LMFDB - Embedded newform 567.2.ba.a.143.7

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			143.7
Character	$\chi$	$=$	567.143
Dual form			567.2.ba.a.341.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.905074 + 1.07862i) q^{2} +(0.00302336 + 0.0171463i) q^{4} +(-1.61655 + 1.35644i) q^{5} +(1.08812 - 2.41164i) q^{7} +(-2.46004 - 1.42030i) q^{8} +O(q^{10})$	\(q+(-0.905074 + 1.07862i) q^{2} +(0.00302336 + 0.0171463i) q^{4} +(-1.61655 + 1.35644i) q^{5} +(1.08812 - 2.41164i) q^{7} +(-2.46004 - 1.42030i) q^{8} -2.97133i q^{10} +(2.38051 - 2.83698i) q^{11} +(2.27684 - 6.25557i) q^{13} +(1.61642 + 3.35639i) q^{14} +(3.72576 - 1.35607i) q^{16} +3.23775 q^{17} +5.32762i q^{19} +(-0.0281454 - 0.0236168i) q^{20} +(0.905502 + 5.13536i) q^{22} +(0.239559 - 0.658182i) q^{23} +(-0.0949575 + 0.538530i) q^{25} +(4.68670 + 8.11761i) q^{26} +(0.0446405 + 0.0113661i) q^{28} +(-1.50083 - 4.12351i) q^{29} +(-1.47986 + 0.260940i) q^{31} +(0.0336848 - 0.0925482i) q^{32} +(-2.93040 + 3.49232i) q^{34} +(1.51224 + 5.37450i) q^{35} +(-3.24831 + 5.62624i) q^{37} +(-5.74650 - 4.82189i) q^{38} +(5.90332 - 1.04091i) q^{40} +(10.4849 + 3.81619i) q^{41} +(1.29121 - 7.32280i) q^{43} +(0.0558409 + 0.0322398i) q^{44} +(0.493113 + 0.854097i) q^{46} +(1.04114 - 5.90462i) q^{47} +(-4.63197 - 5.24832i) q^{49} +(-0.494929 - 0.589833i) q^{50} +(0.114144 + 0.0201266i) q^{52} +(0.766350 + 0.442452i) q^{53} +7.81514i q^{55} +(-6.10208 + 4.38724i) q^{56} +(5.80608 + 2.11324i) q^{58} +(-5.85868 - 2.13238i) q^{59} +(7.32422 + 1.29146i) q^{61} +(1.05793 - 1.83239i) q^{62} +(4.03421 + 6.98746i) q^{64} +(4.80471 + 13.2008i) q^{65} +(8.05809 - 6.76154i) q^{67} +(0.00978888 + 0.0555155i) q^{68} +(-7.16576 - 3.23318i) q^{70} +(3.83248 - 2.21268i) q^{71} +(-2.65123 + 1.53069i) q^{73} +(-3.12864 - 8.59586i) q^{74} +(-0.0913491 + 0.0161073i) q^{76} +(-4.25147 - 8.82791i) q^{77} +(-7.29250 - 6.11913i) q^{79} +(-4.18344 + 7.24593i) q^{80} +(-13.6058 + 7.85533i) q^{82} +(11.4377 - 4.16299i) q^{83} +(-5.23397 + 4.39182i) q^{85} +(6.72991 + 8.02040i) q^{86} +(-9.88551 + 3.59803i) q^{88} +4.35832 q^{89} +(-12.6087 - 12.2977i) q^{91} +(0.0120097 + 0.00211763i) q^{92} +(5.42656 + 6.46712i) q^{94} +(-7.22662 - 8.61234i) q^{95} +(6.85869 + 1.20937i) q^{97} +(9.85324 - 0.246039i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.905074	+	1.07862i	−0.639984	+	0.762703i	−0.984368	−	0.176126i	$-0.943643\pi$
$2$	−0.905074	+	1.07862i	−0.639984	+	0.762703i	0.344384	+	0.938829i	$0.388088\pi$
$3$		0			0
$3$		0			0
$4$	0.00302336	+	0.0171463i	0.00151168	+	0.00857316i
$5$	−1.61655	+	1.35644i	−0.722942	+	0.606620i	−0.928197	−	0.372088i	$-0.878642\pi$
$5$	−1.61655	+	1.35644i	−0.722942	+	0.606620i	0.205256	+	0.978708i	$0.434197\pi$
$6$		0			0
$7$	1.08812	−	2.41164i	0.411273	−	0.911512i
$7$	1.08812	−	2.41164i	0.411273	−	0.911512i
$8$	−2.46004	−	1.42030i	−0.869754	−	0.502153i
$9$		0			0
$10$		−	2.97133i		−	0.939616i
$11$	2.38051	−	2.83698i	0.717751	−	0.855382i	−0.276659	−	0.960968i	$-0.589227\pi$
$11$	2.38051	−	2.83698i	0.717751	−	0.855382i	0.994410	+	0.105586i	$0.0336717\pi$
$12$		0			0
$13$	2.27684	−	6.25557i	0.631482	−	1.73498i	−0.0454806	−	0.998965i	$-0.514482\pi$
$13$	2.27684	−	6.25557i	0.631482	−	1.73498i	0.676963	−	0.736017i	$-0.263296\pi$
$14$	1.61642	+	3.35639i	0.432005	+	0.897032i
$15$		0			0
$16$	3.72576	−	1.35607i	0.931441	−	0.339017i
$17$	3.23775			0.785270			0.392635	−	0.919694i	$-0.371564\pi$
$17$	3.23775			0.785270			0.392635	+	0.919694i	$0.371564\pi$
$18$		0			0
$19$			5.32762i			1.22224i	0.791538	+	0.611120i	$0.209281\pi$
$19$			5.32762i			1.22224i	−0.791538	+	0.611120i	$0.790719\pi$
$20$	−0.0281454	−	0.0236168i	−0.00629351	−	0.00528088i
$21$		0			0
$22$	0.905502	+	5.13536i	0.193054	+	1.09486i
$23$	0.239559	−	0.658182i	0.0499514	−	0.137240i	−0.912208	−	0.409727i	$-0.865624\pi$
$23$	0.239559	−	0.658182i	0.0499514	−	0.137240i	0.962160	+	0.272487i	$0.0878461\pi$
$24$		0			0
$25$	−0.0949575	+	0.538530i	−0.0189915	+	0.107706i
$26$	4.68670	+	8.11761i	0.919138	+	1.59199i
$27$		0			0
$28$	0.0446405	+	0.0113661i	0.00843625	+	0.00214799i
$29$	−1.50083	−	4.12351i	−0.278698	−	0.765716i	−0.997511	−	0.0705128i	$-0.977536\pi$
$29$	−1.50083	−	4.12351i	−0.278698	−	0.765716i	0.718813	−	0.695204i	$-0.244686\pi$
$30$		0			0
$31$	−1.47986	+	0.260940i	−0.265791	+	0.0468662i	−0.304955	−	0.952367i	$-0.598642\pi$
$31$	−1.47986	+	0.260940i	−0.265791	+	0.0468662i	0.0391641	+	0.999233i	$0.487530\pi$
$32$	0.0336848	−	0.0925482i	0.00595468	−	0.0163604i
$33$		0			0
$34$	−2.93040	+	3.49232i	−0.502560	+	0.598927i
$35$	1.51224	+	5.37450i	0.255616	+	0.908456i
$36$		0			0
$37$	−3.24831	+	5.62624i	−0.534019	+	0.924947i	0.465191	+	0.885210i	$0.345985\pi$
$37$	−3.24831	+	5.62624i	−0.534019	+	0.924947i	−0.999210	+	0.0397374i	$0.987348\pi$
$38$	−5.74650	−	4.82189i	−0.932206	−	0.782213i
$39$		0			0
$40$	5.90332	−	1.04091i	0.933397	−	0.164583i
$41$	10.4849	+	3.81619i	1.63746	+	0.595988i	0.986593	−	0.163200i	$-0.0521817\pi$
$41$	10.4849	+	3.81619i	1.63746	+	0.595988i	0.650871	+	0.759188i	$0.274404\pi$
$42$		0			0
$43$	1.29121	−	7.32280i	0.196907	−	1.11672i	−0.712769	−	0.701399i	$-0.752559\pi$
$43$	1.29121	−	7.32280i	0.196907	−	1.11672i	0.909676	−	0.415318i	$-0.136330\pi$
$44$	0.0558409	+	0.0322398i	0.00841834	+	0.00486033i
$45$		0			0
$46$	0.493113	+	0.854097i	0.0727056	+	0.125930i
$47$	1.04114	−	5.90462i	0.151866	−	0.861278i	−0.809728	−	0.586805i	$-0.800386\pi$
$47$	1.04114	−	5.90462i	0.151866	−	0.861278i	0.961595	−	0.274473i	$-0.0885033\pi$
$48$		0			0
$49$	−4.63197	−	5.24832i	−0.661710	−	0.749760i
$50$	−0.494929	−	0.589833i	−0.0699935	−	0.0834150i
$51$		0			0
$52$	0.114144	+	0.0201266i	0.0158289	+	0.00279106i
$53$	0.766350	+	0.442452i	0.105266	+	0.0607755i	0.551709	−	0.834037i	$-0.313976\pi$
$53$	0.766350	+	0.442452i	0.105266	+	0.0607755i	−0.446443	+	0.894812i	$0.647309\pi$
$54$		0			0
$55$			7.81514i			1.05379i
$56$	−6.10208	+	4.38724i	−0.815424	+	0.586270i
$57$		0			0
$58$	5.80608	+	2.11324i	0.762376	+	0.277482i
$59$	−5.85868	−	2.13238i	−0.762735	−	0.277613i	−0.0687807	−	0.997632i	$-0.521911\pi$
$59$	−5.85868	−	2.13238i	−0.762735	−	0.277613i	−0.693954	+	0.720019i	$0.744133\pi$
$60$		0			0
$61$	7.32422	+	1.29146i	0.937771	+	0.165354i	0.621588	−	0.783344i	$-0.286488\pi$
$61$	7.32422	+	1.29146i	0.937771	+	0.165354i	0.316183	+	0.948698i	$0.397599\pi$
$62$	1.05793	−	1.83239i	0.134357	−	0.232713i
$63$		0			0
$64$	4.03421	+	6.98746i	0.504277	+	0.873433i
$65$	4.80471	+	13.2008i	0.595951	+	1.63736i
$66$		0			0
$67$	8.05809	−	6.76154i	0.984453	−	0.826054i	−0.000302478	−	1.00000i	$-0.500096\pi$
$67$	8.05809	−	6.76154i	0.984453	−	0.826054i	0.984755	+	0.173946i	$0.0556518\pi$
$68$	0.00978888	+	0.0555155i	0.00118708	+	0.00673224i
$69$		0			0
$70$	−7.16576	−	3.23318i	−0.856472	−	0.386438i
$71$	3.83248	−	2.21268i	0.454832	−	0.262597i	−0.255037	−	0.966931i	$-0.582088\pi$
$71$	3.83248	−	2.21268i	0.454832	−	0.262597i	0.709869	+	0.704334i	$0.248754\pi$
$72$		0			0
$73$	−2.65123	+	1.53069i	−0.310303	+	0.179154i	−0.647062	−	0.762437i	$-0.724003\pi$
$73$	−2.65123	+	1.53069i	−0.310303	+	0.179154i	0.336759	+	0.941591i	$0.390669\pi$
$74$	−3.12864	−	8.59586i	−0.363697	−	0.999249i
$75$		0			0
$76$	−0.0913491	+	0.0161073i	−0.0104785	+	0.00184763i
$77$	−4.25147	−	8.82791i	−0.484500	−	1.00603i
$78$		0			0
$79$	−7.29250	−	6.11913i	−0.820470	−	0.688456i	0.132612	−	0.991168i	$-0.457664\pi$
$79$	−7.29250	−	6.11913i	−0.820470	−	0.688456i	−0.953082	+	0.302712i	$0.902108\pi$
$80$	−4.18344	+	7.24593i	−0.467723	+	0.810120i
$81$		0			0
