LMFDB - Embedded newform 637.2.q.j.491.3

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			491.3
Character	$\chi$	$=$	637.491
Dual form			637.2.q.j.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.04719 + 1.18194i) q^{2} +(-1.49347 - 2.58676i) q^{3} +(1.79399 - 3.10727i) q^{4} -3.20263i q^{5} +(6.11481 + 3.53039i) q^{6} +3.75379i q^{8} +(-2.96088 + 5.12839i) q^{9} +O(q^{10})$	\(q+(-2.04719 + 1.18194i) q^{2} +(-1.49347 - 2.58676i) q^{3} +(1.79399 - 3.10727i) q^{4} -3.20263i q^{5} +(6.11481 + 3.53039i) q^{6} +3.75379i q^{8} +(-2.96088 + 5.12839i) q^{9} +(3.78533 + 6.55639i) q^{10} +(-3.19878 + 1.84682i) q^{11} -10.7170 q^{12} +(-2.99897 + 2.00154i) q^{13} +(-8.28443 + 4.78302i) q^{15} +(-0.848797 - 1.47016i) q^{16} +(-0.733403 + 1.27029i) q^{17} -13.9984i q^{18} +(5.11958 + 2.95579i) q^{19} +(-9.95145 - 5.74547i) q^{20} +(4.36567 - 7.56157i) q^{22} +(-0.345203 - 0.597908i) q^{23} +(9.71014 - 5.60615i) q^{24} -5.25684 q^{25} +(3.77375 - 7.64215i) q^{26} +8.72707 q^{27} +(2.39239 + 4.14374i) q^{29} +(11.3065 - 19.5835i) q^{30} -2.10879i q^{31} +(-3.02646 - 1.74733i) q^{32} +(9.55454 + 5.51632i) q^{33} -3.46737i q^{34} +(10.6235 + 18.4005i) q^{36} +(1.09027 - 0.629465i) q^{37} -13.9743 q^{38} +(9.65636 + 4.76838i) q^{39} +12.0220 q^{40} +(-0.224704 + 0.129733i) q^{41} +(-2.80608 + 4.86027i) q^{43} +13.2527i q^{44} +(16.4243 + 9.48259i) q^{45} +(1.41339 + 0.816021i) q^{46} -11.6216i q^{47} +(-2.53530 + 4.39126i) q^{48} +(10.7617 - 6.21329i) q^{50} +4.38125 q^{51} +(0.839222 + 12.9094i) q^{52} +0.485623 q^{53} +(-17.8659 + 10.3149i) q^{54} +(5.91467 + 10.2445i) q^{55} -17.6575i q^{57} +(-9.79535 - 5.65535i) q^{58} +(-7.55939 - 4.36441i) q^{59} +34.3226i q^{60} +(-5.73161 + 9.92744i) q^{61} +(2.49247 + 4.31709i) q^{62} +11.6562 q^{64} +(6.41019 + 9.60460i) q^{65} -26.0799 q^{66} +(0.296094 - 0.170950i) q^{67} +(2.63143 + 4.55777i) q^{68} +(-1.03110 + 1.78591i) q^{69} +(-7.10638 - 4.10287i) q^{71} +(-19.2509 - 11.1145i) q^{72} +0.259823i q^{73} +(-1.48799 + 2.57727i) q^{74} +(7.85090 + 13.5982i) q^{75} +(18.3689 - 10.6053i) q^{76} +(-25.4043 + 1.65151i) q^{78} +10.1259 q^{79} +(-4.70838 + 2.71838i) q^{80} +(-4.15094 - 7.18964i) q^{81} +(0.306674 - 0.531175i) q^{82} +10.0995i q^{83} +(4.06827 + 2.34882i) q^{85} -13.2665i q^{86} +(7.14590 - 12.3771i) q^{87} +(-6.93256 - 12.0075i) q^{88} +(-2.16722 + 1.25125i) q^{89} -44.8316 q^{90} -2.47715 q^{92} +(-5.45493 + 3.14941i) q^{93} +(13.7360 + 23.7915i) q^{94} +(9.46631 - 16.3961i) q^{95} +10.4383i q^{96} +(-4.58314 - 2.64607i) q^{97} -21.8728i 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 $

$2$	−2.04719	+	1.18194i	−1.44758	+	0.835761i	−0.998337	−	0.0576484i	$-0.981640\pi$
$2$	−2.04719	+	1.18194i	−1.44758	+	0.835761i	−0.449243	+	0.893409i	$0.648306\pi$
$3$	−1.49347	−	2.58676i	−0.862252	−	1.49347i	−0.869750	−	0.493493i	$-0.835720\pi$
$3$	−1.49347	−	2.58676i	−0.862252	−	1.49347i	0.00749727	−	0.999972i	$-0.497614\pi$
$4$	1.79399	−	3.10727i	0.896993	−	1.55364i
$5$		−	3.20263i		−	1.43226i	−0.697967	−	0.716130i	$-0.745912\pi$
$5$		−	3.20263i		−	1.43226i	0.697967	−	0.716130i	$-0.254088\pi$
$6$	6.11481	+	3.53039i	2.49636	+	1.44127i
$7$		0			0
$7$		0			0
$8$			3.75379i			1.32716i
$9$	−2.96088	+	5.12839i	−0.986959	+	1.70946i
$10$	3.78533	+	6.55639i	1.19703	+	2.07331i
$11$	−3.19878	+	1.84682i	−0.964469	+	0.556837i	−0.897546	−	0.440922i	$-0.854652\pi$
$11$	−3.19878	+	1.84682i	−0.964469	+	0.556837i	−0.0669235	+	0.997758i	$0.521318\pi$
$12$	−10.7170			−3.09374
$13$	−2.99897	+	2.00154i	−0.831765	+	0.555127i
$13$	−2.99897	+	2.00154i	−0.831765	+	0.555127i
$14$		0			0
$15$	−8.28443	+	4.78302i	−2.13903	+	1.23497i
$16$	−0.848797	−	1.47016i	−0.212199	−	0.367540i
$17$	−0.733403	+	1.27029i	−0.177876	+	0.308091i	−0.941153	−	0.337981i	$-0.890256\pi$
$17$	−0.733403	+	1.27029i	−0.177876	+	0.308091i	0.763277	+	0.646072i	$0.223589\pi$
$18$		−	13.9984i		−	3.29945i
$19$	5.11958	+	2.95579i	1.17451	+	0.678105i	0.954739	−	0.297445i	$-0.0961346\pi$
$19$	5.11958	+	2.95579i	1.17451	+	0.678105i	0.219774	+	0.975551i	$0.429468\pi$
$20$	−9.95145	−	5.74547i	−2.22521	−	1.28473i
$21$		0			0
$22$	4.36567	−	7.56157i	0.930764	−	1.61213i
$23$	−0.345203	−	0.597908i	−0.0719797	−	0.124673i	0.827789	−	0.561039i	$-0.189598\pi$
$23$	−0.345203	−	0.597908i	−0.0719797	−	0.124673i	−0.899769	+	0.436367i	$0.856265\pi$
$24$	9.71014	−	5.60615i	1.98207	−	1.14435i
$25$	−5.25684			−1.05137
$26$	3.77375	−	7.64215i	0.740093	−	1.49875i
$27$	8.72707			1.67952
$28$		0			0
$29$	2.39239	+	4.14374i	0.444256	+	0.769474i	0.998000	−	0.0632132i	$-0.0201348\pi$
$29$	2.39239	+	4.14374i	0.444256	+	0.769474i	−0.553744	+	0.832687i	$0.686801\pi$
$30$	11.3065	−	19.5835i	2.06428	−	3.57543i
$31$		−	2.10879i		−	0.378750i	−0.981905	−	0.189375i	$-0.939354\pi$
$31$		−	2.10879i		−	0.378750i	0.981905	−	0.189375i	$-0.0606462\pi$
$32$	−3.02646	−	1.74733i	−0.535007	−	0.308886i
$33$	9.55454	+	5.51632i	1.66323	+	0.960267i
$34$		−	3.46737i		−	0.594649i
$35$		0			0
$36$	10.6235	+	18.4005i	1.77059	+	3.06675i
$37$	1.09027	−	0.629465i	0.179238	−	0.103483i	−0.407696	−	0.913118i	$-0.633668\pi$
$37$	1.09027	−	0.629465i	0.179238	−	0.103483i	0.586935	+	0.809634i	$0.300334\pi$
$38$	−13.9743			−2.26694
$39$	9.65636	+	4.76838i	1.54626	+	0.763552i
$40$	12.0220			1.90084
$41$	−0.224704	+	0.129733i	−0.0350928	+	0.0202609i	−0.517444	−	0.855717i	$-0.673116\pi$
$41$	−0.224704	+	0.129733i	−0.0350928	+	0.0202609i	0.482351	+	0.875978i	$0.339783\pi$
$42$		0			0
$43$	−2.80608	+	4.86027i	−0.427923	+	0.741184i	−0.996688	−	0.0813155i	$-0.974088\pi$
$43$	−2.80608	+	4.86027i	−0.427923	+	0.741184i	0.568766	+	0.822500i	$0.307421\pi$
$44$			13.2527i			1.99791i
$45$	16.4243	+	9.48259i	2.44839	+	1.41358i
$46$	1.41339	+	0.816021i	0.208393	+	0.120316i
$47$		−	11.6216i		−	1.69518i	−0.530653	−	0.847589i	$-0.678053\pi$
$47$		−	11.6216i		−	1.69518i	0.530653	−	0.847589i	$-0.321947\pi$
$48$	−2.53530	+	4.39126i	−0.365939	+	0.633824i
$49$		0			0
$50$	10.7617	−	6.21329i	1.52194	−	0.878692i
$51$	4.38125			0.613497
$52$	0.839222	+	12.9094i	0.116379	+	1.79021i
$53$	0.485623			0.0667055			0.0333527	−	0.999444i	$-0.489382\pi$
$53$	0.485623			0.0667055			0.0333527	+	0.999444i	$0.489382\pi$
$54$	−17.8659	+	10.3149i	−2.43125	+	1.40368i
$55$	5.91467	+	10.2445i	0.797534	+	1.38137i
$56$		0			0
$57$		−	17.6575i		−	2.33879i
$58$	−9.79535	−	5.65535i	−1.28619	−	0.742583i
$59$	−7.55939	−	4.36441i	−0.984148	−	0.568198i	−0.0806283	−	0.996744i	$-0.525693\pi$
$59$	−7.55939	−	4.36441i	−0.984148	−	0.568198i	−0.903520	+	0.428546i	$0.859026\pi$
$60$			34.3226i			4.43103i
$61$	−5.73161	+	9.92744i	−0.733858	+	1.27108i	0.221365	+	0.975191i	$0.428949\pi$
$61$	−5.73161	+	9.92744i	−0.733858	+	1.27108i	−0.955223	+	0.295888i	$0.904385\pi$
$62$	2.49247	+	4.31709i	0.316545	+	0.548271i
$63$		0			0
$64$	11.6562			1.45702
$65$	6.41019	+	9.60460i	0.795087	+	1.19130i
$66$	−26.0799			−3.21022
$67$	0.296094	−	0.170950i	0.0361736	−	0.0208849i	−0.481804	−	0.876279i	$-0.660018\pi$
$67$	0.296094	−	0.170950i	0.0361736	−	0.0208849i	0.517978	+	0.855394i	$0.326685\pi$
$68$	2.63143	+	4.55777i	0.319108	+	0.552711i
$69$	−1.03110	+	1.78591i	−0.124129	+	0.214998i
$70$		0			0
$71$	−7.10638	−	4.10287i	−0.843372	−	0.486921i	0.0150373	−	0.999887i	$-0.495213\pi$
$71$	−7.10638	−	4.10287i	−0.843372	−	0.486921i	−0.858409	+	0.512966i	$0.828547\pi$
$72$	−19.2509	−	11.1145i	−2.26874	−	1.30986i
$73$			0.259823i			0.0304100i	0.999884	+	0.0152050i	$0.00484008\pi$
$73$			0.259823i			0.0304100i	−0.999884	+	0.0152050i	$0.995160\pi$
$74$	−1.48799	+	2.57727i	−0.172975	+	0.299601i
$75$	7.85090	+	13.5982i	0.906544	+	1.57018i
$76$	18.3689	−	10.6053i	2.10706	−	1.21651i
$77$		0			0
$78$	−25.4043	+	1.65151i	−2.87648	+	0.186996i
$79$	10.1259			1.13925			0.569627	−	0.821903i	$-0.307088\pi$
$79$	10.1259			1.13925			0.569627	+	0.821903i	$0.307088\pi$
