LMFDB - Embedded newform 1805.2.a.w.1.13

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 29x^{14} + 339x^{12} - 2038x^{10} + 6639x^{8} - 11261x^{6} + 8701x^{4} - 2592x^{2} + 256 $ x^16 - 29x^14 + 339x^12 - 2038x^10 + 6639x^8 - 11261x^6 + 8701x^4 - 2592*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$2.01896$ 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)

$f(q)$	$=$	$q+2.01896 q^{2} +1.69608 q^{3} +2.07621 q^{4} +1.00000 q^{5} +3.42432 q^{6} +1.43286 q^{7} +0.153862 q^{8} -0.123308 q^{9} +O(q^{10})$	\(q+2.01896 q^{2} +1.69608 q^{3} +2.07621 q^{4} +1.00000 q^{5} +3.42432 q^{6} +1.43286 q^{7} +0.153862 q^{8} -0.123308 q^{9} +2.01896 q^{10} +3.84643 q^{11} +3.52142 q^{12} -1.44713 q^{13} +2.89289 q^{14} +1.69608 q^{15} -3.84178 q^{16} +4.92264 q^{17} -0.248953 q^{18} +2.07621 q^{20} +2.43024 q^{21} +7.76580 q^{22} +5.85823 q^{23} +0.260962 q^{24} +1.00000 q^{25} -2.92170 q^{26} -5.29738 q^{27} +2.97491 q^{28} -7.03515 q^{29} +3.42432 q^{30} +1.72662 q^{31} -8.06412 q^{32} +6.52386 q^{33} +9.93862 q^{34} +1.43286 q^{35} -0.256012 q^{36} -11.6080 q^{37} -2.45445 q^{39} +0.153862 q^{40} +11.8936 q^{41} +4.90657 q^{42} -1.99331 q^{43} +7.98599 q^{44} -0.123308 q^{45} +11.8275 q^{46} -2.91650 q^{47} -6.51596 q^{48} -4.94692 q^{49} +2.01896 q^{50} +8.34920 q^{51} -3.00454 q^{52} +10.4407 q^{53} -10.6952 q^{54} +3.84643 q^{55} +0.220462 q^{56} -14.2037 q^{58} +4.52619 q^{59} +3.52142 q^{60} +0.465044 q^{61} +3.48599 q^{62} -0.176682 q^{63} -8.59761 q^{64} -1.44713 q^{65} +13.1714 q^{66} -2.72787 q^{67} +10.2204 q^{68} +9.93603 q^{69} +2.89289 q^{70} -6.03917 q^{71} -0.0189723 q^{72} +10.3694 q^{73} -23.4361 q^{74} +1.69608 q^{75} +5.51139 q^{77} -4.95544 q^{78} -13.6267 q^{79} -3.84178 q^{80} -8.61487 q^{81} +24.0128 q^{82} -15.7551 q^{83} +5.04569 q^{84} +4.92264 q^{85} -4.02441 q^{86} -11.9322 q^{87} +0.591818 q^{88} +6.11451 q^{89} -0.248953 q^{90} -2.07353 q^{91} +12.1629 q^{92} +2.92850 q^{93} -5.88831 q^{94} -13.6774 q^{96} -4.35718 q^{97} -9.98764 q^{98} -0.474294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	$ 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) $ 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * 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 $

$2$	2.01896	1.42762	0.713811	−	0.700338i	$-0.246968\pi$
$2$	2.01896	1.42762	0.713811	+	0.700338i	$0.246968\pi$
$3$	1.69608	0.979233	0.489617	−	0.871938i	$-0.337137\pi$
$3$	1.69608	0.979233	0.489617	+	0.871938i	$0.337137\pi$
$4$	2.07621	1.03810
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.42432	1.39797
$7$	1.43286	0.541569	0.270785	−	0.962640i	$-0.412717\pi$
$7$	1.43286	0.541569	0.270785	+	0.962640i	$0.412717\pi$
$8$	0.153862	0.0543983
$9$	−0.123308	−0.0411025
$10$	2.01896	0.638452
$11$	3.84643	1.15974	0.579871	−	0.814708i	$-0.303103\pi$
$11$	3.84643	1.15974	0.579871	+	0.814708i	$0.303103\pi$
$12$	3.52142	1.01655
$13$	−1.44713	−0.401361	−0.200681	−	0.979657i	$-0.564315\pi$
$13$	−1.44713	−0.401361	−0.200681	+	0.979657i	$0.564315\pi$
$14$	2.89289	0.773156
$15$	1.69608	0.437926
$16$	−3.84178	−0.960444
$17$	4.92264	1.19392	0.596958	−	0.802273i	$-0.296376\pi$
$17$	4.92264	1.19392	0.596958	+	0.802273i	$0.296376\pi$
$18$	−0.248953	−0.0586789
$19$	0	0
$19$	0	0
$20$	2.07621	0.464254
$21$	2.43024	0.530323
$22$	7.76580	1.65567
$23$	5.85823	1.22153	0.610763	−	0.791814i	$-0.290863\pi$
$23$	5.85823	1.22153	0.610763	+	0.791814i	$0.290863\pi$
$24$	0.260962	0.0532686
$25$	1.00000	0.200000
$26$	−2.92170	−0.572992
$27$	−5.29738	−1.01948
$28$	2.97491	0.562205
$29$	−7.03515	−1.30639	−0.653197	−	0.757188i	$-0.726573\pi$
$29$	−7.03515	−1.30639	−0.653197	+	0.757188i	$0.726573\pi$
$30$	3.42432	0.625193
$31$	1.72662	0.310111	0.155055	−	0.987906i	$-0.450444\pi$
$31$	1.72662	0.310111	0.155055	+	0.987906i	$0.450444\pi$
$32$	−8.06412	−1.42555
$33$	6.52386	1.13566
$34$	9.93862	1.70446
$35$	1.43286	0.242197
$36$	−0.256012	−0.0426687
$37$	−11.6080	−1.90834	−0.954172	−	0.299259i	$-0.903261\pi$
$37$	−11.6080	−1.90834	−0.954172	+	0.299259i	$0.903261\pi$
$38$	0	0
$39$	−2.45445	−0.393026
$40$	0.153862	0.0243277
$41$	11.8936	1.85747	0.928736	−	0.370741i	$-0.120896\pi$
$41$	11.8936	1.85747	0.928736	+	0.370741i	$0.120896\pi$
$42$	4.90657	0.757100
$43$	−1.99331	−0.303976	−0.151988	−	0.988382i	$-0.548568\pi$
$43$	−1.99331	−0.303976	−0.151988	+	0.988382i	$0.548568\pi$
$44$	7.98599	1.20393
$45$	−0.123308	−0.0183816
$46$	11.8275	1.74388
$47$	−2.91650	−0.425416	−0.212708	−	0.977116i	$-0.568228\pi$
$47$	−2.91650	−0.425416	−0.212708	+	0.977116i	$0.568228\pi$
$48$	−6.51596	−0.940498
$49$	−4.94692	−0.706703
$50$	2.01896	0.285524
$51$	8.34920	1.16912
$52$	−3.00454	−0.416655
$53$	10.4407	1.43414	0.717070	−	0.697001i	$-0.245483\pi$
$53$	10.4407	1.43414	0.717070	+	0.697001i	$0.245483\pi$
$54$	−10.6952	−1.45543
$55$	3.84643	0.518653
$56$	0.220462	0.0294605
$57$	0	0
$58$	−14.2037	−1.86504
$59$	4.52619	0.589260	0.294630	−	0.955611i	$-0.404804\pi$
$59$	4.52619	0.589260	0.294630	+	0.955611i	$0.404804\pi$
$60$	3.52142	0.454613
$61$	0.465044	0.0595428	0.0297714	−	0.999557i	$-0.490522\pi$
$61$	0.465044	0.0595428	0.0297714	+	0.999557i	$0.490522\pi$
$62$	3.48599	0.442721
$63$	−0.176682	−0.0222599
$64$	−8.59761	−1.07470
$65$	−1.44713	−0.179494
$66$	13.1714	1.62129
$67$	−2.72787	−0.333262	−0.166631	−	0.986019i	$-0.553289\pi$
$67$	−2.72787	−0.333262	−0.166631	+	0.986019i	$0.553289\pi$
$68$	10.2204	1.23941
$69$	9.93603	1.19616
$70$	2.89289	0.345766
$71$	−6.03917	−0.716718	−0.358359	−	0.933584i	$-0.616664\pi$
$71$	−6.03917	−0.716718	−0.358359	+	0.933584i	$0.616664\pi$
$72$	−0.0189723	−0.00223591
$73$	10.3694	1.21365	0.606823	−	0.794837i	$-0.292444\pi$
