LMFDB - Embedded newform 4235.2.a.bd.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.288385.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} - 2x^{2} + 10x + 3 $ x^5 - 7x^3 - 2x^2 + 10*x + 3
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			1.4
Root			$1.35681$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} -0.329669 q^{6} +1.00000 q^{7} -2.92945 q^{8} -2.94096 q^{9} +O(q^{10})$	\(q+1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} -0.329669 q^{6} +1.00000 q^{7} -2.92945 q^{8} -2.94096 q^{9} +1.35681 q^{10} +0.0386517 q^{12} +2.34529 q^{13} +1.35681 q^{14} -0.242974 q^{15} -3.65654 q^{16} +0.927617 q^{17} -3.99032 q^{18} -1.95659 q^{19} -0.159077 q^{20} -0.242974 q^{21} +2.68368 q^{23} +0.711781 q^{24} +1.00000 q^{25} +3.18211 q^{26} +1.44350 q^{27} -0.159077 q^{28} -0.245772 q^{29} -0.329669 q^{30} +2.99032 q^{31} +0.897683 q^{32} +1.25860 q^{34} +1.00000 q^{35} +0.467840 q^{36} +6.23609 q^{37} -2.65471 q^{38} -0.569845 q^{39} -2.92945 q^{40} -6.05663 q^{41} -0.329669 q^{42} +9.64965 q^{43} -2.94096 q^{45} +3.64123 q^{46} +5.84459 q^{47} +0.888445 q^{48} +1.00000 q^{49} +1.35681 q^{50} -0.225387 q^{51} -0.373082 q^{52} -4.58827 q^{53} +1.95855 q^{54} -2.92945 q^{56} +0.475400 q^{57} -0.333465 q^{58} -9.66792 q^{59} +0.0386517 q^{60} +2.82941 q^{61} +4.05728 q^{62} -2.94096 q^{63} +8.53106 q^{64} +2.34529 q^{65} +15.0109 q^{67} -0.147563 q^{68} -0.652064 q^{69} +1.35681 q^{70} -2.21995 q^{71} +8.61540 q^{72} +0.100173 q^{73} +8.46116 q^{74} -0.242974 q^{75} +0.311248 q^{76} -0.773170 q^{78} +6.31847 q^{79} -3.65654 q^{80} +8.47216 q^{81} -8.21767 q^{82} +16.4112 q^{83} +0.0386517 q^{84} +0.927617 q^{85} +13.0927 q^{86} +0.0597162 q^{87} +2.73384 q^{89} -3.99032 q^{90} +2.34529 q^{91} -0.426912 q^{92} -0.726570 q^{93} +7.92997 q^{94} -1.95659 q^{95} -0.218114 q^{96} +3.11103 q^{97} +1.35681 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} + 9 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 + 9 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	$ 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} + 9 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 3 q^{12} + 6 q^{13} + 2 q^{15} - 6 q^{16} + 2 q^{17} - 3 q^{18} + 7 q^{19} + 4 q^{20} + 2 q^{21} + 5 q^{23} + 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} + 4 q^{28} + 11 q^{29} + 9 q^{30} - 2 q^{31} + 7 q^{32} + 8 q^{34} + 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} + 2 q^{39} + 6 q^{40} + 13 q^{41} + 9 q^{42} + 10 q^{43} + 7 q^{45} + 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} + 30 q^{51} - 8 q^{52} - 14 q^{53} + 16 q^{54} + 6 q^{56} + 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} + 20 q^{61} - 15 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} - 9 q^{67} + 3 q^{68} - 30 q^{69} - 10 q^{71} + 38 q^{72} + 15 q^{73} - 19 q^{74} + 2 q^{75} - 5 q^{76} + 21 q^{78} + 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} + 8 q^{83} + 3 q^{84} + 2 q^{85} - 29 q^{86} - 22 q^{87} + 7 q^{89} - 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} - 14 q^{94} + 7 q^{95} - 18 q^{96} + 21 q^{97}+O(q^{100}) $ 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 + 9 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 3 * q^12 + 6 * q^13 + 2 * q^15 - 6 * q^16 + 2 * q^17 - 3 * q^18 + 7 * q^19 + 4 * q^20 + 2 * q^21 + 5 * q^23 + 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 + 4 * q^28 + 11 * q^29 + 9 * q^30 - 2 * q^31 + 7 * q^32 + 8 * q^34 + 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 + 2 * q^39 + 6 * q^40 + 13 * q^41 + 9 * q^42 + 10 * q^43 + 7 * q^45 + 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 + 30 * q^51 - 8 * q^52 - 14 * q^53 + 16 * q^54 + 6 * q^56 + 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 + 20 * q^61 - 15 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 - 9 * q^67 + 3 * q^68 - 30 * q^69 - 10 * q^71 + 38 * q^72 + 15 * q^73 - 19 * q^74 + 2 * q^75 - 5 * q^76 + 21 * q^78 + 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 + 8 * q^83 + 3 * q^84 + 2 * q^85 - 29 * q^86 - 22 * q^87 + 7 * q^89 - 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 - 14 * q^94 + 7 * q^95 - 18 * q^96 + 21 * q^97

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 $

$2$	1.35681	0.959407	0.479703	−	0.877431i	$-0.340744\pi$
$2$	1.35681	0.959407	0.479703	+	0.877431i	$0.340744\pi$
$3$	−0.242974	−0.140281	−0.0701406	−	0.997537i	$-0.522345\pi$
$3$	−0.242974	−0.140281	−0.0701406	+	0.997537i	$0.522345\pi$
$4$	−0.159077	−0.0795386
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.329669	−0.134587
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.92945	−1.03572
$9$	−2.94096	−0.980321
$10$	1.35681	0.429060
$11$	0	0
$11$	0	0
$12$	0.0386517	0.0111578
$13$	2.34529	0.650467	0.325233	−	0.945634i	$-0.394557\pi$
$13$	2.34529	0.650467	0.325233	+	0.945634i	$0.394557\pi$
$14$	1.35681	0.362622
$15$	−0.242974	−0.0627357
$16$	−3.65654	−0.914135
$17$	0.927617	0.224980	0.112490	−	0.993653i	$-0.464117\pi$
$17$	0.927617	0.224980	0.112490	+	0.993653i	$0.464117\pi$
$18$	−3.99032	−0.940527
$19$	−1.95659	−0.448872	−0.224436	−	0.974489i	$-0.572054\pi$
$19$	−1.95659	−0.448872	−0.224436	+	0.974489i	$0.572054\pi$
$20$	−0.159077	−0.0355707
$21$	−0.242974	−0.0530213
$22$	0	0
$23$	2.68368	0.559585	0.279793	−	0.960060i	$-0.409734\pi$
$23$	2.68368	0.559585	0.279793	+	0.960060i	$0.409734\pi$
$24$	0.711781	0.145292
$25$	1.00000	0.200000
$26$	3.18211	0.624062
$27$	1.44350	0.277802
$28$	−0.159077	−0.0300628
$29$	−0.245772	−0.0456387	−0.0228193	−	0.999740i	$-0.507264\pi$
$29$	−0.245772	−0.0456387	−0.0228193	+	0.999740i	$0.507264\pi$
$30$	−0.329669	−0.0601890
$31$	2.99032	0.537077	0.268538	−	0.963269i	$-0.413459\pi$
$31$	2.99032	0.537077	0.268538	+	0.963269i	$0.413459\pi$
$32$	0.897683	0.158689
$33$	0	0
$34$	1.25860	0.215848
$35$	1.00000	0.169031
$36$	0.467840	0.0779734
$37$	6.23609	1.02521	0.512603	−	0.858626i	$-0.328681\pi$
$37$	6.23609	1.02521	0.512603	+	0.858626i	$0.328681\pi$
