LMFDB - Embedded newform 7935.2.a.bp.1.7

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 = [15,0,-15,12,-15,0,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 21x^{13} + 172x^{11} - 696x^{9} + 1466x^{7} - 1583x^{5} + 803x^{3} - 11x^{2} - 143x + 11 $ x^15 - 21x^13 + 172x^11 - 696x^9 + 1466x^7 - 1583x^5 + 803x^3 - 11x^2 - 143x + 11
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.710736$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.710736 q^{2} -1.00000 q^{3} -1.49485 q^{4} -1.00000 q^{5} +0.710736 q^{6} -4.35754 q^{7} +2.48392 q^{8} +1.00000 q^{9} +0.710736 q^{10} +4.62137 q^{11} +1.49485 q^{12} +1.23026 q^{13} +3.09706 q^{14} +1.00000 q^{15} +1.22430 q^{16} -5.04149 q^{17} -0.710736 q^{18} -2.56771 q^{19} +1.49485 q^{20} +4.35754 q^{21} -3.28457 q^{22} -2.48392 q^{24} +1.00000 q^{25} -0.874388 q^{26} -1.00000 q^{27} +6.51389 q^{28} +1.63095 q^{29} -0.710736 q^{30} -9.36706 q^{31} -5.83799 q^{32} -4.62137 q^{33} +3.58317 q^{34} +4.35754 q^{35} -1.49485 q^{36} +7.73627 q^{37} +1.82497 q^{38} -1.23026 q^{39} -2.48392 q^{40} -6.01986 q^{41} -3.09706 q^{42} -1.39371 q^{43} -6.90828 q^{44} -1.00000 q^{45} -7.40920 q^{47} -1.22430 q^{48} +11.9882 q^{49} -0.710736 q^{50} +5.04149 q^{51} -1.83906 q^{52} +4.71764 q^{53} +0.710736 q^{54} -4.62137 q^{55} -10.8238 q^{56} +2.56771 q^{57} -1.15918 q^{58} +8.57843 q^{59} -1.49485 q^{60} -0.607358 q^{61} +6.65751 q^{62} -4.35754 q^{63} +1.70067 q^{64} -1.23026 q^{65} +3.28457 q^{66} +12.0384 q^{67} +7.53629 q^{68} -3.09706 q^{70} +7.68448 q^{71} +2.48392 q^{72} -12.2426 q^{73} -5.49844 q^{74} -1.00000 q^{75} +3.83836 q^{76} -20.1378 q^{77} +0.874388 q^{78} +14.0056 q^{79} -1.22430 q^{80} +1.00000 q^{81} +4.27853 q^{82} +2.54540 q^{83} -6.51389 q^{84} +5.04149 q^{85} +0.990562 q^{86} -1.63095 q^{87} +11.4791 q^{88} +0.225933 q^{89} +0.710736 q^{90} -5.36090 q^{91} +9.36706 q^{93} +5.26599 q^{94} +2.56771 q^{95} +5.83799 q^{96} +16.9069 q^{97} -8.52041 q^{98} +4.62137 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) $ 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * 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 $

$2$	−0.710736	−0.502566	−0.251283	−	0.967914i	$-0.580852\pi$
$2$	−0.710736	−0.502566	−0.251283	+	0.967914i	$0.580852\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.49485	−0.747427
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.710736	0.290157
$7$	−4.35754	−1.64700	−0.823498	−	0.567320i	$-0.807980\pi$
$7$	−4.35754	−1.64700	−0.823498	+	0.567320i	$0.807980\pi$
$8$	2.48392	0.878198
$9$	1.00000	0.333333
$10$	0.710736	0.224754
$11$	4.62137	1.39340	0.696698	−	0.717365i	$-0.254652\pi$
$11$	4.62137	1.39340	0.696698	+	0.717365i	$0.254652\pi$
$12$	1.49485	0.431527
$13$	1.23026	0.341212	0.170606	−	0.985339i	$-0.445427\pi$
$13$	1.23026	0.341212	0.170606	+	0.985339i	$0.445427\pi$
$14$	3.09706	0.827724
$15$	1.00000	0.258199
$16$	1.22430	0.306075
$17$	−5.04149	−1.22274	−0.611370	−	0.791345i	$-0.709381\pi$
$17$	−5.04149	−1.22274	−0.611370	+	0.791345i	$0.709381\pi$
$18$	−0.710736	−0.167522
$19$	−2.56771	−0.589074	−0.294537	−	0.955640i	$-0.595165\pi$
$19$	−2.56771	−0.589074	−0.294537	+	0.955640i	$0.595165\pi$
$20$	1.49485	0.334260
$21$	4.35754	0.950893
$22$	−3.28457	−0.700273
$23$	0	0
$23$	0	0
$24$	−2.48392	−0.507028
$25$	1.00000	0.200000
$26$	−0.874388	−0.171482
$27$	−1.00000	−0.192450
$28$	6.51389	1.23101
$29$	1.63095	0.302861	0.151430	−	0.988468i	$-0.451612\pi$
$29$	1.63095	0.302861	0.151430	+	0.988468i	$0.451612\pi$
$30$	−0.710736	−0.129762
$31$	−9.36706	−1.68237	−0.841187	−	0.540744i	$-0.818143\pi$
$31$	−9.36706	−1.68237	−0.841187	+	0.540744i	$0.818143\pi$
$32$	−5.83799	−1.03202
$33$	−4.62137	−0.804478
$34$	3.58317	0.614508
$35$	4.35754	0.736559
$36$	−1.49485	−0.249142
$37$	7.73627	1.27183	0.635917	−	0.771757i	$-0.280622\pi$
$37$	7.73627	1.27183	0.635917	+	0.771757i	$0.280622\pi$
$38$	1.82497	0.296048
$39$	−1.23026	−0.196999
$40$	−2.48392	−0.392742
$41$	−6.01986	−0.940145	−0.470072	−	0.882628i	$-0.655772\pi$
$41$	−6.01986	−0.940145	−0.470072	+	0.882628i	$0.655772\pi$
$42$	−3.09706	−0.477887
$43$	−1.39371	−0.212539	−0.106270	−	0.994337i	$-0.533891\pi$
$43$	−1.39371	−0.212539	−0.106270	+	0.994337i	$0.533891\pi$
$44$	−6.90828	−1.04146
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−7.40920	−1.08074	−0.540372	−	0.841426i	$-0.681716\pi$
$47$	−7.40920	−1.08074	−0.540372	+	0.841426i	$0.681716\pi$
$48$	−1.22430	−0.176713
$49$	11.9882	1.71259
$50$	−0.710736	−0.100513
$51$	5.04149	0.705950
$52$	−1.83906	−0.255031
$53$	4.71764	0.648018	0.324009	−	0.946054i	$-0.394969\pi$
$53$	4.71764	0.648018	0.324009	+	0.946054i	$0.394969\pi$
$54$	0.710736	0.0967189
$55$	−4.62137	−0.623146
$56$	−10.8238	−1.44639
$57$	2.56771	0.340102
$58$	−1.15918	−0.152208
$59$	8.57843	1.11682	0.558408	−	0.829566i	$-0.311412\pi$
$59$	8.57843	1.11682	0.558408	+	0.829566i	$0.311412\pi$
$60$	−1.49485	−0.192985
$61$	−0.607358	−0.0777643	−0.0388821	−	0.999244i	$-0.512380\pi$
$61$	−0.607358	−0.0777643	−0.0388821	+	0.999244i	$0.512380\pi$
$62$	6.65751	0.845504
$63$	−4.35754	−0.548998
$64$	1.70067	0.212583
$65$	−1.23026	−0.152595
$66$	3.28457	0.404303
$67$	12.0384	1.47073	0.735364	−	0.677672i	$-0.237011\pi$
$67$	12.0384	1.47073	0.735364	+	0.677672i	$0.237011\pi$
$68$	7.53629	0.913910
$69$	0	0
$70$	−3.09706	−0.370169
$71$	7.68448	0.911980	0.455990	−	0.889985i	$-0.349285\pi$
$71$	7.68448	0.911980	0.455990	+	0.889985i	$0.349285\pi$
$72$	2.48392	0.292733
$73$	−12.2426	−1.43289	−0.716444	−	0.697645i	$-0.754231\pi$
$73$	−12.2426	−1.43289	−0.716444	+	0.697645i	$0.754231\pi$
$74$	−5.49844	−0.639181
$75$	−1.00000	−0.115470
