LMFDB - Embedded newform 5819.2.a.u.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,8] 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:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.53611 q^{2} +1.73986 q^{3} +4.43185 q^{4} +3.67453 q^{5} -4.41248 q^{6} +2.39766 q^{7} -6.16743 q^{8} +0.0271203 q^{9} -9.31902 q^{10} +1.00000 q^{11} +7.71081 q^{12} +3.89159 q^{13} -6.08072 q^{14} +6.39318 q^{15} +6.77759 q^{16} +0.558480 q^{17} -0.0687801 q^{18} -4.09250 q^{19} +16.2850 q^{20} +4.17159 q^{21} -2.53611 q^{22} -10.7305 q^{24} +8.50221 q^{25} -9.86951 q^{26} -5.17240 q^{27} +10.6261 q^{28} -6.82401 q^{29} -16.2138 q^{30} +3.17186 q^{31} -4.85384 q^{32} +1.73986 q^{33} -1.41637 q^{34} +8.81027 q^{35} +0.120193 q^{36} +4.10077 q^{37} +10.3790 q^{38} +6.77084 q^{39} -22.6625 q^{40} -6.56786 q^{41} -10.5796 q^{42} +9.26524 q^{43} +4.43185 q^{44} +0.0996546 q^{45} +13.0742 q^{47} +11.7921 q^{48} -1.25124 q^{49} -21.5625 q^{50} +0.971679 q^{51} +17.2470 q^{52} +9.79621 q^{53} +13.1178 q^{54} +3.67453 q^{55} -14.7874 q^{56} -7.12039 q^{57} +17.3064 q^{58} -8.58826 q^{59} +28.3336 q^{60} -5.44499 q^{61} -8.04420 q^{62} +0.0650253 q^{63} -1.24532 q^{64} +14.2998 q^{65} -4.41248 q^{66} -6.06298 q^{67} +2.47510 q^{68} -22.3438 q^{70} +6.48568 q^{71} -0.167263 q^{72} +2.33785 q^{73} -10.4000 q^{74} +14.7927 q^{75} -18.1373 q^{76} +2.39766 q^{77} -17.1716 q^{78} -4.66919 q^{79} +24.9045 q^{80} -9.08063 q^{81} +16.6568 q^{82} -14.1649 q^{83} +18.4879 q^{84} +2.05216 q^{85} -23.4976 q^{86} -11.8728 q^{87} -6.16743 q^{88} +7.31586 q^{89} -0.252735 q^{90} +9.33070 q^{91} +5.51861 q^{93} -33.1575 q^{94} -15.0380 q^{95} -8.44500 q^{96} +12.9904 q^{97} +3.17329 q^{98} +0.0271203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Coefficient data

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

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

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

$2$	−2.53611	−1.79330	−0.896650	−	0.442740i	$-0.854006\pi$
$2$	−2.53611	−1.79330	−0.896650	+	0.442740i	$0.854006\pi$
$3$	1.73986	1.00451	0.502255	−	0.864720i	$-0.332504\pi$
$3$	1.73986	1.00451	0.502255	+	0.864720i	$0.332504\pi$
$4$	4.43185	2.21592
$5$	3.67453	1.64330	0.821651	−	0.569991i	$-0.193053\pi$
$5$	3.67453	1.64330	0.821651	+	0.569991i	$0.193053\pi$
$6$	−4.41248	−1.80139
$7$	2.39766	0.906229	0.453114	−	0.891452i	$-0.350313\pi$
$7$	2.39766	0.906229	0.453114	+	0.891452i	$0.350313\pi$
$8$	−6.16743	−2.18052
$9$	0.0271203	0.00904011
$10$	−9.31902	−2.94693
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	7.71081	2.22592
$13$	3.89159	1.07933	0.539667	−	0.841879i	$-0.318550\pi$
$13$	3.89159	1.07933	0.539667	+	0.841879i	$0.318550\pi$
$14$	−6.08072	−1.62514
$15$	6.39318	1.65071
$16$	6.77759	1.69440
$17$	0.558480	0.135451	0.0677257	−	0.997704i	$-0.478426\pi$
$17$	0.558480	0.135451	0.0677257	+	0.997704i	$0.478426\pi$
$18$	−0.0687801	−0.0162116
$19$	−4.09250	−0.938884	−0.469442	−	0.882963i	$-0.655545\pi$
$19$	−4.09250	−0.938884	−0.469442	+	0.882963i	$0.655545\pi$
$20$	16.2850	3.64143
$21$	4.17159	0.910316
$22$	−2.53611	−0.540700
$23$	0	0
$23$	0	0
$24$	−10.7305	−2.19035
$25$	8.50221	1.70044
$26$	−9.86951	−1.93557
$27$	−5.17240	−0.995429
$28$	10.6261	2.00813
$29$	−6.82401	−1.26719	−0.633593	−	0.773666i	$-0.718421\pi$
$29$	−6.82401	−1.26719	−0.633593	+	0.773666i	$0.718421\pi$
$30$	−16.2138	−2.96022
$31$	3.17186	0.569684	0.284842	−	0.958575i	$-0.408059\pi$
$31$	3.17186	0.569684	0.284842	+	0.958575i	$0.408059\pi$
$32$	−4.85384	−0.858045
$33$	1.73986	0.302871
$34$	−1.41637	−0.242905
$35$	8.81027	1.48921
$36$	0.120193	0.0200322
$37$	4.10077	0.674163	0.337081	−	0.941475i	$-0.390560\pi$
$37$	4.10077	0.674163	0.337081	+	0.941475i	$0.390560\pi$
$38$	10.3790	1.68370
$39$	6.77084	1.08420
$40$	−22.6625	−3.58325
$41$	−6.56786	−1.02573	−0.512864	−	0.858470i	$-0.671415\pi$
$41$	−6.56786	−1.02573	−0.512864	+	0.858470i	$0.671415\pi$
$42$	−10.5796	−1.63247
$43$	9.26524	1.41294	0.706468	−	0.707745i	$-0.250288\pi$
$43$	9.26524	1.41294	0.706468	+	0.707745i	$0.250288\pi$
$44$	4.43185	0.668126
$45$	0.0996546	0.0148556
$46$	0	0
$47$	13.0742	1.90706	0.953532	−	0.301291i	$-0.0974175\pi$
$47$	13.0742	1.90706	0.953532	+	0.301291i	$0.0974175\pi$
$48$	11.7921	1.70204
$49$	−1.25124	−0.178749
$50$	−21.5625	−3.04940
$51$	0.971679	0.136062
$52$	17.2470	2.39172
$53$	9.79621	1.34561	0.672806	−	0.739819i	$-0.265089\pi$
$53$	9.79621	1.34561	0.672806	+	0.739819i	$0.265089\pi$
$54$	13.1178	1.78510
$55$	3.67453	0.495474
$56$	−14.7874	−1.97605
$57$	−7.12039	−0.943118
$58$	17.3064	2.27244
$59$	−8.58826	−1.11810	−0.559048	−	0.829135i	$-0.688833\pi$
$59$	−8.58826	−1.11810	−0.559048	+	0.829135i	$0.688833\pi$
$60$	28.3336	3.65786
$61$	−5.44499	−0.697160	−0.348580	−	0.937279i	$-0.613336\pi$
$61$	−5.44499	−0.697160	−0.348580	+	0.937279i	$0.613336\pi$
$62$	−8.04420	−1.02161
$63$	0.0650253	0.00819241
$64$	−1.24532	−0.155665
$65$	14.2998	1.77367
$66$	−4.41248	−0.543139
$67$	−6.06298	−0.740710	−0.370355	−	0.928890i	$-0.620764\pi$
$67$	−6.06298	−0.740710	−0.370355	+	0.928890i	$0.620764\pi$
$68$	2.47510	0.300150
$69$	0	0
$70$	−22.3438	−2.67060
$71$	6.48568	0.769708	0.384854	−	0.922977i	$-0.374252\pi$
$71$	6.48568	0.769708	0.384854	+	0.922977i	$0.374252\pi$
$72$	−0.167263	−0.0197121
$73$	2.33785	0.273625	0.136812	−	0.990597i	$-0.456314\pi$
$73$	2.33785	0.273625	0.136812	+	0.990597i	$0.456314\pi$
$74$	−10.4000	−1.20898
