LMFDB - Embedded newform 1805.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1805,2,Mod(1,1805)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1805, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1805 = 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1805.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$14.4129975648$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.7168.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} + 7 $ x^4 - 6*x^2 + 7
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.25928$ of defining polynomial
Character	$\chi$	$=$	1805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.25928 q^{2} -1.78089 q^{3} -0.414214 q^{4} +1.00000 q^{5} +2.24264 q^{6} -0.828427 q^{7} +3.04017 q^{8} +0.171573 q^{9} +O(q^{10})$	\(q-1.25928 q^{2} -1.78089 q^{3} -0.414214 q^{4} +1.00000 q^{5} +2.24264 q^{6} -0.828427 q^{7} +3.04017 q^{8} +0.171573 q^{9} -1.25928 q^{10} +2.00000 q^{11} +0.737669 q^{12} -4.29945 q^{13} +1.04322 q^{14} -1.78089 q^{15} -3.00000 q^{16} +7.65685 q^{17} -0.216058 q^{18} -0.414214 q^{20} +1.47534 q^{21} -2.51856 q^{22} -0.828427 q^{23} -5.41421 q^{24} +1.00000 q^{25} +5.41421 q^{26} +5.03712 q^{27} +0.343146 q^{28} -8.59890 q^{29} +2.24264 q^{30} -3.56178 q^{31} -2.30250 q^{32} -3.56178 q^{33} -9.64212 q^{34} -0.828427 q^{35} -0.0710678 q^{36} -0.737669 q^{37} +7.65685 q^{39} +3.04017 q^{40} -1.85786 q^{42} -4.82843 q^{43} -0.828427 q^{44} +0.171573 q^{45} +1.04322 q^{46} +10.4853 q^{47} +5.34267 q^{48} -6.31371 q^{49} -1.25928 q^{50} -13.6360 q^{51} +1.78089 q^{52} +7.86123 q^{53} -6.34315 q^{54} +2.00000 q^{55} -2.51856 q^{56} +10.8284 q^{58} +7.12356 q^{59} +0.737669 q^{60} -2.82843 q^{61} +4.48528 q^{62} -0.142136 q^{63} +8.89949 q^{64} -4.29945 q^{65} +4.48528 q^{66} -6.81801 q^{67} -3.17157 q^{68} +1.47534 q^{69} +1.04322 q^{70} -13.6360 q^{71} +0.521611 q^{72} -11.6569 q^{73} +0.928932 q^{74} -1.78089 q^{75} -1.65685 q^{77} -9.64212 q^{78} -7.12356 q^{79} -3.00000 q^{80} -9.48528 q^{81} +8.82843 q^{83} -0.611105 q^{84} +7.65685 q^{85} +6.08034 q^{86} +15.3137 q^{87} +6.08034 q^{88} +15.7225 q^{89} -0.216058 q^{90} +3.56178 q^{91} +0.343146 q^{92} +6.34315 q^{93} -13.2039 q^{94} +4.10051 q^{96} -4.29945 q^{97} +7.95073 q^{98} +0.343146 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{4} + 4 q^{5} - 8 q^{6} + 8 q^{7} + 12 q^{9}+O(q^{10}) $ 4 * q + 4 * q^4 + 4 * q^5 - 8 * q^6 + 8 * q^7 + 12 * q^9	$ 4 q + 4 q^{4} + 4 q^{5} - 8 q^{6} + 8 q^{7} + 12 q^{9} + 8 q^{11} - 12 q^{16} + 8 q^{17} + 4 q^{20} + 8 q^{23} - 16 q^{24} + 4 q^{25} + 16 q^{26} + 24 q^{28} - 8 q^{30} + 8 q^{35} + 28 q^{36} + 8 q^{39} - 64 q^{42} - 8 q^{43} + 8 q^{44} + 12 q^{45} + 8 q^{47} + 20 q^{49} - 48 q^{54} + 8 q^{55} + 32 q^{58} - 16 q^{62} + 56 q^{63} - 4 q^{64} - 16 q^{66} - 24 q^{68} - 24 q^{73} + 32 q^{74} + 16 q^{77} - 12 q^{80} - 4 q^{81} + 24 q^{83} + 8 q^{85} + 16 q^{87} + 24 q^{92} + 48 q^{93} + 56 q^{96} + 24 q^{99}+O(q^{100}) $ 4 * q + 4 * q^4 + 4 * q^5 - 8 * q^6 + 8 * q^7 + 12 * q^9 + 8 * q^11 - 12 * q^16 + 8 * q^17 + 4 * q^20 + 8 * q^23 - 16 * q^24 + 4 * q^25 + 16 * q^26 + 24 * q^28 - 8 * q^30 + 8 * q^35 + 28 * q^36 + 8 * q^39 - 64 * q^42 - 8 * q^43 + 8 * q^44 + 12 * q^45 + 8 * q^47 + 20 * q^49 - 48 * q^54 + 8 * q^55 + 32 * q^58 - 16 * q^62 + 56 * q^63 - 4 * q^64 - 16 * q^66 - 24 * q^68 - 24 * q^73 + 32 * q^74 + 16 * q^77 - 12 * q^80 - 4 * q^81 + 24 * q^83 + 8 * q^85 + 16 * q^87 + 24 * q^92 + 48 * q^93 + 56 * q^96 + 24 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.25928	−0.890446	−0.445223	−	0.895420i	$-0.646876\pi$
$2$	−1.25928	−0.890446	−0.445223	+	0.895420i	$0.646876\pi$
$3$	−1.78089	−1.02820	−0.514099	−	0.857731i	$-0.671874\pi$
$3$	−1.78089	−1.02820	−0.514099	+	0.857731i	$0.671874\pi$
$4$	−0.414214	−0.207107
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.24264	0.915554
$7$	−0.828427	−0.313116	−0.156558	−	0.987669i	$-0.550040\pi$
$7$	−0.828427	−0.313116	−0.156558	+	0.987669i	$0.550040\pi$
$8$	3.04017	1.07486
$9$	0.171573	0.0571910
$10$	−1.25928	−0.398219
$11$	2.00000	0.603023	0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000	0.603023	0.301511	+	0.953463i	$0.402509\pi$
$12$	0.737669	0.212947
$13$	−4.29945	−1.19245	−0.596227	−	0.802816i	$-0.703334\pi$
$13$	−4.29945	−1.19245	−0.596227	+	0.802816i	$0.703334\pi$
$14$	1.04322	0.278813
$15$	−1.78089	−0.459824
$16$	−3.00000	−0.750000
$17$	7.65685	1.85706	0.928530	−	0.371257i	$-0.121073\pi$
$17$	7.65685	1.85706	0.928530	+	0.371257i	$0.121073\pi$
$18$	−0.216058	−0.0509254
$19$	0	0
$19$	0	0
$20$	−0.414214	−0.0926210
$21$	1.47534	0.321945
$22$	−2.51856	−0.536959
$23$	−0.828427	−0.172739	−0.0863695	−	0.996263i	$-0.527527\pi$
$23$	−0.828427	−0.172739	−0.0863695	+	0.996263i	$0.527527\pi$
$24$	−5.41421	−1.10517
$25$	1.00000	0.200000
$26$	5.41421	1.06181
$27$	5.03712	0.969394
$28$	0.343146	0.0648485
$29$	−8.59890	−1.59678	−0.798388	−	0.602143i	$-0.794314\pi$
$29$	−8.59890	−1.59678	−0.798388	+	0.602143i	$0.794314\pi$
$30$	2.24264	0.409448
$31$	−3.56178	−0.639715	−0.319857	−	0.947466i	$-0.603635\pi$
$31$	−3.56178	−0.639715	−0.319857	+	0.947466i	$0.603635\pi$
$32$	−2.30250	−0.407029
$33$	−3.56178	−0.620027
$34$	−9.64212	−1.65361
$35$	−0.828427	−0.140030
$36$	−0.0710678	−0.0118446
$37$	−0.737669	−0.121272	−0.0606360	−	0.998160i	$-0.519313\pi$
$37$	−0.737669	−0.121272	−0.0606360	+	0.998160i	$0.519313\pi$
$38$	0	0
$39$	7.65685	1.22608
$40$	3.04017	0.480693
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	−1.85786	−0.286675
$43$	−4.82843	−0.736328	−0.368164	−	0.929761i	$-0.620014\pi$
$43$	−4.82843	−0.736328	−0.368164	+	0.929761i	$0.620014\pi$
$44$	−0.828427	−0.124890
$45$	0.171573	0.0255766
$46$	1.04322	0.153815
$47$	10.4853	1.52944	0.764718	−	0.644365i	$-0.222878\pi$