$80$	−4.70838	+	2.71838i	−0.526413	+	0.303924i
$81$	−4.15094	−	7.18964i	−0.461216	−	0.798849i
$82$	0.306674	−	0.531175i	0.0338665	−	0.0586584i
$83$			10.0995i			1.10857i	0.832327	+	0.554285i	$0.187008\pi$
$83$			10.0995i			1.10857i	−0.832327	+	0.554285i	$0.812992\pi$
$84$		0			0
$85$	4.06827	+	2.34882i	0.441266	+	0.254765i
$86$		−	13.2665i		−	1.43056i
$87$	7.14590	−	12.3771i	0.766121	−	1.32696i
$88$	−6.93256	−	12.0075i	−0.739014	−	1.28001i
$89$	−2.16722	+	1.25125i	−0.229725	+	0.132632i	−0.610445	−	0.792059i	$-0.709009\pi$
$89$	−2.16722	+	1.25125i	−0.229725	+	0.132632i	0.380720	+	0.924690i	$0.375676\pi$
$90$	−44.8316			−4.72566
$91$		0			0
$92$	−2.47715			−0.258261
$93$	−5.45493	+	3.14941i	−0.565650	+	0.326578i
$94$	13.7360	+	23.7915i	1.41676	+	2.45391i
$95$	9.46631	−	16.3961i	0.971223	−	1.68221i
$96$			10.4383i			1.06535i
$97$	−4.58314	−	2.64607i	−0.465347	−	0.268668i	0.248943	−	0.968518i	$-0.419917\pi$
$97$	−4.58314	−	2.64607i	−0.465347	−	0.268668i	−0.714290	+	0.699850i	$0.753250\pi$
$98$		0			0
$99$		−	21.8728i		−	2.19830i
$100$	−9.43069	+	16.3344i	−0.943069	+	1.63344i
$101$	6.00425	+	10.3997i	0.597445	+	1.03480i	0.993197	+	0.116447i	$0.0371507\pi$
$101$	6.00425	+	10.3997i	0.597445	+	1.03480i	−0.395752	+	0.918357i	$0.629516\pi$
$102$	−8.96924	+	5.17839i	−0.888087	+	0.512737i
$103$	8.36022			0.823756			0.411878	−	0.911239i	$-0.364873\pi$
$103$	8.36022			0.823756			0.411878	+	0.911239i	$0.364873\pi$
$104$	−7.51336	−	11.2575i	−0.736745	−	1.10389i
$105$		0			0
$106$	−0.994162	+	0.573980i	−0.0965616	+	0.0557498i
$107$	−5.14150	−	8.90534i	−0.497048	−	0.860912i	0.502947	−	0.864317i	$-0.332249\pi$
$107$	−5.14150	−	8.90534i	−0.497048	−	0.860912i	−0.999994	+	0.00340581i	$0.998916\pi$
$108$	15.6562	−	27.1174i	1.50652	−	2.60937i
$109$			19.7427i			1.89101i	0.325604	+	0.945506i	$0.394432\pi$
$109$			19.7427i			1.89101i	−0.325604	+	0.945506i	$0.605568\pi$
$110$	−24.2169	−	13.9816i	−2.30899	−	1.33310i
$111$	−3.25655	−	1.88017i	−0.309098	−	0.178458i
$112$		0			0
$113$	−1.53549	+	2.65954i	−0.144446	+	0.250189i	−0.929166	−	0.369662i	$-0.879473\pi$
$113$	−1.53549	+	2.65954i	−0.144446	+	0.250189i	0.784720	+	0.619851i	$0.212807\pi$
$114$	20.8702	+	36.1482i	1.95467	+	3.38559i
$115$	−1.91488	+	1.10556i	−0.178563	+	0.103094i
$116$	17.1677			1.59398
$117$	−1.38509	−	21.3062i	−0.128052	−	1.96976i
$118$	20.6340			1.89951
$119$		0			0
$120$	−17.9544	−	31.0980i	−1.63901	−	2.83884i
$121$	1.32147	−	2.28886i	0.120134	−	0.208078i
$122$		−	27.0978i		−	2.45332i
$123$	0.671174	+	0.387503i	0.0605178	+	0.0349399i
$124$	−6.55259	−	3.78314i	−0.588440	−	0.339736i
$125$			0.822557i			0.0735717i
$126$		0			0
$127$	9.23647	+	15.9980i	0.819604	+	1.41960i	0.905974	+	0.423333i	$0.139140\pi$
$127$	9.23647	+	15.9980i	0.819604	+	1.41960i	−0.0863703	+	0.996263i	$0.527527\pi$
$128$	−17.8094	+	10.2823i	−1.57415	+	0.908833i
$129$	16.7631			1.47591
$130$	−24.4750	−	12.0859i	−2.14660	−	1.06001i
$131$	−12.5565			−1.09707			−0.548535	−	0.836128i	$-0.684814\pi$
$131$	−12.5565			−1.09707			−0.548535	+	0.836128i	$0.684814\pi$
$132$	34.2814	−	19.7924i	2.98381	−	1.72271i
$133$		0			0
$134$	−0.404107	+	0.699934i	−0.0349095	+	0.0604650i
$135$		−	27.9496i		−	2.40552i
$136$	−4.76840	−	2.75304i	−0.408887	−	0.236071i
$137$	15.3386	+	8.85577i	1.31047	+	0.756600i	0.982174	−	0.187975i	$-0.0601926\pi$
$137$	15.3386	+	8.85577i	1.31047	+	0.756600i	0.328295	+	0.944575i	$0.393526\pi$
$138$		−	4.87479i		−	0.414970i
$139$	3.73758	−	6.47367i	0.317017	−	0.549090i	−0.662847	−	0.748755i	$-0.730652\pi$
$139$	3.73758	−	6.47367i	0.317017	−	0.549090i	0.979864	+	0.199665i	$0.0639854\pi$
$140$		0			0
$141$	−30.0622	+	17.3564i	−2.53169	+	1.46167i
$142$	19.3974			1.62780
$143$	5.89658	−	11.9410i	0.493097	−	0.998561i
$144$	10.0527			0.837727
$145$	13.2709	−	7.66194i	1.10209	−	0.636290i
$146$	−0.307096	−	0.531906i	−0.0254155	−	0.0440209i
$147$		0			0
$148$		−	4.51700i		−	0.371295i
$149$	6.42234	+	3.70794i	0.526139	+	0.303766i	0.739443	−	0.673220i	$-0.235089\pi$
$149$	6.42234	+	3.70794i	0.526139	+	0.303766i	−0.213304	+	0.976986i	$0.568422\pi$
$150$	−32.1445	−	18.5587i	−2.62459	−	1.51531i
$151$		−	6.07902i		−	0.494703i	−0.968926	−	0.247352i	$-0.920440\pi$
$151$		−	6.07902i		−	0.494703i	0.968926	−	0.247352i	$-0.0795603\pi$
$152$	−11.0954	+	19.2178i	−0.899957	+	1.55877i
$153$	−4.34303	−	7.52235i	−0.351113	−	0.608146i
$154$		0			0
$155$	−6.75368			−0.542468
$156$	32.1400	−	21.4505i	2.57326	−	1.71742i
$157$	−9.38366			−0.748897			−0.374449	−	0.927248i	$-0.622168\pi$
$157$	−9.38366			−0.748897			−0.374449	+	0.927248i	$0.622168\pi$
$158$	−20.7296	+	11.9683i	−1.64916	+	0.952144i
$159$	−0.725261	−	1.25619i	−0.0575170	−	0.0996223i
$160$	−5.59604	+	9.69262i	−0.442405	+	0.766269i
$161$		0			0
$162$	16.9955	+	9.81236i	1.33529	+	0.770932i
$163$	−21.3669	−	12.3362i	−1.67358	−	0.966244i	−0.965606	−	0.260008i	$-0.916275\pi$
$163$	−21.3669	−	12.3362i	−1.67358	−	0.966244i	−0.707977	−	0.706235i	$-0.750392\pi$
$164$			0.930955i			0.0726954i
$165$	17.6667	−	30.5997i	1.37535	−	2.38218i
$166$	−11.9371	−	20.6757i	−0.926499	−	1.60474i
$167$	1.47685	−	0.852661i	0.114282	−	0.0659809i	−0.441769	−	0.897129i	$-0.645649\pi$
$167$	1.47685	−	0.852661i	0.114282	−	0.0659809i	0.556052	+	0.831148i	$0.312316\pi$
$168$		0			0
$169$	4.98767	−	12.0051i	0.383667	−	0.923472i
$170$	−11.1047			−0.851691
$171$	−30.3169	+	17.5035i	−2.31839	+	1.33852i
$172$	10.0681	+	17.4385i	0.767687	+	1.32967i
$173$	1.44853	−	2.50893i	0.110130	−	0.190751i	−0.805693	−	0.592334i	$-0.798207\pi$
$173$	1.44853	−	2.50893i	0.110130	−	0.190751i	0.915823	+	0.401583i	$0.131540\pi$
$174$			33.7842i			2.56118i
$175$		0			0
$176$	5.43023	+	3.13515i	0.409319	+	0.236321i
$177$			26.0724i			1.95972i
$178$	2.95780	−	5.12307i	0.221697	−	0.383990i
$179$	7.75589	+	13.4336i	0.579702	+	1.00407i	0.995513	+	0.0946230i	$0.0301646\pi$
$179$	7.75589	+	13.4336i	0.579702	+	1.00407i	−0.415811	+	0.909451i	$0.636502\pi$
$180$	58.9300	−	34.0233i	4.39238	−	2.53594i
$181$	19.4473			1.44551			0.722754	−	0.691105i	$-0.242876\pi$
$181$	19.4473			1.44551			0.722754	+	0.691105i	$0.242876\pi$
$182$		0			0
$183$	34.2398			2.53108
$184$	2.24442	−	1.29582i	0.165461	−	0.0955289i
$185$	−2.01594	−	3.49172i	−0.148215	−	0.256716i
$186$	7.44485	−	12.8949i	0.545883	−	0.945496i
$187$		−	5.41785i		−	0.396192i
$188$	−36.1114	−	20.8489i	−2.63369	−	1.52056i
$189$		0			0
$190$			44.7546i			3.24684i
$191$	−8.68967	+	15.0510i	−0.628763	+	1.08905i	0.359038	+	0.933323i	$0.383105\pi$
$191$	−8.68967	+	15.0510i	−0.628763	+	1.08905i	−0.987800	+	0.155726i	$0.950228\pi$
$192$	−17.4081	−	30.1516i	−1.25632	−	2.17601i
$193$	−10.0967	+	5.82935i	−0.726778	+	0.419605i	−0.817242	−	0.576294i	$-0.804498\pi$
$193$	−10.0967	+	5.82935i	−0.726778	+	0.419605i	0.0904643	+	0.995900i	$0.471165\pi$
$194$	12.5101			0.898169
$195$	15.2714	−	30.9257i	1.09361	−	2.21464i
$196$		0			0
$197$	−5.36568	+	3.09787i	−0.382289	+	0.220714i	−0.678814	−	0.734311i	$-0.737506\pi$
$197$	−5.36568	+	3.09787i	−0.382289	+	0.220714i	0.296525	+	0.955025i	$0.404172\pi$
$198$	25.8524	+	44.7777i	1.83725	+	3.18221i
$199$	4.74100	−	8.21165i	0.336081	−	0.582109i	−0.647611	−	0.761971i	$-0.724232\pi$
$199$	4.74100	−	8.21165i	0.336081	−	0.582109i	0.983692	+	0.179862i	$0.0575652\pi$
$200$		−	19.7331i		−	1.39534i
$201$	−0.884412	−	0.510616i	−0.0623816	−	0.0360161i
$202$	−24.5836	−	14.1934i	−1.72970	−	0.998642i
$203$		0			0
$204$	7.85990	−	13.6137i	0.550303	−	0.953152i
$205$	0.415486	+	0.719643i	0.0290188	+	0.0502621i
$206$	−17.1149	+	9.88131i	−1.19245	+	0.688464i
$207$	4.08841			0.284164
$208$	5.48810	+	2.71007i	0.380531	+	0.187909i
$209$	−21.8352			−1.51038
$210$		0			0
$211$	1.19094	+	2.06276i	0.0819874	+	0.142006i	0.904104	−	0.427314i	$-0.140540\pi$
$211$	1.19094	+	2.06276i	0.0819874	+	0.142006i	−0.822116	+	0.569320i	$0.807207\pi$
$212$	0.871201	−	1.50896i	0.0598343	−	0.103636i
