LMFDB - Embedded newform 7935.2.a.bu.1.4

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 = [25,1,-25,31,25,-1,-15] 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:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	\(q-2.18378 q^{2} -1.00000 q^{3} +2.76889 q^{4} +1.00000 q^{5} +2.18378 q^{6} -0.993609 q^{7} -1.67909 q^{8} +1.00000 q^{9} -2.18378 q^{10} -5.93300 q^{11} -2.76889 q^{12} -4.13097 q^{13} +2.16982 q^{14} -1.00000 q^{15} -1.87102 q^{16} -7.29277 q^{17} -2.18378 q^{18} +2.31191 q^{19} +2.76889 q^{20} +0.993609 q^{21} +12.9564 q^{22} +1.67909 q^{24} +1.00000 q^{25} +9.02113 q^{26} -1.00000 q^{27} -2.75120 q^{28} -5.22808 q^{29} +2.18378 q^{30} +9.31419 q^{31} +7.44408 q^{32} +5.93300 q^{33} +15.9258 q^{34} -0.993609 q^{35} +2.76889 q^{36} -10.5373 q^{37} -5.04870 q^{38} +4.13097 q^{39} -1.67909 q^{40} -8.24707 q^{41} -2.16982 q^{42} -5.82517 q^{43} -16.4278 q^{44} +1.00000 q^{45} +0.519567 q^{47} +1.87102 q^{48} -6.01274 q^{49} -2.18378 q^{50} +7.29277 q^{51} -11.4382 q^{52} -1.97446 q^{53} +2.18378 q^{54} -5.93300 q^{55} +1.66836 q^{56} -2.31191 q^{57} +11.4170 q^{58} -10.0495 q^{59} -2.76889 q^{60} -4.81217 q^{61} -20.3401 q^{62} -0.993609 q^{63} -12.5142 q^{64} -4.13097 q^{65} -12.9564 q^{66} -7.46264 q^{67} -20.1929 q^{68} +2.16982 q^{70} +0.553134 q^{71} -1.67909 q^{72} +8.22053 q^{73} +23.0112 q^{74} -1.00000 q^{75} +6.40143 q^{76} +5.89508 q^{77} -9.02113 q^{78} -3.22794 q^{79} -1.87102 q^{80} +1.00000 q^{81} +18.0098 q^{82} -17.6316 q^{83} +2.75120 q^{84} -7.29277 q^{85} +12.7209 q^{86} +5.22808 q^{87} +9.96203 q^{88} +2.14296 q^{89} -2.18378 q^{90} +4.10457 q^{91} -9.31419 q^{93} -1.13462 q^{94} +2.31191 q^{95} -7.44408 q^{96} -5.04476 q^{97} +13.1305 q^{98} -5.93300 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19}+ \cdots + 15 q^{99}+O(q^{100}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * 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 $

$2$	−2.18378	−1.54417	−0.772083	−	0.635522i	$-0.780785\pi$
$2$	−2.18378	−1.54417	−0.772083	+	0.635522i	$0.780785\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.76889	1.38445
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.18378	0.891524
$7$	−0.993609	−0.375549	−0.187775	−	0.982212i	$-0.560127\pi$
$7$	−0.993609	−0.375549	−0.187775	+	0.982212i	$0.560127\pi$
$8$	−1.67909	−0.593648
$9$	1.00000	0.333333
$10$	−2.18378	−0.690572
$11$	−5.93300	−1.78887	−0.894433	−	0.447202i	$-0.852420\pi$
$11$	−5.93300	−1.78887	−0.894433	+	0.447202i	$0.852420\pi$
$12$	−2.76889	−0.799310
$13$	−4.13097	−1.14572	−0.572862	−	0.819652i	$-0.694167\pi$
$13$	−4.13097	−1.14572	−0.572862	+	0.819652i	$0.694167\pi$
$14$	2.16982	0.579910
$15$	−1.00000	−0.258199
$16$	−1.87102	−0.467756
$17$	−7.29277	−1.76876	−0.884378	−	0.466771i	$-0.845417\pi$
$17$	−7.29277	−1.76876	−0.884378	+	0.466771i	$0.845417\pi$
$18$	−2.18378	−0.514722
$19$	2.31191	0.530388	0.265194	−	0.964195i	$-0.414564\pi$
$19$	2.31191	0.530388	0.265194	+	0.964195i	$0.414564\pi$
$20$	2.76889	0.619143
$21$	0.993609	0.216823
$22$	12.9564	2.76230
$23$	0	0
$23$	0	0
$24$	1.67909	0.342743
$25$	1.00000	0.200000
$26$	9.02113	1.76919
$27$	−1.00000	−0.192450
$28$	−2.75120	−0.519927
$29$	−5.22808	−0.970831	−0.485415	−	0.874284i	$-0.661332\pi$
$29$	−5.22808	−0.970831	−0.485415	+	0.874284i	$0.661332\pi$
$30$	2.18378	0.398702
$31$	9.31419	1.67288	0.836439	−	0.548061i	$-0.184634\pi$
$31$	9.31419	1.67288	0.836439	+	0.548061i	$0.184634\pi$
$32$	7.44408	1.31594
$33$	5.93300	1.03280
$34$	15.9258	2.73125
$35$	−0.993609	−0.167951
$36$	2.76889	0.461482
$37$	−10.5373	−1.73233	−0.866164	−	0.499759i	$-0.833422\pi$
$37$	−10.5373	−1.73233	−0.866164	+	0.499759i	$0.833422\pi$
$38$	−5.04870	−0.819007
$39$	4.13097	0.661485
$40$	−1.67909	−0.265487
$41$	−8.24707	−1.28798	−0.643988	−	0.765036i	$-0.722721\pi$
$41$	−8.24707	−1.28798	−0.643988	+	0.765036i	$0.722721\pi$
$42$	−2.16982	−0.334811
$43$	−5.82517	−0.888330	−0.444165	−	0.895945i	$-0.646500\pi$
$43$	−5.82517	−0.888330	−0.444165	+	0.895945i	$0.646500\pi$
$44$	−16.4278	−2.47659
$45$	1.00000	0.149071
$46$	0	0
$47$	0.519567	0.0757866	0.0378933	−	0.999282i	$-0.487935\pi$
$47$	0.519567	0.0757866	0.0378933	+	0.999282i	$0.487935\pi$
$48$	1.87102	0.270059
$49$	−6.01274	−0.858963
$50$	−2.18378	−0.308833
$51$	7.29277	1.02119
$52$	−11.4382	−1.58619
$53$	−1.97446	−0.271213	−0.135606	−	0.990763i	$-0.543298\pi$
$53$	−1.97446	−0.271213	−0.135606	+	0.990763i	$0.543298\pi$
$54$	2.18378	0.297175
$55$	−5.93300	−0.800005
$56$	1.66836	0.222944
$57$	−2.31191	−0.306220
$58$	11.4170	1.49912
$59$	−10.0495	−1.30833	−0.654167	−	0.756350i	$-0.726981\pi$
$59$	−10.0495	−1.30833	−0.654167	+	0.756350i	$0.726981\pi$
$60$	−2.76889	−0.357462
$61$	−4.81217	−0.616135	−0.308067	−	0.951365i	$-0.599682\pi$
$61$	−4.81217	−0.616135	−0.308067	+	0.951365i	$0.599682\pi$
$62$	−20.3401	−2.58320
$63$	−0.993609	−0.125183
$64$	−12.5142	−1.56427
$65$	−4.13097	−0.512384
$66$	−12.9564	−1.59482
$67$	−7.46264	−0.911706	−0.455853	−	0.890055i	$-0.650666\pi$
$67$	−7.46264	−0.911706	−0.455853	+	0.890055i	$0.650666\pi$
$68$	−20.1929	−2.44875
$69$	0	0
$70$	2.16982	0.259344
$71$	0.553134	0.0656449	0.0328224	−	0.999461i	$-0.489550\pi$
$71$	0.553134	0.0656449	0.0328224	+	0.999461i	$0.489550\pi$
$72$	−1.67909	−0.197883
$73$	8.22053	0.962140	0.481070	−	0.876682i	$-0.340248\pi$
$73$	8.22053	0.962140	0.481070	+	0.876682i	$0.340248\pi$
$74$	23.0112	2.67500
$75$	−1.00000	−0.115470
$76$	6.40143	0.734294
