LMFDB - Embedded newform 3630.2.a.bq.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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.58059 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.58059 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +5.75608 q^{13} -1.58059 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.17549 q^{17} -1.00000 q^{18} -1.32139 q^{19} -1.00000 q^{20} +1.58059 q^{21} -0.358826 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.75608 q^{26} +1.00000 q^{27} +1.58059 q^{28} -9.67076 q^{29} +1.00000 q^{30} +7.19863 q^{31} -1.00000 q^{32} +7.17549 q^{34} -1.58059 q^{35} +1.00000 q^{36} +9.73294 q^{37} +1.32139 q^{38} +5.75608 q^{39} +1.00000 q^{40} +12.0064 q^{41} -1.58059 q^{42} +6.41156 q^{43} -1.00000 q^{45} +0.358826 q^{46} +6.52001 q^{47} +1.00000 q^{48} -4.50173 q^{49} -1.00000 q^{50} -7.17549 q^{51} +5.75608 q^{52} +2.34453 q^{53} -1.00000 q^{54} -1.58059 q^{56} -1.32139 q^{57} +9.67076 q^{58} +10.3262 q^{59} -1.00000 q^{60} -5.63332 q^{61} -7.19863 q^{62} +1.58059 q^{63} +1.00000 q^{64} -5.75608 q^{65} -5.07747 q^{67} -7.17549 q^{68} -0.358826 q^{69} +1.58059 q^{70} +9.11491 q^{71} -1.00000 q^{72} -6.94427 q^{73} -9.73294 q^{74} +1.00000 q^{75} -1.32139 q^{76} -5.75608 q^{78} -11.5265 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.0064 q^{82} -8.00000 q^{83} +1.58059 q^{84} +7.17549 q^{85} -6.41156 q^{86} -9.67076 q^{87} +7.16764 q^{89} +1.00000 q^{90} +9.09802 q^{91} -0.358826 q^{92} +7.19863 q^{93} -6.52001 q^{94} +1.32139 q^{95} -1.00000 q^{96} -1.92512 q^{97} +4.50173 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.58059	0.597408	0.298704	−	0.954346i	$-0.403446\pi$
$7$	1.58059	0.597408	0.298704	+	0.954346i	$0.403446\pi$
$8$	−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
$13$	5.75608	1.59645	0.798225	−	0.602360i	$-0.205773\pi$
$13$	5.75608	1.59645	0.798225	+	0.602360i	$0.205773\pi$
$14$	−1.58059	−0.422431
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−7.17549	−1.74031	−0.870156	−	0.492777i	$-0.835982\pi$
$17$	−7.17549	−1.74031	−0.870156	+	0.492777i	$0.835982\pi$
$18$	−1.00000	−0.235702
$19$	−1.32139	−0.303147	−0.151573	−	0.988446i	$-0.548434\pi$
$19$	−1.32139	−0.303147	−0.151573	+	0.988446i	$0.548434\pi$
$20$	−1.00000	−0.223607
$21$	1.58059	0.344914
$22$	0	0
$23$	−0.358826	−0.0748205	−0.0374102	−	0.999300i	$-0.511911\pi$
$23$	−0.358826	−0.0748205	−0.0374102	+	0.999300i	$0.511911\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−5.75608	−1.12886
$27$	1.00000	0.192450
$28$	1.58059	0.298704
$29$	−9.67076	−1.79582	−0.897908	−	0.440184i	$-0.854913\pi$
$29$	−9.67076	−1.79582	−0.897908	+	0.440184i	$0.854913\pi$
$30$	1.00000	0.182574
$31$	7.19863	1.29291	0.646456	−	0.762951i	$-0.276250\pi$
$31$	7.19863	1.29291	0.646456	+	0.762951i	$0.276250\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	7.17549	1.23059
$35$	−1.58059	−0.267169
$36$	1.00000	0.166667
$37$	9.73294	1.60009	0.800043	−	0.599943i	$-0.204810\pi$
$37$	9.73294	1.60009	0.800043	+	0.599943i	$0.204810\pi$
$38$	1.32139	0.214357
$39$	5.75608	0.921711
$40$	1.00000	0.158114
$41$	12.0064	1.87509	0.937546	−	0.347861i	$-0.113092\pi$
$41$	12.0064	1.87509	0.937546	+	0.347861i	$0.113092\pi$
$42$	−1.58059	−0.243891
$43$	6.41156	0.977753	0.488877	−	0.872353i	$-0.337407\pi$
$43$	6.41156	0.977753	0.488877	+	0.872353i	$0.337407\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0.358826	0.0529061
$47$	6.52001	0.951042	0.475521	−	0.879704i	$-0.342260\pi$
$47$	6.52001	0.951042	0.475521	+	0.879704i	$0.342260\pi$
$48$	1.00000	0.144338
$49$	−4.50173	−0.643104
$50$	−1.00000	−0.141421
$51$	−7.17549	−1.00477
$52$	5.75608	0.798225
$53$	2.34453	0.322045	0.161023	−	0.986951i	$-0.448521\pi$
$53$	2.34453	0.322045	0.161023	+	0.986951i	$0.448521\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.58059	−0.211216
$57$	−1.32139	−0.175022
$58$	9.67076	1.26983
$59$	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
$61$	−5.63332	−0.721273	−0.360637	−	0.932706i	$-0.617441\pi$
$61$	−5.63332	−0.721273	−0.360637	+	0.932706i	$0.617441\pi$
$62$	−7.19863	−0.914227
$63$	1.58059	0.199136
$64$	1.00000	0.125000
$65$	−5.75608	−0.713954
$66$	0	0
$67$	−5.07747	−0.620311	−0.310156	−	0.950686i	$-0.600381\pi$
$67$	−5.07747	−0.620311	−0.310156	+	0.950686i	$0.600381\pi$
$68$	−7.17549	−0.870156
$69$	−0.358826	−0.0431976
$70$	1.58059	0.188917
$71$	9.11491	1.08174	0.540870	−	0.841106i	$-0.318095\pi$
$71$	9.11491	1.08174	0.540870	+	0.841106i	$0.318095\pi$
$72$	−1.00000	−0.117851
$73$	−6.94427	−0.812766	−0.406383	−	0.913703i	$-0.633210\pi$
$73$	−6.94427	−0.812766	−0.406383	+	0.913703i	$0.633210\pi$
$74$	−9.73294	−1.13143
$75$	1.00000	0.115470
$76$	−1.32139	−0.151573
$77$	0	0
$78$	−5.75608	−0.651748
$79$	−11.5265	−1.29683	−0.648414	−	0.761288i	$-0.724567\pi$
$79$	−11.5265	−1.29683	−0.648414	+	0.761288i	$0.724567\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−12.0064	−1.32589
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	1.58059	0.172457
$85$	7.17549	0.778291
$86$	−6.41156	−0.691376
$87$	−9.67076	−1.03681
$88$	0	0
$89$	7.16764	0.759768	0.379884	−	0.925034i	$-0.375964\pi$
$89$	7.16764	0.759768	0.379884	+	0.925034i	$0.375964\pi$
$90$	1.00000	0.105409
$91$	9.09802	0.953732
$92$	−0.358826	−0.0374102
