LMFDB - Embedded newform 1183.2.c.i.337.2

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:	$12$
Coefficient field:	12.0.58891012706304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$-1.30089 - 0.554694i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.i.337.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10939i q^{2} +2.26165 q^{3} -2.44952 q^{4} -3.60178i q^{5} -4.77070i q^{6} -1.00000i q^{7} +0.948212i q^{8} +2.11505 q^{9} +O(q^{10})$	\(q-2.10939i q^{2} +2.26165 q^{3} -2.44952 q^{4} -3.60178i q^{5} -4.77070i q^{6} -1.00000i q^{7} +0.948212i q^{8} +2.11505 q^{9} -7.59755 q^{10} -0.886384i q^{11} -5.53995 q^{12} -2.10939 q^{14} -8.14596i q^{15} -2.89889 q^{16} +4.96016 q^{17} -4.46147i q^{18} +2.37878i q^{19} +8.82263i q^{20} -2.26165i q^{21} -1.86973 q^{22} +3.85851 q^{23} +2.14452i q^{24} -7.97282 q^{25} -2.00144 q^{27} +2.44952i q^{28} +1.28197 q^{29} -17.1830 q^{30} +8.46921i q^{31} +8.01131i q^{32} -2.00469i q^{33} -10.4629i q^{34} -3.60178 q^{35} -5.18087 q^{36} +9.63812i q^{37} +5.01776 q^{38} +3.41525 q^{40} -12.0841i q^{41} -4.77070 q^{42} +3.64250 q^{43} +2.17122i q^{44} -7.61796i q^{45} -8.13910i q^{46} -2.98229i q^{47} -6.55628 q^{48} -1.00000 q^{49} +16.8178i q^{50} +11.2181 q^{51} +4.92032 q^{53} +4.22181i q^{54} -3.19256 q^{55} +0.948212 q^{56} +5.37995i q^{57} -2.70418i q^{58} +7.32746i q^{59} +19.9537i q^{60} -1.53926 q^{61} +17.8648 q^{62} -2.11505i q^{63} +11.1012 q^{64} -4.22867 q^{66} -8.42649i q^{67} -12.1500 q^{68} +8.72660 q^{69} +7.59755i q^{70} -6.44888i q^{71} +2.00552i q^{72} +7.14859i q^{73} +20.3305 q^{74} -18.0317 q^{75} -5.82686i q^{76} -0.886384 q^{77} +0.757551 q^{79} +10.4412i q^{80} -10.8717 q^{81} -25.4901 q^{82} -4.76766i q^{83} +5.53995i q^{84} -17.8654i q^{85} -7.68344i q^{86} +2.89937 q^{87} +0.840480 q^{88} -3.61884i q^{89} -16.0692 q^{90} -9.45150 q^{92} +19.1544i q^{93} -6.29081 q^{94} +8.56783 q^{95} +18.1188i q^{96} -0.463300i q^{97} +2.10939i q^{98} -1.87475i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 8 q^{9}+O(q^{10}) $ 12 * q - 8 * q^4 + 8 * q^9	$ 12 q - 8 q^{4} + 8 q^{9} - 24 q^{10} - 4 q^{12} - 8 q^{14} + 16 q^{16} + 8 q^{17} - 12 q^{22} + 24 q^{23} - 20 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{30} - 12 q^{35} + 20 q^{36} + 4 q^{38} + 92 q^{40} - 8 q^{42} - 4 q^{43} + 4 q^{48} - 12 q^{49} + 52 q^{51} - 44 q^{53} + 12 q^{55} + 24 q^{56} - 28 q^{61} + 8 q^{62} - 52 q^{64} - 52 q^{66} + 16 q^{68} - 8 q^{69} - 12 q^{74} - 92 q^{75} + 8 q^{77} - 56 q^{79} - 4 q^{81} - 28 q^{82} + 4 q^{87} + 28 q^{88} + 24 q^{90} + 24 q^{92} - 8 q^{94} + 44 q^{95}+O(q^{100}) $ 12 * q - 8 * q^4 + 8 * q^9 - 24 * q^10 - 4 * q^12 - 8 * q^14 + 16 * q^16 + 8 * q^17 - 12 * q^22 + 24 * q^23 - 20 * q^25 + 12 * q^27 - 16 * q^29 - 16 * q^30 - 12 * q^35 + 20 * q^36 + 4 * q^38 + 92 * q^40 - 8 * q^42 - 4 * q^43 + 4 * q^48 - 12 * q^49 + 52 * q^51 - 44 * q^53 + 12 * q^55 + 24 * q^56 - 28 * q^61 + 8 * q^62 - 52 * q^64 - 52 * q^66 + 16 * q^68 - 8 * q^69 - 12 * q^74 - 92 * q^75 + 8 * q^77 - 56 * q^79 - 4 * q^81 - 28 * q^82 + 4 * q^87 + 28 * q^88 + 24 * q^90 + 24 * q^92 - 8 * q^94 + 44 * 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 $

$2$	− 2.10939i	− 1.49156i	−0.666191	−	0.745781i	$-0.732076\pi$
$2$	− 2.10939i	− 1.49156i	0.666191	−	0.745781i	$-0.267924\pi$
$3$	2.26165	1.30576	0.652882	−	0.757460i	$-0.273560\pi$
$3$	2.26165	1.30576	0.652882	+	0.757460i	$0.273560\pi$
$4$	−2.44952	−1.22476
$5$	− 3.60178i	− 1.61076i	−0.592756	−	0.805382i	$-0.701960\pi$
$5$	− 3.60178i	− 1.61076i	0.592756	−	0.805382i	$-0.298040\pi$
$6$	− 4.77070i	− 1.94763i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	0.948212i	0.335243i
$9$	2.11505	0.705018
$10$	−7.59755	−2.40256
$11$	− 0.886384i	− 0.267255i	−0.991032	−	0.133627i	$-0.957337\pi$
$11$	− 0.886384i	− 0.267255i	0.991032	−	0.133627i	$-0.0426626\pi$
$12$	−5.53995	−1.59925
$13$	0	0
$13$	0	0
$14$	−2.10939	−0.563758
$15$	− 8.14596i	− 2.10328i
$16$	−2.89889	−0.724723
$17$	4.96016	1.20302	0.601508	−	0.798867i	$-0.294567\pi$
$17$	4.96016	1.20302	0.601508	+	0.798867i	$0.294567\pi$
$18$	− 4.46147i	− 1.05158i
$19$	2.37878i	0.545729i	0.962053	+	0.272864i	$0.0879710\pi$
$19$	2.37878i	0.545729i	−0.962053	+	0.272864i	$0.912029\pi$
$20$	8.82263i	1.97280i
$21$	− 2.26165i	− 0.493532i
$22$	−1.86973	−0.398628
$23$	3.85851	0.804555	0.402278	−	0.915518i	$-0.368219\pi$
$23$	3.85851	0.804555	0.402278	+	0.915518i	$0.368219\pi$
$24$	2.14452i	0.437749i
$25$	−7.97282	−1.59456
$26$	0	0
$27$	−2.00144	−0.385177
$28$	2.44952i	0.462916i
$29$	1.28197	0.238056	0.119028	−	0.992891i	$-0.462022\pi$
$29$	1.28197	0.238056	0.119028	+	0.992891i	$0.462022\pi$
$30$	−17.1830	−3.13717
$31$	8.46921i	1.52111i	0.649271	+	0.760557i	$0.275074\pi$
$31$	8.46921i	1.52111i	−0.649271	+	0.760557i	$0.724926\pi$
$32$	8.01131i	1.41621i
$33$	− 2.00469i	− 0.348972i
$34$	− 10.4629i	− 1.79437i
$35$	−3.60178	−0.608812
$36$	−5.18087	−0.863478
$37$	9.63812i	1.58450i	0.610198	+	0.792249i	$0.291090\pi$
$37$	9.63812i	1.58450i	−0.610198	+	0.792249i	$0.708910\pi$
$38$	5.01776	0.813988
$39$	0	0
$40$	3.41525	0.539998
$41$	− 12.0841i	− 1.88722i	−0.331053	−	0.943612i	$-0.607404\pi$
$41$	− 12.0841i	− 1.88722i	0.331053	−	0.943612i	$-0.392596\pi$
$42$	−4.77070	−0.736134
$43$	3.64250	0.555476	0.277738	−	0.960657i	$-0.410415\pi$
$43$	3.64250	0.555476	0.277738	+	0.960657i	$0.410415\pi$
$44$	2.17122i	0.327323i
$45$	− 7.61796i	− 1.13562i
$46$	− 8.13910i	− 1.20004i
$47$	− 2.98229i	− 0.435012i	−0.976059	−	0.217506i	$-0.930208\pi$
$47$	− 2.98229i	− 0.435012i	0.976059	−	0.217506i	$-0.0697922\pi$
$48$	−6.55628	−0.946317
$49$	−1.00000	−0.142857
$50$	16.8178i	2.37839i
$51$	11.2181	1.57085
$52$	0	0
$53$	4.92032	0.675858	0.337929	−	0.941172i	$-0.390274\pi$
$53$	4.92032	0.675858	0.337929	+	0.941172i	$0.390274\pi$
$54$	4.22181i	0.574516i
$55$	−3.19256	−0.430485
$56$	0.948212	0.126710
$57$	5.37995i	0.712592i
$58$	− 2.70418i	− 0.355076i
$59$	7.32746i	0.953954i	0.878916	+	0.476977i	$0.158268\pi$
$59$	7.32746i	0.953954i	−0.878916	+	0.476977i	$0.841732\pi$
