LMFDB - Embedded newform 784.2.x.p.165.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.5
Character	$\chi$	$=$	784.165
Dual form			784.2.x.p.765.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.947436 + 1.04994i) q^{2} +(-0.0278645 - 0.103992i) q^{3} +(-0.204729 - 1.98949i) q^{4} +(1.01195 - 3.77665i) q^{5} +(0.135585 + 0.0692696i) q^{6} +(2.28281 + 1.66997i) q^{8} +(2.58804 - 1.49420i) q^{9} +O(q^{10})$	\(q+(-0.947436 + 1.04994i) q^{2} +(-0.0278645 - 0.103992i) q^{3} +(-0.204729 - 1.98949i) q^{4} +(1.01195 - 3.77665i) q^{5} +(0.135585 + 0.0692696i) q^{6} +(2.28281 + 1.66997i) q^{8} +(2.58804 - 1.49420i) q^{9} +(3.00648 + 4.64061i) q^{10} +(4.58934 - 1.22971i) q^{11} +(-0.201186 + 0.0767265i) q^{12} +(-1.87012 + 1.87012i) q^{13} -0.420938 q^{15} +(-3.91617 + 0.814616i) q^{16} +(-1.62511 + 2.81477i) q^{17} +(-0.883183 + 4.13294i) q^{18} +(-2.09607 - 0.561641i) q^{19} +(-7.72079 - 1.24008i) q^{20} +(-3.05699 + 5.98359i) q^{22} +(6.23669 - 3.60076i) q^{23} +(0.110053 - 0.283926i) q^{24} +(-8.90888 - 5.14354i) q^{25} +(-0.191686 - 3.73533i) q^{26} +(-0.455881 - 0.455881i) q^{27} +(-3.46438 + 3.46438i) q^{29} +(0.398812 - 0.441957i) q^{30} +(4.80978 - 8.33078i) q^{31} +(2.85503 - 4.88352i) q^{32} +(-0.255760 - 0.442989i) q^{33} +(-1.41564 - 4.37307i) q^{34} +(-3.50256 - 4.84298i) q^{36} +(0.146341 - 0.546153i) q^{37} +(2.57558 - 1.66862i) q^{38} +(0.246587 + 0.142367i) q^{39} +(8.61695 - 6.93144i) q^{40} +0.425757i q^{41} +(4.63112 + 4.63112i) q^{43} +(-3.38608 - 8.87871i) q^{44} +(-3.02412 - 11.2862i) q^{45} +(-2.12831 + 9.95961i) q^{46} +(-0.163964 - 0.283994i) q^{47} +(0.193836 + 0.384551i) q^{48} +(13.8410 - 4.48057i) q^{50} +(0.337996 + 0.0905657i) q^{51} +(4.10346 + 3.33773i) q^{52} +(-4.64008 + 1.24331i) q^{53} +(0.910564 - 0.0467276i) q^{54} -18.5767i q^{55} +0.233624i q^{57} +(-0.355097 - 6.91965i) q^{58} +(-11.9870 + 3.21190i) q^{59} +(0.0861783 + 0.837453i) q^{60} +(-8.05996 - 2.15966i) q^{61} +(4.18982 + 12.9428i) q^{62} +(2.42243 + 7.62442i) q^{64} +(5.17032 + 8.95525i) q^{65} +(0.707426 + 0.151172i) q^{66} +(0.527697 + 1.96939i) q^{67} +(5.93268 + 2.65688i) q^{68} +(-0.548232 - 0.548232i) q^{69} -0.205828i q^{71} +(8.40327 + 0.910952i) q^{72} +(5.86419 + 3.38569i) q^{73} +(0.434777 + 0.671095i) q^{74} +(-0.286645 + 1.06977i) q^{75} +(-0.688254 + 4.28511i) q^{76} +(-0.383102 + 0.124017i) q^{78} +(-2.01751 - 3.49443i) q^{79} +(-0.886451 + 15.6143i) q^{80} +(4.44791 - 7.70400i) q^{81} +(-0.447017 - 0.403378i) q^{82} +(6.75185 - 6.75185i) q^{83} +(8.98586 + 8.98586i) q^{85} +(-9.25008 + 0.474688i) q^{86} +(0.456800 + 0.263734i) q^{87} +(12.5302 + 4.85685i) q^{88} +(-7.25247 + 4.18722i) q^{89} +(14.7149 + 7.51779i) q^{90} +(-8.44052 - 11.6707i) q^{92} +(-1.00035 - 0.268044i) q^{93} +(0.453520 + 0.0969145i) q^{94} +(-4.24224 + 7.34777i) q^{95} +(-0.587401 - 0.160822i) q^{96} +12.6981 q^{97} +(10.0400 - 10.0400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 4 q^{4}+O(q^{10}) $ 96 * q + 4 * q^4	$ 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) $ 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.947436	+	1.04994i	−0.669939	+	0.742417i
$2$	−0.947436	+	1.04994i	−0.669939	+	0.742417i
$3$	−0.0278645	−	0.103992i	−0.0160876	−	0.0600397i	0.957415	−	0.288714i	$-0.0932276\pi$
$3$	−0.0278645	−	0.103992i	−0.0160876	−	0.0600397i	−0.973503	+	0.228674i	$0.926561\pi$
$4$	−0.204729	−	1.98949i	−0.102365	−	0.994747i
$5$	1.01195	−	3.77665i	0.452557	−	1.68897i	−0.242614	−	0.970123i	$-0.578005\pi$
$5$	1.01195	−	3.77665i	0.452557	−	1.68897i	0.695171	−	0.718844i	$-0.255329\pi$
$6$	0.135585	+	0.0692696i	0.0553522	+	0.0282792i
$7$		0			0
$7$		0			0
$8$	2.28281	+	1.66997i	0.807095	+	0.590422i
$9$	2.58804	−	1.49420i	0.862679	−	0.498068i
$10$	3.00648	+	4.64061i	0.950732	+	1.46749i
$11$	4.58934	−	1.22971i	1.38374	−	0.370772i	0.511261	−	0.859425i	$-0.329178\pi$
$11$	4.58934	−	1.22971i	1.38374	−	0.370772i	0.872478	+	0.488654i	$0.162512\pi$
$12$	−0.201186	+	0.0767265i	−0.0580775	+	0.0221490i
$13$	−1.87012	+	1.87012i	−0.518678	+	0.518678i	−0.917171	−	0.398493i	$-0.869533\pi$
$13$	−1.87012	+	1.87012i	−0.518678	+	0.518678i	0.398493	+	0.917171i	$0.369533\pi$
$14$		0			0
$15$	−0.420938			−0.108686
$16$	−3.91617	+	0.814616i	−0.979043	+	0.203654i
$17$	−1.62511	+	2.81477i	−0.394147	+	0.682682i	−0.992992	−	0.118183i	$-0.962293\pi$
$17$	−1.62511	+	2.81477i	−0.394147	+	0.682682i	0.598845	+	0.800865i	$0.295626\pi$
$18$	−0.883183	+	4.13294i	−0.208168	+	0.974143i
$19$	−2.09607	−	0.561641i	−0.480872	−	0.128849i	0.0102365	−	0.999948i	$-0.496742\pi$
$19$	−2.09607	−	0.561641i	−0.480872	−	0.128849i	−0.491109	+	0.871098i	$0.663408\pi$
$20$	−7.72079	−	1.24008i	−1.72642	−	0.277289i
$21$		0			0
$22$	−3.05699	+	5.98359i	−0.651753	+	1.27571i
$23$	6.23669	−	3.60076i	1.30044	−	0.750810i	0.319961	−	0.947431i	$-0.396330\pi$
$23$	6.23669	−	3.60076i	1.30044	−	0.750810i	0.980480	+	0.196621i	$0.0629969\pi$
$24$	0.110053	−	0.283926i	0.0224646	−	0.0579562i
$25$	−8.90888	−	5.14354i	−1.78178	−	1.02871i
$26$	−0.191686	−	3.73533i	−0.0375928	−	0.732558i
$27$	−0.455881	−	0.455881i	−0.0877344	−	0.0877344i
$28$		0			0
$29$	−3.46438	+	3.46438i	−0.643319	+	0.643319i	−0.951370	−	0.308051i	$-0.900323\pi$
$29$	−3.46438	+	3.46438i	−0.643319	+	0.643319i	0.308051	+	0.951370i	$0.400323\pi$
$30$	0.398812	−	0.441957i	0.0728127	−	0.0806900i
$31$	4.80978	−	8.33078i	0.863862	−	1.49625i	−0.00431170	−	0.999991i	$-0.501372\pi$
$31$	4.80978	−	8.33078i	0.863862	−	1.49625i	0.868173	−	0.496261i	$-0.165294\pi$
$32$	2.85503	−	4.88352i	0.504703	−	0.863293i
$33$	−0.255760	−	0.442989i	−0.0445220	−	0.0771144i
$34$	−1.41564	−	4.37307i	−0.242780	−	0.749976i
$35$		0			0
$36$	−3.50256	−	4.84298i	−0.583760	−	0.807163i
$37$	0.146341	−	0.546153i	0.0240584	−	0.0897871i	−0.952853	−	0.303433i	$-0.901867\pi$
$37$	0.146341	−	0.546153i	0.0240584	−	0.0897871i	0.976911	+	0.213646i	$0.0685338\pi$
$38$	2.57558	−	1.66862i	0.417815	−	0.270686i
$39$	0.246587	+	0.142367i	0.0394856	+	0.0227970i
$40$	8.61695	−	6.93144i	1.36246	−	1.09596i
$41$			0.425757i			0.0664921i	0.999447	+	0.0332460i	$0.0105845\pi$
$41$			0.425757i			0.0664921i	−0.999447	+	0.0332460i	$0.989416\pi$
$42$		0			0
$43$	4.63112	+	4.63112i	0.706240	+	0.706240i	0.965742	−	0.259503i	$-0.0835586\pi$
$43$	4.63112	+	4.63112i	0.706240	+	0.706240i	−0.259503	+	0.965742i	$0.583559\pi$
$44$	−3.38608	−	8.87871i	−0.510470	−	1.33852i
$45$	−3.02412	−	11.2862i	−0.450809	−	1.68244i
$46$	−2.12831	+	9.95961i	−0.313802	+	1.46846i
$47$	−0.163964	−	0.283994i	−0.0239166	−	0.0414247i	0.853819	−	0.520569i	$-0.174280\pi$
$47$	−0.163964	−	0.283994i	−0.0239166	−	0.0414247i	−0.877736	+	0.479145i	$0.840947\pi$
$48$	0.193836	+	0.384551i	0.0279778	+	0.0555051i
$49$		0			0
$50$	13.8410	−	4.48057i	1.95741	−	0.633648i
$51$	0.337996	+	0.0905657i	0.0473289	+	0.0126817i
$52$	4.10346	+	3.33773i	0.569048	+	0.462859i
$53$	−4.64008	+	1.24331i	−0.637364	+	0.170781i	−0.563009	−	0.826451i	$-0.690356\pi$
$53$	−4.64008	+	1.24331i	−0.637364	+	0.170781i	−0.0743548	+	0.997232i	$0.523690\pi$
$54$	0.910564	−	0.0467276i	0.123912	−	0.00635882i
$55$		−	18.5767i		−	2.50489i
$56$		0			0
$57$			0.233624i			0.0309443i
$58$	−0.355097	−	6.91965i	−0.0466265	−	0.908595i
$59$	−11.9870	+	3.21190i	−1.56057	+	0.418154i	−0.932845	−	0.360279i	$-0.882682\pi$
$59$	−11.9870	+	3.21190i	−1.56057	+	0.418154i	−0.627728	+	0.778433i	$0.716015\pi$
$60$	0.0861783	+	0.837453i	0.0111256	+	0.108115i
$61$	−8.05996	−	2.15966i	−1.03197	−	0.276516i	−0.297189	−	0.954819i	$-0.596049\pi$
$61$	−8.05996	−	2.15966i	−1.03197	−	0.276516i	−0.734783	+	0.678303i	$0.762716\pi$
$62$	4.18982	+	12.9428i	0.532108	+	1.64374i
$63$		0			0
$64$	2.42243	+	7.62442i	0.302804	+	0.953053i
$65$	5.17032	+	8.95525i	0.641299	+	1.11076i
$66$	0.707426	+	0.151172i	0.0870781	+	0.0186080i
$67$	0.527697	+	1.96939i	0.0644685	+	0.240600i	0.990640	−	0.136504i	$-0.0435867\pi$
$67$	0.527697	+	1.96939i	0.0644685	+	0.240600i	−0.926171	+	0.377104i	$0.876920\pi$
$68$	5.93268	+	2.65688i	0.719443	+	0.322194i
$69$	−0.548232	−	0.548232i	−0.0659993	−	0.0659993i
$70$		0			0
$71$		−	0.205828i		−	0.0244273i	−0.999925	−	0.0122137i	$-0.996112\pi$
$71$		−	0.205828i		−	0.0244273i	0.999925	−	0.0122137i	$-0.00388783\pi$
$72$	8.40327	+	0.910952i	0.990334	+	0.107357i
$73$	5.86419	+	3.38569i	0.686351	+	0.396265i	0.802244	−	0.596997i	$-0.203639\pi$
$73$	5.86419	+	3.38569i	0.686351	+	0.396265i	−0.115892	+	0.993262i	$0.536973\pi$
$74$	0.434777	+	0.671095i	0.0505418	+	0.0780132i
$75$	−0.286645	+	1.06977i	−0.0330989	+	0.123527i
$76$	−0.688254	+	4.28511i	−0.0789481	+	0.491536i
$77$		0			0
$78$	−0.383102	+	0.124017i	−0.0433778	+	0.0140422i