$75$	14.7927	1.70811
$76$	−18.1373	−2.08050
$77$	2.39766	0.273238
$78$	−17.1716	−1.94430
$79$	−4.66919	−0.525325	−0.262662	−	0.964888i	$-0.584601\pi$
$79$	−4.66919	−0.525325	−0.262662	+	0.964888i	$0.584601\pi$
$80$	24.9045	2.78441
$81$	−9.08063	−1.00896
$82$	16.6568	1.83944
$83$	−14.1649	−1.55480	−0.777399	−	0.629007i	$-0.783461\pi$
$83$	−14.1649	−1.55480	−0.777399	+	0.629007i	$0.783461\pi$
$84$	18.4879	2.01719
$85$	2.05216	0.222588
$86$	−23.4976	−2.53382
$87$	−11.8728	−1.27290
$88$	−6.16743	−0.657451
$89$	7.31586	0.775480	0.387740	−	0.921769i	$-0.373256\pi$
$89$	7.31586	0.775480	0.387740	+	0.921769i	$0.373256\pi$
$90$	−0.252735	−0.0266406
$91$	9.33070	0.978124
$92$	0	0
$93$	5.51861	0.572253
$94$	−33.1575	−3.41994
$95$	−15.0380	−1.54287
$96$	−8.44500	−0.861915
$97$	12.9904	1.31897	0.659486	−	0.751717i	$-0.270774\pi$
$97$	12.9904	1.31897	0.659486	+	0.751717i	$0.270774\pi$
$98$	3.17329	0.320551
$99$	0.0271203	0.00272570
$100$	37.6805	3.76805
$101$	−16.5275	−1.64455	−0.822276	−	0.569089i	$-0.807296\pi$
$101$	−16.5275	−1.64455	−0.822276	+	0.569089i	$0.807296\pi$
$102$	−2.46428	−0.244000
$103$	12.9171	1.27276	0.636380	−	0.771376i	$-0.280431\pi$
$103$	12.9171	1.27276	0.636380	+	0.771376i	$0.280431\pi$
$104$	−24.0012	−2.35351
$105$	15.3287	1.49592
$106$	−24.8443	−2.41309
$107$	2.18792	0.211515	0.105757	−	0.994392i	$-0.466273\pi$
$107$	2.18792	0.211515	0.105757	+	0.994392i	$0.466273\pi$
$108$	−22.9233	−2.20580
$109$	14.1516	1.35548	0.677738	−	0.735303i	$-0.262960\pi$
$109$	14.1516	1.35548	0.677738	+	0.735303i	$0.262960\pi$
$110$	−9.31902	−0.888534
$111$	7.13478	0.677203
$112$	16.2503	1.53551
$113$	13.6362	1.28278	0.641392	−	0.767214i	$-0.278357\pi$
$113$	13.6362	1.28278	0.641392	+	0.767214i	$0.278357\pi$
$114$	18.0581	1.69129
$115$	0	0
$116$	−30.2430	−2.80799
$117$	0.105541	0.00975730
$118$	21.7808	2.00508
$119$	1.33904	0.122750
$120$	−39.4295	−3.59941
$121$	1.00000	0.0909091
$122$	13.8091	1.25022
$123$	−11.4272	−1.03035
$124$	14.0572	1.26238
$125$	12.8690	1.15104
$126$	−0.164911	−0.0146915
$127$	8.70630	0.772559	0.386280	−	0.922382i	$-0.373760\pi$
$127$	8.70630	0.772559	0.386280	+	0.922382i	$0.373760\pi$
$128$	12.8659	1.13720
$129$	16.1202	1.41931
$130$	−36.2658	−3.18073
$131$	10.5888	0.925150	0.462575	−	0.886580i	$-0.346926\pi$
$131$	10.5888	0.925150	0.462575	+	0.886580i	$0.346926\pi$
$132$	7.71081	0.671140
$133$	−9.81241	−0.850844
$134$	15.3764	1.32832
$135$	−19.0062	−1.63579
$136$	−3.44439	−0.295354
$137$	1.38414	0.118255	0.0591276	−	0.998250i	$-0.481168\pi$
$137$	1.38414	0.118255	0.0591276	+	0.998250i	$0.481168\pi$
$138$	0	0
$139$	21.5113	1.82456	0.912281	−	0.409565i	$-0.134319\pi$
$139$	21.5113	1.82456	0.912281	+	0.409565i	$0.134319\pi$
$140$	39.0458	3.29997
$141$	22.7473	1.91567
$142$	−16.4484	−1.38032
$143$	3.89159	0.325431
$144$	0.183811	0.0153175
$145$	−25.0750	−2.08237
$146$	−5.92904	−0.490691
$147$	−2.17699	−0.179555
$148$	18.1740	1.49389
$149$	5.33304	0.436900	0.218450	−	0.975848i	$-0.429900\pi$
$149$	5.33304	0.436900	0.218450	+	0.975848i	$0.429900\pi$
$150$	−37.5158	−3.06315
$151$	10.4293	0.848723	0.424361	−	0.905493i	$-0.360499\pi$
$151$	10.4293	0.848723	0.424361	+	0.905493i	$0.360499\pi$
$152$	25.2402	2.04725
$153$	0.0151462	0.00122450
$154$	−6.08072	−0.489998
$155$	11.6551	0.936162
$156$	30.0073	2.40251
$157$	10.2451	0.817644	0.408822	−	0.912614i	$-0.365940\pi$
$157$	10.2451	0.817644	0.408822	+	0.912614i	$0.365940\pi$
$158$	11.8416	0.942065
$159$	17.0441	1.35168
$160$	−17.8356	−1.41003
$161$	0	0
$162$	23.0295	1.80937
$163$	0.121668	0.00952978	0.00476489	−	0.999989i	$-0.498483\pi$
$163$	0.121668	0.00952978	0.00476489	+	0.999989i	$0.498483\pi$
$164$	−29.1078	−2.27294
$165$	6.39318	0.497709
$166$	35.9237	2.78822
$167$	−11.3523	−0.878468	−0.439234	−	0.898373i	$-0.644750\pi$
$167$	−11.3523	−0.878468	−0.439234	+	0.898373i	$0.644750\pi$
$168$	−25.7280	−1.98496
$169$	2.14450	0.164962
$170$	−5.20449	−0.399166
$171$	−0.110990	−0.00848762
$172$	41.0621	3.13096
$173$	9.32445	0.708924	0.354462	−	0.935070i	$-0.384664\pi$
$173$	9.32445	0.708924	0.354462	+	0.935070i	$0.384664\pi$
$174$	30.1108	2.28269
$175$	20.3854	1.54099
$176$	6.77759	0.510880
$177$	−14.9424	−1.12314
$178$	−18.5538	−1.39067
$179$	16.7636	1.25297	0.626484	−	0.779435i	$-0.284494\pi$
$179$	16.7636	1.25297	0.626484	+	0.779435i	$0.284494\pi$
$180$	0.441654	0.0329190
$181$	−17.6188	−1.30959	−0.654797	−	0.755805i	$-0.727246\pi$
$181$	−17.6188	−1.30959	−0.654797	+	0.755805i	$0.727246\pi$
$182$	−23.6637	−1.75407
$183$	−9.47353	−0.700304
$184$	0	0
$185$	15.0684	1.10785
$186$	−13.9958	−1.02622
$187$	0.558480	0.0408401
$188$	57.9428	4.22591
$189$	−12.4016	−0.902086
$190$	38.1381	2.76683
$191$	−4.11143	−0.297493	−0.148746	−	0.988875i	$-0.547524\pi$
$191$	−4.11143	−0.297493	−0.148746	+	0.988875i	$0.547524\pi$
$192$	−2.16669	−0.156367
$193$	11.5045	0.828109	0.414054	−	0.910252i	$-0.364112\pi$
$193$	11.5045	0.828109	0.414054	+	0.910252i	$0.364112\pi$
$194$	−32.9450	−2.36531
$195$	24.8797	1.78167
$196$	−5.54533	−0.396095
$197$	3.72222	0.265197	0.132599	−	0.991170i	$-0.457668\pi$
$197$	3.72222	0.265197	0.132599	+	0.991170i	$0.457668\pi$
$198$	−0.0687801	−0.00488799
$199$	5.16905	0.366424	0.183212	−	0.983073i	$-0.441350\pi$
$199$	5.16905	0.366424	0.183212	+	0.983073i	$0.441350\pi$
$200$	−52.4368	−3.70784
$201$	−10.5487	−0.744051
$202$	41.9156	2.94917
$203$	−16.3616	−1.14836
$204$	4.30633	0.301504
$205$	−24.1338	−1.68558
