LMFDB - Embedded newform 80.2.q.c.69.8

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			69.8
Root			$-0.238945 - 1.39388i$ of defining polynomial
Character	$\chi$	$=$	80.69
Dual form			80.2.q.c.29.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.39388 + 0.238945i) q^{2} +(0.183790 + 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-2.16225 - 0.569800i) q^{5} +(0.212266 + 0.300098i) q^{6} -3.84853 q^{7} +(2.46943 + 1.37910i) q^{8} -2.93244i q^{9} +O(q^{10})$	\(q+(1.39388 + 0.238945i) q^{2} +(0.183790 + 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-2.16225 - 0.569800i) q^{5} +(0.212266 + 0.300098i) q^{6} -3.84853 q^{7} +(2.46943 + 1.37910i) q^{8} -2.93244i q^{9} +(-2.87777 - 1.31089i) 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} +(-3.69804 - 2.51486i) 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} +(-0.287977 - 0.769836i) q^{30} +2.26371 q^{31} +(3.73822 + 4.24567i) q^{32} +0.588201i q^{33} +(1.18012 - 6.88418i) q^{34} +(8.32149 + 2.19289i) q^{35} +(1.95337 - 5.53003i) q^{36} +(-4.35066 + 4.35066i) q^{37} +(-7.79123 + 5.51092i) q^{38} +0.664493i q^{39} +(-4.55371 - 4.38905i) q^{40} +3.34709i q^{41} +(-0.816913 - 1.15494i) q^{42} +(2.70896 - 2.70896i) q^{43} +(1.95174 + 4.08359i) q^{44} +(-1.67091 + 6.34067i) q^{45} +(-0.187538 - 0.0321487i) q^{46} -7.03343i q^{47} +(0.110310 + 1.03381i) q^{48} +7.81119 q^{49} +(5.47551 + 4.47423i) 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} +(-0.217456 - 1.14187i) 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} +(11.0752 + 5.04502i) q^{70} -9.32899i q^{71} +(4.04414 - 7.24146i) q^{72} -9.82769 q^{73} +(-7.10387 + 5.02473i) q^{74} +(0.346730 + 1.25249i) q^{75} +(-12.1769 + 5.81988i) q^{76} +(-6.15840 - 6.15840i) q^{77} +(-0.158778 + 0.926224i) q^{78} -11.0073 q^{79} +(-5.29859 - 7.20590i) q^{80} -8.39654 q^{81} +(-0.799772 + 4.66544i) q^{82} +(-8.80967 - 8.80967i) q^{83} +(-0.862712 - 1.80504i) q^{84} +(-2.81416 + 10.6790i) q^{85} +(4.42326 - 3.12867i) q^{86} +0.798174 q^{87} +(1.74473 + 6.15840i) q^{88} +1.12125i q^{89} +(-3.84412 + 8.43889i) 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	0.758169	−	0.652058i	$-0.226094\pi$
$3$	0.183790	+	0.183790i	0.106111	+	0.106111i	−0.652058	+	0.758169i	$0.726094\pi$
$4$	1.88581	+	0.666123i	0.942905	+	0.333062i
$5$	−2.16225	−	0.569800i	−0.966988	−	0.254822i
$5$	−2.16225	−	0.569800i	−0.966988	−	0.254822i
$6$	0.212266	+	0.300098i	0.0866573	+	0.122514i
$7$	−3.84853			−1.45461			−0.727304	−	0.686315i	$-0.759227\pi$
$7$	−3.84853			−1.45461			−0.727304	+	0.686315i	$0.759227\pi$
$8$	2.46943	+	1.37910i	0.873075	+	0.487586i
$9$		−	2.93244i		−	0.977481i
$10$	−2.87777	−	1.31089i	−0.910031	−	0.414541i
$11$	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	0.911866	−	0.410487i	$-0.134641\pi$
$13$	1.80775	+	1.80775i	0.501379	+	0.501379i	−0.410487	+	0.911866i	$0.634641\pi$
$14$	−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	$-0.795595\pi$
$17$		−	4.93886i		−	1.19785i	0.800806	−	0.598924i	$-0.204405\pi$
$18$	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	$0.968223\pi$
$20$	−3.69804	−	2.51486i	−0.826906	−	0.562340i
$21$	−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	$-0.504465\pi$
$23$	−0.134544			−0.0280543			−0.0140272	+	0.999902i	$0.504465\pi$
$24$	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	$0.157966\pi$
$30$	−0.287977	−	0.769836i	−0.0525771	−	0.140552i
$31$	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
$35$	8.32149	+	2.19289i	1.40659	+	0.370667i
$36$	1.95337	−	5.53003i	0.325561	−	0.921672i
$37$	−4.35066	+	4.35066i	−0.715243	+	0.715243i	−0.967627	−	0.252384i	$-0.918785\pi$
$37$	−4.35066	+	4.35066i	−0.715243	+	0.715243i	0.252384	+	0.967627i	$0.418785\pi$
$38$	−7.79123	+	5.51092i	−1.26390	+	0.893988i
$39$			0.664493i			0.106404i
$40$	−4.55371	−	4.38905i	−0.720005	−	0.693969i
$41$			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	−0.469709	−	0.882821i	$-0.655641\pi$
$43$	2.70896	−	2.70896i	0.413112	−	0.413112i	0.882821	+	0.469709i	$0.155641\pi$
$44$	1.95174	+	4.08359i	0.294236	+	0.615625i
$45$	−1.67091	+	6.34067i	−0.249084	+	0.945212i
$46$	−0.187538	−	0.0321487i	−0.0276510	−	0.00474006i
$47$		−	7.03343i		−	1.02593i	−0.858409	−	0.512966i	$-0.828547\pi$
$47$		−	7.03343i		−	1.02593i	0.858409	−	0.512966i	$-0.171453\pi$
$48$	0.110310	+	1.03381i	0.0159219	+	0.149217i
$49$	7.81119			1.11588
$50$	5.47551	+	4.47423i	0.774354	+	0.632752i
$51$	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	−0.433905	−	0.900958i	$-0.642865\pi$
$53$	3.40020	−	3.40020i	0.467053	−	0.467053i	0.900958	+	0.433905i	$0.142865\pi$
$54$	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	$0.753139\pi$
$60$	−0.217456	−	1.14187i	−0.0280735	−	0.147415i
