LMFDB - Embedded newform 7935.2.a.bk.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7935,2,Mod(1,7935)] 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("7935.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7935, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,0,-10,16,10,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 18x^{8} + 111x^{6} - 4x^{5} - 270x^{4} + 32x^{3} + 218x^{2} - 60x - 18 $ x^10 - 18x^8 + 111x^6 - 4x^5 - 270x^4 + 32x^3 + 218x^2 - 60*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.80133$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.80133 q^{2} -1.00000 q^{3} +1.24478 q^{4} +1.00000 q^{5} +1.80133 q^{6} -1.16943 q^{7} +1.36039 q^{8} +1.00000 q^{9} -1.80133 q^{10} +4.93264 q^{11} -1.24478 q^{12} -5.72358 q^{13} +2.10653 q^{14} -1.00000 q^{15} -4.94008 q^{16} +5.96836 q^{17} -1.80133 q^{18} +3.76464 q^{19} +1.24478 q^{20} +1.16943 q^{21} -8.88530 q^{22} -1.36039 q^{24} +1.00000 q^{25} +10.3100 q^{26} -1.00000 q^{27} -1.45569 q^{28} +10.2723 q^{29} +1.80133 q^{30} +2.01570 q^{31} +6.17792 q^{32} -4.93264 q^{33} -10.7510 q^{34} -1.16943 q^{35} +1.24478 q^{36} -10.8290 q^{37} -6.78136 q^{38} +5.72358 q^{39} +1.36039 q^{40} +1.84318 q^{41} -2.10653 q^{42} +11.4820 q^{43} +6.14006 q^{44} +1.00000 q^{45} +9.40399 q^{47} +4.94008 q^{48} -5.63243 q^{49} -1.80133 q^{50} -5.96836 q^{51} -7.12461 q^{52} -0.718670 q^{53} +1.80133 q^{54} +4.93264 q^{55} -1.59089 q^{56} -3.76464 q^{57} -18.5039 q^{58} +6.18960 q^{59} -1.24478 q^{60} -4.15996 q^{61} -3.63093 q^{62} -1.16943 q^{63} -1.24830 q^{64} -5.72358 q^{65} +8.88530 q^{66} -15.1497 q^{67} +7.42931 q^{68} +2.10653 q^{70} +9.42763 q^{71} +1.36039 q^{72} +9.34659 q^{73} +19.5065 q^{74} -1.00000 q^{75} +4.68616 q^{76} -5.76838 q^{77} -10.3100 q^{78} +7.30497 q^{79} -4.94008 q^{80} +1.00000 q^{81} -3.32018 q^{82} -11.7083 q^{83} +1.45569 q^{84} +5.96836 q^{85} -20.6828 q^{86} -10.2723 q^{87} +6.71033 q^{88} +3.77295 q^{89} -1.80133 q^{90} +6.69333 q^{91} -2.01570 q^{93} -16.9397 q^{94} +3.76464 q^{95} -6.17792 q^{96} +15.4375 q^{97} +10.1459 q^{98} +4.93264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} + 16 q^{4} + 10 q^{5} + 6 q^{7} + 10 q^{9} - 4 q^{11} - 16 q^{12} - 4 q^{13} - 10 q^{15} + 28 q^{16} + 10 q^{17} + 8 q^{19} + 16 q^{20} - 6 q^{21} - 4 q^{22} + 10 q^{25} - 8 q^{26} - 10 q^{27}+ \cdots - 4 q^{99}+O(q^{100}) $ 10 * q - 10 * q^3 + 16 * q^4 + 10 * q^5 + 6 * q^7 + 10 * q^9 - 4 * q^11 - 16 * q^12 - 4 * q^13 - 10 * q^15 + 28 * q^16 + 10 * q^17 + 8 * q^19 + 16 * q^20 - 6 * q^21 - 4 * q^22 + 10 * q^25 - 8 * q^26 - 10 * q^27 + 76 * q^28 + 2 * q^29 + 2 * q^31 + 20 * q^32 + 4 * q^33 + 8 * q^34 + 6 * q^35 + 16 * q^36 + 2 * q^37 - 56 * q^38 + 4 * q^39 + 6 * q^41 + 44 * q^43 - 24 * q^44 + 10 * q^45 + 8 * q^47 - 28 * q^48 + 12 * q^49 - 10 * q^51 + 2 * q^53 - 4 * q^55 + 8 * q^56 - 8 * q^57 - 20 * q^58 - 14 * q^59 - 16 * q^60 - 8 * q^61 - 28 * q^62 + 6 * q^63 + 40 * q^64 - 4 * q^65 + 4 * q^66 + 2 * q^67 + 84 * q^68 + 6 * q^71 - 12 * q^73 + 40 * q^74 - 10 * q^75 + 44 * q^76 - 16 * q^77 + 8 * q^78 + 28 * q^80 + 10 * q^81 - 4 * q^82 - 62 * q^83 - 76 * q^84 + 10 * q^85 - 4 * q^86 - 2 * q^87 - 12 * q^88 + 56 * q^89 - 2 * q^93 + 20 * q^94 + 8 * q^95 - 20 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

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 $

$2$	−1.80133	−1.27373	−0.636866	−	0.770975i	$-0.719769\pi$
$2$	−1.80133	−1.27373	−0.636866	+	0.770975i	$0.719769\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.24478	0.622391
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.80133	0.735389
$7$	−1.16943	−0.442003	−0.221002	−	0.975273i	$-0.570933\pi$
$7$	−1.16943	−0.442003	−0.221002	+	0.975273i	$0.570933\pi$
$8$	1.36039	0.480972
$9$	1.00000	0.333333
$10$	−1.80133	−0.569630
$11$	4.93264	1.48725	0.743623	−	0.668599i	$-0.233106\pi$
$11$	4.93264	1.48725	0.743623	+	0.668599i	$0.233106\pi$
$12$	−1.24478	−0.359338
$13$	−5.72358	−1.58743	−0.793717	−	0.608287i	$-0.791857\pi$
$13$	−5.72358	−1.58743	−0.793717	+	0.608287i	$0.791857\pi$
$14$	2.10653	0.562993
$15$	−1.00000	−0.258199
$16$	−4.94008	−1.23502
$17$	5.96836	1.44754	0.723770	−	0.690041i	$-0.242408\pi$
$17$	5.96836	1.44754	0.723770	+	0.690041i	$0.242408\pi$
$18$	−1.80133	−0.424577
$19$	3.76464	0.863668	0.431834	−	0.901953i	$-0.357867\pi$
$19$	3.76464	0.863668	0.431834	+	0.901953i	$0.357867\pi$
$20$	1.24478	0.278342
$21$	1.16943	0.255191
$22$	−8.88530	−1.89435
$23$	0	0
$23$	0	0
$24$	−1.36039	−0.277689
$25$	1.00000	0.200000
$26$	10.3100	2.02197
$27$	−1.00000	−0.192450
$28$	−1.45569	−0.275099
$29$	10.2723	1.90753	0.953763	−	0.300559i	$-0.0971731\pi$
$29$	10.2723	1.90753	0.953763	+	0.300559i	$0.0971731\pi$
$30$	1.80133	0.328876
$31$	2.01570	0.362030	0.181015	−	0.983480i	$-0.442062\pi$
$31$	2.01570	0.362030	0.181015	+	0.983480i	$0.442062\pi$
$32$	6.17792	1.09211
$33$	−4.93264	−0.858662
$34$	−10.7510	−1.84378
$35$	−1.16943	−0.197670
$36$	1.24478	0.207464
$37$	−10.8290	−1.78027	−0.890135	−	0.455697i	$-0.849390\pi$
$37$	−10.8290	−1.78027	−0.890135	+	0.455697i	$0.849390\pi$
$38$	−6.78136	−1.10008
$39$	5.72358	0.916506
$40$	1.36039	0.215097
$41$	1.84318	0.287857	0.143929	−	0.989588i	$-0.454026\pi$
$41$	1.84318	0.287857	0.143929	+	0.989588i	$0.454026\pi$
$42$	−2.10653	−0.325044
$43$	11.4820	1.75099	0.875493	−	0.483230i	$-0.160537\pi$
$43$	11.4820	1.75099	0.875493	+	0.483230i	$0.160537\pi$
$44$	6.14006	0.925649
$45$	1.00000	0.149071
$46$	0	0
$47$	9.40399	1.37171	0.685856	−	0.727737i	$-0.259428\pi$
$47$	9.40399	1.37171	0.685856	+	0.727737i	$0.259428\pi$
$48$	4.94008	0.713039
$49$	−5.63243	−0.804633
$50$	−1.80133	−0.254746
$51$	−5.96836	−0.835737
$52$	−7.12461	−0.988006
$53$	−0.718670	−0.0987170	−0.0493585	−	0.998781i	$-0.515718\pi$
