LMFDB - Embedded newform 6762.2.a.cp.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.42048.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 13x^{2} + 8x + 34 $ x^4 - 2x^3 - 13x^2 + 8*x + 34
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.77137$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.82843 q^{10} +4.14794 q^{11} +1.00000 q^{12} -2.18558 q^{13} +1.82843 q^{15} +1.00000 q^{16} -3.35716 q^{17} +1.00000 q^{18} -7.33352 q^{19} +1.82843 q^{20} +4.14794 q^{22} +1.00000 q^{23} +1.00000 q^{24} -1.65685 q^{25} -2.18558 q^{26} +1.00000 q^{27} +5.18558 q^{29} +1.82843 q^{30} +10.5191 q^{31} +1.00000 q^{32} +4.14794 q^{33} -3.35716 q^{34} +1.00000 q^{36} -1.03764 q^{37} -7.33352 q^{38} -2.18558 q^{39} +1.82843 q^{40} +7.33352 q^{41} +5.36098 q^{43} +4.14794 q^{44} +1.82843 q^{45} +1.00000 q^{46} +7.22323 q^{47} +1.00000 q^{48} -1.65685 q^{50} -3.35716 q^{51} -2.18558 q^{52} +4.54274 q^{53} +1.00000 q^{54} +7.58420 q^{55} -7.33352 q^{57} +5.18558 q^{58} -0.471271 q^{59} +1.82843 q^{60} -14.7423 q^{61} +10.5191 q^{62} +1.00000 q^{64} -3.99618 q^{65} +4.14794 q^{66} +13.4050 q^{67} -3.35716 q^{68} +1.00000 q^{69} +14.1856 q^{71} +1.00000 q^{72} +11.5191 q^{73} -1.03764 q^{74} -1.65685 q^{75} -7.33352 q^{76} -2.18558 q^{78} -5.18558 q^{79} +1.82843 q^{80} +1.00000 q^{81} +7.33352 q^{82} +5.80479 q^{83} -6.13831 q^{85} +5.36098 q^{86} +5.18558 q^{87} +4.14794 q^{88} +6.69450 q^{89} +1.82843 q^{90} +1.00000 q^{92} +10.5191 q^{93} +7.22323 q^{94} -13.4088 q^{95} +1.00000 q^{96} -4.47127 q^{97} +4.14794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} + 6 q^{13} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - 4 q^{20} + 6 q^{22} + 4 q^{23} + 4 q^{24} + 16 q^{25} + 6 q^{26} + 4 q^{27} + 6 q^{29} - 4 q^{30} + 2 q^{31} + 4 q^{32} + 6 q^{33} - 10 q^{34} + 4 q^{36} - 4 q^{38} + 6 q^{39} - 4 q^{40} + 4 q^{41} + 20 q^{43} + 6 q^{44} - 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 16 q^{50} - 10 q^{51} + 6 q^{52} + 4 q^{54} + 10 q^{55} - 4 q^{57} + 6 q^{58} + 6 q^{59} - 4 q^{60} + 2 q^{62} + 4 q^{64} - 14 q^{65} + 6 q^{66} + 18 q^{67} - 10 q^{68} + 4 q^{69} + 42 q^{71} + 4 q^{72} + 6 q^{73} + 16 q^{75} - 4 q^{76} + 6 q^{78} - 6 q^{79} - 4 q^{80} + 4 q^{81} + 4 q^{82} - 10 q^{83} + 34 q^{85} + 20 q^{86} + 6 q^{87} + 6 q^{88} - 4 q^{90} + 4 q^{92} + 2 q^{93} + 10 q^{94} - 20 q^{95} + 4 q^{96} - 10 q^{97} + 6 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 + 6 * q^13 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - 4 * q^20 + 6 * q^22 + 4 * q^23 + 4 * q^24 + 16 * q^25 + 6 * q^26 + 4 * q^27 + 6 * q^29 - 4 * q^30 + 2 * q^31 + 4 * q^32 + 6 * q^33 - 10 * q^34 + 4 * q^36 - 4 * q^38 + 6 * q^39 - 4 * q^40 + 4 * q^41 + 20 * q^43 + 6 * q^44 - 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 16 * q^50 - 10 * q^51 + 6 * q^52 + 4 * q^54 + 10 * q^55 - 4 * q^57 + 6 * q^58 + 6 * q^59 - 4 * q^60 + 2 * q^62 + 4 * q^64 - 14 * q^65 + 6 * q^66 + 18 * q^67 - 10 * q^68 + 4 * q^69 + 42 * q^71 + 4 * q^72 + 6 * q^73 + 16 * q^75 - 4 * q^76 + 6 * q^78 - 6 * q^79 - 4 * q^80 + 4 * q^81 + 4 * q^82 - 10 * q^83 + 34 * q^85 + 20 * q^86 + 6 * q^87 + 6 * q^88 - 4 * q^90 + 4 * q^92 + 2 * q^93 + 10 * q^94 - 20 * q^95 + 4 * q^96 - 10 * q^97 + 6 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.82843	0.817697	0.408849	−	0.912602i	$-0.365930\pi$
$5$	1.82843	0.817697	0.408849	+	0.912602i	$0.365930\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.82843	0.578199
$11$	4.14794	1.25065	0.625325	−	0.780364i	$-0.284966\pi$
$11$	4.14794	1.25065	0.625325	+	0.780364i	$0.284966\pi$
$12$	1.00000	0.288675
$13$	−2.18558	−0.606172	−0.303086	−	0.952963i	$-0.598017\pi$
$13$	−2.18558	−0.606172	−0.303086	+	0.952963i	$0.598017\pi$
$14$	0	0
$15$	1.82843	0.472098
$16$	1.00000	0.250000
$17$	−3.35716	−0.814230	−0.407115	−	0.913377i	$-0.633465\pi$
$17$	−3.35716	−0.814230	−0.407115	+	0.913377i	$0.633465\pi$
$18$	1.00000	0.235702
$19$	−7.33352	−1.68243	−0.841213	−	0.540704i	$-0.818158\pi$
$19$	−7.33352	−1.68243	−0.841213	+	0.540704i	$0.818158\pi$
$20$	1.82843	0.408849
$21$	0	0
$22$	4.14794	0.884344
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	−1.65685	−0.331371
$26$	−2.18558	−0.428628
$27$	1.00000	0.192450
$28$	0	0
$29$	5.18558	0.962939	0.481469	−	0.876463i	$-0.340103\pi$
$29$	5.18558	0.962939	0.481469	+	0.876463i	$0.340103\pi$
$30$	1.82843	0.333824
$31$	10.5191	1.88929	0.944643	−	0.328099i	$-0.106408\pi$
$31$	10.5191	1.88929	0.944643	+	0.328099i	$0.106408\pi$
$32$	1.00000	0.176777
$33$	4.14794	0.722063
$34$	−3.35716	−0.575747
$35$	0	0
$36$	1.00000	0.166667
$37$	−1.03764	−0.170588	−0.0852938	−	0.996356i	$-0.527183\pi$
$37$	−1.03764	−0.170588	−0.0852938	+	0.996356i	$0.527183\pi$
$38$	−7.33352	−1.18965
$39$	−2.18558	−0.349973
$40$	1.82843	0.289100
$41$	7.33352	1.14530	0.572652	−	0.819799i	$-0.305915\pi$
$41$	7.33352	1.14530	0.572652	+	0.819799i	$0.305915\pi$
$42$	0	0
$43$	5.36098	0.817541	0.408771	−	0.912637i	$-0.365958\pi$
$43$	5.36098	0.817541	0.408771	+	0.912637i	$0.365958\pi$
$44$	4.14794	0.625325
$45$	1.82843	0.272566
$46$	1.00000	0.147442
$47$	7.22323	1.05362	0.526808	−	0.849984i	$-0.323389\pi$
$47$	7.22323	1.05362	0.526808	+	0.849984i	$0.323389\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−1.65685	−0.234315
$51$	−3.35716	−0.470096
$52$	−2.18558	−0.303086
$53$	4.54274	0.623993	0.311997	−	0.950083i	$-0.399002\pi$
$53$	4.54274	0.623993	0.311997	+	0.950083i	$0.399002\pi$
$54$	1.00000	0.136083
$55$	7.58420	1.02265
$56$	0	0
$57$	−7.33352	−0.971349
$58$	5.18558	0.680900
$59$	−0.471271	−0.0613543	−0.0306771	−	0.999529i	$-0.509766\pi$
