LMFDB - Embedded newform 1183.2.c.i.337.5

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			337.5
Root			$-1.08105 - 0.911778i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.i.337.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.823556i q^{2} +2.66029 q^{3} +1.32176 q^{4} +3.16209i q^{5} -2.19090i q^{6} +1.00000i q^{7} -2.73565i q^{8} +4.07715 q^{9} +O(q^{10})$	\(q-0.823556i q^{2} +2.66029 q^{3} +1.32176 q^{4} +3.16209i q^{5} -2.19090i q^{6} +1.00000i q^{7} -2.73565i q^{8} +4.07715 q^{9} +2.60416 q^{10} -5.94270i q^{11} +3.51626 q^{12} +0.823556 q^{14} +8.41209i q^{15} +0.390549 q^{16} +2.69964 q^{17} -3.35776i q^{18} +1.95705i q^{19} +4.17951i q^{20} +2.66029i q^{21} -4.89414 q^{22} +2.72941 q^{23} -7.27763i q^{24} -4.99883 q^{25} +2.86554 q^{27} +1.32176i q^{28} -5.99845 q^{29} +6.92783 q^{30} +1.15155i q^{31} -5.79294i q^{32} -15.8093i q^{33} -2.22331i q^{34} -3.16209 q^{35} +5.38900 q^{36} +6.50454i q^{37} +1.61174 q^{38} +8.65038 q^{40} +3.73374i q^{41} +2.19090 q^{42} -6.99125 q^{43} -7.85479i q^{44} +12.8923i q^{45} -2.24783i q^{46} -0.456071i q^{47} +1.03897 q^{48} -1.00000 q^{49} +4.11682i q^{50} +7.18184 q^{51} +0.399286 q^{53} -2.35994i q^{54} +18.7914 q^{55} +2.73565 q^{56} +5.20632i q^{57} +4.94006i q^{58} +4.80586i q^{59} +11.1187i q^{60} -1.15703 q^{61} +0.948365 q^{62} +4.07715i q^{63} -3.98971 q^{64} -13.0199 q^{66} +6.27918i q^{67} +3.56827 q^{68} +7.26104 q^{69} +2.60416i q^{70} +4.50720i q^{71} -11.1537i q^{72} -8.30575i q^{73} +5.35685 q^{74} -13.2983 q^{75} +2.58674i q^{76} +5.94270 q^{77} -7.91410 q^{79} +1.23495i q^{80} -4.60828 q^{81} +3.07494 q^{82} -6.19795i q^{83} +3.51626i q^{84} +8.53652i q^{85} +5.75769i q^{86} -15.9576 q^{87} -16.2571 q^{88} -3.56136i q^{89} +10.6176 q^{90} +3.60762 q^{92} +3.06345i q^{93} -0.375600 q^{94} -6.18837 q^{95} -15.4109i q^{96} -3.42751i q^{97} +0.823556i q^{98} -24.2293i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	− 0.823556i	− 0.582342i	−0.956671	−	0.291171i	$-0.905955\pi$
$2$	− 0.823556i	− 0.582342i	0.956671	−	0.291171i	$-0.0940449\pi$
$3$	2.66029	1.53592	0.767960	−	0.640498i	$-0.221272\pi$
$3$	2.66029	1.53592	0.767960	+	0.640498i	$0.221272\pi$
$4$	1.32176	0.660878
$5$	3.16209i	1.41413i	0.707148	+	0.707065i	$0.249981\pi$
$5$	3.16209i	1.41413i	−0.707148	+	0.707065i	$0.750019\pi$
$6$	− 2.19090i	− 0.894431i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 2.73565i	− 0.967199i
$9$	4.07715	1.35905
$10$	2.60416	0.823508
$11$	− 5.94270i	− 1.79179i	−0.444265	−	0.895895i	$-0.646535\pi$
$11$	− 5.94270i	− 1.79179i	0.444265	−	0.895895i	$-0.353465\pi$
$12$	3.51626	1.01506
$13$	0	0
$13$	0	0
$14$	0.823556	0.220105
$15$	8.41209i	2.17199i
$16$	0.390549	0.0976372
$17$	2.69964	0.654760	0.327380	−	0.944893i	$-0.393834\pi$
$17$	2.69964	0.654760	0.327380	+	0.944893i	$0.393834\pi$
$18$	− 3.35776i	− 0.791433i
$19$	1.95705i	0.448978i	0.974477	+	0.224489i	$0.0720712\pi$
$19$	1.95705i	0.448978i	−0.974477	+	0.224489i	$0.927929\pi$
$20$	4.17951i	0.934568i
$21$	2.66029i	0.580523i
$22$	−4.89414	−1.04343
$23$	2.72941	0.569122	0.284561	−	0.958658i	$-0.408152\pi$
$23$	2.72941	0.569122	0.284561	+	0.958658i	$0.408152\pi$
$24$	− 7.27763i	− 1.48554i
$25$	−4.99883	−0.999766
$26$	0	0
$27$	2.86554	0.551474
$28$	1.32176i	0.249788i
$29$	−5.99845	−1.11388	−0.556942	−	0.830551i	$-0.688026\pi$
$29$	−5.99845	−1.11388	−0.556942	+	0.830551i	$0.688026\pi$
$30$	6.92783	1.26484
$31$	1.15155i	0.206824i	0.994639	+	0.103412i	$0.0329760\pi$
$31$	1.15155i	0.206824i	−0.994639	+	0.103412i	$0.967024\pi$
$32$	− 5.79294i	− 1.02406i
$33$	− 15.8093i	− 2.75205i
$34$	− 2.22331i	− 0.381294i
$35$	−3.16209	−0.534491
$36$	5.38900	0.898167
$37$	6.50454i	1.06934i	0.845061	+	0.534670i	$0.179564\pi$
$37$	6.50454i	1.06934i	−0.845061	+	0.534670i	$0.820436\pi$
$38$	1.61174	0.261459
$39$	0	0
$40$	8.65038	1.36775
$41$	3.73374i	0.583112i	0.956554	+	0.291556i	$0.0941730\pi$
$41$	3.73374i	0.583112i	−0.956554	+	0.291556i	$0.905827\pi$
$42$	2.19090	0.338063
$43$	−6.99125	−1.06616	−0.533078	−	0.846066i	$-0.678965\pi$
$43$	−6.99125	−1.06616	−0.533078	+	0.846066i	$0.678965\pi$
$44$	− 7.85479i	− 1.18415i
$45$	12.8923i	1.92188i
$46$	− 2.24783i	− 0.331424i
$47$	− 0.456071i	− 0.0665248i	−0.999447	−	0.0332624i	$-0.989410\pi$
$47$	− 0.456071i	− 0.0665248i	0.999447	−	0.0332624i	$-0.0105897\pi$
$48$	1.03897	0.149963
$49$	−1.00000	−0.142857
$50$	4.11682i	0.582206i
$51$	7.18184	1.00566
$52$	0	0
$53$	0.399286	0.0548462	0.0274231	−	0.999624i	$-0.491270\pi$
$53$	0.399286	0.0548462	0.0274231	+	0.999624i	$0.491270\pi$
$54$	− 2.35994i	− 0.321146i
$55$	18.7914	2.53383
$56$	2.73565	0.365567
$57$	5.20632i	0.689594i
$58$	4.94006i	0.648662i
$59$	4.80586i	0.625670i	0.949807	+	0.312835i	$0.101279\pi$
$59$	4.80586i	0.625670i	−0.949807	+	0.312835i	$0.898721\pi$
$60$	11.1187i	1.43542i
$61$	−1.15703	−0.148142	−0.0740711	−	0.997253i	$-0.523599\pi$
$61$	−1.15703	−0.148142	−0.0740711	+	0.997253i	$0.523599\pi$
$62$	0.948365	0.120442
$63$	4.07715i	0.513673i
$64$	−3.98971	−0.498714
$65$	0	0
$66$	−13.0199	−1.60263
$67$	6.27918i	0.767124i	0.923515	+	0.383562i	$0.125303\pi$
$67$	6.27918i	0.767124i	−0.923515	+	0.383562i	$0.874697\pi$
$68$	3.56827	0.432716
$69$	7.26104	0.874127
$70$	2.60416i	0.311257i
$71$	4.50720i	0.534906i	0.963571	+	0.267453i	$0.0861820\pi$
$71$	4.50720i	0.534906i	−0.963571	+	0.267453i	$0.913818\pi$
$72$	− 11.1537i	− 1.31447i
$73$	− 8.30575i	− 0.972115i	−0.873927	−	0.486057i	$-0.838435\pi$
$73$	− 8.30575i	− 0.972115i	0.873927	−	0.486057i	$-0.161565\pi$
$74$	5.35685	0.622721
$75$	−13.2983	−1.53556
$76$	2.58674i	0.296719i
$77$	5.94270	0.677233
$78$	0	0
$79$	−7.91410	−0.890405	−0.445203	−	0.895430i	$-0.646868\pi$
$79$	−7.91410	−0.890405	−0.445203	+	0.895430i	$0.646868\pi$
$80$	1.23495i	0.138072i
