LMFDB - Embedded newform 7935.2.a.bv.1.10

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 = [25,11,25,31,-25,11,-7] 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			1.10
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)

$f(q)$	$=$	\(q-0.358480 q^{2} +1.00000 q^{3} -1.87149 q^{4} -1.00000 q^{5} -0.358480 q^{6} +2.43554 q^{7} +1.38785 q^{8} +1.00000 q^{9} +0.358480 q^{10} +4.36825 q^{11} -1.87149 q^{12} -5.75501 q^{13} -0.873093 q^{14} -1.00000 q^{15} +3.24547 q^{16} +0.243632 q^{17} -0.358480 q^{18} +3.07550 q^{19} +1.87149 q^{20} +2.43554 q^{21} -1.56593 q^{22} +1.38785 q^{24} +1.00000 q^{25} +2.06306 q^{26} +1.00000 q^{27} -4.55809 q^{28} +2.57379 q^{29} +0.358480 q^{30} +3.73126 q^{31} -3.93914 q^{32} +4.36825 q^{33} -0.0873372 q^{34} -2.43554 q^{35} -1.87149 q^{36} -4.66392 q^{37} -1.10250 q^{38} -5.75501 q^{39} -1.38785 q^{40} +4.81188 q^{41} -0.873093 q^{42} +9.78199 q^{43} -8.17514 q^{44} -1.00000 q^{45} -5.51766 q^{47} +3.24547 q^{48} -1.06814 q^{49} -0.358480 q^{50} +0.243632 q^{51} +10.7705 q^{52} +4.31404 q^{53} -0.358480 q^{54} -4.36825 q^{55} +3.38017 q^{56} +3.07550 q^{57} -0.922653 q^{58} -5.19738 q^{59} +1.87149 q^{60} +9.38738 q^{61} -1.33758 q^{62} +2.43554 q^{63} -5.07883 q^{64} +5.75501 q^{65} -1.56593 q^{66} +1.67416 q^{67} -0.455955 q^{68} +0.873093 q^{70} -11.2396 q^{71} +1.38785 q^{72} +6.99643 q^{73} +1.67192 q^{74} +1.00000 q^{75} -5.75577 q^{76} +10.6390 q^{77} +2.06306 q^{78} -6.05110 q^{79} -3.24547 q^{80} +1.00000 q^{81} -1.72496 q^{82} +12.6294 q^{83} -4.55809 q^{84} -0.243632 q^{85} -3.50665 q^{86} +2.57379 q^{87} +6.06249 q^{88} -12.7019 q^{89} +0.358480 q^{90} -14.0166 q^{91} +3.73126 q^{93} +1.97797 q^{94} -3.07550 q^{95} -3.93914 q^{96} +14.5901 q^{97} +0.382908 q^{98} +4.36825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9} - 11 q^{10} - 9 q^{11} + 31 q^{12} + 18 q^{13} - 11 q^{14} - 25 q^{15} + 39 q^{16} + 8 q^{17} + 11 q^{18} - 11 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) $ 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9 - 11 * q^10 - 9 * q^11 + 31 * q^12 + 18 * q^13 - 11 * q^14 - 25 * q^15 + 39 * q^16 + 8 * q^17 + 11 * q^18 - 11 * q^19 - 31 * q^20 - 7 * q^21 - 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 + 5 * q^28 + 33 * q^29 - 11 * q^30 + 14 * q^31 + 77 * q^32 - 9 * q^33 - 13 * q^34 + 7 * q^35 + 31 * q^36 - 4 * q^37 + 23 * q^38 + 18 * q^39 - 33 * q^40 + 56 * q^41 - 11 * q^42 + 4 * q^43 + 18 * q^44 - 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 + 8 * q^51 + 49 * q^52 - 2 * q^53 + 11 * q^54 + 9 * q^55 - 33 * q^56 - 11 * q^57 + 26 * q^58 + 61 * q^59 - 31 * q^60 - 21 * q^61 + 51 * q^62 - 7 * q^63 + 71 * q^64 - 18 * q^65 - 9 * q^66 - 2 * q^67 + 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 + 47 * q^74 + 25 * q^75 + 8 * q^76 + 49 * q^77 + 35 * q^78 - 35 * q^79 - 39 * q^80 + 25 * q^81 + 35 * q^82 + 26 * q^83 + 5 * q^84 - 8 * q^85 + 33 * q^86 + 33 * q^87 - 9 * q^88 + 7 * q^89 - 11 * q^90 - 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 + 54 * q^97 + 88 * q^98 - 9 * 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 $

$2$	−0.358480	−0.253484	−0.126742	−	0.991936i	$-0.540452\pi$
$2$	−0.358480	−0.253484	−0.126742	+	0.991936i	$0.540452\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.87149	−0.935746
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.358480	−0.146349
$7$	2.43554	0.920548	0.460274	−	0.887777i	$-0.347751\pi$
$7$	2.43554	0.920548	0.460274	+	0.887777i	$0.347751\pi$
$8$	1.38785	0.490680
$9$	1.00000	0.333333
$10$	0.358480	0.113361
$11$	4.36825	1.31708	0.658538	−	0.752547i	$-0.271175\pi$
$11$	4.36825	1.31708	0.658538	+	0.752547i	$0.271175\pi$
$12$	−1.87149	−0.540253
$13$	−5.75501	−1.59615	−0.798077	−	0.602556i	$-0.794149\pi$
$13$	−5.75501	−1.59615	−0.798077	+	0.602556i	$0.794149\pi$
$14$	−0.873093	−0.233344
$15$	−1.00000	−0.258199
$16$	3.24547	0.811367
$17$	0.243632	0.0590894	0.0295447	−	0.999563i	$-0.490594\pi$
$17$	0.243632	0.0590894	0.0295447	+	0.999563i	$0.490594\pi$
$18$	−0.358480	−0.0844946
$19$	3.07550	0.705567	0.352784	−	0.935705i	$-0.385235\pi$
$19$	3.07550	0.705567	0.352784	+	0.935705i	$0.385235\pi$
$20$	1.87149	0.418478
$21$	2.43554	0.531478
$22$	−1.56593	−0.333857
$23$	0	0
$23$	0	0
$24$	1.38785	0.283294
$25$	1.00000	0.200000
$26$	2.06306	0.404599
$27$	1.00000	0.192450
$28$	−4.55809	−0.861399
$29$	2.57379	0.477941	0.238971	−	0.971027i	$-0.423190\pi$
$29$	2.57379	0.477941	0.238971	+	0.971027i	$0.423190\pi$
$30$	0.358480	0.0654492
$31$	3.73126	0.670155	0.335077	−	0.942191i	$-0.391238\pi$
$31$	3.73126	0.670155	0.335077	+	0.942191i	$0.391238\pi$
$32$	−3.93914	−0.696348
$33$	4.36825	0.760414
$34$	−0.0873372	−0.0149782
$35$	−2.43554	−0.411681
$36$	−1.87149	−0.311915
$37$	−4.66392	−0.766744	−0.383372	−	0.923594i	$-0.625237\pi$
$37$	−4.66392	−0.766744	−0.383372	+	0.923594i	$0.625237\pi$
$38$	−1.10250	−0.178850
$39$	−5.75501	−0.921540
$40$	−1.38785	−0.219439
$41$	4.81188	0.751490	0.375745	−	0.926723i	$-0.377387\pi$
$41$	4.81188	0.751490	0.375745	+	0.926723i	$0.377387\pi$
$42$	−0.873093	−0.134721
$43$	9.78199	1.49174	0.745869	−	0.666092i	$-0.232034\pi$
$43$	9.78199	1.49174	0.745869	+	0.666092i	$0.232034\pi$
$44$	−8.17514	−1.23245
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−5.51766	−0.804833	−0.402416	−	0.915457i	$-0.631830\pi$
$47$	−5.51766	−0.804833	−0.402416	+	0.915457i	$0.631830\pi$
$48$	3.24547	0.468443
$49$	−1.06814	−0.152592
$50$	−0.358480	−0.0506967
$51$	0.243632	0.0341153
$52$	10.7705	1.49359
$53$	4.31404	0.592579	0.296289	−	0.955098i	$-0.404251\pi$
$53$	4.31404	0.592579	0.296289	+	0.955098i	$0.404251\pi$
$54$	−0.358480	−0.0487830
$55$	−4.36825	−0.589014
$56$	3.38017	0.451694
$57$	3.07550	0.407360
$58$	−0.922653	−0.121150
$59$	−5.19738	−0.676641	−0.338321	−	0.941031i	$-0.609859\pi$