$82$	−13.6058	+	7.85533i	−1.50251	+	0.867476i
$83$	11.4377	−	4.16299i	1.25545	−	0.456947i	0.373212	−	0.927746i	$-0.378256\pi$
$83$	11.4377	−	4.16299i	1.25545	−	0.456947i	0.882241	+	0.470799i	$0.156034\pi$
$84$		0			0
$85$	−5.23397	+	4.39182i	−0.567704	+	0.476360i
$86$	6.72991	+	8.02040i	0.725705	+	0.864862i
$87$		0			0
$88$	−9.88551	+	3.59803i	−1.05380	+	0.383552i
$89$	4.35832			0.461982			0.230991	−	0.972956i	$-0.425803\pi$
$89$	4.35832			0.461982			0.230991	+	0.972956i	$0.425803\pi$
$90$		0			0
$91$	−12.6087	−	12.2977i	−1.32175	−	1.28915i
$92$	0.0120097	+	0.00211763i	0.00125210	+	0.000220778i
$93$		0			0
$94$	5.42656	+	6.46712i	0.559707	+	0.667033i
$95$	−7.22662	−	8.61234i	−0.741435	−	0.883608i
$96$		0			0
$97$	6.85869	+	1.20937i	0.696394	+	0.122793i	0.510629	−	0.859801i	$-0.329413\pi$
$97$	6.85869	+	1.20937i	0.696394	+	0.122793i	0.185765	+	0.982594i	$0.440524\pi$
$98$	9.85324	−	0.246039i	0.995328	−	0.0248537i
$99$		0			0
$100$	−0.00952091			−0.000952091
$101$	−3.49388	+	1.27167i	−0.347654	+	0.126536i	−0.509945	−	0.860207i	$-0.670334\pi$
$101$	−3.49388	+	1.27167i	−0.347654	+	0.126536i	0.162290	+	0.986743i	$0.448112\pi$
$102$		0			0
$103$	3.98929	+	4.75425i	0.393076	+	0.468450i	0.925896	−	0.377779i	$-0.123312\pi$
$103$	3.98929	+	4.75425i	0.393076	+	0.468450i	−0.532820	+	0.846229i	$0.678868\pi$
$104$	−14.4859	+	12.1551i	−1.42046	+	1.19191i
$105$		0			0
$106$	−1.17084	+	0.426152i	−0.113722	+	0.0413915i
$107$	2.47461	−	1.42872i	0.239230	−	0.138119i	−0.375593	−	0.926785i	$-0.622561\pi$
$107$	2.47461	−	1.42872i	0.239230	−	0.138119i	0.614823	+	0.788665i	$0.289228\pi$
$108$		0			0
$109$	2.81692	−	4.87905i	0.269812	−	0.467328i	−0.699001	−	0.715121i	$-0.746372\pi$
$109$	2.81692	−	4.87905i	0.269812	−	0.467328i	0.968813	+	0.247792i	$0.0797051\pi$
$110$	−8.42961	−	7.07328i	−0.803731	−	0.674411i
$111$		0			0
$112$	0.783757	−	10.4608i	0.0740581	−	0.988448i
$113$	−9.04367	+	1.59464i	−0.850757	+	0.150011i	−0.581992	−	0.813194i	$-0.697727\pi$
$113$	−9.04367	+	1.59464i	−0.850757	+	0.150011i	−0.268765	+	0.963206i	$0.586615\pi$
$114$		0			0
$115$	0.505529	+	1.38893i	0.0471408	+	0.129518i
$116$	0.0661654	−	0.0382006i	0.00614331	−	0.00354684i
$117$		0			0
$118$	7.60258	−	4.38935i	0.699874	−	0.404073i
$119$	3.52308	−	7.80827i	0.322960	−	0.715783i
$120$		0			0
$121$	−0.471507	−	2.67405i	−0.0428643	−	0.243095i
$122$	−8.02196	+	6.73122i	−0.726274	+	0.609416i
$123$		0			0
$124$	−0.00894832	−	0.0245853i	−0.000803582	−	0.00220782i
$125$	−5.85261	−	10.1370i	−0.523474	−	0.906683i
$126$		0			0
$127$	−0.958294	+	1.65981i	−0.0850349	+	0.147285i	−0.905406	−	0.424547i	$-0.860433\pi$
$127$	−0.958294	+	1.65981i	−0.0850349	+	0.147285i	0.820371	+	0.571831i	$0.193767\pi$
$128$	−10.9941	−	1.93856i	−0.971752	−	0.171346i
$129$		0			0
$130$	−18.5873	−	6.76524i	−1.63022	−	0.593351i
$131$	8.18242	+	2.97816i	0.714901	+	0.260203i	0.673760	−	0.738951i	$-0.264678\pi$
$131$	8.18242	+	2.97816i	0.714901	+	0.260203i	0.0411416	+	0.999153i	$0.486901\pi$
$132$		0			0
$133$	12.8483	+	5.79712i	1.11409	+	0.502674i
$134$			14.8114i			1.27951i
$135$		0			0
$136$	−7.96498	−	4.59858i	−0.682991	−	0.394325i
$137$	−6.87107	−	1.21155i	−0.587035	−	0.103510i	−0.127761	−	0.991805i	$-0.540779\pi$
$137$	−6.87107	−	1.21155i	−0.587035	−	0.103510i	−0.459274	+	0.888295i	$0.651890\pi$
$138$		0			0
$139$	6.76177	+	8.05836i	0.573526	+	0.683501i	0.972351	−	0.233526i	$-0.0750263\pi$
$139$	6.76177	+	8.05836i	0.573526	+	0.683501i	−0.398825	+	0.917027i	$0.630582\pi$
$140$	−0.0875808	+	0.0421784i	−0.00740193	+	0.00356473i
$141$		0			0
$142$	−1.08202	+	6.13645i	−0.0908012	+	0.514959i
$143$	−12.3269	−	21.3508i	−1.03083	−	1.78544i
$144$		0			0
$145$	8.01948	+	4.63005i	0.665981	+	0.384504i
$146$	0.748521	−	4.24507i	0.0619480	−	0.351325i
$147$		0			0
$148$	−0.106290	−	0.0386864i	−0.00873699	−	0.00318000i
$149$	−10.9584	+	1.93227i	−0.897750	+	0.158298i	−0.603436	−	0.797411i	$-0.706202\pi$
$149$	−10.9584	+	1.93227i	−0.897750	+	0.158298i	−0.294314	+	0.955709i	$0.595091\pi$
$150$		0			0
$151$	−15.4692	−	12.9802i	−1.25887	−	1.05632i	−0.995802	−	0.0915375i	$-0.970822\pi$
$151$	−15.4692	−	12.9802i	−1.25887	−	1.05632i	−0.263066	−	0.964778i	$-0.584734\pi$
$152$	7.56683	−	13.1061i	0.613751	−	1.06305i
$153$		0			0
$154$	13.3699	+	3.40417i	1.07738	+	0.274316i
$155$	2.03832	−	2.42917i	0.163722	−	0.195116i
$156$		0			0
$157$	1.67332	−	4.59740i	0.133545	−	0.366912i	−0.854838	−	0.518895i	$-0.826344\pi$
$157$	1.67332	−	4.59740i	0.133545	−	0.366912i	0.988383	+	0.151983i	$0.0485658\pi$
$158$	13.2005	−	2.32760i	1.05017	−	0.185174i
$159$		0			0
$160$	0.0710834	+	0.195300i	0.00561963	+	0.0154398i
$161$	−1.32663	−	1.29391i	−0.104553	−	0.101975i
$162$		0			0
$163$	−4.68621	−	8.11676i	−0.367053	−	0.635754i	0.622051	−	0.782977i	$-0.286300\pi$
$163$	−4.68621	−	8.11676i	−0.367053	−	0.635754i	−0.989103	+	0.147223i	$0.952966\pi$
$164$	−0.0337340	+	0.191315i	−0.00263418	+	0.0149392i
$165$		0			0
$166$	−5.86167	+	16.1048i	−0.454954	+	1.24998i
$167$	1.49566	+	8.48231i	0.115738	+	0.656381i	0.986382	+	0.164468i	$0.0525908\pi$
$167$	1.49566	+	8.48231i	0.115738	+	0.656381i	−0.870645	+	0.491912i	$0.836298\pi$
$168$		0			0
$169$	−23.9896	−	20.1296i	−1.84535	−	1.54843i
$170$		−	9.62042i		−	0.737852i
$171$		0			0
$172$	0.129463			0.00987145
$173$	−7.96256	+	2.89813i	−0.605382	+	0.220341i	−0.626481	−	0.779436i	$-0.715506\pi$
$173$	−7.96256	+	2.89813i	−0.605382	+	0.220341i	0.0210995	+	0.999777i	$0.493283\pi$
$174$		0			0
$175$	1.19541	+	0.814991i	0.0903648	+	0.0616075i
$176$	5.02208	−	13.7981i	0.378554	−	1.04007i
$177$		0			0
$178$	−3.94460	+	4.70100i	−0.295661	+	0.352355i
$179$		−	4.83578i		−	0.361443i	−0.983534	−	0.180722i	$-0.942157\pi$
$179$		−	4.83578i		−	0.361443i	0.983534	−	0.180722i	$-0.0578433\pi$
$180$		0			0
$181$	−3.95269	−	2.28209i	−0.293801	−	0.169626i	0.345854	−	0.938288i	$-0.387589\pi$
$181$	−3.95269	−	2.28209i	−0.293801	−	0.169626i	−0.639655	+	0.768662i	$0.720923\pi$
$182$	24.6764	−	2.46965i	1.82914	−	0.183062i
$183$		0			0
$184$	−1.52414	+	1.27891i	−0.112361	+	0.0942822i
$185$	−2.38063	−	13.5012i	−0.175027	−	0.992629i
$186$		0			0
$187$	7.70750	−	9.18544i	0.563628	−	0.671706i
$188$	0.104390			0.00761344
$189$		0			0
$190$	15.8301			1.14844
$191$	−6.64760	+	7.92230i	−0.481003	+	0.573237i	−0.950906	−	0.309481i	$-0.899845\pi$
$191$	−6.64760	+	7.92230i	−0.481003	+	0.573237i	0.469902	+	0.882718i	$0.344289\pi$
$192$		0			0
$193$	1.80685	+	10.2471i	0.130060	+	0.737605i	0.978173	+	0.207791i	$0.0666273\pi$
$193$	1.80685	+	10.2471i	0.130060	+	0.737605i	−0.848114	+	0.529814i	$0.822262\pi$
$194$	−7.51207	+	6.30338i	−0.539335	+	0.452556i
$195$		0			0
$196$	0.0759853	−	0.0952888i	0.00542752	−	0.00680634i
$197$	−12.2795	−	7.08959i	−0.874880	−	0.505112i	−0.00591309	−	0.999983i	$-0.501882\pi$
$197$	−12.2795	−	7.08959i	−0.874880	−	0.505112i	−0.868967	+	0.494870i	$0.835216\pi$
$198$		0			0
$199$			20.1176i			1.42610i	0.701113	+	0.713050i	$0.252687\pi$
$199$			20.1176i			1.42610i	−0.701113	+	0.713050i	$0.747313\pi$
$200$	0.998475	−	1.18994i	0.0706028	−	0.0841412i
$201$		0			0
$202$	1.79057	−	4.91954i	0.125984	−	0.346138i
$203$	−11.5775	−	0.867427i	−0.812581	−	0.0608815i
$204$		0			0
$205$	−22.1257	+	8.05311i	−1.54533	+	0.562454i
$206$	−8.73865			−0.608851
$207$		0			0
$208$		−	26.3943i		−	1.83012i
$209$	15.1144	+	12.6825i	1.04548	+	0.877264i
$210$		0			0
$211$	0.582787	+	3.30515i	0.0401207	+	0.227536i	0.998275	−	0.0587176i	$-0.0187011\pi$
$211$	0.582787	+	3.30515i	0.0401207	+	0.227536i	−0.958154	+	0.286254i	$0.907590\pi$
$212$	−0.00526948	+	0.0144778i	−0.000361909	+	0.000994338i
