LMFDB - Embedded newform 7935.2.a.bj.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:	$1$
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	$-0.429067\pi$
$7$	1.16943	0.442003	0.221002	+	0.975273i	$0.429067\pi$
$8$	1.36039	0.480972
$9$	1.00000	0.333333
$10$	1.80133	0.569630
$11$	−4.93264	−1.48725	−0.743623	−	0.668599i	$-0.766894\pi$
$11$	−4.93264	−1.48725	−0.743623	+	0.668599i	$0.766894\pi$
$12$	−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	$-0.757592\pi$
$17$	−5.96836	−1.44754	−0.723770	+	0.690041i	$0.757592\pi$
$18$	−1.80133	−0.424577
$19$	−3.76464	−0.863668	−0.431834	−	0.901953i	$-0.642133\pi$
$19$	−3.76464	−0.863668	−0.431834	+	0.901953i	$0.642133\pi$
$20$	−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	$-0.150610\pi$
$37$	10.8290	1.78027	0.890135	+	0.455697i	$0.150610\pi$
$38$	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	$-0.839463\pi$
$43$	−11.4820	−1.75099	−0.875493	+	0.483230i	$0.839463\pi$
$44$	−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	$-0.484282\pi$
$53$	0.718670	0.0987170	0.0493585	+	0.998781i	$0.484282\pi$
$54$	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	$-0.414194\pi$
$61$	4.15996	0.532628	0.266314	+	0.963886i	$0.414194\pi$
$62$	−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	$-0.123719\pi$
$67$	15.1497	1.85082	0.925412	+	0.378961i	$0.123719\pi$
$68$	−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	$-0.634798\pi$
$79$	−7.30497	−0.821873	−0.410937	+	0.911664i	$0.634798\pi$
$80$	4.94008	0.552318
$81$	1.00000	0.111111
$82$	−3.32018	−0.366653
$83$	11.7083	1.28515	0.642577	−	0.766221i	$-0.277865\pi$
$83$	11.7083	1.28515	0.642577	+	0.766221i	$0.277865\pi$
$84$	−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	$-0.564083\pi$
$89$	−3.77295	−0.399932	−0.199966	+	0.979803i	$0.564083\pi$
$90$	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	$-0.786681\pi$
$97$	−15.4375	−1.56744	−0.783721	+	0.621112i	$0.786681\pi$
$98$	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	$-0.610338\pi$
$103$	−6.89593	−0.679476	−0.339738	+	0.940520i	$0.610338\pi$
$104$	−7.78632	−0.763511
$105$	1.16943	0.114125
$106$	−1.29456	−0.125739
$107$	1.59496	0.154191	0.0770954	−	0.997024i	$-0.475435\pi$
$107$	1.59496	0.154191	0.0770954	+	0.997024i	$0.475435\pi$
$108$	−1.24478	−0.119779
$109$	7.63337	0.731144	0.365572	−	0.930783i	$-0.380873\pi$
$109$	7.63337	0.731144	0.365572	+	0.930783i	$0.380873\pi$
$110$	−8.88530	−0.847180
$111$	−10.8290	−1.02784
$112$	−5.77708	−0.545883
$113$	−1.38224	−0.130030	−0.0650149	−	0.997884i	$-0.520710\pi$
$113$	−1.38224	−0.130030	−0.0650149	+	0.997884i	$0.520710\pi$
$114$	−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	$-0.759580\pi$
$137$	−17.0436	−1.45613	−0.728066	+	0.685508i	$0.759580\pi$
$138$	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	$-0.360628\pi$
$149$	10.3510	0.847988	0.423994	+	0.905665i	$0.360628\pi$
$150$	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	$-0.569558\pi$
$157$	−5.43266	−0.433573	−0.216787	+	0.976219i	$0.569558\pi$
$158$	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	$-0.409703\pi$
$181$	7.53099	0.559774	0.279887	+	0.960033i	$0.409703\pi$
$182$	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	$-0.561755\pi$
$191$	−5.32898	−0.385591	−0.192796	+	0.981239i	$0.561755\pi$
$192$	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	$-0.523531\pi$
$199$	−2.08378	−0.147715	−0.0738577	+	0.997269i	$0.523531\pi$
$200$	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	$-0.312934\pi$
$227$	16.7068	1.10887	0.554436	+	0.832226i	$0.312934\pi$
$228$	4.68616	0.310349
$229$	6.36253	0.420448	0.210224	−	0.977653i	$-0.432581\pi$
$229$	6.36253	0.420448	0.210224	+	0.977653i	$0.432581\pi$
$230$	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	$-0.363743\pi$
$241$	12.8885	0.830222	0.415111	+	0.909771i	$0.363743\pi$
$242$	−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	$-0.527229\pi$
$251$	−2.70724	−0.170879	−0.0854397	+	0.996343i	$0.527229\pi$
$252$	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	$-0.582360\pi$
$263$	−8.29888	−0.511731	−0.255865	+	0.966712i	$0.582360\pi$
$264$	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	$-0.450402\pi$
