LMFDB - Embedded newform 567.2.u.a.100.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(100,567)]

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([16, 6]))

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

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

chi := DirichletCharacter("567.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.u (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.19
Character	$\chi$	$=$	567.100
Dual form			567.2.u.a.550.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.324131 - 1.83824i) q^{2} +(-1.39467 - 0.507617i) q^{4} +(-1.37479 - 0.500384i) q^{5} +(-2.42382 - 1.06071i) q^{7} +(0.481419 - 0.833843i) q^{8} +O(q^{10})$	\(q+(0.324131 - 1.83824i) q^{2} +(-1.39467 - 0.507617i) q^{4} +(-1.37479 - 0.500384i) q^{5} +(-2.42382 - 1.06071i) q^{7} +(0.481419 - 0.833843i) q^{8} +(-1.36544 + 2.36501i) q^{10} +(-4.29056 + 1.56163i) q^{11} +(0.925783 + 0.336957i) q^{13} +(-2.73547 + 4.11174i) q^{14} +(-3.65064 - 3.06325i) q^{16} +(-0.620234 + 1.07428i) q^{17} +(-0.718027 - 1.24366i) q^{19} +(1.66338 + 1.39574i) q^{20} +(1.47995 + 8.39323i) q^{22} +(-0.165636 - 0.939366i) q^{23} +(-2.19055 - 1.83809i) q^{25} +(0.919482 - 1.59259i) q^{26} +(2.84199 + 2.70971i) q^{28} +(-5.18835 + 1.88840i) q^{29} +(6.28413 + 2.28724i) q^{31} +(-5.33911 + 4.48005i) q^{32} +(1.77374 + 1.48834i) q^{34} +(2.80149 + 2.67110i) q^{35} -2.88764 q^{37} +(-2.51887 + 0.916795i) q^{38} +(-1.07909 + 0.905468i) q^{40} +(-11.1576 - 4.06104i) q^{41} +(0.559660 - 3.17399i) q^{43} +6.77661 q^{44} -1.78046 q^{46} +(10.6381 - 3.87197i) q^{47} +(4.74979 + 5.14193i) q^{49} +(-4.08886 + 3.43096i) q^{50} +(-1.12011 - 0.939887i) q^{52} +(-2.32509 - 4.02717i) q^{53} +6.68005 q^{55} +(-2.05134 + 1.51044i) q^{56} +(1.78963 + 10.1495i) q^{58} +(4.83431 - 4.05647i) q^{59} +(-4.93482 + 1.79613i) q^{61} +(6.24136 - 10.8104i) q^{62} +(1.73924 + 3.01245i) q^{64} +(-1.10415 - 0.926495i) q^{65} +(-2.28146 - 12.9388i) q^{67} +(1.41034 - 1.18342i) q^{68} +(5.81816 - 4.28402i) q^{70} +(5.80593 + 10.0562i) q^{71} +9.93018 q^{73} +(-0.935973 + 5.30816i) q^{74} +(0.370105 + 2.09897i) q^{76} +(12.0560 + 0.765911i) q^{77} +(2.45710 - 13.9349i) q^{79} +(3.48608 + 6.03807i) q^{80} +(-11.0817 + 19.1940i) q^{82} +(7.82112 - 2.84665i) q^{83} +(1.39025 - 1.16656i) q^{85} +(-5.65314 - 2.05757i) q^{86} +(-0.763399 + 4.32945i) q^{88} +(-0.307487 - 0.532584i) q^{89} +(-1.88652 - 1.79871i) q^{91} +(-0.245832 + 1.39418i) q^{92} +(-3.66944 - 20.8104i) q^{94} +(0.364832 + 2.06907i) q^{95} +(-0.991251 + 5.62167i) q^{97} +(10.9916 - 7.06459i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	$ 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) $ 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 + 3 * q^10 + 15 * q^11 - 12 * q^13 + 30 * q^14 + 9 * q^16 - 27 * q^17 + 3 * q^19 + 18 * q^20 - 12 * q^22 + 36 * q^23 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 + 75 * q^32 - 18 * q^34 - 15 * q^35 - 6 * q^37 - 69 * q^38 + 51 * q^40 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 21 * q^47 - 42 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 111 * q^56 - 3 * q^58 - 27 * q^59 - 21 * q^61 - 75 * q^62 - 30 * q^64 + 90 * q^65 - 3 * q^67 + 30 * q^68 + 39 * q^70 + 18 * q^71 - 42 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 + 93 * q^86 - 51 * q^88 - 75 * q^89 - 21 * q^91 + 66 * q^92 + 33 * q^94 - 15 * q^95 - 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	0.324131	−	1.83824i	0.229195	−	1.29983i	−0.625306	−	0.780380i	$-0.715026\pi$
$2$	0.324131	−	1.83824i	0.229195	−	1.29983i	0.854501	−	0.519450i	$-0.173863\pi$
$3$		0			0
$3$		0			0
$4$	−1.39467	−	0.507617i	−0.697333	−	0.253809i
$5$	−1.37479	−	0.500384i	−0.614827	−	0.223779i	0.0157870	−	0.999875i	$-0.494975\pi$
$5$	−1.37479	−	0.500384i	−0.614827	−	0.223779i	−0.630614	+	0.776097i	$0.717197\pi$
$6$		0			0
$7$	−2.42382	−	1.06071i	−0.916117	−	0.400910i
$7$	−2.42382	−	1.06071i	−0.916117	−	0.400910i
$8$	0.481419	−	0.833843i	0.170207	−	0.294808i
$9$		0			0
$10$	−1.36544	+	2.36501i	−0.431789	+	0.747881i
$11$	−4.29056	+	1.56163i	−1.29365	+	0.470851i	−0.894924	−	0.446219i	$-0.852770\pi$
$11$	−4.29056	+	1.56163i	−1.29365	+	0.470851i	−0.398727	+	0.917069i	$0.630548\pi$
$12$		0			0
$13$	0.925783	+	0.336957i	0.256766	+	0.0934552i	0.467196	−	0.884154i	$-0.345264\pi$
$13$	0.925783	+	0.336957i	0.256766	+	0.0934552i	−0.210430	+	0.977609i	$0.567486\pi$
$14$	−2.73547	+	4.11174i	−0.731084	+	1.09891i
$15$		0			0
$16$	−3.65064	−	3.06325i	−0.912661	−	0.765813i
$17$	−0.620234	+	1.07428i	−0.150429	+	0.260550i	−0.931385	−	0.364035i	$-0.881399\pi$
$17$	−0.620234	+	1.07428i	−0.150429	+	0.260550i	0.780956	+	0.624586i	$0.214732\pi$
$18$		0			0
$19$	−0.718027	−	1.24366i	−0.164727	−	0.285315i	0.771832	−	0.635827i	$-0.219341\pi$
$19$	−0.718027	−	1.24366i	−0.164727	−	0.285315i	−0.936558	+	0.350512i	$0.886008\pi$
$20$	1.66338	+	1.39574i	0.371942	+	0.312097i
$21$		0			0
$22$	1.47995	+	8.39323i	0.315527	+	1.78944i
$23$	−0.165636	−	0.939366i	−0.0345374	−	0.195871i	0.962657	−	0.270723i	$-0.0872628\pi$
$23$	−0.165636	−	0.939366i	−0.0345374	−	0.195871i	−0.997195	+	0.0748517i	$0.976152\pi$
$24$		0			0
$25$	−2.19055	−	1.83809i	−0.438109	−	0.367617i
$26$	0.919482	−	1.59259i	0.180325	−	0.312333i
$27$		0			0
$28$	2.84199	+	2.70971i	0.537085	+	0.512087i
$29$	−5.18835	+	1.88840i	−0.963452	+	0.350668i	−0.775385	−	0.631488i	$-0.782444\pi$
$29$	−5.18835	+	1.88840i	−0.963452	+	0.350668i	−0.188067	+	0.982156i	$0.560222\pi$
$30$		0			0
$31$	6.28413	+	2.28724i	1.12866	+	0.410800i	0.837807	−	0.545967i	$-0.183837\pi$
$31$	6.28413	+	2.28724i	1.12866	+	0.410800i	0.290857	+	0.956767i	$0.406060\pi$
$32$	−5.33911	+	4.48005i	−0.943831	+	0.791968i
$33$		0			0
$34$	1.77374	+	1.48834i	0.304194	+	0.255249i
$35$	2.80149	+	2.67110i	0.473538	+	0.451498i
$36$		0			0
$37$	−2.88764			−0.474725			−0.237363	−	0.971421i	$-0.576283\pi$
$37$	−2.88764			−0.474725			−0.237363	+	0.971421i	$0.576283\pi$
$38$	−2.51887	+	0.916795i	−0.408615	+	0.148724i
$39$		0			0
$40$	−1.07909	+	0.905468i	−0.170620	+	0.143167i
$41$	−11.1576	−	4.06104i	−1.74253	−	0.634227i	−0.743135	−	0.669141i	$-0.766662\pi$
$41$	−11.1576	−	4.06104i	−1.74253	−	0.634227i	−0.999390	+	0.0349137i	$0.988884\pi$
$42$		0			0
$43$	0.559660	−	3.17399i	0.0853473	−	0.484029i	−0.911934	−	0.410337i	$-0.865411\pi$
$43$	0.559660	−	3.17399i	0.0853473	−	0.484029i	0.997281	−	0.0736913i	$-0.0234780\pi$
$44$	6.77661			1.02161
$45$		0			0
$46$	−1.78046			−0.262515
$47$	10.6381	−	3.87197i	1.55173	−	0.564785i	0.582909	−	0.812537i	$-0.301914\pi$
$47$	10.6381	−	3.87197i	1.55173	−	0.564785i	0.968823	+	0.247753i	$0.0796920\pi$
$48$		0			0
$49$	4.74979	+	5.14193i	0.678542	+	0.734562i
$50$	−4.08886	+	3.43096i	−0.578252	+	0.485211i
$51$		0			0
$52$	−1.12011	−	0.939887i	−0.155332	−	0.130339i
$53$	−2.32509	−	4.02717i	−0.319376	−	0.553175i	0.660982	−	0.750402i	$-0.270140\pi$
$53$	−2.32509	−	4.02717i	−0.319376	−	0.553175i	−0.980358	+	0.197227i	$0.936806\pi$
$54$		0			0
$55$	6.68005			0.900738
$56$	−2.05134	+	1.51044i	−0.274122	+	0.201841i
$57$		0			0
$58$	1.78963	+	10.1495i	0.234990	+	1.33269i
$59$	4.83431	−	4.05647i	0.629374	−	0.528108i	−0.271360	−	0.962478i	$-0.587473\pi$
$59$	4.83431	−	4.05647i	0.629374	−	0.528108i	0.900734	+	0.434370i	$0.143029\pi$
$60$		0			0
$61$	−4.93482	+	1.79613i	−0.631839	+	0.229970i	−0.638031	−	0.770010i	$-0.720251\pi$
$61$	−4.93482	+	1.79613i	−0.631839	+	0.229970i	0.00619278	+	0.999981i	$0.498029\pi$
$62$	6.24136	−	10.8104i	0.792654	−	1.37292i
$63$		0			0
$64$	1.73924	+	3.01245i	0.217405	+	0.376557i
$65$	−1.10415	−	0.926495i	−0.136953	−	0.114918i
$66$		0			0
$67$	−2.28146	−	12.9388i	−0.278725	−	1.58073i	−0.726875	−	0.686770i	$-0.759028\pi$
$67$	−2.28146	−	12.9388i	−0.278725	−	1.58073i	0.448150	−	0.893958i	$-0.352083\pi$
$68$	1.41034	−	1.18342i	0.171029	−	0.143510i