$73$	10.3694	1.21365	0.606823	+	0.794837i	$0.292444\pi$
$74$	−23.4361	−2.72439
$75$	1.69608	0.195847
$76$	0	0
$77$	5.51139	0.628081
$78$	−4.95544	−0.561093
$79$	−13.6267	−1.53312	−0.766561	−	0.642172i	$-0.778034\pi$
$79$	−13.6267	−1.53312	−0.766561	+	0.642172i	$0.778034\pi$
$80$	−3.84178	−0.429524
$81$	−8.61487	−0.957208
$82$	24.0128	2.65177
$83$	−15.7551	−1.72935	−0.864675	−	0.502332i	$-0.832476\pi$
$83$	−15.7551	−1.72935	−0.864675	+	0.502332i	$0.832476\pi$
$84$	5.04569	0.550530
$85$	4.92264	0.533935
$86$	−4.02441	−0.433963
$87$	−11.9322	−1.27926
$88$	0.591818	0.0630880
$89$	6.11451	0.648137	0.324069	−	0.946034i	$-0.394949\pi$
$89$	6.11451	0.648137	0.324069	+	0.946034i	$0.394949\pi$
$90$	−0.248953	−0.0262420
$91$	−2.07353	−0.217365
$92$	12.1629	1.26807
$93$	2.92850	0.303671
$94$	−5.88831	−0.607333
$95$	0	0
$96$	−13.6774	−1.39594
$97$	−4.35718	−0.442405	−0.221202	−	0.975228i	$-0.570998\pi$
$97$	−4.35718	−0.442405	−0.221202	+	0.975228i	$0.570998\pi$
$98$	−9.98764	−1.00890
$99$	−0.474294	−0.0476684
$100$	2.07621	0.207621
$101$	−18.0554	−1.79658	−0.898291	−	0.439402i	$-0.855190\pi$
$101$	−18.0554	−1.79658	−0.898291	+	0.439402i	$0.855190\pi$
$102$	16.8567	1.66906
$103$	−3.18777	−0.314101	−0.157050	−	0.987591i	$-0.550198\pi$
$103$	−3.18777	−0.314101	−0.157050	+	0.987591i	$0.550198\pi$
$104$	−0.222658	−0.0218334
$105$	2.43024	0.237168
$106$	21.0794	2.04741
$107$	16.7785	1.62204	0.811022	−	0.585016i	$-0.198912\pi$
$107$	16.7785	1.62204	0.811022	+	0.585016i	$0.198912\pi$
$108$	−10.9985	−1.05833
$109$	−6.39265	−0.612305	−0.306152	−	0.951983i	$-0.599042\pi$
$109$	−6.39265	−0.612305	−0.306152	+	0.951983i	$0.599042\pi$
$110$	7.76580	0.740440
$111$	−19.6881	−1.86871
$112$	−5.50472	−0.520147
$113$	−2.68206	−0.252307	−0.126154	−	0.992011i	$-0.540263\pi$
$113$	−2.68206	−0.252307	−0.126154	+	0.992011i	$0.540263\pi$
$114$	0	0
$115$	5.85823	0.546283
$116$	−14.6064	−1.35617
$117$	0.178442	0.0164970
$118$	9.13821	0.841241
$119$	7.05344	0.646588
$120$	0.260962	0.0238225
$121$	3.79503	0.345003
$122$	0.938906	0.0850045
$123$	20.1726	1.81890
$124$	3.58483	0.321927
$125$	1.00000	0.0894427
$126$	−0.356715	−0.0317787
$127$	−14.4322	−1.28065	−0.640326	−	0.768104i	$-0.721201\pi$
$127$	−14.4322	−1.28065	−0.640326	+	0.768104i	$0.721201\pi$
$128$	−1.23000	−0.108718
$129$	−3.38081	−0.297664
$130$	−2.92170	−0.256250
$131$	10.0757	0.880322	0.440161	−	0.897919i	$-0.354921\pi$
$131$	10.0757	0.880322	0.440161	+	0.897919i	$0.354921\pi$
$132$	13.5449	1.17893
$133$	0	0
$134$	−5.50746	−0.475772
$135$	−5.29738	−0.455926
$136$	0.757406	0.0649470
$137$	1.74393	0.148994	0.0744972	−	0.997221i	$-0.476265\pi$
$137$	1.74393	0.148994	0.0744972	+	0.997221i	$0.476265\pi$
$138$	20.0605	1.70766
$139$	−2.92874	−0.248412	−0.124206	−	0.992256i	$-0.539638\pi$
$139$	−2.92874	−0.248412	−0.124206	+	0.992256i	$0.539638\pi$
$140$	2.97491	0.251426
$141$	−4.94663	−0.416581
$142$	−12.1929	−1.02320
$143$	−5.56628	−0.465476
$144$	0.473720	0.0394767
$145$	−7.03515	−0.584237
$146$	20.9354	1.73263
$147$	−8.39038	−0.692027
$148$	−24.1006	−1.98106
$149$	13.6129	1.11521	0.557607	−	0.830105i	$-0.311720\pi$
$149$	13.6129	1.11521	0.557607	+	0.830105i	$0.311720\pi$
$150$	3.42432	0.279595
$151$	−13.1668	−1.07150	−0.535749	−	0.844377i	$-0.679971\pi$
$151$	−13.1668	−1.07150	−0.535749	+	0.844377i	$0.679971\pi$
$152$	0	0
$153$	−0.606999	−0.0490730
$154$	11.1273	0.896662
$155$	1.72662	0.138686
$156$	−5.09594	−0.408002
$157$	−3.18511	−0.254199	−0.127100	−	0.991890i	$-0.540567\pi$
$157$	−3.18511	−0.254199	−0.127100	+	0.991890i	$0.540567\pi$
$158$	−27.5118	−2.18872
$159$	17.7083	1.40436
$160$	−8.06412	−0.637525
$161$	8.39401	0.661541
$162$	−17.3931	−1.36653
$163$	−2.56404	−0.200831	−0.100416	−	0.994946i	$-0.532017\pi$
$163$	−2.56404	−0.200831	−0.100416	+	0.994946i	$0.532017\pi$
$164$	24.6937	1.92825
$165$	6.52386	0.507882
$166$	−31.8090	−2.46886
$167$	−12.1721	−0.941903	−0.470952	−	0.882159i	$-0.656089\pi$
$167$	−12.1721	−0.941903	−0.470952	+	0.882159i	$0.656089\pi$
$168$	0.373921	0.0288487
$169$	−10.9058	−0.838909
$170$	9.93862	0.762258
$171$	0	0
$172$	−4.13852	−0.315559
$173$	−7.98018	−0.606722	−0.303361	−	0.952876i	$-0.598109\pi$
$173$	−7.98018	−0.606722	−0.303361	+	0.952876i	$0.598109\pi$
$174$	−24.0906	−1.82631
$175$	1.43286	0.108314
$176$	−14.7771	−1.11387
$177$	7.67679	0.577023
$178$	12.3450	0.925295
$179$	−11.6075	−0.867586	−0.433793	−	0.901012i	$-0.642825\pi$
$179$	−11.6075	−0.867586	−0.433793	+	0.901012i	$0.642825\pi$
$180$	−0.256012	−0.0190820
$181$	22.4450	1.66832	0.834162	−	0.551519i	$-0.185952\pi$
$181$	22.4450	1.66832	0.834162	+	0.551519i	$0.185952\pi$
$182$	−4.18638	−0.310315
$183$	0.788752	0.0583062
$184$	0.901357	0.0664489
$185$	−11.6080	−0.853437
$186$	5.91252	0.433527
$187$	18.9346	1.38463
$188$	−6.05527	−0.441626
$189$	−7.59040	−0.552120
$190$	0	0
$191$	25.7627	1.86413	0.932063	−	0.362296i	$-0.118007\pi$
$191$	25.7627	1.86413	0.932063	+	0.362296i	$0.118007\pi$
$192$	−14.5822	−1.05238
$193$	−3.55700	−0.256039	−0.128019	−	0.991772i	$-0.540862\pi$
$193$	−3.55700	−0.256039	−0.128019	+	0.991772i	$0.540862\pi$
$194$	−8.79699	−0.631587
$195$	−2.45445	−0.175767
$196$	−10.2708	−0.733631
$197$	22.2789	1.58730	0.793651	−	0.608373i	$-0.208177\pi$
$197$	22.2789	1.58730	0.793651	+	0.608373i	$0.208177\pi$
$198$	−0.957582	−0.0680524
$199$	9.08820	0.644245	0.322123	−	0.946698i	$-0.395604\pi$
$199$	9.08820	0.644245	0.322123	+	0.946698i	$0.395604\pi$
$200$	0.153862	0.0108797
$201$	−4.62668	−0.326341
$202$	−36.4532	−2.56484
$203$	−10.0804	−0.707503
$204$	17.3347	1.21367
$205$	11.8936	0.830687
$206$	−6.43599	−0.448417
$207$	−0.722364	−0.0502078
