LMFDB - Embedded newform 1183.2.c.i.337.12

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			337.12
Root			$-1.12906 + 0.851598i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.i.337.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.70320i q^{2} -0.345949 q^{3} -5.30727 q^{4} +3.25812i q^{5} -0.935168i q^{6} +1.00000i q^{7} -8.94020i q^{8} -2.88032 q^{9} +O(q^{10})$	\(q+2.70320i q^{2} -0.345949 q^{3} -5.30727 q^{4} +3.25812i q^{5} -0.935168i q^{6} +1.00000i q^{7} -8.94020i q^{8} -2.88032 q^{9} -8.80735 q^{10} +1.84603i q^{11} +1.83605 q^{12} -2.70320 q^{14} -1.12715i q^{15} +13.5526 q^{16} -2.15314 q^{17} -7.78607i q^{18} -2.40096i q^{19} -17.2917i q^{20} -0.345949i q^{21} -4.99017 q^{22} -1.81263 q^{23} +3.09285i q^{24} -5.61537 q^{25} +2.03429 q^{27} -5.30727i q^{28} -2.73406 q^{29} +3.04689 q^{30} +1.74236i q^{31} +18.7549i q^{32} -0.638632i q^{33} -5.82036i q^{34} -3.25812 q^{35} +15.2866 q^{36} +5.93565i q^{37} +6.49025 q^{38} +29.1283 q^{40} -4.22131i q^{41} +0.935168 q^{42} +8.68223 q^{43} -9.79737i q^{44} -9.38444i q^{45} -4.89989i q^{46} -5.87774i q^{47} -4.68850 q^{48} -1.00000 q^{49} -15.1794i q^{50} +0.744877 q^{51} -9.30628 q^{53} +5.49909i q^{54} -6.01459 q^{55} +8.94020 q^{56} +0.830609i q^{57} -7.39071i q^{58} +10.7523i q^{59} +5.98206i q^{60} +10.1101 q^{61} -4.70994 q^{62} -2.88032i q^{63} -23.5929 q^{64} +1.72635 q^{66} -0.826916i q^{67} +11.4273 q^{68} +0.627077 q^{69} -8.80735i q^{70} -2.35425i q^{71} +25.7506i q^{72} -3.19482i q^{73} -16.0452 q^{74} +1.94263 q^{75} +12.7425i q^{76} -1.84603 q^{77} +0.801911 q^{79} +44.1559i q^{80} +7.93720 q^{81} +11.4110 q^{82} +9.97031i q^{83} +1.83605i q^{84} -7.01520i q^{85} +23.4698i q^{86} +0.945847 q^{87} +16.5039 q^{88} -15.1135i q^{89} +25.3680 q^{90} +9.62010 q^{92} -0.602768i q^{93} +15.8887 q^{94} +7.82261 q^{95} -6.48823i q^{96} +9.23171i q^{97} -2.70320i q^{98} -5.31715i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.70320i	1.91145i	0.294264	+	0.955724i	$0.404925\pi$
$2$	2.70320i	1.91145i	−0.294264	+	0.955724i	$0.595075\pi$
$3$	−0.345949	−0.199734	−0.0998669	−	0.995001i	$-0.531842\pi$
$3$	−0.345949	−0.199734	−0.0998669	+	0.995001i	$0.531842\pi$
$4$	−5.30727	−2.65363
$5$	3.25812i	1.45708i	0.685005	+	0.728539i	$0.259800\pi$
$5$	3.25812i	1.45708i	−0.685005	+	0.728539i	$0.740200\pi$
$6$	− 0.935168i	− 0.381781i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 8.94020i	− 3.16084i
$9$	−2.88032	−0.960106
$10$	−8.80735	−2.78513
$11$	1.84603i	0.556598i	0.960494	+	0.278299i	$0.0897707\pi$
$11$	1.84603i	0.556598i	−0.960494	+	0.278299i	$0.910229\pi$
$12$	1.83605	0.530021
$13$	0	0
$13$	0	0
$14$	−2.70320	−0.722460
$15$	− 1.12715i	− 0.291028i
$16$	13.5526	3.38814
$17$	−2.15314	−0.522213	−0.261107	−	0.965310i	$-0.584087\pi$
$17$	−2.15314	−0.522213	−0.261107	+	0.965310i	$0.584087\pi$
$18$	− 7.78607i	− 1.83519i
$19$	− 2.40096i	− 0.550817i	−0.961327	−	0.275408i	$-0.911187\pi$
$19$	− 2.40096i	− 0.550817i	0.961327	−	0.275408i	$-0.0888131\pi$
$20$	− 17.2917i	− 3.86655i
$21$	− 0.345949i	− 0.0754923i
$22$	−4.99017	−1.06391
$23$	−1.81263	−0.377959	−0.188979	−	0.981981i	$-0.560518\pi$
$23$	−1.81263	−0.377959	−0.188979	+	0.981981i	$0.560518\pi$
$24$	3.09285i	0.631326i
$25$	−5.61537	−1.12307
$26$	0	0
$27$	2.03429	0.391500
$28$	− 5.30727i	− 1.00298i
$29$	−2.73406	−0.507703	−0.253851	−	0.967243i	$-0.581697\pi$
$29$	−2.73406	−0.507703	−0.253851	+	0.967243i	$0.581697\pi$
$30$	3.04689	0.556284
$31$	1.74236i	0.312937i	0.987683	+	0.156468i	$0.0500110\pi$
$31$	1.74236i	0.312937i	−0.987683	+	0.156468i	$0.949989\pi$
$32$	18.7549i	3.31542i
$33$	− 0.638632i	− 0.111172i
$34$	− 5.82036i	− 0.998183i
$35$	−3.25812	−0.550723
$36$	15.2866	2.54777
$37$	5.93565i	0.975815i	0.872895	+	0.487908i	$0.162240\pi$
$37$	5.93565i	0.975815i	−0.872895	+	0.487908i	$0.837760\pi$
$38$	6.49025	1.05286
$39$	0	0
$40$	29.1283	4.60558
$41$	− 4.22131i	− 0.659259i	−0.944110	−	0.329629i	$-0.893076\pi$
$41$	− 4.22131i	− 0.659259i	0.944110	−	0.329629i	$-0.106924\pi$
$42$	0.935168	0.144300
$43$	8.68223	1.32403	0.662014	−	0.749492i	$-0.269702\pi$
$43$	8.68223	1.32403	0.662014	+	0.749492i	$0.269702\pi$
$44$	− 9.79737i	− 1.47701i
$45$	− 9.38444i	− 1.39895i
$46$	− 4.89989i	− 0.722449i
$47$	− 5.87774i	− 0.857357i	−0.903457	−	0.428678i	$-0.858979\pi$
$47$	− 5.87774i	− 0.857357i	0.903457	−	0.428678i	$-0.141021\pi$
$48$	−4.68850	−0.676727
$49$	−1.00000	−0.142857
$50$	− 15.1794i	− 2.14670i
$51$	0.744877	0.104304
$52$	0	0
$53$	−9.30628	−1.27832	−0.639158	−	0.769076i	$-0.720717\pi$
$53$	−9.30628	−1.27832	−0.639158	+	0.769076i	$0.720717\pi$
$54$	5.49909i	0.748331i
$55$	−6.01459	−0.811007
$56$	8.94020	1.19468
$57$	0.830609i	0.110017i
$58$	− 7.39071i	− 0.970447i
$59$	10.7523i	1.39982i	0.714229	+	0.699912i	$0.246778\pi$
$59$	10.7523i	1.39982i	−0.714229	+	0.699912i	$0.753222\pi$
$60$	5.98206i	0.772281i
$61$	10.1101	1.29446	0.647231	−	0.762294i	$-0.275927\pi$
$61$	10.1101	1.29446	0.647231	+	0.762294i	$0.275927\pi$
$62$	−4.70994	−0.598163
$63$	− 2.88032i	− 0.362886i
$64$	−23.5929	−2.94911
$65$	0	0
$66$	1.72635	0.212499
$67$	− 0.826916i	− 0.101024i	−0.998723	−	0.0505119i	$-0.983915\pi$
$67$	− 0.826916i	− 0.101024i	0.998723	−	0.0505119i	$-0.0160853\pi$
$68$	11.4273	1.38576
$69$	0.627077	0.0754912
$70$	− 8.80735i	− 1.05268i
$71$	− 2.35425i	− 0.279398i	−0.990194	−	0.139699i	$-0.955387\pi$
$71$	− 2.35425i	− 0.279398i	0.990194	−	0.139699i	$-0.0446134\pi$
$72$	25.7506i	3.03474i
$73$	− 3.19482i	− 0.373925i	−0.982367	−	0.186963i	$-0.940136\pi$
$73$	− 3.19482i	− 0.373925i	0.982367	−	0.186963i	$-0.0598644\pi$
$74$	−16.0452	−1.86522
$75$	1.94263	0.224316
$76$	12.7425i	1.46167i
$77$	−1.84603	−0.210374
$78$	0	0
$79$	0.801911	0.0902220	0.0451110	−	0.998982i	$-0.485636\pi$
