LMFDB - Embedded newform 2366.2.d.r.337.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			337.8
Root			$0.500000 - 1.73154i$ of defining polynomial
Character	$\chi$	$=$	2366.337
Dual form			2366.2.d.r.337.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000i q^{2} -0.865515 q^{3} -1.00000 q^{4} -3.71131i q^{5} -0.865515i q^{6} -1.00000i q^{7} -1.00000i q^{8} -2.25088 q^{9} +3.71131 q^{10} +5.77486i q^{11} +0.865515 q^{12} +1.00000 q^{14} +3.21220i q^{15} +1.00000 q^{16} +0.212197 q^{17} -2.25088i q^{18} +2.13714i q^{19} +3.71131i q^{20} +0.865515i q^{21} -5.77486 q^{22} -2.47940 q^{23} +0.865515i q^{24} -8.77384 q^{25} +4.54472 q^{27} +1.00000i q^{28} -0.0985660 q^{29} -3.21220 q^{30} +2.31076i q^{31} +1.00000i q^{32} -4.99823i q^{33} +0.212197i q^{34} -3.71131 q^{35} +2.25088 q^{36} -7.87343i q^{37} -2.13714 q^{38} -3.71131 q^{40} -7.52119i q^{41} -0.865515 q^{42} -4.57973 q^{43} -5.77486i q^{44} +8.35373i q^{45} -2.47940i q^{46} +9.15570i q^{47} -0.865515 q^{48} -1.00000 q^{49} -8.77384i q^{50} -0.183660 q^{51} +12.0948 q^{53} +4.54472i q^{54} +21.4323 q^{55} -1.00000 q^{56} -1.84972i q^{57} -0.0985660i q^{58} -0.231914i q^{59} -3.21220i q^{60} +8.03211 q^{61} -2.31076 q^{62} +2.25088i q^{63} -1.00000 q^{64} +4.99823 q^{66} +12.9700i q^{67} -0.212197 q^{68} +2.14596 q^{69} -3.71131i q^{70} +7.36377i q^{71} +2.25088i q^{72} +5.60414i q^{73} +7.87343 q^{74} +7.59389 q^{75} -2.13714i q^{76} +5.77486 q^{77} -9.19749 q^{79} -3.71131i q^{80} +2.81913 q^{81} +7.52119 q^{82} +3.17186i q^{83} -0.865515i q^{84} -0.787529i q^{85} -4.57973i q^{86} +0.0853103 q^{87} +5.77486 q^{88} +11.8167i q^{89} -8.35373 q^{90} +2.47940 q^{92} -2.00000i q^{93} -9.15570 q^{94} +7.93158 q^{95} -0.865515i q^{96} +14.0819i q^{97} -1.00000i q^{98} -12.9985i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.865515	−0.499705	−0.249853	−	0.968284i	$-0.580382\pi$
$3$	−0.865515	−0.499705	−0.249853	+	0.968284i	$0.580382\pi$
$4$	−1.00000	−0.500000
$5$	− 3.71131i	− 1.65975i	−0.557950	−	0.829875i	$-0.688412\pi$
$5$	− 3.71131i	− 1.65975i	0.557950	−	0.829875i	$-0.311588\pi$
$6$	− 0.865515i	− 0.353345i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 1.00000i	− 0.353553i
$9$	−2.25088	−0.750295
$10$	3.71131	1.17362
$11$	5.77486i	1.74119i	0.492003	+	0.870594i	$0.336265\pi$
$11$	5.77486i	1.74119i	−0.492003	+	0.870594i	$0.663735\pi$
$12$	0.865515	0.249853
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	3.21220i	0.829386i
$16$	1.00000	0.250000
$17$	0.212197	0.0514653	0.0257327	−	0.999669i	$-0.491808\pi$
$17$	0.212197	0.0514653	0.0257327	+	0.999669i	$0.491808\pi$
$18$	− 2.25088i	− 0.530538i
$19$	2.13714i	0.490293i	0.969486	+	0.245146i	$0.0788360\pi$
$19$	2.13714i	0.490293i	−0.969486	+	0.245146i	$0.921164\pi$
$20$	3.71131i	0.829875i
$21$	0.865515i	0.188871i
$22$	−5.77486	−1.23121
$23$	−2.47940	−0.516990	−0.258495	−	0.966013i	$-0.583227\pi$
$23$	−2.47940	−0.516990	−0.258495	+	0.966013i	$0.583227\pi$
$24$	0.865515i	0.176673i
$25$	−8.77384	−1.75477
$26$	0	0
$27$	4.54472	0.874632
$28$	1.00000i	0.188982i
$29$	−0.0985660	−0.0183032	−0.00915162	−	0.999958i	$-0.502913\pi$
$29$	−0.0985660	−0.0183032	−0.00915162	+	0.999958i	$0.502913\pi$
$30$	−3.21220	−0.586464
$31$	2.31076i	0.415025i	0.978232	+	0.207513i	$0.0665368\pi$
$31$	2.31076i	0.415025i	−0.978232	+	0.207513i	$0.933463\pi$
$32$	1.00000i	0.176777i
$33$	− 4.99823i	− 0.870080i
$34$	0.212197i	0.0363915i
$35$	−3.71131	−0.627326
$36$	2.25088	0.375147
$37$	− 7.87343i	− 1.29438i	−0.762327	−	0.647192i	$-0.775943\pi$
$37$	− 7.87343i	− 1.29438i	0.762327	−	0.647192i	$-0.224057\pi$
$38$	−2.13714	−0.346689
$39$	0	0
$40$	−3.71131	−0.586810
$41$	− 7.52119i	− 1.17461i	−0.809365	−	0.587306i	$-0.800188\pi$
$41$	− 7.52119i	− 1.17461i	0.809365	−	0.587306i	$-0.199812\pi$
$42$	−0.865515	−0.133552
$43$	−4.57973	−0.698403	−0.349201	−	0.937048i	$-0.613547\pi$
$43$	−4.57973	−0.698403	−0.349201	+	0.937048i	$0.613547\pi$
$44$	− 5.77486i	− 0.870594i
$45$	8.35373i	1.24530i
$46$	− 2.47940i	− 0.365567i
$47$	9.15570i	1.33550i	0.744388	+	0.667748i	$0.232742\pi$
$47$	9.15570i	1.33550i	−0.744388	+	0.667748i	$0.767258\pi$
$48$	−0.865515	−0.124926
$49$	−1.00000	−0.142857
$50$	− 8.77384i	− 1.24081i
$51$	−0.183660	−0.0257175
$52$	0	0
$53$	12.0948	1.66135	0.830674	−	0.556759i	$-0.187955\pi$
$53$	12.0948	1.66135	0.830674	+	0.556759i	$0.187955\pi$
$54$	4.54472i	0.618458i
$55$	21.4323	2.88993
$56$	−1.00000	−0.133631
$57$	− 1.84972i	− 0.245002i
$58$	− 0.0985660i	− 0.0129423i
$59$	− 0.231914i	− 0.0301926i	−0.999886	−	0.0150963i	$-0.995195\pi$
$59$	− 0.231914i	− 0.0301926i	0.999886	−	0.0150963i	$-0.00480549\pi$
$60$	− 3.21220i	− 0.414693i
$61$	8.03211	1.02841	0.514203	−	0.857668i	$-0.328088\pi$
$61$	8.03211	1.02841	0.514203	+	0.857668i	$0.328088\pi$
$62$	−2.31076	−0.293467
$63$	2.25088i	0.283585i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	4.99823	0.615240
$67$	12.9700i	1.58454i	0.610172	+	0.792269i	$0.291100\pi$
$67$	12.9700i	1.58454i	−0.610172	+	0.792269i	$0.708900\pi$
$68$	−0.212197	−0.0257327
$69$	2.14596	0.258343
$70$	− 3.71131i	− 0.443587i
$71$	7.36377i	0.873918i	0.899481	+	0.436959i	$0.143945\pi$
$71$	7.36377i	0.873918i	−0.899481	+	0.436959i	$0.856055\pi$
$72$	2.25088i	0.265269i
$73$	5.60414i	0.655915i	0.944692	+	0.327958i	$0.106360\pi$
$73$	5.60414i	0.655915i	−0.944692	+	0.327958i	$0.893640\pi$
$74$	7.87343	0.915268
$75$	7.59389	0.876867
$76$	− 2.13714i	− 0.245146i
$77$	5.77486	0.658107
$78$	0	0
$79$	−9.19749	−1.03480	−0.517399	−	0.855744i	$-0.673100\pi$
$79$	−9.19749	−1.03480	−0.517399	+	0.855744i	$0.673100\pi$
$80$	− 3.71131i	− 0.414937i
$81$	2.81913	0.313237
$82$	7.52119	0.830577
$83$	3.17186i	0.348157i	0.984732	+	0.174078i	$0.0556946\pi$
$83$	3.17186i	0.348157i	−0.984732	+	0.174078i	$0.944305\pi$
$84$	− 0.865515i	− 0.0944354i