$208$	5.55954	0.385485
$209$	0	0
$210$	4.90657	0.338586
$211$	13.2606	0.912895	0.456448	−	0.889750i	$-0.349122\pi$
$211$	13.2606	0.912895	0.456448	+	0.889750i	$0.349122\pi$
$212$	21.6771	1.48879
$213$	−10.2429	−0.701834
$214$	33.8753	2.31566
$215$	−1.99331	−0.135942
$216$	−0.815064	−0.0554581
$217$	2.47401	0.167947
$218$	−12.9065	−0.874139
$219$	17.5873	1.18844
$220$	7.98599	0.538415
$221$	−7.12369	−0.479191
$222$	−39.7496	−2.66782
$223$	−13.7775	−0.922612	−0.461306	−	0.887241i	$-0.652619\pi$
$223$	−13.7775	−0.922612	−0.461306	+	0.887241i	$0.652619\pi$
$224$	−11.5547	−0.772034
$225$	−0.123308	−0.00822051
$226$	−5.41498	−0.360199
$227$	9.28710	0.616407	0.308203	−	0.951321i	$-0.400272\pi$
$227$	9.28710	0.616407	0.308203	+	0.951321i	$0.400272\pi$
$228$	0	0
$229$	18.9527	1.25243	0.626216	−	0.779650i	$-0.284603\pi$
$229$	18.9527	1.25243	0.626216	+	0.779650i	$0.284603\pi$
$230$	11.8275	0.779885
$231$	9.34777	0.615038
$232$	−1.08244	−0.0710657
$233$	−15.1163	−0.990302	−0.495151	−	0.868807i	$-0.664887\pi$
$233$	−15.1163	−0.990302	−0.495151	+	0.868807i	$0.664887\pi$
$234$	0.360267	0.0235514
$235$	−2.91650	−0.190252
$236$	9.39732	0.611713
$237$	−23.1120	−1.50128
$238$	14.2406	0.923083
$239$	−28.0462	−1.81416	−0.907079	−	0.420961i	$-0.861693\pi$
$239$	−28.0462	−1.81416	−0.907079	+	0.420961i	$0.861693\pi$
$240$	−6.51596	−0.420604
$241$	10.4493	0.673101	0.336550	−	0.941665i	$-0.390740\pi$
$241$	10.4493	0.673101	0.336550	+	0.941665i	$0.390740\pi$
$242$	7.66202	0.492534
$243$	1.28063	0.0821523
$244$	0.965528	0.0618116
$245$	−4.94692	−0.316047
$246$	40.7276	2.59670
$247$	0	0
$248$	0.265661	0.0168695
$249$	−26.7220	−1.69344
$250$	2.01896	0.127690
$251$	3.20350	0.202203	0.101101	−	0.994876i	$-0.467763\pi$
$251$	3.20350	0.202203	0.101101	+	0.994876i	$0.467763\pi$
$252$	−0.366829	−0.0231081
$253$	22.5333	1.41665
$254$	−29.1381	−1.82829
$255$	8.34920	0.522847
$256$	14.7119	0.919493
$257$	−23.2489	−1.45023	−0.725115	−	0.688628i	$-0.758213\pi$
$257$	−23.2489	−1.45023	−0.725115	+	0.688628i	$0.758213\pi$
$258$	−6.82572	−0.424951
$259$	−16.6326	−1.03350
$260$	−3.00454	−0.186334
$261$	0.867488	0.0536961
$262$	20.3426	1.25677
$263$	14.9822	0.923842	0.461921	−	0.886921i	$-0.347160\pi$
$263$	14.9822	0.923842	0.461921	+	0.886921i	$0.347160\pi$
$264$	1.00377	0.0617779
$265$	10.4407	0.641367
$266$	0	0
$267$	10.3707	0.634677
$268$	−5.66362	−0.345960
$269$	3.98819	0.243164	0.121582	−	0.992581i	$-0.461203\pi$
$269$	3.98819	0.243164	0.121582	+	0.992581i	$0.461203\pi$
$270$	−10.6952	−0.650890
$271$	8.65559	0.525790	0.262895	−	0.964824i	$-0.415323\pi$
$271$	8.65559	0.525790	0.262895	+	0.964824i	$0.415323\pi$
$272$	−18.9117	−1.14669
$273$	−3.51687	−0.212851
$274$	3.52094	0.212708
$275$	3.84643	0.231949
$276$	20.6293	1.24174
$277$	−0.830885	−0.0499230	−0.0249615	−	0.999688i	$-0.507946\pi$
$277$	−0.830885	−0.0499230	−0.0249615	+	0.999688i	$0.507946\pi$
$278$	−5.91301	−0.354639
$279$	−0.212906	−0.0127463
$280$	0.220462	0.0131751
$281$	−0.131759	−0.00786006	−0.00393003	−	0.999992i	$-0.501251\pi$
$281$	−0.131759	−0.00786006	−0.00393003	+	0.999992i	$0.501251\pi$
$282$	−9.98705	−0.594720
$283$	16.0000	0.951099	0.475550	−	0.879689i	$-0.342249\pi$
$283$	16.0000	0.951099	0.475550	+	0.879689i	$0.342249\pi$
$284$	−12.5386	−0.744028
$285$	0	0
$286$	−11.2381	−0.664523
$287$	17.0419	1.00595
$288$	0.994368	0.0585937
$289$	7.23238	0.425434
$290$	−14.2037	−0.834070
$291$	−7.39014	−0.433218
$292$	21.5290	1.25989
$293$	15.8251	0.924511	0.462256	−	0.886747i	$-0.347040\pi$
$293$	15.8251	0.924511	0.462256	+	0.886747i	$0.347040\pi$
$294$	−16.9399	−0.987952
$295$	4.52619	0.263525
$296$	−1.78603	−0.103811
$297$	−20.3760	−1.18234
$298$	27.4840	1.59210
$299$	−8.47761	−0.490273
$300$	3.52142	0.203309
$301$	−2.85612	−0.164624
$302$	−26.5832	−1.52969
$303$	−30.6235	−1.75927
$304$	0	0
$305$	0.465044	0.0266283
$306$	−1.22551	−0.0700576
$307$	−10.4289	−0.595210	−0.297605	−	0.954689i	$-0.596188\pi$
$307$	−10.4289	−0.595210	−0.297605	+	0.954689i	$0.596188\pi$
$308$	11.4428	0.652014
$309$	−5.40672	−0.307578
$310$	3.48599	0.197991
$311$	−26.1146	−1.48082	−0.740412	−	0.672153i	$-0.765369\pi$
$311$	−26.1146	−1.48082	−0.740412	+	0.672153i	$0.765369\pi$
$312$	−0.377645	−0.0213800
$313$	−6.20920	−0.350965	−0.175482	−	0.984483i	$-0.556148\pi$
$313$	−6.20920	−0.350965	−0.175482	+	0.984483i	$0.556148\pi$
$314$	−6.43062	−0.362901
$315$	−0.176682	−0.00995492
$316$	−28.2918	−1.59154
$317$	−4.93800	−0.277346	−0.138673	−	0.990338i	$-0.544284\pi$
$317$	−4.93800	−0.277346	−0.138673	+	0.990338i	$0.544284\pi$
$318$	35.7523	2.00489
$319$	−27.0602	−1.51508
$320$	−8.59761	−0.480621
$321$	28.4578	1.58836
$322$	16.9472	0.944430
$323$	0	0
$324$	−17.8863	−0.993682
$325$	−1.44713	−0.0802722
$326$	−5.17671	−0.286711
$327$	−10.8425	−0.599589
$328$	1.82997	0.101043
$329$	−4.17893	−0.230392
$330$	13.1714	0.725063
$331$	4.61530	0.253680	0.126840	−	0.991923i	$-0.459517\pi$
$331$	4.61530	0.253680	0.126840	+	0.991923i	$0.459517\pi$
$332$	−32.7109	−1.79525
$333$	1.43136	0.0784378
$334$	−24.5750	−1.34468
$335$	−2.72787	−0.149039
$336$	−9.33645	−0.509345
$337$	18.1421	0.988262	0.494131	−	0.869387i	$-0.335486\pi$
$337$	18.1421	0.988262	0.494131	+	0.869387i	$0.335486\pi$
$338$	−22.0184	−1.19765
$339$	−4.54900	−0.247068
$340$	10.2204	0.554280
$341$	6.64134	0.359649
$342$	0	0
$343$	−17.1182	−0.924298
$344$	−0.306693	−0.0165358
$345$	9.93603	0.534938
$346$	−16.1117	−0.866170
$347$	−6.37090	−0.342008	−0.171004	−	0.985270i	$-0.554701\pi$
$347$	−6.37090	−0.342008	−0.171004	+	0.985270i	$0.554701\pi$
$348$	−24.7737	−1.32801
$349$	−8.64857	−0.462947	−0.231474	−	0.972841i	$-0.574355\pi$
