LMFDB - Embedded newform 567.2.ba.a.143.16

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			143.16
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.720590 - 0.858766i) q^{2} +(0.129068 + 0.731979i) q^{4} +(3.14015 - 2.63490i) q^{5} +(0.864922 + 2.50038i) q^{7} +(2.66330 + 1.53766i) q^{8} +O(q^{10})$	\(q+(0.720590 - 0.858766i) q^{2} +(0.129068 + 0.731979i) q^{4} +(3.14015 - 2.63490i) q^{5} +(0.864922 + 2.50038i) q^{7} +(2.66330 + 1.53766i) q^{8} -4.59533i q^{10} +(0.647625 - 0.771809i) q^{11} +(-1.20956 + 3.32323i) q^{13} +(2.77050 + 1.05898i) q^{14} +(1.84274 - 0.670703i) q^{16} -6.15187 q^{17} +2.40834i q^{19} +(2.33398 + 1.95844i) q^{20} +(-0.196131 - 1.11232i) q^{22} +(0.696226 - 1.91287i) q^{23} +(2.04961 - 11.6239i) q^{25} +(1.98228 + 3.43342i) q^{26} +(-1.71859 + 0.955824i) q^{28} +(-0.707925 - 1.94501i) q^{29} +(0.819437 - 0.144489i) q^{31} +(-1.35175 + 3.71391i) q^{32} +(-4.43298 + 5.28302i) q^{34} +(9.30423 + 5.57259i) q^{35} +(1.98418 - 3.43671i) q^{37} +(2.06820 + 1.73543i) q^{38} +(12.4147 - 2.18905i) q^{40} +(-9.37310 - 3.41153i) q^{41} +(1.78960 - 10.1493i) q^{43} +(0.648535 + 0.374432i) q^{44} +(-1.14101 - 1.97629i) q^{46} +(1.26362 - 7.16632i) q^{47} +(-5.50382 + 4.32527i) q^{49} +(-8.50528 - 10.1362i) q^{50} +(-2.58865 - 0.456449i) q^{52} +(3.60509 + 2.08140i) q^{53} -4.13002i q^{55} +(-1.54118 + 7.98922i) q^{56} +(-2.18043 - 0.793611i) q^{58} +(-2.60824 - 0.949323i) q^{59} +(3.70113 + 0.652610i) q^{61} +(0.466396 - 0.807822i) q^{62} +(4.17633 + 7.23361i) q^{64} +(4.95819 + 13.6225i) q^{65} +(-1.49295 + 1.25274i) q^{67} +(-0.794008 - 4.50304i) q^{68} +(11.4901 - 3.97461i) q^{70} +(-5.21039 + 3.00822i) q^{71} +(-6.29382 + 3.63374i) q^{73} +(-1.52154 - 4.18040i) q^{74} +(-1.76286 + 0.310839i) q^{76} +(2.48996 + 0.951754i) q^{77} +(5.62671 + 4.72137i) q^{79} +(4.01925 - 6.96154i) q^{80} +(-9.68386 + 5.59098i) q^{82} +(7.39595 - 2.69190i) q^{83} +(-19.3178 + 16.2095i) q^{85} +(-7.42633 - 8.85035i) q^{86} +(2.91160 - 1.05973i) q^{88} -13.1252 q^{89} +(-9.35552 - 0.150018i) q^{91} +(1.49004 + 0.262734i) q^{92} +(-5.24364 - 6.24913i) q^{94} +(6.34574 + 7.56255i) q^{95} +(-5.98600 - 1.05549i) q^{97} +(-0.251602 + 7.84324i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.720590	−	0.858766i	0.509534	−	0.607239i	−0.448539	−	0.893763i	$-0.648055\pi$
$2$	0.720590	−	0.858766i	0.509534	−	0.607239i	0.958073	+	0.286524i	$0.0924999\pi$
$3$		0			0
$3$		0			0
$4$	0.129068	+	0.731979i	0.0645338	+	0.365990i
$5$	3.14015	−	2.63490i	1.40432	−	1.17836i	0.445172	−	0.895445i	$-0.353142\pi$
$5$	3.14015	−	2.63490i	1.40432	−	1.17836i	0.959144	−	0.282917i	$-0.0913020\pi$
$6$		0			0
$7$	0.864922	+	2.50038i	0.326910	+	0.945056i
$7$	0.864922	+	2.50038i	0.326910	+	0.945056i
$8$	2.66330	+	1.53766i	0.941619	+	0.543644i
$9$		0			0
$10$		−	4.59533i		−	1.45317i
$11$	0.647625	−	0.771809i	0.195266	−	0.232709i	−0.659523	−	0.751684i	$-0.729242\pi$
$11$	0.647625	−	0.771809i	0.195266	−	0.232709i	0.854789	+	0.518975i	$0.173686\pi$
$12$		0			0
$13$	−1.20956	+	3.32323i	−0.335471	+	0.921699i	0.651191	+	0.758914i	$0.274270\pi$
$13$	−1.20956	+	3.32323i	−0.335471	+	0.921699i	−0.986662	+	0.162785i	$0.947952\pi$
$14$	2.77050	+	1.05898i	0.740446	+	0.283026i
$15$		0			0
$16$	1.84274	−	0.670703i	0.460686	−	0.167676i
$17$	−6.15187			−1.49205			−0.746024	−	0.665919i	$-0.768039\pi$
$17$	−6.15187			−1.49205			−0.746024	+	0.665919i	$0.768039\pi$
$18$		0			0
$19$			2.40834i			0.552512i	0.961084	+	0.276256i	$0.0890937\pi$
$19$			2.40834i			0.552512i	−0.961084	+	0.276256i	$0.910906\pi$
$20$	2.33398	+	1.95844i	0.521894	+	0.437921i
$21$		0			0
$22$	−0.196131	−	1.11232i	−0.0418153	−	0.237147i
$23$	0.696226	−	1.91287i	0.145173	−	0.398860i	−0.845700	−	0.533659i	$-0.820817\pi$
$23$	0.696226	−	1.91287i	0.145173	−	0.398860i	0.990873	+	0.134799i	$0.0430388\pi$
$24$		0			0
$25$	2.04961	−	11.6239i	0.409921	−	2.32478i
$26$	1.98228	+	3.43342i	0.388758	+	0.673348i
$27$		0			0
$28$	−1.71859	+	0.955824i	−0.324784	+	0.180634i
$29$	−0.707925	−	1.94501i	−0.131458	−	0.361179i	0.856447	−	0.516234i	$-0.172667\pi$
$29$	−0.707925	−	1.94501i	−0.131458	−	0.361179i	−0.987906	+	0.155055i	$0.950444\pi$
$30$		0			0
$31$	0.819437	−	0.144489i	0.147175	−	0.0259510i	−0.0995751	−	0.995030i	$-0.531748\pi$
$31$	0.819437	−	0.144489i	0.147175	−	0.0259510i	0.246750	+	0.969079i	$0.420637\pi$
$32$	−1.35175	+	3.71391i	−0.238959	+	0.656533i
$33$		0			0
$34$	−4.43298	+	5.28302i	−0.760249	+	0.906030i
$35$	9.30423	+	5.57259i	1.57270	+	0.941939i
$36$		0			0
$37$	1.98418	−	3.43671i	0.326198	−	0.564991i	−0.655556	−	0.755146i	$-0.727566\pi$
$37$	1.98418	−	3.43671i	0.326198	−	0.564991i	0.981754	+	0.190155i	$0.0608992\pi$
$38$	2.06820	+	1.73543i	0.335507	+	0.281524i
$39$		0			0
$40$	12.4147	−	2.18905i	1.96294	−	0.346119i
$41$	−9.37310	−	3.41153i	−1.46383	−	0.532791i	−0.517414	−	0.855735i	$-0.673105\pi$
$41$	−9.37310	−	3.41153i	−1.46383	−	0.532791i	−0.946418	+	0.322944i	$0.895327\pi$
$42$		0			0
$43$	1.78960	−	10.1493i	0.272912	−	1.54776i	−0.472607	−	0.881273i	$-0.656687\pi$
$43$	1.78960	−	10.1493i	0.272912	−	1.54776i	0.745518	−	0.666485i	$-0.232202\pi$
$44$	0.648535	+	0.374432i	0.0977704	+	0.0564478i
$45$		0			0
$46$	−1.14101	−	1.97629i	−0.168233	−	0.291388i
$47$	1.26362	−	7.16632i	0.184317	−	1.04532i	−0.742512	−	0.669833i	$-0.766366\pi$
$47$	1.26362	−	7.16632i	0.184317	−	1.04532i	0.926829	−	0.375483i	$-0.122523\pi$
$48$		0			0
$49$	−5.50382	+	4.32527i	−0.786260	+	0.617896i
$50$	−8.50528	−	10.1362i	−1.20283	−	1.43347i
$51$		0			0
$52$	−2.58865	−	0.456449i	−0.358981	−	0.0632981i
$53$	3.60509	+	2.08140i	0.495197	+	0.285902i	0.726728	−	0.686925i	$-0.241040\pi$
$53$	3.60509	+	2.08140i	0.495197	+	0.285902i	−0.231531	+	0.972828i	$0.574373\pi$
$54$		0			0
$55$		−	4.13002i		−	0.556892i
$56$	−1.54118	+	7.98922i	−0.205949	+	1.06760i
$57$		0			0
$58$	−2.18043	−	0.793611i	−0.286304	−	0.104206i
$59$	−2.60824	−	0.949323i	−0.339564	−	0.123591i	0.166609	−	0.986023i	$-0.446718\pi$
$59$	−2.60824	−	0.949323i	−0.339564	−	0.123591i	−0.506173	+	0.862432i	$0.668940\pi$
$60$		0			0
$61$	3.70113	+	0.652610i	0.473882	+	0.0835581i	0.405488	−	0.914100i	$-0.367102\pi$
$61$	3.70113	+	0.652610i	0.473882	+	0.0835581i	0.0683935	+	0.997658i	$0.478213\pi$
$62$	0.466396	−	0.807822i	0.0592324	−	0.102593i
$63$		0			0
$64$	4.17633	+	7.23361i	0.522041	+	0.904201i
$65$	4.95819	+	13.6225i	0.614987	+	1.68966i
$66$		0			0
$67$	−1.49295	+	1.25274i	−0.182393	+	0.153046i	−0.729413	−	0.684074i	$-0.760207\pi$
$67$	−1.49295	+	1.25274i	−0.182393	+	0.153046i	0.547020	+	0.837120i	$0.315762\pi$
$68$	−0.794008	−	4.50304i	−0.0962876	−	0.546074i
$69$		0			0
$70$	11.4901	−	3.97461i	1.37333	−	0.475056i
$71$	−5.21039	+	3.00822i	−0.618360	+	0.357010i	−0.776230	−	0.630450i	$-0.782871\pi$
$71$	−5.21039	+	3.00822i	−0.618360	+	0.357010i	0.157870	+	0.987460i	$0.449537\pi$
$72$		0			0
$73$	−6.29382	+	3.63374i	−0.736636	+	0.425297i	−0.820845	−	0.571151i	$-0.806497\pi$
$73$	−6.29382	+	3.63374i	−0.736636	+	0.425297i	0.0842090	+	0.996448i	$0.473164\pi$
$74$	−1.52154	−	4.18040i	−0.176876	−	0.485962i
$75$		0			0
$76$	−1.76286	+	0.310839i	−0.202214	+	0.0356557i
$77$	2.48996	+	0.951754i	0.283757	+	0.108462i
$78$		0			0
$79$	5.62671	+	4.72137i	0.633054	+	0.531196i	0.901876	−	0.431994i	$-0.142190\pi$
$79$	5.62671	+	4.72137i	0.633054	+	0.531196i	−0.268822	+	0.963190i	$0.586634\pi$
$80$	4.01925	−	6.96154i	0.449366	−	0.778324i
$81$		0			0
$82$	−9.68386	+	5.59098i	−1.06940	+	0.617421i
