LMFDB - Embedded newform 3381.2.a.bk.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, 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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 100x^{5} + 26x^{4} + 108x^{3} - 33x^{2} - 36x + 14 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 108x^3 - 33x^2 - 36x + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$0.507824$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.507824 q^{2} -1.00000 q^{3} -1.74212 q^{4} -3.36946 q^{5} -0.507824 q^{6} -1.90033 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.507824 q^{2} -1.00000 q^{3} -1.74212 q^{4} -3.36946 q^{5} -0.507824 q^{6} -1.90033 q^{8} +1.00000 q^{9} -1.71109 q^{10} +3.52145 q^{11} +1.74212 q^{12} +0.582156 q^{13} +3.36946 q^{15} +2.51920 q^{16} -4.36722 q^{17} +0.507824 q^{18} -1.57451 q^{19} +5.86999 q^{20} +1.78827 q^{22} -1.00000 q^{23} +1.90033 q^{24} +6.35327 q^{25} +0.295633 q^{26} -1.00000 q^{27} +6.29806 q^{29} +1.71109 q^{30} +3.71809 q^{31} +5.07998 q^{32} -3.52145 q^{33} -2.21778 q^{34} -1.74212 q^{36} -5.02204 q^{37} -0.799574 q^{38} -0.582156 q^{39} +6.40311 q^{40} +11.5320 q^{41} +3.16853 q^{43} -6.13477 q^{44} -3.36946 q^{45} -0.507824 q^{46} +12.5184 q^{47} -2.51920 q^{48} +3.22634 q^{50} +4.36722 q^{51} -1.01418 q^{52} -5.42622 q^{53} -0.507824 q^{54} -11.8654 q^{55} +1.57451 q^{57} +3.19830 q^{58} -12.8936 q^{59} -5.86999 q^{60} -11.9423 q^{61} +1.88813 q^{62} -2.45866 q^{64} -1.96155 q^{65} -1.78827 q^{66} +9.68141 q^{67} +7.60821 q^{68} +1.00000 q^{69} +8.15303 q^{71} -1.90033 q^{72} -3.05034 q^{73} -2.55031 q^{74} -6.35327 q^{75} +2.74298 q^{76} -0.295633 q^{78} -5.16206 q^{79} -8.48833 q^{80} +1.00000 q^{81} +5.85622 q^{82} +0.437777 q^{83} +14.7152 q^{85} +1.60905 q^{86} -6.29806 q^{87} -6.69193 q^{88} -8.36773 q^{89} -1.71109 q^{90} +1.74212 q^{92} -3.71809 q^{93} +6.35714 q^{94} +5.30525 q^{95} -5.07998 q^{96} -6.27355 q^{97} +3.52145 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	$ 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} - 8 q^{12} + 4 q^{15} + 4 q^{16} - 12 q^{17} + 4 q^{18} - 26 q^{19} - 24 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} - 2 q^{25} - 4 q^{26} - 10 q^{27} + 16 q^{29} + 8 q^{30} - 12 q^{31} + 8 q^{32} - 2 q^{33} - 28 q^{34} + 8 q^{36} - 8 q^{37} - 32 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{43} - 16 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 8 q^{50} + 12 q^{51} - 24 q^{52} + 14 q^{53} - 4 q^{54} - 16 q^{55} + 26 q^{57} - 8 q^{58} - 38 q^{59} + 24 q^{60} - 14 q^{61} + 8 q^{62} + 8 q^{64} + 12 q^{65} + 8 q^{66} - 8 q^{68} + 10 q^{69} + 24 q^{71} + 12 q^{72} - 8 q^{73} - 8 q^{74} + 2 q^{75} - 64 q^{76} + 4 q^{78} - 16 q^{79} - 28 q^{80} + 10 q^{81} + 40 q^{82} - 28 q^{83} - 4 q^{85} + 20 q^{86} - 16 q^{87} - 68 q^{88} - 32 q^{89} - 8 q^{90} - 8 q^{92} + 12 q^{93} - 56 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) $ 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 - 8 * q^12 + 4 * q^15 + 4 * q^16 - 12 * q^17 + 4 * q^18 - 26 * q^19 - 24 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 2 * q^25 - 4 * q^26 - 10 * q^27 + 16 * q^29 + 8 * q^30 - 12 * q^31 + 8 * q^32 - 2 * q^33 - 28 * q^34 + 8 * q^36 - 8 * q^37 - 32 * q^38 - 4 * q^40 - 10 * q^41 - 4 * q^43 - 16 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 8 * q^50 + 12 * q^51 - 24 * q^52 + 14 * q^53 - 4 * q^54 - 16 * q^55 + 26 * q^57 - 8 * q^58 - 38 * q^59 + 24 * q^60 - 14 * q^61 + 8 * q^62 + 8 * q^64 + 12 * q^65 + 8 * q^66 - 8 * q^68 + 10 * q^69 + 24 * q^71 + 12 * q^72 - 8 * q^73 - 8 * q^74 + 2 * q^75 - 64 * q^76 + 4 * q^78 - 16 * q^79 - 28 * q^80 + 10 * q^81 + 40 * q^82 - 28 * q^83 - 4 * q^85 + 20 * q^86 - 16 * q^87 - 68 * q^88 - 32 * q^89 - 8 * q^90 - 8 * q^92 + 12 * q^93 - 56 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 + 2 * 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 $

$2$	0.507824	0.359086	0.179543	−	0.983750i	$-0.442538\pi$
$2$	0.507824	0.359086	0.179543	+	0.983750i	$0.442538\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.74212	−0.871058
$5$	−3.36946	−1.50687	−0.753435	−	0.657523i	$-0.771604\pi$
$5$	−3.36946	−1.50687	−0.753435	+	0.657523i	$0.771604\pi$
$6$	−0.507824	−0.207318
$7$	0	0
$7$	0	0
$8$	−1.90033	−0.671870
$9$	1.00000	0.333333
$10$	−1.71109	−0.541095
$11$	3.52145	1.06176	0.530878	−	0.847448i	$-0.321862\pi$
$11$	3.52145	1.06176	0.530878	+	0.847448i	$0.321862\pi$
$12$	1.74212	0.502905
$13$	0.582156	0.161461	0.0807305	−	0.996736i	$-0.474275\pi$
$13$	0.582156	0.161461	0.0807305	+	0.996736i	$0.474275\pi$
$14$	0	0
$15$	3.36946	0.869991
$16$	2.51920	0.629799
$17$	−4.36722	−1.05921	−0.529604	−	0.848245i	$-0.677659\pi$
$17$	−4.36722	−1.05921	−0.529604	+	0.848245i	$0.677659\pi$
$18$	0.507824	0.119695
$19$	−1.57451	−0.361217	−0.180609	−	0.983555i	$-0.557807\pi$
$19$	−1.57451	−0.361217	−0.180609	+	0.983555i	$0.557807\pi$
$20$	5.86999	1.31257
$21$	0	0
$22$	1.78827	0.381261
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.90033	0.387904
$25$	6.35327	1.27065
$26$	0.295633	0.0579783
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.29806	1.16952	0.584760	−	0.811206i	$-0.301189\pi$
$29$	6.29806	1.16952	0.584760	+	0.811206i	$0.301189\pi$
$30$	1.71109	0.312401
$31$	3.71809	0.667788	0.333894	−	0.942611i	$-0.391637\pi$
$31$	3.71809	0.667788	0.333894	+	0.942611i	$0.391637\pi$
$32$	5.07998	0.898021
$33$	−3.52145	−0.613005
$34$	−2.21778	−0.380346
$35$	0	0
$36$	−1.74212	−0.290353
$37$	−5.02204	−0.825619	−0.412809	−	0.910817i	$-0.635452\pi$
$37$	−5.02204	−0.825619	−0.412809	+	0.910817i	$0.635452\pi$
$38$	−0.799574	−0.129708
$39$	−0.582156	−0.0932196
$40$	6.40311	1.01242
$41$	11.5320	1.80100	0.900498	−	0.434860i	$-0.143202\pi$
$41$	11.5320	1.80100	0.900498	+	0.434860i	$0.143202\pi$