$79$	−2.01751	−	3.49443i	−0.226987	−	0.393154i	0.729926	−	0.683526i	$-0.239554\pi$
$79$	−2.01751	−	3.49443i	−0.226987	−	0.393154i	−0.956914	+	0.290372i	$0.906221\pi$
$80$	−0.886451	+	15.6143i	−0.0991082	+	1.74574i
$81$	4.44791	−	7.70400i	0.494212	−	0.856000i
$82$	−0.447017	−	0.403378i	−0.0493648	−	0.0445456i
$83$	6.75185	−	6.75185i	0.741112	−	0.741112i	−0.231680	−	0.972792i	$-0.574422\pi$
$83$	6.75185	−	6.75185i	0.741112	−	0.741112i	0.972792	+	0.231680i	$0.0744222\pi$
$84$		0			0
$85$	8.98586	+	8.98586i	0.974653	+	0.974653i
$86$	−9.25008	+	0.474688i	−0.997462	+	0.0511869i
$87$	0.456800	+	0.263734i	0.0489741	+	0.0282752i
$88$	12.5302	+	4.85685i	1.33572	+	0.517742i
$89$	−7.25247	+	4.18722i	−0.768761	+	0.443844i	−0.832432	−	0.554127i	$-0.813052\pi$
$89$	−7.25247	+	4.18722i	−0.768761	+	0.443844i	0.0636716	+	0.997971i	$0.479719\pi$
$90$	14.7149	+	7.51779i	1.55109	+	0.792444i
$91$		0			0
$92$	−8.44052	−	11.6707i	−0.879985	−	1.21675i
$93$	−1.00035	−	0.268044i	−0.103732	−	0.0277949i
$94$	0.453520	+	0.0969145i	0.0467771	+	0.00999596i
$95$	−4.24224	+	7.34777i	−0.435245	+	0.753866i
$96$	−0.587401	−	0.160822i	−0.0599513	−	0.0164139i
$97$	12.6981			1.28929			0.644647	−	0.764480i	$-0.277004\pi$
$97$	12.6981			1.28929			0.644647	+	0.764480i	$0.277004\pi$
$98$		0			0
$99$	10.0400	−	10.0400i	1.00905	−	1.00905i
$100$	−8.40914	+	18.7772i	−0.840914	+	1.87772i
$101$	6.09459	−	1.63304i	0.606435	−	0.162494i	0.0574812	−	0.998347i	$-0.481693\pi$
$101$	6.09459	−	1.63304i	0.606435	−	0.162494i	0.548953	+	0.835853i	$0.315026\pi$
$102$	−0.415318	+	0.269069i	−0.0411226	+	0.0266418i
$103$	12.3083	−	7.10617i	1.21277	−	0.700192i	0.249407	−	0.968399i	$-0.419764\pi$
$103$	12.3083	−	7.10617i	1.21277	−	0.700192i	0.963361	+	0.268207i	$0.0864311\pi$
$104$	−7.39217	+	1.14609i	−0.724862	+	0.112383i
$105$		0			0
$106$	3.09079	−	6.04974i	0.300204	−	0.587602i
$107$	−3.19377	+	11.9193i	−0.308754	+	1.15228i	0.620912	+	0.783880i	$0.286762\pi$
$107$	−3.19377	+	11.9193i	−0.308754	+	1.15228i	−0.929666	+	0.368404i	$0.879904\pi$
$108$	−0.813641	+	1.00031i	−0.0782926	+	0.0962544i
$109$	−1.74408	−	6.50900i	−0.167053	−	0.623450i	−0.997769	−	0.0667541i	$-0.978736\pi$
$109$	−1.74408	−	6.50900i	−0.167053	−	0.623450i	0.830717	−	0.556695i	$-0.187931\pi$
$110$	19.5044	+	17.6003i	1.85967	+	1.67812i
$111$	−0.0608732			−0.00577783
$112$		0			0
$113$	−9.68827			−0.911396			−0.455698	−	0.890134i	$-0.650610\pi$
$113$	−9.68827			−0.911396			−0.455698	+	0.890134i	$0.650610\pi$
$114$	−0.245291	−	0.221344i	−0.0229736	−	0.0207308i
$115$	−7.28756	−	27.1976i	−0.679569	−	2.53619i
$116$	7.60162	+	6.18310i	0.705792	+	0.574086i
$117$	−2.04560	+	7.63429i	−0.189116	+	0.705790i
$118$	7.98461	−	15.6286i	0.735043	−	1.43873i
$119$		0			0
$120$	−0.960920	−	0.702951i	−0.0877196	−	0.0641704i
$121$	10.0236	−	5.78713i	0.911237	−	0.526103i
$122$	9.90380	−	6.41630i	0.896648	−	0.580904i
$123$	0.0442752	−	0.0118635i	0.00399216	−	0.00106970i
$124$	−17.5587	−	7.86347i	−1.57682	−	0.706160i
$125$	−14.6172	+	14.6172i	−1.30740	+	1.30740i
$126$		0			0
$127$	−9.53241			−0.845865			−0.422932	−	0.906161i	$-0.638999\pi$
$127$	−9.53241			−0.845865			−0.422932	+	0.906161i	$0.638999\pi$
$128$	−10.3003	−	4.68026i	−0.910422	−	0.413681i
$129$	0.352555	−	0.610643i	0.0310407	−	0.0537641i
$130$	−14.3010	−	3.05603i	−1.25428	−	0.268032i
$131$	−6.07909	−	1.62889i	−0.531133	−	0.142317i	−0.0167215	−	0.999860i	$-0.505323\pi$
$131$	−6.07909	−	1.62889i	−0.531133	−	0.142317i	−0.514411	+	0.857544i	$0.671990\pi$
$132$	−0.828962	+	0.599525i	−0.0721519	+	0.0521820i
$133$		0			0
$134$	−2.56769	−	1.31183i	−0.221815	−	0.113324i
$135$	−2.18303	+	1.26037i	−0.187885	+	0.108476i
$136$	−8.41038	+	3.71171i	−0.721184	+	0.318276i
$137$	2.73070	+	1.57657i	0.233300	+	0.134696i	0.612093	−	0.790785i	$-0.290328\pi$
$137$	2.73070	+	1.57657i	0.233300	+	0.134696i	−0.378794	+	0.925481i	$0.623661\pi$
$138$	1.09502	−	0.0561934i	0.0932145	−	0.00478350i
$139$	7.44059	+	7.44059i	0.631103	+	0.631103i	0.948345	−	0.317242i	$-0.102757\pi$
$139$	7.44059	+	7.44059i	0.631103	+	0.631103i	−0.317242	+	0.948345i	$0.602757\pi$
$140$		0			0
$141$	−0.0249642	+	0.0249642i	−0.00210237	+	0.00210237i
$142$	0.216107	+	0.195009i	0.0181353	+	0.0163648i
$143$	−6.28292	+	10.8823i	−0.525404	+	0.910027i
$144$	−8.91800	+	7.95982i	−0.743167	+	0.663318i
$145$	9.57795	+	16.5895i	0.795406	+	1.37768i
$146$	−9.11070	+	2.94929i	−0.754007	+	0.244085i
$147$		0			0
$148$	−1.11653	−	0.179332i	−0.0917782	−	0.0147410i
$149$	4.82515	−	18.0077i	0.395292	−	1.47525i	−0.425992	−	0.904727i	$-0.640075\pi$
$149$	4.82515	−	18.0077i	0.395292	−	1.47525i	0.821283	−	0.570521i	$-0.193259\pi$
$150$	−0.851615	−	1.31450i	−0.0695341	−	0.107328i
$151$	1.40354	+	0.810335i	0.114219	+	0.0659441i	0.556021	−	0.831168i	$-0.312327\pi$
$151$	1.40354	+	0.810335i	0.114219	+	0.0659441i	−0.441802	+	0.897112i	$0.645661\pi$
$152$	−3.84701	−	4.78249i	−0.312034	−	0.387911i
$153$			9.71298i			0.785248i
$154$		0			0
$155$	−26.5951	−	26.5951i	−2.13617	−	2.13617i
$156$	0.232755	−	0.519731i	0.0186353	−	0.0416118i
$157$	3.42633	+	12.7873i	0.273451	+	1.02053i	0.956872	+	0.290509i	$0.0938248\pi$
$157$	3.42633	+	12.7873i	0.273451	+	1.02053i	−0.683421	+	0.730025i	$0.739509\pi$
$158$	5.58038	+	1.19249i	0.443951	+	0.0948696i
$159$	0.258587	+	0.447886i	0.0205073	+	0.0355197i
$160$	−15.5542	−	15.7243i	−1.22967	−	1.24312i
$161$		0			0
$162$	3.87460	+	11.9691i	0.304417	+	0.940379i
$163$	4.19272	+	1.12344i	0.328400	+	0.0879944i	0.419252	−	0.907870i	$-0.362292\pi$
$163$	4.19272	+	1.12344i	0.328400	+	0.0879944i	−0.0908523	+	0.995864i	$0.528959\pi$
$164$	0.847041	−	0.0871650i	0.0661428	−	0.00680644i
$165$	−1.93183	+	0.517632i	−0.150393	+	0.0402976i
$166$	0.692061	+	13.4860i	0.0537144	+	1.04671i
$167$			3.61974i			0.280104i	0.990144	+	0.140052i	$0.0447270\pi$
$167$			3.61974i			0.280104i	−0.990144	+	0.140052i	$0.955273\pi$
$168$		0			0
$169$			6.00529i			0.461945i
$170$	−17.9481	+	0.921045i	−1.37656	+	0.0706410i
$171$	−6.26393	+	1.67841i	−0.479014	+	0.128352i
$172$	8.26547	−	10.1617i	0.630236	−	0.774824i
$173$	−22.5452	−	6.04096i	−1.71408	−	0.459286i	−0.737659	−	0.675173i	$-0.764069\pi$
$173$	−22.5452	−	6.04096i	−1.71408	−	0.459286i	−0.976418	+	0.215888i	$0.930735\pi$
$174$	−0.709692	+	0.229740i	−0.0538016	+	0.0174165i
$175$		0			0
$176$	−16.9709	+	8.55431i	−1.27923	+	0.644805i
$177$	0.668023	+	1.15705i	0.0502117	+	0.0869692i
$178$	2.47495	−	11.5818i	0.185505	−	0.868089i
$179$	3.89515	+	14.5369i	0.291137	+	1.08654i	0.944237	+	0.329267i	$0.106802\pi$
$179$	3.89515	+	14.5369i	0.291137	+	1.08654i	−0.653099	+	0.757272i	$0.726532\pi$
$180$	−21.8346	+	8.32707i	−1.62746	+	0.620663i
$181$	3.54568	+	3.54568i	0.263548	+	0.263548i	0.826494	−	0.562946i	$-0.190332\pi$
$181$	3.54568	+	3.54568i	0.263548	+	0.263548i	−0.562946	+	0.826494i	$0.690332\pi$
$182$		0			0
$183$			0.898347i			0.0664077i
$184$	20.2503	+	2.19523i	1.49287	+	0.161834i
$185$	−1.91454	−	1.10536i	−0.140760	−	0.0812676i
$186$	1.22920	−	0.796353i	0.0901294	−	0.0583915i
$187$	−3.99683	+	14.9164i	−0.292277	+	1.09079i
$188$	−0.531436	+	0.384347i	−0.0387589	+	0.0280314i
$189$		0			0
$190$	−3.69544	−	11.4156i	−0.268095	−	0.828177i
$191$	5.83672	+	10.1095i	0.422331	+	0.731498i	0.996167	−	0.0874720i	$-0.0278788\pi$
$191$	5.83672	+	10.1095i	0.422331	+	0.731498i	−0.573836	+	0.818970i	$0.694545\pi$
$192$	0.725378	−	0.464364i	0.0523496	−	0.0335126i
$193$	4.34510	−	7.52593i	0.312767	−	0.541728i	−0.666193	−	0.745779i	$-0.732077\pi$
$193$	4.34510	−	7.52593i	0.312767	−	0.541728i	0.978960	+	0.204051i	$0.0654108\pi$
$194$	−12.0306	+	13.3322i	−0.863748	+	0.957194i
$195$	0.787205	−	0.787205i	0.0563729	−	0.0563729i
$196$		0			0
$197$	2.77420	+	2.77420i	0.197654	+	0.197654i	0.798993	−	0.601340i	$-0.205366\pi$
$197$	2.77420	+	2.77420i	0.197654	+	0.197654i	−0.601340	+	0.798993i	$0.705366\pi$
$198$	1.02909	+	20.0535i	0.0731342	+	1.42514i
$199$	−11.0757	−	6.39455i	−0.785135	−	0.453298i	0.0531124	−	0.998589i	$-0.483086\pi$
$199$	−11.0757	−	6.39455i	−0.785135	−	0.453298i	−0.838247	+	0.545291i	$0.816419\pi$
$200$	−11.7477	−	26.6193i	−0.830690	−	1.88227i
$201$	0.190097	−	0.109752i	0.0134084	−	0.00774133i
$202$	−4.05965	+	7.94613i	−0.285636	+	0.559088i
$203$		0			0
$204$	0.110982	−	0.690982i	0.00777031	−	0.0483784i
$205$	1.60793	+	0.430844i	0.112303	+	0.0300915i
$206$	−4.20026	+	19.6555i	−0.292646	+	1.36946i
$207$	10.7605	−	18.6378i	0.747909	−	1.29542i
$208$	5.80029	−	8.84715i	0.402178	−	0.613439i
$209$	−10.3103			−0.713175
$210$		0			0
$211$	5.71453	−	5.71453i	0.393405	−	0.393405i	−0.482494	−	0.875899i	$-0.660269\pi$
$211$	5.71453	−	5.71453i	0.393405	−	0.393405i	0.875899	+	0.482494i	$0.160269\pi$
$212$	3.42351	+	8.97687i	0.235128	+	0.616534i
