LMFDB - Embedded newform 637.2.c.g.246.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(246,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("637.246");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.c (of order $2$, degree $1$, 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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 121x^{12} + 296x^{10} + 3468x^{8} - 1748x^{6} + 40192x^{4} - 65056x^{2} + 228484 $ x^16 + 10x^14 + 121x^12 + 296x^10 + 3468x^8 - 1748x^6 + 40192x^4 - 65056*x^2 + 228484
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			246.13
Root			$-1.41421 + 1.65552i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.g.246.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.65552i q^{2} -0.494977 q^{3} -0.740740 q^{4} -2.87389i q^{5} -0.819443i q^{6} +2.08473i q^{8} -2.75500 q^{9} +O(q^{10})$	\(q+1.65552i q^{2} -0.494977 q^{3} -0.740740 q^{4} -2.87389i q^{5} -0.819443i q^{6} +2.08473i q^{8} -2.75500 q^{9} +4.75778 q^{10} -2.58138i q^{11} +0.366649 q^{12} +(3.54562 - 0.654682i) q^{13} +1.42251i q^{15} -4.93278 q^{16} +2.27584 q^{17} -4.56095i q^{18} -4.39571i q^{19} +2.12881i q^{20} +4.27352 q^{22} +7.16926 q^{23} -1.03189i q^{24} -3.25926 q^{25} +(1.08384 + 5.86983i) q^{26} +2.84859 q^{27} +6.19574 q^{29} -2.35499 q^{30} -6.85404i q^{31} -3.99686i q^{32} +1.27772i q^{33} +3.76769i q^{34} +2.04074 q^{36} -5.89241i q^{37} +7.27717 q^{38} +(-1.75500 + 0.324052i) q^{39} +5.99128 q^{40} -3.98014i q^{41} +1.31425 q^{43} +1.91213i q^{44} +7.91757i q^{45} +11.8688i q^{46} -1.35208i q^{47} +2.44161 q^{48} -5.39576i q^{50} -1.12649 q^{51} +(-2.62638 + 0.484949i) q^{52} -8.28778 q^{53} +4.71589i q^{54} -7.41860 q^{55} +2.17577i q^{57} +10.2572i q^{58} +9.61085i q^{59} -1.05371i q^{60} -9.55301 q^{61} +11.3470 q^{62} -3.24870 q^{64} +(-1.88149 - 10.1897i) q^{65} -2.11529 q^{66} +15.9095i q^{67} -1.68581 q^{68} -3.54862 q^{69} +4.79396i q^{71} -5.74342i q^{72} -5.70507i q^{73} +9.75500 q^{74} +1.61326 q^{75} +3.25607i q^{76} +(-0.536475 - 2.90543i) q^{78} -2.01426 q^{79} +14.1763i q^{80} +6.85501 q^{81} +6.58920 q^{82} +3.11798i q^{83} -6.54052i q^{85} +2.17577i q^{86} -3.06675 q^{87} +5.38147 q^{88} +13.0584i q^{89} -13.1077 q^{90} -5.31056 q^{92} +3.39259i q^{93} +2.23839 q^{94} -12.6328 q^{95} +1.97835i q^{96} -14.0382i q^{97} +7.11169i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 20 q^{4} + 16 q^{9}+O(q^{10}) $ 16 * q - 20 * q^4 + 16 * q^9	$ 16 q - 20 q^{4} + 16 q^{9} + 28 q^{16} - 8 q^{22} - 36 q^{23} - 44 q^{25} + 36 q^{29} + 52 q^{36} + 32 q^{39} - 36 q^{43} - 72 q^{51} + 12 q^{53} - 164 q^{64} - 24 q^{65} + 96 q^{74} + 24 q^{78} + 36 q^{79} + 16 q^{81} + 136 q^{88} + 24 q^{92} - 84 q^{95}+O(q^{100}) $ 16 * q - 20 * q^4 + 16 * q^9 + 28 * q^16 - 8 * q^22 - 36 * q^23 - 44 * q^25 + 36 * q^29 + 52 * q^36 + 32 * q^39 - 36 * q^43 - 72 * q^51 + 12 * q^53 - 164 * q^64 - 24 * q^65 + 96 * q^74 + 24 * q^78 + 36 * q^79 + 16 * q^81 + 136 * q^88 + 24 * q^92 - 84 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$197$	$248$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$			1.65552i			1.17063i	0.810807	+	0.585314i	$0.199029\pi$
$2$			1.65552i			1.17063i	−0.810807	+	0.585314i	$0.800971\pi$
$3$	−0.494977			−0.285775			−0.142888	−	0.989739i	$-0.545639\pi$
$3$	−0.494977			−0.285775			−0.142888	+	0.989739i	$0.545639\pi$
$4$	−0.740740			−0.370370
$5$		−	2.87389i		−	1.28524i	−0.766183	−	0.642622i	$-0.777847\pi$
$5$		−	2.87389i		−	1.28524i	0.766183	−	0.642622i	$-0.222153\pi$
$6$		−	0.819443i		−	0.334536i
$7$		0			0
$7$		0			0
$8$			2.08473i			0.737063i
$9$	−2.75500			−0.918333
$10$	4.75778			1.50454
$11$		−	2.58138i		−	0.778315i	−0.921171	−	0.389157i	$-0.872766\pi$
$11$		−	2.58138i		−	0.778315i	0.921171	−	0.389157i	$-0.127234\pi$
$12$	0.366649			0.105842
$13$	3.54562	−	0.654682i	0.983377	−	0.181576i
$13$	3.54562	−	0.654682i	0.983377	−	0.181576i
$14$		0			0
$15$			1.42251i			0.367291i
$16$	−4.93278			−1.23320
$17$	2.27584			0.551972			0.275986	−	0.961162i	$-0.410996\pi$
$17$	2.27584			0.551972			0.275986	+	0.961162i	$0.410996\pi$
$18$		−	4.56095i		−	1.07503i
$19$		−	4.39571i		−	1.00844i	−0.863574	−	0.504222i	$-0.831779\pi$
$19$		−	4.39571i		−	1.00844i	0.863574	−	0.504222i	$-0.168221\pi$
$20$			2.12881i			0.476016i
$21$		0			0
$22$	4.27352			0.911117
$23$	7.16926			1.49489			0.747447	−	0.664321i	$-0.231279\pi$
$23$	7.16926			1.49489			0.747447	+	0.664321i	$0.231279\pi$
$24$		−	1.03189i		−	0.210634i
$25$	−3.25926			−0.651852
$26$	1.08384	+	5.86983i	0.212558	+	1.15117i
$27$	2.84859			0.548212
$28$		0			0
$29$	6.19574			1.15052			0.575260	−	0.817971i	$-0.304901\pi$
$29$	6.19574			1.15052			0.575260	+	0.817971i	$0.304901\pi$
$30$	−2.35499			−0.429961
$31$		−	6.85404i		−	1.23102i	−0.788129	−	0.615511i	$-0.788950\pi$
$31$		−	6.85404i		−	1.23102i	0.788129	−	0.615511i	$-0.211050\pi$
$32$		−	3.99686i		−	0.706551i
$33$			1.27772i			0.222423i
$34$			3.76769i			0.646154i
$35$		0			0
$36$	2.04074			0.340123
$37$		−	5.89241i		−	0.968707i	−0.874872	−	0.484353i	$-0.839055\pi$
$37$		−	5.89241i		−	0.968707i	0.874872	−	0.484353i	$-0.160945\pi$
$38$	7.27717			1.18051
$39$	−1.75500	+	0.324052i	−0.281025	+	0.0518899i
$40$	5.99128			0.947305
$41$		−	3.98014i		−	0.621594i	−0.950476	−	0.310797i	$-0.899404\pi$
$41$		−	3.98014i		−	0.621594i	0.950476	−	0.310797i	$-0.100596\pi$
$42$		0			0
$43$	1.31425			0.200422			0.100211	−	0.994966i	$-0.468048\pi$
$43$	1.31425			0.200422			0.100211	+	0.994966i	$0.468048\pi$
$44$			1.91213i			0.288264i
$45$			7.91757i			1.18028i
$46$			11.8688i			1.74997i
$47$		−	1.35208i		−	0.197221i	−0.995126	−	0.0986106i	$-0.968560\pi$
$47$		−	1.35208i		−	0.197221i	0.995126	−	0.0986106i	$-0.0314398\pi$
$48$	2.44161			0.352417
$49$		0			0
$50$		−	5.39576i		−	0.763076i
$51$	−1.12649			−0.157740
$52$	−2.62638	+	0.484949i	−0.364213	+	0.0672503i
$53$	−8.28778			−1.13841			−0.569207	−	0.822194i	$-0.692750\pi$
$53$	−8.28778			−1.13841			−0.569207	+	0.822194i	$0.692750\pi$
$54$			4.71589i			0.641752i
$55$	−7.41860			−1.00032
$56$		0			0
$57$			2.17577i			0.288188i
$58$			10.2572i			1.34683i
$59$			9.61085i			1.25123i	0.780133	+	0.625613i	$0.215151\pi$
$59$			9.61085i			1.25123i	−0.780133	+	0.625613i	$0.784849\pi$
$60$		−	1.05371i		−	0.136033i
$61$	−9.55301			−1.22314			−0.611569	−	0.791191i	$-0.709461\pi$
$61$	−9.55301			−1.22314			−0.611569	+	0.791191i	$0.709461\pi$