$69$		0			0
$70$	5.81816	−	4.28402i	0.695403	−	0.512038i
$71$	5.80593	+	10.0562i	0.689037	+	1.19345i	0.972150	+	0.234360i	$0.0752995\pi$
$71$	5.80593	+	10.0562i	0.689037	+	1.19345i	−0.283113	+	0.959087i	$0.591367\pi$
$72$		0			0
$73$	9.93018			1.16224			0.581120	−	0.813818i	$-0.302615\pi$
$73$	9.93018			1.16224			0.581120	+	0.813818i	$0.302615\pi$
$74$	−0.935973	+	5.30816i	−0.108805	+	0.617062i
$75$		0			0
$76$	0.370105	+	2.09897i	0.0424540	+	0.240769i
$77$	12.0560	+	0.765911i	1.37391	+	0.0872837i
$78$		0			0
$79$	2.45710	−	13.9349i	0.276445	−	1.56780i	−0.457887	−	0.889010i	$-0.651394\pi$
$79$	2.45710	−	13.9349i	0.276445	−	1.56780i	0.734333	−	0.678790i	$-0.237495\pi$
$80$	3.48608	+	6.03807i	0.389756	+	0.675077i
$81$		0			0
$82$	−11.0817	+	19.1940i	−1.22377	+	2.11962i
$83$	7.82112	−	2.84665i	0.858479	−	0.312461i	0.124987	−	0.992158i	$-0.460111\pi$
$83$	7.82112	−	2.84665i	0.858479	−	0.312461i	0.733493	+	0.679697i	$0.237889\pi$
$84$		0			0
$85$	1.39025	−	1.16656i	0.150793	−	0.126531i
$86$	−5.65314	−	2.05757i	−0.609594	−	0.221874i
$87$		0			0
$88$	−0.763399	+	4.32945i	−0.0813786	+	0.461521i
$89$	−0.307487	−	0.532584i	−0.0325936	−	0.0564538i	0.849268	−	0.527961i	$-0.177043\pi$
$89$	−0.307487	−	0.532584i	−0.0325936	−	0.0564538i	−0.881862	+	0.471507i	$0.843710\pi$
$90$		0			0
$91$	−1.88652	−	1.79871i	−0.197761	−	0.188556i
$92$	−0.245832	+	1.39418i	−0.0256298	+	0.145354i
$93$		0			0
$94$	−3.66944	−	20.8104i	−0.378474	−	2.14643i
$95$	0.364832	+	2.06907i	0.0374310	+	0.212282i
$96$		0			0
$97$	−0.991251	+	5.62167i	−0.100646	+	0.570794i	0.892224	+	0.451593i	$0.149144\pi$
$97$	−0.991251	+	5.62167i	−0.100646	+	0.570794i	−0.992870	+	0.119200i	$0.961967\pi$
$98$	10.9916	−	7.06459i	1.11032	−	0.713631i
$99$		0			0
$100$	2.12204	+	3.67548i	0.212204	+	0.367548i
$101$	2.05653	−	11.6632i	0.204632	−	1.16053i	−0.693385	−	0.720567i	$-0.743881\pi$
$101$	2.05653	−	11.6632i	0.204632	−	1.16053i	0.898017	−	0.439960i	$-0.145007\pi$
$102$		0			0
$103$	−12.0593	−	4.38923i	−1.18824	−	0.432484i	−0.329134	−	0.944283i	$-0.606757\pi$
$103$	−12.0593	−	4.38923i	−1.18824	−	0.432484i	−0.859105	+	0.511800i	$0.828979\pi$
$104$	0.726659	−	0.609740i	0.0712548	−	0.0597899i
$105$		0			0
$106$	−8.15653	+	2.96873i	−0.792232	+	0.288349i
$107$	−5.52411	+	9.56804i	−0.534036	+	0.924977i	0.465173	+	0.885220i	$0.345992\pi$
$107$	−5.52411	+	9.56804i	−0.534036	+	0.924977i	−0.999209	+	0.0397577i	$0.987341\pi$
$108$		0			0
$109$	−9.52408	−	16.4962i	−0.912242	−	1.58005i	−0.810890	−	0.585198i	$-0.801017\pi$
$109$	−9.52408	−	16.4962i	−0.912242	−	1.58005i	−0.101352	−	0.994851i	$-0.532317\pi$
$110$	2.16521	−	12.2795i	0.206445	−	1.17081i
$111$		0			0
$112$	5.59928	+	11.2970i	0.529082	+	1.06747i
$113$	−1.36095	−	7.71833i	−0.128027	−	0.726080i	−0.979464	−	0.201621i	$-0.935379\pi$
$113$	−1.36095	−	7.71833i	−0.128027	−	0.726080i	0.851436	−	0.524458i	$-0.175732\pi$
$114$		0			0
$115$	−0.242329	+	1.37432i	−0.0225973	+	0.128156i
$116$	8.19460			0.760850
$117$		0			0
$118$	−5.88980	−	10.2014i	−0.542200	−	0.939119i
$119$	2.64283	−	1.94596i	0.242268	−	0.178386i
$120$		0			0
$121$	7.54368	−	6.32990i	0.685789	−	0.575445i
$122$	1.70218	+	9.65354i	0.154108	+	0.873990i
$123$		0			0
$124$	−7.60323	−	6.37987i	−0.682790	−	0.572929i
$125$	5.74937	+	9.95820i	0.514239	+	0.890688i
$126$		0			0
$127$	−6.35187	+	11.0018i	−0.563637	+	0.976249i	0.433538	+	0.901136i	$0.357265\pi$
$127$	−6.35187	+	11.0018i	−0.563637	+	0.976249i	−0.997175	+	0.0751132i	$0.976068\pi$
$128$	−6.99744	+	2.54686i	−0.618492	+	0.225113i
$129$		0			0
$130$	−2.06101	+	1.72939i	−0.180762	+	0.151677i
$131$	1.45783	+	8.26775i	0.127371	+	0.722357i	0.979871	+	0.199630i	$0.0639741\pi$
$131$	1.45783	+	8.26775i	0.127371	+	0.722357i	−0.852500	+	0.522727i	$0.824915\pi$
$132$		0			0
$133$	0.421207	+	3.77602i	0.0365233	+	0.327423i
$134$	−24.5241			−2.11856
$135$		0			0
$136$	0.597185	+	1.03436i	0.0512082	+	0.0886953i
$137$	1.77965	+	1.49330i	0.152046	+	0.127581i	0.715637	−	0.698472i	$-0.246136\pi$
$137$	1.77965	+	1.49330i	0.152046	+	0.127581i	−0.563592	+	0.826054i	$0.690581\pi$
$138$		0			0
$139$	16.4618	−	13.8131i	1.39627	−	1.17161i	0.433546	−	0.901131i	$-0.357262\pi$
$139$	16.4618	−	13.8131i	1.39627	−	1.17161i	0.962726	−	0.270480i	$-0.0871824\pi$
$140$	−2.55125	−	5.14738i	−0.215620	−	0.435033i
$141$		0			0
$142$	20.3675	−	7.41316i	1.70920	−	0.622098i
$143$	−4.49833			−0.376169
$144$		0			0
$145$	8.07784			0.670828
$146$	3.21868	−	18.2540i	0.266380	−	1.51071i
$147$		0			0
$148$	4.02730	+	1.46582i	0.331042	+	0.120489i
$149$	−3.36481	+	2.82341i	−0.275656	+	0.231303i	−0.770126	−	0.637892i	$-0.779807\pi$
$149$	−3.36481	+	2.82341i	−0.275656	+	0.231303i	0.494470	+	0.869195i	$0.335362\pi$
$150$		0			0
$151$	−13.9287	+	5.06965i	−1.13351	+	0.412562i	−0.839564	−	0.543261i	$-0.817189\pi$
$151$	−13.9287	+	5.06965i	−1.13351	+	0.412562i	−0.293942	+	0.955823i	$0.594967\pi$
$152$	−1.38269			−0.112151
$153$		0			0
$154$	5.31564	−	21.9135i	0.428346	−	1.76584i
$155$	−7.49490	−	6.28896i	−0.602005	−	0.505142i
$156$		0			0
$157$	0.289738	−	0.243119i	0.0231236	−	0.0194030i	−0.631153	−	0.775659i	$-0.717418\pi$
$157$	0.289738	−	0.243119i	0.0231236	−	0.0194030i	0.654276	+	0.756256i	$0.272973\pi$
$158$	−24.8192	−	9.03346i	−1.97451	−	0.718664i
$159$		0			0
$160$	9.58193	−	3.48754i	0.757518	−	0.275714i
$161$	−0.594923	+	2.45254i	−0.0468865	+	0.193288i
$162$		0			0
$163$	−2.58086	+	4.47018i	−0.202148	+	0.350131i	−0.949220	−	0.314612i	$-0.898126\pi$
$163$	−2.58086	+	4.47018i	−0.202148	+	0.350131i	0.747072	+	0.664743i	$0.231459\pi$
$164$	13.4997	+	11.3276i	1.05415	+	0.884536i
$165$		0			0
$166$	−2.69776	−	15.2998i	−0.209387	−	1.18749i
$167$	1.88838	+	10.7095i	0.146127	+	0.828727i	0.966455	+	0.256834i	$0.0826795\pi$
$167$	1.88838	+	10.7095i	0.146127	+	0.828727i	−0.820329	+	0.571893i	$0.806209\pi$
$168$		0			0
$169$	−9.21504	−	7.73234i	−0.708850	−	0.594795i
$170$	−1.69378	−	2.93372i	−0.129907	−	0.225006i
$171$		0			0
$172$	−2.39171	+	4.14256i	−0.182366	+	0.315868i
$173$	−9.27634	−	7.78377i	−0.705267	−	0.591789i	0.218000	−	0.975949i	$-0.430047\pi$
$173$	−9.27634	−	7.78377i	−0.705267	−	0.591789i	−0.923267	+	0.384160i	$0.874491\pi$
$174$		0			0
$175$	3.35981	+	6.77872i	0.253978	+	0.512423i
$176$	20.4470	+	7.44209i	1.54125	+	0.560969i
$177$		0			0
$178$	−1.07868	+	0.392608i	−0.0808505	+	0.0294272i
$179$	6.18889	−	10.7195i	0.462579	−	0.801211i	−0.536510	−	0.843894i	$-0.680257\pi$
$179$	6.18889	−	10.7195i	0.462579	−	0.801211i	0.999089	+	0.0426837i	$0.0135908\pi$
$180$		0			0
$181$	−7.93495	+	13.7437i	−0.589800	+	1.02156i	0.404458	+	0.914557i	$0.367460\pi$
$181$	−7.93495	+	13.7437i	−0.589800	+	1.02156i	−0.994258	+	0.107007i	$0.965873\pi$
$182$	−3.91793	+	2.88485i	−0.290416	+	0.213839i
$183$		0			0
$184$	−0.863024	−	0.314115i	−0.0636230	−	0.0231569i
$185$	3.96991	+	1.44493i	0.291874	+	0.106233i
$186$		0			0
$187$	0.983521	−	5.57783i	0.0719222	−	0.407891i
$188$	−16.8021			−1.22542
$189$		0			0
$190$	3.92168			0.284509
$191$	2.63991	−	14.9717i	0.191017	−	1.08331i	−0.726960	−	0.686680i	$-0.759068\pi$
$191$	2.63991	−	14.9717i	0.191017	−	1.08331i	0.917977	−	0.396633i	$-0.129821\pi$
$192$		0			0
$193$	17.6672	+	6.43032i	1.27171	+	0.462865i	0.887682	−	0.460456i	$-0.152314\pi$
$193$	17.6672	+	6.43032i	1.27171	+	0.462865i	0.384028	+	0.923321i	$0.374536\pi$
$194$	10.0127	+	3.64431i	0.718867	+	0.261646i
$195$		0			0
$196$	−4.01425	−	9.58236i	−0.286732	−	0.684454i
$197$	−0.130567	+	0.226149i	−0.00930255	+	0.0161125i	−0.870639	−	0.491922i	$-0.836294\pi$
$197$	−0.130567	+	0.226149i	−0.00930255	+	0.0161125i	0.861337	+	0.508035i	$0.169628\pi$
$198$		0			0
$199$	0.818784	−	1.41818i	0.0580421	−	0.100532i	−0.835544	−	0.549423i	$-0.814848\pi$
$199$	0.818784	−	1.41818i	0.0580421	−	0.100532i	0.893586	+	0.448891i	$0.148181\pi$
$200$	−2.58725	+	0.941681i	−0.182946	+	0.0665869i