$59$	−5.19738	−0.676641	−0.338321	+	0.941031i	$0.609859\pi$
$60$	1.87149	0.241609
$61$	9.38738	1.20193	0.600965	−	0.799275i	$-0.294783\pi$
$61$	9.38738	1.20193	0.600965	+	0.799275i	$0.294783\pi$
$62$	−1.33758	−0.169873
$63$	2.43554	0.306849
$64$	−5.07883	−0.634854
$65$	5.75501	0.713821
$66$	−1.56593	−0.192753
$67$	1.67416	0.204531	0.102266	−	0.994757i	$-0.467391\pi$
$67$	1.67416	0.204531	0.102266	+	0.994757i	$0.467391\pi$
$68$	−0.455955	−0.0552927
$69$	0	0
$70$	0.873093	0.104355
$71$	−11.2396	−1.33390	−0.666950	−	0.745103i	$-0.732401\pi$
$71$	−11.2396	−1.33390	−0.666950	+	0.745103i	$0.732401\pi$
$72$	1.38785	0.163560
$73$	6.99643	0.818870	0.409435	−	0.912339i	$-0.365726\pi$
$73$	6.99643	0.818870	0.409435	+	0.912339i	$0.365726\pi$
$74$	1.67192	0.194357
$75$	1.00000	0.115470
$76$	−5.75577	−0.660232
$77$	10.6390	1.21243
$78$	2.06306	0.233595
$79$	−6.05110	−0.680802	−0.340401	−	0.940280i	$-0.610563\pi$
$79$	−6.05110	−0.680802	−0.340401	+	0.940280i	$0.610563\pi$
$80$	−3.24547	−0.362854
$81$	1.00000	0.111111
$82$	−1.72496	−0.190490
$83$	12.6294	1.38626	0.693129	−	0.720813i	$-0.256232\pi$
$83$	12.6294	1.38626	0.693129	+	0.720813i	$0.256232\pi$
$84$	−4.55809	−0.497329
$85$	−0.243632	−0.0264256
$86$	−3.50665	−0.378131
$87$	2.57379	0.275940
$88$	6.06249	0.646263
$89$	−12.7019	−1.34640	−0.673198	−	0.739463i	$-0.735080\pi$
$89$	−12.7019	−1.34640	−0.673198	+	0.739463i	$0.735080\pi$
$90$	0.358480	0.0377871
$91$	−14.0166	−1.46934
$92$	0	0
$93$	3.73126	0.386914
$94$	1.97797	0.204012
$95$	−3.07550	−0.315539
$96$	−3.93914	−0.402037
$97$	14.5901	1.48140	0.740700	−	0.671836i	$-0.234494\pi$
$97$	14.5901	1.48140	0.740700	+	0.671836i	$0.234494\pi$
$98$	0.382908	0.0386796
$99$	4.36825	0.439025
$100$	−1.87149	−0.187149
$101$	12.6691	1.26062	0.630309	−	0.776344i	$-0.282928\pi$
$101$	12.6691	1.26062	0.630309	+	0.776344i	$0.282928\pi$
$102$	−0.0873372	−0.00864767
$103$	−15.3298	−1.51049	−0.755244	−	0.655444i	$-0.772482\pi$
$103$	−15.3298	−1.51049	−0.755244	+	0.655444i	$0.772482\pi$
$104$	−7.98711	−0.783201
$105$	−2.43554	−0.237684
$106$	−1.54650	−0.150209
$107$	−0.156053	−0.0150862	−0.00754312	−	0.999972i	$-0.502401\pi$
$107$	−0.156053	−0.0150862	−0.00754312	+	0.999972i	$0.502401\pi$
$108$	−1.87149	−0.180084
$109$	−14.7059	−1.40857	−0.704284	−	0.709918i	$-0.748732\pi$
$109$	−14.7059	−1.40857	−0.704284	+	0.709918i	$0.748732\pi$
$110$	1.56593	0.149306
$111$	−4.66392	−0.442680
$112$	7.90446	0.746902
$113$	−1.92458	−0.181049	−0.0905247	−	0.995894i	$-0.528854\pi$
$113$	−1.92458	−0.181049	−0.0905247	+	0.995894i	$0.528854\pi$
$114$	−1.10250	−0.103259
$115$	0	0
$116$	−4.81683	−0.447232
$117$	−5.75501	−0.532051
$118$	1.86316	0.171517
$119$	0.593375	0.0543946
$120$	−1.38785	−0.126693
$121$	8.08159	0.734690
$122$	−3.36519	−0.304670
$123$	4.81188	0.433873
$124$	−6.98303	−0.627094
$125$	−1.00000	−0.0894427
$126$	−0.873093	−0.0777813
$127$	10.2076	0.905775	0.452888	−	0.891568i	$-0.350394\pi$
$127$	10.2076	0.905775	0.452888	+	0.891568i	$0.350394\pi$
$128$	9.69894	0.857273
$129$	9.78199	0.861256
$130$	−2.06306	−0.180942
$131$	−5.87457	−0.513264	−0.256632	−	0.966509i	$-0.582613\pi$
$131$	−5.87457	−0.513264	−0.256632	+	0.966509i	$0.582613\pi$
$132$	−8.17514	−0.711555
$133$	7.49050	0.649509
$134$	−0.600153	−0.0518453
$135$	−1.00000	−0.0860663
$136$	0.338125	0.0289940
$137$	10.2776	0.878074	0.439037	−	0.898469i	$-0.355320\pi$
$137$	10.2776	0.878074	0.439037	+	0.898469i	$0.355320\pi$
$138$	0	0
$139$	19.8111	1.68036	0.840180	−	0.542308i	$-0.182450\pi$
$139$	19.8111	1.68036	0.840180	+	0.542308i	$0.182450\pi$
$140$	4.55809	0.385229
$141$	−5.51766	−0.464671
$142$	4.02919	0.338122
$143$	−25.1393	−2.10226
$144$	3.24547	0.270456
$145$	−2.57379	−0.213742
$146$	−2.50808	−0.207570
$147$	−1.06814	−0.0880990
$148$	8.72850	0.717478
$149$	−22.3546	−1.83136	−0.915679	−	0.401910i	$-0.868347\pi$
$149$	−22.3546	−1.83136	−0.915679	+	0.401910i	$0.868347\pi$
$150$	−0.358480	−0.0292698
$151$	−4.80658	−0.391154	−0.195577	−	0.980688i	$-0.562658\pi$
$151$	−4.80658	−0.391154	−0.195577	+	0.980688i	$0.562658\pi$
$152$	4.26834	0.346208
$153$	0.243632	0.0196965
$154$	−3.81389	−0.307332
$155$	−3.73126	−0.299702
$156$	10.7705	0.862327
$157$	−11.3949	−0.909409	−0.454705	−	0.890642i	$-0.650255\pi$
$157$	−11.3949	−0.909409	−0.454705	+	0.890642i	$0.650255\pi$
$158$	2.16920	0.172572
$159$	4.31404	0.342126
$160$	3.93914	0.311416
$161$	0	0
$162$	−0.358480	−0.0281649
$163$	20.1351	1.57710	0.788551	−	0.614969i	$-0.210832\pi$
$163$	20.1351	1.57710	0.788551	+	0.614969i	$0.210832\pi$
$164$	−9.00540	−0.703204
$165$	−4.36825	−0.340068
$166$	−4.52739	−0.351394
$167$	1.00297	0.0776122	0.0388061	−	0.999247i	$-0.487645\pi$
$167$	1.00297	0.0776122	0.0388061	+	0.999247i	$0.487645\pi$
$168$	3.38017	0.260786
$169$	20.1202	1.54771
$170$	0.0873372	0.00669846
$171$	3.07550	0.235189
$172$	−18.3069	−1.39589
$173$	19.4713	1.48038	0.740188	−	0.672400i	$-0.234736\pi$
$173$	19.4713	1.48038	0.740188	+	0.672400i	$0.234736\pi$
$174$	−0.922653	−0.0699462
$175$	2.43554	0.184110
$176$	14.1770	1.06863
$177$	−5.19738	−0.390659
$178$	4.55337	0.341289
$179$	0.452652	0.0338328	0.0169164	−	0.999857i	$-0.494615\pi$
$179$	0.452652	0.0338328	0.0169164	+	0.999857i	$0.494615\pi$
$180$	1.87149	0.139493
$181$	−6.77197	−0.503357	−0.251678	−	0.967811i	$-0.580983\pi$
$181$	−6.77197	−0.503357	−0.251678	+	0.967811i	$0.580983\pi$
$182$	5.02466	0.372453
$183$	9.38738	0.693935
$184$	0	0
$185$	4.66392	0.342899
$186$	−1.33758	−0.0980764
$187$	1.06424	0.0778253
$188$	10.3263	0.753119
$189$	2.43554	0.177159
$190$	1.10250	0.0799841
$191$	10.9469	0.792086	0.396043	−	0.918232i	$-0.370383\pi$
$191$	10.9469	0.792086	0.396043	+	0.918232i	$0.370383\pi$
$192$	−5.07883	−0.366533
$193$	1.12334	0.0808598	0.0404299	−	0.999182i	$-0.487127\pi$
