LMFDB - Embedded newform 3630.2.a.bs.1.3

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			1.3
Root			$-4.17549$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.19863 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.19863 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +6.75608 q^{13} +3.19863 q^{14} -1.00000 q^{15} +1.00000 q^{16} -0.557453 q^{17} +1.00000 q^{18} -6.41156 q^{19} -1.00000 q^{20} +3.19863 q^{21} +2.59489 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.75608 q^{26} +1.00000 q^{27} +3.19863 q^{28} +4.89154 q^{29} -1.00000 q^{30} +2.41941 q^{31} +1.00000 q^{32} -0.557453 q^{34} -3.19863 q^{35} +1.00000 q^{36} -5.73294 q^{37} -6.41156 q^{38} +6.75608 q^{39} -1.00000 q^{40} -1.31979 q^{41} +3.19863 q^{42} +1.32139 q^{43} -1.00000 q^{45} +2.59489 q^{46} -5.99215 q^{47} +1.00000 q^{48} +3.23122 q^{49} +1.00000 q^{50} -0.557453 q^{51} +6.75608 q^{52} -2.43470 q^{53} +1.00000 q^{54} +3.19863 q^{56} -6.41156 q^{57} +4.89154 q^{58} +10.3262 q^{59} -1.00000 q^{60} -3.92512 q^{61} +2.41941 q^{62} +3.19863 q^{63} +1.00000 q^{64} -6.75608 q^{65} +15.1676 q^{67} -0.557453 q^{68} +2.59489 q^{69} -3.19863 q^{70} -6.35097 q^{71} +1.00000 q^{72} +6.94427 q^{73} -5.73294 q^{74} +1.00000 q^{75} -6.41156 q^{76} +6.75608 q^{78} -11.6724 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.31979 q^{82} +8.00000 q^{83} +3.19863 q^{84} +0.557453 q^{85} +1.32139 q^{86} +4.89154 q^{87} -13.0775 q^{89} -1.00000 q^{90} +21.6102 q^{91} +2.59489 q^{92} +2.41941 q^{93} -5.99215 q^{94} +6.41156 q^{95} +1.00000 q^{96} +7.63332 q^{97} +3.23122 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	3.19863	1.20897	0.604484	−	0.796618i	$-0.293379\pi$
$7$	3.19863	1.20897	0.604484	+	0.796618i	$0.293379\pi$
$8$	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
$13$	6.75608	1.87380	0.936900	−	0.349598i	$-0.113682\pi$
$13$	6.75608	1.87380	0.936900	+	0.349598i	$0.113682\pi$
$14$	3.19863	0.854869
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−0.557453	−0.135202	−0.0676012	−	0.997712i	$-0.521535\pi$
$17$	−0.557453	−0.135202	−0.0676012	+	0.997712i	$0.521535\pi$
$18$	1.00000	0.235702
$19$	−6.41156	−1.47091	−0.735456	−	0.677573i	$-0.763032\pi$
$19$	−6.41156	−1.47091	−0.735456	+	0.677573i	$0.763032\pi$
$20$	−1.00000	−0.223607
$21$	3.19863	0.697998
$22$	0	0
$23$	2.59489	0.541073	0.270536	−	0.962710i	$-0.412799\pi$
$23$	2.59489	0.541073	0.270536	+	0.962710i	$0.412799\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	6.75608	1.32498
$27$	1.00000	0.192450
$28$	3.19863	0.604484
$29$	4.89154	0.908337	0.454168	−	0.890916i	$-0.349936\pi$
$29$	4.89154	0.908337	0.454168	+	0.890916i	$0.349936\pi$
$30$	−1.00000	−0.182574
$31$	2.41941	0.434538	0.217269	−	0.976112i	$-0.430285\pi$
$31$	2.41941	0.434538	0.217269	+	0.976112i	$0.430285\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−0.557453	−0.0956025
$35$	−3.19863	−0.540667
$36$	1.00000	0.166667
$37$	−5.73294	−0.942490	−0.471245	−	0.882002i	$-0.656195\pi$
$37$	−5.73294	−0.942490	−0.471245	+	0.882002i	$0.656195\pi$
$38$	−6.41156	−1.04009
$39$	6.75608	1.08184
$40$	−1.00000	−0.158114
$41$	−1.31979	−0.206116	−0.103058	−	0.994675i	$-0.532863\pi$
$41$	−1.31979	−0.206116	−0.103058	+	0.994675i	$0.532863\pi$
$42$	3.19863	0.493559
$43$	1.32139	0.201509	0.100755	−	0.994911i	$-0.467874\pi$
$43$	1.32139	0.201509	0.100755	+	0.994911i	$0.467874\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	2.59489	0.382596
$47$	−5.99215	−0.874045	−0.437022	−	0.899451i	$-0.643967\pi$
$47$	−5.99215	−0.874045	−0.437022	+	0.899451i	$0.643967\pi$
$48$	1.00000	0.144338
$49$	3.23122	0.461602
$50$	1.00000	0.141421
$51$	−0.557453	−0.0780591
$52$	6.75608	0.936900
$53$	−2.43470	−0.334431	−0.167216	−	0.985920i	$-0.553478\pi$
$53$	−2.43470	−0.334431	−0.167216	+	0.985920i	$0.553478\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	3.19863	0.427435
$57$	−6.41156	−0.849231
$58$	4.89154	0.642291
$59$	10.3262	1.34436	0.672181	−	0.740387i	$-0.265358\pi$
$59$	10.3262	1.34436	0.672181	+	0.740387i	$0.265358\pi$
$60$	−1.00000	−0.129099
$61$	−3.92512	−0.502560	−0.251280	−	0.967914i	$-0.580851\pi$
$61$	−3.92512	−0.502560	−0.251280	+	0.967914i	$0.580851\pi$
$62$	2.41941	0.307265
$63$	3.19863	0.402989
$64$	1.00000	0.125000
$65$	−6.75608	−0.837989
$66$	0	0
$67$	15.1676	1.85302	0.926511	−	0.376268i	$-0.122793\pi$
$67$	15.1676	1.85302	0.926511	+	0.376268i	$0.122793\pi$
$68$	−0.557453	−0.0676012
$69$	2.59489	0.312389
$70$	−3.19863	−0.382309
$71$	−6.35097	−0.753722	−0.376861	−	0.926270i	$-0.622997\pi$
$71$	−6.35097	−0.753722	−0.376861	+	0.926270i	$0.622997\pi$
$72$	1.00000	0.117851
$73$	6.94427	0.812766	0.406383	−	0.913703i	$-0.366790\pi$
$73$	6.94427	0.812766	0.406383	+	0.913703i	$0.366790\pi$
$74$	−5.73294	−0.666441
$75$	1.00000	0.115470
$76$	−6.41156	−0.735456
$77$	0	0
$78$	6.75608	0.764975
$79$	−11.6724	−1.31324	−0.656622	−	0.754220i	$-0.728015\pi$
$79$	−11.6724	−1.31324	−0.656622	+	0.754220i	$0.728015\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−1.31979	−0.145746
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	3.19863	0.348999
$85$	0.557453	0.0604643
$86$	1.32139	0.142489
$87$	4.89154	0.524428
$88$	0	0
$89$	−13.0775	−1.38621	−0.693104	−	0.720837i	$-0.743757\pi$
$89$	−13.0775	−1.38621	−0.693104	+	0.720837i	$0.743757\pi$
