LMFDB - Embedded newform 637.2.c.g.246.15

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			246.15
Root			$1.41421 + 2.73420i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.g.246.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.73420i q^{2} -1.15595 q^{3} -5.47586 q^{4} -1.87727i q^{5} -3.16060i q^{6} -9.50370i q^{8} -1.66378 q^{9} +O(q^{10})$	\(q+2.73420i q^{2} -1.15595 q^{3} -5.47586 q^{4} -1.87727i q^{5} -3.16060i q^{6} -9.50370i q^{8} -1.66378 q^{9} +5.13283 q^{10} +2.29974i q^{11} +6.32982 q^{12} +(0.574228 - 3.55953i) q^{13} +2.17003i q^{15} +15.0333 q^{16} +6.07156 q^{17} -4.54911i q^{18} +5.15008i q^{19} +10.2797i q^{20} -6.28794 q^{22} -4.41782 q^{23} +10.9858i q^{24} +1.47586 q^{25} +(9.73248 + 1.57006i) q^{26} +5.39110 q^{27} +7.50488 q^{29} -5.93330 q^{30} -4.33173i q^{31} +22.0967i q^{32} -2.65838i q^{33} +16.6009i q^{34} +9.11062 q^{36} -3.16867i q^{37} -14.0814 q^{38} +(-0.663779 + 4.11464i) q^{39} -17.8410 q^{40} -2.45446i q^{41} -2.17732 q^{43} -12.5930i q^{44} +3.12336i q^{45} -12.0792i q^{46} -8.90462i q^{47} -17.3778 q^{48} +4.03530i q^{50} -7.01842 q^{51} +(-3.14439 + 19.4915i) q^{52} +8.10002 q^{53} +14.7403i q^{54} +4.31722 q^{55} -5.95323i q^{57} +20.5199i q^{58} -7.13955i q^{59} -11.8828i q^{60} +8.00979 q^{61} +11.8438 q^{62} -30.3503 q^{64} +(-6.68220 - 1.07798i) q^{65} +7.26855 q^{66} +1.15732i q^{67} -33.2470 q^{68} +5.10678 q^{69} +5.11328i q^{71} +15.8121i q^{72} -1.96898i q^{73} +8.66378 q^{74} -1.70602 q^{75} -28.2011i q^{76} +(-11.2503 - 1.81491i) q^{78} +3.81208 q^{79} -28.2216i q^{80} -1.24050 q^{81} +6.71098 q^{82} -2.49170i q^{83} -11.3980i q^{85} -5.95323i q^{86} -8.67527 q^{87} +21.8560 q^{88} -10.4291i q^{89} -8.53990 q^{90} +24.1914 q^{92} +5.00726i q^{93} +24.3470 q^{94} +9.66808 q^{95} -25.5427i q^{96} +2.51219i q^{97} -3.82625i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			2.73420i			1.93337i	0.255964	+	0.966686i	$0.417607\pi$
$2$			2.73420i			1.93337i	−0.255964	+	0.966686i	$0.582393\pi$
$3$	−1.15595			−0.667388			−0.333694	−	0.942681i	$-0.608295\pi$
$3$	−1.15595			−0.667388			−0.333694	+	0.942681i	$0.608295\pi$
$4$	−5.47586			−2.73793
$5$		−	1.87727i		−	0.839540i	−0.907630	−	0.419770i	$-0.862111\pi$
$5$		−	1.87727i		−	0.839540i	0.907630	−	0.419770i	$-0.137889\pi$
$6$		−	3.16060i		−	1.29031i
$7$		0			0
$7$		0			0
$8$		−	9.50370i		−	3.36007i
$9$	−1.66378			−0.554593
$10$	5.13283			1.62314
$11$			2.29974i			0.693396i	0.937977	+	0.346698i	$0.112697\pi$
$11$			2.29974i			0.693396i	−0.937977	+	0.346698i	$0.887303\pi$
$12$	6.32982			1.82726
$13$	0.574228	−	3.55953i	0.159262	−	0.987236i
$13$	0.574228	−	3.55953i	0.159262	−	0.987236i
$14$		0			0
$15$			2.17003i			0.560299i
$16$	15.0333			3.75833
$17$	6.07156			1.47257			0.736285	−	0.676672i	$-0.236578\pi$
$17$	6.07156			1.47257			0.736285	+	0.676672i	$0.236578\pi$
$18$		−	4.54911i		−	1.07223i
$19$			5.15008i			1.18151i	0.806851	+	0.590754i	$0.201170\pi$
$19$			5.15008i			1.18151i	−0.806851	+	0.590754i	$0.798830\pi$
$20$			10.2797i			2.29860i
$21$		0			0
$22$	−6.28794			−1.34059
$23$	−4.41782			−0.921180			−0.460590	−	0.887613i	$-0.652362\pi$
$23$	−4.41782			−0.921180			−0.460590	+	0.887613i	$0.652362\pi$
$24$			10.9858i			2.24247i
$25$	1.47586			0.295172
$26$	9.73248	+	1.57006i	1.90870	+	0.307913i
$27$	5.39110			1.03752
$28$		0			0
$29$	7.50488			1.39362			0.696810	−	0.717255i	$-0.254602\pi$
$29$	7.50488			1.39362			0.696810	+	0.717255i	$0.254602\pi$
$30$	−5.93330			−1.08327
$31$		−	4.33173i		−	0.778001i	−0.921238	−	0.389001i	$-0.872820\pi$
$31$		−	4.33173i		−	0.778001i	0.921238	−	0.389001i	$-0.127180\pi$
$32$			22.0967i			3.90619i
$33$		−	2.65838i		−	0.462765i
$34$			16.6009i			2.84703i
$35$		0			0
$36$	9.11062			1.51844
$37$		−	3.16867i		−	0.520926i	−0.965484	−	0.260463i	$-0.916125\pi$
$37$		−	3.16867i		−	0.520926i	0.965484	−	0.260463i	$-0.0838752\pi$
$38$	−14.0814			−2.28430
$39$	−0.663779	+	4.11464i	−0.106290	+	0.658870i
$40$	−17.8410			−2.82091
$41$		−	2.45446i		−	0.383322i	−0.981461	−	0.191661i	$-0.938613\pi$
$41$		−	2.45446i		−	0.383322i	0.981461	−	0.191661i	$-0.0613874\pi$
$42$		0			0
$43$	−2.17732			−0.332038			−0.166019	−	0.986123i	$-0.553091\pi$
$43$	−2.17732			−0.332038			−0.166019	+	0.986123i	$0.553091\pi$
$44$		−	12.5930i		−	1.89847i
$45$			3.12336i			0.465603i
$46$		−	12.0792i		−	1.78098i
$47$		−	8.90462i		−	1.29887i	−0.760416	−	0.649436i	$-0.775005\pi$
$47$		−	8.90462i		−	1.29887i	0.760416	−	0.649436i	$-0.224995\pi$
$48$	−17.3778			−2.50827
$49$		0			0
$50$			4.03530i			0.570677i
$51$	−7.01842			−0.982775
$52$	−3.14439	+	19.4915i	−0.436049	+	2.70298i
$53$	8.10002			1.11262			0.556312	−	0.830974i	$-0.312216\pi$
$53$	8.10002			1.11262			0.556312	+	0.830974i	$0.312216\pi$
$54$			14.7403i			2.00591i
$55$	4.31722			0.582134
$56$		0			0
$57$		−	5.95323i		−	0.788525i
$58$			20.5199i			2.69439i
$59$		−	7.13955i		−	0.929491i	−0.885444	−	0.464745i	$-0.846146\pi$
$59$		−	7.13955i		−	0.929491i	0.885444	−	0.464745i	$-0.153854\pi$
$60$		−	11.8828i		−	1.53406i
$61$	8.00979			1.02555			0.512774	−	0.858523i	$-0.328618\pi$
$61$	8.00979			1.02555			0.512774	+	0.858523i	$0.328618\pi$
$62$	11.8438			1.50417
$63$		0			0
$64$	−30.3503			−3.79379
$65$	−6.68220	−	1.07798i	−0.828825	−	0.133707i
$66$	7.26855			0.894696
$67$			1.15732i			0.141389i	0.997498	+	0.0706947i	$0.0225216\pi$
$67$			1.15732i			0.141389i	−0.997498	+	0.0706947i	$0.977478\pi$
$68$	−33.2470			−4.03179
$69$	5.10678			0.614785
$70$		0			0
$71$			5.11328i			0.606835i	0.952858	+	0.303417i	$0.0981276\pi$
$71$			5.11328i			0.606835i	−0.952858	+	0.303417i	$0.901872\pi$
$72$			15.8121i			1.86347i
$73$		−	1.96898i		−	0.230452i	−0.993339	−	0.115226i	$-0.963241\pi$
$73$		−	1.96898i		−	0.230452i	0.993339	−	0.115226i	$-0.0367593\pi$
$74$	8.66378			1.00714
$75$	−1.70602			−0.196994
$76$		−	28.2011i		−	3.23489i
$77$		0			0
$78$	−11.2503	−	1.81491i	−1.27384	−	0.205498i
$79$	3.81208			0.428893			0.214446	−	0.976736i	$-0.431205\pi$
$79$	3.81208			0.428893			0.214446	+	0.976736i	$0.431205\pi$
$80$		−	28.2216i		−	3.15527i
$81$	−1.24050			−0.137834
$82$	6.71098			0.741104