$53$	−0.718670	−0.0987170	−0.0493585	+	0.998781i	$0.515718\pi$
$54$	1.80133	0.245130
$55$	4.93264	0.665117
$56$	−1.59089	−0.212591
$57$	−3.76464	−0.498639
$58$	−18.5039	−2.42968
$59$	6.18960	0.805818	0.402909	−	0.915240i	$-0.367999\pi$
$59$	6.18960	0.805818	0.402909	+	0.915240i	$0.367999\pi$
$60$	−1.24478	−0.160701
$61$	−4.15996	−0.532628	−0.266314	−	0.963886i	$-0.585806\pi$
$61$	−4.15996	−0.532628	−0.266314	+	0.963886i	$0.585806\pi$
$62$	−3.63093	−0.461129
$63$	−1.16943	−0.147334
$64$	−1.24830	−0.156037
$65$	−5.72358	−0.709922
$66$	8.88530	1.09370
$67$	−15.1497	−1.85082	−0.925412	−	0.378961i	$-0.876281\pi$
$67$	−15.1497	−1.85082	−0.925412	+	0.378961i	$0.876281\pi$
$68$	7.42931	0.900936
$69$	0	0
$70$	2.10653	0.251778
$71$	9.42763	1.11885	0.559427	−	0.828880i	$-0.311021\pi$
$71$	9.42763	1.11885	0.559427	+	0.828880i	$0.311021\pi$
$72$	1.36039	0.160324
$73$	9.34659	1.09394	0.546968	−	0.837154i	$-0.315782\pi$
$73$	9.34659	1.09394	0.546968	+	0.837154i	$0.315782\pi$
$74$	19.5065	2.26759
$75$	−1.00000	−0.115470
$76$	4.68616	0.537540
$77$	−5.76838	−0.657368
$78$	−10.3100	−1.16738
$79$	7.30497	0.821873	0.410937	−	0.911664i	$-0.365202\pi$
$79$	7.30497	0.821873	0.410937	+	0.911664i	$0.365202\pi$
$80$	−4.94008	−0.552318
$81$	1.00000	0.111111
$82$	−3.32018	−0.366653
$83$	−11.7083	−1.28515	−0.642577	−	0.766221i	$-0.722135\pi$
$83$	−11.7083	−1.28515	−0.642577	+	0.766221i	$0.722135\pi$
$84$	1.45569	0.158829
$85$	5.96836	0.647359
$86$	−20.6828	−2.23029
$87$	−10.2723	−1.10131
$88$	6.71033	0.715324
$89$	3.77295	0.399932	0.199966	−	0.979803i	$-0.435917\pi$
$89$	3.77295	0.399932	0.199966	+	0.979803i	$0.435917\pi$
$90$	−1.80133	−0.189877
$91$	6.69333	0.701651
$92$	0	0
$93$	−2.01570	−0.209018
$94$	−16.9397	−1.74719
$95$	3.76464	0.386244
$96$	−6.17792	−0.630531
$97$	15.4375	1.56744	0.783721	−	0.621112i	$-0.213319\pi$
$97$	15.4375	1.56744	0.783721	+	0.621112i	$0.213319\pi$
$98$	10.1459	1.02489
$99$	4.93264	0.495749
$100$	1.24478	0.124478
$101$	−0.00890951	−0.000886530 0	−0.000443265	−	1.00000i	$-0.500141\pi$
$101$	−0.00890951	−0.000886530 0	−0.000443265		1.00000i	$0.500141\pi$
$102$	10.7510	1.06450
$103$	6.89593	0.679476	0.339738	−	0.940520i	$-0.389662\pi$
$103$	6.89593	0.679476	0.339738	+	0.940520i	$0.389662\pi$
$104$	−7.78632	−0.763511
$105$	1.16943	0.114125
$106$	1.29456	0.125739
$107$	−1.59496	−0.154191	−0.0770954	−	0.997024i	$-0.524565\pi$
$107$	−1.59496	−0.154191	−0.0770954	+	0.997024i	$0.524565\pi$
$108$	−1.24478	−0.119779
$109$	−7.63337	−0.731144	−0.365572	−	0.930783i	$-0.619127\pi$
$109$	−7.63337	−0.731144	−0.365572	+	0.930783i	$0.619127\pi$
$110$	−8.88530	−0.847180
$111$	10.8290	1.02784
$112$	5.77708	0.545883
$113$	1.38224	0.130030	0.0650149	−	0.997884i	$-0.479290\pi$
$113$	1.38224	0.130030	0.0650149	+	0.997884i	$0.479290\pi$
$114$	6.78136	0.635132
$115$	0	0
$116$	12.7868	1.18723
$117$	−5.72358	−0.529145
$118$	−11.1495	−1.02640
$119$	−6.97958	−0.639817
$120$	−1.36039	−0.124186
$121$	13.3309	1.21190
$122$	7.49345	0.678425
$123$	−1.84318	−0.166194
$124$	2.50911	0.225324
$125$	1.00000	0.0894427
$126$	2.10653	0.187664
$127$	−6.30514	−0.559491	−0.279745	−	0.960074i	$-0.590250\pi$
$127$	−6.30514	−0.559491	−0.279745	+	0.960074i	$0.590250\pi$
$128$	−10.1072	−0.893363
$129$	−11.4820	−1.01093
$130$	10.3100	0.904250
$131$	15.4861	1.35303	0.676515	−	0.736428i	$-0.263489\pi$
$131$	15.4861	1.35303	0.676515	+	0.736428i	$0.263489\pi$
$132$	−6.14006	−0.534424
$133$	−4.40249	−0.381744
$134$	27.2895	2.35745
$135$	−1.00000	−0.0860663
$136$	8.11932	0.696226
$137$	17.0436	1.45613	0.728066	−	0.685508i	$-0.240420\pi$
$137$	17.0436	1.45613	0.728066	+	0.685508i	$0.240420\pi$
$138$	0	0
$139$	−0.538072	−0.0456387	−0.0228193	−	0.999740i	$-0.507264\pi$
$139$	−0.538072	−0.0456387	−0.0228193	+	0.999740i	$0.507264\pi$
$140$	−1.45569	−0.123028
$141$	−9.40399	−0.791959
$142$	−16.9822	−1.42512
$143$	−28.2323	−2.36091
$144$	−4.94008	−0.411673
$145$	10.2723	0.853072
$146$	−16.8363	−1.39338
$147$	5.63243	0.464555
$148$	−13.4797	−1.10802
$149$	−10.3510	−0.847988	−0.423994	−	0.905665i	$-0.639372\pi$
$149$	−10.3510	−0.847988	−0.423994	+	0.905665i	$0.639372\pi$
$150$	1.80133	0.147078
$151$	−8.46171	−0.688604	−0.344302	−	0.938859i	$-0.611884\pi$
$151$	−8.46171	−0.688604	−0.344302	+	0.938859i	$0.611884\pi$
$152$	5.12140	0.415400
$153$	5.96836	0.482513
$154$	10.3907	0.837310
$155$	2.01570	0.161905
$156$	7.12461	0.570425
$157$	5.43266	0.433573	0.216787	−	0.976219i	$-0.430442\pi$
$157$	5.43266	0.433573	0.216787	+	0.976219i	$0.430442\pi$
$158$	−13.1586	−1.04685
$159$	0.718670	0.0569943
$160$	6.17792	0.488407
$161$	0	0
$162$	−1.80133	−0.141526
$163$	−13.7929	−1.08035	−0.540173	−	0.841554i	$-0.681641\pi$
$163$	−13.7929	−1.08035	−0.540173	+	0.841554i	$0.681641\pi$
$164$	2.29436	0.179160
$165$	−4.93264	−0.384005
$166$	21.0905	1.63694
$167$	12.3352	0.954528	0.477264	−	0.878760i	$-0.341629\pi$
$167$	12.3352	0.954528	0.477264	+	0.878760i	$0.341629\pi$
$168$	1.59089	0.122740
$169$	19.7593	1.51995
$170$	−10.7510	−0.824562
$171$	3.76464	0.287889
$172$	14.2926	1.08980
$173$	−17.2887	−1.31443	−0.657217	−	0.753701i	$-0.728267\pi$
$173$	−17.2887	−1.31443	−0.657217	+	0.753701i	$0.728267\pi$
$174$	18.5039	1.40277
$175$	−1.16943	−0.0884007
$176$	−24.3676	−1.83678
$177$	−6.18960	−0.465239
$178$	−6.79632	−0.509405
$179$	6.09510	0.455569	0.227785	−	0.973712i	$-0.426852\pi$
$179$	6.09510	0.455569	0.227785	+	0.973712i	$0.426852\pi$
$180$	1.24478	0.0927806
$181$	−7.53099	−0.559774	−0.279887	−	0.960033i	$-0.590297\pi$
$181$	−7.53099	−0.559774	−0.279887	+	0.960033i	$0.590297\pi$
$182$	−12.0569	−0.893715
$183$	4.15996	0.307513
$184$	0	0
$185$	−10.8290	−0.796161
$186$	3.63093	0.266233
$187$	29.4398	2.15285
$188$	11.7059	0.853742
$189$	1.16943	0.0850636
