LMFDB - Embedded newform 3630.2.a.bs.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:	$4$
Coefficient field:	4.4.52625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 24x^{2} + 19x + 121 $ x^4 - x^3 - 24x^2 + 19x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.15753$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.10899 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.10899 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} -1.33343 q^{13} -5.10899 q^{14} -1.00000 q^{15} +1.00000 q^{16} -0.775565 q^{17} +1.00000 q^{18} +0.0785371 q^{19} -1.00000 q^{20} -5.10899 q^{21} +6.64849 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.33343 q^{26} +1.00000 q^{27} -5.10899 q^{28} +2.01882 q^{29} -1.00000 q^{30} +8.49096 q^{31} +1.00000 q^{32} -0.775565 q^{34} +5.10899 q^{35} +1.00000 q^{36} -3.93310 q^{37} +0.0785371 q^{38} -1.33343 q^{39} -1.00000 q^{40} +11.8962 q^{41} -5.10899 q^{42} +6.01163 q^{43} -1.00000 q^{45} +6.64849 q^{46} +6.56950 q^{47} +1.00000 q^{48} +19.1018 q^{49} +1.00000 q^{50} -0.775565 q^{51} -1.33343 q^{52} +10.3451 q^{53} +1.00000 q^{54} -5.10899 q^{56} +0.0785371 q^{57} +2.01882 q^{58} -5.32624 q^{59} -1.00000 q^{60} +3.74585 q^{61} +8.49096 q^{62} -5.10899 q^{63} +1.00000 q^{64} +1.33343 q^{65} +0.588036 q^{67} -0.775565 q^{68} +6.64849 q^{69} +5.10899 q^{70} -2.31506 q^{71} +1.00000 q^{72} -10.9443 q^{73} -3.93310 q^{74} +1.00000 q^{75} +0.0785371 q^{76} -1.33343 q^{78} -12.3267 q^{79} -1.00000 q^{80} +1.00000 q^{81} +11.8962 q^{82} +8.00000 q^{83} -5.10899 q^{84} +0.775565 q^{85} +6.01163 q^{86} +2.01882 q^{87} -9.67821 q^{89} -1.00000 q^{90} +6.81247 q^{91} +6.64849 q^{92} +8.49096 q^{93} +6.56950 q^{94} -0.0785371 q^{95} +1.00000 q^{96} -13.4541 q^{97} +19.1018 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{12} + 2 q^{13} + q^{14} - 4 q^{15} + 4 q^{16} + 11 q^{17} + 4 q^{18} + q^{19} - 4 q^{20} + q^{21} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + q^{28} + 9 q^{29} - 4 q^{30} + 17 q^{31} + 4 q^{32} + 11 q^{34} - q^{35} + 4 q^{36} + 8 q^{37} + q^{38} + 2 q^{39} - 4 q^{40} - 11 q^{41} + q^{42} + q^{43} - 4 q^{45} + 10 q^{47} + 4 q^{48} + 31 q^{49} + 4 q^{50} + 11 q^{51} + 2 q^{52} + 11 q^{53} + 4 q^{54} + q^{56} + q^{57} + 9 q^{58} + 10 q^{59} - 4 q^{60} - 10 q^{61} + 17 q^{62} + q^{63} + 4 q^{64} - 2 q^{65} + 9 q^{67} + 11 q^{68} - q^{70} + 10 q^{71} + 4 q^{72} - 8 q^{73} + 8 q^{74} + 4 q^{75} + q^{76} + 2 q^{78} - 7 q^{79} - 4 q^{80} + 4 q^{81} - 11 q^{82} + 32 q^{83} + q^{84} - 11 q^{85} + q^{86} + 9 q^{87} - 23 q^{89} - 4 q^{90} + 48 q^{91} + 17 q^{93} + 10 q^{94} - q^{95} + 4 q^{96} - 2 q^{97} + 31 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^12 + 2 * q^13 + q^14 - 4 * q^15 + 4 * q^16 + 11 * q^17 + 4 * q^18 + q^19 - 4 * q^20 + q^21 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + q^28 + 9 * q^29 - 4 * q^30 + 17 * q^31 + 4 * q^32 + 11 * q^34 - q^35 + 4 * q^36 + 8 * q^37 + q^38 + 2 * q^39 - 4 * q^40 - 11 * q^41 + q^42 + q^43 - 4 * q^45 + 10 * q^47 + 4 * q^48 + 31 * q^49 + 4 * q^50 + 11 * q^51 + 2 * q^52 + 11 * q^53 + 4 * q^54 + q^56 + q^57 + 9 * q^58 + 10 * q^59 - 4 * q^60 - 10 * q^61 + 17 * q^62 + q^63 + 4 * q^64 - 2 * q^65 + 9 * q^67 + 11 * q^68 - q^70 + 10 * q^71 + 4 * q^72 - 8 * q^73 + 8 * q^74 + 4 * q^75 + q^76 + 2 * q^78 - 7 * q^79 - 4 * q^80 + 4 * q^81 - 11 * q^82 + 32 * q^83 + q^84 - 11 * q^85 + q^86 + 9 * q^87 - 23 * q^89 - 4 * q^90 + 48 * q^91 + 17 * q^93 + 10 * q^94 - q^95 + 4 * q^96 - 2 * q^97 + 31 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	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
$7$	−5.10899	−1.93102	−0.965509	−	0.260370i	$-0.916155\pi$
$7$	−5.10899	−1.93102	−0.965509	+	0.260370i	$0.916155\pi$
$8$	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
$13$	−1.33343	−0.369826	−0.184913	−	0.982755i	$-0.559200\pi$
$13$	−1.33343	−0.369826	−0.184913	+	0.982755i	$0.559200\pi$
$14$	−5.10899	−1.36544
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−0.775565	−0.188102	−0.0940511	−	0.995567i	$-0.529982\pi$
$17$	−0.775565	−0.188102	−0.0940511	+	0.995567i	$0.529982\pi$
$18$	1.00000	0.235702
$19$	0.0785371	0.0180176	0.00900882	−	0.999959i	$-0.497132\pi$
$19$	0.0785371	0.0180176	0.00900882	+	0.999959i	$0.497132\pi$
$20$	−1.00000	−0.223607
$21$	−5.10899	−1.11487
$22$	0	0
$23$	6.64849	1.38631	0.693153	−	0.720791i	$-0.256221\pi$
$23$	6.64849	1.38631	0.693153	+	0.720791i	$0.256221\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−1.33343	−0.261507
$27$	1.00000	0.192450
$28$	−5.10899	−0.965509
$29$	2.01882	0.374886	0.187443	−	0.982275i	$-0.439980\pi$
$29$	2.01882	0.374886	0.187443	+	0.982275i	$0.439980\pi$
$30$	−1.00000	−0.182574
$31$	8.49096	1.52502	0.762511	−	0.646976i	$-0.223967\pi$
$31$	8.49096	1.52502	0.762511	+	0.646976i	$0.223967\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−0.775565	−0.133008
$35$	5.10899	0.863577
$36$	1.00000	0.166667
$37$	−3.93310	−0.646597	−0.323298	−	0.946297i	$-0.604792\pi$
$37$	−3.93310	−0.646597	−0.323298	+	0.946297i	$0.604792\pi$
$38$	0.0785371	0.0127404
$39$	−1.33343	−0.213519
$40$	−1.00000	−0.158114
$41$	11.8962	1.85787	0.928936	−	0.370239i	$-0.120724\pi$
$41$	11.8962	1.85787	0.928936	+	0.370239i	$0.120724\pi$
$42$	−5.10899	−0.788335
$43$	6.01163	0.916765	0.458383	−	0.888755i	$-0.348429\pi$
$43$	6.01163	0.916765	0.458383	+	0.888755i	$0.348429\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	6.64849	0.980266
$47$	6.56950	0.958259	0.479130	−	0.877744i	$-0.340952\pi$
$47$	6.56950	0.958259	0.479130	+	0.877744i	$0.340952\pi$
$48$	1.00000	0.144338
$49$	19.1018	2.72883
$50$	1.00000	0.141421
$51$	−0.775565	−0.108601
$52$	−1.33343	−0.184913
$53$	10.3451	1.42100	0.710502	−	0.703696i	$-0.248468\pi$