$213$	−0.0214045	+	0.00573531i	−0.00146661	+	0.000392977i
$214$	−9.48862	−	14.6461i	−0.648629	−	1.00118i
$215$	22.1766	−	12.8037i	1.51243	−	0.873202i
$216$	−0.279384	−	1.80200i	−0.0190096	−	0.122610i
$217$		0			0
$218$	8.48644	+	4.33569i	0.574774	+	0.293650i
$219$	0.188681	−	0.704168i	0.0127499	−	0.0475833i
$220$	−36.9583	+	3.80320i	−2.49173	+	0.256412i
$221$	−2.22481	−	8.30311i	−0.149657	−	0.558528i
$222$	0.0576735	−	0.0639130i	0.00387079	−	0.00428956i
$223$	3.63378			0.243336			0.121668	−	0.992571i	$-0.461176\pi$
$223$	3.63378			0.243336			0.121668	+	0.992571i	$0.461176\pi$
$224$		0			0
$225$	−30.7420			−2.04947
$226$	9.17902	−	10.1721i	0.610579	−	0.676636i
$227$	6.16616	+	23.0124i	0.409262	+	1.52739i	0.796057	+	0.605222i	$0.206916\pi$
$227$	6.16616	+	23.0124i	0.409262	+	1.52739i	−0.386794	+	0.922166i	$0.626418\pi$
$228$	0.464794	−	0.0478298i	0.0307817	−	0.00316760i
$229$	2.53448	−	9.45881i	0.167483	−	0.625056i	−0.830227	−	0.557425i	$-0.811789\pi$
$229$	2.53448	−	9.45881i	0.167483	−	0.625056i	0.997710	−	0.0676308i	$-0.0215440\pi$
$230$	35.4602	+	18.1165i	2.33818	+	1.19457i
$231$		0			0
$232$	−13.6939	+	2.12312i	−0.899049	+	0.139390i
$233$	−22.7274	+	13.1217i	−1.48892	+	0.859629i	−0.999920	−	0.0126550i	$-0.995972\pi$
$233$	−22.7274	+	13.1217i	−1.48892	+	0.859629i	−0.489000	+	0.872284i	$0.662638\pi$
$234$	−6.07744	−	9.38075i	−0.397294	−	0.613239i
$235$	−1.23847	+	0.331846i	−0.0807887	+	0.0216473i
$236$	8.84415	+	23.1905i	0.575705	+	1.50957i
$237$	−0.307175	+	0.307175i	−0.0199531	+	0.0199531i
$238$		0			0
$239$	28.5711			1.84811			0.924055	−	0.382259i	$-0.124854\pi$
$239$	28.5711			1.84811			0.924055	+	0.382259i	$0.124854\pi$
$240$	1.64846	−	0.342902i	0.106408	−	0.0221343i
$241$	−8.25667	+	14.3010i	−0.531859	+	0.921207i	0.467449	+	0.884020i	$0.345173\pi$
$241$	−8.25667	+	14.3010i	−0.531859	+	0.921207i	−0.999308	+	0.0371872i	$0.988160\pi$
$242$	−3.42061	+	16.0071i	−0.219885	+	1.02897i
$243$	−2.79333	−	0.748470i	−0.179192	−	0.0480144i
$244$	−2.64652	+	16.4774i	−0.169426	+	1.05486i
$245$		0			0
$246$	−0.0294920	+	0.0577261i	−0.00188034	+	0.00368048i
$247$	4.97025	−	2.86958i	0.316249	−	0.182587i
$248$	24.8919	−	10.9854i	1.58064	−	0.697574i
$249$	−0.890275	−	0.514000i	−0.0564189	−	0.0325734i
$250$	−1.49825	−	29.1960i	−0.0947579	−	1.84652i
$251$	−11.5207	−	11.5207i	−0.727183	−	0.727183i	0.242875	−	0.970058i	$-0.421910\pi$
$251$	−11.5207	−	11.5207i	−0.727183	−	0.727183i	−0.970058	+	0.242875i	$0.921910\pi$
$252$		0			0
$253$	24.1944	−	24.1944i	1.52109	−	1.52109i
$254$	9.03135	−	10.0084i	0.566678	−	0.627984i
$255$	0.684069	−	1.18484i	0.0428381	−	0.0741977i
$256$	14.6728	−	6.38035i	0.917050	−	0.398772i
$257$	10.3014	+	17.8425i	0.642583	+	1.11299i	0.984854	+	0.173385i	$0.0554704\pi$
$257$	10.3014	+	17.8425i	0.642583	+	1.11299i	−0.342272	+	0.939601i	$0.611196\pi$
$258$	0.307113	+	0.948705i	0.0191200	+	0.0590638i
$259$		0			0
$260$	16.7579	−	12.1197i	1.03928	−	0.751633i
$261$	−3.78945	+	14.1424i	−0.234561	+	0.875394i
$262$	7.46978	−	4.83939i	0.461485	−	0.298978i
$263$	17.6675	+	10.2003i	1.08942	+	0.628979i	0.933423	−	0.358778i	$-0.116806\pi$
$263$	17.6675	+	10.2003i	1.08942	+	0.628979i	0.156001	+	0.987757i	$0.450140\pi$
$264$	0.155926	−	1.43837i	0.00959656	−	0.0885255i
$265$			18.7821i			1.15377i
$266$		0			0
$267$	0.637523	+	0.637523i	0.0390158	+	0.0390158i
$268$	3.81006	−	1.45304i	0.232736	−	0.0887587i
$269$	3.47959	+	12.9860i	0.212154	+	0.791770i	0.987149	+	0.159803i	$0.0510858\pi$
$269$	3.47959	+	12.9860i	0.212154	+	0.791770i	−0.774995	+	0.631968i	$0.782248\pi$
$270$	0.744971	−	3.48616i	0.0453375	−	0.212161i
$271$	−4.74944	−	8.22627i	−0.288508	−	0.499710i	0.684946	−	0.728594i	$-0.259826\pi$
$271$	−4.74944	−	8.22627i	−0.288508	−	0.499710i	−0.973454	+	0.228884i	$0.926492\pi$
$272$	4.07125	−	12.3470i	0.246856	−	0.748645i
$273$		0			0
$274$	−4.24247	+	1.37336i	−0.256297	+	0.0829678i
$275$	−47.2110	−	12.6501i	−2.84693	−	0.762832i
$276$	−0.978464	+	1.20294i	−0.0588966	+	0.0724086i
$277$	−10.5732	+	2.83307i	−0.635279	+	0.170223i	−0.562064	−	0.827094i	$-0.689993\pi$
$277$	−10.5732	+	2.83307i	−0.635279	+	0.170223i	−0.0732151	+	0.997316i	$0.523326\pi$
$278$	−14.8616	+	0.762656i	−0.891341	+	0.0457411i
$279$		−	28.7472i		−	1.72105i
$280$		0			0
$281$			20.2210i			1.20628i	0.797634	+	0.603142i	$0.206085\pi$
$281$			20.2210i			1.20628i	−0.797634	+	0.603142i	$0.793915\pi$
$282$	−0.00255882	−	0.0498629i	−0.000152376	−	0.00296929i
$283$	29.4881	−	7.90130i	1.75288	−	0.469684i	0.767645	−	0.640875i	$-0.221428\pi$
$283$	29.4881	−	7.90130i	1.75288	−	0.469684i	0.985238	+	0.171191i	$0.0547616\pi$
$284$	−0.409494	+	0.0421391i	−0.0242990	+	0.00250050i
$285$	0.882316	+	0.236416i	0.0522639	+	0.0140041i
$286$	−5.47309	−	16.9070i	−0.323630	−	0.999731i
$287$		0			0
$288$	0.0919384	−	16.9047i	0.00541752	−	0.996122i
$289$	3.21805	+	5.57382i	0.189297	+	0.327872i
$290$	−26.4924	−	5.66126i	−1.55569	−	0.332441i
$291$	−0.353826	−	1.32050i	−0.0207416	−	0.0774089i
$292$	5.53524	−	12.3599i	0.323925	−	0.723310i
$293$	1.36393	+	1.36393i	0.0796814	+	0.0796814i	0.745824	−	0.666143i	$-0.232056\pi$
$293$	1.36393	+	1.36393i	0.0796814	+	0.0796814i	−0.666143	+	0.745824i	$0.732056\pi$
$294$		0			0
$295$			48.5209i			2.82499i
$296$	1.24613	−	1.00238i	0.0724297	−	0.0582621i
$297$	−2.65280	−	1.53159i	−0.153931	−	0.0888721i
$298$	14.3354	+	22.1272i	0.830428	+	1.28180i
$299$	−4.92952	+	18.3972i	−0.285082	+	1.06394i
$300$	2.18699	+	0.351264i	0.126266	+	0.0202802i
$301$		0			0
$302$	−2.18057	+	0.705887i	−0.125477	+	0.0406193i
$303$	−0.339646	−	0.588284i	−0.0195121	−	0.0337960i
$304$	8.66611	+	0.491989i	0.497035	+	0.0282175i
$305$	−16.3125	+	28.2541i	−0.934053	+	1.61783i
$306$	−10.1980	−	9.20243i	−0.582981	−	0.526068i
$307$	−17.6399	+	17.6399i	−1.00676	+	1.00676i	−0.00678402	+	0.999977i	$0.502159\pi$
$307$	−17.6399	+	17.6399i	−1.00676	+	1.00676i	−0.999977	+	0.00678402i	$0.997841\pi$
$308$		0			0
$309$	−1.08195	−	1.08195i	−0.0615498	−	0.0615498i
$310$	53.1204	−	2.72599i	3.01704	−	0.154826i
$311$	23.9867	+	13.8487i	1.36016	+	0.785289i	0.989645	−	0.143537i	$-0.0458475\pi$
$311$	23.9867	+	13.8487i	1.36016	+	0.785289i	0.370516	+	0.928826i	$0.379181\pi$
$312$	0.325163	+	0.736790i	0.0184087	+	0.0417125i
$313$	4.27477	−	2.46804i	0.241624	−	0.139502i	−0.374299	−	0.927308i	$-0.622117\pi$
$313$	4.27477	−	2.46804i	0.241624	−	0.139502i	0.615923	+	0.787806i	$0.288783\pi$
$314$	−16.6720	−	8.51768i	−0.940857	−	0.480680i
$315$		0			0
$316$	−6.53910	+	4.72923i	−0.367853	+	0.266040i
$317$	−25.3204	−	6.78457i	−1.42213	−	0.381060i	−0.535894	−	0.844285i	$-0.680025\pi$
$317$	−25.3204	−	6.78457i	−1.42213	−	0.381060i	−0.886240	+	0.463226i	$0.846692\pi$
$318$	−0.715246	−	0.152844i	−0.0401090	−	0.00857104i
$319$	−11.6390	+	20.1594i	−0.651661	+	1.12871i
$320$	31.2461	−	1.43313i	1.74671	−	0.0801142i
$321$	1.32850			0.0741499
$322$		0			0
$323$	4.98724	−	4.98724i	0.277497	−	0.277497i
$324$	−16.2377	−	7.27185i	−0.902094	−	0.403992i
$325$	26.2797	−	7.04164i	1.45774	−	0.390600i
$326$	−5.15188	+	3.33771i	−0.285336	+	0.184858i
$327$	−0.628285	+	0.362741i	−0.0347442	+	0.0200596i
$328$	−0.711000	+	0.971922i	−0.0392584	+	0.0536654i
$329$		0			0
$330$	1.28680	−	2.51872i	0.0708362	−	0.138651i
$331$	0.808626	−	3.01783i	0.0444461	−	0.165875i	−0.940136	−	0.340801i	$-0.889302\pi$
$331$	0.808626	−	3.01783i	0.0444461	−	0.165875i	0.984582	+	0.174926i	$0.0559685\pi$
$332$	−14.8151	−	12.0505i	−0.813083	−	0.661355i
$333$	−0.437328	−	1.63213i	−0.0239654	−	0.0894402i
$334$	−3.80050	−	3.42947i	−0.207954	−	0.187652i
$335$	7.97170			0.435541
$336$		0			0
$337$	−13.1602			−0.716881			−0.358441	−	0.933553i	$-0.616691\pi$
$337$	−13.1602			−0.716881			−0.358441	+	0.933553i	$0.616691\pi$
$338$	−6.30517	−	5.68963i	−0.342956	−	0.309475i
$339$	0.269959	+	1.00750i	0.0146622	+	0.0547199i
$340$	16.0376	−	19.7170i	0.869763	−	1.06930i
$341$	11.8293	−	44.1474i	0.640591	−	2.39072i
$342$	4.17244	−	8.16691i	0.225620	−	0.441616i
$343$		0			0
$344$	2.83815	+	18.3058i	0.153023	+	0.986982i
$345$	−2.62526	+	1.51569i	−0.141339	+	0.0816022i
$346$	27.7027	−	17.9475i	1.48931	−	0.964866i
$347$	11.5508	−	3.09502i	0.620079	−	0.166150i	0.0649151	−	0.997891i	$-0.479322\pi$
$347$	11.5508	−	3.09502i	0.620079	−	0.166150i	0.555164	+	0.831741i	$0.312656\pi$
$348$	0.431176	−	0.962795i	0.0231135	−	0.0516112i
$349$	9.54687	−	9.54687i	0.511032	−	0.511032i	−0.403810	−	0.914843i	$-0.632314\pi$
$349$	9.54687	−	9.54687i	0.511032	−	0.511032i	0.914843	+	0.403810i	$0.132314\pi$
$350$		0			0
$351$	1.70511			0.0910119
$352$	7.09738	−	25.9230i	0.378292	−	1.38170i
$353$	0.707195	−	1.22490i	0.0376402	−	0.0651947i	−0.846592	−	0.532243i	$-0.821349\pi$
