LMFDB - Embedded newform 3630.2.a.bs.1.4

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			1.4
Root			$3.77556$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.49096 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.49096 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +2.33343 q^{13} +4.49096 q^{14} -1.00000 q^{15} +1.00000 q^{16} +5.15753 q^{17} +1.00000 q^{18} +6.01163 q^{19} -1.00000 q^{20} +4.49096 q^{21} -8.88456 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.33343 q^{26} +1.00000 q^{27} +4.49096 q^{28} -7.58113 q^{29} -1.00000 q^{30} -1.10899 q^{31} +1.00000 q^{32} +5.15753 q^{34} -4.49096 q^{35} +1.00000 q^{36} +7.93310 q^{37} +6.01163 q^{38} +2.33343 q^{39} -1.00000 q^{40} -9.56995 q^{41} +4.49096 q^{42} +0.0785371 q^{43} -1.00000 q^{45} -8.88456 q^{46} +2.90264 q^{47} +1.00000 q^{48} +13.1687 q^{49} +1.00000 q^{50} +5.15753 q^{51} +2.33343 q^{52} +0.745110 q^{53} +1.00000 q^{54} +4.49096 q^{56} +6.01163 q^{57} -7.58113 q^{58} -5.32624 q^{59} -1.00000 q^{60} -15.4541 q^{61} -1.10899 q^{62} +4.49096 q^{63} +1.00000 q^{64} -2.33343 q^{65} -1.67821 q^{67} +5.15753 q^{68} -8.88456 q^{69} -4.49096 q^{70} +9.55113 q^{71} +1.00000 q^{72} -10.9443 q^{73} +7.93310 q^{74} +1.00000 q^{75} +6.01163 q^{76} +2.33343 q^{78} +5.47259 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.56995 q^{82} +8.00000 q^{83} +4.49096 q^{84} -5.15753 q^{85} +0.0785371 q^{86} -7.58113 q^{87} -7.41196 q^{89} -1.00000 q^{90} +10.4793 q^{91} -8.88456 q^{92} -1.10899 q^{93} +2.90264 q^{94} -6.01163 q^{95} +1.00000 q^{96} +5.74585 q^{97} +13.1687 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	4.49096	1.69742	0.848711	−	0.528856i	$-0.177379\pi$
$7$	4.49096	1.69742	0.848711	+	0.528856i	$0.177379\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	1.00000	0.288675
$13$	2.33343	0.647176	0.323588	−	0.946198i	$-0.395111\pi$
$13$	2.33343	0.647176	0.323588	+	0.946198i	$0.395111\pi$
$14$	4.49096	1.20026
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	5.15753	1.25088	0.625442	−	0.780270i	$-0.284918\pi$
$17$	5.15753	1.25088	0.625442	+	0.780270i	$0.284918\pi$
$18$	1.00000	0.235702
$19$	6.01163	1.37916	0.689582	−	0.724208i	$-0.257794\pi$
$19$	6.01163	1.37916	0.689582	+	0.724208i	$0.257794\pi$
$20$	−1.00000	−0.223607
$21$	4.49096	0.980007
$22$	0	0
$23$	−8.88456	−1.85256	−0.926279	−	0.376838i	$-0.877011\pi$
$23$	−8.88456	−1.85256	−0.926279	+	0.376838i	$0.877011\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	2.33343	0.457623
$27$	1.00000	0.192450
$28$	4.49096	0.848711
$29$	−7.58113	−1.40778	−0.703890	−	0.710309i	$-0.748555\pi$
$29$	−7.58113	−1.40778	−0.703890	+	0.710309i	$0.748555\pi$
$30$	−1.00000	−0.182574
$31$	−1.10899	−0.199181	−0.0995905	−	0.995029i	$-0.531753\pi$
$31$	−1.10899	−0.199181	−0.0995905	+	0.995029i	$0.531753\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	5.15753	0.884509
$35$	−4.49096	−0.759111
$36$	1.00000	0.166667
$37$	7.93310	1.30419	0.652096	−	0.758136i	$-0.273890\pi$
$37$	7.93310	1.30419	0.652096	+	0.758136i	$0.273890\pi$
$38$	6.01163	0.975216
$39$	2.33343	0.373647
$40$	−1.00000	−0.158114
$41$	−9.56995	−1.49458	−0.747288	−	0.664501i	$-0.768644\pi$
$41$	−9.56995	−1.49458	−0.747288	+	0.664501i	$0.768644\pi$
$42$	4.49096	0.692970
$43$	0.0785371	0.0119768	0.00598839	−	0.999982i	$-0.498094\pi$
$43$	0.0785371	0.0119768	0.00598839	+	0.999982i	$0.498094\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−8.88456	−1.30996
$47$	2.90264	0.423394	0.211697	−	0.977335i	$-0.432101\pi$
$47$	2.90264	0.423394	0.211697	+	0.977335i	$0.432101\pi$
$48$	1.00000	0.144338
$49$	13.1687	1.88124
$50$	1.00000	0.141421
$51$	5.15753	0.722199
$52$	2.33343	0.323588
$53$	0.745110	0.102349	0.0511743	−	0.998690i	$-0.483704\pi$
$53$	0.745110	0.102349	0.0511743	+	0.998690i	$0.483704\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.49096	0.600130
$57$	6.01163	0.796260
$58$	−7.58113	−0.995451
$59$	−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
$61$	−15.4541	−1.97869	−0.989344	−	0.145595i	$-0.953491\pi$
$61$	−15.4541	−1.97869	−0.989344	+	0.145595i	$0.953491\pi$
$62$	−1.10899	−0.140842
$63$	4.49096	0.565808
$64$	1.00000	0.125000
$65$	−2.33343	−0.289426
$66$	0	0
$67$	−1.67821	−0.205025	−0.102513	−	0.994732i	$-0.532688\pi$
$67$	−1.67821	−0.205025	−0.102513	+	0.994732i	$0.532688\pi$
$68$	5.15753	0.625442
$69$	−8.88456	−1.06958
$70$	−4.49096	−0.536772
$71$	9.55113	1.13351	0.566755	−	0.823886i	$-0.308198\pi$
$71$	9.55113	1.13351	0.566755	+	0.823886i	$0.308198\pi$
$72$	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	$0.721258\pi$
$74$	7.93310	0.922204
$75$	1.00000	0.115470
$76$	6.01163	0.689582
$77$	0	0
$78$	2.33343	0.264209
$79$	5.47259	0.615715	0.307857	−	0.951433i	$-0.400388\pi$
$79$	5.47259	0.615715	0.307857	+	0.951433i	$0.400388\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−9.56995	−1.05682
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	4.49096	0.490004
$85$	−5.15753	−0.559413
$86$	0.0785371	0.00846887
$87$	−7.58113	−0.812782
$88$	0	0
$89$	−7.41196	−0.785667	−0.392833	−	0.919610i	$-0.628505\pi$
$89$	−7.41196	−0.785667	−0.392833	+	0.919610i	$0.628505\pi$
$90$	−1.00000	−0.105409
$91$	10.4793	1.09853
$92$	−8.88456	−0.926279
$93$	−1.10899	−0.114997