$42$	0	0
$43$	3.16853	0.483196	0.241598	−	0.970376i	$-0.422328\pi$
$43$	3.16853	0.483196	0.241598	+	0.970376i	$0.422328\pi$
$44$	−6.13477	−0.924851
$45$	−3.36946	−0.502290
$46$	−0.507824	−0.0748745
$47$	12.5184	1.82600	0.912999	−	0.407962i	$-0.133761\pi$
$47$	12.5184	1.82600	0.912999	+	0.407962i	$0.133761\pi$
$48$	−2.51920	−0.363615
$49$	0	0
$50$	3.22634	0.456274
$51$	4.36722	0.611534
$52$	−1.01418	−0.140642
$53$	−5.42622	−0.745348	−0.372674	−	0.927962i	$-0.621559\pi$
$53$	−5.42622	−0.745348	−0.372674	+	0.927962i	$0.621559\pi$
$54$	−0.507824	−0.0691061
$55$	−11.8654	−1.59993
$56$	0	0
$57$	1.57451	0.208549
$58$	3.19830	0.419958
$59$	−12.8936	−1.67860	−0.839302	−	0.543666i	$-0.817036\pi$
$59$	−12.8936	−1.67860	−0.839302	+	0.543666i	$0.817036\pi$
$60$	−5.86999	−0.757812
$61$	−11.9423	−1.52906	−0.764528	−	0.644591i	$-0.777028\pi$
$61$	−11.9423	−1.52906	−0.764528	+	0.644591i	$0.777028\pi$
$62$	1.88813	0.239793
$63$	0	0
$64$	−2.45866	−0.307332
$65$	−1.96155	−0.243301
$66$	−1.78827	−0.220121
$67$	9.68141	1.18277	0.591386	−	0.806389i	$-0.298581\pi$
$67$	9.68141	1.18277	0.591386	+	0.806389i	$0.298581\pi$
$68$	7.60821	0.922630
$69$	1.00000	0.120386
$70$	0	0
$71$	8.15303	0.967587	0.483793	−	0.875182i	$-0.339259\pi$
$71$	8.15303	0.967587	0.483793	+	0.875182i	$0.339259\pi$
$72$	−1.90033	−0.223957
$73$	−3.05034	−0.357015	−0.178508	−	0.983939i	$-0.557127\pi$
$73$	−3.05034	−0.357015	−0.178508	+	0.983939i	$0.557127\pi$
$74$	−2.55031	−0.296468
$75$	−6.35327	−0.733613
$76$	2.74298	0.314641
$77$	0	0
$78$	−0.295633	−0.0334738
$79$	−5.16206	−0.580777	−0.290388	−	0.956909i	$-0.593785\pi$
$79$	−5.16206	−0.580777	−0.290388	+	0.956909i	$0.593785\pi$
$80$	−8.48833	−0.949024
$81$	1.00000	0.111111
$82$	5.85622	0.646712
$83$	0.437777	0.0480523	0.0240262	−	0.999711i	$-0.492352\pi$
$83$	0.437777	0.0480523	0.0240262	+	0.999711i	$0.492352\pi$
$84$	0	0
$85$	14.7152	1.59609
$86$	1.60905	0.173509
$87$	−6.29806	−0.675223
$88$	−6.69193	−0.713362
$89$	−8.36773	−0.886977	−0.443489	−	0.896280i	$-0.646259\pi$
$89$	−8.36773	−0.886977	−0.443489	+	0.896280i	$0.646259\pi$
$90$	−1.71109	−0.180365
$91$	0	0
$92$	1.74212	0.181628
$93$	−3.71809	−0.385548
$94$	6.35714	0.655689
$95$	5.30525	0.544307
$96$	−5.07998	−0.518473
$97$	−6.27355	−0.636983	−0.318491	−	0.947926i	$-0.603176\pi$
$97$	−6.27355	−0.636983	−0.318491	+	0.947926i	$0.603176\pi$
$98$	0	0
$99$	3.52145	0.353919
$100$	−11.0681	−1.10681
$101$	1.47545	0.146813	0.0734065	−	0.997302i	$-0.476613\pi$
$101$	1.47545	0.146813	0.0734065	+	0.997302i	$0.476613\pi$
$102$	2.21778	0.219593
$103$	−10.4958	−1.03419	−0.517093	−	0.855929i	$-0.672986\pi$
$103$	−10.4958	−1.03419	−0.517093	+	0.855929i	$0.672986\pi$
$104$	−1.10629	−0.108481
$105$	0	0
$106$	−2.75556	−0.267644
$107$	−11.2699	−1.08951	−0.544753	−	0.838596i	$-0.683377\pi$
$107$	−11.2699	−1.08951	−0.544753	+	0.838596i	$0.683377\pi$
$108$	1.74212	0.167635
$109$	−14.8940	−1.42659	−0.713294	−	0.700865i	$-0.752798\pi$
$109$	−14.8940	−1.42659	−0.713294	+	0.700865i	$0.752798\pi$
$110$	−6.02552	−0.574511
$111$	5.02204	0.476671
$112$	0	0
$113$	11.2097	1.05452	0.527258	−	0.849705i	$-0.323220\pi$
$113$	11.2097	1.05452	0.527258	+	0.849705i	$0.323220\pi$
$114$	0.799574	0.0748869
$115$	3.36946	0.314204
$116$	−10.9719	−1.01872
$117$	0.582156	0.0538204
$118$	−6.54767	−0.602762
$119$	0	0
$120$	−6.40311	−0.584521
$121$	1.40059	0.127327
$122$	−6.06458	−0.549062
$123$	−11.5320	−1.03981
$124$	−6.47733	−0.581682
$125$	−4.55980	−0.407841
$126$	0	0
$127$	6.83306	0.606336	0.303168	−	0.952937i	$-0.401956\pi$
$127$	6.83306	0.606336	0.303168	+	0.952937i	$0.401956\pi$
$128$	−11.4085	−1.00838
$129$	−3.16853	−0.278973
$130$	−0.996123	−0.0873658
$131$	−5.14200	−0.449259	−0.224629	−	0.974444i	$-0.572117\pi$
$131$	−5.14200	−0.449259	−0.224629	+	0.974444i	$0.572117\pi$
$132$	6.13477	0.533963
$133$	0	0
$134$	4.91645	0.424716
$135$	3.36946	0.289997
$136$	8.29919	0.711649
$137$	−11.9922	−1.02456	−0.512280	−	0.858818i	$-0.671199\pi$
$137$	−11.9922	−1.02456	−0.512280	+	0.858818i	$0.671199\pi$
$138$	0.507824	0.0432288
$139$	−18.8938	−1.60255	−0.801275	−	0.598296i	$-0.795845\pi$
$139$	−18.8938	−1.60255	−0.801275	+	0.598296i	$0.795845\pi$
$140$	0	0
$141$	−12.5184	−1.05424
$142$	4.14030	0.347446
$143$	2.05003	0.171432
$144$	2.51920	0.209933
$145$	−21.2211	−1.76231
$146$	−1.54903	−0.128199
$147$	0	0
$148$	8.74898	0.719162
$149$	−9.67711	−0.792780	−0.396390	−	0.918082i	$-0.629737\pi$
$149$	−9.67711	−0.792780	−0.396390	+	0.918082i	$0.629737\pi$
$150$	−3.22634	−0.263430
$151$	−2.72866	−0.222055	−0.111028	−	0.993817i	$-0.535414\pi$
$151$	−2.72866	−0.222055	−0.111028	+	0.993817i	$0.535414\pi$
$152$	2.99210	0.242691
$153$	−4.36722	−0.353069
$154$	0	0
$155$	−12.5280	−1.00627
$156$	1.01418	0.0811996
$157$	7.52810	0.600808	0.300404	−	0.953812i	$-0.402878\pi$
$157$	7.52810	0.600808	0.300404	+	0.953812i	$0.402878\pi$
$158$	−2.62141	−0.208549
$159$	5.42622	0.430327
$160$	−17.1168	−1.35320
$161$	0	0
$162$	0.507824	0.0398984
$163$	11.1525	0.873530	0.436765	−	0.899576i	$-0.356124\pi$
$163$	11.1525	0.873530	0.436765	+	0.899576i	$0.356124\pi$
$164$	−20.0901	−1.56877
$165$	11.8654	0.923719
$166$	0.222314	0.0172549
$167$	−6.62408	−0.512587	−0.256293	−	0.966599i	$-0.582501\pi$
$167$	−6.62408	−0.512587	−0.256293	+	0.966599i	$0.582501\pi$
$168$	0	0
$169$	−12.6611	−0.973930
$170$	7.47272	0.573132
$171$	−1.57451	−0.120406
$172$	−5.51994	−0.420892
$173$	18.7223	1.42343	0.711714	−	0.702470i	$-0.247919\pi$
$173$	18.7223	1.42343	0.711714	+	0.702470i	$0.247919\pi$
$174$	−3.19830	−0.242463
$175$	0	0
$176$	8.87121	0.668693
$177$	12.8936	0.969142
$178$	−4.24933	−0.318501
$179$	15.9914	1.19526	0.597628	−	0.801774i	$-0.296110\pi$
$179$	15.9914	1.19526	0.597628	+	0.801774i	$0.296110\pi$
$180$	5.86999	0.437523
