LMFDB - Embedded newform 7935.2.a.bd.1.2

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 = [6,0,-6,4,-6,0,2] 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:	$6$
Coefficient field:	6.6.22733568.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 8x^{4} - 2x^{3} + 16x^{2} + 8x - 2 $ x^6 - 8x^4 - 2x^3 + 16x^2 + 8x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.90131$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.90131 q^{2} -1.00000 q^{3} +1.61498 q^{4} -1.00000 q^{5} +1.90131 q^{6} -0.941661 q^{7} +0.732051 q^{8} +1.00000 q^{9} +1.90131 q^{10} -0.344672 q^{11} -1.61498 q^{12} -3.84980 q^{13} +1.79039 q^{14} +1.00000 q^{15} -4.62181 q^{16} -0.110920 q^{17} -1.90131 q^{18} -6.17844 q^{19} -1.61498 q^{20} +0.941661 q^{21} +0.655328 q^{22} -0.732051 q^{24} +1.00000 q^{25} +7.31966 q^{26} -1.00000 q^{27} -1.52076 q^{28} -9.60667 q^{29} -1.90131 q^{30} -2.73037 q^{31} +7.32338 q^{32} +0.344672 q^{33} +0.210892 q^{34} +0.941661 q^{35} +1.61498 q^{36} -5.89894 q^{37} +11.7471 q^{38} +3.84980 q^{39} -0.732051 q^{40} +7.16778 q^{41} -1.79039 q^{42} -0.975678 q^{43} -0.556637 q^{44} -1.00000 q^{45} -2.28186 q^{47} +4.62181 q^{48} -6.11327 q^{49} -1.90131 q^{50} +0.110920 q^{51} -6.21733 q^{52} -13.4086 q^{53} +1.90131 q^{54} +0.344672 q^{55} -0.689344 q^{56} +6.17844 q^{57} +18.2652 q^{58} -13.5660 q^{59} +1.61498 q^{60} +2.16478 q^{61} +5.19128 q^{62} -0.941661 q^{63} -4.68039 q^{64} +3.84980 q^{65} -0.655328 q^{66} +2.89143 q^{67} -0.179132 q^{68} -1.79039 q^{70} +0.0848344 q^{71} +0.732051 q^{72} -2.32129 q^{73} +11.2157 q^{74} -1.00000 q^{75} -9.97803 q^{76} +0.324564 q^{77} -7.31966 q^{78} +6.30863 q^{79} +4.62181 q^{80} +1.00000 q^{81} -13.6282 q^{82} -4.58813 q^{83} +1.52076 q^{84} +0.110920 q^{85} +1.85506 q^{86} +9.60667 q^{87} -0.252317 q^{88} -11.8356 q^{89} +1.90131 q^{90} +3.62521 q^{91} +2.73037 q^{93} +4.33852 q^{94} +6.17844 q^{95} -7.32338 q^{96} +13.6504 q^{97} +11.6232 q^{98} -0.344672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{3} + 4 q^{4} - 6 q^{5} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 4 q^{11} - 4 q^{12} + 10 q^{13} + 8 q^{14} + 6 q^{15} - 8 q^{16} + 8 q^{17} - 4 q^{19} - 4 q^{20} - 2 q^{21} + 2 q^{22} + 6 q^{24} + 6 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 6 * q - 6 * q^3 + 4 * q^4 - 6 * q^5 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 4 * q^11 - 4 * q^12 + 10 * q^13 + 8 * q^14 + 6 * q^15 - 8 * q^16 + 8 * q^17 - 4 * q^19 - 4 * q^20 - 2 * q^21 + 2 * q^22 + 6 * q^24 + 6 * q^25 + 14 * q^26 - 6 * q^27 + 4 * q^28 - 4 * q^29 - 6 * q^31 + 8 * q^32 + 4 * q^33 + 24 * q^34 - 2 * q^35 + 4 * q^36 + 6 * q^37 + 10 * q^38 - 10 * q^39 + 6 * q^40 - 20 * q^41 - 8 * q^42 - 4 * q^43 + 10 * q^44 - 6 * q^45 - 4 * q^47 + 8 * q^48 - 10 * q^49 - 8 * q^51 + 6 * q^52 - 22 * q^53 + 4 * q^55 - 8 * q^56 + 4 * q^57 + 4 * q^58 - 22 * q^59 + 4 * q^60 + 8 * q^61 + 16 * q^62 + 2 * q^63 - 24 * q^64 - 10 * q^65 - 2 * q^66 + 8 * q^67 + 2 * q^68 - 8 * q^70 - 2 * q^71 - 6 * q^72 - 18 * q^73 - 10 * q^74 - 6 * q^75 - 40 * q^76 - 22 * q^77 - 14 * q^78 + 20 * q^79 + 8 * q^80 + 6 * q^81 - 4 * q^82 - 18 * q^83 - 4 * q^84 - 8 * q^85 + 14 * q^86 + 4 * q^87 + 10 * q^88 + 6 * q^89 + 44 * q^91 + 6 * q^93 + 24 * q^94 + 4 * q^95 - 8 * q^96 + 12 * q^97 + 28 * q^98 - 4 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.90131	−1.34443	−0.672214	−	0.740357i	$-0.734657\pi$
$2$	−1.90131	−1.34443	−0.672214	+	0.740357i	$0.734657\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.61498	0.807488
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.90131	0.776206
$7$	−0.941661	−0.355915	−0.177957	−	0.984038i	$-0.556949\pi$
$7$	−0.941661	−0.355915	−0.177957	+	0.984038i	$0.556949\pi$
$8$	0.732051	0.258819
$9$	1.00000	0.333333
$10$	1.90131	0.601247
$11$	−0.344672	−0.103923	−0.0519613	−	0.998649i	$-0.516547\pi$
$11$	−0.344672	−0.103923	−0.0519613	+	0.998649i	$0.516547\pi$
$12$	−1.61498	−0.466203
$13$	−3.84980	−1.06774	−0.533871	−	0.845566i	$-0.679263\pi$
$13$	−3.84980	−1.06774	−0.533871	+	0.845566i	$0.679263\pi$
$14$	1.79039	0.478502
$15$	1.00000	0.258199
$16$	−4.62181	−1.15545
$17$	−0.110920	−0.0269019	−0.0134510	−	0.999910i	$-0.504282\pi$
$17$	−0.110920	−0.0269019	−0.0134510	+	0.999910i	$0.504282\pi$
$18$	−1.90131	−0.448143
$19$	−6.17844	−1.41743	−0.708716	−	0.705494i	$-0.750725\pi$
$19$	−6.17844	−1.41743	−0.708716	+	0.705494i	$0.750725\pi$
$20$	−1.61498	−0.361119
$21$	0.941661	0.205487
$22$	0.655328	0.139716
$23$	0	0
$23$	0	0
$24$	−0.732051	−0.149429
$25$	1.00000	0.200000
$26$	7.31966	1.43550
$27$	−1.00000	−0.192450
$28$	−1.52076	−0.287397
$29$	−9.60667	−1.78391	−0.891957	−	0.452121i	$-0.850668\pi$
$29$	−9.60667	−1.78391	−0.891957	+	0.452121i	$0.850668\pi$
$30$	−1.90131	−0.347130
$31$	−2.73037	−0.490389	−0.245195	−	0.969474i	$-0.578852\pi$
$31$	−2.73037	−0.490389	−0.245195	+	0.969474i	$0.578852\pi$
$32$	7.32338	1.29460
$33$	0.344672	0.0599997
$34$	0.210892	0.0361677
$35$	0.941661	0.159170
$36$	1.61498	0.269163
$37$	−5.89894	−0.969780	−0.484890	−	0.874575i	$-0.661140\pi$
$37$	−5.89894	−0.969780	−0.484890	+	0.874575i	$0.661140\pi$
$38$	11.7471	1.90564
$39$	3.84980	0.616461
$40$	−0.732051	−0.115747
$41$	7.16778	1.11942	0.559710	−	0.828689i	$-0.310913\pi$
$41$	7.16778	1.11942	0.559710	+	0.828689i	$0.310913\pi$
$42$	−1.79039	−0.276263
$43$	−0.975678	−0.148789	−0.0743947	−	0.997229i	$-0.523702\pi$
$43$	−0.975678	−0.148789	−0.0743947	+	0.997229i	$0.523702\pi$
$44$	−0.556637	−0.0839162
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−2.28186	−0.332843	−0.166422	−	0.986055i	$-0.553221\pi$
$47$	−2.28186	−0.332843	−0.166422	+	0.986055i	$0.553221\pi$
$48$	4.62181	0.667100
$49$	−6.11327	−0.873325
$50$	−1.90131	−0.268886
$51$	0.110920	0.0155318
$52$	−6.21733	−0.862189
