LMFDB - Embedded newform 2366.2.d.r.337.9

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			337.9
Root			$0.500000 + 0.399480i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.r.337.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -0.466545 q^{3} -1.00000 q^{4} +3.38938i q^{5} -0.466545i q^{6} -1.00000i q^{7} -1.00000i q^{8} -2.78234 q^{9} -3.38938 q^{10} +0.822730i q^{11} +0.466545 q^{12} +1.00000 q^{14} -1.58130i q^{15} +1.00000 q^{16} -4.58130 q^{17} -2.78234i q^{18} +5.90621i q^{19} -3.38938i q^{20} +0.466545i q^{21} -0.822730 q^{22} +6.13055 q^{23} +0.466545i q^{24} -6.48787 q^{25} +2.69772 q^{27} +1.00000i q^{28} -6.86813 q^{29} +1.58130 q^{30} +4.28683i q^{31} +1.00000i q^{32} -0.383841i q^{33} -4.58130i q^{34} +3.38938 q^{35} +2.78234 q^{36} -9.69086i q^{37} -5.90621 q^{38} +3.38938 q^{40} -0.0893760i q^{41} -0.466545 q^{42} -7.35374 q^{43} -0.822730i q^{44} -9.43038i q^{45} +6.13055i q^{46} -11.1759i q^{47} -0.466545 q^{48} -1.00000 q^{49} -6.48787i q^{50} +2.13738 q^{51} -7.01530 q^{53} +2.69772i q^{54} -2.78854 q^{55} -1.00000 q^{56} -2.75551i q^{57} -6.86813i q^{58} -1.74117i q^{59} +1.58130i q^{60} +2.37945 q^{61} -4.28683 q^{62} +2.78234i q^{63} -1.00000 q^{64} +0.383841 q^{66} +0.291719i q^{67} +4.58130 q^{68} -2.86018 q^{69} +3.38938i q^{70} -10.9484i q^{71} +2.78234i q^{72} +12.7187i q^{73} +9.69086 q^{74} +3.02688 q^{75} -5.90621i q^{76} +0.822730 q^{77} +9.95602 q^{79} +3.38938i q^{80} +7.08840 q^{81} +0.0893760 q^{82} -3.23553i q^{83} -0.466545i q^{84} -15.5277i q^{85} -7.35374i q^{86} +3.20429 q^{87} +0.822730 q^{88} +8.04265i q^{89} +9.43038 q^{90} -6.13055 q^{92} -2.00000i q^{93} +11.1759 q^{94} -20.0184 q^{95} -0.466545i q^{96} -14.7739i q^{97} -1.00000i q^{98} -2.28911i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.466545	−0.269360	−0.134680	−	0.990889i	$-0.543001\pi$
$3$	−0.466545	−0.269360	−0.134680	+	0.990889i	$0.543001\pi$
$4$	−1.00000	−0.500000
$5$	3.38938i	1.51578i	0.652385	+	0.757888i	$0.273768\pi$
$5$	3.38938i	1.51578i	−0.652385	+	0.757888i	$0.726232\pi$
$6$	− 0.466545i	− 0.190466i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−2.78234	−0.927445
$10$	−3.38938	−1.07181
$11$	0.822730i	0.248063i	0.992278	+	0.124031i	$0.0395823\pi$
$11$	0.822730i	0.248063i	−0.992278	+	0.124031i	$0.960418\pi$
$12$	0.466545	0.134680
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	− 1.58130i	− 0.408289i
$16$	1.00000	0.250000
$17$	−4.58130	−1.11113	−0.555564	−	0.831474i	$-0.687498\pi$
$17$	−4.58130	−1.11113	−0.555564	+	0.831474i	$0.687498\pi$
$18$	− 2.78234i	− 0.655803i
$19$	5.90621i	1.35498i	0.735534	+	0.677488i	$0.236932\pi$
$19$	5.90621i	1.35498i	−0.735534	+	0.677488i	$0.763068\pi$
$20$	− 3.38938i	− 0.757888i
$21$	0.466545i	0.101808i
$22$	−0.822730	−0.175407
$23$	6.13055	1.27831	0.639154	−	0.769079i	$-0.279285\pi$
$23$	6.13055	1.27831	0.639154	+	0.769079i	$0.279285\pi$
$24$	0.466545i	0.0952331i
$25$	−6.48787	−1.29757
$26$	0	0
$27$	2.69772	0.519176
$28$	1.00000i	0.188982i
$29$	−6.86813	−1.27538	−0.637690	−	0.770293i	$-0.720110\pi$
$29$	−6.86813	−1.27538	−0.637690	+	0.770293i	$0.720110\pi$
$30$	1.58130	0.288704
$31$	4.28683i	0.769938i	0.922930	+	0.384969i	$0.125788\pi$
$31$	4.28683i	0.769938i	−0.922930	+	0.384969i	$0.874212\pi$
$32$	1.00000i	0.176777i
$33$	− 0.383841i	− 0.0668181i
$34$	− 4.58130i	− 0.785686i
$35$	3.38938	0.572909
$36$	2.78234	0.463723
$37$	− 9.69086i	− 1.59317i	−0.604528	−	0.796584i	$-0.706638\pi$
$37$	− 9.69086i	− 1.59317i	0.604528	−	0.796584i	$-0.293362\pi$
$38$	−5.90621	−0.958113
$39$	0	0
$40$	3.38938	0.535907
$41$	− 0.0893760i	− 0.0139582i	−0.999976	−	0.00697909i	$-0.997778\pi$
$41$	− 0.0893760i	− 0.0139582i	0.999976	−	0.00697909i	$-0.00222153\pi$
$42$	−0.466545	−0.0719895
$43$	−7.35374	−1.12144	−0.560718	−	0.828007i	$-0.689475\pi$
$43$	−7.35374	−1.12144	−0.560718	+	0.828007i	$0.689475\pi$
$44$	− 0.822730i	− 0.124031i
$45$	− 9.43038i	− 1.40580i
$46$	6.13055i	0.903900i
$47$	− 11.1759i	− 1.63018i	−0.579335	−	0.815089i	$-0.696688\pi$
$47$	− 11.1759i	− 1.63018i	0.579335	−	0.815089i	$-0.303312\pi$
$48$	−0.466545	−0.0673400
$49$	−1.00000	−0.142857
$50$	− 6.48787i	− 0.917524i
$51$	2.13738	0.299293
$52$	0	0
$53$	−7.01530	−0.963625	−0.481813	−	0.876274i	$-0.660021\pi$
$53$	−7.01530	−0.963625	−0.481813	+	0.876274i	$0.660021\pi$
$54$	2.69772i	0.367113i
$55$	−2.78854	−0.376007
$56$	−1.00000	−0.133631
$57$	− 2.75551i	− 0.364976i
$58$	− 6.86813i	− 0.901829i
$59$	− 1.74117i	− 0.226681i	−0.993556	−	0.113340i	$-0.963845\pi$
$59$	− 1.74117i	− 0.226681i	0.993556	−	0.113340i	$-0.0361551\pi$
$60$	1.58130i	0.204145i
$61$	2.37945	0.304657	0.152329	−	0.988330i	$-0.451323\pi$
$61$	2.37945	0.304657	0.152329	+	0.988330i	$0.451323\pi$
$62$	−4.28683	−0.544428
$63$	2.78234i	0.350541i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	0.383841	0.0472475
$67$	0.291719i	0.0356391i	0.999841	+	0.0178196i	$0.00567244\pi$
$67$	0.291719i	0.0356391i	−0.999841	+	0.0178196i	$0.994328\pi$
$68$	4.58130	0.555564
$69$	−2.86018	−0.344325
$70$	3.38938i	0.405108i
$71$	− 10.9484i	− 1.29933i	−0.760219	−	0.649667i	$-0.774908\pi$
$71$	− 10.9484i	− 1.29933i	0.760219	−	0.649667i	$-0.225092\pi$
$72$	2.78234i	0.327901i
$73$	12.7187i	1.48861i	0.667841	+	0.744304i	$0.267219\pi$
$73$	12.7187i	1.48861i	−0.667841	+	0.744304i	$0.732781\pi$
$74$	9.69086	1.12654
$75$	3.02688	0.349514
$76$	− 5.90621i	− 0.677488i
$77$	0.822730	0.0937588
$78$	0	0
$79$	9.95602	1.12014	0.560070	−	0.828445i	$-0.310774\pi$
$79$	9.95602	1.12014	0.560070	+	0.828445i	$0.310774\pi$
$80$	3.38938i	0.378944i
$81$	7.08840	0.787600
$82$	0.0893760	0.00986993
$83$	− 3.23553i	− 0.355146i	−0.984108	−	0.177573i	$-0.943175\pi$
$83$	− 3.23553i	− 0.355146i	0.984108	−	0.177573i	$-0.0568246\pi$
$84$	− 0.466545i	− 0.0509042i