$79$	0.801911	0.0902220	0.0451110	+	0.998982i	$0.485636\pi$
$80$	44.1559i	4.93678i
$81$	7.93720	0.881911
$82$	11.4110	1.26014
$83$	9.97031i	1.09438i	0.837007	+	0.547192i	$0.184303\pi$
$83$	9.97031i	1.09438i	−0.837007	+	0.547192i	$0.815697\pi$
$84$	1.83605i	0.200329i
$85$	− 7.01520i	− 0.760905i
$86$	23.4698i	2.53081i
$87$	0.945847	0.101405
$88$	16.5039	1.75932
$89$	− 15.1135i	− 1.60202i	−0.598648	−	0.801012i	$-0.704295\pi$
$89$	− 15.1135i	− 1.60202i	0.598648	−	0.801012i	$-0.295705\pi$
$90$	25.3680	2.67402
$91$	0	0
$92$	9.62010	1.00296
$93$	− 0.602768i	− 0.0625041i
$94$	15.8887	1.63879
$95$	7.82261	0.802583
$96$	− 6.48823i	− 0.662202i
$97$	9.23171i	0.937338i	0.883374	+	0.468669i	$0.155266\pi$
$97$	9.23171i	0.937338i	−0.883374	+	0.468669i	$0.844734\pi$
$98$	− 2.70320i	− 0.273064i
$99$	− 5.31715i	− 0.534394i
$100$	29.8023	2.98023
$101$	−14.8234	−1.47498	−0.737491	−	0.675357i	$-0.763989\pi$
$101$	−14.8234	−1.47498	−0.737491	+	0.675357i	$0.763989\pi$
$102$	2.01355i	0.199371i
$103$	4.28286	0.422003	0.211001	−	0.977486i	$-0.432328\pi$
$103$	4.28286	0.422003	0.211001	+	0.977486i	$0.432328\pi$
$104$	0	0
$105$	1.12715	0.109998
$106$	− 25.1567i	− 2.44343i
$107$	−19.1258	−1.84896	−0.924479	−	0.381233i	$-0.875500\pi$
$107$	−19.1258	−1.84896	−0.924479	+	0.381233i	$0.875500\pi$
$108$	−10.7965	−1.03890
$109$	4.27153i	0.409139i	0.978852	+	0.204569i	$0.0655794\pi$
$109$	4.27153i	0.409139i	−0.978852	+	0.204569i	$0.934421\pi$
$110$	− 16.2586i	− 1.55020i
$111$	− 2.05343i	− 0.194903i
$112$	13.5526i	1.28060i
$113$	2.74976	0.258676	0.129338	−	0.991601i	$-0.458715\pi$
$113$	2.74976	0.258676	0.129338	+	0.991601i	$0.458715\pi$
$114$	−2.24530	−0.210291
$115$	− 5.90576i	− 0.550715i
$116$	14.5104	1.34726
$117$	0	0
$118$	−29.0655	−2.67569
$119$	− 2.15314i	− 0.197378i
$120$	−10.0769	−0.919891
$121$	7.59218	0.690198
$122$	27.3295i	2.47430i
$123$	1.46036i	0.131676i
$124$	− 9.24717i	− 0.830420i
$125$	− 2.00495i	− 0.179329i
$126$	7.78607	0.693638
$127$	9.73438	0.863786	0.431893	−	0.901925i	$-0.357846\pi$
$127$	9.73438	0.863786	0.431893	+	0.901925i	$0.357846\pi$
$128$	− 26.2666i	− 2.32166i
$129$	−3.00361	−0.264453
$130$	0	0
$131$	−18.6615	−1.63046	−0.815230	−	0.579138i	$-0.803389\pi$
$131$	−18.6615	−1.63046	−0.815230	+	0.579138i	$0.803389\pi$
$132$	3.38939i	0.295009i
$133$	2.40096	0.208189
$134$	2.23532	0.193102
$135$	6.62797i	0.570445i
$136$	19.2495i	1.65063i
$137$	− 8.42156i	− 0.719502i	−0.933048	−	0.359751i	$-0.882862\pi$
$137$	− 8.42156i	− 0.719502i	0.933048	−	0.359751i	$-0.117138\pi$
$138$	1.69511i	0.144298i
$139$	−17.6362	−1.49588	−0.747941	−	0.663765i	$-0.768957\pi$
$139$	−17.6362	−1.49588	−0.747941	+	0.663765i	$0.768957\pi$
$140$	17.2917	1.46142
$141$	2.03340i	0.171243i
$142$	6.36399	0.534054
$143$	0	0
$144$	−39.0357	−3.25298
$145$	− 8.90791i	− 0.739762i
$146$	8.63623	0.714739
$147$	0.345949	0.0285334
$148$	− 31.5021i	− 2.58946i
$149$	− 4.02104i	− 0.329416i	−0.986342	−	0.164708i	$-0.947332\pi$
$149$	− 4.02104i	− 0.329416i	0.986342	−	0.164708i	$-0.0526683\pi$
$150$	5.25132i	0.428768i
$151$	− 18.9010i	− 1.53814i	−0.639165	−	0.769069i	$-0.720720\pi$
$151$	− 18.9010i	− 1.53814i	0.639165	−	0.769069i	$-0.279280\pi$
$152$	−21.4650	−1.74104
$153$	6.20173	0.501380
$154$	− 4.99017i	− 0.402120i
$155$	−5.67682	−0.455973
$156$	0	0
$157$	−11.5735	−0.923670	−0.461835	−	0.886966i	$-0.652809\pi$
$157$	−11.5735	−0.923670	−0.461835	+	0.886966i	$0.652809\pi$
$158$	2.16772i	0.172455i
$159$	3.21950	0.255323
$160$	−61.1056	−4.83082
$161$	− 1.81263i	− 0.142855i
$162$	21.4558i	1.68573i
$163$	− 4.40542i	− 0.345059i	−0.985004	−	0.172529i	$-0.944806\pi$
$163$	− 4.40542i	− 0.345059i	0.985004	−	0.172529i	$-0.0551940\pi$
$164$	22.4037i	1.74943i
$165$	2.08074	0.161985
$166$	−26.9517	−2.09186
$167$	9.01909i	0.697918i	0.937138	+	0.348959i	$0.113465\pi$
$167$	9.01909i	0.697918i	−0.937138	+	0.348959i	$0.886535\pi$
$168$	−3.09285	−0.238619
$169$	0	0
$170$	18.9635	1.45443
$171$	6.91552i	0.528843i
$172$	−46.0789	−3.51349
$173$	−6.09200	−0.463166	−0.231583	−	0.972815i	$-0.574391\pi$
$173$	−6.09200	−0.463166	−0.231583	+	0.972815i	$0.574391\pi$
$174$	2.55681i	0.193831i
$175$	− 5.61537i	− 0.424482i
$176$	25.0184i	1.88583i
$177$	− 3.71974i	− 0.279592i
$178$	40.8547	3.06219
$179$	−3.87964	−0.289978	−0.144989	−	0.989433i	$-0.546315\pi$
$179$	−3.87964	−0.289978	−0.144989	+	0.989433i	$0.546315\pi$
$180$	49.8057i	3.71230i
$181$	−6.58392	−0.489379	−0.244690	−	0.969601i	$-0.578686\pi$
$181$	−6.58392	−0.489379	−0.244690	+	0.969601i	$0.578686\pi$
$182$	0	0
$183$	−3.49757	−0.258548
$184$	16.2052i	1.19467i
$185$	−19.3391	−1.42184
$186$	1.62940	0.119473
$187$	− 3.97476i	− 0.290663i
$188$	31.1948i	2.27511i
$189$	2.03429i	0.147973i
$190$	21.1460i	1.53410i
$191$	−13.7434	−0.994435	−0.497218	−	0.867626i	$-0.665645\pi$
$191$	−13.7434	−0.994435	−0.497218	+	0.867626i	$0.665645\pi$
$192$	8.16195	0.589038
$193$	− 22.7530i	− 1.63780i	−0.573937	−	0.818899i	$-0.694585\pi$
$193$	− 22.7530i	− 1.63780i	0.573937	−	0.818899i	$-0.305415\pi$
$194$	−24.9551	−1.79167
$195$	0	0
$196$	5.30727	0.379091
$197$	14.5272i	1.03502i	0.855678	+	0.517509i	$0.173141\pi$
$197$	14.5272i	1.03502i	−0.855678	+	0.517509i	$0.826859\pi$
$198$	14.3733	1.02147
$199$	−23.8404	−1.69000	−0.845001	−	0.534765i	$-0.820400\pi$
$199$	−23.8404	−1.69000	−0.845001	+	0.534765i	$0.820400\pi$
$200$	50.2025i	3.54985i
$201$	0.286071i	0.0201779i
$202$	− 40.0705i	− 2.81935i
$203$	− 2.73406i	− 0.191894i
$204$	−3.95326	−0.276784
$205$	13.7536	0.960591
$206$	11.5774i	0.806637i
$207$	5.22095	0.362881
$208$	0	0
$209$	4.43223	0.306584
$210$	3.04689i	0.210256i
$211$	4.31527	0.297076	0.148538	−	0.988907i	$-0.452543\pi$
$211$	4.31527	0.297076	0.148538	+	0.988907i	$0.452543\pi$
$212$	49.3909	3.39218
$213$	0.814450i	0.0558052i
$214$	− 51.7007i	− 3.53419i