$193$	1.12334	0.0808598	0.0404299	+	0.999182i	$0.487127\pi$
$194$	−5.23026	−0.375511
$195$	5.75501	0.412125
$196$	1.99902	0.142787
$197$	−18.3172	−1.30505	−0.652524	−	0.757768i	$-0.726290\pi$
$197$	−18.3172	−1.30505	−0.652524	+	0.757768i	$0.726290\pi$
$198$	−1.56593	−0.111286
$199$	16.9093	1.19867	0.599336	−	0.800498i	$-0.295431\pi$
$199$	16.9093	1.19867	0.599336	+	0.800498i	$0.295431\pi$
$200$	1.38785	0.0981360
$201$	1.67416	0.118086
$202$	−4.54160	−0.319546
$203$	6.26858	0.439968
$204$	−0.455955	−0.0319232
$205$	−4.81188	−0.336076
$206$	5.49542	0.382884
$207$	0	0
$208$	−18.6777	−1.29507
$209$	13.4345	0.929286
$210$	0.873093	0.0602491
$211$	−17.2386	−1.18675	−0.593377	−	0.804925i	$-0.702206\pi$
$211$	−17.2386	−1.18675	−0.593377	+	0.804925i	$0.702206\pi$
$212$	−8.07369	−0.554503
$213$	−11.2396	−0.770127
$214$	0.0559420	0.00382411
$215$	−9.78199	−0.667126
$216$	1.38785	0.0944314
$217$	9.08764	0.616909
$218$	5.27177	0.357049
$219$	6.99643	0.472775
$220$	8.17514	0.551168
$221$	−1.40210	−0.0943158
$222$	1.67192	0.112212
$223$	−5.28009	−0.353581	−0.176790	−	0.984249i	$-0.556572\pi$
$223$	−5.28009	−0.353581	−0.176790	+	0.984249i	$0.556572\pi$
$224$	−9.59393	−0.641022
$225$	1.00000	0.0666667
$226$	0.689924	0.0458931
$227$	23.0024	1.52672	0.763361	−	0.645973i	$-0.223548\pi$
$227$	23.0024	1.52672	0.763361	+	0.645973i	$0.223548\pi$
$228$	−5.75577	−0.381185
$229$	−3.87336	−0.255959	−0.127979	−	0.991777i	$-0.540849\pi$
$229$	−3.87336	−0.255959	−0.127979	+	0.991777i	$0.540849\pi$
$230$	0	0
$231$	10.6390	0.699998
$232$	3.57205	0.234516
$233$	17.1361	1.12262	0.561310	−	0.827605i	$-0.310297\pi$
$233$	17.1361	1.12262	0.561310	+	0.827605i	$0.310297\pi$
$234$	2.06306	0.134866
$235$	5.51766	0.359932
$236$	9.72685	0.633164
$237$	−6.05110	−0.393061
$238$	−0.212713	−0.0137881
$239$	29.2812	1.89405	0.947023	−	0.321165i	$-0.104074\pi$
$239$	29.2812	1.89405	0.947023	+	0.321165i	$0.104074\pi$
$240$	−3.24547	−0.209494
$241$	−28.4319	−1.83146	−0.915729	−	0.401797i	$-0.868386\pi$
$241$	−28.4319	−1.83146	−0.915729	+	0.401797i	$0.868386\pi$
$242$	−2.89709	−0.186232
$243$	1.00000	0.0641500
$244$	−17.5684	−1.12470
$245$	1.06814	0.0682412
$246$	−1.72496	−0.109980
$247$	−17.6995	−1.12619
$248$	5.17844	0.328831
$249$	12.6294	0.800357
$250$	0.358480	0.0226723
$251$	25.0551	1.58147	0.790733	−	0.612162i	$-0.209700\pi$
$251$	25.0551	1.58147	0.790733	+	0.612162i	$0.209700\pi$
$252$	−4.55809	−0.287133
$253$	0	0
$254$	−3.65921	−0.229599
$255$	−0.243632	−0.0152568
$256$	6.68078	0.417549
$257$	−7.07424	−0.441279	−0.220639	−	0.975355i	$-0.570814\pi$
$257$	−7.07424	−0.441279	−0.220639	+	0.975355i	$0.570814\pi$
$258$	−3.50665	−0.218314
$259$	−11.3592	−0.705825
$260$	−10.7705	−0.667956
$261$	2.57379	0.159314
$262$	2.10592	0.130104
$263$	−3.35421	−0.206830	−0.103415	−	0.994638i	$-0.532977\pi$
$263$	−3.35421	−0.206830	−0.103415	+	0.994638i	$0.532977\pi$
$264$	6.06249	0.373120
$265$	−4.31404	−0.265009
$266$	−2.68519	−0.164640
$267$	−12.7019	−0.777342
$268$	−3.13318	−0.191389
$269$	−4.33125	−0.264081	−0.132040	−	0.991244i	$-0.542153\pi$
$269$	−4.33125	−0.264081	−0.132040	+	0.991244i	$0.542153\pi$
$270$	0.358480	0.0218164
$271$	19.1737	1.16472	0.582359	−	0.812932i	$-0.302130\pi$
$271$	19.1737	1.16472	0.582359	+	0.812932i	$0.302130\pi$
$272$	0.790699	0.0479432
$273$	−14.0166	−0.848321
$274$	−3.68431	−0.222578
$275$	4.36825	0.263415
$276$	0	0
$277$	−24.8789	−1.49483	−0.747413	−	0.664360i	$-0.768704\pi$
$277$	−24.8789	−1.49483	−0.747413	+	0.664360i	$0.768704\pi$
$278$	−7.10190	−0.425944
$279$	3.73126	0.223385
$280$	−3.38017	−0.202004
$281$	−10.2163	−0.609452	−0.304726	−	0.952440i	$-0.598565\pi$
$281$	−10.2163	−0.609452	−0.304726	+	0.952440i	$0.598565\pi$
$282$	1.97797	0.117786
$283$	−9.24893	−0.549792	−0.274896	−	0.961474i	$-0.588643\pi$
$283$	−9.24893	−0.549792	−0.274896	+	0.961474i	$0.588643\pi$
$284$	21.0349	1.24819
$285$	−3.07550	−0.182177
$286$	9.01195	0.532888
$287$	11.7195	0.691782
$288$	−3.93914	−0.232116
$289$	−16.9406	−0.996508
$290$	0.922653	0.0541801
$291$	14.5901	0.855286
$292$	−13.0938	−0.766254
$293$	6.50885	0.380251	0.190125	−	0.981760i	$-0.439111\pi$
$293$	6.50885	0.380251	0.190125	+	0.981760i	$0.439111\pi$
$294$	0.382908	0.0223317
$295$	5.19738	0.302603
$296$	−6.47284	−0.376226
$297$	4.36825	0.253471
$298$	8.01367	0.464219
$299$	0	0
$300$	−1.87149	−0.108051
$301$	23.8244	1.37322
$302$	1.72306	0.0991511
$303$	12.6691	0.727818
$304$	9.98142	0.572474
$305$	−9.38738	−0.537520
$306$	−0.0873372	−0.00499273
$307$	22.5740	1.28836	0.644182	−	0.764872i	$-0.277198\pi$
$307$	22.5740	1.28836	0.644182	+	0.764872i	$0.277198\pi$
$308$	−19.9109	−1.13453
$309$	−15.3298	−0.872080
$310$	1.33758	0.0759696
$311$	−7.54997	−0.428119	−0.214060	−	0.976821i	$-0.568669\pi$
$311$	−7.54997	−0.428119	−0.214060	+	0.976821i	$0.568669\pi$
$312$	−7.98711	−0.452181
$313$	−13.9365	−0.787736	−0.393868	−	0.919167i	$-0.628863\pi$
$313$	−13.9365	−0.787736	−0.393868	+	0.919167i	$0.628863\pi$
$314$	4.08483	0.230520
$315$	−2.43554	−0.137227
$316$	11.3246	0.637058
$317$	23.0604	1.29520	0.647600	−	0.761980i	$-0.275773\pi$
$317$	23.0604	1.29520	0.647600	+	0.761980i	$0.275773\pi$
$318$	−1.54650	−0.0867232
$319$	11.2430	0.629485
$320$	5.07883	0.283915
$321$	−0.156053	−0.00871004
$322$	0	0
$323$	0.749289	0.0416916
$324$	−1.87149	−0.103972
$325$	−5.75501	−0.319231
$326$	−7.21803	−0.399770
$327$	−14.7059	−0.813237
$328$	6.67818	0.368741
$329$	−13.4385	−0.740887
$330$	1.56593	0.0862016
$331$	21.8562	1.20133	0.600664	−	0.799502i	$-0.294903\pi$
$331$	21.8562	1.20133	0.600664	+	0.799502i	$0.294903\pi$
$332$	−23.6359	−1.29719
$333$	−4.66392	−0.255581
$334$	−0.359545	−0.0196734
$335$	−1.67416	−0.0914691
$336$	7.90446	0.431224
$337$	−1.92572	−0.104901	−0.0524504	−	0.998624i	$-0.516703\pi$
$337$	−1.92572	−0.104901	−0.0524504	+	0.998624i	$0.516703\pi$
