LMFDB - Embedded newform 4235.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.23607 q^{2} -1.61803 q^{3} +3.00000 q^{4} -1.00000 q^{5} +3.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} -0.381966 q^{9} +O(q^{10})$	\(q-2.23607 q^{2} -1.61803 q^{3} +3.00000 q^{4} -1.00000 q^{5} +3.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} -0.381966 q^{9} +2.23607 q^{10} -4.85410 q^{12} -2.38197 q^{13} -2.23607 q^{14} +1.61803 q^{15} -1.00000 q^{16} -3.38197 q^{17} +0.854102 q^{18} -1.23607 q^{19} -3.00000 q^{20} -1.61803 q^{21} +4.47214 q^{23} +3.61803 q^{24} +1.00000 q^{25} +5.32624 q^{26} +5.47214 q^{27} +3.00000 q^{28} +5.85410 q^{29} -3.61803 q^{30} -1.23607 q^{31} +6.70820 q^{32} +7.56231 q^{34} -1.00000 q^{35} -1.14590 q^{36} -2.76393 q^{37} +2.76393 q^{38} +3.85410 q^{39} +2.23607 q^{40} +6.47214 q^{41} +3.61803 q^{42} +0.763932 q^{43} +0.381966 q^{45} -10.0000 q^{46} -7.85410 q^{47} +1.61803 q^{48} +1.00000 q^{49} -2.23607 q^{50} +5.47214 q^{51} -7.14590 q^{52} -10.4721 q^{53} -12.2361 q^{54} -2.23607 q^{56} +2.00000 q^{57} -13.0902 q^{58} -4.76393 q^{59} +4.85410 q^{60} +9.23607 q^{61} +2.76393 q^{62} -0.381966 q^{63} -13.0000 q^{64} +2.38197 q^{65} -14.1803 q^{67} -10.1459 q^{68} -7.23607 q^{69} +2.23607 q^{70} +0.673762 q^{71} +0.854102 q^{72} -8.61803 q^{73} +6.18034 q^{74} -1.61803 q^{75} -3.70820 q^{76} -8.61803 q^{78} +13.7984 q^{79} +1.00000 q^{80} -7.70820 q^{81} -14.4721 q^{82} +10.5623 q^{83} -4.85410 q^{84} +3.38197 q^{85} -1.70820 q^{86} -9.47214 q^{87} +17.2361 q^{89} -0.854102 q^{90} -2.38197 q^{91} +13.4164 q^{92} +2.00000 q^{93} +17.5623 q^{94} +1.23607 q^{95} -10.8541 q^{96} +0.326238 q^{97} -2.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{3} + 6 q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{9}+O(q^{10}) $ 2 * q - q^3 + 6 * q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^9	$ 2 q - q^{3} + 6 q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{9} - 3 q^{12} - 7 q^{13} + q^{15} - 2 q^{16} - 9 q^{17} - 5 q^{18} + 2 q^{19} - 6 q^{20} - q^{21} + 5 q^{24} + 2 q^{25} - 5 q^{26} + 2 q^{27} + 6 q^{28} + 5 q^{29} - 5 q^{30} + 2 q^{31} - 5 q^{34} - 2 q^{35} - 9 q^{36} - 10 q^{37} + 10 q^{38} + q^{39} + 4 q^{41} + 5 q^{42} + 6 q^{43} + 3 q^{45} - 20 q^{46} - 9 q^{47} + q^{48} + 2 q^{49} + 2 q^{51} - 21 q^{52} - 12 q^{53} - 20 q^{54} + 4 q^{57} - 15 q^{58} - 14 q^{59} + 3 q^{60} + 14 q^{61} + 10 q^{62} - 3 q^{63} - 26 q^{64} + 7 q^{65} - 6 q^{67} - 27 q^{68} - 10 q^{69} + 17 q^{71} - 5 q^{72} - 15 q^{73} - 10 q^{74} - q^{75} + 6 q^{76} - 15 q^{78} + 3 q^{79} + 2 q^{80} - 2 q^{81} - 20 q^{82} + q^{83} - 3 q^{84} + 9 q^{85} + 10 q^{86} - 10 q^{87} + 30 q^{89} + 5 q^{90} - 7 q^{91} + 4 q^{93} + 15 q^{94} - 2 q^{95} - 15 q^{96} - 15 q^{97}+O(q^{100}) $ 2 * q - q^3 + 6 * q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^9 - 3 * q^12 - 7 * q^13 + q^15 - 2 * q^16 - 9 * q^17 - 5 * q^18 + 2 * q^19 - 6 * q^20 - q^21 + 5 * q^24 + 2 * q^25 - 5 * q^26 + 2 * q^27 + 6 * q^28 + 5 * q^29 - 5 * q^30 + 2 * q^31 - 5 * q^34 - 2 * q^35 - 9 * q^36 - 10 * q^37 + 10 * q^38 + q^39 + 4 * q^41 + 5 * q^42 + 6 * q^43 + 3 * q^45 - 20 * q^46 - 9 * q^47 + q^48 + 2 * q^49 + 2 * q^51 - 21 * q^52 - 12 * q^53 - 20 * q^54 + 4 * q^57 - 15 * q^58 - 14 * q^59 + 3 * q^60 + 14 * q^61 + 10 * q^62 - 3 * q^63 - 26 * q^64 + 7 * q^65 - 6 * q^67 - 27 * q^68 - 10 * q^69 + 17 * q^71 - 5 * q^72 - 15 * q^73 - 10 * q^74 - q^75 + 6 * q^76 - 15 * q^78 + 3 * q^79 + 2 * q^80 - 2 * q^81 - 20 * q^82 + q^83 - 3 * q^84 + 9 * q^85 + 10 * q^86 - 10 * q^87 + 30 * q^89 + 5 * q^90 - 7 * q^91 + 4 * q^93 + 15 * q^94 - 2 * q^95 - 15 * q^96 - 15 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.23607	−1.58114	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	−2.23607	−1.58114	−0.790569	+	0.612372i	$0.790215\pi$
$3$	−1.61803	−0.934172	−0.467086	−	0.884212i	$-0.654696\pi$
$3$	−1.61803	−0.934172	−0.467086	+	0.884212i	$0.654696\pi$
$4$	3.00000	1.50000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.61803	1.47706
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.23607	−0.790569
$9$	−0.381966	−0.127322
$10$	2.23607	0.707107
$11$	0	0
$11$	0	0
$12$	−4.85410	−1.40126
$13$	−2.38197	−0.660639	−0.330319	−	0.943869i	$-0.607156\pi$
$13$	−2.38197	−0.660639	−0.330319	+	0.943869i	$0.607156\pi$
$14$	−2.23607	−0.597614
$15$	1.61803	0.417775
$16$	−1.00000	−0.250000
$17$	−3.38197	−0.820247	−0.410124	−	0.912030i	$-0.634514\pi$
$17$	−3.38197	−0.820247	−0.410124	+	0.912030i	$0.634514\pi$
$18$	0.854102	0.201314
$19$	−1.23607	−0.283573	−0.141787	−	0.989897i	$-0.545285\pi$
$19$	−1.23607	−0.283573	−0.141787	+	0.989897i	$0.545285\pi$
$20$	−3.00000	−0.670820
$21$	−1.61803	−0.353084
$22$	0	0
$23$	4.47214	0.932505	0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214	0.932505	0.466252	+	0.884652i	$0.345604\pi$
$24$	3.61803	0.738528
$25$	1.00000	0.200000
$26$	5.32624	1.04456
$27$	5.47214	1.05311
$28$	3.00000	0.566947
$29$	5.85410	1.08708	0.543540	−	0.839383i	$-0.317084\pi$
$29$	5.85410	1.08708	0.543540	+	0.839383i	$0.317084\pi$
$30$	−3.61803	−0.660560
$31$	−1.23607	−0.222004	−0.111002	−	0.993820i	$-0.535406\pi$
$31$	−1.23607	−0.222004	−0.111002	+	0.993820i	$0.535406\pi$
$32$	6.70820	1.18585
$33$	0	0
$34$	7.56231	1.29692
$35$	−1.00000	−0.169031
$36$	−1.14590	−0.190983
$37$	−2.76393	−0.454388	−0.227194	−	0.973850i	$-0.572955\pi$
$37$	−2.76393	−0.454388	−0.227194	+	0.973850i	$0.572955\pi$
$38$	2.76393	0.448369
$39$	3.85410	0.617150
$40$	2.23607	0.353553
$41$	6.47214	1.01078	0.505389	−	0.862892i	$-0.331349\pi$
$41$	6.47214	1.01078	0.505389	+	0.862892i	$0.331349\pi$
$42$	3.61803	0.558275
$43$	0.763932	0.116499	0.0582493	−	0.998302i	$-0.481448\pi$
$43$	0.763932	0.116499	0.0582493	+	0.998302i	$0.481448\pi$
$44$	0	0
$45$	0.381966	0.0569401
$46$	−10.0000	−1.47442
