LMFDB - Embedded newform 2366.2.d.r.337.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2366,2,Mod(337,2366)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2366, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2366.337"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,4,-12,0,0,0,0,12,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 $ x^12 - 6x^11 + 39x^10 - 140x^9 + 460x^8 - 1066x^7 + 2127x^6 - 3172x^5 + 3842x^4 - 3394x^3 + 2141x^2 - 832*x + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.12
Root			$0.500000 + 2.47866i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.r.337.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} +3.34469 q^{3} -1.00000 q^{4} +1.56356i q^{5} +3.34469i q^{6} -1.00000i q^{7} -1.00000i q^{8} +8.18694 q^{9} -1.56356 q^{10} +2.86614i q^{11} -3.34469 q^{12} +1.00000 q^{14} +5.22961i q^{15} +1.00000 q^{16} +2.22961 q^{17} +8.18694i q^{18} -7.23602i q^{19} -1.56356i q^{20} -3.34469i q^{21} -2.86614 q^{22} +1.66735 q^{23} -3.34469i q^{24} +2.55529 q^{25} +17.3487 q^{27} +1.00000i q^{28} +4.82757 q^{29} -5.22961 q^{30} -0.597963i q^{31} +1.00000i q^{32} +9.58634i q^{33} +2.22961i q^{34} +1.56356 q^{35} -8.18694 q^{36} -0.0385636i q^{37} +7.23602 q^{38} +1.56356 q^{40} +7.95469i q^{41} +3.34469 q^{42} -10.0914 q^{43} -2.86614i q^{44} +12.8007i q^{45} +1.66735i q^{46} +7.02636i q^{47} +3.34469 q^{48} -1.00000 q^{49} +2.55529i q^{50} +7.45736 q^{51} -5.98404 q^{53} +17.3487i q^{54} -4.48137 q^{55} -1.00000 q^{56} -24.2022i q^{57} +4.82757i q^{58} +0.896206i q^{59} -5.22961i q^{60} -14.2569 q^{61} +0.597963 q^{62} -8.18694i q^{63} -1.00000 q^{64} -9.58634 q^{66} +1.64086i q^{67} -2.22961 q^{68} +5.57677 q^{69} +1.56356i q^{70} -2.29466i q^{71} -8.18694i q^{72} +11.2277i q^{73} +0.0385636 q^{74} +8.54664 q^{75} +7.23602i q^{76} +2.86614 q^{77} +4.26098 q^{79} +1.56356i q^{80} +33.4651 q^{81} -7.95469 q^{82} -4.94829i q^{83} +3.34469i q^{84} +3.48613i q^{85} -10.0914i q^{86} +16.1467 q^{87} +2.86614 q^{88} -2.42120i q^{89} -12.8007 q^{90} -1.66735 q^{92} -2.00000i q^{93} -7.02636 q^{94} +11.3139 q^{95} +3.34469i q^{96} -4.88829i q^{97} -1.00000i q^{98} +23.4649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 - 4 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 40 * q^27 + 20 * q^29 - 28 * q^30 - 4 * q^35 - 12 * q^36 + 8 * q^38 - 4 * q^40 + 4 * q^42 - 52 * q^43 + 4 * q^48 - 12 * q^49 - 36 * q^51 + 36 * q^53 + 12 * q^55 - 12 * q^56 + 56 * q^61 + 4 * q^62 - 12 * q^64 + 8 * q^68 - 64 * q^69 + 96 * q^75 - 4 * q^77 + 44 * q^79 + 68 * q^81 - 12 * q^82 - 4 * q^87 - 4 * q^88 + 12 * q^90 - 12 * q^92 - 16 * q^94 - 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2366\mathbb{Z}\right)^\times$.

$n$	$339$	$2199$
$\chi(n)$	$1$	$-1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	3.34469	1.93106	0.965528	−	0.260298i	$-0.0838210\pi$
$3$	3.34469	1.93106	0.965528	+	0.260298i	$0.0838210\pi$
$4$	−1.00000	−0.500000
$5$	1.56356i	0.699244i	0.936891	+	0.349622i	$0.113690\pi$
$5$	1.56356i	0.699244i	−0.936891	+	0.349622i	$0.886310\pi$
$6$	3.34469i	1.36546i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	8.18694	2.72898
$10$	−1.56356	−0.494440
$11$	2.86614i	0.864173i	0.901832	+	0.432087i	$0.142223\pi$
$11$	2.86614i	0.864173i	−0.901832	+	0.432087i	$0.857777\pi$
$12$	−3.34469	−0.965528
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	5.22961i	1.35028i
$16$	1.00000	0.250000
$17$	2.22961	0.540760	0.270380	−	0.962754i	$-0.412851\pi$
$17$	2.22961	0.540760	0.270380	+	0.962754i	$0.412851\pi$
$18$	8.18694i	1.92968i
$19$	− 7.23602i	− 1.66006i	−0.557722	−	0.830028i	$-0.688324\pi$
$19$	− 7.23602i	− 1.66006i	0.557722	−	0.830028i	$-0.311676\pi$
$20$	− 1.56356i	− 0.349622i
$21$	− 3.34469i	− 0.729871i
$22$	−2.86614	−0.611063
$23$	1.66735	0.347667	0.173833	−	0.984775i	$-0.444385\pi$
$23$	1.66735	0.347667	0.173833	+	0.984775i	$0.444385\pi$
$24$	− 3.34469i	− 0.682732i
$25$	2.55529	0.511058
$26$	0	0
$27$	17.3487	3.33876
$28$	1.00000i	0.188982i
$29$	4.82757	0.896458	0.448229	−	0.893919i	$-0.352055\pi$
$29$	4.82757	0.896458	0.448229	+	0.893919i	$0.352055\pi$
$30$	−5.22961	−0.954792
$31$	− 0.597963i	− 0.107397i	−0.998557	−	0.0536987i	$-0.982899\pi$
$31$	− 0.597963i	− 0.107397i	0.998557	−	0.0536987i	$-0.0171010\pi$
$32$	1.00000i	0.176777i
$33$	9.58634i	1.66877i
$34$	2.22961i	0.382375i
$35$	1.56356	0.264289
$36$	−8.18694	−1.36449
$37$	− 0.0385636i	− 0.00633982i	−0.999995	−	0.00316991i	$-0.998991\pi$
$37$	− 0.0385636i	− 0.00633982i	0.999995	−	0.00316991i	$-0.00100902\pi$
$38$	7.23602	1.17384
$39$	0	0
$40$	1.56356	0.247220
$41$	7.95469i	1.24231i	0.783686	+	0.621157i	$0.213337\pi$
$41$	7.95469i	1.24231i	−0.783686	+	0.621157i	$0.786663\pi$
$42$	3.34469	0.516097
$43$	−10.0914	−1.53893	−0.769463	−	0.638691i	$-0.779476\pi$
$43$	−10.0914	−1.53893	−0.769463	+	0.638691i	$0.779476\pi$
$44$	− 2.86614i	− 0.432087i
$45$	12.8007i	1.90822i
$46$	1.66735i	0.245838i
$47$	7.02636i	1.02490i	0.858717	+	0.512450i	$0.171262\pi$
$47$	7.02636i	1.02490i	−0.858717	+	0.512450i	$0.828738\pi$
$48$	3.34469	0.482764
$49$	−1.00000	−0.142857
$50$	2.55529i	0.361372i
$51$	7.45736	1.04424
$52$	0	0
$53$	−5.98404	−0.821971	−0.410985	−	0.911642i	$-0.634815\pi$
$53$	−5.98404	−0.821971	−0.410985	+	0.911642i	$0.634815\pi$
$54$	17.3487i	2.36086i
$55$	−4.48137	−0.604268
$56$	−1.00000	−0.133631
$57$	− 24.2022i	− 3.20566i
$58$	4.82757i	0.633892i
$59$	0.896206i	0.116676i	0.998297	+	0.0583381i	$0.0185801\pi$
$59$	0.896206i	0.116676i	−0.998297	+	0.0583381i	$0.981420\pi$
$60$	− 5.22961i	− 0.675140i
$61$	−14.2569	−1.82541	−0.912706	−	0.408616i	$-0.866011\pi$
$61$	−14.2569	−1.82541	−0.912706	+	0.408616i	$0.866011\pi$
$62$	0.597963	0.0759414
$63$	− 8.18694i	− 1.03146i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−9.58634	−1.18000
$67$	1.64086i	0.200464i	0.994964	+	0.100232i	$0.0319584\pi$
$67$	1.64086i	0.200464i	−0.994964	+	0.100232i	$0.968042\pi$
