LMFDB - Embedded newform 3630.2.a.bg.1.1

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			1.1
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +4.46410 q^{13} -0.267949 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.73205 q^{17} -1.00000 q^{18} +7.00000 q^{19} -1.00000 q^{20} +0.267949 q^{21} -6.73205 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.46410 q^{26} +1.00000 q^{27} +0.267949 q^{28} +5.00000 q^{29} +1.00000 q^{30} +6.19615 q^{31} -1.00000 q^{32} -1.73205 q^{34} -0.267949 q^{35} +1.00000 q^{36} -7.19615 q^{37} -7.00000 q^{38} +4.46410 q^{39} +1.00000 q^{40} -4.19615 q^{41} -0.267949 q^{42} -2.19615 q^{43} -1.00000 q^{45} +6.73205 q^{46} +4.92820 q^{47} +1.00000 q^{48} -6.92820 q^{49} -1.00000 q^{50} +1.73205 q^{51} +4.46410 q^{52} +0.732051 q^{53} -1.00000 q^{54} -0.267949 q^{56} +7.00000 q^{57} -5.00000 q^{58} -11.6603 q^{59} -1.00000 q^{60} +15.1244 q^{61} -6.19615 q^{62} +0.267949 q^{63} +1.00000 q^{64} -4.46410 q^{65} +4.53590 q^{67} +1.73205 q^{68} -6.73205 q^{69} +0.267949 q^{70} -2.46410 q^{71} -1.00000 q^{72} -9.66025 q^{73} +7.19615 q^{74} +1.00000 q^{75} +7.00000 q^{76} -4.46410 q^{78} -10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} +4.19615 q^{82} +9.53590 q^{83} +0.267949 q^{84} -1.73205 q^{85} +2.19615 q^{86} +5.00000 q^{87} +9.46410 q^{89} +1.00000 q^{90} +1.19615 q^{91} -6.73205 q^{92} +6.19615 q^{93} -4.92820 q^{94} -7.00000 q^{95} -1.00000 q^{96} +8.73205 q^{97} +6.92820 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	0.267949	0.101275	0.0506376	−	0.998717i	$-0.483875\pi$
$7$	0.267949	0.101275	0.0506376	+	0.998717i	$0.483875\pi$
$8$	−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
$13$	4.46410	1.23812	0.619060	−	0.785344i	$-0.287514\pi$
$13$	4.46410	1.23812	0.619060	+	0.785344i	$0.287514\pi$
$14$	−0.267949	−0.0716124
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.73205	0.420084	0.210042	−	0.977692i	$-0.432640\pi$
$17$	1.73205	0.420084	0.210042	+	0.977692i	$0.432640\pi$
$18$	−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
$21$	0.267949	0.0584713
$22$	0	0
$23$	−6.73205	−1.40373	−0.701865	−	0.712310i	$-0.747649\pi$
$23$	−6.73205	−1.40373	−0.701865	+	0.712310i	$0.747649\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.46410	−0.875482
$27$	1.00000	0.192450
$28$	0.267949	0.0506376
$29$	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
$31$	6.19615	1.11286	0.556431	−	0.830894i	$-0.312170\pi$
$31$	6.19615	1.11286	0.556431	+	0.830894i	$0.312170\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−1.73205	−0.297044
$35$	−0.267949	−0.0452917
$36$	1.00000	0.166667
$37$	−7.19615	−1.18304	−0.591520	−	0.806290i	$-0.701472\pi$
$37$	−7.19615	−1.18304	−0.591520	+	0.806290i	$0.701472\pi$
$38$	−7.00000	−1.13555
$39$	4.46410	0.714828
$40$	1.00000	0.158114
$41$	−4.19615	−0.655329	−0.327664	−	0.944794i	$-0.606262\pi$
$41$	−4.19615	−0.655329	−0.327664	+	0.944794i	$0.606262\pi$
$42$	−0.267949	−0.0413455
$43$	−2.19615	−0.334910	−0.167455	−	0.985880i	$-0.553555\pi$
$43$	−2.19615	−0.334910	−0.167455	+	0.985880i	$0.553555\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	6.73205	0.992587
$47$	4.92820	0.718852	0.359426	−	0.933174i	$-0.382972\pi$
$47$	4.92820	0.718852	0.359426	+	0.933174i	$0.382972\pi$
$48$	1.00000	0.144338
$49$	−6.92820	−0.989743
$50$	−1.00000	−0.141421
$51$	1.73205	0.242536
$52$	4.46410	0.619060
$53$	0.732051	0.100555	0.0502775	−	0.998735i	$-0.483989\pi$
$53$	0.732051	0.100555	0.0502775	+	0.998735i	$0.483989\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−0.267949	−0.0358062
$57$	7.00000	0.927173
$58$	−5.00000	−0.656532
$59$	−11.6603	−1.51804	−0.759018	−	0.651070i	$-0.774321\pi$
$59$	−11.6603	−1.51804	−0.759018	+	0.651070i	$0.774321\pi$
$60$	−1.00000	−0.129099
$61$	15.1244	1.93648	0.968238	−	0.250032i	$-0.0804410\pi$
$61$	15.1244	1.93648	0.968238	+	0.250032i	$0.0804410\pi$
$62$	−6.19615	−0.786912
$63$	0.267949	0.0337584
$64$	1.00000	0.125000
$65$	−4.46410	−0.553704
$66$	0	0
$67$	4.53590	0.554148	0.277074	−	0.960849i	$-0.410635\pi$
$67$	4.53590	0.554148	0.277074	+	0.960849i	$0.410635\pi$
$68$	1.73205	0.210042
$69$	−6.73205	−0.810444
$70$	0.267949	0.0320261
$71$	−2.46410	−0.292435	−0.146218	−	0.989252i	$-0.546710\pi$
$71$	−2.46410	−0.292435	−0.146218	+	0.989252i	$0.546710\pi$
$72$	−1.00000	−0.117851
$73$	−9.66025	−1.13065	−0.565324	−	0.824869i	$-0.691249\pi$
$73$	−9.66025	−1.13065	−0.565324	+	0.824869i	$0.691249\pi$
$74$	7.19615	0.836536
$75$	1.00000	0.115470
$76$	7.00000	0.802955
$77$	0	0
$78$	−4.46410	−0.505460
$79$	−10.3923	−1.16923	−0.584613	−	0.811312i	$-0.698754\pi$
$79$	−10.3923	−1.16923	−0.584613	+	0.811312i	$0.698754\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	4.19615	0.463388
$83$	9.53590	1.04670	0.523350	−	0.852118i	$-0.324682\pi$
$83$	9.53590	1.04670	0.523350	+	0.852118i	$0.324682\pi$
$84$	0.267949	0.0292357
$85$	−1.73205	−0.187867
$86$	2.19615	0.236817
$87$	5.00000	0.536056
$88$	0	0
$89$	9.46410	1.00319	0.501596	−	0.865102i	$-0.332746\pi$
$89$	9.46410	1.00319	0.501596	+	0.865102i	$0.332746\pi$
$90$	1.00000	0.105409
$91$	1.19615	0.125391
$92$	−6.73205	−0.701865
$93$	6.19615	0.642511
$94$	−4.92820	−0.508305
$95$	−7.00000	−0.718185
