3.79528	+	6.57361i	−0.213501	+	0.369795i
$317$			25.3794i			1.42545i	0.701444	+	0.712725i	$0.252539\pi$
$317$			25.3794i			1.42545i	−0.701444	+	0.712725i	$0.747461\pi$
$318$	9.33182	+	5.38773i	0.523303	+	0.302129i
$319$	−2.26853	−	1.30974i	−0.127013	−	0.0733311i
$320$		−	12.6181i		−	0.705372i
$321$	1.93229	−	3.34682i	0.107850	−	0.186801i
$322$		0			0
$323$	−9.81948	+	5.66928i	−0.546370	+	0.315447i
$324$	3.69450			0.205250
$325$	−4.29797	+	6.61842i	−0.238408	+	0.367124i
$326$	17.5135			0.969984
$327$	−11.9039	+	6.87271i	−0.658286	+	0.380062i
$328$	−1.88417	−	3.26349i	−0.104036	−	0.180196i
$329$		0			0
$330$		−	0.721010i		−	0.0396903i
$331$	12.3751	+	7.14478i	0.680199	+	0.392713i	0.799930	−	0.600093i	$-0.204870\pi$
$331$	12.3751	+	7.14478i	0.680199	+	0.392713i	−0.119731	+	0.992806i	$0.538203\pi$
$332$	7.49475	+	4.32710i	0.411328	+	0.237480i
$333$			3.32778i			0.182361i
$334$	−12.9349	+	22.4039i	−0.707765	+	1.22589i
$335$	8.04603	+	13.9361i	0.439602	+	0.761413i
$336$		0			0
$337$	7.63229			0.415757			0.207879	−	0.978155i	$-0.433344\pi$
$337$	7.63229			0.415757			0.207879	+	0.978155i	$0.433344\pi$
$338$	−10.9384	−	7.94695i	−0.594973	−	0.432257i
$339$	5.82797			0.316532
$340$	7.50583	−	4.33349i	0.407061	−	0.235017i
$341$	−1.01813	−	1.76345i	−0.0551347	−	0.0954961i
$342$	2.52248	−	4.36906i	0.136400	−	0.236252i
$343$		0			0
$344$	−8.58880	−	4.95875i	−0.463077	−	0.267358i
$345$	7.45771	+	4.30571i	0.401510	+	0.231812i
$346$		−	0.161758i		−	0.00869615i
$347$	6.13447	−	10.6252i	0.329315	−	0.570391i	−0.653061	−	0.757305i	$-0.726515\pi$
$347$	6.13447	−	10.6252i	0.329315	−	0.570391i	0.982376	+	0.186914i	$0.0598487\pi$
$348$	−1.72187	−	2.98237i	−0.0923021	−	0.159872i
$349$	−14.5611	+	8.40688i	−0.779440	+	0.450010i	−0.836232	−	0.548376i	$-0.815246\pi$
$349$	−14.5611	+	8.40688i	−0.779440	+	0.450010i	0.0567916	+	0.998386i	$0.481913\pi$
$350$		0			0
$351$	−8.17051	+	12.5817i	−0.436109	+	0.671562i
$352$	2.52447			0.134555
$353$	−9.63221	+	5.56116i	−0.512671	+	0.295991i	−0.733931	−	0.679224i	$-0.762316\pi$
$353$	−9.63221	+	5.56116i	−0.512671	+	0.295991i	0.221260	+	0.975215i	$0.428983\pi$
$354$	3.23115	+	5.59651i	0.171733	+	0.297451i
$355$	−1.27496	+	2.20830i	−0.0676679	+	0.117204i
$356$		−	1.96490i		−	0.104140i
$357$		0			0
$358$	18.3964	+	10.6212i	0.972279	+	0.561346i
$359$		−	34.3599i		−	1.81345i	−0.421727	−	0.906723i	$-0.638576\pi$
$359$		−	34.3599i		−	1.81345i	0.421727	−	0.906723i	$-0.361424\pi$
$360$	−6.12740	+	10.6130i	−0.322942	+	0.559352i
$361$	−7.47117	−	12.9404i	−0.393219	−	0.681076i
$362$	−5.21304	+	3.00975i	−0.273991	+	0.158189i
$363$	−8.24079			−0.432529
$364$		0			0
$365$	26.2320			1.37304
$366$	2.61819	−	1.51161i	0.136855	−	0.0790131i
$367$	11.2748	+	19.5285i	0.588539	+	1.01938i	0.994424	+	0.105455i	$0.0336299\pi$
$367$	11.2748	+	19.5285i	0.588539	+	1.01938i	−0.405885	+	0.913924i	$0.633037\pi$
$368$	4.40603	−	7.63147i	0.229680	−	0.397818i
$369$			2.98978i			0.155642i
$370$	−2.08697	−	1.20491i	−0.108496	−	0.0626404i
$371$		0			0
$372$		−	2.67701i		−	0.138796i
$373$	−6.07186	+	10.5168i	−0.314389	+	0.544537i	−0.979307	−	0.202379i	$-0.935133\pi$
$373$	−6.07186	+	10.5168i	−0.314389	+	0.544537i	0.664919	+	0.746916i	$0.268466\pi$
$374$	−1.57307	−	2.72463i	−0.0813414	−	0.140887i
$375$	−8.03092	+	4.63666i	−0.414715	+	0.239436i
$376$	11.5325			0.594743
$377$	−17.5502	−	0.919613i	−0.903879	−	0.0473625i
$378$		0			0
$379$	13.6752	−	7.89537i	0.702447	−	0.405558i	−0.105811	−	0.994386i	$-0.533744\pi$
$379$	13.6752	−	7.89537i	0.702447	−	0.405558i	0.808258	+	0.588828i	$0.200411\pi$
$380$	−1.55080	−	2.68606i	−0.0795544	−	0.137792i
$381$	4.10535	−	7.11068i	0.210324	−	0.364291i
$382$		−	8.79716i		−	0.450102i
$383$	−22.5661	−	13.0286i	−1.15307	−	0.665728i	−0.203440	−	0.979087i	$-0.565212\pi$
$383$	−22.5661	−	13.0286i	−1.15307	−	0.665728i	−0.949635	+	0.313359i	$0.898546\pi$
$384$	1.04473	+	0.603176i	0.0533137	+	0.0307807i
$385$		0			0
$386$	−0.700273	+	1.21291i	−0.0356430	+	0.0617354i
$387$	3.93424	+	6.81430i	0.199989	+	0.346390i
$388$	5.12526	−	2.95907i	0.260196	−	0.150224i
$389$	−12.9605			−0.657122			−0.328561	−	0.944483i	$-0.606564\pi$
$389$	−12.9605			−0.657122			−0.328561	+	0.944483i	$0.606564\pi$
$390$	−2.19613	−	4.31006i	−0.111205	−	0.218248i
$391$	37.5760			1.90030
$392$		0			0
$393$	−3.46766	−	6.00616i	−0.174920	−	0.302971i
$394$	3.32587	−	5.76058i	0.167555	−	0.290214i
$395$			13.8590i			0.697321i
$396$	−1.02921	−	0.594217i	−0.0517200	−	0.0298605i
$397$	8.34031	+	4.81528i	0.418588	+	0.241672i	0.694473	−	0.719519i	$-0.255638\pi$
$397$	8.34031	+	4.81528i	0.418588	+	0.241672i	−0.275885	+	0.961191i	$0.588971\pi$
$398$			18.2454i			0.914557i
$399$		0			0
$400$	1.44459	+	2.50211i	0.0722296	+	0.125105i
$401$	−9.84837	+	5.68596i	−0.491804	+	0.283943i	−0.725323	−	0.688409i	$-0.758309\pi$
$401$	−9.84837	+	5.68596i	−0.491804	+	0.283943i	0.233518	+	0.972352i	$0.424976\pi$
$402$	7.67961			0.383024
$403$	−11.4575	−	7.44043i	−0.570737	−	0.370634i
$404$	6.78590			0.337611
$405$	5.84176	−	3.37274i	0.290280	−	0.167593i
$406$		0			0
$407$	0.371332	−	0.643166i	0.0184063	−	0.0318806i
$408$		−	13.1442i		−	0.650734i
$409$	18.7856	+	10.8459i	0.928889	+	0.536294i	0.886460	−	0.462805i	$-0.153157\pi$
$409$	18.7856	+	10.8459i	0.928889	+	0.536294i	0.0424291	+	0.999099i	$0.486490\pi$
