LMFDB - Embedded newform 4719.2.a.br.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4719,2,Mod(1,4719)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4719, 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("4719.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4719 = 3 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4719.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:	$37.6814047138$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{17} - 31 x^{16} + 29 x^{15} + 396 x^{14} - 348 x^{13} - 2689 x^{12} + 2242 x^{11} + \cdots + 55 $ x^18 - x^17 - 31x^16 + 29x^15 + 396x^14 - 348x^13 - 2689x^12 + 2242x^11 + 10427x^10 - 8392x^9 - 22969x^8 + 18293x^7 + 26541x^6 - 21589x^5 - 12506x^4 + 11016x^3 + 151x^2 - 630x + 55
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 429)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-1.28332$ of defining polynomial
Character	$\chi$	$=$	4719.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.28332 q^{2} +1.00000 q^{3} -0.353096 q^{4} +0.613240 q^{5} -1.28332 q^{6} -0.715509 q^{7} +3.01977 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.28332 q^{2} +1.00000 q^{3} -0.353096 q^{4} +0.613240 q^{5} -1.28332 q^{6} -0.715509 q^{7} +3.01977 q^{8} +1.00000 q^{9} -0.786982 q^{10} -0.353096 q^{12} +1.00000 q^{13} +0.918226 q^{14} +0.613240 q^{15} -3.16913 q^{16} -4.29493 q^{17} -1.28332 q^{18} +2.10675 q^{19} -0.216533 q^{20} -0.715509 q^{21} +7.24665 q^{23} +3.01977 q^{24} -4.62394 q^{25} -1.28332 q^{26} +1.00000 q^{27} +0.252644 q^{28} -1.84699 q^{29} -0.786982 q^{30} +2.33663 q^{31} -1.97254 q^{32} +5.51176 q^{34} -0.438779 q^{35} -0.353096 q^{36} +2.70097 q^{37} -2.70364 q^{38} +1.00000 q^{39} +1.85184 q^{40} -8.94866 q^{41} +0.918226 q^{42} +8.60453 q^{43} +0.613240 q^{45} -9.29976 q^{46} +11.1121 q^{47} -3.16913 q^{48} -6.48805 q^{49} +5.93398 q^{50} -4.29493 q^{51} -0.353096 q^{52} +12.8770 q^{53} -1.28332 q^{54} -2.16067 q^{56} +2.10675 q^{57} +2.37027 q^{58} -9.28015 q^{59} -0.216533 q^{60} -4.01047 q^{61} -2.99864 q^{62} -0.715509 q^{63} +8.86965 q^{64} +0.613240 q^{65} -1.32563 q^{67} +1.51653 q^{68} +7.24665 q^{69} +0.563093 q^{70} +15.3990 q^{71} +3.01977 q^{72} -14.8027 q^{73} -3.46620 q^{74} -4.62394 q^{75} -0.743887 q^{76} -1.28332 q^{78} +8.78524 q^{79} -1.94344 q^{80} +1.00000 q^{81} +11.4840 q^{82} +9.92077 q^{83} +0.252644 q^{84} -2.63383 q^{85} -11.0423 q^{86} -1.84699 q^{87} -10.7647 q^{89} -0.786982 q^{90} -0.715509 q^{91} -2.55877 q^{92} +2.33663 q^{93} -14.2603 q^{94} +1.29195 q^{95} -1.97254 q^{96} +10.2309 q^{97} +8.32622 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + q^{2} + 18 q^{3} + 27 q^{4} + 10 q^{5} + q^{6} + 7 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) $ 18 * q + q^2 + 18 * q^3 + 27 * q^4 + 10 * q^5 + q^6 + 7 * q^7 + 3 * q^8 + 18 * q^9	$ 18 q + q^{2} + 18 q^{3} + 27 q^{4} + 10 q^{5} + q^{6} + 7 q^{7} + 3 q^{8} + 18 q^{9} - 3 q^{10} + 27 q^{12} + 18 q^{13} + 10 q^{14} + 10 q^{15} + 41 q^{16} - 5 q^{17} + q^{18} + 10 q^{19} + 16 q^{20} + 7 q^{21} + 9 q^{23} + 3 q^{24} + 52 q^{25} + q^{26} + 18 q^{27} + 4 q^{28} - 3 q^{30} + 36 q^{31} + 37 q^{32} + 20 q^{34} - 23 q^{35} + 27 q^{36} + 37 q^{37} + 6 q^{38} + 18 q^{39} - 54 q^{40} + 12 q^{41} + 10 q^{42} - 2 q^{43} + 10 q^{45} + 6 q^{46} + 41 q^{48} + 61 q^{49} - 48 q^{50} - 5 q^{51} + 27 q^{52} + 18 q^{53} + q^{54} + 36 q^{56} + 10 q^{57} + 40 q^{58} + 10 q^{59} + 16 q^{60} - 12 q^{61} - 25 q^{62} + 7 q^{63} + 67 q^{64} + 10 q^{65} + 52 q^{67} - 18 q^{68} + 9 q^{69} - 13 q^{70} + q^{71} + 3 q^{72} + 29 q^{73} - 2 q^{74} + 52 q^{75} + 26 q^{76} + q^{78} - 18 q^{79} + 48 q^{80} + 18 q^{81} - 6 q^{82} - 26 q^{83} + 4 q^{84} + 15 q^{85} + 9 q^{86} + 59 q^{89} - 3 q^{90} + 7 q^{91} + 4 q^{92} + 36 q^{93} - 53 q^{94} - 5 q^{95} + 37 q^{96} + 70 q^{97} + 93 q^{98}+O(q^{100}) $ 18 * q + q^2 + 18 * q^3 + 27 * q^4 + 10 * q^5 + q^6 + 7 * q^7 + 3 * q^8 + 18 * q^9 - 3 * q^10 + 27 * q^12 + 18 * q^13 + 10 * q^14 + 10 * q^15 + 41 * q^16 - 5 * q^17 + q^18 + 10 * q^19 + 16 * q^20 + 7 * q^21 + 9 * q^23 + 3 * q^24 + 52 * q^25 + q^26 + 18 * q^27 + 4 * q^28 - 3 * q^30 + 36 * q^31 + 37 * q^32 + 20 * q^34 - 23 * q^35 + 27 * q^36 + 37 * q^37 + 6 * q^38 + 18 * q^39 - 54 * q^40 + 12 * q^41 + 10 * q^42 - 2 * q^43 + 10 * q^45 + 6 * q^46 + 41 * q^48 + 61 * q^49 - 48 * q^50 - 5 * q^51 + 27 * q^52 + 18 * q^53 + q^54 + 36 * q^56 + 10 * q^57 + 40 * q^58 + 10 * q^59 + 16 * q^60 - 12 * q^61 - 25 * q^62 + 7 * q^63 + 67 * q^64 + 10 * q^65 + 52 * q^67 - 18 * q^68 + 9 * q^69 - 13 * q^70 + q^71 + 3 * q^72 + 29 * q^73 - 2 * q^74 + 52 * q^75 + 26 * q^76 + q^78 - 18 * q^79 + 48 * q^80 + 18 * q^81 - 6 * q^82 - 26 * q^83 + 4 * q^84 + 15 * q^85 + 9 * q^86 + 59 * q^89 - 3 * q^90 + 7 * q^91 + 4 * q^92 + 36 * q^93 - 53 * q^94 - 5 * q^95 + 37 * q^96 + 70 * q^97 + 93 * q^98

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 $

$2$	−1.28332	−0.907442	−0.453721	−	0.891144i	$-0.649904\pi$
$2$	−1.28332	−0.907442	−0.453721	+	0.891144i	$0.649904\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.353096	−0.176548
$5$	0.613240	0.274249	0.137125	−	0.990554i	$-0.456214\pi$
$5$	0.613240	0.274249	0.137125	+	0.990554i	$0.456214\pi$
$6$	−1.28332	−0.523912
$7$	−0.715509	−0.270437	−0.135219	−	0.990816i	$-0.543174\pi$
$7$	−0.715509	−0.270437	−0.135219	+	0.990816i	$0.543174\pi$
$8$	3.01977	1.06765
$9$	1.00000	0.333333
$10$	−0.786982	−0.248866
$11$	0	0
$11$	0	0
$12$	−0.353096	−0.101930
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.918226	0.245406
$15$	0.613240	0.158338
$16$	−3.16913	−0.792283
$17$	−4.29493	−1.04167	−0.520837	−	0.853656i	$-0.674380\pi$
$17$	−4.29493	−1.04167	−0.520837	+	0.853656i	$0.674380\pi$
$18$	−1.28332	−0.302481
$19$	2.10675	0.483323	0.241661	−	0.970361i	$-0.422308\pi$
$19$	2.10675	0.483323	0.241661	+	0.970361i	$0.422308\pi$
$20$	−0.216533	−0.0484182
$21$	−0.715509	−0.156137
$22$	0	0
$23$	7.24665	1.51103	0.755516	−	0.655130i	$-0.227386\pi$
$23$	7.24665	1.51103	0.755516	+	0.655130i	$0.227386\pi$
$24$	3.01977	0.616408
$25$	−4.62394	−0.924787