$201$		0			0
$202$	−20.7731	−	7.56077i	−1.46159	−	0.531974i
$203$	14.5787	+	0.926177i	1.02322	+	0.0650049i
$204$		0			0
$205$	13.3073	+	11.1662i	0.929425	+	0.779880i
$206$	−11.9772	+	20.7452i	−0.834493	+	1.44538i
$207$		0			0
$208$	−2.34752	−	4.06602i	−0.162771	−	0.281928i
$209$	5.02288	+	4.21469i	0.347440	+	0.291536i
$210$		0			0
$211$	1.10692	+	6.27765i	0.0762034	+	0.432171i	0.998910	+	0.0466690i	$0.0148606\pi$
$211$	1.10692	+	6.27765i	0.0762034	+	0.432171i	−0.922707	+	0.385502i	$0.874028\pi$
$212$	1.19846	+	6.79682i	0.0823108	+	0.466808i
$213$		0			0
$214$	15.7978	+	13.2559i	1.07991	+	0.906156i
$215$	−2.35763	+	4.08354i	−0.160789	+	0.278495i
$216$		0			0
$217$	−12.8055	−	12.2095i	−0.869294	−	0.828834i
$218$	−33.4110	+	12.1606i	−2.26288	+	0.823619i
$219$		0			0
$220$	−9.31645	−	3.39091i	−0.628115	−	0.228615i
$221$	−0.936188	+	0.785555i	−0.0629748	+	0.0528421i
$222$		0			0
$223$	4.42813	+	3.71564i	0.296529	+	0.248818i	0.778898	−	0.627151i	$-0.215779\pi$
$223$	4.42813	+	3.71564i	0.296529	+	0.248818i	−0.482369	+	0.875968i	$0.660223\pi$
$224$	17.6931	−	5.19558i	1.18217	−	0.347144i
$225$		0			0
$226$	−14.6292			−0.973123
$227$	12.0490	−	4.38547i	0.799718	−	0.291074i	0.0903484	−	0.995910i	$-0.471202\pi$
$227$	12.0490	−	4.38547i	0.799718	−	0.291074i	0.709370	+	0.704837i	$0.248980\pi$
$228$		0			0
$229$	−4.48966	+	3.76727i	−0.296685	+	0.248948i	−0.778963	−	0.627070i	$-0.784254\pi$
$229$	−4.48966	+	3.76727i	−0.296685	+	0.248948i	0.482278	+	0.876018i	$0.339810\pi$
$230$	2.44777	+	0.890917i	0.161401	+	0.0587453i
$231$		0			0
$232$	−0.923139	+	5.23538i	−0.0606070	+	0.343720i
$233$	−0.971513			−0.0636459			−0.0318230	−	0.999494i	$-0.510131\pi$
$233$	−0.971513			−0.0636459			−0.0318230	+	0.999494i	$0.510131\pi$
$234$		0			0
$235$	−16.5627			−1.08043
$236$	−8.80139	+	3.20345i	−0.572922	+	0.208527i
$237$		0			0
$238$	−2.72052	−	5.48889i	−0.176345	−	0.355792i
$239$	18.1999	−	15.2715i	1.17726	−	0.987834i	0.177262	−	0.984164i	$-0.443276\pi$
$239$	18.1999	−	15.2715i	1.17726	−	0.987834i	0.999993	−	0.00367051i	$-0.00116836\pi$
$240$		0			0
$241$	−0.219263	−	0.183983i	−0.0141239	−	0.0118514i	0.635698	−	0.771938i	$-0.280712\pi$
$241$	−0.219263	−	0.183983i	−0.0141239	−	0.0118514i	−0.649822	+	0.760086i	$0.725157\pi$
$242$	−9.19071	−	15.9188i	−0.590801	−	1.02330i
$243$		0			0
$244$	7.79417			0.498971
$245$	−3.95705	−	9.44582i	−0.252807	−	0.603472i
$246$		0			0
$247$	−0.245677	−	1.39330i	−0.0156320	−	0.0886537i
$248$	4.93250	−	4.13886i	0.313214	−	0.262818i
$249$		0			0
$250$	20.1691	−	7.34094i	1.27560	−	0.464282i
$251$	−3.91719	+	6.78477i	−0.247251	+	0.428251i	−0.962762	−	0.270350i	$-0.912861\pi$
$251$	−3.91719	+	6.78477i	−0.247251	+	0.428251i	0.715511	+	0.698601i	$0.246194\pi$
$252$		0			0
$253$	2.17762	+	3.77174i	0.136906	+	0.237127i
$254$	18.1650	+	15.2423i	1.13977	+	0.956384i
$255$		0			0
$256$	3.62171	+	20.5397i	0.226357	+	1.28373i
$257$	7.40124	−	6.21038i	0.461677	−	0.387393i	−0.382071	−	0.924133i	$-0.624789\pi$
$257$	7.40124	−	6.21038i	0.461677	−	0.387393i	0.843748	+	0.536740i	$0.180344\pi$
$258$		0			0
$259$	6.99912	+	3.06295i	0.434904	+	0.190322i
$260$	1.06962	+	1.85264i	0.0663351	+	0.114896i
$261$		0			0
$262$	15.6706			0.968134
$263$	−3.18277	+	18.0504i	−0.196258	+	1.11304i	0.714358	+	0.699781i	$0.246719\pi$
$263$	−3.18277	+	18.0504i	−0.196258	+	1.11304i	−0.910616	+	0.413254i	$0.864392\pi$
$264$		0			0
$265$	1.18139	+	6.69998i	0.0725720	+	0.411576i
$266$	7.07774	+	0.449647i	0.433964	+	0.0275696i
$267$		0			0
$268$	−3.38609	+	19.2035i	−0.206838	+	1.17304i
$269$	−2.28434	−	3.95659i	−0.139279	−	0.241238i	0.787945	−	0.615745i	$-0.211145\pi$
$269$	−2.28434	−	3.95659i	−0.139279	−	0.241238i	−0.927224	+	0.374508i	$0.877812\pi$
$270$		0			0
$271$	−6.60709	+	11.4438i	−0.401352	+	0.695162i	−0.993889	−	0.110381i	$-0.964793\pi$
$271$	−6.60709	+	11.4438i	−0.401352	+	0.695162i	0.592537	+	0.805543i	$0.298126\pi$
$272$	5.55504	−	2.02187i	0.336824	−	0.122594i
$273$		0			0
$274$	3.32188	−	2.78739i	0.200682	−	0.168392i
$275$	12.2691	+	4.46558i	0.739853	+	0.269285i
$276$		0			0
$277$	−5.27455	+	29.9135i	−0.316917	+	1.79733i	0.244345	+	0.969688i	$0.421427\pi$
$277$	−5.27455	+	29.9135i	−0.316917	+	1.79733i	−0.561262	+	0.827638i	$0.689684\pi$
$278$	−20.0560	−	34.7379i	−1.20288	−	2.08344i
$279$		0			0
$280$	3.57597	−	1.05009i	0.213705	−	0.0627546i
$281$	−3.38213	+	19.1810i	−0.201761	+	1.14424i	0.700695	+	0.713461i	$0.252873\pi$
$281$	−3.38213	+	19.1810i	−0.201761	+	1.14424i	−0.902456	+	0.430782i	$0.858238\pi$
$282$		0			0
$283$	1.33894	+	7.59351i	0.0795917	+	0.451387i	0.998393	+	0.0566670i	$0.0180473\pi$
$283$	1.33894	+	7.59351i	0.0795917	+	0.451387i	−0.918801	+	0.394720i	$0.870842\pi$
$284$	−2.99265	−	16.9722i	−0.177581	−	1.00711i
$285$		0			0
$286$	−1.45805	+	8.26899i	−0.0862161	+	0.488956i
$287$	22.7364	+	21.6782i	1.34209	+	1.27962i
$288$		0			0
$289$	7.73062	+	13.3898i	0.454742	+	0.787637i
$290$	2.61828	−	14.8490i	0.153750	−	0.871962i
$291$		0			0
$292$	−13.8493	−	5.04073i	−0.810469	−	0.294987i
$293$	−10.4784	+	8.79240i	−0.612153	+	0.513657i	−0.895326	−	0.445411i	$-0.853057\pi$
$293$	−10.4784	+	8.79240i	−0.612153	+	0.513657i	0.283173	+	0.959069i	$0.408613\pi$
$294$		0			0
$295$	−8.67599	+	3.15780i	−0.505135	+	0.183854i
$296$	−1.39017	+	2.40784i	−0.0808017	+	0.139953i
$297$		0			0
$298$	4.09946	+	7.10047i	0.237475	+	0.411319i
$299$	0.163184	−	0.925461i	0.00943716	−	0.0535208i
$300$		0			0
$301$	−4.72319	+	7.09954i	−0.272240	+	0.409211i
$302$	4.80448	+	27.2476i	0.276467	+	1.56792i
$303$		0			0
$304$	−1.18838	+	6.73965i	−0.0681584	+	0.386546i
$305$	7.68311			0.439934
$306$		0			0
$307$	8.70668	+	15.0804i	0.496916	+	0.860684i	0.999994	−	0.00355714i	$-0.00113228\pi$
$307$	8.70668	+	15.0804i	0.496916	+	0.860684i	−0.503077	+	0.864241i	$0.667799\pi$
$308$	−16.4253	−	7.18801i	−0.935917	−	0.409575i
$309$		0			0
$310$	−13.9899	+	11.7389i	−0.794575	+	0.666727i
$311$	−5.19029	−	29.4356i	−0.294315	−	1.66914i	−0.669975	−	0.742383i	$-0.733695\pi$
$311$	−5.19029	−	29.4356i	−0.294315	−	1.66914i	0.375661	−	0.926757i	$-0.377416\pi$
$312$		0			0
$313$	2.42961	+	2.03869i	0.137330	+	0.115233i	0.708865	−	0.705344i	$-0.249208\pi$
$313$	2.42961	+	2.03869i	0.137330	+	0.115233i	−0.571535	+	0.820578i	$0.693652\pi$
$314$	−0.352998	−	0.611410i	−0.0199208	−	0.0345039i
$315$		0			0
$316$	−10.5004	+	18.1873i	−0.590696	+	1.02311i
$317$	−6.27590	+	2.28424i	−0.352489	+	0.128296i	−0.512195	−	0.858869i	$-0.671168\pi$
$317$	−6.27590	+	2.28424i	−0.352489	+	0.128296i	0.159706	+	0.987165i	$0.448945\pi$
$318$		0			0
$319$	19.3119	−	16.2046i	1.08126	−	0.907284i
$320$	−0.883715	−	5.01180i	−0.0494012	−	0.280168i
$321$		0			0
$322$	4.31552	+	1.88855i	0.240495	+	0.105245i
$323$	1.78138			0.0991186
$324$		0			0
$325$	−1.40861	−	2.43979i	−0.0781358	−	0.135335i
$326$	7.38070	+	6.19315i	0.408779	+	0.343007i
$327$		0			0
$328$	−8.75776	+	7.34863i	−0.483566	+	0.405760i
$329$	−29.8920	−	1.89903i	−1.64800	−	0.104697i
$330$		0			0
$331$	−4.68844	+	1.70645i	−0.257700	+	0.0937951i	−0.467640	−	0.883919i	$-0.654895\pi$
$331$	−4.68844	+	1.70645i	−0.257700	+	0.0937951i	0.209940	+	0.977714i	$0.432673\pi$
$332$	−12.3529			−0.677952
$333$		0			0
$334$	20.2987			1.11070
$335$	−3.33784	+	18.9298i	−0.182366	+	1.03425i
$336$		0			0
$337$	13.6802	+	4.97920i	0.745209	+	0.271234i	0.686588	−	0.727046i	$-0.259107\pi$
$337$	13.6802	+	4.97920i	0.745209	+	0.271234i	0.0586210	+	0.998280i	$0.481330\pi$
$338$	−17.2007	+	14.4331i	−0.935597	+	0.785059i
$339$		0			0
$340$	−2.53109	+	0.921243i	−0.137268	+	0.0499614i
$341$	−30.5343			−1.65352
$342$		0			0
$343$	−6.05855	−	17.5013i	−0.327131	−	0.944979i
$344$	−2.37718	−	1.99469i	−0.128169	−	0.107546i
$345$		0			0
$346$	−17.3152	+	14.5291i	−0.930868	+	0.781091i
$347$	−8.17009	−	2.97367i	−0.438593	−	0.159635i	0.113280	−	0.993563i	$-0.463864\pi$