$47$	−7.85410	−1.14564	−0.572819	−	0.819682i	$-0.694150\pi$
$47$	−7.85410	−1.14564	−0.572819	+	0.819682i	$0.694150\pi$
$48$	1.61803	0.233543
$49$	1.00000	0.142857
$50$	−2.23607	−0.316228
$51$	5.47214	0.766252
$52$	−7.14590	−0.990958
$53$	−10.4721	−1.43846	−0.719229	−	0.694773i	$-0.755505\pi$
$53$	−10.4721	−1.43846	−0.719229	+	0.694773i	$0.755505\pi$
$54$	−12.2361	−1.66512
$55$	0	0
$56$	−2.23607	−0.298807
$57$	2.00000	0.264906
$58$	−13.0902	−1.71882
$59$	−4.76393	−0.620211	−0.310106	−	0.950702i	$-0.600364\pi$
$59$	−4.76393	−0.620211	−0.310106	+	0.950702i	$0.600364\pi$
$60$	4.85410	0.626662
$61$	9.23607	1.18256	0.591279	−	0.806467i	$-0.298623\pi$
$61$	9.23607	1.18256	0.591279	+	0.806467i	$0.298623\pi$
$62$	2.76393	0.351020
$63$	−0.381966	−0.0481232
$64$	−13.0000	−1.62500
$65$	2.38197	0.295447
$66$	0	0
$67$	−14.1803	−1.73240	−0.866202	−	0.499694i	$-0.833446\pi$
$67$	−14.1803	−1.73240	−0.866202	+	0.499694i	$0.833446\pi$
$68$	−10.1459	−1.23037
$69$	−7.23607	−0.871120
$70$	2.23607	0.267261
$71$	0.673762	0.0799608	0.0399804	−	0.999200i	$-0.487270\pi$
$71$	0.673762	0.0799608	0.0399804	+	0.999200i	$0.487270\pi$
$72$	0.854102	0.100657
$73$	−8.61803	−1.00866	−0.504332	−	0.863510i	$-0.668261\pi$
$73$	−8.61803	−1.00866	−0.504332	+	0.863510i	$0.668261\pi$
$74$	6.18034	0.718450
$75$	−1.61803	−0.186834
$76$	−3.70820	−0.425360
$77$	0	0
$78$	−8.61803	−0.975800
$79$	13.7984	1.55244	0.776219	−	0.630463i	$-0.217135\pi$
$79$	13.7984	1.55244	0.776219	+	0.630463i	$0.217135\pi$
$80$	1.00000	0.111803
$81$	−7.70820	−0.856467
$82$	−14.4721	−1.59818
$83$	10.5623	1.15936	0.579682	−	0.814843i	$-0.303177\pi$
$83$	10.5623	1.15936	0.579682	+	0.814843i	$0.303177\pi$
$84$	−4.85410	−0.529626
$85$	3.38197	0.366826
$86$	−1.70820	−0.184200
$87$	−9.47214	−1.01552
$88$	0	0
$89$	17.2361	1.82702	0.913510	−	0.406817i	$-0.133361\pi$
$89$	17.2361	1.82702	0.913510	+	0.406817i	$0.133361\pi$
$90$	−0.854102	−0.0900303
$91$	−2.38197	−0.249698
$92$	13.4164	1.39876
$93$	2.00000	0.207390
$94$	17.5623	1.81141
$95$	1.23607	0.126818
$96$	−10.8541	−1.10779
$97$	0.326238	0.0331244	0.0165622	−	0.999863i	$-0.494728\pi$
$97$	0.326238	0.0331244	0.0165622	+	0.999863i	$0.494728\pi$
$98$	−2.23607	−0.225877
$99$	0	0
$100$	3.00000	0.300000
$101$	0.291796	0.0290348	0.0145174	−	0.999895i	$-0.495379\pi$
$101$	0.291796	0.0290348	0.0145174	+	0.999895i	$0.495379\pi$
$102$	−12.2361	−1.21155
$103$	−1.67376	−0.164921	−0.0824603	−	0.996594i	$-0.526278\pi$
$103$	−1.67376	−0.164921	−0.0824603	+	0.996594i	$0.526278\pi$
$104$	5.32624	0.522281
$105$	1.61803	0.157904
$106$	23.4164	2.27440
$107$	2.76393	0.267199	0.133600	−	0.991035i	$-0.457346\pi$
$107$	2.76393	0.267199	0.133600	+	0.991035i	$0.457346\pi$
$108$	16.4164	1.57967
$109$	20.4721	1.96087	0.980437	−	0.196831i	$-0.0630649\pi$
$109$	20.4721	1.96087	0.980437	+	0.196831i	$0.0630649\pi$
$110$	0	0
$111$	4.47214	0.424476
$112$	−1.00000	−0.0944911
$113$	1.52786	0.143729	0.0718647	−	0.997414i	$-0.477105\pi$
$113$	1.52786	0.143729	0.0718647	+	0.997414i	$0.477105\pi$
$114$	−4.47214	−0.418854
$115$	−4.47214	−0.417029
$116$	17.5623	1.63062
$117$	0.909830	0.0841138
$118$	10.6525	0.980640
$119$	−3.38197	−0.310024
$120$	−3.61803	−0.330280
$121$	0	0
$122$	−20.6525	−1.86979
$123$	−10.4721	−0.944241
$124$	−3.70820	−0.333007
$125$	−1.00000	−0.0894427
$126$	0.854102	0.0760895
$127$	−4.76393	−0.422731	−0.211365	−	0.977407i	$-0.567791\pi$
$127$	−4.76393	−0.422731	−0.211365	+	0.977407i	$0.567791\pi$
$128$	15.6525	1.38350
$129$	−1.23607	−0.108830
$130$	−5.32624	−0.467142
$131$	−8.00000	−0.698963	−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000	−0.698963	−0.349482	+	0.936943i	$0.613642\pi$
$132$	0	0
$133$	−1.23607	−0.107181
$134$	31.7082	2.73917
$135$	−5.47214	−0.470966
$136$	7.56231	0.648462
$137$	15.4164	1.31711	0.658556	−	0.752531i	$-0.271167\pi$
$137$	15.4164	1.31711	0.658556	+	0.752531i	$0.271167\pi$
$138$	16.1803	1.37736
$139$	−14.4721	−1.22751	−0.613755	−	0.789496i	$-0.710342\pi$
$139$	−14.4721	−1.22751	−0.613755	+	0.789496i	$0.710342\pi$
$140$	−3.00000	−0.253546
$141$	12.7082	1.07022
$142$	−1.50658	−0.126429
$143$	0	0
$144$	0.381966	0.0318305
$145$	−5.85410	−0.486157
$146$	19.2705	1.59484
$147$	−1.61803	−0.133453
$148$	−8.29180	−0.681581
$149$	11.1459	0.913108	0.456554	−	0.889696i	$-0.349084\pi$
$149$	11.1459	0.913108	0.456554	+	0.889696i	$0.349084\pi$
$150$	3.61803	0.295411
$151$	2.61803	0.213053	0.106526	−	0.994310i	$-0.466027\pi$
$151$	2.61803	0.213053	0.106526	+	0.994310i	$0.466027\pi$
$152$	2.76393	0.224184
$153$	1.29180	0.104436
$154$	0	0
$155$	1.23607	0.0992834
$156$	11.5623	0.925725
$157$	−4.90983	−0.391847	−0.195924	−	0.980619i	$-0.562770\pi$
$157$	−4.90983	−0.391847	−0.195924	+	0.980619i	$0.562770\pi$
$158$	−30.8541	−2.45462
$159$	16.9443	1.34377
$160$	−6.70820	−0.530330
$161$	4.47214	0.352454
$162$	17.2361	1.35419
$163$	0.180340	0.0141253	0.00706266	−	0.999975i	$-0.497752\pi$
$163$	0.180340	0.0141253	0.00706266	+	0.999975i	$0.497752\pi$
$164$	19.4164	1.51617
$165$	0	0
$166$	−23.6180	−1.83311
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	3.61803	0.279137
$169$	−7.32624	−0.563557
$170$	−7.56231	−0.580002
$171$	0.472136	0.0361051
$172$	2.29180	0.174748
$173$	−18.5623	−1.41127	−0.705633	−	0.708578i	$-0.749337\pi$
$173$	−18.5623	−1.41127	−0.705633	+	0.708578i	$0.749337\pi$
$174$	21.1803	1.60568
$175$	1.00000	0.0755929
$176$	0	0
$177$	7.70820	0.579384
$178$	−38.5410	−2.88877
$179$	17.3820	1.29919	0.649595	−	0.760281i	$-0.274939\pi$
$179$	17.3820	1.29919	0.649595	+	0.760281i	$0.274939\pi$
$180$	1.14590	0.0854102
$181$	14.4721	1.07571	0.537853	−	0.843039i	$-0.319236\pi$
$181$	14.4721	1.07571	0.537853	+	0.843039i	$0.319236\pi$
$182$	5.32624	0.394807
$183$	−14.9443	−1.10471
$184$	−10.0000	−0.737210
$185$	2.76393	0.203208
$186$	−4.47214	−0.327913
$187$	0	0
$188$	−23.5623	−1.71846
$189$	5.47214	0.398039