$26$	−1.28332	−0.251679
$27$	1.00000	0.192450
$28$	0.252644	0.0477452
$29$	−1.84699	−0.342977	−0.171489	−	0.985186i	$-0.554858\pi$
$29$	−1.84699	−0.342977	−0.171489	+	0.985186i	$0.554858\pi$
$30$	−0.786982	−0.143683
$31$	2.33663	0.419671	0.209836	−	0.977737i	$-0.432707\pi$
$31$	2.33663	0.419671	0.209836	+	0.977737i	$0.432707\pi$
$32$	−1.97254	−0.348699
$33$	0	0
$34$	5.51176	0.945260
$35$	−0.438779	−0.0741672
$36$	−0.353096	−0.0588494
$37$	2.70097	0.444037	0.222018	−	0.975042i	$-0.428735\pi$
$37$	2.70097	0.444037	0.222018	+	0.975042i	$0.428735\pi$
$38$	−2.70364	−0.438588
$39$	1.00000	0.160128
$40$	1.85184	0.292802
$41$	−8.94866	−1.39755	−0.698773	−	0.715343i	$-0.746270\pi$
$41$	−8.94866	−1.39755	−0.698773	+	0.715343i	$0.746270\pi$
$42$	0.918226	0.141685
$43$	8.60453	1.31218	0.656089	−	0.754683i	$-0.272210\pi$
$43$	8.60453	1.31218	0.656089	+	0.754683i	$0.272210\pi$
$44$	0	0
$45$	0.613240	0.0914164
$46$	−9.29976	−1.37117
$47$	11.1121	1.62086	0.810432	−	0.585833i	$-0.199233\pi$
$47$	11.1121	1.62086	0.810432	+	0.585833i	$0.199233\pi$
$48$	−3.16913	−0.457425
$49$	−6.48805	−0.926864
$50$	5.93398	0.839191
$51$	−4.29493	−0.601411
$52$	−0.353096	−0.0489656
$53$	12.8770	1.76879	0.884393	−	0.466742i	$-0.154572\pi$
$53$	12.8770	1.76879	0.884393	+	0.466742i	$0.154572\pi$
$54$	−1.28332	−0.174637
$55$	0	0
$56$	−2.16067	−0.288732
$57$	2.10675	0.279046
$58$	2.37027	0.311232
$59$	−9.28015	−1.20817	−0.604086	−	0.796919i	$-0.706462\pi$
$59$	−9.28015	−1.20817	−0.604086	+	0.796919i	$0.706462\pi$
$60$	−0.216533	−0.0279543
$61$	−4.01047	−0.513489	−0.256744	−	0.966479i	$-0.582650\pi$
$61$	−4.01047	−0.513489	−0.256744	+	0.966479i	$0.582650\pi$
$62$	−2.99864	−0.380828
$63$	−0.715509	−0.0901457
$64$	8.86965	1.10871
$65$	0.613240	0.0760631
$66$	0	0
$67$	−1.32563	−0.161952	−0.0809760	−	0.996716i	$-0.525804\pi$
$67$	−1.32563	−0.161952	−0.0809760	+	0.996716i	$0.525804\pi$
$68$	1.51653	0.183906
$69$	7.24665	0.872395
$70$	0.563093	0.0673025
$71$	15.3990	1.82752	0.913761	−	0.406251i	$-0.133164\pi$
$71$	15.3990	1.82752	0.913761	+	0.406251i	$0.133164\pi$
$72$	3.01977	0.355883
$73$	−14.8027	−1.73252	−0.866262	−	0.499591i	$-0.833484\pi$
$73$	−14.8027	−1.73252	−0.866262	+	0.499591i	$0.833484\pi$
$74$	−3.46620	−0.402938
$75$	−4.62394	−0.533926
$76$	−0.743887	−0.0853297
$77$	0	0
$78$	−1.28332	−0.145307
$79$	8.78524	0.988416	0.494208	−	0.869344i	$-0.335458\pi$
$79$	8.78524	0.988416	0.494208	+	0.869344i	$0.335458\pi$
$80$	−1.94344	−0.217283
$81$	1.00000	0.111111
$82$	11.4840	1.26819
$83$	9.92077	1.08895	0.544473	−	0.838778i	$-0.316730\pi$
$83$	9.92077	1.08895	0.544473	+	0.838778i	$0.316730\pi$
$84$	0.252644	0.0275657
$85$	−2.63383	−0.285679
$86$	−11.0423	−1.19073
$87$	−1.84699	−0.198018
$88$	0	0
$89$	−10.7647	−1.14106	−0.570529	−	0.821277i	$-0.693262\pi$
$89$	−10.7647	−1.14106	−0.570529	+	0.821277i	$0.693262\pi$
$90$	−0.786982	−0.0829552
$91$	−0.715509	−0.0750058
$92$	−2.55877	−0.266770
$93$	2.33663	0.242297
$94$	−14.2603	−1.47084
$95$	1.29195	0.132551
$96$	−1.97254	−0.201321
$97$	10.2309	1.03879	0.519397	−	0.854533i	$-0.326157\pi$
$97$	10.2309	1.03879	0.519397	+	0.854533i	$0.326157\pi$
$98$	8.32622	0.841076
$99$	0	0
$100$	1.63269	0.163269
$101$	−7.69098	−0.765281	−0.382640	−	0.923897i	$-0.624985\pi$
$101$	−7.69098	−0.765281	−0.382640	+	0.923897i	$0.624985\pi$
$102$	5.51176	0.545746
$103$	4.57586	0.450873	0.225436	−	0.974258i	$-0.427619\pi$
$103$	4.57586	0.450873	0.225436	+	0.974258i	$0.427619\pi$
$104$	3.01977	0.296113
$105$	−0.438779	−0.0428205
$106$	−16.5252	−1.60507
$107$	−4.88253	−0.472012	−0.236006	−	0.971752i	$-0.575838\pi$
$107$	−4.88253	−0.472012	−0.236006	+	0.971752i	$0.575838\pi$
$108$	−0.353096	−0.0339767
$109$	3.77364	0.361449	0.180724	−	0.983534i	$-0.442156\pi$
$109$	3.77364	0.361449	0.180724	+	0.983534i	$0.442156\pi$
$110$	0	0
$111$	2.70097	0.256365
$112$	2.26754	0.214263
$113$	12.5254	1.17829	0.589145	−	0.808027i	$-0.299465\pi$
$113$	12.5254	1.17829	0.589145	+	0.808027i	$0.299465\pi$
$114$	−2.70364	−0.253219
$115$	4.44394	0.414399
$116$	0.652165	0.0605520
$117$	1.00000	0.0924500
$118$	11.9094	1.09635
$119$	3.07307	0.281707
$120$	1.85184	0.169049
$121$	0	0
$122$	5.14671	0.465961
$123$	−8.94866	−0.806874
$124$	−0.825056	−0.0740922
$125$	−5.90178	−0.527872
$126$	0.918226	0.0818021
$127$	2.90467	0.257748	0.128874	−	0.991661i	$-0.458864\pi$
$127$	2.90467	0.257748	0.128874	+	0.991661i	$0.458864\pi$
$128$	−7.43750	−0.657389
$129$	8.60453	0.757587
$130$	−0.786982	−0.0690229
$131$	4.60205	0.402083	0.201041	−	0.979583i	$-0.435567\pi$
$131$	4.60205	0.402083	0.201041	+	0.979583i	$0.435567\pi$
$132$	0	0
$133$	−1.50740	−0.130708
$134$	1.70121	0.146962
$135$	0.613240	0.0527793
$136$	−12.9697	−1.11214
$137$	−12.3687	−1.05673	−0.528363	−	0.849019i	$-0.677194\pi$
$137$	−12.3687	−1.05673	−0.528363	+	0.849019i	$0.677194\pi$
$138$	−9.29976	−0.791648
$139$	10.1794	0.863405	0.431702	−	0.902016i	$-0.357913\pi$
$139$	10.1794	0.863405	0.431702	+	0.902016i	$0.357913\pi$
$140$	0.154931	0.0130941
$141$	11.1121	0.935806
$142$	−19.7618	−1.65837
$143$	0	0
$144$	−3.16913	−0.264094
$145$	−1.13265	−0.0940612
$146$	18.9965	1.57217
$147$	−6.48805	−0.535125
$148$	−0.953703	−0.0783939
$149$	−7.33953	−0.601278	−0.300639	−	0.953738i	$-0.597200\pi$
$149$	−7.33953	−0.601278	−0.300639	+	0.953738i	$0.597200\pi$
$150$	5.93398	0.484507
$151$	−14.9151	−1.21378	−0.606889	−	0.794787i	$-0.707583\pi$
$151$	−14.9151	−1.21378	−0.606889	+	0.794787i	$0.707583\pi$
$152$	6.36191	0.516019
$153$	−4.29493	−0.347225
$154$	0	0
$155$	1.43292	0.115095
$156$	−0.353096	−0.0282703
$157$	0.780275	0.0622727	0.0311364	−	0.999515i	$-0.490087\pi$
$157$	0.780275	0.0622727	0.0311364	+	0.999515i	$0.490087\pi$
$158$	−11.2742	−0.896931
$159$	12.8770	1.02121
$160$	−1.20964	−0.0956304
$161$	−5.18505	−0.408639
$162$	−1.28332	−0.100827
$163$	20.4823	1.60430	0.802149	−	0.597124i	$-0.203690\pi$
$163$	20.4823	1.60430	0.802149	+	0.597124i	$0.203690\pi$
$164$	3.15974	0.246734
$165$	0	0
$166$	−12.7315	−0.988156
$167$	−7.98953	−0.618248	−0.309124	−	0.951022i	$-0.600036\pi$
