LMFDB - Embedded newform 3630.2.a.bg.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, 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("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} -2.46410 q^{13} -3.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.73205 q^{17} -1.00000 q^{18} +7.00000 q^{19} -1.00000 q^{20} +3.73205 q^{21} -3.26795 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.46410 q^{26} +1.00000 q^{27} +3.73205 q^{28} +5.00000 q^{29} +1.00000 q^{30} -4.19615 q^{31} -1.00000 q^{32} +1.73205 q^{34} -3.73205 q^{35} +1.00000 q^{36} +3.19615 q^{37} -7.00000 q^{38} -2.46410 q^{39} +1.00000 q^{40} +6.19615 q^{41} -3.73205 q^{42} +8.19615 q^{43} -1.00000 q^{45} +3.26795 q^{46} -8.92820 q^{47} +1.00000 q^{48} +6.92820 q^{49} -1.00000 q^{50} -1.73205 q^{51} -2.46410 q^{52} -2.73205 q^{53} -1.00000 q^{54} -3.73205 q^{56} +7.00000 q^{57} -5.00000 q^{58} +5.66025 q^{59} -1.00000 q^{60} -9.12436 q^{61} +4.19615 q^{62} +3.73205 q^{63} +1.00000 q^{64} +2.46410 q^{65} +11.4641 q^{67} -1.73205 q^{68} -3.26795 q^{69} +3.73205 q^{70} +4.46410 q^{71} -1.00000 q^{72} +7.66025 q^{73} -3.19615 q^{74} +1.00000 q^{75} +7.00000 q^{76} +2.46410 q^{78} +10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.19615 q^{82} +16.4641 q^{83} +3.73205 q^{84} +1.73205 q^{85} -8.19615 q^{86} +5.00000 q^{87} +2.53590 q^{89} +1.00000 q^{90} -9.19615 q^{91} -3.26795 q^{92} -4.19615 q^{93} +8.92820 q^{94} -7.00000 q^{95} -1.00000 q^{96} +5.26795 q^{97} -6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{18} + 14 q^{19} - 2 q^{20} + 4 q^{21} - 10 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + 4 q^{28} + 10 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{32} - 4 q^{35} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 2 q^{39} + 2 q^{40} + 2 q^{41} - 4 q^{42} + 6 q^{43} - 2 q^{45} + 10 q^{46} - 4 q^{47} + 2 q^{48} - 2 q^{50} + 2 q^{52} - 2 q^{53} - 2 q^{54} - 4 q^{56} + 14 q^{57} - 10 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} - 2 q^{62} + 4 q^{63} + 2 q^{64} - 2 q^{65} + 16 q^{67} - 10 q^{69} + 4 q^{70} + 2 q^{71} - 2 q^{72} - 2 q^{73} + 4 q^{74} + 2 q^{75} + 14 q^{76} - 2 q^{78} - 2 q^{80} + 2 q^{81} - 2 q^{82} + 26 q^{83} + 4 q^{84} - 6 q^{86} + 10 q^{87} + 12 q^{89} + 2 q^{90} - 8 q^{91} - 10 q^{92} + 2 q^{93} + 4 q^{94} - 14 q^{95} - 2 q^{96} + 14 q^{97}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^18 + 14 * q^19 - 2 * q^20 + 4 * q^21 - 10 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + 4 * q^28 + 10 * q^29 + 2 * q^30 + 2 * q^31 - 2 * q^32 - 4 * q^35 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 2 * q^39 + 2 * q^40 + 2 * q^41 - 4 * q^42 + 6 * q^43 - 2 * q^45 + 10 * q^46 - 4 * q^47 + 2 * q^48 - 2 * q^50 + 2 * q^52 - 2 * q^53 - 2 * q^54 - 4 * q^56 + 14 * q^57 - 10 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 - 2 * q^62 + 4 * q^63 + 2 * q^64 - 2 * q^65 + 16 * q^67 - 10 * q^69 + 4 * q^70 + 2 * q^71 - 2 * q^72 - 2 * q^73 + 4 * q^74 + 2 * q^75 + 14 * q^76 - 2 * q^78 - 2 * q^80 + 2 * q^81 - 2 * q^82 + 26 * q^83 + 4 * q^84 - 6 * q^86 + 10 * q^87 + 12 * q^89 + 2 * q^90 - 8 * q^91 - 10 * q^92 + 2 * q^93 + 4 * q^94 - 14 * q^95 - 2 * q^96 + 14 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	3.73205	1.41058	0.705291	−	0.708918i	$-0.250816\pi$
$7$	3.73205	1.41058	0.705291	+	0.708918i	$0.250816\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	−2.46410	−0.683419	−0.341709	−	0.939806i	$-0.611006\pi$
$13$	−2.46410	−0.683419	−0.341709	+	0.939806i	$0.611006\pi$
$14$	−3.73205	−0.997433
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.73205	−0.420084	−0.210042	−	0.977692i	$-0.567360\pi$
$17$	−1.73205	−0.420084	−0.210042	+	0.977692i	$0.567360\pi$
$18$	−1.00000	−0.235702
$19$	7.00000	1.60591	0.802955	−	0.596040i	$-0.203260\pi$
$19$	7.00000	1.60591	0.802955	+	0.596040i	$0.203260\pi$
$20$	−1.00000	−0.223607
$21$	3.73205	0.814400
$22$	0	0
$23$	−3.26795	−0.681415	−0.340707	−	0.940169i	$-0.610666\pi$
$23$	−3.26795	−0.681415	−0.340707	+	0.940169i	$0.610666\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.46410	0.483250
$27$	1.00000	0.192450
$28$	3.73205	0.705291
$29$	5.00000	0.928477	0.464238	−	0.885710i	$-0.346328\pi$
$29$	5.00000	0.928477	0.464238	+	0.885710i	$0.346328\pi$
$30$	1.00000	0.182574
$31$	−4.19615	−0.753651	−0.376826	−	0.926284i	$-0.622984\pi$
$31$	−4.19615	−0.753651	−0.376826	+	0.926284i	$0.622984\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.73205	0.297044
$35$	−3.73205	−0.630832
$36$	1.00000	0.166667
$37$	3.19615	0.525444	0.262722	−	0.964872i	$-0.415380\pi$
$37$	3.19615	0.525444	0.262722	+	0.964872i	$0.415380\pi$
$38$	−7.00000	−1.13555
$39$	−2.46410	−0.394572
$40$	1.00000	0.158114
$41$	6.19615	0.967676	0.483838	−	0.875157i	$-0.339242\pi$
$41$	6.19615	0.967676	0.483838	+	0.875157i	$0.339242\pi$
$42$	−3.73205	−0.575868
$43$	8.19615	1.24990	0.624951	−	0.780664i	$-0.285119\pi$
$43$	8.19615	1.24990	0.624951	+	0.780664i	$0.285119\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	3.26795	0.481833
$47$	−8.92820	−1.30231	−0.651156	−	0.758944i	$-0.725716\pi$
$47$	−8.92820	−1.30231	−0.651156	+	0.758944i	$0.725716\pi$
$48$	1.00000	0.144338
$49$	6.92820	0.989743
$50$	−1.00000	−0.141421
$51$	−1.73205	−0.242536
$52$	−2.46410	−0.341709
$53$	−2.73205	−0.375276	−0.187638	−	0.982238i	$-0.560083\pi$
$53$	−2.73205	−0.375276	−0.187638	+	0.982238i	$0.560083\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.73205	−0.498716
$57$	7.00000	0.927173
$58$	−5.00000	−0.656532
$59$	5.66025	0.736902	0.368451	−	0.929647i	$-0.379888\pi$
$59$	5.66025	0.736902	0.368451	+	0.929647i	$0.379888\pi$
$60$	−1.00000	−0.129099
$61$	−9.12436	−1.16825	−0.584127	−	0.811662i	$-0.698563\pi$