$77$	5.89508	0.671807
$78$	−9.02113	−1.02144
$79$	−3.22794	−0.363172	−0.181586	−	0.983375i	$-0.558123\pi$
$79$	−3.22794	−0.363172	−0.181586	+	0.983375i	$0.558123\pi$
$80$	−1.87102	−0.209187
$81$	1.00000	0.111111
$82$	18.0098	1.98885
$83$	−17.6316	−1.93532	−0.967659	−	0.252260i	$-0.918826\pi$
$83$	−17.6316	−1.93532	−0.967659	+	0.252260i	$0.918826\pi$
$84$	2.75120	0.300180
$85$	−7.29277	−0.791012
$86$	12.7209	1.37173
$87$	5.22808	0.560509
$88$	9.96203	1.06196
$89$	2.14296	0.227153	0.113576	−	0.993529i	$-0.463769\pi$
$89$	2.14296	0.227153	0.113576	+	0.993529i	$0.463769\pi$
$90$	−2.18378	−0.230191
$91$	4.10457	0.430276
$92$	0	0
$93$	−9.31419	−0.965836
$94$	−1.13462	−0.117027
$95$	2.31191	0.237197
$96$	−7.44408	−0.759758
$97$	−5.04476	−0.512218	−0.256109	−	0.966648i	$-0.582441\pi$
$97$	−5.04476	−0.512218	−0.256109	+	0.966648i	$0.582441\pi$
$98$	13.1305	1.32638
$99$	−5.93300	−0.596289
$100$	2.76889	0.276889
$101$	5.57461	0.554695	0.277347	−	0.960770i	$-0.410545\pi$
$101$	5.57461	0.554695	0.277347	+	0.960770i	$0.410545\pi$
$102$	−15.9258	−1.57689
$103$	−13.6494	−1.34492	−0.672460	−	0.740134i	$-0.734762\pi$
$103$	−13.6494	−1.34492	−0.672460	+	0.740134i	$0.734762\pi$
$104$	6.93627	0.680157
$105$	0.993609	0.0969663
$106$	4.31178	0.418797
$107$	11.5297	1.11462	0.557308	−	0.830306i	$-0.311834\pi$
$107$	11.5297	1.11462	0.557308	+	0.830306i	$0.311834\pi$
$108$	−2.76889	−0.266437
$109$	6.08637	0.582969	0.291484	−	0.956576i	$-0.405851\pi$
$109$	6.08637	0.582969	0.291484	+	0.956576i	$0.405851\pi$
$110$	12.9564	1.23534
$111$	10.5373	1.00016
$112$	1.85907	0.175665
$113$	−1.20877	−0.113712	−0.0568559	−	0.998382i	$-0.518108\pi$
$113$	−1.20877	−0.113712	−0.0568559	+	0.998382i	$0.518108\pi$
$114$	5.04870	0.472854
$115$	0	0
$116$	−14.4760	−1.34406
$117$	−4.13097	−0.381908
$118$	21.9459	2.02028
$119$	7.24617	0.664255
$120$	1.67909	0.153279
$121$	24.2004	2.20004
$122$	10.5087	0.951414
$123$	8.24707	0.743613
$124$	25.7900	2.31601
$125$	1.00000	0.0894427
$126$	2.16982	0.193303
$127$	−3.46656	−0.307607	−0.153804	−	0.988101i	$-0.549152\pi$
$127$	−3.46656	−0.307607	−0.153804	+	0.988101i	$0.549152\pi$
$128$	12.4400	1.09956
$129$	5.82517	0.512877
$130$	9.02113	0.791205
$131$	7.85244	0.686071	0.343035	−	0.939322i	$-0.388545\pi$
$131$	7.85244	0.686071	0.343035	+	0.939322i	$0.388545\pi$
$132$	16.4278	1.42986
$133$	−2.29713	−0.199187
$134$	16.2968	1.40783
$135$	−1.00000	−0.0860663
$136$	12.2452	1.05002
$137$	−8.36805	−0.714931	−0.357466	−	0.933926i	$-0.616359\pi$
$137$	−8.36805	−0.714931	−0.357466	+	0.933926i	$0.616359\pi$
$138$	0	0
$139$	0.538695	0.0456915	0.0228458	−	0.999739i	$-0.492727\pi$
$139$	0.538695	0.0456915	0.0228458	+	0.999739i	$0.492727\pi$
$140$	−2.75120	−0.232519
$141$	−0.519567	−0.0437554
$142$	−1.20792	−0.101367
$143$	24.5090	2.04955
$144$	−1.87102	−0.155919
$145$	−5.22808	−0.434169
$146$	−17.9518	−1.48570
$147$	6.01274	0.495922
$148$	−29.1768	−2.39832
$149$	1.73900	0.142464	0.0712321	−	0.997460i	$-0.477307\pi$
$149$	1.73900	0.142464	0.0712321	+	0.997460i	$0.477307\pi$
$150$	2.18378	0.178305
$151$	6.20037	0.504579	0.252289	−	0.967652i	$-0.418817\pi$
$151$	6.20037	0.504579	0.252289	+	0.967652i	$0.418817\pi$
$152$	−3.88190	−0.314864
$153$	−7.29277	−0.589586
$154$	−12.8736	−1.03738
$155$	9.31419	0.748133
$156$	11.4382	0.915789
$157$	10.4375	0.833005	0.416503	−	0.909135i	$-0.363256\pi$
$157$	10.4375	0.833005	0.416503	+	0.909135i	$0.363256\pi$
$158$	7.04912	0.560798
$159$	1.97446	0.156585
$160$	7.44408	0.588506
$161$	0	0
$162$	−2.18378	−0.171574
$163$	−2.78139	−0.217855	−0.108928	−	0.994050i	$-0.534742\pi$
$163$	−2.78139	−0.217855	−0.108928	+	0.994050i	$0.534742\pi$
$164$	−22.8352	−1.78313
$165$	5.93300	0.461883
$166$	38.5035	2.98845
$167$	−16.3886	−1.26819	−0.634095	−	0.773255i	$-0.718627\pi$
$167$	−16.3886	−1.26819	−0.634095	+	0.773255i	$0.718627\pi$
$168$	−1.66836	−0.128717
$169$	4.06491	0.312685
$170$	15.9258	1.22145
$171$	2.31191	0.176796
$172$	−16.1293	−1.22984
$173$	3.27198	0.248764	0.124382	−	0.992234i	$-0.460305\pi$
$173$	3.27198	0.248764	0.124382	+	0.992234i	$0.460305\pi$
$174$	−11.4170	−0.865519
$175$	−0.993609	−0.0751098
$176$	11.1008	0.836752
$177$	10.0495	0.755367
$178$	−4.67974	−0.350761
$179$	−20.4215	−1.52638	−0.763188	−	0.646177i	$-0.776367\pi$
$179$	−20.4215	−1.52638	−0.763188	+	0.646177i	$0.776367\pi$
$180$	2.76889	0.206381
$181$	3.18638	0.236841	0.118421	−	0.992964i	$-0.462217\pi$
$181$	3.18638	0.236841	0.118421	+	0.992964i	$0.462217\pi$
$182$	−8.96347	−0.664417
$183$	4.81217	0.355725
$184$	0	0
$185$	−10.5373	−0.774721
$186$	20.3401	1.49141
$187$	43.2680	3.16407
$188$	1.43862	0.104922
$189$	0.993609	0.0722744
$190$	−5.04870	−0.366271
$191$	−11.3085	−0.818255	−0.409128	−	0.912477i	$-0.634167\pi$
$191$	−11.3085	−0.818255	−0.409128	+	0.912477i	$0.634167\pi$
$192$	12.5142	0.903133
$193$	−1.31168	−0.0944170	−0.0472085	−	0.998885i	$-0.515033\pi$
$193$	−1.31168	−0.0944170	−0.0472085	+	0.998885i	$0.515033\pi$
$194$	11.0167	0.790949
$195$	4.13097	0.295825
$196$	−16.6486	−1.18919
$197$	−20.1870	−1.43827	−0.719133	−	0.694873i	$-0.755461\pi$
$197$	−20.1870	−1.43827	−0.719133	+	0.694873i	$0.755461\pi$
$198$	12.9564	0.920768
$199$	7.84740	0.556287	0.278144	−	0.960539i	$-0.410281\pi$
$199$	7.84740	0.556287	0.278144	+	0.960539i	$0.410281\pi$
$200$	−1.67909	−0.118730
$201$	7.46264	0.526374
$202$	−12.1737	−0.856540
$203$	5.19467	0.364595
$204$	20.1929	1.41379
$205$	−8.24707	−0.576000
$206$	29.8074	2.07678