$353$	0.707195	−	1.22490i	0.0376402	−	0.0651947i	0.884232	+	0.467048i	$0.154683\pi$
$354$	−1.84774	−	0.394850i	−0.0982061	−	0.0209860i
$355$	−0.777341	−	0.208288i	−0.0412570	−	0.0110548i
$356$	9.81524	+	13.5715i	0.520207	+	0.719288i
$357$		0			0
$358$	−18.9532	−	9.68313i	−1.00171	−	0.511769i
$359$	8.19593	−	4.73192i	0.432565	−	0.249741i	−0.267874	−	0.963454i	$-0.586321\pi$
$359$	8.19593	−	4.73192i	0.432565	−	0.249741i	0.700439	+	0.713713i	$0.252988\pi$
$360$	11.9440	−	30.8143i	0.629505	−	1.62406i
$361$	−12.3764	−	7.14552i	−0.651389	−	0.376080i
$362$	−7.08203	+	0.363430i	−0.372223	+	0.0191014i
$363$	−0.881117	−	0.881117i	−0.0462466	−	0.0462466i
$364$		0			0
$365$	18.7208	−	18.7208i	0.979892	−	0.979892i
$366$	−0.943207	−	0.851127i	−0.0493022	−	0.0444891i
$367$	−4.93145	+	8.54151i	−0.257419	+	0.445863i	−0.965550	−	0.260218i	$-0.916206\pi$
$367$	−4.93145	+	8.54151i	−0.257419	+	0.445863i	0.708130	+	0.706082i	$0.249539\pi$
$368$	−21.4907	+	19.1817i	−1.12028	+	0.999915i
$369$	0.636168	+	1.10188i	0.0331176	+	0.0573613i
$370$	2.97446	−	0.962884i	0.154635	−	0.0500580i
$371$		0			0
$372$	−0.328470	+	2.04508i	−0.0170304	+	0.106032i
$373$	−3.14248	+	11.7279i	−0.162711	+	0.607248i	0.835610	+	0.549324i	$0.185115\pi$
$373$	−3.14248	+	11.7279i	−0.162711	+	0.607248i	−0.998321	+	0.0579237i	$0.981552\pi$
$374$	−11.8745	−	18.3287i	−0.614015	−	0.947755i
$375$	1.92737	+	1.11277i	0.0995289	+	0.0574631i
$376$	0.0999617	−	0.922117i	0.00515513	−	0.0475546i
$377$		−	12.9576i		−	0.667351i
$378$		0			0
$379$	−20.8501	−	20.8501i	−1.07100	−	1.07100i	−0.997279	−	0.0737177i	$-0.976514\pi$
$379$	−20.8501	−	20.8501i	−1.07100	−	1.07100i	−0.0737177	−	0.997279i	$-0.523486\pi$
$380$	15.4869	+	6.93560i	0.794459	+	0.355789i
$381$	0.265616	+	0.991293i	0.0136079	+	0.0507855i
$382$	−16.1443	−	3.44992i	−0.826012	−	0.176513i
$383$	18.6593	+	32.3189i	0.953447	+	1.65142i	0.737883	+	0.674929i	$0.235826\pi$
$383$	18.6593	+	32.3189i	0.953447	+	1.65142i	0.215564	+	0.976490i	$0.430841\pi$
$384$	−0.199697	+	1.20155i	−0.0101908	+	0.0613166i
$385$		0			0
$386$	3.78504	+	11.6924i	0.192653	+	0.595128i
$387$	18.9054	+	5.06568i	0.961014	+	0.257503i
$388$	−2.59967	−	25.2628i	−0.131978	−	1.28252i
$389$	13.4587	−	3.60626i	0.682385	−	0.182845i	0.0990579	−	0.995082i	$-0.468417\pi$
$389$	13.4587	−	3.60626i	0.682385	−	0.182845i	0.583327	+	0.812237i	$0.301750\pi$
$390$	0.0806880	+	1.57234i	0.00408580	+	0.0796185i
$391$			23.4065i			1.18372i
$392$		0			0
$393$			0.677564i			0.0341786i
$394$	−5.54111	+	0.284354i	−0.279157	+	0.0143255i
$395$	−15.2388	+	4.08323i	−0.766748	+	0.205450i
$396$	−22.0299	−	17.9190i	−1.10704	−	0.900462i
$397$	4.97204	+	1.33225i	0.249539	+	0.0668639i	0.381420	−	0.924402i	$-0.375435\pi$
$397$	4.97204	+	1.33225i	0.249539	+	0.0668639i	−0.131881	+	0.991266i	$0.542102\pi$
$398$	17.2074	−	5.57033i	0.862528	−	0.279215i
$399$		0			0
$400$	39.0787	+	12.8857i	1.95394	+	0.644284i
$401$	−4.13740	−	7.16619i	−0.206612	−	0.357862i	0.744033	−	0.668143i	$-0.232910\pi$
$401$	−4.13740	−	7.16619i	−0.206612	−	0.357862i	−0.950645	+	0.310280i	$0.899577\pi$
$402$	−0.0648715	+	0.303573i	−0.00323550	+	0.0151408i
$403$	6.58470	+	24.5744i	0.328007	+	1.22414i
$404$	−4.49667	−	11.7908i	−0.223718	−	0.586615i
$405$	−24.5942	−	24.5942i	−1.22210	−	1.22210i
$406$		0			0
$407$		−	2.68644i		−	0.133162i
$408$	0.620338	+	0.771186i	0.0307113	+	0.0381794i
$409$	−3.87211	−	2.23557i	−0.191464	−	0.110542i	0.401204	−	0.915989i	$-0.368592\pi$
$409$	−3.87211	−	2.23557i	−0.191464	−	0.110542i	−0.592668	+	0.805447i	$0.701925\pi$
$410$	−1.97577	+	1.28003i	−0.0975765	+	0.0632161i
$411$	0.0878609	−	0.327901i	0.00433386	−	0.0161742i
$412$	−16.6575	−	23.0323i	−0.820658	−	1.13472i
$413$		0			0
$414$	9.37356	+	28.9560i	0.460685	+	1.42311i
$415$	−18.6668	−	32.3319i	−0.916318	−	1.58711i
$416$	3.79353	+	14.4720i	0.185993	+	0.709550i
$417$	0.566432	−	0.981089i	0.0277383	−	0.0480442i
$418$	9.76831	−	10.8251i	0.477784	−	0.529473i
$419$	1.21304	−	1.21304i	0.0592610	−	0.0592610i	−0.676855	−	0.736116i	$-0.736658\pi$
$419$	1.21304	−	1.21304i	0.0592610	−	0.0592610i	0.736116	+	0.676855i	$0.236658\pi$
$420$		0			0
$421$	14.4374	+	14.4374i	0.703638	+	0.703638i	0.965190	−	0.261552i	$-0.0842341\pi$
$421$	14.4374	+	14.4374i	0.703638	+	0.703638i	−0.261552	+	0.965190i	$0.584234\pi$
$422$	0.585736	+	11.4141i	0.0285132	+	0.555627i
$423$	−0.848690	−	0.489991i	−0.0412647	−	0.0238242i
$424$	−12.6687	−	4.91054i	−0.615246	−	0.238477i
$425$	28.9558	−	16.7176i	1.40456	−	0.810924i
$426$	0.0142577	−	0.0279071i	0.000690786	−	0.00135211i
$427$		0			0
$428$	24.3673	+	3.91376i	1.17784	+	0.189179i
$429$	1.30674	+	0.350141i	0.0630902	+	0.0169050i
$430$	−7.56788	+	35.4146i	−0.364956	+	1.70784i
$431$	4.70748	−	8.15360i	0.226751	−	0.392745i	−0.730092	−	0.683349i	$-0.760523\pi$
$431$	4.70748	−	8.15360i	0.226751	−	0.392745i	0.956843	+	0.290604i	$0.0938562\pi$
$432$	2.15668	+	1.41394i	0.103763	+	0.0680283i
$433$	34.1850			1.64283			0.821413	−	0.570333i	$-0.193186\pi$
$433$	34.1850			1.64283			0.821413	+	0.570333i	$0.193186\pi$
$434$		0			0
$435$	1.45829	−	1.45829i	0.0699195	−	0.0699195i
$436$	−12.5926	+	4.80243i	−0.603074	+	0.229995i
$437$	−15.0949	+	4.04467i	−0.722087	+	0.193483i
$438$	0.560568	+	0.865258i	0.0267850	+	0.0413436i
$439$	17.9923	−	10.3879i	0.858727	−	0.495786i	−0.00485902	−	0.999988i	$-0.501547\pi$
$439$	17.9923	−	10.3879i	0.858727	−	0.495786i	0.863586	+	0.504202i	$0.168213\pi$
$440$	31.0225	−	42.4071i	1.47894	−	2.02168i
$441$		0			0
$442$	10.8256	+	5.53076i	0.514921	+	0.263071i
$443$	−1.27873	+	4.77227i	−0.0607542	+	0.226738i	−0.989627	−	0.143661i	$-0.954112\pi$
$443$	−1.27873	+	4.77227i	−0.0607542	+	0.226738i	0.928873	+	0.370399i	$0.120779\pi$
$444$	0.0124625	+	0.121107i	0.000591446	+	0.00574748i
$445$	8.47450	+	31.6273i	0.401730	+	1.49928i
$446$	−3.44277	+	3.81523i	−0.163020	+	0.180657i
$447$	−2.00710			−0.0949327
$448$		0			0
$449$	16.2811			0.768355			0.384177	−	0.923259i	$-0.374485\pi$
$449$	16.2811			0.768355			0.384177	+	0.923259i	$0.374485\pi$
$450$	29.1261	−	32.2772i	1.37302	−	1.52156i
$451$	0.523558	+	1.95395i	0.0246534	+	0.0920077i
$452$	1.98347	+	19.2748i	0.0932948	+	0.906608i
$453$	0.0451592	−	0.168536i	0.00212176	−	0.00791853i
$454$	−30.0036	−	15.3287i	−1.40814	−	0.719413i
$455$		0			0
$456$	−0.390145	+	0.533320i	−0.0182702	+	0.0249750i
$457$	21.1023	−	12.1834i	0.987126	−	0.569917i	0.0827117	−	0.996574i	$-0.473642\pi$
$457$	21.1023	−	12.1834i	0.987126	−	0.569917i	0.904414	+	0.426656i	$0.140309\pi$
$458$	7.52989	+	11.6227i	0.351848	+	0.543091i
$459$	2.02406	−	0.542345i	0.0944749	−	0.0253145i
$460$	−52.6174	+	20.0667i	−2.45330	+	0.935615i
$461$	−12.6919	+	12.6919i	−0.591119	+	0.591119i	−0.937934	−	0.346815i	$-0.887263\pi$
$461$	−12.6919	+	12.6919i	−0.591119	+	0.591119i	0.346815	+	0.937934i	$0.387263\pi$
$462$		0			0
$463$	19.8710			0.923485			0.461742	−	0.887014i	$-0.347224\pi$
$463$	19.8710			0.923485			0.461742	+	0.887014i	$0.347224\pi$
$464$	10.7450	−	16.3892i	0.498822	−	0.760851i
$465$	−2.02462	+	3.50674i	−0.0938893	+	0.162621i
$466$	7.75585	−	36.2942i	0.359283	−	1.68130i
$467$	−15.6773	−	4.20072i	−0.725459	−	0.194386i	−0.122853	−	0.992425i	$-0.539204\pi$
$467$	−15.6773	−	4.20072i	−0.725459	−	0.194386i	−0.602606	+	0.798039i	$0.705871\pi$
$468$	15.6072	+	2.50675i	0.721442	+	0.115875i
$469$		0			0
$470$	0.824951	−	1.61471i	0.0380522	−	0.0744812i
$471$	1.23430	−	0.712621i	0.0568734	−	0.0328359i
$472$	−32.7278	−	12.6857i	−1.50642	−	0.583906i
$473$	26.9488	+	15.5589i	1.23911	+	0.715398i
$474$	−0.0314852	−	0.613542i	−0.00144616	−	0.0281809i
$475$	15.7848	+	15.7848i	0.724258	+	0.724258i
$476$		0			0
$477$	−10.1509	+	10.1509i	−0.464780	+	0.464780i
$478$	−27.0693	+	29.9978i	−1.23812	+	1.37207i
$479$	4.32709	−	7.49474i	0.197710	−	0.342443i	−0.750076	−	0.661352i	$-0.769983\pi$
$479$	4.32709	−	7.49474i	0.197710	−	0.342443i	0.947785	+	0.318909i	$0.103316\pi$
$480$	−1.20179	+	2.05566i	−0.0548539	+	0.0938276i
$481$	0.747697	+	1.29505i	0.0340921	+	0.0590492i
$482$	−7.19244	−	22.2182i	−0.327606	−	1.01201i
$483$		0			0
$484$	−13.5656	−	18.7571i	−0.616618	−	0.852596i
$485$	12.8498	−	47.9561i	0.583480	−	2.17758i
$486$	3.43235	−	2.22369i	0.155694	−	0.100869i
$487$	−22.2974	−	12.8734i	−1.01039	−	0.583350i	−0.0990854	−	0.995079i	$-0.531592\pi$
$487$	−22.2974	−	12.8734i	−1.01039	−	0.583350i	−0.911306	+	0.411729i	$0.864925\pi$
$488$	−14.7928	−	18.3899i	−0.669638	−	0.832473i
$489$		−	0.467313i		−	0.0211326i
$490$		0			0
$491$	24.0762	+	24.0762i	1.08654	+	1.08654i	0.995882	+	0.0906632i	$0.0288987\pi$
$491$	24.0762	+	24.0762i	1.08654	+	1.08654i	0.0906632	+	0.995882i	$0.471101\pi$
$492$	−0.0326668	−	0.0856565i	−0.00147273	−	0.00386169i
$493$	−4.12144	−	15.3814i	−0.185620	−	0.692744i