$53$	−13.4086	−1.84181	−0.920907	−	0.389782i	$-0.872550\pi$
$53$	−13.4086	−1.84181	−0.920907	+	0.389782i	$0.872550\pi$
$54$	1.90131	0.258735
$55$	0.344672	0.0464756
$56$	−0.689344	−0.0921175
$57$	6.17844	0.818355
$58$	18.2652	2.39834
$59$	−13.5660	−1.76615	−0.883074	−	0.469234i	$-0.844530\pi$
$59$	−13.5660	−1.76615	−0.883074	+	0.469234i	$0.844530\pi$
$60$	1.61498	0.208492
$61$	2.16478	0.277172	0.138586	−	0.990350i	$-0.455744\pi$
$61$	2.16478	0.277172	0.138586	+	0.990350i	$0.455744\pi$
$62$	5.19128	0.659293
$63$	−0.941661	−0.118638
$64$	−4.68039	−0.585049
$65$	3.84980	0.477509
$66$	−0.655328	−0.0806653
$67$	2.89143	0.353245	0.176622	−	0.984279i	$-0.443483\pi$
$67$	2.89143	0.353245	0.176622	+	0.984279i	$0.443483\pi$
$68$	−0.179132	−0.0217230
$69$	0	0
$70$	−1.79039	−0.213992
$71$	0.0848344	0.0100680	0.00503400	−	0.999987i	$-0.498398\pi$
$71$	0.0848344	0.0100680	0.00503400	+	0.999987i	$0.498398\pi$
$72$	0.732051	0.0862730
$73$	−2.32129	−0.271686	−0.135843	−	0.990730i	$-0.543374\pi$
$73$	−2.32129	−0.271686	−0.135843	+	0.990730i	$0.543374\pi$
$74$	11.2157	1.30380
$75$	−1.00000	−0.115470
$76$	−9.97803	−1.14456
$77$	0.324564	0.0369875
$78$	−7.31966	−0.828788
$79$	6.30863	0.709776	0.354888	−	0.934909i	$-0.384519\pi$
$79$	6.30863	0.709776	0.354888	+	0.934909i	$0.384519\pi$
$80$	4.62181	0.516734
$81$	1.00000	0.111111
$82$	−13.6282	−1.50498
$83$	−4.58813	−0.503613	−0.251806	−	0.967778i	$-0.581025\pi$
$83$	−4.58813	−0.503613	−0.251806	+	0.967778i	$0.581025\pi$
$84$	1.52076	0.165929
$85$	0.110920	0.0120309
$86$	1.85506	0.200037
$87$	9.60667	1.02994
$88$	−0.252317	−0.0268971
$89$	−11.8356	−1.25457	−0.627285	−	0.778790i	$-0.715834\pi$
$89$	−11.8356	−1.25457	−0.627285	+	0.778790i	$0.715834\pi$
$90$	1.90131	0.200416
$91$	3.62521	0.380025
$92$	0	0
$93$	2.73037	0.283126
$94$	4.33852	0.447484
$95$	6.17844	0.633895
$96$	−7.32338	−0.747439
$97$	13.6504	1.38599	0.692994	−	0.720944i	$-0.256291\pi$
$97$	13.6504	1.38599	0.692994	+	0.720944i	$0.256291\pi$
$98$	11.6232	1.17412
$99$	−0.344672	−0.0346408
$100$	1.61498	0.161498
$101$	−6.88325	−0.684909	−0.342455	−	0.939534i	$-0.611258\pi$
$101$	−6.88325	−0.684909	−0.342455	+	0.939534i	$0.611258\pi$
$102$	−0.210892	−0.0208814
$103$	−1.22097	−0.120306	−0.0601528	−	0.998189i	$-0.519159\pi$
$103$	−1.22097	−0.120306	−0.0601528	+	0.998189i	$0.519159\pi$
$104$	−2.81825	−0.276352
$105$	−0.941661	−0.0918968
$106$	25.4939	2.47619
$107$	7.09838	0.686227	0.343113	−	0.939294i	$-0.388519\pi$
$107$	7.09838	0.686227	0.343113	+	0.939294i	$0.388519\pi$
$108$	−1.61498	−0.155401
$109$	0.640252	0.0613250	0.0306625	−	0.999530i	$-0.490238\pi$
$109$	0.640252	0.0613250	0.0306625	+	0.999530i	$0.490238\pi$
$110$	−0.655328	−0.0624831
$111$	5.89894	0.559902
$112$	4.35218	0.411242
$113$	8.54956	0.804275	0.402137	−	0.915579i	$-0.368267\pi$
$113$	8.54956	0.804275	0.402137	+	0.915579i	$0.368267\pi$
$114$	−11.7471	−1.10022
$115$	0	0
$116$	−15.5145	−1.44049
$117$	−3.84980	−0.355914
$118$	25.7932	2.37446
$119$	0.104449	0.00957479
$120$	0.732051	0.0668268
$121$	−10.8812	−0.989200
$122$	−4.11592	−0.372638
$123$	−7.16778	−0.646297
$124$	−4.40948	−0.395983
$125$	−1.00000	−0.0894427
$126$	1.79039	0.159501
$127$	15.5136	1.37661	0.688304	−	0.725422i	$-0.258355\pi$
$127$	15.5136	1.37661	0.688304	+	0.725422i	$0.258355\pi$
$128$	−5.74788	−0.508046
$129$	0.975678	0.0859036
$130$	−7.31966	−0.641977
$131$	−9.14324	−0.798849	−0.399424	−	0.916766i	$-0.630790\pi$
$131$	−9.14324	−0.798849	−0.399424	+	0.916766i	$0.630790\pi$
$132$	0.556637	0.0484490
$133$	5.81800	0.504485
$134$	−5.49751	−0.474913
$135$	1.00000	0.0860663
$136$	−0.0811987	−0.00696273
$137$	−8.24003	−0.703993	−0.351996	−	0.936001i	$-0.614497\pi$
$137$	−8.24003	−0.703993	−0.351996	+	0.936001i	$0.614497\pi$
$138$	0	0
$139$	13.2150	1.12088	0.560439	−	0.828196i	$-0.310632\pi$
$139$	13.2150	1.12088	0.560439	+	0.828196i	$0.310632\pi$
$140$	1.52076	0.128528
$141$	2.28186	0.192167
$142$	−0.161296	−0.0135357
$143$	1.32692	0.110962
$144$	−4.62181	−0.385150
$145$	9.60667	0.797790
$146$	4.41349	0.365263
$147$	6.11327	0.504214
$148$	−9.52664	−0.783085
$149$	−0.317210	−0.0259869	−0.0129934	−	0.999916i	$-0.504136\pi$
$149$	−0.317210	−0.0259869	−0.0129934	+	0.999916i	$0.504136\pi$
$150$	1.90131	0.155241
$151$	−20.5282	−1.67056	−0.835280	−	0.549824i	$-0.814695\pi$
$151$	−20.5282	−1.67056	−0.835280	+	0.549824i	$0.814695\pi$
$152$	−4.52293	−0.366858
$153$	−0.110920	−0.00896731
$154$	−0.617097	−0.0497271
$155$	2.73037	0.219309
$156$	6.21733	0.497785
$157$	4.24565	0.338840	0.169420	−	0.985544i	$-0.445811\pi$
$157$	4.24565	0.338840	0.169420	+	0.985544i	$0.445811\pi$
$158$	−11.9947	−0.954243
$159$	13.4086	1.06337
$160$	−7.32338	−0.578964
$161$	0	0
$162$	−1.90131	−0.149381
$163$	−7.40104	−0.579694	−0.289847	−	0.957073i	$-0.593604\pi$
$163$	−7.40104	−0.579694	−0.289847	+	0.957073i	$0.593604\pi$
$164$	11.5758	0.903917
$165$	−0.344672	−0.0268327
$166$	8.72346	0.677072
$167$	−3.55092	−0.274778	−0.137389	−	0.990517i	$-0.543871\pi$
$167$	−3.55092	−0.274778	−0.137389	+	0.990517i	$0.543871\pi$
$168$	0.689344	0.0531840
$169$	1.82096	0.140074
$170$	−0.210892	−0.0161747
$171$	−6.17844	−0.472477
$172$	−1.57570	−0.120146
$173$	−17.2570	−1.31203	−0.656013	−	0.754750i	$-0.727758\pi$
$173$	−17.2570	−1.31203	−0.656013	+	0.754750i	$0.727758\pi$
$174$	−18.2652	−1.38468
$175$	−0.941661	−0.0711829
$176$	1.59301	0.120077
$177$	13.5660	1.01969
$178$	22.5031	1.68668
$179$	−12.3387	−0.922238	−0.461119	−	0.887338i	$-0.652552\pi$
$179$	−12.3387	−0.922238	−0.461119	+	0.887338i	$0.652552\pi$
$180$	−1.61498	−0.120373
$181$	−12.5319	−0.931489	−0.465745	−	0.884919i	$-0.654213\pi$
$181$	−12.5319	−0.931489	−0.465745	+	0.884919i	$0.654213\pi$
$182$	−6.89264	−0.510917
$183$	−2.16478	−0.160025
$184$	0	0
$185$	5.89894	0.433699
$186$	−5.19128	−0.380643
$187$	0.0382309	0.00279572
