LMFDB - Embedded newform 80.2.q.c.69.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, 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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			69.1
Root			$0.238945 + 1.39388i$ of defining polynomial
Character	$\chi$	$=$	80.69
Dual form			80.2.q.c.29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39388 - 0.238945i) q^{2} +(-0.183790 - 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(0.212266 + 0.300098i) q^{6} +3.84853 q^{7} +(-2.46943 - 1.37910i) q^{8} -2.93244i q^{9} +O(q^{10})$	\(q+(-1.39388 - 0.238945i) q^{2} +(-0.183790 - 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(0.212266 + 0.300098i) q^{6} +3.84853 q^{7} +(-2.46943 - 1.37910i) q^{8} -2.93244i q^{9} +(0.277574 + 3.15007i) q^{10} +(1.60020 + 1.60020i) q^{11} +(-0.224167 - 0.469021i) q^{12} +(-1.80775 - 1.80775i) q^{13} +(-5.36440 - 0.919589i) q^{14} +(-0.292677 + 0.502125i) q^{15} +(3.11256 + 2.51236i) q^{16} +4.93886i q^{17} +(-0.700694 + 4.08748i) q^{18} +(-4.77162 + 4.77162i) q^{19} +(0.365790 - 4.45715i) q^{20} +(-0.707323 - 0.707323i) q^{21} +(-1.84812 - 2.61284i) q^{22} +0.134544 q^{23} +(0.200391 + 0.707323i) q^{24} +(-4.35066 + 2.46410i) q^{25} +(2.08783 + 2.95174i) q^{26} +(-1.09033 + 1.09033i) q^{27} +(7.25760 + 2.56360i) q^{28} +(2.17142 - 2.17142i) q^{29} +(0.527937 - 0.629968i) q^{30} +2.26371 q^{31} +(-3.73822 - 4.24567i) q^{32} -0.588201i q^{33} +(1.18012 - 6.88418i) q^{34} +(-2.19289 - 8.32149i) q^{35} +(1.95337 - 5.53003i) q^{36} +(4.35066 - 4.35066i) q^{37} +(7.79123 - 5.51092i) q^{38} +0.664493i q^{39} +(-1.57488 + 6.12534i) q^{40} +3.34709i q^{41} +(0.816913 + 1.15494i) q^{42} +(-2.70896 + 2.70896i) q^{43} +(1.95174 + 4.08359i) q^{44} +(-6.34067 + 1.67091i) q^{45} +(-0.187538 - 0.0321487i) q^{46} +7.03343i q^{47} +(-0.110310 - 1.03381i) q^{48} +7.81119 q^{49} +(6.65308 - 2.39510i) q^{50} +(0.907714 - 0.907714i) q^{51} +(-2.20489 - 4.61325i) q^{52} +(-3.40020 + 3.40020i) q^{53} +(1.78031 - 1.25926i) q^{54} +(2.54823 - 4.37182i) q^{55} +(-9.50367 - 5.30752i) q^{56} +1.75396 q^{57} +(-3.54556 + 2.50786i) q^{58} +(-0.107127 - 0.107127i) q^{59} +(-0.886410 + 0.751953i) q^{60} +(-3.46410 + 3.46410i) q^{61} +(-3.15534 - 0.540903i) q^{62} -11.2856i q^{63} +(4.19615 + 6.81119i) q^{64} +(-2.87875 + 4.93886i) q^{65} +(-0.140548 + 0.819883i) q^{66} +(-1.91078 - 1.91078i) q^{67} +(-3.28989 + 9.31375i) q^{68} +(-0.0247279 - 0.0247279i) q^{69} +(1.06825 + 12.1231i) q^{70} -9.32899i q^{71} +(-4.04414 + 7.24146i) q^{72} +9.82769 q^{73} +(-7.10387 + 5.02473i) q^{74} +(1.25249 + 0.346730i) q^{75} +(-12.1769 + 5.81988i) q^{76} +(6.15840 + 6.15840i) q^{77} +(0.158778 - 0.926224i) q^{78} -11.0073 q^{79} +(3.65882 - 8.16168i) q^{80} -8.39654 q^{81} +(0.799772 - 4.66544i) q^{82} +(8.80967 + 8.80967i) q^{83} +(-0.862712 - 1.80504i) q^{84} +(10.6790 - 2.81416i) q^{85} +(4.42326 - 3.12867i) q^{86} -0.798174 q^{87} +(-1.74473 - 6.15840i) q^{88} +1.12125i q^{89} +(9.23740 - 0.813969i) q^{90} +(-6.95717 - 6.95717i) q^{91} +(0.253724 + 0.0896228i) q^{92} +(-0.416048 - 0.416048i) q^{93} +(1.68061 - 9.80377i) q^{94} +(13.0363 + 7.59857i) q^{95} +(-0.0932641 + 1.46736i) q^{96} -6.10461i q^{97} +(-10.8879 - 1.86645i) q^{98} +(4.69248 - 4.69248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	$ 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.39388	−	0.238945i	−0.985623	−	0.168960i
$2$	−1.39388	−	0.238945i	−0.985623	−	0.168960i
$3$	−0.183790	−	0.183790i	−0.106111	−	0.106111i	0.652058	−	0.758169i	$-0.273906\pi$
$3$	−0.183790	−	0.183790i	−0.106111	−	0.106111i	−0.758169	+	0.652058i	$0.773906\pi$
$4$	1.88581	+	0.666123i	0.942905	+	0.333062i
$5$	−0.569800	−	2.16225i	−0.254822	−	0.966988i
$5$	−0.569800	−	2.16225i	−0.254822	−	0.966988i
$6$	0.212266	+	0.300098i	0.0866573	+	0.122514i
$7$	3.84853			1.45461			0.727304	−	0.686315i	$-0.240773\pi$
$7$	3.84853			1.45461			0.727304	+	0.686315i	$0.240773\pi$
$8$	−2.46943	−	1.37910i	−0.873075	−	0.487586i
$9$		−	2.93244i		−	0.977481i
$10$	0.277574	+	3.15007i	0.0877766	+	0.996140i
$11$	1.60020	+	1.60020i	0.482477	+	0.482477i	0.905922	−	0.423445i	$-0.139179\pi$
$11$	1.60020	+	1.60020i	0.482477	+	0.482477i	−0.423445	+	0.905922i	$0.639179\pi$
$12$	−0.224167	−	0.469021i	−0.0647114	−	0.135395i
$13$	−1.80775	−	1.80775i	−0.501379	−	0.501379i	0.410487	−	0.911866i	$-0.365359\pi$
$13$	−1.80775	−	1.80775i	−0.501379	−	0.501379i	−0.911866	+	0.410487i	$0.865359\pi$
$14$	−5.36440	−	0.919589i	−1.43369	−	0.245771i
$15$	−0.292677	+	0.502125i	−0.0755689	+	0.129648i
$16$	3.11256	+	2.51236i	0.778140	+	0.628091i
$17$			4.93886i			1.19785i	0.800806	+	0.598924i	$0.204405\pi$
$17$			4.93886i			1.19785i	−0.800806	+	0.598924i	$0.795595\pi$
$18$	−0.700694	+	4.08748i	−0.165155	+	0.963427i
$19$	−4.77162	+	4.77162i	−1.09468	+	1.09468i	−0.0996636	+	0.995021i	$0.531777\pi$
$19$	−4.77162	+	4.77162i	−1.09468	+	1.09468i	−0.995021	+	0.0996636i	$0.968223\pi$
$20$	0.365790	−	4.45715i	0.0817932	−	0.996649i
$21$	−0.707323	−	0.707323i	−0.154351	−	0.154351i
$22$	−1.84812	−	2.61284i	−0.394021	−	0.557060i
$23$	0.134544			0.0280543			0.0140272	−	0.999902i	$-0.495535\pi$
$23$	0.134544			0.0280543			0.0140272	+	0.999902i	$0.495535\pi$
$24$	0.200391	+	0.707323i	0.0409047	+	0.144382i
$25$	−4.35066	+	2.46410i	−0.870131	+	0.492820i
$26$	2.08783	+	2.95174i	0.409457	+	0.578883i
$27$	−1.09033	+	1.09033i	−0.209833	+	0.209833i
$28$	7.25760	+	2.56360i	1.37156	+	0.484474i
$29$	2.17142	−	2.17142i	0.403223	−	0.403223i	−0.476144	−	0.879367i	$-0.657966\pi$
$29$	2.17142	−	2.17142i	0.403223	−	0.403223i	0.879367	+	0.476144i	$0.157966\pi$
$30$	0.527937	−	0.629968i	0.0963878	−	0.115016i
$31$	2.26371			0.406574			0.203287	−	0.979119i	$-0.434837\pi$
$31$	2.26371			0.406574			0.203287	+	0.979119i	$0.434837\pi$
$32$	−3.73822	−	4.24567i	−0.660830	−	0.750535i
$33$		−	0.588201i		−	0.102393i
$34$	1.18012	−	6.88418i	0.202388	−	1.18063i
$35$	−2.19289	−	8.32149i	−0.370667	−	1.40659i
$36$	1.95337	−	5.53003i	0.325561	−	0.921672i
$37$	4.35066	−	4.35066i	0.715243	−	0.715243i	−0.252384	−	0.967627i	$-0.581215\pi$
$37$	4.35066	−	4.35066i	0.715243	−	0.715243i	0.967627	+	0.252384i	$0.0812146\pi$
$38$	7.79123	−	5.51092i	1.26390	−	0.893988i
$39$			0.664493i			0.106404i
$40$	−1.57488	+	6.12534i	−0.249011	+	0.968501i
$41$			3.34709i			0.522727i	0.965240	+	0.261364i	$0.0841722\pi$
$41$			3.34709i			0.522727i	−0.965240	+	0.261364i	$0.915828\pi$
$42$	0.816913	+	1.15494i	0.126052	+	0.178210i
$43$	−2.70896	+	2.70896i	−0.413112	+	0.413112i	−0.882821	−	0.469709i	$-0.844359\pi$
$43$	−2.70896	+	2.70896i	−0.413112	+	0.413112i	0.469709	+	0.882821i	$0.344359\pi$
$44$	1.95174	+	4.08359i	0.294236	+	0.615625i
$45$	−6.34067	+	1.67091i	−0.945212	+	0.249084i
$46$	−0.187538	−	0.0321487i	−0.0276510	−	0.00474006i
$47$			7.03343i			1.02593i	0.858409	+	0.512966i	$0.171453\pi$
$47$			7.03343i			1.02593i	−0.858409	+	0.512966i	$0.828547\pi$
$48$	−0.110310	−	1.03381i	−0.0159219	−	0.149217i
$49$	7.81119			1.11588
$50$	6.65308	−	2.39510i	0.940888	−	0.338718i
$51$	0.907714	−	0.907714i	0.127105	−	0.127105i
$52$	−2.20489	−	4.61325i	−0.305763	−	0.639743i
$53$	−3.40020	+	3.40020i	−0.467053	+	0.467053i	−0.900958	−	0.433905i	$-0.857135\pi$
$53$	−3.40020	+	3.40020i	−0.467053	+	0.467053i	0.433905	+	0.900958i	$0.357135\pi$
$54$	1.78031	−	1.25926i	0.242270	−	0.171363i
$55$	2.54823	−	4.37182i	0.343604	−	0.589496i
$56$	−9.50367	−	5.30752i	−1.26998	−	0.709247i
$57$	1.75396			0.232317
$58$	−3.54556	+	2.50786i	−0.465555	+	0.329298i
$59$	−0.107127	−	0.107127i	−0.0139468	−	0.0139468i	0.700099	−	0.714046i	$-0.253139\pi$
$59$	−0.107127	−	0.107127i	−0.0139468	−	0.0139468i	−0.714046	+	0.700099i	$0.753139\pi$
$60$	−0.886410	+	0.751953i	−0.114435	+	0.0970767i
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	−0.893197	−	0.449665i	$-0.851543\pi$
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	0.449665	+	0.893197i	$0.351543\pi$
$62$	−3.15534	−	0.540903i	−0.400729	−	0.0686948i
$63$		−	11.2856i		−	1.42185i
$64$	4.19615	+	6.81119i	0.524519	+	0.851399i
$65$	−2.87875	+	4.93886i	−0.357065	+	0.612590i
$66$	−0.140548	+	0.819883i	−0.0173003	+	0.100921i
$67$	−1.91078	−	1.91078i	−0.233440	−	0.233440i	0.580687	−	0.814127i	$-0.302784\pi$
$67$	−1.91078	−	1.91078i	−0.233440	−	0.233440i	−0.814127	+	0.580687i	$0.802784\pi$
$68$	−3.28989	+	9.31375i	−0.398957	+	1.12946i
$69$	−0.0247279	−	0.0247279i	−0.00297689	−	0.00297689i
$70$	1.06825	+	12.1231i	0.127680	+	1.44899i
$71$		−	9.32899i		−	1.10715i	−0.832800	−	0.553573i	$-0.813264\pi$
$71$		−	9.32899i		−	1.10715i	0.832800	−	0.553573i	$-0.186736\pi$
$72$	−4.04414	+	7.24146i	−0.476606	+	0.853414i
$73$	9.82769			1.15024			0.575122	−	0.818068i	$-0.304955\pi$
$73$	9.82769			1.15024			0.575122	+	0.818068i	$0.304955\pi$
$74$	−7.10387	+	5.02473i	−0.825808	+	0.584113i
$75$	1.25249	+	0.346730i	0.144625	+	0.0400370i
$76$	−12.1769	+	5.81988i	−1.39678	+	0.667586i
$77$	6.15840	+	6.15840i	0.701815	+	0.701815i
$78$	0.158778	−	0.926224i	0.0179780	−	0.104874i
$79$	−11.0073			−1.23842			−0.619211	−	0.785224i	$-0.712548\pi$