$83$		−	2.49170i		−	0.273499i	−0.990606	−	0.136750i	$-0.956334\pi$
$83$		−	2.49170i		−	0.273499i	0.990606	−	0.136750i	$-0.0436656\pi$
$84$		0			0
$85$		−	11.3980i		−	1.23628i
$86$		−	5.95323i		−	0.641954i
$87$	−8.67527			−0.930086
$88$	21.8560			2.32986
$89$		−	10.4291i		−	1.10548i	−0.833353	−	0.552742i	$-0.813582\pi$
$89$		−	10.4291i		−	1.10548i	0.833353	−	0.552742i	$-0.186418\pi$
$90$	−8.53990			−0.900185
$91$		0			0
$92$	24.1914			2.52213
$93$			5.00726i			0.519229i
$94$	24.3470			2.51120
$95$	9.66808			0.991924
$96$		−	25.5427i		−	2.60694i
$97$			2.51219i			0.255074i	0.991834	+	0.127537i	$0.0407072\pi$
$97$			2.51219i			0.255074i	−0.991834	+	0.127537i	$0.959293\pi$
$98$		0			0
$99$		−	3.82625i		−	0.384553i
$100$	−8.08160			−0.808160
$101$	−10.6804			−1.06274			−0.531368	−	0.847141i	$-0.678322\pi$
$101$	−10.6804			−1.06274			−0.531368	+	0.847141i	$0.678322\pi$
$102$		−	19.1898i		−	1.90007i
$103$	11.8030			1.16298			0.581492	−	0.813552i	$-0.302469\pi$
$103$	11.8030			1.16298			0.581492	+	0.813552i	$0.302469\pi$
$104$	−33.8287	−	5.45729i	−3.31718	−	0.535131i
$105$		0			0
$106$			22.1471i			2.15112i
$107$	−4.27734			−0.413506			−0.206753	−	0.978393i	$-0.566290\pi$
$107$	−4.27734			−0.413506			−0.206753	+	0.978393i	$0.566290\pi$
$108$	−29.5209			−2.84065
$109$			2.01135i			0.192652i	0.995350	+	0.0963260i	$0.0307091\pi$
$109$			2.01135i			0.192652i	−0.995350	+	0.0963260i	$0.969291\pi$
$110$			11.8042i			1.12548i
$111$			3.66282i			0.347660i
$112$		0			0
$113$	−4.16866			−0.392154			−0.196077	−	0.980588i	$-0.562820\pi$
$113$	−4.16866			−0.392154			−0.196077	+	0.980588i	$0.562820\pi$
$114$	16.2773			1.52451
$115$			8.29344i			0.773368i
$116$	−41.0957			−3.81564
$117$	−0.955388	+	5.92227i	−0.0883257	+	0.547514i
$118$	19.5210			1.79705
$119$		0			0
$120$	20.6233			1.88264
$121$	5.71122			0.519202
$122$			21.9004i			1.98277i
$123$			2.83723i			0.255824i
$124$			23.7199i			2.13011i
$125$		−	12.1569i		−	1.08735i
$126$		0			0
$127$	15.1922			1.34809			0.674046	−	0.738689i	$-0.264555\pi$
$127$	15.1922			1.34809			0.674046	+	0.738689i	$0.264555\pi$
$128$		−	38.7903i		−	3.42861i
$129$	2.51687			0.221598
$130$	2.94742	−	18.2705i	0.258506	−	1.60243i
$131$	−0.950977			−0.0830872			−0.0415436	−	0.999137i	$-0.513228\pi$
$131$	−0.950977			−0.0830872			−0.0415436	+	0.999137i	$0.513228\pi$
$132$			14.5569i			1.26702i
$133$		0			0
$134$	−3.16435			−0.273359
$135$		−	10.1205i		−	0.871037i
$136$		−	57.7023i		−	4.94793i
$137$			12.2379i			1.04555i	0.852469	+	0.522777i	$0.175104\pi$
$137$			12.2379i			1.04555i	−0.852469	+	0.522777i	$0.824896\pi$
$138$			13.9630i			1.18861i
$139$	5.24824			0.445150			0.222575	−	0.974916i	$-0.428554\pi$
$139$	5.24824			0.445150			0.222575	+	0.974916i	$0.428554\pi$
$140$		0			0
$141$			10.2933i			0.866852i
$142$	−13.9807			−1.17324
$143$	8.18598	+	1.32057i	0.684546	+	0.110432i
$144$	−25.0121			−2.08434
$145$		−	14.0887i		−	1.17000i
$146$	5.38360			0.445550
$147$		0			0
$148$			17.3512i			1.42626i
$149$			2.38138i			0.195090i	0.995231	+	0.0975451i	$0.0310990\pi$
$149$			2.38138i			0.195090i	−0.995231	+	0.0975451i	$0.968901\pi$
$150$		−	4.66460i		−	0.380863i
$151$			20.3085i			1.65268i	0.563170	+	0.826341i	$0.309582\pi$
$151$			20.3085i			1.65268i	−0.563170	+	0.826341i	$0.690418\pi$
$152$	48.9448			3.96995
$153$	−10.1017			−0.816677
$154$		0			0
$155$	−8.13182			−0.653163
$156$	3.63476	−	22.5312i	0.291014	−	1.80394i
$157$	11.0405			0.881124			0.440562	−	0.897722i	$-0.354779\pi$
$157$	11.0405			0.881124			0.440562	+	0.897722i	$0.354779\pi$
$158$			10.4230i			0.829209i
$159$	−9.36322			−0.742552
$160$	41.4815			3.27940
$161$		0			0
$162$		−	3.39178i		−	0.266484i
$163$		−	18.9784i		−	1.48651i	−0.669011	−	0.743253i	$-0.733282\pi$
$163$		−	18.9784i		−	1.48651i	0.669011	−	0.743253i	$-0.266718\pi$
$164$			13.4403i			1.04951i
$165$	−4.99049			−0.388509
$166$	6.81280			0.528776
$167$			21.7305i			1.68155i	0.541382	+	0.840776i	$0.317901\pi$
$167$			21.7305i			1.68155i	−0.541382	+	0.840776i	$0.682099\pi$
$168$		0			0
$169$	−12.3405	−	4.08796i	−0.949271	−	0.314459i
$170$	31.1643			2.39019
$171$		−	8.56859i		−	0.655256i
$172$	11.9227			0.909097
$173$	−2.90301			−0.220712			−0.110356	−	0.993892i	$-0.535199\pi$
$173$	−2.90301			−0.220712			−0.110356	+	0.993892i	$0.535199\pi$
$174$		−	23.7199i		−	1.79820i
$175$		0			0
$176$			34.5727i			2.60601i
$177$			8.25297i			0.620331i
$178$	28.5153			2.13731
$179$	−19.3503			−1.44631			−0.723154	−	0.690687i	$-0.757308\pi$
$179$	−19.3503			−1.44631			−0.723154	+	0.690687i	$0.757308\pi$
$180$		−	17.1031i		−	1.27479i
$181$	−9.98016			−0.741820			−0.370910	−	0.928669i	$-0.620954\pi$
$181$	−9.98016			−0.741820			−0.370910	+	0.928669i	$0.620954\pi$
$182$		0			0
$183$	−9.25892			−0.684439
$184$			41.9857i			3.09523i
$185$	−5.94844			−0.437338
$186$	−13.6909			−1.00386
$187$			13.9630i			1.02107i
$188$			48.7604i			3.55622i
$189$		0			0
$190$			26.4345i			1.91776i
$191$	5.40486			0.391082			0.195541	−	0.980696i	$-0.437354\pi$
$191$	5.40486			0.391082			0.195541	+	0.980696i	$0.437354\pi$
$192$	35.0834			2.53193
$193$		−	14.5666i		−	1.04853i	−0.851556	−	0.524264i	$-0.824340\pi$
$193$		−	14.5666i		−	1.04853i	0.851556	−	0.524264i	$-0.175660\pi$
$194$	−6.86883			−0.493153
$195$	7.72429	+	1.24609i	0.553148	+	0.0892345i
$196$		0			0
$197$		−	15.9055i		−	1.13322i	−0.823987	−	0.566609i	$-0.808255\pi$
$197$		−	15.9055i		−	1.13322i	0.823987	−	0.566609i	$-0.191745\pi$
$198$	10.4617			0.743484
$199$	0.373666			0.0264885			0.0132442	−	0.999912i	$-0.495784\pi$
$199$	0.373666			0.0264885			0.0132442	+	0.999912i	$0.495784\pi$
$200$		−	14.0261i		−	0.991797i
$201$		−	1.33781i		−	0.0943617i
$202$		−	29.2023i		−	2.05467i
$203$		0			0
$204$	38.4319			2.69077
$205$	−4.60768			−0.321814
$206$			32.2718i			2.24848i
$207$	7.35028			0.510880
$208$	8.63255	−	53.5116i	0.598560	−	3.71036i
$209$	−11.8438			−0.819254
$210$		0			0
$211$	6.05258			0.416677			0.208339	−	0.978057i	$-0.433194\pi$
$211$	6.05258			0.416677			0.208339	+	0.978057i	$0.433194\pi$
$212$	−44.3546			−3.04629
$213$		−	5.91070i		−	0.404994i
$214$		−	11.6951i		−	0.799462i
$215$			4.08742i			0.278760i