$347$	−8.17009	−	2.97367i	−0.438593	−	0.159635i	−0.551873	+	0.833928i	$0.686087\pi$
$348$		0			0
$349$	−10.4169	+	3.79143i	−0.557602	+	0.202950i	−0.605421	−	0.795906i	$-0.706995\pi$
$349$	−10.4169	+	3.79143i	−0.557602	+	0.202950i	0.0478190	+	0.998856i	$0.484773\pi$
$350$	13.5499	−	3.97894i	0.724273	−	0.212683i
$351$		0			0
$352$	15.9116	−	27.5596i	0.848090	−	1.46893i
$353$	17.7388	+	14.8846i	0.944140	+	0.792228i	0.978301	−	0.207189i	$-0.0664314\pi$
$353$	17.7388	+	14.8846i	0.944140	+	0.792228i	−0.0341608	+	0.999416i	$0.510876\pi$
$354$		0			0
$355$	−2.95001	−	16.7304i	−0.156570	−	0.887955i
$356$	0.158494	+	0.898863i	0.00840015	+	0.0476396i
$357$		0			0
$358$	−17.6989	−	14.8511i	−0.935416	−	0.784907i
$359$	−1.03966	−	1.80074i	−0.0548710	−	0.0950394i	0.837285	−	0.546766i	$-0.184141\pi$
$359$	−1.03966	−	1.80074i	−0.0548710	−	0.0950394i	−0.892156	+	0.451727i	$0.850808\pi$
$360$		0			0
$361$	8.46888	−	14.6685i	0.445730	−	0.772027i
$362$	22.6923	+	19.0411i	1.19268	+	1.00078i
$363$		0			0
$364$	1.71801	+	3.46623i	0.0900480	+	0.181680i
$365$	−13.6520	−	4.96891i	−0.714576	−	0.260085i
$366$		0			0
$367$	14.3862	−	5.23615i	0.750954	−	0.273325i	0.0619470	−	0.998079i	$-0.480269\pi$
$367$	14.3862	−	5.23615i	0.750954	−	0.273325i	0.689007	+	0.724754i	$0.258047\pi$
$368$	−2.27284	+	3.93668i	−0.118480	+	0.205213i
$369$		0			0
$370$	3.94289	−	6.82929i	0.204981	−	0.355038i
$371$	1.36394	+	12.2274i	0.0708121	+	0.634814i
$372$		0			0
$373$	−28.8193	−	10.4894i	−1.49221	−	0.543119i	−0.538177	−	0.842832i	$-0.680887\pi$
$373$	−28.8193	−	10.4894i	−1.49221	−	0.543119i	−0.954029	+	0.299713i	$0.903109\pi$
$374$	−9.93457	−	3.61589i	−0.513704	−	0.186973i
$375$		0			0
$376$	1.89280	−	10.7346i	0.0976135	−	0.553594i
$377$	−5.43960			−0.280153
$378$		0			0
$379$	33.1265			1.70159			0.850797	−	0.525495i	$-0.176120\pi$
$379$	33.1265			1.70159			0.850797	+	0.525495i	$0.176120\pi$
$380$	0.541474	−	3.07085i	0.0277770	−	0.157531i
$381$		0			0
$382$	−26.6658	−	9.70556i	−1.36434	−	0.496580i
$383$	−11.1640	−	4.06336i	−0.570453	−	0.207628i	0.0406578	−	0.999173i	$-0.487055\pi$
$383$	−11.1640	−	4.06336i	−0.570453	−	0.207628i	−0.611110	+	0.791545i	$0.709277\pi$
$384$		0			0
$385$	−16.1912	−	7.08559i	−0.825182	−	0.361115i
$386$	17.5469	−	30.3922i	0.893115	−	1.54692i
$387$		0			0
$388$	4.23612	−	7.33718i	0.215056	−	0.372489i
$389$	21.4924	−	7.82259i	1.08971	−	0.396621i	0.266195	−	0.963919i	$-0.414234\pi$
$389$	21.4924	−	7.82259i	1.08971	−	0.396621i	0.823512	+	0.567298i	$0.192011\pi$
$390$		0			0
$391$	1.11187	+	0.404689i	0.0562298	+	0.0204660i
$392$	6.57421	−	1.48516i	0.332048	−	0.0750117i
$393$		0			0
$394$	0.373395	+	0.313316i	0.0188114	+	0.0157846i
$395$	−10.3508	+	17.9281i	−0.520806	+	0.902063i
$396$		0			0
$397$	−11.1473	−	19.3077i	−0.559466	−	0.969023i	−0.997541	−	0.0700851i	$-0.977673\pi$
$397$	−11.1473	−	19.3077i	−0.559466	−	0.969023i	0.438075	−	0.898938i	$-0.355660\pi$
$398$	−2.34155	−	1.96479i	−0.117371	−	0.0984862i
$399$		0			0
$400$	2.36638	+	13.4204i	0.118319	+	0.671020i
$401$	−0.878529	−	4.98238i	−0.0438716	−	0.248808i	0.954983	−	0.296661i	$-0.0958732\pi$
$401$	−0.878529	−	4.98238i	−0.0438716	−	0.248808i	−0.998854	+	0.0478529i	$0.984762\pi$
$402$		0			0
$403$	5.04704	+	4.23497i	0.251411	+	0.210959i
$404$	−8.78859	+	15.2223i	−0.437249	+	0.757337i
$405$		0			0
$406$	6.42792	−	26.4988i	0.319013	−	1.31511i
$407$	12.3896	−	4.50944i	0.614129	−	0.223525i
$408$		0			0
$409$	−21.3726	−	7.77898i	−1.05681	−	0.384646i	−0.245578	−	0.969377i	$-0.578978\pi$
$409$	−21.3726	−	7.77898i	−1.05681	−	0.384646i	−0.811227	+	0.584731i	$0.801200\pi$
$410$	24.8394	−	20.8427i	1.22673	−	1.02935i
$411$		0			0
$412$	14.5907	+	12.2430i	0.718831	+	0.603171i
$413$	−16.0202	+	4.70435i	−0.788304	+	0.231486i
$414$		0			0
$415$	−12.1769			−0.597738
$416$	−6.45245	+	2.34850i	−0.316357	+	0.115145i
$417$		0			0
$418$	9.37567	−	7.86712i	0.458579	−	0.384793i
$419$	−28.5404	−	10.3878i	−1.39429	−	0.507480i	−0.467811	−	0.883829i	$-0.654957\pi$
$419$	−28.5404	−	10.3878i	−1.39429	−	0.507480i	−0.926478	+	0.376349i	$0.877179\pi$
$420$		0			0
$421$	5.43779	−	30.8393i	0.265022	−	1.50301i	−0.503951	−	0.863732i	$-0.668121\pi$
$421$	5.43779	−	30.8393i	0.265022	−	1.50301i	0.768973	−	0.639281i	$-0.220768\pi$
$422$	11.8986			0.579214
$423$		0			0
$424$	−4.47737			−0.217440
$425$	3.33327	−	1.21321i	0.161687	−	0.0588493i
$426$		0			0
$427$	13.8663	+	0.880919i	0.671036	+	0.0426307i
$428$	12.5612	−	10.5401i	0.607168	−	0.509475i
$429$		0			0
$430$	6.74233	+	5.65748i	0.325144	+	0.272828i
$431$	5.25777	+	9.10673i	0.253258	+	0.438656i	0.964421	−	0.264372i	$-0.0851645\pi$
$431$	5.25777	+	9.10673i	0.253258	+	0.438656i	−0.711163	+	0.703027i	$0.751831\pi$
$432$		0			0
$433$	−6.33812			−0.304591			−0.152295	−	0.988335i	$-0.548667\pi$
$433$	−6.33812			−0.304591			−0.152295	+	0.988335i	$0.548667\pi$
$434$	−26.5946	+	19.5821i	−1.27658	+	0.939970i
$435$		0			0
$436$	4.90917	+	27.8413i	0.235107	+	1.33336i
$437$	−1.04932	+	0.880484i	−0.0501958	+	0.0421193i
$438$		0			0
$439$	−19.0176	+	6.92183i	−0.907659	+	0.330361i	−0.753318	−	0.657657i	$-0.771548\pi$
$439$	−19.0176	+	6.92183i	−0.907659	+	0.330361i	−0.154341	+	0.988018i	$0.549326\pi$
$440$	3.21591	−	5.57011i	0.153312	−	0.265545i
$441$		0			0
$442$	1.14059	+	1.97556i	0.0542523	+	0.0939677i
$443$	−6.80079	−	5.70654i	−0.323115	−	0.271126i	0.466772	−	0.884377i	$-0.345417\pi$
$443$	−6.80079	−	5.70654i	−0.323115	−	0.271126i	−0.789888	+	0.613252i	$0.789861\pi$
$444$		0			0
$445$	0.156235	+	0.886055i	0.00740627	+	0.0420030i
$446$	8.26552	−	6.93559i	0.391384	−	0.328410i
$447$		0			0
$448$	−1.02027	−	9.14647i	−0.0482032	−	0.432130i
$449$	−6.01834	−	10.4241i	−0.284023	−	0.491943i	0.688349	−	0.725380i	$-0.258336\pi$
$449$	−6.01834	−	10.4241i	−0.284023	−	0.491943i	−0.972372	+	0.233437i	$0.925003\pi$
$450$		0			0
$451$	54.2142			2.55285
$452$	−2.01989	+	11.4553i	−0.0950075	+	0.538814i
$453$		0			0
$454$	−4.15608	−	23.5703i	−0.195055	−	1.10621i
$455$	1.69353	+	3.41684i	0.0793937	+	0.160184i
$456$		0			0
$457$	−0.558880	+	3.16957i	−0.0261433	+	0.148266i	−0.995085	−	0.0990224i	$-0.968428\pi$
$457$	−0.558880	+	3.16957i	−0.0261433	+	0.148266i	0.968942	+	0.247289i	$0.0795396\pi$
$458$	5.46990	+	9.47414i	0.255591	+	0.442697i
$459$		0			0
$460$	1.03560	−	1.79370i	0.0482849	−	0.0836319i
$461$	−32.0957	+	11.6819i	−1.49485	+	0.544080i	−0.954720	−	0.297505i	$-0.903846\pi$
$461$	−32.0957	+	11.6819i	−1.49485	+	0.544080i	−0.540126	+	0.841584i	$0.681623\pi$
$462$		0			0
$463$	8.38189	−	7.03324i	0.389539	−	0.326862i	−0.426894	−	0.904302i	$-0.640392\pi$
$463$	8.38189	−	7.03324i	0.389539	−	0.326862i	0.816434	+	0.577439i	$0.195948\pi$
$464$	24.7255	+	8.99933i	1.14785	+	0.417784i
$465$		0			0
$466$	−0.314897	+	1.78587i	−0.0145873	+	0.0827288i
$467$	−20.7032	−	35.8590i	−0.958031	−	1.65936i	−0.727275	−	0.686346i	$-0.759214\pi$
$467$	−20.7032	−	35.8590i	−0.958031	−	1.65936i	−0.230755	−	0.973012i	$-0.574120\pi$
$468$		0			0
$469$	−8.19447	+	33.7813i	−0.378385	+	1.55988i
$470$	−5.36849	+	30.4462i	−0.247630	+	1.40438i
$471$		0			0
$472$	−1.05513	−	5.98392i	−0.0485662	−	0.275432i
$473$	2.55536	+	14.4922i	0.117496	+	0.666350i
$474$		0			0
$475$	−0.713082	+	4.04409i	−0.0327184	+	0.185555i
$476$	−4.67367	+	1.37243i	−0.214217	+	0.0629051i
$477$		0			0
$478$	−22.1736	−	38.4057i	−1.01420	−	1.75664i
$479$	−1.44178	+	8.17673i	−0.0658765	+	0.373604i	0.933990	+	0.357298i	$0.116302\pi$
$479$	−1.44178	+	8.17673i	−0.0658765	+	0.373604i	−0.999867	+	0.0163066i	$0.994809\pi$
$480$		0			0
$481$	−2.67333	−	0.973012i	−0.121893	−	0.0443655i
$482$	−0.409274	+	0.343422i	−0.0186419	+	0.0156424i
$483$		0			0
$484$	−13.7341	+	4.99880i	−0.624277	+	0.227218i
$485$	4.17576	−	7.23263i	0.189612	−	0.328417i
$486$		0			0
$487$	11.9736	+	20.7388i	0.542574	+	0.939766i	0.998755	+	0.0498789i	$0.0158835\pi$