$190$	−2.76393	−0.200517
$191$	11.9098	0.861765	0.430883	−	0.902408i	$-0.358202\pi$
$191$	11.9098	0.861765	0.430883	+	0.902408i	$0.358202\pi$
$192$	21.0344	1.51803
$193$	−4.00000	−0.287926	−0.143963	−	0.989583i	$-0.545985\pi$
$193$	−4.00000	−0.287926	−0.143963	+	0.989583i	$0.545985\pi$
$194$	−0.729490	−0.0523743
$195$	−3.85410	−0.275998
$196$	3.00000	0.214286
$197$	12.0000	0.854965	0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000	0.854965	0.427482	+	0.904024i	$0.359401\pi$
$198$	0	0
$199$	−18.0000	−1.27599	−0.637993	−	0.770042i	$-0.720235\pi$
$199$	−18.0000	−1.27599	−0.637993	+	0.770042i	$0.720235\pi$
$200$	−2.23607	−0.158114
$201$	22.9443	1.61836
$202$	−0.652476	−0.0459080
$203$	5.85410	0.410877
$204$	16.4164	1.14938
$205$	−6.47214	−0.452034
$206$	3.74265	0.260762
$207$	−1.70820	−0.118728
$208$	2.38197	0.165160
$209$	0	0
$210$	−3.61803	−0.249668
$211$	−23.3262	−1.60584	−0.802922	−	0.596084i	$-0.796723\pi$
$211$	−23.3262	−1.60584	−0.802922	+	0.596084i	$0.796723\pi$
$212$	−31.4164	−2.15769
$213$	−1.09017	−0.0746972
$214$	−6.18034	−0.422479
$215$	−0.763932	−0.0520997
$216$	−12.2361	−0.832559
$217$	−1.23607	−0.0839098
$218$	−45.7771	−3.10042
$219$	13.9443	0.942267
$220$	0	0
$221$	8.05573	0.541887
$222$	−10.0000	−0.671156
$223$	10.4721	0.701266	0.350633	−	0.936513i	$-0.385966\pi$
$223$	10.4721	0.701266	0.350633	+	0.936513i	$0.385966\pi$
$224$	6.70820	0.448211
$225$	−0.381966	−0.0254644
$226$	−3.41641	−0.227256
$227$	−13.7984	−0.915830	−0.457915	−	0.888996i	$-0.651404\pi$
$227$	−13.7984	−0.915830	−0.457915	+	0.888996i	$0.651404\pi$
$228$	6.00000	0.397360
$229$	−29.2361	−1.93197	−0.965987	−	0.258591i	$-0.916742\pi$
$229$	−29.2361	−1.93197	−0.965987	+	0.258591i	$0.916742\pi$
$230$	10.0000	0.659380
$231$	0	0
$232$	−13.0902	−0.859412
$233$	24.6525	1.61504	0.807519	−	0.589842i	$-0.200810\pi$
$233$	24.6525	1.61504	0.807519	+	0.589842i	$0.200810\pi$
$234$	−2.03444	−0.132996
$235$	7.85410	0.512345
$236$	−14.2918	−0.930317
$237$	−22.3262	−1.45024
$238$	7.56231	0.490191
$239$	21.9787	1.42168	0.710842	−	0.703351i	$-0.248314\pi$
$239$	21.9787	1.42168	0.710842	+	0.703351i	$0.248314\pi$
$240$	−1.61803	−0.104444
$241$	−23.1246	−1.48959	−0.744794	−	0.667295i	$-0.767452\pi$
$241$	−23.1246	−1.48959	−0.744794	+	0.667295i	$0.767452\pi$
$242$	0	0
$243$	−3.94427	−0.253025
$244$	27.7082	1.77384
$245$	−1.00000	−0.0638877
$246$	23.4164	1.49298
$247$	2.94427	0.187340
$248$	2.76393	0.175510
$249$	−17.0902	−1.08305
$250$	2.23607	0.141421
$251$	5.70820	0.360299	0.180149	−	0.983639i	$-0.442342\pi$
$251$	5.70820	0.360299	0.180149	+	0.983639i	$0.442342\pi$
$252$	−1.14590	−0.0721848
$253$	0	0
$254$	10.6525	0.668396
$255$	−5.47214	−0.342678
$256$	−9.00000	−0.562500
$257$	−4.61803	−0.288065	−0.144033	−	0.989573i	$-0.546007\pi$
$257$	−4.61803	−0.288065	−0.144033	+	0.989573i	$0.546007\pi$
$258$	2.76393	0.172075
$259$	−2.76393	−0.171742
$260$	7.14590	0.443170
$261$	−2.23607	−0.138409
$262$	17.8885	1.10516
$263$	8.18034	0.504421	0.252211	−	0.967672i	$-0.418842\pi$
$263$	8.18034	0.504421	0.252211	+	0.967672i	$0.418842\pi$
$264$	0	0
$265$	10.4721	0.643298
$266$	2.76393	0.169468
$267$	−27.8885	−1.70675
$268$	−42.5410	−2.59861
$269$	12.6525	0.771435	0.385718	−	0.922617i	$-0.373954\pi$
$269$	12.6525	0.771435	0.385718	+	0.922617i	$0.373954\pi$
$270$	12.2361	0.744663
$271$	−18.7639	−1.13983	−0.569914	−	0.821704i	$-0.693023\pi$
$271$	−18.7639	−1.13983	−0.569914	+	0.821704i	$0.693023\pi$
$272$	3.38197	0.205062
$273$	3.85410	0.233261
$274$	−34.4721	−2.08254
$275$	0	0
$276$	−21.7082	−1.30668
$277$	−17.4164	−1.04645	−0.523225	−	0.852194i	$-0.675271\pi$
$277$	−17.4164	−1.04645	−0.523225	+	0.852194i	$0.675271\pi$
$278$	32.3607	1.94086
$279$	0.472136	0.0282660
$280$	2.23607	0.133631
$281$	−0.472136	−0.0281653	−0.0140826	−	0.999901i	$-0.504483\pi$
$281$	−0.472136	−0.0281653	−0.0140826	+	0.999901i	$0.504483\pi$
$282$	−28.4164	−1.69217
$283$	27.5623	1.63841	0.819205	−	0.573501i	$-0.194415\pi$
$283$	27.5623	1.63841	0.819205	+	0.573501i	$0.194415\pi$
$284$	2.02129	0.119941
$285$	−2.00000	−0.118470
$286$	0	0
$287$	6.47214	0.382038
$288$	−2.56231	−0.150985
$289$	−5.56231	−0.327194
$290$	13.0902	0.768681
$291$	−0.527864	−0.0309439
$292$	−25.8541	−1.51300
$293$	−17.4164	−1.01748	−0.508739	−	0.860921i	$-0.669888\pi$
$293$	−17.4164	−1.01748	−0.508739	+	0.860921i	$0.669888\pi$
$294$	3.61803	0.211008
$295$	4.76393	0.277367
$296$	6.18034	0.359225
$297$	0	0
$298$	−24.9230	−1.44375
$299$	−10.6525	−0.616049
$300$	−4.85410	−0.280252
$301$	0.763932	0.0440323
$302$	−5.85410	−0.336866
$303$	−0.472136	−0.0271235
$304$	1.23607	0.0708934
$305$	−9.23607	−0.528856
$306$	−2.88854	−0.165127
$307$	0.437694	0.0249805	0.0124903	−	0.999922i	$-0.496024\pi$
$307$	0.437694	0.0249805	0.0124903	+	0.999922i	$0.496024\pi$
$308$	0	0
$309$	2.70820	0.154064
$310$	−2.76393	−0.156981
$311$	−27.1246	−1.53810	−0.769048	−	0.639191i	$-0.779269\pi$
$311$	−27.1246	−1.53810	−0.769048	+	0.639191i	$0.779269\pi$
$312$	−8.61803	−0.487900
$313$	−18.0000	−1.01742	−0.508710	−	0.860938i	$-0.669877\pi$
$313$	−18.0000	−1.01742	−0.508710	+	0.860938i	$0.669877\pi$
$314$	10.9787	0.619565
$315$	0.381966	0.0215213
$316$	41.3951	2.32866
$317$	−30.4721	−1.71149	−0.855743	−	0.517401i	$-0.826899\pi$
$317$	−30.4721	−1.71149	−0.855743	+	0.517401i	$0.826899\pi$
$318$	−37.8885	−2.12468
$319$	0	0
$320$	13.0000	0.726722
$321$	−4.47214	−0.249610
$322$	−10.0000	−0.557278
$323$	4.18034	0.232600
$324$	−23.1246	−1.28470
$325$	−2.38197	−0.132128
$326$	−0.403252	−0.0223341
$327$	−33.1246	−1.83180
$328$	−14.4721	−0.799090
$329$	−7.85410	−0.433011
$330$	0	0
$331$	19.5066	1.07218	0.536089	−	0.844161i	$-0.319901\pi$
$331$	19.5066	1.07218	0.536089	+	0.844161i	$0.319901\pi$
$332$	31.6869	1.73905
$333$	1.05573	0.0578535
$334$	−26.8328	−1.46823
$335$	14.1803	0.774755
