LMFDB - Embedded newform 7935.2.a.bj.1.1

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 = [10,0,-10,16,-10,0,-6] 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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 18x^{8} + 111x^{6} - 4x^{5} - 270x^{4} + 32x^{3} + 218x^{2} - 60x - 18 $ x^10 - 18x^8 + 111x^6 - 4x^5 - 270x^4 + 32x^3 + 218x^2 - 60*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.57634$ 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)

$f(q)$	$=$	\(q-2.57634 q^{2} -1.00000 q^{3} +4.63755 q^{4} -1.00000 q^{5} +2.57634 q^{6} -2.22333 q^{7} -6.79523 q^{8} +1.00000 q^{9} +2.57634 q^{10} +3.85296 q^{11} -4.63755 q^{12} +5.70765 q^{13} +5.72807 q^{14} +1.00000 q^{15} +8.23175 q^{16} +2.07011 q^{17} -2.57634 q^{18} -6.30815 q^{19} -4.63755 q^{20} +2.22333 q^{21} -9.92654 q^{22} +6.79523 q^{24} +1.00000 q^{25} -14.7049 q^{26} -1.00000 q^{27} -10.3108 q^{28} +7.07159 q^{29} -2.57634 q^{30} +4.00348 q^{31} -7.61737 q^{32} -3.85296 q^{33} -5.33331 q^{34} +2.22333 q^{35} +4.63755 q^{36} -9.82561 q^{37} +16.2520 q^{38} -5.70765 q^{39} +6.79523 q^{40} +9.04057 q^{41} -5.72807 q^{42} +1.69019 q^{43} +17.8683 q^{44} -1.00000 q^{45} -9.81936 q^{47} -8.23175 q^{48} -2.05679 q^{49} -2.57634 q^{50} -2.07011 q^{51} +26.4695 q^{52} -10.5293 q^{53} +2.57634 q^{54} -3.85296 q^{55} +15.1081 q^{56} +6.30815 q^{57} -18.2189 q^{58} -1.83222 q^{59} +4.63755 q^{60} -6.07024 q^{61} -10.3143 q^{62} -2.22333 q^{63} +3.16145 q^{64} -5.70765 q^{65} +9.92654 q^{66} -4.86287 q^{67} +9.60022 q^{68} -5.72807 q^{70} +0.951755 q^{71} -6.79523 q^{72} -7.81309 q^{73} +25.3142 q^{74} -1.00000 q^{75} -29.2543 q^{76} -8.56641 q^{77} +14.7049 q^{78} +6.11017 q^{79} -8.23175 q^{80} +1.00000 q^{81} -23.2916 q^{82} +12.4091 q^{83} +10.3108 q^{84} -2.07011 q^{85} -4.35451 q^{86} -7.07159 q^{87} -26.1817 q^{88} -13.5916 q^{89} +2.57634 q^{90} -12.6900 q^{91} -4.00348 q^{93} +25.2981 q^{94} +6.30815 q^{95} +7.61737 q^{96} -11.0986 q^{97} +5.29899 q^{98} +3.85296 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{3} + 16 q^{4} - 10 q^{5} - 6 q^{7} + 10 q^{9} + 4 q^{11} - 16 q^{12} - 4 q^{13} + 10 q^{15} + 28 q^{16} - 10 q^{17} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 4 q^{22} + 10 q^{25} - 8 q^{26} - 10 q^{27}+ \cdots + 4 q^{99}+O(q^{100}) $ 10 * q - 10 * q^3 + 16 * q^4 - 10 * q^5 - 6 * q^7 + 10 * q^9 + 4 * q^11 - 16 * q^12 - 4 * q^13 + 10 * q^15 + 28 * q^16 - 10 * q^17 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 4 * q^22 + 10 * q^25 - 8 * q^26 - 10 * q^27 - 76 * q^28 + 2 * q^29 + 2 * q^31 + 20 * q^32 - 4 * q^33 - 8 * q^34 + 6 * q^35 + 16 * q^36 - 2 * q^37 + 56 * q^38 + 4 * q^39 + 6 * q^41 - 44 * q^43 + 24 * q^44 - 10 * q^45 + 8 * q^47 - 28 * q^48 + 12 * q^49 + 10 * q^51 - 2 * q^53 - 4 * q^55 - 8 * q^56 + 8 * q^57 - 20 * q^58 - 14 * q^59 + 16 * q^60 + 8 * q^61 - 28 * q^62 - 6 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 2 * q^67 - 84 * q^68 + 6 * q^71 - 12 * q^73 - 40 * q^74 - 10 * q^75 - 44 * q^76 - 16 * q^77 + 8 * q^78 - 28 * q^80 + 10 * q^81 - 4 * q^82 + 62 * q^83 + 76 * q^84 + 10 * q^85 + 4 * q^86 - 2 * q^87 + 12 * q^88 - 56 * q^89 - 2 * q^93 + 20 * q^94 + 8 * q^95 - 20 * q^96 - 56 * q^97 - 4 * 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 $

$2$	−2.57634	−1.82175	−0.910875	−	0.412682i	$-0.864592\pi$
$2$	−2.57634	−1.82175	−0.910875	+	0.412682i	$0.864592\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.63755	2.31877
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.57634	1.05179
$7$	−2.22333	−0.840341	−0.420171	−	0.907445i	$-0.638030\pi$
$7$	−2.22333	−0.840341	−0.420171	+	0.907445i	$0.638030\pi$
$8$	−6.79523	−2.40248
$9$	1.00000	0.333333
$10$	2.57634	0.814711
$11$	3.85296	1.16171	0.580855	−	0.814007i	$-0.302718\pi$
$11$	3.85296	1.16171	0.580855	+	0.814007i	$0.302718\pi$
$12$	−4.63755	−1.33874
$13$	5.70765	1.58302	0.791509	−	0.611157i	$-0.209296\pi$
$13$	5.70765	1.58302	0.791509	+	0.611157i	$0.209296\pi$
$14$	5.72807	1.53089
$15$	1.00000	0.258199
$16$	8.23175	2.05794
$17$	2.07011	0.502075	0.251037	−	0.967977i	$-0.419228\pi$
$17$	2.07011	0.502075	0.251037	+	0.967977i	$0.419228\pi$
$18$	−2.57634	−0.607250
$19$	−6.30815	−1.44719	−0.723594	−	0.690225i	$-0.757511\pi$
$19$	−6.30815	−1.44719	−0.723594	+	0.690225i	$0.757511\pi$
$20$	−4.63755	−1.03699
$21$	2.22333	0.485171
$22$	−9.92654	−2.11635
$23$	0	0
$23$	0	0
$24$	6.79523	1.38707
$25$	1.00000	0.200000
$26$	−14.7049	−2.88386
$27$	−1.00000	−0.192450
$28$	−10.3108	−1.94856
$29$	7.07159	1.31316	0.656581	−	0.754256i	$-0.272002\pi$
$29$	7.07159	1.31316	0.656581	+	0.754256i	$0.272002\pi$
$30$	−2.57634	−0.470374
$31$	4.00348	0.719046	0.359523	−	0.933136i	$-0.382939\pi$
$31$	4.00348	0.719046	0.359523	+	0.933136i	$0.382939\pi$
$32$	−7.61737	−1.34657
$33$	−3.85296	−0.670714
$34$	−5.33331	−0.914654
$35$	2.22333	0.375812
$36$	4.63755	0.772925
$37$	−9.82561	−1.61532	−0.807660	−	0.589648i	$-0.799267\pi$
$37$	−9.82561	−1.61532	−0.807660	+	0.589648i	$0.799267\pi$
$38$	16.2520	2.63642
$39$	−5.70765	−0.913956
$40$	6.79523	1.07442
$41$	9.04057	1.41190	0.705950	−	0.708262i	$-0.250520\pi$
$41$	9.04057	1.41190	0.705950	+	0.708262i	$0.250520\pi$
$42$	−5.72807	−0.883861
$43$	1.69019	0.257752	0.128876	−	0.991661i	$-0.458863\pi$
$43$	1.69019	0.257752	0.128876	+	0.991661i	$0.458863\pi$
$44$	17.8683	2.69374
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−9.81936	−1.43230	−0.716151	−	0.697946i	$-0.754098\pi$
$47$	−9.81936	−1.43230	−0.716151	+	0.697946i	$0.754098\pi$
$48$	−8.23175	−1.18815
$49$	−2.05679	−0.293827
$50$	−2.57634	−0.364350
$51$	−2.07011	−0.289873
$52$	26.4695	3.67066
$53$	−10.5293	−1.44632	−0.723158	−	0.690683i	$-0.757310\pi$
$53$	−10.5293	−1.44632	−0.723158	+	0.690683i	$0.757310\pi$