$190$	−6.78136	−0.491971
$191$	5.32898	0.385591	0.192796	−	0.981239i	$-0.438245\pi$
$191$	5.32898	0.385591	0.192796	+	0.981239i	$0.438245\pi$
$192$	1.24830	0.0900880
$193$	−4.62606	−0.332991	−0.166496	−	0.986042i	$-0.553245\pi$
$193$	−4.62606	−0.332991	−0.166496	+	0.986042i	$0.553245\pi$
$194$	−27.8080	−1.99650
$195$	5.72358	0.409874
$196$	−7.01115	−0.500797
$197$	−21.0697	−1.50116	−0.750578	−	0.660781i	$-0.770225\pi$
$197$	−21.0697	−1.50116	−0.750578	+	0.660781i	$0.770225\pi$
$198$	−8.88530	−0.631451
$199$	2.08378	0.147715	0.0738577	−	0.997269i	$-0.476469\pi$
$199$	2.08378	0.147715	0.0738577	+	0.997269i	$0.476469\pi$
$200$	1.36039	0.0961944
$201$	15.1497	1.06857
$202$	0.0160490	0.00112920
$203$	−12.0128	−0.843133
$204$	−7.42931	−0.520156
$205$	1.84318	0.128734
$206$	−12.4218	−0.865470
$207$	0	0
$208$	28.2749	1.96051
$209$	18.5696	1.28449
$210$	−2.10653	−0.145364
$211$	−15.7435	−1.08383	−0.541914	−	0.840434i	$-0.682300\pi$
$211$	−15.7435	−1.08383	−0.541914	+	0.840434i	$0.682300\pi$
$212$	−0.894588	−0.0614406
$213$	−9.42763	−0.645970
$214$	2.87305	0.196398
$215$	11.4820	0.783065
$216$	−1.36039	−0.0925631
$217$	−2.35722	−0.160019
$218$	13.7502	0.931282
$219$	−9.34659	−0.631584
$220$	6.14006	0.413963
$221$	−34.1604	−2.29787
$222$	−19.5065	−1.30919
$223$	3.79797	0.254331	0.127166	−	0.991882i	$-0.459412\pi$
$223$	3.79797	0.254331	0.127166	+	0.991882i	$0.459412\pi$
$224$	−7.22465	−0.482717
$225$	1.00000	0.0666667
$226$	−2.48986	−0.165623
$227$	−16.7068	−1.10887	−0.554436	−	0.832226i	$-0.687066\pi$
$227$	−16.7068	−1.10887	−0.554436	+	0.832226i	$0.687066\pi$
$228$	−4.68616	−0.310349
$229$	−6.36253	−0.420448	−0.210224	−	0.977653i	$-0.567419\pi$
$229$	−6.36253	−0.420448	−0.210224	+	0.977653i	$0.567419\pi$
$230$	0	0
$231$	5.76838	0.379531
$232$	13.9744	0.917467
$233$	26.5783	1.74120	0.870601	−	0.491991i	$-0.163731\pi$
$233$	26.5783	1.74120	0.870601	+	0.491991i	$0.163731\pi$
$234$	10.3100	0.673988
$235$	9.40399	0.613449
$236$	7.70471	0.501534
$237$	−7.30497	−0.474509
$238$	12.5725	0.814955
$239$	20.8849	1.35093	0.675467	−	0.737390i	$-0.263942\pi$
$239$	20.8849	1.35093	0.675467	+	0.737390i	$0.263942\pi$
$240$	4.94008	0.318881
$241$	−12.8885	−0.830222	−0.415111	−	0.909771i	$-0.636257\pi$
$241$	−12.8885	−0.830222	−0.415111	+	0.909771i	$0.636257\pi$
$242$	−24.0134	−1.54364
$243$	−1.00000	−0.0641500
$244$	−5.17824	−0.331503
$245$	−5.63243	−0.359843
$246$	3.32018	0.211687
$247$	−21.5472	−1.37102
$248$	2.74214	0.174126
$249$	11.7083	0.741984
$250$	−1.80133	−0.113926
$251$	2.70724	0.170879	0.0854397	−	0.996343i	$-0.472771\pi$
$251$	2.70724	0.170879	0.0854397	+	0.996343i	$0.472771\pi$
$252$	−1.45569	−0.0916997
$253$	0	0
$254$	11.3576	0.712641
$255$	−5.96836	−0.373753
$256$	20.7031	1.29394
$257$	−13.3118	−0.830368	−0.415184	−	0.909737i	$-0.636283\pi$
$257$	−13.3118	−0.830368	−0.415184	+	0.909737i	$0.636283\pi$
$258$	20.6828	1.28766
$259$	12.6637	0.786885
$260$	−7.12461	−0.441850
$261$	10.2723	0.635842
$262$	−27.8956	−1.72340
$263$	8.29888	0.511731	0.255865	−	0.966712i	$-0.417640\pi$
$263$	8.29888	0.511731	0.255865	+	0.966712i	$0.417640\pi$
$264$	−6.71033	−0.412992
$265$	−0.718670	−0.0441476
$266$	7.93033	0.486240
$267$	−3.77295	−0.230901
$268$	−18.8580	−1.15194
$269$	−16.7113	−1.01891	−0.509453	−	0.860498i	$-0.670152\pi$
$269$	−16.7113	−1.01891	−0.509453	+	0.860498i	$0.670152\pi$
$270$	1.80133	0.109625
$271$	−15.2463	−0.926147	−0.463073	−	0.886320i	$-0.653253\pi$
$271$	−15.2463	−0.926147	−0.463073	+	0.886320i	$0.653253\pi$
$272$	−29.4842	−1.78774
$273$	−6.69333	−0.405099
$274$	−30.7011	−1.85472
$275$	4.93264	0.297449
$276$	0	0
$277$	−18.6811	−1.12244	−0.561220	−	0.827666i	$-0.689668\pi$
$277$	−18.6811	−1.12244	−0.561220	+	0.827666i	$0.689668\pi$
$278$	0.969244	0.0581314
$279$	2.01570	0.120677
$280$	−1.59089	−0.0950737
$281$	−5.20277	−0.310372	−0.155186	−	0.987885i	$-0.549598\pi$
$281$	−5.20277	−0.310372	−0.155186	+	0.987885i	$0.549598\pi$
$282$	16.9397	1.00874
$283$	−21.7172	−1.29095	−0.645477	−	0.763779i	$-0.723341\pi$
$283$	−21.7172	−1.29095	−0.645477	+	0.763779i	$0.723341\pi$
$284$	11.7353	0.696365
$285$	−3.76464	−0.222998
$286$	50.8557	3.00716
$287$	−2.15548	−0.127234
$288$	6.17792	0.364037
$289$	18.6213	1.09537
$290$	−18.5039	−1.08658
$291$	−15.4375	−0.904964
$292$	11.6345	0.680856
$293$	6.86349	0.400970	0.200485	−	0.979697i	$-0.435748\pi$
$293$	6.86349	0.400970	0.200485	+	0.979697i	$0.435748\pi$
$294$	−10.1459	−0.591718
$295$	6.18960	0.360373
$296$	−14.7316	−0.856260
$297$	−4.93264	−0.286221
$298$	18.6456	1.08011
$299$	0	0
$300$	−1.24478	−0.0718676
$301$	−13.4274	−0.773942
$302$	15.2423	0.877096
$303$	0.00890951	0.000511838 0
$304$	−18.5976	−1.06665
$305$	−4.15996	−0.238198
$306$	−10.7510	−0.614592
$307$	−5.99610	−0.342216	−0.171108	−	0.985252i	$-0.554735\pi$
$307$	−5.99610	−0.342216	−0.171108	+	0.985252i	$0.554735\pi$
$308$	−7.18038	−0.409140
$309$	−6.89593	−0.392296
$310$	−3.63093	−0.206223
$311$	−23.5490	−1.33534	−0.667671	−	0.744457i	$-0.732709\pi$
$311$	−23.5490	−1.33534	−0.667671	+	0.744457i	$0.732709\pi$
$312$	7.78632	0.440814
$313$	7.43120	0.420037	0.210018	−	0.977697i	$-0.432648\pi$
$313$	7.43120	0.420037	0.210018	+	0.977697i	$0.432648\pi$
$314$	−9.78600	−0.552256
$315$	−1.16943	−0.0658900
$316$	9.09310	0.511527
$317$	16.8174	0.944557	0.472278	−	0.881450i	$-0.343432\pi$
$317$	16.8174	0.944557	0.472278	+	0.881450i	$0.343432\pi$
$318$	−1.29456	−0.0725954
$319$	50.6698	2.83696
$320$	−1.24830	−0.0697819
$321$	1.59496	0.0890220
$322$	0	0
$323$	22.4687	1.25019
$324$	1.24478	0.0691546
$325$	−5.72358	−0.317487
$326$	24.8456	1.37607
$327$	7.63337	0.422126
$328$	2.50746	0.138451
$329$	−10.9973	−0.606301
$330$	8.88530	0.489120
$331$	8.38033	0.460625	0.230312	−	0.973117i	$-0.426025\pi$