$90$	−1.00000	−0.105409
$91$	21.6102	2.26536
$92$	2.59489	0.270536
$93$	2.41941	0.250881
$94$	−5.99215	−0.618043
$95$	6.41156	0.657812
$96$	1.00000	0.102062
$97$	7.63332	0.775046	0.387523	−	0.921860i	$-0.373331\pi$
$97$	7.63332	0.775046	0.387523	+	0.921860i	$0.373331\pi$
$98$	3.23122	0.326402
$99$	0	0
$100$	1.00000	0.100000
$101$	−15.9739	−1.58946	−0.794729	−	0.606964i	$-0.792387\pi$
$101$	−15.9739	−1.58946	−0.794729	+	0.606964i	$0.792387\pi$
$102$	−0.557453	−0.0551961
$103$	18.2904	1.80221	0.901103	−	0.433605i	$-0.142759\pi$
$103$	18.2904	1.80221	0.901103	+	0.433605i	$0.142759\pi$
$104$	6.75608	0.662488
$105$	−3.19863	−0.312154
$106$	−2.43470	−0.236478
$107$	−17.1149	−1.65456	−0.827280	−	0.561789i	$-0.810113\pi$
$107$	−17.1149	−1.65456	−0.827280	+	0.561789i	$0.810113\pi$
$108$	1.00000	0.0962250
$109$	−8.94427	−0.856706	−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427	−0.856706	−0.428353	+	0.903612i	$0.640906\pi$
$110$	0	0
$111$	−5.73294	−0.544147
$112$	3.19863	0.302242
$113$	4.81666	0.453113	0.226557	−	0.973998i	$-0.427253\pi$
$113$	4.81666	0.453113	0.226557	+	0.973998i	$0.427253\pi$
$114$	−6.41156	−0.600497
$115$	−2.59489	−0.241975
$116$	4.89154	0.454168
$117$	6.75608	0.624600
$118$	10.3262	0.950607
$119$	−1.78309	−0.163455
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−3.92512	−0.355364
$123$	−1.31979	−0.119001
$124$	2.41941	0.217269
$125$	−1.00000	−0.0894427
$126$	3.19863	0.284956
$127$	16.2155	1.43889	0.719447	−	0.694547i	$-0.244395\pi$
$127$	16.2155	1.43889	0.719447	+	0.694547i	$0.244395\pi$
$128$	1.00000	0.0883883
$129$	1.32139	0.116342
$130$	−6.75608	−0.592547
$131$	−17.2888	−1.51053	−0.755265	−	0.655420i	$-0.772492\pi$
$131$	−17.2888	−1.51053	−0.755265	+	0.655420i	$0.772492\pi$
$132$	0	0
$133$	−20.5082	−1.77828
$134$	15.1676	1.31028
$135$	−1.00000	−0.0860663
$136$	−0.557453	−0.0478012
$137$	7.93157	0.677640	0.338820	−	0.940851i	$-0.389972\pi$
$137$	7.93157	0.677640	0.338820	+	0.940851i	$0.389972\pi$
$138$	2.59489	0.220892
$139$	8.21778	0.697023	0.348512	−	0.937304i	$-0.386687\pi$
$139$	8.21778	0.697023	0.348512	+	0.937304i	$0.386687\pi$
$140$	−3.19863	−0.270333
$141$	−5.99215	−0.504630
$142$	−6.35097	−0.532962
$143$	0	0
$144$	1.00000	0.0833333
$145$	−4.89154	−0.406221
$146$	6.94427	0.574712
$147$	3.23122	0.266506
$148$	−5.73294	−0.471245
$149$	6.08532	0.498529	0.249264	−	0.968435i	$-0.419811\pi$
$149$	6.08532	0.498529	0.249264	+	0.968435i	$0.419811\pi$
$150$	1.00000	0.0816497
$151$	−18.2761	−1.48729	−0.743644	−	0.668576i	$-0.766904\pi$
$151$	−18.2761	−1.48729	−0.743644	+	0.668576i	$0.766904\pi$
$152$	−6.41156	−0.520046
$153$	−0.557453	−0.0450674
$154$	0	0
$155$	−2.41941	−0.194331
$156$	6.75608	0.540919
$157$	18.4874	1.47546	0.737729	−	0.675097i	$-0.235898\pi$
$157$	18.4874	1.47546	0.737729	+	0.675097i	$0.235898\pi$
$158$	−11.6724	−0.928603
$159$	−2.43470	−0.193084
$160$	−1.00000	−0.0790569
$161$	8.30010	0.654139
$162$	1.00000	0.0785674
$163$	11.5480	0.904510	0.452255	−	0.891889i	$-0.350620\pi$
$163$	11.5480	0.904510	0.452255	+	0.891889i	$0.350620\pi$
$164$	−1.31979	−0.103058
$165$	0	0
$166$	8.00000	0.620920
$167$	−2.95212	−0.228442	−0.114221	−	0.993455i	$-0.536437\pi$
$167$	−2.95212	−0.228442	−0.114221	+	0.993455i	$0.536437\pi$
$168$	3.19863	0.246779
$169$	32.6446	2.51112
$170$	0.557453	0.0427547
$171$	−6.41156	−0.490304
$172$	1.32139	0.100755
$173$	−1.84140	−0.139999	−0.0699994	−	0.997547i	$-0.522300\pi$
$173$	−1.84140	−0.139999	−0.0699994	+	0.997547i	$0.522300\pi$
$174$	4.89154	0.370827
$175$	3.19863	0.241793
$176$	0	0
$177$	10.3262	0.776168
$178$	−13.0775	−0.980198
$179$	−18.5623	−1.38741	−0.693706	−	0.720258i	$-0.744023\pi$
$179$	−18.5623	−1.38741	−0.693706	+	0.720258i	$0.744023\pi$
$180$	−1.00000	−0.0745356
$181$	9.52786	0.708201	0.354100	−	0.935207i	$-0.384787\pi$
$181$	9.52786	0.708201	0.354100	+	0.935207i	$0.384787\pi$
$182$	21.6102	1.60185
$183$	−3.92512	−0.290153
$184$	2.59489	0.191298
$185$	5.73294	0.421494
$186$	2.41941	0.177400
$187$	0	0
$188$	−5.99215	−0.437022
$189$	3.19863	0.232666
$190$	6.41156	0.465143
$191$	0.913695	0.0661127	0.0330563	−	0.999453i	$-0.489476\pi$
$191$	0.913695	0.0661127	0.0330563	+	0.999453i	$0.489476\pi$
$192$	1.00000	0.0721688
$193$	−23.2952	−1.67683	−0.838414	−	0.545033i	$-0.816517\pi$
$193$	−23.2952	−1.67683	−0.838414	+	0.545033i	$0.816517\pi$
$194$	7.63332	0.548041
$195$	−6.75608	−0.483813
$196$	3.23122	0.230801
$197$	24.5896	1.75194	0.875969	−	0.482367i	$-0.160223\pi$
$197$	24.5896	1.75194	0.875969	+	0.482367i	$0.160223\pi$
$198$	0	0
$199$	10.5112	0.745117	0.372559	−	0.928009i	$-0.378481\pi$
$199$	10.5112	0.745117	0.372559	+	0.928009i	$0.378481\pi$
$200$	1.00000	0.0707107
$201$	15.1676	1.06984
$202$	−15.9739	−1.12392
$203$	15.6462	1.09815
$204$	−0.557453	−0.0390295
$205$	1.31979	0.0921780
$206$	18.2904	1.27435
$207$	2.59489	0.180358
$208$	6.75608	0.468450
$209$	0	0
$210$	−3.19863	−0.220726
$211$	7.06863	0.486624	0.243312	−	0.969948i	$-0.421766\pi$
$211$	7.06863	0.486624	0.243312	+	0.969948i	$0.421766\pi$
$212$	−2.43470	−0.167216
$213$	−6.35097	−0.435162
$214$	−17.1149	−1.16995
$215$	−1.32139	−0.0901177
$216$	1.00000	0.0680414
$217$	7.73878	0.525343
$218$	−8.94427	−0.605783
$219$	6.94427	0.469250
$220$	0	0
$221$	−3.76620	−0.253342
$222$	−5.73294	−0.384770
$223$	0.801373	0.0536639	0.0268319	−	0.999640i	$-0.491458\pi$