$81$	−4.60828	−0.512031
$82$	3.07494	0.339571
$83$	− 6.19795i	− 0.680313i	−0.940369	−	0.340156i	$-0.889520\pi$
$83$	− 6.19795i	− 0.680313i	0.940369	−	0.340156i	$-0.110480\pi$
$84$	3.51626i	0.383655i
$85$	8.53652i	0.925916i
$86$	5.75769i	0.620867i
$87$	−15.9576	−1.71084
$88$	−16.2571	−1.73302
$89$	− 3.56136i	− 0.377504i	−0.982025	−	0.188752i	$-0.939556\pi$
$89$	− 3.56136i	− 0.377504i	0.982025	−	0.188752i	$-0.0604442\pi$
$90$	10.6176	1.11919
$91$	0	0
$92$	3.60762	0.376120
$93$	3.06345i	0.317665i
$94$	−0.375600	−0.0387402
$95$	−6.18837	−0.634913
$96$	− 15.4109i	− 1.57287i
$97$	− 3.42751i	− 0.348011i	−0.984745	−	0.174005i	$-0.944329\pi$
$97$	− 3.42751i	− 0.348011i	0.984745	−	0.174005i	$-0.0556710\pi$
$98$	0.823556i	0.0831917i
$99$	− 24.2293i	− 2.43513i
$100$	−6.60723	−0.660723
$101$	13.3295	1.32633	0.663167	−	0.748472i	$-0.269212\pi$
$101$	13.3295	1.32633	0.663167	+	0.748472i	$0.269212\pi$
$102$	− 5.91465i	− 0.585637i
$103$	−11.6450	−1.14741	−0.573706	−	0.819061i	$-0.694495\pi$
$103$	−11.6450	−1.14741	−0.573706	+	0.819061i	$0.694495\pi$
$104$	0	0
$105$	−8.41209	−0.820936
$106$	− 0.328834i	− 0.0319392i
$107$	3.92966	0.379894	0.189947	−	0.981794i	$-0.439168\pi$
$107$	3.92966	0.379894	0.189947	+	0.981794i	$0.439168\pi$
$108$	3.78755	0.364457
$109$	− 11.2533i	− 1.07787i	−0.842346	−	0.538936i	$-0.818826\pi$
$109$	− 11.2533i	− 1.07787i	0.842346	−	0.538936i	$-0.181174\pi$
$110$	− 15.4757i	− 1.47555i
$111$	17.3040i	1.64242i
$112$	0.390549i	0.0369034i
$113$	−5.77418	−0.543189	−0.271595	−	0.962412i	$-0.587551\pi$
$113$	−5.77418	−0.543189	−0.271595	+	0.962412i	$0.587551\pi$
$114$	4.28770	0.401579
$115$	8.63066i	0.804813i
$116$	−7.92849	−0.736142
$117$	0	0
$118$	3.95790	0.364354
$119$	2.69964i	0.247476i
$120$	23.0125	2.10075
$121$	−24.3156	−2.21051
$122$	0.952877i	0.0862694i
$123$	9.93284i	0.895614i
$124$	1.52207i	0.136686i
$125$	0.00370455i	0 0.000331345i
$126$	3.35776	0.299133
$127$	−6.13117	−0.544053	−0.272027	−	0.962290i	$-0.587694\pi$
$127$	−6.13117	−0.544053	−0.272027	+	0.962290i	$0.587694\pi$
$128$	− 8.30013i	− 0.733635i
$129$	−18.5988	−1.63753
$130$	0	0
$131$	10.2217	0.893073	0.446537	−	0.894765i	$-0.352657\pi$
$131$	10.2217	0.893073	0.446537	+	0.894765i	$0.352657\pi$
$132$	− 20.8960i	− 1.81877i
$133$	−1.95705	−0.169698
$134$	5.17126	0.446729
$135$	9.06111i	0.779856i
$136$	− 7.38528i	− 0.633283i
$137$	− 19.9475i	− 1.70423i	−0.523353	−	0.852116i	$-0.675319\pi$
$137$	− 19.9475i	− 1.70423i	0.523353	−	0.852116i	$-0.324681\pi$
$138$	− 5.97987i	− 0.509041i
$139$	−20.3275	−1.72415	−0.862077	−	0.506777i	$-0.830837\pi$
$139$	−20.3275	−1.72415	−0.862077	+	0.506777i	$0.830837\pi$
$140$	−4.17951	−0.353233
$141$	− 1.21328i	− 0.102177i
$142$	3.71193	0.311498
$143$	0	0
$144$	1.59233	0.132694
$145$	− 18.9677i	− 1.57518i
$146$	−6.84025	−0.566103
$147$	−2.66029	−0.219417
$148$	8.59741i	0.706703i
$149$	− 10.7162i	− 0.877901i	−0.898511	−	0.438951i	$-0.855350\pi$
$149$	− 10.7162i	− 0.877901i	0.898511	−	0.438951i	$-0.144650\pi$
$150$	10.9519i	0.894221i
$151$	8.74416i	0.711590i	0.934564	+	0.355795i	$0.115790\pi$
$151$	8.74416i	0.711590i	−0.934564	+	0.355795i	$0.884210\pi$
$152$	5.35380	0.434251
$153$	11.0069	0.889852
$154$	− 4.89414i	− 0.394381i
$155$	−3.64130	−0.292476
$156$	0	0
$157$	6.50734	0.519342	0.259671	−	0.965697i	$-0.416386\pi$
$157$	6.50734	0.519342	0.259671	+	0.965697i	$0.416386\pi$
$158$	6.51770i	0.518520i
$159$	1.06222	0.0842393
$160$	18.3178	1.44815
$161$	2.72941i	0.215108i
$162$	3.79518i	0.298177i
$163$	2.61267i	0.204640i	0.994752	+	0.102320i	$0.0326266\pi$
$163$	2.61267i	0.204640i	−0.994752	+	0.102320i	$0.967373\pi$
$164$	4.93509i	0.385366i
$165$	49.9905	3.89175
$166$	−5.10436	−0.396175
$167$	3.88624i	0.300726i	0.988631	+	0.150363i	$0.0480442\pi$
$167$	3.88624i	0.300726i	−0.988631	+	0.150363i	$0.951956\pi$
$168$	7.27763	0.561482
$169$	0	0
$170$	7.03030	0.539200
$171$	7.97919i	0.610184i
$172$	−9.24072	−0.704599
$173$	−13.9768	−1.06263	−0.531317	−	0.847173i	$-0.678303\pi$
$173$	−13.9768	−1.06263	−0.531317	+	0.847173i	$0.678303\pi$
$174$	13.1420i	0.996293i
$175$	− 4.99883i	− 0.377876i
$176$	− 2.32091i	− 0.174945i
$177$	12.7850i	0.960979i
$178$	−2.93298	−0.219836
$179$	25.2843	1.88984	0.944919	−	0.327305i	$-0.106140\pi$
$179$	25.2843	1.88984	0.944919	+	0.327305i	$0.106140\pi$
$180$	17.0405i	1.27013i
$181$	−0.864474	−0.0642559	−0.0321279	−	0.999484i	$-0.510228\pi$
$181$	−0.864474	−0.0642559	−0.0321279	+	0.999484i	$0.510228\pi$
$182$	0	0
$183$	−3.07803	−0.227535
$184$	− 7.46673i	− 0.550454i
$185$	−20.5680	−1.51219
$186$	2.52293	0.184990
$187$	− 16.0432i	− 1.17319i
$188$	− 0.602814i	− 0.0439647i
$189$	2.86554i	0.208438i
$190$	5.09647i	0.369737i
$191$	14.6676	1.06131	0.530657	−	0.847587i	$-0.321945\pi$
$191$	14.6676	1.06131	0.530657	+	0.847587i	$0.321945\pi$
$192$	−10.6138	−0.765985
$193$	− 16.4959i	− 1.18740i	−0.804686	−	0.593700i	$-0.797667\pi$
$193$	− 16.4959i	− 1.18740i	0.804686	−	0.593700i	$-0.202333\pi$
$194$	−2.82275	−0.202661
$195$	0	0
$196$	−1.32176	−0.0944111
$197$	− 11.0102i	− 0.784443i	−0.919871	−	0.392222i	$-0.871707\pi$
$197$	− 11.0102i	− 0.784443i	0.919871	−	0.392222i	$-0.128293\pi$
$198$	−19.9542	−1.41808
$199$	21.2117	1.50366	0.751829	−	0.659358i	$-0.229172\pi$
$199$	21.2117	1.50366	0.751829	+	0.659358i	$0.229172\pi$
$200$	13.6751i	0.966972i
$201$	16.7045i	1.17824i
$202$	− 10.9776i	− 0.772380i
$203$	− 5.99845i	− 0.421009i
$204$	9.49264	0.664617
$205$	−11.8064	−0.824597
$206$	9.59027i	0.668186i
$207$	11.1282	0.773466
$208$	0	0
$209$	11.6301	0.804474
$210$	6.92783i	0.478065i
$211$	−17.9358	−1.23475	−0.617375	−	0.786669i	$-0.711804\pi$
$211$	−17.9358	−1.23475	−0.617375	+	0.786669i	$0.711804\pi$
$212$	0.527759	0.0362466
$213$	11.9905i	0.821572i
$214$	− 3.23629i	− 0.221228i
$215$	− 22.1070i	− 1.50768i