$494$	−1.69613	+	7.93718i	−0.0763123	+	0.357111i
$495$	−27.7574	−	48.0773i	−1.24760	−	2.16091i
$496$	−12.0495	+	36.5429i	−0.541040	+	1.64082i
$497$		0			0
$498$	1.38315	−	0.447749i	0.0619802	−	0.0200641i
$499$	9.09443	+	2.43684i	0.407123	+	0.109088i	0.456568	−	0.889689i	$-0.349079\pi$
$499$	9.09443	+	2.43684i	0.407123	+	0.109088i	−0.0494451	+	0.998777i	$0.515745\pi$
$500$	32.0734	+	26.0883i	1.43437	+	1.16670i
$501$	0.376423	−	0.100862i	0.0168174	−	0.00450620i
$502$	23.0112	−	1.18087i	1.02704	−	0.0527048i
$503$			5.56169i			0.247983i	0.992283	+	0.123992i	$0.0395696\pi$
$503$			5.56169i			0.247983i	−0.992283	+	0.123992i	$0.960430\pi$
$504$		0			0
$505$		−	24.6697i		−	1.09779i
$506$	2.47992	+	48.3253i	0.110246	+	2.14832i
$507$	0.624501	−	0.167335i	0.0277351	−	0.00743159i
$508$	1.95157	+	18.9647i	0.0865867	+	0.841422i
$509$	0.130579	+	0.0349885i	0.00578781	+	0.00155084i	0.261712	−	0.965146i	$-0.415713\pi$
$509$	0.130579	+	0.0349885i	0.00578781	+	0.00155084i	−0.255924	+	0.966697i	$0.582380\pi$
$510$	0.595896	+	1.84079i	0.0263867	+	0.0815116i
$511$		0			0
$512$	−7.20259	+	21.4505i	−0.318312	+	0.947986i
$513$	0.699519	+	1.21160i	0.0308845	+	0.0534936i
$514$	−28.4934	−	6.08886i	−1.25679	−	0.268568i
$515$	−14.3822	−	53.6750i	−0.633754	−	2.36520i
$516$	−1.28705	−	0.576389i	−0.0566592	−	0.0253741i
$517$	−1.10172	−	1.10172i	−0.0484534	−	0.0484534i
$518$		0			0
$519$			2.51284i			0.110301i
$520$	−3.15212	+	29.0774i	−0.138230	+	1.27513i
$521$	32.3309	+	18.6663i	1.41644	+	0.817784i	0.995984	−	0.0895282i	$-0.0285359\pi$
$521$	32.3309	+	18.6663i	1.41644	+	0.817784i	0.420458	+	0.907312i	$0.361869\pi$
$522$	−11.2584	−	17.3777i	−0.492766	−	0.760603i
$523$	5.88406	−	21.9596i	0.257292	−	0.960228i	−0.709509	−	0.704697i	$-0.751083\pi$
$523$	5.88406	−	21.9596i	0.257292	−	0.960228i	0.966801	−	0.255531i	$-0.0822502\pi$
$524$	−1.99609	+	12.4278i	−0.0871998	+	0.542911i
$525$		0			0
$526$	−27.4485	+	8.88557i	−1.19681	+	0.387429i
$527$	15.6328	+	27.0768i	0.680976	+	1.17949i
$528$	1.36246	+	1.52647i	0.0592937	+	0.0664313i
$529$	14.4309	−	24.9950i	0.627430	−	1.08674i
$530$	−19.7200	−	17.7948i	−0.856581	−	0.772958i
$531$	−26.2235	+	26.2235i	−1.13800	+	1.13800i
$532$		0			0
$533$	−0.796217	−	0.796217i	−0.0344880	−	0.0344880i
$534$	−1.27337	+	0.0653457i	−0.0551041	+	0.00282779i
$535$	41.7831	+	24.1235i	1.80644	+	1.04295i
$536$	−2.08419	+	5.37698i	−0.0900232	+	0.232250i
$537$	1.40318	−	0.810128i	0.0605518	−	0.0349596i
$538$	−16.9311	−	8.65006i	−0.729954	−	0.372931i
$539$		0			0
$540$	2.95444	+	4.08509i	0.127139	+	0.175794i
$541$	−5.77189	−	1.54657i	−0.248153	−	0.0664924i	0.132598	−	0.991170i	$-0.457668\pi$
$541$	−5.77189	−	1.54657i	−0.248153	−	0.0664924i	−0.380751	+	0.924677i	$0.624335\pi$
$542$	13.1368	+	2.80726i	0.564276	+	0.120582i
$543$	0.269923	−	0.467520i	0.0115835	−	0.0200632i
$544$	9.10627	+	15.9725i	0.390428	+	0.684815i
$545$	−26.3471			−1.12859
$546$		0			0
$547$	0.794101	−	0.794101i	0.0339533	−	0.0339533i	−0.689926	−	0.723880i	$-0.742357\pi$
$547$	0.794101	−	0.794101i	0.0339533	−	0.0339533i	0.723880	+	0.689926i	$0.242357\pi$
$548$	2.57753	−	5.75549i	0.110106	−	0.245862i
$549$	−24.0865	+	6.45394i	−1.02798	+	0.275448i
$550$	58.0112	−	37.5833i	2.47361	−	1.60256i
$551$	9.20733	−	5.31585i	0.392245	−	0.226463i
$552$	−0.335980	−	2.16704i	−0.0143002	−	0.0922352i
$553$		0			0
$554$	7.04285	−	13.7853i	0.299222	−	0.585681i
$555$	−0.0616006	+	0.229897i	−0.00261480	+	0.00975856i
$556$	13.2797	−	16.3263i	0.563185	−	0.692390i
$557$	4.47037	+	16.6837i	0.189416	+	0.706909i	0.993642	+	0.112586i	$0.0359134\pi$
$557$	4.47037	+	16.6837i	0.189416	+	0.706909i	−0.804226	+	0.594323i	$0.797420\pi$
$558$	30.1827	+	27.2361i	1.27773	+	1.15300i
$559$	−17.3215			−0.732623
$560$		0			0
$561$	1.66255			0.0701929
$562$	−21.2308	−	19.1581i	−0.895565	−	0.808136i
$563$	−1.86914	−	6.97572i	−0.0787748	−	0.293992i	0.915288	−	0.402800i	$-0.131963\pi$
$563$	−1.86914	−	6.97572i	−0.0787748	−	0.293992i	−0.994063	+	0.108809i	$0.965296\pi$
$564$	0.0547771	+	0.0445553i	0.00230653	+	0.00187612i
$565$	−9.80404	+	36.5892i	−0.412459	+	1.53932i
$566$	−19.6422	+	38.4465i	−0.825623	+	1.61603i
$567$		0			0
$568$	0.343726	−	0.469867i	0.0144224	−	0.0197152i
$569$	−14.9666	+	8.64097i	−0.627433	+	0.362248i	−0.779757	−	0.626082i	$-0.784657\pi$
$569$	−14.9666	+	8.64097i	−0.627433	+	0.362248i	0.152324	+	0.988331i	$0.451324\pi$
$570$	−1.08416	+	0.702386i	−0.0454105	+	0.0294197i
$571$	−24.6235	+	6.59784i	−1.03046	+	0.276111i	−0.734155	−	0.678982i	$-0.762421\pi$
$571$	−24.6235	+	6.59784i	−1.03046	+	0.276111i	−0.296305	+	0.955093i	$0.595755\pi$
$572$	22.9366	+	10.2719i	0.959029	+	0.429490i
$573$	0.888668	−	0.888668i	0.0371246	−	0.0371246i
$574$		0			0
$575$	−74.0826			−3.08946
$576$	17.6618	+	16.1127i	0.735908	+	0.671362i
$577$	−3.22470	+	5.58535i	−0.134246	+	0.232521i	−0.925309	−	0.379213i	$-0.876195\pi$
$577$	−3.22470	+	5.58535i	−0.134246	+	0.232521i	0.791063	+	0.611735i	$0.209528\pi$
$578$	−8.90105	−	1.90210i	−0.370235	−	0.0791168i
$579$	−0.903709	−	0.242148i	−0.0375569	−	0.0100633i
$580$	31.0438	−	22.4516i	1.28902	−	0.932253i
$581$		0			0
$582$	1.72166	+	0.879592i	0.0713653	+	0.0364602i
$583$	−19.7660	+	11.4119i	−0.818624	+	0.472633i
$584$	7.73283	+	17.5219i	0.319987	+	0.725061i
$585$	26.7620	+	15.4510i	1.10647	+	0.638821i
$586$	−2.72427	+	0.139802i	−0.112538	+	0.00577515i
$587$	23.4107	+	23.4107i	0.966264	+	0.966264i	0.999449	−	0.0331855i	$-0.0105652\pi$
$587$	23.4107	+	23.4107i	0.966264	+	0.966264i	−0.0331855	+	0.999449i	$0.510565\pi$
$588$		0			0
$589$	−14.7606	+	14.7606i	−0.608198	+	0.608198i
$590$	−50.9438	−	45.9704i	−2.09732	−	1.89257i
$591$	0.211192	−	0.365796i	0.00868729	−	0.0150468i
$592$	−0.128193	+	2.25804i	−0.00526869	+	0.0928050i
$593$	6.99803	+	12.1209i	0.287375	+	0.497748i	0.973182	−	0.230035i	$-0.0738842\pi$
$593$	6.99803	+	12.1209i	0.287375	+	0.497748i	−0.685808	+	0.727783i	$0.740551\pi$
$594$	4.12143	−	1.33418i	0.169104	−	0.0547421i
$595$		0			0
$596$	−36.8141	−	5.91290i	−1.50796	−	0.242202i
$597$	−0.356362	+	1.32996i	−0.0145849	+	0.0544317i
$598$	−14.6455	−	22.6059i	−0.598899	−	0.924423i
$599$	−38.2425	−	22.0793i	−1.56255	−	0.902136i	−0.996998	−	0.0774209i	$-0.975331\pi$
$599$	−38.2425	−	22.0793i	−1.56255	−	0.902136i	−0.565548	−	0.824716i	$-0.691335\pi$
$600$	−2.44084	+	1.96340i	−0.0996468	+	0.0801555i
$601$		−	31.1376i		−	1.27013i	−0.772459	−	0.635065i	$-0.780973\pi$
$601$		−	31.1376i		−	1.27013i	0.772459	−	0.635065i	$-0.219027\pi$
$602$		0			0
$603$	4.30838	+	4.30838i	0.175451	+	0.175451i
$604$	1.32481	−	2.95824i	0.0539058	−	0.120369i
$605$	−11.7126	−	43.7119i	−0.476183	−	1.77714i
$606$	0.939453	+	0.200755i	0.0381627	+	0.00815512i
$607$	4.40831	+	7.63542i	0.178928	+	0.309912i	0.941514	−	0.336975i	$-0.109404\pi$
$607$	4.40831	+	7.63542i	0.178928	+	0.309912i	−0.762586	+	0.646887i	$0.776070\pi$
$608$	−8.72714	+	8.63273i	−0.353932	+	0.350103i
$609$		0			0
$610$	−14.2099	−	43.8961i	−0.575344	−	1.77730i
$611$	0.837735	+	0.224470i	0.0338911	+	0.00908110i
$612$	19.3239	−	1.98853i	0.781123	−	0.0803816i
$613$	−9.24353	+	2.47680i	−0.373343	+	0.100037i	−0.440611	−	0.897698i	$-0.645238\pi$
$613$	−9.24353	+	2.47680i	−0.373343	+	0.100037i	0.0672686	+	0.997735i	$0.478572\pi$
$614$	−1.80808	−	35.2334i	−0.0729681	−	1.42190i
$615$		−	0.179217i		−	0.00722673i
$616$		0			0
$617$		−	25.9915i		−	1.04638i	−0.852216	−	0.523189i	$-0.824742\pi$
$617$		−	25.9915i		−	1.04638i	0.852216	−	0.523189i	$-0.175258\pi$
$618$	2.16105	−	0.110899i	0.0869302	−	0.00446101i
$619$	−23.3633	+	6.26017i	−0.939049	+	0.251617i	−0.695709	−	0.718324i	$-0.744910\pi$
$619$	−23.3633	+	6.26017i	−0.939049	+	0.251617i	−0.243340	+	0.969941i	$0.578243\pi$
$620$	−47.4661	+	58.3557i	−1.90628	+	2.34362i
$621$	−4.48471	−	1.20167i	−0.179965	−	0.0482215i
$622$	−37.2661	+	12.0637i	−1.49424	+	0.483711i
$623$		0			0
$624$	−1.08165	−	0.356661i	−0.0433008	−	0.0142779i
$625$	14.6944	+	25.4514i	0.587775	+	1.01806i
$626$	−1.45879	+	6.82655i	−0.0583050	+	0.272844i
$627$	0.287290	+	1.07218i	0.0114733	+	0.0428188i
$628$	24.7387	−	9.43460i	0.987181	−	0.376482i
$629$	1.29948	+	1.29948i	0.0518135	+	0.0518135i
$630$		0			0
$631$		−	13.2008i		−	0.525514i	−0.964862	−	0.262757i	$-0.915368\pi$
$631$		−	13.2008i		−	0.525514i	0.964862	−	0.262757i	$-0.0846318\pi$
$632$	1.22999	−	11.3463i	0.0489263	−	0.451331i
$633$	−0.753498	−	0.435032i	−0.0299488	−	0.0172910i
$634$	31.1128	−	20.1568i	1.23565	−	0.800529i
$635$	−9.64632	+	36.0005i	−0.382802	+	1.42864i
$636$	0.838126	−	0.606153i	0.0332339	−	0.0240355i
$637$		0			0
$638$	−10.1388	−	31.3200i	−0.401400	−	1.23997i
$639$	−0.307550	−	0.532692i	−0.0121665	−	0.0210730i
$640$	−28.0990	+	34.1642i	−1.11071	+	1.35046i
