LMFDB - Embedded newform 637.2.c.g.246.10

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			246.10
Root			$-1.41421 + 0.680196i$ of defining polynomial
Character	$\chi$	$=$	637.246
Dual form			637.2.c.g.246.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.680196i q^{2} +2.33413 q^{3} +1.53733 q^{4} +3.24613i q^{5} +1.58766i q^{6} +2.40608i q^{8} +2.44815 q^{9} +O(q^{10})$	\(q+0.680196i q^{2} +2.33413 q^{3} +1.53733 q^{4} +3.24613i q^{5} +1.58766i q^{6} +2.40608i q^{8} +2.44815 q^{9} -2.20800 q^{10} -5.33157i q^{11} +3.58833 q^{12} +(1.47728 - 3.28902i) q^{13} +7.57687i q^{15} +1.43806 q^{16} +2.66842 q^{17} +1.66522i q^{18} +0.696519i q^{19} +4.99038i q^{20} +3.62652 q^{22} -8.96087 q^{23} +5.61610i q^{24} -5.53733 q^{25} +(2.23718 + 1.00484i) q^{26} -1.28809 q^{27} -5.28644 q^{29} -5.15376 q^{30} +5.45951i q^{31} +5.79032i q^{32} -12.4446i q^{33} +1.81505i q^{34} +3.76362 q^{36} -6.69197i q^{37} -0.473769 q^{38} +(3.44815 - 7.67699i) q^{39} -7.81044 q^{40} +2.21339i q^{41} +2.39014 q^{43} -8.19640i q^{44} +7.94700i q^{45} -6.09515i q^{46} +5.79573i q^{47} +3.35661 q^{48} -3.76647i q^{50} +6.22843 q^{51} +(2.27106 - 5.05632i) q^{52} -4.71570 q^{53} -0.876153i q^{54} +17.3070 q^{55} +1.62576i q^{57} -3.59581i q^{58} -2.98070i q^{59} +11.6482i q^{60} -2.19465 q^{61} -3.71354 q^{62} -1.06244 q^{64} +(10.6766 + 4.79542i) q^{65} +8.46475 q^{66} -8.70594i q^{67} +4.10225 q^{68} -20.9158 q^{69} -8.56190i q^{71} +5.89045i q^{72} -5.88152i q^{73} +4.55185 q^{74} -12.9248 q^{75} +1.07078i q^{76} +(5.22186 + 2.34542i) q^{78} +0.910817 q^{79} +4.66812i q^{80} -10.3510 q^{81} -1.50554 q^{82} +11.7481i q^{83} +8.66202i q^{85} +1.62576i q^{86} -12.3392 q^{87} +12.8282 q^{88} -0.986019i q^{89} -5.40552 q^{90} -13.7758 q^{92} +12.7432i q^{93} -3.94224 q^{94} -2.26099 q^{95} +13.5154i q^{96} -15.3454i q^{97} -13.0525i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$			0.680196i			0.480971i	0.970653	+	0.240486i	$0.0773067\pi$
$2$			0.680196i			0.480971i	−0.970653	+	0.240486i	$0.922693\pi$
$3$	2.33413			1.34761			0.673804	−	0.738910i	$-0.264659\pi$
$3$	2.33413			1.34761			0.673804	+	0.738910i	$0.264659\pi$
$4$	1.53733			0.768667
$5$			3.24613i			1.45171i	0.687847	+	0.725856i	$0.258556\pi$
$5$			3.24613i			1.45171i	−0.687847	+	0.725856i	$0.741444\pi$
$6$			1.58766i			0.648161i
$7$		0			0
$7$		0			0
$8$			2.40608i			0.850678i
$9$	2.44815			0.816050
$10$	−2.20800			−0.698232
$11$		−	5.33157i		−	1.60753i	−0.594947	−	0.803765i	$-0.702827\pi$
$11$		−	5.33157i		−	1.60753i	0.594947	−	0.803765i	$-0.297173\pi$
$12$	3.58833			1.03586
$13$	1.47728	−	3.28902i	0.409723	−	0.912210i
$13$	1.47728	−	3.28902i	0.409723	−	0.912210i
$14$		0			0
$15$			7.57687i			1.95634i
$16$	1.43806			0.359515
$17$	2.66842			0.647186			0.323593	−	0.946196i	$-0.395109\pi$
$17$	2.66842			0.647186			0.323593	+	0.946196i	$0.395109\pi$
$18$			1.66522i			0.392497i
$19$			0.696519i			0.159792i	0.996803	+	0.0798962i	$0.0254589\pi$
$19$			0.696519i			0.159792i	−0.996803	+	0.0798962i	$0.974541\pi$
$20$			4.99038i			1.11588i
$21$		0			0
$22$	3.62652			0.773176
$23$	−8.96087			−1.86847			−0.934236	−	0.356656i	$-0.883917\pi$
$23$	−8.96087			−1.86847			−0.934236	+	0.356656i	$0.883917\pi$
$24$			5.61610i			1.14638i
$25$	−5.53733			−1.10747
$26$	2.23718	+	1.00484i	0.438747	+	0.197065i
$27$	−1.28809			−0.247893
$28$		0			0
$29$	−5.28644			−0.981667			−0.490833	−	0.871253i	$-0.663308\pi$
$29$	−5.28644			−0.981667			−0.490833	+	0.871253i	$0.663308\pi$
$30$	−5.15376			−0.940943
$31$			5.45951i			0.980557i	0.871566	+	0.490279i	$0.163105\pi$
$31$			5.45951i			0.980557i	−0.871566	+	0.490279i	$0.836895\pi$
$32$			5.79032i			1.02359i
$33$		−	12.4446i		−	2.16632i
$34$			1.81505i			0.311278i
$35$		0			0
$36$	3.76362			0.627270
$37$		−	6.69197i		−	1.10015i	−0.835114	−	0.550076i	$-0.814599\pi$
$37$		−	6.69197i		−	1.10015i	0.835114	−	0.550076i	$-0.185401\pi$
$38$	−0.473769			−0.0768555
$39$	3.44815	−	7.67699i	0.552146	−	1.22930i
$40$	−7.81044			−1.23494
$41$			2.21339i			0.345673i	0.984951	+	0.172836i	$0.0552932\pi$
$41$			2.21339i			0.345673i	−0.984951	+	0.172836i	$0.944707\pi$
$42$		0			0
$43$	2.39014			0.364493			0.182246	−	0.983253i	$-0.441663\pi$
$43$	2.39014			0.364493			0.182246	+	0.983253i	$0.441663\pi$
$44$		−	8.19640i		−	1.23565i
$45$			7.94700i			1.18467i
$46$		−	6.09515i		−	0.898681i
$47$			5.79573i			0.845395i	0.906271	+	0.422697i	$0.138917\pi$
$47$			5.79573i			0.845395i	−0.906271	+	0.422697i	$0.861083\pi$
$48$	3.35661			0.484485
$49$		0			0
$50$		−	3.76647i		−	0.532660i
$51$	6.22843			0.872154
$52$	2.27106	−	5.05632i	0.314940	−	0.701185i
$53$	−4.71570			−0.647751			−0.323876	−	0.946100i	$-0.604986\pi$
$53$	−4.71570			−0.647751			−0.323876	+	0.946100i	$0.604986\pi$
$54$		−	0.876153i		−	0.119229i
$55$	17.3070			2.33367
$56$		0			0
$57$			1.62576i			0.215338i
$58$		−	3.59581i		−	0.472154i
$59$		−	2.98070i		−	0.388054i	−0.980996	−	0.194027i	$-0.937845\pi$
$59$		−	2.98070i		−	0.388054i	0.980996	−	0.194027i	$-0.0621550\pi$
$60$			11.6482i			1.50377i
$61$	−2.19465			−0.280996			−0.140498	−	0.990081i	$-0.544870\pi$
$61$	−2.19465			−0.280996			−0.140498	+	0.990081i	$0.544870\pi$
$62$	−3.71354			−0.471620
$63$		0			0
$64$	−1.06244			−0.132805
$65$	10.6766	+	4.79542i	1.32427	+	0.594799i
$66$	8.46475			1.04194
$67$		−	8.70594i		−	1.06360i	−0.846870	−	0.531800i	$-0.821516\pi$
$67$		−	8.70594i		−	1.06360i	0.846870	−	0.531800i	$-0.178484\pi$
$68$	4.10225			0.497470
$69$	−20.9158			−2.51797
$70$		0			0
$71$		−	8.56190i		−	1.01611i	−0.861325	−	0.508055i	$-0.830365\pi$
$71$		−	8.56190i		−	1.01611i	0.861325	−	0.508055i	$-0.169635\pi$
$72$			5.89045i			0.694196i
$73$		−	5.88152i		−	0.688380i	−0.938900	−	0.344190i	$-0.888154\pi$
$73$		−	5.88152i		−	0.688380i	0.938900	−	0.344190i	$-0.111846\pi$
$74$	4.55185			0.529142
$75$	−12.9248			−1.49243
$76$			1.07078i			0.122827i
$77$		0			0
$78$	5.22186	+	2.34542i	0.591259	+	0.265566i
$79$	0.910817			0.102475			0.0512374	−	0.998687i	$-0.483683\pi$
$79$	0.910817			0.102475			0.0512374	+	0.998687i	$0.483683\pi$
$80$			4.66812i			0.521912i
$81$	−10.3510			−1.15011
$82$	−1.50554			−0.166259
