LMFDB - Embedded newform 1183.2.c.g.337.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, 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("1183.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.11667456256.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 13x^{6} + 44x^{4} + 21x^{2} + 1 $ x^8 + 13x^6 + 44x^4 + 21*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.3
Root			$-0.710287i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.g.337.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.710287i q^{2} +2.40788 q^{3} +1.49549 q^{4} -1.28971i q^{5} -1.71029i q^{6} +1.00000i q^{7} -2.48280i q^{8} +2.79790 q^{9} -0.916066 q^{10} +2.40788i q^{11} +3.60097 q^{12} +0.710287 q^{14} -3.10548i q^{15} +1.22748 q^{16} -3.90338 q^{17} -1.98731i q^{18} -5.89068i q^{19} -1.92876i q^{20} +2.40788i q^{21} +1.71029 q^{22} +6.32395 q^{23} -5.97829i q^{24} +3.33664 q^{25} -0.486640 q^{27} +1.49549i q^{28} +5.61366 q^{29} -2.20578 q^{30} +2.20578i q^{31} -5.83747i q^{32} +5.79790i q^{33} +2.77252i q^{34} +1.28971 q^{35} +4.18424 q^{36} +5.11817i q^{37} -4.18407 q^{38} -3.20210 q^{40} -7.78521i q^{41} +1.71029 q^{42} -0.289713 q^{43} +3.60097i q^{44} -3.60849i q^{45} -4.49182i q^{46} -1.27702i q^{47} +2.95564 q^{48} -1.00000 q^{49} -2.36997i q^{50} -9.39887 q^{51} -13.6225 q^{53} +0.345654i q^{54} +3.10548 q^{55} +2.48280 q^{56} -14.1841i q^{57} -3.98731i q^{58} +4.03056i q^{59} -4.64422i q^{60} -4.60097 q^{61} +1.56674 q^{62} +2.79790i q^{63} -1.69131 q^{64} +4.11817 q^{66} +7.57559i q^{67} -5.83747 q^{68} +15.2273 q^{69} -0.916066i q^{70} +7.22732i q^{71} -6.94662i q^{72} +15.0125i q^{73} +3.63537 q^{74} +8.03424 q^{75} -8.80948i q^{76} -2.40788 q^{77} -9.30758 q^{79} -1.58310i q^{80} -9.56546 q^{81} -5.52973 q^{82} -1.36463i q^{83} +3.60097i q^{84} +5.03424i q^{85} +0.205780i q^{86} +13.5170 q^{87} +5.97829 q^{88} +0.899698i q^{89} -2.56306 q^{90} +9.45742 q^{92} +5.31126i q^{93} -0.907052 q^{94} -7.59729 q^{95} -14.0559i q^{96} +15.6658i q^{97} +0.710287i q^{98} +6.73701i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 10 q^{4} + 14 q^{9} + 22 q^{10} - 24 q^{12} + 2 q^{14} + 38 q^{16} + 8 q^{17} + 10 q^{22} + 4 q^{23} - 10 q^{25} - 52 q^{27} + 2 q^{29} + 8 q^{30} + 14 q^{35} + 68 q^{36} + 46 q^{38} - 34 q^{40}+ \cdots - 42 q^{95}+O(q^{100}) $ 8 * q + 2 * q^3 - 10 * q^4 + 14 * q^9 + 22 * q^10 - 24 * q^12 + 2 * q^14 + 38 * q^16 + 8 * q^17 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 52 * q^27 + 2 * q^29 + 8 * q^30 + 14 * q^35 + 68 * q^36 + 46 * q^38 - 34 * q^40 + 10 * q^42 - 6 * q^43 + 22 * q^48 - 8 * q^49 - 14 * q^51 + 4 * q^53 - 6 * q^55 - 12 * q^56 + 16 * q^61 + 10 * q^62 - 28 * q^64 + 12 * q^66 - 66 * q^68 + 36 * q^69 + 40 * q^74 + 14 * q^75 - 2 * q^77 - 52 * q^79 + 48 * q^81 + 28 * q^82 + 26 * q^87 - 6 * q^88 - 52 * q^90 + 24 * q^92 + 66 * q^94 - 42 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 0.710287i	− 0.502249i	−0.967955	−	0.251124i	$-0.919200\pi$
$2$	− 0.710287i	− 0.502249i	0.967955	−	0.251124i	$-0.0808003\pi$
$3$	2.40788	1.39019	0.695096	−	0.718917i	$-0.255362\pi$
$3$	2.40788	1.39019	0.695096	+	0.718917i	$0.255362\pi$
$4$	1.49549	0.747746
$5$	− 1.28971i	− 0.576777i	−0.957513	−	0.288389i	$-0.906880\pi$
$5$	− 1.28971i	− 0.576777i	0.957513	−	0.288389i	$-0.0931195\pi$
$6$	− 1.71029i	− 0.698222i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 2.48280i	− 0.877803i
$9$	2.79790	0.932632
$10$	−0.916066	−0.289686
$11$	2.40788i	0.726004i	0.931788	+	0.363002i	$0.118248\pi$
$11$	2.40788i	0.726004i	−0.931788	+	0.363002i	$0.881752\pi$
$12$	3.60097	1.03951
$13$	0	0
$13$	0	0
$14$	0.710287	0.189832
$15$	− 3.10548i	− 0.801831i
$16$	1.22748	0.306871
$17$	−3.90338	−0.946708	−0.473354	−	0.880872i	$-0.656957\pi$
$17$	−3.90338	−0.946708	−0.473354	+	0.880872i	$0.656957\pi$
$18$	− 1.98731i	− 0.468413i
$19$	− 5.89068i	− 1.35142i	−0.737170	−	0.675708i	$-0.763838\pi$
$19$	− 5.89068i	− 1.35142i	0.737170	−	0.675708i	$-0.236162\pi$
$20$	− 1.92876i	− 0.431283i
$21$	2.40788i	0.525443i
$22$	1.71029	0.364634
$23$	6.32395	1.31863	0.659317	−	0.751865i	$-0.270845\pi$
$23$	6.32395	1.31863	0.659317	+	0.751865i	$0.270845\pi$
$24$	− 5.97829i	− 1.22031i
$25$	3.33664	0.667328
$26$	0	0
$27$	−0.486640	−0.0936539
$28$	1.49549i	0.282622i
$29$	5.61366	1.04243	0.521215	−	0.853425i	$-0.325479\pi$
$29$	5.61366	1.04243	0.521215	+	0.853425i	$0.325479\pi$
$30$	−2.20578	−0.402718
$31$	2.20578i	0.396170i	0.980185	+	0.198085i	$0.0634722\pi$
$31$	2.20578i	0.396170i	−0.980185	+	0.198085i	$0.936528\pi$
$32$	− 5.83747i	− 1.03193i
$33$	5.79790i	1.00928i
$34$	2.77252i	0.475482i
$35$	1.28971	0.218001
$36$	4.18424	0.697373
$37$	5.11817i	0.841422i	0.907195	+	0.420711i	$0.138219\pi$
$37$	5.11817i	0.841422i	−0.907195	+	0.420711i	$0.861781\pi$
$38$	−4.18407	−0.678746
$39$	0	0
$40$	−3.20210	−0.506297
$41$	− 7.78521i	− 1.21584i	−0.793996	−	0.607922i	$-0.792003\pi$
$41$	− 7.78521i	− 1.21584i	0.793996	−	0.607922i	$-0.207997\pi$
$42$	1.71029	0.263903
$43$	−0.289713	−0.0441809	−0.0220904	−	0.999756i	$-0.507032\pi$
$43$	−0.289713	−0.0441809	−0.0220904	+	0.999756i	$0.507032\pi$
$44$	3.60097i	0.542867i
$45$	− 3.60849i	− 0.537921i
$46$	− 4.49182i	− 0.662282i
$47$	− 1.27702i	− 0.186273i	−0.995653	−	0.0931364i	$-0.970311\pi$
$47$	− 1.27702i	− 0.186273i	0.995653	−	0.0931364i	$-0.0296893\pi$
$48$	2.95564	0.426610
$49$	−1.00000	−0.142857
$50$	− 2.36997i	− 0.335164i
$51$	−9.39887	−1.31610
$52$	0	0
$53$	−13.6225	−1.87120	−0.935598	−	0.353067i	$-0.885139\pi$
$53$	−13.6225	−1.87120	−0.935598	+	0.353067i	$0.885139\pi$
$54$	0.345654i	0.0470375i
$55$	3.10548	0.418743
$56$	2.48280	0.331778
$57$	− 14.1841i	− 1.87873i
$58$	− 3.98731i	− 0.523559i
$59$	4.03056i	0.524734i	0.964968	+	0.262367i	$0.0845031\pi$
$59$	4.03056i	0.524734i	−0.964968	+	0.262367i	$0.915497\pi$
$60$	− 4.64422i	− 0.599566i
$61$	−4.60097	−0.589094	−0.294547	−	0.955637i	$-0.595169\pi$
$61$	−4.60097	−0.589094	−0.294547	+	0.955637i	$0.595169\pi$
$62$	1.56674	0.198976
$63$	2.79790i	0.352502i