$181$	−16.6859	−1.24026	−0.620128	−	0.784501i	$-0.712919\pi$
$181$	−16.6859	−1.24026	−0.620128	+	0.784501i	$0.712919\pi$
$182$	0	0
$183$	11.9423	0.882800
$184$	1.90033	0.140095
$185$	16.9216	1.24410
$186$	−1.88813	−0.138445
$187$	−15.3789	−1.12462
$188$	−21.8085	−1.59055
$189$	0	0
$190$	2.69413	0.195453
$191$	−16.4938	−1.19345	−0.596726	−	0.802445i	$-0.703532\pi$
$191$	−16.4938	−1.19345	−0.596726	+	0.802445i	$0.703532\pi$
$192$	2.45866	0.177438
$193$	−2.49327	−0.179469	−0.0897347	−	0.995966i	$-0.528602\pi$
$193$	−2.49327	−0.179469	−0.0897347	+	0.995966i	$0.528602\pi$
$194$	−3.18586	−0.228731
$195$	1.96155	0.140470
$196$	0	0
$197$	−10.1473	−0.722963	−0.361481	−	0.932379i	$-0.617729\pi$
$197$	−10.1473	−0.722963	−0.361481	+	0.932379i	$0.617729\pi$
$198$	1.78827	0.127087
$199$	−10.6987	−0.758413	−0.379207	−	0.925312i	$-0.623803\pi$
$199$	−10.6987	−0.758413	−0.379207	+	0.925312i	$0.623803\pi$
$200$	−12.0733	−0.853714
$201$	−9.68141	−0.682874
$202$	0.749270	0.0527184
$203$	0	0
$204$	−7.60821	−0.532681
$205$	−38.8566	−2.71387
$206$	−5.33003	−0.371361
$207$	−1.00000	−0.0695048
$208$	1.46656	0.101688
$209$	−5.54456	−0.383525
$210$	0	0
$211$	4.45788	0.306893	0.153447	−	0.988157i	$-0.450963\pi$
$211$	4.45788	0.306893	0.153447	+	0.988157i	$0.450963\pi$
$212$	9.45309	0.649241
$213$	−8.15303	−0.558637
$214$	−5.72314	−0.391226
$215$	−10.6762	−0.728113
$216$	1.90033	0.129301
$217$	0	0
$218$	−7.56354	−0.512267
$219$	3.05034	0.206123
$220$	20.6709	1.39363
$221$	−2.54241	−0.171021
$222$	2.55031	0.171166
$223$	10.5752	0.708166	0.354083	−	0.935214i	$-0.384793\pi$
$223$	10.5752	0.708166	0.354083	+	0.935214i	$0.384793\pi$
$224$	0	0
$225$	6.35327	0.423552
$226$	5.69253	0.378661
$227$	20.8124	1.38137	0.690684	−	0.723157i	$-0.257310\pi$
$227$	20.8124	1.38137	0.690684	+	0.723157i	$0.257310\pi$
$228$	−2.74298	−0.181658
$229$	10.0157	0.661857	0.330928	−	0.943656i	$-0.392638\pi$
$229$	10.0157	0.661857	0.330928	+	0.943656i	$0.392638\pi$
$230$	1.71109	0.112826
$231$	0	0
$232$	−11.9684	−0.785765
$233$	9.84802	0.645165	0.322583	−	0.946541i	$-0.395449\pi$
$233$	9.84802	0.645165	0.322583	+	0.946541i	$0.395449\pi$
$234$	0.295633	0.0193261
$235$	−42.1803	−2.75154
$236$	22.4621	1.46216
$237$	5.16206	0.335312
$238$	0	0
$239$	−3.00670	−0.194487	−0.0972435	−	0.995261i	$-0.531003\pi$
$239$	−3.00670	−0.194487	−0.0972435	+	0.995261i	$0.531003\pi$
$240$	8.48833	0.547919
$241$	−22.5330	−1.45148	−0.725738	−	0.687971i	$-0.758502\pi$
$241$	−22.5330	−1.45148	−0.725738	+	0.687971i	$0.758502\pi$
$242$	0.711254	0.0457211
$243$	−1.00000	−0.0641500
$244$	20.8049	1.33189
$245$	0	0
$246$	−5.85622	−0.373379
$247$	−0.916611	−0.0583226
$248$	−7.06561	−0.448667
$249$	−0.437777	−0.0277430
$250$	−2.31557	−0.146450
$251$	0.240327	0.0151693	0.00758464	−	0.999971i	$-0.497586\pi$
$251$	0.240327	0.0151693	0.00758464	+	0.999971i	$0.497586\pi$
$252$	0	0
$253$	−3.52145	−0.221392
$254$	3.46999	0.217727
$255$	−14.7152	−0.921501
$256$	−0.876200	−0.0547625
$257$	−0.158016	−0.00985675	−0.00492837	−	0.999988i	$-0.501569\pi$
$257$	−0.158016	−0.00985675	−0.00492837	+	0.999988i	$0.501569\pi$
$258$	−1.60905	−0.100175
$259$	0	0
$260$	3.41725	0.211929
$261$	6.29806	0.389840
$262$	−2.61123	−0.161322
$263$	18.4642	1.13855	0.569275	−	0.822147i	$-0.307224\pi$
$263$	18.4642	1.13855	0.569275	+	0.822147i	$0.307224\pi$
$264$	6.69193	0.411860
$265$	18.2834	1.12314
$266$	0	0
$267$	8.36773	0.512096
$268$	−16.8661	−1.03026
$269$	−0.958502	−0.0584409	−0.0292205	−	0.999573i	$-0.509302\pi$
$269$	−0.958502	−0.0584409	−0.0292205	+	0.999573i	$0.509302\pi$
$270$	1.71109	0.104134
$271$	23.5098	1.42812	0.714059	−	0.700086i	$-0.246855\pi$
$271$	23.5098	1.42812	0.714059	+	0.700086i	$0.246855\pi$
$272$	−11.0019	−0.667087
$273$	0	0
$274$	−6.08991	−0.367905
$275$	22.3727	1.34913
$276$	−1.74212	−0.104863
$277$	31.2642	1.87848	0.939240	−	0.343260i	$-0.111531\pi$
$277$	31.2642	1.87848	0.939240	+	0.343260i	$0.111531\pi$
$278$	−9.59471	−0.575452
$279$	3.71809	0.222596
$280$	0	0
$281$	−3.61573	−0.215696	−0.107848	−	0.994167i	$-0.534396\pi$
$281$	−3.61573	−0.215696	−0.107848	+	0.994167i	$0.534396\pi$
$282$	−6.35714	−0.378562
$283$	5.48645	0.326135	0.163068	−	0.986615i	$-0.447861\pi$
$283$	5.48645	0.326135	0.163068	+	0.986615i	$0.447861\pi$
$284$	−14.2035	−0.842824
$285$	−5.30525	−0.314256
$286$	1.04105	0.0615589
$287$	0	0
$288$	5.07998	0.299340
$289$	2.07264	0.121920
$290$	−10.7766	−0.632821
$291$	6.27355	0.367762
$292$	5.31404	0.310981
$293$	18.5359	1.08288	0.541438	−	0.840740i	$-0.317880\pi$
$293$	18.5359	1.08288	0.541438	+	0.840740i	$0.317880\pi$
$294$	0	0
$295$	43.4445	2.52944
$296$	9.54356	0.554708
$297$	−3.52145	−0.204335
$298$	−4.91427	−0.284676
$299$	−0.582156	−0.0336670
$300$	11.0681	0.639019
$301$	0	0
$302$	−1.38568	−0.0797369
$303$	−1.47545	−0.0847625
$304$	−3.96650	−0.227494
$305$	40.2391	2.30409
$306$	−2.21778	−0.126782
$307$	−4.00645	−0.228660	−0.114330	−	0.993443i	$-0.536472\pi$
$307$	−4.00645	−0.228660	−0.114330	+	0.993443i	$0.536472\pi$
$308$	0	0
$309$	10.4958	0.597087
$310$	−6.36199	−0.361337
$311$	−27.7513	−1.57363	−0.786817	−	0.617187i	$-0.788272\pi$
$311$	−27.7513	−1.57363	−0.786817	+	0.617187i	$0.788272\pi$
$312$	1.10629	0.0626314
$313$	28.6113	1.61721	0.808604	−	0.588353i	$-0.200223\pi$
$313$	28.6113	1.61721	0.808604	+	0.588353i	$0.200223\pi$
$314$	3.82295	0.215742
$315$	0	0
$316$	8.99290	0.505890
$317$	1.93708	0.108797	0.0543986	−	0.998519i	$-0.482676\pi$
$317$	1.93708	0.108797	0.0543986	+	0.998519i	$0.482676\pi$
$318$	2.75556	0.154524
$319$	22.1783	1.24174
$320$	8.28435	0.463109
$321$	11.2699	0.629027
$322$	0	0
$323$	6.87624	0.382604
$324$	−1.74212	−0.0967842
$325$	3.69860	0.205161
$326$	5.66349	0.313672
$327$	14.8940	0.823641
$328$	−21.9147	−1.21003
$329$	0	0