$38$	−2.65471	−0.430651
$39$	−0.569845	−0.0912483
$40$	−2.92945	−0.463187
$41$	−6.05663	−0.945886	−0.472943	−	0.881093i	$-0.656808\pi$
$41$	−6.05663	−0.945886	−0.472943	+	0.881093i	$0.656808\pi$
$42$	−0.329669	−0.0508690
$43$	9.64965	1.47156	0.735779	−	0.677221i	$-0.236816\pi$
$43$	9.64965	1.47156	0.735779	+	0.677221i	$0.236816\pi$
$44$	0	0
$45$	−2.94096	−0.438413
$46$	3.64123	0.536870
$47$	5.84459	0.852521	0.426260	−	0.904601i	$-0.359831\pi$
$47$	5.84459	0.852521	0.426260	+	0.904601i	$0.359831\pi$
$48$	0.888445	0.128236
$49$	1.00000	0.142857
$50$	1.35681	0.191881
$51$	−0.225387	−0.0315605
$52$	−0.373082	−0.0517372
$53$	−4.58827	−0.630247	−0.315123	−	0.949051i	$-0.602046\pi$
$53$	−4.58827	−0.630247	−0.315123	+	0.949051i	$0.602046\pi$
$54$	1.95855	0.266525
$55$	0	0
$56$	−2.92945	−0.391464
$57$	0.475400	0.0629683
$58$	−0.333465	−0.0437861
$59$	−9.66792	−1.25866	−0.629328	−	0.777140i	$-0.716670\pi$
$59$	−9.66792	−1.25866	−0.629328	+	0.777140i	$0.716670\pi$
$60$	0.0386517	0.00498991
$61$	2.82941	0.362269	0.181134	−	0.983458i	$-0.442023\pi$
$61$	2.82941	0.362269	0.181134	+	0.983458i	$0.442023\pi$
$62$	4.05728	0.515275
$63$	−2.94096	−0.370527
$64$	8.53106	1.06638
$65$	2.34529	0.290898
$66$	0	0
$67$	15.0109	1.83388	0.916939	−	0.399028i	$-0.130652\pi$
$67$	15.0109	1.83388	0.916939	+	0.399028i	$0.130652\pi$
$68$	−0.147563	−0.0178946
$69$	−0.652064	−0.0784993
$70$	1.35681	0.162169
$71$	−2.21995	−0.263459	−0.131730	−	0.991286i	$-0.542053\pi$
$71$	−2.21995	−0.263459	−0.131730	+	0.991286i	$0.542053\pi$
$72$	8.61540	1.01533
$73$	0.100173	0.0117244	0.00586220	−	0.999983i	$-0.498134\pi$
$73$	0.100173	0.0117244	0.00586220	+	0.999983i	$0.498134\pi$
$74$	8.46116	0.983590
$75$	−0.242974	−0.0280562
$76$	0.311248	0.0357026
$77$	0	0
$78$	−0.773170	−0.0875442
$79$	6.31847	0.710883	0.355442	−	0.934699i	$-0.384331\pi$
$79$	6.31847	0.710883	0.355442	+	0.934699i	$0.384331\pi$
$80$	−3.65654	−0.408814
$81$	8.47216	0.941351
$82$	−8.21767	−0.907490
$83$	16.4112	1.80136	0.900679	−	0.434485i	$-0.143069\pi$
$83$	16.4112	1.80136	0.900679	+	0.434485i	$0.143069\pi$
$84$	0.0386517	0.00421724
$85$	0.927617	0.100614
$86$	13.0927	1.41182
$87$	0.0597162	0.00640225
$88$	0	0
$89$	2.73384	0.289787	0.144893	−	0.989447i	$-0.453716\pi$
$89$	2.73384	0.289787	0.144893	+	0.989447i	$0.453716\pi$
$90$	−3.99032	−0.420616
$91$	2.34529	0.245853
$92$	−0.426912	−0.0445086
$93$	−0.726570	−0.0753418
$94$	7.92997	0.817914
$95$	−1.95659	−0.200742
$96$	−0.218114	−0.0222611
$97$	3.11103	0.315878	0.157939	−	0.987449i	$-0.449515\pi$
$97$	3.11103	0.315878	0.157939	+	0.987449i	$0.449515\pi$
$98$	1.35681	0.137058
$99$	0	0
$100$	−0.159077	−0.0159077
$101$	14.9247	1.48506	0.742531	−	0.669812i	$-0.233625\pi$
$101$	14.9247	1.48506	0.742531	+	0.669812i	$0.233625\pi$
$102$	−0.305807	−0.0302794
$103$	0.991937	0.0977384	0.0488692	−	0.998805i	$-0.484438\pi$
$103$	0.991937	0.0977384	0.0488692	+	0.998805i	$0.484438\pi$
$104$	−6.87041	−0.673699
$105$	−0.242974	−0.0237119
$106$	−6.22539	−0.604663
$107$	−3.31075	−0.320062	−0.160031	−	0.987112i	$-0.551159\pi$
$107$	−3.31075	−0.320062	−0.160031	+	0.987112i	$0.551159\pi$
$108$	−0.229628	−0.0220960
$109$	−6.08363	−0.582706	−0.291353	−	0.956616i	$-0.594105\pi$
$109$	−6.08363	−0.582706	−0.291353	+	0.956616i	$0.594105\pi$
$110$	0	0
$111$	−1.51521	−0.143817
$112$	−3.65654	−0.345511
$113$	−9.54323	−0.897751	−0.448876	−	0.893594i	$-0.648175\pi$
$113$	−9.54323	−0.897751	−0.448876	+	0.893594i	$0.648175\pi$
$114$	0.645026	0.0604122
$115$	2.68368	0.250254
$116$	0.0390967	0.00363004
$117$	−6.89742	−0.637666
$118$	−13.1175	−1.20756
$119$	0.927617	0.0850346
$120$	0.711781	0.0649764
$121$	0	0
$122$	3.83896	0.347563
$123$	1.47160	0.132690
$124$	−0.475691	−0.0427183
$125$	1.00000	0.0894427
$126$	−3.99032	−0.355486
$127$	10.1792	0.903256	0.451628	−	0.892206i	$-0.350843\pi$
$127$	10.1792	0.903256	0.451628	+	0.892206i	$0.350843\pi$
$128$	9.77963	0.864405
$129$	−2.34462	−0.206432
$130$	3.18211	0.279089
$131$	−12.4893	−1.09119	−0.545596	−	0.838048i	$-0.683697\pi$
$131$	−12.4893	−1.09119	−0.545596	+	0.838048i	$0.683697\pi$
$132$	0	0
$133$	−1.95659	−0.169658
$134$	20.3669	1.75943
$135$	1.44350	0.124237
$136$	−2.71741	−0.233016
$137$	16.6161	1.41961	0.709805	−	0.704398i	$-0.248783\pi$
$137$	16.6161	1.41961	0.709805	+	0.704398i	$0.248783\pi$
$138$	−0.884725	−0.0753128
$139$	0.420472	0.0356640	0.0178320	−	0.999841i	$-0.494324\pi$
$139$	0.420472	0.0356640	0.0178320	+	0.999841i	$0.494324\pi$
$140$	−0.159077	−0.0134445
$141$	−1.42008	−0.119593
$142$	−3.01204	−0.252764
$143$	0	0
$144$	10.7538	0.896146
$145$	−0.245772	−0.0204102
$146$	0.135916	0.0112485
$147$	−0.242974	−0.0200402
$148$	−0.992020	−0.0815435
$149$	10.1747	0.833544	0.416772	−	0.909011i	$-0.363161\pi$
$149$	10.1747	0.833544	0.416772	+	0.909011i	$0.363161\pi$
$150$	−0.329669	−0.0269173
$151$	−5.10643	−0.415555	−0.207778	−	0.978176i	$-0.566623\pi$
$151$	−5.10643	−0.415555	−0.207778	+	0.978176i	$0.566623\pi$
$152$	5.73172	0.464904
$153$	−2.72809	−0.220553
$154$	0	0
$155$	2.99032	0.240188
$156$	0.0906494	0.00725776
$157$	3.85612	0.307752	0.153876	−	0.988090i	$-0.450824\pi$
$157$	3.85612	0.307752	0.153876	+	0.988090i	$0.450824\pi$
$158$	8.57293	0.682026
$159$	1.11483	0.0884118
$160$	0.897683	0.0709680
$161$	2.68368	0.211503
$162$	11.4951	0.903138
$163$	−8.98048	−0.703406	−0.351703	−	0.936112i	$-0.614397\pi$
$163$	−8.98048	−0.703406	−0.351703	+	0.936112i	$0.614397\pi$
$164$	0.963471	0.0752345
$165$	0	0
$166$	22.2668	1.72824
$167$	−0.0644782	−0.00498947	−0.00249474	−	0.999997i	$-0.500794\pi$
$167$	−0.0644782	−0.00498947	−0.00249474	+	0.999997i	$0.500794\pi$
$168$	0.711781	0.0549151
$169$	−7.49961	−0.576893
$170$	1.25860	0.0965300
$171$	5.75425	0.440038
$172$	−1.53504	−0.117046
$173$	−17.2202	−1.30923	−0.654613	−	0.755964i	$-0.727168\pi$
$173$	−17.2202	−1.30923	−0.654613	+	0.755964i	$0.727168\pi$
$174$	0.0810233	0.00614236
$175$	1.00000	0.0755929
$176$	0	0
$177$	2.34906	0.176566