$53$	10.3451	1.42100	0.710502	+	0.703696i	$0.248468\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−5.10899	−0.682718
$57$	0.0785371	0.0104025
$58$	2.01882	0.265084
$59$	−5.32624	−0.693417	−0.346709	−	0.937973i	$-0.612701\pi$
$59$	−5.32624	−0.693417	−0.346709	+	0.937973i	$0.612701\pi$
$60$	−1.00000	−0.129099
$61$	3.74585	0.479607	0.239803	−	0.970821i	$-0.422917\pi$
$61$	3.74585	0.479607	0.239803	+	0.970821i	$0.422917\pi$
$62$	8.49096	1.07835
$63$	−5.10899	−0.643673
$64$	1.00000	0.125000
$65$	1.33343	0.165391
$66$	0	0
$67$	0.588036	0.0718400	0.0359200	−	0.999355i	$-0.488564\pi$
$67$	0.588036	0.0718400	0.0359200	+	0.999355i	$0.488564\pi$
$68$	−0.775565	−0.0940511
$69$	6.64849	0.800384
$70$	5.10899	0.610641
$71$	−2.31506	−0.274747	−0.137374	−	0.990519i	$-0.543866\pi$
$71$	−2.31506	−0.274747	−0.137374	+	0.990519i	$0.543866\pi$
$72$	1.00000	0.117851
$73$	−10.9443	−1.28093	−0.640465	−	0.767987i	$-0.721258\pi$
$73$	−10.9443	−1.28093	−0.640465	+	0.767987i	$0.721258\pi$
$74$	−3.93310	−0.457213
$75$	1.00000	0.115470
$76$	0.0785371	0.00900882
$77$	0	0
$78$	−1.33343	−0.150981
$79$	−12.3267	−1.38686	−0.693431	−	0.720523i	$-0.743902\pi$
$79$	−12.3267	−1.38686	−0.693431	+	0.720523i	$0.743902\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	11.8962	1.31371
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	−5.10899	−0.557437
$85$	0.775565	0.0841218
$86$	6.01163	0.648251
$87$	2.01882	0.216440
$88$	0	0
$89$	−9.67821	−1.02589	−0.512944	−	0.858422i	$-0.671445\pi$
$89$	−9.67821	−1.02589	−0.512944	+	0.858422i	$0.671445\pi$
$90$	−1.00000	−0.105409
$91$	6.81247	0.714141
$92$	6.64849	0.693153
$93$	8.49096	0.880471
$94$	6.56950	0.677592
$95$	−0.0785371	−0.00805773
$96$	1.00000	0.102062
$97$	−13.4541	−1.36605	−0.683026	−	0.730394i	$-0.739336\pi$
$97$	−13.4541	−1.36605	−0.683026	+	0.730394i	$0.739336\pi$
$98$	19.1018	1.92957
$99$	0	0
$100$	1.00000	0.100000
$101$	10.6408	1.05880	0.529402	−	0.848371i	$-0.322416\pi$
$101$	10.6408	1.05880	0.529402	+	0.848371i	$0.322416\pi$
$102$	−0.775565	−0.0767924
$103$	16.7087	1.64635	0.823177	−	0.567785i	$-0.192200\pi$
$103$	16.7087	1.64635	0.823177	+	0.567785i	$0.192200\pi$
$104$	−1.33343	−0.130753
$105$	5.10899	0.498587
$106$	10.3451	1.00480
$107$	−17.5511	−1.69673	−0.848366	−	0.529410i	$-0.822413\pi$
$107$	−17.5511	−1.69673	−0.848366	+	0.529410i	$0.822413\pi$
$108$	1.00000	0.0962250
$109$	8.94427	0.856706	0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427	0.856706	0.428353	+	0.903612i	$0.359094\pi$
$110$	0	0
$111$	−3.93310	−0.373313
$112$	−5.10899	−0.482754
$113$	−5.72703	−0.538753	−0.269377	−	0.963035i	$-0.586818\pi$
$113$	−5.72703	−0.538753	−0.269377	+	0.963035i	$0.586818\pi$
$114$	0.0785371	0.00735567
$115$	−6.64849	−0.619975
$116$	2.01882	0.187443
$117$	−1.33343	−0.123275
$118$	−5.32624	−0.490320
$119$	3.96236	0.363229
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	3.74585	0.339133
$123$	11.8962	1.07264
$124$	8.49096	0.762511
$125$	−1.00000	−0.0894427
$126$	−5.10899	−0.455145
$127$	6.96281	0.617850	0.308925	−	0.951086i	$-0.400031\pi$
$127$	6.96281	0.617850	0.308925	+	0.951086i	$0.400031\pi$
$128$	1.00000	0.0883883
$129$	6.01163	0.529295
$130$	1.33343	0.116949
$131$	2.19916	0.192142	0.0960709	−	0.995374i	$-0.469372\pi$
$131$	2.19916	0.192142	0.0960709	+	0.995374i	$0.469372\pi$
$132$	0	0
$133$	−0.401245	−0.0347924
$134$	0.588036	0.0507985
$135$	−1.00000	−0.0860663
$136$	−0.775565	−0.0665041
$137$	−2.17590	−0.185899	−0.0929497	−	0.995671i	$-0.529630\pi$
$137$	−2.17590	−0.185899	−0.0929497	+	0.995671i	$0.529630\pi$
$138$	6.64849	0.565957
$139$	−10.3074	−0.874264	−0.437132	−	0.899397i	$-0.644006\pi$
$139$	−10.3074	−0.874264	−0.437132	+	0.899397i	$0.644006\pi$
$140$	5.10899	0.431789
$141$	6.56950	0.553251
$142$	−2.31506	−0.194276
$143$	0	0
$144$	1.00000	0.0833333
$145$	−2.01882	−0.167654
$146$	−10.9443	−0.905754
$147$	19.1018	1.57549
$148$	−3.93310	−0.323298
$149$	15.2477	1.24914	0.624570	−	0.780969i	$-0.285274\pi$
$149$	15.2477	1.24914	0.624570	+	0.780969i	$0.285274\pi$
$150$	1.00000	0.0816497
$151$	−6.56921	−0.534595	−0.267297	−	0.963614i	$-0.586131\pi$
$151$	−6.56921	−0.534595	−0.267297	+	0.963614i	$0.586131\pi$
$152$	0.0785371	0.00637020
$153$	−0.775565	−0.0627007
$154$	0	0
$155$	−8.49096	−0.682010
$156$	−1.33343	−0.106760
$157$	−9.30815	−0.742872	−0.371436	−	0.928459i	$-0.621134\pi$
$157$	−9.30815	−0.742872	−0.371436	+	0.928459i	$0.621134\pi$
$158$	−12.3267	−0.980659
$159$	10.3451	0.820417
$160$	−1.00000	−0.0790569
$161$	−33.9671	−2.67698
$162$	1.00000	0.0785674
$163$	−18.7018	−1.46483	−0.732417	−	0.680856i	$-0.761608\pi$
$163$	−18.7018	−1.46483	−0.732417	+	0.680856i	$0.761608\pi$
$164$	11.8962	0.928936
$165$	0	0
$166$	8.00000	0.620920
$167$	2.37478	0.183766	0.0918829	−	0.995770i	$-0.470711\pi$
$167$	2.37478	0.183766	0.0918829	+	0.995770i	$0.470711\pi$
$168$	−5.10899	−0.394167
$169$	−11.2220	−0.863229
$170$	0.775565	0.0594831
$171$	0.0785371	0.00600588
$172$	6.01163	0.458383
$173$	−2.91427	−0.221568	−0.110784	−	0.993845i	$-0.535336\pi$
$173$	−2.91427	−0.221568	−0.110784	+	0.993845i	$0.535336\pi$
$174$	2.01882	0.153047
$175$	−5.10899	−0.386204
$176$	0	0
$177$	−5.32624	−0.400345
$178$	−9.67821	−0.725412
$179$	1.56231	0.116772	0.0583861	−	0.998294i	$-0.481405\pi$
$179$	1.56231	0.116772	0.0583861	+	0.998294i	$0.481405\pi$
$180$	−1.00000	−0.0745356
$181$	18.4721	1.37302	0.686512	−	0.727119i	$-0.259141\pi$
$181$	18.4721	1.37302	0.686512	+	0.727119i	$0.259141\pi$
$182$	6.81247	0.504974
$183$	3.74585	0.276901
$184$	6.64849	0.490133
$185$	3.93310	0.289167
$186$	8.49096	0.622587
$187$	0	0
$188$	6.56950	0.479130
$189$	−5.10899	−0.371625
$190$	−0.0785371	−0.00569768
$191$	20.7278	1.49981	0.749904	−	0.661546i	$-0.230100\pi$
$191$	20.7278	1.49981	0.749904	+	0.661546i	$0.230100\pi$
$192$	1.00000	0.0721688