$60$	19.9537i	2.57601i
$61$	−1.53926	−0.197082	−0.0985412	−	0.995133i	$-0.531418\pi$
$61$	−1.53926	−0.197082	−0.0985412	+	0.995133i	$0.531418\pi$
$62$	17.8648	2.26884
$63$	− 2.11505i	− 0.266472i
$64$	11.1012	1.38765
$65$	0	0
$66$	−4.22867	−0.520513
$67$	− 8.42649i	− 1.02946i	−0.857352	−	0.514730i	$-0.827892\pi$
$67$	− 8.42649i	− 1.02946i	0.857352	−	0.514730i	$-0.172108\pi$
$68$	−12.1500	−1.47341
$69$	8.72660	1.05056
$70$	7.59755i	0.908081i
$71$	− 6.44888i	− 0.765342i	−0.923885	−	0.382671i	$-0.875004\pi$
$71$	− 6.44888i	− 0.765342i	0.923885	−	0.382671i	$-0.124996\pi$
$72$	2.00552i	0.236353i
$73$	7.14859i	0.836679i	0.908291	+	0.418340i	$0.137388\pi$
$73$	7.14859i	0.836679i	−0.908291	+	0.418340i	$0.862612\pi$
$74$	20.3305	2.36338
$75$	−18.0317	−2.08212
$76$	− 5.82686i	− 0.668386i
$77$	−0.886384	−0.101013
$78$	0	0
$79$	0.757551	0.0852311	0.0426156	−	0.999092i	$-0.486431\pi$
$79$	0.757551	0.0852311	0.0426156	+	0.999092i	$0.486431\pi$
$80$	10.4412i	1.16736i
$81$	−10.8717	−1.20797
$82$	−25.4901	−2.81491
$83$	− 4.76766i	− 0.523319i	−0.965160	−	0.261659i	$-0.915730\pi$
$83$	− 4.76766i	− 0.523319i	0.965160	−	0.261659i	$-0.0842697\pi$
$84$	5.53995i	0.604458i
$85$	− 17.8654i	− 1.93778i
$86$	− 7.68344i	− 0.828527i
$87$	2.89937	0.310845
$88$	0.840480	0.0895955
$89$	− 3.61884i	− 0.383596i	−0.981434	−	0.191798i	$-0.938568\pi$
$89$	− 3.61884i	− 0.383596i	0.981434	−	0.191798i	$-0.0614318\pi$
$90$	−16.0692	−1.69385
$91$	0	0
$92$	−9.45150	−0.985387
$93$	19.1544i	1.98622i
$94$	−6.29081	−0.648848
$95$	8.56783	0.879040
$96$	18.1188i	1.84924i
$97$	− 0.463300i	− 0.0470409i	−0.999723	−	0.0235205i	$-0.992513\pi$
$97$	− 0.463300i	− 0.0470409i	0.999723	−	0.0235205i	$-0.00748749\pi$
$98$	2.10939i	0.213080i
$99$	− 1.87475i	− 0.188419i
$100$	19.5296	1.95296
$101$	−5.82303	−0.579413	−0.289707	−	0.957115i	$-0.593558\pi$
$101$	−5.82303	−0.579413	−0.289707	+	0.957115i	$0.593558\pi$
$102$	− 23.6634i	− 2.34303i
$103$	−8.23888	−0.811801	−0.405901	−	0.913917i	$-0.633042\pi$
$103$	−8.23888	−0.811801	−0.405901	+	0.913917i	$0.633042\pi$
$104$	0	0
$105$	−8.14596	−0.794964
$106$	− 10.3789i	− 1.00809i
$107$	−3.83260	−0.370511	−0.185256	−	0.982690i	$-0.559311\pi$
$107$	−3.83260	−0.370511	−0.185256	+	0.982690i	$0.559311\pi$
$108$	4.90256	0.471749
$109$	− 10.4180i	− 0.997867i	−0.866640	−	0.498934i	$-0.833725\pi$
$109$	− 10.4180i	− 0.997867i	0.866640	−	0.498934i	$-0.166275\pi$
$110$	6.73435i	0.642095i
$111$	21.7980i	2.06898i
$112$	2.89889i	0.273920i
$113$	−4.91011	−0.461904	−0.230952	−	0.972965i	$-0.574184\pi$
$113$	−4.91011	−0.461904	−0.230952	+	0.972965i	$0.574184\pi$
$114$	11.3484	1.06288
$115$	− 13.8975i	− 1.29595i
$116$	−3.14022	−0.291562
$117$	0	0
$118$	15.4565	1.42288
$119$	− 4.96016i	− 0.454697i
$120$	7.72409	0.705110
$121$	10.2143	0.928575
$122$	3.24690i	0.293961i
$123$	− 27.3301i	− 2.46427i
$124$	− 20.7455i	− 1.86300i
$125$	10.7074i	0.957702i
$126$	−4.46147	−0.397459
$127$	12.3102	1.09235	0.546175	−	0.837671i	$-0.316083\pi$
$127$	12.3102	1.09235	0.546175	+	0.837671i	$0.316083\pi$
$128$	− 7.39409i	− 0.653551i
$129$	8.23805	0.725320
$130$	0	0
$131$	−8.20265	−0.716669	−0.358335	−	0.933593i	$-0.616655\pi$
$131$	−8.20265	−0.716669	−0.358335	+	0.933593i	$0.616655\pi$
$132$	4.91053i	0.427406i
$133$	2.37878	0.206266
$134$	−17.7747	−1.53550
$135$	7.20874i	0.620429i
$136$	4.70328i	0.403303i
$137$	7.45555i	0.636971i	0.947928	+	0.318485i	$0.103174\pi$
$137$	7.45555i	0.636971i	−0.947928	+	0.318485i	$0.896826\pi$
$138$	− 18.4078i	− 1.56697i
$139$	16.6806	1.41483	0.707413	−	0.706800i	$-0.249862\pi$
$139$	16.6806	1.41483	0.707413	+	0.706800i	$0.249862\pi$
$140$	8.82263	0.745648
$141$	− 6.74490i	− 0.568023i
$142$	−13.6032	−1.14156
$143$	0	0
$144$	−6.13131	−0.510943
$145$	− 4.61738i	− 0.383453i
$146$	15.0792	1.24796
$147$	−2.26165	−0.186538
$148$	− 23.6088i	− 1.94063i
$149$	− 2.52163i	− 0.206580i	−0.994651	−	0.103290i	$-0.967063\pi$
$149$	− 2.52163i	− 0.206580i	0.994651	−	0.103290i	$-0.0329370\pi$
$150$	38.0359i	3.10562i
$151$	15.8972i	1.29370i	0.762618	+	0.646849i	$0.223914\pi$
$151$	15.8972i	1.29370i	−0.762618	+	0.646849i	$0.776086\pi$
$152$	−2.25558	−0.182952
$153$	10.4910	0.848148
$154$	1.86973i	0.150667i
$155$	30.5042	2.45016
$156$	0	0
$157$	12.9831	1.03616	0.518082	−	0.855331i	$-0.326646\pi$
$157$	12.9831	1.03616	0.518082	+	0.855331i	$0.326646\pi$
$158$	− 1.59797i	− 0.127128i
$159$	11.1280	0.882511
$160$	28.8550	2.28119
$161$	− 3.85851i	− 0.304093i
$162$	22.9327i	1.80176i
$163$	− 2.31948i	− 0.181676i	−0.995866	−	0.0908378i	$-0.971046\pi$
$163$	− 2.31948i	− 0.181676i	0.995866	−	0.0908378i	$-0.0289545\pi$
$164$	29.6003i	2.31140i
$165$	−7.22045	−0.562111
$166$	−10.0569	−0.780563
$167$	13.7918i	1.06724i	0.845723	+	0.533622i	$0.179169\pi$
$167$	13.7918i	1.06724i	−0.845723	+	0.533622i	$0.820831\pi$
$168$	2.14452	0.165453
$169$	0	0
$170$	−37.6851	−2.89031
$171$	5.03124i	0.384748i
$172$	−8.92237	−0.680324
$173$	3.68432	0.280113	0.140057	−	0.990143i	$-0.455272\pi$
$173$	3.68432	0.280113	0.140057	+	0.990143i	$0.455272\pi$
$174$	− 6.11590i	− 0.463645i
$175$	7.97282i	0.602688i
$176$	2.56953i	0.193686i
$177$	16.5721i	1.24564i
$178$	−7.63353	−0.572157
$179$	5.89277	0.440446	0.220223	−	0.975450i	$-0.429322\pi$
$179$	5.89277	0.440446	0.220223	+	0.975450i	$0.429322\pi$
$180$	18.6603i	1.39086i
$181$	−2.11543	−0.157239	−0.0786193	−	0.996905i	$-0.525051\pi$
$181$	−2.11543	−0.157239	−0.0786193	+	0.996905i	$0.525051\pi$
$182$	0	0
$183$	−3.48127	−0.257343
$184$	3.65869i	0.269722i
$185$	34.7144	2.55225
$186$	40.4040	2.96257
$187$	− 4.39661i	− 0.321512i
$188$	7.30518i	0.532785i
$189$	2.00144i	0.145583i
$190$	− 18.0729i	− 1.31114i
$191$	−11.3667	−0.822462	−0.411231	−	0.911531i	$-0.634901\pi$
$191$	−11.3667	−0.822462	−0.411231	+	0.911531i	$0.634901\pi$
$192$	25.1070	1.81194
$193$	− 14.0894i	− 1.01417i	−0.861895	−	0.507087i	$-0.830722\pi$
$193$	− 14.0894i	− 1.01417i	0.861895	−	0.507087i	$-0.169278\pi$
$194$	−0.977279	−0.0701645
$195$	0	0
$196$	2.44952	0.174966
$197$	22.9571i	1.63563i	0.575482	+	0.817814i	$0.304814\pi$
