LMFDB - Embedded newform 7935.2.a.bt.1.22

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			1.22
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)

$f(q)$	$=$	\(q+2.46508 q^{2} -1.00000 q^{3} +4.07661 q^{4} -1.00000 q^{5} -2.46508 q^{6} -4.49417 q^{7} +5.11900 q^{8} +1.00000 q^{9} -2.46508 q^{10} +1.05963 q^{11} -4.07661 q^{12} +2.71697 q^{13} -11.0785 q^{14} +1.00000 q^{15} +4.46552 q^{16} +3.79273 q^{17} +2.46508 q^{18} -4.64475 q^{19} -4.07661 q^{20} +4.49417 q^{21} +2.61206 q^{22} -5.11900 q^{24} +1.00000 q^{25} +6.69755 q^{26} -1.00000 q^{27} -18.3210 q^{28} +3.82407 q^{29} +2.46508 q^{30} -0.381968 q^{31} +0.769846 q^{32} -1.05963 q^{33} +9.34938 q^{34} +4.49417 q^{35} +4.07661 q^{36} -10.5701 q^{37} -11.4497 q^{38} -2.71697 q^{39} -5.11900 q^{40} +0.415160 q^{41} +11.0785 q^{42} +8.21847 q^{43} +4.31968 q^{44} -1.00000 q^{45} -4.78699 q^{47} -4.46552 q^{48} +13.1976 q^{49} +2.46508 q^{50} -3.79273 q^{51} +11.0760 q^{52} +12.5121 q^{53} -2.46508 q^{54} -1.05963 q^{55} -23.0057 q^{56} +4.64475 q^{57} +9.42663 q^{58} +11.6597 q^{59} +4.07661 q^{60} +7.12915 q^{61} -0.941580 q^{62} -4.49417 q^{63} -7.03330 q^{64} -2.71697 q^{65} -2.61206 q^{66} +3.08483 q^{67} +15.4615 q^{68} +11.0785 q^{70} +8.09757 q^{71} +5.11900 q^{72} +12.4364 q^{73} -26.0561 q^{74} -1.00000 q^{75} -18.9348 q^{76} -4.76214 q^{77} -6.69755 q^{78} -13.4792 q^{79} -4.46552 q^{80} +1.00000 q^{81} +1.02340 q^{82} -1.21364 q^{83} +18.3210 q^{84} -3.79273 q^{85} +20.2592 q^{86} -3.82407 q^{87} +5.42422 q^{88} +12.7167 q^{89} -2.46508 q^{90} -12.2106 q^{91} +0.381968 q^{93} -11.8003 q^{94} +4.64475 q^{95} -0.769846 q^{96} +12.7366 q^{97} +32.5331 q^{98} +1.05963 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.46508	1.74307	0.871537	−	0.490330i	$-0.163124\pi$
$2$	2.46508	1.74307	0.871537	+	0.490330i	$0.163124\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.07661	2.03830
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.46508	−1.00636
$7$	−4.49417	−1.69864	−0.849319	−	0.527880i	$-0.822987\pi$
$7$	−4.49417	−1.69864	−0.849319	+	0.527880i	$0.822987\pi$
$8$	5.11900	1.80984
$9$	1.00000	0.333333
$10$	−2.46508	−0.779526
$11$	1.05963	0.319489	0.159745	−	0.987158i	$-0.448933\pi$
$11$	1.05963	0.319489	0.159745	+	0.987158i	$0.448933\pi$
$12$	−4.07661	−1.17682
$13$	2.71697	0.753553	0.376777	−	0.926304i	$-0.377032\pi$
$13$	2.71697	0.753553	0.376777	+	0.926304i	$0.377032\pi$
$14$	−11.0785	−2.96085
$15$	1.00000	0.258199
$16$	4.46552	1.11638
$17$	3.79273	0.919873	0.459936	−	0.887952i	$-0.347872\pi$
$17$	3.79273	0.919873	0.459936	+	0.887952i	$0.347872\pi$
$18$	2.46508	0.581024
$19$	−4.64475	−1.06558	−0.532790	−	0.846248i	$-0.678856\pi$
$19$	−4.64475	−1.06558	−0.532790	+	0.846248i	$0.678856\pi$
$20$	−4.07661	−0.911557
$21$	4.49417	0.980709
$22$	2.61206	0.556893
$23$	0	0
$23$	0	0
$24$	−5.11900	−1.04491
$25$	1.00000	0.200000
$26$	6.69755	1.31350
$27$	−1.00000	−0.192450
$28$	−18.3210	−3.46234
$29$	3.82407	0.710112	0.355056	−	0.934845i	$-0.384462\pi$
$29$	3.82407	0.710112	0.355056	+	0.934845i	$0.384462\pi$
$30$	2.46508	0.450060
$31$	−0.381968	−0.0686034	−0.0343017	−	0.999412i	$-0.510921\pi$
$31$	−0.381968	−0.0686034	−0.0343017	+	0.999412i	$0.510921\pi$
$32$	0.769846	0.136091
$33$	−1.05963	−0.184457
$34$	9.34938	1.60341
$35$	4.49417	0.759654
$36$	4.07661	0.679435
$37$	−10.5701	−1.73771	−0.868855	−	0.495067i	$-0.835144\pi$
$37$	−10.5701	−1.73771	−0.868855	+	0.495067i	$0.835144\pi$
$38$	−11.4497	−1.85738
$39$	−2.71697	−0.435064
$40$	−5.11900	−0.809385
$41$	0.415160	0.0648372	0.0324186	−	0.999474i	$-0.489679\pi$
$41$	0.415160	0.0648372	0.0324186	+	0.999474i	$0.489679\pi$
$42$	11.0785	1.70945
$43$	8.21847	1.25331	0.626653	−	0.779299i	$-0.284425\pi$
$43$	8.21847	1.25331	0.626653	+	0.779299i	$0.284425\pi$
$44$	4.31968	0.651216
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−4.78699	−0.698255	−0.349127	−	0.937075i	$-0.613522\pi$
$47$	−4.78699	−0.698255	−0.349127	+	0.937075i	$0.613522\pi$
$48$	−4.46552	−0.644542
$49$	13.1976	1.88537
$50$	2.46508	0.348615
$51$	−3.79273	−0.531089
$52$	11.0760	1.53597
$53$	12.5121	1.71866	0.859332	−	0.511418i	$-0.170880\pi$
$53$	12.5121	1.71866	0.859332	+	0.511418i	$0.170880\pi$
$54$	−2.46508	−0.335455
$55$	−1.05963	−0.142880
$56$	−23.0057	−3.07426
$57$	4.64475	0.615213
$58$	9.42663	1.23778
$59$	11.6597	1.51796	0.758981	−	0.651113i	$-0.225698\pi$
$59$	11.6597	1.51796	0.758981	+	0.651113i	$0.225698\pi$
$60$	4.07661	0.526288
$61$	7.12915	0.912794	0.456397	−	0.889776i	$-0.349140\pi$
$61$	7.12915	0.912794	0.456397	+	0.889776i	$0.349140\pi$
$62$	−0.941580	−0.119581
$63$	−4.49417	−0.566213
$64$	−7.03330	−0.879163
$65$	−2.71697	−0.336999
$66$	−2.61206	−0.321522
$67$	3.08483	0.376872	0.188436	−	0.982085i	$-0.439658\pi$
$67$	3.08483	0.376872	0.188436	+	0.982085i	$0.439658\pi$
$68$	15.4615	1.87498
$69$	0	0
$70$	11.0785	1.32413
$71$	8.09757	0.961004	0.480502	−	0.876994i	$-0.340454\pi$
$71$	8.09757	0.961004	0.480502	+	0.876994i	$0.340454\pi$
$72$	5.11900	0.603280
$73$	12.4364	1.45557	0.727785	−	0.685805i	$-0.240550\pi$
$73$	12.4364	1.45557	0.727785	+	0.685805i	$0.240550\pi$
$74$	−26.0561	−3.02896
$75$	−1.00000	−0.115470
$76$	−18.9348	−2.17198
$77$	−4.76214	−0.542697
$78$	−6.69755	−0.758349
$79$	−13.4792	−1.51652	−0.758262	−	0.651950i	$-0.773951\pi$
$79$	−13.4792	−1.51652	−0.758262	+	0.651950i	$0.773951\pi$
$80$	−4.46552	−0.499260
$81$	1.00000	0.111111
$82$	1.02340	0.113016
