LMFDB - Embedded newform 787.2.a.b.1.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [787,2,Mod(1,787)] 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("787.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 787 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	787.a (trivial)

Newform invariants

comment:select newform

sage:traces = [37] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$6.28422663907$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.26
Character	$\chi$	$=$	787.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.66683 q^{2} -2.53460 q^{3} +0.778328 q^{4} +3.86054 q^{5} -4.22476 q^{6} -3.20455 q^{7} -2.03632 q^{8} +3.42421 q^{9} +6.43487 q^{10} +2.80701 q^{11} -1.97275 q^{12} +4.78811 q^{13} -5.34144 q^{14} -9.78494 q^{15} -4.95086 q^{16} +4.18912 q^{17} +5.70758 q^{18} +1.83524 q^{19} +3.00477 q^{20} +8.12225 q^{21} +4.67882 q^{22} +2.98310 q^{23} +5.16127 q^{24} +9.90378 q^{25} +7.98097 q^{26} -1.07521 q^{27} -2.49419 q^{28} +0.918075 q^{29} -16.3098 q^{30} -7.25642 q^{31} -4.17961 q^{32} -7.11466 q^{33} +6.98255 q^{34} -12.3713 q^{35} +2.66516 q^{36} -2.00595 q^{37} +3.05903 q^{38} -12.1360 q^{39} -7.86130 q^{40} +6.76387 q^{41} +13.5384 q^{42} +9.81590 q^{43} +2.18478 q^{44} +13.2193 q^{45} +4.97232 q^{46} +12.5729 q^{47} +12.5485 q^{48} +3.26912 q^{49} +16.5079 q^{50} -10.6177 q^{51} +3.72672 q^{52} -10.0300 q^{53} -1.79219 q^{54} +10.8366 q^{55} +6.52549 q^{56} -4.65160 q^{57} +1.53028 q^{58} -5.69185 q^{59} -7.61589 q^{60} +5.14392 q^{61} -12.0952 q^{62} -10.9730 q^{63} +2.93502 q^{64} +18.4847 q^{65} -11.8589 q^{66} -6.49481 q^{67} +3.26051 q^{68} -7.56097 q^{69} -20.6209 q^{70} -11.0974 q^{71} -6.97279 q^{72} +1.19824 q^{73} -3.34358 q^{74} -25.1022 q^{75} +1.42842 q^{76} -8.99521 q^{77} -20.2286 q^{78} +14.2295 q^{79} -19.1130 q^{80} -7.54741 q^{81} +11.2742 q^{82} -2.26531 q^{83} +6.32178 q^{84} +16.1723 q^{85} +16.3615 q^{86} -2.32696 q^{87} -5.71598 q^{88} -4.17045 q^{89} +22.0344 q^{90} -15.3437 q^{91} +2.32183 q^{92} +18.3921 q^{93} +20.9570 q^{94} +7.08501 q^{95} +10.5937 q^{96} -4.21813 q^{97} +5.44908 q^{98} +9.61180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) $ 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

Coefficient data

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

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

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

$2$	1.66683	1.17863	0.589314	−	0.807904i	$-0.299398\pi$
$2$	1.66683	1.17863	0.589314	+	0.807904i	$0.299398\pi$
$3$	−2.53460	−1.46335	−0.731677	−	0.681652i	$-0.761262\pi$
$3$	−2.53460	−1.46335	−0.731677	+	0.681652i	$0.761262\pi$
$4$	0.778328	0.389164
$5$	3.86054	1.72649	0.863243	−	0.504788i	$-0.168429\pi$
$5$	3.86054	1.72649	0.863243	+	0.504788i	$0.168429\pi$
$6$	−4.22476	−1.72475
$7$	−3.20455	−1.21121	−0.605603	−	0.795767i	$-0.707068\pi$
$7$	−3.20455	−1.21121	−0.605603	+	0.795767i	$0.707068\pi$
$8$	−2.03632	−0.719948
$9$	3.42421	1.14140
$10$	6.43487	2.03489
$11$	2.80701	0.846346	0.423173	−	0.906049i	$-0.360916\pi$
$11$	2.80701	0.846346	0.423173	+	0.906049i	$0.360916\pi$
$12$	−1.97275	−0.569485
$13$	4.78811	1.32798	0.663991	−	0.747740i	$-0.268861\pi$
$13$	4.78811	1.32798	0.663991	+	0.747740i	$0.268861\pi$
$14$	−5.34144	−1.42756
$15$	−9.78494	−2.52646
$16$	−4.95086	−1.23772
$17$	4.18912	1.01601	0.508005	−	0.861354i	$-0.330383\pi$
$17$	4.18912	1.01601	0.508005	+	0.861354i	$0.330383\pi$
$18$	5.70758	1.34529
$19$	1.83524	0.421032	0.210516	−	0.977590i	$-0.432486\pi$
$19$	1.83524	0.421032	0.210516	+	0.977590i	$0.432486\pi$
$20$	3.00477	0.671887
$21$	8.12225	1.77242
$22$	4.67882	0.997528
$23$	2.98310	0.622019	0.311009	−	0.950407i	$-0.399333\pi$
$23$	2.98310	0.622019	0.311009	+	0.950407i	$0.399333\pi$
$24$	5.16127	1.05354
$25$	9.90378	1.98076
$26$	7.98097	1.56520
$27$	−1.07521	−0.206923
$28$	−2.49419	−0.471357
$29$	0.918075	0.170482	0.0852411	−	0.996360i	$-0.472834\pi$
$29$	0.918075	0.170482	0.0852411	+	0.996360i	$0.472834\pi$
$30$	−16.3098	−2.97776
$31$	−7.25642	−1.30329	−0.651646	−	0.758524i	$-0.725921\pi$
$31$	−7.25642	−1.30329	−0.651646	+	0.758524i	$0.725921\pi$
$32$	−4.17961	−0.738858
$33$	−7.11466	−1.23850
$34$	6.98255	1.19750
$35$	−12.3713	−2.09113
$36$	2.66516	0.444193
$37$	−2.00595	−0.329776	−0.164888	−	0.986312i	$-0.552726\pi$
$37$	−2.00595	−0.329776	−0.164888	+	0.986312i	$0.552726\pi$
$38$	3.05903	0.496240
$39$	−12.1360	−1.94331
$40$	−7.86130	−1.24298
$41$	6.76387	1.05634	0.528169	−	0.849139i	$-0.322879\pi$
$41$	6.76387	1.05634	0.528169	+	0.849139i	$0.322879\pi$
$42$	13.5384	2.08903
$43$	9.81590	1.49691	0.748455	−	0.663185i	$-0.230796\pi$
$43$	9.81590	1.49691	0.748455	+	0.663185i	$0.230796\pi$
$44$	2.18478	0.329368
$45$	13.2193	1.97062
$46$	4.97232	0.733129
$47$	12.5729	1.83395	0.916975	−	0.398944i	$-0.130623\pi$
$47$	12.5729	1.83395	0.916975	+	0.398944i	$0.130623\pi$
$48$	12.5485	1.81122
$49$	3.26912	0.467018
$50$	16.5079	2.33458
$51$	−10.6177	−1.48678
$52$	3.72672	0.516803
$53$	−10.0300	−1.37773	−0.688863	−	0.724892i	$-0.741890\pi$
$53$	−10.0300	−1.37773	−0.688863	+	0.724892i	$0.741890\pi$
$54$	−1.79219	−0.243886
$55$	10.8366	1.46121
$56$	6.52549	0.872005
$57$	−4.65160	−0.616119
$58$	1.53028	0.200935
$59$	−5.69185	−0.741016	−0.370508	−	0.928829i	$-0.620816\pi$
$59$	−5.69185	−0.741016	−0.370508	+	0.928829i	$0.620816\pi$
$60$	−7.61589	−0.983208
$61$	5.14392	0.658611	0.329306	−	0.944223i	$-0.393185\pi$
$61$	5.14392	0.658611	0.329306	+	0.944223i	$0.393185\pi$
$62$	−12.0952	−1.53610
$63$	−10.9730	−1.38247
$64$	2.93502	0.366877
