LMFDB - Embedded newform 4263.2.a.m.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4263,2,Mod(1,4263)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4263, 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("4263.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4263 = 3 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4263.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:	$34.0402263817$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.254102$ of defining polynomial
Character	$\chi$	$=$	4263.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} -0.508203 q^{5} -1.93543 q^{6} +0.491797 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} -0.508203 q^{5} -1.93543 q^{6} +0.491797 q^{8} +1.00000 q^{9} +0.983593 q^{10} -0.318669 q^{11} +1.74590 q^{12} -4.18953 q^{13} -0.508203 q^{15} -4.44364 q^{16} -3.17313 q^{17} -1.93543 q^{18} +5.87086 q^{19} -0.887271 q^{20} +0.616763 q^{22} +2.50820 q^{23} +0.491797 q^{24} -4.74173 q^{25} +8.10856 q^{26} +1.00000 q^{27} +1.00000 q^{29} +0.983593 q^{30} -2.50820 q^{31} +7.61676 q^{32} -0.318669 q^{33} +6.14137 q^{34} +1.74590 q^{36} +7.87086 q^{37} -11.3627 q^{38} -4.18953 q^{39} -0.249933 q^{40} -8.72532 q^{41} -10.7253 q^{43} -0.556364 q^{44} -0.508203 q^{45} -4.85446 q^{46} +11.0440 q^{47} -4.44364 q^{48} +9.17730 q^{50} -3.17313 q^{51} -7.31450 q^{52} -8.24993 q^{53} -1.93543 q^{54} +0.161949 q^{55} +5.87086 q^{57} -1.93543 q^{58} +11.3627 q^{59} -0.887271 q^{60} +3.87086 q^{61} +4.85446 q^{62} -5.85446 q^{64} +2.12914 q^{65} +0.616763 q^{66} +7.04399 q^{67} -5.53996 q^{68} +2.50820 q^{69} +6.24993 q^{71} +0.491797 q^{72} +7.87086 q^{73} -15.2335 q^{74} -4.74173 q^{75} +10.2499 q^{76} +8.10856 q^{78} -4.85446 q^{79} +2.25827 q^{80} +1.00000 q^{81} +16.8873 q^{82} +8.37907 q^{83} +1.61259 q^{85} +20.7581 q^{86} +1.00000 q^{87} -0.156721 q^{88} +15.9313 q^{89} +0.983593 q^{90} +4.37907 q^{92} -2.50820 q^{93} -21.3749 q^{94} -2.98359 q^{95} +7.61676 q^{96} -11.2335 q^{97} -0.318669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 8 q^{11} + 6 q^{12} - 4 q^{13} - 4 q^{16} - 4 q^{17} + 2 q^{18} + 2 q^{19} + 16 q^{20} - 13 q^{22} + 6 q^{23} + 3 q^{24} + 17 q^{25} + 11 q^{26} + 3 q^{27} + 3 q^{29} + 6 q^{30} - 6 q^{31} + 8 q^{32} - 8 q^{33} - q^{34} + 6 q^{36} + 8 q^{37} - 20 q^{38} - 4 q^{39} + 32 q^{40} + 2 q^{41} - 4 q^{43} - 11 q^{44} - 2 q^{46} + 12 q^{47} - 4 q^{48} + 54 q^{50} - 4 q^{51} + 3 q^{52} + 8 q^{53} + 2 q^{54} + 10 q^{55} + 2 q^{57} + 2 q^{58} + 20 q^{59} + 16 q^{60} - 4 q^{61} + 2 q^{62} - 5 q^{64} + 22 q^{65} - 13 q^{66} - 29 q^{68} + 6 q^{69} - 14 q^{71} + 3 q^{72} + 8 q^{73} - 16 q^{74} + 17 q^{75} - 2 q^{76} + 11 q^{78} - 2 q^{79} + 38 q^{80} + 3 q^{81} + 32 q^{82} + 8 q^{83} - 42 q^{85} + 28 q^{86} + 3 q^{87} + 2 q^{88} + 8 q^{89} + 6 q^{90} - 4 q^{92} - 6 q^{93} - 15 q^{94} - 12 q^{95} + 8 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 8 * q^11 + 6 * q^12 - 4 * q^13 - 4 * q^16 - 4 * q^17 + 2 * q^18 + 2 * q^19 + 16 * q^20 - 13 * q^22 + 6 * q^23 + 3 * q^24 + 17 * q^25 + 11 * q^26 + 3 * q^27 + 3 * q^29 + 6 * q^30 - 6 * q^31 + 8 * q^32 - 8 * q^33 - q^34 + 6 * q^36 + 8 * q^37 - 20 * q^38 - 4 * q^39 + 32 * q^40 + 2 * q^41 - 4 * q^43 - 11 * q^44 - 2 * q^46 + 12 * q^47 - 4 * q^48 + 54 * q^50 - 4 * q^51 + 3 * q^52 + 8 * q^53 + 2 * q^54 + 10 * q^55 + 2 * q^57 + 2 * q^58 + 20 * q^59 + 16 * q^60 - 4 * q^61 + 2 * q^62 - 5 * q^64 + 22 * q^65 - 13 * q^66 - 29 * q^68 + 6 * q^69 - 14 * q^71 + 3 * q^72 + 8 * q^73 - 16 * q^74 + 17 * q^75 - 2 * q^76 + 11 * q^78 - 2 * q^79 + 38 * q^80 + 3 * q^81 + 32 * q^82 + 8 * q^83 - 42 * q^85 + 28 * q^86 + 3 * q^87 + 2 * q^88 + 8 * q^89 + 6 * q^90 - 4 * q^92 - 6 * q^93 - 15 * q^94 - 12 * q^95 + 8 * q^96 - 4 * q^97 - 8 * q^99

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 $

$2$	−1.93543	−1.36856	−0.684279	−	0.729221i	$-0.739883\pi$
$2$	−1.93543	−1.36856	−0.684279	+	0.729221i	$0.739883\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.74590	0.872949
$5$	−0.508203	−0.227275	−0.113638	−	0.993522i	$-0.536250\pi$
$5$	−0.508203	−0.227275	−0.113638	+	0.993522i	$0.536250\pi$
$6$	−1.93543	−0.790137
$7$	0	0
$7$	0	0
$8$	0.491797	0.173876
$9$	1.00000	0.333333
$10$	0.983593	0.311039
$11$	−0.318669	−0.0960824	−0.0480412	−	0.998845i	$-0.515298\pi$
$11$	−0.318669	−0.0960824	−0.0480412	+	0.998845i	$0.515298\pi$
$12$	1.74590	0.503997
$13$	−4.18953	−1.16197	−0.580984	−	0.813915i	$-0.697332\pi$
$13$	−4.18953	−1.16197	−0.580984	+	0.813915i	$0.697332\pi$
$14$	0	0
$15$	−0.508203	−0.131218
$16$	−4.44364	−1.11091
$17$	−3.17313	−0.769596	−0.384798	−	0.923001i	$-0.625729\pi$
$17$	−3.17313	−0.769596	−0.384798	+	0.923001i	$0.625729\pi$
$18$	−1.93543	−0.456186
$19$	5.87086	1.34687	0.673434	−	0.739247i	$-0.264818\pi$
$19$	5.87086	1.34687	0.673434	+	0.739247i	$0.264818\pi$
$20$	−0.887271	−0.198400
$21$	0	0
$22$	0.616763	0.131494
$23$	2.50820	0.522997	0.261498	−	0.965204i	$-0.415783\pi$
$23$	2.50820	0.522997	0.261498	+	0.965204i	$0.415783\pi$
$24$	0.491797	0.100388
$25$	−4.74173	−0.948346
$26$	8.10856	1.59022
$27$	1.00000	0.192450
$28$	0	0
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	0.983593	0.179579
$31$	−2.50820	−0.450487	−0.225243	−	0.974303i	$-0.572318\pi$
$31$	−2.50820	−0.450487	−0.225243	+	0.974303i	$0.572318\pi$
$32$	7.61676	1.34647
$33$	−0.318669	−0.0554732
$34$	6.14137	1.05324
$35$	0	0
$36$	1.74590	0.290983
$37$	7.87086	1.29396	0.646981	−	0.762506i	$-0.276031\pi$
$37$	7.87086	1.29396	0.646981	+	0.762506i	$0.276031\pi$
$38$	−11.3627	−1.84327
$39$	−4.18953	−0.670862
$40$	−0.249933	−0.0395178
$41$	−8.72532	−1.36267	−0.681333	−	0.731973i	$-0.738600\pi$
$41$	−8.72532	−1.36267	−0.681333	+	0.731973i	$0.738600\pi$
$42$	0	0
$43$	−10.7253	−1.63560	−0.817798	−	0.575505i	$-0.804805\pi$
$43$	−10.7253	−1.63560	−0.817798	+	0.575505i	$0.804805\pi$