$79$	−11.0073			−1.23842			−0.619211	+	0.785224i	$0.712548\pi$
$80$	3.65882	−	8.16168i	0.409069	−	0.912504i
$81$	−8.39654			−0.932949
$82$	0.799772	−	4.66544i	0.0883200	−	0.515212i
$83$	8.80967	+	8.80967i	0.966987	+	0.966987i	0.999472	−	0.0324850i	$-0.0103421\pi$
$83$	8.80967	+	8.80967i	0.966987	+	0.966987i	−0.0324850	+	0.999472i	$0.510342\pi$
$84$	−0.862712	−	1.80504i	−0.0941297	−	0.196946i
$85$	10.6790	−	2.81416i	1.15831	−	0.305239i
$86$	4.42326	−	3.12867i	0.476972	−	0.337374i
$87$	−0.798174			−0.0855732
$88$	−1.74473	−	6.15840i	−0.185989	−	0.656488i
$89$			1.12125i			0.118853i	0.998233	+	0.0594263i	$0.0189271\pi$
$89$			1.12125i			0.118853i	−0.998233	+	0.0594263i	$0.981073\pi$
$90$	9.23740	−	0.813969i	0.973708	−	0.0857999i
$91$	−6.95717	−	6.95717i	−0.729310	−	0.729310i
$92$	0.253724	+	0.0896228i	0.0264526	+	0.00934382i
$93$	−0.416048	−	0.416048i	−0.0431422	−	0.0431422i
$94$	1.68061	−	9.80377i	0.173341	−	1.01118i
$95$	13.0363	+	7.59857i	1.33750	+	0.779597i
$96$	−0.0932641	+	1.46736i	−0.00951873	+	0.149762i
$97$		−	6.10461i		−	0.619829i	−0.950764	−	0.309915i	$-0.899700\pi$
$97$		−	6.10461i		−	0.619829i	0.950764	−	0.309915i	$-0.100300\pi$
$98$	−10.8879	−	1.86645i	−1.09984	−	0.188540i
$99$	4.69248	−	4.69248i	0.471612	−	0.471612i
$100$	−9.84591	+	1.74875i	−0.984591	+	0.174875i
$101$	2.17142	+	2.17142i	0.216065	+	0.216065i	0.806838	−	0.590773i	$-0.201177\pi$
$101$	2.17142	+	2.17142i	0.216065	+	0.216065i	−0.590773	+	0.806838i	$0.701177\pi$
$102$	−1.48214	+	1.04835i	−0.146754	+	0.103802i
$103$	−15.3778			−1.51522			−0.757610	−	0.652707i	$-0.773633\pi$
$103$	−15.3778			−1.51522			−0.757610	+	0.652707i	$0.773633\pi$
$104$	1.97103	+	6.95717i	0.193276	+	0.682207i
$105$	−1.12638	+	1.93244i	−0.109923	+	0.188587i
$106$	5.55193	−	3.92701i	0.539251	−	0.381425i
$107$	6.98419	−	6.98419i	0.675187	−	0.675187i	−0.283720	−	0.958907i	$-0.591569\pi$
$107$	6.98419	−	6.98419i	0.675187	−	0.675187i	0.958907	+	0.283720i	$0.0915688\pi$
$108$	−2.78244	+	1.32986i	−0.267740	+	0.127965i
$109$	8.59694	−	8.59694i	0.823437	−	0.823437i	−0.163162	−	0.986599i	$-0.552169\pi$
$109$	8.59694	−	8.59694i	0.823437	−	0.823437i	0.986599	+	0.163162i	$0.0521694\pi$
$110$	−4.59656	+	5.48490i	−0.438265	+	0.522965i
$111$	−1.59922			−0.151791
$112$	11.9788	+	9.66891i	1.13189	+	0.913626i
$113$		−	14.5329i		−	1.36714i	−0.729883	−	0.683572i	$-0.760426\pi$
$113$		−	14.5329i		−	1.36714i	0.729883	−	0.683572i	$-0.239574\pi$
$114$	−2.44481	−	0.419100i	−0.228977	−	0.0392523i
$115$	−0.0766631	−	0.290918i	−0.00714887	−	0.0271282i
$116$	5.54133	−	2.64846i	0.514500	−	0.245903i
$117$	−5.30111	+	5.30111i	−0.490088	+	0.490088i
$118$	0.123725	+	0.174920i	0.0113898	+	0.0161027i
$119$			19.0073i			1.74240i
$120$	1.41523	−	0.836329i	0.129192	−	0.0763461i
$121$		−	5.87875i		−	0.534432i
$122$	5.65628	−	4.00082i	0.512095	−	0.362217i
$123$	0.615163	−	0.615163i	0.0554673	−	0.0554673i
$124$	4.26893	+	1.50791i	0.383361	+	0.135414i
$125$	7.80701	+	8.00316i	0.698280	+	0.715825i
$126$	−2.69664	+	15.7308i	−0.240236	+	1.40141i
$127$		−	5.96617i		−	0.529412i	−0.964329	−	0.264706i	$-0.914725\pi$
$127$		−	5.96617i		−	0.529412i	0.964329	−	0.264706i	$-0.0852749\pi$
$128$	−4.22144	−	10.4966i	−0.373126	−	0.927781i
$129$	0.995761			0.0876719
$130$	5.19275	−	6.19632i	0.455434	−	0.543453i
$131$	2.37084	−	2.37084i	0.207141	−	0.207141i	−0.595910	−	0.803051i	$-0.703209\pi$
$131$	2.37084	−	2.37084i	0.207141	−	0.207141i	0.803051	+	0.595910i	$0.203209\pi$
$132$	0.391814	−	1.10924i	0.0341031	−	0.0965466i
$133$	−18.3637	+	18.3637i	−1.59234	+	1.59234i
$134$	2.20683	+	3.11998i	0.190641	+	0.269525i
$135$	2.97883	+	1.73629i	0.256376	+	0.149436i
$136$	6.81119	−	12.1962i	0.584055	−	1.04581i
$137$	−18.2745			−1.56129			−0.780646	−	0.624973i	$-0.785110\pi$
$137$	−18.2745			−1.56129			−0.780646	+	0.624973i	$0.785110\pi$
$138$	0.0285591	+	0.0403763i	0.00243111	+	0.00343706i
$139$	−0.136094	−	0.136094i	−0.0115433	−	0.0115433i	0.701312	−	0.712855i	$-0.252598\pi$
$139$	−0.136094	−	0.136094i	−0.0115433	−	0.0115433i	−0.712855	+	0.701312i	$0.752598\pi$
$140$	1.40776	−	17.1535i	0.118977	−	1.44973i
$141$	1.29268	−	1.29268i	0.108863	−	0.108863i
$142$	−2.22912	+	13.0035i	−0.187064	+	1.09123i
$143$		−	5.78550i		−	0.483808i
$144$	7.36736	−	9.12740i	0.613947	−	0.760617i
$145$	−5.93244	−	3.45789i	−0.492663	−	0.287162i
$146$	−13.6986	−	2.34828i	−1.13371	−	0.194345i
$147$	−1.43562	−	1.43562i	−0.118408	−	0.118408i
$148$	11.1026	−	5.30644i	0.912627	−	0.436186i
$149$	−2.40078	−	2.40078i	−0.196680	−	0.196680i	0.601895	−	0.798575i	$-0.294412\pi$
$149$	−2.40078	−	2.40078i	−0.196680	−	0.196680i	−0.798575	+	0.601895i	$0.794412\pi$
$150$	−1.66297	−	0.782577i	−0.135781	−	0.0638972i
$151$			17.9935i			1.46429i	0.681150	+	0.732144i	$0.261480\pi$
$151$			17.9935i			1.46429i	−0.681150	+	0.732144i	$0.738520\pi$
$152$	18.3637	−	5.20262i	1.48950	−	0.421988i
$153$	14.4829			1.17087
$154$	−7.11256	−	10.0556i	−0.573146	−	0.810304i
$155$	−1.28986	−	4.89471i	−0.103604	−	0.393152i
$156$	−0.442634	+	1.25311i	−0.0354391	+	0.100329i
$157$	−12.6359	−	12.6359i	−1.00846	−	1.00846i	−0.999964	−	0.00849213i	$-0.997297\pi$
$157$	−12.6359	−	12.6359i	−1.00846	−	1.00846i	−0.00849213	−	0.999964i	$-0.502703\pi$
$158$	15.3429	+	2.63015i	1.22062	+	0.209244i
$159$	1.24985			0.0991193
$160$	−7.05016	+	10.5022i	−0.557364	+	0.830268i
$161$	0.517796			0.0408081
$162$	11.7038	+	2.00632i	0.919536	+	0.157631i
$163$	15.8470	+	15.8470i	1.24123	+	1.24123i	0.959490	+	0.281743i	$0.0909126\pi$
$163$	15.8470	+	15.8470i	1.24123	+	1.24123i	0.281743	+	0.959490i	$0.409087\pi$
$164$	−2.22957	+	6.31197i	−0.174100	+	0.492882i
$165$	−1.27184	+	0.335157i	−0.0990125	+	0.0260919i
$166$	−10.1746	−	14.3847i	−0.789703	−	1.11647i
$167$	−12.7559			−0.987083			−0.493541	−	0.869722i	$-0.664298\pi$
$167$	−12.7559			−0.987083			−0.493541	+	0.869722i	$0.664298\pi$
$168$	0.771212	+	2.72215i	0.0595003	+	0.210019i
$169$		−	6.46410i		−	0.497239i
$170$	−15.5578	+	1.37090i	−1.19323	+	0.105143i
$171$	13.9925	+	13.9925i	1.07003	+	1.07003i
$172$	−6.91308	+	3.30408i	−0.527118	+	0.251934i
$173$	2.64673	+	2.64673i	0.201227	+	0.201227i	0.800525	−	0.599299i	$-0.204554\pi$
$173$	2.64673	+	2.64673i	0.201227	+	0.201227i	−0.599299	+	0.800525i	$0.704554\pi$
$174$	1.11256	+	0.190720i	0.0843429	+	0.0144584i
$175$	−16.7436	+	9.48317i	−1.26570	+	0.716860i
$176$	0.960431	+	9.00098i	0.0723952	+	0.678474i
$177$			0.0393779i			0.00295983i
$178$	0.267918	−	1.56289i	0.0200813	−	0.117144i
$179$	−11.6497	+	11.6497i	−0.870736	+	0.870736i	−0.992553	−	0.121817i	$-0.961128\pi$
$179$	−11.6497	+	11.6497i	−0.870736	+	0.870736i	0.121817	+	0.992553i	$0.461128\pi$
$180$	−13.0703	−	1.07266i	−0.974206	−	0.0799513i
$181$	1.24322	+	1.24322i	0.0924079	+	0.0924079i	0.751800	−	0.659392i	$-0.229186\pi$
$181$	1.24322	+	1.24322i	0.0924079	+	0.0924079i	−0.659392	+	0.751800i	$0.729186\pi$
$182$	8.03508	+	11.3599i	0.595600	+	0.842048i
$183$	1.27334			0.0941278
$184$	−0.332247	−	0.185550i	−0.0244935	−	0.0136789i
$185$	−11.8862	−	6.92820i	−0.873892	−	0.509372i
$186$	0.480509	+	0.679335i	0.0352326	+	0.0498112i
$187$	−7.90314	+	7.90314i	−0.577935	+	0.577935i
$188$	−4.68513	+	13.2637i	−0.341698	+	0.967356i
$189$	−4.19615	+	4.19615i	−0.305225	+	0.305225i
$190$	−16.3554	−	13.7065i	−1.18655	−	0.994372i
$191$	5.07180			0.366982			0.183491	−	0.983021i	$-0.441260\pi$
$191$	5.07180			0.366982			0.183491	+	0.983021i	$0.441260\pi$
$192$	0.480619	−	2.02304i	0.0346857	−	0.146001i
$193$		−	2.30278i		−	0.165758i	−0.996560	−	0.0828788i	$-0.973589\pi$
$193$		−	2.30278i		−	0.165758i	0.996560	−	0.0828788i	$-0.0264114\pi$
$194$	−1.45867	+	8.50910i	−0.104726	+	0.610918i
$195$	1.43680	−	0.378628i	0.102891	−	0.0271141i
$196$	14.7304	+	5.20322i	1.05217	+	0.371658i
$197$	8.06997	−	8.06997i	0.574961	−	0.574961i	−0.358549	−	0.933511i	$-0.616729\pi$
$197$	8.06997	−	8.06997i	0.574961	−	0.574961i	0.933511	+	0.358549i	$0.116729\pi$
$198$	−7.66201	+	5.41951i	−0.544515	+	0.385148i
$199$		−	21.8564i		−	1.54936i	−0.632354	−	0.774680i	$-0.717911\pi$
$199$		−	21.8564i		−	1.54936i	0.632354	−	0.774680i	$-0.282089\pi$
$200$	14.1419	−	0.0849223i	0.999982	−	0.00600491i
$201$			0.702368i			0.0495412i
$202$	−2.50786	−	3.54556i	−0.176452	−	0.249465i
$203$	8.35679	−	8.35679i	0.586532	−	0.586532i
$204$	2.31643	−	1.10713i	0.162182	−	0.0775144i
$205$	7.23724	−	1.90717i	0.505471	−	0.133203i
$206$	21.4348	+	3.67446i	1.49344	+	0.256012i
$207$		−	0.394542i		−	0.0274226i
$208$	−1.08500	−	10.1684i	−0.0752314	−	0.705054i
$209$	−15.2711			−1.05632
$210$	2.03178	−	2.42445i	0.140206	−	0.167303i
$211$	0.478227	−	0.478227i	0.0329225	−	0.0329225i	−0.690454	−	0.723376i	$-0.742589\pi$
$211$	0.478227	−	0.478227i	0.0329225	−	0.0329225i	0.723376	+	0.690454i	$0.242589\pi$
$212$	−8.67708	+	4.14718i	−0.595944	+	0.284829i
$213$	−1.71458	+	1.71458i	−0.117481	+	0.117481i
$214$	−11.4040	+	8.06629i	−0.779559	+	0.551400i
$215$	7.40101	+	4.31388i	0.504745	+	0.294204i
$216$	4.19615	−	1.18881i	0.285512	−	0.0808883i
$217$	8.71196			0.591406
$218$	−14.0373	+	9.92891i	−0.950726	+	0.672471i