$207$	0	0
$208$	7.72914	0.535919
$209$	−13.7165	−0.948794
$210$	−2.16982	−0.149732
$211$	17.8328	1.22766	0.613829	−	0.789439i	$-0.289629\pi$
$211$	17.8328	1.22766	0.613829	+	0.789439i	$0.289629\pi$
$212$	−5.46706	−0.375479
$213$	−0.553134	−0.0379001
$214$	−25.1783	−1.72115
$215$	−5.82517	−0.397273
$216$	1.67909	0.114248
$217$	−9.25466	−0.628247
$218$	−13.2913	−0.900200
$219$	−8.22053	−0.555492
$220$	−16.4278	−1.10756
$221$	30.1262	2.02651
$222$	−23.0112	−1.54441
$223$	−4.82825	−0.323324	−0.161662	−	0.986846i	$-0.551685\pi$
$223$	−4.82825	−0.323324	−0.161662	+	0.986846i	$0.551685\pi$
$224$	−7.39651	−0.494200
$225$	1.00000	0.0666667
$226$	2.63969	0.175590
$227$	−23.6484	−1.56960	−0.784801	−	0.619748i	$-0.787235\pi$
$227$	−23.6484	−1.56960	−0.784801	+	0.619748i	$0.787235\pi$
$228$	−6.40143	−0.423945
$229$	−11.4495	−0.756602	−0.378301	−	0.925683i	$-0.623492\pi$
$229$	−11.4495	−0.756602	−0.378301	+	0.925683i	$0.623492\pi$
$230$	0	0
$231$	−5.89508	−0.387868
$232$	8.77842	0.576332
$233$	−12.0436	−0.789004	−0.394502	−	0.918895i	$-0.629083\pi$
$233$	−12.0436	−0.789004	−0.394502	+	0.918895i	$0.629083\pi$
$234$	9.02113	0.589729
$235$	0.519567	0.0338928
$236$	−27.8260	−1.81132
$237$	3.22794	0.209678
$238$	−15.8240	−1.02572
$239$	−5.64180	−0.364938	−0.182469	−	0.983212i	$-0.558409\pi$
$239$	−5.64180	−0.364938	−0.182469	+	0.983212i	$0.558409\pi$
$240$	1.87102	0.120774
$241$	13.8293	0.890826	0.445413	−	0.895325i	$-0.353057\pi$
$241$	13.8293	0.890826	0.445413	+	0.895325i	$0.353057\pi$
$242$	−52.8484	−3.39723
$243$	−1.00000	−0.0641500
$244$	−13.3244	−0.853005
$245$	−6.01274	−0.384140
$246$	−18.0098	−1.14826
$247$	−9.55043	−0.607679
$248$	−15.6394	−0.993100
$249$	17.6316	1.11736
$250$	−2.18378	−0.138114
$251$	−26.4002	−1.66636	−0.833182	−	0.552999i	$-0.813483\pi$
$251$	−26.4002	−1.66636	−0.833182	+	0.552999i	$0.813483\pi$
$252$	−2.75120	−0.173309
$253$	0	0
$254$	7.57020	0.474997
$255$	7.29277	0.456691
$256$	−2.13796	−0.133622
$257$	−13.9233	−0.868513	−0.434256	−	0.900789i	$-0.642989\pi$
$257$	−13.9233	−0.868513	−0.434256	+	0.900789i	$0.642989\pi$
$258$	−12.7209	−0.791967
$259$	10.4700	0.650574
$260$	−11.4382	−0.709367
$261$	−5.22808	−0.323610
$262$	−17.1480	−1.05941
$263$	−0.298839	−0.0184272	−0.00921359	−	0.999958i	$-0.502933\pi$
$263$	−0.298839	−0.0184272	−0.00921359	+	0.999958i	$0.502933\pi$
$264$	−9.96203	−0.613121
$265$	−1.97446	−0.121290
$266$	5.01643	0.307577
$267$	−2.14296	−0.131147
$268$	−20.6632	−1.26221
$269$	−25.5063	−1.55514	−0.777572	−	0.628794i	$-0.783549\pi$
$269$	−25.5063	−1.55514	−0.777572	+	0.628794i	$0.783549\pi$
$270$	2.18378	0.132901
$271$	−1.11434	−0.0676914	−0.0338457	−	0.999427i	$-0.510775\pi$
$271$	−1.11434	−0.0676914	−0.0338457	+	0.999427i	$0.510775\pi$
$272$	13.6449	0.827346
$273$	−4.10457	−0.248420
$274$	18.2740	1.10397
$275$	−5.93300	−0.357773
$276$	0	0
$277$	−2.19727	−0.132021	−0.0660105	−	0.997819i	$-0.521027\pi$
$277$	−2.19727	−0.132021	−0.0660105	+	0.997819i	$0.521027\pi$
$278$	−1.17639	−0.0705552
$279$	9.31419	0.557626
$280$	1.66836	0.0997035
$281$	16.4545	0.981593	0.490797	−	0.871274i	$-0.336706\pi$
$281$	16.4545	0.981593	0.490797	+	0.871274i	$0.336706\pi$
$282$	1.13462	0.0675656
$283$	−2.53587	−0.150742	−0.0753708	−	0.997156i	$-0.524014\pi$
$283$	−2.53587	−0.150742	−0.0753708	+	0.997156i	$0.524014\pi$
$284$	1.53157	0.0908818
$285$	−2.31191	−0.136946
$286$	−53.5223	−3.16484
$287$	8.19436	0.483698
$288$	7.44408	0.438647
$289$	36.1845	2.12850
$290$	11.4170	0.670428
$291$	5.04476	0.295729
$292$	22.7617	1.33203
$293$	29.8353	1.74300	0.871499	−	0.490398i	$-0.163148\pi$
$293$	29.8353	1.74300	0.871499	+	0.490398i	$0.163148\pi$
$294$	−13.1305	−0.765786
$295$	−10.0495	−0.585105
$296$	17.6931	1.02839
$297$	5.93300	0.344267
$298$	−3.79758	−0.219988
$299$	0	0
$300$	−2.76889	−0.159862
$301$	5.78794	0.333611
$302$	−13.5402	−0.779153
$303$	−5.57461	−0.320253
$304$	−4.32563	−0.248092
$305$	−4.81217	−0.275544
$306$	15.9258	0.910417
$307$	10.5077	0.599704	0.299852	−	0.953986i	$-0.403063\pi$
$307$	10.5077	0.599704	0.299852	+	0.953986i	$0.403063\pi$
$308$	16.3228	0.930080
$309$	13.6494	0.776490
$310$	−20.3401	−1.15524
$311$	25.4615	1.44379	0.721894	−	0.692004i	$-0.243272\pi$
$311$	25.4615	1.44379	0.721894	+	0.692004i	$0.243272\pi$
$312$	−6.93627	−0.392689
$313$	−14.3344	−0.810227	−0.405114	−	0.914266i	$-0.632768\pi$
$313$	−14.3344	−0.810227	−0.405114	+	0.914266i	$0.632768\pi$
$314$	−22.7933	−1.28630
$315$	−0.993609	−0.0559835
$316$	−8.93783	−0.502792
$317$	−11.7770	−0.661460	−0.330730	−	0.943725i	$-0.607295\pi$
$317$	−11.7770	−0.661460	−0.330730	+	0.943725i	$0.607295\pi$
$318$	−4.31178	−0.241793
$319$	31.0182	1.73669
$320$	−12.5142	−0.699564
$321$	−11.5297	−0.643524
$322$	0	0
$323$	−16.8602	−0.938128
$324$	2.76889	0.153827
$325$	−4.13097	−0.229145
$326$	6.07394	0.336404
$327$	−6.08637	−0.336577
$328$	13.8476	0.764604
$329$	−0.516246	−0.0284616
$330$	−12.9564	−0.713224
$331$	−23.7973	−1.30802	−0.654009	−	0.756487i	$-0.726914\pi$
$331$	−23.7973	−1.30802	−0.654009	+	0.756487i	$0.726914\pi$
$332$	−48.8200	−2.67934
$333$	−10.5373	−0.577443
$334$	35.7891	1.95830
$335$	−7.46264	−0.407727
$336$	−1.85907	−0.101420
$337$	27.8644	1.51787	0.758936	−	0.651165i	$-0.225719\pi$
$337$	27.8644	1.51787	0.758936	+	0.651165i	$0.225719\pi$
$338$	−8.87687	−0.482838
$339$	1.20877	0.0656516
$340$	−20.1929	−1.09511
$341$	−55.2610	−2.99255
$342$	−5.04870	−0.273002
$343$	12.9296	0.698132
$344$	9.78098	0.527355