$85$	− 0.787529i	− 0.0854196i
$86$	− 4.57973i	− 0.493845i
$87$	0.0853103	0.00914623
$88$	5.77486	0.615603
$89$	11.8167i	1.25256i	0.779597	+	0.626282i	$0.215424\pi$
$89$	11.8167i	1.25256i	−0.779597	+	0.626282i	$0.784576\pi$
$90$	−8.35373	−0.880561
$91$	0	0
$92$	2.47940	0.258495
$93$	− 2.00000i	− 0.207390i
$94$	−9.15570	−0.944338
$95$	7.93158	0.813763
$96$	− 0.865515i	− 0.0883363i
$97$	14.0819i	1.42980i	0.699229	+	0.714898i	$0.253527\pi$
$97$	14.0819i	1.42980i	−0.699229	+	0.714898i	$0.746473\pi$
$98$	− 1.00000i	− 0.101015i
$99$	− 12.9985i	− 1.30640i
$100$	8.77384	0.877384
$101$	6.15243	0.612190	0.306095	−	0.952001i	$-0.400977\pi$
$101$	6.15243	0.612190	0.306095	+	0.952001i	$0.400977\pi$
$102$	− 0.183660i	− 0.0181850i
$103$	19.3491	1.90652	0.953260	−	0.302152i	$-0.0977050\pi$
$103$	19.3491	1.90652	0.953260	+	0.302152i	$0.0977050\pi$
$104$	0	0
$105$	3.21220	0.313478
$106$	12.0948i	1.17475i
$107$	11.6501	1.12626	0.563130	−	0.826368i	$-0.309597\pi$
$107$	11.6501	1.12626	0.563130	+	0.826368i	$0.309597\pi$
$108$	−4.54472	−0.437316
$109$	− 5.73307i	− 0.549129i	−0.961569	−	0.274564i	$-0.911466\pi$
$109$	− 5.73307i	− 0.549129i	0.961569	−	0.274564i	$-0.0885336\pi$
$110$	21.4323i	2.04349i
$111$	6.81457i	0.646811i
$112$	− 1.00000i	− 0.0944911i
$113$	16.5194	1.55402	0.777008	−	0.629490i	$-0.216736\pi$
$113$	16.5194	1.55402	0.777008	+	0.629490i	$0.216736\pi$
$114$	1.84972	0.173243
$115$	9.20183i	0.858075i
$116$	0.0985660	0.00915162
$117$	0	0
$118$	0.231914	0.0213494
$119$	− 0.212197i	− 0.0194521i
$120$	3.21220	0.293232
$121$	−22.3491	−2.03173
$122$	8.03211i	0.727193i
$123$	6.50970i	0.586960i
$124$	− 2.31076i	− 0.207513i
$125$	14.0059i	1.25273i
$126$	−2.25088	−0.200525
$127$	11.7884	1.04605	0.523025	−	0.852317i	$-0.324803\pi$
$127$	11.7884	1.04605	0.523025	+	0.852317i	$0.324803\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	3.96383	0.348996
$130$	0	0
$131$	−5.12859	−0.448087	−0.224043	−	0.974579i	$-0.571926\pi$
$131$	−5.12859	−0.448087	−0.224043	+	0.974579i	$0.571926\pi$
$132$	4.99823i	0.435040i
$133$	2.13714	0.185313
$134$	−12.9700	−1.12044
$135$	− 16.8669i	− 1.45167i
$136$	− 0.212197i	− 0.0181957i
$137$	− 9.39328i	− 0.802522i	−0.915964	−	0.401261i	$-0.868572\pi$
$137$	− 9.39328i	− 0.802522i	0.915964	−	0.401261i	$-0.131428\pi$
$138$	2.14596i	0.182676i
$139$	15.1413	1.28427	0.642133	−	0.766594i	$-0.278050\pi$
$139$	15.1413	1.28427	0.642133	+	0.766594i	$0.278050\pi$
$140$	3.71131	0.313663
$141$	− 7.92439i	− 0.667354i
$142$	−7.36377	−0.617954
$143$	0	0
$144$	−2.25088	−0.187574
$145$	0.365809i	0.0303788i
$146$	−5.60414	−0.463802
$147$	0.865515	0.0713865
$148$	7.87343i	0.647192i
$149$	− 20.6027i	− 1.68784i	−0.536470	−	0.843919i	$-0.680243\pi$
$149$	− 20.6027i	− 1.68784i	0.536470	−	0.843919i	$-0.319757\pi$
$150$	7.59389i	0.620039i
$151$	11.9407i	0.971721i	0.874036	+	0.485861i	$0.161494\pi$
$151$	11.9407i	0.971721i	−0.874036	+	0.485861i	$0.838506\pi$
$152$	2.13714	0.173345
$153$	−0.477631	−0.0386142
$154$	5.77486i	0.465352i
$155$	8.57596	0.688838
$156$	0	0
$157$	9.34022	0.745431	0.372715	−	0.927946i	$-0.378427\pi$
$157$	9.34022	0.745431	0.372715	+	0.927946i	$0.378427\pi$
$158$	− 9.19749i	− 0.731713i
$159$	−10.4682	−0.830185
$160$	3.71131	0.293405
$161$	2.47940i	0.195404i
$162$	2.81913i	0.221492i
$163$	4.47730i	0.350689i	0.984507	+	0.175345i	$0.0561040\pi$
$163$	4.47730i	0.350689i	−0.984507	+	0.175345i	$0.943896\pi$
$164$	7.52119i	0.587306i
$165$	−18.5500	−1.44412
$166$	−3.17186	−0.246184
$167$	− 14.7068i	− 1.13805i	−0.822321	−	0.569025i	$-0.807321\pi$
$167$	− 14.7068i	− 1.13805i	0.822321	−	0.569025i	$-0.192679\pi$
$168$	0.865515	0.0667759
$169$	0	0
$170$	0.787529	0.0604008
$171$	− 4.81045i	− 0.367864i
$172$	4.57973	0.349201
$173$	−13.7657	−1.04659	−0.523294	−	0.852152i	$-0.675297\pi$
$173$	−13.7657	−1.04659	−0.523294	+	0.852152i	$0.675297\pi$
$174$	0.0853103i	0.00646736i
$175$	8.77384i	0.663240i
$176$	5.77486i	0.435297i
$177$	0.200725i	0.0150874i
$178$	−11.8167	−0.885696
$179$	−15.2787	−1.14198	−0.570992	−	0.820955i	$-0.693441\pi$
$179$	−15.2787	−1.14198	−0.570992	+	0.820955i	$0.693441\pi$
$180$	− 8.35373i	− 0.622651i
$181$	−1.66748	−0.123943	−0.0619713	−	0.998078i	$-0.519739\pi$
$181$	−1.66748	−0.123943	−0.0619713	+	0.998078i	$0.519739\pi$
$182$	0	0
$183$	−6.95191	−0.513900
$184$	2.47940i	0.182784i
$185$	−29.2208	−2.14835
$186$	2.00000	0.146647
$187$	1.22541i	0.0896108i
$188$	− 9.15570i	− 0.667748i
$189$	− 4.54472i	− 0.330580i
$190$	7.93158i	0.575418i
$191$	0.120976	0.00875351	0.00437676	−	0.999990i	$-0.498607\pi$
$191$	0.120976	0.00875351	0.00437676	+	0.999990i	$0.498607\pi$
$192$	0.865515	0.0624632
$193$	2.75550i	0.198345i	0.995070	+	0.0991725i	$0.0316196\pi$
$193$	2.75550i	0.198345i	−0.995070	+	0.0991725i	$0.968380\pi$
$194$	−14.0819	−1.01102
$195$	0	0
$196$	1.00000	0.0714286
$197$	15.1253i	1.07764i	0.842422	+	0.538818i	$0.181129\pi$
$197$	15.1253i	1.07764i	−0.842422	+	0.538818i	$0.818871\pi$
$198$	12.9985	0.923767
$199$	−5.30640	−0.376161	−0.188080	−	0.982154i	$-0.560227\pi$
$199$	−5.30640	−0.376161	−0.188080	+	0.982154i	$0.560227\pi$
$200$	8.77384i	0.620404i
$201$	− 11.2257i	− 0.791802i
$202$	6.15243i	0.432884i
$203$	0.0985660i	0.00691798i
$204$	0.183660	0.0128587
$205$	−27.9135	−1.94956
$206$	19.3491i	1.34811i
$207$	5.58084	0.387895
$208$	0	0
$209$	−12.3417	−0.853691
$210$	3.21220i	0.221663i
$211$	17.8982	1.23216	0.616081	−	0.787682i	$-0.288719\pi$
$211$	17.8982	1.23216	0.616081	+	0.787682i	$0.288719\pi$
$212$	−12.0948	−0.830674
$213$	− 6.37345i	− 0.436702i
$214$	11.6501i	0.796386i
$215$	16.9968i	1.15917i
$216$	− 4.54472i	− 0.309229i
$217$	2.31076	0.156865
$218$	5.73307	0.388293
$219$	− 4.85047i	− 0.327764i
$220$	−21.4323	−1.44497
$221$	0	0
$222$	−6.81457	−0.457364
$223$	16.4385i	1.10080i	0.834900	+	0.550402i	$0.185525\pi$