$216$	− 7.83913i	− 0.533385i
$217$	−1.15155	−0.0781722
$218$	−9.26774	−0.627691
$219$	− 22.0957i	− 1.49309i
$220$	24.8376	1.67455
$221$	0	0
$222$	14.2508	0.956451
$223$	16.0312i	1.07353i	0.843733	+	0.536763i	$0.180353\pi$
$223$	16.0312i	1.07353i	−0.843733	+	0.536763i	$0.819647\pi$
$224$	5.79294	0.387057
$225$	−20.3810	−1.35873
$226$	4.75536i	0.316322i
$227$	− 16.3750i	− 1.08685i	−0.839458	−	0.543424i	$-0.817127\pi$
$227$	− 16.3750i	− 1.08685i	0.839458	−	0.543424i	$-0.182873\pi$
$228$	6.88148i	0.455737i
$229$	− 27.0104i	− 1.78490i	−0.451148	−	0.892449i	$-0.648985\pi$
$229$	− 27.0104i	− 1.78490i	0.451148	−	0.892449i	$-0.351015\pi$
$230$	7.10783	0.468677
$231$	15.8093	1.04018
$232$	16.4097i	1.07735i
$233$	−11.5681	−0.757853	−0.378926	−	0.925427i	$-0.623707\pi$
$233$	−11.5681	−0.757853	−0.378926	+	0.925427i	$0.623707\pi$
$234$	0	0
$235$	1.44214	0.0940747
$236$	6.35217i	0.413491i
$237$	−21.0538	−1.36759
$238$	2.22331	0.144116
$239$	14.6731i	0.949122i	0.880223	+	0.474561i	$0.157393\pi$
$239$	14.6731i	0.949122i	−0.880223	+	0.474561i	$0.842607\pi$
$240$	3.28533i	0.212067i
$241$	14.3467i	0.924151i	0.886841	+	0.462076i	$0.152895\pi$
$241$	14.3467i	0.924151i	−0.886841	+	0.462076i	$0.847105\pi$
$242$	20.0253i	1.28727i
$243$	−20.8560	−1.33791
$244$	−1.52931	−0.0979039
$245$	− 3.16209i	− 0.202019i
$246$	8.18025	0.521554
$247$	0	0
$248$	3.15024	0.200040
$249$	− 16.4883i	− 1.04491i
$250$	0.00305091	0.000192956 0
$251$	−8.61452	−0.543744	−0.271872	−	0.962333i	$-0.587643\pi$
$251$	−8.61452	−0.543744	−0.271872	+	0.962333i	$0.587643\pi$
$252$	5.38900i	0.339475i
$253$	− 16.2201i	− 1.01975i
$254$	5.04936i	0.316825i
$255$	22.7096i	1.42213i
$256$	−14.8151	−0.925941
$257$	−10.3639	−0.646485	−0.323243	−	0.946316i	$-0.604773\pi$
$257$	−10.3639	−0.646485	−0.323243	+	0.946316i	$0.604773\pi$
$258$	15.3171i	0.953603i
$259$	−6.50454	−0.404172
$260$	0	0
$261$	−24.4566	−1.51383
$262$	− 8.41813i	− 0.520074i
$263$	−22.0826	−1.36167	−0.680835	−	0.732436i	$-0.738383\pi$
$263$	−22.0826	−1.36167	−0.680835	+	0.732436i	$0.738383\pi$
$264$	−43.2488	−2.66178
$265$	1.26258i	0.0775596i
$266$	1.61174i	0.0988220i
$267$	− 9.47427i	− 0.579816i
$268$	8.29954i	0.506975i
$269$	12.9399	0.788960	0.394480	−	0.918905i	$-0.370925\pi$
$269$	12.9399	0.788960	0.394480	+	0.918905i	$0.370925\pi$
$270$	7.46233	0.454143
$271$	17.6749i	1.07367i	0.843686	+	0.536837i	$0.180381\pi$
$271$	17.6749i	1.07367i	−0.843686	+	0.536837i	$0.819619\pi$
$272$	1.05434	0.0639289
$273$	0	0
$274$	−16.4279	−0.992446
$275$	29.7065i	1.79137i
$276$	9.59732	0.577691
$277$	18.0150	1.08242	0.541209	−	0.840888i	$-0.317967\pi$
$277$	18.0150	1.08242	0.541209	+	0.840888i	$0.317967\pi$
$278$	16.7408i	1.00405i
$279$	4.69504i	0.281085i
$280$	8.65038i	0.516959i
$281$	− 2.44178i	− 0.145665i	−0.997344	−	0.0728323i	$-0.976796\pi$
$281$	− 2.44178i	− 0.145665i	0.997344	−	0.0728323i	$-0.0232038\pi$
$282$	−0.999205	−0.0595018
$283$	28.7240	1.70746	0.853732	−	0.520713i	$-0.174334\pi$
$283$	28.7240	1.70746	0.853732	+	0.520713i	$0.174334\pi$
$284$	5.95741i	0.353507i
$285$	−16.4629	−0.975176
$286$	0	0
$287$	−3.73374	−0.220396
$288$	− 23.6187i	− 1.39175i
$289$	−9.71193	−0.571290
$290$	−15.6209	−0.917292
$291$	− 9.11818i	− 0.534517i
$292$	− 10.9782i	− 0.642449i
$293$	29.3309i	1.71353i	0.515710	+	0.856763i	$0.327528\pi$
$293$	29.3309i	1.71353i	−0.515710	+	0.856763i	$0.672472\pi$
$294$	2.19090i	0.127776i
$295$	−15.1966	−0.884779
$296$	17.7942	1.03426
$297$	− 17.0291i	− 0.988126i
$298$	−8.82535	−0.511239
$299$	0	0
$300$	−17.5772	−1.01482
$301$	− 6.99125i	− 0.402969i
$302$	7.20131	0.414389
$303$	35.4603	2.03714
$304$	0.764323i	0.0438369i
$305$	− 3.65863i	− 0.209492i
$306$	− 9.06476i	− 0.518198i
$307$	7.06910i	0.403455i	0.979442	+	0.201728i	$0.0646555\pi$
$307$	7.06910i	0.403455i	−0.979442	+	0.201728i	$0.935344\pi$
$308$	7.85479	0.447568
$309$	−30.9790	−1.76233
$310$	2.99882i	0.170321i
$311$	22.2686	1.26274	0.631368	−	0.775483i	$-0.282494\pi$
$311$	22.2686	1.26274	0.631368	+	0.775483i	$0.282494\pi$
$312$	0	0
$313$	−28.0840	−1.58740	−0.793700	−	0.608309i	$-0.791848\pi$
$313$	−28.0840	−1.58740	−0.793700	+	0.608309i	$0.791848\pi$
$314$	− 5.35916i	− 0.302435i
$315$	−12.8923	−0.726401
$316$	−10.4605	−0.588449
$317$	19.5155i	1.09610i	0.836446	+	0.548049i	$0.184629\pi$
$317$	19.5155i	1.09610i	−0.836446	+	0.548049i	$0.815371\pi$
$318$	− 0.874796i	− 0.0490561i
$319$	35.6470i	1.99585i
$320$	− 12.6158i	− 0.705247i
$321$	10.4540	0.583488
$322$	2.24783	0.125266
$323$	5.28333i	0.293972i
$324$	−6.09102	−0.338390
$325$	0	0
$326$	2.15168	0.119171
$327$	− 29.9371i	− 1.65553i
$328$	10.2142	0.563986
$329$	0.456071	0.0251440
$330$	− 41.1700i	− 2.26633i
$331$	15.6308i	0.859145i	0.903032	+	0.429573i	$0.141336\pi$
$331$	15.6308i	0.859145i	−0.903032	+	0.429573i	$0.858664\pi$
$332$	− 8.19217i	− 0.449604i
$333$	26.5200i	1.45329i
$334$	3.20053	0.175125
$335$	−19.8553	−1.08481
$336$	1.03897i	0.0566807i
$337$	21.7501	1.18480	0.592401	−	0.805643i	$-0.298180\pi$
$337$	21.7501	1.18480	0.592401	+	0.805643i	$0.298180\pi$
$338$	0	0
$339$	−15.3610	−0.834295
$340$	11.2832i	0.611917i
$341$	6.84330	0.370586
$342$	6.57131	0.355336
$343$	− 1.00000i	− 0.0539949i
$344$	19.1256i	1.03118i
$345$	22.9601i	1.23613i
$346$	11.5106i	0.618816i
$347$	−15.9590	−0.856726	−0.428363	−	0.903607i	$-0.640909\pi$
$347$	−15.9590	−0.856726	−0.428363	+	0.903607i	$0.640909\pi$
$348$	−21.0921	−1.13065
$349$	− 6.81706i	− 0.364909i	−0.983214	−	0.182455i	$-0.941596\pi$
$349$	− 6.81706i	− 0.364909i	0.983214	−	0.182455i	$-0.0584042\pi$
$350$	−4.11682	−0.220053
$351$	0	0
$352$	−34.4257	−1.83490
$353$	− 14.0033i	− 0.745318i	−0.927968	−	0.372659i	$-0.878446\pi$
$353$	− 14.0033i	− 0.745318i	0.927968	−	0.372659i	$-0.121554\pi$
$354$	10.5292	0.559619
$355$	−14.2522	−0.756427