$44$	−0.556364	−0.0838751
$45$	−0.508203	−0.0757585
$46$	−4.85446	−0.715751
$47$	11.0440	1.61093	0.805466	−	0.592642i	$-0.201915\pi$
$47$	11.0440	1.61093	0.805466	+	0.592642i	$0.201915\pi$
$48$	−4.44364	−0.641384
$49$	0	0
$50$	9.17730	1.29787
$51$	−3.17313	−0.444327
$52$	−7.31450	−1.01434
$53$	−8.24993	−1.13322	−0.566608	−	0.823988i	$-0.691744\pi$
$53$	−8.24993	−1.13322	−0.566608	+	0.823988i	$0.691744\pi$
$54$	−1.93543	−0.263379
$55$	0.161949	0.0218372
$56$	0	0
$57$	5.87086	0.777615
$58$	−1.93543	−0.254135
$59$	11.3627	1.47929	0.739646	−	0.672996i	$-0.234993\pi$
$59$	11.3627	1.47929	0.739646	+	0.672996i	$0.234993\pi$
$60$	−0.887271	−0.114546
$61$	3.87086	0.495613	0.247807	−	0.968809i	$-0.420290\pi$
$61$	3.87086	0.495613	0.247807	+	0.968809i	$0.420290\pi$
$62$	4.85446	0.616517
$63$	0	0
$64$	−5.85446	−0.731807
$65$	2.12914	0.264087
$66$	0.616763	0.0759183
$67$	7.04399	0.860561	0.430280	−	0.902695i	$-0.358415\pi$
$67$	7.04399	0.860561	0.430280	+	0.902695i	$0.358415\pi$
$68$	−5.53996	−0.671819
$69$	2.50820	0.301952
$70$	0	0
$71$	6.24993	0.741731	0.370865	−	0.928687i	$-0.379061\pi$
$71$	6.24993	0.741731	0.370865	+	0.928687i	$0.379061\pi$
$72$	0.491797	0.0579588
$73$	7.87086	0.921215	0.460608	−	0.887604i	$-0.347632\pi$
$73$	7.87086	0.921215	0.460608	+	0.887604i	$0.347632\pi$
$74$	−15.2335	−1.77086
$75$	−4.74173	−0.547528
$76$	10.2499	1.17575
$77$	0	0
$78$	8.10856	0.918114
$79$	−4.85446	−0.546169	−0.273085	−	0.961990i	$-0.588044\pi$
$79$	−4.85446	−0.546169	−0.273085	+	0.961990i	$0.588044\pi$
$80$	2.25827	0.252482
$81$	1.00000	0.111111
$82$	16.8873	1.86489
$83$	8.37907	0.919722	0.459861	−	0.887991i	$-0.347899\pi$
$83$	8.37907	0.919722	0.459861	+	0.887991i	$0.347899\pi$
$84$	0	0
$85$	1.61259	0.174910
$86$	20.7581	2.23841
$87$	1.00000	0.107211
$88$	−0.156721	−0.0167065
$89$	15.9313	1.68871	0.844355	−	0.535784i	$-0.179984\pi$
$89$	15.9313	1.68871	0.844355	+	0.535784i	$0.179984\pi$
$90$	0.983593	0.103680
$91$	0	0
$92$	4.37907	0.456549
$93$	−2.50820	−0.260089
$94$	−21.3749	−2.20465
$95$	−2.98359	−0.306110
$96$	7.61676	0.777383
$97$	−11.2335	−1.14059	−0.570296	−	0.821439i	$-0.693171\pi$
$97$	−11.2335	−1.14059	−0.570296	+	0.821439i	$0.693171\pi$
$98$	0	0
$99$	−0.318669	−0.0320275
$100$	−8.27858	−0.827858
$101$	−10.9149	−1.08607	−0.543034	−	0.839710i	$-0.682725\pi$
$101$	−10.9149	−1.08607	−0.543034	+	0.839710i	$0.682725\pi$
$102$	6.14137	0.608087
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	−2.06040	−0.202039
$105$	0	0
$106$	15.9672	1.55087
$107$	3.83805	0.371038	0.185519	−	0.982641i	$-0.440603\pi$
$107$	3.83805	0.371038	0.185519	+	0.982641i	$0.440603\pi$
$108$	1.74590	0.167999
$109$	−8.18953	−0.784415	−0.392208	−	0.919877i	$-0.628288\pi$
$109$	−8.18953	−0.784415	−0.392208	+	0.919877i	$0.628288\pi$
$110$	−0.313441	−0.0298854
$111$	7.87086	0.747069
$112$	0	0
$113$	13.2059	1.24231	0.621155	−	0.783688i	$-0.286664\pi$
$113$	13.2059	1.24231	0.621155	+	0.783688i	$0.286664\pi$
$114$	−11.3627	−1.06421
$115$	−1.27468	−0.118864
$116$	1.74590	0.162103
$117$	−4.18953	−0.387323
$118$	−21.9917	−2.02450
$119$	0	0
$120$	−0.249933	−0.0228156
$121$	−10.8984	−0.990768
$122$	−7.49180	−0.678275
$123$	−8.72532	−0.786736
$124$	−4.37907	−0.393252
$125$	4.95078	0.442811
$126$	0	0
$127$	9.39547	0.833714	0.416857	−	0.908972i	$-0.363132\pi$
$127$	9.39547	0.833714	0.416857	+	0.908972i	$0.363132\pi$
$128$	−3.90262	−0.344946
$129$	−10.7253	−0.944312
$130$	−4.12080	−0.361418
$131$	17.0768	1.49201	0.746004	−	0.665942i	$-0.231970\pi$
$131$	17.0768	1.49201	0.746004	+	0.665942i	$0.231970\pi$
$132$	−0.556364	−0.0484253
$133$	0	0
$134$	−13.6332	−1.17773
$135$	−0.508203	−0.0437392
$136$	−1.56053	−0.133815
$137$	15.0164	1.28294	0.641469	−	0.767149i	$-0.278325\pi$
$137$	15.0164	1.28294	0.641469	+	0.767149i	$0.278325\pi$
$138$	−4.85446	−0.413239
$139$	−7.68133	−0.651522	−0.325761	−	0.945452i	$-0.605620\pi$
$139$	−7.68133	−0.651522	−0.325761	+	0.945452i	$0.605620\pi$
$140$	0	0
$141$	11.0440	0.930072
$142$	−12.0963	−1.01510
$143$	1.33508	0.111645
$144$	−4.44364	−0.370303
$145$	−0.508203	−0.0422040
$146$	−15.2335	−1.26074
$147$	0	0
$148$	13.7417	1.12956
$149$	−11.3955	−0.933554	−0.466777	−	0.884375i	$-0.654585\pi$
$149$	−11.3955	−0.933554	−0.466777	+	0.884375i	$0.654585\pi$
$150$	9.17730	0.749323
$151$	−2.03281	−0.165428	−0.0827140	−	0.996573i	$-0.526359\pi$
$151$	−2.03281	−0.165428	−0.0827140	+	0.996573i	$0.526359\pi$
$152$	2.88727	0.234189
$153$	−3.17313	−0.256532
$154$	0	0
$155$	1.27468	0.102385
$156$	−7.31450	−0.585629
$157$	10.7581	0.858593	0.429296	−	0.903164i	$-0.358762\pi$
$157$	10.7581	0.858593	0.429296	+	0.903164i	$0.358762\pi$
$158$	9.39547	0.747464
$159$	−8.24993	−0.654262
$160$	−3.87086	−0.306019
$161$	0	0
$162$	−1.93543	−0.152062
$163$	21.8297	1.70984	0.854918	−	0.518764i	$-0.173608\pi$
$163$	21.8297	1.70984	0.854918	+	0.518764i	$0.173608\pi$
$164$	−15.2335	−1.18954
$165$	0.161949	0.0126077
$166$	−16.2171	−1.25869
$167$	20.4999	1.58633	0.793164	−	0.609009i	$-0.208433\pi$
$167$	20.4999	1.58633	0.793164	+	0.609009i	$0.208433\pi$
$168$	0	0
$169$	4.55220	0.350169
$170$	−3.12107	−0.239375
$171$	5.87086	0.448956
$172$	−18.7253	−1.42779
$173$	−1.62093	−0.123237	−0.0616186	−	0.998100i	$-0.519626\pi$
$173$	−1.62093	−0.123237	−0.0616186	+	0.998100i	$0.519626\pi$
$174$	−1.93543	−0.146725
$175$	0	0
$176$	1.41605	0.106739
$177$	11.3627	0.854070
$178$	−30.8339	−2.31110
$179$	4.47539	0.334506	0.167253	−	0.985914i	$-0.446510\pi$
$179$	4.47539	0.334506	0.167253	+	0.985914i	$0.446510\pi$
$180$	−0.887271	−0.0661333
$181$	−1.20594	−0.0896369	−0.0448184	−	0.998995i	$-0.514271\pi$
$181$	−1.20594	−0.0896369	−0.0448184	+	0.998995i	$0.514271\pi$
$182$	0	0
$183$	3.87086	0.286143
$184$	1.23353	0.0909367
$185$	−4.00000	−0.294086
$186$	4.85446	0.355946
$187$	1.01118	0.0739447
$188$	19.2817	1.40626