$64$	−1.69131	−0.211413
$65$	0	0
$66$	4.11817	0.506912
$67$	7.57559i	0.925505i	0.886487	+	0.462753i	$0.153138\pi$
$67$	7.57559i	0.925505i	−0.886487	+	0.462753i	$0.846862\pi$
$68$	−5.83747	−0.707897
$69$	15.2273	1.83315
$70$	− 0.916066i	− 0.109491i
$71$	7.22732i	0.857726i	0.903370	+	0.428863i	$0.141086\pi$
$71$	7.22732i	0.857726i	−0.903370	+	0.428863i	$0.858914\pi$
$72$	− 6.94662i	− 0.818668i
$73$	15.0125i	1.75708i	0.477665	+	0.878542i	$0.341483\pi$
$73$	15.0125i	1.75708i	−0.477665	+	0.878542i	$0.658517\pi$
$74$	3.63537	0.422603
$75$	8.03424	0.927714
$76$	− 8.80948i	− 1.01052i
$77$	−2.40788	−0.274404
$78$	0	0
$79$	−9.30758	−1.04718	−0.523592	−	0.851969i	$-0.675408\pi$
$79$	−9.30758	−1.04718	−0.523592	+	0.851969i	$0.675408\pi$
$80$	− 1.58310i	− 0.176996i
$81$	−9.56546	−1.06283
$82$	−5.52973	−0.610656
$83$	− 1.36463i	− 0.149788i	−0.997192	−	0.0748940i	$-0.976138\pi$
$83$	− 1.36463i	− 0.149788i	0.997192	−	0.0748940i	$-0.0238618\pi$
$84$	3.60097i	0.392898i
$85$	5.03424i	0.546039i
$86$	0.205780i	0.0221898i
$87$	13.5170	1.44918
$88$	5.97829	0.637288
$89$	0.899698i	0.0953678i	0.998862	+	0.0476839i	$0.0151840\pi$
$89$	0.899698i	0.0953678i	−0.998862	+	0.0476839i	$0.984816\pi$
$90$	−2.56306	−0.270170
$91$	0	0
$92$	9.45742	0.986004
$93$	5.31126i	0.550752i
$94$	−0.907052	−0.0935553
$95$	−7.59729	−0.779466
$96$	− 14.0559i	− 1.43458i
$97$	15.6658i	1.59062i	0.606205	+	0.795309i	$0.292691\pi$
$97$	15.6658i	1.59062i	−0.606205	+	0.795309i	$0.707309\pi$
$98$	0.710287i	0.0717498i
$99$	6.73701i	0.677095i
$100$	4.98992	0.498992
$101$	−0.684905	−0.0681506	−0.0340753	−	0.999419i	$-0.510849\pi$
$101$	−0.684905	−0.0681506	−0.0340753	+	0.999419i	$0.510849\pi$
$102$	6.67589i	0.661012i
$103$	−17.9249	−1.76619	−0.883097	−	0.469190i	$-0.844546\pi$
$103$	−17.9249	−1.76619	−0.883097	+	0.469190i	$0.844546\pi$
$104$	0	0
$105$	3.10548	0.303064
$106$	9.67589i	0.939806i
$107$	8.49549	0.821290	0.410645	−	0.911795i	$-0.365304\pi$
$107$	8.49549	0.821290	0.410645	+	0.911795i	$0.365304\pi$
$108$	−0.727766	−0.0700293
$109$	12.0928i	1.15828i	0.815228	+	0.579139i	$0.196611\pi$
$109$	12.0928i	1.15828i	−0.815228	+	0.579139i	$0.803389\pi$
$110$	− 2.20578i	− 0.210313i
$111$	12.3239i	1.16974i
$112$	1.22748i	0.115986i
$113$	−14.2527	−1.34078	−0.670391	−	0.742008i	$-0.733874\pi$
$113$	−14.2527	−1.34078	−0.670391	+	0.742008i	$0.733874\pi$
$114$	−10.0748	−0.943588
$115$	− 8.15608i	− 0.760558i
$116$	8.39519	0.779474
$117$	0	0
$118$	2.86285	0.263547
$119$	− 3.90338i	− 0.357822i
$120$	−7.71029	−0.703850
$121$	5.20210	0.472918
$122$	3.26801i	0.295872i
$123$	− 18.7459i	− 1.69026i
$124$	3.29873i	0.296234i
$125$	− 10.7519i	− 0.961677i
$126$	1.98731	0.177044
$127$	8.82462	0.783058	0.391529	−	0.920166i	$-0.371946\pi$
$127$	8.82462	0.783058	0.391529	+	0.920166i	$0.371946\pi$
$128$	− 10.4736i	− 0.925747i
$129$	−0.697596	−0.0614199
$130$	0	0
$131$	−19.4294	−1.69756	−0.848778	−	0.528749i	$-0.822661\pi$
$131$	−19.4294	−1.69756	−0.848778	+	0.528749i	$0.822661\pi$
$132$	8.67071i	0.754689i
$133$	5.89068	0.510787
$134$	5.38084	0.464834
$135$	0.627626i	0.0540174i
$136$	9.69131i	0.831023i
$137$	− 10.2362i	− 0.874536i	−0.899331	−	0.437268i	$-0.855946\pi$
$137$	− 10.2362i	− 0.874536i	0.899331	−	0.437268i	$-0.144054\pi$
$138$	− 10.8158i	− 0.920699i
$139$	8.14723	0.691039	0.345519	−	0.938412i	$-0.387703\pi$
$139$	8.14723	0.691039	0.345519	+	0.938412i	$0.387703\pi$
$140$	1.92876	0.163010
$141$	− 3.07492i	− 0.258955i
$142$	5.13347	0.430791
$143$	0	0
$144$	3.43438	0.286198
$145$	− 7.24001i	− 0.601250i
$146$	10.6632	0.882493
$147$	−2.40788	−0.198599
$148$	7.65419i	0.629170i
$149$	− 9.78888i	− 0.801937i	−0.916092	−	0.400968i	$-0.868674\pi$
$149$	− 9.78888i	− 0.801937i	0.916092	−	0.400968i	$-0.131326\pi$
$150$	− 5.70661i	− 0.465943i
$151$	− 14.7407i	− 1.19958i	−0.800158	−	0.599790i	$-0.795251\pi$
$151$	− 14.7407i	− 1.19958i	0.800158	−	0.599790i	$-0.204749\pi$
$152$	−14.6254	−1.18628
$153$	−10.9212	−0.882930
$154$	1.71029i	0.137819i
$155$	2.84482	0.228502
$156$	0	0
$157$	20.5844	1.64282	0.821409	−	0.570340i	$-0.193189\pi$
$157$	20.5844	1.64282	0.821409	+	0.570340i	$0.193189\pi$
$158$	6.61105i	0.525947i
$159$	−32.8014	−2.60132
$160$	−7.52866	−0.595193
$161$	6.32395i	0.498397i
$162$	6.79422i	0.533804i
$163$	3.98086i	0.311805i	0.987772	+	0.155902i	$0.0498286\pi$
$163$	3.98086i	0.311805i	−0.987772	+	0.155902i	$0.950171\pi$
$164$	− 11.6427i	− 0.909144i
$165$	7.47763	0.582132
$166$	−0.969281	−0.0752308
$167$	− 8.67846i	− 0.671559i	−0.941941	−	0.335780i	$-0.891000\pi$
$167$	− 8.67846i	− 0.671559i	0.941941	−	0.335780i	$-0.109000\pi$
$168$	5.97829	0.461235
$169$	0	0
$170$	3.57575	0.274248
$171$	− 16.4815i	− 1.26037i
$172$	−0.433264	−0.0330361
$173$	−0.933934	−0.0710057	−0.0355028	−	0.999370i	$-0.511303\pi$
$173$	−0.933934	−0.0710057	−0.0355028	+	0.999370i	$0.511303\pi$
$174$	− 9.60097i	− 0.727848i
$175$	3.33664i	0.252226i
$176$	2.95564i	0.222790i
$177$	9.70511i	0.729481i
$178$	0.639044	0.0478984
$179$	−13.5461	−1.01248	−0.506241	−	0.862392i	$-0.668966\pi$
$179$	−13.5461	−1.01248	−0.506241	+	0.862392i	$0.668966\pi$
$180$	− 5.39646i	− 0.402229i
$181$	8.86269	0.658759	0.329379	−	0.944198i	$-0.393161\pi$
$181$	8.86269	0.658759	0.329379	+	0.944198i	$0.393161\pi$
$182$	0	0
$183$	−11.0786	−0.818953
$184$	− 15.7011i	− 1.15750i
$185$	6.60097	0.485313
$186$	3.77252	0.276614
$187$	− 9.39887i	− 0.687313i
$188$	− 1.90978i	− 0.139285i
$189$	− 0.486640i	− 0.0353978i
$190$	5.39626i	0.391486i
$191$	−15.3735	−1.11239	−0.556193	−	0.831053i	$-0.687739\pi$
$191$	−15.3735	−1.11239	−0.556193	+	0.831053i	$0.687739\pi$
$192$	−4.07247	−0.293905
$193$	24.4953i	1.76321i	0.471986	+	0.881606i	$0.343537\pi$
$193$	24.4953i	1.76321i	−0.471986	+	0.881606i	$0.656463\pi$
$194$	11.1272	0.798885
$195$	0	0
$196$	−1.49549	−0.106821
$197$	− 6.71412i	− 0.478362i	−0.970975	−	0.239181i	$-0.923121\pi$
$197$	− 6.71412i	− 0.478362i	0.970975	−	0.239181i	$-0.0768789\pi$
$198$	4.78521	0.340070
$199$	4.87282	0.345425	0.172712	−	0.984972i	$-0.444747\pi$
