LMFDB - Embedded newform 9386.2.a.bw.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9386,2,Mod(1,9386)] 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("9386.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9386 = 2 \cdot 13 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9386.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-15,-3,15,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$74.9475873372$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 27 x^{13} + 70 x^{12} + 306 x^{11} - 609 x^{10} - 1854 x^{9} + 2346 x^{8} + \cdots - 24 $ x^15 - 3x^14 - 27x^13 + 70x^12 + 306x^11 - 609x^10 - 1854x^9 + 2346x^8 + 6129x^7 - 3442x^6 - 9735x^5 + 222x^4 + 5181x^3 + 1422x^2 - 36x - 24
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.90071$ of defining polynomial
Character	$\chi$	$=$	9386.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -2.90071 q^{3} +1.00000 q^{4} -3.22232 q^{5} +2.90071 q^{6} +1.61433 q^{7} -1.00000 q^{8} +5.41411 q^{9} +3.22232 q^{10} +2.38696 q^{11} -2.90071 q^{12} +1.00000 q^{13} -1.61433 q^{14} +9.34700 q^{15} +1.00000 q^{16} -0.480530 q^{17} -5.41411 q^{18} -3.22232 q^{20} -4.68269 q^{21} -2.38696 q^{22} +5.30742 q^{23} +2.90071 q^{24} +5.38332 q^{25} -1.00000 q^{26} -7.00262 q^{27} +1.61433 q^{28} -6.49642 q^{29} -9.34700 q^{30} +4.15494 q^{31} -1.00000 q^{32} -6.92389 q^{33} +0.480530 q^{34} -5.20187 q^{35} +5.41411 q^{36} -6.24477 q^{37} -2.90071 q^{39} +3.22232 q^{40} +3.18665 q^{41} +4.68269 q^{42} -4.03431 q^{43} +2.38696 q^{44} -17.4460 q^{45} -5.30742 q^{46} +11.0813 q^{47} -2.90071 q^{48} -4.39395 q^{49} -5.38332 q^{50} +1.39388 q^{51} +1.00000 q^{52} +0.586036 q^{53} +7.00262 q^{54} -7.69155 q^{55} -1.61433 q^{56} +6.49642 q^{58} -7.91358 q^{59} +9.34700 q^{60} -6.14389 q^{61} -4.15494 q^{62} +8.74014 q^{63} +1.00000 q^{64} -3.22232 q^{65} +6.92389 q^{66} -15.5174 q^{67} -0.480530 q^{68} -15.3953 q^{69} +5.20187 q^{70} +14.1554 q^{71} -5.41411 q^{72} +4.24087 q^{73} +6.24477 q^{74} -15.6154 q^{75} +3.85334 q^{77} +2.90071 q^{78} -8.69887 q^{79} -3.22232 q^{80} +4.07023 q^{81} -3.18665 q^{82} -10.0998 q^{83} -4.68269 q^{84} +1.54842 q^{85} +4.03431 q^{86} +18.8442 q^{87} -2.38696 q^{88} +4.41732 q^{89} +17.4460 q^{90} +1.61433 q^{91} +5.30742 q^{92} -12.0523 q^{93} -11.0813 q^{94} +2.90071 q^{96} -7.22109 q^{97} +4.39395 q^{98} +12.9233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{8} + 18 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} + 15 q^{16} + 3 q^{17} - 18 q^{18} + 3 q^{20} - 33 q^{21} + 3 q^{22} + 9 q^{23}+ \cdots + 3 q^{98}+O(q^{100}) $ 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 3 * q^5 + 3 * q^6 - 15 * q^8 + 18 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 + 15 * q^16 + 3 * q^17 - 18 * q^18 + 3 * q^20 - 33 * q^21 + 3 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 15 * q^26 - 42 * q^27 - 12 * q^29 - 24 * q^31 - 15 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 + 18 * q^36 - 30 * q^37 - 3 * q^39 - 3 * q^40 + 24 * q^41 + 33 * q^42 - 12 * q^43 - 3 * q^44 + 21 * q^45 - 9 * q^46 - 6 * q^47 - 3 * q^48 - 3 * q^49 - 24 * q^50 - 48 * q^51 + 15 * q^52 - 9 * q^53 + 42 * q^54 - 60 * q^55 + 12 * q^58 - 12 * q^59 - 12 * q^61 + 24 * q^62 + 15 * q^63 + 15 * q^64 + 3 * q^65 - 3 * q^66 - 48 * q^67 + 3 * q^68 - 18 * q^69 - 6 * q^70 - 21 * q^71 - 18 * q^72 + 21 * q^73 + 30 * q^74 - 21 * q^75 - 9 * q^77 + 3 * q^78 - 45 * q^79 + 3 * q^80 + 15 * q^81 - 24 * q^82 - 33 * q^83 - 33 * q^84 - 6 * q^85 + 12 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 - 21 * q^90 + 9 * q^92 - 3 * q^93 + 6 * q^94 + 3 * q^96 + 24 * q^97 + 3 * q^98

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.90071	−1.67472	−0.837362	−	0.546648i	$-0.815903\pi$
$3$	−2.90071	−1.67472	−0.837362	+	0.546648i	$0.815903\pi$
$4$	1.00000	0.500000
$5$	−3.22232	−1.44106	−0.720532	−	0.693422i	$-0.756102\pi$
$5$	−3.22232	−1.44106	−0.720532	+	0.693422i	$0.756102\pi$
$6$	2.90071	1.18421
$7$	1.61433	0.610158	0.305079	−	0.952327i	$-0.401317\pi$
$7$	1.61433	0.610158	0.305079	+	0.952327i	$0.401317\pi$
$8$	−1.00000	−0.353553
$9$	5.41411	1.80470
$10$	3.22232	1.01899
$11$	2.38696	0.719697	0.359848	−	0.933011i	$-0.382828\pi$
$11$	2.38696	0.719697	0.359848	+	0.933011i	$0.382828\pi$
$12$	−2.90071	−0.837362
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.61433	−0.431447
$15$	9.34700	2.41338
$16$	1.00000	0.250000
$17$	−0.480530	−0.116546	−0.0582728	−	0.998301i	$-0.518559\pi$
$17$	−0.480530	−0.116546	−0.0582728	+	0.998301i	$0.518559\pi$
$18$	−5.41411	−1.27612
$19$	0	0
$19$	0	0
$20$	−3.22232	−0.720532
$21$	−4.68269	−1.02185
$22$	−2.38696	−0.508902
$23$	5.30742	1.10667	0.553337	−	0.832957i	$-0.313354\pi$
$23$	5.30742	1.10667	0.553337	+	0.832957i	$0.313354\pi$
$24$	2.90071	0.592105
$25$	5.38332	1.07666
$26$	−1.00000	−0.196116
$27$	−7.00262	−1.34765
$28$	1.61433	0.305079
$29$	−6.49642	−1.20635	−0.603177	−	0.797607i	$-0.706099\pi$
$29$	−6.49642	−1.20635	−0.603177	+	0.797607i	$0.706099\pi$
$30$	−9.34700	−1.70652
$31$	4.15494	0.746248	0.373124	−	0.927781i	$-0.378287\pi$
$31$	4.15494	0.746248	0.373124	+	0.927781i	$0.378287\pi$
$32$	−1.00000	−0.176777
$33$	−6.92389	−1.20529
$34$	0.480530	0.0824101
$35$	−5.20187	−0.879276
$36$	5.41411	0.902351
$37$	−6.24477	−1.02663	−0.513317	−	0.858199i	$-0.671584\pi$
$37$	−6.24477	−1.02663	−0.513317	+	0.858199i	$0.671584\pi$
$38$	0	0
$39$	−2.90071	−0.464485
$40$	3.22232	0.509493
$41$	3.18665	0.497672	0.248836	−	0.968546i	$-0.419952\pi$
$41$	3.18665	0.497672	0.248836	+	0.968546i	$0.419952\pi$
$42$	4.68269	0.722555
$43$	−4.03431	−0.615226	−0.307613	−	0.951512i	$-0.599530\pi$
$43$	−4.03431	−0.615226	−0.307613	+	0.951512i	$0.599530\pi$
$44$	2.38696	0.359848
$45$	−17.4460	−2.60069
$46$	−5.30742	−0.782537
$47$	11.0813	1.61637	0.808184	−	0.588930i	$-0.200451\pi$