$410$	−1.87500	−	1.08253i	−0.0925996	−	0.0534624i
$411$			3.17709i			0.156714i
$412$	−8.04695	+	13.9377i	−0.396445	+	0.686662i
$413$		0			0
$414$	−14.4791	+	8.35951i	−0.711609	+	0.410848i
$415$	15.8010			0.775640
$416$	15.0908	−	7.68930i	0.739887	−	0.376999i
$417$	15.1653			0.742648
$418$	−0.975048	+	0.562944i	−0.0476912	+	0.0275345i
$419$	−2.95797	−	5.12335i	−0.144506	−	0.250292i	0.784682	−	0.619898i	$-0.212826\pi$
$419$	−2.95797	−	5.12335i	−0.144506	−	0.250292i	−0.929189	+	0.369606i	$0.879493\pi$
$420$		0			0
$421$			1.39103i			0.0677946i	0.999425	+	0.0338973i	$0.0107919\pi$
$421$			1.39103i			0.0677946i	−0.999425	+	0.0338973i	$0.989208\pi$
$422$	−17.8296	−	10.2939i	−0.867932	−	0.501101i
$423$	−7.92396	−	4.57490i	−0.385276	−	0.222439i
$424$			40.8731i			1.98498i
$425$	−6.15997	+	10.6694i	−0.298802	+	0.517541i
$426$	0.608449	+	1.05386i	0.0294794	+	0.0510599i
$427$		0			0
$428$	4.61282			0.222969
$429$	1.32828	−	0.676808i	0.0641301	−	0.0326766i
$430$	−5.69798			−0.274781
$431$	−4.36194	+	2.51837i	−0.210107	+	0.121306i	−0.601361	−	0.798977i	$-0.705375\pi$
$431$	−4.36194	+	2.51837i	−0.210107	+	0.121306i	0.391254	+	0.920283i	$0.372041\pi$
$432$	2.74619	+	4.75654i	0.132126	+	0.228849i
$433$	7.37045	−	12.7660i	0.354201	−	0.613495i	−0.632780	−	0.774332i	$-0.718086\pi$
$433$	7.37045	−	12.7660i	0.354201	−	0.613495i	0.986981	+	0.160837i	$0.0514194\pi$
$434$		0			0
$435$	−5.44527	−	3.14383i	−0.261081	−	0.150735i
$436$	−14.2087	−	8.20337i	−0.680471	−	0.392870i
$437$		−	13.4471i		−	0.643262i
$438$	6.25934	−	10.8415i	0.299083	−	0.518026i
$439$	3.82913	+	6.63225i	0.182755	+	0.316540i	0.942818	−	0.333309i	$-0.108165\pi$
$439$	3.82913	+	6.63225i	0.182755	+	0.316540i	−0.760063	+	0.649849i	$0.774832\pi$
$440$	2.36851	−	1.36746i	0.112914	−	0.0651910i
$441$		0			0
$442$	−17.7025	−	11.4959i	−0.842021	−	0.546805i
$443$	30.0570			1.42805			0.714025	−	0.700121i	$-0.246870\pi$
$443$	30.0570			1.42805			0.714025	+	0.700121i	$0.246870\pi$
$444$	0.845553	−	0.488180i	0.0401282	−	0.0231680i
$445$	−1.79378	−	3.10691i	−0.0850332	−	0.147282i
$446$	13.9644	−	24.1871i	0.661234	−	1.14529i
$447$		−	11.3773i		−	0.538129i
$448$		0			0
$449$	−28.6882	−	16.5632i	−1.35388	−	0.781664i	−0.365091	−	0.930972i	$-0.618962\pi$
$449$	−28.6882	−	16.5632i	−1.35388	−	0.781664i	−0.988791	+	0.149308i	$0.952295\pi$
$450$		−	5.48161i		−	0.258406i
$451$	0.333617	−	0.577841i	0.0157094	−	0.0272095i
$452$	3.47818	+	6.02438i	0.163600	+	0.283363i
$453$	−10.7631	+	6.21407i	−0.505694	+	0.291962i
$454$	−1.70686			−0.0801067
$455$		0			0
$456$	−4.70382			−0.220277
$457$	−19.0992	+	11.0269i	−0.893422	+	0.515817i	−0.875060	−	0.484014i	$-0.839178\pi$
$457$	−19.0992	+	11.0269i	−0.893422	+	0.515817i	−0.0183615	+	0.999831i	$0.505845\pi$
$458$	3.63020	+	6.28769i	0.169628	+	0.293805i
$459$	−11.7102	+	20.2827i	−0.546585	+	0.946713i
$460$			10.2787i			0.479248i
$461$	−19.0689	−	11.0094i	−0.888128	−	0.512761i	−0.0147983	−	0.999890i	$-0.504711\pi$
$461$	−19.0689	−	11.0094i	−0.888128	−	0.512761i	−0.873330	+	0.487130i	$0.838044\pi$
$462$		0			0
$463$			35.0344i			1.62819i	0.580734	+	0.814093i	$0.302766\pi$
$463$			35.0344i			1.62819i	−0.580734	+	0.814093i	$0.697234\pi$
$464$	−3.21707	+	5.57214i	−0.149349	+	0.258680i
$465$	−2.44387	−	4.23290i	−0.113332	−	0.196296i
$466$	−12.9358	+	7.46848i	−0.599239	+	0.345971i
$467$	−19.0158			−0.879948			−0.439974	−	0.898010i	$-0.645012\pi$
$467$	−19.0158			−0.879948			−0.439974	+	0.898010i	$0.645012\pi$
$468$	−7.96238	−	0.417222i	−0.368061	−	0.0192861i
$469$		0			0
$470$	5.73816	−	3.31293i	0.264682	−	0.152814i
$471$	1.12229	+	1.94386i	0.0517123	+	0.0895682i
$472$	−12.2563	+	21.2285i	−0.564141	+	0.977121i
$473$		−	1.75602i		−	0.0807417i
$474$	5.72781	+	3.30695i	0.263087	+	0.151893i
$475$	3.81818	+	2.20443i	0.175190	+	0.101146i
$476$		0			0
$477$	16.2143	−	28.0839i	0.742400	−	1.28587i
$478$	10.3984	+	18.0106i	0.475612	+	0.823784i
$479$	−17.5890	+	10.1550i	−0.803661	+	0.463994i	−0.844750	−	0.535162i	$-0.820251\pi$
$479$	−17.5890	+	10.1550i	−0.803661	+	0.463994i	0.0410890	+	0.999155i	$0.486917\pi$
$480$	6.05962			0.276582
$481$	0.260726	−	4.97577i	0.0118881	−	0.226875i
$482$	28.8109			1.31230
$483$		0			0
$484$	−4.91816	−	8.51851i	−0.223553	−	0.387205i
$485$	5.40272	−	9.35779i	0.245325	−	0.424915i
$486$		−	16.2012i		−	0.734903i
$487$	−5.57260	−	3.21734i	−0.252519	−	0.145792i	0.368398	−	0.929668i	$-0.379906\pi$
$487$	−5.57260	−	3.21734i	−0.252519	−	0.145792i	−0.620917	+	0.783876i	$0.713240\pi$
$488$	9.93122	+	5.73379i	0.449565	+	0.259557i
$489$			12.9556i			0.585870i
$490$		0			0
$491$	0.480213	+	0.831754i	0.0216717	+	0.0375365i	0.876658	−	0.481114i	$-0.159768\pi$
$491$	0.480213	+	0.831754i	0.0216717	+	0.0375365i	−0.854986	+	0.518651i	$0.826434\pi$
$492$	0.759672	−	0.438597i	0.0342486	−	0.0197735i
$493$	−27.4362			−1.23567
$494$	−4.11397	+	6.33508i	−0.185096	+	0.285029i
$495$	−2.16986			−0.0975282
$496$	−4.33152	+	2.50080i	−0.194491	+	0.112289i
$497$		0			0
$498$	3.77035	−	6.53043i	0.168953	−	0.292636i
$499$		−	9.78848i		−	0.438192i	−0.975703	−	0.219096i	$-0.929689\pi$
$499$		−	9.78848i		−	0.438192i	0.975703	−	0.219096i	$-0.0703109\pi$
$500$	−9.58583	−	5.53438i	−0.428691	−	0.247505i
$501$	−16.5732	−	9.56852i	−0.740434	−	0.427490i
$502$		−	9.97982i		−	0.445421i
$503$	6.05845	−	10.4935i	0.270133	−	0.467884i	−0.698763	−	0.715353i	$-0.746266\pi$