$213$			24.5100i			1.67939i
$214$	21.0512	+	12.1539i	1.43903	+	0.830826i
$215$	15.5656	+	8.98683i	1.06157	+	0.612897i
$216$			32.7595i			2.22900i
$217$		0			0
$218$	−23.3348	−	40.4171i	−1.58043	−	2.73739i
$219$	0.672099	−	0.388036i	0.0454162	−	0.0262211i
$220$	42.4434			2.86153
$221$	−0.343084	−	5.27751i	−0.0230783	−	0.355003i
$222$	8.88901			0.596592
$223$	1.99812	−	1.15362i	0.133804	−	0.0772518i	−0.431604	−	0.902063i	$-0.642052\pi$
$223$	1.99812	−	1.15362i	0.133804	−	0.0772518i	0.565408	+	0.824811i	$0.308719\pi$
$224$		0			0
$225$	15.5648	−	26.9591i	1.03766	−	1.79727i
$226$		−	7.25944i		−	0.482891i
$227$	4.52103	+	2.61022i	0.300072	+	0.173246i	0.642475	−	0.766307i	$-0.277908\pi$
$227$	4.52103	+	2.61022i	0.300072	+	0.173246i	−0.342403	+	0.939553i	$0.611241\pi$
$228$	−54.8667	−	31.6773i	−3.63363	−	2.09788i
$229$			15.9037i			1.05095i	0.850810	+	0.525473i	$0.176112\pi$
$229$			15.9037i			1.05095i	−0.850810	+	0.525473i	$0.823888\pi$
$230$	2.61341	−	4.52656i	0.172323	−	0.298473i
$231$		0			0
$232$	−15.5547	+	8.98052i	−1.02122	+	0.589600i
$233$	−18.5787			−1.21713			−0.608564	−	0.793505i	$-0.708254\pi$
$233$	−18.5787			−1.21713			−0.608564	+	0.793505i	$0.708254\pi$
$234$	28.0183	+	41.9807i	1.83161	+	2.74436i
$235$	−37.2196			−2.42794
$236$	−27.1229	+	15.6594i	−1.76555	+	1.01934i
$237$	−15.1227	−	26.1933i	−0.982324	−	1.70144i
$238$		0			0
$239$		−	3.30548i		−	0.213814i	−0.994269	−	0.106907i	$-0.965905\pi$
$239$		−	3.30548i		−	0.213814i	0.994269	−	0.106907i	$-0.0340946\pi$
$240$	14.0636	+	8.11962i	0.907801	+	0.524119i
$241$	−11.3994	−	6.58143i	−0.734298	−	0.423947i	0.0856942	−	0.996321i	$-0.472689\pi$
$241$	−11.3994	−	6.58143i	−0.734298	−	0.423947i	−0.819993	+	0.572374i	$0.806023\pi$
$242$			6.24763i			0.401613i
$243$	0.692028	−	1.19863i	0.0443936	−	0.0768920i
$244$	20.5649	+	35.6194i	1.31653	+	2.28030i
$245$		0			0
$246$	−1.83203			−0.116806
$247$	−21.2696	+	1.38271i	−1.35335	+	0.0879799i
$248$	7.91595			0.502664
$249$	26.1251	−	15.0833i	1.65561	−	0.955866i
$250$	−0.972216	−	1.68393i	−0.0614884	−	0.106501i
$251$	−1.86214	+	3.22532i	−0.117537	+	0.203580i	−0.918791	−	0.394744i	$-0.870833\pi$
$251$	−1.86214	+	3.22532i	−0.117537	+	0.203580i	0.801254	+	0.598324i	$0.204167\pi$
$252$		0			0
$253$	2.20846	+	1.27505i	0.138844	+	0.0801619i
$254$	−37.8176	−	21.8340i	−2.37289	−	1.36999i
$255$		−	14.0315i		−	0.878688i
$256$	12.6500	−	21.9105i	0.790625	−	1.36940i
$257$	8.51637	+	14.7508i	0.531236	+	0.920128i	0.999335	+	0.0364524i	$0.0116057\pi$
$257$	8.51637	+	14.7508i	0.531236	+	0.920128i	−0.468099	+	0.883676i	$0.655061\pi$
$258$	−34.3173	+	19.8131i	−2.13650	+	1.23351i
$259$		0			0
$260$	41.3439	−	2.68772i	2.56404	−	0.166685i
$261$	−28.3343			−1.75385
$262$	25.7056	−	14.8411i	1.58810	−	0.916888i
$263$	−4.64186	−	8.03993i	−0.286229	−	0.495763i	0.686677	−	0.726962i	$-0.259068\pi$
$263$	−4.64186	−	8.03993i	−0.286229	−	0.495763i	−0.972906	+	0.231199i	$0.925735\pi$
$264$	−20.7071	+	35.8657i	−1.27443	+	2.20738i
$265$		−	1.55527i		−	0.0955396i
$266$		0			0
$267$	6.47333	+	3.73738i	0.396162	+	0.228724i
$268$		−	1.22673i		−	0.0749343i
$269$	−11.0680	+	19.1704i	−0.674829	+	1.16884i	0.301690	+	0.953406i	$0.402449\pi$
$269$	−11.0680	+	19.1704i	−0.674829	+	1.16884i	−0.976519	+	0.215431i	$0.930884\pi$
$270$	33.0348	+	57.2180i	2.01044	+	3.48218i
$271$	−23.0544	+	13.3105i	−1.40045	+	0.808553i	−0.994439	−	0.105313i	$-0.966415\pi$
$271$	−23.0544	+	13.3105i	−1.40045	+	0.808553i	−0.406016	+	0.913866i	$0.633082\pi$
$272$	2.49004			0.150981
$273$		0			0
$274$	−41.8681			−2.52935
$275$	16.8155	−	9.70842i	1.01401	−	0.585440i
$276$	3.69954	+	6.40780i	0.222686	+	0.385704i
$277$	−0.840618	+	1.45599i	−0.0505079	+	0.0874822i	−0.890174	−	0.455621i	$-0.849417\pi$
$277$	−0.840618	+	1.45599i	−0.0505079	+	0.0874822i	0.839666	+	0.543103i	$0.182751\pi$
$278$			17.6704i			1.05980i
$279$	10.8147	+	6.24387i	0.647459	+	0.373811i
$280$		0			0
$281$			28.6730i			1.71049i	0.518227	+	0.855243i	$0.326592\pi$
$281$			28.6730i			1.71049i	−0.518227	+	0.855243i	$0.673408\pi$
$282$	41.0286	−	71.0636i	2.44322	−	4.23178i
$283$	−1.79156	−	3.10307i	−0.106497	−	0.184458i	0.807852	−	0.589386i	$-0.200630\pi$
$283$	−1.79156	−	3.10307i	−0.106497	−	0.184458i	−0.914349	+	0.404927i	$0.867297\pi$
$284$	−25.4975	+	14.7210i	−1.51300	+	0.873529i
$285$	−56.5504			−3.34976
$286$	2.04225	+	31.4150i	0.120761	+	1.85761i
$287$		0			0
$288$	17.9219	−	10.3472i	1.05606	−	0.609716i
$289$	7.42424	+	12.8592i	0.436720	+	0.756421i
$290$	−18.1120	+	31.3709i	−1.06357	+	1.84216i
$291$			15.8073i			0.926639i
$292$	0.807341	+	0.466118i	0.0472460	+	0.0272775i
$293$	14.2382	+	8.22041i	0.831803	+	0.480242i	0.854470	−	0.519501i	$-0.173882\pi$
$293$	14.2382	+	8.22041i	0.831803	+	0.480242i	−0.0226667	+	0.999743i	$0.507216\pi$
$294$		0			0
$295$	−13.9776	+	24.2099i	−0.813807	+	1.40956i
$296$	2.36288	+	4.09262i	0.137339	+	0.237879i
$297$	−27.9160	+	16.1173i	−1.61985	+	0.935221i
$298$	−17.5303			−1.01550
$299$	2.23199	+	1.10217i	0.129079	+	0.0637404i
$300$	56.3376			3.25265
$301$		0			0
$302$	7.18506	+	12.4449i	0.413454	+	0.716123i
$303$	17.9343	−	31.0631i	1.03030	−	1.78453i
$304$		−	10.0355i		−	0.575574i
$305$	31.7939	+	18.3562i	1.82051	+	1.05107i
$306$	17.7820	+	10.2664i	1.01653	+	0.586893i
$307$		−	3.52583i		−	0.201230i	−0.994925	−	0.100615i	$-0.967919\pi$
$307$		−	3.52583i		−	0.201230i	0.994925	−	0.100615i	$-0.0320810\pi$
$308$		0			0
$309$	−12.4857	−	21.6258i	−0.710286	−	1.23025i
$310$	13.8260	−	7.98247i	0.785267	−	0.453374i
$311$	14.3241			0.812245			0.406123	−	0.913819i	$-0.366881\pi$
$311$	14.3241			0.812245			0.406123	+	0.913819i	$0.366881\pi$
$312$	−17.8995	+	36.2479i	−1.01336	+	2.05213i
$313$	−6.71897			−0.379779			−0.189889	−	0.981805i	$-0.560813\pi$
$313$	−6.71897			−0.379779			−0.189889	+	0.981805i	$0.560813\pi$
$314$	19.2101	−	11.0910i	1.08409	−	0.625899i
$315$		0			0
$316$	18.1657	−	31.4640i	1.02190	−	1.76999i
$317$			3.95457i			0.222111i	0.993814	+	0.111055i	$0.0354231\pi$
$317$			3.95457i			0.222111i	−0.993814	+	0.111055i	$0.964577\pi$
$318$	2.96949	+	1.71444i	0.166521	+	0.0961409i
$319$	−15.3055	−	8.83662i	−0.856942	−	0.494756i
$320$		−	37.3303i		−	2.08683i
$321$	−15.3573	+	26.5996i	−0.857161	+	1.48465i
$322$		0			0
$323$	−7.50944	+	4.33558i	−0.417836	+	0.241238i
$324$	−29.7869			−1.65483
$325$	15.7651	−	10.5218i	0.874491	−	0.583643i
$326$	58.3227			3.23020
$327$	51.0697	−	29.4851i	2.82416	−	1.63053i
$328$	−0.486989	−	0.843490i	−0.0268895	−	0.0465740i
$329$		0			0
$330$			83.5243i			4.59786i
$331$	10.2189	+	5.89989i	0.561682	+	0.324287i	0.753820	−	0.657080i	$-0.228209\pi$
$331$	10.2189	+	5.89989i	0.561682	+	0.324287i	−0.192138	+	0.981368i	$0.561542\pi$
$332$	31.3821	+	18.1184i	1.72231	+	0.994379i
$333$			7.45507i			0.408535i
$334$	−2.01560	+	3.49111i	−0.110288	+	0.191025i
$335$	−0.547490	−	0.948280i	−0.0299125	−	0.0518101i
$336$		0			0
$337$	27.7135			1.50965			0.754824	−	0.655927i	$-0.227722\pi$
$337$	27.7135			1.50965			0.754824	+	0.655927i	$0.227722\pi$
$338$	3.97870	+	30.4719i	0.216413	+	1.65745i
$339$	9.17278			0.498197
$340$	14.5968	−	8.42749i	0.791625	−	0.457045i
$341$	3.89455	+	6.74556i	0.210902	+	0.365293i
$342$	41.3763	−	71.6658i	2.23737	−	3.87524i
$343$		0			0
$344$	−18.2444	−	10.5334i	−0.983673	−	0.567924i
$345$	5.71961	+	3.30222i	0.307933	+	0.177785i
$346$			6.84834i			0.368169i
$347$	−14.6894	+	25.4428i	−0.788569	+	1.36584i	0.138275	+	0.990394i	$0.455844\pi$
$347$	−14.6894	+	25.4428i	−0.788569	+	1.36584i	−0.926844	+	0.375447i	$0.877489\pi$
$348$	−25.6393	−	44.4086i	−1.37441	−	2.38055i
$349$	−17.7934	+	10.2730i	−0.952458	+	0.549902i	−0.893844	−	0.448379i	$-0.852002\pi$
$349$	−17.7934	+	10.2730i	−0.952458	+	0.549902i	−0.0586146	+	0.998281i	$0.518668\pi$
$350$		0			0
$351$	−26.1722	+	17.4676i	−1.39697	+	0.932350i
$352$	12.9080			0.687997
$353$	−3.02392	+	1.74586i	−0.160947	+	0.0929229i	−0.578310	−	0.815817i	$-0.696288\pi$