$189$	0	0
$190$	5.77454	0.418929
$191$	0.758136	0.0548568	0.0274284	−	0.999624i	$-0.491268\pi$
$191$	0.758136	0.0548568	0.0274284	+	0.999624i	$0.491268\pi$
$192$	−5.85446	−0.422509
$193$	−16.4671	−1.18532	−0.592662	−	0.805451i	$-0.701923\pi$
$193$	−16.4671	−1.18532	−0.592662	+	0.805451i	$0.701923\pi$
$194$	21.7417	1.56097
$195$	2.12914	0.152471
$196$	0	0
$197$	−17.9588	−1.27951	−0.639757	−	0.768577i	$-0.720965\pi$
$197$	−17.9588	−1.27951	−0.639757	+	0.768577i	$0.720965\pi$
$198$	0.616763	0.0438314
$199$	−1.33508	−0.0946410	−0.0473205	−	0.998880i	$-0.515068\pi$
$199$	−1.33508	−0.0946410	−0.0473205	+	0.998880i	$0.515068\pi$
$200$	−2.33197	−0.164895
$201$	7.04399	0.496845
$202$	21.1250	1.48635
$203$	0	0
$204$	−5.53996	−0.387875
$205$	4.43424	0.309701
$206$	15.4835	1.07878
$207$	2.50820	0.174332
$208$	18.6168	1.29084
$209$	−1.87086	−0.129410
$210$	0	0
$211$	8.37907	0.576839	0.288419	−	0.957504i	$-0.406870\pi$
$211$	8.37907	0.576839	0.288419	+	0.957504i	$0.406870\pi$
$212$	−14.4035	−0.989239
$213$	6.24993	0.428238
$214$	−7.42829	−0.507787
$215$	5.45065	0.371731
$216$	0.491797	0.0334625
$217$	0	0
$218$	15.8503	1.07352
$219$	7.87086	0.531864
$220$	0.282746	0.0190627
$221$	13.2939	0.894246
$222$	−15.2335	−1.02241
$223$	6.66492	0.446316	0.223158	−	0.974782i	$-0.428363\pi$
$223$	6.66492	0.446316	0.223158	+	0.974782i	$0.428363\pi$
$224$	0	0
$225$	−4.74173	−0.316115
$226$	−25.5592	−1.70017
$227$	−0.379068	−0.0251596	−0.0125798	−	0.999921i	$-0.504004\pi$
$227$	−0.379068	−0.0251596	−0.0125798	+	0.999921i	$0.504004\pi$
$228$	10.2499	0.678818
$229$	−9.26634	−0.612337	−0.306168	−	0.951977i	$-0.599047\pi$
$229$	−9.26634	−0.612337	−0.306168	+	0.951977i	$0.599047\pi$
$230$	2.46705	0.162673
$231$	0	0
$232$	0.491797	0.0322880
$233$	13.7417	0.900251	0.450125	−	0.892965i	$-0.351379\pi$
$233$	13.7417	0.900251	0.450125	+	0.892965i	$0.351379\pi$
$234$	8.10856	0.530073
$235$	−5.61259	−0.366125
$236$	19.8381	1.29135
$237$	−4.85446	−0.315331
$238$	0	0
$239$	17.8709	1.15597	0.577985	−	0.816047i	$-0.303839\pi$
$239$	17.8709	1.15597	0.577985	+	0.816047i	$0.303839\pi$
$240$	2.25827	0.145771
$241$	14.2223	0.916142	0.458071	−	0.888916i	$-0.348541\pi$
$241$	14.2223	0.916142	0.458071	+	0.888916i	$0.348541\pi$
$242$	21.0932	1.35592
$243$	1.00000	0.0641500
$244$	6.75814	0.432645
$245$	0	0
$246$	16.8873	1.07669
$247$	−24.5962	−1.56502
$248$	−1.23353	−0.0783290
$249$	8.37907	0.531002
$250$	−9.58190	−0.606013
$251$	−8.43947	−0.532694	−0.266347	−	0.963877i	$-0.585817\pi$
$251$	−8.43947	−0.532694	−0.266347	+	0.963877i	$0.585817\pi$
$252$	0	0
$253$	−0.799288	−0.0502508
$254$	−18.1843	−1.14098
$255$	1.61259	0.100985
$256$	19.2622	1.20389
$257$	−25.3627	−1.58208	−0.791040	−	0.611765i	$-0.790460\pi$
$257$	−25.3627	−1.58208	−0.791040	+	0.611765i	$0.790460\pi$
$258$	20.7581	1.29235
$259$	0	0
$260$	3.71725	0.230534
$261$	1.00000	0.0618984
$262$	−33.0510	−2.04190
$263$	23.4835	1.44805	0.724026	−	0.689773i	$-0.242290\pi$
$263$	23.4835	1.44805	0.724026	+	0.689773i	$0.242290\pi$
$264$	−0.156721	−0.00964548
$265$	4.19264	0.257552
$266$	0	0
$267$	15.9313	0.974977
$268$	12.2981	0.751226
$269$	2.10155	0.128134	0.0640669	−	0.997946i	$-0.479593\pi$
$269$	2.10155	0.128134	0.0640669	+	0.997946i	$0.479593\pi$
$270$	0.983593	0.0598596
$271$	−3.10439	−0.188578	−0.0942892	−	0.995545i	$-0.530058\pi$
$271$	−3.10439	−0.188578	−0.0942892	+	0.995545i	$0.530058\pi$
$272$	14.1002	0.854952
$273$	0	0
$274$	−29.0632	−1.75577
$275$	1.51104	0.0911194
$276$	4.37907	0.263589
$277$	−13.9641	−0.839020	−0.419510	−	0.907751i	$-0.637798\pi$
$277$	−13.9641	−0.839020	−0.419510	+	0.907751i	$0.637798\pi$
$278$	14.8667	0.891645
$279$	−2.50820	−0.150162
$280$	0	0
$281$	−14.4342	−0.861074	−0.430537	−	0.902573i	$-0.641676\pi$
$281$	−14.4342	−0.861074	−0.430537	+	0.902573i	$0.641676\pi$
$282$	−21.3749	−1.27286
$283$	−8.25827	−0.490903	−0.245452	−	0.969409i	$-0.578936\pi$
$283$	−8.25827	−0.490903	−0.245452	+	0.969409i	$0.578936\pi$
$284$	10.9117	0.647493
$285$	−2.98359	−0.176733
$286$	−2.58395	−0.152792
$287$	0	0
$288$	7.61676	0.448822
$289$	−6.93126	−0.407721
$290$	0.983593	0.0577586
$291$	−11.2335	−0.658521
$292$	13.7417	0.804174
$293$	12.4478	0.727209	0.363604	−	0.931554i	$-0.381546\pi$
$293$	12.4478	0.727209	0.363604	+	0.931554i	$0.381546\pi$
$294$	0	0
$295$	−5.77454	−0.336207
$296$	3.87086	0.224989
$297$	−0.318669	−0.0184911
$298$	22.0552	1.27762
$299$	−10.5082	−0.607705
$300$	−8.27858	−0.477964
$301$	0	0
$302$	3.93437	0.226398
$303$	−10.9149	−0.627042
$304$	−26.0880	−1.49625
$305$	−1.96719	−0.112641
$306$	6.14137	0.351079
$307$	21.9917	1.25513	0.627565	−	0.778564i	$-0.284052\pi$
$307$	21.9917	1.25513	0.627565	+	0.778564i	$0.284052\pi$
$308$	0	0
$309$	−8.00000	−0.455104
$310$	−2.46705	−0.140119
$311$	19.0440	1.07989	0.539943	−	0.841702i	$-0.318446\pi$
$311$	19.0440	1.07989	0.539943	+	0.841702i	$0.318446\pi$
$312$	−2.06040	−0.116647
$313$	−9.89845	−0.559493	−0.279747	−	0.960074i	$-0.590250\pi$
$313$	−9.89845	−0.559493	−0.279747	+	0.960074i	$0.590250\pi$
$314$	−20.8216	−1.17503
$315$	0	0
$316$	−8.47539	−0.476778
$317$	0.568602	0.0319359	0.0159679	−	0.999873i	$-0.494917\pi$
$317$	0.568602	0.0319359	0.0159679	+	0.999873i	$0.494917\pi$
$318$	15.9672	0.895395
$319$	−0.318669	−0.0178421
$320$	2.97526	0.166322
$321$	3.83805	0.214219
$322$	0	0
$323$	−18.6290	−1.03655
$324$	1.74590	0.0969944
$325$	19.8656	1.10195
$326$	−42.2499	−2.34001
$327$	−8.18953	−0.452882
$328$	−4.29108	−0.236935
$329$	0	0
$330$	−0.313441	−0.0172544
$331$	1.17836	0.0647683	0.0323841	−	0.999475i	$-0.489690\pi$
$331$	1.17836	0.0647683	0.0323841	+	0.999475i	$0.489690\pi$
$332$	14.6290	0.802871
$333$	7.87086	0.431321
$334$	−39.6761	−2.17098
$335$	−3.57978	−0.195584
$336$	0	0
$337$	17.2007	0.936983	0.468491	−	0.883468i	$-0.344798\pi$
$337$	17.2007	0.936983	0.468491	+	0.883468i	$0.344798\pi$