$199$	4.87282	0.345425	0.172712	+	0.984972i	$0.444747\pi$
$200$	− 8.28421i	− 0.585782i
$201$	18.2411i	1.28663i
$202$	0.486479i	0.0342285i
$203$	5.61366i	0.394002i
$204$	−14.0559	−0.984113
$205$	−10.0407	−0.701272
$206$	12.7318i	0.887069i
$207$	17.6938	1.22980
$208$	0	0
$209$	14.1841	0.981133
$210$	− 2.20578i	− 0.152213i
$211$	3.68747	0.253856	0.126928	−	0.991912i	$-0.459488\pi$
$211$	3.68747	0.253856	0.126928	+	0.991912i	$0.459488\pi$
$212$	−20.3724	−1.39918
$213$	17.4025i	1.19240i
$214$	− 6.03424i	− 0.412492i
$215$	0.373647i	0.0254825i
$216$	1.20823i	0.0822096i
$217$	−2.20578	−0.149738
$218$	8.58935	0.581744
$219$	36.1484i	2.44268i
$220$	4.64422	0.313113
$221$	0	0
$222$	8.75354	0.587499
$223$	8.81426i	0.590247i	0.955459	+	0.295123i	$0.0953608\pi$
$223$	8.81426i	0.590247i	−0.955459	+	0.295123i	$0.904639\pi$
$224$	5.83747	0.390032
$225$	9.33557	0.622372
$226$	10.1235i	0.673406i
$227$	− 13.4511i	− 0.892783i	−0.894838	−	0.446391i	$-0.852709\pi$
$227$	− 13.4511i	− 0.892783i	0.894838	−	0.446391i	$-0.147291\pi$
$228$	− 21.2122i	− 1.40481i
$229$	− 6.81576i	− 0.450398i	−0.974313	−	0.225199i	$-0.927697\pi$
$229$	− 6.81576i	− 0.450398i	0.974313	−	0.225199i	$-0.0723033\pi$
$230$	−5.79316	−0.381989
$231$	−5.79790	−0.381474
$232$	− 13.9376i	− 0.915049i
$233$	25.0672	1.64221	0.821105	−	0.570777i	$-0.193358\pi$
$233$	25.0672	1.64221	0.821105	+	0.570777i	$0.193358\pi$
$234$	0	0
$235$	−1.64699	−0.107438
$236$	6.02767i	0.392368i
$237$	−22.4116	−1.45579
$238$	−2.77252	−0.179715
$239$	− 2.78521i	− 0.180160i	−0.995935	−	0.0900800i	$-0.971288\pi$
$239$	− 2.78521i	− 0.180160i	0.995935	−	0.0900800i	$-0.0287123\pi$
$240$	− 3.81193i	− 0.246059i
$241$	− 6.97829i	− 0.449511i	−0.974415	−	0.224756i	$-0.927842\pi$
$241$	− 6.97829i	− 0.449511i	0.974415	−	0.224756i	$-0.0721584\pi$
$242$	− 3.69498i	− 0.237523i
$243$	−21.5726	−1.38388
$244$	−6.88072	−0.440493
$245$	1.28971i	0.0823968i
$246$	−13.3149	−0.848929
$247$	0	0
$248$	5.47651	0.347759
$249$	− 3.28588i	− 0.208234i
$250$	−7.63691	−0.483001
$251$	0.783029	0.0494244	0.0247122	−	0.999695i	$-0.492133\pi$
$251$	0.783029	0.0494244	0.0247122	+	0.999695i	$0.492133\pi$
$252$	4.18424i	0.263582i
$253$	15.2273i	0.957334i
$254$	− 6.26801i	− 0.393290i
$255$	12.1218i	0.759099i
$256$	−10.8219	−0.676368
$257$	−3.25804	−0.203231	−0.101616	−	0.994824i	$-0.532401\pi$
$257$	−3.25804	−0.203231	−0.101616	+	0.994824i	$0.532401\pi$
$258$	0.495493i	0.0308480i
$259$	−5.11817	−0.318028
$260$	0	0
$261$	15.7064	0.972205
$262$	13.8005i	0.852595i
$263$	29.5829	1.82416	0.912081	−	0.410010i	$-0.134475\pi$
$263$	29.5829	1.82416	0.912081	+	0.410010i	$0.134475\pi$
$264$	14.3950	0.885953
$265$	17.5691i	1.07926i
$266$	− 4.18407i	− 0.256542i
$267$	2.16637i	0.132580i
$268$	11.3292i	0.692043i
$269$	1.23650	0.0753907	0.0376953	−	0.999289i	$-0.487998\pi$
$269$	1.23650	0.0753907	0.0376953	+	0.999289i	$0.487998\pi$
$270$	0.445794	0.0271302
$271$	− 25.2071i	− 1.53122i	−0.643303	−	0.765612i	$-0.722436\pi$
$271$	− 25.2071i	− 1.53122i	0.643303	−	0.765612i	$-0.277564\pi$
$272$	−4.79133	−0.290517
$273$	0	0
$274$	−7.27062	−0.439234
$275$	8.03424i	0.484483i
$276$	22.7724	1.37073
$277$	−9.53602	−0.572964	−0.286482	−	0.958086i	$-0.592486\pi$
$277$	−9.53602	−0.572964	−0.286482	+	0.958086i	$0.592486\pi$
$278$	− 5.78687i	− 0.347073i
$279$	6.17154i	0.369481i
$280$	− 3.20210i	− 0.191362i
$281$	− 9.56546i	− 0.570628i	−0.958434	−	0.285314i	$-0.907902\pi$
$281$	− 9.56546i	− 0.570628i	0.958434	−	0.285314i	$-0.0920978\pi$
$282$	−2.18407	−0.130060
$283$	−11.4320	−0.679564	−0.339782	−	0.940504i	$-0.610353\pi$
$283$	−11.4320	−0.679564	−0.339782	+	0.940504i	$0.610353\pi$
$284$	10.8084i	0.641361i
$285$	−18.2934	−1.08361
$286$	0	0
$287$	7.78521	0.459546
$288$	− 16.3326i	− 0.962410i
$289$	−1.76366	−0.103745
$290$	−5.14249	−0.301977
$291$	37.7213i	2.21126i
$292$	22.4511i	1.31385i
$293$	9.35562i	0.546561i	0.961934	+	0.273281i	$0.0881087\pi$
$293$	9.35562i	0.546561i	−0.961934	+	0.273281i	$0.911891\pi$
$294$	1.71029i	0.0997459i
$295$	5.19826	0.302655
$296$	12.7074	0.738603
$297$	− 1.17177i	− 0.0679931i
$298$	−6.95291	−0.402771
$299$	0	0
$300$	12.0151	0.693695
$301$	− 0.289713i	− 0.0166988i
$302$	−10.4701	−0.602487
$303$	−1.64917	−0.0947423
$304$	− 7.23072i	− 0.414711i
$305$	5.93393i	0.339776i
$306$	7.75721i	0.443450i
$307$	− 8.11449i	− 0.463119i	−0.972821	−	0.231559i	$-0.925617\pi$
$307$	− 8.11449i	− 0.463119i	0.972821	−	0.231559i	$-0.0743827\pi$
$308$	−3.60097	−0.205184
$309$	−43.1611	−2.45535
$310$	− 2.02064i	− 0.114765i
$311$	8.64016	0.489938	0.244969	−	0.969531i	$-0.421222\pi$
$311$	8.64016	0.489938	0.244969	+	0.969531i	$0.421222\pi$
$312$	0	0
$313$	−5.22732	−0.295466	−0.147733	−	0.989027i	$-0.547198\pi$
$313$	−5.22732	−0.295466	−0.147733	+	0.989027i	$0.547198\pi$
$314$	− 14.6209i	− 0.825103i
$315$	3.60849	0.203315
$316$	−13.9194	−0.783029
$317$	11.1929i	0.628657i	0.949314	+	0.314329i	$0.101779\pi$
$317$	11.1929i	0.628657i	−0.949314	+	0.314329i	$0.898221\pi$
$318$	23.2984i	1.30651i
$319$	13.5170i	0.756809i
$320$	2.18130i	0.121938i
$321$	20.4561	1.14175
$322$	4.49182	0.250319
$323$	22.9936i	1.27940i
$324$	−14.3051	−0.794727
$325$	0	0
$326$	2.82755	0.156604
$327$	29.1180i	1.61023i
$328$	−19.3291	−1.06727
$329$	1.27702	0.0704045
$330$	− 5.31126i	− 0.292375i
$331$	20.0468i	1.10187i	0.834548	+	0.550935i	$0.185729\pi$
$331$	20.0468i	1.10187i	−0.834548	+	0.550935i	$0.814271\pi$
$332$	− 2.04080i	− 0.112003i
$333$	14.3201i	0.784737i
$334$	−6.16419	−0.337290
$335$	9.77034	0.533811
$336$	2.95564i	0.161243i
$337$	−18.5866	−1.01248	−0.506239	−	0.862393i	$-0.668965\pi$
$337$	−18.5866	−1.01248	−0.506239	+	0.862393i	$0.668965\pi$
$338$	0	0
$339$	−34.3188	−1.86394
$340$	7.52866i	0.408299i
$341$	−5.31126	−0.287621
$342$	−11.7066	−0.633021
$343$	− 1.00000i	− 0.0539949i
$344$	0.719301i	0.0387821i
$345$	− 19.6389i	− 1.05732i
$346$	0.663361i	0.0356625i
$347$	22.3417	1.19936	0.599681	−	0.800239i	$-0.295294\pi$
$347$	22.3417	1.19936	0.599681	+	0.800239i	$0.295294\pi$
