LMFDB - Embedded newform 80.2.q.c.29.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,2,Mod(29,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [16,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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			29.8
Root			$-0.238945 + 1.39388i$ of defining polynomial
Character	$\chi$	$=$	80.29
Dual form			80.2.q.c.69.8

$q$-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} +(-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} - 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}+ \cdots + 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

Character values

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

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

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	$-0.726094\pi$
$3$	0.183790	−	0.183790i	0.106111	−	0.106111i	0.758169	+	0.652058i	$0.226094\pi$
$4$	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	−0.423445	−	0.905922i	$-0.639179\pi$
$11$	1.60020	−	1.60020i	0.482477	−	0.482477i	0.905922	+	0.423445i	$0.139179\pi$
$12$	0.224167	−	0.469021i	0.0647114	−	0.135395i
$13$	1.80775	−	1.80775i	0.501379	−	0.501379i	−0.410487	−	0.911866i	$-0.634641\pi$
$13$	1.80775	−	1.80775i	0.501379	−	0.501379i	0.911866	+	0.410487i	$0.134641\pi$
$14$	−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	−0.995021	−	0.0996636i	$-0.968223\pi$
$19$	−4.77162	−	4.77162i	−1.09468	−	1.09468i	−0.0996636	−	0.995021i	$-0.531777\pi$
$20$	−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	0.879367	−	0.476144i	$-0.157966\pi$
$29$	2.17142	+	2.17142i	0.403223	+	0.403223i	−0.476144	+	0.879367i	$0.657966\pi$
$30$	−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	0.252384	−	0.967627i	$-0.418785\pi$
$37$	−4.35066	−	4.35066i	−0.715243	−	0.715243i	−0.967627	+	0.252384i	$0.918785\pi$
$38$	−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	$-0.915828\pi$
$41$		−	3.34709i		−	0.522727i	0.965240	−	0.261364i	$-0.0841722\pi$
$42$	−0.816913	+	1.15494i	−0.126052	+	0.178210i
$43$	2.70896	+	2.70896i	0.413112	+	0.413112i	0.882821	−	0.469709i	$-0.155641\pi$
$43$	2.70896	+	2.70896i	0.413112	+	0.413112i	−0.469709	+	0.882821i	$0.655641\pi$
$44$	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	$0.171453\pi$
$47$			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
$50$	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	0.900958	−	0.433905i	$-0.142865\pi$
$53$	3.40020	+	3.40020i	0.467053	+	0.467053i	−0.433905	+	0.900958i	$0.642865\pi$
$54$	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	−0.714046	−	0.700099i	$-0.753139\pi$
$59$	−0.107127	+	0.107127i	−0.0139468	+	0.0139468i	0.700099	+	0.714046i	$0.253139\pi$
$60$	−0.217456	+	1.14187i	−0.0280735	+	0.147415i
$61$	−3.46410	−	3.46410i	−0.443533	−	0.443533i	0.449665	−	0.893197i	$-0.351543\pi$
$61$	−3.46410	−	3.46410i	−0.443533	−	0.443533i	−0.893197	+	0.449665i	$0.851543\pi$
$62$	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	$-0.697216\pi$
$67$	1.91078	−	1.91078i	0.233440	−	0.233440i	0.814127	+	0.580687i	$0.197216\pi$
$68$	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	$0.186736\pi$
$71$			9.32899i			1.10715i	−0.832800	+	0.553573i	$0.813264\pi$
$72$	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	−0.999472	−	0.0324850i	$-0.989658\pi$
$83$	−8.80967	+	8.80967i	−0.966987	+	0.966987i	0.0324850	+	0.999472i	$0.489658\pi$
$84$	−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	$-0.981073\pi$
$89$		−	1.12125i		−	0.118853i	0.998233	−	0.0594263i	$-0.0189271\pi$
$90$	−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	$-0.899700\pi$
$97$		−	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
$100$	6.56311	−	7.54490i	0.656311	−	0.754490i
$101$	2.17142	−	2.17142i	0.216065	−	0.216065i	−0.590773	−	0.806838i	$-0.701177\pi$
$101$	2.17142	−	2.17142i	0.216065	−	0.216065i	0.806838	+	0.590773i	$0.201177\pi$