$62$	11.3470			1.44107
$63$		0			0
$64$	−3.24870			−0.406087
$65$	−1.88149	−	10.1897i	−0.233370	−	1.26388i
$66$	−2.11529			−0.260375
$67$			15.9095i			1.94366i	0.235685	+	0.971830i	$0.424267\pi$
$67$			15.9095i			1.94366i	−0.235685	+	0.971830i	$0.575733\pi$
$68$	−1.68581			−0.204434
$69$	−3.54862			−0.427204
$70$		0			0
$71$			4.79396i			0.568938i	0.958685	+	0.284469i	$0.0918173\pi$
$71$			4.79396i			0.568938i	−0.958685	+	0.284469i	$0.908183\pi$
$72$		−	5.74342i		−	0.676869i
$73$		−	5.70507i		−	0.667728i	−0.942621	−	0.333864i	$-0.891647\pi$
$73$		−	5.70507i		−	0.667728i	0.942621	−	0.333864i	$-0.108353\pi$
$74$	9.75500			1.13400
$75$	1.61326			0.186283
$76$			3.25607i			0.373497i
$77$		0			0
$78$	−0.536475	−	2.90543i	−0.0607438	−	0.328975i
$79$	−2.01426			−0.226622			−0.113311	−	0.993560i	$-0.536146\pi$
$79$	−2.01426			−0.226622			−0.113311	+	0.993560i	$0.536146\pi$
$80$			14.1763i			1.58496i
$81$	6.85501			0.761667
$82$	6.58920			0.727655
$83$			3.11798i			0.342243i	0.985250	+	0.171122i	$0.0547391\pi$
$83$			3.11798i			0.342243i	−0.985250	+	0.171122i	$0.945261\pi$
$84$		0			0
$85$		−	6.54052i		−	0.709419i
$86$			2.17577i			0.234620i
$87$	−3.06675			−0.328790
$88$	5.38147			0.573667
$89$			13.0584i			1.38418i	0.721810	+	0.692092i	$0.243311\pi$
$89$			13.0584i			1.38418i	−0.721810	+	0.692092i	$0.756689\pi$
$90$	−13.1077			−1.38167
$91$		0			0
$92$	−5.31056			−0.553664
$93$			3.39259i			0.351795i
$94$	2.23839			0.230873
$95$	−12.6328			−1.29610
$96$			1.97835i			0.201915i
$97$		−	14.0382i		−	1.42536i	−0.701488	−	0.712682i	$-0.747480\pi$
$97$		−	14.0382i		−	1.42536i	0.701488	−	0.712682i	$-0.252520\pi$
$98$		0			0
$99$			7.11169i			0.714752i
$100$	2.41426			0.241426
$101$	−17.4483			−1.73617			−0.868083	−	0.496419i	$-0.834648\pi$
$101$	−17.4483			−1.73617			−0.868083	+	0.496419i	$0.834648\pi$
$102$		−	1.86492i		−	0.184655i
$103$	−6.55698			−0.646078			−0.323039	−	0.946386i	$-0.604705\pi$
$103$	−6.55698			−0.646078			−0.323039	+	0.946386i	$0.604705\pi$
$104$	1.36483	+	7.39164i	0.133833	+	0.724810i
$105$		0			0
$106$		−	13.7206i		−	1.33266i
$107$	15.6020			1.50831			0.754153	−	0.656699i	$-0.228048\pi$
$107$	15.6020			1.50831			0.754153	+	0.656699i	$0.228048\pi$
$108$	−2.11006			−0.203041
$109$		−	10.0171i		−	0.959466i	−0.877414	−	0.479733i	$-0.840733\pi$
$109$		−	10.0171i		−	0.959466i	0.877414	−	0.479733i	$-0.159267\pi$
$110$		−	12.2816i		−	1.17101i
$111$			2.91661i			0.276832i
$112$		0			0
$113$	−3.95074			−0.371654			−0.185827	−	0.982582i	$-0.559496\pi$
$113$	−3.95074			−0.371654			−0.185827	+	0.982582i	$0.559496\pi$
$114$	−3.60203			−0.337361
$115$		−	20.6037i		−	1.92130i
$116$	−4.58943			−0.426118
$117$	−9.76816	+	1.80365i	−0.903067	+	0.166747i
$118$	−15.9109			−1.46472
$119$		0			0
$120$	−2.96555			−0.270716
$121$	4.33649			0.394226
$122$		−	15.8152i		−	1.43184i
$123$			1.97008i			0.177636i
$124$			5.07706i			0.455933i
$125$		−	5.00270i		−	0.447455i
$126$		0			0
$127$	−2.37353			−0.210616			−0.105308	−	0.994440i	$-0.533583\pi$
$127$	−2.37353			−0.210616			−0.105308	+	0.994440i	$0.533583\pi$
$128$		−	13.3720i		−	1.18193i
$129$	−0.650526			−0.0572756
$130$	16.8693	−	3.11483i	1.47953	−	0.273189i
$131$	−2.13546			−0.186576			−0.0932878	−	0.995639i	$-0.529738\pi$
$131$	−2.13546			−0.186576			−0.0932878	+	0.995639i	$0.529738\pi$
$132$		−	0.946460i		−	0.0823788i
$133$		0			0
$134$	−26.3385			−2.27530
$135$		−	8.18655i		−	0.704586i
$136$			4.74451i			0.406838i
$137$		−	0.429210i		−	0.0366699i	−0.999832	−	0.0183349i	$-0.994163\pi$
$137$		−	0.429210i		−	0.0366699i	0.999832	−	0.0183349i	$-0.00583652\pi$
$138$		−	5.87480i		−	0.500096i
$139$	19.4858			1.65276			0.826381	−	0.563112i	$-0.190396\pi$
$139$	19.4858			1.65276			0.826381	+	0.563112i	$0.190396\pi$
$140$		0			0
$141$			0.669248i			0.0563609i
$142$	−7.93648			−0.666015
$143$	−1.68998	−	9.15258i	−0.141323	−	0.765377i
$144$	13.5898			1.13248
$145$		−	17.8059i		−	1.47870i
$146$	9.44485			0.781661
$147$		0			0
$148$			4.36475i			0.358780i
$149$			22.9004i			1.87607i	0.346534	+	0.938037i	$0.387358\pi$
$149$			22.9004i			1.87607i	−0.346534	+	0.938037i	$0.612642\pi$
$150$			2.67078i			0.218068i
$151$		−	11.2207i		−	0.913131i	−0.889690	−	0.456565i	$-0.849079\pi$
$151$		−	11.2207i		−	0.913131i	0.889690	−	0.456565i	$-0.150921\pi$
$152$	9.16385			0.743286
$153$	−6.26993			−0.506894
$154$		0			0
$155$	−19.6978			−1.58216
$156$	1.30000	−	0.240039i	0.104083	−	0.0192185i
$157$	3.78799			0.302315			0.151157	−	0.988510i	$-0.451700\pi$
$157$	3.78799			0.302315			0.151157	+	0.988510i	$0.451700\pi$
$158$		−	3.33464i		−	0.265290i
$159$	4.10226			0.325330
$160$	−11.4865			−0.908091
$161$		0			0
$162$			11.3486i			0.891629i
$163$			19.6130i			1.53621i	0.640326	+	0.768103i	$0.278799\pi$
$163$			19.6130i			1.53621i	−0.640326	+	0.768103i	$0.721201\pi$
$164$			2.94825i			0.230220i
$165$	3.67204			0.285868
$166$	−5.16188			−0.400639
$167$			10.2922i			0.796435i	0.917291	+	0.398217i	$0.130371\pi$
$167$			10.2922i			0.796435i	−0.917291	+	0.398217i	$0.869629\pi$
$168$		0			0
$169$	12.1428	−	4.64250i	0.934060	−	0.357116i
$170$	10.8279			0.830466
$171$			12.1102i			0.926087i
$172$	−0.973521			−0.0742303
$173$	6.00439			0.456505			0.228253	−	0.973602i	$-0.426699\pi$
$173$	6.00439			0.456505			0.228253	+	0.973602i	$0.426699\pi$
$174$		−	5.07706i		−	0.384891i
$175$		0			0
$176$			12.7334i			0.959815i
$177$		−	4.75715i		−	0.357569i
$178$	−21.6184			−1.62036
$179$	7.75130			0.579359			0.289680	−	0.957124i	$-0.406451\pi$
$179$	7.75130			0.579359			0.289680	+	0.957124i	$0.406451\pi$
$180$		−	5.86486i		−	0.437141i
$181$	−19.9999			−1.48658			−0.743289	−	0.668970i	$-0.766735\pi$
$181$	−19.9999			−1.48658			−0.743289	+	0.668970i	$0.766735\pi$
$182$		0			0
$183$	4.72852			0.349542
$184$			14.9460i			1.10183i
$185$	−16.9342			−1.24502
$186$	−5.61649			−0.411821
$187$		−	5.87480i		−	0.429608i
$188$			1.00154i			0.0730448i
$189$		0			0
$190$		−	20.9138i		−	1.51725i
$191$	20.4835			1.48214			0.741068	−	0.671430i	$-0.234320\pi$
$191$	20.4835			1.48214			0.741068	+	0.671430i	$0.234320\pi$
$192$	1.60803			0.116050
$193$		−	12.4329i		−	0.894942i	−0.894298	−	0.447471i	$-0.852325\pi$
$193$		−	12.4329i		−	0.894942i	0.894298	−	0.447471i	$-0.147675\pi$
$194$	23.2405			1.66857
$195$	0.931292	+	5.04368i	0.0666912	+	0.361185i
$196$		0			0
$197$			18.9805i			1.35231i	0.736761	+	0.676154i	$0.236354\pi$