$54$	2.57634	0.350596
$55$	−3.85296	−0.519532
$56$	15.1081	2.01890
$57$	6.30815	0.835535
$58$	−18.2189	−2.39225
$59$	−1.83222	−0.238535	−0.119267	−	0.992862i	$-0.538055\pi$
$59$	−1.83222	−0.238535	−0.119267	+	0.992862i	$0.538055\pi$
$60$	4.63755	0.598705
$61$	−6.07024	−0.777215	−0.388607	−	0.921403i	$-0.627044\pi$
$61$	−6.07024	−0.777215	−0.388607	+	0.921403i	$0.627044\pi$
$62$	−10.3143	−1.30992
$63$	−2.22333	−0.280114
$64$	3.16145	0.395181
$65$	−5.70765	−0.707947
$66$	9.92654	1.22187
$67$	−4.86287	−0.594094	−0.297047	−	0.954863i	$-0.596002\pi$
$67$	−4.86287	−0.594094	−0.297047	+	0.954863i	$0.596002\pi$
$68$	9.60022	1.16420
$69$	0	0
$70$	−5.72807	−0.684636
$71$	0.951755	0.112953	0.0564763	−	0.998404i	$-0.482013\pi$
$71$	0.951755	0.112953	0.0564763	+	0.998404i	$0.482013\pi$
$72$	−6.79523	−0.800825
$73$	−7.81309	−0.914453	−0.457227	−	0.889350i	$-0.651157\pi$
$73$	−7.81309	−0.914453	−0.457227	+	0.889350i	$0.651157\pi$
$74$	25.3142	2.94271
$75$	−1.00000	−0.115470
$76$	−29.2543	−3.35570
$77$	−8.56641	−0.976233
$78$	14.7049	1.66500
$79$	6.11017	0.687448	0.343724	−	0.939071i	$-0.388312\pi$
$79$	6.11017	0.687448	0.343724	+	0.939071i	$0.388312\pi$
$80$	−8.23175	−0.920338
$81$	1.00000	0.111111
$82$	−23.2916	−2.57213
$83$	12.4091	1.36207	0.681037	−	0.732249i	$-0.261529\pi$
$83$	12.4091	1.36207	0.681037	+	0.732249i	$0.261529\pi$
$84$	10.3108	1.12500
$85$	−2.07011	−0.224535
$86$	−4.35451	−0.469559
$87$	−7.07159	−0.758154
$88$	−26.1817	−2.79098
$89$	−13.5916	−1.44071	−0.720355	−	0.693605i	$-0.756021\pi$
$89$	−13.5916	−1.44071	−0.720355	+	0.693605i	$0.756021\pi$
$90$	2.57634	0.271570
$91$	−12.6900	−1.33028
$92$	0	0
$93$	−4.00348	−0.415141
$94$	25.2981	2.60929
$95$	6.30815	0.647203
$96$	7.61737	0.777444
$97$	−11.0986	−1.12689	−0.563446	−	0.826153i	$-0.690525\pi$
$97$	−11.0986	−1.12689	−0.563446	+	0.826153i	$0.690525\pi$
$98$	5.29899	0.535279
$99$	3.85296	0.387237
$100$	4.63755	0.463755
$101$	11.5119	1.14548	0.572740	−	0.819737i	$-0.305880\pi$
$101$	11.5119	1.14548	0.572740	+	0.819737i	$0.305880\pi$
$102$	5.33331	0.528076
$103$	15.4906	1.52633	0.763167	−	0.646201i	$-0.223643\pi$
$103$	15.4906	1.52633	0.763167	+	0.646201i	$0.223643\pi$
$104$	−38.7848	−3.80316
$105$	−2.22333	−0.216975
$106$	27.1272	2.63483
$107$	−1.55180	−0.150018	−0.0750091	−	0.997183i	$-0.523899\pi$
$107$	−1.55180	−0.150018	−0.0750091	+	0.997183i	$0.523899\pi$
$108$	−4.63755	−0.446248
$109$	−0.200796	−0.0192328	−0.00961640	−	0.999954i	$-0.503061\pi$
$109$	−0.200796	−0.0192328	−0.00961640	+	0.999954i	$0.503061\pi$
$110$	9.92654	0.946458
$111$	9.82561	0.932606
$112$	−18.3019	−1.72937
$113$	−10.0237	−0.942954	−0.471477	−	0.881878i	$-0.656279\pi$
$113$	−10.0237	−0.942954	−0.471477	+	0.881878i	$0.656279\pi$
$114$	−16.2520	−1.52214
$115$	0	0
$116$	32.7948	3.04492
$117$	5.70765	0.527673
$118$	4.72043	0.434550
$119$	−4.60254	−0.421914
$120$	−6.79523	−0.620317
$121$	3.84527	0.349570
$122$	15.6390	1.41589
$123$	−9.04057	−0.815161
$124$	18.5663	1.66730
$125$	−1.00000	−0.0894427
$126$	5.72807	0.510297
$127$	−12.0303	−1.06752	−0.533758	−	0.845637i	$-0.679221\pi$
$127$	−12.0303	−1.06752	−0.533758	+	0.845637i	$0.679221\pi$
$128$	7.08975	0.626652
$129$	−1.69019	−0.148813
$130$	14.7049	1.28970
$131$	16.6883	1.45806	0.729031	−	0.684481i	$-0.239971\pi$
$131$	16.6883	1.45806	0.729031	+	0.684481i	$0.239971\pi$
$132$	−17.8683	−1.55523
$133$	14.0251	1.21613
$134$	12.5284	1.08229
$135$	1.00000	0.0860663
$136$	−14.0668	−1.20622
$137$	8.55331	0.730758	0.365379	−	0.930859i	$-0.380939\pi$
$137$	8.55331	0.730758	0.365379	+	0.930859i	$0.380939\pi$
$138$	0	0
$139$	−13.1286	−1.11356	−0.556778	−	0.830661i	$-0.687963\pi$
$139$	−13.1286	−1.11356	−0.556778	+	0.830661i	$0.687963\pi$
$140$	10.3108	0.871423
$141$	9.81936	0.826939
$142$	−2.45205	−0.205771
$143$	21.9913	1.83901
$144$	8.23175	0.685979
$145$	−7.07159	−0.587264
$146$	20.1292	1.66591
$147$	2.05679	0.169641
$148$	−45.5667	−3.74556
$149$	−11.0037	−0.901460	−0.450730	−	0.892660i	$-0.648836\pi$
$149$	−11.0037	−0.901460	−0.450730	+	0.892660i	$0.648836\pi$
$150$	2.57634	0.210358
$151$	−17.2564	−1.40431	−0.702154	−	0.712025i	$-0.747778\pi$
$151$	−17.2564	−1.40431	−0.702154	+	0.712025i	$0.747778\pi$
$152$	42.8653	3.47684
$153$	2.07011	0.167358
$154$	22.0700	1.77845
$155$	−4.00348	−0.321567
$156$	−26.4695	−2.11926
$157$	7.98282	0.637098	0.318549	−	0.947906i	$-0.396804\pi$
$157$	7.98282	0.637098	0.318549	+	0.947906i	$0.396804\pi$
$158$	−15.7419	−1.25236
$159$	10.5293	0.835031
$160$	7.61737	0.602206
$161$	0	0
$162$	−2.57634	−0.202417
$163$	−4.19674	−0.328714	−0.164357	−	0.986401i	$-0.552555\pi$
$163$	−4.19674	−0.328714	−0.164357	+	0.986401i	$0.552555\pi$
$164$	41.9261	3.27388
$165$	3.85296	0.299952
$166$	−31.9700	−2.48136
$167$	25.2458	1.95358	0.976791	−	0.214194i	$-0.0687125\pi$
$167$	25.2458	1.95358	0.976791	+	0.214194i	$0.0687125\pi$
$168$	−15.1081	−1.16561
$169$	19.5773	1.50595
$170$	5.33331	0.409046
$171$	−6.30815	−0.482396
$172$	7.83834	0.597668
$173$	−18.5140	−1.40760	−0.703799	−	0.710400i	$-0.748514\pi$
$173$	−18.5140	−1.40760	−0.703799	+	0.710400i	$0.748514\pi$
$174$	18.2189	1.38117
$175$	−2.22333	−0.168068
$176$	31.7166	2.39073
$177$	1.83222	0.137718
$178$	35.0167	2.62461
$179$	13.3239	0.995877	0.497938	−	0.867212i	$-0.334091\pi$
$179$	13.3239	0.995877	0.497938	+	0.867212i	$0.334091\pi$
$180$	−4.63755	−0.345662
$181$	−25.2946	−1.88013	−0.940066	−	0.340992i	$-0.889237\pi$
$181$	−25.2946	−1.88013	−0.940066	+	0.340992i	$0.889237\pi$
$182$	32.6939	2.42343
$183$	6.07024	0.448725
$184$	0	0
$185$	9.82561	0.722393
$186$	10.3143	0.756284
$187$	7.97603	0.583265
$188$	−45.5378	−3.32118
$189$	2.22333	0.161724
$190$	−16.2520	−1.17904
$191$	10.4473	0.755938	0.377969	−	0.925818i	$-0.376623\pi$