$59$	−0.471271	−0.0613543	−0.0306771	+	0.999529i	$0.509766\pi$
$60$	1.82843	0.236049
$61$	−14.7423	−1.88756	−0.943781	−	0.330571i	$-0.892759\pi$
$61$	−14.7423	−1.88756	−0.943781	+	0.330571i	$0.892759\pi$
$62$	10.5191	1.33593
$63$	0	0
$64$	1.00000	0.125000
$65$	−3.99618	−0.495665
$66$	4.14794	0.510576
$67$	13.4050	1.63768	0.818840	−	0.574022i	$-0.194618\pi$
$67$	13.4050	1.63768	0.818840	+	0.574022i	$0.194618\pi$
$68$	−3.35716	−0.407115
$69$	1.00000	0.120386
$70$	0	0
$71$	14.1856	1.68352	0.841759	−	0.539853i	$-0.181520\pi$
$71$	14.1856	1.68352	0.841759	+	0.539853i	$0.181520\pi$
$72$	1.00000	0.117851
$73$	11.5191	1.34821	0.674105	−	0.738636i	$-0.264530\pi$
$73$	11.5191	1.34821	0.674105	+	0.738636i	$0.264530\pi$
$74$	−1.03764	−0.120624
$75$	−1.65685	−0.191317
$76$	−7.33352	−0.841213
$77$	0	0
$78$	−2.18558	−0.247469
$79$	−5.18558	−0.583424	−0.291712	−	0.956506i	$-0.594225\pi$
$79$	−5.18558	−0.583424	−0.291712	+	0.956506i	$0.594225\pi$
$80$	1.82843	0.204424
$81$	1.00000	0.111111
$82$	7.33352	0.809852
$83$	5.80479	0.637159	0.318579	−	0.947896i	$-0.396794\pi$
$83$	5.80479	0.637159	0.318579	+	0.947896i	$0.396794\pi$
$84$	0	0
$85$	−6.13831	−0.665794
$86$	5.36098	0.578089
$87$	5.18558	0.555953
$88$	4.14794	0.442172
$89$	6.69450	0.709615	0.354808	−	0.934939i	$-0.384546\pi$
$89$	6.69450	0.709615	0.354808	+	0.934939i	$0.384546\pi$
$90$	1.82843	0.192733
$91$	0	0
$92$	1.00000	0.104257
$93$	10.5191	1.09078
$94$	7.22323	0.745019
$95$	−13.4088	−1.37571
$96$	1.00000	0.102062
$97$	−4.47127	−0.453989	−0.226994	−	0.973896i	$-0.572890\pi$
$97$	−4.47127	−0.453989	−0.226994	+	0.973896i	$0.572890\pi$
$98$	0	0
$99$	4.14794	0.416884
$100$	−1.65685	−0.165685
$101$	15.3061	1.52301	0.761505	−	0.648159i	$-0.224461\pi$
$101$	15.3061	1.52301	0.761505	+	0.648159i	$0.224461\pi$
$102$	−3.35716	−0.332408
$103$	7.40499	0.729635	0.364818	−	0.931079i	$-0.381131\pi$
$103$	7.40499	0.729635	0.364818	+	0.931079i	$0.381131\pi$
$104$	−2.18558	−0.214314
$105$	0	0
$106$	4.54274	0.441230
$107$	−5.50127	−0.531828	−0.265914	−	0.963997i	$-0.585674\pi$
$107$	−5.50127	−0.531828	−0.265914	+	0.963997i	$0.585674\pi$
$108$	1.00000	0.0962250
$109$	−18.6951	−1.79066	−0.895331	−	0.445401i	$-0.853061\pi$
$109$	−18.6951	−1.79066	−0.895331	+	0.445401i	$0.853061\pi$
$110$	7.58420	0.723125
$111$	−1.03764	−0.0984888
$112$	0	0
$113$	5.28187	0.496876	0.248438	−	0.968648i	$-0.420083\pi$
$113$	5.28187	0.496876	0.248438	+	0.968648i	$0.420083\pi$
$114$	−7.33352	−0.686847
$115$	1.82843	0.170502
$116$	5.18558	0.481469
$117$	−2.18558	−0.202057
$118$	−0.471271	−0.0433840
$119$	0	0
$120$	1.82843	0.166912
$121$	6.20540	0.564127
$122$	−14.7423	−1.33471
$123$	7.33352	0.661241
$124$	10.5191	0.944643
$125$	−12.1716	−1.08866
$126$	0	0
$127$	6.49108	0.575991	0.287995	−	0.957632i	$-0.407011\pi$
$127$	6.49108	0.575991	0.287995	+	0.957632i	$0.407011\pi$
$128$	1.00000	0.0883883
$129$	5.36098	0.472008
$130$	−3.99618	−0.350488
$131$	−4.40881	−0.385200	−0.192600	−	0.981277i	$-0.561692\pi$
$131$	−4.40881	−0.385200	−0.192600	+	0.981277i	$0.561692\pi$
$132$	4.14794	0.361032
$133$	0	0
$134$	13.4050	1.15801
$135$	1.82843	0.157366
$136$	−3.35716	−0.287874
$137$	1.68049	0.143574	0.0717869	−	0.997420i	$-0.477130\pi$
$137$	1.68049	0.143574	0.0717869	+	0.997420i	$0.477130\pi$
$138$	1.00000	0.0851257
$139$	−13.3137	−1.12925	−0.564627	−	0.825346i	$-0.690980\pi$
$139$	−13.3137	−1.12925	−0.564627	+	0.825346i	$0.690980\pi$
$140$	0	0
$141$	7.22323	0.608305
$142$	14.1856	1.19043
$143$	−9.06566	−0.758109
$144$	1.00000	0.0833333
$145$	9.48146	0.787392
$146$	11.5191	0.953328
$147$	0	0
$148$	−1.03764	−0.0852938
$149$	19.3577	1.58585	0.792923	−	0.609322i	$-0.208558\pi$
$149$	19.3577	1.58585	0.792923	+	0.609322i	$0.208558\pi$
$150$	−1.65685	−0.135282
$151$	5.58420	0.454436	0.227218	−	0.973844i	$-0.427037\pi$
$151$	5.58420	0.454436	0.227218	+	0.973844i	$0.427037\pi$
$152$	−7.33352	−0.594827
$153$	−3.35716	−0.271410
$154$	0	0
$155$	19.2334	1.54487
$156$	−2.18558	−0.174987
$157$	−22.7902	−1.81885	−0.909427	−	0.415864i	$-0.863479\pi$
$157$	−22.7902	−1.81885	−0.909427	+	0.415864i	$0.863479\pi$
$158$	−5.18558	−0.412543
$159$	4.54274	0.360263
$160$	1.82843	0.144550
$161$	0	0
$162$	1.00000	0.0785674
$163$	−25.4368	−1.99237	−0.996183	−	0.0872876i	$-0.972180\pi$
$163$	−25.4368	−1.99237	−0.996183	+	0.0872876i	$0.972180\pi$
$164$	7.33352	0.572652
$165$	7.58420	0.590429
$166$	5.80479	0.450539
$167$	−22.1185	−1.71158	−0.855791	−	0.517323i	$-0.826929\pi$
$167$	−22.1185	−1.71158	−0.855791	+	0.517323i	$0.826929\pi$
$168$	0	0
$169$	−8.22323	−0.632556
$170$	−6.13831	−0.470787
$171$	−7.33352	−0.560808
$172$	5.36098	0.408771
$173$	−13.6849	−1.04044	−0.520221	−	0.854032i	$-0.674150\pi$
$173$	−13.6849	−1.04044	−0.520221	+	0.854032i	$0.674150\pi$
$174$	5.18558	0.393118
$175$	0	0
$176$	4.14794	0.312663
$177$	−0.471271	−0.0354229
$178$	6.69450	0.501774
$179$	−2.77677	−0.207546	−0.103773	−	0.994601i	$-0.533092\pi$
$179$	−2.77677	−0.207546	−0.103773	+	0.994601i	$0.533092\pi$
$180$	1.82843	0.136283
$181$	−20.9629	−1.55816	−0.779081	−	0.626923i	$-0.784314\pi$
$181$	−20.9629	−1.55816	−0.779081	+	0.626923i	$0.784314\pi$
$182$	0	0
$183$	−14.7423	−1.08978
$184$	1.00000	0.0737210
$185$	−1.89726	−0.139489
$186$	10.5191	0.771298
$187$	−13.9253	−1.01832
$188$	7.22323	0.526808
$189$	0	0
$190$	−13.4088	−0.972777
$191$	−8.96236	−0.648493	−0.324247	−	0.945973i	$-0.605111\pi$
$191$	−8.96236	−0.648493	−0.324247	+	0.945973i	$0.605111\pi$
$192$	1.00000	0.0721688
$193$	11.6390	0.837795	0.418898	−	0.908033i	$-0.362417\pi$
$193$	11.6390	0.837795	0.418898	+	0.908033i	$0.362417\pi$