$83$	−1.21364	−0.133215	−0.0666074	−	0.997779i	$-0.521217\pi$
$83$	−1.21364	−0.133215	−0.0666074	+	0.997779i	$0.521217\pi$
$84$	18.3210	1.99898
$85$	−3.79273	−0.411379
$86$	20.2592	2.18460
$87$	−3.82407	−0.409983
$88$	5.42422	0.578224
$89$	12.7167	1.34797	0.673983	−	0.738747i	$-0.264582\pi$
$89$	12.7167	1.34797	0.673983	+	0.738747i	$0.264582\pi$
$90$	−2.46508	−0.259842
$91$	−12.2106	−1.28001
$92$	0	0
$93$	0.381968	0.0396082
$94$	−11.8003	−1.21711
$95$	4.64475	0.476542
$96$	−0.769846	−0.0785721
$97$	12.7366	1.29321	0.646605	−	0.762825i	$-0.276188\pi$
$97$	12.7366	1.29321	0.646605	+	0.762825i	$0.276188\pi$
$98$	32.5331	3.28634
$99$	1.05963	0.106496
$100$	4.07661	0.407661
$101$	9.12078	0.907552	0.453776	−	0.891116i	$-0.350077\pi$
$101$	9.12078	0.907552	0.453776	+	0.891116i	$0.350077\pi$
$102$	−9.34938	−0.925726
$103$	5.99103	0.590314	0.295157	−	0.955449i	$-0.404628\pi$
$103$	5.99103	0.590314	0.295157	+	0.955449i	$0.404628\pi$
$104$	13.9082	1.36381
$105$	−4.49417	−0.438587
$106$	30.8432	2.99576
$107$	11.2412	1.08673	0.543366	−	0.839496i	$-0.317150\pi$
$107$	11.2412	1.08673	0.543366	+	0.839496i	$0.317150\pi$
$108$	−4.07661	−0.392272
$109$	−13.4160	−1.28502	−0.642510	−	0.766278i	$-0.722107\pi$
$109$	−13.4160	−1.28502	−0.642510	+	0.766278i	$0.722107\pi$
$110$	−2.61206	−0.249050
$111$	10.5701	1.00327
$112$	−20.0688	−1.89632
$113$	−9.65606	−0.908365	−0.454183	−	0.890909i	$-0.650069\pi$
$113$	−9.65606	−0.908365	−0.454183	+	0.890909i	$0.650069\pi$
$114$	11.4497	1.07236
$115$	0	0
$116$	15.5892	1.44742
$117$	2.71697	0.251184
$118$	28.7420	2.64592
$119$	−17.0452	−1.56253
$120$	5.11900	0.467299
$121$	−9.87719	−0.897927
$122$	17.5739	1.59107
$123$	−0.415160	−0.0374337
$124$	−1.55713	−0.139835
$125$	−1.00000	−0.0894427
$126$	−11.0785	−0.986950
$127$	−6.79145	−0.602644	−0.301322	−	0.953523i	$-0.597428\pi$
$127$	−6.79145	−0.602644	−0.301322	+	0.953523i	$0.597428\pi$
$128$	−18.8773	−1.66854
$129$	−8.21847	−0.723596
$130$	−6.69755	−0.587414
$131$	−9.39554	−0.820893	−0.410446	−	0.911885i	$-0.634627\pi$
$131$	−9.39554	−0.820893	−0.410446	+	0.911885i	$0.634627\pi$
$132$	−4.31968	−0.375980
$133$	20.8743	1.81003
$134$	7.60434	0.656915
$135$	1.00000	0.0860663
$136$	19.4150	1.66482
$137$	6.86666	0.586658	0.293329	−	0.956012i	$-0.405237\pi$
$137$	6.86666	0.586658	0.293329	+	0.956012i	$0.405237\pi$
$138$	0	0
$139$	−11.8267	−1.00313	−0.501564	−	0.865121i	$-0.667242\pi$
$139$	−11.8267	−1.00313	−0.501564	+	0.865121i	$0.667242\pi$
$140$	18.3210	1.54841
$141$	4.78699	0.403137
$142$	19.9611	1.67510
$143$	2.87898	0.240752
$144$	4.46552	0.372126
$145$	−3.82407	−0.317572
$146$	30.6567	2.53716
$147$	−13.1976	−1.08852
$148$	−43.0901	−3.54198
$149$	16.1167	1.32033	0.660167	−	0.751119i	$-0.270485\pi$
$149$	16.1167	1.32033	0.660167	+	0.751119i	$0.270485\pi$
$150$	−2.46508	−0.201273
$151$	−1.06417	−0.0866010	−0.0433005	−	0.999062i	$-0.513787\pi$
$151$	−1.06417	−0.0866010	−0.0433005	+	0.999062i	$0.513787\pi$
$152$	−23.7765	−1.92853
$153$	3.79273	0.306624
$154$	−11.7391	−0.945960
$155$	0.381968	0.0306804
$156$	−11.0760	−0.886793
$157$	15.8742	1.26690	0.633450	−	0.773784i	$-0.281638\pi$
$157$	15.8742	1.26690	0.633450	+	0.773784i	$0.281638\pi$
$158$	−33.2272	−2.64341
$159$	−12.5121	−0.992271
$160$	−0.769846	−0.0608617
$161$	0	0
$162$	2.46508	0.193675
$163$	17.3304	1.35742	0.678711	−	0.734406i	$-0.262539\pi$
$163$	17.3304	1.35742	0.678711	+	0.734406i	$0.262539\pi$
$164$	1.69245	0.132158
$165$	1.05963	0.0824918
$166$	−2.99173	−0.232203
$167$	9.48647	0.734085	0.367043	−	0.930204i	$-0.380370\pi$
$167$	9.48647	0.734085	0.367043	+	0.930204i	$0.380370\pi$
$168$	23.0057	1.77493
$169$	−5.61805	−0.432158
$170$	−9.34938	−0.717065
$171$	−4.64475	−0.355193
$172$	33.5035	2.55462
$173$	13.2938	1.01071	0.505356	−	0.862911i	$-0.331361\pi$
$173$	13.2938	1.01071	0.505356	+	0.862911i	$0.331361\pi$
$174$	−9.42663	−0.714631
$175$	−4.49417	−0.339728
$176$	4.73178	0.356671
$177$	−11.6597	−0.876396
$178$	31.3476	2.34960
$179$	−10.8091	−0.807908	−0.403954	−	0.914779i	$-0.632364\pi$
$179$	−10.8091	−0.807908	−0.403954	+	0.914779i	$0.632364\pi$
$180$	−4.07661	−0.303852
$181$	−25.4115	−1.88882	−0.944411	−	0.328766i	$-0.893367\pi$
$181$	−25.4115	−1.88882	−0.944411	+	0.328766i	$0.893367\pi$
$182$	−30.1000	−2.23116
$183$	−7.12915	−0.527002
$184$	0	0
$185$	10.5701	0.777128
$186$	0.941580	0.0690400
$187$	4.01888	0.293889
$188$	−19.5147	−1.42325
$189$	4.49417	0.326903
$190$	11.4497	0.830647
$191$	12.8593	0.930465	0.465233	−	0.885189i	$-0.345971\pi$
$191$	12.8593	0.930465	0.465233	+	0.885189i	$0.345971\pi$
$192$	7.03330	0.507585
$193$	9.04279	0.650914	0.325457	−	0.945557i	$-0.394482\pi$
$193$	9.04279	0.650914	0.325457	+	0.945557i	$0.394482\pi$
$194$	31.3968	2.25416
$195$	2.71697	0.194567
$196$	53.8015	3.84296
$197$	11.8999	0.847829	0.423915	−	0.905702i	$-0.360656\pi$
$197$	11.8999	0.847829	0.423915	+	0.905702i	$0.360656\pi$
$198$	2.61206	0.185631
$199$	−1.03969	−0.0737013	−0.0368507	−	0.999321i	$-0.511733\pi$
$199$	−1.03969	−0.0737013	−0.0368507	+	0.999321i	$0.511733\pi$
$200$	5.11900	0.361968
$201$	−3.08483	−0.217587
$202$	22.4834	1.58193
$203$	−17.1860	−1.20622
$204$	−15.4615	−1.08252
$205$	−0.415160	−0.0289961
$206$	14.7684	1.02896
$207$	0	0
$208$	12.1327	0.841251
$209$	−4.92170	−0.340441
$210$	−11.0785	−0.764488
$211$	25.3794	1.74719	0.873595	−	0.486653i	$-0.161782\pi$
$211$	25.3794	1.74719	0.873595	+	0.486653i	$0.161782\pi$
$212$	51.0068	3.50316