$216$		−	51.2354i		−	3.48613i
$217$		0			0
$218$	−5.49943			−0.372468
$219$			2.27605i			0.153801i
$220$	−23.6405			−1.59384
$221$	3.48646	−	21.6119i	0.234525	−	1.45377i
$222$	−10.0149			−0.672156
$223$			7.30624i			0.489262i	0.969616	+	0.244631i	$0.0786668\pi$
$223$			7.30624i			0.489262i	−0.969616	+	0.244631i	$0.921333\pi$
$224$		0			0
$225$	−2.45550			−0.163700
$226$		−	11.3980i		−	0.758180i
$227$		−	15.6914i		−	1.04147i	−0.853717	−	0.520737i	$-0.825657\pi$
$227$		−	15.6914i		−	1.04147i	0.853717	−	0.520737i	$-0.174343\pi$
$228$			32.5991i			2.15893i
$229$		−	25.5632i		−	1.68926i	−0.535347	−	0.844632i	$-0.679819\pi$
$229$		−	25.5632i		−	1.68926i	0.535347	−	0.844632i	$-0.320181\pi$
$230$	−22.6759			−1.49521
$231$		0			0
$232$		−	71.3241i		−	4.68266i
$233$	16.3405			1.07050			0.535252	−	0.844693i	$-0.320217\pi$
$233$	16.3405			1.07050			0.535252	+	0.844693i	$0.320217\pi$
$234$	−16.1927	−	2.61222i	−1.05855	−	0.170766i
$235$	−16.7164			−1.09046
$236$			39.0952i			2.54488i
$237$	−4.40658			−0.286238
$238$		0			0
$239$		−	17.2505i		−	1.11584i	−0.829895	−	0.557920i	$-0.811600\pi$
$239$		−	17.2505i		−	1.11584i	0.829895	−	0.557920i	$-0.188400\pi$
$240$			32.6228i			2.10579i
$241$		−	10.1130i		−	0.651434i	−0.945467	−	0.325717i	$-0.894394\pi$
$241$		−	10.1130i		−	0.651434i	0.945467	−	0.325717i	$-0.105606\pi$
$242$			15.6156i			1.00381i
$243$	−14.7393			−0.945528
$244$	−43.8605			−2.80788
$245$		0			0
$246$	−7.75756			−0.494604
$247$	18.3319	+	2.95732i	1.16643	+	0.188170i
$248$	−41.1674			−2.61414
$249$			2.88028i			0.182530i
$250$	33.2395			2.10225
$251$	−20.8184			−1.31404			−0.657022	−	0.753871i	$-0.728184\pi$
$251$	−20.8184			−1.31404			−0.657022	+	0.753871i	$0.728184\pi$
$252$		0			0
$253$		−	10.1598i		−	0.638743i
$254$			41.5386i			2.60636i
$255$			13.1755i			0.825080i
$256$	45.3600			2.83500
$257$	−28.2296			−1.76091			−0.880456	−	0.474127i	$-0.842764\pi$
$257$	−28.2296			−1.76091			−0.880456	+	0.474127i	$0.842764\pi$
$258$			6.88164i			0.428432i
$259$		0			0
$260$	36.5908	+	5.90287i	2.26926	+	0.366080i
$261$	−12.4865			−0.772892
$262$		−	2.60016i		−	0.160639i
$263$	6.10868			0.376678			0.188339	−	0.982104i	$-0.439690\pi$
$263$	6.10868			0.376678			0.188339	+	0.982104i	$0.439690\pi$
$264$	−25.2645			−1.55492
$265$		−	15.2059i		−	0.934092i
$266$		0			0
$267$			12.0555i			0.737787i
$268$		−	6.33734i		−	0.387114i
$269$	−4.84124			−0.295176			−0.147588	−	0.989049i	$-0.547151\pi$
$269$	−4.84124			−0.295176			−0.147588	+	0.989049i	$0.547151\pi$
$270$	27.6716			1.68404
$271$		−	0.298894i		−	0.0181565i	−0.999959	−	0.00907826i	$-0.997110\pi$
$271$		−	0.298894i		−	0.0181565i	0.999959	−	0.00907826i	$-0.00288974\pi$
$272$	91.2757			5.53440
$273$		0			0
$274$	−33.4609			−2.02145
$275$			3.39409i			0.204671i
$276$	−27.9640			−1.68324
$277$	−8.72696			−0.524352			−0.262176	−	0.965020i	$-0.584440\pi$
$277$	−8.72696			−0.524352			−0.262176	+	0.965020i	$0.584440\pi$
$278$			14.3497i			0.860640i
$279$			7.20704i			0.431474i
$280$		0			0
$281$			24.7012i			1.47355i	0.676137	+	0.736776i	$0.263653\pi$
$281$			24.7012i			1.47355i	−0.676137	+	0.736776i	$0.736347\pi$
$282$	−28.1439			−1.67595
$283$	12.2524			0.728332			0.364166	−	0.931334i	$-0.381354\pi$
$283$	12.2524			0.728332			0.364166	+	0.931334i	$0.381354\pi$
$284$		−	27.9996i		−	1.66147i
$285$	−11.1758			−0.661999
$286$	−3.61071	+	22.3821i	−0.213506	+	1.32348i
$287$		0			0
$288$		−	36.7641i		−	2.16634i
$289$	19.8638			1.16846
$290$	38.5213			2.26205
$291$		−	2.90397i		−	0.170233i
$292$			10.7819i			0.630962i
$293$		−	14.6524i		−	0.856001i	−0.903779	−	0.428000i	$-0.859218\pi$
$293$		−	14.6524i		−	0.856001i	0.903779	−	0.428000i	$-0.140782\pi$
$294$		0			0
$295$	−13.4029			−0.780345
$296$	−30.1141			−1.75035
$297$			12.3981i			0.719410i
$298$	−6.51117			−0.377182
$299$	−2.53684	+	15.7254i	−0.146709	+	0.909422i
$300$	9.34193			0.539357
$301$		0			0
$302$	−55.5275			−3.19525
$303$	12.3460			0.709258
$304$			77.4228i			4.44050i
$305$		−	15.0365i		−	0.860990i
$306$		−	27.6202i		−	1.57894i
$307$			18.8687i			1.07690i	0.842659	+	0.538448i	$0.180989\pi$
$307$			18.8687i			1.07690i	−0.842659	+	0.538448i	$0.819011\pi$
$308$		0			0
$309$	−13.6437			−0.776162
$310$		−	22.2340i		−	1.26281i
$311$	−5.70539			−0.323523			−0.161761	−	0.986830i	$-0.551717\pi$
$311$	−5.70539			−0.323523			−0.161761	+	0.986830i	$0.551717\pi$
$312$	39.1043	+	6.30836i	2.21385	+	0.357140i
$313$	3.94334			0.222891			0.111445	−	0.993771i	$-0.464452\pi$
$313$	3.94334			0.222891			0.111445	+	0.993771i	$0.464452\pi$
$314$			30.1868i			1.70354i
$315$		0			0
$316$	−20.8744			−1.17428
$317$		−	3.84116i		−	0.215741i	−0.994165	−	0.107871i	$-0.965597\pi$
$317$		−	3.84116i		−	0.215741i	0.994165	−	0.107871i	$-0.0344032\pi$
$318$		−	25.6009i		−	1.43563i
$319$			17.2592i			0.966332i
$320$			56.9757i			3.18504i
$321$	4.94439			0.275969
$322$		0			0
$323$			31.2690i			1.73985i
$324$	6.79282			0.377379
$325$	0.847480	−	5.25337i	0.0470097	−	0.291405i
$326$	51.8908			2.87397
$327$		−	2.32502i		−	0.128574i
$328$	−23.3264			−1.28799
$329$		0			0
$330$		−	13.6450i		−	0.751134i
$331$		−	6.12599i		−	0.336715i	−0.985726	−	0.168357i	$-0.946154\pi$
$331$		−	6.12599i		−	0.336715i	0.985726	−	0.168357i	$-0.0538463\pi$
$332$			13.6442i			0.748822i
$333$			5.27196i			0.288902i
$334$	−59.4154			−3.25107
$335$	2.17261			0.118702
$336$		0			0
$337$	20.8026			1.13319			0.566594	−	0.823997i	$-0.308261\pi$
$337$	20.8026			1.13319			0.566594	+	0.823997i	$0.308261\pi$
$338$	11.1773	−	33.7415i	0.607966	−	1.83529i
$339$	4.81876			0.261719
$340$			62.4136i			3.38485i
$341$	9.96183			0.539463
$342$	23.4283			1.26686
$343$		0			0
$344$			20.6926i			1.11567i
$345$		−	9.58681i		−	0.516136i
$346$		−	7.93741i		−	0.426718i
$347$	17.7508			0.952915			0.476457	−	0.879198i	$-0.341921\pi$
$347$	17.7508			0.952915			0.476457	+	0.879198i	$0.341921\pi$
$348$	47.5045			2.54651
$349$		−	1.00552i		−	0.0538245i	−0.999638	−	0.0269122i	$-0.991433\pi$
$349$		−	1.00552i		−	0.0538245i	0.999638	−	0.0269122i	$-0.00856746\pi$
$350$		0			0
$351$	3.09572	−	19.1898i	0.165237	−	1.02427i
$352$	−50.8166			−2.70854