$338$	−7.21268	−0.392318
$339$	−1.92458	−0.104529
$340$	0.455955	0.0247276
$341$	16.2991	0.882645
$342$	−1.10250	−0.0596166
$343$	−19.6503	−1.06102
$344$	13.5760	0.731966
$345$	0	0
$346$	−6.98007	−0.375251
$347$	15.5633	0.835481	0.417740	−	0.908566i	$-0.362822\pi$
$347$	15.5633	0.835481	0.417740	+	0.908566i	$0.362822\pi$
$348$	−4.81683	−0.258209
$349$	−23.4235	−1.25383	−0.626914	−	0.779088i	$-0.715682\pi$
$349$	−23.4235	−1.25383	−0.626914	+	0.779088i	$0.715682\pi$
$350$	−0.873093	−0.0466688
$351$	−5.75501	−0.307180
$352$	−17.2071	−0.917144
$353$	16.0649	0.855050	0.427525	−	0.904004i	$-0.359386\pi$
$353$	16.0649	0.855050	0.427525	+	0.904004i	$0.359386\pi$
$354$	1.86316	0.0990257
$355$	11.2396	0.596538
$356$	23.7714	1.25988
$357$	0.593375	0.0314048
$358$	−0.162267	−0.00857605
$359$	−3.69663	−0.195101	−0.0975503	−	0.995231i	$-0.531101\pi$
$359$	−3.69663	−0.195101	−0.0975503	+	0.995231i	$0.531101\pi$
$360$	−1.38785	−0.0731463
$361$	−9.54132	−0.502175
$362$	2.42762	0.127593
$363$	8.08159	0.424174
$364$	26.2319	1.37492
$365$	−6.99643	−0.366210
$366$	−3.36519	−0.175901
$367$	27.3442	1.42736	0.713678	−	0.700474i	$-0.247028\pi$
$367$	27.3442	1.42736	0.713678	+	0.700474i	$0.247028\pi$
$368$	0	0
$369$	4.81188	0.250497
$370$	−1.67192	−0.0869192
$371$	10.5070	0.545497
$372$	−6.98303	−0.362053
$373$	−1.97252	−0.102133	−0.0510667	−	0.998695i	$-0.516262\pi$
$373$	−1.97252	−0.102133	−0.0510667	+	0.998695i	$0.516262\pi$
$374$	−0.381510	−0.0197274
$375$	−1.00000	−0.0516398
$376$	−7.65769	−0.394915
$377$	−14.8122	−0.762868
$378$	−0.873093	−0.0449070
$379$	16.2454	0.834471	0.417235	−	0.908798i	$-0.362999\pi$
$379$	16.2454	0.834471	0.417235	+	0.908798i	$0.362999\pi$
$380$	5.75577	0.295265
$381$	10.2076	0.522950
$382$	−3.92423	−0.200781
$383$	22.4939	1.14938	0.574692	−	0.818370i	$-0.305122\pi$
$383$	22.4939	1.14938	0.574692	+	0.818370i	$0.305122\pi$
$384$	9.69894	0.494947
$385$	−10.6390	−0.542216
$386$	−0.402695	−0.0204966
$387$	9.78199	0.497246
$388$	−27.3052	−1.38621
$389$	−4.37282	−0.221711	−0.110855	−	0.993837i	$-0.535359\pi$
$389$	−4.37282	−0.221711	−0.110855	+	0.993837i	$0.535359\pi$
$390$	−2.06306	−0.104467
$391$	0	0
$392$	−1.48243	−0.0748738
$393$	−5.87457	−0.296333
$394$	6.56635	0.330808
$395$	6.05110	0.304464
$396$	−8.17514	−0.410816
$397$	17.7483	0.890763	0.445381	−	0.895341i	$-0.353068\pi$
$397$	17.7483	0.890763	0.445381	+	0.895341i	$0.353068\pi$
$398$	−6.06166	−0.303844
$399$	7.49050	0.374994
$400$	3.24547	0.162273
$401$	38.1675	1.90599	0.952996	−	0.302983i	$-0.0979824\pi$
$401$	38.1675	1.90599	0.952996	+	0.302983i	$0.0979824\pi$
$402$	−0.600153	−0.0299329
$403$	−21.4735	−1.06967
$404$	−23.7100	−1.17962
$405$	−1.00000	−0.0496904
$406$	−2.24716	−0.111525
$407$	−20.3732	−1.00986
$408$	0.338125	0.0167397
$409$	−38.1341	−1.88561	−0.942805	−	0.333345i	$-0.891823\pi$
$409$	−38.1341	−1.88561	−0.942805	+	0.333345i	$0.891823\pi$
$410$	1.72496	0.0851899
$411$	10.2776	0.506956
$412$	28.6896	1.41343
$413$	−12.6584	−0.622880
$414$	0	0
$415$	−12.6294	−0.619954
$416$	22.6698	1.11148
$417$	19.8111	0.970156
$418$	−4.81601	−0.235559
$419$	−33.0734	−1.61574	−0.807871	−	0.589359i	$-0.799380\pi$
$419$	−33.0734	−1.61574	−0.807871	+	0.589359i	$0.799380\pi$
$420$	4.55809	0.222412
$421$	1.53236	0.0746827	0.0373414	−	0.999303i	$-0.488111\pi$
$421$	1.53236	0.0746827	0.0373414	+	0.999303i	$0.488111\pi$
$422$	6.17969	0.300823
$423$	−5.51766	−0.268278
$424$	5.98725	0.290767
$425$	0.243632	0.0118179
$426$	4.02919	0.195215
$427$	22.8633	1.10643
$428$	0.292052	0.0141169
$429$	−25.1393	−1.21374
$430$	3.50665	0.169106
$431$	8.17481	0.393767	0.196883	−	0.980427i	$-0.436918\pi$
$431$	8.17481	0.393767	0.196883	+	0.980427i	$0.436918\pi$
$432$	3.24547	0.156148
$433$	25.4801	1.22450	0.612248	−	0.790666i	$-0.290266\pi$
$433$	25.4801	1.22450	0.612248	+	0.790666i	$0.290266\pi$
$434$	−3.25774	−0.156376
$435$	−2.57379	−0.123404
$436$	27.5220	1.31806
$437$	0	0
$438$	−2.50808	−0.119841
$439$	30.3631	1.44915	0.724575	−	0.689196i	$-0.242036\pi$
$439$	30.3631	1.44915	0.724575	+	0.689196i	$0.242036\pi$
$440$	−6.06249	−0.289018
$441$	−1.06814	−0.0508640
$442$	0.502627	0.0239075
$443$	37.5097	1.78214	0.891071	−	0.453865i	$-0.149955\pi$
$443$	37.5097	1.78214	0.891071	+	0.453865i	$0.149955\pi$
$444$	8.72850	0.414236
$445$	12.7019	0.602126
$446$	1.89281	0.0896270
$447$	−22.3546	−1.05734
$448$	−12.3697	−0.584413
$449$	38.4137	1.81286	0.906428	−	0.422361i	$-0.138799\pi$
$449$	38.4137	1.81286	0.906428	+	0.422361i	$0.138799\pi$
$450$	−0.358480	−0.0168989
$451$	21.0195	0.989770
$452$	3.60184	0.169416
$453$	−4.80658	−0.225833
$454$	−8.24589	−0.386999
$455$	14.0166	0.657107
$456$	4.26834	0.199883
$457$	−9.82748	−0.459710	−0.229855	−	0.973225i	$-0.573825\pi$
$457$	−9.82748	−0.459710	−0.229855	+	0.973225i	$0.573825\pi$
$458$	1.38852	0.0648813
$459$	0.243632	0.0113718
$460$	0	0
$461$	26.3896	1.22909	0.614543	−	0.788883i	$-0.289340\pi$
$461$	26.3896	1.22909	0.614543	+	0.788883i	$0.289340\pi$
$462$	−3.81389	−0.177438
$463$	34.7839	1.61654	0.808272	−	0.588809i	$-0.200403\pi$
$463$	34.7839	1.61654	0.808272	+	0.588809i	$0.200403\pi$
$464$	8.35316	0.387786
$465$	−3.73126	−0.173033
$466$	−6.14294	−0.284566
$467$	31.0681	1.43766	0.718831	−	0.695185i	$-0.244677\pi$
$467$	31.0681	1.43766	0.718831	+	0.695185i	$0.244677\pi$
$468$	10.7705	0.497865
$469$	4.07748	0.188281
$470$	−1.97797	−0.0912369
$471$	−11.3949	−0.525048
$472$	−7.21320	−0.332014
$473$	42.7301	1.96473
$474$	2.16920	0.0996346
$475$	3.07550	0.141113
$476$	−1.11050	−0.0508996
$477$	4.31404	0.197526
$478$	−10.4967	−0.480110
$479$	−18.0284	−0.823737	−0.411869	−	0.911243i	$-0.635124\pi$
$479$	−18.0284	−0.823737	−0.411869	+	0.911243i	$0.635124\pi$
$480$	3.93914	0.179796
$481$	26.8409	1.22384
$482$	10.1923	0.464244
$483$	0	0
$484$	−15.1246	−0.687484
