LMFDB - Embedded newform 2366.2.d.r.337.7

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)

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);

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")

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			337.7
Root			$0.500000 - 1.69027i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.r.337.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -2.55629 q^{3} -1.00000 q^{4} -3.48754i q^{5} -2.55629i q^{6} -1.00000i q^{7} -1.00000i q^{8} +3.53463 q^{9} +3.48754 q^{10} -2.68172i q^{11} +2.55629 q^{12} +1.00000 q^{14} +8.91517i q^{15} +1.00000 q^{16} +5.91517 q^{17} +3.53463i q^{18} -5.19793i q^{19} +3.48754i q^{20} +2.55629i q^{21} +2.68172 q^{22} +7.05268 q^{23} +2.55629i q^{24} -7.16292 q^{25} -1.36668 q^{27} +1.00000i q^{28} +7.13278 q^{29} -8.91517 q^{30} +0.782383i q^{31} +1.00000i q^{32} +6.85526i q^{33} +5.91517i q^{34} -3.48754 q^{35} -3.53463 q^{36} +7.81450i q^{37} +5.19793 q^{38} -3.48754 q^{40} +0.157708i q^{41} -2.55629 q^{42} +0.330202 q^{43} +2.68172i q^{44} -12.3272i q^{45} +7.05268i q^{46} -1.60161i q^{47} -2.55629 q^{48} -1.00000 q^{49} -7.16292i q^{50} -15.1209 q^{51} +3.92601 q^{53} -1.36668i q^{54} -9.35259 q^{55} -1.00000 q^{56} +13.2874i q^{57} +7.13278i q^{58} -9.54021i q^{59} -8.91517i q^{60} +15.4105 q^{61} -0.782383 q^{62} -3.53463i q^{63} -1.00000 q^{64} -6.85526 q^{66} +0.966765i q^{67} -5.91517 q^{68} -18.0287 q^{69} -3.48754i q^{70} -4.18658i q^{71} -3.53463i q^{72} -15.0361i q^{73} -7.81450 q^{74} +18.3105 q^{75} +5.19793i q^{76} -2.68172 q^{77} -0.293356 q^{79} -3.48754i q^{80} -7.11027 q^{81} -0.157708 q^{82} -2.87495i q^{83} -2.55629i q^{84} -20.6294i q^{85} +0.330202i q^{86} -18.2335 q^{87} -2.68172 q^{88} +5.21325i q^{89} +12.3272 q^{90} -7.05268 q^{92} -2.00000i q^{93} +1.60161 q^{94} -18.1280 q^{95} -2.55629i q^{96} +3.15946i q^{97} -1.00000i q^{98} -9.47889i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.55629	−1.47588	−0.737938	−	0.674868i	$-0.764200\pi$
$3$	−2.55629	−1.47588	−0.737938	+	0.674868i	$0.764200\pi$
$4$	−1.00000	−0.500000
$5$	− 3.48754i	− 1.55967i	−0.625983	−	0.779837i	$-0.715302\pi$
$5$	− 3.48754i	− 1.55967i	0.625983	−	0.779837i	$-0.284698\pi$
$6$	− 2.55629i	− 1.04360i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	3.53463	1.17821
$10$	3.48754	1.10286
$11$	− 2.68172i	− 0.808569i	−0.914633	−	0.404284i	$-0.867521\pi$
$11$	− 2.68172i	− 0.808569i	0.914633	−	0.404284i	$-0.132479\pi$
$12$	2.55629	0.737938
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	8.91517i	2.30189i
$16$	1.00000	0.250000
$17$	5.91517	1.43464	0.717319	−	0.696745i	$-0.245369\pi$
$17$	5.91517	1.43464	0.717319	+	0.696745i	$0.245369\pi$
$18$	3.53463i	0.833121i
$19$	− 5.19793i	− 1.19249i	−0.802804	−	0.596243i	$-0.796659\pi$
$19$	− 5.19793i	− 1.19249i	0.802804	−	0.596243i	$-0.203341\pi$
$20$	3.48754i	0.779837i
$21$	2.55629i	0.557829i
$22$	2.68172	0.571744
$23$	7.05268	1.47058	0.735292	−	0.677750i	$-0.237045\pi$
$23$	7.05268	1.47058	0.735292	+	0.677750i	$0.237045\pi$
$24$	2.55629i	0.521801i
$25$	−7.16292	−1.43258
$26$	0	0
$27$	−1.36668	−0.263017
$28$	1.00000i	0.188982i
$29$	7.13278	1.32452	0.662262	−	0.749272i	$-0.269596\pi$
$29$	7.13278	1.32452	0.662262	+	0.749272i	$0.269596\pi$
$30$	−8.91517	−1.62768
$31$	0.782383i	0.140520i	0.997529	+	0.0702601i	$0.0223829\pi$
$31$	0.782383i	0.140520i	−0.997529	+	0.0702601i	$0.977617\pi$
$32$	1.00000i	0.176777i
$33$	6.85526i	1.19335i
$34$	5.91517i	1.01444i
$35$	−3.48754	−0.589501
$36$	−3.53463	−0.589105
$37$	7.81450i	1.28470i	0.766413	+	0.642348i	$0.222040\pi$
$37$	7.81450i	1.28470i	−0.766413	+	0.642348i	$0.777960\pi$
$38$	5.19793	0.843215
$39$	0	0
$40$	−3.48754	−0.551428
$41$	0.157708i	0.0246299i	0.999924	+	0.0123149i	$0.00392006\pi$
$41$	0.157708i	0.0246299i	−0.999924	+	0.0123149i	$0.996080\pi$
$42$	−2.55629	−0.394445
$43$	0.330202	0.0503553	0.0251777	−	0.999683i	$-0.491985\pi$
$43$	0.330202	0.0503553	0.0251777	+	0.999683i	$0.491985\pi$
$44$	2.68172i	0.404284i
$45$	− 12.3272i	− 1.83762i
$46$	7.05268i	1.03986i
$47$	− 1.60161i	− 0.233619i	−0.993154	−	0.116810i	$-0.962733\pi$
$47$	− 1.60161i	− 0.233619i	0.993154	−	0.116810i	$-0.0372667\pi$
$48$	−2.55629	−0.368969
$49$	−1.00000	−0.142857
$50$	− 7.16292i	− 1.01299i
$51$	−15.1209	−2.11735
$52$	0	0
$53$	3.92601	0.539279	0.269639	−	0.962961i	$-0.413095\pi$
$53$	3.92601	0.539279	0.269639	+	0.962961i	$0.413095\pi$
$54$	− 1.36668i	− 0.185981i
$55$	−9.35259	−1.26110
$56$	−1.00000	−0.133631
$57$	13.2874i	1.75996i
$58$	7.13278i	0.936580i
$59$	− 9.54021i	− 1.24203i	−0.783799	−	0.621015i	$-0.786721\pi$
$59$	− 9.54021i	− 1.24203i	0.783799	−	0.621015i	$-0.213279\pi$
$60$	− 8.91517i	− 1.15094i
$61$	15.4105	1.97311	0.986556	−	0.163421i	$-0.0522527\pi$
$61$	15.4105	1.97311	0.986556	+	0.163421i	$0.0522527\pi$
$62$	−0.782383	−0.0993627
$63$	− 3.53463i	− 0.445322i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−6.85526	−0.843824
$67$	0.966765i	0.118109i	0.998255	+	0.0590546i	$0.0188086\pi$
$67$	0.966765i	0.118109i	−0.998255	+	0.0590546i	$0.981191\pi$
$68$	−5.91517	−0.717319
$69$	−18.0287	−2.17040
$70$	− 3.48754i	− 0.416840i
$71$	− 4.18658i	− 0.496855i	−0.968650	−	0.248428i	$-0.920086\pi$
$71$	− 4.18658i	− 0.496855i	0.968650	−	0.248428i	$-0.0799138\pi$
$72$	− 3.53463i	− 0.416560i
$73$	− 15.0361i	− 1.75984i	−0.475124	−	0.879919i	$-0.657597\pi$
$73$	− 15.0361i	− 1.75984i	0.475124	−	0.879919i	$-0.342403\pi$
$74$	−7.81450	−0.908417
$75$	18.3105	2.11432
$76$	5.19793i	0.596243i
$77$	−2.68172	−0.305610
$78$	0	0
$79$	−0.293356	−0.0330052	−0.0165026	−	0.999864i	$-0.505253\pi$
$79$	−0.293356	−0.0330052	−0.0165026	+	0.999864i	$0.505253\pi$
$80$	− 3.48754i	− 0.389919i
$81$	−7.11027	−0.790030
