LMFDB - Embedded newform 567.2.ba.a.143.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(143,567)]

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([7, 3]))

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

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

chi := DirichletCharacter("567.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.ba (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			143.9
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.572822 + 0.682663i) q^{2} +(0.209393 + 1.18753i) q^{4} +(1.06212 - 0.891222i) q^{5} +(-1.58403 + 2.11916i) q^{7} +(-2.47415 - 1.42845i) q^{8} +O(q^{10})$	\(q+(-0.572822 + 0.682663i) q^{2} +(0.209393 + 1.18753i) q^{4} +(1.06212 - 0.891222i) q^{5} +(-1.58403 + 2.11916i) q^{7} +(-2.47415 - 1.42845i) q^{8} +1.23558i q^{10} +(0.371978 - 0.443306i) q^{11} +(-1.85992 + 5.11010i) q^{13} +(-0.539301 - 2.29526i) q^{14} +(0.126145 - 0.0459131i) q^{16} -2.31232 q^{17} -3.42394i q^{19} +(1.28075 + 1.07468i) q^{20} +(0.0895514 + 0.507871i) q^{22} +(-2.28843 + 6.28742i) q^{23} +(-0.534425 + 3.03087i) q^{25} +(-2.42307 - 4.19688i) q^{26} +(-2.84824 - 1.43735i) q^{28} +(0.224543 + 0.616928i) q^{29} +(1.71407 - 0.302237i) q^{31} +(1.91332 - 5.25680i) q^{32} +(1.32455 - 1.57853i) q^{34} +(0.206211 + 3.66252i) q^{35} +(0.542537 - 0.939702i) q^{37} +(2.33740 + 1.96131i) q^{38} +(-3.90090 + 0.687834i) q^{40} +(-1.37400 - 0.500093i) q^{41} +(-0.681623 + 3.86568i) q^{43} +(0.604328 + 0.348909i) q^{44} +(-2.98132 - 5.16380i) q^{46} +(-1.07027 + 6.06980i) q^{47} +(-1.98167 - 6.71364i) q^{49} +(-1.76293 - 2.10098i) q^{50} +(-6.45784 - 1.13869i) q^{52} +(-8.16395 - 4.71346i) q^{53} -0.802359i q^{55} +(6.94625 - 2.98040i) q^{56} +(-0.549777 - 0.200103i) q^{58} +(-4.76072 - 1.73276i) q^{59} +(13.3184 + 2.34839i) q^{61} +(-0.775532 + 1.34326i) q^{62} +(2.62687 + 4.54987i) q^{64} +(2.57878 + 7.08513i) q^{65} +(-6.31050 + 5.29514i) q^{67} +(-0.484183 - 2.74594i) q^{68} +(-2.61839 - 1.95720i) q^{70} +(-13.6154 + 7.86086i) q^{71} +(2.07131 - 1.19587i) q^{73} +(0.330722 + 0.908652i) q^{74} +(4.06603 - 0.716950i) q^{76} +(0.350210 + 1.49049i) q^{77} +(-2.05377 - 1.72332i) q^{79} +(0.0930623 - 0.161189i) q^{80} +(1.12845 - 0.651511i) q^{82} +(11.2771 - 4.10455i) q^{83} +(-2.45595 + 2.06079i) q^{85} +(-2.24850 - 2.67966i) q^{86} +(-1.55357 + 0.565453i) q^{88} +11.8321 q^{89} +(-7.88293 - 12.0361i) q^{91} +(-7.94566 - 1.40103i) q^{92} +(-3.53055 - 4.20755i) q^{94} +(-3.05150 - 3.63663i) q^{95} +(18.3532 + 3.23616i) q^{97} +(5.71830 + 2.49291i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.572822	+	0.682663i	−0.405046	+	0.482715i	−0.929552	−	0.368692i	$-0.879806\pi$
$2$	−0.572822	+	0.682663i	−0.405046	+	0.482715i	0.524505	+	0.851407i	$0.324250\pi$
$3$		0			0
$3$		0			0
$4$	0.209393	+	1.18753i	0.104697	+	0.593764i
$5$	1.06212	−	0.891222i	0.474993	−	0.398567i	−0.373619	−	0.927582i	$-0.621883\pi$
$5$	1.06212	−	0.891222i	0.474993	−	0.398567i	0.848612	+	0.529016i	$0.177439\pi$
$6$		0			0
$7$	−1.58403	+	2.11916i	−0.598709	+	0.800967i
$7$	−1.58403	+	2.11916i	−0.598709	+	0.800967i
$8$	−2.47415	−	1.42845i	−0.874743	−	0.505033i
$9$		0			0
$10$			1.23558i			0.390725i
$11$	0.371978	−	0.443306i	0.112156	−	0.133662i	−0.707046	−	0.707168i	$-0.749973\pi$
$11$	0.371978	−	0.443306i	0.112156	−	0.133662i	0.819201	+	0.573506i	$0.194417\pi$
$12$		0			0
$13$	−1.85992	+	5.11010i	−0.515850	+	1.41729i	0.359203	+	0.933260i	$0.383049\pi$
$13$	−1.85992	+	5.11010i	−0.515850	+	1.41729i	−0.875053	+	0.484027i	$0.839174\pi$
$14$	−0.539301	−	2.29526i	−0.144134	−	0.613435i
$15$		0			0
$16$	0.126145	−	0.0459131i	0.0315363	−	0.0114783i
$17$	−2.31232			−0.560820			−0.280410	−	0.959880i	$-0.590470\pi$
$17$	−2.31232			−0.560820			−0.280410	+	0.959880i	$0.590470\pi$
$18$		0			0
$19$		−	3.42394i		−	0.785506i	−0.919644	−	0.392753i	$-0.871523\pi$
$19$		−	3.42394i		−	0.785506i	0.919644	−	0.392753i	$-0.128477\pi$
$20$	1.28075	+	1.07468i	0.286385	+	0.240305i
$21$		0			0
$22$	0.0895514	+	0.507871i	0.0190924	+	0.108279i
$23$	−2.28843	+	6.28742i	−0.477171	+	1.31102i	0.434713	+	0.900569i	$0.356850\pi$
$23$	−2.28843	+	6.28742i	−0.477171	+	1.31102i	−0.911884	+	0.410448i	$0.865372\pi$
$24$		0			0
$25$	−0.534425	+	3.03087i	−0.106885	+	0.606175i
$26$	−2.42307	−	4.19688i	−0.475203	−	0.823076i
$27$		0			0
$28$	−2.84824	−	1.43735i	−0.538268	−	0.271633i
$29$	0.224543	+	0.616928i	0.0416967	+	0.114561i	0.958794	−	0.284104i	$-0.0916960\pi$
$29$	0.224543	+	0.616928i	0.0416967	+	0.114561i	−0.917097	+	0.398664i	$0.869474\pi$
$30$		0			0
$31$	1.71407	−	0.302237i	0.307857	−	0.0542834i	−0.0175856	−	0.999845i	$-0.505598\pi$
$31$	1.71407	−	0.302237i	0.307857	−	0.0542834i	0.325442	+	0.945562i	$0.394487\pi$
$32$	1.91332	−	5.25680i	0.338230	−	0.929280i
$33$		0			0
$34$	1.32455	−	1.57853i	0.227158	−	0.270716i
$35$	0.206211	+	3.66252i	0.0348560	+	0.619079i
$36$		0			0
$37$	0.542537	−	0.939702i	0.0891925	−	0.154486i	−0.817978	−	0.575250i	$-0.804905\pi$
$37$	0.542537	−	0.939702i	0.0891925	−	0.154486i	0.907170	+	0.420764i	$0.138238\pi$
$38$	2.33740	+	1.96131i	0.379176	+	0.318167i
$39$		0			0
$40$	−3.90090	+	0.687834i	−0.616787	+	0.108756i
$41$	−1.37400	−	0.500093i	−0.214582	−	0.0781015i	0.232492	−	0.972598i	$-0.425312\pi$
$41$	−1.37400	−	0.500093i	−0.214582	−	0.0781015i	−0.447074	+	0.894497i	$0.647534\pi$
$42$		0			0
$43$	−0.681623	+	3.86568i	−0.103947	+	0.589510i	0.887689	+	0.460443i	$0.152309\pi$
$43$	−0.681623	+	3.86568i	−0.103947	+	0.589510i	−0.991636	+	0.129067i	$0.958802\pi$
$44$	0.604328	+	0.348909i	0.0911059	+	0.0526000i
$45$		0			0
$46$	−2.98132	−	5.16380i	−0.439572	−	0.761361i
$47$	−1.07027	+	6.06980i	−0.156115	+	0.885372i	0.801645	+	0.597801i	$0.203959\pi$
$47$	−1.07027	+	6.06980i	−0.156115	+	0.885372i	−0.957759	+	0.287571i	$0.907152\pi$
$48$		0			0
$49$	−1.98167	−	6.71364i	−0.283095	−	0.959092i
$50$	−1.76293	−	2.10098i	−0.249316	−	0.297124i
$51$		0			0
$52$	−6.45784	−	1.13869i	−0.895541	−	0.157908i
$53$	−8.16395	−	4.71346i	−1.12141	−	0.647444i	−0.179646	−	0.983731i	$-0.557495\pi$
$53$	−8.16395	−	4.71346i	−1.12141	−	0.647444i	−0.941759	+	0.336288i	$0.890829\pi$
$54$		0			0
$55$		−	0.802359i		−	0.108190i
$56$	6.94625	−	2.98040i	0.928231	−	0.398272i
$57$		0			0
$58$	−0.549777	−	0.200103i	−0.0721893	−	0.0262748i
$59$	−4.76072	−	1.73276i	−0.619792	−	0.225586i	0.0129900	−	0.999916i	$-0.495865\pi$
$59$	−4.76072	−	1.73276i	−0.619792	−	0.225586i	−0.632782	+	0.774330i	$0.718087\pi$
$60$		0			0
$61$	13.3184	+	2.34839i	1.70524	+	0.300680i	0.939521	−	0.342491i	$-0.111271\pi$
$61$	13.3184	+	2.34839i	1.70524	+	0.300680i	0.765722	+	0.643171i	$0.222382\pi$
$62$	−0.775532	+	1.34326i	−0.0984927	+	0.170594i
$63$		0			0
$64$	2.62687	+	4.54987i	0.328359	+	0.568734i
$65$	2.57878	+	7.08513i	0.319858	+	0.878803i
$66$		0			0
$67$	−6.31050	+	5.29514i	−0.770950	+	0.646904i	−0.940952	−	0.338540i	$-0.890067\pi$
$67$	−6.31050	+	5.29514i	−0.770950	+	0.646904i	0.170002	+	0.985444i	$0.445623\pi$
$68$	−0.484183	−	2.74594i	−0.0587159	−	0.332994i
$69$		0			0
$70$	−2.61839	−	1.95720i	−0.312957	−	0.233930i
$71$	−13.6154	+	7.86086i	−1.61585	+	0.932913i	−0.627875	+	0.778314i	$0.716075\pi$
$71$	−13.6154	+	7.86086i	−1.61585	+	0.932913i	−0.987977	+	0.154599i	$0.950592\pi$
$72$		0			0
$73$	2.07131	−	1.19587i	0.242429	−	0.139966i	−0.373864	−	0.927484i	$-0.621967\pi$
$73$	2.07131	−	1.19587i	0.242429	−	0.139966i	0.616292	+	0.787517i	$0.288634\pi$
$74$	0.330722	+	0.908652i	0.0384457	+	0.105629i
$75$		0			0
$76$	4.06603	−	0.716950i	0.466405	−	0.0822398i
$77$	0.350210	+	1.49049i	0.0399102	+	0.169858i
$78$		0			0
$79$	−2.05377	−	1.72332i	−0.231067	−	0.193889i	0.519901	−	0.854226i	$-0.325969\pi$
$79$	−2.05377	−	1.72332i	−0.231067	−	0.193889i	−0.750969	+	0.660338i	$0.770413\pi$