$193$	−1.37079	−0.0986716	−0.0493358	−	0.998782i	$-0.515710\pi$
$193$	−1.37079	−0.0986716	−0.0493358	+	0.998782i	$0.515710\pi$
$194$	−13.4541	−0.965945
$195$	1.33343	0.0954887
$196$	19.1018	1.36441
$197$	5.01135	0.357044	0.178522	−	0.983936i	$-0.442868\pi$
$197$	5.01135	0.357044	0.178522	+	0.983936i	$0.442868\pi$
$198$	0	0
$199$	23.3086	1.65230	0.826152	−	0.563448i	$-0.190525\pi$
$199$	23.3086	1.65230	0.826152	+	0.563448i	$0.190525\pi$
$200$	1.00000	0.0707107
$201$	0.588036	0.0414768
$202$	10.6408	0.748687
$203$	−10.3141	−0.723911
$204$	−0.775565	−0.0543004
$205$	−11.8962	−0.830866
$206$	16.7087	1.16415
$207$	6.64849	0.462102
$208$	−1.33343	−0.0924566
$209$	0	0
$210$	5.10899	0.352554
$211$	20.0842	1.38265	0.691326	−	0.722543i	$-0.257027\pi$
$211$	20.0842	1.38265	0.691326	+	0.722543i	$0.257027\pi$
$212$	10.3451	0.710502
$213$	−2.31506	−0.158625
$214$	−17.5511	−1.19977
$215$	−6.01163	−0.409990
$216$	1.00000	0.0680414
$217$	−43.3802	−2.94484
$218$	8.94427	0.605783
$219$	−10.9443	−0.739545
$220$	0	0
$221$	1.03416	0.0695651
$222$	−3.93310	−0.263972
$223$	9.10899	0.609983	0.304992	−	0.952355i	$-0.401346\pi$
$223$	9.10899	0.609983	0.304992	+	0.952355i	$0.401346\pi$
$224$	−5.10899	−0.341359
$225$	1.00000	0.0666667
$226$	−5.72703	−0.380956
$227$	−20.6901	−1.37325	−0.686626	−	0.727011i	$-0.740909\pi$
$227$	−20.6901	−1.37325	−0.686626	+	0.727011i	$0.740909\pi$
$228$	0.0785371	0.00520124
$229$	10.9819	0.725705	0.362853	−	0.931846i	$-0.381803\pi$
$229$	10.9819	0.725705	0.362853	+	0.931846i	$0.381803\pi$
$230$	−6.64849	−0.438388
$231$	0	0
$232$	2.01882	0.132542
$233$	2.96309	0.194119	0.0970594	−	0.995279i	$-0.469056\pi$
$233$	2.96309	0.194119	0.0970594	+	0.995279i	$0.469056\pi$
$234$	−1.33343	−0.0871689
$235$	−6.56950	−0.428547
$236$	−5.32624	−0.346709
$237$	−12.3267	−0.800705
$238$	3.96236	0.256841
$239$	−8.56978	−0.554333	−0.277166	−	0.960822i	$-0.589395\pi$
$239$	−8.56978	−0.554333	−0.277166	+	0.960822i	$0.589395\pi$
$240$	−1.00000	−0.0645497
$241$	−7.97000	−0.513393	−0.256696	−	0.966492i	$-0.582634\pi$
$241$	−7.97000	−0.513393	−0.256696	+	0.966492i	$0.582634\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	3.74585	0.239803
$245$	−19.1018	−1.22037
$246$	11.8962	0.758473
$247$	−0.104723	−0.00666339
$248$	8.49096	0.539176
$249$	8.00000	0.506979
$250$	−1.00000	−0.0632456
$251$	20.2596	1.27878	0.639388	−	0.768884i	$-0.279188\pi$
$251$	20.2596	1.27878	0.639388	+	0.768884i	$0.279188\pi$
$252$	−5.10899	−0.321836
$253$	0	0
$254$	6.96281	0.436886
$255$	0.775565	0.0485678
$256$	1.00000	0.0625000
$257$	−19.9638	−1.24531	−0.622655	−	0.782497i	$-0.713946\pi$
$257$	−19.9638	−1.24531	−0.622655	+	0.782497i	$0.713946\pi$
$258$	6.01163	0.374268
$259$	20.0942	1.24859
$260$	1.33343	0.0826957
$261$	2.01882	0.124962
$262$	2.19916	0.135865
$263$	0.696114	0.0429242	0.0214621	−	0.999770i	$-0.493168\pi$
$263$	0.696114	0.0429242	0.0214621	+	0.999770i	$0.493168\pi$
$264$	0	0
$265$	−10.3451	−0.635492
$266$	−0.401245	−0.0246019
$267$	−9.67821	−0.592297
$268$	0.588036	0.0359200
$269$	5.92175	0.361055	0.180528	−	0.983570i	$-0.442219\pi$
$269$	5.92175	0.361055	0.180528	+	0.983570i	$0.442219\pi$
$270$	−1.00000	−0.0608581
$271$	13.9146	0.845249	0.422625	−	0.906305i	$-0.361109\pi$
$271$	13.9146	0.845249	0.422625	+	0.906305i	$0.361109\pi$
$272$	−0.775565	−0.0470255
$273$	6.81247	0.412309
$274$	−2.17590	−0.131451
$275$	0	0
$276$	6.64849	0.400192
$277$	10.1025	0.607003	0.303501	−	0.952831i	$-0.401844\pi$
$277$	10.1025	0.607003	0.303501	+	0.952831i	$0.401844\pi$
$278$	−10.3074	−0.618198
$279$	8.49096	0.508340
$280$	5.10899	0.305321
$281$	−28.9081	−1.72451	−0.862256	−	0.506472i	$-0.830949\pi$
$281$	−28.9081	−1.72451	−0.862256	+	0.506472i	$0.830949\pi$
$282$	6.56950	0.391208
$283$	13.1211	0.779967	0.389984	−	0.920822i	$-0.372481\pi$
$283$	13.1211	0.779967	0.389984	+	0.920822i	$0.372481\pi$
$284$	−2.31506	−0.137374
$285$	−0.0785371	−0.00465213
$286$	0	0
$287$	−60.7775	−3.58759
$288$	1.00000	0.0589256
$289$	−16.3985	−0.964618
$290$	−2.01882	−0.118549
$291$	−13.4541	−0.788691
$292$	−10.9443	−0.640465
$293$	−22.6601	−1.32382	−0.661909	−	0.749584i	$-0.730254\pi$
$293$	−22.6601	−1.32382	−0.661909	+	0.749584i	$0.730254\pi$
$294$	19.1018	1.11404
$295$	5.32624	0.310106
$296$	−3.93310	−0.228607
$297$	0	0
$298$	15.2477	0.883276
$299$	−8.86528	−0.512692
$300$	1.00000	0.0577350
$301$	−30.7134	−1.77029
$302$	−6.56921	−0.378016
$303$	10.6408	0.611300
$304$	0.0785371	0.00450441
$305$	−3.74585	−0.214487
$306$	−0.775565	−0.0443361
$307$	29.3158	1.67314	0.836571	−	0.547859i	$-0.184557\pi$
$307$	29.3158	1.67314	0.836571	+	0.547859i	$0.184557\pi$
$308$	0	0
$309$	16.7087	0.950522
$310$	−8.49096	−0.482254
$311$	11.3570	0.643995	0.321998	−	0.946741i	$-0.395646\pi$
$311$	11.3570	0.643995	0.321998	+	0.946741i	$0.395646\pi$
$312$	−1.33343	−0.0754905
$313$	−3.17664	−0.179554	−0.0897770	−	0.995962i	$-0.528615\pi$
$313$	−3.17664	−0.179554	−0.0897770	+	0.995962i	$0.528615\pi$
$314$	−9.30815	−0.525290
$315$	5.10899	0.287859
$316$	−12.3267	−0.693431
$317$	4.73101	0.265720	0.132860	−	0.991135i	$-0.457584\pi$
$317$	4.73101	0.265720	0.132860	+	0.991135i	$0.457584\pi$
$318$	10.3451	0.580122
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−17.5511	−0.979609
$322$	−33.9671	−1.89291
$323$	−0.0609106	−0.00338916
$324$	1.00000	0.0555556
$325$	−1.33343	−0.0739652
$326$	−18.7018	−1.03579
$327$	8.94427	0.494619
$328$	11.8962	0.656857
$329$	−33.5635	−1.85042
$330$	0	0
$331$	30.0424	1.65128	0.825639	−	0.564199i	$-0.190815\pi$
$331$	30.0424	1.65128	0.825639	+	0.564199i	$0.190815\pi$
$332$	8.00000	0.439057
$333$	−3.93310	−0.215532
$334$	2.37478	0.129942
$335$	−0.588036	−0.0321278
$336$	−5.10899	−0.278718
$337$	25.3570	1.38128	0.690641	−	0.723198i	$-0.257328\pi$
$337$	25.3570	1.38128	0.690641	+	0.723198i	$0.257328\pi$