$353$	−3.02392	+	1.74586i	−0.160947	+	0.0929229i	0.417363	+	0.908740i	$0.362954\pi$
$354$	−30.8161	−	53.3751i	−1.63786	−	2.83685i
$355$	−13.1400	+	22.7591i	−0.697397	+	1.20793i
$356$			8.97886i			0.475879i
$357$		0			0
$358$	−31.7555	−	18.3341i	−1.67833	−	0.968985i
$359$		−	24.4864i		−	1.29234i	−0.763193	−	0.646170i	$-0.776370\pi$
$359$		−	24.4864i		−	1.29234i	0.763193	−	0.646170i	$-0.223630\pi$
$360$	−35.5956	+	61.6534i	−1.87605	+	3.24942i
$361$	7.97342	+	13.8104i	0.419654	+	0.726861i
$362$	−39.8123	+	22.9857i	−2.09249	+	1.20810i
$363$	−7.89429			−0.414343
$364$		0			0
$365$	0.832116			0.0435550
$366$	−70.0954	+	40.4696i	−3.66394	+	2.11538i
$367$	−0.750181	−	1.29935i	−0.0391591	−	0.0678256i	0.845782	−	0.533529i	$-0.179135\pi$
$367$	−0.750181	−	1.29935i	−0.0391591	−	0.0678256i	−0.884941	+	0.465704i	$0.845801\pi$
$368$	−0.586014	+	1.01501i	−0.0305481	+	0.0529108i
$369$		−	1.53649i		−	0.0799865i
$370$	8.25403	+	4.76547i	0.429107	+	0.247745i
$371$		0			0
$372$			22.6000i			1.17175i
$373$	−4.53512	+	7.85506i	−0.234820	+	0.406720i	−0.959220	−	0.282660i	$-0.908783\pi$
$373$	−4.53512	+	7.85506i	−0.234820	+	0.406720i	0.724401	+	0.689379i	$0.242117\pi$
$374$	6.40360	+	11.0914i	0.331122	+	0.573520i
$375$	2.12775	−	1.22846i	0.109877	−	0.0634374i
$376$	43.6249			2.24978
$377$	−15.4686	−	7.63850i	−0.796672	−	0.393403i
$378$		0			0
$379$	21.2870	−	12.2900i	1.09344	−	0.631297i	0.158949	−	0.987287i	$-0.449189\pi$
$379$	21.2870	−	12.2900i	1.09344	−	0.631297i	0.934490	+	0.355989i	$0.115856\pi$
$380$	−33.9648	−	58.8288i	−1.74236	−	3.01786i
$381$	27.5887	−	47.7850i	1.41341	−	2.44810i
$382$		−	41.0828i		−	2.10198i
$383$	−4.67467	−	2.69892i	−0.238865	−	0.137909i	0.375790	−	0.926705i	$-0.377371\pi$
$383$	−4.67467	−	2.69892i	−0.238865	−	0.137909i	−0.614655	+	0.788796i	$0.710705\pi$
$384$	53.1955	+	30.7124i	2.71462	+	1.56729i
$385$		0			0
$386$	13.7799	−	23.8675i	0.701380	−	1.21483i
$387$	−16.6169	−	28.7813i	−0.844684	−	1.46304i
$388$	−16.4442	+	9.49404i	−0.834826	+	0.481987i
$389$	−21.2762			−1.07875			−0.539373	−	0.842067i	$-0.681339\pi$
$389$	−21.2762			−1.07875			−0.539373	+	0.842067i	$0.681339\pi$
$390$	5.28916	+	81.3607i	0.267827	+	4.11986i
$391$	1.01269			0.0512140
$392$		0			0
$393$	18.7527	+	32.4807i	0.945951	+	1.63843i
$394$	7.32303	−	12.6839i	0.368929	−	0.639004i
$395$		−	32.4295i		−	1.63171i
$396$	−67.9648	−	39.2395i	−3.41536	−	1.97186i
$397$	−16.3574	−	9.44396i	−0.820955	−	0.473979i	0.0297906	−	0.999556i	$-0.490516\pi$
$397$	−16.3574	−	9.44396i	−0.820955	−	0.473979i	−0.850746	+	0.525578i	$0.823849\pi$
$398$			22.4144i			1.12353i
$399$		0			0
$400$	4.46199	+	7.72839i	0.223099	+	0.386420i
$401$	9.12779	−	5.26993i	0.455820	−	0.263168i	−0.254465	−	0.967082i	$-0.581899\pi$
$401$	9.12779	−	5.26993i	0.455820	−	0.263168i	0.710285	+	0.703914i	$0.248566\pi$
$402$	2.41408			0.120403
$403$	4.22083	+	6.32421i	0.210255	+	0.315031i
$404$	43.0861			2.14361
$405$	−23.0258	+	13.2939i	−1.14416	+	0.660581i
$406$		0			0
$407$	−2.32501	+	4.02704i	−0.115247	+	0.199613i
$408$			16.4463i			0.814212i
$409$	−28.2798	−	16.3274i	−1.39835	−	0.807337i	−0.404128	−	0.914702i	$-0.632425\pi$
$409$	−28.2798	−	16.3274i	−1.39835	−	0.807337i	−0.994220	+	0.107366i	$0.965758\pi$
$410$	−1.70116	−	0.982163i	−0.0840141	−	0.0485056i
$411$		−	52.9031i		−	2.60952i
$412$	14.9981	−	25.9775i	0.738904	−	1.27982i
$413$		0			0
$414$	−8.36974	+	4.83227i	−0.411350	+	0.237493i
$415$	32.3451			1.58776
$416$	12.5736	−	0.817394i	0.616471	−	0.0400760i
$417$	−22.3278			−1.09340
$418$	44.7008	−	25.8080i	2.18639	−	1.26231i
$419$	−18.0683	−	31.2952i	−0.882693	−	1.52887i	−0.848336	−	0.529459i	$-0.822395\pi$
$419$	−18.0683	−	31.2952i	−0.882693	−	1.52887i	−0.0343572	−	0.999410i	$-0.510938\pi$
$420$		0			0
$421$		−	36.6781i		−	1.78758i	−0.448485	−	0.893791i	$-0.648036\pi$
$421$		−	36.6781i		−	1.78758i	0.448485	−	0.893791i	$-0.351964\pi$
$422$	−4.87614	−	2.81524i	−0.237367	−	0.137044i
$423$	59.5999	+	34.4100i	2.89784	+	1.67307i
$424$			1.82293i			0.0885291i
$425$	3.85538	−	6.67772i	0.187013	−	0.323917i
$426$	−28.9694	−	50.1765i	−1.40357	−	2.43106i
$427$		0			0
$428$	−36.8951			−1.78339
$429$	−39.6949	+	2.58052i	−1.91649	+	0.124589i
$430$	−42.4877			−2.04894
$431$	8.91469	−	5.14690i	0.429405	−	0.247917i	−0.269688	−	0.962948i	$-0.586921\pi$
$431$	8.91469	−	5.14690i	0.429405	−	0.247917i	0.699093	+	0.715030i	$0.253587\pi$
$432$	−7.40751	−	12.8302i	−0.356394	−	0.617292i
$433$	−13.9823	+	24.2180i	−0.671946	+	1.16385i	0.305405	+	0.952223i	$0.401208\pi$
$433$	−13.9823	+	24.2180i	−0.671946	+	1.16385i	−0.977351	+	0.211623i	$0.932125\pi$
$434$		0			0
$435$	−39.6392	−	22.8857i	−1.90055	−	1.09728i
$436$	61.3461	+	35.4182i	2.93795	+	1.69622i
$437$		−	4.08139i		−	0.195239i
$438$	−0.917275	+	1.58877i	−0.0438291	+	0.0759142i
$439$	−8.37605	−	14.5077i	−0.399767	−	0.692417i	0.593930	−	0.804517i	$-0.297576\pi$
$439$	−8.37605	−	14.5077i	−0.399767	−	0.692417i	−0.993697	+	0.112100i	$0.964242\pi$
$440$	−38.4557	+	22.2024i	−1.83331	+	1.05846i
$441$		0			0
$442$	6.94008	+	10.3985i	0.330106	+	0.494608i
$443$	6.02660			0.286332			0.143166	−	0.989699i	$-0.454272\pi$
$443$	6.02660			0.286332			0.143166	+	0.989699i	$0.454272\pi$
$444$	−11.6844	+	6.74599i	−0.554517	+	0.320150i
$445$	4.00727	+	6.94080i	0.189963	+	0.329026i
$446$	−2.72702	+	4.72334i	−0.129128	+	0.223657i
$447$		−	22.1507i		−	1.04769i
$448$		0			0
$449$	25.9665	+	14.9918i	1.22544	+	0.707506i	0.966072	−	0.258274i	$-0.0831537\pi$
$449$	25.9665	+	14.9918i	1.22544	+	0.707506i	0.259364	+	0.965780i	$0.416487\pi$
$450$			73.5871i			3.46893i
$451$	0.479186	−	0.829974i	0.0225640	−	0.0390819i
$452$	5.50928	+	9.54236i	0.259135	+	0.448835i
$453$	−15.7249	+	9.07880i	−0.738822	+	0.426559i
$454$	−12.3405			−0.579170
$455$		0			0
$456$	66.2825			3.10396
$457$	25.3924	−	14.6603i	1.18780	−	0.685779i	0.229998	−	0.973191i	$-0.426128\pi$
$457$	25.3924	−	14.6603i	1.18780	−	0.685779i	0.957807	+	0.287412i	$0.0927948\pi$
$458$	−18.7973	−	32.5579i	−0.878340	−	1.52133i
$459$	−6.40046	+	11.0859i	−0.298748	+	0.517446i
$460$			7.93341i			0.369897i
$461$	7.31156	+	4.22133i	0.340533	+	0.196607i	0.660508	−	0.750819i	$-0.270341\pi$
$461$	7.31156	+	4.22133i	0.340533	+	0.196607i	−0.319974	+	0.947426i	$0.603674\pi$
$462$		0			0
$463$		−	5.17390i		−	0.240452i	−0.992747	−	0.120226i	$-0.961638\pi$
$463$		−	5.17390i		−	0.240452i	0.992747	−	0.120226i	$-0.0383619\pi$
$464$	4.06131	−	7.03439i	0.188541	−	0.326563i
$465$	10.0864	+	17.4701i	0.467745	+	0.810158i
$466$	38.0340	−	21.9589i	1.76189	−	1.01723i
$467$	40.3608			1.86768			0.933839	−	0.357694i	$-0.116437\pi$
$467$	40.3608			1.86768			0.933839	+	0.357694i	$0.116437\pi$
$468$	−68.6890	−	33.9192i	−3.17515	−	1.56791i
$469$		0			0
$470$	76.1954	−	43.9914i	3.51463	−	2.02917i
$471$	14.0142	+	24.2732i	0.645739	+	1.11845i
$472$	16.3831	−	28.3763i	0.754092	−	1.30613i
$473$		−	20.7293i		−	0.953132i
$474$	61.9180	+	35.7484i	2.84399	+	1.64198i
$475$	−26.9128	−	15.5381i	−1.23484	−	0.712938i
$476$		0			0
$477$	−1.43787	+	2.49046i	−0.0658356	+	0.114031i
$478$	3.90689	+	6.76693i	0.178697	+	0.309512i
$479$	6.50156	−	3.75368i	0.297064	−	0.171510i	−0.344059	−	0.938948i	$-0.611802\pi$
$479$	6.50156	−	3.75368i	0.297064	−	0.171510i	0.641123	+	0.767438i	$0.278469\pi$
$480$	33.4299			1.52586
$481$	−2.00978	+	4.06996i	−0.0916379	+	0.185574i
$482$	31.1156			1.41727
$483$		0			0
$484$	−4.74140	−	8.21235i	−0.215518	−	0.373289i
$485$	−8.47440	+	14.6781i	−0.384803	+	0.666498i
$486$			3.27176i			0.148410i
$487$	−4.00620	−	2.31298i	−0.181538	−	0.104811i	0.406477	−	0.913661i	$-0.366757\pi$
$487$	−4.00620	−	2.31298i	−0.181538	−	0.104811i	−0.588015	+	0.808850i	$0.700091\pi$
$488$	−37.2655	−	21.5152i	−1.68693	−	0.973950i
$489$			73.6946i			3.33258i
$490$		0			0
$491$	16.5862	+	28.7282i	0.748525	+	1.29648i	0.948529	+	0.316689i	$0.102571\pi$