$167$	−7.98953	−0.618248	−0.309124	+	0.951022i	$0.600036\pi$
$168$	−2.16067	−0.166700
$169$	1.00000	0.0769231
$170$	3.38003	0.259237
$171$	2.10675	0.161108
$172$	−3.03823	−0.231663
$173$	6.66569	0.506783	0.253392	−	0.967364i	$-0.418454\pi$
$173$	6.66569	0.506783	0.253392	+	0.967364i	$0.418454\pi$
$174$	2.37027	0.179690
$175$	3.30847	0.250097
$176$	0	0
$177$	−9.28015	−0.697539
$178$	13.8146	1.03544
$179$	−16.4653	−1.23068	−0.615338	−	0.788263i	$-0.710980\pi$
$179$	−16.4653	−1.23068	−0.615338	+	0.788263i	$0.710980\pi$
$180$	−0.216533	−0.0161394
$181$	−4.11801	−0.306089	−0.153045	−	0.988219i	$-0.548908\pi$
$181$	−4.11801	−0.306089	−0.153045	+	0.988219i	$0.548908\pi$
$182$	0.918226	0.0680634
$183$	−4.01047	−0.296463
$184$	21.8832	1.61325
$185$	1.65634	0.121777
$186$	−2.99864	−0.219871
$187$	0	0
$188$	−3.92363	−0.286160
$189$	−0.715509	−0.0520457
$190$	−1.65798	−0.120282
$191$	−2.35409	−0.170336	−0.0851680	−	0.996367i	$-0.527143\pi$
$191$	−2.35409	−0.170336	−0.0851680	+	0.996367i	$0.527143\pi$
$192$	8.86965	0.640112
$193$	16.1617	1.16335	0.581673	−	0.813423i	$-0.302398\pi$
$193$	16.1617	1.16335	0.581673	+	0.813423i	$0.302398\pi$
$194$	−13.1295	−0.942645
$195$	0.613240	0.0439150
$196$	2.29091	0.163636
$197$	15.4788	1.10282	0.551409	−	0.834235i	$-0.314090\pi$
$197$	15.4788	1.10282	0.551409	+	0.834235i	$0.314090\pi$
$198$	0	0
$199$	21.0230	1.49028	0.745141	−	0.666907i	$-0.232382\pi$
$199$	21.0230	1.49028	0.745141	+	0.666907i	$0.232382\pi$
$200$	−13.9632	−0.987349
$201$	−1.32563	−0.0935030
$202$	9.86997	0.694448
$203$	1.32154	0.0927537
$204$	1.51653	0.106178
$205$	−5.48768	−0.383276
$206$	−5.87228	−0.409141
$207$	7.24665	0.503677
$208$	−3.16913	−0.219740
$209$	0	0
$210$	0.563093	0.0388571
$211$	3.60786	0.248375	0.124188	−	0.992259i	$-0.460368\pi$
$211$	3.60786	0.248375	0.124188	+	0.992259i	$0.460368\pi$
$212$	−4.54681	−0.312276
$213$	15.3990	1.05512
$214$	6.26583	0.428324
$215$	5.27664	0.359864
$216$	3.01977	0.205469
$217$	−1.67188	−0.113495
$218$	−4.84277	−0.327994
$219$	−14.8027	−1.00027
$220$	0	0
$221$	−4.29493	−0.288909
$222$	−3.46620	−0.232636
$223$	27.1970	1.82125	0.910623	−	0.413239i	$-0.135603\pi$
$223$	27.1970	1.82125	0.910623	+	0.413239i	$0.135603\pi$
$224$	1.41137	0.0943011
$225$	−4.62394	−0.308262
$226$	−16.0741	−1.06923
$227$	4.02513	0.267157	0.133579	−	0.991038i	$-0.457353\pi$
$227$	4.02513	0.267157	0.133579	+	0.991038i	$0.457353\pi$
$228$	−0.743887	−0.0492651
$229$	9.45531	0.624825	0.312412	−	0.949947i	$-0.398863\pi$
$229$	9.45531	0.624825	0.312412	+	0.949947i	$0.398863\pi$
$230$	−5.70298	−0.376044
$231$	0	0
$232$	−5.57748	−0.366179
$233$	−24.2765	−1.59041	−0.795204	−	0.606343i	$-0.792636\pi$
$233$	−24.2765	−1.59041	−0.795204	+	0.606343i	$0.792636\pi$
$234$	−1.28332	−0.0838931
$235$	6.81437	0.444521
$236$	3.27679	0.213301
$237$	8.78524	0.570662
$238$	−3.94372	−0.255633
$239$	15.0398	0.972842	0.486421	−	0.873725i	$-0.338302\pi$
$239$	15.0398	0.972842	0.486421	+	0.873725i	$0.338302\pi$
$240$	−1.94344	−0.125448
$241$	21.9238	1.41224	0.706119	−	0.708093i	$-0.250444\pi$
$241$	21.9238	1.41224	0.706119	+	0.708093i	$0.250444\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	1.41608	0.0906555
$245$	−3.97873	−0.254192
$246$	11.4840	0.732191
$247$	2.10675	0.134050
$248$	7.05609	0.448062
$249$	9.92077	0.628703
$250$	7.57386	0.479013
$251$	−9.01089	−0.568762	−0.284381	−	0.958711i	$-0.591788\pi$
$251$	−9.01089	−0.568762	−0.284381	+	0.958711i	$0.591788\pi$
$252$	0.252644	0.0159151
$253$	0	0
$254$	−3.72762	−0.233892
$255$	−2.63383	−0.164937
$256$	−8.19463	−0.512164
$257$	−20.9700	−1.30807	−0.654036	−	0.756464i	$-0.726925\pi$
$257$	−20.9700	−1.30807	−0.654036	+	0.756464i	$0.726925\pi$
$258$	−11.0423	−0.687466
$259$	−1.93257	−0.120084
$260$	−0.216533	−0.0134288
$261$	−1.84699	−0.114326
$262$	−5.90589	−0.364867
$263$	−13.9357	−0.859310	−0.429655	−	0.902993i	$-0.641365\pi$
$263$	−13.9357	−0.859310	−0.429655	+	0.902993i	$0.641365\pi$
$264$	0	0
$265$	7.89667	0.485089
$266$	1.93448	0.118610
$267$	−10.7647	−0.658790
$268$	0.468076	0.0285923
$269$	11.9680	0.729701	0.364850	−	0.931066i	$-0.381120\pi$
$269$	11.9680	0.729701	0.364850	+	0.931066i	$0.381120\pi$
$270$	−0.786982	−0.0478942
$271$	3.57504	0.217168	0.108584	−	0.994087i	$-0.465368\pi$
$271$	3.57504	0.217168	0.108584	+	0.994087i	$0.465368\pi$
$272$	13.6112	0.825301
$273$	−0.715509	−0.0433046
$274$	15.8729	0.958918
$275$	0	0
$276$	−2.55877	−0.154020
$277$	20.3246	1.22119	0.610594	−	0.791944i	$-0.290931\pi$
$277$	20.3246	1.22119	0.610594	+	0.791944i	$0.290931\pi$
$278$	−13.0634	−0.783490
$279$	2.33663	0.139890
$280$	−1.32501	−0.0791846
$281$	13.7722	0.821581	0.410790	−	0.911730i	$-0.365253\pi$
$281$	13.7722	0.821581	0.410790	+	0.911730i	$0.365253\pi$
$282$	−14.2603	−0.849190
$283$	10.3608	0.615884	0.307942	−	0.951405i	$-0.400360\pi$
$283$	10.3608	0.615884	0.307942	+	0.951405i	$0.400360\pi$
$284$	−5.43732	−0.322646
$285$	1.29195	0.0765283
$286$	0	0
$287$	6.40285	0.377948
$288$	−1.97254	−0.116233
$289$	1.44646	0.0850856
$290$	1.45355	0.0853551
$291$	10.2309	0.599748
$292$	5.22677	0.305874
$293$	12.4083	0.724898	0.362449	−	0.932004i	$-0.381941\pi$
$293$	12.4083	0.724898	0.362449	+	0.932004i	$0.381941\pi$
$294$	8.32622	0.485595
$295$	−5.69096	−0.331341
$296$	8.15631	0.474076
$297$	0	0
$298$	9.41895	0.545625
$299$	7.24665	0.419085
$300$	1.63269	0.0942637
$301$	−6.15662	−0.354862
$302$	19.1409	1.10143
$303$	−7.69098	−0.441835
$304$	−6.67658	−0.382928
$305$	−2.45938	−0.140824
$306$	5.51176	0.315087
$307$	17.3394	0.989611	0.494805	−	0.869004i	$-0.335239\pi$
$307$	17.3394	0.989611	0.494805	+	0.869004i	$0.335239\pi$
$308$	0	0
$309$	4.57586	0.260311
$310$	−1.83889	−0.104442
$311$	5.01939	0.284624	0.142312	−	0.989822i	$-0.454546\pi$
$311$	5.01939	0.284624	0.142312	+	0.989822i	$0.454546\pi$
$312$	3.01977	0.170961
$313$	32.6735	1.84682	0.923409	−	0.383817i	$-0.125391\pi$
$313$	32.6735	1.84682	0.923409	+	0.383817i	$0.125391\pi$
$314$	−1.00134	−0.0565089
$315$	−0.438779	−0.0247224
$316$	−3.10203	−0.174503
$317$	16.0745	0.902831	0.451416	−	0.892314i	$-0.350919\pi$