$194$	−4.47127	−0.321019
$195$	−3.99618	−0.286172
$196$	0	0
$197$	9.58157	0.682658	0.341329	−	0.939944i	$-0.389123\pi$
$197$	9.58157	0.682658	0.341329	+	0.939944i	$0.389123\pi$
$198$	4.14794	0.294781
$199$	−9.95273	−0.705530	−0.352765	−	0.935712i	$-0.614759\pi$
$199$	−9.95273	−0.705530	−0.352765	+	0.935712i	$0.614759\pi$
$200$	−1.65685	−0.117157
$201$	13.4050	0.945515
$202$	15.3061	1.07693
$203$	0	0
$204$	−3.35716	−0.235048
$205$	13.4088	0.936512
$206$	7.40499	0.515930
$207$	1.00000	0.0695048
$208$	−2.18558	−0.151543
$209$	−30.4190	−2.10413
$210$	0	0
$211$	0.303519	0.0208951	0.0104476	−	0.999945i	$-0.496674\pi$
$211$	0.303519	0.0208951	0.0104476	+	0.999945i	$0.496674\pi$
$212$	4.54274	0.311997
$213$	14.1856	0.971980
$214$	−5.50127	−0.376059
$215$	9.80216	0.668501
$216$	1.00000	0.0680414
$217$	0	0
$218$	−18.6951	−1.26619
$219$	11.5191	0.778389
$220$	7.58420	0.511327
$221$	7.33734	0.493563
$222$	−1.03764	−0.0696421
$223$	−16.9375	−1.13422	−0.567111	−	0.823642i	$-0.691939\pi$
$223$	−16.9375	−1.13422	−0.567111	+	0.823642i	$0.691939\pi$
$224$	0	0
$225$	−1.65685	−0.110457
$226$	5.28187	0.351345
$227$	−21.5369	−1.42946	−0.714728	−	0.699402i	$-0.753450\pi$
$227$	−21.5369	−1.42946	−0.714728	+	0.699402i	$0.753450\pi$
$228$	−7.33352	−0.485674
$229$	−0.666478	−0.0440421	−0.0220211	−	0.999758i	$-0.507010\pi$
$229$	−0.666478	−0.0440421	−0.0220211	+	0.999758i	$0.507010\pi$
$230$	1.82843	0.120563
$231$	0	0
$232$	5.18558	0.340450
$233$	−1.67667	−0.109842	−0.0549211	−	0.998491i	$-0.517491\pi$
$233$	−1.67667	−0.109842	−0.0549211	+	0.998491i	$0.517491\pi$
$234$	−2.18558	−0.142876
$235$	13.2071	0.861539
$236$	−0.471271	−0.0306771
$237$	−5.18558	−0.336840
$238$	0	0
$239$	10.7220	0.693546	0.346773	−	0.937949i	$-0.387278\pi$
$239$	10.7220	0.693546	0.346773	+	0.937949i	$0.387278\pi$
$240$	1.82843	0.118024
$241$	18.2034	1.17258	0.586292	−	0.810099i	$-0.300587\pi$
$241$	18.2034	1.17258	0.586292	+	0.810099i	$0.300587\pi$
$242$	6.20540	0.398898
$243$	1.00000	0.0641500
$244$	−14.7423	−0.943781
$245$	0	0
$246$	7.33352	0.467568
$247$	16.0280	1.01984
$248$	10.5191	0.667964
$249$	5.80479	0.367864
$250$	−12.1716	−0.769798
$251$	−0.794604	−0.0501549	−0.0250775	−	0.999686i	$-0.507983\pi$
$251$	−0.794604	−0.0501549	−0.0250775	+	0.999686i	$0.507983\pi$
$252$	0	0
$253$	4.14794	0.260779
$254$	6.49108	0.407287
$255$	−6.13831	−0.384396
$256$	1.00000	0.0625000
$257$	−0.591190	−0.0368774	−0.0184387	−	0.999830i	$-0.505870\pi$
$257$	−0.591190	−0.0368774	−0.0184387	+	0.999830i	$0.505870\pi$
$258$	5.36098	0.333760
$259$	0	0
$260$	−3.99618	−0.247833
$261$	5.18558	0.320980
$262$	−4.40881	−0.272377
$263$	2.86725	0.176802	0.0884012	−	0.996085i	$-0.471824\pi$
$263$	2.86725	0.176802	0.0884012	+	0.996085i	$0.471824\pi$
$264$	4.14794	0.255288
$265$	8.30607	0.510238
$266$	0	0
$267$	6.69450	0.409697
$268$	13.4050	0.818840
$269$	−7.17794	−0.437647	−0.218823	−	0.975764i	$-0.570222\pi$
$269$	−7.17794	−0.437647	−0.218823	+	0.975764i	$0.570222\pi$
$270$	1.82843	0.111275
$271$	−10.5191	−0.638990	−0.319495	−	0.947588i	$-0.603513\pi$
$271$	−10.5191	−0.638990	−0.319495	+	0.947588i	$0.603513\pi$
$272$	−3.35716	−0.203557
$273$	0	0
$274$	1.68049	0.101522
$275$	−6.87253	−0.414429
$276$	1.00000	0.0601929
$277$	−30.9285	−1.85831	−0.929156	−	0.369688i	$-0.879465\pi$
$277$	−30.9285	−1.85831	−0.929156	+	0.369688i	$0.879465\pi$
$278$	−13.3137	−0.798503
$279$	10.5191	0.629762
$280$	0	0
$281$	−2.09949	−0.125245	−0.0626225	−	0.998037i	$-0.519946\pi$
$281$	−2.09949	−0.125245	−0.0626225	+	0.998037i	$0.519946\pi$
$282$	7.22323	0.430137
$283$	20.3475	1.20954	0.604768	−	0.796402i	$-0.293266\pi$
$283$	20.3475	1.20954	0.604768	+	0.796402i	$0.293266\pi$
$284$	14.1856	0.841759
$285$	−13.4088	−0.794269
$286$	−9.06566	−0.536064
$287$	0	0
$288$	1.00000	0.0589256
$289$	−5.72950	−0.337030
$290$	9.48146	0.556771
$291$	−4.47127	−0.262111
$292$	11.5191	0.674105
$293$	−31.4853	−1.83939	−0.919695	−	0.392634i	$-0.871564\pi$
$293$	−31.4853	−1.83939	−0.919695	+	0.392634i	$0.871564\pi$
$294$	0	0
$295$	−0.861685	−0.0501693
$296$	−1.03764	−0.0603118
$297$	4.14794	0.240688
$298$	19.3577	1.12136
$299$	−2.18558	−0.126396
$300$	−1.65685	−0.0956585
$301$	0	0
$302$	5.58420	0.321335
$303$	15.3061	0.879311
$304$	−7.33352	−0.420606
$305$	−26.9553	−1.54345
$306$	−3.35716	−0.191916
$307$	1.64865	0.0940933	0.0470466	−	0.998893i	$-0.485019\pi$
$307$	1.64865	0.0940933	0.0470466	+	0.998893i	$0.485019\pi$
$308$	0	0
$309$	7.40499	0.421255
$310$	19.2334	1.09238
$311$	12.1779	0.690548	0.345274	−	0.938502i	$-0.387786\pi$
$311$	12.1779	0.690548	0.345274	+	0.938502i	$0.387786\pi$
$312$	−2.18558	−0.123734
$313$	12.5669	0.710325	0.355163	−	0.934805i	$-0.384425\pi$
$313$	12.5669	0.710325	0.355163	+	0.934805i	$0.384425\pi$
$314$	−22.7902	−1.28612
$315$	0	0
$316$	−5.18558	−0.291712
$317$	−9.17794	−0.515485	−0.257742	−	0.966214i	$-0.582979\pi$
$317$	−9.17794	−0.515485	−0.257742	+	0.966214i	$0.582979\pi$
$318$	4.54274	0.254744
$319$	21.5095	1.20430
$320$	1.82843	0.102212
$321$	−5.50127	−0.307051
$322$	0	0
$323$	24.6198	1.36988
$324$	1.00000	0.0555556
$325$	3.62119	0.200868
$326$	−25.4368	−1.40882
$327$	−18.6951	−1.03384
$328$	7.33352	0.404926
$329$	0	0
$330$	7.58420	0.417497
$331$	−29.3896	−1.61540	−0.807698	−	0.589596i	$-0.799287\pi$
$331$	−29.3896	−1.61540	−0.807698	+	0.589596i	$0.799287\pi$
$332$	5.80479	0.318579
$333$	−1.03764	−0.0568626
$334$	−22.1185	−1.21027
$335$	24.5100	1.33913
$336$	0	0
$337$	8.12048	0.442351	0.221175	−	0.975234i	$-0.429011\pi$
$337$	8.12048	0.442351	0.221175	+	0.975234i	$0.429011\pi$
$338$	−8.22323	−0.447285