$215$	28.2878i	1.92921i
$216$	− 18.1870i	− 1.23747i
$217$	−1.74236	−0.118279
$218$	−11.5468	−0.782047
$219$	1.10525i	0.0746856i
$220$	31.9210	2.15212
$221$	0	0
$222$	5.55083	0.372548
$223$	23.3947i	1.56662i	0.621629	+	0.783312i	$0.286471\pi$
$223$	23.3947i	1.56662i	−0.621629	+	0.783312i	$0.713529\pi$
$224$	−18.7549	−1.25311
$225$	16.1741	1.07827
$226$	7.43315i	0.494446i
$227$	− 26.7229i	− 1.77366i	−0.462097	−	0.886829i	$-0.652903\pi$
$227$	− 26.7229i	− 1.77366i	0.462097	−	0.886829i	$-0.347097\pi$
$228$	− 4.40826i	− 0.291944i
$229$	3.00670i	0.198688i	0.995053	+	0.0993442i	$0.0316745\pi$
$229$	3.00670i	0.198688i	−0.995053	+	0.0993442i	$0.968326\pi$
$230$	15.9644	1.05266
$231$	0.638632	0.0420189
$232$	24.4431i	1.60477i
$233$	11.7148	0.767462	0.383731	−	0.923445i	$-0.374639\pi$
$233$	11.7148	0.767462	0.383731	+	0.923445i	$0.374639\pi$
$234$	0	0
$235$	19.1504	1.24924
$236$	− 57.0651i	− 3.71462i
$237$	−0.277420	−0.0180204
$238$	5.82036	0.377278
$239$	− 1.42797i	− 0.0923677i	−0.998933	−	0.0461838i	$-0.985294\pi$
$239$	− 1.42797i	− 0.0923677i	0.998933	−	0.0461838i	$-0.0147060\pi$
$240$	− 15.2757i	− 0.986043i
$241$	− 2.67969i	− 0.172614i	−0.996269	−	0.0863069i	$-0.972493\pi$
$241$	− 2.67969i	− 0.172614i	0.996269	−	0.0863069i	$-0.0275065\pi$
$242$	20.5232i	1.31928i
$243$	−8.84874	−0.567647
$244$	−53.6569	−3.43503
$245$	− 3.25812i	− 0.208154i
$246$	−3.94764	−0.251692
$247$	0	0
$248$	15.5770	0.989143
$249$	− 3.44922i	− 0.218586i
$250$	5.41978	0.342777
$251$	−10.9339	−0.690143	−0.345072	−	0.938576i	$-0.612145\pi$
$251$	−10.9339	−0.690143	−0.345072	+	0.938576i	$0.612145\pi$
$252$	15.2866i	0.962967i
$253$	− 3.34616i	− 0.210371i
$254$	26.3139i	1.65108i
$255$	2.42690i	0.151978i
$256$	23.8178	1.48861
$257$	−4.15138	−0.258956	−0.129478	−	0.991582i	$-0.541330\pi$
$257$	−4.15138	−0.258956	−0.129478	+	0.991582i	$0.541330\pi$
$258$	− 8.11935i	− 0.505488i
$259$	−5.93565	−0.368823
$260$	0	0
$261$	7.87497	0.487448
$262$	− 50.4456i	− 3.11654i
$263$	4.05360	0.249955	0.124978	−	0.992160i	$-0.460114\pi$
$263$	4.05360	0.249955	0.124978	+	0.992160i	$0.460114\pi$
$264$	−5.70949	−0.351395
$265$	− 30.3210i	− 1.86260i
$266$	6.49025i	0.397943i
$267$	5.22849i	0.319979i
$268$	4.38866i	0.268080i
$269$	4.00022	0.243898	0.121949	−	0.992536i	$-0.461086\pi$
$269$	4.00022	0.243898	0.121949	+	0.992536i	$0.461086\pi$
$270$	−17.9167	−1.09038
$271$	2.78502i	0.169178i	0.996416	+	0.0845888i	$0.0269577\pi$
$271$	2.78502i	0.169178i	−0.996416	+	0.0845888i	$0.973042\pi$
$272$	−29.1806	−1.76933
$273$	0	0
$274$	22.7651	1.37529
$275$	− 10.3661i	− 0.625101i
$276$	−3.32807	−0.200326
$277$	−16.6924	−1.00295	−0.501474	−	0.865173i	$-0.667209\pi$
$277$	−16.6924	−1.00295	−0.501474	+	0.865173i	$0.667209\pi$
$278$	− 47.6741i	− 2.85930i
$279$	− 5.01855i	− 0.300453i
$280$	29.1283i	1.74075i
$281$	− 13.3731i	− 0.797774i	−0.917000	−	0.398887i	$-0.869397\pi$
$281$	− 13.3731i	− 0.797774i	0.917000	−	0.398887i	$-0.130603\pi$
$282$	−5.49668	−0.327322
$283$	18.8862	1.12267	0.561335	−	0.827589i	$-0.310288\pi$
$283$	18.8862	1.12267	0.561335	+	0.827589i	$0.310288\pi$
$284$	12.4946i	0.741419i
$285$	−2.70623	−0.160303
$286$	0	0
$287$	4.22131	0.249176
$288$	− 54.0200i	− 3.18316i
$289$	−12.3640	−0.727293
$290$	24.0798	1.41402
$291$	− 3.19370i	− 0.187218i
$292$	16.9558i	0.992262i
$293$	− 3.41790i	− 0.199676i	−0.995004	−	0.0998380i	$-0.968168\pi$
$293$	− 3.41790i	− 0.199676i	0.995004	−	0.0998380i	$-0.0318325\pi$
$294$	0.935168i	0.0545401i
$295$	−35.0322	−2.03965
$296$	53.0659	3.08439
$297$	3.75536i	0.217908i
$298$	10.8697	0.629663
$299$	0	0
$300$	−10.3101	−0.595252
$301$	8.68223i	0.500435i
$302$	51.0930	2.94007
$303$	5.12814	0.294604
$304$	− 32.5391i	− 1.86625i
$305$	32.9399i	1.88613i
$306$	16.7645i	0.958362i
$307$	16.3679i	0.934165i	0.884214	+	0.467083i	$0.154695\pi$
$307$	16.3679i	0.934165i	−0.884214	+	0.467083i	$0.845305\pi$
$308$	9.79737	0.558257
$309$	−1.48165	−0.0842883
$310$	− 15.3456i	− 0.871569i
$311$	−23.6979	−1.34378	−0.671891	−	0.740650i	$-0.734518\pi$
$311$	−23.6979	−1.34378	−0.671891	+	0.740650i	$0.734518\pi$
$312$	0	0
$313$	−5.18025	−0.292805	−0.146403	−	0.989225i	$-0.546769\pi$
$313$	−5.18025	−0.292805	−0.146403	+	0.989225i	$0.546769\pi$
$314$	− 31.2856i	− 1.76555i
$315$	9.38444	0.528753
$316$	−4.25596	−0.239416
$317$	6.06537i	0.340665i	0.985387	+	0.170332i	$0.0544842\pi$
$317$	6.06537i	0.340665i	−0.985387	+	0.170332i	$0.945516\pi$
$318$	8.70294i	0.488037i
$319$	− 5.04715i	− 0.282586i
$320$	− 76.8686i	− 4.29709i
$321$	6.61655	0.369300
$322$	4.89989	0.273060
$323$	5.16959i	0.287644i
$324$	−42.1248	−2.34027
$325$	0	0
$326$	11.9087	0.659562
$327$	− 1.47773i	− 0.0817188i
$328$	−37.7394	−2.08381
$329$	5.87774	0.324050
$330$	5.62465i	0.309627i
$331$	17.2749i	0.949512i	0.880118	+	0.474756i	$0.157464\pi$
$331$	17.2749i	0.949512i	−0.880118	+	0.474756i	$0.842536\pi$
$332$	− 52.9151i	− 2.90410i
$333$	− 17.0966i	− 0.936886i
$334$	−24.3804	−1.33403
$335$	2.69419	0.147200
$336$	− 4.68850i	− 0.255779i
$337$	−8.35464	−0.455106	−0.227553	−	0.973766i	$-0.573073\pi$
$337$	−8.35464	−0.455106	−0.227553	+	0.973766i	$0.573073\pi$
$338$	0	0
$339$	−0.951279	−0.0516664
$340$	37.2315i	2.01916i
$341$	−3.21644	−0.174180
$342$	−18.6940	−1.01086
$343$	− 1.00000i	− 0.0539949i
$344$	− 77.6208i	− 4.18504i
$345$	2.04309i	0.109997i
$346$	− 16.4679i	− 0.885318i
$347$	28.8220	1.54725	0.773623	−	0.633646i	$-0.218443\pi$
$347$	28.8220	1.54725	0.773623	+	0.633646i	$0.218443\pi$
$348$	−5.01986	−0.269093
$349$	11.7221i	0.627467i	0.949511	+	0.313734i	$0.101580\pi$
$349$	11.7221i	0.627467i	−0.949511	+	0.313734i	$0.898420\pi$
$350$	15.1794	0.811376
$351$	0	0
$352$	−34.6220	−1.84536
$353$	− 17.8362i	− 0.949326i	−0.880168	−	0.474663i	$-0.842570\pi$
$353$	− 17.8362i	− 0.949326i	0.880168	−	0.474663i	$-0.157430\pi$