$61$	−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	0.814127	−	0.580687i	$-0.197216\pi$
$67$	1.91078	+	1.91078i	0.233440	+	0.233440i	−0.580687	+	0.814127i	$0.697216\pi$
$68$	3.28989	−	9.31375i	0.398957	−	1.12946i
$69$	−0.0247279	−	0.0247279i	−0.00297689	−	0.00297689i
$70$	11.0752	+	5.04502i	1.32374	+	0.602995i
$71$		−	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	$-0.695045\pi$
$73$	−9.82769			−1.15024			−0.575122	+	0.818068i	$0.695045\pi$
$74$	−7.10387	+	5.02473i	−0.825808	+	0.584113i
$75$	0.346730	+	1.25249i	0.0400370	+	0.144625i
$76$	−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	$0.712548\pi$
$80$	−5.29859	−	7.20590i	−0.592400	−	0.805644i
$81$	−8.39654			−0.932949
$82$	−0.799772	+	4.66544i	−0.0883200	+	0.515212i
$83$	−8.80967	−	8.80967i	−0.966987	−	0.966987i	0.0324850	−	0.999472i	$-0.489658\pi$
$83$	−8.80967	−	8.80967i	−0.966987	−	0.966987i	−0.999472	+	0.0324850i	$0.989658\pi$
$84$	−0.862712	−	1.80504i	−0.0941297	−	0.196946i
$85$	−2.81416	+	10.6790i	−0.305239	+	1.15831i
$86$	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	$0.981073\pi$
$90$	−3.84412	+	8.43889i	−0.405206	+	0.889537i
$91$	−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	$0.100300\pi$
$97$			6.10461i			0.619829i	−0.950764	+	0.309915i	$0.899700\pi$
$98$	10.8879	+	1.86645i	1.09984	+	0.188540i
$99$	4.69248	−	4.69248i	0.471612	−	0.471612i
$100$	6.56311	+	7.54490i	0.656311	+	0.754490i
$101$	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	$-0.226367\pi$
$103$	15.3778			1.51522			0.757610	+	0.652707i	$0.226367\pi$
$104$	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	−0.958907	−	0.283720i	$-0.908431\pi$
$107$	−6.98419	+	6.98419i	−0.675187	+	0.675187i	0.283720	+	0.958907i	$0.408431\pi$
$108$	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	$0.0521694\pi$
$110$	−2.50731	−	6.70268i	−0.239062	−	0.639076i
$111$	−1.59922			−0.151791
$112$	−11.9788	−	9.66891i	−1.13189	−	0.913626i
$113$			14.5329i			1.36714i	0.729883	+	0.683572i	$0.239574\pi$
$113$			14.5329i			1.36714i	−0.729883	+	0.683572i	$0.760426\pi$
$114$	−2.44481	−	0.419100i	−0.228977	−	0.0392523i
$115$	0.290918	+	0.0766631i	0.0271282	+	0.00714887i
$116$	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
$120$	−0.0302637	−	1.64359i	−0.00276268	−	0.150039i
$121$		−	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
$125$	−8.00316	−	7.80701i	−0.715825	−	0.698280i
$126$	−2.69664	+	15.7308i	−0.240236	+	1.40141i
$127$			5.96617i			0.529412i	0.964329	+	0.264706i	$0.0852749\pi$
$127$			5.96617i			0.529412i	−0.964329	+	0.264706i	$0.914725\pi$
$128$	4.22144	+	10.4966i	0.373126	+	0.927781i
$129$	0.995761			0.0876719
$130$	−2.83251	−	7.57204i	−0.248428	−	0.664112i
$131$	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	$-0.214890\pi$
$137$	18.2745			1.56129			0.780646	+	0.624973i	$0.214890\pi$
$138$	−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	$0.752598\pi$
$140$	14.2320	+	9.67852i	1.20282	+	0.817984i
$141$	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	$0.794412\pi$
$150$	0.184025	+	1.82867i	0.0150256	+	0.149310i
$151$			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
$155$	−4.89471	−	1.28986i	−0.393152	−	0.103604i
$156$	−0.442634	+	1.25311i	−0.0354391	+	0.100329i
$157$	12.6359	+	12.6359i	1.00846	+	1.00846i	0.999964	+	0.00849213i	$0.00270316\pi$
$157$	12.6359	+	12.6359i	1.00846	+	1.00846i	0.00849213	+	0.999964i	$0.497297\pi$
$158$	−15.3429	−	2.63015i	−1.22062	−	0.209244i
$159$	1.24985			0.0991193
$160$	−5.66379	−	11.3102i	−0.447762	−	0.894153i
$161$	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	$-0.909087\pi$
$163$	−15.8470	−	15.8470i	−1.24123	−	1.24123i	−0.281743	−	0.959490i	$-0.590913\pi$
$164$	−2.22957	+	6.31197i	−0.174100	+	0.492882i
$165$	0.335157	−	1.27184i	0.0260919	−	0.0990125i
$166$	−10.1746	−	14.3847i	−0.789703	−	1.11647i
$167$	12.7559			0.987083			0.493541	−	0.869722i	$-0.335702\pi$
$167$	12.7559			0.987083			0.493541	+	0.869722i	$0.335702\pi$
$168$	−0.771212	−	2.72215i	−0.0595003	−	0.210019i
$169$		−	6.46410i		−	0.497239i
$170$	−6.47432	+	14.2129i	−0.496557	+	1.09008i
$171$	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	0.599299	−	0.800525i	$-0.295446\pi$
$173$	−2.64673	−	2.64673i	−0.201227	−	0.201227i	−0.800525	+	0.599299i	$0.795446\pi$
$174$	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	$0.461128\pi$
$180$	−7.37468	+	10.8443i	−0.549676	+	0.808285i
$181$	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
$190$	19.9867	−	7.47654i	1.44999	−	0.542405i
$191$	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	$0.0264114\pi$
$193$			2.30278i			0.165758i	−0.996560	+	0.0828788i	$0.973589\pi$
$194$	−1.45867	+	8.50910i	−0.104726	+	0.610918i
$195$	0.378628	−	1.43680i	0.0271141	−	0.102891i
$196$	14.7304	+	5.20322i	1.05217	+	0.371658i