$348$	20.2146	1.08362
$349$	− 8.78632i	− 0.470321i	−0.971957	−	0.235160i	$-0.924438\pi$
$349$	− 8.78632i	− 0.470321i	0.971957	−	0.235160i	$-0.0755615\pi$
$350$	2.36997	0.126680
$351$	0	0
$352$	14.0559	0.749184
$353$	7.71898i	0.410840i	0.978674	+	0.205420i	$0.0658560\pi$
$353$	7.71898i	0.410840i	−0.978674	+	0.205420i	$0.934144\pi$
$354$	6.89341	0.366381
$355$	9.32118	0.494717
$356$	1.34549i	0.0713110i
$357$	− 9.39887i	− 0.497441i
$358$	9.62161i	0.508518i
$359$	10.5956i	0.559216i	0.960114	+	0.279608i	$0.0902045\pi$
$359$	10.5956i	0.559216i	−0.960114	+	0.279608i	$0.909795\pi$
$360$	−8.95915	−0.472189
$361$	−15.7002	−0.826324
$362$	− 6.29505i	− 0.330861i
$363$	12.5261	0.657447
$364$	0	0
$365$	19.3619	1.01345
$366$	7.86898i	0.411318i
$367$	5.82067	0.303836	0.151918	−	0.988393i	$-0.451455\pi$
$367$	5.82067	0.303836	0.151918	+	0.988393i	$0.451455\pi$
$368$	7.76255	0.404651
$369$	− 21.7822i	− 1.13394i
$370$	− 4.68858i	− 0.243748i
$371$	− 13.6225i	− 0.707246i
$372$	7.94295i	0.411823i
$373$	26.0569	1.34917	0.674587	−	0.738195i	$-0.264322\pi$
$373$	26.0569	1.34917	0.674587	+	0.738195i	$0.264322\pi$
$374$	−6.67589	−0.345202
$375$	− 25.8893i	− 1.33692i
$376$	−3.17059	−0.163511
$377$	0	0
$378$	−0.345654	−0.0177785
$379$	15.6532i	0.804053i	0.915628	+	0.402026i	$0.131694\pi$
$379$	15.6532i	0.804053i	−0.915628	+	0.402026i	$0.868306\pi$
$380$	−11.3617	−0.582843
$381$	21.2486	1.08860
$382$	10.9196i	0.558694i
$383$	− 12.5588i	− 0.641724i	−0.947126	−	0.320862i	$-0.896027\pi$
$383$	− 12.5588i	− 0.641724i	0.947126	−	0.320862i	$-0.103973\pi$
$384$	− 25.2193i	− 1.28696i
$385$	3.10548i	0.158270i
$386$	17.3987	0.885571
$387$	−0.810588	−0.0412045
$388$	23.4280i	1.18938i
$389$	0.503007	0.0255035	0.0127517	−	0.999919i	$-0.495941\pi$
$389$	0.503007	0.0255035	0.0127517	+	0.999919i	$0.495941\pi$
$390$	0	0
$391$	−24.6847	−1.24836
$392$	2.48280i	0.125400i
$393$	−46.7838	−2.35993
$394$	−4.76895	−0.240256
$395$	12.0041i	0.603992i
$396$	10.0751i	0.506295i
$397$	2.35044i	0.117965i	0.998259	+	0.0589827i	$0.0187857\pi$
$397$	2.35044i	0.117965i	−0.998259	+	0.0589827i	$0.981214\pi$
$398$	− 3.46110i	− 0.173489i
$399$	14.1841	0.710092
$400$	4.09567	0.204784
$401$	34.6046i	1.72807i	0.503429	+	0.864037i	$0.332072\pi$
$401$	34.6046i	1.72807i	−0.503429	+	0.864037i	$0.667928\pi$
$402$	12.9564	0.646208
$403$	0	0
$404$	−1.02427	−0.0509593
$405$	12.3367i	0.613016i
$406$	3.98731	0.197887
$407$	−12.3239	−0.610875
$408$	23.3355i	1.15528i
$409$	− 8.02411i	− 0.396767i	−0.980125	−	0.198383i	$-0.936431\pi$
$409$	− 8.02411i	− 0.396767i	0.980125	−	0.198383i	$-0.0635691\pi$
$410$	7.13176i	0.352213i
$411$	− 24.6475i	− 1.21577i
$412$	−26.8066	−1.32067
$413$	−4.03056	−0.198331
$414$	− 12.5676i	− 0.617666i
$415$	−1.75999	−0.0863943
$416$	0	0
$417$	19.6176	0.960676
$418$	− 10.0748i	− 0.492773i
$419$	−11.6694	−0.570090	−0.285045	−	0.958514i	$-0.592008\pi$
$419$	−11.6694	−0.570090	−0.285045	+	0.958514i	$0.592008\pi$
$420$	4.64422	0.226615
$421$	− 18.3381i	− 0.893746i	−0.894597	−	0.446873i	$-0.852538\pi$
$421$	− 18.3381i	− 0.893746i	0.894597	−	0.446873i	$-0.147462\pi$
$422$	− 2.61916i	− 0.127499i
$423$	− 3.57298i	− 0.173724i
$424$	33.8220i	1.64254i
$425$	−13.0242	−0.631764
$426$	12.3608	0.598882
$427$	− 4.60097i	− 0.222657i
$428$	12.7049	0.614117
$429$	0	0
$430$	0.265397	0.0127986
$431$	− 31.2435i	− 1.50495i	−0.658622	−	0.752474i	$-0.728860\pi$
$431$	− 31.2435i	− 1.50495i	0.658622	−	0.752474i	$-0.271140\pi$
$432$	−0.597343	−0.0287397
$433$	30.5513	1.46820	0.734100	−	0.679041i	$-0.237604\pi$
$433$	30.5513	1.46820	0.734100	+	0.679041i	$0.237604\pi$
$434$	1.56674i	0.0752057i
$435$	− 17.4331i	− 0.835853i
$436$	18.0847i	0.866099i
$437$	− 37.2524i	− 1.78202i
$438$	25.6757	1.22683
$439$	12.1472	0.579756	0.289878	−	0.957064i	$-0.406385\pi$
$439$	12.1472	0.579756	0.289878	+	0.957064i	$0.406385\pi$
$440$	− 7.71029i	− 0.367573i
$441$	−2.79790	−0.133233
$442$	0	0
$443$	−8.46532	−0.402200	−0.201100	−	0.979571i	$-0.564452\pi$
$443$	−8.46532	−0.402200	−0.201100	+	0.979571i	$0.564452\pi$
$444$	18.4304i	0.874667i
$445$	1.16035	0.0550060
$446$	6.26065	0.296451
$447$	− 23.5705i	− 1.11485i
$448$	− 1.69131i	− 0.0799068i
$449$	23.3264i	1.10084i	0.834888	+	0.550420i	$0.185533\pi$
$449$	23.3264i	1.10084i	−0.834888	+	0.550420i	$0.814467\pi$
$450$	− 6.63093i	− 0.312585i
$451$	18.7459	0.882708
$452$	−21.3148	−1.00256
$453$	− 35.4938i	− 1.66765i
$454$	−9.55416	−0.448399
$455$	0	0
$456$	−35.2162	−1.64915
$457$	15.4866i	0.724434i	0.932094	+	0.362217i	$0.117980\pi$
$457$	15.4866i	0.724434i	−0.932094	+	0.362217i	$0.882020\pi$
$458$	−4.84115	−0.226212
$459$	1.89954	0.0886628
$460$	− 12.1974i	− 0.568705i
$461$	− 9.28204i	− 0.432308i	−0.976359	−	0.216154i	$-0.930649\pi$
$461$	− 9.28204i	− 0.432308i	0.976359	−	0.216154i	$-0.0693513\pi$
$462$	4.11817i	0.191595i
$463$	− 28.8283i	− 1.33976i	−0.742467	−	0.669882i	$-0.766345\pi$
$463$	− 28.8283i	− 1.33976i	0.742467	−	0.669882i	$-0.233655\pi$
$464$	6.89068	0.319892
$465$	6.85000	0.317661
$466$	− 17.8049i	− 0.824797i
$467$	2.87393	0.132990	0.0664948	−	0.997787i	$-0.478818\pi$
$467$	2.87393	0.132990	0.0664948	+	0.997787i	$0.478818\pi$
$468$	0	0
$469$	−7.57559	−0.349808
$470$	1.16984i	0.0539606i
$471$	49.5649	2.28383
$472$	10.0071	0.460613
$473$	− 0.697596i	− 0.0320755i
$474$	15.9186i	0.731167i
$475$	− 19.6551i	− 0.901837i
$476$	− 5.83747i	− 0.267560i
$477$	−38.1144	−1.74514
$478$	−1.97829	−0.0904851
$479$	22.6082i	1.03299i	0.856289	+	0.516497i	$0.172764\pi$
$479$	22.6082i	1.03299i	−0.856289	+	0.516497i	$0.827236\pi$
$480$	−18.1281	−0.827432
$481$	0	0
$482$	−4.95659	−0.225766
$483$	15.2273i	0.692867i
$484$	7.77971	0.353623
$485$	20.2043	0.917432
$486$	15.3227i	0.695053i
$487$	2.86803i	0.129963i	0.997886	+	0.0649814i	$0.0206988\pi$
$487$	2.86803i	0.129963i	−0.997886	+	0.0649814i	$0.979301\pi$
$488$	11.4233i	0.517108i
$489$	9.58544i	0.433469i
$490$	0.916066	0.0413837
$491$	22.7201	1.02534	0.512672	−	0.858585i	$-0.328656\pi$
$491$	22.7201	1.02534	0.512672	+	0.858585i	$0.328656\pi$