$339$	5.28187	0.286872
$340$	−6.13831	−0.332897
$341$	43.6326	2.36284
$342$	−7.33352	−0.396551
$343$	0	0
$344$	5.36098	0.289044
$345$	1.82843	0.0984392
$346$	−13.6849	−0.735703
$347$	28.2614	1.51715	0.758577	−	0.651584i	$-0.225895\pi$
$347$	28.2614	1.51715	0.758577	+	0.651584i	$0.225895\pi$
$348$	5.18558	0.277976
$349$	24.1307	1.29169	0.645843	−	0.763471i	$-0.276506\pi$
$349$	24.1307	1.29169	0.645843	+	0.763471i	$0.276506\pi$
$350$	0	0
$351$	−2.18558	−0.116658
$352$	4.14794	0.221086
$353$	13.4088	0.713679	0.356839	−	0.934166i	$-0.383854\pi$
$353$	13.4088	0.713679	0.356839	+	0.934166i	$0.383854\pi$
$354$	−0.471271	−0.0250478
$355$	25.9373	1.37661
$356$	6.69450	0.354808
$357$	0	0
$358$	−2.77677	−0.146757
$359$	−3.88509	−0.205047	−0.102523	−	0.994731i	$-0.532692\pi$
$359$	−3.88509	−0.205047	−0.102523	+	0.994731i	$0.532692\pi$
$360$	1.82843	0.0963666
$361$	34.7805	1.83055
$362$	−20.9629	−1.10179
$363$	6.20540	0.325699
$364$	0	0
$365$	21.0618	1.10243
$366$	−14.7423	−0.770594
$367$	−1.43745	−0.0750342	−0.0375171	−	0.999296i	$-0.511945\pi$
$367$	−1.43745	−0.0750342	−0.0375171	+	0.999296i	$0.511945\pi$
$368$	1.00000	0.0521286
$369$	7.33352	0.381768
$370$	−1.89726	−0.0986337
$371$	0	0
$372$	10.5191	0.545390
$373$	18.2959	0.947325	0.473662	−	0.880707i	$-0.342932\pi$
$373$	18.2959	0.947325	0.473662	+	0.880707i	$0.342932\pi$
$374$	−13.9253	−0.720059
$375$	−12.1716	−0.628537
$376$	7.22323	0.372509
$377$	−11.3335	−0.583706
$378$	0	0
$379$	−5.97637	−0.306985	−0.153493	−	0.988150i	$-0.549052\pi$
$379$	−5.97637	−0.306985	−0.153493	+	0.988150i	$0.549052\pi$
$380$	−13.4088	−0.687857
$381$	6.49108	0.332548
$382$	−8.96236	−0.458554
$383$	−5.89726	−0.301336	−0.150668	−	0.988584i	$-0.548142\pi$
$383$	−5.89726	−0.301336	−0.150668	+	0.988584i	$0.548142\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	11.6390	0.592411
$387$	5.36098	0.272514
$388$	−4.47127	−0.226994
$389$	−17.1135	−0.867689	−0.433844	−	0.900988i	$-0.642843\pi$
$389$	−17.1135	−0.867689	−0.433844	+	0.900988i	$0.642843\pi$
$390$	−3.99618	−0.202354
$391$	−3.35716	−0.169779
$392$	0	0
$393$	−4.40881	−0.222395
$394$	9.58157	0.482712
$395$	−9.48146	−0.477064
$396$	4.14794	0.208442
$397$	−12.8450	−0.644671	−0.322336	−	0.946625i	$-0.604468\pi$
$397$	−12.8450	−0.644671	−0.322336	+	0.946625i	$0.604468\pi$
$398$	−9.95273	−0.498885
$399$	0	0
$400$	−1.65685	−0.0828427
$401$	17.4330	0.870563	0.435281	−	0.900294i	$-0.356649\pi$
$401$	17.4330	0.870563	0.435281	+	0.900294i	$0.356649\pi$
$402$	13.4050	0.668580
$403$	−22.9904	−1.14523
$404$	15.3061	0.761505
$405$	1.82843	0.0908553
$406$	0	0
$407$	−4.30408	−0.213346
$408$	−3.35716	−0.166204
$409$	−9.06765	−0.448366	−0.224183	−	0.974547i	$-0.571971\pi$
$409$	−9.06765	−0.448366	−0.224183	+	0.974547i	$0.571971\pi$
$410$	13.4088	0.662214
$411$	1.68049	0.0828924
$412$	7.40499	0.364818
$413$	0	0
$414$	1.00000	0.0491473
$415$	10.6136	0.521003
$416$	−2.18558	−0.107157
$417$	−13.3137	−0.651975
$418$	−30.4190	−1.48784
$419$	−6.63902	−0.324338	−0.162169	−	0.986763i	$-0.551849\pi$
$419$	−6.63902	−0.324338	−0.162169	+	0.986763i	$0.551849\pi$
$420$	0	0
$421$	−0.942543	−0.0459367	−0.0229684	−	0.999736i	$-0.507312\pi$
$421$	−0.942543	−0.0459367	−0.0229684	+	0.999736i	$0.507312\pi$
$422$	0.303519	0.0147751
$423$	7.22323	0.351205
$424$	4.54274	0.220615
$425$	5.56232	0.269812
$426$	14.1856	0.687294
$427$	0	0
$428$	−5.50127	−0.265914
$429$	−9.06566	−0.437694
$430$	9.80216	0.472702
$431$	−35.3697	−1.70370	−0.851850	−	0.523785i	$-0.824519\pi$
$431$	−35.3697	−1.70370	−0.851850	+	0.523785i	$0.824519\pi$
$432$	1.00000	0.0481125
$433$	32.7627	1.57448	0.787238	−	0.616650i	$-0.211510\pi$
$433$	32.7627	1.57448	0.787238	+	0.616650i	$0.211510\pi$
$434$	0	0
$435$	9.48146	0.454601
$436$	−18.6951	−0.895331
$437$	−7.33352	−0.350810
$438$	11.5191	0.550404
$439$	−19.3163	−0.921919	−0.460959	−	0.887421i	$-0.652495\pi$
$439$	−19.3163	−0.921919	−0.460959	+	0.887421i	$0.652495\pi$
$440$	7.58420	0.361563
$441$	0	0
$442$	7.33734	0.349002
$443$	14.4088	0.684583	0.342292	−	0.939594i	$-0.388797\pi$
$443$	14.4088	0.684583	0.342292	+	0.939594i	$0.388797\pi$
$444$	−1.03764	−0.0492444
$445$	12.2404	0.580251
$446$	−16.9375	−0.802016
$447$	19.3577	0.915589
$448$	0	0
$449$	−11.0580	−0.521860	−0.260930	−	0.965358i	$-0.584029\pi$
$449$	−11.0580	−0.521860	−0.260930	+	0.965358i	$0.584029\pi$
$450$	−1.65685	−0.0781049
$451$	30.4190	1.43237
$452$	5.28187	0.248438
$453$	5.58420	0.262369
$454$	−21.5369	−1.01078
$455$	0	0
$456$	−7.33352	−0.343424
$457$	−25.8450	−1.20898	−0.604489	−	0.796614i	$-0.706623\pi$
$457$	−25.8450	−1.20898	−0.604489	+	0.796614i	$0.706623\pi$
$458$	−0.666478	−0.0311425
$459$	−3.35716	−0.156699
$460$	1.82843	0.0852509
$461$	−39.3341	−1.83197	−0.915986	−	0.401211i	$-0.868589\pi$
$461$	−39.3341	−1.83197	−0.915986	+	0.401211i	$0.868589\pi$
$462$	0	0
$463$	25.0778	1.16547	0.582733	−	0.812664i	$-0.301983\pi$
$463$	25.0778	1.16547	0.582733	+	0.812664i	$0.301983\pi$
$464$	5.18558	0.240735
$465$	19.2334	0.891928
$466$	−1.67667	−0.0776701
$467$	−22.9629	−1.06260	−0.531299	−	0.847185i	$-0.678296\pi$
$467$	−22.9629	−1.06260	−0.531299	+	0.847185i	$0.678296\pi$
$468$	−2.18558	−0.101029
$469$	0	0
$470$	13.2071	0.609200
$471$	−22.7902	−1.05012
$472$	−0.471271	−0.0216920
$473$	22.2370	1.02246
$474$	−5.18558	−0.238182
$475$	12.1506	0.557507
$476$	0	0
$477$	4.54274	0.207998
$478$	10.7220	0.490411
$479$	−16.6116	−0.759002	−0.379501	−	0.925191i	$-0.623904\pi$
$479$	−16.6116	−0.759002	−0.379501	+	0.925191i	$0.623904\pi$
$480$	1.82843	0.0834559
$481$	2.26786	0.103405
$482$	18.2034	0.829143
$483$	0	0
$484$	6.20540	0.282063