$76$	3.83836	0.440290
$77$	−20.1378	−2.29492
$78$	0.874388	0.0990049
$79$	14.0056	1.57575	0.787874	−	0.615837i	$-0.211182\pi$
$79$	14.0056	1.57575	0.787874	+	0.615837i	$0.211182\pi$
$80$	−1.22430	−0.136881
$81$	1.00000	0.111111
$82$	4.27853	0.472485
$83$	2.54540	0.279394	0.139697	−	0.990194i	$-0.455387\pi$
$83$	2.54540	0.279394	0.139697	+	0.990194i	$0.455387\pi$
$84$	−6.51389	−0.710724
$85$	5.04149	0.546826
$86$	0.990562	0.106815
$87$	−1.63095	−0.174857
$88$	11.4791	1.22368
$89$	0.225933	0.0239489	0.0119744	−	0.999928i	$-0.496188\pi$
$89$	0.225933	0.0239489	0.0119744	+	0.999928i	$0.496188\pi$
$90$	0.710736	0.0749181
$91$	−5.36090	−0.561975
$92$	0	0
$93$	9.36706	0.971319
$94$	5.26599	0.543145
$95$	2.56771	0.263442
$96$	5.83799	0.595837
$97$	16.9069	1.71664	0.858319	−	0.513117i	$-0.171509\pi$
$97$	16.9069	1.71664	0.858319	+	0.513117i	$0.171509\pi$
$98$	−8.52041	−0.860692
$99$	4.62137	0.464465
$100$	−1.49485	−0.149485
$101$	−8.95130	−0.890687	−0.445344	−	0.895360i	$-0.646919\pi$
$101$	−8.95130	−0.890687	−0.445344	+	0.895360i	$0.646919\pi$
$102$	−3.58317	−0.354786
$103$	9.12324	0.898939	0.449470	−	0.893296i	$-0.351613\pi$
$103$	9.12324	0.898939	0.449470	+	0.893296i	$0.351613\pi$
$104$	3.05586	0.299652
$105$	−4.35754	−0.425252
$106$	−3.35300	−0.325672
$107$	−12.3639	−1.19527	−0.597634	−	0.801769i	$-0.703892\pi$
$107$	−12.3639	−1.19527	−0.597634	+	0.801769i	$0.703892\pi$
$108$	1.49485	0.143842
$109$	11.9404	1.14368	0.571839	−	0.820366i	$-0.306230\pi$
$109$	11.9404	1.14368	0.571839	+	0.820366i	$0.306230\pi$
$110$	3.28457	0.313172
$111$	−7.73627	−0.734294
$112$	−5.33494	−0.504104
$113$	−7.67403	−0.721912	−0.360956	−	0.932583i	$-0.617550\pi$
$113$	−7.67403	−0.721912	−0.360956	+	0.932583i	$0.617550\pi$
$114$	−1.82497	−0.170924
$115$	0	0
$116$	−2.43804	−0.226366
$117$	1.23026	0.113737
$118$	−6.09700	−0.561274
$119$	21.9685	2.01385
$120$	2.48392	0.226750
$121$	10.3571	0.941552
$122$	0.431671	0.0390817
$123$	6.01986	0.542793
$124$	14.0024	1.25745
$125$	−1.00000	−0.0894427
$126$	3.09706	0.275908
$127$	−10.4853	−0.930416	−0.465208	−	0.885201i	$-0.654021\pi$
$127$	−10.4853	−0.930416	−0.465208	+	0.885201i	$0.654021\pi$
$128$	10.4673	0.925183
$129$	1.39371	0.122710
$130$	0.874388	0.0766889
$131$	10.0872	0.881322	0.440661	−	0.897673i	$-0.354744\pi$
$131$	10.0872	0.881322	0.440661	+	0.897673i	$0.354744\pi$
$132$	6.90828	0.601289
$133$	11.1889	0.970202
$134$	−8.55614	−0.739138
$135$	1.00000	0.0860663
$136$	−12.5226	−1.07381
$137$	10.2521	0.875897	0.437948	−	0.899000i	$-0.355705\pi$
$137$	10.2521	0.875897	0.437948	+	0.899000i	$0.355705\pi$
$138$	0	0
$139$	13.5229	1.14699	0.573497	−	0.819208i	$-0.305586\pi$
$139$	13.5229	1.14699	0.573497	+	0.819208i	$0.305586\pi$
$140$	−6.51389	−0.550524
$141$	7.40920	0.623968
$142$	−5.46163	−0.458330
$143$	5.68548	0.475443
$144$	1.22430	0.102025
$145$	−1.63095	−0.135443
$146$	8.70125	0.720121
$147$	−11.9882	−0.988767
$148$	−11.5646	−0.950604
$149$	18.7121	1.53296	0.766479	−	0.642269i	$-0.222007\pi$
$149$	18.7121	1.53296	0.766479	+	0.642269i	$0.222007\pi$
$150$	0.710736	0.0580313
$151$	0.520678	0.0423722	0.0211861	−	0.999776i	$-0.493256\pi$
$151$	0.520678	0.0423722	0.0211861	+	0.999776i	$0.493256\pi$
$152$	−6.37799	−0.517323
$153$	−5.04149	−0.407580
$154$	14.3127	1.15335
$155$	9.36706	0.752381
$156$	1.83906	0.147242
$157$	−18.6916	−1.49175	−0.745876	−	0.666085i	$-0.767969\pi$
$157$	−18.6916	−1.49175	−0.745876	+	0.666085i	$0.767969\pi$
$158$	−9.95425	−0.791917
$159$	−4.71764	−0.374134
$160$	5.83799	0.461534
$161$	0	0
$162$	−0.710736	−0.0558407
$163$	−1.13812	−0.0891448	−0.0445724	−	0.999006i	$-0.514193\pi$
$163$	−1.13812	−0.0891448	−0.0445724	+	0.999006i	$0.514193\pi$
$164$	8.99882	0.702690
$165$	4.62137	0.359773
$166$	−1.80911	−0.140414
$167$	10.6798	0.826425	0.413213	−	0.910635i	$-0.364407\pi$
$167$	10.6798	0.826425	0.413213	+	0.910635i	$0.364407\pi$
$168$	10.8238	0.835072
$169$	−11.4865	−0.883574
$170$	−3.58317	−0.274816
$171$	−2.56771	−0.196358
$172$	2.08340	0.158858
$173$	−13.1391	−0.998951	−0.499475	−	0.866328i	$-0.666474\pi$
$173$	−13.1391	−0.998951	−0.499475	+	0.866328i	$0.666474\pi$
$174$	1.15918	0.0878771
$175$	−4.35754	−0.329399
$176$	5.65795	0.426484
$177$	−8.57843	−0.644795
$178$	−0.160579	−0.0120359
$179$	1.58809	0.118700	0.0593498	−	0.998237i	$-0.481097\pi$
$179$	1.58809	0.118700	0.0593498	+	0.998237i	$0.481097\pi$
$180$	1.49485	0.111420
$181$	−14.6924	−1.09208	−0.546039	−	0.837760i	$-0.683865\pi$
$181$	−14.6924	−1.09208	−0.546039	+	0.837760i	$0.683865\pi$
$182$	3.81018	0.282429
$183$	0.607358	0.0448972
$184$	0	0
$185$	−7.73627	−0.568782
$186$	−6.65751	−0.488152
$187$	−23.2986	−1.70376
$188$	11.0757	0.807777
$189$	4.35754	0.316964
$190$	−1.82497	−0.132397
$191$	−1.65098	−0.119460	−0.0597302	−	0.998215i	$-0.519024\pi$
$191$	−1.65098	−0.119460	−0.0597302	+	0.998215i	$0.519024\pi$
$192$	−1.70067	−0.122735
$193$	3.82901	0.275618	0.137809	−	0.990459i	$-0.455994\pi$
$193$	3.82901	0.275618	0.137809	+	0.990459i	$0.455994\pi$
$194$	−12.0164	−0.862724
$195$	1.23026	0.0881005
$196$	−17.9206	−1.28004
$197$	−17.0473	−1.21457	−0.607287	−	0.794483i	$-0.707742\pi$
$197$	−17.0473	−1.21457	−0.607287	+	0.794483i	$0.707742\pi$
$198$	−3.28457	−0.233424
$199$	26.8408	1.90269	0.951346	−	0.308124i	$-0.0997013\pi$
$199$	26.8408	1.90269	0.951346	+	0.308124i	$0.0997013\pi$
$200$	2.48392	0.175640
$201$	−12.0384	−0.849125
$202$	6.36201	0.447629
$203$	−7.10695	−0.498810
$204$	−7.53629	−0.527646
$205$	6.01986	0.420446
$206$	−6.48421	−0.451776
$207$	0	0
$208$	1.50620	0.104436
$209$	−11.8664	−0.820813
$210$	3.09706	0.213717
$211$	16.6549	1.14657	0.573286	−	0.819355i	$-0.305668\pi$