$213$		0			0
$214$	−0.698655	+	3.96227i	−0.0477591	+	0.270855i
$215$	7.84567	+	13.5891i	0.535070	+	0.926768i
$216$		0			0
$217$	−0.980985	+	3.85283i	−0.0665936	+	0.261547i
$218$	2.71314	+	7.45430i	0.183757	+	0.504869i
$219$		0			0
$220$	−0.134001	+	0.0236280i	−0.00903434	+	0.00159300i
$221$	7.37184	−	20.2540i	0.495884	−	1.36243i
$222$		0			0
$223$	6.45098	−	7.68798i	0.431990	−	0.514825i	−0.505506	−	0.862823i	$-0.668694\pi$
$223$	6.45098	−	7.68798i	0.431990	−	0.514825i	0.937495	+	0.347998i	$0.113138\pi$
$224$	−0.186539	−	0.181939i	−0.0124637	−	0.0121563i
$225$		0			0
$226$	6.46517	−	11.1980i	0.430056	−	0.744880i
$227$	13.5964	+	11.4088i	0.902427	+	0.757226i	0.970663	−	0.240443i	$-0.0772928\pi$
$227$	13.5964	+	11.4088i	0.902427	+	0.757226i	−0.0682365	+	0.997669i	$0.521737\pi$
$228$		0			0
$229$	−12.8653	+	2.26849i	−0.850160	+	0.149906i	−0.581719	−	0.813390i	$-0.697620\pi$
$229$	−12.8653	+	2.26849i	−0.850160	+	0.149906i	−0.268441	+	0.963296i	$0.586509\pi$
$230$	−1.95568	−	0.711808i	−0.128953	−	0.0469352i
$231$		0			0
$232$	−2.16452	+	12.2756i	−0.142108	+	0.805934i
$233$	16.4302	+	9.48596i	1.07638	+	0.621446i	0.929917	−	0.367771i	$-0.119879\pi$
$233$	16.4302	+	9.48596i	1.07638	+	0.621446i	0.146460	+	0.989217i	$0.453212\pi$
$234$		0			0
$235$	6.32623	+	10.9573i	0.412678	+	0.714779i
$236$	0.0188497	−	0.106902i	0.00122701	−	0.00695871i
$237$		0			0
$238$	5.23355	+	10.8671i	0.339241	+	0.704412i
$239$	13.6545	+	16.2728i	0.883236	+	1.05260i	0.998244	+	0.0592349i	$0.0188661\pi$
$239$	13.6545	+	16.2728i	0.883236	+	1.05260i	−0.115008	+	0.993365i	$0.536689\pi$
$240$		0			0
$241$	−11.6046	−	2.04621i	−0.747519	−	0.131808i	−0.213103	−	0.977030i	$-0.568357\pi$
$241$	−11.6046	−	2.04621i	−0.747519	−	0.131808i	−0.534415	+	0.845222i	$0.679468\pi$
$242$	3.31104	+	1.91163i	0.212842	+	0.122884i
$243$		0			0
$244$			0.129488i			0.00828962i
$245$	14.6068	+	2.20115i	0.933197	+	0.140626i
$246$		0			0
$247$	33.3273	+	12.1301i	2.12056	+	0.771822i
$248$	4.01113	+	1.45993i	0.254707	+	0.0927058i
$249$		0			0
$250$	16.2311	+	2.86198i	1.02654	+	0.181007i
$251$	−13.6923	+	23.7157i	−0.864248	+	1.49692i	0.00354445	+	0.999994i	$0.498872\pi$
$251$	−13.6923	+	23.7157i	−0.864248	+	1.49692i	−0.867792	+	0.496927i	$0.834462\pi$
$252$		0			0
$253$	−1.29698	−	2.24643i	−0.0815404	−	0.141232i
$254$	−0.922990	−	2.53589i	−0.0579135	−	0.159116i
$255$		0			0
$256$	−0.320075	+	0.268575i	−0.0200047	+	0.0167859i
$257$	2.77342	+	15.7288i	0.173001	+	0.981138i	0.940426	+	0.339999i	$0.110427\pi$
$257$	2.77342	+	15.7288i	0.173001	+	0.981138i	−0.767425	+	0.641139i	$0.778462\pi$
$258$		0			0
$259$	10.0339	+	13.9558i	0.623474	+	0.867170i
$260$	−0.211819	+	0.122294i	−0.0131365	+	0.00758434i
$261$		0			0
$262$	−10.6180	+	6.13031i	−0.655983	+	0.378732i
$263$	9.86756	+	27.1109i	0.608460	+	1.67173i	0.733592	+	0.679590i	$0.237842\pi$
$263$	9.86756	+	27.1109i	0.608460	+	1.67173i	−0.125132	+	0.992140i	$0.539935\pi$
$264$		0			0
$265$	−1.83900	+	0.324266i	−0.112969	+	0.0199195i
$266$	−17.8815	+	8.61165i	−1.09639	+	0.528014i
$267$		0			0
$268$	0.140298	+	0.117724i	0.00857007	+	0.00719114i
$269$	−4.08105	+	7.06859i	−0.248826	+	0.430979i	−0.963200	−	0.268784i	$-0.913378\pi$
$269$	−4.08105	+	7.06859i	−0.248826	+	0.430979i	0.714374	+	0.699764i	$0.246711\pi$
$270$		0			0
$271$	10.1461	−	5.85783i	0.616329	−	0.355838i	−0.159109	−	0.987261i	$-0.550862\pi$
$271$	10.1461	−	5.85783i	0.616329	−	0.355838i	0.775438	+	0.631423i	$0.217529\pi$
$272$	12.0631	−	4.39061i	0.731432	−	0.266220i
$273$		0			0
$274$	7.52564	−	6.31476i	0.454640	−	0.381488i
$275$	1.30175	+	1.55137i	0.0784987	+	0.0935511i
$276$		0			0
$277$	8.94325	−	3.25508i	0.537348	−	0.195579i	−0.0590684	−	0.998254i	$-0.518813\pi$
$277$	8.94325	−	3.25508i	0.537348	−	0.195579i	0.596416	+	0.802675i	$0.296591\pi$
$278$	−14.8118			−0.888356
$279$		0			0
$280$	3.91324	−	15.3693i	0.233861	−	0.918491i
$281$	−20.5328	−	3.62048i	−1.22488	−	0.215980i	−0.476457	−	0.879198i	$-0.658079\pi$
$281$	−20.5328	−	3.62048i	−1.22488	−	0.215980i	−0.748426	+	0.663218i	$0.769190\pi$
$282$		0			0
$283$	0.946510	+	1.12801i	0.0562642	+	0.0670531i	0.793443	−	0.608645i	$-0.208287\pi$
$283$	0.946510	+	1.12801i	0.0562642	+	0.0670531i	−0.737178	+	0.675698i	$0.763842\pi$
$284$	0.0495263	+	0.0590232i	0.00293885	+	0.00350238i
$285$		0			0
$286$	34.1863	+	6.02796i	2.02148	+	0.356441i
$287$	20.6121	−	21.1332i	1.21669	−	1.24746i
$288$		0			0
$289$	−6.51698			−0.383352
$290$	−12.2523	+	4.45947i	−0.719480	+	0.261869i
$291$		0			0
$292$	−0.0342613	−	0.0408310i	−0.00200499	−	0.00238946i
$293$	4.11874	−	3.45603i	0.240619	−	0.201904i	−0.514501	−	0.857490i	$-0.672023\pi$
$293$	4.11874	−	3.45603i	0.240619	−	0.201904i	0.755120	+	0.655586i	$0.227578\pi$
$294$		0			0
$295$	12.3633	−	4.49987i	0.719818	−	0.261992i
$296$	15.9819	−	9.22716i	0.928930	−	0.536318i
$297$		0			0
$298$	7.83400	−	13.5689i	0.453811	−	0.786024i
$299$	−3.57187	−	2.99715i	−0.206566	−	0.173330i
$300$		0			0
$301$	−16.2549	−	11.0820i	−0.936918	−	0.638758i
$302$	28.0016	−	4.93743i	1.61131	−	0.284117i
$303$		0			0
$304$	7.22461	+	19.8495i	0.414360	+	1.13844i
$305$	−13.5917	+	7.84719i	−0.778261	+	0.449329i
$306$		0			0
$307$	6.76941	−	3.90832i	0.386351	−	0.223060i	−0.294227	−	0.955736i	$-0.595062\pi$
$307$	6.76941	−	3.90832i	0.386351	−	0.223060i	0.680578	+	0.732676i	$0.261729\pi$
$308$	0.138513	−	0.0995871i	0.00789248	−	0.00567450i
$309$		0			0
$310$	0.775338	+	4.39716i	0.0440362	+	0.249742i
$311$	9.50108	−	7.97235i	0.538757	−	0.452071i	−0.332356	−	0.943154i	$-0.607843\pi$
$311$	9.50108	−	7.97235i	0.538757	−	0.452071i	0.871113	+	0.491083i	$0.163399\pi$
$312$		0			0
$313$	2.42423	+	6.66051i	0.137026	+	0.376474i	0.989159	−	0.146850i	$-0.0469136\pi$
$313$	2.42423	+	6.66051i	0.137026	+	0.376474i	−0.852133	+	0.523325i	$0.824691\pi$
$314$	3.44439	+	5.96587i	0.194378	+	0.336673i
$315$		0			0
$316$	0.0828727	−	0.143540i	0.00466196	−	0.00807475i
$317$	−16.6689	−	2.93919i	−0.936221	−	0.165081i	−0.315334	−	0.948981i	$-0.602117\pi$
$317$	−16.6689	−	2.93919i	−0.936221	−	0.165081i	−0.620887	+	0.783900i	$0.713228\pi$
$318$		0			0
$319$	−15.2711	−	5.55822i	−0.855016	−	0.311200i
$320$	−15.9996	−	5.82337i	−0.894404	−	0.325537i
$321$		0			0
$322$	2.59634	−	0.259845i	0.144688	−	0.0144806i
$323$			17.2495i			0.959788i
$324$		0			0
$325$	3.15261	+	1.82016i	0.174875	+	0.100964i
$326$	12.9963	+	2.29160i	0.719799	+	0.126920i
$327$		0			0
$328$	−20.3730	−	24.2797i	−1.12491	−	1.34062i
$329$	−13.1069	−	8.93583i	−0.722607	−	0.492648i
$330$		0			0
$331$	2.51122	−	14.2418i	0.138029	−	0.782801i	−0.834674	−	0.550745i	$-0.814344\pi$
$331$	2.51122	−	14.2418i	0.138029	−	0.782801i	0.972702	−	0.232056i	$-0.0745452\pi$
$332$	0.105960	+	0.183529i	0.00581532	+	0.0100724i
$333$		0			0
$334$	−10.5029	−	6.06386i	−0.574694	−	0.331799i
$335$	−3.85463	+	21.8607i	−0.210601	+	1.19438i
$336$		0			0
$337$	−14.9144	−	5.42839i	−0.812438	−	0.295703i	−0.0978073	−	0.995205i	$-0.531183\pi$
$337$	−14.9144	−	5.42839i	−0.812438	−	0.295703i	−0.714630	+	0.699502i	$0.753405\pi$
$338$	43.4246	−	7.65693i	2.36199	−	0.416482i
$339$		0			0
$340$	−0.0911278	−	0.0764653i	−0.00494210	−	0.00414691i
$341$	−2.78255	+	4.81952i	−0.150683	+	0.260991i
$342$		0			0
$343$	−17.6972	+	5.45979i	−0.955559	+	0.294801i
$344$	−13.5770	+	16.1804i	−0.732023	+	0.872391i
$345$		0			0
$346$	4.08070	−	11.2116i	0.219380	−	0.602741i
$347$	5.06257	−	0.892668i	0.271773	−	0.0479209i	−0.0361006	−	0.999348i	$-0.511494\pi$
$347$	5.06257	−	0.892668i	0.271773	−	0.0479209i	0.307874	+	0.951427i	$0.400383\pi$
$348$		0			0