$65$	18.4847	2.29274
$66$	−11.8589	−1.45974
$67$	−6.49481	−0.793467	−0.396734	−	0.917934i	$-0.629856\pi$
$67$	−6.49481	−0.793467	−0.396734	+	0.917934i	$0.629856\pi$
$68$	3.26051	0.395395
$69$	−7.56097	−0.910233
$70$	−20.6209	−2.46466
$71$	−11.0974	−1.31702	−0.658511	−	0.752571i	$-0.728814\pi$
$71$	−11.0974	−1.31702	−0.658511	+	0.752571i	$0.728814\pi$
$72$	−6.97279	−0.821752
$73$	1.19824	0.140243	0.0701217	−	0.997538i	$-0.477661\pi$
$73$	1.19824	0.140243	0.0701217	+	0.997538i	$0.477661\pi$
$74$	−3.34358	−0.388683
$75$	−25.1022	−2.89855
$76$	1.42842	0.163851
$77$	−8.99521	−1.02510
$78$	−20.2286	−2.29044
$79$	14.2295	1.60094	0.800470	−	0.599373i	$-0.204583\pi$
$79$	14.2295	1.60094	0.800470	+	0.599373i	$0.204583\pi$
$80$	−19.1130	−2.13690
$81$	−7.54741	−0.838602
$82$	11.2742	1.24503
$83$	−2.26531	−0.248650	−0.124325	−	0.992242i	$-0.539677\pi$
$83$	−2.26531	−0.248650	−0.124325	+	0.992242i	$0.539677\pi$
$84$	6.32178	0.689763
$85$	16.1723	1.75413
$86$	16.3615	1.76430
$87$	−2.32696	−0.249476
$88$	−5.71598	−0.609326
$89$	−4.17045	−0.442067	−0.221033	−	0.975266i	$-0.570943\pi$
$89$	−4.17045	−0.442067	−0.221033	+	0.975266i	$0.570943\pi$
$90$	22.0344	2.32263
$91$	−15.3437	−1.60846
$92$	2.32183	0.242067
$93$	18.3921	1.90718
$94$	20.9570	2.16155
$95$	7.08501	0.726907
$96$	10.5937	1.08121
$97$	−4.21813	−0.428286	−0.214143	−	0.976802i	$-0.568696\pi$
$97$	−4.21813	−0.428286	−0.214143	+	0.976802i	$0.568696\pi$
$98$	5.44908	0.550440
$99$	9.61180	0.966023
$100$	7.70839	0.770839
$101$	−16.7717	−1.66885	−0.834424	−	0.551123i	$-0.814200\pi$
$101$	−16.7717	−1.66885	−0.834424	+	0.551123i	$0.814200\pi$
$102$	−17.6980	−1.75236
$103$	−8.79062	−0.866165	−0.433083	−	0.901354i	$-0.642574\pi$
$103$	−8.79062	−0.866165	−0.433083	+	0.901354i	$0.642574\pi$
$104$	−9.75013	−0.956079
$105$	31.3563	3.06006
$106$	−16.7183	−1.62383
$107$	−4.11782	−0.398085	−0.199043	−	0.979991i	$-0.563783\pi$
$107$	−4.11782	−0.398085	−0.199043	+	0.979991i	$0.563783\pi$
$108$	−0.836862	−0.0805271
$109$	−7.85948	−0.752802	−0.376401	−	0.926457i	$-0.622839\pi$
$109$	−7.85948	−0.752802	−0.376401	+	0.926457i	$0.622839\pi$
$110$	18.0628	1.72222
$111$	5.08429	0.482579
$112$	15.8653	1.49913
$113$	−2.37517	−0.223437	−0.111719	−	0.993740i	$-0.535636\pi$
$113$	−2.37517	−0.223437	−0.111719	+	0.993740i	$0.535636\pi$
$114$	−7.75343	−0.726175
$115$	11.5164	1.07391
$116$	0.714564	0.0663456
$117$	16.3955	1.51576
$118$	−9.48736	−0.873382
$119$	−13.4242	−1.23060
$120$	19.9253	1.81892
$121$	−3.12068	−0.283698
$122$	8.57404	0.776258
$123$	−17.1437	−1.54580
$124$	−5.64787	−0.507194
$125$	18.9313	1.69326
$126$	−18.2902	−1.62942
$127$	16.0237	1.42187	0.710935	−	0.703257i	$-0.248272\pi$
$127$	16.0237	1.42187	0.710935	+	0.703257i	$0.248272\pi$
$128$	13.2514	1.17127
$129$	−24.8794	−2.19051
$130$	30.8109	2.70229
$131$	−7.85278	−0.686101	−0.343050	−	0.939317i	$-0.611460\pi$
$131$	−7.85278	−0.686101	−0.343050	+	0.939317i	$0.611460\pi$
$132$	−5.53754	−0.481981
$133$	−5.88110	−0.509956
$134$	−10.8258	−0.935203
$135$	−4.15088	−0.357250
$136$	−8.53039	−0.731475
$137$	−13.6770	−1.16850	−0.584252	−	0.811573i	$-0.698612\pi$
$137$	−13.6770	−1.16850	−0.584252	+	0.811573i	$0.698612\pi$
$138$	−12.6029	−1.07283
$139$	19.8519	1.68382	0.841908	−	0.539621i	$-0.181432\pi$
$139$	19.8519	1.68382	0.841908	+	0.539621i	$0.181432\pi$
$140$	−9.62892	−0.813792
$141$	−31.8674	−2.68372
$142$	−18.4975	−1.55228
$143$	13.4403	1.12393
$144$	−16.9528	−1.41273
$145$	3.54427	0.294335
$146$	1.99726	0.165295
$147$	−8.28593	−0.683412
$148$	−1.56129	−0.128337
$149$	5.27076	0.431798	0.215899	−	0.976416i	$-0.430732\pi$
$149$	5.27076	0.431798	0.215899	+	0.976416i	$0.430732\pi$
$150$	−41.8411	−3.41631
$151$	−13.2677	−1.07971	−0.539854	−	0.841759i	$-0.681521\pi$
$151$	−13.2677	−1.07971	−0.539854	+	0.841759i	$0.681521\pi$
$152$	−3.73713	−0.303122
$153$	14.3444	1.15968
$154$	−14.9935	−1.20821
$155$	−28.0137	−2.25012
$156$	−9.44575	−0.756265
$157$	2.63140	0.210009	0.105004	−	0.994472i	$-0.466514\pi$
$157$	2.63140	0.210009	0.105004	+	0.994472i	$0.466514\pi$
$158$	23.7181	1.88691
$159$	25.4220	2.01610
$160$	−16.1356	−1.27563
$161$	−9.55948	−0.753392
$162$	−12.5803	−0.988399
$163$	8.51020	0.666570	0.333285	−	0.942826i	$-0.391843\pi$
$163$	8.51020	0.666570	0.333285	+	0.942826i	$0.391843\pi$
$164$	5.26451	0.411089
$165$	−27.4665	−2.13826
$166$	−3.77589	−0.293066
$167$	−10.6704	−0.825699	−0.412850	−	0.910799i	$-0.635466\pi$
$167$	−10.6704	−0.825699	−0.412850	+	0.910799i	$0.635466\pi$
$168$	−16.5395	−1.27605
$169$	9.92598	0.763537
$170$	26.9564	2.06746
$171$	6.28424	0.480568
$172$	7.63999	0.582544
$173$	−15.3852	−1.16972	−0.584858	−	0.811136i	$-0.698850\pi$
$173$	−15.3852	−1.16972	−0.584858	+	0.811136i	$0.698850\pi$
$174$	−3.87864	−0.294039
$175$	−31.7371	−2.39910
$176$	−13.8971	−1.04754
$177$	14.4266	1.08437
$178$	−6.95144	−0.521033
$179$	−9.50701	−0.710587	−0.355293	−	0.934755i	$-0.615619\pi$
$179$	−9.50701	−0.710587	−0.355293	+	0.934755i	$0.615619\pi$
$180$	10.2890	0.766894
$181$	8.94492	0.664871	0.332435	−	0.943126i	$-0.392130\pi$
$181$	8.94492	0.664871	0.332435	+	0.943126i	$0.392130\pi$
$182$	−25.5754	−1.89577
$183$	−13.0378	−0.963781
$184$	−6.07454	−0.447821
$185$	−7.74405	−0.569354
$186$	30.6566	2.24785
$187$	11.7589	0.859896
$188$	9.78587	0.713708
$189$	3.44555	0.250627
$190$	11.8095	0.856753
$191$	17.2424	1.24761	0.623806	−	0.781579i	$-0.285585\pi$
$191$	17.2424	1.24761	0.623806	+	0.781579i	$0.285585\pi$
$192$	−7.43910	−0.536871
$193$	2.55620	0.183999	0.0919996	−	0.995759i	$-0.470674\pi$