$191$	10.4473	0.755938	0.377969	+	0.925818i	$0.376623\pi$
$192$	−3.16145	−0.228158
$193$	−8.36824	−0.602359	−0.301180	−	0.953567i	$-0.597380\pi$
$193$	−8.36824	−0.602359	−0.301180	+	0.953567i	$0.597380\pi$
$194$	28.5938	2.05291
$195$	5.70765	0.408734
$196$	−9.53844	−0.681317
$197$	−8.00920	−0.570632	−0.285316	−	0.958434i	$-0.592099\pi$
$197$	−8.00920	−0.570632	−0.285316	+	0.958434i	$0.592099\pi$
$198$	−9.92654	−0.705448
$199$	−16.2030	−1.14860	−0.574298	−	0.818646i	$-0.694725\pi$
$199$	−16.2030	−1.14860	−0.574298	+	0.818646i	$0.694725\pi$
$200$	−6.79523	−0.480495
$201$	4.86287	0.343001
$202$	−29.6587	−2.08678
$203$	−15.7225	−1.10350
$204$	−9.60022	−0.672150
$205$	−9.04057	−0.631421
$206$	−39.9091	−2.78060
$207$	0	0
$208$	46.9840	3.25775
$209$	−24.3050	−1.68121
$210$	5.72807	0.395275
$211$	22.8980	1.57636	0.788180	−	0.615444i	$-0.211023\pi$
$211$	22.8980	1.57636	0.788180	+	0.615444i	$0.211023\pi$
$212$	−48.8303	−3.35368
$213$	−0.951755	−0.0652132
$214$	3.99797	0.273296
$215$	−1.69019	−0.115270
$216$	6.79523	0.462357
$217$	−8.90107	−0.604244
$218$	0.517320	0.0350374
$219$	7.81309	0.527960
$220$	−17.8683	−1.20468
$221$	11.8155	0.794793
$222$	−25.3142	−1.69898
$223$	11.2262	0.751759	0.375880	−	0.926669i	$-0.377341\pi$
$223$	11.2262	0.751759	0.375880	+	0.926669i	$0.377341\pi$
$224$	16.9359	1.13158
$225$	1.00000	0.0666667
$226$	25.8246	1.71783
$227$	−3.47153	−0.230414	−0.115207	−	0.993342i	$-0.536753\pi$
$227$	−3.47153	−0.230414	−0.115207	+	0.993342i	$0.536753\pi$
$228$	29.2543	1.93742
$229$	19.0032	1.25577	0.627885	−	0.778306i	$-0.283921\pi$
$229$	19.0032	1.25577	0.627885	+	0.778306i	$0.283921\pi$
$230$	0	0
$231$	8.56641	0.563628
$232$	−48.0531	−3.15484
$233$	−10.0904	−0.661045	−0.330522	−	0.943798i	$-0.607225\pi$
$233$	−10.0904	−0.661045	−0.330522	+	0.943798i	$0.607225\pi$
$234$	−14.7049	−0.961288
$235$	9.81936	0.640545
$236$	−8.49700	−0.553108
$237$	−6.11017	−0.396898
$238$	11.8577	0.768622
$239$	−0.746340	−0.0482767	−0.0241384	−	0.999709i	$-0.507684\pi$
$239$	−0.746340	−0.0482767	−0.0241384	+	0.999709i	$0.507684\pi$
$240$	8.23175	0.531357
$241$	9.88272	0.636602	0.318301	−	0.947990i	$-0.396888\pi$
$241$	9.88272	0.636602	0.318301	+	0.947990i	$0.396888\pi$
$242$	−9.90674	−0.636829
$243$	−1.00000	−0.0641500
$244$	−28.1510	−1.80219
$245$	2.05679	0.131403
$246$	23.2916	1.48502
$247$	−36.0047	−2.29093
$248$	−27.2045	−1.72749
$249$	−12.4091	−0.786393
$250$	2.57634	0.162942
$251$	−3.53095	−0.222871	−0.111436	−	0.993772i	$-0.535545\pi$
$251$	−3.53095	−0.222871	−0.111436	+	0.993772i	$0.535545\pi$
$252$	−10.3108	−0.649520
$253$	0	0
$254$	30.9942	1.94475
$255$	2.07011	0.129635
$256$	−24.5885	−1.53678
$257$	−24.0303	−1.49897	−0.749484	−	0.662022i	$-0.769698\pi$
$257$	−24.0303	−1.49897	−0.749484	+	0.662022i	$0.769698\pi$
$258$	4.35451	0.271100
$259$	21.8456	1.35742
$260$	−26.4695	−1.64157
$261$	7.07159	0.437721
$262$	−42.9947	−2.65622
$263$	0.757054	0.0466820	0.0233410	−	0.999728i	$-0.492570\pi$
$263$	0.757054	0.0466820	0.0233410	+	0.999728i	$0.492570\pi$
$264$	26.1817	1.61137
$265$	10.5293	0.646812
$266$	−36.1335	−2.21549
$267$	13.5916	0.831795
$268$	−22.5518	−1.37757
$269$	27.1946	1.65809	0.829043	−	0.559185i	$-0.188886\pi$
$269$	27.1946	1.65809	0.829043	+	0.559185i	$0.188886\pi$
$270$	−2.57634	−0.156791
$271$	−2.56803	−0.155996	−0.0779982	−	0.996953i	$-0.524853\pi$
$271$	−2.56803	−0.155996	−0.0779982	+	0.996953i	$0.524853\pi$
$272$	17.0406	1.03324
$273$	12.6900	0.768035
$274$	−22.0363	−1.33126
$275$	3.85296	0.232342
$276$	0	0
$277$	−10.0095	−0.601415	−0.300708	−	0.953716i	$-0.597223\pi$
$277$	−10.0095	−0.601415	−0.300708	+	0.953716i	$0.597223\pi$
$278$	33.8239	2.02862
$279$	4.00348	0.239682
$280$	−15.1081	−0.902880
$281$	12.5059	0.746037	0.373018	−	0.927824i	$-0.378323\pi$
$281$	12.5059	0.746037	0.373018	+	0.927824i	$0.378323\pi$
$282$	−25.2981	−1.50648
$283$	12.1338	0.721279	0.360640	−	0.932705i	$-0.382558\pi$
$283$	12.1338	0.721279	0.360640	+	0.932705i	$0.382558\pi$
$284$	4.41381	0.261911
$285$	−6.30815	−0.373663
$286$	−56.6573	−3.35021
$287$	−20.1002	−1.18648
$288$	−7.61737	−0.448858
$289$	−12.7147	−0.747921
$290$	18.2189	1.06985
$291$	11.0986	0.650611
$292$	−36.2336	−2.12041
$293$	−11.2319	−0.656173	−0.328087	−	0.944648i	$-0.606404\pi$
$293$	−11.2319	−0.656173	−0.328087	+	0.944648i	$0.606404\pi$
$294$	−5.29899	−0.309043
$295$	1.83222	0.106676
$296$	66.7673	3.88077
$297$	−3.85296	−0.223571
$298$	28.3494	1.64224
$299$	0	0
$300$	−4.63755	−0.267749
$301$	−3.75786	−0.216599
$302$	44.4585	2.55830
$303$	−11.5119	−0.661343
$304$	−51.9271	−2.97823
$305$	6.07024	0.347581
$306$	−5.33331	−0.304885
$307$	18.6464	1.06421	0.532104	−	0.846679i	$-0.321401\pi$
$307$	18.6464	1.06421	0.532104	+	0.846679i	$0.321401\pi$
$308$	−39.7271	−2.26366
$309$	−15.4906	−0.881230
$310$	10.3143	0.585815
$311$	14.5596	0.825597	0.412799	−	0.910822i	$-0.364551\pi$
$311$	14.5596	0.825597	0.412799	+	0.910822i	$0.364551\pi$
$312$	38.7848	2.19576
$313$	2.75237	0.155573	0.0777866	−	0.996970i	$-0.475215\pi$
$313$	2.75237	0.155573	0.0777866	+	0.996970i	$0.475215\pi$
$314$	−20.5665	−1.16063
$315$	2.22333	0.125271
$316$	28.3362	1.59404
$317$	−34.5826	−1.94235	−0.971175	−	0.238368i	$-0.923388\pi$
$317$	−34.5826	−1.94235	−0.971175	+	0.238368i	$0.923388\pi$
$318$	−27.1272	−1.52122
$319$	27.2465	1.52551
$320$	−3.16145	−0.176730
$321$	1.55180	0.0866130
$322$	0	0
$323$	−13.0585	−0.726597
$324$	4.63755	0.257642
$325$	5.70765	0.316604
$326$	10.8123	0.598835
$327$	0.200796	0.0111041
$328$	−61.4327	−3.39206
$329$	21.8317	1.20362
$330$	−9.92654	−0.546438
$331$	−14.5713	−0.800909	−0.400454	−	0.916317i	$-0.631148\pi$
$331$	−14.5713	−0.800909	−0.400454	+	0.916317i	$0.631148\pi$
$332$	57.5477	3.15834