$223$	0.801373	0.0536639	0.0268319	+	0.999640i	$0.491458\pi$
$224$	3.19863	0.213717
$225$	1.00000	0.0666667
$226$	4.81666	0.320400
$227$	4.86939	0.323193	0.161596	−	0.986857i	$-0.448336\pi$
$227$	4.86939	0.323193	0.161596	+	0.986857i	$0.448336\pi$
$228$	−6.41156	−0.424616
$229$	−1.16119	−0.0767333	−0.0383667	−	0.999264i	$-0.512215\pi$
$229$	−1.16119	−0.0767333	−0.0383667	+	0.999264i	$0.512215\pi$
$230$	−2.59489	−0.171102
$231$	0	0
$232$	4.89154	0.321146
$233$	−12.0527	−0.789601	−0.394800	−	0.918767i	$-0.629186\pi$
$233$	−12.0527	−0.789601	−0.394800	+	0.918767i	$0.629186\pi$
$234$	6.75608	0.441659
$235$	5.99215	0.390885
$236$	10.3262	0.672181
$237$	−11.6724	−0.758201
$238$	−1.78309	−0.115580
$239$	28.2604	1.82801	0.914006	−	0.405700i	$-0.132972\pi$
$239$	28.2604	1.82801	0.914006	+	0.405700i	$0.132972\pi$
$240$	−1.00000	−0.0645497
$241$	−24.7857	−1.59659	−0.798293	−	0.602270i	$-0.794263\pi$
$241$	−24.7857	−1.59659	−0.798293	+	0.602270i	$0.794263\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−3.92512	−0.251280
$245$	−3.23122	−0.206435
$246$	−1.31979	−0.0841466
$247$	−43.3170	−2.75619
$248$	2.41941	0.153632
$249$	8.00000	0.506979
$250$	−1.00000	−0.0632456
$251$	−17.8615	−1.12741	−0.563705	−	0.825976i	$-0.690625\pi$
$251$	−17.8615	−1.12741	−0.563705	+	0.825976i	$0.690625\pi$
$252$	3.19863	0.201495
$253$	0	0
$254$	16.2155	1.01745
$255$	0.557453	0.0349091
$256$	1.00000	0.0625000
$257$	4.32237	0.269622	0.134811	−	0.990871i	$-0.456957\pi$
$257$	4.32237	0.269622	0.134811	+	0.990871i	$0.456957\pi$
$258$	1.32139	0.0822659
$259$	−18.3375	−1.13944
$260$	−6.75608	−0.418994
$261$	4.89154	0.302779
$262$	−17.2888	−1.06811
$263$	−23.0282	−1.41998	−0.709989	−	0.704212i	$-0.751300\pi$
$263$	−23.0282	−1.41998	−0.709989	+	0.704212i	$0.751300\pi$
$264$	0	0
$265$	2.43470	0.149562
$266$	−20.5082	−1.25744
$267$	−13.0775	−0.800328
$268$	15.1676	0.926511
$269$	−11.8567	−0.722915	−0.361457	−	0.932389i	$-0.617721\pi$
$269$	−11.8567	−0.722915	−0.361457	+	0.932389i	$0.617721\pi$
$270$	−1.00000	−0.0608581
$271$	−11.4268	−0.694131	−0.347066	−	0.937841i	$-0.612822\pi$
$271$	−11.4268	−0.694131	−0.347066	+	0.937841i	$0.612822\pi$
$272$	−0.557453	−0.0338006
$273$	21.6102	1.30791
$274$	7.93157	0.479164
$275$	0	0
$276$	2.59489	0.156194
$277$	−15.0384	−0.903572	−0.451786	−	0.892126i	$-0.649213\pi$
$277$	−15.0384	−0.903572	−0.451786	+	0.892126i	$0.649213\pi$
$278$	8.21778	0.492870
$279$	2.41941	0.144846
$280$	−3.19863	−0.191155
$281$	13.2666	0.791422	0.395711	−	0.918375i	$-0.370498\pi$
$281$	13.2666	0.791422	0.395711	+	0.918375i	$0.370498\pi$
$282$	−5.99215	−0.356827
$283$	15.1214	0.898871	0.449436	−	0.893313i	$-0.351625\pi$
$283$	15.1214	0.898871	0.449436	+	0.893313i	$0.351625\pi$
$284$	−6.35097	−0.376861
$285$	6.41156	0.379788
$286$	0	0
$287$	−4.22151	−0.249188
$288$	1.00000	0.0589256
$289$	−16.6892	−0.981720
$290$	−4.89154	−0.287241
$291$	7.63332	0.447473
$292$	6.94427	0.406383
$293$	−13.9163	−0.812998	−0.406499	−	0.913651i	$-0.633250\pi$
$293$	−13.9163	−0.812998	−0.406499	+	0.913651i	$0.633250\pi$
$294$	3.23122	0.188448
$295$	−10.3262	−0.601217
$296$	−5.73294	−0.333220
$297$	0	0
$298$	6.08532	0.352513
$299$	17.5313	1.01386
$300$	1.00000	0.0577350
$301$	4.22662	0.243618
$302$	−18.2761	−1.05167
$303$	−15.9739	−0.917674
$304$	−6.41156	−0.367728
$305$	3.92512	0.224752
$306$	−0.557453	−0.0318675
$307$	24.0813	1.37439	0.687197	−	0.726471i	$-0.258841\pi$
$307$	24.0813	1.37439	0.687197	+	0.726471i	$0.258841\pi$
$308$	0	0
$309$	18.2904	1.04050
$310$	−2.41941	−0.137413
$311$	−30.3816	−1.72278	−0.861390	−	0.507944i	$-0.830406\pi$
$311$	−30.3816	−1.72278	−0.861390	+	0.507944i	$0.830406\pi$
$312$	6.75608	0.382488
$313$	16.2012	0.915747	0.457873	−	0.889017i	$-0.348611\pi$
$313$	16.2012	0.915747	0.457873	+	0.889017i	$0.348611\pi$
$314$	18.4874	1.04331
$315$	−3.19863	−0.180222
$316$	−11.6724	−0.656622
$317$	−33.0640	−1.85706	−0.928531	−	0.371256i	$-0.878927\pi$
$317$	−33.0640	−1.85706	−0.928531	+	0.371256i	$0.878927\pi$
$318$	−2.43470	−0.136531
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−17.1149	−0.955261
$322$	8.30010	0.462546
$323$	3.57414	0.198871
$324$	1.00000	0.0555556
$325$	6.75608	0.374760
$326$	11.5480	0.639585
$327$	−8.94427	−0.494619
$328$	−1.31979	−0.0728731
$329$	−19.1666	−1.05669
$330$	0	0
$331$	−0.733928	−0.0403403	−0.0201702	−	0.999797i	$-0.506421\pi$
$331$	−0.733928	−0.0403403	−0.0201702	+	0.999797i	$0.506421\pi$
$332$	8.00000	0.439057
$333$	−5.73294	−0.314163
$334$	−2.95212	−0.161533
$335$	−15.1676	−0.828696
$336$	3.19863	0.174499
$337$	−16.3816	−0.892360	−0.446180	−	0.894943i	$-0.647216\pi$
$337$	−16.3816	−0.892360	−0.446180	+	0.894943i	$0.647216\pi$
$338$	32.6446	1.77563
$339$	4.81666	0.261605
$340$	0.557453	0.0302322
$341$	0	0
$342$	−6.41156	−0.346697
$343$	−12.0549	−0.650905
$344$	1.32139	0.0712443
$345$	−2.59489	−0.139704
$346$	−1.84140	−0.0989942
$347$	−16.2012	−0.869727	−0.434863	−	0.900496i	$-0.643203\pi$
$347$	−16.2012	−0.869727	−0.434863	+	0.900496i	$0.643203\pi$
$348$	4.89154	0.262214
$349$	4.19604	0.224609	0.112305	−	0.993674i	$-0.464177\pi$
$349$	4.19604	0.224609	0.112305	+	0.993674i	$0.464177\pi$
$350$	3.19863	0.170974
$351$	6.75608	0.360613
$352$	0	0
$353$	3.32139	0.176780	0.0883898	−	0.996086i	$-0.471828\pi$