$338$	−11.2220	−0.610395
$339$	−5.72703	−0.311049
$340$	0.775565	0.0420609
$341$	0	0
$342$	0.0785371	0.00424680
$343$	−61.8280	−3.33840
$344$	6.01163	0.324126
$345$	−6.64849	−0.357943
$346$	−2.91427	−0.156672
$347$	3.17664	0.170531	0.0852654	−	0.996358i	$-0.472826\pi$
$347$	3.17664	0.170531	0.0852654	+	0.996358i	$0.472826\pi$
$348$	2.01882	0.108220
$349$	6.95865	0.372488	0.186244	−	0.982504i	$-0.440368\pi$
$349$	6.95865	0.372488	0.186244	+	0.982504i	$0.440368\pi$
$350$	−5.10899	−0.273087
$351$	−1.33343	−0.0711731
$352$	0	0
$353$	8.01163	0.426416	0.213208	−	0.977007i	$-0.431609\pi$
$353$	8.01163	0.426416	0.213208	+	0.977007i	$0.431609\pi$
$354$	−5.32624	−0.283086
$355$	2.31506	0.122871
$356$	−9.67821	−0.512944
$357$	3.96236	0.209710
$358$	1.56231	0.0825704
$359$	0.180340	0.00951798	0.00475899	−	0.999989i	$-0.498485\pi$
$359$	0.180340	0.00951798	0.00475899	+	0.999989i	$0.498485\pi$
$360$	−1.00000	−0.0527046
$361$	−18.9938	−0.999675
$362$	18.4721	0.970874
$363$	0	0
$364$	6.81247	0.357070
$365$	10.9443	0.572849
$366$	3.74585	0.195799
$367$	30.8705	1.61142	0.805712	−	0.592307i	$-0.201783\pi$
$367$	30.8705	1.61142	0.805712	+	0.592307i	$0.201783\pi$
$368$	6.64849	0.346576
$369$	11.8962	0.619291
$370$	3.93310	0.204472
$371$	−52.8528	−2.74398
$372$	8.49096	0.440236
$373$	−16.1018	−0.833720	−0.416860	−	0.908971i	$-0.636869\pi$
$373$	−16.1018	−0.833720	−0.416860	+	0.908971i	$0.636869\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	6.56950	0.338796
$377$	−2.69195	−0.138643
$378$	−5.10899	−0.262778
$379$	32.5487	1.67191	0.835956	−	0.548796i	$-0.184914\pi$
$379$	32.5487	1.67191	0.835956	+	0.548796i	$0.184914\pi$
$380$	−0.0785371	−0.00402887
$381$	6.96281	0.356716
$382$	20.7278	1.06052
$383$	2.10825	0.107727	0.0538634	−	0.998548i	$-0.482846\pi$
$383$	2.10825	0.107727	0.0538634	+	0.998548i	$0.482846\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−1.37079	−0.0697714
$387$	6.01163	0.305588
$388$	−13.4541	−0.683026
$389$	−12.6032	−0.639008	−0.319504	−	0.947585i	$-0.603516\pi$
$389$	−12.6032	−0.639008	−0.319504	+	0.947585i	$0.603516\pi$
$390$	1.33343	0.0675207
$391$	−5.15633	−0.260767
$392$	19.1018	0.964787
$393$	2.19916	0.110933
$394$	5.01135	0.252468
$395$	12.3267	0.620223
$396$	0	0
$397$	−30.6341	−1.53748	−0.768741	−	0.639560i	$-0.779116\pi$
$397$	−30.6341	−1.53748	−0.768741	+	0.639560i	$0.779116\pi$
$398$	23.3086	1.16836
$399$	−0.401245	−0.0200874
$400$	1.00000	0.0500000
$401$	−19.9671	−0.997108	−0.498554	−	0.866859i	$-0.666136\pi$
$401$	−19.9671	−0.997108	−0.498554	+	0.866859i	$0.666136\pi$
$402$	0.588036	0.0293285
$403$	−11.3221	−0.563993
$404$	10.6408	0.529402
$405$	−1.00000	−0.0496904
$406$	−10.3141	−0.511883
$407$	0	0
$408$	−0.775565	−0.0383962
$409$	7.13962	0.353032	0.176516	−	0.984298i	$-0.443517\pi$
$409$	7.13962	0.353032	0.176516	+	0.984298i	$0.443517\pi$
$410$	−11.8962	−0.587511
$411$	−2.17590	−0.107329
$412$	16.7087	0.823177
$413$	27.2117	1.33900
$414$	6.64849	0.326755
$415$	−8.00000	−0.392705
$416$	−1.33343	−0.0653767
$417$	−10.3074	−0.504756
$418$	0	0
$419$	−22.3691	−1.09280	−0.546400	−	0.837524i	$-0.684002\pi$
$419$	−22.3691	−1.09280	−0.546400	+	0.837524i	$0.684002\pi$
$420$	5.10899	0.249293
$421$	−6.06091	−0.295391	−0.147695	−	0.989033i	$-0.547186\pi$
$421$	−6.06091	−0.295391	−0.147695	+	0.989033i	$0.547186\pi$
$422$	20.0842	0.977682
$423$	6.56950	0.319420
$424$	10.3451	0.502401
$425$	−0.775565	−0.0376204
$426$	−2.31506	−0.112165
$427$	−19.1375	−0.926129
$428$	−17.5511	−0.848366
$429$	0	0
$430$	−6.01163	−0.289907
$431$	−37.1623	−1.79004	−0.895021	−	0.446023i	$-0.852840\pi$
$431$	−37.1623	−1.79004	−0.895021	+	0.446023i	$0.852840\pi$
$432$	1.00000	0.0481125
$433$	30.6540	1.47314	0.736568	−	0.676364i	$-0.236445\pi$
$433$	30.6540	1.47314	0.736568	+	0.676364i	$0.236445\pi$
$434$	−43.3802	−2.08232
$435$	−2.01882	−0.0967951
$436$	8.94427	0.428353
$437$	0.522153	0.0249780
$438$	−10.9443	−0.522938
$439$	−7.06017	−0.336964	−0.168482	−	0.985705i	$-0.553886\pi$
$439$	−7.06017	−0.336964	−0.168482	+	0.985705i	$0.553886\pi$
$440$	0	0
$441$	19.1018	0.909610
$442$	1.03416	0.0491900
$443$	14.5925	0.693310	0.346655	−	0.937993i	$-0.387318\pi$
$443$	14.5925	0.693310	0.346655	+	0.937993i	$0.387318\pi$
$444$	−3.93310	−0.186656
$445$	9.67821	0.458791
$446$	9.10899	0.431323
$447$	15.2477	0.721192
$448$	−5.10899	−0.241377
$449$	12.7687	0.602590	0.301295	−	0.953531i	$-0.402581\pi$
$449$	12.7687	0.602590	0.301295	+	0.953531i	$0.402581\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−5.72703	−0.269377
$453$	−6.56921	−0.308649
$454$	−20.6901	−0.971035
$455$	−6.81247	−0.319374
$456$	0.0785371	0.00367783
$457$	17.3426	0.811252	0.405626	−	0.914039i	$-0.367053\pi$
$457$	17.3426	0.811252	0.405626	+	0.914039i	$0.367053\pi$
$458$	10.9819	0.513151
$459$	−0.775565	−0.0362003
$460$	−6.64849	−0.309987
$461$	2.99355	0.139424	0.0697118	−	0.997567i	$-0.477792\pi$
$461$	2.99355	0.139424	0.0697118	+	0.997567i	$0.477792\pi$
$462$	0	0
$463$	−16.2589	−0.755614	−0.377807	−	0.925884i	$-0.623322\pi$
$463$	−16.2589	−0.755614	−0.377807	+	0.925884i	$0.623322\pi$
$464$	2.01882	0.0937215
$465$	−8.49096	−0.393759
$466$	2.96309	0.137263
$467$	−18.5707	−0.859349	−0.429675	−	0.902984i	$-0.641372\pi$
$467$	−18.5707	−0.859349	−0.429675	+	0.902984i	$0.641372\pi$
$468$	−1.33343	−0.0616377
$469$	−3.00427	−0.138724
$470$	−6.56950	−0.303028
$471$	−9.30815	−0.428897
$472$	−5.32624	−0.245160
$473$	0	0
$474$	−12.3267	−0.566184
$475$	0.0785371	0.00360353
$476$	3.96236	0.181614
$477$	10.3451	0.473668
$478$	−8.56978	−0.391973
$479$	30.5554	1.39611	0.698056	−	0.716043i	$-0.254049\pi$
$479$	30.5554	1.39611	0.698056	+	0.716043i	$0.254049\pi$
$480$	−1.00000	−0.0456435
$481$	5.24450	0.239129
$482$	−7.97000	−0.363024
$483$	−33.9671	−1.54556
$484$	0	0