$503$	6.05845	−	10.4935i	0.270133	−	0.467884i	0.968896	+	0.247470i	$0.0795990\pi$
$504$		0			0
$505$	10.7299	−	6.19491i	0.477474	−	0.275670i
$506$	3.73120			0.165872
$507$	5.87872	−	8.09166i	0.261083	−	0.359363i
$508$	9.80042			0.434823
$509$	−26.7933	+	15.4691i	−1.18759	+	0.685656i	−0.957758	−	0.287574i	$-0.907151\pi$
$509$	−26.7933	+	15.4691i	−1.18759	+	0.685656i	−0.229833	+	0.973230i	$0.573818\pi$
$510$	−3.77592	−	6.54008i	−0.167200	−	0.289600i
$511$		0			0
$512$		−	14.2139i		−	0.628170i
$513$	7.25843	+	4.19066i	0.320468	+	0.185022i
$514$	−4.42481	−	2.55467i	−0.195170	−	0.112682i
$515$			29.3845i			1.29484i
$516$	1.15429	−	1.99929i	0.0508149	−	0.0880140i
$517$	1.02099	+	1.76840i	0.0449029	+	0.0777741i
$518$		0			0
$519$	0.119660			0.00525247
$520$	9.99331	−	15.3886i	0.438236	−	0.674837i
$521$	−35.0676			−1.53634			−0.768169	−	0.640247i	$-0.778832\pi$
$521$	−35.0676			−1.53634			−0.768169	+	0.640247i	$0.778832\pi$
$522$	10.5720	−	6.10372i	0.462722	−	0.267153i
$523$	−17.2237	−	29.8324i	−0.753142	−	1.30448i	−0.946293	−	0.323311i	$-0.895204\pi$
$523$	−17.2237	−	29.8324i	−0.753142	−	1.30448i	0.193151	−	0.981169i	$-0.438129\pi$
$524$	4.13905	−	7.16904i	0.180815	−	0.313181i
$525$		0			0
$526$	−16.6964	−	9.63969i	−0.727999	−	0.420310i
$527$	−18.4703	−	10.6638i	−0.804579	−	0.464524i
$528$		−	0.545791i		−	0.0237525i
$529$	−10.7819	+	18.6748i	−0.468778	+	0.811947i
$530$	11.7416	+	20.3371i	0.510023	+	0.883385i
$531$	16.8426	−	9.72406i	0.730905	−	0.421988i
$532$		0			0
$533$	0.234244	−	4.47039i	0.0101463	−	0.193634i
$534$	−1.71209			−0.0740893
$535$	7.29380	−	4.21108i	0.315339	−	0.182061i
$536$	14.5650	+	25.2274i	0.629113	+	1.08966i
$537$	−7.85695	+	13.6086i	−0.339053	+	0.587256i
$538$			14.3359i			0.618064i
$539$		0			0
$540$	−5.54821	−	3.20326i	−0.238757	−	0.137846i
$541$			9.77797i			0.420388i	0.977660	+	0.210194i	$0.0674095\pi$
$541$			9.77797i			0.420388i	−0.977660	+	0.210194i	$0.932590\pi$
$542$	10.3984	−	18.0106i	0.446651	−	0.773622i
$543$	−2.22645	−	3.85632i	−0.0955460	−	0.165491i
$544$	22.8988	−	13.2206i	0.981776	−	0.566829i
$545$	−29.9557			−1.28316
$546$		0			0
$547$	19.7876			0.846057			0.423029	−	0.906116i	$-0.360967\pi$
$547$	19.7876			0.846057			0.423029	+	0.906116i	$0.360967\pi$
$548$	−3.28416	+	1.89611i	−0.140292	+	0.0809977i
$549$	−4.54916	−	7.87937i	−0.194153	−	0.336283i
$550$	−0.611669	+	1.05944i	−0.0260816	+	0.0451747i
$551$			9.81844i			0.418280i
$552$	13.5000	+	7.79425i	0.574600	+	0.331745i
$553$		0			0
$554$		−	26.9179i		−	1.14363i
$555$	0.891328	−	1.54383i	0.0378348	−	0.0655317i
$556$	9.05077	+	15.6764i	0.383838	+	0.664827i
$557$	1.09738	−	0.633570i	0.0464973	−	0.0268452i	−0.476571	−	0.879136i	$-0.658121\pi$
$557$	1.09738	−	0.633570i	0.0464973	−	0.0268452i	0.523068	+	0.852291i	$0.324787\pi$
$558$	9.48950			0.401723
$559$	−5.34867	−	10.4971i	−0.226224	−	0.443981i
$560$		0			0
$561$	2.01554	−	1.16367i	0.0850960	−	0.0491302i
$562$	10.5267	+	18.2328i	0.444043	+	0.769106i
$563$	19.9158	−	34.4952i	0.839352	−	1.45380i	−0.0510844	−	0.998694i	$-0.516268\pi$
$563$	19.9158	−	34.4952i	0.839352	−	1.45380i	0.890437	−	0.455107i	$-0.150399\pi$
$564$			2.68452i			0.113039i
$565$	10.9994	+	6.35052i	0.462749	+	0.267168i
$566$	−20.1715	−	11.6460i	−0.847873	−	0.489520i
$567$		0			0
$568$	−2.30795	+	3.99748i	−0.0968394	+	0.167731i
$569$	2.73451	+	4.73631i	0.114637	+	0.198556i	0.917634	−	0.397426i	$-0.130096\pi$
$569$	2.73451	+	4.73631i	0.114637	+	0.198556i	−0.802998	+	0.595982i	$0.796763\pi$
$570$	−2.34046	+	1.35126i	−0.0980311	+	0.0565983i
$571$	4.67594			0.195682			0.0978411	−	0.995202i	$-0.468806\pi$
$571$	4.67594			0.195682			0.0978411	+	0.995202i	$0.468806\pi$
$572$	1.49235	+	0.969123i	0.0623981	+	0.0405211i
$573$	6.50766			0.271861
$574$		0			0
$575$	−7.30549	−	12.6535i	−0.304660	−	0.527687i
$576$	−9.06111	+	15.6943i	−0.377546	+	0.653929i
$577$		−	3.60435i		−	0.150051i	−0.997182	−	0.0750255i	$-0.976096\pi$
$577$		−	3.60435i		−	0.150051i	0.997182	−	0.0750255i	$-0.0239038\pi$
$578$	−13.2259	−	7.63595i	−0.550123	−	0.317614i
$579$	−0.897244	−	0.518024i	−0.0372882	−	0.0215283i
$580$		−	7.50503i		−	0.311630i
$581$		0			0
$582$	−2.57834	−	4.46581i	−0.106876	−	0.185114i
$583$	−6.26751	+	3.61855i	−0.259574	+	0.149865i
$584$	47.4854			1.96496
$585$	−12.9710	+	6.60921i	−0.536286	+	0.273257i
$586$	−23.8400			−0.984823
$587$	20.3274	−	11.7360i	0.839001	−	0.484398i	−0.0179234	−	0.999839i	$-0.505706\pi$
$587$	20.3274	−	11.7360i	0.839001	−	0.484398i	0.856925	+	0.515442i	$0.172372\pi$
$588$		0			0
$589$	−3.81620	+	6.60985i	−0.157244	+	0.272354i
$590$			14.0834i			0.579805i
$591$	4.26136	+	2.46030i	0.175289	+	0.101203i
$592$	−1.57980	−	0.912095i	−0.0649292	−	0.0374869i
$593$		−	34.2267i		−	1.40552i	−0.711427	−	0.702760i	$-0.751951\pi$
$593$		−	34.2267i		−	1.40552i	0.711427	−	0.702760i	$-0.248049\pi$
$594$	−1.16279	+	2.01401i	−0.0477099	+	0.0826360i
$595$		0			0
$596$	11.7608	−	6.79008i	0.481739	−	0.278132i
$597$	−13.4969			−0.552392
$598$	22.3044	−	11.3649i	0.912095	−	0.464745i
$599$	14.9432			0.610564			0.305282	−	0.952262i	$-0.401249\pi$
$599$	14.9432			0.610564			0.305282	+	0.952262i	$0.401249\pi$
$600$	−4.42621	+	2.55548i	−0.180699	+	0.104327i
$601$	1.67229	+	2.89649i	0.0682141	+	0.118150i	0.898115	−	0.439760i	$-0.144937\pi$