$485$	−8.17539	−0.371226
$486$	1.00000	0.0453609
$487$	−14.8226	−0.671677	−0.335839	−	0.941920i	$-0.609020\pi$
$487$	−14.8226	−0.671677	−0.335839	+	0.941920i	$0.609020\pi$
$488$	−14.7423	−0.667354
$489$	−25.4368	−1.15029
$490$	0	0
$491$	22.2466	1.00398	0.501988	−	0.864875i	$-0.332602\pi$
$491$	22.2466	1.00398	0.501988	+	0.864875i	$0.332602\pi$
$492$	7.33352	0.330621
$493$	−17.4088	−0.784053
$494$	16.0280	0.721135
$495$	7.58420	0.340885
$496$	10.5191	0.472322
$497$	0	0
$498$	5.80479	0.260119
$499$	−11.2857	−0.505217	−0.252608	−	0.967569i	$-0.581288\pi$
$499$	−11.2857	−0.505217	−0.252608	+	0.967569i	$0.581288\pi$
$500$	−12.1716	−0.544329
$501$	−22.1185	−0.988182
$502$	−0.794604	−0.0354649
$503$	27.1339	1.20984	0.604920	−	0.796286i	$-0.293205\pi$
$503$	27.1339	1.20984	0.604920	+	0.796286i	$0.293205\pi$
$504$	0	0
$505$	27.9860	1.24536
$506$	4.14794	0.184398
$507$	−8.22323	−0.365206
$508$	6.49108	0.287995
$509$	−38.7952	−1.71957	−0.859783	−	0.510660i	$-0.829401\pi$
$509$	−38.7952	−1.71957	−0.859783	+	0.510660i	$0.829401\pi$
$510$	−6.13831	−0.271809
$511$	0	0
$512$	1.00000	0.0441942
$513$	−7.33352	−0.323783
$514$	−0.591190	−0.0260763
$515$	13.5395	0.596621
$516$	5.36098	0.236004
$517$	29.9615	1.31771
$518$	0	0
$519$	−13.6849	−0.600699
$520$	−3.99618	−0.175244
$521$	1.52991	0.0670266	0.0335133	−	0.999438i	$-0.489330\pi$
$521$	1.52991	0.0670266	0.0335133	+	0.999438i	$0.489330\pi$
$522$	5.18558	0.226967
$523$	8.42282	0.368304	0.184152	−	0.982898i	$-0.441046\pi$
$523$	8.42282	0.368304	0.184152	+	0.982898i	$0.441046\pi$
$524$	−4.40881	−0.192600
$525$	0	0
$526$	2.86725	0.125018
$527$	−35.3143	−1.53831
$528$	4.14794	0.180516
$529$	1.00000	0.0434783
$530$	8.30607	0.360792
$531$	−0.471271	−0.0204514
$532$	0	0
$533$	−16.0280	−0.694251
$534$	6.69450	0.289699
$535$	−10.0587	−0.434875
$536$	13.4050	0.579007
$537$	−2.77677	−0.119827
$538$	−7.17794	−0.309463
$539$	0	0
$540$	1.82843	0.0786830
$541$	−5.65383	−0.243077	−0.121539	−	0.992587i	$-0.538783\pi$
$541$	−5.65383	−0.243077	−0.121539	+	0.992587i	$0.538783\pi$
$542$	−10.5191	−0.451834
$543$	−20.9629	−0.899605
$544$	−3.35716	−0.143937
$545$	−34.1826	−1.46422
$546$	0	0
$547$	−26.2480	−1.12229	−0.561143	−	0.827719i	$-0.689638\pi$
$547$	−26.2480	−1.12229	−0.561143	+	0.827719i	$0.689638\pi$
$548$	1.68049	0.0717869
$549$	−14.7423	−0.629187
$550$	−6.87253	−0.293046
$551$	−38.0286	−1.62007
$552$	1.00000	0.0425628
$553$	0	0
$554$	−30.9285	−1.31403
$555$	−1.89726	−0.0805341
$556$	−13.3137	−0.564627
$557$	37.2422	1.57800	0.789001	−	0.614392i	$-0.210599\pi$
$557$	37.2422	1.57800	0.789001	+	0.614392i	$0.210599\pi$
$558$	10.5191	0.445309
$559$	−11.7169	−0.495570
$560$	0	0
$561$	−13.9253	−0.587926
$562$	−2.09949	−0.0885615
$563$	13.4897	0.568522	0.284261	−	0.958747i	$-0.408252\pi$
$563$	13.4897	0.568522	0.284261	+	0.958747i	$0.408252\pi$
$564$	7.22323	0.304153
$565$	9.65751	0.406294
$566$	20.3475	0.855271
$567$	0	0
$568$	14.1856	0.595214
$569$	−16.7379	−0.701691	−0.350846	−	0.936433i	$-0.614106\pi$
$569$	−16.7379	−0.701691	−0.350846	+	0.936433i	$0.614106\pi$
$570$	−13.4088	−0.561633
$571$	−26.1671	−1.09506	−0.547530	−	0.836786i	$-0.684432\pi$
$571$	−26.1671	−1.09506	−0.547530	+	0.836786i	$0.684432\pi$
$572$	−9.06566	−0.379054
$573$	−8.96236	−0.374408
$574$	0	0
$575$	−1.65685	−0.0690956
$576$	1.00000	0.0416667
$577$	19.7972	0.824166	0.412083	−	0.911146i	$-0.364801\pi$
$577$	19.7972	0.824166	0.412083	+	0.911146i	$0.364801\pi$
$578$	−5.72950	−0.238316
$579$	11.6390	0.483701
$580$	9.48146	0.393696
$581$	0	0
$582$	−4.47127	−0.185340
$583$	18.8430	0.780397
$584$	11.5191	0.476664
$585$	−3.99618	−0.165222
$586$	−31.4853	−1.30064
$587$	−3.20078	−0.132110	−0.0660551	−	0.997816i	$-0.521041\pi$
$587$	−3.20078	−0.132110	−0.0660551	+	0.997816i	$0.521041\pi$
$588$	0	0
$589$	−77.1421	−3.17858
$590$	−0.861685	−0.0354750
$591$	9.58157	0.394133
$592$	−1.03764	−0.0426469
$593$	−32.1033	−1.31832	−0.659162	−	0.752001i	$-0.729089\pi$
$593$	−32.1033	−1.31832	−0.659162	+	0.752001i	$0.729089\pi$
$594$	4.14794	0.170192
$595$	0	0
$596$	19.3577	0.792923
$597$	−9.95273	−0.407338
$598$	−2.18558	−0.0893751
$599$	45.1842	1.84617	0.923087	−	0.384590i	$-0.125657\pi$
$599$	45.1842	1.84617	0.923087	+	0.384590i	$0.125657\pi$
$600$	−1.65685	−0.0676408
$601$	15.5166	0.632934	0.316467	−	0.948604i	$-0.397503\pi$
$601$	15.5166	0.632934	0.316467	+	0.948604i	$0.397503\pi$
$602$	0	0
$603$	13.4050	0.545893
$604$	5.58420	0.227218
$605$	11.3461	0.461285
$606$	15.3061	0.621766
$607$	4.86225	0.197353	0.0986763	−	0.995120i	$-0.468539\pi$
$607$	4.86225	0.197353	0.0986763	+	0.995120i	$0.468539\pi$
$608$	−7.33352	−0.297414
$609$	0	0
$610$	−26.9553	−1.09139
$611$	−15.7870	−0.638672
$612$	−3.35716	−0.135705
$613$	6.80998	0.275052	0.137526	−	0.990498i	$-0.456085\pi$
$613$	6.80998	0.275052	0.137526	+	0.990498i	$0.456085\pi$
$614$	1.64865	0.0665340
$615$	13.4088	0.540695
$616$	0	0
$617$	7.70087	0.310025	0.155013	−	0.987912i	$-0.450458\pi$
$617$	7.70087	0.310025	0.155013	+	0.987912i	$0.450458\pi$
$618$	7.40499	0.297872
$619$	3.13657	0.126069	0.0630346	−	0.998011i	$-0.479922\pi$
$619$	3.13657	0.126069	0.0630346	+	0.998011i	$0.479922\pi$
$620$	19.2334	0.772433
$621$	1.00000	0.0401286
$622$	12.1779	0.488291
$623$	0	0
$624$	−2.18558	−0.0874933
$625$	−13.9706	−0.558823
$626$	12.5669	0.502276
$627$	−30.4190	−1.21482
$628$	−22.7902	−0.909427
$629$	3.48353	0.138898
$630$	0	0
$631$	−22.1045	−0.879966	−0.439983	−	0.898006i	$-0.645016\pi$
$631$	−22.1045	−0.879966	−0.439983	+	0.898006i	$0.645016\pi$
$632$	−5.18558	−0.206271
$633$	0.303519	0.0120638
$634$	−9.17794	−0.364503
