LMFDB - Embedded newform 567.2.bd.a.206.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(17,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([11, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.bd (of order $18$, degree $6$, not minimal)

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:	no
Analytic conductor:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			206.14
Character	$\chi$	$=$	567.206
Dual form			567.2.bd.a.278.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.170792 - 0.469247i) q^{2} +(1.34107 + 1.12529i) q^{4} +(0.000430671 + 0.000361376i) q^{5} +(1.75023 - 1.98411i) q^{7} +(1.62200 - 0.936464i) q^{8} +(0.000243130 - 0.000140371i) q^{10} +(-3.04392 - 3.62761i) q^{11} +(1.77003 - 2.10944i) q^{13} +(-0.632115 - 1.16016i) q^{14} +(0.445582 + 2.52702i) q^{16} +(0.400086 + 0.692969i) q^{17} +(4.50743 + 2.60237i) q^{19} +(0.000170906 + 0.000969257i) q^{20} +(-2.22212 + 0.808787i) q^{22} +(-0.542669 - 1.49097i) q^{23} +(-0.868241 - 4.92404i) q^{25} +(-0.687542 - 1.19086i) q^{26} +(4.57987 - 0.691318i) q^{28} +(5.40692 + 6.44372i) q^{29} +(-5.19122 + 6.18666i) q^{31} +(4.95085 + 0.872968i) q^{32} +(0.393506 - 0.0693856i) q^{34} +(0.00147078 - 0.000222010i) q^{35} +2.05581 q^{37} +(1.99099 - 1.67064i) q^{38} +(0.00103696 + 0.000182845i) q^{40} +(5.20305 + 4.36588i) q^{41} +(-6.39715 - 2.32837i) q^{43} -8.29015i q^{44} -0.792318 q^{46} +(5.68085 - 4.76680i) q^{47} +(-0.873412 - 6.94530i) q^{49} +(-2.45888 - 0.433567i) q^{50} +(4.74745 - 0.837104i) q^{52} +(-9.11266 - 5.26120i) q^{53} -0.00266231i q^{55} +(0.980823 - 4.85726i) q^{56} +(3.94716 - 1.43665i) q^{58} +(-2.29410 + 13.0105i) q^{59} +(-2.33638 - 2.78438i) q^{61} +(2.01645 + 3.49260i) q^{62} +(-1.31080 + 2.27037i) q^{64} +(0.00152460 - 0.000268828i) q^{65} +(-1.99848 + 0.727386i) q^{67} +(-0.243248 + 1.37953i) q^{68} +(0.000147020 - 0.000728078i) q^{70} +(-7.56979 - 4.37042i) q^{71} +7.18246i q^{73} +(0.351116 - 0.964683i) q^{74} +(3.11635 + 8.56210i) q^{76} +(-12.5251 - 0.309645i) q^{77} +(-2.42128 - 0.881273i) q^{79} +(-0.000721305 + 0.00124934i) q^{80} +(2.93732 - 1.69586i) q^{82} +(-1.47761 + 1.23986i) q^{83} +(-7.81169e-5 + 0.000443023i) q^{85} +(-2.18517 + 2.60418i) q^{86} +(-8.33438 - 3.03347i) q^{88} +(1.61790 - 2.80229i) q^{89} +(-1.08741 - 7.20394i) q^{91} +(0.950016 - 2.61015i) q^{92} +(-1.26656 - 3.47986i) q^{94} +(0.00100079 + 0.00274964i) q^{95} +(0.614218 - 1.68755i) q^{97} +(-3.40823 - 0.776355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	0.170792	−	0.469247i	0.120768	−	0.331808i	−0.864547	−	0.502551i	$-0.832395\pi$
$2$	0.170792	−	0.469247i	0.120768	−	0.331808i	0.985316	+	0.170744i	$0.0546169\pi$
$3$		0			0
$3$		0			0
$4$	1.34107	+	1.12529i	0.670533	+	0.562644i
$5$	0.000430671	0	0.000361376i	0.000192602	0	0.000161612i	0.642884	−	0.765964i	$-0.277738\pi$
$5$	0.000430671	0	0.000361376i	0.000192602	0	0.000161612i	−0.642691	+	0.766125i	$0.722182\pi$
$6$		0			0
$7$	1.75023	−	1.98411i	0.661524	−	0.749924i
$7$	1.75023	−	1.98411i	0.661524	−	0.749924i
$8$	1.62200	−	0.936464i	0.573465	−	0.331090i
$9$		0			0
$10$	0.000243130	0	0.000140371i	7.68844e−5	0	4.43892e-5i
$11$	−3.04392	−	3.62761i	−0.917778	−	1.09376i	−0.995306	−	0.0967748i	$-0.969147\pi$
$11$	−3.04392	−	3.62761i	−0.917778	−	1.09376i	0.0775286	−	0.996990i	$-0.475297\pi$
$12$		0			0
$13$	1.77003	−	2.10944i	0.490918	−	0.585053i	−0.462533	−	0.886602i	$-0.653059\pi$
$13$	1.77003	−	2.10944i	0.490918	−	0.585053i	0.953451	+	0.301549i	$0.0975036\pi$
$14$	−0.632115	−	1.16016i	−0.168940	−	0.310066i
$15$		0			0
$16$	0.445582	+	2.52702i	0.111395	+	0.631755i
$17$	0.400086	+	0.692969i	0.0970351	+	0.168070i	0.910456	−	0.413606i	$-0.135731\pi$
$17$	0.400086	+	0.692969i	0.0970351	+	0.168070i	−0.813421	+	0.581675i	$0.802397\pi$
$18$		0			0
$19$	4.50743	+	2.60237i	1.03408	+	0.597024i	0.918150	−	0.396234i	$-0.129683\pi$
$19$	4.50743	+	2.60237i	1.03408	+	0.597024i	0.115926	+	0.993258i	$0.463016\pi$
$20$	0.000170906	0	0.000969257i	3.82158e−5	0	0.000216732i
$21$		0			0
$22$	−2.22212	+	0.808787i	−0.473758	+	0.172434i
$23$	−0.542669	−	1.49097i	−0.113154	−	0.310889i	0.870169	−	0.492753i	$-0.164009\pi$
$23$	−0.542669	−	1.49097i	−0.113154	−	0.310889i	−0.983324	+	0.181864i	$0.941787\pi$
$24$		0			0
$25$	−0.868241	−	4.92404i	−0.173648	−	0.984808i
$26$	−0.687542	−	1.19086i	−0.134838	−	0.233546i
$27$		0			0
$28$	4.57987	−	0.691318i	0.865514	−	0.130647i
$29$	5.40692	+	6.44372i	1.00404	+	1.19657i	0.980434	+	0.196847i	$0.0630702\pi$
$29$	5.40692	+	6.44372i	1.00404	+	1.19657i	0.0236057	+	0.999721i	$0.492485\pi$
$30$		0			0
$31$	−5.19122	+	6.18666i	−0.932371	+	1.11116i	0.0612205	+	0.998124i	$0.480501\pi$
$31$	−5.19122	+	6.18666i	−0.932371	+	1.11116i	−0.993591	+	0.113032i	$0.963944\pi$
$32$	4.95085	+	0.872968i	0.875194	+	0.154320i
$33$		0			0
$34$	0.393506	−	0.0693856i	0.0674856	−	0.0118995i
$35$	0.00147078		0.000222010i	0.000248608		3.75266e-5i
$36$		0			0
$37$	2.05581			0.337973			0.168986	−	0.985618i	$-0.445951\pi$
$37$	2.05581			0.337973			0.168986	+	0.985618i	$0.445951\pi$
$38$	1.99099	−	1.67064i	0.322981	−	0.271013i
$39$		0			0
$40$	0.00103696		0.000182845i	0.000163959		2.89103e-5i
$41$	5.20305	+	4.36588i	0.812580	+	0.681836i	0.951222	−	0.308507i	$-0.0998292\pi$
$41$	5.20305	+	4.36588i	0.812580	+	0.681836i	−0.138642	+	0.990343i	$0.544274\pi$
$42$		0			0
$43$	−6.39715	−	2.32837i	−0.975556	−	0.355073i	−0.195445	−	0.980715i	$-0.562615\pi$
$43$	−6.39715	−	2.32837i	−0.975556	−	0.355073i	−0.780111	+	0.625641i	$0.784837\pi$
$44$		−	8.29015i		−	1.24979i
$45$		0			0
$46$	−0.792318			−0.116821
$47$	5.68085	−	4.76680i	0.828638	−	0.695310i	−0.126340	−	0.991987i	$-0.540323\pi$
$47$	5.68085	−	4.76680i	0.828638	−	0.695310i	0.954978	+	0.296677i	$0.0958786\pi$
$48$		0			0
$49$	−0.873412	−	6.94530i	−0.124773	−	0.992185i
$50$	−2.45888	−	0.433567i	−0.347738	−	0.0613156i
$51$		0			0
$52$	4.74745	−	0.837104i	0.658353	−	0.116085i
$53$	−9.11266	−	5.26120i	−1.25172	−	0.722681i	−0.280269	−	0.959921i	$-0.590424\pi$
$53$	−9.11266	−	5.26120i	−1.25172	−	0.722681i	−0.971451	+	0.237241i	$0.923757\pi$
$54$		0			0
$55$		−	0.00266231i		−	0.000358985i
$56$	0.980823	−	4.85726i	0.131068	−	0.649079i
$57$		0			0
$58$	3.94716	−	1.43665i	0.518287	−	0.188641i
$59$	−2.29410	+	13.0105i	−0.298666	+	1.69382i	0.353251	+	0.935529i	$0.385076\pi$
$59$	−2.29410	+	13.0105i	−0.298666	+	1.69382i	−0.651917	+	0.758291i	$0.726035\pi$
$60$		0			0
$61$	−2.33638	−	2.78438i	−0.299142	−	0.356504i	0.595446	−	0.803395i	$-0.296975\pi$
$61$	−2.33638	−	2.78438i	−0.299142	−	0.356504i	−0.894588	+	0.446892i	$0.852531\pi$
$62$	2.01645	+	3.49260i	0.256090	+	0.443560i
$63$		0			0
$64$	−1.31080	+	2.27037i	−0.163850	+	0.283797i
$65$	0.00152460		0.000268828i	0.000189103		3.33440e-5i
$66$		0			0
$67$	−1.99848	+	0.727386i	−0.244153	+	0.0888644i	−0.461198	−	0.887297i	$-0.652580\pi$
$67$	−1.99848	+	0.727386i	−0.244153	+	0.0888644i	0.217045	+	0.976162i	$0.430358\pi$
$68$	−0.243248	+	1.37953i	−0.0294982	+	0.167292i
$69$		0			0
$70$	0.000147020	0	0.000728078i	1.75723e−5	0	8.70220e-5i
$71$	−7.56979	−	4.37042i	−0.898369	−	0.518673i	−0.0216981	−	0.999765i	$-0.506907\pi$
$71$	−7.56979	−	4.37042i	−0.898369	−	0.518673i	−0.876671	+	0.481091i	$0.840241\pi$
$72$		0			0
$73$			7.18246i			0.840644i	0.907375	+	0.420322i	$0.138083\pi$
$73$			7.18246i			0.840644i	−0.907375	+	0.420322i	$0.861917\pi$
$74$	0.351116	−	0.964683i	0.0408164	−	0.112142i
$75$		0			0
$76$	3.11635	+	8.56210i	0.357470	+	0.982140i
$77$	−12.5251	−	0.309645i	−1.42737	−	0.0352873i
$78$		0			0
$79$	−2.42128	−	0.881273i	−0.272415	−	0.0991510i	0.202201	−	0.979344i	$-0.435191\pi$
$79$	−2.42128	−	0.881273i	−0.272415	−	0.0991510i	−0.474616	+	0.880193i	$0.657413\pi$