$333$	−9.82561	−0.538440
$334$	−65.0420	−3.55894
$335$	4.86287	0.265687
$336$	18.3019	0.998452
$337$	−10.1165	−0.551082	−0.275541	−	0.961289i	$-0.588857\pi$
$337$	−10.1165	−0.551082	−0.275541	+	0.961289i	$0.588857\pi$
$338$	−50.4379	−2.74346
$339$	10.0237	0.544415
$340$	−9.60022	−0.520645
$341$	15.4252	0.835323
$342$	16.2520	0.878806
$343$	20.1363	1.08726
$344$	−11.4852	−0.619242
$345$	0	0
$346$	47.6986	2.56429
$347$	12.9436	0.694851	0.347425	−	0.937708i	$-0.387056\pi$
$347$	12.9436	0.694851	0.347425	+	0.937708i	$0.387056\pi$
$348$	−32.7948	−1.75799
$349$	−26.9395	−1.44204	−0.721019	−	0.692916i	$-0.756326\pi$
$349$	−26.9395	−1.44204	−0.721019	+	0.692916i	$0.756326\pi$
$350$	5.72807	0.306178
$351$	−5.70765	−0.304652
$352$	−29.3494	−1.56433
$353$	−26.2272	−1.39593	−0.697965	−	0.716131i	$-0.745911\pi$
$353$	−26.2272	−1.39593	−0.697965	+	0.716131i	$0.745911\pi$
$354$	−4.72043	−0.250888
$355$	−0.951755	−0.0505139
$356$	−63.0319	−3.34068
$357$	4.60254	0.243592
$358$	−34.3270	−1.81424
$359$	−9.08270	−0.479366	−0.239683	−	0.970851i	$-0.577044\pi$
$359$	−9.08270	−0.479366	−0.239683	+	0.970851i	$0.577044\pi$
$360$	6.79523	0.358140
$361$	20.7928	1.09436
$362$	65.1676	3.42513
$363$	−3.84527	−0.201824
$364$	−58.8506	−3.08461
$365$	7.81309	0.408956
$366$	−15.6390	−0.817465
$367$	12.8673	0.671668	0.335834	−	0.941921i	$-0.390982\pi$
$367$	12.8673	0.671668	0.335834	+	0.941921i	$0.390982\pi$
$368$	0	0
$369$	9.04057	0.470633
$370$	−25.3142	−1.31602
$371$	23.4102	1.21540
$372$	−18.5663	−0.962619
$373$	12.5724	0.650975	0.325488	−	0.945546i	$-0.394472\pi$
$373$	12.5724	0.650975	0.325488	+	0.945546i	$0.394472\pi$
$374$	−20.5490	−1.06256
$375$	1.00000	0.0516398
$376$	66.7248	3.44107
$377$	40.3622	2.07876
$378$	−5.72807	−0.294620
$379$	0.856382	0.0439894	0.0219947	−	0.999758i	$-0.492998\pi$
$379$	0.856382	0.0439894	0.0219947	+	0.999758i	$0.492998\pi$
$380$	29.2543	1.50072
$381$	12.0303	0.616331
$382$	−26.9158	−1.37713
$383$	34.4088	1.75821	0.879103	−	0.476633i	$-0.158143\pi$
$383$	34.4088	1.75821	0.879103	+	0.476633i	$0.158143\pi$
$384$	−7.08975	−0.361797
$385$	8.56641	0.436585
$386$	21.5595	1.09735
$387$	1.69019	0.0859172
$388$	−51.4702	−2.61301
$389$	−25.5349	−1.29467	−0.647336	−	0.762205i	$-0.724117\pi$
$389$	−25.5349	−1.29467	−0.647336	+	0.762205i	$0.724117\pi$
$390$	−14.7049	−0.744610
$391$	0	0
$392$	13.9763	0.705911
$393$	−16.6883	−0.841812
$394$	20.6345	1.03955
$395$	−6.11017	−0.307436
$396$	17.8683	0.897914
$397$	3.80517	0.190976	0.0954880	−	0.995431i	$-0.469559\pi$
$397$	3.80517	0.190976	0.0954880	+	0.995431i	$0.469559\pi$
$398$	41.7444	2.09246
$399$	−14.0251	−0.702134
$400$	8.23175	0.411588
$401$	6.10853	0.305045	0.152523	−	0.988300i	$-0.451260\pi$
$401$	6.10853	0.305045	0.152523	+	0.988300i	$0.451260\pi$
$402$	−12.5284	−0.624861
$403$	22.8505	1.13826
$404$	53.3871	2.65611
$405$	−1.00000	−0.0496904
$406$	40.5066	2.01031
$407$	−37.8577	−1.87653
$408$	14.0668	0.696413
$409$	−5.97720	−0.295554	−0.147777	−	0.989021i	$-0.547212\pi$
$409$	−5.97720	−0.295554	−0.147777	+	0.989021i	$0.547212\pi$
$410$	23.2916	1.15029
$411$	−8.55331	−0.421903
$412$	71.8384	3.53922
$413$	4.07363	0.200450
$414$	0	0
$415$	−12.4091	−0.609138
$416$	−43.4773	−2.13165
$417$	13.1286	0.642912
$418$	62.6181	3.06275
$419$	3.00501	0.146804	0.0734021	−	0.997302i	$-0.476614\pi$
$419$	3.00501	0.146804	0.0734021	+	0.997302i	$0.476614\pi$
$420$	−10.3108	−0.503116
$421$	23.6861	1.15439	0.577195	−	0.816606i	$-0.304147\pi$
$421$	23.6861	1.15439	0.577195	+	0.816606i	$0.304147\pi$
$422$	−58.9930	−2.87174
$423$	−9.81936	−0.477434
$424$	71.5493	3.47474
$425$	2.07011	0.100415
$426$	2.45205	0.118802
$427$	13.4962	0.653126
$428$	−7.19654	−0.347858
$429$	−21.9913	−1.06175
$430$	4.35451	0.209993
$431$	6.51812	0.313967	0.156983	−	0.987601i	$-0.449823\pi$
$431$	6.51812	0.313967	0.156983	+	0.987601i	$0.449823\pi$
$432$	−8.23175	−0.396050
$433$	−30.7910	−1.47972	−0.739860	−	0.672761i	$-0.765108\pi$
$433$	−30.7910	−1.47972	−0.739860	+	0.672761i	$0.765108\pi$
$434$	22.9322	1.10078
$435$	7.07159	0.339057
$436$	−0.931202	−0.0445965
$437$	0	0
$438$	−20.1292	−0.961811
$439$	8.28439	0.395392	0.197696	−	0.980263i	$-0.436654\pi$
$439$	8.28439	0.395392	0.197696	+	0.980263i	$0.436654\pi$
$440$	26.1817	1.24816
$441$	−2.05679	−0.0979422
$442$	−30.4407	−1.44791
$443$	10.2668	0.487790	0.243895	−	0.969802i	$-0.421575\pi$
$443$	10.2668	0.487790	0.243895	+	0.969802i	$0.421575\pi$
$444$	45.5667	2.16250
$445$	13.5916	0.644305
$446$	−28.9224	−1.36952
$447$	11.0037	0.520458
$448$	−7.02896	−0.332087
$449$	−23.7501	−1.12084	−0.560418	−	0.828210i	$-0.689360\pi$
$449$	−23.7501	−1.12084	−0.560418	+	0.828210i	$0.689360\pi$
$450$	−2.57634	−0.121450
$451$	34.8329	1.64022
$452$	−46.4856	−2.18650
$453$	17.2564	0.810778
$454$	8.94385	0.419756
$455$	12.6900	0.594917
$456$	−42.8653	−2.00735
$457$	6.21034	0.290508	0.145254	−	0.989394i	$-0.453600\pi$
$457$	6.21034	0.290508	0.145254	+	0.989394i	$0.453600\pi$
$458$	−48.9589	−2.28770
$459$	−2.07011	−0.0966243
$460$	0	0
$461$	−15.1396	−0.705120	−0.352560	−	0.935789i	$-0.614689\pi$
$461$	−15.1396	−0.705120	−0.352560	+	0.935789i	$0.614689\pi$
$462$	−22.0700	−1.02679
$463$	31.2455	1.45210	0.726051	−	0.687641i	$-0.241354\pi$
$463$	31.2455	1.45210	0.726051	+	0.687641i	$0.241354\pi$
$464$	58.2116	2.70241
$465$	4.00348	0.185657
$466$	25.9964	1.20426
$467$	7.39242	0.342080	0.171040	−	0.985264i	$-0.445287\pi$
$467$	7.39242	0.342080	0.171040	+	0.985264i	$0.445287\pi$
$468$	26.4695	1.22355
$469$	10.8118	0.499242
$470$	−25.2981	−1.16691
$471$	−7.98282	−0.367829
$472$	12.4503	0.573074
$473$	6.51223	0.299433
$474$	15.7419	0.723049
$475$	−6.30815	−0.289438
$476$	−21.3445	−0.978323
$477$	−10.5293	−0.482105
$478$	1.92283	0.0879481