$356$	− 4.70725i	− 0.249484i
$357$	7.18184i	0.380103i
$358$	− 20.8230i	− 1.10053i
$359$	− 5.41494i	− 0.285789i	−0.989738	−	0.142895i	$-0.954359\pi$
$359$	− 5.41494i	− 0.285789i	0.989738	−	0.142895i	$-0.0456410\pi$
$360$	35.2689	1.85884
$361$	15.1700	0.798419
$362$	0.711943i	0.0374189i
$363$	−64.6867	−3.39517
$364$	0	0
$365$	26.2636	1.37470
$366$	2.53493i	0.132503i
$367$	30.0317	1.56764	0.783822	−	0.620985i	$-0.213267\pi$
$367$	30.0317	1.56764	0.783822	+	0.620985i	$0.213267\pi$
$368$	1.06597	0.0555675
$369$	15.2230i	0.792480i
$370$	16.9389i	0.880610i
$371$	0.399286i	0.0207299i
$372$	4.04914i	0.209938i
$373$	21.4098	1.10856	0.554278	−	0.832332i	$-0.312995\pi$
$373$	21.4098	1.10856	0.554278	+	0.832332i	$0.312995\pi$
$374$	−13.2124	−0.683199
$375$	0.00985519i	0 0.000508920i
$376$	−1.24765	−0.0643427
$377$	0	0
$378$	2.35994	0.121382
$379$	9.47655i	0.486778i	0.969929	+	0.243389i	$0.0782591\pi$
$379$	9.47655i	0.486778i	−0.969929	+	0.243389i	$0.921741\pi$
$380$	−8.17951	−0.419600
$381$	−16.3107	−0.835622
$382$	− 12.0796i	− 0.618048i
$383$	− 5.43061i	− 0.277491i	−0.990328	−	0.138746i	$-0.955693\pi$
$383$	− 5.43061i	− 0.277491i	0.990328	−	0.138746i	$-0.0443070\pi$
$384$	− 22.0808i	− 1.12680i
$385$	18.7914i	0.957696i
$386$	−13.5853	−0.691473
$387$	−28.5044	−1.44896
$388$	− 4.53033i	− 0.229993i
$389$	10.6422	0.539580	0.269790	−	0.962919i	$-0.413046\pi$
$389$	10.6422	0.539580	0.269790	+	0.962919i	$0.413046\pi$
$390$	0	0
$391$	7.36845	0.372638
$392$	2.73565i	0.138171i
$393$	27.1927	1.37169
$394$	−9.06750	−0.456814
$395$	− 25.0251i	− 1.25915i
$396$	− 32.0252i	− 1.60933i
$397$	37.1854i	1.86628i	0.359512	+	0.933140i	$0.382943\pi$
$397$	37.1854i	1.86628i	−0.359512	+	0.933140i	$0.617057\pi$
$398$	− 17.4690i	− 0.875644i
$399$	−5.20632	−0.260642
$400$	−1.95229	−0.0976143
$401$	0.896610i	0.0447746i	0.999749	+	0.0223873i	$0.00712669\pi$
$401$	0.896610i	0.0447746i	−0.999749	+	0.0223873i	$0.992873\pi$
$402$	13.7571	0.686139
$403$	0	0
$404$	17.6183	0.876545
$405$	− 14.5718i	− 0.724079i
$406$	−4.94006	−0.245171
$407$	38.6545	1.91603
$408$	− 19.6470i	− 0.972672i
$409$	24.5773i	1.21527i	0.794217	+	0.607635i	$0.207881\pi$
$409$	24.5773i	1.21527i	−0.794217	+	0.607635i	$0.792119\pi$
$410$	9.72326i	0.480198i
$411$	− 53.0662i	− 2.61756i
$412$	−15.3918	−0.758299
$413$	−4.80586	−0.236481
$414$	− 9.16473i	− 0.450422i
$415$	19.5985	0.962052
$416$	0	0
$417$	−54.0770	−2.64816
$418$	− 9.57807i	− 0.468479i
$419$	−7.64558	−0.373511	−0.186755	−	0.982406i	$-0.559797\pi$
$419$	−7.64558	−0.373511	−0.186755	+	0.982406i	$0.559797\pi$
$420$	−11.1187	−0.542538
$421$	− 25.0780i	− 1.22223i	−0.791544	−	0.611113i	$-0.790722\pi$
$421$	− 25.0780i	− 1.22223i	0.791544	−	0.611113i	$-0.209278\pi$
$422$	14.7711i	0.719046i
$423$	− 1.85947i	− 0.0904106i
$424$	− 1.09231i	− 0.0530471i
$425$	−13.4951	−0.654606
$426$	9.87481	0.478436
$427$	− 1.15703i	− 0.0559925i
$428$	5.19405	0.251064
$429$	0	0
$430$	−18.2063	−0.877987
$431$	− 7.75404i	− 0.373499i	−0.982408	−	0.186750i	$-0.940205\pi$
$431$	− 7.75404i	− 0.373499i	0.982408	−	0.186750i	$-0.0597953\pi$
$432$	1.11913	0.0538444
$433$	−35.9760	−1.72890	−0.864448	−	0.502722i	$-0.832332\pi$
$433$	−35.9760	−1.72890	−0.864448	+	0.502722i	$0.832332\pi$
$434$	0.948365i	0.0455230i
$435$	− 50.4595i	− 2.41935i
$436$	− 14.8741i	− 0.712342i
$437$	5.34160i	0.255523i
$438$	−18.1971	−0.869489
$439$	28.2350	1.34758	0.673792	−	0.738921i	$-0.264664\pi$
$439$	28.2350	1.34758	0.673792	+	0.738921i	$0.264664\pi$
$440$	− 51.4066i	− 2.45071i
$441$	−4.07715	−0.194150
$442$	0	0
$443$	28.7918	1.36794	0.683970	−	0.729511i	$-0.260252\pi$
$443$	28.7918	1.36794	0.683970	+	0.729511i	$0.260252\pi$
$444$	22.8716i	1.08544i
$445$	11.2614	0.533840
$446$	13.2026	0.625159
$447$	− 28.5081i	− 1.34839i
$448$	− 3.98971i	− 0.188496i
$449$	− 29.1902i	− 1.37757i	−0.724965	−	0.688785i	$-0.758144\pi$
$449$	− 29.1902i	− 1.37757i	0.724965	−	0.688785i	$-0.241856\pi$
$450$	16.7849i	0.791247i
$451$	22.1885	1.04482
$452$	−7.63205	−0.358982
$453$	23.2620i	1.09295i
$454$	−13.4858	−0.632918
$455$	0	0
$456$	14.2427	0.666974
$457$	31.6848i	1.48215i	0.671420	+	0.741077i	$0.265684\pi$
$457$	31.6848i	1.48215i	−0.671420	+	0.741077i	$0.734316\pi$
$458$	−22.2446	−1.03942
$459$	7.73594	0.361083
$460$	11.4076i	0.531883i
$461$	− 22.1018i	− 1.02938i	−0.857376	−	0.514691i	$-0.827907\pi$
$461$	− 22.1018i	− 1.02938i	0.857376	−	0.514691i	$-0.172093\pi$
$462$	− 13.0199i	− 0.605738i
$463$	38.8811i	1.80696i	0.428632	+	0.903479i	$0.358996\pi$
$463$	38.8811i	1.80696i	−0.428632	+	0.903479i	$0.641004\pi$
$464$	−2.34269	−0.108757
$465$	−9.68693	−0.449220
$466$	9.52699i	0.441329i
$467$	−13.2823	−0.614632	−0.307316	−	0.951607i	$-0.599431\pi$
$467$	−13.2823	−0.614632	−0.307316	+	0.951607i	$0.599431\pi$
$468$	0	0
$469$	−6.27918	−0.289946
$470$	− 1.18768i	− 0.0547837i
$471$	17.3114	0.797668
$472$	13.1472	0.605147
$473$	41.5469i	1.91033i
$474$	17.3390i	0.796406i
$475$	− 9.78295i	− 0.448872i
$476$	3.56827i	0.163551i
$477$	1.62795	0.0745387
$478$	12.0841	0.552714
$479$	− 6.63512i	− 0.303166i	−0.988445	−	0.151583i	$-0.951563\pi$
$479$	− 6.63512i	− 0.303166i	0.988445	−	0.151583i	$-0.0484371\pi$
$480$	48.7307	2.22424
$481$	0	0
$482$	11.8153	0.538172
$483$	7.26104i	0.330389i
$484$	−32.1393	−1.46088
$485$	10.8381	0.492133
$486$	17.1761i	0.779123i
$487$	33.4701i	1.51668i	0.651861	+	0.758338i	$0.273988\pi$
$487$	33.4701i	1.51668i	−0.651861	+	0.758338i	$0.726012\pi$
$488$	3.16522i	0.143283i
$489$	6.95047i	0.314311i
$490$	−2.60416	−0.117644
$491$	37.3287	1.68462	0.842310	−	0.538993i	$-0.181195\pi$
$491$	37.3287	1.68462	0.842310	+	0.538993i	$0.181195\pi$
$492$	13.1288i	0.591891i
$493$	−16.1937	−0.729327
$494$	0	0
$495$	76.6152	3.44360
$496$	0.449736i	0.0201937i
$497$	−4.50720	−0.202175
$498$	−13.5791	−0.608493