$178$	3.70930	0.278023
$179$	−18.2017	−1.36046	−0.680230	−	0.732999i	$-0.738120\pi$
$179$	−18.2017	−1.36046	−0.680230	+	0.732999i	$0.738120\pi$
$180$	0.467840	0.0348708
$181$	−9.54258	−0.709294	−0.354647	−	0.935000i	$-0.615399\pi$
$181$	−9.54258	−0.709294	−0.354647	+	0.935000i	$0.615399\pi$
$182$	3.18211	0.235873
$183$	−0.687473	−0.0508195
$184$	−7.86170	−0.579572
$185$	6.23609	0.458486
$186$	−0.985814	−0.0722834
$187$	0	0
$188$	−0.929741	−0.0678083
$189$	1.44350	0.104999
$190$	−2.65471	−0.192593
$191$	10.0070	0.724078	0.362039	−	0.932163i	$-0.382081\pi$
$191$	10.0070	0.724078	0.362039	+	0.932163i	$0.382081\pi$
$192$	−2.07283	−0.149593
$193$	13.5332	0.974141	0.487071	−	0.873363i	$-0.338065\pi$
$193$	13.5332	0.974141	0.487071	+	0.873363i	$0.338065\pi$
$194$	4.22107	0.303055
$195$	−0.569845	−0.0408075
$196$	−0.159077	−0.0113627
$197$	22.2486	1.58515	0.792575	−	0.609774i	$-0.208740\pi$
$197$	22.2486	1.58515	0.792575	+	0.609774i	$0.208740\pi$
$198$	0	0
$199$	−9.44551	−0.669575	−0.334787	−	0.942294i	$-0.608664\pi$
$199$	−9.44551	−0.669575	−0.334787	+	0.942294i	$0.608664\pi$
$200$	−2.92945	−0.207143
$201$	−3.64727	−0.257259
$202$	20.2499	1.42478
$203$	−0.245772	−0.0172498
$204$	0.0358540	0.00251028
$205$	−6.05663	−0.423013
$206$	1.34587	0.0937709
$207$	−7.89260	−0.548573
$208$	−8.57565	−0.594615
$209$	0	0
$210$	−0.329669	−0.0227493
$211$	4.75884	0.327612	0.163806	−	0.986493i	$-0.447623\pi$
$211$	4.75884	0.327612	0.163806	+	0.986493i	$0.447623\pi$
$212$	0.729889	0.0501290
$213$	0.539389	0.0369584
$214$	−4.49204	−0.307070
$215$	9.64965	0.658101
$216$	−4.22866	−0.287724
$217$	2.99032	0.202996
$218$	−8.25431	−0.559052
$219$	−0.0243395	−0.00164471
$220$	0	0
$221$	2.17553	0.146342
$222$	−2.05584	−0.137979
$223$	19.6049	1.31284	0.656422	−	0.754394i	$-0.272069\pi$
$223$	19.6049	1.31284	0.656422	+	0.754394i	$0.272069\pi$
$224$	0.897683	0.0599789
$225$	−2.94096	−0.196064
$226$	−12.9483	−0.861309
$227$	8.13362	0.539847	0.269924	−	0.962882i	$-0.413002\pi$
$227$	8.13362	0.539847	0.269924	+	0.962882i	$0.413002\pi$
$228$	−0.0756253	−0.00500841
$229$	12.5891	0.831910	0.415955	−	0.909385i	$-0.363447\pi$
$229$	12.5891	0.831910	0.415955	+	0.909385i	$0.363447\pi$
$230$	3.64123	0.240096
$231$	0	0
$232$	0.719976	0.0472688
$233$	2.77199	0.181599	0.0907996	−	0.995869i	$-0.471058\pi$
$233$	2.77199	0.181599	0.0907996	+	0.995869i	$0.471058\pi$
$234$	−9.35846	−0.611782
$235$	5.84459	0.381259
$236$	1.53795	0.100112
$237$	−1.53522	−0.0997235
$238$	1.25860	0.0815827
$239$	−1.04527	−0.0676130	−0.0338065	−	0.999428i	$-0.510763\pi$
$239$	−1.04527	−0.0676130	−0.0338065	+	0.999428i	$0.510763\pi$
$240$	0.888445	0.0573489
$241$	24.2918	1.56477	0.782385	−	0.622796i	$-0.214003\pi$
$241$	24.2918	1.56477	0.782385	+	0.622796i	$0.214003\pi$
$242$	0	0
$243$	−6.38902	−0.409856
$244$	−0.450094	−0.0288143
$245$	1.00000	0.0638877
$246$	1.99668	0.127304
$247$	−4.58877	−0.291976
$248$	−8.75998	−0.556259
$249$	−3.98749	−0.252697
$250$	1.35681	0.0858120
$251$	−15.7101	−0.991610	−0.495805	−	0.868434i	$-0.665127\pi$
$251$	−15.7101	−0.991610	−0.495805	+	0.868434i	$0.665127\pi$
$252$	0.467840	0.0294712
$253$	0	0
$254$	13.8112	0.866590
$255$	−0.225387	−0.0141143
$256$	−3.79306	−0.237066
$257$	24.4875	1.52749	0.763745	−	0.645519i	$-0.223359\pi$
$257$	24.4875	1.52749	0.763745	+	0.645519i	$0.223359\pi$
$258$	−3.18119	−0.198052
$259$	6.23609	0.387492
$260$	−0.373082	−0.0231376
$261$	0.722806	0.0447406
$262$	−16.9455	−1.04690
$263$	−21.7093	−1.33865	−0.669325	−	0.742969i	$-0.733417\pi$
$263$	−21.7093	−1.33865	−0.669325	+	0.742969i	$0.733417\pi$
$264$	0	0
$265$	−4.58827	−0.281855
$266$	−2.65471	−0.162771
$267$	−0.664253	−0.0406516
$268$	−2.38790	−0.145864
$269$	−10.5726	−0.644621	−0.322310	−	0.946634i	$-0.604459\pi$
$269$	−10.5726	−0.644621	−0.322310	+	0.946634i	$0.604459\pi$
$270$	1.95855	0.119194
$271$	23.8119	1.44647	0.723235	−	0.690602i	$-0.242654\pi$
$271$	23.8119	1.44647	0.723235	+	0.690602i	$0.242654\pi$
$272$	−3.39187	−0.205662
$273$	−0.569845	−0.0344886
$274$	22.5448	1.36198
$275$	0	0
$276$	0.103729	0.00624373
$277$	−0.357431	−0.0214759	−0.0107380	−	0.999942i	$-0.503418\pi$
$277$	−0.357431	−0.0214759	−0.0107380	+	0.999942i	$0.503418\pi$
$278$	0.570499	0.0342162
$279$	−8.79441	−0.526508
$280$	−2.92945	−0.175068
$281$	−6.93387	−0.413640	−0.206820	−	0.978379i	$-0.566311\pi$
$281$	−6.93387	−0.413640	−0.206820	+	0.978379i	$0.566311\pi$
$282$	−1.92678	−0.114738
$283$	−12.2813	−0.730050	−0.365025	−	0.930998i	$-0.618939\pi$
$283$	−12.2813	−0.730050	−0.365025	+	0.930998i	$0.618939\pi$
$284$	0.353143	0.0209552
$285$	0.475400	0.0281603
$286$	0	0
$287$	−6.05663	−0.357511
$288$	−2.64005	−0.155567
$289$	−16.1395	−0.949384
$290$	−0.333465	−0.0195817
$291$	−0.755901	−0.0443117
$292$	−0.0159353	−0.000932543 0
$293$	18.4314	1.07678	0.538388	−	0.842697i	$-0.319034\pi$
$293$	18.4314	1.07678	0.538388	+	0.842697i	$0.319034\pi$
$294$	−0.329669	−0.0192267
$295$	−9.66792	−0.562888
$296$	−18.2683	−1.06182
$297$	0	0
$298$	13.8051	0.799708
$299$	6.29401	0.363992
$300$	0.0386517	0.00223155
$301$	9.64965	0.556197
$302$	−6.92843	−0.398686
$303$	−3.62631	−0.208326
$304$	7.15434	0.410329
$305$	2.82941	0.162011
$306$	−3.70149	−0.211600
$307$	27.8266	1.58815	0.794074	−	0.607821i	$-0.207956\pi$
$307$	27.8266	1.58815	0.794074	+	0.607821i	$0.207956\pi$
$308$	0	0
$309$	−0.241015	−0.0137109
$310$	4.05728	0.230438
$311$	−18.5140	−1.04983	−0.524916	−	0.851154i	$-0.675903\pi$
$311$	−18.5140	−1.04983	−0.524916	+	0.851154i	$0.675903\pi$
$312$	1.66933	0.0945074
$313$	−9.40487	−0.531595	−0.265797	−	0.964029i	$-0.585635\pi$
$313$	−9.40487	−0.531595	−0.265797	+	0.964029i	$0.585635\pi$
$314$	5.23201	0.295259
$315$	−2.94096	−0.165705
$316$	−1.00512	−0.0565427
$317$	−14.1532	−0.794924	−0.397462	−	0.917619i	$-0.630109\pi$
$317$	−14.1532	−0.794924	−0.397462	+	0.917619i	$0.630109\pi$
$318$	1.51261	0.0848229
$319$	0	0
$320$	8.53106	0.476901
$321$	0.804426	0.0448987
$322$	3.64123	0.202918
$323$	−1.81496	−0.100987