$197$	22.9571i	1.63563i	−0.575482	+	0.817814i	$0.695186\pi$
$198$	−3.95458	−0.281040
$199$	3.14985	0.223287	0.111643	−	0.993748i	$-0.464389\pi$
$199$	3.14985	0.223287	0.111643	+	0.993748i	$0.464389\pi$
$200$	− 7.55992i	− 0.534567i
$201$	− 19.0578i	− 1.34423i
$202$	12.2830i	0.864231i
$203$	− 1.28197i	− 0.0899768i
$204$	−27.4791	−1.92392
$205$	−43.5244	−3.03987
$206$	17.3790i	1.21085i
$207$	8.16096	0.567226
$208$	0	0
$209$	2.10851	0.145849
$210$	17.1830i	1.18574i
$211$	−14.8638	−1.02327	−0.511634	−	0.859203i	$-0.670960\pi$
$211$	−14.8638	−1.02327	−0.511634	+	0.859203i	$0.670960\pi$
$212$	−12.0524	−0.827764
$213$	− 14.5851i	− 0.999355i
$214$	8.08444i	0.552641i
$215$	− 13.1195i	− 0.894741i
$216$	− 1.89779i	− 0.129128i
$217$	8.46921	0.574927
$218$	−21.9757	−1.48838
$219$	16.1676i	1.09251i
$220$	7.82024	0.527241
$221$	0	0
$222$	45.9805	3.08601
$223$	− 4.38089i	− 0.293366i	−0.989184	−	0.146683i	$-0.953140\pi$
$223$	− 4.38089i	− 0.293366i	0.989184	−	0.146683i	$-0.0468597\pi$
$224$	8.01131	0.535278
$225$	−16.8629	−1.12420
$226$	10.3573i	0.688959i
$227$	13.5663i	0.900428i	0.892921	+	0.450214i	$0.148652\pi$
$227$	13.5663i	0.900428i	−0.892921	+	0.450214i	$0.851348\pi$
$228$	− 13.1783i	− 0.872754i
$229$	− 16.5180i	− 1.09154i	−0.837935	−	0.545770i	$-0.816237\pi$
$229$	− 16.5180i	− 1.09154i	0.837935	−	0.545770i	$-0.183763\pi$
$230$	−29.3152	−1.93299
$231$	−2.00469	−0.131899
$232$	1.21558i	0.0798068i
$233$	16.5026	1.08112	0.540561	−	0.841305i	$-0.318212\pi$
$233$	16.5026	1.08112	0.540561	+	0.841305i	$0.318212\pi$
$234$	0	0
$235$	−10.7416	−0.700702
$236$	− 17.9488i	− 1.16836i
$237$	1.71331	0.111292
$238$	−10.4629	−0.678210
$239$	30.4210i	1.96777i	0.178796	+	0.983886i	$0.442780\pi$
$239$	30.4210i	1.96777i	−0.178796	+	0.983886i	$0.557220\pi$
$240$	23.6143i	1.52429i
$241$	− 29.5143i	− 1.90119i	−0.310440	−	0.950593i	$-0.600476\pi$
$241$	− 29.5143i	− 1.90119i	0.310440	−	0.950593i	$-0.399524\pi$
$242$	− 21.5460i	− 1.38503i
$243$	−18.5837	−1.19214
$244$	3.77046	0.241379
$245$	3.60178i	0.230109i
$246$	−57.6497	−3.67561
$247$	0	0
$248$	−8.03060	−0.509944
$249$	− 10.7828i	− 0.683331i
$250$	22.5861	1.42847
$251$	12.9827	0.819459	0.409730	−	0.912207i	$-0.365623\pi$
$251$	12.9827	0.819459	0.409730	+	0.912207i	$0.365623\pi$
$252$	5.18087i	0.326364i
$253$	− 3.42012i	− 0.215021i
$254$	− 25.9669i	− 1.62931i
$255$	− 40.4053i	− 2.53028i
$256$	6.60537	0.412836
$257$	4.58521	0.286018	0.143009	−	0.989721i	$-0.454322\pi$
$257$	4.58521	0.286018	0.143009	+	0.989721i	$0.454322\pi$
$258$	− 17.3772i	− 1.08186i
$259$	9.63812	0.598884
$260$	0	0
$261$	2.71144	0.167834
$262$	17.3026i	1.06896i
$263$	−2.66499	−0.164330	−0.0821652	−	0.996619i	$-0.526184\pi$
$263$	−2.66499	−0.164330	−0.0821652	+	0.996619i	$0.526184\pi$
$264$	1.90087	0.116990
$265$	− 17.7219i	− 1.08865i
$266$	− 5.01776i	− 0.307659i
$267$	− 8.18453i	− 0.500885i
$268$	20.6409i	1.26084i
$269$	11.9256	0.727119	0.363559	−	0.931571i	$-0.381561\pi$
$269$	11.9256	0.727119	0.363559	+	0.931571i	$0.381561\pi$
$270$	15.2060	0.925409
$271$	13.0283i	0.791414i	0.918377	+	0.395707i	$0.129500\pi$
$271$	13.0283i	0.791414i	−0.918377	+	0.395707i	$0.870500\pi$
$272$	−14.3790	−0.871853
$273$	0	0
$274$	15.7267	0.950082
$275$	7.06698i	0.426155i
$276$	−21.3760	−1.28668
$277$	−21.3649	−1.28369	−0.641846	−	0.766833i	$-0.721831\pi$
$277$	−21.3649	−1.28369	−0.641846	+	0.766833i	$0.721831\pi$
$278$	− 35.1858i	− 2.11030i
$279$	17.9128i	1.07241i
$280$	− 3.41525i	− 0.204100i
$281$	− 17.2678i	− 1.03011i	−0.857158	−	0.515054i	$-0.827772\pi$
$281$	− 17.2678i	− 1.03011i	0.857158	−	0.515054i	$-0.172228\pi$
$282$	−14.2276	−0.847242
$283$	21.2402	1.26260	0.631299	−	0.775539i	$-0.282522\pi$
$283$	21.2402	1.26260	0.631299	+	0.775539i	$0.282522\pi$
$284$	15.7967i	0.937360i
$285$	19.3774	1.14782
$286$	0	0
$287$	−12.0841	−0.713304
$288$	16.9444i	0.998456i
$289$	7.60320	0.447247
$290$	−9.73985	−0.571944
$291$	− 1.04782i	− 0.0614243i
$292$	− 17.5106i	− 1.02473i
$293$	− 0.420060i	− 0.0245402i	−0.999925	−	0.0122701i	$-0.996094\pi$
$293$	− 0.420060i	− 0.0245402i	0.999925	−	0.0122701i	$-0.00390578\pi$
$294$	4.77070i	0.278233i
$295$	26.3919	1.53660
$296$	−9.13898	−0.531192
$297$	1.77404i	0.102940i
$298$	−5.31910	−0.308127
$299$	0	0
$300$	44.1690	2.55010
$301$	− 3.64250i	− 0.209950i
$302$	33.5335	1.92963
$303$	−13.1696	−0.756577
$304$	− 6.89581i	− 0.395502i
$305$	5.54409i	0.317453i
$306$	− 22.1296i	− 1.26507i
$307$	14.0807i	0.803628i	0.915721	+	0.401814i	$0.131620\pi$
$307$	14.0807i	0.803628i	−0.915721	+	0.401814i	$0.868380\pi$
$308$	2.17122	0.123717
$309$	−18.6335	−1.06002
$310$	− 64.3453i	− 3.65456i
$311$	−10.3848	−0.588867	−0.294434	−	0.955672i	$-0.595131\pi$
$311$	−10.3848	−0.588867	−0.294434	+	0.955672i	$0.595131\pi$
$312$	0	0
$313$	6.84759	0.387048	0.193524	−	0.981096i	$-0.438008\pi$
$313$	6.84759	0.387048	0.193524	+	0.981096i	$0.438008\pi$
$314$	− 27.3864i	− 1.54550i
$315$	−7.61796	−0.429223
$316$	−1.85564	−0.104388
$317$	− 0.701249i	− 0.0393861i	−0.999806	−	0.0196930i	$-0.993731\pi$
$317$	− 0.701249i	− 0.0393861i	0.999806	−	0.0196930i	$-0.00626889\pi$
$318$	− 23.4734i	− 1.31632i
$319$	− 1.13632i	− 0.0636217i
$320$	− 39.9840i	− 2.23518i
$321$	−8.66799	−0.483800
$322$	−8.13910	−0.453574
$323$	11.7991i	0.656520i
$324$	26.6305	1.47947
$325$	0	0
$326$	−4.89268	−0.270980
$327$	− 23.5619i	− 1.30298i
$328$	11.4583	0.632680
$329$	−2.98229	−0.164419
$330$	15.2307i	0.838424i
$331$	4.19865i	0.230778i	0.993320	+	0.115389i	$0.0368115\pi$
$331$	4.19865i	0.230778i	−0.993320	+	0.115389i	$0.963188\pi$
$332$	11.6785i	0.640940i
$333$	20.3851i	1.11710i
$334$	29.0923	1.59186
$335$	−30.3504	−1.65822
$336$	6.55628i	0.357674i
$337$	−20.4278	−1.11278	−0.556388	−	0.830923i	$-0.687813\pi$
$337$	−20.4278	−1.11278	−0.556388	+	0.830923i	$0.687813\pi$
$338$	0	0
$339$	−11.1049	−0.603138
$340$	43.7617i	2.37331i
$341$	7.50697	0.406525
$342$	10.6128	0.573876
$343$	1.00000i	0.0539949i
$344$	3.45386i	0.186220i
$345$	− 31.4313i	− 1.69220i
$346$	− 7.77165i	− 0.417807i
$347$	7.97000	0.427852	0.213926	−	0.976850i	$-0.431375\pi$