$83$			11.7481i			1.28952i	0.764387	+	0.644758i	$0.223042\pi$
$83$			11.7481i			1.28952i	−0.764387	+	0.644758i	$0.776958\pi$
$84$		0			0
$85$			8.66202i			0.939528i
$86$			1.62576i			0.175311i
$87$	−12.3392			−1.32290
$88$	12.8282			1.36749
$89$		−	0.986019i		−	0.104518i	−0.998634	−	0.0522589i	$-0.983358\pi$
$89$		−	0.986019i		−	0.104518i	0.998634	−	0.0522589i	$-0.0166421\pi$
$90$	−5.40552			−0.569792
$91$		0			0
$92$	−13.7758			−1.43623
$93$			12.7432i			1.32141i
$94$	−3.94224			−0.406611
$95$	−2.26099			−0.231972
$96$			13.5154i			1.37940i
$97$		−	15.3454i		−	1.55809i	−0.626969	−	0.779044i	$-0.715705\pi$
$97$		−	15.3454i		−	1.55809i	0.626969	−	0.779044i	$-0.284295\pi$
$98$		0			0
$99$		−	13.0525i		−	1.31182i
$100$	−8.51273			−0.851273
$101$	−3.90927			−0.388987			−0.194493	−	0.980904i	$-0.562306\pi$
$101$	−3.90927			−0.388987			−0.194493	+	0.980904i	$0.562306\pi$
$102$			4.23655i			0.419481i
$103$	18.5612			1.82889			0.914443	−	0.404715i	$-0.132629\pi$
$103$	18.5612			1.82889			0.914443	+	0.404715i	$0.132629\pi$
$104$	7.91365	+	3.55444i	0.775997	+	0.348542i
$105$		0			0
$106$		−	3.20760i		−	0.311550i
$107$	13.1058			1.26699			0.633495	−	0.773747i	$-0.281620\pi$
$107$	13.1058			1.26699			0.633495	+	0.773747i	$0.281620\pi$
$108$	−1.98022			−0.190547
$109$			15.3979i			1.47485i	0.675428	+	0.737426i	$0.263959\pi$
$109$			15.3979i			1.47485i	−0.675428	+	0.737426i	$0.736041\pi$
$110$			11.7721i			1.12243i
$111$		−	15.6199i		−	1.48258i
$112$		0			0
$113$	12.7346			1.19797			0.598985	−	0.800761i	$-0.295571\pi$
$113$	12.7346			1.19797			0.598985	+	0.800761i	$0.295571\pi$
$114$	−1.10584			−0.103571
$115$		−	29.0881i		−	2.71248i
$116$	−8.12701			−0.754574
$117$	3.61659	−	8.05201i	0.334354	−	0.744409i
$118$	2.02746			0.186643
$119$		0			0
$120$	−18.2306			−1.66422
$121$	−17.4257			−1.58415
$122$		−	1.49279i		−	0.135151i
$123$			5.16633i			0.465832i
$124$			8.39309i			0.753722i
$125$		−	1.74425i		−	0.156011i
$126$		0			0
$127$	10.2763			0.911878			0.455939	−	0.890011i	$-0.349303\pi$
$127$	10.2763			0.911878			0.455939	+	0.890011i	$0.349303\pi$
$128$			10.8580i			0.959719i
$129$	5.57889			0.491193
$130$	−3.26183	+	7.26217i	−0.286081	+	0.636934i
$131$	12.5813			1.09923			0.549615	−	0.835418i	$-0.314774\pi$
$131$	12.5813			1.09923			0.549615	+	0.835418i	$0.314774\pi$
$132$		−	19.1315i		−	1.66518i
$133$		0			0
$134$	5.92175			0.511561
$135$		−	4.18130i		−	0.359869i
$136$			6.42043i			0.550547i
$137$		−	1.72588i		−	0.147452i	−0.997279	−	0.0737261i	$-0.976511\pi$
$137$		−	1.72588i		−	0.147452i	0.997279	−	0.0737261i	$-0.0234891\pi$
$138$		−	14.2269i		−	1.21107i
$139$	−2.93311			−0.248783			−0.124391	−	0.992233i	$-0.539698\pi$
$139$	−2.93311			−0.248783			−0.124391	+	0.992233i	$0.539698\pi$
$140$		0			0
$141$			13.5280i			1.13926i
$142$	5.82377			0.488720
$143$	−17.5357	−	7.87620i	−1.46641	−	0.658641i
$144$	3.52058			0.293382
$145$		−	17.1604i		−	1.42510i
$146$	4.00059			0.331091
$147$		0			0
$148$		−	10.2878i		−	0.845650i
$149$			13.2399i			1.08465i	0.840168	+	0.542327i	$0.182457\pi$
$149$			13.2399i			1.08465i	−0.840168	+	0.542327i	$0.817543\pi$
$150$		−	8.79143i		−	0.717817i
$151$		−	9.25883i		−	0.753473i	−0.926320	−	0.376736i	$-0.877046\pi$
$151$		−	9.25883i		−	0.753473i	0.926320	−	0.376736i	$-0.122954\pi$
$152$	−1.67588			−0.135932
$153$	6.53268			0.528136
$154$		0			0
$155$	−17.7223			−1.42349
$156$	5.30095	−	11.8021i	0.424416	−	0.944924i
$157$	−1.65626			−0.132184			−0.0660922	−	0.997814i	$-0.521053\pi$
$157$	−1.65626			−0.132184			−0.0660922	+	0.997814i	$0.521053\pi$
$158$			0.619534i			0.0492875i
$159$	−11.0070			−0.872915
$160$	−18.7961			−1.48596
$161$		0			0
$162$		−	7.04072i		−	0.553171i
$163$			9.89957i			0.775394i	0.921787	+	0.387697i	$0.126729\pi$
$163$			9.89957i			0.775394i	−0.921787	+	0.387697i	$0.873271\pi$
$164$			3.40271i			0.265707i
$165$	40.3966			3.14487
$166$	−7.99098			−0.620220
$167$			6.10891i			0.472721i	0.971665	+	0.236361i	$0.0759547\pi$
$167$			6.10891i			0.472721i	−0.971665	+	0.236361i	$0.924045\pi$
$168$		0			0
$169$	−8.63531	−	9.71758i	−0.664255	−	0.747506i
$170$	−5.89187			−0.451886
$171$			1.70518i			0.130398i
$172$	3.67444			0.280173
$173$	−18.7212			−1.42334			−0.711672	−	0.702512i	$-0.752062\pi$
$173$	−18.7212			−1.42334			−0.711672	+	0.702512i	$0.752062\pi$
$174$		−	8.39309i		−	0.636278i
$175$		0			0
$176$		−	7.66712i		−	0.577931i
$177$		−	6.95734i		−	0.522945i
$178$	0.670687			0.0502701
$179$	9.93756			0.742768			0.371384	−	0.928479i	$-0.378883\pi$
$179$	9.93756			0.742768			0.371384	+	0.928479i	$0.378883\pi$
$180$			12.2172i			0.910615i
$181$	−22.6991			−1.68721			−0.843606	−	0.536962i	$-0.819572\pi$
$181$	−22.6991			−1.68721			−0.843606	+	0.536962i	$0.819572\pi$
$182$		0			0
$183$	−5.12259			−0.378673
$184$		−	21.5606i		−	1.58947i
$185$	21.7230			1.59710
$186$	−8.66787			−0.635559
$187$		−	14.2269i		−	1.04037i
$188$			8.90997i			0.649827i
$189$		0			0
$190$		−	1.53791i		−	0.111572i
$191$	5.42926			0.392848			0.196424	−	0.980519i	$-0.437067\pi$
$191$	5.42926			0.392848			0.196424	+	0.980519i	$0.437067\pi$
$192$	−2.47987			−0.178969
$193$			1.97005i			0.141807i	0.997483	+	0.0709037i	$0.0225883\pi$
$193$			1.97005i			0.141807i	−0.997483	+	0.0709037i	$0.977412\pi$
$194$	10.4379			0.749396
$195$	24.9205	+	11.1931i	1.78459	+	0.801557i
$196$		0			0
$197$		−	19.1476i		−	1.36421i	−0.731253	−	0.682107i	$-0.761064\pi$
$197$		−	19.1476i		−	1.36421i	0.731253	−	0.682107i	$-0.238936\pi$
$198$	8.87825			0.630950
$199$	0.194811			0.0138098			0.00690489	−	0.999976i	$-0.497802\pi$
$199$	0.194811			0.0138098			0.00690489	+	0.999976i	$0.497802\pi$
$200$		−	13.3233i		−	0.942097i
$201$		−	20.3208i		−	1.43332i
$202$		−	2.65907i		−	0.187091i
$203$		0			0
$204$	9.57516			0.670396
$205$	−7.18493			−0.501817
$206$			12.6252i			0.879642i
$207$	−21.9376			−1.52477
$208$	2.12441	−	4.72981i	0.147301	−	0.327953i
$209$	3.71354			0.256871
$210$		0			0
$211$	12.2618			0.844139			0.422070	−	0.906563i	$-0.361304\pi$
$211$	12.2618			0.844139			0.422070	+	0.906563i	$0.361304\pi$
$212$	−7.24960			−0.497905
$213$		−	19.9846i		−	1.36932i
$214$			8.91454i			0.609386i
$215$			7.75869i			0.529138i
$216$		−	3.09925i		−	0.210877i