$206$	−32.7592	−2.28244
$207$	0	0
$208$	26.3756	1.82882
$209$	−4.09250	−0.283084
$210$	−38.8751	−2.68264
$211$	−1.25163	−0.0861654	−0.0430827	−	0.999072i	$-0.513718\pi$
$211$	−1.25163	−0.0861654	−0.0430827	+	0.999072i	$0.513718\pi$
$212$	43.4153	2.98178
$213$	11.2842	0.773179
$214$	−5.54882	−0.379309
$215$	34.0454	2.32188
$216$	31.9004	2.17055
$217$	7.60504	0.516264
$218$	−35.8900	−2.43078
$219$	4.06754	0.274859
$220$	16.2850	1.09793
$221$	2.17338	0.146197
$222$	−18.0946	−1.21443
$223$	−2.47683	−0.165861	−0.0829305	−	0.996555i	$-0.526428\pi$
$223$	−2.47683	−0.165861	−0.0829305	+	0.996555i	$0.526428\pi$
$224$	−11.6378	−0.777585
$225$	0.230583	0.0153722
$226$	−34.5828	−2.30041
$227$	−9.21172	−0.611403	−0.305702	−	0.952127i	$-0.598891\pi$
$227$	−9.21172	−0.611403	−0.305702	+	0.952127i	$0.598891\pi$
$228$	−31.5565	−2.08988
$229$	−18.6580	−1.23295	−0.616477	−	0.787373i	$-0.711441\pi$
$229$	−18.6580	−1.23295	−0.616477	+	0.787373i	$0.711441\pi$
$230$	0	0
$231$	4.17159	0.274471
$232$	42.0866	2.76312
$233$	−0.0421319	−0.00276016	−0.00138008	−	0.999999i	$-0.500439\pi$
$233$	−0.0421319	−0.00276016	−0.00138008	+	0.999999i	$0.500439\pi$
$234$	−0.267664	−0.0174978
$235$	48.0415	3.13388
$236$	−38.0619	−2.47762
$237$	−8.12375	−0.527694
$238$	−3.39596	−0.220127
$239$	−0.243749	−0.0157668	−0.00788341	−	0.999969i	$-0.502509\pi$
$239$	−0.243749	−0.0157668	−0.00788341	+	0.999969i	$0.502509\pi$
$240$	43.3304	2.79696
$241$	−20.9205	−1.34761	−0.673804	−	0.738911i	$-0.735341\pi$
$241$	−20.9205	−1.34761	−0.673804	+	0.738911i	$0.735341\pi$
$242$	−2.53611	−0.163027
$243$	−0.281834	−0.0180797
$244$	−24.1314	−1.54485
$245$	−4.59774	−0.293739
$246$	28.9806	1.84773
$247$	−15.9263	−1.01337
$248$	−19.5623	−1.24221
$249$	−24.6450	−1.56181
$250$	−32.6371	−2.06415
$251$	−4.14161	−0.261416	−0.130708	−	0.991421i	$-0.541725\pi$
$251$	−4.14161	−0.261416	−0.130708	+	0.991421i	$0.541725\pi$
$252$	0.288182	0.0181538
$253$	0	0
$254$	−22.0801	−1.38543
$255$	3.57047	0.223591
$256$	−30.1388	−1.88367
$257$	−2.99240	−0.186661	−0.0933304	−	0.995635i	$-0.529751\pi$
$257$	−2.99240	−0.186661	−0.0933304	+	0.995635i	$0.529751\pi$
$258$	−40.8827	−2.54524
$259$	9.83224	0.610946
$260$	63.3746	3.93032
$261$	−0.185069	−0.0114555
$262$	−26.8544	−1.65907
$263$	−16.8197	−1.03715	−0.518574	−	0.855033i	$-0.673537\pi$
$263$	−16.8197	−1.03715	−0.518574	+	0.855033i	$0.673537\pi$
$264$	−10.7305	−0.660416
$265$	35.9965	2.21125
$266$	24.8853	1.52582
$267$	12.7286	0.778977
$268$	−26.8702	−1.64136
$269$	−4.93842	−0.301101	−0.150550	−	0.988602i	$-0.548105\pi$
$269$	−4.93842	−0.301101	−0.150550	+	0.988602i	$0.548105\pi$
$270$	48.2017	2.93346
$271$	−2.81986	−0.171295	−0.0856473	−	0.996326i	$-0.527296\pi$
$271$	−2.81986	−0.171295	−0.0856473	+	0.996326i	$0.527296\pi$
$272$	3.78515	0.229508
$273$	16.2341	0.982535
$274$	−3.51034	−0.212067
$275$	8.50221	0.512702
$276$	0	0
$277$	21.5605	1.29545	0.647724	−	0.761875i	$-0.275721\pi$
$277$	21.5605	1.29545	0.647724	+	0.761875i	$0.275721\pi$
$278$	−54.5549	−3.27199
$279$	0.0860221	0.00515001
$280$	−54.3368	−3.24724
$281$	−23.0804	−1.37686	−0.688430	−	0.725302i	$-0.741700\pi$
$281$	−23.0804	−1.37686	−0.688430	+	0.725302i	$0.741700\pi$
$282$	−57.6895	−3.43536
$283$	−9.27050	−0.551074	−0.275537	−	0.961290i	$-0.588856\pi$
$283$	−9.27050	−0.551074	−0.275537	+	0.961290i	$0.588856\pi$
$284$	28.7435	1.70561
$285$	−26.1641	−1.54983
$286$	−9.86951	−0.583596
$287$	−15.7475	−0.929544
$288$	−0.131638	−0.00775682
$289$	−16.6881	−0.981653
$290$	63.5931	3.73431
$291$	22.6015	1.32492
$292$	10.3610	0.606331
$293$	1.08449	0.0633565	0.0316783	−	0.999498i	$-0.489915\pi$
$293$	1.08449	0.0633565	0.0316783	+	0.999498i	$0.489915\pi$
$294$	5.52109	0.321997
$295$	−31.5578	−1.83737
$296$	−25.2913	−1.47002
$297$	−5.17240	−0.300133
$298$	−13.5252	−0.783493
$299$	0	0
$300$	65.5589	3.78504
$301$	22.2149	1.28044
$302$	−26.4498	−1.52201
$303$	−28.7556	−1.65197
$304$	−27.7373	−1.59084
$305$	−20.0078	−1.14564
$306$	−0.0384124	−0.00219589
$307$	−24.9576	−1.42440	−0.712201	−	0.701975i	$-0.752302\pi$
$307$	−24.9576	−1.42440	−0.712201	+	0.701975i	$0.752302\pi$
$308$	10.6261	0.605475
$309$	22.4740	1.27850
$310$	−29.5587	−1.67882
$311$	3.31914	0.188211	0.0941055	−	0.995562i	$-0.470001\pi$
$311$	3.31914	0.188211	0.0941055	+	0.995562i	$0.470001\pi$
$312$	−41.7587	−2.36412
$313$	25.7907	1.45777	0.728887	−	0.684634i	$-0.240038\pi$
$313$	25.7907	1.45777	0.728887	+	0.684634i	$0.240038\pi$
$314$	−25.9826	−1.46628
$315$	0.238938	0.0134626
$316$	−20.6931	−1.16408
$317$	16.5791	0.931173	0.465587	−	0.885002i	$-0.345843\pi$
$317$	16.5791	0.931173	0.465587	+	0.885002i	$0.345843\pi$
$318$	−43.2256	−2.42397
$319$	−6.82401	−0.382071
$320$	−4.57598	−0.255805
$321$	3.80669	0.212469
$322$	0	0
$323$	−2.28558	−0.127173
$324$	−40.2440	−2.23578
$325$	33.0871	1.83534
$326$	−0.308563	−0.0170898
$327$	24.6218	1.36159
$328$	40.5069	2.23662
$329$	31.3474	1.72824
$330$	−16.2138	−0.892541
$331$	23.8068	1.30854	0.654270	−	0.756261i	$-0.272976\pi$
$331$	23.8068	1.30854	0.654270	+	0.756261i	$0.272976\pi$
$332$	−62.7767	−3.44532
$333$	0.111214	0.00609451
$334$	28.7907	1.57536
$335$	−22.2786	−1.21721
$336$	28.2733	1.54244
$337$	5.18758	0.282585	0.141293	−	0.989968i	$-0.454874\pi$
$337$	5.18758	0.282585	0.141293	+	0.989968i	$0.454874\pi$
$338$	−5.43870	−0.295826
$339$	23.7251	1.28857
$340$	9.09484	0.493237
$341$	3.17186	0.171766
$342$	0.281483	0.0152208
$343$	−19.7836	−1.06822