$211$	16.6549	1.14657	0.573286	+	0.819355i	$0.305668\pi$
$212$	−7.05219	−0.484347
$213$	−7.68448	−0.526532
$214$	8.78750	0.600701
$215$	1.39371	0.0950505
$216$	−2.48392	−0.169009
$217$	40.8174	2.77086
$218$	−8.48643	−0.574774
$219$	12.2426	0.827278
$220$	6.90828	0.465756
$221$	−6.20233	−0.417214
$222$	5.49844	0.369031
$223$	25.1581	1.68471	0.842357	−	0.538920i	$-0.181167\pi$
$223$	25.1581	1.68471	0.842357	+	0.538920i	$0.181167\pi$
$224$	25.4393	1.69973
$225$	1.00000	0.0666667
$226$	5.45421	0.362808
$227$	−6.16143	−0.408949	−0.204474	−	0.978872i	$-0.565548\pi$
$227$	−6.16143	−0.408949	−0.204474	+	0.978872i	$0.565548\pi$
$228$	−3.83836	−0.254201
$229$	−2.39666	−0.158376	−0.0791879	−	0.996860i	$-0.525233\pi$
$229$	−2.39666	−0.158376	−0.0791879	+	0.996860i	$0.525233\pi$
$230$	0	0
$231$	20.1378	1.32497
$232$	4.05116	0.265972
$233$	−5.68435	−0.372394	−0.186197	−	0.982512i	$-0.559616\pi$
$233$	−5.68435	−0.372394	−0.186197	+	0.982512i	$0.559616\pi$
$234$	−0.874388	−0.0571605
$235$	7.40920	0.483323
$236$	−12.8235	−0.834740
$237$	−14.0056	−0.909758
$238$	−15.6138	−1.01209
$239$	27.2177	1.76057	0.880283	−	0.474450i	$-0.157353\pi$
$239$	27.2177	1.76057	0.880283	+	0.474450i	$0.157353\pi$
$240$	1.22430	0.0790282
$241$	0.251294	0.0161873	0.00809363	−	0.999967i	$-0.497424\pi$
$241$	0.251294	0.0161873	0.00809363	+	0.999967i	$0.497424\pi$
$242$	−7.36114	−0.473192
$243$	−1.00000	−0.0641500
$244$	0.907912	0.0581231
$245$	−11.9882	−0.765895
$246$	−4.27853	−0.272789
$247$	−3.15895	−0.200999
$248$	−23.2670	−1.47746
$249$	−2.54540	−0.161308
$250$	0.710736	0.0449509
$251$	−3.41912	−0.215813	−0.107906	−	0.994161i	$-0.534415\pi$
$251$	−3.41912	−0.215813	−0.107906	+	0.994161i	$0.534415\pi$
$252$	6.51389	0.410336
$253$	0	0
$254$	7.45225	0.467596
$255$	−5.04149	−0.315710
$256$	−10.8408	−0.677549
$257$	9.42896	0.588162	0.294081	−	0.955780i	$-0.404986\pi$
$257$	9.42896	0.588162	0.294081	+	0.955780i	$0.404986\pi$
$258$	−0.990562	−0.0616697
$259$	−33.7111	−2.09471
$260$	1.83906	0.114053
$261$	1.63095	0.100954
$262$	−7.16933	−0.442923
$263$	−21.2501	−1.31034	−0.655170	−	0.755482i	$-0.727403\pi$
$263$	−21.2501	−1.31034	−0.655170	+	0.755482i	$0.727403\pi$
$264$	−11.4791	−0.706490
$265$	−4.71764	−0.289803
$266$	−7.95236	−0.487590
$267$	−0.225933	−0.0138269
$268$	−17.9957	−1.09926
$269$	−11.3667	−0.693042	−0.346521	−	0.938042i	$-0.612637\pi$
$269$	−11.3667	−0.693042	−0.346521	+	0.938042i	$0.612637\pi$
$270$	−0.710736	−0.0432540
$271$	−20.0189	−1.21606	−0.608030	−	0.793914i	$-0.708040\pi$
$271$	−20.0189	−1.21606	−0.608030	+	0.793914i	$0.708040\pi$
$272$	−6.17229	−0.374250
$273$	5.36090	0.324456
$274$	−7.28654	−0.440196
$275$	4.62137	0.278679
$276$	0	0
$277$	−6.26539	−0.376451	−0.188225	−	0.982126i	$-0.560274\pi$
$277$	−6.26539	−0.376451	−0.188225	+	0.982126i	$0.560274\pi$
$278$	−9.61118	−0.576440
$279$	−9.36706	−0.560791
$280$	10.8238	0.646844
$281$	−5.30226	−0.316306	−0.158153	−	0.987415i	$-0.550554\pi$
$281$	−5.30226	−0.316306	−0.158153	+	0.987415i	$0.550554\pi$
$282$	−5.26599	−0.313585
$283$	−9.41670	−0.559765	−0.279882	−	0.960034i	$-0.590295\pi$
$283$	−9.41670	−0.559765	−0.279882	+	0.960034i	$0.590295\pi$
$284$	−11.4872	−0.681639
$285$	−2.56771	−0.152098
$286$	−4.04087	−0.238942
$287$	26.2318	1.54841
$288$	−5.83799	−0.344007
$289$	8.41660	0.495094
$290$	1.15918	0.0680693
$291$	−16.9069	−0.991101
$292$	18.3009	1.07098
$293$	−12.1417	−0.709323	−0.354662	−	0.934995i	$-0.615404\pi$
$293$	−12.1417	−0.709323	−0.354662	+	0.934995i	$0.615404\pi$
$294$	8.52041	0.496920
$295$	−8.57843	−0.499456
$296$	19.2163	1.11692
$297$	−4.62137	−0.268159
$298$	−13.2994	−0.770413
$299$	0	0
$300$	1.49485	0.0863055
$301$	6.07316	0.350051
$302$	−0.370065	−0.0212948
$303$	8.95130	0.514239
$304$	−3.14365	−0.180301
$305$	0.607358	0.0347772
$306$	3.58317	0.204836
$307$	−12.9179	−0.737263	−0.368631	−	0.929576i	$-0.620174\pi$
$307$	−12.9179	−0.737263	−0.368631	+	0.929576i	$0.620174\pi$
$308$	30.1031	1.71528
$309$	−9.12324	−0.519003
$310$	−6.65751	−0.378121
$311$	20.5993	1.16808	0.584041	−	0.811724i	$-0.301471\pi$
$311$	20.5993	1.16808	0.584041	+	0.811724i	$0.301471\pi$
$312$	−3.05586	−0.173004
$313$	3.99270	0.225681	0.112840	−	0.993613i	$-0.464005\pi$
$313$	3.99270	0.225681	0.112840	+	0.993613i	$0.464005\pi$
$314$	13.2848	0.749704
$315$	4.35754	0.245520
$316$	−20.9363	−1.17776
$317$	17.0340	0.956722	0.478361	−	0.878163i	$-0.341231\pi$
$317$	17.0340	0.956722	0.478361	+	0.878163i	$0.341231\pi$
$318$	3.35300	0.188027
$319$	7.53725	0.422005
$320$	−1.70067	−0.0950702
$321$	12.3639	0.690088
$322$	0	0
$323$	12.9451	0.720284
$324$	−1.49485	−0.0830475
$325$	1.23026	0.0682424
$326$	0.808906	0.0448012
$327$	−11.9404	−0.660303
$328$	−14.9529	−0.825633
$329$	32.2859	1.77998
$330$	−3.28457	−0.180810
$331$	−6.50273	−0.357423	−0.178711	−	0.983902i	$-0.557193\pi$
$331$	−6.50273	−0.357423	−0.178711	+	0.983902i	$0.557193\pi$
$332$	−3.80500	−0.208827
$333$	7.73627	0.423945
$334$	−7.59049	−0.415333
$335$	−12.0384	−0.657730
$336$	5.33494	0.291045
$337$	−34.9557	−1.90416	−0.952079	−	0.305854i	$-0.901058\pi$
$337$	−34.9557	−1.90416	−0.952079	+	0.305854i	$0.901058\pi$
$338$	8.16384	0.444054
$339$	7.67403	0.416796
$340$	−7.53629	−0.408713
$341$	−43.2887	−2.34421
$342$	1.82497	0.0986828
$343$	−21.7361	−1.17364
$344$	−3.46187	−0.186652
$345$	0	0
$346$	9.33846	0.502039
$347$	−29.5042	−1.58387	−0.791933	−	0.610608i	$-0.790925\pi$
$347$	−29.5042	−1.58387	−0.791933	+	0.610608i	$0.790925\pi$
$348$	2.43804	0.130693
$349$	−24.4744	−1.31009	−0.655043	−	0.755591i	$-0.727350\pi$
$349$	−24.4744	−1.31009	−0.655043	+	0.755591i	$0.727350\pi$
$350$	3.09706	0.165545
