LMFDB - Embedded newform 567.2.bd.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("567.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	567.17
Dual form			567.2.bd.a.467.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10401 + 0.194666i) q^{2} +(-0.698446 + 0.254214i) q^{4} +(3.85196 - 1.40200i) q^{5} +(2.61259 - 0.417595i) q^{7} +(2.66330 - 1.53766i) q^{8} +O(q^{10})$	\(q+(-1.10401 + 0.194666i) q^{2} +(-0.698446 + 0.254214i) q^{4} +(3.85196 - 1.40200i) q^{5} +(2.61259 - 0.417595i) q^{7} +(2.66330 - 1.53766i) q^{8} +(-3.97967 + 2.29767i) q^{10} +(0.344594 - 0.946764i) q^{11} +(1.20956 + 3.32323i) q^{13} +(-2.80303 + 0.969612i) q^{14} +(-1.50222 + 1.26051i) q^{16} +(-3.07593 - 5.32768i) q^{17} +(-2.08569 - 1.20417i) q^{19} +(-2.33398 + 1.95844i) q^{20} +(-0.196131 + 1.11232i) q^{22} +(-2.00470 - 0.353483i) q^{23} +(9.04178 - 7.58696i) q^{25} +(-1.98228 - 3.43342i) q^{26} +(-1.71859 + 0.955824i) q^{28} +(-0.707925 + 1.94501i) q^{29} +(0.284588 + 0.781898i) q^{31} +(-2.54047 + 3.02761i) q^{32} +(4.43298 + 5.28302i) q^{34} +(9.47812 - 5.27141i) q^{35} -3.96837 q^{37} +(2.53703 + 0.923402i) q^{38} +(8.10314 - 9.65694i) q^{40} +(9.37310 - 3.41153i) q^{41} +(1.78960 + 10.1493i) q^{43} +0.748864i q^{44} +2.28202 q^{46} +(6.83803 + 2.48884i) q^{47} +(6.65123 - 2.18201i) q^{49} +(-8.50528 + 10.1362i) q^{50} +(-1.68962 - 2.01361i) q^{52} +(-3.60509 - 2.08140i) q^{53} -4.13002i q^{55} +(6.31599 - 5.12945i) q^{56} +(0.402927 - 2.28511i) q^{58} +(-2.12626 - 1.78414i) q^{59} +(1.28539 - 3.53158i) q^{61} +(-0.466396 - 0.807822i) q^{62} +(4.17633 - 7.23361i) q^{64} +(9.31834 + 11.1052i) q^{65} +(-0.338425 + 1.91930i) q^{67} +(3.50274 + 2.93915i) q^{68} +(-9.43775 + 7.66475i) q^{70} +(-5.21039 - 3.00822i) q^{71} -7.26748i q^{73} +(4.38111 - 0.772507i) q^{74} +(1.76286 + 0.310839i) q^{76} +(0.504917 - 2.61740i) q^{77} +(1.27547 + 7.23356i) q^{79} +(-4.01925 + 6.96154i) q^{80} +(-9.68386 + 5.59098i) q^{82} +(-7.39595 - 2.69190i) q^{83} +(-19.3178 - 16.2095i) q^{85} +(-3.95147 - 10.8566i) q^{86} +(-0.538041 - 3.05138i) q^{88} +(-6.56259 + 11.3667i) q^{89} +(4.54784 + 8.17713i) q^{91} +(1.49004 - 0.262734i) q^{92} +(-8.03373 - 1.41656i) q^{94} +(-9.72223 - 1.71429i) q^{95} +(5.98600 - 1.05549i) q^{97} +(-6.91825 + 3.70373i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−1.10401	+	0.194666i	−0.780652	+	0.137650i	−0.549752	−	0.835328i	$-0.685278\pi$
$2$	−1.10401	+	0.194666i	−0.780652	+	0.137650i	−0.230899	+	0.972978i	$0.574167\pi$
$3$		0			0
$3$		0			0
$4$	−0.698446	+	0.254214i	−0.349223	+	0.127107i
$5$	3.85196	−	1.40200i	1.72265	−	0.626993i	0.724585	−	0.689185i	$-0.242031\pi$
$5$	3.85196	−	1.40200i	1.72265	−	0.626993i	0.998064	+	0.0621920i	$0.0198091\pi$
$6$		0			0
$7$	2.61259	−	0.417595i	0.987465	−	0.157836i
$7$	2.61259	−	0.417595i	0.987465	−	0.157836i
$8$	2.66330	−	1.53766i	0.941619	−	0.543644i
$9$		0			0
$10$	−3.97967	+	2.29767i	−1.25848	+	0.726586i
$11$	0.344594	−	0.946764i	0.103899	−	0.285460i	−0.876840	−	0.480782i	$-0.840353\pi$
$11$	0.344594	−	0.946764i	0.103899	−	0.285460i	0.980739	+	0.195322i	$0.0625751\pi$
$12$		0			0
$13$	1.20956	+	3.32323i	0.335471	+	0.921699i	0.986662	+	0.162785i	$0.0520476\pi$
$13$	1.20956	+	3.32323i	0.335471	+	0.921699i	−0.651191	+	0.758914i	$0.725730\pi$
$14$	−2.80303	+	0.969612i	−0.749140	+	0.259140i
$15$		0			0
$16$	−1.50222	+	1.26051i	−0.375554	+	0.315128i
$17$	−3.07593	−	5.32768i	−0.746024	−	1.29215i	−0.949715	−	0.313116i	$-0.898627\pi$
$17$	−3.07593	−	5.32768i	−0.746024	−	1.29215i	0.203691	−	0.979035i	$-0.434706\pi$
$18$		0			0
$19$	−2.08569	−	1.20417i	−0.478489	−	0.276256i	0.241297	−	0.970451i	$-0.422427\pi$
$19$	−2.08569	−	1.20417i	−0.478489	−	0.276256i	−0.719787	+	0.694195i	$0.755760\pi$
$20$	−2.33398	+	1.95844i	−0.521894	+	0.437921i
$21$		0			0
$22$	−0.196131	+	1.11232i	−0.0418153	+	0.237147i
$23$	−2.00470	−	0.353483i	−0.418010	−	0.0737064i	−0.0393124	−	0.999227i	$-0.512517\pi$
$23$	−2.00470	−	0.353483i	−0.418010	−	0.0737064i	−0.378697	+	0.925521i	$0.623628\pi$
$24$		0			0
$25$	9.04178	−	7.58696i	1.80836	−	1.51739i
$26$	−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	−0.987906	−	0.155055i	$-0.950444\pi$
$29$	−0.707925	+	1.94501i	−0.131458	+	0.361179i	0.856447	+	0.516234i	$0.172667\pi$
$30$		0			0
$31$	0.284588	+	0.781898i	0.0511134	+	0.140433i	0.962622	−	0.270847i	$-0.0873039\pi$
$31$	0.284588	+	0.781898i	0.0511134	+	0.140433i	−0.911509	+	0.411280i	$0.865082\pi$
$32$	−2.54047	+	3.02761i	−0.449095	+	0.535211i
$33$		0			0
$34$	4.43298	+	5.28302i	0.760249	+	0.906030i
$35$	9.47812	−	5.27141i	1.60209	−	0.891030i
$36$		0			0
$37$	−3.96837			−0.652395			−0.326198	−	0.945302i	$-0.605767\pi$
$37$	−3.96837			−0.652395			−0.326198	+	0.945302i	$0.605767\pi$
$38$	2.53703	+	0.923402i	0.411560	+	0.149796i
$39$		0			0
$40$	8.10314	−	9.65694i	1.28122	−	1.52690i
$41$	9.37310	−	3.41153i	1.46383	−	0.532791i	0.517414	−	0.855735i	$-0.326895\pi$
$41$	9.37310	−	3.41153i	1.46383	−	0.532791i	0.946418	+	0.322944i	$0.104673\pi$
$42$		0			0
$43$	1.78960	+	10.1493i	0.272912	+	1.54776i	0.745518	+	0.666485i	$0.232202\pi$
$43$	1.78960	+	10.1493i	0.272912	+	1.54776i	−0.472607	+	0.881273i	$0.656687\pi$
$44$			0.748864i			0.112896i
$45$		0			0
$46$	2.28202			0.336466
$47$	6.83803	+	2.48884i	0.997429	+	0.363034i	0.788592	−	0.614916i	$-0.210810\pi$
$47$	6.83803	+	2.48884i	0.997429	+	0.363034i	0.208836	+	0.977951i	$0.433032\pi$
$48$		0			0
$49$	6.65123	−	2.18201i	0.950175	−	0.311716i
$50$	−8.50528	+	10.1362i	−1.20283	+	1.43347i
$51$		0			0
$52$	−1.68962	−	2.01361i	−0.234309	−	0.279238i
$53$	−3.60509	−	2.08140i	−0.495197	−	0.285902i	0.231531	−	0.972828i	$-0.425627\pi$
$53$	−3.60509	−	2.08140i	−0.495197	−	0.285902i	−0.726728	+	0.686925i	$0.758960\pi$
$54$		0			0
$55$		−	4.13002i		−	0.556892i
$56$	6.31599	−	5.12945i	0.844009	−	0.685451i
$57$		0			0
$58$	0.402927	−	2.28511i	0.0529069	−	0.300050i
$59$	−2.12626	−	1.78414i	−0.276815	−	0.232276i	0.493801	−	0.869575i	$-0.335607\pi$
$59$	−2.12626	−	1.78414i	−0.276815	−	0.232276i	−0.770616	+	0.637299i	$0.780052\pi$
$60$		0			0
$61$	1.28539	−	3.53158i	0.164577	−	0.452173i	−0.829801	−	0.558060i	$-0.811546\pi$
$61$	1.28539	−	3.53158i	0.164577	−	0.452173i	0.994378	+	0.105887i	$0.0337682\pi$
$62$	−0.466396	−	0.807822i	−0.0592324	−	0.102593i
$63$		0			0
$64$	4.17633	−	7.23361i	0.522041	−	0.904201i
$65$	9.31834	+	11.1052i	1.15580	+	1.37743i
$66$		0			0
$67$	−0.338425	+	1.91930i	−0.0413452	+	0.234480i	−0.998477	−	0.0551731i	$-0.982429\pi$
$67$	−0.338425	+	1.91930i	−0.0413452	+	0.234480i	0.957132	+	0.289653i	$0.0935400\pi$
$68$	3.50274	+	2.93915i	0.424770	+	0.356424i
$69$		0			0
$70$	−9.43775	+	7.66475i	−1.12803	+	0.916113i
$71$	−5.21039	−	3.00822i	−0.618360	−	0.357010i	0.157870	−	0.987460i	$-0.449537\pi$
$71$	−5.21039	−	3.00822i	−0.618360	−	0.357010i	−0.776230	+	0.630450i	$0.782871\pi$
$72$		0			0
$73$		−	7.26748i		−	0.850594i	−0.905054	−	0.425297i	$-0.860170\pi$
$73$		−	7.26748i		−	0.850594i	0.905054	−	0.425297i	$-0.139830\pi$
$74$	4.38111	−	0.772507i	0.509293	−	0.0898022i
$75$		0			0
$76$	1.76286	+	0.310839i	0.202214	+	0.0356557i
$77$	0.504917	−	2.61740i	0.0575407	−	0.298281i
$78$		0			0
$79$	1.27547	+	7.23356i	0.143502	+	0.813839i	0.968558	+	0.248788i	$0.0800323\pi$
$79$	1.27547	+	7.23356i	0.143502	+	0.813839i	−0.825056	+	0.565051i	$0.808857\pi$