$93$	7.19863	0.746463
$94$	−6.52001	−0.672488
$95$	1.32139	0.135571
$96$	−1.00000	−0.102062
$97$	−1.92512	−0.195466	−0.0977331	−	0.995213i	$-0.531159\pi$
$97$	−1.92512	−0.195466	−0.0977331	+	0.995213i	$0.531159\pi$
$98$	4.50173	0.454743
$99$	0	0
$100$	1.00000	0.100000
$101$	8.24092	0.820002	0.410001	−	0.912085i	$-0.365528\pi$
$101$	8.24092	0.820002	0.410001	+	0.912085i	$0.365528\pi$
$102$	7.17549	0.710479
$103$	−4.90843	−0.483642	−0.241821	−	0.970321i	$-0.577745\pi$
$103$	−4.90843	−0.483642	−0.241821	+	0.970321i	$0.577745\pi$
$104$	−5.75608	−0.564430
$105$	−1.58059	−0.154250
$106$	−2.34453	−0.227720
$107$	1.64903	0.159417	0.0797086	−	0.996818i	$-0.474601\pi$
$107$	1.64903	0.159417	0.0797086	+	0.996818i	$0.474601\pi$
$108$	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
$111$	9.73294	0.923810
$112$	1.58059	0.149352
$113$	0.0374409	0.00352214	0.00176107	−	0.999998i	$-0.499439\pi$
$113$	0.0374409	0.00352214	0.00176107	+	0.999998i	$0.499439\pi$
$114$	1.32139	0.123759
$115$	0.358826	0.0334607
$116$	−9.67076	−0.897908
$117$	5.75608	0.532150
$118$	−10.3262	−0.950607
$119$	−11.3415	−1.03968
$120$	1.00000	0.0912871
$121$	0	0
$122$	5.63332	0.510017
$123$	12.0064	1.08259
$124$	7.19863	0.646456
$125$	−1.00000	−0.0894427
$126$	−1.58059	−0.140810
$127$	16.5418	1.46784	0.733921	−	0.679234i	$-0.237688\pi$
$127$	16.5418	1.46784	0.733921	+	0.679234i	$0.237688\pi$
$128$	−1.00000	−0.0883883
$129$	6.41156	0.564506
$130$	5.75608	0.504842
$131$	12.5096	1.09297	0.546483	−	0.837470i	$-0.315966\pi$
$131$	12.5096	1.09297	0.546483	+	0.837470i	$0.315966\pi$
$132$	0	0
$133$	−2.08857	−0.181102
$134$	5.07747	0.438626
$135$	−1.00000	−0.0860663
$136$	7.17549	0.615293
$137$	−12.3135	−1.05202	−0.526008	−	0.850480i	$-0.676312\pi$
$137$	−12.3135	−1.05202	−0.526008	+	0.850480i	$0.676312\pi$
$138$	0.358826	0.0305453
$139$	−12.9970	−1.10239	−0.551196	−	0.834376i	$-0.685828\pi$
$139$	−12.9970	−1.10239	−0.551196	+	0.834376i	$0.685828\pi$
$140$	−1.58059	−0.133585
$141$	6.52001	0.549084
$142$	−9.11491	−0.764906
$143$	0	0
$144$	1.00000	0.0833333
$145$	9.67076	0.803113
$146$	6.94427	0.574712
$147$	−4.50173	−0.371296
$148$	9.73294	0.800043
$149$	1.64762	0.134979	0.0674893	−	0.997720i	$-0.478501\pi$
$149$	1.64762	0.134979	0.0674893	+	0.997720i	$0.478501\pi$
$150$	−1.00000	−0.0816497
$151$	−6.74823	−0.549163	−0.274582	−	0.961564i	$-0.588539\pi$
$151$	−6.74823	−0.549163	−0.274582	+	0.961564i	$0.588539\pi$
$152$	1.32139	0.107179
$153$	−7.17549	−0.580104
$154$	0	0
$155$	−7.19863	−0.578208
$156$	5.75608	0.460855
$157$	8.92898	0.712610	0.356305	−	0.934370i	$-0.384036\pi$
$157$	8.92898	0.712610	0.356305	+	0.934370i	$0.384036\pi$
$158$	11.5265	0.916996
$159$	2.34453	0.185933
$160$	1.00000	0.0790569
$161$	−0.567158	−0.0446983
$162$	−1.00000	−0.0785674
$163$	9.72251	0.761525	0.380763	−	0.924673i	$-0.375661\pi$
$163$	9.72251	0.761525	0.380763	+	0.924673i	$0.375661\pi$
$164$	12.0064	0.937546
$165$	0	0
$166$	8.00000	0.620920
$167$	15.4643	1.19666	0.598331	−	0.801249i	$-0.295831\pi$
$167$	15.4643	1.19666	0.598331	+	0.801249i	$0.295831\pi$
$168$	−1.58059	−0.121945
$169$	20.1325	1.54865
$170$	−7.17549	−0.550335
$171$	−1.32139	−0.101049
$172$	6.41156	0.488877
$173$	−18.4037	−1.39921	−0.699604	−	0.714531i	$-0.746640\pi$
$173$	−18.4037	−1.39921	−0.699604	+	0.714531i	$0.746640\pi$
$174$	9.67076	0.733139
$175$	1.58059	0.119482
$176$	0	0
$177$	10.3262	0.776168
$178$	−7.16764	−0.537237
$179$	−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	$0.384787\pi$
$182$	−9.09802	−0.674390
$183$	−5.63332	−0.416427
$184$	0.358826	0.0264530
$185$	−9.73294	−0.715580
$186$	−7.19863	−0.527829
$187$	0	0
$188$	6.52001	0.475521
$189$	1.58059	0.114971
$190$	−1.32139	−0.0958634
$191$	20.0306	1.44936	0.724681	−	0.689085i	$-0.241987\pi$
$191$	20.0306	1.44936	0.724681	+	0.689085i	$0.241987\pi$
$192$	1.00000	0.0721688
$193$	7.82937	0.563570	0.281785	−	0.959478i	$-0.409074\pi$
$193$	7.82937	0.563570	0.281785	+	0.959478i	$0.409074\pi$
$194$	1.92512	0.138215
$195$	−5.75608	−0.412201
$196$	−4.50173	−0.321552
$197$	20.6798	1.47337	0.736687	−	0.676234i	$-0.236389\pi$
$197$	20.6798	1.47337	0.736687	+	0.676234i	$0.236389\pi$
$198$	0	0
$199$	−3.12921	−0.221824	−0.110912	−	0.993830i	$-0.535377\pi$
$199$	−3.12921	−0.221824	−0.110912	+	0.993830i	$0.535377\pi$
$200$	−1.00000	−0.0707107
$201$	−5.07747	−0.358137
$202$	−8.24092	−0.579829
$203$	−15.2855	−1.07283
$204$	−7.17549	−0.502385
$205$	−12.0064	−0.838567
$206$	4.90843	0.341986
$207$	−0.358826	−0.0249402
$208$	5.75608	0.399112
$209$	0	0
$210$	1.58059	0.109071
$211$	14.3047	0.984776	0.492388	−	0.870376i	$-0.336124\pi$
$211$	14.3047	0.984776	0.492388	+	0.870376i	$0.336124\pi$
$212$	2.34453	0.161023
$213$	9.11491	0.624543
$214$	−1.64903	−0.112725
$215$	−6.41156	−0.437264
$216$	−1.00000	−0.0680414
$217$	11.3781	0.772396
$218$	−8.94427	−0.605783
$219$	−6.94427	−0.469250
$220$	0	0
$221$	−41.3027	−2.77832
$222$	−9.73294	−0.653232
$223$	5.58059	0.373704	0.186852	−	0.982388i	$-0.440171\pi$
$223$	5.58059	0.373704	0.186852	+	0.982388i	$0.440171\pi$
$224$	−1.58059	−0.105608
$225$	1.00000	0.0666667
$226$	−0.0374409	−0.00249053
$227$	4.68905	0.311223	0.155612	−	0.987818i	$-0.450265\pi$
$227$	4.68905	0.311223	0.155612	+	0.987818i	$0.450265\pi$
$228$	−1.32139	−0.0875109