$68$	−2.22961	−0.270380
$69$	5.57677	0.671364
$70$	1.56356i	0.186881i
$71$	− 2.29466i	− 0.272326i	−0.990686	−	0.136163i	$-0.956523\pi$
$71$	− 2.29466i	− 0.272326i	0.990686	−	0.136163i	$-0.0434771\pi$
$72$	− 8.18694i	− 0.964840i
$73$	11.2277i	1.31411i	0.753844	+	0.657054i	$0.228198\pi$
$73$	11.2277i	1.31411i	−0.753844	+	0.657054i	$0.771802\pi$
$74$	0.0385636	0.00448293
$75$	8.54664	0.986881
$76$	7.23602i	0.830028i
$77$	2.86614	0.326627
$78$	0	0
$79$	4.26098	0.479397	0.239699	−	0.970847i	$-0.422951\pi$
$79$	4.26098	0.479397	0.239699	+	0.970847i	$0.422951\pi$
$80$	1.56356i	0.174811i
$81$	33.4651	3.71835
$82$	−7.95469	−0.878449
$83$	− 4.94829i	− 0.543145i	−0.962418	−	0.271572i	$-0.912456\pi$
$83$	− 4.94829i	− 0.543145i	0.962418	−	0.271572i	$-0.0875437\pi$
$84$	3.34469i	0.364935i
$85$	3.48613i	0.378123i
$86$	− 10.0914i	− 1.08818i
$87$	16.1467	1.73111
$88$	2.86614	0.305531
$89$	− 2.42120i	− 0.256647i	−0.991732	−	0.128323i	$-0.959040\pi$
$89$	− 2.42120i	− 0.256647i	0.991732	−	0.128323i	$-0.0409595\pi$
$90$	−12.8007	−1.34932
$91$	0	0
$92$	−1.66735	−0.173833
$93$	− 2.00000i	− 0.207390i
$94$	−7.02636	−0.724714
$95$	11.3139	1.16078
$96$	3.34469i	0.341366i
$97$	− 4.88829i	− 0.496330i	−0.968718	−	0.248165i	$-0.920172\pi$
$97$	− 4.88829i	− 0.496330i	0.968718	−	0.248165i	$-0.0798276\pi$
$98$	− 1.00000i	− 0.101015i
$99$	23.4649i	2.35831i
$100$	−2.55529	−0.255529
$101$	−7.36747	−0.733091	−0.366545	−	0.930400i	$-0.619460\pi$
$101$	−7.36747	−0.733091	−0.366545	+	0.930400i	$0.619460\pi$
$102$	7.45736i	0.738388i
$103$	−5.78525	−0.570038	−0.285019	−	0.958522i	$-0.592000\pi$
$103$	−5.78525	−0.570038	−0.285019	+	0.958522i	$0.592000\pi$
$104$	0	0
$105$	5.22961	0.510358
$106$	− 5.98404i	− 0.581221i
$107$	−1.02896	−0.0994729	−0.0497365	−	0.998762i	$-0.515838\pi$
$107$	−1.02896	−0.0994729	−0.0497365	+	0.998762i	$0.515838\pi$
$108$	−17.3487	−1.66938
$109$	− 14.1535i	− 1.35566i	−0.735220	−	0.677829i	$-0.762921\pi$
$109$	− 14.1535i	− 1.35566i	0.735220	−	0.677829i	$-0.237079\pi$
$110$	− 4.48137i	− 0.427282i
$111$	− 0.128983i	− 0.0122426i
$112$	− 1.00000i	− 0.0944911i
$113$	−13.5410	−1.27383	−0.636916	−	0.770933i	$-0.719790\pi$
$113$	−13.5410	−1.27383	−0.636916	+	0.770933i	$0.719790\pi$
$114$	24.2022	2.26675
$115$	2.60700i	0.243104i
$116$	−4.82757	−0.448229
$117$	0	0
$118$	−0.896206	−0.0825025
$119$	− 2.22961i	− 0.204388i
$120$	5.22961	0.477396
$121$	2.78525	0.253205
$122$	− 14.2569i	− 1.29076i
$123$	26.6060i	2.39898i
$124$	0.597963i	0.0536987i
$125$	11.8131i	1.05660i
$126$	8.18694	0.729350
$127$	−9.85165	−0.874193	−0.437096	−	0.899415i	$-0.643993\pi$
$127$	−9.85165	−0.874193	−0.437096	+	0.899415i	$0.643993\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−33.7526	−2.97175
$130$	0	0
$131$	14.7923	1.29241	0.646204	−	0.763165i	$-0.276355\pi$
$131$	14.7923	1.29241	0.646204	+	0.763165i	$0.276355\pi$
$132$	− 9.58634i	− 0.834384i
$133$	−7.23602	−0.627442
$134$	−1.64086	−0.141749
$135$	27.1257i	2.33461i
$136$	− 2.22961i	− 0.191188i
$137$	0.458997i	0.0392148i	0.999808	+	0.0196074i	$0.00624163\pi$
$137$	0.458997i	0.0392148i	−0.999808	+	0.0196074i	$0.993758\pi$
$138$	5.57677i	0.474726i
$139$	15.3146	1.29897	0.649485	−	0.760375i	$-0.274985\pi$
$139$	15.3146	1.29897	0.649485	+	0.760375i	$0.274985\pi$
$140$	−1.56356	−0.132145
$141$	23.5010i	1.97914i
$142$	2.29466	0.192564
$143$	0	0
$144$	8.18694	0.682245
$145$	7.54819i	0.626843i
$146$	−11.2277	−0.929215
$147$	−3.34469	−0.275865
$148$	0.0385636i	0.00316991i
$149$	10.2372i	0.838660i	0.907834	+	0.419330i	$0.137735\pi$
$149$	10.2372i	0.838660i	−0.907834	+	0.419330i	$0.862265\pi$
$150$	8.54664i	0.697830i
$151$	− 15.2110i	− 1.23785i	−0.785448	−	0.618927i	$-0.787568\pi$
$151$	− 15.2110i	− 1.23785i	0.785448	−	0.618927i	$-0.212432\pi$
$152$	−7.23602	−0.586918
$153$	18.2537	1.47572
$154$	2.86614i	0.230960i
$155$	0.934950	0.0750970
$156$	0	0
$157$	−2.27419	−0.181500	−0.0907500	−	0.995874i	$-0.528926\pi$
$157$	−2.27419	−0.181500	−0.0907500	+	0.995874i	$0.528926\pi$
$158$	4.26098i	0.338985i
$159$	−20.0147	−1.58727
$160$	−1.56356	−0.123610
$161$	− 1.66735i	− 0.131406i
$162$	33.4651i	2.62927i
$163$	0.00979262i	0 0.000767017i	1.00000		0.000383509i	$0.000122075\pi$
$163$	0.00979262i	0 0.000767017i	−1.00000		0.000383509i	$0.999878\pi$
$164$	− 7.95469i	− 0.621157i
$165$	−14.9888	−1.16688
$166$	4.94829	0.384061
$167$	− 24.9508i	− 1.93075i	−0.260864	−	0.965376i	$-0.584007\pi$
$167$	− 24.9508i	− 1.93075i	0.260864	−	0.965376i	$-0.415993\pi$
$168$	−3.34469	−0.258048
$169$	0	0
$170$	−3.48613	−0.267374
$171$	− 59.2408i	− 4.53026i
$172$	10.0914	0.769463
$173$	3.20550	0.243709	0.121855	−	0.992548i	$-0.461116\pi$
$173$	3.20550	0.243709	0.121855	+	0.992548i	$0.461116\pi$
$174$	16.1467i	1.22408i
$175$	− 2.55529i	− 0.193162i
$176$	2.86614i	0.216043i
$177$	2.99753i	0.225308i
$178$	2.42120	0.181477
$179$	15.8000	1.18094	0.590472	−	0.807058i	$-0.298942\pi$
$179$	15.8000	1.18094	0.590472	+	0.807058i	$0.298942\pi$
$180$	− 12.8007i	− 0.954111i
$181$	9.11907	0.677815	0.338908	−	0.940820i	$-0.389943\pi$
$181$	9.11907	0.677815	0.338908	+	0.940820i	$0.389943\pi$
$182$	0	0
$183$	−47.6850	−3.52497
$184$	− 1.66735i	− 0.122919i
$185$	0.0602965	0.00443308
$186$	2.00000	0.146647
$187$	6.39038i	0.467311i
$188$	− 7.02636i	− 0.512450i
$189$	− 17.3487i	− 1.26193i
$190$	11.3139i	0.820799i
$191$	−3.26137	−0.235984	−0.117992	−	0.993015i	$-0.537646\pi$
$191$	−3.26137	−0.235984	−0.117992	+	0.993015i	$0.537646\pi$
$192$	−3.34469	−0.241382
$193$	− 22.0730i	− 1.58885i	−0.607361	−	0.794426i	$-0.707772\pi$
$193$	− 22.0730i	− 1.58885i	0.607361	−	0.794426i	$-0.292228\pi$
$194$	4.88829	0.350959
$195$	0	0
$196$	1.00000	0.0714286
$197$	5.27305i	0.375690i	0.982199	+	0.187845i	$0.0601502\pi$
$197$	5.27305i	0.375690i	−0.982199	+	0.187845i	$0.939850\pi$
$198$	−23.4649	−1.66758
$199$	−8.86762	−0.628609	−0.314304	−	0.949322i	$-0.601771\pi$
$199$	−8.86762	−0.628609	−0.314304	+	0.949322i	$0.601771\pi$