$349$	3.81124	+	10.4713i	0.204011	+	0.560516i	0.998932	−	0.0461967i	$-0.0147101\pi$
$349$	3.81124	+	10.4713i	0.204011	+	0.560516i	−0.794921	+	0.606713i	$0.792488\pi$
$350$	−1.96101	+	0.551775i	−0.104820	+	0.0294936i
$351$		0			0
$352$	−0.182371	−	0.315875i	−0.00972038	−	0.0168362i
$353$	0.534901	−	3.03357i	0.0284699	−	0.161461i	−0.967258	−	0.253794i	$-0.918321\pi$
$353$	0.534901	−	3.03357i	0.0284699	−	0.161461i	0.995728	+	0.0923333i	$0.0294325\pi$
$354$		0			0
$355$	−3.19400	+	8.77545i	−0.169520	+	0.465752i
$356$	0.0131768	+	0.0747292i	0.000698368	+	0.00396064i
$357$		0			0
$358$	5.21599	+	4.37674i	0.275674	+	0.231318i
$359$		−	21.9068i		−	1.15620i	−0.815967	−	0.578099i	$-0.803795\pi$
$359$		−	21.9068i		−	1.15620i	0.815967	−	0.578099i	$-0.196205\pi$
$360$		0			0
$361$	−9.38353			−0.493870
$362$	6.03899	−	2.19801i	0.317402	−	0.115525i
$363$		0			0
$364$	0.172741	−	0.253373i	0.00905407	−	0.0132803i
$365$	2.20955	−	6.07068i	0.115653	−	0.317754i
$366$		0			0
$367$	−4.25108	+	5.06624i	−0.221905	+	0.264456i	−0.865499	−	0.500912i	$-0.832998\pi$
$367$	−4.25108	+	5.06624i	−0.221905	+	0.264456i	0.643594	+	0.765367i	$0.277443\pi$
$368$		−	2.77709i		−	0.144766i
$369$		0			0
$370$	16.7174	+	9.65179i	0.869096	+	0.501773i
$371$	1.90092	−	1.36671i	0.0986908	−	0.0709562i
$372$		0			0
$373$	18.8688	−	15.8328i	0.976988	−	0.819790i	−0.00664425	−	0.999978i	$-0.502115\pi$
$373$	18.8688	−	15.8328i	0.976988	−	0.819790i	0.983632	+	0.180188i	$0.0576705\pi$
$374$	2.93179	+	16.6270i	0.151599	+	0.859761i
$375$		0			0
$376$	−10.9476	+	13.0468i	−0.564579	+	0.672839i
$377$	−29.2121			−1.50450
$378$		0			0
$379$	2.06704			0.106176			0.0530882	−	0.998590i	$-0.483094\pi$
$379$	2.06704			0.106176			0.0530882	+	0.998590i	$0.483094\pi$
$380$	0.125821	−	0.149948i	0.00645450	−	0.00769217i
$381$		0			0
$382$	−2.52862	−	14.3405i	−0.129376	−	0.733725i
$383$	−5.29740	+	4.44505i	−0.270685	+	0.227131i	−0.768018	−	0.640428i	$-0.778757\pi$
$383$	−5.29740	+	4.44505i	−0.270685	+	0.227131i	0.497334	+	0.867559i	$0.334313\pi$
$384$		0			0
$385$	18.8473	+	8.50385i	0.960546	+	0.433396i
$386$	−12.6881	−	7.32550i	−0.645810	−	0.372858i
$387$		0			0
$388$			0.121258i			0.00615592i
$389$	8.68514	−	10.3505i	0.440354	−	0.524794i	−0.499526	−	0.866299i	$-0.666492\pi$
$389$	8.68514	−	10.3505i	0.440354	−	0.524794i	0.939880	+	0.341505i	$0.110937\pi$
$390$		0			0
$391$	0.775631	−	2.13103i	0.0392254	−	0.107771i
$392$	3.94061	+	19.4898i	0.199031	+	0.984386i
$393$		0			0
$394$	18.7609	−	6.82840i	0.945159	−	0.344010i
$395$	20.0889			1.01078
$396$		0			0
$397$		−	21.5333i		−	1.08072i	−0.841433	−	0.540362i	$-0.818287\pi$
$397$		−	21.5333i		−	1.08072i	0.841433	−	0.540362i	$-0.181713\pi$
$398$	−21.6994	−	18.2079i	−1.08769	−	0.912681i
$399$		0			0
$400$	0.376494	+	2.13521i	0.0188247	+	0.106760i
$401$	9.04869	−	24.8611i	0.451870	−	1.24150i	−0.479537	−	0.877522i	$-0.659195\pi$
$401$	9.04869	−	24.8611i	0.451870	−	1.24150i	0.931407	−	0.363981i	$-0.118583\pi$
$402$		0			0
$403$	−1.73709	+	9.85151i	−0.0865304	+	0.490738i
$404$	−0.0323677	−	0.0560625i	−0.00161035	−	0.00278921i
$405$		0			0
$406$	11.4141	−	11.7027i	0.566473	−	0.580794i
$407$	8.22890	+	22.6087i	0.407891	+	1.12067i
$408$		0			0
$409$	−24.6998	+	4.35525i	−1.22133	+	0.215353i	−0.746897	−	0.664939i	$-0.768457\pi$
$409$	−24.6998	+	4.35525i	−1.22133	+	0.215353i	−0.474431	+	0.880293i	$0.657346\pi$
$410$	11.3391	−	31.1540i	0.560000	−	1.53859i
$411$		0			0
$412$	−0.0694568	+	0.0827754i	−0.00342189	+	0.00407805i
$413$	−11.5175	+	11.8087i	−0.566740	+	0.581068i
$414$		0			0
$415$	−12.8427	+	22.2443i	−0.630426	+	1.09193i
$416$	−0.502247	−	0.421435i	−0.0246247	−	0.0206625i
$417$		0			0
$418$	−27.3592	+	4.82417i	−1.33818	+	0.235958i
$419$	−22.3814	−	8.14616i	−1.09340	−	0.397966i	−0.268522	−	0.963273i	$-0.586535\pi$
$419$	−22.3814	−	8.14616i	−1.09340	−	0.397966i	−0.824880	+	0.565307i	$0.808758\pi$
$420$		0			0
$421$	−1.34235	+	7.61285i	−0.0654222	+	0.371027i	0.934466	+	0.356053i	$0.115878\pi$
$421$	−1.34235	+	7.61285i	−0.0654222	+	0.371027i	−0.999888	+	0.0149744i	$0.995233\pi$
$422$	−4.09248	−	2.36280i	−0.199219	−	0.115019i
$423$		0			0
$424$	−1.25683	−	2.17690i	−0.0610372	−	0.105719i
$425$	−0.307448	+	1.74363i	−0.0149134	+	0.0845783i
$426$		0			0
$427$	11.0842	−	16.2581i	0.536402	−	0.786784i
$428$	0.0319789	+	0.0381110i	0.00154576	+	0.00184216i
$429$		0			0
$430$	−21.7584	−	3.83660i	−1.04928	−	0.185017i
$431$	−4.73254	−	2.73233i	−0.227959	−	0.131612i	0.381671	−	0.924298i	$-0.375349\pi$
$431$	−4.73254	−	2.73233i	−0.227959	−	0.131612i	−0.609630	+	0.792686i	$0.708682\pi$
$432$		0			0
$433$			35.5423i			1.70805i	0.520229	+	0.854027i	$0.325846\pi$
$433$			35.5423i			1.70805i	−0.520229	+	0.854027i	$0.674154\pi$
$434$	−3.26789	−	4.54521i	−0.156864	−	0.218177i
$435$		0			0
$436$	0.0921743	+	0.0335487i	0.00441435	+	0.00160669i
$437$	3.50654	+	1.27628i	0.167741	+	0.0610526i
$438$		0			0
$439$	−3.99689	−	0.704759i	−0.190761	−	0.0336363i	0.0774513	−	0.996996i	$-0.475322\pi$
$439$	−3.99689	−	0.704759i	−0.190761	−	0.0336363i	−0.268212	+	0.963360i	$0.586433\pi$
$440$	11.0999	−	19.2255i	0.529165	−	0.916541i
$441$		0			0
$442$	15.1744	+	26.2828i	0.721771	+	1.25014i
$443$	−2.83479	−	7.78852i	−0.134685	−	0.370044i	0.853955	−	0.520347i	$-0.174197\pi$
$443$	−2.83479	−	7.78852i	−0.134685	−	0.370044i	−0.988640	+	0.150303i	$0.951975\pi$
$444$		0			0
$445$	−7.04544	+	5.91182i	−0.333986	+	0.280247i
$446$	2.45383	+	13.9164i	0.116192	+	0.658960i
$447$		0			0
$448$	21.2409	−	2.12582i	1.00354	−	0.100435i
$449$	−25.1276	+	14.5074i	−1.18585	+	0.684648i	−0.957359	−	0.288899i	$-0.906711\pi$
$449$	−25.1276	+	14.5074i	−1.18585	+	0.684648i	−0.228486	+	0.973547i	$0.573377\pi$
$450$		0			0
$451$	35.7858	−	20.6610i	1.68509	−	0.972887i
$452$	−0.0546845	−	0.150244i	−0.00257214	−	0.00706691i
$453$		0			0
$454$	−24.6115	+	4.33968i	−1.15508	+	0.203671i
$455$	37.0637	+	2.77695i	1.73757	+	0.130185i
$456$		0			0
$457$	−5.02502	−	4.21649i	−0.235061	−	0.197239i	0.517647	−	0.855594i	$-0.326808\pi$
$457$	−5.02502	−	4.21649i	−0.235061	−	0.197239i	−0.752708	+	0.658355i	$0.771253\pi$
$458$	9.19715	−	15.9299i	0.429755	−	0.744357i
$459$		0			0
$460$	−0.0222866	+	0.0128672i	−0.00103912	+	0.000599936i
$461$	20.7893	−	7.56669i	0.968255	−	0.352416i	0.190992	−	0.981592i	$-0.438830\pi$
$461$	20.7893	−	7.56669i	0.968255	−	0.352416i	0.777263	+	0.629176i	$0.216607\pi$
$462$		0			0
$463$	12.6417	−	10.6077i	0.587511	−	0.492980i	−0.299893	−	0.953973i	$-0.596951\pi$
$463$	12.6417	−	10.6077i	0.587511	−	0.492980i	0.887404	+	0.460993i	$0.152507\pi$
$464$	−11.1835	−	13.3280i	−0.519181	−	0.618736i
$465$		0			0
$466$	−25.1023	+	9.13649i	−1.16284	+	0.423240i
$467$	−1.42626			−0.0659994			−0.0329997	−	0.999455i	$-0.510506\pi$
$467$	−1.42626			−0.0659994			−0.0329997	+	0.999455i	$0.510506\pi$
$468$		0			0
$469$	−7.53816	−	26.7906i	−0.348080	−	1.23707i
$470$	−17.5446	−	3.09358i	−0.809271	−	0.142696i
$471$		0			0
$472$	11.3839	+	13.5668i	0.523988	+	0.624464i
$473$	−17.7009	−	21.0951i	−0.813889	−	0.969955i
$474$		0			0
$475$	−2.86909	−	0.505897i	−0.131643	−	0.0232122i
$476$	0.144535	+	0.0368006i	0.00662473	+	0.00168675i
$477$		0			0
$478$	−29.9106			−1.36808
$479$	−22.5859	+	8.22061i	−1.03198	+	0.375609i	−0.801834	−	0.597547i	$-0.796142\pi$
$479$	−22.5859	+	8.22061i	−1.03198	+	0.375609i	−0.230144	+	0.973157i	$0.573920\pi$
$480$		0			0
$481$	27.7994	+	33.1301i	1.26754	+	1.51060i
$482$	12.7101	−	10.6651i	0.578930	−	0.485780i
$483$		0			0
$484$	0.0444246	−	0.0161692i	0.00201930	−	0.000734965i
$485$	−12.7278	+	7.34842i	−0.577941	+	0.333674i