$338$	−8.81047	−0.479226
$339$	13.2059	0.717248
$340$	2.81543	0.152688
$341$	0.799288	0.0432838
$342$	−11.3627	−0.614422
$343$	0	0
$344$	−5.27468	−0.284392
$345$	−1.27468	−0.0686263
$346$	3.13720	0.168657
$347$	15.2663	0.819540	0.409770	−	0.912189i	$-0.365609\pi$
$347$	15.2663	0.819540	0.409770	+	0.912189i	$0.365609\pi$
$348$	1.74590	0.0935900
$349$	27.7089	1.48322	0.741612	−	0.670829i	$-0.234062\pi$
$349$	27.7089	1.48322	0.741612	+	0.670829i	$0.234062\pi$
$350$	0	0
$351$	−4.18953	−0.223621
$352$	−2.42723	−0.129372
$353$	−2.79929	−0.148991	−0.0744955	−	0.997221i	$-0.523735\pi$
$353$	−2.79929	−0.148991	−0.0744955	+	0.997221i	$0.523735\pi$
$354$	−21.9917	−1.16884
$355$	−3.17624	−0.168577
$356$	27.8144	1.47416
$357$	0	0
$358$	−8.66181	−0.457791
$359$	12.2583	0.646967	0.323483	−	0.946234i	$-0.395146\pi$
$359$	12.2583	0.646967	0.323483	+	0.946234i	$0.395146\pi$
$360$	−0.249933	−0.0131726
$361$	15.4671	0.814055
$362$	2.33402	0.122673
$363$	−10.8984	−0.572020
$364$	0	0
$365$	−4.00000	−0.209370
$366$	−7.49180	−0.391602
$367$	4.25827	0.222280	0.111140	−	0.993805i	$-0.464550\pi$
$367$	4.25827	0.222280	0.111140	+	0.993805i	$0.464550\pi$
$368$	−11.1455	−0.581002
$369$	−8.72532	−0.454222
$370$	7.74173	0.402473
$371$	0	0
$372$	−4.37907	−0.227044
$373$	25.7417	1.33286	0.666428	−	0.745569i	$-0.267822\pi$
$373$	25.7417	1.33286	0.666428	+	0.745569i	$0.267822\pi$
$374$	−1.95707	−0.101198
$375$	4.95078	0.255657
$376$	5.43140	0.280103
$377$	−4.18953	−0.215772
$378$	0	0
$379$	19.6454	1.00912	0.504558	−	0.863378i	$-0.331655\pi$
$379$	19.6454	1.00912	0.504558	+	0.863378i	$0.331655\pi$
$380$	−5.20905	−0.267219
$381$	9.39547	0.481345
$382$	−1.46732	−0.0750747
$383$	22.5634	1.15293	0.576467	−	0.817120i	$-0.304431\pi$
$383$	22.5634	1.15293	0.576467	+	0.817120i	$0.304431\pi$
$384$	−3.90262	−0.199155
$385$	0	0
$386$	31.8709	1.62218
$387$	−10.7253	−0.545199
$388$	−19.6126	−0.995679
$389$	15.8105	0.801622	0.400811	−	0.916161i	$-0.368728\pi$
$389$	15.8105	0.801622	0.400811	+	0.916161i	$0.368728\pi$
$390$	−4.12080	−0.208665
$391$	−7.95885	−0.402496
$392$	0	0
$393$	17.0768	0.861411
$394$	34.7581	1.75109
$395$	2.46705	0.124131
$396$	−0.556364	−0.0279584
$397$	3.27468	0.164351	0.0821757	−	0.996618i	$-0.473813\pi$
$397$	3.27468	0.164351	0.0821757	+	0.996618i	$0.473813\pi$
$398$	2.58395	0.129522
$399$	0	0
$400$	21.0705	1.05353
$401$	2.47539	0.123615	0.0618075	−	0.998088i	$-0.480314\pi$
$401$	2.47539	0.123615	0.0618075	+	0.998088i	$0.480314\pi$
$402$	−13.6332	−0.679961
$403$	10.5082	0.523451
$404$	−19.0562	−0.948083
$405$	−0.508203	−0.0252528
$406$	0	0
$407$	−2.50820	−0.124327
$408$	−1.56053	−0.0772579
$409$	−15.0164	−0.742514	−0.371257	−	0.928530i	$-0.621073\pi$
$409$	−15.0164	−0.742514	−0.371257	+	0.928530i	$0.621073\pi$
$410$	−8.58217	−0.423843
$411$	15.0164	0.740705
$412$	−13.9672	−0.688114
$413$	0	0
$414$	−4.85446	−0.238584
$415$	−4.25827	−0.209030
$416$	−31.9107	−1.56455
$417$	−7.68133	−0.376156
$418$	3.62093	0.177106
$419$	13.8709	0.677636	0.338818	−	0.940852i	$-0.389973\pi$
$419$	13.8709	0.677636	0.338818	+	0.940852i	$0.389973\pi$
$420$	0	0
$421$	−7.45065	−0.363122	−0.181561	−	0.983380i	$-0.558115\pi$
$421$	−7.45065	−0.363122	−0.181561	+	0.983380i	$0.558115\pi$
$422$	−16.2171	−0.789437
$423$	11.0440	0.536977
$424$	−4.05729	−0.197039
$425$	15.0461	0.729844
$426$	−12.0963	−0.586069
$427$	0	0
$428$	6.70085	0.323898
$429$	1.33508	0.0644581
$430$	−10.5494	−0.508735
$431$	14.7253	0.709294	0.354647	−	0.935000i	$-0.384601\pi$
$431$	14.7253	0.709294	0.354647	+	0.935000i	$0.384601\pi$
$432$	−4.44364	−0.213795
$433$	−1.52461	−0.0732681	−0.0366340	−	0.999329i	$-0.511664\pi$
$433$	−1.52461	−0.0732681	−0.0366340	+	0.999329i	$0.511664\pi$
$434$	0	0
$435$	−0.508203	−0.0243665
$436$	−14.2981	−0.684754
$437$	14.7253	0.704408
$438$	−15.2335	−0.727886
$439$	−23.3023	−1.11216	−0.556078	−	0.831130i	$-0.687694\pi$
$439$	−23.3023	−1.11216	−0.556078	+	0.831130i	$0.687694\pi$
$440$	0.0796459	0.00379697
$441$	0	0
$442$	−25.7295	−1.22383
$443$	23.0440	1.09485	0.547427	−	0.836854i	$-0.315608\pi$
$443$	23.0440	1.09485	0.547427	+	0.836854i	$0.315608\pi$
$444$	13.7417	0.652154
$445$	−8.09632	−0.383802
$446$	−12.8995	−0.610809
$447$	−11.3955	−0.538987
$448$	0	0
$449$	−6.53579	−0.308443	−0.154221	−	0.988036i	$-0.549287\pi$
$449$	−6.53579	−0.308443	−0.154221	+	0.988036i	$0.549287\pi$
$450$	9.17730	0.432622
$451$	2.78049	0.130928
$452$	23.0562	1.08447
$453$	−2.03281	−0.0955099
$454$	0.733661	0.0344324
$455$	0	0
$456$	2.88727	0.135209
$457$	10.2223	0.478181	0.239091	−	0.970997i	$-0.423151\pi$
$457$	10.2223	0.478181	0.239091	+	0.970997i	$0.423151\pi$
$458$	17.9344	0.838018
$459$	−3.17313	−0.148109
$460$	−2.22546	−0.103762
$461$	−14.0000	−0.652045	−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000	−0.652045	−0.326023	+	0.945362i	$0.605709\pi$
$462$	0	0
$463$	−24.1812	−1.12380	−0.561898	−	0.827207i	$-0.689929\pi$
$463$	−24.1812	−1.12380	−0.561898	+	0.827207i	$0.689929\pi$
$464$	−4.44364	−0.206291
$465$	1.27468	0.0591118
$466$	−26.5962	−1.23204
$467$	9.96719	0.461226	0.230613	−	0.973046i	$-0.425927\pi$
$467$	9.96719	0.461226	0.230613	+	0.973046i	$0.425927\pi$
$468$	−7.31450	−0.338113
$469$	0	0
$470$	10.8628	0.501063
$471$	10.7581	0.495709
$472$	5.58812	0.257214
$473$	3.41783	0.157152
$474$	9.39547	0.431548
$475$	−27.8381	−1.27730
$476$	0	0
$477$	−8.24993	−0.377738
$478$	−34.5878	−1.58201
$479$	21.7745	0.994904	0.497452	−	0.867491i	$-0.334269\pi$
$479$	21.7745	0.994904	0.497452	+	0.867491i	$0.334269\pi$
$480$	−3.87086	−0.176680
$481$	−32.9753	−1.50354
$482$	−27.5264	−1.25379
$483$	0	0
$484$	−19.0276	−0.864890
$485$	5.70892	0.259229
$486$	−1.93543	−0.0877930
$487$	37.4506	1.69705	0.848525	−	0.529155i	$-0.177491\pi$
$487$	37.4506	1.69705	0.848525	+	0.529155i	$0.177491\pi$