$80$	0.0930623	−	0.161189i	0.0104047	−	0.0180214i
$81$		0			0
$82$	1.12845	−	0.651511i	0.124616	−	0.0719473i
$83$	11.2771	−	4.10455i	1.23783	−	0.450532i	0.361556	−	0.932350i	$-0.382246\pi$
$83$	11.2771	−	4.10455i	1.23783	−	0.450532i	0.876271	+	0.481818i	$0.160023\pi$
$84$		0			0
$85$	−2.45595	+	2.06079i	−0.266386	+	0.223524i
$86$	−2.24850	−	2.67966i	−0.242462	−	0.288956i
$87$		0			0
$88$	−1.55357	+	0.565453i	−0.165611	+	0.0602775i
$89$	11.8321			1.25420			0.627099	−	0.778940i	$-0.284242\pi$
$89$	11.8321			1.25420			0.627099	+	0.778940i	$0.284242\pi$
$90$		0			0
$91$	−7.88293	−	12.0361i	−0.826356	−	1.26172i
$92$	−7.94566	−	1.40103i	−0.828392	−	0.146068i
$93$		0			0
$94$	−3.53055	−	4.20755i	−0.364149	−	0.433976i
$95$	−3.05150	−	3.63663i	−0.313077	−	0.373110i
$96$		0			0
$97$	18.3532	+	3.23616i	1.86348	+	0.328582i	0.987974	−	0.154618i	$-0.0494148\pi$
$97$	18.3532	+	3.23616i	1.86348	+	0.328582i	0.875510	+	0.483201i	$0.160526\pi$
$98$	5.71830	+	2.49291i	0.577635	+	0.251822i
$99$		0			0
$100$	−3.71115			−0.371115
$101$	−11.4438	+	4.16521i	−1.13870	+	0.414454i	−0.841445	−	0.540343i	$-0.818295\pi$
$101$	−11.4438	+	4.16521i	−1.13870	+	0.414454i	−0.297259	+	0.954797i	$0.596072\pi$
$102$		0			0
$103$	8.26065	+	9.84467i	0.813947	+	0.970024i	0.999921	−	0.0125308i	$-0.00398878\pi$
$103$	8.26065	+	9.84467i	0.813947	+	0.970024i	−0.185975	+	0.982554i	$0.559544\pi$
$104$	11.9012	−	9.98633i	1.16701	−	0.979241i
$105$		0			0
$106$	7.89420	−	2.87325i	0.766752	−	0.279075i
$107$	8.97631	−	5.18247i	0.867772	−	0.501009i	0.00116512	−	0.999999i	$-0.499629\pi$
$107$	8.97631	−	5.18247i	0.867772	−	0.501009i	0.866607	+	0.498991i	$0.166296\pi$
$108$		0			0
$109$	8.42552	−	14.5934i	0.807019	−	1.39780i	−0.107901	−	0.994162i	$-0.534413\pi$
$109$	8.42552	−	14.5934i	0.807019	−	1.39780i	0.914920	−	0.403636i	$-0.132254\pi$
$110$	0.547741	+	0.459609i	0.0522250	+	0.0438220i
$111$		0			0
$112$	−0.102521	+	0.340050i	−0.00968735	+	0.0321317i
$113$	20.0144	−	3.52907i	1.88279	−	0.331987i	0.890409	−	0.455162i	$-0.150419\pi$
$113$	20.0144	−	3.52907i	1.88279	−	0.331987i	0.992385	+	0.123174i	$0.0393074\pi$
$114$		0			0
$115$	3.17290	+	8.71748i	0.295875	+	0.812909i
$116$	−0.685601	+	0.395832i	−0.0636564	+	0.0367521i
$117$		0			0
$118$	3.90993	−	2.25740i	0.359939	−	0.207811i
$119$	3.66279	−	4.90017i	0.335768	−	0.449198i
$120$		0			0
$121$	1.85198	+	10.5031i	0.168362	+	0.954826i
$122$	−9.23222	+	7.74675i	−0.835846	+	0.701358i
$123$		0			0
$124$	0.717830	+	1.97222i	0.0644630	+	0.177111i
$125$	5.59980	+	9.69914i	0.500861	+	0.867517i
$126$		0			0
$127$	−0.987545	+	1.71048i	−0.0876305	+	0.151780i	−0.906509	−	0.422186i	$-0.861263\pi$
$127$	−0.987545	+	1.71048i	−0.0876305	+	0.151780i	0.818879	+	0.573967i	$0.194596\pi$
$128$	6.40760	+	1.12983i	0.566358	+	0.0998641i
$129$		0			0
$130$	−6.31394	−	2.29809i	−0.553769	−	0.201555i
$131$	2.09647	+	0.763054i	0.183170	+	0.0666683i	0.431977	−	0.901885i	$-0.357816\pi$
$131$	2.09647	+	0.763054i	0.183170	+	0.0666683i	−0.248807	+	0.968553i	$0.580038\pi$
$132$		0			0
$133$	7.25588	+	5.42365i	0.629165	+	0.470290i
$134$		−	7.34111i		−	0.634176i
$135$		0			0
$136$	5.72102	+	3.30303i	0.490573	+	0.283233i
$137$	−1.31325	−	0.231561i	−0.112198	−	0.0197836i	0.117267	−	0.993100i	$-0.462587\pi$
$137$	−1.31325	−	0.231561i	−0.112198	−	0.0197836i	−0.229465	+	0.973317i	$0.573698\pi$
$138$		0			0
$139$	−9.79765	−	11.6764i	−0.831026	−	0.990378i	−0.999989	−	0.00475527i	$-0.998486\pi$
$139$	−9.79765	−	11.6764i	−0.831026	−	0.990378i	0.168963	−	0.985622i	$-0.445958\pi$
$140$	−4.30617	+	1.01179i	−0.363937	+	0.0855117i
$141$		0			0
$142$	2.43289	−	13.7976i	0.204164	−	1.15787i
$143$	1.57349	+	2.72536i	0.131582	+	0.227906i
$144$		0			0
$145$	0.788312	+	0.455132i	0.0654657	+	0.0377967i
$146$	−0.370115	+	2.09903i	−0.0306310	+	0.173717i
$147$		0			0
$148$	1.22952	+	0.447510i	0.101066	+	0.0367851i
$149$	19.6318	−	3.46162i	1.60830	−	0.283587i	0.703909	−	0.710290i	$-0.251436\pi$
$149$	19.6318	−	3.46162i	1.60830	−	0.283587i	0.904392	+	0.426703i	$0.140325\pi$
$150$		0			0
$151$	−2.21309	−	1.85701i	−0.180099	−	0.151121i	0.548282	−	0.836294i	$-0.315282\pi$
$151$	−2.21309	−	1.85701i	−0.180099	−	0.151121i	−0.728381	+	0.685173i	$0.759727\pi$
$152$	−4.89093	+	8.47134i	−0.396707	+	0.687116i
$153$		0			0
$154$	−1.21811	−	0.614712i	−0.0981583	−	0.0495349i
$155$	1.55119	−	1.84863i	0.124594	−	0.148486i
$156$		0			0
$157$	−2.77826	+	7.63321i	−0.221729	+	0.609197i	−0.999820	−	0.0189550i	$-0.993966\pi$
$157$	−2.77826	+	7.63321i	−0.221729	+	0.609197i	0.778091	+	0.628152i	$0.216188\pi$
$158$	2.35289	−	0.414878i	0.187186	−	0.0330059i
$159$		0			0
$160$	−2.65281	−	7.28853i	−0.209723	−	0.576209i
$161$	−9.69908	−	14.8090i	−0.764394	−	1.16712i
$162$		0			0
$163$	0.518631	+	0.898295i	0.0406223	+	0.0703599i	0.885622	−	0.464407i	$-0.153733\pi$
$163$	0.518631	+	0.898295i	0.0406223	+	0.0703599i	−0.844999	+	0.534767i	$0.820399\pi$
$164$	0.306169	−	1.73637i	0.0239078	−	0.135588i
$165$		0			0
$166$	−3.65778	+	10.0497i	−0.283899	+	0.780005i
$167$	2.43922	+	13.8335i	0.188753	+	1.07047i	0.921038	+	0.389472i	$0.127342\pi$
$167$	2.43922	+	13.8335i	0.188753	+	1.07047i	−0.732286	+	0.680998i	$0.761546\pi$
$168$		0			0
$169$	−12.6952	−	10.6526i	−0.976556	−	0.819428i
$170$		−	2.85705i		−	0.219126i
$171$		0			0
$172$	−4.73332			−0.360912
$173$	5.50262	−	2.00279i	0.418356	−	0.152269i	−0.124260	−	0.992250i	$-0.539656\pi$
$173$	5.50262	−	2.00279i	0.418356	−	0.152269i	0.542617	+	0.839980i	$0.317434\pi$
$174$		0			0
$175$	−5.57635	−	5.93354i	−0.421533	−	0.448533i
$176$	0.0265697	−	0.0729997i	0.00200277	−	0.00550256i
$177$		0			0
$178$	−6.77767	+	8.07732i	−0.508008	+	0.605420i
$179$			8.49786i			0.635160i	0.948232	+	0.317580i	$0.102870\pi$
$179$			8.49786i			0.635160i	−0.948232	+	0.317580i	$0.897130\pi$
$180$		0			0
$181$	5.00733	+	2.89098i	0.372192	+	0.214885i	0.674416	−	0.738352i	$-0.264396\pi$
$181$	5.00733	+	2.89098i	0.372192	+	0.214885i	−0.302224	+	0.953237i	$0.597729\pi$
$182$	12.7321	+	1.51313i	0.943765	+	0.112161i
$183$		0			0
$184$	14.6432	−	12.2871i	1.07951	−	0.905816i
$185$	−0.261245	−	1.48159i	−0.0192071	−	0.108929i
$186$		0			0
$187$	−0.860132	+	1.02507i	−0.0628991	+	0.0749602i
$188$	−7.43216			−0.542046
$189$		0			0
$190$	4.23056			0.306917
$191$	−15.2886	+	18.2202i	−1.10624	+	1.31837i	−0.162864	+	0.986649i	$0.552073\pi$
$191$	−15.2886	+	18.2202i	−1.10624	+	1.31837i	−0.943378	+	0.331719i	$0.892371\pi$
$192$		0			0
$193$	−3.28572	−	18.6342i	−0.236511	−	1.34132i	−0.839408	−	0.543502i	$-0.817098\pi$
$193$	−3.28572	−	18.6342i	−0.236511	−	1.34132i	0.602897	−	0.797819i	$-0.294013\pi$
$194$	−12.7223	+	10.6753i	−0.913409	+	0.766441i
$195$		0			0
$196$	7.55768	−	3.75907i	0.539835	−	0.268505i
$197$	9.22224	+	5.32447i	0.657058	+	0.379352i	0.791155	−	0.611616i	$-0.209480\pi$
$197$	9.22224	+	5.32447i	0.657058	+	0.379352i	−0.134097	+	0.990968i	$0.542813\pi$
$198$		0			0
$199$			10.0273i			0.710813i	0.934712	+	0.355407i	$0.115658\pi$
$199$			10.0273i			0.710813i	−0.934712	+	0.355407i	$0.884342\pi$
$200$	5.65169	−	6.73543i	0.399635	−	0.476267i
$201$		0			0
$202$	3.71184	−	10.1982i	0.261164	−	0.717543i
$203$	−1.66305	−	0.501392i	−0.116723	−	0.0351908i
$204$		0			0
$205$	−1.90504	+	0.693377i	−0.133054	+	0.0484276i
$206$	−11.4525			−0.797931
$207$		0			0
$208$			0.730010i			0.0506171i
$209$	−1.51786	−	1.27363i	−0.104992	−	0.0880990i
$210$		0			0
$211$	−1.04018	−	5.89915i	−0.0716089	−	0.406114i	−0.999451	−	0.0331403i	$-0.989449\pi$
$211$	−1.04018	−	5.89915i	−0.0716089	−	0.406114i	0.927842	−	0.372974i	$-0.121662\pi$
$212$	3.88789	−	10.6819i	0.267021	−	0.733635i
$213$		0			0
$214$	−1.60395	+	9.09643i	−0.109643	+	0.621819i
$215$	2.72121	+	4.71328i	0.185585	+	0.321443i
$216$		0			0