$331$	8.38033	0.460625	0.230312	+	0.973117i	$0.426025\pi$
$332$	−14.5743	−0.799868
$333$	−10.8290	−0.593423
$334$	−22.2198	−1.21581
$335$	−15.1497	−0.827714
$336$	−5.77708	−0.315166
$337$	33.6380	1.83238	0.916190	−	0.400743i	$-0.131248\pi$
$337$	33.6380	1.83238	0.916190	+	0.400743i	$0.131248\pi$
$338$	−35.5930	−1.93601
$339$	−1.38224	−0.0750728
$340$	7.42931	0.402911
$341$	9.94271	0.538428
$342$	−6.78136	−0.366694
$343$	14.7728	0.797654
$344$	15.6200	0.842175
$345$	0	0
$346$	31.1426	1.67424
$347$	−28.4991	−1.52991	−0.764956	−	0.644082i	$-0.777239\pi$
$347$	−28.4991	−1.52991	−0.764956	+	0.644082i	$0.777239\pi$
$348$	−12.7868	−0.685447
$349$	7.85834	0.420647	0.210324	−	0.977632i	$-0.432548\pi$
$349$	7.85834	0.420647	0.210324	+	0.977632i	$0.432548\pi$
$350$	2.10653	0.112599
$351$	5.72358	0.305502
$352$	30.4734	1.62424
$353$	−7.29174	−0.388100	−0.194050	−	0.980992i	$-0.562162\pi$
$353$	−7.29174	−0.388100	−0.194050	+	0.980992i	$0.562162\pi$
$354$	11.1495	0.592590
$355$	9.42763	0.500366
$356$	4.69650	0.248914
$357$	6.97958	0.369399
$358$	−10.9793	−0.580273
$359$	−2.98636	−0.157614	−0.0788071	−	0.996890i	$-0.525111\pi$
$359$	−2.98636	−0.157614	−0.0788071	+	0.996890i	$0.525111\pi$
$360$	1.36039	0.0716991
$361$	−4.82746	−0.254077
$362$	13.5658	0.713001
$363$	−13.3309	−0.699692
$364$	8.33174	0.436702
$365$	9.34659	0.489223
$366$	−7.49345	−0.391689
$367$	−22.9008	−1.19541	−0.597707	−	0.801715i	$-0.703921\pi$
$367$	−22.9008	−1.19541	−0.597707	+	0.801715i	$0.703921\pi$
$368$	0	0
$369$	1.84318	0.0959523
$370$	19.5065	1.01409
$371$	0.840435	0.0436332
$372$	−2.50911	−0.130091
$373$	2.72067	0.140871	0.0704356	−	0.997516i	$-0.477561\pi$
$373$	2.72067	0.140871	0.0704356	+	0.997516i	$0.477561\pi$
$374$	−53.0307	−2.74215
$375$	−1.00000	−0.0516398
$376$	12.7931	0.659755
$377$	−58.7946	−3.02807
$378$	−2.10653	−0.108348
$379$	7.01494	0.360333	0.180167	−	0.983636i	$-0.442336\pi$
$379$	7.01494	0.360333	0.180167	+	0.983636i	$0.442336\pi$
$380$	4.68616	0.240395
$381$	6.30514	0.323022
$382$	−9.59923	−0.491139
$383$	10.5223	0.537666	0.268833	−	0.963187i	$-0.413362\pi$
$383$	10.5223	0.537666	0.268833	+	0.963187i	$0.413362\pi$
$384$	10.1072	0.515783
$385$	−5.76838	−0.293984
$386$	8.33305	0.424141
$387$	11.4820	0.583662
$388$	19.2164	0.975563
$389$	8.16762	0.414115	0.207057	−	0.978329i	$-0.433611\pi$
$389$	8.16762	0.414115	0.207057	+	0.978329i	$0.433611\pi$
$390$	−10.3100	−0.522069
$391$	0	0
$392$	−7.66233	−0.387006
$393$	−15.4861	−0.781173
$394$	37.9535	1.91207
$395$	7.30497	0.367553
$396$	6.14006	0.308550
$397$	16.1626	0.811178	0.405589	−	0.914055i	$-0.367066\pi$
$397$	16.1626	0.811178	0.405589	+	0.914055i	$0.367066\pi$
$398$	−3.75357	−0.188150
$399$	4.40249	0.220400
$400$	−4.94008	−0.247004
$401$	−17.8918	−0.893471	−0.446736	−	0.894666i	$-0.647414\pi$
$401$	−17.8918	−0.893471	−0.446736	+	0.894666i	$0.647414\pi$
$402$	−27.2895	−1.36108
$403$	−11.5370	−0.574699
$404$	−0.0110904	−0.000551768 0
$405$	1.00000	0.0496904
$406$	21.6390	1.07392
$407$	−53.4153	−2.64770
$408$	−8.11932	−0.401966
$409$	−8.01024	−0.396081	−0.198041	−	0.980194i	$-0.563458\pi$
$409$	−8.01024	−0.396081	−0.198041	+	0.980194i	$0.563458\pi$
$410$	−3.32018	−0.163972
$411$	−17.0436	−0.840698
$412$	8.58394	0.422900
$413$	−7.23831	−0.356174
$414$	0	0
$415$	−11.7083	−0.574738
$416$	−35.3598	−1.73366
$417$	0.538072	0.0263495
$418$	−33.4500	−1.63609
$419$	−16.0239	−0.782820	−0.391410	−	0.920216i	$-0.628013\pi$
$419$	−16.0239	−0.782820	−0.391410	+	0.920216i	$0.628013\pi$
$420$	1.45569	0.0710303
$421$	25.5126	1.24341	0.621704	−	0.783252i	$-0.286441\pi$
$421$	25.5126	1.24341	0.621704	+	0.783252i	$0.286441\pi$
$422$	28.3593	1.38051
$423$	9.40399	0.457238
$424$	−0.977675	−0.0474801
$425$	5.96836	0.289508
$426$	16.9822	0.822792
$427$	4.86478	0.235423
$428$	−1.98538	−0.0959670
$429$	28.2323	1.36307
$430$	−20.6828	−0.997414
$431$	−5.19120	−0.250051	−0.125026	−	0.992154i	$-0.539901\pi$
$431$	−5.19120	−0.250051	−0.125026	+	0.992154i	$0.539901\pi$
$432$	4.94008	0.237680
$433$	2.56604	0.123316	0.0616580	−	0.998097i	$-0.480361\pi$
$433$	2.56604	0.123316	0.0616580	+	0.998097i	$0.480361\pi$
$434$	4.24613	0.203821
$435$	−10.2723	−0.492521
$436$	−9.50189	−0.455058
$437$	0	0
$438$	16.8363	0.804468
$439$	−6.69755	−0.319657	−0.159828	−	0.987145i	$-0.551094\pi$
$439$	−6.69755	−0.319657	−0.159828	+	0.987145i	$0.551094\pi$
$440$	6.71033	0.319902
$441$	−5.63243	−0.268211
$442$	61.5340	2.92687
$443$	16.2002	0.769692	0.384846	−	0.922981i	$-0.374254\pi$
$443$	16.2002	0.769692	0.384846	+	0.922981i	$0.374254\pi$
$444$	13.4797	0.639718
$445$	3.77295	0.178855
$446$	−6.84139	−0.323949
$447$	10.3510	0.489586
$448$	1.45980	0.0689689
$449$	18.5691	0.876331	0.438166	−	0.898894i	$-0.355628\pi$
$449$	18.5691	0.876331	0.438166	+	0.898894i	$0.355628\pi$
$450$	−1.80133	−0.0849154
$451$	9.09176	0.428114
$452$	1.72058	0.0809295
$453$	8.46171	0.397566
$454$	30.0945	1.41241
$455$	6.69333	0.313788
$456$	−5.12140	−0.239831
$457$	−14.8197	−0.693238	−0.346619	−	0.938006i	$-0.612670\pi$
$457$	−14.8197	−0.693238	−0.346619	+	0.938006i	$0.612670\pi$
$458$	11.4610	0.535537
$459$	−5.96836	−0.278579
$460$	0	0
$461$	7.32481	0.341150	0.170575	−	0.985345i	$-0.445437\pi$
$461$	7.32481	0.341150	0.170575	+	0.985345i	$0.445437\pi$
$462$	−10.3907	−0.483421
$463$	−21.4397	−0.996388	−0.498194	−	0.867066i	$-0.666003\pi$
$463$	−21.4397	−0.996388	−0.498194	+	0.867066i	$0.666003\pi$
$464$	−50.7462	−2.35583
$465$	−2.01570	−0.0934758
$466$	−47.8762	−2.21782
$467$	−4.00977	−0.185550	−0.0927750	−	0.995687i	$-0.529574\pi$
$467$	−4.00977	−0.185550	−0.0927750	+	0.995687i	$0.529574\pi$
$468$	−7.12461	−0.329335
$469$	17.7165	0.818071
$470$	−16.9397	−0.781369
$471$	−5.43266	−0.250324
$472$	8.42030	0.387576