$485$	−14.5901	−0.662502
$486$	−0.358480	−0.0162610
$487$	11.8058	0.534974	0.267487	−	0.963562i	$-0.413807\pi$
$487$	11.8058	0.534974	0.267487	+	0.963562i	$0.413807\pi$
$488$	13.0283	0.589763
$489$	20.1351	0.910540
$490$	−0.382908	−0.0172980
$491$	27.9703	1.26228	0.631142	−	0.775668i	$-0.282587\pi$
$491$	27.9703	1.26228	0.631142	+	0.775668i	$0.282587\pi$
$492$	−9.00540	−0.405995
$493$	0.627058	0.0282413
$494$	6.34493	0.285472
$495$	−4.36825	−0.196338
$496$	12.1097	0.543741
$497$	−27.3746	−1.22792
$498$	−4.52739	−0.202877
$499$	24.7991	1.11016	0.555080	−	0.831797i	$-0.312688\pi$
$499$	24.7991	1.11016	0.555080	+	0.831797i	$0.312688\pi$
$500$	1.87149	0.0836957
$501$	1.00297	0.0448094
$502$	−8.98176	−0.400876
$503$	2.20613	0.0983665	0.0491832	−	0.998790i	$-0.484338\pi$
$503$	2.20613	0.0983665	0.0491832	+	0.998790i	$0.484338\pi$
$504$	3.38017	0.150565
$505$	−12.6691	−0.563766
$506$	0	0
$507$	20.1202	0.893568
$508$	−19.1034	−0.847576
$509$	−12.9144	−0.572421	−0.286210	−	0.958167i	$-0.592396\pi$
$509$	−12.9144	−0.572421	−0.286210	+	0.958167i	$0.592396\pi$
$510$	0.0873372	0.00386736
$511$	17.0401	0.753809
$512$	−21.7928	−0.963115
$513$	3.07550	0.135787
$514$	2.53597	0.111857
$515$	15.3298	0.675511
$516$	−18.3069	−0.805917
$517$	−24.1025	−1.06003
$518$	4.07204	0.178915
$519$	19.4713	0.854696
$520$	7.98711	0.350258
$521$	−33.9986	−1.48951	−0.744753	−	0.667341i	$-0.767432\pi$
$521$	−33.9986	−1.48951	−0.744753	+	0.667341i	$0.767432\pi$
$522$	−0.922653	−0.0403834
$523$	4.59708	0.201016	0.100508	−	0.994936i	$-0.467953\pi$
$523$	4.59708	0.201016	0.100508	+	0.994936i	$0.467953\pi$
$524$	10.9942	0.480285
$525$	2.43554	0.106296
$526$	1.20242	0.0524280
$527$	0.909055	0.0395990
$528$	14.1770	0.616975
$529$	0	0
$530$	1.54650	0.0671755
$531$	−5.19738	−0.225547
$532$	−14.0184	−0.607775
$533$	−27.6924	−1.19949
$534$	4.55337	0.197043
$535$	0.156053	0.00674677
$536$	2.32349	0.100359
$537$	0.452652	0.0195334
$538$	1.55267	0.0669402
$539$	−4.66592	−0.200975
$540$	1.87149	0.0805362
$541$	−1.35711	−0.0583467	−0.0291734	−	0.999574i	$-0.509287\pi$
$541$	−1.35711	−0.0583467	−0.0291734	+	0.999574i	$0.509287\pi$
$542$	−6.87338	−0.295237
$543$	−6.77197	−0.290613
$544$	−0.959700	−0.0411468
$545$	14.7059	0.629931
$546$	5.02466	0.215036
$547$	−18.3707	−0.785474	−0.392737	−	0.919651i	$-0.628472\pi$
$547$	−18.3707	−0.785474	−0.392737	+	0.919651i	$0.628472\pi$
$548$	−19.2344	−0.821655
$549$	9.38738	0.400644
$550$	−1.56593	−0.0667715
$551$	7.91569	0.337220
$552$	0	0
$553$	−14.7377	−0.626711
$554$	8.91857	0.378914
$555$	4.66392	0.197973
$556$	−37.0764	−1.57239
$557$	20.2332	0.857307	0.428654	−	0.903469i	$-0.358988\pi$
$557$	20.2332	0.857307	0.428654	+	0.903469i	$0.358988\pi$
$558$	−1.33758	−0.0566244
$559$	−56.2955	−2.38104
$560$	−7.90446	−0.334025
$561$	1.06424	0.0449324
$562$	3.66233	0.154486
$563$	−25.3512	−1.06843	−0.534214	−	0.845349i	$-0.679392\pi$
$563$	−25.3512	−1.06843	−0.534214	+	0.845349i	$0.679392\pi$
$564$	10.3263	0.434814
$565$	1.92458	0.0809678
$566$	3.31556	0.139363
$567$	2.43554	0.102283
$568$	−15.5990	−0.654518
$569$	−25.0578	−1.05048	−0.525238	−	0.850955i	$-0.676024\pi$
$569$	−25.0578	−1.05048	−0.525238	+	0.850955i	$0.676024\pi$
$570$	1.10250	0.0461788
$571$	21.0971	0.882885	0.441443	−	0.897290i	$-0.354467\pi$
$571$	21.0971	0.882885	0.441443	+	0.897290i	$0.354467\pi$
$572$	47.0480	1.96718
$573$	10.9469	0.457311
$574$	−4.20122	−0.175355
$575$	0	0
$576$	−5.07883	−0.211618
$577$	39.6939	1.65248	0.826239	−	0.563320i	$-0.190476\pi$
$577$	39.6939	1.65248	0.826239	+	0.563320i	$0.190476\pi$
$578$	6.07288	0.252599
$579$	1.12334	0.0466844
$580$	4.81683	0.200008
$581$	30.7595	1.27612
$582$	−5.23026	−0.216801
$583$	18.8448	0.780472
$584$	9.71001	0.401803
$585$	5.75501	0.237940
$586$	−2.33329	−0.0963874
$587$	40.2992	1.66333	0.831663	−	0.555280i	$-0.187389\pi$
$587$	40.2992	1.66333	0.831663	+	0.555280i	$0.187389\pi$
$588$	1.99902	0.0824383
$589$	11.4755	0.472839
$590$	−1.86316	−0.0767049
$591$	−18.3172	−0.753469
$592$	−15.1366	−0.622111
$593$	−3.30776	−0.135833	−0.0679167	−	0.997691i	$-0.521635\pi$
$593$	−3.30776	−0.135833	−0.0679167	+	0.997691i	$0.521635\pi$
$594$	−1.56593	−0.0642509
$595$	−0.593375	−0.0243260
$596$	41.8364	1.71369
$597$	16.9093	0.692053
$598$	0	0
$599$	18.6014	0.760034	0.380017	−	0.924979i	$-0.375918\pi$
$599$	18.6014	0.760034	0.380017	+	0.924979i	$0.375918\pi$
$600$	1.38785	0.0566588
$601$	−30.4199	−1.24085	−0.620427	−	0.784264i	$-0.713041\pi$
$601$	−30.4199	−1.24085	−0.620427	+	0.784264i	$0.713041\pi$
$602$	−8.54058	−0.348088
$603$	1.67416	0.0681771
$604$	8.99547	0.366020
$605$	−8.08159	−0.328564
$606$	−4.54160	−0.184490
$607$	−5.04798	−0.204891	−0.102446	−	0.994739i	$-0.532667\pi$
$607$	−5.04798	−0.204891	−0.102446	+	0.994739i	$0.532667\pi$
$608$	−12.1148	−0.491321
$609$	6.26858	0.254016
$610$	3.36519	0.136253
$611$	31.7542	1.28464
$612$	−0.455955	−0.0184309
$613$	22.2103	0.897067	0.448534	−	0.893766i	$-0.351946\pi$
$613$	22.2103	0.897067	0.448534	+	0.893766i	$0.351946\pi$
$614$	−8.09232	−0.326579
$615$	−4.81188	−0.194034
$616$	14.7654	0.594916
$617$	25.8134	1.03921	0.519605	−	0.854406i	$-0.326079\pi$
$617$	25.8134	1.03921	0.519605	+	0.854406i	$0.326079\pi$
$618$	5.49542	0.221058
$619$	1.09155	0.0438730	0.0219365	−	0.999759i	$-0.493017\pi$
$619$	1.09155	0.0438730	0.0219365	+	0.999759i	$0.493017\pi$
$620$	6.98303	0.280445
$621$	0	0
$622$	2.70651	0.108521
$623$	−30.9359	−1.23942
$624$	−18.6777	−0.747706
$625$	1.00000	0.0400000
$626$	4.99595	0.199678
$627$	13.4345	0.536524
$628$	21.3254	0.850976
$629$	−1.13628	−0.0453065
$630$	0.873093	0.0347848
$631$	41.4198	1.64890	0.824448	−	0.565938i	$-0.191486\pi$
$631$	41.4198	1.64890	0.824448	+	0.565938i	$0.191486\pi$
$632$	−8.39804	−0.334056
$633$	−17.2386	−0.685173
$634$	−8.26669	−0.328312