$324$	−1.34773	−0.0748737
$325$	2.34529	0.130093
$326$	−12.1848	−0.674852
$327$	1.47817	0.0817427
$328$	17.7426	0.979670
$329$	5.84459	0.322222
$330$	0	0
$331$	−24.4577	−1.34432	−0.672159	−	0.740407i	$-0.734633\pi$
$331$	−24.4577	−1.34432	−0.672159	+	0.740407i	$0.734633\pi$
$332$	−2.61064	−0.143278
$333$	−18.3401	−1.00503
$334$	−0.0874844	−0.00478693
$335$	15.0109	0.820135
$336$	0.888445	0.0484686
$337$	−23.7769	−1.29521	−0.647605	−	0.761976i	$-0.724229\pi$
$337$	−23.7769	−1.29521	−0.647605	+	0.761976i	$0.724229\pi$
$338$	−10.1755	−0.553475
$339$	2.31876	0.125938
$340$	−0.147563	−0.00800272
$341$	0	0
$342$	7.80740	0.422176
$343$	1.00000	0.0539949
$344$	−28.2682	−1.52412
$345$	−0.652064	−0.0351060
$346$	−23.3644	−1.25608
$347$	−2.31154	−0.124090	−0.0620450	−	0.998073i	$-0.519762\pi$
$347$	−2.31154	−0.124090	−0.0620450	+	0.998073i	$0.519762\pi$
$348$	−0.00949949	−0.000509226 0
$349$	36.2674	1.94135	0.970675	−	0.240395i	$-0.0772770\pi$
$349$	36.2674	1.94135	0.970675	+	0.240395i	$0.0772770\pi$
$350$	1.35681	0.0725243
$351$	3.38543	0.180701
$352$	0	0
$353$	−10.6567	−0.567200	−0.283600	−	0.958943i	$-0.591529\pi$
$353$	−10.6567	−0.567200	−0.283600	+	0.958943i	$0.591529\pi$
$354$	3.18721	0.169398
$355$	−2.21995	−0.117822
$356$	−0.434892	−0.0230492
$357$	−0.225387	−0.0119287
$358$	−24.6962	−1.30523
$359$	22.4588	1.18533	0.592664	−	0.805450i	$-0.298076\pi$
$359$	22.4588	1.18533	0.592664	+	0.805450i	$0.298076\pi$
$360$	8.61540	0.454072
$361$	−15.1718	−0.798514
$362$	−12.9474	−0.680502
$363$	0	0
$364$	−0.373082	−0.0195548
$365$	0.100173	0.00524331
$366$	−0.932768	−0.0487566
$367$	15.1093	0.788698	0.394349	−	0.918961i	$-0.370970\pi$
$367$	15.1093	0.788698	0.394349	+	0.918961i	$0.370970\pi$
$368$	−9.81297	−0.511537
$369$	17.8123	0.927272
$370$	8.46116	0.439875
$371$	−4.58827	−0.238211
$372$	0.115581	0.00599258
$373$	−22.7153	−1.17616	−0.588078	−	0.808804i	$-0.700115\pi$
$373$	−22.7153	−1.17616	−0.588078	+	0.808804i	$0.700115\pi$
$374$	0	0
$375$	−0.242974	−0.0125471
$376$	−17.1214	−0.882970
$377$	−0.576407	−0.0296865
$378$	1.95855	0.100737
$379$	−1.50696	−0.0774072	−0.0387036	−	0.999251i	$-0.512323\pi$
$379$	−1.50696	−0.0774072	−0.0387036	+	0.999251i	$0.512323\pi$
$380$	0.311248	0.0159667
$381$	−2.47328	−0.126710
$382$	13.5775	0.694686
$383$	−14.8062	−0.756564	−0.378282	−	0.925690i	$-0.623485\pi$
$383$	−14.8062	−0.756564	−0.378282	+	0.925690i	$0.623485\pi$
$384$	−2.37620	−0.121260
$385$	0	0
$386$	18.3619	0.934598
$387$	−28.3793	−1.44260
$388$	−0.494895	−0.0251245
$389$	−33.6017	−1.70368	−0.851838	−	0.523806i	$-0.824512\pi$
$389$	−33.6017	−1.70368	−0.851838	+	0.523806i	$0.824512\pi$
$390$	−0.773170	−0.0391510
$391$	2.48943	0.125896
$392$	−2.92945	−0.147960
$393$	3.03457	0.153074
$394$	30.1871	1.52080
$395$	6.31847	0.317917
$396$	0	0
$397$	−23.7402	−1.19149	−0.595744	−	0.803174i	$-0.703143\pi$
$397$	−23.7402	−1.19149	−0.595744	+	0.803174i	$0.703143\pi$
$398$	−12.8157	−0.642394
$399$	0.475400	0.0237998
$400$	−3.65654	−0.182827
$401$	25.6299	1.27990	0.639949	−	0.768417i	$-0.278955\pi$
$401$	25.6299	1.27990	0.639949	+	0.768417i	$0.278955\pi$
$402$	−4.94864	−0.246816
$403$	7.01317	0.349351
$404$	−2.37418	−0.118120
$405$	8.47216	0.420985
$406$	−0.333465	−0.0165496
$407$	0	0
$408$	0.660260	0.0326877
$409$	26.5551	1.31306	0.656532	−	0.754299i	$-0.272023\pi$
$409$	26.5551	1.31306	0.656532	+	0.754299i	$0.272023\pi$
$410$	−8.21767	−0.405842
$411$	−4.03728	−0.199145
$412$	−0.157795	−0.00777398
$413$	−9.66792	−0.475727
$414$	−10.7087	−0.526305
$415$	16.4112	0.805592
$416$	2.10533	0.103222
$417$	−0.102164	−0.00500298
$418$	0	0
$419$	−34.6824	−1.69435	−0.847174	−	0.531316i	$-0.821698\pi$
$419$	−34.6824	−1.69435	−0.847174	+	0.531316i	$0.821698\pi$
$420$	0.0386517	0.00188601
$421$	24.7907	1.20823	0.604113	−	0.796899i	$-0.293527\pi$
$421$	24.7907	1.20823	0.604113	+	0.796899i	$0.293527\pi$
$422$	6.45682	0.314313
$423$	−17.1887	−0.835744
$424$	13.4411	0.652757
$425$	0.927617	0.0449961
$426$	0.731847	0.0354581
$427$	2.82941	0.136925
$428$	0.526665	0.0254573
$429$	0	0
$430$	13.0927	0.631387
$431$	−6.59999	−0.317910	−0.158955	−	0.987286i	$-0.550813\pi$
$431$	−6.59999	−0.317910	−0.158955	+	0.987286i	$0.550813\pi$
$432$	−5.27822	−0.253948
$433$	20.0200	0.962101	0.481050	−	0.876693i	$-0.340255\pi$
$433$	20.0200	0.962101	0.481050	+	0.876693i	$0.340255\pi$
$434$	4.05728	0.194756
$435$	0.0597162	0.00286317
$436$	0.967767	0.0463476
$437$	−5.25085	−0.251182
$438$	−0.0330240	−0.00157795
$439$	−26.6216	−1.27058	−0.635290	−	0.772274i	$-0.719119\pi$
$439$	−26.6216	−1.27058	−0.635290	+	0.772274i	$0.719119\pi$
$440$	0	0
$441$	−2.94096	−0.140046
$442$	2.95178	0.140402
$443$	7.35380	0.349389	0.174695	−	0.984623i	$-0.444106\pi$
$443$	7.35380	0.349389	0.174695	+	0.984623i	$0.444106\pi$
$444$	0.241035	0.0114390
$445$	2.73384	0.129597
$446$	26.6001	1.25955
$447$	−2.47219	−0.116931
$448$	8.53106	0.403055
$449$	1.75184	0.0826744	0.0413372	−	0.999145i	$-0.486838\pi$
$449$	1.75184	0.0826744	0.0413372	+	0.999145i	$0.486838\pi$
$450$	−3.99032	−0.188105
$451$	0	0
$452$	1.51811	0.0714059
$453$	1.24073	0.0582946
$454$	11.0357	0.517933
$455$	2.34529	0.109949
$456$	−1.39266	−0.0652173
$457$	17.7181	0.828817	0.414409	−	0.910091i	$-0.363988\pi$
$457$	17.7181	0.828817	0.414409	+	0.910091i	$0.363988\pi$
$458$	17.0809	0.798140
$459$	1.33902	0.0624999
$460$	−0.426912	−0.0199049
$461$	20.6171	0.960235	0.480118	−	0.877204i	$-0.340594\pi$
$461$	20.6171	0.960235	0.480118	+	0.877204i	$0.340594\pi$
$462$	0	0
$463$	−13.1323	−0.610309	−0.305154	−	0.952303i	$-0.598708\pi$
$463$	−13.1323	−0.610309	−0.305154	+	0.952303i	$0.598708\pi$
$464$	0.898675	0.0417199
$465$	−0.726570	−0.0336939
$466$	3.76105	0.174228
$467$	30.8738	1.42867	0.714334	−	0.699805i	$-0.246730\pi$
$467$	30.8738	1.42867	0.714334	+	0.699805i	$0.246730\pi$
$468$	1.09722	0.0507191
$469$	15.0109	0.693141
$470$	7.92997	0.365782
$471$	−0.936938	−0.0431718
$472$	28.3217	1.30361
$473$	0	0
$474$	−2.08300	−0.0956754