$80$	−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	$-0.531065\pi$
$83$	−7.39595	−	2.69190i	−0.811811	−	0.295475i	−0.714372	+	0.699767i	$0.753287\pi$
$84$		0			0
$85$	−19.3178	−	16.2095i	−2.09531	−	1.75817i
$86$	−3.95147	−	10.8566i	−0.426098	−	1.17069i
$87$		0			0
$88$	−0.538041	−	3.05138i	−0.0573554	−	0.325279i
$89$	−6.56259	+	11.3667i	−0.695633	+	1.20487i	0.274334	+	0.961634i	$0.411543\pi$
$89$	−6.56259	+	11.3667i	−0.695633	+	1.20487i	−0.969967	+	0.243237i	$0.921791\pi$
$90$		0			0
$91$	4.54784	+	8.17713i	0.476743	+	0.857196i
$92$	1.49004	−	0.262734i	0.155347	−	0.0273919i
$93$		0			0
$94$	−8.03373	−	1.41656i	−0.828616	−	0.146107i
$95$	−9.72223	−	1.71429i	−0.997480	−	0.175883i
$96$		0			0
$97$	5.98600	−	1.05549i	0.607786	−	0.107169i	0.138719	−	0.990332i	$-0.455701\pi$
$97$	5.98600	−	1.05549i	0.607786	−	0.107169i	0.469067	+	0.883163i	$0.344590\pi$
$98$	−6.91825	+	3.70373i	−0.698848	+	0.374133i
$99$		0			0
$100$	−4.38649	+	7.59763i	−0.438649	+	0.759763i
$101$	0.654061	+	3.70937i	0.0650815	+	0.369096i	0.999902	+	0.0139759i	$0.00444882\pi$
$101$	0.654061	+	3.70937i	0.0650815	+	0.369096i	−0.934821	+	0.355120i	$0.884440\pi$
$102$		0			0
$103$	2.99201	+	8.22048i	0.294812	+	0.809988i	0.995346	+	0.0963692i	$0.0307230\pi$
$103$	2.99201	+	8.22048i	0.294812	+	0.809988i	−0.700534	+	0.713619i	$0.747055\pi$
$104$	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	−0.411228	−	0.911532i	$-0.634900\pi$
$107$	1.78505	−	1.03060i	0.172568	−	0.0996319i	0.583796	+	0.811900i	$0.301567\pi$
$108$		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	$0.173555\pi$
$110$	0.803976	+	4.55957i	0.0766561	+	0.434738i
$111$		0			0
$112$	−3.39829	+	3.92051i	−0.321108	+	0.370454i
$113$	−5.67858	−	1.00129i	−0.534196	−	0.0941931i	−0.0999585	−	0.994992i	$-0.531871\pi$
$113$	−5.67858	−	1.00129i	−0.534196	−	0.0941931i	−0.434237	+	0.900798i	$0.642982\pi$
$114$		0			0
$115$	−8.21763	+	1.44899i	−0.766298	+	0.135119i
$116$		−	1.53845i		−	0.142841i
$117$		0			0
$118$	2.69472	+	1.55580i	0.248069	+	0.143223i
$119$	−10.2610	−	12.6345i	−0.940621	−	1.15820i
$120$		0			0
$121$	7.64887	+	6.41817i	0.695352	+	0.583470i
$122$	−0.731601	+	4.14912i	−0.0662361	+	0.375643i
$123$		0			0
$124$	−0.397538	−	0.473768i	−0.0357000	−	0.0425456i
$125$	13.9438	−	24.1513i	1.24717	−	2.16016i
$126$		0			0
$127$	−0.738713	−	1.27949i	−0.0655502	−	0.113536i	0.831388	−	0.555693i	$-0.187547\pi$
$127$	−0.738713	−	1.27949i	−0.0655502	−	0.113536i	−0.896938	+	0.442157i	$0.854214\pi$
$128$	−0.499050	+	1.37113i	−0.0441102	+	0.121192i
$129$		0			0
$130$	−12.4493	−	10.4462i	−1.09188	−	0.916195i
$131$	0.739169	−	4.19204i	0.0645815	−	0.366260i	−0.935340	−	0.353749i	$-0.884907\pi$
$131$	0.739169	−	4.19204i	0.0645815	−	0.366260i	0.999922	−	0.0125106i	$-0.00398235\pi$
$132$		0			0
$133$	−5.95189	−	2.27503i	−0.516095	−	0.197270i
$134$		−	2.18481i		−	0.188739i
$135$		0			0
$136$	−16.3843	−	9.45947i	−1.40494	−	0.811143i
$137$	3.63320	+	4.32988i	0.310405	+	0.369927i	0.898582	−	0.438806i	$-0.144598\pi$
$137$	3.63320	+	4.32988i	0.310405	+	0.369927i	−0.588177	+	0.808733i	$0.700154\pi$
$138$		0			0
$139$	−10.0379	+	11.9627i	−0.851405	+	1.01466i	0.148265	+	0.988948i	$0.452631\pi$
$139$	−10.0379	+	11.9627i	−0.851405	+	1.01466i	−0.999669	+	0.0257167i	$0.991813\pi$
$140$	−5.27989	+	6.09126i	−0.446232	+	0.514806i
$141$		0			0
$142$	6.33792	+	2.30681i	0.531866	+	0.193583i
$143$	3.56312			0.297963
$144$		0			0
$145$			8.48460i			0.704608i
$146$	1.41473	+	8.02335i	0.117084	+	0.664017i
$147$		0			0
$148$	2.77169	−	1.00881i	0.227832	−	0.0829239i
$149$	−5.50919	+	6.56559i	−0.451330	+	0.537874i	−0.942949	−	0.332936i	$-0.891961\pi$
$149$	−5.50919	+	6.56559i	−0.451330	+	0.537874i	0.491619	+	0.870810i	$0.336405\pi$
$150$		0			0
$151$	−12.3177	−	4.48326i	−1.00240	−	0.364842i	−0.211888	−	0.977294i	$-0.567961\pi$
$151$	−12.3177	−	4.48326i	−1.00240	−	0.364842i	−0.790508	+	0.612451i	$0.790183\pi$
$152$	−7.40641			−0.600739
$153$		0			0
$154$	−0.0479122	+	2.98793i	−0.00386087	+	0.240774i
$155$	2.19244	+	2.61285i	0.176101	+	0.209869i
$156$		0			0
$157$	9.08333	−	10.8251i	0.724929	−	0.863936i	−0.270171	−	0.962812i	$-0.587080\pi$
$157$	9.08333	−	10.8251i	0.724929	−	0.863936i	0.995100	+	0.0988761i	$0.0315248\pi$
$158$	−2.81626	−	7.73762i	−0.224050	−	0.615572i
$159$		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	$0.799307\pi$
$164$	−5.67935	+	4.76554i	−0.443483	+	0.372126i
$165$		0			0
$166$	8.68921	+	1.53214i	0.674413	+	0.118917i
$167$	−3.82643	+	21.7008i	−0.296098	+	1.67926i	0.366608	+	0.930376i	$0.380519\pi$
$167$	−3.82643	+	21.7008i	−0.296098	+	1.67926i	−0.662706	+	0.748880i	$0.730592\pi$
$168$		0			0
$169$	0.377731	−	0.316954i	0.0290562	−	0.0243811i
$170$	24.4824	+	14.1349i	1.87772	+	1.08410i
$171$		0			0
$172$	−3.83004	−	6.63382i	−0.292038	−	0.505824i
$173$	−8.49254	+	7.12609i	−0.645676	+	0.541786i	−0.905755	−	0.423801i	$-0.860696\pi$
$173$	−8.49254	+	7.12609i	−0.645676	+	0.541786i	0.260080	+	0.965587i	$0.416251\pi$
$174$		0			0
$175$	20.4542	−	23.5974i	1.54619	−	1.78380i
$176$	0.675750	+	1.85661i	0.0509366	+	0.139947i
$177$		0			0
$178$	5.03243	−	13.8265i	0.377196	−	1.03634i
$179$	−10.9696	+	6.33328i	−0.819904	+	0.473372i	−0.850383	−	0.526164i	$-0.823630\pi$
$179$	−10.9696	+	6.33328i	−0.819904	+	0.473372i	0.0304796	+	0.999535i	$0.490297\pi$
$180$		0			0
$181$	−1.39406	+	0.804863i	−0.103620	+	0.0598250i	−0.550914	−	0.834562i	$-0.685721\pi$
$181$	−1.39406	+	0.804863i	−0.103620	+	0.0598250i	0.447294	+	0.894387i	$0.352388\pi$
$182$	−6.61267	−	8.14231i	−0.490164	−	0.603548i
$183$		0			0
$184$	−5.88267	+	2.14112i	−0.433676	+	0.157845i
$185$	−15.2860	+	5.56365i	−1.12385	+	0.409047i
$186$		0			0
$187$	−6.10400	+	1.07630i	−0.446369	+	0.0787068i
$188$	−5.40869			−0.394469
$189$		0			0
$190$	11.0671			0.802894
$191$	−12.7926	+	2.25568i	−0.925639	+	0.163215i	−0.616097	−	0.787671i	$-0.711287\pi$
$191$	−12.7926	+	2.25568i	−0.925639	+	0.163215i	−0.309542	+	0.950886i	$0.600176\pi$
$192$		0			0
$193$	13.1923	−	4.80161i	0.949603	−	0.345627i	0.179652	−	0.983730i	$-0.442503\pi$
$193$	13.1923	−	4.80161i	0.949603	−	0.345627i	0.769951	+	0.638103i	$0.220281\pi$
$194$	−6.40312	+	2.33055i	−0.459717	+	0.167323i
$195$		0			0
$196$	−4.09083	+	3.21485i	−0.292202	+	0.229632i
$197$	15.2141	−	8.78387i	1.08396	−	0.625825i	0.151998	−	0.988381i	$-0.451429\pi$
$197$	15.2141	−	8.78387i	1.08396	−	0.625825i	0.931962	+	0.362556i	$0.118096\pi$
$198$		0			0
$199$	−19.2914	+	11.1379i	−1.36753	+	0.789546i	−0.990613	−	0.136700i	$-0.956350\pi$
$199$	−19.2914	+	11.1379i	−1.36753	+	0.789546i	−0.376921	+	0.926245i	$0.623017\pi$
$200$	12.4148	−	34.1095i	0.877862	−	2.41191i
$201$		0			0
$202$	−1.44418	−	3.96785i	−0.101612	−	0.279177i
$203$	−1.03729	+	5.37713i	−0.0728034	+	0.377400i
$204$		0			0
$205$	31.3218	−	26.2822i	2.18761	−	1.83563i
$206$	−4.90346	−	8.49304i	−0.341640	−	0.591738i
$207$		0			0
$208$	−6.00599	−	3.46756i	−0.416440	−	0.240432i
$209$	−1.85878	+	1.55970i	−0.128575	+	0.107887i
$210$		0			0
$211$	−3.52016	+	19.9638i	−0.242338	+	1.37437i	0.584257	+	0.811569i	$0.301386\pi$
$211$	−3.52016	+	19.9638i	−0.242338	+	1.37437i	−0.826595	+	0.562798i	$0.809725\pi$
$212$	3.04708	+	0.537283i	0.209275	+	0.0369008i
$213$		0			0
$214$	−1.77009	+	1.48528i	−0.121001	+	0.101532i
$215$	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