$96$	−1.00000	−0.102062
$97$	8.73205	0.886605	0.443303	−	0.896372i	$-0.353807\pi$
$97$	8.73205	0.886605	0.443303	+	0.896372i	$0.353807\pi$
$98$	6.92820	0.699854
$99$	0	0
$100$	1.00000	0.100000
$101$	−1.53590	−0.152828	−0.0764138	−	0.997076i	$-0.524347\pi$
$101$	−1.53590	−0.152828	−0.0764138	+	0.997076i	$0.524347\pi$
$102$	−1.73205	−0.171499
$103$	3.39230	0.334254	0.167127	−	0.985935i	$-0.446551\pi$
$103$	3.39230	0.334254	0.167127	+	0.985935i	$0.446551\pi$
$104$	−4.46410	−0.437741
$105$	−0.267949	−0.0261492
$106$	−0.732051	−0.0711031
$107$	6.39230	0.617967	0.308984	−	0.951067i	$-0.400011\pi$
$107$	6.39230	0.617967	0.308984	+	0.951067i	$0.400011\pi$
$108$	1.00000	0.0962250
$109$	8.39230	0.803837	0.401919	−	0.915675i	$-0.368344\pi$
$109$	8.39230	0.803837	0.401919	+	0.915675i	$0.368344\pi$
$110$	0	0
$111$	−7.19615	−0.683029
$112$	0.267949	0.0253188
$113$	13.8564	1.30350	0.651751	−	0.758433i	$-0.274035\pi$
$113$	13.8564	1.30350	0.651751	+	0.758433i	$0.274035\pi$
$114$	−7.00000	−0.655610
$115$	6.73205	0.627767
$116$	5.00000	0.464238
$117$	4.46410	0.412706
$118$	11.6603	1.07341
$119$	0.464102	0.0425441
$120$	1.00000	0.0912871
$121$	0	0
$122$	−15.1244	−1.36929
$123$	−4.19615	−0.378354
$124$	6.19615	0.556431
$125$	−1.00000	−0.0894427
$126$	−0.267949	−0.0238708
$127$	6.53590	0.579967	0.289984	−	0.957032i	$-0.406350\pi$
$127$	6.53590	0.579967	0.289984	+	0.957032i	$0.406350\pi$
$128$	−1.00000	−0.0883883
$129$	−2.19615	−0.193360
$130$	4.46410	0.391528
$131$	−3.12436	−0.272976	−0.136488	−	0.990642i	$-0.543582\pi$
$131$	−3.12436	−0.272976	−0.136488	+	0.990642i	$0.543582\pi$
$132$	0	0
$133$	1.87564	0.162639
$134$	−4.53590	−0.391842
$135$	−1.00000	−0.0860663
$136$	−1.73205	−0.148522
$137$	3.53590	0.302092	0.151046	−	0.988527i	$-0.451736\pi$
$137$	3.53590	0.302092	0.151046	+	0.988527i	$0.451736\pi$
$138$	6.73205	0.573070
$139$	7.00000	0.593732	0.296866	−	0.954919i	$-0.404058\pi$
$139$	7.00000	0.593732	0.296866	+	0.954919i	$0.404058\pi$
$140$	−0.267949	−0.0226458
$141$	4.92820	0.415030
$142$	2.46410	0.206783
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.00000	−0.415227
$146$	9.66025	0.799488
$147$	−6.92820	−0.571429
$148$	−7.19615	−0.591520
$149$	12.3923	1.01522	0.507609	−	0.861588i	$-0.330530\pi$
$149$	12.3923	1.01522	0.507609	+	0.861588i	$0.330530\pi$
$150$	−1.00000	−0.0816497
$151$	9.80385	0.797826	0.398913	−	0.916989i	$-0.369388\pi$
$151$	9.80385	0.797826	0.398913	+	0.916989i	$0.369388\pi$
$152$	−7.00000	−0.567775
$153$	1.73205	0.140028
$154$	0	0
$155$	−6.19615	−0.497687
$156$	4.46410	0.357414
$157$	2.66025	0.212311	0.106156	−	0.994350i	$-0.466146\pi$
$157$	2.66025	0.212311	0.106156	+	0.994350i	$0.466146\pi$
$158$	10.3923	0.826767
$159$	0.732051	0.0580554
$160$	1.00000	0.0790569
$161$	−1.80385	−0.142163
$162$	−1.00000	−0.0785674
$163$	−2.19615	−0.172016	−0.0860080	−	0.996294i	$-0.527411\pi$
$163$	−2.19615	−0.172016	−0.0860080	+	0.996294i	$0.527411\pi$
$164$	−4.19615	−0.327664
$165$	0	0
$166$	−9.53590	−0.740129
$167$	−13.4641	−1.04188	−0.520942	−	0.853592i	$-0.674419\pi$
$167$	−13.4641	−1.04188	−0.520942	+	0.853592i	$0.674419\pi$
$168$	−0.267949	−0.0206727
$169$	6.92820	0.532939
$170$	1.73205	0.132842
$171$	7.00000	0.535303
$172$	−2.19615	−0.167455
$173$	6.33975	0.482002	0.241001	−	0.970525i	$-0.422524\pi$
$173$	6.33975	0.482002	0.241001	+	0.970525i	$0.422524\pi$
$174$	−5.00000	−0.379049
$175$	0.267949	0.0202551
$176$	0	0
$177$	−11.6603	−0.876438
$178$	−9.46410	−0.709364
$179$	18.5885	1.38937	0.694683	−	0.719316i	$-0.255545\pi$
$179$	18.5885	1.38937	0.694683	+	0.719316i	$0.255545\pi$
$180$	−1.00000	−0.0745356
$181$	−9.80385	−0.728714	−0.364357	−	0.931259i	$-0.618711\pi$
$181$	−9.80385	−0.728714	−0.364357	+	0.931259i	$0.618711\pi$
$182$	−1.19615	−0.0886647
$183$	15.1244	1.11802
$184$	6.73205	0.496293
$185$	7.19615	0.529072
$186$	−6.19615	−0.454324
$187$	0	0
$188$	4.92820	0.359426
$189$	0.267949	0.0194904
$190$	7.00000	0.507833
$191$	13.9282	1.00781	0.503905	−	0.863759i	$-0.331896\pi$
$191$	13.9282	1.00781	0.503905	+	0.863759i	$0.331896\pi$
$192$	1.00000	0.0721688
$193$	23.3205	1.67865	0.839323	−	0.543632i	$-0.182951\pi$
$193$	23.3205	1.67865	0.839323	+	0.543632i	$0.182951\pi$
$194$	−8.73205	−0.626925
$195$	−4.46410	−0.319681
$196$	−6.92820	−0.494872
$197$	2.53590	0.180675	0.0903376	−	0.995911i	$-0.471205\pi$
$197$	2.53590	0.180675	0.0903376	+	0.995911i	$0.471205\pi$
$198$	0	0
$199$	−15.3205	−1.08604	−0.543021	−	0.839719i	$-0.682720\pi$
$199$	−15.3205	−1.08604	−0.543021	+	0.839719i	$0.682720\pi$
$200$	−1.00000	−0.0707107
$201$	4.53590	0.319938
$202$	1.53590	0.108065
$203$	1.33975	0.0940317
$204$	1.73205	0.121268
$205$	4.19615	0.293072
$206$	−3.39230	−0.236353
$207$	−6.73205	−0.467910
$208$	4.46410	0.309530
$209$	0	0
$210$	0.267949	0.0184903
$211$	27.3923	1.88576	0.942882	−	0.333127i	$-0.108104\pi$
$211$	27.3923	1.88576	0.942882	+	0.333127i	$0.108104\pi$
$212$	0.732051	0.0502775
$213$	−2.46410	−0.168837
$214$	−6.39230	−0.436969
$215$	2.19615	0.149776
$216$	−1.00000	−0.0680414
$217$	1.66025	0.112705
$218$	−8.39230	−0.568399
$219$	−9.66025	−0.652779
$220$	0	0
$221$	7.73205	0.520114
$222$	7.19615	0.482974
$223$	−19.2487	−1.28899	−0.644495	−	0.764609i	$-0.722932\pi$