$200$	− 2.55529i	− 0.180686i
$201$	5.48818i	0.387106i
$202$	− 7.36747i	− 0.518373i
$203$	− 4.82757i	− 0.338829i
$204$	−7.45736	−0.522119
$205$	−12.4376	−0.868681
$206$	− 5.78525i	− 0.403077i
$207$	13.6505	0.948775
$208$	0	0
$209$	20.7394	1.43458
$210$	5.22961i	0.360877i
$211$	6.56907	0.452233	0.226117	−	0.974100i	$-0.427397\pi$
$211$	6.56907	0.452233	0.226117	+	0.974100i	$0.427397\pi$
$212$	5.98404	0.410985
$213$	− 7.67493i	− 0.525877i
$214$	− 1.02896i	− 0.0703380i
$215$	− 15.7785i	− 1.07609i
$216$	− 17.3487i	− 1.18043i
$217$	−0.597963	−0.0405924
$218$	14.1535	0.958594
$219$	37.5533i	2.53762i
$220$	4.48137	0.302134
$221$	0	0
$222$	0.128983	0.00865679
$223$	16.9121i	1.13252i	0.824227	+	0.566260i	$0.191610\pi$
$223$	16.9121i	1.13252i	−0.824227	+	0.566260i	$0.808390\pi$
$224$	1.00000	0.0668153
$225$	20.9200	1.39467
$226$	− 13.5410i	− 0.900736i
$227$	− 16.1322i	− 1.07073i	−0.844620	−	0.535367i	$-0.820173\pi$
$227$	− 16.1322i	− 1.07073i	0.844620	−	0.535367i	$-0.179827\pi$
$228$	24.2022i	1.60283i
$229$	− 6.91184i	− 0.456747i	−0.973574	−	0.228374i	$-0.926659\pi$
$229$	− 6.91184i	− 0.456747i	0.973574	−	0.228374i	$-0.0733408\pi$
$230$	−2.60700	−0.171900
$231$	9.58634	0.630735
$232$	− 4.82757i	− 0.316946i
$233$	7.47405	0.489641	0.244821	−	0.969568i	$-0.421271\pi$
$233$	7.47405	0.489641	0.244821	+	0.969568i	$0.421271\pi$
$234$	0	0
$235$	−10.9861	−0.716656
$236$	− 0.896206i	− 0.0583381i
$237$	14.2516	0.925743
$238$	2.22961	0.144524
$239$	− 19.8696i	− 1.28526i	−0.766179	−	0.642628i	$-0.777844\pi$
$239$	− 19.8696i	− 1.28526i	0.766179	−	0.642628i	$-0.222156\pi$
$240$	5.22961i	0.337570i
$241$	− 10.6445i	− 0.685674i	−0.939395	−	0.342837i	$-0.888612\pi$
$241$	− 10.6445i	− 0.685674i	0.939395	−	0.342837i	$-0.111388\pi$
$242$	2.78525i	0.179043i
$243$	59.8843	3.84158
$244$	14.2569	0.912706
$245$	− 1.56356i	− 0.0998920i
$246$	−26.6060	−1.69633
$247$	0	0
$248$	−0.597963	−0.0379707
$249$	− 16.5505i	− 1.04884i
$250$	−11.8131	−0.747128
$251$	−15.9139	−1.00448	−0.502239	−	0.864729i	$-0.667490\pi$
$251$	−15.9139	−1.00448	−0.502239	+	0.864729i	$0.667490\pi$
$252$	8.18694i	0.515729i
$253$	4.77886i	0.300444i
$254$	− 9.85165i	− 0.618148i
$255$	11.6600i	0.730178i
$256$	1.00000	0.0625000
$257$	31.1018	1.94008	0.970039	−	0.242950i	$-0.0781150\pi$
$257$	31.1018	1.94008	0.970039	+	0.242950i	$0.0781150\pi$
$258$	− 33.7526i	− 2.10135i
$259$	−0.0385636	−0.00239623
$260$	0	0
$261$	39.5230	2.44642
$262$	14.7923i	0.913871i
$263$	−28.3747	−1.74966	−0.874829	−	0.484432i	$-0.839026\pi$
$263$	−28.3747	−1.74966	−0.874829	+	0.484432i	$0.839026\pi$
$264$	9.58634	0.589998
$265$	− 9.35639i	− 0.574758i
$266$	− 7.23602i	− 0.443669i
$267$	− 8.09816i	− 0.495599i
$268$	− 1.64086i	− 0.100232i
$269$	−21.4017	−1.30488	−0.652441	−	0.757840i	$-0.726255\pi$
$269$	−21.4017	−1.30488	−0.652441	+	0.757840i	$0.726255\pi$
$270$	−27.1257	−1.65082
$271$	− 5.74656i	− 0.349079i	−0.984650	−	0.174539i	$-0.944156\pi$
$271$	− 5.74656i	− 0.349079i	0.984650	−	0.174539i	$-0.0558436\pi$
$272$	2.22961	0.135190
$273$	0	0
$274$	−0.458997	−0.0277290
$275$	7.32381i	0.441642i
$276$	−5.57677	−0.335682
$277$	−26.6020	−1.59836	−0.799180	−	0.601092i	$-0.794733\pi$
$277$	−26.6020	−1.59836	−0.799180	+	0.601092i	$0.794733\pi$
$278$	15.3146i	0.918510i
$279$	− 4.89549i	− 0.293085i
$280$	− 1.56356i	− 0.0934404i
$281$	− 6.69143i	− 0.399177i	−0.979880	−	0.199589i	$-0.936039\pi$
$281$	− 6.69143i	− 0.399177i	0.979880	−	0.199589i	$-0.0639606\pi$
$282$	−23.5010	−1.39946
$283$	−19.9338	−1.18494	−0.592472	−	0.805591i	$-0.701848\pi$
$283$	−19.9338	−1.18494	−0.592472	+	0.805591i	$0.701848\pi$
$284$	2.29466i	0.136163i
$285$	37.8416	2.24154
$286$	0	0
$287$	7.95469	0.469550
$288$	8.18694i	0.482420i
$289$	−12.0288	−0.707578
$290$	−7.54819	−0.443245
$291$	− 16.3498i	− 0.958442i
$292$	− 11.2277i	− 0.657054i
$293$	− 8.86088i	− 0.517658i	−0.965923	−	0.258829i	$-0.916663\pi$
$293$	− 8.86088i	− 0.517658i	0.965923	−	0.258829i	$-0.0833367\pi$
$294$	− 3.34469i	− 0.195066i
$295$	−1.40127	−0.0815851
$296$	−0.0385636	−0.00224147
$297$	49.7237i	2.88526i
$298$	−10.2372	−0.593022
$299$	0	0
$300$	−8.54664	−0.493441
$301$	10.0914i	0.581659i
$302$	15.2110	0.875296
$303$	−24.6419	−1.41564
$304$	− 7.23602i	− 0.415014i
$305$	− 22.2915i	− 1.27641i
$306$	18.2537i	1.04349i
$307$	8.34636i	0.476352i	0.971222	+	0.238176i	$0.0765495\pi$
$307$	8.34636i	0.476352i	−0.971222	+	0.238176i	$0.923450\pi$
$308$	−2.86614	−0.163313
$309$	−19.3499	−1.10077
$310$	0.934950i	0.0531016i
$311$	−6.68896	−0.379296	−0.189648	−	0.981852i	$-0.560735\pi$
$311$	−6.68896	−0.379296	−0.189648	+	0.981852i	$0.560735\pi$
$312$	0	0
$313$	−21.3788	−1.20840	−0.604199	−	0.796833i	$-0.706507\pi$
$313$	−21.3788	−1.20840	−0.604199	+	0.796833i	$0.706507\pi$
$314$	− 2.27419i	− 0.128340i
$315$	12.8007	0.721240
$316$	−4.26098	−0.239699
$317$	31.6776i	1.77919i	0.456748	+	0.889596i	$0.349014\pi$
$317$	31.6776i	1.77919i	−0.456748	+	0.889596i	$0.650986\pi$
$318$	− 20.0147i	− 1.12237i
$319$	13.8365i	0.774695i
$320$	− 1.56356i	− 0.0874055i
$321$	−3.44154	−0.192088
$322$	1.66735	0.0929178
$323$	− 16.1335i	− 0.897692i
$324$	−33.4651	−1.85917
$325$	0	0
$326$	−0.00979262	−0.000542363 0
$327$	− 47.3390i	− 2.61785i
$328$	7.95469	0.439224
$329$	7.02636	0.387376
$330$	− 14.9888i	− 0.825106i
$331$	− 24.6695i	− 1.35596i	−0.735081	−	0.677979i	$-0.762856\pi$
$331$	− 24.6695i	− 1.35596i	0.735081	−	0.677979i	$-0.237144\pi$
$332$	4.94829i	0.271572i
$333$	− 0.315718i	− 0.0173012i
$334$	24.9508	1.36525
$335$	−2.56559	−0.140173
$336$	− 3.34469i	− 0.182468i
$337$	28.0871	1.53000	0.765002	−	0.644028i	$-0.222738\pi$
$337$	28.0871	1.53000	0.765002	+	0.644028i	$0.222738\pi$
$338$	0	0
$339$	−45.2905	−2.45984
$340$	− 3.48613i	− 0.189062i
$341$	1.71385	0.0928099
$342$	59.2408	3.20338
$343$	1.00000i	0.0539949i
$344$	10.0914i	0.544092i
$345$	8.71960i	0.469447i
$346$	3.20550i	0.172329i
$347$	−10.1080	−0.542623	−0.271312	−	0.962492i	$-0.587457\pi$