$223$	16.4385i	1.10080i	−0.834900	+	0.550402i	$0.814475\pi$
$224$	1.00000	0.0668153
$225$	19.7489	1.31659
$226$	16.5194i	1.09886i
$227$	− 5.63095i	− 0.373739i	−0.982385	−	0.186870i	$-0.940166\pi$
$227$	− 5.63095i	− 0.373739i	0.982385	−	0.186870i	$-0.0598342\pi$
$228$	1.84972i	0.122501i
$229$	27.7225i	1.83196i	0.401228	+	0.915978i	$0.368584\pi$
$229$	27.7225i	1.83196i	−0.401228	+	0.915978i	$0.631416\pi$
$230$	−9.20183	−0.606750
$231$	−4.99823	−0.328860
$232$	0.0985660i	0.00647117i
$233$	−20.1104	−1.31747	−0.658737	−	0.752374i	$-0.728909\pi$
$233$	−20.1104	−1.31747	−0.658737	+	0.752374i	$0.728909\pi$
$234$	0	0
$235$	33.9797	2.21659
$236$	0.231914i	0.0150963i
$237$	7.96057	0.517094
$238$	0.212197	0.0137547
$239$	6.62968i	0.428838i	0.976742	+	0.214419i	$0.0687858\pi$
$239$	6.62968i	0.428838i	−0.976742	+	0.214419i	$0.931214\pi$
$240$	3.21220i	0.207346i
$241$	1.61687i	0.104151i	0.998643	+	0.0520757i	$0.0165837\pi$
$241$	1.61687i	0.104151i	−0.998643	+	0.0520757i	$0.983416\pi$
$242$	− 22.3491i	− 1.43665i
$243$	−16.0742	−1.03116
$244$	−8.03211	−0.514203
$245$	3.71131i	0.237107i
$246$	−6.50970	−0.415044
$247$	0	0
$248$	2.31076	0.146734
$249$	− 2.74529i	− 0.173976i
$250$	−14.0059	−0.885812
$251$	−0.507011	−0.0320023	−0.0160011	−	0.999872i	$-0.505094\pi$
$251$	−0.507011	−0.0320023	−0.0160011	+	0.999872i	$0.505094\pi$
$252$	− 2.25088i	− 0.141792i
$253$	− 14.3182i	− 0.900177i
$254$	11.7884i	0.739670i
$255$	0.681619i	0.0426846i
$256$	1.00000	0.0625000
$257$	9.64063	0.601366	0.300683	−	0.953724i	$-0.402785\pi$
$257$	9.64063	0.601366	0.300683	+	0.953724i	$0.402785\pi$
$258$	3.96383i	0.246777i
$259$	−7.87343	−0.489231
$260$	0	0
$261$	0.221861	0.0137328
$262$	− 5.12859i	− 0.316845i
$263$	−7.34617	−0.452985	−0.226492	−	0.974013i	$-0.572726\pi$
$263$	−7.34617	−0.452985	−0.226492	+	0.974013i	$0.572726\pi$
$264$	−4.99823	−0.307620
$265$	− 44.8876i	− 2.75742i
$266$	2.13714i	0.131036i
$267$	− 10.2275i	− 0.625912i
$268$	− 12.9700i	− 0.792269i
$269$	22.3541	1.36295	0.681476	−	0.731841i	$-0.261338\pi$
$269$	22.3541	1.36295	0.681476	+	0.731841i	$0.261338\pi$
$270$	16.8669	1.02649
$271$	9.61740i	0.584215i	0.956385	+	0.292108i	$0.0943566\pi$
$271$	9.61740i	0.584215i	−0.956385	+	0.292108i	$0.905643\pi$
$272$	0.212197	0.0128663
$273$	0	0
$274$	9.39328	0.567469
$275$	− 50.6678i	− 3.05538i
$276$	−2.14596	−0.129171
$277$	−10.1789	−0.611590	−0.305795	−	0.952097i	$-0.598922\pi$
$277$	−10.1789	−0.611590	−0.305795	+	0.952097i	$0.598922\pi$
$278$	15.1413i	0.908113i
$279$	− 5.20126i	− 0.311391i
$280$	3.71131i	0.221793i
$281$	14.1692i	0.845265i	0.906301	+	0.422633i	$0.138894\pi$
$281$	14.1692i	0.845265i	−0.906301	+	0.422633i	$0.861106\pi$
$282$	7.92439	0.471891
$283$	−18.9326	−1.12543	−0.562714	−	0.826652i	$-0.690243\pi$
$283$	−18.9326	−1.12543	−0.562714	+	0.826652i	$0.690243\pi$
$284$	− 7.36377i	− 0.436959i
$285$	−6.86490	−0.406642
$286$	0	0
$287$	−7.52119	−0.443962
$288$	− 2.25088i	− 0.132635i
$289$	−16.9550	−0.997351
$290$	−0.365809	−0.0214811
$291$	− 12.1881i	− 0.714477i
$292$	− 5.60414i	− 0.327958i
$293$	3.65982i	0.213809i	0.994269	+	0.106905i	$0.0340939\pi$
$293$	3.65982i	0.213809i	−0.994269	+	0.106905i	$0.965906\pi$
$294$	0.865515i	0.0504779i
$295$	−0.860706	−0.0501122
$296$	−7.87343	−0.457634
$297$	26.2451i	1.52290i
$298$	20.6027	1.19348
$299$	0	0
$300$	−7.59389	−0.438434
$301$	4.57973i	0.263971i
$302$	−11.9407	−0.687111
$303$	−5.32502	−0.305915
$304$	2.13714i	0.122573i
$305$	− 29.8097i	− 1.70690i
$306$	− 0.477631i	− 0.0273043i
$307$	− 19.6987i	− 1.12426i	−0.827048	−	0.562132i	$-0.809981\pi$
$307$	− 19.6987i	− 1.12426i	0.827048	−	0.562132i	$-0.190019\pi$
$308$	−5.77486	−0.329053
$309$	−16.7469	−0.952698
$310$	8.57596i	0.487082i
$311$	16.9685	0.962195	0.481098	−	0.876667i	$-0.340238\pi$
$311$	16.9685	0.962195	0.481098	+	0.876667i	$0.340238\pi$
$312$	0	0
$313$	−4.53794	−0.256500	−0.128250	−	0.991742i	$-0.540936\pi$
$313$	−4.53794	−0.256500	−0.128250	+	0.991742i	$0.540936\pi$
$314$	9.34022i	0.527099i
$315$	8.35373	0.470680
$316$	9.19749	0.517399
$317$	29.1866i	1.63928i	0.572877	+	0.819641i	$0.305827\pi$
$317$	29.1866i	1.63928i	−0.572877	+	0.819641i	$0.694173\pi$
$318$	− 10.4682i	− 0.587029i
$319$	− 0.569205i	− 0.0318694i
$320$	3.71131i	0.207469i
$321$	−10.0834	−0.562798
$322$	−2.47940	−0.138171
$323$	0.453494i	0.0252331i
$324$	−2.81913	−0.156618
$325$	0	0
$326$	−4.47730	−0.247975
$327$	4.96206i	0.274403i
$328$	−7.52119	−0.415288
$329$	9.15570	0.504770
$330$	− 18.5500i	− 1.02114i
$331$	4.80542i	0.264130i	0.991241	+	0.132065i	$0.0421607\pi$
$331$	4.80542i	0.264130i	−0.991241	+	0.132065i	$0.957839\pi$
$332$	− 3.17186i	− 0.174078i
$333$	17.7222i	0.971169i
$334$	14.7068	0.804722
$335$	48.1357	2.62994
$336$	0.865515i	0.0472177i
$337$	17.7312	0.965883	0.482941	−	0.875653i	$-0.339568\pi$
$337$	17.7312	0.965883	0.482941	+	0.875653i	$0.339568\pi$
$338$	0	0
$339$	−14.2978	−0.776550
$340$	0.787529i	0.0427098i
$341$	−13.3443	−0.722637
$342$	4.81045	0.260119
$343$	1.00000i	0.0539949i
$344$	4.57973i	0.246923i
$345$	− 7.96432i	− 0.428784i
$346$	− 13.7657i	− 0.740049i
$347$	−16.7048	−0.896760	−0.448380	−	0.893843i	$-0.647999\pi$
$347$	−16.7048	−0.896760	−0.448380	+	0.893843i	$0.647999\pi$
$348$	−0.0853103	−0.00457311
$349$	− 0.0200475i	− 0.00107312i	−1.00000		0.000536559i	$-0.999829\pi$
$349$	− 0.0200475i	− 0.00107312i	1.00000		0.000536559i	$-0.000170792\pi$
$350$	−8.77384	−0.468982
$351$	0	0
$352$	−5.77486	−0.307801
$353$	− 29.8258i	− 1.58747i	−0.608265	−	0.793734i	$-0.708134\pi$
$353$	− 29.8258i	− 1.58747i	0.608265	−	0.793734i	$-0.291866\pi$
$354$	−0.200725	−0.0106684
$355$	27.3292	1.45049
$356$	− 11.8167i	− 0.626282i
$357$	0.183660i	0.00972030i
$358$	− 15.2787i	− 0.807505i
$359$	− 18.3351i	− 0.967687i	−0.875154	−	0.483844i	$-0.839240\pi$