$336$	1.61803	0.0882710
$337$	4.58359	0.249684	0.124842	−	0.992177i	$-0.460158\pi$
$337$	4.58359	0.249684	0.124842	+	0.992177i	$0.460158\pi$
$338$	16.3820	0.891061
$339$	−2.47214	−0.134268
$340$	10.1459	0.550239
$341$	0	0
$342$	−1.05573	−0.0570872
$343$	1.00000	0.0539949
$344$	−1.70820	−0.0921002
$345$	7.23607	0.389577
$346$	41.5066	2.23141
$347$	10.4721	0.562174	0.281087	−	0.959682i	$-0.409305\pi$
$347$	10.4721	0.562174	0.281087	+	0.959682i	$0.409305\pi$
$348$	−28.4164	−1.52328
$349$	31.8885	1.70695	0.853477	−	0.521130i	$-0.174489\pi$
$349$	31.8885	1.70695	0.853477	+	0.521130i	$0.174489\pi$
$350$	−2.23607	−0.119523
$351$	−13.0344	−0.695727
$352$	0	0
$353$	6.56231	0.349276	0.174638	−	0.984633i	$-0.444124\pi$
$353$	6.56231	0.349276	0.174638	+	0.984633i	$0.444124\pi$
$354$	−17.2361	−0.916087
$355$	−0.673762	−0.0357596
$356$	51.7082	2.74053
$357$	5.47214	0.289616
$358$	−38.8673	−2.05420
$359$	−33.9787	−1.79333	−0.896664	−	0.442712i	$-0.854016\pi$
$359$	−33.9787	−1.79333	−0.896664	+	0.442712i	$0.854016\pi$
$360$	−0.854102	−0.0450151
$361$	−17.4721	−0.919586
$362$	−32.3607	−1.70084
$363$	0	0
$364$	−7.14590	−0.374547
$365$	8.61803	0.451089
$366$	33.4164	1.74670
$367$	24.4508	1.27632	0.638162	−	0.769902i	$-0.279695\pi$
$367$	24.4508	1.27632	0.638162	+	0.769902i	$0.279695\pi$
$368$	−4.47214	−0.233126
$369$	−2.47214	−0.128694
$370$	−6.18034	−0.321301
$371$	−10.4721	−0.543686
$372$	6.00000	0.311086
$373$	29.1246	1.50802	0.754008	−	0.656866i	$-0.228118\pi$
$373$	29.1246	1.50802	0.754008	+	0.656866i	$0.228118\pi$
$374$	0	0
$375$	1.61803	0.0835549
$376$	17.5623	0.905707
$377$	−13.9443	−0.718167
$378$	−12.2361	−0.629355
$379$	−17.7426	−0.911378	−0.455689	−	0.890139i	$-0.650607\pi$
$379$	−17.7426	−0.911378	−0.455689	+	0.890139i	$0.650607\pi$
$380$	3.70820	0.190227
$381$	7.70820	0.394903
$382$	−26.6312	−1.36257
$383$	2.20163	0.112498	0.0562489	−	0.998417i	$-0.482086\pi$
$383$	2.20163	0.112498	0.0562489	+	0.998417i	$0.482086\pi$
$384$	−25.3262	−1.29242
$385$	0	0
$386$	8.94427	0.455251
$387$	−0.291796	−0.0148328
$388$	0.978714	0.0496867
$389$	−13.4377	−0.681318	−0.340659	−	0.940187i	$-0.610650\pi$
$389$	−13.4377	−0.681318	−0.340659	+	0.940187i	$0.610650\pi$
$390$	8.61803	0.436391
$391$	−15.1246	−0.764884
$392$	−2.23607	−0.112938
$393$	12.9443	0.652952
$394$	−26.8328	−1.35182
$395$	−13.7984	−0.694272
$396$	0	0
$397$	−34.1591	−1.71439	−0.857197	−	0.514989i	$-0.827796\pi$
$397$	−34.1591	−1.71439	−0.857197	+	0.514989i	$0.827796\pi$
$398$	40.2492	2.01751
$399$	2.00000	0.100125
$400$	−1.00000	−0.0500000
$401$	−22.5066	−1.12392	−0.561962	−	0.827163i	$-0.689953\pi$
$401$	−22.5066	−1.12392	−0.561962	+	0.827163i	$0.689953\pi$
$402$	−51.3050	−2.55886
$403$	2.94427	0.146665
$404$	0.875388	0.0435522
$405$	7.70820	0.383024
$406$	−13.0902	−0.649654
$407$	0	0
$408$	−12.2361	−0.605776
$409$	−1.23607	−0.0611196	−0.0305598	−	0.999533i	$-0.509729\pi$
$409$	−1.23607	−0.0611196	−0.0305598	+	0.999533i	$0.509729\pi$
$410$	14.4721	0.714728
$411$	−24.9443	−1.23041
$412$	−5.02129	−0.247381
$413$	−4.76393	−0.234418
$414$	3.81966	0.187726
$415$	−10.5623	−0.518483
$416$	−15.9787	−0.783421
$417$	23.4164	1.14671
$418$	0	0
$419$	27.3050	1.33393	0.666967	−	0.745087i	$-0.267592\pi$
$419$	27.3050	1.33393	0.666967	+	0.745087i	$0.267592\pi$
$420$	4.85410	0.236856
$421$	3.50658	0.170900	0.0854501	−	0.996342i	$-0.472767\pi$
$421$	3.50658	0.170900	0.0854501	+	0.996342i	$0.472767\pi$
$422$	52.1591	2.53906
$423$	3.00000	0.145865
$424$	23.4164	1.13720
$425$	−3.38197	−0.164049
$426$	2.43769	0.118107
$427$	9.23607	0.446965
$428$	8.29180	0.400799
$429$	0	0
$430$	1.70820	0.0823769
$431$	−10.3262	−0.497397	−0.248699	−	0.968581i	$-0.580003\pi$
$431$	−10.3262	−0.497397	−0.248699	+	0.968581i	$0.580003\pi$
$432$	−5.47214	−0.263278
$433$	−17.0344	−0.818623	−0.409312	−	0.912395i	$-0.634231\pi$
$433$	−17.0344	−0.818623	−0.409312	+	0.912395i	$0.634231\pi$
$434$	2.76393	0.132673
$435$	9.47214	0.454154
$436$	61.4164	2.94131
$437$	−5.52786	−0.264434
$438$	−31.1803	−1.48985
$439$	−17.7082	−0.845166	−0.422583	−	0.906324i	$-0.638877\pi$
$439$	−17.7082	−0.845166	−0.422583	+	0.906324i	$0.638877\pi$
$440$	0	0
$441$	−0.381966	−0.0181889
$442$	−18.0132	−0.856798
$443$	−34.6525	−1.64639	−0.823194	−	0.567760i	$-0.807810\pi$
$443$	−34.6525	−1.64639	−0.823194	+	0.567760i	$0.807810\pi$
$444$	13.4164	0.636715
$445$	−17.2361	−0.817068
$446$	−23.4164	−1.10880
$447$	−18.0344	−0.853000
$448$	−13.0000	−0.614192
$449$	24.2705	1.14540	0.572698	−	0.819766i	$-0.305897\pi$
$449$	24.2705	1.14540	0.572698	+	0.819766i	$0.305897\pi$
$450$	0.854102	0.0402628
$451$	0	0
$452$	4.58359	0.215594
$453$	−4.23607	−0.199028
$454$	30.8541	1.44805
$455$	2.38197	0.111668
$456$	−4.47214	−0.209427
$457$	−33.7771	−1.58003	−0.790013	−	0.613090i	$-0.789926\pi$
$457$	−33.7771	−1.58003	−0.790013	+	0.613090i	$0.789926\pi$
$458$	65.3738	3.05472
$459$	−18.5066	−0.863813
$460$	−13.4164	−0.625543
$461$	−29.7082	−1.38365	−0.691825	−	0.722066i	$-0.743193\pi$
$461$	−29.7082	−1.38365	−0.691825	+	0.722066i	$0.743193\pi$
$462$	0	0
$463$	23.1246	1.07469	0.537346	−	0.843362i	$-0.319427\pi$
$463$	23.1246	1.07469	0.537346	+	0.843362i	$0.319427\pi$
$464$	−5.85410	−0.271770
$465$	−2.00000	−0.0927478
$466$	−55.1246	−2.55360
$467$	−16.6738	−0.771570	−0.385785	−	0.922589i	$-0.626069\pi$
$467$	−16.6738	−0.771570	−0.385785	+	0.922589i	$0.626069\pi$
$468$	2.72949	0.126171
$469$	−14.1803	−0.654787
$470$	−17.5623	−0.810089
$471$	7.94427	0.366053
$472$	10.6525	0.490320
$473$	0	0
$474$	49.9230	2.29304
$475$	−1.23607	−0.0567147
$476$	−10.1459	−0.465036
$477$	4.00000	0.183147
$478$	−49.1459	−2.24788
$479$	8.65248	0.395342	0.197671	−	0.980268i	$-0.436662\pi$
$479$	8.65248	0.395342	0.197671	+	0.980268i	$0.436662\pi$
$480$	10.8541	0.495420
$481$	6.58359	0.300186
$482$	51.7082	2.35524
$483$	−7.23607	−0.329252