$347$	−10.1080	−0.542623	−0.271312	+	0.962492i	$0.587457\pi$
$348$	−16.1467	−0.865556
$349$	17.3893i	0.930828i	0.885093	+	0.465414i	$0.154095\pi$
$349$	17.3893i	0.930828i	−0.885093	+	0.465414i	$0.845905\pi$
$350$	2.55529	0.136586
$351$	0	0
$352$	−2.86614	−0.152766
$353$	− 3.32659i	− 0.177056i	−0.996074	−	0.0885282i	$-0.971784\pi$
$353$	− 3.32659i	− 0.177056i	0.996074	−	0.0885282i	$-0.0282163\pi$
$354$	−2.99753	−0.159317
$355$	3.58784	0.190423
$356$	2.42120i	0.128323i
$357$	− 7.45736i	− 0.394685i
$358$	15.8000i	0.835053i
$359$	− 8.02414i	− 0.423498i	−0.977324	−	0.211749i	$-0.932084\pi$
$359$	− 8.02414i	− 0.423498i	0.977324	−	0.211749i	$-0.0679159\pi$
$360$	12.8007	0.674659
$361$	−33.3599	−1.75579
$362$	9.11907i	0.479288i
$363$	9.31579	0.488952
$364$	0	0
$365$	−17.5552	−0.918882
$366$	− 47.6850i	− 2.49253i
$367$	1.03908	0.0542395	0.0271198	−	0.999632i	$-0.491366\pi$
$367$	1.03908	0.0542395	0.0271198	+	0.999632i	$0.491366\pi$
$368$	1.66735	0.0869167
$369$	65.1245i	3.39025i
$370$	0.0602965i	0.00313466i
$371$	5.98404i	0.310676i
$372$	2.00000i	0.103695i
$373$	27.3124	1.41418	0.707092	−	0.707122i	$-0.250007\pi$
$373$	27.3124	1.41418	0.707092	+	0.707122i	$0.250007\pi$
$374$	−6.39038	−0.330438
$375$	39.5112i	2.04035i
$376$	7.02636	0.362357
$377$	0	0
$378$	17.3487	0.892320
$379$	2.21166i	0.113605i	0.998385	+	0.0568026i	$0.0180906\pi$
$379$	2.21166i	0.113605i	−0.998385	+	0.0568026i	$0.981909\pi$
$380$	−11.3139	−0.580392
$381$	−32.9507	−1.68812
$382$	− 3.26137i	− 0.166866i
$383$	22.3386i	1.14145i	0.821142	+	0.570724i	$0.193337\pi$
$383$	22.3386i	1.14145i	−0.821142	+	0.570724i	$0.806663\pi$
$384$	− 3.34469i	− 0.170683i
$385$	4.48137i	0.228392i
$386$	22.0730	1.12349
$387$	−82.6178	−4.19970
$388$	4.88829i	0.248165i
$389$	−12.2604	−0.621629	−0.310814	−	0.950471i	$-0.600602\pi$
$389$	−12.2604	−0.621629	−0.310814	+	0.950471i	$0.600602\pi$
$390$	0	0
$391$	3.71755	0.188004
$392$	1.00000i	0.0505076i
$393$	49.4756	2.49571
$394$	−5.27305	−0.265653
$395$	6.66228i	0.335216i
$396$	− 23.4649i	− 1.17916i
$397$	2.93517i	0.147312i	0.997284	+	0.0736561i	$0.0234667\pi$
$397$	2.93517i	0.147312i	−0.997284	+	0.0736561i	$0.976533\pi$
$398$	− 8.86762i	− 0.444493i
$399$	−24.2022	−1.21163
$400$	2.55529	0.127764
$401$	− 21.8502i	− 1.09115i	−0.838062	−	0.545575i	$-0.816311\pi$
$401$	− 21.8502i	− 1.09115i	0.838062	−	0.545575i	$-0.183689\pi$
$402$	−5.48818	−0.273726
$403$	0	0
$404$	7.36747	0.366545
$405$	52.3246i	2.60003i
$406$	4.82757	0.239589
$407$	0.110529	0.00547871
$408$	− 7.45736i	− 0.369194i
$409$	− 7.38191i	− 0.365012i	−0.983205	−	0.182506i	$-0.941579\pi$
$409$	− 7.38191i	− 0.365012i	0.983205	−	0.182506i	$-0.0584208\pi$
$410$	− 12.4376i	− 0.614250i
$411$	1.53520i	0.0757260i
$412$	5.78525	0.285019
$413$	0.896206	0.0440994
$414$	13.6505i	0.670885i
$415$	7.73693	0.379791
$416$	0	0
$417$	51.2226	2.50838
$418$	20.7394i	1.01440i
$419$	−8.58273	−0.419294	−0.209647	−	0.977777i	$-0.567231\pi$
$419$	−8.58273	−0.419294	−0.209647	+	0.977777i	$0.567231\pi$
$420$	−5.22961	−0.255179
$421$	7.49525i	0.365296i	0.983178	+	0.182648i	$0.0584669\pi$
$421$	7.49525i	0.365296i	−0.983178	+	0.182648i	$0.941533\pi$
$422$	6.56907i	0.319777i
$423$	57.5244i	2.79693i
$424$	5.98404i	0.290611i
$425$	5.69730	0.276360
$426$	7.67493	0.371851
$427$	14.2569i	0.689941i
$428$	1.02896	0.0497365
$429$	0	0
$430$	15.7785	0.760907
$431$	16.4791i	0.793772i	0.917868	+	0.396886i	$0.129909\pi$
$431$	16.4791i	0.793772i	−0.917868	+	0.396886i	$0.870091\pi$
$432$	17.3487	0.834689
$433$	25.5610	1.22838	0.614192	−	0.789156i	$-0.289482\pi$
$433$	25.5610	1.22838	0.614192	+	0.789156i	$0.289482\pi$
$434$	− 0.597963i	− 0.0287031i
$435$	25.2463i	1.21047i
$436$	14.1535i	0.677829i
$437$	− 12.0650i	− 0.577146i
$438$	−37.5533	−1.79437
$439$	−9.20839	−0.439493	−0.219746	−	0.975557i	$-0.570523\pi$
$439$	−9.20839	−0.439493	−0.219746	+	0.975557i	$0.570523\pi$
$440$	4.48137i	0.213641i
$441$	−8.18694	−0.389854
$442$	0	0
$443$	−6.20759	−0.294931	−0.147466	−	0.989067i	$-0.547112\pi$
$443$	−6.20759	−0.294931	−0.147466	+	0.989067i	$0.547112\pi$
$444$	0.128983i	0.00612128i
$445$	3.78569	0.179459
$446$	−16.9121	−0.800812
$447$	34.2401i	1.61950i
$448$	1.00000i	0.0472456i
$449$	5.21888i	0.246294i	0.992388	+	0.123147i	$0.0392987\pi$
$449$	5.21888i	0.246294i	−0.992388	+	0.123147i	$0.960701\pi$
$450$	20.9200i	0.986177i
$451$	−22.7992	−1.07357
$452$	13.5410	0.636916
$453$	− 50.8761i	− 2.39037i
$454$	16.1322	0.757123
$455$	0	0
$456$	−24.2022	−1.13337
$457$	33.9332i	1.58733i	0.608357	+	0.793664i	$0.291829\pi$
$457$	33.9332i	1.58733i	−0.608357	+	0.793664i	$0.708171\pi$
$458$	6.91184	0.322969
$459$	38.6808	1.80547
$460$	− 2.60700i	− 0.121552i
$461$	0.844759i	0.0393444i	0.999806	+	0.0196722i	$0.00626225\pi$
$461$	0.844759i	0.0393444i	−0.999806	+	0.0196722i	$0.993738\pi$
$462$	9.58634i	0.445997i
$463$	− 6.50221i	− 0.302183i	−0.988520	−	0.151092i	$-0.951721\pi$
$463$	− 6.50221i	− 0.302183i	0.988520	−	0.151092i	$-0.0482789\pi$
$464$	4.82757	0.224115
$465$	3.12712	0.145016
$466$	7.47405i	0.346229i
$467$	9.52759	0.440884	0.220442	−	0.975400i	$-0.429250\pi$
$467$	9.52759	0.440884	0.220442	+	0.975400i	$0.429250\pi$
$468$	0	0
$469$	1.64086	0.0757681
$470$	− 10.9861i	− 0.506752i
$471$	−7.60645	−0.350487
$472$	0.896206	0.0412512
$473$	− 28.9234i	− 1.32990i
$474$	14.2516i	0.654599i
$475$	− 18.4901i	− 0.848384i
$476$	2.22961i	0.102194i
$477$	−48.9909	−2.24314
$478$	19.8696	0.908813
$479$	2.84198i	0.129854i	0.997890	+	0.0649268i	$0.0206814\pi$
$479$	2.84198i	0.129854i	−0.997890	+	0.0649268i	$0.979319\pi$
$480$	−5.22961	−0.238698
$481$	0	0
$482$	10.6445	0.484844
$483$	− 5.57677i	− 0.253752i
$484$	−2.78525	−0.126602
$485$	7.64312	0.347056
$486$	59.8843i	2.71641i
$487$	− 5.26374i	− 0.238523i	−0.992863	−	0.119261i	$-0.961947\pi$
$487$	− 5.26374i	− 0.238523i	0.992863	−	0.119261i	$-0.0380526\pi$
$488$	14.2569i	0.645381i
$489$	0.0327533i	0.00148115i