$351$	−1.23026	−0.0656663
$352$	−26.9795	−1.43801
$353$	−27.6347	−1.47084	−0.735422	−	0.677609i	$-0.763016\pi$
$353$	−27.6347	−1.47084	−0.735422	+	0.677609i	$0.763016\pi$
$354$	6.09700	0.324052
$355$	−7.68448	−0.407850
$356$	−0.337737	−0.0179000
$357$	−21.9685	−1.16270
$358$	−1.12871	−0.0596544
$359$	3.59097	0.189524	0.0947620	−	0.995500i	$-0.469791\pi$
$359$	3.59097	0.189524	0.0947620	+	0.995500i	$0.469791\pi$
$360$	−2.48392	−0.130914
$361$	−12.4069	−0.652992
$362$	10.4424	0.548841
$363$	−10.3571	−0.543605
$364$	8.01376	0.420035
$365$	12.2426	0.640807
$366$	−0.431671	−0.0225638
$367$	−23.9262	−1.24894	−0.624468	−	0.781051i	$-0.714684\pi$
$367$	−23.9262	−1.24894	−0.624468	+	0.781051i	$0.714684\pi$
$368$	0	0
$369$	−6.01986	−0.313382
$370$	5.49844	0.285850
$371$	−20.5573	−1.06728
$372$	−14.0024	−0.725990
$373$	12.0133	0.622026	0.311013	−	0.950406i	$-0.399332\pi$
$373$	12.0133	0.622026	0.311013	+	0.950406i	$0.399332\pi$
$374$	16.5591	0.856253
$375$	1.00000	0.0516398
$376$	−18.4039	−0.949106
$377$	2.00649	0.103340
$378$	−3.09706	−0.159296
$379$	−25.5283	−1.31130	−0.655651	−	0.755064i	$-0.727606\pi$
$379$	−25.5283	−1.31130	−0.655651	+	0.755064i	$0.727606\pi$
$380$	−3.83836	−0.196904
$381$	10.4853	0.537176
$382$	1.17341	0.0600367
$383$	−8.05312	−0.411495	−0.205747	−	0.978605i	$-0.565963\pi$
$383$	−8.05312	−0.411495	−0.205747	+	0.978605i	$0.565963\pi$
$384$	−10.4673	−0.534155
$385$	20.1378	1.02632
$386$	−2.72141	−0.138516
$387$	−1.39371	−0.0708465
$388$	−25.2734	−1.28306
$389$	0.536041	0.0271784	0.0135892	−	0.999908i	$-0.495674\pi$
$389$	0.536041	0.0271784	0.0135892	+	0.999908i	$0.495674\pi$
$390$	−0.874388	−0.0442763
$391$	0	0
$392$	29.7776	1.50400
$393$	−10.0872	−0.508832
$394$	12.1162	0.610403
$395$	−14.0056	−0.704696
$396$	−6.90828	−0.347154
$397$	3.81955	0.191698	0.0958490	−	0.995396i	$-0.469443\pi$
$397$	3.81955	0.191698	0.0958490	+	0.995396i	$0.469443\pi$
$398$	−19.0767	−0.956228
$399$	−11.1889	−0.560146
$400$	1.22430	0.0612150
$401$	26.2282	1.30977	0.654887	−	0.755727i	$-0.272716\pi$
$401$	26.2282	1.30977	0.654887	+	0.755727i	$0.272716\pi$
$402$	8.55614	0.426742
$403$	−11.5239	−0.574046
$404$	13.3809	0.665724
$405$	−1.00000	−0.0496904
$406$	5.05116	0.250685
$407$	35.7522	1.77217
$408$	12.5226	0.619963
$409$	−28.4413	−1.40633	−0.703166	−	0.711026i	$-0.748231\pi$
$409$	−28.4413	−1.40633	−0.703166	+	0.711026i	$0.748231\pi$
$410$	−4.27853	−0.211302
$411$	−10.2521	−0.505699
$412$	−13.6379	−0.671892
$413$	−37.3809	−1.83939
$414$	0	0
$415$	−2.54540	−0.124949
$416$	−7.18223	−0.352138
$417$	−13.5229	−0.662217
$418$	8.43384	0.412513
$419$	8.29949	0.405456	0.202728	−	0.979235i	$-0.435019\pi$
$419$	8.29949	0.405456	0.202728	+	0.979235i	$0.435019\pi$
$420$	6.51389	0.317845
$421$	1.98187	0.0965906	0.0482953	−	0.998833i	$-0.484621\pi$
$421$	1.98187	0.0965906	0.0482953	+	0.998833i	$0.484621\pi$
$422$	−11.8372	−0.576228
$423$	−7.40920	−0.360248
$424$	11.7182	0.569088
$425$	−5.04149	−0.244548
$426$	5.46163	0.264617
$427$	2.64659	0.128077
$428$	18.4823	0.893376
$429$	−5.68548	−0.274497
$430$	−0.990562	−0.0477692
$431$	21.4346	1.03247	0.516233	−	0.856448i	$-0.327334\pi$
$431$	21.4346	1.03247	0.516233	+	0.856448i	$0.327334\pi$
$432$	−1.22430	−0.0589042
$433$	24.1689	1.16148	0.580741	−	0.814088i	$-0.302763\pi$
$433$	24.1689	1.16148	0.580741	+	0.814088i	$0.302763\pi$
$434$	−29.0103	−1.39254
$435$	1.63095	0.0781983
$436$	−17.8491	−0.854816
$437$	0	0
$438$	−8.70125	−0.415762
$439$	−18.7336	−0.894104	−0.447052	−	0.894508i	$-0.647526\pi$
$439$	−18.7336	−0.894104	−0.447052	+	0.894508i	$0.647526\pi$
$440$	−11.4791	−0.547245
$441$	11.9882	0.570865
$442$	4.40822	0.209677
$443$	−38.5934	−1.83363	−0.916814	−	0.399315i	$-0.869248\pi$
$443$	−38.5934	−1.83363	−0.916814	+	0.399315i	$0.869248\pi$
$444$	11.5646	0.548832
$445$	−0.225933	−0.0107103
$446$	−17.8808	−0.846680
$447$	−18.7121	−0.885054
$448$	−7.41073	−0.350124
$449$	8.03905	0.379386	0.189693	−	0.981843i	$-0.439251\pi$
$449$	8.03905	0.379386	0.189693	+	0.981843i	$0.439251\pi$
$450$	−0.710736	−0.0335044
$451$	−27.8200	−1.30999
$452$	11.4716	0.539577
$453$	−0.520678	−0.0244636
$454$	4.37915	0.205524
$455$	5.36090	0.251323
$456$	6.37799	0.298677
$457$	14.8564	0.694953	0.347476	−	0.937689i	$-0.387039\pi$
$457$	14.8564	0.694953	0.347476	+	0.937689i	$0.387039\pi$
$458$	1.70339	0.0795943
$459$	5.04149	0.235317
$460$	0	0
$461$	−19.0154	−0.885633	−0.442817	−	0.896612i	$-0.646021\pi$
$461$	−19.0154	−0.885633	−0.442817	+	0.896612i	$0.646021\pi$
$462$	−14.3127	−0.665885
$463$	18.0640	0.839508	0.419754	−	0.907638i	$-0.362116\pi$
$463$	18.0640	0.839508	0.419754	+	0.907638i	$0.362116\pi$
$464$	1.99678	0.0926981
$465$	−9.36706	−0.434387
$466$	4.04007	0.187153
$467$	−0.787020	−0.0364190	−0.0182095	−	0.999834i	$-0.505797\pi$
$467$	−0.787020	−0.0364190	−0.0182095	+	0.999834i	$0.505797\pi$
$468$	−1.83906	−0.0850104
$469$	−52.4579	−2.42228
$470$	−5.26599	−0.242902
$471$	18.6916	0.861263
$472$	21.3081	0.980786
$473$	−6.44087	−0.296152
$474$	9.95425	0.457214
$475$	−2.56771	−0.117815
$476$	−32.8397	−1.50521
$477$	4.71764	0.216006
$478$	−19.3446	−0.884800
$479$	−4.79857	−0.219252	−0.109626	−	0.993973i	$-0.534965\pi$
$479$	−4.79857	−0.219252	−0.109626	+	0.993973i	$0.534965\pi$
$480$	−5.83799	−0.266467
$481$	9.51760	0.433965
$482$	−0.178604	−0.00813517
$483$	0	0
$484$	−15.4823	−0.703742
$485$	−16.9069	−0.767704
$486$	0.710736	0.0322396
$487$	13.7237	0.621881	0.310940	−	0.950429i	$-0.399356\pi$
$487$	13.7237	0.621881	0.310940	+	0.950429i	$0.399356\pi$
$488$	−1.50863	−0.0682924
$489$	1.13812	0.0514678
$490$	8.52041	0.384913
$491$	29.3919	1.32644	0.663218	−	0.748426i	$-0.269190\pi$
