LMFDB - Embedded newform 1183.2.c.g.337.6

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

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	$0.0808003\pi$
$2$	0.710287i	0.502249i	−0.967955	+	0.251124i	$0.919200\pi$
$3$	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	$0.0931195\pi$
$5$	1.28971i	0.576777i	−0.957513	+	0.288389i	$0.906880\pi$
$6$	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	$-0.881752\pi$
$11$	− 2.40788i	− 0.726004i	0.931788	−	0.363002i	$-0.118248\pi$
$12$	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	$0.236162\pi$
$19$	5.89068i	1.35142i	−0.737170	+	0.675708i	$0.763838\pi$
$20$	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	$-0.936528\pi$
$31$	− 2.20578i	− 0.396170i	0.980185	−	0.198085i	$-0.0634722\pi$
$32$	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	$-0.861781\pi$
$37$	− 5.11817i	− 0.841422i	0.907195	−	0.420711i	$-0.138219\pi$
$38$	−4.18407	−0.678746
$39$	0	0
$40$	−3.20210	−0.506297
$41$	7.78521i	1.21584i	0.793996	+	0.607922i	$0.207997\pi$
$41$	7.78521i	1.21584i	−0.793996	+	0.607922i	$0.792003\pi$
$42$	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	$0.0296893\pi$
$47$	1.27702i	0.186273i	−0.995653	+	0.0931364i	$0.970311\pi$
$48$	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	$-0.915497\pi$
$59$	− 4.03056i	− 0.524734i	0.964968	−	0.262367i	$-0.0845031\pi$
$60$	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	$-0.846862\pi$
$67$	− 7.57559i	− 0.925505i	0.886487	−	0.462753i	$-0.153138\pi$
$68$	−5.83747	−0.707897
$69$	15.2273	1.83315
$70$	0.916066i	0.109491i
$71$	− 7.22732i	− 0.857726i	−0.903370	−	0.428863i	$-0.858914\pi$
$71$	− 7.22732i	− 0.857726i	0.903370	−	0.428863i	$-0.141086\pi$
$72$	6.94662i	0.818668i
$73$	− 15.0125i	− 1.75708i	−0.477665	−	0.878542i	$-0.658517\pi$
$73$	− 15.0125i	− 1.75708i	0.477665	−	0.878542i	$-0.341483\pi$
$74$	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	$0.0238618\pi$
$83$	1.36463i	0.149788i	−0.997192	+	0.0748940i	$0.976138\pi$
$84$	− 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	$-0.984816\pi$
$89$	− 0.899698i	− 0.0953678i	0.998862	−	0.0476839i	$-0.0151840\pi$
$90$	−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	$-0.707309\pi$
$97$	− 15.6658i	− 1.59062i	0.606205	−	0.795309i	$-0.292691\pi$
$98$	− 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	$-0.803389\pi$
$109$	− 12.0928i	− 1.15828i	0.815228	−	0.579139i	$-0.196611\pi$
$110$	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	$0.144054\pi$
$137$	10.2362i	0.874536i	−0.899331	+	0.437268i	$0.855946\pi$
$138$	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	$0.131326\pi$
$149$	9.78888i	0.801937i	−0.916092	+	0.400968i	$0.868674\pi$
$150$	5.70661i	0.465943i
$151$	14.7407i	1.19958i	0.800158	+	0.599790i	$0.204749\pi$
$151$	14.7407i	1.19958i	−0.800158	+	0.599790i	$0.795251\pi$
$152$	−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	$-0.950171\pi$
$163$	− 3.98086i	− 0.311805i	0.987772	−	0.155902i	$-0.0498286\pi$
$164$	11.6427i	0.909144i
$165$	7.47763	0.582132
$166$	−0.969281	−0.0752308
$167$	8.67846i	0.671559i	0.941941	+	0.335780i	$0.109000\pi$
$167$	8.67846i	0.671559i	−0.941941	+	0.335780i	$0.891000\pi$
$168$	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	$-0.656463\pi$
$193$	− 24.4953i	− 1.76321i	0.471986	−	0.881606i	$-0.343537\pi$
$194$	11.1272	0.798885
$195$	0	0
$196$	−1.49549	−0.106821
$197$	6.71412i	0.478362i	0.970975	+	0.239181i	$0.0768789\pi$
$197$	6.71412i	0.478362i	−0.970975	+	0.239181i	$0.923121\pi$
$198$	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	$-0.904639\pi$