$330$	6.02552	0.331694
$331$	−29.4869	−1.62074	−0.810372	−	0.585916i	$-0.800735\pi$
$331$	−29.4869	−1.62074	−0.810372	+	0.585916i	$0.800735\pi$
$332$	−0.762659	−0.0418563
$333$	−5.02204	−0.275206
$334$	−3.36386	−0.184062
$335$	−32.6211	−1.78228
$336$	0	0
$337$	−17.5959	−0.958510	−0.479255	−	0.877676i	$-0.659093\pi$
$337$	−17.5959	−0.958510	−0.479255	+	0.877676i	$0.659093\pi$
$338$	−6.42960	−0.349724
$339$	−11.2097	−0.608825
$340$	−25.6356	−1.39028
$341$	13.0930	0.709028
$342$	−0.799574	−0.0432360
$343$	0	0
$344$	−6.02127	−0.324645
$345$	−3.36946	−0.181406
$346$	9.50761	0.511132
$347$	−5.99228	−0.321683	−0.160841	−	0.986980i	$-0.551421\pi$
$347$	−5.99228	−0.321683	−0.160841	+	0.986980i	$0.551421\pi$
$348$	10.9719	0.588158
$349$	−31.6524	−1.69431	−0.847156	−	0.531344i	$-0.821687\pi$
$349$	−31.6524	−1.69431	−0.847156	+	0.531344i	$0.821687\pi$
$350$	0	0
$351$	−0.582156	−0.0310732
$352$	17.8889	0.953480
$353$	−31.1107	−1.65585	−0.827927	−	0.560836i	$-0.810480\pi$
$353$	−31.1107	−1.65585	−0.827927	+	0.560836i	$0.810480\pi$
$354$	6.54767	0.348005
$355$	−27.4713	−1.45803
$356$	14.5775	0.772608
$357$	0	0
$358$	8.12082	0.429199
$359$	24.8310	1.31053	0.655266	−	0.755398i	$-0.272557\pi$
$359$	24.8310	1.31053	0.655266	+	0.755398i	$0.272557\pi$
$360$	6.40311	0.337473
$361$	−16.5209	−0.869522
$362$	−8.47351	−0.445358
$363$	−1.40059	−0.0735120
$364$	0	0
$365$	10.2780	0.537975
$366$	6.06458	0.317001
$367$	25.5768	1.33510	0.667548	−	0.744567i	$-0.267344\pi$
$367$	25.5768	1.33510	0.667548	+	0.744567i	$0.267344\pi$
$368$	−2.51920	−0.131322
$369$	11.5320	0.600332
$370$	8.59318	0.446738
$371$	0	0
$372$	6.47733	0.335834
$373$	−16.3483	−0.846485	−0.423242	−	0.906016i	$-0.639108\pi$
$373$	−16.3483	−0.846485	−0.423242	+	0.906016i	$0.639108\pi$
$374$	−7.80979	−0.403835
$375$	4.55980	0.235467
$376$	−23.7892	−1.22683
$377$	3.66645	0.188832
$378$	0	0
$379$	−10.5632	−0.542597	−0.271299	−	0.962495i	$-0.587453\pi$
$379$	−10.5632	−0.542597	−0.271299	+	0.962495i	$0.587453\pi$
$380$	−9.24236	−0.474123
$381$	−6.83306	−0.350068
$382$	−8.37596	−0.428552
$383$	29.1796	1.49101	0.745505	−	0.666500i	$-0.232208\pi$
$383$	29.1796	1.49101	0.745505	+	0.666500i	$0.232208\pi$
$384$	11.4085	0.582188
$385$	0	0
$386$	−1.26614	−0.0644448
$387$	3.16853	0.161065
$388$	10.9293	0.554849
$389$	−10.8298	−0.549091	−0.274545	−	0.961574i	$-0.588527\pi$
$389$	−10.8298	−0.549091	−0.274545	+	0.961574i	$0.588527\pi$
$390$	0.996123	0.0504406
$391$	4.36722	0.220860
$392$	0	0
$393$	5.14200	0.259380
$394$	−5.15302	−0.259605
$395$	17.3934	0.875155
$396$	−6.13477	−0.308284
$397$	16.8982	0.848099	0.424049	−	0.905639i	$-0.360608\pi$
$397$	16.8982	0.848099	0.424049	+	0.905639i	$0.360608\pi$
$398$	−5.43307	−0.272335
$399$	0	0
$400$	16.0051	0.800257
$401$	9.40385	0.469606	0.234803	−	0.972043i	$-0.424556\pi$
$401$	9.40385	0.469606	0.234803	+	0.972043i	$0.424556\pi$
$402$	−4.91645	−0.245210
$403$	2.16451	0.107822
$404$	−2.57041	−0.127883
$405$	−3.36946	−0.167430
$406$	0	0
$407$	−17.6849	−0.876606
$408$	−8.29919	−0.410871
$409$	−28.7565	−1.42192	−0.710959	−	0.703233i	$-0.751739\pi$
$409$	−28.7565	−1.42192	−0.710959	+	0.703233i	$0.751739\pi$
$410$	−19.7323	−0.974510
$411$	11.9922	0.591530
$412$	18.2850	0.900835
$413$	0	0
$414$	−0.507824	−0.0249582
$415$	−1.47507	−0.0724085
$416$	2.95734	0.144995
$417$	18.8938	0.925232
$418$	−2.81566	−0.137718
$419$	−3.08384	−0.150655	−0.0753277	−	0.997159i	$-0.524000\pi$
$419$	−3.08384	−0.150655	−0.0753277	+	0.997159i	$0.524000\pi$
$420$	0	0
$421$	−30.4121	−1.48220	−0.741098	−	0.671397i	$-0.765695\pi$
$421$	−30.4121	−1.48220	−0.741098	+	0.671397i	$0.765695\pi$
$422$	2.26382	0.110201
$423$	12.5184	0.608666
$424$	10.3116	0.500777
$425$	−27.7462	−1.34589
$426$	−4.14030	−0.200598
$427$	0	0
$428$	19.6335	0.949023
$429$	−2.05003	−0.0989765
$430$	−5.42165	−0.261455
$431$	−22.4322	−1.08052	−0.540260	−	0.841498i	$-0.681674\pi$
$431$	−22.4322	−1.08052	−0.540260	+	0.841498i	$0.681674\pi$
$432$	−2.51920	−0.121205
$433$	16.9261	0.813419	0.406709	−	0.913558i	$-0.366676\pi$
$433$	16.9261	0.813419	0.406709	+	0.913558i	$0.366676\pi$
$434$	0	0
$435$	21.2211	1.01747
$436$	25.9471	1.24264
$437$	1.57451	0.0753190
$438$	1.54903	0.0740157
$439$	17.8468	0.851782	0.425891	−	0.904775i	$-0.359961\pi$
$439$	17.8468	0.851782	0.425891	+	0.904775i	$0.359961\pi$
$440$	22.5482	1.07494
$441$	0	0
$442$	−1.29109	−0.0614111
$443$	9.99727	0.474985	0.237492	−	0.971389i	$-0.423675\pi$
$443$	9.99727	0.474985	0.237492	+	0.971389i	$0.423675\pi$
$444$	−8.74898	−0.415208
$445$	28.1947	1.33656
$446$	5.37033	0.254292
$447$	9.67711	0.457712
$448$	0	0
$449$	−12.2739	−0.579239	−0.289620	−	0.957142i	$-0.593529\pi$
$449$	−12.2739	−0.579239	−0.289620	+	0.957142i	$0.593529\pi$
$450$	3.22634	0.152091
$451$	40.6093	1.91222
$452$	−19.5285	−0.918544
$453$	2.72866	0.128204
$454$	10.5690	0.496029
$455$	0	0
$456$	−2.99210	−0.140118
$457$	−7.46202	−0.349059	−0.174529	−	0.984652i	$-0.555840\pi$
$457$	−7.46202	−0.349059	−0.174529	+	0.984652i	$0.555840\pi$
$458$	5.08622	0.237663
$459$	4.36722	0.203845
$460$	−5.86999	−0.273690
$461$	26.5396	1.23607	0.618035	−	0.786150i	$-0.287929\pi$
$461$	26.5396	1.23607	0.618035	+	0.786150i	$0.287929\pi$
$462$	0	0
$463$	15.9728	0.742321	0.371161	−	0.928569i	$-0.378960\pi$
$463$	15.9728	0.742321	0.371161	+	0.928569i	$0.378960\pi$
$464$	15.8660	0.736562
$465$	12.5280	0.580970
$466$	5.00106	0.231670
$467$	14.7648	0.683232	0.341616	−	0.939840i	$-0.389026\pi$
$467$	14.7648	0.683232	0.341616	+	0.939840i	$0.389026\pi$
$468$	−1.01418	−0.0468806
$469$	0	0
$470$	−21.4202	−0.988038
$471$	−7.52810	−0.346877
$472$	24.5022	1.12780
$473$	11.1578	0.513037
$474$	2.62141	0.120406
$475$	−10.0033	−0.458983
$476$	0	0
$477$	−5.42622	−0.248449
$478$	−1.52687	−0.0698375