$354$	10.0552	0.534426
$355$	7.67043	0.407104
$356$	80.2113i	4.25119i
$357$	0.744877i	0.0394231i
$358$	− 10.4874i	− 0.554278i
$359$	5.68162i	0.299864i	0.988696	+	0.149932i	$0.0479055\pi$
$359$	5.68162i	0.299864i	−0.988696	+	0.149932i	$0.952094\pi$
$360$	−83.8987	−4.42185
$361$	13.2354	0.696601
$362$	− 17.7976i	− 0.935423i
$363$	−2.62651	−0.137856
$364$	0	0
$365$	10.4091	0.544838
$366$	− 9.45462i	− 0.494201i
$367$	−19.6316	−1.02476	−0.512381	−	0.858758i	$-0.671236\pi$
$367$	−19.6316	−1.02476	−0.512381	+	0.858758i	$0.671236\pi$
$368$	−24.5658	−1.28058
$369$	12.1587i	0.632958i
$370$	− 52.2773i	− 2.71777i
$371$	− 9.30628i	− 0.483158i
$372$	3.19905i	0.165863i
$373$	32.0645	1.66024	0.830119	−	0.557586i	$-0.188272\pi$
$373$	32.0645	1.66024	0.830119	+	0.557586i	$0.188272\pi$
$374$	10.7445	0.555587
$375$	0.693612i	0.0358180i
$376$	−52.5482	−2.70997
$377$	0	0
$378$	−5.49909	−0.282843
$379$	19.0231i	0.977150i	0.872522	+	0.488575i	$0.162483\pi$
$379$	19.0231i	0.977150i	−0.872522	+	0.488575i	$0.837517\pi$
$380$	−41.5167	−2.12976
$381$	−3.36760	−0.172527
$382$	− 37.1510i	− 1.90081i
$383$	0.699829i	0.0357596i	0.999840	+	0.0178798i	$0.00569162\pi$
$383$	0.699829i	0.0357596i	−0.999840	+	0.0178798i	$0.994308\pi$
$384$	9.08689i	0.463714i
$385$	− 6.01459i	− 0.306532i
$386$	61.5059	3.13057
$387$	−25.0076	−1.27121
$388$	− 48.9951i	− 2.48735i
$389$	20.0547	1.01681	0.508407	−	0.861117i	$-0.330235\pi$
$389$	20.0547	1.01681	0.508407	+	0.861117i	$0.330235\pi$
$390$	0	0
$391$	3.90284	0.197375
$392$	8.94020i	0.451548i
$393$	6.45592	0.325658
$394$	−39.2698	−1.97838
$395$	2.61272i	0.131460i
$396$	28.2195i	1.41809i
$397$	− 22.2803i	− 1.11822i	−0.829095	−	0.559108i	$-0.811144\pi$
$397$	− 22.2803i	− 1.11822i	0.829095	−	0.559108i	$-0.188856\pi$
$398$	− 64.4453i	− 3.23035i
$399$	−0.830609	−0.0415824
$400$	−76.1027	−3.80513
$401$	4.80749i	0.240074i	0.992769	+	0.120037i	$0.0383014\pi$
$401$	4.80749i	0.240074i	−0.992769	+	0.120037i	$0.961699\pi$
$402$	−0.773306	−0.0385690
$403$	0	0
$404$	78.6717	3.91406
$405$	25.8604i	1.28501i
$406$	7.39071	0.366795
$407$	−10.9574	−0.543137
$408$	− 6.65935i	− 0.329687i
$409$	36.8035i	1.81981i	0.414811	+	0.909907i	$0.363848\pi$
$409$	36.8035i	1.81981i	−0.414811	+	0.909907i	$0.636152\pi$
$410$	37.1786i	1.83612i
$411$	2.91343i	0.143709i
$412$	−22.7303	−1.11984
$413$	−10.7523	−0.529084
$414$	14.1132i	0.693628i
$415$	−32.4845	−1.59460
$416$	0	0
$417$	6.10122	0.298778
$418$	11.9812i	0.586019i
$419$	29.2667	1.42977	0.714887	−	0.699240i	$-0.246478\pi$
$419$	29.2667	1.42977	0.714887	+	0.699240i	$0.246478\pi$
$420$	−5.98206	−0.291895
$421$	7.53862i	0.367410i	0.982981	+	0.183705i	$0.0588091\pi$
$421$	7.53862i	0.367410i	−0.982981	+	0.183705i	$0.941191\pi$
$422$	11.6650i	0.567845i
$423$	16.9298i	0.823154i
$424$	83.2000i	4.04055i
$425$	12.0907	0.586484
$426$	−2.20162	−0.106669
$427$	10.1101i	0.489261i
$428$	101.506	4.90646
$429$	0	0
$430$	−76.4674	−3.68759
$431$	31.2261i	1.50411i	0.659101	+	0.752055i	$0.270937\pi$
$431$	31.2261i	1.50411i	−0.659101	+	0.752055i	$0.729063\pi$
$432$	27.5699	1.32646
$433$	−5.88404	−0.282769	−0.141384	−	0.989955i	$-0.545155\pi$
$433$	−5.88404	−0.282769	−0.141384	+	0.989955i	$0.545155\pi$
$434$	− 4.70994i	− 0.226084i
$435$	3.08169i	0.147755i
$436$	− 22.6702i	− 1.08570i
$437$	4.35204i	0.208186i
$438$	−2.98770	−0.142758
$439$	9.95642	0.475194	0.237597	−	0.971364i	$-0.423640\pi$
$439$	9.95642	0.475194	0.237597	+	0.971364i	$0.423640\pi$
$440$	53.7716i	2.56346i
$441$	2.88032	0.137158
$442$	0	0
$443$	−35.8813	−1.70477	−0.852385	−	0.522915i	$-0.824845\pi$
$443$	−35.8813	−1.70477	−0.852385	+	0.522915i	$0.824845\pi$
$444$	10.8981i	0.517202i
$445$	49.2416	2.33427
$446$	−63.2404	−2.99452
$447$	1.39108i	0.0657956i
$448$	− 23.5929i	− 1.11466i
$449$	3.99528i	0.188549i	0.995546	+	0.0942744i	$0.0300531\pi$
$449$	3.99528i	0.188549i	−0.995546	+	0.0942744i	$0.969947\pi$
$450$	43.7217i	2.06106i
$451$	7.79266	0.366942
$452$	−14.5937	−0.686432
$453$	6.53877i	0.307218i
$454$	72.2371	3.39026
$455$	0	0
$456$	7.42580	0.347745
$457$	− 41.2222i	− 1.92829i	−0.265369	−	0.964147i	$-0.585494\pi$
$457$	− 41.2222i	− 1.92829i	0.265369	−	0.964147i	$-0.414506\pi$
$458$	−8.12770	−0.379783
$459$	−4.38011	−0.204446
$460$	31.3435i	1.46140i
$461$	24.7266i	1.15163i	0.817579	+	0.575816i	$0.195316\pi$
$461$	24.7266i	1.15163i	−0.817579	+	0.575816i	$0.804684\pi$
$462$	1.72635i	0.0803169i
$463$	24.4057i	1.13423i	0.823639	+	0.567115i	$0.191940\pi$
$463$	24.4057i	1.13423i	−0.823639	+	0.567115i	$0.808060\pi$
$464$	−37.0536	−1.72017
$465$	1.96389	0.0910733
$466$	31.6674i	1.46696i
$467$	4.44860	0.205857	0.102928	−	0.994689i	$-0.467179\pi$
$467$	4.44860	0.205857	0.102928	+	0.994689i	$0.467179\pi$
$468$	0	0
$469$	0.826916	0.0381834
$470$	51.7673i	2.38785i
$471$	4.00386	0.184488
$472$	96.1273	4.42462
$473$	16.0276i	0.736951i
$474$	− 0.749922i	− 0.0344450i
$475$	13.4823i	0.618608i
$476$	11.4273i	0.523769i
$477$	26.8051	1.22732
$478$	3.86008	0.176556
$479$	31.6766i	1.44734i	0.690145	+	0.723671i	$0.257547\pi$
$479$	31.6766i	1.44734i	−0.690145	+	0.723671i	$0.742453\pi$
$480$	21.1394	0.964879
$481$	0	0
$482$	7.24372	0.329942
$483$	0.627077i	0.0285330i
$484$	−40.2938	−1.83153
$485$	−30.0780	−1.36577
$486$	− 23.9199i	− 1.08503i
$487$	26.9156i	1.21966i	0.792531	+	0.609832i	$0.208763\pi$
$487$	26.9156i	1.21966i	−0.792531	+	0.609832i	$0.791237\pi$
$488$	− 90.3860i	− 4.09158i
$489$	1.52405i	0.0689200i
$490$	8.80735	0.397875
$491$	−9.72716	−0.438980	−0.219490	−	0.975615i	$-0.570439\pi$
$491$	−9.72716	−0.438980	−0.219490	+	0.975615i	$0.570439\pi$
$492$	− 7.75052i	− 0.349421i
$493$	5.88682	0.265129
$494$	0	0
$495$	17.3239	0.778653
$496$	23.6134i	1.06027i
$497$	2.35425	0.105602
$498$	9.32392	0.417815