$217$		0			0
$218$	−10.4736			−0.709362
$219$		−	13.7282i		−	0.927667i
$220$	26.6066			1.79381
$221$	3.94199	−	8.77648i	0.265167	−	0.590370i
$222$	10.6246			0.713076
$223$			27.1733i			1.81966i	0.414981	+	0.909830i	$0.363788\pi$
$223$			27.1733i			1.81966i	−0.414981	+	0.909830i	$0.636212\pi$
$224$		0			0
$225$	−13.5562			−0.903748
$226$			8.66202i			0.576189i
$227$		−	7.21285i		−	0.478733i	−0.970929	−	0.239367i	$-0.923060\pi$
$227$		−	7.21285i		−	0.478733i	0.970929	−	0.239367i	$-0.0769398\pi$
$228$			2.49934i			0.165523i
$229$			17.1127i			1.13084i	0.824804	+	0.565419i	$0.191286\pi$
$229$			17.1127i			1.13084i	−0.824804	+	0.565419i	$0.808714\pi$
$230$	19.7856			1.30463
$231$		0			0
$232$		−	12.7196i		−	0.835082i
$233$	12.6353			0.827767			0.413883	−	0.910330i	$-0.364172\pi$
$233$	12.6353			0.827767			0.413883	+	0.910330i	$0.364172\pi$
$234$	5.47695	+	2.45999i	0.358039	+	0.160815i
$235$	−18.8137			−1.22727
$236$		−	4.58233i		−	0.298284i
$237$	2.12596			0.138096
$238$		0			0
$239$		−	7.70807i		−	0.498594i	−0.968427	−	0.249297i	$-0.919801\pi$
$239$		−	7.70807i		−	0.498594i	0.968427	−	0.249297i	$-0.0801995\pi$
$240$			10.8960i			0.703333i
$241$			19.2022i			1.23693i	0.785814	+	0.618463i	$0.212244\pi$
$241$			19.2022i			1.23693i	−0.785814	+	0.618463i	$0.787756\pi$
$242$		−	11.8529i		−	0.761932i
$243$	−20.2963			−1.30201
$244$	−3.37390			−0.215992
$245$		0			0
$246$	−3.51412			−0.224052
$247$	2.29086	+	1.02895i	0.145764	+	0.0654705i
$248$	−13.1360			−0.834139
$249$			27.4214i			1.73776i
$250$	1.18643			0.0750366
$251$	−17.6761			−1.11570			−0.557851	−	0.829941i	$-0.688374\pi$
$251$	−17.6761			−1.11570			−0.557851	+	0.829941i	$0.688374\pi$
$252$		0			0
$253$			47.7756i			3.00362i
$254$			6.98993i			0.438587i
$255$			20.2183i			1.26612i
$256$	−9.51044			−0.594402
$257$	2.61935			0.163390			0.0816952	−	0.996657i	$-0.473967\pi$
$257$	2.61935			0.163390			0.0816952	+	0.996657i	$0.473967\pi$
$258$			3.79474i			0.236250i
$259$		0			0
$260$	16.4135	+	7.37216i	1.01792	+	0.457202i
$261$	−12.9420			−0.801089
$262$			8.55773i			0.528698i
$263$	5.62875			0.347084			0.173542	−	0.984827i	$-0.444479\pi$
$263$	5.62875			0.347084			0.173542	+	0.984827i	$0.444479\pi$
$264$	29.9426			1.84284
$265$		−	15.3078i		−	0.940348i
$266$		0			0
$267$		−	2.30149i		−	0.140849i
$268$		−	13.3839i		−	0.817554i
$269$	−13.8581			−0.844944			−0.422472	−	0.906376i	$-0.638837\pi$
$269$	−13.8581			−0.844944			−0.422472	+	0.906376i	$0.638837\pi$
$270$	2.84410			0.173087
$271$			8.00871i			0.486495i	0.969964	+	0.243247i	$0.0782127\pi$
$271$			8.00871i			0.486495i	−0.969964	+	0.243247i	$0.921787\pi$
$272$	3.83734			0.232673
$273$		0			0
$274$	1.17394			0.0709203
$275$			29.5227i			1.78029i
$276$	−32.1546			−1.93548
$277$	−18.2930			−1.09912			−0.549560	−	0.835454i	$-0.685205\pi$
$277$	−18.2930			−1.09912			−0.549560	+	0.835454i	$0.685205\pi$
$278$		−	1.99509i		−	0.119657i
$279$			13.3657i			0.800184i
$280$		0			0
$281$			19.3790i			1.15605i	0.816018	+	0.578026i	$0.196177\pi$
$281$			19.3790i			1.15605i	−0.816018	+	0.578026i	$0.803823\pi$
$282$	−9.20168			−0.547952
$283$	−6.43729			−0.382657			−0.191329	−	0.981526i	$-0.561280\pi$
$283$	−6.43729			−0.382657			−0.191329	+	0.981526i	$0.561280\pi$
$284$		−	13.1625i		−	0.781050i
$285$	−5.27743			−0.312608
$286$	5.35737	−	11.9277i	0.316788	−	0.705299i
$287$		0			0
$288$			14.1756i			0.835304i
$289$	−9.87955			−0.581150
$290$	11.6725			0.685431
$291$		−	35.8181i		−	2.09969i
$292$		−	9.04186i		−	0.529135i
$293$			7.66381i			0.447725i	0.974621	+	0.223862i	$0.0718666\pi$
$293$			7.66381i			0.447725i	−0.974621	+	0.223862i	$0.928133\pi$
$294$		0			0
$295$	9.67573			0.563343
$296$	16.1014			0.935876
$297$			6.86754i			0.398495i
$298$	−9.00572			−0.521687
$299$	−13.2377	+	29.4725i	−0.765555	+	1.70444i
$300$	−19.8698			−1.14718
$301$		0			0
$302$	6.29782			0.362399
$303$	−9.12472			−0.524202
$304$			1.00163i			0.0574477i
$305$		−	7.12410i		−	0.407925i
$306$			4.44351i			0.254018i
$307$		−	0.312144i		−	0.0178150i	−0.999960	−	0.00890751i	$-0.997165\pi$
$307$		−	0.312144i		−	0.0178150i	0.999960	−	0.00890751i	$-0.00283539\pi$
$308$		0			0
$309$	43.3241			2.46462
$310$		−	12.0546i		−	0.684656i
$311$	2.81507			0.159628			0.0798141	−	0.996810i	$-0.474567\pi$
$311$	2.81507			0.159628			0.0798141	+	0.996810i	$0.474567\pi$
$312$	18.4715	+	8.29653i	1.04574	+	0.469698i
$313$	−13.2930			−0.751366			−0.375683	−	0.926748i	$-0.622592\pi$
$313$	−13.2930			−0.751366			−0.375683	+	0.926748i	$0.622592\pi$
$314$		−	1.12658i		−	0.0635769i
$315$		0			0
$316$	1.40023			0.0787690
$317$		−	0.972179i		−	0.0546030i	−0.999627	−	0.0273015i	$-0.991309\pi$
$317$		−	0.972179i		−	0.0546030i	0.999627	−	0.0273015i	$-0.00869142\pi$
$318$		−	7.48695i		−	0.419847i
$319$			28.1850i			1.57806i
$320$		−	3.44881i		−	0.192794i
$321$	30.5907			1.70741
$322$		0			0
$323$			1.85860i			0.103415i
$324$	−15.9130			−0.884053
$325$	−8.18017	+	18.2124i	−0.453754	+	1.01024i
$326$	−6.73365			−0.372942
$327$			35.9407i			1.98752i
$328$	−5.32559			−0.294056
$329$		0			0
$330$			27.4776i			1.51259i
$331$		−	7.72092i		−	0.424380i	−0.977228	−	0.212190i	$-0.931940\pi$
$331$		−	7.72092i		−	0.424380i	0.977228	−	0.212190i	$-0.0680596\pi$
$332$			18.0607i			0.991208i
$333$		−	16.3829i		−	0.897779i
$334$	−4.15525			−0.227365
$335$	28.2606			1.54404
$336$		0			0
$337$	−27.4858			−1.49725			−0.748624	−	0.662995i	$-0.769285\pi$
$337$	−27.4858			−1.49725			−0.748624	+	0.662995i	$0.769285\pi$
$338$	6.60986	−	5.87371i	0.359529	−	0.319488i
$339$	29.7241			1.61439
$340$			13.3164i			0.722184i
$341$	29.1078			1.57628
$342$	−1.15986			−0.0627179
$343$		0			0
$344$			5.75086i			0.310066i
$345$		−	67.8954i		−	3.65536i
$346$		−	12.7341i		−	0.684588i
$347$	−3.69546			−0.198383			−0.0991914	−	0.995068i	$-0.531626\pi$
$347$	−3.69546			−0.198383			−0.0991914	+	0.995068i	$0.531626\pi$
$348$	−18.9695			−1.01687
$349$		−	26.7513i		−	1.43197i	−0.698118	−	0.715983i	$-0.745979\pi$
$349$		−	26.7513i		−	1.43197i	0.698118	−	0.715983i	$-0.254021\pi$
$350$		0			0
$351$	−1.90286	+	4.23655i	−0.101567	+	0.226130i
$352$	30.8715			1.64546
$353$		−	2.75332i		−	0.146544i	−0.997312	−	0.0732722i	$-0.976656\pi$