$94$	2.90264	0.299385
$95$	−6.01163	−0.616781
$96$	1.00000	0.102062
$97$	5.74585	0.583403	0.291701	−	0.956509i	$-0.405779\pi$
$97$	5.74585	0.583403	0.291701	+	0.956509i	$0.405779\pi$
$98$	13.1687	1.33024
$99$	0	0
$100$	1.00000	0.100000
$101$	16.5739	1.64917	0.824584	−	0.565739i	$-0.191409\pi$
$101$	16.5739	1.64917	0.824584	+	0.565739i	$0.191409\pi$
$102$	5.15753	0.510672
$103$	−1.09063	−0.107463	−0.0537313	−	0.998555i	$-0.517111\pi$
$103$	−1.09063	−0.107463	−0.0537313	+	0.998555i	$0.517111\pi$
$104$	2.33343	0.228811
$105$	−4.49096	−0.438273
$106$	0.745110	0.0723714
$107$	−5.68494	−0.549584	−0.274792	−	0.961504i	$-0.588609\pi$
$107$	−5.68494	−0.549584	−0.274792	+	0.961504i	$0.588609\pi$
$108$	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
$111$	7.93310	0.752976
$112$	4.49096	0.424356
$113$	3.87292	0.364334	0.182167	−	0.983268i	$-0.441689\pi$
$113$	3.87292	0.364334	0.182167	+	0.983268i	$0.441689\pi$
$114$	6.01163	0.563041
$115$	8.88456	0.828489
$116$	−7.58113	−0.703890
$117$	2.33343	0.215725
$118$	−5.32624	−0.490320
$119$	23.1623	2.12328
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−15.4541	−1.39914
$123$	−9.56995	−0.862894
$124$	−1.10899	−0.0995905
$125$	−1.00000	−0.0894427
$126$	4.49096	0.400086
$127$	8.36343	0.742134	0.371067	−	0.928606i	$-0.378992\pi$
$127$	8.36343	0.742134	0.371067	+	0.928606i	$0.378992\pi$
$128$	1.00000	0.0883883
$129$	0.0785371	0.00691480
$130$	−2.33343	−0.204655
$131$	−7.40079	−0.646610	−0.323305	−	0.946295i	$-0.604794\pi$
$131$	−7.40079	−0.646610	−0.323305	+	0.946295i	$0.604794\pi$
$132$	0	0
$133$	26.9980	2.34102
$134$	−1.67821	−0.144975
$135$	−1.00000	−0.0860663
$136$	5.15753	0.442255
$137$	−4.44214	−0.379517	−0.189759	−	0.981831i	$-0.560771\pi$
$137$	−4.44214	−0.379517	−0.189759	+	0.981831i	$0.560771\pi$
$138$	−8.88456	−0.756304
$139$	−19.9074	−1.68852	−0.844260	−	0.535933i	$-0.819960\pi$
$139$	−19.9074	−1.68852	−0.844260	+	0.535933i	$0.819960\pi$
$140$	−4.49096	−0.379555
$141$	2.90264	0.244446
$142$	9.55113	0.801513
$143$	0	0
$144$	1.00000	0.0833333
$145$	7.58113	0.629578
$146$	−10.9443	−0.905754
$147$	13.1687	1.08614
$148$	7.93310	0.652096
$149$	9.31461	0.763082	0.381541	−	0.924352i	$-0.375393\pi$
$149$	9.31461	0.763082	0.381541	+	0.924352i	$0.375393\pi$
$150$	1.00000	0.0816497
$151$	−13.9029	−1.13140	−0.565702	−	0.824610i	$-0.691395\pi$
$151$	−13.9029	−1.13140	−0.565702	+	0.824610i	$0.691395\pi$
$152$	6.01163	0.487608
$153$	5.15753	0.416962
$154$	0	0
$155$	1.10899	0.0890764
$156$	2.33343	0.186824
$157$	9.89175	0.789447	0.394724	−	0.918800i	$-0.370840\pi$
$157$	9.89175	0.789447	0.394724	+	0.918800i	$0.370840\pi$
$158$	5.47259	0.435376
$159$	0.745110	0.0590910
$160$	−1.00000	−0.0790569
$161$	−39.9002	−3.14457
$162$	1.00000	0.0785674
$163$	6.43124	0.503734	0.251867	−	0.967762i	$-0.418955\pi$
$163$	6.43124	0.503734	0.251867	+	0.967762i	$0.418955\pi$
$164$	−9.56995	−0.747288
$165$	0	0
$166$	8.00000	0.620920
$167$	6.04163	0.467515	0.233758	−	0.972295i	$-0.424898\pi$
$167$	6.04163	0.467515	0.233758	+	0.972295i	$0.424898\pi$
$168$	4.49096	0.346485
$169$	−7.55512	−0.581163
$170$	−5.15753	−0.395565
$171$	6.01163	0.459721
$172$	0.0785371	0.00598839
$173$	−0.648032	−0.0492690	−0.0246345	−	0.999697i	$-0.507842\pi$
$173$	−0.648032	−0.0492690	−0.0246345	+	0.999697i	$0.507842\pi$
$174$	−7.58113	−0.574724
$175$	4.49096	0.339485
$176$	0	0
$177$	−5.32624	−0.400345
$178$	−7.41196	−0.555550
$179$	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	$0.259141\pi$
$182$	10.4793	0.776779
$183$	−15.4541	−1.14240
$184$	−8.88456	−0.654978
$185$	−7.93310	−0.583253
$186$	−1.10899	−0.0813153
$187$	0	0
$188$	2.90264	0.211697
$189$	4.49096	0.326669
$190$	−6.01163	−0.436130
$191$	−17.6720	−1.27870	−0.639352	−	0.768914i	$-0.720797\pi$
$191$	−17.6720	−1.27870	−0.639352	+	0.768914i	$0.720797\pi$
$192$	1.00000	0.0721688
$193$	10.4954	0.755476	0.377738	−	0.925913i	$-0.376702\pi$
$193$	10.4954	0.755476	0.377738	+	0.925913i	$0.376702\pi$
$194$	5.74585	0.412528
$195$	−2.33343	−0.167100
$196$	13.1687	0.940622
$197$	10.0788	0.718086	0.359043	−	0.933321i	$-0.383103\pi$
$197$	10.0788	0.718086	0.359043	+	0.933321i	$0.383103\pi$
$198$	0	0
$199$	−13.6906	−0.970499	−0.485250	−	0.874376i	$-0.661271\pi$
$199$	−13.6906	−0.970499	−0.485250	+	0.874376i	$0.661271\pi$
$200$	1.00000	0.0707107
$201$	−1.67821	−0.118371
$202$	16.5739	1.16614
$203$	−34.0465	−2.38960
$204$	5.15753	0.361099
$205$	9.56995	0.668394
$206$	−1.09063	−0.0759876
$207$	−8.88456	−0.617519
$208$	2.33343	0.161794
$209$	0	0
$210$	−4.49096	−0.309906
$211$	−22.8481	−1.57293	−0.786464	−	0.617636i	$-0.788091\pi$
$211$	−22.8481	−1.57293	−0.786464	+	0.617636i	$0.788091\pi$
$212$	0.745110	0.0511743
$213$	9.55113	0.654433
$214$	−5.68494	−0.388614
$215$	−0.0785371	−0.00535618
$216$	1.00000	0.0680414
$217$	−4.98044	−0.338094
$218$	8.94427	0.605783
$219$	−10.9443	−0.739545
$220$	0	0
$221$	12.0347	0.809543
$222$	7.93310	0.532435
$223$	−0.490958	−0.0328770	−0.0164385	−	0.999865i	$-0.505233\pi$
$223$	−0.490958	−0.0328770	−0.0164385	+	0.999865i	$0.505233\pi$
$224$	4.49096	0.300065
$225$	1.00000	0.0666667
$226$	3.87292	0.257623
$227$	−1.49022	−0.0989093	−0.0494547	−	0.998776i	$-0.515748\pi$
$227$	−1.49022	−0.0989093	−0.0494547	+	0.998776i	$0.515748\pi$