$485$	13.4541	0.610917
$486$	1.00000	0.0453609
$487$	−0.508303	−0.0230334	−0.0115167	−	0.999934i	$-0.503666\pi$
$487$	−0.508303	−0.0230334	−0.0115167	+	0.999934i	$0.503666\pi$
$488$	3.74585	0.169567
$489$	−18.7018	−0.845723
$490$	−19.1018	−0.862931
$491$	−39.3943	−1.77784	−0.888921	−	0.458061i	$-0.848544\pi$
$491$	−39.3943	−1.77784	−0.888921	+	0.458061i	$0.848544\pi$
$492$	11.8962	0.536322
$493$	−1.56573	−0.0705168
$494$	−0.104723	−0.00471173
$495$	0	0
$496$	8.49096	0.381255
$497$	11.8276	0.530542
$498$	8.00000	0.358489
$499$	21.4608	0.960717	0.480358	−	0.877072i	$-0.340507\pi$
$499$	21.4608	0.960717	0.480358	+	0.877072i	$0.340507\pi$
$500$	−1.00000	−0.0447214
$501$	2.37478	0.106097
$502$	20.2596	0.904231
$503$	23.5514	1.05011	0.525053	−	0.851070i	$-0.324046\pi$
$503$	23.5514	1.05011	0.525053	+	0.851070i	$0.324046\pi$
$504$	−5.10899	−0.227573
$505$	−10.6408	−0.473511
$506$	0	0
$507$	−11.2220	−0.498385
$508$	6.96281	0.308925
$509$	38.7178	1.71614	0.858069	−	0.513535i	$-0.171664\pi$
$509$	38.7178	1.71614	0.858069	+	0.513535i	$0.171664\pi$
$510$	0.775565	0.0343426
$511$	55.9142	2.47350
$512$	1.00000	0.0441942
$513$	0.0785371	0.00346750
$514$	−19.9638	−0.880567
$515$	−16.7087	−0.736272
$516$	6.01163	0.264647
$517$	0	0
$518$	20.0942	0.882887
$519$	−2.91427	−0.127922
$520$	1.33343	0.0584747
$521$	2.53921	0.111245	0.0556225	−	0.998452i	$-0.482286\pi$
$521$	2.53921	0.111245	0.0556225	+	0.998452i	$0.482286\pi$
$522$	2.01882	0.0883615
$523$	−37.3202	−1.63190	−0.815950	−	0.578122i	$-0.803786\pi$
$523$	−37.3202	−1.63190	−0.815950	+	0.578122i	$0.803786\pi$
$524$	2.19916	0.0960709
$525$	−5.10899	−0.222975
$526$	0.696114	0.0303520
$527$	−6.58529	−0.286860
$528$	0	0
$529$	21.2024	0.921844
$530$	−10.3451	−0.449361
$531$	−5.32624	−0.231139
$532$	−0.401245	−0.0173962
$533$	−15.8627	−0.687090
$534$	−9.67821	−0.418817
$535$	17.5511	0.758802
$536$	0.588036	0.0253993
$537$	1.56231	0.0674185
$538$	5.92175	0.255305
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	9.23515	0.397050	0.198525	−	0.980096i	$-0.436385\pi$
$541$	9.23515	0.397050	0.198525	+	0.980096i	$0.436385\pi$
$542$	13.9146	0.597681
$543$	18.4721	0.792715
$544$	−0.775565	−0.0332521
$545$	−8.94427	−0.383131
$546$	6.81247	0.291547
$547$	25.3758	1.08499	0.542495	−	0.840059i	$-0.317480\pi$
$547$	25.3758	1.08499	0.542495	+	0.840059i	$0.317480\pi$
$548$	−2.17590	−0.0929497
$549$	3.74585	0.159869
$550$	0	0
$551$	0.158552	0.00675456
$552$	6.64849	0.282978
$553$	62.9770	2.67805
$554$	10.1025	0.429216
$555$	3.93310	0.166951
$556$	−10.3074	−0.437132
$557$	10.6107	0.449589	0.224794	−	0.974406i	$-0.427829\pi$
$557$	10.6107	0.449589	0.224794	+	0.974406i	$0.427829\pi$
$558$	8.49096	0.359451
$559$	−8.01608	−0.339044
$560$	5.10899	0.215894
$561$	0	0
$562$	−28.9081	−1.21941
$563$	4.64450	0.195742	0.0978712	−	0.995199i	$-0.468797\pi$
$563$	4.64450	0.195742	0.0978712	+	0.995199i	$0.468797\pi$
$564$	6.56950	0.276626
$565$	5.72703	0.240938
$566$	13.1211	0.551520
$567$	−5.10899	−0.214558
$568$	−2.31506	−0.0971378
$569$	35.1105	1.47191	0.735954	−	0.677032i	$-0.236734\pi$
$569$	35.1105	1.47191	0.735954	+	0.677032i	$0.236734\pi$
$570$	−0.0785371	−0.00328956
$571$	−17.7758	−0.743896	−0.371948	−	0.928254i	$-0.621310\pi$
$571$	−17.7758	−0.743896	−0.371948	+	0.928254i	$0.621310\pi$
$572$	0	0
$573$	20.7278	0.865915
$574$	−60.7775	−2.53681
$575$	6.64849	0.277261
$576$	1.00000	0.0416667
$577$	3.63439	0.151302	0.0756509	−	0.997134i	$-0.475897\pi$
$577$	3.63439	0.151302	0.0756509	+	0.997134i	$0.475897\pi$
$578$	−16.3985	−0.682088
$579$	−1.37079	−0.0569681
$580$	−2.01882	−0.0838270
$581$	−40.8719	−1.69565
$582$	−13.4541	−0.557688
$583$	0	0
$584$	−10.9443	−0.452877
$585$	1.33343	0.0551304
$586$	−22.6601	−0.936081
$587$	7.39314	0.305148	0.152574	−	0.988292i	$-0.451244\pi$
$587$	7.39314	0.305148	0.152574	+	0.988292i	$0.451244\pi$
$588$	19.1018	0.787745
$589$	0.666855	0.0274773
$590$	5.32624	0.219278
$591$	5.01135	0.206139
$592$	−3.93310	−0.161649
$593$	35.9315	1.47553	0.737766	−	0.675057i	$-0.235881\pi$
$593$	35.9315	1.47553	0.737766	+	0.675057i	$0.235881\pi$
$594$	0	0
$595$	−3.96236	−0.162441
$596$	15.2477	0.624570
$597$	23.3086	0.953958
$598$	−8.86528	−0.362528
$599$	−20.5554	−0.839871	−0.419935	−	0.907554i	$-0.637947\pi$
$599$	−20.5554	−0.839871	−0.419935	+	0.907554i	$0.637947\pi$
$600$	1.00000	0.0408248
$601$	5.12136	0.208905	0.104452	−	0.994530i	$-0.466691\pi$
$601$	5.12136	0.208905	0.104452	+	0.994530i	$0.466691\pi$
$602$	−30.7134	−1.25178
$603$	0.588036	0.0239467
$604$	−6.56921	−0.267297
$605$	0	0
$606$	10.6408	0.432255
$607$	37.3946	1.51780	0.758900	−	0.651207i	$-0.225737\pi$
$607$	37.3946	1.51780	0.758900	+	0.651207i	$0.225737\pi$
$608$	0.0785371	0.00318510
$609$	−10.3141	−0.417950
$610$	−3.74585	−0.151665
$611$	−8.75995	−0.354389
$612$	−0.775565	−0.0313504
$613$	8.39685	0.339145	0.169573	−	0.985518i	$-0.445761\pi$
$613$	8.39685	0.339145	0.169573	+	0.985518i	$0.445761\pi$
$614$	29.3158	1.18309
$615$	−11.8962	−0.479701
$616$	0	0
$617$	−25.9029	−1.04281	−0.521406	−	0.853309i	$-0.674592\pi$
$617$	−25.9029	−1.04281	−0.521406	+	0.853309i	$0.674592\pi$
$618$	16.7087	0.672121
$619$	25.1441	1.01063	0.505313	−	0.862936i	$-0.331377\pi$
$619$	25.1441	1.01063	0.505313	+	0.862936i	$0.331377\pi$
$620$	−8.49096	−0.341005
$621$	6.64849	0.266795
$622$	11.3570	0.455373
$623$	49.4459	1.98101
$624$	−1.33343	−0.0533798
$625$	1.00000	0.0400000
$626$	−3.17664	−0.126964
$627$	0	0
$628$	−9.30815	−0.371436
$629$	3.05037	0.121626
$630$	5.10899	0.203547
$631$	−42.0436	−1.67373	−0.836864	−	0.547411i	$-0.815613\pi$
$631$	−42.0436	−1.67373	−0.836864	+	0.547411i	$0.815613\pi$
$632$	−12.3267	−0.490330
$633$	20.0842	0.798274
$634$	4.73101	0.187893
$635$	−6.96281	−0.276311
$636$	10.3451	0.410208
$637$	−25.4709	−1.00919