$47$	11.0813	1.61637	0.808184	+	0.588930i	$0.200451\pi$
$48$	−2.90071	−0.418681
$49$	−4.39395	−0.627707
$50$	−5.38332	−0.761316
$51$	1.39388	0.195182
$52$	1.00000	0.138675
$53$	0.586036	0.0804982	0.0402491	−	0.999190i	$-0.487185\pi$
$53$	0.586036	0.0804982	0.0402491	+	0.999190i	$0.487185\pi$
$54$	7.00262	0.952936
$55$	−7.69155	−1.03713
$56$	−1.61433	−0.215723
$57$	0	0
$58$	6.49642	0.853022
$59$	−7.91358	−1.03026	−0.515130	−	0.857112i	$-0.672256\pi$
$59$	−7.91358	−1.03026	−0.515130	+	0.857112i	$0.672256\pi$
$60$	9.34700	1.20669
$61$	−6.14389	−0.786644	−0.393322	−	0.919401i	$-0.628674\pi$
$61$	−6.14389	−0.786644	−0.393322	+	0.919401i	$0.628674\pi$
$62$	−4.15494	−0.527677
$63$	8.74014	1.10115
$64$	1.00000	0.125000
$65$	−3.22232	−0.399679
$66$	6.92389	0.852271
$67$	−15.5174	−1.89575	−0.947874	−	0.318646i	$-0.896772\pi$
$67$	−15.5174	−1.89575	−0.947874	+	0.318646i	$0.896772\pi$
$68$	−0.480530	−0.0582728
$69$	−15.3953	−1.85337
$70$	5.20187	0.621742
$71$	14.1554	1.67993	0.839967	−	0.542638i	$-0.182574\pi$
$71$	14.1554	1.67993	0.839967	+	0.542638i	$0.182574\pi$
$72$	−5.41411	−0.638059
$73$	4.24087	0.496356	0.248178	−	0.968714i	$-0.420168\pi$
$73$	4.24087	0.496356	0.248178	+	0.968714i	$0.420168\pi$
$74$	6.24477	0.725940
$75$	−15.6154	−1.80312
$76$	0	0
$77$	3.85334	0.439129
$78$	2.90071	0.328441
$79$	−8.69887	−0.978699	−0.489349	−	0.872088i	$-0.662766\pi$
$79$	−8.69887	−0.978699	−0.489349	+	0.872088i	$0.662766\pi$
$80$	−3.22232	−0.360266
$81$	4.07023	0.452248
$82$	−3.18665	−0.351907
$83$	−10.0998	−1.10860	−0.554298	−	0.832319i	$-0.687013\pi$
$83$	−10.0998	−1.10860	−0.554298	+	0.832319i	$0.687013\pi$
$84$	−4.68269	−0.510923
$85$	1.54842	0.167950
$86$	4.03431	0.435031
$87$	18.8442	2.02031
$88$	−2.38696	−0.254451
$89$	4.41732	0.468235	0.234117	−	0.972208i	$-0.424780\pi$
$89$	4.41732	0.468235	0.234117	+	0.972208i	$0.424780\pi$
$90$	17.4460	1.83897
$91$	1.61433	0.169227
$92$	5.30742	0.553337
$93$	−12.0523	−1.24976
$94$	−11.0813	−1.14294
$95$	0	0
$96$	2.90071	0.296052
$97$	−7.22109	−0.733190	−0.366595	−	0.930381i	$-0.619477\pi$
$97$	−7.22109	−0.733190	−0.366595	+	0.930381i	$0.619477\pi$
$98$	4.39395	0.443856
$99$	12.9233	1.29884
$100$	5.38332	0.538332
$101$	−1.98447	−0.197462	−0.0987311	−	0.995114i	$-0.531478\pi$
$101$	−1.98447	−0.197462	−0.0987311	+	0.995114i	$0.531478\pi$
$102$	−1.39388	−0.138014
$103$	16.4406	1.61994	0.809970	−	0.586471i	$-0.199483\pi$
$103$	16.4406	1.61994	0.809970	+	0.586471i	$0.199483\pi$
$104$	−1.00000	−0.0980581
$105$	15.0891	1.47255
$106$	−0.586036	−0.0569208
$107$	11.3983	1.10192	0.550959	−	0.834532i	$-0.314262\pi$
$107$	11.3983	1.10192	0.550959	+	0.834532i	$0.314262\pi$
$108$	−7.00262	−0.673827
$109$	−17.0126	−1.62951	−0.814757	−	0.579802i	$-0.803130\pi$
$109$	−17.0126	−1.62951	−0.814757	+	0.579802i	$0.803130\pi$
$110$	7.69155	0.733361
$111$	18.1143	1.71933
$112$	1.61433	0.152540
$113$	−8.38862	−0.789135	−0.394567	−	0.918867i	$-0.629106\pi$
$113$	−8.38862	−0.789135	−0.394567	+	0.918867i	$0.629106\pi$
$114$	0	0
$115$	−17.1022	−1.59479
$116$	−6.49642	−0.603177
$117$	5.41411	0.500534
$118$	7.91358	0.728504
$119$	−0.775732	−0.0711112
$120$	−9.34700	−0.853260
$121$	−5.30240	−0.482037
$122$	6.14389	0.556241
$123$	−9.24355	−0.833463
$124$	4.15494	0.373124
$125$	−1.23518	−0.110477
$126$	−8.74014	−0.778633
$127$	13.9561	1.23840	0.619202	−	0.785232i	$-0.287456\pi$
$127$	13.9561	1.23840	0.619202	+	0.785232i	$0.287456\pi$
$128$	−1.00000	−0.0883883
$129$	11.7023	1.03033
$130$	3.22232	0.282616
$131$	11.7378	1.02554	0.512768	−	0.858527i	$-0.328620\pi$
$131$	11.7378	1.02554	0.512768	+	0.858527i	$0.328620\pi$
$132$	−6.92389	−0.602647
$133$	0	0
$134$	15.5174	1.34050
$135$	22.5646	1.94206
$136$	0.480530	0.0412051
$137$	5.35044	0.457119	0.228559	−	0.973530i	$-0.426599\pi$
$137$	5.35044	0.457119	0.228559	+	0.973530i	$0.426599\pi$
$138$	15.3953	1.31053
$139$	−5.10591	−0.433078	−0.216539	−	0.976274i	$-0.569477\pi$
$139$	−5.10591	−0.433078	−0.216539	+	0.976274i	$0.569477\pi$
$140$	−5.20187	−0.439638
$141$	−32.1435	−2.70697
$142$	−14.1554	−1.18789
$143$	2.38696	0.199608
$144$	5.41411	0.451176
$145$	20.9335	1.73843
$146$	−4.24087	−0.350977
$147$	12.7456	1.05124
$148$	−6.24477	−0.513317
$149$	7.17107	0.587477	0.293738	−	0.955886i	$-0.405101\pi$
$149$	7.17107	0.587477	0.293738	+	0.955886i	$0.405101\pi$
$150$	15.6154	1.27500
$151$	−24.0585	−1.95786	−0.978928	−	0.204204i	$-0.934539\pi$
$151$	−24.0585	−1.95786	−0.978928	+	0.204204i	$0.934539\pi$
$152$	0	0
$153$	−2.60164	−0.210330
$154$	−3.85334	−0.310511
$155$	−13.3885	−1.07539
$156$	−2.90071	−0.232243
$157$	24.0177	1.91682	0.958411	−	0.285393i	$-0.0921241\pi$
$157$	24.0177	1.91682	0.958411	+	0.285393i	$0.0921241\pi$
$158$	8.69887	0.692045
$159$	−1.69992	−0.134812
$160$	3.22232	0.254746
$161$	8.56791	0.675246
$162$	−4.07023	−0.319788
$163$	9.70246	0.759955	0.379978	−	0.924996i	$-0.375932\pi$
$163$	9.70246	0.759955	0.379978	+	0.924996i	$0.375932\pi$
$164$	3.18665	0.248836
$165$	22.3109	1.73690
$166$	10.0998	0.783895
$167$	−21.6034	−1.67172	−0.835860	−	0.548943i	$-0.815031\pi$
$167$	−21.6034	−1.67172	−0.835860	+	0.548943i	$0.815031\pi$
$168$	4.68269	0.361277
$169$	1.00000	0.0769231
$170$	−1.54842	−0.118758
$171$	0	0
$172$	−4.03431	−0.307613
$173$	−1.29516	−0.0984692	−0.0492346	−	0.998787i	$-0.515678\pi$
$173$	−1.29516	−0.0984692	−0.0492346	+	0.998787i	$0.515678\pi$
$174$	−18.8442	−1.42858
$175$	8.69043	0.656935
$176$	2.38696	0.179924
$177$	22.9550	1.72540
$178$	−4.41732	−0.331092
$179$	25.3948	1.89810	0.949049	−	0.315128i	$-0.102047\pi$
$179$	25.3948	1.89810	0.949049	+	0.315128i	$0.102047\pi$
$180$	−17.4460	−1.30035
$181$	−14.2965	−1.06265	−0.531327	−	0.847167i	$-0.678306\pi$
$181$	−14.2965	−1.06265	−0.531327	+	0.847167i	$0.678306\pi$
$182$	−1.61433	−0.119662