$217$	−2.07466	+	4.11115i	−0.140837	+	0.279083i
$218$	5.13607	+	14.1112i	0.347858	+	0.955733i
$219$		0			0
$220$	0.952823	−	0.168008i	0.0642393	−	0.0113271i
$221$	4.30074	−	11.8162i	0.289299	−	0.794842i
$222$		0			0
$223$	3.68146	−	4.38739i	0.246528	−	0.293801i	−0.628563	−	0.777759i	$-0.716357\pi$
$223$	3.68146	−	4.38739i	0.246528	−	0.293801i	0.875092	+	0.483957i	$0.160801\pi$
$224$	8.10923	+	12.3816i	0.541821	+	0.827279i
$225$		0			0
$226$	−9.05551	+	15.6846i	−0.602363	+	1.04332i
$227$	−13.5450	−	11.3656i	−0.899011	−	0.754359i	0.0709862	−	0.997477i	$-0.477385\pi$
$227$	−13.5450	−	11.3656i	−0.899011	−	0.754359i	−0.969997	+	0.243118i	$0.921830\pi$
$228$		0			0
$229$	13.5151	−	2.38308i	0.893103	−	0.157478i	0.291781	−	0.956485i	$-0.405752\pi$
$229$	13.5151	−	2.38308i	0.893103	−	0.157478i	0.601322	+	0.799007i	$0.294641\pi$
$230$	−7.76861	−	2.82754i	−0.512247	−	0.186443i
$231$		0			0
$232$	0.325697	−	1.84712i	0.0213831	−	0.121269i
$233$	−7.92072	−	4.57303i	−0.518904	−	0.299589i	0.217582	−	0.976042i	$-0.430183\pi$
$233$	−7.92072	−	4.57303i	−0.518904	−	0.299589i	−0.736486	+	0.676453i	$0.763516\pi$
$234$		0			0
$235$	4.27279	+	7.40069i	0.278726	+	0.482768i
$236$	1.06084	−	6.01631i	0.0690546	−	0.391628i
$237$		0			0
$238$	1.24704	+	5.30738i	0.0808333	+	0.344026i
$239$	−1.62286	−	1.93405i	−0.104974	−	0.125103i	0.710999	−	0.703193i	$-0.248243\pi$
$239$	−1.62286	−	1.93405i	−0.104974	−	0.125103i	−0.815973	+	0.578089i	$0.803798\pi$
$240$		0			0
$241$	7.08366	+	1.24904i	0.456299	+	0.0804578i	0.397073	−	0.917787i	$-0.370026\pi$
$241$	7.08366	+	1.24904i	0.456299	+	0.0804578i	0.0592254	+	0.998245i	$0.481137\pi$
$242$	−8.23092	−	4.75212i	−0.529103	−	0.305478i
$243$		0			0
$244$			16.3077i			1.04399i
$245$	−8.08811	−	5.36457i	−0.516731	−	0.342730i
$246$		0			0
$247$	17.4967	+	6.36828i	1.11329	+	0.405204i
$248$	−4.67260	−	1.70069i	−0.296710	−	0.107994i
$249$		0			0
$250$	−9.82893	−	1.73311i	−0.621636	−	0.109611i
$251$	0.469593	−	0.813359i	0.0296405	−	0.0513388i	−0.850825	−	0.525450i	$-0.823897\pi$
$251$	0.469593	−	0.813359i	0.0296405	−	0.0513388i	0.880465	+	0.474111i	$0.157230\pi$
$252$		0			0
$253$	1.93601	+	3.35326i	0.121716	+	0.210818i
$254$	−0.601992	−	1.65396i	−0.0377724	−	0.103779i
$255$		0			0
$256$	−12.4909	+	10.4811i	−0.780682	+	0.655070i
$257$	3.40273	+	19.2978i	0.212256	+	1.20377i	0.885604	+	0.464441i	$0.153745\pi$
$257$	3.40273	+	19.2978i	0.212256	+	1.20377i	−0.673348	+	0.739326i	$0.735144\pi$
$258$		0			0
$259$	1.13198	+	2.63824i	0.0703378	+	0.163932i
$260$	−7.87381	+	4.54595i	−0.488313	+	0.281928i
$261$		0			0
$262$	−1.72181	+	0.994090i	−0.106374	+	0.0614151i
$263$	−4.07910	−	11.2072i	−0.251528	−	0.691068i	−0.999622	−	0.0274758i	$-0.991253\pi$
$263$	−4.07910	−	11.2072i	−0.251528	−	0.691068i	0.748094	−	0.663593i	$-0.230969\pi$
$264$		0			0
$265$	−12.8718	+	2.26965i	−0.790710	+	0.139423i
$266$	−7.85885	+	1.84654i	−0.481857	+	0.113218i
$267$		0			0
$268$	−7.60949	−	6.38512i	−0.464824	−	0.390033i
$269$	8.21836	−	14.2346i	0.501082	−	0.867900i	−0.498917	−	0.866650i	$-0.666269\pi$
$269$	8.21836	−	14.2346i	0.501082	−	0.867900i	0.999999	−	0.00125014i	$-0.000397931\pi$
$270$		0			0
$271$	−12.7971	+	7.38840i	−0.777367	+	0.448813i	−0.835496	−	0.549496i	$-0.814820\pi$
$271$	−12.7971	+	7.38840i	−0.777367	+	0.448813i	0.0581291	+	0.998309i	$0.481487\pi$
$272$	−0.291688	+	0.106166i	−0.0176862	+	0.00643725i
$273$		0			0
$274$	0.910336	−	0.763863i	0.0549954	−	0.0461466i
$275$	1.14481	+	1.36433i	0.0690347	+	0.0822724i
$276$		0			0
$277$	−26.0466	+	9.48020i	−1.56499	+	0.569610i	−0.971873	−	0.235506i	$-0.924325\pi$
$277$	−26.0466	+	9.48020i	−1.56499	+	0.569610i	−0.593118	+	0.805116i	$0.702103\pi$
$278$	13.5833			0.814674
$279$		0			0
$280$	4.72153	−	9.35618i	0.282166	−	0.559139i
$281$	−6.13171	−	1.08119i	−0.365787	−	0.0644981i	−0.0122663	−	0.999925i	$-0.503905\pi$
$281$	−6.13171	−	1.08119i	−0.365787	−	0.0644981i	−0.353521	+	0.935427i	$0.615016\pi$
$282$		0			0
$283$	3.53087	+	4.20792i	0.209888	+	0.250135i	0.860710	−	0.509095i	$-0.170020\pi$
$283$	3.53087	+	4.20792i	0.209888	+	0.250135i	−0.650822	+	0.759230i	$0.725576\pi$
$284$	−12.1860	−	14.5227i	−0.723104	−	0.861762i
$285$		0			0
$286$	−2.76183	−	0.486986i	−0.163311	−	0.0287961i
$287$	3.23623	−	2.11955i	0.191029	−	0.125113i
$288$		0			0
$289$	−11.6532			−0.685481
$290$	−0.762264	+	0.277441i	−0.0447617	+	0.0162919i
$291$		0			0
$292$	1.85385	+	2.20933i	0.108488	+	0.129291i
$293$	−17.8320	+	14.9629i	−1.04176	+	0.874140i	−0.992203	−	0.124632i	$-0.960225\pi$
$293$	−17.8320	+	14.9629i	−1.04176	+	0.874140i	−0.0495561	+	0.998771i	$0.515781\pi$
$294$		0			0
$295$	−6.60071	+	2.40246i	−0.384308	+	0.139877i
$296$	−2.68463	+	1.54997i	−0.156041	+	0.0900904i
$297$		0			0
$298$	−8.88242	+	15.3848i	−0.514545	+	0.891218i
$299$	−27.8730	−	23.3882i	−1.61194	−	1.35258i
$300$		0			0
$301$	−7.11227	−	7.56783i	−0.409944	−	0.436203i
$302$	2.53542	−	0.447062i	0.145897	−	0.0257255i
$303$		0			0
$304$	−0.157204	−	0.431914i	−0.00901627	−	0.0247720i
$305$	16.2386	−	9.37537i	0.929821	−	0.536832i
$306$		0			0
$307$	15.1010	−	8.71859i	0.861862	−	0.497596i	−0.00277334	−	0.999996i	$-0.500883\pi$
$307$	15.1010	−	8.71859i	0.861862	−	0.497596i	0.864635	+	0.502400i	$0.167549\pi$
$308$	−1.69667	+	0.727983i	−0.0966768	+	0.0414807i
$309$		0			0
$310$	0.373438	+	2.11787i	0.0212099	+	0.120287i
$311$	1.15637	−	0.970311i	0.0655718	−	0.0550213i	−0.609413	−	0.792853i	$-0.708595\pi$
$311$	1.15637	−	0.970311i	0.0655718	−	0.0550213i	0.674985	+	0.737832i	$0.264150\pi$
$312$		0			0
$313$	−9.95908	−	27.3624i	−0.562921	−	1.54661i	−0.815333	−	0.578992i	$-0.803446\pi$
$313$	−9.95908	−	27.3624i	−0.562921	−	1.54661i	0.252413	−	0.967620i	$-0.418776\pi$
$314$	−3.61946	−	6.26909i	−0.204258	−	0.353785i
$315$		0			0
$316$	1.61644	−	2.79976i	0.0909320	−	0.157499i
$317$	−29.9400	−	5.27923i	−1.68160	−	0.296511i	−0.750388	−	0.660997i	$-0.770134\pi$
$317$	−29.9400	−	5.27923i	−1.68160	−	0.296511i	−0.931209	+	0.364486i	$0.881245\pi$
$318$		0			0
$319$	0.357014	+	0.129942i	0.0199889	+	0.00727537i
$320$	6.84500	+	2.49137i	0.382647	+	0.139272i
$321$		0			0
$322$	15.6654	+	1.86174i	0.873000	+	0.103751i
$323$			7.91725i			0.440527i
$324$		0			0
$325$	−14.4941	−	8.36816i	−0.803987	−	0.464182i
$326$	−0.910316	−	0.160513i	−0.0504177	−	0.00889000i
$327$		0			0
$328$	2.68511	+	3.19999i	0.148260	+	0.176690i
$329$	−11.1675	−	11.8828i	−0.615686	−	0.655123i
$330$		0			0
$331$	−4.91465	+	27.8723i	−0.270133	+	1.53200i	0.483875	+	0.875137i	$0.339229\pi$
$331$	−4.91465	+	27.8723i	−0.270133	+	1.53200i	−0.754008	+	0.656865i	$0.771882\pi$
$332$	7.23562	+	12.5325i	0.397106	+	0.687808i
$333$		0			0
$334$	−10.8409	−	6.25898i	−0.593186	−	0.342476i
$335$	−1.98335	+	11.2481i	−0.108362	+	0.614550i
$336$		0			0
$337$	7.63576	+	2.77919i	0.415946	+	0.151392i	0.541512	−	0.840693i	$-0.317852\pi$
$337$	7.63576	+	2.77919i	0.415946	+	0.151392i	−0.125565	+	0.992085i	$0.540074\pi$
$338$	14.5442	−	2.56454i	0.791101	−	0.139492i
$339$		0			0
$340$	−2.96150	−	2.48500i	−0.160610	−	0.134768i
$341$	0.503614	−	0.872285i	0.0272722	−	0.0472369i
$342$		0			0
$343$	17.3663	+	6.43517i	0.937692	+	0.347467i
$344$	7.20836	−	8.59059i	0.388649	−	0.463174i
$345$		0			0
$346$	−1.78479	+	4.90368i	−0.0959510	+	0.263623i
$347$	−13.5586	+	2.39075i	−0.727863	+	0.128342i	−0.525288	−	0.850925i	$-0.676042\pi$
$347$	−13.5586	+	2.39075i	−0.727863	+	0.128342i	−0.202576	+	0.979267i	$0.564931\pi$
$348$		0			0
$349$	0.460133	+	1.26420i	0.0246303	+	0.0676713i	0.951398	−	0.307963i	$-0.0996472\pi$
$349$	0.460133	+	1.26420i	0.0246303	+	0.0676713i	−0.926768	+	0.375634i	$0.877425\pi$
$350$	7.24486	−	0.407907i	0.387254	−	0.0218036i
$351$		0			0
$352$	−1.61866	−	2.80360i	−0.0862749	−	0.149432i