$344$	−57.1427	−3.08093
$345$	0	0
$346$	−23.6478	−1.27131
$347$	−14.3575	−0.770750	−0.385375	−	0.922760i	$-0.625928\pi$
$347$	−14.3575	−0.770750	−0.385375	+	0.922760i	$0.625928\pi$
$348$	−52.6186	−2.82065
$349$	8.96546	0.479910	0.239955	−	0.970784i	$-0.422867\pi$
$349$	8.96546	0.479910	0.239955	+	0.970784i	$0.422867\pi$
$350$	−51.6995	−2.76346
$351$	−20.1289	−1.07440
$352$	−4.85384	−0.258710
$353$	−33.2473	−1.76958	−0.884788	−	0.465995i	$-0.845697\pi$
$353$	−33.2473	−1.76958	−0.884788	+	0.465995i	$0.845697\pi$
$354$	37.8955	2.01412
$355$	23.8318	1.26486
$356$	32.4228	1.71840
$357$	2.32975	0.123304
$358$	−42.5142	−2.24695
$359$	−31.5362	−1.66442	−0.832209	−	0.554462i	$-0.812924\pi$
$359$	−31.5362	−1.66442	−0.832209	+	0.554462i	$0.812924\pi$
$360$	−0.614613	−0.0323930
$361$	−2.25144	−0.118497
$362$	44.6832	2.34849
$363$	1.73986	0.0913191
$364$	41.3523	2.16745
$365$	8.59051	0.449648
$366$	24.0259	1.25585
$367$	−0.720702	−0.0376203	−0.0188102	−	0.999823i	$-0.505988\pi$
$367$	−0.720702	−0.0376203	−0.0188102	+	0.999823i	$0.505988\pi$
$368$	0	0
$369$	−0.178123	−0.00927270
$370$	−38.2152	−1.98671
$371$	23.4879	1.21943
$372$	24.4576	1.26807
$373$	−2.49679	−0.129279	−0.0646395	−	0.997909i	$-0.520590\pi$
$373$	−2.49679	−0.129279	−0.0646395	+	0.997909i	$0.520590\pi$
$374$	−1.41637	−0.0732386
$375$	22.3903	1.15623
$376$	−80.6341	−4.15839
$377$	−26.5563	−1.36772
$378$	31.4519	1.61771
$379$	1.20543	0.0619186	0.0309593	−	0.999521i	$-0.490144\pi$
$379$	1.20543	0.0619186	0.0309593	+	0.999521i	$0.490144\pi$
$380$	−66.6463	−3.41888
$381$	15.1478	0.776043
$382$	10.4270	0.533494
$383$	−32.4156	−1.65636	−0.828181	−	0.560461i	$-0.810624\pi$
$383$	−32.4156	−1.65636	−0.828181	+	0.560461i	$0.810624\pi$
$384$	22.3850	1.14233
$385$	8.81027	0.449013
$386$	−29.1765	−1.48505
$387$	0.251276	0.0127731
$388$	57.5714	2.92274
$389$	−3.67627	−0.186394	−0.0931971	−	0.995648i	$-0.529709\pi$
$389$	−3.67627	−0.186394	−0.0931971	+	0.995648i	$0.529709\pi$
$390$	−63.0976	−3.19507
$391$	0	0
$392$	7.71697	0.389766
$393$	18.4231	0.929322
$394$	−9.43995	−0.475578
$395$	−17.1571	−0.863267
$396$	0.120193	0.00603994
$397$	−17.4558	−0.876080	−0.438040	−	0.898956i	$-0.644327\pi$
$397$	−17.4558	−0.876080	−0.438040	+	0.898956i	$0.644327\pi$
$398$	−13.1093	−0.657109
$399$	−17.0722	−0.854681
$400$	57.6245	2.88122
$401$	4.63145	0.231284	0.115642	−	0.993291i	$-0.463108\pi$
$401$	4.63145	0.231284	0.115642	+	0.993291i	$0.463108\pi$
$402$	26.7528	1.33431
$403$	12.3436	0.614879
$404$	−73.2476	−3.64420
$405$	−33.3671	−1.65802
$406$	41.4949	2.05936
$407$	4.10077	0.203268
$408$	−5.99277	−0.296686
$409$	19.8437	0.981209	0.490605	−	0.871382i	$-0.336776\pi$
$409$	19.8437	0.981209	0.490605	+	0.871382i	$0.336776\pi$
$410$	61.2061	3.02275
$411$	2.40822	0.118789
$412$	57.2467	2.82034
$413$	−20.5917	−1.01325
$414$	0	0
$415$	−52.0494	−2.55500
$416$	−18.8892	−0.926117
$417$	37.4266	1.83279
$418$	10.3790	0.507655
$419$	−22.7150	−1.10970	−0.554851	−	0.831950i	$-0.687225\pi$
$419$	−22.7150	−1.10970	−0.554851	+	0.831950i	$0.687225\pi$
$420$	67.9343	3.31485
$421$	−12.1962	−0.594408	−0.297204	−	0.954814i	$-0.596054\pi$
$421$	−12.1962	−0.594408	−0.297204	+	0.954814i	$0.596054\pi$
$422$	3.17426	0.154520
$423$	0.354576	0.0172401
$424$	−60.4175	−2.93413
$425$	4.74832	0.230327
$426$	−28.6179	−1.38654
$427$	−13.0552	−0.631786
$428$	9.69655	0.468701
$429$	6.77084	0.326899
$430$	−86.3429	−4.16383
$431$	−15.0196	−0.723467	−0.361733	−	0.932282i	$-0.617815\pi$
$431$	−15.0196	−0.723467	−0.361733	+	0.932282i	$0.617815\pi$
$432$	−35.0564	−1.68665
$433$	5.68852	0.273373	0.136687	−	0.990614i	$-0.456355\pi$
$433$	5.68852	0.273373	0.136687	+	0.990614i	$0.456355\pi$
$434$	−19.2872	−0.925816
$435$	−43.6271	−2.09176
$436$	62.7177	3.00363
$437$	0	0
$438$	−10.3157	−0.492904
$439$	3.08851	0.147407	0.0737033	−	0.997280i	$-0.476518\pi$
$439$	3.08851	0.147407	0.0737033	+	0.997280i	$0.476518\pi$
$440$	−22.6625	−1.08039
$441$	−0.0339342	−0.00161591
$442$	−5.51193	−0.262176
$443$	−4.73687	−0.225056	−0.112528	−	0.993649i	$-0.535895\pi$
$443$	−4.73687	−0.225056	−0.112528	+	0.993649i	$0.535895\pi$
$444$	31.6203	1.50063
$445$	26.8824	1.27435
$446$	6.28151	0.297438
$447$	9.27876	0.438870
$448$	−2.98585	−0.141068
$449$	24.3107	1.14729	0.573646	−	0.819104i	$-0.305529\pi$
$449$	24.3107	1.14729	0.573646	+	0.819104i	$0.305529\pi$
$450$	−0.584783	−0.0275669
$451$	−6.56786	−0.309269
$452$	60.4335	2.84255
$453$	18.1455	0.852550
$454$	23.3619	1.09643
$455$	34.2860	1.60735
$456$	43.9145	2.05649
$457$	−5.50157	−0.257352	−0.128676	−	0.991687i	$-0.541073\pi$
$457$	−5.50157	−0.257352	−0.128676	+	0.991687i	$0.541073\pi$
$458$	47.3187	2.21106
$459$	−2.88868	−0.134832
$460$	0	0
$461$	31.8427	1.48306	0.741532	−	0.670917i	$-0.234099\pi$
$461$	31.8427	1.48306	0.741532	+	0.670917i	$0.234099\pi$
$462$	−10.5796	−0.492208
$463$	7.34088	0.341160	0.170580	−	0.985344i	$-0.445436\pi$
$463$	7.34088	0.341160	0.170580	+	0.985344i	$0.445436\pi$
$464$	−46.2503	−2.14712
$465$	20.2783	0.940384
$466$	0.106851	0.00494979
$467$	−11.5380	−0.533916	−0.266958	−	0.963708i	$-0.586018\pi$
$467$	−11.5380	−0.533916	−0.266958	+	0.963708i	$0.586018\pi$
$468$	0.467743	0.0216214
$469$	−14.5369	−0.671253
$470$	−121.839	−5.61999
$471$	17.8250	0.821332
$472$	52.9675	2.43803
$473$	9.26524	0.426016
$474$	20.6027	0.946314
$475$	−34.7953	−1.59652
$476$	5.93444	0.272005
$477$	0.265677	0.0121645
$478$	0.618175	0.0282746