$219$	−1.80623	−	1.80623i	−0.122054	−	0.122054i
$220$	7.71765	−	6.54698i	0.520324	−	0.441397i
$221$	8.92820	−	8.92820i	0.600576	−	0.600576i
$222$	2.22912	+	0.382126i	0.149609	+	0.0256466i
$223$		−	7.50859i		−	0.502813i	−0.967882	−	0.251406i	$-0.919107\pi$
$223$		−	7.50859i		−	0.502813i	0.967882	−	0.251406i	$-0.0808930\pi$
$224$	−14.3867	−	16.3396i	−0.961249	−	1.09173i
$225$	7.22584	+	12.7580i	0.481722	+	0.850536i
$226$	−3.47258	+	20.2572i	−0.230993	+	1.34749i
$227$	−12.8788	−	12.8788i	−0.854798	−	0.854798i	0.135922	−	0.990720i	$-0.456600\pi$
$227$	−12.8788	−	12.8788i	−0.854798	−	0.854798i	−0.990720	+	0.135922i	$0.956600\pi$
$228$	3.30763	+	1.16835i	0.219053	+	0.0773759i
$229$	8.62166	+	8.62166i	0.569736	+	0.569736i	0.932054	−	0.362319i	$-0.118015\pi$
$229$	8.62166	+	8.62166i	0.569736	+	0.569736i	−0.362319	+	0.932054i	$0.618015\pi$
$230$	0.0373459	+	0.423823i	0.00246251	+	0.0279461i
$231$		−	2.26371i		−	0.148941i
$232$	−8.35679	+	2.36756i	−0.548650	+	0.155438i
$233$	4.63429			0.303602			0.151801	−	0.988411i	$-0.451493\pi$
$233$	4.63429			0.303602			0.151801	+	0.988411i	$0.451493\pi$
$234$	8.65580	−	6.12245i	0.565847	−	0.400237i
$235$	15.2080	−	4.00765i	0.992063	−	0.261430i
$236$	−0.130662	−	0.273382i	−0.00850535	−	0.0177956i
$237$	2.02304	+	2.02304i	0.131411	+	0.131411i
$238$	4.54172	−	26.4940i	0.294396	−	1.71735i
$239$	18.4220			1.19162			0.595810	−	0.803126i	$-0.296831\pi$
$239$	18.4220			1.19162			0.595810	+	0.803126i	$0.296831\pi$
$240$	−2.17249	+	0.827582i	−0.140234	+	0.0534202i
$241$	18.3247			1.18040			0.590200	−	0.807257i	$-0.299049\pi$
$241$	18.3247			1.18040			0.590200	+	0.807257i	$0.299049\pi$
$242$	−1.40470	+	8.19428i	−0.0902975	+	0.526748i
$243$	4.81418	+	4.81418i	0.308830	+	0.308830i
$244$	−8.84016	+	4.22512i	−0.565933	+	0.270486i
$245$	−4.45082	−	16.8897i	−0.284352	−	1.07905i
$246$	−1.00445	+	0.710473i	−0.0640416	+	0.0452981i
$247$	17.2518			1.09770
$248$	−5.59007	−	3.12189i	−0.354970	−	0.198240i
$249$		−	3.23827i		−	0.205217i
$250$	−8.96973	−	13.0209i	−0.567295	−	0.823514i
$251$	−16.0222	−	16.0222i	−1.01131	−	1.01131i	−0.999935	−	0.0113760i	$-0.996379\pi$
$251$	−16.0222	−	16.0222i	−1.01131	−	1.01131i	−0.0113760	−	0.999935i	$-0.503621\pi$
$252$	7.51760	−	21.2825i	0.473564	−	1.34067i
$253$	0.215297	+	0.215297i	0.0135356	+	0.0135356i
$254$	−1.42559	+	8.31613i	−0.0894494	+	0.521801i
$255$	−2.47992	−	1.44549i	−0.155299	−	0.0905201i
$256$	3.37605	+	15.6398i	0.211003	+	0.977485i
$257$		−	5.82098i		−	0.363103i	−0.983381	−	0.181551i	$-0.941888\pi$
$257$		−	5.82098i		−	0.363103i	0.983381	−	0.181551i	$-0.0581119\pi$
$258$	−1.38797	−	0.237933i	−0.0864114	−	0.0148130i
$259$	16.7436	−	16.7436i	1.04040	−	1.04040i
$260$	−8.71866	+	7.39615i	−0.540708	+	0.458689i
$261$	−6.36758	−	6.36758i	−0.394143	−	0.394143i
$262$	−3.87117	+	2.73817i	−0.239161	+	0.169164i
$263$	−0.806693			−0.0497428			−0.0248714	−	0.999691i	$-0.507918\pi$
$263$	−0.806693			−0.0497428			−0.0248714	+	0.999691i	$0.507918\pi$
$264$	−0.811190	+	1.45252i	−0.0499253	+	0.0893965i
$265$	9.28951	+	5.41465i	0.570650	+	0.332619i
$266$	29.9848	−	21.2089i	1.83849	−	1.30040i
$267$	0.206075	−	0.206075i	0.0126116	−	0.0126116i
$268$	−2.33056	−	4.87620i	−0.142362	−	0.297861i
$269$	−15.1939	+	15.1939i	−0.926387	+	0.926387i	−0.997470	−	0.0710837i	$-0.977354\pi$
$269$	−15.1939	+	15.1939i	−0.926387	+	0.926387i	0.0710837	+	0.997470i	$0.477354\pi$
$270$	−3.73725	−	3.13196i	−0.227442	−	0.190605i
$271$	−10.8491			−0.659034			−0.329517	−	0.944150i	$-0.606886\pi$
$271$	−10.8491			−0.659034			−0.329517	+	0.944150i	$0.606886\pi$
$272$	−12.4082	+	15.3725i	−0.752358	+	0.932094i
$273$			2.55732i			0.154776i
$274$	25.4724	+	4.36660i	1.53885	+	0.263796i
$275$	−10.9049	−	3.01886i	−0.657593	−	0.182044i
$276$	−0.0301603	−	0.0631039i	−0.00181543	−	0.00379841i
$277$	1.27334	−	1.27334i	0.0765074	−	0.0765074i	−0.667818	−	0.744325i	$-0.732771\pi$
$277$	1.27334	−	1.27334i	0.0765074	−	0.0765074i	0.744325	+	0.667818i	$0.232771\pi$
$278$	0.157180	+	0.222218i	0.00942703	+	0.0133278i
$279$		−	6.63820i		−	0.397419i
$280$	−6.06099	+	23.5735i	−0.362214	+	1.40879i
$281$			20.2174i			1.20607i	0.797716	+	0.603033i	$0.206041\pi$
$281$			20.2174i			1.20607i	−0.797716	+	0.603033i	$0.793959\pi$
$282$	−2.11072	+	1.49296i	−0.125691	+	0.0889044i
$283$	−21.3741	+	21.3741i	−1.27056	+	1.27056i	−0.324759	+	0.945797i	$0.605283\pi$
$283$	−21.3741	+	21.3741i	−1.27056	+	1.27056i	−0.945797	+	0.324759i	$0.894717\pi$
$284$	6.21425	−	17.5927i	0.368748	−	1.04393i
$285$	−0.999404	−	3.79249i	−0.0591996	−	0.224648i
$286$	−1.38242	+	8.06430i	−0.0817441	+	0.476852i
$287$			12.8814i			0.760363i
$288$	−12.4502	+	10.9621i	−0.733634	+	0.645949i
$289$	−7.39230			−0.434841
$290$	7.44287	+	6.23741i	0.437061	+	0.366273i
$291$	−1.12197	+	1.12197i	−0.0657710	+	0.0657710i
$292$	18.5332	+	6.54645i	1.08457	+	0.383102i
$293$	11.1656	−	11.1656i	0.652301	−	0.652301i	−0.301246	−	0.953547i	$-0.597402\pi$
$293$	11.1656	−	11.1656i	0.652301	−	0.652301i	0.953547	+	0.301246i	$0.0974024\pi$
$294$	1.65805	+	2.34412i	0.0966995	+	0.136712i
$295$	−0.170595	+	0.292677i	−0.00993241	+	0.0170403i
$296$	−16.7436	+	4.74363i	−0.973204	+	0.275718i
$297$	−3.48947			−0.202480
$298$	2.77275	+	3.92006i	0.160621	+	0.227083i
$299$	−0.243221	−	0.243221i	−0.0140659	−	0.0140659i
$300$	2.13099	+	1.48818i	0.123033	+	0.0859200i
$301$	−10.4255	+	10.4255i	−0.600916	+	0.600916i
$302$	4.29946	−	25.0808i	0.247406	−	1.44324i
$303$		−	0.798174i		−	0.0458539i
$304$	−26.8400	+	2.86391i	−1.53938	+	0.164256i
$305$	9.46410	+	5.51641i	0.541913	+	0.315869i
$306$	−20.1875	−	3.46063i	−1.15404	−	0.197831i
$307$	2.18143	+	2.18143i	0.124501	+	0.124501i	0.766612	−	0.642111i	$-0.221941\pi$
$307$	2.18143	+	2.18143i	0.124501	+	0.124501i	−0.642111	+	0.766612i	$0.721941\pi$
$308$	7.51132	+	15.7158i	0.427997	+	0.895493i
$309$	2.82629	+	2.82629i	0.160782	+	0.160782i
$310$	0.628347	+	7.13085i	0.0356877	+	0.405005i
$311$		−	11.5517i		−	0.655038i	−0.944845	−	0.327519i	$-0.893787\pi$
$311$		−	11.5517i		−	0.655038i	0.944845	−	0.327519i	$-0.106213\pi$
$312$	0.916404	−	1.64092i	0.0518812	−	0.0928987i
$313$	−10.4265			−0.589343			−0.294671	−	0.955599i	$-0.595210\pi$
$313$	−10.4265			−0.589343			−0.294671	+	0.955599i	$0.595210\pi$
$314$	14.5937	+	20.6323i	0.823569	+	1.16435i
$315$	−24.4023	+	6.43053i	−1.37491	+	0.362320i
$316$	−20.7578	−	7.33225i	−1.16772	−	0.412471i
$317$	10.0785	+	10.0785i	0.566063	+	0.566063i	0.931023	−	0.364960i	$-0.118917\pi$
$317$	10.0785	+	10.0785i	0.566063	+	0.566063i	−0.364960	+	0.931023i	$0.618917\pi$
$318$	−1.74214	−	0.298645i	−0.0976943	−	0.0167472i
$319$	6.94941			0.389092
$320$	12.3365	−	12.9542i	0.689633	−	0.724159i
$321$	−2.56725			−0.143290
$322$	−0.721747	−	0.123725i	−0.0402214	−	0.00689493i
$323$	−23.5663	−	23.5663i	−1.31127	−	1.31127i
$324$	−15.8343	−	5.59313i	−0.879683	−	0.310730i
$325$	12.3194	+	3.41041i	0.683355	+	0.189176i
$326$	−18.3023	−	25.8754i	−1.01367	−	1.43311i
$327$	−3.16007			−0.174752
$328$	4.61598	−	8.26539i	0.254875	−	0.456380i
$329$			27.0684i			1.49233i
$330$	1.85288	−	0.163269i	0.101997	−	0.00898768i
$331$	8.77162	+	8.77162i	0.482132	+	0.482132i	0.905812	−	0.423680i	$-0.139262\pi$
$331$	8.77162	+	8.77162i	0.482132	+	0.482132i	−0.423680	+	0.905812i	$0.639262\pi$
$332$	10.7450	+	22.4817i	0.589711	+	1.23384i
$333$	−12.7580	−	12.7580i	−0.699137	−	0.699137i
$334$	17.7802	+	3.04797i	0.972891	+	0.166777i
$335$	−3.04283	+	5.22036i	−0.166248	+	0.285219i
$336$	−0.424532	−	3.97864i	−0.0231601	−	0.217052i
$337$			33.0226i			1.79885i	0.437072	+	0.899427i	$0.356016\pi$
$337$			33.0226i			1.79885i	−0.437072	+	0.899427i	$0.643984\pi$
$338$	−1.54457	+	9.01019i	−0.0840134	+	0.490090i
$339$	−2.67101	+	2.67101i	−0.145070	+	0.145070i
$340$	22.0132	+	1.80659i	1.19384	+	0.0979759i
$341$	3.62238	+	3.62238i	0.196163	+	0.196163i
$342$	−16.1604	−	22.8473i	−0.873857	−	1.23544i
$343$	3.12189			0.168566
$344$	10.4255	−	2.95365i	0.562106	−	0.159250i
$345$	−0.0393779	+	0.0675578i	−0.00212004	+	0.00363719i
$346$	−3.05680	−	4.32164i	−0.164334	−	0.232333i
$347$	11.1412	−	11.1412i	0.598090	−	0.598090i	−0.341714	−	0.939804i	$-0.611007\pi$
$347$	11.1412	−	11.1412i	0.598090	−	0.598090i	0.939804	+	0.341714i	$0.111007\pi$
$348$	−1.50520	−	0.531682i	−0.0806874	−	0.0285012i
$349$	−10.8656	+	10.8656i	−0.581622	+	0.581622i	−0.935349	−	0.353727i	$-0.884914\pi$
$349$	−10.8656	+	10.8656i	−0.581622	+	0.581622i	0.353727	+	0.935349i	$0.384914\pi$
$350$	25.6046	−	9.21760i	1.36862	−	0.492701i
$351$	3.94207			0.210412
$352$	0.812017	−	12.7758i	0.0432806	−	0.680952i
$353$			11.3480i			0.603995i	0.953309	+	0.301998i	$0.0976534\pi$
$353$			11.3480i			0.603995i	−0.953309	+	0.301998i	$0.902347\pi$
$354$	0.00940917	−	0.0548881i	0.000500092	−	0.00291727i
$355$	−20.1716	+	5.31566i	−1.07060	+	0.282126i
$356$	−0.746892	+	2.11447i	−0.0395852	+	0.112067i
$357$	3.49337	−	3.49337i	0.184889	−	0.184889i
$358$	19.0219	−	13.4546i	1.00534	−	0.711098i
$359$		−	26.5788i		−	1.40278i	−0.712779	−	0.701389i	$-0.752564\pi$
$359$		−	26.5788i		−	1.40278i	0.712779	−	0.701389i	$-0.247436\pi$
