LMFDB - Embedded newform 3381.2.a.bg.1.8

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:	$0$
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} + 100x^{3} - 17x^{2} - 28x - 2 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 100x^5 + 26x^4 + 100x^3 - 17x^2 - 28x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.01915$ 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)

$f(q)$	$=$	$q+1.01915 q^{2} -1.00000 q^{3} -0.961343 q^{4} +2.85504 q^{5} -1.01915 q^{6} -3.01804 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.01915 q^{2} -1.00000 q^{3} -0.961343 q^{4} +2.85504 q^{5} -1.01915 q^{6} -3.01804 q^{8} +1.00000 q^{9} +2.90970 q^{10} +1.04342 q^{11} +0.961343 q^{12} -4.67946 q^{13} -2.85504 q^{15} -1.15313 q^{16} +1.79068 q^{17} +1.01915 q^{18} -2.26257 q^{19} -2.74468 q^{20} +1.06339 q^{22} +1.00000 q^{23} +3.01804 q^{24} +3.15128 q^{25} -4.76905 q^{26} -1.00000 q^{27} +3.86612 q^{29} -2.90970 q^{30} +9.09864 q^{31} +4.86087 q^{32} -1.04342 q^{33} +1.82496 q^{34} -0.961343 q^{36} -1.78621 q^{37} -2.30589 q^{38} +4.67946 q^{39} -8.61663 q^{40} +7.76773 q^{41} -0.798109 q^{43} -1.00308 q^{44} +2.85504 q^{45} +1.01915 q^{46} +12.3065 q^{47} +1.15313 q^{48} +3.21161 q^{50} -1.79068 q^{51} +4.49857 q^{52} -6.50479 q^{53} -1.01915 q^{54} +2.97900 q^{55} +2.26257 q^{57} +3.94014 q^{58} +5.27391 q^{59} +2.74468 q^{60} -3.25902 q^{61} +9.27284 q^{62} +7.26019 q^{64} -13.3601 q^{65} -1.06339 q^{66} -7.52963 q^{67} -1.72146 q^{68} -1.00000 q^{69} -0.379556 q^{71} -3.01804 q^{72} +8.88867 q^{73} -1.82041 q^{74} -3.15128 q^{75} +2.17511 q^{76} +4.76905 q^{78} -9.69344 q^{79} -3.29224 q^{80} +1.00000 q^{81} +7.91644 q^{82} +8.76816 q^{83} +5.11247 q^{85} -0.813389 q^{86} -3.86612 q^{87} -3.14908 q^{88} +12.2032 q^{89} +2.90970 q^{90} -0.961343 q^{92} -9.09864 q^{93} +12.5421 q^{94} -6.45975 q^{95} -4.86087 q^{96} -16.0840 q^{97} +1.04342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 16 q^{13} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 26 q^{19} - 8 q^{22} + 10 q^{23} + 12 q^{24} + 14 q^{25} - 12 q^{26} - 10 q^{27} - 16 q^{29} - 8 q^{30} + 20 q^{31} - 8 q^{32} + 2 q^{33} - 4 q^{34} + 8 q^{36} + 8 q^{37} - 8 q^{38} - 16 q^{39} - 12 q^{40} + 22 q^{41} - 4 q^{43} - 24 q^{44} + 4 q^{45} - 4 q^{46} + 6 q^{47} - 4 q^{48} - 48 q^{50} - 12 q^{51} + 24 q^{52} - 30 q^{53} + 4 q^{54} + 48 q^{55} - 26 q^{57} + 24 q^{58} + 42 q^{59} + 14 q^{61} + 40 q^{62} + 8 q^{64} - 44 q^{65} + 8 q^{66} + 8 q^{68} - 10 q^{69} + 8 q^{71} - 12 q^{72} + 24 q^{73} + 8 q^{74} - 14 q^{75} + 32 q^{76} + 12 q^{78} + 32 q^{79} + 28 q^{80} + 10 q^{81} - 64 q^{82} + 28 q^{83} - 4 q^{85} - 4 q^{86} + 16 q^{87} + 20 q^{88} + 8 q^{90} + 8 q^{92} - 20 q^{93} + 8 q^{94} - 16 q^{95} + 8 q^{96} - 12 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 + 16 * q^13 - 4 * q^15 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 26 * q^19 - 8 * q^22 + 10 * q^23 + 12 * q^24 + 14 * q^25 - 12 * q^26 - 10 * q^27 - 16 * q^29 - 8 * q^30 + 20 * q^31 - 8 * q^32 + 2 * q^33 - 4 * q^34 + 8 * q^36 + 8 * q^37 - 8 * q^38 - 16 * q^39 - 12 * q^40 + 22 * q^41 - 4 * q^43 - 24 * q^44 + 4 * q^45 - 4 * q^46 + 6 * q^47 - 4 * q^48 - 48 * q^50 - 12 * q^51 + 24 * q^52 - 30 * q^53 + 4 * q^54 + 48 * q^55 - 26 * q^57 + 24 * q^58 + 42 * q^59 + 14 * q^61 + 40 * q^62 + 8 * q^64 - 44 * q^65 + 8 * q^66 + 8 * q^68 - 10 * q^69 + 8 * q^71 - 12 * q^72 + 24 * q^73 + 8 * q^74 - 14 * q^75 + 32 * q^76 + 12 * q^78 + 32 * q^79 + 28 * q^80 + 10 * q^81 - 64 * q^82 + 28 * q^83 - 4 * q^85 - 4 * q^86 + 16 * q^87 + 20 * q^88 + 8 * q^90 + 8 * q^92 - 20 * q^93 + 8 * q^94 - 16 * q^95 + 8 * q^96 - 12 * 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 $

$2$	1.01915	0.720644	0.360322	−	0.932828i	$-0.382667\pi$
$2$	1.01915	0.720644	0.360322	+	0.932828i	$0.382667\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.961343	−0.480672
$5$	2.85504	1.27681	0.638407	−	0.769699i	$-0.279594\pi$
$5$	2.85504	1.27681	0.638407	+	0.769699i	$0.279594\pi$
$6$	−1.01915	−0.416064
$7$	0	0
$7$	0	0
$8$	−3.01804	−1.06704
$9$	1.00000	0.333333
$10$	2.90970	0.920129
$11$	1.04342	0.314602	0.157301	−	0.987551i	$-0.449721\pi$
$11$	1.04342	0.314602	0.157301	+	0.987551i	$0.449721\pi$
$12$	0.961343	0.277516
$13$	−4.67946	−1.29785	−0.648925	−	0.760853i	$-0.724781\pi$
$13$	−4.67946	−1.29785	−0.648925	+	0.760853i	$0.724781\pi$
$14$	0	0
$15$	−2.85504	−0.737169
$16$	−1.15313	−0.288283
$17$	1.79068	0.434304	0.217152	−	0.976138i	$-0.430323\pi$
$17$	1.79068	0.434304	0.217152	+	0.976138i	$0.430323\pi$
$18$	1.01915	0.240215
$19$	−2.26257	−0.519070	−0.259535	−	0.965734i	$-0.583569\pi$
$19$	−2.26257	−0.519070	−0.259535	+	0.965734i	$0.583569\pi$
$20$	−2.74468	−0.613729
$21$	0	0
$22$	1.06339	0.226716
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.01804	0.616055
$25$	3.15128	0.630255
$26$	−4.76905	−0.935288
$27$	−1.00000	−0.192450
$28$	0	0
$29$	3.86612	0.717921	0.358960	−	0.933353i	$-0.383131\pi$
$29$	3.86612	0.717921	0.358960	+	0.933353i	$0.383131\pi$
$30$	−2.90970	−0.531237
$31$	9.09864	1.63416	0.817082	−	0.576521i	$-0.195590\pi$
$31$	9.09864	1.63416	0.817082	+	0.576521i	$0.195590\pi$
$32$	4.86087	0.859288
$33$	−1.04342	−0.181636
$34$	1.82496	0.312979
$35$	0	0
$36$	−0.961343	−0.160224
$37$	−1.78621	−0.293652	−0.146826	−	0.989162i	$-0.546906\pi$
$37$	−1.78621	−0.293652	−0.146826	+	0.989162i	$0.546906\pi$
$38$	−2.30589	−0.374065
$39$	4.67946	0.749314
$40$	−8.61663	−1.36241
$41$	7.76773	1.21312	0.606558	−	0.795040i	$-0.292550\pi$
$41$	7.76773	1.21312	0.606558	+	0.795040i	$0.292550\pi$
$42$	0	0
$43$	−0.798109	−0.121710	−0.0608552	−	0.998147i	$-0.519383\pi$
$43$	−0.798109	−0.121710	−0.0608552	+	0.998147i	$0.519383\pi$
$44$	−1.00308	−0.151220
$45$	2.85504	0.425605