$491$	29.3919	1.32644	0.663218	+	0.748426i	$0.269190\pi$
$492$	−8.99882	−0.405698
$493$	−8.22244	−0.370320
$494$	2.24518	0.101015
$495$	−4.62137	−0.207715
$496$	−11.4681	−0.514933
$497$	−33.4854	−1.50203
$498$	1.80911	0.0810679
$499$	−28.8069	−1.28957	−0.644786	−	0.764363i	$-0.723054\pi$
$499$	−28.8069	−1.28957	−0.644786	+	0.764363i	$0.723054\pi$
$500$	1.49485	0.0668519
$501$	−10.6798	−0.477137
$502$	2.43009	0.108460
$503$	35.7496	1.59400	0.796999	−	0.603981i	$-0.206420\pi$
$503$	35.7496	1.59400	0.796999	+	0.603981i	$0.206420\pi$
$504$	−10.8238	−0.482129
$505$	8.95130	0.398328
$506$	0	0
$507$	11.4865	0.510132
$508$	15.6739	0.695419
$509$	27.9504	1.23888	0.619440	−	0.785044i	$-0.287360\pi$
$509$	27.9504	1.23888	0.619440	+	0.785044i	$0.287360\pi$
$510$	3.58317	0.158665
$511$	53.3476	2.35996
$512$	−13.2296	−0.584670
$513$	2.56771	0.113367
$514$	−6.70150	−0.295590
$515$	−9.12324	−0.402018
$516$	−2.08340	−0.0917166
$517$	−34.2407	−1.50590
$518$	23.9597	1.05273
$519$	13.1391	0.576744
$520$	−3.05586	−0.134008
$521$	−11.5528	−0.506135	−0.253068	−	0.967449i	$-0.581440\pi$
$521$	−11.5528	−0.506135	−0.253068	+	0.967449i	$0.581440\pi$
$522$	−1.15918	−0.0507358
$523$	−4.81588	−0.210584	−0.105292	−	0.994441i	$-0.533578\pi$
$523$	−4.81588	−0.210584	−0.105292	+	0.994441i	$0.533578\pi$
$524$	−15.0789	−0.658725
$525$	4.35754	0.190179
$526$	15.1032	0.658532
$527$	47.2239	2.05711
$528$	−5.65795	−0.246230
$529$	0	0
$530$	3.35300	0.145645
$531$	8.57843	0.372272
$532$	−16.7258	−0.725155
$533$	−7.40598	−0.320789
$534$	0.160579	0.00694892
$535$	12.3639	0.534540
$536$	29.9025	1.29159
$537$	−1.58809	−0.0685312
$538$	8.07874	0.348299
$539$	55.4017	2.38632
$540$	−1.49485	−0.0643283
$541$	32.8792	1.41359	0.706794	−	0.707419i	$-0.250141\pi$
$541$	32.8792	1.41359	0.706794	+	0.707419i	$0.250141\pi$
$542$	14.2281	0.611150
$543$	14.6924	0.630511
$544$	29.4322	1.26189
$545$	−11.9404	−0.511468
$546$	−3.81018	−0.163061
$547$	−19.4302	−0.830774	−0.415387	−	0.909645i	$-0.636354\pi$
$547$	−19.4302	−0.830774	−0.415387	+	0.909645i	$0.636354\pi$
$548$	−15.3254	−0.654669
$549$	−0.607358	−0.0259214
$550$	−3.28457	−0.140055
$551$	−4.18782	−0.178407
$552$	0	0
$553$	−61.0298	−2.59525
$554$	4.45304	0.189191
$555$	7.73627	0.328386
$556$	−20.2147	−0.857295
$557$	9.97514	0.422660	0.211330	−	0.977415i	$-0.432220\pi$
$557$	9.97514	0.422660	0.211330	+	0.977415i	$0.432220\pi$
$558$	6.65751	0.281835
$559$	−1.71463	−0.0725210
$560$	5.33494	0.225442
$561$	23.2986	0.983667
$562$	3.76850	0.158965
$563$	43.6138	1.83810	0.919050	−	0.394140i	$-0.128957\pi$
$563$	43.6138	1.83810	0.919050	+	0.394140i	$0.128957\pi$
$564$	−11.0757	−0.466370
$565$	7.67403	0.322849
$566$	6.69278	0.281319
$567$	−4.35754	−0.182999
$568$	19.0876	0.800898
$569$	−17.4593	−0.731930	−0.365965	−	0.930629i	$-0.619261\pi$
$569$	−17.4593	−0.731930	−0.365965	+	0.930629i	$0.619261\pi$
$570$	1.82497	0.0764394
$571$	−27.1394	−1.13575	−0.567874	−	0.823116i	$-0.692234\pi$
$571$	−27.1394	−1.13575	−0.567874	+	0.823116i	$0.692234\pi$
$572$	−8.49896	−0.355359
$573$	1.65098	0.0689705
$574$	−18.6439	−0.778180
$575$	0	0
$576$	1.70067	0.0708612
$577$	−11.4540	−0.476837	−0.238419	−	0.971162i	$-0.576629\pi$
$577$	−11.4540	−0.476837	−0.238419	+	0.971162i	$0.576629\pi$
$578$	−5.98198	−0.248818
$579$	−3.82901	−0.159128
$580$	2.43804	0.101234
$581$	−11.0917	−0.460160
$582$	12.0164	0.498094
$583$	21.8020	0.902946
$584$	−30.4096	−1.25836
$585$	−1.23026	−0.0508649
$586$	8.62951	0.356482
$587$	−0.407382	−0.0168145	−0.00840723	−	0.999965i	$-0.502676\pi$
$587$	−0.407382	−0.0168145	−0.00840723	+	0.999965i	$0.502676\pi$
$588$	17.9206	0.739031
$589$	24.0519	0.991042
$590$	6.09700	0.251009
$591$	17.0473	0.701234
$592$	9.47152	0.389277
$593$	13.7698	0.565458	0.282729	−	0.959200i	$-0.408760\pi$
$593$	13.7698	0.565458	0.282729	+	0.959200i	$0.408760\pi$
$594$	3.28457	0.134768
$595$	−21.9685	−0.900620
$596$	−27.9719	−1.14578
$597$	−26.8408	−1.09852
$598$	0	0
$599$	−18.4867	−0.755348	−0.377674	−	0.925939i	$-0.623276\pi$
$599$	−18.4867	−0.755348	−0.377674	+	0.925939i	$0.623276\pi$
$600$	−2.48392	−0.101406
$601$	−2.70538	−0.110355	−0.0551775	−	0.998477i	$-0.517572\pi$
$601$	−2.70538	−0.110355	−0.0551775	+	0.998477i	$0.517572\pi$
$602$	−4.31641	−0.175924
$603$	12.0384	0.490243
$604$	−0.778339	−0.0316701
$605$	−10.3571	−0.421075
$606$	−6.36201	−0.258439
$607$	−25.6085	−1.03942	−0.519708	−	0.854344i	$-0.673959\pi$
$607$	−25.6085	−1.03942	−0.519708	+	0.854344i	$0.673959\pi$
$608$	14.9903	0.607936
$609$	7.10695	0.287988
$610$	−0.431671	−0.0174779
$611$	−9.11523	−0.368763
$612$	7.53629	0.304637
$613$	20.4529	0.826085	0.413043	−	0.910712i	$-0.364466\pi$
$613$	20.4529	0.826085	0.413043	+	0.910712i	$0.364466\pi$
$614$	9.18121	0.370523
$615$	−6.01986	−0.242744
$616$	−50.0207	−2.01539
$617$	29.1790	1.17470	0.587351	−	0.809332i	$-0.300171\pi$
$617$	29.1790	1.17470	0.587351	+	0.809332i	$0.300171\pi$
$618$	6.48421	0.260833
$619$	30.1589	1.21219	0.606093	−	0.795393i	$-0.292736\pi$
$619$	30.1589	1.21219	0.606093	+	0.795393i	$0.292736\pi$
$620$	−14.0024	−0.562350
$621$	0	0
$622$	−14.6407	−0.587038
$623$	−0.984512	−0.0394437
$624$	−1.50620	−0.0602964
$625$	1.00000	0.0400000
$626$	−2.83775	−0.113419
$627$	11.8664	0.473897
$628$	27.9412	1.11498
$629$	−39.0023	−1.55512
$630$	−3.09706	−0.123390
$631$	−14.7710	−0.588023	−0.294011	−	0.955802i	$-0.594990\pi$
$631$	−14.7710	−0.588023	−0.294011	+	0.955802i	$0.594990\pi$
$632$	34.7886	1.38382
$633$	−16.6549	−0.661974
$634$	−12.1066	−0.480816
$635$	10.4853	0.416095
$636$	7.05219	0.279638
$637$	14.7485	0.584358
$638$	−5.35699	−0.212085
$639$	7.68448	0.303993
$640$	−10.4673	−0.413755