$220$	1.04991	+	2.88460i	0.0707847	+	0.194479i
$221$	13.9846	−	16.6662i	0.940705	−	1.12109i
$222$		0			0
$223$	−15.6660	−	18.6700i	−1.04907	−	1.25024i	−0.967313	−	0.253585i	$-0.918390\pi$
$223$	−15.6660	−	18.6700i	−1.04907	−	1.25024i	−0.0817602	−	0.996652i	$-0.526054\pi$
$224$	−5.37288	+	8.97078i	−0.358990	+	0.599386i
$225$		0			0
$226$	6.46412			0.429987
$227$	−1.21002	−	0.440412i	−0.0803119	−	0.0292312i	0.301552	−	0.953450i	$-0.402495\pi$
$227$	−1.21002	−	0.440412i	−0.0803119	−	0.0292312i	−0.381864	+	0.924219i	$0.624718\pi$
$228$		0			0
$229$	−0.512393	+	0.610646i	−0.0338599	+	0.0403526i	−0.782709	−	0.622388i	$-0.786162\pi$
$229$	−0.512393	+	0.610646i	−0.0338599	+	0.0403526i	0.748849	+	0.662741i	$0.230607\pi$
$230$	8.79026	−	3.19939i	0.579612	−	0.210962i
$231$		0			0
$232$	1.10534	+	6.26868i	0.0725690	+	0.411559i
$233$		−	13.4284i		−	0.879724i	−0.898065	−	0.439862i	$-0.855027\pi$
$233$		−	13.4284i		−	0.879724i	0.898065	−	0.439862i	$-0.144973\pi$
$234$		0			0
$235$	29.8292			1.94584
$236$	1.93863	+	0.705604i	0.126194	+	0.0459309i
$237$		0			0
$238$	13.7877	+	11.9511i	0.893724	+	0.774678i
$239$	11.8688	−	14.1447i	0.767728	−	0.914942i	−0.230583	−	0.973053i	$-0.574063\pi$
$239$	11.8688	−	14.1447i	0.767728	−	0.914942i	0.998310	+	0.0581107i	$0.0185076\pi$
$240$		0			0
$241$	8.79492	+	10.4814i	0.566531	+	0.675165i	0.970915	−	0.239424i	$-0.0769586\pi$
$241$	8.79492	+	10.4814i	0.566531	+	0.675165i	−0.404384	+	0.914589i	$0.632514\pi$
$242$	−9.69382	−	5.59673i	−0.623142	−	0.359771i
$243$		0			0
$244$			2.79338i			0.178828i
$245$	22.5611	−	17.7300i	1.44138	−	1.13273i
$246$		0			0
$247$	1.47898	−	8.38774i	0.0941055	−	0.533699i
$248$	1.96023	+	1.64483i	0.124475	+	0.104447i
$249$		0			0
$250$	−10.6926	+	29.3776i	−0.676258	+	1.85800i
$251$	2.59174	+	4.48902i	0.163589	+	0.283345i	0.936153	−	0.351592i	$-0.114360\pi$
$251$	2.59174	+	4.48902i	0.163589	+	0.283345i	−0.772564	+	0.634937i	$0.781026\pi$
$252$		0			0
$253$	−1.02547	+	1.77617i	−0.0644710	+	0.111667i
$254$	1.06462	+	1.26876i	0.0668001	+	0.0796093i
$255$		0			0
$256$	−2.61680	+	14.8406i	−0.163550	+	0.927540i
$257$	−10.0228	−	8.41016i	−0.625207	−	0.524611i	0.274228	−	0.961665i	$-0.411578\pi$
$257$	−10.0228	−	8.41016i	−0.625207	−	0.524611i	−0.899436	+	0.437053i	$0.856022\pi$
$258$		0			0
$259$	−10.3677	+	1.65717i	−0.644218	+	0.102972i
$260$	−9.33145	−	5.38751i	−0.578712	−	0.334119i
$261$		0			0
$262$			4.77194i			0.294811i
$263$	−13.8717	+	2.44596i	−0.855367	+	0.150824i	−0.584102	−	0.811680i	$-0.698553\pi$
$263$	−13.8717	+	2.44596i	−0.855367	+	0.150824i	−0.271265	+	0.962505i	$0.587442\pi$
$264$		0			0
$265$	−16.8048	−	2.96314i	−1.03231	−	0.182024i
$266$	7.01381	+	1.35302i	0.430044	+	0.0829589i
$267$		0			0
$268$	−0.251542	−	1.42656i	−0.0153653	−	0.0871412i
$269$	−7.46330	+	12.9268i	−0.455045	+	0.788161i	−0.998691	−	0.0511535i	$-0.983710\pi$
$269$	−7.46330	+	12.9268i	−0.455045	+	0.788161i	0.543646	+	0.839315i	$0.317044\pi$
$270$		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
$275$	−4.06731	−	11.1749i	−0.245268	−	0.673869i
$276$		0			0
$277$	−4.23755	−	24.0323i	−0.254609	−	1.44396i	−0.797073	−	0.603883i	$-0.793620\pi$
$277$	−4.23755	−	24.0323i	−0.254609	−	1.44396i	0.542464	−	0.840079i	$-0.317492\pi$
$278$	8.75320	−	15.1610i	0.524982	−	0.909295i
$279$		0			0
$280$	17.1375	−	28.6134i	1.02416	−	1.70998i
$281$	−0.562949	+	0.0992630i	−0.0335827	+	0.00592154i	−0.190414	−	0.981704i	$-0.560983\pi$
$281$	−0.562949	+	0.0992630i	−0.0335827	+	0.00592154i	0.156832	+	0.987625i	$0.449872\pi$
$282$		0			0
$283$	−22.9488	−	4.04649i	−1.36417	−	0.240539i	−0.556827	−	0.830628i	$-0.687981\pi$
$283$	−22.9488	−	4.04649i	−1.36417	−	0.240539i	−0.807338	+	0.590089i	$0.799093\pi$
$284$	4.40391	+	0.776529i	0.261324	+	0.0460785i
$285$		0			0
$286$	−3.93372	+	0.693620i	−0.232606	+	0.0410146i
$287$	23.0634	−	12.8271i	1.36139	−	0.757159i
$288$		0			0
$289$	−10.4227	+	18.0527i	−0.613103	+	1.06193i
$290$	−1.65167	−	9.36707i	−0.0969892	−	0.550053i
$291$		0			0
$292$	1.84749	+	5.07594i	0.108116	+	0.297047i
$293$	12.0512	+	10.1122i	0.704041	+	0.590760i	0.922920	−	0.384992i	$-0.125796\pi$
$293$	12.0512	+	10.1122i	0.704041	+	0.590760i	−0.218879	+	0.975752i	$0.570240\pi$
$294$		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
$299$	−1.25010	−	7.08966i	−0.0722950	−	0.410006i
$300$		0			0
$301$	8.91380	+	25.7687i	0.513783	+	1.48528i
$302$	14.4715	+	2.55172i	0.832743	+	0.146835i
$303$		0			0
$304$	4.65102	−	0.820101i	0.266755	−	0.0470360i
$305$		−	15.4056i		−	0.882124i
$306$		0			0
$307$	30.0731	+	17.3627i	1.71636	+	0.990942i	0.925327	+	0.379170i	$0.123790\pi$
$307$	30.0731	+	17.3627i	1.71636	+	0.990942i	0.791034	+	0.611772i	$0.209543\pi$
$308$	0.312722	+	1.95647i	0.0178190	+	0.111480i
$309$		0			0
$310$	−2.92911	−	2.45781i	−0.166362	−	0.139594i
$311$	1.69468	−	9.61099i	0.0960963	−	0.544989i	−0.898310	−	0.439363i	$-0.855204\pi$
$311$	1.69468	−	9.61099i	0.0960963	−	0.544989i	0.994406	−	0.105626i	$-0.0336847\pi$
$312$		0			0
$313$	6.33689	+	7.55201i	0.358182	+	0.426865i	0.914802	−	0.403903i	$-0.132347\pi$
$313$	6.33689	+	7.55201i	0.358182	+	0.426865i	−0.556620	+	0.830767i	$0.687902\pi$
$314$	−7.92079	+	13.7192i	−0.446996	+	0.774220i
$315$		0			0
$316$	−2.72972	−	4.72801i	−0.153559	−	0.265971i
$317$	3.87202	−	10.6383i	0.217474	−	0.597506i	−0.782200	−	0.623028i	$-0.785902\pi$
$317$	3.87202	−	10.6383i	0.217474	−	0.597506i	0.999674	+	0.0255216i	$0.00812466\pi$
$318$		0			0
$319$	1.59752	+	1.34048i	0.0894437	+	0.0750522i
$320$	5.94553	−	33.7188i	0.332365	−	1.88494i
$321$		0			0
$322$	5.96198	−	0.952962i	0.332248	−	0.0531065i
$323$			14.8158i			0.824374i
$324$		0			0
$325$	36.1498	+	20.8711i	2.00523	+	1.15772i
$326$	−1.96316	−	2.33960i	−0.108729	−	0.129579i
$327$		0			0
$328$	19.7176	−	23.4985i	1.08872	−	1.29749i
$329$	18.9043	+	3.64678i	1.04223	+	0.201053i
$330$		0			0
$331$	3.88443	+	1.41382i	0.213508	+	0.0777104i	0.446560	−	0.894754i	$-0.352649\pi$
$331$	3.88443	+	1.41382i	0.213508	+	0.0777104i	−0.233052	+	0.972464i	$0.574871\pi$
$332$	5.84999			0.321060
$333$		0			0
$334$		−	24.7027i		−	1.35167i
$335$	1.38726	+	7.86756i	0.0757942	+	0.429851i
$336$		0			0
$337$	−13.3670	+	4.86521i	−0.728149	+	0.265025i	−0.679381	−	0.733785i	$-0.737752\pi$
$337$	−13.3670	+	4.86521i	−0.728149	+	0.265025i	−0.0487681	+	0.998810i	$0.515530\pi$
$338$	−0.355318	+	0.423451i	−0.0193267	+	0.0230327i
$339$		0			0
$340$	17.6131	+	6.41065i	0.955206	+	0.347666i
$341$	0.838340			0.0453986
$342$		0			0
$343$	16.4657	−	8.47821i	0.889065	−	0.457780i
$344$	20.3724	+	24.2789i	1.09841	+	1.30903i
$345$		0			0
$346$	7.98862	−	9.52047i	0.429471	−	0.511824i
$347$	2.73573	+	7.51635i	0.146862	+	0.403499i	0.991210	−	0.132295i	$-0.0422346\pi$
$347$	2.73573	+	7.51635i	0.146862	+	0.403499i	−0.844349	+	0.535794i	$0.820012\pi$
$348$		0			0
$349$	−4.85476	+	13.3383i	−0.259869	+	0.713985i	0.739306	+	0.673370i	$0.235154\pi$
$349$	−4.85476	+	13.3383i	−0.259869	+	0.713985i	−0.999175	+	0.0406147i	$0.987068\pi$
$350$	−17.9879	+	30.0335i	−0.961496	+	1.60536i
$351$		0			0
$352$	1.99100	+	3.44852i	0.106121	+	0.183807i
$353$	−12.2139	+	10.2486i	−0.650078	+	0.545480i	−0.907095	−	0.420927i	$-0.861705\pi$
$353$	−12.2139	+	10.2486i	−0.650078	+	0.545480i	0.257017	+	0.966407i	$0.417260\pi$
$354$		0			0
$355$	−24.2878	−	4.28259i	−1.28906	−	0.227296i