$484$	0	0
$485$	−0.326238	−0.0148137
$486$	8.81966	0.400068
$487$	−24.1803	−1.09572	−0.547858	−	0.836571i	$-0.684557\pi$
$487$	−24.1803	−1.09572	−0.547858	+	0.836571i	$0.684557\pi$
$488$	−20.6525	−0.934894
$489$	−0.291796	−0.0131955
$490$	2.23607	0.101015
$491$	−37.8885	−1.70989	−0.854943	−	0.518722i	$-0.826408\pi$
$491$	−37.8885	−1.70989	−0.854943	+	0.518722i	$0.826408\pi$
$492$	−31.4164	−1.41636
$493$	−19.7984	−0.891674
$494$	−6.58359	−0.296210
$495$	0	0
$496$	1.23607	0.0555011
$497$	0.673762	0.0302224
$498$	38.2148	1.71245
$499$	6.03444	0.270139	0.135069	−	0.990836i	$-0.456874\pi$
$499$	6.03444	0.270139	0.135069	+	0.990836i	$0.456874\pi$
$500$	−3.00000	−0.134164
$501$	−19.4164	−0.867461
$502$	−12.7639	−0.569682
$503$	8.09017	0.360723	0.180361	−	0.983600i	$-0.442273\pi$
$503$	8.09017	0.360723	0.180361	+	0.983600i	$0.442273\pi$
$504$	0.854102	0.0380447
$505$	−0.291796	−0.0129848
$506$	0	0
$507$	11.8541	0.526459
$508$	−14.2918	−0.634096
$509$	−18.3607	−0.813823	−0.406911	−	0.913468i	$-0.633394\pi$
$509$	−18.3607	−0.813823	−0.406911	+	0.913468i	$0.633394\pi$
$510$	12.2361	0.541822
$511$	−8.61803	−0.381239
$512$	−11.1803	−0.494106
$513$	−6.76393	−0.298635
$514$	10.3262	0.455471
$515$	1.67376	0.0737548
$516$	−3.70820	−0.163245
$517$	0	0
$518$	6.18034	0.271549
$519$	30.0344	1.31837
$520$	−5.32624	−0.233571
$521$	8.18034	0.358387	0.179194	−	0.983814i	$-0.442651\pi$
$521$	8.18034	0.358387	0.179194	+	0.983814i	$0.442651\pi$
$522$	5.00000	0.218844
$523$	−7.85410	−0.343436	−0.171718	−	0.985146i	$-0.554932\pi$
$523$	−7.85410	−0.343436	−0.171718	+	0.985146i	$0.554932\pi$
$524$	−24.0000	−1.04844
$525$	−1.61803	−0.0706168
$526$	−18.2918	−0.797560
$527$	4.18034	0.182098
$528$	0	0
$529$	−3.00000	−0.130435
$530$	−23.4164	−1.01714
$531$	1.81966	0.0789665
$532$	−3.70820	−0.160771
$533$	−15.4164	−0.667759
$534$	62.3607	2.69861
$535$	−2.76393	−0.119495
$536$	31.7082	1.36959
$537$	−28.1246	−1.21367
$538$	−28.2918	−1.21975
$539$	0	0
$540$	−16.4164	−0.706450
$541$	−12.8541	−0.552641	−0.276321	−	0.961066i	$-0.589115\pi$
$541$	−12.8541	−0.552641	−0.276321	+	0.961066i	$0.589115\pi$
$542$	41.9574	1.80223
$543$	−23.4164	−1.00489
$544$	−22.6869	−0.972694
$545$	−20.4721	−0.876930
$546$	−8.61803	−0.368818
$547$	−40.0689	−1.71322	−0.856611	−	0.515963i	$-0.827434\pi$
$547$	−40.0689	−1.71322	−0.856611	+	0.515963i	$0.827434\pi$
$548$	46.2492	1.97567
$549$	−3.52786	−0.150566
$550$	0	0
$551$	−7.23607	−0.308267
$552$	16.1803	0.688681
$553$	13.7984	0.586767
$554$	38.9443	1.65458
$555$	−4.47214	−0.189832
$556$	−43.4164	−1.84127
$557$	4.29180	0.181849	0.0909246	−	0.995858i	$-0.471018\pi$
$557$	4.29180	0.181849	0.0909246	+	0.995858i	$0.471018\pi$
$558$	−1.05573	−0.0446925
$559$	−1.81966	−0.0769634
$560$	1.00000	0.0422577
$561$	0	0
$562$	1.05573	0.0445332
$563$	21.3820	0.901142	0.450571	−	0.892740i	$-0.351220\pi$
$563$	21.3820	0.901142	0.450571	+	0.892740i	$0.351220\pi$
$564$	38.1246	1.60534
$565$	−1.52786	−0.0642777
$566$	−61.6312	−2.59055
$567$	−7.70820	−0.323714
$568$	−1.50658	−0.0632146
$569$	13.2016	0.553441	0.276720	−	0.960950i	$-0.410752\pi$
$569$	13.2016	0.553441	0.276720	+	0.960950i	$0.410752\pi$
$570$	4.47214	0.187317
$571$	−10.9787	−0.459445	−0.229722	−	0.973256i	$-0.573782\pi$
$571$	−10.9787	−0.459445	−0.229722	+	0.973256i	$0.573782\pi$
$572$	0	0
$573$	−19.2705	−0.805037
$574$	−14.4721	−0.604055
$575$	4.47214	0.186501
$576$	4.96556	0.206898
$577$	−18.2148	−0.758291	−0.379146	−	0.925337i	$-0.623782\pi$
$577$	−18.2148	−0.758291	−0.379146	+	0.925337i	$0.623782\pi$
$578$	12.4377	0.517340
$579$	6.47214	0.268973
$580$	−17.5623	−0.729235
$581$	10.5623	0.438198
$582$	1.18034	0.0489267
$583$	0	0
$584$	19.2705	0.797419
$585$	−0.909830	−0.0376168
$586$	38.9443	1.60877
$587$	40.2705	1.66214	0.831071	−	0.556166i	$-0.187728\pi$
$587$	40.2705	1.66214	0.831071	+	0.556166i	$0.187728\pi$
$588$	−4.85410	−0.200180
$589$	1.52786	0.0629545
$590$	−10.6525	−0.438555
$591$	−19.4164	−0.798684
$592$	2.76393	0.113597
$593$	14.7984	0.607696	0.303848	−	0.952720i	$-0.401728\pi$
$593$	14.7984	0.607696	0.303848	+	0.952720i	$0.401728\pi$
$594$	0	0
$595$	3.38197	0.138647
$596$	33.4377	1.36966
$597$	29.1246	1.19199
$598$	23.8197	0.974058
$599$	−7.27051	−0.297065	−0.148532	−	0.988908i	$-0.547455\pi$
$599$	−7.27051	−0.297065	−0.148532	+	0.988908i	$0.547455\pi$
$600$	3.61803	0.147706
$601$	−11.4164	−0.465685	−0.232842	−	0.972514i	$-0.574803\pi$
$601$	−11.4164	−0.465685	−0.232842	+	0.972514i	$0.574803\pi$
$602$	−1.70820	−0.0696212
$603$	5.41641	0.220573
$604$	7.85410	0.319579
$605$	0	0
$606$	1.05573	0.0428860
$607$	13.0902	0.531314	0.265657	−	0.964068i	$-0.414411\pi$
$607$	13.0902	0.531314	0.265657	+	0.964068i	$0.414411\pi$
$608$	−8.29180	−0.336277
$609$	−9.47214	−0.383830
$610$	20.6525	0.836194
$611$	18.7082	0.756853
$612$	3.87539	0.156653
$613$	−12.8328	−0.518313	−0.259156	−	0.965835i	$-0.583444\pi$
$613$	−12.8328	−0.518313	−0.259156	+	0.965835i	$0.583444\pi$
$614$	−0.978714	−0.0394977
$615$	10.4721	0.422277
$616$	0	0
$617$	−7.23607	−0.291313	−0.145657	−	0.989335i	$-0.546529\pi$
$617$	−7.23607	−0.291313	−0.145657	+	0.989335i	$0.546529\pi$
$618$	−6.05573	−0.243597
$619$	−13.5279	−0.543731	−0.271865	−	0.962335i	$-0.587641\pi$
$619$	−13.5279	−0.543731	−0.271865	+	0.962335i	$0.587641\pi$
$620$	3.70820	0.148925
$621$	24.4721	0.982033
$622$	60.6525	2.43194
$623$	17.2361	0.690548
$624$	−3.85410	−0.154288
$625$	1.00000	0.0400000
$626$	40.2492	1.60868
$627$	0	0
$628$	−14.7295	−0.587771
$629$	9.34752	0.372710
$630$	−0.854102	−0.0340282
$631$	28.5066	1.13483	0.567414	−	0.823432i	$-0.307944\pi$
$631$	28.5066	1.13483	0.567414	+	0.823432i	$0.307944\pi$
$632$	−30.8541	−1.22731
$633$	37.7426	1.50014
$634$	68.1378	2.70610
$635$	4.76393	0.189051
$636$	50.8328	2.01565
$637$	−2.38197	−0.0943769
$638$	0	0
$639$	−0.257354	−0.0101808