$641$	44.7372	1.76701	0.883506	−	0.468421i	$-0.155177\pi$
$641$	44.7372	1.76701	0.883506	+	0.468421i	$0.155177\pi$
$642$	−8.78750	−0.346815
$643$	−3.20427	−0.126364	−0.0631821	−	0.998002i	$-0.520125\pi$
$643$	−3.20427	−0.126364	−0.0631821	+	0.998002i	$0.520125\pi$
$644$	0	0
$645$	−1.39371	−0.0548774
$646$	−9.20054	−0.361990
$647$	−12.5957	−0.495188	−0.247594	−	0.968864i	$-0.579640\pi$
$647$	−12.5957	−0.495188	−0.247594	+	0.968864i	$0.579640\pi$
$648$	2.48392	0.0975775
$649$	39.6441	1.55617
$650$	−0.874388	−0.0342963
$651$	−40.8174	−1.59976
$652$	1.70133	0.0666293
$653$	9.44203	0.369495	0.184748	−	0.982786i	$-0.440853\pi$
$653$	9.44203	0.369495	0.184748	+	0.982786i	$0.440853\pi$
$654$	8.48643	0.331846
$655$	−10.0872	−0.394139
$656$	−7.37012	−0.287755
$657$	−12.2426	−0.477629
$658$	−22.9467	−0.894557
$659$	−39.3544	−1.53303	−0.766515	−	0.642226i	$-0.778011\pi$
$659$	−39.3544	−1.53303	−0.766515	+	0.642226i	$0.778011\pi$
$660$	−6.90828	−0.268904
$661$	−21.9285	−0.852919	−0.426459	−	0.904507i	$-0.640239\pi$
$661$	−21.9285	−0.852919	−0.426459	+	0.904507i	$0.640239\pi$
$662$	4.62172	0.179628
$663$	6.20233	0.240878
$664$	6.32256	0.245363
$665$	−11.1889	−0.433887
$666$	−5.49844	−0.213060
$667$	0	0
$668$	−15.9647	−0.617693
$669$	−25.1581	−0.972670
$670$	8.55614	0.330553
$671$	−2.80683	−0.108356
$672$	−25.4393	−0.981341
$673$	−15.2650	−0.588422	−0.294211	−	0.955741i	$-0.595057\pi$
$673$	−15.2650	−0.588422	−0.294211	+	0.955741i	$0.595057\pi$
$674$	24.8442	0.956965
$675$	−1.00000	−0.0384900
$676$	17.1706	0.660408
$677$	4.06918	0.156391	0.0781957	−	0.996938i	$-0.475084\pi$
$677$	4.06918	0.156391	0.0781957	+	0.996938i	$0.475084\pi$
$678$	−5.45421	−0.209468
$679$	−73.6726	−2.82729
$680$	12.5226	0.480221
$681$	6.16143	0.236107
$682$	30.7668	1.17812
$683$	14.1616	0.541877	0.270938	−	0.962597i	$-0.412666\pi$
$683$	14.1616	0.541877	0.270938	+	0.962597i	$0.412666\pi$
$684$	3.83836	0.146763
$685$	−10.2521	−0.391713
$686$	15.4486	0.589831
$687$	2.39666	0.0914383
$688$	−1.70632	−0.0650530
$689$	5.80392	0.221112
$690$	0	0
$691$	−34.9938	−1.33123	−0.665614	−	0.746297i	$-0.731830\pi$
$691$	−34.9938	−1.33123	−0.665614	+	0.746297i	$0.731830\pi$
$692$	19.6411	0.746643
$693$	−20.1378	−0.764972
$694$	20.9697	0.795997
$695$	−13.5229	−0.512951
$696$	−4.05116	−0.153559
$697$	30.3491	1.14955
$698$	17.3949	0.658405
$699$	5.68435	0.215002
$700$	6.51389	0.246202
$701$	26.9532	1.01801	0.509005	−	0.860764i	$-0.330014\pi$
$701$	26.9532	1.01801	0.509005	+	0.860764i	$0.330014\pi$
$702$	0.874388	0.0330016
$703$	−19.8645	−0.749205
$704$	7.85942	0.296213
$705$	−7.40920	−0.279047
$706$	19.6409	0.739197
$707$	39.0056	1.46696
$708$	12.8235	0.481937
$709$	14.5892	0.547907	0.273954	−	0.961743i	$-0.411669\pi$
$709$	14.5892	0.547907	0.273954	+	0.961743i	$0.411669\pi$
$710$	5.46163	0.204971
$711$	14.0056	0.525249
$712$	0.561199	0.0210318
$713$	0	0
$714$	15.6138	0.584331
$715$	−5.68548	−0.212625
$716$	−2.37397	−0.0887193
$717$	−27.2177	−1.01646
$718$	−2.55223	−0.0952484
$719$	28.3700	1.05802	0.529011	−	0.848615i	$-0.322563\pi$
$719$	28.3700	1.05802	0.529011	+	0.848615i	$0.322563\pi$
$720$	−1.22430	−0.0456270
$721$	−39.7549	−1.48055
$722$	8.81799	0.328172
$723$	−0.251294	−0.00934572
$724$	21.9630	0.816248
$725$	1.63095	0.0605721
$726$	7.36114	0.273198
$727$	44.6184	1.65480	0.827402	−	0.561611i	$-0.189818\pi$
$727$	44.6184	1.65480	0.827402	+	0.561611i	$0.189818\pi$
$728$	−13.3160	−0.493525
$729$	1.00000	0.0370370
$730$	−8.70125	−0.322048
$731$	7.02639	0.259880
$732$	−0.907912	−0.0335574
$733$	37.3118	1.37814	0.689072	−	0.724693i	$-0.258019\pi$
$733$	37.3118	1.37814	0.689072	+	0.724693i	$0.258019\pi$
$734$	17.0052	0.627672
$735$	11.9882	0.442190
$736$	0	0
$737$	55.6341	2.04931
$738$	4.27853	0.157495
$739$	−4.98689	−0.183446	−0.0917228	−	0.995785i	$-0.529237\pi$
$739$	−4.98689	−0.183446	−0.0917228	+	0.995785i	$0.529237\pi$
$740$	11.5646	0.425123
$741$	3.15895	0.116047
$742$	14.6108	0.536380
$743$	−50.4532	−1.85095	−0.925475	−	0.378809i	$-0.876334\pi$
$743$	−50.4532	−1.85095	−0.925475	+	0.378809i	$0.876334\pi$
$744$	23.2670	0.853010
$745$	−18.7121	−0.685560
$746$	−8.53829	−0.312609
$747$	2.54540	0.0931312
$748$	34.8280	1.27344
$749$	53.8764	1.96860
$750$	−0.710736	−0.0259524
$751$	−41.3189	−1.50775	−0.753874	−	0.657019i	$-0.771817\pi$
$751$	−41.3189	−1.50775	−0.753874	+	0.657019i	$0.771817\pi$
$752$	−9.07109	−0.330789
$753$	3.41912	0.124600
$754$	−1.42609	−0.0519350
$755$	−0.520678	−0.0189494
$756$	−6.51389	−0.236908
$757$	−19.3708	−0.704042	−0.352021	−	0.935992i	$-0.614506\pi$
$757$	−19.3708	−0.704042	−0.352021	+	0.935992i	$0.614506\pi$
$758$	18.1439	0.659016
$759$	0	0
$760$	6.37799	0.231354
$761$	8.86082	0.321204	0.160602	−	0.987019i	$-0.448656\pi$
$761$	8.86082	0.321204	0.160602	+	0.987019i	$0.448656\pi$
$762$	−7.45225	−0.269966
$763$	−52.0306	−1.88363
$764$	2.46797	0.0892880
$765$	5.04149	0.182275
$766$	5.72364	0.206803
$767$	10.5537	0.381071
$768$	10.8408	0.391183
$769$	−33.6989	−1.21521	−0.607607	−	0.794238i	$-0.707871\pi$
$769$	−33.6989	−1.21521	−0.607607	+	0.794238i	$0.707871\pi$
$770$	−14.3127	−0.515793
$771$	−9.42896	−0.339576
$772$	−5.72381	−0.206004
$773$	−36.3496	−1.30740	−0.653702	−	0.756752i	$-0.726785\pi$
$773$	−36.3496	−1.30740	−0.653702	+	0.756752i	$0.726785\pi$
$774$	0.990562	0.0356050
$775$	−9.36706	−0.336475
$776$	41.9954	1.50755
$777$	33.7111	1.20938
$778$	−0.380984	−0.0136589
$779$	15.4573	0.553815
$780$	−1.83906	−0.0658488
$781$	35.5128	1.27075
$782$	0	0
$783$	−1.63095	−0.0582856
$784$	14.6771	0.524182
$785$	18.6916	0.667132
$786$	7.16933	0.255722
$787$	−23.7793	−0.847641	−0.423820	−	0.905746i	$-0.639311\pi$