$353$		−	2.75332i		−	0.146544i	0.997312	−	0.0732722i	$-0.0233442\pi$
$354$	4.73235			0.251522
$355$	27.7930			1.47510
$356$		−	1.51584i		−	0.0803394i
$357$		0			0
$358$			6.75949i			0.357250i
$359$			35.0545i			1.85011i	0.379837	+	0.925053i	$0.375980\pi$
$359$			35.0545i			1.85011i	−0.379837	+	0.925053i	$0.624020\pi$
$360$	−19.1211			−1.00777
$361$	18.5149			0.974466
$362$		−	15.4399i		−	0.811501i
$363$	−40.6737			−2.13482
$364$		0			0
$365$	19.0922			0.999329
$366$		−	3.48436i		−	0.182131i
$367$	15.0005			0.783022			0.391511	−	0.920173i	$-0.371953\pi$
$367$	15.0005			0.783022			0.391511	+	0.920173i	$0.371953\pi$
$368$	−12.8863			−0.671743
$369$			5.41870i			0.282086i
$370$			14.7759i			0.768161i
$371$		0			0
$372$			19.5905i			1.01572i
$373$	20.9943			1.08704			0.543521	−	0.839395i	$-0.317091\pi$
$373$	20.9943			1.08704			0.543521	+	0.839395i	$0.317091\pi$
$374$	9.67706			0.500389
$375$		−	4.07130i		−	0.210241i
$376$	−13.9450			−0.719159
$377$	−7.80953	+	17.3872i	−0.402211	+	0.895486i
$378$		0			0
$379$			15.2425i			0.782956i	0.920187	+	0.391478i	$0.128036\pi$
$379$			15.2425i			0.782956i	−0.920187	+	0.391478i	$0.871964\pi$
$380$	−3.47589			−0.178309
$381$	23.9863			1.22886
$382$			3.69296i			0.188948i
$383$		−	24.5760i		−	1.25577i	−0.778305	−	0.627887i	$-0.783920\pi$
$383$		−	24.5760i		−	1.25577i	0.778305	−	0.627887i	$-0.216080\pi$
$384$			25.3439i			1.29333i
$385$		0			0
$386$	−1.34002			−0.0682053
$387$	5.85141			0.297444
$388$		−	23.5910i		−	1.19765i
$389$	−19.2407			−0.975545			−0.487772	−	0.872971i	$-0.662190\pi$
$389$	−19.2407			−0.975545			−0.487772	+	0.872971i	$0.662190\pi$
$390$	−7.61352	+	16.9508i	−0.385526	+	0.858338i
$391$	−23.9114			−1.20925
$392$		0			0
$393$	29.3663			1.48133
$394$	13.0242			0.656147
$395$			2.95663i			0.148764i
$396$		−	20.0660i		−	1.00836i
$397$			0.596764i			0.0299507i	0.999888	+	0.0149754i	$0.00476699\pi$
$397$			0.596764i			0.0299507i	−0.999888	+	0.0149754i	$0.995233\pi$
$398$			0.132510i			0.00664211i
$399$		0			0
$400$	−7.96301			−0.398151
$401$		−	1.59469i		−	0.0796348i	−0.999207	−	0.0398174i	$-0.987322\pi$
$401$		−	1.59469i		−	0.0796348i	0.999207	−	0.0398174i	$-0.0126776\pi$
$402$	13.8221			0.689384
$403$	17.9564	+	8.06521i	0.894474	+	0.401756i
$404$	−6.00984			−0.299001
$405$		−	33.6007i		−	1.66963i
$406$		0			0
$407$	−35.6787			−1.76853
$408$			14.9861i			0.741922i
$409$			28.9884i			1.43338i	0.697390	+	0.716691i	$0.254344\pi$
$409$			28.9884i			1.43338i	−0.697390	+	0.716691i	$0.745656\pi$
$410$		−	4.88716i		−	0.241360i
$411$		−	4.02843i		−	0.198708i
$412$	28.5347			1.40580
$413$		0			0
$414$		−	14.9218i		−	0.733369i
$415$	−38.1357			−1.87201
$416$	19.0445	+	8.55391i	0.933733	+	0.419390i
$417$	−6.84624			−0.335262
$418$			2.52594i			0.123548i
$419$	−5.18611			−0.253358			−0.126679	−	0.991944i	$-0.540432\pi$
$419$	−5.18611			−0.253358			−0.126679	+	0.991944i	$0.540432\pi$
$420$		0			0
$421$		−	2.84363i		−	0.138590i	−0.997596	−	0.0692950i	$-0.977925\pi$
$421$		−	2.84363i		−	0.138590i	0.997596	−	0.0692950i	$-0.0220750\pi$
$422$			8.34045i			0.406007i
$423$			14.1888i			0.689884i
$424$		−	11.3464i		−	0.551028i
$425$	−14.7759			−0.716737
$426$	13.5934			0.658603
$427$		0			0
$428$	20.1480			0.973892
$429$	−40.9304	−	18.3841i	−1.97614	−	0.887591i
$430$	−5.27743			−0.254500
$431$		−	3.98106i		−	0.191761i	−0.995393	−	0.0958804i	$-0.969433\pi$
$431$		−	3.98106i		−	0.191761i	0.995393	−	0.0958804i	$-0.0305666\pi$
$432$	−1.85235			−0.0891211
$433$	7.42082			0.356622			0.178311	−	0.983974i	$-0.442937\pi$
$433$	7.42082			0.356622			0.178311	+	0.983974i	$0.442937\pi$
$434$		0			0
$435$		−	40.0546i		−	1.92047i
$436$			23.6717i			1.13367i
$437$		−	6.24142i		−	0.298567i
$438$	9.33789			0.446181
$439$	30.5670			1.45888			0.729442	−	0.684043i	$-0.239780\pi$
$439$	30.5670			1.45888			0.729442	+	0.684043i	$0.239780\pi$
$440$			41.6419i			1.98520i
$441$		0			0
$442$	5.96973	+	2.68133i	0.283951	+	0.127538i
$443$	−4.30975			−0.204762			−0.102381	−	0.994745i	$-0.532646\pi$
$443$	−4.30975			−0.204762			−0.102381	+	0.994745i	$0.532646\pi$
$444$		−	24.0130i		−	1.13961i
$445$	3.20074			0.151730
$446$	−18.4832			−0.875205
$447$			30.9036i			1.46169i
$448$		0			0
$449$		−	30.7830i		−	1.45274i	−0.687305	−	0.726369i	$-0.741206\pi$
$449$		−	30.7830i		−	1.45274i	0.687305	−	0.726369i	$-0.258794\pi$
$450$		−	9.22089i		−	0.434677i
$451$	11.8008			0.555680
$452$	19.5773			0.920839
$453$		−	21.6113i		−	1.01539i
$454$	4.90615			0.230257
$455$		0			0
$456$	−3.91172			−0.183183
$457$		−	13.4954i		−	0.631287i	−0.948878	−	0.315644i	$-0.897780\pi$
$457$		−	13.4954i		−	0.631287i	0.948878	−	0.315644i	$-0.102220\pi$
$458$	−11.6400			−0.543901
$459$	−3.43716			−0.160433
$460$		−	44.7181i		−	2.08499i
$461$		−	27.4778i		−	1.27977i	−0.768471	−	0.639885i	$-0.778982\pi$
$461$		−	27.4778i		−	1.27977i	0.768471	−	0.639885i	$-0.221018\pi$
$462$		0			0
$463$		−	8.06521i		−	0.374822i	−0.982282	−	0.187411i	$-0.939990\pi$
$463$		−	8.06521i		−	0.374822i	0.982282	−	0.187411i	$-0.0600096\pi$
$464$	−7.60221			−0.352924
$465$	−41.3660			−1.91830
$466$			8.59449i			0.398132i
$467$	12.6325			0.584564			0.292282	−	0.956332i	$-0.405585\pi$
$467$	12.6325			0.584564			0.292282	+	0.956332i	$0.405585\pi$
$468$	5.55991	−	12.3786i	0.257007	−	0.572202i
$469$		0			0
$470$		−	12.7970i		−	0.590281i
$471$	−3.86593			−0.178133
$472$	7.17181			0.330109
$473$		−	12.7432i		−	0.585933i
$474$			1.44607i			0.0664202i
$475$		−	3.85685i		−	0.176965i
$476$		0			0
$477$	−11.5447			−0.528597
$478$	5.24300			0.239809
$479$			31.5380i			1.44101i	0.693451	+	0.720504i	$0.256089\pi$
$479$			31.5380i			1.44101i	−0.693451	+	0.720504i	$0.743911\pi$
$480$	−43.8725			−2.00250
$481$	−22.0100	−	9.88588i	−1.00357	−	0.450757i
$482$	−13.0613			−0.594926
$483$		0			0
$484$	−26.7891			−1.21769
$485$	49.8131			2.26190
$486$		−	13.8055i		−	0.626229i
$487$		−	42.1218i		−	1.90872i	−0.298654	−	0.954362i	$-0.596538\pi$
$487$		−	42.1218i		−	1.90872i	0.298654	−	0.954362i	$-0.403462\pi$
$488$		−	5.28050i		−	0.239037i
$489$			23.1068i			1.04493i
$490$		0			0
$491$	−30.2284			−1.36419			−0.682095	−	0.731264i	$-0.738931\pi$