$229$	8.39725	0.554906	0.277453	−	0.960739i	$-0.410510\pi$
$229$	8.39725	0.554906	0.277453	+	0.960739i	$0.410510\pi$
$230$	−0.358826	−0.0236603
$231$	0	0
$232$	9.67076	0.634917
$233$	7.27351	0.476503	0.238252	−	0.971203i	$-0.423426\pi$
$233$	7.27351	0.476503	0.238252	+	0.971203i	$0.423426\pi$
$234$	−5.75608	−0.376287
$235$	−6.52001	−0.425319
$236$	10.3262	0.672181
$237$	−11.5265	−0.748724
$238$	11.3415	0.735162
$239$	21.7883	1.40937	0.704683	−	0.709523i	$-0.251089\pi$
$239$	21.7883	1.40937	0.704683	+	0.709523i	$0.251089\pi$
$240$	−1.00000	−0.0645497
$241$	4.54057	0.292484	0.146242	−	0.989249i	$-0.453282\pi$
$241$	4.54057	0.292484	0.146242	+	0.989249i	$0.453282\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−5.63332	−0.360637
$245$	4.50173	0.287605
$246$	−12.0064	−0.765503
$247$	−7.60600	−0.483958
$248$	−7.19863	−0.457113
$249$	−8.00000	−0.506979
$250$	1.00000	0.0632456
$251$	4.20906	0.265674	0.132837	−	0.991138i	$-0.457591\pi$
$251$	4.20906	0.265674	0.132837	+	0.991138i	$0.457591\pi$
$252$	1.58059	0.0995680
$253$	0	0
$254$	−16.5418	−1.03792
$255$	7.17549	0.449346
$256$	1.00000	0.0625000
$257$	−14.7945	−0.922856	−0.461428	−	0.887178i	$-0.652663\pi$
$257$	−14.7945	−0.922856	−0.461428	+	0.887178i	$0.652663\pi$
$258$	−6.41156	−0.399166
$259$	15.3838	0.955904
$260$	−5.75608	−0.356977
$261$	−9.67076	−0.598605
$262$	−12.5096	−0.772844
$263$	−7.90358	−0.487355	−0.243678	−	0.969856i	$-0.578354\pi$
$263$	−7.90358	−0.487355	−0.243678	+	0.969856i	$0.578354\pi$
$264$	0	0
$265$	−2.34453	−0.144023
$266$	2.08857	0.128059
$267$	7.16764	0.438652
$268$	−5.07747	−0.310156
$269$	17.9469	1.09424	0.547120	−	0.837054i	$-0.315724\pi$
$269$	17.9469	1.09424	0.547120	+	0.837054i	$0.315724\pi$
$270$	1.00000	0.0608581
$271$	−5.86454	−0.356245	−0.178123	−	0.984008i	$-0.557002\pi$
$271$	−5.86454	−0.356245	−0.178123	+	0.984008i	$0.557002\pi$
$272$	−7.17549	−0.435078
$273$	9.09802	0.550637
$274$	12.3135	0.743888
$275$	0	0
$276$	−0.358826	−0.0215988
$277$	8.43371	0.506732	0.253366	−	0.967370i	$-0.418462\pi$
$277$	8.43371	0.506732	0.253366	+	0.967370i	$0.418462\pi$
$278$	12.9970	0.779508
$279$	7.19863	0.430971
$280$	1.58059	0.0944585
$281$	5.85024	0.348996	0.174498	−	0.984658i	$-0.444170\pi$
$281$	5.85024	0.348996	0.174498	+	0.984658i	$0.444170\pi$
$282$	−6.52001	−0.388261
$283$	11.0312	0.655736	0.327868	−	0.944724i	$-0.393670\pi$
$283$	11.0312	0.655736	0.327868	+	0.944724i	$0.393670\pi$
$284$	9.11491	0.540870
$285$	1.32139	0.0782721
$286$	0	0
$287$	18.9773	1.12020
$288$	−1.00000	−0.0589256
$289$	34.4876	2.02868
$290$	−9.67076	−0.567887
$291$	−1.92512	−0.112852
$292$	−6.94427	−0.406383
$293$	3.22962	0.188676	0.0943382	−	0.995540i	$-0.469927\pi$
$293$	3.22962	0.188676	0.0943382	+	0.995540i	$0.469927\pi$
$294$	4.50173	0.262546
$295$	−10.3262	−0.601217
$296$	−9.73294	−0.565716
$297$	0	0
$298$	−1.64762	−0.0954443
$299$	−2.06543	−0.119447
$300$	1.00000	0.0577350
$301$	10.1341	0.584118
$302$	6.74823	0.388317
$303$	8.24092	0.473429
$304$	−1.32139	−0.0757867
$305$	5.63332	0.322563
$306$	7.17549	0.410195
$307$	−22.9531	−1.31000	−0.655002	−	0.755627i	$-0.727332\pi$
$307$	−22.9531	−1.31000	−0.655002	+	0.755627i	$0.727332\pi$
$308$	0	0
$309$	−4.90843	−0.279231
$310$	7.19863	0.408855
$311$	4.20121	0.238229	0.119114	−	0.992881i	$-0.461994\pi$
$311$	4.20121	0.238229	0.119114	+	0.992881i	$0.461994\pi$
$312$	−5.75608	−0.325874
$313$	−18.3816	−1.03899	−0.519493	−	0.854474i	$-0.673879\pi$
$313$	−18.3816	−1.03899	−0.519493	+	0.854474i	$0.673879\pi$
$314$	−8.92898	−0.503892
$315$	−1.58059	−0.0890563
$316$	−11.5265	−0.648414
$317$	−25.3311	−1.42274	−0.711368	−	0.702820i	$-0.751924\pi$
$317$	−25.3311	−1.42274	−0.711368	+	0.702820i	$0.751924\pi$
$318$	−2.34453	−0.131474
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	1.64903	0.0920396
$322$	0.567158	0.0316065
$323$	9.48158	0.527569
$324$	1.00000	0.0555556
$325$	5.75608	0.319290
$326$	−9.72251	−0.538480
$327$	8.94427	0.494619
$328$	−12.0064	−0.662945
$329$	10.3055	0.568160
$330$	0	0
$331$	26.1159	1.43546	0.717730	−	0.696322i	$-0.245181\pi$
$331$	26.1159	1.43546	0.717730	+	0.696322i	$0.245181\pi$
$332$	−8.00000	−0.439057
$333$	9.73294	0.533362
$334$	−15.4643	−0.846168
$335$	5.07747	0.277412
$336$	1.58059	0.0862284
$337$	−18.2012	−0.991483	−0.495742	−	0.868470i	$-0.665104\pi$
$337$	−18.2012	−0.991483	−0.495742	+	0.868470i	$0.665104\pi$
$338$	−20.1325	−1.09506
$339$	0.0374409	0.00203351
$340$	7.17549	0.389145
$341$	0	0
$342$	1.32139	0.0714523
$343$	−18.1795	−0.981603
$344$	−6.41156	−0.345688
$345$	0.358826	0.0193186
$346$	18.4037	0.989389
$347$	−18.3816	−0.986773	−0.493387	−	0.869810i	$-0.664241\pi$
$347$	−18.3816	−0.986773	−0.493387	+	0.869810i	$0.664241\pi$
$348$	−9.67076	−0.518407
$349$	−29.2204	−1.56413	−0.782065	−	0.623197i	$-0.785834\pi$
$349$	−29.2204	−1.56413	−0.782065	+	0.623197i	$0.785834\pi$
$350$	−1.58059	−0.0844863
$351$	5.75608	0.307237
$352$	0	0
$353$	−4.41156	−0.234803	−0.117402	−	0.993085i	$-0.537457\pi$
$353$	−4.41156	−0.234803	−0.117402	+	0.993085i	$0.537457\pi$
$354$	−10.3262	−0.548833
$355$	−9.11491	−0.483769
$356$	7.16764	0.379884
$357$	−11.3415	−0.600257
$358$	18.5623	0.981048
$359$	22.1803	1.17063	0.585317	−	0.810805i	$-0.300970\pi$
$359$	22.1803	1.17063	0.585317	+	0.810805i	$0.300970\pi$