$213$	−8.09757	−0.554836
$214$	27.7105	1.89425
$215$	−8.21847	−0.560495
$216$	−5.11900	−0.348304
$217$	1.71663	0.116532
$218$	−33.0715	−2.23988
$219$	−12.4364	−0.840374
$220$	−4.31968	−0.291233
$221$	10.3048	0.693173
$222$	26.0561	1.74877
$223$	7.70140	0.515724	0.257862	−	0.966182i	$-0.416982\pi$
$223$	7.70140	0.515724	0.257862	+	0.966182i	$0.416982\pi$
$224$	−3.45982	−0.231169
$225$	1.00000	0.0666667
$226$	−23.8029	−1.58335
$227$	−2.74997	−0.182522	−0.0912610	−	0.995827i	$-0.529090\pi$
$227$	−2.74997	−0.182522	−0.0912610	+	0.995827i	$0.529090\pi$
$228$	18.9348	1.25399
$229$	−2.93094	−0.193682	−0.0968411	−	0.995300i	$-0.530874\pi$
$229$	−2.93094	−0.193682	−0.0968411	+	0.995300i	$0.530874\pi$
$230$	0	0
$231$	4.76214	0.313326
$232$	19.5754	1.28519
$233$	−19.6184	−1.28524	−0.642622	−	0.766183i	$-0.722154\pi$
$233$	−19.6184	−1.28524	−0.642622	+	0.766183i	$0.722154\pi$
$234$	6.69755	0.437833
$235$	4.78699	0.312269
$236$	47.5320	3.09407
$237$	13.4792	0.875566
$238$	−42.0177	−2.72361
$239$	−2.24046	−0.144924	−0.0724618	−	0.997371i	$-0.523086\pi$
$239$	−2.24046	−0.144924	−0.0724618	+	0.997371i	$0.523086\pi$
$240$	4.46552	0.288248
$241$	24.0841	1.55139	0.775697	−	0.631106i	$-0.217399\pi$
$241$	24.0841	1.55139	0.775697	+	0.631106i	$0.217399\pi$
$242$	−24.3480	−1.56515
$243$	−1.00000	−0.0641500
$244$	29.0627	1.86055
$245$	−13.1976	−0.843164
$246$	−1.02340	−0.0652498
$247$	−12.6197	−0.802971
$248$	−1.95529	−0.124161
$249$	1.21364	0.0769116
$250$	−2.46508	−0.155905
$251$	8.77127	0.553638	0.276819	−	0.960922i	$-0.410720\pi$
$251$	8.77127	0.553638	0.276819	+	0.960922i	$0.410720\pi$
$252$	−18.3210	−1.15411
$253$	0	0
$254$	−16.7414	−1.05045
$255$	3.79273	0.237510
$256$	−32.4675	−2.02922
$257$	8.72479	0.544238	0.272119	−	0.962264i	$-0.412276\pi$
$257$	8.72479	0.544238	0.272119	+	0.962264i	$0.412276\pi$
$258$	−20.2592	−1.26128
$259$	47.5038	2.95174
$260$	−11.0760	−0.686907
$261$	3.82407	0.236704
$262$	−23.1607	−1.43088
$263$	24.8439	1.53194	0.765971	−	0.642875i	$-0.222259\pi$
$263$	24.8439	1.53194	0.765971	+	0.642875i	$0.222259\pi$
$264$	−5.42422	−0.333838
$265$	−12.5121	−0.768610
$266$	51.4569	3.15502
$267$	−12.7167	−0.778249
$268$	12.5756	0.768179
$269$	22.8779	1.39489	0.697445	−	0.716638i	$-0.254320\pi$
$269$	22.8779	1.39489	0.697445	+	0.716638i	$0.254320\pi$
$270$	2.46508	0.150020
$271$	−4.16939	−0.253272	−0.126636	−	0.991949i	$-0.540418\pi$
$271$	−4.16939	−0.253272	−0.126636	+	0.991949i	$0.540418\pi$
$272$	16.9365	1.02693
$273$	12.2106	0.739017
$274$	16.9268	1.02259
$275$	1.05963	0.0638978
$276$	0	0
$277$	−29.8462	−1.79329	−0.896643	−	0.442755i	$-0.854001\pi$
$277$	−29.8462	−1.79329	−0.896643	+	0.442755i	$0.854001\pi$
$278$	−29.1537	−1.74852
$279$	−0.381968	−0.0228678
$280$	23.0057	1.37485
$281$	−14.0939	−0.840769	−0.420384	−	0.907346i	$-0.638105\pi$
$281$	−14.0939	−0.840769	−0.420384	+	0.907346i	$0.638105\pi$
$282$	11.8003	0.702698
$283$	−3.26414	−0.194033	−0.0970164	−	0.995283i	$-0.530930\pi$
$283$	−3.26414	−0.194033	−0.0970164	+	0.995283i	$0.530930\pi$
$284$	33.0106	1.95882
$285$	−4.64475	−0.275131
$286$	7.09690	0.419648
$287$	−1.86580	−0.110135
$288$	0.769846	0.0453636
$289$	−2.61519	−0.153835
$290$	−9.42663	−0.553551
$291$	−12.7366	−0.746635
$292$	50.6983	2.96689
$293$	16.9075	0.987746	0.493873	−	0.869534i	$-0.335581\pi$
$293$	16.9075	0.987746	0.493873	+	0.869534i	$0.335581\pi$
$294$	−32.5331	−1.89737
$295$	−11.6597	−0.678853
$296$	−54.1082	−3.14498
$297$	−1.05963	−0.0614857
$298$	39.7290	2.30144
$299$	0	0
$300$	−4.07661	−0.235363
$301$	−36.9352	−2.12891
$302$	−2.62327	−0.150952
$303$	−9.12078	−0.523975
$304$	−20.7412	−1.18959
$305$	−7.12915	−0.408214
$306$	9.34938	0.534468
$307$	13.4258	0.766250	0.383125	−	0.923697i	$-0.374848\pi$
$307$	13.4258	0.766250	0.383125	+	0.923697i	$0.374848\pi$
$308$	−19.4134	−1.10618
$309$	−5.99103	−0.340818
$310$	0.941580	0.0534782
$311$	−12.5633	−0.712402	−0.356201	−	0.934409i	$-0.615928\pi$
$311$	−12.5633	−0.712402	−0.356201	+	0.934409i	$0.615928\pi$
$312$	−13.9082	−0.787396
$313$	−16.4283	−0.928581	−0.464290	−	0.885683i	$-0.653691\pi$
$313$	−16.4283	−0.928581	−0.464290	+	0.885683i	$0.653691\pi$
$314$	39.1312	2.20830
$315$	4.49417	0.253218
$316$	−54.9493	−3.09114
$317$	32.1840	1.80764	0.903818	−	0.427917i	$-0.140753\pi$
$317$	32.1840	1.80764	0.903818	+	0.427917i	$0.140753\pi$
$318$	−30.8432	−1.72960
$319$	4.05208	0.226873
$320$	7.03330	0.393174
$321$	−11.2412	−0.627425
$322$	0	0
$323$	−17.6163	−0.980197
$324$	4.07661	0.226478
$325$	2.71697	0.150711
$326$	42.7208	2.36608
$327$	13.4160	0.741906
$328$	2.12521	0.117345
$329$	21.5136	1.18608
$330$	2.61206	0.143789
$331$	2.34092	0.128669	0.0643343	−	0.997928i	$-0.479508\pi$
$331$	2.34092	0.128669	0.0643343	+	0.997928i	$0.479508\pi$
$332$	−4.94755	−0.271532
$333$	−10.5701	−0.579237
$334$	23.3849	1.27956
$335$	−3.08483	−0.168542
$336$	20.0688	1.09484
$337$	1.87312	0.102035	0.0510177	−	0.998698i	$-0.483754\pi$
$337$	1.87312	0.102035	0.0510177	+	0.998698i	$0.483754\pi$
$338$	−13.8489	−0.753283
$339$	9.65606	0.524445
$340$	−15.4615	−0.838516
$341$	−0.404743	−0.0219181
$342$	−11.4497	−0.619128
$343$	−27.8531	−1.50393
$344$	42.0704	2.26828
$345$	0	0
$346$	32.7703	1.76174
$347$	−19.9731	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$347$	−19.9731	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$348$	−15.5892	−0.835670
$349$	7.61197	0.407459	0.203730	−	0.979027i	$-0.434694\pi$
$349$	7.61197	0.407459	0.203730	+	0.979027i	$0.434694\pi$