$488$	1.90368	0.0861755
$489$	21.8297	0.987174
$490$	0	0
$491$	−16.6925	−0.753322	−0.376661	−	0.926351i	$-0.622928\pi$
$491$	−16.6925	−0.753322	−0.376661	+	0.926351i	$0.622928\pi$
$492$	−15.2335	−0.686780
$493$	−3.17313	−0.142910
$494$	47.6043	2.14182
$495$	0.161949	0.00727906
$496$	11.1455	0.500450
$497$	0	0
$498$	−16.2171	−0.726706
$499$	43.8573	1.96332	0.981661	−	0.190634i	$-0.0610544\pi$
$499$	43.8573	1.96332	0.981661	+	0.190634i	$0.0610544\pi$
$500$	8.64356	0.386552
$501$	20.4999	0.915866
$502$	16.3340	0.729023
$503$	−26.4067	−1.17741	−0.588707	−	0.808346i	$-0.700363\pi$
$503$	−26.4067	−1.17741	−0.588707	+	0.808346i	$0.700363\pi$
$504$	0	0
$505$	5.54697	0.246837
$506$	1.54697	0.0687711
$507$	4.55220	0.202170
$508$	16.4035	0.727790
$509$	36.1432	1.60202	0.801009	−	0.598653i	$-0.204297\pi$
$509$	36.1432	1.60202	0.801009	+	0.598653i	$0.204297\pi$
$510$	−3.12107	−0.138203
$511$	0	0
$512$	−29.4754	−1.30264
$513$	5.87086	0.259205
$514$	49.0877	2.16517
$515$	4.06563	0.179153
$516$	−18.7253	−0.824336
$517$	−3.51938	−0.154782
$518$	0	0
$519$	−1.62093	−0.0711510
$520$	1.04710	0.0459184
$521$	−26.1208	−1.14437	−0.572186	−	0.820124i	$-0.693905\pi$
$521$	−26.1208	−1.14437	−0.572186	+	0.820124i	$0.693905\pi$
$522$	−1.93543	−0.0847116
$523$	2.35148	0.102823	0.0514116	−	0.998678i	$-0.483628\pi$
$523$	2.35148	0.102823	0.0514116	+	0.998678i	$0.483628\pi$
$524$	29.8144	1.30245
$525$	0	0
$526$	−45.4506	−1.98174
$527$	7.95885	0.346693
$528$	1.41605	0.0616257
$529$	−16.7089	−0.726475
$530$	−8.11458	−0.352475
$531$	11.3627	0.493097
$532$	0	0
$533$	36.5550	1.58337
$534$	−30.8339	−1.33431
$535$	−1.95051	−0.0843279
$536$	3.46421	0.149631
$537$	4.47539	0.193127
$538$	−4.06741	−0.175358
$539$	0	0
$540$	−0.887271	−0.0381821
$541$	12.2499	0.526666	0.263333	−	0.964705i	$-0.415178\pi$
$541$	12.2499	0.526666	0.263333	+	0.964705i	$0.415178\pi$
$542$	6.00834	0.258080
$543$	−1.20594	−0.0517519
$544$	−24.1690	−1.03624
$545$	4.16195	0.178278
$546$	0	0
$547$	−11.3023	−0.483250	−0.241625	−	0.970370i	$-0.577680\pi$
$547$	−11.3023	−0.483250	−0.241625	+	0.970370i	$0.577680\pi$
$548$	26.2171	1.11994
$549$	3.87086	0.165204
$550$	−2.92452	−0.124702
$551$	5.87086	0.250107
$552$	1.23353	0.0525024
$553$	0	0
$554$	27.0265	1.14825
$555$	−4.00000	−0.169791
$556$	−13.4108	−0.568746
$557$	32.4671	1.37567	0.687837	−	0.725866i	$-0.258561\pi$
$557$	32.4671	1.37567	0.687837	+	0.725866i	$0.258561\pi$
$558$	4.85446	0.205506
$559$	44.9341	1.90051
$560$	0	0
$561$	1.01118	0.0426920
$562$	27.9365	1.17843
$563$	−11.5439	−0.486516	−0.243258	−	0.969962i	$-0.578216\pi$
$563$	−11.5439	−0.486516	−0.243258	+	0.969962i	$0.578216\pi$
$564$	19.2817	0.811905
$565$	−6.71130	−0.282347
$566$	15.9833	0.671829
$567$	0	0
$568$	3.07370	0.128969
$569$	34.5358	1.44782	0.723908	−	0.689897i	$-0.242344\pi$
$569$	34.5358	1.44782	0.723908	+	0.689897i	$0.242344\pi$
$570$	5.77454	0.241869
$571$	21.7089	0.908490	0.454245	−	0.890877i	$-0.349909\pi$
$571$	21.7089	0.908490	0.454245	+	0.890877i	$0.349909\pi$
$572$	2.33091	0.0974601
$573$	0.758136	0.0316716
$574$	0	0
$575$	−11.8932	−0.495982
$576$	−5.85446	−0.243936
$577$	3.13720	0.130604	0.0653018	−	0.997866i	$-0.479199\pi$
$577$	3.13720	0.130604	0.0653018	+	0.997866i	$0.479199\pi$
$578$	13.4150	0.557990
$579$	−16.4671	−0.684347
$580$	−0.887271	−0.0368419
$581$	0	0
$582$	21.7417	0.901224
$583$	2.62900	0.108882
$584$	3.87086	0.160178
$585$	2.12914	0.0880289
$586$	−24.0919	−0.995227
$587$	−31.5386	−1.30174	−0.650869	−	0.759190i	$-0.725595\pi$
$587$	−31.5386	−1.30174	−0.650869	+	0.759190i	$0.725595\pi$
$588$	0	0
$589$	−14.7253	−0.606746
$590$	11.1762	0.460118
$591$	−17.9588	−0.738728
$592$	−34.9753	−1.43747
$593$	26.9753	1.10774	0.553870	−	0.832603i	$-0.313150\pi$
$593$	26.9753	1.10774	0.553870	+	0.832603i	$0.313150\pi$
$594$	0.616763	0.0253061
$595$	0	0
$596$	−19.8953	−0.814945
$597$	−1.33508	−0.0546410
$598$	20.3379	0.831679
$599$	−20.2364	−0.826836	−0.413418	−	0.910541i	$-0.635665\pi$
$599$	−20.2364	−0.826836	−0.413418	+	0.910541i	$0.635665\pi$
$600$	−2.33197	−0.0952021
$601$	42.7826	1.74514	0.872570	−	0.488490i	$-0.162452\pi$
$601$	42.7826	1.74514	0.872570	+	0.488490i	$0.162452\pi$
$602$	0	0
$603$	7.04399	0.286854
$604$	−3.54909	−0.144410
$605$	5.53863	0.225177
$606$	21.1250	0.858143
$607$	−3.42829	−0.139150	−0.0695750	−	0.997577i	$-0.522164\pi$
$607$	−3.42829	−0.139150	−0.0695750	+	0.997577i	$0.522164\pi$
$608$	44.7170	1.81351
$609$	0	0
$610$	3.80736	0.154155
$611$	−46.2692	−1.87185
$612$	−5.53996	−0.223940
$613$	−21.3267	−0.861379	−0.430689	−	0.902500i	$-0.641730\pi$
$613$	−21.3267	−0.861379	−0.430689	+	0.902500i	$0.641730\pi$
$614$	−42.5634	−1.71772
$615$	4.43424	0.178806
$616$	0	0
$617$	−29.8074	−1.20000	−0.599999	−	0.800000i	$-0.704833\pi$
$617$	−29.8074	−1.20000	−0.599999	+	0.800000i	$0.704833\pi$
$618$	15.4835	0.622836
$619$	−5.87086	−0.235970	−0.117985	−	0.993015i	$-0.537643\pi$
$619$	−5.87086	−0.235970	−0.117985	+	0.993015i	$0.537643\pi$
$620$	2.22546	0.0893765
$621$	2.50820	0.100651
$622$	−36.8584	−1.47789
$623$	0	0
$624$	18.6168	0.745267
$625$	21.1926	0.847706
$626$	19.1578	0.765699
$627$	−1.87086	−0.0747151
$628$	18.7826	0.749508
$629$	−24.9753	−0.995829
$630$	0	0
$631$	20.7529	0.826160	0.413080	−	0.910695i	$-0.364453\pi$
$631$	20.7529	0.826160	0.413080	+	0.910695i	$0.364453\pi$
$632$	−2.38741	−0.0949659
$633$	8.37907	0.333038
$634$	−1.10049	−0.0437061
$635$	−4.77481	−0.189483
$636$	−14.4035	−0.571138
$637$	0	0
$638$	0.616763	0.0244179
$639$	6.24993	0.247244
$640$	1.98332	0.0783978
$641$	−18.9149	−0.747092	−0.373546	−	0.927612i	$-0.621858\pi$
$641$	−18.9149	−0.747092	−0.373546	+	0.927612i	$0.621858\pi$
$642$	−7.42829	−0.293171
$643$	47.1648	1.86000	0.929999	−	0.367562i	$-0.119808\pi$
$643$	47.1648	1.86000	0.929999	+	0.367562i	$0.119808\pi$
$644$	0	0
$645$	5.45065	0.214619