$188$	−3.68514	−0.268767
$189$	0.941661	0.0684958
$190$	−11.7471	−0.852226
$191$	−12.1534	−0.879386	−0.439693	−	0.898148i	$-0.644913\pi$
$191$	−12.1534	−0.879386	−0.439693	+	0.898148i	$0.644913\pi$
$192$	4.68039	0.337778
$193$	11.6399	0.837858	0.418929	−	0.908019i	$-0.362406\pi$
$193$	11.6399	0.837858	0.418929	+	0.908019i	$0.362406\pi$
$194$	−25.9536	−1.86336
$195$	−3.84980	−0.275690
$196$	−9.87279	−0.705199
$197$	−3.20805	−0.228564	−0.114282	−	0.993448i	$-0.536457\pi$
$197$	−3.20805	−0.228564	−0.114282	+	0.993448i	$0.536457\pi$
$198$	0.655328	0.0465721
$199$	12.4391	0.881786	0.440893	−	0.897560i	$-0.354662\pi$
$199$	12.4391	0.881786	0.440893	+	0.897560i	$0.354662\pi$
$200$	0.732051	0.0517638
$201$	−2.89143	−0.203946
$202$	13.0872	0.920811
$203$	9.04623	0.634921
$204$	0.179132	0.0125418
$205$	−7.16778	−0.500619
$206$	2.32144	0.161742
$207$	0	0
$208$	17.7930	1.23372
$209$	2.12954	0.147303
$210$	1.79039	0.123549
$211$	−19.6039	−1.34959	−0.674794	−	0.738006i	$-0.735768\pi$
$211$	−19.6039	−1.34959	−0.674794	+	0.738006i	$0.735768\pi$
$212$	−21.6546	−1.48724
$213$	−0.0848344	−0.00581276
$214$	−13.4962	−0.922583
$215$	0.975678	0.0665407
$216$	−0.732051	−0.0498097
$217$	2.57108	0.174537
$218$	−1.21732	−0.0824471
$219$	2.32129	0.156858
$220$	0.556637	0.0375284
$221$	0.427018	0.0287243
$222$	−11.2157	−0.752749
$223$	1.31636	0.0881501	0.0440751	−	0.999028i	$-0.485966\pi$
$223$	1.31636	0.0881501	0.0440751	+	0.999028i	$0.485966\pi$
$224$	−6.89614	−0.460768
$225$	1.00000	0.0666667
$226$	−16.2554	−1.08129
$227$	−17.7799	−1.18010	−0.590048	−	0.807368i	$-0.700891\pi$
$227$	−17.7799	−1.18010	−0.590048	+	0.807368i	$0.700891\pi$
$228$	9.97803	0.660811
$229$	−7.45996	−0.492968	−0.246484	−	0.969147i	$-0.579275\pi$
$229$	−7.45996	−0.492968	−0.246484	+	0.969147i	$0.579275\pi$
$230$	0	0
$231$	−0.324564	−0.0213548
$232$	−7.03257	−0.461711
$233$	3.05893	0.200397	0.100199	−	0.994967i	$-0.468052\pi$
$233$	3.05893	0.200397	0.100199	+	0.994967i	$0.468052\pi$
$234$	7.31966	0.478501
$235$	2.28186	0.148852
$236$	−21.9088	−1.42614
$237$	−6.30863	−0.409789
$238$	−0.198589	−0.0128726
$239$	14.1780	0.917101	0.458550	−	0.888668i	$-0.348369\pi$
$239$	14.1780	0.917101	0.458550	+	0.888668i	$0.348369\pi$
$240$	−4.62181	−0.298336
$241$	29.2388	1.88343	0.941717	−	0.336405i	$-0.109211\pi$
$241$	29.2388	1.88343	0.941717	+	0.336405i	$0.109211\pi$
$242$	20.6885	1.32991
$243$	−1.00000	−0.0641500
$244$	3.49607	0.223813
$245$	6.11327	0.390563
$246$	13.6282	0.868900
$247$	23.7858	1.51345
$248$	−1.99877	−0.126922
$249$	4.58813	0.290761
$250$	1.90131	0.120249
$251$	−26.8739	−1.69627	−0.848133	−	0.529783i	$-0.822273\pi$
$251$	−26.8739	−1.69627	−0.848133	+	0.529783i	$0.822273\pi$
$252$	−1.52076	−0.0957989
$253$	0	0
$254$	−29.4961	−1.85075
$255$	−0.110920	−0.00694605
$256$	20.2893	1.26808
$257$	23.6429	1.47481	0.737403	−	0.675453i	$-0.236052\pi$
$257$	23.6429	1.47481	0.737403	+	0.675453i	$0.236052\pi$
$258$	−1.85506	−0.115491
$259$	5.55480	0.345159
$260$	6.21733	0.385583
$261$	−9.60667	−0.594638
$262$	17.3841	1.07399
$263$	−11.3133	−0.697605	−0.348803	−	0.937196i	$-0.613412\pi$
$263$	−11.3133	−0.697605	−0.348803	+	0.937196i	$0.613412\pi$
$264$	0.252317	0.0155291
$265$	13.4086	0.823684
$266$	−11.0618	−0.678244
$267$	11.8356	0.724326
$268$	4.66960	0.285241
$269$	−5.84484	−0.356366	−0.178183	−	0.983997i	$-0.557022\pi$
$269$	−5.84484	−0.356366	−0.178183	+	0.983997i	$0.557022\pi$
$270$	−1.90131	−0.115710
$271$	−20.0827	−1.21993	−0.609967	−	0.792427i	$-0.708817\pi$
$271$	−20.0827	−1.21993	−0.609967	+	0.792427i	$0.708817\pi$
$272$	0.512648	0.0310839
$273$	−3.62521	−0.219408
$274$	15.6668	0.946468
$275$	−0.344672	−0.0207845
$276$	0	0
$277$	−22.5451	−1.35460	−0.677302	−	0.735705i	$-0.736851\pi$
$277$	−22.5451	−1.35460	−0.677302	+	0.735705i	$0.736851\pi$
$278$	−25.1257	−1.50694
$279$	−2.73037	−0.163463
$280$	0.689344	0.0411962
$281$	−21.4649	−1.28049	−0.640244	−	0.768172i	$-0.721167\pi$
$281$	−21.4649	−1.28049	−0.640244	+	0.768172i	$0.721167\pi$
$282$	−4.33852	−0.258355
$283$	−25.9275	−1.54123	−0.770616	−	0.637300i	$-0.780051\pi$
$283$	−25.9275	−1.54123	−0.770616	+	0.637300i	$0.780051\pi$
$284$	0.137006	0.00812978
$285$	−6.17844	−0.365979
$286$	−2.52288	−0.149181
$287$	−6.74962	−0.398418
$288$	7.32338	0.431534
$289$	−16.9877	−0.999276
$290$	−18.2652	−1.07257
$291$	−13.6504	−0.800200
$292$	−3.74882	−0.219383
$293$	−20.0884	−1.17358	−0.586790	−	0.809739i	$-0.699608\pi$
$293$	−20.0884	−1.17358	−0.586790	+	0.809739i	$0.699608\pi$
$294$	−11.6232	−0.677880
$295$	13.5660	0.789845
$296$	−4.31832	−0.250997
$297$	0.344672	0.0199999
$298$	0.603115	0.0349375
$299$	0	0
$300$	−1.61498	−0.0932406
$301$	0.918758	0.0529563
$302$	39.0304	2.24595
$303$	6.88325	0.395432
$304$	28.5556	1.63777
$305$	−2.16478	−0.123955
$306$	0.210892	0.0120559
$307$	11.9672	0.683004	0.341502	−	0.939881i	$-0.389064\pi$
$307$	11.9672	0.683004	0.341502	+	0.939881i	$0.389064\pi$
$308$	0.524163	0.0298670
$309$	1.22097	0.0694585
$310$	−5.19128	−0.294845
$311$	2.55209	0.144716	0.0723579	−	0.997379i	$-0.476948\pi$
$311$	2.55209	0.144716	0.0723579	+	0.997379i	$0.476948\pi$
$312$	2.81825	0.159552
$313$	30.7169	1.73622	0.868111	−	0.496370i	$-0.165334\pi$
$313$	30.7169	1.73622	0.868111	+	0.496370i	$0.165334\pi$
$314$	−8.07230	−0.455546
$315$	0.941661	0.0530566
$316$	10.1883	0.573136
$317$	32.9632	1.85140	0.925699	−	0.378260i	$-0.123478\pi$
$317$	32.9632	1.85140	0.925699	+	0.378260i	$0.123478\pi$
$318$	−25.4939	−1.42963
$319$	3.31115	0.185389
$320$	4.68039	0.261642
$321$	−7.09838	−0.396193
$322$	0	0
$323$	0.685310	0.0381317
$324$	1.61498	0.0897209
$325$	−3.84980	−0.213549
$326$	14.0717	0.779357
$327$	−0.640252	−0.0354060
$328$	5.24718	0.289727
$329$	2.14874	0.118464
$330$	0.655328	0.0360746
$331$	22.3176	1.22669	0.613343	−	0.789817i	$-0.289824\pi$