$183$	17.8216	1.31741
$184$	−5.30742	−0.391268
$185$	20.1226	1.47945
$186$	12.0523	0.883714
$187$	−1.14701	−0.0838774
$188$	11.0813	0.808184
$189$	−11.3045	−0.822282
$190$	0	0
$191$	−7.21424	−0.522004	−0.261002	−	0.965338i	$-0.584053\pi$
$191$	−7.21424	−0.522004	−0.261002	+	0.965338i	$0.584053\pi$
$192$	−2.90071	−0.209341
$193$	−2.97961	−0.214477	−0.107238	−	0.994233i	$-0.534201\pi$
$193$	−2.97961	−0.214477	−0.107238	+	0.994233i	$0.534201\pi$
$194$	7.22109	0.518444
$195$	9.34700	0.669352
$196$	−4.39395	−0.313854
$197$	25.8408	1.84108	0.920542	−	0.390644i	$-0.127748\pi$
$197$	25.8408	1.84108	0.920542	+	0.390644i	$0.127748\pi$
$198$	−12.9233	−0.918417
$199$	18.8369	1.33531	0.667655	−	0.744471i	$-0.267298\pi$
$199$	18.8369	1.33531	0.667655	+	0.744471i	$0.267298\pi$
$200$	−5.38332	−0.380658
$201$	45.0113	3.17486
$202$	1.98447	0.139627
$203$	−10.4873	−0.736067
$204$	1.39388	0.0975908
$205$	−10.2684	−0.717176
$206$	−16.4406	−1.14547
$207$	28.7350	1.99722
$208$	1.00000	0.0693375
$209$	0	0
$210$	−15.0891	−1.04125
$211$	−1.51125	−0.104039	−0.0520194	−	0.998646i	$-0.516566\pi$
$211$	−1.51125	−0.104039	−0.0520194	+	0.998646i	$0.516566\pi$
$212$	0.586036	0.0402491
$213$	−41.0606	−2.81343
$214$	−11.3983	−0.779174
$215$	12.9998	0.886580
$216$	7.00262	0.476468
$217$	6.70742	0.455330
$218$	17.0126	1.15224
$219$	−12.3015	−0.831259
$220$	−7.69155	−0.518564
$221$	−0.480530	−0.0323239
$222$	−18.1143	−1.21575
$223$	−1.60290	−0.107338	−0.0536690	−	0.998559i	$-0.517092\pi$
$223$	−1.60290	−0.107338	−0.0536690	+	0.998559i	$0.517092\pi$
$224$	−1.61433	−0.107862
$225$	29.1459	1.94306
$226$	8.38862	0.558003
$227$	12.4678	0.827519	0.413759	−	0.910386i	$-0.364215\pi$
$227$	12.4678	0.827519	0.413759	+	0.910386i	$0.364215\pi$
$228$	0	0
$229$	−10.3992	−0.687197	−0.343598	−	0.939117i	$-0.611646\pi$
$229$	−10.3992	−0.687197	−0.343598	+	0.939117i	$0.611646\pi$
$230$	17.1022	1.12769
$231$	−11.1774	−0.735420
$232$	6.49642	0.426511
$233$	8.08782	0.529851	0.264925	−	0.964269i	$-0.414653\pi$
$233$	8.08782	0.529851	0.264925	+	0.964269i	$0.414653\pi$
$234$	−5.41411	−0.353931
$235$	−35.7073	−2.32929
$236$	−7.91358	−0.515130
$237$	25.2329	1.63905
$238$	0.775732	0.0502832
$239$	−5.47828	−0.354361	−0.177180	−	0.984178i	$-0.556698\pi$
$239$	−5.47828	−0.354361	−0.177180	+	0.984178i	$0.556698\pi$
$240$	9.34700	0.603346
$241$	11.1029	0.715198	0.357599	−	0.933875i	$-0.383595\pi$
$241$	11.1029	0.715198	0.357599	+	0.933875i	$0.383595\pi$
$242$	5.30240	0.340851
$243$	9.20130	0.590264
$244$	−6.14389	−0.393322
$245$	14.1587	0.904566
$246$	9.24355	0.589347
$247$	0	0
$248$	−4.15494	−0.263839
$249$	29.2965	1.85659
$250$	1.23518	0.0781194
$251$	1.85041	0.116797	0.0583985	−	0.998293i	$-0.481401\pi$
$251$	1.85041	0.116797	0.0583985	+	0.998293i	$0.481401\pi$
$252$	8.74014	0.550577
$253$	12.6686	0.796470
$254$	−13.9561	−0.875683
$255$	−4.49151	−0.281269
$256$	1.00000	0.0625000
$257$	24.6849	1.53980	0.769899	−	0.638165i	$-0.220306\pi$
$257$	24.6849	1.53980	0.769899	+	0.638165i	$0.220306\pi$
$258$	−11.7023	−0.728556
$259$	−10.0811	−0.626409
$260$	−3.22232	−0.199840
$261$	−35.1723	−2.17711
$262$	−11.7378	−0.725163
$263$	−10.8873	−0.671340	−0.335670	−	0.941980i	$-0.608963\pi$
$263$	−10.8873	−0.671340	−0.335670	+	0.941980i	$0.608963\pi$
$264$	6.92389	0.426136
$265$	−1.88839	−0.116003
$266$	0	0
$267$	−12.8134	−0.784164
$268$	−15.5174	−0.947874
$269$	−4.68270	−0.285509	−0.142755	−	0.989758i	$-0.545596\pi$
$269$	−4.68270	−0.285509	−0.142755	+	0.989758i	$0.545596\pi$
$270$	−22.5646	−1.37324
$271$	−21.2266	−1.28942	−0.644712	−	0.764426i	$-0.723023\pi$
$271$	−21.2266	−1.28942	−0.644712	+	0.764426i	$0.723023\pi$
$272$	−0.480530	−0.0291364
$273$	−4.68269	−0.283409
$274$	−5.35044	−0.323232
$275$	12.8498	0.774871
$276$	−15.3953	−0.926687
$277$	−14.9983	−0.901163	−0.450581	−	0.892735i	$-0.648783\pi$
$277$	−14.9983	−0.901163	−0.450581	+	0.892735i	$0.648783\pi$
$278$	5.10591	0.306232
$279$	22.4953	1.34676
$280$	5.20187	0.310871
$281$	−10.7525	−0.641438	−0.320719	−	0.947174i	$-0.603925\pi$
$281$	−10.7525	−0.641438	−0.320719	+	0.947174i	$0.603925\pi$
$282$	32.1435	1.91412
$283$	8.21489	0.488325	0.244162	−	0.969734i	$-0.421487\pi$
$283$	8.21489	0.488325	0.244162	+	0.969734i	$0.421487\pi$
$284$	14.1554	0.839967
$285$	0	0
$286$	−2.38696	−0.141144
$287$	5.14430	0.303658
$288$	−5.41411	−0.319029
$289$	−16.7691	−0.986417
$290$	−20.9335	−1.22926
$291$	20.9463	1.22789
$292$	4.24087	0.248178
$293$	31.9264	1.86516	0.932579	−	0.360967i	$-0.117553\pi$
$293$	31.9264	1.86516	0.932579	+	0.360967i	$0.117553\pi$
$294$	−12.7456	−0.743337
$295$	25.5001	1.48467
$296$	6.24477	0.362970
$297$	−16.7150	−0.969903
$298$	−7.17107	−0.415409
$299$	5.30742	0.306936
$300$	−15.6154	−0.901558
$301$	−6.51269	−0.375385
$302$	24.0585	1.38441
$303$	5.75637	0.330695
$304$	0	0
$305$	19.7975	1.13360
$306$	2.60164	0.148726
$307$	−6.07992	−0.346999	−0.173500	−	0.984834i	$-0.555508\pi$
$307$	−6.07992	−0.346999	−0.173500	+	0.984834i	$0.555508\pi$
$308$	3.85334	0.219564
$309$	−47.6894	−2.71295
$310$	13.3885	0.760417
$311$	−25.6708	−1.45566	−0.727829	−	0.685759i	$-0.759470\pi$
$311$	−25.6708	−1.45566	−0.727829	+	0.685759i	$0.759470\pi$
$312$	2.90071	0.164220
$313$	−18.4727	−1.04414	−0.522068	−	0.852904i	$-0.674839\pi$
$313$	−18.4727	−1.04414	−0.522068	+	0.852904i	$0.674839\pi$
$314$	−24.0177	−1.35540
$315$	−28.1635	−1.58683
$316$	−8.69887	−0.489349
$317$	−11.6868	−0.656397	−0.328198	−	0.944609i	$-0.606441\pi$
$317$	−11.6868	−0.656397	−0.328198	+	0.944609i	$0.606441\pi$
$318$	1.69992	0.0953267
$319$	−15.5067	−0.868209
$320$	−3.22232	−0.180133
$321$	−33.0632	−1.84541
$322$	−8.56791	−0.477471
$323$	0	0
$324$	4.07023	0.226124
$325$	5.38332	0.298613
$326$	−9.70246	−0.537369
$327$	49.3487	2.72899
$328$	−3.18665	−0.175954
$329$	17.8888	0.986240