$80$	−0.000721305		0.00124934i	−8.06443e−5		0.000139680i
$81$		0			0
$82$	2.93732	−	1.69586i	0.324373	−	0.187277i
$83$	−1.47761	+	1.23986i	−0.162188	+	0.136092i	−0.720270	−	0.693694i	$-0.755982\pi$
$83$	−1.47761	+	1.23986i	−0.162188	+	0.136092i	0.558082	+	0.829786i	$0.311538\pi$
$84$		0			0
$85$	−7.81169e−5	0	0.000443023i	−8.47297e−6	0	4.80526e-5i
$86$	−2.18517	+	2.60418i	−0.235632	+	0.280816i
$87$		0			0
$88$	−8.33438	−	3.03347i	−0.888448	−	0.323369i
$89$	1.61790	−	2.80229i	0.171498	−	0.297043i	−0.767446	−	0.641114i	$-0.778473\pi$
$89$	1.61790	−	2.80229i	0.171498	−	0.297043i	0.938944	+	0.344071i	$0.111806\pi$
$90$		0			0
$91$	−1.08741	−	7.20394i	−0.113992	−	0.755178i
$92$	0.950016	−	2.61015i	0.0990461	−	0.272127i
$93$		0			0
$94$	−1.26656	−	3.47986i	−0.130636	−	0.358920i
$95$	0.00100079	+	0.00274964i	0.000102679	+	0.000282107i
$96$		0			0
$97$	0.614218	−	1.68755i	0.0623644	−	0.171345i	−0.904597	−	0.426268i	$-0.859828\pi$
$97$	0.614218	−	1.68755i	0.0623644	−	0.171345i	0.966961	+	0.254923i	$0.0820502\pi$
$98$	−3.40823	−	0.776355i	−0.344284	−	0.0784237i
$99$		0			0
$100$	4.37659	−	7.58048i	0.437659	−	0.758048i
$101$	4.00251	+	1.45679i	0.398265	+	0.144957i	0.533385	−	0.845873i	$-0.320920\pi$
$101$	4.00251	+	1.45679i	0.398265	+	0.144957i	−0.135120	+	0.990829i	$0.543142\pi$
$102$		0			0
$103$	−10.3365	+	12.3186i	−1.01849	+	1.21379i	−0.0417981	+	0.999126i	$0.513309\pi$
$103$	−10.3365	+	12.3186i	−1.01849	+	1.21379i	−0.976689	+	0.214660i	$0.931136\pi$
$104$	0.895580	−	5.07909i	0.0878189	−	0.498046i
$105$		0			0
$106$	−4.02517	+	3.37752i	−0.390959	+	0.328054i
$107$	3.48765	−	2.01360i	0.337164	−	0.194662i	−0.321853	−	0.946790i	$-0.604306\pi$
$107$	3.48765	−	2.01360i	0.337164	−	0.194662i	0.659017	+	0.752128i	$0.270972\pi$
$108$		0			0
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	−0.836499	−	0.547969i	$-0.815401\pi$
$109$	0.587845	−	1.01818i	0.0563054	−	0.0975238i	0.892804	+	0.450445i	$0.148735\pi$
$110$	−0.00124928		0.000454701i	−0.000119114		4.33540e-5i
$111$		0			0
$112$	5.79376	+	3.53877i	0.547459	+	0.334383i
$113$	5.04317	+	13.8560i	0.474422	+	1.30346i	0.914166	+	0.405340i	$0.132847\pi$
$113$	5.04317	+	13.8560i	0.474422	+	1.30346i	−0.439745	+	0.898123i	$0.644931\pi$
$114$		0			0
$115$	0.000305089	0	0.000838225i	2.84497e−5	0	7.81649e-5i
$116$			14.7258i			1.36726i
$117$		0			0
$118$	5.71332	+	3.29858i	0.525953	+	0.303659i
$119$	2.07517	+	0.419037i	0.190231	+	0.0384131i
$120$		0			0
$121$	−1.98393	+	11.2514i	−0.180358	+	1.02286i
$122$	−1.70560	+	0.620787i	−0.154418	+	0.0562034i
$123$		0			0
$124$	−13.9235	+	2.45510i	−1.25037	+	0.220474i
$125$	0.00281100	−	0.00486880i	0.000251424	−	0.000435479i
$126$		0			0
$127$	−3.46785	−	6.00649i	−0.307722	−	0.532990i	0.670142	−	0.742233i	$-0.266233\pi$
$127$	−3.46785	−	6.00649i	−0.307722	−	0.532990i	−0.977864	+	0.209243i	$0.932900\pi$
$128$	7.30436	+	8.70500i	0.645621	+	0.769421i
$129$		0			0
$130$	0.000134243	0	0.000761329i	1.17739e−5	0	6.67729e-5i
$131$	−10.3810	+	3.77837i	−0.906990	+	0.330117i	−0.753050	−	0.657963i	$-0.771418\pi$
$131$	−10.3810	+	3.77837i	−0.906990	+	0.330117i	−0.153940	+	0.988080i	$0.549196\pi$
$132$		0			0
$133$	13.0524	−	4.38852i	1.13179	−	0.380533i
$134$			1.06201i			0.0917438i
$135$		0			0
$136$	1.29788	+	0.749332i	0.111292	+	0.0642547i
$137$	−9.89957	+	1.74556i	−0.845777	+	0.149133i	−0.579712	−	0.814822i	$-0.696835\pi$
$137$	−9.89957	+	1.74556i	−0.845777	+	0.149133i	−0.266065	+	0.963955i	$0.585724\pi$
$138$		0			0
$139$	−0.409252	−	0.0721623i	−0.0347123	−	0.00612072i	0.156265	−	0.987715i	$-0.450055\pi$
$139$	−0.409252	−	0.0721623i	−0.0347123	−	0.00612072i	−0.190977	+	0.981594i	$0.561166\pi$
$140$	0.00222224	+	0.00135732i	0.000187814	+	0.000114715i
$141$		0			0
$142$	−3.34367	+	2.80567i	−0.280594	+	0.235447i
$143$	−13.0401			−1.09046
$144$		0			0
$145$			0.00472905i			0.000392726i
$146$	3.37035	+	1.22671i	0.278932	+	0.101523i
$147$		0			0
$148$	2.75697	+	2.31338i	0.226622	+	0.190158i
$149$	0.907098	+	0.159946i	0.0743124	+	0.0131033i	0.210681	−	0.977555i	$-0.432432\pi$
$149$	0.907098	+	0.159946i	0.0743124	+	0.0131033i	−0.136368	+	0.990658i	$0.543543\pi$
$150$		0			0
$151$	−0.922118	+	0.773749i	−0.0750409	+	0.0629668i	−0.679537	−	0.733642i	$-0.737819\pi$
$151$	−0.922118	+	0.773749i	−0.0750409	+	0.0629668i	0.604496	+	0.796608i	$0.293375\pi$
$152$	9.74809			0.790674
$153$		0			0
$154$	−2.28450	+	5.82451i	−0.184090	+	0.469352i
$155$	−0.00447142		0.000788431i	−0.000359153		6.33283e-5i
$156$		0			0
$157$	−11.3485	−	2.00104i	−0.905706	−	0.159700i	−0.298653	−	0.954362i	$-0.596537\pi$
$157$	−11.3485	−	2.00104i	−0.905706	−	0.159700i	−0.607053	+	0.794661i	$0.707648\pi$
$158$	−0.827070	+	0.985664i	−0.0657982	+	0.0784152i
$159$		0			0
$160$	0.00181672	+	0.00216508i	0.000143624	+	0.000171164i
$161$	−3.90805	−	1.53282i	−0.307997	−	0.120803i
$162$		0			0
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	0.700268	−	0.713880i	$-0.253064\pi$
$163$	−3.42292	−	5.92867i	−0.268104	−	0.464369i	−0.968372	+	0.249510i	$0.919730\pi$
$164$	2.06477	+	11.7099i	0.161231	+	0.914387i
$165$		0			0
$166$	0.329437	+	0.905120i	0.0255693	+	0.0702510i
$167$	4.35768	−	1.58606i	0.337207	−	0.122733i	−0.167866	−	0.985810i	$-0.553688\pi$
$167$	4.35768	−	1.58606i	0.337207	−	0.122733i	0.505073	+	0.863076i	$0.331465\pi$
$168$		0			0
$169$	0.940696	+	5.33495i	0.0723613	+	0.410381i
$170$	0.000194546	0	0.000112321i	1.49210e−5	0	8.61462e-6i
$171$		0			0
$172$	−5.95891	−	10.3211i	−0.454363	−	0.786979i
$173$	4.17814	+	23.6954i	0.317658	+	1.80153i	0.556914	+	0.830570i	$0.311985\pi$
$173$	4.17814	+	23.6954i	0.317658	+	1.80153i	−0.239256	+	0.970956i	$0.576904\pi$
$174$		0			0
$175$	−11.2895	−	6.89550i	−0.853404	−	0.521250i
$176$	7.81072	−	9.30846i	0.588755	−	0.701651i
$177$		0			0
$178$	−1.03864	−	1.23781i	−0.0778496	−	0.0927776i
$179$	−21.3630	+	12.3339i	−1.59674	+	0.921880i	−0.604634	+	0.796503i	$0.706681\pi$
$179$	−21.3630	+	12.3339i	−1.59674	+	0.921880i	−0.992109	+	0.125377i	$0.959986\pi$
$180$		0			0
$181$	−7.78429	+	4.49426i	−0.578601	+	0.334056i	−0.760577	−	0.649247i	$-0.775084\pi$
$181$	−7.78429	+	4.49426i	−0.578601	+	0.334056i	0.181976	+	0.983303i	$0.441751\pi$
$182$	−3.56615	−	0.720110i	−0.264341	−	0.0533781i
$183$		0			0
$184$	−2.27645	−	1.91017i	−0.167822	−	0.140820i
$185$	0.000885377	0	0.000742919i	6.50942e−5	0	5.46205e-5i
$186$		0			0
$187$	1.29599	−	3.56070i	0.0947721	−	0.260384i
$188$	12.9824			0.946841
$189$		0			0
$190$	0.00146119			0.000106006
$191$	7.13465	−	19.6023i	0.516245	−	1.41837i	−0.358382	−	0.933575i	$-0.616672\pi$
$191$	7.13465	−	19.6023i	0.516245	−	1.41837i	0.874627	−	0.484796i	$-0.161106\pi$
$192$		0			0
$193$	−14.0017	−	11.7489i	−1.00787	−	0.845701i	−0.0198124	−	0.999804i	$-0.506307\pi$
$193$	−14.0017	−	11.7489i	−1.00787	−	0.845701i	−0.988055	+	0.154103i	$0.950751\pi$
$194$	−0.686975	−	0.576440i	−0.0493219	−	0.0413860i
$195$		0			0
$196$	6.64415	−	10.2969i	0.474582	−	0.735496i
$197$	8.92564	−	5.15322i	0.635925	−	0.367152i	−0.147118	−	0.989119i	$-0.547000\pi$
$197$	8.92564	−	5.15322i	0.635925	−	0.367152i	0.783043	+	0.621967i	$0.213666\pi$
$198$		0			0
$199$	−9.67594	+	5.58641i	−0.685909	+	0.396010i	−0.802078	−	0.597220i	$-0.796272\pi$
$199$	−9.67594	+	5.58641i	−0.685909	+	0.396010i	0.116168	+	0.993230i	$0.462939\pi$
$200$	−6.01947	−	7.17373i	−0.425641	−	0.507259i
$201$		0			0
$202$	1.36719	−	1.62936i	0.0961955	−	0.114641i
$203$	22.2484	+	0.550022i	1.56153	+	0.0386040i
$204$		0			0
$205$	0.000663080		0.00376051i	4.63115e−5		0.000262646i
$206$	4.01507	+	6.95430i	0.279743	+	0.484529i
$207$		0			0
$208$	6.11929	+	3.53297i	0.424297	+	0.244968i
$209$	−4.27991	−	24.2726i	−0.296048	−	1.67897i
$210$		0			0