$46$	1.01915	0.150265
$47$	12.3065	1.79509	0.897544	−	0.440924i	$-0.145349\pi$
$47$	12.3065	1.79509	0.897544	+	0.440924i	$0.145349\pi$
$48$	1.15313	0.166440
$49$	0	0
$50$	3.21161	0.454190
$51$	−1.79068	−0.250745
$52$	4.49857	0.623839
$53$	−6.50479	−0.893502	−0.446751	−	0.894658i	$-0.647419\pi$
$53$	−6.50479	−0.893502	−0.446751	+	0.894658i	$0.647419\pi$
$54$	−1.01915	−0.138688
$55$	2.97900	0.401689
$56$	0	0
$57$	2.26257	0.299685
$58$	3.94014	0.517366
$59$	5.27391	0.686604	0.343302	−	0.939225i	$-0.388455\pi$
$59$	5.27391	0.686604	0.343302	+	0.939225i	$0.388455\pi$
$60$	2.74468	0.354336
$61$	−3.25902	−0.417275	−0.208637	−	0.977993i	$-0.566903\pi$
$61$	−3.25902	−0.417275	−0.208637	+	0.977993i	$0.566903\pi$
$62$	9.27284	1.17765
$63$	0	0
$64$	7.26019	0.907524
$65$	−13.3601	−1.65711
$66$	−1.06339	−0.130895
$67$	−7.52963	−0.919890	−0.459945	−	0.887947i	$-0.652131\pi$
$67$	−7.52963	−0.919890	−0.459945	+	0.887947i	$0.652131\pi$
$68$	−1.72146	−0.208758
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−0.379556	−0.0450451	−0.0225225	−	0.999746i	$-0.507170\pi$
$71$	−0.379556	−0.0450451	−0.0225225	+	0.999746i	$0.507170\pi$
$72$	−3.01804	−0.355679
$73$	8.88867	1.04034	0.520170	−	0.854063i	$-0.325869\pi$
$73$	8.88867	1.04034	0.520170	+	0.854063i	$0.325869\pi$
$74$	−1.82041	−0.211619
$75$	−3.15128	−0.363878
$76$	2.17511	0.249502
$77$	0	0
$78$	4.76905	0.539989
$79$	−9.69344	−1.09060	−0.545299	−	0.838242i	$-0.683584\pi$
$79$	−9.69344	−1.09060	−0.545299	+	0.838242i	$0.683584\pi$
$80$	−3.29224	−0.368084
$81$	1.00000	0.111111
$82$	7.91644	0.874225
$83$	8.76816	0.962431	0.481215	−	0.876602i	$-0.340195\pi$
$83$	8.76816	0.962431	0.481215	+	0.876602i	$0.340195\pi$
$84$	0	0
$85$	5.11247	0.554526
$86$	−0.813389	−0.0877100
$87$	−3.86612	−0.414492
$88$	−3.14908	−0.335693
$89$	12.2032	1.29353	0.646766	−	0.762689i	$-0.276121\pi$
$89$	12.2032	1.29353	0.646766	+	0.762689i	$0.276121\pi$
$90$	2.90970	0.306710
$91$	0	0
$92$	−0.961343	−0.100227
$93$	−9.09864	−0.943486
$94$	12.5421	1.29362
$95$	−6.45975	−0.662756
$96$	−4.86087	−0.496110
$97$	−16.0840	−1.63308	−0.816541	−	0.577287i	$-0.804111\pi$
$97$	−16.0840	−1.63308	−0.816541	+	0.577287i	$0.804111\pi$
$98$	0	0
$99$	1.04342	0.104867
$100$	−3.02946	−0.302946
$101$	8.23439	0.819353	0.409676	−	0.912231i	$-0.365642\pi$
$101$	8.23439	0.819353	0.409676	+	0.912231i	$0.365642\pi$
$102$	−1.82496	−0.180698
$103$	−1.34637	−0.132662	−0.0663308	−	0.997798i	$-0.521129\pi$
$103$	−1.34637	−0.132662	−0.0663308	+	0.997798i	$0.521129\pi$
$104$	14.1228	1.38485
$105$	0	0
$106$	−6.62933	−0.643897
$107$	8.94742	0.864979	0.432490	−	0.901639i	$-0.357635\pi$
$107$	8.94742	0.864979	0.432490	+	0.901639i	$0.357635\pi$
$108$	0.961343	0.0925053
$109$	18.6661	1.78789	0.893945	−	0.448176i	$-0.147926\pi$
$109$	18.6661	1.78789	0.893945	+	0.448176i	$0.147926\pi$
$110$	3.03604	0.289475
$111$	1.78621	0.169540
$112$	0	0
$113$	0.161760	0.0152171	0.00760854	−	0.999971i	$-0.497578\pi$
$113$	0.161760	0.0152171	0.00760854	+	0.999971i	$0.497578\pi$
$114$	2.30589	0.215967
$115$	2.85504	0.266234
$116$	−3.71667	−0.345084
$117$	−4.67946	−0.432616
$118$	5.37487	0.494797
$119$	0	0
$120$	8.61663	0.786587
$121$	−9.91128	−0.901025
$122$	−3.32141	−0.300707
$123$	−7.76773	−0.700392
$124$	−8.74692	−0.785497
$125$	−5.27819	−0.472095
$126$	0	0
$127$	7.43886	0.660092	0.330046	−	0.943965i	$-0.392936\pi$
$127$	7.43886	0.660092	0.330046	+	0.943965i	$0.392936\pi$
$128$	−2.32254	−0.205286
$129$	0.798109	0.0702696
$130$	−13.6159	−1.19419
$131$	13.5570	1.18448	0.592242	−	0.805760i	$-0.298243\pi$
$131$	13.5570	1.18448	0.592242	+	0.805760i	$0.298243\pi$
$132$	1.00308	0.0873071
$133$	0	0
$134$	−7.67378	−0.662914
$135$	−2.85504	−0.245723
$136$	−5.40434	−0.463419
$137$	−1.99426	−0.170381	−0.0851904	−	0.996365i	$-0.527150\pi$
$137$	−1.99426	−0.170381	−0.0851904	+	0.996365i	$0.527150\pi$
$138$	−1.01915	−0.0867554
$139$	6.71469	0.569533	0.284766	−	0.958597i	$-0.408084\pi$
$139$	6.71469	0.569533	0.284766	+	0.958597i	$0.408084\pi$
$140$	0	0
$141$	−12.3065	−1.03639
$142$	−0.386823	−0.0324615
$143$	−4.88263	−0.408306
$144$	−1.15313	−0.0960944
$145$	11.0379	0.916652
$146$	9.05884	0.749715
$147$	0	0
$148$	1.71717	0.141150
$149$	9.56565	0.783649	0.391824	−	0.920040i	$-0.371844\pi$
$149$	9.56565	0.783649	0.391824	+	0.920040i	$0.371844\pi$
$150$	−3.21161	−0.262227
$151$	−1.27075	−0.103412	−0.0517059	−	0.998662i	$-0.516466\pi$
$151$	−1.27075	−0.103412	−0.0517059	+	0.998662i	$0.516466\pi$
$152$	6.82854	0.553868
$153$	1.79068	0.144768
$154$	0	0
$155$	25.9770	2.08653
$156$	−4.49857	−0.360174
$157$	4.99451	0.398605	0.199303	−	0.979938i	$-0.436132\pi$
$157$	4.99451	0.398605	0.199303	+	0.979938i	$0.436132\pi$
$158$	−9.87902	−0.785933
$159$	6.50479	0.515864
$160$	13.8780	1.09715
$161$	0	0
$162$	1.01915	0.0800716
$163$	1.81457	0.142128	0.0710639	−	0.997472i	$-0.477361\pi$
$163$	1.81457	0.142128	0.0710639	+	0.997472i	$0.477361\pi$
$164$	−7.46745	−0.583110
$165$	−2.97900	−0.231915
$166$	8.93603	0.693570
$167$	−3.37935	−0.261502	−0.130751	−	0.991415i	$-0.541739\pi$
$167$	−3.37935	−0.261502	−0.130751	+	0.991415i	$0.541739\pi$
$168$	0	0
$169$	8.89737	0.684413
$170$	5.21035	0.399616
$171$	−2.26257	−0.173023
$172$	0.767257	0.0585028
$173$	22.3854	1.70193	0.850967	−	0.525220i	$-0.176017\pi$
$173$	22.3854	1.70193	0.850967	+	0.525220i	$0.176017\pi$
$174$	−3.94014	−0.298701
$175$	0	0
$176$	−1.20320	−0.0906945
$177$	−5.27391	−0.396411
$178$	12.4368	0.932177
$179$	23.0668	1.72410	0.862049	−	0.506826i	$-0.169181\pi$
$179$	23.0668	1.72410	0.862049	+	0.506826i	$0.169181\pi$
$180$	−2.74468	−0.204576
$181$	−14.7321	−1.09503	−0.547513	−	0.836797i	$-0.684425\pi$
$181$	−14.7321	−1.09503	−0.547513	+	0.836797i	$0.684425\pi$
$182$	0	0