$490$	1.56356	0.0706343
$491$	−22.8913	−1.03307	−0.516536	−	0.856266i	$-0.672779\pi$
$491$	−22.8913	−1.03307	−0.516536	+	0.856266i	$0.672779\pi$
$492$	− 26.6060i	− 1.19949i
$493$	10.7636	0.484769
$494$	0	0
$495$	−36.6887	−1.64903
$496$	− 0.597963i	− 0.0268493i
$497$	−2.29466	−0.102930
$498$	16.5505	0.741644
$499$	6.79877i	0.304355i	0.988353	+	0.152177i	$0.0486285\pi$
$499$	6.79877i	0.304355i	−0.988353	+	0.152177i	$0.951372\pi$
$500$	− 11.8131i	− 0.528299i
$501$	− 83.4527i	− 3.72839i
$502$	− 15.9139i	− 0.710273i
$503$	10.8060	0.481816	0.240908	−	0.970548i	$-0.422555\pi$
$503$	10.8060	0.481816	0.240908	+	0.970548i	$0.422555\pi$
$504$	−8.18694	−0.364675
$505$	− 11.5195i	− 0.512609i
$506$	−4.77886	−0.212446
$507$	0	0
$508$	9.85165	0.437096
$509$	27.3194i	1.21091i	0.795879	+	0.605455i	$0.207009\pi$
$509$	27.3194i	1.21091i	−0.795879	+	0.605455i	$0.792991\pi$
$510$	−11.6600	−0.516314
$511$	11.2277	0.496686
$512$	1.00000i	0.0441942i
$513$	− 125.535i	− 5.54252i
$514$	31.1018i	1.37184i
$515$	− 9.04557i	− 0.398595i
$516$	33.7526	1.48588
$517$	−20.1385	−0.885691
$518$	− 0.0385636i	− 0.00169439i
$519$	10.7214	0.470616
$520$	0	0
$521$	−3.63580	−0.159287	−0.0796437	−	0.996823i	$-0.525378\pi$
$521$	−3.63580	−0.159287	−0.0796437	+	0.996823i	$0.525378\pi$
$522$	39.5230i	1.72988i
$523$	−7.18446	−0.314155	−0.157077	−	0.987586i	$-0.550207\pi$
$523$	−7.18446	−0.314155	−0.157077	+	0.987586i	$0.550207\pi$
$524$	−14.7923	−0.646204
$525$	− 8.54664i	− 0.373006i
$526$	− 28.3747i	− 1.23719i
$527$	− 1.33323i	− 0.0580762i
$528$	9.58634i	0.417192i
$529$	−20.2199	−0.879128
$530$	9.35639	0.406415
$531$	7.33718i	0.318407i
$532$	7.23602	0.313721
$533$	0	0
$534$	8.09816	0.350442
$535$	− 1.60883i	− 0.0695559i
$536$	1.64086	0.0708746
$537$	52.8459	2.28047
$538$	− 21.4017i	− 0.922691i
$539$	− 2.86614i	− 0.123453i
$540$	− 27.1257i	− 1.16730i
$541$	0.445063i	0.0191347i	0.999954	+	0.00956737i	$0.00304543\pi$
$541$	0.445063i	0.0191347i	−0.999954	+	0.00956737i	$0.996955\pi$
$542$	5.74656	0.246836
$543$	30.5004	1.30890
$544$	2.22961i	0.0955938i
$545$	22.1298	0.947935
$546$	0	0
$547$	−5.67129	−0.242487	−0.121243	−	0.992623i	$-0.538688\pi$
$547$	−5.67129	−0.242487	−0.121243	+	0.992623i	$0.538688\pi$
$548$	− 0.458997i	− 0.0196074i
$549$	−116.721	−4.98151
$550$	−7.32381	−0.312288
$551$	− 34.9324i	− 1.48817i
$552$	− 5.57677i	− 0.237363i
$553$	− 4.26098i	− 0.181195i
$554$	− 26.6020i	− 1.13021i
$555$	0.201673	0.00856054
$556$	−15.3146	−0.649485
$557$	− 26.5075i	− 1.12316i	−0.827423	−	0.561579i	$-0.810194\pi$
$557$	− 26.5075i	− 1.12316i	0.827423	−	0.561579i	$-0.189806\pi$
$558$	4.89549	0.207242
$559$	0	0
$560$	1.56356	0.0660724
$561$	21.3738i	0.902403i
$562$	6.69143	0.282261
$563$	11.5376	0.486252	0.243126	−	0.969995i	$-0.421827\pi$
$563$	11.5376	0.486252	0.243126	+	0.969995i	$0.421827\pi$
$564$	− 23.5010i	− 0.989570i
$565$	− 21.1722i	− 0.890720i
$566$	− 19.9338i	− 0.837882i
$567$	− 33.4651i	− 1.40540i
$568$	−2.29466	−0.0962819
$569$	32.1581	1.34814	0.674069	−	0.738668i	$-0.264545\pi$
$569$	32.1581	1.34814	0.674069	+	0.738668i	$0.264545\pi$
$570$	37.8416i	1.58501i
$571$	−11.5540	−0.483521	−0.241761	−	0.970336i	$-0.577725\pi$
$571$	−11.5540	−0.483521	−0.241761	+	0.970336i	$0.577725\pi$
$572$	0	0
$573$	−10.9083	−0.455699
$574$	7.95469i	0.332022i
$575$	4.26056	0.177678
$576$	−8.18694	−0.341122
$577$	− 9.14050i	− 0.380524i	−0.981733	−	0.190262i	$-0.939066\pi$
$577$	− 9.14050i	− 0.380524i	0.981733	−	0.190262i	$-0.0609337\pi$
$578$	− 12.0288i	− 0.500333i
$579$	− 73.8274i	− 3.06816i
$580$	− 7.54819i	− 0.313422i
$581$	−4.94829	−0.205289
$582$	16.3498	0.677721
$583$	− 17.1511i	− 0.710325i
$584$	11.2277	0.464607
$585$	0	0
$586$	8.86088	0.366040
$587$	− 42.7965i	− 1.76640i	−0.468994	−	0.883201i	$-0.655383\pi$
$587$	− 42.7965i	− 1.76640i	0.468994	−	0.883201i	$-0.344617\pi$
$588$	3.34469	0.137933
$589$	−4.32687	−0.178286
$590$	− 1.40127i	− 0.0576894i
$591$	17.6367i	0.725478i
$592$	− 0.0385636i	− 0.00158496i
$593$	14.2439i	0.584927i	0.956277	+	0.292463i	$0.0944750\pi$
$593$	14.2439i	0.584927i	−0.956277	+	0.292463i	$0.905525\pi$
$594$	−49.7237	−2.04019
$595$	3.48613	0.142917
$596$	− 10.2372i	− 0.419330i
$597$	−29.6594	−1.21388
$598$	0	0
$599$	3.74735	0.153113	0.0765563	−	0.997065i	$-0.475608\pi$
$599$	3.74735	0.153113	0.0765563	+	0.997065i	$0.475608\pi$
$600$	− 8.54664i	− 0.348915i
$601$	10.6692	0.435208	0.217604	−	0.976037i	$-0.430176\pi$
$601$	10.6692	0.435208	0.217604	+	0.976037i	$0.430176\pi$
$602$	−10.0914	−0.411295
$603$	13.4337i	0.547061i
$604$	15.2110i	0.618927i
$605$	4.35490i	0.177052i
$606$	− 24.6419i	− 1.00101i
$607$	9.65256	0.391785	0.195893	−	0.980625i	$-0.437240\pi$
$607$	9.65256	0.391785	0.195893	+	0.980625i	$0.437240\pi$
$608$	7.23602	0.293459
$609$	− 16.1467i	− 0.654299i
$610$	22.2915	0.902558
$611$	0	0
$612$	−18.2537	−0.737862
$613$	3.99489i	0.161352i	0.996740	+	0.0806761i	$0.0257079\pi$
$613$	3.99489i	0.161352i	−0.996740	+	0.0806761i	$0.974292\pi$
$614$	−8.34636	−0.336832
$615$	−41.5999	−1.67747
$616$	− 2.86614i	− 0.115480i
$617$	3.23546i	0.130255i	0.997877	+	0.0651273i	$0.0207454\pi$
$617$	3.23546i	0.130255i	−0.997877	+	0.0651273i	$0.979255\pi$
$618$	− 19.3499i	− 0.778365i
$619$	39.2679i	1.57831i	0.614193	+	0.789156i	$0.289482\pi$
$619$	39.2679i	1.57831i	−0.614193	+	0.789156i	$0.710518\pi$
$620$	−0.934950	−0.0375485
$621$	28.9263	1.16077
$622$	− 6.68896i	− 0.268203i
$623$	−2.42120	−0.0970033
$624$	0	0
$625$	−5.69406	−0.227763
$626$	− 21.3788i	− 0.854467i
$627$	69.3669	2.77025
$628$	2.27419	0.0907500
$629$	− 0.0859819i	− 0.00342832i
$630$	12.8007i	0.509994i
$631$	29.4429i	1.17210i	0.810273	+	0.586052i	$0.199319\pi$
$631$	29.4429i	1.17210i	−0.810273	+	0.586052i	$0.800681\pi$
$632$	− 4.26098i	− 0.169493i
$633$	21.9715	0.873288
$634$	−31.6776	−1.25808
$635$	− 15.4036i	− 0.611274i
$636$	20.0147	0.793636
$637$	0	0
$638$	−13.8365	−0.547792
$639$	− 18.7863i	− 0.743173i