$350$	−11.0785	−0.592170
$351$	−2.71697	−0.145021
$352$	0.815749	0.0434796
$353$	6.58204	0.350326	0.175163	−	0.984539i	$-0.443955\pi$
$353$	6.58204	0.350326	0.175163	+	0.984539i	$0.443955\pi$
$354$	−28.7420	−1.52762
$355$	−8.09757	−0.429774
$356$	51.8409	2.74756
$357$	17.0452	0.902128
$358$	−26.6452	−1.40824
$359$	−17.3292	−0.914601	−0.457301	−	0.889312i	$-0.651184\pi$
$359$	−17.3292	−0.914601	−0.457301	+	0.889312i	$0.651184\pi$
$360$	−5.11900	−0.269795
$361$	2.57374	0.135460
$362$	−62.6413	−3.29236
$363$	9.87719	0.518418
$364$	−49.7777	−2.60906
$365$	−12.4364	−0.650951
$366$	−17.5739	−0.918603
$367$	−24.3244	−1.26973	−0.634863	−	0.772625i	$-0.718943\pi$
$367$	−24.3244	−1.26973	−0.634863	+	0.772625i	$0.718943\pi$
$368$	0	0
$369$	0.415160	0.0216124
$370$	26.0561	1.35459
$371$	−56.2314	−2.91939
$372$	1.55713	0.0807336
$373$	−15.3299	−0.793752	−0.396876	−	0.917872i	$-0.629906\pi$
$373$	−15.3299	−0.793752	−0.396876	+	0.917872i	$0.629906\pi$
$374$	9.90684	0.512271
$375$	1.00000	0.0516398
$376$	−24.5046	−1.26373
$377$	10.3899	0.535107
$378$	11.0785	0.569816
$379$	7.52041	0.386297	0.193149	−	0.981169i	$-0.438130\pi$
$379$	7.52041	0.386297	0.193149	+	0.981169i	$0.438130\pi$
$380$	18.9348	0.971337
$381$	6.79145	0.347936
$382$	31.6991	1.62187
$383$	6.08256	0.310805	0.155402	−	0.987851i	$-0.450333\pi$
$383$	6.08256	0.310805	0.155402	+	0.987851i	$0.450333\pi$
$384$	18.8773	0.963330
$385$	4.76214	0.242701
$386$	22.2912	1.13459
$387$	8.21847	0.417768
$388$	51.9223	2.63595
$389$	39.0906	1.98197	0.990985	−	0.133970i	$-0.0427725\pi$
$389$	39.0906	1.98197	0.990985	+	0.133970i	$0.0427725\pi$
$390$	6.69755	0.339144
$391$	0	0
$392$	67.5585	3.41222
$393$	9.39554	0.473943
$394$	29.3341	1.47783
$395$	13.4792	0.678210
$396$	4.31968	0.217072
$397$	−27.8350	−1.39700	−0.698498	−	0.715612i	$-0.746148\pi$
$397$	−27.8350	−1.39700	−0.698498	+	0.715612i	$0.746148\pi$
$398$	−2.56290	−0.128467
$399$	−20.8743	−1.04502
$400$	4.46552	0.223276
$401$	−6.63943	−0.331557	−0.165779	−	0.986163i	$-0.553014\pi$
$401$	−6.63943	−0.331557	−0.165779	+	0.986163i	$0.553014\pi$
$402$	−7.60434	−0.379270
$403$	−1.03780	−0.0516963
$404$	37.1819	1.84987
$405$	−1.00000	−0.0496904
$406$	−42.3649	−2.10253
$407$	−11.2003	−0.555180
$408$	−19.4150	−0.961185
$409$	22.9479	1.13470	0.567351	−	0.823476i	$-0.307968\pi$
$409$	22.9479	1.13470	0.567351	+	0.823476i	$0.307968\pi$
$410$	−1.02340	−0.0505422
$411$	−6.86666	−0.338707
$412$	24.4231	1.20324
$413$	−52.4007	−2.57847
$414$	0	0
$415$	1.21364	0.0595754
$416$	2.09165	0.102552
$417$	11.8267	0.579156
$418$	−12.1324	−0.593414
$419$	6.99875	0.341912	0.170956	−	0.985279i	$-0.445314\pi$
$419$	6.99875	0.341912	0.170956	+	0.985279i	$0.445314\pi$
$420$	−18.3210	−0.893973
$421$	−34.6759	−1.69000	−0.845000	−	0.534766i	$-0.820400\pi$
$421$	−34.6759	−1.69000	−0.845000	+	0.534766i	$0.820400\pi$
$422$	62.5622	3.04548
$423$	−4.78699	−0.232752
$424$	64.0492	3.11051
$425$	3.79273	0.183975
$426$	−19.9611	−0.967120
$427$	−32.0396	−1.55051
$428$	45.8261	2.21509
$429$	−2.87898	−0.138998
$430$	−20.2592	−0.976984
$431$	−18.3973	−0.886166	−0.443083	−	0.896481i	$-0.646115\pi$
$431$	−18.3973	−0.886166	−0.443083	+	0.896481i	$0.646115\pi$
$432$	−4.46552	−0.214847
$433$	9.87626	0.474623	0.237311	−	0.971434i	$-0.423734\pi$
$433$	9.87626	0.474623	0.237311	+	0.971434i	$0.423734\pi$
$434$	4.23163	0.203125
$435$	3.82407	0.183350
$436$	−54.6918	−2.61926
$437$	0	0
$438$	−30.6567	−1.46483
$439$	−4.06457	−0.193991	−0.0969956	−	0.995285i	$-0.530923\pi$
$439$	−4.06457	−0.193991	−0.0969956	+	0.995285i	$0.530923\pi$
$440$	−5.42422	−0.258590
$441$	13.1976	0.628457
$442$	25.4020	1.20825
$443$	−6.21947	−0.295496	−0.147748	−	0.989025i	$-0.547202\pi$
$443$	−6.21947	−0.295496	−0.147748	+	0.989025i	$0.547202\pi$
$444$	43.0901	2.04496
$445$	−12.7167	−0.602829
$446$	18.9846	0.898945
$447$	−16.1167	−0.762295
$448$	31.6089	1.49338
$449$	8.09307	0.381936	0.190968	−	0.981596i	$-0.438837\pi$
$449$	8.09307	0.381936	0.190968	+	0.981596i	$0.438837\pi$
$450$	2.46508	0.116205
$451$	0.439915	0.0207148
$452$	−39.3640	−1.85152
$453$	1.06417	0.0499991
$454$	−6.77890	−0.318149
$455$	12.2106	0.572440
$456$	23.7765	1.11344
$457$	−12.6104	−0.589888	−0.294944	−	0.955515i	$-0.595301\pi$
$457$	−12.6104	−0.589888	−0.294944	+	0.955515i	$0.595301\pi$
$458$	−7.22500	−0.337602
$459$	−3.79273	−0.177030
$460$	0	0
$461$	−23.9496	−1.11544	−0.557722	−	0.830027i	$-0.688325\pi$
$461$	−23.9496	−1.11544	−0.557722	+	0.830027i	$0.688325\pi$
$462$	11.7391	0.546150
$463$	−20.4958	−0.952521	−0.476260	−	0.879304i	$-0.658008\pi$
$463$	−20.4958	−0.952521	−0.476260	+	0.879304i	$0.658008\pi$
$464$	17.0764	0.792754
$465$	−0.381968	−0.0177133
$466$	−48.3609	−2.24028
$467$	−11.9098	−0.551120	−0.275560	−	0.961284i	$-0.588863\pi$
$467$	−11.9098	−0.551120	−0.275560	+	0.961284i	$0.588863\pi$
$468$	11.0760	0.511990
$469$	−13.8638	−0.640169
$470$	11.8003	0.544308
$471$	−15.8742	−0.731445
$472$	59.6859	2.74727
$473$	8.70850	0.400417
$474$	33.2272	1.52617
$475$	−4.64475	−0.213116
$476$	−69.4866	−3.18491
$477$	12.5121	0.572888
$478$	−5.52292	−0.252612
$479$	−6.75560	−0.308671	−0.154336	−	0.988018i	$-0.549324\pi$
$479$	−6.75560	−0.308671	−0.154336	+	0.988018i	$0.549324\pi$
$480$	0.769846	0.0351385
$481$	−28.7186	−1.30946
$482$	59.3692	2.70419
$483$	0	0
$484$	−40.2654	−1.83025
$485$	−12.7366	−0.578341
$486$	−2.46508	−0.111818
$487$	−11.5090	−0.521522	−0.260761	−	0.965403i	$-0.583973\pi$