$353$			12.6219i			0.671797i	0.941898	+	0.335898i	$0.109040\pi$
$353$			12.6219i			0.671797i	−0.941898	+	0.335898i	$0.890960\pi$
$354$	−22.5653			−1.19933
$355$	9.59900			0.509462
$356$			57.1083i			3.02674i
$357$		0			0
$358$		−	52.9076i		−	2.79625i
$359$		−	11.4750i		−	0.605627i	−0.953050	−	0.302813i	$-0.902074\pi$
$359$		−	11.4750i		−	0.605627i	0.953050	−	0.302813i	$-0.0979259\pi$
$360$	29.6835			1.56446
$361$	−7.52330			−0.395963
$362$		−	27.2878i		−	1.43421i
$363$	−6.60188			−0.346509
$364$		0			0
$365$	−3.69631			−0.193474
$366$		−	25.3158i		−	1.32328i
$367$	−28.9114			−1.50917			−0.754583	−	0.656205i	$-0.772161\pi$
$367$	−28.9114			−1.50917			−0.754583	+	0.656205i	$0.772161\pi$
$368$	−66.4146			−3.46210
$369$			4.08367i			0.212588i
$370$		−	16.2642i		−	0.845538i
$371$		0			0
$372$		−	27.4191i		−	1.42161i
$373$	23.4888			1.21621			0.608103	−	0.793858i	$-0.291931\pi$
$373$	23.4888			1.21621			0.608103	+	0.793858i	$0.291931\pi$
$374$	−38.1776			−1.97412
$375$			14.0528i			0.725684i
$376$	−84.6268			−4.36430
$377$	4.30951	−	26.7138i	0.221951	−	1.37583i
$378$		0			0
$379$			37.6063i			1.93171i	0.259088	+	0.965854i	$0.416578\pi$
$379$			37.6063i			1.93171i	−0.259088	+	0.965854i	$0.583422\pi$
$380$	−52.9411			−2.71582
$381$	−17.5615			−0.899701
$382$			14.7780i			0.756107i
$383$			25.3183i			1.29371i	0.762615	+	0.646853i	$0.223915\pi$
$383$			25.3183i			1.29371i	−0.762615	+	0.646853i	$0.776085\pi$
$384$			44.8397i			2.28822i
$385$		0			0
$386$	39.8281			2.02720
$387$	3.62258			0.184146
$388$		−	13.7564i		−	0.698375i
$389$	1.31889			0.0668706			0.0334353	−	0.999441i	$-0.489355\pi$
$389$	1.31889			0.0668706			0.0334353	+	0.999441i	$0.489355\pi$
$390$	−3.40707	+	21.1198i	−0.172524	+	1.06944i
$391$	−26.8231			−1.35650
$392$		0			0
$393$	1.09928			0.0554514
$394$	43.4888			2.19093
$395$		−	7.15630i		−	0.360073i
$396$			20.9520i			1.05288i
$397$			37.3506i			1.87457i	0.348558	+	0.937287i	$0.386671\pi$
$397$			37.3506i			1.87457i	−0.348558	+	0.937287i	$0.613329\pi$
$398$			1.02168i			0.0512121i
$399$		0			0
$400$	22.1871			1.10935
$401$			27.3183i			1.36421i	0.731253	+	0.682106i	$0.238936\pi$
$401$			27.3183i			1.36421i	−0.731253	+	0.682106i	$0.761064\pi$
$402$	3.65784			0.182436
$403$	−15.4189	−	2.48740i	−0.768071	−	0.123906i
$404$	58.4842			2.90970
$405$			2.32876i			0.115717i
$406$		0			0
$407$	7.28710			0.361208
$408$			66.7010i			3.30219i
$409$			23.9071i			1.18213i	0.806624	+	0.591065i	$0.201292\pi$
$409$			23.9071i			1.18213i	−0.806624	+	0.591065i	$0.798708\pi$
$410$		−	12.5983i		−	0.622187i
$411$		−	14.1464i		−	0.697791i
$412$	−64.6315			−3.18417
$413$		0			0
$414$			20.0972i			0.987721i
$415$	−4.67759			−0.229614
$416$	78.6540	+	12.6886i	3.85633	+	0.622108i
$417$	−6.06670			−0.297088
$418$		−	32.3834i		−	1.58392i
$419$	−16.4726			−0.804739			−0.402369	−	0.915477i	$-0.631813\pi$
$419$	−16.4726			−0.804739			−0.402369	+	0.915477i	$0.631813\pi$
$420$		0			0
$421$		−	23.9857i		−	1.16899i	−0.811397	−	0.584495i	$-0.801292\pi$
$421$		−	23.9857i		−	1.16899i	0.811397	−	0.584495i	$-0.198708\pi$
$422$			16.5490i			0.805592i
$423$			14.8153i			0.720345i
$424$		−	76.9802i		−	3.73849i
$425$	8.96077			0.434661
$426$	16.1610			0.783005
$427$		0			0
$428$	23.4221			1.13215
$429$	−9.46259	−	1.52652i	−0.456858	−	0.0737009i
$430$	−11.1758			−0.538946
$431$		−	22.6899i		−	1.09293i	−0.837481	−	0.546467i	$-0.815973\pi$
$431$		−	22.6899i		−	1.09293i	0.837481	−	0.546467i	$-0.184027\pi$
$432$	81.0461			3.89933
$433$	17.0937			0.821470			0.410735	−	0.911755i	$-0.365272\pi$
$433$	17.0937			0.821470			0.410735	+	0.911755i	$0.365272\pi$
$434$		0			0
$435$			16.2858i			0.780845i
$436$		−	11.0138i		−	0.527468i
$437$		−	22.7521i		−	1.08838i
$438$	−6.22318			−0.297355
$439$	35.4013			1.68961			0.844805	−	0.535074i	$-0.179716\pi$
$439$	35.4013			1.68961			0.844805	+	0.535074i	$0.179716\pi$
$440$		−	41.0296i		−	1.95601i
$441$		0			0
$442$	59.0913	+	9.53268i	2.81069	+	0.453423i
$443$	−16.2632			−0.772689			−0.386345	−	0.922355i	$-0.626262\pi$
$443$	−16.2632			−0.772689			−0.386345	+	0.922355i	$0.626262\pi$
$444$		−	20.0571i		−	0.951868i
$445$	−19.5782			−0.928098
$446$	−19.9767			−0.945925
$447$		−	2.75276i		−	0.130201i
$448$		0			0
$449$		−	15.1472i		−	0.714839i	−0.933944	−	0.357419i	$-0.883657\pi$
$449$		−	15.1472i		−	0.714839i	0.933944	−	0.357419i	$-0.116343\pi$
$450$		−	6.71385i		−	0.316494i
$451$	5.64460			0.265794
$452$	22.8270			1.07369
$453$		−	23.4756i		−	1.10298i
$454$	42.9034			2.01356
$455$		0			0
$456$	−56.5778			−2.64950
$457$			39.4983i			1.84765i	0.382813	+	0.923826i	$0.374955\pi$
$457$			39.4983i			1.84765i	−0.382813	+	0.923826i	$0.625045\pi$
$458$	69.8950			3.26598
$459$	32.7324			1.52782
$460$		−	45.4137i		−	2.11743i
$461$		−	19.0149i		−	0.885614i	−0.896617	−	0.442807i	$-0.853983\pi$
$461$		−	19.0149i		−	0.885614i	0.896617	−	0.442807i	$-0.146017\pi$
$462$		0			0
$463$			2.48740i			0.115599i	0.998328	+	0.0577996i	$0.0184084\pi$
$463$			2.48740i			0.115599i	−0.998328	+	0.0577996i	$0.981592\pi$
$464$	112.823			5.23769
$465$	9.39998			0.435913
$466$			44.6783i			2.06968i
$467$	−14.8786			−0.688501			−0.344250	−	0.938878i	$-0.611867\pi$
$467$	−14.8786			−0.688501			−0.344250	+	0.938878i	$0.611867\pi$
$468$	5.23157	−	32.4295i	0.241830	−	1.49906i
$469$		0			0
$470$		−	45.7059i		−	2.10826i
$471$	−12.7622			−0.588052
$472$	−67.8522			−3.12315
$473$		−	5.00726i		−	0.230234i
$474$		−	12.0485i		−	0.553404i
$475$			7.60079i			0.348748i
$476$		0			0
$477$	−13.4766			−0.617053
$478$	47.1662			2.15733
$479$			16.8798i			0.771256i	0.922654	+	0.385628i	$0.126015\pi$
$479$			16.8798i			0.771256i	−0.922654	+	0.385628i	$0.873985\pi$
$480$	−47.9506			−2.18863
$481$	−11.2790	−	1.81954i	−0.514277	−	0.0829638i
$482$	27.6509			1.25947
$483$		0			0
$484$	−31.2738			−1.42154
$485$	4.71606			0.214145
$486$		−	40.3003i		−	1.82806i
$487$		−	4.44539i		−	0.201440i	−0.994915	−	0.100720i	$-0.967885\pi$
$487$		−	4.44539i		−	0.201440i	0.994915	−	0.100720i	$-0.0321146\pi$
$488$		−	76.1227i		−	3.44591i
$489$			21.9381i			0.992076i
$490$		0			0
$491$	−16.9816			−0.766368			−0.383184	−	0.923672i	$-0.625172\pi$