$473$	56.6365	2.60415
$474$	13.1586	0.604397
$475$	3.76464	0.172734
$476$	−8.68807	−0.398217
$477$	−0.718670	−0.0329057
$478$	−37.6206	−1.72073
$479$	12.4853	0.570470	0.285235	−	0.958458i	$-0.407928\pi$
$479$	12.4853	0.570470	0.285235	+	0.958458i	$0.407928\pi$
$480$	−6.17792	−0.281982
$481$	61.9804	2.82606
$482$	23.2164	1.05748
$483$	0	0
$484$	16.5941	0.754277
$485$	15.4375	0.700982
$486$	1.80133	0.0817099
$487$	−2.01019	−0.0910902	−0.0455451	−	0.998962i	$-0.514502\pi$
$487$	−2.01019	−0.0910902	−0.0455451	+	0.998962i	$0.514502\pi$
$488$	−5.65918	−0.256179
$489$	13.7929	0.623738
$490$	10.1459	0.458343
$491$	8.21262	0.370630	0.185315	−	0.982679i	$-0.440669\pi$
$491$	8.21262	0.370630	0.185315	+	0.982679i	$0.440669\pi$
$492$	−2.29436	−0.103438
$493$	61.3091	2.76122
$494$	38.8136	1.74631
$495$	4.93264	0.221706
$496$	−9.95771	−0.447115
$497$	−11.0250	−0.494537
$498$	−21.0905	−0.945088
$499$	40.5552	1.81550	0.907751	−	0.419509i	$-0.137798\pi$
$499$	40.5552	1.81550	0.907751	+	0.419509i	$0.137798\pi$
$500$	1.24478	0.0556684
$501$	−12.3352	−0.551097
$502$	−4.87662	−0.217654
$503$	38.6279	1.72233	0.861166	−	0.508325i	$-0.169735\pi$
$503$	38.6279	1.72233	0.861166	+	0.508325i	$0.169735\pi$
$504$	−1.59089	−0.0708637
$505$	−0.00890951	−0.000396468 0
$506$	0	0
$507$	−19.7593	−0.877543
$508$	−7.84853	−0.348222
$509$	31.4463	1.39383	0.696916	−	0.717152i	$-0.254555\pi$
$509$	31.4463	1.39383	0.696916	+	0.717152i	$0.254555\pi$
$510$	10.7510	0.476061
$511$	−10.9302	−0.483523
$512$	−17.0785	−0.754771
$513$	−3.76464	−0.166213
$514$	23.9789	1.05767
$515$	6.89593	0.303871
$516$	−14.2926	−0.629196
$517$	46.3865	2.04007
$518$	−22.8115	−1.00228
$519$	17.2887	0.758889
$520$	−7.78632	−0.341453
$521$	−33.9586	−1.48775	−0.743876	−	0.668318i	$-0.767015\pi$
$521$	−33.9586	−1.48775	−0.743876	+	0.668318i	$0.767015\pi$
$522$	−18.5039	−0.809892
$523$	15.4202	0.674280	0.337140	−	0.941455i	$-0.390540\pi$
$523$	15.4202	0.674280	0.337140	+	0.941455i	$0.390540\pi$
$524$	19.2769	0.842115
$525$	1.16943	0.0510381
$526$	−14.9490	−0.651807
$527$	12.0304	0.524053
$528$	24.3676	1.06047
$529$	0	0
$530$	1.29456	0.0562321
$531$	6.18960	0.268606
$532$	−5.48014	−0.237594
$533$	−10.5496	−0.456954
$534$	6.79632	0.294105
$535$	−1.59496	−0.0689562
$536$	−20.6095	−0.890195
$537$	−6.09510	−0.263023
$538$	30.1025	1.29781
$539$	−27.7827	−1.19669
$540$	−1.24478	−0.0535669
$541$	18.8236	0.809292	0.404646	−	0.914473i	$-0.367395\pi$
$541$	18.8236	0.809292	0.404646	+	0.914473i	$0.367395\pi$
$542$	27.4636	1.17966
$543$	7.53099	0.323186
$544$	36.8720	1.58088
$545$	−7.63337	−0.326978
$546$	12.0569	0.515987
$547$	−32.9692	−1.40966	−0.704831	−	0.709376i	$-0.748977\pi$
$547$	−32.9692	−1.40966	−0.704831	+	0.709376i	$0.748977\pi$
$548$	21.2156	0.906283
$549$	−4.15996	−0.177543
$550$	−8.88530	−0.378870
$551$	38.6717	1.64747
$552$	0	0
$553$	−8.54265	−0.363271
$554$	33.6509	1.42969
$555$	10.8290	0.459664
$556$	−0.669783	−0.0284051
$557$	20.2861	0.859548	0.429774	−	0.902936i	$-0.358593\pi$
$557$	20.2861	0.859548	0.429774	+	0.902936i	$0.358593\pi$
$558$	−3.63093	−0.153710
$559$	−65.7180	−2.77958
$560$	5.77708	0.244126
$561$	−29.4398	−1.24295
$562$	9.37190	0.395330
$563$	41.0100	1.72836	0.864182	−	0.503179i	$-0.167836\pi$
$563$	41.0100	1.72836	0.864182	+	0.503179i	$0.167836\pi$
$564$	−11.7059	−0.492908
$565$	1.38224	0.0581511
$566$	39.1198	1.64433
$567$	−1.16943	−0.0491115
$568$	12.8253	0.538137
$569$	−12.6489	−0.530269	−0.265135	−	0.964211i	$-0.585416\pi$
$569$	−12.6489	−0.530269	−0.265135	+	0.964211i	$0.585416\pi$
$570$	6.78136	0.284040
$571$	−12.9538	−0.542102	−0.271051	−	0.962565i	$-0.587371\pi$
$571$	−12.9538	−0.542102	−0.271051	+	0.962565i	$0.587371\pi$
$572$	−35.1431	−1.46941
$573$	−5.32898	−0.222621
$574$	3.88272	0.162062
$575$	0	0
$576$	−1.24830	−0.0520124
$577$	−9.25738	−0.385390	−0.192695	−	0.981259i	$-0.561723\pi$
$577$	−9.25738	−0.385390	−0.192695	+	0.981259i	$0.561723\pi$
$578$	−33.5431	−1.39521
$579$	4.62606	0.192252
$580$	12.7868	0.530945
$581$	13.6920	0.568042
$582$	27.8080	1.15268
$583$	−3.54494	−0.146816
$584$	12.7150	0.526152
$585$	−5.72358	−0.236641
$586$	−12.3634	−0.510728
$587$	13.7534	0.567664	0.283832	−	0.958874i	$-0.408394\pi$
$587$	13.7534	0.567664	0.283832	+	0.958874i	$0.408394\pi$
$588$	7.01115	0.289135
$589$	7.58839	0.312674
$590$	−11.1495	−0.459018
$591$	21.0697	0.866693
$592$	53.4959	2.19867
$593$	13.4462	0.552170	0.276085	−	0.961133i	$-0.410963\pi$
$593$	13.4462	0.552170	0.276085	+	0.961133i	$0.410963\pi$
$594$	8.88530	0.364568
$595$	−6.97958	−0.286135
$596$	−12.8848	−0.527780
$597$	−2.08378	−0.0852835
$598$	0	0
$599$	15.5951	0.637200	0.318600	−	0.947889i	$-0.396787\pi$
$599$	15.5951	0.637200	0.318600	+	0.947889i	$0.396787\pi$
$600$	−1.36039	−0.0555379
$601$	−2.46541	−0.100566	−0.0502830	−	0.998735i	$-0.516012\pi$
$601$	−2.46541	−0.100566	−0.0502830	+	0.998735i	$0.516012\pi$
$602$	24.1871	0.985794
$603$	−15.1497	−0.616942
$604$	−10.5330	−0.428581
$605$	13.3309	0.541979
$606$	−0.0160490	−0.000651944 0
$607$	−43.8562	−1.78007	−0.890034	−	0.455894i	$-0.849320\pi$
$607$	−43.8562	−1.78007	−0.890034	+	0.455894i	$0.849320\pi$
$608$	23.2577	0.943223
$609$	12.0128	0.486783
$610$	7.49345	0.303401
$611$	−53.8244	−2.17750
$612$	7.42931	0.300312
$613$	7.88607	0.318516	0.159258	−	0.987237i	$-0.449090\pi$
$613$	7.88607	0.318516	0.159258	+	0.987237i	$0.449090\pi$
$614$	10.8009	0.435891
$615$	−1.84318	−0.0743244
$616$	−7.84727	−0.316175
$617$	−9.42380	−0.379388	−0.189694	−	0.981843i	$-0.560750\pi$
$617$	−9.42380	−0.379388	−0.189694	+	0.981843i	$0.560750\pi$
$618$	12.4218	0.499679
$619$	46.7301	1.87824	0.939120	−	0.343588i	$-0.111642\pi$
$619$	46.7301	1.87824	0.939120	+	0.343588i	$0.111642\pi$
$620$	2.50911	0.100768
$621$	0	0