$281$	5.20277	0.310372	0.155186	+	0.987885i	$0.450402\pi$
$282$	16.9397	1.00874
$283$	21.7172	1.29095	0.645477	−	0.763779i	$-0.276659\pi$
$283$	21.7172	1.29095	0.645477	+	0.763779i	$0.276659\pi$
$284$	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	$-0.564252\pi$
$293$	−6.86349	−0.400970	−0.200485	+	0.979697i	$0.564252\pi$
$294$	−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	$-0.567352\pi$
$313$	−7.43120	−0.420037	−0.210018	+	0.977697i	$0.567352\pi$
$314$	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	$-0.868752\pi$
$337$	−33.6380	−1.83238	−0.916190	+	0.400743i	$0.868752\pi$
$338$	−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	$-0.474889\pi$
$359$	2.98636	0.157614	0.0788071	+	0.996890i	$0.474889\pi$
$360$	−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	$-0.296079\pi$
$367$	22.9008	1.19541	0.597707	+	0.801715i	$0.296079\pi$
$368$	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	$-0.522439\pi$
$373$	−2.72067	−0.140871	−0.0704356	+	0.997516i	$0.522439\pi$
$374$	−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	$-0.557664\pi$
$379$	−7.01494	−0.360333	−0.180167	+	0.983636i	$0.557664\pi$
$380$	4.68616	0.240395
$381$	6.30514	0.323022
$382$	9.59923	0.491139
$383$	−10.5223	−0.537666	−0.268833	−	0.963187i	$-0.586638\pi$
$383$	−10.5223	−0.537666	−0.268833	+	0.963187i	$0.586638\pi$
$384$	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	$-0.566389\pi$
$389$	−8.16762	−0.414115	−0.207057	+	0.978329i	$0.566389\pi$
$390$	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	$-0.352586\pi$
$401$	17.8918	0.893471	0.446736	+	0.894666i	$0.352586\pi$
$402$	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	$-0.371987\pi$
$419$	16.0239	0.782820	0.391410	+	0.920216i	$0.371987\pi$
$420$	1.45569	0.0710303
$421$	−25.5126	−1.24341	−0.621704	−	0.783252i	$-0.713559\pi$
$421$	−25.5126	−1.24341	−0.621704	+	0.783252i	$0.713559\pi$
$422$	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	$-0.460099\pi$
$431$	5.19120	0.250051	0.125026	+	0.992154i	$0.460099\pi$
$432$	4.94008	0.237680
$433$	−2.56604	−0.123316	−0.0616580	−	0.998097i	$-0.519639\pi$
$433$	−2.56604	−0.123316	−0.0616580	+	0.998097i	$0.519639\pi$
$434$	−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	$-0.387330\pi$
$457$	14.8197	0.693238	0.346619	+	0.938006i	$0.387330\pi$
$458$	−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	$-0.470426\pi$
$467$	4.00977	0.185550	0.0927750	+	0.995687i	$0.470426\pi$
$468$	−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	$-0.592072\pi$
$479$	−12.4853	−0.570470	−0.285235	+	0.958458i	$0.592072\pi$
$480$	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	$-0.830265\pi$
$503$	−38.6279	−1.72233	−0.861166	+	0.508325i	$0.830265\pi$
$504$	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	$-0.232985\pi$
$521$	33.9586	1.48775	0.743876	+	0.668318i	$0.232985\pi$
$522$	−18.5039	−0.809892
$523$	−15.4202	−0.674280	−0.337140	−	0.941455i	$-0.609460\pi$
$523$	−15.4202	−0.674280	−0.337140	+	0.941455i	$0.609460\pi$
$524$	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	$-0.641407\pi$
$557$	−20.2861	−0.859548	−0.429774	+	0.902936i	$0.641407\pi$
$558$	−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	$-0.832164\pi$
$563$	−41.0100	−1.72836	−0.864182	+	0.503179i	$0.832164\pi$
$564$	−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	$-0.414584\pi$
$569$	12.6489	0.530269	0.265135	+	0.964211i	$0.414584\pi$
$570$	6.78136	0.284040
$571$	12.9538	0.542102	0.271051	−	0.962565i	$-0.412629\pi$
$571$	12.9538	0.542102	0.271051	+	0.962565i	$0.412629\pi$
$572$	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	$-0.550910\pi$
$613$	−7.88607	−0.318516	−0.159258	+	0.987237i	$0.550910\pi$
$614$	10.8009	0.435891
$615$	1.84318	0.0743244
$616$	−7.84727	−0.316175
$617$	9.42380	0.379388	0.189694	−	0.981843i	$-0.439250\pi$
$617$	9.42380	0.379388	0.189694	+	0.981843i	$0.439250\pi$
$618$	−12.4218	−0.499679
$619$	−46.7301	−1.87824	−0.939120	−	0.343588i	$-0.888358\pi$
$619$	−46.7301	−1.87824	−0.939120	+	0.343588i	$0.888358\pi$
$620$	−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	$-0.330291\pi$
$631$	25.5344	1.01651	0.508255	+	0.861207i	$0.330291\pi$
$632$	−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	$-0.746849\pi$