$492$	− 28.0343i	− 1.26388i
$493$	−21.9122	−0.986877
$494$	0	0
$495$	8.68881	0.390533
$496$	2.70756i	0.121573i
$497$	−7.22732	−0.324190
$498$	−2.33391	−0.104585
$499$	− 18.0151i	− 0.806466i	−0.915097	−	0.403233i	$-0.867886\pi$
$499$	− 18.0151i	− 0.806466i	0.915097	−	0.403233i	$-0.132114\pi$
$500$	− 16.0794i	− 0.719091i
$501$	− 20.8967i	− 0.933596i
$502$	− 0.556175i	− 0.0248233i
$503$	−31.1496	−1.38889	−0.694447	−	0.719544i	$-0.744351\pi$
$503$	−31.1496	−1.38889	−0.694447	+	0.719544i	$0.744351\pi$
$504$	6.94662	0.309427
$505$	0.883331i	0.0393077i
$506$	10.8158	0.480819
$507$	0	0
$508$	13.1972	0.585529
$509$	− 39.5018i	− 1.75089i	−0.483319	−	0.875444i	$-0.660569\pi$
$509$	− 39.5018i	− 1.75089i	0.483319	−	0.875444i	$-0.339431\pi$
$510$	8.60999	0.381257
$511$	−15.0125	−0.664115
$512$	− 13.2606i	− 0.586042i
$513$	2.86664i	0.126565i
$514$	2.31414i	0.102073i
$515$	23.1180i	1.01870i
$516$	−1.04325	−0.0459265
$517$	3.07492	0.135235
$518$	3.63537i	0.159729i
$519$	−2.24880	−0.0987115
$520$	0	0
$521$	−17.7672	−0.778394	−0.389197	−	0.921155i	$-0.627247\pi$
$521$	−17.7672	−0.778394	−0.389197	+	0.921155i	$0.627247\pi$
$522$	− 11.1561i	− 0.488288i
$523$	−1.78904	−0.0782294	−0.0391147	−	0.999235i	$-0.512454\pi$
$523$	−1.78904	−0.0782294	−0.0391147	+	0.999235i	$0.512454\pi$
$524$	−29.0566	−1.26934
$525$	8.03424i	0.350643i
$526$	− 21.0124i	− 0.916183i
$527$	− 8.60999i	− 0.375057i
$528$	7.11683i	0.309720i
$529$	16.9923	0.738797
$530$	12.4791	0.542059
$531$	11.2771i	0.489384i
$532$	8.80948	0.381939
$533$	0	0
$534$	1.53874	0.0665879
$535$	− 10.9568i	− 0.473702i
$536$	18.8087	0.812412
$537$	−32.6174	−1.40754
$538$	− 0.878269i	− 0.0378649i
$539$	− 2.40788i	− 0.103715i
$540$	0.938610i	0.0403913i
$541$	− 15.4027i	− 0.662214i	−0.943593	−	0.331107i	$-0.892578\pi$
$541$	− 15.4027i	− 0.662214i	0.943593	−	0.331107i	$-0.107422\pi$
$542$	−17.9043	−0.769055
$543$	21.3403	0.915801
$544$	22.7858i	0.976935i
$545$	15.5962	0.668069
$546$	0	0
$547$	−3.96944	−0.169721	−0.0848605	−	0.996393i	$-0.527044\pi$
$547$	−3.96944	−0.169721	−0.0848605	+	0.996393i	$0.527044\pi$
$548$	− 15.3081i	− 0.653931i
$549$	−12.8730	−0.549408
$550$	5.70661	0.243331
$551$	− 33.0683i	− 1.40876i
$552$	− 37.8064i	− 1.60915i
$553$	− 9.30758i	− 0.395799i
$554$	6.77331i	0.287770i
$555$	15.8944	0.674678
$556$	12.1841	0.516722
$557$	− 18.6901i	− 0.791924i	−0.918267	−	0.395962i	$-0.870411\pi$
$557$	− 18.6901i	− 0.791924i	0.918267	−	0.395962i	$-0.129589\pi$
$558$	4.38357	0.185571
$559$	0	0
$560$	1.58310	0.0668983
$561$	− 22.6314i	− 0.955497i
$562$	−6.79422	−0.286597
$563$	−36.3059	−1.53011	−0.765056	−	0.643964i	$-0.777289\pi$
$563$	−36.3059	−1.53011	−0.765056	+	0.643964i	$0.777289\pi$
$564$	− 4.59852i	− 0.193633i
$565$	18.3819i	0.773333i
$566$	8.12002i	0.341310i
$567$	− 9.56546i	− 0.401712i
$568$	17.9440	0.752914
$569$	−10.9760	−0.460136	−0.230068	−	0.973175i	$-0.573895\pi$
$569$	−10.9760	−0.460136	−0.230068	+	0.973175i	$0.573895\pi$
$570$	12.9936i	0.544240i
$571$	−31.3363	−1.31138	−0.655692	−	0.755028i	$-0.727623\pi$
$571$	−31.3363	−1.31138	−0.655692	+	0.755028i	$0.727623\pi$
$572$	0	0
$573$	−37.0175	−1.54643
$574$	− 5.52973i	− 0.230806i
$575$	21.1007	0.879962
$576$	−4.73210	−0.197171
$577$	− 42.7876i	− 1.78127i	−0.454717	−	0.890636i	$-0.650260\pi$
$577$	− 42.7876i	− 1.78127i	0.454717	−	0.890636i	$-0.349740\pi$
$578$	1.25271i	0.0521057i
$579$	58.9819i	2.45120i
$580$	− 10.8274i	− 0.449583i
$581$	1.36463	0.0566145
$582$	26.7929	1.11060
$583$	− 32.8014i	− 1.35850i
$584$	37.2731	1.54237
$585$	0	0
$586$	6.64517	0.274509
$587$	− 38.7886i	− 1.60098i	−0.599349	−	0.800488i	$-0.704574\pi$
$587$	− 38.7886i	− 1.60098i	0.599349	−	0.800488i	$-0.295426\pi$
$588$	−3.60097	−0.148502
$589$	12.9936	0.535390
$590$	− 3.69226i	− 0.152008i
$591$	− 16.1668i	− 0.665014i
$592$	6.28247i	0.258208i
$593$	29.9564i	1.23016i	0.788464	+	0.615081i	$0.210877\pi$
$593$	29.9564i	1.23016i	−0.788464	+	0.615081i	$0.789123\pi$
$594$	−0.832293	−0.0341494
$595$	−5.03424	−0.206384
$596$	− 14.6392i	− 0.599645i
$597$	11.7332	0.480207
$598$	0	0
$599$	41.2539	1.68559	0.842794	−	0.538236i	$-0.180909\pi$
$599$	41.2539	1.68559	0.842794	+	0.538236i	$0.180909\pi$
$600$	− 19.9474i	− 0.814350i
$601$	6.61089	0.269664	0.134832	−	0.990868i	$-0.456951\pi$
$601$	6.61089	0.269664	0.134832	+	0.990868i	$0.456951\pi$
$602$	−0.205780	−0.00838695
$603$	21.1957i	0.863156i
$604$	− 22.0446i	− 0.896982i
$605$	− 6.70922i	− 0.272769i
$606$	1.17138i	0.0475842i
$607$	−20.8832	−0.847622	−0.423811	−	0.905751i	$-0.639308\pi$
$607$	−20.8832	−0.847622	−0.423811	+	0.905751i	$0.639308\pi$
$608$	−34.3867	−1.39456
$609$	13.5170i	0.547738i
$610$	4.21479	0.170652
$611$	0	0
$612$	−16.3326	−0.660208
$613$	− 4.29655i	− 0.173536i	−0.996229	−	0.0867680i	$-0.972346\pi$
$613$	− 4.29655i	− 0.173536i	0.996229	−	0.0867680i	$-0.0276539\pi$
$614$	−5.76362	−0.232601
$615$	−24.1768	−0.974902
$616$	5.97829i	0.240872i
$617$	− 30.7380i	− 1.23746i	−0.785602	−	0.618732i	$-0.787647\pi$
$617$	− 30.7380i	− 1.23746i	0.785602	−	0.618732i	$-0.212353\pi$
$618$	30.6568i	1.23320i
$619$	20.6417i	0.829658i	0.909899	+	0.414829i	$0.136159\pi$
$619$	20.6417i	0.829658i	−0.909899	+	0.414829i	$0.863841\pi$
$620$	4.25441	0.170861
$621$	−3.07748	−0.123495
$622$	− 6.13699i	− 0.246071i
$623$	−0.899698	−0.0360457
$624$	0	0
$625$	2.81636	0.112654
$626$	3.71290i	0.148397i
$627$	34.1536	1.36396
$628$	30.7839	1.22841
$629$	− 19.9781i	− 0.796580i
$630$	− 2.56306i	− 0.102115i
$631$	− 29.3366i	− 1.16787i	−0.811799	−	0.583937i	$-0.801512\pi$
$631$	− 29.3366i	− 1.16787i	0.811799	−	0.583937i	$-0.198488\pi$
$632$	23.1089i	0.919222i
$633$	8.87899	0.352908
$634$	7.95019	0.315742
$635$	− 11.3812i	− 0.451650i
$636$	−49.0543	−1.94513
$637$	0	0
$638$	9.60097	0.380106
$639$	20.2213i	0.799943i
$640$	−13.5080	−0.533950
$641$	4.01680	0.158654	0.0793271	−	0.996849i	$-0.474723\pi$
$641$	4.01680	0.158654	0.0793271	+	0.996849i	$0.474723\pi$
$642$	− 14.5297i	− 0.573443i
$643$	− 6.87282i	− 0.271037i	−0.990775	−	0.135519i	$-0.956730\pi$