$82$	−0.157708	−0.0174159
$83$	− 2.87495i	− 0.315566i	−0.987474	−	0.157783i	$-0.949565\pi$
$83$	− 2.87495i	− 0.315566i	0.987474	−	0.157783i	$-0.0504347\pi$
$84$	− 2.55629i	− 0.278914i
$85$	− 20.6294i	− 2.23757i
$86$	0.330202i	0.0356066i
$87$	−18.2335	−1.95483
$88$	−2.68172	−0.285872
$89$	5.21325i	0.552603i	0.961071	+	0.276302i	$0.0891089\pi$
$89$	5.21325i	0.552603i	−0.961071	+	0.276302i	$0.910891\pi$
$90$	12.3272	1.29940
$91$	0	0
$92$	−7.05268	−0.735292
$93$	− 2.00000i	− 0.207390i
$94$	1.60161	0.165194
$95$	−18.1280	−1.85989
$96$	− 2.55629i	− 0.260901i
$97$	3.15946i	0.320794i	0.987053	+	0.160397i	$0.0512775\pi$
$97$	3.15946i	0.320794i	−0.987053	+	0.160397i	$0.948723\pi$
$98$	− 1.00000i	− 0.101015i
$99$	− 9.47889i	− 0.952664i
$100$	7.16292	0.716292
$101$	−3.78650	−0.376771	−0.188386	−	0.982095i	$-0.560325\pi$
$101$	−3.78650	−0.376771	−0.188386	+	0.982095i	$0.560325\pi$
$102$	− 15.1209i	− 1.49719i
$103$	−6.80839	−0.670850	−0.335425	−	0.942067i	$-0.608880\pi$
$103$	−6.80839	−0.670850	−0.335425	+	0.942067i	$0.608880\pi$
$104$	0	0
$105$	8.91517	0.870031
$106$	3.92601i	0.381328i
$107$	14.3017	1.38259	0.691297	−	0.722571i	$-0.257040\pi$
$107$	14.3017	1.38259	0.691297	+	0.722571i	$0.257040\pi$
$108$	1.36668	0.131508
$109$	4.57669i	0.438367i	0.975684	+	0.219184i	$0.0703394\pi$
$109$	4.57669i	0.438367i	−0.975684	+	0.219184i	$0.929661\pi$
$110$	− 9.35259i	− 0.891735i
$111$	− 19.9762i	− 1.89605i
$112$	− 1.00000i	− 0.0944911i
$113$	−3.01297	−0.283436	−0.141718	−	0.989907i	$-0.545263\pi$
$113$	−3.01297	−0.283436	−0.141718	+	0.989907i	$0.545263\pi$
$114$	−13.2874	−1.24448
$115$	− 24.5965i	− 2.29363i
$116$	−7.13278	−0.662262
$117$	0	0
$118$	9.54021	0.878248
$119$	− 5.91517i	− 0.542242i
$120$	8.91517	0.813840
$121$	3.80839	0.346217
$122$	15.4105i	1.39520i
$123$	− 0.403148i	− 0.0363506i
$124$	− 0.782383i	− 0.0702601i
$125$	7.54326i	0.674689i
$126$	3.53463	0.314890
$127$	−11.1256	−0.987233	−0.493616	−	0.869680i	$-0.664325\pi$
$127$	−11.1256	−0.987233	−0.493616	+	0.869680i	$0.664325\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−0.844093	−0.0743183
$130$	0	0
$131$	14.9117	1.30284	0.651420	−	0.758718i	$-0.274174\pi$
$131$	14.9117	1.30284	0.651420	+	0.758718i	$0.274174\pi$
$132$	− 6.85526i	− 0.596674i
$133$	−5.19793	−0.450717
$134$	−0.966765	−0.0835158
$135$	4.76633i	0.410220i
$136$	− 5.91517i	− 0.507221i
$137$	15.4617i	1.32098i	0.750833	+	0.660492i	$0.229652\pi$
$137$	15.4617i	1.32098i	−0.750833	+	0.660492i	$0.770348\pi$
$138$	− 18.0287i	− 1.53471i
$139$	14.3022	1.21310	0.606548	−	0.795046i	$-0.292554\pi$
$139$	14.3022	1.21310	0.606548	+	0.795046i	$0.292554\pi$
$140$	3.48754	0.294751
$141$	4.09419i	0.344793i
$142$	4.18658	0.351330
$143$	0	0
$144$	3.53463	0.294553
$145$	− 24.8758i	− 2.06583i
$146$	15.0361	1.24439
$147$	2.55629	0.210839
$148$	− 7.81450i	− 0.642348i
$149$	3.55717i	0.291415i	0.989328	+	0.145708i	$0.0465458\pi$
$149$	3.55717i	0.291415i	−0.989328	+	0.145708i	$0.953454\pi$
$150$	18.3105i	1.49505i
$151$	− 9.52740i	− 0.775329i	−0.921801	−	0.387664i	$-0.873282\pi$
$151$	− 9.52740i	− 0.775329i	0.921801	−	0.387664i	$-0.126718\pi$
$152$	−5.19793	−0.421608
$153$	20.9079	1.69031
$154$	− 2.68172i	− 0.216099i
$155$	2.72859	0.219166
$156$	0	0
$157$	20.8345	1.66278	0.831388	−	0.555692i	$-0.187547\pi$
$157$	20.8345	1.66278	0.831388	+	0.555692i	$0.187547\pi$
$158$	− 0.293356i	− 0.0233382i
$159$	−10.0360	−0.795909
$160$	3.48754	0.275714
$161$	− 7.05268i	− 0.555829i
$162$	− 7.11027i	− 0.558636i
$163$	− 6.30603i	− 0.493927i	−0.969025	−	0.246963i	$-0.920567\pi$
$163$	− 6.30603i	− 0.493927i	0.969025	−	0.246963i	$-0.0794327\pi$
$164$	− 0.157708i	− 0.0123149i
$165$	23.9080	1.86123
$166$	2.87495	0.223139
$167$	6.66871i	0.516041i	0.966139	+	0.258020i	$0.0830701\pi$
$167$	6.66871i	0.516041i	−0.966139	+	0.258020i	$0.916930\pi$
$168$	2.55629	0.197222
$169$	0	0
$170$	20.6294	1.58220
$171$	− 18.3728i	− 1.40500i
$172$	−0.330202	−0.0251777
$173$	21.3192	1.62087	0.810434	−	0.585830i	$-0.199231\pi$
$173$	21.3192	1.62087	0.810434	+	0.585830i	$0.199231\pi$
$174$	− 18.2335i	− 1.38228i
$175$	7.16292i	0.541466i
$176$	− 2.68172i	− 0.202142i
$177$	24.3876i	1.83308i
$178$	−5.21325	−0.390750
$179$	−15.4384	−1.15392	−0.576961	−	0.816772i	$-0.695761\pi$
$179$	−15.4384	−1.15392	−0.576961	+	0.816772i	$0.695761\pi$
$180$	12.3272i	0.918812i
$181$	−13.2818	−0.987231	−0.493616	−	0.869680i	$-0.664325\pi$
$181$	−13.2818	−0.987231	−0.493616	+	0.869680i	$0.664325\pi$
$182$	0	0
$183$	−39.3938	−2.91207
$184$	− 7.05268i	− 0.519930i
$185$	27.2534	2.00371
$186$	2.00000	0.146647
$187$	− 15.8628i	− 1.16000i
$188$	1.60161i	0.116810i
$189$	1.36668i	0.0994110i
$190$	− 18.1280i	− 1.31514i
$191$	−11.9246	−0.862833	−0.431417	−	0.902153i	$-0.641986\pi$
$191$	−11.9246	−0.862833	−0.431417	+	0.902153i	$0.641986\pi$
$192$	2.55629	0.184485
$193$	5.34936i	0.385055i	0.981292	+	0.192528i	$0.0616685\pi$
$193$	5.34936i	0.385055i	−0.981292	+	0.192528i	$0.938332\pi$
$194$	−3.15946	−0.226836
$195$	0	0
$196$	1.00000	0.0714286
$197$	− 13.1938i	− 0.940017i	−0.882662	−	0.470009i	$-0.844251\pi$
$197$	− 13.1938i	− 0.940017i	0.882662	−	0.470009i	$-0.155749\pi$
$198$	9.47889	0.673635
$199$	−20.0516	−1.42142	−0.710709	−	0.703486i	$-0.751626\pi$
$199$	−20.0516	−1.42142	−0.710709	+	0.703486i	$0.751626\pi$
$200$	7.16292i	0.506495i
$201$	− 2.47133i	− 0.174314i
$202$	− 3.78650i	− 0.266417i
$203$	− 7.13278i	− 0.500623i
$204$	15.1209	1.05867
$205$	0.550013	0.0384146
$206$	− 6.80839i	− 0.474363i
$207$	24.9286	1.73266
$208$	0	0
$209$	−13.9394	−0.964207
$210$	8.91517i	0.615205i
$211$	−7.96144	−0.548088	−0.274044	−	0.961717i	$-0.588361\pi$
$211$	−7.96144	−0.548088	−0.274044	+	0.961717i	$0.588361\pi$
$212$	−3.92601	−0.269639
$213$	10.7021i	0.733297i
$214$	14.3017i	0.977642i