$360$	17.9622	+	4.61826i	0.946691	+	0.243404i
$361$		−	26.5367i		−	1.39667i
$362$	−1.43584	−	2.02997i	−0.0754661	−	0.106693i
$363$	−1.08046	+	1.08046i	−0.0567093	+	0.0567093i
$364$	−8.48557	−	17.7542i	−0.444765	−	0.930575i
$365$	−5.59982	−	21.2499i	−0.293108	−	1.11227i
$366$	−1.77488	−	0.304258i	−0.0927745	−	0.0159038i
$367$		−	2.90729i		−	0.151760i	−0.997117	−	0.0758798i	$-0.975823\pi$
$367$		−	2.90729i		−	0.151760i	0.997117	−	0.0758798i	$-0.0241765\pi$
$368$	0.418776	+	0.338023i	0.0218302	+	0.0176207i
$369$	9.81514			0.510956
$370$	14.9125	+	12.4972i	0.775264	+	0.649701i
$371$	−13.0858	+	13.0858i	−0.679379	+	0.679379i
$372$	−0.507448	−	1.06173i	−0.0263100	−	0.0550480i
$373$	4.65522	−	4.65522i	0.241038	−	0.241038i	−0.576241	−	0.817280i	$-0.695481\pi$
$373$	4.65522	−	4.65522i	0.241038	−	0.241038i	0.817280	+	0.576241i	$0.195481\pi$
$374$	12.9045	−	9.12762i	0.667273	−	0.471978i
$375$	0.0360509	−	2.90576i	0.00186166	−	0.150053i
$376$	9.69982	−	17.3686i	0.500230	−	0.895715i
$377$	−7.85077			−0.404335
$378$	6.85159	−	4.84629i	0.352408	−	0.249266i
$379$	9.52106	+	9.52106i	0.489064	+	0.489064i	0.908011	−	0.418947i	$-0.137601\pi$
$379$	9.52106	+	9.52106i	0.489064	+	0.489064i	−0.418947	+	0.908011i	$0.637601\pi$
$380$	19.5224	+	23.0132i	1.00148	+	1.18055i
$381$	−1.09652	+	1.09652i	−0.0561767	+	0.0561767i
$382$	−7.06948	−	1.21188i	−0.361706	−	0.0620053i
$383$			6.92429i			0.353815i	0.984228	+	0.176907i	$0.0566093\pi$
$383$			6.92429i			0.353815i	−0.984228	+	0.176907i	$0.943391\pi$
$384$	−1.15332	+	2.70504i	−0.0588552	+	0.138041i
$385$	9.80695	−	16.8251i	0.499808	−	0.857485i
$386$	−0.550239	+	3.20980i	−0.0280064	+	0.163375i
$387$	7.94386	+	7.94386i	0.403809	+	0.403809i
$388$	4.06642	−	11.5121i	0.206441	−	0.584440i
$389$	−20.0232	−	20.0232i	−1.01521	−	1.01521i	−0.999882	−	0.0153322i	$-0.995119\pi$
$389$	−20.0232	−	20.0232i	−1.01521	−	1.01521i	−0.0153322	−	0.999882i	$-0.504881\pi$
$390$	−2.09320	+	0.184446i	−0.105993	+	0.00933978i
$391$			0.664493i			0.0336049i
$392$	−19.2892	−	10.7724i	−0.974250	−	0.544090i
$393$	−0.871474			−0.0439601
$394$	−13.1769	+	9.32029i	−0.663840	+	0.469550i
$395$	6.27199	+	23.8006i	0.315578	+	1.19754i
$396$	11.9749	−	5.72336i	0.601761	−	0.287610i
$397$	−3.81625	−	3.81625i	−0.191532	−	0.191532i	0.604826	−	0.796358i	$-0.293243\pi$
$397$	−3.81625	−	3.81625i	−0.191532	−	0.191532i	−0.796358	+	0.604826i	$0.793243\pi$
$398$	−5.22249	+	30.4652i	−0.261780	+	1.52708i
$399$	6.75015			0.337930
$400$	−19.7324	−	3.26077i	−0.986620	−	0.163038i
$401$	1.68031			0.0839108			0.0419554	−	0.999119i	$-0.486641\pi$
$401$	1.68031			0.0839108			0.0419554	+	0.999119i	$0.486641\pi$
$402$	0.167828	−	0.979017i	0.00837048	−	0.0488289i
$403$	−4.09222	−	4.09222i	−0.203848	−	0.203848i
$404$	2.64846	+	5.54133i	0.131766	+	0.275692i
$405$	4.78435	+	18.1554i	0.237736	+	0.902151i
$406$	−13.6452	+	9.65156i	−0.677200	+	0.478999i
$407$	13.9238			0.690177
$408$	−3.49337	+	0.989704i	−0.172947	+	0.0489977i
$409$			20.1317i			0.995448i	0.867335	+	0.497724i	$0.165831\pi$
$409$			20.1317i			0.995448i	−0.867335	+	0.497724i	$0.834169\pi$
$410$	−10.5436	+	0.929064i	−0.520710	+	0.0458832i
$411$	3.35867	+	3.35867i	0.165671	+	0.165671i
$412$	−28.9996	−	10.2435i	−1.42871	−	0.504662i
$413$	−0.412282	−	0.412282i	−0.0202871	−	0.0202871i
$414$	−0.0942741	+	0.549945i	−0.00463332	+	0.0270283i
$415$	14.0290	−	24.0685i	0.688655	−	1.18147i
$416$	−0.917338	+	14.4329i	−0.0449762	+	0.707629i
$417$			0.0500256i			0.00244976i
$418$	21.2860	+	3.64895i	1.04113	+	0.178476i
$419$	22.6570	−	22.6570i	1.10687	−	1.10687i	0.113306	−	0.993560i	$-0.463856\pi$
$419$	22.6570	−	22.6570i	1.10687	−	1.10687i	0.993560	−	0.113306i	$-0.0361442\pi$
$420$	−3.41138	+	2.89391i	−0.166458	+	0.141209i
$421$	−10.1583	−	10.1583i	−0.495084	−	0.495084i	0.414820	−	0.909904i	$-0.363845\pi$
$421$	−10.1583	−	10.1583i	−0.495084	−	0.495084i	−0.909904	+	0.414820i	$0.863845\pi$
$422$	−0.780862	+	0.552321i	−0.0380118	+	0.0268866i
$423$	20.6251			1.00283
$424$	13.0858	−	3.70732i	0.635501	−	0.180044i
$425$	−12.1698	−	21.4873i	−0.590324	−	1.04229i
$426$	2.79961	−	1.98023i	0.135641	−	0.0959423i
$427$	−13.3317	+	13.3317i	−0.645166	+	0.645166i
$428$	17.8232	−	8.51852i	0.861516	−	0.411758i
$429$	−1.06332	+	1.06332i	−0.0513375	+	0.0513375i
$430$	−9.28535	−	7.78148i	−0.447779	−	0.375256i
$431$	−26.1518			−1.25969			−0.629843	−	0.776723i	$-0.716881\pi$
$431$	−26.1518			−1.25969			−0.629843	+	0.776723i	$0.716881\pi$
$432$	−6.13300	+	0.654409i	−0.295074	+	0.0314853i
$433$			9.30795i			0.447312i	0.974668	+	0.223656i	$0.0717992\pi$
$433$			9.30795i			0.447312i	−0.974668	+	0.223656i	$0.928201\pi$
$434$	−12.1434	−	2.08168i	−0.582904	−	0.0999240i
$435$	0.454800	+	1.72585i	0.0218060	+	0.0827483i
$436$	21.9388	−	10.4856i	1.05068	−	0.502168i
$437$	−0.641992	+	0.641992i	−0.0307107	+	0.0307107i
$438$	2.08608	+	2.94927i	0.0996770	+	0.140921i
$439$			30.4799i			1.45473i	0.686252	+	0.727364i	$0.259255\pi$
$439$			30.4799i			1.45473i	−0.686252	+	0.727364i	$0.740745\pi$
$440$	−12.3219	+	7.28161i	−0.587422	+	0.347137i
$441$		−	22.9059i		−	1.09076i
$442$	−14.5782	+	10.3115i	−0.693415	+	0.490468i
$443$	16.7437	−	16.7437i	0.795516	−	0.795516i	−0.186869	−	0.982385i	$-0.559834\pi$
$443$	16.7437	−	16.7437i	0.795516	−	0.795516i	0.982385	+	0.186869i	$0.0598340\pi$
$444$	−3.01582	−	1.06528i	−0.143124	−	0.0505558i
$445$	2.42443	−	0.638890i	0.114929	−	0.0302863i
$446$	−1.79414	+	10.4661i	−0.0849552	+	0.495584i
$447$			0.882482i			0.0417399i
$448$	16.1490	+	26.2131i	0.762970	+	1.23845i
$449$	5.40502			0.255079			0.127539	−	0.991834i	$-0.459292\pi$
$449$	5.40502			0.255079			0.127539	+	0.991834i	$0.459292\pi$
$450$	−7.02348	−	19.5098i	−0.331090	−	0.919700i
$451$	−5.35600	+	5.35600i	−0.252204	+	0.252204i
$452$	9.68073	−	27.4064i	0.455343	−	1.28909i
$453$	3.30703	−	3.30703i	0.155378	−	0.155378i
$454$	14.8742	+	21.0289i	0.698081	+	0.986935i
$455$	−11.0789	+	19.0073i	−0.519389	+	0.891078i
$456$	−4.33127	−	2.41888i	−0.202830	−	0.113275i
$457$	34.5929			1.61819			0.809095	−	0.587678i	$-0.199958\pi$
$457$	34.5929			1.61819			0.809095	+	0.587678i	$0.199958\pi$
$458$	−9.95747	−	14.0777i	−0.465282	−	0.657807i
$459$	−5.38496	−	5.38496i	−0.251349	−	0.251349i
$460$	0.0492149	−	0.599682i	0.00229466	−	0.0279603i
$461$	14.3876	−	14.3876i	0.670099	−	0.670099i	−0.287640	−	0.957739i	$-0.592871\pi$
$461$	14.3876	−	14.3876i	0.670099	−	0.670099i	0.957739	+	0.287640i	$0.0928706\pi$
$462$	−0.540903	+	3.15534i	−0.0251651	+	0.146800i
$463$			20.6591i			0.960108i	0.877239	+	0.480054i	$0.159383\pi$
$463$			20.6591i			0.960108i	−0.877239	+	0.480054i	$0.840617\pi$
$464$	12.2141	−	1.30328i	0.567025	−	0.0605032i
$465$	−0.662536	+	1.13666i	−0.0307244	+	0.0527116i
$466$	−6.45965	−	1.10734i	−0.299237	−	0.0512966i
$467$	16.3222	+	16.3222i	0.755300	+	0.755300i	0.975463	−	0.220163i	$-0.0706590\pi$
$467$	16.3222	+	16.3222i	0.755300	+	0.755300i	−0.220163	+	0.975463i	$0.570659\pi$
$468$	−13.5281	+	6.46570i	−0.625336	+	0.298877i
$469$	−7.35371	−	7.35371i	−0.339563	−	0.339563i
$470$	−22.1558	+	1.95230i	−1.02197	+	0.0900527i
$471$			4.64472i			0.214017i
$472$	0.116804	+	0.412282i	0.00537632	+	0.0189768i
$473$	−8.66973			−0.398635
$474$	−2.33649	−	3.30328i	−0.107318	−	0.151725i
$475$	9.00192	−	32.5174i	0.413036	−	1.49200i
$476$	−12.6612	+	35.8442i	−0.580327	+	1.64292i
$477$	9.97088	+	9.97088i	0.456535	+	0.456535i
$478$	−25.6781	−	4.40185i	−1.17449	−	0.201336i
$479$	−19.5136			−0.891597			−0.445799	−	0.895133i	$-0.647080\pi$
$479$	−19.5136			−0.891597			−0.445799	+	0.895133i	$0.647080\pi$
$480$	3.22595	−	0.634443i	0.147244	−	0.0289582i
$481$	−15.7298			−0.717216
$482$	−25.5425	−	4.37862i	−1.16343	−	0.199440i
$483$	−0.0951660	−	0.0951660i	−0.00433020	−	0.00433020i
$484$	3.91597	−	11.0862i	0.177999	−	0.503918i
$485$	−13.1997	+	3.47841i	−0.599367	+	0.157946i
$486$	−5.56007	−	7.86072i	−0.252210	−	0.356570i
$487$	15.6638			0.709794			0.354897	−	0.934905i	$-0.384516\pi$
$487$	15.6638			0.709794			0.354897	+	0.934905i	$0.384516\pi$
$488$	13.3317	−	3.77700i	0.603498	−	0.170977i
$489$		−	5.82505i		−	0.263418i
$490$	2.16818	+	24.6058i	0.0979485	+	1.11158i
$491$	−17.9076	−	17.9076i	−0.808157	−	0.808157i	0.176198	−	0.984355i	$-0.443620\pi$
$491$	−17.9076	−	17.9076i	−0.808157	−	0.808157i	−0.984355	+	0.176198i	$0.943620\pi$
$492$	1.56985	−	0.750306i	0.0707745	−	0.0338264i
$493$	10.7244	+	10.7244i	0.483001	+	0.483001i
$494$	−24.0469	−	4.12223i	−1.08192	−	0.185468i
$495$	−12.8201	−	7.47254i	−0.576221	−	0.335866i
$496$	7.04593	+	5.68726i	0.316372	+	0.255366i
$497$		−	35.9029i		−	1.61046i
$498$	−0.773769	+	4.51376i	−0.0346734	+	0.202266i
$499$	−2.32067	+	2.32067i	−0.103887	+	0.103887i	−0.757140	−	0.653253i	$-0.773404\pi$
$499$	−2.32067	+	2.32067i	−0.103887	+	0.103887i	0.653253	+	0.757140i	$0.273404\pi$
$500$	9.39145	+	20.2929i	0.419998	+	0.907525i
$501$	2.34441	+	2.34441i	0.104741	+	0.104741i
$502$	18.5046	+	26.1615i	0.825900	+	1.16764i
$503$	−6.18913			−0.275960			−0.137980	−	0.990435i	$-0.544061\pi$
$503$	−6.18913			−0.275960			−0.137980	+	0.990435i	$0.544061\pi$