$356$	1.69404	−	9.60735i	0.0897837	−	0.509189i
$357$		0			0
$358$	10.8776	−	9.12740i	0.574900	−	0.482398i
$359$	12.6803	+	7.32099i	0.669242	+	0.386387i	0.795789	−	0.605574i	$-0.207056\pi$
$359$	12.6803	+	7.32099i	0.669242	+	0.386387i	−0.126547	+	0.991961i	$0.540390\pi$
$360$		0			0
$361$	−6.59994	−	11.4314i	−0.347365	−	0.601654i
$362$	1.38238	−	1.15995i	0.0726562	−	0.0609658i
$363$		0			0
$364$	−5.25516	−	4.55516i	−0.275445	−	0.238755i
$365$	−10.1890	−	27.9940i	−0.533317	−	1.46528i
$366$		0			0
$367$	−3.31307	+	9.10257i	−0.172941	+	0.475150i	−0.995635	−	0.0933336i	$-0.970248\pi$
$367$	−3.31307	+	9.10257i	−0.172941	+	0.475150i	0.822694	+	0.568484i	$0.192470\pi$
$368$	3.45707	−	1.99594i	0.180212	−	0.104046i
$369$		0			0
$370$	15.7928	−	9.11798i	0.821029	−	0.474021i
$371$	−10.2878	−	3.93237i	−0.534116	−	0.204159i
$372$		0			0
$373$	−12.2834	+	4.47080i	−0.636012	+	0.231489i	−0.639846	−	0.768503i	$-0.721002\pi$
$373$	−12.2834	+	4.47080i	−0.636012	+	0.231489i	0.00383399	+	0.999993i	$0.498780\pi$
$374$	6.52934	−	2.37649i	0.337624	−	0.122885i
$375$		0			0
$376$	22.0387	−	3.88602i	1.13656	−	0.200406i
$377$	−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	$0.451874\pi$
$380$	7.22625	−	1.27418i	0.370699	−	0.0653642i
$381$		0			0
$382$	13.6840	−	4.98057i	0.700135	−	0.254828i
$383$	27.2375	−	9.91365i	1.39177	−	0.506564i	0.466048	−	0.884760i	$-0.345678\pi$
$383$	27.2375	−	9.91365i	1.39177	−	0.506564i	0.925726	+	0.378196i	$0.123455\pi$
$384$		0			0
$385$	−1.72468	−	10.7900i	−0.0878977	−	0.549911i
$386$	−13.6297	+	7.86911i	−0.693733	+	0.400527i
$387$		0			0
$388$	−3.91258	+	2.25893i	−0.198631	+	0.114680i
$389$	−12.5930	+	34.5989i	−0.638489	+	1.75423i	0.0179312	+	0.999839i	$0.494292\pi$
$389$	−12.5930	+	34.5989i	−0.638489	+	1.75423i	−0.656420	+	0.754395i	$0.727930\pi$
$390$		0			0
$391$	4.28309	+	11.7677i	0.216605	+	0.595118i
$392$	14.3590	−	16.0387i	0.725241	−	0.810074i
$393$		0			0
$394$	−15.0866	+	12.6591i	−0.760051	+	0.637758i
$395$	15.0545	+	26.0752i	0.757475	+	1.31198i
$396$		0			0
$397$	−30.2038	−	17.4381i	−1.51588	−	0.875195i	−0.999826	−	0.0186410i	$-0.994066\pi$
$397$	−30.2038	−	17.4381i	−1.51588	−	0.875195i	−0.516057	−	0.856554i	$-0.672601\pi$
$398$	19.1297	−	16.0517i	0.958886	−	0.804601i
$399$		0			0
$400$	−4.01929	+	22.7945i	−0.200964	+	1.13973i
$401$	−36.0392	−	6.35469i	−1.79971	−	0.317338i	−0.829303	−	0.558799i	$-0.811262\pi$
$401$	−36.0392	−	6.35469i	−1.79971	−	0.317338i	−0.970411	+	0.241461i	$0.922373\pi$
$402$		0			0
$403$	−2.25420	+	1.89150i	−0.112290	+	0.0942224i
$404$	−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
$409$	12.9837	+	35.6726i	0.642005	+	1.76389i	0.645335	+	0.763900i	$0.276718\pi$
$409$	12.9837	+	35.6726i	0.642005	+	1.76389i	−0.00332951	+	0.999994i	$0.501060\pi$
$410$	−29.4633	+	35.1130i	−1.45509	+	1.73411i
$411$		0			0
$412$	−4.17952	−	4.98096i	−0.205910	−	0.245394i
$413$	−6.30009	−	3.77331i	−0.310007	−	0.185673i
$414$		0			0
$415$	−32.2630			−1.58373
$416$	−13.1343	−	4.78049i	−0.643962	−	0.234383i
$417$		0			0
$418$	1.74849	−	2.08377i	0.0855213	−	0.101920i
$419$	−20.3827	+	7.41869i	−0.995759	+	0.362427i	−0.787948	−	0.615742i	$-0.788856\pi$
$419$	−20.3827	+	7.41869i	−0.995759	+	0.362427i	−0.207811	+	0.978169i	$0.566634\pi$
$420$		0			0
$421$	−4.52904	−	25.6854i	−0.220732	−	1.25183i	−0.870679	−	0.491852i	$-0.836320\pi$
$421$	−4.52904	−	25.6854i	−0.220732	−	1.25183i	0.649947	−	0.759980i	$-0.274791\pi$
$422$		−	22.7255i		−	1.10626i
$423$		0			0
$424$	−12.8019			−0.621716
$425$	−68.2328	−	24.8347i	−3.30978	−	1.20466i
$426$		0			0
$427$	1.88342	−	9.76334i	0.0911452	−	0.472481i
$428$	−0.984771	+	1.17360i	−0.0476007	+	0.0567283i
$429$		0			0
$430$	−30.4418	−	36.2791i	−1.46803	−	1.74953i
$431$	−20.8304	−	12.0264i	−1.00336	−	0.579293i	−0.0941228	−	0.995561i	$-0.530005\pi$
$431$	−20.8304	−	12.0264i	−1.00336	−	0.579293i	−0.909242	+	0.416268i	$0.863338\pi$
$432$		0			0
$433$			3.41498i			0.164114i	0.996628	+	0.0820568i	$0.0261489\pi$
$433$			3.41498i			0.164114i	−0.996628	+	0.0820568i	$0.973851\pi$
$434$	−1.55584	−	1.91574i	−0.0746829	−	0.0919585i
$435$		0			0
$436$	0.0583173	−	0.330734i	0.00279289	−	0.0158393i
$437$	3.75553	+	3.15126i	0.179651	+	0.150745i
$438$		0			0
$439$	−9.31208	+	25.5847i	−0.444441	+	1.22109i	0.492101	+	0.870538i	$0.336229\pi$
$439$	−9.31208	+	25.5847i	−0.444441	+	1.22109i	−0.936542	+	0.350554i	$0.885993\pi$
$440$	−6.35055	−	10.9995i	−0.302751	−	0.524380i
$441$		0			0
$442$	−12.1947	+	21.1219i	−0.580045	+	1.00467i
$443$	−9.61251	−	11.4557i	−0.456704	−	0.544279i	0.487724	−	0.872998i	$-0.337827\pi$
$443$	−9.61251	−	11.4557i	−0.456704	−	0.544279i	−0.944428	+	0.328719i	$0.893383\pi$
$444$		0			0
$445$	−9.34268	+	52.9850i	−0.442885	+	2.51173i
$446$	20.9298	+	17.5622i	0.991056	+	0.831595i
$447$		0			0
$448$	7.89030	−	20.6425i	0.372782	−	0.975265i
$449$	−16.1509	−	9.32474i	−0.762209	−	0.440062i	0.0678793	−	0.997694i	$-0.478377\pi$
$449$	−16.1509	−	9.32474i	−0.762209	−	0.440062i	−0.830088	+	0.557632i	$0.811710\pi$
$450$		0			0
$451$		−	10.0497i		−	0.473222i
$452$	4.22072	−	0.744228i	0.198526	−	0.0350055i
$453$		0			0
$454$	1.42161	+	0.250668i	0.0667193	+	0.0117644i
$455$	28.9824	+	25.1219i	1.35872	+	1.17773i
$456$		0			0
$457$	−5.59634	−	31.7384i	−0.261786	−	1.48466i	−0.778034	−	0.628222i	$-0.783783\pi$
$457$	−5.59634	−	31.7384i	−0.261786	−	1.48466i	0.516248	−	0.856439i	$-0.327328\pi$
$458$	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	$-0.508610\pi$
$461$	−14.8218	−	5.39468i	−0.690318	−	0.251255i	−0.663271	+	0.748379i	$0.730832\pi$
$462$		0			0
$463$	5.32062	+	4.46453i	0.247270	+	0.207484i	0.757996	−	0.652260i	$-0.226179\pi$
$463$	5.32062	+	4.46453i	0.247270	+	0.207484i	−0.510726	+	0.859744i	$0.670623\pi$
$464$	−1.38824	−	3.81417i	−0.0644476	−	0.177068i
$465$		0			0
$466$	2.61406	+	14.8251i	0.121094	+	0.686758i
$467$	−7.13229	+	12.3535i	−0.330043	+	0.571652i	−0.982520	−	0.186157i	$-0.940397\pi$
$467$	−7.13229	+	12.3535i	−0.330043	+	0.571652i	0.652477	+	0.757809i	$0.273730\pi$
$468$		0			0
$469$	−0.0826726	+	5.15567i	−0.00381747	+	0.238067i
$470$	−32.9316	+	5.80674i	−1.51902	+	0.267845i
$471$		0			0
$472$	−8.40627	−	1.48225i	−0.386930	−	0.0682262i
$473$	10.2257	+	1.80307i	0.470178	+	0.0829051i
$474$		0			0
$475$	−27.9943	+	4.93615i	−1.28447	+	0.226486i
$476$	10.3786	+	6.21606i	0.475702	+	0.284913i
$477$		0			0
$478$	−10.3497	+	17.9263i	−0.473386	+	0.819929i
$479$	−1.64157	−	9.30983i	−0.0750055	−	0.425377i	−0.999069	−	0.0431385i	$-0.986264\pi$
$479$	−1.64157	−	9.30983i	−0.0750055	−	0.425377i	0.924064	−	0.382239i	$-0.124847\pi$
$480$		0			0
$481$	−4.79997	−	13.1878i	−0.218860	−	0.601312i
$482$	−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	$0.261452\pi$
$488$	−2.00698	−	11.3822i	−0.0908517	−	0.515246i
$489$		0			0
$490$	−21.4562	+	23.9660i	−0.969292	+	1.08267i
$491$	23.2766	+	4.10430i	1.05046	+	0.185224i	0.672120	−	0.740442i	$-0.265384\pi$
$491$	23.2766	+	4.10430i	1.05046	+	0.185224i	0.378340	+	0.925667i	$0.376495\pi$
$492$		0			0
$493$	12.5399	−	2.21112i	0.564769	−	0.0995839i
$494$			9.54804i			0.429586i
$495$		0			0
$496$	−1.41310	−	0.815855i	−0.0634502	−	0.0366330i
$497$	−14.8688	−	5.68341i	−0.666958	−	0.254936i
$498$		0			0
$499$	−10.1185	−	8.49044i	−0.452967	−	0.380084i	0.387568	−	0.921841i	$-0.373315\pi$
$499$	−10.1185	−	8.49044i	−0.452967	−	0.380084i	−0.840536	+	0.541756i	$0.817760\pi$