$228$	6.01163	0.398130
$229$	−8.21798	−0.543060	−0.271530	−	0.962430i	$-0.587530\pi$
$229$	−8.21798	−0.543060	−0.271530	+	0.962430i	$0.587530\pi$
$230$	8.88456	0.585830
$231$	0	0
$232$	−7.58113	−0.497725
$233$	−6.63686	−0.434795	−0.217397	−	0.976083i	$-0.569757\pi$
$233$	−6.63686	−0.434795	−0.217397	+	0.976083i	$0.569757\pi$
$234$	2.33343	0.152541
$235$	−2.90264	−0.189347
$236$	−5.32624	−0.346709
$237$	5.47259	0.355483
$238$	23.1623	1.50139
$239$	6.09764	0.394424	0.197212	−	0.980361i	$-0.436811\pi$
$239$	6.09764	0.394424	0.197212	+	0.980361i	$0.436811\pi$
$240$	−1.00000	−0.0645497
$241$	−5.70376	−0.367412	−0.183706	−	0.982981i	$-0.558809\pi$
$241$	−5.70376	−0.367412	−0.183706	+	0.982981i	$0.558809\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−15.4541	−0.989344
$245$	−13.1687	−0.841318
$246$	−9.56995	−0.610158
$247$	14.0277	0.892562
$248$	−1.10899	−0.0704211
$249$	8.00000	0.506979
$250$	−1.00000	−0.0632456
$251$	−2.60714	−0.164561	−0.0822806	−	0.996609i	$-0.526220\pi$
$251$	−2.60714	−0.164561	−0.0822806	+	0.996609i	$0.526220\pi$
$252$	4.49096	0.282904
$253$	0	0
$254$	8.36343	0.524768
$255$	−5.15753	−0.322977
$256$	1.00000	0.0625000
$257$	18.4360	1.15000	0.575002	−	0.818152i	$-0.305001\pi$
$257$	18.4360	1.15000	0.575002	+	0.818152i	$0.305001\pi$
$258$	0.0785371	0.00488950
$259$	35.6272	2.21377
$260$	−2.33343	−0.144713
$261$	−7.58113	−0.469260
$262$	−7.40079	−0.457222
$263$	24.4285	1.50633	0.753163	−	0.657834i	$-0.228527\pi$
$263$	24.4285	1.50633	0.753163	+	0.657834i	$0.228527\pi$
$264$	0	0
$265$	−0.745110	−0.0457717
$266$	26.9980	1.65535
$267$	−7.41196	−0.453605
$268$	−1.67821	−0.102513
$269$	−11.0119	−0.671408	−0.335704	−	0.941967i	$-0.608974\pi$
$269$	−11.0119	−0.671408	−0.335704	+	0.941967i	$0.608974\pi$
$270$	−1.00000	−0.0608581
$271$	0.647750	0.0393480	0.0196740	−	0.999806i	$-0.493737\pi$
$271$	0.647750	0.0393480	0.0196740	+	0.999806i	$0.493737\pi$
$272$	5.15753	0.312721
$273$	10.4793	0.634238
$274$	−4.44214	−0.268359
$275$	0	0
$276$	−8.88456	−0.534788
$277$	−24.6304	−1.47990	−0.739949	−	0.672663i	$-0.765150\pi$
$277$	−24.6304	−1.47990	−0.739949	+	0.672663i	$0.765150\pi$
$278$	−19.9074	−1.19396
$279$	−1.10899	−0.0663936
$280$	−4.49096	−0.268386
$281$	9.49170	0.566227	0.283114	−	0.959086i	$-0.408633\pi$
$281$	9.49170	0.566227	0.283114	+	0.959086i	$0.408633\pi$
$282$	2.90264	0.172850
$283$	−20.2113	−1.20143	−0.600717	−	0.799462i	$-0.705118\pi$
$283$	−20.2113	−1.20143	−0.600717	+	0.799462i	$0.705118\pi$
$284$	9.55113	0.566755
$285$	−6.01163	−0.356098
$286$	0	0
$287$	−42.9783	−2.53693
$288$	1.00000	0.0589256
$289$	9.60013	0.564713
$290$	7.58113	0.445179
$291$	5.74585	0.336828
$292$	−10.9443	−0.640465
$293$	−1.19398	−0.0697530	−0.0348765	−	0.999392i	$-0.511104\pi$
$293$	−1.19398	−0.0697530	−0.0348765	+	0.999392i	$0.511104\pi$
$294$	13.1687	0.768015
$295$	5.32624	0.310106
$296$	7.93310	0.461102
$297$	0	0
$298$	9.31461	0.539581
$299$	−20.7315	−1.19893
$300$	1.00000	0.0577350
$301$	0.352707	0.0203297
$302$	−13.9029	−0.800023
$303$	16.5739	0.952148
$304$	6.01163	0.344791
$305$	15.4541	0.884896
$306$	5.15753	0.294836
$307$	−11.3502	−0.647793	−0.323896	−	0.946093i	$-0.604993\pi$
$307$	−11.3502	−0.647793	−0.323896	+	0.946093i	$0.604993\pi$
$308$	0	0
$309$	−1.09063	−0.0620436
$310$	1.10899	0.0629865
$311$	−15.1766	−0.860588	−0.430294	−	0.902689i	$-0.641590\pi$
$311$	−15.1766	−0.860588	−0.430294	+	0.902689i	$0.641590\pi$
$312$	2.33343	0.132104
$313$	23.3570	1.32021	0.660107	−	0.751171i	$-0.270511\pi$
$313$	23.3570	1.32021	0.660107	+	0.751171i	$0.270511\pi$
$314$	9.89175	0.558224
$315$	−4.49096	−0.253037
$316$	5.47259	0.307857
$317$	10.6641	0.598956	0.299478	−	0.954103i	$-0.403187\pi$
$317$	10.6641	0.598956	0.299478	+	0.954103i	$0.403187\pi$
$318$	0.745110	0.0417837
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−5.68494	−0.317302
$322$	−39.9002	−2.22355
$323$	31.0052	1.72517
$324$	1.00000	0.0555556
$325$	2.33343	0.129435
$326$	6.43124	0.356194
$327$	8.94427	0.494619
$328$	−9.56995	−0.528412
$329$	13.0356	0.718678
$330$	0	0
$331$	−2.42434	−0.133254	−0.0666268	−	0.997778i	$-0.521224\pi$
$331$	−2.42434	−0.133254	−0.0666268	+	0.997778i	$0.521224\pi$
$332$	8.00000	0.439057
$333$	7.93310	0.434731
$334$	6.04163	0.330583
$335$	1.67821	0.0916902
$336$	4.49096	0.245002
$337$	−1.17664	−0.0640954	−0.0320477	−	0.999486i	$-0.510203\pi$
$337$	−1.17664	−0.0640954	−0.0320477	+	0.999486i	$0.510203\pi$
$338$	−7.55512	−0.410944
$339$	3.87292	0.210348
$340$	−5.15753	−0.279706
$341$	0	0
$342$	6.01163	0.325072
$343$	27.7034	1.49584
$344$	0.0785371	0.00423443
$345$	8.88456	0.478328
$346$	−0.648032	−0.0348384
$347$	−23.3570	−1.25387	−0.626934	−	0.779072i	$-0.715690\pi$
$347$	−23.3570	−1.25387	−0.626934	+	0.779072i	$0.715690\pi$
$348$	−7.58113	−0.406391
$349$	−0.375059	−0.0200764	−0.0100382	−	0.999950i	$-0.503195\pi$
$349$	−0.375059	−0.0200764	−0.0100382	+	0.999950i	$0.503195\pi$
$350$	4.49096	0.240052
$351$	2.33343	0.124549
$352$	0	0
$353$	2.07854	0.110629	0.0553147	−	0.998469i	$-0.482384\pi$
$353$	2.07854	0.110629	0.0553147	+	0.998469i	$0.482384\pi$
$354$	−5.32624	−0.283086
$355$	−9.55113	−0.506921
$356$	−7.41196	−0.392833
$357$	23.1623	1.22588
$358$	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