$504$	−15.5640	+	27.8690i	−0.693275	+	1.24138i
$505$	3.45789	−	5.93244i	0.153874	−	0.263990i
$506$	−0.248654	−	0.351542i	−0.0110540	−	0.0156279i
$507$	−1.18804	+	1.18804i	−0.0527627	+	0.0527627i
$508$	3.97420	−	11.2511i	0.176327	−	0.499185i
$509$	18.6217	−	18.6217i	0.825391	−	0.825391i	−0.161485	−	0.986875i	$-0.551628\pi$
$509$	18.6217	−	18.6217i	0.825391	−	0.825391i	0.986875	+	0.161485i	$0.0516282\pi$
$510$	3.11132	+	2.60741i	0.137772	+	0.115458i
$511$	37.8222			1.67315
$512$	−0.968769	−	22.6067i	−0.0428139	−	0.999083i
$513$		−	10.4052i		−	0.459403i
$514$	−1.39090	+	8.11375i	−0.0613498	+	0.357882i
$515$	8.76228	+	33.2507i	0.386112	+	1.46520i
$516$	1.87782	+	0.663300i	0.0826663	+	0.0292001i
$517$	−11.2549	+	11.2549i	−0.494988	+	0.494988i
$518$	−27.3395	+	19.3378i	−1.20123	+	0.849655i
$519$		−	0.972885i		−	0.0427049i
$520$	13.9201	−	8.22606i	0.610435	−	0.360737i
$521$			24.0232i			1.05247i	0.850338	+	0.526237i	$0.176397\pi$
$521$			24.0232i			1.05247i	−0.850338	+	0.526237i	$0.823603\pi$
$522$	7.35414	+	10.3972i	0.321882	+	0.455071i
$523$	16.1791	−	16.1791i	0.707463	−	0.707463i	−0.258538	−	0.966001i	$-0.583241\pi$
$523$	16.1791	−	16.1791i	0.707463	−	0.707463i	0.966001	+	0.258538i	$0.0832408\pi$
$524$	6.05022	−	2.89168i	0.264305	−	0.126324i
$525$	4.82023	+	1.33440i	0.210372	+	0.0582381i
$526$	1.12443	+	0.192756i	0.0490277	+	0.00840455i
$527$			11.1801i			0.487015i
$528$	1.47778	−	1.83081i	0.0643119	−	0.0796758i
$529$	−22.9819			−0.999213
$530$	−11.6547	−	9.76706i	−0.506247	−	0.424254i
$531$	−0.314144	+	0.314144i	−0.0136327	+	0.0136327i
$532$	−46.8630	+	22.3980i	−2.03177	+	0.971076i
$533$	6.05069	−	6.05069i	0.262084	−	0.262084i
$534$	−0.336485	+	0.238004i	−0.0145612	+	0.0102994i
$535$	−19.0811	−	11.1220i	−0.824950	−	0.480845i
$536$	2.08338	+	7.35371i	0.0899882	+	0.317632i
$537$	4.28219			0.184790
$538$	24.8090	−	17.5479i	1.06959	−	0.756546i
$539$	12.4994	+	12.4994i	0.538389	+	0.538389i
$540$	4.46092	+	5.25858i	0.191967	+	0.226293i
$541$	6.76526	−	6.76526i	0.290861	−	0.290861i	−0.546559	−	0.837420i	$-0.684063\pi$
$541$	6.76526	−	6.76526i	0.290861	−	0.290861i	0.837420	+	0.546559i	$0.184063\pi$
$542$	15.1223	+	2.59233i	0.649559	+	0.111350i
$543$		−	0.456984i		−	0.0196111i
$544$	20.9688	−	18.4625i	0.899028	−	0.791575i
$545$	−23.4873	−	13.6902i	−1.00608	−	0.586423i
$546$	0.611060	−	3.56460i	0.0261510	−	0.152551i
$547$	4.38359	+	4.38359i	0.187429	+	0.187429i	0.794584	−	0.607155i	$-0.207689\pi$
$547$	4.38359	+	4.38359i	0.187429	+	0.187429i	−0.607155	+	0.794584i	$0.707689\pi$
$548$	−34.4622	−	12.1730i	−1.47215	−	0.520006i
$549$	10.1583	+	10.1583i	0.433545	+	0.433545i
$550$	14.4789	+	6.81361i	0.617381	+	0.290533i
$551$			20.7224i			0.882805i
$552$	0.0269614	+	0.0951660i	0.00114755	+	0.00405053i
$553$	−42.3621			−1.80142
$554$	−2.07914	+	1.47062i	−0.0883341	+	0.0624808i
$555$	0.911234	+	3.45791i	0.0386797	+	0.146780i
$556$	−0.165992	−	0.347303i	−0.00703964	−	0.0147289i
$557$	−3.92396	−	3.92396i	−0.166264	−	0.166264i	0.619071	−	0.785335i	$-0.287509\pi$
$557$	−3.92396	−	3.92396i	−0.166264	−	0.166264i	−0.785335	+	0.619071i	$0.787509\pi$
$558$	−1.58617	+	9.25286i	−0.0671478	+	0.391705i
$559$	9.79422			0.414252
$560$	14.0811	−	31.4105i	0.595035	−	1.32733i
$561$	2.90504			0.122651
$562$	4.83085	−	28.1806i	0.203777	−	1.18873i
$563$	−6.61660	−	6.61660i	−0.278857	−	0.278857i	0.553796	−	0.832652i	$-0.313179\pi$
$563$	−6.61660	−	6.61660i	−0.278857	−	0.278857i	−0.832652	+	0.553796i	$0.813179\pi$
$564$	3.29883	−	1.57666i	0.138906	−	0.0663894i
$565$	−31.4239	+	8.28087i	−1.32201	+	0.348379i
$566$	34.9001	−	24.6857i	1.46696	−	1.03762i
$567$	−32.3144			−1.35708
$568$	−12.8656	+	23.0373i	−0.539830	+	0.966622i
$569$		−	40.2900i		−	1.68904i	−0.535521	−	0.844522i	$-0.679885\pi$
$569$		−	40.2900i		−	1.68904i	0.535521	−	0.844522i	$-0.320115\pi$
$570$	0.486852	+	5.52509i	0.0203920	+	0.231420i
$571$	22.6010	+	22.6010i	0.945823	+	0.945823i	0.998606	−	0.0527829i	$-0.0168091\pi$
$571$	22.6010	+	22.6010i	0.945823	+	0.945823i	−0.0527829	+	0.998606i	$0.516809\pi$
$572$	3.85385	−	10.9104i	0.161138	−	0.456185i
$573$	−0.932147	−	0.932147i	−0.0389410	−	0.0389410i
$574$	3.07795	−	17.9551i	0.128471	−	0.749432i
$575$	−0.585354	+	0.331530i	−0.0244110	+	0.0138257i
$576$	19.9734	−	12.3050i	0.832226	−	0.512707i
$577$			18.8020i			0.782737i	0.920234	+	0.391368i	$0.127998\pi$
$577$			18.8020i			0.782737i	−0.920234	+	0.391368i	$0.872002\pi$
$578$	10.3040	+	1.76636i	0.428590	+	0.0734708i
$579$	−0.423229	+	0.423229i	−0.0175888	+	0.0175888i
$580$	−8.88408	−	10.4727i	−0.368891	−	0.434853i
$581$	33.9043	+	33.9043i	1.40659	+	1.40659i
$582$	1.83198	−	1.29580i	0.0759380	−	0.0537127i
$583$	−10.8820			−0.450685
$584$	−24.2688	−	13.5534i	−1.00425	−	0.560843i
$585$	14.4829	+	8.44176i	0.598795	+	0.349024i
$586$	−18.2315	+	12.8955i	−0.753136	+	0.532710i
$587$	2.71961	−	2.71961i	0.112250	−	0.112250i	−0.648751	−	0.761001i	$-0.724708\pi$
$587$	2.71961	−	2.71961i	0.112250	−	0.112250i	0.761001	+	0.648751i	$0.224708\pi$
$588$	−1.75101	−	3.66361i	−0.0722104	−	0.151085i
$589$	−10.8016	+	10.8016i	−0.445071	+	0.445071i
$590$	0.307723	−	0.367194i	0.0126687	−	0.0151171i
$591$	−2.96636			−0.122020
$592$	24.4721	−	2.61124i	1.00580	−	0.107321i
$593$			4.04894i			0.166270i	0.996538	+	0.0831350i	$0.0264933\pi$
$593$			4.04894i			0.166270i	−0.996538	+	0.0831350i	$0.973507\pi$
$594$	4.86391	+	0.833793i	0.199568	+	0.0342109i
$595$	41.0986	−	10.8304i	1.68488	−	0.444003i
$596$	−2.92820	−	6.12664i	−0.119944	−	0.250957i
$597$	−4.01700	+	4.01700i	−0.164405	+	0.164405i
$598$	0.280905	+	0.397138i	0.0114871	+	0.0162402i
$599$			19.0455i			0.778178i	0.921200	+	0.389089i	$0.127210\pi$
$599$			19.0455i			0.778178i	−0.921200	+	0.389089i	$0.872790\pi$
$600$	−2.61475	−	2.58353i	−0.106747	−	0.105472i
$601$			14.4406i			0.589045i	0.955645	+	0.294522i	$0.0951606\pi$
$601$			14.4406i			0.589045i	−0.955645	+	0.294522i	$0.904839\pi$
$602$	17.0231	−	12.0408i	0.693808	−	0.490746i
$603$	−5.60327	+	5.60327i	−0.228183	+	0.228183i
$604$	−11.9859	+	33.9323i	−0.487698	+	1.38069i
$605$	−12.7113	+	3.34971i	−0.516789	+	0.136185i
$606$	−0.190720	+	1.11256i	−0.00774747	+	0.0451946i
$607$		−	46.3473i		−	1.88118i	−0.339546	−	0.940589i	$-0.610273\pi$
$607$		−	46.3473i		−	1.88118i	0.339546	−	0.940589i	$-0.389727\pi$
$608$	38.0961	+	2.42135i	1.54500	+	0.0981988i
$609$	−3.07180			−0.124475
$610$	−11.8737	−	9.95063i	−0.480753	−	0.402889i
$611$	12.7147	−	12.7147i	0.514380	−	0.514380i
$612$	27.3120	+	9.64740i	1.10402	+	0.389973i
$613$	0.961106	−	0.961106i	0.0388187	−	0.0388187i	−0.687431	−	0.726250i	$-0.741262\pi$
$613$	0.961106	−	0.961106i	0.0388187	−	0.0388187i	0.726250	+	0.687431i	$0.241262\pi$
$614$	−2.51941	−	3.56190i	−0.101675	−	0.143747i
$615$	−1.68066	−	0.979616i	−0.0677706	−	0.0395019i
$616$	−6.71467	−	23.7008i	−0.270542	−	0.954933i
$617$	3.44724			0.138781			0.0693903	−	0.997590i	$-0.477895\pi$
$617$	3.44724			0.138781			0.0693903	+	0.997590i	$0.477895\pi$
$618$	−3.26419	−	4.61485i	−0.131305	−	0.185636i
$619$	−24.5574	−	24.5574i	−0.987044	−	0.987044i	0.0128733	−	0.999917i	$-0.495902\pi$
$619$	−24.5574	−	24.5574i	−0.987044	−	0.987044i	−0.999917	+	0.0128733i	$0.995902\pi$
$620$	0.828044	−	10.0897i	0.0332550	−	0.405212i
$621$	−0.146697	+	0.146697i	−0.00588673	+	0.00588673i
$622$	−2.76023	+	16.1017i	−0.110675	+	0.645620i
$623$			4.31517i			0.172884i
$624$	−1.66945	+	2.06827i	−0.0668314	+	0.0827972i
$625$	12.8564	−	21.4409i	0.514256	−	0.857637i
$626$	14.5334	+	2.49137i	0.580870	+	0.0995753i
$627$	2.80667	+	2.80667i	0.112088	+	0.112088i
$628$	−15.4119	−	32.2460i	−0.615000	−	1.28676i
$629$	21.4873	+	21.4873i	0.856753	+	0.856753i
$630$	35.5504	−	3.13259i	1.41636	−	0.124805i
$631$		−	22.7950i		−	0.907456i	−0.891140	−	0.453728i	$-0.850094\pi$
$631$		−	22.7950i		−	0.907456i	0.891140	−	0.453728i	$-0.149906\pi$
$632$	27.1818	+	15.1803i	1.08124	+	0.603838i
$633$	−0.175787			−0.00698691
$634$	−11.6400	−	16.4564i	−0.462283	−	0.653567i
$635$	−12.9004	+	3.39952i	−0.511935	+	0.134906i
$636$	2.35697	+	0.832552i	0.0934601	+	0.0330128i
$637$	−14.1207	−	14.1207i	−0.559481	−	0.559481i
$638$	−9.68665	−	1.66053i	−0.383498	−	0.0657410i
$639$	−27.3567			−1.08221
$640$	−20.2910	+	15.1088i	−0.802072	+	0.597227i
$641$	30.4468			1.20258			0.601289	−	0.799032i	$-0.294654\pi$
$641$	30.4468			1.20258			0.601289	+	0.799032i	$0.294654\pi$
$642$	3.57844	+	0.613433i	0.141230	+	0.0242103i
$643$	−20.4452	−	20.4452i	−0.806282	−	0.806282i	0.177787	−	0.984069i	$-0.443106\pi$
$643$	−20.4452	−	20.4452i	−0.806282	−	0.806282i	−0.984069	+	0.177787i	$0.943106\pi$
$644$	0.976466	+	0.344916i	0.0384781	+	0.0135916i
$645$	−0.567385	−	2.15308i	−0.0223408	−	0.0847776i
$646$	27.2176	+	38.4798i	1.07086	+	1.51397i
$647$	−29.5876			−1.16321			−0.581604	−	0.813472i	$-0.697575\pi$
$647$	−29.5876			−1.16321			−0.581604	+	0.813472i	$0.697575\pi$
$648$	20.7347	+	11.5797i	0.814534	+	0.454893i
$649$		−	0.342849i		−	0.0134580i
$650$	−16.3568	−	7.69736i	−0.641567	−	0.301915i
$651$	−1.60117	−	1.60117i	−0.0627550	−	0.0627550i