$499$	34.1327i	1.52799i	0.645223	+	0.763994i	$0.276764\pi$
$499$	34.1327i	1.52799i	−0.645223	+	0.763994i	$0.723236\pi$
$500$	0.00489651i	0 0.000218979i
$501$	10.3385i	0.461891i
$502$	7.09454i	0.316645i
$503$	15.3089	0.682592	0.341296	−	0.939956i	$-0.389134\pi$
$503$	15.3089	0.682592	0.341296	+	0.939956i	$0.389134\pi$
$504$	11.1537	0.496824
$505$	42.1491i	1.87561i
$506$	−13.3581	−0.593842
$507$	0	0
$508$	−8.10390	−0.359553
$509$	18.4970i	0.819866i	0.912116	+	0.409933i	$0.134448\pi$
$509$	18.4970i	0.819866i	−0.912116	+	0.409933i	$0.865552\pi$
$510$	18.7027	0.828168
$511$	8.30575	0.367425
$512$	− 4.39924i	− 0.194421i
$513$	5.60801i	0.247599i
$514$	8.53529i	0.376476i
$515$	− 36.8224i	− 1.62259i
$516$	−24.5830	−1.08221
$517$	−2.71029	−0.119198
$518$	5.35685i	0.235367i
$519$	−37.1823	−1.63212
$520$	0	0
$521$	23.5865	1.03334	0.516671	−	0.856184i	$-0.327171\pi$
$521$	23.5865	1.03334	0.516671	+	0.856184i	$0.327171\pi$
$522$	20.1414i	0.881564i
$523$	12.3059	0.538099	0.269049	−	0.963126i	$-0.413291\pi$
$523$	12.3059	0.538099	0.269049	+	0.963126i	$0.413291\pi$
$524$	13.5106	0.590212
$525$	− 13.2983i	− 0.580387i
$526$	18.1862i	0.792958i
$527$	3.10877i	0.135420i
$528$	− 6.17431i	− 0.268702i
$529$	−15.5503	−0.676100
$530$	1.03980	0.0451662
$531$	19.5942i	0.850317i
$532$	−2.58674	−0.112149
$533$	0	0
$534$	−7.80259	−0.337651
$535$	12.4259i	0.537220i
$536$	17.1777	0.741962
$537$	67.2636	2.90264
$538$	− 10.6567i	− 0.459444i
$539$	5.94270i	0.255970i
$540$	11.9766i	0.515390i
$541$	− 19.4411i	− 0.835838i	−0.908484	−	0.417919i	$-0.862760\pi$
$541$	− 19.4411i	− 0.835838i	0.908484	−	0.417919i	$-0.137240\pi$
$542$	14.5563	0.625245
$543$	−2.29975	−0.0986919
$544$	− 15.6389i	− 0.670511i
$545$	35.5841	1.52425
$546$	0	0
$547$	40.2163	1.71953	0.859763	−	0.510693i	$-0.170611\pi$
$547$	40.2163	1.71953	0.859763	+	0.510693i	$0.170611\pi$
$548$	− 26.3658i	− 1.12629i
$549$	−4.71738	−0.201333
$550$	24.4650	1.04319
$551$	− 11.7393i	− 0.500109i
$552$	− 19.8637i	− 0.845454i
$553$	− 7.91410i	− 0.336542i
$554$	− 14.8364i	− 0.630337i
$555$	−54.7168	−2.32260
$556$	−26.8680	−1.13945
$557$	− 7.96399i	− 0.337445i	−0.985664	−	0.168722i	$-0.946036\pi$
$557$	− 7.96399i	− 0.337445i	0.985664	−	0.168722i	$-0.0539642\pi$
$558$	3.86663	0.163687
$559$	0	0
$560$	−1.23495	−0.0521862
$561$	− 42.6795i	− 1.80193i
$562$	−2.01095	−0.0848266
$563$	1.42396	0.0600128	0.0300064	−	0.999550i	$-0.490447\pi$
$563$	1.42396	0.0600128	0.0300064	+	0.999550i	$0.490447\pi$
$564$	− 1.60366i	− 0.0675263i
$565$	− 18.2585i	− 0.768140i
$566$	− 23.6558i	− 0.994327i
$567$	− 4.60828i	− 0.193530i
$568$	12.3301	0.517360
$569$	18.5189	0.776353	0.388177	−	0.921585i	$-0.373105\pi$
$569$	18.5189	0.776353	0.388177	+	0.921585i	$0.373105\pi$
$570$	13.5581i	0.567886i
$571$	−4.35766	−0.182362	−0.0911812	−	0.995834i	$-0.529064\pi$
$571$	−4.35766	−0.182362	−0.0911812	+	0.995834i	$0.529064\pi$
$572$	0	0
$573$	39.0202	1.63009
$574$	3.07494i	0.128346i
$575$	−13.6439	−0.568989
$576$	−16.2667	−0.677778
$577$	− 9.56416i	− 0.398161i	−0.979983	−	0.199081i	$-0.936204\pi$
$577$	− 9.56416i	− 0.398161i	0.979983	−	0.199081i	$-0.0637955\pi$
$578$	7.99832i	0.332686i
$579$	− 43.8839i	− 1.82375i
$580$	− 25.0706i	− 1.04100i
$581$	6.19795	0.257134
$582$	−7.50933	−0.311272
$583$	− 2.37284i	− 0.0982728i
$584$	−22.7216	−0.940228
$585$	0	0
$586$	24.1556	0.997859
$587$	2.36053i	0.0974296i	0.998813	+	0.0487148i	$0.0155125\pi$
$587$	2.36053i	0.0974296i	−0.998813	+	0.0487148i	$0.984487\pi$
$588$	−3.51626	−0.145008
$589$	−2.25364	−0.0928594
$590$	12.5152i	0.515244i
$591$	− 29.2903i	− 1.20484i
$592$	2.54034i	0.104407i
$593$	− 40.4292i	− 1.66023i	−0.557594	−	0.830114i	$-0.688275\pi$
$593$	− 40.4292i	− 1.66023i	0.557594	−	0.830114i	$-0.311725\pi$
$594$	−14.0244	−0.575427
$595$	−8.53652	−0.349963
$596$	− 14.1641i	− 0.580185i
$597$	56.4294	2.30950
$598$	0	0
$599$	−38.5873	−1.57663	−0.788316	−	0.615270i	$-0.789047\pi$
$599$	−38.5873	−1.57663	−0.788316	+	0.615270i	$0.789047\pi$
$600$	36.3796i	1.48519i
$601$	8.16231	0.332948	0.166474	−	0.986046i	$-0.446762\pi$
$601$	8.16231	0.332948	0.166474	+	0.986046i	$0.446762\pi$
$602$	−5.75769	−0.234666
$603$	25.6012i	1.04256i
$604$	11.5576i	0.470274i
$605$	− 76.8883i	− 3.12595i
$606$	− 29.2036i	− 1.18631i
$607$	7.58525	0.307876	0.153938	−	0.988081i	$-0.450804\pi$
$607$	7.58525	0.307876	0.153938	+	0.988081i	$0.450804\pi$
$608$	11.3371	0.459779
$609$	− 15.9576i	− 0.646636i
$610$	−3.01308	−0.121996
$611$	0	0
$612$	14.5484	0.588083
$613$	15.5778i	0.629183i	0.949227	+	0.314592i	$0.101868\pi$
$613$	15.5778i	0.629183i	−0.949227	+	0.314592i	$0.898132\pi$
$614$	5.82180	0.234949
$615$	−31.4086	−1.26652
$616$	− 16.2571i	− 0.655019i
$617$	23.8687i	0.960916i	0.877018	+	0.480458i	$0.159529\pi$
$617$	23.8687i	0.960916i	−0.877018	+	0.480458i	$0.840471\pi$
$618$	25.5129i	1.02628i
$619$	19.4963i	0.783622i	0.920046	+	0.391811i	$0.128151\pi$
$619$	19.4963i	0.783622i	−0.920046	+	0.391811i	$0.871849\pi$
$620$	−4.81291	−0.193291
$621$	7.82126	0.313856
$622$	− 18.3394i	− 0.735344i
$623$	3.56136	0.142683
$624$	0	0
$625$	−25.0059	−1.00023
$626$	23.1287i	0.924410i
$627$	30.9396	1.23561
$628$	8.60111	0.343222
$629$	17.5599i	0.700161i
$630$	10.6176i	0.423014i
$631$	− 25.6619i	− 1.02158i	−0.859704	−	0.510792i	$-0.829352\pi$
$631$	− 25.6619i	− 1.02158i	0.859704	−	0.510792i	$-0.170648\pi$
$632$	21.6502i	0.861199i
$633$	−47.7144	−1.89648
$634$	16.0721	0.638304
$635$	− 19.3873i	− 0.769362i
$636$	1.40399	0.0556719
$637$	0	0
$638$	29.3573	1.16227
$639$	18.3765i	0.726964i
$640$	26.2458	1.03746
$641$	1.10604	0.0436860	0.0218430	−	0.999761i	$-0.493047\pi$
$641$	1.10604	0.0436860	0.0218430	+	0.999761i	$0.493047\pi$
$642$	− 8.60949i	− 0.339789i
$643$	12.6367i	0.498341i	0.968460	+	0.249171i	$0.0801580\pi$