$223$	−19.2487	−1.28899	−0.644495	+	0.764609i	$0.722932\pi$
$224$	−0.267949	−0.0179031
$225$	1.00000	0.0666667
$226$	−13.8564	−0.921714
$227$	−20.5359	−1.36302	−0.681508	−	0.731811i	$-0.738675\pi$
$227$	−20.5359	−1.36302	−0.681508	+	0.731811i	$0.738675\pi$
$228$	7.00000	0.463586
$229$	21.8564	1.44431	0.722156	−	0.691730i	$-0.243151\pi$
$229$	21.8564	1.44431	0.722156	+	0.691730i	$0.243151\pi$
$230$	−6.73205	−0.443898
$231$	0	0
$232$	−5.00000	−0.328266
$233$	−22.9282	−1.50208	−0.751038	−	0.660259i	$-0.770447\pi$
$233$	−22.9282	−1.50208	−0.751038	+	0.660259i	$0.770447\pi$
$234$	−4.46410	−0.291827
$235$	−4.92820	−0.321481
$236$	−11.6603	−0.759018
$237$	−10.3923	−0.675053
$238$	−0.464102	−0.0300832
$239$	−7.19615	−0.465480	−0.232740	−	0.972539i	$-0.574769\pi$
$239$	−7.19615	−0.465480	−0.232740	+	0.972539i	$0.574769\pi$
$240$	−1.00000	−0.0645497
$241$	11.1962	0.721208	0.360604	−	0.932719i	$-0.382571\pi$
$241$	11.1962	0.721208	0.360604	+	0.932719i	$0.382571\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	15.1244	0.968238
$245$	6.92820	0.442627
$246$	4.19615	0.267537
$247$	31.2487	1.98831
$248$	−6.19615	−0.393456
$249$	9.53590	0.604313
$250$	1.00000	0.0632456
$251$	−3.32051	−0.209589	−0.104794	−	0.994494i	$-0.533418\pi$
$251$	−3.32051	−0.209589	−0.104794	+	0.994494i	$0.533418\pi$
$252$	0.267949	0.0168792
$253$	0	0
$254$	−6.53590	−0.410099
$255$	−1.73205	−0.108465
$256$	1.00000	0.0625000
$257$	−21.7846	−1.35889	−0.679443	−	0.733728i	$-0.737779\pi$
$257$	−21.7846	−1.35889	−0.679443	+	0.733728i	$0.737779\pi$
$258$	2.19615	0.136726
$259$	−1.92820	−0.119813
$260$	−4.46410	−0.276852
$261$	5.00000	0.309492
$262$	3.12436	0.193023
$263$	−6.73205	−0.415116	−0.207558	−	0.978223i	$-0.566552\pi$
$263$	−6.73205	−0.415116	−0.207558	+	0.978223i	$0.566552\pi$
$264$	0	0
$265$	−0.732051	−0.0449695
$266$	−1.87564	−0.115003
$267$	9.46410	0.579194
$268$	4.53590	0.277074
$269$	−29.9808	−1.82796	−0.913980	−	0.405760i	$-0.867007\pi$
$269$	−29.9808	−1.82796	−0.913980	+	0.405760i	$0.867007\pi$
$270$	1.00000	0.0608581
$271$	−3.85641	−0.234260	−0.117130	−	0.993117i	$-0.537369\pi$
$271$	−3.85641	−0.234260	−0.117130	+	0.993117i	$0.537369\pi$
$272$	1.73205	0.105021
$273$	1.19615	0.0723944
$274$	−3.53590	−0.213611
$275$	0	0
$276$	−6.73205	−0.405222
$277$	−29.8564	−1.79390	−0.896949	−	0.442134i	$-0.854221\pi$
$277$	−29.8564	−1.79390	−0.896949	+	0.442134i	$0.854221\pi$
$278$	−7.00000	−0.419832
$279$	6.19615	0.370954
$280$	0.267949	0.0160130
$281$	21.1244	1.26017	0.630087	−	0.776525i	$-0.283019\pi$
$281$	21.1244	1.26017	0.630087	+	0.776525i	$0.283019\pi$
$282$	−4.92820	−0.293470
$283$	12.3923	0.736646	0.368323	−	0.929698i	$-0.379932\pi$
$283$	12.3923	0.736646	0.368323	+	0.929698i	$0.379932\pi$
$284$	−2.46410	−0.146218
$285$	−7.00000	−0.414644
$286$	0	0
$287$	−1.12436	−0.0663686
$288$	−1.00000	−0.0589256
$289$	−14.0000	−0.823529
$290$	5.00000	0.293610
$291$	8.73205	0.511882
$292$	−9.66025	−0.565324
$293$	−1.07180	−0.0626150	−0.0313075	−	0.999510i	$-0.509967\pi$
$293$	−1.07180	−0.0626150	−0.0313075	+	0.999510i	$0.509967\pi$
$294$	6.92820	0.404061
$295$	11.6603	0.678886
$296$	7.19615	0.418268
$297$	0	0
$298$	−12.3923	−0.717867
$299$	−30.0526	−1.73798
$300$	1.00000	0.0577350
$301$	−0.588457	−0.0339181
$302$	−9.80385	−0.564148
$303$	−1.53590	−0.0882351
$304$	7.00000	0.401478
$305$	−15.1244	−0.866018
$306$	−1.73205	−0.0990148
$307$	14.5885	0.832607	0.416304	−	0.909226i	$-0.363325\pi$
$307$	14.5885	0.832607	0.416304	+	0.909226i	$0.363325\pi$
$308$	0	0
$309$	3.39230	0.192981
$310$	6.19615	0.351918
$311$	26.9282	1.52696	0.763479	−	0.645832i	$-0.223490\pi$
$311$	26.9282	1.52696	0.763479	+	0.645832i	$0.223490\pi$
$312$	−4.46410	−0.252730
$313$	22.1962	1.25460	0.627300	−	0.778777i	$-0.284160\pi$
$313$	22.1962	1.25460	0.627300	+	0.778777i	$0.284160\pi$
$314$	−2.66025	−0.150127
$315$	−0.267949	−0.0150972
$316$	−10.3923	−0.584613
$317$	−2.19615	−0.123348	−0.0616741	−	0.998096i	$-0.519644\pi$
$317$	−2.19615	−0.123348	−0.0616741	+	0.998096i	$0.519644\pi$
$318$	−0.732051	−0.0410514
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	6.39230	0.356784
$322$	1.80385	0.100524
$323$	12.1244	0.674617
$324$	1.00000	0.0555556
$325$	4.46410	0.247624
$326$	2.19615	0.121634
$327$	8.39230	0.464096
$328$	4.19615	0.231694
$329$	1.32051	0.0728020
$330$	0	0
$331$	30.1244	1.65578	0.827892	−	0.560887i	$-0.189540\pi$
$331$	30.1244	1.65578	0.827892	+	0.560887i	$0.189540\pi$
$332$	9.53590	0.523350
$333$	−7.19615	−0.394347
$334$	13.4641	0.736723
$335$	−4.53590	−0.247823
$336$	0.267949	0.0146178
$337$	−19.8038	−1.07878	−0.539392	−	0.842055i	$-0.681346\pi$
$337$	−19.8038	−1.07878	−0.539392	+	0.842055i	$0.681346\pi$
$338$	−6.92820	−0.376845
$339$	13.8564	0.752577
$340$	−1.73205	−0.0939336
$341$	0	0
$342$	−7.00000	−0.378517
$343$	−3.73205	−0.201512
$344$	2.19615	0.118409
$345$	6.73205	0.362441
$346$	−6.33975	−0.340827
$347$	−7.53590	−0.404548	−0.202274	−	0.979329i	$-0.564833\pi$
$347$	−7.53590	−0.404548	−0.202274	+	0.979329i	$0.564833\pi$
$348$	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	$0.136090\pi$
$350$	−0.267949	−0.0143225
$351$	4.46410	0.238276
$352$	0	0
$353$	−25.8564	−1.37620	−0.688099	−	0.725617i	$-0.741554\pi$