$601$	1.67229	+	2.89649i	0.0682141	+	0.118150i	−0.829901	+	0.557911i	$0.811603\pi$
$602$		0			0
$603$		−	23.1116i		−	0.941178i
$604$	−12.8470	−	7.41720i	−0.522736	−	0.301802i
$605$	−15.5532	−	8.97967i	−0.632329	−	0.365075i
$606$		−	5.91279i		−	0.240191i
$607$	3.05262	−	5.28729i	0.123902	−	0.214605i	−0.797401	−	0.603450i	$-0.793792\pi$
$607$	3.05262	−	5.28729i	0.123902	−	0.214605i	0.921303	+	0.388845i	$0.127126\pi$
$608$	−4.73117	−	8.19464i	−0.191874	−	0.332336i
$609$		0			0
$610$	6.58857			0.266764
$611$	11.4896	+	7.46132i	0.464821	+	0.301853i
$612$	−12.4476			−0.503165
$613$	−6.06230	+	3.50007i	−0.244854	+	0.141366i	−0.617406	−	0.786645i	$-0.711816\pi$
$613$	−6.06230	+	3.50007i	−0.244854	+	0.141366i	0.372552	+	0.928011i	$0.378483\pi$
$614$	15.0370	+	26.0449i	0.606844	+	1.05109i
$615$	0.800797	−	1.38702i	0.0322913	−	0.0559301i
$616$		0			0
$617$	17.5343	+	10.1234i	0.705903	+	0.407553i	0.809542	−	0.587062i	$-0.199715\pi$
$617$	17.5343	+	10.1234i	0.705903	+	0.407553i	−0.103639	+	0.994615i	$0.533049\pi$
$618$	12.1444	+	7.01158i	0.488520	+	0.282047i
$619$		−	38.2583i		−	1.53773i	−0.639411	−	0.768865i	$-0.720822\pi$
$619$		−	38.2583i		−	1.53773i	0.639411	−	0.768865i	$-0.279178\pi$
$620$	2.91703	−	5.05245i	0.117151	−	0.202911i
$621$	−13.8879	−	24.0545i	−0.557301	−	0.965273i
$622$	−4.71641	+	2.72302i	−0.189111	+	0.109183i
$623$		0			0
$624$	−1.66243	−	3.26263i	−0.0665505	−	0.130610i
$625$	−9.26598			−0.370639
$626$	−14.1557	+	8.17277i	−0.565774	+	0.326650i
$627$	−0.416435	−	0.721287i	−0.0166308	−	0.0288054i
$628$	−1.33958	+	2.32022i	−0.0534550	+	0.0925868i
$629$		−	7.77864i		−	0.310155i
$630$		0			0
$631$	16.8935	+	9.75349i	0.672521	+	0.388280i	0.797031	−	0.603938i	$-0.206403\pi$
$631$	16.8935	+	9.75349i	0.672521	+	0.388280i	−0.124510	+	0.992218i	$0.539736\pi$
$632$			25.0877i			0.997934i
$633$	7.61489	−	13.1894i	0.302665	−	0.524230i
$634$	13.1978	+	22.8592i	0.524150	+	0.907855i
$635$	15.4965	−	8.94689i	0.614958	−	0.355046i
$636$	−9.51442			−0.377271
$637$		0			0
$638$	−2.72435			−0.107858
$639$	3.17158	−	1.83111i	0.125466	−	0.0724377i
$640$	1.31452	+	2.27681i	0.0519608	+	0.0899987i
$641$	13.8958	−	24.0682i	0.548851	−	0.950637i	−0.449503	−	0.893279i	$-0.648399\pi$
$641$	13.8958	−	24.0682i	0.548851	−	0.950637i	0.998354	−	0.0573584i	$-0.0182678\pi$
$642$		−	4.01930i		−	0.158629i
$643$	−37.4573	−	21.6260i	−1.47717	−	0.852846i	−0.477506	−	0.878629i	$-0.658459\pi$
$643$	−37.4573	−	21.6260i	−1.47717	−	0.852846i	−0.999668	+	0.0257823i	$0.991792\pi$
$644$		0			0
$645$		−	4.21506i		−	0.165968i
$646$	−5.89626	+	10.2126i	−0.231985	+	0.401810i
$647$	−9.00502	−	15.5972i	−0.354024	−	0.613187i	0.632927	−	0.774212i	$-0.281854\pi$
$647$	−9.00502	−	15.5972i	−0.354024	−	0.613187i	−0.986950	+	0.161024i	$0.948520\pi$
$648$	10.5748	−	6.10538i	0.415419	−	0.239842i
$649$	−4.34026			−0.170370
$650$	−0.429475	+	8.19622i	−0.0168454	+	0.321482i
$651$		0			0
$652$	−13.3922	+	7.73197i	−0.524478	+	0.302807i
$653$	11.9625	+	20.7197i	0.468130	+	0.810825i	0.999337	−	0.0364170i	$-0.0115945\pi$
$653$	11.9625	+	20.7197i	0.468130	+	0.810825i	−0.531206	+	0.847242i	$0.678261\pi$
$654$	−7.14788	+	12.3805i	−0.279504	+	0.484115i
$655$		−	15.1143i		−	0.590564i
$656$	−1.41934	−	0.819455i	−0.0554158	−	0.0319944i
$657$	−32.6272	−	18.8373i	−1.27291	−	0.734914i
$658$		0			0
$659$	3.41860	−	5.92119i	0.133170	−	0.230657i	−0.791727	−	0.610875i	$-0.790818\pi$
$659$	3.41860	−	5.92119i	0.133170	−	0.230657i	0.924897	+	0.380218i	$0.124151\pi$
$660$	0.318316	+	0.551339i	0.0123904	+	0.0214608i
$661$	25.2880	−	14.6000i	0.983587	−	0.567874i	0.0802361	−	0.996776i	$-0.474433\pi$
$661$	25.2880	−	14.6000i	0.983587	−	0.567874i	0.903351	+	0.428901i	$0.141099\pi$
$662$	14.8617			0.577616
$663$	8.50405	−	13.0953i	0.330270	−	0.508581i
$664$	28.6031			1.11002
$665$		0			0
$666$	1.73051	+	2.99733i	0.0670558	+	0.116144i
$667$	16.2692	−	28.1790i	0.629945	−	1.09110i
$668$		−	22.8422i		−	0.883793i
$669$	17.8923	+	10.3301i	0.691756	+	0.399385i
$670$	14.4941	+	8.36817i	0.559956	+	0.323291i
$671$			2.03048i			0.0783858i
$672$		0			0
$673$	−2.75416	−	4.77034i	−0.106165	−	0.183883i	0.808049	−	0.589116i	$-0.200524\pi$
$673$	−2.75416	−	4.77034i	−0.106165	−	0.183883i	−0.914214	+	0.405233i	$0.867191\pi$
$674$	6.87439	−	3.96893i	0.264792	−	0.152878i
$675$	9.10674			0.350519
$676$	11.8728	+	1.24768i	0.456647	+	0.0479876i
$677$	9.80946			0.377008			0.188504	−	0.982072i	$-0.439636\pi$
$677$	9.80946			0.377008			0.188504	+	0.982072i	$0.439636\pi$
$678$	5.24925	−	3.03065i	0.201596	−	0.116392i
$679$		0			0
$680$	14.3227	−	24.8076i	0.549250	−	0.951330i
$681$		−	1.26264i		−	0.0483844i
$682$	−1.83405	−	1.05889i	−0.0702295	−	0.0405470i
$683$	−8.57514	−	4.95086i	−0.328119	−	0.189439i	0.326887	−	0.945063i	$-0.394000\pi$
$683$	−8.57514	−	4.95086i	−0.328119	−	0.189439i	−0.655006	+	0.755624i	$0.727334\pi$
$684$			4.45455i			0.170324i
$685$	−3.46195	+	5.99627i	−0.132274	+	0.229106i
$686$		0			0
$687$	−4.65129	+	2.68542i	−0.177458	+	0.102455i
$688$	−4.31326			−0.164442
$689$	−26.4442	+	40.7213i	−1.00744	+	1.55136i
$690$	8.95620			0.340957
$691$	35.9527	−	20.7573i	1.36771	−	0.789646i	0.377071	−	0.926184i	$-0.376931\pi$
$691$	35.9527	−	20.7573i	1.36771	−	0.789646i	0.990635	+	0.136539i	$0.0435978\pi$
$692$	0.0714137	+	0.123692i	0.00271474	+	0.00470207i
$693$		0			0