$622$	42.4195	1.70087
$623$	−4.41220	−0.176771
$624$	−28.2749	−1.13190
$625$	1.00000	0.0400000
$626$	−13.3860	−0.535014
$627$	−18.5696	−0.741599
$628$	6.76248	0.269852
$629$	−64.6311	−2.57701
$630$	2.10653	0.0839261
$631$	−25.5344	−1.01651	−0.508255	−	0.861207i	$-0.669709\pi$
$631$	−25.5344	−1.01651	−0.508255	+	0.861207i	$0.669709\pi$
$632$	9.93763	0.395298
$633$	15.7435	0.625749
$634$	−30.2936	−1.20311
$635$	−6.30514	−0.250212
$636$	0.894588	0.0354727
$637$	32.2377	1.27730
$638$	−91.2729	−3.61353
$639$	9.42763	0.372951
$640$	−10.1072	−0.399524
$641$	35.4489	1.40015	0.700073	−	0.714072i	$-0.253151\pi$
$641$	35.4489	1.40015	0.700073	+	0.714072i	$0.253151\pi$
$642$	−2.87305	−0.113390
$643$	−14.5158	−0.572446	−0.286223	−	0.958163i	$-0.592400\pi$
$643$	−14.5158	−0.572446	−0.286223	+	0.958163i	$0.592400\pi$
$644$	0	0
$645$	−11.4820	−0.452103
$646$	−40.4736	−1.59241
$647$	−4.12441	−0.162147	−0.0810737	−	0.996708i	$-0.525835\pi$
$647$	−4.12441	−0.162147	−0.0810737	+	0.996708i	$0.525835\pi$
$648$	1.36039	0.0534413
$649$	30.5311	1.19845
$650$	10.3100	0.404393
$651$	2.35722	0.0923867
$652$	−17.1692	−0.672398
$653$	−2.99421	−0.117173	−0.0585863	−	0.998282i	$-0.518659\pi$
$653$	−2.99421	−0.117173	−0.0585863	+	0.998282i	$0.518659\pi$
$654$	−13.7502	−0.537676
$655$	15.4861	0.605094
$656$	−9.10548	−0.355509
$657$	9.34659	0.364645
$658$	19.8098	0.772265
$659$	−9.54973	−0.372005	−0.186002	−	0.982549i	$-0.559553\pi$
$659$	−9.54973	−0.372005	−0.186002	+	0.982549i	$0.559553\pi$
$660$	−6.14006	−0.239002
$661$	12.6193	0.490832	0.245416	−	0.969418i	$-0.421075\pi$
$661$	12.6193	0.490832	0.245416	+	0.969418i	$0.421075\pi$
$662$	−15.0957	−0.586712
$663$	34.1604	1.32668
$664$	−15.9279	−0.618123
$665$	−4.40249	−0.170721
$666$	19.5065	0.755862
$667$	0	0
$668$	15.3547	0.594090
$669$	−3.79797	−0.146838
$670$	27.2895	1.05429
$671$	−20.5196	−0.792149
$672$	7.22465	0.278697
$673$	−22.7988	−0.878830	−0.439415	−	0.898284i	$-0.644814\pi$
$673$	−22.7988	−0.878830	−0.439415	+	0.898284i	$0.644814\pi$
$674$	−60.5931	−2.33396
$675$	−1.00000	−0.0384900
$676$	24.5961	0.946003
$677$	−1.30088	−0.0499967	−0.0249984	−	0.999687i	$-0.507958\pi$
$677$	−1.30088	−0.0499967	−0.0249984	+	0.999687i	$0.507958\pi$
$678$	2.48986	0.0956225
$679$	−18.0531	−0.692815
$680$	8.11932	0.311362
$681$	16.7068	0.640208
$682$	−17.9101	−0.685813
$683$	−3.52866	−0.135020	−0.0675102	−	0.997719i	$-0.521506\pi$
$683$	−3.52866	−0.135020	−0.0675102	+	0.997719i	$0.521506\pi$
$684$	4.68616	0.179180
$685$	17.0436	0.651202
$686$	−26.6106	−1.01600
$687$	6.36253	0.242746
$688$	−56.7220	−2.16250
$689$	4.11336	0.156707
$690$	0	0
$691$	−22.9943	−0.874745	−0.437372	−	0.899281i	$-0.644091\pi$
$691$	−22.9943	−0.874745	−0.437372	+	0.899281i	$0.644091\pi$
$692$	−21.5207	−0.818093
$693$	−5.76838	−0.219123
$694$	51.3363	1.94870
$695$	−0.538072	−0.0204102
$696$	−13.9744	−0.529700
$697$	11.0008	0.416685
$698$	−14.1554	−0.535791
$699$	−26.5783	−1.00528
$700$	−1.45569	−0.0550198
$701$	20.5637	0.776680	0.388340	−	0.921516i	$-0.373049\pi$
$701$	20.5637	0.776680	0.388340	+	0.921516i	$0.373049\pi$
$702$	−10.3100	−0.389127
$703$	−40.7672	−1.53756
$704$	−6.15739	−0.232066
$705$	−9.40399	−0.354175
$706$	13.1348	0.494335
$707$	0.0104191	0.000391849 0
$708$	−7.70471	−0.289561
$709$	40.6832	1.52789	0.763945	−	0.645281i	$-0.223260\pi$
$709$	40.6832	1.52789	0.763945	+	0.645281i	$0.223260\pi$
$710$	−16.9822	−0.637332
$711$	7.30497	0.273958
$712$	5.13269	0.192356
$713$	0	0
$714$	−12.5725	−0.470515
$715$	−28.2323	−1.05583
$716$	7.58707	0.283542
$717$	−20.8849	−0.779962
$718$	5.37942	0.200758
$719$	13.6807	0.510206	0.255103	−	0.966914i	$-0.417891\pi$
$719$	13.6807	0.510206	0.255103	+	0.966914i	$0.417891\pi$
$720$	−4.94008	−0.184106
$721$	−8.06431	−0.300331
$722$	8.69584	0.323626
$723$	12.8885	0.479329
$724$	−9.37444	−0.348398
$725$	10.2723	0.381505
$726$	24.0134	0.891219
$727$	16.1935	0.600583	0.300292	−	0.953847i	$-0.402916\pi$
$727$	16.1935	0.600583	0.300292	+	0.953847i	$0.402916\pi$
$728$	9.10556	0.337475
$729$	1.00000	0.0370370
$730$	−16.8363	−0.623138
$731$	68.5286	2.53462
$732$	5.17824	0.191393
$733$	10.5359	0.389151	0.194576	−	0.980887i	$-0.437667\pi$
$733$	10.5359	0.389151	0.194576	+	0.980887i	$0.437667\pi$
$734$	41.2519	1.52264
$735$	5.63243	0.207755
$736$	0	0
$737$	−74.7278	−2.75263
$738$	−3.32018	−0.122218
$739$	39.8626	1.46637	0.733184	−	0.680030i	$-0.238033\pi$
$739$	39.8626	1.46637	0.733184	+	0.680030i	$0.238033\pi$
$740$	−13.4797	−0.495524
$741$	21.5472	0.791557
$742$	−1.51390	−0.0555770
$743$	7.32384	0.268686	0.134343	−	0.990935i	$-0.457108\pi$
$743$	7.32384	0.268686	0.134343	+	0.990935i	$0.457108\pi$
$744$	−2.74214	−0.100532
$745$	−10.3510	−0.379232
$746$	−4.90082	−0.179432
$747$	−11.7083	−0.428384
$748$	36.6461	1.33991
$749$	1.86520	0.0681528
$750$	1.80133	0.0657752
$751$	−15.0521	−0.549261	−0.274630	−	0.961550i	$-0.588555\pi$
$751$	−15.0521	−0.549261	−0.274630	+	0.961550i	$0.588555\pi$
$752$	−46.4565	−1.69409
$753$	−2.70724	−0.0986572
$754$	105.908	3.85695
$755$	−8.46171	−0.307953
$756$	1.45569	0.0529428
$757$	−38.5540	−1.40127	−0.700634	−	0.713521i	$-0.747099\pi$
$757$	−38.5540	−1.40127	−0.700634	+	0.713521i	$0.747099\pi$
$758$	−12.6362	−0.458968
$759$	0	0
$760$	5.12140	0.185773
$761$	−6.58967	−0.238875	−0.119438	−	0.992842i	$-0.538109\pi$
$761$	−6.58967	−0.238875	−0.119438	+	0.992842i	$0.538109\pi$
$762$	−11.3576	−0.411444
$763$	8.92670	0.323168
$764$	6.63342	0.239989
$765$	5.96836	0.215786
$766$	−18.9542	−0.684842
$767$	−35.4267	−1.27918
$768$	−20.7031	−0.747057
$769$	−8.13233	−0.293259	−0.146630	−	0.989191i	$-0.546843\pi$
$769$	−8.13233	−0.293259	−0.146630	+	0.989191i	$0.546843\pi$
$770$	10.3907	0.374456
$771$	13.3118	0.479413
$772$	−5.75844	−0.207251