$330$	−22.3109	−1.22818
$331$	27.6056	1.51734	0.758671	−	0.651474i	$-0.225849\pi$
$331$	27.6056	1.51734	0.758671	+	0.651474i	$0.225849\pi$
$332$	−10.0998	−0.554298
$333$	−33.8099	−1.85277
$334$	21.6034	1.18208
$335$	50.0019	2.73189
$336$	−4.68269	−0.255462
$337$	−13.9431	−0.759527	−0.379764	−	0.925084i	$-0.623995\pi$
$337$	−13.9431	−0.759527	−0.379764	+	0.925084i	$0.623995\pi$
$338$	−1.00000	−0.0543928
$339$	24.3329	1.32158
$340$	1.54842	0.0839748
$341$	9.91768	0.537073
$342$	0	0
$343$	−18.3936	−0.993159
$344$	4.03431	0.217515
$345$	49.6085	2.67083
$346$	1.29516	0.0696283
$347$	18.0715	0.970127	0.485063	−	0.874479i	$-0.338797\pi$
$347$	18.0715	0.970127	0.485063	+	0.874479i	$0.338797\pi$
$348$	18.8442	1.01016
$349$	6.85462	0.366919	0.183460	−	0.983027i	$-0.441270\pi$
$349$	6.85462	0.366919	0.183460	+	0.983027i	$0.441270\pi$
$350$	−8.69043	−0.464523
$351$	−7.00262	−0.373772
$352$	−2.38696	−0.127226
$353$	23.5277	1.25225	0.626126	−	0.779722i	$-0.284640\pi$
$353$	23.5277	1.25225	0.626126	+	0.779722i	$0.284640\pi$
$354$	−22.9550	−1.22004
$355$	−45.6131	−2.42089
$356$	4.41732	0.234117
$357$	2.25017	0.119092
$358$	−25.3948	−1.34216
$359$	−25.6994	−1.35636	−0.678182	−	0.734894i	$-0.737232\pi$
$359$	−25.6994	−1.35636	−0.678182	+	0.734894i	$0.737232\pi$
$360$	17.4460	0.919483
$361$	0	0
$362$	14.2965	0.751410
$363$	15.3807	0.807279
$364$	1.61433	0.0846137
$365$	−13.6654	−0.715280
$366$	−17.8216	−0.931551
$367$	9.42932	0.492207	0.246103	−	0.969244i	$-0.420850\pi$
$367$	9.42932	0.492207	0.246103	+	0.969244i	$0.420850\pi$
$368$	5.30742	0.276669
$369$	17.2529	0.898149
$370$	−20.1226	−1.04613
$371$	0.946053	0.0491166
$372$	−12.0523	−0.624880
$373$	−10.8902	−0.563873	−0.281936	−	0.959433i	$-0.590977\pi$
$373$	−10.8902	−0.563873	−0.281936	+	0.959433i	$0.590977\pi$
$374$	1.14701	0.0593103
$375$	3.58288	0.185019
$376$	−11.0813	−0.571472
$377$	−6.49642	−0.334583
$378$	11.3045	0.581441
$379$	31.3484	1.61026	0.805130	−	0.593099i	$-0.202096\pi$
$379$	31.3484	1.61026	0.805130	+	0.593099i	$0.202096\pi$
$380$	0	0
$381$	−40.4826	−2.07398
$382$	7.21424	0.369113
$383$	−15.1855	−0.775941	−0.387971	−	0.921672i	$-0.626824\pi$
$383$	−15.1855	−0.775941	−0.387971	+	0.921672i	$0.626824\pi$
$384$	2.90071	0.148026
$385$	−12.4167	−0.632812
$386$	2.97961	0.151658
$387$	−21.8422	−1.11030
$388$	−7.22109	−0.366595
$389$	−4.37696	−0.221921	−0.110960	−	0.993825i	$-0.535393\pi$
$389$	−4.37696	−0.221921	−0.110960	+	0.993825i	$0.535393\pi$
$390$	−9.34700	−0.473304
$391$	−2.55037	−0.128978
$392$	4.39395	0.221928
$393$	−34.0479	−1.71749
$394$	−25.8408	−1.30184
$395$	28.0305	1.41037
$396$	12.9233	0.649419
$397$	−13.7731	−0.691251	−0.345625	−	0.938373i	$-0.612333\pi$
$397$	−13.7731	−0.691251	−0.345625	+	0.938373i	$0.612333\pi$
$398$	−18.8369	−0.944207
$399$	0	0
$400$	5.38332	0.269166
$401$	8.89253	0.444072	0.222036	−	0.975039i	$-0.428730\pi$
$401$	8.89253	0.444072	0.222036	+	0.975039i	$0.428730\pi$
$402$	−45.0113	−2.24496
$403$	4.15494	0.206972
$404$	−1.98447	−0.0987311
$405$	−13.1156	−0.651718
$406$	10.4873	0.520478
$407$	−14.9060	−0.738865
$408$	−1.39388	−0.0690071
$409$	32.6858	1.61621	0.808105	−	0.589038i	$-0.200493\pi$
$409$	32.6858	1.61621	0.808105	+	0.589038i	$0.200493\pi$
$410$	10.2684	0.507120
$411$	−15.5201	−0.765548
$412$	16.4406	0.809970
$413$	−12.7751	−0.628622
$414$	−28.7350	−1.41225
$415$	32.5447	1.59756
$416$	−1.00000	−0.0490290
$417$	14.8108	0.725286
$418$	0	0
$419$	−19.0007	−0.928246	−0.464123	−	0.885771i	$-0.653630\pi$
$419$	−19.0007	−0.928246	−0.464123	+	0.885771i	$0.653630\pi$
$420$	15.0891	0.736273
$421$	35.0992	1.71063	0.855316	−	0.518107i	$-0.173363\pi$
$421$	35.0992	1.71063	0.855316	+	0.518107i	$0.173363\pi$
$422$	1.51125	0.0735665
$423$	59.9951	2.91706
$424$	−0.586036	−0.0284604
$425$	−2.58684	−0.125480
$426$	41.0606	1.98939
$427$	−9.91824	−0.479977
$428$	11.3983	0.550959
$429$	−6.92389	−0.334288
$430$	−12.9998	−0.626907
$431$	−1.63152	−0.0785878	−0.0392939	−	0.999228i	$-0.512511\pi$
$431$	−1.63152	−0.0785878	−0.0392939	+	0.999228i	$0.512511\pi$
$432$	−7.00262	−0.336914
$433$	−5.60635	−0.269424	−0.134712	−	0.990885i	$-0.543011\pi$
$433$	−5.60635	−0.269424	−0.134712	+	0.990885i	$0.543011\pi$
$434$	−6.70742	−0.321967
$435$	−60.7220	−2.91140
$436$	−17.0126	−0.814757
$437$	0	0
$438$	12.3015	0.587789
$439$	−24.5930	−1.17376	−0.586880	−	0.809674i	$-0.699644\pi$
$439$	−24.5930	−1.17376	−0.586880	+	0.809674i	$0.699644\pi$
$440$	7.69155	0.366680
$441$	−23.7893	−1.13282
$442$	0.480530	0.0228565
$443$	−19.0053	−0.902969	−0.451485	−	0.892279i	$-0.649105\pi$
$443$	−19.0053	−0.902969	−0.451485	+	0.892279i	$0.649105\pi$
$444$	18.1143	0.859665
$445$	−14.2340	−0.674756
$446$	1.60290	0.0758994
$447$	−20.8012	−0.983862
$448$	1.61433	0.0762698
$449$	−2.13840	−0.100917	−0.0504587	−	0.998726i	$-0.516068\pi$
$449$	−2.13840	−0.100917	−0.0504587	+	0.998726i	$0.516068\pi$
$450$	−29.1459	−1.37395
$451$	7.60643	0.358173
$452$	−8.38862	−0.394567
$453$	69.7868	3.27887
$454$	−12.4678	−0.585144
$455$	−5.20187	−0.243867
$456$	0	0
$457$	−16.7817	−0.785016	−0.392508	−	0.919749i	$-0.628392\pi$
$457$	−16.7817	−0.785016	−0.392508	+	0.919749i	$0.628392\pi$
$458$	10.3992	0.485922
$459$	3.36497	0.157063
$460$	−17.1022	−0.797394
$461$	−11.2496	−0.523946	−0.261973	−	0.965075i	$-0.584373\pi$
$461$	−11.2496	−0.523946	−0.261973	+	0.965075i	$0.584373\pi$
$462$	11.1774	0.520020
$463$	30.9991	1.44065	0.720326	−	0.693636i	$-0.243992\pi$
$463$	30.9991	1.44065	0.720326	+	0.693636i	$0.243992\pi$
$464$	−6.49642	−0.301589
$465$	38.8362	1.80098
$466$	−8.08782	−0.374661
$467$	−7.22785	−0.334465	−0.167233	−	0.985917i	$-0.553483\pi$
$467$	−7.22785	−0.334465	−0.167233	+	0.985917i	$0.553483\pi$
$468$	5.41411	0.250267
$469$	−25.0501	−1.15671
$470$	35.7073	1.64706
$471$	−69.6683	−3.21015