$211$	22.3190	−	8.12346i	1.53651	−	0.559242i	0.571302	−	0.820740i	$-0.306439\pi$
$211$	22.3190	−	8.12346i	1.53651	−	0.559242i	0.965204	+	0.261498i	$0.0842165\pi$
$212$	−6.30032	−	17.3100i	−0.432707	−	1.18885i
$213$		0			0
$214$	−0.349212	−	1.98048i	−0.0238716	−	0.135383i
$215$	−0.00191365	−	0.00331454i	−0.000130510	−	0.000226050i
$216$		0			0
$217$	3.18921	+	21.1280i	0.216498	+	1.43426i
$218$	−0.377378	−	0.449742i	−0.0255593	−	0.0304603i
$219$		0			0
$220$	0.00299586	−	0.00357033i	0.000201981	−	0.000240711i
$221$	2.16994	+	0.382619i	0.145966	+	0.0257378i
$222$		0			0
$223$	23.8004	−	4.19666i	1.59380	−	0.281029i	0.694871	−	0.719134i	$-0.255461\pi$
$223$	23.8004	−	4.19666i	1.59380	−	0.281029i	0.898924	+	0.438105i	$0.144350\pi$
$224$	10.3972	−	8.29515i	0.694690	−	0.554243i
$225$		0			0
$226$	7.36322			0.489794
$227$	3.27753	−	2.75018i	0.217537	−	0.182536i	−0.527506	−	0.849551i	$-0.676873\pi$
$227$	3.27753	−	2.75018i	0.217537	−	0.182536i	0.745044	+	0.667015i	$0.232428\pi$
$228$		0			0
$229$	12.7575	+	2.24949i	0.843037	+	0.148650i	0.578456	−	0.815713i	$-0.303655\pi$
$229$	12.7575	+	2.24949i	0.843037	+	0.148650i	0.264581	+	0.964364i	$0.414766\pi$
$230$	−0.000341228	0	0.000286324i	−2.24999e−5	0	1.88797e-5i
$231$		0			0
$232$	14.8044	+	5.38834i	0.971953	+	0.353762i
$233$			11.2048i			0.734052i	0.930211	+	0.367026i	$0.119624\pi$
$233$			11.2048i			0.734052i	−0.930211	+	0.367026i	$0.880376\pi$
$234$		0			0
$235$	0.00416919			0.000271968
$236$	−17.7171	+	14.8664i	−1.15328	+	0.967719i
$237$		0			0
$238$	0.551055	−	0.902200i	0.0357196	−	0.0584810i
$239$	−12.3508	−	2.17779i	−0.798909	−	0.140869i	−0.240733	−	0.970591i	$-0.577388\pi$
$239$	−12.3508	−	2.17779i	−0.798909	−	0.140869i	−0.558177	+	0.829722i	$0.688499\pi$
$240$		0			0
$241$	−19.7697	+	3.48594i	−1.27348	+	0.224549i	−0.769209	−	0.638997i	$-0.779350\pi$
$241$	−19.7697	+	3.48594i	−1.27348	+	0.224549i	−0.504271	+	0.863546i	$0.668239\pi$
$242$	4.94087	+	2.85261i	0.317611	+	0.183373i
$243$		0			0
$244$		−	6.36314i		−	0.407358i
$245$	0.00213371	−	0.00330677i	0.000136318	−	0.000211262i
$246$		0			0
$247$	13.4678	−	4.90189i	0.856937	−	0.311900i
$248$	−2.62660	+	14.8962i	−0.166789	+	0.945908i
$249$		0			0
$250$	−0.00180458	−	0.00215061i	−0.000114131	−	0.000136016i
$251$	−11.2730	−	19.5255i	−0.711547	−	1.23244i	−0.964276	−	0.264899i	$-0.914661\pi$
$251$	−11.2730	−	19.5255i	−0.711547	−	1.23244i	0.252729	−	0.967537i	$-0.418672\pi$
$252$		0			0
$253$	−3.75681	+	6.50699i	−0.236189	+	0.409091i
$254$	−3.41081	+	0.601418i	−0.214013	+	0.0377363i
$255$		0			0
$256$	0.405328	−	0.147528i	0.0253330	−	0.00922047i
$257$	5.10311	−	28.9412i	0.318323	−	1.80530i	−0.234627	−	0.972085i	$-0.575387\pi$
$257$	5.10311	−	28.9412i	0.318323	−	1.80530i	0.552950	−	0.833214i	$-0.313502\pi$
$258$		0			0
$259$	3.59813	−	4.07896i	0.223577	−	0.253454i
$260$	0.00234710	+	0.00135510i	0.000145561	+	8.40396e-5i
$261$		0			0
$262$			5.51656i			0.340814i
$263$	5.73330	−	15.7521i	0.353531	−	0.971318i	−0.627696	−	0.778459i	$-0.716002\pi$
$263$	5.73330	−	15.7521i	0.353531	−	0.971318i	0.981227	−	0.192859i	$-0.0617760\pi$
$264$		0			0
$265$	−0.00202329	−	0.00555894i	−0.000124290	−	0.000341483i
$266$	0.169947	−	6.87434i	0.0104201	−	0.421493i
$267$		0			0
$268$	−3.49861	−	1.27339i	−0.213711	−	0.0777846i
$269$	−4.71711	+	8.17027i	−0.287607	+	0.498150i	−0.973238	−	0.229799i	$-0.926193\pi$
$269$	−4.71711	+	8.17027i	−0.287607	+	0.498150i	0.685631	+	0.727949i	$0.259526\pi$
$270$		0			0
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	−0.599719	−	0.800211i	$-0.704721\pi$
$271$	−3.40065	+	1.96337i	−0.206575	+	0.119266i	0.393144	+	0.919477i	$0.371388\pi$
$272$	−1.57288	+	1.31980i	−0.0953696	+	0.0800246i
$273$		0			0
$274$	−0.871668	+	4.94347i	−0.0526594	+	0.298646i
$275$	−15.2196	+	18.1380i	−0.917778	+	1.09376i
$276$		0			0
$277$	21.5582	+	7.84655i	1.29531	+	0.471454i	0.895466	−	0.445130i	$-0.146843\pi$
$277$	21.5582	+	7.84655i	1.29531	+	0.471454i	0.399843	+	0.916584i	$0.369065\pi$
$278$	−0.103759	+	0.179716i	−0.00622305	+	0.0107786i
$279$		0			0
$280$	0.00217771	−	0.00173744i	0.000130143	−	0.000103832i
$281$	−0.608889	+	1.67291i	−0.0363233	+	0.0997974i	−0.956528	−	0.291639i	$-0.905799\pi$
$281$	−0.608889	+	1.67291i	−0.0363233	+	0.0997974i	0.920205	+	0.391436i	$0.128022\pi$
$282$		0			0
$283$	−1.52431	−	4.18800i	−0.0906106	−	0.248951i	0.886107	−	0.463482i	$-0.153400\pi$
$283$	−1.52431	−	4.18800i	−0.0906106	−	0.248951i	−0.976717	+	0.214531i	$0.931178\pi$
$284$	−5.23361	−	14.3792i	−0.310557	−	0.853249i
$285$		0			0
$286$	−2.22714	+	6.11901i	−0.131693	+	0.361825i
$287$	17.7689	−	2.68217i	1.04887	−	0.158323i
$288$		0			0
$289$	8.17986	−	14.1679i	0.481168	−	0.833408i
$290$	0.00221909		0.000807684i	0.000130310		4.74289e-5i
$291$		0			0
$292$	−8.08234	+	9.63216i	−0.472983	+	0.563679i
$293$	1.23196	−	6.98681i	0.0719721	−	0.408174i	−0.927443	−	0.373965i	$-0.877998\pi$
$293$	1.23196	−	6.98681i	0.0719721	−	0.408174i	0.999415	−	0.0342085i	$-0.0108910\pi$
$294$		0			0
$295$	−0.00568967	+	0.00477420i	−0.000331265	+	0.000277965i
$296$	3.33453	−	1.92519i	0.193815	−	0.111899i
$297$		0			0
$298$	0.229979	−	0.398336i	0.0133223	−	0.0230750i
$299$	−4.10565	−	1.49434i	−0.237436	−	0.0864197i
$300$		0			0
$301$	−15.8162	+	8.61749i	−0.911632	+	0.496704i
$302$	0.205589	+	0.564852i	0.0118303	+	0.0325036i
$303$		0			0
$304$	−4.56780	+	12.5499i	−0.261981	+	0.719788i
$305$		−	0.00204346i		−	0.000117008i
$306$		0			0
$307$	6.20672	+	3.58345i	0.354236	+	0.204518i	0.666549	−	0.745461i	$-0.267771\pi$
$307$	6.20672	+	3.58345i	0.354236	+	0.204518i	−0.312313	+	0.949979i	$0.601104\pi$
$308$	−16.4486	−	14.5096i	−0.937246	−	0.826764i
$309$		0			0
$310$	−0.000393713		0.00223286i	−2.23614e−5		0.000126818i
$311$	21.8466	−	7.95150i	1.23881	−	0.450888i	0.362201	−	0.932100i	$-0.382025\pi$
$311$	21.8466	−	7.95150i	1.23881	−	0.450888i	0.876605	+	0.481212i	$0.159803\pi$
$312$		0			0
$313$	23.5238	−	4.14788i	1.32964	−	0.234452i	0.536713	−	0.843765i	$-0.319666\pi$
$313$	23.5238	−	4.14788i	1.32964	−	0.234452i	0.792930	+	0.609313i	$0.208555\pi$
$314$	−2.87721	+	4.98347i	−0.162370	+	0.281234i
$315$		0			0
$316$	−2.25541	−	3.90648i	−0.126877	−	0.219757i
$317$	18.4623	+	22.0025i	1.03695	+	1.23579i	0.971279	+	0.237944i	$0.0764735\pi$
$317$	18.4623	+	22.0025i	1.03695	+	1.23579i	0.0656685	+	0.997841i	$0.479082\pi$
$318$		0			0
$319$	6.91702	−	39.2284i	0.387279	−	2.19637i
$320$	−0.00138498		0.000504092i	−7.74228e−5		2.81796e-5i
$321$		0			0
$322$	−1.38674	+	1.57205i	−0.0772798	+	0.0876068i
$323$			4.16468i			0.231729i
$324$		0			0
$325$	−11.9238	−	6.88420i	−0.661412	−	0.381866i
$326$	−3.36662	+	0.593626i	−0.186460	+	0.0328779i
$327$		0			0
$328$	12.5279	+	2.20900i	0.691735	+	0.121972i
$329$	0.484906	−	19.6144i	0.0267337	−	1.08138i
$330$		0			0
$331$	−19.9199	+	16.7148i	−1.09490	+	0.918726i	−0.997071	−	0.0764775i	$-0.975633\pi$
$331$	−19.9199	+	16.7148i	−1.09490	+	0.918726i	−0.0978240	+	0.995204i	$0.531188\pi$
$332$	−3.37676			−0.185324
$333$		0			0
$334$		−	2.31571i		−	0.126710i
$335$	−0.00112355		0.000408937i	−6.13858e−5		2.23426e-5i
$336$		0			0
$337$	5.30836	+	4.45424i	0.289165	+	0.242638i	0.775817	−	0.630958i	$-0.217338\pi$
$337$	5.30836	+	4.45424i	0.289165	+	0.242638i	−0.486653	+	0.873596i	$0.661782\pi$
$338$	2.66408	+	0.469749i	0.144907	+	0.0255510i
$339$		0			0
$340$	−0.000603288	0	0.000506219i	−3.27179e−5	0	2.74536e-5i
$341$	38.2444			2.07105
$342$		0			0
$343$	−15.3089	−	10.4229i	−0.826604	−	0.562783i
$344$	−12.5566	+	2.21407i	−0.677008	+	0.119375i
$345$		0			0
$346$	11.8326	+	2.08640i	0.636124	+	0.112166i
$347$	1.01656	−	1.21149i	0.0545718	−	0.0650361i	−0.738068	−	0.674726i	$-0.764262\pi$