$652$	19.3284	+	40.4405i	0.756958	+	1.58377i
$653$	21.2334	+	21.2334i	0.830928	+	0.830928i	0.987644	−	0.156716i	$-0.0500908\pi$
$653$	21.2334	+	21.2334i	0.830928	+	0.830928i	−0.156716	+	0.987644i	$0.550091\pi$
$654$	4.40476	+	0.755084i	0.172240	+	0.0295261i
$655$	−6.47725	−	3.77544i	−0.253087	−	0.147519i
$656$	−8.40910	+	10.4180i	−0.328320	+	0.406755i
$657$		−	28.8191i		−	1.12434i
$658$	6.46787	−	37.7301i	0.252144	−	1.47087i
$659$	−20.0222	+	20.0222i	−0.779954	+	0.779954i	−0.979823	−	0.199869i	$-0.935948\pi$
$659$	−20.0222	+	20.0222i	−0.779954	+	0.779954i	0.199869	+	0.979823i	$0.435948\pi$
$660$	−2.62170	−	0.215158i	−0.102050	−	0.00837503i
$661$	−19.9536	−	19.9536i	−0.776107	−	0.776107i	0.203059	−	0.979166i	$-0.434912\pi$
$661$	−19.9536	−	19.9536i	−0.776107	−	0.776107i	−0.979166	+	0.203059i	$0.934912\pi$
$662$	−10.1307	−	14.3225i	−0.393739	−	0.556661i
$663$	−3.28184			−0.127456
$664$	−9.60541	−	33.9043i	−0.372762	−	1.31574i
$665$	50.1706	+	29.2433i	1.94553	+	1.13401i
$666$	14.7347	+	20.8317i	0.570959	+	0.807211i
$667$	0.292152	−	0.292152i	0.0113122	−	0.0113122i
$668$	−24.0552	−	8.49701i	−0.930725	−	0.328759i
$669$	−1.38001	+	1.38001i	−0.0533542	+	0.0533542i
$670$	5.48873	−	6.54949i	0.212048	−	0.253029i
$671$	−11.0865			−0.427989
$672$	−0.358930	+	5.64719i	−0.0138460	+	0.217845i
$673$			2.91192i			0.112246i	0.998424	+	0.0561231i	$0.0178739\pi$
$673$			2.91192i			0.112246i	−0.998424	+	0.0561231i	$0.982126\pi$
$674$	7.89059	−	46.0295i	0.303934	−	1.77299i
$675$	2.05696	−	7.43031i	0.0791724	−	0.285993i
$676$	4.30589	−	12.1901i	0.165611	−	0.468849i
$677$	−34.6045	+	34.6045i	−1.32996	+	1.32996i	−0.424558	+	0.905401i	$0.639570\pi$
$677$	−34.6045	+	34.6045i	−1.32996	+	1.32996i	−0.905401	+	0.424558i	$0.860430\pi$
$678$	4.36130	−	3.08485i	0.167495	−	0.118473i
$679$		−	23.4938i		−	0.901609i
$680$	−30.2522	−	7.77813i	−1.16012	−	0.298278i
$681$			4.73401i			0.181408i
$682$	−4.18362	−	5.91472i	−0.160199	−	0.226486i
$683$	−24.7435	+	24.7435i	−0.946785	+	0.946785i	−0.998654	−	0.0518690i	$-0.983482\pi$
$683$	−24.7435	+	24.7435i	−0.946785	+	0.946785i	0.0518690	+	0.998654i	$0.483482\pi$
$684$	17.0665	+	35.7079i	0.652553	+	1.36533i
$685$	10.4128	+	39.5140i	0.397852	+	1.50975i
$686$	−4.35154	−	0.745961i	−0.166143	−	0.0284809i
$687$		−	3.16916i		−	0.120911i
$688$	−15.2377	+	1.62591i	−0.580931	+	0.0619871i
$689$	12.2934			0.468341
$690$	0.0710308	−	0.0847584i	0.00270410	−	0.00322670i
$691$	25.3782	−	25.3782i	0.965431	−	0.965431i	−0.0339907	−	0.999422i	$-0.510822\pi$
$691$	25.3782	−	25.3782i	0.965431	−	0.965431i	0.999422	+	0.0339907i	$0.0108217\pi$
$692$	3.22818	+	6.75427i	0.122717	+	0.256759i
$693$	18.0592	−	18.0592i	0.686011	−	0.686011i
$694$	−18.1916	+	12.8673i	−0.690544	+	0.488438i
$695$	−0.216723	+	0.371816i	−0.00822077	+	0.0141038i
$696$	1.97103	+	1.10076i	0.0747118	+	0.0417243i
$697$	−16.5308			−0.626148
$698$	17.7416	−	12.5491i	0.671531	−	0.474989i
$699$	−0.851738	−	0.851738i	−0.0322157	−	0.0322157i
$700$	−37.8923	+	6.73014i	−1.43219	+	0.254375i
$701$	−32.3544	+	32.3544i	−1.22201	+	1.22201i	−0.255094	+	0.966916i	$0.582106\pi$
$701$	−32.3544	+	32.3544i	−1.22201	+	1.22201i	−0.966916	+	0.255094i	$0.917894\pi$
$702$	−5.49477	−	0.941939i	−0.207387	−	0.0355512i
$703$			41.5194i			1.56593i
$704$	−4.18457	+	17.6139i	−0.157712	+	0.663849i
$705$	−3.53166	−	2.05852i	−0.133010	−	0.0775285i
$706$	2.71156	−	15.8178i	0.102051	−	0.595311i
$707$	8.35679	+	8.35679i	0.314290	+	0.314290i
$708$	−0.0262305	+	0.0742593i	−0.000985804	+	0.00279083i
$709$	6.64939	+	6.64939i	0.249723	+	0.249723i	0.820857	−	0.571134i	$-0.193496\pi$
$709$	6.64939	+	6.64939i	0.249723	+	0.249723i	−0.571134	+	0.820857i	$0.693496\pi$
$710$	29.3870	−	2.58948i	1.10287	−	0.0971815i
$711$			32.2784i			1.21053i
$712$	1.54632	−	2.76885i	0.0579509	−	0.103767i
$713$	0.304568			0.0114062
$714$	−5.70406	+	4.03461i	−0.213469	+	0.150992i
$715$	−12.5097	+	3.29658i	−0.467836	+	0.123285i
$716$	−29.7291	+	14.2089i	−1.11103	+	0.531013i
$717$	−3.38578	−	3.38578i	−0.126444	−	0.126444i
$718$	−6.35089	+	37.0477i	−0.237013	+	1.38261i
$719$	45.0785			1.68115			0.840573	−	0.541699i	$-0.182219\pi$
$719$	45.0785			1.68115			0.840573	+	0.541699i	$0.182219\pi$
$720$	−23.9337	−	10.7293i	−0.891955	−	0.399857i
$721$	−59.1820			−2.20405
$722$	−6.34083	+	36.9890i	−0.235981	+	1.37659i
$723$	−3.36791	−	3.36791i	−0.125254	−	0.125254i
$724$	1.51634	+	3.17262i	0.0563544	+	0.117909i
$725$	−4.09651	+	14.7977i	−0.152141	+	0.549574i
$726$	1.76420	−	1.24786i	0.0654756	−	0.0463124i
$727$	−18.6075			−0.690116			−0.345058	−	0.938581i	$-0.612141\pi$
$727$	−18.6075			−0.690116			−0.345058	+	0.938581i	$0.612141\pi$
$728$	7.58558	+	26.7749i	0.281140	+	0.992343i
$729$			23.4200i			0.867409i
$730$	2.72791	+	30.9579i	0.100964	+	1.14580i
$731$	−13.3792	−	13.3792i	−0.494846	−	0.494846i
$732$	2.40127	+	0.848199i	0.0887536	+	0.0313504i
$733$	7.95550	+	7.95550i	0.293843	+	0.293843i	0.838596	−	0.544753i	$-0.183377\pi$
$733$	7.95550	+	7.95550i	0.293843	+	0.293843i	−0.544753	+	0.838596i	$0.683377\pi$
$734$	−0.694685	+	4.05242i	−0.0256413	+	0.149578i
$735$	−2.28616	+	3.92219i	−0.0843261	+	0.144672i
$736$	−0.502955	−	0.571229i	−0.0185392	−	0.0210558i
$737$		−	6.11526i		−	0.225258i
$738$	−13.6811	−	2.34528i	−0.503610	−	0.0863311i
$739$	−15.2636	+	15.2636i	−0.561479	+	0.561479i	−0.929727	−	0.368249i	$-0.879958\pi$
$739$	−15.2636	+	15.2636i	−0.561479	+	0.561479i	0.368249	+	0.929727i	$0.379958\pi$
$740$	−17.8001	−	20.9830i	−0.654345	−	0.771349i
$741$	−3.17071	−	3.17071i	−0.116479	−	0.116479i
$742$	21.3668	−	15.1132i	0.784399	−	0.554824i
$743$	33.3017			1.22172			0.610861	−	0.791738i	$-0.290823\pi$
$743$	33.3017			1.22172			0.610861	+	0.791738i	$0.290823\pi$
$744$	0.453628	+	1.60117i	0.0166308	+	0.0587019i
$745$	−3.82313	+	6.55906i	−0.140069	+	0.240305i
$746$	−7.60117	+	5.37648i	−0.278299	+	0.196847i
$747$	25.8339	−	25.8339i	0.945211	−	0.945211i
$748$	−20.1683	+	9.63935i	−0.737425	+	0.352450i
$749$	26.8789	−	26.8789i	0.982132	−	0.982132i
$750$	−0.744568	+	4.04167i	−0.0271878	+	0.147581i
$751$	1.17214			0.0427720			0.0213860	−	0.999771i	$-0.493192\pi$
$751$	1.17214			0.0427720			0.0213860	+	0.999771i	$0.493192\pi$
$752$	−17.6705	+	21.8920i	−0.644378	+	0.798318i
$753$			5.88945i			0.214623i
$754$	10.9430	+	1.87591i	0.398522	+	0.0683165i
$755$	38.9064	−	10.2527i	1.41595	−	0.373134i
$756$	−10.7083	+	5.11799i	−0.389457	+	0.186140i
$757$	17.9408	−	17.9408i	0.652069	−	0.652069i	−0.301422	−	0.953491i	$-0.597461\pi$
$757$	17.9408	−	17.9408i	0.652069	−	0.652069i	0.953491	+	0.301422i	$0.0974612\pi$
$758$	−10.9962	−	15.5462i	−0.399400	−	0.564665i
$759$		−	0.0791389i		−	0.00287256i
$760$	−21.7130	−	36.7425i	−0.787614	−	1.33279i
$761$		−	15.4641i		−	0.560573i	−0.959916	−	0.280287i	$-0.909570\pi$
$761$		−	15.4641i		−	0.560573i	0.959916	−	0.280287i	$-0.0904295\pi$
$762$	1.79043	−	1.26642i	0.0648606	−	0.0458774i
$763$	33.0856	−	33.0856i	1.19778	−	1.19778i
$764$	9.56445	+	3.37844i	0.346030	+	0.122228i
$765$	−8.25237	−	31.3157i	−0.298365	−	1.13222i
$766$	1.65453	−	9.65164i	0.0597805	−	0.348728i
$767$			0.387318i			0.0139852i
$768$	2.25395	−	3.49492i	0.0813325	−	0.126112i
$769$	14.9777			0.540108			0.270054	−	0.962845i	$-0.412958\pi$
$769$	14.9777			0.540108			0.270054	+	0.962845i	$0.412958\pi$
$770$	−17.6900	+	21.1088i	−0.637503	+	0.760709i
$771$	−1.06984	+	1.06984i	−0.0385293	+	0.0385293i
$772$	1.53393	−	4.34260i	0.0552075	−	0.156294i
$773$	33.0120	−	33.0120i	1.18736	−	1.18736i	0.209566	−	0.977794i	$-0.432795\pi$
$773$	33.0120	−	33.0120i	1.18736	−	1.18736i	0.977794	−	0.209566i	$-0.0672052\pi$
$774$	−9.17465	−	12.9710i	−0.329776	−	0.466231i
$775$	−9.84862	+	5.57801i	−0.353773	+	0.200368i
$776$	−8.41888	+	15.0749i	−0.302220	+	0.541157i
$777$	−6.15464			−0.220796
$778$	23.1255	+	32.6944i	0.829088	+	1.17215i
$779$	−15.9710	−	15.9710i	−0.572222	−	0.572222i
$780$	2.96175	+	0.243065i	0.106048	+	0.00870313i
$781$	14.9282	−	14.9282i	0.534173	−	0.534173i
$782$	0.158778	−	0.926224i	0.00567788	−	0.0331217i
$783$			4.73512i			0.169219i
$784$	24.3128	+	19.6246i	0.868314	+	0.700877i
$785$	−20.1221	+	34.5220i	−0.718188	+	1.23214i
$786$	1.21473	+	0.208235i	0.0433280	+	0.00742749i
$787$	−28.8326	−	28.8326i	−1.02777	−	1.02777i	−0.999603	−	0.0281690i	$-0.991032\pi$
$787$	−28.8326	−	28.8326i	−1.02777	−	1.02777i	−0.0281690	−	0.999603i	$-0.508968\pi$
$788$	20.5940	−	9.84283i	0.733631	−	0.350636i
$789$	0.148262	+	0.148262i	0.00527828	+	0.00527828i
$790$	−3.05535	−	34.6739i	−0.108704	−	1.23364i
$791$		−	55.9305i		−	1.98866i
$792$	−18.0592	+	5.11633i	−0.641704	+	0.181801i
$793$	12.5244			0.444756
$794$	4.40752	+	6.23127i	0.156417	+	0.221139i
$795$	−0.712163	−	2.70248i	−0.0252578	−	0.0958472i
$796$	14.5591	−	41.2170i	0.516032	−	1.46090i
$797$	23.1556	+	23.1556i	0.820214	+	0.820214i	0.986139	−	0.165924i	$-0.0530607\pi$
$797$	23.1556	+	23.1556i	0.820214	+	0.820214i	−0.165924	+	0.986139i	$0.553061\pi$
$798$	−9.40891	−	1.61292i	−0.333072	−	0.0570967i
$799$	−34.7371			−1.22891
$800$	26.7255	+	9.26009i	0.944888	+	0.327394i
$801$	3.28801			0.116176