$360$	1.00000	0.0527046
$361$	−17.2539	−0.908102
$362$	−9.52786	−0.500773
$363$	0	0
$364$	9.09802	0.476866
$365$	6.94427	0.363480
$366$	5.63332	0.294458
$367$	−7.49129	−0.391042	−0.195521	−	0.980700i	$-0.562640\pi$
$367$	−7.49129	−0.391042	−0.195521	+	0.980700i	$0.562640\pi$
$368$	−0.358826	−0.0187051
$369$	12.0064	0.625031
$370$	9.73294	0.505991
$371$	3.70574	0.192392
$372$	7.19863	0.373231
$373$	−7.50173	−0.388425	−0.194212	−	0.980960i	$-0.562215\pi$
$373$	−7.50173	−0.388425	−0.194212	+	0.980960i	$0.562215\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−6.52001	−0.336244
$377$	−55.6657	−2.86693
$378$	−1.58059	−0.0812969
$379$	−22.6589	−1.16391	−0.581955	−	0.813221i	$-0.697712\pi$
$379$	−22.6589	−1.16391	−0.581955	+	0.813221i	$0.697712\pi$
$380$	1.32139	0.0677856
$381$	16.5418	0.847460
$382$	−20.0306	−1.02485
$383$	−6.48742	−0.331492	−0.165746	−	0.986168i	$-0.553003\pi$
$383$	−6.48742	−0.331492	−0.165746	+	0.986168i	$0.553003\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−7.82937	−0.398504
$387$	6.41156	0.325918
$388$	−1.92512	−0.0977331
$389$	21.5824	1.09427	0.547137	−	0.837043i	$-0.315718\pi$
$389$	21.5824	1.09427	0.547137	+	0.837043i	$0.315718\pi$
$390$	5.75608	0.291470
$391$	2.57475	0.130211
$392$	4.50173	0.227371
$393$	12.5096	0.631025
$394$	−20.6798	−1.04183
$395$	11.5265	0.579959
$396$	0	0
$397$	16.5235	0.829289	0.414644	−	0.909984i	$-0.363906\pi$
$397$	16.5235	0.829289	0.414644	+	0.909984i	$0.363906\pi$
$398$	3.12921	0.156853
$399$	−2.08857	−0.104559
$400$	1.00000	0.0500000
$401$	14.5672	0.727449	0.363725	−	0.931507i	$-0.381505\pi$
$401$	14.5672	0.727449	0.363725	+	0.931507i	$0.381505\pi$
$402$	5.07747	0.253241
$403$	41.4359	2.06407
$404$	8.24092	0.410001
$405$	−1.00000	−0.0496904
$406$	15.2855	0.758609
$407$	0	0
$408$	7.17549	0.355240
$409$	22.6287	1.11892	0.559458	−	0.828859i	$-0.311009\pi$
$409$	22.6287	1.11892	0.559458	+	0.828859i	$0.311009\pi$
$410$	12.0064	0.592956
$411$	−12.3135	−0.607382
$412$	−4.90843	−0.241821
$413$	16.3216	0.803132
$414$	0.358826	0.0176354
$415$	8.00000	0.392705
$416$	−5.75608	−0.282215
$417$	−12.9970	−0.636466
$418$	0	0
$419$	5.41057	0.264324	0.132162	−	0.991228i	$-0.457808\pi$
$419$	5.41057	0.264324	0.132162	+	0.991228i	$0.457808\pi$
$420$	−1.58059	−0.0771250
$421$	3.48158	0.169682	0.0848410	−	0.996395i	$-0.472962\pi$
$421$	3.48158	0.169682	0.0848410	+	0.996395i	$0.472962\pi$
$422$	−14.3047	−0.696342
$423$	6.52001	0.317014
$424$	−2.34453	−0.113860
$425$	−7.17549	−0.348062
$426$	−9.11491	−0.441619
$427$	−8.90399	−0.430894
$428$	1.64903	0.0797086
$429$	0	0
$430$	6.41156	0.309193
$431$	12.2169	0.588468	0.294234	−	0.955733i	$-0.404935\pi$
$431$	12.2169	0.588468	0.294234	+	0.955733i	$0.404935\pi$
$432$	1.00000	0.0481125
$433$	9.48356	0.455751	0.227875	−	0.973690i	$-0.426822\pi$
$433$	9.48356	0.455751	0.227875	+	0.973690i	$0.426822\pi$
$434$	−11.3781	−0.546166
$435$	9.67076	0.463678
$436$	8.94427	0.428353
$437$	0.474148	0.0226816
$438$	6.94427	0.331810
$439$	−7.54960	−0.360323	−0.180161	−	0.983637i	$-0.557662\pi$
$439$	−7.54960	−0.360323	−0.180161	+	0.983637i	$0.557662\pi$
$440$	0	0
$441$	−4.50173	−0.214368
$442$	41.3027	1.96457
$443$	−23.5713	−1.11991	−0.559954	−	0.828524i	$-0.689181\pi$
$443$	−23.5713	−1.11991	−0.559954	+	0.828524i	$0.689181\pi$
$444$	9.73294	0.461905
$445$	−7.16764	−0.339779
$446$	−5.58059	−0.264249
$447$	1.64762	0.0779299
$448$	1.58059	0.0746760
$449$	−1.98956	−0.0938933	−0.0469467	−	0.998897i	$-0.514949\pi$
$449$	−1.98956	−0.0938933	−0.0469467	+	0.998897i	$0.514949\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	0.0374409	0.00176107
$453$	−6.74823	−0.317059
$454$	−4.68905	−0.220068
$455$	−9.09802	−0.426522
$456$	1.32139	0.0618795
$457$	29.9634	1.40163	0.700815	−	0.713343i	$-0.252820\pi$
$457$	29.9634	1.40163	0.700815	+	0.713343i	$0.252820\pi$
$458$	−8.39725	−0.392378
$459$	−7.17549	−0.334923
$460$	0.358826	0.0167304
$461$	12.0143	0.559562	0.279781	−	0.960064i	$-0.409738\pi$
$461$	12.0143	0.559562	0.279781	+	0.960064i	$0.409738\pi$
$462$	0	0
$463$	4.85895	0.225815	0.112907	−	0.993606i	$-0.463984\pi$
$463$	4.85895	0.225815	0.112907	+	0.993606i	$0.463984\pi$
$464$	−9.67076	−0.448954
$465$	−7.19863	−0.333828
$466$	−7.27351	−0.336939
$467$	−15.3878	−0.712063	−0.356031	−	0.934474i	$-0.615870\pi$
$467$	−15.3878	−0.712063	−0.356031	+	0.934474i	$0.615870\pi$
$468$	5.75608	0.266075
$469$	−8.02541	−0.370579
$470$	6.52001	0.300746
$471$	8.92898	0.411426
$472$	−10.3262	−0.475304
$473$	0	0
$474$	11.5265	0.529428
$475$	−1.32139	−0.0606293
$476$	−11.3415	−0.519838
$477$	2.34453	0.107348
$478$	−21.7883	−0.996572
$479$	−3.62362	−0.165567	−0.0827836	−	0.996568i	$-0.526381\pi$
$479$	−3.62362	−0.165567	−0.0827836	+	0.996568i	$0.526381\pi$
$480$	1.00000	0.0456435
$481$	56.0236	2.55446
$482$	−4.54057	−0.206817
$483$	−0.567158	−0.0258066
$484$	0	0
$485$	1.92512	0.0874151
$486$	−1.00000	−0.0453609
$487$	3.26664	0.148026	0.0740129	−	0.997257i	$-0.476419\pi$
$487$	3.26664	0.148026	0.0740129	+	0.997257i	$0.476419\pi$
$488$	5.63332	0.255009
$489$	9.72251	0.439667
$490$	−4.50173	−0.203367
$491$	34.2745	1.54679	0.773393	−	0.633927i	$-0.218558\pi$
$491$	34.2745	1.54679	0.773393	+	0.633927i	$0.218558\pi$
$492$	12.0064	0.541293