$694$		−	12.7601i		−	0.484368i
$695$	28.6222	+	16.5251i	1.08570	+	0.626831i
$696$	−9.85709	−	5.69099i	−0.373632	−	0.215716i
$697$		−	6.98858i		−	0.264711i
$698$	−8.74347	+	15.1441i	−0.330945	+	0.573214i
$699$	−5.52477	−	9.56919i	−0.208966	−	0.361940i
$700$		0			0
$701$	−26.0138			−0.982527			−0.491263	−	0.871011i	$-0.663465\pi$
$701$	−26.0138			−0.982527			−0.491263	+	0.871011i	$0.663465\pi$
$702$	−0.816439	+	15.5811i	−0.0308145	+	0.588073i
$703$	−2.78369			−0.104989
$704$	3.50251	−	2.02218i	0.132006	−	0.0762137i
$705$	2.45072	+	4.24478i	0.0922996	+	0.159868i
$706$	−5.78381	+	10.0179i	−0.217677	+	0.377027i
$707$		0			0
$708$	−4.94156	−	2.85301i	−0.185715	−	0.107223i
$709$	−29.0171	−	16.7530i	−1.08976	−	0.629173i	−0.156247	−	0.987718i	$-0.549940\pi$
$709$	−29.0171	−	16.7530i	−1.08976	−	0.629173i	−0.933513	+	0.358545i	$0.883273\pi$
$710$			2.65201i			0.0995282i
$711$	9.95221	−	17.2377i	0.373237	−	0.646465i
$712$	−3.24712	−	5.62417i	−0.121691	−	0.210775i
$713$	21.9051	−	12.6469i	0.820352	−	0.473631i
$714$		0			0
$715$	3.24443	+	0.170005i	0.121335	+	0.00635783i
$716$	−18.7563			−0.700958
$717$	−13.3232	+	7.69217i	−0.497565	+	0.287269i
$718$	−17.8678	−	30.9479i	−0.666820	−	1.15497i
$719$	−13.2460	+	22.9428i	−0.493994	+	0.855623i	−0.999976	−	0.00692138i	$-0.997797\pi$
$719$	−13.2460	+	22.9428i	−0.493994	+	0.855623i	0.505982	+	0.862544i	$0.331130\pi$
$720$			5.32979i			0.198630i
$721$		0			0
$722$	−13.4585	−	7.77029i	−0.500875	−	0.289180i
$723$			21.3127i			0.792628i
$724$	2.65752	−	4.60296i	0.0987660	−	0.171068i
$725$	5.33412	+	9.23897i	0.198104	+	0.343127i
$726$	−7.42247	+	4.28536i	−0.275474	+	0.159045i
$727$	14.6388			0.542922			0.271461	−	0.962449i	$-0.412493\pi$
$727$	14.6388			0.542922			0.271461	+	0.962449i	$0.412493\pi$
$728$		0			0
$729$	−0.0845074			−0.00312990
$730$	23.6271	−	13.6411i	0.874478	−	0.504880i
$731$	−9.19623	−	15.9283i	−0.340135	−	0.589131i
$732$	−1.33471	+	2.31178i	−0.0493322	+	0.0854459i
$733$		−	24.3546i		−	0.899557i	−0.893140	−	0.449779i	$-0.851503\pi$
$733$		−	24.3546i		−	0.899557i	0.893140	−	0.449779i	$-0.148497\pi$
$734$	20.3104	+	11.7262i	0.749669	+	0.432822i
$735$		0			0
$736$			31.3583i			1.15588i
$737$	−2.57892	+	4.46682i	−0.0949958	+	0.164537i
$738$	1.55474	+	2.69290i	0.0572309	+	0.0991268i
$739$	−41.0177	+	23.6816i	−1.50886	+	0.871140i	−0.508912	+	0.860818i	$0.669952\pi$
$739$	−41.0177	+	23.6816i	−1.50886	+	0.871140i	−0.999947	+	0.0103217i	$0.996714\pi$
$740$	2.12780			0.0782197
$741$	−4.68635	−	3.04329i	−0.172157	−	0.111798i
$742$		0			0
$743$	−19.9140	+	11.4973i	−0.730573	+	0.421796i	−0.818632	−	0.574319i	$-0.805267\pi$
$743$	−19.9140	+	11.4973i	−0.730573	+	0.421796i	0.0880590	+	0.996115i	$0.471934\pi$
$744$	−4.42391	−	7.66244i	−0.162189	−	0.280919i
$745$	12.3974	−	21.4730i	0.454207	−	0.786710i
$746$			12.6299i			0.462414i
$747$	−19.6532	−	11.3468i	−0.719073	−	0.415157i
$748$	2.40577	+	1.38897i	0.0879638	+	0.0507859i
$749$		0			0
$750$	−4.82229	+	8.35246i	−0.176085	+	0.304989i
$751$	−6.60896	−	11.4470i	−0.241164	−	0.417709i	0.719882	−	0.694097i	$-0.244196\pi$
$751$	−6.60896	−	11.4470i	−0.241164	−	0.417709i	−0.961046	+	0.276388i	$0.910863\pi$
$752$	4.34368	−	2.50782i	0.158398	−	0.0914509i
$753$	7.38253			0.269034
$754$	−16.2856	+	8.29811i	−0.593087	+	0.302199i
$755$	−27.0849			−0.985721
$756$		0			0
$757$	−0.408563	−	0.707653i	−0.0148495	−	0.0257201i	0.858505	−	0.512805i	$-0.171394\pi$
$757$	−0.408563	−	0.707653i	−0.0148495	−	0.0257201i	−0.873355	+	0.487085i	$0.838060\pi$
$758$	8.21148	−	14.2227i	0.298254	−	0.516592i
$759$			2.76014i			0.100187i
$760$	−8.87776	−	5.12558i	−0.322030	−	0.185924i
$761$	−37.6791	−	21.7541i	−1.36587	−	0.788584i	−0.375471	−	0.926834i	$-0.622519\pi$
$761$	−37.6791	−	21.7541i	−1.36587	−	0.788584i	−0.990397	+	0.138250i	$0.955852\pi$
$762$		−	8.53944i		−	0.309351i
$763$		0			0
$764$	3.88382	+	6.72697i	0.140512	+	0.243373i
$765$	−19.6822	+	11.3635i	−0.711613	+	0.410850i
$766$	−27.1004			−0.979176
$767$	−25.9452	+	13.2200i	−0.936827	+	0.477348i
$768$	12.8345			0.463124
$769$	17.0148	−	9.82351i	0.613570	−	0.354245i	−0.160791	−	0.986988i	$-0.551405\pi$
$769$	17.0148	−	9.82351i	0.613570	−	0.354245i	0.774361	+	0.632743i	$0.218071\pi$
$770$		0			0
$771$	1.88980	−	3.27323i	0.0680596	−	0.117883i
$772$		−	1.23664i		−	0.0445077i
$773$	19.2232	+	11.0985i	0.691410	+	0.399186i	0.804140	−	0.594440i	$-0.202626\pi$
$773$	19.2232	+	11.0985i	0.691410	+	0.399186i	−0.112730	+	0.993626i	$0.535959\pi$
$774$	7.08713	+	4.09175i	0.254742	+	0.147075i
$775$			8.29300i			0.297894i
$776$	9.78007	−	16.9396i	0.351084	−	0.608096i
$777$		0			0
$778$	−11.6735	+	6.73968i	−0.418514	+	0.241629i
$779$	−2.50096			−0.0896062
$780$	3.58216	+	2.32624i	0.128262	+	0.0832926i
$781$	−0.817302			−0.0292454
$782$	33.8447	−	19.5402i	1.21028	−	0.698758i
$783$	10.1403	+	17.5634i	0.362383	+	0.627666i
$784$		0			0
$785$			4.89165i			0.174591i
$786$	−6.24663	−	3.60649i	−0.222810	−	0.128639i
$787$	−7.47595	−	4.31624i	−0.266489	−	0.153857i	0.360802	−	0.932642i	$-0.382503\pi$
$787$	−7.47595	−	4.31624i	−0.266489	−	0.153857i	−0.627291	+	0.778785i	$0.715836\pi$
$788$			5.87330i			0.209228i
$789$	7.13092	−	12.3511i	0.253867	−	0.439711i
$790$	7.20692	+	12.4828i	0.256411	+	0.444117i
$791$		0			0
$792$	−3.92791			−0.139572
$793$	6.18466	+	12.1378i	0.219624	+	0.431026i