$85$	− 15.5277i	− 1.68422i
$86$	− 7.35374i	− 0.792974i
$87$	3.20429	0.343536
$88$	0.822730	0.0877033
$89$	8.04265i	0.852519i	0.904601	+	0.426260i	$0.140169\pi$
$89$	8.04265i	0.852519i	−0.904601	+	0.426260i	$0.859831\pi$
$90$	9.43038	0.994050
$91$	0	0
$92$	−6.13055	−0.639154
$93$	− 2.00000i	− 0.207390i
$94$	11.1759	1.15271
$95$	−20.0184	−2.05384
$96$	− 0.466545i	− 0.0476166i
$97$	− 14.7739i	− 1.50006i	−0.661405	−	0.750029i	$-0.730039\pi$
$97$	− 14.7739i	− 1.50006i	0.661405	−	0.750029i	$-0.269961\pi$
$98$	− 1.00000i	− 0.101015i
$99$	− 2.28911i	− 0.230064i
$100$	6.48787	0.648787
$101$	8.23976	0.819887	0.409943	−	0.912111i	$-0.365548\pi$
$101$	8.23976	0.819887	0.409943	+	0.912111i	$0.365548\pi$
$102$	2.13738i	0.211632i
$103$	−13.3231	−1.31277	−0.656383	−	0.754428i	$-0.727914\pi$
$103$	−13.3231	−1.31277	−0.656383	+	0.754428i	$0.727914\pi$
$104$	0	0
$105$	−1.58130	−0.154319
$106$	− 7.01530i	− 0.681386i
$107$	−9.02649	−0.872624	−0.436312	−	0.899795i	$-0.643716\pi$
$107$	−9.02649	−0.872624	−0.436312	+	0.899795i	$0.643716\pi$
$108$	−2.69772	−0.259588
$109$	0.397192i	0.0380441i	0.999819	+	0.0190220i	$0.00605527\pi$
$109$	0.397192i	0.0380441i	−0.999819	+	0.0190220i	$0.993945\pi$
$110$	− 2.78854i	− 0.265877i
$111$	4.52122i	0.429135i
$112$	− 1.00000i	− 0.0944911i
$113$	4.47322	0.420805	0.210402	−	0.977615i	$-0.432523\pi$
$113$	4.47322	0.420805	0.210402	+	0.977615i	$0.432523\pi$
$114$	2.75551	0.258077
$115$	20.7787i	1.93763i
$116$	6.86813	0.637690
$117$	0	0
$118$	1.74117	0.160288
$119$	4.58130i	0.419967i
$120$	−1.58130	−0.144352
$121$	10.3231	0.938465
$122$	2.37945i	0.215425i
$123$	0.0416979i	0.00375978i
$124$	− 4.28683i	− 0.384969i
$125$	− 5.04295i	− 0.451056i
$126$	−2.78234	−0.247870
$127$	0.540127	0.0479285	0.0239642	−	0.999713i	$-0.492371\pi$
$127$	0.540127	0.0479285	0.0239642	+	0.999713i	$0.492371\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	3.43085	0.302070
$130$	0	0
$131$	−7.72615	−0.675037	−0.337518	−	0.941319i	$-0.609587\pi$
$131$	−7.72615	−0.675037	−0.337518	+	0.941319i	$0.609587\pi$
$132$	0.383841i	0.0334090i
$133$	5.90621	0.512133
$134$	−0.291719	−0.0252007
$135$	9.14359i	0.786955i
$136$	4.58130i	0.392843i
$137$	− 12.5401i	− 1.07137i	−0.844417	−	0.535687i	$-0.820053\pi$
$137$	− 12.5401i	− 1.07137i	0.844417	−	0.535687i	$-0.179947\pi$
$138$	− 2.86018i	− 0.243474i
$139$	12.0974	1.02608	0.513042	−	0.858363i	$-0.328518\pi$
$139$	12.0974	1.02608	0.513042	+	0.858363i	$0.328518\pi$
$140$	−3.38938	−0.286455
$141$	5.21408i	0.439105i
$142$	10.9484	0.918768
$143$	0	0
$144$	−2.78234	−0.231861
$145$	− 23.2787i	− 1.93319i
$146$	−12.7187	−1.05261
$147$	0.466545	0.0384800
$148$	9.69086i	0.796584i
$149$	− 17.0078i	− 1.39333i	−0.717395	−	0.696666i	$-0.754666\pi$
$149$	− 17.0078i	− 1.39333i	0.717395	−	0.696666i	$-0.245334\pi$
$150$	3.02688i	0.247144i
$151$	− 5.54567i	− 0.451300i	−0.974208	−	0.225650i	$-0.927549\pi$
$151$	− 5.54567i	− 0.451300i	0.974208	−	0.225650i	$-0.0724506\pi$
$152$	5.90621	0.479057
$153$	12.7467	1.03051
$154$	0.822730i	0.0662975i
$155$	−14.5297	−1.16705
$156$	0	0
$157$	2.29353	0.183044	0.0915218	−	0.995803i	$-0.470827\pi$
$157$	2.29353	0.183044	0.0915218	+	0.995803i	$0.470827\pi$
$158$	9.95602i	0.792059i
$159$	3.27295	0.259562
$160$	−3.38938	−0.267954
$161$	− 6.13055i	− 0.483155i
$162$	7.08840i	0.556917i
$163$	23.3560i	1.82938i	0.404155	+	0.914691i	$0.367566\pi$
$163$	23.3560i	1.82938i	−0.404155	+	0.914691i	$0.632434\pi$
$164$	0.0893760i	0.00697909i
$165$	1.30098	0.101281
$166$	3.23553	0.251126
$167$	− 21.7780i	− 1.68523i	−0.538517	−	0.842614i	$-0.681015\pi$
$167$	− 21.7780i	− 1.68523i	0.538517	−	0.842614i	$-0.318985\pi$
$168$	0.466545	0.0359947
$169$	0	0
$170$	15.5277	1.19092
$171$	− 16.4330i	− 1.25667i
$172$	7.35374	0.560718
$173$	−8.09733	−0.615629	−0.307814	−	0.951446i	$-0.599598\pi$
$173$	−8.09733	−0.615629	−0.307814	+	0.951446i	$0.599598\pi$
$174$	3.20429i	0.242917i
$175$	6.48787i	0.490437i
$176$	0.822730i	0.0620156i
$177$	0.812334i	0.0610588i
$178$	−8.04265	−0.602822
$179$	−9.90883	−0.740621	−0.370310	−	0.928908i	$-0.620749\pi$
$179$	−9.90883	−0.740621	−0.370310	+	0.928908i	$0.620749\pi$
$180$	9.43038i	0.702899i
$181$	1.27902	0.0950685	0.0475343	−	0.998870i	$-0.484864\pi$
$181$	1.27902	0.0950685	0.0475343	+	0.998870i	$0.484864\pi$
$182$	0	0
$183$	−1.11012	−0.0820624
$184$	− 6.13055i	− 0.451950i
$185$	32.8460	2.41488
$186$	2.00000	0.146647
$187$	− 3.76917i	− 0.275629i
$188$	11.1759i	0.815089i
$189$	− 2.69772i	− 0.196230i
$190$	− 20.0184i	− 1.45228i
$191$	−10.0342	−0.726050	−0.363025	−	0.931779i	$-0.618256\pi$
$191$	−10.0342	−0.726050	−0.363025	+	0.931779i	$0.618256\pi$
$192$	0.466545	0.0336700
$193$	− 15.8582i	− 1.14150i	−0.821124	−	0.570750i	$-0.806653\pi$
$193$	− 15.8582i	− 1.14150i	0.821124	−	0.570750i	$-0.193347\pi$
$194$	14.7739	1.06070
$195$	0	0
$196$	1.00000	0.0714286
$197$	14.8081i	1.05503i	0.849546	+	0.527515i	$0.176876\pi$
$197$	14.8081i	1.05503i	−0.849546	+	0.527515i	$0.823124\pi$
$198$	2.28911	0.162680
$199$	2.55543	0.181149	0.0905747	−	0.995890i	$-0.471130\pi$
$199$	2.55543	0.181149	0.0905747	+	0.995890i	$0.471130\pi$
$200$	6.48787i	0.458762i
$201$	− 0.136100i	− 0.00959974i
$202$	8.23976i	0.579748i
$203$	6.86813i	0.482048i
$204$	−2.13738	−0.149647
$205$	0.302929	0.0211575
$206$	− 13.3231i	− 0.928265i
$207$	−17.0572	−1.18556
$208$	0	0
$209$	−4.85921	−0.336119
$210$	− 1.58130i	− 0.109120i
$211$	−8.63648	−0.594560	−0.297280	−	0.954790i	$-0.596080\pi$
$211$	−8.63648	−0.594560	−0.297280	+	0.954790i	$0.596080\pi$
$212$	7.01530	0.481813
$213$	5.10792i	0.349989i
$214$	− 9.02649i	− 0.617038i
$215$	− 24.9246i	− 1.69984i
$216$	− 2.69772i	− 0.183557i
$217$	4.28683	0.291009
$218$	−0.397192	−0.0269012
$219$	− 5.93384i	− 0.400971i
$220$	2.78854	0.188003