$47$	10.4853	1.52944	0.764718	+	0.644365i	$0.222878\pi$
$48$	5.34267	0.771148
$49$	−6.31371	−0.901958
$50$	−1.25928	−0.178089
$51$	−13.6360	−1.90943
$52$	1.78089	0.246965
$53$	7.86123	1.07982	0.539912	−	0.841722i	$-0.318458\pi$
$53$	7.86123	1.07982	0.539912	+	0.841722i	$0.318458\pi$
$54$	−6.34315	−0.863193
$55$	2.00000	0.269680
$56$	−2.51856	−0.336557
$57$	0	0
$58$	10.8284	1.42184
$59$	7.12356	0.927409	0.463705	−	0.885990i	$-0.346520\pi$
$59$	7.12356	0.927409	0.463705	+	0.885990i	$0.346520\pi$
$60$	0.737669	0.0952327
$61$	−2.82843	−0.362143	−0.181071	−	0.983470i	$-0.557957\pi$
$61$	−2.82843	−0.362143	−0.181071	+	0.983470i	$0.557957\pi$
$62$	4.48528	0.569631
$63$	−0.142136	−0.0179074
$64$	8.89949	1.11244
$65$	−4.29945	−0.533281
$66$	4.48528	0.552100
$67$	−6.81801	−0.832953	−0.416476	−	0.909147i	$-0.636735\pi$
$67$	−6.81801	−0.832953	−0.416476	+	0.909147i	$0.636735\pi$
$68$	−3.17157	−0.384610
$69$	1.47534	0.177610
$70$	1.04322	0.124689
$71$	−13.6360	−1.61830	−0.809149	−	0.587603i	$-0.800072\pi$
$71$	−13.6360	−1.61830	−0.809149	+	0.587603i	$0.800072\pi$
$72$	0.521611	0.0614724
$73$	−11.6569	−1.36433	−0.682166	−	0.731198i	$-0.738962\pi$
$73$	−11.6569	−1.36433	−0.682166	+	0.731198i	$0.738962\pi$
$74$	0.928932	0.107986
$75$	−1.78089	−0.205640
$76$	0	0
$77$	−1.65685	−0.188816
$78$	−9.64212	−1.09176
$79$	−7.12356	−0.801464	−0.400732	−	0.916195i	$-0.631244\pi$
$79$	−7.12356	−0.801464	−0.400732	+	0.916195i	$0.631244\pi$
$80$	−3.00000	−0.335410
$81$	−9.48528	−1.05392
$82$	0	0
$83$	8.82843	0.969046	0.484523	−	0.874779i	$-0.338993\pi$
$83$	8.82843	0.969046	0.484523	+	0.874779i	$0.338993\pi$
$84$	−0.611105	−0.0666770
$85$	7.65685	0.830502
$86$	6.08034	0.655660
$87$	15.3137	1.64180
$88$	6.08034	0.648167
$89$	15.7225	1.66658	0.833289	−	0.552838i	$-0.186455\pi$
$89$	15.7225	1.66658	0.833289	+	0.552838i	$0.186455\pi$
$90$	−0.216058	−0.0227745
$91$	3.56178	0.373376
$92$	0.343146	0.0357754
$93$	6.34315	0.657754
$94$	−13.2039	−1.36188
$95$	0	0
$96$	4.10051	0.418506
$97$	−4.29945	−0.436543	−0.218272	−	0.975888i	$-0.570042\pi$
$97$	−4.29945	−0.436543	−0.218272	+	0.975888i	$0.570042\pi$
$98$	7.95073	0.803145
$99$	0.343146	0.0344874
$100$	−0.414214	−0.0414214
$101$	0.485281	0.0482873	0.0241437	−	0.999708i	$-0.492314\pi$
$101$	0.485281	0.0482873	0.0241437	+	0.999708i	$0.492314\pi$
$102$	17.1716	1.70024
$103$	5.34267	0.526429	0.263215	−	0.964737i	$-0.415217\pi$
$103$	5.34267	0.526429	0.263215	+	0.964737i	$0.415217\pi$
$104$	−13.0711	−1.28172
$105$	1.47534	0.143978
$106$	−9.89949	−0.961524
$107$	13.9416	1.34778	0.673891	−	0.738830i	$-0.264622\pi$
$107$	13.9416	1.34778	0.673891	+	0.738830i	$0.264622\pi$
$108$	−2.08644	−0.200768
$109$	18.6731	1.78856	0.894281	−	0.447505i	$-0.147687\pi$
$109$	18.6731	1.78856	0.894281	+	0.447505i	$0.147687\pi$
$110$	−2.51856	−0.240135
$111$	1.31371	0.124692
$112$	2.48528	0.234837
$113$	9.33657	0.878311	0.439155	−	0.898411i	$-0.355278\pi$
$113$	9.33657	0.878311	0.439155	+	0.898411i	$0.355278\pi$
$114$	0	0
$115$	−0.828427	−0.0772512
$116$	3.56178	0.330703
$117$	−0.737669	−0.0681975
$118$	−8.97056	−0.825807
$119$	−6.34315	−0.581475
$120$	−5.41421	−0.494248
$121$	−7.00000	−0.636364
$122$	3.56178	0.322469
$123$	0	0
$124$	1.47534	0.132489
$125$	1.00000	0.0894427
$126$	0.178989	0.0159456
$127$	17.5034	1.55317	0.776586	−	0.630011i	$-0.216950\pi$
$127$	17.5034	1.55317	0.776586	+	0.630011i	$0.216950\pi$
$128$	−6.60195	−0.583536
$129$	8.59890	0.757091
$130$	5.41421	0.474858
$131$	15.3137	1.33796	0.668982	−	0.743278i	$-0.266730\pi$
$131$	15.3137	1.33796	0.668982	+	0.743278i	$0.266730\pi$
$132$	1.47534	0.128412
$133$	0	0
$134$	8.58579	0.741699
$135$	5.03712	0.433526
$136$	23.2781	1.99608
$137$	−2.00000	−0.170872	−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000	−0.170872	−0.0854358	+	0.996344i	$0.527228\pi$
$138$	−1.85786	−0.158152
$139$	19.6569	1.66727	0.833636	−	0.552314i	$-0.186255\pi$
$139$	19.6569	1.66727	0.833636	+	0.552314i	$0.186255\pi$
$140$	0.343146	0.0290011
$141$	−18.6731	−1.57256
$142$	17.1716	1.44101
$143$	−8.59890	−0.719076
$144$	−0.514719	−0.0428932
$145$	−8.59890	−0.714100
$146$	14.6792	1.21486
$147$	11.2440	0.927392
$148$	0.305553	0.0251163
$149$	−14.8284	−1.21479	−0.607396	−	0.794399i	$-0.707786\pi$
$149$	−14.8284	−1.21479	−0.607396	+	0.794399i	$0.707786\pi$
$150$	2.24264	0.183111
$151$	10.6853	0.869561	0.434781	−	0.900536i	$-0.356826\pi$
$151$	10.6853	0.869561	0.434781	+	0.900536i	$0.356826\pi$
$152$	0	0
$153$	1.31371	0.106207
$154$	2.08644	0.168130
$155$	−3.56178	−0.286089
$156$	−3.17157	−0.253929
$157$	18.0000	1.43656	0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000	1.43656	0.718278	+	0.695756i	$0.244931\pi$
$158$	8.97056	0.713660
$159$	−14.0000	−1.11027
$160$	−2.30250	−0.182029
$161$	0.686292	0.0540873
$162$	11.9446	0.938458
$163$	7.17157	0.561721	0.280860	−	0.959749i	$-0.409380\pi$
$163$	7.17157	0.561721	0.280860	+	0.959749i	$0.409380\pi$
$164$	0	0
$165$	−3.56178	−0.277284
$166$	−11.1175	−0.862882
$167$	16.8923	1.30716	0.653581	−	0.756857i	$-0.273266\pi$
$167$	16.8923	1.30716	0.653581	+	0.756857i	$0.273266\pi$
$168$	4.48528	0.346047
$169$	5.48528	0.421945
$170$	−9.64212	−0.739517
$171$	0	0
$172$	2.00000	0.152499
$173$	−2.82411	−0.214713	−0.107357	−	0.994221i	$-0.534239\pi$
$173$	−2.82411	−0.214713	−0.107357	+	0.994221i	$0.534239\pi$
$174$	−19.2842	−1.46194
$175$	−0.828427	−0.0626232
$176$	−6.00000	−0.452267
$177$	−12.6863	−0.953560
$178$	−19.7990	−1.48400
$179$	−17.1978	−1.28542	−0.642712	−	0.766108i	$-0.722191\pi$
$179$	−17.1978	−1.28542	−0.642712	+	0.766108i	$0.722191\pi$
$180$	−0.0710678	−0.00529708
$181$	10.0742	0.748812	0.374406	−	0.927265i	$-0.377847\pi$
$181$	10.0742	0.748812	0.374406	+	0.927265i	$0.377847\pi$
$182$	−4.48528	−0.332471
$183$	5.03712	0.372355
$184$	−2.51856	−0.185671