$61$	−9.12436	−1.16825	−0.584127	+	0.811662i	$0.698563\pi$
$62$	4.19615	0.532912
$63$	3.73205	0.470194
$64$	1.00000	0.125000
$65$	2.46410	0.305634
$66$	0	0
$67$	11.4641	1.40056	0.700281	−	0.713867i	$-0.253058\pi$
$67$	11.4641	1.40056	0.700281	+	0.713867i	$0.253058\pi$
$68$	−1.73205	−0.210042
$69$	−3.26795	−0.393415
$70$	3.73205	0.446065
$71$	4.46410	0.529791	0.264896	−	0.964277i	$-0.414662\pi$
$71$	4.46410	0.529791	0.264896	+	0.964277i	$0.414662\pi$
$72$	−1.00000	−0.117851
$73$	7.66025	0.896565	0.448282	−	0.893892i	$-0.352036\pi$
$73$	7.66025	0.896565	0.448282	+	0.893892i	$0.352036\pi$
$74$	−3.19615	−0.371545
$75$	1.00000	0.115470
$76$	7.00000	0.802955
$77$	0	0
$78$	2.46410	0.279005
$79$	10.3923	1.16923	0.584613	−	0.811312i	$-0.301246\pi$
$79$	10.3923	1.16923	0.584613	+	0.811312i	$0.301246\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−6.19615	−0.684251
$83$	16.4641	1.80717	0.903585	−	0.428409i	$-0.140926\pi$
$83$	16.4641	1.80717	0.903585	+	0.428409i	$0.140926\pi$
$84$	3.73205	0.407200
$85$	1.73205	0.187867
$86$	−8.19615	−0.883814
$87$	5.00000	0.536056
$88$	0	0
$89$	2.53590	0.268805	0.134402	−	0.990927i	$-0.457089\pi$
$89$	2.53590	0.268805	0.134402	+	0.990927i	$0.457089\pi$
$90$	1.00000	0.105409
$91$	−9.19615	−0.964019
$92$	−3.26795	−0.340707
$93$	−4.19615	−0.435121
$94$	8.92820	0.920874
$95$	−7.00000	−0.718185
$96$	−1.00000	−0.102062
$97$	5.26795	0.534879	0.267440	−	0.963575i	$-0.413822\pi$
$97$	5.26795	0.534879	0.267440	+	0.963575i	$0.413822\pi$
$98$	−6.92820	−0.699854
$99$	0	0
$100$	1.00000	0.100000
$101$	−8.46410	−0.842210	−0.421105	−	0.907012i	$-0.638358\pi$
$101$	−8.46410	−0.842210	−0.421105	+	0.907012i	$0.638358\pi$
$102$	1.73205	0.171499
$103$	−17.3923	−1.71371	−0.856857	−	0.515554i	$-0.827586\pi$
$103$	−17.3923	−1.71371	−0.856857	+	0.515554i	$0.827586\pi$
$104$	2.46410	0.241625
$105$	−3.73205	−0.364211
$106$	2.73205	0.265360
$107$	−14.3923	−1.39136	−0.695678	−	0.718353i	$-0.744896\pi$
$107$	−14.3923	−1.39136	−0.695678	+	0.718353i	$0.744896\pi$
$108$	1.00000	0.0962250
$109$	−12.3923	−1.18697	−0.593484	−	0.804846i	$-0.702248\pi$
$109$	−12.3923	−1.18697	−0.593484	+	0.804846i	$0.702248\pi$
$110$	0	0
$111$	3.19615	0.303365
$112$	3.73205	0.352646
$113$	−13.8564	−1.30350	−0.651751	−	0.758433i	$-0.725965\pi$
$113$	−13.8564	−1.30350	−0.651751	+	0.758433i	$0.725965\pi$
$114$	−7.00000	−0.655610
$115$	3.26795	0.304738
$116$	5.00000	0.464238
$117$	−2.46410	−0.227806
$118$	−5.66025	−0.521069
$119$	−6.46410	−0.592563
$120$	1.00000	0.0912871
$121$	0	0
$122$	9.12436	0.826080
$123$	6.19615	0.558688
$124$	−4.19615	−0.376826
$125$	−1.00000	−0.0894427
$126$	−3.73205	−0.332478
$127$	13.4641	1.19475	0.597373	−	0.801964i	$-0.296211\pi$
$127$	13.4641	1.19475	0.597373	+	0.801964i	$0.296211\pi$
$128$	−1.00000	−0.0883883
$129$	8.19615	0.721631
$130$	−2.46410	−0.216116
$131$	21.1244	1.84564	0.922822	−	0.385227i	$-0.125877\pi$
$131$	21.1244	1.84564	0.922822	+	0.385227i	$0.125877\pi$
$132$	0	0
$133$	26.1244	2.26527
$134$	−11.4641	−0.990348
$135$	−1.00000	−0.0860663
$136$	1.73205	0.148522
$137$	10.4641	0.894009	0.447004	−	0.894532i	$-0.352491\pi$
$137$	10.4641	0.894009	0.447004	+	0.894532i	$0.352491\pi$
$138$	3.26795	0.278186
$139$	7.00000	0.593732	0.296866	−	0.954919i	$-0.404058\pi$
$139$	7.00000	0.593732	0.296866	+	0.954919i	$0.404058\pi$
$140$	−3.73205	−0.315416
$141$	−8.92820	−0.751890
$142$	−4.46410	−0.374619
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.00000	−0.415227
$146$	−7.66025	−0.633967
$147$	6.92820	0.571429
$148$	3.19615	0.262722
$149$	−8.39230	−0.687524	−0.343762	−	0.939057i	$-0.611701\pi$
$149$	−8.39230	−0.687524	−0.343762	+	0.939057i	$0.611701\pi$
$150$	−1.00000	−0.0816497
$151$	20.1962	1.64354	0.821770	−	0.569820i	$-0.192987\pi$
$151$	20.1962	1.64354	0.821770	+	0.569820i	$0.192987\pi$
$152$	−7.00000	−0.567775
$153$	−1.73205	−0.140028
$154$	0	0
$155$	4.19615	0.337043
$156$	−2.46410	−0.197286
$157$	−14.6603	−1.17002	−0.585008	−	0.811028i	$-0.698909\pi$
$157$	−14.6603	−1.17002	−0.585008	+	0.811028i	$0.698909\pi$
$158$	−10.3923	−0.826767
$159$	−2.73205	−0.216666
$160$	1.00000	0.0790569
$161$	−12.1962	−0.961191
$162$	−1.00000	−0.0785674
$163$	8.19615	0.641972	0.320986	−	0.947084i	$-0.395986\pi$
$163$	8.19615	0.641972	0.320986	+	0.947084i	$0.395986\pi$
$164$	6.19615	0.483838
$165$	0	0
$166$	−16.4641	−1.27786
$167$	−6.53590	−0.505763	−0.252882	−	0.967497i	$-0.581378\pi$
$167$	−6.53590	−0.505763	−0.252882	+	0.967497i	$0.581378\pi$
$168$	−3.73205	−0.287934
$169$	−6.92820	−0.532939
$170$	−1.73205	−0.132842
$171$	7.00000	0.535303
$172$	8.19615	0.624951
$173$	23.6603	1.79886	0.899428	−	0.437069i	$-0.143984\pi$
$173$	23.6603	1.79886	0.899428	+	0.437069i	$0.143984\pi$
$174$	−5.00000	−0.379049
$175$	3.73205	0.282117
$176$	0	0
$177$	5.66025	0.425451
$178$	−2.53590	−0.190074
$179$	−12.5885	−0.940905	−0.470453	−	0.882425i	$-0.655909\pi$
$179$	−12.5885	−0.940905	−0.470453	+	0.882425i	$0.655909\pi$
$180$	−1.00000	−0.0745356
$181$	−20.1962	−1.50117	−0.750584	−	0.660775i	$-0.770228\pi$
$181$	−20.1962	−1.50117	−0.750584	+	0.660775i	$0.770228\pi$
$182$	9.19615	0.681664
$183$	−9.12436	−0.674492
$184$	3.26795	0.240916
$185$	−3.19615	−0.234986
$186$	4.19615	0.307677
$187$	0	0
$188$	−8.92820	−0.651156
$189$	3.73205	0.271467
$190$	7.00000	0.507833
$191$	0.0717968	0.00519503	0.00259752	−	0.999997i	$-0.499173\pi$
$191$	0.0717968	0.00519503	0.00259752	+	0.999997i	$0.499173\pi$
$192$	1.00000	0.0721688
$193$	−11.3205	−0.814868	−0.407434	−	0.913235i	$-0.633576\pi$
$193$	−11.3205	−0.814868	−0.407434	+	0.913235i	$0.633576\pi$
$194$	−5.26795	−0.378217
$195$	2.46410	0.176458
$196$	6.92820	0.494872