$221$	0	0
$222$	−4.52122	−0.303445
$223$	− 19.9277i	− 1.33446i	−0.744854	−	0.667228i	$-0.767481\pi$
$223$	− 19.9277i	− 1.33446i	0.744854	−	0.667228i	$-0.232519\pi$
$224$	1.00000	0.0668153
$225$	18.0514	1.20343
$226$	4.47322i	0.297554i
$227$	− 0.352624i	− 0.0234045i	−0.999932	−	0.0117022i	$-0.996275\pi$
$227$	− 0.352624i	− 0.0234045i	0.999932	−	0.0117022i	$-0.00372502\pi$
$228$	2.75551i	0.182488i
$229$	8.31317i	0.549350i	0.961537	+	0.274675i	$0.0885702\pi$
$229$	8.31317i	0.549350i	−0.961537	+	0.274675i	$0.911430\pi$
$230$	−20.7787	−1.37011
$231$	−0.383841	−0.0252549
$232$	6.86813i	0.450915i
$233$	−15.3798	−1.00756	−0.503781	−	0.863831i	$-0.668058\pi$
$233$	−15.3798	−1.00756	−0.503781	+	0.863831i	$0.668058\pi$
$234$	0	0
$235$	37.8795	2.47098
$236$	1.74117i	0.113340i
$237$	−4.64493	−0.301721
$238$	−4.58130	−0.296961
$239$	− 2.88606i	− 0.186684i	−0.995634	−	0.0933418i	$-0.970245\pi$
$239$	− 2.88606i	− 0.186684i	0.995634	−	0.0933418i	$-0.0297549\pi$
$240$	− 1.58130i	− 0.102072i
$241$	6.26744i	0.403722i	0.979414	+	0.201861i	$0.0646988\pi$
$241$	6.26744i	0.403722i	−0.979414	+	0.201861i	$0.935301\pi$
$242$	10.3231i	0.663595i
$243$	−11.4002	−0.731324
$244$	−2.37945	−0.152329
$245$	− 3.38938i	− 0.216539i
$246$	−0.0416979	−0.00265856
$247$	0	0
$248$	4.28683	0.272214
$249$	1.50952i	0.0956621i
$250$	5.04295	0.318944
$251$	−17.2665	−1.08985	−0.544926	−	0.838484i	$-0.683442\pi$
$251$	−17.2665	−1.08985	−0.544926	+	0.838484i	$0.683442\pi$
$252$	− 2.78234i	− 0.175271i
$253$	5.04379i	0.317100i
$254$	0.540127i	0.0338906i
$255$	7.24439i	0.453661i
$256$	1.00000	0.0625000
$257$	11.1931	0.698206	0.349103	−	0.937084i	$-0.386486\pi$
$257$	11.1931	0.698206	0.349103	+	0.937084i	$0.386486\pi$
$258$	3.43085i	0.213595i
$259$	−9.69086	−0.602161
$260$	0	0
$261$	19.1094	1.18284
$262$	− 7.72615i	− 0.477323i
$263$	−28.5826	−1.76248	−0.881240	−	0.472668i	$-0.843291\pi$
$263$	−28.5826	−1.76248	−0.881240	+	0.472668i	$0.843291\pi$
$264$	−0.383841	−0.0236238
$265$	− 23.7775i	− 1.46064i
$266$	5.90621i	0.362133i
$267$	− 3.75226i	− 0.229635i
$268$	− 0.291719i	− 0.0178196i
$269$	−18.3754	−1.12037	−0.560183	−	0.828369i	$-0.689269\pi$
$269$	−18.3754	−1.12037	−0.560183	+	0.828369i	$0.689269\pi$
$270$	−9.14359	−0.556461
$271$	20.3825i	1.23815i	0.785332	+	0.619075i	$0.212492\pi$
$271$	20.3825i	1.23815i	−0.785332	+	0.619075i	$0.787508\pi$
$272$	−4.58130	−0.277782
$273$	0	0
$274$	12.5401	0.757575
$275$	− 5.33777i	− 0.321880i
$276$	2.86018	0.172162
$277$	−7.23219	−0.434540	−0.217270	−	0.976112i	$-0.569715\pi$
$277$	−7.23219	−0.434540	−0.217270	+	0.976112i	$0.569715\pi$
$278$	12.0974i	0.725551i
$279$	− 11.9274i	− 0.714075i
$280$	− 3.38938i	− 0.202554i
$281$	− 12.4585i	− 0.743215i	−0.928390	−	0.371607i	$-0.878807\pi$
$281$	− 12.4585i	− 0.743215i	0.928390	−	0.371607i	$-0.121193\pi$
$282$	−5.21408	−0.310494
$283$	−13.0607	−0.776378	−0.388189	−	0.921580i	$-0.626899\pi$
$283$	−13.0607	−0.776378	−0.388189	+	0.921580i	$0.626899\pi$
$284$	10.9484i	0.649667i
$285$	9.33946	0.553222
$286$	0	0
$287$	−0.0893760	−0.00527570
$288$	− 2.78234i	− 0.163951i
$289$	3.98828	0.234605
$290$	23.2787	1.36697
$291$	6.89267i	0.404056i
$292$	− 12.7187i	− 0.744304i
$293$	14.5582i	0.850498i	0.905076	+	0.425249i	$0.139813\pi$
$293$	14.5582i	0.850498i	−0.905076	+	0.425249i	$0.860187\pi$
$294$	0.466545i	0.0272095i
$295$	5.90148	0.343597
$296$	−9.69086	−0.563270
$297$	2.21950i	0.128788i
$298$	17.0078	0.985235
$299$	0	0
$300$	−3.02688	−0.174757
$301$	7.35374i	0.423863i
$302$	5.54567	0.319117
$303$	−3.84422	−0.220845
$304$	5.90621i	0.338744i
$305$	8.06485i	0.461792i
$306$	12.7467i	0.728681i
$307$	3.24267i	0.185069i	0.995709	+	0.0925345i	$0.0294968\pi$
$307$	3.24267i	0.185069i	−0.995709	+	0.0925345i	$0.970503\pi$
$308$	−0.822730	−0.0468794
$309$	6.21583	0.353606
$310$	− 14.5297i	− 0.825231i
$311$	−10.2709	−0.582408	−0.291204	−	0.956661i	$-0.594056\pi$
$311$	−10.2709	−0.582408	−0.291204	+	0.956661i	$0.594056\pi$
$312$	0	0
$313$	−6.13382	−0.346704	−0.173352	−	0.984860i	$-0.555460\pi$
$313$	−6.13382	−0.346704	−0.173352	+	0.984860i	$0.555460\pi$
$314$	2.29353i	0.129431i
$315$	−9.43038	−0.531342
$316$	−9.95602	−0.560070
$317$	− 5.04487i	− 0.283348i	−0.989913	−	0.141674i	$-0.954752\pi$
$317$	− 5.04487i	− 0.283348i	0.989913	−	0.141674i	$-0.0452485\pi$
$318$	3.27295i	0.183538i
$319$	− 5.65062i	− 0.316374i
$320$	− 3.38938i	− 0.189472i
$321$	4.21127	0.235050
$322$	6.13055	0.341642
$323$	− 27.0581i	− 1.50555i
$324$	−7.08840	−0.393800
$325$	0	0
$326$	−23.3560	−1.29357
$327$	− 0.185308i	− 0.0102475i
$328$	−0.0893760	−0.00493496
$329$	−11.1759	−0.616150
$330$	1.30098i	0.0716166i
$331$	23.0874i	1.26900i	0.772924	+	0.634499i	$0.218793\pi$
$331$	23.0874i	1.26900i	−0.772924	+	0.634499i	$0.781207\pi$
$332$	3.23553i	0.177573i
$333$	26.9632i	1.47758i
$334$	21.7780	1.19164
$335$	−0.988744	−0.0540209
$336$	0.466545i	0.0254521i
$337$	29.1429	1.58751	0.793757	−	0.608235i	$-0.208122\pi$
$337$	29.1429	1.58751	0.793757	+	0.608235i	$0.208122\pi$
$338$	0	0
$339$	−2.08696	−0.113348
$340$	15.5277i	0.842110i
$341$	−3.52691	−0.190993
$342$	16.4330	0.888597
$343$	1.00000i	0.0539949i
$344$	7.35374i	0.396487i
$345$	− 9.69421i	− 0.521919i
$346$	− 8.09733i	− 0.435315i
$347$	−29.1082	−1.56261	−0.781306	−	0.624148i	$-0.785446\pi$
$347$	−29.1082	−1.56261	−0.781306	+	0.624148i	$0.785446\pi$
$348$	−3.20429	−0.171768
$349$	25.7802i	1.37998i	0.723817	+	0.689992i	$0.242386\pi$
$349$	25.7802i	1.37998i	−0.723817	+	0.689992i	$0.757614\pi$
$350$	−6.48787	−0.346791
$351$	0	0
$352$	−0.822730	−0.0438517
$353$	− 9.91779i	− 0.527871i	−0.964540	−	0.263935i	$-0.914979\pi$
$353$	− 9.91779i	− 0.527871i	0.964540	−	0.263935i	$-0.0850206\pi$
$354$	−0.812334	−0.0431751
$355$	37.1082	1.96950
$356$	− 8.04265i	− 0.426260i