$487$	11.9736	+	20.7388i	0.542574	+	0.939766i	−0.456181	+	0.889887i	$0.650783\pi$
$488$	−0.878029	+	4.97955i	−0.0397465	+	0.225414i
$489$		0			0
$490$	−18.6463	+	4.21231i	−0.842352	+	0.190293i
$491$	−6.82562	−	38.7100i	−0.308036	−	1.74696i	−0.608859	−	0.793278i	$-0.708373\pi$
$491$	−6.82562	−	38.7100i	−0.308036	−	1.74696i	0.300823	−	0.953680i	$-0.402739\pi$
$492$		0			0
$493$	1.18932	−	6.74498i	0.0535643	−	0.303778i
$494$	−2.64085			−0.118817
$495$		0			0
$496$	−15.9347	−	27.5998i	−0.715491	−	1.23927i
$497$	−3.40586	−	30.5327i	−0.152774	−	1.36958i
$498$		0			0
$499$	−4.79773	+	4.02577i	−0.214776	+	0.180218i	−0.743828	−	0.668371i	$-0.766992\pi$
$499$	−4.79773	+	4.02577i	−0.214776	+	0.180218i	0.529052	+	0.848589i	$0.322548\pi$
$500$	−2.96350	−	16.8068i	−0.132532	−	0.751625i
$501$		0			0
$502$	11.2023	+	9.39988i	0.499985	+	0.419537i
$503$	1.54894	+	2.68284i	0.0690637	+	0.119622i	0.898489	−	0.438995i	$-0.144665\pi$
$503$	1.54894	+	2.68284i	0.0690637	+	0.119622i	−0.829426	+	0.558617i	$0.811332\pi$
$504$		0			0
$505$	−8.66337	+	15.0054i	−0.385515	+	0.667731i
$506$	7.63918	−	2.78044i	0.339603	−	0.123605i
$507$		0			0
$508$	14.4434	−	12.1195i	0.640824	−	0.537715i
$509$	0.840121	+	4.76457i	0.0372377	+	0.211186i	0.997749	−	0.0670543i	$-0.0213601\pi$
$509$	0.840121	+	4.76457i	0.0372377	+	0.211186i	−0.960512	+	0.278240i	$0.910249\pi$
$510$		0			0
$511$	−24.0690	−	10.5330i	−1.06475	−	0.465954i
$512$	24.0378			1.06233
$513$		0			0
$514$	−9.01718	−	15.6182i	−0.397731	−	0.688890i
$515$	14.3828	+	12.0686i	0.633781	+	0.531805i
$516$		0			0
$517$	−39.5970	+	33.2258i	−1.74147	+	1.46127i
$518$	7.89904	−	11.8732i	0.347064	−	0.521680i
$519$		0			0
$520$	−1.30411	+	0.474658i	−0.0571891	+	0.0208151i
$521$	30.4398			1.33359			0.666796	−	0.745240i	$-0.267665\pi$
$521$	30.4398			1.33359			0.666796	+	0.745240i	$0.267665\pi$
$522$		0			0
$523$	33.7422			1.47545			0.737723	−	0.675104i	$-0.235901\pi$
$523$	33.7422			1.47545			0.737723	+	0.675104i	$0.235901\pi$
$524$	2.16367	−	12.2708i	0.0945203	−	0.536051i
$525$		0			0
$526$	32.1493	+	11.7014i	1.40177	+	0.510204i
$527$	−6.35476	+	5.33228i	−0.276818	+	0.232278i
$528$		0			0
$529$	20.7580	−	7.55528i	0.902520	−	0.328490i
$530$	12.6991			0.551612
$531$		0			0
$532$	1.32933	−	5.48010i	0.0576338	−	0.237593i
$533$	−8.96113	−	7.51928i	−0.388149	−	0.325696i
$534$		0			0
$535$	12.3822	−	10.3899i	0.535330	−	0.449195i
$536$	−11.8873	−	4.32662i	−0.513452	−	0.186881i
$537$		0			0
$538$	−8.01357	+	2.91670i	−0.345490	+	0.125748i
$539$	−28.4091	−	14.6443i	−1.22367	−	0.630775i
$540$		0			0
$541$	7.87553	−	13.6408i	0.338596	−	0.586465i	−0.645573	−	0.763698i	$-0.723382\pi$
$541$	7.87553	−	13.6408i	0.338596	−	0.586465i	0.984169	+	0.177234i	$0.0567148\pi$
$542$	18.8949	+	15.8547i	0.811604	+	0.681017i
$543$		0			0
$544$	−1.50131	−	8.51437i	−0.0643683	−	0.365050i
$545$	4.83922	+	27.4446i	0.207289	+	1.17560i
$546$		0			0
$547$	−16.6514	−	13.9722i	−0.711963	−	0.597408i	0.213186	−	0.977012i	$-0.431616\pi$
$547$	−16.6514	−	13.9722i	−0.711963	−	0.597408i	−0.925149	+	0.379603i	$0.876060\pi$
$548$	−1.72399	−	2.98604i	−0.0736452	−	0.127557i
$549$		0			0
$550$	12.1856	−	21.1060i	0.519595	−	0.899964i
$551$	6.07390	+	5.09661i	0.258757	+	0.217123i
$552$		0			0
$553$	−20.7364	+	31.1694i	−0.881803	+	1.32546i
$554$	53.2784	+	19.3918i	2.26358	+	0.823877i
$555$		0			0
$556$	−29.9705	+	10.9084i	−1.27103	+	0.462618i
$557$	12.3971	−	21.4723i	0.525280	−	0.909811i	−0.474287	−	0.880370i	$-0.657294\pi$
$557$	12.3971	−	21.4723i	0.525280	−	0.909811i	0.999567	−	0.0294409i	$-0.00937270\pi$
$558$		0			0
$559$	1.58762	−	2.74984i	0.0671493	−	0.116306i
$560$	−2.04499	−	18.3329i	−0.0864168	−	0.774707i
$561$		0			0
$562$	34.1630	+	12.4343i	1.44108	+	0.524509i
$563$	17.9677	+	6.53971i	0.757248	+	0.275616i	0.691652	−	0.722230i	$-0.256883\pi$
$563$	17.9677	+	6.53971i	0.757248	+	0.275616i	0.0655957	+	0.997846i	$0.479105\pi$
$564$		0			0
$565$	−1.99111	+	11.2921i	−0.0837665	+	0.475063i
$566$	14.3927			0.604968
$567$		0			0
$568$	11.1803			0.469117
$569$	3.50374	−	19.8707i	0.146884	−	0.833022i	−0.818951	−	0.573864i	$-0.805444\pi$
$569$	3.50374	−	19.8707i	0.146884	−	0.833022i	0.965835	−	0.259158i	$-0.0834451\pi$
$570$		0			0
$571$	−1.27023	−	0.462325i	−0.0531574	−	0.0193477i	0.315305	−	0.948991i	$-0.397893\pi$
$571$	−1.27023	−	0.462325i	−0.0531574	−	0.0193477i	−0.368462	+	0.929643i	$0.620116\pi$
$572$	6.27367	+	2.28343i	0.262315	+	0.0954750i
$573$		0			0
$574$	47.2192	−	34.7684i	1.97089	−	1.45120i
$575$	−1.36380	+	2.36218i	−0.0568746	+	0.0985096i
$576$		0			0
$577$	−6.07544	+	10.5230i	−0.252924	+	0.438077i	−0.964330	−	0.264705i	$-0.914726\pi$
$577$	−6.07544	+	10.5230i	−0.252924	+	0.438077i	0.711406	+	0.702782i	$0.248059\pi$
$578$	27.1194	−	9.87065i	1.12802	−	0.410565i
$579$		0			0
$580$	−11.2659	−	4.10045i	−0.467791	−	0.170262i
$581$	−21.9764	−	1.39616i	−0.911737	−	0.0579223i
$582$		0			0
$583$	16.2649	+	13.6479i	0.673623	+	0.565237i
$584$	4.78058	−	8.28021i	0.197822	−	0.342638i
$585$		0			0
$586$	12.7661	+	22.1116i	0.527365	+	0.913422i
$587$	36.1996	+	30.3750i	1.49412	+	1.25371i	0.889282	+	0.457360i	$0.151205\pi$
$587$	36.1996	+	30.3750i	1.49412	+	1.25371i	0.604834	+	0.796352i	$0.293239\pi$
$588$		0			0
$589$	−1.66763	−	9.45762i	−0.0687136	−	0.389694i
$590$	2.99263	+	16.9721i	0.123205	+	0.698728i
$591$		0			0
$592$	10.5417	+	8.84557i	0.433263	+	0.363551i
$593$	−5.30960	+	9.19649i	−0.218039	+	0.377655i	−0.954208	−	0.299143i	$-0.903299\pi$
$593$	−5.30960	+	9.19649i	−0.218039	+	0.377655i	0.736169	+	0.676797i	$0.236633\pi$
$594$		0			0
$595$	−4.60708	+	1.35287i	−0.188872	+	0.0554623i
$596$	6.12600	−	2.22968i	0.250931	−	0.0913314i
$597$		0			0
$598$	−1.64832	−	0.599941i	−0.0674050	−	0.0245334i
$599$	−7.85627	+	6.59219i	−0.320999	+	0.269350i	−0.789020	−	0.614367i	$-0.789411\pi$
$599$	−7.85627	+	6.59219i	−0.320999	+	0.269350i	0.468022	+	0.883717i	$0.344967\pi$
$600$		0			0
$601$	−19.1642	−	16.0807i	−0.781724	−	0.655945i	0.161958	−	0.986798i	$-0.448219\pi$
$601$	−19.1642	−	16.0807i	−0.781724	−	0.655945i	−0.943682	+	0.330853i	$0.892664\pi$
$602$	11.5197	+	10.9835i	0.469508	+	0.447655i
$603$		0			0
$604$	21.9994			0.895143
$605$	−13.5384	+	4.92757i	−0.550414	+	0.200334i
$606$		0			0
$607$	0.503454	−	0.422448i	0.0204346	−	0.0171466i	−0.632513	−	0.774550i	$-0.717977\pi$
$607$	0.503454	−	0.422448i	0.0204346	−	0.0171466i	0.652948	+	0.757403i	$0.273532\pi$
$608$	9.40528	+	3.42324i	0.381434	+	0.138831i
$609$		0			0
$610$	2.49033	−	14.1234i	0.100831	−	0.571839i
$611$	11.1533			0.451214
$612$		0			0
$613$	−27.7448			−1.12060			−0.560301	−	0.828289i	$-0.689314\pi$
$613$	−27.7448			−1.12060			−0.560301	+	0.828289i	$0.689314\pi$
$614$	30.5435	−	11.1169i	1.23263	−	0.448642i
$615$		0			0
$616$	6.44263	−	9.68406i	0.259581	−	0.390182i
$617$	−12.7820	+	10.7253i	−0.514582	+	0.431786i	−0.862738	−	0.505651i	$-0.831252\pi$
$617$	−12.7820	+	10.7253i	−0.514582	+	0.431786i	0.348156	+	0.937437i	$0.386808\pi$
$618$		0			0
$619$	−7.28444	−	6.11237i	−0.292787	−	0.245677i	0.484548	−	0.874765i	$-0.338984\pi$
$619$	−7.28444	−	6.11237i	−0.292787	−	0.245677i	−0.777334	+	0.629088i	$0.783429\pi$
$620$	7.26050	+	12.5755i	0.291589	+	0.505046i
$621$		0			0
$622$	−55.7920			−2.23705
$623$	0.180377	+	1.61704i	0.00722667	+	0.0647854i
$624$		0			0
$625$	−0.438492	−	2.48681i	−0.0175397	−	0.0994725i
$626$	4.53510	−	3.80540i	0.181259	−	0.152094i
$627$		0			0
$628$	−0.527500	+	0.191994i	−0.0210495	+	0.00766141i
$629$	1.79101	−	3.10213i	0.0714124	−	0.123690i
$630$		0			0
$631$	−22.9465	−	39.7445i	−0.913486	−	1.58220i	−0.809103	−	0.587667i	$-0.800047\pi$
$631$	−22.9465	−	39.7445i	−0.913486	−	1.58220i	−0.104383	−	0.994537i	$-0.533287\pi$
$632$	−10.4366	−	8.75737i	−0.415147	−	0.348349i
$633$		0			0
$634$	2.16476	+	12.2770i	0.0859737	+	0.487581i
$635$	14.2376	−	11.9468i	0.565003	−	0.474094i
$636$		0			0
$637$	2.66467	+	6.36079i	0.105578	+	0.252024i