$646$	36.0552	1.41857
$647$	−7.20071	−0.283089	−0.141545	−	0.989932i	$-0.545207\pi$
$647$	−7.20071	−0.283089	−0.141545	+	0.989932i	$0.545207\pi$
$648$	0.491797	0.0193196
$649$	−3.62093	−0.142134
$650$	−38.4486	−1.50808
$651$	0	0
$652$	38.1125	1.49260
$653$	42.5191	1.66390	0.831951	−	0.554850i	$-0.187224\pi$
$653$	42.5191	1.66390	0.831951	+	0.554850i	$0.187224\pi$
$654$	15.8503	0.619795
$655$	−8.67849	−0.339097
$656$	38.7722	1.51380
$657$	7.87086	0.307072
$658$	0	0
$659$	−1.90679	−0.0742779	−0.0371390	−	0.999310i	$-0.511824\pi$
$659$	−1.90679	−0.0742779	−0.0371390	+	0.999310i	$0.511824\pi$
$660$	0.282746	0.0110059
$661$	−35.9969	−1.40012	−0.700058	−	0.714086i	$-0.746843\pi$
$661$	−35.9969	−1.40012	−0.700058	+	0.714086i	$0.746843\pi$
$662$	−2.28063	−0.0886391
$663$	13.2939	0.516293
$664$	4.12080	0.159918
$665$	0	0
$666$	−15.2335	−0.590287
$667$	2.50820	0.0971180
$668$	35.7907	1.38478
$669$	6.66492	0.257681
$670$	6.92842	0.267668
$671$	−1.23353	−0.0476197
$672$	0	0
$673$	9.46421	0.364819	0.182409	−	0.983223i	$-0.441610\pi$
$673$	9.46421	0.364819	0.182409	+	0.983223i	$0.441610\pi$
$674$	−33.2908	−1.28231
$675$	−4.74173	−0.182509
$676$	7.94767	0.305680
$677$	3.81047	0.146448	0.0732241	−	0.997316i	$-0.476671\pi$
$677$	3.81047	0.146448	0.0732241	+	0.997316i	$0.476671\pi$
$678$	−25.5592	−0.981595
$679$	0	0
$680$	0.793068	0.0304128
$681$	−0.379068	−0.0145259
$682$	−1.54697	−0.0592364
$683$	32.9341	1.26019	0.630094	−	0.776519i	$-0.283016\pi$
$683$	32.9341	1.26019	0.630094	+	0.776519i	$0.283016\pi$
$684$	10.2499	0.391916
$685$	−7.63139	−0.291580
$686$	0	0
$687$	−9.26634	−0.353533
$688$	47.6594	1.81700
$689$	34.5634	1.31676
$690$	2.46705	0.0939191
$691$	−0.752908	−0.0286420	−0.0143210	−	0.999897i	$-0.504559\pi$
$691$	−0.752908	−0.0286420	−0.0143210	+	0.999897i	$0.504559\pi$
$692$	−2.82998	−0.107580
$693$	0	0
$694$	−29.5470	−1.12159
$695$	3.90368	0.148075
$696$	0.491797	0.0186415
$697$	27.6866	1.04870
$698$	−53.6287	−2.02988
$699$	13.7417	0.519760
$700$	0	0
$701$	−27.3543	−1.03316	−0.516579	−	0.856239i	$-0.672795\pi$
$701$	−27.3543	−1.03316	−0.516579	+	0.856239i	$0.672795\pi$
$702$	8.10856	0.306038
$703$	46.2088	1.74280
$704$	1.86564	0.0703138
$705$	−5.61259	−0.211383
$706$	5.41783	0.203903
$707$	0	0
$708$	19.8381	0.745560
$709$	50.1760	1.88440	0.942199	−	0.335054i	$-0.108754\pi$
$709$	50.1760	1.88440	0.942199	+	0.335054i	$0.108754\pi$
$710$	6.14739	0.230707
$711$	−4.85446	−0.182056
$712$	7.83494	0.293627
$713$	−6.29108	−0.235603
$714$	0	0
$715$	−0.678490	−0.0253741
$716$	7.81358	0.292007
$717$	17.8709	0.667400
$718$	−23.7251	−0.885411
$719$	−30.4014	−1.13378	−0.566891	−	0.823793i	$-0.691854\pi$
$719$	−30.4014	−1.13378	−0.566891	+	0.823793i	$0.691854\pi$
$720$	2.25827	0.0841608
$721$	0	0
$722$	−29.9354	−1.11408
$723$	14.2223	0.528935
$724$	−2.10545	−0.0782484
$725$	−4.74173	−0.176103
$726$	21.0932	0.782843
$727$	46.1676	1.71226	0.856131	−	0.516758i	$-0.172861\pi$
$727$	46.1676	1.71226	0.856131	+	0.516758i	$0.172861\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	7.74173	0.286534
$731$	34.0328	1.25875
$732$	6.75814	0.249788
$733$	34.1208	1.26028	0.630140	−	0.776481i	$-0.282997\pi$
$733$	34.1208	1.26028	0.630140	+	0.776481i	$0.282997\pi$
$734$	−8.24159	−0.304203
$735$	0	0
$736$	19.1044	0.704197
$737$	−2.24470	−0.0826847
$738$	16.8873	0.621629
$739$	−40.7826	−1.50021	−0.750106	−	0.661317i	$-0.769998\pi$
$739$	−40.7826	−1.50021	−0.750106	+	0.661317i	$0.769998\pi$
$740$	−6.98359	−0.256722
$741$	−24.5962	−0.903564
$742$	0	0
$743$	−14.3515	−0.526505	−0.263252	−	0.964727i	$-0.584795\pi$
$743$	−14.3515	−0.526505	−0.263252	+	0.964727i	$0.584795\pi$
$744$	−1.23353	−0.0452233
$745$	5.79122	0.212174
$746$	−49.8214	−1.82409
$747$	8.37907	0.306574
$748$	1.76541	0.0645500
$749$	0	0
$750$	−9.58190	−0.349881
$751$	−21.4506	−0.782745	−0.391373	−	0.920232i	$-0.628000\pi$
$751$	−21.4506	−0.782745	−0.391373	+	0.920232i	$0.628000\pi$
$752$	−49.0755	−1.78960
$753$	−8.43947	−0.307551
$754$	8.10856	0.295296
$755$	1.03308	0.0375977
$756$	0	0
$757$	0.862796	0.0313588	0.0156794	−	0.999877i	$-0.495009\pi$
$757$	0.862796	0.0313588	0.0156794	+	0.999877i	$0.495009\pi$
$758$	−38.0224	−1.38103
$759$	−0.799288	−0.0290123
$760$	−1.46732	−0.0532253
$761$	−25.4423	−0.922283	−0.461141	−	0.887327i	$-0.652560\pi$
$761$	−25.4423	−0.922283	−0.461141	+	0.887327i	$0.652560\pi$
$762$	−18.1843	−0.658748
$763$	0	0
$764$	1.32363	0.0478872
$765$	1.61259	0.0583035
$766$	−43.6699	−1.57786
$767$	−47.6043	−1.71889
$768$	19.2622	0.695064
$769$	0.194762	0.00702331	0.00351165	−	0.999994i	$-0.498882\pi$
$769$	0.194762	0.00702331	0.00351165	+	0.999994i	$0.498882\pi$
$770$	0	0
$771$	−25.3627	−0.913414
$772$	−28.7498	−1.03473
$773$	−44.5327	−1.60173	−0.800865	−	0.598846i	$-0.795626\pi$
$773$	−44.5327	−1.60173	−0.800865	+	0.598846i	$0.795626\pi$
$774$	20.7581	0.746136
$775$	11.8932	0.427217
$776$	−5.52461	−0.198322
$777$	0	0
$778$	−30.6001	−1.09707
$779$	−51.2252	−1.83533
$780$	3.71725	0.133099
$781$	−1.99166	−0.0712673
$782$	15.4038	0.550839
$783$	1.00000	0.0357371
$784$	0	0
$785$	−5.46732	−0.195137
$786$	−33.0510	−1.17889
$787$	24.4999	0.873326	0.436663	−	0.899625i	$-0.356160\pi$
$787$	24.4999	0.873326	0.436663	+	0.899625i	$0.356160\pi$
$788$	−31.3543	−1.11695
$789$	23.4835	0.836033
$790$	−4.77481	−0.169880
$791$	0	0
$792$	−0.156721	−0.00556882
$793$	−16.2171	−0.575887
$794$	−6.33792	−0.224924
$795$	4.19264	0.148698
$796$	−2.33091	−0.0826168
$797$	−12.7253	−0.450754	−0.225377	−	0.974272i	$-0.572361\pi$
$797$	−12.7253	−0.450754	−0.225377	+	0.974272i	$0.572361\pi$
$798$	0	0
$799$	−35.0440	−1.23977
$800$	−36.1166	−1.27692
$801$	15.9313	0.562904
$802$	−4.79095	−0.169174
$803$	−2.50820	−0.0885126
$804$	12.2981	0.433720
$805$	0	0
$806$	−20.3379	−0.716373
$807$	2.10155	0.0739781
$808$	−5.36789	−0.188842