$183$	3.25902	0.240914
$184$	−3.01804	−0.222493
$185$	−5.09972	−0.374939
$186$	−9.27284	−0.679918
$187$	1.86843	0.136633
$188$	−11.8308	−0.862848
$189$	0	0
$190$	−6.58342	−0.477612
$191$	−5.69954	−0.412404	−0.206202	−	0.978509i	$-0.566110\pi$
$191$	−5.69954	−0.412404	−0.206202	+	0.978509i	$0.566110\pi$
$192$	−7.26019	−0.523959
$193$	−6.38029	−0.459263	−0.229632	−	0.973278i	$-0.573752\pi$
$193$	−6.38029	−0.459263	−0.229632	+	0.973278i	$0.573752\pi$
$194$	−16.3919	−1.17687
$195$	13.3601	0.956735
$196$	0	0
$197$	15.5744	1.10963	0.554814	−	0.831974i	$-0.312789\pi$
$197$	15.5744	1.10963	0.554814	+	0.831974i	$0.312789\pi$
$198$	1.06339	0.0755721
$199$	23.6231	1.67460	0.837298	−	0.546747i	$-0.184134\pi$
$199$	23.6231	1.67460	0.837298	+	0.546747i	$0.184134\pi$
$200$	−9.51067	−0.672506
$201$	7.52963	0.531099
$202$	8.39204	0.590462
$203$	0	0
$204$	1.72146	0.120526
$205$	22.1772	1.54892
$206$	−1.37215	−0.0956019
$207$	1.00000	0.0695048
$208$	5.39604	0.374148
$209$	−2.36081	−0.163301
$210$	0	0
$211$	−3.03523	−0.208954	−0.104477	−	0.994527i	$-0.533317\pi$
$211$	−3.03523	−0.208954	−0.104477	+	0.994527i	$0.533317\pi$
$212$	6.25334	0.429481
$213$	0.379556	0.0260068
$214$	9.11872	0.623343
$215$	−2.27864	−0.155402
$216$	3.01804	0.205352
$217$	0	0
$218$	19.0235	1.28843
$219$	−8.88867	−0.600640
$220$	−2.86385	−0.193080
$221$	−8.37943	−0.563661
$222$	1.82041	0.122178
$223$	3.17544	0.212643	0.106321	−	0.994332i	$-0.466093\pi$
$223$	3.17544	0.212643	0.106321	+	0.994332i	$0.466093\pi$
$224$	0	0
$225$	3.15128	0.210085
$226$	0.164857	0.0109661
$227$	15.3902	1.02148	0.510742	−	0.859734i	$-0.329371\pi$
$227$	15.3902	1.02148	0.510742	+	0.859734i	$0.329371\pi$
$228$	−2.17511	−0.144050
$229$	11.5216	0.761369	0.380685	−	0.924705i	$-0.375688\pi$
$229$	11.5216	0.761369	0.380685	+	0.924705i	$0.375688\pi$
$230$	2.90970	0.191860
$231$	0	0
$232$	−11.6681	−0.766049
$233$	−23.4506	−1.53630	−0.768150	−	0.640270i	$-0.778822\pi$
$233$	−23.4506	−1.53630	−0.768150	+	0.640270i	$0.778822\pi$
$234$	−4.76905	−0.311763
$235$	35.1356	2.29200
$236$	−5.07003	−0.330031
$237$	9.69344	0.629657
$238$	0	0
$239$	−9.20694	−0.595548	−0.297774	−	0.954636i	$-0.596244\pi$
$239$	−9.20694	−0.595548	−0.297774	+	0.954636i	$0.596244\pi$
$240$	3.29224	0.212513
$241$	−19.9299	−1.28380	−0.641900	−	0.766789i	$-0.721853\pi$
$241$	−19.9299	−1.28380	−0.641900	+	0.766789i	$0.721853\pi$
$242$	−10.1010	−0.649319
$243$	−1.00000	−0.0641500
$244$	3.13304	0.200572
$245$	0	0
$246$	−7.91644	−0.504734
$247$	10.5876	0.673675
$248$	−27.4601	−1.74372
$249$	−8.76816	−0.555660
$250$	−5.37924	−0.340213
$251$	−2.24319	−0.141589	−0.0707944	−	0.997491i	$-0.522553\pi$
$251$	−2.24319	−0.141589	−0.0707944	+	0.997491i	$0.522553\pi$
$252$	0	0
$253$	1.04342	0.0655991
$254$	7.58128	0.475692
$255$	−5.11247	−0.320155
$256$	−16.8874	−1.05546
$257$	−4.43044	−0.276363	−0.138182	−	0.990407i	$-0.544126\pi$
$257$	−4.43044	−0.276363	−0.138182	+	0.990407i	$0.544126\pi$
$258$	0.813389	0.0506394
$259$	0	0
$260$	12.8436	0.796527
$261$	3.86612	0.239307
$262$	13.8166	0.853591
$263$	−7.70557	−0.475146	−0.237573	−	0.971370i	$-0.576352\pi$
$263$	−7.70557	−0.475146	−0.237573	+	0.971370i	$0.576352\pi$
$264$	3.14908	0.193812
$265$	−18.5715	−1.14084
$266$	0	0
$267$	−12.2032	−0.746821
$268$	7.23856	0.442165
$269$	10.8217	0.659809	0.329904	−	0.944014i	$-0.392984\pi$
$269$	10.8217	0.659809	0.329904	+	0.944014i	$0.392984\pi$
$270$	−2.90970	−0.177079
$271$	−29.8769	−1.81489	−0.907446	−	0.420168i	$-0.861971\pi$
$271$	−29.8769	−1.81489	−0.907446	+	0.420168i	$0.861971\pi$
$272$	−2.06489	−0.125202
$273$	0	0
$274$	−2.03244	−0.122784
$275$	3.28810	0.198280
$276$	0.961343	0.0578661
$277$	−4.15136	−0.249431	−0.124716	−	0.992193i	$-0.539802\pi$
$277$	−4.15136	−0.249431	−0.124716	+	0.992193i	$0.539802\pi$
$278$	6.84324	0.410430
$279$	9.09864	0.544722
$280$	0	0
$281$	15.4199	0.919872	0.459936	−	0.887952i	$-0.347872\pi$
$281$	15.4199	0.919872	0.459936	+	0.887952i	$0.347872\pi$
$282$	−12.5421	−0.746872
$283$	−12.2255	−0.726729	−0.363365	−	0.931647i	$-0.618372\pi$
$283$	−12.2255	−0.726729	−0.363365	+	0.931647i	$0.618372\pi$
$284$	0.364884	0.0216519
$285$	6.45975	0.382643
$286$	−4.97611	−0.294244
$287$	0	0
$288$	4.86087	0.286429
$289$	−13.7935	−0.811380
$290$	11.2493	0.660580
$291$	16.0840	0.942861
$292$	−8.54506	−0.500062
$293$	−12.1797	−0.711544	−0.355772	−	0.934573i	$-0.615782\pi$
$293$	−12.1797	−0.711544	−0.355772	+	0.934573i	$0.615782\pi$
$294$	0	0
$295$	15.0572	0.876666
$296$	5.39086	0.313338
$297$	−1.04342	−0.0605452
$298$	9.74879	0.564732
$299$	−4.67946	−0.270620
$300$	3.02946	0.174906
$301$	0	0
$302$	−1.29508	−0.0745232
$303$	−8.23439	−0.473053
$304$	2.60905	0.149639
$305$	−9.30464	−0.532782
$306$	1.82496	0.104326
$307$	24.2359	1.38322	0.691609	−	0.722272i	$-0.256902\pi$
$307$	24.2359	1.38322	0.691609	+	0.722272i	$0.256902\pi$
$308$	0	0
$309$	1.34637	0.0765922
$310$	26.4744	1.50364
$311$	24.2837	1.37700	0.688500	−	0.725236i	$-0.258269\pi$
$311$	24.2837	1.37700	0.688500	+	0.725236i	$0.258269\pi$
$312$	−14.1228	−0.799546
$313$	−27.5204	−1.55554	−0.777772	−	0.628547i	$-0.783650\pi$
$313$	−27.5204	−1.55554	−0.777772	+	0.628547i	$0.783650\pi$
$314$	5.09013	0.287253
$315$	0	0
$316$	9.31872	0.524219
$317$	10.9475	0.614871	0.307435	−	0.951569i	$-0.400529\pi$
$317$	10.9475	0.614871	0.307435	+	0.951569i	$0.400529\pi$
$318$	6.62933	0.371754
$319$	4.03398	0.225860
$320$	20.7282	1.15874
$321$	−8.94742	−0.499396
$322$	0	0
$323$	−4.05155	−0.225434
$324$	−0.961343	−0.0534080
$325$	−14.7463	−0.817976
$326$	1.84931	0.102424
$327$	−18.6661	−1.03224
$328$	−23.4433	−1.29444
$329$	0	0
$330$	−3.03604	−0.167128
$331$	29.9489	1.64614	0.823071	−	0.567939i	$-0.192259\pi$
$331$	29.9489	1.64614	0.823071	+	0.567939i	$0.192259\pi$