$185$	−0.737669	−0.0542345
$186$	−7.98780	−0.585694
$187$	15.3137	1.11985
$188$	−4.34315	−0.316756
$189$	−4.17289	−0.303533
$190$	0	0
$191$	−2.34315	−0.169544	−0.0847720	−	0.996400i	$-0.527016\pi$
$191$	−2.34315	−0.169544	−0.0847720	+	0.996400i	$0.527016\pi$
$192$	−15.8490	−1.14381
$193$	20.0219	1.44121	0.720605	−	0.693346i	$-0.243864\pi$
$193$	20.0219	1.44121	0.720605	+	0.693346i	$0.243864\pi$
$194$	5.41421	0.388718
$195$	7.65685	0.548319
$196$	2.61522	0.186802
$197$	9.31371	0.663574	0.331787	−	0.943354i	$-0.392348\pi$
$197$	9.31371	0.663574	0.331787	+	0.943354i	$0.392348\pi$
$198$	−0.432117	−0.0307092
$199$	−4.00000	−0.283552	−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000	−0.283552	−0.141776	+	0.989899i	$0.545281\pi$
$200$	3.04017	0.214973
$201$	12.1421	0.856440
$202$	−0.611105	−0.0429972
$203$	7.12356	0.499976
$204$	5.64823	0.395455
$205$	0	0
$206$	−6.72792	−0.468757
$207$	−0.142136	−0.00987911
$208$	12.8984	0.894340
$209$	0	0
$210$	−1.85786	−0.128205
$211$	13.6360	0.938743	0.469371	−	0.883001i	$-0.344481\pi$
$211$	13.6360	0.938743	0.469371	+	0.883001i	$0.344481\pi$
$212$	−3.25623	−0.223639
$213$	24.2843	1.66393
$214$	−17.5563	−1.20013
$215$	−4.82843	−0.329296
$216$	15.3137	1.04197
$217$	2.95068	0.200305
$218$	−23.5147	−1.59262
$219$	20.7596	1.40280
$220$	−0.828427	−0.0558525
$221$	−32.9203	−2.21446
$222$	−1.65433	−0.111031
$223$	−0.305553	−0.0204613	−0.0102307	−	0.999948i	$-0.503257\pi$
$223$	−0.305553	−0.0204613	−0.0102307	+	0.999948i	$0.503257\pi$
$224$	1.90746	0.127447
$225$	0.171573	0.0114382
$226$	−11.7574	−0.782088
$227$	16.8923	1.12118	0.560589	−	0.828094i	$-0.310575\pi$
$227$	16.8923	1.12118	0.560589	+	0.828094i	$0.310575\pi$
$228$	0	0
$229$	−4.48528	−0.296396	−0.148198	−	0.988958i	$-0.547347\pi$
$229$	−4.48528	−0.296396	−0.148198	+	0.988958i	$0.547347\pi$
$230$	1.04322	0.0687880
$231$	2.95068	0.194140
$232$	−26.1421	−1.71632
$233$	−9.31371	−0.610161	−0.305081	−	0.952327i	$-0.598683\pi$
$233$	−9.31371	−0.610161	−0.305081	+	0.952327i	$0.598683\pi$
$234$	0.928932	0.0607262
$235$	10.4853	0.683984
$236$	−2.95068	−0.192073
$237$	12.6863	0.824063
$238$	7.98780	0.517772
$239$	9.65685	0.624650	0.312325	−	0.949975i	$-0.398892\pi$
$239$	9.65685	0.624650	0.312325	+	0.949975i	$0.398892\pi$
$240$	5.34267	0.344868
$241$	−24.3214	−1.56668	−0.783339	−	0.621595i	$-0.786485\pi$
$241$	−24.3214	−1.56668	−0.783339	+	0.621595i	$0.786485\pi$
$242$	8.81496	0.566647
$243$	1.78089	0.114244
$244$	1.17157	0.0750023
$245$	−6.31371	−0.403368
$246$	0	0
$247$	0	0
$248$	−10.8284	−0.687606
$249$	−15.7225	−0.996371
$250$	−1.25928	−0.0796439
$251$	20.9706	1.32365	0.661825	−	0.749658i	$-0.269782\pi$
$251$	20.9706	1.32365	0.661825	+	0.749658i	$0.269782\pi$
$252$	0.0588745	0.00370875
$253$	−1.65685	−0.104166
$254$	−22.0416	−1.38301
$255$	−13.6360	−0.853921
$256$	−9.48528	−0.592830
$257$	−20.0219	−1.24893	−0.624466	−	0.781052i	$-0.714684\pi$
$257$	−20.0219	−1.24893	−0.624466	+	0.781052i	$0.714684\pi$
$258$	−10.8284	−0.674148
$259$	0.611105	0.0379722
$260$	1.78089	0.110446
$261$	−1.47534	−0.0913212
$262$	−19.2842	−1.19138
$263$	−16.1421	−0.995367	−0.497683	−	0.867359i	$-0.665816\pi$
$263$	−16.1421	−0.995367	−0.497683	+	0.867359i	$0.665816\pi$
$264$	−10.8284	−0.666444
$265$	7.86123	0.482912
$266$	0	0
$267$	−28.0000	−1.71357
$268$	2.82411	0.172510
$269$	−8.59890	−0.524284	−0.262142	−	0.965029i	$-0.584429\pi$
$269$	−8.59890	−0.524284	−0.262142	+	0.965029i	$0.584429\pi$
$270$	−6.34315	−0.386032
$271$	30.9706	1.88133	0.940664	−	0.339340i	$-0.110204\pi$
$271$	30.9706	1.88133	0.940664	+	0.339340i	$0.110204\pi$
$272$	−22.9706	−1.39279
$273$	−6.34315	−0.383905
$274$	2.51856	0.152152
$275$	2.00000	0.120605
$276$	−0.611105	−0.0367842
$277$	−17.3137	−1.04028	−0.520140	−	0.854081i	$-0.674120\pi$
$277$	−17.3137	−1.04028	−0.520140	+	0.854081i	$0.674120\pi$
$278$	−24.7535	−1.48462
$279$	−0.611105	−0.0365859
$280$	−2.51856	−0.150513
$281$	−14.2471	−0.849912	−0.424956	−	0.905214i	$-0.639711\pi$
$281$	−14.2471	−0.849912	−0.424956	+	0.905214i	$0.639711\pi$
$282$	23.5147	1.40028
$283$	−9.79899	−0.582489	−0.291245	−	0.956649i	$-0.594069\pi$
$283$	−9.79899	−0.582489	−0.291245	+	0.956649i	$0.594069\pi$
$284$	5.64823	0.335161
$285$	0	0
$286$	10.8284	0.640298
$287$	0	0
$288$	−0.395047	−0.0232784
$289$	41.6274	2.44867
$290$	10.8284	0.635867
$291$	7.65685	0.448853
$292$	4.82843	0.282562
$293$	17.9355	1.04780	0.523901	−	0.851779i	$-0.324476\pi$
$293$	17.9355	1.04780	0.523901	+	0.851779i	$0.324476\pi$
$294$	−14.1594	−0.825792
$295$	7.12356	0.414750
$296$	−2.24264	−0.130351
$297$	10.0742	0.584567
$298$	18.6731	1.08171
$299$	3.56178	0.205983
$300$	0.737669	0.0425894
$301$	4.00000	0.230556
$302$	−13.4558	−0.774297
$303$	−0.864233	−0.0496489
$304$	0	0
$305$	−2.82843	−0.161955
$306$	−1.65433	−0.0945716
$307$	−3.25623	−0.185843	−0.0929214	−	0.995673i	$-0.529621\pi$
$307$	−3.25623	−0.185843	−0.0929214	+	0.995673i	$0.529621\pi$
$308$	0.686292	0.0391051
$309$	−9.51472	−0.541273
$310$	4.48528	0.254747
$311$	−20.3431	−1.15355	−0.576777	−	0.816902i	$-0.695690\pi$
$311$	−20.3431	−1.15355	−0.576777	+	0.816902i	$0.695690\pi$
$312$	23.2781	1.31787
$313$	24.6274	1.39202	0.696012	−	0.718030i	$-0.254956\pi$
$313$	24.6274	1.39202	0.696012	+	0.718030i	$0.254956\pi$
$314$	−22.6670	−1.27918
$315$	−0.142136	−0.00800844
$316$	2.95068	0.165989
$317$	5.77479	0.324345	0.162172	−	0.986762i	$-0.448150\pi$
$317$	5.77479	0.324345	0.162172	+	0.986762i	$0.448150\pi$
$318$	17.6299	0.988637
$319$	−17.1978	−0.962892
$320$	8.89949	0.497497
$321$	−24.8284	−1.38579
$322$	−0.864233	−0.0481618
$323$	0	0
$324$	3.92893	0.218274
$325$	−4.29945	−0.238491
$326$	−9.03102	−0.500182
$327$	−33.2548	−1.83900
$328$	0	0
$329$	−8.68629	−0.478891
$330$	4.48528	0.246907