$193$	2.55620	0.183999	0.0919996	+	0.995759i	$0.470674\pi$
$194$	−7.03092	−0.504790
$195$	−46.8514	−3.35510
$196$	2.54445	0.181747
$197$	18.7963	1.33918	0.669590	−	0.742731i	$-0.266470\pi$
$197$	18.7963	1.33918	0.669590	+	0.742731i	$0.266470\pi$
$198$	16.0213	1.13858
$199$	15.1475	1.07377	0.536887	−	0.843654i	$-0.319600\pi$
$199$	15.1475	1.07377	0.536887	+	0.843654i	$0.319600\pi$
$200$	−20.1673	−1.42604
$201$	16.4618	1.16112
$202$	−27.9556	−1.96695
$203$	−2.94202	−0.206489
$204$	−8.26409	−0.578602
$205$	26.1122	1.82375
$206$	−14.6525	−1.02089
$207$	10.2148	0.709974
$208$	−23.7053	−1.64366
$209$	5.15154	0.356339
$210$	52.2657	3.60667
$211$	−22.5349	−1.55136	−0.775682	−	0.631124i	$-0.782594\pi$
$211$	−22.5349	−1.55136	−0.775682	+	0.631124i	$0.782594\pi$
$212$	−7.80662	−0.536161
$213$	28.1276	1.92727
$214$	−6.86372	−0.469194
$215$	37.8947	2.58440
$216$	2.18946	0.148974
$217$	23.2535	1.57855
$218$	−13.1004	−0.887274
$219$	−3.03706	−0.205226
$220$	8.43442	0.568649
$221$	20.0579	1.34924
$222$	8.47465	0.568781
$223$	19.6240	1.31412	0.657060	−	0.753839i	$-0.271800\pi$
$223$	19.6240	1.31412	0.657060	+	0.753839i	$0.271800\pi$
$224$	13.3938	0.894908
$225$	33.9126	2.26084
$226$	−3.95901	−0.263349
$227$	−21.1158	−1.40151	−0.700753	−	0.713404i	$-0.747153\pi$
$227$	−21.1158	−1.40151	−0.700753	+	0.713404i	$0.747153\pi$
$228$	−3.62047	−0.239771
$229$	−22.4595	−1.48417	−0.742083	−	0.670308i	$-0.766162\pi$
$229$	−22.4595	−1.48417	−0.742083	+	0.670308i	$0.766162\pi$
$230$	19.1959	1.26574
$231$	22.7993	1.50008
$232$	−1.86950	−0.122738
$233$	14.1100	0.924380	0.462190	−	0.886781i	$-0.347064\pi$
$233$	14.1100	0.924380	0.462190	+	0.886781i	$0.347064\pi$
$234$	27.3285	1.78652
$235$	48.5383	3.16629
$236$	−4.43013	−0.288377
$237$	−36.0660	−2.34274
$238$	−22.3759	−1.45042
$239$	20.2618	1.31063	0.655313	−	0.755357i	$-0.272537\pi$
$239$	20.2618	1.31063	0.655313	+	0.755357i	$0.272537\pi$
$240$	48.4439	3.12704
$241$	−22.5673	−1.45369	−0.726844	−	0.686802i	$-0.759014\pi$
$241$	−22.5673	−1.45369	−0.726844	+	0.686802i	$0.759014\pi$
$242$	−5.20164	−0.334374
$243$	22.3553	1.43409
$244$	4.00366	0.256308
$245$	12.6206	0.806300
$246$	−28.5757	−1.82192
$247$	8.78731	0.559123
$248$	14.7764	0.938302
$249$	5.74166	0.363863
$250$	31.5552	1.99573
$251$	−30.7968	−1.94388	−0.971940	−	0.235229i	$-0.924416\pi$
$251$	−30.7968	−1.94388	−0.971940	+	0.235229i	$0.924416\pi$
$252$	−8.54063	−0.538009
$253$	8.37359	0.526443
$254$	26.7088	1.67586
$255$	−40.9902	−2.56691
$256$	16.2178	1.01361
$257$	4.66616	0.291067	0.145533	−	0.989353i	$-0.453510\pi$
$257$	4.66616	0.291067	0.145533	+	0.989353i	$0.453510\pi$
$258$	−41.4698	−2.58180
$259$	6.42816	0.399427
$260$	14.3872	0.892254
$261$	3.14368	0.194589
$262$	−13.0893	−0.808658
$263$	19.7919	1.22042	0.610210	−	0.792239i	$-0.291085\pi$
$263$	19.7919	1.22042	0.610210	+	0.792239i	$0.291085\pi$
$264$	14.4877	0.891659
$265$	−38.7212	−2.37862
$266$	−9.80281	−0.601049
$267$	10.5704	0.646900
$268$	−5.05509	−0.308789
$269$	1.46870	0.0895483	0.0447741	−	0.998997i	$-0.485743\pi$
$269$	1.46870	0.0895483	0.0447741	+	0.998997i	$0.485743\pi$
$270$	−6.91881	−0.421065
$271$	−28.6120	−1.73806	−0.869028	−	0.494763i	$-0.835255\pi$
$271$	−28.6120	−1.73806	−0.869028	+	0.494763i	$0.835255\pi$
$272$	−20.7397	−1.25753
$273$	38.8902	2.35374
$274$	−22.7972	−1.37723
$275$	27.8001	1.67641
$276$	−5.88491	−0.354230
$277$	3.22181	0.193580	0.0967900	−	0.995305i	$-0.469142\pi$
$277$	3.22181	0.193580	0.0967900	+	0.995305i	$0.469142\pi$
$278$	33.0898	1.98459
$279$	−24.8475	−1.48758
$280$	25.1919	1.50551
$281$	18.4370	1.09986	0.549931	−	0.835210i	$-0.314654\pi$
$281$	18.4370	1.09986	0.549931	+	0.835210i	$0.314654\pi$
$282$	−53.1176	−3.16311
$283$	−18.0818	−1.07485	−0.537425	−	0.843312i	$-0.680603\pi$
$283$	−18.0818	−1.07485	−0.537425	+	0.843312i	$0.680603\pi$
$284$	−8.63744	−0.512538
$285$	−17.9577	−1.06372
$286$	22.4027	1.32470
$287$	−21.6751	−1.27944
$288$	−14.3119	−0.843335
$289$	0.548693	0.0322761
$290$	5.90770	0.346912
$291$	10.6913	0.626734
$292$	0.932624	0.0545777
$293$	14.5657	0.850937	0.425468	−	0.904973i	$-0.360109\pi$
$293$	14.5657	0.850937	0.425468	+	0.904973i	$0.360109\pi$
$294$	−13.8113	−0.805489
$295$	−21.9736	−1.27935
$296$	4.08476	0.237422
$297$	−3.01812	−0.175129
$298$	8.78548	0.508929
$299$	14.2834	0.826030
$300$	−19.5377	−1.12801
$301$	−31.4555	−1.81307
$302$	−22.1150	−1.27257
$303$	42.5096	2.44211
$304$	−9.08601	−0.521118
$305$	19.8583	1.13708
$306$	23.9097	1.36683
$307$	30.9927	1.76885	0.884423	−	0.466687i	$-0.154552\pi$
$307$	30.9927	1.76885	0.884423	+	0.466687i	$0.154552\pi$
$308$	−7.00122	−0.398932
$309$	22.2807	1.26751
$310$	−46.6941	−2.65205
$311$	8.88597	0.503877	0.251938	−	0.967743i	$-0.418932\pi$
$311$	8.88597	0.503877	0.251938	+	0.967743i	$0.418932\pi$
$312$	24.7127	1.39908
$313$	19.5433	1.10465	0.552326	−	0.833628i	$-0.313741\pi$
$313$	19.5433	1.10465	0.552326	+	0.833628i	$0.313741\pi$
$314$	4.38611	0.247522
$315$	−42.3619	−2.38682
$316$	11.0752	0.623028
$317$	26.3640	1.48075	0.740376	−	0.672193i	$-0.234647\pi$
$317$	26.3640	1.48075	0.740376	+	0.672193i	$0.234647\pi$
$318$	42.3743	2.37623
$319$	2.57705	0.144287
$320$	11.3308	0.633408
$321$	10.4370	0.582539
$322$	−15.9340	−0.887969
$323$	7.68802	0.427773
$324$	−5.87436	−0.326354
$325$	47.4204	2.63041
$326$	14.1851	0.785638
$327$	19.9207	1.10162
$328$	−13.7734	−0.760509
$329$	−40.2906	−2.22129
$330$	−45.7820	−2.52021
$331$	−10.4756	−0.575791	−0.287895	−	0.957662i	$-0.592956\pi$
$331$	−10.4756	−0.575791	−0.287895	+	0.957662i	$0.592956\pi$
$332$	−1.76316	−0.0967657