$347$	7.97000	0.427852	0.213926	+	0.976850i	$0.431375\pi$
$348$	−7.10207	−0.380711
$349$	− 21.5972i	− 1.15607i	−0.816011	−	0.578037i	$-0.803819\pi$
$349$	− 21.5972i	− 1.15607i	0.816011	−	0.578037i	$-0.196181\pi$
$350$	16.8178	0.898947
$351$	0	0
$352$	7.10110	0.378490
$353$	− 21.6176i	− 1.15059i	−0.817946	−	0.575295i	$-0.804887\pi$
$353$	− 21.6176i	− 1.15059i	0.817946	−	0.575295i	$-0.195113\pi$
$354$	34.9571	1.85795
$355$	−23.2275	−1.23279
$356$	8.86441i	0.469813i
$357$	− 11.2181i	− 0.593727i
$358$	− 12.4301i	− 0.656953i
$359$	− 13.6834i	− 0.722180i	−0.932531	−	0.361090i	$-0.882405\pi$
$359$	− 13.6834i	− 0.722180i	0.932531	−	0.361090i	$-0.117595\pi$
$360$	7.22344	0.380708
$361$	13.3414	0.702180
$362$	4.46226i	0.234531i
$363$	23.1012	1.21250
$364$	0	0
$365$	25.7477	1.34769
$366$	7.34335i	0.383843i
$367$	−11.4128	−0.595741	−0.297871	−	0.954606i	$-0.596276\pi$
$367$	−11.4128	−0.595741	−0.297871	+	0.954606i	$0.596276\pi$
$368$	−11.1854	−0.583080
$369$	− 25.5586i	− 1.33053i
$370$	− 73.2261i	− 3.80685i
$371$	− 4.92032i	− 0.255450i
$372$	− 46.9190i	− 2.43264i
$373$	−31.2808	−1.61966	−0.809830	−	0.586664i	$-0.800441\pi$
$373$	−31.2808	−1.61966	−0.809830	+	0.586664i	$0.800441\pi$
$374$	−9.27416	−0.479555
$375$	24.2164i	1.25053i
$376$	2.82784	0.145835
$377$	0	0
$378$	4.22181	0.217146
$379$	− 27.4151i	− 1.40822i	−0.710093	−	0.704108i	$-0.751347\pi$
$379$	− 27.4151i	− 1.40822i	0.710093	−	0.704108i	$-0.248653\pi$
$380$	−20.9871	−1.07661
$381$	27.8412	1.42635
$382$	23.9767i	1.22675i
$383$	16.1006i	0.822705i	0.911476	+	0.411352i	$0.134943\pi$
$383$	16.1006i	0.822705i	−0.911476	+	0.411352i	$0.865057\pi$
$384$	− 16.7228i	− 0.853383i
$385$	3.19256i	0.162708i
$386$	−29.7199	−1.51271
$387$	7.70408	0.391620
$388$	1.13486i	0.0576139i
$389$	−21.1380	−1.07174	−0.535870	−	0.844301i	$-0.680016\pi$
$389$	−21.1380	−1.07174	−0.535870	+	0.844301i	$0.680016\pi$
$390$	0	0
$391$	19.1388	0.967893
$392$	− 0.948212i	− 0.0478919i
$393$	−18.5515	−0.935800
$394$	48.4255	2.43964
$395$	− 2.72853i	− 0.137287i
$396$	4.59224i	0.230769i
$397$	13.0984i	0.657390i	0.944436	+	0.328695i	$0.106609\pi$
$397$	13.0984i	0.657390i	−0.944436	+	0.328695i	$0.893391\pi$
$398$	− 6.64426i	− 0.333046i
$399$	5.37995	0.269335
$400$	23.1123	1.15562
$401$	− 19.4447i	− 0.971022i	−0.874230	−	0.485511i	$-0.838633\pi$
$401$	− 19.4447i	− 0.971022i	0.874230	−	0.485511i	$-0.161367\pi$
$402$	−40.2002	−2.00501
$403$	0	0
$404$	14.2636	0.709642
$405$	39.1575i	1.94575i
$406$	−2.70418	−0.134206
$407$	8.54308	0.423465
$408$	10.6372i	0.526618i
$409$	24.0559i	1.18949i	0.803916	+	0.594743i	$0.202746\pi$
$409$	24.0559i	1.18949i	−0.803916	+	0.594743i	$0.797254\pi$
$410$	91.8098i	4.53416i
$411$	16.8618i	0.831733i
$412$	20.1813	0.994261
$413$	7.32746	0.360561
$414$	− 17.2146i	− 0.846053i
$415$	−17.1721	−0.842944
$416$	0	0
$417$	37.7256	1.84743
$418$	− 4.44767i	− 0.217542i
$419$	39.0238	1.90644	0.953218	−	0.302283i	$-0.0977487\pi$
$419$	39.0238	1.90644	0.953218	+	0.302283i	$0.0977487\pi$
$420$	19.9537	0.973640
$421$	22.0284i	1.07360i	0.843710	+	0.536799i	$0.180367\pi$
$421$	22.0284i	1.07360i	−0.843710	+	0.536799i	$0.819633\pi$
$422$	31.3536i	1.52627i
$423$	− 6.30771i	− 0.306691i
$424$	4.66551i	0.226577i
$425$	−39.5465	−1.91828
$426$	−30.7657	−1.49060
$427$	1.53926i	0.0744902i
$428$	9.38803	0.453787
$429$	0	0
$430$	−27.6741	−1.33456
$431$	35.8797i	1.72826i	0.503267	+	0.864131i	$0.332131\pi$
$431$	35.8797i	1.72826i	−0.503267	+	0.864131i	$0.667869\pi$
$432$	5.80195	0.279147
$433$	−12.2136	−0.586946	−0.293473	−	0.955967i	$-0.594811\pi$
$433$	−12.2136	−0.586946	−0.293473	+	0.955967i	$0.594811\pi$
$434$	− 17.8648i	− 0.857540i
$435$	− 10.4429i	− 0.500699i
$436$	25.5192i	1.22215i
$437$	9.17853i	0.439069i
$438$	34.1037	1.62954
$439$	15.7553	0.751960	0.375980	−	0.926628i	$-0.377306\pi$
$439$	15.7553	0.751960	0.375980	+	0.926628i	$0.377306\pi$
$440$	− 3.02722i	− 0.144317i
$441$	−2.11505	−0.100717
$442$	0	0
$443$	−15.0706	−0.716028	−0.358014	−	0.933716i	$-0.616546\pi$
$443$	−15.0706	−0.716028	−0.358014	+	0.933716i	$0.616546\pi$
$444$	− 53.3947i	− 2.53400i
$445$	−13.0342	−0.617883
$446$	−9.24099	−0.437574
$447$	− 5.70305i	− 0.269745i
$448$	− 11.1012i	− 0.524482i
$449$	30.7826i	1.45272i	0.687315	+	0.726360i	$0.258789\pi$
$449$	30.7826i	1.45272i	−0.687315	+	0.726360i	$0.741211\pi$
$450$	35.5705i	1.67681i
$451$	−10.7112	−0.504370
$452$	12.0274	0.565722
$453$	35.9540i	1.68926i
$454$	28.6166	1.34304
$455$	0	0
$456$	−5.10133	−0.238892
$457$	7.75597i	0.362809i	0.983409	+	0.181405i	$0.0580643\pi$
$457$	7.75597i	0.362809i	−0.983409	+	0.181405i	$0.941936\pi$
$458$	−34.8429	−1.62810
$459$	−9.92745	−0.463374
$460$	34.0422i	1.58723i
$461$	1.47222i	0.0685681i	0.999412	+	0.0342840i	$0.0109151\pi$
$461$	1.47222i	0.0685681i	−0.999412	+	0.0342840i	$0.989085\pi$
$462$	4.22867i	0.196735i
$463$	14.0366i	0.652335i	0.945312	+	0.326168i	$0.105757\pi$
$463$	14.0366i	0.652335i	−0.945312	+	0.326168i	$0.894243\pi$
$464$	−3.71630	−0.172525
$465$	68.9898	3.19933
$466$	− 34.8104i	− 1.61256i
$467$	−31.3806	−1.45212	−0.726060	−	0.687631i	$-0.758651\pi$
$467$	−31.3806	−1.45212	−0.726060	+	0.687631i	$0.758651\pi$
$468$	0	0
$469$	−8.42649	−0.389099
$470$	22.6581i	1.04514i
$471$	29.3632	1.35298
$472$	−6.94798	−0.319807
$473$	− 3.22865i	− 0.148454i
$474$	− 3.61404i	− 0.165999i
$475$	− 18.9655i	− 0.870199i
$476$	12.1500i	0.556895i
$477$	10.4067	0.476492
$478$	64.1698	2.93506
$479$	− 41.1951i	− 1.88225i	−0.338059	−	0.941125i	$-0.609770\pi$
$479$	− 41.1951i	− 1.88225i	0.338059	−	0.941125i	$-0.390230\pi$
$480$	65.2598	2.97869
$481$	0	0
$482$	−62.2572	−2.83574
$483$	− 8.72660i	− 0.397074i
$484$	−25.0202	−1.13728
$485$	−1.66870	−0.0757719
$486$	39.2002i	1.77816i
$487$	28.3265i	1.28360i	0.766874	+	0.641798i	$0.221811\pi$
$487$	28.3265i	1.28360i	−0.766874	+	0.641798i	$0.778189\pi$
$488$	− 1.45955i	− 0.0660706i
$489$	− 5.24584i	− 0.237225i
$490$	7.59755	0.343222
$491$	−34.7863	−1.56988	−0.784941	−	0.619571i	$-0.787307\pi$
$491$	−34.7863	−1.56988	−0.784941	+	0.619571i	$0.787307\pi$
$492$	66.9455i	3.01814i