$493$	69.3924	3.12528
$494$	7.60600	0.342210
$495$	0	0
$496$	7.19863	0.323228
$497$	14.4070	0.646240
$498$	8.00000	0.358489
$499$	38.2077	1.71041	0.855205	−	0.518290i	$-0.173431\pi$
$499$	38.2077	1.71041	0.855205	+	0.518290i	$0.173431\pi$
$500$	−1.00000	−0.0447214
$501$	15.4643	0.690893
$502$	−4.20906	−0.187860
$503$	−20.9173	−0.932655	−0.466327	−	0.884612i	$-0.654423\pi$
$503$	−20.9173	−0.932655	−0.466327	+	0.884612i	$0.654423\pi$
$504$	−1.58059	−0.0704052
$505$	−8.24092	−0.366716
$506$	0	0
$507$	20.1325	0.894114
$508$	16.5418	0.733921
$509$	−34.6279	−1.53486	−0.767428	−	0.641135i	$-0.778464\pi$
$509$	−34.6279	−1.53486	−0.767428	+	0.641135i	$0.778464\pi$
$510$	−7.17549	−0.317736
$511$	−10.9761	−0.485553
$512$	−1.00000	−0.0441942
$513$	−1.32139	−0.0583406
$514$	14.7945	0.652558
$515$	4.90843	0.216291
$516$	6.41156	0.282253
$517$	0	0
$518$	−15.3838	−0.675926
$519$	−18.4037	−0.807833
$520$	5.75608	0.252421
$521$	−14.2077	−0.622449	−0.311224	−	0.950336i	$-0.600739\pi$
$521$	−14.2077	−0.622449	−0.311224	+	0.950336i	$0.600739\pi$
$522$	9.67076	0.423278
$523$	−1.54076	−0.0673729	−0.0336864	−	0.999432i	$-0.510725\pi$
$523$	−1.54076	−0.0673729	−0.0336864	+	0.999432i	$0.510725\pi$
$524$	12.5096	0.546483
$525$	1.58059	0.0689827
$526$	7.90358	0.344612
$527$	−51.6537	−2.25007
$528$	0	0
$529$	−22.8712	−0.994402
$530$	2.34453	0.101840
$531$	10.3262	0.448121
$532$	−2.08857	−0.0905511
$533$	69.1101	2.99349
$534$	−7.16764	−0.310174
$535$	−1.64903	−0.0712936
$536$	5.07747	0.219313
$537$	−18.5623	−0.801023
$538$	−17.9469	−0.773744
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−21.1644	−0.909928	−0.454964	−	0.890510i	$-0.650348\pi$
$541$	−21.1644	−0.909928	−0.454964	+	0.890510i	$0.650348\pi$
$542$	5.86454	0.251903
$543$	9.52786	0.408880
$544$	7.17549	0.307646
$545$	−8.94427	−0.383131
$546$	−9.09802	−0.389359
$547$	−25.8720	−1.10621	−0.553103	−	0.833113i	$-0.686556\pi$
$547$	−25.8720	−1.10621	−0.553103	+	0.833113i	$0.686556\pi$
$548$	−12.3135	−0.526008
$549$	−5.63332	−0.240424
$550$	0	0
$551$	12.7788	0.544395
$552$	0.358826	0.0152727
$553$	−18.2186	−0.774736
$554$	−8.43371	−0.358314
$555$	−9.73294	−0.413140
$556$	−12.9970	−0.551196
$557$	−9.76811	−0.413888	−0.206944	−	0.978353i	$-0.566352\pi$
$557$	−9.76811	−0.413888	−0.206944	+	0.978353i	$0.566352\pi$
$558$	−7.19863	−0.304742
$559$	36.9054	1.56093
$560$	−1.58059	−0.0667923
$561$	0	0
$562$	−5.85024	−0.246777
$563$	−21.9348	−0.924443	−0.462221	−	0.886765i	$-0.652947\pi$
$563$	−21.9348	−0.924443	−0.462221	+	0.886765i	$0.652947\pi$
$564$	6.52001	0.274542
$565$	−0.0374409	−0.00157515
$566$	−11.0312	−0.463675
$567$	1.58059	0.0663787
$568$	−9.11491	−0.382453
$569$	−41.7166	−1.74885	−0.874426	−	0.485159i	$-0.838762\pi$
$569$	−41.7166	−1.74885	−0.874426	+	0.485159i	$0.838762\pi$
$570$	−1.32139	−0.0553467
$571$	23.0928	0.966402	0.483201	−	0.875510i	$-0.339474\pi$
$571$	23.0928	0.966402	0.483201	+	0.875510i	$0.339474\pi$
$572$	0	0
$573$	20.0306	0.836789
$574$	−18.9773	−0.792098
$575$	−0.358826	−0.0149641
$576$	1.00000	0.0416667
$577$	−30.2552	−1.25954	−0.629771	−	0.776781i	$-0.716851\pi$
$577$	−30.2552	−1.25954	−0.629771	+	0.776781i	$0.716851\pi$
$578$	−34.4876	−1.43450
$579$	7.82937	0.325377
$580$	9.67076	0.401557
$581$	−12.6447	−0.524592
$582$	1.92512	0.0797987
$583$	0	0
$584$	6.94427	0.287356
$585$	−5.75608	−0.237985
$586$	−3.22962	−0.133414
$587$	5.40670	0.223159	0.111579	−	0.993756i	$-0.464409\pi$
$587$	5.40670	0.223159	0.111579	+	0.993756i	$0.464409\pi$
$588$	−4.50173	−0.185648
$589$	−9.51216	−0.391942
$590$	10.3262	0.425124
$591$	20.6798	0.850653
$592$	9.73294	0.400021
$593$	33.4413	1.37327	0.686636	−	0.727002i	$-0.259087\pi$
$593$	33.4413	1.37327	0.686636	+	0.727002i	$0.259087\pi$
$594$	0	0
$595$	11.3415	0.464957
$596$	1.64762	0.0674893
$597$	−3.12921	−0.128070
$598$	2.06543	0.0844618
$599$	6.37638	0.260532	0.130266	−	0.991479i	$-0.458417\pi$
$599$	6.37638	0.260532	0.130266	+	0.991479i	$0.458417\pi$
$600$	−1.00000	−0.0408248
$601$	5.76294	0.235075	0.117538	−	0.993068i	$-0.462500\pi$
$601$	5.76294	0.235075	0.117538	+	0.993068i	$0.462500\pi$
$602$	−10.1341	−0.413033
$603$	−5.07747	−0.206770
$604$	−6.74823	−0.274582
$605$	0	0
$606$	−8.24092	−0.334765
$607$	−45.5427	−1.84852	−0.924261	−	0.381760i	$-0.875318\pi$
$607$	−45.5427	−1.84852	−0.924261	+	0.381760i	$0.875318\pi$
$608$	1.32139	0.0535893
$609$	−15.2855	−0.619401
$610$	−5.63332	−0.228087
$611$	37.5297	1.51829
$612$	−7.17549	−0.290052
$613$	31.1552	1.25835	0.629173	−	0.777265i	$-0.283394\pi$
$613$	31.1552	1.25835	0.629173	+	0.777265i	$0.283394\pi$
$614$	22.9531	0.926312
$615$	−12.0064	−0.484147
$616$	0	0
$617$	−30.2761	−1.21887	−0.609435	−	0.792836i	$-0.708604\pi$
$617$	−30.2761	−1.21887	−0.609435	+	0.792836i	$0.708604\pi$
$618$	4.90843	0.197446
$619$	−37.1225	−1.49208	−0.746040	−	0.665901i	$-0.768047\pi$
$619$	−37.1225	−1.49208	−0.746040	+	0.665901i	$0.768047\pi$
$620$	−7.19863	−0.289104
$621$	−0.358826	−0.0143992
$622$	−4.20121	−0.168453
$623$	11.3291	0.453891
$624$	5.75608	0.230428
$625$	1.00000	0.0400000
$626$	18.3816	0.734675
$627$	0	0
$628$	8.92898	0.356305
$629$	−69.8386	−2.78465
$630$	1.58059	0.0629723
$631$	−34.9837	−1.39268	−0.696339	−	0.717713i	$-0.745189\pi$
$631$	−34.9837	−1.39268	−0.696339	+	0.717713i	$0.745189\pi$