$638$	0	0
$639$	−2.31506	−0.0915824
$640$	−1.00000	−0.0395285
$641$	−2.11562	−0.0835619	−0.0417809	−	0.999127i	$-0.513303\pi$
$641$	−2.11562	−0.0835619	−0.0417809	+	0.999127i	$0.513303\pi$
$642$	−17.5511	−0.692688
$643$	−39.4827	−1.55704	−0.778522	−	0.627617i	$-0.784030\pi$
$643$	−39.4827	−1.55704	−0.778522	+	0.627617i	$0.784030\pi$
$644$	−33.9671	−1.33849
$645$	−6.01163	−0.236708
$646$	−0.0609106	−0.00239649
$647$	−16.1454	−0.634743	−0.317371	−	0.948301i	$-0.602800\pi$
$647$	−16.1454	−0.634743	−0.317371	+	0.948301i	$0.602800\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−1.33343	−0.0523013
$651$	−43.3802	−1.70021
$652$	−18.7018	−0.732417
$653$	−1.29134	−0.0505340	−0.0252670	−	0.999681i	$-0.508044\pi$
$653$	−1.29134	−0.0505340	−0.0252670	+	0.999681i	$0.508044\pi$
$654$	8.94427	0.349749
$655$	−2.19916	−0.0859284
$656$	11.8962	0.464468
$657$	−10.9443	−0.426977
$658$	−33.5635	−1.30844
$659$	23.7015	0.923278	0.461639	−	0.887068i	$-0.347262\pi$
$659$	23.7015	0.923278	0.461639	+	0.887068i	$0.347262\pi$
$660$	0	0
$661$	−17.0796	−0.664318	−0.332159	−	0.943223i	$-0.607777\pi$
$661$	−17.0796	−0.664318	−0.332159	+	0.943223i	$0.607777\pi$
$662$	30.0424	1.16763
$663$	1.03416	0.0401634
$664$	8.00000	0.310460
$665$	0.401245	0.0155596
$666$	−3.93310	−0.152404
$667$	13.4221	0.519707
$668$	2.37478	0.0918829
$669$	9.10899	0.352174
$670$	−0.588036	−0.0227178
$671$	0	0
$672$	−5.10899	−0.197084
$673$	8.51069	0.328063	0.164032	−	0.986455i	$-0.447550\pi$
$673$	8.51069	0.328063	0.164032	+	0.986455i	$0.447550\pi$
$674$	25.3570	0.976714
$675$	1.00000	0.0384900
$676$	−11.2220	−0.431614
$677$	−22.7125	−0.872911	−0.436456	−	0.899726i	$-0.643766\pi$
$677$	−22.7125	−0.872911	−0.436456	+	0.899726i	$0.643766\pi$
$678$	−5.72703	−0.219945
$679$	68.7367	2.63787
$680$	0.775565	0.0297416
$681$	−20.6901	−0.792847
$682$	0	0
$683$	−11.0419	−0.422507	−0.211254	−	0.977431i	$-0.567755\pi$
$683$	−11.0419	−0.422507	−0.211254	+	0.977431i	$0.567755\pi$
$684$	0.0785371	0.00300294
$685$	2.17590	0.0831367
$686$	−61.8280	−2.36060
$687$	10.9819	0.418986
$688$	6.01163	0.229191
$689$	−13.7944	−0.525524
$690$	−6.64849	−0.253104
$691$	9.49934	0.361372	0.180686	−	0.983541i	$-0.442168\pi$
$691$	9.49934	0.361372	0.180686	+	0.983541i	$0.442168\pi$
$692$	−2.91427	−0.110784
$693$	0	0
$694$	3.17664	0.120583
$695$	10.3074	0.390983
$696$	2.01882	0.0765233
$697$	−9.22627	−0.349470
$698$	6.95865	0.263389
$699$	2.96309	0.112075
$700$	−5.10899	−0.193102
$701$	−25.7924	−0.974165	−0.487082	−	0.873356i	$-0.661939\pi$
$701$	−25.7924	−0.974165	−0.487082	+	0.873356i	$0.661939\pi$
$702$	−1.33343	−0.0503270
$703$	−0.308894	−0.0116501
$704$	0	0
$705$	−6.56950	−0.247422
$706$	8.01163	0.301522
$707$	−54.3640	−2.04457
$708$	−5.32624	−0.200172
$709$	−13.7924	−0.517984	−0.258992	−	0.965880i	$-0.583390\pi$
$709$	−13.7924	−0.517984	−0.258992	+	0.965880i	$0.583390\pi$
$710$	2.31506	0.0868827
$711$	−12.3267	−0.462287
$712$	−9.67821	−0.362706
$713$	56.4520	2.11415
$714$	3.96236	0.148287
$715$	0	0
$716$	1.56231	0.0583861
$717$	−8.56978	−0.320044
$718$	0.180340	0.00673022
$719$	−19.4035	−0.723629	−0.361814	−	0.932250i	$-0.617843\pi$
$719$	−19.4035	−0.723629	−0.361814	+	0.932250i	$0.617843\pi$
$720$	−1.00000	−0.0372678
$721$	−85.3644	−3.17914
$722$	−18.9938	−0.706877
$723$	−7.97000	−0.296408
$724$	18.4721	0.686512
$725$	2.01882	0.0749772
$726$	0	0
$727$	−1.37752	−0.0510895	−0.0255447	−	0.999674i	$-0.508132\pi$
$727$	−1.37752	−0.0510895	−0.0255447	+	0.999674i	$0.508132\pi$
$728$	6.81247	0.252487
$729$	1.00000	0.0370370
$730$	10.9443	0.405066
$731$	−4.66241	−0.172446
$732$	3.74585	0.138451
$733$	−21.8778	−0.808076	−0.404038	−	0.914742i	$-0.632394\pi$
$733$	−21.8778	−0.808076	−0.404038	+	0.914742i	$0.632394\pi$
$734$	30.8705	1.13945
$735$	−19.1018	−0.704581
$736$	6.64849	0.245067
$737$	0	0
$738$	11.8962	0.437905
$739$	−0.525400	−0.0193272	−0.00966358	−	0.999953i	$-0.503076\pi$
$739$	−0.525400	−0.0193272	−0.00966358	+	0.999953i	$0.503076\pi$
$740$	3.93310	0.144583
$741$	−0.104723	−0.00384711
$742$	−52.8528	−1.94029
$743$	−47.8868	−1.75680	−0.878399	−	0.477929i	$-0.841388\pi$
$743$	−47.8868	−1.75680	−0.878399	+	0.477929i	$0.841388\pi$
$744$	8.49096	0.311294
$745$	−15.2477	−0.558633
$746$	−16.1018	−0.589529
$747$	8.00000	0.292705
$748$	0	0
$749$	89.6686	3.27642
$750$	−1.00000	−0.0365148
$751$	36.1543	1.31929	0.659645	−	0.751577i	$-0.270707\pi$
$751$	36.1543	1.31929	0.659645	+	0.751577i	$0.270707\pi$
$752$	6.56950	0.239565
$753$	20.2596	0.738301
$754$	−2.69195	−0.0980352
$755$	6.56921	0.239078
$756$	−5.10899	−0.185812
$757$	−43.6114	−1.58508	−0.792542	−	0.609818i	$-0.791243\pi$
$757$	−43.6114	−1.58508	−0.792542	+	0.609818i	$0.791243\pi$
$758$	32.5487	1.18222
$759$	0	0
$760$	−0.0785371	−0.00284884
$761$	1.10226	0.0399569	0.0199784	−	0.999800i	$-0.493640\pi$
$761$	1.10226	0.0399569	0.0199784	+	0.999800i	$0.493640\pi$
$762$	6.96281	0.252236
$763$	−45.6962	−1.65431
$764$	20.7278	0.749904
$765$	0.775565	0.0280406
$766$	2.10825	0.0761743
$767$	7.10215	0.256444
$768$	1.00000	0.0360844
$769$	26.9983	0.973583	0.486791	−	0.873518i	$-0.338167\pi$
$769$	26.9983	0.973583	0.486791	+	0.873518i	$0.338167\pi$
$770$	0	0
$771$	−19.9638	−0.718980
$772$	−1.37079	−0.0493358
$773$	−23.5077	−0.845512	−0.422756	−	0.906244i	$-0.638937\pi$
$773$	−23.5077	−0.845512	−0.422756	+	0.906244i	$0.638937\pi$
$774$	6.01163	0.216084
$775$	8.49096	0.305004
$776$	−13.4541	−0.482972
$777$	20.0942	0.720874
$778$	−12.6032	−0.451847
$779$	0.934292	0.0334745
$780$	1.33343	0.0477444
$781$	0	0
$782$	−5.15633	−0.184390
$783$	2.01882	0.0721468
$784$	19.1018	0.682207
$785$	9.30815	0.332222
$786$	2.19916	0.0784415
$787$	32.3634	1.15363	0.576816	−	0.816874i	$-0.304295\pi$
$787$	32.3634	1.15363	0.576816	+	0.816874i	$0.304295\pi$
$788$	5.01135	0.178522