$331$	22.3176	1.22669	0.613343	+	0.789817i	$0.289824\pi$
$332$	−7.40972	−0.406661
$333$	−5.89894	−0.323260
$334$	6.75139	0.369420
$335$	−2.89143	−0.157976
$336$	−4.35218	−0.237431
$337$	−17.4215	−0.949010	−0.474505	−	0.880253i	$-0.657373\pi$
$337$	−17.4215	−0.949010	−0.474505	+	0.880253i	$0.657373\pi$
$338$	−3.46221	−0.188320
$339$	−8.54956	−0.464348
$340$	0.179132	0.00971481
$341$	0.941082	0.0509625
$342$	11.7471	0.635212
$343$	12.3483	0.666744
$344$	−0.714246	−0.0385095
$345$	0	0
$346$	32.8109	1.76392
$347$	−25.5751	−1.37294	−0.686471	−	0.727157i	$-0.740841\pi$
$347$	−25.5751	−1.37294	−0.686471	+	0.727157i	$0.740841\pi$
$348$	15.5145	0.831666
$349$	−25.3037	−1.35447	−0.677237	−	0.735765i	$-0.736823\pi$
$349$	−25.3037	−1.35447	−0.677237	+	0.735765i	$0.736823\pi$
$350$	1.79039	0.0957003
$351$	3.84980	0.205487
$352$	−2.52416	−0.134538
$353$	17.7951	0.947135	0.473568	−	0.880757i	$-0.342966\pi$
$353$	17.7951	0.947135	0.473568	+	0.880757i	$0.342966\pi$
$354$	−25.7932	−1.37089
$355$	−0.0848344	−0.00450254
$356$	−19.1142	−1.01305
$357$	−0.104449	−0.00552801
$358$	23.4597	1.23988
$359$	−20.8242	−1.09906	−0.549530	−	0.835474i	$-0.685193\pi$
$359$	−20.8242	−1.09906	−0.549530	+	0.835474i	$0.685193\pi$
$360$	−0.732051	−0.0385825
$361$	19.1731	1.00911
$362$	23.8270	1.25232
$363$	10.8812	0.571115
$364$	5.85462	0.306866
$365$	2.32129	0.121502
$366$	4.11592	0.215143
$367$	6.24844	0.326166	0.163083	−	0.986612i	$-0.447856\pi$
$367$	6.24844	0.326166	0.163083	+	0.986612i	$0.447856\pi$
$368$	0	0
$369$	7.16778	0.373140
$370$	−11.2157	−0.583077
$371$	12.6264	0.655529
$372$	4.40948	0.228621
$373$	2.04949	0.106119	0.0530593	−	0.998591i	$-0.483103\pi$
$373$	2.04949	0.106119	0.0530593	+	0.998591i	$0.483103\pi$
$374$	−0.0726887	−0.00375864
$375$	1.00000	0.0516398
$376$	−1.67044	−0.0861461
$377$	36.9838	1.90476
$378$	−1.79039	−0.0920877
$379$	−20.7709	−1.06693	−0.533464	−	0.845823i	$-0.679110\pi$
$379$	−20.7709	−1.06693	−0.533464	+	0.845823i	$0.679110\pi$
$380$	9.97803	0.511862
$381$	−15.5136	−0.794785
$382$	23.1073	1.18227
$383$	21.6361	1.10555	0.552776	−	0.833330i	$-0.313569\pi$
$383$	21.6361	1.10555	0.552776	+	0.833330i	$0.313569\pi$
$384$	5.74788	0.293320
$385$	−0.324564	−0.0165413
$386$	−22.1310	−1.12644
$387$	−0.975678	−0.0495965
$388$	22.0450	1.11917
$389$	33.6439	1.70582	0.852908	−	0.522061i	$-0.174837\pi$
$389$	33.6439	1.70582	0.852908	+	0.522061i	$0.174837\pi$
$390$	7.31966	0.370645
$391$	0	0
$392$	−4.47523	−0.226033
$393$	9.14324	0.461215
$394$	6.09950	0.307288
$395$	−6.30863	−0.317422
$396$	−0.556637	−0.0279721
$397$	15.5549	0.780679	0.390340	−	0.920671i	$-0.372358\pi$
$397$	15.5549	0.780679	0.390340	+	0.920671i	$0.372358\pi$
$398$	−23.6506	−1.18550
$399$	−5.81800	−0.291264
$400$	−4.62181	−0.231090
$401$	−38.5160	−1.92340	−0.961699	−	0.274108i	$-0.911617\pi$
$401$	−38.5160	−1.92340	−0.961699	+	0.274108i	$0.911617\pi$
$402$	5.49751	0.274191
$403$	10.5114	0.523609
$404$	−11.1163	−0.553056
$405$	−1.00000	−0.0496904
$406$	−17.1997	−0.853605
$407$	2.03320	0.100782
$408$	0.0811987	0.00401994
$409$	−35.6798	−1.76425	−0.882126	−	0.471014i	$-0.843888\pi$
$409$	−35.6798	−1.76425	−0.882126	+	0.471014i	$0.843888\pi$
$410$	13.6282	0.673047
$411$	8.24003	0.406451
$412$	−1.97183	−0.0971453
$413$	12.7746	0.628598
$414$	0	0
$415$	4.58813	0.225223
$416$	−28.1935	−1.38230
$417$	−13.2150	−0.647139
$418$	−4.04891	−0.198038
$419$	28.0247	1.36909	0.684547	−	0.728969i	$-0.260000\pi$
$419$	28.0247	1.36909	0.684547	+	0.728969i	$0.260000\pi$
$420$	−1.52076	−0.0742055
$421$	29.8972	1.45710	0.728551	−	0.684991i	$-0.240194\pi$
$421$	29.8972	1.45710	0.728551	+	0.684991i	$0.240194\pi$
$422$	37.2731	1.81442
$423$	−2.28186	−0.110948
$424$	−9.81578	−0.476697
$425$	−0.110920	−0.00538039
$426$	0.161296	0.00781484
$427$	−2.03849	−0.0986495
$428$	11.4637	0.554120
$429$	−1.32692	−0.0640642
$430$	−1.85506	−0.0894591
$431$	2.99611	0.144318	0.0721588	−	0.997393i	$-0.477011\pi$
$431$	2.99611	0.144318	0.0721588	+	0.997393i	$0.477011\pi$
$432$	4.62181	0.222367
$433$	−3.55693	−0.170935	−0.0854677	−	0.996341i	$-0.527238\pi$
$433$	−3.55693	−0.170935	−0.0854677	+	0.996341i	$0.527238\pi$
$434$	−4.88843	−0.234652
$435$	−9.60667	−0.460604
$436$	1.03399	0.0495192
$437$	0	0
$438$	−4.41349	−0.210884
$439$	−8.50958	−0.406140	−0.203070	−	0.979164i	$-0.565092\pi$
$439$	−8.50958	−0.406140	−0.203070	+	0.979164i	$0.565092\pi$
$440$	0.252317	0.0120288
$441$	−6.11327	−0.291108
$442$	−0.811893	−0.0386178
$443$	−14.9149	−0.708629	−0.354315	−	0.935126i	$-0.615286\pi$
$443$	−14.9149	−0.708629	−0.354315	+	0.935126i	$0.615286\pi$
$444$	9.52664	0.452114
$445$	11.8356	0.561061
$446$	−2.50281	−0.118511
$447$	0.317210	0.0150035
$448$	4.40735	0.208227
$449$	−22.6007	−1.06659	−0.533296	−	0.845928i	$-0.679047\pi$
$449$	−22.6007	−1.06659	−0.533296	+	0.845928i	$0.679047\pi$
$450$	−1.90131	−0.0896286
$451$	−2.47053	−0.116333
$452$	13.8073	0.649442
$453$	20.5282	0.964499
$454$	33.8052	1.58655
$455$	−3.62521	−0.169952
$456$	4.52293	0.211806
$457$	39.3091	1.83880	0.919400	−	0.393323i	$-0.128675\pi$
$457$	39.3091	1.83880	0.919400	+	0.393323i	$0.128675\pi$
$458$	14.1837	0.662760
$459$	0.110920	0.00517728
$460$	0	0
$461$	20.2367	0.942516	0.471258	−	0.881995i	$-0.343800\pi$
$461$	20.2367	0.942516	0.471258	+	0.881995i	$0.343800\pi$
$462$	0.617097	0.0287100
$463$	−36.4822	−1.69547	−0.847736	−	0.530419i	$-0.822035\pi$
$463$	−36.4822	−1.69547	−0.847736	+	0.530419i	$0.822035\pi$
$464$	44.4001	2.06122
$465$	−2.73037	−0.126618
$466$	−5.81598	−0.269420
$467$	19.5589	0.905077	0.452538	−	0.891745i	$-0.350519\pi$
$467$	19.5589	0.905077	0.452538	+	0.891745i	$0.350519\pi$
$468$	−6.21733	−0.287396
$469$	−2.72275	−0.125725
$470$	−4.33852	−0.200121
$471$	−4.24565	−0.195629
$472$	−9.93103	−0.457113
$473$	0.336289	0.0154626