$491$	16.5862	+	28.7282i	0.748525	+	1.29648i	−0.200004	+	0.979795i	$0.564096\pi$
$492$	2.40815	−	1.39035i	0.108568	−	0.0626818i
$493$	−7.01835			−0.316090
$494$	41.9086	−	27.9702i	1.88556	−	1.25844i
$495$	−70.0505			−3.14853
$496$	−3.10026	+	1.78994i	−0.139206	+	0.0803705i
$497$		0			0
$498$	−35.6553	+	61.7568i	−1.59775	+	2.76739i
$499$			28.3940i			1.27109i	0.772063	+	0.635546i	$0.219225\pi$
$499$			28.3940i			1.27109i	−0.772063	+	0.635546i	$0.780775\pi$
$500$	2.55591	+	1.47565i	0.114304	+	0.0659933i
$501$	−4.41125	−	2.54684i	−0.197080	−	0.113784i
$502$		−	8.80378i		−	0.392932i
$503$	−15.2455	+	26.4059i	−0.679762	+	1.17738i	0.295290	+	0.955408i	$0.404584\pi$
$503$	−15.2455	+	26.4059i	−0.679762	+	1.17738i	−0.975052	+	0.221975i	$0.928750\pi$
$504$		0			0
$505$	33.3063	−	19.2294i	1.48211	−	0.855696i
$506$	−6.02817			−0.267985
$507$	−38.5033	+	5.02735i	−1.70999	+	0.223272i
$508$	66.2804			2.94072
$509$	−15.3716	+	8.87482i	−0.681336	+	0.393370i	−0.800358	−	0.599522i	$-0.795357\pi$
$509$	−15.3716	+	8.87482i	−0.681336	+	0.393370i	0.119022	+	0.992892i	$0.462024\pi$
$510$	16.5845	+	28.7251i	0.734373	+	1.27197i
$511$		0			0
$512$			18.6773i			0.825428i
$513$	44.6789	+	25.7954i	1.97262	+	1.13889i
$514$	−34.8692	−	20.1317i	−1.53801	−	0.887973i
$515$		−	26.7747i		−	1.17983i
$516$	30.0728	−	52.0876i	1.32388	−	2.29303i
$517$	21.4629	+	37.1748i	0.943937	+	1.63495i
$518$		0			0
$519$	−8.65333			−0.379839
$520$	−36.0536	+	24.0625i	−1.58106	+	1.05521i
$521$	3.82051			0.167380			0.0836898	−	0.996492i	$-0.473330\pi$
$521$	3.82051			0.167380			0.0836898	+	0.996492i	$0.473330\pi$
$522$	58.0056	−	33.4895i	2.53884	−	1.46580i
$523$	−9.98769	−	17.2992i	−0.436731	−	0.756441i	0.560704	−	0.828016i	$-0.310531\pi$
$523$	−9.98769	−	17.2992i	−0.436731	−	0.756441i	−0.997435	+	0.0715758i	$0.977197\pi$
$524$	−22.5262	+	39.0166i	−0.984063	+	1.70445i
$525$		0			0
$526$	19.0055	+	10.9728i	0.828679	+	0.478438i
$527$	2.67878	+	1.54659i	0.116689	+	0.0673707i
$528$		−	18.7289i		−	0.815072i
$529$	11.2617	−	19.5058i	0.489638	−	0.848078i
$530$	1.83824	+	3.18393i	0.0798483	+	0.138301i
$531$	44.7648	−	25.8450i	1.94263	−	1.12158i
$532$		0			0
$533$	0.414215	−	0.838819i	0.0179416	−	0.0363333i
$534$	−17.6695			−0.764634
$535$	−28.5205	+	16.4663i	−1.23305	+	0.711901i
$536$	0.641710	+	1.11147i	0.0277176	+	0.0480084i
$537$	23.1663	−	40.1252i	0.999700	−	1.73153i
$538$		−	52.3271i		−	2.25598i
$539$		0			0
$540$	−86.8469	−	50.1411i	−3.73730	−	2.15773i
$541$		−	35.0586i		−	1.50729i	−0.657284	−	0.753643i	$-0.728295\pi$
$541$		−	35.0586i		−	1.50729i	0.657284	−	0.753643i	$-0.271705\pi$
$542$	31.4645	−	54.4980i	1.35151	−	2.34089i
$543$	−29.0439	−	50.3055i	−1.24639	−	2.15882i
$544$	4.43922	−	2.56299i	0.190330	−	0.109887i
$545$	63.2287			2.70842
$546$		0			0
$547$	−38.0737			−1.62792			−0.813958	−	0.580924i	$-0.802691\pi$
$547$	−38.0737			−1.62792			−0.813958	+	0.580924i	$0.802691\pi$
$548$	55.0346	−	31.7743i	2.35096	−	1.35733i
$549$	−33.9412	−	58.7878i	−1.44857	−	2.50900i
$550$	−22.9496	+	39.7499i	−0.978576	+	1.69494i
$551$			28.2856i			1.20501i
$552$	−6.70393	−	3.87051i	−0.285338	−	0.164740i
$553$		0			0
$554$		−	3.97426i		−	0.168850i
$555$	−6.02148	+	10.4295i	−0.255598	+	0.442708i
$556$	−13.4103	−	23.2274i	−0.568724	−	0.985059i
$557$	−19.4379	+	11.2225i	−0.823610	+	0.475511i	−0.851660	−	0.524095i	$-0.824404\pi$
$557$	−19.4379	+	11.2225i	−0.823610	+	0.475511i	0.0280499	+	0.999607i	$0.491070\pi$
$558$	−29.5196			−1.24967
$559$	−1.31268	−	20.1923i	−0.0555203	−	0.854043i
$560$		0			0
$561$	−14.0147	+	8.09137i	−0.591699	+	0.341618i
$562$	−33.8899	−	58.6990i	−1.42956	−	2.47607i
$563$	−15.1092	+	26.1700i	−0.636779	+	1.10293i	0.349357	+	0.936990i	$0.386400\pi$
$563$	−15.1092	+	26.1700i	−0.636779	+	1.10293i	−0.986135	+	0.165943i	$0.946933\pi$
$564$			124.548i			5.24444i
$565$	8.51753	+	4.91760i	0.358335	+	0.206885i
$566$	7.33531	+	4.23504i	0.308326	+	0.178012i
$567$		0			0
$568$	15.4013	−	26.6758i	0.646224	−	1.11929i
$569$	−7.50755	−	13.0035i	−0.314733	−	0.545134i	0.664648	−	0.747157i	$-0.268582\pi$
$569$	−7.50755	−	13.0035i	−0.314733	−	0.545134i	−0.979381	+	0.202023i	$0.935248\pi$
$570$	115.769	−	66.8394i	4.84904	−	2.79960i
$571$	−24.1365			−1.01008			−0.505041	−	0.863096i	$-0.668523\pi$
$571$	−24.1365			−1.01008			−0.505041	+	0.863096i	$0.668523\pi$
$572$	−26.5257	−	39.7444i	−1.10910	−	1.66180i
$573$	51.9109			2.16861
$574$		0			0
$575$	1.81467	+	3.14311i	0.0756771	+	0.131077i
$576$	−34.5124	+	59.7773i	−1.43802	+	2.49072i
$577$			45.4117i			1.89051i	0.326326	+	0.945257i	$0.394189\pi$
$577$			45.4117i			1.89051i	−0.326326	+	0.945257i	$0.605811\pi$
$578$	−30.3976	−	17.5501i	−1.26437	−	0.729987i
$579$	30.1582	+	17.4118i	1.25333	+	0.723612i
$580$		−	54.9816i		−	2.28299i
$581$		0			0
$582$	−18.6833	−	32.3605i	−0.774449	−	1.34138i
$583$	−1.55340	+	0.896858i	−0.0643354	+	0.0371441i
$584$	−0.975320			−0.0403590
$585$	−68.2359	+	4.43593i	−2.82121	+	0.183403i
$586$	−38.8643			−1.60547
$587$	−26.2185	+	15.1373i	−1.08215	+	0.624781i	−0.931476	−	0.363802i	$-0.881479\pi$
$587$	−26.2185	+	15.1373i	−1.08215	+	0.624781i	−0.150677	+	0.988583i	$0.548145\pi$
$588$		0			0
$589$	6.23315	−	10.7961i	0.256832	−	0.444847i
$590$		−	66.0830i		−	2.72059i
$591$	16.0269	+	9.25313i	0.659259	+	0.380623i
$592$	−1.85083	−	1.06858i	−0.0760685	−	0.0439182i
$593$			29.8218i			1.22463i	0.790612	+	0.612317i	$0.209762\pi$
$593$			29.8218i			1.22463i	−0.790612	+	0.612317i	$0.790238\pi$
$594$	38.0995	−	65.9903i	1.56324	−	2.70761i
$595$		0			0
$596$	23.0432	−	13.3040i	0.943885	−	0.544952i
$597$	−28.3221			−1.15915
$598$	−5.87201	+	0.381732i	−0.240124	+	0.0156102i
$599$	22.6191			0.924191			0.462096	−	0.886830i	$-0.347098\pi$
$599$	22.6191			0.924191			0.462096	+	0.886830i	$0.347098\pi$
$600$	−51.0446	+	29.4706i	−2.08389	+	1.20313i
$601$	−22.3912	−	38.7826i	−0.913355	−	1.58198i	−0.809292	−	0.587406i	$-0.800149\pi$
$601$	−22.3912	−	38.7826i	−0.913355	−	1.58198i	−0.104062	−	0.994571i	$-0.533184\pi$
$602$		0			0
$603$			2.02465i			0.0824500i
$604$	−18.8892	−	10.9057i	−0.768589	−	0.443745i
$605$	−7.33036	−	4.23219i	−0.298022	−	0.172063i
$606$			84.7892i			3.44433i
$607$	−2.15014	+	3.72415i	−0.0872715	+	0.151159i	−0.906357	−	0.422513i	$-0.861148\pi$
$607$	−2.15014	+	3.72415i	−0.0872715	+	0.151159i	0.819085	+	0.573672i	$0.194481\pi$
$608$	−10.3295	−	17.8912i	−0.418915	−	0.725582i
$609$		0			0
$610$	−86.7842			−3.51379
$611$	23.2610	+	34.8527i	0.941040	+	1.40999i
$612$	−31.1653			−1.25978
$613$	−20.5300	+	11.8530i	−0.829201	+	0.478739i	−0.853579	−	0.520964i	$-0.825573\pi$
$613$	−20.5300	+	11.8530i	−0.829201	+	0.478739i	0.0243783	+	0.999703i	$0.492239\pi$
$614$	4.16734	+	7.21805i	0.168180	+	0.291297i
$615$	1.24103	−	2.14952i	0.0500431	−	0.0866772i
$616$		0			0
$617$	10.2808	+	5.93560i	0.413888	+	0.238958i	0.692459	−	0.721458i	$-0.256527\pi$
$617$	10.2808	+	5.93560i	0.413888	+	0.238958i	−0.278571	+	0.960416i	$0.589861\pi$
$618$	51.1211	+	29.5148i	2.05639	+	1.18726i
$619$		−	6.30946i		−	0.253599i	−0.991928	−	0.126799i	$-0.959530\pi$
$619$		−	6.30946i		−	0.253599i	0.991928	−	0.126799i	$-0.0404704\pi$
$620$	−12.1160	+	20.9855i	−0.486590	+	0.842799i
$621$	−3.01261	−	5.21799i	−0.120892	−	0.209391i
$622$	−29.3241	+	16.9303i	−1.17579	+	0.678843i
$623$		0			0
$624$	−1.18601	−	18.2438i	−0.0474782	−	0.730336i
$625$	−23.6498			−0.945994
$626$	13.7550	−	7.94145i	0.549760	−	0.317404i
$627$	32.6102	+	56.4825i	1.30232	+	2.25569i
$628$	−16.8341	+	29.1576i	−0.671756	+	1.16351i
$629$			1.84661i			0.0736290i
$630$		0			0
$631$	−11.2293	−	6.48324i	−0.447032	−	0.258094i	0.259544	−	0.965731i	$-0.416428\pi$
$631$	−11.2293	−	6.48324i	−0.447032	−	0.258094i	−0.706576	+	0.707637i	$0.749761\pi$
$632$			38.0105i			1.51198i
$633$	3.55724	−	6.16132i	0.141388	−	0.244891i
$634$	−4.67408	−	8.09574i	−0.185631	−	0.321523i