$635$	11.8685	0.470986
$636$	4.54274	0.180131
$637$	0	0
$638$	21.5095	0.851568
$639$	14.1856	0.561173
$640$	1.82843	0.0722749
$641$	−18.5483	−0.732614	−0.366307	−	0.930494i	$-0.619378\pi$
$641$	−18.5483	−0.732614	−0.366307	+	0.930494i	$0.619378\pi$
$642$	−5.50127	−0.217118
$643$	−12.4114	−0.489456	−0.244728	−	0.969592i	$-0.578699\pi$
$643$	−12.4114	−0.489456	−0.244728	+	0.969592i	$0.578699\pi$
$644$	0	0
$645$	9.80216	0.385959
$646$	24.6198	0.968652
$647$	37.8202	1.48686	0.743432	−	0.668811i	$-0.233197\pi$
$647$	37.8202	1.48686	0.743432	+	0.668811i	$0.233197\pi$
$648$	1.00000	0.0392837
$649$	−1.95480	−0.0767328
$650$	3.62119	0.142035
$651$	0	0
$652$	−25.4368	−0.996183
$653$	19.5095	0.763465	0.381732	−	0.924273i	$-0.375328\pi$
$653$	19.5095	0.763465	0.381732	+	0.924273i	$0.375328\pi$
$654$	−18.6951	−0.731035
$655$	−8.06119	−0.314977
$656$	7.33352	0.286326
$657$	11.5191	0.449403
$658$	0	0
$659$	−33.6772	−1.31188	−0.655939	−	0.754814i	$-0.727727\pi$
$659$	−33.6772	−1.31188	−0.655939	+	0.754814i	$0.727727\pi$
$660$	7.58420	0.295215
$661$	27.3966	1.06561	0.532803	−	0.846239i	$-0.321139\pi$
$661$	27.3966	1.06561	0.532803	+	0.846239i	$0.321139\pi$
$662$	−29.3896	−1.14226
$663$	7.33734	0.284959
$664$	5.80479	0.225270
$665$	0	0
$666$	−1.03764	−0.0402079
$667$	5.18558	0.200787
$668$	−22.1185	−0.855791
$669$	−16.9375	−0.654843
$670$	24.5100	0.946906
$671$	−61.1503	−2.36068
$672$	0	0
$673$	7.79715	0.300558	0.150279	−	0.988644i	$-0.451983\pi$
$673$	7.79715	0.300558	0.150279	+	0.988644i	$0.451983\pi$
$674$	8.12048	0.312789
$675$	−1.65685	−0.0637723
$676$	−8.22323	−0.316278
$677$	−0.0566580	−0.00217755	−0.00108877	−	0.999999i	$-0.500347\pi$
$677$	−0.0566580	−0.00217755	−0.00108877	+	0.999999i	$0.500347\pi$
$678$	5.28187	0.202849
$679$	0	0
$680$	−6.13831	−0.235394
$681$	−21.5369	−0.825297
$682$	43.6326	1.67078
$683$	−35.9635	−1.37610	−0.688052	−	0.725661i	$-0.741534\pi$
$683$	−35.9635	−1.37610	−0.688052	+	0.725661i	$0.741534\pi$
$684$	−7.33352	−0.280404
$685$	3.07265	0.117400
$686$	0	0
$687$	−0.666478	−0.0254277
$688$	5.36098	0.204385
$689$	−9.92853	−0.378247
$690$	1.82843	0.0696070
$691$	−22.0362	−0.838298	−0.419149	−	0.907918i	$-0.637671\pi$
$691$	−22.0362	−0.838298	−0.419149	+	0.907918i	$0.637671\pi$
$692$	−13.6849	−0.520221
$693$	0	0
$694$	28.2614	1.07279
$695$	−24.3431	−0.923388
$696$	5.18558	0.196559
$697$	−24.6198	−0.932540
$698$	24.1307	0.913359
$699$	−1.67667	−0.0634174
$700$	0	0
$701$	37.5337	1.41763	0.708814	−	0.705396i	$-0.249231\pi$
$701$	37.5337	1.41763	0.708814	+	0.705396i	$0.249231\pi$
$702$	−2.18558	−0.0824895
$703$	7.60959	0.287001
$704$	4.14794	0.156331
$705$	13.2071	0.497410
$706$	13.4088	0.504647
$707$	0	0
$708$	−0.471271	−0.0177115
$709$	40.9788	1.53899	0.769495	−	0.638653i	$-0.220508\pi$
$709$	40.9788	1.53899	0.769495	+	0.638653i	$0.220508\pi$
$710$	25.9373	0.973410
$711$	−5.18558	−0.194475
$712$	6.69450	0.250887
$713$	10.5191	0.393944
$714$	0	0
$715$	−16.5759	−0.619904
$716$	−2.77677	−0.103773
$717$	10.7220	0.400419
$718$	−3.88509	−0.144990
$719$	17.7397	0.661579	0.330789	−	0.943705i	$-0.392685\pi$
$719$	17.7397	0.661579	0.330789	+	0.943705i	$0.392685\pi$
$720$	1.82843	0.0681415
$721$	0	0
$722$	34.7805	1.29440
$723$	18.2034	0.676992
$724$	−20.9629	−0.779081
$725$	−8.59176	−0.319090
$726$	6.20540	0.230304
$727$	14.4240	0.534957	0.267478	−	0.963564i	$-0.413810\pi$
$727$	14.4240	0.534957	0.267478	+	0.963564i	$0.413810\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	21.0618	0.779534
$731$	−17.9976	−0.665667
$732$	−14.7423	−0.544892
$733$	−31.6854	−1.17033	−0.585164	−	0.810915i	$-0.698970\pi$
$733$	−31.6854	−1.17033	−0.585164	+	0.810915i	$0.698970\pi$
$734$	−1.43745	−0.0530572
$735$	0	0
$736$	1.00000	0.0368605
$737$	55.6031	2.04817
$738$	7.33352	0.269951
$739$	−4.20021	−0.154507	−0.0772536	−	0.997011i	$-0.524615\pi$
$739$	−4.20021	−0.154507	−0.0772536	+	0.997011i	$0.524615\pi$
$740$	−1.89726	−0.0697445
$741$	16.0280	0.588804
$742$	0	0
$743$	−42.3168	−1.55245	−0.776227	−	0.630454i	$-0.782869\pi$
$743$	−42.3168	−1.55245	−0.776227	+	0.630454i	$0.782869\pi$
$744$	10.5191	0.385649
$745$	35.3942	1.29674
$746$	18.2959	0.669860
$747$	5.80479	0.212386
$748$	−13.9253	−0.509159
$749$	0	0
$750$	−12.1716	−0.444443
$751$	16.4444	0.600064	0.300032	−	0.953929i	$-0.403003\pi$
$751$	16.4444	0.600064	0.300032	+	0.953929i	$0.403003\pi$
$752$	7.22323	0.263404
$753$	−0.794604	−0.0289570
$754$	−11.3335	−0.412743
$755$	10.2103	0.371591
$756$	0	0
$757$	45.4215	1.65087	0.825437	−	0.564494i	$-0.190929\pi$
$757$	45.4215	1.65087	0.825437	+	0.564494i	$0.190929\pi$
$758$	−5.97637	−0.217071
$759$	4.14794	0.150561
$760$	−13.4088	−0.486389
$761$	15.6421	0.567027	0.283513	−	0.958968i	$-0.408500\pi$
$761$	15.6421	0.567027	0.283513	+	0.958968i	$0.408500\pi$
$762$	6.49108	0.235147
$763$	0	0
$764$	−8.96236	−0.324247
$765$	−6.13831	−0.221931
$766$	−5.89726	−0.213077
$767$	1.03000	0.0371912
$768$	1.00000	0.0360844
$769$	−14.1205	−0.509198	−0.254599	−	0.967047i	$-0.581943\pi$
$769$	−14.1205	−0.509198	−0.254599	+	0.967047i	$0.581943\pi$
$770$	0	0
$771$	−0.591190	−0.0212912
$772$	11.6390	0.418898
$773$	17.6052	0.633215	0.316608	−	0.948557i	$-0.397456\pi$
$773$	17.6052	0.633215	0.316608	+	0.948557i	$0.397456\pi$
$774$	5.36098	0.192696
$775$	−17.4286	−0.626055
$776$	−4.47127	−0.160509
$777$	0	0
$778$	−17.1135	−0.613549
$779$	−53.7805	−1.92689
$780$	−3.99618	−0.143086
$781$	58.8409	2.10549
$782$	−3.35716	−0.120052
$783$	5.18558	0.185318
$784$	0	0
$785$	−41.6702	−1.48727
$786$	−4.40881	−0.157257
$787$	−8.75832	−0.312201	−0.156100	−	0.987741i	$-0.549892\pi$