$641$	−35.4489	−1.40015	−0.700073	+	0.714072i	$0.746849\pi$
$642$	2.87305	0.113390
$643$	14.5158	0.572446	0.286223	−	0.958163i	$-0.407600\pi$
$643$	14.5158	0.572446	0.286223	+	0.958163i	$0.407600\pi$
$644$	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	$-0.440447\pi$
$659$	9.54973	0.372005	0.186002	+	0.982549i	$0.440447\pi$
$660$	−6.14006	−0.239002
$661$	−12.6193	−0.490832	−0.245416	−	0.969418i	$-0.578925\pi$
$661$	−12.6193	−0.490832	−0.245416	+	0.969418i	$0.578925\pi$
$662$	−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	$-0.492042\pi$
$677$	1.30088	0.0499967	0.0249984	+	0.999687i	$0.492042\pi$
$678$	−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	$-0.626951\pi$
$701$	−20.5637	−0.776680	−0.388340	+	0.921516i	$0.626951\pi$
$702$	−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	$-0.776740\pi$
$709$	−40.6832	−1.52789	−0.763945	+	0.645281i	$0.776740\pi$
$710$	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	$-0.597084\pi$
$727$	−16.1935	−0.600583	−0.300292	+	0.953847i	$0.597084\pi$
$728$	−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	$-0.562333\pi$
$733$	−10.5359	−0.389151	−0.194576	+	0.980887i	$0.562333\pi$
$734$	−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	$-0.542892\pi$
$743$	−7.32384	−0.268686	−0.134343	+	0.990935i	$0.542892\pi$
$744$	−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	$-0.411445\pi$
$751$	15.0521	0.549261	0.274630	+	0.961550i	$0.411445\pi$
$752$	−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	$-0.252901\pi$
$757$	38.5540	1.40127	0.700634	+	0.713521i	$0.252901\pi$
$758$	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	$-0.453157\pi$
$769$	8.13233	0.293259	0.146630	+	0.989191i	$0.453157\pi$
$770$	−10.3907	−0.374456
$771$	13.3118	0.479413
$772$	−5.75844	−0.207251
$773$	−5.20702	−0.187284	−0.0936418	−	0.995606i	$-0.529851\pi$
$773$	−5.20702	−0.187284	−0.0936418	+	0.995606i	$0.529851\pi$
$774$	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	$-0.160233\pi$
$787$	49.1472	1.75191	0.875954	+	0.482395i	$0.160233\pi$
$788$	−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	$-0.620119\pi$
$797$	−20.8049	−0.736946	−0.368473	+	0.929639i	$0.620119\pi$
$798$	−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	$-0.517518\pi$
$827$	−3.16378	−0.110016	−0.0550078	+	0.998486i	$0.517518\pi$
$828$	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	$-0.274073\pi$
$839$	37.7512	1.30332	0.651659	+	0.758512i	$0.274073\pi$
$840$	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	$-0.658786\pi$
$881$	−28.3999	−0.956817	−0.478408	+	0.878137i	$0.658786\pi$
$882$	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	$-0.636522\pi$
$907$	−25.0489	−0.831736	−0.415868	+	0.909425i	$0.636522\pi$
$908$	20.7964	0.690153
$909$	−0.00890951	−0.000295510 0
$910$	−12.0569	−0.399682
$911$	−26.4675	−0.876906	−0.438453	−	0.898754i	$-0.644473\pi$
$911$	−26.4675	−0.876906	−0.438453	+	0.898754i	$0.644473\pi$
$912$	−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	$-0.473519\pi$
$919$	5.03813	0.166193	0.0830963	+	0.996542i	$0.473519\pi$
$920$	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	$-0.840643\pi$
$937$	−53.7077	−1.75456	−0.877278	+	0.479983i	$0.840643\pi$
$938$	−31.9132	−1.04200
$939$	7.43120	0.242508
$940$	−11.7059	−0.381805
$941$	18.8802	0.615475	0.307738	−	0.951471i	$-0.400428\pi$
$941$	18.8802	0.615475	0.307738	+	0.951471i	$0.400428\pi$
$942$	−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	$-0.529973\pi$
$953$	−5.80510	−0.188046	−0.0940228	+	0.995570i	$0.529973\pi$
$954$	−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	$-0.510254\pi$
$971$	−2.00731	−0.0644175	−0.0322088	+	0.999481i	$0.510254\pi$
$972$	−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	$-0.682054\pi$
$977$	−33.8365	−1.08253	−0.541263	+	0.840854i	$0.682054\pi$
$978$	−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	$-0.643241\pi$
$983$	−27.2751	−0.869939	−0.434970	+	0.900445i	$0.643241\pi$
$984$	−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.bj.1.3	✓	10
23.22	odd	2		7935.2.a.bk.1.3	yes	10

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

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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