$643$	12.6367i	0.498341i	−0.968460	+	0.249171i	$0.919842\pi$
$644$	3.60762i	0.142160i
$645$	− 58.8110i	− 2.31568i
$646$	4.35112	0.171192
$647$	−25.7148	−1.01095	−0.505477	−	0.862840i	$-0.668683\pi$
$647$	−25.7148	−1.01095	−0.505477	+	0.862840i	$0.668683\pi$
$648$	12.6066i	0.495236i
$649$	28.5598	1.12107
$650$	0	0
$651$	−3.06345	−0.120066
$652$	3.45331i	0.135242i
$653$	25.2607	0.988527	0.494263	−	0.869312i	$-0.335438\pi$
$653$	25.2607	0.988527	0.494263	+	0.869312i	$0.335438\pi$
$654$	−24.6549	−0.964083
$655$	32.3219i	1.26292i
$656$	1.45821i	0.0569335i
$657$	− 33.8638i	− 1.32115i
$658$	− 0.375600i	− 0.0146424i
$659$	22.9764	0.895034	0.447517	−	0.894275i	$-0.352308\pi$
$659$	22.9764	0.895034	0.447517	+	0.894275i	$0.352308\pi$
$660$	66.0752	2.57197
$661$	− 30.4326i	− 1.18369i	−0.806051	−	0.591845i	$-0.798400\pi$
$661$	− 30.4326i	− 1.18369i	0.806051	−	0.591845i	$-0.201600\pi$
$662$	12.8728	0.500316
$663$	0	0
$664$	−16.9554	−0.657998
$665$	− 6.18837i	− 0.239975i
$666$	21.8407	0.846310
$667$	−16.3723	−0.633937
$668$	5.13665i	0.198743i
$669$	42.6475i	1.64885i
$670$	16.3520i	0.631733i
$671$	6.87586i	0.265440i
$672$	15.4109	0.594489
$673$	−10.8387	−0.417800	−0.208900	−	0.977937i	$-0.566988\pi$
$673$	−10.8387	−0.417800	−0.208900	+	0.977937i	$0.566988\pi$
$674$	− 17.9124i	− 0.689960i
$675$	−14.3244	−0.551345
$676$	0	0
$677$	−18.1209	−0.696442	−0.348221	−	0.937412i	$-0.613214\pi$
$677$	−18.1209	−0.696442	−0.348221	+	0.937412i	$0.613214\pi$
$678$	12.6506i	0.485845i
$679$	3.42751	0.131536
$680$	23.3529	0.895545
$681$	− 43.5624i	− 1.66931i
$682$	− 5.63584i	− 0.215808i
$683$	37.8352i	1.44772i	0.689946	+	0.723861i	$0.257634\pi$
$683$	37.8352i	1.44772i	−0.689946	+	0.723861i	$0.742366\pi$
$684$	10.5465i	0.403257i
$685$	63.0759	2.41001
$686$	−0.823556	−0.0314435
$687$	− 71.8556i	− 2.74146i
$688$	−2.73042	−0.104096
$689$	0	0
$690$	18.9089	0.719850
$691$	− 30.0261i	− 1.14225i	−0.820864	−	0.571124i	$-0.806508\pi$
$691$	− 30.0261i	− 1.14225i	0.820864	−	0.571124i	$-0.193492\pi$
$692$	−18.4739	−0.702271
$693$	24.2293	0.920394
$694$	13.1432i	0.498907i
$695$	− 64.2774i	− 2.43818i
$696$	43.6545i	1.65472i
$697$	10.0798i	0.381798i
$698$	−5.61423	−0.212502
$699$	−30.7746	−1.16400
$700$	− 6.60723i	− 0.249730i
$701$	0.116177	0.00438796	0.00219398	−	0.999998i	$-0.499302\pi$
$701$	0.116177	0.00438796	0.00219398	+	0.999998i	$0.499302\pi$
$702$	0	0
$703$	−12.7297	−0.480110
$704$	23.7097i	0.893591i
$705$	3.83651	0.144491
$706$	−11.5325	−0.434030
$707$	13.3295i	0.501307i
$708$	16.8986i	0.635090i
$709$	6.72993i	0.252748i	0.991983	+	0.126374i	$0.0403339\pi$
$709$	6.72993i	0.252748i	−0.991983	+	0.126374i	$0.959666\pi$
$710$	11.7375i	0.440499i
$711$	−32.2670	−1.21011
$712$	−9.74265	−0.365121
$713$	3.14305i	0.117708i
$714$	5.91465	0.221350
$715$	0	0
$716$	33.4197	1.24895
$717$	39.0347i	1.45778i
$718$	−4.45950	−0.166427
$719$	−46.8078	−1.74564	−0.872818	−	0.488046i	$-0.837710\pi$
$719$	−46.8078	−1.74564	−0.872818	+	0.488046i	$0.837710\pi$
$720$	5.03509i	0.187647i
$721$	− 11.6450i	− 0.433681i
$722$	− 12.4933i	− 0.464953i
$723$	38.1664i	1.41942i
$724$	−1.14262	−0.0424653
$725$	29.9852	1.11362
$726$	53.2731i	1.97715i
$727$	13.3362	0.494611	0.247305	−	0.968938i	$-0.420455\pi$
$727$	13.3362	0.494611	0.247305	+	0.968938i	$0.420455\pi$
$728$	0	0
$729$	−41.6582	−1.54290
$730$	− 21.6295i	− 0.800544i
$731$	−18.8739	−0.698076
$732$	−4.06840	−0.150373
$733$	− 29.4612i	− 1.08817i	−0.839029	−	0.544087i	$-0.816876\pi$
$733$	− 29.4612i	− 1.08817i	0.839029	−	0.544087i	$-0.183124\pi$
$734$	− 24.7328i	− 0.912905i
$735$	− 8.41209i	− 0.310285i
$736$	− 15.8113i	− 0.582814i
$737$	37.3153	1.37453
$738$	12.5370	0.461494
$739$	12.0302i	0.442537i	0.975213	+	0.221269i	$0.0710198\pi$
$739$	12.0302i	0.442537i	−0.975213	+	0.221269i	$0.928980\pi$
$740$	−27.1858	−0.999370
$741$	0	0
$742$	0.328834	0.0120719
$743$	21.8826i	0.802796i	0.915904	+	0.401398i	$0.131476\pi$
$743$	21.8826i	0.802796i	−0.915904	+	0.401398i	$0.868524\pi$
$744$	8.38055	0.307246
$745$	33.8855	1.24147
$746$	− 17.6321i	− 0.645558i
$747$	− 25.2700i	− 0.924580i
$748$	− 21.2051i	− 0.775337i
$749$	3.92966i	0.143587i
$750$	0.00811630	0.000296365 0
$751$	−34.7492	−1.26802	−0.634008	−	0.773327i	$-0.718591\pi$
$751$	−34.7492	−1.26802	−0.634008	+	0.773327i	$0.718591\pi$
$752$	− 0.178118i	− 0.00649529i
$753$	−22.9172	−0.835147
$754$	0	0
$755$	−27.6498	−1.00628
$756$	3.78755i	0.137752i
$757$	43.9263	1.59653	0.798265	−	0.602307i	$-0.205752\pi$
$757$	43.9263	1.59653	0.798265	+	0.602307i	$0.205752\pi$
$758$	7.80447	0.283471
$759$	− 43.1502i	− 1.56625i
$760$	16.9292i	0.614087i
$761$	0.141391i	0.00512543i	0.999997	+	0.00256272i	$0.000815739\pi$
$761$	0.141391i	0.00512543i	−0.999997	+	0.00256272i	$0.999184\pi$
$762$	13.4328i	0.486618i
$763$	11.2533	0.407398
$764$	19.3870	0.701399
$765$	34.8047i	1.25837i
$766$	−4.47241	−0.161595
$767$	0	0
$768$	−39.4124	−1.42217
$769$	− 13.6486i	− 0.492180i	−0.969247	−	0.246090i	$-0.920854\pi$
$769$	− 13.6486i	− 0.492180i	0.969247	−	0.246090i	$-0.0791459\pi$
$770$	15.4757	0.557707
$771$	−27.5711	−0.992950
$772$	− 21.8035i	− 0.784726i
$773$	17.5894i	0.632646i	0.948652	+	0.316323i	$0.102448\pi$
$773$	17.5894i	0.632646i	−0.948652	+	0.316323i	$0.897552\pi$
$774$	23.4750i	0.843790i
$775$	− 5.75639i	− 0.206776i
$776$	−9.37647	−0.336596
$777$	−17.3040	−0.620777
$778$	− 8.76443i	− 0.314220i
$779$	−7.30711	−0.261804
$780$	0	0
$781$	26.7849	0.958439
$782$	− 6.06833i	− 0.217003i
$783$	−17.1888	−0.614278
$784$	−0.390549	−0.0139482
$785$	20.5768i	0.734418i
$786$	− 22.3947i	− 0.798792i
$787$	2.96845i	0.105814i	0.998599	+	0.0529069i	$0.0168487\pi$
$787$	2.96845i	0.105814i	−0.998599	+	0.0529069i	$0.983151\pi$
$788$	− 14.5528i	− 0.518421i
$789$	−58.7461	−2.09142
$790$	−20.6096	−0.733256
$791$	− 5.77418i	− 0.205306i