$347$	1.01656	−	1.21149i	0.0545718	−	0.0650361i	0.792640	+	0.609690i	$0.208706\pi$
$348$		0			0
$349$	11.3433	+	13.5184i	0.607194	+	0.723626i	0.978812	−	0.204760i	$-0.0656414\pi$
$349$	11.3433	+	13.5184i	0.607194	+	0.723626i	−0.371618	+	0.928386i	$0.621197\pi$
$350$	−5.16384	+	4.11986i	−0.276019	+	0.220216i
$351$		0			0
$352$	−11.9032	−	20.6170i	−0.634444	−	1.09889i
$353$	0.472599	+	2.68024i	0.0251539	+	0.142655i	0.994798	−	0.101865i	$-0.0324809\pi$
$353$	0.472599	+	2.68024i	0.0251539	+	0.142655i	−0.969644	+	0.244520i	$0.921370\pi$
$354$		0			0
$355$	−0.00168072	−	0.00461775i	−8.92035e−5	−	0.000245085i
$356$	5.32310	−	1.93745i	0.282124	−	0.102685i
$357$		0			0
$358$	2.13903	+	12.1311i	0.113051	+	0.641146i
$359$	−19.8115	−	11.4382i	−1.04561	−	0.603683i	−0.124193	−	0.992258i	$-0.539634\pi$
$359$	−19.8115	−	11.4382i	−1.04561	−	0.603683i	−0.921417	+	0.388575i	$0.872968\pi$
$360$		0			0
$361$	4.04462	+	7.00549i	0.212875	+	0.368710i
$362$	0.779425	+	4.42034i	0.0409657	+	0.232328i
$363$		0			0
$364$	6.64821	−	10.8846i	0.348461	−	0.570509i
$365$	−0.00259557	+	0.00309328i	−0.000135858	+	0.000161910i
$366$		0			0
$367$	4.74994	+	5.66075i	0.247945	+	0.295489i	0.875634	−	0.482975i	$-0.160444\pi$
$367$	4.74994	+	5.66075i	0.247945	+	0.295489i	−0.627690	+	0.778464i	$0.715999\pi$
$368$	3.52591	−	2.03569i	0.183801	−	0.106117i
$369$		0			0
$370$	0.000499828	0	0.000288576i	2.59848e−5	0	1.50023e-5i
$371$	−26.3880	+	8.87226i	−1.37000	+	0.460625i
$372$		0			0
$373$	24.8147	+	20.8220i	1.28486	+	1.07812i	0.992555	+	0.121797i	$0.0388658\pi$
$373$	24.8147	+	20.8220i	1.28486	+	1.07812i	0.292302	+	0.956326i	$0.405579\pi$
$374$	−1.44950	−	1.21628i	−0.0749521	−	0.0628923i
$375$		0			0
$376$	4.75042	−	13.0517i	0.244984	−	0.673089i
$377$	23.1631			1.19296
$378$		0			0
$379$	−6.72815			−0.345602			−0.172801	−	0.984957i	$-0.555282\pi$
$379$	−6.72815			−0.345602			−0.172801	+	0.984957i	$0.555282\pi$
$380$	−0.00175201	+	0.00481362i	−8.98764e−5	+	0.000246933i
$381$		0			0
$382$	−7.97978	−	6.69583i	−0.408281	−	0.342588i
$383$	0.217502	+	0.182506i	0.0111138	+	0.00932560i	0.648328	−	0.761361i	$-0.275469\pi$
$383$	0.217502	+	0.182506i	0.0111138	+	0.00932560i	−0.637214	+	0.770687i	$0.719913\pi$
$384$		0			0
$385$	−0.00528232	−	0.00465964i	−0.000269212	−	0.000237477i
$386$	−7.90450	+	4.56367i	−0.402329	+	0.232285i
$387$		0			0
$388$	2.72269	−	1.57194i	0.138223	−	0.0798033i
$389$	−0.478715	−	0.570510i	−0.0242718	−	0.0289260i	0.753772	−	0.657136i	$-0.228232\pi$
$389$	−0.478715	−	0.570510i	−0.0242718	−	0.0289260i	−0.778044	+	0.628210i	$0.783788\pi$
$390$		0			0
$391$	0.816083	−	0.972570i	0.0412711	−	0.0491850i
$392$	−7.92070	−	10.4474i	−0.400056	−	0.527672i
$393$		0			0
$394$	−0.893706	−	5.06846i	−0.0450243	−	0.255345i
$395$	−0.000724303	−	0.00125453i	−3.64437e−5	−	6.31223e-5i
$396$		0			0
$397$	14.4875	+	8.36439i	0.727109	+	0.419797i	0.817364	−	0.576122i	$-0.195435\pi$
$397$	14.4875	+	8.36439i	0.727109	+	0.419797i	−0.0902545	+	0.995919i	$0.528768\pi$
$398$	0.968833	+	5.49452i	0.0485632	+	0.275416i
$399$		0			0
$400$	12.0563	−	4.38812i	0.602814	−	0.219406i
$401$	6.32052	+	17.3655i	0.315632	+	0.867191i	0.991493	+	0.130162i	$0.0415498\pi$
$401$	6.32052	+	17.3655i	0.315632	+	0.867191i	−0.675861	+	0.737029i	$0.736228\pi$
$402$		0			0
$403$	3.86176	+	21.9011i	0.192368	+	1.09097i
$404$	3.72832	+	6.45763i	0.185491	+	0.321279i
$405$		0			0
$406$	4.05795	−	10.3461i	0.201393	−	0.513467i
$407$	−6.25772	−	7.45767i	−0.310184	−	0.369663i
$408$		0			0
$409$	11.4565	−	13.6534i	0.566489	−	0.675116i	−0.404417	−	0.914575i	$-0.632526\pi$
$409$	11.4565	−	13.6534i	0.566489	−	0.675116i	0.970906	+	0.239459i	$0.0769701\pi$
$410$	0.00187786		0.000331117i	9.27409e−5		1.63527e-5i
$411$		0			0
$412$	−27.7239	+	4.88847i	−1.36586	+	0.240838i
$413$	21.7991	+	27.3230i	1.07266	+	1.34448i
$414$		0			0
$415$	−0.00108442			−5.32319e−5
$416$	10.6046	−	8.89834i	0.519934	−	0.436277i
$417$		0			0
$418$	−12.1208	−	2.13723i	−0.592849	−	0.104535i
$419$	0.812929	+	0.682129i	0.0397142	+	0.0333242i	0.662429	−	0.749125i	$-0.269526\pi$
$419$	0.812929	+	0.682129i	0.0397142	+	0.0333242i	−0.622715	+	0.782449i	$0.713970\pi$
$420$		0			0
$421$	−14.4175	−	5.24755i	−0.702667	−	0.255750i	−0.0341181	−	0.999418i	$-0.510862\pi$
$421$	−14.4175	−	5.24755i	−0.702667	−	0.255750i	−0.668549	+	0.743668i	$0.733084\pi$
$422$		−	11.8606i		−	0.577364i
$423$		0			0
$424$	−19.7077			−0.957090
$425$	3.06484	−	2.57170i	0.148666	−	0.124746i
$426$		0			0
$427$	−9.61372	−	0.237669i	−0.465241	−	0.0115016i
$428$	6.94305	+	1.22425i	0.335605	+	0.0591762i
$429$		0			0
$430$	−0.00188217		0.000331878i	−9.07665e−5		1.60046e-5i
$431$	−3.29736	−	1.90373i	−0.158828	−	0.0916996i	0.418479	−	0.908226i	$-0.362563\pi$
$431$	−3.29736	−	1.90373i	−0.158828	−	0.0916996i	−0.577308	+	0.816527i	$0.695897\pi$
$432$		0			0
$433$			29.5261i			1.41893i	0.704739	+	0.709467i	$0.251064\pi$
$433$			29.5261i			1.41893i	−0.704739	+	0.709467i	$0.748936\pi$
$434$	10.4590	+	2.11197i	0.502046	+	0.101378i
$435$		0			0
$436$	1.93408	−	0.703949i	0.0926258	−	0.0337130i
$437$	1.43401	−	8.13267i	0.0685980	−	0.389038i
$438$		0			0
$439$	−10.6109	−	12.6456i	−0.506432	−	0.603543i	0.450885	−	0.892582i	$-0.351109\pi$
$439$	−10.6109	−	12.6456i	−0.506432	−	0.603543i	−0.957317	+	0.289040i	$0.906664\pi$
$440$	−0.00249315	−	0.00431827i	−0.000118856	−	0.000205865i
$441$		0			0
$442$	0.550152	−	0.952891i	0.0261681	−	0.0453244i
$443$	27.5106	−	4.85086i	1.30707	−	0.230471i	0.523632	−	0.851945i	$-0.324577\pi$
$443$	27.5106	−	4.85086i	1.30707	−	0.230471i	0.783435	+	0.621474i	$0.213466\pi$
$444$		0			0
$445$	0.00170947		0.000622194i	8.10364e−5		2.94948e-5i
$446$	2.09565	−	11.8850i	0.0992321	−	0.562773i
$447$		0			0
$448$	2.21048	+	6.57444i	0.104435	+	0.310613i
$449$	−20.1252	−	11.6193i	−0.949765	−	0.548347i	−0.0567572	−	0.998388i	$-0.518076\pi$
$449$	−20.1252	−	11.6193i	−0.949765	−	0.548347i	−0.893008	+	0.450041i	$0.851409\pi$
$450$		0			0
$451$		−	32.1640i		−	1.51455i
$452$	−8.82876	+	24.2568i	−0.415270	+	1.14094i
$453$		0			0
$454$	−0.730736	−	2.00768i	−0.0342952	−	0.0942252i
$455$	0.00213501	−	0.00349549i	0.000100091	−	0.000163871i
$456$		0			0
$457$	−17.0320	−	6.19915i	−0.796724	−	0.289984i	−0.0885960	−	0.996068i	$-0.528238\pi$
$457$	−17.0320	−	6.19915i	−0.796724	−	0.289984i	−0.708128	+	0.706084i	$0.750460\pi$
$458$	3.23444	−	5.60221i	0.151135	−	0.261774i
$459$		0			0
$460$	0.00135239		0.000780802i	6.30555e−5		3.64051e-5i
$461$	−0.780576	+	0.654981i	−0.0363550	+	0.0305055i	−0.660784	−	0.750576i	$-0.729776\pi$
$461$	−0.780576	+	0.654981i	−0.0363550	+	0.0305055i	0.624429	+	0.781081i	$0.285332\pi$
$462$		0			0
$463$	5.96496	−	33.8290i	0.277215	−	1.57216i	−0.454621	−	0.890685i	$-0.650225\pi$
$463$	5.96496	−	33.8290i	0.277215	−	1.57216i	0.731837	−	0.681480i	$-0.238663\pi$
$464$	−13.8742	+	16.5346i	−0.644093	+	0.767600i
$465$		0			0
$466$	5.25783	+	1.91369i	0.243564	+	0.0886502i
$467$	0.712541	−	1.23416i	0.0329724	−	0.0571100i	−0.849068	−	0.528283i	$-0.822836\pi$
$467$	0.712541	−	1.23416i	0.0329724	−	0.0571100i	0.882041	+	0.471173i	$0.156169\pi$
$468$		0			0
$469$	−2.05457	+	5.23830i	−0.0948713	+	0.241882i
$470$	0.000712064	−	0.00195638i	3.28451e−5	−	9.02410e-5i
$471$		0			0
$472$	8.46280	+	23.2514i	0.389532	+	1.07023i
$473$	11.0260	+	30.2937i	0.506977	+	1.39291i
$474$		0			0
$475$	8.90062	−	24.4542i	0.408388	−	1.12204i
$476$	2.31140	+	2.89712i	0.105943	+	0.132789i
$477$		0			0
$478$	−3.13135	+	5.42365i	−0.143224	+	0.248072i
$479$	−33.6340	−	12.2418i	−1.53678	−	0.559341i	−0.571507	−	0.820597i	$-0.693641\pi$
$479$	−33.6340	−	12.2418i	−1.53678	−	0.559341i	−0.965270	+	0.261256i	$0.915863\pi$
$480$		0			0
$481$	3.63884	−	4.33660i	0.165917	−	0.197732i
$482$	−1.74075	+	9.87226i	−0.0792888	+	0.449669i