$640$	1.56356	0.0618050
$641$	−4.09119	−0.161592	−0.0807961	−	0.996731i	$-0.525746\pi$
$641$	−4.09119	−0.161592	−0.0807961	+	0.996731i	$0.525746\pi$
$642$	− 3.44154i	− 0.135827i
$643$	22.2479i	0.877370i	0.898641	+	0.438685i	$0.144556\pi$
$643$	22.2479i	0.877370i	−0.898641	+	0.438685i	$0.855444\pi$
$644$	1.66735i	0.0657028i
$645$	− 52.7742i	− 2.07798i
$646$	16.1335	0.634764
$647$	49.8583	1.96013	0.980066	−	0.198670i	$-0.0636622\pi$
$647$	49.8583	1.96013	0.980066	+	0.198670i	$0.0636622\pi$
$648$	− 33.4651i	− 1.31463i
$649$	−2.56865	−0.100828
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	− 0.00979262i	0 0.000383509i
$653$	7.40353	0.289723	0.144861	−	0.989452i	$-0.453726\pi$
$653$	7.40353	0.289723	0.144861	+	0.989452i	$0.453726\pi$
$654$	47.3390	1.85110
$655$	23.1286i	0.903709i
$656$	7.95469i	0.310578i
$657$	91.9208i	3.58617i
$658$	7.02636i	0.273916i
$659$	30.0820	1.17183	0.585914	−	0.810373i	$-0.300736\pi$
$659$	30.0820	1.17183	0.585914	+	0.810373i	$0.300736\pi$
$660$	14.9888	0.583438
$661$	− 26.6319i	− 1.03586i	−0.855423	−	0.517931i	$-0.826702\pi$
$661$	− 26.6319i	− 1.03586i	0.855423	−	0.517931i	$-0.173298\pi$
$662$	24.6695	0.958807
$663$	0	0
$664$	−4.94829	−0.192031
$665$	− 11.3139i	− 0.438735i
$666$	0.315718	0.0122338
$667$	8.04926	0.311669
$668$	24.9508i	0.965376i
$669$	56.5657i	2.18696i
$670$	− 2.56559i	− 0.0991172i
$671$	− 40.8623i	− 1.57747i
$672$	3.34469	0.129024
$673$	3.69305	0.142357	0.0711783	−	0.997464i	$-0.477324\pi$
$673$	3.69305	0.142357	0.0711783	+	0.997464i	$0.477324\pi$
$674$	28.0871i	1.08188i
$675$	44.3309	1.70630
$676$	0	0
$677$	−35.6533	−1.37027	−0.685134	−	0.728417i	$-0.740256\pi$
$677$	−35.6533	−1.37027	−0.685134	+	0.728417i	$0.740256\pi$
$678$	− 45.2905i	− 1.73937i
$679$	−4.88829	−0.187595
$680$	3.48613	0.133687
$681$	− 53.9572i	− 2.06765i
$682$	1.71385i	0.0656265i
$683$	− 30.2653i	− 1.15807i	−0.815304	−	0.579034i	$-0.803430\pi$
$683$	− 30.2653i	− 1.15807i	0.815304	−	0.579034i	$-0.196570\pi$
$684$	59.2408i	2.26513i
$685$	−0.717669	−0.0274207
$686$	−1.00000	−0.0381802
$687$	− 23.1179i	− 0.882004i
$688$	−10.0914	−0.384731
$689$	0	0
$690$	−8.71960	−0.331949
$691$	− 3.50309i	− 0.133264i	−0.997778	−	0.0666320i	$-0.978775\pi$
$691$	− 3.50309i	− 0.133264i	0.997778	−	0.0666320i	$-0.0212253\pi$
$692$	−3.20550	−0.121855
$693$	23.4649	0.891358
$694$	− 10.1080i	− 0.383693i
$695$	23.9453i	0.908297i
$696$	− 16.1467i	− 0.612040i
$697$	17.7359i	0.671794i
$698$	−17.3893	−0.658195
$699$	24.9984	0.945525
$700$	2.55529i	0.0965808i
$701$	−45.2243	−1.70810	−0.854048	−	0.520194i	$-0.825860\pi$
$701$	−45.2243	−1.70810	−0.854048	+	0.520194i	$0.825860\pi$
$702$	0	0
$703$	−0.279047	−0.0105245
$704$	− 2.86614i	− 0.108022i
$705$	−36.7451	−1.38390
$706$	3.32659	0.125198
$707$	7.36747i	0.277082i
$708$	− 2.99753i	− 0.112654i
$709$	2.99826i	0.112602i	0.998414	+	0.0563009i	$0.0179306\pi$
$709$	2.99826i	0.112602i	−0.998414	+	0.0563009i	$0.982069\pi$
$710$	3.58784i	0.134649i
$711$	34.8843	1.30827
$712$	−2.42120	−0.0907383
$713$	− 0.997014i	− 0.0373385i
$714$	7.45736	0.279085
$715$	0	0
$716$	−15.8000	−0.590472
$717$	− 66.4575i	− 2.48190i
$718$	8.02414	0.299458
$719$	20.0794	0.748834	0.374417	−	0.927260i	$-0.377843\pi$
$719$	20.0794	0.748834	0.374417	+	0.927260i	$0.377843\pi$
$720$	12.8007i	0.477056i
$721$	5.78525i	0.215454i
$722$	− 33.3599i	− 1.24153i
$723$	− 35.6026i	− 1.32407i
$724$	−9.11907	−0.338908
$725$	12.3358	0.458142
$726$	9.31579i	0.345741i
$727$	−32.5895	−1.20868	−0.604338	−	0.796728i	$-0.706562\pi$
$727$	−32.5895	−1.20868	−0.604338	+	0.796728i	$0.706562\pi$
$728$	0	0
$729$	99.8990	3.69996
$730$	− 17.5552i	− 0.649748i
$731$	−22.4999	−0.832190
$732$	47.6850	1.76249
$733$	− 18.5190i	− 0.684017i	−0.939697	−	0.342008i	$-0.888893\pi$
$733$	− 18.5190i	− 0.684017i	0.939697	−	0.342008i	$-0.111107\pi$
$734$	1.03908i	0.0383531i
$735$	− 5.22961i	− 0.192897i
$736$	1.66735i	0.0614594i
$737$	−4.70294	−0.173235
$738$	−65.1245	−2.39727
$739$	− 15.9312i	− 0.586038i	−0.956107	−	0.293019i	$-0.905340\pi$
$739$	− 15.9312i	− 0.586038i	0.956107	−	0.293019i	$-0.0946600\pi$
$740$	−0.0602965	−0.00221654
$741$	0	0
$742$	−5.98404	−0.219681
$743$	− 12.2355i	− 0.448876i	−0.974488	−	0.224438i	$-0.927945\pi$
$743$	− 12.2355i	− 0.448876i	0.974488	−	0.224438i	$-0.0720546\pi$
$744$	−2.00000	−0.0733236
$745$	−16.0064	−0.586428
$746$	27.3124i	0.999979i
$747$	− 40.5113i	− 1.48223i
$748$	− 6.39038i	− 0.233655i
$749$	1.02896i	0.0375972i
$750$	−39.5112	−1.44275
$751$	20.8213	0.759782	0.379891	−	0.925031i	$-0.375962\pi$
$751$	20.8213	0.759782	0.379891	+	0.925031i	$0.375962\pi$
$752$	7.02636i	0.256225i
$753$	−53.2271	−1.93970
$754$	0	0
$755$	23.7833	0.865563
$756$	17.3487i	0.630966i
$757$	27.1151	0.985514	0.492757	−	0.870167i	$-0.335989\pi$
$757$	27.1151	0.985514	0.492757	+	0.870167i	$0.335989\pi$
$758$	−2.21166	−0.0803310
$759$	15.9838i	0.580175i
$760$	− 11.3139i	− 0.410399i
$761$	48.3727i	1.75351i	0.480937	+	0.876755i	$0.340297\pi$
$761$	48.3727i	1.75351i	−0.480937	+	0.876755i	$0.659703\pi$
$762$	− 32.9507i	− 1.19368i
$763$	−14.1535	−0.512390
$764$	3.26137	0.117992
$765$	28.5407i	1.03189i
$766$	−22.3386	−0.807125
$767$	0	0
$768$	3.34469	0.120691
$769$	17.3453i	0.625486i	0.949838	+	0.312743i	$0.101248\pi$
$769$	17.3453i	0.625486i	−0.949838	+	0.312743i	$0.898752\pi$
$770$	−4.48137	−0.161497
$771$	104.026	3.74640
$772$	22.0730i	0.794426i
$773$	− 14.0480i	− 0.505270i	−0.967562	−	0.252635i	$-0.918703\pi$
$773$	− 14.0480i	− 0.505270i	0.967562	−	0.252635i	$-0.0812971\pi$
$774$	− 82.6178i	− 2.96963i
$775$	− 1.52797i	− 0.0548862i
$776$	−4.88829	−0.175479
$777$	−0.128983	−0.00462725
$778$	− 12.2604i	− 0.439558i
$779$	57.5603	2.06231
$780$	0	0
$781$	6.57682	0.235337
$782$	3.71755i	0.132939i
$783$	83.7521	2.99305
$784$	−1.00000	−0.0357143
$785$	− 3.55582i	− 0.126913i
$786$	49.4756i	1.76474i
$787$	− 7.75577i	− 0.276463i	−0.990400	−	0.138232i	$-0.955858\pi$