$472$	7.91358	0.364252
$473$	−9.62975	−0.442776
$474$	−25.2329	−1.15898
$475$	0	0
$476$	−0.775732	−0.0355556
$477$	3.17286	0.145275
$478$	5.47828	0.250571
$479$	−8.40367	−0.383973	−0.191987	−	0.981398i	$-0.561493\pi$
$479$	−8.40367	−0.383973	−0.191987	+	0.981398i	$0.561493\pi$
$480$	−9.34700	−0.426630
$481$	−6.24477	−0.284737
$482$	−11.1029	−0.505721
$483$	−24.8530	−1.13085
$484$	−5.30240	−0.241018
$485$	23.2686	1.05657
$486$	−9.20130	−0.417380
$487$	−39.0864	−1.77117	−0.885587	−	0.464473i	$-0.846244\pi$
$487$	−39.0864	−1.77117	−0.885587	+	0.464473i	$0.846244\pi$
$488$	6.14389	0.278121
$489$	−28.1440	−1.27272
$490$	−14.1587	−0.639625
$491$	−34.1244	−1.54001	−0.770006	−	0.638037i	$-0.779747\pi$
$491$	−34.1244	−1.54001	−0.770006	+	0.638037i	$0.779747\pi$
$492$	−9.24355	−0.416731
$493$	3.12172	0.140595
$494$	0	0
$495$	−41.6429	−1.87171
$496$	4.15494	0.186562
$497$	22.8514	1.02502
$498$	−29.2965	−1.31281
$499$	−16.1855	−0.724562	−0.362281	−	0.932069i	$-0.618002\pi$
$499$	−16.1855	−0.724562	−0.362281	+	0.932069i	$0.618002\pi$
$500$	−1.23518	−0.0552387
$501$	62.6651	2.79967
$502$	−1.85041	−0.0825879
$503$	−21.9120	−0.977009	−0.488504	−	0.872561i	$-0.662457\pi$
$503$	−21.9120	−0.977009	−0.488504	+	0.872561i	$0.662457\pi$
$504$	−8.74014	−0.389317
$505$	6.39459	0.284556
$506$	−12.6686	−0.563189
$507$	−2.90071	−0.128825
$508$	13.9561	0.619202
$509$	−34.3483	−1.52246	−0.761231	−	0.648481i	$-0.775405\pi$
$509$	−34.3483	−1.52246	−0.761231	+	0.648481i	$0.775405\pi$
$510$	4.49151	0.198887
$511$	6.84614	0.302855
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−24.6849	−1.08880
$515$	−52.9768	−2.33444
$516$	11.7023	0.515167
$517$	26.4506	1.16329
$518$	10.0811	0.442938
$519$	3.75688	0.164909
$520$	3.22232	0.141308
$521$	35.6790	1.56313	0.781563	−	0.623827i	$-0.214423\pi$
$521$	35.6790	1.56313	0.781563	+	0.623827i	$0.214423\pi$
$522$	35.1723	1.53945
$523$	−8.02294	−0.350819	−0.175409	−	0.984496i	$-0.556125\pi$
$523$	−8.02294	−0.350819	−0.175409	+	0.984496i	$0.556125\pi$
$524$	11.7378	0.512768
$525$	−25.2084	−1.10019
$526$	10.8873	0.474709
$527$	−1.99657	−0.0869719
$528$	−6.92389	−0.301323
$529$	5.16874	0.224728
$530$	1.88839	0.0820265
$531$	−42.8450	−1.85931
$532$	0	0
$533$	3.18665	0.138029
$534$	12.8134	0.554488
$535$	−36.7290	−1.58793
$536$	15.5174	0.670248
$537$	−73.6630	−3.17879
$538$	4.68270	0.201886
$539$	−10.4882	−0.451759
$540$	22.5646	0.971028
$541$	−31.5951	−1.35838	−0.679189	−	0.733963i	$-0.737668\pi$
$541$	−31.5951	−1.35838	−0.679189	+	0.733963i	$0.737668\pi$
$542$	21.2266	0.911760
$543$	41.4701	1.77965
$544$	0.480530	0.0206025
$545$	54.8201	2.34823
$546$	4.68269	0.200401
$547$	18.3126	0.782992	0.391496	−	0.920180i	$-0.371958\pi$
$547$	18.3126	0.782992	0.391496	+	0.920180i	$0.371958\pi$
$548$	5.35044	0.228559
$549$	−33.2637	−1.41966
$550$	−12.8498	−0.547917
$551$	0	0
$552$	15.3953	0.655267
$553$	−14.0428	−0.597161
$554$	14.9983	0.637218
$555$	−58.3699	−2.47766
$556$	−5.10591	−0.216539
$557$	−13.1018	−0.555141	−0.277570	−	0.960705i	$-0.589529\pi$
$557$	−13.1018	−0.555141	−0.277570	+	0.960705i	$0.589529\pi$
$558$	−22.4953	−0.952301
$559$	−4.03431	−0.170633
$560$	−5.20187	−0.219819
$561$	3.32713	0.140472
$562$	10.7525	0.453565
$563$	10.3286	0.435301	0.217650	−	0.976027i	$-0.430161\pi$
$563$	10.3286	0.435301	0.217650	+	0.976027i	$0.430161\pi$
$564$	−32.1435	−1.35349
$565$	27.0308	1.13719
$566$	−8.21489	−0.345298
$567$	6.57068	0.275943
$568$	−14.1554	−0.593946
$569$	−9.62426	−0.403470	−0.201735	−	0.979440i	$-0.564658\pi$
$569$	−9.62426	−0.403470	−0.201735	+	0.979440i	$0.564658\pi$
$570$	0	0
$571$	46.0612	1.92760	0.963801	−	0.266622i	$-0.0859076\pi$
$571$	46.0612	1.92760	0.963801	+	0.266622i	$0.0859076\pi$
$572$	2.38696	0.0998040
$573$	20.9264	0.874214
$574$	−5.14430	−0.214719
$575$	28.5716	1.19152
$576$	5.41411	0.225588
$577$	−26.4621	−1.10163	−0.550816	−	0.834626i	$-0.685684\pi$
$577$	−26.4621	−1.10163	−0.550816	+	0.834626i	$0.685684\pi$
$578$	16.7691	0.697502
$579$	8.64297	0.359189
$580$	20.9335	0.869217
$581$	−16.3043	−0.676418
$582$	−20.9463	−0.868251
$583$	1.39885	0.0579343
$584$	−4.24087	−0.175488
$585$	−17.4460	−0.721302
$586$	−31.9264	−1.31887
$587$	1.90301	0.0785456	0.0392728	−	0.999229i	$-0.487496\pi$
$587$	1.90301	0.0785456	0.0392728	+	0.999229i	$0.487496\pi$
$588$	12.7456	0.525618
$589$	0	0
$590$	−25.5001	−1.04982
$591$	−74.9567	−3.08331
$592$	−6.24477	−0.256659
$593$	−21.7482	−0.893092	−0.446546	−	0.894761i	$-0.647346\pi$
$593$	−21.7482	−0.893092	−0.446546	+	0.894761i	$0.647346\pi$
$594$	16.7150	0.685825
$595$	2.49965	0.102476
$596$	7.17107	0.293738
$597$	−54.6403	−2.23628
$598$	−5.30742	−0.217037
$599$	−18.4707	−0.754694	−0.377347	−	0.926072i	$-0.623164\pi$
$599$	−18.4707	−0.754694	−0.377347	+	0.926072i	$0.623164\pi$
$600$	15.6154	0.637498
$601$	−20.8248	−0.849461	−0.424730	−	0.905320i	$-0.639631\pi$
$601$	−20.8248	−0.849461	−0.424730	+	0.905320i	$0.639631\pi$
$602$	6.51269	0.265437
$603$	−84.0127	−3.42126
$604$	−24.0585	−0.978928
$605$	17.0860	0.694645
$606$	−5.75637	−0.233837
$607$	37.1365	1.50732	0.753661	−	0.657263i	$-0.228286\pi$
$607$	37.1365	1.50732	0.753661	+	0.657263i	$0.228286\pi$
$608$	0	0
$609$	30.4207	1.23271
$610$	−19.7975	−0.801579
$611$	11.0813	0.448300
$612$	−2.60164	−0.105165
$613$	28.3288	1.14419	0.572094	−	0.820188i	$-0.306131\pi$
$613$	28.3288	1.14419	0.572094	+	0.820188i	$0.306131\pi$
$614$	6.07992	0.245366
$615$	29.7856	1.20107
$616$	−3.85334	−0.155255
$617$	−3.31640	−0.133513	−0.0667567	−	0.997769i	$-0.521265\pi$
$617$	−3.31640	−0.133513	−0.0667567	+	0.997769i	$0.521265\pi$
$618$	47.6894	1.91835
$619$	24.2555	0.974909	0.487455	−	0.873148i	$-0.337925\pi$
$619$	24.2555	0.974909	0.487455	+	0.873148i	$0.337925\pi$
$620$	−13.3885	−0.537696
$621$	−37.1659	−1.49141
$622$	25.6708	1.02931