$809$	13.6402	0.479563	0.239782	−	0.970827i	$-0.422924\pi$
$809$	13.6402	0.479563	0.239782	+	0.970827i	$0.422924\pi$
$810$	0.983593	0.0345599
$811$	−15.9948	−0.561652	−0.280826	−	0.959759i	$-0.590608\pi$
$811$	−15.9948	−0.561652	−0.280826	+	0.959759i	$0.590608\pi$
$812$	0	0
$813$	−3.10439	−0.108876
$814$	4.85446	0.170149
$815$	−11.0939	−0.388604
$816$	14.1002	0.493606
$817$	−62.9669	−2.20293
$818$	29.0632	1.01617
$819$	0	0
$820$	7.74173	0.270353
$821$	−3.70892	−0.129442	−0.0647210	−	0.997903i	$-0.520616\pi$
$821$	−3.70892	−0.129442	−0.0647210	+	0.997903i	$0.520616\pi$
$822$	−29.0632	−1.01370
$823$	−48.8685	−1.70345	−0.851724	−	0.523991i	$-0.824443\pi$
$823$	−48.8685	−1.70345	−0.851724	+	0.523991i	$0.824443\pi$
$824$	−3.93437	−0.137060
$825$	1.51104	0.0526078
$826$	0	0
$827$	1.20905	0.0420428	0.0210214	−	0.999779i	$-0.493308\pi$
$827$	1.20905	0.0420428	0.0210214	+	0.999779i	$0.493308\pi$
$828$	4.37907	0.152183
$829$	4.67015	0.162201	0.0811005	−	0.996706i	$-0.474157\pi$
$829$	4.67015	0.162201	0.0811005	+	0.996706i	$0.474157\pi$
$830$	8.24159	0.286070
$831$	−13.9641	−0.484408
$832$	24.5275	0.850336
$833$	0	0
$834$	14.8667	0.514792
$835$	−10.4181	−0.360533
$836$	−3.26634	−0.112969
$837$	−2.50820	−0.0866962
$838$	−26.8461	−0.927384
$839$	10.8513	0.374630	0.187315	−	0.982300i	$-0.440021\pi$
$839$	10.8513	0.374630	0.187315	+	0.982300i	$0.440021\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	14.4202	0.496954
$843$	−14.4342	−0.497142
$844$	14.6290	0.503551
$845$	−2.31344	−0.0795848
$846$	−21.3749	−0.734884
$847$	0	0
$848$	36.6597	1.25890
$849$	−8.25827	−0.283423
$850$	−29.1207	−0.998833
$851$	19.7417	0.676738
$852$	10.9117	0.373830
$853$	−44.3296	−1.51782	−0.758908	−	0.651198i	$-0.774267\pi$
$853$	−44.3296	−1.51782	−0.758908	+	0.651198i	$0.774267\pi$
$854$	0	0
$855$	−2.98359	−0.102037
$856$	1.88754	0.0645148
$857$	−3.23353	−0.110455	−0.0552276	−	0.998474i	$-0.517588\pi$
$857$	−3.23353	−0.110455	−0.0552276	+	0.998474i	$0.517588\pi$
$858$	−2.58395	−0.0882146
$859$	−38.3463	−1.30836	−0.654179	−	0.756340i	$-0.726986\pi$
$859$	−38.3463	−1.30836	−0.654179	+	0.756340i	$0.726986\pi$
$860$	9.51627	0.324502
$861$	0	0
$862$	−28.4999	−0.970709
$863$	41.4751	1.41183	0.705915	−	0.708297i	$-0.250536\pi$
$863$	41.4751	1.41183	0.705915	+	0.708297i	$0.250536\pi$
$864$	7.61676	0.259128
$865$	0.823763	0.0280088
$866$	2.95078	0.100272
$867$	−6.93126	−0.235398
$868$	0	0
$869$	1.54697	0.0524773
$870$	0.983593	0.0333469
$871$	−29.5110	−0.999944
$872$	−4.02759	−0.136391
$873$	−11.2335	−0.380197
$874$	−28.4999	−0.964022
$875$	0	0
$876$	13.7417	0.464290
$877$	13.0492	0.440641	0.220320	−	0.975428i	$-0.429290\pi$
$877$	13.0492	0.440641	0.220320	+	0.975428i	$0.429290\pi$
$878$	45.1000	1.52205
$879$	12.4478	0.419854
$880$	−0.719642	−0.0242591
$881$	39.6074	1.33441	0.667203	−	0.744876i	$-0.267491\pi$
$881$	39.6074	1.33441	0.667203	+	0.744876i	$0.267491\pi$
$882$	0	0
$883$	29.9505	1.00791	0.503957	−	0.863728i	$-0.331877\pi$
$883$	29.9505	1.00791	0.503957	+	0.863728i	$0.331877\pi$
$884$	23.2098	0.780631
$885$	−5.77454	−0.194109
$886$	−44.6001	−1.49837
$887$	−47.5439	−1.59637	−0.798183	−	0.602415i	$-0.794205\pi$
$887$	−47.5439	−1.59637	−0.798183	+	0.602415i	$0.794205\pi$
$888$	3.87086	0.129898
$889$	0	0
$890$	15.6699	0.525256
$891$	−0.318669	−0.0106758
$892$	11.6363	0.389611
$893$	64.8378	2.16971
$894$	22.0552	0.737635
$895$	−2.27441	−0.0760251
$896$	0	0
$897$	−10.5082	−0.350859
$898$	12.6496	0.422122
$899$	−2.50820	−0.0836533
$900$	−8.27858	−0.275953
$901$	26.1781	0.872119
$902$	−5.38146	−0.179183
$903$	0	0
$904$	6.49464	0.216008
$905$	0.612863	0.0203723
$906$	3.93437	0.130711
$907$	14.8628	0.493511	0.246756	−	0.969078i	$-0.420636\pi$
$907$	14.8628	0.493511	0.246756	+	0.969078i	$0.420636\pi$
$908$	−0.661814	−0.0219631
$909$	−10.9149	−0.362023
$910$	0	0
$911$	−28.5603	−0.946244	−0.473122	−	0.880997i	$-0.656873\pi$
$911$	−28.5603	−0.946244	−0.473122	+	0.880997i	$0.656873\pi$
$912$	−26.0880	−0.863859
$913$	−2.67015	−0.0883691
$914$	−19.7847	−0.654418
$915$	−1.96719	−0.0650332
$916$	−16.1781	−0.534539
$917$	0	0
$918$	6.14137	0.202696
$919$	−9.32462	−0.307591	−0.153795	−	0.988103i	$-0.549150\pi$
$919$	−9.32462	−0.307591	−0.153795	+	0.988103i	$0.549150\pi$
$920$	−0.626882	−0.0206677
$921$	21.9917	0.724650
$922$	27.0961	0.892361
$923$	−26.1843	−0.861867
$924$	0	0
$925$	−37.3215	−1.22712
$926$	46.8011	1.53798
$927$	−8.00000	−0.262754
$928$	7.61676	0.250032
$929$	4.29108	0.140786	0.0703930	−	0.997519i	$-0.477575\pi$
$929$	4.29108	0.140786	0.0703930	+	0.997519i	$0.477575\pi$
$930$	−2.46705	−0.0808978
$931$	0	0
$932$	23.9917	0.785873
$933$	19.0440	0.623472
$934$	−19.2908	−0.631215
$935$	−0.513884	−0.0168058
$936$	−2.06040	−0.0673462
$937$	4.94767	0.161633	0.0808167	−	0.996729i	$-0.474247\pi$
$937$	4.94767	0.161633	0.0808167	+	0.996729i	$0.474247\pi$
$938$	0	0
$939$	−9.89845	−0.323024
$940$	−9.79902	−0.319609
$941$	17.7969	0.580162	0.290081	−	0.957002i	$-0.406318\pi$
$941$	17.7969	0.580162	0.290081	+	0.957002i	$0.406318\pi$
$942$	−20.8216	−0.678406
$943$	−21.8849	−0.712670
$944$	−50.4915	−1.64336
$945$	0	0
$946$	−6.61498	−0.215072
$947$	−53.7693	−1.74727	−0.873634	−	0.486584i	$-0.838243\pi$
$947$	−53.7693	−1.74727	−0.873634	+	0.486584i	$0.838243\pi$
$948$	−8.47539	−0.275268
$949$	−32.9753	−1.07042
$950$	53.8787	1.74805
$951$	0.568602	0.0184382
$952$	0	0
$953$	50.5550	1.63764	0.818819	−	0.574052i	$-0.194629\pi$
$953$	50.5550	1.63764	0.818819	+	0.574052i	$0.194629\pi$
$954$	15.9672	0.516957
$955$	−0.385287	−0.0124676
$956$	31.2007	1.00910
$957$	−0.318669	−0.0103011
$958$	−42.1432	−1.36158
$959$	0	0
$960$	2.97526	0.0960260
$961$	−24.7089	−0.797062
$962$	63.8214	2.05768
$963$	3.83805	0.123679
$964$	24.8308	0.799745
$965$	8.36861	0.269395
$966$	0	0
$967$	−13.1784	−0.423787	−0.211894	−	0.977293i	$-0.567963\pi$