$353$	−25.8564	−1.37620	−0.688099	+	0.725617i	$0.741554\pi$
$354$	11.6603	0.619736
$355$	2.46410	0.130781
$356$	9.46410	0.501596
$357$	0.464102	0.0245629
$358$	−18.5885	−0.982430
$359$	31.1769	1.64545	0.822727	−	0.568436i	$-0.192451\pi$
$359$	31.1769	1.64545	0.822727	+	0.568436i	$0.192451\pi$
$360$	1.00000	0.0527046
$361$	30.0000	1.57895
$362$	9.80385	0.515279
$363$	0	0
$364$	1.19615	0.0626954
$365$	9.66025	0.505641
$366$	−15.1244	−0.790563
$367$	−17.0000	−0.887393	−0.443696	−	0.896177i	$-0.646333\pi$
$367$	−17.0000	−0.887393	−0.443696	+	0.896177i	$0.646333\pi$
$368$	−6.73205	−0.350932
$369$	−4.19615	−0.218443
$370$	−7.19615	−0.374110
$371$	0.196152	0.0101837
$372$	6.19615	0.321256
$373$	−3.39230	−0.175647	−0.0878234	−	0.996136i	$-0.527991\pi$
$373$	−3.39230	−0.175647	−0.0878234	+	0.996136i	$0.527991\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−4.92820	−0.254153
$377$	22.3205	1.14956
$378$	−0.267949	−0.0137818
$379$	−18.1244	−0.930986	−0.465493	−	0.885052i	$-0.654123\pi$
$379$	−18.1244	−0.930986	−0.465493	+	0.885052i	$0.654123\pi$
$380$	−7.00000	−0.359092
$381$	6.53590	0.334844
$382$	−13.9282	−0.712629
$383$	−31.8564	−1.62779	−0.813893	−	0.581015i	$-0.802656\pi$
$383$	−31.8564	−1.62779	−0.813893	+	0.581015i	$0.802656\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−23.3205	−1.18698
$387$	−2.19615	−0.111637
$388$	8.73205	0.443303
$389$	35.7128	1.81071	0.905356	−	0.424654i	$-0.139604\pi$
$389$	35.7128	1.81071	0.905356	+	0.424654i	$0.139604\pi$
$390$	4.46410	0.226049
$391$	−11.6603	−0.589684
$392$	6.92820	0.349927
$393$	−3.12436	−0.157603
$394$	−2.53590	−0.127757
$395$	10.3923	0.522894
$396$	0	0
$397$	−23.9808	−1.20356	−0.601780	−	0.798662i	$-0.705542\pi$
$397$	−23.9808	−1.20356	−0.601780	+	0.798662i	$0.705542\pi$
$398$	15.3205	0.767948
$399$	1.87564	0.0938997
$400$	1.00000	0.0500000
$401$	31.2679	1.56145	0.780723	−	0.624877i	$-0.214851\pi$
$401$	31.2679	1.56145	0.780723	+	0.624877i	$0.214851\pi$
$402$	−4.53590	−0.226230
$403$	27.6603	1.37786
$404$	−1.53590	−0.0764138
$405$	−1.00000	−0.0496904
$406$	−1.33975	−0.0664905
$407$	0	0
$408$	−1.73205	−0.0857493
$409$	−0.928203	−0.0458967	−0.0229483	−	0.999737i	$-0.507305\pi$
$409$	−0.928203	−0.0458967	−0.0229483	+	0.999737i	$0.507305\pi$
$410$	−4.19615	−0.207233
$411$	3.53590	0.174413
$412$	3.39230	0.167127
$413$	−3.12436	−0.153739
$414$	6.73205	0.330862
$415$	−9.53590	−0.468099
$416$	−4.46410	−0.218871
$417$	7.00000	0.342791
$418$	0	0
$419$	28.2487	1.38004	0.690020	−	0.723790i	$-0.257602\pi$
$419$	28.2487	1.38004	0.690020	+	0.723790i	$0.257602\pi$
$420$	−0.267949	−0.0130746
$421$	1.66025	0.0809158	0.0404579	−	0.999181i	$-0.487118\pi$
$421$	1.66025	0.0809158	0.0404579	+	0.999181i	$0.487118\pi$
$422$	−27.3923	−1.33344
$423$	4.92820	0.239617
$424$	−0.732051	−0.0355515
$425$	1.73205	0.0840168
$426$	2.46410	0.119386
$427$	4.05256	0.196117
$428$	6.39230	0.308984
$429$	0	0
$430$	−2.19615	−0.105908
$431$	−37.4449	−1.80366	−0.901828	−	0.432096i	$-0.857774\pi$
$431$	−37.4449	−1.80366	−0.901828	+	0.432096i	$0.857774\pi$
$432$	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	$0.469359\pi$
$434$	−1.66025	−0.0796947
$435$	−5.00000	−0.239732
$436$	8.39230	0.401919
$437$	−47.1244	−2.25426
$438$	9.66025	0.461585
$439$	−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
$442$	−7.73205	−0.367776
$443$	21.1962	1.00706	0.503530	−	0.863978i	$-0.332034\pi$
$443$	21.1962	1.00706	0.503530	+	0.863978i	$0.332034\pi$
$444$	−7.19615	−0.341514
$445$	−9.46410	−0.448641
$446$	19.2487	0.911453
$447$	12.3923	0.586136
$448$	0.267949	0.0126594
$449$	−29.3205	−1.38372	−0.691860	−	0.722032i	$-0.743209\pi$
$449$	−29.3205	−1.38372	−0.691860	+	0.722032i	$0.743209\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	13.8564	0.651751
$453$	9.80385	0.460625
$454$	20.5359	0.963797
$455$	−1.19615	−0.0560765
$456$	−7.00000	−0.327805
$457$	−24.7321	−1.15692	−0.578458	−	0.815712i	$-0.696345\pi$
$457$	−24.7321	−1.15692	−0.578458	+	0.815712i	$0.696345\pi$
$458$	−21.8564	−1.02128
$459$	1.73205	0.0808452
$460$	6.73205	0.313883
$461$	−15.3923	−0.716891	−0.358446	−	0.933551i	$-0.616693\pi$
$461$	−15.3923	−0.716891	−0.358446	+	0.933551i	$0.616693\pi$
$462$	0	0
$463$	24.2487	1.12693	0.563467	−	0.826139i	$-0.309467\pi$
$463$	24.2487	1.12693	0.563467	+	0.826139i	$0.309467\pi$
$464$	5.00000	0.232119
$465$	−6.19615	−0.287340
$466$	22.9282	1.06213
$467$	39.1962	1.81378	0.906891	−	0.421366i	$-0.138449\pi$
$467$	39.1962	1.81378	0.906891	+	0.421366i	$0.138449\pi$
$468$	4.46410	0.206353
$469$	1.21539	0.0561215
$470$	4.92820	0.227321
$471$	2.66025	0.122578
$472$	11.6603	0.536707
$473$	0	0
$474$	10.3923	0.477334
$475$	7.00000	0.321182
$476$	0.464102	0.0212721
$477$	0.732051	0.0335183
$478$	7.19615	0.329144
$479$	−25.9808	−1.18709	−0.593546	−	0.804800i	$-0.702272\pi$
$479$	−25.9808	−1.18709	−0.593546	+	0.804800i	$0.702272\pi$
$480$	1.00000	0.0456435
$481$	−32.1244	−1.46474
$482$	−11.1962	−0.509971
$483$	−1.80385	−0.0820779
$484$	0	0
$485$	−8.73205	−0.396502
$486$	−1.00000	−0.0453609
$487$	−40.3205	−1.82710	−0.913548	−	0.406730i	$-0.866669\pi$
$487$	−40.3205	−1.82710	−0.913548	+	0.406730i	$0.866669\pi$
$488$	−15.1244	−0.684647