$332$	−8.42921	−0.462613
$333$	−1.78621	−0.0978839
$334$	−3.44405	−0.188450
$335$	−21.4974	−1.17453
$336$	0	0
$337$	−23.4521	−1.27752	−0.638760	−	0.769406i	$-0.720552\pi$
$337$	−23.4521	−1.27752	−0.638760	+	0.769406i	$0.720552\pi$
$338$	9.06771	0.493219
$339$	−0.161760	−0.00878558
$340$	−4.91484	−0.266545
$341$	9.49369	0.514112
$342$	−2.30589	−0.124688
$343$	0	0
$344$	2.40872	0.129870
$345$	−2.85504	−0.153710
$346$	22.8140	1.22649
$347$	−2.95663	−0.158720	−0.0793602	−	0.996846i	$-0.525288\pi$
$347$	−2.95663	−0.158720	−0.0793602	+	0.996846i	$0.525288\pi$
$348$	3.71667	0.199234
$349$	−30.0033	−1.60604	−0.803020	−	0.595952i	$-0.796775\pi$
$349$	−30.0033	−1.60604	−0.803020	+	0.595952i	$0.796775\pi$
$350$	0	0
$351$	4.67946	0.249771
$352$	5.07192	0.270334
$353$	8.07484	0.429780	0.214890	−	0.976638i	$-0.431061\pi$
$353$	8.07484	0.429780	0.214890	+	0.976638i	$0.431061\pi$
$354$	−5.37487	−0.285671
$355$	−1.08365	−0.0575142
$356$	−11.7314	−0.621764
$357$	0	0
$358$	23.5085	1.24246
$359$	−4.45604	−0.235181	−0.117590	−	0.993062i	$-0.537517\pi$
$359$	−4.45604	−0.235181	−0.117590	+	0.993062i	$0.537517\pi$
$360$	−8.61663	−0.454136
$361$	−13.8808	−0.730566
$362$	−15.0141	−0.789124
$363$	9.91128	0.520207
$364$	0	0
$365$	25.3775	1.32832
$366$	3.32141	0.173613
$367$	20.0161	1.04483	0.522415	−	0.852691i	$-0.325031\pi$
$367$	20.0161	1.04483	0.522415	+	0.852691i	$0.325031\pi$
$368$	−1.15313	−0.0601112
$369$	7.76773	0.404372
$370$	−5.19735	−0.270198
$371$	0	0
$372$	8.74692	0.453507
$373$	−31.5718	−1.63472	−0.817362	−	0.576124i	$-0.804565\pi$
$373$	−31.5718	−1.63472	−0.817362	+	0.576124i	$0.804565\pi$
$374$	1.90420	0.0984638
$375$	5.27819	0.272564
$376$	−37.1415	−1.91543
$377$	−18.0914	−0.931753
$378$	0	0
$379$	−1.88867	−0.0970145	−0.0485073	−	0.998823i	$-0.515446\pi$
$379$	−1.88867	−0.0970145	−0.0485073	+	0.998823i	$0.515446\pi$
$380$	6.21004	0.318568
$381$	−7.43886	−0.381105
$382$	−5.80866	−0.297197
$383$	−16.5772	−0.847053	−0.423527	−	0.905884i	$-0.639208\pi$
$383$	−16.5772	−0.847053	−0.423527	+	0.905884i	$0.639208\pi$
$384$	2.32254	0.118522
$385$	0	0
$386$	−6.50244	−0.330965
$387$	−0.798109	−0.0405702
$388$	15.4622	0.784977
$389$	−1.96070	−0.0994113	−0.0497056	−	0.998764i	$-0.515828\pi$
$389$	−1.96070	−0.0994113	−0.0497056	+	0.998764i	$0.515828\pi$
$390$	13.6159	0.689465
$391$	1.79068	0.0905586
$392$	0	0
$393$	−13.5570	−0.683862
$394$	15.8725	0.799647
$395$	−27.6752	−1.39249
$396$	−1.00308	−0.0504068
$397$	−6.70599	−0.336564	−0.168282	−	0.985739i	$-0.553822\pi$
$397$	−6.70599	−0.336564	−0.168282	+	0.985739i	$0.553822\pi$
$398$	24.0753	1.20679
$399$	0	0
$400$	−3.63384	−0.181692
$401$	−20.6383	−1.03063	−0.515315	−	0.857001i	$-0.672325\pi$
$401$	−20.6383	−1.03063	−0.515315	+	0.857001i	$0.672325\pi$
$402$	7.67378	0.382733
$403$	−42.5768	−2.12090
$404$	−7.91608	−0.393840
$405$	2.85504	0.141868
$406$	0	0
$407$	−1.86377	−0.0923835
$408$	5.40434	0.267555
$409$	23.2536	1.14982	0.574909	−	0.818217i	$-0.305037\pi$
$409$	23.2536	1.14982	0.574909	+	0.818217i	$0.305037\pi$
$410$	22.6018	1.11622
$411$	1.99426	0.0983695
$412$	1.29432	0.0637667
$413$	0	0
$414$	1.01915	0.0500882
$415$	25.0335	1.22885
$416$	−22.7462	−1.11523
$417$	−6.71469	−0.328820
$418$	−2.40601	−0.117682
$419$	28.4386	1.38932	0.694658	−	0.719341i	$-0.255556\pi$
$419$	28.4386	1.38932	0.694658	+	0.719341i	$0.255556\pi$
$420$	0	0
$421$	7.98691	0.389258	0.194629	−	0.980877i	$-0.437650\pi$
$421$	7.98691	0.389258	0.194629	+	0.980877i	$0.437650\pi$
$422$	−3.09334	−0.150581
$423$	12.3065	0.598363
$424$	19.6317	0.953400
$425$	5.64293	0.273722
$426$	0.386823	0.0187416
$427$	0	0
$428$	−8.60154	−0.415771
$429$	4.88263	0.235736
$430$	−2.32226	−0.111989
$431$	19.2608	0.927761	0.463880	−	0.885898i	$-0.346457\pi$
$431$	19.2608	0.927761	0.463880	+	0.885898i	$0.346457\pi$
$432$	1.15313	0.0554801
$433$	16.9368	0.813930	0.406965	−	0.913444i	$-0.366587\pi$
$433$	16.9368	0.813930	0.406965	+	0.913444i	$0.366587\pi$
$434$	0	0
$435$	−11.0379	−0.529229
$436$	−17.9446	−0.859388
$437$	−2.26257	−0.108234
$438$	−9.05884	−0.432848
$439$	2.88388	0.137640	0.0688199	−	0.997629i	$-0.478077\pi$
$439$	2.88388	0.137640	0.0688199	+	0.997629i	$0.478077\pi$
$440$	−8.99075	−0.428617
$441$	0	0
$442$	−8.53985	−0.406199
$443$	−23.6271	−1.12256	−0.561279	−	0.827627i	$-0.689690\pi$
$443$	−23.6271	−1.12256	−0.561279	+	0.827627i	$0.689690\pi$
$444$	−1.71717	−0.0814930
$445$	34.8405	1.65160
$446$	3.23623	0.153240
$447$	−9.56565	−0.452440
$448$	0	0
$449$	−40.2794	−1.90090	−0.950451	−	0.310874i	$-0.899378\pi$
$449$	−40.2794	−1.90090	−0.950451	+	0.310874i	$0.899378\pi$
$450$	3.21161	0.151397
$451$	8.10498	0.381649
$452$	−0.155507	−0.00731442
$453$	1.27075	0.0597049
$454$	15.6849	0.736127
$455$	0	0
$456$	−6.82854	−0.319776
$457$	34.0390	1.59228	0.796138	−	0.605115i	$-0.206873\pi$
$457$	34.0390	1.59228	0.796138	+	0.605115i	$0.206873\pi$
$458$	11.7422	0.548676
$459$	−1.79068	−0.0835818
$460$	−2.74468	−0.127971
$461$	−21.1476	−0.984941	−0.492471	−	0.870329i	$-0.663906\pi$
$461$	−21.1476	−0.984941	−0.492471	+	0.870329i	$0.663906\pi$
$462$	0	0
$463$	9.99149	0.464344	0.232172	−	0.972675i	$-0.425417\pi$
$463$	9.99149	0.464344	0.232172	+	0.972675i	$0.425417\pi$
$464$	−4.45815	−0.206964
$465$	−25.9770	−1.20466
$466$	−23.8996	−1.10713
$467$	−21.9657	−1.01645	−0.508225	−	0.861224i	$-0.669698\pi$
$467$	−21.9657	−1.01645	−0.508225	+	0.861224i	$0.669698\pi$
$468$	4.49857	0.207946
$469$	0	0
$470$	35.8083	1.65171
$471$	−4.99451	−0.230135
$472$	−15.9168	−0.732632
$473$	−0.832761	−0.0382904
$474$	9.87902	0.453758
$475$	−7.13000	−0.327147
$476$	0	0
$477$	−6.50479	−0.297834
$478$	−9.38321	−0.429178
$479$	−12.7784	−0.583860	−0.291930	−	0.956440i	$-0.594297\pi$