$331$	17.8089	0.978866	0.489433	−	0.872041i	$-0.337204\pi$
$331$	17.8089	0.978866	0.489433	+	0.872041i	$0.337204\pi$
$332$	−3.65685	−0.200696
$333$	−0.126564	−0.00693567
$334$	−21.2721	−1.16396
$335$	−6.81801	−0.372508
$336$	−4.42602	−0.241459
$337$	13.5095	0.735907	0.367954	−	0.929844i	$-0.380059\pi$
$337$	13.5095	0.735907	0.367954	+	0.929844i	$0.380059\pi$
$338$	−6.90751	−0.375719
$339$	−16.6274	−0.903077
$340$	−3.17157	−0.172003
$341$	−7.12356	−0.385763
$342$	0	0
$343$	11.0294	0.595534
$344$	−14.6792	−0.791452
$345$	1.47534	0.0794296
$346$	3.55635	0.191191
$347$	19.1716	1.02918	0.514592	−	0.857435i	$-0.327943\pi$
$347$	19.1716	1.02918	0.514592	+	0.857435i	$0.327943\pi$
$348$	−6.34315	−0.340028
$349$	−29.3137	−1.56913	−0.784563	−	0.620049i	$-0.787113\pi$
$349$	−29.3137	−1.56913	−0.784563	+	0.620049i	$0.787113\pi$
$350$	1.04322	0.0557626
$351$	−21.6569	−1.15596
$352$	−4.60500	−0.245448
$353$	7.65685	0.407533	0.203767	−	0.979019i	$-0.434682\pi$
$353$	7.65685	0.407533	0.203767	+	0.979019i	$0.434682\pi$
$354$	15.9756	0.849093
$355$	−13.6360	−0.723725
$356$	−6.51246	−0.345160
$357$	11.2965	0.597872
$358$	21.6569	1.14460
$359$	−2.68629	−0.141777	−0.0708885	−	0.997484i	$-0.522583\pi$
$359$	−2.68629	−0.141777	−0.0708885	+	0.997484i	$0.522583\pi$
$360$	0.521611	0.0274913
$361$	0	0
$362$	−12.6863	−0.666777
$363$	12.4662	0.654308
$364$	−1.47534	−0.0773287
$365$	−11.6569	−0.610148
$366$	−6.34315	−0.331562
$367$	3.17157	0.165555	0.0827774	−	0.996568i	$-0.473621\pi$
$367$	3.17157	0.165555	0.0827774	+	0.996568i	$0.473621\pi$
$368$	2.48528	0.129554
$369$	0	0
$370$	0.928932	0.0482929
$371$	−6.51246	−0.338110
$372$	−2.62742	−0.136225
$373$	10.8119	0.559819	0.279910	−	0.960026i	$-0.409695\pi$
$373$	10.8119	0.559819	0.279910	+	0.960026i	$0.409695\pi$
$374$	−19.2842	−0.997165
$375$	−1.78089	−0.0919648
$376$	31.8771	1.64393
$377$	36.9706	1.90408
$378$	5.25483	0.270279
$379$	17.1978	0.883392	0.441696	−	0.897165i	$-0.354377\pi$
$379$	17.1978	0.883392	0.441696	+	0.897165i	$0.354377\pi$
$380$	0	0
$381$	−31.1716	−1.59697
$382$	2.95068	0.150970
$383$	−32.6147	−1.66653	−0.833267	−	0.552871i	$-0.813532\pi$
$383$	−32.6147	−1.66653	−0.833267	+	0.552871i	$0.813532\pi$
$384$	11.7574	0.599990
$385$	−1.65685	−0.0844411
$386$	−25.2132	−1.28332
$387$	−0.828427	−0.0421113
$388$	1.78089	0.0904110
$389$	−20.6274	−1.04585	−0.522926	−	0.852378i	$-0.675160\pi$
$389$	−20.6274	−1.04585	−0.522926	+	0.852378i	$0.675160\pi$
$390$	−9.64212	−0.488248
$391$	−6.34315	−0.320787
$392$	−19.1948	−0.969482
$393$	−27.2720	−1.37569
$394$	−11.7286	−0.590877
$395$	−7.12356	−0.358425
$396$	−0.142136	−0.00714258
$397$	−14.0000	−0.702640	−0.351320	−	0.936255i	$-0.614267\pi$
$397$	−14.0000	−0.702640	−0.351320	+	0.936255i	$0.614267\pi$
$398$	5.03712	0.252488
$399$	0	0
$400$	−3.00000	−0.150000
$401$	10.0742	0.503084	0.251542	−	0.967846i	$-0.419062\pi$
$401$	10.0742	0.503084	0.251542	+	0.967846i	$0.419062\pi$
$402$	−15.2904	−0.762613
$403$	15.3137	0.762830
$404$	−0.201010	−0.0100006
$405$	−9.48528	−0.471327
$406$	−8.97056	−0.445202
$407$	−1.47534	−0.0731298
$408$	−41.4558	−2.05237
$409$	−12.7718	−0.631524	−0.315762	−	0.948838i	$-0.602260\pi$
$409$	−12.7718	−0.631524	−0.315762	+	0.948838i	$0.602260\pi$
$410$	0	0
$411$	3.56178	0.175690
$412$	−2.21301	−0.109027
$413$	−5.90135	−0.290387
$414$	0.178989	0.00879681
$415$	8.82843	0.433370
$416$	9.89949	0.485363
$417$	−35.0067	−1.71429
$418$	0	0
$419$	−24.9706	−1.21989	−0.609946	−	0.792443i	$-0.708809\pi$
$419$	−24.9706	−1.21989	−0.609946	+	0.792443i	$0.708809\pi$
$420$	−0.611105	−0.0298189
$421$	10.0742	0.490988	0.245494	−	0.969398i	$-0.421050\pi$
$421$	10.0742	0.490988	0.245494	+	0.969398i	$0.421050\pi$
$422$	−17.1716	−0.835899
$423$	1.79899	0.0874699
$424$	23.8995	1.16066
$425$	7.65685	0.371412
$426$	−30.5807	−1.48164
$427$	2.34315	0.113393
$428$	−5.77479	−0.279135
$429$	15.3137	0.739353
$430$	6.08034	0.293220
$431$	−3.56178	−0.171565	−0.0857825	−	0.996314i	$-0.527339\pi$
$431$	−3.56178	−0.171565	−0.0857825	+	0.996314i	$0.527339\pi$
$432$	−15.1114	−0.727046
$433$	−4.91056	−0.235986	−0.117993	−	0.993014i	$-0.537646\pi$
$433$	−4.91056	−0.235986	−0.117993	+	0.993014i	$0.537646\pi$
$434$	−3.71573	−0.178361
$435$	15.3137	0.734236
$436$	−7.73467	−0.370423
$437$	0	0
$438$	−26.1421	−1.24912
$439$	−2.95068	−0.140828	−0.0704141	−	0.997518i	$-0.522432\pi$
$439$	−2.95068	−0.140828	−0.0704141	+	0.997518i	$0.522432\pi$
$440$	6.08034	0.289869
$441$	−1.08326	−0.0515839
$442$	41.4558	1.97185
$443$	20.1421	0.956982	0.478491	−	0.878093i	$-0.341184\pi$
$443$	20.1421	0.956982	0.478491	+	0.878093i	$0.341184\pi$
$444$	−0.544156	−0.0258245
$445$	15.7225	0.745316
$446$	0.384776	0.0182197
$447$	26.4078	1.24905
$448$	−7.37258	−0.348322
$449$	8.59890	0.405807	0.202904	−	0.979199i	$-0.434962\pi$
$449$	8.59890	0.405807	0.202904	+	0.979199i	$0.434962\pi$
$450$	−0.216058	−0.0101851
$451$	0	0
$452$	−3.86733	−0.181904
$453$	−19.0294	−0.894081
$454$	−21.2721	−0.998348
$455$	3.56178	0.166979
$456$	0	0
$457$	5.31371	0.248565	0.124282	−	0.992247i	$-0.460337\pi$
$457$	5.31371	0.248565	0.124282	+	0.992247i	$0.460337\pi$
$458$	5.64823	0.263924
$459$	38.5685	1.80022
$460$	0.343146	0.0159993
$461$	−10.6863	−0.497710	−0.248855	−	0.968541i	$-0.580054\pi$
$461$	−10.6863	−0.497710	−0.248855	+	0.968541i	$0.580054\pi$
$462$	−3.71573	−0.172871
$463$	−32.8284	−1.52567	−0.762833	−	0.646595i	$-0.776192\pi$
$463$	−32.8284	−1.52567	−0.762833	+	0.646595i	$0.776192\pi$
$464$	25.7967	1.19758
$465$	6.34315	0.294156
$466$	11.7286	0.543315
$467$	38.4853	1.78089	0.890443	−	0.455094i	$-0.150394\pi$
$467$	38.4853	1.78089	0.890443	+	0.455094i	$0.150394\pi$
$468$	0.305553	0.0141242
$469$	5.64823	0.260811
$470$	−13.2039	−0.609051
$471$	−32.0560	−1.47706
$472$	21.6569	0.996838
$473$	−9.65685	−0.444023