$491$	−16.9816			−0.766368			−0.383184	+	0.923672i	$0.625172\pi$
$492$		−	15.5363i		−	0.700430i
$493$	45.5663			2.05220
$494$	−8.08591	+	50.1230i	−0.363802	+	2.25514i
$495$	−7.18290			−0.322848
$496$		−	65.1202i		−	2.92399i
$497$		0			0
$498$	−7.87526			−0.352899
$499$		−	41.0011i		−	1.83546i	−0.397203	−	0.917731i	$-0.630019\pi$
$499$		−	41.0011i		−	1.83546i	0.397203	−	0.917731i	$-0.369981\pi$
$500$			66.5697i			2.97709i
$501$		−	25.1193i		−	1.12225i
$502$		−	56.9217i		−	2.54054i
$503$	37.2910			1.66272			0.831361	−	0.555732i	$-0.187562\pi$
$503$	37.2910			1.66272			0.831361	+	0.555732i	$0.187562\pi$
$504$		0			0
$505$			20.0499i			0.892210i
$506$	27.7790			1.23493
$507$	14.2650	+	4.72548i	0.633532	+	0.209866i
$508$	−83.1905			−3.69098
$509$			8.21571i			0.364155i	0.983284	+	0.182077i	$0.0582821\pi$
$509$			8.21571i			0.364155i	−0.983284	+	0.182077i	$0.941718\pi$
$510$	−36.0244			−1.59519
$511$		0			0
$512$			46.4428i			2.05250i
$513$			27.7646i			1.22584i
$514$		−	77.1854i		−	3.40450i
$515$		−	22.1574i		−	0.976372i
$516$	−13.7821			−0.606721
$517$	20.4783			0.900633
$518$		0			0
$519$	3.35573			0.147300
$520$	−10.2448	+	63.5056i	−0.449264	+	2.78491i
$521$	−33.9993			−1.48954			−0.744768	−	0.667323i	$-0.767440\pi$
$521$	−33.9993			−1.48954			−0.744768	+	0.667323i	$0.767440\pi$
$522$		−	34.1405i		−	1.49429i
$523$	22.8782			1.00039			0.500197	−	0.865912i	$-0.333261\pi$
$523$	22.8782			1.00039			0.500197	+	0.865912i	$0.333261\pi$
$524$	5.20742			0.227487
$525$		0			0
$526$			16.7024i			0.728258i
$527$		−	26.3003i		−	1.14566i
$528$		−	39.9643i		−	1.73922i
$529$	−3.48284			−0.151428
$530$	41.5761			1.80595
$531$			11.8786i			0.515489i
$532$		0			0
$533$	−8.73672	−	1.40942i	−0.378429	−	0.0610487i
$534$	−32.9623			−1.42642
$535$			8.02972i			0.347155i
$536$	10.9989			0.475078
$537$	22.3680			0.965249
$538$		−	13.2369i		−	0.570685i
$539$		0			0
$540$			55.4187i			2.38484i
$541$			39.4983i			1.69816i	0.528261	+	0.849082i	$0.322844\pi$
$541$			39.4983i			1.69816i	−0.528261	+	0.849082i	$0.677156\pi$
$542$	0.817236			0.0351033
$543$	11.5366			0.495082
$544$			134.162i			5.75213i
$545$	3.77584			0.161739
$546$		0			0
$547$	37.0129			1.58256			0.791279	−	0.611455i	$-0.209416\pi$
$547$	37.0129			1.58256			0.791279	+	0.611455i	$0.209416\pi$
$548$		−	67.0131i		−	2.86266i
$549$	−13.3265			−0.568762
$550$	−9.28012			−0.395706
$551$			38.6507i			1.64658i
$552$		−	48.5334i		−	2.06572i
$553$		0			0
$554$		−	23.8613i		−	1.01377i
$555$	6.87611			0.291874
$556$	−28.7386			−1.21879
$557$			24.0867i			1.02059i	0.860001	+	0.510293i	$0.170463\pi$
$557$			24.0867i			1.02059i	−0.860001	+	0.510293i	$0.829537\pi$
$558$	−19.7055			−0.834200
$559$	−1.25028	+	7.75024i	−0.0528811	+	0.327800i
$560$		0			0
$561$		−	16.1405i		−	0.681453i
$562$	−67.5381			−2.84892
$563$	6.49397			0.273688			0.136844	−	0.990593i	$-0.456304\pi$
$563$	6.49397			0.273688			0.136844	+	0.990593i	$0.456304\pi$
$564$		−	56.3646i		−	2.37338i
$565$			7.82569i			0.329229i
$566$			33.5006i			1.40814i
$567$		0			0
$568$	48.5951			2.03900
$569$	−28.7638			−1.20584			−0.602921	−	0.797801i	$-0.705996\pi$
$569$	−28.7638			−1.20584			−0.602921	+	0.797801i	$0.705996\pi$
$570$		−	30.5570i		−	1.27989i
$571$	2.48615			0.104042			0.0520211	−	0.998646i	$-0.483434\pi$
$571$	2.48615			0.104042			0.0520211	+	0.998646i	$0.483434\pi$
$572$	−44.8253	−	7.23127i	−1.87424	−	0.302355i
$573$	−6.24775			−0.261003
$574$		0			0
$575$	−6.52009			−0.271906
$576$	50.4962			2.10401
$577$		−	14.5747i		−	0.606755i	−0.952871	−	0.303377i	$-0.901886\pi$
$577$		−	14.5747i		−	0.606755i	0.952871	−	0.303377i	$-0.0981142\pi$
$578$			54.3117i			2.25907i
$579$			16.8383i			0.699775i
$580$			77.1476i			3.20338i
$581$		0			0
$582$	7.94003			0.329125
$583$			18.6279i			0.771489i
$584$	−18.7126			−0.774335
$585$	11.1177	+	1.79352i	0.459660	+	0.0741530i
$586$	40.0625			1.65497
$587$		−	8.69744i		−	0.358982i	−0.983760	−	0.179491i	$-0.942555\pi$
$587$		−	8.69744i		−	0.358982i	0.983760	−	0.179491i	$-0.0574450\pi$
$588$		0			0
$589$	22.3087			0.919215
$590$		−	36.6461i		−	1.50870i
$591$			18.3859i			0.756296i
$592$		−	47.6356i		−	1.95781i
$593$		−	18.0299i		−	0.740399i	−0.928952	−	0.370200i	$-0.879289\pi$
$593$		−	18.0299i		−	0.740399i	0.928952	−	0.370200i	$-0.120711\pi$
$594$	−33.8989			−1.39089
$595$		0			0
$596$		−	13.0401i		−	0.534143i
$597$	−0.431939			−0.0176781
$598$	−42.9964	−	6.93623i	−1.75825	−	0.283643i
$599$	0.0141162			0.000576774			0.000288387	−	1.00000i	$-0.499908\pi$
$599$	0.0141162			0.000576774			0.000288387		1.00000i	$0.499908\pi$
$600$			16.2135i			0.661914i
$601$	13.7533			0.561007			0.280504	−	0.959853i	$-0.409499\pi$
$601$	13.7533			0.561007			0.280504	+	0.959853i	$0.409499\pi$
$602$		0			0
$603$		−	1.92553i		−	0.0784136i
$604$		−	111.207i		−	4.52493i
$605$		−	10.7215i		−	0.435891i
$606$			33.7564i			1.37126i
$607$	23.7484			0.963918			0.481959	−	0.876194i	$-0.339925\pi$
$607$	23.7484			0.963918			0.481959	+	0.876194i	$0.339925\pi$
$608$	−113.800			−4.61519
$609$		0			0
$610$	41.1129			1.66461
$611$	−31.6963	−	5.11328i	−1.28229	−	0.206861i
$612$	55.3157			2.23600
$613$		−	2.18410i		−	0.0882149i	−0.999027	−	0.0441075i	$-0.985956\pi$
$613$		−	2.18410i		−	0.0882149i	0.999027	−	0.0441075i	$-0.0140444\pi$
$614$	−51.5910			−2.08204
$615$	5.32625			0.214775
$616$		0			0
$617$			14.6673i			0.590485i	0.955422	+	0.295243i	$0.0954005\pi$
$617$			14.6673i			0.590485i	−0.955422	+	0.295243i	$0.904600\pi$
$618$		−	37.3046i		−	1.50061i
$619$			21.2649i			0.854708i	0.904084	+	0.427354i	$0.140554\pi$
$619$			21.2649i			0.854708i	−0.904084	+	0.427354i	$0.859446\pi$
$620$	44.5287			1.78832
$621$	−23.8169			−0.955740
$622$		−	15.5997i		−	0.625490i
$623$		0			0
$624$	−9.97880	+	61.8567i	−0.399472	+	2.47625i
$625$	−15.4425			−0.617702
$626$			10.7819i			0.430931i
$627$	13.6909			0.546760
$628$	−60.4560			−2.41246
$629$		−	19.2388i		−	0.767099i
$630$		0			0
$631$		−	34.4910i		−	1.37307i	−0.727099	−	0.686533i	$-0.759132\pi$
$631$		−	34.4910i		−	1.37307i	0.727099	−	0.686533i	$-0.240868\pi$
$632$		−	36.2289i		−	1.44111i