$357$	− 2.13738i	− 0.113122i
$358$	− 9.90883i	− 0.523698i
$359$	25.2683i	1.33361i	0.745233	+	0.666804i	$0.232338\pi$
$359$	25.2683i	1.33361i	−0.745233	+	0.666804i	$0.767662\pi$
$360$	−9.43038	−0.497025
$361$	−15.8833	−0.835962
$362$	1.27902i	0.0672236i
$363$	−4.81620	−0.252785
$364$	0	0
$365$	−43.1084	−2.25640
$366$	− 1.11012i	− 0.0580269i
$367$	35.7838	1.86790	0.933950	−	0.357404i	$-0.116338\pi$
$367$	35.7838	1.86790	0.933950	+	0.357404i	$0.116338\pi$
$368$	6.13055	0.319577
$369$	0.248674i	0.0129455i
$370$	32.8460i	1.70758i
$371$	7.01530i	0.364216i
$372$	2.00000i	0.103695i
$373$	−23.3304	−1.20800	−0.604000	−	0.796984i	$-0.706427\pi$
$373$	−23.3304	−1.20800	−0.604000	+	0.796984i	$0.706427\pi$
$374$	3.76917	0.194899
$375$	2.35277i	0.121496i
$376$	−11.1759	−0.576355
$377$	0	0
$378$	2.69772	0.138756
$379$	24.3066i	1.24855i	0.781206	+	0.624274i	$0.214605\pi$
$379$	24.3066i	1.24855i	−0.781206	+	0.624274i	$0.785395\pi$
$380$	20.0184	1.02692
$381$	−0.251993	−0.0129100
$382$	− 10.0342i	− 0.513395i
$383$	− 4.91150i	− 0.250966i	−0.992096	−	0.125483i	$-0.959952\pi$
$383$	− 4.91150i	− 0.250966i	0.992096	−	0.125483i	$-0.0400480\pi$
$384$	0.466545i	0.0238083i
$385$	2.78854i	0.142117i
$386$	15.8582	0.807162
$387$	20.4606	1.04007
$388$	14.7739i	0.750029i
$389$	−5.14522	−0.260873	−0.130437	−	0.991457i	$-0.541638\pi$
$389$	−5.14522	−0.260873	−0.130437	+	0.991457i	$0.541638\pi$
$390$	0	0
$391$	−28.0858	−1.42036
$392$	1.00000i	0.0505076i
$393$	3.60460	0.181828
$394$	−14.8081	−0.746019
$395$	33.7447i	1.69788i
$396$	2.28911i	0.115032i
$397$	12.3500i	0.619827i	0.950765	+	0.309913i	$0.100300\pi$
$397$	12.3500i	0.619827i	−0.950765	+	0.309913i	$0.899700\pi$
$398$	2.55543i	0.128092i
$399$	−2.75551	−0.137948
$400$	−6.48787	−0.324394
$401$	32.4894i	1.62244i	0.584739	+	0.811221i	$0.301197\pi$
$401$	32.4894i	1.62244i	−0.584739	+	0.811221i	$0.698803\pi$
$402$	0.136100	0.00678804
$403$	0	0
$404$	−8.23976	−0.409943
$405$	24.0253i	1.19382i
$406$	−6.86813	−0.340859
$407$	7.97296	0.395205
$408$	− 2.13738i	− 0.105816i
$409$	− 3.76834i	− 0.186332i	−0.995651	−	0.0931662i	$-0.970301\pi$
$409$	− 3.76834i	− 0.186332i	0.995651	−	0.0931662i	$-0.0296988\pi$
$410$	0.302929i	0.0149606i
$411$	5.85052i	0.288585i
$412$	13.3231	0.656383
$413$	−1.74117	−0.0856774
$414$	− 17.0572i	− 0.838317i
$415$	10.9664	0.538321
$416$	0	0
$417$	−5.64396	−0.276386
$418$	− 4.85921i	− 0.237672i
$419$	−10.5301	−0.514428	−0.257214	−	0.966354i	$-0.582805\pi$
$419$	−10.5301	−0.514428	−0.257214	+	0.966354i	$0.582805\pi$
$420$	1.58130	0.0771594
$421$	− 24.9973i	− 1.21830i	−0.793057	−	0.609148i	$-0.791512\pi$
$421$	− 24.9973i	− 1.21830i	0.793057	−	0.609148i	$-0.208488\pi$
$422$	− 8.63648i	− 0.420417i
$423$	31.0952i	1.51190i
$424$	7.01530i	0.340693i
$425$	29.7229	1.44177
$426$	−5.10792	−0.247479
$427$	− 2.37945i	− 0.115150i
$428$	9.02649	0.436312
$429$	0	0
$430$	24.9246	1.20197
$431$	11.9784i	0.576979i	0.957483	+	0.288489i	$0.0931530\pi$
$431$	11.9784i	0.576979i	−0.957483	+	0.288489i	$0.906847\pi$
$432$	2.69772	0.129794
$433$	−7.96950	−0.382990	−0.191495	−	0.981494i	$-0.561334\pi$
$433$	−7.96950	−0.382990	−0.191495	+	0.981494i	$0.561334\pi$
$434$	4.28683i	0.205775i
$435$	10.8605i	0.520723i
$436$	− 0.397192i	− 0.0190220i
$437$	36.2083i	1.73208i
$438$	5.93384	0.283530
$439$	−4.35655	−0.207927	−0.103963	−	0.994581i	$-0.533152\pi$
$439$	−4.35655	−0.207927	−0.103963	+	0.994581i	$0.533152\pi$
$440$	2.78854i	0.132939i
$441$	2.78234	0.132492
$442$	0	0
$443$	−11.4823	−0.545542	−0.272771	−	0.962079i	$-0.587940\pi$
$443$	−11.4823	−0.545542	−0.272771	+	0.962079i	$0.587940\pi$
$444$	− 4.52122i	− 0.214568i
$445$	−27.2596	−1.29223
$446$	19.9277	0.943603
$447$	7.93490i	0.375308i
$448$	1.00000i	0.0472456i
$449$	29.5248i	1.39336i	0.717382	+	0.696680i	$0.245340\pi$
$449$	29.5248i	1.39336i	−0.717382	+	0.696680i	$0.754660\pi$
$450$	18.0514i	0.850953i
$451$	0.0735323	0.00346250
$452$	−4.47322	−0.210402
$453$	2.58730i	0.121562i
$454$	0.352624	0.0165495
$455$	0	0
$456$	−2.75551	−0.129039
$457$	− 16.5981i	− 0.776428i	−0.921569	−	0.388214i	$-0.873092\pi$
$457$	− 16.5981i	− 0.776428i	0.921569	−	0.388214i	$-0.126908\pi$
$458$	−8.31317	−0.388449
$459$	−12.3591	−0.576871
$460$	− 20.7787i	− 0.968813i
$461$	− 26.4422i	− 1.23154i	−0.787927	−	0.615769i	$-0.788846\pi$
$461$	− 26.4422i	− 1.23154i	0.787927	−	0.615769i	$-0.211154\pi$
$462$	− 0.383841i	− 0.0178579i
$463$	− 10.4717i	− 0.486663i	−0.969943	−	0.243331i	$-0.921760\pi$
$463$	− 10.4717i	− 0.486663i	0.969943	−	0.243331i	$-0.0782403\pi$
$464$	−6.86813	−0.318845
$465$	6.77875	0.314357
$466$	− 15.3798i	− 0.712454i
$467$	27.9010	1.29110	0.645551	−	0.763717i	$-0.276628\pi$
$467$	27.9010	1.29110	0.645551	+	0.763717i	$0.276628\pi$
$468$	0	0
$469$	0.291719	0.0134703
$470$	37.8795i	1.74725i
$471$	−1.07003	−0.0493046
$472$	−1.74117	−0.0801438
$473$	− 6.05015i	− 0.278186i
$474$	− 4.64493i	− 0.213349i
$475$	− 38.3187i	− 1.75818i
$476$	− 4.58130i	− 0.209983i
$477$	19.5189	0.893710
$478$	2.88606	0.132005
$479$	− 6.88133i	− 0.314416i	−0.987566	−	0.157208i	$-0.949751\pi$
$479$	− 6.88133i	− 0.314416i	0.987566	−	0.157208i	$-0.0502493\pi$
$480$	1.58130	0.0721760
$481$	0	0
$482$	−6.26744	−0.285474
$483$	2.86018i	0.130142i
$484$	−10.3231	−0.469232
$485$	50.0742	2.27375
$486$	− 11.4002i	− 0.517124i
$487$	40.8062i	1.84911i	0.381053	+	0.924553i	$0.375562\pi$
$487$	40.8062i	1.84911i	−0.381053	+	0.924553i	$0.624438\pi$
$488$	− 2.37945i	− 0.107713i
$489$	− 10.8966i	− 0.492762i
$490$	3.38938	0.153116
$491$	−6.72706	−0.303588	−0.151794	−	0.988412i	$-0.548505\pi$
$491$	−6.72706	−0.303588	−0.151794	+	0.988412i	$0.548505\pi$
$492$	− 0.0416979i	− 0.00187989i
$493$	31.4649	1.41711
$494$	0	0
$495$	7.75866	0.348726
$496$	4.28683i	0.192484i
$497$	−10.9484	−0.491102