$353$	−2.73545	+	15.5135i	−0.145593	+	0.825701i	0.821295	+	0.570503i	$0.193252\pi$
$353$	−2.73545	+	15.5135i	−0.145593	+	0.825701i	−0.966889	+	0.255198i	$0.917859\pi$
$354$		0			0
$355$	−7.45539	+	20.4835i	−0.395691	+	1.08715i
$356$	2.47755	+	14.0509i	0.131310	+	0.744697i
$357$		0			0
$358$	−5.80117	−	4.86776i	−0.306601	−	0.257269i
$359$		−	29.9732i		−	1.58192i	−0.611866	−	0.790962i	$-0.709581\pi$
$359$		−	29.9732i		−	1.58192i	0.611866	−	0.790962i	$-0.290419\pi$
$360$		0			0
$361$	7.27661			0.382980
$362$	−4.84188	+	1.76230i	−0.254483	+	0.0926244i
$363$		0			0
$364$	12.6425	−	11.8815i	0.662647	−	0.622758i
$365$	1.13419	−	3.11616i	0.0593661	−	0.163107i
$366$		0			0
$367$	−3.07129	+	3.66022i	−0.160320	+	0.191062i	−0.840225	−	0.542239i	$-0.817577\pi$
$367$	−3.07129	+	3.66022i	−0.160320	+	0.191062i	0.679904	+	0.733301i	$0.262021\pi$
$368$			0.898197i			0.0468218i
$369$		0			0
$370$	1.16108	+	0.670348i	0.0603615	+	0.0348497i
$371$	22.9206	−	9.83443i	1.18998	−	0.510578i
$372$		0			0
$373$	10.5947	−	8.89000i	0.548572	−	0.460307i	−0.325885	−	0.945409i	$-0.605662\pi$
$373$	10.5947	−	8.89000i	0.548572	−	0.460307i	0.874457	+	0.485103i	$0.161218\pi$
$374$	−0.207071	−	1.17436i	−0.0107074	−	0.0607247i
$375$		0			0
$376$	11.3184	−	13.4888i	0.583703	−	0.695630i
$377$	−3.57020			−0.183875
$378$		0			0
$379$	−8.84194			−0.454180			−0.227090	−	0.973874i	$-0.572921\pi$
$379$	−8.84194			−0.454180			−0.227090	+	0.973874i	$0.572921\pi$
$380$	3.67963	−	4.38522i	0.188761	−	0.224957i
$381$		0			0
$382$	−3.68063	−	20.8739i	−0.188317	−	1.06800i
$383$	−23.0477	+	19.3393i	−1.17768	+	0.988193i	−0.177691	+	0.984086i	$0.556863\pi$
$383$	−23.0477	+	19.3393i	−1.17768	+	0.988193i	−0.999992	+	0.00410677i	$0.998693\pi$
$384$		0			0
$385$	1.70033	+	1.27096i	0.0866566	+	0.0647743i
$386$	14.6030	+	8.43106i	0.743274	+	0.429130i
$387$		0			0
$388$			22.4725i			1.14087i
$389$	−6.35574	+	7.57448i	−0.322249	+	0.384041i	−0.902712	−	0.430245i	$-0.858427\pi$
$389$	−6.35574	+	7.57448i	−0.322249	+	0.384041i	0.580463	+	0.814286i	$0.302872\pi$
$390$		0			0
$391$	5.29159	−	14.5385i	0.267607	−	0.735244i
$392$	−4.68716	+	19.4413i	−0.236737	+	0.981932i
$393$		0			0
$394$	−8.91752	+	3.24571i	−0.449258	+	0.163517i
$395$	−3.71721			−0.187033
$396$		0			0
$397$		−	11.4899i		−	0.576660i	−0.957531	−	0.288330i	$-0.906900\pi$
$397$		−	11.4899i		−	0.576660i	0.957531	−	0.288330i	$-0.0931000\pi$
$398$	−6.84523	−	5.74383i	−0.343121	−	0.287912i
$399$		0			0
$400$	0.0717417	+	0.406867i	0.00358709	+	0.0203434i
$401$	−5.63819	+	15.4908i	−0.281558	+	0.773573i	0.715620	+	0.698490i	$0.246144\pi$
$401$	−5.63819	+	15.4908i	−0.281558	+	0.773573i	−0.997177	+	0.0750829i	$0.976078\pi$
$402$		0			0
$403$	−1.64358	+	9.32122i	−0.0818727	+	0.464323i
$404$	−7.34256	−	12.7177i	−0.365306	−	0.632729i
$405$		0			0
$406$	1.29492	−	0.848096i	0.0642656	−	0.0420903i
$407$	−0.214764	−	0.590059i	−0.0106454	−	0.0292481i
$408$		0			0
$409$	8.98833	−	1.58489i	0.444444	−	0.0783675i	0.0530527	−	0.998592i	$-0.483105\pi$
$409$	8.98833	−	1.58489i	0.444444	−	0.0783675i	0.391392	+	0.920224i	$0.371994\pi$
$410$	0.617905	−	1.69768i	0.0305162	−	0.0838425i
$411$		0			0
$412$	−9.96108	+	11.8712i	−0.490747	+	0.584850i
$413$	11.2131	−	7.34396i	0.551762	−	0.361373i
$414$		0			0
$415$	8.31959	−	14.4100i	0.408393	−	0.707357i
$416$	23.3041	+	19.5545i	1.14258	+	0.958738i
$417$		0			0
$418$	1.73892	−	0.306619i	0.0850535	−	0.0149972i
$419$	27.5287	+	10.0196i	1.34487	+	0.489492i	0.911342	−	0.411650i	$-0.135047\pi$
$419$	27.5287	+	10.0196i	1.34487	+	0.489492i	0.433525	+	0.901142i	$0.357270\pi$
$420$		0			0
$421$	2.05835	−	11.6735i	0.100318	−	0.568930i	−0.892670	−	0.450711i	$-0.851171\pi$
$421$	2.05835	−	11.6735i	0.100318	−	0.568930i	0.992988	−	0.118219i	$-0.0377184\pi$
$422$	4.62297	+	2.66907i	0.225042	+	0.129928i
$423$		0			0
$424$	13.4659	+	23.3236i	0.653961	+	1.13269i
$425$	1.23576	−	7.00834i	0.0599432	−	0.339955i
$426$		0			0
$427$	−26.0734	+	24.5038i	−1.26178	+	1.18582i
$428$	8.03390	+	9.57443i	0.388333	+	0.462798i
$429$		0			0
$430$	−4.77635	−	0.842200i	−0.230336	−	0.0406145i
$431$	10.4044	+	6.00699i	0.501163	+	0.289347i	0.729194	−	0.684307i	$-0.239895\pi$
$431$	10.4044	+	6.00699i	0.501163	+	0.289347i	−0.228031	+	0.973654i	$0.573229\pi$
$432$		0			0
$433$			1.86378i			0.0895673i	0.998997	+	0.0447837i	$0.0142599\pi$
$433$			1.86378i			0.0895673i	−0.998997	+	0.0447837i	$0.985740\pi$
$434$	−1.61811	−	3.77125i	−0.0776720	−	0.181026i
$435$		0			0
$436$	19.0943	+	6.94977i	0.914453	+	0.332834i
$437$	21.5278	+	7.83546i	1.02981	+	0.374821i
$438$		0			0
$439$	25.7176	+	4.53471i	1.22744	+	0.216430i	0.749524	−	0.661978i	$-0.230283\pi$
$439$	25.7176	+	4.53471i	1.22744	+	0.216430i	0.477912	+	0.878408i	$0.341394\pi$
$440$	−1.14613	+	1.98515i	−0.0546396	+	0.0946385i
$441$		0			0
$442$	5.60291	+	9.70452i	0.266503	+	0.461597i
$443$	2.67757	+	7.35657i	0.127215	+	0.349521i	0.986907	−	0.161293i	$-0.0515664\pi$
$443$	2.67757	+	7.35657i	0.127215	+	0.349521i	−0.859691	+	0.510814i	$0.829344\pi$
$444$		0			0
$445$	12.5671	−	10.5450i	0.595735	−	0.499881i
$446$	0.886287	+	5.02638i	0.0419669	+	0.238006i
$447$		0			0
$448$	−13.8030	−	1.64040i	−0.652129	−	0.0775017i
$449$	−2.53492	+	1.46354i	−0.119630	+	0.0690687i	−0.558621	−	0.829423i	$-0.688669\pi$
$449$	−2.53492	+	1.46354i	−0.119630	+	0.0690687i	0.438991	+	0.898492i	$0.355336\pi$
$450$		0			0
$451$	−0.732791	+	0.423077i	−0.0345058	+	0.0199219i
$452$	8.38174	+	23.0286i	0.394244	+	1.08318i
$453$		0			0
$454$	15.5177	−	2.73619i	0.728282	−	0.128416i
$455$	−19.0994	−	5.75826i	−0.895394	−	0.269951i
$456$		0			0
$457$	−18.8614	−	15.8266i	−0.882297	−	0.740335i	0.0843528	−	0.996436i	$-0.473118\pi$
$457$	−18.8614	−	15.8266i	−0.882297	−	0.740335i	−0.966650	+	0.256101i	$0.917562\pi$
$458$	−6.11491	+	10.5913i	−0.285731	+	0.494900i
$459$		0			0
$460$	−9.68786	+	5.59329i	−0.451699	+	0.260788i
$461$	35.5416	−	12.9361i	1.65534	−	0.602493i	0.665717	−	0.746204i	$-0.268126\pi$
$461$	35.5416	−	12.9361i	1.65534	−	0.602493i	0.989620	+	0.143711i	$0.0459036\pi$
$462$		0			0
$463$	−8.27501	+	6.94356i	−0.384572	+	0.322695i	−0.814494	−	0.580171i	$-0.802986\pi$
$463$	−8.27501	+	6.94356i	−0.384572	+	0.322695i	0.429922	+	0.902866i	$0.358541\pi$
$464$	0.0566502	+	0.0675131i	0.00262992	+	0.00313422i
$465$		0			0
$466$	7.65900	−	2.78765i	0.354796	−	0.129135i
$467$	29.0369			1.34367			0.671833	−	0.740702i	$-0.265507\pi$
$467$	29.0369			1.34367			0.671833	+	0.740702i	$0.265507\pi$
$468$		0			0
$469$	−1.22519	−	21.7606i	−0.0565739	−	1.00481i
$470$	−7.49973	−	1.32240i	−0.345937	−	0.0609979i
$471$		0			0
$472$	9.30356	+	11.0875i	0.428231	+	0.510346i
$473$	1.46013	+	1.74012i	0.0671369	+	0.0800106i
$474$		0			0
$475$	10.3775	+	1.82984i	0.476154	+	0.0839588i
$476$	6.58605	+	3.32360i	0.301871	+	0.152337i
$477$		0			0
$478$	2.24991			0.102909
$479$	12.8160	−	4.66466i	0.585580	−	0.213134i	−0.0322044	−	0.999481i	$-0.510253\pi$
$479$	12.8160	−	4.66466i	0.585580	−	0.213134i	0.617784	+	0.786348i	$0.288031\pi$
$480$		0			0
$481$	3.79289	+	4.52019i	0.172941	+	0.206103i
$482$	−4.91035	+	4.12027i	−0.223660	+	0.187673i
$483$		0			0
$484$	−12.0849	+	4.39855i	−0.549314	+	0.199934i
$485$	22.3774	−	12.9196i	1.01610	−	0.586648i
$486$		0			0
$487$	16.0866	−	27.8628i	0.728954	−	1.26259i	−0.228371	−	0.973574i	$-0.573340\pi$
$487$	16.0866	−	27.8628i	0.728954	−	1.26259i	0.957325	−	0.289012i	$-0.0933267\pi$
$488$	−29.5971	−	24.8349i	−1.33980	−	1.12422i
$489$		0			0
$490$	8.29524	−	2.44851i	0.374741	−	0.110612i
$491$	−24.2362	+	4.27350i	−1.09377	+	0.192860i	−0.691295	−	0.722573i	$-0.742959\pi$
$491$	−24.2362	+	4.27350i	−1.09377	+	0.192860i	−0.402470	+	0.915433i	$0.631848\pi$
$492$		0			0
$493$	−0.519216	−	1.42653i	−0.0233843	−	0.0642479i