$345$	0	0
$346$	−7.14529	−0.384133
$347$	24.6620	1.32393	0.661963	−	0.749537i	$-0.269724\pi$
$347$	24.6620	1.32393	0.661963	+	0.749537i	$0.269724\pi$
$348$	14.4760	0.775995
$349$	25.9763	1.39048	0.695240	−	0.718777i	$-0.255298\pi$
$349$	25.9763	1.39048	0.695240	+	0.718777i	$0.255298\pi$
$350$	2.16982	0.115982
$351$	4.13097	0.220495
$352$	−44.1657	−2.35404
$353$	2.16457	0.115209	0.0576043	−	0.998339i	$-0.481654\pi$
$353$	2.16457	0.115209	0.0576043	+	0.998339i	$0.481654\pi$
$354$	−21.9459	−1.16641
$355$	0.553134	0.0293573
$356$	5.93361	0.314481
$357$	−7.24617	−0.383508
$358$	44.5961	2.35698
$359$	−17.9334	−0.946487	−0.473244	−	0.880932i	$-0.656917\pi$
$359$	−17.9334	−0.946487	−0.473244	+	0.880932i	$0.656917\pi$
$360$	−1.67909	−0.0884958
$361$	−13.6551	−0.718688
$362$	−6.95834	−0.365722
$363$	−24.2004	−1.27019
$364$	11.3651	0.595694
$365$	8.22053	0.430282
$366$	−10.5087	−0.549299
$367$	−12.6785	−0.661811	−0.330906	−	0.943664i	$-0.607354\pi$
$367$	−12.6785	−0.661811	−0.330906	+	0.943664i	$0.607354\pi$
$368$	0	0
$369$	−8.24707	−0.429325
$370$	23.0112	1.19630
$371$	1.96184	0.101854
$372$	−25.7900	−1.33715
$373$	−0.574898	−0.0297671	−0.0148836	−	0.999889i	$-0.504738\pi$
$373$	−0.574898	−0.0297671	−0.0148836	+	0.999889i	$0.504738\pi$
$374$	−94.4877	−4.88584
$375$	−1.00000	−0.0516398
$376$	−0.872399	−0.0449906
$377$	21.5971	1.11230
$378$	−2.16982	−0.111604
$379$	12.6878	0.651728	0.325864	−	0.945417i	$-0.394345\pi$
$379$	12.6878	0.651728	0.325864	+	0.945417i	$0.394345\pi$
$380$	6.40143	0.328386
$381$	3.46656	0.177597
$382$	24.6953	1.26352
$383$	26.6855	1.36356	0.681782	−	0.731555i	$-0.261205\pi$
$383$	26.6855	1.36356	0.681782	+	0.731555i	$0.261205\pi$
$384$	−12.4400	−0.634829
$385$	5.89508	0.300441
$386$	2.86442	0.145795
$387$	−5.82517	−0.296110
$388$	−13.9684	−0.709138
$389$	2.08920	0.105927	0.0529633	−	0.998596i	$-0.483133\pi$
$389$	2.08920	0.105927	0.0529633	+	0.998596i	$0.483133\pi$
$390$	−9.02113	−0.456802
$391$	0	0
$392$	10.0959	0.509921
$393$	−7.85244	−0.396103
$394$	44.0840	2.22092
$395$	−3.22794	−0.162415
$396$	−16.4278	−0.825529
$397$	−21.3991	−1.07399	−0.536995	−	0.843586i	$-0.680441\pi$
$397$	−21.3991	−1.07399	−0.536995	+	0.843586i	$0.680441\pi$
$398$	−17.1370	−0.859000
$399$	2.29713	0.115001
$400$	−1.87102	−0.0935511
$401$	4.08016	0.203753	0.101877	−	0.994797i	$-0.467515\pi$
$401$	4.08016	0.203753	0.101877	+	0.994797i	$0.467515\pi$
$402$	−16.2968	−0.812808
$403$	−38.4766	−1.91666
$404$	15.4355	0.767945
$405$	1.00000	0.0496904
$406$	−11.3440	−0.562994
$407$	62.5180	3.09890
$408$	−12.2452	−0.606229
$409$	15.1625	0.749739	0.374870	−	0.927078i	$-0.377687\pi$
$409$	15.1625	0.749739	0.374870	+	0.927078i	$0.377687\pi$
$410$	18.0098	0.889439
$411$	8.36805	0.412766
$412$	−37.7938	−1.86197
$413$	9.98528	0.491344
$414$	0	0
$415$	−17.6316	−0.865501
$416$	−30.7513	−1.50770
$417$	−0.538695	−0.0263800
$418$	29.9539	1.46509
$419$	11.0826	0.541420	0.270710	−	0.962661i	$-0.412742\pi$
$419$	11.0826	0.541420	0.270710	+	0.962661i	$0.412742\pi$
$420$	2.75120	0.134245
$421$	12.8358	0.625578	0.312789	−	0.949823i	$-0.398737\pi$
$421$	12.8358	0.625578	0.312789	+	0.949823i	$0.398737\pi$
$422$	−38.9428	−1.89571
$423$	0.519567	0.0252622
$424$	3.31529	0.161005
$425$	−7.29277	−0.353751
$426$	1.20792	0.0585240
$427$	4.78141	0.231389
$428$	31.9245	1.54313
$429$	−24.5090	−1.18331
$430$	12.7209	0.613455
$431$	17.5460	0.845162	0.422581	−	0.906325i	$-0.361124\pi$
$431$	17.5460	0.845162	0.422581	+	0.906325i	$0.361124\pi$
$432$	1.87102	0.0900196
$433$	−10.0965	−0.485209	−0.242604	−	0.970125i	$-0.578002\pi$
$433$	−10.0965	−0.485209	−0.242604	+	0.970125i	$0.578002\pi$
$434$	20.2101	0.970118
$435$	5.22808	0.250667
$436$	16.8525	0.807089
$437$	0	0
$438$	17.9518	0.857771
$439$	5.75514	0.274678	0.137339	−	0.990524i	$-0.456145\pi$
$439$	5.75514	0.274678	0.137339	+	0.990524i	$0.456145\pi$
$440$	9.96203	0.474921
$441$	−6.01274	−0.286321
$442$	−65.7890	−3.12926
$443$	−32.2581	−1.53263	−0.766314	−	0.642467i	$-0.777911\pi$
$443$	−32.2581	−1.53263	−0.766314	+	0.642467i	$0.777911\pi$
$444$	29.1768	1.38467
$445$	2.14296	0.101586
$446$	10.5438	0.499265
$447$	−1.73900	−0.0822517
$448$	12.4342	0.587461
$449$	−18.9929	−0.896330	−0.448165	−	0.893951i	$-0.647922\pi$
$449$	−18.9929	−0.896330	−0.448165	+	0.893951i	$0.647922\pi$
$450$	−2.18378	−0.102944
$451$	48.9298	2.30402
$452$	−3.34696	−0.157428
$453$	−6.20037	−0.291319
$454$	51.6430	2.42372
$455$	4.10457	0.192425
$456$	3.88190	0.181787
$457$	−5.67575	−0.265500	−0.132750	−	0.991150i	$-0.542381\pi$
$457$	−5.67575	−0.265500	−0.132750	+	0.991150i	$0.542381\pi$
$458$	25.0031	1.16832
$459$	7.29277	0.340397
$460$	0	0
$461$	−1.81839	−0.0846907	−0.0423453	−	0.999103i	$-0.513483\pi$
$461$	−1.81839	−0.0846907	−0.0423453	+	0.999103i	$0.513483\pi$
$462$	12.8736	0.598932
$463$	16.7397	0.777961	0.388981	−	0.921246i	$-0.372827\pi$
$463$	16.7397	0.777961	0.388981	+	0.921246i	$0.372827\pi$
$464$	9.78186	0.454112
$465$	−9.31419	−0.431935
$466$	26.3006	1.21835
$467$	−19.4592	−0.900466	−0.450233	−	0.892911i	$-0.648659\pi$
$467$	−19.4592	−0.900466	−0.450233	+	0.892911i	$0.648659\pi$
$468$	−11.4382	−0.528731
$469$	7.41495	0.342390
$470$	−1.13462	−0.0523361
$471$	−10.4375	−0.480936
$472$	16.8740	0.776690
$473$	34.5607	1.58910
$474$	−7.04912	−0.323777
$475$	2.31191	0.106078
$476$	20.0638	0.919625
$477$	−1.97446	−0.0904043
$478$	12.3205	0.563524
$479$	−9.09672	−0.415640	−0.207820	−	0.978167i	$-0.566637\pi$