$486$		0			0
$487$	17.7620	−	30.7647i	0.804874	−	1.39408i	−0.111501	−	0.993764i	$-0.535566\pi$
$487$	17.7620	−	30.7647i	0.804874	−	1.39408i	0.916376	−	0.400319i	$-0.131101\pi$
$488$	−16.1836	−	13.5796i	−0.732597	−	0.614722i
$489$		0			0
$490$	−15.5945	+	13.7631i	−0.704487	+	0.621753i
$491$	30.5498	−	5.38675i	1.37869	−	0.243101i	0.565334	−	0.824862i	$-0.308747\pi$
$491$	30.5498	−	5.38675i	1.37869	−	0.243101i	0.813360	+	0.581761i	$0.197636\pi$
$492$		0			0
$493$	−4.85933	−	13.3509i	−0.218853	−	0.601294i
$494$	−43.2475	+	24.9690i	−1.94580	+	1.12341i
$495$		0			0
$496$	−5.15977	+	2.97899i	−0.231681	+	0.133761i
$497$	−1.16597	−	11.6502i	−0.0523008	−	0.522584i
$498$		0			0
$499$	6.32386	+	35.8644i	0.283095	+	1.60551i	0.712012	+	0.702167i	$0.247784\pi$
$499$	6.32386	+	35.8644i	0.283095	+	1.60551i	−0.428917	+	0.903344i	$0.641105\pi$
$500$	0.156118	−	0.130999i	0.00698181	−	0.00585844i
$501$		0			0
$502$	−13.1878	−	36.2332i	−0.588601	−	1.61717i
$503$	9.30116	+	16.1101i	0.414718	+	0.718313i	0.995399	−	0.0958185i	$-0.0305468\pi$
$503$	9.30116	+	16.1101i	0.414718	+	0.718313i	−0.580681	+	0.814131i	$0.697213\pi$
$504$		0			0
$505$	3.92308	−	6.79497i	0.174575	−	0.302372i
$506$	3.59692	+	0.634234i	0.159903	+	0.0281951i
$507$		0			0
$508$	−0.0313570	−	0.0114130i	−0.00139124	−	0.000506370i
$509$	−4.20101	−	1.52904i	−0.186207	−	0.0677737i	0.247234	−	0.968956i	$-0.420478\pi$
$509$	−4.20101	−	1.52904i	−0.186207	−	0.0677737i	−0.433441	+	0.901182i	$0.642701\pi$
$510$		0			0
$511$	0.806593	+	8.05939i	0.0356816	+	0.356526i
$512$		−	22.9158i		−	1.01274i
$513$		0			0
$514$	−19.4757	−	11.2443i	−0.859034	−	0.495964i
$515$	−12.8977	−	2.27422i	−0.568343	−	0.100214i
$516$		0			0
$517$	−14.2729	−	17.0097i	−0.627719	−	0.748087i
$518$	−24.1344	−	1.80824i	−1.06041	−	0.0794494i
$519$		0			0
$520$	6.92941	−	39.2986i	0.303875	−	1.72336i
$521$	17.3340	+	30.0233i	0.759415	+	1.31535i	0.943149	+	0.332369i	$0.107848\pi$
$521$	17.3340	+	30.0233i	0.759415	+	1.31535i	−0.183735	+	0.982976i	$0.558819\pi$
$522$		0			0
$523$	−22.2749	−	12.8604i	−0.974015	−	0.562348i	−0.0735572	−	0.997291i	$-0.523435\pi$
$523$	−22.2749	−	12.8604i	−0.974015	−	0.562348i	−0.900458	+	0.434943i	$0.856768\pi$
$524$	−0.0263260	+	0.149302i	−0.00115006	+	0.00652231i
$525$		0			0
$526$	−38.1734	−	13.8940i	−1.66444	−	0.605806i
$527$	−4.79143	+	0.844858i	−0.208718	+	0.0368026i
$528$		0			0
$529$	17.2432	+	14.4688i	0.749705	+	0.629077i
$530$	1.31467	−	2.27708i	0.0571057	−	0.0989099i
$531$		0			0
$532$	−0.0605542	+	0.237827i	−0.00262536	+	0.0103111i
$533$	47.7448	−	56.9001i	2.06806	−	2.46462i
$534$		0			0
$535$	−2.06235	+	5.66626i	−0.0891632	+	0.244974i
$536$	−29.4266	+	5.18871i	−1.27104	+	0.224118i
$537$		0			0
$538$	−3.93070	−	10.7995i	−0.169465	−	0.465600i
$539$	−25.9158	+	0.647128i	−1.11627	+	0.0278738i
$540$		0			0
$541$	13.1658	+	22.8039i	0.566044	+	0.980416i	0.996952	+	0.0780204i	$0.0248599\pi$
$541$	13.1658	+	22.8039i	0.566044	+	0.980416i	−0.430908	+	0.902396i	$0.641807\pi$
$542$	−2.86453	+	16.2455i	−0.123042	+	0.697806i
$543$		0			0
$544$	0.109063	−	0.299648i	0.00467603	−	0.0128473i
$545$	2.06447	+	11.7082i	0.0884323	+	0.501524i
$546$		0			0
$547$	13.7395	+	11.5288i	0.587459	+	0.492937i	0.887387	−	0.461025i	$-0.152518\pi$
$547$	13.7395	+	11.5288i	0.587459	+	0.492937i	−0.299928	+	0.953962i	$0.596963\pi$
$548$		−	0.121477i		−	0.00518922i
$549$		0			0
$550$	−2.85153			−0.121590
$551$	21.9685	−	7.99587i	0.935889	−	0.340636i
$552$		0			0
$553$	−22.6923	+	10.9285i	−0.964973	+	0.464726i
$554$	−4.58329	+	12.5925i	−0.194725	+	0.535004i
$555$		0			0
$556$	−0.117728	+	0.140303i	−0.00499278	+	0.00595016i
$557$			1.14693i			0.0485968i	0.999705	+	0.0242984i	$0.00773518\pi$
$557$			1.14693i			0.0485968i	−0.999705	+	0.0242984i	$0.992265\pi$
$558$		0			0
$559$	−42.8684	−	24.7501i	−1.81314	−	1.04682i
$560$	12.9224	+	17.9734i	0.546073	+	0.759516i
$561$		0			0
$562$	22.4888	−	18.8704i	0.948634	−	0.795998i
$563$	1.56861	+	8.89601i	0.0661089	+	0.374922i	0.999856	+	0.0169880i	$0.00540771\pi$
$563$	1.56861	+	8.89601i	0.0661089	+	0.374922i	−0.933747	+	0.357934i	$0.883481\pi$
$564$		0			0
$565$	12.4565	−	14.8450i	0.524048	−	0.624536i
$566$	−2.07336			−0.0871497
$567$		0			0
$568$	−12.5707			−0.527455
$569$	−27.5657	+	32.8516i	−1.15562	+	1.37721i	−0.242178	+	0.970232i	$0.577862\pi$
$569$	−27.5657	+	32.8516i	−1.15562	+	1.37721i	−0.913438	+	0.406978i	$0.866583\pi$
$570$		0			0
$571$	−5.74972	−	32.6083i	−0.240618	−	1.36461i	−0.830453	−	0.557089i	$-0.811918\pi$
$571$	−5.74972	−	32.6083i	−0.240618	−	1.36461i	0.589834	−	0.807524i	$-0.299193\pi$
$572$	0.328819	−	0.275912i	0.0137486	−	0.0115365i
$573$		0			0
$574$	4.13934	+	41.3599i	0.172773	+	1.72633i
$575$	0.331703	+	0.191509i	0.0138330	+	0.00798648i
$576$		0			0
$577$			41.8339i			1.74157i	0.491665	+	0.870784i	$0.336388\pi$
$577$			41.8339i			1.74157i	−0.491665	+	0.870784i	$0.663612\pi$
$578$	5.89835	−	7.02938i	0.245339	−	0.292383i
$579$		0			0
$580$	−0.0551425	+	0.151503i	−0.00228967	+	0.00629081i
$581$	2.40606	−	32.1135i	0.0998200	−	1.33229i
$582$		0			0
$583$	3.07953	−	1.12086i	0.127541	−	0.0464212i
$584$	8.69617			0.359850
$585$		0			0
$586$			7.57054i			0.312736i
$587$	−10.1800	−	8.54200i	−0.420172	−	0.352566i	0.408057	−	0.912957i	$-0.366207\pi$
$587$	−10.1800	−	8.54200i	−0.420172	−	0.352566i	−0.828228	+	0.560391i	$0.810651\pi$
$588$		0			0
$589$	−1.39019	−	7.88415i	−0.0572817	−	0.324861i
$590$	−6.33602	+	17.4081i	−0.260850	+	0.716678i
$591$		0			0
$592$	−4.47288	+	25.3670i	−0.183834	+	1.04258i
$593$	−6.07625	−	10.5244i	−0.249522	−	0.432184i	0.713872	−	0.700277i	$-0.246940\pi$
$593$	−6.07625	−	10.5244i	−0.249522	−	0.432184i	−0.963393	+	0.268093i	$0.913607\pi$
$594$		0			0
$595$	4.89626	+	17.4013i	0.200727	+	0.713383i
$596$	−0.0662626	−	0.182055i	−0.00271422	−	0.00745726i
$597$		0			0
$598$	6.46560	−	1.14006i	0.264398	−	0.0466205i
$599$	−10.4793	+	28.7916i	−0.428172	+	1.17639i	0.518749	+	0.854927i	$0.326398\pi$
$599$	−10.4793	+	28.7916i	−0.428172	+	1.17639i	−0.946921	+	0.321466i	$0.895824\pi$
$600$		0			0
$601$	0.739101	−	0.880827i	0.0301486	−	0.0359297i	−0.750759	−	0.660576i	$-0.770312\pi$
$601$	0.739101	−	0.880827i	0.0301486	−	0.0359297i	0.780908	+	0.624646i	$0.214757\pi$
$602$	26.6653	−	7.50290i	1.08679	−	0.305795i
$603$		0			0
$604$	0.175794	−	0.304484i	0.00715296	−	0.0123893i
$605$	4.38941	+	3.68315i	0.178455	+	0.149741i
$606$		0			0
$607$	2.97007	−	0.523704i	0.120552	−	0.0212565i	−0.113047	−	0.993590i	$-0.536061\pi$
$607$	2.97007	−	0.523704i	0.120552	−	0.0212565i	0.233598	+	0.972333i	$0.424950\pi$
$608$	0.493061	+	0.179460i	0.0199963	+	0.00727805i
$609$		0			0
$610$	3.83735	−	21.7627i	0.155370	−	0.881145i
$611$	−34.5662	−	19.9568i	−1.39840	−	0.807367i
$612$		0			0
$613$	20.0456	+	34.7199i	0.809633	+	1.40232i	0.913119	+	0.407694i	$0.133667\pi$
$613$	20.0456	+	34.7199i	0.809633	+	1.40232i	−0.103486	+	0.994631i	$0.533000\pi$
$614$	−1.91120	+	10.8390i	−0.0771299	+	0.437425i
$615$		0			0
$616$	−2.07953	+	27.7554i	−0.0837867	+	1.11830i
$617$	−6.57249	−	7.83278i	−0.264598	−	0.315336i	0.617344	−	0.786693i	$-0.288209\pi$
$617$	−6.57249	−	7.83278i	−0.264598	−	0.315336i	−0.881942	+	0.471357i	$0.843764\pi$
$618$		0			0
$619$	38.3209	+	6.75702i	1.54025	+	0.271587i	0.878354	−	0.478010i	$-0.158642\pi$
$619$	38.3209	+	6.75702i	1.54025	+	0.271587i	0.661894	+	0.749597i	$0.269753\pi$
$620$	0.0478139	+	0.0276054i	0.00192025	+	0.00110866i
$621$		0			0
$622$			17.4637i			0.700229i
$623$	4.74240	−	10.5107i	0.190000	−	0.421102i
$624$		0			0
$625$	20.6420	+	7.51308i	0.825681	+	0.300523i