$215$	− 1.15159i	− 0.0785379i
$216$	1.36668i	0.0929905i
$217$	0.782383	0.0531116
$218$	−4.57669	−0.309972
$219$	38.4366i	2.59730i
$220$	9.35259	0.630552
$221$	0	0
$222$	19.9762	1.34071
$223$	− 21.5417i	− 1.44254i	−0.692653	−	0.721271i	$-0.743558\pi$
$223$	− 21.5417i	− 1.44254i	0.692653	−	0.721271i	$-0.256442\pi$
$224$	1.00000	0.0668153
$225$	−25.3183	−1.68789
$226$	− 3.01297i	− 0.200419i
$227$	− 3.65771i	− 0.242771i	−0.992605	−	0.121385i	$-0.961266\pi$
$227$	− 3.65771i	− 0.242771i	0.992605	−	0.121385i	$-0.0387337\pi$
$228$	− 13.2874i	− 0.879981i
$229$	9.74752i	0.644134i	0.946717	+	0.322067i	$0.104378\pi$
$229$	9.74752i	0.644134i	−0.946717	+	0.322067i	$0.895622\pi$
$230$	24.5965	1.62184
$231$	6.85526	0.451043
$232$	− 7.13278i	− 0.468290i
$233$	−2.72895	−0.178779	−0.0893897	−	0.995997i	$-0.528492\pi$
$233$	−2.72895	−0.178779	−0.0893897	+	0.995997i	$0.528492\pi$
$234$	0	0
$235$	−5.58568	−0.364370
$236$	9.54021i	0.621015i
$237$	0.749905	0.0487115
$238$	5.91517	0.383423
$239$	12.2347i	0.791400i	0.918380	+	0.395700i	$0.129498\pi$
$239$	12.2347i	0.791400i	−0.918380	+	0.395700i	$0.870502\pi$
$240$	8.91517i	0.575471i
$241$	24.2176i	1.56000i	0.625782	+	0.779998i	$0.284780\pi$
$241$	24.2176i	1.56000i	−0.625782	+	0.779998i	$0.715220\pi$
$242$	3.80839i	0.244812i
$243$	22.2760	1.42900
$244$	−15.4105	−0.986556
$245$	3.48754i	0.222811i
$246$	0.403148	0.0257038
$247$	0	0
$248$	0.782383	0.0496814
$249$	7.34921i	0.465737i
$250$	−7.54326	−0.477077
$251$	−2.01371	−0.127104	−0.0635521	−	0.997979i	$-0.520243\pi$
$251$	−2.01371	−0.127104	−0.0635521	+	0.997979i	$0.520243\pi$
$252$	3.53463i	0.222661i
$253$	− 18.9133i	− 1.18907i
$254$	− 11.1256i	− 0.698079i
$255$	52.7347i	3.30237i
$256$	1.00000	0.0625000
$257$	2.14218	0.133625	0.0668127	−	0.997766i	$-0.478717\pi$
$257$	2.14218	0.133625	0.0668127	+	0.997766i	$0.478717\pi$
$258$	− 0.844093i	− 0.0525509i
$259$	7.81450	0.485570
$260$	0	0
$261$	25.2118	1.56057
$262$	14.9117i	0.921247i
$263$	−10.8626	−0.669818	−0.334909	−	0.942250i	$-0.608706\pi$
$263$	−10.8626	−0.669818	−0.334909	+	0.942250i	$0.608706\pi$
$264$	6.85526	0.421912
$265$	− 13.6921i	− 0.841099i
$266$	− 5.19793i	− 0.318705i
$267$	− 13.3266i	− 0.815574i
$268$	− 0.966765i	− 0.0590546i
$269$	−14.8051	−0.902686	−0.451343	−	0.892351i	$-0.649055\pi$
$269$	−14.8051	−0.902686	−0.451343	+	0.892351i	$0.649055\pi$
$270$	−4.76633	−0.290070
$271$	0.0646361i	0.00392636i	0.999998	+	0.00196318i	$0.000624900\pi$
$271$	0.0646361i	0.00392636i	−0.999998	+	0.00196318i	$0.999375\pi$
$272$	5.91517	0.358660
$273$	0	0
$274$	−15.4617	−0.934077
$275$	19.2089i	1.15834i
$276$	18.0287	1.08520
$277$	−4.25115	−0.255427	−0.127713	−	0.991811i	$-0.540764\pi$
$277$	−4.25115	−0.255427	−0.127713	+	0.991811i	$0.540764\pi$
$278$	14.3022i	0.857789i
$279$	2.76544i	0.165562i
$280$	3.48754i	0.208420i
$281$	− 11.0454i	− 0.658916i	−0.944170	−	0.329458i	$-0.893134\pi$
$281$	− 11.0454i	− 0.658916i	0.944170	−	0.329458i	$-0.106866\pi$
$282$	−4.09419	−0.243805
$283$	−11.2854	−0.670849	−0.335424	−	0.942067i	$-0.608880\pi$
$283$	−11.2854	−0.670849	−0.335424	+	0.942067i	$0.608880\pi$
$284$	4.18658i	0.248428i
$285$	46.3404	2.74497
$286$	0	0
$287$	0.157708	0.00930922
$288$	3.53463i	0.208280i
$289$	17.9892	1.05819
$290$	24.8758	1.46076
$291$	− 8.07650i	− 0.473453i
$292$	15.0361i	0.879919i
$293$	26.0442i	1.52152i	0.649036	+	0.760758i	$0.275172\pi$
$293$	26.0442i	1.52152i	−0.649036	+	0.760758i	$0.724828\pi$
$294$	2.55629i	0.149086i
$295$	−33.2719	−1.93716
$296$	7.81450	0.454209
$297$	3.66504i	0.212667i
$298$	−3.55717	−0.206062
$299$	0	0
$300$	−18.3105	−1.05716
$301$	− 0.330202i	− 0.0190325i
$302$	9.52740	0.548240
$303$	9.67941	0.556067
$304$	− 5.19793i	− 0.298122i
$305$	− 53.7447i	− 3.07741i
$306$	20.9079i	1.19523i
$307$	− 25.0551i	− 1.42997i	−0.699139	−	0.714986i	$-0.746433\pi$
$307$	− 25.0551i	− 1.42997i	0.699139	−	0.714986i	$-0.253567\pi$
$308$	2.68172	0.152805
$309$	17.4042	0.990092
$310$	2.72859i	0.154974i
$311$	−32.4330	−1.83911	−0.919554	−	0.392964i	$-0.871450\pi$
$311$	−32.4330	−1.83911	−0.919554	+	0.392964i	$0.871450\pi$
$312$	0	0
$313$	2.22517	0.125774	0.0628870	−	0.998021i	$-0.479969\pi$
$313$	2.22517	0.125774	0.0628870	+	0.998021i	$0.479969\pi$
$314$	20.8345i	1.17576i
$315$	−12.3272	−0.694557
$316$	0.293356	0.0165026
$317$	3.83753i	0.215537i	0.994176	+	0.107769i	$0.0343706\pi$
$317$	3.83753i	0.215537i	−0.994176	+	0.107769i	$0.965629\pi$
$318$	− 10.0360i	− 0.562793i
$319$	− 19.1281i	− 1.07097i
$320$	3.48754i	0.194959i
$321$	−36.5592	−2.04054
$322$	7.05268	0.393030
$323$	− 30.7466i	− 1.71079i
$324$	7.11027	0.395015
$325$	0	0
$326$	6.30603	0.349259
$327$	− 11.6994i	− 0.646976i
$328$	0.157708	0.00870797
$329$	−1.60161	−0.0882997
$330$	23.9080i	1.31609i
$331$	− 6.08365i	− 0.334387i	−0.985924	−	0.167194i	$-0.946529\pi$
$331$	− 6.08365i	− 0.334387i	0.985924	−	0.167194i	$-0.0534705\pi$
$332$	2.87495i	0.157783i
$333$	27.6214i	1.51364i
$334$	−6.66871	−0.364896
$335$	3.37163	0.184212
$336$	2.55629i	0.139457i
$337$	−19.3746	−1.05540	−0.527700	−	0.849431i	$-0.676946\pi$
$337$	−19.3746	−1.05540	−0.527700	+	0.849431i	$0.676946\pi$
$338$	0	0
$339$	7.70202	0.418316
$340$	20.6294i	1.11878i
$341$	2.09813	0.113620
$342$	18.3728	0.993485
$343$	1.00000i	0.0539949i
$344$	− 0.330202i	− 0.0178033i
$345$	62.8758i	3.38512i
$346$	21.3192i	1.14613i
$347$	−9.02056	−0.484249	−0.242124	−	0.970245i	$-0.577844\pi$
$347$	−9.02056	−0.484249	−0.242124	+	0.970245i	$0.577844\pi$
$348$	18.2335	0.977417
$349$	6.97685i	0.373462i	0.982411	+	0.186731i	$0.0597893\pi$
$349$	6.97685i	0.373462i	−0.982411	+	0.186731i	$0.940211\pi$
$350$	−7.16292	−0.382874
$351$	0	0
$352$	2.68172	0.142936
$353$	− 25.0386i	− 1.33267i	−0.745653	−	0.666335i	$-0.767862\pi$