$494$	−14.3699	+	8.29645i	−0.646531	+	0.373275i
$495$		0			0
$496$	0.202346	−	0.116824i	0.00908558	−	0.00524556i
$497$	4.90887	−	41.3051i	0.220193	−	1.85279i
$498$		0			0
$499$	−4.54776	−	25.7916i	−0.203586	−	1.15459i	−0.899650	−	0.436613i	$-0.856178\pi$
$499$	−4.54776	−	25.7916i	−0.203586	−	1.15459i	0.696064	−	0.717980i	$-0.254933\pi$
$500$	−10.3454	+	8.68085i	−0.462662	+	0.388219i
$501$		0			0
$502$	0.286257	+	0.786484i	0.0127763	+	0.0351025i
$503$	−3.69643	−	6.40240i	−0.164815	−	0.285469i	0.771774	−	0.635897i	$-0.219370\pi$
$503$	−3.69643	−	6.40240i	−0.164815	−	0.285469i	−0.936590	+	0.350428i	$0.886036\pi$
$504$		0			0
$505$	−8.44256	+	14.6229i	−0.375689	+	0.650713i
$506$	−3.39813	−	0.599182i	−0.151065	−	0.0266369i
$507$		0			0
$508$	−2.23803	−	0.814575i	−0.0992963	−	0.0361409i
$509$	15.1126	+	5.50053i	0.669853	+	0.243807i	0.654485	−	0.756075i	$-0.272886\pi$
$509$	15.1126	+	5.50053i	0.669853	+	0.243807i	0.0153687	+	0.999882i	$0.495108\pi$
$510$		0			0
$511$	−0.746786	+	6.28374i	−0.0330359	+	0.277976i
$512$		−	1.51799i		−	0.0670865i
$513$		0			0
$514$	−15.1231	−	8.73131i	−0.667050	−	0.385122i
$515$	17.5476	+	3.09411i	0.773238	+	0.136343i
$516$		0			0
$517$	2.29267	+	2.73229i	0.100831	+	0.120166i
$518$	−2.44945	−	0.738483i	−0.107623	−	0.0324471i
$519$		0			0
$520$	3.74048	−	21.2133i	0.164031	−	0.930266i
$521$	−8.46473	−	14.6613i	−0.370847	−	0.642325i	0.618849	−	0.785510i	$-0.287599\pi$
$521$	−8.46473	−	14.6613i	−0.370847	−	0.642325i	−0.989696	+	0.143184i	$0.954266\pi$
$522$		0			0
$523$	−8.72367	−	5.03662i	−0.381460	−	0.220236i	0.296994	−	0.954879i	$-0.404016\pi$
$523$	−8.72367	−	5.03662i	−0.381460	−	0.220236i	−0.678453	+	0.734644i	$0.737349\pi$
$524$	−0.467160	+	2.64940i	−0.0204080	+	0.115739i
$525$		0			0
$526$	9.98737	+	3.63511i	0.435470	+	0.158498i
$527$	−3.96348	+	0.698869i	−0.172652	+	0.0304432i
$528$		0			0
$529$	−16.6757	−	13.9925i	−0.725029	−	0.608372i
$530$	5.82386	−	10.0872i	0.252972	−	0.438161i
$531$		0			0
$532$	−4.92139	+	9.75223i	−0.213370	+	0.422813i
$533$	5.11105	−	6.09112i	0.221384	−	0.263836i
$534$		0			0
$535$	4.91516	−	13.5043i	0.212501	−	0.583841i
$536$	23.1769	−	4.08672i	1.00109	−	0.176519i
$537$		0			0
$538$	5.00978	+	13.7643i	0.215987	+	0.593420i
$539$	−3.71334	−	1.61884i	−0.159945	−	0.0697285i
$540$		0			0
$541$	9.39785	+	16.2776i	0.404045	+	0.699827i	0.994210	−	0.107456i	$-0.0342705\pi$
$541$	9.39785	+	16.2776i	0.404045	+	0.699827i	−0.590165	+	0.807283i	$0.700937\pi$
$542$	2.28667	−	12.9683i	0.0982207	−	0.557037i
$543$		0			0
$544$	−4.42420	+	12.1554i	−0.189686	+	0.521158i
$545$	−4.05710	−	23.0090i	−0.173787	−	0.985595i
$546$		0			0
$547$	−9.76636	−	8.19495i	−0.417579	−	0.350391i	0.409662	−	0.912237i	$-0.365647\pi$
$547$	−9.76636	−	8.19495i	−0.417579	−	0.350391i	−0.827241	+	0.561847i	$0.810091\pi$
$548$		−	1.60801i		−	0.0686906i
$549$		0			0
$550$	−1.58715			−0.0676764
$551$	2.11233	−	0.768824i	0.0899881	−	0.0327530i
$552$		0			0
$553$	6.90523	−	1.62247i	0.293640	−	0.0689945i
$554$	8.44831	−	23.2115i	0.358934	−	0.986164i
$555$		0			0
$556$	11.8145	−	14.0799i	0.501045	−	0.597122i
$557$			27.3089i			1.15711i	0.815642	+	0.578557i	$0.196384\pi$
$557$			27.3089i			1.15711i	−0.815642	+	0.578557i	$0.803616\pi$
$558$		0			0
$559$	−18.4862	−	10.6730i	−0.781884	−	0.451421i
$560$	0.194170	+	0.452542i	0.00820520	+	0.0191234i
$561$		0			0
$562$	4.25046	−	3.56656i	0.179295	−	0.150446i
$563$	−4.09167	−	23.2050i	−0.172443	−	0.977974i	−0.941054	−	0.338257i	$-0.890163\pi$
$563$	−4.09167	−	23.2050i	−0.172443	−	0.977974i	0.768611	−	0.639717i	$-0.220948\pi$
$564$		0			0
$565$	18.1124	−	21.5855i	0.761996	−	0.908111i
$566$	−4.89515			−0.205759
$567$		0			0
$568$	44.9154			1.88461
$569$	−8.50590	+	10.1369i	−0.356586	+	0.424963i	−0.914279	−	0.405084i	$-0.867242\pi$
$569$	−8.50590	+	10.1369i	−0.356586	+	0.424963i	0.557693	+	0.830047i	$0.311687\pi$
$570$		0			0
$571$	1.15073	+	6.52612i	0.0481566	+	0.273110i	0.999373	−	0.0354159i	$-0.0112756\pi$
$571$	1.15073	+	6.52612i	0.0481566	+	0.273110i	−0.951216	+	0.308525i	$0.900164\pi$
$572$	−2.90696	+	2.43923i	−0.121546	+	0.101989i
$573$		0			0
$574$	−0.406849	+	3.42338i	−0.0169815	+	0.142889i
$575$	−17.8334	−	10.2961i	−0.743703	−	0.429377i
$576$		0			0
$577$		−	1.50126i		−	0.0624981i	−0.999512	−	0.0312490i	$-0.990052\pi$
$577$		−	1.50126i		−	0.0624981i	0.999512	−	0.0312490i	$-0.00994850\pi$
$578$	6.67520	−	7.95519i	0.277652	−	0.330892i
$579$		0			0
$580$	−0.375415	+	1.03144i	−0.0155882	+	0.0428283i
$581$	−9.16521	+	30.3998i	−0.380237	+	1.26120i
$582$		0			0
$583$	−5.12632	+	1.86583i	−0.212311	+	0.0772747i
$584$	−6.83297			−0.282750
$585$		0			0
$586$		−	20.7443i		−	0.856940i
$587$	2.83790	+	2.38128i	0.117133	+	0.0982861i	0.699473	−	0.714659i	$-0.253418\pi$
$587$	2.83790	+	2.38128i	0.117133	+	0.0982861i	−0.582340	+	0.812945i	$0.697863\pi$
$588$		0			0
$589$	−1.03484	−	5.86889i	−0.0426400	−	0.241823i
$590$	2.14096	−	5.88225i	0.0881420	−	0.242168i
$591$		0			0
$592$	0.0252938	−	0.143449i	0.00103957	−	0.00589570i
$593$	13.5970	+	23.5507i	0.558362	+	0.967112i	0.997633	+	0.0687572i	$0.0219034\pi$
$593$	13.5970	+	23.5507i	0.558362	+	0.967112i	−0.439271	+	0.898355i	$0.644763\pi$
$594$		0			0
$595$	−0.476825	−	8.46892i	−0.0195479	−	0.347192i
$596$	8.22153	+	22.5885i	0.336767	+	0.925260i
$597$		0			0
$598$	31.9326	−	5.63057i	1.30582	−	0.230251i
$599$	−0.718887	+	1.97512i	−0.0293729	+	0.0807014i	−0.953512	−	0.301354i	$-0.902561\pi$
$599$	−0.718887	+	1.97512i	−0.0293729	+	0.0807014i	0.924139	+	0.382055i	$0.124784\pi$
$600$		0			0
$601$	−6.40627	+	7.63469i	−0.261317	+	0.311426i	−0.880710	−	0.473655i	$-0.842934\pi$
$601$	−6.40627	+	7.63469i	−0.261317	+	0.311426i	0.619393	+	0.785081i	$0.287379\pi$
$602$	9.24034	−	0.520259i	0.376608	−	0.0212042i
$603$		0			0
$604$	1.74184	−	3.01695i	0.0708744	−	0.122758i
$605$	11.3276	+	9.50499i	0.460532	+	0.386433i
$606$		0			0
$607$	−22.3484	+	3.94062i	−0.907092	+	0.159945i	−0.607683	−	0.794180i	$-0.707901\pi$
$607$	−22.3484	+	3.94062i	−0.907092	+	0.159945i	−0.299409	+	0.954125i	$0.596790\pi$
$608$	−17.9990	−	6.55109i	−0.729955	−	0.265682i
$609$		0			0
$610$	−2.90162	+	16.4559i	−0.117483	+	0.666281i
$611$	−29.0267	−	16.7586i	−1.17429	−	0.677979i
$612$		0			0
$613$	14.3002	+	24.7687i	0.577581	+	1.00040i	0.995756	+	0.0920328i	$0.0293365\pi$
$613$	14.3002	+	24.7687i	0.577581	+	1.00040i	−0.418175	+	0.908366i	$0.637330\pi$
$614$	−2.69835	+	15.3031i	−0.108897	+	0.617584i
$615$		0			0
$616$	1.26262	−	4.18796i	0.0508726	−	0.168738i
$617$	−0.142287	−	0.169571i	−0.00572826	−	0.00682668i	0.763173	−	0.646195i	$-0.223641\pi$
$617$	−0.142287	−	0.169571i	−0.00572826	−	0.00682668i	−0.768901	+	0.639368i	$0.779196\pi$
$618$		0			0
$619$	−23.5424	−	4.15115i	−0.946247	−	0.166849i	−0.320828	−	0.947138i	$-0.603961\pi$
$619$	−23.5424	−	4.15115i	−0.946247	−	0.166849i	−0.625420	+	0.780289i	$0.715072\pi$
$620$	2.52011	+	1.45498i	0.101210	+	0.0584336i
$621$		0			0
$622$			1.34523i			0.0539387i
$623$	−18.7424	+	25.0740i	−0.750899	+	1.00457i
$624$		0			0
$625$	0.131608	+	0.0479015i	0.00526433	+	0.00191606i
$626$	24.3840	+	8.87506i	0.974582	+	0.354719i
$627$		0			0
$628$	−9.64640	−	1.70092i	−0.384933	−	0.0678741i
$629$	−1.25452	+	2.17289i	−0.0500209	+	0.0866388i
$630$		0			0
$631$	8.84858	+	15.3262i	0.352256	+	0.610126i	0.986644	−	0.162889i	$-0.0520812\pi$
$631$	8.84858	+	15.3262i	0.352256	+	0.610126i	−0.634388	+	0.773015i	$0.718748\pi$
$632$	2.61966	+	7.19745i	0.104204	+	0.286299i
$633$		0			0
$634$	20.7542	−	17.4149i	0.824255	−	0.691632i
$635$	0.475528	+	2.69685i	0.0188707	+	0.107021i
$636$		0			0
$637$	37.9931	+	2.36034i	1.50534	+	0.0935202i
$638$	−0.293212	+	0.169286i	−0.0116084	+	0.00670210i
$639$		0			0
$640$	7.81256	−	4.51058i	0.308819	−	0.178296i