$333$	−6.86880	−0.376408
$334$	−17.7857	−0.973192
$335$	−25.0735	−1.36991
$336$	−40.2122	−2.19375
$337$	10.6302	0.579062	0.289531	−	0.957169i	$-0.406501\pi$
$337$	10.6302	0.579062	0.289531	+	0.957169i	$0.406501\pi$
$338$	16.5449	0.899926
$339$	6.02011	0.326968
$340$	12.5873	0.682643
$341$	−20.3689	−1.10304
$342$	10.4748	0.566411
$343$	11.9558	0.645551
$344$	−19.9883	−1.07770
$345$	−29.1894	−1.57151
$346$	−25.6446	−1.37866
$347$	10.3770	0.557069	0.278535	−	0.960426i	$-0.410151\pi$
$347$	10.3770	0.557069	0.278535	+	0.960426i	$0.410151\pi$
$348$	−1.81114	−0.0970870
$349$	−20.3187	−1.08763	−0.543817	−	0.839204i	$-0.683021\pi$
$349$	−20.3187	−1.08763	−0.543817	+	0.839204i	$0.683021\pi$
$350$	−52.9005	−2.82765
$351$	−5.14820	−0.274791
$352$	−11.7322	−0.625330
$353$	3.29442	0.175344	0.0876721	−	0.996149i	$-0.472057\pi$
$353$	3.29442	0.175344	0.0876721	+	0.996149i	$0.472057\pi$
$354$	24.0467	1.27807
$355$	−42.8421	−2.27382
$356$	−3.24598	−0.172037
$357$	34.0251	1.80080
$358$	−15.8466	−0.837518
$359$	−0.297088	−0.0156797	−0.00783985	−	0.999969i	$-0.502496\pi$
$359$	−0.297088	−0.0156797	−0.00783985	+	0.999969i	$0.502496\pi$
$360$	−26.9188	−1.41874
$361$	−15.6319	−0.822732
$362$	14.9097	0.783635
$363$	7.90967	0.415150
$364$	−11.9424	−0.625954
$365$	4.62586	0.242128
$366$	−21.7318	−1.13594
$367$	−24.3748	−1.27236	−0.636178	−	0.771542i	$-0.719486\pi$
$367$	−24.3748	−1.27236	−0.636178	+	0.771542i	$0.719486\pi$
$368$	−14.7689	−0.769882
$369$	23.1609	1.20571
$370$	−12.9080	−0.671057
$371$	32.1416	1.66871
$372$	14.3151	0.742204
$373$	27.1931	1.40801	0.704003	−	0.710197i	$-0.251394\pi$
$373$	27.1931	1.40801	0.704003	+	0.710197i	$0.251394\pi$
$374$	19.6001	1.01350
$375$	−47.9832	−2.47784
$376$	−25.6025	−1.32035
$377$	4.39584	0.226397
$378$	5.74315	0.295396
$379$	15.4141	0.791772	0.395886	−	0.918300i	$-0.370438\pi$
$379$	15.4141	0.791772	0.395886	+	0.918300i	$0.370438\pi$
$380$	5.51446	0.282886
$381$	−40.6136	−2.08070
$382$	28.7401	1.47047
$383$	−23.1298	−1.18188	−0.590938	−	0.806717i	$-0.701242\pi$
$383$	−23.1298	−1.18188	−0.590938	+	0.806717i	$0.701242\pi$
$384$	−33.5870	−1.71398
$385$	−34.7264	−1.76982
$386$	4.26075	0.216867
$387$	33.6117	1.70858
$388$	−3.28309	−0.166674
$389$	10.1990	0.517107	0.258554	−	0.965997i	$-0.416754\pi$
$389$	10.1990	0.517107	0.258554	+	0.965997i	$0.416754\pi$
$390$	−78.0933	−3.95441
$391$	12.4965	0.631977
$392$	−6.65699	−0.336229
$393$	19.9037	1.00401
$394$	31.3302	1.57839
$395$	54.9334	2.76400
$396$	7.48114	0.375941
$397$	−14.2227	−0.713818	−0.356909	−	0.934139i	$-0.616169\pi$
$397$	−14.2227	−0.713818	−0.356909	+	0.934139i	$0.616169\pi$
$398$	25.2483	1.26558
$399$	14.9063	0.746247
$400$	−49.0323	−2.45161
$401$	−36.7125	−1.83333	−0.916667	−	0.399652i	$-0.869131\pi$
$401$	−36.7125	−1.83333	−0.916667	+	0.399652i	$0.869131\pi$
$402$	27.4390	1.36853
$403$	−34.7445	−1.73075
$404$	−13.0539	−0.649456
$405$	−29.1371	−1.44783
$406$	−4.90385	−0.243374
$407$	−5.63073	−0.279105
$408$	21.6211	1.07041
$409$	12.1724	0.601885	0.300943	−	0.953642i	$-0.402699\pi$
$409$	12.1724	0.601885	0.300943	+	0.953642i	$0.402699\pi$
$410$	43.5246	2.14953
$411$	34.6657	1.70993
$412$	−6.84198	−0.337080
$413$	18.2398	0.897522
$414$	17.0263	0.836796
$415$	−8.74533	−0.429291
$416$	−20.0124	−0.981190
$417$	−50.3167	−2.46402
$418$	8.58674	0.419991
$419$	5.36250	0.261975	0.130988	−	0.991384i	$-0.458185\pi$
$419$	5.36250	0.261975	0.130988	+	0.991384i	$0.458185\pi$
$420$	24.4055	1.19087
$421$	4.97168	0.242305	0.121152	−	0.992634i	$-0.461341\pi$
$421$	4.97168	0.242305	0.121152	+	0.992634i	$0.461341\pi$
$422$	−37.5618	−1.82848
$423$	43.0524	2.09328
$424$	20.4243	0.991891
$425$	41.4881	2.01247
$426$	46.8839	2.27153
$427$	−16.4839	−0.797713
$428$	−3.20502	−0.154920
$429$	−34.0658	−1.64471
$430$	63.1641	3.04604
$431$	−0.904823	−0.0435838	−0.0217919	−	0.999763i	$-0.506937\pi$
$431$	−0.904823	−0.0435838	−0.0217919	+	0.999763i	$0.506937\pi$
$432$	5.32319	0.256112
$433$	−28.3440	−1.36213	−0.681063	−	0.732224i	$-0.738482\pi$
$433$	−28.3440	−1.36213	−0.681063	+	0.732224i	$0.738482\pi$
$434$	38.7597	1.86053
$435$	−8.98331	−0.430717
$436$	−6.11726	−0.292964
$437$	5.47469	0.261890
$438$	−5.06227	−0.241885
$439$	−29.4511	−1.40562	−0.702812	−	0.711375i	$-0.748073\pi$
$439$	−29.4511	−1.40562	−0.702812	+	0.711375i	$0.748073\pi$
$440$	−22.0668	−1.05199
$441$	11.1942	0.533056
$442$	33.4332	1.59026
$443$	−27.0607	−1.28569	−0.642847	−	0.765994i	$-0.722247\pi$
$443$	−27.0607	−1.28569	−0.642847	+	0.765994i	$0.722247\pi$
$444$	3.95724	0.187802
$445$	−16.1002	−0.763223
$446$	32.7099	1.54886
$447$	−13.3593	−0.631873
$448$	−9.40540	−0.444363
$449$	14.4606	0.682439	0.341219	−	0.939984i	$-0.389160\pi$
$449$	14.4606	0.682439	0.341219	+	0.939984i	$0.389160\pi$
$450$	56.5267	2.66469
$451$	18.9863	0.894028
$452$	−1.84866	−0.0869537
$453$	33.6283	1.57999
$454$	−35.1965	−1.65185
$455$	−59.2351	−2.77698
$456$	9.47215	0.443574
$457$	−35.5623	−1.66353	−0.831767	−	0.555125i	$-0.812670\pi$
$457$	−35.5623	−1.66353	−0.831767	+	0.555125i	$0.812670\pi$
$458$	−37.4362	−1.74928
$459$	−4.50416	−0.210236
$460$	8.96351	0.417926
$461$	−26.4731	−1.23297	−0.616487	−	0.787365i	$-0.711445\pi$
$461$	−26.4731	−1.23297	−0.616487	+	0.787365i	$0.711445\pi$
$462$	38.0026	1.76804
$463$	31.8071	1.47820	0.739101	−	0.673595i	$-0.235251\pi$
$463$	31.8071	1.47820	0.739101	+	0.673595i	$0.235251\pi$
$464$	−4.54526	−0.211009
$465$	71.0036	3.29271
$466$	23.5191	1.08950
$467$	−31.4629	−1.45593	−0.727964	−	0.685616i	$-0.759533\pi$
$467$	−31.4629	−1.45593	−0.727964	+	0.685616i	$0.759533\pi$