$641$	12.0211	−	20.8211i	0.474805	−	0.822386i	−0.524779	−	0.851239i	$-0.675852\pi$
$641$	12.0211	−	20.8211i	0.474805	−	0.822386i	0.999584	+	0.0288526i	$0.00918535\pi$
$642$	−1.25867	+	1.39484i	−0.0496759	+	0.0550501i
$643$	17.9930	−	17.9930i	0.709573	−	0.709573i	−0.256872	−	0.966445i	$-0.582692\pi$
$643$	17.9930	−	17.9930i	0.709573	−	0.709573i	0.966445	+	0.256872i	$0.0826920\pi$
$644$		0			0
$645$	−1.94941	−	1.94941i	−0.0767581	−	0.0767581i
$646$	0.511189	+	9.96137i	0.0201125	+	0.391925i
$647$	−21.3332	−	12.3167i	−0.838695	−	0.484221i	0.0181252	−	0.999836i	$-0.494230\pi$
$647$	−21.3332	−	12.3167i	−0.838695	−	0.484221i	−0.856821	+	0.515615i	$0.827564\pi$
$648$	23.0191	−	10.1589i	0.904278	−	0.399080i
$649$	−51.0627	+	29.4810i	−2.00439	+	1.15723i
$650$	−17.5051	+	34.2635i	−0.686607	+	1.34393i
$651$		0			0
$652$	1.37670	−	8.57140i	0.0539156	−	0.335682i
$653$	−16.8853	−	4.52441i	−0.660774	−	0.177054i	−0.0871785	−	0.996193i	$-0.527785\pi$
$653$	−16.8853	−	4.52441i	−0.660774	−	0.177054i	−0.573595	+	0.819139i	$0.694452\pi$
$654$	0.214406	−	1.00333i	0.00838393	−	0.0392334i
$655$	−12.3035	+	21.3102i	−0.480736	+	0.832659i
$656$	−0.346828	−	1.66734i	−0.0135414	−	0.0650986i
$657$	20.2357			0.789468
$658$		0			0
$659$	−22.2113	+	22.2113i	−0.865229	+	0.865229i	−0.991940	−	0.126711i	$-0.959558\pi$
$659$	−22.2113	+	22.2113i	−0.865229	+	0.865229i	0.126711	+	0.991940i	$0.459558\pi$
$660$	1.42533	+	3.73738i	0.0554808	+	0.145477i
$661$	21.7330	−	5.82333i	0.845314	−	0.226501i	0.189931	−	0.981798i	$-0.439174\pi$
$661$	21.7330	−	5.82333i	0.845314	−	0.226501i	0.655384	+	0.755296i	$0.272507\pi$
$662$	2.40241	+	3.70821i	0.0933723	+	0.144124i
$663$	−0.801462	+	0.462724i	−0.0311262	+	0.0179707i
$664$	26.6886	−	4.13782i	1.03572	−	0.160579i
$665$		0			0
$666$	2.12797	+	1.08717i	0.0824572	+	0.0421271i
$667$	−9.13188	+	34.0806i	−0.353588	+	1.31961i
$668$	7.20145	−	0.741068i	0.278633	−	0.0286728i
$669$	−0.101253	−	0.377883i	−0.00391469	−	0.0146098i
$670$	−7.55268	+	8.36977i	−0.291785	+	0.323352i
$671$	−39.6457			−1.53050
$672$		0			0
$673$	−4.76133			−0.183536			−0.0917679	−	0.995780i	$-0.529252\pi$
$673$	−4.76133			−0.183536			−0.0917679	+	0.995780i	$0.529252\pi$
$674$	12.4684	−	13.8174i	0.480266	−	0.532225i
$675$	1.71655	+	6.40624i	0.0660699	+	0.246576i
$676$	11.9475	−	1.22946i	0.459519	−	0.0472869i
$677$	−0.936462	+	3.49493i	−0.0359912	+	0.134321i	−0.981584	−	0.191032i	$-0.938817\pi$
$677$	−0.936462	+	3.49493i	−0.0359912	+	0.134321i	0.945593	+	0.325353i	$0.105483\pi$
$678$	−1.31358	−	0.671103i	−0.0504477	−	0.0257736i
$679$		0			0
$680$	5.50692	+	35.5191i	0.211181	+	1.36209i
$681$	2.22129	−	1.28246i	0.0851199	−	0.0491440i
$682$	35.1445	+	54.2469i	1.34575	+	2.07722i
$683$	−3.94113	+	1.05602i	−0.150803	+	0.0404076i	−0.333431	−	0.942775i	$-0.608206\pi$
$683$	−3.94113	+	1.05602i	−0.150803	+	0.0404076i	0.182628	+	0.983182i	$0.441540\pi$
$684$	4.62160	+	12.1184i	0.176711	+	0.463359i
$685$	8.71749	−	8.71749i	0.333078	−	0.333078i
$686$		0			0
$687$	−1.05426			−0.0402226
$688$	−21.9089	−	14.3637i	−0.835268	−	0.547611i
$689$	6.35238	−	11.0026i	0.242006	−	0.419167i
$690$	0.895884	−	4.19238i	0.0341057	−	0.159601i
$691$	−32.6372	−	8.74512i	−1.24158	−	0.332680i	−0.422501	−	0.906363i	$-0.638848\pi$
$691$	−32.6372	−	8.74512i	−1.24158	−	0.332680i	−0.819078	+	0.573683i	$0.805514\pi$
$692$	−7.40279	+	46.0902i	−0.281412	+	1.75209i
$693$		0			0
$694$	−7.69406	+	15.0599i	−0.292062	+	0.571667i
$695$	35.6300	−	20.5710i	1.35152	−	0.780302i
$696$	0.602361	+	1.36489i	0.0228324	+	0.0517362i
$697$	−1.19841	−	0.691901i	−0.0453929	−	0.0262076i
$698$	0.978548	+	19.0686i	0.0370386	+	0.721759i
$699$	1.99783	+	1.99783i	0.0755650	+	0.0755650i
$700$		0			0
$701$	−8.85253	+	8.85253i	−0.334355	+	0.334355i	−0.854238	−	0.519882i	$-0.825976\pi$
$701$	−8.85253	+	8.85253i	−0.334355	+	0.334355i	0.519882	+	0.854238i	$0.325976\pi$
$702$	−1.61548	+	1.79025i	−0.0609724	+	0.0675687i
$703$	−0.613485	+	1.06259i	−0.0231380	+	0.0400762i
$704$	20.4932	+	32.0122i	0.772366	+	1.20651i
$705$	0.0690186	+	0.119544i	0.00259939	+	0.00450227i
$706$	0.616042	+	1.90302i	0.0231850	+	0.0716212i
$707$		0			0
$708$	2.16518	−	1.56591i	0.0813724	−	0.0588505i
$709$	−12.1752	+	45.4386i	−0.457250	+	1.70648i	0.224137	+	0.974558i	$0.428044\pi$
$709$	−12.1752	+	45.4386i	−0.457250	+	1.70648i	−0.681387	+	0.731923i	$0.738623\pi$
$710$	0.955169	−	0.618818i	0.0358469	−	0.0232238i
$711$	−10.4428	−	6.02914i	−0.391635	−	0.226110i
$712$	−23.5485	−	2.55277i	−0.882518	−	0.0956690i
$713$		−	69.2753i		−	2.59438i
$714$		0			0
$715$	34.7407	+	34.7407i	1.29923	+	1.29923i
$716$	28.1236	−	10.7255i	1.05103	−	0.400831i
$717$	−0.796120	−	2.97116i	−0.0297316	−	0.110960i
$718$	−2.79691	+	13.0884i	−0.104380	+	0.488454i
$719$	11.2893	+	19.5536i	0.421020	+	0.729228i	0.996040	−	0.0889118i	$-0.0283389\pi$
$719$	11.2893	+	19.5536i	0.421020	+	0.729228i	−0.575020	+	0.818140i	$0.695006\pi$
$720$	21.0369	+	41.7351i	0.783997	+	1.55537i
$721$		0			0
$722$	19.2282	−	6.22450i	0.715599	−	0.231652i
$723$	1.71725	+	0.460137i	0.0638653	+	0.0171127i
$724$	6.32820	−	7.78000i	0.235186	−	0.289142i
$725$	48.6829	−	13.0445i	1.80804	−	0.484462i
$726$	1.75992	−	0.0903140i	0.0653167	−	0.00335187i
$727$			8.36564i			0.310265i	0.987894	+	0.155132i	$0.0495804\pi$
$727$			8.36564i			0.310265i	−0.987894	+	0.155132i	$0.950420\pi$
$728$		0			0
$729$		−	26.3761i		−	0.976893i
$730$	1.91887	+	37.3924i	0.0710207	+	1.38396i
$731$	−20.5616	+	5.50947i	−0.760499	+	0.203775i
$732$	1.78726	−	0.183918i	0.0660589	−	0.00679781i
$733$	1.22544	+	0.328355i	0.0452625	+	0.0121281i	0.281379	−	0.959597i	$-0.409208\pi$
$733$	1.22544	+	0.328355i	0.0452625	+	0.0121281i	−0.236117	+	0.971725i	$0.575875\pi$
$734$	−4.29581	−	13.2702i	−0.158561	−	0.489814i
$735$		0			0
$736$	0.221555	−	40.7373i	0.00816661	−	1.50160i
$737$	4.84357	+	8.38930i	0.178415	+	0.309024i
$738$	−1.75963	−	0.376021i	−0.0647728	−	0.0138415i
$739$	−5.21579	−	19.4656i	−0.191866	−	0.716053i	−0.993056	−	0.117643i	$-0.962466\pi$
$739$	−5.21579	−	19.4656i	−0.191866	−	0.716053i	0.801190	−	0.598410i	$-0.204201\pi$
$740$	−1.80714	+	4.03526i	−0.0664319	+	0.148339i
$741$	−0.436906	−	0.436906i	−0.0160501	−	0.0160501i
$742$		0			0
$743$		−	22.0688i		−	0.809625i	−0.914400	−	0.404813i	$-0.867337\pi$
$743$		−	22.0688i		−	0.809625i	0.914400	−	0.404813i	$-0.132663\pi$
$744$	−1.83599	−	2.28245i	−0.0673108	−	0.0836787i
$745$	−63.1259	−	36.4457i	−2.31275	−	1.33527i
$746$	−9.33624	−	14.4108i	−0.341824	−	0.527618i
$747$	7.38541	−	27.5627i	0.270218	−	1.00847i
$748$	30.4943	+	4.89784i	1.11498	+	0.179083i
$749$		0			0
$750$	−2.99439	+	0.969338i	−0.109340	+	0.0353952i
$751$	−10.2941	−	17.8298i	−0.375636	−	0.650620i	0.614786	−	0.788694i	$-0.289242\pi$
$751$	−10.2941	−	17.8298i	−0.375636	−	0.650620i	−0.990422	+	0.138074i	$0.955909\pi$
$752$	0.873457	+	0.978601i	0.0318517	+	0.0356859i
$753$	−0.877043	+	1.51908i	−0.0319612	+	0.0553585i
$754$	13.6047	+	12.2765i	0.495453	+	0.447084i
$755$	4.48066	−	4.48066i	0.163068	−	0.163068i
$756$		0			0
$757$	−15.3679	−	15.3679i	−0.558556	−	0.558556i	0.370340	−	0.928896i	$-0.379241\pi$
$757$	−15.3679	−	15.3679i	−0.558556	−	0.558556i	−0.928896	+	0.370340i	$0.879241\pi$
$758$	41.6454	−	2.13712i	1.51263	−	0.0776237i
$759$	−3.19019	−	1.84186i	−0.115797	−	0.0668552i
$760$	−21.9548	+	9.68917i	−0.796383	+	0.351463i
$761$	9.59011	−	5.53685i	0.347641	−	0.200711i	−0.316005	−	0.948758i	$-0.602342\pi$
$761$	9.59011	−	5.53685i	0.347641	−	0.200711i	0.663646	+	0.748047i	$0.269008\pi$
$762$	−1.29245	−	0.660307i	−0.0468204	−	0.0239204i
$763$		0			0
$764$	18.9178	−	13.6818i	0.684424	−	0.494992i
$765$	36.6825	+	9.82904i	1.32626	+	0.355370i
$766$	−51.6113	−	11.0290i	−1.86479	−	0.398494i
$767$	16.4105	−	28.4238i	0.592548	−	1.02632i
$768$	−1.07235	−	1.34807i	−0.0386953	−	0.0486441i
$769$	36.7776			1.32623			0.663117	−	0.748515i	$-0.269233\pi$
$769$	36.7776			1.32623			0.663117	+	0.748515i	$0.269233\pi$
$770$		0			0
$771$	1.56843	−	1.56843i	0.0564857	−	0.0564857i
$772$	−15.8624	−	7.10376i	−0.570899	−	0.255670i
$773$	−12.7966	+	3.42883i	−0.460261	+	0.123326i	−0.481496	−	0.876448i	$-0.659907\pi$
$773$	−12.7966	+	3.42883i	−0.460261	+	0.123326i	0.0212359	+	0.999774i	$0.493240\pi$
$774$	−23.2303	+	15.0500i	−0.834995	+	0.540962i
$775$	−85.6995	+	49.4786i	−3.07842	+	1.77732i
$776$	28.9873	+	21.2054i	1.04058	+	0.761228i
$777$		0			0
$778$	−8.96496	+	17.5475i	−0.321409	+	0.629109i
$779$	0.239123	−	0.892418i	0.00856746	−	0.0319742i
$780$	−1.72730	−	1.40497i	−0.0618473	−	0.0503062i
$781$	−0.253109	−	0.944617i	−0.00905696	−	0.0338011i
$782$	−24.5753	−	22.1761i	−0.878811	−	0.793017i
$783$	3.15869			0.112882
$784$		0			0
$785$	51.7602			1.84740