$487$	−11.5090	−0.521522	−0.260761	+	0.965403i	$0.583973\pi$
$488$	36.4941	1.65201
$489$	−17.3304	−0.783708
$490$	−32.5331	−1.46970
$491$	−40.9226	−1.84681	−0.923404	−	0.383828i	$-0.874605\pi$
$491$	−40.9226	−1.84681	−0.923404	+	0.383828i	$0.874605\pi$
$492$	−1.69245	−0.0763014
$493$	14.5037	0.653212
$494$	−31.1085	−1.39964
$495$	−1.05963	−0.0476266
$496$	−1.70568	−0.0765875
$497$	−36.3919	−1.63240
$498$	2.99173	0.134063
$499$	9.62367	0.430815	0.215407	−	0.976524i	$-0.430892\pi$
$499$	9.62367	0.430815	0.215407	+	0.976524i	$0.430892\pi$
$500$	−4.07661	−0.182311
$501$	−9.48647	−0.423824
$502$	21.6219	0.965031
$503$	21.2606	0.947964	0.473982	−	0.880535i	$-0.342816\pi$
$503$	21.2606	0.947964	0.473982	+	0.880535i	$0.342816\pi$
$504$	−23.0057	−1.02475
$505$	−9.12078	−0.405869
$506$	0	0
$507$	5.61805	0.249506
$508$	−27.6861	−1.22837
$509$	−34.5160	−1.52989	−0.764947	−	0.644093i	$-0.777235\pi$
$509$	−34.5160	−1.52989	−0.764947	+	0.644093i	$0.777235\pi$
$510$	9.34938	0.413997
$511$	−55.8913	−2.47249
$512$	−42.2802	−1.86854
$513$	4.64475	0.205071
$514$	21.5073	0.948646
$515$	−5.99103	−0.263996
$516$	−33.5035	−1.47491
$517$	−5.07242	−0.223085
$518$	117.100	5.14510
$519$	−13.2938	−0.583535
$520$	−13.9082	−0.609915
$521$	−0.246034	−0.0107789	−0.00538947	−	0.999985i	$-0.501716\pi$
$521$	−0.246034	−0.0107789	−0.00538947	+	0.999985i	$0.501716\pi$
$522$	9.42663	0.412592
$523$	−4.34525	−0.190005	−0.0950023	−	0.995477i	$-0.530286\pi$
$523$	−4.34525	−0.190005	−0.0950023	+	0.995477i	$0.530286\pi$
$524$	−38.3020	−1.67323
$525$	4.49417	0.196142
$526$	61.2422	2.67029
$527$	−1.44870	−0.0631064
$528$	−4.73178	−0.205924
$529$	0	0
$530$	−30.8432	−1.33974
$531$	11.6597	0.505987
$532$	85.0965	3.68940
$533$	1.12798	0.0488582
$534$	−31.3476	−1.35654
$535$	−11.2412	−0.486001
$536$	15.7912	0.682078
$537$	10.8091	0.466446
$538$	56.3958	2.43139
$539$	13.9845	0.602356
$540$	4.07661	0.175429
$541$	10.4580	0.449623	0.224812	−	0.974402i	$-0.427823\pi$
$541$	10.4580	0.449623	0.224812	+	0.974402i	$0.427823\pi$
$542$	−10.2779	−0.441472
$543$	25.4115	1.09051
$544$	2.91982	0.125186
$545$	13.4160	0.574678
$546$	30.1000	1.28816
$547$	0.443683	0.0189705	0.00948526	−	0.999955i	$-0.496981\pi$
$547$	0.443683	0.0189705	0.00948526	+	0.999955i	$0.496981\pi$
$548$	27.9927	1.19579
$549$	7.12915	0.304265
$550$	2.61206	0.111379
$551$	−17.7619	−0.756681
$552$	0	0
$553$	60.5777	2.57603
$554$	−73.5732	−3.12583
$555$	−10.5701	−0.448675
$556$	−48.2128	−2.04468
$557$	1.77163	0.0750666	0.0375333	−	0.999295i	$-0.488050\pi$
$557$	1.77163	0.0750666	0.0375333	+	0.999295i	$0.488050\pi$
$558$	−0.941580	−0.0398603
$559$	22.3294	0.944432
$560$	20.0688	0.848062
$561$	−4.01888	−0.169677
$562$	−34.7424	−1.46552
$563$	−37.2279	−1.56897	−0.784485	−	0.620148i	$-0.787073\pi$
$563$	−37.2279	−1.56897	−0.784485	+	0.620148i	$0.787073\pi$
$564$	19.5147	0.821717
$565$	9.65606	0.406233
$566$	−8.04635	−0.338213
$567$	−4.49417	−0.188738
$568$	41.4514	1.73926
$569$	−8.69454	−0.364494	−0.182247	−	0.983253i	$-0.558337\pi$
$569$	−8.69454	−0.364494	−0.182247	+	0.983253i	$0.558337\pi$
$570$	−11.4497	−0.479574
$571$	−8.45548	−0.353851	−0.176925	−	0.984224i	$-0.556615\pi$
$571$	−8.45548	−0.353851	−0.176925	+	0.984224i	$0.556615\pi$
$572$	11.7365	0.490726
$573$	−12.8593	−0.537204
$574$	−4.59935	−0.191973
$575$	0	0
$576$	−7.03330	−0.293054
$577$	24.3076	1.01194	0.505969	−	0.862551i	$-0.331135\pi$
$577$	24.3076	1.01194	0.505969	+	0.862551i	$0.331135\pi$
$578$	−6.44664	−0.268145
$579$	−9.04279	−0.375805
$580$	−15.5892	−0.647307
$581$	5.45433	0.226284
$582$	−31.3968	−1.30144
$583$	13.2581	0.549094
$584$	63.6619	2.63435
$585$	−2.71697	−0.112333
$586$	41.6783	1.72171
$587$	16.9986	0.701609	0.350804	−	0.936449i	$-0.385908\pi$
$587$	16.9986	0.701609	0.350804	+	0.936449i	$0.385908\pi$
$588$	−53.8015	−2.21873
$589$	1.77415	0.0731024
$590$	−28.7420	−1.18329
$591$	−11.8999	−0.489494
$592$	−47.2009	−1.93994
$593$	33.1814	1.36260	0.681298	−	0.732006i	$-0.261416\pi$
$593$	33.1814	1.36260	0.681298	+	0.732006i	$0.261416\pi$
$594$	−2.61206	−0.107174
$595$	17.0452	0.698785
$596$	65.7016	2.69124
$597$	1.03969	0.0425515
$598$	0	0
$599$	9.03872	0.369312	0.184656	−	0.982803i	$-0.440883\pi$
$599$	9.03872	0.369312	0.184656	+	0.982803i	$0.440883\pi$
$600$	−5.11900	−0.208982
$601$	−18.1738	−0.741326	−0.370663	−	0.928767i	$-0.620870\pi$
$601$	−18.1738	−0.741326	−0.370663	+	0.928767i	$0.620870\pi$
$602$	−91.0483	−3.71085
$603$	3.08483	0.125624
$604$	−4.33821	−0.176519
$605$	9.87719	0.401565
$606$	−22.4834	−0.913327
$607$	4.57162	0.185556	0.0927782	−	0.995687i	$-0.470425\pi$
$607$	4.57162	0.185556	0.0927782	+	0.995687i	$0.470425\pi$
$608$	−3.57575	−0.145016
$609$	17.1860	0.696413
$610$	−17.5739	−0.711547
$611$	−13.0061	−0.526172
$612$	15.4615	0.624993
$613$	45.6151	1.84238	0.921189	−	0.389115i	$-0.127219\pi$
$613$	45.6151	1.84238	0.921189	+	0.389115i	$0.127219\pi$
$614$	33.0956	1.33563
$615$	0.415160	0.0167409
$616$	−24.3774	−0.982194
$617$	17.7245	0.713560	0.356780	−	0.934188i	$-0.383875\pi$
$617$	17.7245	0.713560	0.356780	+	0.934188i	$0.383875\pi$
$618$	−14.7684	−0.594070
$619$	41.0036	1.64807	0.824037	−	0.566537i	$-0.191717\pi$
$619$	41.0036	1.64807	0.824037	+	0.566537i	$0.191717\pi$
$620$	1.55713	0.0625360
$621$	0	0
$622$	−30.9696	−1.24177
$623$	−57.1510	−2.28971
$624$	−12.1327	−0.485697
$625$	1.00000	0.0400000
$626$	−40.4970	−1.61858
$627$	4.92170	0.196554
$628$	64.7129	2.58233