$491$	−30.2284			−1.36419			−0.682095	+	0.731264i	$0.738931\pi$
$492$			7.94236i			0.358069i
$493$	−14.1064			−0.635321
$494$	−0.699888	+	1.55824i	−0.0314894	+	0.0701084i
$495$	42.3700			1.90439
$496$			7.85110i			0.352525i
$497$		0			0
$498$	−18.6520			−0.835815
$499$			3.50797i			0.157038i	0.996913	+	0.0785191i	$0.0250192\pi$
$499$			3.50797i			0.157038i	−0.996913	+	0.0785191i	$0.974981\pi$
$500$		−	2.68149i		−	0.119920i
$501$			14.2590i			0.637043i
$502$		−	12.0232i		−	0.536621i
$503$	22.8622			1.01937			0.509687	−	0.860360i	$-0.329761\pi$
$503$	22.8622			1.01937			0.509687	+	0.860360i	$0.329761\pi$
$504$		0			0
$505$		−	12.6900i		−	0.564696i
$506$	−32.4968			−1.44466
$507$	−20.1559	−	22.6821i	−0.895156	−	1.00735i
$508$	15.7982			0.700930
$509$			21.7755i			0.965183i	0.875846	+	0.482592i	$0.160304\pi$
$509$			21.7755i			0.965183i	−0.875846	+	0.482592i	$0.839696\pi$
$510$	−13.7524			−0.608966
$511$		0			0
$512$			15.2470i			0.673829i
$513$		−	0.897178i		−	0.0396114i
$514$			1.78167i			0.0785861i
$515$			60.2519i			2.65501i
$516$	8.57660			0.377564
$517$	30.9004			1.35900
$518$		0			0
$519$	−43.6976			−1.91811
$520$	−11.5382	+	25.6887i	−0.505982	+	1.12652i
$521$	−14.5235			−0.636287			−0.318144	−	0.948042i	$-0.603059\pi$
$521$	−14.5235			−0.636287			−0.318144	+	0.948042i	$0.603059\pi$
$522$		−	8.80309i		−	0.385301i
$523$	−16.4188			−0.717945			−0.358973	−	0.933348i	$-0.616873\pi$
$523$	−16.4188			−0.717945			−0.358973	+	0.933348i	$0.616873\pi$
$524$	19.3416			0.844942
$525$		0			0
$526$			3.82865i			0.166937i
$527$			14.5683i			0.634603i
$528$		−	17.8960i		−	0.778825i
$529$	57.2973			2.49119
$530$	10.4123			0.452280
$531$		−	7.29720i		−	0.316672i
$532$		0			0
$533$	7.27987	+	3.26978i	0.315326	+	0.141630i
$534$	1.56547			0.0677444
$535$			42.5432i			1.83930i
$536$	20.9472			0.904781
$537$	23.1955			1.00096
$538$		−	9.42623i		−	0.406394i
$539$		0			0
$540$		−	6.42805i		−	0.276619i
$541$		−	13.4954i		−	0.580212i	−0.956995	−	0.290106i	$-0.906309\pi$
$541$		−	13.4954i		−	0.580212i	0.956995	−	0.290106i	$-0.0936905\pi$
$542$	−5.44750			−0.233990
$543$	−52.9826			−2.27370
$544$			15.4510i			0.662456i
$545$	−49.9835			−2.14106
$546$		0			0
$547$	13.5615			0.579847			0.289924	−	0.957050i	$-0.406370\pi$
$547$	13.5615			0.579847			0.289924	+	0.957050i	$0.406370\pi$
$548$		−	2.65326i		−	0.113342i
$549$	−5.37283			−0.229307
$550$	−20.0812			−0.856267
$551$		−	3.68210i		−	0.156863i
$552$		−	50.3252i		−	2.14198i
$553$		0			0
$554$		−	12.4428i		−	0.528645i
$555$	50.7042			2.15227
$556$	−4.50916			−0.191231
$557$			35.2736i			1.49459i	0.664493	+	0.747294i	$0.268648\pi$
$557$			35.2736i			1.49459i	−0.664493	+	0.747294i	$0.731352\pi$
$558$	−9.09130			−0.384865
$559$	3.53089	−	7.86121i	0.149341	−	0.332494i
$560$		0			0
$561$		−	33.2073i		−	1.40201i
$562$	−13.1815			−0.556028
$563$	36.1102			1.52186			0.760931	−	0.648833i	$-0.224742\pi$
$563$	36.1102			1.52186			0.760931	+	0.648833i	$0.224742\pi$
$564$			20.7970i			0.875712i
$565$			41.3381i			1.73911i
$566$		−	4.37862i		−	0.184047i
$567$		0			0
$568$	20.6006			0.864383
$569$	−11.8362			−0.496197			−0.248099	−	0.968735i	$-0.579806\pi$
$569$	−11.8362			−0.496197			−0.248099	+	0.968735i	$0.579806\pi$
$570$		−	3.58969i		−	0.150356i
$571$	45.9414			1.92259			0.961294	−	0.275526i	$-0.0888521\pi$
$571$	45.9414			1.92259			0.961294	+	0.275526i	$0.0888521\pi$
$572$	−26.9581	−	12.1084i	−1.12718	−	0.506276i
$573$	12.6726			0.529405
$574$		0			0
$575$	49.6193			2.06927
$576$	−2.60101			−0.108375
$577$		−	29.7470i		−	1.23838i	−0.785240	−	0.619192i	$-0.787460\pi$
$577$		−	29.7470i		−	1.23838i	0.785240	−	0.619192i	$-0.212540\pi$
$578$		−	6.72003i		−	0.279517i
$579$			4.59835i			0.191101i
$580$		−	26.3813i		−	1.09542i
$581$		0			0
$582$	24.3633			1.00989
$583$			25.1421i			1.04128i
$584$	14.1514			0.585590
$585$	26.1379	+	11.7399i	1.08067	+	0.485386i
$586$	−5.21290			−0.215343
$587$		−	11.3406i		−	0.468078i	−0.972227	−	0.234039i	$-0.924806\pi$
$587$		−	11.3406i		−	0.468078i	0.972227	−	0.234039i	$-0.0751943\pi$
$588$		0			0
$589$	−3.80265			−0.156686
$590$			6.58140i			0.270952i
$591$		−	44.6930i		−	1.83843i
$592$		−	9.62344i		−	0.395521i
$593$			2.87084i			0.117891i	0.998261	+	0.0589455i	$0.0187738\pi$
$593$			2.87084i			0.117891i	−0.998261	+	0.0589455i	$0.981226\pi$
$594$	−4.67128			−0.191665
$595$		0			0
$596$			20.3541i			0.833737i
$597$	0.454713			0.0186102
$598$	−20.0471	−	9.00422i	−0.819786	−	0.368210i
$599$	−5.41559			−0.221275			−0.110637	−	0.993861i	$-0.535289\pi$
$599$	−5.41559			−0.221275			−0.110637	+	0.993861i	$0.535289\pi$
$600$		−	31.0982i		−	1.26958i
$601$	−34.1648			−1.39361			−0.696805	−	0.717261i	$-0.745396\pi$
$601$	−34.1648			−1.39361			−0.696805	+	0.717261i	$0.745396\pi$
$602$		0			0
$603$		−	21.3134i		−	0.867951i
$604$		−	14.2339i		−	0.579169i
$605$		−	56.5659i		−	2.29973i
$606$		−	6.20660i		−	0.252126i
$607$	−22.0430			−0.894697			−0.447349	−	0.894360i	$-0.647632\pi$
$607$	−22.0430			−0.894697			−0.447349	+	0.894360i	$0.647632\pi$
$608$	−4.03307			−0.163562
$609$		0			0
$610$	4.84579			0.196200
$611$	19.0623	+	8.56190i	0.771178	+	0.346377i
$612$	10.0429			0.405961
$613$		−	24.7446i		−	0.999424i	−0.866191	−	0.499712i	$-0.833439\pi$
$613$		−	24.7446i		−	0.999424i	0.866191	−	0.499712i	$-0.166561\pi$
$614$	0.212320			0.00856852
$615$	−16.7705			−0.676254
$616$		0			0
$617$		−	19.9659i		−	0.803797i	−0.915684	−	0.401898i	$-0.868350\pi$
$617$		−	19.9659i		−	0.803797i	0.915684	−	0.401898i	$-0.131650\pi$
$618$			29.4689i			1.18541i
$619$		−	10.0750i		−	0.404949i	−0.979288	−	0.202474i	$-0.935102\pi$
$619$		−	10.0750i		−	0.404949i	0.979288	−	0.202474i	$-0.0648983\pi$
$620$	−27.2450			−1.09419
$621$	11.5424			0.463181
$622$			1.91480i			0.0767766i
$623$		0			0
$624$	4.95864	−	11.0400i	0.198505	−	0.441952i
$625$	−22.0246			−0.880984
$626$		−	9.04186i		−	0.361385i
$627$	8.66787			0.346162
$628$	−2.54623			−0.101606
$629$		−	17.8570i		−	0.712004i
$630$		0			0
$631$			26.2386i			1.04454i	0.852780	+	0.522271i	$0.174915\pi$
$631$			26.2386i			1.04454i	−0.852780	+	0.522271i	$0.825085\pi$
$632$			2.19150i			0.0871731i
$633$	28.6207			1.13757
$634$	0.661273			0.0262625