$489$	−2.19615	−0.0993134
$490$	−6.92820	−0.312984
$491$	−4.73205	−0.213554	−0.106777	−	0.994283i	$-0.534053\pi$
$491$	−4.73205	−0.213554	−0.106777	+	0.994283i	$0.534053\pi$
$492$	−4.19615	−0.189177
$493$	8.66025	0.390038
$494$	−31.2487	−1.40595
$495$	0	0
$496$	6.19615	0.278215
$497$	−0.660254	−0.0296164
$498$	−9.53590	−0.427314
$499$	−16.8038	−0.752244	−0.376122	−	0.926570i	$-0.622743\pi$
$499$	−16.8038	−0.752244	−0.376122	+	0.926570i	$0.622743\pi$
$500$	−1.00000	−0.0447214
$501$	−13.4641	−0.601532
$502$	3.32051	0.148202
$503$	41.9090	1.86863	0.934314	−	0.356451i	$-0.116013\pi$
$503$	41.9090	1.86863	0.934314	+	0.356451i	$0.116013\pi$
$504$	−0.267949	−0.0119354
$505$	1.53590	0.0683466
$506$	0	0
$507$	6.92820	0.307692
$508$	6.53590	0.289984
$509$	−15.8564	−0.702823	−0.351411	−	0.936221i	$-0.614298\pi$
$509$	−15.8564	−0.702823	−0.351411	+	0.936221i	$0.614298\pi$
$510$	1.73205	0.0766965
$511$	−2.58846	−0.114507
$512$	−1.00000	−0.0441942
$513$	7.00000	0.309058
$514$	21.7846	0.960878
$515$	−3.39230	−0.149483
$516$	−2.19615	−0.0966802
$517$	0	0
$518$	1.92820	0.0847204
$519$	6.33975	0.278284
$520$	4.46410	0.195764
$521$	12.5885	0.551510	0.275755	−	0.961228i	$-0.411072\pi$
$521$	12.5885	0.551510	0.275755	+	0.961228i	$0.411072\pi$
$522$	−5.00000	−0.218844
$523$	−27.1244	−1.18607	−0.593033	−	0.805178i	$-0.702069\pi$
$523$	−27.1244	−1.18607	−0.593033	+	0.805178i	$0.702069\pi$
$524$	−3.12436	−0.136488
$525$	0.267949	0.0116943
$526$	6.73205	0.293531
$527$	10.7321	0.467495
$528$	0	0
$529$	22.3205	0.970457
$530$	0.732051	0.0317983
$531$	−11.6603	−0.506012
$532$	1.87564	0.0813195
$533$	−18.7321	−0.811375
$534$	−9.46410	−0.409552
$535$	−6.39230	−0.276363
$536$	−4.53590	−0.195921
$537$	18.5885	0.802151
$538$	29.9808	1.29256
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	27.2679	1.17234	0.586170	−	0.810188i	$-0.300635\pi$
$541$	27.2679	1.17234	0.586170	+	0.810188i	$0.300635\pi$
$542$	3.85641	0.165647
$543$	−9.80385	−0.420723
$544$	−1.73205	−0.0742611
$545$	−8.39230	−0.359487
$546$	−1.19615	−0.0511906
$547$	3.85641	0.164888	0.0824440	−	0.996596i	$-0.473727\pi$
$547$	3.85641	0.164888	0.0824440	+	0.996596i	$0.473727\pi$
$548$	3.53590	0.151046
$549$	15.1244	0.645492
$550$	0	0
$551$	35.0000	1.49105
$552$	6.73205	0.286535
$553$	−2.78461	−0.118414
$554$	29.8564	1.26848
$555$	7.19615	0.305460
$556$	7.00000	0.296866
$557$	−2.67949	−0.113534	−0.0567669	−	0.998387i	$-0.518079\pi$
$557$	−2.67949	−0.113534	−0.0567669	+	0.998387i	$0.518079\pi$
$558$	−6.19615	−0.262304
$559$	−9.80385	−0.414659
$560$	−0.267949	−0.0113229
$561$	0	0
$562$	−21.1244	−0.891077
$563$	12.4641	0.525299	0.262650	−	0.964891i	$-0.415404\pi$
$563$	12.4641	0.525299	0.262650	+	0.964891i	$0.415404\pi$
$564$	4.92820	0.207515
$565$	−13.8564	−0.582943
$566$	−12.3923	−0.520887
$567$	0.267949	0.0112528
$568$	2.46410	0.103391
$569$	6.33975	0.265776	0.132888	−	0.991131i	$-0.457575\pi$
$569$	6.33975	0.265776	0.132888	+	0.991131i	$0.457575\pi$
$570$	7.00000	0.293198
$571$	11.4641	0.479758	0.239879	−	0.970803i	$-0.422892\pi$
$571$	11.4641	0.479758	0.239879	+	0.970803i	$0.422892\pi$
$572$	0	0
$573$	13.9282	0.581859
$574$	1.12436	0.0469297
$575$	−6.73205	−0.280746
$576$	1.00000	0.0416667
$577$	45.0333	1.87476	0.937381	−	0.348306i	$-0.113243\pi$
$577$	45.0333	1.87476	0.937381	+	0.348306i	$0.113243\pi$
$578$	14.0000	0.582323
$579$	23.3205	0.969167
$580$	−5.00000	−0.207614
$581$	2.55514	0.106005
$582$	−8.73205	−0.361955
$583$	0	0
$584$	9.66025	0.399744
$585$	−4.46410	−0.184568
$586$	1.07180	0.0442755
$587$	−26.1244	−1.07827	−0.539134	−	0.842220i	$-0.681248\pi$
$587$	−26.1244	−1.07827	−0.539134	+	0.842220i	$0.681248\pi$
$588$	−6.92820	−0.285714
$589$	43.3731	1.78716
$590$	−11.6603	−0.480045
$591$	2.53590	0.104313
$592$	−7.19615	−0.295760
$593$	−6.78461	−0.278611	−0.139305	−	0.990249i	$-0.544487\pi$
$593$	−6.78461	−0.278611	−0.139305	+	0.990249i	$0.544487\pi$
$594$	0	0
$595$	−0.464102	−0.0190263
$596$	12.3923	0.507609
$597$	−15.3205	−0.627027
$598$	30.0526	1.22894
$599$	−8.24871	−0.337033	−0.168517	−	0.985699i	$-0.553898\pi$
$599$	−8.24871	−0.337033	−0.168517	+	0.985699i	$0.553898\pi$
$600$	−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	$0.351887\pi$
$602$	0.588457	0.0239837
$603$	4.53590	0.184716
$604$	9.80385	0.398913
$605$	0	0
$606$	1.53590	0.0623916
$607$	3.87564	0.157308	0.0786538	−	0.996902i	$-0.474938\pi$
$607$	3.87564	0.157308	0.0786538	+	0.996902i	$0.474938\pi$
$608$	−7.00000	−0.283887
$609$	1.33975	0.0542892
$610$	15.1244	0.612367
$611$	22.0000	0.890025
$612$	1.73205	0.0700140
$613$	−22.4641	−0.907317	−0.453658	−	0.891176i	$-0.649881\pi$
$613$	−22.4641	−0.907317	−0.453658	+	0.891176i	$0.649881\pi$
$614$	−14.5885	−0.588742
$615$	4.19615	0.169205
$616$	0	0
$617$	35.1051	1.41328	0.706639	−	0.707574i	$-0.250210\pi$
$617$	35.1051	1.41328	0.706639	+	0.707574i	$0.250210\pi$
$618$	−3.39230	−0.136459
$619$	−36.1244	−1.45196	−0.725980	−	0.687716i	$-0.758614\pi$
$619$	−36.1244	−1.45196	−0.725980	+	0.687716i	$0.758614\pi$
$620$	−6.19615	−0.248843
$621$	−6.73205	−0.270148
$622$	−26.9282	−1.07972
$623$	2.53590	0.101599
$624$	4.46410	0.178707
$625$	1.00000	0.0400000
$626$	−22.1962	−0.887137
$627$	0	0
$628$	2.66025	0.106156