$640$	−15.6525	−0.618718
$641$	−25.9787	−1.02610	−0.513049	−	0.858359i	$-0.671484\pi$
$641$	−25.9787	−1.02610	−0.513049	+	0.858359i	$0.671484\pi$
$642$	10.0000	0.394669
$643$	−13.7984	−0.544155	−0.272077	−	0.962275i	$-0.587711\pi$
$643$	−13.7984	−0.544155	−0.272077	+	0.962275i	$0.587711\pi$
$644$	13.4164	0.528681
$645$	1.23607	0.0486701
$646$	−9.34752	−0.367773
$647$	−40.1459	−1.57830	−0.789149	−	0.614202i	$-0.789478\pi$
$647$	−40.1459	−1.57830	−0.789149	+	0.614202i	$0.789478\pi$
$648$	17.2361	0.677097
$649$	0	0
$650$	5.32624	0.208912
$651$	2.00000	0.0783862
$652$	0.541020	0.0211880
$653$	−15.8197	−0.619071	−0.309536	−	0.950888i	$-0.600174\pi$
$653$	−15.8197	−0.619071	−0.309536	+	0.950888i	$0.600174\pi$
$654$	74.0689	2.89632
$655$	8.00000	0.312586
$656$	−6.47214	−0.252694
$657$	3.29180	0.128425
$658$	17.5623	0.684650
$659$	−25.0344	−0.975203	−0.487602	−	0.873066i	$-0.662128\pi$
$659$	−25.0344	−0.975203	−0.487602	+	0.873066i	$0.662128\pi$
$660$	0	0
$661$	−33.4164	−1.29975	−0.649874	−	0.760042i	$-0.725178\pi$
$661$	−33.4164	−1.29975	−0.649874	+	0.760042i	$0.725178\pi$
$662$	−43.6180	−1.69526
$663$	−13.0344	−0.506216
$664$	−23.6180	−0.916557
$665$	1.23607	0.0479327
$666$	−2.36068	−0.0914745
$667$	26.1803	1.01371
$668$	36.0000	1.39288
$669$	−16.9443	−0.655103
$670$	−31.7082	−1.22499
$671$	0	0
$672$	−10.8541	−0.418706
$673$	13.8885	0.535364	0.267682	−	0.963507i	$-0.413742\pi$
$673$	13.8885	0.535364	0.267682	+	0.963507i	$0.413742\pi$
$674$	−10.2492	−0.394785
$675$	5.47214	0.210623
$676$	−21.9787	−0.845335
$677$	−42.1459	−1.61980	−0.809899	−	0.586569i	$-0.800478\pi$
$677$	−42.1459	−1.61980	−0.809899	+	0.586569i	$0.800478\pi$
$678$	5.52786	0.212296
$679$	0.326238	0.0125199
$680$	−7.56231	−0.290001
$681$	22.3262	0.855543
$682$	0	0
$683$	39.2361	1.50133	0.750663	−	0.660685i	$-0.229734\pi$
$683$	39.2361	1.50133	0.750663	+	0.660685i	$0.229734\pi$
$684$	1.41641	0.0541577
$685$	−15.4164	−0.589031
$686$	−2.23607	−0.0853735
$687$	47.3050	1.80480
$688$	−0.763932	−0.0291246
$689$	24.9443	0.950301
$690$	−16.1803	−0.615975
$691$	26.8328	1.02077	0.510384	−	0.859946i	$-0.329503\pi$
$691$	26.8328	1.02077	0.510384	+	0.859946i	$0.329503\pi$
$692$	−55.6869	−2.11690
$693$	0	0
$694$	−23.4164	−0.888875
$695$	14.4721	0.548959
$696$	21.1803	0.802839
$697$	−21.8885	−0.829088
$698$	−71.3050	−2.69893
$699$	−39.8885	−1.50872
$700$	3.00000	0.113389
$701$	−11.3050	−0.426982	−0.213491	−	0.976945i	$-0.568483\pi$
$701$	−11.3050	−0.426982	−0.213491	+	0.976945i	$0.568483\pi$
$702$	29.1459	1.10004
$703$	3.41641	0.128852
$704$	0	0
$705$	−12.7082	−0.478619
$706$	−14.6738	−0.552254
$707$	0.291796	0.0109741
$708$	23.1246	0.869076
$709$	42.7426	1.60523	0.802617	−	0.596495i	$-0.203440\pi$
$709$	42.7426	1.60523	0.802617	+	0.596495i	$0.203440\pi$
$710$	1.50658	0.0565409
$711$	−5.27051	−0.197660
$712$	−38.5410	−1.44439
$713$	−5.52786	−0.207020
$714$	−12.2361	−0.457923
$715$	0	0
$716$	52.1459	1.94878
$717$	−35.5623	−1.32810
$718$	75.9787	2.83550
$719$	−13.8885	−0.517955	−0.258978	−	0.965883i	$-0.583386\pi$
$719$	−13.8885	−0.517955	−0.258978	+	0.965883i	$0.583386\pi$
$720$	−0.381966	−0.0142350
$721$	−1.67376	−0.0623342
$722$	39.0689	1.45399
$723$	37.4164	1.39153
$724$	43.4164	1.61356
$725$	5.85410	0.217416
$726$	0	0
$727$	−21.4377	−0.795080	−0.397540	−	0.917585i	$-0.630136\pi$
$727$	−21.4377	−0.795080	−0.397540	+	0.917585i	$0.630136\pi$
$728$	5.32624	0.197404
$729$	29.5066	1.09284
$730$	−19.2705	−0.713234
$731$	−2.58359	−0.0955576
$732$	−44.8328	−1.65707
$733$	47.8673	1.76802	0.884009	−	0.467470i	$-0.154835\pi$
$733$	47.8673	1.76802	0.884009	+	0.467470i	$0.154835\pi$
$734$	−54.6738	−2.01805
$735$	1.61803	0.0596821
$736$	30.0000	1.10581
$737$	0	0
$738$	5.52786	0.203483
$739$	−12.0000	−0.441427	−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000	−0.441427	−0.220714	+	0.975339i	$0.570839\pi$
$740$	8.29180	0.304812
$741$	−4.76393	−0.175007
$742$	23.4164	0.859643
$743$	−36.6525	−1.34465	−0.672324	−	0.740257i	$-0.734704\pi$
$743$	−36.6525	−1.34465	−0.672324	+	0.740257i	$0.734704\pi$
$744$	−4.47214	−0.163956
$745$	−11.1459	−0.408354
$746$	−65.1246	−2.38438
$747$	−4.03444	−0.147613
$748$	0	0
$749$	2.76393	0.100992
$750$	−3.61803	−0.132112
$751$	21.6738	0.790887	0.395443	−	0.918490i	$-0.370591\pi$
$751$	21.6738	0.790887	0.395443	+	0.918490i	$0.370591\pi$
$752$	7.85410	0.286410
$753$	−9.23607	−0.336581
$754$	31.1803	1.13552
$755$	−2.61803	−0.0952800
$756$	16.4164	0.597059
$757$	−18.1803	−0.660776	−0.330388	−	0.943845i	$-0.607180\pi$
$757$	−18.1803	−0.660776	−0.330388	+	0.943845i	$0.607180\pi$
$758$	39.6738	1.44102
$759$	0	0
$760$	−2.76393	−0.100258
$761$	4.83282	0.175189	0.0875947	−	0.996156i	$-0.472082\pi$
$761$	4.83282	0.175189	0.0875947	+	0.996156i	$0.472082\pi$
$762$	−17.2361	−0.624397
$763$	20.4721	0.741141
$764$	35.7295	1.29265
$765$	−1.29180	−0.0467050
$766$	−4.92299	−0.177875
$767$	11.3475	0.409735
$768$	14.5623	0.525472
$769$	1.70820	0.0615994	0.0307997	−	0.999526i	$-0.490195\pi$
$769$	1.70820	0.0615994	0.0307997	+	0.999526i	$0.490195\pi$
$770$	0	0
$771$	7.47214	0.269102
$772$	−12.0000	−0.431889
$773$	−29.6180	−1.06529	−0.532643	−	0.846340i	$-0.678801\pi$
$773$	−29.6180	−1.06529	−0.532643	+	0.846340i	$0.678801\pi$
$774$	0.652476	0.0234528
$775$	−1.23607	−0.0444009
$776$	−0.729490	−0.0261872
$777$	4.47214	0.160437
$778$	30.0476	1.07726
$779$	−8.00000	−0.286630
$780$	−11.5623	−0.413997
$781$	0	0
$782$	33.8197	1.20939
$783$	32.0344	1.14482
$784$	−1.00000	−0.0357143
$785$	4.90983	0.175239
$786$	−28.9443	−1.03241
$787$	−10.9656	−0.390880	−0.195440	−	0.980716i	$-0.562613\pi$
$787$	−10.9656	−0.390880	−0.195440	+	0.980716i	$0.562613\pi$
$788$	36.0000	1.28245
$789$	−13.2361	−0.471216
$790$	30.8541	1.09774
$791$	1.52786	0.0543246
$792$	0	0
$793$	−22.0000	−0.781243
$794$	76.3820	2.71069
$795$	−16.9443	−0.600951