$83$	7.39595	−	2.69190i	0.811811	−	0.295475i	0.0974392	−	0.995241i	$-0.468935\pi$
$83$	7.39595	−	2.69190i	0.811811	−	0.295475i	0.714372	+	0.699767i	$0.246713\pi$
$84$		0			0
$85$	−19.3178	+	16.2095i	−2.09531	+	1.75817i
$86$	−7.42633	−	8.85035i	−0.800802	−	0.954358i
$87$		0			0
$88$	2.91160	−	1.05973i	0.310377	−	0.112968i
$89$	−13.1252			−1.39127			−0.695633	−	0.718397i	$-0.744876\pi$
$89$	−13.1252			−1.39127			−0.695633	+	0.718397i	$0.744876\pi$
$90$		0			0
$91$	−9.35552	−	0.150018i	−0.980725	−	0.0157262i
$92$	1.49004	+	0.262734i	0.155347	+	0.0273919i
$93$		0			0
$94$	−5.24364	−	6.24913i	−0.540841	−	0.644549i
$95$	6.34574	+	7.56255i	0.651059	+	0.775902i
$96$		0			0
$97$	−5.98600	−	1.05549i	−0.607786	−	0.107169i	−0.138719	−	0.990332i	$-0.544299\pi$
$97$	−5.98600	−	1.05549i	−0.607786	−	0.107169i	−0.469067	+	0.883163i	$0.655410\pi$
$98$	−0.251602	+	7.84324i	−0.0254156	+	0.792287i
$99$		0			0
$100$	8.77298			0.877298
$101$	3.53944	−	1.28825i	0.352187	−	0.128186i	−0.159868	−	0.987138i	$-0.551107\pi$
$101$	3.53944	−	1.28825i	0.352187	−	0.128186i	0.512055	+	0.858953i	$0.328885\pi$
$102$		0			0
$103$	−5.62314	−	6.70140i	−0.554065	−	0.660308i	0.414215	−	0.910179i	$-0.364056\pi$
$103$	−5.62314	−	6.70140i	−0.554065	−	0.660308i	−0.968279	+	0.249871i	$0.919612\pi$
$104$	−8.33141	+	6.99088i	−0.816962	+	0.685512i
$105$		0			0
$106$	4.38523	−	1.59609i	0.425931	−	0.155026i
$107$	−1.78505	+	1.03060i	−0.172568	+	0.0996319i	−0.583796	−	0.811900i	$-0.698433\pi$
$107$	−1.78505	+	1.03060i	−0.172568	+	0.0996319i	0.411228	+	0.911532i	$0.365100\pi$
$108$		0			0
$109$	−0.225918	+	0.391301i	−0.0216390	+	0.0374798i	−0.876642	−	0.481143i	$-0.840222\pi$
$109$	−0.225918	+	0.391301i	−0.0216390	+	0.0374798i	0.855003	+	0.518623i	$0.173555\pi$
$110$	−3.54672	−	2.97605i	−0.338166	−	0.283755i
$111$		0			0
$112$	3.27084	+	4.02745i	0.309066	+	0.380559i
$113$	−5.67858	+	1.00129i	−0.534196	+	0.0941931i	−0.434237	−	0.900798i	$-0.642982\pi$
$113$	−5.67858	+	1.00129i	−0.534196	+	0.0941931i	−0.0999585	+	0.994992i	$0.531871\pi$
$114$		0			0
$115$	−2.85395	−	7.84117i	−0.266132	−	0.731193i
$116$	1.33233	−	0.769224i	0.123704	−	0.0714206i
$117$		0			0
$118$	−2.69472	+	1.55580i	−0.248069	+	0.143223i
$119$	−5.32089	−	15.3820i	−0.487765	−	1.41007i
$120$		0			0
$121$	1.73386	+	9.83320i	0.157624	+	0.893927i
$122$	3.22744	−	2.70814i	0.292199	−	0.245184i
$123$		0			0
$124$	0.211526	+	0.581162i	0.0189956	+	0.0521899i
$125$	−13.9438	−	24.1513i	−1.24717	−	2.16016i
$126$		0			0
$127$	−0.738713	+	1.27949i	−0.0655502	+	0.113536i	−0.896938	−	0.442157i	$-0.854214\pi$
$127$	−0.738713	+	1.27949i	−0.0655502	+	0.113536i	0.831388	+	0.555693i	$0.187547\pi$
$128$	1.43696	+	0.253374i	0.127010	+	0.0223953i
$129$		0			0
$130$	15.2714	+	5.55832i	1.33939	+	0.487497i
$131$	4.00000	+	1.45588i	0.349481	+	0.127201i	0.510795	−	0.859702i	$-0.329351\pi$
$131$	4.00000	+	1.45588i	0.349481	+	0.127201i	−0.161314	+	0.986903i	$0.551573\pi$
$132$		0			0
$133$	−6.02178	+	2.08303i	−0.522154	+	0.180622i
$134$			2.18481i			0.188739i
$135$		0			0
$136$	−16.3843	−	9.45947i	−1.40494	−	0.811143i
$137$	−5.56639	−	0.981504i	−0.475568	−	0.0838556i	−0.0692738	−	0.997598i	$-0.522068\pi$
$137$	−5.56639	−	0.981504i	−0.475568	−	0.0838556i	−0.406295	+	0.913742i	$0.633179\pi$
$138$		0			0
$139$	10.0379	+	11.9627i	0.851405	+	1.01466i	0.999669	+	0.0257167i	$0.00818678\pi$
$139$	10.0379	+	11.9627i	0.851405	+	1.01466i	−0.148265	+	0.988948i	$0.547369\pi$
$140$	−2.87814	+	7.52975i	−0.243247	+	0.636380i
$141$		0			0
$142$	−1.17120	+	6.64220i	−0.0982849	+	0.557401i
$143$	1.78156	+	3.08575i	0.148982	+	0.258044i
$144$		0			0
$145$	−7.34788	−	4.24230i	−0.610208	−	0.352304i
$146$	−1.41473	+	8.02335i	−0.117084	+	0.664017i
$147$		0			0
$148$	2.77169	+	1.00881i	0.227832	+	0.0829239i
$149$	8.44056	−	1.48830i	0.691478	−	0.121926i	0.183144	−	0.983086i	$-0.441373\pi$
$149$	8.44056	−	1.48830i	0.691478	−	0.121926i	0.508334	+	0.861160i	$0.330262\pi$
$150$		0			0
$151$	10.0414	+	8.42577i	0.817161	+	0.685679i	0.952305	−	0.305146i	$-0.0987054\pi$
$151$	10.0414	+	8.42577i	0.817161	+	0.685679i	−0.135144	+	0.990826i	$0.543150\pi$
$152$	−3.70321	+	6.41414i	−0.300370	+	0.520256i
$153$		0			0
$154$	2.61158	−	1.45247i	0.210447	−	0.117043i
$155$	2.19244	−	2.61285i	0.176101	−	0.209869i
$156$		0			0
$157$	−4.83314	+	13.2789i	−0.385726	+	1.05977i	0.583179	+	0.812344i	$0.301809\pi$
$157$	−4.83314	+	13.2789i	−0.385726	+	1.05977i	−0.968906	+	0.247431i	$0.920414\pi$
$158$	8.10910	−	1.42985i	0.645126	−	0.113753i
$159$		0			0
$160$	5.54107	+	15.2240i	0.438060	+	1.20356i
$161$	5.38508	+	0.0863512i	0.424404	+	0.00680543i
$162$		0			0
$163$	1.36219	+	2.35938i	0.106695	+	0.184801i	0.914429	−	0.404745i	$-0.132640\pi$
$163$	1.36219	+	2.35938i	0.106695	+	0.184801i	−0.807734	+	0.589546i	$0.799307\pi$
$164$	1.28740	−	7.30123i	0.100529	−	0.570130i
$165$		0			0
$166$	3.01773	−	8.29115i	0.234221	−	0.643518i
$167$	3.82643	+	21.7008i	0.296098	+	1.67926i	0.662706	+	0.748880i	$0.269408\pi$
$167$	3.82643	+	21.7008i	0.296098	+	1.67926i	−0.366608	+	0.930376i	$0.619481\pi$
$168$		0			0
$169$	0.377731	+	0.316954i	0.0290562	+	0.0243811i
$170$			28.2699i			2.16820i
$171$		0			0
$172$	7.66008			0.584075
$173$	−10.4176	+	3.79171i	−0.792038	+	0.288278i	−0.706183	−	0.708029i	$-0.749585\pi$
$173$	−10.4176	+	3.79171i	−0.792038	+	0.288278i	−0.0858553	+	0.996308i	$0.527362\pi$
$174$		0			0
$175$	30.8369	−	4.92897i	2.33105	−	0.372595i
$176$	0.675750	−	1.85661i	0.0509366	−	0.139947i
$177$		0			0
$178$	−9.45787	+	11.2715i	−0.708897	+	0.844831i
$179$			12.6666i			0.946743i	0.880863	+	0.473372i	$0.156963\pi$
$179$			12.6666i			0.946743i	−0.880863	+	0.473372i	$0.843037\pi$
$180$		0			0
$181$	1.39406	+	0.804863i	0.103620	+	0.0598250i	0.550914	−	0.834562i	$-0.314279\pi$
$181$	1.39406	+	0.804863i	0.103620	+	0.0598250i	−0.447294	+	0.894387i	$0.647612\pi$
$182$	−6.87033	+	7.92610i	−0.509263	+	0.587522i
$183$		0			0
$184$	4.79559	−	4.02398i	0.353536	−	0.296652i
$185$	−2.82474	−	16.0199i	−0.207679	−	1.17780i
$186$		0			0
$187$	−3.98410	+	4.74807i	−0.291346	+	0.347213i
$188$	5.40869			0.394469
$189$		0			0
$190$	11.0671			0.802894
$191$	8.34977	−	9.95086i	0.604168	−	0.720019i	−0.374094	−	0.927391i	$-0.622046\pi$
$191$	8.34977	−	9.95086i	0.604168	−	0.720019i	0.978262	+	0.207371i	$0.0664908\pi$
$192$		0			0
$193$	−2.43784	−	13.8257i	−0.175480	−	0.995194i	−0.937589	−	0.347746i	$-0.886947\pi$
$193$	−2.43784	−	13.8257i	−0.175480	−	0.995194i	0.762109	−	0.647448i	$-0.224164\pi$
$194$	−5.21987	+	4.37999i	−0.374765	+	0.314465i
$195$		0			0
$196$	−3.87637	−	3.47043i	−0.276884	−	0.247888i
$197$	15.2141	+	8.78387i	1.08396	+	0.625825i	0.931962	−	0.362556i	$-0.118096\pi$
$197$	15.2141	+	8.78387i	1.08396	+	0.625825i	0.151998	+	0.988381i	$0.451429\pi$
$198$		0			0
$199$		−	22.2758i		−	1.57909i	−0.613692	−	0.789546i	$-0.710316\pi$
$199$		−	22.2758i		−	1.57909i	0.613692	−	0.789546i	$-0.289684\pi$
$200$	23.3323	−	27.8063i	1.64984	−	1.96620i
$201$		0			0
$202$	1.44418	−	3.96785i	0.101612	−	0.279177i
$203$	4.25096	−	3.45236i	0.298359	−	0.242308i
$204$		0			0
$205$	−38.4219	+	13.9844i	−2.68350	+	0.976716i
$206$	−9.80691			−0.683280
$207$		0			0
$208$			6.93512i			0.480864i
$209$	1.85878	+	1.55970i	0.128575	+	0.107887i
$210$		0			0
$211$	−3.52016	−	19.9638i	−0.242338	−	1.37437i	−0.826595	−	0.562798i	$-0.809725\pi$
$211$	−3.52016	−	19.9638i	−0.242338	−	1.37437i	0.584257	−	0.811569i	$-0.301386\pi$
$212$	−1.05824	+	2.90749i	−0.0726803	+	0.199688i
$213$		0			0
$214$	−0.401247	+	2.27558i	−0.0274287	+	0.155556i