$353$	3.32139	0.176780	0.0883898	+	0.996086i	$0.471828\pi$
$354$	10.3262	0.548833
$355$	6.35097	0.337075
$356$	−13.0775	−0.693104
$357$	−1.78309	−0.0943709
$358$	−18.5623	−0.981048
$359$	−22.1803	−1.17063	−0.585317	−	0.810805i	$-0.699030\pi$
$359$	−22.1803	−1.17063	−0.585317	+	0.810805i	$0.699030\pi$
$360$	−1.00000	−0.0527046
$361$	22.1080	1.16358
$362$	9.52786	0.500773
$363$	0	0
$364$	21.6102	1.13268
$365$	−6.94427	−0.363480
$366$	−3.92512	−0.205169
$367$	−17.0497	−0.889989	−0.444994	−	0.895533i	$-0.646794\pi$
$367$	−17.0497	−0.889989	−0.444994	+	0.895533i	$0.646794\pi$
$368$	2.59489	0.135268
$369$	−1.31979	−0.0687054
$370$	5.73294	0.298041
$371$	−7.78768	−0.404316
$372$	2.41941	0.125440
$373$	−0.231215	−0.0119719	−0.00598594	−	0.999982i	$-0.501905\pi$
$373$	−0.231215	−0.0119719	−0.00598594	+	0.999982i	$0.501905\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−5.99215	−0.309021
$377$	33.0477	1.70204
$378$	3.19863	0.164520
$379$	−11.9723	−0.614974	−0.307487	−	0.951552i	$-0.599488\pi$
$379$	−11.9723	−0.614974	−0.307487	+	0.951552i	$0.599488\pi$
$380$	6.41156	0.328906
$381$	16.2155	0.830746
$382$	0.913695	0.0467487
$383$	3.07102	0.156922	0.0784608	−	0.996917i	$-0.474999\pi$
$383$	3.07102	0.156922	0.0784608	+	0.996917i	$0.474999\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−23.2952	−1.18570
$387$	1.32139	0.0671698
$388$	7.63332	0.387523
$389$	19.7569	1.00172	0.500858	−	0.865529i	$-0.333018\pi$
$389$	19.7569	1.00172	0.500858	+	0.865529i	$0.333018\pi$
$390$	−6.75608	−0.342107
$391$	−1.44653	−0.0731543
$392$	3.23122	0.163201
$393$	−17.2888	−0.872104
$394$	24.5896	1.23881
$395$	11.6724	0.587300
$396$	0	0
$397$	−11.4546	−0.574889	−0.287444	−	0.957797i	$-0.592806\pi$
$397$	−11.4546	−0.574889	−0.287444	+	0.957797i	$0.592806\pi$
$398$	10.5112	0.526878
$399$	−20.5082	−1.02669
$400$	1.00000	0.0500000
$401$	22.3001	1.11361	0.556807	−	0.830642i	$-0.312026\pi$
$401$	22.3001	1.11361	0.556807	+	0.830642i	$0.312026\pi$
$402$	15.1676	0.756493
$403$	16.3457	0.814238
$404$	−15.9739	−0.794729
$405$	−1.00000	−0.0496904
$406$	15.6462	0.776509
$407$	0	0
$408$	−0.557453	−0.0275981
$409$	36.2811	1.79399	0.896993	−	0.442044i	$-0.145746\pi$
$409$	36.2811	1.79399	0.896993	+	0.442044i	$0.145746\pi$
$410$	1.31979	0.0651797
$411$	7.93157	0.391235
$412$	18.2904	0.901103
$413$	33.0298	1.62529
$414$	2.59489	0.127532
$415$	−8.00000	−0.392705
$416$	6.75608	0.331244
$417$	8.21778	0.402426
$418$	0	0
$419$	9.06157	0.442687	0.221343	−	0.975196i	$-0.428956\pi$
$419$	9.06157	0.442687	0.221343	+	0.975196i	$0.428956\pi$
$420$	−3.19863	−0.156077
$421$	−2.42586	−0.118229	−0.0591145	−	0.998251i	$-0.518828\pi$
$421$	−2.42586	−0.118229	−0.0591145	+	0.998251i	$0.518828\pi$
$422$	7.06863	0.344095
$423$	−5.99215	−0.291348
$424$	−2.43470	−0.118239
$425$	−0.557453	−0.0270405
$426$	−6.35097	−0.307706
$427$	−12.5550	−0.607579
$428$	−17.1149	−0.827280
$429$	0	0
$430$	−1.32139	−0.0637229
$431$	−2.65847	−0.128054	−0.0640271	−	0.997948i	$-0.520394\pi$
$431$	−2.65847	−0.128054	−0.0640271	+	0.997948i	$0.520394\pi$
$432$	1.00000	0.0481125
$433$	−19.1918	−0.922297	−0.461149	−	0.887323i	$-0.652563\pi$
$433$	−19.1918	−0.922297	−0.461149	+	0.887323i	$0.652563\pi$
$434$	7.73878	0.371473
$435$	−4.89154	−0.234532
$436$	−8.94427	−0.428353
$437$	−16.6373	−0.795870
$438$	6.94427	0.331810
$439$	−12.6955	−0.605923	−0.302962	−	0.953003i	$-0.597975\pi$
$439$	−12.6955	−0.605923	−0.302962	+	0.953003i	$0.597975\pi$
$440$	0	0
$441$	3.23122	0.153867
$442$	−3.76620	−0.179140
$443$	16.9189	0.803839	0.401920	−	0.915675i	$-0.368343\pi$
$443$	16.9189	0.803839	0.401920	+	0.915675i	$0.368343\pi$
$444$	−5.73294	−0.272073
$445$	13.0775	0.619931
$446$	0.801373	0.0379461
$447$	6.08532	0.287826
$448$	3.19863	0.151121
$449$	−19.2809	−0.909924	−0.454962	−	0.890511i	$-0.650347\pi$
$449$	−19.2809	−0.909924	−0.454962	+	0.890511i	$0.650347\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	4.81666	0.226557
$453$	−18.2761	−0.858686
$454$	4.86939	0.228532
$455$	−21.6102	−1.01310
$456$	−6.41156	−0.300249
$457$	−39.5219	−1.84875	−0.924377	−	0.381479i	$-0.875415\pi$
$457$	−39.5219	−1.84875	−0.924377	+	0.381479i	$0.875415\pi$
$458$	−1.16119	−0.0542587
$459$	−0.557453	−0.0260197
$460$	−2.59489	−0.120988
$461$	−13.8398	−0.644584	−0.322292	−	0.946640i	$-0.604453\pi$
$461$	−13.8398	−0.644584	−0.322292	+	0.946640i	$0.604453\pi$
$462$	0	0
$463$	12.5919	0.585195	0.292598	−	0.956236i	$-0.405480\pi$
$463$	12.5919	0.585195	0.292598	+	0.956236i	$0.405480\pi$
$464$	4.89154	0.227084
$465$	−2.41941	−0.112197
$466$	−12.0527	−0.558332
$467$	−11.7368	−0.543115	−0.271557	−	0.962422i	$-0.587539\pi$
$467$	−11.7368	−0.543115	−0.271557	+	0.962422i	$0.587539\pi$
$468$	6.75608	0.312300
$469$	48.5156	2.24024
$470$	5.99215	0.276397
$471$	18.4874	0.851856
$472$	10.3262	0.475304
$473$	0	0
$474$	−11.6724	−0.536129
$475$	−6.41156	−0.294182
$476$	−1.78309	−0.0817276
$477$	−2.43470	−0.111477
$478$	28.2604	1.29260
$479$	−21.4007	−0.977823	−0.488912	−	0.872333i	$-0.662606\pi$
$479$	−21.4007	−0.977823	−0.488912	+	0.872333i	$0.662606\pi$
$480$	−1.00000	−0.0456435
$481$	−38.7322	−1.76604
$482$	−24.7857	−1.12896
$483$	8.30010	0.377668
$484$	0	0
$485$	−7.63332	−0.346611
$486$	1.00000	0.0453609
$487$	−15.8502	−0.718243	−0.359121	−	0.933291i	$-0.616924\pi$
$487$	−15.8502	−0.718243	−0.359121	+	0.933291i	$0.616924\pi$