$468$	12.7611	0.589881
$469$	20.8129	0.961052
$470$	80.9052	3.73188
$471$	−6.66956	−0.307317
$472$	11.5904	0.533493
$473$	27.5534	1.26691
$474$	−60.1160	−2.76122
$475$	18.1758	0.833963
$476$	−10.4484	−0.478904
$477$	−34.3448	−1.57254
$478$	33.7730	1.54474
$479$	−31.4633	−1.43760	−0.718798	−	0.695219i	$-0.755307\pi$
$479$	−31.4633	−1.43760	−0.718798	+	0.695219i	$0.755307\pi$
$480$	40.8972	1.86669
$481$	−9.60471	−0.437937
$482$	−37.6159	−1.71336
$483$	24.2295	1.10248
$484$	−2.42891	−0.110405
$485$	−16.2843	−0.739431
$486$	37.2625	1.69026
$487$	−22.1074	−1.00178	−0.500892	−	0.865510i	$-0.666995\pi$
$487$	−22.1074	−1.00178	−0.500892	+	0.865510i	$0.666995\pi$
$488$	−10.4747	−0.474166
$489$	−21.5700	−0.975427
$490$	21.0364	0.950328
$491$	−5.73930	−0.259011	−0.129506	−	0.991579i	$-0.541339\pi$
$491$	−5.73930	−0.259011	−0.129506	+	0.991579i	$0.541339\pi$
$492$	−13.3434	−0.601569
$493$	3.84592	0.173212
$494$	14.6470	0.658999
$495$	37.1068	1.66783
$496$	35.9255	1.61310
$497$	35.5622	1.59518
$498$	9.57039	0.428859
$499$	3.50798	0.157039	0.0785193	−	0.996913i	$-0.474981\pi$
$499$	3.50798	0.157039	0.0785193	+	0.996913i	$0.474981\pi$
$500$	14.7347	0.658957
$501$	27.0452	1.20829
$502$	−51.3332	−2.29111
$503$	11.3637	0.506683	0.253342	−	0.967377i	$-0.418470\pi$
$503$	11.3637	0.506683	0.253342	+	0.967377i	$0.418470\pi$
$504$	22.3446	0.995310
$505$	−64.7479	−2.88124
$506$	13.9574	0.620481
$507$	−25.1584	−1.11732
$508$	12.4717	0.553341
$509$	−33.4533	−1.48279	−0.741397	−	0.671067i	$-0.765836\pi$
$509$	−33.4533	−1.48279	−0.741397	+	0.671067i	$0.765836\pi$
$510$	−68.3238	−3.02543
$511$	−3.83982	−0.169864
$512$	0.529579	0.0234043
$513$	−1.97326	−0.0871214
$514$	7.77770	0.343060
$515$	−33.9365	−1.49542
$516$	−19.3643	−0.852468
$517$	35.2924	1.55216
$518$	10.7147	0.470775
$519$	38.9954	1.71171
$520$	−37.6408	−1.65066
$521$	20.0560	0.878670	0.439335	−	0.898323i	$-0.355214\pi$
$521$	20.0560	0.878670	0.439335	+	0.898323i	$0.355214\pi$
$522$	5.23999	0.229348
$523$	29.8001	1.30307	0.651534	−	0.758620i	$-0.274126\pi$
$523$	29.8001	1.30307	0.651534	+	0.758620i	$0.274126\pi$
$524$	−6.11204	−0.267006
$525$	80.4411	3.51074
$526$	32.9898	1.43842
$527$	−30.3980	−1.32416
$528$	35.2237	1.53292
$529$	−14.1011	−0.613093
$530$	−64.5417	−2.80351
$531$	−19.4901	−0.845798
$532$	−4.57743	−0.198457
$533$	32.3861	1.40280
$534$	17.6191	0.762455
$535$	−15.8970	−0.687289
$536$	13.2255	0.571256
$537$	24.0965	1.03984
$538$	2.44808	0.105544
$539$	9.17648	0.395259
$540$	−3.23074	−0.139029
$541$	−1.04233	−0.0448134	−0.0224067	−	0.999749i	$-0.507133\pi$
$541$	−1.04233	−0.0448134	−0.0224067	+	0.999749i	$0.507133\pi$
$542$	−47.6914	−2.04852
$543$	−22.6718	−0.972941
$544$	−17.5089	−0.750687
$545$	−30.3419	−1.29970
$546$	64.8235	2.77419
$547$	−15.2991	−0.654142	−0.327071	−	0.945000i	$-0.606062\pi$
$547$	−15.2991	−0.654142	−0.327071	+	0.945000i	$0.606062\pi$
$548$	−10.6452	−0.454739
$549$	17.6139	0.751741
$550$	46.3380	1.97586
$551$	1.68489	0.0717785
$552$	15.3966	0.655321
$553$	−45.5990	−1.93907
$554$	5.37022	0.228159
$555$	19.6281	0.833166
$556$	15.4513	0.655281
$557$	−23.9575	−1.01511	−0.507556	−	0.861619i	$-0.669451\pi$
$557$	−23.9575	−1.01511	−0.507556	+	0.861619i	$0.669451\pi$
$558$	−41.4166	−1.75330
$559$	46.9996	1.98787
$560$	61.2485	2.58822
$561$	−29.8042	−1.25833
$562$	30.7314	1.29633
$563$	7.28767	0.307139	0.153569	−	0.988138i	$-0.450923\pi$
$563$	7.28767	0.307139	0.153569	+	0.988138i	$0.450923\pi$
$564$	−24.8033	−1.04441
$565$	−9.16944	−0.385761
$566$	−30.1393	−1.26685
$567$	24.1860	1.01572
$568$	22.5979	0.948188
$569$	14.7716	0.619258	0.309629	−	0.950857i	$-0.399795\pi$
$569$	14.7716	0.619258	0.309629	+	0.950857i	$0.399795\pi$
$570$	−29.9324	−1.25373
$571$	−10.6241	−0.444603	−0.222301	−	0.974978i	$-0.571357\pi$
$571$	−10.6241	−0.444603	−0.222301	+	0.974978i	$0.571357\pi$
$572$	10.4610	0.437394
$573$	−43.7025	−1.82570
$574$	−36.1288	−1.50799
$575$	29.5439	1.23207
$576$	10.0501	0.418755
$577$	−12.9800	−0.540363	−0.270182	−	0.962809i	$-0.587084\pi$
$577$	−12.9800	−0.540363	−0.270182	+	0.962809i	$0.587084\pi$
$578$	0.914579	0.0380415
$579$	−6.47895	−0.269256
$580$	2.75860	0.114545
$581$	7.25930	0.301166
$582$	17.8206	0.738687
$583$	−28.1543	−1.16603
$584$	−2.44000	−0.100968
$585$	63.2955	2.61695
$586$	24.2786	1.00294
$587$	19.6060	0.809228	0.404614	−	0.914488i	$-0.367406\pi$
$587$	19.6060	0.809228	0.404614	+	0.914488i	$0.367406\pi$
$588$	−6.44917	−0.265959
$589$	−13.3172	−0.548728
$590$	−36.6263	−1.50788
$591$	−47.6411	−1.95969
$592$	9.93118	0.408169
$593$	−11.2121	−0.460425	−0.230213	−	0.973140i	$-0.573942\pi$
$593$	−11.2121	−0.460425	−0.230213	+	0.973140i	$0.573942\pi$
$594$	−5.03069	−0.206412
$595$	−51.8248	−2.12461
$596$	4.10238	0.168040
$597$	−38.3928	−1.57131
$598$	23.8080	0.973582
$599$	−5.75836	−0.235280	−0.117640	−	0.993056i	$-0.537533\pi$
$599$	−5.75836	−0.235280	−0.117640	+	0.993056i	$0.537533\pi$
$600$	51.1161	2.08680
$601$	−32.1574	−1.31173	−0.655864	−	0.754879i	$-0.727696\pi$
$601$	−32.1574	−1.31173	−0.655864	+	0.754879i	$0.727696\pi$
$602$	−52.4311	−2.13693
$603$	−22.2396	−0.905666
$604$	−10.3266	−0.420184
$605$	−12.0475	−0.489801
$606$	70.8564	2.87835
$607$	−33.1331	−1.34483	−0.672415	−	0.740174i	$-0.734743\pi$
$607$	−33.1331	−1.34483	−0.672415	+	0.740174i	$0.734743\pi$
$608$	−7.67058	−0.311083
$609$	7.45684	0.302166
$610$	33.1005	1.34020
$611$	60.2006	2.43545
$612$	11.1647	0.451305
$613$	15.2948	0.617749	0.308875	−	0.951103i	$-0.400048\pi$
$613$	15.2948	0.617749	0.308875	+	0.951103i	$0.400048\pi$
$614$	51.6596	2.08481