$794$	10.0161			0.355460
$795$	−15.0442	+	8.68580i	−0.533564	+	0.308054i
$796$	−8.05506	−	13.9518i	−0.285504	−	0.494507i
$797$	−19.7592	+	34.2240i	−0.699908	+	1.21228i	0.268590	+	0.963255i	$0.413442\pi$
$797$	−19.7592	+	34.2240i	−0.699908	+	1.21228i	−0.968498	+	0.249022i	$0.919891\pi$
$798$		0			0
$799$	18.5221	+	10.6938i	0.655266	+	0.378318i
$800$	−8.90390	−	5.14067i	−0.314800	−	0.181750i
$801$			5.15249i			0.182054i
$802$	−5.91361	+	10.2427i	−0.208817	+	0.361681i
$803$	4.20395	+	7.28145i	0.148354	+	0.256957i
$804$	−5.87241	+	3.39044i	−0.207104	+	0.119571i
$805$		0			0
$806$	−14.1889	−	0.743486i	−0.499782	−	0.0261882i
$807$	−10.6049			−0.373311
$808$	19.4234	−	11.2141i	0.683313	−	0.394511i
$809$	−12.2583	−	21.2320i	−0.430979	−	0.746478i	0.565979	−	0.824420i	$-0.308498\pi$
$809$	−12.2583	−	21.2320i	−0.430979	−	0.746478i	−0.996958	+	0.0779419i	$0.975165\pi$
$810$	3.50778	−	6.07565i	0.123251	−	0.213477i
$811$			19.0854i			0.670179i	0.942186	+	0.335089i	$0.108767\pi$
$811$			19.0854i			0.670179i	−0.942186	+	0.335089i	$0.891233\pi$
$812$		0			0
$813$	13.3233	+	7.69219i	0.467267	+	0.269777i
$814$		−	0.772398i		−	0.0270726i
$815$	−14.1172	+	24.4516i	−0.494503	+	0.856504i
$816$	−2.85830	−	4.95072i	−0.100060	−	0.173310i
$817$	−5.70017	+	3.29100i	−0.199424	+	0.115137i
$818$	22.5602			0.788800
$819$		0			0
$820$	1.91169			0.0667590
$821$	−7.06462	+	4.07876i	−0.246557	+	0.142350i	−0.618187	−	0.786031i	$-0.712132\pi$
$821$	−7.06462	+	4.07876i	−0.246557	+	0.142350i	0.371630	+	0.928381i	$0.378799\pi$
$822$	1.65214	+	2.86160i	0.0576251	+	0.0998096i
$823$	24.2676	−	42.0328i	0.845917	−	1.46517i	−0.0389057	−	0.999243i	$-0.512387\pi$
$823$	24.2676	−	42.0328i	0.845917	−	1.46517i	0.884823	−	0.465928i	$-0.154279\pi$
$824$			53.1922i			1.85304i
$825$	−0.783717	−	0.452479i	−0.0272855	−	0.0157533i
$826$		0			0
$827$		−	2.45879i		−	0.0855004i	−0.999086	−	0.0427502i	$-0.986388\pi$
$827$		−	2.45879i		−	0.0855004i	0.999086	−	0.0427502i	$-0.0136120\pi$
$828$	7.38121	−	12.7846i	0.256515	−	0.444297i
$829$	18.0097	+	31.1938i	0.625504	+	1.08340i	0.988443	+	0.151592i	$0.0484399\pi$
$829$	18.0097	+	31.1938i	0.625504	+	1.08340i	−0.362939	+	0.931813i	$0.618227\pi$
$830$	14.2319	−	8.21680i	0.493997	−	0.285209i
$831$	19.9124			0.690754
$832$	14.7780	−	22.7565i	0.512334	−	0.788941i
$833$		0			0
$834$	13.6594	−	7.88624i	0.472985	−	0.273078i
$835$	−20.8529	−	36.1183i	−0.721644	−	1.24992i
$836$	0.497064	−	0.860939i	0.0171913	−	0.0297762i
$837$			15.7651i			0.544923i
$838$	−5.32847	−	3.07639i	−0.184069	−	0.106272i
$839$	28.7901	+	16.6220i	0.993945	+	0.573855i	0.906451	−	0.422310i	$-0.138781\pi$
$839$	28.7901	+	16.6220i	0.993945	+	0.573855i	0.0874940	+	0.996165i	$0.472114\pi$
$840$		0			0
$841$	2.62102	−	4.53973i	0.0903799	−	0.156543i
$842$	0.723361	+	1.25290i	0.0249287	+	0.0431777i
$843$	−13.4877	+	7.78710i	−0.464540	+	0.268202i
$844$	18.1785			0.625729
$845$	19.9124	−	8.86597i	0.685006	−	0.304999i
$846$	−9.51614			−0.327172
$847$		0			0
$848$	8.88817	+	15.3948i	0.305221	+	0.528658i
$849$	8.61510	−	14.9218i	0.295670	−	0.512115i
$850$			12.8132i			0.439489i
$851$	7.98924	+	4.61259i	0.273868	+	0.158118i
$852$	−0.930531	−	0.537243i	−0.0318795	−	0.0184056i
$853$		−	3.02993i		−	0.103743i	−0.998654	−	0.0518714i	$-0.983481\pi$
$853$		−	3.02993i		−	0.103743i	0.998654	−	0.0518714i	$-0.0165186\pi$
$854$		0			0
$855$	4.06660	+	7.04356i	0.139075	+	0.240885i
$856$	13.2033	−	7.62295i	0.451281	−	0.260547i
$857$	35.8756			1.22549			0.612744	−	0.790282i	$-0.290066\pi$
$857$	35.8756			1.22549			0.612744	+	0.790282i	$0.290066\pi$
$858$	0.844430	−	1.30033i	0.0288284	−	0.0443926i
$859$	16.1467			0.550918			0.275459	−	0.961313i	$-0.411170\pi$
$859$	16.1467			0.550918			0.275459	+	0.961313i	$0.411170\pi$
$860$	4.35711	−	2.51558i	0.148576	−	0.0857805i
$861$		0			0
$862$	−2.61920	+	4.53658i	−0.0892102	+	0.154517i
$863$		−	8.12050i		−	0.276425i	−0.990403	−	0.138212i	$-0.955864\pi$
$863$		−	8.12050i		−	0.276425i	0.990403	−	0.138212i	$-0.0441357\pi$
$864$	−16.9265	−	9.77250i	−0.575850	−	0.332467i
$865$	0.225839	+	0.130388i	0.00767877	+	0.00443334i
$866$		−	15.3311i		−	0.520972i
$867$	5.64866	−	9.78376i	0.191838	−	0.332274i
$868$		0			0
$869$	−3.84696	+	2.22104i	−0.130499	+	0.0753437i
$870$	−6.53939			−0.221706
$871$	−1.81075	+	34.5570i	−0.0613551	+	1.17092i
$872$	−54.2262			−1.83633
$873$	−13.4398	+	7.75945i	−0.454867	+	0.262618i
$874$	−6.99275	−	12.1118i	−0.236533	−	0.409687i
$875$		0			0
$876$			11.0536i			0.373467i
$877$	18.9143	+	10.9202i	0.638692	+	0.368749i	0.784110	−	0.620621i	$-0.213120\pi$
$877$	18.9143	+	10.9202i	0.638692	+	0.368749i	−0.145419	+	0.989370i	$0.546453\pi$
$878$	6.89779	+	3.98244i	0.232789	+	0.134401i
$879$		−	17.6356i		−	0.594833i
$880$	0.594727	−	1.03010i	0.0200483	−	0.0347246i
$881$	20.4350	+	35.3945i	0.688473	+	1.19247i	0.972332	+	0.233604i	$0.0750518\pi$
$881$	20.4350	+	35.3945i	0.688473	+	1.19247i	−0.283859	+	0.958866i	$0.591615\pi$
$882$		0			0
$883$	7.78501			0.261986			0.130993	−	0.991383i	$-0.458183\pi$
$883$	7.78501			0.261986			0.130993	+	0.991383i	$0.458183\pi$
$884$	18.6119	+	0.975250i	0.625987	+	0.0328012i
$885$	−10.4181			−0.350202
$886$	27.0723	−	15.6302i	0.909511	−	0.525106i
$887$	0.241085	+	0.417572i	0.00809486	+	0.0140207i	0.870044	−	0.492973i	$-0.164090\pi$