$197$			18.9805i			1.35231i	−0.736761	+	0.676154i	$0.763646\pi$
$198$	−11.7735			−0.836709
$199$	12.8188			0.908701			0.454350	−	0.890823i	$-0.349871\pi$
$199$	12.8188			0.908701			0.454350	+	0.890823i	$0.349871\pi$
$200$		−	6.79467i		−	0.480456i
$201$		−	7.87485i		−	0.555449i
$202$		−	28.8859i		−	2.03241i
$203$		0			0
$204$	0.834435			0.0584221
$205$	−11.4385			−0.798900
$206$		−	10.8552i		−	0.756317i
$207$	−19.7513			−1.37281
$208$	−17.4898	+	3.22940i	−1.21270	+	0.223919i
$209$	−11.3470			−0.784887
$210$		0			0
$211$	−7.86926			−0.541743			−0.270871	−	0.962616i	$-0.587312\pi$
$211$	−7.86926			−0.541743			−0.270871	+	0.962616i	$0.587312\pi$
$212$	6.13909			0.421634
$213$		−	2.37290i		−	0.162588i
$214$			25.8294i			1.76566i
$215$		−	3.77703i		−	0.257591i
$216$			5.93854i			0.404066i
$217$		0			0
$218$	16.5835			1.12318
$219$			2.82388i			0.190820i
$220$	5.49526			0.370490
$221$	8.06925	−	1.48995i	0.542797	−	0.100225i
$222$	−4.82850			−0.324068
$223$		−	7.77059i		−	0.520357i	−0.965560	−	0.260179i	$-0.916219\pi$
$223$		−	7.77059i		−	0.520357i	0.965560	−	0.260179i	$-0.0837815\pi$
$224$		0			0
$225$	8.97925			0.598617
$226$		−	6.54052i		−	0.435069i
$227$			25.5431i			1.69536i	0.530511	+	0.847678i	$0.322000\pi$
$227$			25.5431i			1.69536i	−0.530511	+	0.847678i	$0.678000\pi$
$228$		−	1.61168i		−	0.106736i
$229$			12.8986i			0.852362i	0.904638	+	0.426181i	$0.140141\pi$
$229$			12.8986i			0.852362i	−0.904638	+	0.426181i	$0.859859\pi$
$230$	34.1098			2.24913
$231$		0			0
$232$			12.9164i			0.848005i
$233$	−8.14278			−0.533451			−0.266726	−	0.963772i	$-0.585942\pi$
$233$	−8.14278			−0.533451			−0.266726	+	0.963772i	$0.585942\pi$
$234$	−2.98597	−	16.1714i	−0.195199	−	1.05716i
$235$	−3.88573			−0.253477
$236$		−	7.11914i		−	0.463417i
$237$	0.997011			0.0647628
$238$		0			0
$239$		−	23.8122i		−	1.54028i	−0.637875	−	0.770140i	$-0.720186\pi$
$239$		−	23.8122i		−	1.54028i	0.637875	−	0.770140i	$-0.279814\pi$
$240$		−	7.01694i		−	0.452941i
$241$		−	0.288546i		−	0.0185869i	−0.999957	−	0.00929346i	$-0.997042\pi$
$241$		−	0.288546i		−	0.0185869i	0.999957	−	0.00929346i	$-0.00295824\pi$
$242$			7.17913i			0.461492i
$243$	−11.9388			−0.765877
$244$	7.07630			0.453013
$245$		0			0
$246$	−3.26150			−0.207946
$247$	−2.87779	−	15.5855i	−0.183109	−	0.991681i
$248$	14.2888			0.907340
$249$		−	1.54333i		−	0.0978045i
$250$	8.28206			0.523803
$251$	−7.61843			−0.480871			−0.240435	−	0.970665i	$-0.577290\pi$
$251$	−7.61843			−0.480871			−0.240435	+	0.970665i	$0.577290\pi$
$252$		0			0
$253$		−	18.5066i		−	1.16350i
$254$		−	3.92942i		−	0.246554i
$255$			3.23741i			0.202734i
$256$	15.6402			0.977511
$257$	−11.6560			−0.727082			−0.363541	−	0.931578i	$-0.618432\pi$
$257$	−11.6560			−0.727082			−0.363541	+	0.931578i	$0.618432\pi$
$258$		−	1.07696i		−	0.0670484i
$259$		0			0
$260$	1.39369	+	7.54793i	0.0864331	+	0.468103i
$261$	−17.0693			−1.05656
$262$		−	3.53529i		−	0.218411i
$263$	−13.5528			−0.835700			−0.417850	−	0.908516i	$-0.637216\pi$
$263$	−13.5528			−0.835700			−0.417850	+	0.908516i	$0.637216\pi$
$264$	−2.66370			−0.163940
$265$			23.8182i			1.46314i
$266$		0			0
$267$		−	6.46359i		−	0.395565i
$268$		−	11.7848i		−	0.719873i
$269$	17.8332			1.08731			0.543656	−	0.839308i	$-0.317040\pi$
$269$	17.8332			1.08731			0.543656	+	0.839308i	$0.317040\pi$
$270$	13.5530			0.824808
$271$			30.3743i			1.84511i	0.385866	+	0.922555i	$0.373903\pi$
$271$			30.3743i			1.84511i	−0.385866	+	0.922555i	$0.626097\pi$
$272$	−11.2262			−0.680690
$273$		0			0
$274$	0.710564			0.0429268
$275$			8.41338i			0.507346i
$276$	2.62860			0.158223
$277$	−5.21425			−0.313294			−0.156647	−	0.987655i	$-0.550068\pi$
$277$	−5.21425			−0.313294			−0.156647	+	0.987655i	$0.550068\pi$
$278$			32.2591i			1.93477i
$279$			18.8829i			1.13049i
$280$		0			0
$281$			1.66255i			0.0991794i	0.998770	+	0.0495897i	$0.0157914\pi$
$281$			1.66255i			0.0991794i	−0.998770	+	0.0495897i	$0.984209\pi$
$282$	−1.10795			−0.0659776
$283$	−13.7957			−0.820066			−0.410033	−	0.912071i	$-0.634483\pi$
$283$	−13.7957			−0.820066			−0.410033	+	0.912071i	$0.634483\pi$
$284$		−	3.55107i		−	0.210718i
$285$	6.25294			0.370392
$286$	15.1523	−	2.79780i	0.895972	−	0.165437i
$287$		0			0
$288$			11.0113i			0.648849i
$289$	−11.8206			−0.695327
$290$	29.4780			1.73101
$291$			6.94859i			0.407333i
$292$			4.22597i			0.247306i
$293$			12.8576i			0.751149i	0.926792	+	0.375574i	$0.122555\pi$
$293$			12.8576i			0.751149i	−0.926792	+	0.375574i	$0.877445\pi$
$294$		0			0
$295$	27.6206			1.60813
$296$	12.2841			0.713998
$297$		−	7.35329i		−	0.426681i
$298$	−37.9120			−2.19619
$299$	25.4194	−	4.69359i	1.47004	−	0.271437i
$300$	−1.19500			−0.0689936
$301$		0			0
$302$	18.5761			1.06894
$303$	8.63648			0.496153
$304$			21.6831i			1.24361i
$305$			27.4543i			1.57203i
$306$		−	10.3800i		−	0.593384i
$307$		−	20.9016i		−	1.19292i	−0.802644	−	0.596458i	$-0.796574\pi$
$307$		−	20.9016i		−	1.19292i	0.802644	−	0.596458i	$-0.203426\pi$
$308$		0			0
$309$	3.24555			0.184633
$310$		−	32.6100i		−	1.85212i
$311$	17.1392			0.971876			0.485938	−	0.873993i	$-0.338478\pi$
$311$	17.1392			0.971876			0.485938	+	0.873993i	$0.338478\pi$
$312$	−0.675561	−	3.65869i	−0.0382461	−	0.207133i
$313$	2.55266			0.144285			0.0721424	−	0.997394i	$-0.477016\pi$
$313$	2.55266			0.144285			0.0721424	+	0.997394i	$0.477016\pi$
$314$			6.27109i			0.353898i
$315$		0			0
$316$	1.49204			0.0839339
$317$		−	27.2888i		−	1.53269i	−0.642430	−	0.766345i	$-0.722073\pi$
$317$		−	27.2888i		−	1.53269i	0.642430	−	0.766345i	$-0.277927\pi$
$318$			6.79136i			0.380841i
$319$		−	15.9936i		−	0.895467i
$320$			9.33641i			0.521921i
$321$	−7.72264			−0.431036
$322$		0			0
$323$		−	10.0039i		−	0.556633i
$324$	−5.07778			−0.282099
$325$	−11.5561	+	2.13378i	−0.641016	+	0.118361i
$326$	−32.4696			−1.79833
$327$			4.95824i			0.274192i
$328$	8.29751			0.458154
$329$		0			0
$330$			6.07912i			0.334645i
$331$			9.69307i			0.532779i	0.963865	+	0.266390i	$0.0858308\pi$
$331$			9.69307i			0.532779i	−0.963865	+	0.266390i	$0.914169\pi$
$332$		−	2.30961i		−	0.126757i
$333$			16.2336i			0.889595i
$334$	−17.0389			−0.932329
$335$	45.7223			2.49808
$336$		0			0
$337$	6.31370			0.343929			0.171965	−	0.985103i	$-0.444988\pi$
$337$	6.31370			0.343929			0.171965	+	0.985103i	$0.444988\pi$
$338$	7.68575	+	20.1026i	0.418049	+	1.09344i
$339$	1.95552			0.106210
$340$			4.84482i			0.262747i