$635$	−10.2076	−0.405075
$636$	−8.07369	−0.320143
$637$	6.14718	0.243560
$638$	−4.03038	−0.159564
$639$	−11.2396	−0.444633
$640$	−9.69894	−0.383384
$641$	−22.8918	−0.904171	−0.452085	−	0.891975i	$-0.649320\pi$
$641$	−22.8918	−0.904171	−0.452085	+	0.891975i	$0.649320\pi$
$642$	0.0559420	0.00220785
$643$	−14.1854	−0.559417	−0.279708	−	0.960085i	$-0.590238\pi$
$643$	−14.1854	−0.559417	−0.279708	+	0.960085i	$0.590238\pi$
$644$	0	0
$645$	−9.78199	−0.385165
$646$	−0.268605	−0.0105681
$647$	3.90531	0.153534	0.0767669	−	0.997049i	$-0.475540\pi$
$647$	3.90531	0.153534	0.0767669	+	0.997049i	$0.475540\pi$
$648$	1.38785	0.0545200
$649$	−22.7034	−0.891188
$650$	2.06306	0.0809198
$651$	9.08764	0.356173
$652$	−37.6827	−1.47577
$653$	1.55233	0.0607475	0.0303737	−	0.999539i	$-0.490330\pi$
$653$	1.55233	0.0607475	0.0303737	+	0.999539i	$0.490330\pi$
$654$	5.27177	0.206142
$655$	5.87457	0.229539
$656$	15.6168	0.609734
$657$	6.99643	0.272957
$658$	4.81742	0.187803
$659$	−11.0466	−0.430313	−0.215156	−	0.976580i	$-0.569026\pi$
$659$	−11.0466	−0.430313	−0.215156	+	0.976580i	$0.569026\pi$
$660$	8.17514	0.318217
$661$	−8.91816	−0.346876	−0.173438	−	0.984845i	$-0.555488\pi$
$661$	−8.91816	−0.346876	−0.173438	+	0.984845i	$0.555488\pi$
$662$	−7.83502	−0.304517
$663$	−1.40210	−0.0544532
$664$	17.5278	0.680209
$665$	−7.49050	−0.290469
$666$	1.67192	0.0647857
$667$	0	0
$668$	−1.87705	−0.0726253
$669$	−5.28009	−0.204140
$670$	0.600153	0.0231859
$671$	41.0064	1.58303
$672$	−9.59393	−0.370094
$673$	−13.3250	−0.513642	−0.256821	−	0.966459i	$-0.582675\pi$
$673$	−13.3250	−0.513642	−0.256821	+	0.966459i	$0.582675\pi$
$674$	0.690333	0.0265906
$675$	1.00000	0.0384900
$676$	−37.6547	−1.44826
$677$	9.56405	0.367576	0.183788	−	0.982966i	$-0.441164\pi$
$677$	9.56405	0.367576	0.183788	+	0.982966i	$0.441164\pi$
$678$	0.689924	0.0264964
$679$	35.5348	1.36370
$680$	−0.338125	−0.0129665
$681$	23.0024	0.881453
$682$	−5.84290	−0.223736
$683$	−37.2215	−1.42424	−0.712120	−	0.702058i	$-0.752265\pi$
$683$	−37.2215	−1.42424	−0.712120	+	0.702058i	$0.752265\pi$
$684$	−5.75577	−0.220077
$685$	−10.2776	−0.392687
$686$	7.04424	0.268950
$687$	−3.87336	−0.147778
$688$	31.7471	1.21035
$689$	−24.8273	−0.945847
$690$	0	0
$691$	5.50408	0.209385	0.104693	−	0.994505i	$-0.466614\pi$
$691$	5.50408	0.209385	0.104693	+	0.994505i	$0.466614\pi$
$692$	−36.4404	−1.38526
$693$	10.6390	0.404144
$694$	−5.57913	−0.211781
$695$	−19.8111	−0.751479
$696$	3.57205	0.135398
$697$	1.17233	0.0444051
$698$	8.39684	0.317825
$699$	17.1361	0.648145
$700$	−4.55809	−0.172280
$701$	27.2799	1.03035	0.515174	−	0.857085i	$-0.327727\pi$
$701$	27.2799	1.03035	0.515174	+	0.857085i	$0.327727\pi$
$702$	2.06306	0.0778651
$703$	−14.3439	−0.540990
$704$	−22.1856	−0.836151
$705$	5.51766	0.207807
$706$	−5.75895	−0.216741
$707$	30.8560	1.16046
$708$	9.72685	0.365558
$709$	20.0339	0.752389	0.376195	−	0.926541i	$-0.377232\pi$
$709$	20.0339	0.752389	0.376195	+	0.926541i	$0.377232\pi$
$710$	−4.02919	−0.151213
$711$	−6.05110	−0.226934
$712$	−17.6283	−0.660649
$713$	0	0
$714$	−0.212713	−0.00796059
$715$	25.1393	0.940157
$716$	−0.847134	−0.0316589
$717$	29.2812	1.09353
$718$	1.32517	0.0494548
$719$	−18.8220	−0.701941	−0.350971	−	0.936387i	$-0.614148\pi$
$719$	−18.8220	−0.701941	−0.350971	+	0.936387i	$0.614148\pi$
$720$	−3.24547	−0.120951
$721$	−37.3363	−1.39048
$722$	3.42037	0.127293
$723$	−28.4319	−1.05739
$724$	12.6737	0.471014
$725$	2.57379	0.0955883
$726$	−2.89709	−0.107521
$727$	9.15600	0.339577	0.169789	−	0.985481i	$-0.445692\pi$
$727$	9.15600	0.339577	0.169789	+	0.985481i	$0.445692\pi$
$728$	−19.4529	−0.720973
$729$	1.00000	0.0370370
$730$	2.50808	0.0928282
$731$	2.38320	0.0881460
$732$	−17.5684	−0.649347
$733$	−44.6965	−1.65090	−0.825451	−	0.564474i	$-0.809079\pi$
$733$	−44.6965	−1.65090	−0.825451	+	0.564474i	$0.809079\pi$
$734$	−9.80235	−0.361811
$735$	1.06814	0.0393991
$736$	0	0
$737$	7.31315	0.269383
$738$	−1.72496	−0.0634968
$739$	−1.40814	−0.0517991	−0.0258996	−	0.999665i	$-0.508245\pi$
$739$	−1.40814	−0.0517991	−0.0258996	+	0.999665i	$0.508245\pi$
$740$	−8.72850	−0.320866
$741$	−17.6995	−0.650208
$742$	−3.76656	−0.138275
$743$	−40.1457	−1.47280	−0.736402	−	0.676544i	$-0.763477\pi$
$743$	−40.1457	−1.47280	−0.736402	+	0.676544i	$0.763477\pi$
$744$	5.17844	0.189851
$745$	22.3546	0.819008
$746$	0.707110	0.0258891
$747$	12.6294	0.462086
$748$	−1.99173	−0.0728247
$749$	−0.380074	−0.0138876
$750$	0.358480	0.0130898
$751$	34.6691	1.26509	0.632546	−	0.774522i	$-0.282010\pi$
$751$	34.6691	1.26509	0.632546	+	0.774522i	$0.282010\pi$
$752$	−17.9074	−0.653015
$753$	25.0551	0.913059
$754$	5.30988	0.193375
$755$	4.80658	0.174929
$756$	−4.55809	−0.165776
$757$	−18.8333	−0.684509	−0.342254	−	0.939607i	$-0.611190\pi$
$757$	−18.8333	−0.684509	−0.342254	+	0.939607i	$0.611190\pi$
$758$	−5.82366	−0.211525
$759$	0	0
$760$	−4.26834	−0.154829
$761$	−6.69122	−0.242556	−0.121278	−	0.992619i	$-0.538699\pi$
$761$	−6.69122	−0.242556	−0.121278	+	0.992619i	$0.538699\pi$
$762$	−3.65921	−0.132559
$763$	−35.8168	−1.29665
$764$	−20.4869	−0.741192
$765$	−0.243632	−0.00880853
$766$	−8.06361	−0.291350
$767$	29.9110	1.08002
$768$	6.68078	0.241072
$769$	−17.2361	−0.621551	−0.310776	−	0.950483i	$-0.600589\pi$
$769$	−17.2361	−0.621551	−0.310776	+	0.950483i	$0.600589\pi$
$770$	3.81389	0.137443
$771$	−7.07424	−0.254773
$772$	−2.10232	−0.0756643
$773$	38.9240	1.40000	0.699999	−	0.714144i	$-0.253184\pi$
$773$	38.9240	1.40000	0.699999	+	0.714144i	$0.253184\pi$
$774$	−3.50665	−0.126044
$775$	3.73126	0.134031
$776$	20.2489	0.726893
$777$	−11.3592	−0.407508
$778$	1.56757	0.0562001
$779$	14.7989	0.530227
$780$	−10.7705	−0.385644
$781$	−49.0975	−1.75685
$782$	0	0
$783$	2.57379	0.0919799
$784$	−3.46662	−0.123808
$785$	11.3949	0.406700
$786$	2.10592	0.0751156