$802$	−2.34216	−	0.401503i	−0.0827044	−	0.0141776i
$803$	15.7262	+	15.7262i	0.554966	+	0.554966i
$804$	−0.467863	+	1.32453i	−0.0165003	+	0.0467126i
$805$	−0.295040	−	1.11961i	−0.0103988	−	0.0394609i
$806$	4.72625	+	6.68188i	0.166475	+	0.235359i
$807$	5.58497			0.196600
$808$	−2.36756	−	8.35679i	−0.0832905	−	0.293991i
$809$		−	36.2210i		−	1.27346i	−0.771086	−	0.636731i	$-0.780286\pi$
$809$		−	36.2210i		−	1.27346i	0.771086	−	0.636731i	$-0.219714\pi$
$810$	−2.33066	−	26.4497i	−0.0818911	−	0.929348i
$811$	9.17312	+	9.17312i	0.322112	+	0.322112i	0.849577	−	0.527465i	$-0.176857\pi$
$811$	9.17312	+	9.17312i	0.322112	+	0.322112i	−0.527465	+	0.849577i	$0.676857\pi$
$812$	21.3260	−	10.1927i	0.748395	−	0.357693i
$813$	1.99395	+	1.99395i	0.0699310	+	0.0699310i
$814$	−19.4081	−	3.32703i	−0.680254	−	0.116612i
$815$	25.2356	−	43.2948i	0.883963	−	1.51655i
$816$	5.10582	−	0.544806i	0.178740	−	0.0190720i
$817$		−	25.8522i		−	0.904456i
$818$	4.81038	−	28.0612i	0.168191	−	0.981137i
$819$	−20.4015	+	20.4015i	−0.712886	+	0.712886i
$820$	14.9185	+	1.22433i	0.520976	+	0.0427556i
$821$	7.26795	+	7.26795i	0.253653	+	0.253653i	0.822467	−	0.568813i	$-0.192597\pi$
$821$	7.26795	+	7.26795i	0.253653	+	0.253653i	−0.568813	+	0.822467i	$0.692597\pi$
$822$	−3.87905	−	5.48412i	−0.135297	−	0.191281i
$823$	28.2974			0.986384			0.493192	−	0.869920i	$-0.335830\pi$
$823$	28.2974			0.986384			0.493192	+	0.869920i	$0.335830\pi$
$824$	37.9744	+	21.2076i	1.32290	+	0.738801i
$825$	1.44939	+	2.55906i	0.0504612	+	0.0890951i
$826$	0.476160	+	0.673186i	0.0165677	+	0.0234231i
$827$	−18.1661	+	18.1661i	−0.631697	+	0.631697i	−0.948494	−	0.316797i	$-0.897393\pi$
$827$	−18.1661	+	18.1661i	−0.631697	+	0.631697i	0.316797	+	0.948494i	$0.397393\pi$
$828$	0.262814	−	0.744032i	0.00913341	−	0.0258569i
$829$	11.0865	−	11.0865i	0.385049	−	0.385049i	−0.487868	−	0.872917i	$-0.662225\pi$
$829$	11.0865	−	11.0865i	0.385049	−	0.385049i	0.872917	+	0.487868i	$0.162225\pi$
$830$	−25.3058	+	30.1964i	−0.878376	+	1.04813i
$831$	−0.468054			−0.0162366
$832$	4.72733	−	19.8985i	0.163891	−	0.689856i
$833$			38.5783i			1.33666i
$834$	0.0119534	−	0.0697297i	0.000413912	−	0.00241454i
$835$	7.26832	+	27.5815i	0.251531	+	0.954497i
$836$	−28.7983	−	10.1724i	−0.996010	−	0.351820i
$837$	−2.46818	+	2.46818i	−0.0853128	+	0.0853128i
$838$	−36.9949	+	26.1674i	−1.27797	+	0.903937i
$839$			11.9093i			0.411153i	0.978641	+	0.205577i	$0.0659069\pi$
$839$			11.9093i			0.411153i	−0.978641	+	0.205577i	$0.934093\pi$
$840$	5.44654	−	3.21864i	0.187924	−	0.111054i
$841$			19.5698i			0.674822i
$842$	11.7322	+	16.5867i	0.404317	+	0.571616i
$843$	3.71576	−	3.71576i	0.127977	−	0.127977i
$844$	1.22040	−	0.583287i	0.0420080	−	0.0200776i
$845$	−13.9770	+	3.68325i	−0.480824	+	0.126708i
$846$	−28.7490	−	4.92828i	−0.988410	−	0.169438i
$847$		−	22.6245i		−	0.777388i
$848$	−19.1259	+	2.04078i	−0.656784	+	0.0700808i
$849$	7.85669			0.269641
$850$	11.8290	+	32.8586i	0.405733	+	1.12704i
$851$	0.585354	−	0.585354i	0.0200657	−	0.0200657i
$852$	−4.37549	+	2.09125i	−0.149902	+	0.0716450i
$853$	2.44597	−	2.44597i	0.0837485	−	0.0837485i	−0.663992	−	0.747740i	$-0.731139\pi$
$853$	2.44597	−	2.44597i	0.0837485	−	0.0837485i	0.747740	+	0.663992i	$0.231139\pi$
$854$	21.7684	−	15.3973i	0.744898	−	0.526883i
$855$	22.2824	−	38.2282i	0.762041	−	1.30738i
$856$	−26.8789	+	7.61504i	−0.918700	+	0.260277i
$857$	2.57862			0.0880839			0.0440419	−	0.999030i	$-0.485976\pi$
$857$	2.57862			0.0880839			0.0440419	+	0.999030i	$0.485976\pi$
$858$	1.73622	−	1.22807i	0.0592734	−	0.0419254i
$859$	33.0076	+	33.0076i	1.12620	+	1.12620i	0.990789	+	0.135416i	$0.0432371\pi$
$859$	33.0076	+	33.0076i	1.12620	+	1.12620i	0.135416	+	0.990789i	$0.456763\pi$
$860$	11.0833	+	13.0651i	0.377938	+	0.445518i
$861$	2.36747	−	2.36747i	0.0806832	−	0.0806832i
$862$	36.4524	+	6.24884i	1.24158	+	0.212836i
$863$			23.5500i			0.801652i	0.916154	+	0.400826i	$0.131277\pi$
$863$			23.5500i			0.801652i	−0.916154	+	0.400826i	$0.868723\pi$
$864$	8.70504	+	0.553284i	0.296152	+	0.0188231i
$865$	4.21478	−	7.23099i	0.143307	−	0.245861i
$866$	2.22409	−	12.9742i	0.0755778	−	0.440881i
$867$	1.35863	+	1.35863i	0.0461416	+	0.0461416i
$868$	16.4291	+	5.80324i	0.557640	+	0.196975i
$869$	−17.6139	−	17.6139i	−0.597511	−	0.597511i
$870$	−0.221552	−	2.51431i	−0.00751132	−	0.0852429i
$871$			6.90843i			0.234083i
$872$	−33.0856	+	9.37346i	−1.12042	+	0.317425i
$873$	−17.9014			−0.605871
$874$	1.04826	−	0.741460i	0.0354580	−	0.0250803i
$875$	30.0455	+	30.8004i	1.01572	+	1.04124i
$876$	−2.20304	−	4.60939i	−0.0744338	−	0.155737i
$877$	−34.2135	−	34.2135i	−1.15531	−	1.15531i	−0.985472	−	0.169836i	$-0.945676\pi$
$877$	−34.2135	−	34.2135i	−1.15531	−	1.15531i	−0.169836	−	0.985472i	$-0.554324\pi$
$878$	7.28304	−	42.4854i	0.245791	−	1.43381i
$879$	−4.10426			−0.138433
$880$	18.9151	−	7.20545i	0.637628	−	0.242896i
$881$	40.6823			1.37062			0.685310	−	0.728251i	$-0.259667\pi$
$881$	40.6823			1.37062			0.685310	+	0.728251i	$0.259667\pi$
$882$	−5.47325	+	31.9281i	−0.184294	+	1.07507i
$883$	−35.8531	−	35.8531i	−1.20655	−	1.20655i	−0.972137	−	0.234415i	$-0.924682\pi$
$883$	−35.8531	−	35.8531i	−1.20655	−	1.20655i	−0.234415	−	0.972137i	$-0.575318\pi$
$884$	22.7842	−	10.8896i	0.766315	−	0.366257i
$885$	0.0851449	−	0.0224375i	0.00286211	−	0.000754230i
$886$	−27.3395	+	19.3379i	−0.918489	+	0.649668i
$887$	−9.33231			−0.313348			−0.156674	−	0.987650i	$-0.550077\pi$
$887$	−9.33231			−0.313348			−0.156674	+	0.987650i	$0.550077\pi$
$888$	3.94915	+	2.20548i	0.132525	+	0.0740112i
$889$		−	22.9610i		−	0.770087i
$890$	−3.53203	+	0.311230i	−0.118394	+	0.0104325i
$891$	−13.4361	−	13.4361i	−0.450127	−	0.450127i
$892$	5.00165	−	14.1598i	0.167468	−	0.474105i
$893$	−33.5609	−	33.5609i	−1.12307	−	1.12307i
$894$	0.210865	−	1.23007i	0.00705238	−	0.0411398i
$895$	31.8274	+	18.5515i	1.06387	+	0.620108i
$896$	−16.2463	−	40.3966i	−0.542752	−	1.34956i
$897$			0.0894035i			0.00298510i
$898$	−7.53396	−	1.29151i	−0.251411	−	0.0430981i
$899$	4.91548	−	4.91548i	0.163940	−	0.163940i
$900$	5.12812	+	28.8725i	0.170937	+	0.962418i
$901$	−16.7931	−	16.7931i	−0.559459	−	0.559459i
$902$	8.74541	−	6.18583i	0.291190	−	0.205966i
$903$	3.83222			0.127528
$904$	−20.0424	+	35.8880i	−0.666601	+	1.19362i
$905$	1.97977	−	3.39654i	0.0658097	−	0.112905i
$906$	−5.39980	+	3.81941i	−0.179396	+	0.126891i
$907$	−33.2170	+	33.2170i	−1.10295	+	1.10295i	−0.108899	+	0.994053i	$0.534733\pi$
$907$	−33.2170	+	33.2170i	−1.10295	+	1.10295i	−0.994053	+	0.108899i	$0.965267\pi$
$908$	−15.7081	−	32.8659i	−0.521293	−	1.09069i
$909$	6.36758	−	6.36758i	0.211199	−	0.211199i
$910$	19.9845	−	23.8467i	0.662478	−	0.790511i
$911$	5.77870			0.191457			0.0957284	−	0.995407i	$-0.469482\pi$
$911$	5.77870			0.191457			0.0957284	+	0.995407i	$0.469482\pi$
$912$	5.45929	+	4.40658i	0.180775	+	0.145916i
$913$			28.1944i			0.933098i
$914$	−48.2184	−	8.26582i	−1.59492	−	0.273409i
$915$	−0.725548	−	2.75327i	−0.0239859	−	0.0910204i
$916$	10.5157	+	22.0019i	0.347449	+	0.726964i
$917$	9.12424	−	9.12424i	0.301309	−	0.301309i
$918$	6.21929	+	8.79271i	0.205267	+	0.290203i
$919$			50.8572i			1.67763i	0.544420	+	0.838813i	$0.316750\pi$
$919$			50.8572i			1.67763i	−0.544420	+	0.838813i	$0.683250\pi$
$920$	−0.211891	+	0.824127i	−0.00698584	+	0.0271706i
$921$		−	0.801852i		−	0.0264219i
$922$	−23.4925	+	16.6168i	−0.773685	+	0.547245i
$923$	−16.8644	+	16.8644i	−0.555100	+	0.555100i
$924$	1.50791	−	4.26893i	0.0496066	−	0.140437i
$925$	−8.20775	+	29.6487i	−0.269869	+	0.974842i
$926$	4.93639	−	28.7963i	0.162220	−	0.946304i
$927$			45.0945i			1.48110i
$928$	−17.3364	−	1.10189i	−0.569096	−	0.0361712i
$929$	21.6815			0.711346			0.355673	−	0.934611i	$-0.384252\pi$
$929$	21.6815			0.711346			0.355673	+	0.934611i	$0.384252\pi$
$930$	1.19510	−	1.42607i	0.0391888	−	0.0467625i
$931$	−37.2720	+	37.2720i	−1.22154	+	1.22154i
$932$	8.73939	+	3.08701i	0.286268	+	0.101118i
$933$	−2.12309	+	2.12309i	−0.0695070	+	0.0695070i
$934$	−18.8511	−	26.6513i	−0.616825	−	0.872056i
$935$	21.5918	+	12.5854i	0.706126	+	0.411585i
$936$	20.4015	−	5.77994i	0.666844	−	0.188923i
$937$	19.7948			0.646668			0.323334	−	0.946285i	$-0.395196\pi$
$937$	19.7948			0.646668			0.323334	+	0.946285i	$0.395196\pi$
$938$	8.49307	+	12.0073i	0.277308	+	0.392054i
$939$	1.91630	+	1.91630i	0.0625360	+	0.0625360i
$940$	31.3491	+	2.57276i	1.02249	+	0.0839142i
$941$	−29.4510	+	29.4510i	−0.960074	+	0.960074i	−0.999233	−	0.0391593i	$-0.987532\pi$
$941$	−29.4510	+	29.4510i	−0.960074	+	0.960074i	0.0391593	+	0.999233i	$0.487532\pi$
$942$	1.10983	−	6.47419i	0.0361604	−	0.210940i
$943$			0.450330i			0.0146648i
$944$	−0.0642973	−	0.602583i	−0.00209270	−	0.0196124i
$945$	11.4641	+	6.68216i	0.372927	+	0.217371i
$946$	12.0846	+	2.07159i	0.392903	+	0.0673533i
$947$	−4.11783	−	4.11783i	−0.133811	−	0.133811i	0.637029	−	0.770840i	$-0.280163\pi$
$947$	−4.11783	−	4.11783i	−0.133811	−	0.133811i	−0.770840	+	0.637029i	$0.780163\pi$
$948$	2.46748	+	5.16267i	0.0801400	+	0.167676i
$949$	−17.7660	−	17.7660i	−0.576708	−	0.576708i