$341$	−17.6929			−0.958122
$342$	−20.0486			−1.08410
$343$		0			0
$344$			2.73986i			0.147724i
$345$			10.1984i			0.549061i
$346$			9.94038i			0.534398i
$347$	29.1200			1.56324			0.781622	−	0.623753i	$-0.214393\pi$
$347$	29.1200			1.56324			0.781622	+	0.623753i	$0.214393\pi$
$348$	2.27166			0.121774
$349$			20.3297i			1.08822i	0.839013	+	0.544112i	$0.183133\pi$
$349$			20.3297i			1.08822i	−0.839013	+	0.544112i	$0.816867\pi$
$350$		0			0
$351$	10.1000	−	1.86492i	0.539099	−	0.0995421i
$352$	−10.3174			−0.549919
$353$			14.1980i			0.755683i	0.925870	+	0.377841i	$0.123334\pi$
$353$			14.1980i			0.755683i	−0.925870	+	0.377841i	$0.876666\pi$
$354$	7.87555			0.418581
$355$	13.7773			0.731224
$356$		−	9.67285i		−	0.512660i
$357$		0			0
$358$			12.8324i			0.678214i
$359$			7.50164i			0.395921i	0.980210	+	0.197961i	$0.0634318\pi$
$359$			7.50164i			0.395921i	−0.980210	+	0.197961i	$0.936568\pi$
$360$	−16.5060			−0.869941
$361$	−0.322229			−0.0169594
$362$		−	33.1101i		−	1.74023i
$363$	−2.14646			−0.112660
$364$		0			0
$365$	−16.3958			−0.858193
$366$			7.82815i			0.409184i
$367$	28.5883			1.49230			0.746149	−	0.665779i	$-0.231901\pi$
$367$	28.5883			1.49230			0.746149	+	0.665779i	$0.231901\pi$
$368$	−35.3644			−1.84350
$369$			10.9653i			0.570830i
$370$		−	28.0348i		−	1.45746i
$371$		0			0
$372$		−	2.51303i		−	0.130294i
$373$	−7.91204			−0.409670			−0.204835	−	0.978797i	$-0.565666\pi$
$373$	−7.91204			−0.409670			−0.204835	+	0.978797i	$0.565666\pi$
$374$	9.72584			0.502911
$375$			2.47622i			0.127871i
$376$	2.81872			0.145364
$377$	21.9677	−	4.05624i	1.13139	−	0.208907i
$378$		0			0
$379$			1.78091i			0.0914791i	0.998953	+	0.0457395i	$0.0145644\pi$
$379$			1.78091i			0.0914791i	−0.998953	+	0.0457395i	$0.985436\pi$
$380$	9.35761			0.480035
$381$	1.17484			0.0601889
$382$			33.9108i			1.73503i
$383$			14.1997i			0.725572i	0.931872	+	0.362786i	$0.118174\pi$
$383$			14.1997i			0.725572i	−0.931872	+	0.362786i	$0.881826\pi$
$384$			6.61883i			0.337766i
$385$		0			0
$386$	20.5829			1.04764
$387$	−3.62077			−0.184054
$388$			10.3987i			0.527912i
$389$	6.77499			0.343506			0.171753	−	0.985140i	$-0.445057\pi$
$389$	6.77499			0.343506			0.171753	+	0.985140i	$0.445057\pi$
$390$	−8.34990	+	1.54177i	−0.422813	+	0.0780706i
$391$	16.3161			0.825140
$392$		0			0
$393$	1.05700			0.0533187
$394$	−31.4226			−1.58305
$395$			5.78876i			0.291264i
$396$		−	5.26791i		−	0.264723i
$397$		−	29.0023i		−	1.45558i	−0.685798	−	0.727792i	$-0.740547\pi$
$397$		−	29.0023i		−	1.45558i	0.685798	−	0.727792i	$-0.259453\pi$
$398$			21.2218i			1.06375i
$399$		0			0
$400$	16.0772			0.803861
$401$			21.9604i			1.09665i	0.836265	+	0.548326i	$0.184735\pi$
$401$			21.9604i			1.09665i	−0.836265	+	0.548326i	$0.815265\pi$
$402$	13.0370			0.650224
$403$	−4.48721	−	24.3018i	−0.223524	−	1.21056i
$404$	12.9246			0.643024
$405$		−	19.7006i		−	0.978928i
$406$		0			0
$407$	−15.2105			−0.753959
$408$		−	2.34842i		−	0.116264i
$409$		−	4.00290i		−	0.197931i	−0.995091	−	0.0989653i	$-0.968447\pi$
$409$		−	4.00290i		−	0.197931i	0.995091	−	0.0989653i	$-0.0315533\pi$
$410$		−	18.9366i		−	0.935214i
$411$			0.212449i			0.0104793i
$412$	4.85702			0.239288
$413$		0			0
$414$		−	32.6986i		−	1.60705i
$415$	8.96075			0.439866
$416$	−2.61667	−	14.1713i	−0.128293	−	0.694806i
$417$	−9.64501			−0.472318
$418$		−	18.7851i		−	0.918811i
$419$	−1.75047			−0.0855162			−0.0427581	−	0.999085i	$-0.513614\pi$
$419$	−1.75047			−0.0855162			−0.0427581	+	0.999085i	$0.513614\pi$
$420$		0			0
$421$			16.2204i			0.790533i	0.918566	+	0.395267i	$0.129348\pi$
$421$			16.2204i			0.790533i	−0.918566	+	0.395267i	$0.870652\pi$
$422$		−	13.0277i		−	0.634179i
$423$			3.72498i			0.181115i
$424$		−	17.2778i		−	0.839082i
$425$	−7.41755			−0.359804
$426$	3.92837			0.190330
$427$		0			0
$428$	−11.5570			−0.558631
$429$	0.836502	+	4.53031i	0.0403867	+	0.218726i
$430$	6.25294			0.301543
$431$		−	11.6797i		−	0.562590i	−0.959621	−	0.281295i	$-0.909236\pi$
$431$		−	11.6797i		−	0.562590i	0.959621	−	0.281295i	$-0.0907639\pi$
$432$	−14.0515			−0.676052
$433$	−31.6289			−1.51999			−0.759994	−	0.649930i	$-0.774798\pi$
$433$	−31.6289			−1.51999			−0.759994	+	0.649930i	$0.774798\pi$
$434$		0			0
$435$			8.81351i			0.422575i
$436$			7.42008i			0.355357i
$437$		−	31.5140i		−	1.50752i
$438$	−4.67498			−0.223379
$439$	9.71539			0.463690			0.231845	−	0.972753i	$-0.425524\pi$
$439$	9.71539			0.463690			0.231845	+	0.972753i	$0.425524\pi$
$440$		−	15.4658i		−	0.737302i
$441$		0			0
$442$	2.46664	+	13.3588i	0.117326	+	0.635413i
$443$	21.1163			1.00327			0.501633	−	0.865081i	$-0.332733\pi$
$443$	21.1163			1.00327			0.501633	+	0.865081i	$0.332733\pi$
$444$		−	2.16045i		−	0.102530i
$445$	37.5283			1.77901
$446$	12.8644			0.609145
$447$		−	11.3352i		−	0.536135i
$448$		0			0
$449$		−	13.4710i		−	0.635735i	−0.948135	−	0.317867i	$-0.897033\pi$
$449$		−	13.4710i		−	0.635735i	0.948135	−	0.317867i	$-0.102967\pi$
$450$			14.8653i			0.700758i
$451$	−10.2743			−0.483796
$452$	2.92647			0.137650
$453$			5.55401i			0.260950i
$454$	−42.2871			−1.98463
$455$		0			0
$456$	−4.53589			−0.212413
$457$		−	9.35582i		−	0.437647i	−0.975764	−	0.218823i	$-0.929778\pi$
$457$		−	9.35582i		−	0.437647i	0.975764	−	0.218823i	$-0.0702218\pi$
$458$	−21.3538			−0.997798
$459$	6.48294			0.302598
$460$			15.2620i			0.711593i
$461$			8.14109i			0.379168i	0.981864	+	0.189584i	$0.0607140\pi$
$461$			8.14109i			0.379168i	−0.981864	+	0.189584i	$0.939286\pi$
$462$		0			0
$463$			24.3018i			1.12940i	0.825296	+	0.564700i	$0.191008\pi$
$463$			24.3018i			1.12940i	−0.825296	+	0.564700i	$0.808992\pi$
$464$	−30.5623			−1.41882
$465$	9.74994			0.452143
$466$		−	13.4805i		−	0.624473i
$467$	32.7935			1.51750			0.758751	−	0.651381i	$-0.225810\pi$
$467$	32.7935			1.51750			0.758751	+	0.651381i	$0.225810\pi$
$468$	7.23567	−	1.33603i	0.334469	−	0.0617582i
$469$		0			0
$470$		−	6.43290i		−	0.296728i
$471$	−1.87497			−0.0863940
$472$	−20.0360			−0.922232
$473$		−	3.39259i		−	0.155991i
$474$			1.65057i			0.0758132i
$475$			14.3267i			0.657356i
$476$		0			0
$477$	22.8328			1.04544
$478$	39.4215			1.80310
$479$		−	2.48109i		−	0.113364i	−0.998392	−	0.0566819i	$-0.981948\pi$
$479$		−	2.48109i		−	0.113364i	0.998392	−	0.0566819i	$-0.0180521\pi$
$480$	5.68557			0.259510
$481$	−3.85766	−	20.8922i	−0.175894	−	0.952604i
$482$	0.477694			0.0217584
$483$		0			0