$787$	− 7.75577i	− 0.276463i	0.990400	−	0.138232i	$-0.0441419\pi$
$788$	− 5.27305i	− 0.187845i
$789$	−94.9044	−3.37869
$790$	−6.66228	−0.237033
$791$	13.5410i	0.481464i
$792$	23.4649	0.833789
$793$	0	0
$794$	−2.93517	−0.104165
$795$	− 31.2942i	− 1.10989i
$796$	8.86762	0.314304
$797$	33.8492	1.19900	0.599500	−	0.800375i	$-0.295366\pi$
$797$	33.8492	1.19900	0.599500	+	0.800375i	$0.295366\pi$
$798$	− 24.2022i	− 0.856749i
$799$	15.6661i	0.554225i
$800$	2.55529i	0.0903431i
$801$	− 19.8222i	− 0.700383i
$802$	21.8502	0.771559
$803$	−32.1803	−1.13562
$804$	− 5.48818i	− 0.193553i
$805$	2.60700	0.0918847
$806$	0	0
$807$	−71.5819	−2.51980
$808$	7.36747i	0.259187i
$809$	−32.8340	−1.15438	−0.577191	−	0.816609i	$-0.695851\pi$
$809$	−32.8340	−1.15438	−0.577191	+	0.816609i	$0.695851\pi$
$810$	−52.3246	−1.83850
$811$	12.2083i	0.428690i	0.976758	+	0.214345i	$0.0687617\pi$
$811$	12.2083i	0.428690i	−0.976758	+	0.214345i	$0.931238\pi$
$812$	4.82757i	0.169415i
$813$	− 19.2205i	− 0.674091i
$814$	0.110529i	0.00387403i
$815$	−0.0153113	−0.000536332 0
$816$	7.45736	0.261060
$817$	73.0216i	2.55470i
$818$	7.38191	0.258102
$819$	0	0
$820$	12.4376	0.434340
$821$	− 47.4868i	− 1.65730i	−0.559767	−	0.828650i	$-0.689109\pi$
$821$	− 47.4868i	− 1.65730i	0.559767	−	0.828650i	$-0.310891\pi$
$822$	−1.53520	−0.0535463
$823$	−22.0459	−0.768471	−0.384235	−	0.923235i	$-0.625535\pi$
$823$	−22.0459	−0.768471	−0.384235	+	0.923235i	$0.625535\pi$
$824$	5.78525i	0.201539i
$825$	24.4959i	0.852836i
$826$	0.896206i	0.0311830i
$827$	45.9092i	1.59642i	0.602380	+	0.798209i	$0.294219\pi$
$827$	45.9092i	1.59642i	−0.602380	+	0.798209i	$0.705781\pi$
$828$	−13.6505	−0.474388
$829$	−26.7766	−0.929991	−0.464996	−	0.885313i	$-0.653944\pi$
$829$	−26.7766	−0.929991	−0.464996	+	0.885313i	$0.653944\pi$
$830$	7.73693i	0.268553i
$831$	−88.9754	−3.08652
$832$	0	0
$833$	−2.22961	−0.0772515
$834$	51.2226i	1.77369i
$835$	39.0120	1.35007
$836$	−20.7394	−0.717288
$837$	− 10.3739i	− 0.358574i
$838$	− 8.58273i	− 0.296486i
$839$	− 28.4010i	− 0.980511i	−0.871579	−	0.490255i	$-0.836904\pi$
$839$	− 28.4010i	− 0.980511i	0.871579	−	0.490255i	$-0.163096\pi$
$840$	− 5.22961i	− 0.180439i
$841$	−5.69452	−0.196363
$842$	−7.49525	−0.258304
$843$	− 22.3807i	− 0.770834i
$844$	−6.56907	−0.226117
$845$	0	0
$846$	−57.5244	−1.97773
$847$	− 2.78525i	− 0.0957023i
$848$	−5.98404	−0.205493
$849$	−66.6725	−2.28819
$850$	5.69730i	0.195416i
$851$	− 0.0642991i	− 0.00220415i
$852$	7.67493i	0.262939i
$853$	21.3316i	0.730379i	0.930933	+	0.365189i	$0.118996\pi$
$853$	21.3316i	0.730379i	−0.930933	+	0.365189i	$0.881004\pi$
$854$	−14.2569	−0.487862
$855$	92.6264	3.16776
$856$	1.02896i	0.0351690i
$857$	−41.0823	−1.40335	−0.701673	−	0.712499i	$-0.747563\pi$
$857$	−41.0823	−1.40335	−0.701673	+	0.712499i	$0.747563\pi$
$858$	0	0
$859$	28.8618	0.984752	0.492376	−	0.870383i	$-0.336129\pi$
$859$	28.8618	0.984752	0.492376	+	0.870383i	$0.336129\pi$
$860$	15.7785i	0.538043i
$861$	26.6060	0.906728
$862$	−16.4791	−0.561281
$863$	22.7332i	0.773847i	0.922112	+	0.386923i	$0.126462\pi$
$863$	22.7332i	0.773847i	−0.922112	+	0.386923i	$0.873538\pi$
$864$	17.3487i	0.590214i
$865$	5.01198i	0.170412i
$866$	25.5610i	0.868599i
$867$	−40.2327	−1.36637
$868$	0.597963	0.0202962
$869$	12.2125i	0.414282i
$870$	−25.2463	−0.855931
$871$	0	0
$872$	−14.1535	−0.479297
$873$	− 40.0201i	− 1.35448i
$874$	12.0650	0.408104
$875$	11.8131	0.399357
$876$	− 37.5533i	− 1.26881i
$877$	29.4178i	0.993368i	0.867932	+	0.496684i	$0.165449\pi$
$877$	29.4178i	0.993368i	−0.867932	+	0.496684i	$0.834551\pi$
$878$	− 9.20839i	− 0.310768i
$879$	− 29.6369i	− 0.999627i
$880$	−4.48137	−0.151067
$881$	−4.22209	−0.142246	−0.0711229	−	0.997468i	$-0.522658\pi$
$881$	−4.22209	−0.142246	−0.0711229	+	0.997468i	$0.522658\pi$
$882$	− 8.18694i	− 0.275668i
$883$	37.1982	1.25182	0.625910	−	0.779895i	$-0.284728\pi$
$883$	37.1982	1.25182	0.625910	+	0.779895i	$0.284728\pi$
$884$	0	0
$885$	−4.68681	−0.157545
$886$	− 6.20759i	− 0.208548i
$887$	−56.1894	−1.88665	−0.943327	−	0.331865i	$-0.892322\pi$
$887$	−56.1894	−1.88665	−0.943327	+	0.331865i	$0.892322\pi$
$888$	−0.128983	−0.00432840
$889$	9.85165i	0.330414i
$890$	3.78569i	0.126896i
$891$	95.9157i	3.21330i
$892$	− 16.9121i	− 0.566260i
$893$	50.8429	1.70139
$894$	−34.2401	−1.14516
$895$	24.7041i	0.825768i
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−5.21888	−0.174156
$899$	− 2.88671i	− 0.0962772i
$900$	−20.9200	−0.697333
$901$	−13.3421	−0.444489
$902$	− 22.7992i	− 0.759132i
$903$	33.7526i	1.12322i
$904$	13.5410i	0.450368i
$905$	14.2582i	0.473958i
$906$	50.8761	1.69025
$907$	0.653612	0.0217028	0.0108514	−	0.999941i	$-0.496546\pi$
$907$	0.653612	0.0217028	0.0108514	+	0.999941i	$0.496546\pi$
$908$	16.1322i	0.535367i
$909$	−60.3170	−2.00059
$910$	0	0
$911$	39.7806	1.31799	0.658995	−	0.752147i	$-0.270982\pi$
$911$	39.7806	1.31799	0.658995	+	0.752147i	$0.270982\pi$
$912$	− 24.2022i	− 0.801415i
$913$	14.1825	0.469371
$914$	−33.9332	−1.12241
$915$	− 74.5582i	− 2.46482i
$916$	6.91184i	0.228374i
$917$	− 14.7923i	− 0.488484i
$918$	38.6808i	1.27666i
$919$	34.6056	1.14153	0.570767	−	0.821112i	$-0.306646\pi$
$919$	34.6056	1.14153	0.570767	+	0.821112i	$0.306646\pi$
$920$	2.60700	0.0859502
$921$	27.9160i	0.919863i
$922$	−0.844759	−0.0278207
$923$	0	0
$924$	−9.58634	−0.315367
$925$	− 0.0985412i	− 0.00324001i
$926$	6.50221	0.213676
$927$	−47.3635	−1.55562
$928$	4.82757i	0.158473i
$929$	19.2707i	0.632252i	0.948717	+	0.316126i	$0.102382\pi$
$929$	19.2707i	0.632252i	−0.948717	+	0.316126i	$0.897618\pi$
$930$	3.12712i	0.102542i
$931$	7.23602i	0.237151i
$932$	−7.47405	−0.244821
$933$	−22.3725	−0.732442
$934$	9.52759i	0.311752i
$935$	−9.99172	−0.326764
$936$	0	0
$937$	−50.9507	−1.66449	−0.832244	−	0.554410i	$-0.812944\pi$
$937$	−50.9507	−1.66449	−0.832244	+	0.554410i	$0.812944\pi$
$938$	1.64086i	0.0535761i
$939$	−71.5052	−2.33349
$940$	10.9861	0.358328
$941$	− 24.3014i	− 0.792204i	−0.918207	−	0.396102i	$-0.870363\pi$