$488$	−3.92512	−0.177682
$489$	11.5480	0.522219
$490$	−3.23122	−0.145971
$491$	−27.6698	−1.24872	−0.624360	−	0.781137i	$-0.714640\pi$
$491$	−27.6698	−1.24872	−0.624360	+	0.781137i	$0.714640\pi$
$492$	−1.31979	−0.0595007
$493$	−2.72681	−0.122809
$494$	−43.3170	−1.94892
$495$	0	0
$496$	2.41941	0.108635
$497$	−20.3144	−0.911225
$498$	8.00000	0.358489
$499$	−7.06176	−0.316128	−0.158064	−	0.987429i	$-0.550525\pi$
$499$	−7.06176	−0.316128	−0.158064	+	0.987429i	$0.550525\pi$
$500$	−1.00000	−0.0447214
$501$	−2.95212	−0.131891
$502$	−17.8615	−0.797199
$503$	−1.15333	−0.0514247	−0.0257123	−	0.999669i	$-0.508185\pi$
$503$	−1.15333	−0.0514247	−0.0257123	+	0.999669i	$0.508185\pi$
$504$	3.19863	0.142478
$505$	15.9739	0.710827
$506$	0	0
$507$	32.6446	1.44980
$508$	16.2155	0.719447
$509$	−8.47539	−0.375665	−0.187833	−	0.982201i	$-0.560146\pi$
$509$	−8.47539	−0.375665	−0.187833	+	0.982201i	$0.560146\pi$
$510$	0.557453	0.0246845
$511$	22.2121	0.982607
$512$	1.00000	0.0441942
$513$	−6.41156	−0.283077
$514$	4.32237	0.190652
$515$	−18.2904	−0.805971
$516$	1.32139	0.0581708
$517$	0	0
$518$	−18.3375	−0.805705
$519$	−1.84140	−0.0808284
$520$	−6.75608	−0.296274
$521$	31.0618	1.36084	0.680420	−	0.732822i	$-0.261797\pi$
$521$	31.0618	1.36084	0.680420	+	0.732822i	$0.261797\pi$
$522$	4.89154	0.214097
$523$	−19.8326	−0.867217	−0.433609	−	0.901101i	$-0.642760\pi$
$523$	−19.8326	−0.867217	−0.433609	+	0.901101i	$0.642760\pi$
$524$	−17.2888	−0.755265
$525$	3.19863	0.139600
$526$	−23.0282	−1.00408
$527$	−1.34871	−0.0587506
$528$	0	0
$529$	−16.2665	−0.707240
$530$	2.43470	0.105756
$531$	10.3262	0.448121
$532$	−20.5082	−0.889142
$533$	−8.91660	−0.386221
$534$	−13.0775	−0.565917
$535$	17.1149	0.739942
$536$	15.1676	0.655142
$537$	−18.5623	−0.801023
$538$	−11.8567	−0.511178
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−25.2333	−1.08486	−0.542431	−	0.840100i	$-0.682496\pi$
$541$	−25.2333	−1.08486	−0.542431	+	0.840100i	$0.682496\pi$
$542$	−11.4268	−0.490825
$543$	9.52786	0.408880
$544$	−0.557453	−0.0239006
$545$	8.94427	0.383131
$546$	21.6102	0.924830
$547$	−13.4900	−0.576791	−0.288396	−	0.957511i	$-0.593122\pi$
$547$	−13.4900	−0.576791	−0.288396	+	0.957511i	$0.593122\pi$
$548$	7.93157	0.338820
$549$	−3.92512	−0.167520
$550$	0	0
$551$	−31.3624	−1.33608
$552$	2.59489	0.110446
$553$	−37.3355	−1.58767
$554$	−15.0384	−0.638922
$555$	5.73294	0.243350
$556$	8.21778	0.348512
$557$	−38.4550	−1.62939	−0.814696	−	0.579888i	$-0.803096\pi$
$557$	−38.4550	−1.62939	−0.814696	+	0.579888i	$0.803096\pi$
$558$	2.41941	0.102422
$559$	8.92739	0.377588
$560$	−3.19863	−0.135167
$561$	0	0
$562$	13.2666	0.559620
$563$	27.8423	1.17341	0.586706	−	0.809800i	$-0.300425\pi$
$563$	27.8423	1.17341	0.586706	+	0.809800i	$0.300425\pi$
$564$	−5.99215	−0.252315
$565$	−4.81666	−0.202638
$566$	15.1214	0.635598
$567$	3.19863	0.134330
$568$	−6.35097	−0.266481
$569$	8.26209	0.346365	0.173182	−	0.984890i	$-0.444595\pi$
$569$	8.26209	0.346365	0.173182	+	0.984890i	$0.444595\pi$
$570$	6.41156	0.268551
$571$	6.71079	0.280838	0.140419	−	0.990092i	$-0.455155\pi$
$571$	6.71079	0.280838	0.140419	+	0.990092i	$0.455155\pi$
$572$	0	0
$573$	0.913695	0.0381702
$574$	−4.22151	−0.176202
$575$	2.59489	0.108215
$576$	1.00000	0.0416667
$577$	−39.8137	−1.65746	−0.828732	−	0.559645i	$-0.810937\pi$
$577$	−39.8137	−1.65746	−0.828732	+	0.559645i	$0.810937\pi$
$578$	−16.6892	−0.694181
$579$	−23.2952	−0.968117
$580$	−4.89154	−0.203110
$581$	25.5890	1.06161
$582$	7.63332	0.316411
$583$	0	0
$584$	6.94427	0.287356
$585$	−6.75608	−0.279330
$586$	−13.9163	−0.574876
$587$	−10.0592	−0.415187	−0.207593	−	0.978215i	$-0.566563\pi$
$587$	−10.0592	−0.415187	−0.207593	+	0.978215i	$0.566563\pi$
$588$	3.23122	0.133253
$589$	−15.5122	−0.639167
$590$	−10.3262	−0.425124
$591$	24.5896	1.01148
$592$	−5.73294	−0.235622
$593$	23.6430	0.970900	0.485450	−	0.874264i	$-0.338656\pi$
$593$	23.6430	0.970900	0.485450	+	0.874264i	$0.338656\pi$
$594$	0	0
$595$	1.78309	0.0730994
$596$	6.08532	0.249264
$597$	10.5112	0.430194
$598$	17.5313	0.716909
$599$	31.4007	1.28300	0.641499	−	0.767124i	$-0.278313\pi$
$599$	31.4007	1.28300	0.641499	+	0.767124i	$0.278313\pi$
$600$	1.00000	0.0408248
$601$	−17.1469	−0.699436	−0.349718	−	0.936855i	$-0.613723\pi$
$601$	−17.1469	−0.699436	−0.349718	+	0.936855i	$0.613723\pi$
$602$	4.22662	0.172264
$603$	15.1676	0.617674
$604$	−18.2761	−0.743644
$605$	0	0
$606$	−15.9739	−0.648894
$607$	1.40153	0.0568865	0.0284433	−	0.999595i	$-0.490945\pi$
$607$	1.40153	0.0568865	0.0284433	+	0.999595i	$0.490945\pi$
$608$	−6.41156	−0.260023
$609$	15.6462	0.634017
$610$	3.92512	0.158923
$611$	−40.4834	−1.63778
$612$	−0.557453	−0.0225337
$613$	−12.0383	−0.486223	−0.243111	−	0.969998i	$-0.578168\pi$
$613$	−12.0383	−0.486223	−0.243111	+	0.969998i	$0.578168\pi$
$614$	24.0813	0.971843
$615$	1.31979	0.0532190
$616$	0	0
$617$	−5.25177	−0.211428	−0.105714	−	0.994397i	$-0.533713\pi$
$617$	−5.25177	−0.211428	−0.105714	+	0.994397i	$0.533713\pi$
$618$	18.2904	0.735748
$619$	42.0324	1.68942	0.844712	−	0.535221i	$-0.179772\pi$
$619$	42.0324	1.68942	0.844712	+	0.535221i	$0.179772\pi$
$620$	−2.41941	−0.0971657
$621$	2.59489	0.104130
$622$	−30.3816	−1.21819
$623$	−41.8299	−1.67588
$624$	6.75608	0.270460
$625$	1.00000	0.0400000
$626$	16.2012	0.647531
$627$	0	0