$474$	11.9947	0.550933
$475$	−6.17844	−0.283486
$476$	0.168682	0.00773153
$477$	−13.4086	−0.613938
$478$	−26.9568	−1.23298
$479$	−16.7397	−0.764856	−0.382428	−	0.923985i	$-0.624912\pi$
$479$	−16.7397	−0.764856	−0.382428	+	0.923985i	$0.624912\pi$
$480$	7.32338	0.334265
$481$	22.7097	1.03547
$482$	−55.5919	−2.53214
$483$	0	0
$484$	−17.5729	−0.798767
$485$	−13.6504	−0.619832
$486$	1.90131	0.0862451
$487$	1.26249	0.0572087	0.0286044	−	0.999591i	$-0.490894\pi$
$487$	1.26249	0.0572087	0.0286044	+	0.999591i	$0.490894\pi$
$488$	1.58473	0.0717374
$489$	7.40104	0.334687
$490$	−11.6232	−0.525084
$491$	1.58626	0.0715871	0.0357935	−	0.999359i	$-0.488604\pi$
$491$	1.58626	0.0715871	0.0357935	+	0.999359i	$0.488604\pi$
$492$	−11.5758	−0.521877
$493$	1.06557	0.0479907
$494$	−45.2241	−2.03473
$495$	0.344672	0.0154919
$496$	12.6192	0.566621
$497$	−0.0798853	−0.00358335
$498$	−8.72346	−0.390907
$499$	−13.9364	−0.623877	−0.311939	−	0.950102i	$-0.600978\pi$
$499$	−13.9364	−0.623877	−0.311939	+	0.950102i	$0.600978\pi$
$500$	−1.61498	−0.0722239
$501$	3.55092	0.158643
$502$	51.0956	2.28051
$503$	−16.5341	−0.737219	−0.368609	−	0.929584i	$-0.620166\pi$
$503$	−16.5341	−0.737219	−0.368609	+	0.929584i	$0.620166\pi$
$504$	−0.689344	−0.0307058
$505$	6.88325	0.306301
$506$	0	0
$507$	−1.82096	−0.0808718
$508$	25.0541	1.11159
$509$	6.67931	0.296055	0.148028	−	0.988983i	$-0.452708\pi$
$509$	6.67931	0.296055	0.148028	+	0.988983i	$0.452708\pi$
$510$	0.210892	0.00933847
$511$	2.18587	0.0966971
$512$	−27.0804	−1.19680
$513$	6.17844	0.272785
$514$	−44.9525	−1.98277
$515$	1.22097	0.0538023
$516$	1.57570	0.0693661
$517$	0.786492	0.0345899
$518$	−10.5614	−0.464041
$519$	17.2570	0.757499
$520$	2.81825	0.123588
$521$	31.1155	1.36320	0.681598	−	0.731727i	$-0.261285\pi$
$521$	31.1155	1.36320	0.681598	+	0.731727i	$0.261285\pi$
$522$	18.2652	0.799448
$523$	4.20093	0.183694	0.0918470	−	0.995773i	$-0.470723\pi$
$523$	4.20093	0.183694	0.0918470	+	0.995773i	$0.470723\pi$
$524$	−14.7661	−0.645060
$525$	0.941661	0.0410975
$526$	21.5100	0.937881
$527$	0.302851	0.0131924
$528$	−1.59301	−0.0693267
$529$	0	0
$530$	−25.4939	−1.10738
$531$	−13.5660	−0.588716
$532$	9.39593	0.407365
$533$	−27.5945	−1.19525
$534$	−22.5031	−0.973804
$535$	−7.09838	−0.306890
$536$	2.11668	0.0914265
$537$	12.3387	0.532454
$538$	11.1129	0.479109
$539$	2.10707	0.0907581
$540$	1.61498	0.0694975
$541$	13.0314	0.560265	0.280133	−	0.959961i	$-0.409622\pi$
$541$	13.0314	0.560265	0.280133	+	0.959961i	$0.409622\pi$
$542$	38.1833	1.64011
$543$	12.5319	0.537796
$544$	−0.812306	−0.0348273
$545$	−0.640252	−0.0274254
$546$	6.89264	0.294978
$547$	24.4746	1.04646	0.523228	−	0.852193i	$-0.324728\pi$
$547$	24.4746	1.04646	0.523228	+	0.852193i	$0.324728\pi$
$548$	−13.3074	−0.568466
$549$	2.16478	0.0923907
$550$	0.655328	0.0279433
$551$	59.3542	2.52858
$552$	0	0
$553$	−5.94059	−0.252620
$554$	42.8652	1.82117
$555$	−5.89894	−0.250396
$556$	21.3418	0.905096
$557$	−32.6808	−1.38473	−0.692364	−	0.721548i	$-0.743431\pi$
$557$	−32.6808	−1.38473	−0.692364	+	0.721548i	$0.743431\pi$
$558$	5.19128	0.219764
$559$	3.75616	0.158869
$560$	−4.35218	−0.183913
$561$	−0.0382309	−0.00161411
$562$	40.8114	1.72152
$563$	32.4830	1.36899	0.684497	−	0.729016i	$-0.260022\pi$
$563$	32.4830	1.36899	0.684497	+	0.729016i	$0.260022\pi$
$564$	3.68514	0.155173
$565$	−8.54956	−0.359683
$566$	49.2962	2.07207
$567$	−0.941661	−0.0395461
$568$	0.0621031	0.00260579
$569$	−13.2468	−0.555334	−0.277667	−	0.960677i	$-0.589561\pi$
$569$	−13.2468	−0.555334	−0.277667	+	0.960677i	$0.589561\pi$
$570$	11.7471	0.492033
$571$	36.5638	1.53015	0.765074	−	0.643942i	$-0.222702\pi$
$571$	36.5638	1.53015	0.765074	+	0.643942i	$0.222702\pi$
$572$	2.14294	0.0896008
$573$	12.1534	0.507714
$574$	12.8331	0.535644
$575$	0	0
$576$	−4.68039	−0.195016
$577$	−3.59443	−0.149638	−0.0748191	−	0.997197i	$-0.523838\pi$
$577$	−3.59443	−0.149638	−0.0748191	+	0.997197i	$0.523838\pi$
$578$	32.2989	1.34346
$579$	−11.6399	−0.483738
$580$	15.5145	0.644206
$581$	4.32047	0.179243
$582$	25.9536	1.07581
$583$	4.62157	0.191406
$584$	−1.69930	−0.0703176
$585$	3.84980	0.159170
$586$	38.1943	1.57779
$587$	12.7193	0.524980	0.262490	−	0.964935i	$-0.415456\pi$
$587$	12.7193	0.524980	0.262490	+	0.964935i	$0.415456\pi$
$588$	9.87279	0.407147
$589$	16.8694	0.695093
$590$	−25.7932	−1.06189
$591$	3.20805	0.131962
$592$	27.2637	1.12053
$593$	−9.87033	−0.405326	−0.202663	−	0.979249i	$-0.564960\pi$
$593$	−9.87033	−0.405326	−0.202663	+	0.979249i	$0.564960\pi$
$594$	−0.655328	−0.0268884
$595$	−0.104449	−0.00428198
$596$	−0.512287	−0.0209841
$597$	−12.4391	−0.509099
$598$	0	0
$599$	−42.1809	−1.72346	−0.861732	−	0.507364i	$-0.830620\pi$
$599$	−42.1809	−1.72346	−0.861732	+	0.507364i	$0.830620\pi$
$600$	−0.732051	−0.0298858
$601$	−23.0857	−0.941684	−0.470842	−	0.882218i	$-0.656050\pi$
$601$	−23.0857	−0.941684	−0.470842	+	0.882218i	$0.656050\pi$
$602$	−1.74684	−0.0711960
$603$	2.89143	0.117748
$604$	−33.1525	−1.34896
$605$	10.8812	0.442384
$606$	−13.0872	−0.531631
$607$	41.7202	1.69337	0.846685	−	0.532095i	$-0.178595\pi$
$607$	41.7202	1.69337	0.846685	+	0.532095i	$0.178595\pi$
$608$	−45.2471	−1.83501
$609$	−9.04623	−0.366572
$610$	4.11592	0.166649
$611$	8.78470	0.355391
$612$	−0.179132	−0.00724099
$613$	6.36682	0.257153	0.128577	−	0.991700i	$-0.458959\pi$
$613$	6.36682	0.257153	0.128577	+	0.991700i	$0.458959\pi$
$614$	−22.7533	−0.918250
$615$	7.16778	0.289033
$616$	0.237598	0.00957308
$617$	33.2714	1.33946	0.669728	−	0.742607i	$-0.266411\pi$
$617$	33.2714	1.33946	0.669728	+	0.742607i	$0.266411\pi$
$618$	−2.32144	−0.0933819
$619$	43.7641	1.75903	0.879515	−	0.475872i	$-0.157867\pi$
$619$	43.7641	1.75903	0.879515	+	0.475872i	$0.157867\pi$
$620$	4.40948	0.177089
$621$	0	0
$622$	−4.85231	−0.194560
$623$	11.1451	0.446520