$197$	−8.06997	+	8.06997i	−0.574961	+	0.574961i	−0.933511	−	0.358549i	$-0.883271\pi$
$197$	−8.06997	+	8.06997i	−0.574961	+	0.574961i	0.358549	+	0.933511i	$0.383271\pi$
$198$	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	$-0.282089\pi$
$200$	7.34538	+	12.0849i	0.519397	+	0.854533i
$201$			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
$205$	1.90717	−	7.23724i	0.133203	−	0.505471i
$206$	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
$210$	1.10829	+	2.96274i	0.0764791	+	0.204448i
$211$	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
$220$	−1.89331	−	9.94185i	−0.127647	−	0.670279i
$221$	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	$0.0808930\pi$
$223$			7.50859i			0.502813i	−0.967882	+	0.251406i	$0.919107\pi$
$224$	−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	0.990720	−	0.135922i	$-0.0433997\pi$
$227$	12.8788	+	12.8788i	0.854798	+	0.854798i	−0.135922	+	0.990720i	$0.543400\pi$
$228$	−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	$0.618015\pi$
$230$	0.387186	+	0.176373i	0.0255303	+	0.0116297i
$231$		−	2.26371i		−	0.148941i
$232$	8.35679	−	2.36756i	0.548650	−	0.155438i
$233$	−4.63429			−0.303602			−0.151801	−	0.988411i	$-0.548507\pi$
$233$	−4.63429			−0.303602			−0.151801	+	0.988411i	$0.548507\pi$
$234$	8.65580	−	6.12245i	0.565847	−	0.400237i
$235$	−4.00765	+	15.2080i	−0.261430	+	0.992063i
$236$	−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	$0.296831\pi$
$240$	0.350545	−	2.29820i	0.0226276	−	0.148348i
$241$	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
$245$	−16.8897	−	4.45082i	−1.07905	−	0.284352i
$246$	−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
$250$	−9.29001	−	12.7944i	−0.587552	−	0.809187i
$251$	−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	$0.0581119\pi$
$257$			5.82098i			0.363103i	−0.983381	+	0.181551i	$0.941888\pi$
$258$	1.38797	+	0.237933i	0.0864114	+	0.0148130i
$259$	16.7436	−	16.7436i	1.04040	−	1.04040i
$260$	−2.13888	−	11.2313i	−0.132648	−	0.696539i
$261$	−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	$-0.492082\pi$
$263$	0.806693			0.0497428			0.0248714	+	0.999691i	$0.492082\pi$
$264$	−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	$0.477354\pi$
$270$	−4.56701	+	1.70840i	−0.277939	+	0.103970i
$271$	−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
$275$	3.01886	+	10.9049i	0.182044	+	0.657593i
$276$	−0.0301603	−	0.0631039i	−0.00181543	−	0.00379841i
$277$	−1.27334	+	1.27334i	−0.0765074	+	0.0765074i	−0.744325	−	0.667818i	$-0.767229\pi$
$277$	−1.27334	+	1.27334i	−0.0765074	+	0.0765074i	0.667818	+	0.744325i	$0.267229\pi$
$278$	−0.157180	−	0.222218i	−0.00942703	−	0.0133278i
$279$		−	6.63820i		−	0.397419i
$280$	17.5251	+	16.8914i	1.04732	+	1.00945i
$281$			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	$-0.394717\pi$
$283$	21.3741	−	21.3741i	1.27056	−	1.27056i	0.945797	−	0.324759i	$-0.105283\pi$
$284$	6.21425	−	17.5927i	0.368748	−	1.04393i
$285$	3.79249	+	0.999404i	0.224648	+	0.0591996i
$286$	−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
$290$	−9.09537	+	3.40235i	−0.534098	+	0.199793i
$291$	−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	−0.953547	−	0.301246i	$-0.902598\pi$
$293$	−11.1656	+	11.1656i	−0.652301	+	0.652301i	0.301246	+	0.953547i	$0.402598\pi$
$294$	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
$300$	−0.180443	+	2.59292i	−0.0104179	+	0.149702i
$301$	−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	0.642111	−	0.766612i	$-0.278059\pi$
$307$	−2.18143	−	2.18143i	−0.124501	−	0.124501i	−0.766612	+	0.642111i	$0.778059\pi$
$308$	−7.51132	−	15.7158i	−0.427997	−	0.895493i
$309$	2.82629	+	2.82629i	0.160782	+	0.160782i
$310$	−6.51444	−	2.96748i	−0.369995	−	0.168542i
$311$		−	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	$-0.404790\pi$
$313$	10.4265			0.589343			0.294671	+	0.955599i	$0.404790\pi$
$314$	14.5937	+	20.6323i	0.823569	+	1.16435i
$315$	6.43053	−	24.4023i	0.362320	−	1.37491i
$316$	−20.7578	−	7.33225i	−1.16772	−	0.412471i
$317$	−10.0785	−	10.0785i	−0.566063	−	0.566063i	0.364960	−	0.931023i	$-0.381083\pi$
$317$	−10.0785	−	10.0785i	−0.566063	−	0.566063i	−0.931023	+	0.364960i	$0.881083\pi$
$318$	1.74214	+	0.298645i	0.0976943	+	0.0167472i
$319$	6.94941			0.389092
$320$	−5.19212	−	17.1185i	−0.290248	−	0.956951i
$321$	−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
$325$	3.41041	+	12.3194i	0.189176	+	0.683355i
$326$	−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
$330$	0.771069	−	1.69271i	0.0424460	−	0.0931805i
$331$	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	$-0.643984\pi$
$337$		−	33.0226i		−	1.79885i	0.437072	−	0.899427i	$-0.356016\pi$
$338$	1.54457	−	9.01019i	0.0840134	−	0.490090i
$339$	−2.67101	+	2.67101i	−0.145070	+	0.145070i
$340$	−12.4205	+	18.2641i	−0.673598	+	0.990509i