$635$			33.3583i			1.32378i
$636$	−16.9215			−0.670981
$637$		0			0
$638$	−19.1714			−0.759001
$639$		−	20.9608i		−	0.829197i
$640$	−35.2464			−1.39324
$641$	−37.2213			−1.47015			−0.735077	−	0.677984i	$-0.762854\pi$
$641$	−37.2213			−1.47015			−0.735077	+	0.677984i	$0.762854\pi$
$642$			20.8077i			0.821213i
$643$			10.8569i			0.428155i	0.976817	+	0.214077i	$0.0686744\pi$
$643$			10.8569i			0.428155i	−0.976817	+	0.214077i	$0.931326\pi$
$644$		0			0
$645$			18.1098i			0.713071i
$646$	−1.26421			−0.0497398
$647$	11.2388			0.441841			0.220921	−	0.975292i	$-0.429094\pi$
$647$	11.2388			0.441841			0.220921	+	0.975292i	$0.429094\pi$
$648$		−	24.9054i		−	0.978375i
$649$	−15.8918			−0.623809
$650$	−12.3880	−	5.56412i	−0.485898	−	0.218243i
$651$		0			0
$652$			15.2189i			0.596019i
$653$	−15.8246			−0.619265			−0.309632	−	0.950856i	$-0.600206\pi$
$653$	−15.8246			−0.619265			−0.309632	+	0.950856i	$0.600206\pi$
$654$	−24.4467			−0.955942
$655$			40.8404i			1.59577i
$656$			3.18298i			0.124274i
$657$		−	14.3988i		−	0.561753i
$658$		0			0
$659$	−27.8237			−1.08386			−0.541928	−	0.840425i	$-0.682306\pi$
$659$	−27.8237			−1.08386			−0.541928	+	0.840425i	$0.682306\pi$
$660$	62.1031			2.41736
$661$		−	17.4521i		−	0.678808i	−0.940641	−	0.339404i	$-0.889775\pi$
$661$		−	17.4521i		−	0.678808i	0.940641	−	0.339404i	$-0.110225\pi$
$662$	5.25174			0.204115
$663$	9.20110	−	20.4854i	0.357341	−	0.795588i
$664$	−28.2668			−1.09696
$665$		0			0
$666$	11.1436			0.431806
$667$	47.3711			1.83422
$668$			9.39142i			0.363365i
$669$			63.4260i			2.45219i
$670$			19.2227i			0.742639i
$671$			11.7009i			0.451709i
$672$		0			0
$673$	−30.6883			−1.18295			−0.591474	−	0.806324i	$-0.701454\pi$
$673$	−30.6883			−1.18295			−0.591474	+	0.806324i	$0.701454\pi$
$674$		−	18.6958i		−	0.720134i
$675$	7.13258			0.274533
$676$	−13.2754	−	14.9392i	−0.510590	−	0.574583i
$677$	3.47556			0.133577			0.0667883	−	0.997767i	$-0.478725\pi$
$677$	3.47556			0.133577			0.0667883	+	0.997767i	$0.478725\pi$
$678$			20.2183i			0.776477i
$679$		0			0
$680$	−20.8415			−0.799236
$681$		−	16.8357i		−	0.645145i
$682$			19.7990i			0.758143i
$683$		−	2.98767i		−	0.114320i	−0.998365	−	0.0571601i	$-0.981795\pi$
$683$		−	2.98767i		−	0.114320i	0.998365	−	0.0571601i	$-0.0182045\pi$
$684$			2.62143i			0.100233i
$685$	5.60244			0.214058
$686$		0			0
$687$			39.9432i			1.52393i
$688$	3.43716			0.131040
$689$	−6.96639	+	15.5100i	−0.265398	+	0.590885i
$690$	46.1822			1.75813
$691$		−	11.4913i		−	0.437150i	−0.975820	−	0.218575i	$-0.929859\pi$
$691$		−	11.4913i		−	0.437150i	0.975820	−	0.218575i	$-0.0701408\pi$
$692$	−28.7807			−1.09408
$693$		0			0
$694$		−	2.51364i		−	0.0954164i
$695$		−	9.52123i		−	0.361161i
$696$		−	29.6891i		−	1.12536i
$697$			5.90624i			0.223715i
$698$	18.1961			0.688734
$699$	29.4924			1.11551
$700$		0			0
$701$	−0.977624			−0.0369244			−0.0184622	−	0.999830i	$-0.505877\pi$
$701$	−0.977624			−0.0369244			−0.0184622	+	0.999830i	$0.505877\pi$
$702$	−2.88169	−	1.29432i	−0.108762	−	0.0488510i
$703$	4.66108			0.175796
$704$			5.66447i			0.213488i
$705$	−43.9135			−1.65388
$706$	1.87280			0.0704836
$707$		0			0
$708$		−	10.6957i		−	0.401971i
$709$		−	9.85564i		−	0.370136i	−0.982726	−	0.185068i	$-0.940749\pi$
$709$		−	9.85564i		−	0.370136i	0.982726	−	0.185068i	$-0.0592506\pi$
$710$			18.9047i			0.709480i
$711$	2.22982			0.0836246
$712$	2.37244			0.0889110
$713$		−	48.9220i		−	1.83214i
$714$		0			0
$715$	25.5672	−	56.9229i	0.956157	−	2.12880i
$716$	15.2773			0.570941
$717$		−	17.9916i		−	0.671909i
$718$	−23.8440			−0.889848
$719$	19.5346			0.728517			0.364258	−	0.931298i	$-0.381322\pi$
$719$	19.5346			0.728517			0.364258	+	0.931298i	$0.381322\pi$
$720$			11.4283i			0.425906i
$721$		0			0
$722$			12.5937i			0.468690i
$723$			44.8205i			1.66689i
$724$	−34.8961			−1.29690
$725$	29.2728			1.08716
$726$		−	27.6661i		−	1.02679i
$727$	24.4958			0.908498			0.454249	−	0.890875i	$-0.349908\pi$
$727$	24.4958			0.908498			0.454249	+	0.890875i	$0.349908\pi$
$728$		0			0
$729$	−16.3211			−0.604486
$730$			12.9864i			0.480649i
$731$	6.37788			0.235895
$732$	−7.87512			−0.291073
$733$			30.8279i			1.13865i	0.822111	+	0.569327i	$0.192796\pi$
$733$			30.8279i			1.13865i	−0.822111	+	0.569327i	$0.807204\pi$
$734$			10.2033i			0.376611i
$735$		0			0
$736$		−	51.8864i		−	1.91256i
$737$	−46.4164			−1.70977
$738$	−3.68578			−0.135675
$739$		−	2.69864i		−	0.0992710i	−0.998767	−	0.0496355i	$-0.984194\pi$
$739$		−	2.69864i		−	0.0992710i	0.998767	−	0.0496355i	$-0.0158060\pi$
$740$	33.3954			1.22764
$741$	5.34717	+	2.40170i	0.196433	+	0.0882287i
$742$		0			0
$743$			15.2204i			0.558382i	0.960236	+	0.279191i	$0.0900662\pi$
$743$			15.2204i			0.558382i	−0.960236	+	0.279191i	$0.909934\pi$
$744$	−30.6612			−1.12409
$745$	−42.9783			−1.57460
$746$			14.2802i			0.522836i
$747$			28.7610i			1.05231i
$748$		−	21.8714i		−	0.799699i
$749$		0			0
$750$	2.76929			0.101120
$751$	24.5482			0.895777			0.447888	−	0.894089i	$-0.352176\pi$
$751$	24.5482			0.895777			0.447888	+	0.894089i	$0.352176\pi$
$752$			8.33461i			0.303932i
$753$	−41.2581			−1.50353
$754$	−11.8267	−	5.31201i	−0.430703	−	0.193452i
$755$	30.0553			1.09383
$756$		0			0
$757$	11.0892			0.403043			0.201522	−	0.979484i	$-0.435411\pi$
$757$	11.0892			0.403043			0.201522	+	0.979484i	$0.435411\pi$
$758$	−10.3679			−0.376580
$759$			111.514i			4.04771i
$760$		−	5.44012i		−	0.197334i
$761$		−	16.9512i		−	0.614481i	−0.951632	−	0.307241i	$-0.900594\pi$
$761$		−	16.9512i		−	0.614481i	0.951632	−	0.307241i	$-0.0994057\pi$
$762$			16.3154i			0.591044i
$763$		0			0
$764$	8.34659			0.301969
$765$			21.2059i			0.766702i
$766$	16.7165			0.603991
$767$	−9.80359	−	4.40332i	−0.353987	−	0.158995i
$768$	−22.1986			−0.801022
$769$			50.7371i			1.82962i	0.403879	+	0.914812i	$0.367662\pi$
$769$			50.7371i			1.82962i	−0.403879	+	0.914812i	$0.632338\pi$
$770$		0			0
$771$	6.11389			0.220186
$772$			3.02863i			0.109003i
$773$		−	30.8560i		−	1.10981i	−0.831912	−	0.554907i	$-0.812754\pi$
$773$		−	30.8560i		−	1.10981i	0.831912	−	0.554907i	$-0.187246\pi$
$774$			3.98011i			0.143062i
$775$		−	30.2311i		−	1.08593i
$776$	36.9223			1.32543
$777$		0			0
$778$		−	13.0875i		−	0.469209i