$624$	−17.7930	−0.712291
$625$	1.00000	0.0400000
$626$	−58.4023	−2.33423
$627$	−2.12954	−0.0850455
$628$	6.85663	0.273609
$629$	0.654307	0.0260889
$630$	−1.79039	−0.0713308
$631$	29.3769	1.16948	0.584738	−	0.811222i	$-0.301197\pi$
$631$	29.3769	1.16948	0.584738	+	0.811222i	$0.301197\pi$
$632$	4.61824	0.183704
$633$	19.6039	0.779185
$634$	−62.6732	−2.48907
$635$	−15.5136	−0.615638
$636$	21.6546	0.858660
$637$	23.5349	0.932486
$638$	−6.29552	−0.249242
$639$	0.0848344	0.00335600
$640$	5.74788	0.227205
$641$	−44.1549	−1.74401	−0.872007	−	0.489493i	$-0.837182\pi$
$641$	−44.1549	−1.74401	−0.872007	+	0.489493i	$0.837182\pi$
$642$	13.4962	0.532653
$643$	29.7768	1.17428	0.587142	−	0.809484i	$-0.300253\pi$
$643$	29.7768	1.17428	0.587142	+	0.809484i	$0.300253\pi$
$644$	0	0
$645$	−0.975678	−0.0384173
$646$	−1.30299	−0.0512653
$647$	−31.4784	−1.23754	−0.618772	−	0.785571i	$-0.712369\pi$
$647$	−31.4784	−1.23754	−0.618772	+	0.785571i	$0.712369\pi$
$648$	0.732051	0.0287577
$649$	4.67583	0.183543
$650$	7.31966	0.287101
$651$	−2.57108	−0.100769
$652$	−11.9525	−0.468096
$653$	−11.8058	−0.461998	−0.230999	−	0.972954i	$-0.574199\pi$
$653$	−11.8058	−0.461998	−0.230999	+	0.972954i	$0.574199\pi$
$654$	1.21732	0.0476009
$655$	9.14324	0.357256
$656$	−33.1281	−1.29343
$657$	−2.32129	−0.0905621
$658$	−4.08541	−0.159266
$659$	22.9082	0.892379	0.446189	−	0.894939i	$-0.352781\pi$
$659$	22.9082	0.892379	0.446189	+	0.894939i	$0.352781\pi$
$660$	−0.556637	−0.0216671
$661$	−20.0826	−0.781123	−0.390562	−	0.920577i	$-0.627719\pi$
$661$	−20.0826	−0.781123	−0.390562	+	0.920577i	$0.627719\pi$
$662$	−42.4326	−1.64919
$663$	−0.427018	−0.0165840
$664$	−3.35875	−0.130345
$665$	−5.81800	−0.225612
$666$	11.2157	0.434600
$667$	0	0
$668$	−5.73464	−0.221880
$669$	−1.31636	−0.0508935
$670$	5.49751	0.212387
$671$	−0.746140	−0.0288044
$672$	6.89614	0.266024
$673$	31.2670	1.20526	0.602628	−	0.798023i	$-0.294120\pi$
$673$	31.2670	1.20526	0.602628	+	0.798023i	$0.294120\pi$
$674$	33.1237	1.27588
$675$	−1.00000	−0.0384900
$676$	2.94081	0.113108
$677$	21.8318	0.839065	0.419533	−	0.907740i	$-0.362194\pi$
$677$	21.8318	0.839065	0.419533	+	0.907740i	$0.362194\pi$
$678$	16.2554	0.624283
$679$	−12.8540	−0.493293
$680$	0.0811987	0.00311383
$681$	17.7799	0.681329
$682$	−1.78929	−0.0685154
$683$	−4.96284	−0.189898	−0.0949488	−	0.995482i	$-0.530269\pi$
$683$	−4.96284	−0.189898	−0.0949488	+	0.995482i	$0.530269\pi$
$684$	−9.97803	−0.381520
$685$	8.24003	0.314835
$686$	−23.4779	−0.896389
$687$	7.45996	0.284615
$688$	4.50939	0.171919
$689$	51.6205	1.96658
$690$	0	0
$691$	43.0193	1.63653	0.818266	−	0.574840i	$-0.194936\pi$
$691$	43.0193	1.63653	0.818266	+	0.574840i	$0.194936\pi$
$692$	−27.8696	−1.05944
$693$	0.324564	0.0123292
$694$	48.6261	1.84582
$695$	−13.2150	−0.501272
$696$	7.03257	0.266569
$697$	−0.795047	−0.0301145
$698$	48.1101	1.82099
$699$	−3.05893	−0.115699
$700$	−1.52076	−0.0574793
$701$	2.19600	0.0829419	0.0414709	−	0.999140i	$-0.486796\pi$
$701$	2.19600	0.0829419	0.0414709	+	0.999140i	$0.486796\pi$
$702$	−7.31966	−0.276263
$703$	36.4463	1.37460
$704$	1.61320	0.0607998
$705$	−2.28186	−0.0859397
$706$	−33.8339	−1.27336
$707$	6.48169	0.243769
$708$	21.9088	0.823384
$709$	18.5085	0.695100	0.347550	−	0.937662i	$-0.387014\pi$
$709$	18.5085	0.695100	0.347550	+	0.937662i	$0.387014\pi$
$710$	0.161296	0.00605335
$711$	6.30863	0.236592
$712$	−8.66425	−0.324706
$713$	0	0
$714$	0.198589	0.00743201
$715$	−1.32692	−0.0496239
$716$	−19.9267	−0.744696
$717$	−14.1780	−0.529488
$718$	39.5933	1.47761
$719$	9.96118	0.371489	0.185745	−	0.982598i	$-0.440530\pi$
$719$	9.96118	0.371489	0.185745	+	0.982598i	$0.440530\pi$
$720$	4.62181	0.172245
$721$	1.14974	0.0428185
$722$	−36.4541	−1.35668
$723$	−29.2388	−1.08740
$724$	−20.2387	−0.752166
$725$	−9.60667	−0.356783
$726$	−20.6885	−0.767823
$727$	−31.8475	−1.18116	−0.590579	−	0.806980i	$-0.701100\pi$
$727$	−31.8475	−1.18116	−0.590579	+	0.806980i	$0.701100\pi$
$728$	2.65384	0.0983577
$729$	1.00000	0.0370370
$730$	−4.41349	−0.163350
$731$	0.108222	0.00400272
$732$	−3.49607	−0.129218
$733$	11.0828	0.409354	0.204677	−	0.978830i	$-0.434386\pi$
$733$	11.0828	0.409354	0.204677	+	0.978830i	$0.434386\pi$
$734$	−11.8802	−0.438506
$735$	−6.11327	−0.225491
$736$	0	0
$737$	−0.996597	−0.0367101
$738$	−13.6282	−0.501660
$739$	−33.3039	−1.22510	−0.612551	−	0.790431i	$-0.709857\pi$
$739$	−33.3039	−1.22510	−0.612551	+	0.790431i	$0.709857\pi$
$740$	9.52664	0.350206
$741$	−23.7858	−0.873792
$742$	−24.0066	−0.881311
$743$	−31.8767	−1.16944	−0.584721	−	0.811234i	$-0.698796\pi$
$743$	−31.8767	−1.16944	−0.584721	+	0.811234i	$0.698796\pi$
$744$	1.99877	0.0732785
$745$	0.317210	0.0116217
$746$	−3.89671	−0.142669
$747$	−4.58813	−0.167871
$748$	0.0617419	0.00225751
$749$	−6.68427	−0.244238
$750$	−1.90131	−0.0694260
$751$	−4.00249	−0.146053	−0.0730264	−	0.997330i	$-0.523266\pi$
$751$	−4.00249	−0.146053	−0.0730264	+	0.997330i	$0.523266\pi$
$752$	10.5463	0.384584
$753$	26.8739	0.979340
$754$	−70.3175	−2.56081
$755$	20.5282	0.747097
$756$	1.52076	0.0553095
$757$	−24.2980	−0.883124	−0.441562	−	0.897231i	$-0.645576\pi$
$757$	−24.2980	−0.883124	−0.441562	+	0.897231i	$0.645576\pi$
$758$	39.4918	1.43441
$759$	0	0
$760$	4.52293	0.164064
$761$	24.2036	0.877379	0.438689	−	0.898639i	$-0.355443\pi$
$761$	24.2036	0.877379	0.438689	+	0.898639i	$0.355443\pi$
$762$	29.4961	1.06853
$763$	−0.602901	−0.0218265
$764$	−19.6274	−0.710094
$765$	0.110920	0.00401030
$766$	−41.1368	−1.48633
$767$	52.2265	1.88579
$768$	−20.2893	−0.732127
$769$	13.9566	0.503288	0.251644	−	0.967820i	$-0.419029\pi$
$769$	13.9566	0.503288	0.251644	+	0.967820i	$0.419029\pi$
$770$	0.617097	0.0222386
$771$	−23.6429	−0.851480
$772$	18.7981	0.676560
$773$	−13.9560	−0.501962	−0.250981	−	0.967992i	$-0.580753\pi$