$483$		0			0
$484$	−15.3217	+	12.8564i	−0.696441	+	0.584383i
$485$	0.000874365	0	0.000504815i	3.97029e−5	0	2.29225e-5i
$486$		0			0
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	0.133625	+	0.991032i	$0.457338\pi$
$487$	−17.4657	+	30.2515i	−0.791446	+	1.37082i	−0.925071	+	0.379793i	$0.875995\pi$
$488$	−6.39708	−	2.32835i	−0.289582	−	0.105399i
$489$		0			0
$490$	−0.00118727	−	0.00156601i	−5.36354e−5	−	7.07450e-5i
$491$	3.72269	+	10.2280i	0.168003	+	0.461584i	0.994912	−	0.100752i	$-0.0321249\pi$
$491$	3.72269	+	10.2280i	0.168003	+	0.461584i	−0.826909	+	0.562336i	$0.809903\pi$
$492$		0			0
$493$	−2.30206	+	6.32487i	−0.103680	+	0.284858i
$494$		−	7.15694i		−	0.322006i
$495$		0			0
$496$	−17.9469	−	10.3617i	−0.805841	−	0.465252i
$497$	−21.9203	+	7.37009i	−0.983258	+	0.330594i
$498$		0			0
$499$	1.10201	−	6.24980i	0.0493326	−	0.279779i	−0.950155	−	0.311777i	$-0.899076\pi$
$499$	1.10201	−	6.24980i	0.0493326	−	0.279779i	0.999488	+	0.0319977i	$0.0101869\pi$
$500$	0.00924854	−	0.00336619i	0.000413607	−	0.000150541i
$501$		0			0
$502$	−11.0876	+	1.95505i	−0.494864	+	0.0872579i
$503$	−6.72425	+	11.6468i	−0.299820	+	0.519303i	−0.976095	−	0.217346i	$-0.930260\pi$
$503$	−6.72425	+	11.6468i	−0.299820	+	0.519303i	0.676275	+	0.736649i	$0.263593\pi$
$504$		0			0
$505$	0.00119731	+	0.00207381i	5.32798e−5	+	9.22833e-5i
$506$	2.41176	+	2.87422i	0.107216	+	0.127775i
$507$		0			0
$508$	2.10842	−	11.9574i	0.0935459	−	0.530525i
$509$	−16.2407	+	5.91114i	−0.719857	+	0.262007i	−0.675865	−	0.737025i	$-0.736230\pi$
$509$	−16.2407	+	5.91114i	−0.719857	+	0.262007i	−0.0439919	+	0.999032i	$0.514008\pi$
$510$		0			0
$511$	14.2508	+	12.5709i	0.630419	+	0.556106i
$512$			22.5118i			0.994888i
$513$		0			0
$514$	−12.7090	−	7.33754i	−0.560570	−	0.323645i
$515$	−0.00890327	+	0.00156989i	−0.000392325	+	6.91775e-5i
$516$		0			0
$517$	−34.5842	−	6.09812i	−1.52101	−	0.268195i
$518$	−1.29951	−	2.38507i	−0.0570971	−	0.104794i
$519$		0			0
$520$	0.00222116	−	0.00186377i	9.74043e−5	−	8.17319e-5i
$521$	28.5570			1.25111			0.625553	−	0.780182i	$-0.284874\pi$
$521$	28.5570			1.25111			0.625553	+	0.780182i	$0.284874\pi$
$522$		0			0
$523$			15.1785i			0.663708i	0.943331	+	0.331854i	$0.107674\pi$
$523$			15.1785i			0.663708i	−0.943331	+	0.331854i	$0.892326\pi$
$524$	−18.1733	−	6.61455i	−0.793905	−	0.288958i
$525$		0			0
$526$	−6.41244	−	5.38068i	−0.279596	−	0.234609i
$527$	−6.36410	−	1.12216i	−0.277224	−	0.0488822i
$528$		0			0
$529$	15.6905	−	13.1659i	0.682196	−	0.572431i
$530$	−0.00295408			−0.000128317
$531$		0			0
$532$	22.4425	+	8.80243i	0.973006	+	0.381634i
$533$	18.4191	−	3.24779i	0.797821	−	0.140677i
$534$		0			0
$535$	0.00222969		0.000393155i	9.63981e−5		1.69976e-5i
$536$	−2.56036	+	3.05132i	−0.110591	+	0.131797i
$537$		0			0
$538$	3.02823	+	3.60891i	0.130556	+	0.155591i
$539$	−22.5362	+	24.3094i	−0.970703	+	1.04708i
$540$		0			0
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	0.991076	−	0.133301i	$-0.0425577\pi$
$541$	8.84080	+	15.3127i	0.380096	+	0.658345i	−0.610980	+	0.791646i	$0.709224\pi$
$542$	0.340501	+	1.93108i	0.0146258	+	0.0829468i
$543$		0			0
$544$	1.37582	+	3.78005i	0.0589880	+	0.162068i
$545$	0.000621113	0	0.000226067i	2.66055e−5	0	9.68363e-6i
$546$		0			0
$547$	−1.23750	−	7.01822i	−0.0529117	−	0.300077i	0.946855	−	0.321660i	$-0.104241\pi$
$547$	−1.23750	−	7.01822i	−0.0529117	−	0.300077i	−0.999767	+	0.0215823i	$0.993130\pi$
$548$	−15.2402	−	8.79895i	−0.651030	−	0.375873i
$549$		0			0
$550$	5.91184	+	10.2396i	0.252082	+	0.436618i
$551$	7.60241	+	43.1154i	0.323873	+	1.83678i
$552$		0			0
$553$	−5.98633	+	3.26166i	−0.254565	+	0.138700i
$554$	7.36395	−	8.77601i	0.312864	−	0.372857i
$555$		0			0
$556$	−0.467631	−	0.557301i	−0.0198320	−	0.0236348i
$557$	6.62385	−	3.82428i	0.280662	−	0.162040i	−0.353061	−	0.935600i	$-0.614859\pi$
$557$	6.62385	−	3.82428i	0.280662	−	0.162040i	0.633723	+	0.773560i	$0.281526\pi$
$558$		0			0
$559$	−16.2347	+	9.37312i	−0.686655	+	0.396441i
$560$	0.00121638	+	0.00361777i	5.14014e−5	+	0.000152879i
$561$		0			0
$562$	0.681015	+	0.571439i	0.0287269	+	0.0241047i
$563$	−27.7146	−	23.2553i	−1.16803	−	0.980095i	−0.168048	−	0.985779i	$-0.553746\pi$
$563$	−27.7146	−	23.2553i	−1.16803	−	0.980095i	−0.999984	+	0.00568387i	$0.998191\pi$
$564$		0			0
$565$	−0.00283527	+	0.00778985i	−0.000119281	+	0.000327722i
$566$	−2.22555			−0.0935467
$567$		0			0
$568$	−16.3710			−0.686910
$569$	−1.82595	+	5.01676i	−0.0765478	+	0.210313i	−0.972064	−	0.234715i	$-0.924584\pi$
$569$	−1.82595	+	5.01676i	−0.0765478	+	0.210313i	0.895516	+	0.445029i	$0.146806\pi$
$570$		0			0
$571$	28.4696	+	23.8889i	1.19142	+	0.999718i	0.999834	+	0.0182416i	$0.00580681\pi$
$571$	28.4696	+	23.8889i	1.19142	+	0.999718i	0.191584	+	0.981476i	$0.438638\pi$
$572$	−17.4876	−	14.6738i	−0.731192	−	0.613543i
$573$		0			0
$574$	1.77619	−	8.79611i	0.0741368	−	0.367143i
$575$	−6.87043	+	3.96664i	−0.286517	+	0.165421i
$576$		0			0
$577$	21.9589	−	12.6780i	0.914161	−	0.527791i	0.0323932	−	0.999475i	$-0.489687\pi$
$577$	21.9589	−	12.6780i	0.914161	−	0.527791i	0.881768	+	0.471684i	$0.156354\pi$
$578$	−5.25121	−	6.25815i	−0.218422	−	0.260305i
$579$		0			0
$580$	−0.00532154	+	0.00634197i	−0.000220965	+	0.000263336i
$581$	−0.126125	+	5.10177i	−0.00523256	+	0.211657i
$582$		0			0
$583$	8.65269	+	49.0718i	0.358358	+	2.03235i
$584$	6.72612	+	11.6500i	0.278329	+	0.482080i
$585$		0			0
$586$	−3.06813	−	1.77139i	−0.126743	−	0.0731754i
$587$	2.85469	+	16.1897i	0.117826	+	0.668222i	0.985312	+	0.170762i	$0.0546229\pi$
$587$	2.85469	+	16.1897i	0.117826	+	0.668222i	−0.867487	+	0.497460i	$0.834266\pi$
$588$		0			0
$589$	−39.4990	+	14.3765i	−1.62753	+	0.592372i
$590$	0.00126853	+	0.00348526i	5.22246e−5	+	0.000143486i
$591$		0			0
$592$	0.916031	+	5.19507i	0.0376486	+	0.213516i
$593$	−15.3209	−	26.5365i	−0.629153	−	1.08973i	−0.987722	−	0.156222i	$-0.950068\pi$
$593$	−15.3209	−	26.5365i	−0.629153	−	1.08973i	0.358569	−	0.933503i	$-0.383265\pi$
$594$		0			0
$595$	0.000742286	0	0.000930384i	3.04307e−5	0	3.81420e-5i
$596$	1.03649	+	1.23524i	0.0424564	+	0.0505976i
$597$		0			0
$598$	−1.40243	+	1.67135i	−0.0573495	+	0.0683465i
$599$	19.2428	+	3.39302i	0.786239	+	0.138635i	0.552332	−	0.833624i	$-0.313738\pi$
$599$	19.2428	+	3.39302i	0.786239	+	0.138635i	0.233906	+	0.972259i	$0.424849\pi$
$600$		0			0
$601$	20.6262	−	3.63695i	0.841360	−	0.148354i	0.263672	−	0.964612i	$-0.415066\pi$
$601$	20.6262	−	3.63695i	0.841360	−	0.148354i	0.577688	+	0.816258i	$0.303955\pi$
$602$	1.34245	+	8.89352i	0.0547142	+	0.362473i
$603$		0			0
$604$	−2.10731			−0.0857453
$605$	−0.00492042	+	0.00412872i	−0.000200043	+	0.000167856i
$606$		0			0
$607$	−26.5691	−	4.68485i	−1.07841	−	0.190152i	−0.393896	−	0.919155i	$-0.628873\pi$
$607$	−26.5691	−	4.68485i	−1.07841	−	0.190152i	−0.684511	+	0.729003i	$0.739984\pi$
$608$	20.0438	+	16.8188i	0.812884	+	0.682091i
$609$		0			0
$610$	−0.000958889	0	0.000349007i	−3.88243e−5	0	1.41309e-5i
$611$		−	20.4208i		−	0.826138i
$612$		0			0
$613$	−26.9051			−1.08669			−0.543343	−	0.839511i	$-0.682842\pi$
$613$	−26.9051			−1.08669			−0.543343	+	0.839511i	$0.682842\pi$
$614$	2.74158	−	2.30046i	0.110641	−	0.0928390i
$615$		0			0
$616$	−20.6058	+	11.2271i	−0.830231	+	0.452353i
$617$	22.1664	+	3.90853i	0.892386	+	0.157352i	0.600995	−	0.799253i	$-0.294771\pi$
$617$	22.1664	+	3.90853i	0.892386	+	0.157352i	0.291390	+	0.956604i	$0.405882\pi$
$618$		0			0
$619$	10.5751	−	1.86467i	0.425047	−	0.0749473i	0.0429671	−	0.999076i	$-0.486319\pi$
$619$	10.5751	−	1.86467i	0.425047	−	0.0749473i	0.382080	+	0.924129i	$0.375208\pi$
$620$	−0.00688367	−	0.00397429i	−0.000276455	−	0.000159611i
$621$		0			0
$622$		−	11.6095i		−	0.465499i