$341$	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	−0.939804	−	0.341714i	$-0.888993\pi$
$347$	−11.1412	+	11.1412i	−0.598090	+	0.598090i	0.341714	+	0.939804i	$0.388993\pi$
$348$	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	$0.384914\pi$
$350$	−21.0727	−	17.2192i	−1.12638	−	0.920407i
$351$	3.94207			0.210412
$352$	−0.812017	+	12.7758i	−0.0432806	+	0.680952i
$353$		−	11.3480i		−	0.603995i	−0.953309	−	0.301998i	$-0.902347\pi$
$353$		−	11.3480i		−	0.603995i	0.953309	−	0.301998i	$-0.0976534\pi$
$354$	0.00940917	−	0.0548881i	0.000500092	−	0.00291727i
$355$	−5.31566	+	20.1716i	−0.282126	+	1.07060i
$356$	−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	$-0.247436\pi$
$360$	−12.8706	+	13.3535i	−0.678341	+	0.703791i
$361$		−	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
$365$	21.2499	+	5.59982i	1.11227	+	0.293108i
$366$	−1.77488	−	0.304258i	−0.0927745	−	0.0159038i
$367$			2.90729i			0.151760i	0.997117	+	0.0758798i	$0.0241765\pi$
$367$			2.90729i			0.151760i	−0.997117	+	0.0758798i	$0.975823\pi$
$368$	−0.418776	−	0.338023i	−0.0218302	−	0.0176207i
$369$	9.81514			0.510956
$370$	18.2234	−	6.81694i	0.947391	−	0.354396i
$371$	−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	−0.817280	−	0.576241i	$-0.804519\pi$
$373$	−4.65522	+	4.65522i	−0.241038	+	0.241038i	0.576241	+	0.817280i	$0.304519\pi$
$374$	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	$0.637601\pi$
$380$	29.6456	−	5.64567i	1.52079	−	0.289617i
$381$	−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	$-0.943391\pi$
$383$		−	6.92429i		−	0.353815i	0.984228	−	0.176907i	$-0.0566093\pi$
$384$	−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	$-0.504881\pi$
$390$	0.871080	−	1.91226i	0.0441088	−	0.0968309i
$391$			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
$395$	23.8006	+	6.27199i	1.19754	+	0.315578i
$396$	11.9749	−	5.72336i	0.601761	−	0.287610i
$397$	3.81625	+	3.81625i	0.191532	+	0.191532i	0.796358	−	0.604826i	$-0.206757\pi$
$397$	3.81625	+	3.81625i	0.191532	+	0.191532i	−0.604826	+	0.796358i	$0.706757\pi$
$398$	5.22249	−	30.4652i	0.261780	−	1.52708i
$399$	6.75015			0.337930
$400$	7.35095	+	18.6001i	0.367548	+	0.930005i
$401$	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
$405$	18.1554	+	4.78435i	0.902151	+	0.237736i
$406$	−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	$0.834169\pi$
$410$	4.38768	−	9.63215i	0.216692	−	0.475698i
$411$	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	$-0.0361442\pi$
$420$	0.836888	+	4.39452i	0.0408359	+	0.214431i
$421$	−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
$430$	−11.3469	+	4.24460i	−0.547197	+	0.204693i
$431$	−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	$-0.928201\pi$
$433$		−	9.30795i		−	0.447312i	0.974668	−	0.223656i	$-0.0717992\pi$
$434$	−12.1434	−	2.08168i	−0.582904	−	0.0999240i
$435$	−1.72585	−	0.454800i	−0.0827483	−	0.0218060i
$436$	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	$0.740745\pi$
$440$	−0.263495	−	14.3102i	−0.0125616	−	0.682210i
$441$		−	22.9059i		−	1.09076i
$442$	14.5782	−	10.3115i	0.693415	−	0.490468i
$443$	−16.7437	+	16.7437i	−0.795516	+	0.795516i	−0.982385	−	0.186869i	$-0.940166\pi$
$443$	−16.7437	+	16.7437i	−0.795516	+	0.795516i	0.186869	+	0.982385i	$0.440166\pi$
$444$	−3.01582	−	1.06528i	−0.143124	−	0.0505558i
$445$	0.638890	−	2.42443i	0.0302863	−	0.114929i
$446$	−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	$0.459292\pi$
$450$	13.1204	−	16.0566i	0.618503	−	0.756916i
$451$	−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	$-0.800042\pi$
$457$	−34.5929			−1.61819			−0.809095	+	0.587678i	$0.800042\pi$
$458$	9.95747	+	14.0777i	0.465282	+	0.657807i
$459$	−5.38496	−	5.38496i	−0.251349	−	0.251349i
$460$	0.497548	+	0.338359i	0.0231983	+	0.0157761i
$461$	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	$-0.840617\pi$
$463$		−	20.6591i		−	0.960108i	0.877239	−	0.480054i	$-0.159383\pi$
$464$	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	0.220163	−	0.975463i	$-0.429341\pi$
$467$	−16.3222	−	16.3222i	−0.755300	−	0.755300i	−0.975463	+	0.220163i	$0.929341\pi$
$468$	13.5281	−	6.46570i	0.625336	−	0.298877i
$469$	−7.35371	−	7.35371i	−0.339563	−	0.339563i
$470$	−9.22008	+	20.2406i	−0.425291	+	0.933629i
$471$			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
$475$	−32.5174	+	9.00192i	−1.49200	+	0.413036i
$476$	−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	$0.647080\pi$
$480$	1.03776	−	3.11966i	0.0473672	−	0.142392i
$481$	−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
$485$	3.47841	−	13.1997i	0.157946	−	0.599367i
$486$	−5.56007	−	7.86072i	−0.252210	−	0.356570i
$487$	−15.6638			−0.709794			−0.354897	−	0.934905i	$-0.615484\pi$
$487$	−15.6638			−0.709794			−0.354897	+	0.934905i	$0.615484\pi$