$479$	−9.09672	−0.415640	−0.207820	+	0.978167i	$0.566637\pi$
$480$	−7.44408	−0.339774
$481$	43.5294	1.98477
$482$	−30.2002	−1.37558
$483$	0	0
$484$	67.0084	3.04584
$485$	−5.04476	−0.229071
$486$	2.18378	0.0990582
$487$	24.4485	1.10787	0.553934	−	0.832560i	$-0.313126\pi$
$487$	24.4485	1.10787	0.553934	+	0.832560i	$0.313126\pi$
$488$	8.08006	0.365767
$489$	2.78139	0.125779
$490$	13.1305	0.593175
$491$	−26.1208	−1.17882	−0.589408	−	0.807835i	$-0.700639\pi$
$491$	−26.1208	−1.17882	−0.589408	+	0.807835i	$0.700639\pi$
$492$	22.8352	1.02949
$493$	38.1272	1.71716
$494$	20.8560	0.938357
$495$	−5.93300	−0.266668
$496$	−17.4270	−0.782498
$497$	−0.549599	−0.0246529
$498$	−38.5035	−1.72538
$499$	−9.98200	−0.446856	−0.223428	−	0.974720i	$-0.571725\pi$
$499$	−9.98200	−0.446856	−0.223428	+	0.974720i	$0.571725\pi$
$500$	2.76889	0.123829
$501$	16.3886	0.732190
$502$	57.6521	2.57314
$503$	20.4576	0.912160	0.456080	−	0.889939i	$-0.349253\pi$
$503$	20.4576	0.912160	0.456080	+	0.889939i	$0.349253\pi$
$504$	1.66836	0.0743146
$505$	5.57461	0.248067
$506$	0	0
$507$	−4.06491	−0.180529
$508$	−9.59853	−0.425866
$509$	5.69695	0.252513	0.126256	−	0.991998i	$-0.459704\pi$
$509$	5.69695	0.252513	0.126256	+	0.991998i	$0.459704\pi$
$510$	−15.9258	−0.705206
$511$	−8.16799	−0.361331
$512$	−20.2113	−0.893220
$513$	−2.31191	−0.102073
$514$	30.4054	1.34113
$515$	−13.6494	−0.601466
$516$	16.1293	0.710051
$517$	−3.08259	−0.135572
$518$	−22.8642	−1.00459
$519$	−3.27198	−0.143624
$520$	6.93627	0.304175
$521$	−27.2617	−1.19436	−0.597178	−	0.802109i	$-0.703711\pi$
$521$	−27.2617	−1.19436	−0.597178	+	0.802109i	$0.703711\pi$
$522$	11.4170	0.499708
$523$	−31.4682	−1.37601	−0.688003	−	0.725708i	$-0.741513\pi$
$523$	−31.4682	−1.37601	−0.688003	+	0.725708i	$0.741513\pi$
$524$	21.7426	0.949828
$525$	0.993609	0.0433647
$526$	0.652597	0.0284546
$527$	−67.9262	−2.95891
$528$	−11.1008	−0.483099
$529$	0	0
$530$	4.31178	0.187292
$531$	−10.0495	−0.436111
$532$	−6.36052	−0.275763
$533$	34.0684	1.47567
$534$	4.67974	0.202512
$535$	11.5297	0.498472
$536$	12.5304	0.541232
$537$	20.4215	0.881253
$538$	55.7000	2.40140
$539$	35.6736	1.53657
$540$	−2.76889	−0.119154
$541$	−8.16607	−0.351087	−0.175543	−	0.984472i	$-0.556168\pi$
$541$	−8.16607	−0.351087	−0.175543	+	0.984472i	$0.556168\pi$
$542$	2.43348	0.104527
$543$	−3.18638	−0.136740
$544$	−54.2880	−2.32758
$545$	6.08637	0.260712
$546$	8.96347	0.383601
$547$	11.0363	0.471878	0.235939	−	0.971768i	$-0.424183\pi$
$547$	11.0363	0.471878	0.235939	+	0.971768i	$0.424183\pi$
$548$	−23.1702	−0.989783
$549$	−4.81217	−0.205378
$550$	12.9564	0.552461
$551$	−12.0869	−0.514917
$552$	0	0
$553$	3.20732	0.136389
$554$	4.79835	0.203862
$555$	10.5373	0.447285
$556$	1.49159	0.0632574
$557$	4.47498	0.189611	0.0948054	−	0.995496i	$-0.469777\pi$
$557$	4.47498	0.189611	0.0948054	+	0.995496i	$0.469777\pi$
$558$	−20.3401	−0.861066
$559$	24.0636	1.01778
$560$	1.85907	0.0785598
$561$	−43.2680	−1.82678
$562$	−35.9330	−1.51574
$563$	−14.1615	−0.596836	−0.298418	−	0.954435i	$-0.596459\pi$
$563$	−14.1615	−0.596836	−0.298418	+	0.954435i	$0.596459\pi$
$564$	−1.43862	−0.0605770
$565$	−1.20877	−0.0508535
$566$	5.53777	0.232770
$567$	−0.993609	−0.0417277
$568$	−0.928761	−0.0389699
$569$	−43.5373	−1.82518	−0.912588	−	0.408880i	$-0.865920\pi$
$569$	−43.5373	−1.82518	−0.912588	+	0.408880i	$0.865920\pi$
$570$	5.04870	0.211467
$571$	−3.77915	−0.158152	−0.0790762	−	0.996869i	$-0.525197\pi$
$571$	−3.77915	−0.158152	−0.0790762	+	0.996869i	$0.525197\pi$
$572$	67.8628	2.83749
$573$	11.3085	0.472420
$574$	−17.8947	−0.746910
$575$	0	0
$576$	−12.5142	−0.521424
$577$	−7.51831	−0.312991	−0.156496	−	0.987679i	$-0.550020\pi$
$577$	−7.51831	−0.312991	−0.156496	+	0.987679i	$0.550020\pi$
$578$	−79.0190	−3.28676
$579$	1.31168	0.0545117
$580$	−14.4760	−0.601083
$581$	17.5189	0.726807
$582$	−11.0167	−0.456655
$583$	11.7145	0.485163
$584$	−13.8030	−0.571172
$585$	−4.13097	−0.170795
$586$	−65.1537	−2.69148
$587$	−30.0303	−1.23948	−0.619741	−	0.784806i	$-0.712762\pi$
$587$	−30.0303	−1.23948	−0.619741	+	0.784806i	$0.712762\pi$
$588$	16.6486	0.686578
$589$	21.5336	0.887275
$590$	21.9459	0.903498
$591$	20.1870	0.830383
$592$	19.7156	0.810306
$593$	36.4535	1.49697	0.748483	−	0.663154i	$-0.230783\pi$
$593$	36.4535	1.49697	0.748483	+	0.663154i	$0.230783\pi$
$594$	−12.9564	−0.531606
$595$	7.24617	0.297064
$596$	4.81509	0.197234
$597$	−7.84740	−0.321173
$598$	0	0
$599$	25.0497	1.02350	0.511752	−	0.859133i	$-0.328997\pi$
$599$	25.0497	1.02350	0.511752	+	0.859133i	$0.328997\pi$
$600$	1.67909	0.0685485
$601$	8.90866	0.363392	0.181696	−	0.983355i	$-0.441841\pi$
$601$	8.90866	0.363392	0.181696	+	0.983355i	$0.441841\pi$
$602$	−12.6396	−0.515151
$603$	−7.46264	−0.303902
$604$	17.1681	0.698562
$605$	24.2004	0.983888
$606$	12.1737	0.494524
$607$	12.2852	0.498642	0.249321	−	0.968421i	$-0.419793\pi$
$607$	12.2852	0.498642	0.249321	+	0.968421i	$0.419793\pi$
$608$	17.2100	0.697959
$609$	−5.19467	−0.210499
$610$	10.5087	0.425485
$611$	−2.14631	−0.0868306
$612$	−20.1929	−0.816249
$613$	−35.7470	−1.44381	−0.721904	−	0.691994i	$-0.756733\pi$
$613$	−35.7470	−1.44381	−0.721904	+	0.691994i	$0.756733\pi$
$614$	−22.9464	−0.926042
$615$	8.24707	0.332554
$616$	−9.89837	−0.398817
$617$	−31.8097	−1.28061	−0.640304	−	0.768121i	$-0.721192\pi$
$617$	−31.8097	−1.28061	−0.640304	+	0.768121i	$0.721192\pi$
$618$	−29.8074	−1.19903
$619$	−4.64692	−0.186775	−0.0933877	−	0.995630i	$-0.529770\pi$