$475$	−1.95659	−0.0897743
$476$	−0.147563	−0.00676353
$477$	13.4939	0.617844
$478$	−1.41823	−0.0648684
$479$	−36.4945	−1.66748	−0.833739	−	0.552159i	$-0.813804\pi$
$479$	−36.4945	−1.66748	−0.833739	+	0.552159i	$0.813804\pi$
$480$	−0.218114	−0.00995548
$481$	14.6254	0.666863
$482$	32.9592	1.50125
$483$	−0.652064	−0.0296700
$484$	0	0
$485$	3.11103	0.141265
$486$	−8.66866	−0.393218
$487$	−29.0277	−1.31537	−0.657685	−	0.753293i	$-0.728464\pi$
$487$	−29.0277	−1.31537	−0.657685	+	0.753293i	$0.728464\pi$
$488$	−8.28861	−0.375208
$489$	2.18203	0.0986746
$490$	1.35681	0.0612943
$491$	28.1964	1.27249	0.636244	−	0.771488i	$-0.280487\pi$
$491$	28.1964	1.27249	0.636244	+	0.771488i	$0.280487\pi$
$492$	−0.234099	−0.0105540
$493$	−0.227982	−0.0102678
$494$	−6.22607	−0.280124
$495$	0	0
$496$	−10.9342	−0.490961
$497$	−2.21995	−0.0995782
$498$	−5.41025	−0.242439
$499$	−12.1817	−0.545326	−0.272663	−	0.962110i	$-0.587904\pi$
$499$	−12.1817	−0.545326	−0.272663	+	0.962110i	$0.587904\pi$
$500$	−0.159077	−0.00711415
$501$	0.0156665	0.000699929 0
$502$	−21.3155	−0.951357
$503$	9.57390	0.426879	0.213439	−	0.976956i	$-0.431533\pi$
$503$	9.57390	0.426879	0.213439	+	0.976956i	$0.431533\pi$
$504$	8.61540	0.383761
$505$	14.9247	0.664140
$506$	0	0
$507$	1.82221	0.0809272
$508$	−1.61927	−0.0718437
$509$	−28.2988	−1.25432	−0.627161	−	0.778889i	$-0.715783\pi$
$509$	−28.2988	−1.25432	−0.627161	+	0.778889i	$0.715783\pi$
$510$	−0.305807	−0.0135413
$511$	0.100173	0.00443141
$512$	−24.7057	−1.09185
$513$	−2.82433	−0.124697
$514$	33.2248	1.46548
$515$	0.991937	0.0437100
$516$	0.372975	0.0164193
$517$	0	0
$518$	8.46116	0.371762
$519$	4.18406	0.183660
$520$	−6.87041	−0.301288
$521$	−6.04860	−0.264994	−0.132497	−	0.991183i	$-0.542299\pi$
$521$	−6.04860	−0.264994	−0.132497	+	0.991183i	$0.542299\pi$
$522$	0.980708	0.0429244
$523$	15.3496	0.671192	0.335596	−	0.942006i	$-0.391062\pi$
$523$	15.3496	0.671192	0.335596	+	0.942006i	$0.391062\pi$
$524$	1.98676	0.0867919
$525$	−0.242974	−0.0106043
$526$	−29.4553	−1.28431
$527$	2.77387	0.120832
$528$	0	0
$529$	−15.7979	−0.686864
$530$	−6.22539	−0.270414
$531$	28.4330	1.23389
$532$	0.311248	0.0134943
$533$	−14.2046	−0.615268
$534$	−0.901263	−0.0390015
$535$	−3.31075	−0.143136
$536$	−43.9738	−1.89938
$537$	4.42254	0.190847
$538$	−14.3449	−0.618453
$539$	0	0
$540$	−0.229628	−0.00988162
$541$	−31.1468	−1.33911	−0.669553	−	0.742765i	$-0.733514\pi$
$541$	−31.1468	−1.33911	−0.669553	+	0.742765i	$0.733514\pi$
$542$	32.3081	1.38775
$543$	2.31860	0.0995006
$544$	0.832706	0.0357020
$545$	−6.08363	−0.260594
$546$	−0.773170	−0.0330886
$547$	2.82444	0.120764	0.0603821	−	0.998175i	$-0.480768\pi$
$547$	2.82444	0.120764	0.0603821	+	0.998175i	$0.480768\pi$
$548$	−2.64324	−0.112914
$549$	−8.32119	−0.355140
$550$	0	0
$551$	0.480874	0.0204859
$552$	1.91019	0.0813030
$553$	6.31847	0.268689
$554$	−0.484965	−0.0206042
$555$	−1.51521	−0.0643170
$556$	−0.0668875	−0.00283666
$557$	5.32104	0.225460	0.112730	−	0.993626i	$-0.464041\pi$
$557$	5.32104	0.225460	0.112730	+	0.993626i	$0.464041\pi$
$558$	−11.9323	−0.505135
$559$	22.6313	0.957200
$560$	−3.65654	−0.154517
$561$	0	0
$562$	−9.40792	−0.396849
$563$	1.88609	0.0794893	0.0397447	−	0.999210i	$-0.487346\pi$
$563$	1.88609	0.0794893	0.0397447	+	0.999210i	$0.487346\pi$
$564$	0.225903	0.00951223
$565$	−9.54323	−0.401487
$566$	−16.6634	−0.700415
$567$	8.47216	0.355797
$568$	6.50322	0.272869
$569$	4.30097	0.180306	0.0901529	−	0.995928i	$-0.471264\pi$
$569$	4.30097	0.180306	0.0901529	+	0.995928i	$0.471264\pi$
$570$	0.645026	0.0270171
$571$	−10.5416	−0.441153	−0.220577	−	0.975370i	$-0.570794\pi$
$571$	−10.5416	−0.441153	−0.220577	+	0.975370i	$0.570794\pi$
$572$	0	0
$573$	−2.43143	−0.101575
$574$	−8.21767	−0.342999
$575$	2.68368	0.111917
$576$	−25.0895	−1.04540
$577$	−2.05286	−0.0854618	−0.0427309	−	0.999087i	$-0.513606\pi$
$577$	−2.05286	−0.0854618	−0.0427309	+	0.999087i	$0.513606\pi$
$578$	−21.8982	−0.910845
$579$	−3.28822	−0.136654
$580$	0.0390967	0.00162340
$581$	16.4112	0.680849
$582$	−1.02561	−0.0425129
$583$	0	0
$584$	−0.293453	−0.0121432
$585$	−6.89742	−0.285173
$586$	25.0079	1.03307
$587$	25.9972	1.07302	0.536510	−	0.843894i	$-0.319742\pi$
$587$	25.9972	1.07302	0.536510	+	0.843894i	$0.319742\pi$
$588$	0.0386517	0.00159397
$589$	−5.85081	−0.241079
$590$	−13.1175	−0.540039
$591$	−5.40585	−0.222367
$592$	−22.8025	−0.937177
$593$	−11.1931	−0.459645	−0.229823	−	0.973233i	$-0.573815\pi$
$593$	−11.1931	−0.459645	−0.229823	+	0.973233i	$0.573815\pi$
$594$	0	0
$595$	0.927617	0.0380286
$596$	−1.61856	−0.0662989
$597$	2.29502	0.0939287
$598$	8.53975	0.349216
$599$	33.8637	1.38363	0.691817	−	0.722073i	$-0.256811\pi$
$599$	33.8637	1.38363	0.691817	+	0.722073i	$0.256811\pi$
$600$	0.711781	0.0290583
$601$	42.1489	1.71929	0.859645	−	0.510892i	$-0.170685\pi$
$601$	42.1489	1.71929	0.859645	+	0.510892i	$0.170685\pi$
$602$	13.0927	0.533619
$603$	−44.1466	−1.79779
$604$	0.812316	0.0330527
$605$	0	0
$606$	−4.92020	−0.199870
$607$	−22.4797	−0.912422	−0.456211	−	0.889872i	$-0.650794\pi$
$607$	−22.4797	−0.912422	−0.456211	+	0.889872i	$0.650794\pi$
$608$	−1.75639	−0.0712312
$609$	0.0597162	0.00241982
$610$	3.83896	0.155435
$611$	13.7073	0.554536
$612$	0.433977	0.0175425
$613$	−8.61975	−0.348148	−0.174074	−	0.984733i	$-0.555693\pi$
$613$	−8.61975	−0.348148	−0.174074	+	0.984733i	$0.555693\pi$
$614$	37.7553	1.52368
$615$	1.47160	0.0593408
$616$	0	0
$617$	−1.79131	−0.0721154	−0.0360577	−	0.999350i	$-0.511480\pi$
$617$	−1.79131	−0.0721154	−0.0360577	+	0.999350i	$0.511480\pi$
$618$	−0.327011	−0.0131543
$619$	12.4154	0.499016	0.249508	−	0.968373i	$-0.419731\pi$
$619$	12.4154	0.499016	0.249508	+	0.968373i	$0.419731\pi$
$620$	−0.475691	−0.0191042
$621$	3.87389	0.155454
$622$	−25.1199	−1.00722
$623$	2.73384	0.109529
$624$	2.08366	0.0834132
$625$	1.00000	0.0400000
$626$	−12.7606	−0.510016
$627$	0	0
$628$	−0.613421	−0.0244782
$629$	5.78471	0.230651
$630$	−3.99032	−0.158978
$631$	−6.81348	−0.271240	−0.135620	−	0.990761i	$-0.543303\pi$