$215$	−21.1228	−	36.5858i	−1.44056	−	2.49513i
$216$		0			0
$217$	1.07003	+	1.92393i	0.0726381	+	0.130605i
$218$	0.173242	+	0.475978i	0.0117334	+	0.0322373i
$219$		0			0
$220$	3.02309	−	0.533052i	0.203816	−	0.0359383i
$221$	7.44104	−	20.4441i	0.500539	−	1.37522i
$222$		0			0
$223$	15.6660	−	18.6700i	1.04907	−	1.25024i	0.0817602	−	0.996652i	$-0.473946\pi$
$223$	15.6660	−	18.6700i	1.04907	−	1.25024i	0.967313	−	0.253585i	$-0.0816097\pi$
$224$	−10.4554	−	0.167655i	−0.698578	−	0.0112019i
$225$		0			0
$226$	−3.23206	+	5.59809i	−0.214993	+	0.372379i
$227$	−0.986418	−	0.827703i	−0.0654709	−	0.0549366i	0.609465	−	0.792813i	$-0.291384\pi$
$227$	−0.986418	−	0.827703i	−0.0654709	−	0.0549366i	−0.674936	+	0.737876i	$0.735829\pi$
$228$		0			0
$229$	−0.785032	+	0.138422i	−0.0518764	+	0.00914720i	−0.199526	−	0.979893i	$-0.563940\pi$
$229$	−0.785032	+	0.138422i	−0.0518764	+	0.00914720i	0.147650	+	0.989040i	$0.452829\pi$
$230$	−8.79026	−	3.19939i	−0.579612	−	0.210962i
$231$		0			0
$232$	1.10534	−	6.26868i	0.0725690	−	0.411559i
$233$	−11.6293	−	6.71420i	−0.761863	−	0.439862i	0.0681010	−	0.997678i	$-0.478306\pi$
$233$	−11.6293	−	6.71420i	−0.761863	−	0.439862i	−0.829964	+	0.557816i	$0.811639\pi$
$234$		0			0
$235$	−14.9146	−	25.8328i	−0.972920	−	1.68515i
$236$	0.358245	−	2.03171i	0.0233197	−	0.132253i
$237$		0			0
$238$	−17.0437	−	6.51474i	−1.10478	−	0.422288i
$239$	11.8688	+	14.1447i	0.767728	+	0.914942i	0.998310	−	0.0581107i	$-0.0185076\pi$
$239$	11.8688	+	14.1447i	0.767728	+	0.914942i	−0.230583	+	0.973053i	$0.574063\pi$
$240$		0			0
$241$	13.4746	+	2.37594i	0.867975	+	0.153047i	0.589865	−	0.807502i	$-0.299181\pi$
$241$	13.4746	+	2.37594i	0.867975	+	0.153047i	0.278110	+	0.960549i	$0.410292\pi$
$242$	9.69382	+	5.59673i	0.623142	+	0.359771i
$243$		0			0
$244$			2.79338i			0.178828i
$245$	−5.88616	+	28.0840i	−0.376053	+	1.79422i
$246$		0			0
$247$	−8.00348	−	2.91303i	−0.509250	−	0.185352i
$248$	2.40458	+	0.875196i	0.152691	+	0.0555750i
$249$		0			0
$250$	−30.7880	−	5.42876i	−1.94721	−	0.343345i
$251$	−2.59174	+	4.48902i	−0.163589	+	0.283345i	−0.936153	−	0.351592i	$-0.885640\pi$
$251$	−2.59174	+	4.48902i	−0.163589	+	0.283345i	0.772564	+	0.634937i	$0.218974\pi$
$252$		0			0
$253$	−1.02547	−	1.77617i	−0.0644710	−	0.111667i
$254$	0.566472	+	1.55637i	0.0355436	+	0.0976552i
$255$		0			0
$256$	−11.5440	+	9.68654i	−0.721498	+	0.605408i
$257$	2.27199	+	12.8851i	0.141723	+	0.803751i	0.969940	+	0.243344i	$0.0782443\pi$
$257$	2.27199	+	12.8851i	0.141723	+	0.803751i	−0.828217	+	0.560407i	$0.810645\pi$
$258$		0			0
$259$	10.3092	+	1.98873i	0.640585	+	0.123574i
$260$	−9.33145	+	5.38751i	−0.578712	+	0.334119i
$261$		0			0
$262$	4.13262	−	2.38597i	0.255314	−	0.147406i
$263$	4.81760	+	13.2362i	0.297066	+	0.816182i	0.994987	+	0.100007i	$0.0318865\pi$
$263$	4.81760	+	13.2362i	0.297066	+	0.816182i	−0.697921	+	0.716175i	$0.745891\pi$
$264$		0			0
$265$	16.8048	−	2.96314i	1.03231	−	0.182024i
$266$	−2.55040	+	6.67231i	−0.156375	+	0.409105i
$267$		0			0
$268$	−1.10967	−	0.931123i	−0.0677838	−	0.0568774i
$269$	7.46330	−	12.9268i	0.455045	−	0.788161i	−0.543646	−	0.839315i	$-0.682956\pi$
$269$	7.46330	−	12.9268i	0.455045	−	0.788161i	0.998691	+	0.0511535i	$0.0162898\pi$
$270$		0			0
$271$	8.04155	−	4.64279i	0.488489	−	0.282029i	−0.235458	−	0.971884i	$-0.575659\pi$
$271$	8.04155	−	4.64279i	0.488489	−	0.282029i	0.723948	+	0.689855i	$0.242326\pi$
$272$	−11.3363	+	4.12608i	−0.687365	+	0.250180i
$273$		0			0
$274$	−4.85396	+	4.07296i	−0.293239	+	0.246057i
$275$	−7.64405	−	9.10982i	−0.460953	−	0.549343i
$276$		0			0
$277$	22.9314	−	8.34633i	1.37781	−	0.501483i	0.456298	−	0.889827i	$-0.349175\pi$
$277$	22.9314	−	8.34633i	1.37781	−	0.501483i	0.921514	+	0.388344i	$0.126953\pi$
$278$	17.5064			1.04996
$279$		0			0
$280$	16.2112	+	29.1482i	0.968807	+	1.74194i
$281$	−0.562949	−	0.0992630i	−0.0335827	−	0.00592154i	0.156832	−	0.987625i	$-0.449872\pi$
$281$	−0.562949	−	0.0992630i	−0.0335827	−	0.00592154i	−0.190414	+	0.981704i	$0.560983\pi$
$282$		0			0
$283$	−14.9788	−	17.8510i	−0.890396	−	1.06113i	−0.997759	−	0.0669124i	$-0.978685\pi$
$283$	−14.9788	−	17.8510i	−0.890396	−	1.06113i	0.107363	−	0.994220i	$-0.465759\pi$
$284$	−2.87445	−	3.42564i	−0.170567	−	0.203274i
$285$		0			0
$286$	3.93372	+	0.693620i	0.232606	+	0.0410146i
$287$	0.423123	−	26.3870i	0.0249762	−	1.55758i
$288$		0			0
$289$	20.8455			1.22621
$290$	−8.93796	+	3.25315i	−0.524855	+	0.191032i
$291$		0			0
$292$	−3.47215	−	4.13795i	−0.203192	−	0.242155i
$293$	−12.0512	+	10.1122i	−0.704041	+	0.590760i	−0.922920	−	0.384992i	$-0.874204\pi$
$293$	−12.0512	+	10.1122i	−0.704041	+	0.590760i	0.218879	+	0.975752i	$0.429760\pi$
$294$		0			0
$295$	−10.6916	+	3.89144i	−0.622491	+	0.226568i
$296$	10.5689	−	6.10199i	0.614308	−	0.354671i
$297$		0			0
$298$	4.80409	−	8.32092i	0.278293	−	0.482018i
$299$	5.51477	+	4.62745i	0.318928	+	0.267612i
$300$		0			0
$301$	26.9251	−	4.30370i	1.55194	−	0.248061i
$302$	14.4715	−	2.55172i	0.832743	−	0.146835i
$303$		0			0
$304$	1.61528	+	4.43796i	0.0926429	+	0.254534i
$305$	13.3417	−	7.70281i	0.763942	−	0.441062i
$306$		0			0
$307$	−30.0731	+	17.3627i	−1.71636	+	0.990942i	−0.791034	+	0.611772i	$0.790457\pi$
$307$	−30.0731	+	17.3627i	−1.71636	+	0.990942i	−0.925327	+	0.379170i	$0.876210\pi$
$308$	−0.375291	+	1.94544i	−0.0213842	+	0.110852i
$309$		0			0
$310$	−0.663974	−	3.76559i	−0.0377112	−	0.213871i
$311$	−7.47602	+	6.27313i	−0.423926	+	0.355716i	−0.829654	−	0.558277i	$-0.811462\pi$
$311$	−7.47602	+	6.27313i	−0.423926	+	0.355716i	0.405728	+	0.913994i	$0.367018\pi$
$312$		0			0
$313$	−3.37179	−	9.26391i	−0.190585	−	0.523627i	0.807191	−	0.590291i	$-0.200987\pi$
$313$	−3.37179	−	9.26391i	−0.190585	−	0.523627i	−0.997776	+	0.0666635i	$0.978765\pi$
$314$	7.92079	+	13.7192i	0.446996	+	0.774220i
$315$		0			0
$316$	−2.72972	+	4.72801i	−0.153559	+	0.265971i
$317$	−11.1490	−	1.96588i	−0.626193	−	0.110415i	−0.148458	−	0.988919i	$-0.547431\pi$
$317$	−11.1490	−	1.96588i	−0.626193	−	0.110415i	−0.477735	+	0.878504i	$0.658542\pi$
$318$		0			0
$319$	−1.95964	−	0.713252i	−0.109719	−	0.0399344i
$320$	32.1741	+	11.7104i	1.79859	+	0.654632i
$321$		0			0
$322$	3.95459	−	4.56230i	0.220381	−	0.254247i
$323$		−	14.8158i		−	0.824374i
$324$		0			0
$325$	36.1498	+	20.8711i	2.00523	+	1.15772i
$326$	3.00774	+	0.530345i	0.166583	+	0.0293731i
$327$		0			0
$328$	−19.7176	−	23.4985i	−1.08872	−	1.29749i
$329$	19.0115	−	3.03879i	1.04814	−	0.167534i
$330$		0			0
$331$	−0.717814	+	4.07092i	−0.0394546	+	0.223758i	−0.998159	−	0.0606449i	$-0.980684\pi$
$331$	−0.717814	+	4.07092i	−0.0394546	+	0.223758i	0.958705	+	0.284403i	$0.0917954\pi$
$332$	2.92500	+	5.06624i	0.160530	+	0.278046i
$333$		0			0
$334$	21.3932	+	12.3513i	1.17058	+	0.675836i
$335$	−1.38726	+	7.86756i	−0.0757942	+	0.429851i
$336$		0			0
$337$	−13.3670	−	4.86521i	−0.728149	−	0.265025i	−0.0487681	−	0.998810i	$-0.515530\pi$
$337$	−13.3670	−	4.86521i	−0.728149	−	0.265025i	−0.679381	+	0.733785i	$0.737752\pi$
$338$	0.544378	−	0.0959885i	0.0296103	−	0.00522109i
$339$		0			0
$340$	−14.3583	−	12.0481i	−0.778691	−	0.653399i
$341$	0.419170	−	0.726023i	0.0226993	−	0.0393164i
$342$		0			0
$343$	−15.5752	−	10.0206i	−0.840982	−	0.541063i
$344$	20.3724	−	24.2789i	1.09841	−	1.30903i
$345$		0			0
$346$	−4.25066	+	11.6786i	−0.228517	+	0.627844i
$347$	−7.87722	+	1.38897i	−0.422871	+	0.0745636i	−0.381034	−	0.924561i	$-0.624432\pi$
$347$	−7.87722	+	1.38897i	−0.422871	+	0.0745636i	−0.0418368	+	0.999124i	$0.513321\pi$
$348$		0			0