$359$	− 18.3351i	− 0.967687i	0.875154	−	0.483844i	$-0.160760\pi$
$360$	8.35373	0.440280
$361$	14.4326	0.759613
$362$	− 1.66748i	− 0.0876407i
$363$	19.3434	1.01527
$364$	0	0
$365$	20.7987	1.08866
$366$	− 6.95191i	− 0.363382i
$367$	1.34485	0.0702007	0.0351004	−	0.999384i	$-0.488825\pi$
$367$	1.34485	0.0702007	0.0351004	+	0.999384i	$0.488825\pi$
$368$	−2.47940	−0.129248
$369$	16.9293i	0.881306i
$370$	− 29.2208i	− 1.51912i
$371$	− 12.0948i	− 0.627931i
$372$	2.00000i	0.103695i
$373$	−11.0715	−0.573261	−0.286630	−	0.958041i	$-0.592535\pi$
$373$	−11.0715	−0.573261	−0.286630	+	0.958041i	$0.592535\pi$
$374$	−1.22541	−0.0633644
$375$	− 12.1223i	− 0.625994i
$376$	9.15570	0.472169
$377$	0	0
$378$	4.54472	0.233755
$379$	− 16.8105i	− 0.863495i	−0.901995	−	0.431747i	$-0.857897\pi$
$379$	− 16.8105i	− 0.863495i	0.901995	−	0.431747i	$-0.142103\pi$
$380$	−7.93158	−0.406882
$381$	−10.2030	−0.522717
$382$	0.120976i	0.00618967i
$383$	16.5771i	0.847051i	0.905884	+	0.423525i	$0.139208\pi$
$383$	16.5771i	0.847051i	−0.905884	+	0.423525i	$0.860792\pi$
$384$	0.865515i	0.0441681i
$385$	− 21.4323i	− 1.09229i
$386$	−2.75550	−0.140251
$387$	10.3084	0.524008
$388$	− 14.0819i	− 0.714898i
$389$	−1.17013	−0.0593280	−0.0296640	−	0.999560i	$-0.509444\pi$
$389$	−1.17013	−0.0593280	−0.0296640	+	0.999560i	$0.509444\pi$
$390$	0	0
$391$	−0.526121	−0.0266071
$392$	1.00000i	0.0505076i
$393$	4.43887	0.223911
$394$	−15.1253	−0.762003
$395$	34.1348i	1.71751i
$396$	12.9985i	0.653202i
$397$	26.1975i	1.31481i	0.753536	+	0.657406i	$0.228346\pi$
$397$	26.1975i	1.31481i	−0.753536	+	0.657406i	$0.771654\pi$
$398$	− 5.30640i	− 0.265986i
$399$	−1.84972	−0.0926020
$400$	−8.77384	−0.438692
$401$	11.3687i	0.567726i	0.958865	+	0.283863i	$0.0916162\pi$
$401$	11.3687i	0.567726i	−0.958865	+	0.283863i	$0.908384\pi$
$402$	11.2257	0.559888
$403$	0	0
$404$	−6.15243	−0.306095
$405$	− 10.4627i	− 0.519894i
$406$	−0.0985660	−0.00489175
$407$	45.4680	2.25376
$408$	0.183660i	0.00909251i
$409$	− 23.3314i	− 1.15366i	−0.816863	−	0.576832i	$-0.804289\pi$
$409$	− 23.3314i	− 1.15366i	0.816863	−	0.576832i	$-0.195711\pi$
$410$	− 27.9135i	− 1.37855i
$411$	8.13003i	0.401025i
$412$	−19.3491	−0.953260
$413$	−0.231914	−0.0114117
$414$	5.58084i	0.274283i
$415$	11.7718	0.577853
$416$	0	0
$417$	−13.1050	−0.641754
$418$	− 12.3417i	− 0.603651i
$419$	−12.6680	−0.618875	−0.309437	−	0.950920i	$-0.600141\pi$
$419$	−12.6680	−0.618875	−0.309437	+	0.950920i	$0.600141\pi$
$420$	−3.21220	−0.156739
$421$	27.6625i	1.34819i	0.738646	+	0.674094i	$0.235466\pi$
$421$	27.6625i	1.34819i	−0.738646	+	0.674094i	$0.764534\pi$
$422$	17.8982i	0.871271i
$423$	− 20.6084i	− 1.00202i
$424$	− 12.0948i	− 0.587375i
$425$	−1.86178	−0.0903098
$426$	6.37345	0.308795
$427$	− 8.03211i	− 0.388701i
$428$	−11.6501	−0.563130
$429$	0	0
$430$	−16.9968	−0.819660
$431$	− 6.41393i	− 0.308948i	−0.987997	−	0.154474i	$-0.950632\pi$
$431$	− 6.41393i	− 0.308948i	0.987997	−	0.154474i	$-0.0493683\pi$
$432$	4.54472	0.218658
$433$	0.0650270	0.00312500	0.00156250	−	0.999999i	$-0.499503\pi$
$433$	0.0650270	0.00312500	0.00156250	+	0.999999i	$0.499503\pi$
$434$	2.31076i	0.110920i
$435$	− 0.316613i	− 0.0151804i
$436$	5.73307i	0.274564i
$437$	− 5.29881i	− 0.253477i
$438$	4.85047	0.231764
$439$	−36.7778	−1.75531	−0.877655	−	0.479294i	$-0.840893\pi$
$439$	−36.7778	−1.75531	−0.877655	+	0.479294i	$0.840893\pi$
$440$	− 21.4323i	− 1.02175i
$441$	2.25088	0.107185
$442$	0	0
$443$	−8.46383	−0.402129	−0.201064	−	0.979578i	$-0.564440\pi$
$443$	−8.46383	−0.402129	−0.201064	+	0.979578i	$0.564440\pi$
$444$	− 6.81457i	− 0.323405i
$445$	43.8553	2.07894
$446$	−16.4385	−0.778385
$447$	17.8319i	0.843422i
$448$	1.00000i	0.0472456i
$449$	− 22.6303i	− 1.06799i	−0.845488	−	0.533995i	$-0.820690\pi$
$449$	− 22.6303i	− 1.06799i	0.845488	−	0.533995i	$-0.179310\pi$
$450$	19.7489i	0.930972i
$451$	43.4339	2.04522
$452$	−16.5194	−0.777008
$453$	− 10.3349i	− 0.485574i
$454$	5.63095	0.264274
$455$	0	0
$456$	−1.84972	−0.0866213
$457$	16.3170i	0.763278i	0.924311	+	0.381639i	$0.124640\pi$
$457$	16.3170i	0.763278i	−0.924311	+	0.381639i	$0.875360\pi$
$458$	−27.7225	−1.29539
$459$	0.964376	0.0450132
$460$	− 9.20183i	− 0.429037i
$461$	19.2778i	0.897858i	0.893567	+	0.448929i	$0.148194\pi$
$461$	19.2778i	0.897858i	−0.893567	+	0.448929i	$0.851806\pi$
$462$	− 4.99823i	− 0.232539i
$463$	− 2.70218i	− 0.125581i	−0.998027	−	0.0627904i	$-0.980000\pi$
$463$	− 2.70218i	− 0.125581i	0.998027	−	0.0627904i	$-0.0200000\pi$
$464$	−0.0985660	−0.00457581
$465$	−7.42263	−0.344216
$466$	− 20.1104i	− 0.931594i
$467$	−18.3906	−0.851014	−0.425507	−	0.904955i	$-0.639904\pi$
$467$	−18.3906	−0.851014	−0.425507	+	0.904955i	$0.639904\pi$
$468$	0	0
$469$	12.9700	0.598899
$470$	33.9797i	1.56736i
$471$	−8.08410	−0.372496
$472$	−0.231914	−0.0106747
$473$	− 26.4473i	− 1.21605i
$474$	7.96057i	0.365641i
$475$	− 18.7509i	− 0.860350i
$476$	0.212197i	0.00972603i
$477$	−27.2240	−1.24650
$478$	−6.62968	−0.303234
$479$	− 40.8708i	− 1.86743i	−0.358012	−	0.933717i	$-0.616545\pi$
$479$	− 40.8708i	− 1.86743i	0.358012	−	0.933717i	$-0.383455\pi$
$480$	−3.21220	−0.146616
$481$	0	0
$482$	−1.61687	−0.0736462
$483$	− 2.14596i	− 0.0976444i
$484$	22.3491	1.01587
$485$	52.2622	2.37310
$486$	− 16.0742i	− 0.729138i
$487$	17.6293i	0.798861i	0.916764	+	0.399430i	$0.130792\pi$
$487$	17.6293i	0.798861i	−0.916764	+	0.399430i	$0.869208\pi$
$488$	− 8.03211i	− 0.363597i
$489$	− 3.87517i	− 0.175241i
$490$	−3.71131	−0.167660
$491$	18.8599	0.851137	0.425569	−	0.904926i	$-0.360074\pi$
$491$	18.8599	0.851137	0.425569	+	0.904926i	$0.360074\pi$
$492$	− 6.50970i	− 0.293480i
$493$	−0.0209154	−0.000941982 0
$494$	0	0
$495$	−48.2417	−2.16830
$496$	2.31076i	0.103756i
$497$	7.36377	0.330310
$498$	2.74529	0.123019
$499$	2.10742i	0.0943410i	0.998887	+	0.0471705i	$0.0150204\pi$
$499$	2.10742i	0.0943410i	−0.998887	+	0.0471705i	$0.984980\pi$