$102$	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	0.283720	−	0.958907i	$-0.408431\pi$
$107$	−6.98419	−	6.98419i	−0.675187	−	0.675187i	−0.958907	+	0.283720i	$0.908431\pi$
$108$	2.78244	+	1.32986i	0.267740	+	0.127965i
$109$	8.59694	+	8.59694i	0.823437	+	0.823437i	0.986599	−	0.163162i	$-0.0521694\pi$
$109$	8.59694	+	8.59694i	0.823437	+	0.823437i	−0.163162	+	0.986599i	$0.552169\pi$
$110$	−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	$-0.760426\pi$
$113$		−	14.5329i		−	1.36714i	0.729883	−	0.683572i	$-0.239574\pi$
$114$	−2.44481	+	0.419100i	−0.228977	+	0.0392523i
$115$	0.290918	−	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	$-0.914725\pi$
$127$		−	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
$130$	−2.83251	+	7.57204i	−0.248428	+	0.664112i
$131$	2.37084	+	2.37084i	0.207141	+	0.207141i	0.803051	−	0.595910i	$-0.203209\pi$
$131$	2.37084	+	2.37084i	0.207141	+	0.207141i	−0.595910	+	0.803051i	$0.703209\pi$
$132$	−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	−0.712855	−	0.701312i	$-0.752598\pi$
$139$	−0.136094	+	0.136094i	−0.0115433	+	0.0115433i	0.701312	+	0.712855i	$0.252598\pi$
$140$	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	−0.798575	−	0.601895i	$-0.794412\pi$
$149$	−2.40078	+	2.40078i	−0.196680	+	0.196680i	0.601895	+	0.798575i	$0.294412\pi$
$150$	0.184025	−	1.82867i	0.0150256	−	0.149310i
$151$		−	17.9935i		−	1.46429i	−0.681150	−	0.732144i	$-0.738520\pi$
$151$		−	17.9935i		−	1.46429i	0.681150	−	0.732144i	$-0.261480\pi$
$152$	−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	0.00849213	−	0.999964i	$-0.497297\pi$
$157$	12.6359	−	12.6359i	1.00846	−	1.00846i	0.999964	−	0.00849213i	$-0.00270316\pi$
$158$	−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	−0.281743	+	0.959490i	$0.590913\pi$
$163$	−15.8470	+	15.8470i	−1.24123	+	1.24123i	−0.959490	+	0.281743i	$0.909087\pi$
$164$	−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	−0.800525	−	0.599299i	$-0.795446\pi$
$173$	−2.64673	+	2.64673i	−0.201227	+	0.201227i	0.599299	+	0.800525i	$0.295446\pi$
$174$	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	0.121817	−	0.992553i	$-0.461128\pi$
$179$	−11.6497	−	11.6497i	−0.870736	−	0.870736i	−0.992553	+	0.121817i	$0.961128\pi$
$180$	−7.37468	−	10.8443i	−0.549676	−	0.808285i
$181$	1.24322	−	1.24322i	0.0924079	−	0.0924079i	−0.659392	−	0.751800i	$-0.729186\pi$
$181$	1.24322	−	1.24322i	0.0924079	−	0.0924079i	0.751800	+	0.659392i	$0.229186\pi$
$182$	−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	$-0.973589\pi$
$193$		−	2.30278i		−	0.165758i	0.996560	−	0.0828788i	$-0.0264114\pi$
$194$	−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	0.358549	−	0.933511i	$-0.383271\pi$
$197$	−8.06997	−	8.06997i	−0.574961	−	0.574961i	−0.933511	+	0.358549i	$0.883271\pi$
$198$	7.66201	+	5.41951i	0.544515	+	0.385148i
$199$			21.8564i			1.54936i	0.632354	+	0.774680i	$0.282089\pi$
$199$			21.8564i			1.54936i	−0.632354	+	0.774680i	$0.717911\pi$
$200$	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	0.723376	−	0.690454i	$-0.242589\pi$
$211$	0.478227	+	0.478227i	0.0329225	+	0.0329225i	−0.690454	+	0.723376i	$0.742589\pi$
$212$	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	$-0.919107\pi$
$223$		−	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	$-0.543400\pi$
$227$	12.8788	−	12.8788i	0.854798	−	0.854798i	0.990720	+	0.135922i	$0.0433997\pi$
$228$	−3.30763	+	1.16835i	−0.219053	+	0.0773759i
$229$	8.62166	−	8.62166i	0.569736	−	0.569736i	−0.362319	−	0.932054i	$-0.618015\pi$
$229$	8.62166	−	8.62166i	0.569736	−	0.569736i	0.932054	+	0.362319i	$0.118015\pi$
$230$	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	−0.0113760	+	0.999935i	$0.503621\pi$
$251$	−16.0222	+	16.0222i	−1.01131	+	1.01131i	−0.999935	+	0.0113760i	$0.996379\pi$
$252$	−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
$260$	−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	0.0710837	−	0.997470i	$-0.477354\pi$