$641$	6.54891	+	17.9930i	0.258666	+	0.710680i	0.999250	+	0.0387161i	$0.0123268\pi$
$641$	6.54891	+	17.9930i	0.258666	+	0.710680i	−0.740584	+	0.671964i	$0.765451\pi$
$642$		0			0
$643$	−29.5375	+	5.20825i	−1.16484	+	0.205393i	−0.722447	−	0.691426i	$-0.756983\pi$
$643$	−29.5375	+	5.20825i	−1.16484	+	0.205393i	−0.442396	+	0.896820i	$0.645872\pi$
$644$	15.5552	−	14.6188i	0.612961	−	0.576063i
$645$		0			0
$646$	−5.40481	−	4.53517i	−0.212649	−	0.178434i
$647$	−0.0112934	+	0.0195607i	−0.000443989	+	0.000769011i	−0.866247	−	0.499615i	$-0.833475\pi$
$647$	−0.0112934	+	0.0195607i	−0.000443989	+	0.000769011i	0.865803	+	0.500384i	$0.166808\pi$
$648$		0			0
$649$	−2.53903	+	1.46591i	−0.0996655	+	0.0575419i
$650$	14.0152	−	5.10110i	0.549720	−	0.200082i
$651$		0			0
$652$	−0.958152	+	0.803985i	−0.0375241	+	0.0314865i
$653$	19.3776	+	23.0933i	0.758304	+	0.903712i	0.997739	−	0.0672006i	$-0.0214067\pi$
$653$	19.3776	+	23.0933i	0.758304	+	0.903712i	−0.239435	+	0.970912i	$0.576962\pi$
$654$		0			0
$655$	2.90675	−	1.05797i	0.113576	−	0.0413383i
$656$	−0.196284			−0.00766360
$657$		0			0
$658$	14.5090	−	0.816899i	0.565619	−	0.0318460i
$659$	−17.6905	−	3.11932i	−0.689126	−	0.121511i	−0.181890	−	0.983319i	$-0.558222\pi$
$659$	−17.6905	−	3.11932i	−0.689126	−	0.121511i	−0.507236	+	0.861807i	$0.669333\pi$
$660$		0			0
$661$	−22.0195	−	26.2418i	−0.856459	−	1.02069i	−0.999520	−	0.0309742i	$-0.990139\pi$
$661$	−22.0195	−	26.2418i	−0.856459	−	1.02069i	0.143061	−	0.989714i	$-0.454305\pi$
$662$	−16.2122	−	19.3209i	−0.630105	−	0.750929i
$663$		0			0
$664$	−33.7645	−	5.95359i	−1.31032	−	0.231044i
$665$	12.5403	−	0.706054i	0.486291	−	0.0273796i
$666$		0			0
$667$	−4.39274			−0.170087
$668$	−15.9169	+	5.79328i	−0.615844	+	0.224149i
$669$		0			0
$670$	−6.54256	−	7.79712i	−0.252761	−	0.301229i
$671$	5.99520	−	5.03057i	0.231442	−	0.194203i
$672$		0			0
$673$	−16.8698	+	6.14009i	−0.650282	+	0.236683i	−0.646035	−	0.763308i	$-0.723574\pi$
$673$	−16.8698	+	6.14009i	−0.650282	+	0.236683i	−0.00424668	+	0.999991i	$0.501352\pi$
$674$	−6.27118	+	3.62067i	−0.241557	+	0.139463i
$675$		0			0
$676$	9.99192	−	17.3065i	0.384304	−	0.665635i
$677$	−2.57495	−	2.16064i	−0.0989635	−	0.0830403i	0.591963	−	0.805965i	$-0.298353\pi$
$677$	−2.57495	−	2.16064i	−0.0989635	−	0.0830403i	−0.690927	+	0.722925i	$0.742797\pi$
$678$		0			0
$679$	−35.9300	+	33.7671i	−1.37887	+	1.29586i
$680$	9.02013	−	1.59049i	0.345906	−	0.0609926i
$681$		0			0
$682$	0.306995	+	0.843463i	0.0117555	+	0.0322979i
$683$	−35.1068	+	20.2689i	−1.34333	+	0.775570i	−0.987294	−	0.158904i	$-0.949204\pi$
$683$	−35.1068	+	20.2689i	−1.34333	+	0.775570i	−0.356032	+	0.934474i	$0.615871\pi$
$684$		0			0
$685$	−1.60120	+	0.924452i	−0.0611786	+	0.0353215i
$686$	−14.3409	+	8.16912i	−0.547536	+	0.311898i
$687$		0			0
$688$	0.0915018	+	0.518932i	0.00348847	+	0.0197841i
$689$	39.2706	−	32.9519i	1.49609	−	1.25537i
$690$		0			0
$691$	14.3836	+	39.5186i	0.547178	+	1.50336i	0.837504	+	0.546431i	$0.184014\pi$
$691$	14.3836	+	39.5186i	0.547178	+	1.50336i	−0.290327	+	0.956928i	$0.593764\pi$
$692$	3.53058	+	6.11514i	0.134212	+	0.232463i
$693$		0			0
$694$	6.13459	−	10.6254i	0.232866	−	0.403335i
$695$	−20.8125	−	3.66981i	−0.789463	−	0.139204i
$696$		0			0
$697$	3.17711	+	1.15638i	0.120342	+	0.0438008i
$698$	−1.12660	−	0.410049i	−0.0426424	−	0.0155206i
$699$		0			0
$700$	5.87859	−	7.86451i	0.222190	−	0.297251i
$701$		−	33.4343i		−	1.26280i	−0.775459	−	0.631398i	$-0.782481\pi$
$701$		−	33.4343i		−	1.26280i	0.775459	−	0.631398i	$-0.217519\pi$
$702$		0			0
$703$	−3.21749	−	1.85762i	−0.121350	−	0.0700613i
$704$	2.99413	+	0.527946i	0.112845	+	0.0198977i
$705$		0			0
$706$	−9.02357	−	10.7539i	−0.339607	−	0.404727i
$707$	9.30068	−	30.8491i	0.349788	−	1.16020i
$708$		0			0
$709$	6.70491	−	38.0254i	0.251808	−	1.42807i	−0.552327	−	0.833628i	$-0.686260\pi$
$709$	6.70491	−	38.0254i	0.251808	−	1.42807i	0.804135	−	0.594447i	$-0.202629\pi$
$710$	−9.71272	−	16.8229i	−0.364512	−	0.631353i
$711$		0			0
$712$	−29.2743	−	16.9015i	−1.09710	−	0.633411i
$713$	−2.02225	+	11.4687i	−0.0757338	+	0.429508i
$714$		0			0
$715$	4.10014	+	1.49233i	0.153336	+	0.0558099i
$716$	−10.0914	+	1.77939i	−0.377135	+	0.0664990i
$717$		0			0
$718$	20.4616	+	17.1693i	0.763619	+	0.640752i
$719$	10.3735	−	17.9674i	0.386866	−	0.670072i	−0.605160	−	0.796104i	$-0.706891\pi$
$719$	10.3735	−	17.9674i	0.386866	−	0.670072i	0.992026	+	0.126032i	$0.0402241\pi$
$720$		0			0
$721$	−33.9476	+	1.91135i	−1.26427	+	0.0711823i
$722$	−4.16820	+	4.96747i	−0.155124	+	0.184870i
$723$		0			0
$724$	−2.38462	+	6.55169i	−0.0886237	+	0.243492i
$725$	−1.98983	+	0.350861i	−0.0739005	+	0.0130307i
$726$		0			0
$727$	6.23885	+	17.1411i	0.231386	+	0.635729i	0.999992	−	0.00399420i	$-0.00127140\pi$
$727$	6.23885	+	17.1411i	0.231386	+	0.635729i	−0.768606	+	0.639723i	$0.779049\pi$
$728$	2.31064	+	41.0393i	0.0856379	+	1.52102i
$729$		0			0
$730$	1.47760	+	2.55927i	0.0546883	+	0.0947228i
$731$	1.57613	−	8.93868i	0.0582953	−	0.330609i
$732$		0			0
$733$	9.34633	−	25.6788i	0.345214	−	0.948469i	−0.638641	−	0.769505i	$-0.720503\pi$
$733$	9.34633	−	25.6788i	0.345214	−	0.948469i	0.983856	−	0.178964i	$-0.0572746\pi$
$734$	−0.739395	−	4.19331i	−0.0272916	−	0.154778i
$735$		0			0
$736$	28.6732	+	24.0597i	1.05691	+	0.886851i
$737$			4.76716i			0.175601i
$738$		0			0
$739$	14.1363			0.520012			0.260006	−	0.965607i	$-0.416275\pi$
$739$	14.1363			0.520012			0.260006	+	0.965607i	$0.416275\pi$
$740$	1.70473	−	0.620471i	0.0626671	−	0.0228090i
$741$		0			0
$742$	−6.41580	+	21.2804i	−0.235532	+	0.781228i
$743$	−3.05230	+	8.38613i	−0.111978	+	0.307657i	−0.983005	−	0.183578i	$-0.941232\pi$
$743$	−3.05230	+	8.38613i	−0.111978	+	0.307657i	0.871027	+	0.491235i	$0.163454\pi$
$744$		0			0
$745$	17.7662	−	21.1730i	0.650904	−	0.775717i
$746$			12.3250i			0.451250i
$747$		0			0
$748$	−1.39740	−	0.806789i	−0.0510940	−	0.0294991i
$749$	−3.23630	+	27.2314i	−0.118252	+	0.995015i
$750$		0			0
$751$	−2.72115	+	2.28332i	−0.0992962	+	0.0833194i	−0.691084	−	0.722774i	$-0.742867\pi$
$751$	−2.72115	+	2.28332i	−0.0992962	+	0.0833194i	0.591788	+	0.806094i	$0.298422\pi$
$752$	0.143674	+	0.814816i	0.00523926	+	0.0297133i
$753$		0			0
$754$	2.04509	−	2.43724i	0.0744777	−	0.0887591i
$755$	−4.00557			−0.145778
$756$		0			0
$757$	−21.6011			−0.785104			−0.392552	−	0.919730i	$-0.628408\pi$
$757$	−21.6011			−0.785104			−0.392552	+	0.919730i	$0.628408\pi$
$758$	5.06486	−	6.03606i	0.183964	−	0.219240i
$759$		0			0
$760$	2.35511	+	13.3565i	0.0854287	+	0.484490i
$761$	7.74438	−	6.49831i	0.280734	−	0.235563i	−0.491538	−	0.870856i	$-0.663565\pi$
$761$	7.74438	−	6.49831i	0.280734	−	0.235563i	0.772271	+	0.635293i	$0.219121\pi$
$762$		0			0
$763$	17.5795	+	40.9715i	0.636420	+	1.48327i
$764$	−24.8383	−	14.3404i	−0.898618	−	0.518818i
$765$		0			0
$766$		−	26.8118i		−	0.968750i
$767$	17.7091	−	21.1049i	0.639440	−	0.762055i
$768$		0			0
$769$	−12.2720	+	33.7171i	−0.442540	+	1.21587i	0.495276	+	0.868736i	$0.335067\pi$
$769$	−12.2720	+	33.7171i	−0.442540	+	1.21587i	−0.937816	+	0.347133i	$0.887155\pi$
$770$	−1.84162	+	0.432713i	−0.0663675	+	0.0155939i
$771$		0			0
$772$	21.4406	−	7.80375i	0.771665	−	0.280863i
$773$	35.8360			1.28893			0.644466	−	0.764633i	$-0.277080\pi$
$773$	35.8360			1.28893			0.644466	+	0.764633i	$0.277080\pi$
$774$		0			0
$775$			5.35666i			0.192417i
$776$	−40.7858	−	34.2233i	−1.46412	−	1.22855i
$777$		0			0
$778$	−1.53010	−	8.67765i	−0.0548569	−	0.311109i
$779$	−1.71229	+	4.70448i	−0.0613492	+	0.168556i
$780$		0			0
$781$	−1.57987	+	8.95987i	−0.0565321	+	0.320609i
$782$	6.89376	+	11.9403i	0.246520	+	0.426986i
$783$		0			0
$784$	−0.558222	−	0.755910i	−0.0199365	−	0.0269968i
$785$	3.85205	+	10.5834i	0.137486	+	0.377738i
$786$		0			0