$317$	16.0745	0.902831	0.451416	+	0.892314i	$0.350919\pi$
$318$	−16.5252	−0.926689
$319$	0	0
$320$	5.43923	0.304062
$321$	−4.88253	−0.272516
$322$	6.65406	0.370816
$323$	−9.04837	−0.503465
$324$	−0.353096	−0.0196165
$325$	−4.62394	−0.256490
$326$	−26.2853	−1.45581
$327$	3.77364	0.208683
$328$	−27.0229	−1.49209
$329$	−7.95080	−0.438342
$330$	0	0
$331$	−12.3506	−0.678851	−0.339426	−	0.940633i	$-0.610233\pi$
$331$	−12.3506	−0.678851	−0.339426	+	0.940633i	$0.610233\pi$
$332$	−3.50299	−0.192251
$333$	2.70097	0.148012
$334$	10.2531	0.561025
$335$	−0.812932	−0.0444152
$336$	2.26754	0.123705
$337$	−16.5033	−0.898990	−0.449495	−	0.893283i	$-0.648396\pi$
$337$	−16.5033	−0.898990	−0.449495	+	0.893283i	$0.648396\pi$
$338$	−1.28332	−0.0698033
$339$	12.5254	0.680286
$340$	0.929994	0.0504360
$341$	0	0
$342$	−2.70364	−0.146196
$343$	9.65082	0.521096
$344$	25.9837	1.40095
$345$	4.44394	0.239254
$346$	−8.55420	−0.459877
$347$	−22.6843	−1.21776	−0.608879	−	0.793263i	$-0.708381\pi$
$347$	−22.6843	−1.21776	−0.608879	+	0.793263i	$0.708381\pi$
$348$	0.652165	0.0349597
$349$	31.6785	1.69571	0.847856	−	0.530226i	$-0.177893\pi$
$349$	31.6785	1.69571	0.847856	+	0.530226i	$0.177893\pi$
$350$	−4.24582	−0.226949
$351$	1.00000	0.0533761
$352$	0	0
$353$	−1.18584	−0.0631159	−0.0315580	−	0.999502i	$-0.510047\pi$
$353$	−1.18584	−0.0631159	−0.0315580	+	0.999502i	$0.510047\pi$
$354$	11.9094	0.632976
$355$	9.44327	0.501197
$356$	3.80098	0.201452
$357$	3.07307	0.162644
$358$	21.1302	1.11677
$359$	17.9760	0.948740	0.474370	−	0.880326i	$-0.342676\pi$
$359$	17.9760	0.948740	0.474370	+	0.880326i	$0.342676\pi$
$360$	1.85184	0.0976007
$361$	−14.5616	−0.766399
$362$	5.28471	0.277758
$363$	0	0
$364$	0.252644	0.0132421
$365$	−9.07760	−0.475143
$366$	5.14671	0.269023
$367$	−8.17659	−0.426815	−0.213407	−	0.976963i	$-0.568456\pi$
$367$	−8.17659	−0.426815	−0.213407	+	0.976963i	$0.568456\pi$
$368$	−22.9656	−1.19716
$369$	−8.94866	−0.465849
$370$	−2.12561	−0.110505
$371$	−9.21359	−0.478346
$372$	−0.825056	−0.0427772
$373$	−13.8857	−0.718975	−0.359487	−	0.933150i	$-0.617048\pi$
$373$	−13.8857	−0.718975	−0.359487	+	0.933150i	$0.617048\pi$
$374$	0	0
$375$	−5.90178	−0.304767
$376$	33.5559	1.73051
$377$	−1.84699	−0.0951247
$378$	0.918226	0.0472284
$379$	−15.6657	−0.804695	−0.402347	−	0.915487i	$-0.631806\pi$
$379$	−15.6657	−0.804695	−0.402347	+	0.915487i	$0.631806\pi$
$380$	−0.456182	−0.0234016
$381$	2.90467	0.148811
$382$	3.02104	0.154570
$383$	−17.7356	−0.906248	−0.453124	−	0.891448i	$-0.649691\pi$
$383$	−17.7356	−0.906248	−0.453124	+	0.891448i	$0.649691\pi$
$384$	−7.43750	−0.379544
$385$	0	0
$386$	−20.7406	−1.05567
$387$	8.60453	0.437393
$388$	−3.61250	−0.183397
$389$	35.4102	1.79537	0.897685	−	0.440638i	$-0.145248\pi$
$389$	35.4102	1.79537	0.897685	+	0.440638i	$0.145248\pi$
$390$	−0.786982	−0.0398504
$391$	−31.1239	−1.57400
$392$	−19.5924	−0.989566
$393$	4.60205	0.232142
$394$	−19.8642	−1.00074
$395$	5.38746	0.271072
$396$	0	0
$397$	−5.20301	−0.261131	−0.130566	−	0.991440i	$-0.541679\pi$
$397$	−5.20301	−0.261131	−0.130566	+	0.991440i	$0.541679\pi$
$398$	−26.9792	−1.35235
$399$	−1.50740	−0.0754645
$400$	14.6539	0.732693
$401$	0.596052	0.0297654	0.0148827	−	0.999889i	$-0.495263\pi$
$401$	0.596052	0.0297654	0.0148827	+	0.999889i	$0.495263\pi$
$402$	1.70121	0.0848486
$403$	2.33663	0.116396
$404$	2.71566	0.135109
$405$	0.613240	0.0304721
$406$	−1.69595	−0.0841687
$407$	0	0
$408$	−12.9697	−0.642096
$409$	0.820901	0.0405910	0.0202955	−	0.999794i	$-0.493539\pi$
$409$	0.820901	0.0405910	0.0202955	+	0.999794i	$0.493539\pi$
$410$	7.04243	0.347801
$411$	−12.3687	−0.610101
$412$	−1.61572	−0.0796007
$413$	6.64004	0.326735
$414$	−9.29976	−0.457058
$415$	6.08382	0.298643
$416$	−1.97254	−0.0967117
$417$	10.1794	0.498487
$418$	0	0
$419$	12.2868	0.600250	0.300125	−	0.953900i	$-0.402972\pi$
$419$	12.2868	0.600250	0.300125	+	0.953900i	$0.402972\pi$
$420$	0.154931	0.00755987
$421$	0.845143	0.0411898	0.0205949	−	0.999788i	$-0.493444\pi$
$421$	0.845143	0.0411898	0.0205949	+	0.999788i	$0.493444\pi$
$422$	−4.63003	−0.225386
$423$	11.1121	0.540288
$424$	38.8855	1.88844
$425$	19.8595	0.963327
$426$	−19.7618	−0.957461
$427$	2.86953	0.138866
$428$	1.72400	0.0833328
$429$	0	0
$430$	−6.77161	−0.326556
$431$	−2.20629	−0.106273	−0.0531367	−	0.998587i	$-0.516922\pi$
$431$	−2.20629	−0.106273	−0.0531367	+	0.998587i	$0.516922\pi$
$432$	−3.16913	−0.152475
$433$	27.0388	1.29940	0.649700	−	0.760190i	$-0.274894\pi$
$433$	27.0388	1.29940	0.649700	+	0.760190i	$0.274894\pi$
$434$	2.14556	0.102990
$435$	−1.13265	−0.0543063
$436$	−1.33246	−0.0638131
$437$	15.2669	0.730316
$438$	18.9965	0.907690
$439$	29.4751	1.40677	0.703384	−	0.710810i	$-0.251671\pi$
$439$	29.4751	1.40677	0.703384	+	0.710810i	$0.251671\pi$
$440$	0	0
$441$	−6.48805	−0.308955
$442$	5.51176	0.262168
$443$	2.94794	0.140061	0.0700304	−	0.997545i	$-0.477690\pi$
$443$	2.94794	0.140061	0.0700304	+	0.997545i	$0.477690\pi$
$444$	−0.953703	−0.0452607
$445$	−6.60136	−0.312934
$446$	−34.9024	−1.65268
$447$	−7.33953	−0.347148
$448$	−6.34632	−0.299836
$449$	−24.9460	−1.17728	−0.588638	−	0.808397i	$-0.700336\pi$
$449$	−24.9460	−1.17728	−0.588638	+	0.808397i	$0.700336\pi$
$450$	5.93398	0.279730
$451$	0	0
$452$	−4.42267	−0.208025
$453$	−14.9151	−0.700775
$454$	−5.16552	−0.242430
$455$	−0.438779	−0.0205703
$456$	6.36191	0.297924
$457$	−26.1704	−1.22420	−0.612099	−	0.790781i	$-0.709675\pi$
$457$	−26.1704	−1.22420	−0.612099	+	0.790781i	$0.709675\pi$
$458$	−12.1342	−0.566992
$459$	−4.29493	−0.200470
$460$	−1.56914	−0.0731615
$461$	28.1349	1.31037	0.655187	−	0.755466i	$-0.272590\pi$
$461$	28.1349	1.31037	0.655187	+	0.755466i	$0.272590\pi$
$462$	0	0
$463$	5.79921	0.269512	0.134756	−	0.990879i	$-0.456975\pi$
$463$	5.79921	0.269512	0.134756	+	0.990879i	$0.456975\pi$
$464$	5.85335	0.271735
$465$	1.43292	0.0664499
$466$	31.1545	1.44320
$467$	−13.3544	−0.617967	−0.308983	−	0.951067i	$-0.599989\pi$
$467$	−13.3544	−0.617967	−0.308983	+	0.951067i	$0.599989\pi$
$468$	−0.353096	−0.0163219
$469$	0.948504	0.0437978