$787$	−23.7793	−0.847641	−0.423820	+	0.905746i	$0.639311\pi$
$788$	25.4833	0.907805
$789$	21.2501	0.756525
$790$	9.95425	0.354156
$791$	33.4399	1.18899
$792$	11.4791	0.407892
$793$	−0.747207	−0.0265341
$794$	−2.71469	−0.0963409
$795$	4.71764	0.167318
$796$	−40.1231	−1.42212
$797$	−35.8378	−1.26944	−0.634720	−	0.772742i	$-0.718885\pi$
$797$	−35.8378	−1.26944	−0.634720	+	0.772742i	$0.718885\pi$
$798$	7.95236	0.281510
$799$	37.3534	1.32147
$800$	−5.83799	−0.206404
$801$	0.225933	0.00798295
$802$	−18.6413	−0.658248
$803$	−56.5776	−1.99658
$804$	17.9957	0.634659
$805$	0	0
$806$	8.19044	0.288496
$807$	11.3667	0.400128
$808$	−22.2343	−0.782200
$809$	−18.5287	−0.651435	−0.325717	−	0.945467i	$-0.605606\pi$
$809$	−18.5287	−0.651435	−0.325717	+	0.945467i	$0.605606\pi$
$810$	0.710736	0.0249727
$811$	−30.5749	−1.07363	−0.536815	−	0.843700i	$-0.680373\pi$
$811$	−30.5749	−1.07363	−0.536815	+	0.843700i	$0.680373\pi$
$812$	10.6239	0.372824
$813$	20.0189	0.702092
$814$	−25.4103	−0.890632
$815$	1.13812	0.0398668
$816$	6.17229	0.216074
$817$	3.57866	0.125201
$818$	20.2142	0.706775
$819$	−5.36090	−0.187325
$820$	−8.99882	−0.314253
$821$	28.4203	0.991877	0.495938	−	0.868358i	$-0.334824\pi$
$821$	28.4203	0.991877	0.495938	+	0.868358i	$0.334824\pi$
$822$	7.28654	0.254147
$823$	−31.0144	−1.08110	−0.540548	−	0.841313i	$-0.681783\pi$
$823$	−31.0144	−1.08110	−0.540548	+	0.841313i	$0.681783\pi$
$824$	22.6614	0.789446
$825$	−4.62137	−0.160896
$826$	26.5679	0.924416
$827$	0.982592	0.0341681	0.0170840	−	0.999854i	$-0.494562\pi$
$827$	0.982592	0.0341681	0.0170840	+	0.999854i	$0.494562\pi$
$828$	0	0
$829$	−31.9397	−1.10931	−0.554656	−	0.832080i	$-0.687150\pi$
$829$	−31.9397	−1.10931	−0.554656	+	0.832080i	$0.687150\pi$
$830$	1.80911	0.0627950
$831$	6.26539	0.217344
$832$	2.09226	0.0725360
$833$	−60.4381	−2.09406
$834$	9.61118	0.332808
$835$	−10.6798	−0.369589
$836$	17.7385	0.613498
$837$	9.36706	0.323773
$838$	−5.89874	−0.203769
$839$	−32.3100	−1.11546	−0.557732	−	0.830021i	$-0.688328\pi$
$839$	−32.3100	−1.11546	−0.557732	+	0.830021i	$0.688328\pi$
$840$	−10.8238	−0.373456
$841$	−26.3400	−0.908275
$842$	−1.40859	−0.0485431
$843$	5.30226	0.182619
$844$	−24.8967	−0.856980
$845$	11.4865	0.395146
$846$	5.26599	0.181048
$847$	−45.1314	−1.55073
$848$	5.77581	0.198342
$849$	9.41670	0.323180
$850$	3.58317	0.122902
$851$	0	0
$852$	11.4872	0.393544
$853$	20.1864	0.691168	0.345584	−	0.938388i	$-0.387681\pi$
$853$	20.1864	0.691168	0.345584	+	0.938388i	$0.387681\pi$
$854$	−1.88102	−0.0643673
$855$	2.56771	0.0878139
$856$	−30.7110	−1.04968
$857$	−27.6286	−0.943774	−0.471887	−	0.881659i	$-0.656427\pi$
$857$	−27.6286	−0.943774	−0.471887	+	0.881659i	$0.656427\pi$
$858$	4.04087	0.137953
$859$	28.6578	0.977792	0.488896	−	0.872342i	$-0.337400\pi$
$859$	28.6578	0.977792	0.488896	+	0.872342i	$0.337400\pi$
$860$	−2.08340	−0.0710433
$861$	−26.2318	−0.893977
$862$	−15.2343	−0.518883
$863$	10.2972	0.350520	0.175260	−	0.984522i	$-0.443923\pi$
$863$	10.2972	0.350520	0.175260	+	0.984522i	$0.443923\pi$
$864$	5.83799	0.198612
$865$	13.1391	0.446744
$866$	−17.1777	−0.583722
$867$	−8.41660	−0.285843
$868$	−61.0160	−2.07102
$869$	64.7249	2.19564
$870$	−1.15918	−0.0392998
$871$	14.8104	0.501830
$872$	29.6589	1.00438
$873$	16.9069	0.572213
$874$	0	0
$875$	4.35754	0.147312
$876$	−18.3009	−0.618330
$877$	−24.2742	−0.819683	−0.409842	−	0.912157i	$-0.634416\pi$
$877$	−24.2742	−0.819683	−0.409842	+	0.912157i	$0.634416\pi$
$878$	13.3146	0.449346
$879$	12.1417	0.409528
$880$	−5.65795	−0.190729
$881$	−0.586128	−0.0197471	−0.00987357	−	0.999951i	$-0.503143\pi$
$881$	−0.586128	−0.0197471	−0.00987357	+	0.999951i	$0.503143\pi$
$882$	−8.52041	−0.286897
$883$	−34.9956	−1.17770	−0.588848	−	0.808244i	$-0.700418\pi$
$883$	−34.9956	−1.17770	−0.588848	+	0.808244i	$0.700418\pi$
$884$	9.27158	0.311837
$885$	8.57843	0.288361
$886$	27.4297	0.921519
$887$	−7.29228	−0.244851	−0.122425	−	0.992478i	$-0.539067\pi$
$887$	−7.29228	−0.244851	−0.122425	+	0.992478i	$0.539067\pi$
$888$	−19.2163	−0.644855
$889$	45.6899	1.53239
$890$	0.160579	0.00538261
$891$	4.62137	0.154822
$892$	−37.6078	−1.25920
$893$	19.0247	0.636638
$894$	13.2994	0.444798
$895$	−1.58809	−0.0530840
$896$	−45.6115	−1.52377
$897$	0	0
$898$	−5.71364	−0.190667
$899$	−15.2773	−0.509525
$900$	−1.49485	−0.0498285
$901$	−23.7839	−0.792358
$902$	19.7727	0.658359
$903$	−6.07316	−0.202102
$904$	−19.0617	−0.633981
$905$	14.6924	0.488392
$906$	0.370065	0.0122946
$907$	5.23401	0.173792	0.0868962	−	0.996217i	$-0.472305\pi$
$907$	5.23401	0.173792	0.0868962	+	0.996217i	$0.472305\pi$
$908$	9.21045	0.305659
$909$	−8.95130	−0.296896
$910$	−3.81018	−0.126306
$911$	49.2471	1.63163	0.815815	−	0.578313i	$-0.196289\pi$
$911$	49.2471	1.63163	0.815815	+	0.578313i	$0.196289\pi$
$912$	3.14365	0.104097
$913$	11.7632	0.389306
$914$	−10.5590	−0.349260
$915$	−0.607358	−0.0200786
$916$	3.58266	0.118374
$917$	−43.9554	−1.45153
$918$	−3.58317	−0.118262
$919$	31.8816	1.05168	0.525838	−	0.850585i	$-0.323752\pi$
$919$	31.8816	1.05168	0.525838	+	0.850585i	$0.323752\pi$
$920$	0	0
$921$	12.9179	0.425659
$922$	13.5149	0.445089
$923$	9.45388	0.311178
$924$	−30.1031	−0.990319
$925$	7.73627	0.254367
$926$	−12.8388	−0.421908
$927$	9.12324	0.299646
$928$	−9.52150	−0.312559
$929$	−53.1883	−1.74505	−0.872525	−	0.488569i	$-0.837519\pi$
$929$	−53.1883	−1.74505	−0.872525	+	0.488569i	$0.837519\pi$
$930$	6.65751	0.218308
$931$	−30.7821	−1.00884
$932$	8.49728	0.278338
$933$	−20.5993	−0.674392
$934$	0.559364	0.0183029
$935$	23.2986	0.761945
$936$	3.05586	0.0998838
$937$	−9.83038	−0.321145	−0.160572	−	0.987024i	$-0.551334\pi$