$643$	− 6.87282i	− 0.271037i	0.990775	−	0.135519i	$-0.0432701\pi$
$644$	9.45742i	0.372675i
$645$	0.899698i	0.0354256i
$646$	16.3320	0.642574
$647$	33.7431	1.32658	0.663289	−	0.748363i	$-0.269160\pi$
$647$	33.7431	1.32658	0.663289	+	0.748363i	$0.269160\pi$
$648$	23.7491i	0.932955i
$649$	−9.70511	−0.380959
$650$	0	0
$651$	−5.31126	−0.208165
$652$	5.95335i	0.233151i
$653$	32.4002	1.26792	0.633958	−	0.773367i	$-0.281429\pi$
$653$	32.4002	1.26792	0.633958	+	0.773367i	$0.281429\pi$
$654$	20.6821	0.808735
$655$	25.0584i	0.979112i
$656$	− 9.55622i	− 0.373108i
$657$	42.0035i	1.63871i
$658$	− 0.907052i	− 0.0353606i
$659$	4.01035	0.156221	0.0781106	−	0.996945i	$-0.475111\pi$
$659$	4.01035	0.156221	0.0781106	+	0.996945i	$0.475111\pi$
$660$	11.1827	0.435287
$661$	1.81794i	0.0707097i	0.999375	+	0.0353549i	$0.0112561\pi$
$661$	1.81794i	0.0707097i	−0.999375	+	0.0353549i	$0.988744\pi$
$662$	14.2389	0.553412
$663$	0	0
$664$	−3.38811	−0.131484
$665$	− 7.59729i	− 0.294610i
$666$	10.1714	0.394133
$667$	35.5005	1.37459
$668$	− 12.9786i	− 0.502156i
$669$	21.2237i	0.820556i
$670$	− 6.93974i	− 0.268106i
$671$	− 11.0786i	− 0.427684i
$672$	14.0559	0.542220
$673$	22.9743	0.885594	0.442797	−	0.896622i	$-0.353986\pi$
$673$	22.9743	0.885594	0.442797	+	0.896622i	$0.353986\pi$
$674$	13.2018i	0.508515i
$675$	−1.62374	−0.0624978
$676$	0	0
$677$	38.0276	1.46152	0.730760	−	0.682634i	$-0.239166\pi$
$677$	38.0276	1.46152	0.730760	+	0.682634i	$0.239166\pi$
$678$	24.3762i	0.936163i
$679$	−15.6658	−0.601197
$680$	12.4990	0.479315
$681$	− 32.3887i	− 1.24114i
$682$	3.77252i	0.144457i
$683$	40.7786i	1.56035i	0.625560	+	0.780176i	$0.284870\pi$
$683$	40.7786i	1.56035i	−0.625560	+	0.780176i	$0.715130\pi$
$684$	− 24.6480i	− 0.942440i
$685$	−13.2017	−0.504412
$686$	−0.710287	−0.0271189
$687$	− 16.4116i	− 0.626140i
$688$	−0.355619	−0.0135578
$689$	0	0
$690$	−13.9492	−0.531038
$691$	− 3.12868i	− 0.119021i	−0.998228	−	0.0595104i	$-0.981046\pi$
$691$	− 3.12868i	− 0.119021i	0.998228	−	0.0595104i	$-0.0189539\pi$
$692$	−1.39669	−0.0530942
$693$	−6.73701	−0.255918
$694$	− 15.8690i	− 0.602378i
$695$	− 10.5076i	− 0.398576i
$696$	− 33.5601i	− 1.27209i
$697$	30.3886i	1.15105i
$698$	−6.24080	−0.236218
$699$	60.3590	2.28299
$700$	4.98992i	0.188601i
$701$	−9.61382	−0.363109	−0.181555	−	0.983381i	$-0.558113\pi$
$701$	−9.61382	−0.363109	−0.181555	+	0.983381i	$0.558113\pi$
$702$	0	0
$703$	30.1495	1.13711
$704$	− 4.07247i	− 0.153487i
$705$	−3.96576	−0.149359
$706$	5.48269	0.206344
$707$	− 0.684905i	− 0.0257585i
$708$	14.5139i	0.545467i
$709$	− 28.1294i	− 1.05642i	−0.849113	−	0.528211i	$-0.822863\pi$
$709$	− 28.1294i	− 1.05642i	0.849113	−	0.528211i	$-0.177137\pi$
$710$	− 6.62071i	− 0.248471i
$711$	−26.0417	−0.976638
$712$	2.23377	0.0837142
$713$	13.9492i	0.522403i
$714$	−6.67589	−0.249839
$715$	0	0
$716$	−20.2581	−0.757080
$717$	− 6.70645i	− 0.250457i
$718$	7.52594	0.280865
$719$	−24.9044	−0.928779	−0.464389	−	0.885631i	$-0.653726\pi$
$719$	−24.9044	−0.928779	−0.464389	+	0.885631i	$0.653726\pi$
$720$	− 4.42936i	− 0.165073i
$721$	− 17.9249i	− 0.667559i
$722$	11.1516i	0.415020i
$723$	− 16.8029i	− 0.624907i
$724$	13.2541	0.492584
$725$	18.7308	0.695643
$726$	− 8.89709i	− 0.330202i
$727$	24.2120	0.897974	0.448987	−	0.893538i	$-0.351785\pi$
$727$	24.2120	0.897974	0.448987	+	0.893538i	$0.351785\pi$
$728$	0	0
$729$	−23.2479	−0.861032
$730$	− 13.7525i	− 0.509002i
$731$	1.13086	0.0418264
$732$	−16.5680	−0.612369
$733$	− 12.3989i	− 0.457963i	−0.973431	−	0.228981i	$-0.926461\pi$
$733$	− 12.3989i	− 0.457963i	0.973431	−	0.228981i	$-0.0735395\pi$
$734$	− 4.13434i	− 0.152601i
$735$	3.10548i	0.114547i
$736$	− 36.9159i	− 1.36074i
$737$	−18.2411	−0.671921
$738$	−15.4716	−0.569518
$739$	10.9604i	0.403184i	0.979470	+	0.201592i	$0.0646115\pi$
$739$	10.9604i	0.403184i	−0.979470	+	0.201592i	$0.935388\pi$
$740$	9.87170	0.362891
$741$	0	0
$742$	−9.67589	−0.355213
$743$	40.6925i	1.49286i	0.665463	+	0.746431i	$0.268234\pi$
$743$	40.6925i	1.49286i	−0.665463	+	0.746431i	$0.731766\pi$
$744$	13.1868	0.483452
$745$	−12.6249	−0.462539
$746$	− 18.5079i	− 0.677621i
$747$	− 3.81810i	− 0.139697i
$748$	− 14.0559i	− 0.513936i
$749$	8.49549i	0.310419i
$750$	−18.3888	−0.671464
$751$	−9.40472	−0.343183	−0.171592	−	0.985168i	$-0.554891\pi$
$751$	−9.40472	−0.343183	−0.171592	+	0.985168i	$0.554891\pi$
$752$	− 1.56753i	− 0.0571618i
$753$	1.88544	0.0687093
$754$	0	0
$755$	−19.0113	−0.691890
$756$	− 0.727766i	− 0.0264686i
$757$	−29.5808	−1.07513	−0.537566	−	0.843222i	$-0.680656\pi$
$757$	−29.5808	−1.07513	−0.537566	+	0.843222i	$0.680656\pi$
$758$	11.1183	0.403834
$759$	36.6656i	1.33088i
$760$	18.8626i	0.684218i
$761$	− 16.9417i	− 0.614137i	−0.951687	−	0.307068i	$-0.900652\pi$
$761$	− 16.9417i	− 0.614137i	0.951687	−	0.307068i	$-0.0993481\pi$
$762$	− 15.0926i	− 0.546748i
$763$	−12.0928	−0.437788
$764$	−22.9909	−0.831783
$765$	14.0853i	0.509254i
$766$	−8.92034	−0.322305
$767$	0	0
$768$	−26.0578	−0.940281
$769$	7.36574i	0.265616i	0.991142	+	0.132808i	$0.0423993\pi$
$769$	7.36574i	0.265616i	−0.991142	+	0.132808i	$0.957601\pi$
$770$	2.20578	0.0794908
$771$	−7.84498	−0.282530
$772$	36.6326i	1.31844i
$773$	− 44.7734i	− 1.61039i	−0.593012	−	0.805194i	$-0.702061\pi$
$773$	− 44.7734i	− 1.61039i	0.593012	−	0.805194i	$-0.297939\pi$
$774$	0.575750i	0.0206949i
$775$	7.35989i	0.264375i
$776$	38.8950	1.39625
$777$	−12.3239	−0.442119
$778$	− 0.357279i	− 0.0128091i
$779$	−45.8602	−1.64311
$780$	0	0
$781$	−17.4025	−0.622712
$782$	17.5332i	0.626988i
$783$	−2.73183	−0.0976277
$784$	−1.22748	−0.0438387
$785$	− 26.5480i	− 0.947540i
$786$	33.2299i	1.18527i
$787$	18.7682i	0.669016i	0.942393	+	0.334508i	$0.108570\pi$
$787$	18.7682i	0.669016i	−0.942393	+	0.334508i	$0.891430\pi$
$788$	− 10.0409i	− 0.357693i
$789$	71.2322	2.53594
$790$	8.52636	0.303354
$791$	− 14.2527i	− 0.506768i
$792$	16.7267	0.594356
$793$	0	0
$794$	1.66949	0.0592479
$795$	42.3044i	1.50038i
$796$	7.28726	0.258290
$797$	−7.21697	−0.255638	−0.127819	−	0.991797i	$-0.540798\pi$