$479$	−9.59664	−0.438482	−0.219241	−	0.975671i	$-0.570358\pi$
$479$	−9.59664	−0.438482	−0.219241	+	0.975671i	$0.570358\pi$
$480$	−31.0315	−1.41639
$481$	15.9585	0.727647
$482$	53.0566	2.41666
$483$	0	0
$484$	4.43185	0.201448
$485$	47.7336	2.16747
$486$	0.714762	0.0324223
$487$	17.3524	0.786313	0.393157	−	0.919472i	$-0.371383\pi$
$487$	17.3524	0.786313	0.393157	+	0.919472i	$0.371383\pi$
$488$	33.5816	1.52017
$489$	0.211686	0.00957276
$490$	11.6604	0.526762
$491$	−20.1424	−0.909012	−0.454506	−	0.890744i	$-0.650184\pi$
$491$	−20.1424	−0.909012	−0.454506	+	0.890744i	$0.650184\pi$
$492$	−50.6435	−2.28319
$493$	−3.81107	−0.171642
$494$	40.3910	1.81728
$495$	0.0996546	0.00447914
$496$	21.4976	0.965271
$497$	15.5504	0.697532
$498$	62.5023	2.80079
$499$	−8.96128	−0.401162	−0.200581	−	0.979677i	$-0.564283\pi$
$499$	−8.96128	−0.401162	−0.200581	+	0.979677i	$0.564283\pi$
$500$	57.0334	2.55061
$501$	−19.7515	−0.882430
$502$	10.5036	0.468797
$503$	−18.7542	−0.836210	−0.418105	−	0.908399i	$-0.637306\pi$
$503$	−18.7542	−0.836210	−0.418105	+	0.908399i	$0.637306\pi$
$504$	−0.401039	−0.0178637
$505$	−60.7310	−2.70250
$506$	0	0
$507$	3.73114	0.165706
$508$	38.5850	1.71193
$509$	−25.6921	−1.13878	−0.569392	−	0.822066i	$-0.692821\pi$
$509$	−25.6921	−1.13878	−0.569392	+	0.822066i	$0.692821\pi$
$510$	−9.05510	−0.400966
$511$	5.60536	0.247966
$512$	50.7034	2.24079
$513$	21.1680	0.934592
$514$	7.58905	0.334739
$515$	47.4643	2.09153
$516$	71.4424	3.14508
$517$	13.0742	0.575002
$518$	−24.9356	−1.09561
$519$	16.2232	0.712122
$520$	−88.1931	−3.86752
$521$	19.1296	0.838082	0.419041	−	0.907967i	$-0.362366\pi$
$521$	19.1296	0.838082	0.419041	+	0.907967i	$0.362366\pi$
$522$	0.469356	0.0205432
$523$	−6.95089	−0.303941	−0.151971	−	0.988385i	$-0.548562\pi$
$523$	−6.95089	−0.303941	−0.151971	+	0.988385i	$0.548562\pi$
$524$	46.9281	2.05006
$525$	35.4677	1.54794
$526$	42.6567	1.85992
$527$	1.77142	0.0771645
$528$	11.7921	0.513184
$529$	0	0
$530$	−91.2911	−3.96543
$531$	−0.232916	−0.0101077
$532$	−43.4871	−1.88541
$533$	−25.5595	−1.10710
$534$	−32.2811	−1.39694
$535$	8.03960	0.347582
$536$	37.3930	1.61513
$537$	29.1663	1.25862
$538$	12.5244	0.539964
$539$	−1.25124	−0.0538949
$540$	−84.2325	−3.62479
$541$	−20.5351	−0.882872	−0.441436	−	0.897293i	$-0.645531\pi$
$541$	−20.5351	−0.882872	−0.441436	+	0.897293i	$0.645531\pi$
$542$	7.15148	0.307182
$543$	−30.6543	−1.31550
$544$	−2.71077	−0.116223
$545$	52.0005	2.22746
$546$	−41.1716	−1.76198
$547$	3.15578	0.134931	0.0674657	−	0.997722i	$-0.478509\pi$
$547$	3.15578	0.134931	0.0674657	+	0.997722i	$0.478509\pi$
$548$	6.13431	0.262045
$549$	−0.147670	−0.00630240
$550$	−21.5625	−0.919429
$551$	27.9272	1.18974
$552$	0	0
$553$	−11.1951	−0.476065
$554$	−54.6799	−2.32313
$555$	26.2170	1.11285
$556$	95.3347	4.04309
$557$	−13.4861	−0.571425	−0.285712	−	0.958315i	$-0.592230\pi$
$557$	−13.4861	−0.571425	−0.285712	+	0.958315i	$0.592230\pi$
$558$	−0.218161	−0.00923551
$559$	36.0565	1.52503
$560$	59.7124	2.52331
$561$	0.971679	0.0410243
$562$	58.5344	2.46912
$563$	8.09071	0.340983	0.170491	−	0.985359i	$-0.445464\pi$
$563$	8.09071	0.340983	0.170491	+	0.985359i	$0.445464\pi$
$564$	100.812	4.24497
$565$	50.1066	2.10800
$566$	23.5110	0.988241
$567$	−21.7722	−0.914347
$568$	−40.0000	−1.67836
$569$	7.18366	0.301155	0.150577	−	0.988598i	$-0.451887\pi$
$569$	7.18366	0.301155	0.150577	+	0.988598i	$0.451887\pi$
$570$	66.3550	2.77931
$571$	−22.2721	−0.932059	−0.466030	−	0.884769i	$-0.654316\pi$
$571$	−22.2721	−0.932059	−0.466030	+	0.884769i	$0.654316\pi$
$572$	17.2470	0.721132
$573$	−7.15333	−0.298834
$574$	39.9373	1.66695
$575$	0	0
$576$	−0.0337736	−0.00140723
$577$	−21.5325	−0.896409	−0.448204	−	0.893931i	$-0.647936\pi$
$577$	−21.5325	−0.896409	−0.448204	+	0.893931i	$0.647936\pi$
$578$	42.3228	1.76040
$579$	20.0162	0.831843
$580$	−111.129	−4.61437
$581$	−33.9625	−1.40900
$582$	−57.3198	−2.37598
$583$	9.79621	0.405718
$584$	−14.4185	−0.596643
$585$	0.387815	0.0160342
$586$	−2.75038	−0.113617
$587$	−33.5783	−1.38593	−0.692963	−	0.720973i	$-0.743695\pi$
$587$	−33.5783	−1.38593	−0.692963	+	0.720973i	$0.743695\pi$
$588$	−9.64811	−0.397881
$589$	−12.9809	−0.534867
$590$	80.0341	3.29495
$591$	6.47615	0.266393
$592$	27.7934	1.14230
$593$	33.9610	1.39461	0.697306	−	0.716774i	$-0.254382\pi$
$593$	33.9610	1.39461	0.697306	+	0.716774i	$0.254382\pi$
$594$	13.1178	0.538229
$595$	4.92036	0.201715
$596$	23.6352	0.968137
$597$	8.99344	0.368077
$598$	0	0
$599$	−48.6293	−1.98694	−0.993469	−	0.114098i	$-0.963602\pi$
$599$	−48.6293	−1.98694	−0.993469	+	0.114098i	$0.963602\pi$
$600$	−91.2328	−3.72456
$601$	−14.3657	−0.585991	−0.292995	−	0.956114i	$-0.594652\pi$
$601$	−14.3657	−0.585991	−0.292995	+	0.956114i	$0.594652\pi$
$602$	−56.3393	−2.29622
$603$	−0.164430	−0.00669611
$604$	46.2210	1.88071
$605$	3.67453	0.149391
$606$	72.9274	2.96248
$607$	−9.69370	−0.393455	−0.196728	−	0.980458i	$-0.563031\pi$
$607$	−9.69370	−0.393455	−0.196728	+	0.980458i	$0.563031\pi$
$608$	19.8643	0.805605
$609$	−28.4670	−1.15354
$610$	50.7420	2.05448
$611$	50.8794	2.05836
$612$	0.0671256	0.00271339
$613$	0.659730	0.0266462	0.0133231	−	0.999911i	$-0.495759\pi$
$613$	0.659730	0.0266462	0.0133231	+	0.999911i	$0.495759\pi$
$614$	63.2951	2.55438
$615$	−41.9896	−1.69318
$616$	−14.7874	−0.595801
$617$	−48.2586	−1.94282	−0.971409	−	0.237413i	$-0.923700\pi$
$617$	−48.2586	−1.94282	−0.971409	+	0.237413i	$0.923700\pi$
$618$	−56.9965	−2.29273