$361$	17.1397	0.902091
$362$	18.4721	0.970874
$363$	0	0
$364$	10.4793	0.549266
$365$	10.9443	0.572849
$366$	−15.4541	−0.807796
$367$	11.6706	0.609198	0.304599	−	0.952481i	$-0.401478\pi$
$367$	11.6706	0.609198	0.304599	+	0.952481i	$0.401478\pi$
$368$	−8.88456	−0.463140
$369$	−9.56995	−0.498192
$370$	−7.93310	−0.412422
$371$	3.34626	0.173729
$372$	−1.10899	−0.0574986
$373$	−10.1687	−0.526516	−0.263258	−	0.964726i	$-0.584797\pi$
$373$	−10.1687	−0.526516	−0.263258	+	0.964726i	$0.584797\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	2.90264	0.149692
$377$	−17.6900	−0.911082
$378$	4.49096	0.230990
$379$	11.0825	0.569271	0.284636	−	0.958636i	$-0.408127\pi$
$379$	11.0825	0.569271	0.284636	+	0.958636i	$0.408127\pi$
$380$	−6.01163	−0.308390
$381$	8.36343	0.428471
$382$	−17.6720	−0.904180
$383$	21.3082	1.08880	0.544398	−	0.838827i	$-0.316758\pi$
$383$	21.3082	1.08880	0.544398	+	0.838827i	$0.316758\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	10.4954	0.534202
$387$	0.0785371	0.00399226
$388$	5.74585	0.291701
$389$	−37.7362	−1.91330	−0.956651	−	0.291238i	$-0.905933\pi$
$389$	−37.7362	−1.91330	−0.956651	+	0.291238i	$0.905933\pi$
$390$	−2.33343	−0.118158
$391$	−45.8224	−2.31734
$392$	13.1687	0.665120
$393$	−7.40079	−0.373320
$394$	10.0788	0.507764
$395$	−5.47259	−0.275356
$396$	0	0
$397$	−22.4348	−1.12597	−0.562985	−	0.826467i	$-0.690347\pi$
$397$	−22.4348	−1.12597	−0.562985	+	0.826467i	$0.690347\pi$
$398$	−13.6906	−0.686247
$399$	26.9980	1.35159
$400$	1.00000	0.0500000
$401$	−25.9002	−1.29339	−0.646697	−	0.762747i	$-0.723850\pi$
$401$	−25.9002	−1.29339	−0.646697	+	0.762747i	$0.723850\pi$
$402$	−1.67821	−0.0837013
$403$	−2.58775	−0.128905
$404$	16.5739	0.824584
$405$	−1.00000	−0.0496904
$406$	−34.0465	−1.68970
$407$	0	0
$408$	5.15753	0.255336
$409$	−24.7921	−1.22589	−0.612945	−	0.790125i	$-0.710015\pi$
$409$	−24.7921	−1.22589	−0.612945	+	0.790125i	$0.710015\pi$
$410$	9.56995	0.472626
$411$	−4.44214	−0.219114
$412$	−1.09063	−0.0537313
$413$	−23.9199	−1.17702
$414$	−8.88456	−0.436652
$415$	−8.00000	−0.392705
$416$	2.33343	0.114406
$417$	−19.9074	−0.974868
$418$	0	0
$419$	27.8969	1.36285	0.681427	−	0.731886i	$-0.261360\pi$
$419$	27.8969	1.36285	0.681427	+	0.731886i	$0.261360\pi$
$420$	−4.49096	−0.219136
$421$	25.0052	1.21868	0.609339	−	0.792910i	$-0.291435\pi$
$421$	25.0052	1.21868	0.609339	+	0.792910i	$0.291435\pi$
$422$	−22.8481	−1.11223
$423$	2.90264	0.141131
$424$	0.745110	0.0361857
$425$	5.15753	0.250177
$426$	9.55113	0.462754
$427$	−69.4035	−3.35867
$428$	−5.68494	−0.274792
$429$	0	0
$430$	−0.0785371	−0.00378739
$431$	−17.9624	−0.865216	−0.432608	−	0.901582i	$-0.642407\pi$
$431$	−17.9624	−0.865216	−0.432608	+	0.901582i	$0.642407\pi$
$432$	1.00000	0.0481125
$433$	−26.9458	−1.29493	−0.647465	−	0.762095i	$-0.724171\pi$
$433$	−26.9458	−1.29493	−0.647465	+	0.762095i	$0.724171\pi$
$434$	−4.98044	−0.239069
$435$	7.58113	0.363487
$436$	8.94427	0.428353
$437$	−53.4107	−2.55498
$438$	−10.9443	−0.522938
$439$	−4.79393	−0.228802	−0.114401	−	0.993435i	$-0.536495\pi$
$439$	−4.79393	−0.228802	−0.114401	+	0.993435i	$0.536495\pi$
$440$	0	0
$441$	13.1687	0.627081
$442$	12.0347	0.572433
$443$	10.0600	0.477965	0.238982	−	0.971024i	$-0.423186\pi$
$443$	10.0600	0.477965	0.238982	+	0.971024i	$0.423186\pi$
$444$	7.93310	0.376488
$445$	7.41196	0.351361
$446$	−0.490958	−0.0232476
$447$	9.31461	0.440566
$448$	4.49096	0.212178
$449$	−0.498148	−0.0235091	−0.0117545	−	0.999931i	$-0.503742\pi$
$449$	−0.498148	−0.0235091	−0.0117545	+	0.999931i	$0.503742\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	3.87292	0.182167
$453$	−13.9029	−0.653216
$454$	−1.49022	−0.0699395
$455$	−10.4793	−0.491278
$456$	6.01163	0.281521
$457$	−1.85730	−0.0868811	−0.0434405	−	0.999056i	$-0.513832\pi$
$457$	−1.85730	−0.0868811	−0.0434405	+	0.999056i	$0.513832\pi$
$458$	−8.21798	−0.384001
$459$	5.15753	0.240733
$460$	8.88456	0.414245
$461$	−22.1394	−1.03114	−0.515568	−	0.856848i	$-0.672419\pi$
$461$	−22.1394	−1.03114	−0.515568	+	0.856848i	$0.672419\pi$
$462$	0	0
$463$	−22.1920	−1.03135	−0.515674	−	0.856785i	$-0.672459\pi$
$463$	−22.1920	−1.03135	−0.515674	+	0.856785i	$0.672459\pi$
$464$	−7.58113	−0.351945
$465$	1.10899	0.0514283
$466$	−6.63686	−0.307446
$467$	31.6953	1.46668	0.733342	−	0.679860i	$-0.237959\pi$
$467$	31.6953	1.46668	0.733342	+	0.679860i	$0.237959\pi$
$468$	2.33343	0.107863
$469$	−7.53675	−0.348015
$470$	−2.90264	−0.133889
$471$	9.89175	0.455788
$472$	−5.32624	−0.245160
$473$	0	0
$474$	5.47259	0.251365
$475$	6.01163	0.275833
$476$	23.1623	1.06164
$477$	0.745110	0.0341162
$478$	6.09764	0.278900
$479$	23.2217	1.06103	0.530513	−	0.847677i	$-0.321999\pi$
$479$	23.2217	1.06103	0.530513	+	0.847677i	$0.321999\pi$
$480$	−1.00000	−0.0456435
$481$	18.5113	0.844043
$482$	−5.70376	−0.259799
$483$	−39.9002	−1.81552
$484$	0	0
$485$	−5.74585	−0.260906
$486$	1.00000	0.0453609
$487$	−38.9081	−1.76309	−0.881547	−	0.472096i	$-0.843498\pi$
$487$	−38.9081	−1.76309	−0.881547	+	0.472096i	$0.843498\pi$
$488$	−15.4541	−0.699572
$489$	6.43124	0.290831
$490$	−13.1687	−0.594902
$491$	−4.66139	−0.210366	−0.105183	−	0.994453i	$-0.533543\pi$
$491$	−4.66139	−0.210366	−0.105183	+	0.994453i	$0.533543\pi$
$492$	−9.56995	−0.431447