$269$	−15.1939	−	15.1939i	−0.926387	−	0.926387i	−0.997470	+	0.0710837i	$0.977354\pi$
$270$	−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	0.667818	−	0.744325i	$-0.267229\pi$
$277$	−1.27334	−	1.27334i	−0.0765074	−	0.0765074i	−0.744325	+	0.667818i	$0.767229\pi$
$278$	−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	$-0.793959\pi$
$281$		−	20.2174i		−	1.20607i	0.797716	−	0.603033i	$-0.206041\pi$
$282$	2.11072	+	1.49296i	0.125691	+	0.0889044i
$283$	21.3741	+	21.3741i	1.27056	+	1.27056i	0.945797	+	0.324759i	$0.105283\pi$
$283$	21.3741	+	21.3741i	1.27056	+	1.27056i	0.324759	+	0.945797i	$0.394717\pi$
$284$	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	0.301246	−	0.953547i	$-0.402598\pi$
$293$	−11.1656	−	11.1656i	−0.652301	−	0.652301i	−0.953547	+	0.301246i	$0.902598\pi$
$294$	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	−0.766612	−	0.642111i	$-0.778059\pi$
$307$	−2.18143	+	2.18143i	−0.124501	+	0.124501i	0.642111	+	0.766612i	$0.278059\pi$
$308$	−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	$0.106213\pi$
$311$			11.5517i			0.655038i	−0.944845	+	0.327519i	$0.893787\pi$
$312$	−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	−0.931023	−	0.364960i	$-0.881083\pi$
$317$	−10.0785	+	10.0785i	−0.566063	+	0.566063i	0.364960	+	0.931023i	$0.381083\pi$
$318$	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	−0.423680	−	0.905812i	$-0.639262\pi$
$331$	8.77162	−	8.77162i	0.482132	−	0.482132i	0.905812	+	0.423680i	$0.139262\pi$
$332$	−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
$340$	−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	0.341714	−	0.939804i	$-0.388993\pi$
$347$	−11.1412	−	11.1412i	−0.598090	−	0.598090i	−0.939804	+	0.341714i	$0.888993\pi$
$348$	1.50520	−	0.531682i	0.0806874	−	0.0285012i
$349$	−10.8656	−	10.8656i	−0.581622	−	0.581622i	0.353727	−	0.935349i	$-0.384914\pi$
$349$	−10.8656	−	10.8656i	−0.581622	−	0.581622i	−0.935349	+	0.353727i	$0.884914\pi$
$350$	−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	$0.0976534\pi$
$353$			11.3480i			0.603995i	−0.953309	+	0.301998i	$0.902347\pi$
$354$	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	$0.247436\pi$
$359$			26.5788i			1.40278i	−0.712779	+	0.701389i	$0.752564\pi$
$360$	−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	$-0.975823\pi$
$367$		−	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
$370$	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	0.576241	−	0.817280i	$-0.304519\pi$
$373$	−4.65522	−	4.65522i	−0.241038	−	0.241038i	−0.817280	+	0.576241i	$0.804519\pi$
$374$	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	−0.418947	−	0.908011i	$-0.637601\pi$
$379$	9.52106	−	9.52106i	0.489064	−	0.489064i	0.908011	+	0.418947i	$0.137601\pi$
$380$	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	$0.0566093\pi$
$383$			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	−0.0153322	+	0.999882i	$0.504881\pi$
$389$	−20.0232	+	20.0232i	−1.01521	+	1.01521i	−0.999882	+	0.0153322i	$0.995119\pi$
$390$	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	−0.604826	−	0.796358i	$-0.706757\pi$
$397$	3.81625	−	3.81625i	0.191532	−	0.191532i	0.796358	+	0.604826i	$0.206757\pi$
$398$	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	$-0.834169\pi$
$409$		−	20.1317i		−	0.995448i	0.867335	−	0.497724i	$-0.165831\pi$
$410$	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	0.993560	+	0.113306i	$0.0361442\pi$
$419$	22.6570	+	22.6570i	1.10687	+	1.10687i	0.113306	+	0.993560i	$0.463856\pi$
$420$	0.836888	−	4.39452i	0.0408359	−	0.214431i
$421$	−10.1583	+	10.1583i	−0.495084	+	0.495084i	−0.909904	−	0.414820i	$-0.863845\pi$
$421$	−10.1583	+	10.1583i	−0.495084	+	0.495084i	0.414820	+	0.909904i	$0.363845\pi$
$422$	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	$0.0717992\pi$
$433$			9.30795i			0.447312i	−0.974668	+	0.223656i	$0.928201\pi$
$434$	−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	$-0.740745\pi$