$484$	−3.21221			−0.146009
$485$	−40.3443			−1.83194
$486$		−	19.7650i		−	0.896557i
$487$		−	22.9216i		−	1.03867i	−0.854569	−	0.519337i	$-0.826179\pi$
$487$		−	22.9216i		−	1.03867i	0.854569	−	0.519337i	$-0.173821\pi$
$488$		−	19.9154i		−	0.901529i
$489$		−	9.70797i		−	0.439010i
$490$		0			0
$491$	−22.8735			−1.03227			−0.516134	−	0.856508i	$-0.672629\pi$
$491$	−22.8735			−1.03227			−0.516134	+	0.856508i	$0.672629\pi$
$492$		−	1.45932i		−	0.0657910i
$493$	14.1005			0.635055
$494$	25.8020	−	4.76423i	1.16089	−	0.214353i
$495$	20.4382			0.918631
$496$			33.8095i			1.51809i
$497$		0			0
$498$	2.55501			0.114493
$499$			8.48087i			0.379656i	0.981817	+	0.189828i	$0.0607930\pi$
$499$			8.48087i			0.379656i	−0.981817	+	0.189828i	$0.939207\pi$
$500$			3.70570i			0.165724i
$501$		−	5.09440i		−	0.227601i
$502$		−	12.6124i		−	0.562921i
$503$	9.36890			0.417739			0.208869	−	0.977944i	$-0.433022\pi$
$503$	9.36890			0.417739			0.208869	+	0.977944i	$0.433022\pi$
$504$		0			0
$505$			50.1444i			2.23140i
$506$	30.6380			1.36202
$507$	−6.01040	+	2.29793i	−0.266931	+	0.102055i
$508$	1.75817			0.0780060
$509$			21.5402i			0.954753i	0.878699	+	0.477376i	$0.158412\pi$
$509$			21.5402i			0.954753i	−0.878699	+	0.477376i	$0.841588\pi$
$510$	−5.35958			−0.237326
$511$		0			0
$512$		−	0.851388i		−	0.0376264i
$513$		−	12.5216i		−	0.552841i
$514$		−	19.2967i		−	0.851143i
$515$			18.8441i			0.830368i
$516$	0.481870			0.0212132
$517$	−3.49023			−0.153500
$518$		0			0
$519$	−2.97203			−0.130458
$520$	21.2428	−	3.92239i	0.931558	−	0.172008i
$521$	−15.7470			−0.689889			−0.344944	−	0.938623i	$-0.612102\pi$
$521$	−15.7470			−0.689889			−0.344944	+	0.938623i	$0.612102\pi$
$522$		−	28.2585i		−	1.23684i
$523$	−17.9404			−0.784477			−0.392238	−	0.919864i	$-0.628299\pi$
$523$	−17.9404			−0.784477			−0.392238	+	0.919864i	$0.628299\pi$
$524$	1.58182			0.0691020
$525$		0			0
$526$		−	22.4369i		−	0.978293i
$527$		−	15.5987i		−	0.679489i
$528$		−	6.30273i		−	0.274291i
$529$	28.3983			1.23471
$530$	−39.4314			−1.71279
$531$		−	26.4779i		−	1.14904i
$532$		0			0
$533$	−2.60573	−	14.1121i	−0.112867	−	0.611261i
$534$	10.7006			0.463060
$535$		−	44.8386i		−	1.93854i
$536$	−33.1671			−1.43260
$537$	−3.83672			−0.165566
$538$			29.5232i			1.27284i
$539$		0			0
$540$			6.06410i			0.260957i
$541$		−	9.35582i		−	0.402238i	−0.979567	−	0.201119i	$-0.935542\pi$
$541$		−	9.35582i		−	0.402238i	0.979567	−	0.201119i	$-0.0644578\pi$
$542$	−50.2853			−2.15994
$543$	9.89947			0.424827
$544$		−	9.09621i		−	0.389997i
$545$	−28.7881			−1.23315
$546$		0			0
$547$	−33.1634			−1.41796			−0.708981	−	0.705227i	$-0.750845\pi$
$547$	−33.1634			−1.41796			−0.708981	+	0.705227i	$0.750845\pi$
$548$			0.317933i			0.0135814i
$549$	26.3185			1.12325
$550$	−13.9285			−0.593914
$551$		−	27.2347i		−	1.16024i
$552$		−	7.39790i		−	0.314876i
$553$		0			0
$554$		−	8.63228i		−	0.366750i
$555$	8.38202			0.355797
$556$	−14.4339			−0.612133
$557$			11.1532i			0.472578i	0.971683	+	0.236289i	$0.0759312\pi$
$557$			11.1532i			0.472578i	−0.971683	+	0.236289i	$0.924069\pi$
$558$	−31.2609			−1.32338
$559$	4.65984	−	0.860419i	0.197090	−	0.0363918i
$560$		0			0
$561$			2.90789i			0.122771i
$562$	−2.75238			−0.116102
$563$	−19.1778			−0.808247			−0.404124	−	0.914704i	$-0.632423\pi$
$563$	−19.1778			−0.808247			−0.404124	+	0.914704i	$0.632423\pi$
$564$		−	0.495739i		−	0.0208744i
$565$			11.3540i			0.477666i
$566$		−	22.8389i		−	0.959993i
$567$		0			0
$568$	−9.99409			−0.419343
$569$	−13.4672			−0.564575			−0.282288	−	0.959330i	$-0.591093\pi$
$569$	−13.4672			−0.564575			−0.282288	+	0.959330i	$0.591093\pi$
$570$			10.3519i			0.433591i
$571$	−25.1608			−1.05295			−0.526473	−	0.850192i	$-0.676486\pi$
$571$	−25.1608			−1.05295			−0.526473	+	0.850192i	$0.676486\pi$
$572$	1.25184	+	6.77968i	0.0523419	+	0.283473i
$573$	−10.1389			−0.423557
$574$		0			0
$575$	−23.3665			−0.974450
$576$	8.95016			0.372923
$577$			21.6484i			0.901235i	0.892717	+	0.450617i	$0.148796\pi$
$577$			21.6484i			0.901235i	−0.892717	+	0.450617i	$0.851204\pi$
$578$		−	19.5691i		−	0.813969i
$579$			6.15401i			0.255752i
$580$			13.1895i			0.547666i
$581$		0			0
$582$	−11.5035			−0.476836
$583$			21.3939i			0.886044i
$584$	11.8935			0.492157
$585$	5.18349	+	28.0727i	0.214311	+	1.16066i
$586$	−21.2860			−0.879316
$587$		−	34.5576i		−	1.42634i	−0.700989	−	0.713172i	$-0.747258\pi$
$587$		−	34.5576i		−	1.42634i	0.700989	−	0.713172i	$-0.252742\pi$
$588$		0			0
$589$	−30.1283			−1.24142
$590$			45.7263i			1.88252i
$591$		−	9.39493i		−	0.386456i
$592$			29.0660i			1.19461i
$593$		−	1.26839i		−	0.0520865i	−0.999661	−	0.0260432i	$-0.991709\pi$
$593$		−	1.26839i		−	0.0520865i	0.999661	−	0.0260432i	$-0.00829075\pi$
$594$	12.1735			0.499485
$595$		0			0
$596$		−	16.9632i		−	0.694842i
$597$	−6.34501			−0.259684
$598$	7.77032	+	42.0824i	0.317752	+	1.72088i
$599$	17.5143			0.715614			0.357807	−	0.933796i	$-0.383525\pi$
$599$	17.5143			0.715614			0.357807	+	0.933796i	$0.383525\pi$
$600$			3.36320i			0.137302i
$601$	9.02164			0.368000			0.184000	−	0.982926i	$-0.441095\pi$
$601$	9.02164			0.368000			0.184000	+	0.982926i	$0.441095\pi$
$602$		0			0
$603$		−	43.8307i		−	1.78493i
$604$			8.31165i			0.338196i
$605$		−	12.4626i		−	0.506677i
$606$			14.2979i			0.580811i
$607$	15.8290			0.642479			0.321239	−	0.946998i	$-0.395901\pi$
$607$	15.8290			0.642479			0.321239	+	0.946998i	$0.395901\pi$
$608$	−17.5690			−0.712517
$609$		0			0
$610$	−45.4511			−1.84026
$611$	−0.885182	−	4.79396i	−0.0358106	−	0.193943i
$612$	4.64439			0.187738
$613$			17.5344i			0.708209i	0.935206	+	0.354104i	$0.115214\pi$
$613$			17.5344i			0.708209i	−0.935206	+	0.354104i	$0.884786\pi$
$614$	34.6029			1.39646
$615$	5.66179			0.228306
$616$		0			0
$617$		−	7.01448i		−	0.282392i	−0.989982	−	0.141196i	$-0.954905\pi$
$617$		−	7.01448i		−	0.282392i	0.989982	−	0.141196i	$-0.0450948\pi$
$618$			5.37307i			0.216137i
$619$			38.8263i			1.56056i	0.625430	+	0.780280i	$0.284923\pi$
$619$			38.8263i			1.56056i	−0.625430	+	0.780280i	$0.715077\pi$
$620$	14.5909			0.585985
$621$	20.4223			0.819518
$622$			28.3743i			1.13771i
$623$		0			0
$624$	8.65703	−	1.59848i	0.346558	−	0.0639904i
$625$	−30.6735			−1.22694
$626$			4.22597i			0.168904i
$627$	5.61649			0.224301
$628$	−2.80592			−0.111968
$629$		−	13.4102i		−	0.534699i
$630$		0			0
$631$			12.7484i			0.507506i	0.967269	+	0.253753i	$0.0816650\pi$