$349$	4.85476	+	13.3383i	0.259869	+	0.713985i	0.999175	+	0.0406147i	$0.0129316\pi$
$349$	4.85476	+	13.3383i	0.259869	+	0.713985i	−0.739306	+	0.673370i	$0.764846\pi$
$350$	17.9879	−	30.0335i	0.961496	−	1.60536i
$351$		0			0
$352$	1.99100	+	3.44852i	0.106121	+	0.183807i
$353$	2.76866	−	15.7018i	0.147361	−	0.835724i	−0.818081	−	0.575103i	$-0.804962\pi$
$353$	2.76866	−	15.7018i	0.147361	−	0.835724i	0.965441	−	0.260620i	$-0.0839271\pi$
$354$		0			0
$355$	−8.43505	+	23.1751i	−0.447686	+	1.23001i
$356$	−1.69404	−	9.60735i	−0.0897837	−	0.509189i
$357$		0			0
$358$	10.8776	+	9.12740i	0.574900	+	0.482398i
$359$			14.6420i			0.772774i	0.922337	+	0.386387i	$0.126277\pi$
$359$			14.6420i			0.772774i	−0.922337	+	0.386387i	$0.873723\pi$
$360$		0			0
$361$	13.1999			0.694731
$362$	1.69574	−	0.617198i	0.0891260	−	0.0324392i
$363$		0			0
$364$	−1.09769	−	6.86741i	−0.0575344	−	0.359950i
$365$	−10.1890	+	27.9940i	−0.533317	+	1.46528i
$366$		0			0
$367$	6.22653	−	7.42049i	0.325022	−	0.387346i	−0.578647	−	0.815578i	$-0.696419\pi$
$367$	6.22653	−	7.42049i	0.325022	−	0.387346i	0.903669	+	0.428232i	$0.140863\pi$
$368$		−	3.99188i		−	0.208091i
$369$		0			0
$370$	−15.7928	−	9.11798i	−0.821029	−	0.474021i
$371$	−2.08617	+	10.8144i	−0.108309	+	0.561453i
$372$		0			0
$373$	10.0135	−	8.40236i	0.518482	−	0.435058i	−0.345620	−	0.938374i	$-0.612332\pi$
$373$	10.0135	−	8.40236i	0.518482	−	0.435058i	0.864102	+	0.503317i	$0.167887\pi$
$374$	1.20657	+	6.84282i	0.0623905	+	0.353834i
$375$		0			0
$376$	14.3847	−	17.1431i	0.741836	−	0.884086i
$377$	7.31999			0.376999
$378$		0			0
$379$	5.86445			0.301236			0.150618	−	0.988592i	$-0.451874\pi$
$379$	5.86445			0.301236			0.150618	+	0.988592i	$0.451874\pi$
$380$	−4.71660	+	5.62103i	−0.241957	+	0.288353i
$381$		0			0
$382$	−2.52870	−	14.3410i	−0.129380	−	0.733749i
$383$	22.2042	−	18.6316i	1.13458	−	0.952029i	0.135336	−	0.990800i	$-0.456789\pi$
$383$	22.2042	−	18.6316i	1.13458	−	0.952029i	0.999248	+	0.0387708i	$0.0123442\pi$
$384$		0			0
$385$	10.3266	−	3.57214i	0.526293	−	0.182053i
$386$	−13.6297	−	7.86911i	−0.693733	−	0.400527i
$387$		0			0
$388$		−	4.51786i		−	0.229359i
$389$	−23.6671	+	28.2053i	−1.19997	+	1.43007i	−0.325115	+	0.945674i	$0.605403\pi$
$389$	−23.6671	+	28.2053i	−1.19997	+	1.43007i	−0.874852	+	0.484391i	$0.839041\pi$
$390$		0			0
$391$	−4.28309	+	11.7677i	−0.216605	+	0.595118i
$392$	−21.3091	+	3.05651i	−1.07627	+	0.154377i
$393$		0			0
$394$	18.5064	−	6.73579i	0.932340	−	0.339344i
$395$	30.1090			1.51495
$396$		0			0
$397$			34.8763i			1.75039i	0.483770	+	0.875195i	$0.339267\pi$
$397$			34.8763i			1.75039i	−0.483770	+	0.875195i	$0.660733\pi$
$398$	−19.1297	−	16.0517i	−0.958886	−	0.804601i
$399$		0			0
$400$	−4.01929	−	22.7945i	−0.200964	−	1.13973i
$401$	12.5163	−	34.3882i	0.625034	−	1.71727i	−0.0692825	−	0.997597i	$-0.522071\pi$
$401$	12.5163	−	34.3882i	0.625034	−	1.71727i	0.694316	−	0.719670i	$-0.255707\pi$
$402$		0			0
$403$	−0.510986	+	2.89795i	−0.0254540	+	0.144357i
$404$	1.39980	+	2.42452i	0.0696426	+	0.120624i
$405$		0			0
$406$	0.0984296	−	6.13832i	0.00488498	−	0.304640i
$407$	−1.36747	−	3.75710i	−0.0677832	−	0.186233i
$408$		0			0
$409$	37.3852	−	6.59202i	1.84858	−	0.325955i	0.864356	−	0.502881i	$-0.167726\pi$
$409$	37.3852	−	6.59202i	1.84858	−	0.325955i	0.984224	+	0.176926i	$0.0566154\pi$
$410$	−15.6771	+	43.0725i	−0.774237	+	2.12720i
$411$		0			0
$412$	4.17952	−	4.98096i	0.205910	−	0.245394i
$413$	0.117742	−	7.34269i	0.00579371	−	0.361310i
$414$		0			0
$415$	16.1315	−	27.9405i	0.791863	−	1.37155i
$416$	−10.7072	−	8.98439i	−0.524963	−	0.440496i
$417$		0			0
$418$	2.67884	−	0.472351i	0.131026	−	0.0231035i
$419$	20.3827	+	7.41869i	0.995759	+	0.362427i	0.787948	−	0.615742i	$-0.211144\pi$
$419$	20.3827	+	7.41869i	0.995759	+	0.362427i	0.207811	+	0.978169i	$0.433366\pi$
$420$		0			0
$421$	−4.52904	+	25.6854i	−0.220732	+	1.25183i	0.649947	+	0.759980i	$0.274791\pi$
$421$	−4.52904	+	25.6854i	−0.220732	+	1.25183i	−0.870679	+	0.491852i	$0.836320\pi$
$422$	−19.6808	−	11.3627i	−0.958049	−	0.553130i
$423$		0			0
$424$	6.40096	+	11.0868i	0.310858	+	0.538422i
$425$	−12.6089	+	71.5087i	−0.611622	+	3.46868i
$426$		0			0
$427$	1.56942	+	9.81870i	0.0759495	+	0.475160i
$428$	−0.984771	−	1.17360i	−0.0476007	−	0.0567283i
$429$		0			0
$430$	−46.6395	−	8.22381i	−2.24916	−	0.396587i
$431$	20.8304	+	12.0264i	1.00336	+	0.579293i	0.909242	−	0.416268i	$-0.136662\pi$
$431$	20.8304	+	12.0264i	1.00336	+	0.579293i	0.0941228	+	0.995561i	$0.469995\pi$
$432$		0			0
$433$			3.41498i			0.164114i	0.996628	+	0.0820568i	$0.0261489\pi$
$433$			3.41498i			0.164114i	−0.996628	+	0.0820568i	$0.973851\pi$
$434$	2.42326	+	0.467465i	0.116320	+	0.0224391i
$435$		0			0
$436$	−0.315583	−	0.114863i	−0.0151137	−	0.00550093i
$437$	4.60684	+	1.67675i	0.220375	+	0.0802099i
$438$		0			0
$439$	−26.8131	−	4.72787i	−1.27972	−	0.225649i	−0.507858	−	0.861441i	$-0.669562\pi$
$439$	−26.8131	−	4.72787i	−1.27972	−	0.225649i	−0.771860	+	0.635792i	$0.780673\pi$
$440$	6.35055	−	10.9995i	0.302751	−	0.524380i
$441$		0			0
$442$	−12.1947	−	21.1219i	−0.580045	−	1.00467i
$443$	−5.11471	−	14.0525i	−0.243007	−	0.667657i	−0.999900	−	0.0141181i	$-0.995506\pi$
$443$	−5.11471	−	14.0525i	−0.243007	−	0.667657i	0.756893	−	0.653539i	$-0.226716\pi$
$444$		0			0
$445$	−41.2150	+	34.5835i	−1.95378	+	1.63941i
$446$	−4.74441	−	26.9069i	−0.224654	−	1.27408i
$447$		0			0
$448$	−14.4746	+	16.6989i	−0.683860	+	0.788950i
$449$	−16.1509	+	9.32474i	−0.762209	+	0.440062i	−0.830088	−	0.557632i	$-0.811710\pi$
$449$	−16.1509	+	9.32474i	−0.762209	+	0.440062i	0.0678793	+	0.997694i	$0.478377\pi$
$450$		0			0
$451$	−8.70330	+	5.02485i	−0.409822	+	0.236611i
$452$	−1.46584	−	4.02737i	−0.0689474	−	0.189431i
$453$		0			0
$454$	−1.42161	+	0.250668i	−0.0667193	+	0.0117644i
$455$	−29.7730	+	24.1798i	−1.39578	+	1.13356i
$456$		0			0
$457$	−24.6881	−	20.7158i	−1.15486	−	0.969044i	−0.155039	−	0.987908i	$-0.549550\pi$
$457$	−24.6881	−	20.7158i	−1.15486	−	0.969044i	−0.999822	+	0.0188644i	$0.993995\pi$
$458$	−0.446814	+	0.773904i	−0.0208782	+	0.0361622i
$459$		0			0
$460$	5.37122	−	3.10107i	0.250434	−	0.144588i
$461$	14.8218	−	5.39468i	0.690318	−	0.251255i	0.0270466	−	0.999634i	$-0.491390\pi$
$461$	14.8218	−	5.39468i	0.690318	−	0.251255i	0.663271	+	0.748379i	$0.269168\pi$
$462$		0			0
$463$	5.32062	−	4.46453i	0.247270	−	0.207484i	−0.510726	−	0.859744i	$-0.670623\pi$
$463$	5.32062	−	4.46453i	0.247270	−	0.207484i	0.757996	+	0.652260i	$0.226179\pi$
$464$	−2.60905	−	3.10934i	−0.121122	−	0.144348i
$465$		0			0
$466$	−14.1459	+	5.14869i	−0.655297	+	0.238509i
$467$	−14.2646			−0.660086			−0.330043	−	0.943966i	$-0.607063\pi$
$467$	−14.2646			−0.660086			−0.330043	+	0.943966i	$0.607063\pi$
$468$		0			0
$469$	−4.42361	−	2.64943i	−0.204263	−	0.122339i
$470$	−32.9316	−	5.80674i	−1.51902	−	0.267845i
$471$		0			0
$472$	−5.48680	−	6.53891i	−0.252550	−	0.300978i
$473$	−6.67435	−	7.95419i	−0.306887	−	0.365734i
$474$		0			0
$475$	27.9943	+	4.93615i	1.28447	+	0.226486i
$476$	10.5726	−	5.88010i	0.484593	−	0.269514i
$477$		0			0
$478$	20.6995			0.946772
$479$	−8.88334	+	3.23327i	−0.405890	+	0.147732i	−0.536894	−	0.843650i	$-0.680402\pi$
$479$	−8.88334	+	3.23327i	−0.405890	+	0.147732i	0.131003	+	0.991382i	$0.458180\pi$
$480$		0			0
$481$	9.02099	+	10.7508i	0.411322	+	0.490194i
$482$	11.7500	−	9.85945i	0.535199	−	0.449086i
$483$		0			0
$484$	−6.97391	+	2.53830i	−0.316996	+	0.115377i
$485$	−21.5780	+	12.4581i	−0.979808	+	0.565692i
$486$		0			0