$628$	18.4874	0.737729
$629$	3.19585	0.127427
$630$	−3.19863	−0.127436
$631$	−16.9950	−0.676561	−0.338281	−	0.941045i	$-0.609845\pi$
$631$	−16.9950	−0.676561	−0.338281	+	0.941045i	$0.609845\pi$
$632$	−11.6724	−0.464302
$633$	7.06863	0.280953
$634$	−33.0640	−1.31314
$635$	−16.2155	−0.643493
$636$	−2.43470	−0.0965419
$637$	21.8304	0.864950
$638$	0	0
$639$	−6.35097	−0.251241
$640$	−1.00000	−0.0395285
$641$	−49.9080	−1.97125	−0.985624	−	0.168954i	$-0.945961\pi$
$641$	−49.9080	−1.97125	−0.985624	+	0.168954i	$0.945961\pi$
$642$	−17.1149	−0.675471
$643$	−26.7579	−1.05523	−0.527614	−	0.849484i	$-0.676913\pi$
$643$	−26.7579	−1.05523	−0.527614	+	0.849484i	$0.676913\pi$
$644$	8.30010	0.327070
$645$	−1.32139	−0.0520295
$646$	3.57414	0.140623
$647$	−7.85550	−0.308832	−0.154416	−	0.988006i	$-0.549350\pi$
$647$	−7.85550	−0.308832	−0.154416	+	0.988006i	$0.549350\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	6.75608	0.264995
$651$	7.73878	0.303307
$652$	11.5480	0.452255
$653$	0.290394	0.0113640	0.00568200	−	0.999984i	$-0.498191\pi$
$653$	0.290394	0.0113640	0.00568200	+	0.999984i	$0.498191\pi$
$654$	−8.94427	−0.349749
$655$	17.2888	0.675529
$656$	−1.31979	−0.0515291
$657$	6.94427	0.270922
$658$	−19.1666	−0.747194
$659$	17.7202	0.690282	0.345141	−	0.938551i	$-0.387831\pi$
$659$	17.7202	0.690282	0.345141	+	0.938551i	$0.387831\pi$
$660$	0	0
$661$	22.9494	0.892630	0.446315	−	0.894876i	$-0.352736\pi$
$661$	22.9494	0.892630	0.446315	+	0.894876i	$0.352736\pi$
$662$	−0.733928	−0.0285249
$663$	−3.76620	−0.146267
$664$	8.00000	0.310460
$665$	20.5082	0.795273
$666$	−5.73294	−0.222147
$667$	12.6930	0.491476
$668$	−2.95212	−0.114221
$669$	0.801373	0.0309829
$670$	−15.1676	−0.585977
$671$	0	0
$672$	3.19863	0.123390
$673$	35.3081	1.36103	0.680515	−	0.732735i	$-0.261756\pi$
$673$	35.3081	1.36103	0.680515	+	0.732735i	$0.261756\pi$
$674$	−16.3816	−0.630994
$675$	1.00000	0.0384900
$676$	32.6446	1.25556
$677$	42.2238	1.62279	0.811397	−	0.584496i	$-0.198708\pi$
$677$	42.2238	1.62279	0.811397	+	0.584496i	$0.198708\pi$
$678$	4.81666	0.184983
$679$	24.4162	0.937006
$680$	0.557453	0.0213774
$681$	4.86939	0.186595
$682$	0	0
$683$	34.7325	1.32900	0.664502	−	0.747287i	$-0.268644\pi$
$683$	34.7325	1.32900	0.664502	+	0.747287i	$0.268644\pi$
$684$	−6.41156	−0.245152
$685$	−7.93157	−0.303050
$686$	−12.0549	−0.460260
$687$	−1.16119	−0.0443020
$688$	1.32139	0.0503773
$689$	−16.4490	−0.626657
$690$	−2.59489	−0.0987859
$691$	16.7185	0.636002	0.318001	−	0.948090i	$-0.396988\pi$
$691$	16.7185	0.636002	0.318001	+	0.948090i	$0.396988\pi$
$692$	−1.84140	−0.0699994
$693$	0	0
$694$	−16.2012	−0.614990
$695$	−8.21778	−0.311718
$696$	4.89154	0.185413
$697$	0.735720	0.0278674
$698$	4.19604	0.158823
$699$	−12.0527	−0.455876
$700$	3.19863	0.120897
$701$	0.639577	0.0241565	0.0120782	−	0.999927i	$-0.496155\pi$
$701$	0.639577	0.0241565	0.0120782	+	0.999927i	$0.496155\pi$
$702$	6.75608	0.254992
$703$	36.7571	1.38632
$704$	0	0
$705$	5.99215	0.225677
$706$	3.32139	0.125002
$707$	−51.0944	−1.92160
$708$	10.3262	0.388084
$709$	12.6396	0.474689	0.237345	−	0.971426i	$-0.423723\pi$
$709$	12.6396	0.474689	0.237345	+	0.971426i	$0.423723\pi$
$710$	6.35097	0.238348
$711$	−11.6724	−0.437748
$712$	−13.0775	−0.490099
$713$	6.27811	0.235117
$714$	−1.78309	−0.0667303
$715$	0	0
$716$	−18.5623	−0.693706
$717$	28.2604	1.05540
$718$	−22.1803	−0.827763
$719$	41.0960	1.53262	0.766311	−	0.642469i	$-0.222090\pi$
$719$	41.0960	1.53262	0.766311	+	0.642469i	$0.222090\pi$
$720$	−1.00000	−0.0372678
$721$	58.5042	2.17881
$722$	22.1080	0.822776
$723$	−24.7857	−0.921789
$724$	9.52786	0.354100
$725$	4.89154	0.181667
$726$	0	0
$727$	−15.8668	−0.588467	−0.294234	−	0.955734i	$-0.595064\pi$
$727$	−15.8668	−0.588467	−0.294234	+	0.955734i	$0.595064\pi$
$728$	21.6102	0.800927
$729$	1.00000	0.0370370
$730$	−6.94427	−0.257019
$731$	−0.736611	−0.0272445
$732$	−3.92512	−0.145077
$733$	−20.7873	−0.767795	−0.383898	−	0.923376i	$-0.625418\pi$
$733$	−20.7873	−0.767795	−0.383898	+	0.923376i	$0.625418\pi$
$734$	−17.0497	−0.629317
$735$	−3.23122	−0.119185
$736$	2.59489	0.0956491
$737$	0	0
$738$	−1.31979	−0.0485821
$739$	34.6150	1.27333	0.636667	−	0.771139i	$-0.280312\pi$
$739$	34.6150	1.27333	0.636667	+	0.771139i	$0.280312\pi$
$740$	5.73294	0.210747
$741$	−43.3170	−1.59129
$742$	−7.78768	−0.285895
$743$	41.2454	1.51315	0.756573	−	0.653910i	$-0.226872\pi$
$743$	41.2454	1.51315	0.756573	+	0.653910i	$0.226872\pi$
$744$	2.41941	0.0886998
$745$	−6.08532	−0.222949
$746$	−0.231215	−0.00846540
$747$	8.00000	0.292705
$748$	0	0
$749$	−54.7442	−2.00031
$750$	−1.00000	−0.0365148
$751$	3.35796	0.122534	0.0612668	−	0.998121i	$-0.480486\pi$
$751$	3.35796	0.122534	0.0612668	+	0.998121i	$0.480486\pi$
$752$	−5.99215	−0.218511
$753$	−17.8615	−0.650911
$754$	33.0477	1.20352
$755$	18.2761	0.665135
$756$	3.19863	0.116333
$757$	14.7247	0.535177	0.267589	−	0.963533i	$-0.413773\pi$
$757$	14.7247	0.535177	0.267589	+	0.963533i	$0.413773\pi$
$758$	−11.9723	−0.434852
$759$	0	0
$760$	6.41156	0.232572
$761$	0.229814	0.00833074	0.00416537	−	0.999991i	$-0.498674\pi$
$761$	0.229814	0.00833074	0.00416537	+	0.999991i	$0.498674\pi$
$762$	16.2155	0.587426
$763$	−28.6094	−1.03573
$764$	0.913695	0.0330563
$765$	0.557453	0.0201548
$766$	3.07102	0.110960
$767$	69.7649	2.51906
$768$	1.00000	0.0360844