$498$	−1.50952	−0.0676433
$499$	− 1.16200i	− 0.0520184i	−0.999662	−	0.0260092i	$-0.991720\pi$
$499$	− 1.16200i	− 0.0520184i	0.999662	−	0.0260092i	$-0.00827993\pi$
$500$	5.04295i	0.225528i
$501$	10.1604i	0.453933i
$502$	− 17.2665i	− 0.770641i
$503$	9.95053	0.443672	0.221836	−	0.975084i	$-0.428795\pi$
$503$	9.95053	0.443672	0.221836	+	0.975084i	$0.428795\pi$
$504$	2.78234	0.123935
$505$	27.9277i	1.24276i
$506$	−5.04379	−0.224224
$507$	0	0
$508$	−0.540127	−0.0239642
$509$	− 0.0522003i	− 0.00231374i	−0.999999	−	0.00115687i	$-0.999632\pi$
$509$	− 0.0522003i	− 0.00231374i	0.999999	−	0.00115687i	$-0.000368243\pi$
$510$	−7.24439	−0.320787
$511$	12.7187	0.562641
$512$	1.00000i	0.0441942i
$513$	15.9333i	0.703472i
$514$	11.1931i	0.493706i
$515$	− 45.1570i	− 1.98986i
$516$	−3.43085	−0.151035
$517$	9.19479	0.404386
$518$	− 9.69086i	− 0.425792i
$519$	3.77777	0.165826
$520$	0	0
$521$	26.0984	1.14339	0.571695	−	0.820466i	$-0.306286\pi$
$521$	26.0984	1.14339	0.571695	+	0.820466i	$0.306286\pi$
$522$	19.1094i	0.836397i
$523$	−19.5321	−0.854080	−0.427040	−	0.904233i	$-0.640444\pi$
$523$	−19.5321	−0.854080	−0.427040	+	0.904233i	$0.640444\pi$
$524$	7.72615	0.337518
$525$	− 3.02688i	− 0.132104i
$526$	− 28.5826i	− 1.24626i
$527$	− 19.6392i	− 0.855499i
$528$	− 0.383841i	− 0.0167045i
$529$	14.5836	0.634069
$530$	23.7775	1.03283
$531$	4.84452i	0.210234i
$532$	−5.90621	−0.256067
$533$	0	0
$534$	3.75226	0.162376
$535$	− 30.5942i	− 1.32270i
$536$	0.291719	0.0126003
$537$	4.62292	0.199494
$538$	− 18.3754i	− 0.792219i
$539$	− 0.822730i	− 0.0354375i
$540$	− 9.14359i	− 0.393477i
$541$	32.8802i	1.41363i	0.707399	+	0.706814i	$0.249868\pi$
$541$	32.8802i	1.41363i	−0.707399	+	0.706814i	$0.750132\pi$
$542$	−20.3825	−0.875504
$543$	−0.596719	−0.0256077
$544$	− 4.58130i	− 0.196421i
$545$	−1.34623	−0.0576662
$546$	0	0
$547$	−39.0180	−1.66829	−0.834144	−	0.551546i	$-0.814038\pi$
$547$	−39.0180	−1.66829	−0.834144	+	0.551546i	$0.814038\pi$
$548$	12.5401i	0.535687i
$549$	−6.62043	−0.282553
$550$	5.33777	0.227603
$551$	− 40.5646i	− 1.72811i
$552$	2.86018i	0.121737i
$553$	− 9.95602i	− 0.423373i
$554$	− 7.23219i	− 0.307266i
$555$	−15.3241	−0.650473
$556$	−12.0974	−0.513042
$557$	− 29.5492i	− 1.25204i	−0.779807	−	0.626020i	$-0.784683\pi$
$557$	− 29.5492i	− 1.25204i	0.779807	−	0.626020i	$-0.215317\pi$
$558$	11.9274	0.504927
$559$	0	0
$560$	3.38938	0.143227
$561$	1.75849i	0.0742434i
$562$	12.4585	0.525532
$563$	27.1323	1.14349	0.571745	−	0.820431i	$-0.306267\pi$
$563$	27.1323	1.14349	0.571745	+	0.820431i	$0.306267\pi$
$564$	− 5.21408i	− 0.219552i
$565$	15.1614i	0.637845i
$566$	− 13.0607i	− 0.548982i
$567$	− 7.08840i	− 0.297685i
$568$	−10.9484	−0.459384
$569$	−42.4594	−1.77999	−0.889996	−	0.455969i	$-0.849293\pi$
$569$	−42.4594	−1.77999	−0.889996	+	0.455969i	$0.849293\pi$
$570$	9.33946i	0.391187i
$571$	−11.2678	−0.471543	−0.235771	−	0.971809i	$-0.575762\pi$
$571$	−11.2678	−0.471543	−0.235771	+	0.971809i	$0.575762\pi$
$572$	0	0
$573$	4.68141	0.195569
$574$	− 0.0893760i	− 0.00373048i
$575$	−39.7742	−1.65870
$576$	2.78234	0.115931
$577$	− 22.8987i	− 0.953286i	−0.879097	−	0.476643i	$-0.841853\pi$
$577$	− 22.8987i	− 0.953286i	0.879097	−	0.476643i	$-0.158147\pi$
$578$	3.98828i	0.165890i
$579$	7.39857i	0.307474i
$580$	23.2787i	0.966594i
$581$	−3.23553	−0.134233
$582$	−6.89267	−0.285710
$583$	− 5.77170i	− 0.239039i
$584$	12.7187	0.526303
$585$	0	0
$586$	−14.5582	−0.601393
$587$	35.8019i	1.47770i	0.673868	+	0.738852i	$0.264632\pi$
$587$	35.8019i	1.47770i	−0.673868	+	0.738852i	$0.735368\pi$
$588$	−0.466545	−0.0192400
$589$	−25.3189	−1.04325
$590$	5.90148i	0.242960i
$591$	− 6.90862i	− 0.284183i
$592$	− 9.69086i	− 0.398292i
$593$	− 14.6093i	− 0.599931i	−0.953950	−	0.299965i	$-0.903025\pi$
$593$	− 14.6093i	− 0.599931i	0.953950	−	0.299965i	$-0.0969752\pi$
$594$	−2.21950	−0.0910670
$595$	−15.5277	−0.636575
$596$	17.0078i	0.696666i
$597$	−1.19222	−0.0487944
$598$	0	0
$599$	−37.5729	−1.53519	−0.767594	−	0.640936i	$-0.778546\pi$
$599$	−37.5729	−1.53519	−0.767594	+	0.640936i	$0.778546\pi$
$600$	− 3.02688i	− 0.123572i
$601$	−5.45158	−0.222375	−0.111187	−	0.993799i	$-0.535465\pi$
$601$	−5.45158	−0.222375	−0.111187	+	0.993799i	$0.535465\pi$
$602$	−7.35374	−0.299716
$603$	− 0.811659i	− 0.0330533i
$604$	5.54567i	0.225650i
$605$	34.9889i	1.42250i
$606$	− 3.84422i	− 0.156161i
$607$	−39.9387	−1.62106	−0.810531	−	0.585696i	$-0.800821\pi$
$607$	−39.9387	−1.62106	−0.810531	+	0.585696i	$0.800821\pi$
$608$	−5.90621	−0.239528
$609$	− 3.20429i	− 0.129844i
$610$	−8.06485	−0.326536
$611$	0	0
$612$	−12.7467	−0.515255
$613$	16.6552i	0.672696i	0.941738	+	0.336348i	$0.109192\pi$
$613$	16.6552i	0.672696i	−0.941738	+	0.336348i	$0.890808\pi$
$614$	−3.24267	−0.130864
$615$	−0.141330	−0.00569897
$616$	− 0.822730i	− 0.0331487i
$617$	26.9652i	1.08558i	0.839869	+	0.542788i	$0.182631\pi$
$617$	26.9652i	1.08558i	−0.839869	+	0.542788i	$0.817369\pi$
$618$	6.21583i	0.250037i
$619$	− 12.7533i	− 0.512597i	−0.966598	−	0.256298i	$-0.917497\pi$
$619$	− 12.7533i	− 0.512597i	0.966598	−	0.256298i	$-0.0825029\pi$
$620$	14.5297	0.583526
$621$	16.5385	0.663667
$622$	− 10.2709i	− 0.411825i
$623$	8.04265	0.322222
$624$	0	0
$625$	−15.3469	−0.613875
$626$	− 6.13382i	− 0.245157i
$627$	2.26704	0.0905369
$628$	−2.29353	−0.0915218
$629$	44.3967i	1.77021i
$630$	− 9.43038i	− 0.375715i
$631$	− 37.5529i	− 1.49496i	−0.664286	−	0.747479i	$-0.731264\pi$
$631$	− 37.5529i	− 1.49496i	0.664286	−	0.747479i	$-0.268736\pi$
$632$	− 9.95602i	− 0.396029i
$633$	4.02931	0.160151
$634$	5.04487	0.200357
$635$	1.83069i	0.0726488i
$636$	−3.27295	−0.129781
$637$	0	0
$638$	5.65062	0.223710
$639$	30.4621i	1.20506i
$640$	3.38938	0.133977
$641$	−1.97623	−0.0780564	−0.0390282	−	0.999238i	$-0.512426\pi$