$500$	− 14.0059i	− 0.626364i
$501$	12.7290i	0.568689i
$502$	− 0.507011i	− 0.0226290i
$503$	21.7884	0.971498	0.485749	−	0.874098i	$-0.338547\pi$
$503$	21.7884	0.971498	0.485749	+	0.874098i	$0.338547\pi$
$504$	2.25088	0.100262
$505$	− 22.8336i	− 1.01608i
$506$	14.3182	0.636521
$507$	0	0
$508$	−11.7884	−0.523025
$509$	12.1977i	0.540655i	0.962768	+	0.270328i	$0.0871321\pi$
$509$	12.1977i	0.540655i	−0.962768	+	0.270328i	$0.912868\pi$
$510$	−0.681619	−0.0301826
$511$	5.60414	0.247913
$512$	1.00000i	0.0441942i
$513$	9.71268i	0.428826i
$514$	9.64063i	0.425230i
$515$	− 71.8104i	− 3.16435i
$516$	−3.96383	−0.174498
$517$	−52.8729	−2.32535
$518$	− 7.87343i	− 0.345939i
$519$	11.9144	0.522986
$520$	0	0
$521$	−26.9765	−1.18186	−0.590932	−	0.806722i	$-0.701240\pi$
$521$	−26.9765	−1.18186	−0.590932	+	0.806722i	$0.701240\pi$
$522$	0.221861i	0.00971057i
$523$	−3.75365	−0.164136	−0.0820679	−	0.996627i	$-0.526152\pi$
$523$	−3.75365	−0.164136	−0.0820679	+	0.996627i	$0.526152\pi$
$524$	5.12859	0.224043
$525$	− 7.59389i	− 0.331425i
$526$	− 7.34617i	− 0.320308i
$527$	0.490337i	0.0213594i
$528$	− 4.99823i	− 0.217520i
$529$	−16.8526	−0.732721
$530$	44.8876	1.94979
$531$	0.522012i	0.0226534i
$532$	−2.13714	−0.0926566
$533$	0	0
$534$	10.2275	0.442587
$535$	− 43.2372i	− 1.86931i
$536$	12.9700	0.560219
$537$	13.2240	0.570656
$538$	22.3541i	0.963752i
$539$	− 5.77486i	− 0.248741i
$540$	16.8669i	0.725835i
$541$	− 0.0135705i	0 0.000583440i	−1.00000		0.000291720i	$-0.999907\pi$
$541$	− 0.0135705i	0 0.000583440i	1.00000		0.000291720i	$-9.28574e-5\pi$
$542$	−9.61740	−0.413103
$543$	1.44323	0.0619348
$544$	0.212197i	0.00909787i
$545$	−21.2772	−0.911416
$546$	0	0
$547$	−9.66115	−0.413081	−0.206540	−	0.978438i	$-0.566220\pi$
$547$	−9.66115	−0.413081	−0.206540	+	0.978438i	$0.566220\pi$
$548$	9.39328i	0.401261i
$549$	−18.0793	−0.771608
$550$	50.6678	2.16048
$551$	− 0.210649i	− 0.00897395i
$552$	− 2.14596i	− 0.0913380i
$553$	9.19749i	0.391117i
$554$	− 10.1789i	− 0.432460i
$555$	25.2910	1.07354
$556$	−15.1413	−0.642133
$557$	24.9582i	1.05751i	0.848773	+	0.528757i	$0.177342\pi$
$557$	24.9582i	1.05751i	−0.848773	+	0.528757i	$0.822658\pi$
$558$	5.20126	0.220187
$559$	0	0
$560$	−3.71131	−0.156832
$561$	− 1.06061i	− 0.0447790i
$562$	−14.1692	−0.597693
$563$	−15.8994	−0.670080	−0.335040	−	0.942204i	$-0.608750\pi$
$563$	−15.8994	−0.670080	−0.335040	+	0.942204i	$0.608750\pi$
$564$	7.92439i	0.333677i
$565$	− 61.3088i	− 2.57928i
$566$	− 18.9326i	− 0.795798i
$567$	− 2.81913i	− 0.118392i
$568$	7.36377	0.308977
$569$	17.9093	0.750797	0.375398	−	0.926864i	$-0.377506\pi$
$569$	17.9093	0.750797	0.375398	+	0.926864i	$0.377506\pi$
$570$	− 6.86490i	− 0.287539i
$571$	−12.5123	−0.523623	−0.261812	−	0.965119i	$-0.584320\pi$
$571$	−12.5123	−0.523623	−0.261812	+	0.965119i	$0.584320\pi$
$572$	0	0
$573$	−0.104707	−0.00437418
$574$	− 7.52119i	− 0.313928i
$575$	21.7539	0.907199
$576$	2.25088	0.0937868
$577$	22.0910i	0.919662i	0.888007	+	0.459831i	$0.152090\pi$
$577$	22.0910i	0.919662i	−0.888007	+	0.459831i	$0.847910\pi$
$578$	− 16.9550i	− 0.705234i
$579$	− 2.38492i	− 0.0991141i
$580$	− 0.365809i	− 0.0151894i
$581$	3.17186	0.131591
$582$	12.1881	0.505211
$583$	69.8458i	2.89272i
$584$	5.60414	0.231901
$585$	0	0
$586$	−3.65982	−0.151186
$587$	21.1319i	0.872205i	0.899897	+	0.436102i	$0.143641\pi$
$587$	21.1319i	0.872205i	−0.899897	+	0.436102i	$0.856359\pi$
$588$	−0.865515	−0.0356932
$589$	−4.93842	−0.203484
$590$	− 0.860706i	− 0.0354347i
$591$	− 13.0912i	− 0.538500i
$592$	− 7.87343i	− 0.323596i
$593$	− 8.95493i	− 0.367735i	−0.982951	−	0.183867i	$-0.941138\pi$
$593$	− 8.95493i	− 0.367735i	0.982951	−	0.183867i	$-0.0588617\pi$
$594$	−26.2451	−1.07685
$595$	−0.787529	−0.0322856
$596$	20.6027i	0.843919i
$597$	4.59277	0.187970
$598$	0	0
$599$	41.7996	1.70788	0.853942	−	0.520368i	$-0.174205\pi$
$599$	41.7996	1.70788	0.853942	+	0.520368i	$0.174205\pi$
$600$	− 7.59389i	− 0.310019i
$601$	15.2896	0.623676	0.311838	−	0.950135i	$-0.399055\pi$
$601$	15.2896	0.623676	0.311838	+	0.950135i	$0.399055\pi$
$602$	−4.57973	−0.186656
$603$	− 29.1940i	− 1.18887i
$604$	− 11.9407i	− 0.485861i
$605$	82.9444i	3.37217i
$606$	− 5.32502i	− 0.216314i
$607$	14.6087	0.592948	0.296474	−	0.955041i	$-0.404189\pi$
$607$	14.6087	0.592948	0.296474	+	0.955041i	$0.404189\pi$
$608$	−2.13714	−0.0866723
$609$	− 0.0853103i	− 0.00345695i
$610$	29.8097	1.20696
$611$	0	0
$612$	0.477631	0.0193071
$613$	39.2163i	1.58393i	0.610566	+	0.791965i	$0.290942\pi$
$613$	39.2163i	1.58393i	−0.610566	+	0.791965i	$0.709058\pi$
$614$	19.6987	0.794975
$615$	24.1595	0.974207
$616$	− 5.77486i	− 0.232676i
$617$	9.35868i	0.376766i	0.982096	+	0.188383i	$0.0603247\pi$
$617$	9.35868i	0.376766i	−0.982096	+	0.188383i	$0.939675\pi$
$618$	− 16.7469i	− 0.673659i
$619$	43.7075i	1.75675i	0.477970	+	0.878376i	$0.341373\pi$
$619$	43.7075i	1.75675i	−0.477970	+	0.878376i	$0.658627\pi$
$620$	−8.57596	−0.344419
$621$	−11.2682	−0.452176
$622$	16.9685i	0.680375i
$623$	11.8167	0.473424
$624$	0	0
$625$	8.11112	0.324445
$626$	− 4.53794i	− 0.181373i
$627$	10.6819	0.426594
$628$	−9.34022	−0.372715
$629$	− 1.67072i	− 0.0666159i
$630$	8.35373i	0.332821i
$631$	− 20.7957i	− 0.827864i	−0.910308	−	0.413932i	$-0.864155\pi$
$631$	− 20.7957i	− 0.827864i	0.910308	−	0.413932i	$-0.135845\pi$
$632$	9.19749i	0.365857i
$633$	−15.4912	−0.615718
$634$	−29.1866	−1.15915
$635$	− 43.7504i	− 1.73618i
$636$	10.4682	0.415092
$637$	0	0
$638$	0.569205	0.0225350
$639$	− 16.5750i	− 0.655696i
$640$	−3.71131	−0.146703
$641$	7.23795	0.285882	0.142941	−	0.989731i	$-0.454344\pi$
$641$	7.23795	0.285882	0.142941	+	0.989731i	$0.454344\pi$
$642$	− 10.0834i	− 0.397958i
$643$	40.1718i	1.58422i	0.610377	+	0.792111i	$0.291018\pi$
$643$	40.1718i	1.58422i	−0.610377	+	0.792111i	$0.708982\pi$