$349$	−8.64857	−0.462947	−0.231474	+	0.972841i	$0.574355\pi$
$350$	2.89289	0.154631
$351$	7.66599	0.409180
$352$	−31.0181	−1.65327
$353$	−33.1398	−1.76385	−0.881926	−	0.471388i	$-0.843753\pi$
$353$	−33.1398	−1.76385	−0.881926	+	0.471388i	$0.843753\pi$
$354$	15.4992	0.823771
$355$	−6.03917	−0.320526
$356$	12.6950	0.672834
$357$	11.9632	0.633160
$358$	−23.4351	−1.23859
$359$	13.6900	0.722530	0.361265	−	0.932463i	$-0.382345\pi$
$359$	13.6900	0.722530	0.361265	+	0.932463i	$0.382345\pi$
$360$	−0.0189723	−0.000999929 0
$361$	0	0
$362$	45.3156	2.38174
$363$	6.43668	0.337838
$364$	−4.30508	−0.225647
$365$	10.3694	0.542759
$366$	1.59246	0.0832393
$367$	10.2997	0.537640	0.268820	−	0.963190i	$-0.413366\pi$
$367$	10.2997	0.537640	0.268820	+	0.963190i	$0.413366\pi$
$368$	−22.5060	−1.17321
$369$	−1.46658	−0.0763468
$370$	−23.4361	−1.21839
$371$	14.9600	0.776686
$372$	6.08017	0.315242
$373$	10.2751	0.532025	0.266012	−	0.963970i	$-0.414294\pi$
$373$	10.2751	0.532025	0.266012	+	0.963970i	$0.414294\pi$
$374$	38.2282	1.97673
$375$	1.69608	0.0875853
$376$	−0.448738	−0.0231419
$377$	10.1808	0.524336
$378$	−15.3247	−0.788219
$379$	−17.1320	−0.880012	−0.440006	−	0.897995i	$-0.645024\pi$
$379$	−17.1320	−0.880012	−0.440006	+	0.897995i	$0.645024\pi$
$380$	0	0
$381$	−24.4782	−1.25406
$382$	52.0140	2.66127
$383$	17.9887	0.919178	0.459589	−	0.888132i	$-0.347997\pi$
$383$	17.9887	0.919178	0.459589	+	0.888132i	$0.347997\pi$
$384$	−2.08618	−0.106460
$385$	5.51139	0.280886
$386$	−7.18146	−0.365526
$387$	0.245790	0.0124942
$388$	−9.04642	−0.459262
$389$	14.0159	0.710636	0.355318	−	0.934746i	$-0.384373\pi$
$389$	14.0159	0.710636	0.355318	+	0.934746i	$0.384373\pi$
$390$	−4.95544	−0.250928
$391$	28.8380	1.45840
$392$	−0.761141	−0.0384434
$393$	17.0893	0.862041
$394$	44.9802	2.26607
$395$	−13.6267	−0.685633
$396$	−0.984734	−0.0494847
$397$	15.2254	0.764140	0.382070	−	0.924133i	$-0.375211\pi$
$397$	15.2254	0.764140	0.382070	+	0.924133i	$0.375211\pi$
$398$	18.3487	0.919739
$399$	0	0
$400$	−3.84178	−0.192089
$401$	−3.66356	−0.182950	−0.0914748	−	0.995807i	$-0.529158\pi$
$401$	−3.66356	−0.182950	−0.0914748	+	0.995807i	$0.529158\pi$
$402$	−9.34110	−0.465892
$403$	−2.49865	−0.124466
$404$	−37.4868	−1.86504
$405$	−8.61487	−0.428076
$406$	−20.3519	−1.01005
$407$	−44.6494	−2.21319
$408$	1.28462	0.0635982
$409$	26.5833	1.31446	0.657229	−	0.753691i	$-0.271729\pi$
$409$	26.5833	1.31446	0.657229	+	0.753691i	$0.271729\pi$
$410$	24.0128	1.18591
$411$	2.95786	0.145900
$412$	−6.61848	−0.326069
$413$	6.48539	0.319125
$414$	−1.45843	−0.0716777
$415$	−15.7551	−0.773389
$416$	11.6698	0.572160
$417$	−4.96737	−0.243253
$418$	0	0
$419$	−0.269516	−0.0131667	−0.00658336	−	0.999978i	$-0.502096\pi$
$419$	−0.269516	−0.0131667	−0.00658336	+	0.999978i	$0.502096\pi$
$420$	5.04569	0.246205
$421$	−10.5249	−0.512954	−0.256477	−	0.966550i	$-0.582562\pi$
$421$	−10.5249	−0.512954	−0.256477	+	0.966550i	$0.582562\pi$
$422$	26.7726	1.30327
$423$	0.359627	0.0174857
$424$	1.60642	0.0780148
$425$	4.92264	0.238783
$426$	−20.6801	−1.00195
$427$	0.666342	0.0322465
$428$	34.8358	1.68385
$429$	−9.44086	−0.455809
$430$	−4.02441	−0.194074
$431$	13.4105	0.645962	0.322981	−	0.946406i	$-0.395315\pi$
$431$	13.4105	0.645962	0.322981	+	0.946406i	$0.395315\pi$
$432$	20.3514	0.979155
$433$	9.80120	0.471016	0.235508	−	0.971872i	$-0.424325\pi$
$433$	9.80120	0.471016	0.235508	+	0.971872i	$0.424325\pi$
$434$	4.99493	0.239764
$435$	−11.9322	−0.572105
$436$	−13.2725	−0.635636
$437$	0	0
$438$	35.5082	1.69665
$439$	1.18525	0.0565689	0.0282844	−	0.999600i	$-0.490996\pi$
$439$	1.18525	0.0565689	0.0282844	+	0.999600i	$0.490996\pi$
$440$	0.591818	0.0282138
$441$	0.609993	0.0290473
$442$	−14.3825	−0.684104
$443$	31.7654	1.50922	0.754610	−	0.656174i	$-0.227826\pi$
$443$	31.7654	1.50922	0.754610	+	0.656174i	$0.227826\pi$
$444$	−40.8766	−1.93992
$445$	6.11451	0.289856
$446$	−27.8163	−1.31714
$447$	23.0886	1.09205
$448$	−12.3192	−0.582025
$449$	15.8902	0.749904	0.374952	−	0.927044i	$-0.377659\pi$
$449$	15.8902	0.749904	0.374952	+	0.927044i	$0.377659\pi$
$450$	−0.248953	−0.0117358
$451$	45.7480	2.15419
$452$	−5.56852	−0.261921
$453$	−22.3319	−1.04925
$454$	18.7503	0.879996
$455$	−2.07353	−0.0972085
$456$	0	0
$457$	−19.4620	−0.910395	−0.455197	−	0.890391i	$-0.650431\pi$
$457$	−19.4620	−0.910395	−0.455197	+	0.890391i	$0.650431\pi$
$458$	38.2648	1.78800
$459$	−26.0771	−1.21718
$460$	12.1629	0.567098
$461$	13.1076	0.610483	0.305241	−	0.952275i	$-0.401263\pi$
$461$	13.1076	0.610483	0.305241	+	0.952275i	$0.401263\pi$
$462$	18.8728	0.878041
$463$	5.20630	0.241957	0.120979	−	0.992655i	$-0.461397\pi$
$463$	5.20630	0.241957	0.120979	+	0.992655i	$0.461397\pi$
$464$	27.0275	1.25472
$465$	2.92850	0.135806
$466$	−30.5192	−1.41378
$467$	38.1971	1.76755	0.883776	−	0.467910i	$-0.154993\pi$
$467$	38.1971	1.76755	0.883776	+	0.467910i	$0.154993\pi$
$468$	0.370483	0.0171256
$469$	−3.90864	−0.180484
$470$	−5.88831	−0.271607
$471$	−5.40221	−0.248921
$472$	0.696408	0.0320548
$473$	−7.66711	−0.352534
$474$	−46.6622	−2.14327
$475$	0	0
$476$	14.6444	0.671226
$477$	−1.28742	−0.0589468
$478$	−56.6242	−2.58993
$479$	−22.5548	−1.03056	−0.515279	−	0.857023i	$-0.672312\pi$
$479$	−22.5548	−1.03056	−0.515279	+	0.857023i	$0.672312\pi$
$480$	−13.6774	−0.624285
$481$	16.7983	0.765935
$482$	21.0968	0.960934
$483$	14.2369	0.647803
$484$	7.87927	0.358149
$485$	−4.35718	−0.197850
$486$	2.58554	0.117282
$487$	−0.744678	−0.0337446	−0.0168723	−	0.999858i	$-0.505371\pi$
$487$	−0.744678	−0.0337446	−0.0168723	+	0.999858i	$0.505371\pi$
$488$	0.0715524	0.00323903
$489$	−4.34883	−0.196661
$490$	−9.98764	−0.451196
$491$	11.7055	0.528260	0.264130	−	0.964487i	$-0.414915\pi$