$197$	9.46410	0.674289	0.337145	−	0.941453i	$-0.390539\pi$
$197$	9.46410	0.674289	0.337145	+	0.941453i	$0.390539\pi$
$198$	0	0
$199$	19.3205	1.36959	0.684797	−	0.728734i	$-0.259891\pi$
$199$	19.3205	1.36959	0.684797	+	0.728734i	$0.259891\pi$
$200$	−1.00000	−0.0707107
$201$	11.4641	0.808615
$202$	8.46410	0.595532
$203$	18.6603	1.30969
$204$	−1.73205	−0.121268
$205$	−6.19615	−0.432758
$206$	17.3923	1.21178
$207$	−3.26795	−0.227138
$208$	−2.46410	−0.170855
$209$	0	0
$210$	3.73205	0.257536
$211$	6.60770	0.454892	0.227446	−	0.973791i	$-0.426962\pi$
$211$	6.60770	0.454892	0.227446	+	0.973791i	$0.426962\pi$
$212$	−2.73205	−0.187638
$213$	4.46410	0.305875
$214$	14.3923	0.983838
$215$	−8.19615	−0.558973
$216$	−1.00000	−0.0680414
$217$	−15.6603	−1.06309
$218$	12.3923	0.839313
$219$	7.66025	0.517632
$220$	0	0
$221$	4.26795	0.287093
$222$	−3.19615	−0.214512
$223$	29.2487	1.95864	0.979319	−	0.202321i	$-0.0648484\pi$
$223$	29.2487	1.95864	0.979319	+	0.202321i	$0.0648484\pi$
$224$	−3.73205	−0.249358
$225$	1.00000	0.0666667
$226$	13.8564	0.921714
$227$	−27.4641	−1.82286	−0.911428	−	0.411459i	$-0.865019\pi$
$227$	−27.4641	−1.82286	−0.911428	+	0.411459i	$0.865019\pi$
$228$	7.00000	0.463586
$229$	−5.85641	−0.387002	−0.193501	−	0.981100i	$-0.561984\pi$
$229$	−5.85641	−0.387002	−0.193501	+	0.981100i	$0.561984\pi$
$230$	−3.26795	−0.215482
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−9.07180	−0.594313	−0.297157	−	0.954829i	$-0.596038\pi$
$233$	−9.07180	−0.594313	−0.297157	+	0.954829i	$0.596038\pi$
$234$	2.46410	0.161083
$235$	8.92820	0.582412
$236$	5.66025	0.368451
$237$	10.3923	0.675053
$238$	6.46410	0.419005
$239$	3.19615	0.206742	0.103371	−	0.994643i	$-0.467037\pi$
$239$	3.19615	0.206742	0.103371	+	0.994643i	$0.467037\pi$
$240$	−1.00000	−0.0645497
$241$	0.803848	0.0517804	0.0258902	−	0.999665i	$-0.491758\pi$
$241$	0.803848	0.0517804	0.0258902	+	0.999665i	$0.491758\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−9.12436	−0.584127
$245$	−6.92820	−0.442627
$246$	−6.19615	−0.395052
$247$	−17.2487	−1.09751
$248$	4.19615	0.266456
$249$	16.4641	1.04337
$250$	1.00000	0.0632456
$251$	31.3205	1.97693	0.988466	−	0.151440i	$-0.0483910\pi$
$251$	31.3205	1.97693	0.988466	+	0.151440i	$0.0483910\pi$
$252$	3.73205	0.235097
$253$	0	0
$254$	−13.4641	−0.844813
$255$	1.73205	0.108465
$256$	1.00000	0.0625000
$257$	19.7846	1.23413	0.617065	−	0.786912i	$-0.288322\pi$
$257$	19.7846	1.23413	0.617065	+	0.786912i	$0.288322\pi$
$258$	−8.19615	−0.510270
$259$	11.9282	0.741182
$260$	2.46410	0.152817
$261$	5.00000	0.309492
$262$	−21.1244	−1.30507
$263$	−3.26795	−0.201510	−0.100755	−	0.994911i	$-0.532126\pi$
$263$	−3.26795	−0.201510	−0.100755	+	0.994911i	$0.532126\pi$
$264$	0	0
$265$	2.73205	0.167829
$266$	−26.1244	−1.60179
$267$	2.53590	0.155194
$268$	11.4641	0.700281
$269$	21.9808	1.34019	0.670095	−	0.742275i	$-0.266253\pi$
$269$	21.9808	1.34019	0.670095	+	0.742275i	$0.266253\pi$
$270$	1.00000	0.0608581
$271$	23.8564	1.44917	0.724587	−	0.689184i	$-0.242031\pi$
$271$	23.8564	1.44917	0.724587	+	0.689184i	$0.242031\pi$
$272$	−1.73205	−0.105021
$273$	−9.19615	−0.556576
$274$	−10.4641	−0.632159
$275$	0	0
$276$	−3.26795	−0.196707
$277$	−2.14359	−0.128796	−0.0643980	−	0.997924i	$-0.520513\pi$
$277$	−2.14359	−0.128796	−0.0643980	+	0.997924i	$0.520513\pi$
$278$	−7.00000	−0.419832
$279$	−4.19615	−0.251217
$280$	3.73205	0.223033
$281$	−3.12436	−0.186383	−0.0931917	−	0.995648i	$-0.529707\pi$
$281$	−3.12436	−0.186383	−0.0931917	+	0.995648i	$0.529707\pi$
$282$	8.92820	0.531667
$283$	−8.39230	−0.498871	−0.249435	−	0.968391i	$-0.580245\pi$
$283$	−8.39230	−0.498871	−0.249435	+	0.968391i	$0.580245\pi$
$284$	4.46410	0.264896
$285$	−7.00000	−0.414644
$286$	0	0
$287$	23.1244	1.36499
$288$	−1.00000	−0.0589256
$289$	−14.0000	−0.823529
$290$	5.00000	0.293610
$291$	5.26795	0.308813
$292$	7.66025	0.448282
$293$	−14.9282	−0.872115	−0.436057	−	0.899919i	$-0.643626\pi$
$293$	−14.9282	−0.872115	−0.436057	+	0.899919i	$0.643626\pi$
$294$	−6.92820	−0.404061
$295$	−5.66025	−0.329553
$296$	−3.19615	−0.185773
$297$	0	0
$298$	8.39230	0.486153
$299$	8.05256	0.465692
$300$	1.00000	0.0577350
$301$	30.5885	1.76309
$302$	−20.1962	−1.16216
$303$	−8.46410	−0.486250
$304$	7.00000	0.401478
$305$	9.12436	0.522459
$306$	1.73205	0.0990148
$307$	−16.5885	−0.946753	−0.473377	−	0.880860i	$-0.656965\pi$
$307$	−16.5885	−0.946753	−0.473377	+	0.880860i	$0.656965\pi$
$308$	0	0
$309$	−17.3923	−0.989414
$310$	−4.19615	−0.238325
$311$	13.0718	0.741234	0.370617	−	0.928786i	$-0.379146\pi$
$311$	13.0718	0.741234	0.370617	+	0.928786i	$0.379146\pi$
$312$	2.46410	0.139502
$313$	11.8038	0.667193	0.333596	−	0.942716i	$-0.391738\pi$
$313$	11.8038	0.667193	0.333596	+	0.942716i	$0.391738\pi$
$314$	14.6603	0.827326
$315$	−3.73205	−0.210277
$316$	10.3923	0.584613
$317$	8.19615	0.460342	0.230171	−	0.973150i	$-0.426071\pi$
$317$	8.19615	0.460342	0.230171	+	0.973150i	$0.426071\pi$
$318$	2.73205	0.153206
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−14.3923	−0.803300
$322$	12.1962	0.679665
$323$	−12.1244	−0.674617
$324$	1.00000	0.0555556
$325$	−2.46410	−0.136684
$326$	−8.19615	−0.453943
$327$	−12.3923	−0.685296
$328$	−6.19615	−0.342125
$329$	−33.3205	−1.83702
$330$	0	0
$331$	5.87564	0.322955	0.161477	−	0.986876i	$-0.448374\pi$
$331$	5.87564	0.322955	0.161477	+	0.986876i	$0.448374\pi$
$332$	16.4641	0.903585
$333$	3.19615	0.175148
$334$	6.53590	0.357628
$335$	−11.4641	−0.626351
$336$	3.73205	0.203600
$337$	−30.1962	−1.64489	−0.822445	−	0.568845i	$-0.807390\pi$
$337$	−30.1962	−1.64489	−0.822445	+	0.568845i	$0.807390\pi$
$338$	6.92820	0.376845
$339$	−13.8564	−0.752577
$340$	1.73205	0.0939336
$341$	0	0