$787$	−23.3675	+	4.12032i	−0.832962	+	0.146874i	−0.573836	−	0.818970i	$-0.694545\pi$
$787$	−23.3675	+	4.12032i	−0.832962	+	0.146874i	−0.259125	+	0.965844i	$0.583434\pi$
$788$	−4.39187	+	12.0666i	−0.156454	+	0.429854i
$789$		0			0
$790$	2.12930	−	2.53760i	0.0757570	−	0.0902837i
$791$	−24.2248	+	48.0038i	−0.861335	+	1.70682i
$792$		0			0
$793$	−36.7717	+	63.6904i	−1.30580	+	2.26171i
$794$	7.84370	+	6.58165i	0.278363	+	0.233574i
$795$		0			0
$796$	−11.9076	+	2.09964i	−0.422055	+	0.0744197i
$797$	−25.1031	−	9.13677i	−0.889196	−	0.323641i	−0.143281	−	0.989682i	$-0.545765\pi$
$797$	−25.1031	−	9.13677i	−0.889196	−	0.323641i	−0.745915	+	0.666041i	$0.767988\pi$
$798$		0			0
$799$	2.47481	−	14.0353i	0.0875523	−	0.496534i
$800$	14.9102	+	8.60839i	0.527154	+	0.304353i
$801$		0			0
$802$	−7.34531	−	12.7224i	−0.259372	−	0.449245i
$803$	0.240345	−	1.36306i	0.00848159	−	0.0481015i
$804$		0			0
$805$	−23.4997	−	7.08490i	−0.828256	−	0.249710i
$806$	−5.42177	−	6.46141i	−0.190974	−	0.227594i
$807$		0			0
$808$	34.2635	+	6.04158i	1.20539	+	0.212542i
$809$	−17.2909	−	9.98289i	−0.607915	−	0.350980i	0.164234	−	0.986421i	$-0.447485\pi$
$809$	−17.2909	−	9.98289i	−0.607915	−	0.350980i	−0.772149	+	0.635442i	$0.780818\pi$
$810$		0			0
$811$			13.5611i			0.476196i	0.971241	+	0.238098i	$0.0765239\pi$
$811$			13.5611i			0.476196i	−0.971241	+	0.238098i	$0.923476\pi$
$812$	0.247185	−	2.07991i	0.00867449	−	0.0729905i
$813$		0			0
$814$	0.525833	+	0.191387i	0.0184304	+	0.00670813i
$815$	1.35143	+	0.491879i	0.0473384	+	0.0172298i
$816$		0			0
$817$	13.2359	+	2.33384i	0.463064	+	0.0816507i
$818$	−4.06677	+	7.04386i	−0.142191	+	0.246283i
$819$		0			0
$820$	−1.22231	−	2.11710i	−0.0426848	−	0.0739322i
$821$	11.6528	+	32.0157i	0.406684	+	1.11735i	0.958922	+	0.283669i	$0.0915516\pi$
$821$	11.6528	+	32.0157i	0.406684	+	1.11735i	−0.552238	+	0.833686i	$0.686226\pi$
$822$		0			0
$823$	6.62637	−	5.56019i	0.230981	−	0.193816i	−0.519950	−	0.854197i	$-0.674050\pi$
$823$	6.62637	−	5.56019i	0.230981	−	0.193816i	0.750931	+	0.660381i	$0.229605\pi$
$824$	−6.37547	−	36.1571i	−0.222100	−	1.25959i
$825$		0			0
$826$	−1.40968	+	11.8616i	−0.0490490	+	0.412717i
$827$	34.8581	−	20.1253i	1.21213	−	0.699826i	0.248911	−	0.968526i	$-0.419927\pi$
$827$	34.8581	−	20.1253i	1.21213	−	0.699826i	0.963224	+	0.268700i	$0.0865941\pi$
$828$		0			0
$829$	35.8294	−	20.6861i	1.24441	−	0.718458i	0.274417	−	0.961611i	$-0.411515\pi$
$829$	35.8294	−	20.6861i	1.24441	−	0.718458i	0.969988	+	0.243153i	$0.0781817\pi$
$830$	5.07149	+	13.9338i	0.176034	+	0.483650i
$831$		0			0
$832$	−28.1361	+	4.96115i	−0.975444	+	0.171997i
$833$	4.58225	+	15.5241i	0.158766	+	0.537877i
$834$		0			0
$835$	14.9195	+	12.5189i	0.516310	+	0.433235i
$836$	1.19464	−	2.06919i	0.0413176	−	0.0715643i
$837$		0			0
$838$	−22.6091	+	13.0534i	−0.781019	+	0.450921i
$839$	25.4475	−	9.26215i	0.878547	−	0.319765i	0.136924	−	0.990582i	$-0.456278\pi$
$839$	25.4475	−	9.26215i	0.878547	−	0.319765i	0.741623	+	0.670817i	$0.234056\pi$
$840$		0			0
$841$	21.8851	−	18.3638i	0.754659	−	0.633234i
$842$	6.78997	+	8.09197i	0.233998	+	0.278868i
$843$		0			0
$844$	6.78759	−	2.47048i	0.233639	−	0.0850375i
$845$	−22.9776			−0.790455
$846$		0			0
$847$	−25.1913	−	12.7126i	−0.865583	−	0.436811i
$848$	−1.24625	−	0.219748i	−0.0427965	−	0.00754619i
$849$		0			0
$850$	4.07646	+	4.85814i	0.139822	+	0.166633i
$851$	4.66674	+	5.56160i	0.159974	+	0.190649i
$852$		0			0
$853$	−19.5183	−	3.44160i	−0.668293	−	0.117838i	−0.170800	−	0.985306i	$-0.554635\pi$
$853$	−19.5183	−	3.44160i	−0.668293	−	0.117838i	−0.497494	+	0.867468i	$0.665746\pi$
$854$	−1.79244	−	31.8357i	−0.0613361	−	1.08939i
$855$		0			0
$856$	−29.6116			−1.01210
$857$	−29.8153	+	10.8519i	−1.01847	+	0.370693i	−0.796680	−	0.604402i	$-0.793412\pi$
$857$	−29.8153	+	10.8519i	−1.01847	+	0.370693i	−0.221790	+	0.975094i	$0.571190\pi$
$858$		0			0
$859$	1.68873	+	2.01255i	0.0576187	+	0.0686673i	0.794084	−	0.607808i	$-0.207951\pi$
$859$	1.68873	+	2.01255i	0.0576187	+	0.0686673i	−0.736465	+	0.676475i	$0.763507\pi$
$860$	−5.02734	+	4.21844i	−0.171431	+	0.143848i
$861$		0			0
$862$	−10.0606	+	3.66177i	−0.342666	+	0.124720i
$863$	−32.4638	+	18.7430i	−1.10508	+	0.638018i	−0.937551	−	0.347849i	$-0.886912\pi$
$863$	−32.4638	+	18.7430i	−1.10508	+	0.638018i	−0.167529	+	0.985867i	$0.553579\pi$
$864$		0			0
$865$	4.05950	−	7.03126i	0.138027	−	0.239070i
$866$	−1.27233	−	1.06761i	−0.0432355	−	0.0362789i
$867$		0			0
$868$	−5.31652	−	1.60287i	−0.180454	−	0.0544050i
$869$	−1.52792	+	0.269413i	−0.0518310	+	0.00913921i
$870$		0			0
$871$	−15.3216	−	42.0958i	−0.519154	−	1.42636i
$872$	−41.6920	+	24.0709i	−1.41187	+	0.815142i
$873$		0			0
$874$	−17.6806	+	10.2079i	−0.598054	+	0.345286i
$875$	−29.4243	−	3.49691i	−0.994723	−	0.118217i
$876$		0			0
$877$	6.49296	+	36.8234i	0.219252	+	1.24344i	0.873374	+	0.487049i	$0.161927\pi$
$877$	6.49296	+	36.8234i	0.219252	+	1.24344i	−0.654123	+	0.756388i	$0.726962\pi$
$878$	−17.8273	+	14.9589i	−0.601642	+	0.504838i
$879$		0			0
$880$	−0.0368388	−	0.101214i	−0.00124184	−	0.00341192i
$881$	−3.30548	−	5.72527i	−0.111365	−	0.192889i	0.804956	−	0.593334i	$-0.202189\pi$
$881$	−3.30548	−	5.72527i	−0.111365	−	0.192889i	−0.916321	+	0.400445i	$0.868855\pi$
$882$		0			0
$883$	27.7285	−	48.0272i	0.933140	−	1.61625i	0.155222	−	0.987880i	$-0.450391\pi$
$883$	27.7285	−	48.0272i	0.933140	−	1.61625i	0.777918	−	0.628366i	$-0.216276\pi$
$884$	14.9326	+	2.63302i	0.502237	+	0.0885579i
$885$		0			0
$886$	−6.55582	−	2.38613i	−0.220247	−	0.0801634i
$887$	−25.8689	−	9.41552i	−0.868594	−	0.316142i	−0.130996	−	0.991383i	$-0.541818\pi$
$887$	−25.8689	−	9.41552i	−0.868594	−	0.316142i	−0.737598	+	0.675241i	$0.764040\pi$
$888$		0			0
$889$	−2.06047	−	4.80222i	−0.0691060	−	0.161061i
$890$			14.6195i			0.490046i
$891$		0			0
$892$	5.98101	+	3.45314i	0.200259	+	0.115620i
$893$	20.7827	+	3.66454i	0.695465	+	0.122629i
$894$		0			0
$895$	7.57348	+	9.02572i	0.253154	+	0.301697i
$896$	−12.5442	+	11.7890i	−0.419071	+	0.393844i
$897$		0			0
$898$	0.452957	−	2.56885i	0.0151154	−	0.0857235i
$899$	0.571342	+	0.989594i	0.0190553	+	0.0330048i
$900$		0			0
$901$	18.8777	+	10.8990i	0.628906	+	0.363099i
$902$	0.130940	−	0.742597i	0.00435982	−	0.0247258i
$903$		0			0
$904$	−54.5596	−	19.8581i	−1.81463	−	0.660470i
$905$	7.89488	−	1.39208i	0.262435	−	0.0462743i
$906$		0			0
$907$	31.0373	+	26.0433i	1.03058	+	0.864755i	0.990919	−	0.134458i	$-0.0429294\pi$
$907$	31.0373	+	26.0433i	1.03058	+	0.864755i	0.0396558	+	0.999213i	$0.487374\pi$
$908$	10.6607	−	18.4649i	0.353788	−	0.612779i
$909$		0			0
$910$	14.8715	−	9.73999i	0.492986	−	0.322878i
$911$	32.6169	−	38.8713i	1.08064	−	1.28786i	0.125380	−	0.992109i	$-0.459985\pi$
$911$	32.6169	−	38.8713i	1.08064	−	1.28786i	0.955264	−	0.295753i	$-0.0955706\pi$
$912$		0			0
$913$	2.37528	−	6.52604i	0.0786104	−	0.215980i
$914$	21.6084	−	3.81015i	0.714743	−	0.126028i
$915$		0			0
$916$	5.65994	+	15.5505i	0.187010	+	0.513805i
$917$	−4.93792	+	3.23406i	−0.163064	+	0.106798i
$918$		0			0
$919$	27.9766	+	48.4569i	0.922864	+	1.59845i	0.794962	+	0.606660i	$0.207491\pi$
$919$	27.9766	+	48.4569i	0.922864	+	1.59845i	0.127902	+	0.991787i	$0.459176\pi$
$920$	4.60225	−	26.1007i	0.151732	−	0.860513i
$921$		0			0
$922$	−11.5280	+	31.6730i	−0.379655	+	1.04309i
$923$	−14.8462	−	84.1968i	−0.488667	−	2.77137i
$924$		0			0
$925$	2.55817	+	2.14656i	0.0841121	+	0.0705785i
$926$		−	9.62647i		−	0.316345i
$927$		0			0
$928$	3.67269			0.120562
$929$	21.4697	−	7.81435i	0.704399	−	0.256380i	0.0351113	−	0.999383i	$-0.488821\pi$
$929$	21.4697	−	7.81435i	0.704399	−	0.256380i	0.669288	+	0.743003i	$0.266599\pi$
$930$		0			0
$931$	−22.9871	+	6.78512i	−0.753373	+	0.222373i
$932$	3.77205	−	10.3636i	0.123558	−	0.339472i
$933$		0			0