$491$	11.7055	0.528260	0.264130	+	0.964487i	$0.414915\pi$
$492$	41.8824	1.88821
$493$	−34.6315	−1.55972
$494$	0	0
$495$	−0.474294	−0.0213179
$496$	−6.63330	−0.297844
$497$	−8.65328	−0.388153
$498$	−53.9507	−2.41759
$499$	38.4818	1.72268	0.861341	−	0.508028i	$-0.169625\pi$
$499$	38.4818	1.72268	0.861341	+	0.508028i	$0.169625\pi$
$500$	2.07621	0.0928509
$501$	−20.6448	−0.922343
$502$	6.46774	0.288669
$503$	−20.7221	−0.923951	−0.461975	−	0.886893i	$-0.652859\pi$
$503$	−20.7221	−0.923951	−0.461975	+	0.886893i	$0.652859\pi$
$504$	−0.0271846	−0.00121090
$505$	−18.0554	−0.803456
$506$	45.4938	2.02245
$507$	−18.4972	−0.821488
$508$	−29.9643	−1.32945
$509$	−1.53979	−0.0682501	−0.0341251	−	0.999418i	$-0.510864\pi$
$509$	−1.53979	−0.0682501	−0.0341251	+	0.999418i	$0.510864\pi$
$510$	16.8567	0.746428
$511$	14.8579	0.657273
$512$	32.1628	1.42141
$513$	0	0
$514$	−46.9387	−2.07038
$515$	−3.18777	−0.140470
$516$	−7.01926	−0.309006
$517$	−11.2181	−0.493373
$518$	−33.5806	−1.47545
$519$	−13.5350	−0.594122
$520$	−0.222658	−0.00976418
$521$	−18.1497	−0.795151	−0.397576	−	0.917569i	$-0.630148\pi$
$521$	−18.1497	−0.795151	−0.397576	+	0.917569i	$0.630148\pi$
$522$	1.75142	0.0766578
$523$	−27.6172	−1.20762	−0.603808	−	0.797130i	$-0.706351\pi$
$523$	−27.6172	−1.20762	−0.603808	+	0.797130i	$0.706351\pi$
$524$	20.9194	0.913866
$525$	2.43024	0.106065
$526$	30.2485	1.31890
$527$	8.49955	0.370246
$528$	−25.0632	−1.09074
$529$	11.3189	0.492124
$530$	21.0794	0.915629
$531$	−0.558114	−0.0242201
$532$	0	0
$533$	−17.2116	−0.745517
$534$	20.9381	0.906079
$535$	16.7785	0.725400
$536$	−0.419714	−0.0181289
$537$	−19.6873	−0.849569
$538$	8.05201	0.347147
$539$	−19.0280	−0.819593
$540$	−10.9985	−0.473299
$541$	−33.1485	−1.42517	−0.712583	−	0.701588i	$-0.752475\pi$
$541$	−33.1485	−1.42517	−0.712583	+	0.701588i	$0.752475\pi$
$542$	17.4753	0.750629
$543$	38.0686	1.63368
$544$	−39.6968	−1.70198
$545$	−6.39265	−0.273831
$546$	−7.10044	−0.303871
$547$	−3.95014	−0.168896	−0.0844479	−	0.996428i	$-0.526913\pi$
$547$	−3.95014	−0.168896	−0.0844479	+	0.996428i	$0.526913\pi$
$548$	3.62077	0.154672
$549$	−0.0573434	−0.00244736
$550$	7.76580	0.331135
$551$	0	0
$552$	1.52877	0.0650690
$553$	−19.5251	−0.830292
$554$	−1.67753	−0.0712712
$555$	−19.6881	−0.835714
$556$	−6.08067	−0.257878
$557$	15.8255	0.670549	0.335274	−	0.942121i	$-0.391171\pi$
$557$	15.8255	0.670549	0.335274	+	0.942121i	$0.391171\pi$
$558$	−0.429849	−0.0181970
$559$	2.88457	0.122004
$560$	−5.50472	−0.232617
$561$	32.1146	1.35588
$562$	−0.266016	−0.0112212
$563$	38.3847	1.61772	0.808861	−	0.588000i	$-0.200084\pi$
$563$	38.3847	1.61772	0.808861	+	0.588000i	$0.200084\pi$
$564$	−10.2702	−0.432455
$565$	−2.68206	−0.112835
$566$	32.3033	1.35781
$567$	−12.3439	−0.518395
$568$	−0.929198	−0.0389883
$569$	36.1468	1.51535	0.757676	−	0.652630i	$-0.226335\pi$
$569$	36.1468	1.51535	0.757676	+	0.652630i	$0.226335\pi$
$570$	0	0
$571$	15.0479	0.629735	0.314867	−	0.949136i	$-0.398040\pi$
$571$	15.0479	0.629735	0.314867	+	0.949136i	$0.398040\pi$
$572$	−11.5568	−0.483212
$573$	43.6957	1.82541
$574$	34.4069	1.43612
$575$	5.85823	0.244305
$576$	1.06015	0.0441729
$577$	10.6236	0.442267	0.221133	−	0.975244i	$-0.429024\pi$
$577$	10.6236	0.442267	0.221133	+	0.975244i	$0.429024\pi$
$578$	14.6019	0.607359
$579$	−6.03297	−0.250722
$580$	−14.6064	−0.606499
$581$	−22.5749	−0.936563
$582$	−14.9204	−0.618471
$583$	40.1594	1.66323
$584$	1.59545	0.0660203
$585$	0.178442	0.00737767
$586$	31.9502	1.31985
$587$	36.8310	1.52018	0.760089	−	0.649819i	$-0.225156\pi$
$587$	36.8310	1.52018	0.760089	+	0.649819i	$0.225156\pi$
$588$	−17.4202	−0.718396
$589$	0	0
$590$	9.13821	0.376214
$591$	37.7868	1.55434
$592$	44.5953	1.83286
$593$	−2.20754	−0.0906530	−0.0453265	−	0.998972i	$-0.514433\pi$
$593$	−2.20754	−0.0906530	−0.0453265	+	0.998972i	$0.514433\pi$
$594$	−41.1384	−1.68793
$595$	7.05344	0.289163
$596$	28.2633	1.15771
$597$	15.4143	0.630866
$598$	−17.1160	−0.699924
$599$	−29.7287	−1.21468	−0.607341	−	0.794441i	$-0.707764\pi$
$599$	−29.7287	−1.21468	−0.607341	+	0.794441i	$0.707764\pi$
$600$	0.260962	0.0106537
$601$	−29.0988	−1.18697	−0.593483	−	0.804847i	$-0.702248\pi$
$601$	−29.0988	−1.18697	−0.593483	+	0.804847i	$0.702248\pi$
$602$	−5.76640	−0.235021
$603$	0.336367	0.0136979
$604$	−27.3370	−1.11233
$605$	3.79503	0.154290
$606$	−61.8276	−2.51158
$607$	9.43622	0.383005	0.191502	−	0.981492i	$-0.438664\pi$
$607$	9.43622	0.383005	0.191502	+	0.981492i	$0.438664\pi$
$608$	0	0
$609$	−17.0971	−0.692811
$610$	0.938906	0.0380152
$611$	4.22055	0.170745
$612$	−1.26026	−0.0509428
$613$	4.15678	0.167891	0.0839455	−	0.996470i	$-0.473248\pi$
$613$	4.15678	0.167891	0.0839455	+	0.996470i	$0.473248\pi$
$614$	−21.0556	−0.849735
$615$	20.1726	0.813436
$616$	0.847992	0.0341666
$617$	−2.67219	−0.107579	−0.0537893	−	0.998552i	$-0.517130\pi$
$617$	−2.67219	−0.107579	−0.0537893	+	0.998552i	$0.517130\pi$
$618$	−10.9160	−0.439105
$619$	26.6090	1.06950	0.534752	−	0.845009i	$-0.320405\pi$
$619$	26.6090	1.06950	0.534752	+	0.845009i	$0.320405\pi$
$620$	3.58483	0.143970
$621$	−31.0333	−1.24532
$622$	−52.7244	−2.11406
$623$	8.76123	0.351011
$624$	9.42944	0.377480
$625$	1.00000	0.0400000
$626$	−12.5361	−0.501045
$627$	0	0
$628$	−6.61295	−0.263886
$629$	−57.1420	−2.27840
$630$	−0.356715	−0.0142119
$631$	−14.0062	−0.557576	−0.278788	−	0.960353i	$-0.589933\pi$
$631$	−14.0062	−0.557576	−0.278788	+	0.960353i	$0.589933\pi$
$632$	−2.09662	−0.0833993
$633$	22.4910	0.893937
$634$	−9.96964	−0.395945
$635$	−14.4322	−0.572725
$636$	36.7661	1.45787
$637$	7.15882	0.283643
$638$	−54.6336	−2.16296
$639$	0.744676	0.0294589
$640$	−1.23000	−0.0486200