$342$	−7.00000	−0.378517
$343$	−0.267949	−0.0144679
$344$	−8.19615	−0.441907
$345$	3.26795	0.175940
$346$	−23.6603	−1.27198
$347$	−14.4641	−0.776474	−0.388237	−	0.921560i	$-0.626916\pi$
$347$	−14.4641	−0.776474	−0.388237	+	0.921560i	$0.626916\pi$
$348$	5.00000	0.268028
$349$	34.0000	1.81998	0.909989	−	0.414632i	$-0.136090\pi$
$349$	34.0000	1.81998	0.909989	+	0.414632i	$0.136090\pi$
$350$	−3.73205	−0.199487
$351$	−2.46410	−0.131524
$352$	0	0
$353$	1.85641	0.0988065	0.0494033	−	0.998779i	$-0.484268\pi$
$353$	1.85641	0.0988065	0.0494033	+	0.998779i	$0.484268\pi$
$354$	−5.66025	−0.300839
$355$	−4.46410	−0.236930
$356$	2.53590	0.134402
$357$	−6.46410	−0.342117
$358$	12.5885	0.665321
$359$	−31.1769	−1.64545	−0.822727	−	0.568436i	$-0.807549\pi$
$359$	−31.1769	−1.64545	−0.822727	+	0.568436i	$0.807549\pi$
$360$	1.00000	0.0527046
$361$	30.0000	1.57895
$362$	20.1962	1.06149
$363$	0	0
$364$	−9.19615	−0.482009
$365$	−7.66025	−0.400956
$366$	9.12436	0.476938
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	−3.26795	−0.170354
$369$	6.19615	0.322559
$370$	3.19615	0.166160
$371$	−10.1962	−0.529358
$372$	−4.19615	−0.217560
$373$	17.3923	0.900539	0.450270	−	0.892893i	$-0.351328\pi$
$373$	17.3923	0.900539	0.450270	+	0.892893i	$0.351328\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	8.92820	0.460437
$377$	−12.3205	−0.634538
$378$	−3.73205	−0.191956
$379$	6.12436	0.314587	0.157294	−	0.987552i	$-0.449723\pi$
$379$	6.12436	0.314587	0.157294	+	0.987552i	$0.449723\pi$
$380$	−7.00000	−0.359092
$381$	13.4641	0.689787
$382$	−0.0717968	−0.00367344
$383$	−4.14359	−0.211728	−0.105864	−	0.994381i	$-0.533761\pi$
$383$	−4.14359	−0.211728	−0.105864	+	0.994381i	$0.533761\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	11.3205	0.576199
$387$	8.19615	0.416634
$388$	5.26795	0.267440
$389$	−19.7128	−0.999479	−0.499740	−	0.866176i	$-0.666571\pi$
$389$	−19.7128	−0.999479	−0.499740	+	0.866176i	$0.666571\pi$
$390$	−2.46410	−0.124775
$391$	5.66025	0.286251
$392$	−6.92820	−0.349927
$393$	21.1244	1.06558
$394$	−9.46410	−0.476795
$395$	−10.3923	−0.522894
$396$	0	0
$397$	27.9808	1.40431	0.702157	−	0.712022i	$-0.252220\pi$
$397$	27.9808	1.40431	0.702157	+	0.712022i	$0.252220\pi$
$398$	−19.3205	−0.968450
$399$	26.1244	1.30785
$400$	1.00000	0.0500000
$401$	34.7321	1.73444	0.867218	−	0.497929i	$-0.165906\pi$
$401$	34.7321	1.73444	0.867218	+	0.497929i	$0.165906\pi$
$402$	−11.4641	−0.571777
$403$	10.3397	0.515059
$404$	−8.46410	−0.421105
$405$	−1.00000	−0.0496904
$406$	−18.6603	−0.926093
$407$	0	0
$408$	1.73205	0.0857493
$409$	12.9282	0.639259	0.319629	−	0.947543i	$-0.396442\pi$
$409$	12.9282	0.639259	0.319629	+	0.947543i	$0.396442\pi$
$410$	6.19615	0.306006
$411$	10.4641	0.516156
$412$	−17.3923	−0.856857
$413$	21.1244	1.03946
$414$	3.26795	0.160611
$415$	−16.4641	−0.808191
$416$	2.46410	0.120813
$417$	7.00000	0.342791
$418$	0	0
$419$	−20.2487	−0.989214	−0.494607	−	0.869117i	$-0.664688\pi$
$419$	−20.2487	−0.989214	−0.494607	+	0.869117i	$0.664688\pi$
$420$	−3.73205	−0.182105
$421$	−15.6603	−0.763234	−0.381617	−	0.924321i	$-0.624633\pi$
$421$	−15.6603	−0.763234	−0.381617	+	0.924321i	$0.624633\pi$
$422$	−6.60770	−0.321658
$423$	−8.92820	−0.434104
$424$	2.73205	0.132680
$425$	−1.73205	−0.0840168
$426$	−4.46410	−0.216286
$427$	−34.0526	−1.64792
$428$	−14.3923	−0.695678
$429$	0	0
$430$	8.19615	0.395254
$431$	21.4449	1.03296	0.516481	−	0.856298i	$-0.327242\pi$
$431$	21.4449	1.03296	0.516481	+	0.856298i	$0.327242\pi$
$432$	1.00000	0.0481125
$433$	4.00000	0.192228	0.0961139	−	0.995370i	$-0.469359\pi$
$433$	4.00000	0.192228	0.0961139	+	0.995370i	$0.469359\pi$
$434$	15.6603	0.751716
$435$	−5.00000	−0.239732
$436$	−12.3923	−0.593484
$437$	−22.8756	−1.09429
$438$	−7.66025	−0.366021
$439$	−14.0000	−0.668184	−0.334092	−	0.942541i	$-0.608430\pi$
$439$	−14.0000	−0.668184	−0.334092	+	0.942541i	$0.608430\pi$
$440$	0	0
$441$	6.92820	0.329914
$442$	−4.26795	−0.203006
$443$	10.8038	0.513306	0.256653	−	0.966504i	$-0.417380\pi$
$443$	10.8038	0.513306	0.256653	+	0.966504i	$0.417380\pi$
$444$	3.19615	0.151683
$445$	−2.53590	−0.120213
$446$	−29.2487	−1.38497
$447$	−8.39230	−0.396942
$448$	3.73205	0.176323
$449$	5.32051	0.251090	0.125545	−	0.992088i	$-0.459932\pi$
$449$	5.32051	0.251090	0.125545	+	0.992088i	$0.459932\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	−13.8564	−0.651751
$453$	20.1962	0.948898
$454$	27.4641	1.28895
$455$	9.19615	0.431122
$456$	−7.00000	−0.327805
$457$	−21.2679	−0.994873	−0.497436	−	0.867500i	$-0.665725\pi$
$457$	−21.2679	−0.994873	−0.497436	+	0.867500i	$0.665725\pi$
$458$	5.85641	0.273652
$459$	−1.73205	−0.0808452
$460$	3.26795	0.152369
$461$	5.39230	0.251145	0.125572	−	0.992084i	$-0.459923\pi$
$461$	5.39230	0.251145	0.125572	+	0.992084i	$0.459923\pi$
$462$	0	0
$463$	−24.2487	−1.12693	−0.563467	−	0.826139i	$-0.690533\pi$
$463$	−24.2487	−1.12693	−0.563467	+	0.826139i	$0.690533\pi$
$464$	5.00000	0.232119
$465$	4.19615	0.194592
$466$	9.07180	0.420243
$467$	28.8038	1.33288	0.666442	−	0.745557i	$-0.267817\pi$
$467$	28.8038	1.33288	0.666442	+	0.745557i	$0.267817\pi$
$468$	−2.46410	−0.113903
$469$	42.7846	1.97561
$470$	−8.92820	−0.411827
$471$	−14.6603	−0.675509
$472$	−5.66025	−0.260534
$473$	0	0
$474$	−10.3923	−0.477334
$475$	7.00000	0.321182
$476$	−6.46410	−0.296282
$477$	−2.73205	−0.125092
$478$	−3.19615	−0.146189
$479$	25.9808	1.18709	0.593546	−	0.804800i	$-0.297728\pi$
$479$	25.9808	1.18709	0.593546	+	0.804800i	$0.297728\pi$
$480$	1.00000	0.0456435
$481$	−7.87564	−0.359098
$482$	−0.803848	−0.0366143
$483$	−12.1962	−0.554944
$484$	0	0
$485$	−5.26795	−0.239205
$486$	−1.00000	−0.0453609
$487$	−5.67949	−0.257362	−0.128681	−	0.991686i	$-0.541074\pi$