$499$	− 7.87525i	− 0.352545i	−0.984341	−	0.176272i	$-0.943596\pi$
$499$	− 7.87525i	− 0.352545i	0.984341	−	0.176272i	$-0.0564039\pi$
$500$	10.6408i	0.475872i
$501$	− 3.12015i	− 0.139398i
$502$	− 29.5565i	− 1.31917i
$503$	−9.75206	−0.434823	−0.217411	−	0.976080i	$-0.569761\pi$
$503$	−9.75206	−0.434823	−0.217411	+	0.976080i	$0.569761\pi$
$504$	−25.7506	−1.14702
$505$	− 48.2964i	− 2.14916i
$506$	9.04533	0.402114
$507$	0	0
$508$	−51.6630	−2.29217
$509$	23.0256i	1.02059i	0.859999	+	0.510295i	$0.170464\pi$
$509$	23.0256i	1.02059i	−0.859999	+	0.510295i	$0.829536\pi$
$510$	−6.56039	−0.290499
$511$	3.19482	0.141331
$512$	11.8512i	0.523752i
$513$	− 4.88424i	− 0.215645i
$514$	− 11.2220i	− 0.494981i
$515$	13.9541i	0.614891i
$516$	15.9410	0.701762
$517$	10.8505	0.477203
$518$	− 16.0452i	− 0.704987i
$519$	2.10752	0.0925100
$520$	0	0
$521$	0.486481	0.0213131	0.0106566	−	0.999943i	$-0.496608\pi$
$521$	0.486481	0.0213131	0.0106566	+	0.999943i	$0.496608\pi$
$522$	21.2876i	0.931733i
$523$	−34.6270	−1.51413	−0.757065	−	0.653339i	$-0.773368\pi$
$523$	−34.6270	−1.51413	−0.757065	+	0.653339i	$0.773368\pi$
$524$	99.0414	4.32664
$525$	1.94263i	0.0847834i
$526$	10.9577i	0.477777i
$527$	− 3.75154i	− 0.163420i
$528$	− 8.65510i	− 0.376665i
$529$	−19.7144	−0.857147
$530$	81.9636	3.56027
$531$	− 30.9699i	− 1.34398i
$532$	−12.7425	−0.552458
$533$	0	0
$534$	−14.1336	−0.611622
$535$	− 62.3141i	− 2.69408i
$536$	−7.39279	−0.319320
$537$	1.34216	0.0579185
$538$	10.8134i	0.466198i
$539$	− 1.84603i	− 0.0795140i
$540$	− 35.1764i	− 1.51375i
$541$	− 22.5384i	− 0.969002i	−0.874791	−	0.484501i	$-0.839001\pi$
$541$	− 22.5384i	− 0.969002i	0.874791	−	0.484501i	$-0.160999\pi$
$542$	−7.52844	−0.323374
$543$	2.27770	0.0977456
$544$	− 40.3818i	− 1.73136i
$545$	−13.9172	−0.596146
$546$	0	0
$547$	39.3716	1.68341	0.841704	−	0.539940i	$-0.181553\pi$
$547$	39.3716	1.68341	0.841704	+	0.539940i	$0.181553\pi$
$548$	44.6955i	1.90930i
$549$	−29.1202	−1.24282
$550$	28.0217	1.19485
$551$	6.56436i	0.279651i
$552$	− 5.60619i	− 0.238615i
$553$	0.801911i	0.0341007i
$554$	− 45.1227i	− 1.91708i
$555$	6.69034	0.283989
$556$	93.6000	3.96952
$557$	− 0.726975i	− 0.0308029i	−0.999881	−	0.0154015i	$-0.995097\pi$
$557$	− 0.726975i	− 0.0308029i	0.999881	−	0.0154015i	$-0.00490263\pi$
$558$	13.5661	0.574300
$559$	0	0
$560$	−44.1559	−1.86593
$561$	1.37506i	0.0580552i
$562$	36.1502	1.52490
$563$	−41.6077	−1.75355	−0.876777	−	0.480897i	$-0.840311\pi$
$563$	−41.6077	−1.75355	−0.876777	+	0.480897i	$0.840311\pi$
$564$	− 10.7918i	− 0.454417i
$565$	8.95907i	0.376911i
$566$	51.0532i	2.14593i
$567$	7.93720i	0.333331i
$568$	−21.0474	−0.883130
$569$	25.3888	1.06435	0.532177	−	0.846633i	$-0.321374\pi$
$569$	25.3888	1.06435	0.532177	+	0.846633i	$0.321374\pi$
$570$	− 7.31546i	− 0.306411i
$571$	−16.9992	−0.711393	−0.355697	−	0.934602i	$-0.615756\pi$
$571$	−16.9992	−0.711393	−0.355697	+	0.934602i	$0.615756\pi$
$572$	0	0
$573$	4.75451	0.198622
$574$	11.4110i	0.476288i
$575$	10.1786	0.424476
$576$	67.9551	2.83146
$577$	15.9759i	0.665084i	0.943088	+	0.332542i	$0.107906\pi$
$577$	15.9759i	0.665084i	−0.943088	+	0.332542i	$0.892094\pi$
$578$	− 33.4223i	− 1.39018i
$579$	7.87139i	0.327124i
$580$	47.2767i	1.96306i
$581$	−9.97031	−0.413638
$582$	8.63320	0.357858
$583$	− 17.1796i	− 0.711508i
$584$	−28.5623	−1.18192
$585$	0	0
$586$	9.23926	0.381670
$587$	15.9815i	0.659627i	0.944046	+	0.329814i	$0.106986\pi$
$587$	15.9815i	0.659627i	−0.944046	+	0.329814i	$0.893014\pi$
$588$	−1.83605	−0.0757172
$589$	4.18333	0.172371
$590$	− 94.6989i	− 3.89869i
$591$	− 5.02566i	− 0.206728i
$592$	80.4433i	3.30620i
$593$	29.0532i	1.19307i	0.802586	+	0.596536i	$0.203457\pi$
$593$	29.0532i	1.19307i	−0.802586	+	0.596536i	$0.796543\pi$
$594$	−10.1515	−0.416520
$595$	7.01520	0.287595
$596$	21.3407i	0.874151i
$597$	8.24757	0.337551
$598$	0	0
$599$	3.45554	0.141190	0.0705948	−	0.997505i	$-0.477510\pi$
$599$	3.45554	0.141190	0.0705948	+	0.997505i	$0.477510\pi$
$600$	− 17.3675i	− 0.709026i
$601$	15.5304	0.633497	0.316748	−	0.948510i	$-0.397409\pi$
$601$	15.5304	0.633497	0.316748	+	0.948510i	$0.397409\pi$
$602$	−23.4698	−0.956556
$603$	2.38178i	0.0969936i
$604$	100.313i	4.08166i
$605$	24.7363i	1.00567i
$606$	13.8624i	0.563120i
$607$	15.4784	0.628250	0.314125	−	0.949382i	$-0.398289\pi$
$607$	15.4784	0.628250	0.314125	+	0.949382i	$0.398289\pi$
$608$	45.0296	1.82619
$609$	0.945847i	0.0383276i
$610$	−89.0429	−3.60524
$611$	0	0
$612$	−32.9142	−1.33048
$613$	7.13223i	0.288068i	0.989573	+	0.144034i	$0.0460075\pi$
$613$	7.13223i	0.288068i	−0.989573	+	0.144034i	$0.953993\pi$
$614$	−44.2456	−1.78561
$615$	−4.75803	−0.191862
$616$	16.5039i	0.664959i
$617$	− 4.96685i	− 0.199958i	−0.994990	−	0.0999789i	$-0.968122\pi$
$617$	− 4.96685i	− 0.199958i	0.994990	−	0.0999789i	$-0.0318775\pi$
$618$	− 4.00520i	− 0.161113i
$619$	42.3570i	1.70247i	0.524784	+	0.851235i	$0.324146\pi$
$619$	42.3570i	1.70247i	−0.524784	+	0.851235i	$0.675854\pi$
$620$	30.1284	1.20999
$621$	−3.68741	−0.147971
$622$	− 64.0600i	− 2.56857i
$623$	15.1135	0.605508
$624$	0	0
$625$	−21.5445	−0.861779
$626$	− 14.0032i	− 0.559682i
$627$	−1.53333	−0.0612352
$628$	61.4239	2.45108
$629$	− 12.7803i	− 0.509583i
$630$	25.3680i	1.01068i
$631$	− 6.26775i	− 0.249515i	−0.992187	−	0.124758i	$-0.960185\pi$
$631$	− 6.26775i	− 0.249515i	0.992187	−	0.124758i	$-0.0398153\pi$
$632$	− 7.16924i	− 0.285177i
$633$	−1.49286	−0.0593361
$634$	−16.3959	−0.651163
$635$	31.7158i	1.25860i
$636$	−17.0868	−0.677534
$637$	0	0
$638$	13.6434	0.540149
$639$	6.78098i	0.268251i
$640$	85.5797	3.38283
$641$	31.5637	1.24669	0.623345	−	0.781947i	$-0.285773\pi$
$641$	31.5637	1.24669	0.623345	+	0.781947i	$0.285773\pi$
$642$	17.8858i	0.705897i
$643$	18.2504i	0.719725i	0.933005	+	0.359863i	$0.117176\pi$