$488$	−13.3317	+	3.77700i	−0.603498	+	0.170977i
$489$		−	5.82505i		−	0.263418i
$490$	−22.4788	−	10.2396i	−1.01549	−	0.462580i
$491$	−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	$0.273404\pi$
$500$	−9.89201	−	20.0536i	−0.442384	−	0.896826i
$501$	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	$-0.455939\pi$
$503$	6.18913			0.275960			0.137980	+	0.990435i	$0.455939\pi$
$504$	−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	$0.0516282\pi$
$510$	−3.80211	+	1.42228i	−0.168360	+	0.0629794i
$511$	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
$515$	−33.2507	−	8.76228i	−1.46520	−	0.386112i
$516$	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
$520$	−0.297671	−	16.1662i	−0.0130537	−	0.708937i
$521$			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	−0.966001	−	0.258538i	$-0.916759\pi$
$523$	−16.1791	+	16.1791i	−0.707463	+	0.707463i	0.258538	+	0.966001i	$0.416759\pi$
$524$	6.05022	−	2.89168i	0.264305	−	0.126324i
$525$	−1.33440	−	4.82023i	−0.0582381	−	0.210372i
$526$	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
$530$	−14.2423	+	5.32769i	−0.618645	+	0.231420i
$531$	−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
$540$	−6.77408	+	1.29005i	−0.291510	+	0.0555148i
$541$	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	0.607155	−	0.794584i	$-0.292311\pi$
$547$	−4.38359	−	4.38359i	−0.187429	−	0.187429i	−0.794584	+	0.607155i	$0.792311\pi$
$548$	34.4622	+	12.1730i	1.47215	+	0.520006i
$549$	10.1583	+	10.1583i	0.433545	+	0.433545i
$550$	1.60224	+	15.9215i	0.0683197	+	0.678897i
$551$			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
$555$	3.45791	+	0.911234i	0.146780	+	0.0386797i
$556$	−0.165992	−	0.347303i	−0.00703964	−	0.0147289i
$557$	3.92396	+	3.92396i	0.166264	+	0.166264i	0.785335	−	0.619071i	$-0.212491\pi$
$557$	3.92396	+	3.92396i	0.166264	+	0.166264i	−0.619071	+	0.785335i	$0.712491\pi$
$558$	1.58617	−	9.25286i	0.0671478	−	0.391705i
$559$	9.79422			0.414252
$560$	20.3918	+	27.7321i	0.861710	+	1.17190i
$561$	2.90504			0.122651
$562$	−4.83085	+	28.1806i	−0.203777	+	1.18873i
$563$	6.61660	+	6.61660i	0.278857	+	0.278857i	0.832652	−	0.553796i	$-0.186821\pi$
$563$	6.61660	+	6.61660i	0.278857	+	0.278857i	−0.553796	+	0.832652i	$0.686821\pi$
$564$	3.29883	−	1.57666i	0.138906	−	0.0663894i
$565$	8.28087	−	31.4239i	0.348379	−	1.32201i
$566$	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	$-0.320115\pi$
$570$	5.04748	+	2.29925i	0.211416	+	0.0963050i
$571$	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	$-0.872002\pi$
$577$		−	18.8020i		−	0.782737i	0.920234	−	0.391368i	$-0.127998\pi$
$578$	−10.3040	−	1.76636i	−0.428590	−	0.0734708i
$579$	−0.423229	+	0.423229i	−0.0175888	+	0.0175888i
$580$	−13.4908	+	2.56918i	−0.560177	+	0.106679i
$581$	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	−0.761001	−	0.648751i	$-0.775292\pi$
$587$	−2.71961	+	2.71961i	−0.112250	+	0.112250i	0.648751	+	0.761001i	$0.275292\pi$
$588$	1.75101	+	3.66361i	0.0722104	+	0.151085i
$589$	−10.8016	+	10.8016i	−0.445071	+	0.445071i
$590$	0.167855	+	0.448720i	0.00691048	+	0.0184735i
$591$	−2.96636			−0.122020
$592$	−24.4721	+	2.61124i	−1.00580	+	0.107321i
$593$		−	4.04894i		−	0.166270i	−0.996538	−	0.0831350i	$-0.973507\pi$
$593$		−	4.04894i		−	0.166270i	0.996538	−	0.0831350i	$-0.0264933\pi$
$594$	4.86391	+	0.833793i	0.199568	+	0.0342109i
$595$	10.8304	−	41.0986i	0.444003	−	1.68488i
$596$	−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	$0.872790\pi$
$600$	−0.871082	+	3.57110i	−0.0355618	+	0.145790i
$601$			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
$605$	−3.34971	+	12.7113i	−0.136185	+	0.516789i
$606$	−0.190720	+	1.11256i	−0.00774747	+	0.0451946i
$607$			46.3473i			1.88118i	0.339546	+	0.940589i	$0.389727\pi$
$607$			46.3473i			1.88118i	−0.339546	+	0.940589i	$0.610273\pi$
$608$	−38.0961	−	2.42135i	−1.54500	−	0.0981988i
$609$	−3.07180			−0.124475
$610$	14.5100	−	5.42782i	0.587491	−	0.219766i
$611$	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	−0.726250	−	0.687431i	$-0.758738\pi$
$613$	−0.961106	+	0.961106i	−0.0388187	+	0.0388187i	0.687431	+	0.726250i	$0.258738\pi$
$614$	−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	$-0.522105\pi$
$617$	−3.44724			−0.138781			−0.0693903	+	0.997590i	$0.522105\pi$
$618$	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	$0.995902\pi$
$620$	−8.37128	−	5.69292i	−0.336199	−	0.228633i
$621$	−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
$630$	14.7942	−	32.4773i	0.589416	−	1.29393i
$631$		−	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
$635$	3.39952	−	12.9004i	0.134906	−	0.511935i
$636$	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
$640$	−3.14681	−	25.1017i	−0.124389	−	0.992234i
$641$	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	0.984069	−	0.177787i	$-0.0568939\pi$