$487$	−6.47468	+	11.2145i	−0.293396	+	0.508177i	−0.974610	−	0.223907i	$-0.928119\pi$
$487$	−6.47468	+	11.2145i	−0.293396	+	0.508177i	0.681215	+	0.732084i	$0.261452\pi$
$488$	8.85374	+	7.42917i	0.400790	+	0.336303i
$489$		0			0
$490$	19.8761	+	25.2919i	0.897909	+	1.14257i
$491$	23.2766	−	4.10430i	1.05046	−	0.185224i	0.378340	−	0.925667i	$-0.376495\pi$
$491$	23.2766	−	4.10430i	1.05046	−	0.185224i	0.672120	+	0.740442i	$0.265384\pi$
$492$		0			0
$493$	4.35506	+	11.9654i	0.196142	+	0.538896i
$494$	−8.26884	+	4.77402i	−0.372033	+	0.214793i
$495$		0			0
$496$	1.41310	−	0.815855i	0.0634502	−	0.0366330i
$497$	−12.0283	−	10.4261i	−0.539543	−	0.467674i
$498$		0			0
$499$	−2.29368	−	13.0081i	−0.102679	−	0.582323i	−0.992122	−	0.125276i	$-0.960018\pi$
$499$	−2.29368	−	13.0081i	−0.102679	−	0.582323i	0.889443	−	0.457047i	$-0.151093\pi$
$500$	15.8786	−	13.3237i	0.710111	−	0.595854i
$501$		0			0
$502$	1.98744	+	5.46044i	0.0887037	+	0.243711i
$503$	12.0725	+	20.9102i	0.538286	+	0.932339i	0.998996	+	0.0447884i	$0.0142614\pi$
$503$	12.0725	+	20.9102i	0.538286	+	0.932339i	−0.460710	+	0.887551i	$0.652405\pi$
$504$		0			0
$505$	7.71995	−	13.3713i	0.343533	−	0.595017i
$506$	−2.26426	−	0.399251i	−0.100659	−	0.0177489i
$507$		0			0
$508$	−1.03190	−	0.375582i	−0.0457833	−	0.0166638i
$509$	−15.0961	−	5.49452i	−0.669122	−	0.243540i	−0.0149520	−	0.999888i	$-0.504760\pi$
$509$	−15.0961	−	5.49452i	−0.669122	−	0.243540i	−0.654170	+	0.756348i	$0.726982\pi$
$510$		0			0
$511$	−14.5294	−	12.5941i	−0.642743	−	0.557128i
$512$			19.8118i			0.875568i
$513$		0			0
$514$	12.7025	+	7.33377i	0.560282	+	0.323479i
$515$	−35.3150	−	6.22699i	−1.55616	−	0.274394i
$516$		0			0
$517$	−4.71268	−	5.61636i	−0.207264	−	0.247007i
$518$	9.13659	−	7.42016i	0.401439	−	0.326023i
$519$		0			0
$520$	−7.74160	+	43.9048i	−0.339492	+	1.92535i
$521$	4.79393	+	8.30333i	0.210026	+	0.363776i	0.951722	−	0.306960i	$-0.0993118\pi$
$521$	4.79393	+	8.30333i	0.210026	+	0.363776i	−0.741696	+	0.670736i	$0.765978\pi$
$522$		0			0
$523$	22.7408	+	13.1294i	0.994384	+	0.574108i	0.906582	−	0.422030i	$-0.138682\pi$
$523$	22.7408	+	13.1294i	0.994384	+	0.574108i	0.0878023	+	0.996138i	$0.472016\pi$
$524$	−0.549403	+	3.11582i	−0.0240008	+	0.136115i
$525$		0			0
$526$	14.8383	+	5.40072i	0.646983	+	0.235482i
$527$	−5.04107	+	0.888877i	−0.219592	+	0.0387201i
$528$		0			0
$529$	14.4447	+	12.1205i	0.628030	+	0.526980i
$530$	9.56473	−	16.5666i	0.415465	−	0.719607i
$531$		0			0
$532$	−2.30195	−	4.13896i	−0.0998022	−	0.179447i
$533$	22.6746	−	27.0225i	0.982146	−	1.17048i
$534$		0			0
$535$	−2.88980	+	7.93967i	−0.124937	+	0.343262i
$536$	−5.90246	+	1.04076i	−0.254948	+	0.0449541i
$537$		0			0
$538$	−5.72312	−	15.7242i	−0.246741	−	0.677916i
$539$	−0.226125	+	7.04905i	−0.00973989	+	0.303624i
$540$		0			0
$541$	−12.0613	−	20.8908i	−0.518556	−	0.898166i	−0.999768	−	0.0215613i	$-0.993136\pi$
$541$	−12.0613	−	20.8908i	−0.518556	−	0.898166i	0.481211	−	0.876605i	$-0.340197\pi$
$542$	1.80759	−	10.2514i	0.0776427	−	0.440333i
$543$		0			0
$544$	8.31581	−	22.8475i	0.356538	−	0.979579i
$545$	0.321622	+	1.82401i	0.0137768	+	0.0781321i
$546$		0			0
$547$	21.4421	+	17.9921i	0.916799	+	0.769286i	0.973400	−	0.229111i	$-0.0735818\pi$
$547$	21.4421	+	17.9921i	0.916799	+	0.769286i	−0.0566010	+	0.998397i	$0.518026\pi$
$548$		−	4.20116i		−	0.179465i
$549$		0			0
$550$	−13.3314			−0.568454
$551$	4.68424	−	1.70493i	0.199556	−	0.0726323i
$552$		0			0
$553$	−6.93856	+	18.1525i	−0.295058	+	0.771925i
$554$	9.35657	−	25.7070i	0.397522	−	1.09218i
$555$		0			0
$556$	−7.46089	+	8.89154i	−0.316412	+	0.377085i
$557$		−	5.93171i		−	0.251334i	−0.992072	−	0.125667i	$-0.959893\pi$
$557$		−	5.93171i		−	0.251334i	0.992072	−	0.125667i	$-0.0401072\pi$
$558$		0			0
$559$	31.5640	+	18.2235i	1.33501	+	0.770770i
$560$	20.8829	+	4.02846i	0.882462	+	0.170234i
$561$		0			0
$562$	−0.490899	+	0.411913i	−0.0207073	+	0.0173755i
$563$	−1.83078	−	10.3828i	−0.0771580	−	0.437585i	−0.998775	−	0.0494840i	$-0.984242\pi$
$563$	−1.83078	−	10.3828i	−0.0771580	−	0.437585i	0.921617	−	0.388101i	$-0.126869\pi$
$564$		0			0
$565$	−15.1933	+	18.1067i	−0.639187	+	0.761753i
$566$	−26.1234			−1.09805
$567$		0			0
$568$	−18.5025			−0.776346
$569$	−9.09551	+	10.8396i	−0.381303	+	0.454420i	−0.922225	−	0.386653i	$-0.873631\pi$
$569$	−9.09551	+	10.8396i	−0.381303	+	0.454420i	0.540922	+	0.841073i	$0.318075\pi$
$570$		0			0
$571$	4.10726	+	23.2934i	0.171884	+	0.974800i	0.941680	+	0.336510i	$0.109247\pi$
$571$	4.10726	+	23.2934i	0.171884	+	0.974800i	−0.769796	+	0.638290i	$0.779642\pi$
$572$	−2.02877	+	1.70234i	−0.0848270	+	0.0711783i
$573$		0			0
$574$	−22.3554	−	19.3776i	−0.933096	−	0.808805i
$575$	−20.8080	−	12.0135i	−0.867752	−	0.500997i
$576$		0			0
$577$			44.6938i			1.86063i	0.366765	+	0.930313i	$0.380465\pi$
$577$			44.6938i			1.86063i	−0.366765	+	0.930313i	$0.619535\pi$
$578$	15.0211	−	17.9014i	0.624794	−	0.744600i
$579$		0			0
$580$	2.15690	−	5.92604i	0.0895605	−	0.246065i
$581$	13.1277	+	16.1644i	0.544629	+	0.670613i
$582$		0			0
$583$	3.94119	−	1.43448i	0.163227	−	0.0594099i
$584$	−22.3498			−0.924840
$585$		0			0
$586$			17.6359i			0.728534i
$587$	−21.3980	−	17.9551i	−0.883191	−	0.741085i	0.0836420	−	0.996496i	$-0.473345\pi$
$587$	−21.3980	−	17.9551i	−0.883191	−	0.741085i	−0.966833	+	0.255411i	$0.917789\pi$
$588$		0			0
$589$	0.347979	+	1.97349i	0.0143382	+	0.0813161i
$590$	−4.36245	+	11.9857i	−0.179599	+	0.493445i
$591$		0			0
$592$	1.35133	−	7.66376i	0.0555392	−	0.314979i
$593$	−2.10565	−	3.64710i	−0.0864689	−	0.149768i	0.819547	−	0.573012i	$-0.194225\pi$
$593$	−2.10565	−	3.64710i	−0.0864689	−	0.149768i	−0.906016	+	0.423243i	$0.860892\pi$
$594$		0			0
$595$	−57.2384	−	34.2818i	−2.34655	−	1.40542i
$596$	2.17881	+	5.98622i	0.0892474	+	0.245205i
$597$		0			0
$598$	7.94778	−	1.40141i	0.325009	−	0.0573079i
$599$	−2.62407	+	7.20957i	−0.107217	+	0.294575i	−0.981686	−	0.190505i	$-0.938987\pi$
$599$	−2.62407	+	7.20957i	−0.107217	+	0.294575i	0.874470	+	0.485080i	$0.161210\pi$
$600$		0			0
$601$	−17.3311	+	20.6544i	−0.706949	+	0.842509i	−0.993294	−	0.115617i	$-0.963115\pi$
$601$	−17.3311	+	20.6544i	−0.706949	+	0.842509i	0.286344	+	0.958127i	$0.407560\pi$
$602$	15.7061	−	26.2235i	0.640132	−	1.06879i
$603$		0			0
$604$	−4.87146	+	8.43762i	−0.198217	+	0.343322i
$605$	31.3540	+	26.3092i	1.27472	+	1.06962i
$606$		0			0
$607$	2.86956	−	0.505981i	0.116472	−	0.0205371i	−0.115108	−	0.993353i	$-0.536722\pi$
$607$	2.86956	−	0.505981i	0.116472	−	0.0205371i	0.231580	+	0.972816i	$0.425610\pi$
$608$	−8.94438	−	3.25549i	−0.362742	−	0.132027i
$609$		0			0
$610$	2.99896	−	17.0079i	0.121424	−	0.688631i
$611$	22.2869	+	12.8674i	0.901633	+	0.520558i
$612$		0			0
$613$	−17.2809	−	29.9315i	−0.697971	−	1.20892i	−0.969169	−	0.246397i	$-0.920753\pi$
$613$	−17.2809	−	29.9315i	−0.697971	−	1.20892i	0.271198	−	0.962523i	$-0.412580\pi$
$614$	−6.75987	+	38.3371i	−0.272806	+	1.54716i
$615$		0			0
$616$	5.16805	+	6.36351i	0.208226	+	0.256393i
$617$	16.2205	+	19.3308i	0.653011	+	0.778228i	0.986365	−	0.164574i	$-0.0526248\pi$
$617$	16.2205	+	19.3308i	0.653011	+	0.778228i	−0.333354	+	0.942802i	$0.608180\pi$
$618$		0			0
$619$	38.8625	+	6.85252i	1.56202	+	0.275426i	0.886786	−	0.462180i	$-0.152933\pi$
$619$	38.8625	+	6.85252i	1.56202	+	0.275426i	0.675231	+	0.737606i	$0.264044\pi$
$620$	2.19552	+	1.26759i	0.0881744	+	0.0509075i
$621$		0			0
$622$			10.9405i			0.438674i
$623$	−11.3523	−	32.8179i	−0.454819	−	1.31482i
$624$		0			0
$625$	−51.9647	−	18.9136i	−2.07859	−	0.756544i
$626$	−10.3852	−	3.77990i	−0.415076	−	0.151075i