$786$	−0.711399	−	0.641949i	−0.0253747	−	0.0228975i
$787$	−6.76707	−	25.2550i	−0.241220	−	0.900245i	−0.975246	−	0.221123i	$-0.929028\pi$
$787$	−6.76707	−	25.2550i	−0.241220	−	0.900245i	0.734026	−	0.679121i	$-0.237639\pi$
$788$	4.95130	−	6.08722i	0.176383	−	0.216848i
$789$	0.568455	−	2.12150i	0.0202375	−	0.0755275i
$790$	10.1507	−	19.8684i	0.361145	−	0.706885i
$791$		0			0
$792$	39.6857	−	6.15291i	1.41017	−	0.218634i
$793$	19.1119	−	11.0343i	0.678684	−	0.391839i
$794$	−6.10947	+	3.95810i	−0.216817	+	0.140468i
$795$	1.95318	−	0.523354i	0.0692723	−	0.0185615i
$796$	−10.4544	+	23.3442i	−0.370546	+	0.827412i
$797$	19.5355	−	19.5355i	0.691984	−	0.691984i	−0.270684	−	0.962668i	$-0.587250\pi$
$797$	19.5355	−	19.5355i	0.691984	−	0.691984i	0.962668	+	0.270684i	$0.0872500\pi$
$798$		0			0
$799$	1.06584			0.0377066
$800$	−50.5537	+	28.8218i	−1.78734	+	1.01900i
$801$	−12.5131	+	21.6734i	−0.442129	+	0.765791i
$802$	11.4440	+	2.44550i	0.404100	+	0.0863536i
$803$	31.0762	+	8.32684i	1.09666	+	0.293848i
$804$	−0.257270	−	0.355727i	−0.00907321	−	0.0125455i
$805$		0			0
$806$	−32.0402	−	16.3692i	−1.12857	−	0.576580i
$807$	1.25348	−	0.723697i	0.0441246	−	0.0254753i
$808$	16.6399	+	6.44984i	0.585390	+	0.226905i
$809$	−35.1150	−	20.2736i	−1.23458	−	0.712783i	−0.266596	−	0.963808i	$-0.585899\pi$
$809$	−35.1150	−	20.2736i	−1.23458	−	0.712783i	−0.967980	+	0.251026i	$0.919232\pi$
$810$	49.1238	−	2.52089i	1.72604	−	0.0885752i
$811$	11.3534	+	11.3534i	0.398672	+	0.398672i	0.877764	−	0.479092i	$-0.159034\pi$
$811$	11.3534	+	11.3534i	0.398672	+	0.398672i	−0.479092	+	0.877764i	$0.659034\pi$
$812$		0			0
$813$	−0.723124	+	0.723124i	−0.0253611	+	0.0253611i
$814$	2.82059	+	2.54523i	0.0988617	+	0.0892104i
$815$	8.48565	−	14.6976i	0.297239	−	0.514834i
$816$	−1.39743	−	0.0793341i	−0.0489197	−	0.00277725i
$817$	−7.10615	−	12.3082i	−0.248613	−	0.430610i
$818$	6.01578	−	1.94741i	0.210337	−	0.0680898i
$819$		0			0
$820$	0.527971	−	3.28718i	0.0184375	−	0.114793i
$821$	1.89736	−	7.08103i	0.0662182	−	0.247130i	−0.924881	−	0.380257i	$-0.875835\pi$
$821$	1.89736	−	7.08103i	0.0662182	−	0.247130i	0.991099	+	0.133128i	$0.0425021\pi$
$822$	0.261033	+	0.402914i	0.00910456	+	0.0140532i
$823$	−22.2136	−	12.8250i	−0.774318	−	0.447053i	0.0600947	−	0.998193i	$-0.480860\pi$
$823$	−22.2136	−	12.8250i	−0.774318	−	0.447053i	−0.834413	+	0.551140i	$0.814193\pi$
$824$	39.9644	+	4.33233i	1.39223	+	0.150924i
$825$			5.26205i			0.183201i
$826$		0			0
$827$	−17.0664	−	17.0664i	−0.593456	−	0.593456i	0.345108	−	0.938563i	$-0.387842\pi$
$827$	−17.0664	−	17.0664i	−0.593456	−	0.593456i	−0.938563	+	0.345108i	$0.887842\pi$
$828$	−39.2828	−	17.5923i	−1.36517	−	0.611375i
$829$	−5.17304	−	19.3060i	−0.179667	−	0.670526i	−0.995709	−	0.0925344i	$-0.970503\pi$
$829$	−5.17304	−	19.3060i	−0.179667	−	0.670526i	0.816043	−	0.577992i	$-0.196163\pi$
$830$	51.6320	+	11.0334i	1.79217	+	0.382976i
$831$	0.589232	+	1.02058i	0.0204402	+	0.0354035i
$832$	−18.7888	−	9.72836i	−0.651386	−	0.337270i
$833$		0			0
$834$	0.493422	+	1.52424i	0.0170858	+	0.0527800i
$835$	13.6705	+	3.66299i	0.473086	+	0.126763i
$836$	2.11081	+	20.5122i	0.0730040	+	0.709429i
$837$	−5.99053	+	1.60516i	−0.207063	+	0.0554824i
$838$	0.124336	+	2.42290i	0.00429512	+	0.0836975i
$839$			33.7897i			1.16655i	0.812275	+	0.583275i	$0.198229\pi$
$839$			33.7897i			1.16655i	−0.812275	+	0.583275i	$0.801771\pi$
$840$		0			0
$841$			4.99618i			0.172282i
$842$	−28.8369	+	1.47983i	−0.993787	+	0.0509983i
$843$	2.10282	−	0.563449i	0.0724249	−	0.0194062i
$844$	−12.5390	−	10.1991i	−0.431609	−	0.351067i
$845$	22.6798	+	6.07705i	0.780211	+	0.209057i
$846$	1.31854	−	0.426834i	0.0453323	−	0.0146749i
$847$		0			0
$848$	17.1585	−	8.64888i	0.589226	−	0.297004i
$849$	−1.64334	−	2.84635i	−0.0563993	−	0.0976865i
$850$	−9.88132	+	46.2406i	−0.338927	+	1.58604i
$851$	−1.05388	−	3.93313i	−0.0361265	−	0.134826i
$852$	0.0157925	+	0.0414099i	0.000541042	+	0.00141868i
$853$	27.3617	+	27.3617i	0.936845	+	0.936845i	0.998121	−	0.0612756i	$-0.0195169\pi$
$853$	27.3617	+	27.3617i	0.936845	+	0.936845i	−0.0612756	+	0.998121i	$0.519517\pi$
$854$		0			0
$855$			25.3551i			0.867126i
$856$	−27.1956	+	21.8760i	−0.929528	+	0.747708i
$857$	−2.43604	−	1.40645i	−0.0832136	−	0.0480434i	0.457816	−	0.889047i	$-0.348632\pi$
$857$	−2.43604	−	1.40645i	−0.0832136	−	0.0480434i	−0.541029	+	0.841004i	$0.681965\pi$
$858$	−1.60568	+	1.04026i	−0.0548171	+	0.0355139i
$859$	−9.66838	+	36.0829i	−0.329881	+	1.23113i	0.579432	+	0.815020i	$0.303274\pi$
$859$	−9.66838	+	36.0829i	−0.329881	+	1.23113i	−0.909313	+	0.416112i	$0.863392\pi$
$860$	−30.0130	−	41.4989i	−1.02343	−	1.41510i
$861$		0			0
$862$	4.10071	+	12.6676i	0.139671	+	0.431459i
$863$	21.6095	+	37.4288i	0.735597	+	1.27409i	0.954461	+	0.298336i	$0.0964317\pi$
$863$	21.6095	+	37.4288i	0.735597	+	1.27409i	−0.218864	+	0.975755i	$0.570235\pi$
$864$	−3.52786	+	0.924753i	−0.120020	+	0.0314607i
$865$	−45.6291	+	79.0319i	−1.55144	+	2.68717i
$866$	−32.3881	+	35.8921i	−1.10059	+	1.21966i
$867$	0.489962	−	0.489962i	0.0166400	−	0.0166400i
$868$		0			0
$869$	−13.5562	−	13.5562i	−0.459862	−	0.459862i
$870$	0.149474	+	2.91274i	0.00506763	+	0.0987512i
$871$	−4.66986	−	2.69615i	−0.158232	−	0.0913554i
$872$	6.88841	−	17.7714i	0.233271	−	0.601814i
$873$	32.8631	−	18.9735i	1.11225	−	0.642157i
$874$	10.0548	−	19.6807i	0.340109	−	0.665711i
$875$		0			0
$876$	−1.43957	−	0.231216i	−0.0486385	−	0.00781208i
$877$	−9.87251	−	2.64533i	−0.333371	−	0.0893265i	0.0882507	−	0.996098i	$-0.471872\pi$
$877$	−9.87251	−	2.64533i	−0.333371	−	0.0893265i	−0.421622	+	0.906772i	$0.638539\pi$
$878$	−6.13998	+	28.7326i	−0.207214	+	0.969679i
$879$	0.103832	−	0.179842i	0.00350217	−	0.00606593i
$880$	15.1329	+	72.7496i	0.510130	+	2.45239i
$881$	−38.6974			−1.30375			−0.651875	−	0.758327i	$-0.726017\pi$
$881$	−38.6974			−1.30375			−0.651875	+	0.758327i	$0.726017\pi$
$882$		0			0
$883$	9.08807	−	9.08807i	0.305838	−	0.305838i	−0.537455	−	0.843293i	$-0.680614\pi$
$883$	9.08807	−	9.08807i	0.305838	−	0.305838i	0.843293	+	0.537455i	$0.180614\pi$
$884$	−16.0635	+	6.12614i	−0.540274	+	0.206044i
$885$	5.04577	−	1.35201i	0.169612	−	0.0454473i
$886$	−3.79907	−	5.86401i	−0.127632	−	0.197005i
$887$	−20.3494	+	11.7487i	−0.683265	+	0.394483i	−0.801084	−	0.598552i	$-0.795743\pi$
$887$	−20.3494	+	11.7487i	−0.683265	+	0.394483i	0.117819	+	0.993035i	$0.462410\pi$
$888$	−0.138962	−	0.101656i	−0.00466326	−	0.00341136i
$889$		0			0
$890$	−41.2357	−	21.0671i	−1.38222	−	0.706172i
$891$	10.9393	−	40.8260i	0.366480	−	1.36772i
$892$	−0.743941	−	7.22938i	−0.0249090	−	0.242058i
$893$	0.184178	+	0.687361i	0.00616327	+	0.0230017i
$894$	1.90160	−	2.10733i	0.0635991	−	0.0704796i
$895$	58.8424			1.96689
$896$		0			0
$897$	2.05052			0.0684648
$898$	−15.4253	+	17.0942i	−0.514750	+	0.570439i
$899$	12.1981	+	45.5238i	0.406829	+	1.51831i
$900$	6.29380	+	61.1611i	0.209793	+	2.03870i
$901$	4.04101	−	15.0813i	0.134626	−	0.502430i
$902$	−2.54755	−	1.30154i	−0.0848243	−	0.0433364i
$903$		0			0
$904$	−22.1165	−	16.1791i	−0.735583	−	0.538108i
$905$	16.9788	−	9.80272i	0.564394	−	0.325853i
$906$	0.134167	+	0.207092i	0.00445740	+	0.00688016i
$907$	18.5581	−	4.97263i	0.616211	−	0.165113i	0.0628064	−	0.998026i	$-0.479995\pi$
$907$	18.5581	−	4.97263i	0.616211	−	0.165113i	0.553405	+	0.832912i	$0.313328\pi$
$908$	44.5207	−	16.9789i	1.47747	−	0.563463i
$909$	13.3329	−	13.3329i	0.442226	−	0.442226i
$910$		0			0
$911$	10.6476			0.352770			0.176385	−	0.984321i	$-0.443560\pi$
$911$	10.6476			0.352770			0.176385	+	0.984321i	$0.443560\pi$
$912$	−0.190314	−	0.914913i	−0.00630193	−	0.0302958i
$913$	22.6837	−	39.2894i	0.750723	−	1.30029i
$914$	−7.20129	+	33.6991i	−0.238197	+	1.11467i
$915$	3.39274	+	0.909082i	0.112160	+	0.0300533i
$916$	−19.3371	−	3.10584i	−0.638917	−	0.102620i
$917$		0			0
$918$	−1.34824	+	2.63897i	−0.0444985	+	0.0870989i
$919$	33.9084	−	19.5770i	1.11854	−	0.645787i	0.177509	−	0.984119i	$-0.443196\pi$
$919$	33.9084	−	19.5770i	1.11854	−	0.645787i	0.941027	+	0.338332i	$0.109863\pi$
$920$	28.7829	−	74.2568i	0.948943	−	2.44817i
$921$	2.32593	+	1.34288i	0.0766420	+	0.0442493i
$922$	−1.30091	−	25.3504i	−0.0428431	−	0.834869i
$923$	0.384924	+	0.384924i	0.0126699	+	0.0126699i
$924$		0			0
$925$	−4.11290	+	4.11290i	−0.135231	+	0.135231i
$926$	−18.8265	+	20.8633i	−0.618678	+	0.685611i
$927$	21.2362	−	36.7821i	0.697487	−	1.20808i
$928$	7.02748	+	26.8093i	0.230688	+	0.880057i
$929$	−28.6023	−	49.5406i	−0.938411	−	1.62538i	−0.768435	−	0.639927i	$-0.778964\pi$
$929$	−28.6023	−	49.5406i	−0.938411	−	1.62538i	−0.169976	−	0.985448i	$-0.554369\pi$
$930$	−1.76365	−	5.44813i	−0.0578325	−	0.178651i
$931$		0			0
$932$	30.7584	+	42.5296i	1.00753	+	1.39310i