$629$	−12.4641	−0.496976
$630$	0.267949	0.0106754
$631$	−24.9808	−0.994468	−0.497234	−	0.867616i	$-0.665651\pi$
$631$	−24.9808	−0.994468	−0.497234	+	0.867616i	$0.665651\pi$
$632$	10.3923	0.413384
$633$	27.3923	1.08875
$634$	2.19615	0.0872204
$635$	−6.53590	−0.259369
$636$	0.732051	0.0290277
$637$	−30.9282	−1.22542
$638$	0	0
$639$	−2.46410	−0.0974784
$640$	1.00000	0.0395285
$641$	4.14359	0.163662	0.0818311	−	0.996646i	$-0.473923\pi$
$641$	4.14359	0.163662	0.0818311	+	0.996646i	$0.473923\pi$
$642$	−6.39230	−0.252284
$643$	3.21539	0.126803	0.0634013	−	0.997988i	$-0.479805\pi$
$643$	3.21539	0.126803	0.0634013	+	0.997988i	$0.479805\pi$
$644$	−1.80385	−0.0710816
$645$	2.19615	0.0864734
$646$	−12.1244	−0.477026
$647$	−33.4641	−1.31561	−0.657805	−	0.753188i	$-0.728515\pi$
$647$	−33.4641	−1.31561	−0.657805	+	0.753188i	$0.728515\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−4.46410	−0.175096
$651$	1.66025	0.0650705
$652$	−2.19615	−0.0860080
$653$	39.5167	1.54641	0.773203	−	0.634158i	$-0.218653\pi$
$653$	39.5167	1.54641	0.773203	+	0.634158i	$0.218653\pi$
$654$	−8.39230	−0.328165
$655$	3.12436	0.122079
$656$	−4.19615	−0.163832
$657$	−9.66025	−0.376882
$658$	−1.32051	−0.0514788
$659$	32.2487	1.25623	0.628116	−	0.778120i	$-0.283826\pi$
$659$	32.2487	1.25623	0.628116	+	0.778120i	$0.283826\pi$
$660$	0	0
$661$	18.4449	0.717422	0.358711	−	0.933449i	$-0.383216\pi$
$661$	18.4449	0.717422	0.358711	+	0.933449i	$0.383216\pi$
$662$	−30.1244	−1.17082
$663$	7.73205	0.300288
$664$	−9.53590	−0.370065
$665$	−1.87564	−0.0727344
$666$	7.19615	0.278845
$667$	−33.6603	−1.30333
$668$	−13.4641	−0.520942
$669$	−19.2487	−0.744198
$670$	4.53590	0.175237
$671$	0	0
$672$	−0.267949	−0.0103364
$673$	30.9282	1.19219	0.596097	−	0.802912i	$-0.296717\pi$
$673$	30.9282	1.19219	0.596097	+	0.802912i	$0.296717\pi$
$674$	19.8038	0.762816
$675$	1.00000	0.0384900
$676$	6.92820	0.266469
$677$	−2.87564	−0.110520	−0.0552600	−	0.998472i	$-0.517599\pi$
$677$	−2.87564	−0.110520	−0.0552600	+	0.998472i	$0.517599\pi$
$678$	−13.8564	−0.532152
$679$	2.33975	0.0897912
$680$	1.73205	0.0664211
$681$	−20.5359	−0.786937
$682$	0	0
$683$	30.3731	1.16219	0.581097	−	0.813835i	$-0.302624\pi$
$683$	30.3731	1.16219	0.581097	+	0.813835i	$0.302624\pi$
$684$	7.00000	0.267652
$685$	−3.53590	−0.135100
$686$	3.73205	0.142490
$687$	21.8564	0.833874
$688$	−2.19615	−0.0837275
$689$	3.26795	0.124499
$690$	−6.73205	−0.256285
$691$	−32.5167	−1.23699	−0.618496	−	0.785788i	$-0.712258\pi$
$691$	−32.5167	−1.23699	−0.618496	+	0.785788i	$0.712258\pi$
$692$	6.33975	0.241001
$693$	0	0
$694$	7.53590	0.286059
$695$	−7.00000	−0.265525
$696$	−5.00000	−0.189525
$697$	−7.26795	−0.275293
$698$	−34.0000	−1.28692
$699$	−22.9282	−0.867224
$700$	0.267949	0.0101275
$701$	−45.2487	−1.70902	−0.854510	−	0.519435i	$-0.826143\pi$
$701$	−45.2487	−1.70902	−0.854510	+	0.519435i	$0.826143\pi$
$702$	−4.46410	−0.168487
$703$	−50.3731	−1.89986
$704$	0	0
$705$	−4.92820	−0.185607
$706$	25.8564	0.973119
$707$	−0.411543	−0.0154777
$708$	−11.6603	−0.438219
$709$	−21.2679	−0.798735	−0.399367	−	0.916791i	$-0.630770\pi$
$709$	−21.2679	−0.798735	−0.399367	+	0.916791i	$0.630770\pi$
$710$	−2.46410	−0.0924761
$711$	−10.3923	−0.389742
$712$	−9.46410	−0.354682
$713$	−41.7128	−1.56216
$714$	−0.464102	−0.0173686
$715$	0	0
$716$	18.5885	0.694683
$717$	−7.19615	−0.268745
$718$	−31.1769	−1.16351
$719$	−25.6077	−0.955006	−0.477503	−	0.878630i	$-0.658458\pi$
$719$	−25.6077	−0.955006	−0.477503	+	0.878630i	$0.658458\pi$
$720$	−1.00000	−0.0372678
$721$	0.908965	0.0338516
$722$	−30.0000	−1.11648
$723$	11.1962	0.416389
$724$	−9.80385	−0.364357
$725$	5.00000	0.185695
$726$	0	0
$727$	−48.8564	−1.81198	−0.905992	−	0.423295i	$-0.860873\pi$
$727$	−48.8564	−1.81198	−0.905992	+	0.423295i	$0.860873\pi$
$728$	−1.19615	−0.0443324
$729$	1.00000	0.0370370
$730$	−9.66025	−0.357542
$731$	−3.80385	−0.140690
$732$	15.1244	0.559012
$733$	36.7846	1.35867	0.679335	−	0.733828i	$-0.262268\pi$
$733$	36.7846	1.35867	0.679335	+	0.733828i	$0.262268\pi$
$734$	17.0000	0.627481
$735$	6.92820	0.255551
$736$	6.73205	0.248147
$737$	0	0
$738$	4.19615	0.154463
$739$	−19.0000	−0.698926	−0.349463	−	0.936950i	$-0.613636\pi$
$739$	−19.0000	−0.698926	−0.349463	+	0.936950i	$0.613636\pi$
$740$	7.19615	0.264536
$741$	31.2487	1.14795
$742$	−0.196152	−0.00720098
$743$	−8.73205	−0.320348	−0.160174	−	0.987089i	$-0.551206\pi$
$743$	−8.73205	−0.320348	−0.160174	+	0.987089i	$0.551206\pi$
$744$	−6.19615	−0.227162
$745$	−12.3923	−0.454019
$746$	3.39230	0.124201
$747$	9.53590	0.348900
$748$	0	0
$749$	1.71281	0.0625848
$750$	1.00000	0.0365148
$751$	15.6603	0.571451	0.285725	−	0.958312i	$-0.407765\pi$
$751$	15.6603	0.571451	0.285725	+	0.958312i	$0.407765\pi$
$752$	4.92820	0.179713
$753$	−3.32051	−0.121006
$754$	−22.3205	−0.812865
$755$	−9.80385	−0.356799
$756$	0.267949	0.00974522
$757$	15.4641	0.562052	0.281026	−	0.959700i	$-0.409325\pi$
$757$	15.4641	0.562052	0.281026	+	0.959700i	$0.409325\pi$
$758$	18.1244	0.658306
$759$	0	0
$760$	7.00000	0.253917
$761$	2.24871	0.0815157	0.0407579	−	0.999169i	$-0.487023\pi$
$761$	2.24871	0.0815157	0.0407579	+	0.999169i	$0.487023\pi$
$762$	−6.53590	−0.236771
$763$	2.24871	0.0814088
$764$	13.9282	0.503905