$633$	−6.99649			−0.278085
$634$	10.5025			0.417108
$635$		−	28.5199i		−	1.13178i
$636$	51.2717			2.03305
$637$		0			0
$638$	−47.1902			−1.86828
$639$		−	8.50737i		−	0.336546i
$640$	−72.8199			−2.87846
$641$	−21.7944			−0.860829			−0.430414	−	0.902631i	$-0.641633\pi$
$641$	−21.7944			−0.860829			−0.430414	+	0.902631i	$0.641633\pi$
$642$			13.5190i			0.533551i
$643$			5.81898i			0.229478i	0.993396	+	0.114739i	$0.0366032\pi$
$643$			5.81898i			0.229478i	−0.993396	+	0.114739i	$0.963397\pi$
$644$		0			0
$645$		−	4.72485i		−	0.186041i
$646$	−85.4957			−3.36379
$647$	33.0708			1.30015			0.650074	−	0.759871i	$-0.274738\pi$
$647$	33.0708			1.30015			0.650074	+	0.759871i	$0.274738\pi$
$648$			11.7894i			0.463130i
$649$	16.4191			0.644505
$650$	14.3638	+	2.31718i	0.563394	+	0.0908873i
$651$		0			0
$652$			103.923i			4.06995i
$653$	−1.73993			−0.0680886			−0.0340443	−	0.999420i	$-0.510839\pi$
$653$	−1.73993			−0.0680886			−0.0340443	+	0.999420i	$0.510839\pi$
$654$	6.35706			0.248581
$655$			1.78524i			0.0697551i
$656$		−	36.8986i		−	1.44065i
$657$			3.27596i			0.127807i
$658$		0			0
$659$	27.9823			1.09003			0.545017	−	0.838425i	$-0.316523\pi$
$659$	27.9823			1.09003			0.545017	+	0.838425i	$0.316523\pi$
$660$	27.3273			1.06371
$661$			20.8334i			0.810325i	0.914245	+	0.405163i	$0.132785\pi$
$661$			20.8334i			0.810325i	−0.914245	+	0.405163i	$0.867215\pi$
$662$	16.7497			0.650995
$663$	−4.03017	+	24.9823i	−0.156519	+	0.970232i
$664$	−23.6804			−0.918976
$665$		0			0
$666$	−14.4146			−0.558555
$667$	−33.1552			−1.28378
$668$		−	118.993i		−	4.60397i
$669$		−	8.44565i		−	0.326528i
$670$			5.94034i			0.229496i
$671$			18.4204i			0.711112i
$672$		0			0
$673$	−7.06203			−0.272221			−0.136111	−	0.990694i	$-0.543460\pi$
$673$	−7.06203			−0.272221			−0.136111	+	0.990694i	$0.543460\pi$
$674$			56.8784i			2.19088i
$675$	7.95650			0.306246
$676$	67.5750	+	22.3851i	2.59904	+	0.860966i
$677$	5.22990			0.201001			0.100501	−	0.994937i	$-0.467956\pi$
$677$	5.22990			0.201001			0.100501	+	0.994937i	$0.467956\pi$
$678$			13.1755i			0.506001i
$679$		0			0
$680$	−108.323			−4.15399
$681$			18.1385i			0.695068i
$682$			27.2376i			1.04298i
$683$		−	27.9416i		−	1.06916i	−0.845119	−	0.534579i	$-0.820470\pi$
$683$		−	27.9416i		−	1.06916i	0.845119	−	0.534579i	$-0.179530\pi$
$684$			46.9204i			1.79405i
$685$	22.9738			0.877785
$686$		0			0
$687$			29.5498i			1.12740i
$688$	−32.7324			−1.24791
$689$	4.65126	−	28.8323i	0.177199	−	1.09842i
$690$	26.2123			0.997884
$691$		−	25.4515i		−	0.968220i	−0.875007	−	0.484110i	$-0.839143\pi$
$691$		−	25.4515i		−	0.968220i	0.875007	−	0.484110i	$-0.160857\pi$
$692$	15.8965			0.604293
$693$		0			0
$694$			48.5344i			1.84234i
$695$		−	9.85235i		−	0.373721i
$696$			82.4472i			3.12515i
$697$		−	14.9024i		−	0.564468i
$698$	2.74931			0.104063
$699$	−18.8888			−0.714441
$700$		0			0
$701$	−17.9541			−0.678117			−0.339058	−	0.940765i	$-0.610108\pi$
$701$	−17.9541			−0.678117			−0.339058	+	0.940765i	$0.610108\pi$
$702$	52.4687	+	8.46432i	1.98030	+	0.319465i
$703$	16.3189			0.615478
$704$		−	69.7976i		−	2.63060i
$705$	19.3233			0.727757
$706$	−34.5109			−1.29883
$707$		0			0
$708$		−	45.1921i		−	1.69842i
$709$			29.2191i			1.09734i	0.836037	+	0.548672i	$0.184867\pi$
$709$			29.2191i			1.09734i	−0.836037	+	0.548672i	$0.815133\pi$
$710$			26.2456i			0.984980i
$711$	−6.34246			−0.237861
$712$	−99.1152			−3.71450
$713$			19.1368i			0.716679i
$714$		0			0
$715$	2.47907	−	15.3673i	0.0927120	−	0.574704i
$716$	105.959			3.95989
$717$			19.9407i			0.744698i
$718$	31.3749			1.17090
$719$	−38.7200			−1.44401			−0.722005	−	0.691887i	$-0.756779\pi$
$719$	−38.7200			−1.44401			−0.722005	+	0.691887i	$0.756779\pi$
$720$			46.9545i			1.74989i
$721$		0			0
$722$		−	20.5702i		−	0.765544i
$723$			11.6901i			0.434760i
$724$	54.6500			2.03105
$725$	11.0761			0.411358
$726$		−	18.0509i		−	0.669931i
$727$	27.9441			1.03639			0.518194	−	0.855263i	$-0.326604\pi$
$727$	27.9441			1.03639			0.518194	+	0.855263i	$0.326604\pi$
$728$		0			0
$729$	20.7594			0.768868
$730$		−	10.1065i		−	0.374057i
$731$	−13.2197			−0.488949
$732$	50.7006			1.87395
$733$			43.7436i			1.61571i	0.589382	+	0.807854i	$0.299371\pi$
$733$			43.7436i			1.61571i	−0.589382	+	0.807854i	$0.700629\pi$
$734$		−	79.0497i		−	2.91778i
$735$		0			0
$736$		−	97.6195i		−	3.59830i
$737$	−2.66154			−0.0980389
$738$	−11.1656			−0.411011
$739$		−	7.24471i		−	0.266501i	−0.991082	−	0.133251i	$-0.957459\pi$
$739$		−	7.24471i		−	0.266501i	0.991082	−	0.133251i	$-0.0425415\pi$
$740$	32.5728			1.19740
$741$	−21.1907	−	3.41851i	−0.778461	−	0.125582i
$742$		0			0
$743$			33.9142i			1.24419i	0.782941	+	0.622096i	$0.213719\pi$
$743$			33.9142i			1.24419i	−0.782941	+	0.622096i	$0.786281\pi$
$744$	47.5875			1.74464
$745$	4.47049			0.163786
$746$			64.2232i			2.35138i
$747$			4.14563i			0.151681i
$748$		−	76.4593i		−	2.79563i
$749$		0			0
$750$	−38.4232			−1.40302
$751$	−38.4973			−1.40479			−0.702393	−	0.711789i	$-0.747885\pi$
$751$	−38.4973			−1.40479			−0.702393	+	0.711789i	$0.747885\pi$
$752$		−	133.866i		−	4.88159i
$753$	24.0650			0.876978
$754$	73.0411	+	11.7831i	2.66000	+	0.429114i
$755$	38.1245			1.38749
$756$		0			0
$757$	8.18792			0.297595			0.148797	−	0.988868i	$-0.452460\pi$
$757$	8.18792			0.297595			0.148797	+	0.988868i	$0.452460\pi$
$758$	−102.823			−3.73471
$759$			11.7443i			0.426289i
$760$		−	91.8826i		−	3.33293i
$761$		−	10.0596i		−	0.364660i	−0.983237	−	0.182330i	$-0.941636\pi$
$761$		−	10.0596i		−	0.364660i	0.983237	−	0.182330i	$-0.0583639\pi$
$762$		−	48.0166i		−	1.73946i
$763$		0			0
$764$	−29.5962			−1.07075
$765$			18.9637i			0.685633i
$766$	−69.2254			−2.50121
$767$	−25.4135	−	4.09973i	−0.917627	−	0.148033i
$768$	−52.4339			−1.89205
$769$		−	2.53594i		−	0.0914482i	−0.998954	−	0.0457241i	$-0.985440\pi$
$769$		−	2.53594i		−	0.0914482i	0.998954	−	0.0457241i	$-0.0145595\pi$
$770$		0			0
$771$	32.6320			1.17521
$772$			79.7648i			2.87080i
$773$		−	29.2195i		−	1.05095i	−0.850808	−	0.525477i	$-0.823887\pi$
$773$		−	29.2195i		−	1.05095i	0.850808	−	0.525477i	$-0.176113\pi$
$774$			9.90486i			0.356023i
$775$		−	6.39302i		−	0.229644i