$479$	1.85487	0.0847514	0.0423757	−	0.999102i	$-0.486507\pi$
$479$	1.85487	0.0847514	0.0423757	+	0.999102i	$0.486507\pi$
$480$	17.1168	0.781271
$481$	−2.92361	−0.133305
$482$	−11.4428	−0.521204
$483$	0	0
$484$	−2.43999	−0.110909
$485$	21.1385	0.959850
$486$	−0.507824	−0.0230354
$487$	−23.3766	−1.05930	−0.529648	−	0.848218i	$-0.677676\pi$
$487$	−23.3766	−1.05930	−0.529648	+	0.848218i	$0.677676\pi$
$488$	22.6944	1.02733
$489$	−11.1525	−0.504333
$490$	0	0
$491$	−34.4930	−1.55665	−0.778325	−	0.627862i	$-0.783930\pi$
$491$	−34.4930	−1.55665	−0.778325	+	0.627862i	$0.783930\pi$
$492$	20.0901	0.905730
$493$	−27.5050	−1.23876
$494$	−0.465477	−0.0209428
$495$	−11.8654	−0.533309
$496$	9.36659	0.420572
$497$	0	0
$498$	−0.222314	−0.00996212
$499$	−33.3579	−1.49331	−0.746653	−	0.665214i	$-0.768340\pi$
$499$	−33.3579	−1.49331	−0.746653	+	0.665214i	$0.768340\pi$
$500$	7.94370	0.355253
$501$	6.62408	0.295942
$502$	0.122044	0.00544707
$503$	−39.1129	−1.74396	−0.871979	−	0.489544i	$-0.837163\pi$
$503$	−39.1129	−1.74396	−0.871979	+	0.489544i	$0.837163\pi$
$504$	0	0
$505$	−4.97148	−0.221228
$506$	−1.78827	−0.0794985
$507$	12.6611	0.562299
$508$	−11.9040	−0.528154
$509$	−28.3813	−1.25798	−0.628990	−	0.777413i	$-0.716531\pi$
$509$	−28.3813	−1.25798	−0.628990	+	0.777413i	$0.716531\pi$
$510$	−7.47272	−0.330898
$511$	0	0
$512$	22.3721	0.988716
$513$	1.57451	0.0695163
$514$	−0.0802441	−0.00353942
$515$	35.3653	1.55838
$516$	5.51994	0.243002
$517$	44.0829	1.93876
$518$	0	0
$519$	−18.7223	−0.821816
$520$	3.72761	0.163466
$521$	−0.701087	−0.0307152	−0.0153576	−	0.999882i	$-0.504889\pi$
$521$	−0.701087	−0.0307152	−0.0153576	+	0.999882i	$0.504889\pi$
$522$	3.19830	0.139986
$523$	−14.0416	−0.613997	−0.306999	−	0.951710i	$-0.599325\pi$
$523$	−14.0416	−0.613997	−0.306999	+	0.951710i	$0.599325\pi$
$524$	8.95796	0.391330
$525$	0	0
$526$	9.37654	0.408837
$527$	−16.2377	−0.707326
$528$	−8.87121	−0.386070
$529$	1.00000	0.0434783
$530$	9.28476	0.403304
$531$	−12.8936	−0.559534
$532$	0	0
$533$	6.71343	0.290791
$534$	4.24933	0.183886
$535$	37.9736	1.64174
$536$	−18.3979	−0.794669
$537$	−15.9914	−0.690081
$538$	−0.486750	−0.0209853
$539$	0	0
$540$	−5.86999	−0.252604
$541$	−7.90191	−0.339730	−0.169865	−	0.985467i	$-0.554333\pi$
$541$	−7.90191	−0.339730	−0.169865	+	0.985467i	$0.554333\pi$
$542$	11.9388	0.512816
$543$	16.6859	0.716062
$544$	−22.1854	−0.951191
$545$	50.1848	2.14968
$546$	0	0
$547$	−31.7535	−1.35768	−0.678841	−	0.734285i	$-0.737518\pi$
$547$	−31.7535	−1.35768	−0.678841	+	0.734285i	$0.737518\pi$
$548$	20.8918	0.892451
$549$	−11.9423	−0.509685
$550$	11.3614	0.484452
$551$	−9.91636	−0.422451
$552$	−1.90033	−0.0808836
$553$	0	0
$554$	15.8767	0.674535
$555$	−16.9216	−0.718281
$556$	32.9151	1.39591
$557$	−40.5194	−1.71686	−0.858430	−	0.512930i	$-0.828560\pi$
$557$	−40.5194	−1.71686	−0.858430	+	0.512930i	$0.828560\pi$
$558$	1.88813	0.0799310
$559$	1.84458	0.0780174
$560$	0	0
$561$	15.3789	0.649300
$562$	−1.83615	−0.0774535
$563$	−11.6983	−0.493026	−0.246513	−	0.969139i	$-0.579285\pi$
$563$	−11.6983	−0.493026	−0.246513	+	0.969139i	$0.579285\pi$
$564$	21.8085	0.918304
$565$	−37.7705	−1.58902
$566$	2.78615	0.117111
$567$	0	0
$568$	−15.4935	−0.650092
$569$	2.88940	0.121130	0.0605649	−	0.998164i	$-0.480710\pi$
$569$	2.88940	0.121130	0.0605649	+	0.998164i	$0.480710\pi$
$570$	−2.69413	−0.112845
$571$	7.00219	0.293033	0.146516	−	0.989208i	$-0.453194\pi$
$571$	7.00219	0.293033	0.146516	+	0.989208i	$0.453194\pi$
$572$	−3.57139	−0.149327
$573$	16.4938	0.689040
$574$	0	0
$575$	−6.35327	−0.264950
$576$	−2.45866	−0.102444
$577$	21.0327	0.875602	0.437801	−	0.899072i	$-0.355757\pi$
$577$	21.0327	0.875602	0.437801	+	0.899072i	$0.355757\pi$
$578$	1.05254	0.0437797
$579$	2.49327	0.103617
$580$	36.9695	1.53508
$581$	0	0
$582$	3.18586	0.132058
$583$	−19.1081	−0.791378
$584$	5.79666	0.239868
$585$	−1.96155	−0.0811002
$586$	9.41295	0.388845
$587$	−24.1793	−0.997986	−0.498993	−	0.866606i	$-0.666297\pi$
$587$	−24.1793	−0.997986	−0.498993	+	0.866606i	$0.666297\pi$
$588$	0	0
$589$	−5.85417	−0.241217
$590$	22.0621	0.908284
$591$	10.1473	0.417403
$592$	−12.6515	−0.519974
$593$	−24.3877	−1.00148	−0.500742	−	0.865597i	$-0.666939\pi$
$593$	−24.3877	−1.00148	−0.500742	+	0.865597i	$0.666939\pi$
$594$	−1.78827	−0.0733738
$595$	0	0
$596$	16.8586	0.690557
$597$	10.6987	0.437870
$598$	−0.295633	−0.0120893
$599$	31.2133	1.27534	0.637670	−	0.770310i	$-0.279898\pi$
$599$	31.2133	1.27534	0.637670	+	0.770310i	$0.279898\pi$
$600$	12.0733	0.492892
$601$	−8.22360	−0.335448	−0.167724	−	0.985834i	$-0.553642\pi$
$601$	−8.22360	−0.335448	−0.167724	+	0.985834i	$0.553642\pi$
$602$	0	0
$603$	9.68141	0.394257
$604$	4.75364	0.193423
$605$	−4.71924	−0.191864
$606$	−0.749270	−0.0304370
$607$	15.0851	0.612286	0.306143	−	0.951986i	$-0.400961\pi$
$607$	15.0851	0.612286	0.306143	+	0.951986i	$0.400961\pi$
$608$	−7.99848	−0.324381
$609$	0	0
$610$	20.4344	0.827364
$611$	7.28767	0.294827
$612$	7.60821	0.307543
$613$	−25.1438	−1.01555	−0.507773	−	0.861491i	$-0.669531\pi$
$613$	−25.1438	−1.01555	−0.507773	+	0.861491i	$0.669531\pi$
$614$	−2.03457	−0.0821085
$615$	38.8566	1.56685
$616$	0	0
$617$	−25.3212	−1.01939	−0.509696	−	0.860354i	$-0.670242\pi$
$617$	−25.3212	−1.01939	−0.509696	+	0.860354i	$0.670242\pi$
$618$	5.33003	0.214405
$619$	−2.77129	−0.111388	−0.0556938	−	0.998448i	$-0.517737\pi$
$619$	−2.77129	−0.111388	−0.0556938	+	0.998448i	$0.517737\pi$
$620$	21.8251	0.876518
$621$	1.00000	0.0401286
$622$	−14.0928	−0.565069
$623$	0	0
$624$	−1.46656	−0.0587096
$625$	−16.4023	−0.656092
$626$	14.5295	0.580716
$627$	5.54456	0.221428
$628$	−13.1148	−0.523338
$629$	21.9324	0.874502
$630$	0	0
$631$	−34.0907	−1.35713	−0.678564	−	0.734541i	$-0.737397\pi$
$631$	−34.0907	−1.35713	−0.678564	+	0.734541i	$0.737397\pi$