$638$	−23.5283	−	40.7523i	−0.931495	−	1.61340i
$639$		0			0
$640$	10.8945			0.430641
$641$	4.98155	−	28.2518i	0.196759	−	1.11588i	−0.713132	−	0.701030i	$-0.752724\pi$
$641$	4.98155	−	28.2518i	0.196759	−	1.11588i	0.909891	−	0.414847i	$-0.136165\pi$
$642$		0			0
$643$	0.172431	+	0.977906i	0.00680002	+	0.0385648i	0.988019	−	0.154332i	$-0.0493227\pi$
$643$	0.172431	+	0.977906i	0.00680002	+	0.0385648i	−0.981219	+	0.192897i	$0.938212\pi$
$644$	2.07467	−	3.11849i	0.0817536	−	0.122886i
$645$		0			0
$646$	0.577400	−	3.27460i	0.0227175	−	0.128837i
$647$	−8.87356	−	15.3695i	−0.348856	−	0.604236i	0.637191	−	0.770706i	$-0.280096\pi$
$647$	−8.87356	−	15.3695i	−0.348856	−	0.604236i	−0.986046	+	0.166470i	$0.946763\pi$
$648$		0			0
$649$	−14.4072	+	24.9540i	−0.565531	+	0.979528i
$650$	−4.94148	+	1.79855i	−0.193821	+	0.0705451i
$651$		0			0
$652$	5.86857	−	4.92432i	0.229831	−	0.192851i
$653$	−17.1213	−	6.23165i	−0.670008	−	0.243863i	−0.0154569	−	0.999881i	$-0.504920\pi$
$653$	−17.1213	−	6.23165i	−0.670008	−	0.243863i	−0.654552	+	0.756017i	$0.727143\pi$
$654$		0			0
$655$	2.13284	−	12.0959i	0.0833370	−	0.472627i
$656$	28.2925	+	49.0040i	1.10463	+	1.91328i
$657$		0			0
$658$	−13.1798	+	54.3330i	−0.513800	+	2.11812i
$659$	0.516836	−	2.93112i	0.0201331	−	0.114180i	−0.973085	−	0.230446i	$-0.925981\pi$
$659$	0.516836	−	2.93112i	0.0201331	−	0.114180i	0.993218	+	0.116266i	$0.0370925\pi$
$660$		0			0
$661$	4.25035	+	24.1049i	0.165320	+	0.937574i	0.948734	+	0.316075i	$0.102365\pi$
$661$	4.25035	+	24.1049i	0.165320	+	0.937574i	−0.783415	+	0.621499i	$0.786524\pi$
$662$	1.61720	+	9.17158i	0.0628541	+	0.356463i
$663$		0			0
$664$	1.39158	−	7.89202i	0.0540036	−	0.306270i
$665$	1.31039	−	5.40202i	0.0508147	−	0.209481i
$666$		0			0
$667$	2.63328	+	4.56097i	0.101961	+	0.176602i
$668$	2.80268	−	15.8948i	0.108439	−	0.614987i
$669$		0			0
$670$	33.7156	+	12.2715i	1.30255	+	0.474089i
$671$	18.3682	−	15.4128i	0.709097	−	0.595003i
$672$		0			0
$673$	23.3965	−	8.51562i	0.901868	−	0.328253i	0.150867	−	0.988554i	$-0.451794\pi$
$673$	23.3965	−	8.51562i	0.901868	−	0.328253i	0.751001	+	0.660301i	$0.229571\pi$
$674$	13.5871	−	23.5336i	0.523356	−	0.906480i
$675$		0			0
$676$	8.92685	+	15.4618i	0.343340	+	0.594683i
$677$	−1.53657	+	8.71430i	−0.0590550	+	0.334918i	−0.999993	−	0.00366049i	$-0.998835\pi$
$677$	−1.53657	+	8.71430i	−0.0590550	+	0.334918i	0.940938	+	0.338578i	$0.109946\pi$
$678$		0			0
$679$	8.36556	−	12.5745i	0.321041	−	0.482564i
$680$	−0.303432	−	1.72085i	−0.0116361	−	0.0659916i
$681$		0			0
$682$	−9.89709	+	56.1292i	−0.378979	+	2.14930i
$683$	−6.28032			−0.240310			−0.120155	−	0.992755i	$-0.538339\pi$
$683$	−6.28032			−0.240310			−0.120155	+	0.992755i	$0.538339\pi$
$684$		0			0
$685$	−1.69943	−	2.94349i	−0.0649317	−	0.112465i
$686$	−34.1352	+	5.46435i	−1.30329	+	0.208630i
$687$		0			0
$688$	−11.7658	+	9.87272i	−0.448569	+	0.376394i
$689$	−0.795542	−	4.51174i	−0.0303077	−	0.171884i
$690$		0			0
$691$	−8.61563	−	7.22938i	−0.327754	−	0.275018i	0.464030	−	0.885820i	$-0.346403\pi$
$691$	−8.61563	−	7.22938i	−0.327754	−	0.275018i	−0.791784	+	0.610801i	$0.790847\pi$
$692$	8.98622	+	15.5646i	0.341605	+	0.591677i
$693$		0			0
$694$	−8.11448	+	14.0547i	−0.308022	+	0.533509i
$695$	−29.5435	+	10.7529i	−1.12065	+	0.407882i
$696$		0			0
$697$	11.2830	−	9.46757i	0.427374	−	0.358610i
$698$	3.59312	+	20.3776i	0.136001	+	0.771302i
$699$		0			0
$700$	−1.24482	−	11.1596i	−0.0470499	−	0.421791i
$701$	−11.0400			−0.416976			−0.208488	−	0.978025i	$-0.566854\pi$
$701$	−11.0400			−0.416976			−0.208488	+	0.978025i	$0.566854\pi$
$702$		0			0
$703$	2.07340	+	3.59124i	0.0781999	+	0.135446i
$704$	−12.1667	−	10.2090i	−0.458549	−	0.384768i
$705$		0			0
$706$	33.1111	−	27.7835i	1.24615	−	1.04565i
$707$	−17.3559	+	26.0880i	−0.652735	+	0.981140i
$708$		0			0
$709$	17.8195	−	6.48575i	0.669224	−	0.243577i	0.0150100	−	0.999887i	$-0.495222\pi$
$709$	17.8195	−	6.48575i	0.669224	−	0.243577i	0.654214	+	0.756310i	$0.273000\pi$
$710$	−31.7105			−1.19008
$711$		0			0
$712$	−0.592121			−0.0221907
$713$	1.10768	−	6.28195i	0.0414828	−	0.235261i
$714$		0			0
$715$	6.18428	+	2.25089i	0.231279	+	0.0841786i
$716$	−14.0728	+	11.8085i	−0.525926	+	0.441304i
$717$		0			0
$718$	−3.64717	+	1.32746i	−0.136111	+	0.0495404i
$719$	−3.54116			−0.132063			−0.0660316	−	0.997818i	$-0.521034\pi$
$719$	−3.54116			−0.132063			−0.0660316	+	0.997818i	$0.521034\pi$
$720$		0			0
$721$	24.5739	+	23.4301i	0.915179	+	0.872583i
$722$	−24.2192	−	20.3223i	−0.901345	−	0.756318i
$723$		0			0
$724$	18.0432	−	15.1400i	0.670569	−	0.562674i
$725$	14.8364	+	5.40000i	0.551009	+	0.200551i
$726$		0			0
$727$	34.1662	−	12.4355i	1.26715	−	0.461206i	0.380990	−	0.924579i	$-0.375583\pi$
$727$	34.1662	−	12.4355i	1.26715	−	0.461206i	0.886163	+	0.463373i	$0.153361\pi$
$728$	−2.40805	+	0.707124i	−0.0892481	+	0.0262078i
$729$		0			0
$730$	−13.5590	+	23.4850i	−0.501843	+	0.869217i
$731$	3.06262	+	2.56985i	0.113275	+	0.0950492i
$732$		0			0
$733$	−3.73447	−	21.1792i	−0.137936	−	0.782272i	−0.972770	−	0.231771i	$-0.925548\pi$
$733$	−3.73447	−	21.1792i	−0.137936	−	0.782272i	0.834835	−	0.550501i	$-0.185563\pi$
$734$	−4.96227	−	28.1425i	−0.183161	−	1.03876i
$735$		0			0
$736$	5.09275	+	4.27333i	0.187721	+	0.157517i
$737$	29.9945	+	51.9519i	1.10486	+	1.91367i
$738$		0			0
$739$	−3.59765	+	6.23131i	−0.132342	+	0.229223i	−0.924579	−	0.380991i	$-0.875583\pi$
$739$	−3.59765	+	6.23131i	−0.132342	+	0.229223i	0.792237	+	0.610213i	$0.208916\pi$
$740$	−4.80323	−	4.03039i	−0.176570	−	0.148160i
$741$		0			0
$742$	22.9189	+	1.45603i	0.841380	+	0.0534525i
$743$	5.28136	+	1.92226i	0.193754	+	0.0705207i	0.437075	−	0.899425i	$-0.356015\pi$
$743$	5.28136	+	1.92226i	0.193754	+	0.0705207i	−0.243321	+	0.969946i	$0.578237\pi$
$744$		0			0
$745$	6.03872	−	2.19791i	0.221242	−	0.0805253i
$746$	−28.6232	+	49.5768i	−1.04797	+	1.81513i
$747$		0			0
$748$	−4.20308	+	7.27996i	−0.153680	+	0.266182i
$749$	23.5383	−	17.3317i	0.860072	−	0.633287i
$750$		0			0
$751$	−40.3558	−	14.6883i	−1.47260	−	0.535984i	−0.523797	−	0.851843i	$-0.675485\pi$
$751$	−40.3558	−	14.6883i	−1.47260	−	0.535984i	−0.948806	+	0.315860i	$0.897707\pi$
$752$	−50.6969	−	18.4522i	−1.84873	−	0.672881i
$753$		0			0
$754$	−1.76314	+	9.99926i	−0.0642098	+	0.364152i
$755$	21.6859			0.789232
$756$		0			0
$757$	−18.7190			−0.680354			−0.340177	−	0.940361i	$-0.610487\pi$
$757$	−18.7190			−0.680354			−0.340177	+	0.940361i	$0.610487\pi$
$758$	10.7373	−	60.8943i	0.389997	−	2.21178i
$759$		0			0
$760$	1.90091	+	0.691876i	0.0689533	+	0.0250970i
$761$	−11.7685	−	4.28340i	−0.426609	−	0.155273i	0.119787	−	0.992800i	$-0.461779\pi$
$761$	−11.7685	−	4.28340i	−0.426609	−	0.155273i	−0.546397	+	0.837526i	$0.684001\pi$
$762$		0			0
$763$	5.58699	+	50.0861i	0.202263	+	1.81324i
$764$	−11.2817	+	19.5404i	−0.408157	+	0.706948i
$765$		0			0
$766$	−11.0880	+	19.2050i	−0.400626	+	0.693904i
$767$	5.84238	−	2.12645i	0.210956	−	0.0767818i
$768$		0			0
$769$	18.4388	+	6.71117i	0.664920	+	0.242011i	0.652359	−	0.757910i	$-0.273779\pi$
$769$	18.4388	+	6.71117i	0.664920	+	0.242011i	0.0125608	+	0.999921i	$0.496002\pi$
$770$	−18.2731	+	27.4667i	−0.658516	+	0.989830i
$771$		0			0
$772$	−21.3757	−	17.9363i	−0.769327	−	0.645542i
$773$	5.39853	−	9.35052i	0.194171	−	0.336315i	−0.752457	−	0.658641i	$-0.771132\pi$
$773$	5.39853	−	9.35052i	0.194171	−	0.336315i	0.946629	+	0.322326i	$0.104465\pi$
$774$		0			0
$775$	−9.56154	−	16.5611i	−0.343461	−	0.594891i
$776$	4.21038	+	3.53293i	0.151144	+	0.126825i
$777$		0			0
$778$	−7.41343	−	42.0436i	−0.265784	−	1.50734i
$779$	2.96092	+	16.7922i	0.106086	+	0.601643i
$780$		0			0
$781$	−40.6147	−	34.0798i	−1.45331	−	1.21947i
$782$	1.10431	−	1.91271i	0.0394899	−	0.0683985i
$783$		0			0
$784$	−1.58876	−	33.3212i	−0.0567415	−	1.19004i
$785$	−0.519984	+	0.189259i	−0.0185590	+	0.00675493i