$470$	−8.74501	−0.403377
$471$	0.780275	0.0359532
$472$	−28.0239	−1.28991
$473$	0	0
$474$	−11.2742	−0.517843
$475$	−9.74150	−0.446971
$476$	−1.08509	−0.0497349
$477$	12.8770	0.589596
$478$	−19.3008	−0.882798
$479$	7.74056	0.353675	0.176838	−	0.984240i	$-0.443413\pi$
$479$	7.74056	0.353675	0.176838	+	0.984240i	$0.443413\pi$
$480$	−1.20964	−0.0552123
$481$	2.70097	0.123154
$482$	−28.1352	−1.28153
$483$	−5.18505	−0.235928
$484$	0	0
$485$	6.27402	0.284888
$486$	−1.28332	−0.0582125
$487$	12.8604	0.582760	0.291380	−	0.956607i	$-0.405886\pi$
$487$	12.8604	0.582760	0.291380	+	0.956607i	$0.405886\pi$
$488$	−12.1107	−0.548226
$489$	20.4823	0.926242
$490$	5.10597	0.230664
$491$	12.4772	0.563090	0.281545	−	0.959548i	$-0.409153\pi$
$491$	12.4772	0.563090	0.281545	+	0.959548i	$0.409153\pi$
$492$	3.15974	0.142452
$493$	7.93269	0.357270
$494$	−2.70364	−0.121642
$495$	0	0
$496$	−7.40509	−0.332498
$497$	−11.0181	−0.494230
$498$	−12.7315	−0.570512
$499$	−27.3206	−1.22304	−0.611520	−	0.791229i	$-0.709442\pi$
$499$	−27.3206	−1.22304	−0.611520	+	0.791229i	$0.709442\pi$
$500$	2.08390	0.0931948
$501$	−7.98953	−0.356946
$502$	11.5638	0.516119
$503$	−32.5324	−1.45055	−0.725275	−	0.688460i	$-0.758287\pi$
$503$	−32.5324	−1.45055	−0.725275	+	0.688460i	$0.758287\pi$
$504$	−2.16067	−0.0962441
$505$	−4.71642	−0.209878
$506$	0	0
$507$	1.00000	0.0444116
$508$	−1.02563	−0.0455049
$509$	23.1786	1.02737	0.513686	−	0.857978i	$-0.328280\pi$
$509$	23.1786	1.02737	0.513686	+	0.857978i	$0.328280\pi$
$510$	3.38003	0.149670
$511$	10.5915	0.468539
$512$	25.3913	1.12215
$513$	2.10675	0.0930155
$514$	26.9111	1.18700
$515$	2.80610	0.123652
$516$	−3.03823	−0.133750
$517$	0	0
$518$	2.48010	0.108969
$519$	6.66569	0.292591
$520$	1.85184	0.0812087
$521$	−20.2529	−0.887295	−0.443647	−	0.896201i	$-0.646316\pi$
$521$	−20.2529	−0.887295	−0.443647	+	0.896201i	$0.646316\pi$
$522$	2.37027	0.103744
$523$	21.3917	0.935393	0.467696	−	0.883889i	$-0.345084\pi$
$523$	21.3917	0.935393	0.467696	+	0.883889i	$0.345084\pi$
$524$	−1.62497	−0.0709869
$525$	3.30847	0.144393
$526$	17.8839	0.779775
$527$	−10.0357	−0.437161
$528$	0	0
$529$	29.5140	1.28322
$530$	−10.1339	−0.440190
$531$	−9.28015	−0.402724
$532$	0.532258	0.0230763
$533$	−8.94866	−0.387610
$534$	13.8146	0.597814
$535$	−2.99416	−0.129449
$536$	−4.00311	−0.172908
$537$	−16.4653	−0.710531
$538$	−15.3587	−0.662162
$539$	0	0
$540$	−0.216533	−0.00931809
$541$	12.3305	0.530128	0.265064	−	0.964231i	$-0.414607\pi$
$541$	12.3305	0.530128	0.265064	+	0.964231i	$0.414607\pi$
$542$	−4.58791	−0.197068
$543$	−4.11801	−0.176721
$544$	8.47192	0.363231
$545$	2.31414	0.0991271
$546$	0.918226	0.0392964
$547$	34.7306	1.48497	0.742487	−	0.669860i	$-0.233646\pi$
$547$	34.7306	1.48497	0.742487	+	0.669860i	$0.233646\pi$
$548$	4.36733	0.186563
$549$	−4.01047	−0.171163
$550$	0	0
$551$	−3.89115	−0.165769
$552$	21.8832	0.931412
$553$	−6.28592	−0.267304
$554$	−26.0829	−1.10816
$555$	1.65634	0.0703079
$556$	−3.59430	−0.152432
$557$	10.5804	0.448304	0.224152	−	0.974554i	$-0.428039\pi$
$557$	10.5804	0.448304	0.224152	+	0.974554i	$0.428039\pi$
$558$	−2.99864	−0.126943
$559$	8.60453	0.363933
$560$	1.39055	0.0587614
$561$	0	0
$562$	−17.6741	−0.745537
$563$	−42.9147	−1.80864	−0.904320	−	0.426854i	$-0.859622\pi$
$563$	−42.9147	−1.80864	−0.904320	+	0.426854i	$0.859622\pi$
$564$	−3.92363	−0.165215
$565$	7.68108	0.323145
$566$	−13.2962	−0.558880
$567$	−0.715509	−0.0300486
$568$	46.5014	1.95115
$569$	−27.2785	−1.14358	−0.571788	−	0.820401i	$-0.693750\pi$
$569$	−27.2785	−1.14358	−0.571788	+	0.820401i	$0.693750\pi$
$570$	−1.65798	−0.0694450
$571$	−9.46788	−0.396218	−0.198109	−	0.980180i	$-0.563480\pi$
$571$	−9.46788	−0.396218	−0.198109	+	0.980180i	$0.563480\pi$
$572$	0	0
$573$	−2.35409	−0.0983435
$574$	−8.21689	−0.342966
$575$	−33.5081	−1.39738
$576$	8.86965	0.369569
$577$	32.1780	1.33959	0.669795	−	0.742546i	$-0.266382\pi$
$577$	32.1780	1.33959	0.669795	+	0.742546i	$0.266382\pi$
$578$	−1.85626	−0.0772103
$579$	16.1617	0.671658
$580$	0.399934	0.0166063
$581$	−7.09841	−0.294492
$582$	−13.1295	−0.544237
$583$	0	0
$584$	−44.7007	−1.84973
$585$	0.613240	0.0253544
$586$	−15.9237	−0.657803
$587$	5.76068	0.237769	0.118884	−	0.992908i	$-0.462068\pi$
$587$	5.76068	0.237769	0.118884	+	0.992908i	$0.462068\pi$
$588$	2.29091	0.0944753
$589$	4.92271	0.202837
$590$	7.30331	0.300673
$591$	15.4788	0.636713
$592$	−8.55973	−0.351803
$593$	44.7785	1.83883	0.919417	−	0.393285i	$-0.128661\pi$
$593$	44.7785	1.83883	0.919417	+	0.393285i	$0.128661\pi$
$594$	0	0
$595$	1.88453	0.0772581
$596$	2.59156	0.106155
$597$	21.0230	0.860415
$598$	−9.29976	−0.380295
$599$	23.7620	0.970888	0.485444	−	0.874268i	$-0.338658\pi$
$599$	23.7620	0.970888	0.485444	+	0.874268i	$0.338658\pi$
$600$	−13.9632	−0.570046
$601$	33.7334	1.37601	0.688007	−	0.725704i	$-0.258486\pi$
$601$	33.7334	1.37601	0.688007	+	0.725704i	$0.258486\pi$
$602$	7.90090	0.322017
$603$	−1.32563	−0.0539840
$604$	5.26648	0.214290
$605$	0	0
$606$	9.86997	0.400940
$607$	25.4596	1.03337	0.516686	−	0.856175i	$-0.327166\pi$
$607$	25.4596	1.03337	0.516686	+	0.856175i	$0.327166\pi$
$608$	−4.15566	−0.168534
$609$	1.32154	0.0535514
$610$	3.15617	0.127790
$611$	11.1121	0.449547
$612$	1.51653	0.0613019
$613$	20.7198	0.836864	0.418432	−	0.908248i	$-0.362580\pi$
$613$	20.7198	0.836864	0.418432	+	0.908248i	$0.362580\pi$
$614$	−22.2519	−0.898015
$615$	−5.48768	−0.221285
$616$	0	0
$617$	−10.3915	−0.418348	−0.209174	−	0.977878i	$-0.567077\pi$
$617$	−10.3915	−0.418348	−0.209174	+	0.977878i	$0.567077\pi$
$618$	−5.87228	−0.236218
$619$	−24.5446	−0.986533	−0.493266	−	0.869878i	$-0.664197\pi$
$619$	−24.5446	−0.986533	−0.493266	+	0.869878i	$0.664197\pi$
$620$	−0.505957	−0.0203197
$621$	7.24665	0.290798
$622$	−6.44148	−0.258280
$623$	7.70226	0.308585
$624$	−3.16913	−0.126867
$625$	19.5005	0.780019
$626$	−41.9305	−1.67588
$627$	0	0
$628$	−0.275512	−0.0109941
$629$	−11.6005	−0.462542
$630$	0.563093	0.0224342
$631$	1.74712	0.0695519	0.0347759	−	0.999395i	$-0.488928\pi$
$631$	1.74712	0.0695519	0.0347759	+	0.999395i	$0.488928\pi$