$487$	−5.67949	−0.257362	−0.128681	+	0.991686i	$0.541074\pi$
$488$	9.12436	0.413040
$489$	8.19615	0.370643
$490$	6.92820	0.312984
$491$	−1.26795	−0.0572217	−0.0286109	−	0.999591i	$-0.509108\pi$
$491$	−1.26795	−0.0572217	−0.0286109	+	0.999591i	$0.509108\pi$
$492$	6.19615	0.279344
$493$	−8.66025	−0.390038
$494$	17.2487	0.776056
$495$	0	0
$496$	−4.19615	−0.188413
$497$	16.6603	0.747315
$498$	−16.4641	−0.737774
$499$	−27.1962	−1.21747	−0.608733	−	0.793375i	$-0.708322\pi$
$499$	−27.1962	−1.21747	−0.608733	+	0.793375i	$0.708322\pi$
$500$	−1.00000	−0.0447214
$501$	−6.53590	−0.292002
$502$	−31.3205	−1.39790
$503$	−23.9090	−1.06605	−0.533024	−	0.846100i	$-0.678944\pi$
$503$	−23.9090	−1.06605	−0.533024	+	0.846100i	$0.678944\pi$
$504$	−3.73205	−0.166239
$505$	8.46410	0.376648
$506$	0	0
$507$	−6.92820	−0.307692
$508$	13.4641	0.597373
$509$	11.8564	0.525526	0.262763	−	0.964860i	$-0.415366\pi$
$509$	11.8564	0.525526	0.262763	+	0.964860i	$0.415366\pi$
$510$	−1.73205	−0.0766965
$511$	28.5885	1.26468
$512$	−1.00000	−0.0441942
$513$	7.00000	0.309058
$514$	−19.7846	−0.872662
$515$	17.3923	0.766397
$516$	8.19615	0.360815
$517$	0	0
$518$	−11.9282	−0.524095
$519$	23.6603	1.03857
$520$	−2.46410	−0.108058
$521$	−18.5885	−0.814375	−0.407188	−	0.913345i	$-0.633490\pi$
$521$	−18.5885	−0.814375	−0.407188	+	0.913345i	$0.633490\pi$
$522$	−5.00000	−0.218844
$523$	−2.87564	−0.125743	−0.0628716	−	0.998022i	$-0.520026\pi$
$523$	−2.87564	−0.125743	−0.0628716	+	0.998022i	$0.520026\pi$
$524$	21.1244	0.922822
$525$	3.73205	0.162880
$526$	3.26795	0.142489
$527$	7.26795	0.316597
$528$	0	0
$529$	−12.3205	−0.535674
$530$	−2.73205	−0.118673
$531$	5.66025	0.245634
$532$	26.1244	1.13263
$533$	−15.2679	−0.661328
$534$	−2.53590	−0.109739
$535$	14.3923	0.622234
$536$	−11.4641	−0.495174
$537$	−12.5885	−0.543232
$538$	−21.9808	−0.947658
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	30.7321	1.32127	0.660637	−	0.750705i	$-0.270286\pi$
$541$	30.7321	1.32127	0.660637	+	0.750705i	$0.270286\pi$
$542$	−23.8564	−1.02472
$543$	−20.1962	−0.866700
$544$	1.73205	0.0742611
$545$	12.3923	0.530828
$546$	9.19615	0.393559
$547$	−23.8564	−1.02003	−0.510013	−	0.860167i	$-0.670359\pi$
$547$	−23.8564	−1.02003	−0.510013	+	0.860167i	$0.670359\pi$
$548$	10.4641	0.447004
$549$	−9.12436	−0.389418
$550$	0	0
$551$	35.0000	1.49105
$552$	3.26795	0.139093
$553$	38.7846	1.64929
$554$	2.14359	0.0910726
$555$	−3.19615	−0.135669
$556$	7.00000	0.296866
$557$	−37.3205	−1.58132	−0.790660	−	0.612255i	$-0.790263\pi$
$557$	−37.3205	−1.58132	−0.790660	+	0.612255i	$0.790263\pi$
$558$	4.19615	0.177637
$559$	−20.1962	−0.854206
$560$	−3.73205	−0.157708
$561$	0	0
$562$	3.12436	0.131793
$563$	5.53590	0.233310	0.116655	−	0.993172i	$-0.462783\pi$
$563$	5.53590	0.233310	0.116655	+	0.993172i	$0.462783\pi$
$564$	−8.92820	−0.375945
$565$	13.8564	0.582943
$566$	8.39230	0.352755
$567$	3.73205	0.156731
$568$	−4.46410	−0.187310
$569$	23.6603	0.991889	0.495945	−	0.868354i	$-0.334822\pi$
$569$	23.6603	0.991889	0.495945	+	0.868354i	$0.334822\pi$
$570$	7.00000	0.293198
$571$	4.53590	0.189821	0.0949107	−	0.995486i	$-0.469743\pi$
$571$	4.53590	0.189821	0.0949107	+	0.995486i	$0.469743\pi$
$572$	0	0
$573$	0.0717968	0.00299935
$574$	−23.1244	−0.965192
$575$	−3.26795	−0.136283
$576$	1.00000	0.0416667
$577$	−45.0333	−1.87476	−0.937381	−	0.348306i	$-0.886757\pi$
$577$	−45.0333	−1.87476	−0.937381	+	0.348306i	$0.886757\pi$
$578$	14.0000	0.582323
$579$	−11.3205	−0.470464
$580$	−5.00000	−0.207614
$581$	61.4449	2.54916
$582$	−5.26795	−0.218364
$583$	0	0
$584$	−7.66025	−0.316984
$585$	2.46410	0.101878
$586$	14.9282	0.616678
$587$	−1.87564	−0.0774161	−0.0387081	−	0.999251i	$-0.512324\pi$
$587$	−1.87564	−0.0774161	−0.0387081	+	0.999251i	$0.512324\pi$
$588$	6.92820	0.285714
$589$	−29.3731	−1.21030
$590$	5.66025	0.233029
$591$	9.46410	0.389301
$592$	3.19615	0.131361
$593$	34.7846	1.42843	0.714216	−	0.699925i	$-0.246783\pi$
$593$	34.7846	1.42843	0.714216	+	0.699925i	$0.246783\pi$
$594$	0	0
$595$	6.46410	0.265002
$596$	−8.39230	−0.343762
$597$	19.3205	0.790736
$598$	−8.05256	−0.329294
$599$	40.2487	1.64452	0.822259	−	0.569114i	$-0.192714\pi$
$599$	40.2487	1.64452	0.822259	+	0.569114i	$0.192714\pi$
$600$	−1.00000	−0.0408248
$601$	22.0000	0.897399	0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000	0.897399	0.448699	+	0.893683i	$0.351887\pi$
$602$	−30.5885	−1.24669
$603$	11.4641	0.466854
$604$	20.1962	0.821770
$605$	0	0
$606$	8.46410	0.343831
$607$	28.1244	1.14153	0.570766	−	0.821113i	$-0.306646\pi$
$607$	28.1244	1.14153	0.570766	+	0.821113i	$0.306646\pi$
$608$	−7.00000	−0.283887
$609$	18.6603	0.756152
$610$	−9.12436	−0.369434
$611$	22.0000	0.890025
$612$	−1.73205	−0.0700140
$613$	−15.5359	−0.627489	−0.313745	−	0.949507i	$-0.601584\pi$
$613$	−15.5359	−0.627489	−0.313745	+	0.949507i	$0.601584\pi$
$614$	16.5885	0.669456
$615$	−6.19615	−0.249853
$616$	0	0
$617$	−41.1051	−1.65483	−0.827415	−	0.561591i	$-0.810189\pi$
$617$	−41.1051	−1.65483	−0.827415	+	0.561591i	$0.810189\pi$
$618$	17.3923	0.699621
$619$	−11.8756	−0.477322	−0.238661	−	0.971103i	$-0.576709\pi$
$619$	−11.8756	−0.477322	−0.238661	+	0.971103i	$0.576709\pi$
$620$	4.19615	0.168522
$621$	−3.26795	−0.131138
$622$	−13.0718	−0.524131
$623$	9.46410	0.379171
$624$	−2.46410	−0.0986430
$625$	1.00000	0.0400000
$626$	−11.8038	−0.471777
$627$	0	0
$628$	−14.6603	−0.585008
$629$	−5.53590	−0.220731
$630$	3.73205	0.148688
$631$	26.9808	1.07409	0.537044	−	0.843554i	$-0.319541\pi$
$631$	26.9808	1.07409	0.537044	+	0.843554i	$0.319541\pi$
$632$	−10.3923	−0.413384
$633$	6.60770	0.262632
$634$	−8.19615	−0.325511
$635$	−13.4641	−0.534307
$636$	−2.73205	−0.108333
$637$	−17.0718	−0.676409