$493$	6.35879	0.286386
$494$	0	0
$495$	−6.75244	−0.303499
$496$	− 24.5513i	− 1.10239i
$497$	−6.44888	−0.289272
$498$	−22.7451	−1.01923
$499$	0.0694885i	0.00311073i	0.999999	+	0.00155537i	$0.000495089\pi$
$499$	0.0694885i	0.00311073i	−0.999999	+	0.00155537i	$0.999505\pi$
$500$	− 26.2281i	− 1.17295i
$501$	31.1923i	1.39357i
$502$	− 27.3855i	− 1.22228i
$503$	25.7372	1.14756	0.573782	−	0.819008i	$-0.305476\pi$
$503$	25.7372	1.14756	0.573782	+	0.819008i	$0.305476\pi$
$504$	2.00552	0.0893329
$505$	20.9733i	0.933299i
$506$	−7.21437	−0.320718
$507$	0	0
$508$	−30.1540	−1.33787
$509$	7.04000i	0.312042i	0.987754	+	0.156021i	$0.0498668\pi$
$509$	7.04000i	0.312042i	−0.987754	+	0.156021i	$0.950133\pi$
$510$	−85.2304	−3.77407
$511$	7.14859	0.316235
$512$	− 28.7215i	− 1.26932i
$513$	− 4.76097i	− 0.210202i
$514$	− 9.67199i	− 0.426613i
$515$	29.6746i	1.30762i
$516$	−20.1793	−0.888342
$517$	−2.64346	−0.116259
$518$	− 20.3305i	− 0.893273i
$519$	8.33263	0.365762
$520$	0	0
$521$	16.3253	0.715225	0.357613	−	0.933870i	$-0.383591\pi$
$521$	16.3253	0.715225	0.357613	+	0.933870i	$0.383591\pi$
$522$	− 5.71948i	− 0.250335i
$523$	−7.08946	−0.310000	−0.155000	−	0.987914i	$-0.549538\pi$
$523$	−7.08946	−0.310000	−0.155000	+	0.987914i	$0.549538\pi$
$524$	20.0926	0.877748
$525$	18.0317i	0.786968i
$526$	5.62150i	0.245109i
$527$	42.0086i	1.82993i
$528$	5.81138i	0.252908i
$529$	−8.11189	−0.352691
$530$	−37.3824	−1.62379
$531$	15.4980i	0.672555i
$532$	−5.82686	−0.252626
$533$	0	0
$534$	−17.2644	−0.747102
$535$	13.8042i	0.596807i
$536$	7.99010	0.345120
$537$	13.3274	0.575118
$538$	− 25.1558i	− 1.08454i
$539$	0.886384i	0.0381793i
$540$	− 17.6579i	− 0.759877i
$541$	25.5162i	1.09703i	0.836141	+	0.548515i	$0.184806\pi$
$541$	25.5162i	1.09703i	−0.836141	+	0.548515i	$0.815194\pi$
$542$	27.4818	1.18044
$543$	−4.78436	−0.205316
$544$	39.7374i	1.70373i
$545$	−37.5235	−1.60733
$546$	0	0
$547$	−13.3073	−0.568978	−0.284489	−	0.958679i	$-0.591824\pi$
$547$	−13.3073	−0.568978	−0.284489	+	0.958679i	$0.591824\pi$
$548$	− 18.2625i	− 0.780136i
$549$	−3.25562	−0.138947
$550$	14.9070	0.635637
$551$	3.04952i	0.129914i
$552$	8.27466i	0.352193i
$553$	− 0.757551i	− 0.0322143i
$554$	45.0669i	1.91471i
$555$	78.5118	3.33264
$556$	−40.8594	−1.73282
$557$	17.0071i	0.720612i	0.932834	+	0.360306i	$0.117328\pi$
$557$	17.0071i	0.720612i	−0.932834	+	0.360306i	$0.882672\pi$
$558$	37.7851	1.59957
$559$	0	0
$560$	10.4412	0.441220
$561$	− 9.94358i	− 0.419818i
$562$	−36.4244	−1.53647
$563$	24.9193	1.05022	0.525111	−	0.851034i	$-0.324024\pi$
$563$	24.9193	1.05022	0.525111	+	0.851034i	$0.324024\pi$
$564$	16.5218i	0.695691i
$565$	17.6851i	0.744019i
$566$	− 44.8038i	− 1.88325i
$567$	10.8717i	0.456569i
$568$	6.11491	0.256576
$569$	−5.88129	−0.246557	−0.123278	−	0.992372i	$-0.539341\pi$
$569$	−5.88129	−0.246557	−0.123278	+	0.992372i	$0.539341\pi$
$570$	− 40.8745i	− 1.71204i
$571$	−8.92622	−0.373551	−0.186775	−	0.982403i	$-0.559804\pi$
$571$	−8.92622	−0.373551	−0.186775	+	0.982403i	$0.559804\pi$
$572$	0	0
$573$	−25.7074	−1.07394
$574$	25.4901i	1.06394i
$575$	−30.7632	−1.28291
$576$	23.4796	0.978317
$577$	− 36.1933i	− 1.50675i	−0.657592	−	0.753374i	$-0.728425\pi$
$577$	− 36.1933i	− 1.50675i	0.657592	−	0.753374i	$-0.271575\pi$
$578$	− 16.0381i	− 0.667097i
$579$	− 31.8652i	− 1.32427i
$580$	11.3104i	0.469638i
$581$	−4.76766	−0.197796
$582$	−2.21026	−0.0916183
$583$	− 4.36130i	− 0.180626i
$584$	−6.77838	−0.280491
$585$	0	0
$586$	−0.886069	−0.0366032
$587$	− 36.4895i	− 1.50608i	−0.657974	−	0.753041i	$-0.728586\pi$
$587$	− 36.4895i	− 1.50608i	0.657974	−	0.753041i	$-0.271414\pi$
$588$	5.53995	0.228464
$589$	−20.1463	−0.830116
$590$	− 55.6708i	− 2.29193i
$591$	51.9210i	2.13574i
$592$	− 27.9399i	− 1.14832i
$593$	34.9930i	1.43699i	0.695533	+	0.718495i	$0.255168\pi$
$593$	34.9930i	1.43699i	−0.695533	+	0.718495i	$0.744832\pi$
$594$	3.74215	0.153542
$595$	−17.8654	−0.732410
$596$	6.17679i	0.253011i
$597$	7.12385	0.291560
$598$	0	0
$599$	−32.5052	−1.32812	−0.664062	−	0.747677i	$-0.731169\pi$
$599$	−32.5052	−1.32812	−0.664062	+	0.747677i	$0.731169\pi$
$600$	− 17.0979i	− 0.698018i
$601$	20.0780	0.819000	0.409500	−	0.912310i	$-0.365703\pi$
$601$	20.0780	0.819000	0.409500	+	0.912310i	$0.365703\pi$
$602$	−7.68344	−0.313154
$603$	− 17.8225i	− 0.725788i
$604$	− 38.9406i	− 1.58447i
$605$	− 36.7897i	− 1.49572i
$606$	27.7799i	1.12848i
$607$	9.71601	0.394361	0.197180	−	0.980367i	$-0.436822\pi$
$607$	9.71601	0.394361	0.197180	+	0.980367i	$0.436822\pi$
$608$	−19.0571	−0.772868
$609$	− 2.89937i	− 0.117488i
$610$	11.6946	0.473502
$611$	0	0
$612$	−25.6979	−1.03878
$613$	11.8816i	0.479893i	0.970786	+	0.239947i	$0.0771299\pi$
$613$	11.8816i	0.479893i	−0.970786	+	0.239947i	$0.922870\pi$
$614$	29.7017	1.19866
$615$	−98.4368	−3.96936
$616$	− 0.840480i	− 0.0338639i
$617$	− 19.9884i	− 0.804705i	−0.915485	−	0.402352i	$-0.868193\pi$
$617$	− 19.9884i	− 0.804705i	0.915485	−	0.402352i	$-0.131807\pi$
$618$	39.3052i	1.58109i
$619$	41.7176i	1.67677i	0.545078	+	0.838386i	$0.316500\pi$
$619$	41.7176i	1.67677i	−0.545078	+	0.838386i	$0.683500\pi$
$620$	−74.7207	−3.00086
$621$	−7.72257	−0.309896
$622$	21.9056i	0.878333i
$623$	−3.61884	−0.144986
$624$	0	0
$625$	−1.29828	−0.0519312
$626$	− 14.4442i	− 0.577307i
$627$	4.76871	0.190444
$628$	−31.8023	−1.26905
$629$	47.8066i	1.90618i
$630$	16.0692i	0.640213i
$631$	17.6415i	0.702296i	0.936320	+	0.351148i	$0.114209\pi$
$631$	17.6415i	0.702296i	−0.936320	+	0.351148i	$0.885791\pi$
$632$	0.718319i	0.0285732i
$633$	−33.6168	−1.33615
$634$	−1.47921	−0.0587468
$635$	− 44.3385i	− 1.75952i
$636$	−27.2584	−1.08086
$637$	0	0
$638$	−2.39694	−0.0948958
$639$	− 13.6397i	− 0.539580i
$640$	−26.6319	−1.05272
$641$	10.9202	0.431324	0.215662	−	0.976468i	$-0.430809\pi$
$641$	10.9202	0.431324	0.215662	+	0.976468i	$0.430809\pi$
$642$	18.2842i	0.721618i
$643$	17.6351i	0.695462i	0.937594	+	0.347731i	$0.113048\pi$
$643$	17.6351i	0.695462i	−0.937594	+	0.347731i	$0.886952\pi$
$644$	9.45150i	0.372441i
$645$	− 29.6716i	− 1.16832i
$646$	24.8889	0.979241