$635$	51.2358	−	29.5810i	2.03323	−	1.17389i
$636$	−5.20443			−0.206369
$637$		0			0
$638$	41.7776			1.65399
$639$	42.0822	−	24.2962i	1.66475	−	0.961141i
$640$	32.9303	+	57.0370i	1.30169	+	2.25459i
$641$	16.7277	−	28.9732i	0.660704	−	1.14437i	−0.319727	−	0.947510i	$-0.603591\pi$
$641$	16.7277	−	28.9732i	0.660704	−	1.14437i	0.980431	−	0.196863i	$-0.0630754\pi$
$642$		−	72.6059i		−	2.86553i
$643$	5.35385	+	3.09105i	0.211135	+	0.121899i	0.601839	−	0.798618i	$-0.294435\pi$
$643$	5.35385	+	3.09105i	0.211135	+	0.121899i	−0.390704	+	0.920517i	$0.627768\pi$
$644$		0			0
$645$		−	53.6861i		−	2.11389i
$646$	10.2488	−	17.7515i	0.403234	−	0.698422i
$647$	18.2114	+	31.5430i	0.715963	+	1.24008i	0.962587	+	0.270974i	$0.0873456\pi$
$647$	18.2114	+	31.5430i	0.715963	+	1.24008i	−0.246623	+	0.969111i	$0.579321\pi$
$648$	26.9884	−	15.5817i	1.06020	−	0.612109i
$649$	32.2411			1.26557
$650$	−19.8380	+	40.1735i	−0.778110	+	1.57574i
$651$		0			0
$652$	−76.6638	+	44.2618i	−3.00238	+	1.73343i
$653$	20.0564	+	34.7387i	0.784867	+	1.35943i	0.929079	+	0.369882i	$0.120602\pi$
$653$	20.0564	+	34.7387i	0.784867	+	1.35943i	−0.144212	+	0.989547i	$0.546065\pi$
$654$	−69.6995	+	120.723i	−2.72547	+	4.72065i
$655$			40.2139i			1.57129i
$656$	0.381456	+	0.220234i	0.0148933	+	0.00859868i
$657$	−1.33247	−	0.769303i	−0.0519847	−	0.0300134i
$658$		0			0
$659$	−12.0636	+	20.8948i	−0.469933	+	0.813948i	−0.999409	−	0.0343773i	$-0.989055\pi$
$659$	−12.0636	+	20.8948i	−0.469933	+	0.813948i	0.529476	+	0.848325i	$0.322389\pi$
$660$	−63.3877	−	109.791i	−2.46736	−	4.27360i
$661$	−6.99297	+	4.03739i	−0.271995	+	0.157036i	−0.629794	−	0.776762i	$-0.716861\pi$
$661$	−6.99297	+	4.03739i	−0.271995	+	0.157036i	0.357799	+	0.933799i	$0.383527\pi$
$662$	−27.8934			−1.08411
$663$	−13.1392	+	8.76924i	−0.510286	+	0.340569i
$664$	−37.9115			−1.47125
$665$		0			0
$666$	−8.81148	−	15.2619i	−0.341438	−	0.591388i
$667$	1.65172	−	2.86086i	0.0639548	−	0.110773i
$668$		−	6.11864i		−	0.236737i
$669$	−5.96825	−	3.44577i	−0.230746	−	0.133221i
$670$	2.24163	+	1.29420i	0.0866016	+	0.0499995i
$671$		−	42.3410i		−	1.63455i
$672$		0			0
$673$	0.130865	+	0.226665i	0.00504449	+	0.00873731i	0.868537	−	0.495625i	$-0.165061\pi$
$673$	0.130865	+	0.226665i	0.00504449	+	0.00873731i	−0.863492	+	0.504362i	$0.831728\pi$
$674$	−56.7347	+	32.7558i	−2.18534	+	1.26171i
$675$	−45.8768			−1.76580
$676$	−28.3554	−	37.0351i	−1.09059	−	1.42443i
$677$	−13.8129			−0.530874			−0.265437	−	0.964128i	$-0.585516\pi$
$677$	−13.8129			−0.530874			−0.265437	+	0.964128i	$0.585516\pi$
$678$	−18.7784	+	10.8417i	−0.721181	+	0.416374i
$679$		0			0
$680$	−8.81697	+	15.2714i	−0.338115	+	0.585633i
$681$		−	15.5931i		−	0.597528i
$682$	−15.9458	−	9.20629i	−0.610595	−	0.352527i
$683$	−15.2050	−	8.77861i	−0.581803	−	0.335904i	0.180046	−	0.983658i	$-0.442375\pi$
$683$	−15.2050	−	8.77861i	−0.581803	−	0.335904i	−0.761850	+	0.647754i	$0.775709\pi$
$684$			125.604i			4.80258i
$685$	28.3618	−	49.1240i	1.08365	−	1.87693i
$686$		0			0
$687$	41.1390	−	23.7516i	1.56955	−	0.906181i
$688$	9.52716			0.363220
$689$	−1.45637	+	0.971995i	−0.0554833	+	0.0370301i
$690$	−15.6122			−0.594345
$691$	−32.1966	+	18.5887i	−1.22482	+	0.707148i	−0.965941	−	0.258763i	$-0.916685\pi$
$691$	−32.1966	+	18.5887i	−1.22482	+	0.707148i	−0.258875	+	0.965911i	$0.583352\pi$
$692$	−5.19729	−	9.00198i	−0.197571	−	0.342204i
$693$		0			0
$694$		−	69.4483i		−	2.63622i
$695$	−20.7328	−	11.9701i	−0.786439	−	0.454051i
$696$	46.4609	+	26.8242i	1.76109	+	1.01677i
$697$		−	0.380586i		−	0.0144157i
$698$	24.2843	−	42.0616i	0.919173	−	1.59206i
$699$	27.7466	+	48.0585i	1.04947	+	1.81774i
$700$		0			0
$701$	−43.8575			−1.65647			−0.828237	−	0.560378i	$-0.810656\pi$
$701$	−43.8575			−1.65647			−0.828237	+	0.560378i	$0.810656\pi$
$702$	32.9338	−	66.6935i	1.24300	−	2.51719i
$703$	7.44227			0.280691
$704$	−37.2855	+	21.5268i	−1.40525	+	0.811322i
$705$	55.5861	+	96.2779i	2.09349	+	3.62604i
$706$	4.12703	−	7.14822i	0.155323	−	0.269027i
$707$		0			0
$708$	81.0141	+	46.7735i	3.04470	+	1.75786i
$709$	30.8017	+	17.7834i	1.15678	+	0.667870i	0.950531	−	0.310629i	$-0.100540\pi$
$709$	30.8017	+	17.7834i	1.15678	+	0.667870i	0.206253	+	0.978499i	$0.433873\pi$
$710$		−	62.1228i		−	2.33143i
$711$	−29.9816	+	51.9296i	−1.12440	+	1.94751i
$712$	−4.69691	−	8.13528i	−0.176024	−	0.304883i
$713$	−1.26086	+	0.727960i	−0.0472197	+	0.0272623i
$714$		0			0
$715$	−38.2428	−	18.8846i	−1.43020	−	0.706243i
$716$	55.6558			2.07996
$717$	−8.55047	+	4.93661i	−0.319323	+	0.184361i
$718$	28.9415	+	50.1282i	1.08009	+	1.87077i
$719$	4.99828	−	8.65727i	0.186404	−	0.322862i	−0.757645	−	0.652667i	$-0.773650\pi$
$719$	4.99828	−	8.65727i	0.186404	−	0.322862i	0.944049	+	0.329806i	$0.106983\pi$
$720$		−	32.1952i		−	1.19984i
$721$		0			0
$722$	−32.6462	−	18.8483i	−1.21496	−	0.701460i
$723$			39.3166i			1.46220i
$724$	34.8882	−	60.4282i	1.29661	−	2.24580i
$725$	−12.5764	−	21.7830i	−0.467076	−	0.809000i
$726$	16.1611	−	9.33061i	0.599795	−	0.346292i
$727$	−39.8985			−1.47975			−0.739877	−	0.672742i	$-0.765116\pi$
$727$	−39.8985			−1.47975			−0.739877	+	0.672742i	$0.765116\pi$
$728$		0			0
$729$	−29.0397			−1.07555
$730$	−1.70350	+	0.983515i	−0.0630493	+	0.0364015i
$731$	−4.11597	−	7.12907i	−0.152235	−	0.263678i
$732$	61.4258	−	106.393i	2.27036	−	3.93238i
$733$			6.81455i			0.251701i	0.992049	+	0.125850i	$0.0401660\pi$
$733$			6.81455i			0.251701i	−0.992049	+	0.125850i	$0.959834\pi$
$734$	3.07152	+	1.77335i	0.113372	+	0.0654554i
$735$		0			0
$736$			2.41272i			0.0889342i
$737$	−0.631427	+	1.09366i	−0.0232589	+	0.0402856i
$738$	1.81605	+	3.14548i	0.0668496	+	0.115787i
$739$	22.4174	−	12.9427i	0.824638	−	0.476105i	−0.0273755	−	0.999625i	$-0.508715\pi$
$739$	22.4174	−	12.9427i	0.824638	−	0.476105i	0.852013	+	0.523520i	$0.175382\pi$
$740$	−14.4663			−0.531791
$741$	35.3422	+	52.9543i	1.29833	+	1.94533i
$742$		0			0
$743$	−2.38738	+	1.37836i	−0.0875846	+	0.0505670i	−0.543153	−	0.839634i	$-0.682770\pi$
$743$	−2.38738	+	1.37836i	−0.0875846	+	0.0505670i	0.455568	+	0.890201i	$0.349436\pi$
$744$	−11.8222	−	20.4766i	−0.433423	−	0.750710i
$745$	11.8752	−	20.5684i	0.435072	−	0.753567i
$746$		−	21.4410i		−	0.785012i
$747$	−51.7944	−	29.9035i	−1.89506	−	1.09411i
$748$	−16.8347	−	9.71954i	−0.615539	−	0.355382i
$749$		0			0
$750$	−2.90394	+	5.02978i	−0.106037	+	0.183661i
$751$	13.1874	+	22.8413i	0.481216	+	0.833491i	0.999768	−	0.0215556i	$-0.00686189\pi$
$751$	13.1874	+	22.8413i	0.481216	+	0.833491i	−0.518552	+	0.855046i	$0.673529\pi$
$752$	−17.0855	+	9.86435i	−0.623046	+	0.359716i
$753$	11.1242			0.405387
$754$	40.6954	−	2.64556i	1.48204	−	0.0963455i
$755$	−19.4688			−0.708544
$756$		0			0
$757$	−7.39345	−	12.8058i	−0.268720	−	0.465436i	0.699812	−	0.714327i	$-0.253267\pi$
$757$	−7.39345	−	12.8058i	−0.268720	−	0.465436i	−0.968531	+	0.248891i	$0.919934\pi$
$758$	−29.0523	+	50.3201i	−1.05523	+	1.82771i
$759$		−	7.61699i		−	0.276479i
$760$	61.5476	+	35.5345i	2.23257	+	1.28897i
$761$	−20.4564	−	11.8105i	−0.741543	−	0.428130i	0.0810874	−	0.996707i	$-0.474161\pi$
$761$	−20.4564	−	11.8105i	−0.741543	−	0.428130i	−0.822630	+	0.568577i	$0.807494\pi$
$762$			130.433i			4.72510i
$763$		0			0
$764$	31.1783	+	54.0024i	1.12799	+	1.95374i
$765$	−24.0913	+	13.9091i	−0.871023	+	0.502885i
$766$	12.7599			0.461034
$767$	31.4059	−	2.04166i	1.13400	−	0.0737201i
$768$	−75.5694			−2.72687
$769$	0.990062	−	0.571613i	0.0357026	−	0.0206129i	−0.482042	−	0.876148i	$-0.660105\pi$
$769$	0.990062	−	0.571613i	0.0357026	−	0.0206129i	0.517745	+	0.855535i	$0.326772\pi$
$770$		0			0
$771$	25.4378	−	44.0596i	0.916120	−	1.58677i
$772$			41.8310i			1.50553i
$773$	15.0236	+	8.67389i	0.540362	+	0.311978i	0.745226	−	0.666812i	$-0.232342\pi$
$773$	15.0236	+	8.67389i	0.540362	+	0.311978i	−0.204864	+	0.978791i	$0.565675\pi$
$774$	68.0358	+	39.2805i	2.44550	+	1.41191i
$775$			11.0856i			0.398206i