$786$		0			0
$787$	−39.4055	−	14.3424i	−1.40465	−	0.511252i	−0.475097	−	0.879933i	$-0.657587\pi$
$787$	−39.4055	−	14.3424i	−1.40465	−	0.511252i	−0.929556	+	0.368681i	$0.879809\pi$
$788$	0.296895	−	0.249125i	0.0105765	−	0.00887471i
$789$		0			0
$790$	29.6012	+	24.8383i	1.05316	+	0.883708i
$791$	−4.88821	+	20.1514i	−0.173805	+	0.716502i
$792$		0			0
$793$	−5.17379			−0.183727
$794$	−39.1052	+	14.2331i	−1.38779	+	0.505115i
$795$		0			0
$796$	−1.86182	+	1.56225i	−0.0659905	+	0.0553726i
$797$	12.2053	+	4.44238i	0.432335	+	0.157357i	0.549015	−	0.835812i	$-0.315003\pi$
$797$	12.2053	+	4.44238i	0.432335	+	0.157357i	−0.116680	+	0.993170i	$0.537225\pi$
$798$		0			0
$799$	−2.43857	+	13.8298i	−0.0862705	+	0.489265i
$800$	19.9303			0.704642
$801$		0			0
$802$	−9.44356			−0.333464
$803$	−42.6060	+	15.5073i	−1.50353	+	0.547241i
$804$		0			0
$805$	2.04511	−	3.07406i	0.0720808	−	0.108346i
$806$	9.42078	−	7.90497i	0.331833	−	0.278441i
$807$		0			0
$808$	−8.73519	−	7.32969i	−0.307303	−	0.257858i
$809$	14.8787	+	25.7707i	0.523109	+	0.906051i	0.999638	+	0.0268927i	$0.00856125\pi$
$809$	14.8787	+	25.7707i	0.523109	+	0.906051i	−0.476529	+	0.879159i	$0.658105\pi$
$810$		0			0
$811$	38.9051			1.36614			0.683072	−	0.730351i	$-0.260643\pi$
$811$	38.9051			1.36614			0.683072	+	0.730351i	$0.260643\pi$
$812$	−19.8622	−	8.69209i	−0.697028	−	0.305033i
$813$		0			0
$814$	−4.27357	−	24.2366i	−0.149789	−	0.849493i
$815$	5.78496	−	4.85415i	0.202638	−	0.170034i
$816$		0			0
$817$	−4.34921	+	1.58298i	−0.152160	+	0.0553816i
$818$	−21.2271	+	36.7664i	−0.742188	+	1.28551i
$819$		0			0
$820$	−12.8912	−	22.3281i	−0.450179	−	0.779733i
$821$	−30.4574	−	25.5568i	−1.06297	−	0.891939i	−0.0685747	−	0.997646i	$-0.521845\pi$
$821$	−30.4574	−	25.5568i	−1.06297	−	0.891939i	−0.994397	+	0.105707i	$0.966290\pi$
$822$		0			0
$823$	−6.77095	−	38.3999i	−0.236020	−	1.33854i	−0.840454	−	0.541883i	$-0.817712\pi$
$823$	−6.77095	−	38.3999i	−0.236020	−	1.33854i	0.604434	−	0.796655i	$-0.293399\pi$
$824$	−9.46551	+	7.94251i	−0.329747	+	0.276690i
$825$		0			0
$826$	3.45506	+	30.9738i	0.120217	+	1.07772i
$827$	−15.3937	−	26.6626i	−0.535290	−	0.927150i	−0.999149	−	0.0412408i	$-0.986869\pi$
$827$	−15.3937	−	26.6626i	−0.535290	−	0.927150i	0.463859	−	0.885909i	$-0.346464\pi$
$828$		0			0
$829$	−25.5293			−0.886669			−0.443335	−	0.896356i	$-0.646205\pi$
$829$	−25.5293			−0.886669			−0.443335	+	0.896356i	$0.646205\pi$
$830$	−3.94689	+	22.3839i	−0.136999	+	0.776958i
$831$		0			0
$832$	0.595091	+	3.37493i	0.0206311	+	0.117005i
$833$	−8.46984	+	1.91339i	−0.293463	+	0.0662951i
$834$		0			0
$835$	2.76274	−	15.6683i	0.0956087	−	0.542224i
$836$	−4.86579	−	8.42779i	−0.168287	−	0.291481i
$837$		0			0
$838$	−28.3461	+	49.0969i	−0.979201	+	1.69603i
$839$	15.4625	−	5.62791i	0.533826	−	0.194297i	−0.0610197	−	0.998137i	$-0.519435\pi$
$839$	15.4625	−	5.62791i	0.533826	−	0.194297i	0.594846	+	0.803840i	$0.297213\pi$
$840$		0			0
$841$	1.13760	−	0.954559i	0.0392275	−	0.0329158i
$842$	−54.9273	−	19.9919i	−1.89292	−	0.688966i
$843$		0			0
$844$	1.64286	−	9.31712i	0.0565495	−	0.320708i
$845$	8.79965	+	15.2414i	0.302717	+	0.524322i
$846$		0			0
$847$	−24.9987	+	7.34088i	−0.858965	+	0.252236i
$848$	−3.84818	+	21.8241i	−0.132147	+	0.749443i
$849$		0			0
$850$	−1.14975	−	6.52057i	−0.0394362	−	0.223654i
$851$	0.478296	+	2.71255i	0.0163958	+	0.0929851i
$852$		0			0
$853$	−1.40699	+	7.97942i	−0.0481743	+	0.273210i	−0.999374	−	0.0353643i	$-0.988741\pi$
$853$	−1.40699	+	7.97942i	−0.0481743	+	0.273210i	0.951200	+	0.308575i	$0.0998519\pi$
$854$	6.11382	−	25.2039i	0.209211	−	0.862461i
$855$		0			0
$856$	5.31883	+	9.21248i	0.181794	+	0.314876i
$857$	1.18534	−	6.72238i	0.0404903	−	0.229632i	−0.957847	−	0.287280i	$-0.907249\pi$
$857$	1.18534	−	6.72238i	0.0404903	−	0.229632i	0.998337	+	0.0576480i	$0.0183601\pi$
$858$		0			0
$859$	42.9069	+	15.6168i	1.46397	+	0.532840i	0.946455	−	0.322837i	$-0.104636\pi$
$859$	42.9069	+	15.6168i	1.46397	+	0.532840i	0.517511	+	0.855677i	$0.326859\pi$
$860$	5.36099	−	4.49840i	0.182808	−	0.153394i
$861$		0			0
$862$	18.4445	−	6.71326i	0.628223	−	0.228655i
$863$	−0.791478	+	1.37088i	−0.0269422	+	0.0466653i	−0.879182	−	0.476486i	$-0.841910\pi$
$863$	−0.791478	+	1.37088i	−0.0269422	+	0.0466653i	0.852240	+	0.523151i	$0.175244\pi$
$864$		0			0
$865$	8.85818	+	15.3428i	0.301187	+	0.521672i
$866$	−2.05438	+	11.6510i	−0.0698107	+	0.395916i
$867$		0			0
$868$	11.6617	+	23.5285i	0.395823	+	0.798608i
$869$	11.2189	+	63.6256i	0.380575	+	2.15835i
$870$		0			0
$871$	2.24769	−	12.7473i	0.0761601	−	0.431926i
$872$	−18.3403			−0.621081
$873$		0			0
$874$	1.27842	+	2.21429i	0.0432433	+	0.0748995i
$875$	−3.37268	−	30.2353i	−0.114017	−	1.02214i
$876$		0			0
$877$	17.0243	−	14.2851i	0.574869	−	0.482372i	−0.308389	−	0.951260i	$-0.599790\pi$
$877$	17.0243	−	14.2851i	0.574869	−	0.482372i	0.883257	+	0.468888i	$0.155345\pi$
$878$	6.55978	+	37.2024i	0.221382	+	1.25552i
$879$		0			0
$880$	−24.3865	−	20.4627i	−0.822068	−	0.689797i
$881$	−12.8210	−	22.2065i	−0.431949	−	0.748158i	0.565092	−	0.825028i	$-0.308841\pi$
$881$	−12.8210	−	22.2065i	−0.431949	−	0.748158i	−0.997041	+	0.0768702i	$0.975507\pi$
$882$		0			0
$883$	−17.2315	+	29.8458i	−0.579886	+	1.00439i	0.415606	+	0.909545i	$0.363569\pi$
$883$	−17.2315	+	29.8458i	−0.579886	+	1.00439i	−0.995492	+	0.0948467i	$0.969764\pi$
$884$	1.70443	−	0.620362i	0.0573262	−	0.0208650i
$885$		0			0
$886$	−12.6943	+	10.6518i	−0.426474	+	0.357854i
$887$	−2.16361	−	12.2704i	−0.0726469	−	0.412001i	−0.999345	−	0.0361938i	$-0.988477\pi$
$887$	−2.16361	−	12.2704i	−0.0726469	−	0.412001i	0.926698	−	0.375807i	$-0.122634\pi$
$888$		0			0
$889$	27.0655	−	19.9288i	0.907746	−	0.668390i
$890$	1.67942			0.0562943
$891$		0			0
$892$	−4.28964	−	7.42988i	−0.143628	−	0.248771i
$893$	−12.4539	−	10.4500i	−0.416753	−	0.349697i
$894$		0			0
$895$	−13.8723	+	11.6402i	−0.463700	+	0.389090i
$896$	19.6620	+	1.24912i	0.656861	+	0.0417302i
$897$		0			0
$898$	−21.1127	+	7.68438i	−0.704538	+	0.256431i
$899$	−36.9235			−1.23147
$900$		0			0
$901$	5.76840			0.192173
$902$	17.5725	−	99.6585i	0.585100	−	3.31827i
$903$		0			0
$904$	−7.09106	−	2.58094i	−0.235845	−	0.0858407i
$905$	17.7861	−	14.9243i	0.591229	−	0.496100i
$906$		0			0
$907$	−19.0510	+	6.93399i	−0.632577	+	0.230239i	−0.638353	−	0.769744i	$-0.720384\pi$
$907$	−19.0510	+	6.93399i	−0.632577	+	0.230239i	0.00577554	+	0.999983i	$0.498162\pi$
$908$	−19.0304			−0.631547
$909$		0			0
$910$	6.82988	−	2.00560i	0.226408	−	0.0664850i
$911$	16.6560	+	13.9761i	0.551838	+	0.463047i	0.875563	−	0.483104i	$-0.160491\pi$
$911$	16.6560	+	13.9761i	0.551838	+	0.463047i	−0.323725	+	0.946151i	$0.604935\pi$
$912$		0			0
$913$	−29.1115	+	24.4275i	−0.963451	+	0.808431i
$914$	5.64526	+	2.05471i	0.186729	+	0.0679637i
$915$		0			0
$916$	8.17391	−	2.97506i	0.270073	−	0.0982987i
$917$	5.23617	−	21.5859i	0.172913	−	0.712828i
$918$		0			0
$919$	−8.04117	+	13.9277i	−0.265254	+	0.459433i	−0.967630	−	0.252373i	$-0.918789\pi$
$919$	−8.04117	+	13.9277i	−0.265254	+	0.459433i	0.702376	+	0.711806i	$0.252122\pi$
$920$	1.02930	+	0.863688i	0.0339351	+	0.0284749i
$921$		0			0
$922$	11.0709	+	62.7860i	0.364599	+	2.06775i
$923$	1.98653	+	11.2662i	0.0653874	+	0.370831i
$924$		0			0
$925$	6.32551	+	5.30773i	0.207981	+	0.174517i
$926$	−10.2119	−	17.6876i	−0.335585	−	0.581250i
$927$		0			0
$928$	19.2410	−	33.3265i	0.631618	−	1.09399i
$929$	34.8423	+	29.2361i	1.14314	+	0.959206i	0.999537	−	0.0304292i	$-0.00968743\pi$
$929$	34.8423	+	29.2361i	1.14314	+	0.959206i	0.143601	+	0.989636i	$0.454132\pi$
$930$		0			0
$931$	2.98433	−	9.59917i	0.0978075	−	0.314600i
$932$	1.35494	+	0.493157i	0.0443824	+	0.0161539i
$933$		0			0
$934$	−72.6279	+	26.4344i	−2.37646	+	0.864960i
$935$	−4.14320	+	7.17623i	−0.135497	+	0.234688i
$936$		0			0
$937$	19.6409	−	34.0190i	0.641639	−	1.11135i	−0.343428	−	0.939179i	$-0.611588\pi$