$776$	23.8751			0.857066
$777$		0			0
$778$			3.60612i			0.129286i
$779$	12.6406			0.452898
$780$	−42.2971	−	6.82342i	−1.51448	−	0.244318i
$781$	−11.7592			−0.420777
$782$		−	73.3397i		−	2.62262i
$783$	40.4595			1.44591
$784$		0			0
$785$		−	20.7259i		−	0.739739i
$786$			3.00566i			0.107208i
$787$		−	0.149447i		−	0.00532721i	−0.999996	−	0.00266360i	$-0.999152\pi$
$787$		−	0.149447i		−	0.00532721i	0.999996	−	0.00266360i	$-0.000847853\pi$
$788$			87.0961i			3.10267i
$789$	−7.06134			−0.251390
$790$	19.5668			0.696155
$791$		0			0
$792$	−36.3636			−1.29212
$793$	4.59945	−	28.5111i	0.163331	−	1.01246i
$794$	−102.124			−3.62425
$795$			17.5773i			0.623402i
$796$	−2.04614			−0.0725236
$797$	−29.7429			−1.05355			−0.526773	−	0.850006i	$-0.676598\pi$
$797$	−29.7429			−1.05355			−0.526773	+	0.850006i	$0.676598\pi$
$798$		0			0
$799$		−	54.0649i		−	1.91268i
$800$			32.6117i			1.15300i
$801$			17.3517i			0.613093i
$802$	−74.6938			−2.63753
$803$	4.52814			0.159795
$804$			7.32565i			0.258356i
$805$		0			0
$806$	6.80105	−	42.1584i	0.239557	−	1.48497i
$807$	5.59624			0.196997
$808$			101.503i			3.57087i
$809$	34.8902			1.22667			0.613336	−	0.789822i	$-0.289827\pi$
$809$	34.8902			1.22667			0.613336	+	0.789822i	$0.289827\pi$
$810$	−6.36729			−0.223724
$811$		−	31.6196i		−	1.11031i	−0.831745	−	0.555157i	$-0.812658\pi$
$811$		−	31.6196i		−	1.11031i	0.831745	−	0.555157i	$-0.187342\pi$
$812$		0			0
$813$			0.345507i			0.0121174i
$814$			19.9244i			0.698350i
$815$	−35.6276			−1.24798
$816$	−105.510			−3.69359
$817$		−	11.2134i		−	0.392306i
$818$	−65.3668			−2.28550
$819$		0			0
$820$	25.2310			0.881105
$821$		−	5.70873i		−	0.199236i	−0.995026	−	0.0996181i	$-0.968238\pi$
$821$		−	5.70873i		−	0.199236i	0.995026	−	0.0996181i	$-0.0317621\pi$
$822$	38.6791			1.34909
$823$	−0.00866314			−0.000301978			−0.000150989	−	1.00000i	$-0.500048\pi$
$823$	−0.00866314			−0.000301978			−0.000150989		1.00000i	$0.500048\pi$
$824$		−	112.172i		−	3.90770i
$825$		−	3.92340i		−	0.136595i
$826$		0			0
$827$			52.4236i			1.82295i	0.411359	+	0.911473i	$0.365054\pi$
$827$			52.4236i			1.82295i	−0.411359	+	0.911473i	$0.634946\pi$
$828$	−40.2491			−1.39875
$829$	17.4723			0.606839			0.303419	−	0.952857i	$-0.401872\pi$
$829$	17.4723			0.606839			0.303419	+	0.952857i	$0.401872\pi$
$830$		−	12.7895i		−	0.443929i
$831$	10.0879			0.349947
$832$	−17.4280	+	108.033i	−0.604206	+	3.74536i
$833$		0			0
$834$		−	16.5876i		−	0.574381i
$835$	40.7939			1.41173
$836$	64.8551			2.24306
$837$		−	23.3528i		−	0.807189i
$838$		−	45.0394i		−	1.55586i
$839$		−	19.7237i		−	0.680939i	−0.940256	−	0.340470i	$-0.889414\pi$
$839$		−	19.7237i		−	0.680939i	0.940256	−	0.340470i	$-0.110586\pi$
$840$		0			0
$841$	27.3232			0.942179
$842$	65.5817			2.26010
$843$		−	28.5534i		−	0.983431i
$844$	−33.1431			−1.14083
$845$	−7.67421	+	23.1665i	−0.264001	+	0.796951i
$846$	−40.5081			−1.39270
$847$		0			0
$848$	121.770			4.18161
$849$	−14.1632			−0.486080
$850$			24.5006i			0.840362i
$851$			13.9986i			0.479866i
$852$			32.3661i			1.10885i
$853$			1.74842i			0.0598648i	0.999552	+	0.0299324i	$0.00952921\pi$
$853$			1.74842i			0.0598648i	−0.999552	+	0.0299324i	$0.990471\pi$
$854$		0			0
$855$	−16.0856			−0.550114
$856$			40.6506i			1.38941i
$857$	−3.35601			−0.114639			−0.0573196	−	0.998356i	$-0.518255\pi$
$857$	−3.35601			−0.114639			−0.0573196	+	0.998356i	$0.518255\pi$
$858$	4.17380	−	25.8726i	0.142491	−	0.883277i
$859$	−29.8216			−1.01750			−0.508750	−	0.860914i	$-0.669892\pi$
$859$	−29.8216			−1.01750			−0.508750	+	0.860914i	$0.669892\pi$
$860$		−	22.3821i		−	0.763224i
$861$		0			0
$862$	62.0387			2.11305
$863$		−	0.392880i		−	0.0133738i	−0.999978	−	0.00668690i	$-0.997871\pi$
$863$		−	0.392880i		−	0.0133738i	0.999978	−	0.00668690i	$-0.00212852\pi$
$864$			119.126i			4.05274i
$865$			5.44973i			0.185296i
$866$			46.7376i			1.58821i
$867$	−22.9616			−0.779817
$868$		0			0
$869$			8.76678i			0.297393i
$870$	−44.5287			−1.50966
$871$	4.11953	+	0.664567i	0.139585	+	0.0225180i
$872$	19.1152			0.647323
$873$		−	4.17973i		−	0.141462i
$874$	62.2089			2.10425
$875$		0			0
$876$		−	12.4633i		−	0.421097i
$877$		−	51.9082i		−	1.75282i	−0.481568	−	0.876409i	$-0.659933\pi$
$877$		−	51.9082i		−	1.75282i	0.481568	−	0.876409i	$-0.340067\pi$
$878$			96.7942i			3.26665i
$879$			16.9374i			0.571285i
$880$	64.9022			2.18785
$881$	10.0487			0.338548			0.169274	−	0.985569i	$-0.445858\pi$
$881$	10.0487			0.338548			0.169274	+	0.985569i	$0.445858\pi$
$882$		0			0
$883$	−57.1835			−1.92438			−0.962189	−	0.272383i	$-0.912188\pi$
$883$	−57.1835			−1.92438			−0.962189	+	0.272383i	$0.912188\pi$
$884$	−19.0914	+	118.344i	−0.642112	+	3.98033i
$885$	15.4930			0.520793
$886$		−	44.4669i		−	1.49390i
$887$	−0.707920			−0.0237696			−0.0118848	−	0.999929i	$-0.503783\pi$
$887$	−0.707920			−0.0237696			−0.0118848	+	0.999929i	$0.503783\pi$
$888$	34.8104			1.16816
$889$		0			0
$890$		−	53.5309i		−	1.79436i
$891$		−	2.85283i		−	0.0955733i
$892$		−	40.0079i		−	1.33956i
$893$	45.8595			1.53463
$894$	7.52659			0.251727
$895$			36.3257i			1.21423i
$896$		0			0
$897$	2.93246	−	18.1778i	0.0979119	−	0.606938i
$898$	41.4154			1.38205
$899$		−	32.5091i		−	1.08424i
$900$	13.4460			0.448200
$901$	49.1798			1.63842
$902$			15.4335i			0.513879i
$903$		0			0
$904$			39.6177i			1.31766i
$905$			18.7355i			0.622788i
$906$	64.1871			2.13247
$907$	−44.3793			−1.47359			−0.736795	−	0.676116i	$-0.763662\pi$
$907$	−44.3793			−1.47359			−0.736795	+	0.676116i	$0.763662\pi$
$908$			85.9239i			2.85148i
$909$	17.7698			0.589386
$910$		0			0
$911$	28.9184			0.958109			0.479055	−	0.877785i	$-0.340980\pi$
$911$	28.9184			0.958109			0.479055	+	0.877785i	$0.340980\pi$
$912$		−	89.4969i		−	2.96354i
$913$	5.73025			0.189643
$914$	−107.996			−3.57220
$915$			17.3815i			0.574614i
$916$			139.981i			4.62509i
$917$		0			0
$918$			89.4969i			2.95384i
$919$	25.7611			0.849781			0.424891	−	0.905245i	$-0.360313\pi$
$919$	25.7611			0.849781			0.424891	+	0.905245i	$0.360313\pi$
$920$	78.8184			2.59857
$921$		−	21.8113i		−	0.718708i
$922$	51.9907			1.71222
$923$	18.2009	+	2.93619i	0.599089	+	0.0966458i