$941$	− 24.3014i	− 0.792204i	0.918207	−	0.396102i	$-0.129637\pi$
$942$	− 7.60645i	− 0.247831i
$943$	13.2633i	0.431911i
$944$	0.896206i	0.0291690i
$945$	27.1257	0.882398
$946$	28.9234	0.940380
$947$	− 25.6665i	− 0.834049i	−0.908895	−	0.417024i	$-0.863073\pi$
$947$	− 25.6665i	− 0.834049i	0.908895	−	0.417024i	$-0.136927\pi$
$948$	−14.2516	−0.462872
$949$	0	0
$950$	18.4901	0.599898
$951$	105.952i	3.43572i
$952$	−2.22961	−0.0722621
$953$	−4.80983	−0.155806	−0.0779029	−	0.996961i	$-0.524822\pi$
$953$	−4.80983	−0.155806	−0.0779029	+	0.996961i	$0.524822\pi$
$954$	− 48.9909i	− 1.58614i
$955$	− 5.09934i	− 0.165011i
$956$	19.8696i	0.642628i
$957$	46.2788i	1.49598i
$958$	−2.84198	−0.0918203
$959$	0.458997	0.0148218
$960$	− 5.22961i	− 0.168785i
$961$	30.6424	0.988466
$962$	0	0
$963$	−8.42400	−0.271460
$964$	10.6445i	0.342837i
$965$	34.5125	1.11100
$966$	5.57677	0.179430
$967$	58.2044i	1.87173i	0.352362	+	0.935864i	$0.385378\pi$
$967$	58.2044i	1.87173i	−0.352362	+	0.935864i	$0.614622\pi$
$968$	− 2.78525i	− 0.0895213i
$969$	− 53.9615i	− 1.73349i
$970$	7.64312i	0.245406i
$971$	−36.1337	−1.15959	−0.579793	−	0.814764i	$-0.696867\pi$
$971$	−36.1337	−1.15959	−0.579793	+	0.814764i	$0.696867\pi$
$972$	−59.8843	−1.92079
$973$	− 15.3146i	− 0.490964i
$974$	5.26374	0.168661
$975$	0	0
$976$	−14.2569	−0.456353
$977$	− 16.7194i	− 0.534901i	−0.963572	−	0.267451i	$-0.913819\pi$
$977$	− 16.7194i	− 0.534901i	0.963572	−	0.267451i	$-0.0861812\pi$
$978$	−0.0327533	−0.00104733
$979$	6.93950	0.221787
$980$	1.56356i	0.0499460i
$981$	− 115.874i	− 3.69956i
$982$	− 22.8913i	− 0.730492i
$983$	− 46.4764i	− 1.48237i	−0.671303	−	0.741183i	$-0.734265\pi$
$983$	− 46.4764i	− 1.48237i	0.671303	−	0.741183i	$-0.265735\pi$
$984$	26.6060	0.848167
$985$	−8.24472	−0.262699
$986$	10.7636i	0.342783i
$987$	23.5010	0.748045
$988$	0	0
$989$	−16.8259	−0.535033
$990$	− 36.6887i	− 1.16604i
$991$	35.3510	1.12296	0.561480	−	0.827490i	$-0.310232\pi$
$991$	35.3510	1.12296	0.561480	+	0.827490i	$0.310232\pi$
$992$	0.597963	0.0189853
$993$	− 82.5118i	− 2.61843i
$994$	− 2.29466i	− 0.0727823i
$995$	− 13.8650i	− 0.439551i
$996$	16.5505i	0.524422i
$997$	1.48780	0.0471190	0.0235595	−	0.999722i	$-0.492500\pi$
$997$	1.48780	0.0471190	0.0235595	+	0.999722i	$0.492500\pi$
$998$	−6.79877	−0.215211
$999$	− 0.669028i	− 0.0211671i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.r.337.12		12
13.3	even	3		182.2.m.b.43.1	✓	12
13.4	even	6		182.2.m.b.127.1	yes	12
13.5	odd	4		2366.2.a.bh.1.6		6
13.8	odd	4		2366.2.a.bf.1.6		6
13.12	even	2	inner	2366.2.d.r.337.6		12
39.17	odd	6		1638.2.bj.g.127.6		12
39.29	odd	6		1638.2.bj.g.1135.4		12
52.3	odd	6		1456.2.cc.d.225.6		12
52.43	odd	6		1456.2.cc.d.673.6		12
91.3	odd	6		1274.2.v.d.667.4		12
91.4	even	6		1274.2.o.d.569.1		12
91.16	even	3		1274.2.o.d.459.4		12
91.17	odd	6		1274.2.o.e.569.3		12
91.30	even	6		1274.2.v.e.361.6		12
91.55	odd	6		1274.2.m.c.589.3		12
91.68	odd	6		1274.2.o.e.459.6		12
91.69	odd	6		1274.2.m.c.491.3		12
91.81	even	3		1274.2.v.e.667.6		12
91.82	odd	6		1274.2.v.d.361.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.1	✓	12	13.3	even	3
182.2.m.b.127.1	yes	12	13.4	even	6
1274.2.m.c.491.3		12	91.69	odd	6
1274.2.m.c.589.3		12	91.55	odd	6
1274.2.o.d.459.4		12	91.16	even	3
1274.2.o.d.569.1		12	91.4	even	6
1274.2.o.e.459.6		12	91.68	odd	6
1274.2.o.e.569.3		12	91.17	odd	6
1274.2.v.d.361.4		12	91.82	odd	6
1274.2.v.d.667.4		12	91.3	odd	6
1274.2.v.e.361.6		12	91.30	even	6
1274.2.v.e.667.6		12	91.81	even	3
1456.2.cc.d.225.6		12	52.3	odd	6
1456.2.cc.d.673.6		12	52.43	odd	6
1638.2.bj.g.127.6		12	39.17	odd	6
1638.2.bj.g.1135.4		12	39.29	odd	6
2366.2.a.bf.1.6		6	13.8	odd	4
2366.2.a.bh.1.6		6	13.5	odd	4
2366.2.d.r.337.6		12	13.12	even	2	inner
2366.2.d.r.337.12		12	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +3.34469 q^{3} -1.00000 q^{4} +1.56356i q^{5} +3.34469i q^{6} -1.00000i q^{7} -1.00000i q^{8} +8.18694 q^{9} -1.56356 q^{10} +2.86614i q^{11} -3.34469 q^{12} +1.00000 q^{14} +5.22961i q^{15} +1.00000 q^{16} +2.22961 q^{17} +8.18694i q^{18} -7.23602i q^{19} -1.56356i q^{20} -3.34469i q^{21} -2.86614 q^{22} +1.66735 q^{23} -3.34469i q^{24} +2.55529 q^{25} +17.3487 q^{27} +1.00000i q^{28} +4.82757 q^{29} -5.22961 q^{30} -0.597963i q^{31} +1.00000i q^{32} +9.58634i q^{33} +2.22961i q^{34} +1.56356 q^{35} -8.18694 q^{36} -0.0385636i q^{37} +7.23602 q^{38} +1.56356 q^{40} +7.95469i q^{41} +3.34469 q^{42} -10.0914 q^{43} -2.86614i q^{44} +12.8007i q^{45} +1.66735i q^{46} +7.02636i q^{47} +3.34469 q^{48} -1.00000 q^{49} +2.55529i q^{50} +7.45736 q^{51} -5.98404 q^{53} +17.3487i q^{54} -4.48137 q^{55} -1.00000 q^{56} -24.2022i q^{57} +4.82757i q^{58} +0.896206i q^{59} -5.22961i q^{60} -14.2569 q^{61} +0.597963 q^{62} -8.18694i q^{63} -1.00000 q^{64} -9.58634 q^{66} +1.64086i q^{67} -2.22961 q^{68} +5.57677 q^{69} +1.56356i q^{70} -2.29466i q^{71} -8.18694i q^{72} +11.2277i q^{73} +0.0385636 q^{74} +8.54664 q^{75} +7.23602i q^{76} +2.86614 q^{77} +4.26098 q^{79} +1.56356i q^{80} +33.4651 q^{81} -7.95469 q^{82} -4.94829i q^{83} +3.34469i q^{84} +3.48613i q^{85} -10.0914i q^{86} +16.1467 q^{87} +2.86614 q^{88} -2.42120i q^{89} -12.8007 q^{90} -1.66735 q^{92} -2.00000i q^{93} -7.02636 q^{94} +11.3139 q^{95} +3.34469i q^{96} -4.88829i q^{97} -1.00000i q^{98} +23.4649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 + 12 * q^9 + 4 * q^10 - 4 * q^12 + 12 * q^14 + 12 * q^16 - 8 * q^17 + 4 * q^22 + 12 * q^23 - 24 * q^25 + 40 * q^27 + 20 * q^29 - 28 * q^30 - 4 * q^35 - 12 * q^36 + 8 * q^38 - 4 * q^40 + 4 * q^42 - 52 * q^43 + 4 * q^48 - 12 * q^49 - 36 * q^51 + 36 * q^53 + 12 * q^55 - 12 * q^56 + 56 * q^61 + 4 * q^62 - 12 * q^64 + 8 * q^68 - 64 * q^69 + 96 * q^75 - 4 * q^77 + 44 * q^79 + 68 * q^81 - 12 * q^82 - 4 * q^87 - 4 * q^88 + 12 * q^90 - 12 * q^92 - 16 * q^94 - 64 * q^95

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