$934$	−16.6330	+	19.8224i	−0.544247	+	0.648609i
$935$			1.85531i			0.0606751i
$936$		0			0
$937$	−34.1439	−	19.7130i	−1.11543	−	0.643995i	−0.175201	−	0.984533i	$-0.556057\pi$
$937$	−34.1439	−	19.7130i	−1.11543	−	0.643995i	−0.940231	+	0.340538i	$0.889391\pi$
$938$	15.5570	+	11.6286i	0.507954	+	0.379687i
$939$		0			0
$940$	−7.89383	+	6.62371i	−0.257468	+	0.216042i
$941$	2.36221	+	13.3968i	0.0770059	+	0.436722i	0.998797	+	0.0490354i	$0.0156147\pi$
$941$	2.36221	+	13.3968i	0.0770059	+	0.436722i	−0.921791	+	0.387687i	$0.873274\pi$
$942$		0			0
$943$	6.28859	−	7.49445i	0.204785	−	0.244053i
$944$	−0.680098			−0.0221353
$945$		0			0
$946$	−2.02431			−0.0658159
$947$	−3.05054	+	3.63549i	−0.0991292	+	0.118138i	−0.813328	−	0.581805i	$-0.802347\pi$
$947$	−3.05054	+	3.63549i	−0.0991292	+	0.118138i	0.714199	+	0.699943i	$0.246791\pi$
$948$		0			0
$949$	2.25854	+	12.8088i	0.0733155	+	0.415793i
$950$	−7.19365	+	6.03619i	−0.233393	+	0.195840i
$951$		0			0
$952$	−16.0619	+	6.89163i	−0.520570	+	0.223359i
$953$	−25.1568	−	14.5243i	−0.814909	−	0.470488i	0.0337488	−	0.999430i	$-0.489255\pi$
$953$	−25.1568	−	14.5243i	−0.814909	−	0.470488i	−0.848658	+	0.528942i	$0.822589\pi$
$954$		0			0
$955$			32.9775i			1.06713i
$956$	1.95692	−	2.33217i	0.0632913	−	0.0754277i
$957$		0			0
$958$	−4.15692	+	11.4210i	−0.134304	+	0.368997i
$959$	2.57095	−	2.41618i	0.0830202	−	0.0780226i
$960$		0			0
$961$	−26.2838	+	9.56651i	−0.847864	+	0.308597i
$962$	−5.25842			−0.169538
$963$		0			0
$964$			8.67358i			0.279357i
$965$	−20.0971	−	16.8634i	−0.646947	−	0.542853i
$966$		0			0
$967$	−0.574034	−	3.25551i	−0.0184597	−	0.104690i	0.974186	−	0.225748i	$-0.0724825\pi$
$967$	−0.574034	−	3.25551i	−0.0184597	−	0.104690i	−0.992645	+	0.121058i	$0.961371\pi$
$968$	10.4211	−	28.6316i	0.334946	−	0.920256i
$969$		0			0
$970$	−3.99854	+	22.6768i	−0.128385	+	0.728109i
$971$	−7.79202	−	13.4962i	−0.250058	−	0.433113i	0.713484	−	0.700672i	$-0.247116\pi$
$971$	−7.79202	−	13.4962i	−0.250058	−	0.433113i	−0.963541	+	0.267559i	$0.913783\pi$
$972$		0			0
$973$	40.2639	−	2.26698i	1.29080	−	0.0726760i
$974$	9.80616	+	26.9422i	0.314209	+	0.863283i
$975$		0			0
$976$	1.78787	−	0.315250i	0.0572284	−	0.0100909i
$977$	10.4385	−	28.6796i	0.333958	−	0.917542i	−0.653113	−	0.757260i	$-0.726537\pi$
$977$	10.4385	−	28.6796i	0.333958	−	0.917542i	0.987071	−	0.160282i	$-0.0512403\pi$
$978$		0			0
$979$	4.40127	−	5.24524i	0.140665	−	0.167638i
$980$	4.67698	−	10.7282i	0.149401	−	0.342698i
$981$		0			0
$982$	10.9657	−	18.9931i	0.349929	−	0.606095i
$983$	14.4341	+	12.1117i	0.460377	+	0.386303i	0.843270	−	0.537490i	$-0.180628\pi$
$983$	14.4341	+	12.1117i	0.460377	+	0.386303i	−0.382892	+	0.923793i	$0.625072\pi$
$984$		0			0
$985$	14.5404	−	2.56386i	0.463295	−	0.0816915i
$986$	1.27126	+	0.462701i	0.0404852	+	0.0147354i
$987$		0			0
$988$	−3.89881	+	22.1113i	−0.124038	+	0.703453i
$989$	−22.7453	−	13.1320i	−0.723258	−	0.417573i
$990$		0			0
$991$	9.66991	+	16.7488i	0.307175	+	0.532042i	0.977743	−	0.209805i	$-0.0672831\pi$
$991$	9.66991	+	16.7488i	0.307175	+	0.532042i	−0.670568	+	0.741848i	$0.733950\pi$
$992$	1.69077	−	9.58881i	0.0536819	−	0.304445i
$993$		0			0
$994$	25.3855	+	27.0116i	0.805181	+	0.856755i
$995$	8.93652	+	10.6501i	0.283307	+	0.337632i
$996$		0			0
$997$	9.92283	+	1.74966i	0.314259	+	0.0554124i	0.328553	−	0.944485i	$-0.393439\pi$
$997$	9.92283	+	1.74966i	0.314259	+	0.0554124i	−0.0142940	+	0.999898i	$0.504550\pi$
$998$	20.2121	+	11.6694i	0.639801	+	0.369390i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.9		132
3.2	odd	2		189.2.ba.a.101.14	✓	132
7.5	odd	6		567.2.bd.a.467.14		132
21.5	even	6		189.2.bd.a.47.9	yes	132
27.4	even	9		189.2.bd.a.185.9	yes	132
27.23	odd	18		567.2.bd.a.17.14		132
189.131	even	18	inner	567.2.ba.a.341.9		132
189.166	odd	18		189.2.ba.a.131.14	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.14	✓	132	3.2	odd	2
189.2.ba.a.131.14	yes	132	189.166	odd	18
189.2.bd.a.47.9	yes	132	21.5	even	6
189.2.bd.a.185.9	yes	132	27.4	even	9
567.2.ba.a.143.9		132	1.1	even	1	trivial
567.2.ba.a.341.9		132	189.131	even	18	inner
567.2.bd.a.17.14		132	27.23	odd	18
567.2.bd.a.467.14		132	7.5	odd	6

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.ba (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.572822 + 0.682663i) q^{2} +(0.209393 + 1.18753i) q^{4} +(1.06212 - 0.891222i) q^{5} +(-1.58403 + 2.11916i) q^{7} +(-2.47415 - 1.42845i) q^{8} +O(q^{10})\)	\(q+(-0.572822 + 0.682663i) q^{2} +(0.209393 + 1.18753i) q^{4} +(1.06212 - 0.891222i) q^{5} +(-1.58403 + 2.11916i) q^{7} +(-2.47415 - 1.42845i) q^{8} +1.23558i q^{10} +(0.371978 - 0.443306i) q^{11} +(-1.85992 + 5.11010i) q^{13} +(-0.539301 - 2.29526i) q^{14} +(0.126145 - 0.0459131i) q^{16} -2.31232 q^{17} -3.42394i q^{19} +(1.28075 + 1.07468i) q^{20} +(0.0895514 + 0.507871i) q^{22} +(-2.28843 + 6.28742i) q^{23} +(-0.534425 + 3.03087i) q^{25} +(-2.42307 - 4.19688i) q^{26} +(-2.84824 - 1.43735i) q^{28} +(0.224543 + 0.616928i) q^{29} +(1.71407 - 0.302237i) q^{31} +(1.91332 - 5.25680i) q^{32} +(1.32455 - 1.57853i) q^{34} +(0.206211 + 3.66252i) q^{35} +(0.542537 - 0.939702i) q^{37} +(2.33740 + 1.96131i) q^{38} +(-3.90090 + 0.687834i) q^{40} +(-1.37400 - 0.500093i) q^{41} +(-0.681623 + 3.86568i) q^{43} +(0.604328 + 0.348909i) q^{44} +(-2.98132 - 5.16380i) q^{46} +(-1.07027 + 6.06980i) q^{47} +(-1.98167 - 6.71364i) q^{49} +(-1.76293 - 2.10098i) q^{50} +(-6.45784 - 1.13869i) q^{52} +(-8.16395 - 4.71346i) q^{53} -0.802359i q^{55} +(6.94625 - 2.98040i) q^{56} +(-0.549777 - 0.200103i) q^{58} +(-4.76072 - 1.73276i) q^{59} +(13.3184 + 2.34839i) q^{61} +(-0.775532 + 1.34326i) q^{62} +(2.62687 + 4.54987i) q^{64} +(2.57878 + 7.08513i) q^{65} +(-6.31050 + 5.29514i) q^{67} +(-0.484183 - 2.74594i) q^{68} +(-2.61839 - 1.95720i) q^{70} +(-13.6154 + 7.86086i) q^{71} +(2.07131 - 1.19587i) q^{73} +(0.330722 + 0.908652i) q^{74} +(4.06603 - 0.716950i) q^{76} +(0.350210 + 1.49049i) q^{77} +(-2.05377 - 1.72332i) q^{79} +(0.0930623 - 0.161189i) q^{80} +(1.12845 - 0.651511i) q^{82} +(11.2771 - 4.10455i) q^{83} +(-2.45595 + 2.06079i) q^{85} +(-2.24850 - 2.67966i) q^{86} +(-1.55357 + 0.565453i) q^{88} +11.8321 q^{89} +(-7.88293 - 12.0361i) q^{91} +(-7.94566 - 1.40103i) q^{92} +(-3.53055 - 4.20755i) q^{94} +(-3.05150 - 3.63663i) q^{95} +(18.3532 + 3.23616i) q^{97} +(5.71830 + 2.49291i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} + 9 q^{11} - 3 q^{14} + 3 q^{16} + 18 q^{17} - 18 q^{20} - 12 q^{22} + 6 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} - 3 q^{32} - 18 q^{34} - 18 q^{35} + 3 q^{37} + 99 q^{38} - 54 q^{40} - 12 q^{43} + 9 q^{44} + 3 q^{46} - 45 q^{47} - 24 q^{49} + 9 q^{50} - 9 q^{52} + 45 q^{53} - 3 q^{56} - 3 q^{58} - 36 q^{59} - 9 q^{61} + 99 q^{62} + 18 q^{64} - 69 q^{65} - 3 q^{67} - 36 q^{68} + 66 q^{70} - 18 q^{71} - 9 q^{73} - 75 q^{74} + 36 q^{76} - 15 q^{77} - 21 q^{79} - 72 q^{80} - 18 q^{82} + 90 q^{83} + 9 q^{85} + 105 q^{86} - 63 q^{88} + 18 q^{89} + 6 q^{91} - 150 q^{92} - 9 q^{94} - 45 q^{95} - 27 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 + 9 * q^11 - 3 * q^14 + 3 * q^16 + 18 * q^17 - 18 * q^20 - 12 * q^22 + 6 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 - 3 * q^32 - 18 * q^34 - 18 * q^35 + 3 * q^37 + 99 * q^38 - 54 * q^40 - 12 * q^43 + 9 * q^44 + 3 * q^46 - 45 * q^47 - 24 * q^49 + 9 * q^50 - 9 * q^52 + 45 * q^53 - 3 * q^56 - 3 * q^58 - 36 * q^59 - 9 * q^61 + 99 * q^62 + 18 * q^64 - 69 * q^65 - 3 * q^67 - 36 * q^68 + 66 * q^70 - 18 * q^71 - 9 * q^73 - 75 * q^74 + 36 * q^76 - 15 * q^77 - 21 * q^79 - 72 * q^80 - 18 * q^82 + 90 * q^83 + 9 * q^85 + 105 * q^86 - 63 * q^88 + 18 * q^89 + 6 * q^91 - 150 * q^92 - 9 * q^94 - 45 * q^95 - 27 * q^98

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