$937$	−9.83038	−0.321145	−0.160572	+	0.987024i	$0.551334\pi$
$938$	37.2837	1.21736
$939$	−3.99270	−0.130297
$940$	−11.0757	−0.361249
$941$	−50.2189	−1.63709	−0.818544	−	0.574444i	$-0.805218\pi$
$941$	−50.2189	−1.63709	−0.818544	+	0.574444i	$0.805218\pi$
$942$	−13.2848	−0.432842
$943$	0	0
$944$	10.5026	0.341830
$945$	−4.35754	−0.141751
$946$	4.57776	0.148836
$947$	38.2604	1.24330	0.621648	−	0.783297i	$-0.286463\pi$
$947$	38.2604	1.24330	0.621648	+	0.783297i	$0.286463\pi$
$948$	20.9363	0.679978
$949$	−15.0615	−0.488918
$950$	1.82497	0.0592097
$951$	−17.0340	−0.552364
$952$	54.5679	1.76856
$953$	−35.7573	−1.15829	−0.579146	−	0.815224i	$-0.696614\pi$
$953$	−35.7573	−1.15829	−0.579146	+	0.815224i	$0.696614\pi$
$954$	−3.35300	−0.108557
$955$	1.65098	0.0534243
$956$	−40.6865	−1.31589
$957$	−7.53725	−0.243645
$958$	3.41051	0.110189
$959$	−44.6740	−1.44260
$960$	1.70067	0.0548888
$961$	56.7419	1.83038
$962$	−6.76450	−0.218096
$963$	−12.3639	−0.398422
$964$	−0.375648	−0.0120988
$965$	−3.82901	−0.123260
$966$	0	0
$967$	−49.2572	−1.58400	−0.792002	−	0.610518i	$-0.790961\pi$
$967$	−49.2572	−1.58400	−0.792002	+	0.610518i	$0.790961\pi$
$968$	25.7261	0.826869
$969$	−12.9451	−0.415856
$970$	12.0164	0.385822
$971$	16.7731	0.538275	0.269137	−	0.963102i	$-0.413261\pi$
$971$	16.7731	0.538275	0.269137	+	0.963102i	$0.413261\pi$
$972$	1.49485	0.0479475
$973$	−58.9264	−1.88909
$974$	−9.75393	−0.312536
$975$	−1.23026	−0.0393998
$976$	−0.743589	−0.0238017
$977$	−14.1872	−0.453887	−0.226944	−	0.973908i	$-0.572873\pi$
$977$	−14.1872	−0.453887	−0.226944	+	0.973908i	$0.572873\pi$
$978$	−0.808906	−0.0258660
$979$	1.04412	0.0333702
$980$	17.9206	0.572451
$981$	11.9404	0.381226
$982$	−20.8899	−0.666622
$983$	−9.82377	−0.313329	−0.156665	−	0.987652i	$-0.550074\pi$
$983$	−9.82377	−0.313329	−0.156665	+	0.987652i	$0.550074\pi$
$984$	14.9529	0.476679
$985$	17.0473	0.543174
$986$	5.84398	0.186110
$987$	−32.2859	−1.02767
$988$	4.72217	0.150232
$989$	0	0
$990$	3.28457	0.104391
$991$	44.9906	1.42917	0.714586	−	0.699548i	$-0.246615\pi$
$991$	44.9906	1.42917	0.714586	+	0.699548i	$0.246615\pi$
$992$	54.6848	1.73624
$993$	6.50273	0.206358
$994$	23.7993	0.754867
$995$	−26.8408	−0.850910
$996$	3.80500	0.120566
$997$	47.3434	1.49938	0.749691	−	0.661788i	$-0.230202\pi$
$997$	47.3434	1.49938	0.749691	+	0.661788i	$0.230202\pi$
$998$	20.4741	0.648096
$999$	−7.73627	−0.244765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bp.1.7		15
23.13	even	11		345.2.m.a.31.3	✓	30
23.16	even	11		345.2.m.a.256.3	yes	30
23.22	odd	2		7935.2.a.bq.1.7		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.a.31.3	✓	30	23.13	even	11
345.2.m.a.256.3	yes	30	23.16	even	11
7935.2.a.bp.1.7		15	1.1	even	1	trivial
7935.2.a.bq.1.7		15	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)

\(f(q)\)	\(=\)	\(q-0.710736 q^{2} -1.00000 q^{3} -1.49485 q^{4} -1.00000 q^{5} +0.710736 q^{6} -4.35754 q^{7} +2.48392 q^{8} +1.00000 q^{9} +0.710736 q^{10} +4.62137 q^{11} +1.49485 q^{12} +1.23026 q^{13} +3.09706 q^{14} +1.00000 q^{15} +1.22430 q^{16} -5.04149 q^{17} -0.710736 q^{18} -2.56771 q^{19} +1.49485 q^{20} +4.35754 q^{21} -3.28457 q^{22} -2.48392 q^{24} +1.00000 q^{25} -0.874388 q^{26} -1.00000 q^{27} +6.51389 q^{28} +1.63095 q^{29} -0.710736 q^{30} -9.36706 q^{31} -5.83799 q^{32} -4.62137 q^{33} +3.58317 q^{34} +4.35754 q^{35} -1.49485 q^{36} +7.73627 q^{37} +1.82497 q^{38} -1.23026 q^{39} -2.48392 q^{40} -6.01986 q^{41} -3.09706 q^{42} -1.39371 q^{43} -6.90828 q^{44} -1.00000 q^{45} -7.40920 q^{47} -1.22430 q^{48} +11.9882 q^{49} -0.710736 q^{50} +5.04149 q^{51} -1.83906 q^{52} +4.71764 q^{53} +0.710736 q^{54} -4.62137 q^{55} -10.8238 q^{56} +2.56771 q^{57} -1.15918 q^{58} +8.57843 q^{59} -1.49485 q^{60} -0.607358 q^{61} +6.65751 q^{62} -4.35754 q^{63} +1.70067 q^{64} -1.23026 q^{65} +3.28457 q^{66} +12.0384 q^{67} +7.53629 q^{68} -3.09706 q^{70} +7.68448 q^{71} +2.48392 q^{72} -12.2426 q^{73} -5.49844 q^{74} -1.00000 q^{75} +3.83836 q^{76} -20.1378 q^{77} +0.874388 q^{78} +14.0056 q^{79} -1.22430 q^{80} +1.00000 q^{81} +4.27853 q^{82} +2.54540 q^{83} -6.51389 q^{84} +5.04149 q^{85} +0.990562 q^{86} -1.63095 q^{87} +11.4791 q^{88} +0.225933 q^{89} +0.710736 q^{90} -5.36090 q^{91} +9.36706 q^{93} +5.26599 q^{94} +2.56771 q^{95} +5.83799 q^{96} +16.9069 q^{97} -8.52041 q^{98} +4.62137 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{3} + 12 q^{4} - 15 q^{5} - 5 q^{7} + 15 q^{9} + 13 q^{11} - 12 q^{12} - 24 q^{13} + 15 q^{14} + 15 q^{15} + 2 q^{16} + 2 q^{17} + 13 q^{19} - 12 q^{20} + 5 q^{21} - 9 q^{22} + 15 q^{25} - 9 q^{26}+ \cdots + 13 q^{99}+O(q^{100}) \) 15 * q - 15 * q^3 + 12 * q^4 - 15 * q^5 - 5 * q^7 + 15 * q^9 + 13 * q^11 - 12 * q^12 - 24 * q^13 + 15 * q^14 + 15 * q^15 + 2 * q^16 + 2 * q^17 + 13 * q^19 - 12 * q^20 + 5 * q^21 - 9 * q^22 + 15 * q^25 - 9 * q^26 - 15 * q^27 + q^28 - 3 * q^29 - 22 * q^31 - 13 * q^33 + q^34 + 5 * q^35 + 12 * q^36 - 6 * q^37 - 17 * q^38 + 24 * q^39 - 20 * q^41 - 15 * q^42 - 4 * q^43 - 18 * q^44 - 15 * q^45 + 7 * q^47 - 2 * q^48 - 10 * q^49 - 2 * q^51 - 55 * q^52 + 4 * q^53 - 13 * q^55 + 25 * q^56 - 13 * q^57 + 2 * q^58 + 9 * q^59 + 12 * q^60 + 13 * q^61 - 7 * q^62 - 5 * q^63 - 26 * q^64 + 24 * q^65 + 9 * q^66 - 32 * q^67 + 27 * q^68 - 15 * q^70 + 14 * q^71 - 43 * q^73 - 11 * q^74 - 15 * q^75 + 88 * q^76 - 21 * q^77 + 9 * q^78 + 33 * q^79 - 2 * q^80 + 15 * q^81 - 35 * q^82 - 12 * q^83 - q^84 - 2 * q^85 + 77 * q^86 + 3 * q^87 - 37 * q^88 + 29 * q^89 + 20 * q^91 + 22 * q^93 - 20 * q^94 - 13 * q^95 + 18 * q^97 - 19 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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