$779$	−1.54166			−0.0552359
$780$	38.3111	+	17.2076i	1.37176	+	0.616130i
$781$	−45.6484			−1.63343
$782$		−	16.2644i		−	0.581614i
$783$	6.80940			0.243348
$784$		0			0
$785$		−	5.37644i		−	0.191893i
$786$			19.9748i			0.712479i
$787$			4.00436i			0.142740i	0.997450	+	0.0713700i	$0.0227371\pi$
$787$			4.00436i			0.142740i	−0.997450	+	0.0713700i	$0.977263\pi$
$788$		−	29.4363i		−	1.04862i
$789$	13.1382			0.467733
$790$	−2.01109			−0.0715512
$791$		0			0
$792$	31.4053			1.11594
$793$	−3.24210	+	7.21824i	−0.115130	+	0.256327i
$794$	−0.405917			−0.0144054
$795$		−	35.7302i		−	1.26722i
$796$	0.299489			0.0106151
$797$	17.3993			0.616316			0.308158	−	0.951335i	$-0.400287\pi$
$797$	17.3993			0.616316			0.308158	+	0.951335i	$0.400287\pi$
$798$		0			0
$799$			15.4654i			0.547128i
$800$		−	32.0630i		−	1.13360i
$801$		−	2.41392i		−	0.0852918i
$802$	1.08470			0.0383021
$803$	−31.3578			−1.10659
$804$		−	31.2398i		−	1.10174i
$805$		0			0
$806$	−5.48592	+	12.2139i	−0.193233	+	0.430217i
$807$	−32.3466			−1.13865
$808$		−	9.40601i		−	0.330902i
$809$	45.3185			1.59331			0.796656	−	0.604433i	$-0.206600\pi$
$809$	45.3185			1.59331			0.796656	+	0.604433i	$0.206600\pi$
$810$	22.8551			0.803045
$811$			3.47248i			0.121935i	0.998140	+	0.0609676i	$0.0194186\pi$
$811$			3.47248i			0.121935i	−0.998140	+	0.0609676i	$0.980581\pi$
$812$		0			0
$813$			18.6934i			0.655605i
$814$		−	24.2685i		−	0.850611i
$815$	−32.1352			−1.12565
$816$	8.95684			0.313552
$817$			1.66478i			0.0582431i
$818$	−19.7178			−0.689416
$819$		0			0
$820$	−11.0456			−0.385730
$821$		−	12.1108i		−	0.422670i	−0.977414	−	0.211335i	$-0.932219\pi$
$821$		−	12.1108i		−	0.422670i	0.977414	−	0.211335i	$-0.0677812\pi$
$822$	2.74013			0.0955729
$823$	−12.3444			−0.430300			−0.215150	−	0.976581i	$-0.569024\pi$
$823$	−12.3444			−0.430300			−0.215150	+	0.976581i	$0.569024\pi$
$824$			44.6597i			1.55579i
$825$			68.9097i			2.39913i
$826$		0			0
$827$		−	33.0214i		−	1.14827i	−0.818762	−	0.574133i	$-0.805339\pi$
$827$		−	33.0214i		−	1.14827i	0.818762	−	0.574133i	$-0.194661\pi$
$828$	−33.7253			−1.17204
$829$	25.8518			0.897870			0.448935	−	0.893565i	$-0.351804\pi$
$829$	25.8518			0.897870			0.448935	+	0.893565i	$0.351804\pi$
$830$		−	25.9397i		−	0.900381i
$831$	−42.6982			−1.48118
$832$	−1.56951	+	3.49438i	−0.0544131	+	0.121146i
$833$		0			0
$834$		−	4.65679i		−	0.161251i
$835$	−19.8303			−0.686255
$836$	5.70895			0.197448
$837$		−	7.03234i		−	0.243073i
$838$		−	3.52757i		−	0.121858i
$839$			24.3723i			0.841424i	0.907194	+	0.420712i	$0.138220\pi$
$839$			24.3723i			0.841424i	−0.907194	+	0.420712i	$0.861780\pi$
$840$		0			0
$841$	−1.05359			−0.0363305
$842$	1.93423			0.0666578
$843$			45.2330i			1.55791i
$844$	18.8505			0.648861
$845$	31.5445	−	28.0313i	1.08516	−	0.964306i
$846$	−9.65118			−0.331815
$847$		0			0
$848$	−6.78145			−0.232876
$849$	−15.0255			−0.515672
$850$		−	10.0505i		−	0.344730i
$851$			59.9659i			2.05560i
$852$		−	30.7229i		−	1.05255i
$853$		−	16.2919i		−	0.557825i	−0.960316	−	0.278913i	$-0.910026\pi$
$853$		−	16.2919i		−	0.557825i	0.960316	−	0.278913i	$-0.0899740\pi$
$854$		0			0
$855$	−5.53523			−0.189301
$856$			31.5337i			1.07780i
$857$	−28.2966			−0.966593			−0.483296	−	0.875457i	$-0.660561\pi$
$857$	−28.2966			−0.966593			−0.483296	+	0.875457i	$0.660561\pi$
$858$	12.5048	−	27.8407i	0.426906	−	0.950467i
$859$	5.30710			0.181076			0.0905380	−	0.995893i	$-0.471141\pi$
$859$	5.30710			0.181076			0.0905380	+	0.995893i	$0.471141\pi$
$860$			11.9277i			0.406731i
$861$		0			0
$862$	2.70790			0.0922314
$863$		−	35.4867i		−	1.20798i	−0.796992	−	0.603990i	$-0.793577\pi$
$863$		−	35.4867i		−	1.20798i	0.796992	−	0.603990i	$-0.206423\pi$
$864$		−	7.45845i		−	0.253742i
$865$		−	60.7713i		−	2.06629i
$866$			5.04761i			0.171525i
$867$	−23.0601			−0.783163
$868$		0			0
$869$		−	4.85609i		−	0.164731i
$870$	27.2450			0.923693
$871$	−28.6340	−	12.8611i	−0.970227	−	0.435781i
$872$	−37.0486			−1.25462
$873$		−	37.5678i		−	1.27148i
$874$	4.24539			0.143602
$875$		0			0
$876$		−	21.1048i		−	0.713067i
$877$		−	42.3986i		−	1.43170i	−0.698254	−	0.715850i	$-0.746040\pi$
$877$		−	42.3986i		−	1.43170i	0.698254	−	0.715850i	$-0.253960\pi$
$878$			20.7916i			0.701681i
$879$			17.8883i			0.603358i
$880$	24.8884			0.838989
$881$	33.1997			1.11853			0.559263	−	0.828990i	$-0.311084\pi$
$881$	33.1997			1.11853			0.559263	+	0.828990i	$0.311084\pi$
$882$		0			0
$883$	−11.9618			−0.402546			−0.201273	−	0.979535i	$-0.564508\pi$
$883$	−11.9618			−0.402546			−0.201273	+	0.979535i	$0.564508\pi$
$884$	6.06015	−	13.4924i	0.203825	−	0.453798i
$885$	22.5844			0.759166
$886$		−	2.93148i		−	0.0984849i
$887$	−6.32663			−0.212427			−0.106214	−	0.994343i	$-0.533873\pi$
$887$	−6.32663			−0.212427			−0.106214	+	0.994343i	$0.533873\pi$
$888$	37.5827			1.26119
$889$		0			0
$890$			2.17713i			0.0729777i
$891$			55.1872i			1.84884i
$892$			41.7745i			1.39871i
$893$	−4.03684			−0.135088
$894$	−21.0205			−0.703031
$895$			32.2586i			1.07829i
$896$		0			0
$897$	−30.8984	+	68.7926i	−1.03167	+	2.29692i
$898$	20.9385			0.698726
$899$		−	28.8614i		−	0.962580i
$900$	−20.8404			−0.694681
$901$	−12.5835			−0.419216
$902$			8.02688i			0.267266i
$903$		0			0
$904$			30.6404i			1.01909i
$905$		−	73.6842i		−	2.44935i
$906$	14.6999			0.488372
$907$	−9.31333			−0.309244			−0.154622	−	0.987974i	$-0.549416\pi$
$907$	−9.31333			−0.309244			−0.154622	+	0.987974i	$0.549416\pi$
$908$		−	11.0885i		−	0.367986i
$909$	−9.57047			−0.317432
$910$		0			0
$911$	28.4873			0.943826			0.471913	−	0.881645i	$-0.343564\pi$
$911$	28.4873			0.943826			0.471913	+	0.881645i	$0.343564\pi$
$912$			2.33794i			0.0774170i
$913$	62.6356			2.07294
$914$	9.17951			0.303631
$915$		−	16.6286i		−	0.549723i
$916$			26.3079i			0.869238i
$917$		0			0
$918$		−	2.33794i		−	0.0771636i
$919$	54.7833			1.80713			0.903566	−	0.428448i	$-0.140940\pi$
$919$	54.7833			1.80713			0.903566	+	0.428448i	$0.140940\pi$
$920$	69.9884			2.30745
$921$		−	0.728585i		−	0.0240077i
$922$	18.6903			0.615533
$923$	−28.1603	−	12.6483i	−0.926906	−	0.416323i
$924$		0			0
$925$			37.0556i			1.21838i
$926$	5.48592			0.180279
$927$	45.4405			1.49246
$928$		−	30.6102i		−	1.00483i