$627$		0			0
$628$	−10.3437	−	1.82387i	−0.412759	−	0.0727805i
$629$	−12.2064	+	21.1422i	−0.486702	+	0.842993i
$630$		0			0
$631$	9.73033	+	16.8534i	0.387358	+	0.670924i	0.992093	−	0.125503i	$-0.0400544\pi$
$631$	9.73033	+	16.8534i	0.387358	+	0.670924i	−0.604735	+	0.796427i	$0.706721\pi$
$632$	7.72577	+	21.2264i	0.307315	+	0.844340i
$633$		0			0
$634$	−9.72212	+	8.15782i	−0.386115	+	0.323989i
$635$	1.05165	+	5.96421i	0.0417335	+	0.236683i
$636$		0			0
$637$	−7.71670	−	23.5221i	−0.305747	−	0.931981i
$638$	−2.02462	+	1.16891i	−0.0801553	+	0.0462777i
$639$		0			0
$640$	5.17987	−	2.99060i	0.204752	−	0.118214i
$641$	−16.4862	−	45.2954i	−0.651165	−	1.78906i	−0.613398	−	0.789774i	$-0.710198\pi$
$641$	−16.4862	−	45.2954i	−0.651165	−	1.78906i	−0.0377667	−	0.999287i	$-0.512024\pi$
$642$		0			0
$643$	−16.8028	+	2.96278i	−0.662636	+	0.116841i	−0.494844	−	0.868982i	$-0.664775\pi$
$643$	−16.8028	+	2.96278i	−0.662636	+	0.116841i	−0.167792	+	0.985822i	$0.553664\pi$
$644$	0.631832	+	3.95291i	0.0248977	+	0.155766i
$645$		0			0
$646$	−12.7233	−	10.6761i	−0.500592	−	0.420047i
$647$	−6.85799	+	11.8784i	−0.269616	+	0.466988i	−0.968763	−	0.247990i	$-0.920230\pi$
$647$	−6.85799	+	11.8784i	−0.269616	+	0.466988i	0.699147	+	0.714978i	$0.253563\pi$
$648$		0			0
$649$	−2.42186	+	1.39826i	−0.0950662	+	0.0548865i
$650$	43.9726	−	16.0047i	1.72475	−	0.627756i
$651$		0			0
$652$	−1.55120	+	1.30161i	−0.0607498	+	0.0509752i
$653$	−21.3576	−	25.4530i	−0.835787	−	0.996053i	−0.999954	−	0.00962007i	$-0.996938\pi$
$653$	−21.3576	−	25.4530i	−0.835787	−	0.996053i	0.164166	−	0.986433i	$-0.447507\pi$
$654$		0			0
$655$	16.3967	−	5.96790i	0.640671	−	0.233185i
$656$	−19.5603			−0.763703
$657$		0			0
$658$	11.0899	−	18.5161i	0.432328	−	0.721834i
$659$	1.85923	+	0.327832i	0.0724252	+	0.0127705i	0.209743	−	0.977756i	$-0.432737\pi$
$659$	1.85923	+	0.327832i	0.0724252	+	0.0127705i	−0.137318	+	0.990527i	$0.543848\pi$
$660$		0			0
$661$	−30.0773	−	35.8448i	−1.16987	−	1.39420i	−0.902545	−	0.430595i	$-0.858304\pi$
$661$	−30.0773	−	35.8448i	−1.16987	−	1.39420i	−0.267328	−	0.963606i	$-0.586141\pi$
$662$	2.97872	+	3.54990i	0.115771	+	0.137971i
$663$		0			0
$664$	23.8369	+	4.20308i	0.925050	+	0.163111i
$665$	−13.4207	+	22.4078i	−0.520432	+	0.868936i
$666$		0			0
$667$	−4.21342			−0.163144
$668$	−15.3906	+	5.60173i	−0.595482	+	0.216738i
$669$		0			0
$670$	5.75674	+	6.86062i	0.222402	+	0.265049i
$671$	2.90064	−	2.43392i	0.111978	−	0.0939605i
$672$		0			0
$673$	19.5365	−	7.11069i	0.753075	−	0.274097i	0.0631762	−	0.998002i	$-0.479877\pi$
$673$	19.5365	−	7.11069i	0.753075	−	0.274097i	0.689899	+	0.723905i	$0.257655\pi$
$674$	−13.8102	+	7.97334i	−0.531950	+	0.307122i
$675$		0			0
$676$	−0.183251	+	0.317400i	−0.00704810	+	0.0122077i
$677$	−29.3952	−	24.6655i	−1.12975	−	0.947973i	−0.130695	−	0.991423i	$-0.541721\pi$
$677$	−29.3952	−	24.6655i	−1.12975	−	0.947973i	−0.999056	+	0.0434493i	$0.986165\pi$
$678$		0			0
$679$	−2.53829	−	15.8802i	−0.0974105	−	0.609426i
$680$	−76.3738	+	13.4668i	−2.92880	+	0.516427i
$681$		0			0
$682$	−0.321434	−	0.883134i	−0.0123084	−	0.0338169i
$683$	12.1220	−	6.99865i	0.463836	−	0.267796i	−0.249820	−	0.968292i	$-0.580371\pi$
$683$	12.1220	−	6.99865i	0.463836	−	0.267796i	0.713656	+	0.700496i	$0.247038\pi$
$684$		0			0
$685$	−20.0654	+	11.5848i	−0.766661	+	0.442632i
$686$	−19.8287	+	6.15469i	−0.757064	+	0.234987i
$687$		0			0
$688$	−3.50942	−	19.9029i	−0.133795	−	0.758791i
$689$	−11.2775	+	9.46299i	−0.429640	+	0.360511i
$690$		0			0
$691$	−15.8752	−	43.6168i	−0.603922	−	1.65926i	−0.743248	−	0.669016i	$-0.766716\pi$
$691$	−15.8752	−	43.6168i	−0.603922	−	1.65926i	0.139326	−	0.990247i	$-0.455506\pi$
$692$	−4.12003	−	7.13611i	−0.156620	−	0.271274i
$693$		0			0
$694$	−4.48345	+	7.76556i	−0.170189	+	0.294777i
$695$	63.0410	+	11.1158i	2.39128	+	0.421648i
$696$		0			0
$697$	57.6621	+	20.9873i	2.18411	+	0.794950i
$698$	14.9528	+	5.44237i	0.565972	+	0.205997i
$699$		0			0
$700$	7.58795	+	21.9358i	0.286798	+	0.829096i
$701$		−	25.1102i		−	0.948399i	−0.880417	−	0.474199i	$-0.842738\pi$
$701$		−	25.1102i		−	0.948399i	0.880417	−	0.474199i	$-0.157262\pi$
$702$		0			0
$703$	8.27676	+	4.77859i	0.312164	+	0.180228i
$704$	8.28766	+	1.46134i	0.312353	+	0.0550762i
$705$		0			0
$706$	−11.4891	−	13.6922i	−0.432399	−	0.515313i
$707$	6.28245	+	7.73571i	0.236276	+	0.290931i
$708$		0			0
$709$	3.87398	−	21.9704i	0.145490	−	0.825116i	−0.821482	−	0.570234i	$-0.806852\pi$
$709$	3.87398	−	21.9704i	0.145490	−	0.825116i	0.966972	−	0.254882i	$-0.0820365\pi$
$710$	13.8238	+	23.9435i	0.518797	+	0.898583i
$711$		0			0
$712$	−34.9563	−	20.1820i	−1.31004	−	0.756353i
$713$	0.294126	−	1.66807i	0.0110151	−	0.0624697i
$714$		0			0
$715$	13.7250	+	4.99550i	0.513286	+	0.186821i
$716$	−9.27166	+	1.63484i	−0.346498	+	0.0610970i
$717$		0			0
$718$	12.5740	+	10.5509i	0.469259	+	0.393755i
$719$	1.57773	−	2.73271i	0.0588395	−	0.101913i	−0.835105	−	0.550090i	$-0.814593\pi$
$719$	1.57773	−	2.73271i	0.0588395	−	0.101913i	0.893945	+	0.448177i	$0.147927\pi$
$720$		0			0
$721$	11.8925	−	19.8562i	0.442899	−	0.739483i
$722$	9.51171	−	11.3356i	0.353989	−	0.421868i
$723$		0			0
$724$	−0.409215	+	1.12431i	−0.0152083	+	0.0417846i
$725$	−24.0595	+	4.24234i	−0.893548	+	0.157557i
$726$		0			0
$727$	−2.93771	−	8.07129i	−0.108954	−	0.299348i	0.873219	−	0.487328i	$-0.162028\pi$
$727$	−2.93771	−	8.07129i	−0.108954	−	0.299348i	−0.982173	+	0.187980i	$0.939806\pi$
$728$	−24.6859	−	14.7851i	−0.914920	−	0.547974i
$729$		0			0
$730$	16.6982	+	28.9222i	0.618029	+	1.07046i
$731$	−11.0094	+	62.4374i	−0.407197	+	2.30933i
$732$		0			0
$733$	9.57552	−	26.3085i	0.353680	−	0.971727i	−0.627498	−	0.778619i	$-0.715921\pi$
$733$	9.57552	−	26.3085i	0.353680	−	0.971727i	0.981177	−	0.193109i	$-0.0618570\pi$
$734$	−1.88569	−	10.6943i	−0.0696019	−	0.394732i
$735$		0			0
$736$	6.16309	+	5.17145i	0.227175	+	0.190622i
$737$			1.96358i			0.0723293i
$738$		0			0
$739$	20.6207			0.758546			0.379273	−	0.925285i	$-0.376174\pi$
$739$	20.6207			0.758546			0.379273	+	0.925285i	$0.376174\pi$
$740$	11.3616	−	4.13530i	0.417662	−	0.152017i
$741$		0			0
$742$	7.78373	+	9.58425i	0.285750	+	0.351849i
$743$	−2.11075	+	5.79924i	−0.0774359	+	0.212753i	−0.972370	−	0.233445i	$-0.925000\pi$
$743$	−2.11075	+	5.79924i	−0.0774359	+	0.212753i	0.894934	+	0.446198i	$0.147222\pi$
$744$		0			0
$745$	22.5831	−	26.9135i	0.827381	−	0.986034i
$746$		−	14.6539i		−	0.536519i
$747$		0			0
$748$	−3.98971	−	2.30346i	−0.145878	−	0.0842227i
$749$	−4.12083	−	3.57192i	−0.150572	−	0.130515i
$750$		0			0
$751$	−15.2733	+	12.8158i	−0.557330	+	0.467656i	−0.877414	−	0.479734i	$-0.840733\pi$
$751$	−15.2733	+	12.8158i	−0.557330	+	0.467656i	0.320084	+	0.947389i	$0.396289\pi$
$752$	−2.47796	−	14.0532i	−0.0903618	−	0.512467i
$753$		0			0
$754$	5.27471	−	6.28616i	0.192094	−	0.228928i
$755$	53.7326			1.95553
$756$		0			0
$757$	14.8634			0.540221			0.270110	−	0.962829i	$-0.412940\pi$
$757$	14.8634			0.540221			0.270110	+	0.962829i	$0.412940\pi$
$758$	4.22586	−	5.03619i	0.153490	−	0.182923i
$759$		0			0
$760$	5.27199	+	29.8989i	0.191235	+	1.08455i
$761$	−11.7805	+	9.88505i	−0.427044	+	0.358333i	−0.830835	−	0.556519i	$-0.812137\pi$
$761$	−11.7805	+	9.88505i	−0.427044	+	0.358333i	0.403791	+	0.914851i	$0.367692\pi$
$762$		0			0
$763$	−1.17380	−	0.226436i	−0.0424945	−	0.00819752i
$764$	8.36151	+	4.82752i	0.302509	+	0.174654i
$765$		0			0
$766$		−	32.4940i		−	1.17406i
$767$	6.30964	−	7.51954i	0.227828	−	0.271515i
$768$		0			0