$632$	9.80964	0.390206
$633$	−4.45788	−0.177185
$634$	0.983695	0.0390675
$635$	−23.0237	−0.913669
$636$	−9.45309	−0.374839
$637$	0	0
$638$	11.2627	0.445893
$639$	8.15303	0.322529
$640$	38.4406	1.51950
$641$	41.0169	1.62007	0.810034	−	0.586383i	$-0.199449\pi$
$641$	41.0169	1.62007	0.810034	+	0.586383i	$0.199449\pi$
$642$	5.72314	0.225874
$643$	−12.5304	−0.494153	−0.247076	−	0.968996i	$-0.579470\pi$
$643$	−12.5304	−0.494153	−0.247076	+	0.968996i	$0.579470\pi$
$644$	0	0
$645$	10.6762	0.420377
$646$	3.49192	0.137388
$647$	23.4635	0.922444	0.461222	−	0.887285i	$-0.347411\pi$
$647$	23.4635	0.922444	0.461222	+	0.887285i	$0.347411\pi$
$648$	−1.90033	−0.0746522
$649$	−45.4041	−1.78227
$650$	1.87823	0.0736704
$651$	0	0
$652$	−19.4289	−0.760895
$653$	−42.1303	−1.64868	−0.824342	−	0.566092i	$-0.808455\pi$
$653$	−42.1303	−1.64868	−0.824342	+	0.566092i	$0.808455\pi$
$654$	7.56354	0.295758
$655$	17.3258	0.676974
$656$	29.0514	1.13427
$657$	−3.05034	−0.119005
$658$	0	0
$659$	15.6112	0.608126	0.304063	−	0.952652i	$-0.401657\pi$
$659$	15.6112	0.608126	0.304063	+	0.952652i	$0.401657\pi$
$660$	−20.6709	−0.804612
$661$	10.1039	0.392997	0.196498	−	0.980504i	$-0.437043\pi$
$661$	10.1039	0.392997	0.196498	+	0.980504i	$0.437043\pi$
$662$	−14.9741	−0.581986
$663$	2.54241	0.0987389
$664$	−0.831924	−0.0322849
$665$	0	0
$666$	−2.55031	−0.0988226
$667$	−6.29806	−0.243862
$668$	11.5399	0.446492
$669$	−10.5752	−0.408860
$670$	−16.5658	−0.639992
$671$	−42.0542	−1.62348
$672$	0	0
$673$	−37.5723	−1.44830	−0.724152	−	0.689640i	$-0.757769\pi$
$673$	−37.5723	−1.44830	−0.724152	+	0.689640i	$0.757769\pi$
$674$	−8.93561	−0.344187
$675$	−6.35327	−0.244538
$676$	22.0571	0.848349
$677$	37.6674	1.44768	0.723838	−	0.689970i	$-0.242376\pi$
$677$	37.6674	1.44768	0.723838	+	0.689970i	$0.242376\pi$
$678$	−5.69253	−0.218620
$679$	0	0
$680$	−27.9638	−1.07236
$681$	−20.8124	−0.797533
$682$	6.64896	0.254602
$683$	32.1942	1.23188	0.615938	−	0.787795i	$-0.288777\pi$
$683$	32.1942	1.23188	0.615938	+	0.787795i	$0.288777\pi$
$684$	2.74298	0.104880
$685$	40.4072	1.54388
$686$	0	0
$687$	−10.0157	−0.382123
$688$	7.98214	0.304316
$689$	−3.15890	−0.120345
$690$	−1.71109	−0.0651402
$691$	1.85398	0.0705286	0.0352643	−	0.999378i	$-0.488773\pi$
$691$	1.85398	0.0705286	0.0352643	+	0.999378i	$0.488773\pi$
$692$	−32.6163	−1.23989
$693$	0	0
$694$	−3.04302	−0.115512
$695$	63.6619	2.41483
$696$	11.9684	0.453662
$697$	−50.3628	−1.90763
$698$	−16.0738	−0.608403
$699$	−9.84802	−0.372486
$700$	0	0
$701$	32.2504	1.21808	0.609040	−	0.793139i	$-0.291555\pi$
$701$	32.2504	1.21808	0.609040	+	0.793139i	$0.291555\pi$
$702$	−0.295633	−0.0111579
$703$	7.90726	0.298228
$704$	−8.65803	−0.326312
$705$	42.1803	1.58860
$706$	−15.7987	−0.594593
$707$	0	0
$708$	−22.4621	−0.844179
$709$	−39.2019	−1.47226	−0.736130	−	0.676841i	$-0.763349\pi$
$709$	−39.2019	−1.47226	−0.736130	+	0.676841i	$0.763349\pi$
$710$	−13.9506	−0.523556
$711$	−5.16206	−0.193592
$712$	15.9015	0.595933
$713$	−3.71809	−0.139243
$714$	0	0
$715$	−6.90750	−0.258326
$716$	−27.8589	−1.04114
$717$	3.00670	0.112287
$718$	12.6098	0.470593
$719$	−44.4526	−1.65780	−0.828901	−	0.559396i	$-0.811033\pi$
$719$	−44.4526	−1.65780	−0.828901	+	0.559396i	$0.811033\pi$
$720$	−8.48833	−0.316341
$721$	0	0
$722$	−8.38971	−0.312233
$723$	22.5330	0.838010
$724$	29.0688	1.08033
$725$	40.0133	1.48606
$726$	−0.711254	−0.0263971
$727$	−19.5784	−0.726123	−0.363062	−	0.931765i	$-0.618269\pi$
$727$	−19.5784	−0.726123	−0.363062	+	0.931765i	$0.618269\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	5.21941	0.193179
$731$	−13.8377	−0.511805
$732$	−20.8049	−0.768970
$733$	3.23986	0.119667	0.0598335	−	0.998208i	$-0.480943\pi$
$733$	3.23986	0.119667	0.0598335	+	0.998208i	$0.480943\pi$
$734$	12.9885	0.479414
$735$	0	0
$736$	−5.07998	−0.187250
$737$	34.0926	1.25582
$738$	5.85622	0.215571
$739$	−23.6779	−0.871004	−0.435502	−	0.900188i	$-0.643429\pi$
$739$	−23.6779	−0.871004	−0.435502	+	0.900188i	$0.643429\pi$
$740$	−29.4794	−1.08368
$741$	0.916611	0.0336725
$742$	0	0
$743$	−49.0714	−1.80026	−0.900128	−	0.435625i	$-0.856527\pi$
$743$	−49.0714	−1.80026	−0.900128	+	0.435625i	$0.856527\pi$
$744$	7.06561	0.259038
$745$	32.6067	1.19462
$746$	−8.30207	−0.303961
$747$	0.437777	0.0160174
$748$	26.7919	0.979609
$749$	0	0
$750$	2.31557	0.0845528
$751$	23.8607	0.870690	0.435345	−	0.900264i	$-0.356626\pi$
$751$	23.8607	0.870690	0.435345	+	0.900264i	$0.356626\pi$
$752$	31.5363	1.15001
$753$	−0.240327	−0.00875799
$754$	1.86191	0.0678068
$755$	9.19413	0.334608
$756$	0	0
$757$	−15.4095	−0.560068	−0.280034	−	0.959990i	$-0.590346\pi$
$757$	−15.4095	−0.560068	−0.280034	+	0.959990i	$0.590346\pi$
$758$	−5.36426	−0.194839
$759$	3.52145	0.127820
$760$	−10.0818	−0.365704
$761$	39.3607	1.42683	0.713413	−	0.700744i	$-0.247149\pi$
$761$	39.3607	1.42683	0.713413	+	0.700744i	$0.247149\pi$
$762$	−3.46999	−0.125705
$763$	0	0
$764$	28.7342	1.03957
$765$	14.7152	0.532029
$766$	14.8181	0.535400
$767$	−7.50609	−0.271029
$768$	0.876200	0.0316171
$769$	−18.1247	−0.653592	−0.326796	−	0.945095i	$-0.605969\pi$
$769$	−18.1247	−0.653592	−0.326796	+	0.945095i	$0.605969\pi$
$770$	0	0
$771$	0.158016	0.00569079
$772$	4.34356	0.156328
$773$	−26.5742	−0.955807	−0.477903	−	0.878412i	$-0.658603\pi$
$773$	−26.5742	−0.955807	−0.477903	+	0.878412i	$0.658603\pi$
$774$	1.60905	0.0578363
$775$	23.6220	0.848528
$776$	11.9219	0.427969
$777$	0	0
$778$	−5.49961	−0.197171
$779$	−18.1573	−0.650551
$780$	−3.41725	−0.122357
$781$	28.7105	1.02734
$782$	2.21778	0.0793076
$783$	−6.29806	−0.225074
$784$	0	0
$785$	−25.3657	−0.905339
$786$	2.61123	0.0931395
$787$	−38.1617	−1.36032	−0.680160	−	0.733064i	$-0.738090\pi$
$787$	−38.1617	−1.36032	−0.680160	+	0.733064i	$0.738090\pi$
$788$	17.6777	0.629742
$789$	−18.4642	−0.657342