$933$	0.771776	−	2.88031i	0.0252668	−	0.0942971i
$934$	19.2637	−	12.4802i	0.630328	−	0.408366i
$935$	52.2892	+	30.1892i	1.71004	+	0.987292i
$936$	−17.4187	+	14.0115i	−0.569349	+	0.457981i
$937$			23.0753i			0.753837i	0.926246	+	0.376919i	$0.123016\pi$
$937$			23.0753i			0.753837i	−0.926246	+	0.376919i	$0.876984\pi$
$938$		0			0
$939$	−0.375770	−	0.375770i	−0.0122628	−	0.0122628i
$940$	0.913757	+	2.39598i	0.0298035	+	0.0781484i
$941$	−6.29666	−	23.4995i	−0.205265	−	0.766060i	−0.989369	−	0.145430i	$-0.953543\pi$
$941$	−6.29666	−	23.4995i	−0.205265	−	0.766060i	0.784103	−	0.620630i	$-0.213123\pi$
$942$	−0.421211	+	1.97110i	−0.0137238	+	0.0642218i
$943$	1.53305	+	2.65532i	0.0499229	+	0.0864690i
$944$	44.3266	−	22.3432i	1.44271	−	0.727208i
$945$		0			0
$946$	−41.8681	+	13.5534i	−1.36125	+	0.440660i
$947$	15.7694	+	4.22540i	0.512436	+	0.137307i	0.505766	−	0.862671i	$-0.331210\pi$
$947$	15.7694	+	4.22540i	0.512436	+	0.137307i	0.00667058	+	0.999978i	$0.497877\pi$
$948$	0.674010	+	0.548235i	0.0218908	+	0.0178058i
$949$	−17.2984	+	4.63509i	−0.561530	+	0.150461i
$950$	−31.5282	+	1.61794i	−1.02291	+	0.0524928i
$951$			2.82216i			0.0915148i
$952$		0			0
$953$			7.30572i			0.236656i	0.992975	+	0.118328i	$0.0377534\pi$
$953$			7.30572i			0.236656i	−0.992975	+	0.118328i	$0.962247\pi$
$954$	−1.04047	−	20.2752i	−0.0336863	−	0.656434i
$955$	44.0865	−	11.8129i	1.42660	−	0.382258i
$956$	−5.84934	−	56.8420i	−0.189181	−	1.83840i
$957$	2.42073	+	0.648632i	0.0782510	+	0.0209673i
$958$	3.76935	+	11.6440i	0.121782	+	0.376199i
$959$		0			0
$960$	−1.01969	−	3.20941i	−0.0329104	−	0.103583i
$961$	−30.7679	−	53.2916i	−0.992513	−	1.71908i
$962$	−2.06811	−	0.441943i	−0.0666787	−	0.0142488i
$963$	9.54430	+	35.6198i	0.307561	+	1.14783i
$964$	30.1421	+	13.4988i	0.970812	+	0.434766i
$965$	−24.0257	−	24.0257i	−0.773416	−	0.773416i
$966$		0			0
$967$		−	32.6337i		−	1.04943i	−0.851279	−	0.524714i	$-0.824172\pi$
$967$		−	32.6337i		−	1.04943i	0.851279	−	0.524714i	$-0.175828\pi$
$968$	32.5463	+	3.52816i	1.04608	+	0.113400i
$969$	−0.657599	−	0.379665i	−0.0211251	−	0.0121966i
$970$	38.1765	+	58.9269i	1.22577	+	1.89203i
$971$	6.78495	−	25.3218i	0.217740	−	0.812615i	−0.767445	−	0.641115i	$-0.778472\pi$
$971$	6.78495	−	25.3218i	0.217740	−	0.812615i	0.985184	−	0.171500i	$-0.0548613\pi$
$972$	−0.917200	+	5.71054i	−0.0294192	+	0.183166i
$973$		0			0
$974$	34.6416	−	11.2141i	1.10999	−	0.359323i
$975$	−1.46454	−	2.53667i	−0.0469030	−	0.0812383i
$976$	33.3235	+	1.89183i	1.06666	+	0.0605559i
$977$	21.1362	−	36.6090i	0.676207	−	1.17123i	−0.299907	−	0.953968i	$-0.596956\pi$
$977$	21.1362	−	36.6090i	0.676207	−	1.17123i	0.976114	−	0.217257i	$-0.0697109\pi$
$978$	0.490649	+	0.442749i	0.0156892	+	0.0141576i
$979$	−28.1350	+	28.1350i	−0.899199	+	0.899199i
$980$		0			0
$981$	−14.2395	−	14.2395i	−0.454633	−	0.454633i
$982$	−48.0892	+	2.46780i	−1.53459	+	0.0787506i
$983$	−34.0579	−	19.6634i	−1.08628	−	0.627164i	−0.153696	−	0.988118i	$-0.549118\pi$
$983$	−34.0579	−	19.6634i	−1.08628	−	0.627164i	−0.932583	+	0.360954i	$0.882451\pi$
$984$	0.120884	+	0.0468560i	0.00385363	+	0.00149371i
$985$	13.2845	−	7.66982i	0.423280	−	0.244381i
$986$	20.0543	+	10.2457i	0.638659	+	0.326288i
$987$		0			0
$988$	−6.72656	−	9.30080i	−0.214000	−	0.295898i
$989$	45.5585	+	12.2074i	1.44867	+	0.388171i
$990$	76.7764	+	16.4066i	2.44012	+	0.521437i
$991$	11.6473	−	20.1737i	0.369988	−	0.640838i	−0.619575	−	0.784937i	$-0.712695\pi$
$991$	11.6473	−	20.1737i	0.369988	−	0.640838i	0.989563	+	0.144099i	$0.0460285\pi$
$992$	−26.9515	−	47.2733i	−0.855711	−	1.50093i
$993$	−0.336362			−0.0106741
$994$		0			0
$995$	−35.3580	+	35.3580i	−1.12092	+	1.12092i
$996$	−0.840335	+	1.87643i	−0.0266270	+	0.0594569i
$997$	−44.4973	+	11.9230i	−1.40924	+	0.377606i	−0.881656	−	0.471893i	$-0.843571\pi$
$997$	−44.4973	+	11.9230i	−1.40924	+	0.377606i	−0.527589	+	0.849500i	$0.676904\pi$
$998$	−11.1749	+	7.23981i	−0.353736	+	0.229172i
$999$	−0.315695	+	0.182267i	−0.00998816	+	0.00576667i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.p.165.5		96
7.2	even	3	inner	784.2.x.p.373.24		96
7.3	odd	6		784.2.m.l.197.10	yes	48
7.4	even	3		784.2.m.l.197.9	✓	48
7.5	odd	6	inner	784.2.x.p.373.23		96
7.6	odd	2	inner	784.2.x.p.165.6		96
16.13	even	4	inner	784.2.x.p.557.24		96
112.13	odd	4	inner	784.2.x.p.557.23		96
112.45	odd	12		784.2.m.l.589.10	yes	48
112.61	odd	12	inner	784.2.x.p.765.6		96
112.93	even	12	inner	784.2.x.p.765.5		96
112.109	even	12		784.2.m.l.589.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
784.2.m.l.197.9	✓	48	7.4	even	3
784.2.m.l.197.10	yes	48	7.3	odd	6
784.2.m.l.589.9	yes	48	112.109	even	12
784.2.m.l.589.10	yes	48	112.45	odd	12
784.2.x.p.165.5		96	1.1	even	1	trivial
784.2.x.p.165.6		96	7.6	odd	2	inner
784.2.x.p.373.23		96	7.5	odd	6	inner
784.2.x.p.373.24		96	7.2	even	3	inner
784.2.x.p.557.23		96	112.13	odd	4	inner
784.2.x.p.557.24		96	16.13	even	4	inner
784.2.x.p.765.5		96	112.93	even	12	inner
784.2.x.p.765.6		96	112.61	odd	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.947436 + 1.04994i) q^{2} +(-0.0278645 - 0.103992i) q^{3} +(-0.204729 - 1.98949i) q^{4} +(1.01195 - 3.77665i) q^{5} +(0.135585 + 0.0692696i) q^{6} +(2.28281 + 1.66997i) q^{8} +(2.58804 - 1.49420i) q^{9} +O(q^{10})\)	\(q+(-0.947436 + 1.04994i) q^{2} +(-0.0278645 - 0.103992i) q^{3} +(-0.204729 - 1.98949i) q^{4} +(1.01195 - 3.77665i) q^{5} +(0.135585 + 0.0692696i) q^{6} +(2.28281 + 1.66997i) q^{8} +(2.58804 - 1.49420i) q^{9} +(3.00648 + 4.64061i) q^{10} +(4.58934 - 1.22971i) q^{11} +(-0.201186 + 0.0767265i) q^{12} +(-1.87012 + 1.87012i) q^{13} -0.420938 q^{15} +(-3.91617 + 0.814616i) q^{16} +(-1.62511 + 2.81477i) q^{17} +(-0.883183 + 4.13294i) q^{18} +(-2.09607 - 0.561641i) q^{19} +(-7.72079 - 1.24008i) q^{20} +(-3.05699 + 5.98359i) q^{22} +(6.23669 - 3.60076i) q^{23} +(0.110053 - 0.283926i) q^{24} +(-8.90888 - 5.14354i) q^{25} +(-0.191686 - 3.73533i) q^{26} +(-0.455881 - 0.455881i) q^{27} +(-3.46438 + 3.46438i) q^{29} +(0.398812 - 0.441957i) q^{30} +(4.80978 - 8.33078i) q^{31} +(2.85503 - 4.88352i) q^{32} +(-0.255760 - 0.442989i) q^{33} +(-1.41564 - 4.37307i) q^{34} +(-3.50256 - 4.84298i) q^{36} +(0.146341 - 0.546153i) q^{37} +(2.57558 - 1.66862i) q^{38} +(0.246587 + 0.142367i) q^{39} +(8.61695 - 6.93144i) q^{40} +0.425757i q^{41} +(4.63112 + 4.63112i) q^{43} +(-3.38608 - 8.87871i) q^{44} +(-3.02412 - 11.2862i) q^{45} +(-2.12831 + 9.95961i) q^{46} +(-0.163964 - 0.283994i) q^{47} +(0.193836 + 0.384551i) q^{48} +(13.8410 - 4.48057i) q^{50} +(0.337996 + 0.0905657i) q^{51} +(4.10346 + 3.33773i) q^{52} +(-4.64008 + 1.24331i) q^{53} +(0.910564 - 0.0467276i) q^{54} -18.5767i q^{55} +0.233624i q^{57} +(-0.355097 - 6.91965i) q^{58} +(-11.9870 + 3.21190i) q^{59} +(0.0861783 + 0.837453i) q^{60} +(-8.05996 - 2.15966i) q^{61} +(4.18982 + 12.9428i) q^{62} +(2.42243 + 7.62442i) q^{64} +(5.17032 + 8.95525i) q^{65} +(0.707426 + 0.151172i) q^{66} +(0.527697 + 1.96939i) q^{67} +(5.93268 + 2.65688i) q^{68} +(-0.548232 - 0.548232i) q^{69} -0.205828i q^{71} +(8.40327 + 0.910952i) q^{72} +(5.86419 + 3.38569i) q^{73} +(0.434777 + 0.671095i) q^{74} +(-0.286645 + 1.06977i) q^{75} +(-0.688254 + 4.28511i) q^{76} +(-0.383102 + 0.124017i) q^{78} +(-2.01751 - 3.49443i) q^{79} +(-0.886451 + 15.6143i) q^{80} +(4.44791 - 7.70400i) q^{81} +(-0.447017 - 0.403378i) q^{82} +(6.75185 - 6.75185i) q^{83} +(8.98586 + 8.98586i) q^{85} +(-9.25008 + 0.474688i) q^{86} +(0.456800 + 0.263734i) q^{87} +(12.5302 + 4.85685i) q^{88} +(-7.25247 + 4.18722i) q^{89} +(14.7149 + 7.51779i) q^{90} +(-8.44052 - 11.6707i) q^{92} +(-1.00035 - 0.268044i) q^{93} +(0.453520 + 0.0969145i) q^{94} +(-4.24224 + 7.34777i) q^{95} +(-0.587401 - 0.160822i) q^{96} +12.6981 q^{97} +(10.0400 - 10.0400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 4 q^{4}+O(q^{10}) \) 96 * q + 4 * q^4	\( 96 q + 4 q^{4} + 8 q^{11} + 64 q^{15} - 36 q^{16} - 20 q^{18} - 56 q^{22} - 32 q^{29} - 96 q^{30} - 40 q^{32} + 80 q^{36} + 16 q^{37} + 16 q^{43} - 4 q^{44} - 64 q^{46} - 56 q^{50} - 16 q^{53} + 20 q^{58} - 8 q^{60} + 88 q^{64} - 40 q^{67} + 196 q^{72} + 28 q^{74} + 112 q^{78} - 80 q^{79} + 48 q^{81} + 108 q^{86} + 100 q^{88} + 128 q^{95} - 80 q^{99}+O(q^{100}) \) 96 * q + 4 * q^4 + 8 * q^11 + 64 * q^15 - 36 * q^16 - 20 * q^18 - 56 * q^22 - 32 * q^29 - 96 * q^30 - 40 * q^32 + 80 * q^36 + 16 * q^37 + 16 * q^43 - 4 * q^44 - 64 * q^46 - 56 * q^50 - 16 * q^53 + 20 * q^58 - 8 * q^60 + 88 * q^64 - 40 * q^67 + 196 * q^72 + 28 * q^74 + 112 * q^78 - 80 * q^79 + 48 * q^81 + 108 * q^86 + 100 * q^88 + 128 * q^95 - 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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