$769$	−26.3568	−0.950451	−0.475226	−	0.879864i	$-0.657634\pi$
$769$	−26.3568	−0.950451	−0.475226	+	0.879864i	$0.657634\pi$
$770$	0	0
$771$	4.32237	0.155666
$772$	−23.2952	−0.838414
$773$	−54.7575	−1.96949	−0.984744	−	0.174007i	$-0.944329\pi$
$773$	−54.7575	−1.96949	−0.984744	+	0.174007i	$0.944329\pi$
$774$	1.32139	0.0474962
$775$	2.41941	0.0869077
$776$	7.63332	0.274020
$777$	−18.3375	−0.657856
$778$	19.7569	0.708321
$779$	8.46190	0.303179
$780$	−6.75608	−0.241906
$781$	0	0
$782$	−1.44653	−0.0517279
$783$	4.89154	0.174809
$784$	3.23122	0.115401
$785$	−18.4874	−0.659844
$786$	−17.2888	−0.616671
$787$	7.45825	0.265858	0.132929	−	0.991126i	$-0.457562\pi$
$787$	7.45825	0.265858	0.132929	+	0.991126i	$0.457562\pi$
$788$	24.5896	0.875969
$789$	−23.0282	−0.819825
$790$	11.6724	0.415284
$791$	15.4067	0.547799
$792$	0	0
$793$	−26.5184	−0.941697
$794$	−11.4546	−0.406508
$795$	2.43470	0.0863497
$796$	10.5112	0.372559
$797$	35.0946	1.24311	0.621557	−	0.783369i	$-0.286500\pi$
$797$	35.0946	1.24311	0.621557	+	0.783369i	$0.286500\pi$
$798$	−20.5082	−0.725982
$799$	3.34034	0.118173
$800$	1.00000	0.0353553
$801$	−13.0775	−0.462070
$802$	22.3001	0.787444
$803$	0	0
$804$	15.1676	0.534921
$805$	−8.30010	−0.292540
$806$	16.3457	0.575753
$807$	−11.8567	−0.417375
$808$	−15.9739	−0.561958
$809$	−22.7625	−0.800288	−0.400144	−	0.916452i	$-0.631040\pi$
$809$	−22.7625	−0.800288	−0.400144	+	0.916452i	$0.631040\pi$
$810$	−1.00000	−0.0351364
$811$	21.7665	0.764326	0.382163	−	0.924095i	$-0.375179\pi$
$811$	21.7665	0.764326	0.382163	+	0.924095i	$0.375179\pi$
$812$	15.6462	0.549075
$813$	−11.4268	−0.400757
$814$	0	0
$815$	−11.5480	−0.404509
$816$	−0.557453	−0.0195148
$817$	−8.47214	−0.296403
$818$	36.2811	1.26854
$819$	21.6102	0.755121
$820$	1.31979	0.0460890
$821$	35.5251	1.23983	0.619917	−	0.784668i	$-0.287166\pi$
$821$	35.5251	1.23983	0.619917	+	0.784668i	$0.287166\pi$
$822$	7.93157	0.276645
$823$	39.6319	1.38148	0.690741	−	0.723102i	$-0.257284\pi$
$823$	39.6319	1.38148	0.690741	+	0.723102i	$0.257284\pi$
$824$	18.2904	0.637176
$825$	0	0
$826$	33.0298	1.14925
$827$	17.6236	0.612833	0.306417	−	0.951898i	$-0.400870\pi$
$827$	17.6236	0.612833	0.306417	+	0.951898i	$0.400870\pi$
$828$	2.59489	0.0901788
$829$	7.04973	0.244847	0.122424	−	0.992478i	$-0.460933\pi$
$829$	7.04973	0.244847	0.122424	+	0.992478i	$0.460933\pi$
$830$	−8.00000	−0.277684
$831$	−15.0384	−0.521677
$832$	6.75608	0.234225
$833$	−1.80125	−0.0624097
$834$	8.21778	0.284558
$835$	2.95212	0.102162
$836$	0	0
$837$	2.41941	0.0836269
$838$	9.06157	0.313027
$839$	−22.5599	−0.778855	−0.389427	−	0.921057i	$-0.627327\pi$
$839$	−22.5599	−0.778855	−0.389427	+	0.921057i	$0.627327\pi$
$840$	−3.19863	−0.110363
$841$	−5.07281	−0.174924
$842$	−2.42586	−0.0836005
$843$	13.2666	0.456928
$844$	7.06863	0.243312
$845$	−32.6446	−1.12301
$846$	−5.99215	−0.206014
$847$	0	0
$848$	−2.43470	−0.0836078
$849$	15.1214	0.518964
$850$	−0.557453	−0.0191205
$851$	−14.8764	−0.509956
$852$	−6.35097	−0.217581
$853$	−18.3884	−0.629607	−0.314804	−	0.949157i	$-0.601939\pi$
$853$	−18.3884	−0.629607	−0.314804	+	0.949157i	$0.601939\pi$
$854$	−12.5550	−0.429623
$855$	6.41156	0.219271
$856$	−17.1149	−0.584975
$857$	−21.9179	−0.748700	−0.374350	−	0.927287i	$-0.622134\pi$
$857$	−21.9179	−0.748700	−0.374350	+	0.927287i	$0.622134\pi$
$858$	0	0
$859$	−32.0841	−1.09470	−0.547348	−	0.836905i	$-0.684363\pi$
$859$	−32.0841	−1.09470	−0.547348	+	0.836905i	$0.684363\pi$
$860$	−1.32139	−0.0450589
$861$	−4.22151	−0.143869
$862$	−2.65847	−0.0905480
$863$	0.406288	0.0138302	0.00691511	−	0.999976i	$-0.497799\pi$
$863$	0.406288	0.0138302	0.00691511	+	0.999976i	$0.497799\pi$
$864$	1.00000	0.0340207
$865$	1.84140	0.0626094
$866$	−19.1918	−0.652163
$867$	−16.6892	−0.566796
$868$	7.73878	0.262671
$869$	0	0
$870$	−4.89154	−0.165839
$871$	102.474	3.47219
$872$	−8.94427	−0.302891
$873$	7.63332	0.258349
$874$	−16.6373	−0.562765
$875$	−3.19863	−0.108133
$876$	6.94427	0.234625
$877$	6.38542	0.215620	0.107810	−	0.994172i	$-0.465616\pi$
$877$	6.38542	0.215620	0.107810	+	0.994172i	$0.465616\pi$
$878$	−12.6955	−0.428452
$879$	−13.9163	−0.469384
$880$	0	0
$881$	−39.6551	−1.33601	−0.668006	−	0.744155i	$-0.732852\pi$
$881$	−39.6551	−1.33601	−0.668006	+	0.744155i	$0.732852\pi$
$882$	3.23122	0.108801
$883$	−4.90523	−0.165074	−0.0825371	−	0.996588i	$-0.526302\pi$
$883$	−4.90523	−0.165074	−0.0825371	+	0.996588i	$0.526302\pi$
$884$	−3.76620	−0.126671
$885$	−10.3262	−0.347113
$886$	16.9189	0.568400
$887$	7.61724	0.255762	0.127881	−	0.991790i	$-0.459182\pi$
$887$	7.61724	0.255762	0.127881	+	0.991790i	$0.459182\pi$
$888$	−5.73294	−0.192385
$889$	51.8674	1.73958
$890$	13.0775	0.438358
$891$	0	0
$892$	0.801373	0.0268319
$893$	38.4190	1.28564
$894$	6.08532	0.203523
$895$	18.5623	0.620469
$896$	3.19863	0.106859
$897$	17.5313	0.585354
$898$	−19.2809	−0.643413
$899$	11.8346	0.394707
$900$	1.00000	0.0333333
$901$	1.35723	0.0452159
$902$	0	0
$903$	4.22662	0.140653
$904$	4.81666	0.160200
$905$	−9.52786	−0.316717
$906$	−18.2761	−0.607183
$907$	−51.7186	−1.71729	−0.858645	−	0.512571i	$-0.828693\pi$
$907$	−51.7186	−1.71729	−0.858645	+	0.512571i	$0.828693\pi$
$908$	4.86939	0.161596
$909$	−15.9739	−0.529820
$910$	−21.6102	−0.716371
$911$	−32.2012	−1.06687	−0.533437	−	0.845840i	$-0.679100\pi$