$631$	−6.81348	−0.271240	−0.135620	+	0.990761i	$0.543303\pi$
$632$	−18.5096	−0.736273
$633$	−1.15627	−0.0459578
$634$	−19.2032	−0.762655
$635$	10.1792	0.403948
$636$	−0.177344	−0.00703215
$637$	2.34529	0.0929238
$638$	0	0
$639$	6.52878	0.258274
$640$	9.77963	0.386574
$641$	−48.3163	−1.90838	−0.954190	−	0.299202i	$-0.903280\pi$
$641$	−48.3163	−1.90838	−0.954190	+	0.299202i	$0.903280\pi$
$642$	1.09145	0.0430761
$643$	−45.7624	−1.80469	−0.902346	−	0.431012i	$-0.858157\pi$
$643$	−45.7624	−1.80469	−0.902346	+	0.431012i	$0.858157\pi$
$644$	−0.426912	−0.0168227
$645$	−2.34462	−0.0923192
$646$	−2.46255	−0.0968879
$647$	−14.5828	−0.573310	−0.286655	−	0.958034i	$-0.592543\pi$
$647$	−14.5828	−0.573310	−0.286655	+	0.958034i	$0.592543\pi$
$648$	−24.8188	−0.974973
$649$	0	0
$650$	3.18211	0.124812
$651$	−0.726570	−0.0284765
$652$	1.42859	0.0559479
$653$	17.5533	0.686913	0.343456	−	0.939169i	$-0.388402\pi$
$653$	17.5533	0.686913	0.343456	+	0.939169i	$0.388402\pi$
$654$	2.00558	0.0784245
$655$	−12.4893	−0.487996
$656$	22.1463	0.864668
$657$	−0.294606	−0.0114937
$658$	7.92997	0.309142
$659$	15.1180	0.588915	0.294458	−	0.955665i	$-0.404861\pi$
$659$	15.1180	0.588915	0.294458	+	0.955665i	$0.404861\pi$
$660$	0	0
$661$	−38.6231	−1.50226	−0.751132	−	0.660152i	$-0.770492\pi$
$661$	−38.6231	−1.50226	−0.751132	+	0.660152i	$0.770492\pi$
$662$	−33.1844	−1.28975
$663$	−0.528598	−0.0205291
$664$	−48.0756	−1.86570
$665$	−1.95659	−0.0758732
$666$	−24.8840	−0.964234
$667$	−0.659572	−0.0255387
$668$	0.0102570	0.000396856 0
$669$	−4.76349	−0.184167
$670$	20.3669	0.786843
$671$	0	0
$672$	−0.218114	−0.00841392
$673$	41.8975	1.61503	0.807515	−	0.589847i	$-0.200812\pi$
$673$	41.8975	1.61503	0.807515	+	0.589847i	$0.200812\pi$
$674$	−32.2606	−1.24263
$675$	1.44350	0.0555604
$676$	1.19302	0.0458853
$677$	−15.8363	−0.608637	−0.304318	−	0.952570i	$-0.598429\pi$
$677$	−15.8363	−0.608637	−0.304318	+	0.952570i	$0.598429\pi$
$678$	3.14611	0.120825
$679$	3.11103	0.119391
$680$	−2.71741	−0.104208
$681$	−1.97626	−0.0757304
$682$	0	0
$683$	16.7634	0.641434	0.320717	−	0.947175i	$-0.396076\pi$
$683$	16.7634	0.641434	0.320717	+	0.947175i	$0.396076\pi$
$684$	−0.915370	−0.0350000
$685$	16.6161	0.634869
$686$	1.35681	0.0518031
$687$	−3.05882	−0.116701
$688$	−35.2843	−1.34520
$689$	−10.7608	−0.409955
$690$	−0.884725	−0.0336809
$691$	−0.259485	−0.00987129	−0.00493564	−	0.999988i	$-0.501571\pi$
$691$	−0.259485	−0.00987129	−0.00493564	+	0.999988i	$0.501571\pi$
$692$	2.73934	0.104134
$693$	0	0
$694$	−3.13631	−0.119053
$695$	0.420472	0.0159494
$696$	−0.174936	−0.00663092
$697$	−5.61823	−0.212806
$698$	49.2079	1.86254
$699$	−0.673522	−0.0254750
$700$	−0.159077	−0.00601255
$701$	−14.0986	−0.532498	−0.266249	−	0.963904i	$-0.585784\pi$
$701$	−14.0986	−0.532498	−0.266249	+	0.963904i	$0.585784\pi$
$702$	4.59337	0.173366
$703$	−12.2014	−0.460186
$704$	0	0
$705$	−1.42008	−0.0534834
$706$	−14.4591	−0.544176
$707$	14.9247	0.561301
$708$	−0.373681	−0.0140438
$709$	18.0034	0.676131	0.338065	−	0.941123i	$-0.390227\pi$
$709$	18.0034	0.676131	0.338065	+	0.941123i	$0.390227\pi$
$710$	−3.01204	−0.113040
$711$	−18.5824	−0.696894
$712$	−8.00865	−0.300137
$713$	8.02505	0.300540
$714$	−0.305807	−0.0114445
$715$	0	0
$716$	2.89548	0.108209
$717$	0.253974	0.00948483
$718$	30.4722	1.13721
$719$	−20.5769	−0.767387	−0.383694	−	0.923460i	$-0.625348\pi$
$719$	−20.5769	−0.767387	−0.383694	+	0.923460i	$0.625348\pi$
$720$	10.7538	0.400769
$721$	0.991937	0.0369417
$722$	−20.5851	−0.766100
$723$	−5.90227	−0.219508
$724$	1.51801	0.0564163
$725$	−0.245772	−0.00912774
$726$	0	0
$727$	−2.37912	−0.0882368	−0.0441184	−	0.999026i	$-0.514048\pi$
$727$	−2.37912	−0.0882368	−0.0441184	+	0.999026i	$0.514048\pi$
$728$	−6.87041	−0.254634
$729$	−23.8641	−0.883856
$730$	0.135916	0.00503047
$731$	8.95119	0.331072
$732$	0.109361	0.00404211
$733$	−9.09774	−0.336033	−0.168016	−	0.985784i	$-0.553736\pi$
$733$	−9.09774	−0.336033	−0.168016	+	0.985784i	$0.553736\pi$
$734$	20.5004	0.756682
$735$	−0.242974	−0.00896224
$736$	2.40909	0.0888002
$737$	0	0
$738$	24.1679	0.889631
$739$	−12.3131	−0.452944	−0.226472	−	0.974018i	$-0.572719\pi$
$739$	−12.3131	−0.452944	−0.226472	+	0.974018i	$0.572719\pi$
$740$	−0.992020	−0.0364674
$741$	1.11495	0.0409588
$742$	−6.22539	−0.228541
$743$	−51.7175	−1.89733	−0.948666	−	0.316279i	$-0.897566\pi$
$743$	−51.7175	−1.89733	−0.948666	+	0.316279i	$0.897566\pi$
$744$	2.12845	0.0780327
$745$	10.1747	0.372772
$746$	−30.8203	−1.12841
$747$	−48.2646	−1.76591
$748$	0	0
$749$	−3.31075	−0.120972
$750$	−0.329669	−0.0120378
$751$	13.7321	0.501093	0.250546	−	0.968105i	$-0.419390\pi$
$751$	13.7321	0.501093	0.250546	+	0.968105i	$0.419390\pi$
$752$	−21.3710	−0.779319
$753$	3.81714	0.139104
$754$	−0.782072	−0.0284814
$755$	−5.10643	−0.185842
$756$	−0.229628	−0.00835149
$757$	−49.2807	−1.79114	−0.895568	−	0.444924i	$-0.853231\pi$
$757$	−49.2807	−1.79114	−0.895568	+	0.444924i	$0.853231\pi$
$758$	−2.04465	−0.0742650
$759$	0	0
$760$	5.73172	0.207911
$761$	12.4590	0.451637	0.225818	−	0.974169i	$-0.427494\pi$
$761$	12.4590	0.451637	0.225818	+	0.974169i	$0.427494\pi$
$762$	−3.35576	−0.121566
$763$	−6.08363	−0.220242
$764$	−1.59188	−0.0575922
$765$	−2.72809	−0.0986343
$766$	−20.0892	−0.725853
$767$	−22.6741	−0.818714
$768$	0.921616	0.0332559
$769$	−21.9501	−0.791540	−0.395770	−	0.918350i	$-0.629522\pi$
$769$	−21.9501	−0.791540	−0.395770	+	0.918350i	$0.629522\pi$
$770$	0	0
$771$	−5.94983	−0.214278
$772$	−2.15282	−0.0774819
$773$	23.0657	0.829617	0.414808	−	0.909909i	$-0.363849\pi$
$773$	23.0657	0.829617	0.414808	+	0.909909i	$0.363849\pi$
$774$	−38.5052	−1.38404
$775$	2.99032	0.107415
$776$	−9.11362	−0.327160
$777$	−1.51521	−0.0543578
$778$	−45.5910	−1.63452
$779$	11.8503	0.424582
$780$	0.0906494	0.00324577
$781$	0	0
$782$	3.37767	0.120785
$783$	−0.354772	−0.0126785
$784$	−3.65654	−0.130591
$785$	3.85612	0.137631
$786$	4.11732	0.146860
$787$	−46.7274	−1.66565	−0.832826	−	0.553534i	$-0.813279\pi$