$643$	18.2504i	0.719725i	−0.933005	+	0.359863i	$0.882824\pi$
$644$	9.62010i	0.379085i
$645$	− 9.78613i	− 0.385329i
$646$	−13.9744	−0.549816
$647$	−23.0273	−0.905298	−0.452649	−	0.891689i	$-0.649521\pi$
$647$	−23.0273	−0.905298	−0.452649	+	0.891689i	$0.649521\pi$
$648$	− 70.9601i	− 2.78758i
$649$	−19.8490	−0.779140
$650$	0	0
$651$	0.602768	0.0236243
$652$	23.3807i	0.915660i
$653$	28.8124	1.12752	0.563759	−	0.825939i	$-0.309355\pi$
$653$	28.8124	1.12752	0.563759	+	0.825939i	$0.309355\pi$
$654$	3.99460	0.156201
$655$	− 60.8014i	− 2.37571i
$656$	− 57.2096i	− 2.23366i
$657$	9.20210i	0.359008i
$658$	15.8887i	0.619406i
$659$	−31.2228	−1.21627	−0.608134	−	0.793835i	$-0.708082\pi$
$659$	−31.2228	−1.21627	−0.608134	+	0.793835i	$0.708082\pi$
$660$	−11.0431	−0.429850
$661$	26.5582i	1.03299i	0.856289	+	0.516496i	$0.172764\pi$
$661$	26.5582i	1.03299i	−0.856289	+	0.516496i	$0.827236\pi$
$662$	−46.6973	−1.81494
$663$	0	0
$664$	89.1366	3.45917
$665$	7.82261i	0.303348i
$666$	46.2154	1.79081
$667$	4.95584	0.191891
$668$	− 47.8667i	− 1.85202i
$669$	− 8.09337i	− 0.312908i
$670$	7.28293i	0.281364i
$671$	18.6635i	0.720495i
$672$	6.48823	0.250289
$673$	19.7386	0.760867	0.380434	−	0.924808i	$-0.375775\pi$
$673$	19.7386	0.760867	0.380434	+	0.924808i	$0.375775\pi$
$674$	− 22.5842i	− 0.869912i
$675$	−11.4233	−0.439683
$676$	0	0
$677$	−13.1440	−0.505163	−0.252582	−	0.967576i	$-0.581280\pi$
$677$	−13.1440	−0.505163	−0.252582	+	0.967576i	$0.581280\pi$
$678$	− 2.57149i	− 0.0987576i
$679$	−9.23171	−0.354280
$680$	−62.7172	−2.40510
$681$	9.24475i	0.354260i
$682$	− 8.69468i	− 0.332936i
$683$	− 6.76255i	− 0.258762i	−0.991595	−	0.129381i	$-0.958701\pi$
$683$	− 6.76255i	− 0.258762i	0.991595	−	0.129381i	$-0.0412990\pi$
$684$	− 36.7025i	− 1.40336i
$685$	27.4385	1.04837
$686$	2.70320	0.103209
$687$	− 1.04017i	− 0.0396848i
$688$	117.666	4.48599
$689$	0	0
$690$	−5.52288	−0.210253
$691$	− 9.17090i	− 0.348877i	−0.984668	−	0.174439i	$-0.944189\pi$
$691$	− 9.17090i	− 0.348877i	0.984668	−	0.174439i	$-0.0558111\pi$
$692$	32.3319	1.22907
$693$	5.31715	0.201982
$694$	77.9115i	2.95748i
$695$	− 57.4609i	− 2.17962i
$696$	− 8.45605i	− 0.320526i
$697$	9.08908i	0.344273i
$698$	−31.6870	−1.19937
$699$	−4.05272	−0.153288
$700$	29.8023i	1.12642i
$701$	47.4700	1.79292	0.896459	−	0.443127i	$-0.146131\pi$
$701$	47.4700	1.79292	0.896459	+	0.443127i	$0.146131\pi$
$702$	0	0
$703$	14.2512	0.537495
$704$	− 43.5532i	− 1.64147i
$705$	−6.62507	−0.249515
$706$	48.2148	1.81459
$707$	− 14.8234i	− 0.557491i
$708$	19.7416i	0.741936i
$709$	34.9719i	1.31340i	0.754153	+	0.656699i	$0.228048\pi$
$709$	34.9719i	1.31340i	−0.754153	+	0.656699i	$0.771952\pi$
$710$	20.7347i	0.778158i
$711$	−2.30976	−0.0866227
$712$	−135.117	−5.06374
$713$	− 3.15825i	− 0.118277i
$714$	−2.01355	−0.0753552
$715$	0	0
$716$	20.5903	0.769496
$717$	0.494005i	0.0184490i
$718$	−15.3585	−0.573175
$719$	8.36101	0.311813	0.155907	−	0.987772i	$-0.450170\pi$
$719$	8.36101	0.311813	0.155907	+	0.987772i	$0.450170\pi$
$720$	− 127.183i	− 4.73984i
$721$	4.28286i	0.159502i
$722$	35.7779i	1.33152i
$723$	0.927035i	0.0344768i
$724$	34.9427	1.29863
$725$	15.3528	0.570188
$726$	− 7.09997i	− 0.263505i
$727$	−27.4014	−1.01626	−0.508131	−	0.861280i	$-0.669663\pi$
$727$	−27.4014	−1.01626	−0.508131	+	0.861280i	$0.669663\pi$
$728$	0	0
$729$	−20.7504	−0.768532
$730$	28.1379i	1.04143i
$731$	−18.6941	−0.691425
$732$	18.5625	0.686092
$733$	12.1569i	0.449026i	0.974471	+	0.224513i	$0.0720792\pi$
$733$	12.1569i	0.449026i	−0.974471	+	0.224513i	$0.927921\pi$
$734$	− 53.0681i	− 1.95878i
$735$	1.12715i	0.0415754i
$736$	− 33.9956i	− 1.25309i
$737$	1.52651	0.0562297
$738$	−32.8674	−1.20987
$739$	48.4439i	1.78204i	0.453966	+	0.891019i	$0.350009\pi$
$739$	48.4439i	1.78204i	−0.453966	+	0.891019i	$0.649991\pi$
$740$	102.638	3.77304
$741$	0	0
$742$	25.1567	0.923531
$743$	16.9906i	0.623326i	0.950193	+	0.311663i	$0.100886\pi$
$743$	16.9906i	0.623326i	−0.950193	+	0.311663i	$0.899114\pi$
$744$	−5.38886	−0.197565
$745$	13.1010	0.479985
$746$	86.6767i	3.17346i
$747$	− 28.7177i	− 1.05073i
$748$	21.0951i	0.771313i
$749$	− 19.1258i	− 0.698841i
$750$	−1.87497	−0.0684642
$751$	−43.0323	−1.57027	−0.785136	−	0.619323i	$-0.787407\pi$
$751$	−43.0323	−1.57027	−0.785136	+	0.619323i	$0.787407\pi$
$752$	− 79.6585i	− 2.90485i
$753$	3.78258	0.137845
$754$	0	0
$755$	61.5817	2.24119
$756$	− 10.7965i	− 0.392666i
$757$	29.1785	1.06051	0.530255	−	0.847838i	$-0.322096\pi$
$757$	29.1785	1.06051	0.530255	+	0.847838i	$0.322096\pi$
$758$	−51.4231	−1.86777
$759$	1.15760i	0.0420183i
$760$	− 69.9357i	− 2.53683i
$761$	− 29.4251i	− 1.06666i	−0.845907	−	0.533330i	$-0.820941\pi$
$761$	− 29.4251i	− 1.06666i	0.845907	−	0.533330i	$-0.179059\pi$
$762$	− 9.10328i	− 0.329777i
$763$	−4.27153	−0.154640
$764$	72.9398	2.63887
$765$	20.2060i	0.730550i
$766$	−1.89178	−0.0683526
$767$	0	0
$768$	−8.23976	−0.297327
$769$	− 17.1864i	− 0.619759i	−0.950776	−	0.309879i	$-0.899711\pi$
$769$	− 17.1864i	− 0.619759i	0.950776	−	0.309879i	$-0.100289\pi$
$770$	16.2586	0.585920
$771$	1.43617	0.0517223
$772$	120.756i	4.34612i
$773$	21.9601i	0.789851i	0.918713	+	0.394926i	$0.129230\pi$
$773$	21.9601i	0.789851i	−0.918713	+	0.394926i	$0.870770\pi$
$774$	− 67.6004i	− 2.42985i
$775$	− 9.78399i	− 0.351451i
$776$	82.5333	2.96277
$777$	2.05343	0.0736665
$778$	54.2118i	1.94359i
$779$	−10.1352	−0.363131
$780$	0	0
$781$	4.34600	0.155512
$782$	10.5501i	0.377272i
$783$	−5.56188	−0.198765
$784$	−13.5526	−0.484020
$785$	− 37.7081i	− 1.34586i
$786$	17.4516i	0.622478i
$787$	− 2.33567i	− 0.0832578i	−0.999133	−	0.0416289i	$-0.986745\pi$
$787$	− 2.33567i	− 0.0832578i	0.999133	−	0.0416289i	$-0.0132547\pi$
$788$	− 77.0996i	− 2.74656i
$789$	−1.40234	−0.0499246
$790$	−7.06271	−0.251280
$791$	2.74976i	0.0977704i
$792$	−47.5364	−1.68913