$629$	−40.0895	−1.59847
$630$	11.0785	0.441378
$631$	11.6296	0.462969	0.231485	−	0.972839i	$-0.425642\pi$
$631$	11.6296	0.462969	0.231485	+	0.972839i	$0.425642\pi$
$632$	−68.9998	−2.74467
$633$	−25.3794	−1.00874
$634$	79.3362	3.15084
$635$	6.79145	0.269510
$636$	−51.0068	−2.02255
$637$	35.8576	1.42073
$638$	9.98869	0.395456
$639$	8.09757	0.320335
$640$	18.8773	0.746192
$641$	19.0735	0.753357	0.376678	−	0.926344i	$-0.377066\pi$
$641$	19.0735	0.753357	0.376678	+	0.926344i	$0.377066\pi$
$642$	−27.7105	−1.09365
$643$	29.2335	1.15286	0.576429	−	0.817148i	$-0.304446\pi$
$643$	29.2335	1.15286	0.576429	+	0.817148i	$0.304446\pi$
$644$	0	0
$645$	8.21847	0.323602
$646$	−43.4256	−1.70856
$647$	1.33879	0.0526332	0.0263166	−	0.999654i	$-0.491622\pi$
$647$	1.33879	0.0526332	0.0263166	+	0.999654i	$0.491622\pi$
$648$	5.11900	0.201093
$649$	12.3549	0.484972
$650$	6.69755	0.262700
$651$	−1.71663	−0.0672800
$652$	70.6492	2.76684
$653$	−46.4199	−1.81655	−0.908275	−	0.418374i	$-0.862600\pi$
$653$	−46.4199	−1.81655	−0.908275	+	0.418374i	$0.862600\pi$
$654$	33.0715	1.29320
$655$	9.39554	0.367114
$656$	1.85391	0.0723829
$657$	12.4364	0.485190
$658$	53.0326	2.06743
$659$	−17.1595	−0.668439	−0.334219	−	0.942495i	$-0.608473\pi$
$659$	−17.1595	−0.668439	−0.334219	+	0.942495i	$0.608473\pi$
$660$	4.31968	0.168143
$661$	6.47531	0.251860	0.125930	−	0.992039i	$-0.459808\pi$
$661$	6.47531	0.251860	0.125930	+	0.992039i	$0.459808\pi$
$662$	5.77055	0.224279
$663$	−10.3048	−0.400203
$664$	−6.21264	−0.241097
$665$	−20.8743	−0.809472
$666$	−26.0561	−1.00965
$667$	0	0
$668$	38.6726	1.49629
$669$	−7.70140	−0.297754
$670$	−7.60434	−0.293781
$671$	7.55423	0.291628
$672$	3.45982	0.133466
$673$	22.2651	0.858258	0.429129	−	0.903243i	$-0.358821\pi$
$673$	22.2651	0.858258	0.429129	+	0.903243i	$0.358821\pi$
$674$	4.61738	0.177855
$675$	−1.00000	−0.0384900
$676$	−22.9026	−0.880869
$677$	16.9998	0.653356	0.326678	−	0.945136i	$-0.394071\pi$
$677$	16.9998	0.653356	0.326678	+	0.945136i	$0.394071\pi$
$678$	23.8029	0.914146
$679$	−57.2407	−2.19670
$680$	−19.4150	−0.744531
$681$	2.74997	0.105379
$682$	−0.997723	−0.0382048
$683$	−31.9822	−1.22377	−0.611883	−	0.790948i	$-0.709588\pi$
$683$	−31.9822	−1.22377	−0.611883	+	0.790948i	$0.709588\pi$
$684$	−18.9348	−0.723992
$685$	−6.86666	−0.262362
$686$	−68.6601	−2.62145
$687$	2.93094	0.111822
$688$	36.6997	1.39916
$689$	33.9949	1.29510
$690$	0	0
$691$	−35.4966	−1.35035	−0.675177	−	0.737655i	$-0.735933\pi$
$691$	−35.4966	−1.35035	−0.675177	+	0.737655i	$0.735933\pi$
$692$	54.1938	2.06014
$693$	−4.76214	−0.180899
$694$	−49.2354	−1.86895
$695$	11.8267	0.448612
$696$	−19.5754	−0.742004
$697$	1.57459	0.0596419
$698$	18.7641	0.710231
$699$	19.6184	0.742036
$700$	−18.3210	−0.692468
$701$	−0.331760	−0.0125304	−0.00626520	−	0.999980i	$-0.501994\pi$
$701$	−0.331760	−0.0125304	−0.00626520	+	0.999980i	$0.501994\pi$
$702$	−6.69755	−0.252783
$703$	49.0954	1.85167
$704$	−7.45267	−0.280883
$705$	−4.78699	−0.180289
$706$	16.2252	0.610645
$707$	−40.9904	−1.54160
$708$	−47.5320	−1.78636
$709$	−1.80586	−0.0678206	−0.0339103	−	0.999425i	$-0.510796\pi$
$709$	−1.80586	−0.0678206	−0.0339103	+	0.999425i	$0.510796\pi$
$710$	−19.9611	−0.749128
$711$	−13.4792	−0.505508
$712$	65.0967	2.43960
$713$	0	0
$714$	42.0177	1.57247
$715$	−2.87898	−0.107668
$716$	−44.0643	−1.64676
$717$	2.24046	0.0836717
$718$	−42.7179	−1.59422
$719$	16.9292	0.631351	0.315676	−	0.948867i	$-0.397769\pi$
$719$	16.9292	0.631351	0.315676	+	0.948867i	$0.397769\pi$
$720$	−4.46552	−0.166420
$721$	−26.9247	−1.00273
$722$	6.34447	0.236117
$723$	−24.0841	−0.895697
$724$	−103.593	−3.84999
$725$	3.82407	0.142022
$726$	24.3480	0.903641
$727$	−49.2693	−1.82730	−0.913649	−	0.406505i	$-0.866748\pi$
$727$	−49.2693	−1.82730	−0.913649	+	0.406505i	$0.866748\pi$
$728$	−62.5058	−2.31662
$729$	1.00000	0.0370370
$730$	−30.6567	−1.13465
$731$	31.1705	1.15288
$732$	−29.0627	−1.07419
$733$	5.21430	0.192594	0.0962972	−	0.995353i	$-0.469300\pi$
$733$	5.21430	0.192594	0.0962972	+	0.995353i	$0.469300\pi$
$734$	−59.9617	−2.21323
$735$	13.1976	0.486801
$736$	0	0
$737$	3.26876	0.120406
$738$	1.02340	0.0376720
$739$	7.55599	0.277952	0.138976	−	0.990296i	$-0.455619\pi$
$739$	7.55599	0.277952	0.138976	+	0.990296i	$0.455619\pi$
$740$	43.0901	1.58402
$741$	12.6197	0.463595
$742$	−138.615	−5.08871
$743$	−20.0428	−0.735297	−0.367649	−	0.929965i	$-0.619837\pi$
$743$	−20.0428	−0.735297	−0.367649	+	0.929965i	$0.619837\pi$
$744$	1.95529	0.0716845
$745$	−16.1167	−0.590471
$746$	−37.7894	−1.38357
$747$	−1.21364	−0.0444049
$748$	16.3834	0.599036
$749$	−50.5201	−1.84596
$750$	2.46508	0.0900119
$751$	−15.9637	−0.582523	−0.291262	−	0.956643i	$-0.594075\pi$
$751$	−15.9637	−0.582523	−0.291262	+	0.956643i	$0.594075\pi$
$752$	−21.3764	−0.779517
$753$	−8.77127	−0.319643
$754$	25.6119	0.932730
$755$	1.06417	0.0387292
$756$	18.3210	0.666328
$757$	−3.40154	−0.123631	−0.0618156	−	0.998088i	$-0.519689\pi$
$757$	−3.40154	−0.123631	−0.0618156	+	0.998088i	$0.519689\pi$
$758$	18.5384	0.673345
$759$	0	0
$760$	23.7765	0.862464
$761$	24.1546	0.875604	0.437802	−	0.899071i	$-0.355757\pi$
$761$	24.1546	0.875604	0.437802	+	0.899071i	$0.355757\pi$
$762$	16.7414	0.606479
$763$	60.2938	2.18278
$764$	52.4223	1.89657
$765$	−3.79273	−0.137126
$766$	14.9940	0.541755
$767$	31.6791	1.14386
$768$	32.4675	1.17157
$769$	−2.62218	−0.0945583	−0.0472792	−	0.998882i	$-0.515055\pi$
$769$	−2.62218	−0.0945583	−0.0472792	+	0.998882i	$0.515055\pi$