$632$	11.5265	0.458498
$633$	14.3047	0.568561
$634$	25.3311	1.00603
$635$	−16.5418	−0.656439
$636$	2.34453	0.0929665
$637$	−25.9123	−1.02668
$638$	0	0
$639$	9.11491	0.360580
$640$	1.00000	0.0395285
$641$	7.87357	0.310987	0.155494	−	0.987837i	$-0.450303\pi$
$641$	7.87357	0.310987	0.155494	+	0.987837i	$0.450303\pi$
$642$	−1.64903	−0.0650818
$643$	45.7923	1.80587	0.902936	−	0.429774i	$-0.141407\pi$
$643$	45.7923	1.80587	0.902936	+	0.429774i	$0.141407\pi$
$644$	−0.567158	−0.0223492
$645$	−6.41156	−0.252455
$646$	−9.48158	−0.373048
$647$	−31.0543	−1.22087	−0.610436	−	0.792066i	$-0.709006\pi$
$647$	−31.0543	−1.22087	−0.610436	+	0.792066i	$0.709006\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−5.75608	−0.225772
$651$	11.3781	0.445943
$652$	9.72251	0.380763
$653$	−22.9084	−0.896476	−0.448238	−	0.893914i	$-0.647948\pi$
$653$	−22.9084	−0.896476	−0.448238	+	0.893914i	$0.647948\pi$
$654$	−8.94427	−0.349749
$655$	−12.5096	−0.488790
$656$	12.0064	0.468773
$657$	−6.94427	−0.270922
$658$	−10.3055	−0.401750
$659$	17.9907	0.700820	0.350410	−	0.936596i	$-0.386042\pi$
$659$	17.9907	0.700820	0.350410	+	0.936596i	$0.386042\pi$
$660$	0	0
$661$	−36.6576	−1.42582	−0.712909	−	0.701257i	$-0.752623\pi$
$661$	−36.6576	−1.42582	−0.712909	+	0.701257i	$0.752623\pi$
$662$	−26.1159	−1.01502
$663$	−41.3027	−1.60406
$664$	8.00000	0.310460
$665$	2.08857	0.0809914
$666$	−9.73294	−0.377144
$667$	3.47012	0.134364
$668$	15.4643	0.598331
$669$	5.58059	0.215758
$670$	−5.07747	−0.196160
$671$	0	0
$672$	−1.58059	−0.0609727
$673$	1.53106	0.0590180	0.0295090	−	0.999565i	$-0.490606\pi$
$673$	1.53106	0.0590180	0.0295090	+	0.999565i	$0.490606\pi$
$674$	18.2012	0.701084
$675$	1.00000	0.0384900
$676$	20.1325	0.774326
$677$	−1.73361	−0.0666281	−0.0333141	−	0.999445i	$-0.510606\pi$
$677$	−1.73361	−0.0666281	−0.0333141	+	0.999445i	$0.510606\pi$
$678$	−0.0374409	−0.00143791
$679$	−3.04283	−0.116773
$680$	−7.17549	−0.275167
$681$	4.68905	0.179685
$682$	0	0
$683$	−15.3161	−0.586055	−0.293027	−	0.956104i	$-0.594663\pi$
$683$	−15.3161	−0.586055	−0.293027	+	0.956104i	$0.594663\pi$
$684$	−1.32139	−0.0505244
$685$	12.3135	0.470476
$686$	18.1795	0.694098
$687$	8.39725	0.320375
$688$	6.41156	0.244438
$689$	13.4953	0.514129
$690$	−0.358826	−0.0136603
$691$	25.1487	0.956703	0.478352	−	0.878168i	$-0.341234\pi$
$691$	25.1487	0.956703	0.478352	+	0.878168i	$0.341234\pi$
$692$	−18.4037	−0.699604
$693$	0	0
$694$	18.3816	0.697754
$695$	12.9970	0.493004
$696$	9.67076	0.366569
$697$	−86.1521	−3.26324
$698$	29.2204	1.10601
$699$	7.27351	0.275109
$700$	1.58059	0.0597408
$701$	−22.0129	−0.831416	−0.415708	−	0.909498i	$-0.636466\pi$
$701$	−22.0129	−0.831416	−0.415708	+	0.909498i	$0.636466\pi$
$702$	−5.75608	−0.217249
$703$	−12.8610	−0.485061
$704$	0	0
$705$	−6.52001	−0.245558
$706$	4.41156	0.166031
$707$	13.0255	0.489876
$708$	10.3262	0.388084
$709$	34.0129	1.27738	0.638691	−	0.769464i	$-0.279476\pi$
$709$	34.0129	1.27738	0.638691	+	0.769464i	$0.279476\pi$
$710$	9.11491	0.342076
$711$	−11.5265	−0.432276
$712$	−7.16764	−0.268619
$713$	−2.58306	−0.0967362
$714$	11.3415	0.424446
$715$	0	0
$716$	−18.5623	−0.693706
$717$	21.7883	0.813697
$718$	−22.1803	−0.827763
$719$	37.4450	1.39646	0.698232	−	0.715872i	$-0.253971\pi$
$719$	37.4450	1.39646	0.698232	+	0.715872i	$0.253971\pi$
$720$	−1.00000	−0.0372678
$721$	−7.75823	−0.288932
$722$	17.2539	0.642125
$723$	4.54057	0.168866
$724$	9.52786	0.354100
$725$	−9.67076	−0.359163
$726$	0	0
$727$	−36.1119	−1.33932	−0.669658	−	0.742669i	$-0.733559\pi$
$727$	−36.1119	−1.33932	−0.669658	+	0.742669i	$0.733559\pi$
$728$	−9.09802	−0.337195
$729$	1.00000	0.0370370
$730$	−6.94427	−0.257019
$731$	−46.0060	−1.70159
$732$	−5.63332	−0.208214
$733$	−17.8774	−0.660318	−0.330159	−	0.943925i	$-0.607102\pi$
$733$	−17.8774	−0.660318	−0.330159	+	0.943925i	$0.607102\pi$
$734$	7.49129	0.276509
$735$	4.50173	0.166049
$736$	0.358826	0.0132265
$737$	0	0
$738$	−12.0064	−0.441964
$739$	−29.8358	−1.09753	−0.548764	−	0.835977i	$-0.684901\pi$
$739$	−29.8358	−1.09753	−0.548764	+	0.835977i	$0.684901\pi$
$740$	−9.73294	−0.357790
$741$	−7.60600	−0.279413
$742$	−3.70574	−0.136042
$743$	−22.1285	−0.811815	−0.405908	−	0.913914i	$-0.633045\pi$
$743$	−22.1285	−0.811815	−0.405908	+	0.913914i	$0.633045\pi$
$744$	−7.19863	−0.263914
$745$	−1.64762	−0.0603642
$746$	7.50173	0.274658
$747$	−8.00000	−0.292705
$748$	0	0
$749$	2.60644	0.0952372
$750$	1.00000	0.0365148
$751$	−13.9334	−0.508438	−0.254219	−	0.967147i	$-0.581818\pi$
$751$	−13.9334	−0.508438	−0.254219	+	0.967147i	$0.581818\pi$
$752$	6.52001	0.237760
$753$	4.20906	0.153387
$754$	55.6657	2.02722
$755$	6.74823	0.245593
$756$	1.58059	0.0574856
$757$	−47.8361	−1.73863	−0.869317	−	0.494255i	$-0.835441\pi$
$757$	−47.8361	−1.73863	−0.869317	+	0.494255i	$0.835441\pi$
$758$	22.6589	0.823009
$759$	0	0
$760$	−1.32139	−0.0479317
$761$	30.7019	1.11294	0.556472	−	0.830866i	$-0.312154\pi$
$761$	30.7019	1.11294	0.556472	+	0.830866i	$0.312154\pi$
$762$	−16.5418	−0.599244
$763$	14.1373	0.511803
$764$	20.0306	0.724681
$765$	7.17549	0.259430
$766$	6.48742	0.234400
$767$	59.4387	2.14621
$768$	1.00000	0.0360844
$769$	7.23993	0.261079	0.130539	−	0.991443i	$-0.458329\pi$
$769$	7.23993	0.261079	0.130539	+	0.991443i	$0.458329\pi$
$770$	0	0