$353$	− 25.0386i	− 1.33267i	0.745653	−	0.666335i	$-0.232138\pi$
$354$	−24.3876	−1.29619
$355$	−14.6008	−0.774932
$356$	− 5.21325i	− 0.276302i
$357$	15.1209i	0.800283i
$358$	− 15.4384i	− 0.815946i
$359$	37.6090i	1.98493i	0.122545	+	0.992463i	$0.460894\pi$
$359$	37.6090i	1.98493i	−0.122545	+	0.992463i	$0.539106\pi$
$360$	−12.3272	−0.649698
$361$	−8.01845	−0.422024
$362$	− 13.2818i	− 0.698078i
$363$	−9.73535	−0.510973
$364$	0	0
$365$	−52.4388	−2.74477
$366$	− 39.3938i	− 2.05914i
$367$	21.0910	1.10094	0.550470	−	0.834855i	$-0.314449\pi$
$367$	21.0910	1.10094	0.550470	+	0.834855i	$0.314449\pi$
$368$	7.05268	0.367646
$369$	0.557440i	0.0290192i
$370$	27.2534i	1.41684i
$371$	− 3.92601i	− 0.203828i
$372$	2.00000i	0.103695i
$373$	14.0942	0.729768	0.364884	−	0.931053i	$-0.381109\pi$
$373$	14.0942	0.729768	0.364884	+	0.931053i	$0.381109\pi$
$374$	15.8628	0.820246
$375$	− 19.2828i	− 0.995758i
$376$	−1.60161	−0.0825968
$377$	0	0
$378$	−1.36668	−0.0702942
$379$	33.1137i	1.70093i	0.526028	+	0.850467i	$0.323681\pi$
$379$	33.1137i	1.70093i	−0.526028	+	0.850467i	$0.676319\pi$
$380$	18.1280	0.929945
$381$	28.4402	1.45703
$382$	− 11.9246i	− 0.610115i
$383$	25.9321i	1.32507i	0.749032	+	0.662534i	$0.230519\pi$
$383$	25.9321i	1.32507i	−0.749032	+	0.662534i	$0.769481\pi$
$384$	2.55629i	0.130450i
$385$	9.35259i	0.476652i
$386$	−5.34936	−0.272275
$387$	1.16714	0.0593292
$388$	− 3.15946i	− 0.160397i
$389$	−30.5647	−1.54969	−0.774847	−	0.632149i	$-0.782173\pi$
$389$	−30.5647	−1.54969	−0.774847	+	0.632149i	$0.782173\pi$
$390$	0	0
$391$	41.7178	2.10976
$392$	1.00000i	0.0505076i
$393$	−38.1186	−1.92283
$394$	13.1938	0.664692
$395$	1.02309i	0.0514773i
$396$	9.47889i	0.476332i
$397$	− 22.4614i	− 1.12731i	−0.826012	−	0.563653i	$-0.809396\pi$
$397$	− 22.4614i	− 1.12731i	0.826012	−	0.563653i	$-0.190604\pi$
$398$	− 20.0516i	− 1.00509i
$399$	13.2874	0.665203
$400$	−7.16292	−0.358146
$401$	− 17.0288i	− 0.850376i	−0.905105	−	0.425188i	$-0.860208\pi$
$401$	− 17.0288i	− 0.850376i	0.905105	−	0.425188i	$-0.139792\pi$
$402$	2.47133	0.123259
$403$	0	0
$404$	3.78650	0.188386
$405$	24.7973i	1.23219i
$406$	7.13278	0.353994
$407$	20.9563	1.03876
$408$	15.1209i	0.748596i
$409$	− 5.13532i	− 0.253925i	−0.991908	−	0.126963i	$-0.959477\pi$
$409$	− 5.13532i	− 0.253925i	0.991908	−	0.126963i	$-0.0405228\pi$
$410$	0.550013i	0.0271632i
$411$	− 39.5247i	− 1.94961i
$412$	6.80839	0.335425
$413$	−9.54021	−0.469443
$414$	24.9286i	1.22517i
$415$	−10.0265	−0.492181
$416$	0	0
$417$	−36.5606	−1.79038
$418$	− 13.9394i	− 0.681797i
$419$	−31.8836	−1.55762	−0.778808	−	0.627263i	$-0.784175\pi$
$419$	−31.8836	−1.55762	−0.778808	+	0.627263i	$0.784175\pi$
$420$	−8.91517	−0.435016
$421$	− 14.7648i	− 0.719594i	−0.933031	−	0.359797i	$-0.882846\pi$
$421$	− 14.7648i	− 0.719594i	0.933031	−	0.359797i	$-0.117154\pi$
$422$	− 7.96144i	− 0.387557i
$423$	− 5.66111i	− 0.275252i
$424$	− 3.92601i	− 0.190664i
$425$	−42.3698	−2.05524
$426$	−10.7021	−0.518519
$427$	− 15.4105i	− 0.745767i
$428$	−14.3017	−0.691297
$429$	0	0
$430$	1.15159	0.0555347
$431$	35.1088i	1.69113i	0.533872	+	0.845565i	$0.320736\pi$
$431$	35.1088i	1.69113i	−0.533872	+	0.845565i	$0.679264\pi$
$432$	−1.36668	−0.0657542
$433$	3.97251	0.190907	0.0954533	−	0.995434i	$-0.469570\pi$
$433$	3.97251	0.190907	0.0954533	+	0.995434i	$0.469570\pi$
$434$	0.782383i	0.0375556i
$435$	63.5899i	3.04890i
$436$	− 4.57669i	− 0.219184i
$437$	− 36.6593i	− 1.75365i
$438$	−38.4366	−1.83657
$439$	−5.75277	−0.274565	−0.137282	−	0.990532i	$-0.543837\pi$
$439$	−5.75277	−0.274565	−0.137282	+	0.990532i	$0.543837\pi$
$440$	9.35259i	0.445867i
$441$	−3.53463	−0.168316
$442$	0	0
$443$	−27.0804	−1.28663	−0.643315	−	0.765602i	$-0.722441\pi$
$443$	−27.0804	−1.28663	−0.643315	+	0.765602i	$0.722441\pi$
$444$	19.9762i	0.948026i
$445$	18.1814	0.861881
$446$	21.5417	1.02003
$447$	− 9.09318i	− 0.430092i
$448$	1.00000i	0.0472456i
$449$	− 8.24914i	− 0.389301i	−0.980873	−	0.194650i	$-0.937643\pi$
$449$	− 8.24914i	− 0.389301i	0.980873	−	0.194650i	$-0.0623573\pi$
$450$	− 25.3183i	− 1.19351i
$451$	0.422929	0.0199149
$452$	3.01297	0.141718
$453$	24.3548i	1.14429i
$454$	3.65771	0.171665
$455$	0	0
$456$	13.2874	0.622241
$457$	38.6967i	1.81015i	0.425247	+	0.905077i	$0.360187\pi$
$457$	38.6967i	1.81015i	−0.425247	+	0.905077i	$0.639813\pi$
$458$	−9.74752	−0.455472
$459$	−8.08411	−0.377334
$460$	24.5965i	1.14682i
$461$	− 13.1348i	− 0.611751i	−0.952072	−	0.305875i	$-0.901051\pi$
$461$	− 13.1348i	− 0.611751i	0.952072	−	0.305875i	$-0.0989491\pi$
$462$	6.85526i	0.318935i
$463$	− 6.98417i	− 0.324582i	−0.986743	−	0.162291i	$-0.948112\pi$
$463$	− 6.98417i	− 0.324582i	0.986743	−	0.162291i	$-0.0518883\pi$
$464$	7.13278	0.331131
$465$	−6.97507	−0.323461
$466$	− 2.72895i	− 0.126416i
$467$	5.62691	0.260382	0.130191	−	0.991489i	$-0.458441\pi$
$467$	5.62691	0.260382	0.130191	+	0.991489i	$0.458441\pi$
$468$	0	0
$469$	0.966765	0.0446411
$470$	− 5.58568i	− 0.257648i
$471$	−53.2591	−2.45405
$472$	−9.54021	−0.439124
$473$	− 0.885509i	− 0.0407158i
$474$	0.749905i	0.0344443i
$475$	37.2323i	1.70834i
$476$	5.91517i	0.271121i
$477$	13.8770	0.635384
$478$	−12.2347	−0.559604
$479$	25.1191i	1.14772i	0.818953	+	0.573861i	$0.194555\pi$
$479$	25.1191i	1.14772i	−0.818953	+	0.573861i	$0.805445\pi$
$480$	−8.91517	−0.406920
$481$	0	0
$482$	−24.2176	−1.10308
$483$	18.0287i	0.820334i
$484$	−3.80839	−0.173108
$485$	11.0187	0.500334
$486$	22.2760i	1.01046i
$487$	17.6758i	0.800968i	0.916304	+	0.400484i	$0.131158\pi$
$487$	17.6758i	0.800968i	−0.916304	+	0.400484i	$0.868842\pi$
$488$	− 15.4105i	− 0.697601i
$489$	16.1201i	0.728975i
$490$	−3.48754	−0.157551
$491$	−31.9949	−1.44391	−0.721956	−	0.691939i	$-0.756757\pi$
$491$	−31.9949	−1.44391	−0.721956	+	0.691939i	$0.756757\pi$