$937$	19.6409	−	34.0190i	0.641639	−	1.11135i	0.985067	−	0.172172i	$-0.0550784\pi$
$938$	59.4420	+	26.0129i	1.94085	+	0.849352i
$939$		0			0
$940$	23.0995	+	8.40753i	0.753423	+	0.274223i
$941$	−34.2173	−	12.4541i	−1.11545	−	0.405991i	−0.282461	−	0.959279i	$-0.591151\pi$
$941$	−34.2173	−	12.4541i	−1.11545	−	0.405991i	−0.832990	+	0.553288i	$0.813373\pi$
$942$		0			0
$943$	−1.96670	+	11.1537i	−0.0640447	+	0.363216i
$944$	−30.0744			−0.978837
$945$		0			0
$946$	27.4683			0.893071
$947$	−2.93396	+	16.6393i	−0.0953410	+	0.540705i	0.899301	+	0.437329i	$0.144076\pi$
$947$	−2.93396	+	16.6393i	−0.0953410	+	0.540705i	−0.994642	+	0.103376i	$0.967035\pi$
$948$		0			0
$949$	9.19319	+	3.34605i	0.298424	+	0.108617i
$950$	7.20286	+	2.62163i	0.233691	+	0.0850567i
$951$		0			0
$952$	−0.350319	−	3.14053i	−0.0113539	−	0.101785i
$953$	10.9661	−	18.9938i	0.355226	−	0.615270i	−0.631930	−	0.775025i	$-0.717737\pi$
$953$	10.9661	−	18.9938i	0.355226	−	0.615270i	0.987157	+	0.159755i	$0.0510705\pi$
$954$		0			0
$955$	−11.1209	+	19.2620i	−0.359865	+	0.623304i
$956$	−33.1349	+	12.0601i	−1.07166	+	0.390052i
$957$		0			0
$958$	14.5634	+	5.30066i	0.470523	+	0.171257i
$959$	−2.72958	−	5.50718i	−0.0881429	−	0.177836i
$960$		0			0
$961$	10.5115	+	8.82019i	0.339081	+	0.284522i
$962$	−2.65513	+	4.59883i	−0.0856049	+	0.148272i
$963$		0			0
$964$	0.212405	+	0.367897i	0.00684111	+	0.0118492i
$965$	−21.0711	−	17.6808i	−0.678303	−	0.569164i
$966$		0			0
$967$	2.64027	+	14.9737i	0.0849053	+	0.481522i	0.997377	+	0.0723820i	$0.0230601\pi$
$967$	2.64027	+	14.9737i	0.0849053	+	0.481522i	−0.912472	+	0.409140i	$0.865829\pi$
$968$	−1.64647	−	9.33758i	−0.0529195	−	0.300121i
$969$		0			0
$970$	−11.9418	−	10.0204i	−0.383428	−	0.321734i
$971$	12.0551	−	20.8800i	0.386866	−	0.670072i	−0.605160	−	0.796104i	$-0.706891\pi$
$971$	12.0551	−	20.8800i	0.386866	−	0.670072i	0.992026	+	0.126032i	$0.0402241\pi$
$972$		0			0
$973$	−54.5521	+	16.0193i	−1.74886	+	0.513554i
$974$	42.0039	−	15.2882i	1.34589	−	0.489864i
$975$		0			0
$976$	23.5172	+	8.55958i	0.752769	+	0.273985i
$977$	−22.0256	+	18.4817i	−0.704662	+	0.591282i	−0.923096	−	0.384570i	$-0.874350\pi$
$977$	−22.0256	+	18.4817i	−0.704662	+	0.591282i	0.218434	+	0.975852i	$0.429905\pi$
$978$		0			0
$979$	2.15099	+	1.80490i	0.0687460	+	0.0576848i
$980$	0.723903	+	15.1824i	0.0231242	+	0.484985i
$981$		0			0
$982$	−73.3705			−2.34135
$983$	4.51817	−	1.64448i	0.144107	−	0.0524508i	−0.268960	−	0.963151i	$-0.586680\pi$
$983$	4.51817	−	1.64448i	0.144107	−	0.0524508i	0.413067	+	0.910701i	$0.364458\pi$
$984$		0			0
$985$	0.292665	−	0.245575i	0.00932509	−	0.00782468i
$986$	−12.0134	−	4.37251i	−0.382583	−	0.139249i
$987$		0			0
$988$	−0.364627	+	2.06790i	−0.0116003	+	0.0657887i
$989$	−3.07424			−0.0977551
$990$		0			0
$991$	52.7537			1.67578			0.837888	−	0.545842i	$-0.183790\pi$
$991$	52.7537			1.67578			0.837888	+	0.545842i	$0.183790\pi$
$992$	−43.7986	+	15.9414i	−1.39061	+	0.506140i
$993$		0			0
$994$	−57.2303	−	3.63582i	−1.81523	−	0.115321i
$995$	−1.83529	+	1.53999i	−0.0581827	+	0.0488211i
$996$		0			0
$997$	39.3451	+	33.0144i	1.24607	+	1.04558i	0.997024	+	0.0770861i	$0.0245616\pi$
$997$	39.3451	+	33.0144i	1.24607	+	1.04558i	0.249046	+	0.968492i	$0.419883\pi$
$998$	5.84523	+	10.1242i	0.185028	+	0.320477i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.u.a.100.19		132
3.2	odd	2		189.2.u.a.142.4	yes	132
7.4	even	3		567.2.w.a.424.19		132
21.11	odd	6		189.2.w.a.88.4	yes	132
27.4	even	9		567.2.w.a.226.19		132
27.23	odd	18		189.2.w.a.58.4	yes	132
189.4	even	9	inner	567.2.u.a.550.19		132
189.158	odd	18		189.2.u.a.4.4	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.4	✓	132	189.158	odd	18
189.2.u.a.142.4	yes	132	3.2	odd	2
189.2.w.a.58.4	yes	132	27.23	odd	18
189.2.w.a.88.4	yes	132	21.11	odd	6
567.2.u.a.100.19		132	1.1	even	1	trivial
567.2.u.a.550.19		132	189.4	even	9	inner
567.2.w.a.226.19		132	27.4	even	9
567.2.w.a.424.19		132	7.4	even	3

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.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.324131 - 1.83824i) q^{2} +(-1.39467 - 0.507617i) q^{4} +(-1.37479 - 0.500384i) q^{5} +(-2.42382 - 1.06071i) q^{7} +(0.481419 - 0.833843i) q^{8} +O(q^{10})\)	\(q+(0.324131 - 1.83824i) q^{2} +(-1.39467 - 0.507617i) q^{4} +(-1.37479 - 0.500384i) q^{5} +(-2.42382 - 1.06071i) q^{7} +(0.481419 - 0.833843i) q^{8} +(-1.36544 + 2.36501i) q^{10} +(-4.29056 + 1.56163i) q^{11} +(0.925783 + 0.336957i) q^{13} +(-2.73547 + 4.11174i) q^{14} +(-3.65064 - 3.06325i) q^{16} +(-0.620234 + 1.07428i) q^{17} +(-0.718027 - 1.24366i) q^{19} +(1.66338 + 1.39574i) q^{20} +(1.47995 + 8.39323i) q^{22} +(-0.165636 - 0.939366i) q^{23} +(-2.19055 - 1.83809i) q^{25} +(0.919482 - 1.59259i) q^{26} +(2.84199 + 2.70971i) q^{28} +(-5.18835 + 1.88840i) q^{29} +(6.28413 + 2.28724i) q^{31} +(-5.33911 + 4.48005i) q^{32} +(1.77374 + 1.48834i) q^{34} +(2.80149 + 2.67110i) q^{35} -2.88764 q^{37} +(-2.51887 + 0.916795i) q^{38} +(-1.07909 + 0.905468i) q^{40} +(-11.1576 - 4.06104i) q^{41} +(0.559660 - 3.17399i) q^{43} +6.77661 q^{44} -1.78046 q^{46} +(10.6381 - 3.87197i) q^{47} +(4.74979 + 5.14193i) q^{49} +(-4.08886 + 3.43096i) q^{50} +(-1.12011 - 0.939887i) q^{52} +(-2.32509 - 4.02717i) q^{53} +6.68005 q^{55} +(-2.05134 + 1.51044i) q^{56} +(1.78963 + 10.1495i) q^{58} +(4.83431 - 4.05647i) q^{59} +(-4.93482 + 1.79613i) q^{61} +(6.24136 - 10.8104i) q^{62} +(1.73924 + 3.01245i) q^{64} +(-1.10415 - 0.926495i) q^{65} +(-2.28146 - 12.9388i) q^{67} +(1.41034 - 1.18342i) q^{68} +(5.81816 - 4.28402i) q^{70} +(5.80593 + 10.0562i) q^{71} +9.93018 q^{73} +(-0.935973 + 5.30816i) q^{74} +(0.370105 + 2.09897i) q^{76} +(12.0560 + 0.765911i) q^{77} +(2.45710 - 13.9349i) q^{79} +(3.48608 + 6.03807i) q^{80} +(-11.0817 + 19.1940i) q^{82} +(7.82112 - 2.84665i) q^{83} +(1.39025 - 1.16656i) q^{85} +(-5.65314 - 2.05757i) q^{86} +(-0.763399 + 4.32945i) q^{88} +(-0.307487 - 0.532584i) q^{89} +(-1.88652 - 1.79871i) q^{91} +(-0.245832 + 1.39418i) q^{92} +(-3.66944 - 20.8104i) q^{94} +(0.364832 + 2.06907i) q^{95} +(-0.991251 + 5.62167i) q^{97} +(10.9916 - 7.06459i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8}+O(q^{10}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8	\( 132 q + 3 q^{2} - 3 q^{4} + 3 q^{5} - 6 q^{7} + 6 q^{8} + 3 q^{10} + 15 q^{11} - 12 q^{13} + 30 q^{14} + 9 q^{16} - 27 q^{17} + 3 q^{19} + 18 q^{20} - 12 q^{22} + 36 q^{23} - 3 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 3 q^{31} + 75 q^{32} - 18 q^{34} - 15 q^{35} - 6 q^{37} - 69 q^{38} + 51 q^{40} - 12 q^{43} + 6 q^{44} - 6 q^{46} + 21 q^{47} - 42 q^{49} + 39 q^{50} + 9 q^{52} - 9 q^{53} - 24 q^{55} - 111 q^{56} - 3 q^{58} - 27 q^{59} - 21 q^{61} - 75 q^{62} - 30 q^{64} + 90 q^{65} - 3 q^{67} + 30 q^{68} + 39 q^{70} + 18 q^{71} - 42 q^{73} - 51 q^{74} - 24 q^{76} - 15 q^{77} + 15 q^{79} - 102 q^{80} - 6 q^{82} + 42 q^{83} - 63 q^{85} + 93 q^{86} - 51 q^{88} - 75 q^{89} - 21 q^{91} + 66 q^{92} + 33 q^{94} - 15 q^{95} - 12 q^{97} + 36 q^{98}+O(q^{100}) \) 132 * q + 3 * q^2 - 3 * q^4 + 3 * q^5 - 6 * q^7 + 6 * q^8 + 3 * q^10 + 15 * q^11 - 12 * q^13 + 30 * q^14 + 9 * q^16 - 27 * q^17 + 3 * q^19 + 18 * q^20 - 12 * q^22 + 36 * q^23 - 3 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 3 * q^31 + 75 * q^32 - 18 * q^34 - 15 * q^35 - 6 * q^37 - 69 * q^38 + 51 * q^40 - 12 * q^43 + 6 * q^44 - 6 * q^46 + 21 * q^47 - 42 * q^49 + 39 * q^50 + 9 * q^52 - 9 * q^53 - 24 * q^55 - 111 * q^56 - 3 * q^58 - 27 * q^59 - 21 * q^61 - 75 * q^62 - 30 * q^64 + 90 * q^65 - 3 * q^67 + 30 * q^68 + 39 * q^70 + 18 * q^71 - 42 * q^73 - 51 * q^74 - 24 * q^76 - 15 * q^77 + 15 * q^79 - 102 * q^80 - 6 * q^82 + 42 * q^83 - 63 * q^85 + 93 * q^86 - 51 * q^88 - 75 * q^89 - 21 * q^91 + 66 * q^92 + 33 * q^94 - 15 * q^95 - 12 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more