$641$	42.9165	1.69510	0.847550	−	0.530716i	$-0.178077\pi$
$641$	42.9165	1.69510	0.847550	+	0.530716i	$0.178077\pi$
$642$	57.4552	2.26758
$643$	−35.3393	−1.39364	−0.696822	−	0.717244i	$-0.745403\pi$
$643$	−35.3393	−1.39364	−0.696822	+	0.717244i	$0.745403\pi$
$644$	17.4277	0.686748
$645$	−3.38081	−0.133119
$646$	0	0
$647$	11.9287	0.468968	0.234484	−	0.972120i	$-0.424660\pi$
$647$	11.9287	0.468968	0.234484	+	0.972120i	$0.424660\pi$
$648$	−1.32550	−0.0520705
$649$	17.4097	0.683390
$650$	−2.92170	−0.114598
$651$	4.19612	0.164459
$652$	−5.32349	−0.208484
$653$	−21.0076	−0.822092	−0.411046	−	0.911615i	$-0.634836\pi$
$653$	−21.0076	−0.822092	−0.411046	+	0.911615i	$0.634836\pi$
$654$	−21.8905	−0.855986
$655$	10.0757	0.393692
$656$	−45.6927	−1.78400
$657$	−1.27863	−0.0498839
$658$	−8.43711	−0.328913
$659$	−30.3339	−1.18164	−0.590820	−	0.806804i	$-0.701196\pi$
$659$	−30.3339	−1.18164	−0.590820	+	0.806804i	$0.701196\pi$
$660$	13.5449	0.527234
$661$	34.1539	1.32843	0.664215	−	0.747541i	$-0.268766\pi$
$661$	34.1539	1.32843	0.664215	+	0.747541i	$0.268766\pi$
$662$	9.31812	0.362159
$663$	−12.0824	−0.469240
$664$	−2.42411	−0.0940737
$665$	0	0
$666$	2.88985	0.111979
$667$	−41.2135	−1.59579
$668$	−25.2718	−0.977794
$669$	−23.3678	−0.903452
$670$	−5.50746	−0.212772
$671$	1.78876	0.0690543
$672$	−19.5978	−0.756001
$673$	−29.1541	−1.12381	−0.561903	−	0.827203i	$-0.689931\pi$
$673$	−29.1541	−1.12381	−0.561903	+	0.827203i	$0.689931\pi$
$674$	36.6282	1.41086
$675$	−5.29738	−0.203896
$676$	−22.6428	−0.870875
$677$	−3.41061	−0.131081	−0.0655403	−	0.997850i	$-0.520877\pi$
$677$	−3.41061	−0.131081	−0.0655403	+	0.997850i	$0.520877\pi$
$678$	−9.18425	−0.352719
$679$	−6.24323	−0.239593
$680$	0.757406	0.0290452
$681$	15.7517	0.603606
$682$	13.4086	0.513442
$683$	33.2020	1.27044	0.635220	−	0.772331i	$-0.280909\pi$
$683$	33.2020	1.27044	0.635220	+	0.772331i	$0.280909\pi$
$684$	0	0
$685$	1.74393	0.0666323
$686$	−34.5611	−1.31955
$687$	32.1454	1.22642
$688$	7.65783	0.291952
$689$	−15.1090	−0.575608
$690$	20.0605	0.763689
$691$	46.1595	1.75599	0.877995	−	0.478669i	$-0.158881\pi$
$691$	46.1595	1.75599	0.877995	+	0.478669i	$0.158881\pi$
$692$	−16.5685	−0.629841
$693$	−0.679596	−0.0258157
$694$	−12.8626	−0.488258
$695$	−2.92874	−0.111093
$696$	−1.83591	−0.0695899
$697$	58.5480	2.21767
$698$	−17.4611	−0.660914
$699$	−25.6385	−0.969736
$700$	2.97491	0.112441
$701$	−17.0310	−0.643252	−0.321626	−	0.946867i	$-0.604229\pi$
$701$	−17.0310	−0.643252	−0.321626	+	0.946867i	$0.604229\pi$
$702$	15.4774	0.584155
$703$	0	0
$704$	−33.0701	−1.24638
$705$	−4.94663	−0.186301
$706$	−66.9079	−2.51811
$707$	−25.8709	−0.972974
$708$	15.9386	0.599010
$709$	−44.7336	−1.68001	−0.840003	−	0.542582i	$-0.817447\pi$
$709$	−44.7336	−1.68001	−0.840003	+	0.542582i	$0.817447\pi$
$710$	−12.1929	−0.457590
$711$	1.68027	0.0630152
$712$	0.940789	0.0352576
$713$	10.1150	0.378808
$714$	24.1533	0.903914
$715$	−5.56628	−0.208167
$716$	−24.0996	−0.900645
$717$	−47.5686	−1.77648
$718$	27.6396	1.03150
$719$	−0.198530	−0.00740391	−0.00370196	−	0.999993i	$-0.501178\pi$
$719$	−0.198530	−0.00740391	−0.00370196	+	0.999993i	$0.501178\pi$
$720$	0.473720	0.0176545
$721$	−4.56762	−0.170107
$722$	0	0
$723$	17.7229	0.659123
$724$	46.6005	1.73189
$725$	−7.03515	−0.261279
$726$	12.9954	0.482305
$727$	23.9627	0.888727	0.444364	−	0.895846i	$-0.353430\pi$
$727$	23.9627	0.888727	0.444364	+	0.895846i	$0.353430\pi$
$728$	−0.319037	−0.0118243
$729$	28.0167	1.03765
$730$	20.9354	0.774854
$731$	−9.81232	−0.362922
$732$	1.63761	0.0605280
$733$	41.7562	1.54230	0.771150	−	0.636654i	$-0.219682\pi$
$733$	41.7562	1.54230	0.771150	+	0.636654i	$0.219682\pi$
$734$	20.7947	0.767546
$735$	−8.39038	−0.309484
$736$	−47.2415	−1.74134
$737$	−10.4925	−0.386498
$738$	−2.96096	−0.108994
$739$	−46.3175	−1.70382	−0.851908	−	0.523691i	$-0.824555\pi$
$739$	−46.3175	−1.70382	−0.851908	+	0.523691i	$0.824555\pi$
$740$	−24.1006	−0.885957
$741$	0	0
$742$	30.2037	1.10881
$743$	36.1089	1.32471	0.662354	−	0.749191i	$-0.269557\pi$
$743$	36.1089	1.32471	0.662354	+	0.749191i	$0.269557\pi$
$744$	0.450583	0.0165192
$745$	13.6129	0.498739
$746$	20.7450	0.759530
$747$	1.94273	0.0710807
$748$	39.3122	1.43739
$749$	24.0413	0.878449
$750$	3.42432	0.125039
$751$	−20.5615	−0.750298	−0.375149	−	0.926964i	$-0.622408\pi$
$751$	−20.5615	−0.750298	−0.375149	+	0.926964i	$0.622408\pi$
$752$	11.2045	0.408588
$753$	5.43339	0.198004
$754$	20.5546	0.748554
$755$	−13.1668	−0.479188
$756$	−15.7592	−0.573158
$757$	37.5478	1.36470	0.682349	−	0.731027i	$-0.260959\pi$
$757$	37.5478	1.36470	0.682349	+	0.731027i	$0.260959\pi$
$758$	−34.5889	−1.25633
$759$	38.2183	1.38724
$760$	0	0
$761$	19.5623	0.709134	0.354567	−	0.935031i	$-0.384628\pi$
$761$	19.5623	0.709134	0.354567	+	0.935031i	$0.384628\pi$
$762$	−49.4206	−1.79032
$763$	−9.15976	−0.331605
$764$	53.4888	1.93516
$765$	−0.606999	−0.0219461
$766$	36.3185	1.31224
$767$	−6.54998	−0.236506
$768$	24.9526	0.900398
$769$	−6.94671	−0.250505	−0.125252	−	0.992125i	$-0.539974\pi$
$769$	−6.94671	−0.250505	−0.125252	+	0.992125i	$0.539974\pi$
$770$	11.1273	0.401000
$771$	−39.4321	−1.42011
$772$	−7.38508	−0.265795
$773$	−15.9395	−0.573304	−0.286652	−	0.958035i	$-0.592542\pi$
$773$	−15.9395	−0.573304	−0.286652	+	0.958035i	$0.592542\pi$
$774$	0.496240	0.0178370
$775$	1.72662	0.0620222
$776$	−0.670404	−0.0240661
$777$	−28.2103	−1.01204
$778$	28.2976	1.01452
$779$	0	0
$780$	−5.09594	−0.182464
$781$	−23.2293	−0.831209
$782$	58.2227	2.08204
$783$	37.2679	1.33185
$784$	19.0049	0.678748
$785$	−3.18511	−0.113681
$786$	34.5026	1.23067
$787$	−3.40109	−0.121236	−0.0606178	−	0.998161i	$-0.519307\pi$