$493$	−39.0999	−1.76097
$494$	14.0277	0.631136
$495$	0	0
$496$	−1.10899	−0.0497952
$497$	42.8937	1.92405
$498$	8.00000	0.358489
$499$	16.3933	0.733866	0.366933	−	0.930247i	$-0.380408\pi$
$499$	16.3933	0.733866	0.366933	+	0.930247i	$0.380408\pi$
$500$	−1.00000	−0.0447214
$501$	6.04163	0.269920
$502$	−2.60714	−0.116362
$503$	0.684656	0.0305273	0.0152636	−	0.999884i	$-0.495141\pi$
$503$	0.684656	0.0305273	0.0152636	+	0.999884i	$0.495141\pi$
$504$	4.49096	0.200043
$505$	−16.5739	−0.737531
$506$	0	0
$507$	−7.55512	−0.335534
$508$	8.36343	0.371067
$509$	5.38550	0.238708	0.119354	−	0.992852i	$-0.461918\pi$
$509$	5.38550	0.238708	0.119354	+	0.992852i	$0.461918\pi$
$510$	−5.15753	−0.228379
$511$	−49.1503	−2.17428
$512$	1.00000	0.0441942
$513$	6.01163	0.265420
$514$	18.4360	0.813176
$515$	1.09063	0.0480588
$516$	0.0785371	0.00345740
$517$	0	0
$518$	35.6272	1.56537
$519$	−0.648032	−0.0284455
$520$	−2.33343	−0.102328
$521$	7.60668	0.333255	0.166627	−	0.986020i	$-0.446712\pi$
$521$	7.60668	0.333255	0.166627	+	0.986020i	$0.446712\pi$
$522$	−7.58113	−0.331817
$523$	5.61204	0.245397	0.122699	−	0.992444i	$-0.460845\pi$
$523$	5.61204	0.245397	0.122699	+	0.992444i	$0.460845\pi$
$524$	−7.40079	−0.323305
$525$	4.49096	0.196001
$526$	24.4285	1.06513
$527$	−5.71966	−0.249152
$528$	0	0
$529$	55.9354	2.43197
$530$	−0.745110	−0.0323655
$531$	−5.32624	−0.231139
$532$	26.9980	1.17051
$533$	−22.3308	−0.967254
$534$	−7.41196	−0.320747
$535$	5.68494	0.245781
$536$	−1.67821	−0.0724874
$537$	1.56231	0.0674185
$538$	−11.0119	−0.474757
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	44.8337	1.92755	0.963776	−	0.266712i	$-0.0859372\pi$
$541$	44.8337	1.92755	0.963776	+	0.266712i	$0.0859372\pi$
$542$	0.647750	0.0278233
$543$	18.4721	0.792715
$544$	5.15753	0.221127
$545$	−8.94427	−0.383131
$546$	10.4793	0.448474
$547$	−10.7578	−0.459969	−0.229984	−	0.973194i	$-0.573868\pi$
$547$	−10.7578	−0.459969	−0.229984	+	0.973194i	$0.573868\pi$
$548$	−4.44214	−0.189759
$549$	−15.4541	−0.659563
$550$	0	0
$551$	−45.5750	−1.94156
$552$	−8.88456	−0.378152
$553$	24.5772	1.04513
$554$	−24.6304	−1.04645
$555$	−7.93310	−0.336741
$556$	−19.9074	−0.844260
$557$	21.0762	0.893029	0.446515	−	0.894776i	$-0.352665\pi$
$557$	21.0762	0.893029	0.446515	+	0.894776i	$0.352665\pi$
$558$	−1.10899	−0.0469474
$559$	0.183261	0.00775109
$560$	−4.49096	−0.189778
$561$	0	0
$562$	9.49170	0.400383
$563$	−26.4216	−1.11354	−0.556769	−	0.830668i	$-0.687959\pi$
$563$	−26.4216	−1.11354	−0.556769	+	0.830668i	$0.687959\pi$
$564$	2.90264	0.122223
$565$	−3.87292	−0.162935
$566$	−20.2113	−0.849542
$567$	4.49096	0.188603
$568$	9.55113	0.400757
$569$	−32.0892	−1.34525	−0.672624	−	0.739984i	$-0.734833\pi$
$569$	−32.0892	−1.34525	−0.672624	+	0.739984i	$0.734833\pi$
$570$	−6.01163	−0.251800
$571$	−0.842187	−0.0352444	−0.0176222	−	0.999845i	$-0.505610\pi$
$571$	−0.842187	−0.0352444	−0.0176222	+	0.999845i	$0.505610\pi$
$572$	0	0
$573$	−17.6720	−0.738260
$574$	−42.9783	−1.79388
$575$	−8.88456	−0.370512
$576$	1.00000	0.0416667
$577$	−15.5655	−0.648001	−0.324000	−	0.946057i	$-0.605028\pi$
$577$	−15.5655	−0.648001	−0.324000	+	0.946057i	$0.605028\pi$
$578$	9.60013	0.399313
$579$	10.4954	0.436174
$580$	7.58113	0.314789
$581$	35.9277	1.49053
$582$	5.74585	0.238173
$583$	0	0
$584$	−10.9443	−0.452877
$585$	−2.33343	−0.0964754
$586$	−1.19398	−0.0493229
$587$	19.2593	0.794918	0.397459	−	0.917620i	$-0.369892\pi$
$587$	19.2593	0.794918	0.397459	+	0.917620i	$0.369892\pi$
$588$	13.1687	0.543068
$589$	−6.66685	−0.274703
$590$	5.32624	0.219278
$591$	10.0788	0.414587
$592$	7.93310	0.326048
$593$	−21.1332	−0.867835	−0.433918	−	0.900953i	$-0.642869\pi$
$593$	−21.1332	−0.867835	−0.433918	+	0.900953i	$0.642869\pi$
$594$	0	0
$595$	−23.1623	−0.949560
$596$	9.31461	0.381541
$597$	−13.6906	−0.560318
$598$	−20.7315	−0.847773
$599$	−13.2217	−0.540224	−0.270112	−	0.962829i	$-0.587061\pi$
$599$	−13.2217	−0.540224	−0.270112	+	0.962829i	$0.587061\pi$
$600$	1.00000	0.0408248
$601$	−39.2115	−1.59947	−0.799736	−	0.600352i	$-0.795027\pi$
$601$	−39.2115	−1.59947	−0.799736	+	0.600352i	$0.795027\pi$
$602$	0.352707	0.0143752
$603$	−1.67821	−0.0683418
$604$	−13.9029	−0.565702
$605$	0	0
$606$	16.5739	0.673270
$607$	−8.33889	−0.338465	−0.169233	−	0.985576i	$-0.554129\pi$
$607$	−8.33889	−0.338465	−0.169233	+	0.985576i	$0.554129\pi$
$608$	6.01163	0.243804
$609$	−34.0465	−1.37964
$610$	15.4541	0.625716
$611$	6.77310	0.274010
$612$	5.15753	0.208481
$613$	46.7966	1.89010	0.945049	−	0.326927i	$-0.106013\pi$
$613$	46.7966	1.89010	0.945049	+	0.326927i	$0.106013\pi$
$614$	−11.3502	−0.458059
$615$	9.56995	0.385898
$616$	0	0
$617$	−18.5692	−0.747568	−0.373784	−	0.927516i	$-0.621940\pi$
$617$	−18.5692	−0.747568	−0.373784	+	0.927516i	$0.621940\pi$
$618$	−1.09063	−0.0438714
$619$	−9.05390	−0.363907	−0.181953	−	0.983307i	$-0.558242\pi$
$619$	−9.05390	−0.363907	−0.181953	+	0.983307i	$0.558242\pi$
$620$	1.10899	0.0445382
$621$	−8.88456	−0.356525
$622$	−15.1766	−0.608528
$623$	−33.2868	−1.33361
$624$	2.33343	0.0934119
$625$	1.00000	0.0400000
$626$	23.3570	0.933532
$627$	0	0
$628$	9.89175	0.394724
$629$	40.9152	1.63140
$630$	−4.49096	−0.178924
$631$	37.0223	1.47383	0.736917	−	0.675983i	$-0.236281\pi$