$929$		−	13.3363i		−	0.437551i	−0.975775	−	0.218776i	$-0.929794\pi$
$929$		−	13.3363i		−	0.437551i	0.975775	−	0.218776i	$-0.0702063\pi$
$930$		−	28.1370i		−	0.922649i
$931$		0			0
$932$	19.4247			0.636277
$933$	6.57074			0.215116
$934$			8.59260i			0.281158i
$935$	46.1822			1.51032
$936$	19.3738	+	8.70181i	0.633252	+	0.284428i
$937$	15.4989			0.506327			0.253164	−	0.967423i	$-0.418529\pi$
$937$	15.4989			0.506327			0.253164	+	0.967423i	$0.418529\pi$
$938$		0			0
$939$	−31.0276			−1.01255
$940$	−28.9229			−0.943361
$941$			21.7664i			0.709566i	0.934949	+	0.354783i	$0.115445\pi$
$941$			21.7664i			0.709566i	−0.934949	+	0.354783i	$0.884555\pi$
$942$		−	2.62959i		−	0.0856768i
$943$		−	19.8339i		−	0.645880i
$944$		−	4.28642i		−	0.139511i
$945$		0			0
$946$	8.66787			0.281817
$947$		−	16.2266i		−	0.527294i	−0.964619	−	0.263647i	$-0.915075\pi$
$947$		−	16.2266i		−	0.527294i	0.964619	−	0.263647i	$-0.0849254\pi$
$948$	3.26831			0.106150
$949$	−19.3444	−	8.68863i	−0.627947	−	0.282045i
$950$	2.62342			0.0851149
$951$		−	2.26919i		−	0.0735835i
$952$		0			0
$953$	25.2125			0.816712			0.408356	−	0.912823i	$-0.366102\pi$
$953$	25.2125			0.816712			0.408356	+	0.912823i	$0.366102\pi$
$954$		−	7.85269i		−	0.254240i
$955$			17.6241i			0.570302i
$956$		−	11.8499i		−	0.383252i
$957$			65.7874i			2.12661i
$958$	−21.4520			−0.693083
$959$		0			0
$960$		−	8.04996i		−	0.259811i
$961$	1.19373			0.0385073
$962$	6.72434	−	14.9711i	0.216801	−	0.482689i
$963$	32.0851			1.03393
$964$			29.5202i			0.950783i
$965$	−6.39504			−0.205863
$966$		0			0
$967$			32.6302i			1.04932i	0.851313	+	0.524658i	$0.175807\pi$
$967$			32.6302i			1.04932i	−0.851313	+	0.524658i	$0.824193\pi$
$968$		−	41.9276i		−	1.34760i
$969$			4.33821i			0.139363i
$970$			33.8827i			1.08791i
$971$	−34.0324			−1.09215			−0.546077	−	0.837735i	$-0.683879\pi$
$971$	−34.0324			−1.09215			−0.546077	+	0.837735i	$0.683879\pi$
$972$	−31.2022			−1.00081
$973$		0			0
$974$	28.6511			0.918041
$975$	−19.0936	+	42.5101i	−0.611483	+	1.36141i
$976$	−3.15603			−0.101022
$977$		−	4.85551i		−	0.155342i	−0.996979	−	0.0776708i	$-0.975252\pi$
$977$		−	4.85551i		−	0.155342i	0.996979	−	0.0776708i	$-0.0247483\pi$
$978$	−15.7172			−0.502580
$979$	−5.25703			−0.168016
$980$		0			0
$981$			37.6964i			1.20355i
$982$		−	20.5613i		−	0.656136i
$983$		−	27.5856i		−	0.879845i	−0.898036	−	0.439922i	$-0.855006\pi$
$983$		−	27.5856i		−	0.879845i	0.898036	−	0.439922i	$-0.144994\pi$
$984$	−12.4306			−0.396273
$985$	62.1557			1.98044
$986$		−	9.59513i		−	0.305571i
$987$		0			0
$988$	3.52182	+	1.58184i	0.112044	+	0.0503250i
$989$	−21.4177			−0.681044
$990$			28.8199i			0.915958i
$991$	−1.99210			−0.0632813			−0.0316406	−	0.999499i	$-0.510073\pi$
$991$	−1.99210			−0.0632813			−0.0316406	+	0.999499i	$0.510073\pi$
$992$	−31.6123			−1.00369
$993$		−	18.0216i		−	0.571898i
$994$		0			0
$995$			0.632380i			0.0200478i
$996$			42.1559i			1.33576i
$997$	31.5600			0.999516			0.499758	−	0.866165i	$-0.333422\pi$
$997$	31.5600			0.999516			0.499758	+	0.866165i	$0.333422\pi$
$998$	−2.38611			−0.0755309
$999$			8.61985i			0.272720i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.c.g.246.10	yes	16
7.2	even	3		637.2.r.g.116.9		32
7.3	odd	6		637.2.r.g.324.8		32
7.4	even	3		637.2.r.g.324.7		32
7.5	odd	6		637.2.r.g.116.10		32
7.6	odd	2	inner	637.2.c.g.246.9	yes	16
13.5	odd	4		8281.2.a.cs.1.10		16
13.8	odd	4		8281.2.a.cs.1.8		16
13.12	even	2	inner	637.2.c.g.246.8	yes	16
91.12	odd	6		637.2.r.g.116.8		32
91.25	even	6		637.2.r.g.324.9		32
91.34	even	4		8281.2.a.cs.1.7		16
91.38	odd	6		637.2.r.g.324.10		32
91.51	even	6		637.2.r.g.116.7		32
91.83	even	4		8281.2.a.cs.1.9		16
91.90	odd	2	inner	637.2.c.g.246.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.c.g.246.7	✓	16	91.90	odd	2	inner
637.2.c.g.246.8	yes	16	13.12	even	2	inner
637.2.c.g.246.9	yes	16	7.6	odd	2	inner
637.2.c.g.246.10	yes	16	1.1	even	1	trivial
637.2.r.g.116.7		32	91.51	even	6
637.2.r.g.116.8		32	91.12	odd	6
637.2.r.g.116.9		32	7.2	even	3
637.2.r.g.116.10		32	7.5	odd	6
637.2.r.g.324.7		32	7.4	even	3
637.2.r.g.324.8		32	7.3	odd	6
637.2.r.g.324.9		32	91.25	even	6
637.2.r.g.324.10		32	91.38	odd	6
8281.2.a.cs.1.7		16	91.34	even	4
8281.2.a.cs.1.8		16	13.8	odd	4
8281.2.a.cs.1.9		16	91.83	even	4
8281.2.a.cs.1.10		16	13.5	odd	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)

\(f(q)\)	\(=\)	\(q+0.680196i q^{2} +2.33413 q^{3} +1.53733 q^{4} +3.24613i q^{5} +1.58766i q^{6} +2.40608i q^{8} +2.44815 q^{9} +O(q^{10})\)	\(q+0.680196i q^{2} +2.33413 q^{3} +1.53733 q^{4} +3.24613i q^{5} +1.58766i q^{6} +2.40608i q^{8} +2.44815 q^{9} -2.20800 q^{10} -5.33157i q^{11} +3.58833 q^{12} +(1.47728 - 3.28902i) q^{13} +7.57687i q^{15} +1.43806 q^{16} +2.66842 q^{17} +1.66522i q^{18} +0.696519i q^{19} +4.99038i q^{20} +3.62652 q^{22} -8.96087 q^{23} +5.61610i q^{24} -5.53733 q^{25} +(2.23718 + 1.00484i) q^{26} -1.28809 q^{27} -5.28644 q^{29} -5.15376 q^{30} +5.45951i q^{31} +5.79032i q^{32} -12.4446i q^{33} +1.81505i q^{34} +3.76362 q^{36} -6.69197i q^{37} -0.473769 q^{38} +(3.44815 - 7.67699i) q^{39} -7.81044 q^{40} +2.21339i q^{41} +2.39014 q^{43} -8.19640i q^{44} +7.94700i q^{45} -6.09515i q^{46} +5.79573i q^{47} +3.35661 q^{48} -3.76647i q^{50} +6.22843 q^{51} +(2.27106 - 5.05632i) q^{52} -4.71570 q^{53} -0.876153i q^{54} +17.3070 q^{55} +1.62576i q^{57} -3.59581i q^{58} -2.98070i q^{59} +11.6482i q^{60} -2.19465 q^{61} -3.71354 q^{62} -1.06244 q^{64} +(10.6766 + 4.79542i) q^{65} +8.46475 q^{66} -8.70594i q^{67} +4.10225 q^{68} -20.9158 q^{69} -8.56190i q^{71} +5.89045i q^{72} -5.88152i q^{73} +4.55185 q^{74} -12.9248 q^{75} +1.07078i q^{76} +(5.22186 + 2.34542i) q^{78} +0.910817 q^{79} +4.66812i q^{80} -10.3510 q^{81} -1.50554 q^{82} +11.7481i q^{83} +8.66202i q^{85} +1.62576i q^{86} -12.3392 q^{87} +12.8282 q^{88} -0.986019i q^{89} -5.40552 q^{90} -13.7758 q^{92} +12.7432i q^{93} -3.94224 q^{94} -2.26099 q^{95} +13.5154i q^{96} -15.3454i q^{97} -13.0525i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 20 q^{4} + 16 q^{9}+O(q^{10}) \) 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

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