$787$	−3.40109	−0.121236	−0.0606178	+	0.998161i	$0.519307\pi$
$788$	46.2555	1.64779
$789$	25.4110	0.904657
$790$	−27.5118	−0.978825
$791$	−3.84302	−0.136642
$792$	−0.0729757	−0.00259308
$793$	−0.672978	−0.0238981
$794$	30.7395	1.09090
$795$	17.7083	0.628048
$796$	18.8690	0.668794
$797$	22.2164	0.786946	0.393473	−	0.919336i	$-0.371274\pi$
$797$	22.2164	0.786946	0.393473	+	0.919336i	$0.371274\pi$
$798$	0	0
$799$	−14.3569	−0.507910
$800$	−8.06412	−0.285110
$801$	−0.753966	−0.0266401
$802$	−7.39659	−0.261183
$803$	39.8852	1.40752
$804$	−9.60596	−0.338776
$805$	8.39401	0.295850
$806$	−5.04467	−0.177691
$807$	6.76430	0.238115
$808$	−2.77804	−0.0977310
$809$	−2.65819	−0.0934570	−0.0467285	−	0.998908i	$-0.514880\pi$
$809$	−2.65819	−0.0934570	−0.0467285	+	0.998908i	$0.514880\pi$
$810$	−17.3931	−0.611131
$811$	−46.9135	−1.64736	−0.823678	−	0.567058i	$-0.808082\pi$
$811$	−46.9135	−1.64736	−0.823678	+	0.567058i	$0.808082\pi$
$812$	−20.9290	−0.734462
$813$	14.6806	0.514871
$814$	−90.1454	−3.15960
$815$	−2.56404	−0.0898145
$816$	−32.0757	−1.12288
$817$	0	0
$818$	53.6706	1.87655
$819$	0.255682	0.00893425
$820$	24.6937	0.862340
$821$	25.3475	0.884635	0.442317	−	0.896859i	$-0.354156\pi$
$821$	25.3475	0.884635	0.442317	+	0.896859i	$0.354156\pi$
$822$	5.97180	0.208290
$823$	−38.6392	−1.34688	−0.673439	−	0.739243i	$-0.735183\pi$
$823$	−38.6392	−1.34688	−0.673439	+	0.739243i	$0.735183\pi$
$824$	−0.490476	−0.0170865
$825$	6.52386	0.227132
$826$	13.0938	0.455590
$827$	44.9129	1.56178	0.780888	−	0.624671i	$-0.214767\pi$
$827$	44.9129	1.56178	0.780888	+	0.624671i	$0.214767\pi$
$828$	−1.49978	−0.0521209
$829$	−8.72624	−0.303075	−0.151537	−	0.988452i	$-0.548422\pi$
$829$	−8.72624	−0.303075	−0.151537	+	0.988452i	$0.548422\pi$
$830$	−31.8090	−1.10411
$831$	−1.40925	−0.0488863
$832$	12.4418	0.431343
$833$	−24.3519	−0.843743
$834$	−10.0289	−0.347274
$835$	−12.1721	−0.421232
$836$	0	0
$837$	−9.14659	−0.316152
$838$	−0.544142	−0.0187971
$839$	−46.7489	−1.61395	−0.806976	−	0.590584i	$-0.798898\pi$
$839$	−46.7489	−1.61395	−0.806976	+	0.590584i	$0.798898\pi$
$840$	0.373921	0.0129015
$841$	20.4933	0.706667
$842$	−21.2494	−0.732304
$843$	−0.223473	−0.00769683
$844$	27.5317	0.947680
$845$	−10.9058	−0.375172
$846$	0.726073	0.0249629
$847$	5.43774	0.186843
$848$	−40.1108	−1.37741
$849$	27.1372	0.931348
$850$	9.93862	0.340892
$851$	−68.0023	−2.33109
$852$	−21.2665	−0.728577
$853$	−4.21689	−0.144383	−0.0721917	−	0.997391i	$-0.522999\pi$
$853$	−4.21689	−0.144383	−0.0721917	+	0.997391i	$0.522999\pi$
$854$	1.34532	0.0460359
$855$	0	0
$856$	2.58158	0.0882364
$857$	36.9234	1.26128	0.630639	−	0.776076i	$-0.282793\pi$
$857$	36.9234	1.26128	0.630639	+	0.776076i	$0.282793\pi$
$858$	−19.0607	−0.650723
$859$	37.8989	1.29309	0.646547	−	0.762874i	$-0.276213\pi$
$859$	37.8989	1.29309	0.646547	+	0.762874i	$0.276213\pi$
$860$	−4.13852	−0.141122
$861$	28.9044	0.985060
$862$	27.0753	0.922189
$863$	−2.78585	−0.0948315	−0.0474157	−	0.998875i	$-0.515099\pi$
$863$	−2.78585	−0.0948315	−0.0474157	+	0.998875i	$0.515099\pi$
$864$	42.7188	1.45332
$865$	−7.98018	−0.271334
$866$	19.7882	0.672432
$867$	12.2667	0.416599
$868$	5.13655	0.174346
$869$	−52.4141	−1.77803
$870$	−24.0906	−0.816749
$871$	3.94757	0.133758
$872$	−0.983584	−0.0333083
$873$	0.537274	0.0181840
$874$	0	0
$875$	1.43286	0.0484394
$876$	36.5150	1.23373
$877$	7.09624	0.239623	0.119811	−	0.992797i	$-0.461771\pi$
$877$	7.09624	0.239623	0.119811	+	0.992797i	$0.461771\pi$
$878$	2.39297	0.0807590
$879$	26.8406	0.905312
$880$	−14.7771	−0.498137
$881$	−41.9836	−1.41447	−0.707233	−	0.706981i	$-0.750057\pi$
$881$	−41.9836	−1.41447	−0.707233	+	0.706981i	$0.750057\pi$
$882$	1.23155	0.0414685
$883$	17.2680	0.581115	0.290558	−	0.956857i	$-0.406159\pi$
$883$	17.2680	0.581115	0.290558	+	0.956857i	$0.406159\pi$
$884$	−14.7903	−0.497450
$885$	7.67679	0.258053
$886$	64.1331	2.15460
$887$	0.515778	0.0173181	0.00865906	−	0.999963i	$-0.497244\pi$
$887$	0.515778	0.0173181	0.00865906	+	0.999963i	$0.497244\pi$
$888$	−3.02925	−0.101655
$889$	−20.6793	−0.693561
$890$	12.3450	0.413804
$891$	−33.1365	−1.11011
$892$	−28.6050	−0.957767
$893$	0	0
$894$	46.6150	1.55904
$895$	−11.6075	−0.387996
$896$	−1.76242	−0.0588782
$897$	−14.3787	−0.480091
$898$	32.0817	1.07058
$899$	−12.1471	−0.405127
$900$	−0.256012	−0.00853374
$901$	51.3958	1.71224
$902$	92.3635	3.07537
$903$	−4.84422	−0.161205
$904$	−0.412667	−0.0137251
$905$	22.4450	0.746097
$906$	−45.0873	−1.49793
$907$	5.58491	0.185444	0.0927220	−	0.995692i	$-0.470443\pi$
$907$	5.58491	0.185444	0.0927220	+	0.995692i	$0.470443\pi$
$908$	19.2820	0.639894
$909$	2.22637	0.0738441
$910$	−4.18638	−0.138777
$911$	8.10096	0.268397	0.134198	−	0.990954i	$-0.457154\pi$
$911$	8.10096	0.268397	0.134198	+	0.990954i	$0.457154\pi$
$912$	0	0
$913$	−60.6010	−2.00560
$914$	−39.2931	−1.29970
$915$	0.788752	0.0260753
$916$	39.3498	1.30015
$917$	14.4371	0.476756
$918$	−52.6487	−1.73767
$919$	54.0976	1.78452	0.892258	−	0.451525i	$-0.149120\pi$
$919$	54.0976	1.78452	0.892258	+	0.451525i	$0.149120\pi$
$920$	0.901357	0.0297169
$921$	−17.6883	−0.582850
$922$	26.4638	0.871538
$923$	8.73946	0.287663
$924$	19.4079	0.638473
$925$	−11.6080	−0.381669
$926$	10.5113	0.345423
$927$	0.393077	0.0129103
$928$	56.7323	1.86233
$929$	−32.0625	−1.05194	−0.525969	−	0.850504i	$-0.676297\pi$
$929$	−32.0625	−1.05194	−0.525969	+	0.850504i	$0.676297\pi$
$930$	5.91252	0.193879
$931$	0	0
$932$	−31.3846	−1.02804
$933$	−44.2925	−1.45007
$934$	77.1185	2.52340
$935$	18.9346	0.619227
$936$	0.0274554	0.000897407 0
$937$	−15.6055	−0.509809	−0.254905	−	0.966966i	$-0.582044\pi$
$937$	−15.6055	−0.509809	−0.254905	+	0.966966i	$0.582044\pi$
$938$	−7.89140	−0.257664