$769$	4.80418	−	13.1994i	0.173243	−	0.475982i	−0.822434	−	0.568860i	$-0.807385\pi$
$769$	4.80418	−	13.1994i	0.173243	−	0.475982i	0.995677	+	0.0928784i	$0.0296068\pi$
$770$	4.37363	−	11.4422i	0.157615	−	0.412348i
$771$		0			0
$772$	9.80546	−	3.56890i	0.352906	−	0.128447i
$773$	−20.4197			−0.734446			−0.367223	−	0.930133i	$-0.619691\pi$
$773$	−20.4197			−0.734446			−0.367223	+	0.930133i	$0.619691\pi$
$774$		0			0
$775$		−	9.82119i		−	0.352788i
$776$	−14.3195	−	12.0155i	−0.514041	−	0.431332i
$777$		0			0
$778$	7.16750	+	40.6489i	0.256967	+	1.45733i
$779$	8.21613	−	22.5736i	0.294373	−	0.808784i
$780$		0			0
$781$	−1.05261	+	5.96963i	−0.0376652	+	0.213610i
$782$	7.01935	+	12.1579i	0.251011	+	0.434764i
$783$		0			0
$784$	−7.24115	+	11.6618i	−0.258612	+	0.416493i
$785$	19.8119	+	54.4326i	0.707116	+	1.94278i
$786$		0			0
$787$	−28.5055	+	5.02629i	−1.01611	+	0.179168i	−0.656812	−	0.754054i	$-0.728096\pi$
$787$	−28.5055	+	5.02629i	−1.01611	+	0.179168i	−0.359300	+	0.933222i	$0.616984\pi$
$788$	−4.46596	+	12.2701i	−0.159093	+	0.437105i
$789$		0			0
$790$	21.6963	−	25.8566i	0.771918	−	0.919937i
$791$	−7.41513	−	13.3326i	−0.263652	−	0.474052i
$792$		0			0
$793$	−6.64551	+	11.5104i	−0.235989	+	0.408745i
$794$	29.9506	+	25.1315i	1.06291	+	0.891884i
$795$		0			0
$796$	16.3054	−	2.87509i	0.577931	−	0.101905i
$797$	44.1173	+	16.0574i	1.56271	+	0.568781i	0.971356	−	0.237628i	$-0.0763700\pi$
$797$	44.1173	+	16.0574i	1.56271	+	0.568781i	0.591357	+	0.806410i	$0.298592\pi$
$798$		0			0
$799$	−7.77360	+	44.0863i	−0.275010	+	1.55966i
$800$	40.3996	+	23.3247i	1.42834	+	0.824653i
$801$		0			0
$802$	−20.5123	−	35.5284i	−0.724315	−	1.25455i
$803$	−1.27148	+	7.21092i	−0.0448696	+	0.254468i
$804$		0			0
$805$	17.1375	−	13.9180i	0.604016	−	0.490544i
$806$	2.12045	+	2.52705i	0.0746896	+	0.0890115i
$807$		0			0
$808$	11.4075	+	2.01144i	0.401313	+	0.0707624i
$809$	−16.7570	−	9.67464i	−0.589144	−	0.340142i	0.175615	−	0.984459i	$-0.443809\pi$
$809$	−16.7570	−	9.67464i	−0.589144	−	0.340142i	−0.764759	+	0.644317i	$0.777142\pi$
$810$		0			0
$811$		−	46.9758i		−	1.64954i	−0.565466	−	0.824771i	$-0.691304\pi$
$811$		−	46.9758i		−	1.64954i	0.565466	−	0.824771i	$-0.308696\pi$
$812$	3.07572	+	2.66603i	0.107937	+	0.0935592i
$813$		0			0
$814$	−4.21186	−	1.53299i	−0.147626	−	0.0537313i
$815$	10.4942	+	3.81958i	0.367596	+	0.133794i
$816$		0			0
$817$	24.4431	+	4.30997i	0.855155	+	0.150787i
$818$	21.2784	−	36.8553i	0.743982	−	1.28862i
$819$		0			0
$820$	−15.1953	−	26.3191i	−0.530645	−	0.919103i
$821$	6.79548	+	18.6704i	0.237164	+	0.651603i	0.999988	+	0.00499598i	$0.00159028\pi$
$821$	6.79548	+	18.6704i	0.237164	+	0.651603i	−0.762824	+	0.646607i	$0.776188\pi$
$822$		0			0
$823$	2.44422	−	2.05094i	0.0852001	−	0.0714914i	−0.599193	−	0.800605i	$-0.704512\pi$
$823$	2.44422	−	2.05094i	0.0852001	−	0.0714914i	0.684393	+	0.729113i	$0.260067\pi$
$824$	−4.67166	−	26.4943i	−0.162745	−	0.922973i
$825$		0			0
$826$	−6.22081	−	5.39218i	−0.216450	−	0.187618i
$827$	22.4378	−	12.9545i	0.780239	−	0.450471i	−0.0562757	−	0.998415i	$-0.517923\pi$
$827$	22.4378	−	12.9545i	0.780239	−	0.450471i	0.836515	+	0.547944i	$0.184589\pi$
$828$		0			0
$829$	−26.0612	+	15.0464i	−0.905143	+	0.522585i	−0.878865	−	0.477070i	$-0.841699\pi$
$829$	−26.0612	+	15.0464i	−0.905143	+	0.522585i	−0.0262778	+	0.999655i	$0.508365\pi$
$830$	−12.3702	−	33.9868i	−0.429376	−	1.17970i
$831$		0			0
$832$	−29.0905	+	5.12944i	−1.00853	+	0.177831i
$833$	33.8588	−	26.6085i	1.17314	−	0.921930i
$834$		0			0
$835$	69.1948	+	58.0613i	2.39459	+	2.00930i
$836$	−0.901761	+	1.56190i	−0.0311881	+	0.0540193i
$837$		0			0
$838$	21.0585	−	12.1581i	0.727453	−	0.419995i
$839$	25.0830	−	9.12945i	0.865960	−	0.315184i	0.129430	−	0.991589i	$-0.458685\pi$
$839$	25.0830	−	9.12945i	0.865960	−	0.315184i	0.736530	+	0.676405i	$0.236463\pi$
$840$		0			0
$841$	18.9334	−	15.8870i	0.652876	−	0.547828i
$842$	18.7942	+	22.3981i	0.647691	+	0.771888i
$843$		0			0
$844$	14.1588	−	5.15337i	0.487365	−	0.177386i
$845$	2.02127			0.0695338
$846$		0			0
$847$	−23.0871	+	12.8403i	−0.793282	+	0.441197i
$848$	8.03926	+	1.41754i	0.276069	+	0.0486785i
$849$		0			0
$850$	52.3233	+	62.3565i	1.79468	+	2.13881i
$851$	−5.19252	−	6.18820i	−0.177997	−	0.212129i
$852$		0			0
$853$	−36.3817	−	6.41508i	−1.24569	−	0.219648i	−0.488335	−	0.872656i	$-0.662396\pi$
$853$	−36.3817	−	6.41508i	−1.24569	−	0.219648i	−0.757351	+	0.653008i	$0.773507\pi$
$854$	9.56288	+	5.72750i	0.327235	+	0.195991i
$855$		0			0
$856$	−6.33884			−0.216657
$857$	20.6042	−	7.49932i	0.703827	−	0.256172i	0.0347829	−	0.999395i	$-0.488926\pi$
$857$	20.6042	−	7.49932i	0.703827	−	0.256172i	0.669044	+	0.743223i	$0.266704\pi$
$858$		0			0
$859$	1.54908	+	1.84613i	0.0528541	+	0.0629890i	0.791824	−	0.610750i	$-0.209132\pi$
$859$	1.54908	+	1.84613i	0.0528541	+	0.0629890i	−0.738970	+	0.673739i	$0.764687\pi$
$860$	24.0538	−	20.1835i	0.820227	−	0.688252i
$861$		0			0
$862$	25.3381	−	9.22230i	0.863018	−	0.314113i
$863$	−37.5953	+	21.7057i	−1.27976	+	0.738869i	−0.976804	−	0.214135i	$-0.931307\pi$
$863$	−37.5953	+	21.7057i	−1.27976	+	0.738869i	−0.302955	+	0.953005i	$0.597973\pi$
$864$		0			0
$865$	−22.7222	+	39.3559i	−0.772577	+	1.33814i
$866$	2.93267	+	2.46080i	0.0996562	+	0.0836215i
$867$		0			0
$868$	−1.27017	+	1.03155i	−0.0431125	+	0.0350133i
$869$	7.28799	−	1.28507i	0.247228	−	0.0435930i
$870$		0			0
$871$	−2.35732	−	6.47669i	−0.0798748	−	0.219454i
$872$	−1.20337	+	0.694768i	−0.0407513	+	0.0235278i
$873$		0			0
$874$	4.75958	−	2.74794i	0.160995	−	0.0929506i
$875$	48.3272	−	55.7537i	1.63376	−	1.88482i
$876$		0			0
$877$	−1.09135	−	6.18938i	−0.0368524	−	0.209000i	0.960821	−	0.277168i	$-0.0893959\pi$
$877$	−1.09135	−	6.18938i	−0.0368524	−	0.209000i	−0.997674	+	0.0681675i	$0.978285\pi$
$878$	−23.3814	+	19.6193i	−0.789083	+	0.662119i
$879$		0			0
$880$	−2.77002	−	7.61056i	−0.0933773	−	0.256552i
$881$	−6.18255	−	10.7085i	−0.208295	−	0.360778i	0.742882	−	0.669422i	$-0.233458\pi$
$881$	−6.18255	−	10.7085i	−0.208295	−	0.360778i	−0.951178	+	0.308644i	$0.900125\pi$
$882$		0			0
$883$	9.12997	−	15.8136i	0.307248	−	0.532169i	−0.670511	−	0.741899i	$-0.733925\pi$
$883$	9.12997	−	15.8136i	0.307248	−	0.532169i	0.977759	+	0.209730i	$0.0672586\pi$
$884$	15.9251	+	2.80802i	0.535617	+	0.0944438i
$885$		0			0
$886$	−15.7535	−	5.73379i	−0.529248	−	0.192630i
$887$	7.91282	+	2.88003i	0.265686	+	0.0967020i	0.471428	−	0.881904i	$-0.343739\pi$
$887$	7.91282	+	2.88003i	0.265686	+	0.0967020i	−0.205742	+	0.978606i	$0.565961\pi$
$888$		0			0
$889$	−3.83814	−	0.740406i	−0.128727	−	0.0248324i
$890$			60.3145i			2.02175i
$891$		0			0
$892$	15.6880	+	9.05749i	0.525274	+	0.303267i
$893$	17.2590	+	3.04322i	0.577549	+	0.101838i
$894$		0			0
$895$	33.3751	+	39.7749i	1.11561	+	1.32953i
$896$	0.609324	+	3.81209i	0.0203561	+	0.127353i
$897$		0			0
$898$	−3.63043	+	20.5892i	−0.121149	+	0.687069i
$899$	−0.861132	−	1.49152i	−0.0287204	−	0.0497451i
$900$		0			0
$901$	−22.1781	−	12.8045i	−0.738858	−	0.426580i
$902$	−1.95634	+	11.0950i	−0.0651390	+	0.369421i
$903$		0			0
$904$	−16.6634	−	6.06498i	−0.554216	−	0.201718i
$905$	6.49830	−	1.14583i	0.216011	−	0.0380885i
$906$		0			0
$907$	−10.0928	−	8.46887i	−0.335126	−	0.281204i	0.459659	−	0.888096i	$-0.347972\pi$
$907$	−10.0928	−	8.46887i	−0.335126	−	0.281204i	−0.794785	+	0.606892i	$0.792416\pi$
$908$	0.478547	−	0.828867i	0.0158811	−	0.0275069i
$909$		0			0
$910$	−0.689384	+	42.9917i	−0.0228529	+	1.42516i
$911$	15.2020	−	18.1170i	0.503664	−	0.600244i	−0.452973	−	0.891524i	$-0.649637\pi$