$787$	−8.75832	−0.312201	−0.156100	+	0.987741i	$0.549892\pi$
$788$	9.58157	0.341329
$789$	2.86725	0.102077
$790$	−9.48146	−0.337335
$791$	0	0
$792$	4.14794	0.147391
$793$	32.2206	1.14419
$794$	−12.8450	−0.455851
$795$	8.30607	0.294586
$796$	−9.95273	−0.352765
$797$	16.5708	0.586966	0.293483	−	0.955964i	$-0.405186\pi$
$797$	16.5708	0.586966	0.293483	+	0.955964i	$0.405186\pi$
$798$	0	0
$799$	−24.2495	−0.857886
$800$	−1.65685	−0.0585786
$801$	6.69450	0.236538
$802$	17.4330	0.615581
$803$	47.7805	1.68614
$804$	13.4050	0.472758
$805$	0	0
$806$	−22.9904	−0.809801
$807$	−7.17794	−0.252676
$808$	15.3061	0.538466
$809$	27.8553	0.979339	0.489669	−	0.871908i	$-0.337117\pi$
$809$	27.8553	0.979339	0.489669	+	0.871908i	$0.337117\pi$
$810$	1.82843	0.0642444
$811$	31.5623	1.10830	0.554151	−	0.832416i	$-0.313043\pi$
$811$	31.5623	1.10830	0.554151	+	0.832416i	$0.313043\pi$
$812$	0	0
$813$	−10.5191	−0.368921
$814$	−4.30408	−0.150858
$815$	−46.5094	−1.62915
$816$	−3.35716	−0.117524
$817$	−39.3148	−1.37545
$818$	−9.06765	−0.317043
$819$	0	0
$820$	13.4088	0.468256
$821$	−24.9930	−0.872262	−0.436131	−	0.899883i	$-0.643652\pi$
$821$	−24.9930	−0.872262	−0.436131	+	0.899883i	$0.643652\pi$
$822$	1.68049	0.0586138
$823$	−8.08803	−0.281931	−0.140965	−	0.990015i	$-0.545021\pi$
$823$	−8.08803	−0.281931	−0.140965	+	0.990015i	$0.545021\pi$
$824$	7.40499	0.257965
$825$	−6.87253	−0.239271
$826$	0	0
$827$	−19.3864	−0.674130	−0.337065	−	0.941481i	$-0.609434\pi$
$827$	−19.3864	−0.674130	−0.337065	+	0.941481i	$0.609434\pi$
$828$	1.00000	0.0347524
$829$	26.8252	0.931677	0.465838	−	0.884870i	$-0.345753\pi$
$829$	26.8252	0.931677	0.465838	+	0.884870i	$0.345753\pi$
$830$	10.6136	0.368405
$831$	−30.9285	−1.07290
$832$	−2.18558	−0.0757715
$833$	0	0
$834$	−13.3137	−0.461016
$835$	−40.4421	−1.39956
$836$	−30.4190	−1.05206
$837$	10.5191	0.363593
$838$	−6.63902	−0.229341
$839$	−4.82979	−0.166743	−0.0833715	−	0.996519i	$-0.526569\pi$
$839$	−4.82979	−0.166743	−0.0833715	+	0.996519i	$0.526569\pi$
$840$	0	0
$841$	−2.10973	−0.0727493
$842$	−0.942543	−0.0324822
$843$	−2.09949	−0.0723102
$844$	0.303519	0.0104476
$845$	−15.0356	−0.517239
$846$	7.22323	0.248340
$847$	0	0
$848$	4.54274	0.155998
$849$	20.3475	0.698325
$850$	5.56232	0.190786
$851$	−1.03764	−0.0355700
$852$	14.1856	0.485990
$853$	15.3330	0.524990	0.262495	−	0.964933i	$-0.415455\pi$
$853$	15.3330	0.524990	0.262495	+	0.964933i	$0.415455\pi$
$854$	0	0
$855$	−13.4088	−0.458572
$856$	−5.50127	−0.188030
$857$	−37.6025	−1.28448	−0.642239	−	0.766505i	$-0.721994\pi$
$857$	−37.6025	−1.28448	−0.642239	+	0.766505i	$0.721994\pi$
$858$	−9.06566	−0.309497
$859$	37.1257	1.26671	0.633356	−	0.773861i	$-0.281677\pi$
$859$	37.1257	1.26671	0.633356	+	0.773861i	$0.281677\pi$
$860$	9.80216	0.334251
$861$	0	0
$862$	−35.3697	−1.20470
$863$	33.1461	1.12831	0.564154	−	0.825670i	$-0.309202\pi$
$863$	33.1461	1.12831	0.564154	+	0.825670i	$0.309202\pi$
$864$	1.00000	0.0340207
$865$	−25.0218	−0.850767
$866$	32.7627	1.11332
$867$	−5.72950	−0.194584
$868$	0	0
$869$	−21.5095	−0.729659
$870$	9.48146	0.321452
$871$	−29.2977	−0.992715
$872$	−18.6951	−0.633095
$873$	−4.47127	−0.151330
$874$	−7.33352	−0.248060
$875$	0	0
$876$	11.5191	0.389194
$877$	32.8603	1.10961	0.554806	−	0.831980i	$-0.312792\pi$
$877$	32.8603	1.10961	0.554806	+	0.831980i	$0.312792\pi$
$878$	−19.3163	−0.651895
$879$	−31.4853	−1.06197
$880$	7.58420	0.255663
$881$	10.6907	0.360178	0.180089	−	0.983650i	$-0.442361\pi$
$881$	10.6907	0.360178	0.180089	+	0.983650i	$0.442361\pi$
$882$	0	0
$883$	5.83725	0.196439	0.0982196	−	0.995165i	$-0.468685\pi$
$883$	5.83725	0.196439	0.0982196	+	0.995165i	$0.468685\pi$
$884$	7.33734	0.246782
$885$	−0.861685	−0.0289652
$886$	14.4088	0.484073
$887$	54.0917	1.81622	0.908111	−	0.418730i	$-0.137525\pi$
$887$	54.0917	1.81622	0.908111	+	0.418730i	$0.137525\pi$
$888$	−1.03764	−0.0348211
$889$	0	0
$890$	12.2404	0.410299
$891$	4.14794	0.138961
$892$	−16.9375	−0.567111
$893$	−52.9717	−1.77263
$894$	19.3577	0.647419
$895$	−5.07713	−0.169710
$896$	0	0
$897$	−2.18558	−0.0729745
$898$	−11.0580	−0.369011
$899$	54.5477	1.81927
$900$	−1.65685	−0.0552285
$901$	−15.2507	−0.508074
$902$	30.4190	1.01284
$903$	0	0
$904$	5.28187	0.175672
$905$	−38.3292	−1.27410
$906$	5.58420	0.185523
$907$	−13.1289	−0.435939	−0.217969	−	0.975956i	$-0.569943\pi$
$907$	−13.1289	−0.435939	−0.217969	+	0.975956i	$0.569943\pi$
$908$	−21.5369	−0.714728
$909$	15.3061	0.507670
$910$	0	0
$911$	2.77432	0.0919172	0.0459586	−	0.998943i	$-0.485366\pi$
$911$	2.77432	0.0919172	0.0459586	+	0.998943i	$0.485366\pi$
$912$	−7.33352	−0.242837
$913$	24.0779	0.796863
$914$	−25.8450	−0.854876
$915$	−26.9553	−0.891114
$916$	−0.666478	−0.0220211
$917$	0	0
$918$	−3.35716	−0.110803
$919$	−21.1868	−0.698887	−0.349443	−	0.936957i	$-0.613629\pi$
$919$	−21.1868	−0.698887	−0.349443	+	0.936957i	$0.613629\pi$
$920$	1.82843	0.0602815
$921$	1.64865	0.0543248
$922$	−39.3341	−1.29540
$923$	−31.0038	−1.02050
$924$	0	0
$925$	1.71923	0.0565278
$926$	25.0778	0.824109
$927$	7.40499	0.243212
$928$	5.18558	0.170225
$929$	−36.0478	−1.18269	−0.591346	−	0.806418i	$-0.701403\pi$
$929$	−36.0478	−1.18269	−0.591346	+	0.806418i	$0.701403\pi$
$930$	19.2334	0.630689
$931$	0	0
$932$	−1.67667	−0.0549211
$933$	12.1779	0.398688
$934$	−22.9629	−0.751370
$935$	−25.4614	−0.832675
$936$	−2.18558	−0.0714380
$937$	−14.4789	−0.473005	−0.236503	−	0.971631i	$-0.576001\pi$
$937$	−14.4789	−0.473005	−0.236503	+	0.971631i	$0.576001\pi$
$938$	0	0
$939$	12.5669	0.410107
$940$	13.2071	0.430770
$941$	−40.2996	−1.31373	−0.656865	−	0.754008i	$-0.728118\pi$