$631$			12.7484i			0.507506i	−0.967269	+	0.253753i	$0.918335\pi$
$632$		−	4.19918i		−	0.167034i
$633$	3.89510			0.154816
$634$	45.1770			1.79421
$635$			6.82126i			0.270694i
$636$	−3.03871			−0.120493
$637$		0			0
$638$	26.4776			1.04826
$639$		−	13.2073i		−	0.522474i
$640$	−38.4297			−1.51907
$641$	9.71429			0.383691			0.191846	−	0.981425i	$-0.438553\pi$
$641$	9.71429			0.383691			0.191846	+	0.981425i	$0.438553\pi$
$642$		−	12.7850i		−	0.504583i
$643$		−	0.458279i		−	0.0180728i	−0.999959	−	0.00903639i	$-0.997124\pi$
$643$		−	0.458279i		−	0.0180728i	0.999959	−	0.00903639i	$-0.00287641\pi$
$644$		0			0
$645$			1.86954i			0.0736131i
$646$	16.5617			0.651610
$647$	−6.17722			−0.242852			−0.121426	−	0.992601i	$-0.538747\pi$
$647$	−6.17722			−0.242852			−0.121426	+	0.992601i	$0.538747\pi$
$648$			14.2908i			0.561397i
$649$	24.8093			0.973848
$650$	−3.53251	−	19.1313i	−0.138556	−	0.750392i
$651$		0			0
$652$		−	14.5281i		−	0.568965i
$653$	28.4385			1.11289			0.556443	−	0.830886i	$-0.312166\pi$
$653$	28.4385			1.11289			0.556443	+	0.830886i	$0.312166\pi$
$654$	−8.20846			−0.320976
$655$			6.13707i			0.239795i
$656$			19.6332i			0.766547i
$657$			15.7175i			0.613196i
$658$		0			0
$659$	−25.9818			−1.01211			−0.506054	−	0.862502i	$-0.668897\pi$
$659$	−25.9818			−1.01211			−0.506054	+	0.862502i	$0.668897\pi$
$660$	−2.72002			−0.105877
$661$			37.2752i			1.44984i	0.688835	+	0.724918i	$0.258122\pi$
$661$			37.2752i			1.44984i	−0.688835	+	0.724918i	$0.741878\pi$
$662$	−16.0471			−0.623686
$663$	−3.99409	+	0.737491i	−0.155118	+	0.0286418i
$664$	−6.50015			−0.252255
$665$		0			0
$666$	−26.8750			−1.04139
$667$	44.4189			1.71991
$668$		−	7.62385i		−	0.294976i
$669$			3.84626i			0.148705i
$670$			75.6941i			2.92432i
$671$			24.6599i			0.951986i
$672$		0			0
$673$	41.7078			1.60772			0.803859	−	0.594820i	$-0.202777\pi$
$673$	41.7078			1.60772			0.803859	+	0.594820i	$0.202777\pi$
$674$			10.4525i			0.402613i
$675$	−9.28430			−0.357353
$676$	−8.99464	+	3.43889i	−0.345948	+	0.132265i
$677$	−18.2069			−0.699750			−0.349875	−	0.936796i	$-0.613776\pi$
$677$	−18.2069			−0.699750			−0.349875	+	0.936796i	$0.613776\pi$
$678$			3.23741i			0.124332i
$679$		0			0
$680$	13.6352			0.522886
$681$		−	12.6432i		−	0.484490i
$682$		−	29.2908i		−	1.12160i
$683$			27.3360i			1.04598i	0.852338	+	0.522991i	$0.175184\pi$
$683$			27.3360i			1.04598i	−0.852338	+	0.522991i	$0.824816\pi$
$684$		−	8.97048i		−	0.342995i
$685$	−1.23350			−0.0471297
$686$		0			0
$687$		−	6.38449i		−	0.243584i
$688$	−6.48294			−0.247160
$689$	−29.3853	+	5.42586i	−1.11949	+	0.206709i
$690$	−16.8836			−0.642746
$691$		−	8.39581i		−	0.319392i	−0.987166	−	0.159696i	$-0.948949\pi$
$691$		−	8.39581i		−	0.319392i	0.987166	−	0.159696i	$-0.0510513\pi$
$692$	−4.44769			−0.169076
$693$		0			0
$694$			48.2087i			1.82998i
$695$		−	56.0000i		−	2.12420i
$696$		−	6.39334i		−	0.242339i
$697$		−	9.05817i		−	0.343102i
$698$	−33.6562			−1.27391
$699$	4.03049			0.152447
$700$		0			0
$701$	27.4998			1.03865			0.519327	−	0.854576i	$-0.326183\pi$
$701$	27.4998			1.03865			0.519327	+	0.854576i	$0.326183\pi$
$702$	3.08741	+	16.7207i	0.116527	+	0.631084i
$703$	−25.9013			−0.976887
$704$			8.38612i			0.316064i
$705$	1.92335			0.0724375
$706$	−23.5050			−0.884623
$707$		0			0
$708$			3.52381i			0.132433i
$709$		−	28.9820i		−	1.08844i	−0.838942	−	0.544221i	$-0.816825\pi$
$709$		−	28.9820i		−	1.08844i	0.838942	−	0.544221i	$-0.183175\pi$
$710$			22.8086i			0.855991i
$711$	5.54928			0.208114
$712$	−27.2231			−1.02023
$713$		−	49.1384i		−	1.84025i
$714$		0			0
$715$	−26.3035	+	4.85683i	−0.983696	+	0.181635i
$716$	−5.74170			−0.214577
$717$			11.7865i			0.440174i
$718$	−12.4191			−0.463476
$719$	−17.5522			−0.654588			−0.327294	−	0.944923i	$-0.606137\pi$
$719$	−17.5522			−0.654588			−0.327294	+	0.944923i	$0.606137\pi$
$720$		−	39.0557i		−	1.45552i
$721$		0			0
$722$		−	0.533456i		−	0.0198532i
$723$			0.142824i			0.00531168i
$724$	14.8147			0.550584
$725$	−20.1935			−0.749969
$726$		−	3.55350i		−	0.131883i
$727$	22.1403			0.821139			0.410569	−	0.911829i	$-0.365330\pi$
$727$	22.1403			0.821139			0.410569	+	0.911829i	$0.365330\pi$
$728$		0			0
$729$	−14.6556			−0.542799
$730$		−	27.1435i		−	1.00463i
$731$	2.99103			0.110627
$732$	−3.50260			−0.129460
$733$		−	51.3414i		−	1.89634i	−0.317768	−	0.948169i	$-0.602933\pi$
$733$		−	51.3414i		−	1.89634i	0.317768	−	0.948169i	$-0.397067\pi$
$734$			47.3285i			1.74693i
$735$		0			0
$736$		−	28.6545i		−	1.05622i
$737$	41.0685			1.51278
$738$	−18.1532			−0.668229
$739$			22.7787i			0.837929i	0.908003	+	0.418965i	$0.137607\pi$
$739$			22.7787i			0.837929i	−0.908003	+	0.418965i	$0.862393\pi$
$740$	12.5438			0.461120
$741$	1.42444	+	7.71445i	0.0523281	+	0.283398i
$742$		0			0
$743$		−	27.6199i		−	1.01328i	−0.862159	−	0.506638i	$-0.830888\pi$
$743$		−	27.6199i		−	1.01328i	0.862159	−	0.506638i	$-0.169112\pi$
$744$	−7.07262			−0.259295
$745$	65.8133			2.41121
$746$		−	13.0985i		−	0.479571i
$747$		−	8.59004i		−	0.314293i
$748$			4.35170i			0.159114i
$749$		0			0
$750$	−4.09943			−0.149690
$751$	−41.1172			−1.50039			−0.750194	−	0.661218i	$-0.770040\pi$
$751$	−41.1172			−1.50039			−0.750194	+	0.661218i	$0.770040\pi$
$752$			6.66952i			0.243212i
$753$	3.77095			0.137421
$754$	6.71518	+	36.3680i	0.244552	+	1.32444i
$755$	−32.2472			−1.17360
$756$		0			0
$757$	14.0143			0.509357			0.254678	−	0.967026i	$-0.418030\pi$
$757$	14.0143			0.509357			0.254678	+	0.967026i	$0.418030\pi$
$758$	−2.94832			−0.107088
$759$			9.16033i			0.332499i
$760$		−	26.3359i		−	0.955304i
$761$			34.1648i			1.23847i	0.785205	+	0.619236i	$0.212558\pi$
$761$			34.1648i			1.23847i	−0.785205	+	0.619236i	$0.787442\pi$
$762$			1.94497i			0.0704588i
$763$		0			0
$764$	−15.1730			−0.548938
$765$			18.0191i			0.651483i
$766$	−23.5079			−0.849375
$767$	6.29205	+	34.0764i	0.227193	+	1.23043i
$768$	−7.74153			−0.279348
$769$			52.9061i			1.90784i	0.300059	+	0.953921i	$0.402994\pi$
$769$			52.9061i			1.90784i	−0.300059	+	0.953921i	$0.597006\pi$
$770$		0			0
$771$	5.76946			0.207782
$772$			9.20957i			0.331460i
$773$		−	45.9133i		−	1.65139i	−0.564118	−	0.825694i	$-0.690784\pi$
$773$		−	45.9133i		−	1.65139i	0.564118	−	0.825694i	$-0.309216\pi$
$774$		−	5.99425i		−	0.215459i
$775$			22.3391i			0.802444i
$776$	29.2658			1.05058
$777$		0			0
$778$			11.2161i			0.402117i
$779$	−17.4955			−0.626843