$644$	− 2.47940i	− 0.0977020i
$645$	− 14.7110i	− 0.579245i
$646$	−0.453494	−0.0178425
$647$	−14.5512	−0.572068	−0.286034	−	0.958220i	$-0.592337\pi$
$647$	−14.5512	−0.572068	−0.286034	+	0.958220i	$0.592337\pi$
$648$	− 2.81913i	− 0.110746i
$649$	1.33927	0.0525710
$650$	0	0
$651$	−2.00000	−0.0783862
$652$	− 4.47730i	− 0.175345i
$653$	−49.7267	−1.94596	−0.972978	−	0.230896i	$-0.925834\pi$
$653$	−49.7267	−1.94596	−0.972978	+	0.230896i	$0.925834\pi$
$654$	−4.96206	−0.194032
$655$	19.0338i	0.743712i
$656$	− 7.52119i	− 0.293653i
$657$	− 12.6143i	− 0.492130i
$658$	9.15570i	0.356926i
$659$	−31.5977	−1.23087	−0.615436	−	0.788187i	$-0.711020\pi$
$659$	−31.5977	−1.23087	−0.615436	+	0.788187i	$0.711020\pi$
$660$	18.5500	0.722058
$661$	24.8712i	0.967379i	0.875240	+	0.483689i	$0.160704\pi$
$661$	24.8712i	0.967379i	−0.875240	+	0.483689i	$0.839296\pi$
$662$	−4.80542	−0.186768
$663$	0	0
$664$	3.17186	0.123092
$665$	− 7.93158i	− 0.307574i
$666$	−17.7222	−0.686720
$667$	0.244384	0.00946260
$668$	14.7068i	0.569025i
$669$	− 14.2278i	− 0.550077i
$670$	48.1357i	1.85964i
$671$	46.3843i	1.79065i
$672$	−0.865515	−0.0333880
$673$	21.6490	0.834508	0.417254	−	0.908790i	$-0.362993\pi$
$673$	21.6490	0.834508	0.417254	+	0.908790i	$0.362993\pi$
$674$	17.7312i	0.682982i
$675$	−39.8747	−1.53478
$676$	0	0
$677$	14.3935	0.553187	0.276594	−	0.960987i	$-0.410794\pi$
$677$	14.3935	0.553187	0.276594	+	0.960987i	$0.410794\pi$
$678$	− 14.2978i	− 0.549104i
$679$	14.0819	0.540412
$680$	−0.787529	−0.0302004
$681$	4.87367i	0.186759i
$682$	− 13.3443i	− 0.510981i
$683$	− 42.3738i	− 1.62139i	−0.585471	−	0.810694i	$-0.699090\pi$
$683$	− 42.3738i	− 1.62139i	0.585471	−	0.810694i	$-0.300910\pi$
$684$	4.81045i	0.183932i
$685$	−34.8614	−1.33199
$686$	−1.00000	−0.0381802
$687$	− 23.9943i	− 0.915438i
$688$	−4.57973	−0.174601
$689$	0	0
$690$	7.96432	0.303196
$691$	22.9382i	0.872610i	0.899799	+	0.436305i	$0.143713\pi$
$691$	22.9382i	0.872610i	−0.899799	+	0.436305i	$0.856287\pi$
$692$	13.7657	0.523294
$693$	−12.9985	−0.493774
$694$	− 16.7048i	− 0.634105i
$695$	− 56.1940i	− 2.13156i
$696$	− 0.0853103i	− 0.00323368i
$697$	− 1.59597i	− 0.0604518i
$698$	0.0200475	0.000758808 0
$699$	17.4058	0.658348
$700$	− 8.77384i	− 0.331620i
$701$	1.70699	0.0644723	0.0322361	−	0.999480i	$-0.489737\pi$
$701$	1.70699	0.0644723	0.0322361	+	0.999480i	$0.489737\pi$
$702$	0	0
$703$	16.8266	0.634627
$704$	− 5.77486i	− 0.217648i
$705$	−29.4099	−1.10764
$706$	29.8258	1.12251
$707$	− 6.15243i	− 0.231386i
$708$	− 0.200725i	− 0.00754371i
$709$	− 18.2131i	− 0.684009i	−0.939698	−	0.342005i	$-0.888894\pi$
$709$	− 18.2131i	− 0.684009i	0.939698	−	0.342005i	$-0.111106\pi$
$710$	27.3292i	1.02565i
$711$	20.7025	0.776404
$712$	11.8167	0.442848
$713$	− 5.72930i	− 0.214564i
$714$	−0.183660	−0.00687329
$715$	0	0
$716$	15.2787	0.570992
$717$	− 5.73808i	− 0.214293i
$718$	18.3351	0.684258
$719$	−3.58214	−0.133591	−0.0667956	−	0.997767i	$-0.521278\pi$
$719$	−3.58214	−0.133591	−0.0667956	+	0.997767i	$0.521278\pi$
$720$	8.35373i	0.311325i
$721$	− 19.3491i	− 0.720597i
$722$	14.4326i	0.537128i
$723$	− 1.39942i	− 0.0520450i
$724$	1.66748	0.0619713
$725$	0.864802	0.0321180
$726$	19.3434i	0.717903i
$727$	3.21747	0.119329	0.0596647	−	0.998218i	$-0.480997\pi$
$727$	3.21747	0.119329	0.0596647	+	0.998218i	$0.480997\pi$
$728$	0	0
$729$	5.45503	0.202038
$730$	20.7987i	0.769796i
$731$	−0.971806	−0.0359435
$732$	6.95191	0.256950
$733$	− 4.79233i	− 0.177009i	−0.996076	−	0.0885043i	$-0.971791\pi$
$733$	− 4.79233i	− 0.177009i	0.996076	−	0.0885043i	$-0.0282087\pi$
$734$	1.34485i	0.0496394i
$735$	− 3.21220i	− 0.118484i
$736$	− 2.47940i	− 0.0913919i
$737$	−74.9000	−2.75898
$738$	−16.9293	−0.623177
$739$	− 11.1989i	− 0.411958i	−0.978556	−	0.205979i	$-0.933962\pi$
$739$	− 11.1989i	− 0.411958i	0.978556	−	0.205979i	$-0.0660379\pi$
$740$	29.2208	1.07418
$741$	0	0
$742$	12.0948	0.444014
$743$	38.2570i	1.40351i	0.712417	+	0.701757i	$0.247601\pi$
$743$	38.2570i	1.40351i	−0.712417	+	0.701757i	$0.752399\pi$
$744$	−2.00000	−0.0733236
$745$	−76.4630	−2.80139
$746$	− 11.0715i	− 0.405357i
$747$	− 7.13948i	− 0.261220i
$748$	− 1.22541i	− 0.0448054i
$749$	− 11.6501i	− 0.425686i
$750$	12.1223	0.442645
$751$	1.84025	0.0671517	0.0335758	−	0.999436i	$-0.489310\pi$
$751$	1.84025	0.0671517	0.0335758	+	0.999436i	$0.489310\pi$
$752$	9.15570i	0.333874i
$753$	0.438826	0.0159917
$754$	0	0
$755$	44.3157	1.61281
$756$	4.54472i	0.165290i
$757$	−21.1921	−0.770241	−0.385120	−	0.922866i	$-0.625840\pi$
$757$	−21.1921	−0.770241	−0.385120	+	0.922866i	$0.625840\pi$
$758$	16.8105	0.610583
$759$	12.3926i	0.449823i
$760$	− 7.93158i	− 0.287709i
$761$	− 14.1313i	− 0.512260i	−0.966642	−	0.256130i	$-0.917553\pi$
$761$	− 14.1313i	− 0.512260i	0.966642	−	0.256130i	$-0.0824475\pi$
$762$	− 10.2030i	− 0.369617i
$763$	−5.73307	−0.207551
$764$	−0.120976	−0.00437676
$765$	1.77264i	0.0640898i
$766$	−16.5771	−0.598955
$767$	0	0
$768$	−0.865515	−0.0312316
$769$	30.6249i	1.10436i	0.833725	+	0.552181i	$0.186204\pi$
$769$	30.6249i	1.10436i	−0.833725	+	0.552181i	$0.813796\pi$
$770$	21.4323	0.772368
$771$	−8.34411	−0.300506
$772$	− 2.75550i	− 0.0991725i
$773$	− 9.79479i	− 0.352294i	−0.984364	−	0.176147i	$-0.943637\pi$
$773$	− 9.79479i	− 0.352294i	0.984364	−	0.176147i	$-0.0563634\pi$
$774$	10.3084i	0.370529i
$775$	− 20.2743i	− 0.728273i
$776$	14.0819	0.505509
$777$	6.81457	0.244471
$778$	− 1.17013i	− 0.0419512i
$779$	16.0738	0.575904
$780$	0	0
$781$	−42.5248	−1.52166
$782$	− 0.526121i	− 0.0188140i
$783$	−0.447955	−0.0160086
$784$	−1.00000	−0.0357143
$785$	− 34.6645i	− 1.23723i
$786$	4.43887i	0.158329i
$787$	20.6305i	0.735397i	0.929945	+	0.367699i	$0.119854\pi$
$787$	20.6305i	0.735397i	−0.929945	+	0.367699i	$0.880146\pi$
$788$	− 15.1253i	− 0.538818i
$789$	6.35822	0.226359
$790$	−34.1348	−1.21446
$791$	− 16.5194i	− 0.587363i