$479$	−4.43812	−0.202783	−0.101392	−	0.994847i	$-0.532329\pi$
$479$	−4.43812	−0.202783	−0.101392	+	0.994847i	$0.532329\pi$
$480$	−7.61737	−0.347684
$481$	−56.0812	−2.55708
$482$	−25.4613	−1.15973
$483$	0	0
$484$	17.8326	0.810574
$485$	11.0986	0.503961
$486$	2.57634	0.116865
$487$	20.6904	0.937571	0.468785	−	0.883312i	$-0.344692\pi$
$487$	20.6904	0.937571	0.468785	+	0.883312i	$0.344692\pi$
$488$	41.2487	1.86724
$489$	4.19674	0.189783
$490$	−5.29899	−0.239384
$491$	2.13813	0.0964925	0.0482462	−	0.998835i	$-0.484637\pi$
$491$	2.13813	0.0964925	0.0482462	+	0.998835i	$0.484637\pi$
$492$	−41.9261	−1.89017
$493$	14.6389	0.659305
$494$	92.7606	4.17350
$495$	−3.85296	−0.173177
$496$	32.9556	1.47975
$497$	−2.11607	−0.0949187
$498$	31.9700	1.43261
$499$	−30.8994	−1.38325	−0.691623	−	0.722259i	$-0.743104\pi$
$499$	−30.8994	−1.38325	−0.691623	+	0.722259i	$0.743104\pi$
$500$	−4.63755	−0.207397
$501$	−25.2458	−1.12790
$502$	9.09693	0.406016
$503$	−0.210342	−0.00937869	−0.00468935	−	0.999989i	$-0.501493\pi$
$503$	−0.210342	−0.00937869	−0.00468935	+	0.999989i	$0.501493\pi$
$504$	15.1081	0.672967
$505$	−11.5119	−0.512274
$506$	0	0
$507$	−19.5773	−0.869459
$508$	−55.7910	−2.47533
$509$	−18.8512	−0.835564	−0.417782	−	0.908547i	$-0.637192\pi$
$509$	−18.8512	−0.835564	−0.417782	+	0.908547i	$0.637192\pi$
$510$	−5.33331	−0.236163
$511$	17.3711	0.768453
$512$	49.1690	2.17298
$513$	6.30815	0.278512
$514$	61.9103	2.73075
$515$	−15.4906	−0.682598
$516$	−7.83834	−0.345064
$517$	−37.8336	−1.66392
$518$	−56.2818	−2.47288
$519$	18.5140	0.812677
$520$	38.7848	1.70083
$521$	14.5923	0.639302	0.319651	−	0.947535i	$-0.396434\pi$
$521$	14.5923	0.639302	0.319651	+	0.947535i	$0.396434\pi$
$522$	−18.2189	−0.797418
$523$	36.5014	1.59609	0.798047	−	0.602595i	$-0.205867\pi$
$523$	36.5014	1.59609	0.798047	+	0.602595i	$0.205867\pi$
$524$	77.3927	3.38091
$525$	2.22333	0.0970343
$526$	−1.95043	−0.0850429
$527$	8.28762	0.361015
$528$	−31.7166	−1.38029
$529$	0	0
$530$	−27.1272	−1.17833
$531$	−1.83222	−0.0795115
$532$	65.0422	2.81994
$533$	51.6004	2.23506
$534$	−35.0167	−1.51532
$535$	1.55180	0.0670901
$536$	33.0443	1.42730
$537$	−13.3239	−0.574970
$538$	−70.0627	−3.02062
$539$	−7.92471	−0.341341
$540$	4.63755	0.199568
$541$	46.1380	1.98363	0.991813	−	0.127698i	$-0.0407589\pi$
$541$	46.1380	1.98363	0.991813	+	0.127698i	$0.0407589\pi$
$542$	6.61612	0.284187
$543$	25.2946	1.08550
$544$	−15.7688	−0.676080
$545$	0.200796	0.00860117
$546$	−32.6939	−1.39917
$547$	−6.83035	−0.292045	−0.146022	−	0.989281i	$-0.546647\pi$
$547$	−6.83035	−0.292045	−0.146022	+	0.989281i	$0.546647\pi$
$548$	39.6664	1.69446
$549$	−6.07024	−0.259072
$550$	−9.92654	−0.423269
$551$	−44.6087	−1.90039
$552$	0	0
$553$	−13.5849	−0.577691
$554$	25.7880	1.09563
$555$	−9.82561	−0.417074
$556$	−60.8846	−2.58208
$557$	18.2801	0.774553	0.387277	−	0.921964i	$-0.373416\pi$
$557$	18.2801	0.774553	0.387277	+	0.921964i	$0.373416\pi$
$558$	−10.3143	−0.436641
$559$	9.64702	0.408025
$560$	18.3019	0.773398
$561$	−7.97603	−0.336748
$562$	−32.2194	−1.35909
$563$	−8.28316	−0.349094	−0.174547	−	0.984649i	$-0.555846\pi$
$563$	−8.28316	−0.349094	−0.174547	+	0.984649i	$0.555846\pi$
$564$	45.5378	1.91749
$565$	10.0237	0.421702
$566$	−31.2608	−1.31399
$567$	−2.22333	−0.0933713
$568$	−6.46740	−0.271366
$569$	7.04869	0.295497	0.147748	−	0.989025i	$-0.452797\pi$
$569$	7.04869	0.295497	0.147748	+	0.989025i	$0.452797\pi$
$570$	16.2520	0.680720
$571$	9.17289	0.383874	0.191937	−	0.981407i	$-0.438523\pi$
$571$	9.17289	0.383874	0.191937	+	0.981407i	$0.438523\pi$
$572$	101.986	4.26424
$573$	−10.4473	−0.436441
$574$	51.7850	2.16147
$575$	0	0
$576$	3.16145	0.131727
$577$	2.97732	0.123947	0.0619737	−	0.998078i	$-0.480260\pi$
$577$	2.97732	0.123947	0.0619737	+	0.998078i	$0.480260\pi$
$578$	32.7573	1.36253
$579$	8.36824	0.347772
$580$	−32.7948	−1.36173
$581$	−27.5895	−1.14461
$582$	−28.5938	−1.18525
$583$	−40.5691	−1.68020
$584$	53.0917	2.19695
$585$	−5.70765	−0.235982
$586$	28.9372	1.19538
$587$	7.78628	0.321374	0.160687	−	0.987005i	$-0.448629\pi$
$587$	7.78628	0.321374	0.160687	+	0.987005i	$0.448629\pi$
$588$	9.53844	0.393359
$589$	−25.2545	−1.04059
$590$	−4.72043	−0.194337
$591$	8.00920	0.329455
$592$	−80.8820	−3.32423
$593$	−23.6189	−0.969911	−0.484956	−	0.874539i	$-0.661164\pi$
$593$	−23.6189	−0.969911	−0.484956	+	0.874539i	$0.661164\pi$
$594$	9.92654	0.407291
$595$	4.60254	0.188686
$596$	−51.0303	−2.09028
$597$	16.2030	0.663143
$598$	0	0
$599$	−0.214192	−0.00875165	−0.00437582	−	0.999990i	$-0.501393\pi$
$599$	−0.214192	−0.00875165	−0.00437582	+	0.999990i	$0.501393\pi$
$600$	6.79523	0.277414
$601$	−8.11936	−0.331196	−0.165598	−	0.986193i	$-0.552955\pi$
$601$	−8.11936	−0.331196	−0.165598	+	0.986193i	$0.552955\pi$
$602$	9.68153	0.394590
$603$	−4.86287	−0.198031
$604$	−80.0275	−3.25627
$605$	−3.84527	−0.156332
$606$	29.6587	1.20480
$607$	−42.1273	−1.70989	−0.854946	−	0.518716i	$-0.826410\pi$
$607$	−42.1273	−1.70989	−0.854946	+	0.518716i	$0.826410\pi$
$608$	48.0515	1.94875
$609$	15.7225	0.637108
$610$	−15.6390	−0.633206
$611$	−56.0455	−2.26736
$612$	9.60022	0.388066
$613$	−47.6665	−1.92523	−0.962616	−	0.270869i	$-0.912689\pi$
$613$	−47.6665	−1.92523	−0.962616	+	0.270869i	$0.912689\pi$
$614$	−48.0396	−1.93872
$615$	9.04057	0.364551
$616$	58.2107	2.34538
$617$	−10.3245	−0.415648	−0.207824	−	0.978166i	$-0.566638\pi$
$617$	−10.3245	−0.415648	−0.207824	+	0.978166i	$0.566638\pi$
$618$	39.9091	1.60538
$619$	−38.0148	−1.52794	−0.763972	−	0.645250i	$-0.776753\pi$
$619$	−38.0148	−1.52794	−0.763972	+	0.645250i	$0.776753\pi$
$620$	−18.5663	−0.745641
$621$	0	0
$622$	−37.5105	−1.50403
$623$	30.2187	1.21069
$624$	−46.9840	−1.88087
$625$	1.00000	0.0400000
$626$	−7.09105	−0.283416