$479$	−12.7784	−0.583860	−0.291930	+	0.956440i	$0.594297\pi$
$480$	−13.8780	−0.633441
$481$	8.35852	0.381116
$482$	−20.3115	−0.925163
$483$	0	0
$484$	9.52814	0.433097
$485$	−45.9205	−2.08514
$486$	−1.01915	−0.0462294
$487$	−1.84572	−0.0836378	−0.0418189	−	0.999125i	$-0.513315\pi$
$487$	−1.84572	−0.0836378	−0.0418189	+	0.999125i	$0.513315\pi$
$488$	9.83584	0.445248
$489$	−1.81457	−0.0820575
$490$	0	0
$491$	32.9129	1.48534	0.742669	−	0.669658i	$-0.233559\pi$
$491$	32.9129	1.48534	0.742669	+	0.669658i	$0.233559\pi$
$492$	7.46745	0.336659
$493$	6.92299	0.311796
$494$	10.7903	0.485480
$495$	2.97900	0.133896
$496$	−10.4919	−0.471102
$497$	0	0
$498$	−8.93603	−0.400433
$499$	7.55799	0.338342	0.169171	−	0.985587i	$-0.445891\pi$
$499$	7.55799	0.338342	0.169171	+	0.985587i	$0.445891\pi$
$500$	5.07415	0.226923
$501$	3.37935	0.150978
$502$	−2.28614	−0.102035
$503$	−37.9876	−1.69378	−0.846891	−	0.531767i	$-0.821528\pi$
$503$	−37.9876	−1.69378	−0.846891	+	0.531767i	$0.821528\pi$
$504$	0	0
$505$	23.5096	1.04616
$506$	1.06339	0.0472736
$507$	−8.89737	−0.395146
$508$	−7.15130	−0.317288
$509$	2.75321	0.122034	0.0610170	−	0.998137i	$-0.480566\pi$
$509$	2.75321	0.122034	0.0610170	+	0.998137i	$0.480566\pi$
$510$	−5.21035	−0.230718
$511$	0	0
$512$	−12.5656	−0.555327
$513$	2.26257	0.0998951
$514$	−4.51526	−0.199159
$515$	−3.84394	−0.169384
$516$	−0.767257	−0.0337766
$517$	12.8408	0.564739
$518$	0	0
$519$	−22.3854	−0.982612
$520$	40.3212	1.76820
$521$	3.06342	0.134211	0.0671054	−	0.997746i	$-0.478624\pi$
$521$	3.06342	0.134211	0.0671054	+	0.997746i	$0.478624\pi$
$522$	3.94014	0.172455
$523$	−2.61418	−0.114310	−0.0571552	−	0.998365i	$-0.518203\pi$
$523$	−2.61418	−0.114310	−0.0571552	+	0.998365i	$0.518203\pi$
$524$	−13.0330	−0.569348
$525$	0	0
$526$	−7.85309	−0.342411
$527$	16.2928	0.709724
$528$	1.20320	0.0523625
$529$	1.00000	0.0434783
$530$	−18.9270	−0.822137
$531$	5.27391	0.228868
$532$	0	0
$533$	−36.3488	−1.57444
$534$	−12.4368	−0.538192
$535$	25.5453	1.10442
$536$	22.7247	0.981558
$537$	−23.0668	−0.995408
$538$	11.0288	0.475487
$539$	0	0
$540$	2.74468	0.118112
$541$	13.0646	0.561691	0.280846	−	0.959753i	$-0.409385\pi$
$541$	13.0646	0.561691	0.280846	+	0.959753i	$0.409385\pi$
$542$	−30.4489	−1.30789
$543$	14.7321	0.632214
$544$	8.70426	0.373192
$545$	53.2926	2.28280
$546$	0	0
$547$	14.6162	0.624942	0.312471	−	0.949927i	$-0.398843\pi$
$547$	14.6162	0.624942	0.312471	+	0.949927i	$0.398843\pi$
$548$	1.91717	0.0818973
$549$	−3.25902	−0.139092
$550$	3.35105	0.142889
$551$	−8.74739	−0.372651
$552$	3.01804	0.128456
$553$	0	0
$554$	−4.23084	−0.179751
$555$	5.09972	0.216471
$556$	−6.45512	−0.273758
$557$	24.9955	1.05909	0.529547	−	0.848281i	$-0.322362\pi$
$557$	24.9955	1.05909	0.529547	+	0.848281i	$0.322362\pi$
$558$	9.27284	0.392551
$559$	3.73472	0.157962
$560$	0	0
$561$	−1.86843	−0.0788851
$562$	15.7151	0.662901
$563$	−43.4546	−1.83139	−0.915697	−	0.401868i	$-0.868361\pi$
$563$	−43.4546	−1.83139	−0.915697	+	0.401868i	$0.868361\pi$
$564$	11.8308	0.498166
$565$	0.461831	0.0194294
$566$	−12.4595	−0.523713
$567$	0	0
$568$	1.14552	0.0480648
$569$	−21.6971	−0.909590	−0.454795	−	0.890596i	$-0.650288\pi$
$569$	−21.6971	−0.909590	−0.454795	+	0.890596i	$0.650288\pi$
$570$	6.58342	0.275749
$571$	32.8262	1.37373	0.686867	−	0.726784i	$-0.258986\pi$
$571$	32.8262	1.37373	0.686867	+	0.726784i	$0.258986\pi$
$572$	4.69389	0.196261
$573$	5.69954	0.238102
$574$	0	0
$575$	3.15128	0.131417
$576$	7.26019	0.302508
$577$	−17.5189	−0.729323	−0.364661	−	0.931140i	$-0.618815\pi$
$577$	−17.5189	−0.729323	−0.364661	+	0.931140i	$0.618815\pi$
$578$	−14.0575	−0.584717
$579$	6.38029	0.265156
$580$	−10.6113	−0.440609
$581$	0	0
$582$	16.3919	0.679467
$583$	−6.78722	−0.281098
$584$	−26.8263	−1.11008
$585$	−13.3601	−0.552371
$586$	−12.4128	−0.512770
$587$	25.1480	1.03797	0.518985	−	0.854783i	$-0.326310\pi$
$587$	25.1480	1.03797	0.518985	+	0.854783i	$0.326310\pi$
$588$	0	0
$589$	−20.5864	−0.848246
$590$	15.3455	0.631764
$591$	−15.5744	−0.640644
$592$	2.05974	0.0846549
$593$	−8.52453	−0.350061	−0.175030	−	0.984563i	$-0.556002\pi$
$593$	−8.52453	−0.350061	−0.175030	+	0.984563i	$0.556002\pi$
$594$	−1.06339	−0.0436316
$595$	0	0
$596$	−9.19588	−0.376678
$597$	−23.6231	−0.966828
$598$	−4.76905	−0.195021
$599$	−38.4684	−1.57178	−0.785889	−	0.618368i	$-0.787794\pi$
$599$	−38.4684	−1.57178	−0.785889	+	0.618368i	$0.787794\pi$
$600$	9.51067	0.388272
$601$	26.9508	1.09935	0.549673	−	0.835380i	$-0.314752\pi$
$601$	26.9508	1.09935	0.549673	+	0.835380i	$0.314752\pi$
$602$	0	0
$603$	−7.52963	−0.306630
$604$	1.22162	0.0497072
$605$	−28.2971	−1.15044
$606$	−8.39204	−0.340903
$607$	11.5776	0.469920	0.234960	−	0.972005i	$-0.424504\pi$
$607$	11.5776	0.469920	0.234960	+	0.972005i	$0.424504\pi$
$608$	−10.9981	−0.446031
$609$	0	0
$610$	−9.48278	−0.383947
$611$	−57.5878	−2.32975
$612$	−1.72146	−0.0695859
$613$	38.6512	1.56111	0.780553	−	0.625090i	$-0.214938\pi$
$613$	38.6512	1.56111	0.780553	+	0.625090i	$0.214938\pi$
$614$	24.6999	0.996808
$615$	−22.1772	−0.894271
$616$	0	0
$617$	−32.4322	−1.30567	−0.652836	−	0.757499i	$-0.726421\pi$
$617$	−32.4322	−1.30567	−0.652836	+	0.757499i	$0.726421\pi$
$618$	1.37215	0.0551958
$619$	−2.04093	−0.0820317	−0.0410159	−	0.999158i	$-0.513059\pi$
$619$	−2.04093	−0.0820317	−0.0410159	+	0.999158i	$0.513059\pi$
$620$	−24.9728	−1.00293
$621$	−1.00000	−0.0401286
$622$	24.7486	0.992328
$623$	0	0
$624$	−5.39604	−0.216015
$625$	−30.8258	−1.23303
$626$	−28.0473	−1.12099
$627$	2.36081	0.0942817
$628$	−4.80144	−0.191598
$629$	−3.19854	−0.127534
$630$	0	0
$631$	−49.2098	−1.95901	−0.979506	−	0.201416i	$-0.935446\pi$
$631$	−49.2098	−1.95901	−0.979506	+	0.201416i	$0.935446\pi$
$632$	29.2552	1.16371
$633$	3.03523	0.120640