$615$	−66.1840	−2.66880
$616$	18.3171	0.738018
$617$	7.08811	0.285357	0.142678	−	0.989769i	$-0.454429\pi$
$617$	7.08811	0.285357	0.142678	+	0.989769i	$0.454429\pi$
$618$	37.1382	1.49392
$619$	32.7113	1.31478	0.657388	−	0.753552i	$-0.271661\pi$
$619$	32.7113	1.31478	0.657388	+	0.753552i	$0.271661\pi$
$620$	−21.8039	−0.875664
$621$	−3.20744	−0.128710
$622$	14.8114	0.593884
$623$	13.3644	0.535434
$624$	60.0834	2.40526
$625$	23.5660	0.942641
$626$	32.5754	1.30197
$627$	−13.0571	−0.521450
$628$	2.04810	0.0817279
$629$	−8.40316	−0.335056
$630$	−70.6102	−2.81318
$631$	31.5065	1.25426	0.627128	−	0.778917i	$-0.284230\pi$
$631$	31.5065	1.25426	0.627128	+	0.778917i	$0.284230\pi$
$632$	−28.9758	−1.15259
$633$	57.1169	2.27019
$634$	43.9444	1.74526
$635$	61.8600	2.45484
$636$	19.7867	0.784593
$637$	15.6529	0.620191
$638$	4.29551	0.170061
$639$	−37.9999	−1.50325
$640$	51.1576	2.02218
$641$	−41.3023	−1.63134	−0.815672	−	0.578514i	$-0.803633\pi$
$641$	−41.3023	−1.63134	−0.815672	+	0.578514i	$0.803633\pi$
$642$	17.3968	0.686597
$643$	−36.6735	−1.44626	−0.723131	−	0.690710i	$-0.757298\pi$
$643$	−36.6735	−1.44626	−0.723131	+	0.690710i	$0.757298\pi$
$644$	−7.44041	−0.293193
$645$	−96.0480	−3.78189
$646$	12.8146	0.504185
$647$	13.4592	0.529134	0.264567	−	0.964367i	$-0.414771\pi$
$647$	13.4592	0.529134	0.264567	+	0.964367i	$0.414771\pi$
$648$	15.3690	0.603750
$649$	−15.9771	−0.627156
$650$	79.0418	3.10027
$651$	−58.9385	−2.30998
$652$	6.62372	0.259405
$653$	45.0315	1.76222	0.881109	−	0.472914i	$-0.156798\pi$
$653$	45.0315	1.76222	0.881109	+	0.472914i	$0.156798\pi$
$654$	33.2044	1.29840
$655$	−30.3160	−1.18454
$656$	−33.4870	−1.30745
$657$	4.10303	0.160074
$658$	−67.1576	−2.61808
$659$	−49.5281	−1.92934	−0.964671	−	0.263456i	$-0.915138\pi$
$659$	−49.5281	−1.92934	−0.964671	+	0.263456i	$0.915138\pi$
$660$	−21.3779	−0.832134
$661$	29.4145	1.14409	0.572046	−	0.820221i	$-0.306150\pi$
$661$	29.4145	1.14409	0.572046	+	0.820221i	$0.306150\pi$
$662$	−17.4610	−0.678643
$663$	−50.8389	−1.97442
$664$	4.61290	0.179015
$665$	−22.7043	−0.880433
$666$	−11.4491	−0.443645
$667$	2.73871	0.106043
$668$	−8.30506	−0.321332
$669$	−49.7390	−1.92302
$670$	−41.7933	−1.61462
$671$	14.4390	0.557413
$672$	−33.9479	−1.30957
$673$	−26.3408	−1.01536	−0.507682	−	0.861545i	$-0.669497\pi$
$673$	−26.3408	−1.01536	−0.507682	+	0.861545i	$0.669497\pi$
$674$	17.7187	0.682499
$675$	−10.6486	−0.409865
$676$	7.72567	0.297141
$677$	26.6543	1.02441	0.512204	−	0.858864i	$-0.328829\pi$
$677$	26.6543	1.02441	0.512204	+	0.858864i	$0.328829\pi$
$678$	10.0345	0.385373
$679$	13.5172	0.518743
$680$	−32.9319	−1.26288
$681$	53.5202	2.05090
$682$	−33.9515	−1.30007
$683$	30.1313	1.15294	0.576471	−	0.817118i	$-0.304429\pi$
$683$	30.1313	1.15294	0.576471	+	0.817118i	$0.304429\pi$
$684$	4.89120	0.187020
$685$	−52.8006	−2.01741
$686$	19.9283	0.760864
$687$	56.9260	2.17186
$688$	−48.5972	−1.85275
$689$	−48.0247	−1.82959
$690$	−48.6539	−1.85222
$691$	31.1678	1.18568	0.592839	−	0.805321i	$-0.298007\pi$
$691$	31.1678	1.18568	0.592839	+	0.805321i	$0.298007\pi$
$692$	−11.9747	−0.455211
$693$	−30.8015	−1.17005
$694$	17.2968	0.656577
$695$	76.6391	2.90709
$696$	4.73843	0.179610
$697$	28.3346	1.07325
$698$	−33.8678	−1.28192
$699$	−35.7634	−1.35269
$700$	−24.7019	−0.933645
$701$	−6.74845	−0.254885	−0.127443	−	0.991846i	$-0.540677\pi$
$701$	−6.74845	−0.254885	−0.127443	+	0.991846i	$0.540677\pi$
$702$	−8.58118	−0.323876
$703$	−3.68139	−0.138846
$704$	8.23863	0.310505
$705$	−123.025	−4.63340
$706$	5.49124	0.206666
$707$	53.7458	2.02132
$708$	11.2286	0.421997
$709$	11.7702	0.442038	0.221019	−	0.975270i	$-0.429062\pi$
$709$	11.7702	0.442038	0.221019	+	0.975270i	$0.429062\pi$
$710$	−71.4106	−2.67999
$711$	48.7247	1.82732
$712$	8.49238	0.318265
$713$	−21.6466	−0.810672
$714$	56.7141	2.12247
$715$	51.8868	1.94046
$716$	−7.39957	−0.276535
$717$	−51.3556	−1.91791
$718$	−0.495196	−0.0184805
$719$	−52.4809	−1.95721	−0.978604	−	0.205752i	$-0.934036\pi$
$719$	−52.4809	−1.95721	−0.978604	+	0.205752i	$0.934036\pi$
$720$	−65.4470	−2.43906
$721$	28.1699	1.04910
$722$	−26.0558	−0.969695
$723$	57.1992	2.12726
$724$	6.96208	0.258744
$725$	9.09242	0.337684
$726$	13.1841	0.489308
$727$	−25.1949	−0.934426	−0.467213	−	0.884145i	$-0.654742\pi$
$727$	−25.1949	−0.934426	−0.467213	+	0.884145i	$0.654742\pi$
$728$	31.2447	1.15801
$729$	−34.0196	−1.25998
$730$	7.71052	0.285379
$731$	41.1199	1.52088
$732$	−10.1477	−0.375069
$733$	−27.7624	−1.02543	−0.512713	−	0.858560i	$-0.671359\pi$
$733$	−27.7624	−1.02543	−0.512713	+	0.858560i	$0.671359\pi$
$734$	−40.6287	−1.49963
$735$	−31.9882	−1.17990
$736$	−12.4682	−0.459583
$737$	−18.2310	−0.671548
$738$	38.6053	1.42108
$739$	30.7604	1.13154	0.565770	−	0.824563i	$-0.308579\pi$
$739$	30.7604	1.13154	0.565770	+	0.824563i	$0.308579\pi$
$740$	−6.02742	−0.221572
$741$	−22.2724	−0.818195
$742$	53.5746	1.96679
$743$	−43.6331	−1.60074	−0.800371	−	0.599505i	$-0.795364\pi$
$743$	−43.6331	−1.60074	−0.800371	+	0.599505i	$0.795364\pi$
$744$	−37.4523	−1.37307
$745$	20.3480	0.745493
$746$	45.3263	1.65951
$747$	−7.75690	−0.283810
$748$	9.15229	0.334641
$749$	13.1958	0.482163
$750$	−79.9800	−2.92046
$751$	−26.3342	−0.960949	−0.480474	−	0.877009i	$-0.659535\pi$
$751$	−26.3342	−0.960949	−0.480474	+	0.877009i	$0.659535\pi$
$752$	−62.2469	−2.26991
$753$	78.0578	2.84458
$754$	7.32713	0.266838
$755$	−51.2204	−1.86410
$756$	2.68177	0.0975349
$757$	−37.5467	−1.36466	−0.682329	−	0.731045i	$-0.739033\pi$
$757$	−37.5467	−1.36466	−0.682329	+	0.731045i	$0.739033\pi$
$758$	25.6928	0.933204