$631$	37.0223	1.47383	0.736917	+	0.675983i	$0.236281\pi$
$632$	5.47259	0.217688
$633$	−22.8481	−0.908131
$634$	10.6641	0.423526
$635$	−8.36343	−0.331892
$636$	0.745110	0.0295455
$637$	30.7282	1.21750
$638$	0	0
$639$	9.55113	0.377837
$640$	−1.00000	−0.0395285
$641$	−10.8499	−0.428547	−0.214273	−	0.976774i	$-0.568738\pi$
$641$	−10.8499	−0.428547	−0.214273	+	0.976774i	$0.568738\pi$
$642$	−5.68494	−0.224367
$643$	29.4482	1.16132	0.580662	−	0.814144i	$-0.302794\pi$
$643$	29.4482	1.16132	0.580662	+	0.814144i	$0.302794\pi$
$644$	−39.9002	−1.57229
$645$	−0.0785371	−0.00309239
$646$	31.0052	1.21988
$647$	−33.9447	−1.33450	−0.667252	−	0.744832i	$-0.732530\pi$
$647$	−33.9447	−1.33450	−0.667252	+	0.744832i	$0.732530\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	2.33343	0.0915246
$651$	−4.98044	−0.195199
$652$	6.43124	0.251867
$653$	−19.0906	−0.747074	−0.373537	−	0.927615i	$-0.621855\pi$
$653$	−19.0906	−0.747074	−0.373537	+	0.927615i	$0.621855\pi$
$654$	8.94427	0.349749
$655$	7.40079	0.289173
$656$	−9.56995	−0.373644
$657$	−10.9443	−0.426977
$658$	13.0356	0.508182
$659$	9.56904	0.372757	0.186378	−	0.982478i	$-0.440325\pi$
$659$	9.56904	0.372757	0.186378	+	0.982478i	$0.440325\pi$
$660$	0	0
$661$	16.7878	0.652968	0.326484	−	0.945203i	$-0.394136\pi$
$661$	16.7878	0.652968	0.326484	+	0.945203i	$0.394136\pi$
$662$	−2.42434	−0.0942245
$663$	12.0347	0.467390
$664$	8.00000	0.310460
$665$	−26.9980	−1.04694
$666$	7.93310	0.307401
$667$	67.3550	2.60799
$668$	6.04163	0.233758
$669$	−0.490958	−0.0189815
$670$	1.67821	0.0648347
$671$	0	0
$672$	4.49096	0.173242
$673$	−46.2878	−1.78426	−0.892131	−	0.451776i	$-0.850791\pi$
$673$	−46.2878	−1.78426	−0.892131	+	0.451776i	$0.850791\pi$
$674$	−1.17664	−0.0453223
$675$	1.00000	0.0384900
$676$	−7.55512	−0.290581
$677$	−27.2450	−1.04711	−0.523554	−	0.851992i	$-0.675394\pi$
$677$	−27.2450	−1.04711	−0.523554	+	0.851992i	$0.675394\pi$
$678$	3.87292	0.148739
$679$	25.8044	0.990281
$680$	−5.15753	−0.197782
$681$	−1.49022	−0.0571053
$682$	0	0
$683$	3.62551	0.138726	0.0693631	−	0.997591i	$-0.477903\pi$
$683$	3.62551	0.138726	0.0693631	+	0.997591i	$0.477903\pi$
$684$	6.01163	0.229861
$685$	4.44214	0.169725
$686$	27.7034	1.05772
$687$	−8.21798	−0.313536
$688$	0.0785371	0.00299420
$689$	1.73866	0.0662376
$690$	8.88456	0.338229
$691$	−50.3666	−1.91604	−0.958018	−	0.286708i	$-0.907439\pi$
$691$	−50.3666	−1.91604	−0.958018	+	0.286708i	$0.907439\pi$
$692$	−0.648032	−0.0246345
$693$	0	0
$694$	−23.3570	−0.886619
$695$	19.9074	0.755129
$696$	−7.58113	−0.287362
$697$	−49.3573	−1.86954
$698$	−0.375059	−0.0141962
$699$	−6.63686	−0.251029
$700$	4.49096	0.169742
$701$	17.1399	0.647365	0.323683	−	0.946166i	$-0.395079\pi$
$701$	17.1399	0.647365	0.323683	+	0.946166i	$0.395079\pi$
$702$	2.33343	0.0880695
$703$	47.6909	1.79869
$704$	0	0
$705$	−2.90264	−0.109320
$706$	2.07854	0.0782268
$707$	74.4329	2.79934
$708$	−5.32624	−0.200172
$709$	29.1399	1.09437	0.547186	−	0.837011i	$-0.315699\pi$
$709$	29.1399	1.09437	0.547186	+	0.837011i	$0.315699\pi$
$710$	−9.55113	−0.358448
$711$	5.47259	0.205238
$712$	−7.41196	−0.277775
$713$	9.85291	0.368994
$714$	23.1623	0.866826
$715$	0	0
$716$	1.56231	0.0583861
$717$	6.09764	0.227721
$718$	0.180340	0.00673022
$719$	30.8625	1.15098	0.575488	−	0.817810i	$-0.304812\pi$
$719$	30.8625	1.15098	0.575488	+	0.817810i	$0.304812\pi$
$720$	−1.00000	−0.0372678
$721$	−4.89796	−0.182410
$722$	17.1397	0.637875
$723$	−5.70376	−0.212125
$724$	18.4721	0.686512
$725$	−7.58113	−0.281556
$726$	0	0
$727$	−3.64376	−0.135140	−0.0675699	−	0.997715i	$-0.521525\pi$
$727$	−3.64376	−0.135140	−0.0675699	+	0.997715i	$0.521525\pi$
$728$	10.4793	0.388390
$729$	1.00000	0.0370370
$730$	10.9443	0.405066
$731$	0.405057	0.0149816
$732$	−15.4541	−0.571198
$733$	7.78765	0.287644	0.143822	−	0.989604i	$-0.454061\pi$
$733$	7.78765	0.287644	0.143822	+	0.989604i	$0.454061\pi$
$734$	11.6706	0.430768
$735$	−13.1687	−0.485735
$736$	−8.88456	−0.327489
$737$	0	0
$738$	−9.56995	−0.352275
$739$	9.07455	0.333813	0.166906	−	0.985973i	$-0.446622\pi$
$739$	9.07455	0.333813	0.166906	+	0.985973i	$0.446622\pi$
$740$	−7.93310	−0.291626
$741$	14.0277	0.515321
$742$	3.34626	0.122845
$743$	−9.48702	−0.348045	−0.174022	−	0.984742i	$-0.555677\pi$
$743$	−9.48702	−0.348045	−0.174022	+	0.984742i	$0.555677\pi$
$744$	−1.10899	−0.0406576
$745$	−9.31461	−0.341261
$746$	−10.1687	−0.372303
$747$	8.00000	0.292705
$748$	0	0
$749$	−25.5308	−0.932876
$750$	−1.00000	−0.0365148
$751$	49.4211	1.80340	0.901701	−	0.432359i	$-0.142319\pi$
$751$	49.4211	1.80340	0.901701	+	0.432359i	$0.142319\pi$
$752$	2.90264	0.105848
$753$	−2.60714	−0.0950095
$754$	−17.6900	−0.644232
$755$	13.9029	0.505979
$756$	4.49096	0.163335
$757$	−25.2771	−0.918713	−0.459357	−	0.888252i	$-0.651920\pi$
$757$	−25.2771	−0.918713	−0.459357	+	0.888252i	$0.651920\pi$
$758$	11.0825	0.402535
$759$	0	0
$760$	−6.01163	−0.218065
$761$	−22.6301	−0.820341	−0.410171	−	0.912009i	$-0.634531\pi$
$761$	−22.6301	−0.820341	−0.410171	+	0.912009i	$0.634531\pi$
$762$	8.36343	0.302975
$763$	40.1684	1.45419
$764$	−17.6720	−0.639352
$765$	−5.15753	−0.186471
$766$	21.3082	0.769895
$767$	−12.4284	−0.448763
$768$	1.00000	0.0360844
$769$	−11.4015	−0.411150	−0.205575	−	0.978641i	$-0.565906\pi$