$223$	− 8.81426i	− 0.590247i	0.955459	−	0.295123i	$-0.0953608\pi$
$224$	5.83747	0.390032
$225$	9.33557	0.622372
$226$	− 10.1235i	− 0.673406i
$227$	13.4511i	0.892783i	0.894838	+	0.446391i	$0.147291\pi$
$227$	13.4511i	0.892783i	−0.894838	+	0.446391i	$0.852709\pi$
$228$	21.2122i	1.40481i
$229$	6.81576i	0.450398i	0.974313	+	0.225199i	$0.0723033\pi$
$229$	6.81576i	0.450398i	−0.974313	+	0.225199i	$0.927697\pi$
$230$	−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	$0.0287123\pi$
$239$	2.78521i	0.180160i	−0.995935	+	0.0900800i	$0.971288\pi$
$240$	3.81193i	0.246059i
$241$	6.97829i	0.449511i	0.974415	+	0.224756i	$0.0721584\pi$
$241$	6.97829i	0.449511i	−0.974415	+	0.224756i	$0.927842\pi$
$242$	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	$0.277564\pi$
$271$	25.2071i	1.53122i	−0.643303	+	0.765612i	$0.722436\pi$
$272$	−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	$0.0920978\pi$
$281$	9.56546i	0.570628i	−0.958434	+	0.285314i	$0.907902\pi$
$282$	−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	$-0.911891\pi$
$293$	− 9.35562i	− 0.546561i	0.961934	−	0.273281i	$-0.0881087\pi$
$294$	− 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	$0.0743827\pi$
$307$	8.11449i	0.463119i	−0.972821	+	0.231559i	$0.925617\pi$
$308$	−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	$-0.898221\pi$
$317$	− 11.1929i	− 0.628657i	0.949314	−	0.314329i	$-0.101779\pi$
$318$	− 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	$-0.814271\pi$
$331$	− 20.0468i	− 1.10187i	0.834548	−	0.550935i	$-0.185729\pi$
$332$	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	$0.0755615\pi$
$349$	8.78632i	0.470321i	−0.971957	+	0.235160i	$0.924438\pi$
$350$	2.36997	0.126680
$351$	0	0
$352$	14.0559	0.749184
$353$	− 7.71898i	− 0.410840i	−0.978674	−	0.205420i	$-0.934144\pi$
$353$	− 7.71898i	− 0.410840i	0.978674	−	0.205420i	$-0.0658560\pi$
$354$	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	$-0.909795\pi$
$359$	− 10.5956i	− 0.559216i	0.960114	−	0.279608i	$-0.0902045\pi$
$360$	−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	$-0.868306\pi$
$379$	− 15.6532i	− 0.804053i	0.915628	−	0.402026i	$-0.131694\pi$
$380$	−11.3617	−0.582843
$381$	21.2486	1.08860
$382$	− 10.9196i	− 0.558694i
$383$	12.5588i	0.641724i	0.947126	+	0.320862i	$0.103973\pi$
$383$	12.5588i	0.641724i	−0.947126	+	0.320862i	$0.896027\pi$
$384$	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	$-0.981214\pi$
$397$	− 2.35044i	− 0.117965i	0.998259	−	0.0589827i	$-0.0187857\pi$
$398$	3.46110i	0.173489i
$399$	14.1841	0.710092
$400$	4.09567	0.204784
$401$	− 34.6046i	− 1.72807i	−0.503429	−	0.864037i	$-0.667928\pi$
$401$	− 34.6046i	− 1.72807i	0.503429	−	0.864037i	$-0.332072\pi$
$402$	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	$0.0635691\pi$
$409$	8.02411i	0.396767i	−0.980125	+	0.198383i	$0.936431\pi$
$410$	− 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	$0.147462\pi$
$421$	18.3381i	0.893746i	−0.894597	+	0.446873i	$0.852538\pi$
$422$	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	$0.271140\pi$
$431$	31.2435i	1.50495i	−0.658622	+	0.752474i	$0.728860\pi$
$432$	−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	$-0.814467\pi$
$449$	− 23.3264i	− 1.10084i	0.834888	−	0.550420i	$-0.185533\pi$
$450$	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	$-0.882020\pi$
$457$	− 15.4866i	− 0.724434i	0.932094	−	0.362217i	$-0.117980\pi$
$458$	−4.84115	−0.226212
$459$	1.89954	0.0886628
$460$	12.1974i	0.568705i
$461$	9.28204i	0.432308i	0.976359	+	0.216154i	$0.0693513\pi$
$461$	9.28204i	0.432308i	−0.976359	+	0.216154i	$0.930649\pi$
$462$	− 4.11817i	− 0.191595i