$623$	7.13099	0.285697
$624$	−2.90071	−0.116121
$625$	−22.9365	−0.917459
$626$	18.4727	0.738316
$627$	0	0
$628$	24.0177	0.958411
$629$	3.00080	0.119650
$630$	28.1635	1.12206
$631$	38.9655	1.55119	0.775595	−	0.631231i	$-0.217450\pi$
$631$	38.9655	1.55119	0.775595	+	0.631231i	$0.217450\pi$
$632$	8.69887	0.346022
$633$	4.38369	0.174236
$634$	11.6868	0.464143
$635$	−44.9709	−1.78462
$636$	−1.69992	−0.0674062
$637$	−4.39395	−0.174095
$638$	15.5067	0.613917
$639$	76.6387	3.03178
$640$	3.22232	0.127373
$641$	5.93366	0.234365	0.117183	−	0.993110i	$-0.462614\pi$
$641$	5.93366	0.234365	0.117183	+	0.993110i	$0.462614\pi$
$642$	33.0632	1.30490
$643$	20.0765	0.791738	0.395869	−	0.918307i	$-0.370443\pi$
$643$	20.0765	0.791738	0.395869	+	0.918307i	$0.370443\pi$
$644$	8.56791	0.337623
$645$	−37.7087	−1.48478
$646$	0	0
$647$	−3.89165	−0.152996	−0.0764982	−	0.997070i	$-0.524374\pi$
$647$	−3.89165	−0.152996	−0.0764982	+	0.997070i	$0.524374\pi$
$648$	−4.07023	−0.159894
$649$	−18.8894	−0.741475
$650$	−5.38332	−0.211151
$651$	−19.4563	−0.762551
$652$	9.70246	0.379978
$653$	−12.3661	−0.483924	−0.241962	−	0.970286i	$-0.577791\pi$
$653$	−12.3661	−0.483924	−0.241962	+	0.970286i	$0.577791\pi$
$654$	−49.3487	−1.92969
$655$	−37.8229	−1.47786
$656$	3.18665	0.124418
$657$	22.9605	0.895774
$658$	−17.8888	−0.697377
$659$	13.4769	0.524986	0.262493	−	0.964934i	$-0.415455\pi$
$659$	13.4769	0.524986	0.262493	+	0.964934i	$0.415455\pi$
$660$	22.3109	0.868452
$661$	7.37597	0.286892	0.143446	−	0.989658i	$-0.454182\pi$
$661$	7.37597	0.286892	0.143446	+	0.989658i	$0.454182\pi$
$662$	−27.6056	−1.07292
$663$	1.39388	0.0541337
$664$	10.0998	0.391948
$665$	0	0
$666$	33.8099	1.31011
$667$	−34.4792	−1.33504
$668$	−21.6034	−0.835860
$669$	4.64954	0.179761
$670$	−50.0019	−1.93174
$671$	−14.6652	−0.566145
$672$	4.68269	0.180639
$673$	6.27761	0.241984	0.120992	−	0.992653i	$-0.461392\pi$
$673$	6.27761	0.241984	0.120992	+	0.992653i	$0.461392\pi$
$674$	13.9431	0.537067
$675$	−37.6973	−1.45097
$676$	1.00000	0.0384615
$677$	0.692027	0.0265967	0.0132984	−	0.999912i	$-0.495767\pi$
$677$	0.692027	0.0265967	0.0132984	+	0.999912i	$0.495767\pi$
$678$	−24.3329	−0.934501
$679$	−11.6572	−0.447362
$680$	−1.54842	−0.0593791
$681$	−36.1655	−1.38587
$682$	−9.91768	−0.379768
$683$	−42.5373	−1.62764	−0.813822	−	0.581114i	$-0.802617\pi$
$683$	−42.5373	−1.62764	−0.813822	+	0.581114i	$0.802617\pi$
$684$	0	0
$685$	−17.2408	−0.658737
$686$	18.3936	0.702269
$687$	30.1650	1.15087
$688$	−4.03431	−0.153807
$689$	0.586036	0.0223262
$690$	−49.6085	−1.88856
$691$	−7.56745	−0.287880	−0.143940	−	0.989586i	$-0.545977\pi$
$691$	−7.56745	−0.287880	−0.143940	+	0.989586i	$0.545977\pi$
$692$	−1.29516	−0.0492346
$693$	20.8624	0.792497
$694$	−18.0715	−0.685983
$695$	16.4529	0.624093
$696$	−18.8442	−0.714288
$697$	−1.53128	−0.0580014
$698$	−6.85462	−0.259451
$699$	−23.4604	−0.887354
$700$	8.69043	0.328468
$701$	−28.1528	−1.06332	−0.531658	−	0.846959i	$-0.678431\pi$
$701$	−28.1528	−1.06332	−0.531658	+	0.846959i	$0.678431\pi$
$702$	7.00262	0.264297
$703$	0	0
$704$	2.38696	0.0899621
$705$	103.576	3.90092
$706$	−23.5277	−0.885475
$707$	−3.20358	−0.120483
$708$	22.9550	0.862701
$709$	−20.6522	−0.775611	−0.387806	−	0.921741i	$-0.626767\pi$
$709$	−20.6522	−0.775611	−0.387806	+	0.921741i	$0.626767\pi$
$710$	45.6131	1.71183
$711$	−47.0966	−1.76626
$712$	−4.41732	−0.165546
$713$	22.0520	0.825854
$714$	−2.25017	−0.0842105
$715$	−7.69155	−0.287648
$716$	25.3948	0.949049
$717$	15.8909	0.593457
$718$	25.6994	0.959094
$719$	0.386691	0.0144211	0.00721057	−	0.999974i	$-0.497705\pi$
$719$	0.386691	0.0144211	0.00721057	+	0.999974i	$0.497705\pi$
$720$	−17.4460	−0.650173
$721$	26.5405	0.988419
$722$	0	0
$723$	−32.2062	−1.19776
$724$	−14.2965	−0.531327
$725$	−34.9723	−1.29884
$726$	−15.3807	−0.570832
$727$	−36.2780	−1.34548	−0.672738	−	0.739880i	$-0.734882\pi$
$727$	−36.2780	−1.34548	−0.672738	+	0.739880i	$0.734882\pi$
$728$	−1.61433	−0.0598309
$729$	−38.9010	−1.44078
$730$	13.6654	0.505779
$731$	1.93860	0.0717019
$732$	17.8216	0.658706
$733$	−3.37369	−0.124610	−0.0623051	−	0.998057i	$-0.519845\pi$
$733$	−3.37369	−0.124610	−0.0623051	+	0.998057i	$0.519845\pi$
$734$	−9.42932	−0.348043
$735$	−41.0702	−1.51490
$736$	−5.30742	−0.195634
$737$	−37.0394	−1.36436
$738$	−17.2529	−0.635087
$739$	−28.7986	−1.05937	−0.529687	−	0.848193i	$-0.677690\pi$
$739$	−28.7986	−1.05937	−0.529687	+	0.848193i	$0.677690\pi$
$740$	20.1226	0.739723
$741$	0	0
$742$	−0.946053	−0.0347307
$743$	2.60303	0.0954959	0.0477479	−	0.998859i	$-0.484796\pi$
$743$	2.60303	0.0954959	0.0477479	+	0.998859i	$0.484796\pi$
$744$	12.0523	0.441857
$745$	−23.1074	−0.846591
$746$	10.8902	0.398718
$747$	−54.6813	−2.00068
$748$	−1.14701	−0.0419387
$749$	18.4006	0.672344
$750$	−3.58288	−0.130828
$751$	−29.3147	−1.06971	−0.534854	−	0.844944i	$-0.679634\pi$
$751$	−29.3147	−1.06971	−0.534854	+	0.844944i	$0.679634\pi$
$752$	11.0813	0.404092
$753$	−5.36750	−0.195603
$754$	6.49642	0.236586
$755$	77.5242	2.82140
$756$	−11.3045	−0.411141
$757$	−10.9189	−0.396853	−0.198426	−	0.980116i	$-0.563583\pi$
$757$	−10.9189	−0.396853	−0.198426	+	0.980116i	$0.563583\pi$
$758$	−31.3484	−1.13863
$759$	−36.7480	−1.33387
$760$	0	0
$761$	29.8756	1.08299	0.541495	−	0.840704i	$-0.317859\pi$
$761$	29.8756	1.08299	0.541495	+	0.840704i	$0.317859\pi$
$762$	40.4826	1.46653
$763$	−27.4639	−0.994261
$764$	−7.21424	−0.261002
$765$	8.38330	0.303099
$766$	15.1855	0.548673
$767$	−7.91358	−0.285743
$768$	−2.90071	−0.104670
$769$	36.7846	1.32649	0.663244	−	0.748403i	$-0.269179\pi$
$769$	36.7846	1.32649	0.663244	+	0.748403i	$0.269179\pi$
$770$	12.4167	0.447466
$771$	−71.6035	−2.57874
$772$	−2.97961	−0.107238
$773$	−28.5296	−1.02614	−0.513069	−	0.858347i	$-0.671492\pi$
$773$	−28.5296	−1.02614	−0.513069	+	0.858347i	$0.671492\pi$