$641$	−1.97623	−0.0780564	−0.0390282	+	0.999238i	$0.512426\pi$
$642$	4.21127i	0.166205i
$643$	39.0704i	1.54079i	0.637568	+	0.770394i	$0.279940\pi$
$643$	39.0704i	1.54079i	−0.637568	+	0.770394i	$0.720060\pi$
$644$	6.13055i	0.241577i
$645$	11.6284i	0.457870i
$646$	27.0581	1.06459
$647$	−12.1051	−0.475900	−0.237950	−	0.971277i	$-0.576475\pi$
$647$	−12.1051	−0.475900	−0.237950	+	0.971277i	$0.576475\pi$
$648$	− 7.08840i	− 0.278459i
$649$	1.43251	0.0562311
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	− 23.3560i	− 0.914691i
$653$	40.2464	1.57496	0.787481	−	0.616338i	$-0.211385\pi$
$653$	40.2464	1.57496	0.787481	+	0.616338i	$0.211385\pi$
$654$	0.185308	0.00724611
$655$	− 26.1868i	− 1.02320i
$656$	− 0.0893760i	− 0.00348955i
$657$	− 35.3876i	− 1.38060i
$658$	− 11.1759i	− 0.435684i
$659$	−3.62327	−0.141143	−0.0705714	−	0.997507i	$-0.522482\pi$
$659$	−3.62327	−0.141143	−0.0705714	+	0.997507i	$0.522482\pi$
$660$	−1.30098	−0.0506406
$661$	− 23.6365i	− 0.919352i	−0.888087	−	0.459676i	$-0.847965\pi$
$661$	− 23.6365i	− 0.919352i	0.888087	−	0.459676i	$-0.152035\pi$
$662$	−23.0874	−0.897317
$663$	0	0
$664$	−3.23553	−0.125563
$665$	20.0184i	0.776278i
$666$	−26.9632	−1.04480
$667$	−42.1054	−1.63033
$668$	21.7780i	0.842614i
$669$	9.29716i	0.359449i
$670$	− 0.988744i	− 0.0381985i
$671$	1.95764i	0.0755740i
$672$	−0.466545	−0.0179974
$673$	−46.8710	−1.80674	−0.903372	−	0.428859i	$-0.858916\pi$
$673$	−46.8710	−1.80674	−0.903372	+	0.428859i	$0.858916\pi$
$674$	29.1429i	1.12254i
$675$	−17.5025	−0.673670
$676$	0	0
$677$	−13.7304	−0.527704	−0.263852	−	0.964563i	$-0.584993\pi$
$677$	−13.7304	−0.527704	−0.263852	+	0.964563i	$0.584993\pi$
$678$	− 2.08696i	− 0.0801491i
$679$	−14.7739	−0.566969
$680$	−15.5277	−0.595462
$681$	0.164515i	0.00630423i
$682$	− 3.52691i	− 0.135052i
$683$	− 3.50578i	− 0.134145i	−0.997748	−	0.0670725i	$-0.978634\pi$
$683$	− 3.50578i	− 0.134145i	0.997748	−	0.0670725i	$-0.0213659\pi$
$684$	16.4330i	0.628333i
$685$	42.5031	1.62396
$686$	−1.00000	−0.0381802
$687$	− 3.87847i	− 0.147973i
$688$	−7.35374	−0.280359
$689$	0	0
$690$	9.69421	0.369052
$691$	− 31.7769i	− 1.20885i	−0.796662	−	0.604426i	$-0.793403\pi$
$691$	− 31.7769i	− 1.20885i	0.796662	−	0.604426i	$-0.206597\pi$
$692$	8.09733	0.307814
$693$	−2.28911	−0.0869562
$694$	− 29.1082i	− 1.10493i
$695$	41.0025i	1.55531i
$696$	− 3.20429i	− 0.121458i
$697$	0.409458i	0.0155093i
$698$	−25.7802	−0.975796
$699$	7.17535	0.271397
$700$	− 6.48787i	− 0.245218i
$701$	−31.6828	−1.19664	−0.598322	−	0.801256i	$-0.704166\pi$
$701$	−31.6828	−1.19664	−0.598322	+	0.801256i	$0.704166\pi$
$702$	0	0
$703$	57.2362	2.15870
$704$	− 0.822730i	− 0.0310078i
$705$	−17.6725	−0.665584
$706$	9.91779	0.373261
$707$	− 8.23976i	− 0.309888i
$708$	− 0.812334i	− 0.0305294i
$709$	35.3147i	1.32627i	0.748498	+	0.663137i	$0.230775\pi$
$709$	35.3147i	1.32627i	−0.748498	+	0.663137i	$0.769225\pi$
$710$	37.1082i	1.39265i
$711$	−27.7010	−1.03887
$712$	8.04265	0.301411
$713$	26.2806i	0.984217i
$714$	2.13738	0.0799895
$715$	0	0
$716$	9.90883	0.370310
$717$	1.34648i	0.0502850i
$718$	−25.2683	−0.943003
$719$	1.21956	0.0454818	0.0227409	−	0.999741i	$-0.492761\pi$
$719$	1.21956	0.0454818	0.0227409	+	0.999741i	$0.492761\pi$
$720$	− 9.43038i	− 0.351450i
$721$	13.3231i	0.496179i
$722$	− 15.8833i	− 0.591114i
$723$	− 2.92404i	− 0.108746i
$724$	−1.27902	−0.0475343
$725$	44.5595	1.65490
$726$	− 4.81620i	− 0.178746i
$727$	5.75380	0.213397	0.106698	−	0.994291i	$-0.465972\pi$
$727$	5.75380	0.213397	0.106698	+	0.994291i	$0.465972\pi$
$728$	0	0
$729$	−15.9465	−0.590611
$730$	− 43.1084i	− 1.59551i
$731$	33.6897	1.24606
$732$	1.11012	0.0410312
$733$	35.2258i	1.30110i	0.759466	+	0.650548i	$0.225461\pi$
$733$	35.2258i	1.30110i	−0.759466	+	0.650548i	$0.774539\pi$
$734$	35.7838i	1.32080i
$735$	1.58130i	0.0583270i
$736$	6.13055i	0.225975i
$737$	−0.240006	−0.00884073
$738$	−0.248674	−0.00915382
$739$	− 29.3524i	− 1.07975i	−0.841746	−	0.539873i	$-0.818472\pi$
$739$	− 29.3524i	− 1.07975i	0.841746	−	0.539873i	$-0.181528\pi$
$740$	−32.8460	−1.20744
$741$	0	0
$742$	−7.01530	−0.257540
$743$	− 14.9838i	− 0.549702i	−0.961487	−	0.274851i	$-0.911371\pi$
$743$	− 14.9838i	− 0.549702i	0.961487	−	0.274851i	$-0.0886286\pi$
$744$	−2.00000	−0.0733236
$745$	57.6458	2.11198
$746$	− 23.3304i	− 0.854185i
$747$	9.00234i	0.329378i
$748$	3.76917i	0.137815i
$749$	9.02649i	0.329821i
$750$	−2.35277	−0.0859108
$751$	−43.8390	−1.59971	−0.799855	−	0.600194i	$-0.795090\pi$
$751$	−43.8390	−1.59971	−0.799855	+	0.600194i	$0.795090\pi$
$752$	− 11.1759i	− 0.407545i
$753$	8.05560	0.293562
$754$	0	0
$755$	18.7963	0.684069
$756$	2.69772i	0.0981151i
$757$	−36.3597	−1.32152	−0.660758	−	0.750599i	$-0.729765\pi$
$757$	−36.3597	−1.32152	−0.660758	+	0.750599i	$0.729765\pi$
$758$	−24.3066	−0.882856
$759$	− 2.35315i	− 0.0854140i
$760$	20.0184i	0.726142i
$761$	18.2335i	0.660962i	0.943813	+	0.330481i	$0.107211\pi$
$761$	18.2335i	0.660962i	−0.943813	+	0.330481i	$0.892789\pi$
$762$	− 0.251993i	− 0.00912876i
$763$	0.397192	0.0143793
$764$	10.0342	0.363025
$765$	43.2034i	1.56202i
$766$	4.91150	0.177460
$767$	0	0
$768$	−0.466545	−0.0168350
$769$	− 6.54565i	− 0.236042i	−0.993011	−	0.118021i	$-0.962345\pi$
$769$	− 6.54565i	− 0.236042i	0.993011	−	0.118021i	$-0.0376551\pi$
$770$	−2.78854	−0.100492
$771$	−5.22208	−0.188069
$772$	15.8582i	0.570750i
$773$	− 44.6466i	− 1.60583i	−0.596097	−	0.802913i	$-0.703282\pi$
$773$	− 44.6466i	− 1.60583i	0.596097	−	0.802913i	$-0.296718\pi$
$774$	20.4606i	0.735440i
$775$	− 27.8124i	− 0.999051i
$776$	−14.7739	−0.530351
$777$	4.52122	0.162198
$778$	− 5.14522i	− 0.184465i
$779$	0.527873	0.0189130
$780$	0	0
$781$	9.00757	0.322316
$782$	− 28.0858i	− 1.00435i
$783$	−18.5283	−0.662147
$784$	−1.00000	−0.0357143
$785$	7.77363i	0.277453i
$786$	3.60460i	0.128572i