$634$	11.1571	0.443103
$635$	21.2383	0.842816
$636$	−6.25334	−0.247961
$637$	0	0
$638$	4.11121	0.162764
$639$	−0.379556	−0.0150150
$640$	−6.63097	−0.262112
$641$	−7.68209	−0.303424	−0.151712	−	0.988425i	$-0.548479\pi$
$641$	−7.68209	−0.303424	−0.151712	+	0.988425i	$0.548479\pi$
$642$	−9.11872	−0.359887
$643$	8.84243	0.348711	0.174356	−	0.984683i	$-0.444216\pi$
$643$	8.84243	0.348711	0.174356	+	0.984683i	$0.444216\pi$
$644$	0	0
$645$	2.27864	0.0897212
$646$	−4.12912	−0.162458
$647$	−31.1218	−1.22353	−0.611763	−	0.791041i	$-0.709539\pi$
$647$	−31.1218	−1.22353	−0.611763	+	0.791041i	$0.709539\pi$
$648$	−3.01804	−0.118560
$649$	5.50289	0.216007
$650$	−15.0286	−0.589470
$651$	0	0
$652$	−1.74442	−0.0683168
$653$	6.60593	0.258510	0.129255	−	0.991611i	$-0.458741\pi$
$653$	6.60593	0.258510	0.129255	+	0.991611i	$0.458741\pi$
$654$	−19.0235	−0.743877
$655$	38.7059	1.51237
$656$	−8.95722	−0.349721
$657$	8.88867	0.346780
$658$	0	0
$659$	−46.2685	−1.80237	−0.901183	−	0.433439i	$-0.857300\pi$
$659$	−46.2685	−1.80237	−0.901183	+	0.433439i	$0.857300\pi$
$660$	2.86385	0.111475
$661$	−50.5909	−1.96776	−0.983879	−	0.178834i	$-0.942768\pi$
$661$	−50.5909	−1.96776	−0.983879	+	0.178834i	$0.942768\pi$
$662$	30.5223	1.18628
$663$	8.37943	0.325430
$664$	−26.4627	−1.02695
$665$	0	0
$666$	−1.82041	−0.0705395
$667$	3.86612	0.149697
$668$	3.24871	0.125697
$669$	−3.17544	−0.122769
$670$	−21.9090	−0.846418
$671$	−3.40052	−0.131276
$672$	0	0
$673$	−22.8274	−0.879931	−0.439966	−	0.898015i	$-0.645009\pi$
$673$	−22.8274	−0.879931	−0.439966	+	0.898015i	$0.645009\pi$
$674$	−23.9011	−0.920637
$675$	−3.15128	−0.121293
$676$	−8.55343	−0.328978
$677$	−8.44454	−0.324550	−0.162275	−	0.986746i	$-0.551883\pi$
$677$	−8.44454	−0.324550	−0.162275	+	0.986746i	$0.551883\pi$
$678$	−0.164857	−0.00633128
$679$	0	0
$680$	−15.4296	−0.591700
$681$	−15.3902	−0.589754
$682$	9.67545	0.370492
$683$	−11.3985	−0.436153	−0.218076	−	0.975932i	$-0.569978\pi$
$683$	−11.3985	−0.436153	−0.218076	+	0.975932i	$0.569978\pi$
$684$	2.17511	0.0831674
$685$	−5.69369	−0.217545
$686$	0	0
$687$	−11.5216	−0.439577
$688$	0.920325	0.0350871
$689$	30.4389	1.15963
$690$	−2.90970	−0.110771
$691$	21.9369	0.834519	0.417259	−	0.908787i	$-0.362991\pi$
$691$	21.9369	0.834519	0.417259	+	0.908787i	$0.362991\pi$
$692$	−21.5201	−0.818071
$693$	0	0
$694$	−3.01324	−0.114381
$695$	19.1707	0.727187
$696$	11.6681	0.442278
$697$	13.9095	0.526861
$698$	−30.5777	−1.15738
$699$	23.4506	0.886983
$700$	0	0
$701$	−31.3551	−1.18427	−0.592134	−	0.805840i	$-0.701714\pi$
$701$	−31.3551	−1.18427	−0.592134	+	0.805840i	$0.701714\pi$
$702$	4.76905	0.179996
$703$	4.04144	0.152426
$704$	7.57542	0.285509
$705$	−35.1356	−1.32328
$706$	8.22943	0.309719
$707$	0	0
$708$	5.07003	0.190544
$709$	−17.3234	−0.650593	−0.325297	−	0.945612i	$-0.605464\pi$
$709$	−17.3234	−0.650593	−0.325297	+	0.945612i	$0.605464\pi$
$710$	−1.10440	−0.0414473
$711$	−9.69344	−0.363532
$712$	−36.8296	−1.38025
$713$	9.09864	0.340747
$714$	0	0
$715$	−13.9401	−0.521332
$716$	−22.1752	−0.828725
$717$	9.20694	0.343840
$718$	−4.54135	−0.169482
$719$	16.4930	0.615085	0.307542	−	0.951534i	$-0.400493\pi$
$719$	16.4930	0.615085	0.307542	+	0.951534i	$0.400493\pi$
$720$	−3.29224	−0.122695
$721$	0	0
$722$	−14.1465	−0.526478
$723$	19.9299	0.741202
$724$	14.1626	0.526348
$725$	12.1832	0.452473
$726$	10.1010	0.374884
$727$	−31.8066	−1.17964	−0.589820	−	0.807535i	$-0.700801\pi$
$727$	−31.8066	−1.17964	−0.589820	+	0.807535i	$0.700801\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	25.8634	0.957247
$731$	−1.42916	−0.0528593
$732$	−3.13304	−0.115800
$733$	7.78447	0.287526	0.143763	−	0.989612i	$-0.454080\pi$
$733$	7.78447	0.287526	0.143763	+	0.989612i	$0.454080\pi$
$734$	20.3993	0.752951
$735$	0	0
$736$	4.86087	0.179174
$737$	−7.85655	−0.289400
$738$	7.91644	0.291408
$739$	38.3045	1.40905	0.704527	−	0.709678i	$-0.251159\pi$
$739$	38.3045	1.40905	0.704527	+	0.709678i	$0.251159\pi$
$740$	4.90258	0.180222
$741$	−10.5876	−0.388946
$742$	0	0
$743$	−17.8234	−0.653878	−0.326939	−	0.945046i	$-0.606017\pi$
$743$	−17.8234	−0.653878	−0.326939	+	0.945046i	$0.606017\pi$
$744$	27.4601	1.00673
$745$	27.3104	1.00057
$746$	−32.1762	−1.17806
$747$	8.76816	0.320810
$748$	−1.79620	−0.0656756
$749$	0	0
$750$	5.37924	0.196422
$751$	25.8847	0.944546	0.472273	−	0.881452i	$-0.343434\pi$
$751$	25.8847	0.944546	0.472273	+	0.881452i	$0.343434\pi$
$752$	−14.1910	−0.517494
$753$	2.24319	0.0817464
$754$	−18.4377	−0.671463
$755$	−3.62804	−0.132038
$756$	0	0
$757$	−33.3830	−1.21333	−0.606663	−	0.794959i	$-0.707492\pi$
$757$	−33.3830	−1.21333	−0.606663	+	0.794959i	$0.707492\pi$
$758$	−1.92483	−0.0699130
$759$	−1.04342	−0.0378737
$760$	19.4958	0.707186
$761$	20.5987	0.746703	0.373352	−	0.927690i	$-0.378208\pi$
$761$	20.5987	0.746703	0.373352	+	0.927690i	$0.378208\pi$
$762$	−7.58128	−0.274641
$763$	0	0
$764$	5.47921	0.198231
$765$	5.11247	0.184842
$766$	−16.8945	−0.610424
$767$	−24.6790	−0.891109
$768$	16.8874	0.609371
$769$	−52.5860	−1.89630	−0.948150	−	0.317825i	$-0.897048\pi$
$769$	−52.5860	−1.89630	−0.948150	+	0.317825i	$0.897048\pi$
$770$	0	0
$771$	4.43044	0.159558
$772$	6.13365	0.220755
$773$	34.3933	1.23704	0.618520	−	0.785769i	$-0.287733\pi$
$773$	34.3933	1.23704	0.618520	+	0.785769i	$0.287733\pi$
$774$	−0.813389	−0.0292367
$775$	28.6723	1.02994
$776$	48.5421	1.74256
$777$	0	0
$778$	−1.99823	−0.0716402
$779$	−17.5751	−0.629692
$780$	−12.8436	−0.459875
$781$	−0.396036	−0.0141713
$782$	1.82496	0.0652606
$783$	−3.86612	−0.138164
$784$	0	0
$785$	14.2596	0.508945
$786$	−13.8166	−0.492821
$787$	15.5797	0.555355	0.277678	−	0.960674i	$-0.410435\pi$
$787$	15.5797	0.555355	0.277678	+	0.960674i	$0.410435\pi$
$788$	−14.9723	−0.533367
$789$	7.70557	0.274325