$492$	0.403148i	0.0181753i
$493$	42.1916	1.90021
$494$	0	0
$495$	−33.0580	−1.48585
$496$	0.782383i	0.0351300i
$497$	−4.18658	−0.187794
$498$	−7.34921	−0.329326
$499$	− 11.6416i	− 0.521149i	−0.965454	−	0.260574i	$-0.916088\pi$
$499$	− 11.6416i	− 0.521149i	0.965454	−	0.260574i	$-0.0839119\pi$
$500$	− 7.54326i	− 0.337345i
$501$	− 17.0472i	− 0.761612i
$502$	− 2.01371i	− 0.0898762i
$503$	15.0353	0.670390	0.335195	−	0.942149i	$-0.391198\pi$
$503$	15.0353	0.670390	0.335195	+	0.942149i	$0.391198\pi$
$504$	−3.53463	−0.157445
$505$	13.2056i	0.587640i
$506$	18.9133	0.840798
$507$	0	0
$508$	11.1256	0.493616
$509$	2.56096i	0.113513i	0.998388	+	0.0567563i	$0.0180758\pi$
$509$	2.56096i	0.113513i	−0.998388	+	0.0567563i	$0.981924\pi$
$510$	−52.7347	−2.33513
$511$	−15.0361	−0.665156
$512$	1.00000i	0.0441942i
$513$	7.10388i	0.313644i
$514$	2.14218i	0.0944874i
$515$	23.7445i	1.04631i
$516$	0.844093	0.0371591
$517$	−4.29507	−0.188897
$518$	7.81450i	0.343349i
$519$	−54.4981	−2.39220
$520$	0	0
$521$	−31.0544	−1.36052	−0.680259	−	0.732972i	$-0.738133\pi$
$521$	−31.0544	−1.36052	−0.680259	+	0.732972i	$0.738133\pi$
$522$	25.2118i	1.10349i
$523$	−4.36360	−0.190807	−0.0954035	−	0.995439i	$-0.530414\pi$
$523$	−4.36360	−0.190807	−0.0954035	+	0.995439i	$0.530414\pi$
$524$	−14.9117	−0.651420
$525$	− 18.3105i	− 0.799136i
$526$	− 10.8626i	− 0.473633i
$527$	4.62793i	0.201596i
$528$	6.85526i	0.298337i
$529$	26.7402	1.16262
$530$	13.6921	0.594747
$531$	− 33.7211i	− 1.46337i
$532$	5.19793	0.225359
$533$	0	0
$534$	13.3266	0.576698
$535$	− 49.8776i	− 2.15640i
$536$	0.966765	0.0417579
$537$	39.4651	1.70305
$538$	− 14.8051i	− 0.638295i
$539$	2.68172i	0.115510i
$540$	− 4.76633i	− 0.205110i
$541$	17.2191i	0.740305i	0.928971	+	0.370152i	$0.120695\pi$
$541$	17.2191i	0.740305i	−0.928971	+	0.370152i	$0.879305\pi$
$542$	−0.0646361	−0.00277636
$543$	33.9523	1.45703
$544$	5.91517i	0.253611i
$545$	15.9614	0.683710
$546$	0	0
$547$	42.8331	1.83141	0.915706	−	0.401849i	$-0.131632\pi$
$547$	42.8331	1.83141	0.915706	+	0.401849i	$0.131632\pi$
$548$	− 15.4617i	− 0.660492i
$549$	54.4705	2.32474
$550$	−19.2089	−0.819071
$551$	− 37.0757i	− 1.57948i
$552$	18.0287i	0.767353i
$553$	0.293356i	0.0124748i
$554$	− 4.25115i	− 0.180614i
$555$	−69.6676	−2.95722
$556$	−14.3022	−0.606548
$557$	− 24.2206i	− 1.02626i	−0.858312	−	0.513129i	$-0.828486\pi$
$557$	− 24.2206i	− 1.02626i	0.858312	−	0.513129i	$-0.171514\pi$
$558$	−2.76544	−0.117070
$559$	0	0
$560$	−3.48754	−0.147375
$561$	40.5500i	1.71202i
$562$	11.0454	0.465924
$563$	13.2481	0.558341	0.279170	−	0.960242i	$-0.409941\pi$
$563$	13.2481	0.558341	0.279170	+	0.960242i	$0.409941\pi$
$564$	− 4.09419i	− 0.172396i
$565$	10.5078i	0.442068i
$566$	− 11.2854i	− 0.474362i
$567$	7.11027i	0.298603i
$568$	−4.18658	−0.175665
$569$	24.9921	1.04772	0.523861	−	0.851804i	$-0.324491\pi$
$569$	24.9921	1.04772	0.523861	+	0.851804i	$0.324491\pi$
$570$	46.3404i	1.94099i
$571$	22.5276	0.942750	0.471375	−	0.881933i	$-0.343758\pi$
$571$	22.5276	0.942750	0.471375	+	0.881933i	$0.343758\pi$
$572$	0	0
$573$	30.4827	1.27344
$574$	0.157708i	0.00658261i
$575$	−50.5177	−2.10674
$576$	−3.53463	−0.147276
$577$	12.9848i	0.540564i	0.962781	+	0.270282i	$0.0871170\pi$
$577$	12.9848i	0.540564i	−0.962781	+	0.270282i	$0.912883\pi$
$578$	17.9892i	0.748252i
$579$	− 13.6745i	− 0.568294i
$580$	24.8758i	1.03291i
$581$	−2.87495	−0.119273
$582$	8.07650	0.334782
$583$	− 10.5285i	− 0.436044i
$584$	−15.0361	−0.622197
$585$	0	0
$586$	−26.0442	−1.07587
$587$	3.49432i	0.144226i	0.997396	+	0.0721131i	$0.0229742\pi$
$587$	3.49432i	0.144226i	−0.997396	+	0.0721131i	$0.977026\pi$
$588$	−2.55629	−0.105420
$589$	4.06677	0.167568
$590$	− 33.2719i	− 1.36978i
$591$	33.7271i	1.38735i
$592$	7.81450i	0.321174i
$593$	23.2140i	0.953283i	0.879098	+	0.476642i	$0.158146\pi$
$593$	23.2140i	0.953283i	−0.879098	+	0.476642i	$0.841854\pi$
$594$	−3.66504	−0.150378
$595$	−20.6294	−0.845721
$596$	− 3.55717i	− 0.145708i
$597$	51.2577	2.09784
$598$	0	0
$599$	18.3645	0.750354	0.375177	−	0.926953i	$-0.377582\pi$
$599$	18.3645	0.750354	0.375177	+	0.926953i	$0.377582\pi$
$600$	− 18.3105i	− 0.747524i
$601$	−4.75965	−0.194150	−0.0970751	−	0.995277i	$-0.530949\pi$
$601$	−4.75965	−0.194150	−0.0970751	+	0.995277i	$0.530949\pi$
$602$	0.330202	0.0134580
$603$	3.41716i	0.139157i
$604$	9.52740i	0.387664i
$605$	− 13.2819i	− 0.539986i
$606$	9.67941i	0.393199i
$607$	20.9656	0.850968	0.425484	−	0.904966i	$-0.360104\pi$
$607$	20.9656	0.850968	0.425484	+	0.904966i	$0.360104\pi$
$608$	5.19793	0.210804
$609$	18.2335i	0.738858i
$610$	53.7447	2.17606
$611$	0	0
$612$	−20.9079	−0.845153
$613$	− 29.3124i	− 1.18392i	−0.805968	−	0.591959i	$-0.798355\pi$
$613$	− 29.3124i	− 1.18392i	0.805968	−	0.591959i	$-0.201645\pi$
$614$	25.0551	1.01114
$615$	−1.40599	−0.0566952
$616$	2.68172i	0.108050i
$617$	5.26343i	0.211898i	0.994372	+	0.105949i	$0.0337880\pi$
$617$	5.26343i	0.211898i	−0.994372	+	0.105949i	$0.966212\pi$
$618$	17.4042i	0.700101i
$619$	10.9663i	0.440774i	0.975413	+	0.220387i	$0.0707320\pi$
$619$	10.9663i	0.440774i	−0.975413	+	0.220387i	$0.929268\pi$
$620$	−2.72859	−0.109583
$621$	−9.63872	−0.386788
$622$	− 32.4330i	− 1.30045i
$623$	5.21325	0.208864
$624$	0	0
$625$	−9.50720	−0.380288
$626$	2.22517i	0.0889357i
$627$	35.6331	1.42305
$628$	−20.8345	−0.831388
$629$	46.2241i	1.84307i
$630$	− 12.3272i	− 0.491126i
$631$	24.3229i	0.968278i	0.874991	+	0.484139i	$0.160867\pi$
$631$	24.3229i	0.968278i	−0.874991	+	0.484139i	$0.839133\pi$
$632$	0.293356i	0.0116691i
$633$	20.3518	0.808910
$634$	−3.83753	−0.152408
$635$	38.8008i	1.53976i
$636$	10.0360	0.397954
$637$	0	0
$638$	19.1281	0.757289
$639$	− 14.7980i	− 0.585400i
$640$	−3.48754	−0.137857
$641$	−1.30118	−0.0513937	−0.0256968	−	0.999670i	$-0.508180\pi$