$626$	−9.37830	−	3.41342i	−0.374832	−	0.136428i
$627$		0			0
$628$	0.0838875	+	0.0147916i	0.00334748	+	0.000590250i
$629$	−10.5172	+	18.2163i	−0.419349	+	0.726333i
$630$		0			0
$631$	5.94429	+	10.2958i	0.236639	+	0.409870i	0.959748	−	0.280864i	$-0.0906210\pi$
$631$	5.94429	+	10.2958i	0.236639	+	0.409870i	−0.723109	+	0.690734i	$0.757288\pi$
$632$	9.24879	+	25.4108i	0.367897	+	1.01079i
$633$		0			0
$634$	18.2569	−	15.3194i	0.725074	−	0.608409i
$635$	−0.702317	−	3.98304i	−0.0278706	−	0.158062i
$636$		0			0
$637$	−43.3775	+	17.0260i	−1.71868	+	0.674595i
$638$	19.8167	−	11.4412i	0.784550	−	0.452960i
$639$		0			0
$640$	20.4021	−	11.7791i	0.806462	−	0.465611i
$641$	17.0872	+	46.9468i	0.674906	+	1.85429i	0.490509	+	0.871436i	$0.336811\pi$
$641$	17.0872	+	46.9468i	0.674906	+	1.85429i	0.184396	+	0.982852i	$0.440967\pi$
$642$		0			0
$643$	−7.32572	+	1.29172i	−0.288898	+	0.0509406i	−0.316219	−	0.948686i	$-0.602414\pi$
$643$	−7.32572	+	1.29172i	−0.288898	+	0.0509406i	0.0273209	+	0.999627i	$0.491302\pi$
$644$	0.0181750	−	0.0266587i	0.000716194	−	0.00105050i
$645$		0			0
$646$	−18.6057	−	15.6121i	−0.732033	−	0.614248i
$647$	9.06934	−	15.7086i	0.356553	−	0.617567i	−0.630830	−	0.775921i	$-0.717285\pi$
$647$	9.06934	−	15.7086i	0.356553	−	0.617567i	0.987382	+	0.158354i	$0.0506187\pi$
$648$		0			0
$649$	−19.9962	+	11.5448i	−0.784919	+	0.453173i
$650$	−4.81662	+	1.75310i	−0.188923	+	0.0687624i
$651$		0			0
$652$	0.125004	−	0.104891i	0.00489555	−	0.00410786i
$653$	14.2828	+	17.0215i	0.558928	+	0.666104i	0.969319	−	0.245805i	$-0.0790524\pi$
$653$	14.2828	+	17.0215i	0.558928	+	0.666104i	−0.410392	+	0.911909i	$0.634608\pi$
$654$		0			0
$655$	−17.2670	+	6.28466i	−0.674676	+	0.245562i
$656$	44.2392			1.72725
$657$		0			0
$658$	21.5011	−	6.04984i	0.838200	−	0.235847i
$659$	−21.2896	−	3.75393i	−0.829324	−	0.146232i	−0.257157	−	0.966370i	$-0.582786\pi$
$659$	−21.2896	−	3.75393i	−0.829324	−	0.146232i	−0.572167	+	0.820137i	$0.693897\pi$
$660$		0			0
$661$	3.08248	+	3.67356i	0.119895	+	0.142885i	0.822653	−	0.568544i	$-0.192493\pi$
$661$	3.08248	+	3.67356i	0.119895	+	0.142885i	−0.702758	+	0.711428i	$0.748049\pi$
$662$	13.0887	+	15.5986i	0.508708	+	0.606255i
$663$		0			0
$664$	−34.0499	−	6.00391i	−1.32139	−	0.232997i
$665$	−28.6333	+	8.05665i	−1.11035	+	0.312424i
$666$		0			0
$667$	−3.07356			−0.119009
$668$	−0.140918	+	0.0512901i	−0.00545230	+	0.00198447i
$669$		0			0
$670$	−20.0908	−	23.9432i	−0.776174	−	0.925008i
$671$	21.0992	−	17.7044i	0.814527	−	0.683469i
$672$		0			0
$673$	−41.8330	+	15.2260i	−1.61255	+	0.586918i	−0.981941	−	0.189186i	$-0.939415\pi$
$673$	−41.8330	+	15.2260i	−1.61255	+	0.586918i	−0.630604	+	0.776105i	$0.717193\pi$
$674$	19.3538	−	11.1739i	0.745480	−	0.430403i
$675$		0			0
$676$	0.272620	−	0.472192i	0.0104854	−	0.0181612i
$677$	−30.7338	−	25.7887i	−1.18120	−	0.991142i	−0.999970	−	0.00770076i	$-0.997549\pi$
$677$	−30.7338	−	25.7887i	−1.18120	−	0.991142i	−0.181227	−	0.983441i	$-0.558007\pi$
$678$		0			0
$679$	10.3797	−	15.2247i	0.398335	−	0.584270i
$680$	19.1135	−	3.37022i	0.732968	−	0.129242i
$681$		0			0
$682$	−2.68004	−	7.36334i	−0.102624	−	0.281957i
$683$	28.5877	−	16.5051i	1.09388	−	0.631550i	0.159271	−	0.987235i	$-0.449086\pi$
$683$	28.5877	−	16.5051i	1.09388	−	0.631550i	0.934606	+	0.355685i	$0.115752\pi$
$684$		0			0
$685$	12.7508	−	7.36168i	0.487183	−	0.281275i
$686$	10.1282	−	24.0301i	0.386696	−	0.917475i
$687$		0			0
$688$	−5.11947	−	29.0340i	−0.195178	−	1.10691i
$689$	4.51265	−	3.78656i	0.171918	−	0.144257i
$690$		0			0
$691$	1.00124	+	2.75087i	0.0380888	+	0.104648i	0.957279	−	0.289165i	$-0.0933778\pi$
$691$	1.00124	+	2.75087i	0.0380888	+	0.104648i	−0.919190	+	0.393814i	$0.871156\pi$
$692$	−0.0737660	−	0.127766i	−0.00280416	−	0.00485695i
$693$		0			0
$694$	−3.61915	+	6.26854i	−0.137381	+	0.237951i
$695$	−21.8614	−	3.85476i	−0.829251	−	0.146219i
$696$		0			0
$697$	33.9474	+	12.3559i	1.28585	+	0.468011i
$698$	−14.7441	−	5.36640i	−0.558071	−	0.203121i
$699$		0			0
$700$	−0.0103599	+	0.0229609i	−0.000391569	+	0.000867842i
$701$			6.39386i			0.241493i	0.992683	+	0.120746i	$0.0385288\pi$
$701$			6.39386i			0.241493i	−0.992683	+	0.120746i	$0.961471\pi$
$702$		0			0
$703$	−29.9744	−	17.3058i	−1.13051	−	0.652699i
$704$	29.4268	+	5.18874i	1.10906	+	0.195558i
$705$		0			0
$706$	2.78796	+	3.32257i	0.104926	+	0.125046i
$707$	−0.734978	+	9.80970i	−0.0276417	+	0.368932i
$708$		0			0
$709$	−6.22575	+	35.3080i	−0.233813	+	1.32602i	0.611287	+	0.791409i	$0.290652\pi$
$709$	−6.22575	+	35.3080i	−0.233813	+	1.32602i	−0.845099	+	0.534609i	$0.820459\pi$
$710$	−6.57461	−	11.3876i	−0.246741	−	0.427367i
$711$		0			0
$712$	−10.7216	−	6.19014i	−0.401810	−	0.231985i
$713$	−0.182768	+	1.03653i	−0.00684472	+	0.0388184i
$714$		0			0
$715$	48.8882	+	17.7938i	1.82831	+	0.665452i
$716$	0.0829158	−	0.0146203i	0.00309871	−	0.000546386i
$717$		0			0
$718$	23.6292	+	19.8273i	0.881836	+	0.739948i
$719$	17.8398	−	30.8994i	0.665311	−	1.15235i	−0.313890	−	0.949459i	$-0.601632\pi$
$719$	17.8398	−	30.8994i	0.665311	−	1.15235i	0.979201	−	0.202893i	$-0.0650344\pi$
$720$		0			0
$721$	15.8064	−	4.44749i	0.588660	−	0.165633i
$722$	8.49278	−	10.1213i	0.316069	−	0.376676i
$723$		0			0
$724$	0.0271790	−	0.0746736i	0.00101010	−	0.00277522i
$725$	2.36315	−	0.416687i	0.0877652	−	0.0154754i
$726$		0			0
$727$	−0.773622	−	2.12551i	−0.0286921	−	0.0788308i	0.924520	−	0.381135i	$-0.124467\pi$
$727$	−0.773622	−	2.12551i	−0.0286921	−	0.0788308i	−0.953212	+	0.302304i	$0.902244\pi$
$728$	13.5512	+	48.1610i	0.502242	+	1.78497i
$729$		0			0
$730$	4.54818	+	7.87768i	0.168336	+	0.291566i
$731$	4.18060	−	23.7094i	0.154625	−	0.876923i
$732$		0			0
$733$	5.51496	−	15.1522i	0.203700	−	0.559661i	−0.795210	−	0.606334i	$-0.792640\pi$
$733$	5.51496	−	15.1522i	0.203700	−	0.559661i	0.998910	+	0.0466729i	$0.0148618\pi$
$734$	−1.61703	−	9.17065i	−0.0596858	−	0.338495i
$735$		0			0
$736$	−0.0528441	−	0.0443414i	−0.00194786	−	0.00163445i
$737$		−	38.9566i		−	1.43498i
$738$		0			0
$739$	24.5989			0.904884			0.452442	−	0.891794i	$-0.350553\pi$
$739$	24.5989			0.904884			0.452442	+	0.891794i	$0.350553\pi$
$740$	0.224299	−	0.0816381i	0.00824538	−	0.00300107i
$741$		0			0
$742$	−0.246300	+	3.28735i	−0.00904197	+	0.120683i
$743$	−8.41237	+	23.1128i	−0.308620	+	0.847926i	0.684307	+	0.729194i	$0.260105\pi$
$743$	−8.41237	+	23.1128i	−0.308620	+	0.847926i	−0.992926	+	0.118732i	$0.962117\pi$
$744$		0			0
$745$	15.0938	−	17.9881i	0.552994	−	0.659033i
$746$			34.6822i			1.26980i
$747$		0			0
$748$	0.180799	+	0.104384i	0.00661066	+	0.00381667i
$749$	−0.752859	−	7.52248i	−0.0275089	−	0.274866i
$750$		0			0
$751$	−28.0407	+	23.5290i	−1.02322	+	0.858584i	−0.990029	−	0.140865i	$-0.955012\pi$
$751$	−28.0407	+	23.5290i	−1.02322	+	0.858584i	−0.0331922	+	0.999449i	$0.510567\pi$
$752$	−4.12801	−	23.4111i	−0.150533	−	0.853715i
$753$		0			0
$754$	26.4391	−	31.5088i	0.962854	−	1.14748i
$755$	42.6137			1.55087
$756$		0			0
$757$	−38.6682			−1.40542			−0.702709	−	0.711477i	$-0.748027\pi$
$757$	−38.6682			−1.40542			−0.702709	+	0.711477i	$0.748027\pi$
$758$	−1.87082	+	2.22956i	−0.0679512	+	0.0809811i
$759$		0			0
$760$	5.54560	+	31.4506i	0.201160	+	1.14083i
$761$	−36.9741	+	31.0250i	−1.34031	+	1.12465i	−0.358765	+	0.933428i	$0.616802\pi$
$761$	−36.9741	+	31.0250i	−1.34031	+	1.12465i	−0.981546	+	0.191226i	$0.938754\pi$
$762$		0			0
$763$	−8.70132	−	12.1024i	−0.315009	−	0.438136i
$764$	−0.155936	−	0.0900299i	−0.00564158	−	0.00325717i
$765$		0			0
$766$		−	9.73700i		−	0.351812i
$767$	−26.6786	+	31.7943i	−0.963307	+	1.14802i