$774$	21.8422	0.785101
$775$	22.3673	0.803459
$776$	7.22109	0.259222
$777$	29.2423	1.04906
$778$	4.37696	0.156922
$779$	0	0
$780$	9.34700	0.334676
$781$	33.7884	1.20904
$782$	2.55037	0.0912012
$783$	45.4919	1.62575
$784$	−4.39395	−0.156927
$785$	−77.3926	−2.76226
$786$	34.0479	1.21445
$787$	−15.2974	−0.545292	−0.272646	−	0.962114i	$-0.587899\pi$
$787$	−15.2974	−0.545292	−0.272646	+	0.962114i	$0.587899\pi$
$788$	25.8408	0.920542
$789$	31.5809	1.12431
$790$	−28.0305	−0.997280
$791$	−13.5420	−0.481497
$792$	−12.9233	−0.459209
$793$	−6.14389	−0.218176
$794$	13.7731	0.488788
$795$	5.47767	0.194273
$796$	18.8369	0.667655
$797$	22.1294	0.783863	0.391931	−	0.919994i	$-0.371807\pi$
$797$	22.1294	0.783863	0.391931	+	0.919994i	$0.371807\pi$
$798$	0	0
$799$	−5.32487	−0.188380
$800$	−5.38332	−0.190329
$801$	23.9158	0.845025
$802$	−8.89253	−0.314006
$803$	10.1228	0.357226
$804$	45.0113	1.58743
$805$	−27.6085	−0.973073
$806$	−4.15494	−0.146351
$807$	13.5831	0.478150
$808$	1.98447	0.0698134
$809$	23.3963	0.822569	0.411284	−	0.911507i	$-0.365080\pi$
$809$	23.3963	0.822569	0.411284	+	0.911507i	$0.365080\pi$
$810$	13.1156	0.460834
$811$	−4.04053	−0.141882	−0.0709411	−	0.997481i	$-0.522600\pi$
$811$	−4.04053	−0.141882	−0.0709411	+	0.997481i	$0.522600\pi$
$812$	−10.4873	−0.368033
$813$	61.5721	2.15943
$814$	14.9060	0.522457
$815$	−31.2644	−1.09514
$816$	1.39388	0.0487954
$817$	0	0
$818$	−32.6858	−1.14283
$819$	8.74014	0.305405
$820$	−10.2684	−0.358588
$821$	22.6358	0.789993	0.394997	−	0.918683i	$-0.370746\pi$
$821$	22.6358	0.789993	0.394997	+	0.918683i	$0.370746\pi$
$822$	15.5201	0.541324
$823$	32.0170	1.11604	0.558021	−	0.829827i	$-0.311561\pi$
$823$	32.0170	1.11604	0.558021	+	0.829827i	$0.311561\pi$
$824$	−16.4406	−0.572735
$825$	−37.2735	−1.29770
$826$	12.7751	0.444503
$827$	−10.5760	−0.367765	−0.183882	−	0.982948i	$-0.558867\pi$
$827$	−10.5760	−0.367765	−0.183882	+	0.982948i	$0.558867\pi$
$828$	28.7350	0.998609
$829$	10.9830	0.381455	0.190727	−	0.981643i	$-0.438915\pi$
$829$	10.9830	0.381455	0.190727	+	0.981643i	$0.438915\pi$
$830$	−32.5447	−1.12964
$831$	43.5058	1.50920
$832$	1.00000	0.0346688
$833$	2.11142	0.0731565
$834$	−14.8108	−0.512855
$835$	69.6129	2.40905
$836$	0	0
$837$	−29.0954	−1.00569
$838$	19.0007	0.656369
$839$	44.4742	1.53542	0.767711	−	0.640797i	$-0.221396\pi$
$839$	44.4742	1.53542	0.767711	+	0.640797i	$0.221396\pi$
$840$	−15.0891	−0.520624
$841$	13.2035	0.455291
$842$	−35.0992	−1.20960
$843$	31.1898	1.07423
$844$	−1.51125	−0.0520194
$845$	−3.22232	−0.110851
$846$	−59.9951	−2.06267
$847$	−8.55981	−0.294118
$848$	0.586036	0.0201246
$849$	−23.8290	−0.817809
$850$	2.58684	0.0887280
$851$	−33.1437	−1.13615
$852$	−41.0606	−1.40671
$853$	12.2291	0.418716	0.209358	−	0.977839i	$-0.432863\pi$
$853$	12.2291	0.418716	0.209358	+	0.977839i	$0.432863\pi$
$854$	9.91824	0.339395
$855$	0	0
$856$	−11.3983	−0.389587
$857$	54.5003	1.86170	0.930848	−	0.365406i	$-0.119070\pi$
$857$	54.5003	1.86170	0.930848	+	0.365406i	$0.119070\pi$
$858$	6.92389	0.236378
$859$	−38.1826	−1.30277	−0.651386	−	0.758746i	$-0.725812\pi$
$859$	−38.1826	−1.30277	−0.651386	+	0.758746i	$0.725812\pi$
$860$	12.9998	0.443290
$861$	−14.9221	−0.508544
$862$	1.63152	0.0555699
$863$	27.6662	0.941768	0.470884	−	0.882195i	$-0.343935\pi$
$863$	27.6662	0.941768	0.470884	+	0.882195i	$0.343935\pi$
$864$	7.00262	0.238234
$865$	4.17342	0.141900
$866$	5.60635	0.190511
$867$	48.6422	1.65198
$868$	6.70742	0.227665
$869$	−20.7639	−0.704366
$870$	60.7220	2.05867
$871$	−15.5174	−0.525786
$872$	17.0126	0.576120
$873$	−39.0957	−1.32319
$874$	0	0
$875$	−1.99398	−0.0674087
$876$	−12.3015	−0.415630
$877$	−7.66019	−0.258666	−0.129333	−	0.991601i	$-0.541284\pi$
$877$	−7.66019	−0.258666	−0.129333	+	0.991601i	$0.541284\pi$
$878$	24.5930	0.829973
$879$	−92.6090	−3.12362
$880$	−7.69155	−0.259282
$881$	−20.1132	−0.677631	−0.338815	−	0.940853i	$-0.610026\pi$
$881$	−20.1132	−0.677631	−0.338815	+	0.940853i	$0.610026\pi$
$882$	23.7893	0.801028
$883$	0.971252	0.0326852	0.0163426	−	0.999866i	$-0.494798\pi$
$883$	0.971252	0.0326852	0.0163426	+	0.999866i	$0.494798\pi$
$884$	−0.480530	−0.0161620
$885$	−73.9682	−2.48641
$886$	19.0053	0.638496
$887$	−31.0454	−1.04240	−0.521201	−	0.853434i	$-0.674516\pi$
$887$	−31.0454	−1.04240	−0.521201	+	0.853434i	$0.674516\pi$
$888$	−18.1143	−0.607875
$889$	22.5297	0.755622
$890$	14.2340	0.477125
$891$	9.71550	0.325481
$892$	−1.60290	−0.0536690
$893$	0	0
$894$	20.8012	0.695695
$895$	−81.8302	−2.73528
$896$	−1.61433	−0.0539309
$897$	−15.3953	−0.514034
$898$	2.13840	0.0713593
$899$	−26.9922	−0.900240
$900$	29.1459	0.971529
$901$	−0.281607	−0.00938171
$902$	−7.60643	−0.253266
$903$	18.8914	0.628667
$904$	8.38862	0.279001
$905$	46.0680	1.53135
$906$	−69.7868	−2.31851
$907$	3.77407	0.125316	0.0626580	−	0.998035i	$-0.480042\pi$
$907$	3.77407	0.125316	0.0626580	+	0.998035i	$0.480042\pi$
$908$	12.4678	0.413759
$909$	−10.7441	−0.356360
$910$	5.20187	0.172440
$911$	−44.8830	−1.48704	−0.743519	−	0.668715i	$-0.766845\pi$
$911$	−44.8830	−1.48704	−0.743519	+	0.668715i	$0.766845\pi$
$912$	0	0
$913$	−24.1078	−0.797852
$914$	16.7817	0.555090
$915$	−57.4269	−1.89847
$916$	−10.3992	−0.343598
$917$	18.9486	0.625739
$918$	−3.36497	−0.111060
$919$	−35.7410	−1.17899	−0.589493	−	0.807773i	$-0.700672\pi$
$919$	−35.7410	−1.17899	−0.589493	+	0.807773i	$0.700672\pi$
$920$	17.1022	0.563843
$921$	17.6361	0.581129
$922$	11.2496	0.370485
$923$	14.1554	0.465930
$924$	−11.1774	−0.367710
$925$	−33.6176	−1.10534
$926$	−30.9991	−1.01869
$927$	89.0111	2.92351
$928$	6.49642	0.213255
$929$	9.22422	0.302637	0.151318	−	0.988485i	$-0.451648\pi$
$929$	9.22422	0.302637	0.151318	+	0.988485i	$0.451648\pi$
$930$	−38.8362	−1.27349
$931$	0	0
$932$	8.08782	0.264925
$933$	74.4635	2.43783
$934$	7.22785	0.236503