$641$	−1.30118	−0.0513937	−0.0256968	+	0.999670i	$0.508180\pi$
$642$	− 36.5592i	− 1.44288i
$643$	− 5.62971i	− 0.222014i	−0.993820	−	0.111007i	$-0.964592\pi$
$643$	− 5.62971i	− 0.222014i	0.993820	−	0.111007i	$-0.0354076\pi$
$644$	7.05268i	0.277914i
$645$	2.94381i	0.115912i
$646$	30.7466	1.20971
$647$	11.8127	0.464405	0.232202	−	0.972667i	$-0.425407\pi$
$647$	11.8127	0.464405	0.232202	+	0.972667i	$0.425407\pi$
$648$	7.11027i	0.279318i
$649$	−25.5842	−1.00427
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	6.30603i	0.246963i
$653$	−3.12013	−0.122100	−0.0610500	−	0.998135i	$-0.519445\pi$
$653$	−3.12013	−0.122100	−0.0610500	+	0.998135i	$0.519445\pi$
$654$	11.6994	0.457481
$655$	− 52.0050i	− 2.03201i
$656$	0.157708i	0.00615747i
$657$	− 53.1469i	− 2.07346i
$658$	− 1.60161i	− 0.0624373i
$659$	37.5067	1.46105	0.730526	−	0.682885i	$-0.239275\pi$
$659$	37.5067	1.46105	0.730526	+	0.682885i	$0.239275\pi$
$660$	−23.9080	−0.930616
$661$	35.7746i	1.39147i	0.718299	+	0.695735i	$0.244921\pi$
$661$	35.7746i	1.39147i	−0.718299	+	0.695735i	$0.755079\pi$
$662$	6.08365	0.236448
$663$	0	0
$664$	−2.87495	−0.111570
$665$	18.1280i	0.702972i
$666$	−27.6214	−1.07031
$667$	50.3052	1.94783
$668$	− 6.66871i	− 0.258020i
$669$	55.0670i	2.12901i
$670$	3.37163i	0.130257i
$671$	− 41.3266i	− 1.59540i
$672$	−2.55629	−0.0986111
$673$	8.62162	0.332339	0.166170	−	0.986097i	$-0.446860\pi$
$673$	8.62162	0.332339	0.166170	+	0.986097i	$0.446860\pi$
$674$	− 19.3746i	− 0.746281i
$675$	9.78938	0.376793
$676$	0	0
$677$	−15.5551	−0.597829	−0.298915	−	0.954280i	$-0.596625\pi$
$677$	−15.5551	−0.597829	−0.298915	+	0.954280i	$0.596625\pi$
$678$	7.70202i	0.295794i
$679$	3.15946	0.121249
$680$	−20.6294	−0.791100
$681$	9.35019i	0.358300i
$682$	2.09813i	0.0803416i
$683$	8.89795i	0.340471i	0.985403	+	0.170235i	$0.0544528\pi$
$683$	8.89795i	0.340471i	−0.985403	+	0.170235i	$0.945547\pi$
$684$	18.3728i	0.702500i
$685$	53.9233	2.06030
$686$	−1.00000	−0.0381802
$687$	− 24.9175i	− 0.950663i
$688$	0.330202	0.0125888
$689$	0	0
$690$	−62.8758	−2.39364
$691$	− 38.1797i	− 1.45243i	−0.687470	−	0.726213i	$-0.741279\pi$
$691$	− 38.1797i	− 1.45243i	0.687470	−	0.726213i	$-0.258721\pi$
$692$	−21.3192	−0.810434
$693$	−9.47889	−0.360073
$694$	− 9.02056i	− 0.342416i
$695$	− 49.8795i	− 1.89204i
$696$	18.2335i	0.691138i
$697$	0.932870i	0.0353350i
$698$	−6.97685	−0.264078
$699$	6.97600	0.263856
$700$	− 7.16292i	− 0.270733i
$701$	44.0952	1.66545	0.832727	−	0.553684i	$-0.186779\pi$
$701$	44.0952	1.66545	0.832727	+	0.553684i	$0.186779\pi$
$702$	0	0
$703$	40.6192	1.53198
$704$	2.68172i	0.101071i
$705$	14.2786	0.537765
$706$	25.0386	0.942340
$707$	3.78650i	0.142406i
$708$	− 24.3876i	− 0.916541i
$709$	− 12.2637i	− 0.460573i	−0.973123	−	0.230287i	$-0.926034\pi$
$709$	− 12.2637i	− 0.460573i	0.973123	−	0.230287i	$-0.0739663\pi$
$710$	− 14.6008i	− 0.547960i
$711$	−1.03691	−0.0388870
$712$	5.21325	0.195375
$713$	5.51789i	0.206647i
$714$	−15.1209	−0.565885
$715$	0	0
$716$	15.4384	0.576961
$717$	− 31.2756i	− 1.16801i
$718$	−37.6090	−1.40355
$719$	−27.1933	−1.01414	−0.507070	−	0.861905i	$-0.669272\pi$
$719$	−27.1933	−1.01414	−0.507070	+	0.861905i	$0.669272\pi$
$720$	− 12.3272i	− 0.459406i
$721$	6.80839i	0.253558i
$722$	− 8.01845i	− 0.298416i
$723$	− 61.9074i	− 2.30236i
$724$	13.2818	0.493616
$725$	−51.0915	−1.89749
$726$	− 9.73535i	− 0.361313i
$727$	−18.5289	−0.687200	−0.343600	−	0.939116i	$-0.611646\pi$
$727$	−18.5289	−0.687200	−0.343600	+	0.939116i	$0.611646\pi$
$728$	0	0
$729$	−35.6131	−1.31900
$730$	− 52.4388i	− 1.94085i
$731$	1.95320	0.0722417
$732$	39.3938	1.45604
$733$	− 50.8986i	− 1.87998i	−0.341196	−	0.939992i	$-0.610832\pi$
$733$	− 50.8986i	− 1.87998i	0.341196	−	0.939992i	$-0.389168\pi$
$734$	21.0910i	0.778482i
$735$	− 8.91517i	− 0.328841i
$736$	7.05268i	0.259965i
$737$	2.59259	0.0954993
$738$	−0.557440	−0.0205197
$739$	− 8.58969i	− 0.315977i	−0.987441	−	0.157988i	$-0.949499\pi$
$739$	− 8.58969i	− 0.315977i	0.987441	−	0.157988i	$-0.0505009\pi$
$740$	−27.2534	−1.00185
$741$	0	0
$742$	3.92601	0.144128
$743$	38.1873i	1.40095i	0.713675	+	0.700477i	$0.247029\pi$
$743$	38.1873i	1.40095i	−0.713675	+	0.700477i	$0.752971\pi$
$744$	−2.00000	−0.0733236
$745$	12.4058	0.454512
$746$	14.0942i	0.516024i
$747$	− 10.1619i	− 0.371804i
$748$	15.8628i	0.580002i
$749$	− 14.3017i	− 0.522572i
$750$	19.2828	0.704107
$751$	2.84971	0.103987	0.0519937	−	0.998647i	$-0.483442\pi$
$751$	2.84971	0.103987	0.0519937	+	0.998647i	$0.483442\pi$
$752$	− 1.60161i	− 0.0584048i
$753$	5.14763	0.187590
$754$	0	0
$755$	−33.2272	−1.20926
$756$	− 1.36668i	− 0.0497055i
$757$	19.2790	0.700707	0.350354	−	0.936618i	$-0.386061\pi$
$757$	19.2790	0.700707	0.350354	+	0.936618i	$0.386061\pi$
$758$	−33.1137	−1.20274
$759$	48.3479i	1.75492i
$760$	18.1280i	0.657570i
$761$	11.5840i	0.419919i	0.977710	+	0.209959i	$0.0673332\pi$
$761$	11.5840i	0.419919i	−0.977710	+	0.209959i	$0.932667\pi$
$762$	28.4402i	1.03028i
$763$	4.57669	0.165687
$764$	11.9246	0.431417
$765$	− 72.9172i	− 2.63633i
$766$	−25.9321	−0.936964
$767$	0	0
$768$	−2.55629	−0.0922423
$769$	24.4203i	0.880619i	0.897846	+	0.440310i	$0.145131\pi$
$769$	24.4203i	0.880619i	−0.897846	+	0.440310i	$0.854869\pi$
$770$	−9.35259	−0.337044
$771$	−5.47603	−0.197214
$772$	− 5.34936i	− 0.192528i
$773$	− 6.98615i	− 0.251275i	−0.992076	−	0.125637i	$-0.959902\pi$
$773$	− 6.98615i	− 0.251275i	0.992076	−	0.125637i	$-0.0400975\pi$
$774$	1.16714i	0.0419521i
$775$	− 5.60415i	− 0.201307i
$776$	3.15946	0.113418
$777$	−19.9762	−0.716640
$778$	− 30.5647i	− 1.09580i
$779$	0.819755	0.0293708
$780$	0	0
$781$	−11.2272	−0.401741
$782$	41.7178i	1.49182i
$783$	−9.74820	−0.348372
$784$	−1.00000	−0.0357143
$785$	− 72.6612i	− 2.59339i
$786$	− 38.1186i	− 1.35965i