$632$	26.5294	1.05528
$633$	3.60786	0.143399
$634$	−20.6286	−0.819267
$635$	1.78126	0.0706872
$636$	−4.54681	−0.180293
$637$	−6.48805	−0.257066
$638$	0	0
$639$	15.3990	0.609174
$640$	−4.56098	−0.180288
$641$	−3.42460	−0.135264	−0.0676318	−	0.997710i	$-0.521544\pi$
$641$	−3.42460	−0.135264	−0.0676318	+	0.997710i	$0.521544\pi$
$642$	6.26583	0.247293
$643$	18.3908	0.725262	0.362631	−	0.931933i	$-0.381879\pi$
$643$	18.3908	0.725262	0.362631	+	0.931933i	$0.381879\pi$
$644$	1.83082	0.0721445
$645$	5.27664	0.207768
$646$	11.6119	0.456865
$647$	−43.1858	−1.69781	−0.848905	−	0.528546i	$-0.822737\pi$
$647$	−43.1858	−1.69781	−0.848905	+	0.528546i	$0.822737\pi$
$648$	3.01977	0.118628
$649$	0	0
$650$	5.93398	0.232750
$651$	−1.67188	−0.0655262
$652$	−7.23222	−0.283236
$653$	−12.9625	−0.507260	−0.253630	−	0.967301i	$-0.581625\pi$
$653$	−12.9625	−0.507260	−0.253630	+	0.967301i	$0.581625\pi$
$654$	−4.84277	−0.189367
$655$	2.82216	0.110271
$656$	28.3595	1.10725
$657$	−14.8027	−0.577508
$658$	10.2034	0.397770
$659$	51.0453	1.98844	0.994222	−	0.107347i	$-0.0342356\pi$
$659$	51.0453	1.98844	0.994222	+	0.107347i	$0.0342356\pi$
$660$	0	0
$661$	32.7762	1.27485	0.637424	−	0.770513i	$-0.280000\pi$
$661$	32.7762	1.27485	0.637424	+	0.770513i	$0.280000\pi$
$662$	15.8498	0.616019
$663$	−4.29493	−0.166801
$664$	29.9584	1.16261
$665$	−0.924400	−0.0358467
$666$	−3.46620	−0.134313
$667$	−13.3845	−0.518249
$668$	2.82107	0.109151
$669$	27.1970	1.05150
$670$	1.04325	0.0403043
$671$	0	0
$672$	1.41137	0.0544448
$673$	−40.5502	−1.56310	−0.781549	−	0.623844i	$-0.785570\pi$
$673$	−40.5502	−1.56310	−0.781549	+	0.623844i	$0.785570\pi$
$674$	21.1789	0.815781
$675$	−4.62394	−0.177975
$676$	−0.353096	−0.0135806
$677$	38.6857	1.48681	0.743406	−	0.668840i	$-0.233209\pi$
$677$	38.6857	1.48681	0.743406	+	0.668840i	$0.233209\pi$
$678$	−16.0741	−0.617321
$679$	−7.32033	−0.280928
$680$	−7.95355	−0.305005
$681$	4.02513	0.154243
$682$	0	0
$683$	−8.39921	−0.321387	−0.160693	−	0.987004i	$-0.551373\pi$
$683$	−8.39921	−0.321387	−0.160693	+	0.987004i	$0.551373\pi$
$684$	−0.743887	−0.0284432
$685$	−7.58496	−0.289806
$686$	−12.3851	−0.472864
$687$	9.45531	0.360743
$688$	−27.2689	−1.03962
$689$	12.8770	0.490573
$690$	−5.70298	−0.217109
$691$	39.1444	1.48912	0.744561	−	0.667554i	$-0.232659\pi$
$691$	39.1444	1.48912	0.744561	+	0.667554i	$0.232659\pi$
$692$	−2.35363	−0.0894716
$693$	0	0
$694$	29.1112	1.10505
$695$	6.24241	0.236788
$696$	−5.57748	−0.211414
$697$	38.4339	1.45579
$698$	−40.6536	−1.53876
$699$	−24.2765	−0.918222
$700$	−1.16821	−0.0441541
$701$	−20.6076	−0.778337	−0.389169	−	0.921167i	$-0.627238\pi$
$701$	−20.6076	−0.778337	−0.389169	+	0.921167i	$0.627238\pi$
$702$	−1.28332	−0.0484357
$703$	5.69028	0.214613
$704$	0	0
$705$	6.81437	0.256644
$706$	1.52181	0.0572741
$707$	5.50297	0.206960
$708$	3.27679	0.123149
$709$	−44.1739	−1.65899	−0.829493	−	0.558517i	$-0.811371\pi$
$709$	−44.1739	−1.65899	−0.829493	+	0.558517i	$0.811371\pi$
$710$	−12.1187	−0.454807
$711$	8.78524	0.329472
$712$	−32.5070	−1.21825
$713$	16.9328	0.634137
$714$	−3.94372	−0.147590
$715$	0	0
$716$	5.81385	0.217274
$717$	15.0398	0.561670
$718$	−23.0690	−0.860927
$719$	−10.9116	−0.406933	−0.203467	−	0.979082i	$-0.565221\pi$
$719$	−10.9116	−0.406933	−0.203467	+	0.979082i	$0.565221\pi$
$720$	−1.94344	−0.0724277
$721$	−3.27407	−0.121933
$722$	18.6871	0.695463
$723$	21.9238	0.815356
$724$	1.45405	0.0540395
$725$	8.54035	0.317181
$726$	0	0
$727$	8.35175	0.309749	0.154875	−	0.987934i	$-0.450503\pi$
$727$	8.35175	0.309749	0.154875	+	0.987934i	$0.450503\pi$
$728$	−2.16067	−0.0800799
$729$	1.00000	0.0370370
$730$	11.6494	0.431165
$731$	−36.9559	−1.36686
$732$	1.41608	0.0523400
$733$	25.6442	0.947191	0.473596	−	0.880742i	$-0.342956\pi$
$733$	25.6442	0.947191	0.473596	+	0.880742i	$0.342956\pi$
$734$	10.4932	0.387310
$735$	−3.97873	−0.146758
$736$	−14.2943	−0.526895
$737$	0	0
$738$	11.4840	0.422731
$739$	−0.950373	−0.0349600	−0.0174800	−	0.999847i	$-0.505564\pi$
$739$	−0.950373	−0.0349600	−0.0174800	+	0.999847i	$0.505564\pi$
$740$	−0.584849	−0.0214995
$741$	2.10675	0.0773936
$742$	11.8240	0.434071
$743$	−35.9926	−1.32044	−0.660219	−	0.751073i	$-0.729537\pi$
$743$	−35.9926	−1.32044	−0.660219	+	0.751073i	$0.729537\pi$
$744$	7.05609	0.258689
$745$	−4.50090	−0.164900
$746$	17.8198	0.652428
$747$	9.92077	0.362982
$748$	0	0
$749$	3.49350	0.127650
$750$	7.57386	0.276558
$751$	−47.3843	−1.72908	−0.864539	−	0.502567i	$-0.832389\pi$
$751$	−47.3843	−1.72908	−0.864539	+	0.502567i	$0.832389\pi$
$752$	−35.2156	−1.28418
$753$	−9.01089	−0.328375
$754$	2.37027	0.0863202
$755$	−9.14657	−0.332878
$756$	0.252644	0.00918856
$757$	16.7276	0.607976	0.303988	−	0.952676i	$-0.401682\pi$
$757$	16.7276	0.607976	0.303988	+	0.952676i	$0.401682\pi$
$758$	20.1041	0.730214
$759$	0	0
$760$	3.90138	0.141518
$761$	17.1407	0.621351	0.310676	−	0.950516i	$-0.399445\pi$
$761$	17.1407	0.621351	0.310676	+	0.950516i	$0.399445\pi$
$762$	−3.72762	−0.135037
$763$	−2.70007	−0.0977492
$764$	0.831220	0.0300725
$765$	−2.63383	−0.0952262
$766$	22.7604	0.822368
$767$	−9.28015	−0.335087
$768$	−8.19463	−0.295698
$769$	−3.13638	−0.113101	−0.0565504	−	0.998400i	$-0.518010\pi$
$769$	−3.13638	−0.113101	−0.0565504	+	0.998400i	$0.518010\pi$
$770$	0	0
$771$	−20.9700	−0.755215
$772$	−5.70665	−0.205387
$773$	21.0395	0.756738	0.378369	−	0.925655i	$-0.376485\pi$
$773$	21.0395	0.756738	0.378369	+	0.925655i	$0.376485\pi$
$774$	−11.0423	−0.396909
$775$	−10.8044	−0.388107
$776$	30.8951	1.10907
$777$	−1.93257	−0.0693306
$778$	−45.4426	−1.62919
$779$	−18.8526	−0.675466
$780$	−0.216533	−0.00775312
$781$	0	0
$782$	39.9418	1.42832
$783$	−1.84699	−0.0660060
$784$	20.5615	0.734338
$785$	0.478496	0.0170782
$786$	−5.90589	−0.210656
$787$	8.92698	0.318212	0.159106	−	0.987261i	$-0.449139\pi$
$787$	8.92698	0.318212	0.159106	+	0.987261i	$0.449139\pi$
$788$	−5.46551	−0.194701
$789$	−13.9357	−0.496123
$790$	−6.91382	−0.245983
$791$	−8.96204	−0.318654
$792$	0	0
$793$	−4.01047	−0.142416
$794$	6.67711	0.236962
$795$	7.89667	0.280066
$796$	−7.42315	−0.263107