$768$		0			0
$769$	−16.2750	+	44.7151i	−0.586891	+	1.61247i	0.189264	+	0.981926i	$0.439390\pi$
$769$	−16.2750	+	44.7151i	−0.586891	+	1.61247i	−0.776155	+	0.630543i	$0.782832\pi$
$770$	−26.2306	+	12.6325i	−0.945286	+	0.455244i
$771$		0			0
$772$	−0.170238	+	0.0619615i	−0.00612700	+	0.00223004i
$773$	−3.58933			−0.129099			−0.0645496	−	0.997914i	$-0.520561\pi$
$773$	−3.58933			−0.129099			−0.0645496	+	0.997914i	$0.520561\pi$
$774$		0			0
$775$		−	0.821730i		−	0.0295174i
$776$	−15.1549	−	12.7165i	−0.544031	−	0.456496i
$777$		0			0
$778$	3.30367	+	18.7360i	0.118442	+	0.671719i
$779$	−20.3312	+	55.8595i	−0.728440	+	2.00137i
$780$		0			0
$781$	2.84592	−	16.1400i	0.101835	−	0.577534i
$782$	1.59658	+	2.76535i	0.0570935	+	0.0988888i
$783$		0			0
$784$	−24.3747	−	13.2727i	−0.870525	−	0.474027i
$785$	3.53112	+	9.70167i	0.126031	+	0.346267i
$786$		0			0
$787$	30.5240	−	5.38221i	1.08806	−	0.191855i	0.399286	−	0.916827i	$-0.369258\pi$
$787$	30.5240	−	5.38221i	1.08806	−	0.191855i	0.688779	+	0.724971i	$0.258147\pi$
$788$	0.0844349	−	0.231983i	0.00300787	−	0.00826405i
$789$		0			0
$790$	−18.1819	+	21.6684i	−0.646885	+	0.770927i
$791$	−5.99495	+	23.5452i	−0.213156	+	0.837171i
$792$		0			0
$793$	24.7549	−	42.8767i	0.879072	−	1.52260i
$794$	23.2263	+	19.4892i	0.824271	+	0.691645i
$795$		0			0
$796$	−0.344943	+	0.0608228i	−0.0122262	+	0.00215581i
$797$	−18.1049	−	6.58966i	−0.641310	−	0.233418i	0.000836476	−	1.00000i	$-0.499734\pi$
$797$	−18.1049	−	6.58966i	−0.641310	−	0.233418i	−0.642147	+	0.766582i	$0.721956\pi$
$798$		0			0
$799$	3.37096	−	19.1177i	0.119256	−	0.676335i
$800$	0.0466414	+	0.0269284i	0.00164902	+	0.000952063i
$801$		0			0
$802$	18.6260	+	32.2612i	0.657708	+	1.13918i
$803$	−1.96875	+	11.1653i	−0.0694756	+	0.394016i
$804$		0			0
$805$	3.89967	+	0.292177i	0.137445	+	0.0102979i
$806$	−9.05389	−	10.7900i	−0.318910	−	0.380062i
$807$		0			0
$808$	10.4012	+	1.83402i	0.365914	+	0.0645205i
$809$	10.9220	+	6.30585i	0.383999	+	0.221702i	0.679557	−	0.733623i	$-0.262172\pi$
$809$	10.9220	+	6.30585i	0.383999	+	0.221702i	−0.295558	+	0.955325i	$0.595506\pi$
$810$		0			0
$811$		−	43.6085i		−	1.53130i	−0.643256	−	0.765652i	$-0.722417\pi$
$811$		−	43.6085i		−	1.53130i	0.643256	−	0.765652i	$-0.277583\pi$
$812$	−0.0201297	−	0.201134i	−0.000706415	−	0.00705842i
$813$		0			0
$814$	−31.8341	−	11.5867i	−1.11578	−	0.406112i
$815$	18.5854	+	6.76454i	0.651019	+	0.236951i
$816$		0			0
$817$	39.0131	+	6.87906i	1.36489	+	0.240668i
$818$	17.6575	−	30.5837i	0.617380	−	1.06933i
$819$		0			0
$820$	−0.204975	−	0.355028i	−0.00715805	−	0.0123981i
$821$	−9.39965	−	25.8253i	−0.328050	−	0.901310i	−0.988605	−	0.150532i	$-0.951901\pi$
$821$	−9.39965	−	25.8253i	−0.328050	−	0.901310i	0.660555	−	0.750778i	$-0.270321\pi$
$822$		0			0
$823$	−3.92941	+	3.29717i	−0.136971	+	0.114932i	−0.708699	−	0.705511i	$-0.750718\pi$
$823$	−3.92941	+	3.29717i	−0.136971	+	0.114932i	0.571728	+	0.820443i	$0.306273\pi$
$824$	−3.06132	−	17.3616i	−0.106646	−	0.604821i
$825$		0			0
$826$	−2.31296	−	23.1108i	−0.0804781	−	0.804128i
$827$	−22.7209	+	13.1179i	−0.790082	+	0.456154i	−0.839991	−	0.542600i	$-0.817440\pi$
$827$	−22.7209	+	13.1179i	−0.790082	+	0.456154i	0.0499094	+	0.998754i	$0.484107\pi$
$828$		0			0
$829$	13.7370	−	7.93108i	0.477107	−	0.275458i	−0.242103	−	0.970251i	$-0.577837\pi$
$829$	13.7370	−	7.93108i	0.477107	−	0.275458i	0.719210	+	0.694793i	$0.244504\pi$
$830$	−12.3696	−	33.9852i	−0.429355	−	1.17964i
$831$		0			0
$832$	52.8958	−	9.32696i	1.83383	−	0.323354i
$833$	−14.9972	−	16.9927i	−0.519621	−	0.588764i
$834$		0			0
$835$	−13.9236	−	11.6833i	−0.481845	−	0.404316i
$836$	−0.171761	+	0.297499i	−0.00594049	+	0.0102892i
$837$		0			0
$838$	29.0435	−	16.7682i	1.00329	−	0.579249i
$839$	43.7933	−	15.9395i	1.51191	−	0.550291i	0.552800	−	0.833314i	$-0.313560\pi$
$839$	43.7933	−	15.9395i	1.51191	−	0.550291i	0.959113	+	0.283023i	$0.0913373\pi$
$840$		0			0
$841$	7.46447	−	6.26343i	0.257395	−	0.215980i
$842$	−6.99648	−	8.33808i	−0.241115	−	0.287349i
$843$		0			0
$844$	−0.0549092	+	0.0199853i	−0.00189005	+	0.000687923i
$845$	66.0849			2.27339
$846$		0			0
$847$	−6.96189	−	1.77260i	−0.239213	−	0.0609071i
$848$	3.45523	+	0.609251i	0.118653	+	0.0209218i
$849$		0			0
$850$	−1.60246	−	1.90973i	−0.0549638	−	0.0655033i
$851$	2.92493	+	3.48579i	0.100265	+	0.119491i
$852$		0			0
$853$	−33.3113	−	5.87368i	−1.14056	−	0.201111i	−0.428708	−	0.903443i	$-0.641031\pi$
$853$	−33.3113	−	5.87368i	−1.14056	−	0.201111i	−0.711850	+	0.702332i	$0.752142\pi$
$854$	7.50436	+	26.6705i	0.256794	+	0.912644i
$855$		0			0
$856$	−8.11684			−0.277428
$857$	41.3614	−	15.0543i	1.41288	−	0.514246i	0.480905	−	0.876773i	$-0.340308\pi$
$857$	41.3614	−	15.0543i	1.41288	−	0.514246i	0.931973	+	0.362527i	$0.118086\pi$
$858$		0			0
$859$	29.8856	+	35.6162i	1.01968	+	1.21521i	0.976360	+	0.216149i	$0.0693496\pi$
$859$	29.8856	+	35.6162i	1.01968	+	1.21521i	0.0433218	+	0.999061i	$0.486206\pi$
$860$	−0.209283	+	0.175609i	−0.00713648	+	0.00598822i
$861$		0			0
$862$	7.23046	−	2.63167i	0.246271	−	0.0896351i
$863$	6.24515	−	3.60564i	0.212587	−	0.122737i	−0.389926	−	0.920846i	$-0.627499\pi$
$863$	6.24515	−	3.60564i	0.212587	−	0.122737i	0.602513	+	0.798109i	$0.294166\pi$
$864$		0			0
$865$	8.94069	−	15.4857i	0.303992	−	0.526530i
$866$	−38.3368	−	32.1684i	−1.30274	−	1.09313i
$867$		0			0
$868$	−0.0690276	−	0.00517180i	−0.00234295	−	0.000175542i
$869$	−34.7197	+	6.12203i	−1.17779	+	0.207676i
$870$		0			0
$871$	−23.9503	−	65.8029i	−0.811525	−	2.22965i
$872$	−13.8594	+	8.00176i	−0.469340	+	0.270974i
$873$		0			0
$874$	−4.55031	+	2.62712i	−0.153916	+	0.0888637i
$875$	−30.8152	+	3.08402i	−1.04174	+	0.104259i
$876$		0			0
$877$	−7.82720	−	44.3903i	−0.264306	−	1.49895i	−0.771005	−	0.636829i	$-0.780246\pi$
$877$	−7.82720	−	44.3903i	−0.264306	−	1.49895i	0.506699	−	0.862123i	$-0.330866\pi$
$878$	4.37765	−	3.67328i	0.147739	−	0.123967i
$879$		0			0
$880$	10.5979	+	29.1174i	0.357254	+	0.981547i
$881$	−17.2527	−	29.8826i	−0.581259	−	1.00677i	−0.995330	−	0.0965261i	$-0.969227\pi$
$881$	−17.2527	−	29.8826i	−0.581259	−	1.00677i	0.414071	−	0.910245i	$-0.364106\pi$
$882$		0			0
$883$	−19.2076	+	33.2686i	−0.646388	+	1.11958i	0.337591	+	0.941293i	$0.390388\pi$
$883$	−19.2076	+	33.2686i	−0.646388	+	1.11958i	−0.983979	+	0.178284i	$0.942945\pi$
$884$	0.369569	+	0.0651649i	0.0124299	+	0.00219173i
$885$		0			0
$886$	10.9666	+	3.99151i	0.368429	+	0.134097i
$887$	25.3610	+	9.23065i	0.851539	+	0.309935i	0.730668	−	0.682733i	$-0.239209\pi$
$887$	25.3610	+	9.23065i	0.851539	+	0.309935i	0.120871	+	0.992668i	$0.461431\pi$
$888$		0			0
$889$	2.96012	+	4.11714i	0.0992793	+	0.138084i
$890$		−	12.9500i		−	0.434085i
$891$		0			0
$892$	0.151324	+	0.0873671i	0.00506671	+	0.00292527i
$893$	31.4576	+	5.54682i	1.05269	+	0.185617i
$894$		0			0
$895$	6.55946	+	7.81726i	0.219259	+	0.261302i
$896$	−16.6381	+	24.4044i	−0.555839	+	0.815294i
$897$		0			0
$898$	7.09426	−	40.2335i	0.236739	−	1.34261i
$899$	3.29702	+	5.71060i	0.109962	+	0.190459i
$900$		0			0
$901$	2.48125	+	1.43255i	0.0826624	+	0.0477252i
$902$	−10.1034	+	57.2992i	−0.336406	+	1.90785i
$903$		0			0
$904$	24.5126	+	8.92187i	0.815278	+	0.296737i
$905$	9.48522	−	1.67250i	0.315299	−	0.0555958i
$906$		0			0
$907$	−27.8874	−	23.4003i	−0.925987	−	0.776996i	0.0491052	−	0.998794i	$-0.484363\pi$
$907$	−27.8874	−	23.4003i	−0.925987	−	0.776996i	−0.975093	+	0.221798i	$0.928807\pi$
$908$	−0.154511	+	0.267621i	−0.00512764	+	0.00888133i
$909$		0			0
$910$	−36.5406	+	37.4645i	−1.21131	+	1.24194i
$911$	−17.9098	+	21.3441i	−0.593378	+	0.707160i	−0.976251	−	0.216640i	$-0.930490\pi$