$793$	0	0
$794$	60.2280	2.13741
$795$	10.4895i	0.372025i
$796$	126.527	4.48465
$797$	−27.8040	−0.984869	−0.492434	−	0.870350i	$-0.663893\pi$
$797$	−27.8040	−0.984869	−0.492434	+	0.870350i	$0.663893\pi$
$798$	− 2.24530i	− 0.0794827i
$799$	12.6556i	0.447723i
$800$	− 105.315i	− 3.72346i
$801$	43.5316i	1.53811i
$802$	−12.9956	−0.458890
$803$	5.89773	0.208126
$804$	− 1.51825i	− 0.0535447i
$805$	5.90576	0.208151
$806$	0	0
$807$	−1.38387	−0.0487147
$808$	132.524i	4.66218i
$809$	15.0203	0.528087	0.264043	−	0.964511i	$-0.414944\pi$
$809$	15.0203	0.528087	0.264043	+	0.964511i	$0.414944\pi$
$810$	−69.9056	−2.45623
$811$	− 43.6933i	− 1.53428i	−0.641481	−	0.767139i	$-0.721680\pi$
$811$	− 43.6933i	− 1.53428i	0.641481	−	0.767139i	$-0.278320\pi$
$812$	14.5104i	0.509215i
$813$	− 0.963474i	− 0.0337905i
$814$	− 29.6199i	− 1.03818i
$815$	14.3534	0.502778
$816$	10.0950	0.353395
$817$	− 20.8456i	− 0.729297i
$818$	−99.4870	−3.47848
$819$	0	0
$820$	−72.9939	−2.54906
$821$	− 18.0701i	− 0.630651i	−0.948984	−	0.315326i	$-0.897886\pi$
$821$	− 18.0701i	− 0.630651i	0.948984	−	0.315326i	$-0.102114\pi$
$822$	−7.87557	−0.274692
$823$	−4.45550	−0.155309	−0.0776544	−	0.996980i	$-0.524743\pi$
$823$	−4.45550	−0.155309	−0.0776544	+	0.996980i	$0.524743\pi$
$824$	− 38.2896i	− 1.33388i
$825$	3.58615i	0.124854i
$826$	− 29.0655i	− 1.01132i
$827$	− 11.8352i	− 0.411549i	−0.978599	−	0.205774i	$-0.934029\pi$
$827$	− 11.8352i	− 0.411549i	0.978599	−	0.205774i	$-0.0659713\pi$
$828$	−27.7090	−0.962953
$829$	3.53894	0.122913	0.0614563	−	0.998110i	$-0.480426\pi$
$829$	3.53894	0.122913	0.0614563	+	0.998110i	$0.480426\pi$
$830$	− 87.8120i	− 3.04800i
$831$	5.77471	0.200323
$832$	0	0
$833$	2.15314	0.0746019
$834$	16.4928i	0.571099i
$835$	−29.3853	−1.01692
$836$	−23.5230	−0.813561
$837$	3.54447i	0.122515i
$838$	79.1137i	2.73294i
$839$	− 33.4853i	− 1.15604i	−0.816023	−	0.578020i	$-0.803826\pi$
$839$	− 33.4853i	− 1.15604i	0.816023	−	0.578020i	$-0.196174\pi$
$840$	− 10.0769i	− 0.347686i
$841$	−21.5249	−0.742238
$842$	−20.3784	−0.702285
$843$	4.62642i	0.159343i
$844$	−22.9023	−0.788330
$845$	0	0
$846$	−45.7645	−1.57342
$847$	7.59218i	0.260870i
$848$	−126.124	−4.33112
$849$	−6.53368	−0.224235
$850$	32.6835i	1.12103i
$851$	− 10.7591i	− 0.368818i
$852$	− 4.32250i	− 0.148087i
$853$	− 22.0871i	− 0.756248i	−0.925755	−	0.378124i	$-0.876569\pi$
$853$	− 22.0871i	− 0.756248i	0.925755	−	0.378124i	$-0.123431\pi$
$854$	−27.3295	−0.935196
$855$	−22.5316	−0.770565
$856$	170.988i	5.84426i
$857$	6.89363	0.235482	0.117741	−	0.993044i	$-0.462435\pi$
$857$	6.89363	0.235482	0.117741	+	0.993044i	$0.462435\pi$
$858$	0	0
$859$	−37.4834	−1.27892	−0.639459	−	0.768825i	$-0.720842\pi$
$859$	−37.4834	−1.27892	−0.639459	+	0.768825i	$0.720842\pi$
$860$	− 150.131i	− 5.11942i
$861$	−1.46036	−0.0497689
$862$	−84.4103	−2.87503
$863$	17.5248i	0.596552i	0.954480	+	0.298276i	$0.0964115\pi$
$863$	17.5248i	0.596552i	−0.954480	+	0.298276i	$0.903588\pi$
$864$	38.1528i	1.29799i
$865$	− 19.8485i	− 0.674869i
$866$	− 15.9057i	− 0.540498i
$867$	4.27731	0.145265
$868$	9.24717	0.313869
$869$	1.48035i	0.0502174i
$870$	−8.33040	−0.282427
$871$	0	0
$872$	38.1883	1.29322
$873$	− 26.5903i	− 0.899944i
$874$	−11.7644	−0.397937
$875$	2.00495	0.0677798
$876$	− 5.86584i	− 0.198188i
$877$	− 46.7491i	− 1.57860i	−0.614005	−	0.789302i	$-0.710443\pi$
$877$	− 46.7491i	− 1.57860i	0.614005	−	0.789302i	$-0.289557\pi$
$878$	26.9142i	0.908309i
$879$	1.18242i	0.0398821i
$880$	−81.5131	−2.74781
$881$	2.91875	0.0983350	0.0491675	−	0.998791i	$-0.484343\pi$
$881$	2.91875	0.0983350	0.0491675	+	0.998791i	$0.484343\pi$
$882$	7.78607i	0.262171i
$883$	28.5505	0.960801	0.480400	−	0.877049i	$-0.340491\pi$
$883$	28.5505	0.960801	0.480400	+	0.877049i	$0.340491\pi$
$884$	0	0
$885$	12.1194	0.407388
$886$	− 96.9941i	− 3.25858i
$887$	0.422914	0.0142001	0.00710004	−	0.999975i	$-0.497740\pi$
$887$	0.422914	0.0142001	0.00710004	+	0.999975i	$0.497740\pi$
$888$	−18.3581	−0.616058
$889$	9.73438i	0.326480i
$890$	133.110i	4.46184i
$891$	14.6523i	0.490870i
$892$	− 124.162i	− 4.15725i
$893$	−14.1122	−0.472247
$894$	−3.76035	−0.125765
$895$	− 12.6404i	− 0.422521i
$896$	26.2666	0.877504
$897$	0	0
$898$	−10.8000	−0.360401
$899$	− 4.76372i	− 0.158879i
$900$	−85.8401	−2.86134
$901$	20.0377	0.667553
$902$	21.0651i	0.701391i
$903$	− 3.00361i	− 0.0999539i
$904$	− 24.5834i	− 0.817633i
$905$	− 21.4512i	− 0.713063i
$906$	−17.6756	−0.587232
$907$	22.4284	0.744723	0.372361	−	0.928088i	$-0.378548\pi$
$907$	22.4284	0.744723	0.372361	+	0.928088i	$0.378548\pi$
$908$	141.825i	4.70664i
$909$	42.6961	1.41614
$910$	0	0
$911$	−32.5788	−1.07938	−0.539692	−	0.841863i	$-0.681459\pi$
$911$	−32.5788	−1.07938	−0.539692	+	0.841863i	$0.681459\pi$
$912$	11.2569i	0.372752i
$913$	−18.4055	−0.609132
$914$	111.432	3.68583
$915$	− 11.3955i	− 0.376724i
$916$	− 15.9574i	− 0.527247i
$917$	− 18.6615i	− 0.616256i
$918$	− 11.8403i	− 0.390788i
$919$	−9.87913	−0.325883	−0.162941	−	0.986636i	$-0.552098\pi$
$919$	−9.87913	−0.325883	−0.162941	+	0.986636i	$0.552098\pi$
$920$	−52.7987	−1.74072
$921$	− 5.66246i	− 0.186584i
$922$	−66.8408	−2.20129
$923$	0	0
$924$	−3.38939	−0.111503
$925$	− 33.3309i	− 1.09591i
$926$	−65.9734	−2.16802
$927$	−12.3360	−0.405168
$928$	− 51.2769i	− 1.68325i
$929$	29.9136i	0.981434i	0.871319	+	0.490717i	$0.163265\pi$
$929$	29.9136i	0.981434i	−0.871319	+	0.490717i	$0.836735\pi$
$930$	5.30878i	0.174082i
$931$	2.40096i	0.0786881i
$932$	−62.1736	−2.03656
$933$	8.19826	0.268399
$934$	12.0255i	0.393485i
$935$	12.9502	0.423518
$936$	0	0
$937$	−31.8296	−1.03983	−0.519914	−	0.854219i	$-0.674036\pi$
$937$	−31.8296	−1.03983	−0.519914	+	0.854219i	$0.674036\pi$
$938$	2.23532i	0.0729856i
$939$	1.79210	0.0584831
$940$	−101.636	−3.31501