$773$	−13.9560	−0.501962	−0.250981	+	0.967992i	$0.580753\pi$
$774$	1.85506	0.0666789
$775$	−2.73037	−0.0980778
$776$	9.99278	0.358720
$777$	−5.55480	−0.199277
$778$	−63.9675	−2.29335
$779$	−44.2857	−1.58670
$780$	−6.21733	−0.222616
$781$	−0.0292401	−0.00104629
$782$	0	0
$783$	9.60667	0.343314
$784$	28.2544	1.00908
$785$	−4.24565	−0.151534
$786$	−17.3841	−0.620071
$787$	−53.1643	−1.89510	−0.947551	−	0.319605i	$-0.896450\pi$
$787$	−53.1643	−1.89510	−0.947551	+	0.319605i	$0.896450\pi$
$788$	−5.18093	−0.184563
$789$	11.3133	0.402763
$790$	11.9947	0.426751
$791$	−8.05079	−0.286253
$792$	−0.252317	−0.00896571
$793$	−8.33398	−0.295948
$794$	−29.5747	−1.04957
$795$	−13.4086	−0.475554
$796$	20.0889	0.712031
$797$	12.7288	0.450876	0.225438	−	0.974258i	$-0.427619\pi$
$797$	12.7288	0.450876	0.225438	+	0.974258i	$0.427619\pi$
$798$	11.0618	0.391584
$799$	0.253103	0.00895413
$800$	7.32338	0.258921
$801$	−11.8356	−0.418190
$802$	73.2308	2.58587
$803$	0.800083	0.0282343
$804$	−4.66960	−0.164684
$805$	0	0
$806$	−19.9854	−0.703955
$807$	5.84484	0.205748
$808$	−5.03889	−0.177268
$809$	−8.00024	−0.281273	−0.140637	−	0.990061i	$-0.544915\pi$
$809$	−8.00024	−0.281273	−0.140637	+	0.990061i	$0.544915\pi$
$810$	1.90131	0.0668052
$811$	−35.6166	−1.25067	−0.625334	−	0.780357i	$-0.715037\pi$
$811$	−35.6166	−1.25067	−0.625334	+	0.780357i	$0.715037\pi$
$812$	14.6094	0.512691
$813$	20.0827	0.704329
$814$	−3.86574	−0.135494
$815$	7.40104	0.259247
$816$	−0.512648	−0.0179463
$817$	6.02817	0.210899
$818$	67.8383	2.37191
$819$	3.62521	0.126675
$820$	−11.5758	−0.404244
$821$	32.9309	1.14930	0.574648	−	0.818401i	$-0.305139\pi$
$821$	32.9309	1.14930	0.574648	+	0.818401i	$0.305139\pi$
$822$	−15.6668	−0.546444
$823$	−10.3159	−0.359588	−0.179794	−	0.983704i	$-0.557543\pi$
$823$	−10.3159	−0.359588	−0.179794	+	0.983704i	$0.557543\pi$
$824$	−0.893811	−0.0311374
$825$	0.344672	0.0119999
$826$	−24.2885	−0.845105
$827$	19.6441	0.683093	0.341546	−	0.939865i	$-0.389049\pi$
$827$	19.6441	0.683093	0.341546	+	0.939865i	$0.389049\pi$
$828$	0	0
$829$	−40.0323	−1.39038	−0.695190	−	0.718826i	$-0.744680\pi$
$829$	−40.0323	−1.39038	−0.695190	+	0.718826i	$0.744680\pi$
$830$	−8.72346	−0.302796
$831$	22.5451	0.782081
$832$	18.0186	0.624682
$833$	0.678081	0.0234941
$834$	25.1257	0.870033
$835$	3.55092	0.122885
$836$	3.43915	0.118945
$837$	2.73037	0.0943754
$838$	−53.2835	−1.84065
$839$	38.1380	1.31667	0.658335	−	0.752725i	$-0.271261\pi$
$839$	38.1380	1.31667	0.658335	+	0.752725i	$0.271261\pi$
$840$	−0.689344	−0.0237846
$841$	63.2881	2.18235
$842$	−56.8439	−1.95897
$843$	21.4649	0.739290
$844$	−31.6598	−1.08978
$845$	−1.82096	−0.0626430
$846$	4.33852	0.149161
$847$	10.2464	0.352071
$848$	61.9720	2.12813
$849$	25.9275	0.889830
$850$	0.210892	0.00723355
$851$	0	0
$852$	−0.137006	−0.00469373
$853$	15.3040	0.523998	0.261999	−	0.965068i	$-0.415618\pi$
$853$	15.3040	0.523998	0.261999	+	0.965068i	$0.415618\pi$
$854$	3.87580	0.132627
$855$	6.17844	0.211298
$856$	5.19638	0.177609
$857$	−20.8576	−0.712483	−0.356242	−	0.934394i	$-0.615942\pi$
$857$	−20.8576	−0.712483	−0.356242	+	0.934394i	$0.615942\pi$
$858$	2.52288	0.0861298
$859$	−48.2744	−1.64710	−0.823551	−	0.567242i	$-0.808010\pi$
$859$	−48.2744	−1.64710	−0.823551	+	0.567242i	$0.808010\pi$
$860$	1.57570	0.0537308
$861$	6.74962	0.230027
$862$	−5.69653	−0.194025
$863$	−38.4817	−1.30993	−0.654966	−	0.755659i	$-0.727317\pi$
$863$	−38.4817	−1.30993	−0.654966	+	0.755659i	$0.727317\pi$
$864$	−7.32338	−0.249146
$865$	17.2570	0.586756
$866$	6.76283	0.229810
$867$	16.9877	0.576932
$868$	4.15224	0.140936
$869$	−2.17441	−0.0737617
$870$	18.2652	0.619250
$871$	−11.1314	−0.377175
$872$	0.468697	0.0158721
$873$	13.6504	0.461996
$874$	0	0
$875$	0.941661	0.0318340
$876$	3.74882	0.126661
$877$	−0.202222	−0.00682856	−0.00341428	−	0.999994i	$-0.501087\pi$
$877$	−0.202222	−0.00682856	−0.00341428	+	0.999994i	$0.501087\pi$
$878$	16.1793	0.546026
$879$	20.0884	0.677566
$880$	−1.59301	−0.0537003
$881$	57.9770	1.95329	0.976647	−	0.214850i	$-0.0689263\pi$
$881$	57.9770	1.95329	0.976647	+	0.214850i	$0.0689263\pi$
$882$	11.6232	0.391374
$883$	−39.6491	−1.33430	−0.667149	−	0.744924i	$-0.732486\pi$
$883$	−39.6491	−1.33430	−0.667149	+	0.744924i	$0.732486\pi$
$884$	0.689624	0.0231946
$885$	−13.5660	−0.456017
$886$	28.3579	0.952702
$887$	−5.67369	−0.190504	−0.0952520	−	0.995453i	$-0.530366\pi$
$887$	−5.67369	−0.190504	−0.0952520	+	0.995453i	$0.530366\pi$
$888$	4.31832	0.144913
$889$	−14.6086	−0.489955
$890$	−22.5031	−0.754306
$891$	−0.344672	−0.0115469
$892$	2.12589	0.0711801
$893$	14.0983	0.471782
$894$	−0.603115	−0.0201712
$895$	12.3387	0.412437
$896$	5.41256	0.180821
$897$	0	0
$898$	42.9709	1.43396
$899$	26.2298	0.874812
$900$	1.61498	0.0538325
$901$	1.48728	0.0495484
$902$	4.69725	0.156401
$903$	−0.918758	−0.0305744
$904$	6.25871	0.208162
$905$	12.5319	0.416575
$906$	−39.0304	−1.29670
$907$	−22.5215	−0.747814	−0.373907	−	0.927466i	$-0.621982\pi$
$907$	−22.5215	−0.747814	−0.373907	+	0.927466i	$0.621982\pi$
$908$	−28.7142	−0.952913
$909$	−6.88325	−0.228303
$910$	6.89264	0.228489
$911$	−42.7622	−1.41678	−0.708388	−	0.705823i	$-0.750577\pi$
$911$	−42.7622	−1.41678	−0.708388	+	0.705823i	$0.750577\pi$
$912$	−28.5556	−0.945569
$913$	1.58140	0.0523367
$914$	−74.7387	−2.47214
$915$	2.16478	0.0715655
$916$	−12.0477	−0.398066
$917$	8.60984	0.284322
$918$	−0.210892	−0.00696048
$919$	40.2318	1.32713	0.663563	−	0.748120i	$-0.269043\pi$
$919$	40.2318	1.32713	0.663563	+	0.748120i	$0.269043\pi$
$920$	0	0
$921$	−11.9672	−0.394333
$922$	−38.4762	−1.26715
$923$	−0.326596	−0.0107500
$924$	−0.524163	−0.0172437
$925$	−5.89894	−0.193956
$926$	69.3639	2.27944
$927$	−1.22097	−0.0401019
$928$	−70.3533	−2.30946
$929$	−8.72947	−0.286405	−0.143202	−	0.989693i	$-0.545740\pi$
$929$	−8.72947	−0.286405	−0.143202	+	0.989693i	$0.545740\pi$