$474$	−15.9756	−0.733783
$475$	0	0
$476$	2.62742	0.120427
$477$	1.34877	0.0617561
$478$	−12.1607	−0.556217
$479$	10.0000	0.456912	0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000	0.456912	0.228456	+	0.973554i	$0.426632\pi$
$480$	4.10051	0.187162
$481$	3.17157	0.144611
$482$	30.6274	1.39504
$483$	−1.22221	−0.0556125
$484$	2.89949	0.131795
$485$	−4.29945	−0.195228
$486$	−2.24264	−0.101728
$487$	29.6640	1.34421	0.672103	−	0.740458i	$-0.265391\pi$
$487$	29.6640	1.34421	0.672103	+	0.740458i	$0.265391\pi$
$488$	−8.59890	−0.389254
$489$	−12.7718	−0.577560
$490$	7.95073	0.359177
$491$	32.2843	1.45697	0.728484	−	0.685062i	$-0.240225\pi$
$491$	32.2843	1.45697	0.728484	+	0.685062i	$0.240225\pi$
$492$	0	0
$493$	−65.8405	−2.96531
$494$	0	0
$495$	0.343146	0.0154233
$496$	10.6853	0.479786
$497$	11.2965	0.506715
$498$	19.7990	0.887214
$499$	1.02944	0.0460839	0.0230420	−	0.999734i	$-0.492665\pi$
$499$	1.02944	0.0460839	0.0230420	+	0.999734i	$0.492665\pi$
$500$	−0.414214	−0.0185242
$501$	−30.0833	−1.34402
$502$	−26.4078	−1.17864
$503$	2.48528	0.110813	0.0554066	−	0.998464i	$-0.482354\pi$
$503$	2.48528	0.110813	0.0554066	+	0.998464i	$0.482354\pi$
$504$	−0.432117	−0.0192480
$505$	0.485281	0.0215947
$506$	2.08644	0.0927537
$507$	−9.76869	−0.433843
$508$	−7.25013	−0.321672
$509$	32.9203	1.45917	0.729583	−	0.683893i	$-0.239714\pi$
$509$	32.9203	1.45917	0.729583	+	0.683893i	$0.239714\pi$
$510$	17.1716	0.760370
$511$	9.65685	0.427194
$512$	25.1485	1.11142
$513$	0	0
$514$	25.2132	1.11211
$515$	5.34267	0.235426
$516$	−3.56178	−0.156799
$517$	20.9706	0.922284
$518$	−0.769553	−0.0338122
$519$	5.02944	0.220768
$520$	−13.0711	−0.573204
$521$	17.1978	0.753450	0.376725	−	0.926325i	$-0.377050\pi$
$521$	17.1978	0.753450	0.376725	+	0.926325i	$0.377050\pi$
$522$	1.85786	0.0813165
$523$	−15.4169	−0.674135	−0.337067	−	0.941481i	$-0.609435\pi$
$523$	−15.4169	−0.674135	−0.337067	+	0.941481i	$0.609435\pi$
$524$	−6.34315	−0.277102
$525$	1.47534	0.0643890
$526$	20.3275	0.886320
$527$	−27.2720	−1.18799
$528$	10.6853	0.465020
$529$	−22.3137	−0.970161
$530$	−9.89949	−0.430007
$531$	1.22221	0.0530394
$532$	0	0
$533$	0	0
$534$	35.2598	1.52584
$535$	13.9416	0.602747
$536$	−20.7279	−0.895310
$537$	30.6274	1.32167
$538$	10.8284	0.466847
$539$	−12.6274	−0.543901
$540$	−2.08644	−0.0897862
$541$	22.1421	0.951965	0.475982	−	0.879455i	$-0.342093\pi$
$541$	22.1421	0.951965	0.475982	+	0.879455i	$0.342093\pi$
$542$	−39.0006	−1.67522
$543$	−17.9411	−0.769927
$544$	−17.6299	−0.755877
$545$	18.6731	0.799870
$546$	7.98780	0.341846
$547$	−11.8551	−0.506889	−0.253444	−	0.967350i	$-0.581563\pi$
$547$	−11.8551	−0.506889	−0.253444	+	0.967350i	$0.581563\pi$
$548$	0.828427	0.0353887
$549$	−0.485281	−0.0207113
$550$	−2.51856	−0.107392
$551$	0	0
$552$	4.48528	0.190906
$553$	5.90135	0.250951
$554$	21.8028	0.926313
$555$	1.31371	0.0557638
$556$	−8.14214	−0.345303
$557$	−28.6274	−1.21298	−0.606491	−	0.795090i	$-0.707424\pi$
$557$	−28.6274	−1.21298	−0.606491	+	0.795090i	$0.707424\pi$
$558$	0.769553	0.0325778
$559$	20.7596	0.878037
$560$	2.48528	0.105022
$561$	−27.2720	−1.15143
$562$	17.9411	0.756801
$563$	26.1023	1.10008	0.550040	−	0.835139i	$-0.314613\pi$
$563$	26.1023	1.10008	0.550040	+	0.835139i	$0.314613\pi$
$564$	7.73467	0.325688
$565$	9.33657	0.392793
$566$	12.3397	0.518675
$567$	7.85786	0.329999
$568$	−41.4558	−1.73945
$569$	15.7225	0.659120	0.329560	−	0.944135i	$-0.393100\pi$
$569$	15.7225	0.659120	0.329560	+	0.944135i	$0.393100\pi$
$570$	0	0
$571$	13.3137	0.557161	0.278581	−	0.960413i	$-0.410136\pi$
$571$	13.3137	0.557161	0.278581	+	0.960413i	$0.410136\pi$
$572$	3.56178	0.148926
$573$	4.17289	0.174325
$574$	0	0
$575$	−0.828427	−0.0345478
$576$	1.52691	0.0636213
$577$	10.0000	0.416305	0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000	0.416305	0.208153	+	0.978096i	$0.433255\pi$
$578$	−52.4206	−2.18041
$579$	−35.6569	−1.48185
$580$	3.56178	0.147895
$581$	−7.31371	−0.303424
$582$	−9.64212	−0.399679
$583$	15.7225	0.651158
$584$	−35.4388	−1.46647
$585$	−0.737669	−0.0304989
$586$	−22.5858	−0.933010
$587$	18.4853	0.762969	0.381485	−	0.924375i	$-0.375413\pi$
$587$	18.4853	0.762969	0.381485	+	0.924375i	$0.375413\pi$
$588$	−4.65743	−0.192069
$589$	0	0
$590$	−8.97056	−0.369312
$591$	−16.5867	−0.682286
$592$	2.21301	0.0909541
$593$	−9.31371	−0.382468	−0.191234	−	0.981544i	$-0.561249\pi$
$593$	−9.31371	−0.382468	−0.191234	+	0.981544i	$0.561249\pi$
$594$	−12.6863	−0.520525
$595$	−6.34315	−0.260044
$596$	6.14214	0.251592
$597$	7.12356	0.291548
$598$	−4.48528	−0.183417
$599$	34.3956	1.40537	0.702683	−	0.711503i	$-0.251985\pi$
$599$	34.3956	1.40537	0.702683	+	0.711503i	$0.251985\pi$
$600$	−5.41421	−0.221034
$601$	17.1978	0.701513	0.350757	−	0.936467i	$-0.385924\pi$
$601$	17.1978	0.701513	0.350757	+	0.936467i	$0.385924\pi$
$602$	−5.03712	−0.205298
$603$	−1.16979	−0.0476374
$604$	−4.42602	−0.180092
$605$	−7.00000	−0.284590
$606$	1.08831	0.0442096
$607$	−33.2258	−1.34859	−0.674297	−	0.738460i	$-0.735553\pi$
$607$	−33.2258	−1.34859	−0.674297	+	0.738460i	$0.735553\pi$
$608$	0	0
$609$	−12.6863	−0.514074
$610$	3.56178	0.144212
$611$	−45.0810	−1.82378
$612$	−0.544156	−0.0219962
$613$	−14.2843	−0.576936	−0.288468	−	0.957489i	$-0.593146\pi$
$613$	−14.2843	−0.576936	−0.288468	+	0.957489i	$0.593146\pi$
$614$	4.10051	0.165483
$615$	0	0
$616$	−5.03712	−0.202951
$617$	30.2843	1.21920	0.609599	−	0.792710i	$-0.291330\pi$
$617$	30.2843	1.21920	0.609599	+	0.792710i	$0.291330\pi$
$618$	11.9817	0.481975
$619$	−18.9706	−0.762491	−0.381246	−	0.924474i	$-0.624505\pi$
$619$	−18.9706	−0.762491	−0.381246	+	0.924474i	$0.624505\pi$
$620$	1.47534	0.0592510
$621$	−4.17289	−0.167452
$622$	25.6177	1.02718
$623$	−13.0249	−0.521832
$624$	−22.9706	−0.919558
$625$	1.00000	0.0400000