$911$	15.2020	−	18.1170i	0.503664	−	0.600244i	0.956638	+	0.291280i	$0.0940812\pi$
$912$		0			0
$913$	2.71216	−	7.45160i	0.0897594	−	0.246612i
$914$	−35.5800	+	6.27372i	−1.17688	+	0.207516i
$915$		0			0
$916$	−0.202644	−	0.556761i	−0.00669556	−	0.0183959i
$917$	−0.180569	+	11.2607i	−0.00596291	+	0.371862i
$918$		0			0
$919$	−2.87139	−	4.97339i	−0.0947183	−	0.164057i	0.814773	−	0.579780i	$-0.196862\pi$
$919$	−2.87139	−	4.97339i	−0.0947183	−	0.164057i	−0.909491	+	0.415724i	$0.863528\pi$
$920$	4.45610	−	25.2718i	0.146913	−	0.833186i
$921$		0			0
$922$	6.04764	−	16.6158i	0.199169	−	0.547211i
$923$	−3.69475	−	20.9540i	−0.121614	−	0.689708i
$924$		0			0
$925$	−35.8811	−	30.1078i	−1.17976	−	0.989939i
$926$		−	7.78626i		−	0.255872i
$927$		0			0
$928$	8.18053			0.268539
$929$	31.8850	−	11.6052i	1.04611	−	0.380754i	0.238918	−	0.971040i	$-0.423207\pi$
$929$	31.8850	−	11.6052i	1.04611	−	0.380754i	0.807194	+	0.590286i	$0.200985\pi$
$930$		0			0
$931$	−10.4167	−	13.2551i	−0.341395	−	0.434418i
$932$	3.41368	−	9.37902i	0.111819	−	0.307220i
$933$		0			0
$934$	−10.2789	+	12.2499i	−0.336337	+	0.400830i
$935$			25.4073i			0.830909i
$936$		0			0
$937$	−1.87049	−	1.07993i	−0.0611062	−	0.0352797i	0.469136	−	0.883126i	$-0.344566\pi$
$937$	−1.87049	−	1.07993i	−0.0611062	−	0.0352797i	−0.530242	+	0.847846i	$0.677899\pi$
$938$	−5.46285	+	1.88969i	−0.178368	+	0.0617005i
$939$		0			0
$940$	16.9841	−	14.2513i	0.553960	−	0.464828i
$941$	1.85768	+	10.5354i	0.0605587	+	0.343446i	1.00000		0.000734985i	$0.000233953\pi$
$941$	1.85768	+	10.5354i	0.0605587	+	0.343446i	−0.939441	+	0.342711i	$0.888655\pi$
$942$		0			0
$943$	−13.0516	+	15.5543i	−0.425018	+	0.506517i
$944$	−5.44303			−0.177156
$945$		0			0
$946$	−11.6403			−0.378457
$947$	20.1759	−	24.0447i	0.655630	−	0.781349i	−0.331122	−	0.943588i	$-0.607427\pi$
$947$	20.1759	−	24.0447i	0.655630	−	0.781349i	0.986751	+	0.162239i	$0.0518716\pi$
$948$		0			0
$949$	−4.46302	−	25.3110i	−0.144876	−	0.821631i
$950$	24.4114	−	20.4836i	0.792011	−	0.664576i
$951$		0			0
$952$	9.48115	−	49.1487i	0.307286	−	1.59292i
$953$	7.86126	+	4.53870i	0.254651	+	0.147023i	0.621892	−	0.783103i	$-0.286364\pi$
$953$	7.86126	+	4.53870i	0.254651	+	0.147023i	−0.367241	+	0.930126i	$0.619698\pi$
$954$		0			0
$955$		−	53.2480i		−	1.72306i
$956$	−8.82172	+	10.5133i	−0.285315	+	0.340025i
$957$		0			0
$958$	−3.62462	+	9.95857i	−0.117106	+	0.321747i
$959$	−2.36036	−	14.7670i	−0.0762199	−	0.476852i
$960$		0			0
$961$	−28.4799	+	10.3658i	−0.918706	+	0.334381i
$962$	15.7329			0.507247
$963$		0			0
$964$			10.1698i			0.327547i
$965$	−44.0844	−	36.9912i	−1.41913	−	1.19079i
$966$		0			0
$967$	5.45036	+	30.9105i	0.175272	+	0.994016i	0.937830	+	0.347096i	$0.112832\pi$
$967$	5.45036	+	30.9105i	0.175272	+	0.994016i	−0.762558	+	0.646920i	$0.776057\pi$
$968$	−10.5023	+	28.8548i	−0.337557	+	0.927430i
$969$		0			0
$970$	−4.85034	+	27.5077i	−0.155735	+	0.883217i
$971$	14.1550	+	24.5172i	0.454255	+	0.786793i	0.998645	−	0.0520390i	$-0.0165720\pi$
$971$	14.1550	+	24.5172i	0.454255	+	0.786793i	−0.544390	+	0.838832i	$0.683239\pi$
$972$		0			0
$973$	−21.2293	+	35.4454i	−0.680582	+	1.13633i
$974$	4.96502	+	13.6413i	0.159090	+	0.437095i
$975$		0			0
$976$	7.25794	−	1.27977i	0.232321	−	0.0409645i
$977$	−3.25337	+	8.93857i	−0.104085	+	0.285970i	−0.980793	−	0.195052i	$-0.937512\pi$
$977$	−3.25337	+	8.93857i	−0.104085	+	0.285970i	0.876708	+	0.481023i	$0.159735\pi$
$978$		0			0
$979$	−8.50019	+	10.1301i	−0.271667	+	0.323760i
$980$	−21.3166	−	0.683811i	−0.680934	−	0.0218435i
$981$		0			0
$982$	13.2483	−	22.9467i	0.422770	−	0.732258i
$983$	−27.5518	−	23.1187i	−0.878765	−	0.737371i	0.0871597	−	0.996194i	$-0.472221\pi$
$983$	−27.5518	−	23.1187i	−0.878765	−	0.737371i	−0.965925	+	0.258823i	$0.916665\pi$
$984$		0			0
$985$	70.9191	−	12.5050i	2.25967	−	0.398441i
$986$	13.4137	+	4.88219i	0.427180	+	0.155481i
$987$		0			0
$988$	1.09929	−	6.23436i	0.0349730	−	0.198341i
$989$	−18.1683	−	10.4895i	−0.577720	−	0.333547i
$990$		0			0
$991$	10.9977	+	19.0485i	0.349352	+	0.605095i	0.986134	−	0.165948i	$-0.0530684\pi$
$991$	10.9977	+	19.0485i	0.349352	+	0.605095i	−0.636783	+	0.771043i	$0.719735\pi$
$992$	−0.571058	+	3.23863i	−0.0181311	+	0.102827i
$993$		0			0
$994$	−17.6210	+	2.81654i	−0.558906	+	0.0893353i
$995$	−58.6945	−	69.9494i	−1.86074	−	2.21754i
$996$		0			0
$997$	21.0010	+	3.70304i	0.665108	+	0.117277i	0.496002	−	0.868321i	$-0.334801\pi$
$997$	21.0010	+	3.70304i	0.665108	+	0.117277i	0.169106	+	0.985598i	$0.445912\pi$
$998$	−12.8237	−	7.40378i	−0.405928	−	0.234363i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.16		132
3.2	odd	2		189.2.ba.a.101.7	✓	132
7.5	odd	6		567.2.bd.a.467.7		132
21.5	even	6		189.2.bd.a.47.16	yes	132
27.4	even	9		189.2.bd.a.185.16	yes	132
27.23	odd	18		567.2.bd.a.17.7		132
189.131	even	18	inner	567.2.ba.a.341.16		132
189.166	odd	18		189.2.ba.a.131.7	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.7	✓	132	3.2	odd	2
189.2.ba.a.131.7	yes	132	189.166	odd	18
189.2.bd.a.47.16	yes	132	21.5	even	6
189.2.bd.a.185.16	yes	132	27.4	even	9
567.2.ba.a.143.16		132	1.1	even	1	trivial
567.2.ba.a.341.16		132	189.131	even	18	inner
567.2.bd.a.17.7		132	27.23	odd	18
567.2.bd.a.467.7		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)

\(f(q)\)	\(=\)	\(q+(0.720590 - 0.858766i) q^{2} +(0.129068 + 0.731979i) q^{4} +(3.14015 - 2.63490i) q^{5} +(0.864922 + 2.50038i) q^{7} +(2.66330 + 1.53766i) q^{8} +O(q^{10})\)	\(q+(0.720590 - 0.858766i) q^{2} +(0.129068 + 0.731979i) q^{4} +(3.14015 - 2.63490i) q^{5} +(0.864922 + 2.50038i) q^{7} +(2.66330 + 1.53766i) q^{8} -4.59533i q^{10} +(0.647625 - 0.771809i) q^{11} +(-1.20956 + 3.32323i) q^{13} +(2.77050 + 1.05898i) q^{14} +(1.84274 - 0.670703i) q^{16} -6.15187 q^{17} +2.40834i q^{19} +(2.33398 + 1.95844i) q^{20} +(-0.196131 - 1.11232i) q^{22} +(0.696226 - 1.91287i) q^{23} +(2.04961 - 11.6239i) q^{25} +(1.98228 + 3.43342i) q^{26} +(-1.71859 + 0.955824i) q^{28} +(-0.707925 - 1.94501i) q^{29} +(0.819437 - 0.144489i) q^{31} +(-1.35175 + 3.71391i) q^{32} +(-4.43298 + 5.28302i) q^{34} +(9.30423 + 5.57259i) q^{35} +(1.98418 - 3.43671i) q^{37} +(2.06820 + 1.73543i) q^{38} +(12.4147 - 2.18905i) q^{40} +(-9.37310 - 3.41153i) q^{41} +(1.78960 - 10.1493i) q^{43} +(0.648535 + 0.374432i) q^{44} +(-1.14101 - 1.97629i) q^{46} +(1.26362 - 7.16632i) q^{47} +(-5.50382 + 4.32527i) q^{49} +(-8.50528 - 10.1362i) q^{50} +(-2.58865 - 0.456449i) q^{52} +(3.60509 + 2.08140i) q^{53} -4.13002i q^{55} +(-1.54118 + 7.98922i) q^{56} +(-2.18043 - 0.793611i) q^{58} +(-2.60824 - 0.949323i) q^{59} +(3.70113 + 0.652610i) q^{61} +(0.466396 - 0.807822i) q^{62} +(4.17633 + 7.23361i) q^{64} +(4.95819 + 13.6225i) q^{65} +(-1.49295 + 1.25274i) q^{67} +(-0.794008 - 4.50304i) q^{68} +(11.4901 - 3.97461i) q^{70} +(-5.21039 + 3.00822i) q^{71} +(-6.29382 + 3.63374i) q^{73} +(-1.52154 - 4.18040i) q^{74} +(-1.76286 + 0.310839i) q^{76} +(2.48996 + 0.951754i) q^{77} +(5.62671 + 4.72137i) q^{79} +(4.01925 - 6.96154i) q^{80} +(-9.68386 + 5.59098i) q^{82} +(7.39595 - 2.69190i) q^{83} +(-19.3178 + 16.2095i) q^{85} +(-7.42633 - 8.85035i) q^{86} +(2.91160 - 1.05973i) q^{88} -13.1252 q^{89} +(-9.35552 - 0.150018i) q^{91} +(1.49004 + 0.262734i) q^{92} +(-5.24364 - 6.24913i) q^{94} +(6.34574 + 7.56255i) q^{95} +(-5.98600 - 1.05549i) q^{97} +(-0.251602 + 7.84324i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 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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