$787$	2.63419	0.0938986	0.0469493	−	0.998897i	$-0.485050\pi$
$787$	2.63419	0.0938986	0.0469493	+	0.998897i	$0.485050\pi$
$788$	34.2805	1.22119
$789$	−3.35421	−0.119413
$790$	−2.16920	−0.0771767
$791$	−4.68740	−0.166665
$792$	6.06249	0.215421
$793$	−54.0245	−1.91847
$794$	−6.36242	−0.225794
$795$	−4.31404	−0.153003
$796$	−31.6457	−1.12165
$797$	−1.51945	−0.0538216	−0.0269108	−	0.999638i	$-0.508567\pi$
$797$	−1.51945	−0.0538216	−0.0269108	+	0.999638i	$0.508567\pi$
$798$	−2.68519	−0.0950548
$799$	−1.34428	−0.0475571
$800$	−3.93914	−0.139270
$801$	−12.7019	−0.448798
$802$	−13.6823	−0.483138
$803$	30.5621	1.07851
$804$	−3.13318	−0.110499
$805$	0	0
$806$	7.69781	0.271144
$807$	−4.33125	−0.152467
$808$	17.5828	0.618560
$809$	43.9687	1.54586	0.772928	−	0.634494i	$-0.218791\pi$
$809$	43.9687	1.54586	0.772928	+	0.634494i	$0.218791\pi$
$810$	0.358480	0.0125957
$811$	−33.7672	−1.18573	−0.592864	−	0.805303i	$-0.702003\pi$
$811$	−33.7672	−1.18573	−0.592864	+	0.805303i	$0.702003\pi$
$812$	−11.7316	−0.411698
$813$	19.1737	0.672450
$814$	7.30338	0.255983
$815$	−20.1351	−0.705301
$816$	0.790699	0.0276800
$817$	30.0845	1.05252
$818$	13.6703	0.477971
$819$	−14.0166	−0.489778
$820$	9.00540	0.314482
$821$	10.3581	0.361499	0.180749	−	0.983529i	$-0.442148\pi$
$821$	10.3581	0.361499	0.180749	+	0.983529i	$0.442148\pi$
$822$	−3.68431	−0.128505
$823$	−0.443035	−0.0154432	−0.00772161	−	0.999970i	$-0.502458\pi$
$823$	−0.443035	−0.0154432	−0.00772161	+	0.999970i	$0.502458\pi$
$824$	−21.2755	−0.741166
$825$	4.36825	0.152083
$826$	4.53779	0.157890
$827$	−2.81514	−0.0978922	−0.0489461	−	0.998801i	$-0.515586\pi$
$827$	−2.81514	−0.0978922	−0.0489461	+	0.998801i	$0.515586\pi$
$828$	0	0
$829$	−31.9240	−1.10877	−0.554384	−	0.832261i	$-0.687046\pi$
$829$	−31.9240	−1.10877	−0.554384	+	0.832261i	$0.687046\pi$
$830$	4.52739	0.157148
$831$	−24.8789	−0.863038
$832$	29.2287	1.01332
$833$	−0.260234	−0.00901657
$834$	−7.10190	−0.245919
$835$	−1.00297	−0.0347092
$836$	−25.1426	−0.869576
$837$	3.73126	0.128971
$838$	11.8562	0.409564
$839$	42.2531	1.45874	0.729369	−	0.684120i	$-0.239814\pi$
$839$	42.2531	1.45874	0.729369	+	0.684120i	$0.239814\pi$
$840$	−3.38017	−0.116627
$841$	−22.3756	−0.771572
$842$	−0.549321	−0.0189308
$843$	−10.2163	−0.351867
$844$	32.2619	1.11050
$845$	−20.1202	−0.692155
$846$	1.97797	0.0680040
$847$	19.6830	0.676318
$848$	14.0011	0.480799
$849$	−9.24893	−0.317422
$850$	−0.0873372	−0.00299564
$851$	0	0
$852$	21.0349	0.720644
$853$	−43.8133	−1.50014	−0.750069	−	0.661359i	$-0.769980\pi$
$853$	−43.8133	−1.50014	−0.750069	+	0.661359i	$0.769980\pi$
$854$	−8.19605	−0.280463
$855$	−3.07550	−0.105180
$856$	−0.216579	−0.00740251
$857$	6.15482	0.210245	0.105122	−	0.994459i	$-0.466477\pi$
$857$	6.15482	0.210245	0.105122	+	0.994459i	$0.466477\pi$
$858$	9.01195	0.307663
$859$	−34.4506	−1.17544	−0.587719	−	0.809065i	$-0.699974\pi$
$859$	−34.4506	−1.17544	−0.587719	+	0.809065i	$0.699974\pi$
$860$	18.3069	0.624260
$861$	11.7195	0.399401
$862$	−2.93050	−0.0998134
$863$	−44.5246	−1.51563	−0.757817	−	0.652467i	$-0.773734\pi$
$863$	−44.5246	−1.51563	−0.757817	+	0.652467i	$0.773734\pi$
$864$	−3.93914	−0.134012
$865$	−19.4713	−0.662044
$866$	−9.13411	−0.310390
$867$	−16.9406	−0.575334
$868$	−17.0074	−0.577270
$869$	−26.4327	−0.896669
$870$	0.922653	0.0312809
$871$	−9.63481	−0.326463
$872$	−20.4096	−0.691156
$873$	14.5901	0.493800
$874$	0	0
$875$	−2.43554	−0.0823363
$876$	−13.0938	−0.442397
$877$	8.73143	0.294839	0.147420	−	0.989074i	$-0.452903\pi$
$877$	8.73143	0.294839	0.147420	+	0.989074i	$0.452903\pi$
$878$	−10.8846	−0.367336
$879$	6.50885	0.219538
$880$	−14.1770	−0.477907
$881$	35.8407	1.20751	0.603753	−	0.797172i	$-0.293671\pi$
$881$	35.8407	1.20751	0.603753	+	0.797172i	$0.293671\pi$
$882$	0.382908	0.0128932
$883$	−41.0695	−1.38210	−0.691049	−	0.722808i	$-0.742851\pi$
$883$	−41.0695	−1.38210	−0.691049	+	0.722808i	$0.742851\pi$
$884$	2.62403	0.0882556
$885$	5.19738	0.174708
$886$	−13.4465	−0.451744
$887$	−30.9390	−1.03883	−0.519415	−	0.854522i	$-0.673850\pi$
$887$	−30.9390	−1.03883	−0.519415	+	0.854522i	$0.673850\pi$
$888$	−6.47284	−0.217214
$889$	24.8609	0.833809
$890$	−4.55337	−0.152629
$891$	4.36825	0.146342
$892$	9.88165	0.330862
$893$	−16.9695	−0.567864
$894$	8.01367	0.268017
$895$	−0.452652	−0.0151305
$896$	23.6222	0.789161
$897$	0	0
$898$	−13.7705	−0.459529
$899$	9.60350	0.320295
$900$	−1.87149	−0.0623831
$901$	1.05104	0.0350151
$902$	−7.53507	−0.250890
$903$	23.8244	0.792827
$904$	−2.67104	−0.0888373
$905$	6.77197	0.225108
$906$	1.72306	0.0572449
$907$	17.3031	0.574540	0.287270	−	0.957850i	$-0.407252\pi$
$907$	17.3031	0.574540	0.287270	+	0.957850i	$0.407252\pi$
$908$	−43.0488	−1.42862
$909$	12.6691	0.420206
$910$	−5.02466	−0.166566
$911$	−28.1741	−0.933449	−0.466724	−	0.884403i	$-0.654566\pi$
$911$	−28.1741	−0.933449	−0.466724	+	0.884403i	$0.654566\pi$
$912$	9.98142	0.330518
$913$	55.1684	1.82581
$914$	3.52296	0.116529
$915$	−9.38738	−0.310337
$916$	7.24895	0.239512
$917$	−14.3078	−0.472484
$918$	−0.0873372	−0.00288256
$919$	−31.0178	−1.02318	−0.511591	−	0.859229i	$-0.670944\pi$
$919$	−31.0178	−1.02318	−0.511591	+	0.859229i	$0.670944\pi$
$920$	0	0
$921$	22.5740	0.743838
$922$	−9.46015	−0.311553
$923$	64.6843	2.12911
$924$	−19.9109	−0.655020
$925$	−4.66392	−0.153349
$926$	−12.4693	−0.409768
$927$	−15.3298	−0.503496
$928$	−10.1385	−0.332814
$929$	−13.1852	−0.432594	−0.216297	−	0.976328i	$-0.569398\pi$
$929$	−13.1852	−0.432594	−0.216297	+	0.976328i	$0.569398\pi$
$930$	1.33758	0.0438611
$931$	−3.28507	−0.107664
$932$	−32.0700	−1.05049
$933$	−7.54997	−0.247175
$934$	−11.1373	−0.364424
$935$	−1.06424	−0.0348045
$936$	−7.98711	−0.261067
$937$	−42.2092	−1.37891	−0.689457	−	0.724327i	$-0.742151\pi$
$937$	−42.2092	−1.37891	−0.689457	+	0.724327i	$0.742151\pi$
$938$	−1.46170	−0.0477261