$623$	−2.72837	−	8.11476i	−0.109310	−	0.325111i
$624$		0			0
$625$	−23.4923	+	8.55050i	−0.939692	+	0.342020i
$626$	2.07130	−	11.7469i	0.0827856	−	0.469500i
$627$		0			0
$628$	−12.9673	−	15.4538i	−0.517451	−	0.616674i
$629$	0.822500	+	1.42461i	0.0327952	+	0.0568030i
$630$		0			0
$631$	−0.130873	+	0.226679i	−0.00520998	+	0.00902394i	−0.868619	−	0.495481i	$-0.834992\pi$
$631$	−0.130873	+	0.226679i	−0.00520998	+	0.00902394i	0.863409	+	0.504505i	$0.168325\pi$
$632$	−4.75260	+	0.838012i	−0.189048	+	0.0333343i
$633$		0			0
$634$	13.4779	−	4.90554i	0.535274	−	0.194824i
$635$	0.000677099	−	0.00384002i	2.68698e−5	−	0.000152386i
$636$		0			0
$637$	−16.1967	−	10.4510i	−0.641735	−	0.414083i
$638$	−17.2264	−	9.94569i	−0.682001	−	0.393754i
$639$		0			0
$640$			0.00638861i			0.000252532i
$641$	17.0992	−	46.9798i	0.675379	−	1.85559i	0.188626	−	0.982049i	$-0.439596\pi$
$641$	17.0992	−	46.9798i	0.675379	−	1.85559i	0.486753	−	0.873540i	$-0.338181\pi$
$642$		0			0
$643$	−5.42130	−	14.8949i	−0.213795	−	0.587397i	0.785718	−	0.618584i	$-0.212294\pi$
$643$	−5.42130	−	14.8949i	−0.213795	−	0.587397i	−0.999514	+	0.0311869i	$0.990071\pi$
$644$	−3.51609	−	6.45329i	−0.138553	−	0.254295i
$645$		0			0
$646$	1.95427	+	0.711295i	0.0768896	+	0.0279855i
$647$	7.51759	−	13.0208i	0.295547	−	0.511902i	−0.679565	−	0.733615i	$-0.737831\pi$
$647$	7.51759	−	13.0208i	0.295547	−	0.511902i	0.975112	+	0.221713i	$0.0711648\pi$
$648$		0			0
$649$	54.1799	−	31.2808i	2.12675	−	1.22788i
$650$	−5.26688	+	4.41943i	−0.206584	+	0.173344i
$651$		0			0
$652$	2.08110	−	11.8025i	0.0815022	−	0.462222i
$653$	9.89082	−	11.7874i	0.387058	−	0.461277i	−0.536971	−	0.843601i	$-0.680432\pi$
$653$	9.89082	−	11.7874i	0.387058	−	0.461277i	0.924029	+	0.382323i	$0.124876\pi$
$654$		0			0
$655$	−0.00583619	−	0.00212420i	−0.000228039	−	8.29994e-5i
$656$	−8.71428	+	15.0936i	−0.340236	+	0.589305i
$657$		0			0
$658$	−9.12121	−	3.57753i	−0.355582	−	0.139467i
$659$	5.58157	−	15.3352i	0.217427	−	0.597376i	−0.782245	−	0.622971i	$-0.785926\pi$
$659$	5.58157	−	15.3352i	0.217427	−	0.597376i	0.999672	+	0.0255942i	$0.00814779\pi$
$660$		0			0
$661$	10.2996	+	28.2979i	0.400608	+	1.10066i	0.961985	+	0.273102i	$0.0880496\pi$
$661$	10.2996	+	28.2979i	0.400608	+	1.10066i	−0.561377	+	0.827560i	$0.689728\pi$
$662$	4.44120	+	12.2021i	0.172612	+	0.474248i
$663$		0			0
$664$	−1.23560	+	3.39478i	−0.0479505	+	0.131743i
$665$	0.00720720	+	0.00282682i	0.000279483	+	0.000109619i
$666$		0			0
$667$	6.67323	−	11.5584i	0.258388	−	0.447542i
$668$	7.62871	+	2.77662i	0.295164	+	0.107431i
$669$		0			0
$670$	−0.000383785	0	0.000457377i	−1.48269e−5	0	1.76700e-5i
$671$	−2.98890	+	16.9509i	−0.115385	+	0.654383i
$672$		0			0
$673$	8.51271	−	7.14301i	0.328141	−	0.275343i	−0.463801	−	0.885939i	$-0.653515\pi$
$673$	8.51271	−	7.14301i	0.328141	−	0.275343i	0.791942	+	0.610597i	$0.209070\pi$
$674$	2.99677	−	1.73018i	0.115431	−	0.0666442i
$675$		0			0
$676$	−4.74182	+	8.21308i	−0.182378	+	0.315888i
$677$	−29.2132	−	10.6327i	−1.12276	−	0.408650i	−0.287099	−	0.957901i	$-0.592691\pi$
$677$	−29.2132	−	10.6327i	−1.12276	−	0.408650i	−0.835657	+	0.549251i	$0.814913\pi$
$678$		0			0
$679$	−2.27327	−	4.17227i	−0.0872401	−	0.160117i
$680$	0.000288169	0	0.000791738i	1.10508e−5	0	3.03618e-5i
$681$		0			0
$682$	6.53185	−	17.9461i	0.250117	−	0.687192i
$683$			20.0528i			0.767298i	0.923479	+	0.383649i	$0.125333\pi$
$683$			20.0528i			0.767298i	−0.923479	+	0.383649i	$0.874667\pi$
$684$		0			0
$685$	−0.00489426	−	0.00282570i	−0.000187000	−	0.000107965i
$686$	−7.50556	+	5.40353i	−0.286564	+	0.206308i
$687$		0			0
$688$	3.03339	−	17.2032i	0.115647	−	0.655866i
$689$	−27.2279	+	9.91013i	−1.03730	+	0.377546i
$690$		0			0
$691$	−5.23641	+	0.923321i	−0.199203	+	0.0351248i	−0.272359	−	0.962196i	$-0.587804\pi$
$691$	−5.23641	+	0.923321i	−0.199203	+	0.0351248i	0.0731565	+	0.997320i	$0.476693\pi$
$692$	−21.0610	+	36.4787i	−0.800618	+	1.38671i
$693$		0			0
$694$	−0.394867	−	0.683930i	−0.0149890	−	0.0259616i
$695$	−0.000150175	0	0.000178972i	−5.69648e−6	0	6.78880e-6i
$696$		0			0
$697$	−0.943752	+	5.35228i	−0.0357472	+	0.202732i
$698$	8.28084	−	3.01398i	0.313435	−	0.114081i
$699$		0			0
$700$	−7.38050	−	21.9512i	−0.278957	−	0.829678i
$701$			16.0144i			0.604857i	0.953172	+	0.302428i	$0.0977973\pi$
$701$			16.0144i			0.604857i	−0.953172	+	0.302428i	$0.902203\pi$
$702$		0			0
$703$	9.26641	+	5.34997i	0.349489	+	0.201778i
$704$	12.2260	−	2.15577i	0.460785	−	0.0812488i
$705$		0			0
$706$	1.33841	+	0.235998i	0.0503718	+	0.00888192i
$707$	9.89575	−	5.39171i	0.372168	−	0.202776i
$708$		0			0
$709$	0.187155	−	0.157041i	0.00702874	−	0.00589781i	−0.639266	−	0.768985i	$-0.720762\pi$
$709$	0.187155	−	0.157041i	0.00702874	−	0.00589781i	0.646295	+	0.763087i	$0.276317\pi$
$710$	−0.00245392			−9.20940e−5
$711$		0			0
$712$		−	6.06044i		−	0.227125i
$713$	12.0412	+	4.38265i	0.450948	+	0.164132i
$714$		0			0
$715$	−0.00561597	−	0.00471236i	−0.000210025	−	0.000176232i
$716$	−42.5283	−	7.49890i	−1.58936	−	0.280247i
$717$		0			0
$718$	−8.75097	+	7.34294i	−0.326583	+	0.274036i
$719$	35.2732			1.31547			0.657734	−	0.753250i	$-0.271515\pi$
$719$	35.2732			1.31547			0.657734	+	0.753250i	$0.271515\pi$
$720$		0			0
$721$	6.35021	+	42.0691i	0.236494	+	1.56674i
$722$	3.97810	−	0.701446i	0.148049	−	0.0261051i
$723$		0			0
$724$	−15.4966	−	2.73246i	−0.575926	−	0.101551i
$725$	27.0346	−	32.2186i	1.00404	−	1.19657i
$726$		0			0
$727$	−28.8861	−	34.4251i	−1.07133	−	1.27676i	−0.959098	−	0.283075i	$-0.908645\pi$
$727$	−28.8861	−	34.4251i	−1.07133	−	1.27676i	−0.112229	−	0.993682i	$-0.535799\pi$
$728$	−8.51002	−	10.6665i	−0.315402	−	0.395326i
$729$		0			0
$730$	0.00100821	+	0.00174627i	3.73155e−5	+	6.46324e-5i
$731$	−0.945920	−	5.36458i	−0.0349861	−	0.198416i
$732$		0			0
$733$	14.9455	+	41.0625i	0.552025	+	1.51668i	0.830941	+	0.556361i	$0.187803\pi$
$733$	14.9455	+	41.0625i	0.552025	+	1.51668i	−0.278915	+	0.960316i	$0.589975\pi$
$734$	3.46755	−	1.26208i	0.127989	−	0.0465843i
$735$		0			0
$736$	−1.38510	−	7.85530i	−0.0510555	−	0.289550i
$737$	8.72188	+	5.03558i	0.321275	+	0.185488i
$738$		0			0
$739$	−17.7049	−	30.6658i	−0.651286	−	1.12806i	−0.982811	−	0.184613i	$-0.940897\pi$
$739$	−17.7049	−	30.6658i	−0.651286	−	1.12806i	0.331526	−	0.943446i	$-0.392437\pi$
$740$	0.000351350		0.00199261i	1.29159e−5		7.32497e-5i
$741$		0			0
$742$	−0.343580	+	13.8978i	−0.0126132	+	0.510205i
$743$	−14.2073	+	16.9316i	−0.521216	+	0.621161i	−0.960868	−	0.277007i	$-0.910657\pi$
$743$	−14.2073	+	16.9316i	−0.521216	+	0.621161i	0.439652	+	0.898168i	$0.355102\pi$
$744$		0			0
$745$	0.000332860	0	0.000396687i	1.21951e−5	0	1.45335e-5i
$746$	14.0088	−	8.08800i	0.512900	−	0.296123i
$747$		0			0
$748$	5.74482	−	3.31677i	0.210051	−	0.121273i
$749$	2.10898	−	10.4441i	0.0770603	−	0.381621i
$750$		0			0
$751$	32.1560	+	26.9821i	1.17339	+	0.984589i	1.00000		0.000264372i	$-8.41522e-5\pi$
$751$	32.1560	+	26.9821i	1.17339	+	0.984589i	0.173388	+	0.984854i	$0.444529\pi$
$752$	14.5771	+	12.2316i	0.531572	+	0.446042i
$753$		0			0
$754$	3.95607	−	10.8692i	0.144071	−	0.395833i
$755$	−0.000676743	0		−2.46292e−5	0
$756$		0			0
$757$	7.91633			0.287724			0.143862	−	0.989598i	$-0.454048\pi$
$757$	7.91633			0.287724			0.143862	+	0.989598i	$0.454048\pi$
$758$	−1.14912	+	3.15717i	−0.0417377	+	0.114673i
$759$		0			0
$760$	0.00419822	+	0.00352272i	0.000152285	+	0.000127783i
$761$	−25.3022	−	21.2310i	−0.917202	−	0.769624i	0.0562731	−	0.998415i	$-0.482078\pi$
$761$	−25.3022	−	21.2310i	−0.917202	−	0.769624i	−0.973476	+	0.228791i	$0.926523\pi$
$762$		0			0
$763$	−0.991318	−	2.94839i	−0.0358881	−	0.106739i
$764$	31.6262	−	18.2594i	1.14420	−	0.660602i
$765$		0			0
$766$	0.122788	−	0.0708916i	0.00443651	−	0.00256142i