$950$	−20.3175	+	43.1745i	−0.659187	+	1.40076i
$951$		−	3.70465i		−	0.120131i
$952$	26.2131	−	46.9373i	0.849571	−	1.52125i
$953$	−40.3245			−1.30624			−0.653119	−	0.757255i	$-0.726540\pi$
$953$	−40.3245			−1.30624			−0.653119	+	0.757255i	$0.726540\pi$
$954$	−11.5157	−	16.2807i	−0.372836	−	0.527108i
$955$	−2.88991	−	10.9665i	−0.0935153	−	0.354867i
$956$	34.7404	+	12.2713i	1.12358	+	0.396883i
$957$	−1.27723	−	1.27723i	−0.0412871	−	0.0412871i
$958$	27.1996	+	4.66268i	0.878779	+	0.150644i
$959$	−70.3298			−2.27107
$960$	−4.64818	+	0.113513i	−0.150019	+	0.00366360i
$961$	−25.8756			−0.834697
$962$	21.9254	+	3.75856i	0.706904	+	0.121181i
$963$	−20.4807	−	20.4807i	−0.659982	−	0.659982i
$964$	34.5570	+	12.2065i	1.11301	+	0.393146i
$965$	−4.97919	+	1.31212i	−0.160286	+	0.0422388i
$966$	0.109911	+	0.155390i	0.00353632	+	0.00499958i
$967$	58.1740			1.87075			0.935375	−	0.353656i	$-0.115062\pi$
$967$	58.1740			1.87075			0.935375	+	0.353656i	$0.115062\pi$
$968$	−8.10740	+	14.5171i	−0.260582	+	0.466599i
$969$			8.66254i			0.278281i
$970$	19.2300	−	1.69448i	0.617437	−	0.0544065i
$971$	−1.70830	−	1.70830i	−0.0548220	−	0.0548220i	0.679164	−	0.733986i	$-0.262342\pi$
$971$	−1.70830	−	1.70830i	−0.0548220	−	0.0548220i	−0.733986	+	0.679164i	$0.762342\pi$
$972$	5.87179	+	12.2855i	0.188338	+	0.394057i
$973$	−0.523762	−	0.523762i	−0.0167910	−	0.0167910i
$974$	−21.8335	−	3.74279i	−0.699589	−	0.119927i
$975$	−1.63738	−	2.89098i	−0.0524381	−	0.0925855i
$976$	−19.4853	+	2.07914i	−0.623709	+	0.0665516i
$977$			35.1811i			1.12554i	0.826612	+	0.562772i	$0.190265\pi$
$977$			35.1811i			1.12554i	−0.826612	+	0.562772i	$0.809735\pi$
$978$	−1.39187	+	8.11943i	−0.0445071	+	0.259631i
$979$	−1.79422	+	1.79422i	−0.0573436	+	0.0573436i
$980$	2.85726	−	34.8157i	0.0912718	−	1.11215i
$981$	−25.2100	−	25.2100i	−0.804894	−	0.804894i
$982$	20.6821	+	29.2399i	0.659992	+	0.933084i
$983$	27.7257			0.884312			0.442156	−	0.896938i	$-0.354214\pi$
$983$	27.7257			0.884312			0.442156	+	0.896938i	$0.354214\pi$
$984$	−2.36747	+	0.670728i	−0.0754723	+	0.0213820i
$985$	−22.0476	−	12.8510i	−0.702494	−	0.409468i
$986$	−12.3859	−	17.5110i	−0.394449	−	0.557664i
$987$	4.97491	−	4.97491i	0.158353	−	0.158353i
$988$	32.5336	+	11.4918i	1.03503	+	0.365603i
$989$	−0.364474	+	0.364474i	−0.0115896	+	0.0115896i
$990$	16.0842	+	13.4791i	0.511188	+	0.428395i
$991$	−7.02711			−0.223224			−0.111612	−	0.993752i	$-0.535601\pi$
$991$	−7.02711			−0.223224			−0.111612	+	0.993752i	$0.535601\pi$
$992$	−8.46225	−	9.61096i	−0.268677	−	0.305148i
$993$		−	3.22428i		−	0.102319i
$994$	−8.57883	+	50.0444i	−0.272104	+	1.58731i
$995$	−47.2590	+	12.4538i	−1.49821	+	0.394812i
$996$	2.15708	−	6.10675i	0.0683498	−	0.193500i
$997$	14.2467	−	14.2467i	0.451197	−	0.451197i	−0.444555	−	0.895752i	$-0.646638\pi$
$997$	14.2467	−	14.2467i	0.451197	−	0.451197i	0.895752	+	0.444555i	$0.146638\pi$
$998$	3.78924	−	2.68022i	0.119946	−	0.0848409i
$999$			9.48726i			0.300164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.q.c.69.1	yes	16
3.2	odd	2		720.2.bm.f.469.8		16
4.3	odd	2		320.2.q.c.49.5		16
5.2	odd	4		400.2.l.i.101.5		16
5.3	odd	4		400.2.l.i.101.4		16
5.4	even	2	inner	80.2.q.c.69.8	yes	16
8.3	odd	2		640.2.q.f.609.4		16
8.5	even	2		640.2.q.e.609.5		16
15.14	odd	2		720.2.bm.f.469.1		16
16.3	odd	4		320.2.q.c.209.4		16
16.5	even	4		640.2.q.e.289.4		16
16.11	odd	4		640.2.q.f.289.5		16
16.13	even	4	inner	80.2.q.c.29.8	yes	16
20.3	even	4		1600.2.l.h.1201.4		16
20.7	even	4		1600.2.l.h.1201.5		16
20.19	odd	2		320.2.q.c.49.4		16
40.19	odd	2		640.2.q.f.609.5		16
40.29	even	2		640.2.q.e.609.4		16
48.29	odd	4		720.2.bm.f.109.1		16
80.3	even	4		1600.2.l.h.401.4		16
80.13	odd	4		400.2.l.i.301.4		16
80.19	odd	4		320.2.q.c.209.5		16
80.29	even	4	inner	80.2.q.c.29.1	✓	16
80.59	odd	4		640.2.q.f.289.4		16
80.67	even	4		1600.2.l.h.401.5		16
80.69	even	4		640.2.q.e.289.5		16
80.77	odd	4		400.2.l.i.301.5		16
240.29	odd	4		720.2.bm.f.109.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.1	✓	16	80.29	even	4	inner
80.2.q.c.29.8	yes	16	16.13	even	4	inner
80.2.q.c.69.1	yes	16	1.1	even	1	trivial
80.2.q.c.69.8	yes	16	5.4	even	2	inner
320.2.q.c.49.4		16	20.19	odd	2
320.2.q.c.49.5		16	4.3	odd	2
320.2.q.c.209.4		16	16.3	odd	4
320.2.q.c.209.5		16	80.19	odd	4
400.2.l.i.101.4		16	5.3	odd	4
400.2.l.i.101.5		16	5.2	odd	4
400.2.l.i.301.4		16	80.13	odd	4
400.2.l.i.301.5		16	80.77	odd	4
640.2.q.e.289.4		16	16.5	even	4
640.2.q.e.289.5		16	80.69	even	4
640.2.q.e.609.4		16	40.29	even	2
640.2.q.e.609.5		16	8.5	even	2
640.2.q.f.289.4		16	80.59	odd	4
640.2.q.f.289.5		16	16.11	odd	4
640.2.q.f.609.4		16	8.3	odd	2
640.2.q.f.609.5		16	40.19	odd	2
720.2.bm.f.109.1		16	48.29	odd	4
720.2.bm.f.109.8		16	240.29	odd	4
720.2.bm.f.469.1		16	15.14	odd	2
720.2.bm.f.469.8		16	3.2	odd	2
1600.2.l.h.401.4		16	80.3	even	4
1600.2.l.h.401.5		16	80.67	even	4
1600.2.l.h.1201.4		16	20.3	even	4
1600.2.l.h.1201.5		16	20.7	even	4

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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39388 - 0.238945i) q^{2} +(-0.183790 - 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(0.212266 + 0.300098i) q^{6} +3.84853 q^{7} +(-2.46943 - 1.37910i) q^{8} -2.93244i q^{9} +O(q^{10})\)	\(q+(-1.39388 - 0.238945i) q^{2} +(-0.183790 - 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-0.569800 - 2.16225i) q^{5} +(0.212266 + 0.300098i) q^{6} +3.84853 q^{7} +(-2.46943 - 1.37910i) q^{8} -2.93244i q^{9} +(0.277574 + 3.15007i) q^{10} +(1.60020 + 1.60020i) q^{11} +(-0.224167 - 0.469021i) q^{12} +(-1.80775 - 1.80775i) q^{13} +(-5.36440 - 0.919589i) q^{14} +(-0.292677 + 0.502125i) q^{15} +(3.11256 + 2.51236i) q^{16} +4.93886i q^{17} +(-0.700694 + 4.08748i) q^{18} +(-4.77162 + 4.77162i) q^{19} +(0.365790 - 4.45715i) q^{20} +(-0.707323 - 0.707323i) q^{21} +(-1.84812 - 2.61284i) q^{22} +0.134544 q^{23} +(0.200391 + 0.707323i) q^{24} +(-4.35066 + 2.46410i) q^{25} +(2.08783 + 2.95174i) q^{26} +(-1.09033 + 1.09033i) q^{27} +(7.25760 + 2.56360i) q^{28} +(2.17142 - 2.17142i) q^{29} +(0.527937 - 0.629968i) q^{30} +2.26371 q^{31} +(-3.73822 - 4.24567i) q^{32} -0.588201i q^{33} +(1.18012 - 6.88418i) q^{34} +(-2.19289 - 8.32149i) q^{35} +(1.95337 - 5.53003i) q^{36} +(4.35066 - 4.35066i) q^{37} +(7.79123 - 5.51092i) q^{38} +0.664493i q^{39} +(-1.57488 + 6.12534i) q^{40} +3.34709i q^{41} +(0.816913 + 1.15494i) q^{42} +(-2.70896 + 2.70896i) q^{43} +(1.95174 + 4.08359i) q^{44} +(-6.34067 + 1.67091i) q^{45} +(-0.187538 - 0.0321487i) q^{46} +7.03343i q^{47} +(-0.110310 - 1.03381i) q^{48} +7.81119 q^{49} +(6.65308 - 2.39510i) q^{50} +(0.907714 - 0.907714i) q^{51} +(-2.20489 - 4.61325i) q^{52} +(-3.40020 + 3.40020i) q^{53} +(1.78031 - 1.25926i) q^{54} +(2.54823 - 4.37182i) q^{55} +(-9.50367 - 5.30752i) q^{56} +1.75396 q^{57} +(-3.54556 + 2.50786i) q^{58} +(-0.107127 - 0.107127i) q^{59} +(-0.886410 + 0.751953i) q^{60} +(-3.46410 + 3.46410i) q^{61} +(-3.15534 - 0.540903i) q^{62} -11.2856i q^{63} +(4.19615 + 6.81119i) q^{64} +(-2.87875 + 4.93886i) q^{65} +(-0.140548 + 0.819883i) q^{66} +(-1.91078 - 1.91078i) q^{67} +(-3.28989 + 9.31375i) q^{68} +(-0.0247279 - 0.0247279i) q^{69} +(1.06825 + 12.1231i) q^{70} -9.32899i q^{71} +(-4.04414 + 7.24146i) q^{72} +9.82769 q^{73} +(-7.10387 + 5.02473i) q^{74} +(1.25249 + 0.346730i) q^{75} +(-12.1769 + 5.81988i) q^{76} +(6.15840 + 6.15840i) q^{77} +(0.158778 - 0.926224i) q^{78} -11.0073 q^{79} +(3.65882 - 8.16168i) q^{80} -8.39654 q^{81} +(0.799772 - 4.66544i) q^{82} +(8.80967 + 8.80967i) q^{83} +(-0.862712 - 1.80504i) q^{84} +(10.6790 - 2.81416i) q^{85} +(4.42326 - 3.12867i) q^{86} -0.798174 q^{87} +(-1.74473 - 6.15840i) q^{88} +1.12125i q^{89} +(9.23740 - 0.813969i) q^{90} +(-6.95717 - 6.95717i) q^{91} +(0.253724 + 0.0896228i) q^{92} +(-0.416048 - 0.416048i) q^{93} +(1.68061 - 9.80377i) q^{94} +(13.0363 + 7.59857i) q^{95} +(-0.0932641 + 1.46736i) q^{96} -6.10461i q^{97} +(-10.8879 - 1.86645i) q^{98} +(4.69248 - 4.69248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6}+O(q^{10}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36} + 24 q^{40} - 8 q^{44} + 8 q^{45} - 28 q^{46} + 16 q^{49} + 24 q^{50} - 16 q^{51} + 40 q^{54} - 56 q^{56} - 24 q^{59} + 48 q^{60} - 16 q^{64} - 72 q^{66} + 32 q^{69} + 20 q^{70} + 48 q^{75} - 88 q^{76} + 16 q^{79} + 16 q^{80} - 16 q^{81} - 80 q^{84} - 28 q^{86} - 84 q^{90} - 16 q^{91} + 12 q^{94} + 32 q^{95} + 56 q^{96} + 88 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 8 * q^5 - 4 * q^6 - 12 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 4 * q^20 - 16 * q^21 - 32 * q^24 + 32 * q^26 - 16 * q^29 - 36 * q^30 + 16 * q^31 + 48 * q^34 - 24 * q^35 + 60 * q^36 + 24 * q^40 - 8 * q^44 + 8 * q^45 - 28 * q^46 + 16 * q^49 + 24 * q^50 - 16 * q^51 + 40 * q^54 - 56 * q^56 - 24 * q^59 + 48 * q^60 - 16 * q^64 - 72 * q^66 + 32 * q^69 + 20 * q^70 + 48 * q^75 - 88 * q^76 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 80 * q^84 - 28 * q^86 - 84 * q^90 - 16 * q^91 + 12 * q^94 + 32 * q^95 + 56 * q^96 + 88 * q^99

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