$647$	−16.6726	−0.655469	−0.327735	−	0.944770i	$-0.606285\pi$
$647$	−16.6726	−0.655469	−0.327735	+	0.944770i	$0.606285\pi$
$648$	− 10.3087i	− 0.404963i
$649$	6.49495	0.254949
$650$	0	0
$651$	19.1544	0.750719
$652$	5.68161i	0.222509i
$653$	−6.77329	−0.265059	−0.132530	−	0.991179i	$-0.542310\pi$
$653$	−6.77329	−0.265059	−0.132530	+	0.991179i	$0.542310\pi$
$654$	−49.7013	−1.94347
$655$	29.5441i	1.15439i
$656$	35.0306i	1.36772i
$657$	15.1197i	0.589874i
$658$	6.29081i	0.245241i
$659$	33.5361	1.30638	0.653190	−	0.757194i	$-0.273430\pi$
$659$	33.5361	1.30638	0.653190	+	0.757194i	$0.273430\pi$
$660$	17.6866	0.688451
$661$	25.1661i	0.978848i	0.872046	+	0.489424i	$0.162793\pi$
$661$	25.1661i	0.978848i	−0.872046	+	0.489424i	$0.837207\pi$
$662$	8.85657	0.344221
$663$	0	0
$664$	4.52075	0.175439
$665$	− 8.56783i	− 0.332246i
$666$	43.0002	1.66622
$667$	4.94651	0.191529
$668$	− 33.7833i	− 1.30712i
$669$	− 9.90802i	− 0.383066i
$670$	64.0207i	2.47334i
$671$	1.36438i	0.0526713i
$672$	18.1188	0.698947
$673$	1.85468	0.0714927	0.0357464	−	0.999361i	$-0.488619\pi$
$673$	1.85468	0.0714927	0.0357464	+	0.999361i	$0.488619\pi$
$674$	43.0902i	1.65977i
$675$	15.9571	0.614189
$676$	0	0
$677$	−14.7209	−0.565770	−0.282885	−	0.959154i	$-0.591291\pi$
$677$	−14.7209	−0.565770	−0.282885	+	0.959154i	$0.591291\pi$
$678$	23.4246i	0.899618i
$679$	−0.463300	−0.0177798
$680$	16.9402	0.649627
$681$	30.6822i	1.17575i
$682$	− 15.8351i	− 0.606358i
$683$	7.94353i	0.303951i	0.988384	+	0.151975i	$0.0485634\pi$
$683$	7.94353i	0.303951i	−0.988384	+	0.151975i	$0.951437\pi$
$684$	− 12.3241i	− 0.471224i
$685$	26.8533	1.02601
$686$	2.10939	0.0805368
$687$	− 37.3579i	− 1.42529i
$688$	−10.5592	−0.402566
$689$	0	0
$690$	−66.3008	−2.52403
$691$	− 10.2307i	− 0.389193i	−0.980883	−	0.194597i	$-0.937660\pi$
$691$	− 10.2307i	− 0.389193i	0.980883	−	0.194597i	$-0.0623397\pi$
$692$	−9.02481	−0.343072
$693$	−1.87475	−0.0712159
$694$	− 16.8118i	− 0.638168i
$695$	− 60.0797i	− 2.27895i
$696$	2.74922i	0.104209i
$697$	− 59.9392i	− 2.27036i
$698$	−45.5570	−1.72436
$699$	37.3231	1.41169
$700$	− 19.5296i	− 0.738148i
$701$	−16.5978	−0.626891	−0.313445	−	0.949606i	$-0.601483\pi$
$701$	−16.5978	−0.626891	−0.313445	+	0.949606i	$0.601483\pi$
$702$	0	0
$703$	−22.9269	−0.864706
$704$	− 9.83992i	− 0.370856i
$705$	−24.2936	−0.914951
$706$	−45.5999	−1.71618
$707$	5.82303i	0.218998i
$708$	− 40.5938i	− 1.52561i
$709$	47.8659i	1.79764i	0.438318	+	0.898820i	$0.355574\pi$
$709$	47.8659i	1.79764i	−0.438318	+	0.898820i	$0.644426\pi$
$710$	48.9957i	1.83878i
$711$	1.60226	0.0600895
$712$	3.43142	0.128598
$713$	32.6785i	1.22382i
$714$	−23.6634	−0.885581
$715$	0	0
$716$	−14.4344	−0.539441
$717$	68.8017i	2.56944i
$718$	−28.8635	−1.07718
$719$	38.0922	1.42060	0.710300	−	0.703899i	$-0.248559\pi$
$719$	38.0922	1.42060	0.710300	+	0.703899i	$0.248559\pi$
$720$	22.0836i	0.823009i
$721$	8.23888i	0.306832i
$722$	− 28.1423i	− 1.04735i
$723$	− 66.7511i	− 2.48250i
$724$	5.18179	0.192580
$725$	−10.2209	−0.379596
$726$	− 48.7294i	− 1.80852i
$727$	15.4059	0.571374	0.285687	−	0.958323i	$-0.407778\pi$
$727$	15.4059	0.571374	0.285687	+	0.958323i	$0.407778\pi$
$728$	0	0
$729$	−9.41460	−0.348689
$730$	− 54.3118i	− 2.01017i
$731$	18.0674	0.668246
$732$	8.52744	0.315183
$733$	11.6298i	0.429557i	0.976663	+	0.214778i	$0.0689029\pi$
$733$	11.6298i	0.429557i	−0.976663	+	0.214778i	$0.931097\pi$
$734$	24.0740i	0.888586i
$735$	8.14596i	0.300468i
$736$	30.9117i	1.13942i
$737$	−7.46911	−0.275128
$738$	−53.9130	−1.98456
$739$	− 2.68901i	− 0.0989168i	−0.998776	−	0.0494584i	$-0.984250\pi$
$739$	− 2.68901i	− 0.0989168i	0.998776	−	0.0494584i	$-0.0157495\pi$
$740$	−85.0336	−3.12590
$741$	0	0
$742$	−10.3789	−0.381020
$743$	2.46720i	0.0905126i	0.998975	+	0.0452563i	$0.0144105\pi$
$743$	2.46720i	0.0905126i	−0.998975	+	0.0452563i	$0.985590\pi$
$744$	−18.1624	−0.665866
$745$	−9.08236	−0.332752
$746$	65.9835i	2.41583i
$747$	− 10.0839i	− 0.368949i
$748$	10.7696i	0.393775i
$749$	3.83260i	0.140040i
$750$	51.0819	1.86525
$751$	37.9185	1.38366	0.691832	−	0.722058i	$-0.256804\pi$
$751$	37.9185	1.38366	0.691832	+	0.722058i	$0.256804\pi$
$752$	8.64534i	0.315263i
$753$	29.3623	1.07002
$754$	0	0
$755$	57.2583	2.08384
$756$	− 4.90256i	− 0.178304i
$757$	34.6451	1.25920	0.629598	−	0.776921i	$-0.283219\pi$
$757$	34.6451	1.25920	0.629598	+	0.776921i	$0.283219\pi$
$758$	−57.8290	−2.10044
$759$	− 7.73512i	− 0.280767i
$760$	8.12411i	0.294692i
$761$	22.8595i	0.828655i	0.910128	+	0.414328i	$0.135983\pi$
$761$	22.8595i	0.828655i	−0.910128	+	0.414328i	$0.864017\pi$
$762$	− 58.7280i	− 2.12749i
$763$	−10.4180	−0.377158
$764$	27.8428	1.00732
$765$	− 37.7863i	− 1.36617i
$766$	33.9625	1.22712
$767$	0	0
$768$	14.9390	0.539065
$769$	51.8275i	1.86895i	0.356034	+	0.934473i	$0.384129\pi$
$769$	51.8275i	1.86895i	−0.356034	+	0.934473i	$0.615871\pi$
$770$	6.73435	0.242689
$771$	10.3701	0.373471
$772$	34.5122i	1.24212i
$773$	− 5.69966i	− 0.205003i	−0.994733	−	0.102501i	$-0.967315\pi$
$773$	− 5.69966i	− 0.205003i	0.994733	−	0.102501i	$-0.0326846\pi$
$774$	− 16.2509i	− 0.584126i
$775$	− 67.5234i	− 2.42551i
$776$	0.439306	0.0157702
$777$	21.7980	0.782001
$778$	44.5883i	1.59857i
$779$	28.7454	1.02991
$780$	0	0
$781$	−5.71619	−0.204541
$782$	− 40.3712i	− 1.44367i
$783$	−2.56579	−0.0916938
$784$	2.89889	0.103532
$785$	− 46.7622i	− 1.66902i
$786$	39.1324i	1.39580i
$787$	− 16.8141i	− 0.599358i	−0.954040	−	0.299679i	$-0.903120\pi$
$787$	− 16.8141i	− 0.599358i	0.954040	−	0.299679i	$-0.0968796\pi$
$788$	− 56.2340i	− 2.00325i
$789$	−6.02727	−0.214577
$790$	−5.75553	−0.204773
$791$	4.91011i	0.174583i
$792$	1.77766	0.0631664
$793$	0	0
$794$	27.6296	0.980539
$795$	− 40.0807i	− 1.42152i
$796$	−7.71562	−0.273473
$797$	−42.1301	−1.49233	−0.746163	−	0.665764i	$-0.768106\pi$
$797$	−42.1301	−1.49233	−0.746163	+	0.665764i	$0.768106\pi$
$798$	− 11.3484i	− 0.401729i
$799$	− 14.7926i	− 0.523326i
$800$	− 63.8727i	− 2.25824i
$801$	− 7.65403i	− 0.270442i
$802$	−41.0164	−1.44834
$803$	6.33640	0.223607
$804$	46.6824i	1.64636i
$805$	−13.8975	−0.489823
$806$	0	0