$759$	−21.2237	−0.770373
$760$	−14.4274	−0.523335
$761$	25.3904	0.920403	0.460201	−	0.887815i	$-0.347777\pi$
$761$	25.3904	0.920403	0.460201	+	0.887815i	$0.347777\pi$
$762$	−67.6961	−2.45237
$763$	25.1861	0.911798
$764$	13.4202	0.485526
$765$	55.3772	2.00217
$766$	−38.5534	−1.39299
$767$	−27.2532	−0.984056
$768$	−41.1057	−1.48328
$769$	32.1010	1.15759	0.578796	−	0.815473i	$-0.303523\pi$
$769$	32.1010	1.15759	0.578796	+	0.815473i	$0.303523\pi$
$770$	−57.8830	−2.08596
$771$	−11.8269	−0.425934
$772$	1.98956	0.0716058
$773$	−21.9262	−0.788631	−0.394315	−	0.918975i	$-0.629018\pi$
$773$	−21.9262	−0.788631	−0.394315	+	0.918975i	$0.629018\pi$
$774$	56.0251	2.01378
$775$	−71.8660	−2.58150
$776$	8.58947	0.308344
$777$	−16.2928	−0.584502
$778$	16.9999	0.609477
$779$	12.4133	0.444753
$780$	−36.4657	−1.30568
$781$	−31.1506	−1.11466
$782$	20.8296	0.744866
$783$	−0.987119	−0.0352768
$784$	−16.1850	−0.578035
$785$	10.1586	0.362578
$786$	33.1761	1.18335
$787$	1.00000	0.0356462
$787$	1.00000	0.0356462
$788$	14.6297	0.521161
$789$	−50.1646	−1.78591
$790$	91.5648	3.25773
$791$	7.61134	0.270628
$792$	−19.5727	−0.695487
$793$	24.6296	0.874624
$794$	−23.7069	−0.841325
$795$	98.1429	3.48077
$796$	11.7897	0.417874
$797$	15.5117	0.549451	0.274726	−	0.961523i	$-0.411413\pi$
$797$	15.5117	0.549451	0.274726	+	0.961523i	$0.411413\pi$
$798$	24.8462	0.879547
$799$	52.6695	1.86331
$800$	−41.3940	−1.46350
$801$	−14.2805	−0.504577
$802$	−61.1935	−2.16082
$803$	3.36348	0.118695
$804$	12.8127	0.451867
$805$	−36.9048	−1.30072
$806$	−57.9133	−2.03991
$807$	−3.72257	−0.131041
$808$	34.1526	1.20148
$809$	12.0551	0.423834	0.211917	−	0.977288i	$-0.432029\pi$
$809$	12.0551	0.423834	0.211917	+	0.977288i	$0.432029\pi$
$810$	−48.5667	−1.70646
$811$	42.4490	1.49059	0.745294	−	0.666736i	$-0.232309\pi$
$811$	42.4490	1.49059	0.745294	+	0.666736i	$0.232309\pi$
$812$	−2.28985	−0.0803581
$813$	72.5201	2.54339
$814$	−9.38548	−0.328961
$815$	32.8540	1.15082
$816$	52.5670	1.84021
$817$	18.0145	0.630248
$818$	20.2893	0.709399
$819$	−52.5401	−1.83590
$820$	20.3239	0.709740
$821$	5.71748	0.199541	0.0997707	−	0.995010i	$-0.468189\pi$
$821$	5.71748	0.199541	0.0997707	+	0.995010i	$0.468189\pi$
$822$	57.7819	2.01538
$823$	−15.9661	−0.556542	−0.278271	−	0.960503i	$-0.589761\pi$
$823$	−15.9661	−0.556542	−0.278271	+	0.960503i	$0.589761\pi$
$824$	17.9005	0.623594
$825$	−70.4621	−2.45318
$826$	30.4027	1.05784
$827$	45.0917	1.56799	0.783996	−	0.620766i	$-0.213178\pi$
$827$	45.0917	1.56799	0.783996	+	0.620766i	$0.213178\pi$
$828$	7.95043	0.276296
$829$	27.2197	0.945378	0.472689	−	0.881229i	$-0.343283\pi$
$829$	27.2197	0.945378	0.472689	+	0.881229i	$0.343283\pi$
$830$	−14.5770	−0.505975
$831$	−8.16602	−0.283276
$832$	14.0532	0.487206
$833$	13.6947	0.474495
$834$	−83.8694	−2.90416
$835$	−41.1935	−1.42556
$836$	4.00958	0.138674
$837$	7.80214	0.269681
$838$	8.93838	0.308771
$839$	−3.00966	−0.103905	−0.0519525	−	0.998650i	$-0.516544\pi$
$839$	−3.00966	−0.103905	−0.0519525	+	0.998650i	$0.516544\pi$
$840$	−63.8515	−2.20309
$841$	−28.1571	−0.970936
$842$	8.28695	0.285587
$843$	−46.7306	−1.60949
$844$	−17.5395	−0.603735
$845$	38.3197	1.31824
$846$	71.7611	2.46720
$847$	10.0004	0.343616
$848$	49.6571	1.70523
$849$	45.8301	1.57289
$850$	69.1537	2.37195
$851$	−5.98394	−0.205127
$852$	21.8925	0.750024
$853$	−26.9576	−0.923012	−0.461506	−	0.887137i	$-0.652691\pi$
$853$	−26.9576	−0.923012	−0.461506	+	0.887137i	$0.652691\pi$
$854$	−27.4759	−0.940207
$855$	24.2606	0.829694
$856$	8.38521	0.286601
$857$	4.71792	0.161161	0.0805805	−	0.996748i	$-0.474323\pi$
$857$	4.71792	0.161161	0.0805805	+	0.996748i	$0.474323\pi$
$858$	−56.7819	−1.93850
$859$	37.0573	1.26438	0.632190	−	0.774814i	$-0.282156\pi$
$859$	37.0573	1.26438	0.632190	+	0.774814i	$0.282156\pi$
$860$	29.4945	1.00575
$861$	54.9379	1.87228
$862$	−1.50819	−0.0513691
$863$	−7.46742	−0.254194	−0.127097	−	0.991890i	$-0.540566\pi$
$863$	−7.46742	−0.254194	−0.127097	+	0.991890i	$0.540566\pi$
$864$	4.49394	0.152887
$865$	−59.3953	−2.01950
$866$	−47.2447	−1.60544
$867$	−1.39072	−0.0472313
$868$	18.0989	0.614316
$869$	39.9423	1.35495
$870$	−14.9737	−0.507655
$871$	−31.0979	−1.05371
$872$	16.0044	0.541979
$873$	−14.4438	−0.488848
$874$	9.12539	0.308671
$875$	−60.6661	−2.05089
$876$	−2.36383	−0.0798665
$877$	27.2535	0.920286	0.460143	−	0.887845i	$-0.347798\pi$
$877$	27.2535	0.920286	0.460143	+	0.887845i	$0.347798\pi$
$878$	−49.0900	−1.65671
$879$	−36.9182	−1.24522
$880$	−53.6505	−1.80856
$881$	0.0482393	0.00162522	0.000812611	−	1.00000i	$-0.499741\pi$
$881$	0.0482393	0.00162522	0.000812611		1.00000i	$0.499741\pi$
$882$	18.6588	0.628275
$883$	−32.0734	−1.07936	−0.539678	−	0.841871i	$-0.681454\pi$
$883$	−32.0734	−1.07936	−0.539678	+	0.841871i	$0.681454\pi$
$884$	15.6117	0.525077
$885$	55.6944	1.87215
$886$	−45.1057	−1.51536
$887$	17.8876	0.600606	0.300303	−	0.953844i	$-0.402912\pi$
$887$	17.8876	0.600606	0.300303	+	0.953844i	$0.402912\pi$
$888$	−10.3532	−0.347432
$889$	−51.3486	−1.72218
$890$	−26.8363	−0.899556
$891$	−21.1857	−0.709747
$892$	15.2739	0.511408
$893$	23.0743	0.772153
$894$	−22.2677	−0.744743
$895$	−36.7022	−1.22682
$896$	−42.4647	−1.41865
$897$	−36.2027	−1.20877
$898$	24.1034	0.804341
$899$	−6.66194	−0.222188
$900$	26.3952	0.879839
$901$	−42.0168	−1.39978
$902$	31.6469	1.05373
$903$	79.7272	2.65316
$904$	4.83661	0.160863
$905$	34.5322	1.14789
$906$	56.0527	1.86223
$907$	−14.1222	−0.468919	−0.234460	−	0.972126i	$-0.575332\pi$
$907$	−14.1222	−0.468919	−0.234460	+	0.972126i	$0.575332\pi$
$908$	−16.4350	−0.545416