$790$	−28.2050	−1.00349
$791$	0	0
$792$	−3.14908	−0.111898
$793$	15.2505	0.541560
$794$	−6.83438	−0.242543
$795$	18.5715	0.658662
$796$	−22.7099	−0.804931
$797$	−4.36454	−0.154600	−0.0772999	−	0.997008i	$-0.524630\pi$
$797$	−4.36454	−0.154600	−0.0772999	+	0.997008i	$0.524630\pi$
$798$	0	0
$799$	22.0370	0.779614
$800$	15.3179	0.541571
$801$	12.2032	0.431177
$802$	−21.0335	−0.742718
$803$	9.27459	0.327293
$804$	−7.23856	−0.255284
$805$	0	0
$806$	−43.3919	−1.52841
$807$	−10.8217	−0.380941
$808$	−24.8517	−0.874280
$809$	6.90210	0.242665	0.121332	−	0.992612i	$-0.461283\pi$
$809$	6.90210	0.242665	0.121332	+	0.992612i	$0.461283\pi$
$810$	2.90970	0.102237
$811$	−28.1935	−0.990008	−0.495004	−	0.868891i	$-0.664833\pi$
$811$	−28.1935	−0.990008	−0.495004	+	0.868891i	$0.664833\pi$
$812$	0	0
$813$	29.8769	1.04783
$814$	−1.89945	−0.0665757
$815$	5.18067	0.181471
$816$	2.06489	0.0722857
$817$	1.80578	0.0631763
$818$	23.6988	0.828610
$819$	0	0
$820$	−21.3199	−0.744523
$821$	−3.32469	−0.116033	−0.0580163	−	0.998316i	$-0.518478\pi$
$821$	−3.32469	−0.116033	−0.0580163	+	0.998316i	$0.518478\pi$
$822$	2.03244	0.0708894
$823$	−1.44459	−0.0503552	−0.0251776	−	0.999683i	$-0.508015\pi$
$823$	−1.44459	−0.0503552	−0.0251776	+	0.999683i	$0.508015\pi$
$824$	4.06339	0.141555
$825$	−3.28810	−0.114477
$826$	0	0
$827$	−19.9119	−0.692405	−0.346203	−	0.938160i	$-0.612529\pi$
$827$	−19.9119	−0.692405	−0.346203	+	0.938160i	$0.612529\pi$
$828$	−0.961343	−0.0334090
$829$	33.3647	1.15880	0.579402	−	0.815042i	$-0.303286\pi$
$829$	33.3647	1.15880	0.579402	+	0.815042i	$0.303286\pi$
$830$	25.5128	0.885561
$831$	4.15136	0.144009
$832$	−33.9738	−1.17783
$833$	0	0
$834$	−6.84324	−0.236962
$835$	−9.64819	−0.333889
$836$	2.26955	0.0784940
$837$	−9.09864	−0.314495
$838$	28.9830	1.00120
$839$	48.1980	1.66398	0.831991	−	0.554790i	$-0.187201\pi$
$839$	48.1980	1.66398	0.831991	+	0.554790i	$0.187201\pi$
$840$	0	0
$841$	−14.0531	−0.484590
$842$	8.13982	0.280517
$843$	−15.4199	−0.531089
$844$	2.91790	0.100438
$845$	25.4024	0.873869
$846$	12.5421	0.431207
$847$	0	0
$848$	7.50089	0.257582
$849$	12.2255	0.419577
$850$	5.75096	0.197256
$851$	−1.78621	−0.0612306
$852$	−0.364884	−0.0125007
$853$	−17.8327	−0.610580	−0.305290	−	0.952259i	$-0.598753\pi$
$853$	−17.8327	−0.610580	−0.305290	+	0.952259i	$0.598753\pi$
$854$	0	0
$855$	−6.45975	−0.220919
$856$	−27.0036	−0.922966
$857$	−1.04471	−0.0356865	−0.0178432	−	0.999841i	$-0.505680\pi$
$857$	−1.04471	−0.0356865	−0.0178432	+	0.999841i	$0.505680\pi$
$858$	4.97611	0.169882
$859$	52.0934	1.77740	0.888701	−	0.458487i	$-0.151608\pi$
$859$	52.0934	1.77740	0.888701	+	0.458487i	$0.151608\pi$
$860$	2.19055	0.0746972
$861$	0	0
$862$	19.6296	0.668586
$863$	40.3838	1.37468	0.687340	−	0.726336i	$-0.258778\pi$
$863$	40.3838	1.37468	0.687340	+	0.726336i	$0.258778\pi$
$864$	−4.86087	−0.165370
$865$	63.9114	2.17305
$866$	17.2610	0.586554
$867$	13.7935	0.468451
$868$	0	0
$869$	−10.1143	−0.343104
$870$	−11.2493	−0.381386
$871$	35.2346	1.19388
$872$	−56.3351	−1.90775
$873$	−16.0840	−0.544361
$874$	−2.30589	−0.0779980
$875$	0	0
$876$	8.54506	0.288711
$877$	25.7819	0.870593	0.435297	−	0.900287i	$-0.356643\pi$
$877$	25.7819	0.870593	0.435297	+	0.900287i	$0.356643\pi$
$878$	2.93909	0.0991894
$879$	12.1797	0.410810
$880$	−3.43519	−0.115800
$881$	−52.9086	−1.78253	−0.891267	−	0.453478i	$-0.850183\pi$
$881$	−52.9086	−1.78253	−0.891267	+	0.453478i	$0.850183\pi$
$882$	0	0
$883$	8.10188	0.272650	0.136325	−	0.990664i	$-0.456471\pi$
$883$	8.10188	0.272650	0.136325	+	0.990664i	$0.456471\pi$
$884$	8.05550	0.270936
$885$	−15.0572	−0.506143
$886$	−24.0794	−0.808965
$887$	−37.3698	−1.25475	−0.627377	−	0.778716i	$-0.715872\pi$
$887$	−37.3698	−1.25475	−0.627377	+	0.778716i	$0.715872\pi$
$888$	−5.39086	−0.180906
$889$	0	0
$890$	35.5076	1.19022
$891$	1.04342	0.0349558
$892$	−3.05269	−0.102211
$893$	−27.8444	−0.931777
$894$	−9.74879	−0.326048
$895$	65.8569	2.20135
$896$	0	0
$897$	4.67946	0.156243
$898$	−41.0506	−1.36987
$899$	35.1765	1.17320
$900$	−3.02946	−0.100982
$901$	−11.6480	−0.388051
$902$	8.26015	0.275033
$903$	0	0
$904$	−0.488197	−0.0162372
$905$	−42.0607	−1.39814
$906$	1.29508	0.0430260
$907$	21.3707	0.709602	0.354801	−	0.934942i	$-0.384549\pi$
$907$	21.3707	0.709602	0.354801	+	0.934942i	$0.384549\pi$
$908$	−14.7953	−0.490998
$909$	8.23439	0.273118
$910$	0	0
$911$	−5.78530	−0.191676	−0.0958378	−	0.995397i	$-0.530553\pi$
$911$	−5.78530	−0.191676	−0.0958378	+	0.995397i	$0.530553\pi$
$912$	−2.60905	−0.0863942
$913$	9.14886	0.302783
$914$	34.6906	1.14746
$915$	9.30464	0.307602
$916$	−11.0762	−0.365969
$917$	0	0
$918$	−1.82496	−0.0602328
$919$	1.06651	0.0351810	0.0175905	−	0.999845i	$-0.494400\pi$
$919$	1.06651	0.0351810	0.0175905	+	0.999845i	$0.494400\pi$
$920$	−8.61663	−0.284082
$921$	−24.2359	−0.798601
$922$	−21.5525	−0.709792
$923$	1.77612	0.0584617
$924$	0	0
$925$	−5.62885	−0.185076
$926$	10.1828	0.334627
$927$	−1.34637	−0.0442206
$928$	18.7927	0.616901
$929$	−8.63760	−0.283391	−0.141695	−	0.989910i	$-0.545255\pi$
$929$	−8.63760	−0.283391	−0.141695	+	0.989910i	$0.545255\pi$
$930$	−26.4744	−0.868129
$931$	0	0
$932$	22.5441	0.738456
$933$	−24.2837	−0.795012
$934$	−22.3862	−0.732499
$935$	5.33445	0.174455
$936$	14.1228	0.461618
$937$	52.2887	1.70820	0.854098	−	0.520112i	$-0.174110\pi$
$937$	52.2887	1.70820	0.854098	+	0.520112i	$0.174110\pi$
$938$	0	0
$939$	27.5204	0.898093
$940$	−33.7774	−1.10170
$941$	−14.2321	−0.463954	−0.231977	−	0.972721i	$-0.574519\pi$
$941$	−14.2321	−0.463954	−0.231977	+	0.972721i	$0.574519\pi$
$942$	−5.09013	−0.165845
$943$	7.76773	0.252952
$944$	−6.08151	−0.197936
$945$	0	0
$946$	−0.848704	−0.0275938
$947$	42.5248	1.38187	0.690936	−	0.722916i	$-0.257199\pi$