$500$	−3.59938	+	20.4131i	−0.160969	+	0.912901i
$501$		0			0
$502$	−3.73516	−	4.45139i	−0.166708	−	0.198675i
$503$	−12.0725	+	20.9102i	−0.538286	+	0.932339i	0.460710	+	0.887551i	$0.347595\pi$
$503$	−12.0725	+	20.9102i	−0.538286	+	0.932339i	−0.998996	+	0.0447884i	$0.985739\pi$
$504$		0			0
$505$	7.71995	+	13.3713i	0.343533	+	0.595017i
$506$	0.786370	−	2.16053i	0.0349584	−	0.0960475i
$507$		0			0
$508$	0.841215	+	0.705863i	0.0373229	+	0.0313176i
$509$	−2.78964	+	15.8208i	−0.123649	+	0.701246i	0.858453	+	0.512893i	$0.171426\pi$
$509$	−2.78964	+	15.8208i	−0.123649	+	0.701246i	−0.982101	+	0.188354i	$0.939685\pi$
$510$		0			0
$511$	−3.03487	−	18.9869i	−0.134255	−	0.839932i
$512$		−	19.8118i		−	0.875568i
$513$		0			0
$514$	12.7025	+	7.33377i	0.560282	+	0.323479i
$515$	23.0502	+	27.4702i	1.01571	+	1.21048i
$516$		0			0
$517$	4.71268	−	5.61636i	0.207264	−	0.247007i
$518$	11.1234	−	3.84777i	0.488736	−	0.169061i
$519$		0			0
$520$	41.8935	+	15.2480i	1.83715	+	0.668668i
$521$	9.58786			0.420052			0.210026	−	0.977696i	$-0.432645\pi$
$521$	9.58786			0.420052			0.210026	+	0.977696i	$0.432645\pi$
$522$		0			0
$523$		−	26.2588i		−	1.14822i	−0.818780	−	0.574108i	$-0.805349\pi$
$523$		−	26.2588i		−	1.14822i	0.818780	−	0.574108i	$-0.194651\pi$
$524$	0.549403	+	3.11582i	0.0240008	+	0.136115i
$525$		0			0
$526$	14.8383	−	5.40072i	0.646983	−	0.235482i
$527$	3.29032	−	3.92126i	0.143329	−	0.170813i
$528$		0			0
$529$	−17.7190	−	6.44920i	−0.770393	−	0.280400i
$530$	19.1295			0.830931
$531$		0			0
$532$	4.73542	+	0.0759338i	0.205307	+	0.00329215i
$533$	22.6746	+	27.0225i	0.982146	+	1.17048i
$534$		0			0
$535$	5.43105	−	6.47248i	0.234805	−	0.279830i
$536$	2.04990	+	5.63206i	0.0885424	+	0.243268i
$537$		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	$-0.340197\pi$
$542$	−7.97414	+	6.69110i	−0.342519	+	0.287407i
$543$		0			0
$544$	23.9444	+	4.22205i	1.02661	+	0.181019i
$545$	−0.321622	+	1.82401i	−0.0137768	+	0.0781321i
$546$		0			0
$547$	21.4421	−	17.9921i	0.916799	−	0.769286i	−0.0566010	−	0.998397i	$-0.518026\pi$
$547$	21.4421	−	17.9921i	0.916799	−	0.769286i	0.973400	+	0.229111i	$0.0735818\pi$
$548$	−3.63831	−	2.10058i	−0.155421	−	0.0897323i
$549$		0			0
$550$	6.66571	+	11.5454i	0.284227	+	0.492296i
$551$	3.81863	−	3.20421i	0.162679	−	0.136504i
$552$		0			0
$553$	6.35298	+	18.3657i	0.270156	+	0.780988i
$554$	9.35657	+	25.7070i	0.397522	+	1.09218i
$555$		0			0
$556$	3.96986	−	10.9071i	0.168359	−	0.462564i
$557$	5.13701	−	2.96585i	0.217662	−	0.125667i	−0.387205	−	0.921994i	$-0.626560\pi$
$557$	5.13701	−	2.96585i	0.217662	−	0.125667i	0.604867	+	0.796326i	$0.293226\pi$
$558$		0			0
$559$	−31.5640	+	18.2235i	−1.33501	+	0.770770i
$560$	−7.59353	+	19.8661i	−0.320885	+	0.839494i
$561$		0			0
$562$	0.602177	−	0.219174i	0.0254013	−	0.00924531i
$563$	−9.90720	+	3.60593i	−0.417539	+	0.151972i	−0.542242	−	0.840222i	$-0.682424\pi$
$563$	−9.90720	+	3.60593i	−0.417539	+	0.151972i	0.124703	+	0.992194i	$0.460202\pi$
$564$		0			0
$565$	−23.2775	+	4.10445i	−0.979291	+	0.172675i
$566$	26.1234			1.09805
$567$		0			0
$568$	−18.5025			−0.776346
$569$	13.9351	−	2.45714i	0.584191	−	0.103009i	0.126261	−	0.991997i	$-0.459702\pi$
$569$	13.9351	−	2.45714i	0.584191	−	0.103009i	0.457930	+	0.888988i	$0.348591\pi$
$570$		0			0
$571$	−22.2263	+	8.08973i	−0.930144	+	0.338545i	−0.762266	−	0.647263i	$-0.775913\pi$
$571$	−22.2263	+	8.08973i	−0.930144	+	0.338545i	−0.167877	+	0.985808i	$0.553691\pi$
$572$	−2.48865	+	0.905795i	−0.104056	+	0.0378732i
$573$		0			0
$574$	−22.9652	+	18.6509i	−0.958548	+	0.778472i
$575$	−20.8080	+	12.0135i	−0.867752	+	0.500997i
$576$		0			0
$577$	38.7060	−	22.3469i	1.61135	−	0.930313i	0.622292	−	0.782785i	$-0.286202\pi$
$577$	38.7060	−	22.3469i	1.61135	−	0.930313i	0.989058	−	0.147529i	$-0.0471318\pi$
$578$	7.99254	−	21.9593i	0.332446	−	0.913387i
$579$		0			0
$580$	−2.15690	−	5.92604i	−0.0895605	−	0.246065i
$581$	−20.4467	−	3.94432i	−0.848272	−	0.163638i
$582$		0			0
$583$	−3.21289	+	2.69593i	−0.133064	+	0.111654i
$584$	−11.1749	−	19.3555i	−0.462420	−	0.800935i
$585$		0			0
$586$	−15.2732	−	8.81797i	−0.630929	−	0.364267i
$587$	21.3980	−	17.9551i	0.883191	−	0.741085i	−0.0836420	−	0.996496i	$-0.526655\pi$
$587$	21.3980	−	17.9551i	0.883191	−	0.741085i	0.966833	+	0.255411i	$0.0822108\pi$
$588$		0			0
$589$	0.347979	−	1.97349i	0.0143382	−	0.0813161i
$590$	12.5612	+	2.21488i	0.517136	+	0.0911850i
$591$		0			0
$592$	5.96135	−	5.00216i	0.245010	−	0.205588i
$593$	2.10565	+	3.64710i	0.0864689	+	0.149768i	0.906016	−	0.423243i	$-0.139108\pi$
$593$	2.10565	+	3.64710i	0.0864689	+	0.149768i	−0.819547	+	0.573012i	$0.805775\pi$
$594$		0			0
$595$	−57.2384	−	34.2818i	−2.34655	−	1.40542i
$596$	2.17881	−	5.98622i	0.0892474	−	0.245205i
$597$		0			0
$598$	2.76024	+	7.58369i	0.112874	+	0.310120i
$599$	−4.93164	+	5.87730i	−0.201501	+	0.240140i	−0.857327	−	0.514773i	$-0.827876\pi$
$599$	−4.93164	+	5.87730i	−0.201501	+	0.240140i	0.655825	+	0.754913i	$0.272321\pi$
$600$		0			0
$601$	17.3311	+	20.6544i	0.706949	+	0.842509i	0.993294	−	0.115617i	$-0.0368846\pi$
$601$	17.3311	+	20.6544i	0.706949	+	0.842509i	−0.286344	+	0.958127i	$0.592440\pi$
$602$	−14.8572	−	26.7136i	−0.605535	−	1.08877i
$603$		0			0
$604$	9.74293			0.396434
$605$	38.4614	+	13.9988i	1.56368	+	0.569133i
$606$		0			0
$607$	1.87297	−	2.23212i	0.0760216	−	0.0905991i	−0.726693	−	0.686962i	$-0.758944\pi$
$607$	1.87297	−	2.23212i	0.0760216	−	0.0905991i	0.802715	+	0.596363i	$0.203388\pi$
$608$	8.94438	−	3.25549i	0.362742	−	0.132027i
$609$		0			0
$610$	2.99896	+	17.0079i	0.121424	+	0.688631i
$611$			25.7347i			1.04112i
$612$		0			0
$613$	34.5619			1.39594			0.697971	−	0.716126i	$-0.254087\pi$
$613$	34.5619			1.39594			0.697971	+	0.716126i	$0.254087\pi$
$614$	−36.5809	−	13.3143i	−1.47628	−	0.537323i
$615$		0			0
$616$	−2.67992	−	7.74732i	−0.107977	−	0.312149i
$617$	16.2205	−	19.3308i	0.653011	−	0.778228i	−0.333354	−	0.942802i	$-0.608180\pi$
$617$	16.2205	−	19.3308i	0.653011	−	0.778228i	0.986365	+	0.164574i	$0.0526248\pi$
$618$		0			0
$619$	25.3657	+	30.2297i	1.01953	+	1.21503i	0.976401	+	0.215965i	$0.0692896\pi$
$619$	25.3657	+	30.2297i	1.01953	+	1.21503i	0.0431333	+	0.999069i	$0.486266\pi$
$620$	−2.19552	−	1.26759i	−0.0881744	−	0.0509075i
$621$		0			0
$622$			10.9405i			0.438674i
$623$	−12.3986	+	32.4371i	−0.496741	+	1.29956i
$624$		0			0
$625$	9.60269	−	54.4596i	0.384108	−	2.17838i
$626$	−8.46609	−	7.10390i	−0.338373	−	0.283929i
$627$		0			0
$628$	−3.59233	+	9.86985i	−0.143350	+	0.393850i
$629$	12.2064	+	21.1422i	0.486702	+	0.842993i
$630$		0			0
$631$	9.73033	−	16.8534i	0.387358	−	0.670924i	−0.604735	−	0.796427i	$-0.706721\pi$
$631$	9.73033	−	16.8534i	0.387358	−	0.670924i	0.992093	+	0.125503i	$0.0400544\pi$
$632$	14.5197	+	17.3039i	0.577563	+	0.688312i
$633$		0			0
$634$	−2.20382	+	12.4985i	−0.0875251	+	0.496379i
$635$	−4.63934	−	3.89286i	−0.184106	−	0.154484i
$636$		0			0
$637$	15.2964	+	19.4643i	0.606064	+	0.771204i
$638$	−2.02462	−	1.16891i	−0.0801553	−	0.0462777i
$639$		0			0
$640$			5.98120i			0.236428i
$641$	47.4700	−	8.37025i	1.87495	−	0.330605i	0.884291	−	0.466936i	$-0.154642\pi$
$641$	47.4700	−	8.37025i	1.87495	−	0.330605i	0.990663	+	0.136331i	$0.0435312\pi$
$642$		0			0
$643$	16.8028	+	2.96278i	0.662636	+	0.116841i	0.494844	−	0.868982i	$-0.335225\pi$