$792$	−12.9985	−0.461883
$793$	0	0
$794$	−26.1975	−0.929713
$795$	38.8509i	1.37790i
$796$	5.30640	0.188080
$797$	−7.77168	−0.275287	−0.137643	−	0.990482i	$-0.543953\pi$
$797$	−7.77168	−0.275287	−0.137643	+	0.990482i	$0.543953\pi$
$798$	− 1.84972i	− 0.0654795i
$799$	1.94281i	0.0687317i
$800$	− 8.77384i	− 0.310202i
$801$	− 26.5979i	− 0.939791i
$802$	−11.3687	−0.401443
$803$	−32.3632	−1.14207
$804$	11.2257i	0.395901i
$805$	9.20183	0.324322
$806$	0	0
$807$	−19.3478	−0.681074
$808$	− 6.15243i	− 0.216442i
$809$	42.5430	1.49573	0.747866	−	0.663850i	$-0.231078\pi$
$809$	42.5430	1.49573	0.747866	+	0.663850i	$0.231078\pi$
$810$	10.4627	0.367621
$811$	22.1131i	0.776494i	0.921555	+	0.388247i	$0.126919\pi$
$811$	22.1131i	0.776494i	−0.921555	+	0.388247i	$0.873081\pi$
$812$	− 0.0985660i	− 0.00345899i
$813$	− 8.32400i	− 0.291936i
$814$	45.4680i	1.59365i
$815$	16.6167	0.582056
$816$	−0.183660	−0.00642937
$817$	− 9.78752i	− 0.342422i
$818$	23.3314	0.815763
$819$	0	0
$820$	27.9135	0.974782
$821$	− 24.3549i	− 0.849992i	−0.905195	−	0.424996i	$-0.860275\pi$
$821$	− 24.3549i	− 0.849992i	0.905195	−	0.424996i	$-0.139725\pi$
$822$	−8.13003	−0.283567
$823$	4.75914	0.165893	0.0829465	−	0.996554i	$-0.473567\pi$
$823$	4.75914	0.165893	0.0829465	+	0.996554i	$0.473567\pi$
$824$	− 19.3491i	− 0.674056i
$825$	43.8537i	1.52679i
$826$	− 0.231914i	− 0.00806932i
$827$	− 7.00333i	− 0.243530i	−0.992559	−	0.121765i	$-0.961145\pi$
$827$	− 7.00333i	− 0.243530i	0.992559	−	0.121765i	$-0.0388554\pi$
$828$	−5.58084	−0.193948
$829$	5.75238	0.199788	0.0998941	−	0.994998i	$-0.468150\pi$
$829$	5.75238	0.199788	0.0998941	+	0.994998i	$0.468150\pi$
$830$	11.7718i	0.408604i
$831$	8.80998	0.305615
$832$	0	0
$833$	−0.212197	−0.00735219
$834$	− 13.1050i	− 0.453789i
$835$	−54.5817	−1.88888
$836$	12.3417	0.426846
$837$	10.5018i	0.362994i
$838$	− 12.6680i	− 0.437610i
$839$	− 41.2070i	− 1.42262i	−0.702877	−	0.711311i	$-0.748102\pi$
$839$	− 41.2070i	− 1.42262i	0.702877	−	0.711311i	$-0.251898\pi$
$840$	− 3.21220i	− 0.110831i
$841$	−28.9903	−0.999665
$842$	−27.6625	−0.953312
$843$	− 12.2637i	− 0.422384i
$844$	−17.8982	−0.616081
$845$	0	0
$846$	20.6084	0.708532
$847$	22.3491i	0.767923i
$848$	12.0948	0.415337
$849$	16.3865	0.562382
$850$	− 1.86178i	− 0.0638586i
$851$	19.5214i	0.669184i
$852$	6.37345i	0.218351i
$853$	2.38939i	0.0818113i	0.999163	+	0.0409056i	$0.0130243\pi$
$853$	2.38939i	0.0818113i	−0.999163	+	0.0409056i	$0.986976\pi$
$854$	8.03211	0.274853
$855$	−17.8531	−0.610562
$856$	− 11.6501i	− 0.398193i
$857$	−13.8037	−0.471526	−0.235763	−	0.971811i	$-0.575759\pi$
$857$	−13.8037	−0.471526	−0.235763	+	0.971811i	$0.575759\pi$
$858$	0	0
$859$	−37.7276	−1.28725	−0.643624	−	0.765342i	$-0.722570\pi$
$859$	−37.7276	−1.28725	−0.643624	+	0.765342i	$0.722570\pi$
$860$	− 16.9968i	− 0.579587i
$861$	6.50970	0.221850
$862$	6.41393	0.218459
$863$	− 25.5180i	− 0.868643i	−0.900758	−	0.434322i	$-0.856988\pi$
$863$	− 25.5180i	− 0.868643i	0.900758	−	0.434322i	$-0.143012\pi$
$864$	4.54472i	0.154614i
$865$	51.0889i	1.73707i
$866$	0.0650270i	0.00220971i
$867$	14.6748	0.498382
$868$	−2.31076	−0.0784324
$869$	− 53.1143i	− 1.80178i
$870$	0.316613	0.0107342
$871$	0	0
$872$	−5.73307	−0.194146
$873$	− 31.6966i	− 1.07277i
$874$	5.29881	0.179235
$875$	14.0059	0.473486
$876$	4.85047i	0.163882i
$877$	12.4391i	0.420039i	0.977697	+	0.210019i	$0.0673527\pi$
$877$	12.4391i	0.420039i	−0.977697	+	0.210019i	$0.932647\pi$
$878$	− 36.7778i	− 1.24119i
$879$	− 3.16763i	− 0.106842i
$880$	21.4323	0.722484
$881$	22.5419	0.759457	0.379728	−	0.925098i	$-0.376017\pi$
$881$	22.5419	0.759457	0.379728	+	0.925098i	$0.376017\pi$
$882$	2.25088i	0.0757912i
$883$	−15.1548	−0.509998	−0.254999	−	0.966941i	$-0.582075\pi$
$883$	−15.1548	−0.509998	−0.254999	+	0.966941i	$0.582075\pi$
$884$	0	0
$885$	0.744954	0.0250413
$886$	− 8.46383i	− 0.284348i
$887$	41.7749	1.40266	0.701332	−	0.712835i	$-0.252589\pi$
$887$	41.7749	1.40266	0.701332	+	0.712835i	$0.252589\pi$
$888$	6.81457	0.228682
$889$	− 11.7884i	− 0.395370i
$890$	43.8553i	1.47003i
$891$	16.2801i	0.545404i
$892$	− 16.4385i	− 0.550402i
$893$	−19.5670	−0.654784
$894$	−17.8319	−0.596389
$895$	56.7041i	1.89541i
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	22.6303	0.755183
$899$	− 0.227763i	− 0.00759631i
$900$	−19.7489	−0.658297
$901$	2.56648	0.0855018
$902$	43.4339i	1.44619i
$903$	− 3.96383i	− 0.131908i
$904$	− 16.5194i	− 0.549428i
$905$	6.18853i	0.205714i
$906$	10.3349	0.343353
$907$	−4.28751	−0.142365	−0.0711823	−	0.997463i	$-0.522677\pi$
$907$	−4.28751	−0.142365	−0.0711823	+	0.997463i	$0.522677\pi$
$908$	5.63095i	0.186870i
$909$	−13.8484	−0.459323
$910$	0	0
$911$	−3.87618	−0.128423	−0.0642117	−	0.997936i	$-0.520453\pi$
$911$	−3.87618	−0.128423	−0.0642117	+	0.997936i	$0.520453\pi$
$912$	− 1.84972i	− 0.0612505i
$913$	−18.3171	−0.606206
$914$	−16.3170	−0.539719
$915$	25.8007i	0.852945i
$916$	− 27.7225i	− 0.915978i
$917$	5.12859i	0.169361i
$918$	0.964376i	0.0318291i
$919$	45.9047	1.51426	0.757129	−	0.653266i	$-0.226601\pi$
$919$	45.9047	1.51426	0.757129	+	0.653266i	$0.226601\pi$
$920$	9.20183	0.303375
$921$	17.0495i	0.561801i
$922$	−19.2778	−0.634882
$923$	0	0
$924$	4.99823	0.164430
$925$	69.0802i	2.27134i
$926$	2.70218	0.0887990
$927$	−43.5525	−1.43045
$928$	− 0.0985660i	− 0.00323559i
$929$	9.83612i	0.322713i	0.986896	+	0.161356i	$0.0515869\pi$
$929$	9.83612i	0.322713i	−0.986896	+	0.161356i	$0.948413\pi$
$930$	− 7.42263i	− 0.243397i
$931$	− 2.13714i	− 0.0700418i
$932$	20.1104	0.658737
$933$	−14.6865	−0.480814
$934$	− 18.3906i	− 0.601758i
$935$	4.54788	0.148731
$936$	0	0
$937$	21.5135	0.702815	0.351407	−	0.936223i	$-0.385703\pi$
$937$	21.5135	0.702815	0.351407	+	0.936223i	$0.385703\pi$
$938$	12.9700i	0.423485i
$939$	3.92766	0.128174
$940$	−33.9797	−1.10829