$787$	−46.7274	−1.66565	−0.832826	+	0.553534i	$0.813279\pi$
$788$	−3.53925	−0.126081
$789$	5.27479	0.187788
$790$	8.57293	0.305011
$791$	−9.54323	−0.339318
$792$	0	0
$793$	6.63579	0.235644
$794$	−32.2109	−1.14312
$795$	1.11483	0.0395390
$796$	1.50257	0.0532570
$797$	49.0362	1.73695	0.868475	−	0.495732i	$-0.165100\pi$
$797$	49.0362	1.73695	0.868475	+	0.495732i	$0.165100\pi$
$798$	0.645026	0.0228337
$799$	5.42154	0.191800
$800$	0.897683	0.0317379
$801$	−8.04013	−0.284084
$802$	34.7749	1.22794
$803$	0	0
$804$	0.580198	0.0204620
$805$	2.68368	0.0945872
$806$	9.51551	0.335169
$807$	2.56886	0.0904282
$808$	−43.7211	−1.53810
$809$	−9.38528	−0.329969	−0.164984	−	0.986296i	$-0.552757\pi$
$809$	−9.38528	−0.329969	−0.164984	+	0.986296i	$0.552757\pi$
$810$	11.4951	0.403896
$811$	9.21722	0.323660	0.161830	−	0.986819i	$-0.448260\pi$
$811$	9.21722	0.323660	0.161830	+	0.986819i	$0.448260\pi$
$812$	0.0390967	0.00137203
$813$	−5.78568	−0.202913
$814$	0	0
$815$	−8.98048	−0.314573
$816$	0.824137	0.0288506
$817$	−18.8804	−0.660541
$818$	36.0301	1.25976
$819$	−6.89742	−0.241015
$820$	0.963471	0.0336459
$821$	−17.3336	−0.604946	−0.302473	−	0.953158i	$-0.597812\pi$
$821$	−17.3336	−0.604946	−0.302473	+	0.953158i	$0.597812\pi$
$822$	−5.47781	−0.191061
$823$	−42.7706	−1.49089	−0.745445	−	0.666567i	$-0.767763\pi$
$823$	−42.7706	−1.49089	−0.745445	+	0.666567i	$0.767763\pi$
$824$	−2.90583	−0.101229
$825$	0	0
$826$	−13.1175	−0.456416
$827$	19.0832	0.663589	0.331794	−	0.943352i	$-0.392346\pi$
$827$	19.0832	0.663589	0.331794	+	0.943352i	$0.392346\pi$
$828$	1.25553	0.0436328
$829$	−40.8201	−1.41774	−0.708870	−	0.705340i	$-0.750795\pi$
$829$	−40.8201	−1.41774	−0.708870	+	0.705340i	$0.750795\pi$
$830$	22.2668	0.772890
$831$	0.0868465	0.00301267
$832$	20.0078	0.693647
$833$	0.927617	0.0321400
$834$	−0.138617	−0.00479990
$835$	−0.0644782	−0.00223136
$836$	0	0
$837$	4.31653	0.149201
$838$	−47.0573	−1.62557
$839$	33.0074	1.13954	0.569771	−	0.821804i	$-0.307032\pi$
$839$	33.0074	1.13954	0.569771	+	0.821804i	$0.307032\pi$
$840$	0.711781	0.0245588
$841$	−28.9396	−0.997917
$842$	33.6362	1.15918
$843$	1.68475	0.0580259
$844$	−0.757022	−0.0260578
$845$	−7.49961	−0.257994
$846$	−23.3218	−0.801818
$847$	0	0
$848$	16.7772	0.576131
$849$	2.98405	0.102412
$850$	1.25860	0.0431695
$851$	16.7357	0.573691
$852$	−0.0858046	−0.00293962
$853$	48.6092	1.66435	0.832173	−	0.554516i	$-0.187097\pi$
$853$	48.6092	1.66435	0.832173	+	0.554516i	$0.187097\pi$
$854$	3.83896	0.131366
$855$	5.75425	0.196791
$856$	9.69867	0.331494
$857$	18.1003	0.618294	0.309147	−	0.951014i	$-0.399957\pi$
$857$	18.1003	0.618294	0.309147	+	0.951014i	$0.399957\pi$
$858$	0	0
$859$	−7.23154	−0.246737	−0.123368	−	0.992361i	$-0.539370\pi$
$859$	−7.23154	−0.246737	−0.123368	+	0.992361i	$0.539370\pi$
$860$	−1.53504	−0.0523444
$861$	1.47160	0.0501521
$862$	−8.95491	−0.305005
$863$	30.3494	1.03310	0.516552	−	0.856256i	$-0.327215\pi$
$863$	30.3494	1.03310	0.516552	+	0.856256i	$0.327215\pi$
$864$	1.29581	0.0440842
$865$	−17.2202	−0.585504
$866$	27.1633	0.923046
$867$	3.92149	0.133181
$868$	−0.475691	−0.0161460
$869$	0	0
$870$	0.0810233	0.00274695
$871$	35.2050	1.19288
$872$	17.8217	0.603519
$873$	−9.14944	−0.309662
$874$	−7.12438	−0.240986
$875$	1.00000	0.0338062
$876$	0.00387187	0.000130818 0
$877$	32.3026	1.09078	0.545391	−	0.838182i	$-0.316381\pi$
$877$	32.3026	1.09078	0.545391	+	0.838182i	$0.316381\pi$
$878$	−36.1203	−1.21900
$879$	−4.47836	−0.151051
$880$	0	0
$881$	23.1158	0.778792	0.389396	−	0.921070i	$-0.372684\pi$
$881$	23.1158	0.778792	0.389396	+	0.921070i	$0.372684\pi$
$882$	−3.99032	−0.134361
$883$	47.4436	1.59661	0.798303	−	0.602257i	$-0.205732\pi$
$883$	47.4436	1.59661	0.798303	+	0.602257i	$0.205732\pi$
$884$	−0.346078	−0.0116399
$885$	2.34906	0.0789626
$886$	9.97768	0.335207
$887$	−49.3267	−1.65623	−0.828114	−	0.560560i	$-0.810586\pi$
$887$	−49.3267	−1.65623	−0.828114	+	0.560560i	$0.810586\pi$
$888$	4.43873	0.148954
$889$	10.1792	0.341399
$890$	3.70930	0.124336
$891$	0	0
$892$	−3.11870	−0.104422
$893$	−11.4354	−0.382672
$894$	−3.35428	−0.112184
$895$	−18.2017	−0.608416
$896$	9.77963	0.326715
$897$	−1.52928	−0.0510612
$898$	2.37691	0.0793184
$899$	−0.734936	−0.0245115
$900$	0.467840	0.0155947
$901$	−4.25616	−0.141793
$902$	0	0
$903$	−2.34462	−0.0780240
$904$	27.9564	0.929816
$905$	−9.54258	−0.317206
$906$	1.68343	0.0559282
$907$	32.7141	1.08625	0.543126	−	0.839651i	$-0.317240\pi$
$907$	32.7141	1.08625	0.543126	+	0.839651i	$0.317240\pi$
$908$	−1.29387	−0.0429387
$909$	−43.8930	−1.45584
$910$	3.18211	0.105486
$911$	−15.9930	−0.529870	−0.264935	−	0.964266i	$-0.585351\pi$
$911$	−15.9930	−0.529870	−0.264935	+	0.964266i	$0.585351\pi$
$912$	−1.73832	−0.0575615
$913$	0	0
$914$	24.0400	0.795173
$915$	−0.687473	−0.0227272
$916$	−2.00264	−0.0661689
$917$	−12.4893	−0.412432
$918$	1.81679	0.0599629
$919$	47.6485	1.57178	0.785890	−	0.618366i	$-0.212205\pi$
$919$	47.6485	1.57178	0.785890	+	0.618366i	$0.212205\pi$
$920$	−7.86170	−0.259192
$921$	−6.76115	−0.222787
$922$	27.9734	0.921256
$923$	−5.20642	−0.171371
$924$	0	0
$925$	6.23609	0.205041
$926$	−17.8179	−0.585534
$927$	−2.91725	−0.0958151
$928$	−0.220625	−0.00724237
$929$	53.3770	1.75124	0.875622	−	0.482998i	$-0.160452\pi$
$929$	53.3770	1.75124	0.875622	+	0.482998i	$0.160452\pi$
$930$	−0.985814	−0.0323261
$931$	−1.95659	−0.0641245
$932$	−0.440961	−0.0144441
$933$	4.49842	0.147272
$934$	41.8897	1.37067
$935$	0	0
$936$	20.2056	0.660442
$937$	13.0806	0.427326	0.213663	−	0.976907i	$-0.431461\pi$
$937$	13.0806	0.427326	0.213663	+	0.976907i	$0.431461\pi$
$938$	20.3669	0.665004
$939$	2.28514	0.0745727
$940$	−0.929741	−0.0303248
$941$	−40.1799	−1.30983	−0.654913	−	0.755704i	$-0.727295\pi$
$941$	−40.1799	−1.30983	−0.654913	+	0.755704i	$0.727295\pi$
$942$	−1.27124	−0.0414193
$943$	−16.2540	−0.529304
$944$	35.3511	1.15058
$945$	1.44350	0.0469571
$946$	0	0
$947$	21.1138	0.686105	0.343053	−	0.939316i	$-0.388539\pi$
$947$	21.1138	0.686105	0.343053	+	0.939316i	$0.388539\pi$