$643$	20.4452	+	20.4452i	0.806282	+	0.806282i	−0.177787	+	0.984069i	$0.556894\pi$
$644$	0.976466	+	0.344916i	0.0384781	+	0.0135916i
$645$	−2.15308	−	0.567385i	−0.0847776	−	0.0223408i
$646$	27.2176	+	38.4798i	1.07086	+	1.51397i
$647$	29.5876			1.16321			0.581604	−	0.813472i	$-0.302425\pi$
$647$	29.5876			1.16321			0.581604	+	0.813472i	$0.302425\pi$
$648$	−20.7347	−	11.5797i	−0.814534	−	0.454893i
$649$		−	0.342849i		−	0.0134580i
$650$	1.81006	+	17.9866i	0.0709962	+	0.705493i
$651$	−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	0.156716	−	0.987644i	$-0.449909\pi$
$653$	−21.2334	−	21.2334i	−0.830928	−	0.830928i	−0.987644	+	0.156716i	$0.949909\pi$
$654$	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	$0.435948\pi$
$660$	1.47924	−	2.17519i	0.0575795	−	0.0846691i
$661$	−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
$670$	−2.99396	−	8.00363i	−0.115667	−	0.309207i
$671$	−11.0865			−0.427989
$672$	0.358930	−	5.64719i	0.0138460	−	0.217845i
$673$		−	2.91192i		−	0.112246i	−0.998424	−	0.0561231i	$-0.982126\pi$
$673$		−	2.91192i		−	0.112246i	0.998424	−	0.0561231i	$-0.0178739\pi$
$674$	7.89059	−	46.0295i	0.303934	−	1.77299i
$675$	7.43031	−	2.05696i	0.285993	−	0.0791724i
$676$	4.30589	−	12.1901i	0.165611	−	0.468849i
$677$	34.6045	−	34.6045i	1.32996	−	1.32996i	0.424558	−	0.905401i	$-0.360430\pi$
$677$	34.6045	−	34.6045i	1.32996	−	1.32996i	0.905401	−	0.424558i	$-0.139570\pi$
$678$	−4.36130	+	3.08485i	−0.167495	+	0.118473i
$679$		−	23.4938i		−	0.901609i
$680$	−21.6769	+	22.4901i	−0.831270	+	0.862457i
$681$			4.73401i			0.181408i
$682$	4.18362	+	5.91472i	0.160199	+	0.226486i
$683$	24.7435	−	24.7435i	0.946785	−	0.946785i	−0.0518690	−	0.998654i	$-0.516518\pi$
$683$	24.7435	−	24.7435i	0.946785	−	0.946785i	0.998654	+	0.0518690i	$0.0165178\pi$
$684$	17.0665	+	35.7079i	0.652553	+	1.36533i
$685$	−39.5140	−	10.4128i	−1.50975	−	0.397852i
$686$	−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
$690$	0.0387455	+	0.103577i	0.00147502	+	0.00394310i
$691$	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
$700$	−25.2583	−	29.0368i	−0.954676	−	1.09749i
$701$	−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	$0.693496\pi$
$710$	−12.2293	+	26.8467i	−0.458958	+	1.00754i
$711$			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
$715$	3.29658	−	12.5097i	0.123285	−	0.467836i
$716$	−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	$0.182219\pi$
$720$	−21.1309	+	15.5378i	−0.787501	+	0.579060i
$721$	−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
$725$	14.7977	−	4.09651i	0.549574	−	0.152141i
$726$	1.76420	−	1.24786i	0.0654756	−	0.0463124i
$727$	18.6075			0.690116			0.345058	−	0.938581i	$-0.387859\pi$
$727$	18.6075			0.690116			0.345058	+	0.938581i	$0.387859\pi$
$728$	−7.58558	−	26.7749i	−0.281140	−	0.992343i
$729$			23.4200i			0.867409i
$730$	28.2818	+	12.8831i	1.04676	+	0.476823i
$731$	−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	0.544753	−	0.838596i	$-0.316623\pi$
$733$	−7.95550	−	7.95550i	−0.293843	−	0.293843i	−0.838596	+	0.544753i	$0.816623\pi$
$734$	−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	$0.379958\pi$
$740$	27.0302	−	5.14759i	0.993649	−	0.189229i
$741$	−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	$-0.709177\pi$
$743$	−33.3017			−1.22172			−0.610861	+	0.791738i	$0.709177\pi$
$744$	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
$750$	0.644067	−	4.05890i	0.0235180	−	0.148210i
$751$	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
$755$	10.2527	−	38.9064i	0.373134	−	1.41595i
$756$	−10.7083	+	5.11799i	−0.389457	+	0.186140i
$757$	−17.9408	+	17.9408i	−0.652069	+	0.652069i	−0.953491	−	0.301422i	$-0.902539\pi$
$757$	−17.9408	+	17.9408i	−0.652069	+	0.652069i	0.301422	+	0.953491i	$0.402539\pi$
$758$	10.9962	+	15.5462i	0.399400	+	0.564665i
$759$		−	0.0791389i		−	0.00287256i
$760$	42.6714	−	0.785714i	1.54786	−	0.0285008i
$761$		−	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
$765$	31.3157	+	8.25237i	1.13222	+	0.298365i
$766$	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	$0.412958\pi$
$770$	9.64945	+	25.7955i	0.347742	+	0.929604i
$771$	−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	$0.567205\pi$
$773$	−33.0120	+	33.0120i	−1.18736	+	1.18736i	−0.977794	+	0.209566i	$0.932795\pi$
$774$	−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
$780$	1.67111	−	2.45732i	0.0598352	−	0.0879862i
$781$	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	$0.00896767\pi$
$787$	28.8326	+	28.8326i	1.02777	+	1.02777i	0.0281690	+	0.999603i	$0.491032\pi$
$788$	−20.5940	+	9.84283i	−0.733631	+	0.350636i
$789$	0.148262	+	0.148262i	0.00527828	+	0.00527828i
$790$	31.6766	+	14.4295i	1.12700	+	0.513377i
$791$		−	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