$792$	−66.2829	−2.35526
$793$	0	0
$794$	30.6242	1.08681
$795$	3.35883i	0.119125i
$796$	28.0367	0.993735
$797$	−9.45221	−0.334815	−0.167407	−	0.985888i	$-0.553539\pi$
$797$	−9.45221	−0.334815	−0.167407	+	0.985888i	$0.553539\pi$
$798$	4.28770i	0.151783i
$799$	− 1.23123i	− 0.0435577i
$800$	28.9579i	1.02382i
$801$	− 14.5202i	− 0.513047i
$802$	0.738409	0.0260741
$803$	−49.3586	−1.74183
$804$	22.0792i	0.778674i
$805$	−8.63066	−0.304191
$806$	0	0
$807$	34.4239	1.21178
$808$	− 36.4648i	− 1.28283i
$809$	−1.16255	−0.0408729	−0.0204365	−	0.999791i	$-0.506506\pi$
$809$	−1.16255	−0.0408729	−0.0204365	+	0.999791i	$0.506506\pi$
$810$	−12.0007	−0.421662
$811$	− 19.5561i	− 0.686706i	−0.939206	−	0.343353i	$-0.888437\pi$
$811$	− 19.5561i	− 0.686706i	0.939206	−	0.343353i	$-0.111563\pi$
$812$	− 7.92849i	− 0.278235i
$813$	47.0204i	1.64908i
$814$	− 31.8342i	− 1.11579i
$815$	−8.26151	−0.289388
$816$	2.80486	0.0981897
$817$	− 13.6822i	− 0.478680i
$818$	20.2408	0.707702
$819$	0	0
$820$	−15.6052	−0.544958
$821$	− 12.6189i	− 0.440403i	−0.975454	−	0.220201i	$-0.929329\pi$
$821$	− 12.6189i	− 0.440403i	0.975454	−	0.220201i	$-0.0706714\pi$
$822$	−43.7030	−1.52432
$823$	6.56808	0.228949	0.114474	−	0.993426i	$-0.463482\pi$
$823$	6.56808	0.228949	0.114474	+	0.993426i	$0.463482\pi$
$824$	31.8565i	1.10978i
$825$	79.0280i	2.75140i
$826$	3.95790i	0.137713i
$827$	17.3050i	0.601754i	0.953663	+	0.300877i	$0.0972794\pi$
$827$	17.3050i	0.601754i	−0.953663	+	0.300877i	$0.902721\pi$
$828$	14.7088	0.511167
$829$	3.75674	0.130477	0.0652385	−	0.997870i	$-0.479219\pi$
$829$	3.75674	0.130477	0.0652385	+	0.997870i	$0.479219\pi$
$830$	− 16.1404i	− 0.560243i
$831$	47.9252	1.66251
$832$	0	0
$833$	−2.69964	−0.0935371
$834$	44.5355i	1.54214i
$835$	−12.2886	−0.425266
$836$	15.3722	0.531659
$837$	3.29981i	0.114058i
$838$	6.29656i	0.217511i
$839$	− 46.3427i	− 1.59993i	−0.600047	−	0.799965i	$-0.704852\pi$
$839$	− 46.3427i	− 1.59993i	0.600047	−	0.799965i	$-0.295148\pi$
$840$	23.0125i	0.794008i
$841$	6.98142	0.240739
$842$	−20.6531	−0.711753
$843$	− 6.49586i	− 0.223729i
$844$	−23.7067	−0.816018
$845$	0	0
$846$	−1.53138	−0.0526499
$847$	− 24.3156i	− 0.835495i
$848$	0.155941	0.00535503
$849$	76.4142	2.62253
$850$	11.1139i	0.381205i
$851$	17.7536i	0.608585i
$852$	15.8485i	0.542959i
$853$	15.3103i	0.524215i	0.965039	+	0.262107i	$0.0844174\pi$
$853$	15.3103i	0.524215i	−0.965039	+	0.262107i	$0.915583\pi$
$854$	−0.952877	−0.0326068
$855$	−25.2309	−0.862879
$856$	− 10.7502i	− 0.367433i
$857$	−2.59248	−0.0885574	−0.0442787	−	0.999019i	$-0.514099\pi$
$857$	−2.59248	−0.0885574	−0.0442787	+	0.999019i	$0.514099\pi$
$858$	0	0
$859$	−13.7738	−0.469955	−0.234978	−	0.972001i	$-0.575502\pi$
$859$	−13.7738	−0.469955	−0.234978	+	0.972001i	$0.575502\pi$
$860$	− 29.2200i	− 0.996394i
$861$	−9.93284	−0.338510
$862$	−6.38589	−0.217504
$863$	− 29.7592i	− 1.01302i	−0.862235	−	0.506508i	$-0.830936\pi$
$863$	− 29.7592i	− 1.01302i	0.862235	−	0.506508i	$-0.169064\pi$
$864$	− 16.5999i	− 0.564741i
$865$	− 44.1958i	− 1.50270i
$866$	29.6282i	1.00681i
$867$	−25.8366	−0.877456
$868$	−1.52207	−0.0516623
$869$	47.0311i	1.59542i
$870$	−41.5562	−1.40889
$871$	0	0
$872$	−30.7852	−1.04252
$873$	− 13.9745i	− 0.472965i
$874$	4.39910	0.148802
$875$	−0.00370455	−0.000125237 0
$876$	− 29.2051i	− 0.986750i
$877$	− 1.44332i	− 0.0487374i	−0.999703	−	0.0243687i	$-0.992242\pi$
$877$	− 1.44332i	− 0.0487374i	0.999703	−	0.0243687i	$-0.00775757\pi$
$878$	− 23.2531i	− 0.784755i
$879$	78.0286i	2.63184i
$880$	7.33894	0.247396
$881$	35.8804	1.20884	0.604420	−	0.796666i	$-0.293405\pi$
$881$	35.8804	1.20884	0.604420	+	0.796666i	$0.293405\pi$
$882$	3.35776i	0.113062i
$883$	10.5626	0.355458	0.177729	−	0.984079i	$-0.443125\pi$
$883$	10.5626	0.355458	0.177729	+	0.984079i	$0.443125\pi$
$884$	0	0
$885$	−40.4273	−1.35895
$886$	− 23.7116i	− 0.796608i
$887$	12.2280	0.410577	0.205288	−	0.978702i	$-0.434187\pi$
$887$	12.2280	0.410577	0.205288	+	0.978702i	$0.434187\pi$
$888$	47.3377	1.58855
$889$	− 6.13117i	− 0.205633i
$890$	− 9.27436i	− 0.310877i
$891$	27.3856i	0.917452i
$892$	21.1893i	0.709469i
$893$	0.892553	0.0298681
$894$	−23.4780	−0.785222
$895$	79.9513i	2.67248i
$896$	8.30013	0.277288
$897$	0	0
$898$	−24.0398	−0.802217
$899$	− 6.90751i	− 0.230378i
$900$	−26.9387	−0.897956
$901$	1.07793	0.0359110
$902$	− 18.2735i	− 0.608440i
$903$	− 18.5988i	− 0.618928i
$904$	15.7961i	0.525372i
$905$	− 2.73355i	− 0.0908662i
$906$	19.1576	0.636468
$907$	−4.52555	−0.150269	−0.0751343	−	0.997173i	$-0.523939\pi$
$907$	−4.52555	−0.150269	−0.0751343	+	0.997173i	$0.523939\pi$
$908$	− 21.6438i	− 0.718274i
$909$	54.3464	1.80256
$910$	0	0
$911$	−57.2723	−1.89751	−0.948757	−	0.316006i	$-0.897658\pi$
$911$	−57.2723	−1.89751	−0.948757	+	0.316006i	$0.897658\pi$
$912$	2.03332i	0.0673300i
$913$	−36.8325	−1.21898
$914$	26.0942	0.863120
$915$	− 9.73302i	− 0.321764i
$916$	− 35.7012i	− 1.17960i
$917$	10.2217i	0.337550i
$918$	− 6.37098i	− 0.210274i
$919$	−40.7551	−1.34439	−0.672193	−	0.740376i	$-0.734648\pi$
$919$	−40.7551	−1.34439	−0.672193	+	0.740376i	$0.734648\pi$
$920$	23.6105	0.778415
$921$	18.8059i	0.619675i
$922$	−18.2021	−0.599453
$923$	0	0
$924$	20.8960	0.687429
$925$	− 32.5151i	− 1.06909i
$926$	32.0208	1.05227
$927$	−47.4783	−1.55939
$928$	34.7487i	1.14068i
$929$	52.2791i	1.71522i	0.514298	+	0.857611i	$0.328052\pi$
$929$	52.2791i	1.71522i	−0.514298	+	0.857611i	$0.671948\pi$
$930$	7.97773i	0.261600i
$931$	− 1.95705i	− 0.0641397i
$932$	−15.2902	−0.500848
$933$	59.2410	1.93946
$934$	10.9387i	0.357926i
$935$	50.7300	1.65905
$936$	0	0
$937$	−6.38634	−0.208633	−0.104316	−	0.994544i	$-0.533265\pi$
$937$	−6.38634	−0.208633	−0.104316	+	0.994544i	$0.533265\pi$
$938$	5.17126i	0.168848i
$939$	−74.7116	−2.43812
$940$	1.90615	0.0621719