$776$	9.93280	−	17.2041i	0.356567	−	0.617592i
$777$		0			0
$778$	43.5564	−	25.1473i	1.56157	−	0.901574i
$779$	−1.53385			−0.0549560
$780$	−68.6982	−	102.933i	−2.45979	−	3.68558i
$781$	30.3090			1.08454
$782$	−2.07317	+	1.19694i	−0.0741363	+	0.0428026i
$783$	20.8785	+	36.1627i	0.746138	+	1.29235i
$784$		0			0
$785$			30.0524i			1.07262i
$786$	−76.7808	−	44.3294i	−2.73868	−	1.58118i
$787$	0.953072	+	0.550256i	0.0339734	+	0.0196145i	0.516890	−	0.856052i	$-0.327089\pi$
$787$	0.953072	+	0.550256i	0.0339734	+	0.0196145i	−0.482917	+	0.875666i	$0.660423\pi$
$788$			22.2302i			0.791917i
$789$	−13.8649	+	24.0147i	−0.493603	+	0.854946i
$790$	38.3299	+	66.3894i	1.36372	+	2.36203i
$791$		0			0
$792$	82.1058			2.91750
$793$	−2.68123	−	41.2442i	−0.0952134	−	1.46462i
$794$	44.6489			1.58453
$795$	−4.02311	+	2.32274i	−0.142685	+	0.0823792i
$796$	−17.0106	−	29.4632i	−0.602924	−	1.04429i
$797$	6.31738	−	10.9420i	0.223773	−	0.387587i	−0.732177	−	0.681114i	$-0.761496\pi$
$797$	6.31738	−	10.9420i	0.223773	−	0.387587i	0.955951	+	0.293527i	$0.0948292\pi$
$798$		0			0
$799$	14.7628	+	8.52329i	0.522269	+	0.301532i
$800$	15.9096	+	9.18541i	0.562489	+	0.324753i
$801$		−	14.8191i		−	0.523608i
$802$	−12.4575	+	21.5771i	−0.439891	+	0.761913i
$803$	−0.479845	−	0.831117i	−0.0169334	−	0.0293295i
$804$	−3.17325	+	1.83207i	−0.111912	+	0.0646123i
$805$		0			0
$806$	−16.1157	−	7.95805i	−0.567651	−	0.280310i
$807$	66.1188			2.32749
$808$	−39.0381	+	22.5387i	−1.37336	+	0.792907i
$809$	−20.6805	−	35.8197i	−0.727088	−	1.25935i	−0.958109	−	0.286404i	$-0.907540\pi$
$809$	−20.6805	−	35.8197i	−0.727088	−	1.25935i	0.231021	−	0.972949i	$-0.425793\pi$
$810$	31.4254	−	54.4303i	1.10417	−	1.91249i
$811$		−	15.3408i		−	0.538687i	−0.963044	−	0.269343i	$-0.913193\pi$
$811$		−	15.3408i		−	0.538687i	0.963044	−	0.269343i	$-0.0868067\pi$
$812$		0			0
$813$	68.8619	+	39.7574i	2.41509	+	1.39435i
$814$		−	10.9921i		−	0.385275i
$815$	−39.5082	+	68.4302i	−1.38391	+	2.39701i
$816$	−3.71879	−	6.44113i	−0.130184	−	0.225485i
$817$	−28.7319	+	16.5884i	−1.00520	+	0.580354i
$818$	77.1922			2.69896
$819$		0			0
$820$	2.98150			0.104119
$821$	−28.4471	+	16.4240i	−0.992812	+	0.573200i	−0.906114	−	0.423034i	$-0.860965\pi$
$821$	−28.4471	+	16.4240i	−0.992812	+	0.573200i	−0.0866982	+	0.996235i	$0.527632\pi$
$822$	62.5286	+	108.303i	2.18093	+	3.77749i
$823$	−16.2971	+	28.2273i	−0.568080	+	0.983943i	0.428676	+	0.903458i	$0.358980\pi$
$823$	−16.2971	+	28.2273i	−0.568080	+	0.983943i	−0.996756	+	0.0804850i	$0.974353\pi$
$824$			31.3825i			1.09326i
$825$	−50.2267	−	28.9984i	−1.74867	−	1.00959i
$826$		0			0
$827$		−	6.24226i		−	0.217065i	−0.994093	−	0.108532i	$-0.965385\pi$
$827$		−	6.24226i		−	0.217065i	0.994093	−	0.108532i	$-0.0346151\pi$
$828$	7.33454	−	12.7038i	0.254893	−	0.441488i
$829$	−10.8516	−	18.7954i	−0.376890	−	0.652792i	0.613718	−	0.789525i	$-0.289673\pi$
$829$	−10.8516	−	18.7954i	−0.376890	−	0.652792i	−0.990608	+	0.136733i	$0.956340\pi$
$830$	−66.2165	+	38.2301i	−2.29841	+	1.32699i
$831$	5.02174			0.174202
$832$	−34.9565	+	23.3303i	−1.21190	+	0.808831i
$833$		0			0
$834$	45.7091	−	26.3902i	1.58278	−	0.913817i
$835$	−2.73076	−	4.72981i	−0.0945017	−	0.163682i
$836$	−39.1721	+	67.8481i	−1.35480	+	2.34657i
$837$		−	18.4036i		−	0.636120i
$838$	73.9783	+	42.7114i	2.55554	+	1.47544i
$839$	−2.86335	−	1.65316i	−0.0988540	−	0.0570734i	0.449758	−	0.893150i	$-0.351510\pi$
$839$	−2.86335	−	1.65316i	−0.0988540	−	0.0570734i	−0.548612	+	0.836077i	$0.684844\pi$
$840$		0			0
$841$	3.05294	−	5.28784i	0.105274	−	0.182339i
$842$	43.3515	+	75.0870i	1.49399	+	2.58767i
$843$	74.1700	−	42.8221i	2.55455	−	1.47487i
$844$	8.54608			0.294168
$845$	−38.4480	−	15.9737i	−1.32265	−	0.549511i
$846$	−162.683			−5.59315
$847$		0			0
$848$	−0.412196	−	0.713944i	−0.0141549	−	0.0245169i
$849$	−5.35126	+	9.26865i	−0.183655	+	0.318099i
$850$			18.2274i			0.625194i
$851$	−0.752725	−	0.434586i	−0.0258031	−	0.0148974i
$852$	76.1592	+	43.9705i	2.60917	+	1.50640i
$853$			1.65549i			0.0566828i	0.999598	+	0.0283414i	$0.00902255\pi$
$853$			1.65549i			0.0566828i	−0.999598	+	0.0283414i	$0.990977\pi$
$854$		0			0
$855$	56.0571	+	97.0938i	1.91711	+	3.32054i
$856$	33.4287	−	19.3001i	1.14257	−	0.659664i
$857$	−48.2809			−1.64924			−0.824622	−	0.565683i	$-0.808612\pi$
$857$	−48.2809			−1.64924			−0.824622	+	0.565683i	$0.808612\pi$
$858$	78.2129	−	52.2000i	2.67015	−	1.78208i
$859$	16.1342			0.550492			0.275246	−	0.961374i	$-0.411241\pi$
$859$	16.1342			0.550492			0.275246	+	0.961374i	$0.411241\pi$
$860$	55.8491	−	32.2445i	1.90444	−	1.09953i
$861$		0			0
$862$	−12.1667	+	21.0733i	−0.414399	+	0.717761i
$863$		−	1.89828i		−	0.0646181i	−0.999478	−	0.0323090i	$-0.989714\pi$
$863$		−	1.89828i		−	0.0646181i	0.999478	−	0.0323090i	$-0.0102861\pi$
$864$	−26.4121	−	15.2490i	−0.898557	−	0.518782i
$865$	−8.03518	−	4.63911i	−0.273204	−	0.157735i
$866$		−	66.1052i		−	2.24635i
$867$	22.1757	−	38.4094i	0.753126	−	1.30445i
$868$		0			0
$869$	−32.3906	+	18.7007i	−1.09878	+	0.634378i
$870$	108.198			3.66827
$871$	−0.545815	+	1.10532i	−0.0184942	+	0.0374523i
$872$	−74.1101			−2.50968
$873$	27.1402	−	15.6694i	0.918556	−	0.530329i
$874$	4.82398	+	8.35537i	0.163173	+	0.282625i
$875$		0			0
$876$		−	2.78453i		−	0.0940804i
$877$	−5.50805	−	3.18007i	−0.185994	−	0.107383i	0.404112	−	0.914709i	$-0.367581\pi$
$877$	−5.50805	−	3.18007i	−0.185994	−	0.107383i	−0.590106	+	0.807326i	$0.700914\pi$
$878$	34.2947	+	19.8001i	1.15739	+	0.668219i
$879$		−	49.1076i		−	1.65636i
$880$	10.0407	−	17.3910i	0.338472	−	0.586251i
$881$	−10.8083	−	18.7205i	−0.364140	−	0.630709i	0.624498	−	0.781027i	$-0.285304\pi$
$881$	−10.8083	−	18.7205i	−0.364140	−	0.630709i	−0.988638	+	0.150318i	$0.951970\pi$
$882$		0			0
$883$	6.14172			0.206685			0.103343	−	0.994646i	$-0.467046\pi$
$883$	6.14172			0.206685			0.103343	+	0.994646i	$0.467046\pi$
$884$	−17.0141	−	8.40171i	−0.572248	−	0.282580i
$885$	83.5002			2.80683
$886$	−12.3376	+	7.12311i	−0.414489	+	0.239306i
$887$	16.9316	+	29.3265i	0.568509	+	0.984686i	0.996714	+	0.0810044i	$0.0258128\pi$
$887$	16.9316	+	29.3265i	0.568509	+	0.984686i	−0.428205	+	0.903682i	$0.640854\pi$
$888$	7.05775	−	12.2244i	0.236843	−	0.410223i
$889$		0			0
$890$	−16.4073	−	9.47275i	−0.549974	−	0.317527i
$891$	26.5559	+	15.3321i	0.889657	+	0.513643i
$892$		−	8.27828i		−	0.277177i
$893$	34.3509	−	59.4975i	1.14951	−	1.99101i
$894$	26.1809	+	45.3467i	0.875621	+	1.51662i
$895$	43.0228	−	24.8392i	1.43809	−	0.830284i
$896$		0			0
$897$	−0.482344	−	7.41968i	−0.0161050	−	0.247736i
$898$	−70.8778			−2.36522
$899$	8.73829	−	5.04505i	0.291438	−	0.168262i
$900$	−55.8462	−	96.7285i	−1.86154	−	3.22428i
$901$	−0.356158	+	0.616883i	−0.0118653	+	0.0205514i
$902$			2.26548i			0.0754323i
$903$		0			0
$904$	−9.98335	−	5.76389i	−0.332041	−	0.191704i
$905$		−	62.2826i		−	2.07034i
$906$	21.4613	−	37.1720i	0.713003	−	1.23496i
$907$	−6.15858	−	10.6670i	−0.204492	−	0.354191i	0.745479	−	0.666530i	$-0.232221\pi$
$907$	−6.15858	−	10.6670i	−0.204492	−	0.354191i	−0.949971	+	0.312339i	$0.898888\pi$
$908$	16.2213	−	9.36539i	0.538324	−	0.310802i
$909$	−71.1113			−2.35861
$910$		0			0
$911$	17.7667			0.588636			0.294318	−	0.955708i	$-0.404908\pi$
$911$	17.7667			0.588636			0.294318	+	0.955708i	$0.404908\pi$
$912$	−25.9593	+	14.9876i	−0.859599	+	0.496290i
$913$	−18.6520	−	32.3062i	−0.617292	−	1.06918i
$914$	−34.6553	+	60.0247i	−1.14630	+	1.98544i
$915$		−	109.658i		−	3.62517i
$916$	49.4172	+	28.5310i	1.63279	+	0.942691i
$917$		0			0
$918$		−	30.2599i		−	0.998727i
$919$	12.1237	−	20.9988i	0.399924	−	0.692688i	−0.593792	−	0.804618i	$-0.702370\pi$
$919$	12.1237	−	20.9988i	0.399924	−	0.692688i	0.993716	+	0.111930i	$0.0357033\pi$
$920$	−4.15002	−	7.18805i	−0.136822	−	0.236983i
$921$	−9.12048	+	5.26571i	−0.300530	+	0.173511i
$922$	−19.9575			−0.657266
$923$	29.5239	−	1.91931i	0.971790	−	0.0631749i
$924$		0			0