$911$	−32.2012	−1.06687	−0.533437	+	0.845840i	$0.679100\pi$
$912$	−6.41156	−0.212308
$913$	0	0
$914$	−39.5219	−1.30727
$915$	3.92512	0.129760
$916$	−1.16119	−0.0383667
$917$	−55.3004	−1.82618
$918$	−0.557453	−0.0183987
$919$	31.5512	1.04078	0.520389	−	0.853929i	$-0.325787\pi$
$919$	31.5512	1.04078	0.520389	+	0.853929i	$0.325787\pi$
$920$	−2.59489	−0.0855511
$921$	24.0813	0.793507
$922$	−13.8398	−0.455790
$923$	−42.9077	−1.41232
$924$	0	0
$925$	−5.73294	−0.188498
$926$	12.5919	0.413795
$927$	18.2904	0.600735
$928$	4.89154	0.160573
$929$	26.7857	0.878809	0.439405	−	0.898289i	$-0.355189\pi$
$929$	26.7857	0.878809	0.439405	+	0.898289i	$0.355189\pi$
$930$	−2.41941	−0.0793355
$931$	−20.7171	−0.678976
$932$	−12.0527	−0.394800
$933$	−30.3816	−0.994647
$934$	−11.7368	−0.384040
$935$	0	0
$936$	6.75608	0.220829
$937$	−21.3572	−0.697710	−0.348855	−	0.937177i	$-0.613429\pi$
$937$	−21.3572	−0.697710	−0.348855	+	0.937177i	$0.613429\pi$
$938$	48.5156	1.58409
$939$	16.2012	0.528707
$940$	5.99215	0.195442
$941$	−41.5778	−1.35540	−0.677699	−	0.735340i	$-0.737023\pi$
$941$	−41.5778	−1.35540	−0.677699	+	0.735340i	$0.737023\pi$
$942$	18.4874	0.602353
$943$	−3.42471	−0.111524
$944$	10.3262	0.336090
$945$	−3.19863	−0.104051
$946$	0	0
$947$	8.59847	0.279413	0.139706	−	0.990193i	$-0.455384\pi$
$947$	8.59847	0.279413	0.139706	+	0.990193i	$0.455384\pi$
$948$	−11.6724	−0.379101
$949$	46.9161	1.52296
$950$	−6.41156	−0.208018
$951$	−33.0640	−1.07217
$952$	−1.78309	−0.0577901
$953$	5.86067	0.189846	0.0949229	−	0.995485i	$-0.469740\pi$
$953$	5.86067	0.189846	0.0949229	+	0.995485i	$0.469740\pi$
$954$	−2.43470	−0.0788262
$955$	−0.913695	−0.0295665
$956$	28.2604	0.914006
$957$	0	0
$958$	−21.4007	−0.691425
$959$	25.3701	0.819244
$960$	−1.00000	−0.0322749
$961$	−25.1465	−0.811176
$962$	−38.7322	−1.24878
$963$	−17.1149	−0.551520
$964$	−24.7857	−0.798293
$965$	23.2952	0.749901
$966$	8.30010	0.267051
$967$	24.7496	0.795894	0.397947	−	0.917408i	$-0.369723\pi$
$967$	24.7496	0.795894	0.397947	+	0.917408i	$0.369723\pi$
$968$	0	0
$969$	3.57414	0.114818
$970$	−7.63332	−0.245091
$971$	43.1418	1.38449	0.692243	−	0.721664i	$-0.256622\pi$
$971$	43.1418	1.38449	0.692243	+	0.721664i	$0.256622\pi$
$972$	1.00000	0.0320750
$973$	26.2856	0.842678
$974$	−15.8502	−0.507874
$975$	6.75608	0.216368
$976$	−3.92512	−0.125640
$977$	−42.5522	−1.36137	−0.680683	−	0.732579i	$-0.738317\pi$
$977$	−42.5522	−1.36137	−0.680683	+	0.732579i	$0.738317\pi$
$978$	11.5480	0.369264
$979$	0	0
$980$	−3.23122	−0.103217
$981$	−8.94427	−0.285569
$982$	−27.6698	−0.882978
$983$	18.3473	0.585188	0.292594	−	0.956237i	$-0.405482\pi$
$983$	18.3473	0.585188	0.292594	+	0.956237i	$0.405482\pi$
$984$	−1.31979	−0.0420733
$985$	−24.5896	−0.783491
$986$	−2.72681	−0.0868392
$987$	−19.1666	−0.610081
$988$	−43.3170	−1.37810
$989$	3.42886	0.109031
$990$	0	0
$991$	1.48883	0.0472941	0.0236471	−	0.999720i	$-0.492472\pi$
$991$	1.48883	0.0472941	0.0236471	+	0.999720i	$0.492472\pi$
$992$	2.41941	0.0768162
$993$	−0.733928	−0.0232905
$994$	−20.3144	−0.644334
$995$	−10.5112	−0.333227
$996$	8.00000	0.253490
$997$	55.9405	1.77165	0.885826	−	0.464017i	$-0.153592\pi$
$997$	55.9405	1.77165	0.885826	+	0.464017i	$0.153592\pi$
$998$	−7.06176	−0.223536
$999$	−5.73294	−0.181382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bs.1.3		4
11.7	odd	10		330.2.m.f.181.2	yes	8
11.8	odd	10		330.2.m.f.31.2	✓	8
11.10	odd	2		3630.2.a.bq.1.2		4
33.8	even	10		990.2.n.i.361.2		8
33.29	even	10		990.2.n.i.181.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.31.2	✓	8	11.8	odd	10
330.2.m.f.181.2	yes	8	11.7	odd	10
990.2.n.i.181.2		8	33.29	even	10
990.2.n.i.361.2		8	33.8	even	10
3630.2.a.bq.1.2		4	11.10	odd	2
3630.2.a.bs.1.3		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.19863 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.19863 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{12} +6.75608 q^{13} +3.19863 q^{14} -1.00000 q^{15} +1.00000 q^{16} -0.557453 q^{17} +1.00000 q^{18} -6.41156 q^{19} -1.00000 q^{20} +3.19863 q^{21} +2.59489 q^{23} +1.00000 q^{24} +1.00000 q^{25} +6.75608 q^{26} +1.00000 q^{27} +3.19863 q^{28} +4.89154 q^{29} -1.00000 q^{30} +2.41941 q^{31} +1.00000 q^{32} -0.557453 q^{34} -3.19863 q^{35} +1.00000 q^{36} -5.73294 q^{37} -6.41156 q^{38} +6.75608 q^{39} -1.00000 q^{40} -1.31979 q^{41} +3.19863 q^{42} +1.32139 q^{43} -1.00000 q^{45} +2.59489 q^{46} -5.99215 q^{47} +1.00000 q^{48} +3.23122 q^{49} +1.00000 q^{50} -0.557453 q^{51} +6.75608 q^{52} -2.43470 q^{53} +1.00000 q^{54} +3.19863 q^{56} -6.41156 q^{57} +4.89154 q^{58} +10.3262 q^{59} -1.00000 q^{60} -3.92512 q^{61} +2.41941 q^{62} +3.19863 q^{63} +1.00000 q^{64} -6.75608 q^{65} +15.1676 q^{67} -0.557453 q^{68} +2.59489 q^{69} -3.19863 q^{70} -6.35097 q^{71} +1.00000 q^{72} +6.94427 q^{73} -5.73294 q^{74} +1.00000 q^{75} -6.41156 q^{76} +6.75608 q^{78} -11.6724 q^{79} -1.00000 q^{80} +1.00000 q^{81} -1.31979 q^{82} +8.00000 q^{83} +3.19863 q^{84} +0.557453 q^{85} +1.32139 q^{86} +4.89154 q^{87} -13.0775 q^{89} -1.00000 q^{90} +21.6102 q^{91} +2.59489 q^{92} +2.41941 q^{93} -5.99215 q^{94} +6.41156 q^{95} +1.00000 q^{96} +7.63332 q^{97} +3.23122 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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

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