$941$	42.0885i	1.37205i	0.727580	+	0.686023i	$0.240645\pi$
$941$	42.0885i	1.37205i	−0.727580	+	0.686023i	$0.759355\pi$
$942$	10.8232i	0.352640i
$943$	7.65167i	0.249173i
$944$	145.721i	4.74280i
$945$	−6.62797	−0.215608
$946$	−43.3258	−1.40864
$947$	− 60.3377i	− 1.96071i	−0.197234	−	0.980357i	$-0.563196\pi$
$947$	− 60.3377i	− 1.96071i	0.197234	−	0.980357i	$-0.436804\pi$
$948$	1.47234	0.0478195
$949$	0	0
$950$	−36.4452	−1.18244
$951$	− 2.09831i	− 0.0680423i
$952$	−19.2495	−0.623880
$953$	17.3754	0.562844	0.281422	−	0.959584i	$-0.409194\pi$
$953$	17.3754	0.562844	0.281422	+	0.959584i	$0.409194\pi$
$954$	72.4593i	2.34596i
$955$	− 44.7776i	− 1.44897i
$956$	7.57862i	0.245110i
$957$	1.74606i	0.0564421i
$958$	−85.6281	−2.76652
$959$	8.42156	0.271946
$960$	26.5926i	0.858274i
$961$	27.9642	0.902070
$962$	0	0
$963$	55.0883	1.77520
$964$	14.2218i	0.458054i
$965$	74.1322	2.38640
$966$	−1.69511	−0.0545393
$967$	− 18.8630i	− 0.606594i	−0.952896	−	0.303297i	$-0.901913\pi$
$967$	− 18.8630i	− 0.606594i	0.952896	−	0.303297i	$-0.0980874\pi$
$968$	− 67.8756i	− 2.18160i
$969$	− 1.78842i	− 0.0574522i
$970$	− 81.3068i	− 2.61061i
$971$	−1.56446	−0.0502060	−0.0251030	−	0.999685i	$-0.507991\pi$
$971$	−1.56446	−0.0502060	−0.0251030	+	0.999685i	$0.507991\pi$
$972$	46.9626	1.50633
$973$	− 17.6362i	− 0.565390i
$974$	−72.7582	−2.33132
$975$	0	0
$976$	137.017	4.38582
$977$	27.8755i	0.891817i	0.895078	+	0.445909i	$0.147119\pi$
$977$	27.8755i	0.891817i	−0.895078	+	0.445909i	$0.852881\pi$
$978$	−4.11981	−0.131737
$979$	27.8999	0.891684
$980$	17.2917i	0.552364i
$981$	− 12.3034i	− 0.392817i
$982$	− 26.2944i	− 0.839088i
$983$	− 33.4239i	− 1.06606i	−0.846097	−	0.533029i	$-0.821054\pi$
$983$	− 33.4239i	− 1.06606i	0.846097	−	0.533029i	$-0.178946\pi$
$984$	13.0559	0.416207
$985$	−47.3313	−1.50810
$986$	15.9132i	0.506780i
$987$	−2.03340	−0.0647238
$988$	0	0
$989$	−15.7376	−0.500428
$990$	46.8300i	1.48835i
$991$	−18.9110	−0.600726	−0.300363	−	0.953825i	$-0.597108\pi$
$991$	−18.9110	−0.600726	−0.300363	+	0.953825i	$0.597108\pi$
$992$	−32.6777	−1.03752
$993$	− 5.97622i	− 0.189650i
$994$	6.36399i	0.201853i
$995$	− 77.6750i	− 2.46246i
$996$	18.3059i	0.580046i
$997$	43.5775	1.38011	0.690057	−	0.723755i	$-0.257585\pi$
$997$	43.5775	1.38011	0.690057	+	0.723755i	$0.257585\pi$
$998$	21.2884	0.673871
$999$	12.0748i	0.382031i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.i.337.12		12
13.3	even	3		91.2.q.a.43.1	yes	12
13.4	even	6		91.2.q.a.36.1	✓	12
13.5	odd	4		1183.2.a.p.1.6		6
13.8	odd	4		1183.2.a.m.1.1		6
13.12	even	2	inner	1183.2.c.i.337.1		12
39.17	odd	6		819.2.ct.a.127.6		12
39.29	odd	6		819.2.ct.a.316.6		12
52.3	odd	6		1456.2.cc.c.225.4		12
52.43	odd	6		1456.2.cc.c.673.4		12
91.3	odd	6		637.2.u.i.30.6		12
91.4	even	6		637.2.k.h.569.1		12
91.16	even	3		637.2.k.h.459.6		12
91.17	odd	6		637.2.k.g.569.1		12
91.30	even	6		637.2.u.h.361.6		12
91.34	even	4		8281.2.a.by.1.1		6
91.55	odd	6		637.2.q.h.589.1		12
91.68	odd	6		637.2.k.g.459.6		12
91.69	odd	6		637.2.q.h.491.1		12
91.81	even	3		637.2.u.h.30.6		12
91.82	odd	6		637.2.u.i.361.6		12
91.83	even	4		8281.2.a.ch.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.1	✓	12	13.4	even	6
91.2.q.a.43.1	yes	12	13.3	even	3
637.2.k.g.459.6		12	91.68	odd	6
637.2.k.g.569.1		12	91.17	odd	6
637.2.k.h.459.6		12	91.16	even	3
637.2.k.h.569.1		12	91.4	even	6
637.2.q.h.491.1		12	91.69	odd	6
637.2.q.h.589.1		12	91.55	odd	6
637.2.u.h.30.6		12	91.81	even	3
637.2.u.h.361.6		12	91.30	even	6
637.2.u.i.30.6		12	91.3	odd	6
637.2.u.i.361.6		12	91.82	odd	6
819.2.ct.a.127.6		12	39.17	odd	6
819.2.ct.a.316.6		12	39.29	odd	6
1183.2.a.m.1.1		6	13.8	odd	4
1183.2.a.p.1.6		6	13.5	odd	4
1183.2.c.i.337.1		12	13.12	even	2	inner
1183.2.c.i.337.12		12	1.1	even	1	trivial
1456.2.cc.c.225.4		12	52.3	odd	6
1456.2.cc.c.673.4		12	52.43	odd	6
8281.2.a.by.1.1		6	91.34	even	4
8281.2.a.ch.1.6		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)

\(f(q)\)	\(=\)	\(q+2.70320i q^{2} -0.345949 q^{3} -5.30727 q^{4} +3.25812i q^{5} -0.935168i q^{6} +1.00000i q^{7} -8.94020i q^{8} -2.88032 q^{9} +O(q^{10})\)	\(q+2.70320i q^{2} -0.345949 q^{3} -5.30727 q^{4} +3.25812i q^{5} -0.935168i q^{6} +1.00000i q^{7} -8.94020i q^{8} -2.88032 q^{9} -8.80735 q^{10} +1.84603i q^{11} +1.83605 q^{12} -2.70320 q^{14} -1.12715i q^{15} +13.5526 q^{16} -2.15314 q^{17} -7.78607i q^{18} -2.40096i q^{19} -17.2917i q^{20} -0.345949i q^{21} -4.99017 q^{22} -1.81263 q^{23} +3.09285i q^{24} -5.61537 q^{25} +2.03429 q^{27} -5.30727i q^{28} -2.73406 q^{29} +3.04689 q^{30} +1.74236i q^{31} +18.7549i q^{32} -0.638632i q^{33} -5.82036i q^{34} -3.25812 q^{35} +15.2866 q^{36} +5.93565i q^{37} +6.49025 q^{38} +29.1283 q^{40} -4.22131i q^{41} +0.935168 q^{42} +8.68223 q^{43} -9.79737i q^{44} -9.38444i q^{45} -4.89989i q^{46} -5.87774i q^{47} -4.68850 q^{48} -1.00000 q^{49} -15.1794i q^{50} +0.744877 q^{51} -9.30628 q^{53} +5.49909i q^{54} -6.01459 q^{55} +8.94020 q^{56} +0.830609i q^{57} -7.39071i q^{58} +10.7523i q^{59} +5.98206i q^{60} +10.1101 q^{61} -4.70994 q^{62} -2.88032i q^{63} -23.5929 q^{64} +1.72635 q^{66} -0.826916i q^{67} +11.4273 q^{68} +0.627077 q^{69} -8.80735i q^{70} -2.35425i q^{71} +25.7506i q^{72} -3.19482i q^{73} -16.0452 q^{74} +1.94263 q^{75} +12.7425i q^{76} -1.84603 q^{77} +0.801911 q^{79} +44.1559i q^{80} +7.93720 q^{81} +11.4110 q^{82} +9.97031i q^{83} +1.83605i q^{84} -7.01520i q^{85} +23.4698i q^{86} +0.945847 q^{87} +16.5039 q^{88} -15.1135i q^{89} +25.3680 q^{90} +9.62010 q^{92} -0.602768i q^{93} +15.8887 q^{94} +7.82261 q^{95} -6.48823i q^{96} +9.23171i q^{97} -2.70320i q^{98} -5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 8 q^{9}+O(q^{10}) \) 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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