$771$	−14.7945	−0.532811
$772$	7.82937	0.281785
$773$	52.3755	1.88382	0.941908	−	0.335872i	$-0.109031\pi$
$773$	52.3755	1.88382	0.941908	+	0.335872i	$0.109031\pi$
$774$	−6.41156	−0.230459
$775$	7.19863	0.258582
$776$	1.92512	0.0691077
$777$	15.3838	0.551891
$778$	−21.5824	−0.773768
$779$	−15.8651	−0.568428
$780$	−5.75608	−0.206101
$781$	0	0
$782$	−2.57475	−0.0920730
$783$	−9.67076	−0.345605
$784$	−4.50173	−0.160776
$785$	−8.92898	−0.318689
$786$	−12.5096	−0.446202
$787$	−40.2155	−1.43353	−0.716764	−	0.697316i	$-0.754378\pi$
$787$	−40.2155	−1.43353	−0.716764	+	0.697316i	$0.754378\pi$
$788$	20.6798	0.736687
$789$	−7.90358	−0.281375
$790$	−11.5265	−0.410093
$791$	0.0591788	0.00210415
$792$	0	0
$793$	−32.4259	−1.15148
$794$	−16.5235	−0.586396
$795$	−2.34453	−0.0831517
$796$	−3.12921	−0.110912
$797$	8.24479	0.292045	0.146023	−	0.989281i	$-0.453353\pi$
$797$	8.24479	0.292045	0.146023	+	0.989281i	$0.453353\pi$
$798$	2.08857	0.0739347
$799$	−46.7843	−1.65511
$800$	−1.00000	−0.0353553
$801$	7.16764	0.253256
$802$	−14.5672	−0.514384
$803$	0	0
$804$	−5.07747	−0.179068
$805$	0.567158	0.0199897
$806$	−41.4359	−1.45952
$807$	17.9469	0.631759
$808$	−8.24092	−0.289915
$809$	−0.436292	−0.0153392	−0.00766961	−	0.999971i	$-0.502441\pi$
$809$	−0.436292	−0.0153392	−0.00766961	+	0.999971i	$0.502441\pi$
$810$	1.00000	0.0351364
$811$	8.03703	0.282218	0.141109	−	0.989994i	$-0.454933\pi$
$811$	8.03703	0.282218	0.141109	+	0.989994i	$0.454933\pi$
$812$	−15.2855	−0.536417
$813$	−5.86454	−0.205678
$814$	0	0
$815$	−9.72251	−0.340564
$816$	−7.17549	−0.251192
$817$	−8.47214	−0.296403
$818$	−22.6287	−0.791193
$819$	9.09802	0.317911
$820$	−12.0064	−0.419283
$821$	10.8726	0.379456	0.189728	−	0.981837i	$-0.439239\pi$
$821$	10.8726	0.379456	0.189728	+	0.981837i	$0.439239\pi$
$822$	12.3135	0.429484
$823$	6.87466	0.239635	0.119818	−	0.992796i	$-0.461769\pi$
$823$	6.87466	0.239635	0.119818	+	0.992796i	$0.461769\pi$
$824$	4.90843	0.170993
$825$	0	0
$826$	−16.3216	−0.567900
$827$	7.40070	0.257348	0.128674	−	0.991687i	$-0.458928\pi$
$827$	7.40070	0.257348	0.128674	+	0.991687i	$0.458928\pi$
$828$	−0.358826	−0.0124701
$829$	−2.50871	−0.0871311	−0.0435656	−	0.999051i	$-0.513872\pi$
$829$	−2.50871	−0.0871311	−0.0435656	+	0.999051i	$0.513872\pi$
$830$	−8.00000	−0.277684
$831$	8.43371	0.292562
$832$	5.75608	0.199556
$833$	32.3021	1.11920
$834$	12.9970	0.450049
$835$	−15.4643	−0.535164
$836$	0	0
$837$	7.19863	0.248821
$838$	−5.41057	−0.186905
$839$	−10.7450	−0.370960	−0.185480	−	0.982648i	$-0.559384\pi$
$839$	−10.7450	−0.370960	−0.185480	+	0.982648i	$0.559384\pi$
$840$	1.58059	0.0545356
$841$	64.5237	2.22495
$842$	−3.48158	−0.119983
$843$	5.85024	0.201493
$844$	14.3047	0.492388
$845$	−20.1325	−0.692578
$846$	−6.52001	−0.224163
$847$	0	0
$848$	2.34453	0.0805113
$849$	11.0312	0.378589
$850$	7.17549	0.246117
$851$	−3.49244	−0.119719
$852$	9.11491	0.312272
$853$	7.70175	0.263703	0.131852	−	0.991269i	$-0.457908\pi$
$853$	7.70175	0.263703	0.131852	+	0.991269i	$0.457908\pi$
$854$	8.90399	0.304688
$855$	1.32139	0.0451904
$856$	−1.64903	−0.0563625
$857$	−7.18839	−0.245551	−0.122775	−	0.992434i	$-0.539179\pi$
$857$	−7.18839	−0.245551	−0.122775	+	0.992434i	$0.539179\pi$
$858$	0	0
$859$	40.4661	1.38068	0.690342	−	0.723483i	$-0.257460\pi$
$859$	40.4661	1.38068	0.690342	+	0.723483i	$0.257460\pi$
$860$	−6.41156	−0.218632
$861$	18.9773	0.646745
$862$	−12.2169	−0.416110
$863$	−49.6424	−1.68985	−0.844923	−	0.534888i	$-0.820354\pi$
$863$	−49.6424	−1.68985	−0.844923	+	0.534888i	$0.820354\pi$
$864$	−1.00000	−0.0340207
$865$	18.4037	0.625745
$866$	−9.48356	−0.322264
$867$	34.4876	1.17126
$868$	11.3781	0.386198
$869$	0	0
$870$	−9.67076	−0.327870
$871$	−29.2263	−0.990296
$872$	−8.94427	−0.302891
$873$	−1.92512	−0.0651554
$874$	−0.474148	−0.0160383
$875$	−1.58059	−0.0534338
$876$	−6.94427	−0.234625
$877$	9.08046	0.306626	0.153313	−	0.988178i	$-0.451006\pi$
$877$	9.08046	0.306626	0.153313	+	0.988178i	$0.451006\pi$
$878$	7.54960	0.254787
$879$	3.22962	0.108932
$880$	0	0
$881$	−9.85152	−0.331906	−0.165953	−	0.986134i	$-0.553070\pi$
$881$	−9.85152	−0.331906	−0.165953	+	0.986134i	$0.553070\pi$
$882$	4.50173	0.151581
$883$	−18.5456	−0.624110	−0.312055	−	0.950064i	$-0.601017\pi$
$883$	−18.5456	−0.624110	−0.312055	+	0.950064i	$0.601017\pi$
$884$	−41.3027	−1.38916
$885$	−10.3262	−0.347113
$886$	23.5713	0.791895
$887$	22.6172	0.759413	0.379706	−	0.925107i	$-0.376025\pi$
$887$	22.6172	0.759413	0.379706	+	0.925107i	$0.376025\pi$
$888$	−9.73294	−0.326616
$889$	26.1458	0.876901
$890$	7.16764	0.240260
$891$	0	0
$892$	5.58059	0.186852
$893$	−8.61545	−0.288305
$894$	−1.64762	−0.0551048
$895$	18.5623	0.620469
$896$	−1.58059	−0.0528039
$897$	−2.06543	−0.0689628
$898$	1.98956	0.0663926
$899$	−69.6162	−2.32183
$900$	1.00000	0.0333333
$901$	−16.8231	−0.560459
$902$	0	0
$903$	10.1341	0.337240
$904$	−0.0374409	−0.00124526
$905$	−9.52786	−0.316717
$906$	6.74823	0.224195
$907$	−34.4273	−1.14314	−0.571569	−	0.820554i	$-0.693665\pi$
$907$	−34.4273	−1.14314	−0.571569	+	0.820554i	$0.693665\pi$
$908$	4.68905	0.155612
$909$	8.24092	0.273334
$910$	9.09802	0.301596
$911$	2.38155	0.0789043	0.0394522	−	0.999221i	$-0.487439\pi$
$911$	2.38155	0.0789043	0.0394522	+	0.999221i	$0.487439\pi$
$912$	−1.32139	−0.0437554