$935$	3.69602	0.120873
$936$	−5.41411	−0.176966
$937$	−22.0910	−0.721682	−0.360841	−	0.932627i	$-0.617510\pi$
$937$	−22.0910	−0.721682	−0.360841	+	0.932627i	$0.617510\pi$
$938$	25.0501	0.817914
$939$	53.5838	1.74864
$940$	−35.7073	−1.16464
$941$	37.2279	1.21360	0.606798	−	0.794856i	$-0.292454\pi$
$941$	37.2279	1.21360	0.606798	+	0.794856i	$0.292454\pi$
$942$	69.6683	2.26992
$943$	16.9129	0.550760
$944$	−7.91358	−0.257565
$945$	36.4267	1.18496
$946$	9.62975	0.313090
$947$	14.2094	0.461744	0.230872	−	0.972984i	$-0.425842\pi$
$947$	14.2094	0.461744	0.230872	+	0.972984i	$0.425842\pi$
$948$	25.2329	0.819526
$949$	4.24087	0.137664
$950$	0	0
$951$	33.9000	1.09928
$952$	0.775732	0.0251416
$953$	−55.2027	−1.78819	−0.894095	−	0.447878i	$-0.852180\pi$
$953$	−55.2027	−1.78819	−0.894095	+	0.447878i	$0.852180\pi$
$954$	−3.17286	−0.102725
$955$	23.2466	0.752241
$956$	−5.47828	−0.177180
$957$	44.9805	1.45401
$958$	8.40367	0.271510
$959$	8.63735	0.278915
$960$	9.34700	0.301673
$961$	−13.7365	−0.443113
$962$	6.24477	0.201340
$963$	61.7118	1.98863
$964$	11.1029	0.357599
$965$	9.60123	0.309075
$966$	24.8530	0.799633
$967$	−4.87359	−0.156724	−0.0783621	−	0.996925i	$-0.524969\pi$
$967$	−4.87359	−0.156724	−0.0783621	+	0.996925i	$0.524969\pi$
$968$	5.30240	0.170426
$969$	0	0
$970$	−23.2686	−0.747110
$971$	24.1961	0.776489	0.388244	−	0.921556i	$-0.373082\pi$
$971$	24.1961	0.776489	0.388244	+	0.921556i	$0.373082\pi$
$972$	9.20130	0.295132
$973$	−8.24261	−0.264246
$974$	39.0864	1.25241
$975$	−15.6154	−0.500094
$976$	−6.14389	−0.196661
$977$	57.0584	1.82546	0.912731	−	0.408562i	$-0.133970\pi$
$977$	57.0584	1.82546	0.912731	+	0.408562i	$0.133970\pi$
$978$	28.1440	0.899946
$979$	10.5440	0.336987
$980$	14.1587	0.452283
$981$	−92.1082	−2.94079
$982$	34.1244	1.08895
$983$	48.0041	1.53109	0.765547	−	0.643380i	$-0.222468\pi$
$983$	48.0041	1.53109	0.765547	+	0.643380i	$0.222468\pi$
$984$	9.24355	0.294674
$985$	−83.2673	−2.65312
$986$	−3.12172	−0.0994158
$987$	−51.8901	−1.65168
$988$	0	0
$989$	−21.4118	−0.680855
$990$	41.6429	1.32350
$991$	−0.421547	−0.0133909	−0.00669544	−	0.999978i	$-0.502131\pi$
$991$	−0.421547	−0.0133909	−0.00669544	+	0.999978i	$0.502131\pi$
$992$	−4.15494	−0.131919
$993$	−80.0758	−2.54113
$994$	−22.8514	−0.724802
$995$	−60.6983	−1.92427
$996$	29.2965	0.928296
$997$	34.4456	1.09090	0.545452	−	0.838142i	$-0.316358\pi$
$997$	34.4456	1.09090	0.545452	+	0.838142i	$0.316358\pi$
$998$	16.1855	0.512342
$999$	43.7298	1.38355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9386.2.a.bw.1.3		15
19.2	odd	18		494.2.x.d.365.4	yes	30
19.10	odd	18		494.2.x.d.157.4	✓	30
19.18	odd	2		9386.2.a.bz.1.13		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.x.d.157.4	✓	30	19.10	odd	18
494.2.x.d.365.4	yes	30	19.2	odd	18
9386.2.a.bw.1.3		15	1.1	even	1	trivial
9386.2.a.bz.1.13		15	19.18	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:	\( N \)	\(=\)	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9386.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.90071 q^{3} +1.00000 q^{4} -3.22232 q^{5} +2.90071 q^{6} +1.61433 q^{7} -1.00000 q^{8} +5.41411 q^{9} +3.22232 q^{10} +2.38696 q^{11} -2.90071 q^{12} +1.00000 q^{13} -1.61433 q^{14} +9.34700 q^{15} +1.00000 q^{16} -0.480530 q^{17} -5.41411 q^{18} -3.22232 q^{20} -4.68269 q^{21} -2.38696 q^{22} +5.30742 q^{23} +2.90071 q^{24} +5.38332 q^{25} -1.00000 q^{26} -7.00262 q^{27} +1.61433 q^{28} -6.49642 q^{29} -9.34700 q^{30} +4.15494 q^{31} -1.00000 q^{32} -6.92389 q^{33} +0.480530 q^{34} -5.20187 q^{35} +5.41411 q^{36} -6.24477 q^{37} -2.90071 q^{39} +3.22232 q^{40} +3.18665 q^{41} +4.68269 q^{42} -4.03431 q^{43} +2.38696 q^{44} -17.4460 q^{45} -5.30742 q^{46} +11.0813 q^{47} -2.90071 q^{48} -4.39395 q^{49} -5.38332 q^{50} +1.39388 q^{51} +1.00000 q^{52} +0.586036 q^{53} +7.00262 q^{54} -7.69155 q^{55} -1.61433 q^{56} +6.49642 q^{58} -7.91358 q^{59} +9.34700 q^{60} -6.14389 q^{61} -4.15494 q^{62} +8.74014 q^{63} +1.00000 q^{64} -3.22232 q^{65} +6.92389 q^{66} -15.5174 q^{67} -0.480530 q^{68} -15.3953 q^{69} +5.20187 q^{70} +14.1554 q^{71} -5.41411 q^{72} +4.24087 q^{73} +6.24477 q^{74} -15.6154 q^{75} +3.85334 q^{77} +2.90071 q^{78} -8.69887 q^{79} -3.22232 q^{80} +4.07023 q^{81} -3.18665 q^{82} -10.0998 q^{83} -4.68269 q^{84} +1.54842 q^{85} +4.03431 q^{86} +18.8442 q^{87} -2.38696 q^{88} +4.41732 q^{89} +17.4460 q^{90} +1.61433 q^{91} +5.30742 q^{92} -12.0523 q^{93} -11.0813 q^{94} +2.90071 q^{96} -7.22109 q^{97} +4.39395 q^{98} +12.9233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - 3 q^{3} + 15 q^{4} + 3 q^{5} + 3 q^{6} - 15 q^{8} + 18 q^{9} - 3 q^{10} - 3 q^{11} - 3 q^{12} + 15 q^{13} + 15 q^{16} + 3 q^{17} - 18 q^{18} + 3 q^{20} - 33 q^{21} + 3 q^{22} + 9 q^{23}+ \cdots + 3 q^{98}+O(q^{100}) \) 15 * q - 15 * q^2 - 3 * q^3 + 15 * q^4 + 3 * q^5 + 3 * q^6 - 15 * q^8 + 18 * q^9 - 3 * q^10 - 3 * q^11 - 3 * q^12 + 15 * q^13 + 15 * q^16 + 3 * q^17 - 18 * q^18 + 3 * q^20 - 33 * q^21 + 3 * q^22 + 9 * q^23 + 3 * q^24 + 24 * q^25 - 15 * q^26 - 42 * q^27 - 12 * q^29 - 24 * q^31 - 15 * q^32 + 3 * q^33 - 3 * q^34 + 6 * q^35 + 18 * q^36 - 30 * q^37 - 3 * q^39 - 3 * q^40 + 24 * q^41 + 33 * q^42 - 12 * q^43 - 3 * q^44 + 21 * q^45 - 9 * q^46 - 6 * q^47 - 3 * q^48 - 3 * q^49 - 24 * q^50 - 48 * q^51 + 15 * q^52 - 9 * q^53 + 42 * q^54 - 60 * q^55 + 12 * q^58 - 12 * q^59 - 12 * q^61 + 24 * q^62 + 15 * q^63 + 15 * q^64 + 3 * q^65 - 3 * q^66 - 48 * q^67 + 3 * q^68 - 18 * q^69 - 6 * q^70 - 21 * q^71 - 18 * q^72 + 21 * q^73 + 30 * q^74 - 21 * q^75 - 9 * q^77 + 3 * q^78 - 45 * q^79 + 3 * q^80 + 15 * q^81 - 24 * q^82 - 33 * q^83 - 33 * q^84 - 6 * q^85 + 12 * q^86 + 9 * q^87 + 3 * q^88 + 12 * q^89 - 21 * q^90 + 9 * q^92 - 3 * q^93 + 6 * q^94 + 3 * q^96 + 24 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more