$626$	−31.0128	−1.23952
$627$	0	0
$628$	−7.45584	−0.297521
$629$	−5.64823	−0.225210
$630$	0.178989	0.00713108
$631$	18.2843	0.727885	0.363943	−	0.931421i	$-0.381430\pi$
$631$	18.2843	0.727885	0.363943	+	0.931421i	$0.381430\pi$
$632$	−21.6569	−0.861463
$633$	−24.2843	−0.965213
$634$	−7.27208	−0.288811
$635$	17.5034	0.694600
$636$	5.79899	0.229945
$637$	27.1455	1.07554
$638$	21.6569	0.857403
$639$	−2.33957	−0.0925520
$640$	−6.60195	−0.260965
$641$	21.3707	0.844092	0.422046	−	0.906575i	$-0.361312\pi$
$641$	21.3707	0.844092	0.422046	+	0.906575i	$0.361312\pi$
$642$	31.2659	1.23397
$643$	9.51472	0.375224	0.187612	−	0.982243i	$-0.439925\pi$
$643$	9.51472	0.375224	0.187612	+	0.982243i	$0.439925\pi$
$644$	−0.284271	−0.0112019
$645$	8.59890	0.338581
$646$	0	0
$647$	−27.1716	−1.06822	−0.534112	−	0.845413i	$-0.679354\pi$
$647$	−27.1716	−1.06822	−0.534112	+	0.845413i	$0.679354\pi$
$648$	−28.8369	−1.13282
$649$	14.2471	0.559249
$650$	5.41421	0.212363
$651$	−5.25483	−0.205953
$652$	−2.97056	−0.116336
$653$	27.6569	1.08230	0.541148	−	0.840927i	$-0.317990\pi$
$653$	27.6569	1.08230	0.541148	+	0.840927i	$0.317990\pi$
$654$	41.8772	1.63753
$655$	15.3137	0.598356
$656$	0	0
$657$	−2.00000	−0.0780274
$658$	10.9385	0.426426
$659$	20.1485	0.784873	0.392437	−	0.919779i	$-0.371632\pi$
$659$	20.1485	0.784873	0.392437	+	0.919779i	$0.371632\pi$
$660$	1.47534	0.0574275
$661$	−2.95068	−0.114768	−0.0573840	−	0.998352i	$-0.518276\pi$
$661$	−2.95068	−0.114768	−0.0573840	+	0.998352i	$0.518276\pi$
$662$	−22.4264	−0.871627
$663$	58.6274	2.27690
$664$	26.8399	1.04159
$665$	0	0
$666$	0.159380	0.00617583
$667$	7.12356	0.275826
$668$	−6.99700	−0.270722
$669$	0.544156	0.0210383
$670$	8.58579	0.331698
$671$	−5.65685	−0.218380
$672$	−3.39697	−0.131041
$673$	−50.8557	−1.96034	−0.980172	−	0.198146i	$-0.936508\pi$
$673$	−50.8557	−1.96034	−0.980172	+	0.198146i	$0.936508\pi$
$674$	−17.0122	−0.655285
$675$	5.03712	0.193879
$676$	−2.27208	−0.0873876
$677$	−2.21301	−0.0850528	−0.0425264	−	0.999095i	$-0.513541\pi$
$677$	−2.21301	−0.0850528	−0.0425264	+	0.999095i	$0.513541\pi$
$678$	20.9386	0.804141
$679$	3.56178	0.136689
$680$	23.2781	0.892676
$681$	−30.0833	−1.15279
$682$	8.97056	0.343501
$683$	11.8551	0.453624	0.226812	−	0.973939i	$-0.427170\pi$
$683$	11.8551	0.453624	0.226812	+	0.973939i	$0.427170\pi$
$684$	0	0
$685$	−2.00000	−0.0764161
$686$	−13.8892	−0.530290
$687$	7.98780	0.304753
$688$	14.4853	0.552246
$689$	−33.7990	−1.28764
$690$	−1.85786	−0.0707277
$691$	16.6274	0.632537	0.316268	−	0.948670i	$-0.397570\pi$
$691$	16.6274	0.632537	0.316268	+	0.948670i	$0.397570\pi$
$692$	1.16979	0.0444686
$693$	−0.284271	−0.0107986
$694$	−24.1424	−0.916432
$695$	19.6569	0.745627
$696$	46.5563	1.76471
$697$	0	0
$698$	36.9142	1.39722
$699$	16.5867	0.627367
$700$	0.343146	0.0129697
$701$	−24.4853	−0.924796	−0.462398	−	0.886672i	$-0.653011\pi$
$701$	−24.4853	−0.924796	−0.462398	+	0.886672i	$0.653011\pi$
$702$	27.2720	1.02932
$703$	0	0
$704$	17.7990	0.670825
$705$	−18.6731	−0.703271
$706$	−9.64212	−0.362886
$707$	−0.402020	−0.0151195
$708$	5.25483	0.197489
$709$	−5.31371	−0.199561	−0.0997803	−	0.995009i	$-0.531814\pi$
$709$	−5.31371	−0.199561	−0.0997803	+	0.995009i	$0.531814\pi$
$710$	17.1716	0.644438
$711$	−1.22221	−0.0458365
$712$	47.7990	1.79134
$713$	2.95068	0.110504
$714$	−14.2254	−0.532372
$715$	−8.59890	−0.321581
$716$	7.12356	0.266220
$717$	−17.1978	−0.642264
$718$	3.38279	0.126245
$719$	31.9411	1.19120	0.595601	−	0.803280i	$-0.296914\pi$
$719$	31.9411	1.19120	0.595601	+	0.803280i	$0.296914\pi$
$720$	−0.514719	−0.0191824
$721$	−4.42602	−0.164833
$722$	0	0
$723$	43.3137	1.61085
$724$	−4.17289	−0.155084
$725$	−8.59890	−0.319355
$726$	−15.6985	−0.582625
$727$	6.48528	0.240526	0.120263	−	0.992742i	$-0.461626\pi$
$727$	6.48528	0.240526	0.120263	+	0.992742i	$0.461626\pi$
$728$	10.8284	0.401328
$729$	25.2843	0.936454
$730$	14.6792	0.543303
$731$	−36.9706	−1.36741
$732$	−2.08644	−0.0771172
$733$	−35.6569	−1.31702	−0.658508	−	0.752574i	$-0.728812\pi$
$733$	−35.6569	−1.31702	−0.658508	+	0.752574i	$0.728812\pi$
$734$	−3.99390	−0.147417
$735$	11.2440	0.414742
$736$	1.90746	0.0703097
$737$	−13.6360	−0.502289
$738$	0	0
$739$	1.37258	0.0504913	0.0252456	−	0.999681i	$-0.491963\pi$
$739$	1.37258	0.0504913	0.0252456	+	0.999681i	$0.491963\pi$
$740$	0.305553	0.0112323
$741$	0	0
$742$	8.20101	0.301069
$743$	−6.81801	−0.250129	−0.125064	−	0.992149i	$-0.539914\pi$
$743$	−6.81801	−0.250129	−0.125064	+	0.992149i	$0.539914\pi$
$744$	19.2842	0.706995
$745$	−14.8284	−0.543272
$746$	−13.6152	−0.498489
$747$	1.51472	0.0554207
$748$	−6.34315	−0.231928
$749$	−11.5496	−0.422012
$750$	2.24264	0.0818897
$751$	6.51246	0.237643	0.118822	−	0.992916i	$-0.462088\pi$
$751$	6.51246	0.237643	0.118822	+	0.992916i	$0.462088\pi$
$752$	−31.4558	−1.14708
$753$	−37.3463	−1.36097
$754$	−46.5563	−1.69548
$755$	10.6853	0.388880
$756$	1.72847	0.0628637
$757$	−6.68629	−0.243017	−0.121509	−	0.992590i	$-0.538773\pi$
$757$	−6.68629	−0.243017	−0.121509	+	0.992590i	$0.538773\pi$
$758$	−21.6569	−0.786612
$759$	2.95068	0.107103
$760$	0	0
$761$	−9.17157	−0.332469	−0.166235	−	0.986086i	$-0.553161\pi$
$761$	−9.17157	−0.332469	−0.166235	+	0.986086i	$0.553161\pi$
$762$	39.2537	1.42201
$763$	−15.4693	−0.560028
$764$	0.970563	0.0351137
$765$	1.31371	0.0474972
$766$	41.0711	1.48396
$767$	−30.6274	−1.10589
$768$	16.8923	0.609547
$769$	14.1421	0.509978	0.254989	−	0.966944i	$-0.417928\pi$
$769$	14.1421	0.509978	0.254989	+	0.966944i	$0.417928\pi$
$770$	2.08644	0.0751902
$771$	35.6569	1.28415
$772$	−8.29335	−0.298484
$773$	−18.5466	−0.667074	−0.333537	−	0.942737i	$-0.608242\pi$
$773$	−18.5466	−0.667074	−0.333537	+	0.942737i	$0.608242\pi$
$774$	1.04322	0.0374978
$775$	−3.56178	−0.127943
$776$	−13.0711	−0.469224
$777$	−1.08831	−0.0390430