$765$	−1.73205	−0.0626224
$766$	31.8564	1.15102
$767$	−52.0526	−1.87951
$768$	1.00000	0.0360844
$769$	−31.8372	−1.14808	−0.574039	−	0.818828i	$-0.694624\pi$
$769$	−31.8372	−1.14808	−0.574039	+	0.818828i	$0.694624\pi$
$770$	0	0
$771$	−21.7846	−0.784554
$772$	23.3205	0.839323
$773$	−12.3397	−0.443830	−0.221915	−	0.975066i	$-0.571231\pi$
$773$	−12.3397	−0.443830	−0.221915	+	0.975066i	$0.571231\pi$
$774$	2.19615	0.0789391
$775$	6.19615	0.222572
$776$	−8.73205	−0.313462
$777$	−1.92820	−0.0691739
$778$	−35.7128	−1.28037
$779$	−29.3731	−1.05240
$780$	−4.46410	−0.159840
$781$	0	0
$782$	11.6603	0.416970
$783$	5.00000	0.178685
$784$	−6.92820	−0.247436
$785$	−2.66025	−0.0949485
$786$	3.12436	0.111442
$787$	−27.8038	−0.991100	−0.495550	−	0.868579i	$-0.665033\pi$
$787$	−27.8038	−0.991100	−0.495550	+	0.868579i	$0.665033\pi$
$788$	2.53590	0.0903376
$789$	−6.73205	−0.239667
$790$	−10.3923	−0.369742
$791$	3.71281	0.132012
$792$	0	0
$793$	67.5167	2.39759
$794$	23.9808	0.851045
$795$	−0.732051	−0.0259632
$796$	−15.3205	−0.543021
$797$	−26.8756	−0.951984	−0.475992	−	0.879450i	$-0.657911\pi$
$797$	−26.8756	−0.951984	−0.475992	+	0.879450i	$0.657911\pi$
$798$	−1.87564	−0.0663971
$799$	8.53590	0.301978
$800$	−1.00000	−0.0353553
$801$	9.46410	0.334398
$802$	−31.2679	−1.10411
$803$	0	0
$804$	4.53590	0.159969
$805$	1.80385	0.0635773
$806$	−27.6603	−0.974291
$807$	−29.9808	−1.05537
$808$	1.53590	0.0540327
$809$	−8.19615	−0.288161	−0.144081	−	0.989566i	$-0.546022\pi$
$809$	−8.19615	−0.288161	−0.144081	+	0.989566i	$0.546022\pi$
$810$	1.00000	0.0351364
$811$	18.1769	0.638278	0.319139	−	0.947708i	$-0.396606\pi$
$811$	18.1769	0.638278	0.319139	+	0.947708i	$0.396606\pi$
$812$	1.33975	0.0470159
$813$	−3.85641	−0.135250
$814$	0	0
$815$	2.19615	0.0769279
$816$	1.73205	0.0606339
$817$	−15.3731	−0.537836
$818$	0.928203	0.0324539
$819$	1.19615	0.0417969
$820$	4.19615	0.146536
$821$	−44.3923	−1.54930	−0.774651	−	0.632389i	$-0.782074\pi$
$821$	−44.3923	−1.54930	−0.774651	+	0.632389i	$0.782074\pi$
$822$	−3.53590	−0.123329
$823$	−36.3205	−1.26605	−0.633027	−	0.774130i	$-0.718188\pi$
$823$	−36.3205	−1.26605	−0.633027	+	0.774130i	$0.718188\pi$
$824$	−3.39230	−0.118177
$825$	0	0
$826$	3.12436	0.108710
$827$	−21.0000	−0.730242	−0.365121	−	0.930960i	$-0.618972\pi$
$827$	−21.0000	−0.730242	−0.365121	+	0.930960i	$0.618972\pi$
$828$	−6.73205	−0.233955
$829$	10.5885	0.367752	0.183876	−	0.982949i	$-0.441135\pi$
$829$	10.5885	0.367752	0.183876	+	0.982949i	$0.441135\pi$
$830$	9.53590	0.330996
$831$	−29.8564	−1.03571
$832$	4.46410	0.154765
$833$	−12.0000	−0.415775
$834$	−7.00000	−0.242390
$835$	13.4641	0.465944
$836$	0	0
$837$	6.19615	0.214170
$838$	−28.2487	−0.975836
$839$	−22.4641	−0.775547	−0.387773	−	0.921755i	$-0.626756\pi$
$839$	−22.4641	−0.775547	−0.387773	+	0.921755i	$0.626756\pi$
$840$	0.267949	0.00924513
$841$	−4.00000	−0.137931
$842$	−1.66025	−0.0572161
$843$	21.1244	0.727561
$844$	27.3923	0.942882
$845$	−6.92820	−0.238337
$846$	−4.92820	−0.169435
$847$	0	0
$848$	0.732051	0.0251387
$849$	12.3923	0.425303
$850$	−1.73205	−0.0594089
$851$	48.4449	1.66067
$852$	−2.46410	−0.0844187
$853$	28.7128	0.983108	0.491554	−	0.870847i	$-0.336429\pi$
$853$	28.7128	0.983108	0.491554	+	0.870847i	$0.336429\pi$
$854$	−4.05256	−0.138676
$855$	−7.00000	−0.239395
$856$	−6.39230	−0.218484
$857$	36.5167	1.24739	0.623693	−	0.781670i	$-0.285632\pi$
$857$	36.5167	1.24739	0.623693	+	0.781670i	$0.285632\pi$
$858$	0	0
$859$	−2.67949	−0.0914231	−0.0457115	−	0.998955i	$-0.514556\pi$
$859$	−2.67949	−0.0914231	−0.0457115	+	0.998955i	$0.514556\pi$
$860$	2.19615	0.0748882
$861$	−1.12436	−0.0383179
$862$	37.4449	1.27538
$863$	−11.4641	−0.390243	−0.195121	−	0.980779i	$-0.562510\pi$
$863$	−11.4641	−0.390243	−0.195121	+	0.980779i	$0.562510\pi$
$864$	−1.00000	−0.0340207
$865$	−6.33975	−0.215558
$866$	−4.00000	−0.135926
$867$	−14.0000	−0.475465
$868$	1.66025	0.0563527
$869$	0	0
$870$	5.00000	0.169516
$871$	20.2487	0.686101
$872$	−8.39230	−0.284199
$873$	8.73205	0.295535
$874$	47.1244	1.59401
$875$	−0.267949	−0.00905834
$876$	−9.66025	−0.326390
$877$	−22.4641	−0.758559	−0.379279	−	0.925282i	$-0.623828\pi$
$877$	−22.4641	−0.758559	−0.379279	+	0.925282i	$0.623828\pi$
$878$	14.0000	0.472477
$879$	−1.07180	−0.0361508
$880$	0	0
$881$	−26.5885	−0.895788	−0.447894	−	0.894087i	$-0.647826\pi$
$881$	−26.5885	−0.895788	−0.447894	+	0.894087i	$0.647826\pi$
$882$	6.92820	0.233285
$883$	26.0526	0.876738	0.438369	−	0.898795i	$-0.355556\pi$
$883$	26.0526	0.876738	0.438369	+	0.898795i	$0.355556\pi$
$884$	7.73205	0.260057
$885$	11.6603	0.391955
$886$	−21.1962	−0.712099
$887$	−36.7846	−1.23511	−0.617553	−	0.786529i	$-0.711876\pi$
$887$	−36.7846	−1.23511	−0.617553	+	0.786529i	$0.711876\pi$
$888$	7.19615	0.241487
$889$	1.75129	0.0587363
$890$	9.46410	0.317237
$891$	0	0
$892$	−19.2487	−0.644495
$893$	34.4974	1.15441
$894$	−12.3923	−0.414461
$895$	−18.5885	−0.621344
$896$	−0.267949	−0.00895155
$897$	−30.0526	−1.00343
$898$	29.3205	0.978438
$899$	30.9808	1.03327
$900$	1.00000	0.0333333
$901$	1.26795	0.0422415
$902$	0	0
$903$	−0.588457	−0.0195826
$904$	−13.8564	−0.460857
$905$	9.80385	0.325891
$906$	−9.80385	−0.325711