$796$	−54.0000	−1.91398
$797$	−43.1033	−1.52680	−0.763399	−	0.645927i	$-0.776471\pi$
$797$	−43.1033	−1.52680	−0.763399	+	0.645927i	$0.776471\pi$
$798$	−4.47214	−0.158312
$799$	26.5623	0.939707
$800$	6.70820	0.237171
$801$	−6.58359	−0.232620
$802$	50.3262	1.77708
$803$	0	0
$804$	68.8328	2.42755
$805$	−4.47214	−0.157622
$806$	−6.58359	−0.231897
$807$	−20.4721	−0.720653
$808$	−0.652476	−0.0229540
$809$	−8.09017	−0.284435	−0.142218	−	0.989835i	$-0.545423\pi$
$809$	−8.09017	−0.284435	−0.142218	+	0.989835i	$0.545423\pi$
$810$	−17.2361	−0.605614
$811$	−4.58359	−0.160952	−0.0804758	−	0.996757i	$-0.525644\pi$
$811$	−4.58359	−0.160952	−0.0804758	+	0.996757i	$0.525644\pi$
$812$	17.5623	0.616316
$813$	30.3607	1.06480
$814$	0	0
$815$	−0.180340	−0.00631703
$816$	−5.47214	−0.191563
$817$	−0.944272	−0.0330359
$818$	2.76393	0.0966386
$819$	0.909830	0.0317920
$820$	−19.4164	−0.678050
$821$	−28.3262	−0.988593	−0.494296	−	0.869294i	$-0.664574\pi$
$821$	−28.3262	−0.988593	−0.494296	+	0.869294i	$0.664574\pi$
$822$	55.7771	1.94545
$823$	−20.0000	−0.697156	−0.348578	−	0.937280i	$-0.613335\pi$
$823$	−20.0000	−0.697156	−0.348578	+	0.937280i	$0.613335\pi$
$824$	3.74265	0.130381
$825$	0	0
$826$	10.6525	0.370647
$827$	2.11146	0.0734225	0.0367113	−	0.999326i	$-0.488312\pi$
$827$	2.11146	0.0734225	0.0367113	+	0.999326i	$0.488312\pi$
$828$	−5.12461	−0.178093
$829$	−1.88854	−0.0655918	−0.0327959	−	0.999462i	$-0.510441\pi$
$829$	−1.88854	−0.0655918	−0.0327959	+	0.999462i	$0.510441\pi$
$830$	23.6180	0.819794
$831$	28.1803	0.977565
$832$	30.9656	1.07354
$833$	−3.38197	−0.117178
$834$	−52.3607	−1.81310
$835$	−12.0000	−0.415277
$836$	0	0
$837$	−6.76393	−0.233796
$838$	−61.0557	−2.10914
$839$	52.3607	1.80769	0.903846	−	0.427859i	$-0.140732\pi$
$839$	52.3607	1.80769	0.903846	+	0.427859i	$0.140732\pi$
$840$	−3.61803	−0.124834
$841$	5.27051	0.181742
$842$	−7.84095	−0.270217
$843$	0.763932	0.0263112
$844$	−69.9787	−2.40877
$845$	7.32624	0.252030
$846$	−6.70820	−0.230633
$847$	0	0
$848$	10.4721	0.359615
$849$	−44.5967	−1.53056
$850$	7.56231	0.259385
$851$	−12.3607	−0.423719
$852$	−3.27051	−0.112046
$853$	−38.5623	−1.32035	−0.660174	−	0.751113i	$-0.729518\pi$
$853$	−38.5623	−1.32035	−0.660174	+	0.751113i	$0.729518\pi$
$854$	−20.6525	−0.706713
$855$	−0.472136	−0.0161467
$856$	−6.18034	−0.211240
$857$	−41.1935	−1.40714	−0.703572	−	0.710624i	$-0.748413\pi$
$857$	−41.1935	−1.40714	−0.703572	+	0.710624i	$0.748413\pi$
$858$	0	0
$859$	−28.9443	−0.987566	−0.493783	−	0.869585i	$-0.664386\pi$
$859$	−28.9443	−0.987566	−0.493783	+	0.869585i	$0.664386\pi$
$860$	−2.29180	−0.0781496
$861$	−10.4721	−0.356889
$862$	23.0902	0.786454
$863$	20.9443	0.712951	0.356476	−	0.934305i	$-0.383978\pi$
$863$	20.9443	0.712951	0.356476	+	0.934305i	$0.383978\pi$
$864$	36.7082	1.24884
$865$	18.5623	0.631137
$866$	38.0902	1.29436
$867$	9.00000	0.305656
$868$	−3.70820	−0.125865
$869$	0	0
$870$	−21.1803	−0.718081
$871$	33.7771	1.14449
$872$	−45.7771	−1.55021
$873$	−0.124612	−0.00421747
$874$	12.3607	0.418106
$875$	−1.00000	−0.0338062
$876$	41.8328	1.41340
$877$	21.0132	0.709564	0.354782	−	0.934949i	$-0.384555\pi$
$877$	21.0132	0.709564	0.354782	+	0.934949i	$0.384555\pi$
$878$	39.5967	1.33633
$879$	28.1803	0.950499
$880$	0	0
$881$	−0.763932	−0.0257375	−0.0128688	−	0.999917i	$-0.504096\pi$
$881$	−0.763932	−0.0257375	−0.0128688	+	0.999917i	$0.504096\pi$
$882$	0.854102	0.0287591
$883$	12.1803	0.409901	0.204951	−	0.978772i	$-0.434297\pi$
$883$	12.1803	0.409901	0.204951	+	0.978772i	$0.434297\pi$
$884$	24.1672	0.812830
$885$	−7.70820	−0.259108
$886$	77.4853	2.60317
$887$	27.8541	0.935249	0.467625	−	0.883927i	$-0.345110\pi$
$887$	27.8541	0.935249	0.467625	+	0.883927i	$0.345110\pi$
$888$	−10.0000	−0.335578
$889$	−4.76393	−0.159777
$890$	38.5410	1.29190
$891$	0	0
$892$	31.4164	1.05190
$893$	9.70820	0.324873
$894$	40.3262	1.34871
$895$	−17.3820	−0.581015
$896$	15.6525	0.522913
$897$	17.2361	0.575496
$898$	−54.2705	−1.81103
$899$	−7.23607	−0.241336
$900$	−1.14590	−0.0381966
$901$	35.4164	1.17989
$902$	0	0
$903$	−1.23607	−0.0411338
$904$	−3.41641	−0.113628
$905$	−14.4721	−0.481070
$906$	9.47214	0.314691
$907$	−7.88854	−0.261935	−0.130967	−	0.991387i	$-0.541808\pi$
$907$	−7.88854	−0.261935	−0.130967	+	0.991387i	$0.541808\pi$
$908$	−41.3951	−1.37375
$909$	−0.111456	−0.00369677
$910$	−5.32624	−0.176563
$911$	36.5066	1.20952	0.604758	−	0.796409i	$-0.293270\pi$
$911$	36.5066	1.20952	0.604758	+	0.796409i	$0.293270\pi$
$912$	−2.00000	−0.0662266
$913$	0	0
$914$	75.5279	2.49824
$915$	14.9443	0.494042
$916$	−87.7082	−2.89796
$917$	−8.00000	−0.264183
$918$	41.3820	1.36581
$919$	31.2705	1.03152	0.515759	−	0.856733i	$-0.327510\pi$
$919$	31.2705	1.03152	0.515759	+	0.856733i	$0.327510\pi$
$920$	10.0000	0.329690
$921$	−0.708204	−0.0233361
$922$	66.4296	2.18774
$923$	−1.60488	−0.0528252
$924$	0	0
$925$	−2.76393	−0.0908775
$926$	−51.7082	−1.69924
$927$	0.639320	0.0209980
$928$	39.2705	1.28912
$929$	17.8885	0.586904	0.293452	−	0.955974i	$-0.405196\pi$
$929$	17.8885	0.586904	0.293452	+	0.955974i	$0.405196\pi$
$930$	4.47214	0.146647
$931$	−1.23607	−0.0405105
$932$	73.9574	2.42256
$933$	43.8885	1.43685
$934$	37.2837	1.21996
$935$	0	0
$936$	−2.03444	−0.0664978
$937$	−56.4508	−1.84417	−0.922084	−	0.386989i	$-0.873515\pi$
$937$	−56.4508	−1.84417	−0.922084	+	0.386989i	$0.873515\pi$
$938$	31.7082	1.03531
$939$	29.1246	0.950446
$940$	23.5623	0.768518
$941$	−36.5410	−1.19120	−0.595602	−	0.803280i	$-0.703086\pi$
$941$	−36.5410	−1.19120	−0.595602	+	0.803280i	$0.703086\pi$
$942$	−17.7639	−0.578780
$943$	28.9443	0.942555
$944$	4.76393	0.155053
$945$	−5.47214	−0.178009
$946$	0	0
$947$	−24.0689	−0.782134	−0.391067	−	0.920362i	$-0.627894\pi$
$947$	−24.0689	−0.782134	−0.391067	+	0.920362i	$0.627894\pi$
$948$	−66.9787	−2.17537
$949$	20.5279	0.666363
$950$	2.76393	0.0896738