$948$	0.244219	0.00793187
$949$	0.234936	0.00762634
$950$	−2.65471	−0.0861301
$951$	3.43887	0.111513
$952$	−2.71741	−0.0880717
$953$	−36.3562	−1.17769	−0.588846	−	0.808245i	$-0.700418\pi$
$953$	−36.3562	−1.17769	−0.588846	+	0.808245i	$0.700418\pi$
$954$	18.3086	0.592764
$955$	10.0070	0.323818
$956$	0.166279	0.00537784
$957$	0	0
$958$	−49.5160	−1.59979
$959$	16.6161	0.536562
$960$	−2.07283	−0.0669002
$961$	−22.0580	−0.711548
$962$	19.8439	0.639793
$963$	9.73679	0.313764
$964$	−3.86426	−0.124460
$965$	13.5332	0.435649
$966$	−0.884725	−0.0284656
$967$	−3.01730	−0.0970299	−0.0485149	−	0.998822i	$-0.515449\pi$
$967$	−3.01730	−0.0970299	−0.0485149	+	0.998822i	$0.515449\pi$
$968$	0	0
$969$	0.440989	0.0141666
$970$	4.22107	0.135530
$971$	49.6294	1.59268	0.796341	−	0.604847i	$-0.206766\pi$
$971$	49.6294	1.59268	0.796341	+	0.604847i	$0.206766\pi$
$972$	1.01635	0.0325994
$973$	0.420472	0.0134797
$974$	−39.3849	−1.26197
$975$	−0.569845	−0.0182497
$976$	−10.3458	−0.331162
$977$	−11.0956	−0.354979	−0.177490	−	0.984123i	$-0.556798\pi$
$977$	−11.0956	−0.354979	−0.177490	+	0.984123i	$0.556798\pi$
$978$	2.96058	0.0946691
$979$	0	0
$980$	−0.159077	−0.00508154
$981$	17.8917	0.571239
$982$	38.2571	1.22083
$983$	16.2497	0.518283	0.259142	−	0.965839i	$-0.416560\pi$
$983$	16.2497	0.518283	0.259142	+	0.965839i	$0.416560\pi$
$984$	−4.31099	−0.137429
$985$	22.2486	0.708901
$986$	−0.309328	−0.00985100
$987$	−1.42008	−0.0452018
$988$	0.729968	0.0232234
$989$	25.8966	0.823463
$990$	0	0
$991$	−31.8831	−1.01280	−0.506400	−	0.862299i	$-0.669024\pi$
$991$	−31.8831	−1.01280	−0.506400	+	0.862299i	$0.669024\pi$
$992$	2.68436	0.0852284
$993$	5.94259	0.188582
$994$	−3.01204	−0.0955360
$995$	−9.44551	−0.299443
$996$	0.634318	0.0200991
$997$	−10.3751	−0.328584	−0.164292	−	0.986412i	$-0.552534\pi$
$997$	−10.3751	−0.328584	−0.164292	+	0.986412i	$0.552534\pi$
$998$	−16.5282	−0.523190
$999$	9.00180	0.284804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bd.1.4	yes	5
11.10	odd	2		4235.2.a.bc.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bc.1.2	✓	5	11.10	odd	2
4235.2.a.bd.1.4	yes	5	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q+1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} -0.329669 q^{6} +1.00000 q^{7} -2.92945 q^{8} -2.94096 q^{9} +O(q^{10})\)	\(q+1.35681 q^{2} -0.242974 q^{3} -0.159077 q^{4} +1.00000 q^{5} -0.329669 q^{6} +1.00000 q^{7} -2.92945 q^{8} -2.94096 q^{9} +1.35681 q^{10} +0.0386517 q^{12} +2.34529 q^{13} +1.35681 q^{14} -0.242974 q^{15} -3.65654 q^{16} +0.927617 q^{17} -3.99032 q^{18} -1.95659 q^{19} -0.159077 q^{20} -0.242974 q^{21} +2.68368 q^{23} +0.711781 q^{24} +1.00000 q^{25} +3.18211 q^{26} +1.44350 q^{27} -0.159077 q^{28} -0.245772 q^{29} -0.329669 q^{30} +2.99032 q^{31} +0.897683 q^{32} +1.25860 q^{34} +1.00000 q^{35} +0.467840 q^{36} +6.23609 q^{37} -2.65471 q^{38} -0.569845 q^{39} -2.92945 q^{40} -6.05663 q^{41} -0.329669 q^{42} +9.64965 q^{43} -2.94096 q^{45} +3.64123 q^{46} +5.84459 q^{47} +0.888445 q^{48} +1.00000 q^{49} +1.35681 q^{50} -0.225387 q^{51} -0.373082 q^{52} -4.58827 q^{53} +1.95855 q^{54} -2.92945 q^{56} +0.475400 q^{57} -0.333465 q^{58} -9.66792 q^{59} +0.0386517 q^{60} +2.82941 q^{61} +4.05728 q^{62} -2.94096 q^{63} +8.53106 q^{64} +2.34529 q^{65} +15.0109 q^{67} -0.147563 q^{68} -0.652064 q^{69} +1.35681 q^{70} -2.21995 q^{71} +8.61540 q^{72} +0.100173 q^{73} +8.46116 q^{74} -0.242974 q^{75} +0.311248 q^{76} -0.773170 q^{78} +6.31847 q^{79} -3.65654 q^{80} +8.47216 q^{81} -8.21767 q^{82} +16.4112 q^{83} +0.0386517 q^{84} +0.927617 q^{85} +13.0927 q^{86} +0.0597162 q^{87} +2.73384 q^{89} -3.99032 q^{90} +2.34529 q^{91} -0.426912 q^{92} -0.726570 q^{93} +7.92997 q^{94} -1.95659 q^{95} -0.218114 q^{96} +3.11103 q^{97} +1.35681 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} + 9 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 + 9 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9	\( 5 q + 2 q^{3} + 4 q^{4} + 5 q^{5} + 9 q^{6} + 5 q^{7} + 6 q^{8} + 7 q^{9} + 3 q^{12} + 6 q^{13} + 2 q^{15} - 6 q^{16} + 2 q^{17} - 3 q^{18} + 7 q^{19} + 4 q^{20} + 2 q^{21} + 5 q^{23} + 8 q^{24} + 5 q^{25} + 9 q^{26} - 7 q^{27} + 4 q^{28} + 11 q^{29} + 9 q^{30} - 2 q^{31} + 7 q^{32} + 8 q^{34} + 5 q^{35} + q^{36} + 2 q^{37} - 19 q^{38} + 2 q^{39} + 6 q^{40} + 13 q^{41} + 9 q^{42} + 10 q^{43} + 7 q^{45} + 2 q^{46} - 2 q^{47} + 32 q^{48} + 5 q^{49} + 30 q^{51} - 8 q^{52} - 14 q^{53} + 16 q^{54} + 6 q^{56} + 6 q^{57} + 4 q^{58} + 6 q^{59} + 3 q^{60} + 20 q^{61} - 15 q^{62} + 7 q^{63} - 6 q^{64} + 6 q^{65} - 9 q^{67} + 3 q^{68} - 30 q^{69} - 10 q^{71} + 38 q^{72} + 15 q^{73} - 19 q^{74} + 2 q^{75} - 5 q^{76} + 21 q^{78} + 23 q^{79} - 6 q^{80} + 13 q^{81} - 16 q^{82} + 8 q^{83} + 3 q^{84} + 2 q^{85} - 29 q^{86} - 22 q^{87} + 7 q^{89} - 3 q^{90} + 6 q^{91} + 26 q^{92} - 45 q^{93} - 14 q^{94} + 7 q^{95} - 18 q^{96} + 21 q^{97}+O(q^{100}) \) 5 * q + 2 * q^3 + 4 * q^4 + 5 * q^5 + 9 * q^6 + 5 * q^7 + 6 * q^8 + 7 * q^9 + 3 * q^12 + 6 * q^13 + 2 * q^15 - 6 * q^16 + 2 * q^17 - 3 * q^18 + 7 * q^19 + 4 * q^20 + 2 * q^21 + 5 * q^23 + 8 * q^24 + 5 * q^25 + 9 * q^26 - 7 * q^27 + 4 * q^28 + 11 * q^29 + 9 * q^30 - 2 * q^31 + 7 * q^32 + 8 * q^34 + 5 * q^35 + q^36 + 2 * q^37 - 19 * q^38 + 2 * q^39 + 6 * q^40 + 13 * q^41 + 9 * q^42 + 10 * q^43 + 7 * q^45 + 2 * q^46 - 2 * q^47 + 32 * q^48 + 5 * q^49 + 30 * q^51 - 8 * q^52 - 14 * q^53 + 16 * q^54 + 6 * q^56 + 6 * q^57 + 4 * q^58 + 6 * q^59 + 3 * q^60 + 20 * q^61 - 15 * q^62 + 7 * q^63 - 6 * q^64 + 6 * q^65 - 9 * q^67 + 3 * q^68 - 30 * q^69 - 10 * q^71 + 38 * q^72 + 15 * q^73 - 19 * q^74 + 2 * q^75 - 5 * q^76 + 21 * q^78 + 23 * q^79 - 6 * q^80 + 13 * q^81 - 16 * q^82 + 8 * q^83 + 3 * q^84 + 2 * q^85 - 29 * q^86 - 22 * q^87 + 7 * q^89 - 3 * q^90 + 6 * q^91 + 26 * q^92 - 45 * q^93 - 14 * q^94 + 7 * q^95 - 18 * q^96 + 21 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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