$797$	−7.21697	−0.255638	−0.127819	+	0.991797i	$0.540798\pi$
$798$	− 10.0748i	− 0.356643i
$799$	4.98470i	0.176346i
$800$	− 19.4775i	− 0.688635i
$801$	2.51726i	0.0889431i
$802$	24.5792	0.867922
$803$	−36.1484	−1.27565
$804$	27.2795i	0.962073i
$805$	8.15608	0.287464
$806$	0	0
$807$	2.97734	0.104807
$808$	1.70048i	0.0598228i
$809$	14.8318	0.521459	0.260729	−	0.965412i	$-0.416037\pi$
$809$	14.8318	0.521459	0.260729	+	0.965412i	$0.416037\pi$
$810$	8.76260	0.307886
$811$	18.5831i	0.652541i	0.945276	+	0.326271i	$0.105792\pi$
$811$	18.5831i	0.652541i	−0.945276	+	0.326271i	$0.894208\pi$
$812$	8.39519i	0.294613i
$813$	− 60.6958i	− 2.12869i
$814$	8.75354i	0.306811i
$815$	5.13417	0.179842
$816$	−11.5370	−0.403875
$817$	1.70661i	0.0597067i
$818$	−5.69942	−0.199275
$819$	0	0
$820$	−15.0158	−0.524374
$821$	− 26.6236i	− 0.929169i	−0.885529	−	0.464585i	$-0.846204\pi$
$821$	− 26.6236i	− 0.929169i	0.885529	−	0.464585i	$-0.153796\pi$
$822$	−17.5068	−0.610620
$823$	−6.75136	−0.235338	−0.117669	−	0.993053i	$-0.537542\pi$
$823$	−6.75136	−0.235338	−0.117669	+	0.993053i	$0.537542\pi$
$824$	44.5040i	1.55037i
$825$	19.3455i	0.673524i
$826$	2.86285i	0.0996114i
$827$	21.7430i	0.756079i	0.925789	+	0.378039i	$0.123402\pi$
$827$	21.7430i	0.756079i	−0.925789	+	0.378039i	$0.876598\pi$
$828$	26.4609	0.919579
$829$	14.6216	0.507828	0.253914	−	0.967227i	$-0.418282\pi$
$829$	14.6216	0.507828	0.253914	+	0.967227i	$0.418282\pi$
$830$	1.25009i	0.0433914i
$831$	−22.9616	−0.796529
$832$	0	0
$833$	3.90338	0.135244
$834$	− 13.9341i	− 0.482498i
$835$	−11.1927	−0.387340
$836$	21.2122	0.733639
$837$	− 1.07342i	− 0.0371028i
$838$	8.28865i	0.286327i
$839$	10.7469i	0.371023i	0.982642	+	0.185511i	$0.0593942\pi$
$839$	10.7469i	0.371023i	−0.982642	+	0.185511i	$0.940606\pi$
$840$	− 7.71029i	− 0.266030i
$841$	2.51320	0.0866620
$842$	−13.0253	−0.448883
$843$	− 23.0325i	− 0.793282i
$844$	5.51458	0.189820
$845$	0	0
$846$	−2.53784	−0.0872527
$847$	5.20210i	0.178746i
$848$	−16.7214	−0.574216
$849$	−27.5270	−0.944724
$850$	9.25088i	0.317303i
$851$	32.3670i	1.10953i
$852$	26.0254i	0.891615i
$853$	31.7709i	1.08782i	0.839145	+	0.543908i	$0.183056\pi$
$853$	31.7709i	1.08782i	−0.839145	+	0.543908i	$0.816944\pi$
$854$	−3.26801	−0.111829
$855$	−21.2564	−0.726955
$856$	− 21.0926i	− 0.720931i
$857$	0.648105	0.0221388	0.0110694	−	0.999939i	$-0.496476\pi$
$857$	0.648105	0.0221388	0.0110694	+	0.999939i	$0.496476\pi$
$858$	0	0
$859$	−43.1902	−1.47363	−0.736815	−	0.676095i	$-0.763671\pi$
$859$	−43.1902	−1.47363	−0.736815	+	0.676095i	$0.763671\pi$
$860$	0.558787i	0.0190545i
$861$	18.7459	0.638857
$862$	−22.1919	−0.755858
$863$	21.6094i	0.735592i	0.929906	+	0.367796i	$0.119888\pi$
$863$	21.6094i	0.735592i	−0.929906	+	0.367796i	$0.880112\pi$
$864$	2.84074i	0.0966441i
$865$	1.20451i	0.0409545i
$866$	− 21.7002i	− 0.737401i
$867$	−4.24669	−0.144225
$868$	−3.29873	−0.111966
$869$	− 22.4116i	− 0.760260i
$870$	−12.3825	−0.419806
$871$	0	0
$872$	30.0240	1.01674
$873$	43.8312i	1.48346i
$874$	−26.4599	−0.895018
$875$	10.7519	0.363480
$876$	54.0597i	1.82651i
$877$	− 0.880766i	− 0.0297413i	−0.999889	−	0.0148707i	$-0.995266\pi$
$877$	− 0.880766i	− 0.0297413i	0.999889	−	0.0148707i	$-0.00473366\pi$
$878$	− 8.62801i	− 0.291181i
$879$	22.5272i	0.759825i
$880$	3.81193	0.128500
$881$	0.140035	0.00471791	0.00235895	−	0.999997i	$-0.499249\pi$
$881$	0.140035	0.00471791	0.00235895	+	0.999997i	$0.499249\pi$
$882$	1.98731i	0.0669162i
$883$	18.8253	0.633522	0.316761	−	0.948505i	$-0.397405\pi$
$883$	18.8253	0.633522	0.316761	+	0.948505i	$0.397405\pi$
$884$	0	0
$885$	12.5168	0.420748
$886$	6.01281i	0.202004i
$887$	−33.3010	−1.11814	−0.559069	−	0.829121i	$-0.688841\pi$
$887$	−33.3010	−1.11814	−0.559069	+	0.829121i	$0.688841\pi$
$888$	30.5979	1.02680
$889$	8.82462i	0.295968i
$890$	− 0.824183i	− 0.0276267i
$891$	− 23.0325i	− 0.771618i
$892$	13.1817i	0.441355i
$893$	−7.52254	−0.251732
$894$	−16.7418	−0.559929
$895$	17.4706i	0.583977i
$896$	10.4736	0.349899
$897$	0	0
$898$	16.5684	0.552896
$899$	12.3825i	0.412980i
$900$	13.9613	0.465376
$901$	53.1738	1.77148
$902$	− 13.3149i	− 0.443339i
$903$	− 0.697596i	− 0.0232145i
$904$	35.3866i	1.17694i
$905$	− 11.4303i	− 0.379957i
$906$	−25.2108	−0.837573
$907$	−11.5870	−0.384740	−0.192370	−	0.981322i	$-0.561617\pi$
$907$	−11.5870	−0.384740	−0.192370	+	0.981322i	$0.561617\pi$
$908$	− 20.1161i	− 0.667575i
$909$	−1.91629	−0.0635594
$910$	0	0
$911$	52.5489	1.74102	0.870512	−	0.492147i	$-0.163788\pi$
$911$	52.5489	1.74102	0.870512	+	0.492147i	$0.163788\pi$
$912$	− 17.4107i	− 0.576527i
$913$	3.28588	0.108747
$914$	11.0000	0.363846
$915$	14.2882i	0.472354i
$916$	− 10.1929i	− 0.336784i
$917$	− 19.4294i	− 0.641616i
$918$	− 1.34922i	− 0.0445308i
$919$	−20.0534	−0.661502	−0.330751	−	0.943718i	$-0.607302\pi$
$919$	−20.0534	−0.661502	−0.330751	+	0.943718i	$0.607302\pi$
$920$	−20.2499	−0.667621
$921$	− 19.5387i	− 0.643823i
$922$	−6.59291	−0.217126
$923$	0	0
$924$	−8.67071	−0.285246
$925$	17.0775i	0.561504i
$926$	−20.4764	−0.672895
$927$	−50.1521	−1.64721
$928$	− 32.7696i	− 1.07571i
$929$	− 15.9085i	− 0.521941i	−0.965347	−	0.260971i	$-0.915957\pi$
$929$	− 15.9085i	− 0.521941i	0.965347	−	0.260971i	$-0.0840426\pi$
$930$	− 4.86546i	− 0.159545i
$931$	5.89068i	0.193059i
$932$	37.4879	1.22796
$933$	20.8045	0.681108
$934$	− 2.04131i	− 0.0667938i
$935$	−12.1218	−0.396427
$936$	0	0
$937$	26.1978	0.855846	0.427923	−	0.903815i	$-0.359245\pi$
$937$	26.1978	0.855846	0.427923	+	0.903815i	$0.359245\pi$
$938$	5.38084i	0.175691i
$939$	−12.5868	−0.410754
$940$	−2.46307	−0.0803364
$941$	− 36.3059i	− 1.18354i	−0.806108	−	0.591769i	$-0.798430\pi$
$941$	− 36.3059i	− 1.18354i	0.806108	−	0.591769i	$-0.201570\pi$
$942$	− 35.2053i	− 1.14705i
$943$	− 49.2332i	− 1.60325i
$944$	4.94745i	0.161026i
$945$	−0.627626	−0.0204167
$946$	−0.495493	−0.0161099
$947$	0.918839i	0.0298582i	0.999889	+	0.0149291i	$0.00475226\pi$
$947$	0.918839i	0.0298582i	−0.999889	+	0.0149291i	$0.995248\pi$
$948$	−33.5163	−1.08856