$627$	24.3050	0.970649
$628$	37.0207	1.47729
$629$	−20.3401	−0.811011
$630$	−5.72807	−0.228212
$631$	−29.9890	−1.19384	−0.596922	−	0.802299i	$-0.703610\pi$
$631$	−29.9890	−1.19384	−0.596922	+	0.802299i	$0.703610\pi$
$632$	−41.5200	−1.65158
$633$	−22.8980	−0.910112
$634$	89.0965	3.53848
$635$	12.0303	0.477408
$636$	48.8303	1.93625
$637$	−11.7394	−0.465133
$638$	−70.1964	−2.77910
$639$	0.951755	0.0376509
$640$	−7.08975	−0.280247
$641$	20.9929	0.829170	0.414585	−	0.910011i	$-0.363927\pi$
$641$	20.9929	0.829170	0.414585	+	0.910011i	$0.363927\pi$
$642$	−3.99797	−0.157787
$643$	−45.1488	−1.78050	−0.890248	−	0.455476i	$-0.849469\pi$
$643$	−45.1488	−1.78050	−0.890248	+	0.455476i	$0.849469\pi$
$644$	0	0
$645$	1.69019	0.0665512
$646$	33.6433	1.32368
$647$	−24.9572	−0.981169	−0.490585	−	0.871394i	$-0.663217\pi$
$647$	−24.9572	−0.981169	−0.490585	+	0.871394i	$0.663217\pi$
$648$	−6.79523	−0.266942
$649$	−7.05946	−0.277108
$650$	−14.7049	−0.576773
$651$	8.90107	0.348860
$652$	−19.4626	−0.762214
$653$	23.8399	0.932925	0.466463	−	0.884541i	$-0.345528\pi$
$653$	23.8399	0.932925	0.466463	+	0.884541i	$0.345528\pi$
$654$	−0.517320	−0.0202288
$655$	−16.6883	−0.652065
$656$	74.4197	2.90560
$657$	−7.81309	−0.304818
$658$	−56.2460	−2.19270
$659$	−8.97697	−0.349693	−0.174847	−	0.984596i	$-0.555943\pi$
$659$	−8.97697	−0.349693	−0.174847	+	0.984596i	$0.555943\pi$
$660$	17.8683	0.695521
$661$	−44.9308	−1.74761	−0.873803	−	0.486280i	$-0.838354\pi$
$661$	−44.9308	−1.74761	−0.873803	+	0.486280i	$0.838354\pi$
$662$	37.5406	1.45906
$663$	−11.8155	−0.458874
$664$	−84.3225	−3.27235
$665$	−14.0251	−0.543871
$666$	25.3142	0.980904
$667$	0	0
$668$	117.079	4.52992
$669$	−11.2262	−0.434028
$670$	−12.5284	−0.484016
$671$	−23.3884	−0.902898
$672$	−16.9359	−0.653318
$673$	50.3579	1.94116	0.970578	−	0.240788i	$-0.0774057\pi$
$673$	50.3579	1.94116	0.970578	+	0.240788i	$0.0774057\pi$
$674$	26.0636	1.00393
$675$	−1.00000	−0.0384900
$676$	90.7907	3.49195
$677$	−29.6193	−1.13836	−0.569181	−	0.822212i	$-0.692740\pi$
$677$	−29.6193	−1.13836	−0.569181	+	0.822212i	$0.692740\pi$
$678$	−25.8246	−0.991788
$679$	24.6759	0.946973
$680$	14.0668	0.539439
$681$	3.47153	0.133029
$682$	−39.7407	−1.52175
$683$	0.363453	0.0139071	0.00695356	−	0.999976i	$-0.497787\pi$
$683$	0.363453	0.0139071	0.00695356	+	0.999976i	$0.497787\pi$
$684$	−29.2543	−1.11857
$685$	−8.55331	−0.326805
$686$	−51.8779	−1.98071
$687$	−19.0032	−0.725019
$688$	13.9132	0.530437
$689$	−60.0978	−2.28954
$690$	0	0
$691$	−7.60415	−0.289276	−0.144638	−	0.989485i	$-0.546202\pi$
$691$	−7.60415	−0.289276	−0.144638	+	0.989485i	$0.546202\pi$
$692$	−85.8598	−3.26390
$693$	−8.56641	−0.325411
$694$	−33.3473	−1.26584
$695$	13.1286	0.497997
$696$	48.0531	1.82145
$697$	18.7149	0.708879
$698$	69.4054	2.62703
$699$	10.0904	0.381654
$700$	−10.3108	−0.389712
$701$	29.0793	1.09831	0.549154	−	0.835721i	$-0.314950\pi$
$701$	29.0793	1.09831	0.549154	+	0.835721i	$0.314950\pi$
$702$	14.7049	0.555000
$703$	61.9814	2.33767
$704$	12.1809	0.459086
$705$	−9.81936	−0.369819
$706$	67.5702	2.54304
$707$	−25.5949	−0.962594
$708$	8.49700	0.319337
$709$	−9.36886	−0.351855	−0.175927	−	0.984403i	$-0.556292\pi$
$709$	−9.36886	−0.351855	−0.175927	+	0.984403i	$0.556292\pi$
$710$	2.45205	0.0920238
$711$	6.11017	0.229149
$712$	92.3583	3.46127
$713$	0	0
$714$	−11.8577	−0.443764
$715$	−21.9913	−0.822429
$716$	61.7903	2.30921
$717$	0.746340	0.0278726
$718$	23.4002	0.873286
$719$	34.3557	1.28125	0.640626	−	0.767853i	$-0.278675\pi$
$719$	34.3557	1.28125	0.640626	+	0.767853i	$0.278675\pi$
$720$	−8.23175	−0.306779
$721$	−34.4408	−1.28264
$722$	−53.5693	−1.99364
$723$	−9.88272	−0.367542
$724$	−117.305	−4.35960
$725$	7.07159	0.262632
$726$	9.90674	0.367674
$727$	49.5581	1.83801	0.919003	−	0.394250i	$-0.128996\pi$
$727$	49.5581	1.83801	0.919003	+	0.394250i	$0.128996\pi$
$728$	86.2316	3.19596
$729$	1.00000	0.0370370
$730$	−20.1292	−0.745015
$731$	3.49887	0.129410
$732$	28.1510	1.04049
$733$	−23.7820	−0.878409	−0.439205	−	0.898387i	$-0.644740\pi$
$733$	−23.7820	−0.878409	−0.439205	+	0.898387i	$0.644740\pi$
$734$	−33.1506	−1.22361
$735$	−2.05679	−0.0758657
$736$	0	0
$737$	−18.7364	−0.690165
$738$	−23.2916	−0.857376
$739$	−38.5883	−1.41949	−0.709747	−	0.704456i	$-0.751191\pi$
$739$	−38.5883	−1.41949	−0.709747	+	0.704456i	$0.751191\pi$
$740$	45.5667	1.67507
$741$	36.0047	1.32267
$742$	−60.3128	−2.21415
$743$	−39.0138	−1.43128	−0.715638	−	0.698471i	$-0.753864\pi$
$743$	−39.0138	−1.43128	−0.715638	+	0.698471i	$0.753864\pi$
$744$	27.2045	0.997367
$745$	11.0037	0.403145
$746$	−32.3909	−1.18591
$747$	12.4091	0.454024
$748$	36.9892	1.35246
$749$	3.45017	0.126066
$750$	−2.57634	−0.0940748
$751$	−39.1497	−1.42859	−0.714297	−	0.699842i	$-0.753254\pi$
$751$	−39.1497	−1.42859	−0.714297	+	0.699842i	$0.753254\pi$
$752$	−80.8306	−2.94759
$753$	3.53095	0.128675
$754$	−103.987	−3.78698
$755$	17.2564	0.628026
$756$	10.3108	0.375001
$757$	27.3944	0.995667	0.497833	−	0.867273i	$-0.334129\pi$
$757$	27.3944	0.995667	0.497833	+	0.867273i	$0.334129\pi$
$758$	−2.20633	−0.0801376
$759$	0	0
$760$	−42.8653	−1.55489
$761$	4.52175	0.163913	0.0819567	−	0.996636i	$-0.473883\pi$
$761$	4.52175	0.163913	0.0819567	+	0.996636i	$0.473883\pi$
$762$	−30.9942	−1.12280
$763$	0.446437	0.0161621
$764$	48.4497	1.75285
$765$	−2.07011	−0.0748449
$766$	−88.6488	−3.20301
$767$	−10.4577	−0.377605
$768$	24.5885	0.887262
$769$	−9.30471	−0.335536	−0.167768	−	0.985826i	$-0.553656\pi$
$769$	−9.30471	−0.335536	−0.167768	+	0.985826i	$0.553656\pi$
$770$	−22.0700	−0.795348
$771$	24.0303	0.865430
$772$	−38.8081	−1.39673
$773$	−32.0452	−1.15259	−0.576293	−	0.817243i	$-0.695501\pi$
$773$	−32.0452	−1.15259	−0.576293	+	0.817243i	$0.695501\pi$
$774$	−4.35451	−0.156520