$770$	11.7391	0.423046
$771$	−8.72479	−0.314216
$772$	36.8639	1.32676
$773$	−41.5899	−1.49588	−0.747942	−	0.663764i	$-0.768958\pi$
$773$	−41.5899	−1.49588	−0.747942	+	0.663764i	$0.768958\pi$
$774$	20.2592	0.728201
$775$	−0.381968	−0.0137207
$776$	65.1988	2.34050
$777$	−47.5038	−1.70419
$778$	96.3613	3.45472
$779$	−1.92832	−0.0690892
$780$	11.0760	0.396586
$781$	8.58039	0.307030
$782$	0	0
$783$	−3.82407	−0.136661
$784$	58.9341	2.10479
$785$	−15.8742	−0.566575
$786$	23.1607	0.826117
$787$	37.9159	1.35155	0.675777	−	0.737106i	$-0.263808\pi$
$787$	37.9159	1.35155	0.675777	+	0.737106i	$0.263808\pi$
$788$	48.5110	1.72813
$789$	−24.8439	−0.884467
$790$	33.2272	1.18217
$791$	43.3960	1.54298
$792$	5.42422	0.192741
$793$	19.3697	0.687839
$794$	−68.6154	−2.43507
$795$	12.5121	0.443757
$796$	−4.23839	−0.150226
$797$	−34.4820	−1.22141	−0.610707	−	0.791857i	$-0.709115\pi$
$797$	−34.4820	−1.22141	−0.610707	+	0.791857i	$0.709115\pi$
$798$	−51.4569	−1.82155
$799$	−18.1558	−0.642305
$800$	0.769846	0.0272182
$801$	12.7167	0.449322
$802$	−16.3667	−0.577929
$803$	13.1779	0.465039
$804$	−12.5756	−0.443508
$805$	0	0
$806$	−2.55825	−0.0901105
$807$	−22.8779	−0.805340
$808$	46.6893	1.64252
$809$	−23.2506	−0.817449	−0.408724	−	0.912658i	$-0.634026\pi$
$809$	−23.2506	−0.817449	−0.408724	+	0.912658i	$0.634026\pi$
$810$	−2.46508	−0.0866140
$811$	9.57534	0.336236	0.168118	−	0.985767i	$-0.446231\pi$
$811$	9.57534	0.336236	0.168118	+	0.985767i	$0.446231\pi$
$812$	−70.0607	−2.45865
$813$	4.16939	0.146227
$814$	−27.6097	−0.967719
$815$	−17.3304	−0.607057
$816$	−16.9365	−0.592896
$817$	−38.1728	−1.33550
$818$	56.5684	1.97787
$819$	−12.2106	−0.426671
$820$	−1.69245	−0.0591028
$821$	−24.4923	−0.854789	−0.427394	−	0.904065i	$-0.640568\pi$
$821$	−24.4923	−0.854789	−0.427394	+	0.904065i	$0.640568\pi$
$822$	−16.9268	−0.590392
$823$	−51.1554	−1.78317	−0.891583	−	0.452857i	$-0.850405\pi$
$823$	−51.1554	−1.78317	−0.891583	+	0.452857i	$0.850405\pi$
$824$	30.6681	1.06837
$825$	−1.05963	−0.0368914
$826$	−129.172	−4.49446
$827$	19.4775	0.677300	0.338650	−	0.940912i	$-0.390030\pi$
$827$	19.4775	0.677300	0.338650	+	0.940912i	$0.390030\pi$
$828$	0	0
$829$	−18.1914	−0.631814	−0.315907	−	0.948790i	$-0.602309\pi$
$829$	−18.1914	−0.631814	−0.315907	+	0.948790i	$0.602309\pi$
$830$	2.99173	0.103844
$831$	29.8462	1.03535
$832$	−19.1093	−0.662496
$833$	50.0550	1.73430
$834$	29.1537	1.00951
$835$	−9.48647	−0.328293
$836$	−20.0638	−0.693923
$837$	0.381968	0.0132027
$838$	17.2525	0.595977
$839$	−6.41227	−0.221376	−0.110688	−	0.993855i	$-0.535305\pi$
$839$	−6.41227	−0.221376	−0.110688	+	0.993855i	$0.535305\pi$
$840$	−23.0057	−0.793771
$841$	−14.3765	−0.495741
$842$	−85.4788	−2.94579
$843$	14.0939	0.485418
$844$	103.462	3.56131
$845$	5.61805	0.193267
$846$	−11.8003	−0.405703
$847$	44.3898	1.52525
$848$	55.8728	1.91868
$849$	3.26414	0.112025
$850$	9.34938	0.320681
$851$	0	0
$852$	−33.0106	−1.13092
$853$	−1.91188	−0.0654615	−0.0327308	−	0.999464i	$-0.510420\pi$
$853$	−1.91188	−0.0654615	−0.0327308	+	0.999464i	$0.510420\pi$
$854$	−78.9802	−2.70265
$855$	4.64475	0.158847
$856$	57.5439	1.96681
$857$	−15.4003	−0.526063	−0.263031	−	0.964787i	$-0.584722\pi$
$857$	−15.4003	−0.526063	−0.263031	+	0.964787i	$0.584722\pi$
$858$	−7.09690	−0.242284
$859$	−40.4530	−1.38024	−0.690120	−	0.723695i	$-0.742442\pi$
$859$	−40.4530	−1.38024	−0.690120	+	0.723695i	$0.742442\pi$
$860$	−33.5035	−1.14246
$861$	1.86580	0.0635864
$862$	−45.3507	−1.54465
$863$	−46.2998	−1.57606	−0.788031	−	0.615635i	$-0.788899\pi$
$863$	−46.2998	−1.57606	−0.788031	+	0.615635i	$0.788899\pi$
$864$	−0.769846	−0.0261907
$865$	−13.2938	−0.452004
$866$	24.3457	0.827302
$867$	2.61519	0.0888164
$868$	6.99803	0.237529
$869$	−14.2829	−0.484513
$870$	9.42663	0.319593
$871$	8.38140	0.283993
$872$	−68.6765	−2.32568
$873$	12.7366	0.431070
$874$	0	0
$875$	4.49417	0.151931
$876$	−50.6983	−1.71294
$877$	−4.97428	−0.167970	−0.0839848	−	0.996467i	$-0.526765\pi$
$877$	−4.97428	−0.167970	−0.0839848	+	0.996467i	$0.526765\pi$
$878$	−10.0195	−0.338141
$879$	−16.9075	−0.570275
$880$	−4.73178	−0.159508
$881$	−13.7398	−0.462907	−0.231454	−	0.972846i	$-0.574348\pi$
$881$	−13.7398	−0.462907	−0.231454	+	0.972846i	$0.574348\pi$
$882$	32.5331	1.09545
$883$	−18.8961	−0.635904	−0.317952	−	0.948107i	$-0.602995\pi$
$883$	−18.8961	−0.635904	−0.317952	+	0.948107i	$0.602995\pi$
$884$	42.0084	1.41290
$885$	11.6597	0.391936
$886$	−15.3315	−0.515071
$887$	−54.5154	−1.83045	−0.915224	−	0.402946i	$-0.867986\pi$
$887$	−54.5154	−1.83045	−0.915224	+	0.402946i	$0.867986\pi$
$888$	54.1082	1.81575
$889$	30.5219	1.02367
$890$	−31.3476	−1.05077
$891$	1.05963	0.0354988
$892$	31.3956	1.05120
$893$	22.2344	0.744046
$894$	−39.7290	−1.32874
$895$	10.8091	0.361307
$896$	84.8380	2.83424
$897$	0	0
$898$	19.9500	0.665742
$899$	−1.46067	−0.0487161
$900$	4.07661	0.135887
$901$	47.4549	1.58095
$902$	1.08442	0.0361074
$903$	36.9352	1.22913
$904$	−49.4294	−1.64400
$905$	25.4115	0.844707
$906$	2.62327	0.0871521
$907$	8.34585	0.277120	0.138560	−	0.990354i	$-0.455753\pi$
$907$	8.34585	0.277120	0.138560	+	0.990354i	$0.455753\pi$
$908$	−11.2106	−0.372035
$909$	9.12078	0.302517
$910$	30.1000	0.997804
$911$	6.04817	0.200385	0.100192	−	0.994968i	$-0.468054\pi$
$911$	6.04817	0.200385	0.100192	+	0.994968i	$0.468054\pi$
$912$	20.7412	0.686811
$913$	−1.28601	−0.0425607
$914$	−31.0855	−1.02822
$915$	7.12915	0.235682
$916$	−11.9483	−0.394783