$911$	−17.9098	+	21.3441i	−0.593378	+	0.707160i	0.382873	+	0.923801i	$0.374935\pi$
$912$		0			0
$913$	15.4173	−	42.3586i	0.510238	−	1.40187i
$914$	9.09603	−	1.60388i	0.300870	−	0.0530515i
$915$		0			0
$916$	−0.0777926	−	0.213733i	−0.00257034	−	0.00706195i
$917$	16.0857	−	16.4924i	0.531197	−	0.544627i
$918$		0			0
$919$	24.7371	+	42.8459i	0.816001	+	1.41336i	0.908607	+	0.417653i	$0.137147\pi$
$919$	24.7371	+	42.8459i	0.816001	+	1.41336i	−0.0926055	+	0.995703i	$0.529520\pi$
$920$	0.729081	−	4.13482i	0.0240371	−	0.136321i
$921$		0			0
$922$	−10.6542	+	29.2723i	−0.350879	+	0.964031i
$923$	−5.11565	−	29.0123i	−0.168384	−	0.954950i
$924$		0			0
$925$	−2.72145	−	2.28357i	−0.0894807	−	0.0750832i
$926$			23.2364i			0.763595i
$927$		0			0
$928$	−0.432178			−0.0141870
$929$	29.3067	−	10.6668i	0.961522	−	0.349966i	0.186892	−	0.982380i	$-0.440158\pi$
$929$	29.3067	−	10.6668i	0.961522	−	0.349966i	0.774630	+	0.632415i	$0.217936\pi$
$930$		0			0
$931$	27.9611	−	24.6774i	0.916387	−	0.808768i
$932$	−0.112975	+	0.310396i	−0.00370062	+	0.0101674i
$933$		0			0
$934$	1.29087	−	1.53840i	0.0422386	−	0.0503380i
$935$			25.3035i			0.827512i
$936$		0			0
$937$	15.9634	+	9.21646i	0.521501	+	0.301089i	0.737548	−	0.675294i	$-0.235983\pi$
$937$	15.9634	+	9.21646i	0.521501	+	0.301089i	−0.216048	+	0.976383i	$0.569317\pi$
$938$	35.7196	+	16.1166i	1.16629	+	0.526226i
$939$		0			0
$940$	−0.168752	+	0.141600i	−0.00550407	+	0.00461847i
$941$	3.99360	+	22.6488i	0.130188	+	0.738331i	0.978091	+	0.208180i	$0.0667539\pi$
$941$	3.99360	+	22.6488i	0.130188	+	0.738331i	−0.847903	+	0.530152i	$0.822135\pi$
$942$		0			0
$943$	5.02349	−	5.98676i	0.163587	−	0.194956i
$944$	−24.7197			−0.804558
$945$		0			0
$946$	38.7744			1.26066
$947$	11.7046	−	13.9490i	0.380349	−	0.453282i	−0.541575	−	0.840652i	$-0.682172\pi$
$947$	11.7046	−	13.9490i	0.380349	−	0.453282i	0.921924	+	0.387370i	$0.126616\pi$
$948$		0			0
$949$	3.53890	+	20.0701i	0.114878	+	0.651503i
$950$	3.14241	−	2.63679i	0.101953	−	0.0855488i
$951$		0			0
$952$	−19.7570	+	14.2048i	−0.640328	+	0.460380i
$953$	20.4233	+	11.7914i	0.661576	+	0.381961i	0.792877	−	0.609381i	$-0.208582\pi$
$953$	20.4233	+	11.7914i	0.661576	+	0.381961i	−0.131301	+	0.991343i	$0.541915\pi$
$954$		0			0
$955$		−	21.8239i		−	0.706203i
$956$	−0.237736	+	0.283323i	−0.00768893	+	0.00916331i
$957$		0			0
$958$	11.5750	−	31.8020i	0.373971	−	1.02748i
$959$	−10.3984	+	15.2522i	−0.335782	+	0.492519i
$960$		0			0
$961$	−27.0086	+	9.83031i	−0.871244	+	0.317107i
$962$	−60.8954			−1.96335
$963$		0			0
$964$		−	0.205163i		−	0.00660785i
$965$	−16.8205	−	14.1141i	−0.541472	−	0.454349i
$966$		0			0
$967$	−6.40078	−	36.3006i	−0.205835	−	1.16735i	−0.896120	−	0.443811i	$-0.853626\pi$
$967$	−6.40078	−	36.3006i	−0.205835	−	1.16735i	0.690285	−	0.723537i	$-0.257485\pi$
$968$	−2.63803	+	7.24794i	−0.0847896	+	0.232958i
$969$		0			0
$970$	3.59344	−	20.3794i	0.115378	−	0.654343i
$971$	6.28287	+	10.8822i	0.201627	+	0.349228i	0.949053	−	0.315117i	$-0.102044\pi$
$971$	6.28287	+	10.8822i	0.201627	+	0.349228i	−0.747426	+	0.664345i	$0.768711\pi$
$972$		0			0
$973$	26.7915	−	7.53842i	0.858895	−	0.241671i
$974$	17.1077	+	47.0029i	0.548165	+	1.50607i
$975$		0			0
$976$	29.0396	−	5.12047i	0.929536	−	0.163902i
$977$	−5.53944	+	15.2195i	−0.177222	+	0.486914i	−0.996218	−	0.0868850i	$-0.972309\pi$
$977$	−5.53944	+	15.2195i	−0.177222	+	0.486914i	0.818996	+	0.573799i	$0.194531\pi$
$978$		0			0
$979$	10.3750	−	12.3645i	0.331588	−	0.395171i
$980$	0.00642009	+	0.257108i	0.000205082	+	0.00821303i
$981$		0			0
$982$	−21.8395	+	37.8272i	−0.696927	+	1.20711i
$983$	0.923122	+	0.774591i	0.0294430	+	0.0247056i	0.657390	−	0.753550i	$-0.271660\pi$
$983$	0.923122	+	0.774591i	0.0294430	+	0.0247056i	−0.627947	+	0.778256i	$0.716105\pi$
$984$		0			0
$985$	29.4670	−	5.19584i	0.938898	−	0.165553i
$986$	18.7986	+	6.84215i	0.598671	+	0.217898i
$987$		0			0
$988$	−0.107227	+	0.608114i	−0.00341134	+	0.0193467i
$989$	−4.51042	−	2.60409i	−0.143423	−	0.0828052i
$990$		0			0
$991$	26.7781	+	46.3810i	0.850635	+	1.47334i	0.880636	+	0.473793i	$0.157115\pi$
$991$	26.7781	+	46.3810i	0.850635	+	1.47334i	−0.0300019	+	0.999550i	$0.509551\pi$
$992$	−0.0256994	+	0.145748i	−0.000815956	+	0.00462752i
$993$		0			0
$994$	13.6215	+	9.28666i	0.432048	+	0.294555i
$995$	−27.2884	−	32.5211i	−0.865101	−	1.03099i
$996$		0			0
$997$	−2.68170	−	0.472857i	−0.0849304	−	0.0149755i	0.131021	−	0.991380i	$-0.458174\pi$
$997$	−2.68170	−	0.472857i	−0.0849304	−	0.0149755i	−0.215952	+	0.976404i	$0.569285\pi$
$998$	−44.4078	−	25.6388i	−1.40570	−	0.811584i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.ba.a.143.7		132
3.2	odd	2		189.2.ba.a.101.16	✓	132
7.5	odd	6		567.2.bd.a.467.16		132
21.5	even	6		189.2.bd.a.47.7	yes	132
27.4	even	9		189.2.bd.a.185.7	yes	132
27.23	odd	18		567.2.bd.a.17.16		132
189.131	even	18	inner	567.2.ba.a.341.7		132
189.166	odd	18		189.2.ba.a.131.16	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.16	✓	132	3.2	odd	2
189.2.ba.a.131.16	yes	132	189.166	odd	18
189.2.bd.a.47.7	yes	132	21.5	even	6
189.2.bd.a.185.7	yes	132	27.4	even	9
567.2.ba.a.143.7		132	1.1	even	1	trivial
567.2.ba.a.341.7		132	189.131	even	18	inner
567.2.bd.a.17.16		132	27.23	odd	18
567.2.bd.a.467.16		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)

\(f(q)\)	\(=\)	\(q+(-0.905074 + 1.07862i) q^{2} +(0.00302336 + 0.0171463i) q^{4} +(-1.61655 + 1.35644i) q^{5} +(1.08812 - 2.41164i) q^{7} +(-2.46004 - 1.42030i) q^{8} +O(q^{10})\)	\(q+(-0.905074 + 1.07862i) q^{2} +(0.00302336 + 0.0171463i) q^{4} +(-1.61655 + 1.35644i) q^{5} +(1.08812 - 2.41164i) q^{7} +(-2.46004 - 1.42030i) q^{8} -2.97133i q^{10} +(2.38051 - 2.83698i) q^{11} +(2.27684 - 6.25557i) q^{13} +(1.61642 + 3.35639i) q^{14} +(3.72576 - 1.35607i) q^{16} +3.23775 q^{17} +5.32762i q^{19} +(-0.0281454 - 0.0236168i) q^{20} +(0.905502 + 5.13536i) q^{22} +(0.239559 - 0.658182i) q^{23} +(-0.0949575 + 0.538530i) q^{25} +(4.68670 + 8.11761i) q^{26} +(0.0446405 + 0.0113661i) q^{28} +(-1.50083 - 4.12351i) q^{29} +(-1.47986 + 0.260940i) q^{31} +(0.0336848 - 0.0925482i) q^{32} +(-2.93040 + 3.49232i) q^{34} +(1.51224 + 5.37450i) q^{35} +(-3.24831 + 5.62624i) q^{37} +(-5.74650 - 4.82189i) q^{38} +(5.90332 - 1.04091i) q^{40} +(10.4849 + 3.81619i) q^{41} +(1.29121 - 7.32280i) q^{43} +(0.0558409 + 0.0322398i) q^{44} +(0.493113 + 0.854097i) q^{46} +(1.04114 - 5.90462i) q^{47} +(-4.63197 - 5.24832i) q^{49} +(-0.494929 - 0.589833i) q^{50} +(0.114144 + 0.0201266i) q^{52} +(0.766350 + 0.442452i) q^{53} +7.81514i q^{55} +(-6.10208 + 4.38724i) q^{56} +(5.80608 + 2.11324i) q^{58} +(-5.85868 - 2.13238i) q^{59} +(7.32422 + 1.29146i) q^{61} +(1.05793 - 1.83239i) q^{62} +(4.03421 + 6.98746i) q^{64} +(4.80471 + 13.2008i) q^{65} +(8.05809 - 6.76154i) q^{67} +(0.00978888 + 0.0555155i) q^{68} +(-7.16576 - 3.23318i) q^{70} +(3.83248 - 2.21268i) q^{71} +(-2.65123 + 1.53069i) q^{73} +(-3.12864 - 8.59586i) q^{74} +(-0.0913491 + 0.0161073i) q^{76} +(-4.25147 - 8.82791i) q^{77} +(-7.29250 - 6.11913i) q^{79} +(-4.18344 + 7.24593i) q^{80} +(-13.6058 + 7.85533i) q^{82} +(11.4377 - 4.16299i) q^{83} +(-5.23397 + 4.39182i) q^{85} +(6.72991 + 8.02040i) q^{86} +(-9.88551 + 3.59803i) q^{88} +4.35832 q^{89} +(-12.6087 - 12.2977i) q^{91} +(0.0120097 + 0.00211763i) q^{92} +(5.42656 + 6.46712i) q^{94} +(-7.22662 - 8.61234i) q^{95} +(6.85869 + 1.20937i) q^{97} +(9.85324 - 0.246039i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 9 q^{5} - 6 q^{7} + 18 q^{8}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more