$769$	−11.4015	−0.411150	−0.205575	+	0.978641i	$0.565906\pi$
$770$	0	0
$771$	18.4360	0.663955
$772$	10.4954	0.377738
$773$	18.8896	0.679413	0.339706	−	0.940532i	$-0.389672\pi$
$773$	18.8896	0.679413	0.339706	+	0.940532i	$0.389672\pi$
$774$	0.0785371	0.00282296
$775$	−1.10899	−0.0398362
$776$	5.74585	0.206264
$777$	35.6272	1.27812
$778$	−37.7362	−1.35291
$779$	−57.5310	−2.06126
$780$	−2.33343	−0.0835501
$781$	0	0
$782$	−45.8224	−1.63860
$783$	−7.58113	−0.270927
$784$	13.1687	0.470311
$785$	−9.89175	−0.353052
$786$	−7.40079	−0.263977
$787$	30.9628	1.10371	0.551853	−	0.833942i	$-0.313921\pi$
$787$	30.9628	1.10371	0.551853	+	0.833942i	$0.313921\pi$
$788$	10.0788	0.359043
$789$	24.4285	0.869678
$790$	−5.47259	−0.194706
$791$	17.3931	0.618429
$792$	0	0
$793$	−36.0609	−1.28056
$794$	−22.4348	−0.796180
$795$	−0.745110	−0.0264263
$796$	−13.6906	−0.485250
$797$	−7.93634	−0.281120	−0.140560	−	0.990072i	$-0.544890\pi$
$797$	−7.93634	−0.281120	−0.140560	+	0.990072i	$0.544890\pi$
$798$	26.9980	0.955719
$799$	14.9705	0.529617
$800$	1.00000	0.0353553
$801$	−7.41196	−0.261889
$802$	−25.9002	−0.914567
$803$	0	0
$804$	−1.67821	−0.0591857
$805$	39.9002	1.40630
$806$	−2.58775	−0.0911497
$807$	−11.0119	−0.387638
$808$	16.5739	0.583069
$809$	5.56276	0.195576	0.0977882	−	0.995207i	$-0.468823\pi$
$809$	5.56276	0.195576	0.0977882	+	0.995207i	$0.468823\pi$
$810$	−1.00000	−0.0351364
$811$	32.1021	1.12726	0.563628	−	0.826029i	$-0.309405\pi$
$811$	32.1021	1.12726	0.563628	+	0.826029i	$0.309405\pi$
$812$	−34.0465	−1.19480
$813$	0.647750	0.0227176
$814$	0	0
$815$	−6.43124	−0.225277
$816$	5.15753	0.180550
$817$	0.472136	0.0165179
$818$	−24.7921	−0.866835
$819$	10.4793	0.366177
$820$	9.56995	0.334197
$821$	−21.1255	−0.737286	−0.368643	−	0.929571i	$-0.620177\pi$
$821$	−21.1255	−0.737286	−0.368643	+	0.929571i	$0.620177\pi$
$822$	−4.44214	−0.154937
$823$	4.94702	0.172442	0.0862211	−	0.996276i	$-0.472521\pi$
$823$	4.94702	0.172442	0.0862211	+	0.996276i	$0.472521\pi$
$824$	−1.09063	−0.0379938
$825$	0	0
$826$	−23.9199	−0.832280
$827$	44.5554	1.54934	0.774672	−	0.632364i	$-0.217915\pi$
$827$	44.5554	1.54934	0.774672	+	0.632364i	$0.217915\pi$
$828$	−8.88456	−0.308760
$829$	−21.6706	−0.752650	−0.376325	−	0.926488i	$-0.622812\pi$
$829$	−21.6706	−0.752650	−0.376325	+	0.926488i	$0.622812\pi$
$830$	−8.00000	−0.277684
$831$	−24.6304	−0.854419
$832$	2.33343	0.0808970
$833$	67.9180	2.35322
$834$	−19.9074	−0.689336
$835$	−6.04163	−0.209079
$836$	0	0
$837$	−1.10899	−0.0383324
$838$	27.8969	0.963683
$839$	45.7186	1.57838	0.789190	−	0.614149i	$-0.210501\pi$
$839$	45.7186	1.57838	0.789190	+	0.614149i	$0.210501\pi$
$840$	−4.49096	−0.154953
$841$	28.4735	0.981845
$842$	25.0052	0.861735
$843$	9.49170	0.326911
$844$	−22.8481	−0.786464
$845$	7.55512	0.259904
$846$	2.90264	0.0997948
$847$	0	0
$848$	0.745110	0.0255872
$849$	−20.2113	−0.693648
$850$	5.15753	0.176902
$851$	−70.4820	−2.41609
$852$	9.55113	0.327216
$853$	3.27816	0.112242	0.0561210	−	0.998424i	$-0.482127\pi$
$853$	3.27816	0.112242	0.0561210	+	0.998424i	$0.482127\pi$
$854$	−69.4035	−2.37494
$855$	−6.01163	−0.205594
$856$	−5.68494	−0.194307
$857$	0.297435	0.0101602	0.00508010	−	0.999987i	$-0.498383\pi$
$857$	0.297435	0.0101602	0.00508010	+	0.999987i	$0.498383\pi$
$858$	0	0
$859$	39.7745	1.35709	0.678544	−	0.734560i	$-0.262611\pi$
$859$	39.7745	1.35709	0.678544	+	0.734560i	$0.262611\pi$
$860$	−0.0785371	−0.00267809
$861$	−42.9783	−1.46470
$862$	−17.9624	−0.611800
$863$	−15.0483	−0.512249	−0.256124	−	0.966644i	$-0.582446\pi$
$863$	−15.0483	−0.512249	−0.256124	+	0.966644i	$0.582446\pi$
$864$	1.00000	0.0340207
$865$	0.648032	0.0220338
$866$	−26.9458	−0.915654
$867$	9.60013	0.326037
$868$	−4.98044	−0.169047
$869$	0	0
$870$	7.58113	0.257024
$871$	−3.91597	−0.132688
$872$	8.94427	0.302891
$873$	5.74585	0.194468
$874$	−53.4107	−1.80664
$875$	−4.49096	−0.151822
$876$	−10.9443	−0.369773
$877$	−38.5856	−1.30294	−0.651471	−	0.758673i	$-0.725848\pi$
$877$	−38.5856	−1.30294	−0.651471	+	0.758673i	$0.725848\pi$
$878$	−4.79393	−0.161787
$879$	−1.19398	−0.0402719
$880$	0	0
$881$	−14.2135	−0.478866	−0.239433	−	0.970913i	$-0.576962\pi$
$881$	−14.2135	−0.478866	−0.239433	+	0.970913i	$0.576962\pi$
$882$	13.1687	0.443413
$883$	−2.27417	−0.0765319	−0.0382660	−	0.999268i	$-0.512183\pi$
$883$	−2.27417	−0.0765319	−0.0382660	+	0.999268i	$0.512183\pi$
$884$	12.0347	0.404772
$885$	5.32624	0.179040
$886$	10.0600	0.337972
$887$	−52.2657	−1.75491	−0.877455	−	0.479658i	$-0.840761\pi$
$887$	−52.2657	−1.75491	−0.877455	+	0.479658i	$0.840761\pi$
$888$	7.93310	0.266217
$889$	37.5598	1.25972
$890$	7.41196	0.248450
$891$	0	0
$892$	−0.490958	−0.0164385
$893$	17.4496	0.583929
$894$	9.31461	0.311527
$895$	−1.56231	−0.0522221
$896$	4.49096	0.150032
$897$	−20.7315	−0.692204
$898$	−0.498148	−0.0166234
$899$	8.40741	0.280403
$900$	1.00000	0.0333333
$901$	3.84293	0.128026
$902$	0	0
$903$	0.352707	0.0117373
$904$	3.87292	0.128812
$905$	−18.4721	−0.614035
$906$	−13.9029	−0.461894
$907$	−53.0605	−1.76184	−0.880922	−	0.473262i	$-0.843076\pi$
$907$	−53.0605	−1.76184	−0.880922	+	0.473262i	$0.843076\pi$
$908$	−1.49022	−0.0494547
$909$	16.5739	0.549723
$910$	−10.4793	−0.347386
$911$	−39.3570	−1.30395	−0.651977	−	0.758238i	$-0.726060\pi$