$789$	0.696114	0.0247823
$790$	12.3267	0.438564
$791$	29.2593	1.04034
$792$	0	0
$793$	−4.99482	−0.177371
$794$	−30.6341	−1.08716
$795$	−10.3451	−0.366901
$796$	23.3086	0.826152
$797$	−40.4031	−1.43115	−0.715575	−	0.698536i	$-0.753835\pi$
$797$	−40.4031	−1.43115	−0.715575	+	0.698536i	$0.753835\pi$
$798$	−0.401245	−0.0142039
$799$	−5.09507	−0.180251
$800$	1.00000	0.0353553
$801$	−9.67821	−0.341963
$802$	−19.9671	−0.705062
$803$	0	0
$804$	0.588036	0.0207384
$805$	33.9671	1.19718
$806$	−11.3221	−0.398803
$807$	5.92175	0.208455
$808$	10.6408	0.374344
$809$	−12.2365	−0.430213	−0.215107	−	0.976591i	$-0.569010\pi$
$809$	−12.2365	−0.430213	−0.215107	+	0.976591i	$0.569010\pi$
$810$	−1.00000	−0.0351364
$811$	15.1684	0.532635	0.266318	−	0.963885i	$-0.414193\pi$
$811$	15.1684	0.532635	0.266318	+	0.963885i	$0.414193\pi$
$812$	−10.3141	−0.361956
$813$	13.9146	0.488005
$814$	0	0
$815$	18.7018	0.655094
$816$	−0.775565	−0.0271502
$817$	0.472136	0.0165179
$818$	7.13962	0.249631
$819$	6.81247	0.238047
$820$	−11.8962	−0.415433
$821$	14.4730	0.505113	0.252556	−	0.967582i	$-0.418729\pi$
$821$	14.4730	0.505113	0.252556	+	0.967582i	$0.418729\pi$
$822$	−2.17590	−0.0758931
$823$	3.54640	0.123620	0.0618099	−	0.998088i	$-0.480313\pi$
$823$	3.54640	0.123620	0.0618099	+	0.998088i	$0.480313\pi$
$824$	16.7087	0.582074
$825$	0	0
$826$	27.2117	0.946816
$827$	37.2217	1.29432	0.647162	−	0.762352i	$-0.275956\pi$
$827$	37.2217	1.29432	0.647162	+	0.762352i	$0.275956\pi$
$828$	6.64849	0.231051
$829$	−40.8705	−1.41949	−0.709745	−	0.704459i	$-0.751190\pi$
$829$	−40.8705	−1.41949	−0.709745	+	0.704459i	$0.751190\pi$
$830$	−8.00000	−0.277684
$831$	10.1025	0.350453
$832$	−1.33343	−0.0462283
$833$	−14.8147	−0.513299
$834$	−10.3074	−0.356917
$835$	−2.37478	−0.0821825
$836$	0	0
$837$	8.49096	0.293490
$838$	−22.3691	−0.772727
$839$	−16.4136	−0.566661	−0.283330	−	0.959022i	$-0.591439\pi$
$839$	−16.4136	−0.566661	−0.283330	+	0.959022i	$0.591439\pi$
$840$	5.10899	0.176277
$841$	−24.9244	−0.859461
$842$	−6.06091	−0.208873
$843$	−28.9081	−0.995648
$844$	20.0842	0.691326
$845$	11.2220	0.386048
$846$	6.56950	0.225864
$847$	0	0
$848$	10.3451	0.355251
$849$	13.1211	0.450314
$850$	−0.775565	−0.0266017
$851$	−26.1491	−0.896381
$852$	−2.31506	−0.0793127
$853$	−18.1880	−0.622745	−0.311372	−	0.950288i	$-0.600789\pi$
$853$	−18.1880	−0.622745	−0.311372	+	0.950288i	$0.600789\pi$
$854$	−19.1375	−0.654872
$855$	−0.0785371	−0.00268591
$856$	−17.5511	−0.599885
$857$	−48.5679	−1.65905	−0.829525	−	0.558470i	$-0.811389\pi$
$857$	−48.5679	−1.65905	−0.829525	+	0.558470i	$0.811389\pi$
$858$	0	0
$859$	−29.1564	−0.994805	−0.497402	−	0.867520i	$-0.665713\pi$
$859$	−29.1564	−0.994805	−0.497402	+	0.867520i	$0.665713\pi$
$860$	−6.01163	−0.204995
$861$	−60.7775	−2.07129
$862$	−37.1623	−1.26575
$863$	−29.7157	−1.01153	−0.505767	−	0.862670i	$-0.668790\pi$
$863$	−29.7157	−1.01153	−0.505767	+	0.862670i	$0.668790\pi$
$864$	1.00000	0.0340207
$865$	2.91427	0.0990883
$866$	30.6540	1.04166
$867$	−16.3985	−0.556922
$868$	−43.3802	−1.47242
$869$	0	0
$870$	−2.01882	−0.0684445
$871$	−0.784103	−0.0265683
$872$	8.94427	0.302891
$873$	−13.4541	−0.455351
$874$	0.522153	0.0176621
$875$	5.10899	0.172715
$876$	−10.9443	−0.369773
$877$	−26.7194	−0.902249	−0.451125	−	0.892461i	$-0.648977\pi$
$877$	−26.7194	−0.902249	−0.451125	+	0.892461i	$0.648977\pi$
$878$	−7.06017	−0.238269
$879$	−22.6601	−0.764307
$880$	0	0
$881$	2.72012	0.0916431	0.0458216	−	0.998950i	$-0.485409\pi$
$881$	2.72012	0.0916431	0.0458216	+	0.998950i	$0.485409\pi$
$882$	19.1018	0.643191
$883$	34.7250	1.16859	0.584295	−	0.811541i	$-0.301371\pi$
$883$	34.7250	1.16859	0.584295	+	0.811541i	$0.301371\pi$
$884$	1.03416	0.0347825
$885$	5.32624	0.179040
$886$	14.5925	0.490244
$887$	37.2657	1.25126	0.625630	−	0.780120i	$-0.284842\pi$
$887$	37.2657	1.25126	0.625630	+	0.780120i	$0.284842\pi$
$888$	−3.93310	−0.131986
$889$	−35.5730	−1.19308
$890$	9.67821	0.324414
$891$	0	0
$892$	9.10899	0.304992
$893$	0.515949	0.0172656
$894$	15.2477	0.509959
$895$	−1.56231	−0.0522221
$896$	−5.10899	−0.170679
$897$	−8.86528	−0.296003
$898$	12.7687	0.426096
$899$	17.1417	0.571709
$900$	1.00000	0.0333333
$901$	−8.02327	−0.267294
$902$	0	0
$903$	−30.7134	−1.02208
$904$	−5.72703	−0.190478
$905$	−18.4721	−0.614035
$906$	−6.56921	−0.218247
$907$	−39.7936	−1.32133	−0.660663	−	0.750682i	$-0.729725\pi$
$907$	−39.7936	−1.32133	−0.660663	+	0.750682i	$0.729725\pi$
$908$	−20.6901	−0.686626
$909$	10.6408	0.352934
$910$	−6.81247	−0.225831
$911$	−12.8234	−0.424857	−0.212429	−	0.977177i	$-0.568137\pi$
$911$	−12.8234	−0.424857	−0.212429	+	0.977177i	$0.568137\pi$
$912$	0.0785371	0.00260062
$913$	0	0
$914$	17.3426	0.573642
$915$	−3.74585	−0.123834
$916$	10.9819	0.362853
$917$	−11.2355	−0.371029
$918$	−0.775565	−0.0255975
$919$	37.1139	1.22427	0.612137	−	0.790752i	$-0.290310\pi$
$919$	37.1139	1.22427	0.612137	+	0.790752i	$0.290310\pi$
$920$	−6.64849	−0.219194
$921$	29.3158	0.965988
$922$	2.99355	0.0985873
$923$	3.08697	0.101609
$924$	0	0
$925$	−3.93310	−0.129319
$926$	−16.2589	−0.534300
$927$	16.7087	0.548784
$928$	2.01882	0.0662711
$929$	9.97000	0.327105	0.163553	−	0.986535i	$-0.447705\pi$
$929$	9.97000	0.327105	0.163553	+	0.986535i	$0.447705\pi$
$930$	−8.49096	−0.278429
$931$	1.50020	0.0491670
$932$	2.96309	0.0970594
$933$	11.3570	0.371811
$934$	−18.5707	−0.607652
$935$	0	0
$936$	−1.33343	−0.0435844
$937$	−11.9767	−0.391263	−0.195631	−	0.980677i	$-0.562676\pi$
$937$	−11.9767	−0.391263	−0.195631	+	0.980677i	$0.562676\pi$
$938$	−3.00427	−0.0980929
$939$	−3.17664	−0.103666
$940$	−6.56950	−0.214273
$941$	−5.50996	−0.179619	−0.0898097	−	0.995959i	$-0.528626\pi$
$941$	−5.50996	−0.179619	−0.0898097	+	0.995959i	$0.528626\pi$
$942$	−9.30815	−0.303276
$943$	79.0917	2.57558
$944$	−5.32624	−0.173354