$907$	−48.9282	−1.62463	−0.812317	−	0.583216i	$-0.801794\pi$
$907$	−48.9282	−1.62463	−0.812317	+	0.583216i	$0.801794\pi$
$908$	−20.5359	−0.681508
$909$	−1.53590	−0.0509425
$910$	1.19615	0.0396521
$911$	45.1051	1.49440	0.747200	−	0.664600i	$-0.231398\pi$
$911$	45.1051	1.49440	0.747200	+	0.664600i	$0.231398\pi$
$912$	7.00000	0.231793
$913$	0	0
$914$	24.7321	0.818064
$915$	−15.1244	−0.499996
$916$	21.8564	0.722156
$917$	−0.837169	−0.0276457
$918$	−1.73205	−0.0571662
$919$	36.0526	1.18926	0.594632	−	0.803998i	$-0.297298\pi$
$919$	36.0526	1.18926	0.594632	+	0.803998i	$0.297298\pi$
$920$	−6.73205	−0.221949
$921$	14.5885	0.480706
$922$	15.3923	0.506919
$923$	−11.0000	−0.362069
$924$	0	0
$925$	−7.19615	−0.236608
$926$	−24.2487	−0.796862
$927$	3.39230	0.111418
$928$	−5.00000	−0.164133
$929$	−31.1244	−1.02116	−0.510578	−	0.859831i	$-0.670569\pi$
$929$	−31.1244	−1.02116	−0.510578	+	0.859831i	$0.670569\pi$
$930$	6.19615	0.203180
$931$	−48.4974	−1.58944
$932$	−22.9282	−0.751038
$933$	26.9282	0.881590
$934$	−39.1962	−1.28254
$935$	0	0
$936$	−4.46410	−0.145914
$937$	8.92820	0.291672	0.145836	−	0.989309i	$-0.453413\pi$
$937$	8.92820	0.291672	0.145836	+	0.989309i	$0.453413\pi$
$938$	−1.21539	−0.0396839
$939$	22.1962	0.724344
$940$	−4.92820	−0.160740
$941$	−19.9282	−0.649641	−0.324820	−	0.945776i	$-0.605304\pi$
$941$	−19.9282	−0.649641	−0.324820	+	0.945776i	$0.605304\pi$
$942$	−2.66025	−0.0866758
$943$	28.2487	0.919905
$944$	−11.6603	−0.379509
$945$	−0.267949	−0.00871639
$946$	0	0
$947$	−28.3731	−0.922001	−0.461000	−	0.887400i	$-0.652509\pi$
$947$	−28.3731	−0.922001	−0.461000	+	0.887400i	$0.652509\pi$
$948$	−10.3923	−0.337526
$949$	−43.1244	−1.39988
$950$	−7.00000	−0.227110
$951$	−2.19615	−0.0712151
$952$	−0.464102	−0.0150416
$953$	−30.7846	−0.997211	−0.498606	−	0.866829i	$-0.666154\pi$
$953$	−30.7846	−0.997211	−0.498606	+	0.866829i	$0.666154\pi$
$954$	−0.732051	−0.0237010
$955$	−13.9282	−0.450706
$956$	−7.19615	−0.232740
$957$	0	0
$958$	25.9808	0.839400
$959$	0.947441	0.0305945
$960$	−1.00000	−0.0322749
$961$	7.39230	0.238461
$962$	32.1244	1.03573
$963$	6.39230	0.205989
$964$	11.1962	0.360604
$965$	−23.3205	−0.750714
$966$	1.80385	0.0580378
$967$	−15.1769	−0.488057	−0.244028	−	0.969768i	$-0.578469\pi$
$967$	−15.1769	−0.488057	−0.244028	+	0.969768i	$0.578469\pi$
$968$	0	0
$969$	12.1244	0.389490
$970$	8.73205	0.280369
$971$	−60.3923	−1.93808	−0.969041	−	0.246901i	$-0.920588\pi$
$971$	−60.3923	−1.93808	−0.969041	+	0.246901i	$0.920588\pi$
$972$	1.00000	0.0320750
$973$	1.87564	0.0601304
$974$	40.3205	1.29195
$975$	4.46410	0.142966
$976$	15.1244	0.484119
$977$	55.8564	1.78700	0.893502	−	0.449058i	$-0.148241\pi$
$977$	55.8564	1.78700	0.893502	+	0.449058i	$0.148241\pi$
$978$	2.19615	0.0702252
$979$	0	0
$980$	6.92820	0.221313
$981$	8.39230	0.267946
$982$	4.73205	0.151006
$983$	−41.9090	−1.33669	−0.668344	−	0.743852i	$-0.732997\pi$
$983$	−41.9090	−1.33669	−0.668344	+	0.743852i	$0.732997\pi$
$984$	4.19615	0.133768
$985$	−2.53590	−0.0808004
$986$	−8.66025	−0.275799
$987$	1.32051	0.0420322
$988$	31.2487	0.994154
$989$	14.7846	0.470123
$990$	0	0
$991$	−1.21539	−0.0386081	−0.0193041	−	0.999814i	$-0.506145\pi$
$991$	−1.21539	−0.0386081	−0.0193041	+	0.999814i	$0.506145\pi$
$992$	−6.19615	−0.196728
$993$	30.1244	0.955968
$994$	0.660254	0.0209420
$995$	15.3205	0.485693
$996$	9.53590	0.302157
$997$	−48.7128	−1.54275	−0.771375	−	0.636381i	$-0.780431\pi$
$997$	−48.7128	−1.54275	−0.771375	+	0.636381i	$0.780431\pi$
$998$	16.8038	0.531917
$999$	−7.19615	−0.227676

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3630.2.a.bg.1.1	✓	2	1.1	even	1	trivial
3630.2.a.bo.1.2	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.267949 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +4.46410 q^{13} -0.267949 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.73205 q^{17} -1.00000 q^{18} +7.00000 q^{19} -1.00000 q^{20} +0.267949 q^{21} -6.73205 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.46410 q^{26} +1.00000 q^{27} +0.267949 q^{28} +5.00000 q^{29} +1.00000 q^{30} +6.19615 q^{31} -1.00000 q^{32} -1.73205 q^{34} -0.267949 q^{35} +1.00000 q^{36} -7.19615 q^{37} -7.00000 q^{38} +4.46410 q^{39} +1.00000 q^{40} -4.19615 q^{41} -0.267949 q^{42} -2.19615 q^{43} -1.00000 q^{45} +6.73205 q^{46} +4.92820 q^{47} +1.00000 q^{48} -6.92820 q^{49} -1.00000 q^{50} +1.73205 q^{51} +4.46410 q^{52} +0.732051 q^{53} -1.00000 q^{54} -0.267949 q^{56} +7.00000 q^{57} -5.00000 q^{58} -11.6603 q^{59} -1.00000 q^{60} +15.1244 q^{61} -6.19615 q^{62} +0.267949 q^{63} +1.00000 q^{64} -4.46410 q^{65} +4.53590 q^{67} +1.73205 q^{68} -6.73205 q^{69} +0.267949 q^{70} -2.46410 q^{71} -1.00000 q^{72} -9.66025 q^{73} +7.19615 q^{74} +1.00000 q^{75} +7.00000 q^{76} -4.46410 q^{78} -10.3923 q^{79} -1.00000 q^{80} +1.00000 q^{81} +4.19615 q^{82} +9.53590 q^{83} +0.267949 q^{84} -1.73205 q^{85} +2.19615 q^{86} +5.00000 q^{87} +9.46410 q^{89} +1.00000 q^{90} +1.19615 q^{91} -6.73205 q^{92} +6.19615 q^{93} -4.92820 q^{94} -7.00000 q^{95} -1.00000 q^{96} +8.73205 q^{97} +6.92820 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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Database

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