$947$	42.5248	1.38187	0.690936	+	0.722916i	$0.257199\pi$
$948$	−9.31872	−0.302658
$949$	−41.5942	−1.35020
$950$	−7.26650	−0.235756
$951$	−10.9475	−0.354996
$952$	0	0
$953$	−37.6680	−1.22019	−0.610094	−	0.792329i	$-0.708868\pi$
$953$	−37.6680	−1.22019	−0.610094	+	0.792329i	$0.708868\pi$
$954$	−6.62933	−0.214632
$955$	−16.2724	−0.526563
$956$	8.85103	0.286263
$957$	−4.03398	−0.130400
$958$	−13.0230	−0.420755
$959$	0	0
$960$	−20.7282	−0.668999
$961$	51.7853	1.67049
$962$	8.51855	0.274649
$963$	8.94742	0.288326
$964$	19.1595	0.617086
$965$	−18.2160	−0.586394
$966$	0	0
$967$	−11.5544	−0.371565	−0.185782	−	0.982591i	$-0.559482\pi$
$967$	−11.5544	−0.371565	−0.185782	+	0.982591i	$0.559482\pi$
$968$	29.9126	0.961428
$969$	4.05155	0.130155
$970$	−46.7997	−1.50265
$971$	−22.8798	−0.734248	−0.367124	−	0.930172i	$-0.619658\pi$
$971$	−22.8798	−0.734248	−0.367124	+	0.930172i	$0.619658\pi$
$972$	0.961343	0.0308351
$973$	0	0
$974$	−1.88106	−0.0602731
$975$	14.7463	0.472259
$976$	3.75808	0.120293
$977$	12.6228	0.403839	0.201920	−	0.979402i	$-0.435282\pi$
$977$	12.6228	0.403839	0.201920	+	0.979402i	$0.435282\pi$
$978$	−1.84931	−0.0591343
$979$	12.7330	0.406948
$980$	0	0
$981$	18.6661	0.595963
$982$	33.5430	1.07040
$983$	58.0230	1.85065	0.925324	−	0.379178i	$-0.123793\pi$
$983$	58.0230	1.85065	0.925324	+	0.379178i	$0.123793\pi$
$984$	23.4433	0.747345
$985$	44.4655	1.41679
$986$	7.05553	0.224694
$987$	0	0
$988$	−10.1784	−0.323816
$989$	−0.798109	−0.0253784
$990$	3.03604	0.0964916
$991$	46.0361	1.46238	0.731192	−	0.682172i	$-0.238965\pi$
$991$	46.0361	1.46238	0.731192	+	0.682172i	$0.238965\pi$
$992$	44.2273	1.40422
$993$	−29.9489	−0.950400
$994$	0	0
$995$	67.4449	2.13815
$996$	8.42921	0.267090
$997$	−1.09138	−0.0345642	−0.0172821	−	0.999851i	$-0.505501\pi$
$997$	−1.09138	−0.0345642	−0.0172821	+	0.999851i	$0.505501\pi$
$998$	7.70268	0.243824
$999$	1.78621	0.0565133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bg.1.8	✓	10
7.6	odd	2		3381.2.a.bh.1.8	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3381.2.a.bg.1.8	✓	10	1.1	even	1	trivial
3381.2.a.bh.1.8	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)

\(f(q)\)	\(=\)	\(q+1.01915 q^{2} -1.00000 q^{3} -0.961343 q^{4} +2.85504 q^{5} -1.01915 q^{6} -3.01804 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.01915 q^{2} -1.00000 q^{3} -0.961343 q^{4} +2.85504 q^{5} -1.01915 q^{6} -3.01804 q^{8} +1.00000 q^{9} +2.90970 q^{10} +1.04342 q^{11} +0.961343 q^{12} -4.67946 q^{13} -2.85504 q^{15} -1.15313 q^{16} +1.79068 q^{17} +1.01915 q^{18} -2.26257 q^{19} -2.74468 q^{20} +1.06339 q^{22} +1.00000 q^{23} +3.01804 q^{24} +3.15128 q^{25} -4.76905 q^{26} -1.00000 q^{27} +3.86612 q^{29} -2.90970 q^{30} +9.09864 q^{31} +4.86087 q^{32} -1.04342 q^{33} +1.82496 q^{34} -0.961343 q^{36} -1.78621 q^{37} -2.30589 q^{38} +4.67946 q^{39} -8.61663 q^{40} +7.76773 q^{41} -0.798109 q^{43} -1.00308 q^{44} +2.85504 q^{45} +1.01915 q^{46} +12.3065 q^{47} +1.15313 q^{48} +3.21161 q^{50} -1.79068 q^{51} +4.49857 q^{52} -6.50479 q^{53} -1.01915 q^{54} +2.97900 q^{55} +2.26257 q^{57} +3.94014 q^{58} +5.27391 q^{59} +2.74468 q^{60} -3.25902 q^{61} +9.27284 q^{62} +7.26019 q^{64} -13.3601 q^{65} -1.06339 q^{66} -7.52963 q^{67} -1.72146 q^{68} -1.00000 q^{69} -0.379556 q^{71} -3.01804 q^{72} +8.88867 q^{73} -1.82041 q^{74} -3.15128 q^{75} +2.17511 q^{76} +4.76905 q^{78} -9.69344 q^{79} -3.29224 q^{80} +1.00000 q^{81} +7.91644 q^{82} +8.76816 q^{83} +5.11247 q^{85} -0.813389 q^{86} -3.86612 q^{87} -3.14908 q^{88} +12.2032 q^{89} +2.90970 q^{90} -0.961343 q^{92} -9.09864 q^{93} +12.5421 q^{94} -6.45975 q^{95} -4.86087 q^{96} -16.0840 q^{97} +1.04342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 10 * q^3 + 8 * q^4 + 4 * q^5 + 4 * q^6 - 12 * q^8 + 10 * q^9	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} + 4 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9} + 8 q^{10} - 2 q^{11} - 8 q^{12} + 16 q^{13} - 4 q^{15} + 4 q^{16} + 12 q^{17} - 4 q^{18} + 26 q^{19} - 8 q^{22} + 10 q^{23} + 12 q^{24} + 14 q^{25} - 12 q^{26} - 10 q^{27} - 16 q^{29} - 8 q^{30} + 20 q^{31} - 8 q^{32} + 2 q^{33} - 4 q^{34} + 8 q^{36} + 8 q^{37} - 8 q^{38} - 16 q^{39} - 12 q^{40} + 22 q^{41} - 4 q^{43} - 24 q^{44} + 4 q^{45} - 4 q^{46} + 6 q^{47} - 4 q^{48} - 48 q^{50} - 12 q^{51} + 24 q^{52} - 30 q^{53} + 4 q^{54} + 48 q^{55} - 26 q^{57} + 24 q^{58} + 42 q^{59} + 14 q^{61} + 40 q^{62} + 8 q^{64} - 44 q^{65} + 8 q^{66} + 8 q^{68} - 10 q^{69} + 8 q^{71} - 12 q^{72} + 24 q^{73} + 8 q^{74} - 14 q^{75} + 32 q^{76} + 12 q^{78} + 32 q^{79} + 28 q^{80} + 10 q^{81} - 64 q^{82} + 28 q^{83} - 4 q^{85} - 4 q^{86} + 16 q^{87} + 20 q^{88} + 8 q^{90} + 8 q^{92} - 20 q^{93} + 8 q^{94} - 16 q^{95} + 8 q^{96} - 12 q^{97} - 2 q^{99}+O(q^{100}) \) 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 + 16 * q^13 - 4 * q^15 + 4 * q^16 + 12 * q^17 - 4 * q^18 + 26 * q^19 - 8 * q^22 + 10 * q^23 + 12 * q^24 + 14 * q^25 - 12 * q^26 - 10 * q^27 - 16 * q^29 - 8 * q^30 + 20 * q^31 - 8 * q^32 + 2 * q^33 - 4 * q^34 + 8 * q^36 + 8 * q^37 - 8 * q^38 - 16 * q^39 - 12 * q^40 + 22 * q^41 - 4 * q^43 - 24 * q^44 + 4 * q^45 - 4 * q^46 + 6 * q^47 - 4 * q^48 - 48 * q^50 - 12 * q^51 + 24 * q^52 - 30 * q^53 + 4 * q^54 + 48 * q^55 - 26 * q^57 + 24 * q^58 + 42 * q^59 + 14 * q^61 + 40 * q^62 + 8 * q^64 - 44 * q^65 + 8 * q^66 + 8 * q^68 - 10 * q^69 + 8 * q^71 - 12 * q^72 + 24 * q^73 + 8 * q^74 - 14 * q^75 + 32 * q^76 + 12 * q^78 + 32 * q^79 + 28 * q^80 + 10 * q^81 - 64 * q^82 + 28 * q^83 - 4 * q^85 - 4 * q^86 + 16 * q^87 + 20 * q^88 + 8 * q^90 + 8 * q^92 - 20 * q^93 + 8 * q^94 - 16 * q^95 + 8 * q^96 - 12 * q^97 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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