$638$	0	0
$639$	4.46410	0.176597
$640$	1.00000	0.0395285
$641$	31.8564	1.25825	0.629126	−	0.777303i	$-0.283413\pi$
$641$	31.8564	1.25825	0.629126	+	0.777303i	$0.283413\pi$
$642$	14.3923	0.568019
$643$	44.7846	1.76613	0.883066	−	0.469248i	$-0.155475\pi$
$643$	44.7846	1.76613	0.883066	+	0.469248i	$0.155475\pi$
$644$	−12.1962	−0.480596
$645$	−8.19615	−0.322723
$646$	12.1244	0.477026
$647$	−26.5359	−1.04323	−0.521617	−	0.853180i	$-0.674671\pi$
$647$	−26.5359	−1.04323	−0.521617	+	0.853180i	$0.674671\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	2.46410	0.0966500
$651$	−15.6603	−0.613774
$652$	8.19615	0.320986
$653$	−5.51666	−0.215884	−0.107942	−	0.994157i	$-0.534426\pi$
$653$	−5.51666	−0.215884	−0.107942	+	0.994157i	$0.534426\pi$
$654$	12.3923	0.484577
$655$	−21.1244	−0.825397
$656$	6.19615	0.241919
$657$	7.66025	0.298855
$658$	33.3205	1.29897
$659$	−16.2487	−0.632960	−0.316480	−	0.948599i	$-0.602501\pi$
$659$	−16.2487	−0.632960	−0.316480	+	0.948599i	$0.602501\pi$
$660$	0	0
$661$	−40.4449	−1.57312	−0.786561	−	0.617512i	$-0.788141\pi$
$661$	−40.4449	−1.57312	−0.786561	+	0.617512i	$0.788141\pi$
$662$	−5.87564	−0.228363
$663$	4.26795	0.165753
$664$	−16.4641	−0.638931
$665$	−26.1244	−1.01306
$666$	−3.19615	−0.123848
$667$	−16.3397	−0.632677
$668$	−6.53590	−0.252882
$669$	29.2487	1.13082
$670$	11.4641	0.442897
$671$	0	0
$672$	−3.73205	−0.143967
$673$	17.0718	0.658069	0.329035	−	0.944318i	$-0.393277\pi$
$673$	17.0718	0.658069	0.329035	+	0.944318i	$0.393277\pi$
$674$	30.1962	1.16311
$675$	1.00000	0.0384900
$676$	−6.92820	−0.266469
$677$	−27.1244	−1.04247	−0.521237	−	0.853412i	$-0.674529\pi$
$677$	−27.1244	−1.04247	−0.521237	+	0.853412i	$0.674529\pi$
$678$	13.8564	0.532152
$679$	19.6603	0.754491
$680$	−1.73205	−0.0664211
$681$	−27.4641	−1.05243
$682$	0	0
$683$	−42.3731	−1.62136	−0.810680	−	0.585489i	$-0.800902\pi$
$683$	−42.3731	−1.62136	−0.810680	+	0.585489i	$0.800902\pi$
$684$	7.00000	0.267652
$685$	−10.4641	−0.399813
$686$	0.267949	0.0102303
$687$	−5.85641	−0.223436
$688$	8.19615	0.312475
$689$	6.73205	0.256471
$690$	−3.26795	−0.124409
$691$	12.5167	0.476156	0.238078	−	0.971246i	$-0.423483\pi$
$691$	12.5167	0.476156	0.238078	+	0.971246i	$0.423483\pi$
$692$	23.6603	0.899428
$693$	0	0
$694$	14.4641	0.549050
$695$	−7.00000	−0.265525
$696$	−5.00000	−0.189525
$697$	−10.7321	−0.406505
$698$	−34.0000	−1.28692
$699$	−9.07180	−0.343127
$700$	3.73205	0.141058
$701$	3.24871	0.122702	0.0613511	−	0.998116i	$-0.480459\pi$
$701$	3.24871	0.122702	0.0613511	+	0.998116i	$0.480459\pi$
$702$	2.46410	0.0930015
$703$	22.3731	0.843816
$704$	0	0
$705$	8.92820	0.336256
$706$	−1.85641	−0.0698668
$707$	−31.5885	−1.18801
$708$	5.66025	0.212725
$709$	−24.7321	−0.928832	−0.464416	−	0.885617i	$-0.653736\pi$
$709$	−24.7321	−0.928832	−0.464416	+	0.885617i	$0.653736\pi$
$710$	4.46410	0.167535
$711$	10.3923	0.389742
$712$	−2.53590	−0.0950368
$713$	13.7128	0.513549
$714$	6.46410	0.241913
$715$	0	0
$716$	−12.5885	−0.470453
$717$	3.19615	0.119362
$718$	31.1769	1.16351
$719$	−46.3923	−1.73014	−0.865071	−	0.501650i	$-0.832726\pi$
$719$	−46.3923	−1.73014	−0.865071	+	0.501650i	$0.832726\pi$
$720$	−1.00000	−0.0372678
$721$	−64.9090	−2.41734
$722$	−30.0000	−1.11648
$723$	0.803848	0.0298954
$724$	−20.1962	−0.750584
$725$	5.00000	0.185695
$726$	0	0
$727$	−21.1436	−0.784172	−0.392086	−	0.919928i	$-0.628247\pi$
$727$	−21.1436	−0.784172	−0.392086	+	0.919928i	$0.628247\pi$
$728$	9.19615	0.340832
$729$	1.00000	0.0370370
$730$	7.66025	0.283519
$731$	−14.1962	−0.525064
$732$	−9.12436	−0.337246
$733$	−4.78461	−0.176724	−0.0883618	−	0.996088i	$-0.528163\pi$
$733$	−4.78461	−0.176724	−0.0883618	+	0.996088i	$0.528163\pi$
$734$	17.0000	0.627481
$735$	−6.92820	−0.255551
$736$	3.26795	0.120458
$737$	0	0
$738$	−6.19615	−0.228084
$739$	−19.0000	−0.698926	−0.349463	−	0.936950i	$-0.613636\pi$
$739$	−19.0000	−0.698926	−0.349463	+	0.936950i	$0.613636\pi$
$740$	−3.19615	−0.117493
$741$	−17.2487	−0.633647
$742$	10.1962	0.374313
$743$	−5.26795	−0.193262	−0.0966312	−	0.995320i	$-0.530807\pi$
$743$	−5.26795	−0.193262	−0.0966312	+	0.995320i	$0.530807\pi$
$744$	4.19615	0.153838
$745$	8.39230	0.307470
$746$	−17.3923	−0.636778
$747$	16.4641	0.602390
$748$	0	0
$749$	−53.7128	−1.96262
$750$	1.00000	0.0365148
$751$	−1.66025	−0.0605835	−0.0302918	−	0.999541i	$-0.509644\pi$
$751$	−1.66025	−0.0605835	−0.0302918	+	0.999541i	$0.509644\pi$
$752$	−8.92820	−0.325578
$753$	31.3205	1.14138
$754$	12.3205	0.448686
$755$	−20.1962	−0.735013
$756$	3.73205	0.135733
$757$	8.53590	0.310243	0.155121	−	0.987895i	$-0.450423\pi$
$757$	8.53590	0.310243	0.155121	+	0.987895i	$0.450423\pi$
$758$	−6.12436	−0.222447
$759$	0	0
$760$	7.00000	0.253917
$761$	−46.2487	−1.67651	−0.838257	−	0.545275i	$-0.816425\pi$
$761$	−46.2487	−1.67651	−0.838257	+	0.545275i	$0.816425\pi$
$762$	−13.4641	−0.487753
$763$	−46.2487	−1.67432
$764$	0.0717968	0.00259752
$765$	1.73205	0.0626224
$766$	4.14359	0.149714
$767$	−13.9474	−0.503613
$768$	1.00000	0.0360844
$769$	47.8372	1.72505	0.862526	−	0.506012i	$-0.168881\pi$
$769$	47.8372	1.72505	0.862526	+	0.506012i	$0.168881\pi$
$770$	0	0
$771$	19.7846	0.712525
$772$	−11.3205	−0.407434
$773$	−29.6603	−1.06681	−0.533403	−	0.845861i	$-0.679087\pi$
$773$	−29.6603	−1.06681	−0.533403	+	0.845861i	$0.679087\pi$
$774$	−8.19615	−0.294605
$775$	−4.19615	−0.150730
$776$	−5.26795	−0.189108
$777$	11.9282	0.427922
$778$	19.7128	0.706739
$779$	43.3731	1.55400
$780$	2.46410	0.0882290
$781$	0	0
$782$	−5.66025	−0.202410
$783$	5.00000	0.178685
$784$	6.92820	0.247436
$785$	14.6603	0.523247
$786$	−21.1244	−0.753481
$787$	−38.1962	−1.36155	−0.680773	−	0.732495i	$-0.738356\pi$