$778$	25.9757	0.931274
$779$	0	0
$780$	−3.17157	−0.113561
$781$	−27.2720	−0.975871
$782$	7.98780	0.285643
$783$	−43.3137	−1.54791
$784$	18.9411	0.676469
$785$	18.0000	0.642448
$786$	34.3431	1.22498
$787$	−46.2507	−1.64866	−0.824330	−	0.566109i	$-0.808448\pi$
$787$	−46.2507	−1.64866	−0.824330	+	0.566109i	$0.808448\pi$
$788$	−3.85786	−0.137431
$789$	28.7474	1.02343
$790$	8.97056	0.319158
$791$	−7.73467	−0.275013
$792$	1.04322	0.0370693
$793$	12.1607	0.431839
$794$	17.6299	0.625663
$795$	−14.0000	−0.496529
$796$	1.65685	0.0587256
$797$	0.737669	0.0261296	0.0130648	−	0.999915i	$-0.495841\pi$
$797$	0.737669	0.0261296	0.0130648	+	0.999915i	$0.495841\pi$
$798$	0	0
$799$	80.2843	2.84025
$800$	−2.30250	−0.0814057
$801$	2.69755	0.0953132
$802$	−12.6863	−0.447969
$803$	−23.3137	−0.822723
$804$	−5.02944	−0.177375
$805$	0.686292	0.0241886
$806$	−19.2842	−0.679259
$807$	15.3137	0.539068
$808$	1.47534	0.0519022
$809$	−13.3137	−0.468085	−0.234043	−	0.972226i	$-0.575196\pi$
$809$	−13.3137	−0.468085	−0.234043	+	0.972226i	$0.575196\pi$
$810$	11.9446	0.419691
$811$	33.7845	1.18633	0.593167	−	0.805079i	$-0.297877\pi$
$811$	33.7845	1.18633	0.593167	+	0.805079i	$0.297877\pi$
$812$	−2.95068	−0.103548
$813$	−55.1552	−1.93438
$814$	1.85786	0.0651181
$815$	7.17157	0.251209
$816$	40.9081	1.43207
$817$	0	0
$818$	16.0833	0.562338
$819$	0.611105	0.0213537
$820$	0	0
$821$	2.68629	0.0937522	0.0468761	−	0.998901i	$-0.485073\pi$
$821$	2.68629	0.0937522	0.0468761	+	0.998901i	$0.485073\pi$
$822$	−4.48528	−0.156442
$823$	42.0833	1.46693	0.733465	−	0.679727i	$-0.237902\pi$
$823$	42.0833	1.46693	0.733465	+	0.679727i	$0.237902\pi$
$824$	16.2426	0.565839
$825$	−3.56178	−0.124005
$826$	7.43146	0.258573
$827$	18.9787	0.659954	0.329977	−	0.943989i	$-0.392959\pi$
$827$	18.9787	0.659954	0.329977	+	0.943989i	$0.392959\pi$
$828$	0.0588745	0.00204603
$829$	−42.9945	−1.49326	−0.746631	−	0.665239i	$-0.768330\pi$
$829$	−42.9945	−1.49326	−0.746631	+	0.665239i	$0.768330\pi$
$830$	−11.1175	−0.385893
$831$	30.8338	1.06961
$832$	−38.2629	−1.32653
$833$	−48.3431	−1.67499
$834$	44.0833	1.52648
$835$	16.8923	0.584581
$836$	0	0
$837$	−17.9411	−0.620136
$838$	31.4449	1.08625
$839$	31.4449	1.08560	0.542800	−	0.839862i	$-0.317364\pi$
$839$	31.4449	1.08560	0.542800	+	0.839862i	$0.317364\pi$
$840$	4.48528	0.154757
$841$	44.9411	1.54969
$842$	−12.6863	−0.437198
$843$	25.3726	0.873878
$844$	−5.64823	−0.194420
$845$	5.48528	0.188699
$846$	−2.26543	−0.0778872
$847$	5.79899	0.199256
$848$	−23.5837	−0.809868
$849$	17.4509	0.598914
$850$	−9.64212	−0.330722
$851$	0.611105	0.0209484
$852$	−10.0589	−0.344611
$853$	36.3431	1.24437	0.622183	−	0.782872i	$-0.286246\pi$
$853$	36.3431	1.24437	0.622183	+	0.782872i	$0.286246\pi$
$854$	−2.95068	−0.100970
$855$	0	0
$856$	42.3848	1.44868
$857$	−17.0712	−0.583142	−0.291571	−	0.956549i	$-0.594178\pi$
$857$	−17.0712	−0.583142	−0.291571	+	0.956549i	$0.594178\pi$
$858$	−19.2842	−0.658353
$859$	−44.2843	−1.51096	−0.755480	−	0.655172i	$-0.772596\pi$
$859$	−44.2843	−1.51096	−0.755480	+	0.655172i	$0.772596\pi$
$860$	2.00000	0.0681994
$861$	0	0
$862$	4.48528	0.152769
$863$	24.6269	0.838310	0.419155	−	0.907915i	$-0.362326\pi$
$863$	24.6269	0.838310	0.419155	+	0.907915i	$0.362326\pi$
$864$	−11.5980	−0.394571
$865$	−2.82411	−0.0960227
$866$	6.18377	0.210133
$867$	−74.1339	−2.51772
$868$	−1.22221	−0.0414845
$869$	−14.2471	−0.483301
$870$	−19.2842	−0.653797
$871$	29.3137	0.993257
$872$	56.7696	1.92246
$873$	−0.737669	−0.0249663
$874$	0	0
$875$	−0.828427	−0.0280059
$876$	−8.59890	−0.290530
$877$	10.8119	0.365092	0.182546	−	0.983197i	$-0.441566\pi$
$877$	10.8119	0.365092	0.182546	+	0.983197i	$0.441566\pi$
$878$	3.71573	0.125400
$879$	−31.9411	−1.07735
$880$	−6.00000	−0.202260
$881$	4.48528	0.151113	0.0755565	−	0.997142i	$-0.475927\pi$
$881$	4.48528	0.151113	0.0755565	+	0.997142i	$0.475927\pi$
$882$	1.36413	0.0459326
$883$	3.85786	0.129827	0.0649137	−	0.997891i	$-0.479323\pi$
$883$	3.85786	0.129827	0.0649137	+	0.997891i	$0.479323\pi$
$884$	13.6360	0.458629
$885$	−12.6863	−0.426445
$886$	−25.3646	−0.852140
$887$	−1.16979	−0.0392776	−0.0196388	−	0.999807i	$-0.506252\pi$
$887$	−1.16979	−0.0392776	−0.0196388	+	0.999807i	$0.506252\pi$
$888$	3.99390	0.134026
$889$	−14.5003	−0.486323
$890$	−19.7990	−0.663664
$891$	−18.9706	−0.635538
$892$	0.126564	0.00423768
$893$	0	0
$894$	−33.2548	−1.11221
$895$	−17.1978	−0.574859
$896$	5.46924	0.182714
$897$	−6.34315	−0.211791
$898$	−10.8284	−0.361349
$899$	30.6274	1.02148
$900$	−0.0710678	−0.00236893
$901$	60.1923	2.00530
$902$	0	0
$903$	−7.12356	−0.237057
$904$	28.3848	0.944064
$905$	10.0742	0.334879
$906$	23.9634	0.796130
$907$	−30.5283	−1.01367	−0.506837	−	0.862042i	$-0.669186\pi$
$907$	−30.5283	−1.01367	−0.506837	+	0.862042i	$0.669186\pi$
$908$	−6.99700	−0.232204
$909$	0.0832611	0.00276160
$910$	−4.48528	−0.148686
$911$	26.6609	0.883316	0.441658	−	0.897183i	$-0.354390\pi$
$911$	26.6609	0.883316	0.441658	+	0.897183i	$0.354390\pi$
$912$	0	0
$913$	17.6569	0.584357
$914$	−6.69145	−0.221333
$915$	5.03712	0.166522
$916$	1.85786	0.0613856
$917$	−12.6863	−0.418938
$918$	−48.5685	−1.60300
$919$	0.284271	0.00937724	0.00468862	−	0.999989i	$-0.498508\pi$
$919$	0.284271	0.00937724	0.00468862	+	0.999989i	$0.498508\pi$
$920$	−2.51856	−0.0830345
$921$	5.79899	0.191083
$922$	13.4570	0.443184
$923$	58.6274	1.92974
$924$	−1.22221	−0.0402078
$925$	−0.737669	−0.0242544
$926$	41.3402	1.35852
$927$	0.916658	0.0301070
$928$	19.7990	0.649934
$929$	−6.00000	−0.196854	−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000	−0.196854	−0.0984268	+	0.995144i	$0.531381\pi$
$930$	−7.98780	−0.261930
$931$	0	0
$932$	3.85786	0.126369
$933$	36.2289	1.18608
$934$	−48.4638	−1.58578
$935$	15.3137	0.500812
$936$	−2.24264	−0.0733030