$787$	− 25.0526i	− 0.893028i	−0.894777	−	0.446514i	$-0.852665\pi$
$787$	− 25.0526i	− 0.893028i	0.894777	−	0.446514i	$-0.147335\pi$
$788$	− 14.8081i	− 0.527515i
$789$	13.3351	0.474742
$790$	−33.7447	−1.20058
$791$	− 4.47322i	− 0.159049i
$792$	−2.28911	−0.0813400
$793$	0	0
$794$	−12.3500	−0.438284
$795$	11.0933i	0.393438i
$796$	−2.55543	−0.0905747
$797$	−27.8264	−0.985662	−0.492831	−	0.870125i	$-0.664038\pi$
$797$	−27.8264	−0.985662	−0.492831	+	0.870125i	$0.664038\pi$
$798$	− 2.75551i	− 0.0975440i
$799$	51.2003i	1.81134i
$800$	− 6.48787i	− 0.229381i
$801$	− 22.3774i	− 0.790665i
$802$	−32.4894	−1.14724
$803$	−10.4640	−0.369268
$804$	0.136100i	0.00479987i
$805$	20.7787	0.732354
$806$	0	0
$807$	8.57294	0.301782
$808$	− 8.23976i	− 0.289874i
$809$	7.49650	0.263563	0.131781	−	0.991279i	$-0.457930\pi$
$809$	7.49650	0.263563	0.131781	+	0.991279i	$0.457930\pi$
$810$	−24.0253	−0.844161
$811$	− 9.88726i	− 0.347189i	−0.984817	−	0.173594i	$-0.944462\pi$
$811$	− 9.88726i	− 0.347189i	0.984817	−	0.173594i	$-0.0555381\pi$
$812$	− 6.86813i	− 0.241024i
$813$	− 9.50936i	− 0.333508i
$814$	7.97296i	0.279452i
$815$	−79.1622	−2.77293
$816$	2.13738	0.0748233
$817$	− 43.4327i	− 1.51952i
$818$	3.76834	0.131757
$819$	0	0
$820$	−0.302929	−0.0105787
$821$	14.3675i	0.501430i	0.968061	+	0.250715i	$0.0806657\pi$
$821$	14.3675i	0.501430i	−0.968061	+	0.250715i	$0.919334\pi$
$822$	−5.85052	−0.204060
$823$	−11.8869	−0.414350	−0.207175	−	0.978304i	$-0.566427\pi$
$823$	−11.8869	−0.414350	−0.207175	+	0.978304i	$0.566427\pi$
$824$	13.3231i	0.464133i
$825$	2.49031i	0.0867014i
$826$	− 1.74117i	− 0.0605830i
$827$	29.0884i	1.01150i	0.862679	+	0.505752i	$0.168785\pi$
$827$	29.0884i	1.01150i	−0.862679	+	0.505752i	$0.831215\pi$
$828$	17.0572	0.592780
$829$	49.6286	1.72367	0.861836	−	0.507187i	$-0.169315\pi$
$829$	49.6286	1.72367	0.861836	+	0.507187i	$0.169315\pi$
$830$	10.9664i	0.380651i
$831$	3.37414	0.117048
$832$	0	0
$833$	4.58130	0.158733
$834$	− 5.64396i	− 0.195434i
$835$	73.8137	2.55443
$836$	4.85921	0.168059
$837$	11.5647i	0.399734i
$838$	− 10.5301i	− 0.363755i
$839$	4.61692i	0.159394i	0.996819	+	0.0796969i	$0.0253952\pi$
$839$	4.61692i	0.159394i	−0.996819	+	0.0796969i	$0.974605\pi$
$840$	1.58130i	0.0545599i
$841$	18.1712	0.626593
$842$	24.9973	0.861465
$843$	5.81247i	0.200192i
$844$	8.63648	0.297280
$845$	0	0
$846$	−31.0952	−1.06908
$847$	− 10.3231i	− 0.354706i
$848$	−7.01530	−0.240906
$849$	6.09341	0.209125
$850$	29.7229i	1.01949i
$851$	− 59.4103i	− 2.03656i
$852$	− 5.10792i	− 0.174994i
$853$	− 37.8266i	− 1.29516i	−0.761999	−	0.647579i	$-0.775782\pi$
$853$	− 37.8266i	− 1.29516i	0.761999	−	0.647579i	$-0.224218\pi$
$854$	2.37945	0.0814231
$855$	55.6978	1.90482
$856$	9.02649i	0.308519i
$857$	30.1652	1.03042	0.515211	−	0.857063i	$-0.327713\pi$
$857$	30.1652	1.03042	0.515211	+	0.857063i	$0.327713\pi$
$858$	0	0
$859$	10.6316	0.362745	0.181372	−	0.983414i	$-0.441946\pi$
$859$	10.6316	0.362745	0.181372	+	0.983414i	$0.441946\pi$
$860$	24.9246i	0.849922i
$861$	0.0416979	0.00142106
$862$	−11.9784	−0.407986
$863$	23.8352i	0.811360i	0.914015	+	0.405680i	$0.132965\pi$
$863$	23.8352i	0.811360i	−0.914015	+	0.405680i	$0.867035\pi$
$864$	2.69772i	0.0917783i
$865$	− 27.4449i	− 0.933154i
$866$	− 7.96950i	− 0.270814i
$867$	−1.86071	−0.0631931
$868$	−4.28683	−0.145505
$869$	8.19112i	0.277865i
$870$	−10.8605	−0.368207
$871$	0	0
$872$	0.397192	0.0134506
$873$	41.1059i	1.39122i
$874$	−36.2083	−1.22476
$875$	−5.04295	−0.170483
$876$	5.93384i	0.200486i
$877$	− 28.4246i	− 0.959829i	−0.877315	−	0.479915i	$-0.840668\pi$
$877$	− 28.4246i	− 0.959829i	0.877315	−	0.479915i	$-0.159332\pi$
$878$	− 4.35655i	− 0.147026i
$879$	− 6.79205i	− 0.229090i
$880$	−2.78854	−0.0940017
$881$	−55.1829	−1.85916	−0.929580	−	0.368621i	$-0.879830\pi$
$881$	−55.1829	−1.85916	−0.929580	+	0.368621i	$0.879830\pi$
$882$	2.78234i	0.0936861i
$883$	9.18216	0.309004	0.154502	−	0.987992i	$-0.450623\pi$
$883$	9.18216	0.309004	0.154502	+	0.987992i	$0.450623\pi$
$884$	0	0
$885$	−2.75331	−0.0925514
$886$	− 11.4823i	− 0.385757i
$887$	33.5715	1.12722	0.563610	−	0.826041i	$-0.309412\pi$
$887$	33.5715	1.12722	0.563610	+	0.826041i	$0.309412\pi$
$888$	4.52122	0.151722
$889$	− 0.540127i	− 0.0181153i
$890$	− 27.2596i	− 0.913743i
$891$	5.83184i	0.195374i
$892$	19.9277i	0.667228i
$893$	66.0074	2.20885
$894$	−7.93490	−0.265383
$895$	− 33.5848i	− 1.12261i
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−29.5248	−0.985255
$899$	− 29.4425i	− 0.981963i
$900$	−18.0514	−0.601715
$901$	32.1392	1.07071
$902$	0.0735323i	0.00244836i
$903$	− 3.43085i	− 0.114172i
$904$	− 4.47322i	− 0.148777i
$905$	4.33507i	0.144103i
$906$	−2.58730	−0.0859574
$907$	−11.0349	−0.366409	−0.183205	−	0.983075i	$-0.558647\pi$
$907$	−11.0349	−0.366409	−0.183205	+	0.983075i	$0.558647\pi$
$908$	0.352624i	0.0117022i
$909$	−22.9258	−0.760400
$910$	0	0
$911$	59.9931	1.98766	0.993830	−	0.110917i	$-0.0353789\pi$
$911$	59.9931	1.98766	0.993830	+	0.110917i	$0.0353789\pi$
$912$	− 2.75551i	− 0.0912441i
$913$	2.66197	0.0880984
$914$	16.5981	0.549018
$915$	− 3.76261i	− 0.124388i
$916$	− 8.31317i	− 0.274675i
$917$	7.72615i	0.255140i
$918$	− 12.3591i	− 0.407910i
$919$	35.6537	1.17611	0.588053	−	0.808822i	$-0.299895\pi$
$919$	35.6537	1.17611	0.588053	+	0.808822i	$0.299895\pi$
$920$	20.7787	0.685054
$921$	− 1.51285i	− 0.0498502i
$922$	26.4422	0.870828
$923$	0	0
$924$	0.383841	0.0126274
$925$	62.8730i	2.06725i
$926$	10.4717	0.344123
$927$	37.0694	1.21752
$928$	− 6.86813i	− 0.225457i
$929$	− 29.0302i	− 0.952450i	−0.879324	−	0.476225i	$-0.842005\pi$
$929$	− 29.0302i	− 0.952450i	0.879324	−	0.476225i	$-0.157995\pi$
$930$	6.77875i	0.222284i
$931$	− 5.90621i	− 0.193568i
$932$	15.3798	0.503781
$933$	4.79183	0.156877
$934$	27.9010i	0.912947i