$773$	5.20702	0.187284	0.0936418	−	0.995606i	$-0.470149\pi$
$773$	5.20702	0.187284	0.0936418	+	0.995606i	$0.470149\pi$
$774$	−20.6828	−0.743429
$775$	2.01570	0.0724060
$776$	21.0011	0.753896
$777$	−12.6637	−0.454308
$778$	−14.7126	−0.527471
$779$	6.93893	0.248613
$780$	7.12461	0.255102
$781$	46.5031	1.66401
$782$	0	0
$783$	−10.2723	−0.367104
$784$	27.8247	0.993738
$785$	5.43266	0.193900
$786$	27.8956	0.995004
$787$	−49.1472	−1.75191	−0.875954	−	0.482395i	$-0.839767\pi$
$787$	−49.1472	−1.75191	−0.875954	+	0.482395i	$0.839767\pi$
$788$	−26.2272	−0.934307
$789$	−8.29888	−0.295448
$790$	−13.1586	−0.468164
$791$	−1.61643	−0.0574736
$792$	6.71033	0.238441
$793$	23.8098	0.845512
$794$	−29.1142	−1.03322
$795$	0.718670	0.0254886
$796$	2.59386	0.0919368
$797$	20.8049	0.736946	0.368473	−	0.929639i	$-0.379881\pi$
$797$	20.8049	0.736946	0.368473	+	0.929639i	$0.379881\pi$
$798$	−7.93033	−0.280731
$799$	56.1264	1.98561
$800$	6.17792	0.218422
$801$	3.77295	0.133311
$802$	32.2289	1.13804
$803$	46.1033	1.62695
$804$	18.8580	0.665071
$805$	0	0
$806$	20.7819	0.732012
$807$	16.7113	0.588266
$808$	−0.0121204	−0.000426396 0
$809$	45.5051	1.59987	0.799936	−	0.600085i	$-0.204867\pi$
$809$	45.5051	1.59987	0.799936	+	0.600085i	$0.204867\pi$
$810$	−1.80133	−0.0632922
$811$	−41.9687	−1.47372	−0.736860	−	0.676045i	$-0.763692\pi$
$811$	−41.9687	−1.47372	−0.736860	+	0.676045i	$0.763692\pi$
$812$	−14.9533	−0.524759
$813$	15.2463	0.534711
$814$	96.2185	3.37246
$815$	−13.7929	−0.483145
$816$	29.4842	1.03215
$817$	43.2256	1.51227
$818$	14.4291	0.504501
$819$	6.69333	0.233884
$820$	2.29436	0.0801227
$821$	18.9558	0.661562	0.330781	−	0.943708i	$-0.392688\pi$
$821$	18.9558	0.661562	0.330781	+	0.943708i	$0.392688\pi$
$822$	30.7011	1.07082
$823$	12.2743	0.427855	0.213927	−	0.976850i	$-0.431374\pi$
$823$	12.2743	0.427855	0.213927	+	0.976850i	$0.431374\pi$
$824$	9.38118	0.326809
$825$	−4.93264	−0.171732
$826$	13.0386	0.453670
$827$	3.16378	0.110016	0.0550078	−	0.998486i	$-0.482482\pi$
$827$	3.16378	0.110016	0.0550078	+	0.998486i	$0.482482\pi$
$828$	0	0
$829$	35.3042	1.22616	0.613082	−	0.790019i	$-0.289929\pi$
$829$	35.3042	1.22616	0.613082	+	0.790019i	$0.289929\pi$
$830$	21.0905	0.732062
$831$	18.6811	0.648042
$832$	7.14472	0.247699
$833$	−33.6164	−1.16474
$834$	−0.969244	−0.0335622
$835$	12.3352	0.426878
$836$	23.1151	0.799454
$837$	−2.01570	−0.0696727
$838$	28.8643	0.997102
$839$	−37.7512	−1.30332	−0.651659	−	0.758512i	$-0.725927\pi$
$839$	−37.7512	−1.30332	−0.651659	+	0.758512i	$0.725927\pi$
$840$	1.59089	0.0548908
$841$	76.5211	2.63866
$842$	−45.9566	−1.58377
$843$	5.20277	0.179193
$844$	−19.5973	−0.674566
$845$	19.7593	0.679742
$846$	−16.9397	−0.582398
$847$	−15.5896	−0.535664
$848$	3.55029	0.121917
$849$	21.7172	0.745333
$850$	−10.7510	−0.368755
$851$	0	0
$852$	−11.7353	−0.402046
$853$	−20.9667	−0.717885	−0.358943	−	0.933360i	$-0.616863\pi$
$853$	−20.9667	−0.717885	−0.358943	+	0.933360i	$0.616863\pi$
$854$	−8.76307	−0.299866
$855$	3.76464	0.128748
$856$	−2.16978	−0.0741614
$857$	48.1896	1.64612	0.823062	−	0.567951i	$-0.192264\pi$
$857$	48.1896	1.64612	0.823062	+	0.567951i	$0.192264\pi$
$858$	−50.8557	−1.73618
$859$	42.5110	1.45046	0.725228	−	0.688509i	$-0.241734\pi$
$859$	42.5110	1.45046	0.725228	+	0.688509i	$0.241734\pi$
$860$	14.2926	0.487373
$861$	2.15548	0.0734584
$862$	9.35106	0.318498
$863$	51.5990	1.75645	0.878226	−	0.478247i	$-0.158727\pi$
$863$	51.5990	1.75645	0.878226	+	0.478247i	$0.158727\pi$
$864$	−6.17792	−0.210177
$865$	−17.2887	−0.587833
$866$	−4.62228	−0.157071
$867$	−18.6213	−0.632413
$868$	−2.93423	−0.0995941
$869$	36.0328	1.22233
$870$	18.5039	0.627340
$871$	86.7102	2.93806
$872$	−10.3844	−0.351660
$873$	15.4375	0.522481
$874$	0	0
$875$	−1.16943	−0.0395340
$876$	−11.6345	−0.393092
$877$	33.2526	1.12286	0.561431	−	0.827524i	$-0.310251\pi$
$877$	33.2526	1.12286	0.561431	+	0.827524i	$0.310251\pi$
$878$	12.0645	0.407157
$879$	−6.86349	−0.231500
$880$	−24.3676	−0.821433
$881$	28.3999	0.956817	0.478408	−	0.878137i	$-0.341214\pi$
$881$	28.3999	0.956817	0.478408	+	0.878137i	$0.341214\pi$
$882$	10.1459	0.341629
$883$	19.5877	0.659178	0.329589	−	0.944125i	$-0.393090\pi$
$883$	19.5877	0.659178	0.329589	+	0.944125i	$0.393090\pi$
$884$	−42.5222	−1.43018
$885$	−6.18960	−0.208061
$886$	−29.1818	−0.980381
$887$	−20.5286	−0.689283	−0.344641	−	0.938734i	$-0.611999\pi$
$887$	−20.5286	−0.689283	−0.344641	+	0.938734i	$0.611999\pi$
$888$	14.7316	0.494362
$889$	7.37343	0.247297
$890$	−6.79632	−0.227813
$891$	4.93264	0.165250
$892$	4.72765	0.158293
$893$	35.4027	1.18470
$894$	−18.6456	−0.623601
$895$	6.09510	0.203737
$896$	11.8197	0.394869
$897$	0	0
$898$	−33.4491	−1.11621
$899$	20.7060	0.690582
$900$	1.24478	0.0414928
$901$	−4.28928	−0.142897
$902$	−16.3772	−0.545303
$903$	13.4274	0.446836
$904$	1.88039	0.0625407
$905$	−7.53099	−0.250338
$906$	−15.2423	−0.506392
$907$	25.0489	0.831736	0.415868	−	0.909425i	$-0.363478\pi$
$907$	25.0489	0.831736	0.415868	+	0.909425i	$0.363478\pi$
$908$	−20.7964	−0.690153
$909$	−0.00890951	−0.000295510 0
$910$	−12.0569	−0.399682
$911$	26.4675	0.876906	0.438453	−	0.898754i	$-0.355527\pi$
$911$	26.4675	0.876906	0.438453	+	0.898754i	$0.355527\pi$
$912$	18.5976	0.615830
$913$	−57.7528	−1.91134
$914$	26.6952	0.882999
$915$	4.15996	0.137524
$916$	−7.91997	−0.261683
$917$	−18.1100	−0.598044
$918$	10.7510	0.354835
$919$	−5.03813	−0.166193	−0.0830963	−	0.996542i	$-0.526481\pi$
$919$	−5.03813	−0.166193	−0.0830963	+	0.996542i	$0.526481\pi$
$920$	0	0
$921$	5.99610	0.197578
$922$	−13.1944	−0.434534
$923$	−53.9597	−1.77611
$924$	7.18038	0.236217
$925$	−10.8290	−0.356054
$926$	38.6200	1.26913
$927$	6.89593	0.226492
$928$	63.4617	2.08323
$929$	35.4018	1.16149	0.580747	−	0.814084i	$-0.302761\pi$