$767$	23.3842	+	27.8682i	0.844354	+	1.00626i
$768$		0			0
$769$	19.7511	−	23.5384i	0.712241	−	0.848816i	−0.281611	−	0.959529i	$-0.590869\pi$
$769$	19.7511	−	23.5384i	0.712241	−	0.848816i	0.993852	+	0.110713i	$0.0353133\pi$
$770$	−0.00308870	+	0.00168288i	−0.000111309	+	6.06469e-5i
$771$		0			0
$772$	−5.55641	−	31.5120i	−0.199980	−	1.13414i
$773$	−15.7630	−	27.3023i	−0.566956	−	0.981997i	−0.996865	−	0.0791245i	$-0.974788\pi$
$773$	−15.7630	−	27.3023i	−0.566956	−	0.981997i	0.429909	−	0.902872i	$-0.358546\pi$
$774$		0			0
$775$	34.9706	+	20.1903i	1.25618	+	0.725256i
$776$	−0.584066	−	3.31240i	−0.0209668	−	0.118908i
$777$		0			0
$778$	−0.349471	+	0.127197i	−0.0125291	+	0.00456023i
$779$	12.0908	+	33.2192i	0.433197	+	1.19020i
$780$		0			0
$781$	7.18770	+	40.7635i	0.257196	+	1.45863i
$782$	−0.316995	−	0.549052i	−0.0113357	−	0.0196341i
$783$		0			0
$784$	17.1617	−	5.30183i	0.612919	−	0.189351i
$785$	−0.00416432	−	0.00496285i	−0.000148631	−	0.000177132i
$786$		0			0
$787$	30.6724	−	36.5539i	1.09335	−	1.30301i	0.143726	−	0.989618i	$-0.454092\pi$
$787$	30.6724	−	36.5539i	1.09335	−	1.30301i	0.949625	−	0.313388i	$-0.101464\pi$
$788$	17.7687	+	3.13310i	0.632984	+	0.111612i
$789$		0			0
$790$	−0.000712390	0	0.000125614i	−2.53457e−5	0	4.46913e-6i
$791$	36.3186	+	14.2449i	1.29134	+	0.506491i
$792$		0			0
$793$	−10.0089			−0.355428
$794$	6.39933	−	5.36967i	0.227104	−	0.190563i
$795$		0			0
$796$	−19.2624	−	3.39648i	−0.682737	−	0.120385i
$797$	−29.5128	−	24.7642i	−1.04540	−	0.877192i	−0.0527949	−	0.998605i	$-0.516813\pi$
$797$	−29.5128	−	24.7642i	−1.04540	−	0.877192i	−0.992602	+	0.121413i	$0.961257\pi$
$798$		0			0
$799$	5.57608	+	2.02953i	0.197267	+	0.0717995i
$800$		−	25.1361i		−	0.888696i
$801$		0			0
$802$	9.22821			0.325859
$803$	26.0552	−	21.8629i	0.919467	−	0.771524i
$804$		0			0
$805$	−0.00112916	−	0.00207242i	−3.97976e−5	−	7.30430e-5i
$806$	10.9366	+	1.92842i	0.385226	+	0.0679257i
$807$		0			0
$808$	7.85632	−	1.38528i	0.276384	−	0.0487340i
$809$	−36.7753	−	21.2322i	−1.29295	−	0.746486i	−0.313775	−	0.949497i	$-0.601594\pi$
$809$	−36.7753	−	21.2322i	−1.29295	−	0.746486i	−0.979176	+	0.203011i	$0.934927\pi$
$810$		0			0
$811$		−	22.9043i		−	0.804277i	−0.915579	−	0.402139i	$-0.868267\pi$
$811$		−	22.9043i		−	0.804277i	0.915579	−	0.402139i	$-0.131733\pi$
$812$	29.2176	+	25.7735i	1.02534	+	0.904472i
$813$		0			0
$814$	−4.56826	+	1.66271i	−0.160117	+	0.0582780i
$815$	0.000668326	−	0.00379027i	2.34104e−5	−	0.000132767i
$816$		0			0
$817$	−22.7754	−	27.1427i	−0.796812	−	0.949603i
$818$	−4.45012	−	7.70784i	−0.155595	−	0.269498i
$819$		0			0
$820$	−0.00334243	+	0.00578925i	−0.000116723	+	0.000202169i
$821$	2.02629	−	0.357290i	0.0707180	−	0.0124695i	−0.138177	−	0.990408i	$-0.544124\pi$
$821$	2.02629	−	0.357290i	0.0707180	−	0.0124695i	0.208895	+	0.977938i	$0.433013\pi$
$822$		0			0
$823$	−3.04598	+	1.10865i	−0.106176	+	0.0386450i	−0.394562	−	0.918869i	$-0.629104\pi$
$823$	−3.04598	+	1.10865i	−0.106176	+	0.0386450i	0.288386	+	0.957514i	$0.406881\pi$
$824$	−5.22995	+	29.6605i	−0.182194	+	1.03327i
$825$		0			0
$826$	16.5444	−	5.56260i	0.575652	−	0.193547i
$827$	−47.0423	−	27.1599i	−1.63582	−	0.944441i	−0.982251	−	0.187574i	$-0.939938\pi$
$827$	−47.0423	−	27.1599i	−1.63582	−	0.944441i	−0.653569	−	0.756867i	$-0.726729\pi$
$828$		0			0
$829$		−	8.47998i		−	0.294522i	−0.989098	−	0.147261i	$-0.952954\pi$
$829$		−	8.47998i		−	0.294522i	0.989098	−	0.147261i	$-0.0470457\pi$
$830$	−0.000185210	0	0.000508859i	−6.42872e−6	0	1.76628e-5i
$831$		0			0
$832$	2.46906	+	6.78368i	0.0855992	+	0.235182i
$833$	4.46344	−	3.38396i	0.154649	−	0.117247i
$834$		0			0
$835$	0.00244989		0.000891687i	8.47819e−5		3.08581e-5i
$836$	21.5740	−	37.3673i	0.746153	−	1.29237i
$837$		0			0
$838$	0.458929	−	0.264963i	0.0158534	−	0.00915299i
$839$	−11.5622	+	9.70185i	−0.399172	+	0.334945i	−0.820173	−	0.572115i	$-0.806123\pi$
$839$	−11.5622	+	9.70185i	−0.399172	+	0.334945i	0.421002	+	0.907060i	$0.361679\pi$
$840$		0			0
$841$	−7.25090	+	41.1219i	−0.250031	+	1.41800i
$842$	−4.92480	+	5.86915i	−0.169720	+	0.202264i
$843$		0			0
$844$	39.0725	+	14.2212i	1.34493	+	0.489515i
$845$	−0.00152279	+	0.00263755i	−5.23856e−5	+	9.07346e-5i
$846$		0			0
$847$	18.8518	+	23.6289i	0.647756	+	0.811899i
$848$	9.23471	−	25.3722i	0.317121	−	0.871284i
$849$		0			0
$850$	−0.683315	−	1.87739i	−0.0234375	−	0.0643940i
$851$	−1.11562	−	3.06515i	−0.0382431	−	0.105072i
$852$		0			0
$853$	−5.23344	+	14.3788i	−0.179190	+	0.492319i	−0.996473	−	0.0839170i	$-0.973257\pi$
$853$	−5.23344	+	14.3788i	−0.179190	+	0.492319i	0.817283	+	0.576236i	$0.195479\pi$
$854$	−1.75347	+	4.47062i	−0.0600026	+	0.152982i
$855$		0			0
$856$	3.77132	−	6.53212i	0.128901	−	0.223263i
$857$	16.4933	+	6.00308i	0.563401	+	0.205061i	0.607991	−	0.793944i	$-0.291976\pi$
$857$	16.4933	+	6.00308i	0.563401	+	0.205061i	−0.0445895	+	0.999005i	$0.514198\pi$
$858$		0			0
$859$	−10.1924	+	12.1469i	−0.347761	+	0.414446i	−0.911365	−	0.411600i	$-0.864970\pi$
$859$	−10.1924	+	12.1469i	−0.347761	+	0.414446i	0.563604	+	0.826045i	$0.309415\pi$
$860$	0.00116348	−	0.00659842i	3.96743e−5	−	0.000225004i
$861$		0			0
$862$	−1.45649	+	1.22214i	−0.0496081	+	0.0416261i
$863$	−1.76440	+	1.01868i	−0.0600610	+	0.0346762i	−0.529730	−	0.848166i	$-0.677707\pi$
$863$	−1.76440	+	1.01868i	−0.0600610	+	0.0346762i	0.469669	+	0.882843i	$0.344373\pi$
$864$		0			0
$865$	−0.00676353	+	0.0117148i	−0.000229967	+	0.000398315i
$866$	13.8550	+	5.04282i	0.470813	+	0.171362i
$867$		0			0
$868$	−19.4982	+	31.9229i	−0.661811	+	1.08353i
$869$	4.17328	+	11.4660i	0.141569	+	0.388957i
$870$		0			0
$871$	−2.00299	+	5.50316i	−0.0678686	+	0.186468i
$872$		−	2.20198i		−	0.0745686i
$873$		0			0
$874$	−3.57132	−	2.06190i	−0.120802	−	0.0697448i
$875$	−0.00474036	−	0.0140989i	−0.000160253	−	0.000476628i
$876$		0			0
$877$	−3.15820	+	17.9111i	−0.106645	+	0.604814i	0.883906	+	0.467665i	$0.154905\pi$
$877$	−3.15820	+	17.9111i	−0.106645	+	0.604814i	−0.990551	+	0.137148i	$0.956206\pi$
$878$	−7.74619	+	2.81938i	−0.261421	+	0.0951495i
$879$		0			0
$880$	0.00672770	−	0.00118627i	0.000226791	−	3.99893e-5i
$881$	−13.3725	+	23.1618i	−0.450530	+	0.780341i	−0.998419	−	0.0562101i	$-0.982098\pi$
$881$	−13.3725	+	23.1618i	−0.450530	+	0.780341i	0.547889	+	0.836551i	$0.315432\pi$
$882$		0			0
$883$	10.5208	+	18.2226i	0.354054	+	0.613240i	0.986956	−	0.160992i	$-0.0514694\pi$
$883$	10.5208	+	18.2226i	0.354054	+	0.613240i	−0.632901	+	0.774232i	$0.718136\pi$
$884$	2.47948	+	2.95493i	0.0833939	+	0.0993849i
$885$		0			0
$886$	2.42234	−	13.7378i	0.0813800	−	0.461529i
$887$	20.9254	−	7.61624i	0.702608	−	0.255728i	0.0340838	−	0.999419i	$-0.489149\pi$
$887$	20.9254	−	7.61624i	0.702608	−	0.255728i	0.668524	+	0.743691i	$0.266926\pi$
$888$		0			0
$889$	−17.9871	−	3.63212i	−0.603267	−	0.121817i
$890$		0	0.000908428i		0	3.04506e-5i
$891$		0			0
$892$	36.6404	+	21.1543i	1.22681	+	0.708300i
$893$	38.0110	−	6.70237i	1.27199	−	0.224286i
$894$		0			0
$895$	−0.0136576	−	0.00240820i	−0.000456523	−	8.04973e-5i
$896$	30.0560	+	0.743041i	1.00410	+	0.0248233i
$897$		0			0
$898$	−8.88953	+	7.45920i	−0.296647	+	0.248917i
$899$	−67.9336			−2.26571
$900$		0			0
$901$		−	8.41972i		−	0.280502i
$902$	−15.0929	−	5.49336i	−0.502538	−	0.182909i
$903$		0			0
$904$	21.1557	+	17.7517i	0.703627	+	0.590414i
$905$	−0.00497658		0.000877506i	−0.000165427		2.91693e-5i
$906$		0			0
$907$	2.75474	−	2.31150i	0.0914695	−	0.0767520i	−0.595906	−	0.803054i	$-0.703207\pi$
$907$	2.75474	−	2.31150i	0.0914695	−	0.0767520i	0.687376	+	0.726302i	$0.258763\pi$
$908$	7.49013			0.248569
$909$		0			0
$910$	−0.00127561	−	0.00159885i	−4.22860e−5	−	5.30014e-5i
$911$	51.8774	−	9.14738i	1.71877	−	0.303066i	0.774585	−	0.632470i	$-0.217959\pi$