$787$	17.3473i	0.618364i	0.951003	+	0.309182i	$0.100055\pi$
$787$	17.3473i	0.618364i	−0.951003	+	0.309182i	$0.899945\pi$
$788$	13.1938i	0.470009i
$789$	27.7681	0.988569
$790$	−1.02309	−0.0363999
$791$	3.01297i	0.107129i
$792$	−9.47889	−0.336818
$793$	0	0
$794$	22.4614	0.797125
$795$	35.0010i	1.24136i
$796$	20.0516	0.710709
$797$	−40.3340	−1.42871	−0.714353	−	0.699786i	$-0.753279\pi$
$797$	−40.3340	−1.42871	−0.714353	+	0.699786i	$0.753279\pi$
$798$	13.2874i	0.470370i
$799$	− 9.47380i	− 0.335159i
$800$	− 7.16292i	− 0.253247i
$801$	18.4269i	0.651083i
$802$	17.0288	0.601307
$803$	−40.3225	−1.42295
$804$	2.47133i	0.0871572i
$805$	−24.5965	−0.866912
$806$	0	0
$807$	37.8463	1.33225
$808$	3.78650i	0.133209i
$809$	2.71050	0.0952961	0.0476481	−	0.998864i	$-0.484827\pi$
$809$	2.71050	0.0952961	0.0476481	+	0.998864i	$0.484827\pi$
$810$	−24.7973	−0.871290
$811$	29.7449i	1.04448i	0.852797	+	0.522242i	$0.174904\pi$
$811$	29.7449i	1.04448i	−0.852797	+	0.522242i	$0.825096\pi$
$812$	7.13278i	0.250312i
$813$	− 0.165229i	− 0.00579483i
$814$	20.9563i	0.734518i
$815$	−21.9925	−0.770365
$816$	−15.1209	−0.529337
$817$	− 1.71637i	− 0.0600481i
$818$	5.13532	0.179552
$819$	0	0
$820$	−0.550013	−0.0192073
$821$	17.3317i	0.604880i	0.953168	+	0.302440i	$0.0978011\pi$
$821$	17.3317i	0.604880i	−0.953168	+	0.302440i	$0.902199\pi$
$822$	39.5247	1.37858
$823$	−11.4589	−0.399432	−0.199716	−	0.979854i	$-0.564002\pi$
$823$	−11.4589	−0.399432	−0.199716	+	0.979854i	$0.564002\pi$
$824$	6.80839i	0.237181i
$825$	− 49.1036i	− 1.70957i
$826$	− 9.54021i	− 0.331946i
$827$	− 5.41259i	− 0.188214i	−0.995562	−	0.0941070i	$-0.970000\pi$
$827$	− 5.41259i	− 0.188214i	0.995562	−	0.0941070i	$-0.0299996\pi$
$828$	−24.9286	−0.866329
$829$	−34.8694	−1.21107	−0.605533	−	0.795820i	$-0.707040\pi$
$829$	−34.8694	−1.21107	−0.605533	+	0.795820i	$0.707040\pi$
$830$	− 10.0265i	− 0.348024i
$831$	10.8672	0.376979
$832$	0	0
$833$	−5.91517	−0.204948
$834$	− 36.5606i	− 1.26599i
$835$	23.2574	0.804855
$836$	13.9394	0.482103
$837$	− 1.06926i	− 0.0369592i
$838$	− 31.8836i	− 1.10140i
$839$	− 24.7350i	− 0.853947i	−0.904264	−	0.426973i	$-0.859580\pi$
$839$	− 24.7350i	− 0.853947i	0.904264	−	0.426973i	$-0.140420\pi$
$840$	− 8.91517i	− 0.307602i
$841$	21.8766	0.754365
$842$	14.7648	0.508830
$843$	28.2354i	0.972478i
$844$	7.96144	0.274044
$845$	0	0
$846$	5.66111	0.194633
$847$	− 3.80839i	− 0.130858i
$848$	3.92601	0.134820
$849$	28.8488	0.990089
$850$	− 42.3698i	− 1.45327i
$851$	55.1132i	1.88925i
$852$	− 10.7021i	− 0.366648i
$853$	− 6.14219i	− 0.210304i	−0.994456	−	0.105152i	$-0.966467\pi$
$853$	− 6.14219i	− 0.210304i	0.994456	−	0.105152i	$-0.0335330\pi$
$854$	15.4105	0.527337
$855$	−64.0757	−2.19134
$856$	− 14.3017i	− 0.488821i
$857$	32.2072	1.10018	0.550088	−	0.835106i	$-0.314594\pi$
$857$	32.2072	1.10018	0.550088	+	0.835106i	$0.314594\pi$
$858$	0	0
$859$	−17.3714	−0.592705	−0.296352	−	0.955079i	$-0.595770\pi$
$859$	−17.3714	−0.592705	−0.296352	+	0.955079i	$0.595770\pi$
$860$	1.15159i	0.0392690i
$861$	−0.403148	−0.0137393
$862$	−35.1088	−1.19581
$863$	0.309300i	0.0105287i	0.999986	+	0.00526435i	$0.00167570\pi$
$863$	0.309300i	0.0105287i	−0.999986	+	0.00526435i	$0.998324\pi$
$864$	− 1.36668i	− 0.0464952i
$865$	− 74.3515i	− 2.52803i
$866$	3.97251i	0.134991i
$867$	−45.9856	−1.56175
$868$	−0.782383	−0.0265558
$869$	0.786699i	0.0266869i
$870$	−63.5899	−2.15590
$871$	0	0
$872$	4.57669	0.154986
$873$	11.1675i	0.377963i
$874$	36.6593	1.24002
$875$	7.54326	0.255009
$876$	− 38.4366i	− 1.29865i
$877$	21.8148i	0.736633i	0.929701	+	0.368316i	$0.120066\pi$
$877$	21.8148i	0.736633i	−0.929701	+	0.368316i	$0.879934\pi$
$878$	− 5.75277i	− 0.194147i
$879$	− 66.5765i	− 2.24557i
$880$	−9.35259	−0.315276
$881$	10.3626	0.349126	0.174563	−	0.984646i	$-0.444149\pi$
$881$	10.3626	0.349126	0.174563	+	0.984646i	$0.444149\pi$
$882$	− 3.53463i	− 0.119017i
$883$	47.4366	1.59637	0.798184	−	0.602414i	$-0.205794\pi$
$883$	47.4366	1.59637	0.798184	+	0.602414i	$0.205794\pi$
$884$	0	0
$885$	85.0526	2.85901
$886$	− 27.0804i	− 0.909785i
$887$	20.3479	0.683216	0.341608	−	0.939843i	$-0.389028\pi$
$887$	20.3479	0.683216	0.341608	+	0.939843i	$0.389028\pi$
$888$	−19.9762	−0.670356
$889$	11.1256i	0.373139i
$890$	18.1814i	0.609442i
$891$	19.0678i	0.638794i
$892$	21.5417i	0.721271i
$893$	−8.32506	−0.278588
$894$	9.09318	0.304121
$895$	53.8421i	1.79974i
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	8.24914	0.275277
$899$	5.58057i	0.186122i
$900$	25.3183	0.843943
$901$	23.2230	0.773670
$902$	0.422929i	0.0140820i
$903$	0.844093i	0.0280897i
$904$	3.01297i	0.100210i
$905$	46.3209i	1.53976i
$906$	−24.3548	−0.809135
$907$	17.0130	0.564908	0.282454	−	0.959281i	$-0.408852\pi$
$907$	17.0130	0.564908	0.282454	+	0.959281i	$0.408852\pi$
$908$	3.65771i	0.121385i
$909$	−13.3839	−0.443916
$910$	0	0
$911$	12.8289	0.425040	0.212520	−	0.977157i	$-0.431833\pi$
$911$	12.8289	0.425040	0.212520	+	0.977157i	$0.431833\pi$
$912$	13.2874i	0.439991i
$913$	−7.70980	−0.255157
$914$	−38.6967	−1.27997
$915$	137.387i	4.54188i
$916$	− 9.74752i	− 0.322067i
$917$	− 14.9117i	− 0.492427i
$918$	− 8.08411i	− 0.266815i
$919$	−38.5765	−1.27252	−0.636261	−	0.771474i	$-0.719520\pi$
$919$	−38.5765	−1.27252	−0.636261	+	0.771474i	$0.719520\pi$
$920$	−24.5965	−0.810922
$921$	64.0482i	2.11046i
$922$	13.1348	0.432573
$923$	0	0
$924$	−6.85526	−0.225521
$925$	− 55.9746i	− 1.84043i
$926$	6.98417	0.229514
$927$	−24.0651	−0.790403
$928$	7.13278i	0.234145i
$929$	4.34958i	0.142705i	0.997451	+	0.0713526i	$0.0227316\pi$
$929$	4.34958i	0.142705i	−0.997451	+	0.0713526i	$0.977268\pi$
$930$	− 6.97507i	− 0.228722i
$931$	5.19793i	0.170355i
$932$	2.72895	0.0893897
$933$	82.9083	2.71430
$934$	5.62691i	0.184118i
$935$	−55.3221	−1.80923