$643$	16.8028	+	2.96278i	0.662636	+	0.116841i	0.167792	+	0.985822i	$0.446336\pi$
$644$	3.78314	−	1.30865i	0.149077	−	0.0515680i
$645$		0			0
$646$	−2.88414	−	16.3568i	−0.113475	−	0.643549i
$647$	6.85799	−	11.8784i	0.269616	−	0.466988i	−0.699147	−	0.714978i	$-0.746437\pi$
$647$	6.85799	−	11.8784i	0.269616	−	0.466988i	0.968763	+	0.247990i	$0.0797700\pi$
$648$		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
$653$	−11.3641	−	31.2227i	−0.444713	−	1.22184i	−0.936359	−	0.351044i	$-0.885827\pi$
$653$	−11.3641	−	31.2227i	−0.444713	−	1.22184i	0.491646	−	0.870795i	$-0.336396\pi$
$654$		0			0
$655$	−3.02998	−	17.1839i	−0.118391	−	0.671430i
$656$	−9.78016	+	16.9397i	−0.381851	+	0.661386i
$657$		0			0
$658$	−21.5804	−	0.346047i	−0.841290	−	0.0134903i
$659$	1.85923	−	0.327832i	0.0724252	−	0.0127705i	−0.137318	−	0.990527i	$-0.543848\pi$
$659$	1.85923	−	0.327832i	0.0724252	−	0.0127705i	0.209743	+	0.977756i	$0.432737\pi$
$660$		0			0
$661$	−46.0812	−	8.12535i	−1.79235	−	0.316040i	−0.824179	−	0.566330i	$-0.808363\pi$
$661$	−46.0812	−	8.12535i	−1.79235	−	0.316040i	−0.968171	+	0.250290i	$0.919474\pi$
$662$	−4.56366	−	0.804697i	−0.177372	−	0.0312754i
$663$		0			0
$664$	−23.8369	+	4.20308i	−0.925050	+	0.163111i
$665$	−26.1161	−	0.418778i	−1.01274	−	0.0162395i
$666$		0			0
$667$	2.10671	−	3.64892i	0.0815721	−	0.141287i
$668$	−2.84407	−	16.1295i	−0.110041	−	0.624071i
$669$		0			0
$670$	−3.06310	−	8.41579i	−0.118338	−	0.325130i
$671$	−2.90064	−	2.43392i	−0.111978	−	0.0939605i
$672$		0			0
$673$	19.5365	+	7.11069i	0.753075	+	0.274097i	0.689899	−	0.723905i	$-0.257655\pi$
$673$	19.5365	+	7.11069i	0.753075	+	0.274097i	0.0631762	+	0.998002i	$0.479877\pi$
$674$	13.8102	−	7.97334i	0.531950	−	0.307122i
$675$		0			0
$676$	−0.183251	+	0.317400i	−0.00704810	+	0.0122077i
$677$	6.66336	+	37.7898i	0.256094	+	1.45238i	0.793250	+	0.608896i	$0.208388\pi$
$677$	6.66336	+	37.7898i	0.256094	+	1.45238i	−0.537156	+	0.843483i	$0.680501\pi$
$678$		0			0
$679$	15.1982	−	5.25729i	0.583252	−	0.201756i
$680$	−76.3738	−	13.4668i	−2.92880	−	0.516427i
$681$		0			0
$682$	−0.925534	+	0.163197i	−0.0354405	+	0.00624912i
$683$		−	13.9973i		−	0.535592i	−0.963476	−	0.267796i	$-0.913705\pi$
$683$		−	13.9973i		−	0.535592i	0.963476	−	0.267796i	$-0.0862953\pi$
$684$		0			0
$685$	20.0654	+	11.5848i	0.766661	+	0.442632i
$686$	−16.5279	+	12.5653i	−0.631037	+	0.479747i
$687$		0			0
$688$	−15.4817	−	12.9907i	−0.590234	−	0.495265i
$689$	2.55641	−	14.4981i	0.0973916	−	0.552335i
$690$		0			0
$691$	29.8357	+	35.5568i	1.13500	+	1.35264i	0.927242	+	0.374463i	$0.122173\pi$
$691$	29.8357	+	35.5568i	1.13500	+	1.35264i	0.207760	+	0.978180i	$0.433383\pi$
$692$	4.12003	−	7.13611i	0.156620	−	0.271274i
$693$		0			0
$694$	−4.48345	−	7.76556i	−0.170189	−	0.294777i
$695$	−21.8939	+	60.1531i	−0.830484	+	2.28174i
$696$		0			0
$697$	−47.0065	−	39.4432i	−1.78050	−	1.49402i
$698$	2.76316	−	15.6707i	0.104587	−	0.593144i
$699$		0			0
$700$	−8.28736	+	21.6812i	−0.313233	+	0.819474i
$701$			25.1102i			0.948399i	0.880417	+	0.474199i	$0.157262\pi$
$701$			25.1102i			0.948399i	−0.880417	+	0.474199i	$0.842738\pi$
$702$		0			0
$703$	8.27676	+	4.77859i	0.312164	+	0.180228i
$704$	−5.40938	−	6.44665i	−0.203874	−	0.242967i
$705$		0			0
$706$	11.4891	−	13.6922i	0.432399	−	0.515313i
$707$	3.25781	+	9.41791i	0.122522	+	0.354197i
$708$		0			0
$709$	−20.9639	−	7.63024i	−0.787316	−	0.286560i	−0.0830964	−	0.996542i	$-0.526481\pi$
$709$	−20.9639	−	7.63024i	−0.787316	−	0.286560i	−0.704220	+	0.709982i	$0.748703\pi$
$710$	27.6476			1.03759
$711$		0			0
$712$			40.3640i			1.51271i
$713$	−0.294126	−	1.66807i	−0.0110151	−	0.0624697i
$714$		0			0
$715$	13.7250	−	4.99550i	0.513286	−	0.186821i
$716$	6.05165	−	7.21207i	0.226161	−	0.269528i
$717$		0			0
$718$	−15.4243	−	5.61400i	−0.575631	−	0.209513i
$719$	3.15546			0.117679			0.0588395	−	0.998267i	$-0.481260\pi$
$719$	3.15546			0.117679			0.0588395	+	0.998267i	$0.481260\pi$
$720$		0			0
$721$	11.2497	+	20.2273i	0.418962	+	0.753303i
$722$	9.51171	+	11.3356i	0.353989	+	0.421868i
$723$		0			0
$724$	0.769072	−	0.916544i	0.0285823	−	0.0340631i
$725$	8.35578	+	22.9573i	0.310326	+	0.852614i
$726$		0			0
$727$	2.93771	−	8.07129i	0.108954	−	0.299348i	−0.873219	−	0.487328i	$-0.837972\pi$
$727$	2.93771	−	8.07129i	0.108954	−	0.299348i	0.982173	+	0.187980i	$0.0601940\pi$
$728$	24.6859	+	14.7851i	0.914920	+	0.547974i
$729$		0			0
$730$	16.6982	+	28.9222i	0.618029	+	1.07046i
$731$	48.5676	−	40.7531i	1.79634	−	1.50731i
$732$		0			0
$733$	27.5716	+	4.86162i	1.01838	+	0.179568i	0.657826	−	0.753170i	$-0.271476\pi$
$733$	27.5716	+	4.86162i	1.01838	+	0.179568i	0.360555	+	0.932738i	$0.382587\pi$
$734$	1.88569	−	10.6943i	0.0696019	−	0.394732i
$735$		0			0
$736$	6.16309	−	5.17145i	0.227175	−	0.190622i
$737$	1.70051	+	0.981789i	0.0626390	+	0.0361647i
$738$		0			0
$739$	−10.3104	−	17.8581i	−0.379273	−	0.656921i	0.611683	−	0.791103i	$-0.290493\pi$
$739$	−10.3104	−	17.8581i	−0.379273	−	0.656921i	−0.990957	+	0.134182i	$0.957159\pi$
$740$	9.26209	−	7.77182i	0.340481	−	0.285698i
$741$		0			0
$742$	12.1233	+	2.33868i	0.445061	+	0.0858557i
$743$	−2.11075	−	5.79924i	−0.0774359	−	0.212753i	0.894934	−	0.446198i	$-0.147222\pi$
$743$	−2.11075	−	5.79924i	−0.0774359	−	0.212753i	−0.972370	+	0.233445i	$0.925000\pi$
$744$		0			0
$745$	−12.0162	+	33.0143i	−0.440240	+	1.20955i
$746$	12.6907	−	7.32697i	0.464639	−	0.268260i
$747$		0			0
$748$	3.98971	−	2.30346i	0.145878	−	0.0842227i
$749$	4.23323	−	3.43796i	0.154679	−	0.125620i
$750$		0			0
$751$	18.7355	−	6.81915i	0.683667	−	0.248834i	0.0232457	−	0.999730i	$-0.492600\pi$
$751$	18.7355	−	6.81915i	0.683667	−	0.248834i	0.660421	+	0.750895i	$0.270378\pi$
$752$	−13.4094	+	4.88063i	−0.488991	+	0.177978i
$753$		0			0
$754$	8.08133	−	1.42496i	0.294305	−	0.0518938i
$755$	−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	$0.412940\pi$
$758$	−6.47440	+	1.14161i	−0.235161	+	0.0414652i
$759$		0			0
$760$	−28.5292	+	10.3838i	−1.03486	+	0.376659i
$761$	−14.4510	+	5.25972i	−0.523847	+	0.190665i	−0.590389	−	0.807119i	$-0.701026\pi$
$761$	−14.4510	+	5.25972i	−0.523847	+	0.190665i	0.0665417	+	0.997784i	$0.478803\pi$
$762$		0			0
$763$	−0.426824	+	1.11665i	−0.0154521	+	0.0404254i
$764$	8.36151	−	4.82752i	0.302509	−	0.174654i
$765$		0			0
$766$	−28.1406	+	16.2470i	−1.01676	+	0.587028i
$767$	3.35729	−	9.22408i	0.121225	−	0.333062i
$768$		0			0
$769$	−4.80418	−	13.1994i	−0.173243	−	0.475982i	0.822434	−	0.568860i	$-0.192615\pi$
$769$	−4.80418	−	13.1994i	−0.173243	−	0.475982i	−0.995677	+	0.0928784i	$0.970393\pi$
$770$	4.00451	+	11.5765i	0.144313	+	0.417190i
$771$		0			0
$772$	−7.99348	+	6.70733i	−0.287692	+	0.241402i
$773$	−10.2099	−	17.6840i	−0.367223	−	0.636049i	0.621907	−	0.783091i	$-0.286358\pi$
$773$	−10.2099	−	17.6840i	−0.367223	−	0.636049i	−0.989130	+	0.147042i	$0.953025\pi$
$774$		0			0
$775$	8.50540	+	4.91060i	0.305523	+	0.176394i
$776$	14.3195	−	12.0155i	0.514041	−	0.431332i
$777$		0			0
$778$	7.16750	−	40.6489i	0.256967	−	1.45733i
$779$	−23.6574	−	4.17144i	−0.847614	−	0.149457i
$780$		0			0
$781$	−4.64355	+	3.89640i	−0.166159	+	0.139424i
$782$	−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
$787$	−9.89986	−	27.1997i	−0.352892	−	0.969563i	−0.981436	−	0.191789i	$-0.938571\pi$
$787$	−9.89986	−	27.1997i	−0.352892	−	0.969563i	0.628544	−	0.777774i	$-0.283651\pi$