$925$	−5.73135	+	3.30899i	−0.188446	+	0.108799i
$926$	6.11527	+	10.5920i	0.200960	+	0.348073i
$927$	−24.7536	+	42.8744i	−0.813013	+	1.40818i
$928$		−	16.7211i		−	0.548898i
$929$	−40.7740	−	23.5409i	−1.33775	−	0.772351i	−0.351277	−	0.936271i	$-0.614253\pi$
$929$	−40.7740	−	23.5409i	−1.33775	−	0.772351i	−0.986474	+	0.163921i	$0.947586\pi$
$930$	−41.2974	−	23.8431i	−1.35420	−	0.781846i
$931$		0			0
$932$	−33.3299	+	57.7290i	−1.09176	+	1.89098i
$933$	−21.3925	−	37.0530i	−0.700360	−	1.21306i
$934$	−82.6262	+	47.7043i	−2.70361	+	1.56093i
$935$	−17.3514			−0.567450
$936$	79.9790	−	5.19933i	2.61419	−	0.169945i
$937$	−29.4852			−0.963240			−0.481620	−	0.876380i	$-0.659952\pi$
$937$	−29.4852			−0.963240			−0.481620	+	0.876380i	$0.659952\pi$
$938$		0			0
$939$	10.0345	+	17.3803i	0.327465	+	0.567186i
$940$	−66.7713	+	115.651i	−2.17784	+	3.77213i
$941$		−	48.3265i		−	1.57540i	−0.616059	−	0.787700i	$-0.711272\pi$
$941$		−	48.3265i		−	1.57540i	0.616059	−	0.787700i	$-0.288728\pi$
$942$	−57.3793	−	33.1279i	−1.86952	−	1.07937i
$943$	0.155137	+	0.0895682i	0.00505194	+	0.00291674i
$944$			14.8180i			0.482285i
$945$		0			0
$946$	24.5008	+	42.4367i	0.796591	+	1.37974i
$947$	−2.35762	+	1.36117i	−0.0766125	+	0.0442322i	−0.537817	−	0.843062i	$-0.680751\pi$
$947$	−2.35762	+	1.36117i	−0.0766125	+	0.0442322i	0.461204	+	0.887294i	$0.347417\pi$
$948$	−108.520			−3.52455
$949$	−0.520046	−	0.779201i	−0.0168814	−	0.0252939i
$950$	73.4608			2.38338
$951$	10.2295	−	5.90601i	0.331714	−	0.191515i
$952$		0			0
$953$	19.8192	−	34.3279i	0.642008	−	1.11199i	−0.342976	−	0.939344i	$-0.611435\pi$
$953$	19.8192	−	34.3279i	0.642008	−	1.11199i	0.984984	−	0.172646i	$-0.0552316\pi$
$954$		−	6.79793i		−	0.220091i
$955$	48.2026	+	27.8298i	1.55980	+	0.900551i
$956$	−10.2710	−	5.92998i	−0.332189	−	0.191789i
$957$			52.7887i			1.70642i
$958$	−8.87327	+	15.3690i	−0.286682	+	0.496549i
$959$		0			0
$960$	−96.5645	+	55.7516i	−3.11661	+	1.79937i
$961$	26.5530			0.856548
$962$	−0.696076	−	10.7074i	−0.0224424	−	0.345221i
$963$	60.8934			1.96226
$964$	−40.9006	+	23.6140i	−1.31732	+	0.760555i
$965$	18.6692	+	32.3361i	0.600984	+	1.04093i
$966$		0			0
$967$			23.7830i			0.764810i	0.923995	+	0.382405i	$0.124904\pi$
$967$			23.7830i			0.764810i	−0.923995	+	0.382405i	$0.875096\pi$
$968$	8.59188	+	4.96053i	0.276154	+	0.159437i
$969$	22.4302	+	12.9501i	0.720561	+	0.416016i
$970$		−	40.0651i		−	1.28641i
$971$	−18.6704	+	32.3380i	−0.599160	+	1.03778i	0.393785	+	0.919203i	$0.371165\pi$
$971$	−18.6704	+	32.3380i	−0.599160	+	1.03778i	−0.992945	+	0.118573i	$0.962168\pi$
$972$	−2.48298	−	4.30064i	−0.0796416	−	0.137943i
$973$		0			0
$974$	10.9353			0.350389
$975$	−50.7619	−	25.0666i	−1.62568	−	0.802774i
$976$	19.4599			0.622896
$977$	43.7185	−	25.2409i	1.39868	−	0.807527i	0.404423	−	0.914572i	$-0.367472\pi$
$977$	43.7185	−	25.2409i	1.39868	−	0.807527i	0.994254	+	0.107045i	$0.0341389\pi$
$978$	−87.1029	−	150.867i	−2.78524	−	4.82418i
$979$	4.62164	−	8.00492i	0.147708	−	0.255838i
$980$		0			0
$981$	−101.248	−	58.4558i	−3.23261	−	1.86635i
$982$	−67.9102	−	39.2080i	−2.16710	−	1.25118i
$983$			7.90270i			0.252057i	0.992027	+	0.126028i	$0.0402231\pi$
$983$			7.90270i			0.252057i	−0.992027	+	0.126028i	$0.959777\pi$
$984$	−1.45460	+	2.51945i	−0.0463710	+	0.0803170i
$985$	9.92135	+	17.1843i	0.316120	+	0.547536i
$986$	14.3679	−	8.29530i	0.457566	−	0.264176i
$987$		0			0
$988$	−33.8609	+	68.5711i	−1.07726	+	2.18154i
$989$	3.87466			0.123207
$990$	143.406	−	82.7957i	4.55776	−	2.63142i
$991$	−2.93261	−	5.07942i	−0.0931573	−	0.161353i	0.815681	−	0.578502i	$-0.196363\pi$
$991$	−2.93261	−	5.07942i	−0.0931573	−	0.161353i	−0.908838	+	0.417149i	$0.863029\pi$
$992$	−3.68474	+	6.38216i	−0.116991	+	0.202634i
$993$		−	35.2451i		−	1.11847i
$994$		0			0
$995$	−26.2989	−	15.1837i	−0.833731	−	0.481355i
$996$		−	108.237i		−	3.42962i
$997$	−25.6600	+	44.4443i	−0.812659	+	1.40757i	0.0983379	+	0.995153i	$0.468647\pi$
$997$	−25.6600	+	44.4443i	−0.812659	+	1.40757i	−0.910997	+	0.412413i	$0.864686\pi$
$998$	−33.5602	−	58.1279i	−1.06233	−	1.84001i
$999$	9.51482	−	5.49338i	0.301035	−	0.173803i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.j.491.3	✓	32
7.2	even	3		637.2.u.j.361.14		32
7.3	odd	6		637.2.k.j.569.4		32
7.4	even	3		637.2.k.j.569.3		32
7.5	odd	6		637.2.u.j.361.13		32
7.6	odd	2	inner	637.2.q.j.491.4	yes	32
13.2	odd	12		8281.2.a.cx.1.6		32
13.4	even	6	inner	637.2.q.j.589.3	yes	32
13.11	odd	12		8281.2.a.cx.1.28		32
91.4	even	6		637.2.u.j.30.14		32
91.17	odd	6		637.2.u.j.30.13		32
91.30	even	6		637.2.k.j.459.13		32
91.41	even	12		8281.2.a.cx.1.5		32
91.69	odd	6	inner	637.2.q.j.589.4	yes	32
91.76	even	12		8281.2.a.cx.1.27		32
91.82	odd	6		637.2.k.j.459.14		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.k.j.459.13		32	91.30	even	6
637.2.k.j.459.14		32	91.82	odd	6
637.2.k.j.569.3		32	7.4	even	3
637.2.k.j.569.4		32	7.3	odd	6
637.2.q.j.491.3	✓	32	1.1	even	1	trivial
637.2.q.j.491.4	yes	32	7.6	odd	2	inner
637.2.q.j.589.3	yes	32	13.4	even	6	inner
637.2.q.j.589.4	yes	32	91.69	odd	6	inner
637.2.u.j.30.13		32	91.17	odd	6
637.2.u.j.30.14		32	91.4	even	6
637.2.u.j.361.13		32	7.5	odd	6
637.2.u.j.361.14		32	7.2	even	3
8281.2.a.cx.1.5		32	91.41	even	12
8281.2.a.cx.1.6		32	13.2	odd	12
8281.2.a.cx.1.27		32	91.76	even	12
8281.2.a.cx.1.28		32	13.11	odd	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)

\(f(q)\)	\(=\)	\(q+(-2.04719 + 1.18194i) q^{2} +(-1.49347 - 2.58676i) q^{3} +(1.79399 - 3.10727i) q^{4} -3.20263i q^{5} +(6.11481 + 3.53039i) q^{6} +3.75379i q^{8} +(-2.96088 + 5.12839i) q^{9} +O(q^{10})\)	\(q+(-2.04719 + 1.18194i) q^{2} +(-1.49347 - 2.58676i) q^{3} +(1.79399 - 3.10727i) q^{4} -3.20263i q^{5} +(6.11481 + 3.53039i) q^{6} +3.75379i q^{8} +(-2.96088 + 5.12839i) q^{9} +(3.78533 + 6.55639i) q^{10} +(-3.19878 + 1.84682i) q^{11} -10.7170 q^{12} +(-2.99897 + 2.00154i) q^{13} +(-8.28443 + 4.78302i) q^{15} +(-0.848797 - 1.47016i) q^{16} +(-0.733403 + 1.27029i) q^{17} -13.9984i q^{18} +(5.11958 + 2.95579i) q^{19} +(-9.95145 - 5.74547i) q^{20} +(4.36567 - 7.56157i) q^{22} +(-0.345203 - 0.597908i) q^{23} +(9.71014 - 5.60615i) q^{24} -5.25684 q^{25} +(3.77375 - 7.64215i) q^{26} +8.72707 q^{27} +(2.39239 + 4.14374i) q^{29} +(11.3065 - 19.5835i) q^{30} -2.10879i q^{31} +(-3.02646 - 1.74733i) q^{32} +(9.55454 + 5.51632i) q^{33} -3.46737i q^{34} +(10.6235 + 18.4005i) q^{36} +(1.09027 - 0.629465i) q^{37} -13.9743 q^{38} +(9.65636 + 4.76838i) q^{39} +12.0220 q^{40} +(-0.224704 + 0.129733i) q^{41} +(-2.80608 + 4.86027i) q^{43} +13.2527i q^{44} +(16.4243 + 9.48259i) q^{45} +(1.41339 + 0.816021i) q^{46} -11.6216i q^{47} +(-2.53530 + 4.39126i) q^{48} +(10.7617 - 6.21329i) q^{50} +4.38125 q^{51} +(0.839222 + 12.9094i) q^{52} +0.485623 q^{53} +(-17.8659 + 10.3149i) q^{54} +(5.91467 + 10.2445i) q^{55} -17.6575i q^{57} +(-9.79535 - 5.65535i) q^{58} +(-7.55939 - 4.36441i) q^{59} +34.3226i q^{60} +(-5.73161 + 9.92744i) q^{61} +(2.49247 + 4.31709i) q^{62} +11.6562 q^{64} +(6.41019 + 9.60460i) q^{65} -26.0799 q^{66} +(0.296094 - 0.170950i) q^{67} +(2.63143 + 4.55777i) q^{68} +(-1.03110 + 1.78591i) q^{69} +(-7.10638 - 4.10287i) q^{71} +(-19.2509 - 11.1145i) q^{72} +0.259823i q^{73} +(-1.48799 + 2.57727i) q^{74} +(7.85090 + 13.5982i) q^{75} +(18.3689 - 10.6053i) q^{76} +(-25.4043 + 1.65151i) q^{78} +10.1259 q^{79} +(-4.70838 + 2.71838i) q^{80} +(-4.15094 - 7.18964i) q^{81} +(0.306674 - 0.531175i) q^{82} +10.0995i q^{83} +(4.06827 + 2.34882i) q^{85} -13.2665i q^{86} +(7.14590 - 12.3771i) q^{87} +(-6.93256 - 12.0075i) q^{88} +(-2.16722 + 1.25125i) q^{89} -44.8316 q^{90} -2.47715 q^{92} +(-5.45493 + 3.14941i) q^{93} +(13.7360 + 23.7915i) q^{94} +(9.46631 - 16.3961i) q^{95} +10.4383i q^{96} +(-4.58314 - 2.64607i) q^{97} -21.8728i 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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