$929$	35.4018	1.16149	0.580747	+	0.814084i	$0.302761\pi$
$930$	3.63093	0.119063
$931$	−21.2041	−0.694936
$932$	33.0842	1.08371
$933$	23.5490	0.770960
$934$	7.22291	0.236341
$935$	29.4398	0.962783
$936$	−7.78632	−0.254504
$937$	53.7077	1.75456	0.877278	−	0.479983i	$-0.159357\pi$
$937$	53.7077	1.75456	0.877278	+	0.479983i	$0.159357\pi$
$938$	−31.9132	−1.04200
$939$	−7.43120	−0.242508
$940$	11.7059	0.381805
$941$	−18.8802	−0.615475	−0.307738	−	0.951471i	$-0.599572\pi$
$941$	−18.8802	−0.615475	−0.307738	+	0.951471i	$0.599572\pi$
$942$	9.78600	0.318845
$943$	0	0
$944$	−30.5771	−0.995201
$945$	1.16943	0.0380416
$946$	−102.021	−3.31699
$947$	−0.0162488	−0.000528015 0	−0.000264007	−	1.00000i	$-0.500084\pi$
$947$	−0.0162488	−0.000528015 0	−0.000264007		1.00000i	$0.500084\pi$
$948$	−9.09310	−0.295330
$949$	−53.4959	−1.73655
$950$	−6.78136	−0.220016
$951$	−16.8174	−0.545340
$952$	−9.49498	−0.307734
$953$	5.80510	0.188046	0.0940228	−	0.995570i	$-0.470027\pi$
$953$	5.80510	0.188046	0.0940228	+	0.995570i	$0.470027\pi$
$954$	1.29456	0.0419130
$955$	5.32898	0.172442
$956$	25.9972	0.840810
$957$	−50.6698	−1.63792
$958$	−22.4902	−0.726626
$959$	−19.9313	−0.643615
$960$	1.24830	0.0402886
$961$	−26.9370	−0.868934
$962$	−111.647	−3.59964
$963$	−1.59496	−0.0513969
$964$	−16.0434	−0.516723
$965$	−4.62606	−0.148918
$966$	0	0
$967$	−12.0594	−0.387805	−0.193902	−	0.981021i	$-0.562115\pi$
$967$	−12.0594	−0.387805	−0.193902	+	0.981021i	$0.562115\pi$
$968$	18.1353	0.582890
$969$	−22.4687	−0.721800
$970$	−27.8080	−0.892862
$971$	2.00731	0.0644175	0.0322088	−	0.999481i	$-0.489746\pi$
$971$	2.00731	0.0644175	0.0322088	+	0.999481i	$0.489746\pi$
$972$	−1.24478	−0.0399264
$973$	0.629238	0.0201724
$974$	3.62100	0.116024
$975$	5.72358	0.183301
$976$	20.5505	0.657806
$977$	33.8365	1.08253	0.541263	−	0.840854i	$-0.317946\pi$
$977$	33.8365	1.08253	0.541263	+	0.840854i	$0.317946\pi$
$978$	−24.8456	−0.794474
$979$	18.6106	0.594797
$980$	−7.01115	−0.223963
$981$	−7.63337	−0.243715
$982$	−14.7936	−0.472084
$983$	27.2751	0.869939	0.434970	−	0.900445i	$-0.356759\pi$
$983$	27.2751	0.869939	0.434970	+	0.900445i	$0.356759\pi$
$984$	−2.50746	−0.0799348
$985$	−21.0697	−0.671338
$986$	−110.438	−3.51705
$987$	10.9973	0.350048
$988$	−26.8216	−0.853309
$989$	0	0
$990$	−8.88530	−0.282393
$991$	−20.6046	−0.654526	−0.327263	−	0.944933i	$-0.606126\pi$
$991$	−20.6046	−0.654526	−0.327263	+	0.944933i	$0.606126\pi$
$992$	12.4528	0.395378
$993$	−8.38033	−0.265942
$994$	19.8596	0.629907
$995$	2.08378	0.0660603
$996$	14.5743	0.461804
$997$	−52.6168	−1.66639	−0.833196	−	0.552978i	$-0.813491\pi$
$997$	−52.6168	−1.66639	−0.833196	+	0.552978i	$0.813491\pi$
$998$	−73.0533	−2.31246
$999$	10.8290	0.342613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bk.1.3	yes	10
23.22	odd	2		7935.2.a.bj.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bj.1.3	✓	10	23.22	odd	2
7935.2.a.bk.1.3	yes	10	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.80133 q^{2} -1.00000 q^{3} +1.24478 q^{4} +1.00000 q^{5} +1.80133 q^{6} -1.16943 q^{7} +1.36039 q^{8} +1.00000 q^{9} -1.80133 q^{10} +4.93264 q^{11} -1.24478 q^{12} -5.72358 q^{13} +2.10653 q^{14} -1.00000 q^{15} -4.94008 q^{16} +5.96836 q^{17} -1.80133 q^{18} +3.76464 q^{19} +1.24478 q^{20} +1.16943 q^{21} -8.88530 q^{22} -1.36039 q^{24} +1.00000 q^{25} +10.3100 q^{26} -1.00000 q^{27} -1.45569 q^{28} +10.2723 q^{29} +1.80133 q^{30} +2.01570 q^{31} +6.17792 q^{32} -4.93264 q^{33} -10.7510 q^{34} -1.16943 q^{35} +1.24478 q^{36} -10.8290 q^{37} -6.78136 q^{38} +5.72358 q^{39} +1.36039 q^{40} +1.84318 q^{41} -2.10653 q^{42} +11.4820 q^{43} +6.14006 q^{44} +1.00000 q^{45} +9.40399 q^{47} +4.94008 q^{48} -5.63243 q^{49} -1.80133 q^{50} -5.96836 q^{51} -7.12461 q^{52} -0.718670 q^{53} +1.80133 q^{54} +4.93264 q^{55} -1.59089 q^{56} -3.76464 q^{57} -18.5039 q^{58} +6.18960 q^{59} -1.24478 q^{60} -4.15996 q^{61} -3.63093 q^{62} -1.16943 q^{63} -1.24830 q^{64} -5.72358 q^{65} +8.88530 q^{66} -15.1497 q^{67} +7.42931 q^{68} +2.10653 q^{70} +9.42763 q^{71} +1.36039 q^{72} +9.34659 q^{73} +19.5065 q^{74} -1.00000 q^{75} +4.68616 q^{76} -5.76838 q^{77} -10.3100 q^{78} +7.30497 q^{79} -4.94008 q^{80} +1.00000 q^{81} -3.32018 q^{82} -11.7083 q^{83} +1.45569 q^{84} +5.96836 q^{85} -20.6828 q^{86} -10.2723 q^{87} +6.71033 q^{88} +3.77295 q^{89} -1.80133 q^{90} +6.69333 q^{91} -2.01570 q^{93} -16.9397 q^{94} +3.76464 q^{95} -6.17792 q^{96} +15.4375 q^{97} +10.1459 q^{98} +4.93264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} + 16 q^{4} + 10 q^{5} + 6 q^{7} + 10 q^{9} - 4 q^{11} - 16 q^{12} - 4 q^{13} - 10 q^{15} + 28 q^{16} + 10 q^{17} + 8 q^{19} + 16 q^{20} - 6 q^{21} - 4 q^{22} + 10 q^{25} - 8 q^{26} - 10 q^{27}+ \cdots - 4 q^{99}+O(q^{100}) \) 10 * q - 10 * q^3 + 16 * q^4 + 10 * q^5 + 6 * q^7 + 10 * q^9 - 4 * q^11 - 16 * q^12 - 4 * q^13 - 10 * q^15 + 28 * q^16 + 10 * q^17 + 8 * q^19 + 16 * q^20 - 6 * q^21 - 4 * q^22 + 10 * q^25 - 8 * q^26 - 10 * q^27 + 76 * q^28 + 2 * q^29 + 2 * q^31 + 20 * q^32 + 4 * q^33 + 8 * q^34 + 6 * q^35 + 16 * q^36 + 2 * q^37 - 56 * q^38 + 4 * q^39 + 6 * q^41 + 44 * q^43 - 24 * q^44 + 10 * q^45 + 8 * q^47 - 28 * q^48 + 12 * q^49 - 10 * q^51 + 2 * q^53 - 4 * q^55 + 8 * q^56 - 8 * q^57 - 20 * q^58 - 14 * q^59 - 16 * q^60 - 8 * q^61 - 28 * q^62 + 6 * q^63 + 40 * q^64 - 4 * q^65 + 4 * q^66 + 2 * q^67 + 84 * q^68 + 6 * q^71 - 12 * q^73 + 40 * q^74 - 10 * q^75 + 44 * q^76 - 16 * q^77 + 8 * q^78 + 28 * q^80 + 10 * q^81 - 4 * q^82 - 62 * q^83 - 76 * q^84 + 10 * q^85 - 4 * q^86 - 2 * q^87 - 12 * q^88 + 56 * q^89 - 2 * q^93 + 20 * q^94 + 8 * q^95 - 20 * q^96 + 56 * q^97 - 4 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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