$463$	28.8283i	1.33976i	0.742467	+	0.669882i	$0.233655\pi$
$463$	28.8283i	1.33976i	−0.742467	+	0.669882i	$0.766345\pi$
$464$	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	$-0.827236\pi$
$479$	− 22.6082i	− 1.03299i	0.856289	−	0.516497i	$-0.172764\pi$
$480$	−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	$-0.979301\pi$
$487$	− 2.86803i	− 0.129963i	0.997886	−	0.0649814i	$-0.0206988\pi$
$488$	− 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	$0.132114\pi$
$499$	18.0151i	0.806466i	−0.915097	+	0.403233i	$0.867886\pi$
$500$	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	$0.339431\pi$
$509$	39.5018i	1.75089i	−0.483319	+	0.875444i	$0.660569\pi$
$510$	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	$0.107422\pi$
$541$	15.4027i	0.662214i	−0.943593	+	0.331107i	$0.892578\pi$
$542$	−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	$0.129589\pi$
$557$	18.6901i	0.791924i	−0.918267	+	0.395962i	$0.870411\pi$
$558$	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	$0.349740\pi$
$577$	42.7876i	1.78127i	−0.454717	+	0.890636i	$0.650260\pi$
$578$	− 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	$0.295426\pi$
$587$	38.7886i	1.60098i	−0.599349	+	0.800488i	$0.704574\pi$
$588$	−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	$-0.789123\pi$
$593$	− 29.9564i	− 1.23016i	0.788464	−	0.615081i	$-0.210877\pi$
$594$	−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	$0.0276539\pi$
$613$	4.29655i	0.173536i	−0.996229	+	0.0867680i	$0.972346\pi$
$614$	−5.76362	−0.232601
$615$	−24.1768	−0.974902
$616$	− 5.97829i	− 0.240872i
$617$	30.7380i	1.23746i	0.785602	+	0.618732i	$0.212353\pi$
$617$	30.7380i	1.23746i	−0.785602	+	0.618732i	$0.787647\pi$
$618$	− 30.6568i	− 1.23320i
$619$	− 20.6417i	− 0.829658i	−0.909899	−	0.414829i	$-0.863841\pi$
$619$	− 20.6417i	− 0.829658i	0.909899	−	0.414829i	$-0.136159\pi$
$620$	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	$0.198488\pi$
$631$	29.3366i	1.16787i	−0.811799	+	0.583937i	$0.801512\pi$
$632$	− 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	$0.0432701\pi$
$643$	6.87282i	0.271037i	−0.990775	+	0.135519i	$0.956730\pi$
$644$	− 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	$-0.988744\pi$
$661$	− 1.81794i	− 0.0707097i	0.999375	−	0.0353549i	$-0.0112561\pi$
$662$	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	$-0.715130\pi$
$683$	− 40.7786i	− 1.56035i	0.625560	−	0.780176i	$-0.284870\pi$
$684$	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	$0.0189539\pi$
$691$	3.12868i	0.119021i	−0.998228	+	0.0595104i	$0.981046\pi$
$692$	−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	$0.177137\pi$
$709$	28.1294i	1.05642i	−0.849113	+	0.528211i	$0.822863\pi$
$710$	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	$0.0735395\pi$
$733$	12.3989i	0.457963i	−0.973431	+	0.228981i	$0.926461\pi$
$734$	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	$-0.935388\pi$
$739$	− 10.9604i	− 0.403184i	0.979470	−	0.201592i	$-0.0646115\pi$
$740$	9.87170	0.362891
$741$	0	0
$742$	−9.67589	−0.355213
$743$	− 40.6925i	− 1.49286i	−0.665463	−	0.746431i	$-0.731766\pi$
$743$	− 40.6925i	− 1.49286i	0.665463	−	0.746431i	$-0.268234\pi$
$744$	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	$0.0993481\pi$
$761$	16.9417i	0.614137i	−0.951687	+	0.307068i	$0.900652\pi$
$762$	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	$-0.957601\pi$
$769$	− 7.36574i	− 0.265616i	0.991142	−	0.132808i	$-0.0423993\pi$
$770$	2.20578	0.0794908
$771$	−7.84498	−0.282530
$772$	− 36.6326i	− 1.31844i
$773$	44.7734i	1.61039i	0.593012	+	0.805194i	$0.297939\pi$