$913$	0	0
$914$	−29.9634	−0.991102
$915$	5.63332	0.186232
$916$	8.39725	0.277453
$917$	19.7726	0.652947
$918$	7.17549	0.236826
$919$	7.11351	0.234653	0.117326	−	0.993093i	$-0.462568\pi$
$919$	7.11351	0.234653	0.117326	+	0.993093i	$0.462568\pi$
$920$	−0.358826	−0.0118302
$921$	−22.9531	−0.756331
$922$	−12.0143	−0.395670
$923$	52.4661	1.72694
$924$	0	0
$925$	9.73294	0.320017
$926$	−4.85895	−0.159675
$927$	−4.90843	−0.161214
$928$	9.67076	0.317458
$929$	6.54057	0.214589	0.107295	−	0.994227i	$-0.465781\pi$
$929$	6.54057	0.214589	0.107295	+	0.994227i	$0.465781\pi$
$930$	7.19863	0.236052
$931$	5.94851	0.194955
$932$	7.27351	0.238252
$933$	4.20121	0.137541
$934$	15.3878	0.503504
$935$	0	0
$936$	−5.75608	−0.188143
$937$	36.8231	1.20296	0.601479	−	0.798888i	$-0.294578\pi$
$937$	36.8231	1.20296	0.601479	+	0.798888i	$0.294578\pi$
$938$	8.02541	0.262039
$939$	−18.3816	−0.599859
$940$	−6.52001	−0.212659
$941$	−9.59908	−0.312921	−0.156460	−	0.987684i	$-0.550008\pi$
$941$	−9.59908	−0.312921	−0.156460	+	0.987684i	$0.550008\pi$
$942$	−8.92898	−0.290922
$943$	−4.30823	−0.140295
$944$	10.3262	0.336090
$945$	−1.58059	−0.0514167
$946$	0	0
$947$	−35.5427	−1.15498	−0.577492	−	0.816396i	$-0.695968\pi$
$947$	−35.5427	−1.15498	−0.577492	+	0.816396i	$0.695968\pi$
$948$	−11.5265	−0.374362
$949$	−39.9718	−1.29754
$950$	1.32139	0.0428714
$951$	−25.3311	−0.821417
$952$	11.3415	0.367581
$953$	30.5476	0.989534	0.494767	−	0.869026i	$-0.335253\pi$
$953$	30.5476	0.989534	0.494767	+	0.869026i	$0.335253\pi$
$954$	−2.34453	−0.0759068
$955$	−20.0306	−0.648174
$956$	21.7883	0.704683
$957$	0	0
$958$	3.62362	0.117074
$959$	−19.4627	−0.628483
$960$	−1.00000	−0.0322749
$961$	20.8202	0.671620
$962$	−56.0236	−1.80627
$963$	1.64903	0.0531391
$964$	4.54057	0.146242
$965$	−7.82937	−0.252036
$966$	0.567158	0.0182480
$967$	−22.9241	−0.737190	−0.368595	−	0.929590i	$-0.620161\pi$
$967$	−22.9241	−0.737190	−0.368595	+	0.929590i	$0.620161\pi$
$968$	0	0
$969$	9.48158	0.304592
$970$	−1.92512	−0.0618118
$971$	−52.1763	−1.67442	−0.837208	−	0.546885i	$-0.815814\pi$
$971$	−52.1763	−1.67442	−0.837208	+	0.546885i	$0.815814\pi$
$972$	1.00000	0.0320750
$973$	−20.5430	−0.658577
$974$	−3.26664	−0.104670
$975$	5.75608	0.184342
$976$	−5.63332	−0.180318
$977$	7.49646	0.239833	0.119916	−	0.992784i	$-0.461737\pi$
$977$	7.49646	0.239833	0.119916	+	0.992784i	$0.461737\pi$
$978$	−9.72251	−0.310891
$979$	0	0
$980$	4.50173	0.143802
$981$	8.94427	0.285569
$982$	−34.2745	−1.09374
$983$	−57.8539	−1.84525	−0.922626	−	0.385695i	$-0.873962\pi$
$983$	−57.8539	−1.84525	−0.922626	+	0.385695i	$0.873962\pi$
$984$	−12.0064	−0.382752
$985$	−20.6798	−0.658913
$986$	−69.3924	−2.20991
$987$	10.3055	0.328027
$988$	−7.60600	−0.241979
$989$	−2.30063	−0.0731559
$990$	0	0
$991$	15.1292	0.480595	0.240298	−	0.970699i	$-0.422755\pi$
$991$	15.1292	0.480595	0.240298	+	0.970699i	$0.422755\pi$
$992$	−7.19863	−0.228557
$993$	26.1159	0.828763
$994$	−14.4070	−0.456961
$995$	3.12921	0.0992026
$996$	−8.00000	−0.253490
$997$	−20.9268	−0.662758	−0.331379	−	0.943498i	$-0.607514\pi$
$997$	−20.9268	−0.662758	−0.331379	+	0.943498i	$0.607514\pi$
$998$	−38.2077	−1.20944
$999$	9.73294	0.307937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bq.1.3		4
11.3	even	5		330.2.m.f.31.1	✓	8
11.4	even	5		330.2.m.f.181.1	yes	8
11.10	odd	2		3630.2.a.bs.1.2		4
33.14	odd	10		990.2.n.i.361.1		8
33.26	odd	10		990.2.n.i.181.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.f.31.1	✓	8	11.3	even	5
330.2.m.f.181.1	yes	8	11.4	even	5
990.2.n.i.181.1		8	33.26	odd	10
990.2.n.i.361.1		8	33.14	odd	10
3630.2.a.bq.1.3		4	1.1	even	1	trivial
3630.2.a.bs.1.2		4	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.58059 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.58059 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{12} +5.75608 q^{13} -1.58059 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.17549 q^{17} -1.00000 q^{18} -1.32139 q^{19} -1.00000 q^{20} +1.58059 q^{21} -0.358826 q^{23} -1.00000 q^{24} +1.00000 q^{25} -5.75608 q^{26} +1.00000 q^{27} +1.58059 q^{28} -9.67076 q^{29} +1.00000 q^{30} +7.19863 q^{31} -1.00000 q^{32} +7.17549 q^{34} -1.58059 q^{35} +1.00000 q^{36} +9.73294 q^{37} +1.32139 q^{38} +5.75608 q^{39} +1.00000 q^{40} +12.0064 q^{41} -1.58059 q^{42} +6.41156 q^{43} -1.00000 q^{45} +0.358826 q^{46} +6.52001 q^{47} +1.00000 q^{48} -4.50173 q^{49} -1.00000 q^{50} -7.17549 q^{51} +5.75608 q^{52} +2.34453 q^{53} -1.00000 q^{54} -1.58059 q^{56} -1.32139 q^{57} +9.67076 q^{58} +10.3262 q^{59} -1.00000 q^{60} -5.63332 q^{61} -7.19863 q^{62} +1.58059 q^{63} +1.00000 q^{64} -5.75608 q^{65} -5.07747 q^{67} -7.17549 q^{68} -0.358826 q^{69} +1.58059 q^{70} +9.11491 q^{71} -1.00000 q^{72} -6.94427 q^{73} -9.73294 q^{74} +1.00000 q^{75} -1.32139 q^{76} -5.75608 q^{78} -11.5265 q^{79} -1.00000 q^{80} +1.00000 q^{81} -12.0064 q^{82} -8.00000 q^{83} +1.58059 q^{84} +7.17549 q^{85} -6.41156 q^{86} -9.67076 q^{87} +7.16764 q^{89} +1.00000 q^{90} +9.09802 q^{91} -0.358826 q^{92} +7.19863 q^{93} -6.52001 q^{94} +1.32139 q^{95} -1.00000 q^{96} -1.92512 q^{97} +4.50173 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} - q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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