$619$	−4.64692	−0.186775	−0.0933877	+	0.995630i	$0.529770\pi$
$620$	25.7900	1.03575
$621$	0	0
$622$	−55.6023	−2.22945
$623$	−2.12926	−0.0853070
$624$	−7.72914	−0.309413
$625$	1.00000	0.0400000
$626$	31.3031	1.25112
$627$	13.7165	0.547786
$628$	28.9004	1.15325
$629$	76.8464	3.06407
$630$	2.16982	0.0864478
$631$	−9.24710	−0.368121	−0.184061	−	0.982915i	$-0.558924\pi$
$631$	−9.24710	−0.368121	−0.184061	+	0.982915i	$0.558924\pi$
$632$	5.42001	0.215596
$633$	−17.8328	−0.708788
$634$	25.7183	1.02140
$635$	−3.46656	−0.137566
$636$	5.46706	0.216783
$637$	24.8384	0.984135
$638$	−67.7369	−2.68173
$639$	0.553134	0.0218816
$640$	12.4400	0.491736
$641$	−7.77407	−0.307057	−0.153529	−	0.988144i	$-0.549064\pi$
$641$	−7.77407	−0.307057	−0.153529	+	0.988144i	$0.549064\pi$
$642$	25.1783	0.993708
$643$	−35.1494	−1.38616	−0.693078	−	0.720862i	$-0.743746\pi$
$643$	−35.1494	−1.38616	−0.693078	+	0.720862i	$0.743746\pi$
$644$	0	0
$645$	5.82517	0.229366
$646$	36.8190	1.44862
$647$	−30.4323	−1.19642	−0.598209	−	0.801340i	$-0.704121\pi$
$647$	−30.4323	−1.19642	−0.598209	+	0.801340i	$0.704121\pi$
$648$	−1.67909	−0.0659609
$649$	59.6237	2.34043
$650$	9.02113	0.353838
$651$	9.25466	0.362719
$652$	−7.70137	−0.301609
$653$	18.7925	0.735409	0.367704	−	0.929943i	$-0.380144\pi$
$653$	18.7925	0.735409	0.367704	+	0.929943i	$0.380144\pi$
$654$	13.2913	0.519731
$655$	7.85244	0.306820
$656$	15.4304	0.602458
$657$	8.22053	0.320713
$658$	1.12737	0.0439494
$659$	8.83579	0.344194	0.172097	−	0.985080i	$-0.444946\pi$
$659$	8.83579	0.344194	0.172097	+	0.985080i	$0.444946\pi$
$660$	16.4278	0.639452
$661$	−16.2098	−0.630488	−0.315244	−	0.949011i	$-0.602086\pi$
$661$	−16.2098	−0.630488	−0.315244	+	0.949011i	$0.602086\pi$
$662$	51.9680	2.01979
$663$	−30.1262	−1.17001
$664$	29.6050	1.14890
$665$	−2.29713	−0.0890791
$666$	23.0112	0.891667
$667$	0	0
$668$	−45.3783	−1.75574
$669$	4.82825	0.186671
$670$	16.2968	0.629599
$671$	28.5506	1.10218
$672$	7.39651	0.285326
$673$	41.2347	1.58948	0.794741	−	0.606949i	$-0.207607\pi$
$673$	41.2347	1.58948	0.794741	+	0.606949i	$0.207607\pi$
$674$	−60.8498	−2.34385
$675$	−1.00000	−0.0384900
$676$	11.2553	0.432896
$677$	−23.2626	−0.894055	−0.447027	−	0.894520i	$-0.647517\pi$
$677$	−23.2626	−0.894055	−0.447027	+	0.894520i	$0.647517\pi$
$678$	−2.63969	−0.101377
$679$	5.01252	0.192363
$680$	12.2452	0.469583
$681$	23.6484	0.906210
$682$	120.678	4.62100
$683$	−28.3910	−1.08635	−0.543176	−	0.839619i	$-0.682778\pi$
$683$	−28.3910	−1.08635	−0.543176	+	0.839619i	$0.682778\pi$
$684$	6.40143	0.244765
$685$	−8.36805	−0.319727
$686$	−28.2353	−1.07803
$687$	11.4495	0.436824
$688$	10.8990	0.415521
$689$	8.15643	0.310735
$690$	0	0
$691$	−32.0697	−1.21999	−0.609995	−	0.792406i	$-0.708828\pi$
$691$	−32.0697	−1.21999	−0.609995	+	0.792406i	$0.708828\pi$
$692$	9.05976	0.344400
$693$	5.89508	0.223936
$694$	−53.8564	−2.04436
$695$	0.538695	0.0204339
$696$	−8.77842	−0.332745
$697$	60.1440	2.27812
$698$	−56.7266	−2.14713
$699$	12.0436	0.455531
$700$	−2.75120	−0.103985
$701$	47.9070	1.80942	0.904711	−	0.426027i	$-0.140087\pi$
$701$	47.9070	1.80942	0.904711	+	0.426027i	$0.140087\pi$
$702$	−9.02113	−0.340480
$703$	−24.3614	−0.918807
$704$	74.2466	2.79827
$705$	−0.519567	−0.0195680
$706$	−4.72695	−0.177901
$707$	−5.53899	−0.208315
$708$	27.8260	1.04576
$709$	31.7378	1.19194	0.595969	−	0.803008i	$-0.296768\pi$
$709$	31.7378	1.19194	0.595969	+	0.803008i	$0.296768\pi$
$710$	−1.20792	−0.0453325
$711$	−3.22794	−0.121057
$712$	−3.59821	−0.134849
$713$	0	0
$714$	15.8240	0.592199
$715$	24.5090	0.916586
$716$	−56.5450	−2.11318
$717$	5.64180	0.210697
$718$	39.1625	1.46153
$719$	47.4294	1.76882	0.884409	−	0.466712i	$-0.154562\pi$
$719$	47.4294	1.76882	0.884409	+	0.466712i	$0.154562\pi$
$720$	−1.87102	−0.0697289
$721$	13.5622	0.505083
$722$	29.8197	1.10977
$723$	−13.8293	−0.514318
$724$	8.82273	0.327894
$725$	−5.22808	−0.194166
$726$	52.8484	1.96139
$727$	−15.8313	−0.587152	−0.293576	−	0.955936i	$-0.594845\pi$
$727$	−15.8313	−0.587152	−0.293576	+	0.955936i	$0.594845\pi$
$728$	−6.89194	−0.255432
$729$	1.00000	0.0370370
$730$	−17.9518	−0.664427
$731$	42.4816	1.57124
$732$	13.3244	0.492483
$733$	−1.79899	−0.0664471	−0.0332236	−	0.999448i	$-0.510577\pi$
$733$	−1.79899	−0.0664471	−0.0332236	+	0.999448i	$0.510577\pi$
$734$	27.6870	1.02195
$735$	6.01274	0.221783
$736$	0	0
$737$	44.2758	1.63092
$738$	18.0098	0.662949
$739$	−29.9310	−1.10103	−0.550515	−	0.834825i	$-0.685569\pi$
$739$	−29.9310	−1.10103	−0.550515	+	0.834825i	$0.685569\pi$
$740$	−29.1768	−1.07256
$741$	9.55043	0.350844
$742$	−4.28423	−0.157279
$743$	25.6694	0.941719	0.470860	−	0.882208i	$-0.343944\pi$
$743$	25.6694	0.941719	0.470860	+	0.882208i	$0.343944\pi$
$744$	15.6394	0.573366
$745$	1.73900	0.0637119
$746$	1.25545	0.0459653
$747$	−17.6316	−0.645106
$748$	119.804	4.38048
$749$	−11.4560	−0.418593
$750$	2.18378	0.0797403
$751$	−18.0346	−0.658092	−0.329046	−	0.944314i	$-0.606727\pi$
$751$	−18.0346	−0.658092	−0.329046	+	0.944314i	$0.606727\pi$
$752$	−0.972121	−0.0354496
$753$	26.4002	0.962076
$754$	−47.1632	−1.71758
$755$	6.20037	0.225654
$756$	2.75120	0.100060
$757$	21.6790	0.787938	0.393969	−	0.919124i	$-0.371102\pi$
$757$	21.6790	0.787938	0.393969	+	0.919124i	$0.371102\pi$
$758$	−27.7073	−1.00638
$759$	0	0
$760$	−3.88190	−0.140811
$761$	33.5881	1.21757	0.608783	−	0.793337i	$-0.291658\pi$
$761$	33.5881	1.21757	0.608783	+	0.793337i	$0.291658\pi$
$762$	−7.57020	−0.274239
$763$	−6.04748	−0.218933