$780$	−0.689845	−	3.73605i	−0.0247004	−	0.133772i
$781$	12.3750			0.442813
$782$			27.0116i			0.965932i
$783$	17.6491			0.630728
$784$		0			0
$785$		−	10.8863i		−	0.388548i
$786$			1.74989i			0.0624163i
$787$			15.1872i			0.541364i	0.962669	+	0.270682i	$0.0872492\pi$
$787$			15.1872i			0.541364i	−0.962669	+	0.270682i	$0.912751\pi$
$788$		−	14.0596i		−	0.500854i
$789$	6.70831			0.238822
$790$	−9.58340			−0.340962
$791$		0			0
$792$	−14.8259			−0.526817
$793$	−33.8713	+	6.25418i	−1.20281	+	0.222093i
$794$	48.0138			1.70395
$795$		−	11.7894i		−	0.418129i
$796$	−9.49540			−0.336555
$797$	−16.3006			−0.577398			−0.288699	−	0.957420i	$-0.593223\pi$
$797$	−16.3006			−0.577398			−0.288699	+	0.957420i	$0.593223\pi$
$798$		0			0
$799$		−	3.07712i		−	0.108861i
$800$			13.0268i			0.460567i
$801$		−	35.9758i		−	1.27114i
$802$	−36.3559			−1.28377
$803$	−14.7269			−0.519703
$804$			5.83322i			0.205722i
$805$		0			0
$806$	40.2320	−	7.42866i	1.41711	−	0.261663i
$807$	−8.82704			−0.310727
$808$		−	36.3749i		−	1.27966i
$809$	10.3857			0.365142			0.182571	−	0.983193i	$-0.441558\pi$
$809$	10.3857			0.365142			0.182571	+	0.983193i	$0.441558\pi$
$810$	32.6146			1.14596
$811$			10.9705i			0.385227i	0.981275	+	0.192614i	$0.0616964\pi$
$811$			10.9705i			0.385227i	−0.981275	+	0.192614i	$0.938304\pi$
$812$		0			0
$813$		−	15.0346i		−	0.527286i
$814$		−	25.1813i		−	0.882605i
$815$	56.3656			1.97440
$816$	5.55672			0.194524
$817$		−	5.77708i		−	0.202114i
$818$	6.62687			0.231703
$819$		0			0
$820$	8.47296			0.295888
$821$		−	40.2325i		−	1.40412i	−0.712117	−	0.702061i	$-0.752263\pi$
$821$		−	40.2325i		−	1.40412i	0.712117	−	0.702061i	$-0.247737\pi$
$822$	−0.351713			−0.0122674
$823$	3.26499			0.113811			0.0569053	−	0.998380i	$-0.481877\pi$
$823$	3.26499			0.113811			0.0569053	+	0.998380i	$0.481877\pi$
$824$		−	13.6695i		−	0.476200i
$825$		−	4.16443i		−	0.144987i
$826$		0			0
$827$			46.0118i			1.59999i	0.600009	+	0.799993i	$0.295164\pi$
$827$			46.0118i			1.59999i	−0.600009	+	0.799993i	$0.704836\pi$
$828$	14.6306			0.508448
$829$	−30.3865			−1.05537			−0.527683	−	0.849441i	$-0.676939\pi$
$829$	−30.3865			−1.05537			−0.527683	+	0.849441i	$0.676939\pi$
$830$			14.8347i			0.514919i
$831$	2.58093			0.0895315
$832$	−11.5186	+	2.12686i	−0.399337	+	0.0737358i
$833$		0			0
$834$		−	15.9675i		−	0.552909i
$835$	29.5787			1.02361
$836$	8.40516			0.290699
$837$		−	19.5243i		−	0.674860i
$838$		−	2.89794i		−	0.100108i
$839$			1.52007i			0.0524787i	0.999656	+	0.0262394i	$0.00835321\pi$
$839$			1.52007i			0.0524787i	−0.999656	+	0.0262394i	$0.991647\pi$
$840$		0			0
$841$	9.38720			0.323697
$842$	−26.8531			−0.925420
$843$		−	0.822923i		−	0.0283430i
$844$	5.82908			0.200645
$845$	−13.3421	−	34.8971i	−0.458981	−	1.20050i
$846$	−6.16677			−0.212018
$847$		0			0
$848$	40.8818			1.40389
$849$	6.82853			0.234354
$850$		−	12.2799i		−	0.421197i
$851$		−	42.2443i		−	1.44811i
$852$			1.75770i			0.0602178i
$853$		−	43.7939i		−	1.49947i	−0.661736	−	0.749737i	$-0.730180\pi$
$853$		−	43.7939i		−	1.49947i	0.661736	−	0.749737i	$-0.269820\pi$
$854$		0			0
$855$	34.8033			1.19025
$856$			32.5260i			1.11172i
$857$	−14.8521			−0.507338			−0.253669	−	0.967291i	$-0.581637\pi$
$857$	−14.8521			−0.507338			−0.253669	+	0.967291i	$0.581637\pi$
$858$	−7.50002	+	1.38484i	−0.256046	+	0.0472778i
$859$	44.3568			1.51343			0.756717	−	0.653742i	$-0.226802\pi$
$859$	44.3568			1.51343			0.756717	+	0.653742i	$0.226802\pi$
$860$			2.79780i			0.0954040i
$861$		0			0
$862$	19.3359			0.658584
$863$			25.8451i			0.879778i	0.898052	+	0.439889i	$0.144982\pi$
$863$			25.8451i			0.879778i	−0.898052	+	0.439889i	$0.855018\pi$
$864$		−	11.3854i		−	0.387340i
$865$		−	17.2560i		−	0.586721i
$866$		−	52.3622i		−	1.77934i
$867$	5.85090			0.198707
$868$		0			0
$869$			5.19956i			0.176383i
$870$	−14.5909			−0.494678
$871$	10.4157	+	56.4091i	0.352922	+	1.91135i
$872$	20.8830			0.707187
$873$			38.6752i			1.30896i
$874$	52.1719			1.76474
$875$		0			0
$876$		−	2.09176i		−	0.0706740i
$877$		−	1.37284i		−	0.0463575i	−0.999731	−	0.0231788i	$-0.992621\pi$
$877$		−	1.37284i		−	0.0463575i	0.999731	−	0.0231788i	$-0.00737869\pi$
$878$			16.0840i			0.542809i
$879$		−	6.36421i		−	0.214660i
$880$	36.5944			1.23360
$881$	−16.2514			−0.547524			−0.273762	−	0.961797i	$-0.588268\pi$
$881$	−16.2514			−0.547524			−0.273762	+	0.961797i	$0.588268\pi$
$882$		0			0
$883$	0.619110			0.0208347			0.0104174	−	0.999946i	$-0.496684\pi$
$883$	0.619110			0.0208347			0.0104174	+	0.999946i	$0.496684\pi$
$884$	−5.97722	+	1.10367i	−0.201036	+	0.0371203i
$885$	−13.6715			−0.459564
$886$			34.9584i			1.17445i
$887$	31.9379			1.07237			0.536185	−	0.844100i	$-0.319865\pi$
$887$	31.9379			1.07237			0.536185	+	0.844100i	$0.319865\pi$
$888$	−6.08034			−0.204043
$889$		0			0
$890$			62.1288i			2.08256i
$891$		−	17.6954i		−	0.592817i
$892$			5.75599i			0.192725i
$893$	−5.94335			−0.198886
$894$	18.7656			0.627615
$895$		−	22.2764i		−	0.744618i
$896$		0			0
$897$	−12.5820	+	2.32322i	−0.420102	+	0.0775700i
$898$	22.3015			0.744209
$899$		−	42.4658i		−	1.41631i
$900$	−6.65129			−0.221710
$901$	−18.8616			−0.628373
$902$		−	17.0092i		−	0.566345i
$903$		0			0
$904$		−	8.23621i		−	0.273932i
$905$			57.4775i			1.91062i
$906$	−9.19476			−0.305475
$907$	−20.7037			−0.687455			−0.343728	−	0.939069i	$-0.611690\pi$
$907$	−20.7037			−0.687455			−0.343728	+	0.939069i	$0.611690\pi$
$908$		−	18.9208i		−	0.627909i
$909$	48.0699			1.59438
$910$		0			0
$911$	39.4143			1.30585			0.652926	−	0.757421i	$-0.273541\pi$
$911$	39.4143			1.30585			0.652926	+	0.757421i	$0.273541\pi$
$912$		−	10.7326i		−	0.355392i
$913$	8.04869			0.266373
$914$	15.4887			0.512321
$915$		−	13.5893i		−	0.449247i
$916$		−	9.55449i		−	0.315689i
$917$		0			0
$918$			10.7326i			0.354229i
$919$	14.2185			0.469025			0.234512	−	0.972113i	$-0.424651\pi$
$919$	14.2185			0.469025			0.234512	+	0.972113i	$0.424651\pi$
$920$	42.9531			1.41612
$921$			10.3458i			0.340906i
$922$	−13.4777			−0.443865
$923$	3.13852	+	16.9975i	0.103306	+	0.559480i
$924$		0			0
$925$			19.2049i			0.631454i
$926$	−40.2320			−1.32211
$927$	18.0645			0.593315
$928$		−	24.7635i		−	0.812902i
$929$		−	28.7478i		−	0.943185i	−0.881817	−	0.471593i	$-0.843679\pi$
$929$		−	28.7478i		−	0.943185i	0.881817	−	0.471593i	$-0.156321\pi$
$930$			16.1412i			0.529291i
$931$		0			0
$932$	6.03168			0.197574
$933$	−8.48352			−0.277738