$935$	12.7751	0.417792
$936$	0	0
$937$	38.2635	1.25001	0.625006	−	0.780620i	$-0.285096\pi$
$937$	38.2635	1.25001	0.625006	+	0.780620i	$0.285096\pi$
$938$	0.291719i	0.00952495i
$939$	2.86170	0.0933882
$940$	−37.8795	−1.23549
$941$	4.14746i	0.135203i	0.997712	+	0.0676017i	$0.0215347\pi$
$941$	4.14746i	0.135203i	−0.997712	+	0.0676017i	$0.978465\pi$
$942$	− 1.07003i	− 0.0348636i
$943$	− 0.547924i	− 0.0178428i
$944$	− 1.74117i	− 0.0566702i
$945$	9.14359	0.297441
$946$	6.05015	0.196707
$947$	1.00792i	0.0327530i	0.999866	+	0.0163765i	$0.00521303\pi$
$947$	1.00792i	0.0327530i	−0.999866	+	0.0163765i	$0.994787\pi$
$948$	4.64493	0.150860
$949$	0	0
$950$	38.3187	1.24322
$951$	2.35366i	0.0763226i
$952$	4.58130	0.148481
$953$	−16.5029	−0.534582	−0.267291	−	0.963616i	$-0.586129\pi$
$953$	−16.5029	−0.534582	−0.267291	+	0.963616i	$0.586129\pi$
$954$	19.5189i	0.631948i
$955$	− 34.0097i	− 1.10053i
$956$	2.88606i	0.0933418i
$957$	2.63627i	0.0852184i
$958$	6.88133	0.222326
$959$	−12.5401	−0.404941
$960$	1.58130i	0.0510361i
$961$	12.6231	0.407196
$962$	0	0
$963$	25.1147	0.809311
$964$	− 6.26744i	− 0.201861i
$965$	53.7495	1.73026
$966$	−2.86018	−0.0920246
$967$	− 37.7765i	− 1.21481i	−0.794392	−	0.607406i	$-0.792210\pi$
$967$	− 37.7765i	− 1.21481i	0.794392	−	0.607406i	$-0.207790\pi$
$968$	− 10.3231i	− 0.331797i
$969$	12.6238i	0.405535i
$970$	50.0742i	1.60779i
$971$	−48.3122	−1.55041	−0.775206	−	0.631709i	$-0.782354\pi$
$971$	−48.3122	−1.55041	−0.775206	+	0.631709i	$0.782354\pi$
$972$	11.4002	0.365662
$973$	− 12.0974i	− 0.387823i
$974$	−40.8062	−1.30752
$975$	0	0
$976$	2.37945	0.0761643
$977$	− 16.3041i	− 0.521615i	−0.965391	−	0.260807i	$-0.916011\pi$
$977$	− 16.3041i	− 0.521615i	0.965391	−	0.260807i	$-0.0839888\pi$
$978$	10.8966	0.348435
$979$	−6.61693	−0.211478
$980$	3.38938i	0.108270i
$981$	− 1.10512i	− 0.0352838i
$982$	− 6.72706i	− 0.214669i
$983$	29.5121i	0.941291i	0.882322	+	0.470645i	$0.155979\pi$
$983$	29.5121i	0.941291i	−0.882322	+	0.470645i	$0.844021\pi$
$984$	0.0416979	0.00132928
$985$	−50.1901	−1.59919
$986$	31.4649i	1.00205i
$987$	5.21408	0.165966
$988$	0	0
$989$	−45.0825	−1.43354
$990$	7.75866i	0.246586i
$991$	4.39245	0.139531	0.0697653	−	0.997563i	$-0.477775\pi$
$991$	4.39245	0.139531	0.0697653	+	0.997563i	$0.477775\pi$
$992$	−4.28683	−0.136107
$993$	− 10.7713i	− 0.341817i
$994$	− 10.9484i	− 0.347262i
$995$	8.66130i	0.274582i
$996$	− 1.50952i	− 0.0478310i
$997$	46.3338	1.46741	0.733704	−	0.679470i	$-0.237790\pi$
$997$	46.3338	1.46741	0.733704	+	0.679470i	$0.237790\pi$
$998$	1.16200	0.0367826
$999$	− 26.1432i	− 0.827135i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.r.337.9		12
13.5	odd	4		2366.2.a.bh.1.3		6
13.8	odd	4		2366.2.a.bf.1.3		6
13.9	even	3		182.2.m.b.127.5	yes	12
13.10	even	6		182.2.m.b.43.5	✓	12
13.12	even	2	inner	2366.2.d.r.337.3		12
39.23	odd	6		1638.2.bj.g.1135.3		12
39.35	odd	6		1638.2.bj.g.127.1		12
52.23	odd	6		1456.2.cc.d.225.3		12
52.35	odd	6		1456.2.cc.d.673.3		12
91.9	even	3		1274.2.v.e.361.2		12
91.10	odd	6		1274.2.v.d.667.2		12
91.23	even	6		1274.2.o.d.459.2		12
91.48	odd	6		1274.2.m.c.491.5		12
91.61	odd	6		1274.2.v.d.361.2		12
91.62	odd	6		1274.2.m.c.589.5		12
91.74	even	3		1274.2.o.d.569.5		12
91.75	odd	6		1274.2.o.e.459.2		12
91.87	odd	6		1274.2.o.e.569.5		12
91.88	even	6		1274.2.v.e.667.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.5	✓	12	13.10	even	6
182.2.m.b.127.5	yes	12	13.9	even	3
1274.2.m.c.491.5		12	91.48	odd	6
1274.2.m.c.589.5		12	91.62	odd	6
1274.2.o.d.459.2		12	91.23	even	6
1274.2.o.d.569.5		12	91.74	even	3
1274.2.o.e.459.2		12	91.75	odd	6
1274.2.o.e.569.5		12	91.87	odd	6
1274.2.v.d.361.2		12	91.61	odd	6
1274.2.v.d.667.2		12	91.10	odd	6
1274.2.v.e.361.2		12	91.9	even	3
1274.2.v.e.667.2		12	91.88	even	6
1456.2.cc.d.225.3		12	52.23	odd	6
1456.2.cc.d.673.3		12	52.35	odd	6
1638.2.bj.g.127.1		12	39.35	odd	6
1638.2.bj.g.1135.3		12	39.23	odd	6
2366.2.a.bf.1.3		6	13.8	odd	4
2366.2.a.bh.1.3		6	13.5	odd	4
2366.2.d.r.337.3		12	13.12	even	2	inner
2366.2.d.r.337.9		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.466545 q^{3} -1.00000 q^{4} +3.38938i q^{5} -0.466545i q^{6} -1.00000i q^{7} -1.00000i q^{8} -2.78234 q^{9} -3.38938 q^{10} +0.822730i q^{11} +0.466545 q^{12} +1.00000 q^{14} -1.58130i q^{15} +1.00000 q^{16} -4.58130 q^{17} -2.78234i q^{18} +5.90621i q^{19} -3.38938i q^{20} +0.466545i q^{21} -0.822730 q^{22} +6.13055 q^{23} +0.466545i q^{24} -6.48787 q^{25} +2.69772 q^{27} +1.00000i q^{28} -6.86813 q^{29} +1.58130 q^{30} +4.28683i q^{31} +1.00000i q^{32} -0.383841i q^{33} -4.58130i q^{34} +3.38938 q^{35} +2.78234 q^{36} -9.69086i q^{37} -5.90621 q^{38} +3.38938 q^{40} -0.0893760i q^{41} -0.466545 q^{42} -7.35374 q^{43} -0.822730i q^{44} -9.43038i q^{45} +6.13055i q^{46} -11.1759i q^{47} -0.466545 q^{48} -1.00000 q^{49} -6.48787i q^{50} +2.13738 q^{51} -7.01530 q^{53} +2.69772i q^{54} -2.78854 q^{55} -1.00000 q^{56} -2.75551i q^{57} -6.86813i q^{58} -1.74117i q^{59} +1.58130i q^{60} +2.37945 q^{61} -4.28683 q^{62} +2.78234i q^{63} -1.00000 q^{64} +0.383841 q^{66} +0.291719i q^{67} +4.58130 q^{68} -2.86018 q^{69} +3.38938i q^{70} -10.9484i q^{71} +2.78234i q^{72} +12.7187i q^{73} +9.69086 q^{74} +3.02688 q^{75} -5.90621i q^{76} +0.822730 q^{77} +9.95602 q^{79} +3.38938i q^{80} +7.08840 q^{81} +0.0893760 q^{82} -3.23553i q^{83} -0.466545i q^{84} -15.5277i q^{85} -7.35374i q^{86} +3.20429 q^{87} +0.822730 q^{88} +8.04265i q^{89} +9.43038 q^{90} -6.13055 q^{92} -2.00000i q^{93} +11.1759 q^{94} -20.0184 q^{95} -0.466545i q^{96} -14.7739i q^{97} -1.00000i q^{98} -2.28911i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) \) 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

Introduction

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