$951$	49.3050	1.59882
$952$	7.56231	0.245096
$953$	−25.0557	−0.811635	−0.405817	−	0.913954i	$-0.633013\pi$
$953$	−25.0557	−0.811635	−0.405817	+	0.913954i	$0.633013\pi$
$954$	−8.94427	−0.289581
$955$	−11.9098	−0.385393
$956$	65.9361	2.13253
$957$	0	0
$958$	−19.3475	−0.625090
$959$	15.4164	0.497822
$960$	−21.0344	−0.678884
$961$	−29.4721	−0.950714
$962$	−14.7214	−0.474636
$963$	−1.05573	−0.0340204
$964$	−69.3738	−2.23438
$965$	4.00000	0.128765
$966$	16.1803	0.520594
$967$	21.2361	0.682906	0.341453	−	0.939899i	$-0.389081\pi$
$967$	21.2361	0.682906	0.341453	+	0.939899i	$0.389081\pi$
$968$	0	0
$969$	−6.76393	−0.217289
$970$	0.729490	0.0234225
$971$	−29.4164	−0.944017	−0.472009	−	0.881594i	$-0.656471\pi$
$971$	−29.4164	−0.944017	−0.472009	+	0.881594i	$0.656471\pi$
$972$	−11.8328	−0.379538
$973$	−14.4721	−0.463955
$974$	54.0689	1.73248
$975$	3.85410	0.123430
$976$	−9.23607	−0.295639
$977$	36.7639	1.17618	0.588091	−	0.808795i	$-0.299880\pi$
$977$	36.7639	1.17618	0.588091	+	0.808795i	$0.299880\pi$
$978$	0.652476	0.0208639
$979$	0	0
$980$	−3.00000	−0.0958315
$981$	−7.81966	−0.249663
$982$	84.7214	2.70357
$983$	18.9787	0.605327	0.302663	−	0.953097i	$-0.402124\pi$
$983$	18.9787	0.605327	0.302663	+	0.953097i	$0.402124\pi$
$984$	23.4164	0.746488
$985$	−12.0000	−0.382352
$986$	44.2705	1.40986
$987$	12.7082	0.404507
$988$	8.83282	0.281009
$989$	3.41641	0.108635
$990$	0	0
$991$	7.14590	0.226997	0.113498	−	0.993538i	$-0.463794\pi$
$991$	7.14590	0.226997	0.113498	+	0.993538i	$0.463794\pi$
$992$	−8.29180	−0.263265
$993$	−31.5623	−1.00160
$994$	−1.50658	−0.0477857
$995$	18.0000	0.570638
$996$	−51.2705	−1.62457
$997$	−26.2148	−0.830230	−0.415115	−	0.909769i	$-0.636259\pi$
$997$	−26.2148	−0.830230	−0.415115	+	0.909769i	$0.636259\pi$
$998$	−13.4934	−0.427127
$999$	−15.1246	−0.478522

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.k.1.1		2
11.7	odd	10		385.2.n.b.71.1	✓	4
11.8	odd	10		385.2.n.b.141.1	yes	4
11.10	odd	2		4235.2.a.j.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.b.71.1	✓	4	11.7	odd	10
385.2.n.b.141.1	yes	4	11.8	odd	10
4235.2.a.j.1.2		2	11.10	odd	2
4235.2.a.k.1.1		2	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:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-2.23607 q^{2} -1.61803 q^{3} +3.00000 q^{4} -1.00000 q^{5} +3.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} -0.381966 q^{9} +O(q^{10})\)	\(q-2.23607 q^{2} -1.61803 q^{3} +3.00000 q^{4} -1.00000 q^{5} +3.61803 q^{6} +1.00000 q^{7} -2.23607 q^{8} -0.381966 q^{9} +2.23607 q^{10} -4.85410 q^{12} -2.38197 q^{13} -2.23607 q^{14} +1.61803 q^{15} -1.00000 q^{16} -3.38197 q^{17} +0.854102 q^{18} -1.23607 q^{19} -3.00000 q^{20} -1.61803 q^{21} +4.47214 q^{23} +3.61803 q^{24} +1.00000 q^{25} +5.32624 q^{26} +5.47214 q^{27} +3.00000 q^{28} +5.85410 q^{29} -3.61803 q^{30} -1.23607 q^{31} +6.70820 q^{32} +7.56231 q^{34} -1.00000 q^{35} -1.14590 q^{36} -2.76393 q^{37} +2.76393 q^{38} +3.85410 q^{39} +2.23607 q^{40} +6.47214 q^{41} +3.61803 q^{42} +0.763932 q^{43} +0.381966 q^{45} -10.0000 q^{46} -7.85410 q^{47} +1.61803 q^{48} +1.00000 q^{49} -2.23607 q^{50} +5.47214 q^{51} -7.14590 q^{52} -10.4721 q^{53} -12.2361 q^{54} -2.23607 q^{56} +2.00000 q^{57} -13.0902 q^{58} -4.76393 q^{59} +4.85410 q^{60} +9.23607 q^{61} +2.76393 q^{62} -0.381966 q^{63} -13.0000 q^{64} +2.38197 q^{65} -14.1803 q^{67} -10.1459 q^{68} -7.23607 q^{69} +2.23607 q^{70} +0.673762 q^{71} +0.854102 q^{72} -8.61803 q^{73} +6.18034 q^{74} -1.61803 q^{75} -3.70820 q^{76} -8.61803 q^{78} +13.7984 q^{79} +1.00000 q^{80} -7.70820 q^{81} -14.4721 q^{82} +10.5623 q^{83} -4.85410 q^{84} +3.38197 q^{85} -1.70820 q^{86} -9.47214 q^{87} +17.2361 q^{89} -0.854102 q^{90} -2.38197 q^{91} +13.4164 q^{92} +2.00000 q^{93} +17.5623 q^{94} +1.23607 q^{95} -10.8541 q^{96} +0.326238 q^{97} -2.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{3} + 6 q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) 2 * q - q^3 + 6 * q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^9	\( 2 q - q^{3} + 6 q^{4} - 2 q^{5} + 5 q^{6} + 2 q^{7} - 3 q^{9} - 3 q^{12} - 7 q^{13} + q^{15} - 2 q^{16} - 9 q^{17} - 5 q^{18} + 2 q^{19} - 6 q^{20} - q^{21} + 5 q^{24} + 2 q^{25} - 5 q^{26} + 2 q^{27} + 6 q^{28} + 5 q^{29} - 5 q^{30} + 2 q^{31} - 5 q^{34} - 2 q^{35} - 9 q^{36} - 10 q^{37} + 10 q^{38} + q^{39} + 4 q^{41} + 5 q^{42} + 6 q^{43} + 3 q^{45} - 20 q^{46} - 9 q^{47} + q^{48} + 2 q^{49} + 2 q^{51} - 21 q^{52} - 12 q^{53} - 20 q^{54} + 4 q^{57} - 15 q^{58} - 14 q^{59} + 3 q^{60} + 14 q^{61} + 10 q^{62} - 3 q^{63} - 26 q^{64} + 7 q^{65} - 6 q^{67} - 27 q^{68} - 10 q^{69} + 17 q^{71} - 5 q^{72} - 15 q^{73} - 10 q^{74} - q^{75} + 6 q^{76} - 15 q^{78} + 3 q^{79} + 2 q^{80} - 2 q^{81} - 20 q^{82} + q^{83} - 3 q^{84} + 9 q^{85} + 10 q^{86} - 10 q^{87} + 30 q^{89} + 5 q^{90} - 7 q^{91} + 4 q^{93} + 15 q^{94} - 2 q^{95} - 15 q^{96} - 15 q^{97}+O(q^{100}) \) 2 * q - q^3 + 6 * q^4 - 2 * q^5 + 5 * q^6 + 2 * q^7 - 3 * q^9 - 3 * q^12 - 7 * q^13 + q^15 - 2 * q^16 - 9 * q^17 - 5 * q^18 + 2 * q^19 - 6 * q^20 - q^21 + 5 * q^24 + 2 * q^25 - 5 * q^26 + 2 * q^27 + 6 * q^28 + 5 * q^29 - 5 * q^30 + 2 * q^31 - 5 * q^34 - 2 * q^35 - 9 * q^36 - 10 * q^37 + 10 * q^38 + q^39 + 4 * q^41 + 5 * q^42 + 6 * q^43 + 3 * q^45 - 20 * q^46 - 9 * q^47 + q^48 + 2 * q^49 + 2 * q^51 - 21 * q^52 - 12 * q^53 - 20 * q^54 + 4 * q^57 - 15 * q^58 - 14 * q^59 + 3 * q^60 + 14 * q^61 + 10 * q^62 - 3 * q^63 - 26 * q^64 + 7 * q^65 - 6 * q^67 - 27 * q^68 - 10 * q^69 + 17 * q^71 - 5 * q^72 - 15 * q^73 - 10 * q^74 - q^75 + 6 * q^76 - 15 * q^78 + 3 * q^79 + 2 * q^80 - 2 * q^81 - 20 * q^82 + q^83 - 3 * q^84 + 9 * q^85 + 10 * q^86 - 10 * q^87 + 30 * q^89 + 5 * q^90 - 7 * q^91 + 4 * q^93 + 15 * q^94 - 2 * q^95 - 15 * q^96 - 15 * q^97

Introduction

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