$795$	−2.70248	−	0.712163i	−0.0958472	−	0.0252578i
$796$	14.5591	−	41.2170i	0.516032	−	1.46090i
$797$	−23.1556	−	23.1556i	−0.820214	−	0.820214i	0.165924	−	0.986139i	$-0.446939\pi$
$797$	−23.1556	−	23.1556i	−0.820214	−	0.820214i	−0.986139	+	0.165924i	$0.946939\pi$
$798$	9.40891	+	1.61292i	0.333072	+	0.0570967i
$799$	−34.7371			−1.22891
$800$	5.80195	+	27.6828i	0.205130	+	0.978735i
$801$	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
$805$	−1.11961	−	0.295040i	−0.0394609	−	0.0103988i
$806$	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	$-0.219714\pi$
$810$	24.1633	+	11.0070i	0.849012	+	0.386746i
$811$	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
$820$	8.41746	−	12.3777i	0.293950	−	0.432246i
$821$	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	$-0.664170\pi$
$823$	−28.2974			−0.986384			−0.493192	+	0.869920i	$0.664170\pi$
$824$	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	−0.316797	−	0.948494i	$-0.602607\pi$
$827$	18.1661	−	18.1661i	0.631697	−	0.631697i	0.948494	+	0.316797i	$0.102607\pi$
$828$	−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	$0.162225\pi$
$830$	13.8037	+	36.9008i	0.479132	+	1.28084i
$831$	−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
$835$	−27.5815	−	7.26832i	−0.954497	−	0.251531i
$836$	−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	$0.934093\pi$
$840$	0.116471	+	6.32542i	0.00401862	+	0.218248i
$841$			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
$845$	−3.68325	+	13.9770i	−0.126708	+	0.480824i
$846$	−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
$850$	22.0976	−	27.0428i	0.757942	−	0.927559i
$851$	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	−0.747740	−	0.663992i	$-0.768861\pi$
$853$	−2.44597	+	2.44597i	−0.0837485	+	0.0837485i	0.663992	+	0.747740i	$0.268861\pi$
$854$	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	$-0.514024\pi$
$857$	−2.57862			−0.0880839			−0.0440419	+	0.999030i	$0.514024\pi$
$858$	−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	$0.456763\pi$
$860$	−16.8305	+	3.20518i	−0.573915	+	0.109296i
$861$	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	$-0.868723\pi$
$863$		−	23.5500i		−	0.801652i	0.916154	−	0.400826i	$-0.131277\pi$
$864$	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
$870$	−2.29696	−	1.04632i	−0.0778743	−	0.0354736i
$871$			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
$875$	30.8004	+	30.0455i	1.04124	+	1.01572i
$876$	−2.20304	−	4.60939i	−0.0744338	−	0.155737i
$877$	34.2135	+	34.2135i	1.15531	+	1.15531i	0.985472	+	0.169836i	$0.0543237\pi$
$877$	34.2135	+	34.2135i	1.15531	+	1.15531i	0.169836	+	0.985472i	$0.445676\pi$
$878$	−7.28304	+	42.4854i	−0.245791	+	1.43381i
$879$	−4.10426			−0.138433
$880$	3.05207	−	20.0096i	0.102885	−	0.674524i
$881$	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	$0.0753176\pi$
$883$	35.8531	+	35.8531i	1.20655	+	1.20655i	0.234415	+	0.972137i	$0.424682\pi$
$884$	22.7842	−	10.8896i	0.766315	−	0.366257i
$885$	−0.0224375	+	0.0851449i	−0.000754230	+	0.00286211i
$886$	−27.3395	+	19.3379i	−0.918489	+	0.649668i
$887$	9.33231			0.313348			0.156674	−	0.987650i	$-0.449923\pi$
$887$	9.33231			0.313348			0.156674	+	0.987650i	$0.449923\pi$
$888$	−3.94915	−	2.20548i	−0.132525	−	0.0740112i
$889$		−	22.9610i		−	0.770087i
$890$	1.46984	−	3.22671i	0.0492692	−	0.108159i
$891$	−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
$900$	22.1250	−	19.2460i	0.737499	−	0.641532i
$901$	−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	$-0.465267\pi$
$907$	33.2170	−	33.2170i	1.10295	−	1.10295i	0.994053	−	0.108899i	$-0.0347327\pi$
$908$	15.7081	+	32.8659i	0.521293	+	1.09069i
$909$	6.36758	−	6.36758i	0.211199	−	0.211199i
$910$	10.9010	+	29.1412i	0.361365	+	0.966023i
$911$	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
$915$	2.75327	+	0.725548i	0.0910204	+	0.0239859i
$916$	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	$0.683250\pi$
$920$	0.612674	+	0.590519i	0.0201993	+	0.0194688i
$921$		−	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
$925$	−29.6487	+	8.20775i	−0.974842	+	0.269869i
$926$	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	$0.384252\pi$
$930$	−0.651896	−	1.74269i	−0.0213765	−	0.0571449i
$931$	−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	$-0.604804\pi$
$937$	−19.7948			−0.646668			−0.323334	+	0.946285i	$0.604804\pi$
$938$	−8.49307	−	12.0073i	−0.277308	−	0.392054i
$939$	1.91630	+	1.91630i	0.0625360	+	0.0625360i
$940$	−17.6881	+	26.0099i	−0.576922	+	0.848349i
$941$	−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	0.770840	−	0.637029i	$-0.219837\pi$
$947$	4.11783	+	4.11783i	0.133811	+	0.133811i	−0.637029	+	0.770840i	$0.719837\pi$
$948$	−2.46748	−	5.16267i	−0.0801400	−	0.167676i