$788$	−8.39326	+	10.0027i	−0.298998	+	0.356331i
$789$		0			0
$790$	−21.6963	−	25.8566i	−0.771918	−	0.919937i
$791$	−15.2539	−	0.244601i	−0.542367	−	0.00869700i
$792$		0			0
$793$	13.2910			0.471978
$794$	36.7398	+	13.3722i	1.30385	+	0.474562i
$795$		0			0
$796$	10.6426	−	12.6834i	0.377218	−	0.449551i
$797$	−44.1173	+	16.0574i	−1.56271	+	0.568781i	−0.971356	−	0.237628i	$-0.923630\pi$
$797$	−44.1173	+	16.0574i	−1.56271	+	0.568781i	−0.591357	+	0.806410i	$0.701408\pi$
$798$		0			0
$799$	−7.77360	−	44.0863i	−0.275010	−	1.55966i
$800$			46.6494i			1.64931i
$801$		0			0
$802$	41.0247			1.44863
$803$	−6.88058	−	2.50433i	−0.242811	−	0.0883758i
$804$		0			0
$805$	−20.8642	+	7.21726i	−0.735366	+	0.254375i
$806$	2.12045	−	2.52705i	0.0746896	−	0.0890115i
$807$		0			0
$808$	7.44570	+	8.87343i	0.261939	+	0.312166i
$809$	16.7570	+	9.67464i	0.589144	+	0.340142i	0.764759	−	0.644317i	$-0.222858\pi$
$809$	16.7570	+	9.67464i	0.589144	+	0.340142i	−0.175615	+	0.984459i	$0.556191\pi$
$810$		0			0
$811$		−	46.9758i		−	1.64954i	−0.565466	−	0.824771i	$-0.691304\pi$
$811$		−	46.9758i		−	1.64954i	0.565466	−	0.824771i	$-0.308696\pi$
$812$	−0.642449	−	4.01933i	−0.0225455	−	0.141051i
$813$		0			0
$814$	0.778321	−	4.41408i	0.0272801	−	0.154713i
$815$	8.55496	+	7.17846i	0.299667	+	0.251451i
$816$		0			0
$817$	8.48899	−	23.3233i	0.296992	−	0.815979i
$818$	−21.2784	−	36.8553i	−0.743982	−	1.28862i
$819$		0			0
$820$	−15.1953	+	26.3191i	−0.530645	+	0.919103i
$821$	12.7713	+	15.2203i	0.445723	+	0.531191i	0.941390	−	0.337321i	$-0.109521\pi$
$821$	12.7713	+	15.2203i	0.445723	+	0.531191i	−0.495667	+	0.868513i	$0.665076\pi$
$822$		0			0
$823$	0.554059	−	3.14223i	0.0193133	−	0.109531i	−0.973627	−	0.228145i	$-0.926734\pi$
$823$	0.554059	−	3.14223i	0.0193133	−	0.109531i	0.992940	+	0.118614i	$0.0378451\pi$
$824$	20.6089	+	17.2929i	0.717945	+	0.602428i
$825$		0			0
$826$	7.68989	+	2.93935i	0.267565	+	0.102273i
$827$	22.4378	+	12.9545i	0.780239	+	0.450471i	0.836515	−	0.547944i	$-0.184589\pi$
$827$	22.4378	+	12.9545i	0.780239	+	0.450471i	−0.0562757	+	0.998415i	$0.517923\pi$
$828$		0			0
$829$		−	30.0929i		−	1.04517i	−0.852587	−	0.522585i	$-0.824968\pi$
$829$		−	30.0929i		−	1.04517i	0.852587	−	0.522585i	$-0.175032\pi$
$830$	35.6186	−	6.28051i	1.23634	−	0.218000i
$831$		0			0
$832$	29.0905	+	5.12944i	1.00853	+	0.177831i
$833$	−32.0838	−	28.7239i	−1.11164	−	0.995223i
$834$		0			0
$835$	15.6852	+	88.9551i	0.542808	+	3.07842i
$836$	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	$-0.541315\pi$
$839$	−25.0830	−	9.12945i	−0.865960	−	0.315184i	−0.736530	+	0.676405i	$0.763537\pi$
$840$		0			0
$841$	18.9334	+	15.8870i	0.652876	+	0.547828i
$842$	10.0002	+	27.4753i	0.344629	+	0.946861i
$843$		0			0
$844$	−2.61643	−	14.8385i	−0.0900614	−	0.510763i
$845$	1.01064	−	1.75047i	0.0347669	−	0.0602181i
$846$		0			0
$847$	22.6635	+	13.5739i	0.778729	+	0.466404i
$848$	8.03926	−	1.41754i	0.276069	−	0.0486785i
$849$		0			0
$850$	80.1640	+	14.1351i	2.74960	+	0.484829i
$851$	7.95540	+	1.40275i	0.272708	+	0.0480857i
$852$		0			0
$853$	36.3817	−	6.41508i	1.24569	−	0.219648i	0.488335	−	0.872656i	$-0.337604\pi$
$853$	36.3817	−	6.41508i	1.24569	−	0.219648i	0.757351	+	0.653008i	$0.226493\pi$
$854$	−0.178720	+	11.1454i	−0.00611568	+	0.381389i
$855$		0			0
$856$	3.16942	−	5.48960i	0.108329	−	0.187631i
$857$	3.80751	+	21.5934i	0.130062	+	0.737618i	0.978172	+	0.207798i	$0.0666295\pi$
$857$	3.80751	+	21.5934i	0.130062	+	0.737618i	−0.848110	+	0.529820i	$0.822259\pi$
$858$		0			0
$859$	−0.824251	−	2.26461i	−0.0281231	−	0.0772675i	0.924837	−	0.380365i	$-0.124202\pi$
$859$	−0.824251	−	2.26461i	−0.0281231	−	0.0772675i	−0.952960	+	0.303097i	$0.901979\pi$
$860$	−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	0.302955	−	0.953005i	$-0.402027\pi$
$863$	37.5953	−	21.7057i	1.27976	−	0.738869i	0.976804	+	0.214135i	$0.0686934\pi$
$864$		0			0
$865$	−22.7222	+	39.3559i	−0.772577	+	1.33814i
$866$	−0.664782	−	3.77017i	−0.0225902	−	0.128116i
$867$		0			0
$868$	−1.23645	−	1.07175i	−0.0419677	−	0.0363775i
$869$	7.28799	+	1.28507i	0.247228	+	0.0435930i
$870$		0			0
$871$	−6.78764	+	1.19684i	−0.229990	+	0.0405535i
$872$			1.38954i			0.0470556i
$873$		0			0
$874$	−4.75958	−	2.74794i	−0.160995	−	0.0929506i
$875$	26.3438	−	68.9202i	0.890584	−	2.32993i
$876$		0			0
$877$	−4.81448	−	4.03983i	−0.162574	−	0.136415i	0.557872	−	0.829927i	$-0.311618\pi$
$877$	−4.81448	−	4.03983i	−0.162574	−	0.136415i	−0.720445	+	0.693512i	$0.756063\pi$
$878$	5.30012	−	30.0585i	0.178871	−	1.01443i
$879$		0			0
$880$	5.20593	+	6.20419i	0.175492	+	0.209143i
$881$	6.18255	−	10.7085i	0.208295	−	0.360778i	−0.742882	−	0.669422i	$-0.766542\pi$
$881$	6.18255	−	10.7085i	0.208295	−	0.360778i	0.951178	+	0.308644i	$0.0998752\pi$
$882$		0			0
$883$	9.12997	+	15.8136i	0.307248	+	0.532169i	0.977759	−	0.209730i	$-0.0672586\pi$
$883$	9.12997	+	15.8136i	0.307248	+	0.532169i	−0.670511	+	0.741899i	$0.733925\pi$
$884$	−5.53071	+	15.1955i	−0.186018	+	0.511080i
$885$		0			0
$886$	12.8423	+	10.7760i	0.431447	+	0.362027i
$887$	1.46223	−	8.29272i	0.0490969	−	0.278442i	−0.950369	−	0.311125i	$-0.899294\pi$
$887$	1.46223	−	8.29272i	0.0490969	−	0.278442i	0.999466	+	0.0326831i	$0.0104052\pi$
$888$		0			0
$889$	−2.46426	−	3.03429i	−0.0826487	−	0.101767i
$890$		−	60.3145i		−	2.02175i
$891$		0			0
$892$	15.6880	+	9.05749i	0.525274	+	0.303267i
$893$	−11.2650	−	13.4251i	−0.376968	−	0.449254i
$894$		0			0
$895$	−33.3751	+	39.7749i	−1.11561	+	1.32953i
$896$	−0.731235	+	3.79059i	−0.0244288	+	0.126635i
$897$		0			0
$898$	19.6460	+	7.15054i	0.655594	+	0.238617i
$899$	−1.72226			−0.0574407
$900$		0			0
$901$			25.6090i			0.853160i
$902$	1.95634	+	11.0950i	0.0651390	+	0.369421i
$903$		0			0
$904$	−16.6634	+	6.06498i	−0.554216	+	0.201718i
$905$	−4.24146	+	5.05478i	−0.140991	+	0.168027i
$906$		0			0
$907$	12.3807	+	4.50619i	0.411093	+	0.149626i	0.539284	−	0.842124i	$-0.318695\pi$
$907$	12.3807	+	4.50619i	0.411093	+	0.149626i	−0.128191	+	0.991749i	$0.540917\pi$
$908$	0.957094			0.0317623
$909$		0			0
$910$	−36.8873	−	22.0929i	−1.22280	−	0.732372i
$911$	15.2020	+	18.1170i	0.503664	+	0.600244i	0.956638	−	0.291280i	$-0.0940812\pi$
$911$	15.2020	+	18.1170i	0.503664	+	0.600244i	−0.452973	+	0.891524i	$0.649637\pi$
$912$		0			0
$913$	−5.09720	+	6.07460i	−0.168693	+	0.201040i
$914$	12.3568	+	33.9501i	0.408727	+	1.12297i
$915$		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	$0.863528\pi$
$920$	−19.6580	+	16.4950i	−0.648104	+	0.543824i
$921$		0			0
$922$	17.4135	+	3.07047i	0.573483	+	0.101121i
$923$	3.69475	−	20.9540i	0.121614	−	0.689708i
$924$		0			0
$925$	−35.8811	+	30.1078i	−1.17976	+	0.989939i
$926$	−6.74310	−	3.89313i	−0.221592	−	0.127936i
$927$		0			0
$928$	−4.09027	−	7.08455i	−0.134270	−	0.232562i
$929$	25.9929	−	21.8106i	0.852798	−	0.715583i	−0.107606	−	0.994194i	$-0.534318\pi$
$929$	25.9929	−	21.8106i	0.852798	−	0.715583i	0.960404	+	0.278611i	$0.0898740\pi$
$930$		0			0
$931$	−16.4999	−	3.45823i	−0.540762	−	0.113339i
$932$	3.41368	+	9.37902i	0.111819	+	0.307220i
$933$		0			0
$934$	5.46930	−	15.0268i	0.178961	−	0.491691i
$935$	−22.0034	+	12.7037i	−0.719588	+	0.415454i
$936$		0			0
$937$	1.87049	−	1.07993i	0.0611062	−	0.0352797i	−0.469136	−	0.883126i	$-0.655434\pi$
$937$	1.87049	−	1.07993i	0.0611062	−	0.0352797i	0.530242	+	0.847846i	$0.322101\pi$