$807$	26.9716	0.949445
$808$	− 5.52147i	− 0.194245i
$809$	−30.1686	−1.06067	−0.530336	−	0.847787i	$-0.677934\pi$
$809$	−30.1686	−1.06067	−0.530336	+	0.847787i	$0.677934\pi$
$810$	82.5984	2.90221
$811$	− 23.7929i	− 0.835480i	−0.908567	−	0.417740i	$-0.862822\pi$
$811$	− 23.7929i	− 0.835480i	0.908567	−	0.417740i	$-0.137178\pi$
$812$	3.14022i	0.110200i
$813$	29.4655i	1.03340i
$814$	− 18.0207i	− 0.631624i
$815$	−8.35425	−0.292637
$816$	−32.5202	−1.13843
$817$	8.66468i	0.303139i
$818$	50.7432	1.77419
$819$	0	0
$820$	106.614	3.72312
$821$	35.8847i	1.25239i	0.779668	+	0.626193i	$0.215388\pi$
$821$	35.8847i	1.25239i	−0.779668	+	0.626193i	$0.784612\pi$
$822$	35.5682	1.24058
$823$	12.2346	0.426470	0.213235	−	0.977001i	$-0.431600\pi$
$823$	12.2346	0.426470	0.213235	+	0.977001i	$0.431600\pi$
$824$	− 7.81220i	− 0.272151i
$825$	15.9830i	0.556457i
$826$	− 15.4565i	− 0.537799i
$827$	27.3474i	0.950962i	0.879726	+	0.475481i	$0.157726\pi$
$827$	27.3474i	0.950962i	−0.879726	+	0.475481i	$0.842274\pi$
$828$	−19.9904	−0.694715
$829$	−23.5738	−0.818751	−0.409376	−	0.912366i	$-0.634253\pi$
$829$	−23.5738	−0.818751	−0.409376	+	0.912366i	$0.634253\pi$
$830$	36.2226i	1.25730i
$831$	−48.3199	−1.67620
$832$	0	0
$833$	−4.96016	−0.171859
$834$	− 79.5779i	− 2.75556i
$835$	49.6751	1.71908
$836$	−5.16483	−0.178630
$837$	− 16.9506i	− 0.585898i
$838$	− 82.3163i	− 2.84357i
$839$	10.5883i	0.365549i	0.983155	+	0.182775i	$0.0585078\pi$
$839$	10.5883i	0.365549i	−0.983155	+	0.182775i	$0.941492\pi$
$840$	− 7.72409i	− 0.266507i
$841$	−27.3565	−0.943329
$842$	46.4664	1.60134
$843$	− 39.0536i	− 1.34508i
$844$	36.4092	1.25326
$845$	0	0
$846$	−13.3054	−0.457449
$847$	− 10.2143i	− 0.350968i
$848$	−14.2635	−0.489810
$849$	48.0379	1.64866
$850$	83.4188i	2.86124i
$851$	37.1888i	1.27482i
$852$	35.7265i	1.22397i
$853$	21.3925i	0.732464i	0.930524	+	0.366232i	$0.119352\pi$
$853$	21.3925i	0.732464i	−0.930524	+	0.366232i	$0.880648\pi$
$854$	3.24690	0.111107
$855$	18.1214	0.619739
$856$	− 3.63412i	− 0.124212i
$857$	−7.22129	−0.246675	−0.123337	−	0.992365i	$-0.539360\pi$
$857$	−7.22129	−0.246675	−0.123337	+	0.992365i	$0.539360\pi$
$858$	0	0
$859$	57.1073	1.94848	0.974238	−	0.225524i	$-0.0724095\pi$
$859$	57.1073	1.94848	0.974238	+	0.225524i	$0.0724095\pi$
$860$	32.1364i	1.09584i
$861$	−27.3301	−0.931406
$862$	75.6841	2.57781
$863$	− 51.3361i	− 1.74750i	−0.486374	−	0.873751i	$-0.661681\pi$
$863$	− 51.3361i	− 1.74750i	0.486374	−	0.873751i	$-0.338319\pi$
$864$	− 16.0341i	− 0.545493i
$865$	− 13.2701i	− 0.451197i
$866$	25.7631i	0.875467i
$867$	17.1958	0.583999
$868$	−20.7455	−0.704148
$869$	− 0.671481i	− 0.0227784i
$870$	−22.0281	−0.746823
$871$	0	0
$872$	9.87851	0.334528
$873$	− 0.979903i	− 0.0331647i
$874$	19.3611	0.654899
$875$	10.7074	0.361977
$876$	− 39.6029i	− 1.33806i
$877$	− 21.4277i	− 0.723563i	−0.932263	−	0.361781i	$-0.882169\pi$
$877$	− 21.4277i	− 0.723563i	0.932263	−	0.361781i	$-0.117831\pi$
$878$	− 33.2341i	− 1.12160i
$879$	− 0.950027i	− 0.0320436i
$880$	9.25489	0.311982
$881$	−29.0619	−0.979120	−0.489560	−	0.871970i	$-0.662843\pi$
$881$	−29.0619	−0.979120	−0.489560	+	0.871970i	$0.662843\pi$
$882$	4.46147i	0.150225i
$883$	4.83594	0.162742	0.0813711	−	0.996684i	$-0.474070\pi$
$883$	4.83594	0.162742	0.0813711	+	0.996684i	$0.474070\pi$
$884$	0	0
$885$	59.6892	2.00643
$886$	31.7899i	1.06800i
$887$	−24.9898	−0.839075	−0.419538	−	0.907738i	$-0.637808\pi$
$887$	−24.9898	−0.839075	−0.419538	+	0.907738i	$0.637808\pi$
$888$	−20.6692	−0.693612
$889$	− 12.3102i	− 0.412869i
$890$	27.4943i	0.921611i
$891$	9.63651i	0.322835i
$892$	10.7311i	0.359303i
$893$	7.09420	0.237398
$894$	−12.0299	−0.402341
$895$	− 21.2244i	− 0.709455i
$896$	−7.39409	−0.247019
$897$	0	0
$898$	64.9324	2.16682
$899$	10.8573i	0.362111i
$900$	41.3061	1.37687
$901$	24.4056	0.813068
$902$	22.5940i	0.752300i
$903$	− 8.23805i	− 0.274145i
$904$	− 4.65582i	− 0.154850i
$905$	7.61931i	0.253274i
$906$	75.8409	2.51964
$907$	−15.0412	−0.499435	−0.249717	−	0.968319i	$-0.580338\pi$
$907$	−15.0412	−0.499435	−0.249717	+	0.968319i	$0.580338\pi$
$908$	− 33.2310i	− 1.10281i
$909$	−12.3160	−0.408497
$910$	0	0
$911$	−9.22150	−0.305522	−0.152761	−	0.988263i	$-0.548816\pi$
$911$	−9.22150	−0.305522	−0.152761	+	0.988263i	$0.548816\pi$
$912$	− 15.5959i	− 0.516432i
$913$	−4.22598	−0.139860
$914$	16.3604	0.541153
$915$	12.5388i	0.414519i
$916$	40.4612i	1.33687i
$917$	8.20265i	0.270875i
$918$	20.9409i	0.691151i
$919$	−45.0803	−1.48706	−0.743531	−	0.668701i	$-0.766851\pi$
$919$	−45.0803	−1.48706	−0.743531	+	0.668701i	$0.766851\pi$
$920$	13.1778	0.434459
$921$	31.8456i	1.04935i
$922$	3.10548	0.102274
$923$	0	0
$924$	4.91053	0.161544
$925$	− 76.8430i	− 2.52658i
$926$	29.6086	0.972999
$927$	−17.4257	−0.572334
$928$	10.2703i	0.337139i
$929$	− 46.9169i	− 1.53929i	−0.638469	−	0.769647i	$-0.720432\pi$
$929$	− 46.9169i	− 1.53929i	0.638469	−	0.769647i	$-0.279568\pi$
$930$	− 145.526i	− 4.77200i
$931$	− 2.37878i	− 0.0779612i
$932$	−40.4235	−1.32412
$933$	−23.4867	−0.768921
$934$	66.1939i	2.16593i
$935$	−15.8356	−0.517880
$936$	0	0
$937$	−28.3912	−0.927501	−0.463750	−	0.885966i	$-0.653497\pi$
$937$	−28.3912	−0.927501	−0.463750	+	0.885966i	$0.653497\pi$
$938$	17.7747i	0.580366i
$939$	15.4868	0.505394
$940$	26.3117	0.858192
$941$	− 17.8718i	− 0.582603i	−0.956631	−	0.291302i	$-0.905912\pi$
$941$	− 17.8718i	− 0.582603i	0.956631	−	0.291302i	$-0.0940883\pi$
$942$	− 61.9384i	− 2.01806i
$943$	− 46.6268i	− 1.51838i
$944$	− 21.2415i	− 0.691353i
$945$	7.20874	0.234500
$946$	−6.81048	−0.221428
$947$	− 9.52234i	− 0.309435i	−0.987959	−	0.154717i	$-0.950553\pi$
$947$	− 9.52234i	− 0.309435i	0.987959	−	0.154717i	$-0.0494467\pi$
$948$	−4.19680	−0.136306
$949$	0	0
$950$	−40.0057	−1.29796
$951$	− 1.58598i	− 0.0514289i
$952$	4.70328	0.152434
$953$	13.4180	0.434652	0.217326	−	0.976099i	$-0.430267\pi$
$953$	13.4180	0.434652	0.217326	+	0.976099i	$0.430267\pi$
$954$	− 21.9519i	− 0.710718i
$955$	40.9402i	1.32479i
$956$	− 74.5169i	− 2.41005i
$957$	− 2.56996i	− 0.0830749i
$958$	−86.8964	−2.80749
$959$	7.45555	0.240752