$790$	8.83276	0.314255
$791$	0	0
$792$	−6.69193	−0.237787
$793$	−6.95228	−0.246883
$794$	8.58133	0.304540
$795$	−18.2834	−0.648446
$796$	18.6384	0.660621
$797$	21.2237	0.751780	0.375890	−	0.926664i	$-0.377337\pi$
$797$	21.2237	0.751780	0.375890	+	0.926664i	$0.377337\pi$
$798$	0	0
$799$	−54.6707	−1.93411
$800$	32.2745	1.14108
$801$	−8.36773	−0.295659
$802$	4.77550	0.168629
$803$	−10.7416	−0.379063
$804$	16.8661	0.594822
$805$	0	0
$806$	1.09919	0.0387172
$807$	0.958502	0.0337409
$808$	−2.80385	−0.0986392
$809$	48.7399	1.71360	0.856801	−	0.515647i	$-0.172448\pi$
$809$	48.7399	1.71360	0.856801	+	0.515647i	$0.172448\pi$
$810$	−1.71109	−0.0601217
$811$	−20.6607	−0.725496	−0.362748	−	0.931887i	$-0.618161\pi$
$811$	−20.6607	−0.725496	−0.362748	+	0.931887i	$0.618161\pi$
$812$	0	0
$813$	−23.5098	−0.824524
$814$	−8.98079	−0.314777
$815$	−37.5779	−1.31629
$816$	11.0019	0.385143
$817$	−4.98888	−0.174539
$818$	−14.6032	−0.510590
$819$	0	0
$820$	67.6927	2.36393
$821$	−16.5527	−0.577694	−0.288847	−	0.957375i	$-0.593272\pi$
$821$	−16.5527	−0.577694	−0.288847	+	0.957375i	$0.593272\pi$
$822$	6.08991	0.212410
$823$	−56.3756	−1.96513	−0.982565	−	0.185921i	$-0.940473\pi$
$823$	−56.3756	−1.96513	−0.982565	+	0.185921i	$0.940473\pi$
$824$	19.9456	0.694838
$825$	−22.3727	−0.778918
$826$	0	0
$827$	−29.5907	−1.02897	−0.514485	−	0.857499i	$-0.672017\pi$
$827$	−29.5907	−1.02897	−0.514485	+	0.857499i	$0.672017\pi$
$828$	1.74212	0.0605427
$829$	−23.1935	−0.805544	−0.402772	−	0.915300i	$-0.631953\pi$
$829$	−23.1935	−0.805544	−0.402772	+	0.915300i	$0.631953\pi$
$830$	−0.749078	−0.0260009
$831$	−31.2642	−1.08454
$832$	−1.43132	−0.0496222
$833$	0	0
$834$	9.59471	0.332238
$835$	22.3196	0.772401
$836$	9.65925	0.334072
$837$	−3.71809	−0.128516
$838$	−1.56605	−0.0540982
$839$	38.4657	1.32798	0.663992	−	0.747739i	$-0.268861\pi$
$839$	38.4657	1.32798	0.663992	+	0.747739i	$0.268861\pi$
$840$	0	0
$841$	10.6655	0.367776
$842$	−15.4440	−0.532235
$843$	3.61573	0.124532
$844$	−7.76615	−0.267322
$845$	42.6611	1.46759
$846$	6.35714	0.218563
$847$	0	0
$848$	−13.6697	−0.469419
$849$	−5.48645	−0.188294
$850$	−14.0902	−0.483288
$851$	5.02204	0.172153
$852$	14.2035	0.486605
$853$	−20.7509	−0.710499	−0.355249	−	0.934772i	$-0.615604\pi$
$853$	−20.7509	−0.710499	−0.355249	+	0.934772i	$0.615604\pi$
$854$	0	0
$855$	5.30525	0.181436
$856$	21.4167	0.732006
$857$	16.1412	0.551372	0.275686	−	0.961248i	$-0.411095\pi$
$857$	16.1412	0.551372	0.275686	+	0.961248i	$0.411095\pi$
$858$	−1.04105	−0.0355410
$859$	−42.5954	−1.45334	−0.726668	−	0.686989i	$-0.758932\pi$
$859$	−42.5954	−1.45334	−0.726668	+	0.686989i	$0.758932\pi$
$860$	18.5992	0.634229
$861$	0	0
$862$	−11.3916	−0.387999
$863$	−34.7858	−1.18412	−0.592061	−	0.805893i	$-0.701686\pi$
$863$	−34.7858	−1.18412	−0.592061	+	0.805893i	$0.701686\pi$
$864$	−5.07998	−0.172824
$865$	−63.0839	−2.14492
$866$	8.59550	0.292087
$867$	−2.07264	−0.0703905
$868$	0	0
$869$	−18.1779	−0.616643
$870$	10.7766	0.365359
$871$	5.63609	0.190972
$872$	28.3036	0.958482
$873$	−6.27355	−0.212328
$874$	0.799574	0.0270460
$875$	0	0
$876$	−5.31404	−0.179545
$877$	−10.9171	−0.368643	−0.184322	−	0.982866i	$-0.559009\pi$
$877$	−10.9171	−0.368643	−0.184322	+	0.982866i	$0.559009\pi$
$878$	9.06303	0.305863
$879$	−18.5359	−0.625199
$880$	−29.8912	−1.00763
$881$	40.9354	1.37915	0.689575	−	0.724214i	$-0.257797\pi$
$881$	40.9354	1.37915	0.689575	+	0.724214i	$0.257797\pi$
$882$	0	0
$883$	18.8540	0.634486	0.317243	−	0.948344i	$-0.397243\pi$
$883$	18.8540	0.634486	0.317243	+	0.948344i	$0.397243\pi$
$884$	4.42916	0.148969
$885$	−43.4445	−1.46037
$886$	5.07685	0.170560
$887$	−0.248770	−0.00835289	−0.00417645	−	0.999991i	$-0.501329\pi$
$887$	−0.248770	−0.00835289	−0.00417645	+	0.999991i	$0.501329\pi$
$888$	−9.54356	−0.320261
$889$	0	0
$890$	14.3180	0.479939
$891$	3.52145	0.117973
$892$	−18.4232	−0.616854
$893$	−19.7104	−0.659582
$894$	4.91427	0.164358
$895$	−53.8825	−1.80109
$896$	0	0
$897$	0.582156	0.0194376
$898$	−6.23296	−0.207996
$899$	23.4167	0.780991
$900$	−11.0681	−0.368938
$901$	23.6975	0.789478
$902$	20.6224	0.686650
$903$	0	0
$904$	−21.3021	−0.708497
$905$	56.2226	1.86890
$906$	1.38568	0.0460361
$907$	53.4014	1.77316	0.886582	−	0.462572i	$-0.153073\pi$
$907$	53.4014	1.77316	0.886582	+	0.462572i	$0.153073\pi$
$908$	−36.2576	−1.20325
$909$	1.47545	0.0489377
$910$	0	0
$911$	−25.0659	−0.830471	−0.415235	−	0.909714i	$-0.636301\pi$
$911$	−25.0659	−0.830471	−0.415235	+	0.909714i	$0.636301\pi$
$912$	3.96650	0.131344
$913$	1.54161	0.0510198
$914$	−3.78939	−0.125342
$915$	−40.2391	−1.33026
$916$	−17.4485	−0.576516
$917$	0	0
$918$	2.21778	0.0731976
$919$	−7.51211	−0.247802	−0.123901	−	0.992295i	$-0.539540\pi$
$919$	−7.51211	−0.247802	−0.123901	+	0.992295i	$0.539540\pi$
$920$	−6.40311	−0.211104
$921$	4.00645	0.132017
$922$	13.4774	0.443855
$923$	4.74634	0.156228
$924$	0	0
$925$	−31.9064	−1.04908
$926$	8.11139	0.266557
$927$	−10.4958	−0.344729
$928$	31.9940	1.05025
$929$	41.5253	1.36240	0.681201	−	0.732096i	$-0.261458\pi$
$929$	41.5253	1.36240	0.681201	+	0.732096i	$0.261458\pi$
$930$	6.36199	0.208618
$931$	0	0
$932$	−17.1564	−0.561976
$933$	27.7513	0.908538
$934$	7.49790	0.245339
$935$	51.8188	1.69466
$936$	−1.10629	−0.0361603
$937$	−0.268875	−0.00878377	−0.00439188	−	0.999990i	$-0.501398\pi$
$937$	−0.268875	−0.00878377	−0.00439188	+	0.999990i	$0.501398\pi$
$938$	0	0
$939$	−28.6113	−0.933696
$940$	73.4829	2.39675
$941$	43.1875	1.40787	0.703937	−	0.710263i	$-0.251424\pi$
$941$	43.1875	1.40787	0.703937	+	0.710263i	$0.251424\pi$
$942$	−3.82295	−0.124558
$943$	−11.5320	−0.375534
$944$	−32.4815	−1.05718
$945$	0	0
$946$	5.66620	0.184224
$947$	−3.35228	−0.108934	−0.0544672	−	0.998516i	$-0.517346\pi$
$947$	−3.35228	−0.108934	−0.0544672	+	0.998516i	$0.517346\pi$