$934$			54.2902i			1.77643i
$935$	−16.8836			−0.552151
$936$	−3.76011	−	20.3640i	−0.122903	−	0.665617i
$937$	19.8495			0.648456			0.324228	−	0.945979i	$-0.394895\pi$
$937$	19.8495			0.648456			0.324228	+	0.945979i	$0.394895\pi$
$938$		0			0
$939$	−1.26351			−0.0412330
$940$	2.87832			0.0938804
$941$			45.2320i			1.47452i	0.675609	+	0.737260i	$0.263881\pi$
$941$			45.2320i			1.47452i	−0.675609	+	0.737260i	$0.736119\pi$
$942$		−	3.10404i		−	0.101135i
$943$		−	28.5347i		−	0.929217i
$944$		−	47.4083i		−	1.54301i
$945$		0			0
$946$	5.61649			0.182608
$947$			22.1095i			0.718462i	0.933249	+	0.359231i	$0.116961\pi$
$947$			22.1095i			0.718462i	−0.933249	+	0.359231i	$0.883039\pi$
$948$	−0.738526			−0.0239862
$949$	−3.73501	−	20.2280i	−0.121243	−	0.656628i
$950$	−23.7182			−0.769520
$951$			13.5073i			0.438004i
$952$		0			0
$953$	−34.3502			−1.11271			−0.556356	−	0.830944i	$-0.687801\pi$
$953$	−34.3502			−1.11271			−0.556356	+	0.830944i	$0.687801\pi$
$954$			37.8001i			1.22382i
$955$		−	58.8674i		−	1.90491i
$956$			17.6386i			0.570474i
$957$			7.91644i			0.255902i
$958$	4.10749			0.132707
$959$		0			0
$960$		−	4.62131i		−	0.149152i
$961$	−15.9778			−0.515413
$962$	34.5875	−	6.38642i	1.11514	−	0.205906i
$963$	−42.9836			−1.38513
$964$			0.213738i			0.00688403i
$965$	−35.7309			−1.15022
$966$		0			0
$967$			23.8805i			0.767945i	0.923344	+	0.383973i	$0.125444\pi$
$967$			23.8805i			0.767945i	−0.923344	+	0.383973i	$0.874556\pi$
$968$			9.04039i			0.290569i
$969$			4.95171i			0.159072i
$970$		−	66.7907i		−	2.14452i
$971$	−25.9377			−0.832381			−0.416190	−	0.909277i	$-0.636635\pi$
$971$	−25.9377			−0.832381			−0.416190	+	0.909277i	$0.636635\pi$
$972$	8.84358			0.283658
$973$		0			0
$974$	37.9470			1.21590
$975$	5.71999	−	1.05617i	0.183186	−	0.0338245i
$976$	47.1229			1.50837
$977$		−	45.2971i		−	1.44918i	−0.689178	−	0.724592i	$-0.742028\pi$
$977$		−	45.2971i		−	1.44918i	0.689178	−	0.724592i	$-0.257972\pi$
$978$	16.0717			0.513917
$979$	33.7086			1.07733
$980$		0			0
$981$			27.5971i			0.881109i
$982$		−	37.8675i		−	1.20840i
$983$		−	2.03101i		−	0.0647792i	−0.999475	−	0.0323896i	$-0.989688\pi$
$983$		−	2.03101i		−	0.0647792i	0.999475	−	0.0323896i	$-0.0103117\pi$
$984$	−4.10708			−0.130929
$985$	54.5480			1.73804
$986$			23.3437i			0.743413i
$987$		0			0
$988$	2.13169	+	11.5448i	0.0678182	+	0.367289i
$989$	9.42224			0.299610
$990$			33.8359i			1.07537i
$991$	−26.9665			−0.856618			−0.428309	−	0.903632i	$-0.640890\pi$
$991$	−26.9665			−0.856618			−0.428309	+	0.903632i	$0.640890\pi$
$992$	−27.3946			−0.869780
$993$		−	4.79785i		−	0.152255i
$994$		0			0
$995$		−	36.8399i		−	1.16790i
$996$			1.14321i			0.0362239i
$997$	−6.65574			−0.210789			−0.105395	−	0.994430i	$-0.533611\pi$
$997$	−6.65574			−0.210789			−0.105395	+	0.994430i	$0.533611\pi$
$998$	−14.0402			−0.444436
$999$		−	16.7851i		−	0.531056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.g.246.13	yes	16
7.2	even	3		637.2.r.g.116.14		32
7.3	odd	6		637.2.r.g.324.3		32
7.4	even	3		637.2.r.g.324.4		32
7.5	odd	6		637.2.r.g.116.13		32
7.6	odd	2	inner	637.2.c.g.246.14	yes	16
13.5	odd	4		8281.2.a.cs.1.13		16
13.8	odd	4		8281.2.a.cs.1.3		16
13.12	even	2	inner	637.2.c.g.246.3	✓	16
91.12	odd	6		637.2.r.g.116.3		32
91.25	even	6		637.2.r.g.324.14		32
91.34	even	4		8281.2.a.cs.1.4		16
91.38	odd	6		637.2.r.g.324.13		32
91.51	even	6		637.2.r.g.116.4		32
91.83	even	4		8281.2.a.cs.1.14		16
91.90	odd	2	inner	637.2.c.g.246.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.3	✓	16	13.12	even	2	inner
637.2.c.g.246.4	yes	16	91.90	odd	2	inner
637.2.c.g.246.13	yes	16	1.1	even	1	trivial
637.2.c.g.246.14	yes	16	7.6	odd	2	inner
637.2.r.g.116.3		32	91.12	odd	6
637.2.r.g.116.4		32	91.51	even	6
637.2.r.g.116.13		32	7.5	odd	6
637.2.r.g.116.14		32	7.2	even	3
637.2.r.g.324.3		32	7.3	odd	6
637.2.r.g.324.4		32	7.4	even	3
637.2.r.g.324.13		32	91.38	odd	6
637.2.r.g.324.14		32	91.25	even	6
8281.2.a.cs.1.3		16	13.8	odd	4
8281.2.a.cs.1.4		16	91.34	even	4
8281.2.a.cs.1.13		16	13.5	odd	4
8281.2.a.cs.1.14		16	91.83	even	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.65552i q^{2} -0.494977 q^{3} -0.740740 q^{4} -2.87389i q^{5} -0.819443i q^{6} +2.08473i q^{8} -2.75500 q^{9} +O(q^{10})\)	\(q+1.65552i q^{2} -0.494977 q^{3} -0.740740 q^{4} -2.87389i q^{5} -0.819443i q^{6} +2.08473i q^{8} -2.75500 q^{9} +4.75778 q^{10} -2.58138i q^{11} +0.366649 q^{12} +(3.54562 - 0.654682i) q^{13} +1.42251i q^{15} -4.93278 q^{16} +2.27584 q^{17} -4.56095i q^{18} -4.39571i q^{19} +2.12881i q^{20} +4.27352 q^{22} +7.16926 q^{23} -1.03189i q^{24} -3.25926 q^{25} +(1.08384 + 5.86983i) q^{26} +2.84859 q^{27} +6.19574 q^{29} -2.35499 q^{30} -6.85404i q^{31} -3.99686i q^{32} +1.27772i q^{33} +3.76769i q^{34} +2.04074 q^{36} -5.89241i q^{37} +7.27717 q^{38} +(-1.75500 + 0.324052i) q^{39} +5.99128 q^{40} -3.98014i q^{41} +1.31425 q^{43} +1.91213i q^{44} +7.91757i q^{45} +11.8688i q^{46} -1.35208i q^{47} +2.44161 q^{48} -5.39576i q^{50} -1.12649 q^{51} +(-2.62638 + 0.484949i) q^{52} -8.28778 q^{53} +4.71589i q^{54} -7.41860 q^{55} +2.17577i q^{57} +10.2572i q^{58} +9.61085i q^{59} -1.05371i q^{60} -9.55301 q^{61} +11.3470 q^{62} -3.24870 q^{64} +(-1.88149 - 10.1897i) q^{65} -2.11529 q^{66} +15.9095i q^{67} -1.68581 q^{68} -3.54862 q^{69} +4.79396i q^{71} -5.74342i q^{72} -5.70507i q^{73} +9.75500 q^{74} +1.61326 q^{75} +3.25607i q^{76} +(-0.536475 - 2.90543i) q^{78} -2.01426 q^{79} +14.1763i q^{80} +6.85501 q^{81} +6.58920 q^{82} +3.11798i q^{83} -6.54052i q^{85} +2.17577i q^{86} -3.06675 q^{87} +5.38147 q^{88} +13.0584i q^{89} -13.1077 q^{90} -5.31056 q^{92} +3.39259i q^{93} +2.23839 q^{94} -12.6328 q^{95} +1.97835i q^{96} -14.0382i q^{97} +7.11169i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 16 * q - 20 * q^4 + 16 * q^9	\( 16 q - 20 q^{4} + 16 q^{9} + 28 q^{16} - 8 q^{22} - 36 q^{23} - 44 q^{25} + 36 q^{29} + 52 q^{36} + 32 q^{39} - 36 q^{43} - 72 q^{51} + 12 q^{53} - 164 q^{64} - 24 q^{65} + 96 q^{74} + 24 q^{78} + 36 q^{79} + 16 q^{81} + 136 q^{88} + 24 q^{92} - 84 q^{95}+O(q^{100}) \) 16 * q - 20 * q^4 + 16 * q^9 + 28 * q^16 - 8 * q^22 - 36 * q^23 - 44 * q^25 + 36 * q^29 + 52 * q^36 + 32 * q^39 - 36 * q^43 - 72 * q^51 + 12 * q^53 - 164 * q^64 - 24 * q^65 + 96 * q^74 + 24 * q^78 + 36 * q^79 + 16 * q^81 + 136 * q^88 + 24 * q^92 - 84 * q^95

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