$960$	− 90.4298i	− 2.91861i
$961$	−40.7275	−1.31379
$962$	0	0
$963$	−8.10615	−0.261217
$964$	72.2960i	2.32850i
$965$	−50.7468	−1.63360
$966$	−18.4078	−0.592261
$967$	12.9316i	0.415851i	0.978145	+	0.207926i	$0.0666712\pi$
$967$	12.9316i	0.415851i	−0.978145	+	0.207926i	$0.933329\pi$
$968$	9.68534i	0.311299i
$969$	26.6854i	0.857260i
$970$	3.51994i	0.113019i
$971$	47.5213	1.52503	0.762516	−	0.646969i	$-0.223964\pi$
$971$	47.5213	1.52503	0.762516	+	0.646969i	$0.223964\pi$
$972$	45.5211	1.46009
$973$	− 16.6806i	− 0.534754i
$974$	59.7515	1.91456
$975$	0	0
$976$	4.46216	0.142830
$977$	− 36.4942i	− 1.16755i	−0.811915	−	0.583776i	$-0.801575\pi$
$977$	− 36.4942i	− 1.16755i	0.811915	−	0.583776i	$-0.198425\pi$
$978$	−11.0655	−0.353836
$979$	−3.20768	−0.102518
$980$	− 8.82263i	− 0.281829i
$981$	− 22.0347i	− 0.703514i
$982$	73.3777i	2.34158i
$983$	− 44.1843i	− 1.40926i	−0.709576	−	0.704629i	$-0.751113\pi$
$983$	− 44.1843i	− 1.40926i	0.709576	−	0.704629i	$-0.248887\pi$
$984$	25.9147	0.826130
$985$	82.6865	2.63461
$986$	− 13.4132i	− 0.427162i
$987$	−6.74490	−0.214692
$988$	0	0
$989$	14.0546	0.446911
$990$	14.2435i	0.452689i
$991$	−50.7097	−1.61085	−0.805424	−	0.592699i	$-0.798062\pi$
$991$	−50.7097	−1.61085	−0.805424	+	0.592699i	$0.798062\pi$
$992$	−67.8495	−2.15422
$993$	9.49586i	0.301342i
$994$	13.6032i	0.431467i
$995$	− 11.3451i	− 0.359663i
$996$	26.4126i	0.836916i
$997$	−50.2768	−1.59228	−0.796141	−	0.605111i	$-0.793129\pi$
$997$	−50.2768	−1.59228	−0.796141	+	0.605111i	$0.793129\pi$
$998$	0.146578	0.00463985
$999$	− 19.2901i	− 0.610312i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.i.337.2		12
13.3	even	3		91.2.q.a.43.6	yes	12
13.4	even	6		91.2.q.a.36.6	✓	12
13.5	odd	4		1183.2.a.m.1.2		6
13.8	odd	4		1183.2.a.p.1.5		6
13.12	even	2	inner	1183.2.c.i.337.11		12
39.17	odd	6		819.2.ct.a.127.1		12
39.29	odd	6		819.2.ct.a.316.1		12
52.3	odd	6		1456.2.cc.c.225.5		12
52.43	odd	6		1456.2.cc.c.673.5		12
91.3	odd	6		637.2.u.i.30.1		12
91.4	even	6		637.2.k.h.569.6		12
91.16	even	3		637.2.k.h.459.1		12
91.17	odd	6		637.2.k.g.569.6		12
91.30	even	6		637.2.u.h.361.1		12
91.34	even	4		8281.2.a.ch.1.5		6
91.55	odd	6		637.2.q.h.589.6		12
91.68	odd	6		637.2.k.g.459.1		12
91.69	odd	6		637.2.q.h.491.6		12
91.81	even	3		637.2.u.h.30.1		12
91.82	odd	6		637.2.u.i.361.1		12
91.83	even	4		8281.2.a.by.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.6	✓	12	13.4	even	6
91.2.q.a.43.6	yes	12	13.3	even	3
637.2.k.g.459.1		12	91.68	odd	6
637.2.k.g.569.6		12	91.17	odd	6
637.2.k.h.459.1		12	91.16	even	3
637.2.k.h.569.6		12	91.4	even	6
637.2.q.h.491.6		12	91.69	odd	6
637.2.q.h.589.6		12	91.55	odd	6
637.2.u.h.30.1		12	91.81	even	3
637.2.u.h.361.1		12	91.30	even	6
637.2.u.i.30.1		12	91.3	odd	6
637.2.u.i.361.1		12	91.82	odd	6
819.2.ct.a.127.1		12	39.17	odd	6
819.2.ct.a.316.1		12	39.29	odd	6
1183.2.a.m.1.2		6	13.5	odd	4
1183.2.a.p.1.5		6	13.8	odd	4
1183.2.c.i.337.2		12	1.1	even	1	trivial
1183.2.c.i.337.11		12	13.12	even	2	inner
1456.2.cc.c.225.5		12	52.3	odd	6
1456.2.cc.c.673.5		12	52.43	odd	6
8281.2.a.by.1.2		6	91.83	even	4
8281.2.a.ch.1.5		6	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)

\(f(q)\)	\(=\)	\(q-2.10939i q^{2} +2.26165 q^{3} -2.44952 q^{4} -3.60178i q^{5} -4.77070i q^{6} -1.00000i q^{7} +0.948212i q^{8} +2.11505 q^{9} +O(q^{10})\)	\(q-2.10939i q^{2} +2.26165 q^{3} -2.44952 q^{4} -3.60178i q^{5} -4.77070i q^{6} -1.00000i q^{7} +0.948212i q^{8} +2.11505 q^{9} -7.59755 q^{10} -0.886384i q^{11} -5.53995 q^{12} -2.10939 q^{14} -8.14596i q^{15} -2.89889 q^{16} +4.96016 q^{17} -4.46147i q^{18} +2.37878i q^{19} +8.82263i q^{20} -2.26165i q^{21} -1.86973 q^{22} +3.85851 q^{23} +2.14452i q^{24} -7.97282 q^{25} -2.00144 q^{27} +2.44952i q^{28} +1.28197 q^{29} -17.1830 q^{30} +8.46921i q^{31} +8.01131i q^{32} -2.00469i q^{33} -10.4629i q^{34} -3.60178 q^{35} -5.18087 q^{36} +9.63812i q^{37} +5.01776 q^{38} +3.41525 q^{40} -12.0841i q^{41} -4.77070 q^{42} +3.64250 q^{43} +2.17122i q^{44} -7.61796i q^{45} -8.13910i q^{46} -2.98229i q^{47} -6.55628 q^{48} -1.00000 q^{49} +16.8178i q^{50} +11.2181 q^{51} +4.92032 q^{53} +4.22181i q^{54} -3.19256 q^{55} +0.948212 q^{56} +5.37995i q^{57} -2.70418i q^{58} +7.32746i q^{59} +19.9537i q^{60} -1.53926 q^{61} +17.8648 q^{62} -2.11505i q^{63} +11.1012 q^{64} -4.22867 q^{66} -8.42649i q^{67} -12.1500 q^{68} +8.72660 q^{69} +7.59755i q^{70} -6.44888i q^{71} +2.00552i q^{72} +7.14859i q^{73} +20.3305 q^{74} -18.0317 q^{75} -5.82686i q^{76} -0.886384 q^{77} +0.757551 q^{79} +10.4412i q^{80} -10.8717 q^{81} -25.4901 q^{82} -4.76766i q^{83} +5.53995i q^{84} -17.8654i q^{85} -7.68344i q^{86} +2.89937 q^{87} +0.840480 q^{88} -3.61884i q^{89} -16.0692 q^{90} -9.45150 q^{92} +19.1544i q^{93} -6.29081 q^{94} +8.56783 q^{95} +18.1188i q^{96} -0.463300i q^{97} +2.10939i q^{98} -1.87475i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 8 q^{9}+O(q^{10}) \) 12 * q - 8 * q^4 + 8 * q^9	\( 12 q - 8 q^{4} + 8 q^{9} - 24 q^{10} - 4 q^{12} - 8 q^{14} + 16 q^{16} + 8 q^{17} - 12 q^{22} + 24 q^{23} - 20 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{30} - 12 q^{35} + 20 q^{36} + 4 q^{38} + 92 q^{40} - 8 q^{42} - 4 q^{43} + 4 q^{48} - 12 q^{49} + 52 q^{51} - 44 q^{53} + 12 q^{55} + 24 q^{56} - 28 q^{61} + 8 q^{62} - 52 q^{64} - 52 q^{66} + 16 q^{68} - 8 q^{69} - 12 q^{74} - 92 q^{75} + 8 q^{77} - 56 q^{79} - 4 q^{81} - 28 q^{82} + 4 q^{87} + 28 q^{88} + 24 q^{90} + 24 q^{92} - 8 q^{94} + 44 q^{95}+O(q^{100}) \) 12 * q - 8 * q^4 + 8 * q^9 - 24 * q^10 - 4 * q^12 - 8 * q^14 + 16 * q^16 + 8 * q^17 - 12 * q^22 + 24 * q^23 - 20 * q^25 + 12 * q^27 - 16 * q^29 - 16 * q^30 - 12 * q^35 + 20 * q^36 + 4 * q^38 + 92 * q^40 - 8 * q^42 - 4 * q^43 + 4 * q^48 - 12 * q^49 + 52 * q^51 - 44 * q^53 + 12 * q^55 + 24 * q^56 - 28 * q^61 + 8 * q^62 - 52 * q^64 - 52 * q^66 + 16 * q^68 - 8 * q^69 - 12 * q^74 - 92 * q^75 + 8 * q^77 - 56 * q^79 - 4 * q^81 - 28 * q^82 + 4 * q^87 + 28 * q^88 + 24 * q^90 + 24 * q^92 - 8 * q^94 + 44 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more