$775$	4.00348	0.143809
$776$	75.4175	2.70733
$777$	−21.8456	−0.783707
$778$	65.7867	2.35857
$779$	−57.0293	−2.04329
$780$	26.4695	0.947761
$781$	3.66707	0.131218
$782$	0	0
$783$	−7.07159	−0.252718
$784$	−16.9310	−0.604677
$785$	−7.98282	−0.284919
$786$	42.9947	1.53357
$787$	−13.5428	−0.482748	−0.241374	−	0.970432i	$-0.577598\pi$
$787$	−13.5428	−0.482748	−0.241374	+	0.970432i	$0.577598\pi$
$788$	−37.1431	−1.32317
$789$	−0.757054	−0.0269518
$790$	15.7419	0.560072
$791$	22.2861	0.792403
$792$	−26.1817	−0.930327
$793$	−34.6468	−1.23035
$794$	−9.80343	−0.347911
$795$	−10.5293	−0.373437
$796$	−75.1420	−2.66334
$797$	18.0192	0.638274	0.319137	−	0.947709i	$-0.396607\pi$
$797$	18.0192	0.638274	0.319137	+	0.947709i	$0.396607\pi$
$798$	36.1335	1.27911
$799$	−20.3271	−0.719122
$800$	−7.61737	−0.269315
$801$	−13.5916	−0.480237
$802$	−15.7377	−0.555717
$803$	−30.1035	−1.06233
$804$	22.5518	0.795341
$805$	0	0
$806$	−58.8706	−2.07363
$807$	−27.1946	−0.957297
$808$	−78.2262	−2.75199
$809$	−23.7507	−0.835031	−0.417516	−	0.908670i	$-0.637099\pi$
$809$	−23.7507	−0.835031	−0.417516	+	0.908670i	$0.637099\pi$
$810$	2.57634	0.0905235
$811$	−19.9626	−0.700981	−0.350490	−	0.936566i	$-0.613985\pi$
$811$	−19.9626	−0.700981	−0.350490	+	0.936566i	$0.613985\pi$
$812$	−72.9139	−2.55878
$813$	2.56803	0.0900646
$814$	97.5343	3.41858
$815$	4.19674	0.147006
$816$	−17.0406	−0.596540
$817$	−10.6620	−0.373015
$818$	15.3993	0.538425
$819$	−12.6900	−0.443425
$820$	−41.9261	−1.46412
$821$	24.1735	0.843662	0.421831	−	0.906674i	$-0.361388\pi$
$821$	24.1735	0.843662	0.421831	+	0.906674i	$0.361388\pi$
$822$	22.0363	0.768603
$823$	10.4432	0.364027	0.182013	−	0.983296i	$-0.441739\pi$
$823$	10.4432	0.364027	0.182013	+	0.983296i	$0.441739\pi$
$824$	−105.262	−3.66698
$825$	−3.85296	−0.134143
$826$	−10.4951	−0.365171
$827$	−2.24062	−0.0779140	−0.0389570	−	0.999241i	$-0.512404\pi$
$827$	−2.24062	−0.0779140	−0.0389570	+	0.999241i	$0.512404\pi$
$828$	0	0
$829$	9.11773	0.316672	0.158336	−	0.987385i	$-0.449387\pi$
$829$	9.11773	0.316672	0.158336	+	0.987385i	$0.449387\pi$
$830$	31.9700	1.10970
$831$	10.0095	0.347227
$832$	18.0445	0.625579
$833$	−4.25777	−0.147523
$834$	−33.8239	−1.17122
$835$	−25.2458	−0.873669
$836$	−112.716	−3.89835
$837$	−4.00348	−0.138380
$838$	−7.74193	−0.267440
$839$	0.637012	0.0219921	0.0109961	−	0.999940i	$-0.496500\pi$
$839$	0.637012	0.0219921	0.0109961	+	0.999940i	$0.496500\pi$
$840$	15.1081	0.521278
$841$	21.0074	0.724394
$842$	−61.0235	−2.10301
$843$	−12.5059	−0.430724
$844$	106.190	3.65522
$845$	−19.5773	−0.673480
$846$	25.2981	0.869765
$847$	−8.54932	−0.293758
$848$	−86.6749	−2.97643
$849$	−12.1338	−0.416431
$850$	−5.33331	−0.182931
$851$	0	0
$852$	−4.41381	−0.151215
$853$	−3.30135	−0.113036	−0.0565180	−	0.998402i	$-0.518000\pi$
$853$	−3.30135	−0.113036	−0.0565180	+	0.998402i	$0.518000\pi$
$854$	−34.7708	−1.18983
$855$	6.30815	0.215734
$856$	10.5448	0.360415
$857$	−7.98037	−0.272604	−0.136302	−	0.990667i	$-0.543522\pi$
$857$	−7.98037	−0.272604	−0.136302	+	0.990667i	$0.543522\pi$
$858$	56.6573	1.93425
$859$	−27.7698	−0.947492	−0.473746	−	0.880662i	$-0.657099\pi$
$859$	−27.7698	−0.947492	−0.473746	+	0.880662i	$0.657099\pi$
$860$	−7.83834	−0.267285
$861$	20.1002	0.685013
$862$	−16.7929	−0.571969
$863$	−28.6753	−0.976119	−0.488059	−	0.872810i	$-0.662295\pi$
$863$	−28.6753	−0.976119	−0.488059	+	0.872810i	$0.662295\pi$
$864$	7.61737	0.259148
$865$	18.5140	0.629497
$866$	79.3281	2.69568
$867$	12.7147	0.431812
$868$	−41.2791	−1.40110
$869$	23.5422	0.798615
$870$	−18.2189	−0.617677
$871$	−27.7556	−0.940462
$872$	1.36446	0.0462063
$873$	−11.0986	−0.375630
$874$	0	0
$875$	2.22333	0.0751624
$876$	36.2336	1.22422
$877$	13.8484	0.467626	0.233813	−	0.972282i	$-0.424880\pi$
$877$	13.8484	0.467626	0.233813	+	0.972282i	$0.424880\pi$
$878$	−21.3434	−0.720306
$879$	11.2319	0.378842
$880$	−31.7166	−1.06917
$881$	−29.9638	−1.00950	−0.504752	−	0.863264i	$-0.668416\pi$
$881$	−29.9638	−1.00950	−0.504752	+	0.863264i	$0.668416\pi$
$882$	5.29899	0.178426
$883$	29.6813	0.998856	0.499428	−	0.866355i	$-0.333544\pi$
$883$	29.6813	0.998856	0.499428	+	0.866355i	$0.333544\pi$
$884$	54.7947	1.84295
$885$	−1.83222	−0.0615894
$886$	−26.4508	−0.888631
$887$	−20.1448	−0.676395	−0.338198	−	0.941075i	$-0.609817\pi$
$887$	−20.1448	−0.676395	−0.338198	+	0.941075i	$0.609817\pi$
$888$	−66.7673	−2.24056
$889$	26.7474	0.897078
$890$	−35.0167	−1.17376
$891$	3.85296	0.129079
$892$	52.0618	1.74316
$893$	61.9420	2.07281
$894$	−28.3494	−0.948145
$895$	−13.3239	−0.445370
$896$	−15.7629	−0.526601
$897$	0	0
$898$	61.1884	2.04188
$899$	28.3110	0.944223
$900$	4.63755	0.154585
$901$	−21.7968	−0.726158
$902$	−89.7416	−2.98807
$903$	3.75786	0.125054
$904$	68.1136	2.26542
$905$	25.2946	0.840821
$906$	−44.4585	−1.47703
$907$	−19.5795	−0.650127	−0.325063	−	0.945692i	$-0.605386\pi$
$907$	−19.5795	−0.650127	−0.325063	+	0.945692i	$0.605386\pi$
$908$	−16.0994	−0.534277
$909$	11.5119	0.381827
$910$	−32.6939	−1.08379
$911$	−43.2187	−1.43190	−0.715949	−	0.698152i	$-0.754006\pi$
$911$	−43.2187	−1.43190	−0.715949	+	0.698152i	$0.754006\pi$
$912$	51.9271	1.71948
$913$	47.8116	1.58233
$914$	−16.0000	−0.529232
$915$	−6.07024	−0.200676
$916$	88.1284	2.91184
$917$	−37.1036	−1.22527
$918$	5.33331	0.176025
$919$	−44.5514	−1.46962	−0.734808	−	0.678275i	$-0.762728\pi$
$919$	−44.5514	−1.46962	−0.734808	+	0.678275i	$0.762728\pi$
$920$	0	0
$921$	−18.6464	−0.614421
$922$	39.0048	1.28455
$923$	5.43229	0.178806
$924$	39.7271	1.30693
$925$	−9.82561	−0.323064
$926$	−80.4991	−2.64537
$927$	15.4906	0.508778
$928$	−53.8669	−1.76827
$929$	−27.0033	−0.885951	−0.442976	−	0.896534i	$-0.646077\pi$
$929$	−27.0033	−0.885951	−0.442976	+	0.896534i	$0.646077\pi$