$764$	−31.3120	−1.13283
$765$	−7.29277	−0.263671
$766$	−58.2752	−2.10557
$767$	41.5142	1.49899
$768$	2.13796	0.0771470
$769$	40.9159	1.47547	0.737733	−	0.675093i	$-0.235896\pi$
$769$	40.9159	1.47547	0.737733	+	0.675093i	$0.235896\pi$
$770$	−12.8736	−0.463931
$771$	13.9233	0.501436
$772$	−3.63191	−0.130715
$773$	−24.6478	−0.886519	−0.443260	−	0.896393i	$-0.646178\pi$
$773$	−24.6478	−0.886519	−0.443260	+	0.896393i	$0.646178\pi$
$774$	12.7209	0.457242
$775$	9.31419	0.334575
$776$	8.47061	0.304077
$777$	−10.4700	−0.375609
$778$	−4.56235	−0.163568
$779$	−19.0665	−0.683127
$780$	11.4382	0.409554
$781$	−3.28174	−0.117430
$782$	0	0
$783$	5.22808	0.186836
$784$	11.2500	0.401785
$785$	10.4375	0.372531
$786$	17.1480	0.611649
$787$	−26.4403	−0.942493	−0.471247	−	0.882001i	$-0.656196\pi$
$787$	−26.4403	−0.942493	−0.471247	+	0.882001i	$0.656196\pi$
$788$	−55.8957	−1.99120
$789$	0.298839	0.0106389
$790$	7.04912	0.250796
$791$	1.20105	0.0427044
$792$	9.96203	0.353985
$793$	19.8789	0.705921
$794$	46.7309	1.65842
$795$	1.97446	0.0700268
$796$	21.7286	0.770150
$797$	−1.72152	−0.0609793	−0.0304897	−	0.999535i	$-0.509707\pi$
$797$	−1.72152	−0.0609793	−0.0304897	+	0.999535i	$0.509707\pi$
$798$	−5.01643	−0.177580
$799$	−3.78908	−0.134048
$800$	7.44408	0.263188
$801$	2.14296	0.0757176
$802$	−8.91017	−0.314629
$803$	−48.7724	−1.72114
$804$	20.6632	0.728736
$805$	0	0
$806$	84.0244	2.95963
$807$	25.5063	0.897863
$808$	−9.36028	−0.329293
$809$	9.85919	0.346631	0.173315	−	0.984866i	$-0.444552\pi$
$809$	9.85919	0.346631	0.173315	+	0.984866i	$0.444552\pi$
$810$	−2.18378	−0.0767302
$811$	20.5675	0.722222	0.361111	−	0.932523i	$-0.382398\pi$
$811$	20.5675	0.722222	0.361111	+	0.932523i	$0.382398\pi$
$812$	14.3835	0.504761
$813$	1.11434	0.0390817
$814$	−136.526	−4.78522
$815$	−2.78139	−0.0974278
$816$	−13.6449	−0.477668
$817$	−13.4673	−0.471160
$818$	−33.1116	−1.15772
$819$	4.10457	0.143425
$820$	−22.8352	−0.797441
$821$	−26.6950	−0.931661	−0.465830	−	0.884874i	$-0.654244\pi$
$821$	−26.6950	−0.931661	−0.465830	+	0.884874i	$0.654244\pi$
$822$	−18.2740	−0.637378
$823$	−54.6288	−1.90424	−0.952120	−	0.305723i	$-0.901102\pi$
$823$	−54.6288	−1.90424	−0.952120	+	0.305723i	$0.901102\pi$
$824$	22.9186	0.798409
$825$	5.93300	0.206560
$826$	−21.8056	−0.758715
$827$	4.09290	0.142324	0.0711621	−	0.997465i	$-0.477329\pi$
$827$	4.09290	0.142324	0.0711621	+	0.997465i	$0.477329\pi$
$828$	0	0
$829$	45.7661	1.58952	0.794761	−	0.606923i	$-0.207596\pi$
$829$	45.7661	1.58952	0.794761	+	0.606923i	$0.207596\pi$
$830$	38.5035	1.33648
$831$	2.19727	0.0762224
$832$	51.6957	1.79223
$833$	43.8495	1.51930
$834$	1.17639	0.0407351
$835$	−16.3886	−0.567152
$836$	−37.9796	−1.31355
$837$	−9.31419	−0.321945
$838$	−24.2019	−0.836042
$839$	−6.09180	−0.210312	−0.105156	−	0.994456i	$-0.533534\pi$
$839$	−6.09180	−0.210312	−0.105156	+	0.994456i	$0.533534\pi$
$840$	−1.66836	−0.0575639
$841$	−1.66714	−0.0574876
$842$	−28.0305	−0.965996
$843$	−16.4545	−0.566723
$844$	49.3770	1.69962
$845$	4.06491	0.139837
$846$	−1.13462	−0.0390090
$847$	−24.0458	−0.826223
$848$	3.69426	0.126861
$849$	2.53587	0.0870307
$850$	15.9258	0.546250
$851$	0	0
$852$	−1.53157	−0.0524706
$853$	−8.05785	−0.275895	−0.137948	−	0.990440i	$-0.544051\pi$
$853$	−8.05785	−0.275895	−0.137948	+	0.990440i	$0.544051\pi$
$854$	−10.4415	−0.357302
$855$	2.31191	0.0790656
$856$	−19.3594	−0.661690
$857$	38.4610	1.31380	0.656902	−	0.753976i	$-0.271866\pi$
$857$	38.4610	1.31380	0.656902	+	0.753976i	$0.271866\pi$
$858$	53.5223	1.82722
$859$	4.75760	0.162327	0.0811636	−	0.996701i	$-0.474136\pi$
$859$	4.75760	0.162327	0.0811636	+	0.996701i	$0.474136\pi$
$860$	−16.1293	−0.550003
$861$	−8.19436	−0.279263
$862$	−38.3166	−1.30507
$863$	37.8469	1.28832	0.644161	−	0.764890i	$-0.277206\pi$
$863$	37.8469	1.28832	0.644161	+	0.764890i	$0.277206\pi$
$864$	−7.44408	−0.253253
$865$	3.27198	0.111251
$866$	22.0486	0.749243
$867$	−36.1845	−1.22889
$868$	−25.6252	−0.869775
$869$	19.1514	0.649666
$870$	−11.4170	−0.387072
$871$	30.8279	1.04456
$872$	−10.2196	−0.346078
$873$	−5.04476	−0.170739
$874$	0	0
$875$	−0.993609	−0.0335901
$876$	−22.7617	−0.769048
$877$	−5.70872	−0.192770	−0.0963849	−	0.995344i	$-0.530728\pi$
$877$	−5.70872	−0.192770	−0.0963849	+	0.995344i	$0.530728\pi$
$878$	−12.5680	−0.424148
$879$	−29.8353	−1.00632
$880$	11.1008	0.374207
$881$	3.54321	0.119374	0.0596869	−	0.998217i	$-0.480990\pi$
$881$	3.54321	0.119374	0.0596869	+	0.998217i	$0.480990\pi$
$882$	13.1305	0.442127
$883$	22.8803	0.769982	0.384991	−	0.922920i	$-0.374205\pi$
$883$	22.8803	0.769982	0.384991	+	0.922920i	$0.374205\pi$
$884$	83.4162	2.80559
$885$	10.0495	0.337810
$886$	70.4445	2.36663
$887$	−6.10700	−0.205053	−0.102526	−	0.994730i	$-0.532693\pi$
$887$	−6.10700	−0.205053	−0.102526	+	0.994730i	$0.532693\pi$
$888$	−17.6931	−0.593743
$889$	3.44441	0.115522
$890$	−4.67974	−0.156865
$891$	−5.93300	−0.198763
$892$	−13.3689	−0.447624
$893$	1.20119	0.0401963
$894$	3.79758	0.127010
$895$	−20.4215	−0.682616
$896$	−12.3605	−0.412937
$897$	0	0
$898$	41.4763	1.38408
$899$	−48.6953	−1.62408
$900$	2.76889	0.0922964
$901$	14.3993	0.479709
$902$	−106.852	−3.55778
$903$	−5.78794	−0.192611
$904$	2.02964	0.0675048
$905$	3.18638	0.105919
$906$	13.5402	0.449844
$907$	−9.28792	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$907$	−9.28792	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$908$	−65.4799	−2.17303
$909$	5.57461	0.184898
$910$	−8.96347	−0.297136