$941$	25.3711i	0.827073i	0.910488	+	0.413536i	$0.135707\pi$
$941$	25.3711i	0.827073i	−0.910488	+	0.413536i	$0.864293\pi$
$942$	− 14.2569i	− 0.464516i
$943$	10.1909i	0.331862i
$944$	1.87692i	0.0610887i
$945$	−9.06111	−0.294758
$946$	34.2162	1.11246
$947$	− 27.2061i	− 0.884080i	−0.896995	−	0.442040i	$-0.854255\pi$
$947$	− 27.2061i	− 0.884080i	0.896995	−	0.442040i	$-0.145745\pi$
$948$	−27.8280	−0.903811
$949$	0	0
$950$	−8.05681	−0.261397
$951$	51.9169i	1.68352i
$952$	7.38528	0.239358
$953$	−26.5879	−0.861265	−0.430633	−	0.902527i	$-0.641710\pi$
$953$	−26.5879	−0.861265	−0.430633	+	0.902527i	$0.641710\pi$
$954$	− 1.34071i	− 0.0434070i
$955$	46.3805i	1.50084i
$956$	19.3942i	0.627254i
$957$	94.8314i	3.06546i
$958$	−5.46439	−0.176546
$959$	19.9475	0.644139
$960$	− 33.5618i	− 1.08320i
$961$	29.6739	0.957224
$962$	0	0
$963$	16.0218	0.516296
$964$	18.9628i	0.610751i
$965$	52.1615	1.67914
$966$	5.97987	0.192399
$967$	− 35.2467i	− 1.13346i	−0.823904	−	0.566729i	$-0.808209\pi$
$967$	− 35.2467i	− 1.13346i	0.823904	−	0.566729i	$-0.191791\pi$
$968$	66.5191i	2.13801i
$969$	14.0552i	0.451518i
$970$	− 8.92578i	− 0.286590i
$971$	36.9783	1.18669	0.593344	−	0.804949i	$-0.297807\pi$
$971$	36.9783	1.18669	0.593344	+	0.804949i	$0.297807\pi$
$972$	−27.5665	−0.884197
$973$	− 20.3275i	− 0.651669i
$974$	27.5645	0.883224
$975$	0	0
$976$	−0.451876	−0.0144642
$977$	24.7525i	0.791902i	0.918272	+	0.395951i	$0.129585\pi$
$977$	24.7525i	0.791902i	−0.918272	+	0.395951i	$0.870415\pi$
$978$	5.72410	0.183036
$979$	−21.1641	−0.676408
$980$	− 4.17951i	− 0.133510i
$981$	− 45.8815i	− 1.46488i
$982$	− 30.7423i	− 0.981025i
$983$	− 4.55736i	− 0.145357i	−0.997355	−	0.0726786i	$-0.976845\pi$
$983$	− 4.55736i	− 0.145357i	0.997355	−	0.0726786i	$-0.0231547\pi$
$984$	27.1728	0.866237
$985$	34.8152	1.10930
$986$	13.3364i	0.424718i
$987$	1.21328	0.0386192
$988$	0	0
$989$	−19.0820	−0.606773
$990$	− 63.0969i	− 2.00535i
$991$	−27.1963	−0.863919	−0.431960	−	0.901893i	$-0.642178\pi$
$991$	−27.1963	−0.863919	−0.431960	+	0.901893i	$0.642178\pi$
$992$	6.67085	0.211800
$993$	41.5824i	1.31958i
$994$	3.71193i	0.117735i
$995$	67.0734i	2.12637i
$996$	− 21.7936i	− 0.690556i
$997$	−30.2274	−0.957312	−0.478656	−	0.878002i	$-0.658876\pi$
$997$	−30.2274	−0.957312	−0.478656	+	0.878002i	$0.658876\pi$
$998$	28.1102	0.889812
$999$	18.6390i	0.589713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.i.337.5		12
13.3	even	3		91.2.q.a.43.4	yes	12
13.4	even	6		91.2.q.a.36.4	✓	12
13.5	odd	4		1183.2.a.p.1.2		6
13.8	odd	4		1183.2.a.m.1.5		6
13.12	even	2	inner	1183.2.c.i.337.8		12
39.17	odd	6		819.2.ct.a.127.3		12
39.29	odd	6		819.2.ct.a.316.3		12
52.3	odd	6		1456.2.cc.c.225.6		12
52.43	odd	6		1456.2.cc.c.673.6		12
91.3	odd	6		637.2.u.i.30.3		12
91.4	even	6		637.2.k.h.569.4		12
91.16	even	3		637.2.k.h.459.3		12
91.17	odd	6		637.2.k.g.569.4		12
91.30	even	6		637.2.u.h.361.3		12
91.34	even	4		8281.2.a.by.1.5		6
91.55	odd	6		637.2.q.h.589.4		12
91.68	odd	6		637.2.k.g.459.3		12
91.69	odd	6		637.2.q.h.491.4		12
91.81	even	3		637.2.u.h.30.3		12
91.82	odd	6		637.2.u.i.361.3		12
91.83	even	4		8281.2.a.ch.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.4	✓	12	13.4	even	6
91.2.q.a.43.4	yes	12	13.3	even	3
637.2.k.g.459.3		12	91.68	odd	6
637.2.k.g.569.4		12	91.17	odd	6
637.2.k.h.459.3		12	91.16	even	3
637.2.k.h.569.4		12	91.4	even	6
637.2.q.h.491.4		12	91.69	odd	6
637.2.q.h.589.4		12	91.55	odd	6
637.2.u.h.30.3		12	91.81	even	3
637.2.u.h.361.3		12	91.30	even	6
637.2.u.i.30.3		12	91.3	odd	6
637.2.u.i.361.3		12	91.82	odd	6
819.2.ct.a.127.3		12	39.17	odd	6
819.2.ct.a.316.3		12	39.29	odd	6
1183.2.a.m.1.5		6	13.8	odd	4
1183.2.a.p.1.2		6	13.5	odd	4
1183.2.c.i.337.5		12	1.1	even	1	trivial
1183.2.c.i.337.8		12	13.12	even	2	inner
1456.2.cc.c.225.6		12	52.3	odd	6
1456.2.cc.c.673.6		12	52.43	odd	6
8281.2.a.by.1.5		6	91.34	even	4
8281.2.a.ch.1.2		6	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)

\(f(q)\)	\(=\)	\(q-0.823556i q^{2} +2.66029 q^{3} +1.32176 q^{4} +3.16209i q^{5} -2.19090i q^{6} +1.00000i q^{7} -2.73565i q^{8} +4.07715 q^{9} +O(q^{10})\)	\(q-0.823556i q^{2} +2.66029 q^{3} +1.32176 q^{4} +3.16209i q^{5} -2.19090i q^{6} +1.00000i q^{7} -2.73565i q^{8} +4.07715 q^{9} +2.60416 q^{10} -5.94270i q^{11} +3.51626 q^{12} +0.823556 q^{14} +8.41209i q^{15} +0.390549 q^{16} +2.69964 q^{17} -3.35776i q^{18} +1.95705i q^{19} +4.17951i q^{20} +2.66029i q^{21} -4.89414 q^{22} +2.72941 q^{23} -7.27763i q^{24} -4.99883 q^{25} +2.86554 q^{27} +1.32176i q^{28} -5.99845 q^{29} +6.92783 q^{30} +1.15155i q^{31} -5.79294i q^{32} -15.8093i q^{33} -2.22331i q^{34} -3.16209 q^{35} +5.38900 q^{36} +6.50454i q^{37} +1.61174 q^{38} +8.65038 q^{40} +3.73374i q^{41} +2.19090 q^{42} -6.99125 q^{43} -7.85479i q^{44} +12.8923i q^{45} -2.24783i q^{46} -0.456071i q^{47} +1.03897 q^{48} -1.00000 q^{49} +4.11682i q^{50} +7.18184 q^{51} +0.399286 q^{53} -2.35994i q^{54} +18.7914 q^{55} +2.73565 q^{56} +5.20632i q^{57} +4.94006i q^{58} +4.80586i q^{59} +11.1187i q^{60} -1.15703 q^{61} +0.948365 q^{62} +4.07715i q^{63} -3.98971 q^{64} -13.0199 q^{66} +6.27918i q^{67} +3.56827 q^{68} +7.26104 q^{69} +2.60416i q^{70} +4.50720i q^{71} -11.1537i q^{72} -8.30575i q^{73} +5.35685 q^{74} -13.2983 q^{75} +2.58674i q^{76} +5.94270 q^{77} -7.91410 q^{79} +1.23495i q^{80} -4.60828 q^{81} +3.07494 q^{82} -6.19795i q^{83} +3.51626i q^{84} +8.53652i q^{85} +5.75769i q^{86} -15.9576 q^{87} -16.2571 q^{88} -3.56136i q^{89} +10.6176 q^{90} +3.60762 q^{92} +3.06345i q^{93} -0.375600 q^{94} -6.18837 q^{95} -15.4109i q^{96} -3.42751i q^{97} +0.823556i q^{98} -24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 8 q^{9}+O(q^{10}) \) 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

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