$911$	−39.3570	−1.30395	−0.651977	+	0.758238i	$0.726060\pi$
$912$	6.01163	0.199065
$913$	0	0
$914$	−1.85730	−0.0614342
$915$	15.4541	0.510895
$916$	−8.21798	−0.271530
$917$	−33.2366	−1.09757
$918$	5.15753	0.170224
$919$	7.44841	0.245700	0.122850	−	0.992425i	$-0.460797\pi$
$919$	7.44841	0.245700	0.122850	+	0.992425i	$0.460797\pi$
$920$	8.88456	0.292915
$921$	−11.3502	−0.374003
$922$	−22.1394	−0.729124
$923$	22.2869	0.733581
$924$	0	0
$925$	7.93310	0.260839
$926$	−22.1920	−0.729273
$927$	−1.09063	−0.0358209
$928$	−7.58113	−0.248863
$929$	7.70376	0.252752	0.126376	−	0.991982i	$-0.459665\pi$
$929$	7.70376	0.252752	0.126376	+	0.991982i	$0.459665\pi$
$930$	1.10899	0.0363653
$931$	79.1654	2.59454
$932$	−6.63686	−0.217397
$933$	−15.1766	−0.496861
$934$	31.6953	1.03710
$935$	0	0
$936$	2.33343	0.0762705
$937$	−23.8429	−0.778914	−0.389457	−	0.921045i	$-0.627337\pi$
$937$	−23.8429	−0.778914	−0.389457	+	0.921045i	$0.627337\pi$
$938$	−7.53675	−0.246084
$939$	23.3570	0.762226
$940$	−2.90264	−0.0946737
$941$	20.4887	0.667912	0.333956	−	0.942589i	$-0.391616\pi$
$941$	20.4887	0.667912	0.333956	+	0.942589i	$0.391616\pi$
$942$	9.89175	0.322291
$943$	85.0248	2.76879
$944$	−5.32624	−0.173354
$945$	−4.49096	−0.146091
$946$	0	0
$947$	18.3389	0.595934	0.297967	−	0.954576i	$-0.403691\pi$
$947$	18.3389	0.595934	0.297967	+	0.954576i	$0.403691\pi$
$948$	5.47259	0.177742
$949$	−25.5377	−0.828988
$950$	6.01163	0.195043
$951$	10.6641	0.345807
$952$	23.1623	0.750693
$953$	43.6768	1.41483	0.707415	−	0.706799i	$-0.249861\pi$
$953$	43.6768	1.41483	0.707415	+	0.706799i	$0.249861\pi$
$954$	0.745110	0.0241238
$955$	17.6720	0.571854
$956$	6.09764	0.197212
$957$	0	0
$958$	23.2217	0.750259
$959$	−19.9495	−0.644201
$960$	−1.00000	−0.0322749
$961$	−29.7701	−0.960327
$962$	18.5113	0.596828
$963$	−5.68494	−0.183195
$964$	−5.70376	−0.183706
$965$	−10.4954	−0.337859
$966$	−39.9002	−1.28377
$967$	44.2296	1.42233	0.711164	−	0.703026i	$-0.248168\pi$
$967$	44.2296	1.42233	0.711164	+	0.703026i	$0.248168\pi$
$968$	0	0
$969$	31.0052	0.996030
$970$	−5.74585	−0.184488
$971$	19.8847	0.638129	0.319065	−	0.947733i	$-0.396631\pi$
$971$	19.8847	0.638129	0.319065	+	0.947733i	$0.396631\pi$
$972$	1.00000	0.0320750
$973$	−89.4032	−2.86613
$974$	−38.9081	−1.24670
$975$	2.33343	0.0747295
$976$	−15.4541	−0.494672
$977$	−33.8058	−1.08154	−0.540772	−	0.841169i	$-0.681868\pi$
$977$	−33.8058	−1.08154	−0.540772	+	0.841169i	$0.681868\pi$
$978$	6.43124	0.205648
$979$	0	0
$980$	−13.1687	−0.420659
$981$	8.94427	0.285569
$982$	−4.66139	−0.148751
$983$	−10.0792	−0.321476	−0.160738	−	0.986997i	$-0.551387\pi$
$983$	−10.0792	−0.321476	−0.160738	+	0.986997i	$0.551387\pi$
$984$	−9.56995	−0.305079
$985$	−10.0788	−0.321138
$986$	−39.0999	−1.24519
$987$	13.0356	0.414929
$988$	14.0277	0.446281
$989$	−0.697767	−0.0221877
$990$	0	0
$991$	25.6906	0.816088	0.408044	−	0.912962i	$-0.366211\pi$
$991$	25.6906	0.816088	0.408044	+	0.912962i	$0.366211\pi$
$992$	−1.10899	−0.0352105
$993$	−2.42434	−0.0769340
$994$	42.8937	1.36051
$995$	13.6906	0.434020
$996$	8.00000	0.253490
$997$	−42.8994	−1.35864	−0.679318	−	0.733844i	$-0.737724\pi$
$997$	−42.8994	−1.35864	−0.679318	+	0.733844i	$0.737724\pi$
$998$	16.3933	0.518921
$999$	7.93310	0.250992

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bs.1.4		4
11.2	odd	10		330.2.m.f.301.1	yes	8
11.6	odd	10		330.2.m.f.91.1	✓	8
11.10	odd	2		3630.2.a.bq.1.1		4
33.2	even	10		990.2.n.i.631.1		8
33.17	even	10		990.2.n.i.91.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.91.1	✓	8	11.6	odd	10
330.2.m.f.301.1	yes	8	11.2	odd	10
990.2.n.i.91.1		8	33.17	even	10
990.2.n.i.631.1		8	33.2	even	10
3630.2.a.bq.1.1		4	11.10	odd	2
3630.2.a.bs.1.4		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.49096 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +4.49096 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +2.33343 q^{13} +4.49096 q^{14} -1.00000 q^{15} +1.00000 q^{16} +5.15753 q^{17} +1.00000 q^{18} +6.01163 q^{19} -1.00000 q^{20} +4.49096 q^{21} -8.88456 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.33343 q^{26} +1.00000 q^{27} +4.49096 q^{28} -7.58113 q^{29} -1.00000 q^{30} -1.10899 q^{31} +1.00000 q^{32} +5.15753 q^{34} -4.49096 q^{35} +1.00000 q^{36} +7.93310 q^{37} +6.01163 q^{38} +2.33343 q^{39} -1.00000 q^{40} -9.56995 q^{41} +4.49096 q^{42} +0.0785371 q^{43} -1.00000 q^{45} -8.88456 q^{46} +2.90264 q^{47} +1.00000 q^{48} +13.1687 q^{49} +1.00000 q^{50} +5.15753 q^{51} +2.33343 q^{52} +0.745110 q^{53} +1.00000 q^{54} +4.49096 q^{56} +6.01163 q^{57} -7.58113 q^{58} -5.32624 q^{59} -1.00000 q^{60} -15.4541 q^{61} -1.10899 q^{62} +4.49096 q^{63} +1.00000 q^{64} -2.33343 q^{65} -1.67821 q^{67} +5.15753 q^{68} -8.88456 q^{69} -4.49096 q^{70} +9.55113 q^{71} +1.00000 q^{72} -10.9443 q^{73} +7.93310 q^{74} +1.00000 q^{75} +6.01163 q^{76} +2.33343 q^{78} +5.47259 q^{79} -1.00000 q^{80} +1.00000 q^{81} -9.56995 q^{82} +8.00000 q^{83} +4.49096 q^{84} -5.15753 q^{85} +0.0785371 q^{86} -7.58113 q^{87} -7.41196 q^{89} -1.00000 q^{90} +10.4793 q^{91} -8.88456 q^{92} -1.10899 q^{93} +2.90264 q^{94} -6.01163 q^{95} +1.00000 q^{96} +5.74585 q^{97} +13.1687 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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