$787$	−38.1962	−1.36155	−0.680773	+	0.732495i	$0.738356\pi$
$788$	9.46410	0.337145
$789$	−3.26795	−0.116342
$790$	10.3923	0.369742
$791$	−51.7128	−1.83870
$792$	0	0
$793$	22.4833	0.798407
$794$	−27.9808	−0.993000
$795$	2.73205	0.0968959
$796$	19.3205	0.684797
$797$	−51.1244	−1.81092	−0.905459	−	0.424434i	$-0.860473\pi$
$797$	−51.1244	−1.81092	−0.905459	+	0.424434i	$0.860473\pi$
$798$	−26.1244	−0.924792
$799$	15.4641	0.547081
$800$	−1.00000	−0.0353553
$801$	2.53590	0.0896016
$802$	−34.7321	−1.22643
$803$	0	0
$804$	11.4641	0.404308
$805$	12.1962	0.429858
$806$	−10.3397	−0.364202
$807$	21.9808	0.773759
$808$	8.46410	0.297766
$809$	2.19615	0.0772126	0.0386063	−	0.999254i	$-0.487708\pi$
$809$	2.19615	0.0772126	0.0386063	+	0.999254i	$0.487708\pi$
$810$	1.00000	0.0351364
$811$	−44.1769	−1.55126	−0.775631	−	0.631187i	$-0.782568\pi$
$811$	−44.1769	−1.55126	−0.775631	+	0.631187i	$0.782568\pi$
$812$	18.6603	0.654847
$813$	23.8564	0.836681
$814$	0	0
$815$	−8.19615	−0.287099
$816$	−1.73205	−0.0606339
$817$	57.3731	2.00723
$818$	−12.9282	−0.452024
$819$	−9.19615	−0.321340
$820$	−6.19615	−0.216379
$821$	−23.6077	−0.823914	−0.411957	−	0.911203i	$-0.635155\pi$
$821$	−23.6077	−0.823914	−0.411957	+	0.911203i	$0.635155\pi$
$822$	−10.4641	−0.364977
$823$	−1.67949	−0.0585434	−0.0292717	−	0.999571i	$-0.509319\pi$
$823$	−1.67949	−0.0585434	−0.0292717	+	0.999571i	$0.509319\pi$
$824$	17.3923	0.605890
$825$	0	0
$826$	−21.1244	−0.735010
$827$	−21.0000	−0.730242	−0.365121	−	0.930960i	$-0.618972\pi$
$827$	−21.0000	−0.730242	−0.365121	+	0.930960i	$0.618972\pi$
$828$	−3.26795	−0.113569
$829$	−20.5885	−0.715067	−0.357533	−	0.933900i	$-0.616382\pi$
$829$	−20.5885	−0.715067	−0.357533	+	0.933900i	$0.616382\pi$
$830$	16.4641	0.571477
$831$	−2.14359	−0.0743604
$832$	−2.46410	−0.0854274
$833$	−12.0000	−0.415775
$834$	−7.00000	−0.242390
$835$	6.53590	0.226184
$836$	0	0
$837$	−4.19615	−0.145040
$838$	20.2487	0.699480
$839$	−15.5359	−0.536359	−0.268179	−	0.963369i	$-0.586422\pi$
$839$	−15.5359	−0.536359	−0.268179	+	0.963369i	$0.586422\pi$
$840$	3.73205	0.128768
$841$	−4.00000	−0.137931
$842$	15.6603	0.539688
$843$	−3.12436	−0.107609
$844$	6.60770	0.227446
$845$	6.92820	0.238337
$846$	8.92820	0.306958
$847$	0	0
$848$	−2.73205	−0.0938190
$849$	−8.39230	−0.288023
$850$	1.73205	0.0594089
$851$	−10.4449	−0.358045
$852$	4.46410	0.152938
$853$	−26.7128	−0.914629	−0.457315	−	0.889305i	$-0.651189\pi$
$853$	−26.7128	−0.914629	−0.457315	+	0.889305i	$0.651189\pi$
$854$	34.0526	1.16525
$855$	−7.00000	−0.239395
$856$	14.3923	0.491919
$857$	−8.51666	−0.290924	−0.145462	−	0.989364i	$-0.546467\pi$
$857$	−8.51666	−0.290924	−0.145462	+	0.989364i	$0.546467\pi$
$858$	0	0
$859$	−37.3205	−1.27336	−0.636680	−	0.771128i	$-0.719693\pi$
$859$	−37.3205	−1.27336	−0.636680	+	0.771128i	$0.719693\pi$
$860$	−8.19615	−0.279486
$861$	23.1244	0.788076
$862$	−21.4449	−0.730415
$863$	−4.53590	−0.154404	−0.0772019	−	0.997015i	$-0.524599\pi$
$863$	−4.53590	−0.154404	−0.0772019	+	0.997015i	$0.524599\pi$
$864$	−1.00000	−0.0340207
$865$	−23.6603	−0.804473
$866$	−4.00000	−0.135926
$867$	−14.0000	−0.475465
$868$	−15.6603	−0.531544
$869$	0	0
$870$	5.00000	0.169516
$871$	−28.2487	−0.957171
$872$	12.3923	0.419656
$873$	5.26795	0.178293
$874$	22.8756	0.773780
$875$	−3.73205	−0.126166
$876$	7.66025	0.258816
$877$	−15.5359	−0.524610	−0.262305	−	0.964985i	$-0.584483\pi$
$877$	−15.5359	−0.524610	−0.262305	+	0.964985i	$0.584483\pi$
$878$	14.0000	0.472477
$879$	−14.9282	−0.503516
$880$	0	0
$881$	4.58846	0.154589	0.0772945	−	0.997008i	$-0.475372\pi$
$881$	4.58846	0.154589	0.0772945	+	0.997008i	$0.475372\pi$
$882$	−6.92820	−0.233285
$883$	−12.0526	−0.405601	−0.202800	−	0.979220i	$-0.565004\pi$
$883$	−12.0526	−0.405601	−0.202800	+	0.979220i	$0.565004\pi$
$884$	4.26795	0.143547
$885$	−5.66025	−0.190267
$886$	−10.8038	−0.362962
$887$	4.78461	0.160651	0.0803257	−	0.996769i	$-0.474404\pi$
$887$	4.78461	0.160651	0.0803257	+	0.996769i	$0.474404\pi$
$888$	−3.19615	−0.107256
$889$	50.2487	1.68529
$890$	2.53590	0.0850035
$891$	0	0
$892$	29.2487	0.979319
$893$	−62.4974	−2.09140
$894$	8.39230	0.280681
$895$	12.5885	0.420786
$896$	−3.73205	−0.124679
$897$	8.05256	0.268867
$898$	−5.32051	−0.177548
$899$	−20.9808	−0.699748
$900$	1.00000	0.0333333
$901$	4.73205	0.157647
$902$	0	0
$903$	30.5885	1.01792
$904$	13.8564	0.460857
$905$	20.1962	0.671343
$906$	−20.1962	−0.670972
$907$	−35.0718	−1.16454	−0.582270	−	0.812996i	$-0.697835\pi$
$907$	−35.0718	−1.16454	−0.582270	+	0.812996i	$0.697835\pi$
$908$	−27.4641	−0.911428
$909$	−8.46410	−0.280737
$910$	−9.19615	−0.304849
$911$	−31.1051	−1.03056	−0.515279	−	0.857022i	$-0.672312\pi$
$911$	−31.1051	−1.03056	−0.515279	+	0.857022i	$0.672312\pi$
$912$	7.00000	0.231793
$913$	0	0
$914$	21.2679	0.703481
$915$	9.12436	0.301642
$916$	−5.85641	−0.193501
$917$	78.8372	2.60343
$918$	1.73205	0.0571662
$919$	−2.05256	−0.0677077	−0.0338538	−	0.999427i	$-0.510778\pi$
$919$	−2.05256	−0.0677077	−0.0338538	+	0.999427i	$0.510778\pi$
$920$	−3.26795	−0.107741
$921$	−16.5885	−0.546608
$922$	−5.39230	−0.177586
$923$	−11.0000	−0.362069
$924$	0	0
$925$	3.19615	0.105089
$926$	24.2487	0.796862
$927$	−17.3923	−0.571238
$928$	−5.00000	−0.164133
$929$	−6.87564	−0.225583	−0.112791	−	0.993619i	$-0.535979\pi$
$929$	−6.87564	−0.225583	−0.112791	+	0.993619i	$0.535979\pi$
$930$	−4.19615	−0.137597
$931$	48.4974	1.58944
$932$	−9.07180	−0.297157
$933$	13.0718	0.427951
$934$	−28.8038	−0.942491
$935$	0	0
$936$	2.46410	0.0805417
$937$	−4.92820	−0.160997	−0.0804987	−	0.996755i	$-0.525651\pi$
$937$	−4.92820	−0.160997	−0.0804987	+	0.996755i	$0.525651\pi$
$938$	−42.7846	−1.39697
$939$	11.8038	0.385204
$940$	8.92820	0.291206