$939$	−10.5313	−0.343676
$940$	−6.05527	−0.197501
$941$	−38.6654	−1.26046	−0.630228	−	0.776410i	$-0.717039\pi$
$941$	−38.6654	−1.26046	−0.630228	+	0.776410i	$0.717039\pi$
$942$	−10.9069	−0.355364
$943$	69.6756	2.26895
$944$	−17.3886	−0.565951
$945$	−7.59040	−0.246916
$946$	−15.4796	−0.503285
$947$	−42.4362	−1.37899	−0.689496	−	0.724290i	$-0.742168\pi$
$947$	−42.4362	−1.37899	−0.689496	+	0.724290i	$0.742168\pi$
$948$	−47.9853	−1.55849
$949$	−15.0058	−0.487110
$950$	0	0
$951$	−8.37526	−0.271586
$952$	1.08525	0.0351733
$953$	5.39691	0.174823	0.0874115	−	0.996172i	$-0.472140\pi$
$953$	5.39691	0.174823	0.0874115	+	0.996172i	$0.472140\pi$
$954$	−2.59925	−0.0841537
$955$	25.7627	0.833662
$956$	−58.2297	−1.88328
$957$	−45.8963	−1.48362
$958$	−45.5374	−1.47125
$959$	2.49881	0.0806908
$960$	−14.5822	−0.470640
$961$	−28.0188	−0.903831
$962$	33.9151	1.09347
$963$	−2.06892	−0.0666701
$964$	21.6950	0.698749
$965$	−3.55700	−0.114504
$966$	28.7438	0.924817
$967$	23.4644	0.754563	0.377282	−	0.926099i	$-0.376859\pi$
$967$	23.4644	0.754563	0.377282	+	0.926099i	$0.376859\pi$
$968$	0.583910	0.0187676
$969$	0	0
$970$	−8.79699	−0.282454
$971$	17.5032	0.561704	0.280852	−	0.959751i	$-0.409383\pi$
$971$	17.5032	0.561704	0.280852	+	0.959751i	$0.409383\pi$
$972$	2.65885	0.0852826
$973$	−4.19646	−0.134532
$974$	−1.50348	−0.0481745
$975$	−2.45445	−0.0786052
$976$	−1.78659	−0.0571875
$977$	35.0456	1.12121	0.560604	−	0.828084i	$-0.310569\pi$
$977$	35.0456	1.12121	0.560604	+	0.828084i	$0.310569\pi$
$978$	−8.78012	−0.280757
$979$	23.5191	0.751672
$980$	−10.2708	−0.328090
$981$	0.788262	0.0251673
$982$	23.6329	0.754155
$983$	22.0422	0.703038	0.351519	−	0.936181i	$-0.385665\pi$
$983$	22.0422	0.703038	0.351519	+	0.936181i	$0.385665\pi$
$984$	3.10378	0.0989450
$985$	22.2789	0.709863
$986$	−69.9197	−2.22670
$987$	−7.08781	−0.225608
$988$	0	0
$989$	−11.6772	−0.371315
$990$	−0.957582	−0.0304340
$991$	13.4570	0.427477	0.213738	−	0.976891i	$-0.431436\pi$
$991$	13.4570	0.427477	0.213738	+	0.976891i	$0.431436\pi$
$992$	−13.9237	−0.442078
$993$	7.82793	0.248412
$994$	−17.4706	−0.554135
$995$	9.08820	0.288115
$996$	−55.4804	−1.75796
$997$	17.4572	0.552875	0.276438	−	0.961032i	$-0.410846\pi$
$997$	17.4572	0.552875	0.276438	+	0.961032i	$0.410846\pi$
$998$	77.6933	2.45934
$999$	61.4921	1.94552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1805.2.a.w.1.13	yes	16
5.4	even	2		9025.2.a.cm.1.4		16
19.18	odd	2	inner	1805.2.a.w.1.4	✓	16
95.94	odd	2		9025.2.a.cm.1.13		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.a.w.1.4	✓	16	19.18	odd	2	inner
1805.2.a.w.1.13	yes	16	1.1	even	1	trivial
9025.2.a.cm.1.4		16	5.4	even	2
9025.2.a.cm.1.13		16	95.94	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+2.01896 q^{2} +1.69608 q^{3} +2.07621 q^{4} +1.00000 q^{5} +3.42432 q^{6} +1.43286 q^{7} +0.153862 q^{8} -0.123308 q^{9} +O(q^{10})\)	\(q+2.01896 q^{2} +1.69608 q^{3} +2.07621 q^{4} +1.00000 q^{5} +3.42432 q^{6} +1.43286 q^{7} +0.153862 q^{8} -0.123308 q^{9} +2.01896 q^{10} +3.84643 q^{11} +3.52142 q^{12} -1.44713 q^{13} +2.89289 q^{14} +1.69608 q^{15} -3.84178 q^{16} +4.92264 q^{17} -0.248953 q^{18} +2.07621 q^{20} +2.43024 q^{21} +7.76580 q^{22} +5.85823 q^{23} +0.260962 q^{24} +1.00000 q^{25} -2.92170 q^{26} -5.29738 q^{27} +2.97491 q^{28} -7.03515 q^{29} +3.42432 q^{30} +1.72662 q^{31} -8.06412 q^{32} +6.52386 q^{33} +9.93862 q^{34} +1.43286 q^{35} -0.256012 q^{36} -11.6080 q^{37} -2.45445 q^{39} +0.153862 q^{40} +11.8936 q^{41} +4.90657 q^{42} -1.99331 q^{43} +7.98599 q^{44} -0.123308 q^{45} +11.8275 q^{46} -2.91650 q^{47} -6.51596 q^{48} -4.94692 q^{49} +2.01896 q^{50} +8.34920 q^{51} -3.00454 q^{52} +10.4407 q^{53} -10.6952 q^{54} +3.84643 q^{55} +0.220462 q^{56} -14.2037 q^{58} +4.52619 q^{59} +3.52142 q^{60} +0.465044 q^{61} +3.48599 q^{62} -0.176682 q^{63} -8.59761 q^{64} -1.44713 q^{65} +13.1714 q^{66} -2.72787 q^{67} +10.2204 q^{68} +9.93603 q^{69} +2.89289 q^{70} -6.03917 q^{71} -0.0189723 q^{72} +10.3694 q^{73} -23.4361 q^{74} +1.69608 q^{75} +5.51139 q^{77} -4.95544 q^{78} -13.6267 q^{79} -3.84178 q^{80} -8.61487 q^{81} +24.0128 q^{82} -15.7551 q^{83} +5.04569 q^{84} +4.92264 q^{85} -4.02441 q^{86} -11.9322 q^{87} +0.591818 q^{88} +6.11451 q^{89} -0.248953 q^{90} -2.07353 q^{91} +12.1629 q^{92} +2.92850 q^{93} -5.88831 q^{94} -13.6774 q^{96} -4.35718 q^{97} -9.98764 q^{98} -0.474294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9	\( 16 q + 26 q^{4} + 16 q^{5} - 2 q^{6} + 22 q^{7} + 18 q^{9} + 12 q^{11} + 42 q^{16} + 22 q^{17} + 26 q^{20} + 42 q^{23} - 14 q^{24} + 16 q^{25} - 26 q^{26} + 46 q^{28} - 2 q^{30} + 22 q^{35} - 8 q^{36} - 38 q^{39} + 74 q^{42} + 88 q^{43} - 48 q^{44} + 18 q^{45} + 32 q^{47} + 30 q^{49} - 22 q^{54} + 12 q^{55} - 2 q^{58} + 20 q^{61} + 6 q^{62} - 6 q^{63} + 24 q^{64} - 24 q^{66} + 84 q^{68} + 44 q^{73} - 122 q^{74} + 4 q^{77} + 42 q^{80} - 36 q^{81} - 50 q^{82} + 56 q^{83} + 22 q^{85} + 34 q^{87} + 6 q^{92} - 58 q^{93} - 96 q^{96} + 6 q^{99}+O(q^{100}) \) 16 * q + 26 * q^4 + 16 * q^5 - 2 * q^6 + 22 * q^7 + 18 * q^9 + 12 * q^11 + 42 * q^16 + 22 * q^17 + 26 * q^20 + 42 * q^23 - 14 * q^24 + 16 * q^25 - 26 * q^26 + 46 * q^28 - 2 * q^30 + 22 * q^35 - 8 * q^36 - 38 * q^39 + 74 * q^42 + 88 * q^43 - 48 * q^44 + 18 * q^45 + 32 * q^47 + 30 * q^49 - 22 * q^54 + 12 * q^55 - 2 * q^58 + 20 * q^61 + 6 * q^62 - 6 * q^63 + 24 * q^64 - 24 * q^66 + 84 * q^68 + 44 * q^73 - 122 * q^74 + 4 * q^77 + 42 * q^80 - 36 * q^81 - 50 * q^82 + 56 * q^83 + 22 * q^85 + 34 * q^87 + 6 * q^92 - 58 * q^93 - 96 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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