$941$	− 6.41845i	− 0.209236i	−0.994513	−	0.104618i	$-0.966638\pi$
$941$	− 6.41845i	− 0.209236i	0.994513	−	0.104618i	$-0.0333619\pi$
$942$	− 8.08410i	− 0.263394i
$943$	18.6480i	0.607264i
$944$	− 0.231914i	− 0.00754816i
$945$	−16.8669	−0.548679
$946$	26.4473	0.859877
$947$	− 7.57266i	− 0.246078i	−0.992402	−	0.123039i	$-0.960736\pi$
$947$	− 7.57266i	− 0.246078i	0.992402	−	0.123039i	$-0.0392641\pi$
$948$	−7.96057	−0.258547
$949$	0	0
$950$	18.7509	0.608360
$951$	− 25.2614i	− 0.819158i
$952$	−0.212197	−0.00687734
$953$	35.8044	1.15982	0.579909	−	0.814681i	$-0.303088\pi$
$953$	35.8044	1.15982	0.579909	+	0.814681i	$0.303088\pi$
$954$	− 27.2240i	− 0.881409i
$955$	− 0.448980i	− 0.0145286i
$956$	− 6.62968i	− 0.214419i
$957$	0.492656i	0.0159253i
$958$	40.8708	1.32048
$959$	−9.39328	−0.303325
$960$	− 3.21220i	− 0.103673i
$961$	25.6604	0.827754
$962$	0	0
$963$	−26.2231	−0.845027
$964$	− 1.61687i	− 0.0520757i
$965$	10.2265	0.329203
$966$	2.14596	0.0690450
$967$	32.3876i	1.04152i	0.853704	+	0.520758i	$0.174351\pi$
$967$	32.3876i	1.04152i	−0.853704	+	0.520758i	$0.825649\pi$
$968$	22.3491i	0.718326i
$969$	− 0.392506i	− 0.0126091i
$970$	52.2622i	1.67804i
$971$	34.4065	1.10416	0.552079	−	0.833792i	$-0.313835\pi$
$971$	34.4065	1.10416	0.552079	+	0.833792i	$0.313835\pi$
$972$	16.0742	0.515579
$973$	− 15.1413i	− 0.485407i
$974$	−17.6293	−0.564880
$975$	0	0
$976$	8.03211	0.257102
$977$	− 23.1484i	− 0.740583i	−0.928916	−	0.370291i	$-0.879258\pi$
$977$	− 23.1484i	− 0.740583i	0.928916	−	0.370291i	$-0.120742\pi$
$978$	3.87517	0.123914
$979$	−68.2396	−2.18095
$980$	− 3.71131i	− 0.118554i
$981$	12.9045i	0.412008i
$982$	18.8599i	0.601845i
$983$	− 47.0579i	− 1.50092i	−0.660919	−	0.750458i	$-0.729833\pi$
$983$	− 47.0579i	− 1.50092i	0.660919	−	0.750458i	$-0.270167\pi$
$984$	6.50970	0.207522
$985$	56.1349	1.78861
$986$	− 0.0209154i	0 0.000666082i
$987$	−7.92439	−0.252236
$988$	0	0
$989$	11.3550	0.361068
$990$	− 48.2417i	− 1.53322i
$991$	−11.9010	−0.378049	−0.189025	−	0.981972i	$-0.560533\pi$
$991$	−11.9010	−0.378049	−0.189025	+	0.981972i	$0.560533\pi$
$992$	−2.31076	−0.0733668
$993$	− 4.15916i	− 0.131987i
$994$	7.36377i	0.233565i
$995$	19.6937i	0.624333i
$996$	2.74529i	0.0869879i
$997$	13.0143	0.412166	0.206083	−	0.978534i	$-0.433928\pi$
$997$	13.0143	0.412166	0.206083	+	0.978534i	$0.433928\pi$
$998$	−2.10742	−0.0667092
$999$	− 35.7825i	− 1.13211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.d.r.337.8		12
13.3	even	3		182.2.m.b.43.3	✓	12
13.4	even	6		182.2.m.b.127.3	yes	12
13.5	odd	4		2366.2.a.bh.1.2		6
13.8	odd	4		2366.2.a.bf.1.2		6
13.12	even	2	inner	2366.2.d.r.337.2		12
39.17	odd	6		1638.2.bj.g.127.4		12
39.29	odd	6		1638.2.bj.g.1135.6		12
52.3	odd	6		1456.2.cc.d.225.2		12
52.43	odd	6		1456.2.cc.d.673.2		12
91.3	odd	6		1274.2.v.d.667.6		12
91.4	even	6		1274.2.o.d.569.3		12
91.16	even	3		1274.2.o.d.459.6		12
91.17	odd	6		1274.2.o.e.569.1		12
91.30	even	6		1274.2.v.e.361.4		12
91.55	odd	6		1274.2.m.c.589.1		12
91.68	odd	6		1274.2.o.e.459.4		12
91.69	odd	6		1274.2.m.c.491.1		12
91.81	even	3		1274.2.v.e.667.4		12
91.82	odd	6		1274.2.v.d.361.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.b.43.3	✓	12	13.3	even	3
182.2.m.b.127.3	yes	12	13.4	even	6
1274.2.m.c.491.1		12	91.69	odd	6
1274.2.m.c.589.1		12	91.55	odd	6
1274.2.o.d.459.6		12	91.16	even	3
1274.2.o.d.569.3		12	91.4	even	6
1274.2.o.e.459.4		12	91.68	odd	6
1274.2.o.e.569.1		12	91.17	odd	6
1274.2.v.d.361.6		12	91.82	odd	6
1274.2.v.d.667.6		12	91.3	odd	6
1274.2.v.e.361.4		12	91.30	even	6
1274.2.v.e.667.4		12	91.81	even	3
1456.2.cc.d.225.2		12	52.3	odd	6
1456.2.cc.d.673.2		12	52.43	odd	6
1638.2.bj.g.127.4		12	39.17	odd	6
1638.2.bj.g.1135.6		12	39.29	odd	6
2366.2.a.bf.1.2		6	13.8	odd	4
2366.2.a.bh.1.2		6	13.5	odd	4
2366.2.d.r.337.2		12	13.12	even	2	inner
2366.2.d.r.337.8		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)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -0.865515 q^{3} -1.00000 q^{4} -3.71131i q^{5} -0.865515i q^{6} -1.00000i q^{7} -1.00000i q^{8} -2.25088 q^{9} +3.71131 q^{10} +5.77486i q^{11} +0.865515 q^{12} +1.00000 q^{14} +3.21220i q^{15} +1.00000 q^{16} +0.212197 q^{17} -2.25088i q^{18} +2.13714i q^{19} +3.71131i q^{20} +0.865515i q^{21} -5.77486 q^{22} -2.47940 q^{23} +0.865515i q^{24} -8.77384 q^{25} +4.54472 q^{27} +1.00000i q^{28} -0.0985660 q^{29} -3.21220 q^{30} +2.31076i q^{31} +1.00000i q^{32} -4.99823i q^{33} +0.212197i q^{34} -3.71131 q^{35} +2.25088 q^{36} -7.87343i q^{37} -2.13714 q^{38} -3.71131 q^{40} -7.52119i q^{41} -0.865515 q^{42} -4.57973 q^{43} -5.77486i q^{44} +8.35373i q^{45} -2.47940i q^{46} +9.15570i q^{47} -0.865515 q^{48} -1.00000 q^{49} -8.77384i q^{50} -0.183660 q^{51} +12.0948 q^{53} +4.54472i q^{54} +21.4323 q^{55} -1.00000 q^{56} -1.84972i q^{57} -0.0985660i q^{58} -0.231914i q^{59} -3.21220i q^{60} +8.03211 q^{61} -2.31076 q^{62} +2.25088i q^{63} -1.00000 q^{64} +4.99823 q^{66} +12.9700i q^{67} -0.212197 q^{68} +2.14596 q^{69} -3.71131i q^{70} +7.36377i q^{71} +2.25088i q^{72} +5.60414i q^{73} +7.87343 q^{74} +7.59389 q^{75} -2.13714i q^{76} +5.77486 q^{77} -9.19749 q^{79} -3.71131i q^{80} +2.81913 q^{81} +7.52119 q^{82} +3.17186i q^{83} -0.865515i q^{84} -0.787529i q^{85} -4.57973i q^{86} +0.0853103 q^{87} +5.77486 q^{88} +11.8167i q^{89} -8.35373 q^{90} +2.47940 q^{92} -2.00000i q^{93} -9.15570 q^{94} +7.93158 q^{95} -0.865515i q^{96} +14.0819i q^{97} -1.00000i q^{98} -12.9985i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} + 12 q^{9} + 4 q^{10} - 4 q^{12} + 12 q^{14} + 12 q^{16} - 8 q^{17} + 4 q^{22} + 12 q^{23} - 24 q^{25} + 40 q^{27} + 20 q^{29} - 28 q^{30} - 4 q^{35} - 12 q^{36} + 8 q^{38} - 4 q^{40}+ \cdots - 64 q^{95}+O(q^{100}) \) 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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