$941$	−6.07180	−0.197935	−0.0989675	−	0.995091i	$-0.531554\pi$
$941$	−6.07180	−0.197935	−0.0989675	+	0.995091i	$0.531554\pi$
$942$	14.6603	0.477657
$943$	−20.2487	−0.659389
$944$	5.66025	0.184226
$945$	−3.73205	−0.121404
$946$	0	0
$947$	44.3731	1.44193	0.720965	−	0.692971i	$-0.243699\pi$
$947$	44.3731	1.44193	0.720965	+	0.692971i	$0.243699\pi$
$948$	10.3923	0.337526
$949$	−18.8756	−0.612729
$950$	−7.00000	−0.227110
$951$	8.19615	0.265778
$952$	6.46410	0.209503
$953$	10.7846	0.349348	0.174674	−	0.984626i	$-0.444113\pi$
$953$	10.7846	0.349348	0.174674	+	0.984626i	$0.444113\pi$
$954$	2.73205	0.0884534
$955$	−0.0717968	−0.00232329
$956$	3.19615	0.103371
$957$	0	0
$958$	−25.9808	−0.839400
$959$	39.0526	1.26107
$960$	−1.00000	−0.0322749
$961$	−13.3923	−0.432010
$962$	7.87564	0.253921
$963$	−14.3923	−0.463786
$964$	0.803848	0.0258902
$965$	11.3205	0.364420
$966$	12.1962	0.392405
$967$	47.1769	1.51711	0.758554	−	0.651611i	$-0.225906\pi$
$967$	47.1769	1.51711	0.758554	+	0.651611i	$0.225906\pi$
$968$	0	0
$969$	−12.1244	−0.389490
$970$	5.26795	0.169144
$971$	−39.6077	−1.27107	−0.635536	−	0.772071i	$-0.719221\pi$
$971$	−39.6077	−1.27107	−0.635536	+	0.772071i	$0.719221\pi$
$972$	1.00000	0.0320750
$973$	26.1244	0.837508
$974$	5.67949	0.181983
$975$	−2.46410	−0.0789144
$976$	−9.12436	−0.292064
$977$	28.1436	0.900393	0.450197	−	0.892929i	$-0.351354\pi$
$977$	28.1436	0.900393	0.450197	+	0.892929i	$0.351354\pi$
$978$	−8.19615	−0.262084
$979$	0	0
$980$	−6.92820	−0.221313
$981$	−12.3923	−0.395656
$982$	1.26795	0.0404619
$983$	23.9090	0.762578	0.381289	−	0.924456i	$-0.375480\pi$
$983$	23.9090	0.762578	0.381289	+	0.924456i	$0.375480\pi$
$984$	−6.19615	−0.197526
$985$	−9.46410	−0.301551
$986$	8.66025	0.275799
$987$	−33.3205	−1.06060
$988$	−17.2487	−0.548755
$989$	−26.7846	−0.851701
$990$	0	0
$991$	−42.7846	−1.35910	−0.679549	−	0.733630i	$-0.737824\pi$
$991$	−42.7846	−1.35910	−0.679549	+	0.733630i	$0.737824\pi$
$992$	4.19615	0.133228
$993$	5.87564	0.186458
$994$	−16.6603	−0.528431
$995$	−19.3205	−0.612501
$996$	16.4641	0.521685
$997$	6.71281	0.212597	0.106298	−	0.994334i	$-0.466100\pi$
$997$	6.71281	0.212597	0.106298	+	0.994334i	$0.466100\pi$
$998$	27.1962	0.860879
$999$	3.19615	0.101122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bg.1.2	✓	2
11.10	odd	2		3630.2.a.bo.1.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.bg.1.2	✓	2	1.1	even	1	trivial
3630.2.a.bo.1.1	yes	2	11.10	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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.73205 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} -2.46410 q^{13} -3.73205 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.73205 q^{17} -1.00000 q^{18} +7.00000 q^{19} -1.00000 q^{20} +3.73205 q^{21} -3.26795 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.46410 q^{26} +1.00000 q^{27} +3.73205 q^{28} +5.00000 q^{29} +1.00000 q^{30} -4.19615 q^{31} -1.00000 q^{32} +1.73205 q^{34} -3.73205 q^{35} +1.00000 q^{36} +3.19615 q^{37} -7.00000 q^{38} -2.46410 q^{39} +1.00000 q^{40} +6.19615 q^{41} -3.73205 q^{42} +8.19615 q^{43} -1.00000 q^{45} +3.26795 q^{46} -8.92820 q^{47} +1.00000 q^{48} +6.92820 q^{49} -1.00000 q^{50} -1.73205 q^{51} -2.46410 q^{52} -2.73205 q^{53} -1.00000 q^{54} -3.73205 q^{56} +7.00000 q^{57} -5.00000 q^{58} +5.66025 q^{59} -1.00000 q^{60} -9.12436 q^{61} +4.19615 q^{62} +3.73205 q^{63} +1.00000 q^{64} +2.46410 q^{65} +11.4641 q^{67} -1.73205 q^{68} -3.26795 q^{69} +3.73205 q^{70} +4.46410 q^{71} -1.00000 q^{72} +7.66025 q^{73} -3.19615 q^{74} +1.00000 q^{75} +7.00000 q^{76} +2.46410 q^{78} +10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} -6.19615 q^{82} +16.4641 q^{83} +3.73205 q^{84} +1.73205 q^{85} -8.19615 q^{86} +5.00000 q^{87} +2.53590 q^{89} +1.00000 q^{90} -9.19615 q^{91} -3.26795 q^{92} -4.19615 q^{93} +8.92820 q^{94} -7.00000 q^{95} -1.00000 q^{96} +5.26795 q^{97} -6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + 2 q^{16} - 2 q^{18} + 14 q^{19} - 2 q^{20} + 4 q^{21} - 10 q^{23} - 2 q^{24} + 2 q^{25} - 2 q^{26} + 2 q^{27} + 4 q^{28} + 10 q^{29} + 2 q^{30} + 2 q^{31} - 2 q^{32} - 4 q^{35} + 2 q^{36} - 4 q^{37} - 14 q^{38} + 2 q^{39} + 2 q^{40} + 2 q^{41} - 4 q^{42} + 6 q^{43} - 2 q^{45} + 10 q^{46} - 4 q^{47} + 2 q^{48} - 2 q^{50} + 2 q^{52} - 2 q^{53} - 2 q^{54} - 4 q^{56} + 14 q^{57} - 10 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} - 2 q^{62} + 4 q^{63} + 2 q^{64} - 2 q^{65} + 16 q^{67} - 10 q^{69} + 4 q^{70} + 2 q^{71} - 2 q^{72} - 2 q^{73} + 4 q^{74} + 2 q^{75} + 14 q^{76} - 2 q^{78} - 2 q^{80} + 2 q^{81} - 2 q^{82} + 26 q^{83} + 4 q^{84} - 6 q^{86} + 10 q^{87} + 12 q^{89} + 2 q^{90} - 8 q^{91} - 10 q^{92} + 2 q^{93} + 4 q^{94} - 14 q^{95} - 2 q^{96} + 14 q^{97}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + 2 * q^16 - 2 * q^18 + 14 * q^19 - 2 * q^20 + 4 * q^21 - 10 * q^23 - 2 * q^24 + 2 * q^25 - 2 * q^26 + 2 * q^27 + 4 * q^28 + 10 * q^29 + 2 * q^30 + 2 * q^31 - 2 * q^32 - 4 * q^35 + 2 * q^36 - 4 * q^37 - 14 * q^38 + 2 * q^39 + 2 * q^40 + 2 * q^41 - 4 * q^42 + 6 * q^43 - 2 * q^45 + 10 * q^46 - 4 * q^47 + 2 * q^48 - 2 * q^50 + 2 * q^52 - 2 * q^53 - 2 * q^54 - 4 * q^56 + 14 * q^57 - 10 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 - 2 * q^62 + 4 * q^63 + 2 * q^64 - 2 * q^65 + 16 * q^67 - 10 * q^69 + 4 * q^70 + 2 * q^71 - 2 * q^72 - 2 * q^73 + 4 * q^74 + 2 * q^75 + 14 * q^76 - 2 * q^78 - 2 * q^80 + 2 * q^81 - 2 * q^82 + 26 * q^83 + 4 * q^84 - 6 * q^86 + 10 * q^87 + 12 * q^89 + 2 * q^90 - 8 * q^91 - 10 * q^92 + 2 * q^93 + 4 * q^94 - 14 * q^95 - 2 * q^96 + 14 * q^97

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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