$619$	−31.8073	−1.27844	−0.639222	−	0.769022i	$-0.720743\pi$
$619$	−31.8073	−1.27844	−0.639222	+	0.769022i	$0.720743\pi$
$620$	51.6538	2.07447
$621$	0	0
$622$	−8.41769	−0.337519
$623$	17.5409	0.702762
$624$	45.8900	1.83707
$625$	4.77648	0.191059
$626$	−65.4080	−2.61423
$627$	−7.12039	−0.284361
$628$	45.4045	1.81184
$629$	2.29020	0.0913163
$630$	−0.605972	−0.0241425
$631$	−33.1624	−1.32017	−0.660087	−	0.751189i	$-0.729481\pi$
$631$	−33.1624	−1.32017	−0.660087	+	0.751189i	$0.729481\pi$
$632$	28.7969	1.14548
$633$	−2.17766	−0.0865540
$634$	−42.0463	−1.66987
$635$	31.9916	1.26955
$636$	75.5367	2.99522
$637$	−4.86934	−0.192930
$638$	17.3064	0.685168
$639$	0.175894	0.00695825
$640$	47.2764	1.86876
$641$	−45.9455	−1.81474	−0.907369	−	0.420335i	$-0.861912\pi$
$641$	−45.9455	−1.81474	−0.907369	+	0.420335i	$0.861912\pi$
$642$	−9.65417	−0.381020
$643$	38.9242	1.53502	0.767511	−	0.641036i	$-0.221495\pi$
$643$	38.9242	1.53502	0.767511	+	0.641036i	$0.221495\pi$
$644$	0	0
$645$	59.2344	2.33235
$646$	5.79648	0.228060
$647$	−28.7663	−1.13092	−0.565460	−	0.824776i	$-0.691301\pi$
$647$	−28.7663	−1.13092	−0.565460	+	0.824776i	$0.691301\pi$
$648$	56.0042	2.20005
$649$	−8.58826	−0.337119
$650$	−83.9126	−3.29132
$651$	13.2317	0.518592
$652$	0.539215	0.0211173
$653$	5.55935	0.217554	0.108777	−	0.994066i	$-0.465307\pi$
$653$	5.55935	0.217554	0.108777	+	0.994066i	$0.465307\pi$
$654$	−62.4436	−2.44174
$655$	38.9090	1.52030
$656$	−44.5143	−1.73799
$657$	0.0634033	0.00247360
$658$	−79.5004	−3.09925
$659$	−6.77816	−0.264040	−0.132020	−	0.991247i	$-0.542146\pi$
$659$	−6.77816	−0.264040	−0.132020	+	0.991247i	$0.542146\pi$
$660$	28.3336	1.10288
$661$	−15.5799	−0.605989	−0.302994	−	0.952992i	$-0.597986\pi$
$661$	−15.5799	−0.605989	−0.302994	+	0.952992i	$0.597986\pi$
$662$	−60.3766	−2.34660
$663$	3.78138	0.146857
$664$	87.3610	3.39027
$665$	−36.0560	−1.39819
$666$	−0.282052	−0.0109293
$667$	0	0
$668$	−50.3117	−1.94662
$669$	−4.30935	−0.166609
$670$	56.5010	2.18282
$671$	−5.44499	−0.210202
$672$	−20.2482	−0.781092
$673$	28.1133	1.08369	0.541844	−	0.840479i	$-0.317726\pi$
$673$	28.1133	1.08369	0.541844	+	0.840479i	$0.317726\pi$
$674$	−13.1563	−0.506760
$675$	−43.9768	−1.69267
$676$	9.50412	0.365543
$677$	−10.5970	−0.407275	−0.203637	−	0.979046i	$-0.565276\pi$
$677$	−10.5970	−0.407275	−0.203637	+	0.979046i	$0.565276\pi$
$678$	−60.1693	−2.31079
$679$	31.1465	1.19529
$680$	−12.6565	−0.485356
$681$	−16.0271	−0.614161
$682$	−8.04420	−0.308028
$683$	3.87202	0.148159	0.0740793	−	0.997252i	$-0.476398\pi$
$683$	3.87202	0.148159	0.0740793	+	0.997252i	$0.476398\pi$
$684$	−0.491891	−0.0188079
$685$	5.08608	0.194329
$686$	50.1735	1.91563
$687$	−32.4623	−1.23851
$688$	62.7960	2.39407
$689$	38.1229	1.45237
$690$	0	0
$691$	−4.59634	−0.174853	−0.0874264	−	0.996171i	$-0.527864\pi$
$691$	−4.59634	−0.174853	−0.0874264	+	0.996171i	$0.527864\pi$
$692$	41.3245	1.57092
$693$	0.0650253	0.00247011
$694$	36.4121	1.38219
$695$	79.0439	2.99831
$696$	73.2249	2.77558
$697$	−3.66802	−0.138936
$698$	−22.7374	−0.860623
$699$	−0.0733038	−0.00277260
$700$	90.3449	3.41472
$701$	−16.8335	−0.635794	−0.317897	−	0.948125i	$-0.602977\pi$
$701$	−16.8335	−0.635794	−0.317897	+	0.948125i	$0.602977\pi$
$702$	51.0490	1.92672
$703$	−16.7824	−0.632961
$704$	−1.24532	−0.0469349
$705$	83.5856	3.14802
$706$	84.3188	3.17338
$707$	−39.6274	−1.49034
$708$	−66.2224	−2.48879
$709$	−5.12826	−0.192596	−0.0962979	−	0.995353i	$-0.530700\pi$
$709$	−5.12826	−0.192596	−0.0962979	+	0.995353i	$0.530700\pi$
$710$	−60.4401	−2.26828
$711$	−0.126630	−0.00474900
$712$	−45.1201	−1.69095
$713$	0	0
$714$	−5.90850	−0.221120
$715$	14.2998	0.534782
$716$	74.2936	2.77648
$717$	−0.424090	−0.0158379
$718$	79.9793	2.98480
$719$	18.4479	0.687991	0.343996	−	0.938971i	$-0.388219\pi$
$719$	18.4479	0.687991	0.343996	+	0.938971i	$0.388219\pi$
$720$	0.675418	0.0251713
$721$	30.9708	1.15341
$722$	5.70991	0.212501
$723$	−36.3988	−1.35368
$724$	−78.0838	−2.90196
$725$	−58.0191	−2.15478
$726$	−4.41248	−0.163763
$727$	7.40243	0.274541	0.137270	−	0.990534i	$-0.456167\pi$
$727$	7.40243	0.274541	0.137270	+	0.990534i	$0.456167\pi$
$728$	−57.5465	−2.13282
$729$	26.7515	0.990797
$730$	−21.7865	−0.806353
$731$	5.17445	0.191384
$732$	−41.9853	−1.55182
$733$	21.4571	0.792537	0.396269	−	0.918135i	$-0.370305\pi$
$733$	21.4571	0.792537	0.396269	+	0.918135i	$0.370305\pi$
$734$	1.82778	0.0674646
$735$	−7.99944	−0.295064
$736$	0	0
$737$	−6.06298	−0.223333
$738$	0.451739	0.0166287
$739$	36.6430	1.34793	0.673967	−	0.738762i	$-0.264589\pi$
$739$	36.6430	1.34793	0.673967	+	0.738762i	$0.264589\pi$
$740$	66.7810	2.45492
$741$	−27.7097	−1.01794
$742$	−59.5680	−2.18681
$743$	10.5207	0.385968	0.192984	−	0.981202i	$-0.438183\pi$
$743$	10.5207	0.385968	0.192984	+	0.981202i	$0.438183\pi$
$744$	−34.0357	−1.24781
$745$	19.5965	0.717958
$746$	6.33214	0.231836
$747$	−0.384157	−0.0140556
$748$	2.47510	0.0904986
$749$	5.24589	0.191681
$750$	−56.7841	−2.07346
$751$	12.4571	0.454568	0.227284	−	0.973829i	$-0.427016\pi$
$751$	12.4571	0.454568	0.227284	+	0.973829i	$0.427016\pi$
$752$	88.6114	3.23133
$753$	−7.20582	−0.262595
$754$	67.3496	2.45273
$755$	38.3227	1.39471
$756$	−54.9622	−1.99896
$757$	−26.7123	−0.970875	−0.485437	−	0.874271i	$-0.661340\pi$
$757$	−26.7123	−0.970875	−0.485437	+	0.874271i	$0.661340\pi$
$758$	−3.05709	−0.111039
$759$	0	0
$760$	92.7461	3.36425
$761$	−36.6373	−1.32810	−0.664050	−	0.747688i	$-0.731164\pi$