$917$	42.2252	1.39440
$918$	−9.34938	−0.308575
$919$	−28.5122	−0.940529	−0.470265	−	0.882525i	$-0.655842\pi$
$919$	−28.5122	−0.940529	−0.470265	+	0.882525i	$0.655842\pi$
$920$	0	0
$921$	−13.4258	−0.442394
$922$	−59.0377	−1.94430
$923$	22.0009	0.724168
$924$	19.4134	0.638654
$925$	−10.5701	−0.347542
$926$	−50.5237	−1.66031
$927$	5.99103	0.196771
$928$	2.94395	0.0966397
$929$	13.0644	0.428629	0.214315	−	0.976765i	$-0.431248\pi$
$929$	13.0644	0.428629	0.214315	+	0.976765i	$0.431248\pi$
$930$	−0.941580	−0.0308756
$931$	−61.2996	−2.00901
$932$	−79.9766	−2.61972
$933$	12.5633	0.411305
$934$	−29.3586	−0.960643
$935$	−4.01888	−0.131431
$936$	13.9082	0.454603
$937$	57.5576	1.88032	0.940162	−	0.340729i	$-0.110674\pi$
$937$	57.5576	1.88032	0.940162	+	0.340729i	$0.110674\pi$
$938$	−34.1752	−1.11586
$939$	16.4283	0.536116
$940$	19.5147	0.636499
$941$	−25.3489	−0.826352	−0.413176	−	0.910651i	$-0.635580\pi$
$941$	−25.3489	−0.826352	−0.413176	+	0.910651i	$0.635580\pi$
$942$	−39.1312	−1.27496
$943$	0	0
$944$	52.0665	1.69462
$945$	−4.49417	−0.146196
$946$	21.4671	0.697957
$947$	47.0537	1.52904	0.764521	−	0.644599i	$-0.222976\pi$
$947$	47.0537	1.52904	0.764521	+	0.644599i	$0.222976\pi$
$948$	54.9493	1.78467
$949$	33.7894	1.09685
$950$	−11.4497	−0.371477
$951$	−32.1840	−1.04364
$952$	−87.2544	−2.82793
$953$	47.7427	1.54654	0.773269	−	0.634079i	$-0.218620\pi$
$953$	47.7427	1.54654	0.773269	+	0.634079i	$0.218620\pi$
$954$	30.8432	0.998585
$955$	−12.8593	−0.416117
$956$	−9.13350	−0.295398
$957$	−4.05208	−0.130985
$958$	−16.6531	−0.538036
$959$	−30.8600	−0.996520
$960$	−7.03330	−0.226999
$961$	−30.8541	−0.995294
$962$	−70.7937	−2.28248
$963$	11.2412	0.362244
$964$	98.1815	3.16221
$965$	−9.04279	−0.291098
$966$	0	0
$967$	−14.9460	−0.480632	−0.240316	−	0.970695i	$-0.577251\pi$
$967$	−14.9460	−0.480632	−0.240316	+	0.970695i	$0.577251\pi$
$968$	−50.5614	−1.62510
$969$	17.6163	0.565917
$970$	−31.3968	−1.00809
$971$	−6.50678	−0.208813	−0.104406	−	0.994535i	$-0.533294\pi$
$971$	−6.50678	−0.208813	−0.104406	+	0.994535i	$0.533294\pi$
$972$	−4.07661	−0.130757
$973$	53.1512	1.70395
$974$	−28.3705	−0.909051
$975$	−2.71697	−0.0870128
$976$	31.8353	1.01902
$977$	45.2595	1.44798	0.723990	−	0.689810i	$-0.242306\pi$
$977$	45.2595	1.44798	0.723990	+	0.689810i	$0.242306\pi$
$978$	−42.7208	−1.36606
$979$	13.4749	0.430661
$980$	−53.8015	−1.71862
$981$	−13.4160	−0.428340
$982$	−100.877	−3.21912
$983$	11.4195	0.364225	0.182113	−	0.983278i	$-0.441706\pi$
$983$	11.4195	0.364225	0.182113	+	0.983278i	$0.441706\pi$
$984$	−2.12521	−0.0677491
$985$	−11.8999	−0.379161
$986$	35.7527	1.13860
$987$	−21.5136	−0.684785
$988$	−51.4455	−1.63670
$989$	0	0
$990$	−2.61206	−0.0830167
$991$	22.7751	0.723475	0.361737	−	0.932280i	$-0.382184\pi$
$991$	22.7751	0.723475	0.361737	+	0.932280i	$0.382184\pi$
$992$	−0.294057	−0.00933630
$993$	−2.34092	−0.0742868
$994$	−89.7088	−2.84539
$995$	1.03969	0.0329602
$996$	4.94755	0.156769
$997$	−7.19037	−0.227721	−0.113861	−	0.993497i	$-0.536322\pi$
$997$	−7.19037	−0.227721	−0.113861	+	0.993497i	$0.536322\pi$
$998$	23.7231	0.750942
$999$	10.5701	0.334422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bt.1.22		25
23.17	odd	22		345.2.m.d.151.1	yes	50
23.19	odd	22		345.2.m.d.16.1	✓	50
23.22	odd	2		7935.2.a.bu.1.22		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.16.1	✓	50	23.19	odd	22
345.2.m.d.151.1	yes	50	23.17	odd	22
7935.2.a.bt.1.22		25	1.1	even	1	trivial
7935.2.a.bu.1.22		25	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)

\(f(q)\)	\(=\)	\(q+2.46508 q^{2} -1.00000 q^{3} +4.07661 q^{4} -1.00000 q^{5} -2.46508 q^{6} -4.49417 q^{7} +5.11900 q^{8} +1.00000 q^{9} -2.46508 q^{10} +1.05963 q^{11} -4.07661 q^{12} +2.71697 q^{13} -11.0785 q^{14} +1.00000 q^{15} +4.46552 q^{16} +3.79273 q^{17} +2.46508 q^{18} -4.64475 q^{19} -4.07661 q^{20} +4.49417 q^{21} +2.61206 q^{22} -5.11900 q^{24} +1.00000 q^{25} +6.69755 q^{26} -1.00000 q^{27} -18.3210 q^{28} +3.82407 q^{29} +2.46508 q^{30} -0.381968 q^{31} +0.769846 q^{32} -1.05963 q^{33} +9.34938 q^{34} +4.49417 q^{35} +4.07661 q^{36} -10.5701 q^{37} -11.4497 q^{38} -2.71697 q^{39} -5.11900 q^{40} +0.415160 q^{41} +11.0785 q^{42} +8.21847 q^{43} +4.31968 q^{44} -1.00000 q^{45} -4.78699 q^{47} -4.46552 q^{48} +13.1976 q^{49} +2.46508 q^{50} -3.79273 q^{51} +11.0760 q^{52} +12.5121 q^{53} -2.46508 q^{54} -1.05963 q^{55} -23.0057 q^{56} +4.64475 q^{57} +9.42663 q^{58} +11.6597 q^{59} +4.07661 q^{60} +7.12915 q^{61} -0.941580 q^{62} -4.49417 q^{63} -7.03330 q^{64} -2.71697 q^{65} -2.61206 q^{66} +3.08483 q^{67} +15.4615 q^{68} +11.0785 q^{70} +8.09757 q^{71} +5.11900 q^{72} +12.4364 q^{73} -26.0561 q^{74} -1.00000 q^{75} -18.9348 q^{76} -4.76214 q^{77} -6.69755 q^{78} -13.4792 q^{79} -4.46552 q^{80} +1.00000 q^{81} +1.02340 q^{82} -1.21364 q^{83} +18.3210 q^{84} -3.79273 q^{85} +20.2592 q^{86} -3.82407 q^{87} +5.42422 q^{88} +12.7167 q^{89} -2.46508 q^{90} -12.2106 q^{91} +0.381968 q^{93} -11.8003 q^{94} +4.64475 q^{95} -0.769846 q^{96} +12.7366 q^{97} +32.5331 q^{98} +1.05963 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9} - q^{10} - 15 q^{11} - 31 q^{12} + 24 q^{13} - 5 q^{14} + 25 q^{15} + 39 q^{16} + 6 q^{17} + q^{18} - 13 q^{19}+ \cdots - 15 q^{99}+O(q^{100}) \) 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

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Database

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