$909$	−57.4299	−1.90483
$910$	−98.7349	−3.27303
$911$	33.3802	1.10594	0.552968	−	0.833203i	$-0.313495\pi$
$911$	33.3802	1.10594	0.552968	+	0.833203i	$0.313495\pi$
$912$	23.0294	0.762580
$913$	−6.35876	−0.210444
$914$	−59.2764	−1.96069
$915$	−50.3329	−1.66396
$916$	−17.4809	−0.577584
$917$	25.1646	0.831009
$918$	−7.50768	−0.247790
$919$	−54.3593	−1.79315	−0.896574	−	0.442895i	$-0.853952\pi$
$919$	−54.3593	−1.79315	−0.896574	+	0.442895i	$0.853952\pi$
$920$	−23.4510	−0.773158
$921$	−78.5541	−2.58845
$922$	−44.1262	−1.45322
$923$	−53.1357	−1.74898
$924$	17.7453	0.583778
$925$	−19.8665	−0.653206
$926$	53.0171	1.74225
$927$	−30.1009	−0.988644
$928$	−3.83720	−0.125962
$929$	21.9733	0.720921	0.360460	−	0.932775i	$-0.382620\pi$
$929$	21.9733	0.720921	0.360460	+	0.932775i	$0.382620\pi$
$930$	118.351	3.88089
$931$	5.99962	0.196630
$932$	10.9822	0.359735
$933$	−22.5224	−0.737350
$934$	−52.4433	−1.71600
$935$	45.3957	1.48460
$936$	−33.3865	−1.09127
$937$	−47.6420	−1.55640	−0.778199	−	0.628018i	$-0.783866\pi$
$937$	−47.6420	−1.55640	−0.778199	+	0.628018i	$0.783866\pi$
$938$	34.6916	1.13272
$939$	−49.5344	−1.61650
$940$	37.7788	1.23221
$941$	31.2675	1.01929	0.509646	−	0.860384i	$-0.329776\pi$
$941$	31.2675	1.01929	0.509646	+	0.860384i	$0.329776\pi$
$942$	−11.1170	−0.362213
$943$	20.1773	0.657062
$944$	28.1796	0.917167
$945$	13.3017	0.432704
$946$	45.9268	1.49321
$947$	38.7780	1.26011	0.630057	−	0.776548i	$-0.283031\pi$
$947$	38.7780	1.26011	0.630057	+	0.776548i	$0.283031\pi$
$948$	−28.0712	−0.911710
$949$	5.73730	0.186241
$950$	30.2960	0.982932
$951$	−66.8224	−2.16686
$952$	27.3360	0.885966
$953$	9.68668	0.313782	0.156891	−	0.987616i	$-0.449853\pi$
$953$	9.68668	0.313782	0.156891	+	0.987616i	$0.449853\pi$
$954$	−57.2470	−1.85344
$955$	66.5648	2.15399
$956$	15.7703	0.510049
$957$	−6.53180	−0.211143
$958$	−52.4441	−1.69439
$959$	43.8285	1.41530
$960$	−28.7190	−0.926900
$961$	21.6556	0.698568
$962$	−16.0094	−0.516165
$963$	−14.1003	−0.454376
$964$	−17.5648	−0.565723
$965$	9.86831	0.317672
$966$	40.3865	1.29941
$967$	6.85278	0.220371	0.110185	−	0.993911i	$-0.464856\pi$
$967$	6.85278	0.220371	0.110185	+	0.993911i	$0.464856\pi$
$968$	6.35470	0.204248
$969$	−19.4861	−0.625983
$970$	−27.1431	−0.871514
$971$	−31.3435	−1.00586	−0.502931	−	0.864326i	$-0.667745\pi$
$971$	−31.3435	−1.00586	−0.502931	+	0.864326i	$0.667745\pi$
$972$	17.3998	0.558098
$973$	−63.6164	−2.03945
$974$	−36.8494	−1.18073
$975$	−120.192	−3.84922
$976$	−25.4668	−0.815173
$977$	33.0727	1.05809	0.529045	−	0.848594i	$-0.322550\pi$
$977$	33.0727	1.05809	0.529045	+	0.848594i	$0.322550\pi$
$978$	−35.9535	−1.14967
$979$	−11.7065	−0.374142
$980$	9.82296	0.313783
$981$	−26.9125	−0.859251
$982$	−9.56645	−0.305278
$983$	40.8024	1.30139	0.650697	−	0.759337i	$-0.274477\pi$
$983$	40.8024	1.30139	0.650697	+	0.759337i	$0.274477\pi$
$984$	34.9101	1.11289
$985$	72.5638	2.31208
$986$	6.41051	0.204152
$987$	102.121	3.25053
$988$	6.83941	0.217591
$989$	29.2818	0.931107
$990$	61.8508	1.96575
$991$	−9.46998	−0.300824	−0.150412	−	0.988623i	$-0.548060\pi$
$991$	−9.46998	−0.300824	−0.150412	+	0.988623i	$0.548060\pi$
$992$	30.3290	0.962947
$993$	26.5515	0.842585
$994$	59.2763	1.88013
$995$	58.4774	1.85386
$996$	4.46890	0.141602
$997$	−6.06563	−0.192100	−0.0960502	−	0.995376i	$-0.530621\pi$
$997$	−6.06563	−0.192100	−0.0960502	+	0.995376i	$0.530621\pi$
$998$	5.84721	0.185090
$999$	2.15681	0.0682384

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	787.2.a.b.1.26	✓	37
3.2	odd	2		7083.2.a.g.1.12		37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
787.2.a.b.1.26	✓	37	1.1	even	1	trivial
7083.2.a.g.1.12		37	3.2	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:	\( N \)	\(=\)	\( 787 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	787.a (trivial)

\(f(q)\)	\(=\)	\(q+1.66683 q^{2} -2.53460 q^{3} +0.778328 q^{4} +3.86054 q^{5} -4.22476 q^{6} -3.20455 q^{7} -2.03632 q^{8} +3.42421 q^{9} +6.43487 q^{10} +2.80701 q^{11} -1.97275 q^{12} +4.78811 q^{13} -5.34144 q^{14} -9.78494 q^{15} -4.95086 q^{16} +4.18912 q^{17} +5.70758 q^{18} +1.83524 q^{19} +3.00477 q^{20} +8.12225 q^{21} +4.67882 q^{22} +2.98310 q^{23} +5.16127 q^{24} +9.90378 q^{25} +7.98097 q^{26} -1.07521 q^{27} -2.49419 q^{28} +0.918075 q^{29} -16.3098 q^{30} -7.25642 q^{31} -4.17961 q^{32} -7.11466 q^{33} +6.98255 q^{34} -12.3713 q^{35} +2.66516 q^{36} -2.00595 q^{37} +3.05903 q^{38} -12.1360 q^{39} -7.86130 q^{40} +6.76387 q^{41} +13.5384 q^{42} +9.81590 q^{43} +2.18478 q^{44} +13.2193 q^{45} +4.97232 q^{46} +12.5729 q^{47} +12.5485 q^{48} +3.26912 q^{49} +16.5079 q^{50} -10.6177 q^{51} +3.72672 q^{52} -10.0300 q^{53} -1.79219 q^{54} +10.8366 q^{55} +6.52549 q^{56} -4.65160 q^{57} +1.53028 q^{58} -5.69185 q^{59} -7.61589 q^{60} +5.14392 q^{61} -12.0952 q^{62} -10.9730 q^{63} +2.93502 q^{64} +18.4847 q^{65} -11.8589 q^{66} -6.49481 q^{67} +3.26051 q^{68} -7.56097 q^{69} -20.6209 q^{70} -11.0974 q^{71} -6.97279 q^{72} +1.19824 q^{73} -3.34358 q^{74} -25.1022 q^{75} +1.42842 q^{76} -8.99521 q^{77} -20.2286 q^{78} +14.2295 q^{79} -19.1130 q^{80} -7.54741 q^{81} +11.2742 q^{82} -2.26531 q^{83} +6.32178 q^{84} +16.1723 q^{85} +16.3615 q^{86} -2.32696 q^{87} -5.71598 q^{88} -4.17045 q^{89} +22.0344 q^{90} -15.3437 q^{91} +2.32183 q^{92} +18.3921 q^{93} +20.9570 q^{94} +7.08501 q^{95} +10.5937 q^{96} -4.21813 q^{97} +5.44908 q^{98} +9.61180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) \) 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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