$967$	−13.1784	−0.423787	−0.211894	+	0.977293i	$0.567963\pi$
$968$	−5.35982	−0.172271
$969$	−18.6290	−0.598450
$970$	−11.0492	−0.354769
$971$	16.3686	0.525294	0.262647	−	0.964892i	$-0.415405\pi$
$971$	16.3686	0.525294	0.262647	+	0.964892i	$0.415405\pi$
$972$	1.74590	0.0559997
$973$	0	0
$974$	−72.4832	−2.32251
$975$	19.8656	0.636210
$976$	−17.2007	−0.550581
$977$	−59.7229	−1.91071	−0.955353	−	0.295467i	$-0.904525\pi$
$977$	−59.7229	−1.91071	−0.955353	+	0.295467i	$0.904525\pi$
$978$	−42.2499	−1.35100
$979$	−5.07681	−0.162255
$980$	0	0
$981$	−8.18953	−0.261472
$982$	32.3072	1.03096
$983$	−55.4835	−1.76965	−0.884824	−	0.465926i	$-0.845721\pi$
$983$	−55.4835	−1.76965	−0.884824	+	0.465926i	$0.845721\pi$
$984$	−4.29108	−0.136795
$985$	9.12675	0.290802
$986$	6.14137	0.195581
$987$	0	0
$988$	−42.9424	−1.36618
$989$	−26.9013	−0.855411
$990$	−0.313441	−0.00996181
$991$	12.8737	0.408947	0.204473	−	0.978872i	$-0.434452\pi$
$991$	12.8737	0.408947	0.204473	+	0.978872i	$0.434452\pi$
$992$	−19.1044	−0.606565
$993$	1.17836	0.0373940
$994$	0	0
$995$	0.678490	0.0215096
$996$	14.6290	0.463538
$997$	16.0880	0.509512	0.254756	−	0.967005i	$-0.418005\pi$
$997$	16.0880	0.509512	0.254756	+	0.967005i	$0.418005\pi$
$998$	−84.8828	−2.68692
$999$	7.87086	0.249023

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4263.2.a.m.1.1		3
7.6	odd	2		87.2.a.b.1.1	✓	3
21.20	even	2		261.2.a.e.1.3		3
28.27	even	2		1392.2.a.u.1.2		3
35.13	even	4		2175.2.c.l.349.5		6
35.27	even	4		2175.2.c.l.349.2		6
35.34	odd	2		2175.2.a.t.1.3		3
56.13	odd	2		5568.2.a.cb.1.2		3
56.27	even	2		5568.2.a.bx.1.2		3
84.83	odd	2		4176.2.a.bx.1.2		3
105.104	even	2		6525.2.a.bg.1.1		3
203.202	odd	2		2523.2.a.h.1.3		3
609.608	even	2		7569.2.a.t.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.a.b.1.1	✓	3	7.6	odd	2
261.2.a.e.1.3		3	21.20	even	2
1392.2.a.u.1.2		3	28.27	even	2
2175.2.a.t.1.3		3	35.34	odd	2
2175.2.c.l.349.2		6	35.27	even	4
2175.2.c.l.349.5		6	35.13	even	4
2523.2.a.h.1.3		3	203.202	odd	2
4176.2.a.bx.1.2		3	84.83	odd	2
4263.2.a.m.1.1		3	1.1	even	1	trivial
5568.2.a.bx.1.2		3	56.27	even	2
5568.2.a.cb.1.2		3	56.13	odd	2
6525.2.a.bg.1.1		3	105.104	even	2
7569.2.a.t.1.1		3	609.608	even	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:	\( N \)	\(=\)	\( 4263 = 3 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4263.a (trivial)

\(f(q)\)	\(=\)	\(q-1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} -0.508203 q^{5} -1.93543 q^{6} +0.491797 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.93543 q^{2} +1.00000 q^{3} +1.74590 q^{4} -0.508203 q^{5} -1.93543 q^{6} +0.491797 q^{8} +1.00000 q^{9} +0.983593 q^{10} -0.318669 q^{11} +1.74590 q^{12} -4.18953 q^{13} -0.508203 q^{15} -4.44364 q^{16} -3.17313 q^{17} -1.93543 q^{18} +5.87086 q^{19} -0.887271 q^{20} +0.616763 q^{22} +2.50820 q^{23} +0.491797 q^{24} -4.74173 q^{25} +8.10856 q^{26} +1.00000 q^{27} +1.00000 q^{29} +0.983593 q^{30} -2.50820 q^{31} +7.61676 q^{32} -0.318669 q^{33} +6.14137 q^{34} +1.74590 q^{36} +7.87086 q^{37} -11.3627 q^{38} -4.18953 q^{39} -0.249933 q^{40} -8.72532 q^{41} -10.7253 q^{43} -0.556364 q^{44} -0.508203 q^{45} -4.85446 q^{46} +11.0440 q^{47} -4.44364 q^{48} +9.17730 q^{50} -3.17313 q^{51} -7.31450 q^{52} -8.24993 q^{53} -1.93543 q^{54} +0.161949 q^{55} +5.87086 q^{57} -1.93543 q^{58} +11.3627 q^{59} -0.887271 q^{60} +3.87086 q^{61} +4.85446 q^{62} -5.85446 q^{64} +2.12914 q^{65} +0.616763 q^{66} +7.04399 q^{67} -5.53996 q^{68} +2.50820 q^{69} +6.24993 q^{71} +0.491797 q^{72} +7.87086 q^{73} -15.2335 q^{74} -4.74173 q^{75} +10.2499 q^{76} +8.10856 q^{78} -4.85446 q^{79} +2.25827 q^{80} +1.00000 q^{81} +16.8873 q^{82} +8.37907 q^{83} +1.61259 q^{85} +20.7581 q^{86} +1.00000 q^{87} -0.156721 q^{88} +15.9313 q^{89} +0.983593 q^{90} +4.37907 q^{92} -2.50820 q^{93} -21.3749 q^{94} -2.98359 q^{95} +7.61676 q^{96} -11.2335 q^{97} -0.318669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} + 6 q^{4} + 2 q^{6} + 3 q^{8} + 3 q^{9} + 6 q^{10} - 8 q^{11} + 6 q^{12} - 4 q^{13} - 4 q^{16} - 4 q^{17} + 2 q^{18} + 2 q^{19} + 16 q^{20} - 13 q^{22} + 6 q^{23} + 3 q^{24} + 17 q^{25} + 11 q^{26} + 3 q^{27} + 3 q^{29} + 6 q^{30} - 6 q^{31} + 8 q^{32} - 8 q^{33} - q^{34} + 6 q^{36} + 8 q^{37} - 20 q^{38} - 4 q^{39} + 32 q^{40} + 2 q^{41} - 4 q^{43} - 11 q^{44} - 2 q^{46} + 12 q^{47} - 4 q^{48} + 54 q^{50} - 4 q^{51} + 3 q^{52} + 8 q^{53} + 2 q^{54} + 10 q^{55} + 2 q^{57} + 2 q^{58} + 20 q^{59} + 16 q^{60} - 4 q^{61} + 2 q^{62} - 5 q^{64} + 22 q^{65} - 13 q^{66} - 29 q^{68} + 6 q^{69} - 14 q^{71} + 3 q^{72} + 8 q^{73} - 16 q^{74} + 17 q^{75} - 2 q^{76} + 11 q^{78} - 2 q^{79} + 38 q^{80} + 3 q^{81} + 32 q^{82} + 8 q^{83} - 42 q^{85} + 28 q^{86} + 3 q^{87} + 2 q^{88} + 8 q^{89} + 6 q^{90} - 4 q^{92} - 6 q^{93} - 15 q^{94} - 12 q^{95} + 8 q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 + 6 * q^4 + 2 * q^6 + 3 * q^8 + 3 * q^9 + 6 * q^10 - 8 * q^11 + 6 * q^12 - 4 * q^13 - 4 * q^16 - 4 * q^17 + 2 * q^18 + 2 * q^19 + 16 * q^20 - 13 * q^22 + 6 * q^23 + 3 * q^24 + 17 * q^25 + 11 * q^26 + 3 * q^27 + 3 * q^29 + 6 * q^30 - 6 * q^31 + 8 * q^32 - 8 * q^33 - q^34 + 6 * q^36 + 8 * q^37 - 20 * q^38 - 4 * q^39 + 32 * q^40 + 2 * q^41 - 4 * q^43 - 11 * q^44 - 2 * q^46 + 12 * q^47 - 4 * q^48 + 54 * q^50 - 4 * q^51 + 3 * q^52 + 8 * q^53 + 2 * q^54 + 10 * q^55 + 2 * q^57 + 2 * q^58 + 20 * q^59 + 16 * q^60 - 4 * q^61 + 2 * q^62 - 5 * q^64 + 22 * q^65 - 13 * q^66 - 29 * q^68 + 6 * q^69 - 14 * q^71 + 3 * q^72 + 8 * q^73 - 16 * q^74 + 17 * q^75 - 2 * q^76 + 11 * q^78 - 2 * q^79 + 38 * q^80 + 3 * q^81 + 32 * q^82 + 8 * q^83 - 42 * q^85 + 28 * q^86 + 3 * q^87 + 2 * q^88 + 8 * q^89 + 6 * q^90 - 4 * q^92 - 6 * q^93 - 15 * q^94 - 12 * q^95 + 8 * q^96 - 4 * q^97 - 8 * q^99

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