$945$	5.10899	0.166196
$946$	0	0
$947$	−27.3946	−0.890206	−0.445103	−	0.895479i	$-0.646833\pi$
$947$	−27.3946	−0.890206	−0.445103	+	0.895479i	$0.646833\pi$
$948$	−12.3267	−0.400352
$949$	14.5934	0.473722
$950$	0.0785371	0.00254808
$951$	4.73101	0.153414
$952$	3.96236	0.128421
$953$	−7.98985	−0.258816	−0.129408	−	0.991591i	$-0.541308\pi$
$953$	−7.98985	−0.258816	−0.129408	+	0.991591i	$0.541308\pi$
$954$	10.3451	0.334934
$955$	−20.7278	−0.670735
$956$	−8.56978	−0.277166
$957$	0	0
$958$	30.5554	0.987200
$959$	11.1166	0.358975
$960$	−1.00000	−0.0322749
$961$	41.0964	1.32569
$962$	5.24450	0.169089
$963$	−17.5511	−0.565577
$964$	−7.97000	−0.256696
$965$	1.37079	0.0441273
$966$	−33.9671	−1.09287
$967$	19.0966	0.614106	0.307053	−	0.951692i	$-0.400657\pi$
$967$	19.0966	0.614106	0.307053	+	0.951692i	$0.400657\pi$
$968$	0	0
$969$	−0.0609106	−0.00195673
$970$	13.4541	0.431984
$971$	0.149777	0.00480656	0.00240328	−	0.999997i	$-0.499235\pi$
$971$	0.149777	0.00480656	0.00240328	+	0.999997i	$0.499235\pi$
$972$	1.00000	0.0320750
$973$	52.6605	1.68822
$974$	−0.508303	−0.0162871
$975$	−1.33343	−0.0427039
$976$	3.74585	0.119902
$977$	−19.1384	−0.612292	−0.306146	−	0.951984i	$-0.599040\pi$
$977$	−19.1384	−0.612292	−0.306146	+	0.951984i	$0.599040\pi$
$978$	−18.7018	−0.598016
$979$	0	0
$980$	−19.1018	−0.610185
$981$	8.94427	0.285569
$982$	−39.3943	−1.25712
$983$	8.58575	0.273843	0.136921	−	0.990582i	$-0.456279\pi$
$983$	8.58575	0.273843	0.136921	+	0.990582i	$0.456279\pi$
$984$	11.8962	0.379237
$985$	−5.01135	−0.159675
$986$	−1.56573	−0.0498629
$987$	−33.5635	−1.06834
$988$	−0.104723	−0.00333170
$989$	39.9683	1.27092
$990$	0	0
$991$	−11.3086	−0.359230	−0.179615	−	0.983737i	$-0.557485\pi$
$991$	−11.3086	−0.359230	−0.179615	+	0.983737i	$0.557485\pi$
$992$	8.49096	0.269588
$993$	30.0424	0.953366
$994$	11.8276	0.375150
$995$	−23.3086	−0.738933
$996$	8.00000	0.253490
$997$	37.0321	1.17282	0.586409	−	0.810015i	$-0.300541\pi$
$997$	37.0321	1.17282	0.586409	+	0.810015i	$0.300541\pi$
$998$	21.4608	0.679329
$999$	−3.93310	−0.124438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bs.1.1		4
11.2	odd	10		330.2.m.f.301.2	yes	8
11.6	odd	10		330.2.m.f.91.2	✓	8
11.10	odd	2		3630.2.a.bq.1.4		4
33.2	even	10		990.2.n.i.631.2		8
33.17	even	10		990.2.n.i.91.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.91.2	✓	8	11.6	odd	10
330.2.m.f.301.2	yes	8	11.2	odd	10
990.2.n.i.91.2		8	33.17	even	10
990.2.n.i.631.2		8	33.2	even	10
3630.2.a.bq.1.4		4	11.10	odd	2
3630.2.a.bs.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.10899 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -5.10899 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} -1.33343 q^{13} -5.10899 q^{14} -1.00000 q^{15} +1.00000 q^{16} -0.775565 q^{17} +1.00000 q^{18} +0.0785371 q^{19} -1.00000 q^{20} -5.10899 q^{21} +6.64849 q^{23} +1.00000 q^{24} +1.00000 q^{25} -1.33343 q^{26} +1.00000 q^{27} -5.10899 q^{28} +2.01882 q^{29} -1.00000 q^{30} +8.49096 q^{31} +1.00000 q^{32} -0.775565 q^{34} +5.10899 q^{35} +1.00000 q^{36} -3.93310 q^{37} +0.0785371 q^{38} -1.33343 q^{39} -1.00000 q^{40} +11.8962 q^{41} -5.10899 q^{42} +6.01163 q^{43} -1.00000 q^{45} +6.64849 q^{46} +6.56950 q^{47} +1.00000 q^{48} +19.1018 q^{49} +1.00000 q^{50} -0.775565 q^{51} -1.33343 q^{52} +10.3451 q^{53} +1.00000 q^{54} -5.10899 q^{56} +0.0785371 q^{57} +2.01882 q^{58} -5.32624 q^{59} -1.00000 q^{60} +3.74585 q^{61} +8.49096 q^{62} -5.10899 q^{63} +1.00000 q^{64} +1.33343 q^{65} +0.588036 q^{67} -0.775565 q^{68} +6.64849 q^{69} +5.10899 q^{70} -2.31506 q^{71} +1.00000 q^{72} -10.9443 q^{73} -3.93310 q^{74} +1.00000 q^{75} +0.0785371 q^{76} -1.33343 q^{78} -12.3267 q^{79} -1.00000 q^{80} +1.00000 q^{81} +11.8962 q^{82} +8.00000 q^{83} -5.10899 q^{84} +0.775565 q^{85} +6.01163 q^{86} +2.01882 q^{87} -9.67821 q^{89} -1.00000 q^{90} +6.81247 q^{91} +6.64849 q^{92} +8.49096 q^{93} +6.56950 q^{94} -0.0785371 q^{95} +1.00000 q^{96} -13.4541 q^{97} +19.1018 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{12} + 2 q^{13} + q^{14} - 4 q^{15} + 4 q^{16} + 11 q^{17} + 4 q^{18} + q^{19} - 4 q^{20} + q^{21} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + q^{28} + 9 q^{29} - 4 q^{30} + 17 q^{31} + 4 q^{32} + 11 q^{34} - q^{35} + 4 q^{36} + 8 q^{37} + q^{38} + 2 q^{39} - 4 q^{40} - 11 q^{41} + q^{42} + q^{43} - 4 q^{45} + 10 q^{47} + 4 q^{48} + 31 q^{49} + 4 q^{50} + 11 q^{51} + 2 q^{52} + 11 q^{53} + 4 q^{54} + q^{56} + q^{57} + 9 q^{58} + 10 q^{59} - 4 q^{60} - 10 q^{61} + 17 q^{62} + q^{63} + 4 q^{64} - 2 q^{65} + 9 q^{67} + 11 q^{68} - q^{70} + 10 q^{71} + 4 q^{72} - 8 q^{73} + 8 q^{74} + 4 q^{75} + q^{76} + 2 q^{78} - 7 q^{79} - 4 q^{80} + 4 q^{81} - 11 q^{82} + 32 q^{83} + q^{84} - 11 q^{85} + q^{86} + 9 q^{87} - 23 q^{89} - 4 q^{90} + 48 q^{91} + 17 q^{93} + 10 q^{94} - q^{95} + 4 q^{96} - 2 q^{97} + 31 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^12 + 2 * q^13 + q^14 - 4 * q^15 + 4 * q^16 + 11 * q^17 + 4 * q^18 + q^19 - 4 * q^20 + q^21 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + q^28 + 9 * q^29 - 4 * q^30 + 17 * q^31 + 4 * q^32 + 11 * q^34 - q^35 + 4 * q^36 + 8 * q^37 + q^38 + 2 * q^39 - 4 * q^40 - 11 * q^41 + q^42 + q^43 - 4 * q^45 + 10 * q^47 + 4 * q^48 + 31 * q^49 + 4 * q^50 + 11 * q^51 + 2 * q^52 + 11 * q^53 + 4 * q^54 + q^56 + q^57 + 9 * q^58 + 10 * q^59 - 4 * q^60 - 10 * q^61 + 17 * q^62 + q^63 + 4 * q^64 - 2 * q^65 + 9 * q^67 + 11 * q^68 - q^70 + 10 * q^71 + 4 * q^72 - 8 * q^73 + 8 * q^74 + 4 * q^75 + q^76 + 2 * q^78 - 7 * q^79 - 4 * q^80 + 4 * q^81 - 11 * q^82 + 32 * q^83 + q^84 - 11 * q^85 + q^86 + 9 * q^87 - 23 * q^89 - 4 * q^90 + 48 * q^91 + 17 * q^93 + 10 * q^94 - q^95 + 4 * q^96 - 2 * q^97 + 31 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more