$761$	−36.6373	−1.32810	−0.664050	+	0.747688i	$0.731164\pi$
$762$	−38.4164	−1.39168
$763$	33.9307	1.22837
$764$	−18.2212	−0.659222
$765$	0.0556552	0.00201222
$766$	82.2096	2.97035
$767$	−33.4220	−1.20680
$768$	−52.4373	−1.89217
$769$	42.9581	1.54911	0.774555	−	0.632507i	$-0.217974\pi$
$769$	42.9581	1.54911	0.774555	+	0.632507i	$0.217974\pi$
$770$	−22.3438	−0.805215
$771$	−5.20636	−0.187503
$772$	50.9860	1.83503
$773$	13.5566	0.487597	0.243798	−	0.969826i	$-0.421607\pi$
$773$	13.5566	0.487597	0.243798	+	0.969826i	$0.421607\pi$
$774$	−0.637264	−0.0229060
$775$	26.9679	0.968714
$776$	−80.1173	−2.87604
$777$	17.1067	0.613701
$778$	9.32342	0.334261
$779$	26.8790	0.963039
$780$	110.263	3.94805
$781$	6.48568	0.232076
$782$	0	0
$783$	35.2965	1.26139
$784$	−8.48042	−0.302872
$785$	37.6458	1.34364
$786$	−46.7230	−1.66655
$787$	20.9843	0.748011	0.374005	−	0.927427i	$-0.377984\pi$
$787$	20.9843	0.748011	0.374005	+	0.927427i	$0.377984\pi$
$788$	16.4963	0.587657
$789$	−29.2640	−1.04183
$790$	43.5123	1.54810
$791$	32.6949	1.16250
$792$	−0.167263	−0.00594343
$793$	−21.1897	−0.752468
$794$	44.2697	1.57107
$795$	62.6290	2.22122
$796$	22.9085	0.811969
$797$	−28.0624	−0.994020	−0.497010	−	0.867745i	$-0.665569\pi$
$797$	−28.0624	−0.994020	−0.497010	+	0.867745i	$0.665569\pi$
$798$	43.2971	1.53270
$799$	7.30167	0.258315
$800$	−41.2683	−1.45906
$801$	0.198409	0.00701042
$802$	−11.7459	−0.414761
$803$	2.33785	0.0825009
$804$	−46.7504	−1.64876
$805$	0	0
$806$	−31.3047	−1.10266
$807$	−8.59217	−0.302459
$808$	101.933	3.58597
$809$	−53.8989	−1.89498	−0.947492	−	0.319780i	$-0.896391\pi$
$809$	−53.8989	−1.89498	−0.947492	+	0.319780i	$0.896391\pi$
$810$	84.6225	2.97333
$811$	24.3372	0.854594	0.427297	−	0.904111i	$-0.359466\pi$
$811$	24.3372	0.854594	0.427297	+	0.904111i	$0.359466\pi$
$812$	−72.5122	−2.54468
$813$	−4.90617	−0.172067
$814$	−10.4000	−0.364520
$815$	0.447074	0.0156603
$816$	6.58564	0.230544
$817$	−37.9180	−1.32658
$818$	−50.3259	−1.75960
$819$	0.253052	0.00884235
$820$	−106.958	−3.73512
$821$	19.9197	0.695201	0.347601	−	0.937643i	$-0.386997\pi$
$821$	19.9197	0.695201	0.347601	+	0.937643i	$0.386997\pi$
$822$	−6.10750	−0.213024
$823$	−5.24102	−0.182690	−0.0913451	−	0.995819i	$-0.529117\pi$
$823$	−5.24102	−0.182690	−0.0913451	+	0.995819i	$0.529117\pi$
$824$	−79.6654	−2.77528
$825$	14.7927	0.515015
$826$	52.2228	1.81706
$827$	−12.4250	−0.432061	−0.216030	−	0.976387i	$-0.569311\pi$
$827$	−12.4250	−0.432061	−0.216030	+	0.976387i	$0.569311\pi$
$828$	0	0
$829$	21.9923	0.763825	0.381913	−	0.924198i	$-0.375266\pi$
$829$	21.9923	0.763825	0.381913	+	0.924198i	$0.375266\pi$
$830$	132.003	4.58189
$831$	37.5124	1.30129
$832$	−4.84629	−0.168015
$833$	−0.698796	−0.0242118
$834$	−94.9181	−3.28674
$835$	−41.7145	−1.44359
$836$	−18.1373	−0.627293
$837$	−16.4062	−0.567080
$838$	57.6078	1.99003
$839$	−39.8548	−1.37594	−0.687970	−	0.725739i	$-0.741498\pi$
$839$	−39.8548	−1.37594	−0.687970	+	0.725739i	$0.741498\pi$
$840$	−94.5385	−3.26189
$841$	17.5671	0.605761
$842$	30.9310	1.06595
$843$	−40.1567	−1.38307
$844$	−5.54701	−0.190936
$845$	7.88006	0.271082
$846$	−0.899244	−0.0309166
$847$	2.39766	0.0823844
$848$	66.3947	2.28000
$849$	−16.1294	−0.553559
$850$	−12.0422	−0.413046
$851$	0	0
$852$	50.0098	1.71331
$853$	44.1121	1.51037	0.755185	−	0.655512i	$-0.227547\pi$
$853$	44.1121	1.51037	0.755185	+	0.655512i	$0.227547\pi$
$854$	33.1095	1.13298
$855$	−0.407837	−0.0139477
$856$	−13.4939	−0.461211
$857$	17.0132	0.581159	0.290580	−	0.956851i	$-0.406152\pi$
$857$	17.0132	0.581159	0.290580	+	0.956851i	$0.406152\pi$
$858$	−17.1716	−0.586228
$859$	−3.29151	−0.112305	−0.0561525	−	0.998422i	$-0.517883\pi$
$859$	−3.29151	−0.112305	−0.0561525	+	0.998422i	$0.517883\pi$
$860$	150.884	5.14511
$861$	−27.3984	−0.933736
$862$	38.0912	1.29739
$863$	−14.7933	−0.503570	−0.251785	−	0.967783i	$-0.581018\pi$
$863$	−14.7933	−0.503570	−0.251785	+	0.967783i	$0.581018\pi$
$864$	25.1060	0.854123
$865$	34.2630	1.16498
$866$	−14.4267	−0.490240
$867$	−29.0350	−0.986080
$868$	33.7044	1.14400
$869$	−4.66919	−0.158391
$870$	110.643	3.75115
$871$	−23.5946	−0.799474
$872$	−87.2790	−2.95564
$873$	0.352303	0.0119237
$874$	0	0
$875$	30.8554	1.04310
$876$	18.0267	0.609066
$877$	19.2347	0.649509	0.324754	−	0.945798i	$-0.394718\pi$
$877$	19.2347	0.649509	0.324754	+	0.945798i	$0.394718\pi$
$878$	−7.83280	−0.264344
$879$	1.88686	0.0636423
$880$	24.9045	0.839530
$881$	54.5257	1.83702	0.918510	−	0.395399i	$-0.129394\pi$
$881$	54.5257	1.83702	0.918510	+	0.395399i	$0.129394\pi$
$882$	0.0860608	0.00289782
$883$	31.1937	1.04975	0.524875	−	0.851179i	$-0.324112\pi$
$883$	31.1937	1.04975	0.524875	+	0.851179i	$0.324112\pi$
$884$	9.63209	0.323962
$885$	−54.9063	−1.84565
$886$	12.0132	0.403592
$887$	−5.63009	−0.189040	−0.0945199	−	0.995523i	$-0.530132\pi$
$887$	−5.63009	−0.189040	−0.0945199	+	0.995523i	$0.530132\pi$
$888$	−44.0033	−1.47665
$889$	20.8747	0.700115
$890$	−68.1767	−2.28529
$891$	−9.08063	−0.304212
$892$	−10.9769	−0.367535
$893$	−53.5061	−1.79051
$894$	−23.5319	−0.787026
$895$	61.5983	2.05900
$896$	30.8481	1.03056
$897$	0	0
$898$	−61.6545	−2.05744
$899$	−21.6448	−0.721895
$900$	1.02191	0.0340636
$901$	5.47099	0.182265
$902$	16.6568	0.554611
$903$	38.6508	1.28622
$904$	−84.1002	−2.79713
$905$	−64.7408	−2.15206
$906$	−46.0190	−1.52888
$907$	5.85106	0.194281	0.0971406	−	0.995271i	$-0.469030\pi$
$907$	5.85106	0.194281	0.0971406	+	0.995271i	$0.469030\pi$