$936$	0	0
$937$	−13.5931	−0.444068	−0.222034	−	0.975039i	$-0.571270\pi$
$937$	−13.5931	−0.444068	−0.222034	+	0.975039i	$0.571270\pi$
$938$	0.966765i	0.0315660i
$939$	−5.68819	−0.185627
$940$	5.58568	0.182185
$941$	24.5649i	0.800792i	0.916342	+	0.400396i	$0.131127\pi$
$941$	24.5649i	0.800792i	−0.916342	+	0.400396i	$0.868873\pi$
$942$	− 53.2591i	− 1.73528i
$943$	1.11226i	0.0362203i
$944$	− 9.54021i	− 0.310508i
$945$	4.76633	0.155049
$946$	0.885509	0.0287904
$947$	− 2.09781i	− 0.0681697i	−0.999419	−	0.0340848i	$-0.989148\pi$
$947$	− 2.09781i	− 0.0681697i	0.999419	−	0.0340848i	$-0.0108516\pi$
$948$	−0.749905	−0.0243558
$949$	0	0
$950$	−37.2323	−1.20798
$951$	− 9.80985i	− 0.318106i
$952$	−5.91517	−0.191712
$953$	40.3398	1.30673	0.653367	−	0.757042i	$-0.273356\pi$
$953$	40.3398	1.30673	0.653367	+	0.757042i	$0.273356\pi$
$954$	13.8770i	0.449284i
$955$	41.5875i	1.34574i
$956$	− 12.2347i	− 0.395700i
$957$	48.8971i	1.58062i
$958$	−25.1191	−0.811562
$959$	15.4617	0.499285
$960$	− 8.91517i	− 0.287736i
$961$	30.3879	0.980254
$962$	0	0
$963$	50.5511	1.62899
$964$	− 24.2176i	− 0.779998i
$965$	18.6561	0.600560
$966$	−18.0287	−0.580064
$967$	2.90536i	0.0934300i	0.998908	+	0.0467150i	$0.0148753\pi$
$967$	2.90536i	0.0934300i	−0.998908	+	0.0467150i	$0.985125\pi$
$968$	− 3.80839i	− 0.122406i
$969$	78.5973i	2.52491i
$970$	11.0187i	0.353790i
$971$	−11.7552	−0.377242	−0.188621	−	0.982050i	$-0.560402\pi$
$971$	−11.7552	−0.377242	−0.188621	+	0.982050i	$0.560402\pi$
$972$	−22.2760	−0.714502
$973$	− 14.3022i	− 0.458508i
$974$	−17.6758	−0.566370
$975$	0	0
$976$	15.4105	0.493278
$977$	20.0905i	0.642751i	0.946952	+	0.321375i	$0.104145\pi$
$977$	20.0905i	0.642751i	−0.946952	+	0.321375i	$0.895855\pi$
$978$	−16.1201	−0.515463
$979$	13.9805	0.446818
$980$	− 3.48754i	− 0.111405i
$981$	16.1769i	0.516489i
$982$	− 31.9949i	− 1.02100i
$983$	30.8037i	0.982487i	0.871022	+	0.491243i	$0.163457\pi$
$983$	30.8037i	0.982487i	−0.871022	+	0.491243i	$0.836543\pi$
$984$	−0.403148	−0.0128519
$985$	−46.0138	−1.46612
$986$	42.1916i	1.34365i
$987$	4.09419	0.130319
$988$	0	0
$989$	2.32881	0.0740518
$990$	− 33.0580i	− 1.05065i
$991$	−42.6457	−1.35469	−0.677343	−	0.735668i	$-0.736869\pi$
$991$	−42.6457	−1.35469	−0.677343	+	0.735668i	$0.736869\pi$
$992$	−0.782383	−0.0248407
$993$	15.5516i	0.493514i
$994$	− 4.18658i	− 0.132790i
$995$	69.9306i	2.21695i
$996$	− 7.34921i	− 0.232868i
$997$	−31.5540	−0.999326	−0.499663	−	0.866220i	$-0.666543\pi$
$997$	−31.5540	−0.999326	−0.499663	+	0.866220i	$0.666543\pi$
$998$	11.6416	0.368508
$999$	− 10.6799i	− 0.337897i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.r.337.7		12
13.5	odd	4		2366.2.a.bh.1.1		6
13.8	odd	4		2366.2.a.bf.1.1		6
13.9	even	3		182.2.m.b.127.6	yes	12
13.10	even	6		182.2.m.b.43.6	✓	12
13.12	even	2	inner	2366.2.d.r.337.1		12
39.23	odd	6		1638.2.bj.g.1135.1		12
39.35	odd	6		1638.2.bj.g.127.3		12
52.23	odd	6		1456.2.cc.d.225.1		12
52.35	odd	6		1456.2.cc.d.673.1		12
91.9	even	3		1274.2.v.e.361.1		12
91.10	odd	6		1274.2.v.d.667.3		12
91.23	even	6		1274.2.o.d.459.3		12
91.48	odd	6		1274.2.m.c.491.4		12
91.61	odd	6		1274.2.v.d.361.3		12
91.62	odd	6		1274.2.m.c.589.4		12
91.74	even	3		1274.2.o.d.569.6		12
91.75	odd	6		1274.2.o.e.459.1		12
91.87	odd	6		1274.2.o.e.569.4		12
91.88	even	6		1274.2.v.e.667.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.6	✓	12	13.10	even	6
182.2.m.b.127.6	yes	12	13.9	even	3
1274.2.m.c.491.4		12	91.48	odd	6
1274.2.m.c.589.4		12	91.62	odd	6
1274.2.o.d.459.3		12	91.23	even	6
1274.2.o.d.569.6		12	91.74	even	3
1274.2.o.e.459.1		12	91.75	odd	6
1274.2.o.e.569.4		12	91.87	odd	6
1274.2.v.d.361.3		12	91.61	odd	6
1274.2.v.d.667.3		12	91.10	odd	6
1274.2.v.e.361.1		12	91.9	even	3
1274.2.v.e.667.1		12	91.88	even	6
1456.2.cc.d.225.1		12	52.23	odd	6
1456.2.cc.d.673.1		12	52.35	odd	6
1638.2.bj.g.127.3		12	39.35	odd	6
1638.2.bj.g.1135.1		12	39.23	odd	6
2366.2.a.bf.1.1		6	13.8	odd	4
2366.2.a.bh.1.1		6	13.5	odd	4
2366.2.d.r.337.1		12	13.12	even	2	inner
2366.2.d.r.337.7		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -2.55629 q^{3} -1.00000 q^{4} -3.48754i q^{5} -2.55629i q^{6} -1.00000i q^{7} -1.00000i q^{8} +3.53463 q^{9} +3.48754 q^{10} -2.68172i q^{11} +2.55629 q^{12} +1.00000 q^{14} +8.91517i q^{15} +1.00000 q^{16} +5.91517 q^{17} +3.53463i q^{18} -5.19793i q^{19} +3.48754i q^{20} +2.55629i q^{21} +2.68172 q^{22} +7.05268 q^{23} +2.55629i q^{24} -7.16292 q^{25} -1.36668 q^{27} +1.00000i q^{28} +7.13278 q^{29} -8.91517 q^{30} +0.782383i q^{31} +1.00000i q^{32} +6.85526i q^{33} +5.91517i q^{34} -3.48754 q^{35} -3.53463 q^{36} +7.81450i q^{37} +5.19793 q^{38} -3.48754 q^{40} +0.157708i q^{41} -2.55629 q^{42} +0.330202 q^{43} +2.68172i q^{44} -12.3272i q^{45} +7.05268i q^{46} -1.60161i q^{47} -2.55629 q^{48} -1.00000 q^{49} -7.16292i q^{50} -15.1209 q^{51} +3.92601 q^{53} -1.36668i q^{54} -9.35259 q^{55} -1.00000 q^{56} +13.2874i q^{57} +7.13278i q^{58} -9.54021i q^{59} -8.91517i q^{60} +15.4105 q^{61} -0.782383 q^{62} -3.53463i q^{63} -1.00000 q^{64} -6.85526 q^{66} +0.966765i q^{67} -5.91517 q^{68} -18.0287 q^{69} -3.48754i q^{70} -4.18658i q^{71} -3.53463i q^{72} -15.0361i q^{73} -7.81450 q^{74} +18.3105 q^{75} +5.19793i q^{76} -2.68172 q^{77} -0.293356 q^{79} -3.48754i q^{80} -7.11027 q^{81} -0.157708 q^{82} -2.87495i q^{83} -2.55629i q^{84} -20.6294i q^{85} +0.330202i q^{86} -18.2335 q^{87} -2.68172 q^{88} +5.21325i q^{89} +12.3272 q^{90} -7.05268 q^{92} -2.00000i q^{93} +1.60161 q^{94} -18.1280 q^{95} -2.55629i q^{96} +3.15946i q^{97} -1.00000i q^{98} -9.47889i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) \) 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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