$939$	−13.9365	−0.454799
$940$	−10.3263	−0.336805
$941$	−45.6332	−1.48760	−0.743800	−	0.668402i	$-0.766979\pi$
$941$	−45.6332	−1.48760	−0.743800	+	0.668402i	$0.766979\pi$
$942$	4.08483	0.133091
$943$	0	0
$944$	−16.8679	−0.549004
$945$	−2.43554	−0.0792281
$946$	−15.3179	−0.498028
$947$	−17.8510	−0.580079	−0.290040	−	0.957015i	$-0.593668\pi$
$947$	−17.8510	−0.580079	−0.290040	+	0.957015i	$0.593668\pi$
$948$	11.3246	0.367806
$949$	−40.2645	−1.30704
$950$	−1.10250	−0.0357700
$951$	23.0604	0.747785
$952$	0.823518	0.0266904
$953$	−5.36993	−0.173949	−0.0869746	−	0.996211i	$-0.527720\pi$
$953$	−5.36993	−0.173949	−0.0869746	+	0.996211i	$0.527720\pi$
$954$	−1.54650	−0.0500697
$955$	−10.9469	−0.354232
$956$	−54.7996	−1.77235
$957$	11.2430	0.363434
$958$	6.46281	0.208804
$959$	25.0315	0.808309
$960$	5.07883	0.163919
$961$	−17.0777	−0.550893
$962$	−9.62194	−0.310224
$963$	−0.156053	−0.00502874
$964$	53.2100	1.71378
$965$	−1.12334	−0.0361616
$966$	0	0
$967$	−7.96373	−0.256096	−0.128048	−	0.991768i	$-0.540871\pi$
$967$	−7.96373	−0.256096	−0.128048	+	0.991768i	$0.540871\pi$
$968$	11.2161	0.360498
$969$	0.749289	0.0240706
$970$	5.23026	0.167933
$971$	3.02181	0.0969745	0.0484873	−	0.998824i	$-0.484560\pi$
$971$	3.02181	0.0969745	0.0484873	+	0.998824i	$0.484560\pi$
$972$	−1.87149	−0.0600281
$973$	48.2508	1.54685
$974$	−4.23216	−0.135607
$975$	−5.75501	−0.184308
$976$	30.4664	0.975207
$977$	−29.7411	−0.951502	−0.475751	−	0.879580i	$-0.657824\pi$
$977$	−29.7411	−0.951502	−0.475751	+	0.879580i	$0.657824\pi$
$978$	−7.21803	−0.230807
$979$	−55.4849	−1.77331
$980$	−1.99902	−0.0638564
$981$	−14.7059	−0.469523
$982$	−10.0268	−0.319968
$983$	16.7234	0.533393	0.266697	−	0.963781i	$-0.414068\pi$
$983$	16.7234	0.533393	0.266697	+	0.963781i	$0.414068\pi$
$984$	6.67818	0.212893
$985$	18.3172	0.583635
$986$	−0.224788	−0.00715870
$987$	−13.4385	−0.427751
$988$	33.1245	1.05383
$989$	0	0
$990$	1.56593	0.0497685
$991$	−12.9342	−0.410868	−0.205434	−	0.978671i	$-0.565861\pi$
$991$	−12.9342	−0.410868	−0.205434	+	0.978671i	$0.565861\pi$
$992$	−14.6980	−0.466661
$993$	21.8562	0.693587
$994$	9.81325	0.311257
$995$	−16.9093	−0.536062
$996$	−23.6359	−0.748931
$997$	−8.85083	−0.280309	−0.140154	−	0.990130i	$-0.544760\pi$
$997$	−8.85083	−0.280309	−0.140154	+	0.990130i	$0.544760\pi$
$998$	−8.88998	−0.281407
$999$	−4.66392	−0.147560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bv.1.10		25
23.13	even	11		345.2.m.c.31.4	✓	50
23.16	even	11		345.2.m.c.256.4	yes	50
23.22	odd	2		7935.2.a.bw.1.10		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.c.31.4	✓	50	23.13	even	11
345.2.m.c.256.4	yes	50	23.16	even	11
7935.2.a.bv.1.10		25	1.1	even	1	trivial
7935.2.a.bw.1.10		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)

\(f(q)\)	\(=\)	\(q-0.358480 q^{2} +1.00000 q^{3} -1.87149 q^{4} -1.00000 q^{5} -0.358480 q^{6} +2.43554 q^{7} +1.38785 q^{8} +1.00000 q^{9} +0.358480 q^{10} +4.36825 q^{11} -1.87149 q^{12} -5.75501 q^{13} -0.873093 q^{14} -1.00000 q^{15} +3.24547 q^{16} +0.243632 q^{17} -0.358480 q^{18} +3.07550 q^{19} +1.87149 q^{20} +2.43554 q^{21} -1.56593 q^{22} +1.38785 q^{24} +1.00000 q^{25} +2.06306 q^{26} +1.00000 q^{27} -4.55809 q^{28} +2.57379 q^{29} +0.358480 q^{30} +3.73126 q^{31} -3.93914 q^{32} +4.36825 q^{33} -0.0873372 q^{34} -2.43554 q^{35} -1.87149 q^{36} -4.66392 q^{37} -1.10250 q^{38} -5.75501 q^{39} -1.38785 q^{40} +4.81188 q^{41} -0.873093 q^{42} +9.78199 q^{43} -8.17514 q^{44} -1.00000 q^{45} -5.51766 q^{47} +3.24547 q^{48} -1.06814 q^{49} -0.358480 q^{50} +0.243632 q^{51} +10.7705 q^{52} +4.31404 q^{53} -0.358480 q^{54} -4.36825 q^{55} +3.38017 q^{56} +3.07550 q^{57} -0.922653 q^{58} -5.19738 q^{59} +1.87149 q^{60} +9.38738 q^{61} -1.33758 q^{62} +2.43554 q^{63} -5.07883 q^{64} +5.75501 q^{65} -1.56593 q^{66} +1.67416 q^{67} -0.455955 q^{68} +0.873093 q^{70} -11.2396 q^{71} +1.38785 q^{72} +6.99643 q^{73} +1.67192 q^{74} +1.00000 q^{75} -5.75577 q^{76} +10.6390 q^{77} +2.06306 q^{78} -6.05110 q^{79} -3.24547 q^{80} +1.00000 q^{81} -1.72496 q^{82} +12.6294 q^{83} -4.55809 q^{84} -0.243632 q^{85} -3.50665 q^{86} +2.57379 q^{87} +6.06249 q^{88} -12.7019 q^{89} +0.358480 q^{90} -14.0166 q^{91} +3.73126 q^{93} +1.97797 q^{94} -3.07550 q^{95} -3.93914 q^{96} +14.5901 q^{97} +0.382908 q^{98} +4.36825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 11 q^{2} + 25 q^{3} + 31 q^{4} - 25 q^{5} + 11 q^{6} - 7 q^{7} + 33 q^{8} + 25 q^{9} - 11 q^{10} - 9 q^{11} + 31 q^{12} + 18 q^{13} - 11 q^{14} - 25 q^{15} + 39 q^{16} + 8 q^{17} + 11 q^{18} - 11 q^{19}+ \cdots - 9 q^{99}+O(q^{100}) \) 25 * q + 11 * q^2 + 25 * q^3 + 31 * q^4 - 25 * q^5 + 11 * q^6 - 7 * q^7 + 33 * q^8 + 25 * q^9 - 11 * q^10 - 9 * q^11 + 31 * q^12 + 18 * q^13 - 11 * q^14 - 25 * q^15 + 39 * q^16 + 8 * q^17 + 11 * q^18 - 11 * q^19 - 31 * q^20 - 7 * q^21 - 9 * q^22 + 33 * q^24 + 25 * q^25 + 35 * q^26 + 25 * q^27 + 5 * q^28 + 33 * q^29 - 11 * q^30 + 14 * q^31 + 77 * q^32 - 9 * q^33 - 13 * q^34 + 7 * q^35 + 31 * q^36 - 4 * q^37 + 23 * q^38 + 18 * q^39 - 33 * q^40 + 56 * q^41 - 11 * q^42 + 4 * q^43 + 18 * q^44 - 25 * q^45 + 43 * q^47 + 39 * q^48 + 40 * q^49 + 11 * q^50 + 8 * q^51 + 49 * q^52 - 2 * q^53 + 11 * q^54 + 9 * q^55 - 33 * q^56 - 11 * q^57 + 26 * q^58 + 61 * q^59 - 31 * q^60 - 21 * q^61 + 51 * q^62 - 7 * q^63 + 71 * q^64 - 18 * q^65 - 9 * q^66 - 2 * q^67 + 33 * q^68 + 11 * q^70 + 66 * q^71 + 33 * q^72 + 53 * q^73 + 47 * q^74 + 25 * q^75 + 8 * q^76 + 49 * q^77 + 35 * q^78 - 35 * q^79 - 39 * q^80 + 25 * q^81 + 35 * q^82 + 26 * q^83 + 5 * q^84 - 8 * q^85 + 33 * q^86 + 33 * q^87 - 9 * q^88 + 7 * q^89 - 11 * q^90 - 28 * q^91 + 14 * q^93 + 24 * q^94 + 11 * q^95 + 77 * q^96 + 54 * q^97 + 88 * q^98 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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