$908$	−40.8250	−1.35482
$909$	−0.448233	−0.0148669
$910$	−86.9530	−2.88247
$911$	6.27524	0.207908	0.103954	−	0.994582i	$-0.466851\pi$
$911$	6.27524	0.207908	0.103954	+	0.994582i	$0.466851\pi$
$912$	−48.2590	−1.59802
$913$	−14.1649	−0.468789
$914$	13.9526	0.461510
$915$	−34.8108	−1.15081
$916$	−82.6894	−2.73213
$917$	25.3884	0.838397
$918$	7.32602	0.241795
$919$	−27.0874	−0.893531	−0.446765	−	0.894651i	$-0.647424\pi$
$919$	−27.0874	−0.893531	−0.446765	+	0.894651i	$0.647424\pi$
$920$	0	0
$921$	−43.4227	−1.43083
$922$	−80.7567	−2.65958
$923$	25.2396	0.830772
$924$	18.4879	0.608206
$925$	34.8656	1.14637
$926$	−18.6173	−0.611802
$927$	0.350316	0.0115059
$928$	33.1226	1.08730
$929$	5.45463	0.178960	0.0894802	−	0.995989i	$-0.471479\pi$
$929$	5.45463	0.178960	0.0894802	+	0.995989i	$0.471479\pi$
$930$	−51.4280	−1.68639
$931$	5.12072	0.167825
$932$	−0.186722	−0.00611630
$933$	5.77484	0.189060
$934$	29.2617	0.957471
$935$	2.05216	0.0671127
$936$	−0.650919	−0.0212760
$937$	12.1415	0.396647	0.198324	−	0.980137i	$-0.436450\pi$
$937$	12.1415	0.396647	0.198324	+	0.980137i	$0.436450\pi$
$938$	36.8672	1.20376
$939$	44.8722	1.46435
$940$	212.913	6.94445
$941$	3.53600	0.115270	0.0576352	−	0.998338i	$-0.481644\pi$
$941$	3.53600	0.115270	0.0576352	+	0.998338i	$0.481644\pi$
$942$	−45.2061	−1.47289
$943$	0	0
$944$	−58.2077	−1.89450
$945$	−45.5703	−1.48240
$946$	−23.4976	−0.763974
$947$	49.8400	1.61958	0.809791	−	0.586718i	$-0.199580\pi$
$947$	49.8400	1.61958	0.809791	+	0.586718i	$0.199580\pi$
$948$	−36.0032	−1.16933
$949$	9.09796	0.295332
$950$	88.2446	2.86303
$951$	28.8453	0.935373
$952$	−8.25847	−0.267658
$953$	33.8454	1.09636	0.548181	−	0.836360i	$-0.315321\pi$
$953$	33.8454	1.09636	0.548181	+	0.836360i	$0.315321\pi$
$954$	−0.673785	−0.0218146
$955$	−15.1076	−0.488871
$956$	−1.08026	−0.0349381
$957$	−11.8728	−0.383794
$958$	24.3381	0.786329
$959$	3.31870	0.107166
$960$	−7.96158	−0.256959
$961$	−20.9393	−0.675460
$962$	−40.4726	−1.30489
$963$	0.0593373	0.00191212
$964$	−92.7165	−2.98620
$965$	42.2735	1.36083
$966$	0	0
$967$	−32.0898	−1.03194	−0.515970	−	0.856607i	$-0.672568\pi$
$967$	−32.0898	−1.03194	−0.515970	+	0.856607i	$0.672568\pi$
$968$	−6.16743	−0.198229
$969$	−3.97660	−0.127747
$970$	−121.058	−3.88692
$971$	−9.81772	−0.315066	−0.157533	−	0.987514i	$-0.550354\pi$
$971$	−9.81772	−0.315066	−0.157533	+	0.987514i	$0.550354\pi$
$972$	−1.24905	−0.0400632
$973$	51.5766	1.65347
$974$	−44.0076	−1.41010
$975$	57.5671	1.84362
$976$	−36.9039	−1.18127
$977$	47.5399	1.52094	0.760468	−	0.649375i	$-0.224970\pi$
$977$	47.5399	1.52094	0.760468	+	0.649375i	$0.224970\pi$
$978$	−0.536858	−0.0171668
$979$	7.31586	0.233816
$980$	−20.3765	−0.650903
$981$	0.383796	0.0122537
$982$	51.0832	1.63013
$983$	−59.3006	−1.89140	−0.945698	−	0.325045i	$-0.894620\pi$
$983$	−59.3006	−1.89140	−0.945698	+	0.325045i	$0.894620\pi$
$984$	70.4764	2.24670
$985$	13.6774	0.435799
$986$	9.66530	0.307806
$987$	54.5401	1.73603
$988$	−70.5832	−2.24555
$989$	0	0
$990$	−0.252735	−0.00803245
$991$	18.9246	0.601161	0.300580	−	0.953757i	$-0.402820\pi$
$991$	18.9246	0.601161	0.300580	+	0.953757i	$0.402820\pi$
$992$	−15.3957	−0.488814
$993$	41.4205	1.31444
$994$	−39.4376	−1.25088
$995$	18.9939	0.602146
$996$	−109.223	−3.46085
$997$	22.0326	0.697778	0.348889	−	0.937164i	$-0.386559\pi$
$997$	22.0326	0.697778	0.348889	+	0.937164i	$0.386559\pi$
$998$	22.7268	0.719403
$999$	−21.2108	−0.671081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.5		60
23.4	even	11		253.2.i.b.177.12	✓	120
23.6	even	11		253.2.i.b.243.12	yes	120
23.22	odd	2		5819.2.a.t.1.5		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.177.12	✓	120	23.4	even	11
253.2.i.b.243.12	yes	120	23.6	even	11
5819.2.a.t.1.5		60	23.22	odd	2
5819.2.a.u.1.5		60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53611 q^{2} +1.73986 q^{3} +4.43185 q^{4} +3.67453 q^{5} -4.41248 q^{6} +2.39766 q^{7} -6.16743 q^{8} +0.0271203 q^{9} -9.31902 q^{10} +1.00000 q^{11} +7.71081 q^{12} +3.89159 q^{13} -6.08072 q^{14} +6.39318 q^{15} +6.77759 q^{16} +0.558480 q^{17} -0.0687801 q^{18} -4.09250 q^{19} +16.2850 q^{20} +4.17159 q^{21} -2.53611 q^{22} -10.7305 q^{24} +8.50221 q^{25} -9.86951 q^{26} -5.17240 q^{27} +10.6261 q^{28} -6.82401 q^{29} -16.2138 q^{30} +3.17186 q^{31} -4.85384 q^{32} +1.73986 q^{33} -1.41637 q^{34} +8.81027 q^{35} +0.120193 q^{36} +4.10077 q^{37} +10.3790 q^{38} +6.77084 q^{39} -22.6625 q^{40} -6.56786 q^{41} -10.5796 q^{42} +9.26524 q^{43} +4.43185 q^{44} +0.0996546 q^{45} +13.0742 q^{47} +11.7921 q^{48} -1.25124 q^{49} -21.5625 q^{50} +0.971679 q^{51} +17.2470 q^{52} +9.79621 q^{53} +13.1178 q^{54} +3.67453 q^{55} -14.7874 q^{56} -7.12039 q^{57} +17.3064 q^{58} -8.58826 q^{59} +28.3336 q^{60} -5.44499 q^{61} -8.04420 q^{62} +0.0650253 q^{63} -1.24532 q^{64} +14.2998 q^{65} -4.41248 q^{66} -6.06298 q^{67} +2.47510 q^{68} -22.3438 q^{70} +6.48568 q^{71} -0.167263 q^{72} +2.33785 q^{73} -10.4000 q^{74} +14.7927 q^{75} -18.1373 q^{76} +2.39766 q^{77} -17.1716 q^{78} -4.66919 q^{79} +24.9045 q^{80} -9.08063 q^{81} +16.6568 q^{82} -14.1649 q^{83} +18.4879 q^{84} +2.05216 q^{85} -23.4976 q^{86} -11.8728 q^{87} -6.16743 q^{88} +7.31586 q^{89} -0.252735 q^{90} +9.33070 q^{91} +5.51861 q^{93} -33.1575 q^{94} -15.0380 q^{95} -8.44500 q^{96} +12.9904 q^{97} +3.17329 q^{98} +0.0271203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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