$797$	−51.1002	−1.81006	−0.905031	−	0.425345i	$-0.860153\pi$
$797$	−51.1002	−1.81006	−0.905031	+	0.425345i	$0.860153\pi$
$798$	1.93448	0.0684797
$799$	−47.7257	−1.68841
$800$	9.12089	0.322472
$801$	−10.7647	−0.380353
$802$	−0.764924	−0.0270104
$803$	0	0
$804$	0.468076	0.0165078
$805$	−3.17968	−0.112069
$806$	−2.99864	−0.105623
$807$	11.9680	0.421293
$808$	−23.2250	−0.817052
$809$	−12.4035	−0.436085	−0.218042	−	0.975939i	$-0.569967\pi$
$809$	−12.4035	−0.436085	−0.218042	+	0.975939i	$0.569967\pi$
$810$	−0.786982	−0.0276517
$811$	−40.9574	−1.43821	−0.719105	−	0.694901i	$-0.755448\pi$
$811$	−40.9574	−1.43821	−0.719105	+	0.694901i	$0.755448\pi$
$812$	−0.466630	−0.0163755
$813$	3.57504	0.125382
$814$	0	0
$815$	12.5606	0.439978
$816$	13.6112	0.476487
$817$	18.1276	0.634206
$818$	−1.05348	−0.0368340
$819$	−0.715509	−0.0250019
$820$	1.93768	0.0676667
$821$	7.00104	0.244338	0.122169	−	0.992509i	$-0.461015\pi$
$821$	7.00104	0.244338	0.122169	+	0.992509i	$0.461015\pi$
$822$	15.8729	0.553631
$823$	−5.89937	−0.205639	−0.102820	−	0.994700i	$-0.532786\pi$
$823$	−5.89937	−0.205639	−0.102820	+	0.994700i	$0.532786\pi$
$824$	13.8180	0.481374
$825$	0	0
$826$	−8.52127	−0.296493
$827$	5.28787	0.183877	0.0919386	−	0.995765i	$-0.470694\pi$
$827$	5.28787	0.183877	0.0919386	+	0.995765i	$0.470694\pi$
$828$	−2.55877	−0.0889233
$829$	−4.87126	−0.169186	−0.0845929	−	0.996416i	$-0.526959\pi$
$829$	−4.87126	−0.169186	−0.0845929	+	0.996416i	$0.526959\pi$
$830$	−7.80747	−0.271001
$831$	20.3246	0.705053
$832$	8.86965	0.307500
$833$	27.8657	0.965490
$834$	−13.0634	−0.452348
$835$	−4.89950	−0.169554
$836$	0	0
$837$	2.33663	0.0807658
$838$	−15.7679	−0.544692
$839$	−38.9362	−1.34423	−0.672113	−	0.740449i	$-0.734613\pi$
$839$	−38.9362	−1.34423	−0.672113	+	0.740449i	$0.734613\pi$
$840$	−1.32501	−0.0457173
$841$	−25.5886	−0.882367
$842$	−1.08459	−0.0373773
$843$	13.7722	0.474340
$844$	−1.27392	−0.0438502
$845$	0.613240	0.0210961
$846$	−14.2603	−0.490280
$847$	0	0
$848$	−40.8088	−1.40138
$849$	10.3608	0.355581
$850$	−25.4860	−0.874164
$851$	19.5730	0.670954
$852$	−5.43732	−0.186280
$853$	−10.3532	−0.354488	−0.177244	−	0.984167i	$-0.556718\pi$
$853$	−10.3532	−0.354488	−0.177244	+	0.984167i	$0.556718\pi$
$854$	−3.68252	−0.126013
$855$	1.29195	0.0441836
$856$	−14.7441	−0.503943
$857$	−15.2858	−0.522152	−0.261076	−	0.965318i	$-0.584077\pi$
$857$	−15.2858	−0.522152	−0.261076	+	0.965318i	$0.584077\pi$
$858$	0	0
$859$	−19.4227	−0.662692	−0.331346	−	0.943509i	$-0.607503\pi$
$859$	−19.4227	−0.662692	−0.331346	+	0.943509i	$0.607503\pi$
$860$	−1.86316	−0.0635333
$861$	6.40285	0.218209
$862$	2.83137	0.0964370
$863$	13.5372	0.460812	0.230406	−	0.973095i	$-0.425994\pi$
$863$	13.5372	0.460812	0.230406	+	0.973095i	$0.425994\pi$
$864$	−1.97254	−0.0671071
$865$	4.08767	0.138985
$866$	−34.6993	−1.17913
$867$	1.44646	0.0491242
$868$	0.590335	0.0200373
$869$	0	0
$870$	1.45355	0.0492798
$871$	−1.32563	−0.0449174
$872$	11.3955	0.385901
$873$	10.2309	0.346265
$874$	−19.5923	−0.662720
$875$	4.22278	0.142756
$876$	5.22677	0.176596
$877$	−5.20415	−0.175732	−0.0878658	−	0.996132i	$-0.528005\pi$
$877$	−5.20415	−0.175732	−0.0878658	+	0.996132i	$0.528005\pi$
$878$	−37.8259	−1.27656
$879$	12.4083	0.418520
$880$	0	0
$881$	27.3624	0.921862	0.460931	−	0.887436i	$-0.347516\pi$
$881$	27.3624	0.921862	0.460931	+	0.887436i	$0.347516\pi$
$882$	8.32622	0.280359
$883$	26.8526	0.903662	0.451831	−	0.892104i	$-0.350771\pi$
$883$	26.8526	0.903662	0.451831	+	0.892104i	$0.350771\pi$
$884$	1.51653	0.0510063
$885$	−5.69096	−0.191300
$886$	−3.78314	−0.127097
$887$	−14.0319	−0.471146	−0.235573	−	0.971857i	$-0.575697\pi$
$887$	−14.0319	−0.471146	−0.235573	+	0.971857i	$0.575697\pi$
$888$	8.15631	0.273708
$889$	−2.07832	−0.0697046
$890$	8.47164	0.283970
$891$	0	0
$892$	−9.60316	−0.321538
$893$	23.4104	0.783400
$894$	9.41895	0.315017
$895$	−10.0972	−0.337512
$896$	5.32160	0.177782
$897$	7.24665	0.241959
$898$	32.0137	1.06831
$899$	−4.31573	−0.143938
$900$	1.63269	0.0544232
$901$	−55.3057	−1.84250
$902$	0	0
$903$	−6.15662	−0.204880
$904$	37.8238	1.25800
$905$	−2.52533	−0.0839447
$906$	19.1409	0.635913
$907$	−40.4357	−1.34264	−0.671322	−	0.741166i	$-0.734273\pi$
$907$	−40.4357	−1.34264	−0.671322	+	0.741166i	$0.734273\pi$
$908$	−1.42126	−0.0471661
$909$	−7.69098	−0.255094
$910$	0.563093	0.0186663
$911$	20.7844	0.688617	0.344309	−	0.938856i	$-0.388113\pi$
$911$	20.7844	0.688617	0.344309	+	0.938856i	$0.388113\pi$
$912$	−6.67658	−0.221084
$913$	0	0
$914$	33.5849	1.11089
$915$	−2.45938	−0.0813047
$916$	−3.33864	−0.110312
$917$	−3.29281	−0.108738
$918$	5.51176	0.181915
$919$	−12.1220	−0.399869	−0.199935	−	0.979809i	$-0.564073\pi$
$919$	−12.1220	−0.399869	−0.199935	+	0.979809i	$0.564073\pi$
$920$	13.4197	0.442433
$921$	17.3394	0.571352
$922$	−36.1061	−1.18909
$923$	15.3990	0.506864
$924$	0	0
$925$	−12.4891	−0.410640
$926$	−7.44223	−0.244567
$927$	4.57586	0.150291
$928$	3.64326	0.119596
$929$	−8.51575	−0.279393	−0.139696	−	0.990194i	$-0.544613\pi$
$929$	−8.51575	−0.279393	−0.139696	+	0.990194i	$0.544613\pi$
$930$	−1.83889	−0.0602995
$931$	−13.6687	−0.447974
$932$	8.57195	0.280783
$933$	5.01939	0.164328
$934$	17.1379	0.560769
$935$	0	0
$936$	3.01977	0.0987043
$937$	−26.1003	−0.852661	−0.426331	−	0.904567i	$-0.640194\pi$
$937$	−26.1003	−0.852661	−0.426331	+	0.904567i	$0.640194\pi$
$938$	−1.21723	−0.0397440
$939$	32.6735	1.06626
$940$	−2.40613	−0.0784793
$941$	−25.0575	−0.816853	−0.408426	−	0.912791i	$-0.633922\pi$
$941$	−25.0575	−0.816853	−0.408426	+	0.912791i	$0.633922\pi$
$942$	−1.00134	−0.0326254
$943$	−64.8478	−2.11174
$944$	29.4100	0.957214
$945$	−0.438779	−0.0142735
$946$	0	0
$947$	−15.1877	−0.493534	−0.246767	−	0.969075i	$-0.579368\pi$
$947$	−15.1877	−0.493534	−0.246767	+	0.969075i	$0.579368\pi$
$948$	−3.10203	−0.100749
$949$	−14.8027	−0.480516
$950$	12.5014	0.405600
$951$	16.0745	0.521250
$952$	9.27995	0.300765
$953$	22.5895	0.731746	0.365873	−	0.930665i	$-0.380771\pi$
$953$	22.5895	0.731746	0.365873	+	0.930665i	$0.380771\pi$
$954$	−16.5252	−0.535024
$955$	−1.44362	−0.0467145