$938$	−0.912365	−	5.70800i	−0.0297898	−	0.186373i
$939$		0			0
$940$	−20.8341	+	7.58298i	−0.679532	+	0.247330i
$941$	10.0528	−	3.65892i	0.327712	−	0.119277i	−0.172924	−	0.984935i	$-0.555322\pi$
$941$	10.0528	−	3.65892i	0.327712	−	0.119277i	0.500636	+	0.865658i	$0.333099\pi$
$942$		0			0
$943$	−19.9962	+	3.52587i	−0.651166	+	0.114818i
$944$	5.44303			0.177156
$945$		0			0
$946$	−11.6403			−0.378457
$947$	−30.9113	+	5.45050i	−1.00448	+	0.177117i	−0.651610	−	0.758554i	$-0.725906\pi$
$947$	−30.9113	+	5.45050i	−1.00448	+	0.177117i	−0.352873	+	0.935671i	$0.614795\pi$
$948$		0			0
$949$	24.1515	−	8.79043i	0.783992	−	0.285350i
$950$	29.9450	−	10.8991i	0.971546	−	0.353614i
$951$		0			0
$952$	−46.7556	−	17.8717i	−1.51536	−	0.579225i
$953$	7.86126	−	4.53870i	0.254651	−	0.147023i	−0.367241	−	0.930126i	$-0.619698\pi$
$953$	7.86126	−	4.53870i	0.254651	−	0.147023i	0.621892	+	0.783103i	$0.286364\pi$
$954$		0			0
$955$	−46.1141	+	26.6240i	−1.49222	+	0.861532i
$956$	−4.69394	+	12.8965i	−0.151813	+	0.417102i
$957$		0			0
$958$	3.62462	+	9.95857i	0.117106	+	0.321747i
$959$	11.3002	+	9.79498i	0.364902	+	0.316296i
$960$		0			0
$961$	23.2170	−	19.4814i	0.748936	−	0.628432i
$962$	7.86643	+	13.6250i	0.253624	+	0.439289i
$963$		0			0
$964$	−8.80729	−	5.08489i	−0.283664	−	0.163773i
$965$	44.0844	−	36.9912i	1.41913	−	1.19079i
$966$		0			0
$967$	5.45036	−	30.9105i	0.175272	−	0.994016i	−0.762558	−	0.646920i	$-0.776057\pi$
$967$	5.45036	−	30.9105i	0.175272	−	0.994016i	0.937830	−	0.347096i	$-0.112832\pi$
$968$	30.2402	+	5.33216i	0.971956	+	0.171382i
$969$		0			0
$970$	−21.3972	+	17.9543i	−0.687021	+	0.576479i
$971$	−14.1550	−	24.5172i	−0.454255	−	0.786793i	0.544390	−	0.838832i	$-0.316761\pi$
$971$	−14.1550	−	24.5172i	−0.454255	−	0.786793i	−0.998645	+	0.0520390i	$0.983428\pi$
$972$		0			0
$973$	−21.2293	+	35.4454i	−0.680582	+	1.13633i
$974$	4.96502	−	13.6413i	0.159090	−	0.437095i
$975$		0			0
$976$	2.52066	+	6.92545i	0.0806843	+	0.221678i
$977$	−6.11434	+	7.28679i	−0.195615	+	0.233125i	−0.854932	−	0.518740i	$-0.826401\pi$
$977$	−6.11434	+	7.28679i	−0.195615	+	0.233125i	0.659317	+	0.751865i	$0.270846\pi$
$978$		0			0
$979$	8.50019	+	10.1301i	0.271667	+	0.323760i
$980$	−11.2505	+	18.1188i	−0.359384	+	0.578784i
$981$		0			0
$982$	−26.4966			−0.845539
$983$	−33.7973	−	12.3012i	−1.07796	−	0.392347i	−0.258815	−	0.965927i	$-0.583332\pi$
$983$	−33.7973	−	12.3012i	−1.07796	−	0.392347i	−0.819150	+	0.573580i	$0.805554\pi$
$984$		0			0
$985$	46.2892	−	55.1653i	1.47490	−	1.75771i
$986$	−13.4137	+	4.88219i	−0.427180	+	0.155481i
$987$		0			0
$988$	1.09929	+	6.23436i	0.0349730	+	0.198341i
$989$		−	20.9790i		−	0.667093i
$990$		0			0
$991$	−21.9953			−0.698704			−0.349352	−	0.936992i	$-0.613598\pi$
$991$	−21.9953			−0.698704			−0.349352	+	0.936992i	$0.613598\pi$
$992$	−3.09027	−	1.12477i	−0.0981161	−	0.0357113i
$993$		0			0
$994$	17.5217	+	3.38007i	0.555754	+	0.107209i
$995$	−58.6945	+	69.9494i	−1.86074	+	2.21754i
$996$		0			0
$997$	13.7074	+	16.3359i	0.434119	+	0.517362i	0.938106	−	0.346349i	$-0.112579\pi$
$997$	13.7074	+	16.3359i	0.434119	+	0.517362i	−0.503987	+	0.863711i	$0.668134\pi$
$998$	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.bd.a.17.7		132
3.2	odd	2		189.2.bd.a.185.16	yes	132
7.5	odd	6		567.2.ba.a.341.16		132
21.5	even	6		189.2.ba.a.131.7	yes	132
27.7	even	9		189.2.ba.a.101.7	✓	132
27.20	odd	18		567.2.ba.a.143.16		132
189.47	even	18	inner	567.2.bd.a.467.7		132
189.61	odd	18		189.2.bd.a.47.16	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.7	✓	132	27.7	even	9
189.2.ba.a.131.7	yes	132	21.5	even	6
189.2.bd.a.47.16	yes	132	189.61	odd	18
189.2.bd.a.185.16	yes	132	3.2	odd	2
567.2.ba.a.143.16		132	27.20	odd	18
567.2.ba.a.341.16		132	7.5	odd	6
567.2.bd.a.17.7		132	1.1	even	1	trivial
567.2.bd.a.467.7		132	189.47	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.10401 + 0.194666i) q^{2} +(-0.698446 + 0.254214i) q^{4} +(3.85196 - 1.40200i) q^{5} +(2.61259 - 0.417595i) q^{7} +(2.66330 - 1.53766i) q^{8} +O(q^{10})\)	\(q+(-1.10401 + 0.194666i) q^{2} +(-0.698446 + 0.254214i) q^{4} +(3.85196 - 1.40200i) q^{5} +(2.61259 - 0.417595i) q^{7} +(2.66330 - 1.53766i) q^{8} +(-3.97967 + 2.29767i) q^{10} +(0.344594 - 0.946764i) q^{11} +(1.20956 + 3.32323i) q^{13} +(-2.80303 + 0.969612i) q^{14} +(-1.50222 + 1.26051i) q^{16} +(-3.07593 - 5.32768i) q^{17} +(-2.08569 - 1.20417i) q^{19} +(-2.33398 + 1.95844i) q^{20} +(-0.196131 + 1.11232i) q^{22} +(-2.00470 - 0.353483i) q^{23} +(9.04178 - 7.58696i) q^{25} +(-1.98228 - 3.43342i) q^{26} +(-1.71859 + 0.955824i) q^{28} +(-0.707925 + 1.94501i) q^{29} +(0.284588 + 0.781898i) q^{31} +(-2.54047 + 3.02761i) q^{32} +(4.43298 + 5.28302i) q^{34} +(9.47812 - 5.27141i) q^{35} -3.96837 q^{37} +(2.53703 + 0.923402i) q^{38} +(8.10314 - 9.65694i) q^{40} +(9.37310 - 3.41153i) q^{41} +(1.78960 + 10.1493i) q^{43} +0.748864i q^{44} +2.28202 q^{46} +(6.83803 + 2.48884i) q^{47} +(6.65123 - 2.18201i) q^{49} +(-8.50528 + 10.1362i) q^{50} +(-1.68962 - 2.01361i) q^{52} +(-3.60509 - 2.08140i) q^{53} -4.13002i q^{55} +(6.31599 - 5.12945i) q^{56} +(0.402927 - 2.28511i) q^{58} +(-2.12626 - 1.78414i) q^{59} +(1.28539 - 3.53158i) q^{61} +(-0.466396 - 0.807822i) q^{62} +(4.17633 - 7.23361i) q^{64} +(9.31834 + 11.1052i) q^{65} +(-0.338425 + 1.91930i) q^{67} +(3.50274 + 2.93915i) q^{68} +(-9.43775 + 7.66475i) q^{70} +(-5.21039 - 3.00822i) q^{71} -7.26748i q^{73} +(4.38111 - 0.772507i) q^{74} +(1.76286 + 0.310839i) q^{76} +(0.504917 - 2.61740i) q^{77} +(1.27547 + 7.23356i) q^{79} +(-4.01925 + 6.96154i) q^{80} +(-9.68386 + 5.59098i) q^{82} +(-7.39595 - 2.69190i) q^{83} +(-19.3178 - 16.2095i) q^{85} +(-3.95147 - 10.8566i) q^{86} +(-0.538041 - 3.05138i) q^{88} +(-6.56259 + 11.3667i) q^{89} +(4.54784 + 8.17713i) q^{91} +(1.49004 - 0.262734i) q^{92} +(-8.03373 - 1.41656i) q^{94} +(-9.72223 - 1.71429i) q^{95} +(5.98600 - 1.05549i) q^{97} +(-6.91825 + 3.70373i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8} - 9 q^{10} - 9 q^{11} + 42 q^{14} - 15 q^{16} + 9 q^{17} - 9 q^{19} + 18 q^{20} - 12 q^{22} - 30 q^{23} - 3 q^{25} - 12 q^{28} - 6 q^{29} - 9 q^{31} + 51 q^{32} + 18 q^{34} + 9 q^{35} - 6 q^{37} + 9 q^{38} - 9 q^{40} - 12 q^{43} - 6 q^{46} - 45 q^{47} + 30 q^{49} + 9 q^{50} - 9 q^{52} - 45 q^{53} + 51 q^{56} - 3 q^{58} + 9 q^{59} - 63 q^{61} - 99 q^{62} + 18 q^{64} + 102 q^{65} - 3 q^{67} - 144 q^{68} - 15 q^{70} - 18 q^{71} + 33 q^{74} - 36 q^{76} + 57 q^{77} - 21 q^{79} + 72 q^{80} - 18 q^{82} - 90 q^{83} + 9 q^{85} + 33 q^{86} + 45 q^{88} + 9 q^{89} - 21 q^{91} - 150 q^{92} - 9 q^{94} - 27 q^{95} + 180 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 9 * q^5 - 6 * q^7 + 18 * q^8 - 9 * q^10 - 9 * q^11 + 42 * q^14 - 15 * q^16 + 9 * q^17 - 9 * q^19 + 18 * q^20 - 12 * q^22 - 30 * q^23 - 3 * q^25 - 12 * q^28 - 6 * q^29 - 9 * q^31 + 51 * q^32 + 18 * q^34 + 9 * q^35 - 6 * q^37 + 9 * q^38 - 9 * q^40 - 12 * q^43 - 6 * q^46 - 45 * q^47 + 30 * q^49 + 9 * q^50 - 9 * q^52 - 45 * q^53 + 51 * q^56 - 3 * q^58 + 9 * q^59 - 63 * q^61 - 99 * q^62 + 18 * q^64 + 102 * q^65 - 3 * q^67 - 144 * q^68 - 15 * q^70 - 18 * q^71 + 33 * q^74 - 36 * q^76 + 57 * q^77 - 21 * q^79 + 72 * q^80 - 18 * q^82 - 90 * q^83 + 9 * q^85 + 33 * q^86 + 45 * q^88 + 9 * q^89 - 21 * q^91 - 150 * q^92 - 9 * q^94 - 27 * q^95 + 180 * q^98

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