$930$	5.19128	0.170229
$931$	37.7705	1.23788
$932$	4.94010	0.161818
$933$	−2.55209	−0.0835517
$934$	−37.1875	−1.21681
$935$	−0.0382309	−0.00125028
$936$	−2.81825	−0.0921174
$937$	58.5218	1.91182	0.955912	−	0.293653i	$-0.0948711\pi$
$937$	58.5218	1.91182	0.955912	+	0.293653i	$0.0948711\pi$
$938$	5.17679	0.169028
$939$	−30.7169	−1.00241
$940$	3.68514	0.120196
$941$	8.73847	0.284866	0.142433	−	0.989804i	$-0.454507\pi$
$941$	8.73847	0.284866	0.142433	+	0.989804i	$0.454507\pi$
$942$	8.07230	0.263010
$943$	0	0
$944$	62.6996	2.04070
$945$	−0.941661	−0.0306323
$946$	−0.639389	−0.0207883
$947$	35.4912	1.15331	0.576654	−	0.816988i	$-0.304358\pi$
$947$	35.4912	1.15331	0.576654	+	0.816988i	$0.304358\pi$
$948$	−10.1883	−0.330900
$949$	8.93649	0.290091
$950$	11.7471	0.381127
$951$	−32.9632	−1.06891
$952$	0.0764617	0.00247814
$953$	59.0366	1.91238	0.956191	−	0.292744i	$-0.0945682\pi$
$953$	59.0366	1.91238	0.956191	+	0.292744i	$0.0945682\pi$
$954$	25.4939	0.825396
$955$	12.1534	0.393274
$956$	22.8972	0.740548
$957$	−3.31115	−0.107034
$958$	31.8273	1.02829
$959$	7.75932	0.250561
$960$	−4.68039	−0.151059
$961$	−23.5451	−0.759519
$962$	−43.1782	−1.39212
$963$	7.09838	0.228742
$964$	47.2199	1.52085
$965$	−11.6399	−0.374702
$966$	0	0
$967$	−10.2838	−0.330704	−0.165352	−	0.986235i	$-0.552876\pi$
$967$	−10.2838	−0.330704	−0.165352	+	0.986235i	$0.552876\pi$
$968$	−7.96559	−0.256024
$969$	−0.685310	−0.0220153
$970$	25.9536	0.833320
$971$	29.3045	0.940428	0.470214	−	0.882553i	$-0.344177\pi$
$971$	29.3045	0.940428	0.470214	+	0.882553i	$0.344177\pi$
$972$	−1.61498	−0.0518004
$973$	−12.4440	−0.398937
$974$	−2.40038	−0.0769130
$975$	3.84980	0.123292
$976$	−10.0052	−0.320259
$977$	49.6960	1.58991	0.794957	−	0.606666i	$-0.207493\pi$
$977$	49.6960	1.58991	0.794957	+	0.606666i	$0.207493\pi$
$978$	−14.0717	−0.449962
$979$	4.07939	0.130378
$980$	9.87279	0.315375
$981$	0.640252	0.0204417
$982$	−3.01598	−0.0962437
$983$	−46.8606	−1.49462	−0.747310	−	0.664475i	$-0.768655\pi$
$983$	−46.8606	−1.49462	−0.747310	+	0.664475i	$0.768655\pi$
$984$	−5.24718	−0.167274
$985$	3.20805	0.102217
$986$	−2.02597	−0.0645201
$987$	−2.14874	−0.0683951
$988$	38.4134	1.22209
$989$	0	0
$990$	−0.655328	−0.0208277
$991$	49.5901	1.57528	0.787640	−	0.616135i	$-0.211303\pi$
$991$	49.5901	1.57528	0.787640	+	0.616135i	$0.211303\pi$
$992$	−19.9955	−0.634859
$993$	−22.3176	−0.708227
$994$	0.151887	0.00481755
$995$	−12.4391	−0.394346
$996$	7.40972	0.234786
$997$	−28.5373	−0.903787	−0.451893	−	0.892072i	$-0.649251\pi$
$997$	−28.5373	−0.903787	−0.451893	+	0.892072i	$0.649251\pi$
$998$	26.4973	0.838758
$999$	5.89894	0.186634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bd.1.2	✓	6
23.22	odd	2		7935.2.a.be.1.2	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bd.1.2	✓	6	1.1	even	1	trivial
7935.2.a.be.1.2	yes	6	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.90131 q^{2} -1.00000 q^{3} +1.61498 q^{4} -1.00000 q^{5} +1.90131 q^{6} -0.941661 q^{7} +0.732051 q^{8} +1.00000 q^{9} +1.90131 q^{10} -0.344672 q^{11} -1.61498 q^{12} -3.84980 q^{13} +1.79039 q^{14} +1.00000 q^{15} -4.62181 q^{16} -0.110920 q^{17} -1.90131 q^{18} -6.17844 q^{19} -1.61498 q^{20} +0.941661 q^{21} +0.655328 q^{22} -0.732051 q^{24} +1.00000 q^{25} +7.31966 q^{26} -1.00000 q^{27} -1.52076 q^{28} -9.60667 q^{29} -1.90131 q^{30} -2.73037 q^{31} +7.32338 q^{32} +0.344672 q^{33} +0.210892 q^{34} +0.941661 q^{35} +1.61498 q^{36} -5.89894 q^{37} +11.7471 q^{38} +3.84980 q^{39} -0.732051 q^{40} +7.16778 q^{41} -1.79039 q^{42} -0.975678 q^{43} -0.556637 q^{44} -1.00000 q^{45} -2.28186 q^{47} +4.62181 q^{48} -6.11327 q^{49} -1.90131 q^{50} +0.110920 q^{51} -6.21733 q^{52} -13.4086 q^{53} +1.90131 q^{54} +0.344672 q^{55} -0.689344 q^{56} +6.17844 q^{57} +18.2652 q^{58} -13.5660 q^{59} +1.61498 q^{60} +2.16478 q^{61} +5.19128 q^{62} -0.941661 q^{63} -4.68039 q^{64} +3.84980 q^{65} -0.655328 q^{66} +2.89143 q^{67} -0.179132 q^{68} -1.79039 q^{70} +0.0848344 q^{71} +0.732051 q^{72} -2.32129 q^{73} +11.2157 q^{74} -1.00000 q^{75} -9.97803 q^{76} +0.324564 q^{77} -7.31966 q^{78} +6.30863 q^{79} +4.62181 q^{80} +1.00000 q^{81} -13.6282 q^{82} -4.58813 q^{83} +1.52076 q^{84} +0.110920 q^{85} +1.85506 q^{86} +9.60667 q^{87} -0.252317 q^{88} -11.8356 q^{89} +1.90131 q^{90} +3.62521 q^{91} +2.73037 q^{93} +4.33852 q^{94} +6.17844 q^{95} -7.32338 q^{96} +13.6504 q^{97} +11.6232 q^{98} -0.344672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{3} + 4 q^{4} - 6 q^{5} + 2 q^{7} - 6 q^{8} + 6 q^{9} - 4 q^{11} - 4 q^{12} + 10 q^{13} + 8 q^{14} + 6 q^{15} - 8 q^{16} + 8 q^{17} - 4 q^{19} - 4 q^{20} - 2 q^{21} + 2 q^{22} + 6 q^{24} + 6 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^3 + 4 * q^4 - 6 * q^5 + 2 * q^7 - 6 * q^8 + 6 * q^9 - 4 * q^11 - 4 * q^12 + 10 * q^13 + 8 * q^14 + 6 * q^15 - 8 * q^16 + 8 * q^17 - 4 * q^19 - 4 * q^20 - 2 * q^21 + 2 * q^22 + 6 * q^24 + 6 * q^25 + 14 * q^26 - 6 * q^27 + 4 * q^28 - 4 * q^29 - 6 * q^31 + 8 * q^32 + 4 * q^33 + 24 * q^34 - 2 * q^35 + 4 * q^36 + 6 * q^37 + 10 * q^38 - 10 * q^39 + 6 * q^40 - 20 * q^41 - 8 * q^42 - 4 * q^43 + 10 * q^44 - 6 * q^45 - 4 * q^47 + 8 * q^48 - 10 * q^49 - 8 * q^51 + 6 * q^52 - 22 * q^53 + 4 * q^55 - 8 * q^56 + 4 * q^57 + 4 * q^58 - 22 * q^59 + 4 * q^60 + 8 * q^61 + 16 * q^62 + 2 * q^63 - 24 * q^64 - 10 * q^65 - 2 * q^66 + 8 * q^67 + 2 * q^68 - 8 * q^70 - 2 * q^71 - 6 * q^72 - 18 * q^73 - 10 * q^74 - 6 * q^75 - 40 * q^76 - 22 * q^77 - 14 * q^78 + 20 * q^79 + 8 * q^80 + 6 * q^81 - 4 * q^82 - 18 * q^83 - 4 * q^84 - 8 * q^85 + 14 * q^86 + 4 * q^87 + 10 * q^88 + 6 * q^89 + 44 * q^91 + 6 * q^93 + 24 * q^94 + 4 * q^95 - 8 * q^96 + 12 * q^97 + 28 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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