$887$	0.241085	+	0.417572i	0.00809486	+	0.0140207i	−0.861950	+	0.506994i	$0.830757\pi$
$888$	1.61349	−	2.79465i	0.0541453	−	0.0937824i
$889$		0			0
$890$	−3.23131	−	1.86560i	−0.108314	−	0.0625349i
$891$	1.87241	+	1.08103i	0.0627280	+	0.0362160i
$892$			24.6604i			0.825690i
$893$	3.82691	−	6.62841i	0.128063	−	0.221811i
$894$	−5.91642	−	10.2475i	−0.197875	−	0.342729i
$895$	−29.6576	+	17.1228i	−0.991345	+	0.572353i
$896$		0			0
$897$	8.40713	+	16.4996i	0.280706	+	0.550905i
$898$	−34.4526			−1.14970
$899$	−15.9941	+	9.23417i	−0.533432	+	0.307977i
$900$	2.42005	+	4.19166i	0.0806685	+	0.139722i
$901$	−37.9006	+	65.6457i	−1.26265	+	2.18698i
$902$		−	0.693947i		−	0.0231059i
$903$		0			0
$904$	19.9113	+	11.4958i	0.662239	+	0.382344i
$905$		−	9.70429i		−	0.322582i
$906$	−6.46286	+	11.1940i	−0.214714	+	0.371896i
$907$	2.95150	+	5.11215i	0.0980030	+	0.169746i	0.910858	−	0.412720i	$-0.135421\pi$
$907$	2.95150	+	5.11215i	0.0980030	+	0.169746i	−0.812855	+	0.582466i	$0.802088\pi$
$908$	1.30519	−	0.753552i	0.0433143	−	0.0250075i
$909$	−17.7944			−0.590203
$910$		0			0
$911$	−39.3536			−1.30384			−0.651921	−	0.758287i	$-0.726037\pi$
$911$	−39.3536			−1.30384			−0.651921	+	0.758287i	$0.726037\pi$
$912$	−1.77168	+	1.02288i	−0.0586663	+	0.0338710i
$913$	2.53227	+	4.38602i	0.0838059	+	0.145156i
$914$	−11.4684	+	19.8638i	−0.379341	+	0.657038i
$915$			4.87387i			0.161125i
$916$	−5.55185	−	3.20536i	−0.183438	−	0.105908i
$917$		0			0
$918$			24.3581i			0.803937i
$919$	9.22582	−	15.9796i	0.304332	−	0.527118i	−0.672781	−	0.739842i	$-0.734900\pi$
$919$	9.22582	−	15.9796i	0.304332	−	0.527118i	0.977112	+	0.212724i	$0.0682335\pi$
$920$	16.9862	+	29.4209i	0.560018	+	0.969980i
$921$	−19.2666	+	11.1236i	−0.634855	+	0.366534i
$922$	−22.9005			−0.754187
$923$	−4.88568	+	2.48943i	−0.160814	+	0.0819406i
$924$		0			0
$925$	−2.61941	+	1.51232i	−0.0861256	+	0.0497246i
$926$	18.2185	+	31.5554i	0.598698	+	1.03698i
$927$	21.1012	−	36.5483i	0.693054	−	1.20041i
$928$		−	22.8963i		−	0.751609i
$929$	−3.00647	−	1.73579i	−0.0986390	−	0.0569493i	0.449869	−	0.893095i	$-0.351471\pi$
$929$	−3.00647	−	1.73579i	−0.0986390	−	0.0569493i	−0.548508	+	0.836145i	$0.684804\pi$
$930$	−4.40237	−	2.54171i	−0.144359	−	0.0833460i
$931$		0			0
$932$	6.59445	−	11.4219i	0.216008	−	0.374137i
$933$	−2.01434	−	3.48894i	−0.0659466	−	0.114223i
$934$	−17.1275	+	9.88859i	−0.560430	+	0.323565i
$935$	5.07203			0.165873
$936$	−23.4803	+	11.9641i	−0.767478	+	0.391058i
$937$	−16.7987			−0.548789			−0.274395	−	0.961617i	$-0.588477\pi$
$937$	−16.7987			−0.548789			−0.274395	+	0.961617i	$0.588477\pi$
$938$		0			0
$939$	−6.04577	−	10.4716i	−0.197296	−	0.341727i
$940$	−2.92522	+	5.06663i	−0.0954102	+	0.165255i
$941$			1.56115i			0.0508922i	0.999676	+	0.0254461i	$0.00810061\pi$
$941$			1.56115i			0.0508922i	−0.999676	+	0.0254461i	$0.991899\pi$
$942$	2.02168	+	1.16722i	0.0658700	+	0.0380301i
$943$	7.17779	+	4.14410i	0.233741	+	0.134950i
$944$			10.6609i			0.346982i
$945$		0			0
$946$	−0.913161	−	1.58164i	−0.0296894	−	0.0514236i
$947$	38.2656	−	22.0927i	1.24347	−	0.717915i	0.273668	−	0.961824i	$-0.411763\pi$
$947$	38.2656	−	22.0927i	1.24347	−	0.717915i	0.969798	+	0.243909i	$0.0784298\pi$
$948$	−5.83989			−0.189671
$949$	47.3090	+	30.7222i	1.53572	+	0.997286i
$950$	4.58538			0.148769
$951$	−16.9100	+	9.76299i	−0.548344	+	0.316587i
$952$		0			0
$953$	−7.17547	+	12.4283i	−0.232436	+	0.402591i	−0.958525	−	0.285010i	$-0.908003\pi$
$953$	−7.17547	+	12.4283i	−0.232436	+	0.402591i	0.726088	+	0.687602i	$0.241336\pi$
$954$		−	33.7269i		−	1.09195i
$955$	12.2822	+	7.09114i	0.397443	+	0.229464i
$956$	−15.9028	−	9.18149i	−0.514333	−	0.296951i
$957$		−	2.01532i		−	0.0651461i
$958$	−10.5616	+	18.2932i	−0.341229	+	0.591026i
$959$		0			0
$960$	8.40727	−	4.85394i	0.271343	−	0.156660i
$961$	16.6436			0.536889
$962$	−2.35266	−	4.61725i	−0.0758527	−	0.148866i
$963$	−12.0960			−0.389788
$964$	−22.0310	+	12.7196i	−0.709570	+	0.409670i
$965$	−1.12894	−	1.95538i	−0.0363419	−	0.0629460i
$966$		0			0
$967$			46.1818i			1.48511i	0.669787	+	0.742553i	$0.266385\pi$
$967$			46.1818i			1.48511i	−0.669787	+	0.742553i	$0.733615\pi$
$968$	−28.1547	−	16.2551i	−0.904925	−	0.522459i
$969$	−7.55474	−	4.36173i	−0.242693	−	0.140119i
$970$		−	11.2381i		−	0.360832i
$971$	−20.9662	+	36.3146i	−0.672839	+	1.16539i	0.304257	+	0.952590i	$0.401592\pi$
$971$	−20.9662	+	36.3146i	−0.672839	+	1.16539i	−0.977096	+	0.212801i	$0.931742\pi$
$972$	7.15261	+	12.3887i	0.229420	+	0.397367i
$973$		0			0
$974$	−6.69231			−0.214436
$975$	−6.06312	−	0.317702i	−0.194175	−	0.0101746i
$976$	4.98742			0.159644
$977$	−2.72433	+	1.57290i	−0.0871592	+	0.0503214i	−0.542946	−	0.839768i	$-0.682691\pi$
$977$	−2.72433	+	1.57290i	−0.0871592	+	0.0503214i	0.455787	+	0.890089i	$0.349358\pi$
$978$	6.73713	+	11.6690i	0.215430	+	0.373135i
$979$	0.574943	−	0.995830i	0.0183753	−	0.0318269i
$980$		0			0
$981$	37.2588	+	21.5114i	1.18958	+	0.686805i
$982$	0.865055	+	0.499440i	0.0276050	+	0.0159378i
$983$			49.4907i			1.57851i	0.614067	+	0.789254i	$0.289533\pi$
$983$			49.4907i			1.57851i	−0.614067	+	0.789254i	$0.710467\pi$
$984$	1.44961	−	2.51080i	0.0462120	−	0.0800415i
$985$	5.36178	+	9.28688i	0.170841	+	0.295905i
$986$	−24.7118	+	14.2674i	−0.786983	+	0.454365i
$987$		0			0
$988$	0.349007	−	6.66054i	0.0111034	−	0.211900i
$989$	21.8128			0.693606