$773$	44.7734i	1.61039i	−0.593012	+	0.805194i	$0.702061\pi$
$774$	− 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	$-0.891430\pi$
$787$	− 18.7682i	− 0.669016i	0.942393	−	0.334508i	$-0.108570\pi$
$788$	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	$-0.894208\pi$
$811$	− 18.5831i	− 0.652541i	0.945276	−	0.326271i	$-0.105792\pi$
$812$	− 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	$0.153796\pi$
$821$	26.6236i	0.929169i	−0.885529	+	0.464585i	$0.846204\pi$
$822$	−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	$-0.876598\pi$
$827$	− 21.7430i	− 0.756079i	0.925789	−	0.378039i	$-0.123402\pi$
$828$	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	$-0.940606\pi$
$839$	− 10.7469i	− 0.371023i	0.982642	−	0.185511i	$-0.0593942\pi$
$840$	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	$-0.816944\pi$
$853$	− 31.7709i	− 1.08782i	0.839145	−	0.543908i	$-0.183056\pi$
$854$	−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	$-0.880112\pi$
$863$	− 21.6094i	− 0.735592i	0.929906	−	0.367796i	$-0.119888\pi$
$864$	− 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	$0.00473366\pi$
$877$	0.880766i	0.0297413i	−0.999889	+	0.0148707i	$0.995266\pi$
$878$	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	$0.0840426\pi$
$929$	15.9085i	0.521941i	−0.965347	+	0.260971i	$0.915957\pi$
$930$	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	$0.201570\pi$
$941$	36.3059i	1.18354i	−0.806108	+	0.591769i	$0.798430\pi$
$942$	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	$-0.995248\pi$
$947$	− 0.918839i	− 0.0298582i	0.999889	−	0.0149291i	$-0.00475226\pi$
$948$	−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	$-0.935103\pi$
$967$	− 12.5923i	− 0.404940i	0.979288	−	0.202470i	$-0.0648969\pi$
$968$	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	$0.237454\pi$
$977$	42.4279i	1.35739i	−0.734420	+	0.678695i	$0.762546\pi$
$978$	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	$0.0106498\pi$
$983$	2.09758i	0.0669023i	−0.999440	+	0.0334511i	$0.989350\pi$
$984$	−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.337.6		8
13.5	odd	4		1183.2.a.l.1.3		4
13.7	odd	12		91.2.f.c.29.3	yes	8
13.8	odd	4		1183.2.a.k.1.2		4
13.11	odd	12		91.2.f.c.22.3	✓	8
13.12	even	2	inner	1183.2.c.g.337.3		8
39.11	even	12		819.2.o.h.568.2		8
39.20	even	12		819.2.o.h.757.2		8
52.7	even	12		1456.2.s.q.1121.4		8
52.11	even	12		1456.2.s.q.113.4		8
91.11	odd	12		637.2.g.k.373.3		8
91.20	even	12		637.2.f.i.393.3		8
91.24	even	12		637.2.g.j.373.3		8
91.33	even	12		637.2.g.j.263.3		8
91.34	even	4		8281.2.a.bp.1.2		4
91.37	odd	12		637.2.h.h.165.2		8
91.46	odd	12		637.2.h.h.471.2		8
91.59	even	12		637.2.h.i.471.2		8
91.72	odd	12		637.2.g.k.263.3		8
91.76	even	12		637.2.f.i.295.3		8
91.83	even	4		8281.2.a.bt.1.3		4
91.89	even	12		637.2.h.i.165.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.3	✓	8	13.11	odd	12
91.2.f.c.29.3	yes	8	13.7	odd	12
637.2.f.i.295.3		8	91.76	even	12
637.2.f.i.393.3		8	91.20	even	12
637.2.g.j.263.3		8	91.33	even	12
637.2.g.j.373.3		8	91.24	even	12
637.2.g.k.263.3		8	91.72	odd	12
637.2.g.k.373.3		8	91.11	odd	12
637.2.h.h.165.2		8	91.37	odd	12
637.2.h.h.471.2		8	91.46	odd	12
637.2.h.i.165.2		8	91.89	even	12
637.2.h.i.471.2		8	91.59	even	12
819.2.o.h.568.2		8	39.11	even	12
819.2.o.h.757.2		8	39.20	even	12
1183.2.a.k.1.2		4	13.8	odd	4
1183.2.a.l.1.3		4	13.5	odd	4
1183.2.c.g.337.3		8	13.12	even	2	inner
1183.2.c.g.337.6		8	1.1	even	1	trivial
1456.2.s.q.113.4		8	52.11	even	12
1456.2.s.q.1121.4		8	52.7	even	12
8281.2.a.bp.1.2		4	91.34	even	4
8281.2.a.bt.1.3		4	91.83	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more