$949$	−17.7660	−	17.7660i	−0.576708	−	0.576708i
$950$	−47.4764	+	4.77771i	−1.54034	+	0.155009i
$951$		−	3.70465i		−	0.120131i
$952$	−26.2131	+	46.9373i	−0.849571	+	1.52125i
$953$	40.3245			1.30624			0.653119	−	0.757255i	$-0.273460\pi$
$953$	40.3245			1.30624			0.653119	+	0.757255i	$0.273460\pi$
$954$	−11.5157	−	16.2807i	−0.372836	−	0.527108i
$955$	−10.9665	−	2.88991i	−0.354867	−	0.0935153i
$956$	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
$960$	2.19195	−	4.10047i	0.0707448	−	0.132342i
$961$	−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
$965$	1.31212	−	4.97919i	0.0422388	−	0.160286i
$966$	0.109911	+	0.155390i	0.00353632	+	0.00499958i
$967$	−58.1740			−1.87075			−0.935375	−	0.353656i	$-0.884938\pi$
$967$	−58.1740			−1.87075			−0.935375	+	0.353656i	$0.884938\pi$
$968$	8.10740	−	14.5171i	0.260582	−	0.466599i
$969$			8.66254i			0.278281i
$970$	8.00250	−	17.5677i	0.256945	−	0.564064i
$971$	−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	$-0.809735\pi$
$977$		−	35.1811i		−	1.12554i	0.826612	−	0.562772i	$-0.190265\pi$
$978$	1.39187	−	8.11943i	0.0445071	−	0.259631i
$979$	−1.79422	+	1.79422i	−0.0573436	+	0.0573436i
$980$	−28.8861	−	19.6441i	−0.922732	−	0.627506i
$981$	−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	$-0.645786\pi$
$983$	−27.7257			−0.884312			−0.442156	+	0.896938i	$0.645786\pi$
$984$	−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
$990$	−19.6552	+	7.35254i	−0.624684	+	0.233679i
$991$	−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
$995$	−12.4538	+	47.2590i	−0.394812	+	1.49821i
$996$	2.15708	−	6.10675i	0.0683498	−	0.193500i
$997$	−14.2467	+	14.2467i	−0.451197	+	0.451197i	−0.895752	−	0.444555i	$-0.853362\pi$
$997$	−14.2467	+	14.2467i	−0.451197	+	0.451197i	0.444555	+	0.895752i	$0.353362\pi$
$998$	−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.69.8	yes	16
3.2	odd	2		720.2.bm.f.469.1		16
4.3	odd	2		320.2.q.c.49.4		16
5.2	odd	4		400.2.l.i.101.4		16
5.3	odd	4		400.2.l.i.101.5		16
5.4	even	2	inner	80.2.q.c.69.1	yes	16
8.3	odd	2		640.2.q.f.609.5		16
8.5	even	2		640.2.q.e.609.4		16
15.14	odd	2		720.2.bm.f.469.8		16
16.3	odd	4		320.2.q.c.209.5		16
16.5	even	4		640.2.q.e.289.5		16
16.11	odd	4		640.2.q.f.289.4		16
16.13	even	4	inner	80.2.q.c.29.1	✓	16
20.3	even	4		1600.2.l.h.1201.5		16
20.7	even	4		1600.2.l.h.1201.4		16
20.19	odd	2		320.2.q.c.49.5		16
40.19	odd	2		640.2.q.f.609.4		16
40.29	even	2		640.2.q.e.609.5		16
48.29	odd	4		720.2.bm.f.109.8		16
80.3	even	4		1600.2.l.h.401.5		16
80.13	odd	4		400.2.l.i.301.5		16
80.19	odd	4		320.2.q.c.209.4		16
80.29	even	4	inner	80.2.q.c.29.8	yes	16
80.59	odd	4		640.2.q.f.289.5		16
80.67	even	4		1600.2.l.h.401.4		16
80.69	even	4		640.2.q.e.289.4		16
80.77	odd	4		400.2.l.i.301.4		16
240.29	odd	4		720.2.bm.f.109.1		16

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

\(f(q)\)	\(=\)	\(q+(1.39388 + 0.238945i) q^{2} +(0.183790 + 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-2.16225 - 0.569800i) q^{5} +(0.212266 + 0.300098i) q^{6} -3.84853 q^{7} +(2.46943 + 1.37910i) q^{8} -2.93244i q^{9} +O(q^{10})\)	\(q+(1.39388 + 0.238945i) q^{2} +(0.183790 + 0.183790i) q^{3} +(1.88581 + 0.666123i) q^{4} +(-2.16225 - 0.569800i) q^{5} +(0.212266 + 0.300098i) q^{6} -3.84853 q^{7} +(2.46943 + 1.37910i) q^{8} -2.93244i q^{9} +(-2.87777 - 1.31089i) 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} +(-3.69804 - 2.51486i) 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} +(-0.287977 - 0.769836i) q^{30} +2.26371 q^{31} +(3.73822 + 4.24567i) q^{32} +0.588201i q^{33} +(1.18012 - 6.88418i) q^{34} +(8.32149 + 2.19289i) q^{35} +(1.95337 - 5.53003i) q^{36} +(-4.35066 + 4.35066i) q^{37} +(-7.79123 + 5.51092i) q^{38} +0.664493i q^{39} +(-4.55371 - 4.38905i) q^{40} +3.34709i q^{41} +(-0.816913 - 1.15494i) q^{42} +(2.70896 - 2.70896i) q^{43} +(1.95174 + 4.08359i) q^{44} +(-1.67091 + 6.34067i) q^{45} +(-0.187538 - 0.0321487i) q^{46} -7.03343i q^{47} +(0.110310 + 1.03381i) q^{48} +7.81119 q^{49} +(5.47551 + 4.47423i) 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} +(-0.217456 - 1.14187i) 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} +(11.0752 + 5.04502i) q^{70} -9.32899i q^{71} +(4.04414 - 7.24146i) q^{72} -9.82769 q^{73} +(-7.10387 + 5.02473i) q^{74} +(0.346730 + 1.25249i) q^{75} +(-12.1769 + 5.81988i) q^{76} +(-6.15840 - 6.15840i) q^{77} +(-0.158778 + 0.926224i) q^{78} -11.0073 q^{79} +(-5.29859 - 7.20590i) q^{80} -8.39654 q^{81} +(-0.799772 + 4.66544i) q^{82} +(-8.80967 - 8.80967i) q^{83} +(-0.862712 - 1.80504i) q^{84} +(-2.81416 + 10.6790i) q^{85} +(4.42326 - 3.12867i) q^{86} +0.798174 q^{87} +(1.74473 + 6.15840i) q^{88} +1.12125i q^{89} +(-3.84412 + 8.43889i) 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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