$956$	−5.31049	−0.171753
$957$	0	0
$958$	−9.93360	−0.320940
$959$	8.84989	0.285778
$960$	5.43923	0.175550
$961$	−25.5402	−0.823876
$962$	−3.46620	−0.111755
$963$	−4.88253	−0.157337
$964$	−7.74123	−0.249328
$965$	9.91102	0.319047
$966$	6.65406	0.214091
$967$	51.1691	1.64549	0.822743	−	0.568413i	$-0.192443\pi$
$967$	51.1691	1.64549	0.822743	+	0.568413i	$0.192443\pi$
$968$	0	0
$969$	−9.04837	−0.290676
$970$	−8.05156	−0.258520
$971$	−35.5938	−1.14226	−0.571130	−	0.820859i	$-0.693495\pi$
$971$	−35.5938	−1.14226	−0.571130	+	0.820859i	$0.693495\pi$
$972$	−0.353096	−0.0113256
$973$	−7.28345	−0.233497
$974$	−16.5040	−0.528821
$975$	−4.62394	−0.148084
$976$	12.7097	0.406828
$977$	−5.40781	−0.173011	−0.0865056	−	0.996251i	$-0.527570\pi$
$977$	−5.40781	−0.173011	−0.0865056	+	0.996251i	$0.527570\pi$
$978$	−26.2853	−0.840511
$979$	0	0
$980$	1.40488	0.0448771
$981$	3.77364	0.120483
$982$	−16.0123	−0.510972
$983$	−51.9524	−1.65703	−0.828513	−	0.559970i	$-0.810813\pi$
$983$	−51.9524	−1.65703	−0.828513	+	0.559970i	$0.810813\pi$
$984$	−27.0229	−0.861458
$985$	9.49222	0.302447
$986$	−10.1802	−0.324202
$987$	−7.95080	−0.253077
$988$	−0.743887	−0.0236662
$989$	62.3540	1.98274
$990$	0	0
$991$	−6.37256	−0.202431	−0.101215	−	0.994865i	$-0.532273\pi$
$991$	−6.37256	−0.202431	−0.101215	+	0.994865i	$0.532273\pi$
$992$	−4.60910	−0.146339
$993$	−12.3506	−0.391935
$994$	14.1397	0.448485
$995$	12.8922	0.408709
$996$	−3.50299	−0.110996
$997$	10.1915	0.322767	0.161384	−	0.986892i	$-0.448404\pi$
$997$	10.1915	0.322767	0.161384	+	0.986892i	$0.448404\pi$
$998$	35.0611	1.10984
$999$	2.70097	0.0854549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4719.2.a.br.1.7		18
11.7	odd	10		429.2.n.d.313.6	yes	36
11.8	odd	10		429.2.n.d.196.6	✓	36
11.10	odd	2		4719.2.a.bq.1.12		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.196.6	✓	36	11.8	odd	10
429.2.n.d.313.6	yes	36	11.7	odd	10
4719.2.a.bq.1.12		18	11.10	odd	2
4719.2.a.br.1.7		18	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:	\( N \)	\(=\)	\( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4719.a (trivial)

\(f(q)\)	\(=\)	\(q-1.28332 q^{2} +1.00000 q^{3} -0.353096 q^{4} +0.613240 q^{5} -1.28332 q^{6} -0.715509 q^{7} +3.01977 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.28332 q^{2} +1.00000 q^{3} -0.353096 q^{4} +0.613240 q^{5} -1.28332 q^{6} -0.715509 q^{7} +3.01977 q^{8} +1.00000 q^{9} -0.786982 q^{10} -0.353096 q^{12} +1.00000 q^{13} +0.918226 q^{14} +0.613240 q^{15} -3.16913 q^{16} -4.29493 q^{17} -1.28332 q^{18} +2.10675 q^{19} -0.216533 q^{20} -0.715509 q^{21} +7.24665 q^{23} +3.01977 q^{24} -4.62394 q^{25} -1.28332 q^{26} +1.00000 q^{27} +0.252644 q^{28} -1.84699 q^{29} -0.786982 q^{30} +2.33663 q^{31} -1.97254 q^{32} +5.51176 q^{34} -0.438779 q^{35} -0.353096 q^{36} +2.70097 q^{37} -2.70364 q^{38} +1.00000 q^{39} +1.85184 q^{40} -8.94866 q^{41} +0.918226 q^{42} +8.60453 q^{43} +0.613240 q^{45} -9.29976 q^{46} +11.1121 q^{47} -3.16913 q^{48} -6.48805 q^{49} +5.93398 q^{50} -4.29493 q^{51} -0.353096 q^{52} +12.8770 q^{53} -1.28332 q^{54} -2.16067 q^{56} +2.10675 q^{57} +2.37027 q^{58} -9.28015 q^{59} -0.216533 q^{60} -4.01047 q^{61} -2.99864 q^{62} -0.715509 q^{63} +8.86965 q^{64} +0.613240 q^{65} -1.32563 q^{67} +1.51653 q^{68} +7.24665 q^{69} +0.563093 q^{70} +15.3990 q^{71} +3.01977 q^{72} -14.8027 q^{73} -3.46620 q^{74} -4.62394 q^{75} -0.743887 q^{76} -1.28332 q^{78} +8.78524 q^{79} -1.94344 q^{80} +1.00000 q^{81} +11.4840 q^{82} +9.92077 q^{83} +0.252644 q^{84} -2.63383 q^{85} -11.0423 q^{86} -1.84699 q^{87} -10.7647 q^{89} -0.786982 q^{90} -0.715509 q^{91} -2.55877 q^{92} +2.33663 q^{93} -14.2603 q^{94} +1.29195 q^{95} -1.97254 q^{96} +10.2309 q^{97} +8.32622 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + q^{2} + 18 q^{3} + 27 q^{4} + 10 q^{5} + q^{6} + 7 q^{7} + 3 q^{8} + 18 q^{9}+O(q^{10}) \) 18 * q + q^2 + 18 * q^3 + 27 * q^4 + 10 * q^5 + q^6 + 7 * q^7 + 3 * q^8 + 18 * q^9	\( 18 q + q^{2} + 18 q^{3} + 27 q^{4} + 10 q^{5} + q^{6} + 7 q^{7} + 3 q^{8} + 18 q^{9} - 3 q^{10} + 27 q^{12} + 18 q^{13} + 10 q^{14} + 10 q^{15} + 41 q^{16} - 5 q^{17} + q^{18} + 10 q^{19} + 16 q^{20} + 7 q^{21} + 9 q^{23} + 3 q^{24} + 52 q^{25} + q^{26} + 18 q^{27} + 4 q^{28} - 3 q^{30} + 36 q^{31} + 37 q^{32} + 20 q^{34} - 23 q^{35} + 27 q^{36} + 37 q^{37} + 6 q^{38} + 18 q^{39} - 54 q^{40} + 12 q^{41} + 10 q^{42} - 2 q^{43} + 10 q^{45} + 6 q^{46} + 41 q^{48} + 61 q^{49} - 48 q^{50} - 5 q^{51} + 27 q^{52} + 18 q^{53} + q^{54} + 36 q^{56} + 10 q^{57} + 40 q^{58} + 10 q^{59} + 16 q^{60} - 12 q^{61} - 25 q^{62} + 7 q^{63} + 67 q^{64} + 10 q^{65} + 52 q^{67} - 18 q^{68} + 9 q^{69} - 13 q^{70} + q^{71} + 3 q^{72} + 29 q^{73} - 2 q^{74} + 52 q^{75} + 26 q^{76} + q^{78} - 18 q^{79} + 48 q^{80} + 18 q^{81} - 6 q^{82} - 26 q^{83} + 4 q^{84} + 15 q^{85} + 9 q^{86} + 59 q^{89} - 3 q^{90} + 7 q^{91} + 4 q^{92} + 36 q^{93} - 53 q^{94} - 5 q^{95} + 37 q^{96} + 70 q^{97} + 93 q^{98}+O(q^{100}) \) 18 * q + q^2 + 18 * q^3 + 27 * q^4 + 10 * q^5 + q^6 + 7 * q^7 + 3 * q^8 + 18 * q^9 - 3 * q^10 + 27 * q^12 + 18 * q^13 + 10 * q^14 + 10 * q^15 + 41 * q^16 - 5 * q^17 + q^18 + 10 * q^19 + 16 * q^20 + 7 * q^21 + 9 * q^23 + 3 * q^24 + 52 * q^25 + q^26 + 18 * q^27 + 4 * q^28 - 3 * q^30 + 36 * q^31 + 37 * q^32 + 20 * q^34 - 23 * q^35 + 27 * q^36 + 37 * q^37 + 6 * q^38 + 18 * q^39 - 54 * q^40 + 12 * q^41 + 10 * q^42 - 2 * q^43 + 10 * q^45 + 6 * q^46 + 41 * q^48 + 61 * q^49 - 48 * q^50 - 5 * q^51 + 27 * q^52 + 18 * q^53 + q^54 + 36 * q^56 + 10 * q^57 + 40 * q^58 + 10 * q^59 + 16 * q^60 - 12 * q^61 - 25 * q^62 + 7 * q^63 + 67 * q^64 + 10 * q^65 + 52 * q^67 - 18 * q^68 + 9 * q^69 - 13 * q^70 + q^71 + 3 * q^72 + 29 * q^73 - 2 * q^74 + 52 * q^75 + 26 * q^76 + q^78 - 18 * q^79 + 48 * q^80 + 18 * q^81 - 6 * q^82 - 26 * q^83 + 4 * q^84 + 15 * q^85 + 9 * q^86 + 59 * q^89 - 3 * q^90 + 7 * q^91 + 4 * q^92 + 36 * q^93 - 53 * q^94 - 5 * q^95 + 37 * q^96 + 70 * q^97 + 93 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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