$941$	−40.2996	−1.31373	−0.656865	+	0.754008i	$0.728118\pi$
$942$	−22.7902	−0.742544
$943$	7.33352	0.238812
$944$	−0.471271	−0.0153386
$945$	0	0
$946$	22.2370	0.722987
$947$	−55.4602	−1.80222	−0.901108	−	0.433595i	$-0.857245\pi$
$947$	−55.4602	−1.80222	−0.901108	+	0.433595i	$0.857245\pi$
$948$	−5.18558	−0.168420
$949$	−25.1760	−0.817246
$950$	12.1506	0.394217
$951$	−9.17794	−0.297615
$952$	0	0
$953$	−42.0164	−1.36105	−0.680523	−	0.732727i	$-0.738247\pi$
$953$	−42.0164	−1.36105	−0.680523	+	0.732727i	$0.738247\pi$
$954$	4.54274	0.147077
$955$	−16.3870	−0.530271
$956$	10.7220	0.346773
$957$	21.5095	0.695303
$958$	−16.6116	−0.536695
$959$	0	0
$960$	1.82843	0.0590122
$961$	79.6516	2.56941
$962$	2.26786	0.0731187
$963$	−5.50127	−0.177276
$964$	18.2034	0.586292
$965$	21.2811	0.685063
$966$	0	0
$967$	6.71167	0.215833	0.107916	−	0.994160i	$-0.465582\pi$
$967$	6.71167	0.215833	0.107916	+	0.994160i	$0.465582\pi$
$968$	6.20540	0.199449
$969$	24.6198	0.790901
$970$	−8.17539	−0.262496
$971$	37.4616	1.20220	0.601101	−	0.799173i	$-0.294729\pi$
$971$	37.4616	1.20220	0.601101	+	0.799173i	$0.294729\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−14.8226	−0.474948
$975$	3.62119	0.115971
$976$	−14.7423	−0.471891
$977$	53.2632	1.70404	0.852020	−	0.523509i	$-0.175377\pi$
$977$	53.2632	1.70404	0.852020	+	0.523509i	$0.175377\pi$
$978$	−25.4368	−0.813380
$979$	27.7684	0.887481
$980$	0	0
$981$	−18.6951	−0.596887
$982$	22.2466	0.709918
$983$	−15.9049	−0.507287	−0.253644	−	0.967298i	$-0.581629\pi$
$983$	−15.9049	−0.507287	−0.253644	+	0.967298i	$0.581629\pi$
$984$	7.33352	0.233784
$985$	17.5192	0.558208
$986$	−17.4088	−0.554409
$987$	0	0
$988$	16.0280	0.509919
$989$	5.36098	0.170469
$990$	7.58420	0.241042
$991$	15.5969	0.495453	0.247727	−	0.968830i	$-0.420317\pi$
$991$	15.5969	0.495453	0.247727	+	0.968830i	$0.420317\pi$
$992$	10.5191	0.333982
$993$	−29.3896	−0.932650
$994$	0	0
$995$	−18.1978	−0.576910
$996$	5.80479	0.183932
$997$	−8.75450	−0.277258	−0.138629	−	0.990344i	$-0.544270\pi$
$997$	−8.75450	−0.277258	−0.138629	+	0.990344i	$0.544270\pi$
$998$	−11.2857	−0.357242
$999$	−1.03764	−0.0328296

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cp.1.4		4
7.2	even	3		966.2.i.l.277.1	✓	8
7.4	even	3		966.2.i.l.415.1	yes	8
7.6	odd	2		6762.2.a.cm.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.l.277.1	✓	8	7.2	even	3
966.2.i.l.415.1	yes	8	7.4	even	3
6762.2.a.cm.1.2		4	7.6	odd	2
6762.2.a.cp.1.4		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.82843 q^{5} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +1.82843 q^{10} +4.14794 q^{11} +1.00000 q^{12} -2.18558 q^{13} +1.82843 q^{15} +1.00000 q^{16} -3.35716 q^{17} +1.00000 q^{18} -7.33352 q^{19} +1.82843 q^{20} +4.14794 q^{22} +1.00000 q^{23} +1.00000 q^{24} -1.65685 q^{25} -2.18558 q^{26} +1.00000 q^{27} +5.18558 q^{29} +1.82843 q^{30} +10.5191 q^{31} +1.00000 q^{32} +4.14794 q^{33} -3.35716 q^{34} +1.00000 q^{36} -1.03764 q^{37} -7.33352 q^{38} -2.18558 q^{39} +1.82843 q^{40} +7.33352 q^{41} +5.36098 q^{43} +4.14794 q^{44} +1.82843 q^{45} +1.00000 q^{46} +7.22323 q^{47} +1.00000 q^{48} -1.65685 q^{50} -3.35716 q^{51} -2.18558 q^{52} +4.54274 q^{53} +1.00000 q^{54} +7.58420 q^{55} -7.33352 q^{57} +5.18558 q^{58} -0.471271 q^{59} +1.82843 q^{60} -14.7423 q^{61} +10.5191 q^{62} +1.00000 q^{64} -3.99618 q^{65} +4.14794 q^{66} +13.4050 q^{67} -3.35716 q^{68} +1.00000 q^{69} +14.1856 q^{71} +1.00000 q^{72} +11.5191 q^{73} -1.03764 q^{74} -1.65685 q^{75} -7.33352 q^{76} -2.18558 q^{78} -5.18558 q^{79} +1.82843 q^{80} +1.00000 q^{81} +7.33352 q^{82} +5.80479 q^{83} -6.13831 q^{85} +5.36098 q^{86} +5.18558 q^{87} +4.14794 q^{88} +6.69450 q^{89} +1.82843 q^{90} +1.00000 q^{92} +10.5191 q^{93} +7.22323 q^{94} -13.4088 q^{95} +1.00000 q^{96} -4.47127 q^{97} +4.14794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 6 q^{11} + 4 q^{12} + 6 q^{13} - 4 q^{15} + 4 q^{16} - 10 q^{17} + 4 q^{18} - 4 q^{19} - 4 q^{20} + 6 q^{22} + 4 q^{23} + 4 q^{24} + 16 q^{25} + 6 q^{26} + 4 q^{27} + 6 q^{29} - 4 q^{30} + 2 q^{31} + 4 q^{32} + 6 q^{33} - 10 q^{34} + 4 q^{36} - 4 q^{38} + 6 q^{39} - 4 q^{40} + 4 q^{41} + 20 q^{43} + 6 q^{44} - 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 16 q^{50} - 10 q^{51} + 6 q^{52} + 4 q^{54} + 10 q^{55} - 4 q^{57} + 6 q^{58} + 6 q^{59} - 4 q^{60} + 2 q^{62} + 4 q^{64} - 14 q^{65} + 6 q^{66} + 18 q^{67} - 10 q^{68} + 4 q^{69} + 42 q^{71} + 4 q^{72} + 6 q^{73} + 16 q^{75} - 4 q^{76} + 6 q^{78} - 6 q^{79} - 4 q^{80} + 4 q^{81} + 4 q^{82} - 10 q^{83} + 34 q^{85} + 20 q^{86} + 6 q^{87} + 6 q^{88} - 4 q^{90} + 4 q^{92} + 2 q^{93} + 10 q^{94} - 20 q^{95} + 4 q^{96} - 10 q^{97} + 6 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 6 * q^11 + 4 * q^12 + 6 * q^13 - 4 * q^15 + 4 * q^16 - 10 * q^17 + 4 * q^18 - 4 * q^19 - 4 * q^20 + 6 * q^22 + 4 * q^23 + 4 * q^24 + 16 * q^25 + 6 * q^26 + 4 * q^27 + 6 * q^29 - 4 * q^30 + 2 * q^31 + 4 * q^32 + 6 * q^33 - 10 * q^34 + 4 * q^36 - 4 * q^38 + 6 * q^39 - 4 * q^40 + 4 * q^41 + 20 * q^43 + 6 * q^44 - 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 16 * q^50 - 10 * q^51 + 6 * q^52 + 4 * q^54 + 10 * q^55 - 4 * q^57 + 6 * q^58 + 6 * q^59 - 4 * q^60 + 2 * q^62 + 4 * q^64 - 14 * q^65 + 6 * q^66 + 18 * q^67 - 10 * q^68 + 4 * q^69 + 42 * q^71 + 4 * q^72 + 6 * q^73 + 16 * q^75 - 4 * q^76 + 6 * q^78 - 6 * q^79 - 4 * q^80 + 4 * q^81 + 4 * q^82 - 10 * q^83 + 34 * q^85 + 20 * q^86 + 6 * q^87 + 6 * q^88 - 4 * q^90 + 4 * q^92 + 2 * q^93 + 10 * q^94 - 20 * q^95 + 4 * q^96 - 10 * q^97 + 6 * q^99

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