$911$	51.8774	−	9.14738i	1.71877	−	0.303066i	0.944189	+	0.329403i	$0.106848\pi$
$912$		0			0
$913$	8.99544	+	1.58614i	0.297706	+	0.0524935i
$914$	−5.81787	+	6.93347i	−0.192438	+	0.229339i
$915$		0			0
$916$	14.5773	+	17.3725i	0.481647	+	0.574005i
$917$	−10.6724	+	27.2100i	−0.352432	+	0.898555i
$918$		0			0
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.827969	−	0.560774i	$-0.810504\pi$
$919$	−27.2723	−	47.2370i	−0.899629	−	1.55820i	−0.0716603	−	0.997429i	$-0.522830\pi$
$920$	−0.000290112	−	0.00164531i	−9.56472e−6	−	5.42442e-5i
$921$		0			0
$922$	0.174032	+	0.478149i	0.00573144	+	0.0157470i
$923$	−22.6179	+	8.23224i	−0.744477	+	0.270968i
$924$		0			0
$925$	−1.78494	−	10.1229i	−0.0586884	−	0.332838i
$926$	−14.8554	−	8.57676i	−0.488178	−	0.281850i
$927$		0			0
$928$	21.1437	+	36.6219i	0.694075	+	1.20217i
$929$	−7.27715	−	41.2707i	−0.238755	−	1.35405i	−0.834559	−	0.550919i	$-0.814277\pi$
$929$	−7.27715	−	41.2707i	−0.238755	−	1.35405i	0.595803	−	0.803130i	$-0.296834\pi$
$930$		0			0
$931$	14.1374	−	33.5784i	0.463333	−	1.10049i
$932$	−12.6086	+	15.0264i	−0.413010	+	0.492206i
$933$		0			0
$934$	−0.457428	−	0.545142i	−0.0149675	−	0.0178376i
$935$	0.00184490	−	0.00106515i	6.03345e−5	−	3.48342e-5i
$936$		0			0
$937$	24.5420	−	14.1693i	0.801751	−	0.462891i	−0.0423320	−	0.999104i	$-0.513479\pi$
$937$	24.5420	−	14.1693i	0.801751	−	0.462891i	0.844083	+	0.536212i	$0.180145\pi$
$938$	2.10715	+	1.85876i	0.0688009	+	0.0606907i
$939$		0			0
$940$	0.00559115	+	0.00469153i	0.000182363	+	0.000153021i
$941$	12.4382	+	10.4369i	0.405473	+	0.340232i	0.822604	−	0.568614i	$-0.192520\pi$
$941$	12.4382	+	10.4369i	0.405473	+	0.340232i	−0.417132	+	0.908846i	$0.636965\pi$
$942$		0			0
$943$	3.68586	−	10.1268i	0.120028	−	0.329775i
$944$	−33.8999			−1.10335
$945$		0			0
$946$	16.0984			0.523405
$947$	3.35614	−	9.22091i	0.109060	−	0.299639i	−0.873143	−	0.487465i	$-0.837922\pi$
$947$	3.35614	−	9.22091i	0.109060	−	0.299639i	0.982202	+	0.187825i	$0.0601439\pi$
$948$		0			0
$949$	15.1510	+	12.7132i	0.491822	+	0.412687i
$950$	−9.95493	−	8.35318i	−0.322981	−	0.271013i
$951$		0			0
$952$	3.75835	−	1.26364i	0.121809	−	0.0409549i
$953$	34.8176	−	20.1019i	1.12785	−	0.651166i	0.184458	−	0.982840i	$-0.440947\pi$
$953$	34.8176	−	20.1019i	1.12785	−	0.651166i	0.943394	+	0.331675i	$0.107614\pi$
$954$		0			0
$955$	0.0101565	−	0.00586384i	0.000328656	−	0.000189749i
$956$	−14.1126	−	16.8188i	−0.456436	−	0.543959i
$957$		0			0
$958$	−11.4888	+	13.6919i	−0.371188	+	0.442364i
$959$	−13.8631	+	22.6970i	−0.447663	+	0.732924i
$960$		0			0
$961$	−5.94285	−	33.7036i	−0.191705	−	1.08721i
$962$	−1.41345	−	2.44818i	−0.0455716	−	0.0789323i
$963$		0			0
$964$	−30.4352	−	17.5718i	−0.980251	−	0.565948i
$965$	−0.00178439	−	0.0101198i	−5.74415e−5	−	0.000325767i
$966$		0			0
$967$	−6.39685	+	2.32826i	−0.205709	+	0.0748719i	−0.442820	−	0.896611i	$-0.646022\pi$
$967$	−6.39685	+	2.32826i	−0.205709	+	0.0748719i	0.237111	+	0.971483i	$0.423800\pi$
$968$	7.31862	+	20.1078i	0.235229	+	0.646288i
$969$		0			0
$970$	−8.75485e−5	0	0.000496512i	−2.81101e−6	0	1.59420e-5i
$971$	−14.6415	−	25.3599i	−0.469869	−	0.813836i	0.529538	−	0.848286i	$-0.322365\pi$
$971$	−14.6415	−	25.3599i	−0.469869	−	0.813836i	−0.999406	+	0.0344500i	$0.989032\pi$
$972$		0			0
$973$	−0.859463	+	0.685703i	−0.0275531	+	0.0219826i
$974$	11.2124	+	13.3624i	0.359269	+	0.428160i
$975$		0			0
$976$	5.99515	−	7.14474i	0.191900	−	0.228698i
$977$	−7.70964	−	1.35942i	−0.246653	−	0.0434916i	0.0489546	−	0.998801i	$-0.484411\pi$
$977$	−7.70964	−	1.35942i	−0.246653	−	0.0434916i	−0.295608	+	0.955309i	$0.595522\pi$
$978$		0			0
$979$	−15.0904	+	2.66085i	−0.482291	+	0.0850410i
$980$	0.00658251	−	0.00203356i	0.000210270	−	6.49595e-5i
$981$		0			0
$982$	5.43528			0.173447
$983$	−4.61869	+	3.87554i	−0.147313	+	0.123611i	−0.713466	−	0.700690i	$-0.752876\pi$
$983$	−4.61869	+	3.87554i	−0.147313	+	0.123611i	0.566153	+	0.824300i	$0.308431\pi$
$984$		0			0
$985$	0.00570626	+	0.00100617i	0.000181817	+	3.20592e-5i
$986$	2.57475	+	2.16048i	0.0819969	+	0.0688036i
$987$		0			0
$988$	23.5773	+	8.58143i	0.750093	+	0.273012i
$989$			10.8015i			0.343468i
$990$		0			0
$991$	22.6935			0.720884			0.360442	−	0.932782i	$-0.382626\pi$
$991$	22.6935			0.720884			0.360442	+	0.932782i	$0.382626\pi$
$992$	−31.1017	+	26.0974i	−0.987480	+	0.828594i
$993$		0			0
$994$	−0.285409	+	11.5448i	−0.00905261	+	0.366178i
$995$	−0.00618594	−	0.00109075i	−0.000196107	−	3.45790e-5i
$996$		0			0
$997$	9.60364	−	1.69338i	0.304150	−	0.0536299i	−0.0194901	−	0.999810i	$-0.506204\pi$
$997$	9.60364	−	1.69338i	0.304150	−	0.0536299i	0.323640	+	0.946180i	$0.395093\pi$
$998$	−2.74449	−	1.58453i	−0.0868752	−	0.0501574i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.bd.a.206.14		132
3.2	odd	2		189.2.bd.a.59.9	yes	132
7.5	odd	6		567.2.ba.a.530.9		132
21.5	even	6		189.2.ba.a.5.14	✓	132
27.11	odd	18		567.2.ba.a.521.9		132
27.16	even	9		189.2.ba.a.38.14	yes	132
189.124	odd	18		189.2.bd.a.173.9	yes	132
189.173	even	18	inner	567.2.bd.a.278.14		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.14	✓	132	21.5	even	6
189.2.ba.a.38.14	yes	132	27.16	even	9
189.2.bd.a.59.9	yes	132	3.2	odd	2
189.2.bd.a.173.9	yes	132	189.124	odd	18
567.2.ba.a.521.9		132	27.11	odd	18
567.2.ba.a.530.9		132	7.5	odd	6
567.2.bd.a.206.14		132	1.1	even	1	trivial
567.2.bd.a.278.14		132	189.173	even	18	inner

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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.bd (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.170792 - 0.469247i) q^{2} +(1.34107 + 1.12529i) q^{4} +(0.000430671 + 0.000361376i) q^{5} +(1.75023 - 1.98411i) q^{7} +(1.62200 - 0.936464i) q^{8} +(0.000243130 - 0.000140371i) q^{10} +(-3.04392 - 3.62761i) q^{11} +(1.77003 - 2.10944i) q^{13} +(-0.632115 - 1.16016i) q^{14} +(0.445582 + 2.52702i) q^{16} +(0.400086 + 0.692969i) q^{17} +(4.50743 + 2.60237i) q^{19} +(0.000170906 + 0.000969257i) q^{20} +(-2.22212 + 0.808787i) q^{22} +(-0.542669 - 1.49097i) q^{23} +(-0.868241 - 4.92404i) q^{25} +(-0.687542 - 1.19086i) q^{26} +(4.57987 - 0.691318i) q^{28} +(5.40692 + 6.44372i) q^{29} +(-5.19122 + 6.18666i) q^{31} +(4.95085 + 0.872968i) q^{32} +(0.393506 - 0.0693856i) q^{34} +(0.00147078 - 0.000222010i) q^{35} +2.05581 q^{37} +(1.99099 - 1.67064i) q^{38} +(0.00103696 + 0.000182845i) q^{40} +(5.20305 + 4.36588i) q^{41} +(-6.39715 - 2.32837i) q^{43} -8.29015i q^{44} -0.792318 q^{46} +(5.68085 - 4.76680i) q^{47} +(-0.873412 - 6.94530i) q^{49} +(-2.45888 - 0.433567i) q^{50} +(4.74745 - 0.837104i) q^{52} +(-9.11266 - 5.26120i) q^{53} -0.00266231i q^{55} +(0.980823 - 4.85726i) q^{56} +(3.94716 - 1.43665i) q^{58} +(-2.29410 + 13.0105i) q^{59} +(-2.33638 - 2.78438i) q^{61} +(2.01645 + 3.49260i) q^{62} +(-1.31080 + 2.27037i) q^{64} +(0.00152460 - 0.000268828i) q^{65} +(-1.99848 + 0.727386i) q^{67} +(-0.243248 + 1.37953i) q^{68} +(0.000147020 - 0.000728078i) q^{70} +(-7.56979 - 4.37042i) q^{71} +7.18246i q^{73} +(0.351116 - 0.964683i) q^{74} +(3.11635 + 8.56210i) q^{76} +(-12.5251 - 0.309645i) q^{77} +(-2.42128 - 0.881273i) q^{79} +(-0.000721305 + 0.00124934i) q^{80} +(2.93732 - 1.69586i) q^{82} +(-1.47761 + 1.23986i) q^{83} +(-7.81169e-5 + 0.000443023i) q^{85} +(-2.18517 + 2.60418i) q^{86} +(-8.33438 - 3.03347i) q^{88} +(1.61790 - 2.80229i) q^{89} +(-1.08741 - 7.20394i) q^{91} +(0.950016 - 2.61015i) q^{92} +(-1.26656 - 3.47986i) q^{94} +(0.00100079 + 0.00274964i) q^{95} +(0.614218 - 1.68755i) q^{97} +(-3.40823 - 0.776355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31}+ \cdots + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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