$949$	0	0
$950$	−13.9607	−0.452946
$951$	26.9513i	0.873954i
$952$	−9.69131	−0.314097
$953$	18.3589	0.594702	0.297351	−	0.954768i	$-0.403897\pi$
$953$	18.3589	0.594702	0.297351	+	0.954768i	$0.403897\pi$
$954$	27.0721i	0.876493i
$955$	19.8274i	0.641599i
$956$	− 4.16526i	− 0.134714i
$957$	32.5474i	1.05211i
$958$	16.0583	0.518819
$959$	10.2362	0.330543
$960$	5.25232i	0.169518i
$961$	26.1345	0.843050
$962$	0	0
$963$	23.7695	0.765962
$964$	− 10.4360i	− 0.336121i
$965$	31.5920	1.01698
$966$	10.8158	0.347992
$967$	12.5923i	0.404940i	0.979288	+	0.202470i	$0.0648969\pi$
$967$	12.5923i	0.404940i	−0.979288	+	0.202470i	$0.935103\pi$
$968$	− 12.9158i	− 0.415129i
$969$	55.3658i	1.77860i
$970$	− 14.3509i	− 0.460779i
$971$	−21.3308	−0.684537	−0.342269	−	0.939602i	$-0.611195\pi$
$971$	−21.3308	−0.684537	−0.342269	+	0.939602i	$0.611195\pi$
$972$	−32.2617	−1.03479
$973$	8.14723i	0.261188i
$974$	2.03712	0.0652736
$975$	0	0
$976$	−5.64762	−0.180776
$977$	− 42.4279i	− 1.35739i	−0.734420	−	0.678695i	$-0.762546\pi$
$977$	− 42.4279i	− 1.35739i	0.734420	−	0.678695i	$-0.237454\pi$
$978$	6.80841	0.217709
$979$	−2.16637	−0.0692374
$980$	1.92876i	0.0616119i
$981$	33.8344i	1.08025i
$982$	− 16.1378i	− 0.514977i
$983$	− 2.09758i	− 0.0669023i	−0.999440	−	0.0334511i	$-0.989350\pi$
$983$	− 2.09758i	− 0.0669023i	0.999440	−	0.0334511i	$-0.0106498\pi$
$984$	−46.5423	−1.48371
$985$	−8.65930	−0.275908
$986$	15.5640i	0.495658i
$987$	3.07492	0.0978758
$988$	0	0
$989$	−1.83213	−0.0582584
$990$	− 6.17154i	− 0.196145i
$991$	−27.6349	−0.877851	−0.438926	−	0.898523i	$-0.644641\pi$
$991$	−27.6349	−0.877851	−0.438926	+	0.898523i	$0.644641\pi$
$992$	12.8762	0.408819
$993$	48.2703i	1.53181i
$994$	5.13347i	0.162824i
$995$	− 6.28454i	− 0.199233i
$996$	− 4.91400i	− 0.155706i
$997$	−2.02783	−0.0642221	−0.0321110	−	0.999484i	$-0.510223\pi$
$997$	−2.02783	−0.0642221	−0.0321110	+	0.999484i	$0.510223\pi$
$998$	−12.7959	−0.405047
$999$	− 2.49070i	− 0.0788024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.g.337.3		8
13.2	odd	12		91.2.f.c.22.3	✓	8
13.5	odd	4		1183.2.a.k.1.2		4
13.6	odd	12		91.2.f.c.29.3	yes	8
13.8	odd	4		1183.2.a.l.1.3		4
13.12	even	2	inner	1183.2.c.g.337.6		8
39.2	even	12		819.2.o.h.568.2		8
39.32	even	12		819.2.o.h.757.2		8
52.15	even	12		1456.2.s.q.113.4		8
52.19	even	12		1456.2.s.q.1121.4		8
91.2	odd	12		637.2.h.h.165.2		8
91.6	even	12		637.2.f.i.393.3		8
91.19	even	12		637.2.g.j.263.3		8
91.32	odd	12		637.2.h.h.471.2		8
91.34	even	4		8281.2.a.bt.1.3		4
91.41	even	12		637.2.f.i.295.3		8
91.45	even	12		637.2.h.i.471.2		8
91.54	even	12		637.2.h.i.165.2		8
91.58	odd	12		637.2.g.k.263.3		8
91.67	odd	12		637.2.g.k.373.3		8
91.80	even	12		637.2.g.j.373.3		8
91.83	even	4		8281.2.a.bp.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.3	✓	8	13.2	odd	12
91.2.f.c.29.3	yes	8	13.6	odd	12
637.2.f.i.295.3		8	91.41	even	12
637.2.f.i.393.3		8	91.6	even	12
637.2.g.j.263.3		8	91.19	even	12
637.2.g.j.373.3		8	91.80	even	12
637.2.g.k.263.3		8	91.58	odd	12
637.2.g.k.373.3		8	91.67	odd	12
637.2.h.h.165.2		8	91.2	odd	12
637.2.h.h.471.2		8	91.32	odd	12
637.2.h.i.165.2		8	91.54	even	12
637.2.h.i.471.2		8	91.45	even	12
819.2.o.h.568.2		8	39.2	even	12
819.2.o.h.757.2		8	39.32	even	12
1183.2.a.k.1.2		4	13.5	odd	4
1183.2.a.l.1.3		4	13.8	odd	4
1183.2.c.g.337.3		8	1.1	even	1	trivial
1183.2.c.g.337.6		8	13.12	even	2	inner
1456.2.s.q.113.4		8	52.15	even	12
1456.2.s.q.1121.4		8	52.19	even	12
8281.2.a.bp.1.2		4	91.83	even	4
8281.2.a.bt.1.3		4	91.34	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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.710287i q^{2} +2.40788 q^{3} +1.49549 q^{4} -1.28971i q^{5} -1.71029i q^{6} +1.00000i q^{7} -2.48280i q^{8} +2.79790 q^{9} -0.916066 q^{10} +2.40788i q^{11} +3.60097 q^{12} +0.710287 q^{14} -3.10548i q^{15} +1.22748 q^{16} -3.90338 q^{17} -1.98731i q^{18} -5.89068i q^{19} -1.92876i q^{20} +2.40788i q^{21} +1.71029 q^{22} +6.32395 q^{23} -5.97829i q^{24} +3.33664 q^{25} -0.486640 q^{27} +1.49549i q^{28} +5.61366 q^{29} -2.20578 q^{30} +2.20578i q^{31} -5.83747i q^{32} +5.79790i q^{33} +2.77252i q^{34} +1.28971 q^{35} +4.18424 q^{36} +5.11817i q^{37} -4.18407 q^{38} -3.20210 q^{40} -7.78521i q^{41} +1.71029 q^{42} -0.289713 q^{43} +3.60097i q^{44} -3.60849i q^{45} -4.49182i q^{46} -1.27702i q^{47} +2.95564 q^{48} -1.00000 q^{49} -2.36997i q^{50} -9.39887 q^{51} -13.6225 q^{53} +0.345654i q^{54} +3.10548 q^{55} +2.48280 q^{56} -14.1841i q^{57} -3.98731i q^{58} +4.03056i q^{59} -4.64422i q^{60} -4.60097 q^{61} +1.56674 q^{62} +2.79790i q^{63} -1.69131 q^{64} +4.11817 q^{66} +7.57559i q^{67} -5.83747 q^{68} +15.2273 q^{69} -0.916066i q^{70} +7.22732i q^{71} -6.94662i q^{72} +15.0125i q^{73} +3.63537 q^{74} +8.03424 q^{75} -8.80948i q^{76} -2.40788 q^{77} -9.30758 q^{79} -1.58310i q^{80} -9.56546 q^{81} -5.52973 q^{82} -1.36463i q^{83} +3.60097i q^{84} +5.03424i q^{85} +0.205780i q^{86} +13.5170 q^{87} +5.97829 q^{88} +0.899698i q^{89} -2.56306 q^{90} +9.45742 q^{92} +5.31126i q^{93} -0.907052 q^{94} -7.59729 q^{95} -14.0559i q^{96} +15.6658i q^{97} +0.710287i q^{98} +6.73701i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 10 q^{4} + 14 q^{9} + 22 q^{10} - 24 q^{12} + 2 q^{14} + 38 q^{16} + 8 q^{17} + 10 q^{22} + 4 q^{23} - 10 q^{25} - 52 q^{27} + 2 q^{29} + 8 q^{30} + 14 q^{35} + 68 q^{36} + 46 q^{38} - 34 q^{40}+ \cdots - 42 q^{95}+O(q^{100}) \) 8 * q + 2 * q^3 - 10 * q^4 + 14 * q^9 + 22 * q^10 - 24 * q^12 + 2 * q^14 + 38 * q^16 + 8 * q^17 + 10 * q^22 + 4 * q^23 - 10 * q^25 - 52 * q^27 + 2 * q^29 + 8 * q^30 + 14 * q^35 + 68 * q^36 + 46 * q^38 - 34 * q^40 + 10 * q^42 - 6 * q^43 + 22 * q^48 - 8 * q^49 - 14 * q^51 + 4 * q^53 - 6 * q^55 - 12 * q^56 + 16 * q^61 + 10 * q^62 - 28 * q^64 + 12 * q^66 - 66 * q^68 + 36 * q^69 + 40 * q^74 + 14 * q^75 - 2 * q^77 - 52 * q^79 + 48 * q^81 + 28 * q^82 + 26 * q^87 - 6 * q^88 - 52 * q^90 + 24 * q^92 + 66 * q^94 - 42 * q^95

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