$990$	−1.95439	+	1.12837i	−0.0621147	+	0.0358619i
$991$	−8.28076	−	14.3427i	−0.263047	−	0.455611i	0.704003	−	0.710197i	$-0.251394\pi$
$991$	−8.28076	−	14.3427i	−0.263047	−	0.455611i	−0.967050	+	0.254586i	$0.918061\pi$
$992$	8.89927	−	15.4140i	0.282552	−	0.489395i
$993$			10.9939i			0.348880i
$994$		0			0
$995$	−25.4734	−	14.7071i	−0.807561	−	0.466245i
$996$			6.65822i			0.210974i
$997$	−12.1716	+	21.0819i	−0.385479	+	0.667669i	−0.991836	−	0.127524i	$-0.959297\pi$
$997$	−12.1716	+	21.0819i	−0.385479	+	0.667669i	0.606356	+	0.795193i	$0.292630\pi$
$998$	−5.09019	−	8.81647i	−0.161127	−	0.279080i
$999$	−4.97953	+	2.87494i	−0.157545	+	0.0909589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.j.491.12	yes	32
7.2	even	3		637.2.u.j.361.5		32
7.3	odd	6		637.2.k.j.569.11		32
7.4	even	3		637.2.k.j.569.12		32
7.5	odd	6		637.2.u.j.361.6		32
7.6	odd	2	inner	637.2.q.j.491.11	✓	32
13.2	odd	12		8281.2.a.cx.1.21		32
13.4	even	6	inner	637.2.q.j.589.12	yes	32
13.11	odd	12		8281.2.a.cx.1.11		32
91.4	even	6		637.2.u.j.30.5		32
91.17	odd	6		637.2.u.j.30.6		32
91.30	even	6		637.2.k.j.459.6		32
91.41	even	12		8281.2.a.cx.1.22		32
91.69	odd	6	inner	637.2.q.j.589.11	yes	32
91.76	even	12		8281.2.a.cx.1.12		32
91.82	odd	6		637.2.k.j.459.5		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.5		32	91.82	odd	6
637.2.k.j.459.6		32	91.30	even	6
637.2.k.j.569.11		32	7.3	odd	6
637.2.k.j.569.12		32	7.4	even	3
637.2.q.j.491.11	✓	32	7.6	odd	2	inner
637.2.q.j.491.12	yes	32	1.1	even	1	trivial
637.2.q.j.589.11	yes	32	91.69	odd	6	inner
637.2.q.j.589.12	yes	32	13.4	even	6	inner
637.2.u.j.30.5		32	91.4	even	6
637.2.u.j.30.6		32	91.17	odd	6
637.2.u.j.361.5		32	7.2	even	3
637.2.u.j.361.6		32	7.5	odd	6
8281.2.a.cx.1.11		32	13.11	odd	12
8281.2.a.cx.1.12		32	91.76	even	12
8281.2.a.cx.1.21		32	13.2	odd	12
8281.2.a.cx.1.22		32	91.41	even	12

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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.900699 - 0.520019i) q^{2} +(0.384681 + 0.666288i) q^{3} +(-0.459161 + 0.795291i) q^{4} +1.67669i q^{5} +(0.692964 + 0.400083i) q^{6} +3.03516i q^{8} +(1.20404 - 2.08546i) q^{9} +O(q^{10})\)	\(q+(0.900699 - 0.520019i) q^{2} +(0.384681 + 0.666288i) q^{3} +(-0.459161 + 0.795291i) q^{4} +1.67669i q^{5} +(0.692964 + 0.400083i) q^{6} +3.03516i q^{8} +(1.20404 - 2.08546i) q^{9} +(0.871910 + 1.51019i) q^{10} +(-0.465414 + 0.268707i) q^{11} -0.706523 q^{12} +(-1.96370 + 3.02389i) q^{13} +(-1.11716 + 0.644991i) q^{15} +(0.660019 + 1.14319i) q^{16} +(-2.81443 + 4.87473i) q^{17} -2.50449i q^{18} +(1.74449 + 1.00718i) q^{19} +(-1.33346 - 0.769871i) q^{20} +(-0.279465 + 0.484048i) q^{22} +(-3.33781 - 5.78125i) q^{23} +(-2.02229 + 1.16757i) q^{24} +2.18871 q^{25} +(-0.196223 + 3.74477i) q^{26} +4.16078 q^{27} +(2.43711 + 4.22119i) q^{29} +(-0.670815 + 1.16189i) q^{30} +3.78899i q^{31} +(-4.06810 - 2.34872i) q^{32} +(-0.358072 - 0.206733i) q^{33} +5.85422i q^{34} +(1.10570 + 1.91512i) q^{36} +(-1.19678 + 0.690961i) q^{37} +2.09501 q^{38} +(-2.77018 - 0.145155i) q^{39} -5.08903 q^{40} +(-1.07523 + 0.620782i) q^{41} +(-1.63377 + 2.82976i) q^{43} -0.493519i q^{44} +(3.49667 + 2.01880i) q^{45} +(-6.01271 - 3.47144i) q^{46} -3.79963i q^{47} +(-0.507794 + 0.879525i) q^{48} +(1.97137 - 1.13817i) q^{50} -4.33063 q^{51} +(-1.50322 - 2.95016i) q^{52} +13.4665 q^{53} +(3.74760 - 2.16368i) q^{54} +(-0.450538 - 0.780355i) q^{55} +1.54978i q^{57} +(4.39020 + 2.53468i) q^{58} +(6.99419 + 4.03810i) q^{59} -1.18462i q^{60} +(1.88912 - 3.27205i) q^{61} +(1.97034 + 3.41274i) q^{62} -7.52559 q^{64} +(-5.07012 - 3.29251i) q^{65} -0.430020 q^{66} +(8.31170 - 4.79876i) q^{67} +(-2.58455 - 4.47658i) q^{68} +(2.56798 - 4.44788i) q^{69} +(1.31706 + 0.760403i) q^{71} +(6.32971 + 3.65446i) q^{72} -15.6451i q^{73} +(-0.718625 + 1.24470i) q^{74} +(0.841957 + 1.45831i) q^{75} +(-1.60200 + 0.924918i) q^{76} +(-2.57058 + 1.30980i) q^{78} +8.26567 q^{79} +(-1.91677 + 1.10665i) q^{80} +(-2.01155 - 3.48410i) q^{81} +(-0.645636 + 1.11827i) q^{82} -9.42392i q^{83} +(-8.17341 - 4.71892i) q^{85} +3.39835i q^{86} +(-1.87502 + 3.24763i) q^{87} +(-0.815570 - 1.41261i) q^{88} +(-1.85300 + 1.06983i) q^{89} +4.19926 q^{90} +6.13037 q^{92} +(-2.52456 + 1.45755i) q^{93} +(-1.97588 - 3.42232i) q^{94} +(-1.68873 + 2.92497i) q^{95} -3.61403i q^{96} +(-5.58111 - 3.22225i) q^{97} +1.29414i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4} - 28 q^{9}+O(q^{10}) \) 32 * q + 20 * q^4 - 28 * q^9	\( 32 q + 20 q^{4} - 28 q^{9} - 12 q^{15} - 28 q^{16} + 8 q^{22} + 24 q^{23} - 40 q^{25} - 24 q^{29} + 24 q^{30} - 60 q^{32} + 92 q^{36} - 32 q^{39} + 12 q^{43} - 24 q^{46} + 12 q^{50} + 72 q^{53} - 132 q^{58} + 32 q^{64} + 48 q^{67} - 48 q^{71} + 72 q^{72} + 24 q^{74} - 156 q^{78} + 96 q^{79} - 64 q^{81} + 12 q^{85} + 56 q^{88} + 168 q^{92} - 48 q^{93} + 84 q^{95}+O(q^{100}) \) 32 * q + 20 * q^4 - 28 * q^9 - 12 * q^15 - 28 * q^16 + 8 * q^22 + 24 * q^23 - 40 * q^25 - 24 * q^29 + 24 * q^30 - 60 * q^32 + 92 * q^36 - 32 * q^39 + 12 * q^43 - 24 * q^46 + 12 * q^50 + 72 * q^53 - 132 * q^58 + 32 * q^64 + 48 * q^67 - 48 * q^71 + 72 * q^72 + 24 * q^74 - 156 * q^78 + 96 * q^79 - 64 * q^81 + 12 * q^85 + 56 * q^88 + 168 * q^92 - 48 * q^93 + 84 * q^95

Introduction

L-functions

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