$930$	−10.3143	−0.338220
$931$	12.9745	0.425223
$932$	−46.7948	−1.53281
$933$	−14.5596	−0.476659
$934$	−19.0454	−0.623185
$935$	−7.97603	−0.260844
$936$	−38.7848	−1.26772
$937$	6.47123	0.211406	0.105703	−	0.994398i	$-0.466291\pi$
$937$	6.47123	0.211406	0.105703	+	0.994398i	$0.466291\pi$
$938$	−27.8549	−0.909494
$939$	−2.75237	−0.0898202
$940$	45.5378	1.48528
$941$	−15.2810	−0.498147	−0.249073	−	0.968485i	$-0.580126\pi$
$941$	−15.2810	−0.498147	−0.249073	+	0.968485i	$0.580126\pi$
$942$	20.5665	0.670092
$943$	0	0
$944$	−15.0824	−0.490889
$945$	−2.22333	−0.0723251
$946$	−16.7777	−0.545491
$947$	−44.7053	−1.45273	−0.726364	−	0.687311i	$-0.758791\pi$
$947$	−44.7053	−1.45273	−0.726364	+	0.687311i	$0.758791\pi$
$948$	−28.3362	−0.920317
$949$	−44.5944	−1.44760
$950$	16.2520	0.527283
$951$	34.5826	1.12142
$952$	31.2753	1.01364
$953$	−20.6174	−0.667862	−0.333931	−	0.942598i	$-0.608375\pi$
$953$	−20.6174	−0.667862	−0.333931	+	0.942598i	$0.608375\pi$
$954$	27.1272	0.878275
$955$	−10.4473	−0.338066
$956$	−3.46119	−0.111943
$957$	−27.2465	−0.880755
$958$	11.4341	0.369420
$959$	−19.0169	−0.614086
$960$	3.16145	0.102035
$961$	−14.9722	−0.482973
$962$	144.484	4.65837
$963$	−1.55180	−0.0500060
$964$	45.8316	1.47614
$965$	8.36824	0.269383
$966$	0	0
$967$	−7.72807	−0.248518	−0.124259	−	0.992250i	$-0.539655\pi$
$967$	−7.72807	−0.248518	−0.124259	+	0.992250i	$0.539655\pi$
$968$	−26.1295	−0.839834
$969$	13.0585	0.419501
$970$	−28.5938	−0.918091
$971$	−30.0298	−0.963704	−0.481852	−	0.876253i	$-0.660036\pi$
$971$	−30.0298	−0.963704	−0.481852	+	0.876253i	$0.660036\pi$
$972$	−4.63755	−0.148749
$973$	29.1893	0.935767
$974$	−53.3055	−1.70802
$975$	−5.70765	−0.182791
$976$	−49.9687	−1.59946
$977$	−24.5148	−0.784298	−0.392149	−	0.919902i	$-0.628268\pi$
$977$	−24.5148	−0.784298	−0.392149	+	0.919902i	$0.628268\pi$
$978$	−10.8123	−0.345738
$979$	−52.3680	−1.67369
$980$	9.53844	0.304694
$981$	−0.200796	−0.00641093
$982$	−5.50856	−0.175785
$983$	−0.365112	−0.0116453	−0.00582263	−	0.999983i	$-0.501853\pi$
$983$	−0.365112	−0.0116453	−0.00582263	+	0.999983i	$0.501853\pi$
$984$	61.4327	1.95840
$985$	8.00920	0.255194
$986$	−37.7150	−1.20109
$987$	−21.8317	−0.694911
$988$	−166.974	−5.31214
$989$	0	0
$990$	9.92654	0.315486
$991$	−35.5339	−1.12877	−0.564386	−	0.825511i	$-0.690887\pi$
$991$	−35.5339	−1.12877	−0.564386	+	0.825511i	$0.690887\pi$
$992$	−30.4959	−0.968247
$993$	14.5713	0.462405
$994$	5.45172	0.172918
$995$	16.2030	0.513668
$996$	−57.5477	−1.82347
$997$	−47.0929	−1.49145	−0.745724	−	0.666255i	$-0.767896\pi$
$997$	−47.0929	−1.49145	−0.745724	+	0.666255i	$0.767896\pi$
$998$	79.6074	2.51993
$999$	9.82561	0.310869

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bj.1.1	✓	10
23.22	odd	2		7935.2.a.bk.1.1	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bj.1.1	✓	10	1.1	even	1	trivial
7935.2.a.bk.1.1	yes	10	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.57634 q^{2} -1.00000 q^{3} +4.63755 q^{4} -1.00000 q^{5} +2.57634 q^{6} -2.22333 q^{7} -6.79523 q^{8} +1.00000 q^{9} +2.57634 q^{10} +3.85296 q^{11} -4.63755 q^{12} +5.70765 q^{13} +5.72807 q^{14} +1.00000 q^{15} +8.23175 q^{16} +2.07011 q^{17} -2.57634 q^{18} -6.30815 q^{19} -4.63755 q^{20} +2.22333 q^{21} -9.92654 q^{22} +6.79523 q^{24} +1.00000 q^{25} -14.7049 q^{26} -1.00000 q^{27} -10.3108 q^{28} +7.07159 q^{29} -2.57634 q^{30} +4.00348 q^{31} -7.61737 q^{32} -3.85296 q^{33} -5.33331 q^{34} +2.22333 q^{35} +4.63755 q^{36} -9.82561 q^{37} +16.2520 q^{38} -5.70765 q^{39} +6.79523 q^{40} +9.04057 q^{41} -5.72807 q^{42} +1.69019 q^{43} +17.8683 q^{44} -1.00000 q^{45} -9.81936 q^{47} -8.23175 q^{48} -2.05679 q^{49} -2.57634 q^{50} -2.07011 q^{51} +26.4695 q^{52} -10.5293 q^{53} +2.57634 q^{54} -3.85296 q^{55} +15.1081 q^{56} +6.30815 q^{57} -18.2189 q^{58} -1.83222 q^{59} +4.63755 q^{60} -6.07024 q^{61} -10.3143 q^{62} -2.22333 q^{63} +3.16145 q^{64} -5.70765 q^{65} +9.92654 q^{66} -4.86287 q^{67} +9.60022 q^{68} -5.72807 q^{70} +0.951755 q^{71} -6.79523 q^{72} -7.81309 q^{73} +25.3142 q^{74} -1.00000 q^{75} -29.2543 q^{76} -8.56641 q^{77} +14.7049 q^{78} +6.11017 q^{79} -8.23175 q^{80} +1.00000 q^{81} -23.2916 q^{82} +12.4091 q^{83} +10.3108 q^{84} -2.07011 q^{85} -4.35451 q^{86} -7.07159 q^{87} -26.1817 q^{88} -13.5916 q^{89} +2.57634 q^{90} -12.6900 q^{91} -4.00348 q^{93} +25.2981 q^{94} +6.30815 q^{95} +7.61737 q^{96} -11.0986 q^{97} +5.29899 q^{98} +3.85296 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{3} + 16 q^{4} - 10 q^{5} - 6 q^{7} + 10 q^{9} + 4 q^{11} - 16 q^{12} - 4 q^{13} + 10 q^{15} + 28 q^{16} - 10 q^{17} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 4 q^{22} + 10 q^{25} - 8 q^{26} - 10 q^{27}+ \cdots + 4 q^{99}+O(q^{100}) \) 10 * q - 10 * q^3 + 16 * q^4 - 10 * q^5 - 6 * q^7 + 10 * q^9 + 4 * q^11 - 16 * q^12 - 4 * q^13 + 10 * q^15 + 28 * q^16 - 10 * q^17 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 4 * q^22 + 10 * q^25 - 8 * q^26 - 10 * q^27 - 76 * q^28 + 2 * q^29 + 2 * q^31 + 20 * q^32 - 4 * q^33 - 8 * q^34 + 6 * q^35 + 16 * q^36 - 2 * q^37 + 56 * q^38 + 4 * q^39 + 6 * q^41 - 44 * q^43 + 24 * q^44 - 10 * q^45 + 8 * q^47 - 28 * q^48 + 12 * q^49 + 10 * q^51 - 2 * q^53 - 4 * q^55 - 8 * q^56 + 8 * q^57 - 20 * q^58 - 14 * q^59 + 16 * q^60 + 8 * q^61 - 28 * q^62 - 6 * q^63 + 40 * q^64 + 4 * q^65 - 4 * q^66 - 2 * q^67 - 84 * q^68 + 6 * q^71 - 12 * q^73 - 40 * q^74 - 10 * q^75 - 44 * q^76 - 16 * q^77 + 8 * q^78 - 28 * q^80 + 10 * q^81 - 4 * q^82 + 62 * q^83 + 76 * q^84 + 10 * q^85 + 4 * q^86 - 2 * q^87 + 12 * q^88 - 56 * q^89 - 2 * q^93 + 20 * q^94 + 8 * q^95 - 20 * q^96 - 56 * q^97 - 4 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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