$937$	10.9706	0.358393	0.179196	−	0.983813i	$-0.442650\pi$
$937$	10.9706	0.358393	0.179196	+	0.983813i	$0.442650\pi$
$938$	−7.11270	−0.232238
$939$	−43.8587	−1.43128
$940$	−4.34315	−0.141658
$941$	−2.95068	−0.0961893	−0.0480947	−	0.998843i	$-0.515315\pi$
$941$	−2.95068	−0.0961893	−0.0480947	+	0.998843i	$0.515315\pi$
$942$	40.3675	1.31525
$943$	0	0
$944$	−21.3707	−0.695557
$945$	−4.17289	−0.135744
$946$	12.1607	0.395378
$947$	−4.14214	−0.134601	−0.0673007	−	0.997733i	$-0.521439\pi$
$947$	−4.14214	−0.134601	−0.0673007	+	0.997733i	$0.521439\pi$
$948$	−5.25483	−0.170669
$949$	50.1181	1.62690
$950$	0	0
$951$	−10.2843	−0.333490
$952$	−19.2842	−0.625006
$953$	1.34877	0.0436911	0.0218455	−	0.999761i	$-0.493046\pi$
$953$	1.34877	0.0436911	0.0218455	+	0.999761i	$0.493046\pi$
$954$	−1.69848	−0.0549905
$955$	−2.34315	−0.0758224
$956$	−4.00000	−0.129369
$957$	30.6274	0.990044
$958$	−12.5928	−0.406855
$959$	1.65685	0.0535026
$960$	−15.8490	−0.511525
$961$	−18.3137	−0.590765
$962$	−3.99390	−0.128768
$963$	2.39200	0.0770810
$964$	10.0742	0.324469
$965$	20.0219	0.644528
$966$	1.53911	0.0495199
$967$	21.5147	0.691867	0.345933	−	0.938259i	$-0.387562\pi$
$967$	21.5147	0.691867	0.345933	+	0.938259i	$0.387562\pi$
$968$	−21.2812	−0.684004
$969$	0	0
$970$	5.41421	0.173840
$971$	−7.73467	−0.248217	−0.124109	−	0.992269i	$-0.539607\pi$
$971$	−7.73467	−0.248217	−0.124109	+	0.992269i	$0.539607\pi$
$972$	−0.737669	−0.0236608
$973$	−16.2843	−0.522050
$974$	−37.3553	−1.19694
$975$	7.65685	0.245216
$976$	8.48528	0.271607
$977$	−47.9051	−1.53262	−0.766309	−	0.642472i	$-0.777909\pi$
$977$	−47.9051	−1.53262	−0.766309	+	0.642472i	$0.777909\pi$
$978$	16.0833	0.514286
$979$	31.4449	1.00498
$980$	2.61522	0.0835403
$981$	3.20380	0.102290
$982$	−40.6549	−1.29735
$983$	−33.8369	−1.07923	−0.539615	−	0.841912i	$-0.681430\pi$
$983$	−33.8369	−1.07923	−0.539615	+	0.841912i	$0.681430\pi$
$984$	0	0
$985$	9.31371	0.296759
$986$	82.9117	2.64045
$987$	15.4693	0.492394
$988$	0	0
$989$	4.00000	0.127193
$990$	−0.432117	−0.0137336
$991$	−27.8832	−0.885737	−0.442869	−	0.896586i	$-0.646039\pi$
$991$	−27.8832	−0.885737	−0.442869	+	0.896586i	$0.646039\pi$
$992$	8.20101	0.260382
$993$	−31.7157	−1.00647
$994$	−14.2254	−0.451202
$995$	−4.00000	−0.126809
$996$	6.51246	0.206355
$997$	−7.65685	−0.242495	−0.121248	−	0.992622i	$-0.538689\pi$
$997$	−7.65685	−0.242495	−0.121248	+	0.992622i	$0.538689\pi$
$998$	−1.29635	−0.0410352
$999$	−3.71573	−0.117560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.m.1.2	✓	4
5.4	even	2		9025.2.a.bn.1.3		4
19.18	odd	2	inner	1805.2.a.m.1.3	yes	4
95.94	odd	2		9025.2.a.bn.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.m.1.2	✓	4	1.1	even	1	trivial
1805.2.a.m.1.3	yes	4	19.18	odd	2	inner
9025.2.a.bn.1.2		4	95.94	odd	2
9025.2.a.bn.1.3		4	5.4	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.25928 q^{2} -1.78089 q^{3} -0.414214 q^{4} +1.00000 q^{5} +2.24264 q^{6} -0.828427 q^{7} +3.04017 q^{8} +0.171573 q^{9} +O(q^{10})\)	\(q-1.25928 q^{2} -1.78089 q^{3} -0.414214 q^{4} +1.00000 q^{5} +2.24264 q^{6} -0.828427 q^{7} +3.04017 q^{8} +0.171573 q^{9} -1.25928 q^{10} +2.00000 q^{11} +0.737669 q^{12} -4.29945 q^{13} +1.04322 q^{14} -1.78089 q^{15} -3.00000 q^{16} +7.65685 q^{17} -0.216058 q^{18} -0.414214 q^{20} +1.47534 q^{21} -2.51856 q^{22} -0.828427 q^{23} -5.41421 q^{24} +1.00000 q^{25} +5.41421 q^{26} +5.03712 q^{27} +0.343146 q^{28} -8.59890 q^{29} +2.24264 q^{30} -3.56178 q^{31} -2.30250 q^{32} -3.56178 q^{33} -9.64212 q^{34} -0.828427 q^{35} -0.0710678 q^{36} -0.737669 q^{37} +7.65685 q^{39} +3.04017 q^{40} -1.85786 q^{42} -4.82843 q^{43} -0.828427 q^{44} +0.171573 q^{45} +1.04322 q^{46} +10.4853 q^{47} +5.34267 q^{48} -6.31371 q^{49} -1.25928 q^{50} -13.6360 q^{51} +1.78089 q^{52} +7.86123 q^{53} -6.34315 q^{54} +2.00000 q^{55} -2.51856 q^{56} +10.8284 q^{58} +7.12356 q^{59} +0.737669 q^{60} -2.82843 q^{61} +4.48528 q^{62} -0.142136 q^{63} +8.89949 q^{64} -4.29945 q^{65} +4.48528 q^{66} -6.81801 q^{67} -3.17157 q^{68} +1.47534 q^{69} +1.04322 q^{70} -13.6360 q^{71} +0.521611 q^{72} -11.6569 q^{73} +0.928932 q^{74} -1.78089 q^{75} -1.65685 q^{77} -9.64212 q^{78} -7.12356 q^{79} -3.00000 q^{80} -9.48528 q^{81} +8.82843 q^{83} -0.611105 q^{84} +7.65685 q^{85} +6.08034 q^{86} +15.3137 q^{87} +6.08034 q^{88} +15.7225 q^{89} -0.216058 q^{90} +3.56178 q^{91} +0.343146 q^{92} +6.34315 q^{93} -13.2039 q^{94} +4.10051 q^{96} -4.29945 q^{97} +7.95073 q^{98} +0.343146 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{4} + 4 q^{5} - 8 q^{6} + 8 q^{7} + 12 q^{9}+O(q^{10}) \) 4 * q + 4 * q^4 + 4 * q^5 - 8 * q^6 + 8 * q^7 + 12 * q^9	\( 4 q + 4 q^{4} + 4 q^{5} - 8 q^{6} + 8 q^{7} + 12 q^{9} + 8 q^{11} - 12 q^{16} + 8 q^{17} + 4 q^{20} + 8 q^{23} - 16 q^{24} + 4 q^{25} + 16 q^{26} + 24 q^{28} - 8 q^{30} + 8 q^{35} + 28 q^{36} + 8 q^{39} - 64 q^{42} - 8 q^{43} + 8 q^{44} + 12 q^{45} + 8 q^{47} + 20 q^{49} - 48 q^{54} + 8 q^{55} + 32 q^{58} - 16 q^{62} + 56 q^{63} - 4 q^{64} - 16 q^{66} - 24 q^{68} - 24 q^{73} + 32 q^{74} + 16 q^{77} - 12 q^{80} - 4 q^{81} + 24 q^{83} + 8 q^{85} + 16 q^{87} + 24 q^{92} + 48 q^{93} + 56 q^{96} + 24 q^{99}+O(q^{100}) \) 4 * q + 4 * q^4 + 4 * q^5 - 8 * q^6 + 8 * q^7 + 12 * q^9 + 8 * q^11 - 12 * q^16 + 8 * q^17 + 4 * q^20 + 8 * q^23 - 16 * q^24 + 4 * q^25 + 16 * q^26 + 24 * q^28 - 8 * q^30 + 8 * q^35 + 28 * q^36 + 8 * q^39 - 64 * q^42 - 8 * q^43 + 8 * q^44 + 12 * q^45 + 8 * q^47 + 20 * q^49 - 48 * q^54 + 8 * q^55 + 32 * q^58 - 16 * q^62 + 56 * q^63 - 4 * q^64 - 16 * q^66 - 24 * q^68 - 24 * q^73 + 32 * q^74 + 16 * q^77 - 12 * q^80 - 4 * q^81 + 24 * q^83 + 8 * q^85 + 16 * q^87 + 24 * q^92 + 48 * q^93 + 56 * q^96 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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