$924$		0			0
$925$		−	4.67651i		−	0.153763i
$926$	−6.80105			−0.223496
$927$	−19.6376			−0.644983
$928$			165.833i			5.44374i
$929$		−	54.9117i		−	1.80159i	−0.434240	−	0.900797i	$-0.642983\pi$
$929$		−	54.9117i		−	1.80159i	0.434240	−	0.900797i	$-0.357017\pi$
$930$			25.7014i			0.842783i
$931$		0			0
$932$	−89.4784			−2.93096
$933$	6.59514			0.215915
$934$		−	40.6812i		−	1.33113i
$935$	26.2123			0.857233
$936$	56.2835	+	9.07973i	1.83968	+	0.296780i
$937$	−23.1364			−0.755835			−0.377917	−	0.925839i	$-0.623360\pi$
$937$	−23.1364			−0.755835			−0.377917	+	0.925839i	$0.623360\pi$
$938$		0			0
$939$	−4.55830			−0.148755
$940$	91.5365			2.98559
$941$			0.349519i			0.0113940i	0.999984	+	0.00569699i	$0.00181342\pi$
$941$			0.349519i			0.0113940i	−0.999984	+	0.00569699i	$0.998187\pi$
$942$		−	34.8945i		−	1.13692i
$943$			10.8434i			0.353108i
$944$		−	107.331i		−	3.49333i
$945$		0			0
$946$	13.6909			0.445128
$947$		−	17.5380i		−	0.569909i	−0.958541	−	0.284954i	$-0.908022\pi$
$947$		−	17.5380i		−	0.569909i	0.958541	−	0.284954i	$-0.0919784\pi$
$948$	24.1298			0.783699
$949$	−7.00866	−	1.13065i	−0.227511	−	0.0367023i
$950$	−20.7821			−0.674260
$951$			4.44019i			0.143983i
$952$		0			0
$953$	−47.8790			−1.55095			−0.775477	−	0.631376i	$-0.782491\pi$
$953$	−47.8790			−1.55095			−0.775477	+	0.631376i	$0.782491\pi$
$954$		−	36.8479i		−	1.19299i
$955$		−	10.1464i		−	0.328329i
$956$			94.4611i			3.05509i
$957$		−	19.9508i		−	0.644918i
$958$	−46.1527			−1.49112
$959$		0			0
$960$		−	65.8610i		−	2.12566i
$961$	12.2361			0.394714
$962$	4.97498	−	30.8390i	0.160400	−	0.994289i
$963$	7.11655			0.229328
$964$			55.3773i			1.78358i
$965$	−27.3455			−0.880282
$966$		0			0
$967$		−	12.4683i		−	0.400955i	−0.979698	−	0.200477i	$-0.935751\pi$
$967$		−	12.4683i		−	0.400955i	0.979698	−	0.200477i	$-0.0642493\pi$
$968$		−	54.2777i		−	1.74455i
$969$		−	36.1454i		−	1.16116i
$970$			12.8946i			0.414022i
$971$	39.2379			1.25920			0.629602	−	0.776918i	$-0.283218\pi$
$971$	39.2379			1.25920			0.629602	+	0.776918i	$0.283218\pi$
$972$	80.7105			2.58879
$973$		0			0
$974$	12.1546			0.389458
$975$	−0.979645	+	6.07263i	−0.0313737	+	0.194480i
$976$	120.414			3.85435
$977$			24.4082i			0.780889i	0.920627	+	0.390444i	$0.127679\pi$
$977$			24.4082i			0.780889i	−0.920627	+	0.390444i	$0.872321\pi$
$978$	−59.9832			−1.91805
$979$	23.9842			0.766538
$980$		0			0
$981$		−	3.34643i		−	0.106843i
$982$		−	46.4311i		−	1.48167i
$983$			54.8232i			1.74859i	0.485395	+	0.874295i	$0.338676\pi$
$983$			54.8232i			1.74859i	−0.485395	+	0.874295i	$0.661324\pi$
$984$	26.9642			0.859587
$985$	−29.8589			−0.951382
$986$			124.587i			3.96767i
$987$		0			0
$988$	−100.383	−	16.1939i	−3.19360	−	0.515195i
$989$	9.61902			0.305867
$990$		−	19.6395i		−	0.624185i
$991$	−38.1372			−1.21147			−0.605734	−	0.795667i	$-0.707121\pi$
$991$	−38.1372			−1.21147			−0.605734	+	0.795667i	$0.707121\pi$
$992$	95.7170			3.03902
$993$			7.08134i			0.224719i
$994$		0			0
$995$		−	0.701472i		−	0.0222382i
$996$		−	15.7720i		−	0.499755i
$997$	−53.0260			−1.67935			−0.839676	−	0.543088i	$-0.817255\pi$
$997$	−53.0260			−1.67935			−0.839676	+	0.543088i	$0.817255\pi$
$998$	112.105			3.54863
$999$		−	17.0826i		−	0.540469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.g.246.15	yes	16
7.2	even	3		637.2.r.g.116.16		32
7.3	odd	6		637.2.r.g.324.1		32
7.4	even	3		637.2.r.g.324.2		32
7.5	odd	6		637.2.r.g.116.15		32
7.6	odd	2	inner	637.2.c.g.246.16	yes	16
13.5	odd	4		8281.2.a.cs.1.15		16
13.8	odd	4		8281.2.a.cs.1.1		16
13.12	even	2	inner	637.2.c.g.246.1	✓	16
91.12	odd	6		637.2.r.g.116.1		32
91.25	even	6		637.2.r.g.324.16		32
91.34	even	4		8281.2.a.cs.1.2		16
91.38	odd	6		637.2.r.g.324.15		32
91.51	even	6		637.2.r.g.116.2		32
91.83	even	4		8281.2.a.cs.1.16		16
91.90	odd	2	inner	637.2.c.g.246.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.1	✓	16	13.12	even	2	inner
637.2.c.g.246.2	yes	16	91.90	odd	2	inner
637.2.c.g.246.15	yes	16	1.1	even	1	trivial
637.2.c.g.246.16	yes	16	7.6	odd	2	inner
637.2.r.g.116.1		32	91.12	odd	6
637.2.r.g.116.2		32	91.51	even	6
637.2.r.g.116.15		32	7.5	odd	6
637.2.r.g.116.16		32	7.2	even	3
637.2.r.g.324.1		32	7.3	odd	6
637.2.r.g.324.2		32	7.4	even	3
637.2.r.g.324.15		32	91.38	odd	6
637.2.r.g.324.16		32	91.25	even	6
8281.2.a.cs.1.1		16	13.8	odd	4
8281.2.a.cs.1.2		16	91.34	even	4
8281.2.a.cs.1.15		16	13.5	odd	4
8281.2.a.cs.1.16		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)

\(f(q)\)	\(=\)	\(q+2.73420i q^{2} -1.15595 q^{3} -5.47586 q^{4} -1.87727i q^{5} -3.16060i q^{6} -9.50370i q^{8} -1.66378 q^{9} +O(q^{10})\)	\(q+2.73420i q^{2} -1.15595 q^{3} -5.47586 q^{4} -1.87727i q^{5} -3.16060i q^{6} -9.50370i q^{8} -1.66378 q^{9} +5.13283 q^{10} +2.29974i q^{11} +6.32982 q^{12} +(0.574228 - 3.55953i) q^{13} +2.17003i q^{15} +15.0333 q^{16} +6.07156 q^{17} -4.54911i q^{18} +5.15008i q^{19} +10.2797i q^{20} -6.28794 q^{22} -4.41782 q^{23} +10.9858i q^{24} +1.47586 q^{25} +(9.73248 + 1.57006i) q^{26} +5.39110 q^{27} +7.50488 q^{29} -5.93330 q^{30} -4.33173i q^{31} +22.0967i q^{32} -2.65838i q^{33} +16.6009i q^{34} +9.11062 q^{36} -3.16867i q^{37} -14.0814 q^{38} +(-0.663779 + 4.11464i) q^{39} -17.8410 q^{40} -2.45446i q^{41} -2.17732 q^{43} -12.5930i q^{44} +3.12336i q^{45} -12.0792i q^{46} -8.90462i q^{47} -17.3778 q^{48} +4.03530i q^{50} -7.01842 q^{51} +(-3.14439 + 19.4915i) q^{52} +8.10002 q^{53} +14.7403i q^{54} +4.31722 q^{55} -5.95323i q^{57} +20.5199i q^{58} -7.13955i q^{59} -11.8828i q^{60} +8.00979 q^{61} +11.8438 q^{62} -30.3503 q^{64} +(-6.68220 - 1.07798i) q^{65} +7.26855 q^{66} +1.15732i q^{67} -33.2470 q^{68} +5.10678 q^{69} +5.11328i q^{71} +15.8121i q^{72} -1.96898i q^{73} +8.66378 q^{74} -1.70602 q^{75} -28.2011i q^{76} +(-11.2503 - 1.81491i) q^{78} +3.81208 q^{79} -28.2216i q^{80} -1.24050 q^{81} +6.71098 q^{82} -2.49170i q^{83} -11.3980i q^{85} -5.95323i q^{86} -8.67527 q^{87} +21.8560 q^{88} -10.4291i q^{89} -8.53990 q^{90} +24.1914 q^{92} +5.00726i q^{93} +24.3470 q^{94} +9.66808 q^{95} -25.5427i q^{96} +2.51219i q^{97} -3.82625i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more