$948$	−8.99290	−0.292076
$949$	−1.77577	−0.0576440
$950$	−5.07991	−0.164814
$951$	−1.93708	−0.0628141
$952$	0	0
$953$	53.5918	1.73601	0.868004	−	0.496558i	$-0.165403\pi$
$953$	53.5918	1.73601	0.868004	+	0.496558i	$0.165403\pi$
$954$	−2.75556	−0.0892146
$955$	55.5754	1.79838
$956$	5.23801	0.169409
$957$	−22.1783	−0.716922
$958$	0.941949	0.0304330
$959$	0	0
$960$	−8.28435	−0.267376
$961$	−17.1758	−0.554059
$962$	−1.48468	−0.0478680
$963$	−11.2699	−0.363169
$964$	39.2550	1.26432
$965$	8.40097	0.270437
$966$	0	0
$967$	15.7474	0.506401	0.253201	−	0.967414i	$-0.418517\pi$
$967$	15.7474	0.506401	0.253201	+	0.967414i	$0.418517\pi$
$968$	−2.66159	−0.0855469
$969$	−6.87624	−0.220897
$970$	10.7346	0.344668
$971$	−30.6603	−0.983935	−0.491967	−	0.870614i	$-0.663722\pi$
$971$	−30.6603	−0.983935	−0.491967	+	0.870614i	$0.663722\pi$
$972$	1.74212	0.0558784
$973$	0	0
$974$	−11.8712	−0.380378
$975$	−3.69860	−0.118450
$976$	−30.0850	−0.962997
$977$	−14.8183	−0.474081	−0.237040	−	0.971500i	$-0.576177\pi$
$977$	−14.8183	−0.474081	−0.237040	+	0.971500i	$0.576177\pi$
$978$	−5.66349	−0.181099
$979$	−29.4665	−0.941754
$980$	0	0
$981$	−14.8940	−0.475529
$982$	−17.5164	−0.558970
$983$	−27.7690	−0.885692	−0.442846	−	0.896598i	$-0.646031\pi$
$983$	−27.7690	−0.885692	−0.442846	+	0.896598i	$0.646031\pi$
$984$	21.9147	0.698614
$985$	34.1908	1.08941
$986$	−13.9677	−0.444822
$987$	0	0
$988$	1.59684	0.0508023
$989$	−3.16853	−0.100753
$990$	−6.02552	−0.191504
$991$	38.5662	1.22510	0.612548	−	0.790433i	$-0.290145\pi$
$991$	38.5662	1.22510	0.612548	+	0.790433i	$0.290145\pi$
$992$	18.8878	0.599688
$993$	29.4869	0.935737
$994$	0	0
$995$	36.0490	1.14283
$996$	0.762659	0.0241658
$997$	−45.2497	−1.43307	−0.716536	−	0.697550i	$-0.754273\pi$
$997$	−45.2497	−1.43307	−0.716536	+	0.697550i	$0.754273\pi$
$998$	−16.9399	−0.536225
$999$	5.02204	0.158890

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bk.1.5	✓	10
7.6	odd	2		3381.2.a.bl.1.5	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bk.1.5	✓	10	1.1	even	1	trivial
3381.2.a.bl.1.5	yes	10	7.6	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.507824 q^{2} -1.00000 q^{3} -1.74212 q^{4} -3.36946 q^{5} -0.507824 q^{6} -1.90033 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.507824 q^{2} -1.00000 q^{3} -1.74212 q^{4} -3.36946 q^{5} -0.507824 q^{6} -1.90033 q^{8} +1.00000 q^{9} -1.71109 q^{10} +3.52145 q^{11} +1.74212 q^{12} +0.582156 q^{13} +3.36946 q^{15} +2.51920 q^{16} -4.36722 q^{17} +0.507824 q^{18} -1.57451 q^{19} +5.86999 q^{20} +1.78827 q^{22} -1.00000 q^{23} +1.90033 q^{24} +6.35327 q^{25} +0.295633 q^{26} -1.00000 q^{27} +6.29806 q^{29} +1.71109 q^{30} +3.71809 q^{31} +5.07998 q^{32} -3.52145 q^{33} -2.21778 q^{34} -1.74212 q^{36} -5.02204 q^{37} -0.799574 q^{38} -0.582156 q^{39} +6.40311 q^{40} +11.5320 q^{41} +3.16853 q^{43} -6.13477 q^{44} -3.36946 q^{45} -0.507824 q^{46} +12.5184 q^{47} -2.51920 q^{48} +3.22634 q^{50} +4.36722 q^{51} -1.01418 q^{52} -5.42622 q^{53} -0.507824 q^{54} -11.8654 q^{55} +1.57451 q^{57} +3.19830 q^{58} -12.8936 q^{59} -5.86999 q^{60} -11.9423 q^{61} +1.88813 q^{62} -2.45866 q^{64} -1.96155 q^{65} -1.78827 q^{66} +9.68141 q^{67} +7.60821 q^{68} +1.00000 q^{69} +8.15303 q^{71} -1.90033 q^{72} -3.05034 q^{73} -2.55031 q^{74} -6.35327 q^{75} +2.74298 q^{76} -0.295633 q^{78} -5.16206 q^{79} -8.48833 q^{80} +1.00000 q^{81} +5.85622 q^{82} +0.437777 q^{83} +14.7152 q^{85} +1.60905 q^{86} -6.29806 q^{87} -6.69193 q^{88} -8.36773 q^{89} -1.71109 q^{90} +1.74212 q^{92} -3.71809 q^{93} +6.35714 q^{94} +5.30525 q^{95} -5.07998 q^{96} -6.27355 q^{97} +3.52145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9	\( 10 q + 4 q^{2} - 10 q^{3} + 8 q^{4} - 4 q^{5} - 4 q^{6} + 12 q^{8} + 10 q^{9} - 8 q^{10} + 2 q^{11} - 8 q^{12} + 4 q^{15} + 4 q^{16} - 12 q^{17} + 4 q^{18} - 26 q^{19} - 24 q^{20} - 8 q^{22} - 10 q^{23} - 12 q^{24} - 2 q^{25} - 4 q^{26} - 10 q^{27} + 16 q^{29} + 8 q^{30} - 12 q^{31} + 8 q^{32} - 2 q^{33} - 28 q^{34} + 8 q^{36} - 8 q^{37} - 32 q^{38} - 4 q^{40} - 10 q^{41} - 4 q^{43} - 16 q^{44} - 4 q^{45} - 4 q^{46} - 2 q^{47} - 4 q^{48} - 8 q^{50} + 12 q^{51} - 24 q^{52} + 14 q^{53} - 4 q^{54} - 16 q^{55} + 26 q^{57} - 8 q^{58} - 38 q^{59} + 24 q^{60} - 14 q^{61} + 8 q^{62} + 8 q^{64} + 12 q^{65} + 8 q^{66} - 8 q^{68} + 10 q^{69} + 24 q^{71} + 12 q^{72} - 8 q^{73} - 8 q^{74} + 2 q^{75} - 64 q^{76} + 4 q^{78} - 16 q^{79} - 28 q^{80} + 10 q^{81} + 40 q^{82} - 28 q^{83} - 4 q^{85} + 20 q^{86} - 16 q^{87} - 68 q^{88} - 32 q^{89} - 8 q^{90} - 8 q^{92} + 12 q^{93} - 56 q^{94} + 8 q^{95} - 8 q^{96} - 4 q^{97} + 2 q^{99}+O(q^{100}) \) 10 * q + 4 * q^2 - 10 * q^3 + 8 * q^4 - 4 * q^5 - 4 * q^6 + 12 * q^8 + 10 * q^9 - 8 * q^10 + 2 * q^11 - 8 * q^12 + 4 * q^15 + 4 * q^16 - 12 * q^17 + 4 * q^18 - 26 * q^19 - 24 * q^20 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 2 * q^25 - 4 * q^26 - 10 * q^27 + 16 * q^29 + 8 * q^30 - 12 * q^31 + 8 * q^32 - 2 * q^33 - 28 * q^34 + 8 * q^36 - 8 * q^37 - 32 * q^38 - 4 * q^40 - 10 * q^41 - 4 * q^43 - 16 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 - 8 * q^50 + 12 * q^51 - 24 * q^52 + 14 * q^53 - 4 * q^54 - 16 * q^55 + 26 * q^57 - 8 * q^58 - 38 * q^59 + 24 * q^60 - 14 * q^61 + 8 * q^62 + 8 * q^64 + 12 * q^65 + 8 * q^66 - 8 * q^68 + 10 * q^69 + 24 * q^71 + 12 * q^72 - 8 * q^73 - 8 * q^74 + 2 * q^75 - 64 * q^76 + 4 * q^78 - 16 * q^79 - 28 * q^80 + 10 * q^81 + 40 * q^82 - 28 * q^83 - 4 * q^85 + 20 * q^86 - 16 * q^87 - 68 * q^88 - 32 * q^89 - 8 * q^90 - 8 * q^92 + 12 * q^93 - 56 * q^94 + 8 * q^95 - 8 * q^96 - 4 * q^97 + 2 * q^99

Introduction

L-functions

Modular forms

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Database

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