$911$	−31.3503	−1.03868	−0.519341	−	0.854567i	$-0.673823\pi$
$911$	−31.3503	−1.03868	−0.519341	+	0.854567i	$0.673823\pi$
$912$	4.32563	0.143236
$913$	104.608	3.46203
$914$	12.3946	0.409976
$915$	4.81217	0.159085
$916$	−31.7023	−1.04747
$917$	−7.80226	−0.257653
$918$	−15.9258	−0.525630
$919$	−8.58564	−0.283214	−0.141607	−	0.989923i	$-0.545227\pi$
$919$	−8.58564	−0.283214	−0.141607	+	0.989923i	$0.545227\pi$
$920$	0	0
$921$	−10.5077	−0.346239
$922$	3.97095	0.130776
$923$	−2.28498	−0.0752110
$924$	−16.3228	−0.536982
$925$	−10.5373	−0.346466
$926$	−36.5559	−1.20130
$927$	−13.6494	−0.448307
$928$	−38.9183	−1.27755
$929$	28.6555	0.940158	0.470079	−	0.882624i	$-0.344225\pi$
$929$	28.6555	0.940158	0.470079	+	0.882624i	$0.344225\pi$
$930$	20.3401	0.666979
$931$	−13.9009	−0.455584
$932$	−33.3475	−1.09233
$933$	−25.4615	−0.833571
$934$	42.4947	1.39047
$935$	43.2680	1.41501
$936$	6.93627	0.226719
$937$	−34.8604	−1.13884	−0.569420	−	0.822047i	$-0.692832\pi$
$937$	−34.8604	−1.13884	−0.569420	+	0.822047i	$0.692832\pi$
$938$	−16.1926	−0.528707
$939$	14.3344	0.467785
$940$	1.43862	0.0469227
$941$	−40.3556	−1.31556	−0.657778	−	0.753212i	$-0.728504\pi$
$941$	−40.3556	−1.31556	−0.657778	+	0.753212i	$0.728504\pi$
$942$	22.7933	0.742644
$943$	0	0
$944$	18.8028	0.611980
$945$	0.993609	0.0323221
$946$	−75.4729	−2.45384
$947$	−4.13862	−0.134487	−0.0672435	−	0.997737i	$-0.521420\pi$
$947$	−4.13862	−0.134487	−0.0672435	+	0.997737i	$0.521420\pi$
$948$	8.93783	0.290287
$949$	−33.9587	−1.10235
$950$	−5.04870	−0.163801
$951$	11.7770	0.381894
$952$	−12.1670	−0.394333
$953$	47.1255	1.52654	0.763272	−	0.646077i	$-0.223591\pi$
$953$	47.1255	1.52654	0.763272	+	0.646077i	$0.223591\pi$
$954$	4.31178	0.139599
$955$	−11.3085	−0.365935
$956$	−15.6215	−0.505237
$957$	−31.0182	−1.00268
$958$	19.8652	0.641816
$959$	8.31458	0.268492
$960$	12.5142	0.403893
$961$	55.7541	1.79852
$962$	−95.0587	−3.06482
$963$	11.5297	0.371539
$964$	38.2919	1.23330
$965$	−1.31168	−0.0422245
$966$	0	0
$967$	9.38576	0.301826	0.150913	−	0.988547i	$-0.451779\pi$
$967$	9.38576	0.301826	0.150913	+	0.988547i	$0.451779\pi$
$968$	−40.6347	−1.30605
$969$	16.8602	0.541628
$970$	11.0167	0.353723
$971$	−19.1640	−0.615003	−0.307501	−	0.951548i	$-0.599493\pi$
$971$	−19.1640	−0.615003	−0.307501	+	0.951548i	$0.599493\pi$
$972$	−2.76889	−0.0888122
$973$	−0.535252	−0.0171594
$974$	−53.3902	−1.71073
$975$	4.13097	0.132297
$976$	9.00367	0.288200
$977$	−22.2225	−0.710962	−0.355481	−	0.934683i	$-0.615683\pi$
$977$	−22.2225	−0.710962	−0.355481	+	0.934683i	$0.615683\pi$
$978$	−6.07394	−0.194223
$979$	−12.7141	−0.406346
$980$	−16.6486	−0.531821
$981$	6.08637	0.194323
$982$	57.0421	1.82029
$983$	−12.6701	−0.404114	−0.202057	−	0.979374i	$-0.564763\pi$
$983$	−12.6701	−0.404114	−0.202057	+	0.979374i	$0.564763\pi$
$984$	−13.8476	−0.441444
$985$	−20.1870	−0.643212
$986$	−83.2614	−2.65158
$987$	0.516246	0.0164323
$988$	−26.4441	−0.841299
$989$	0	0
$990$	12.9564	0.411780
$991$	−12.4113	−0.394257	−0.197128	−	0.980378i	$-0.563162\pi$
$991$	−12.4113	−0.394257	−0.197128	+	0.980378i	$0.563162\pi$
$992$	69.3355	2.20141
$993$	23.7973	0.755184
$994$	1.20020	0.0380681
$995$	7.84740	0.248779
$996$	48.8200	1.54692
$997$	20.4653	0.648142	0.324071	−	0.946033i	$-0.394948\pi$
$997$	20.4653	0.648142	0.324071	+	0.946033i	$0.394948\pi$
$998$	21.7985	0.690019
$999$	10.5373	0.333387

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.4		25
23.3	even	11		345.2.m.d.331.5	yes	50
23.8	even	11		345.2.m.d.271.5	✓	50
23.22	odd	2		7935.2.a.bt.1.4		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.271.5	✓	50	23.8	even	11
345.2.m.d.331.5	yes	50	23.3	even	11
7935.2.a.bt.1.4		25	23.22	odd	2
7935.2.a.bu.1.4		25	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)

\(f(q)\)	\(=\)	\(q-2.18378 q^{2} -1.00000 q^{3} +2.76889 q^{4} +1.00000 q^{5} +2.18378 q^{6} -0.993609 q^{7} -1.67909 q^{8} +1.00000 q^{9} -2.18378 q^{10} -5.93300 q^{11} -2.76889 q^{12} -4.13097 q^{13} +2.16982 q^{14} -1.00000 q^{15} -1.87102 q^{16} -7.29277 q^{17} -2.18378 q^{18} +2.31191 q^{19} +2.76889 q^{20} +0.993609 q^{21} +12.9564 q^{22} +1.67909 q^{24} +1.00000 q^{25} +9.02113 q^{26} -1.00000 q^{27} -2.75120 q^{28} -5.22808 q^{29} +2.18378 q^{30} +9.31419 q^{31} +7.44408 q^{32} +5.93300 q^{33} +15.9258 q^{34} -0.993609 q^{35} +2.76889 q^{36} -10.5373 q^{37} -5.04870 q^{38} +4.13097 q^{39} -1.67909 q^{40} -8.24707 q^{41} -2.16982 q^{42} -5.82517 q^{43} -16.4278 q^{44} +1.00000 q^{45} +0.519567 q^{47} +1.87102 q^{48} -6.01274 q^{49} -2.18378 q^{50} +7.29277 q^{51} -11.4382 q^{52} -1.97446 q^{53} +2.18378 q^{54} -5.93300 q^{55} +1.66836 q^{56} -2.31191 q^{57} +11.4170 q^{58} -10.0495 q^{59} -2.76889 q^{60} -4.81217 q^{61} -20.3401 q^{62} -0.993609 q^{63} -12.5142 q^{64} -4.13097 q^{65} -12.9564 q^{66} -7.46264 q^{67} -20.1929 q^{68} +2.16982 q^{70} +0.553134 q^{71} -1.67909 q^{72} +8.22053 q^{73} +23.0112 q^{74} -1.00000 q^{75} +6.40143 q^{76} +5.89508 q^{77} -9.02113 q^{78} -3.22794 q^{79} -1.87102 q^{80} +1.00000 q^{81} +18.0098 q^{82} -17.6316 q^{83} +2.75120 q^{84} -7.29277 q^{85} +12.7209 q^{86} +5.22808 q^{87} +9.96203 q^{88} +2.14296 q^{89} -2.18378 q^{90} +4.10457 q^{91} -9.31419 q^{93} -1.13462 q^{94} +2.31191 q^{95} -7.44408 q^{96} -5.04476 q^{97} +13.1305 q^{98} -5.93300 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19}+ \cdots + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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