$439$		−	30.4799i		−	1.45473i	0.686252	−	0.727364i	$-0.259255\pi$
$440$	−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	0.186869	−	0.982385i	$-0.440166\pi$
$443$	−16.7437	−	16.7437i	−0.795516	−	0.795516i	−0.982385	+	0.186869i	$0.940166\pi$
$444$	−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	0.957739	−	0.287640i	$-0.0928706\pi$
$461$	14.3876	+	14.3876i	0.670099	+	0.670099i	−0.287640	+	0.957739i	$0.592871\pi$
$462$	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	$-0.929341\pi$
$467$	−16.3222	+	16.3222i	−0.755300	+	0.755300i	0.220163	+	0.975463i	$0.429341\pi$
$468$	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	−0.984355	−	0.176198i	$-0.943620\pi$
$491$	−17.9076	+	17.9076i	−0.808157	+	0.808157i	0.176198	+	0.984355i	$0.443620\pi$
$492$	−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	0.653253	−	0.757140i	$-0.273404\pi$
$499$	−2.32067	−	2.32067i	−0.103887	−	0.103887i	−0.757140	+	0.653253i	$0.773404\pi$
$500$	−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	0.986875	−	0.161485i	$-0.0516282\pi$
$509$	18.6217	+	18.6217i	0.825391	+	0.825391i	−0.161485	+	0.986875i	$0.551628\pi$
$510$	−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	$-0.823603\pi$
$521$		−	24.0232i		−	1.05247i	0.850338	−	0.526237i	$-0.176397\pi$
$522$	−7.35414	+	10.3972i	−0.321882	+	0.455071i
$523$	−16.1791	−	16.1791i	−0.707463	−	0.707463i	0.258538	−	0.966001i	$-0.416759\pi$
$523$	−16.1791	−	16.1791i	−0.707463	−	0.707463i	−0.966001	+	0.258538i	$0.916759\pi$
$524$	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	0.837420	−	0.546559i	$-0.184063\pi$
$541$	6.76526	+	6.76526i	0.290861	+	0.290861i	−0.546559	+	0.837420i	$0.684063\pi$
$542$	−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	$-0.792311\pi$
$547$	−4.38359	+	4.38359i	−0.187429	+	0.187429i	0.607155	+	0.794584i	$0.292311\pi$
$548$	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	−0.619071	−	0.785335i	$-0.712491\pi$
$557$	3.92396	−	3.92396i	0.166264	−	0.166264i	0.785335	+	0.619071i	$0.212491\pi$
$558$	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	−0.553796	−	0.832652i	$-0.686821\pi$
$563$	6.61660	−	6.61660i	0.278857	−	0.278857i	0.832652	+	0.553796i	$0.186821\pi$
$564$	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	$0.320115\pi$
$569$			40.2900i			1.68904i	−0.535521	+	0.844522i	$0.679885\pi$
$570$	5.04748	−	2.29925i	0.211416	−	0.0963050i
$571$	22.6010	−	22.6010i	0.945823	−	0.945823i	−0.0527829	−	0.998606i	$-0.516809\pi$
$571$	22.6010	−	22.6010i	0.945823	−	0.945823i	0.998606	+	0.0527829i	$0.0168091\pi$
$572$	−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
$580$	−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	0.648751	−	0.761001i	$-0.275292\pi$
$587$	−2.71961	−	2.71961i	−0.112250	−	0.112250i	−0.761001	+	0.648751i	$0.775292\pi$
$588$	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	$0.0264933\pi$
$593$			4.04894i			0.166270i	−0.996538	+	0.0831350i	$0.973507\pi$
$594$	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	$-0.872790\pi$
$599$		−	19.0455i		−	0.778178i	0.921200	−	0.389089i	$-0.127210\pi$
$600$	−0.871082	−	3.57110i	−0.0355618	−	0.145790i
$601$		−	14.4406i		−	0.589045i	−0.955645	−	0.294522i	$-0.904839\pi$
$601$		−	14.4406i		−	0.589045i	0.955645	−	0.294522i	$-0.0951606\pi$
$602$	−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	$-0.610273\pi$
$607$		−	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
$610$	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	0.687431	−	0.726250i	$-0.258738\pi$
$613$	−0.961106	−	0.961106i	−0.0388187	−	0.0388187i	−0.726250	+	0.687431i	$0.758738\pi$
$614$	−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	−0.999917	−	0.0128733i	$-0.995902\pi$
$619$	−24.5574	+	24.5574i	−0.987044	+	0.987044i	0.0128733	+	0.999917i	$0.495902\pi$
$620$	−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	$0.149906\pi$
$631$			22.7950i			0.907456i	−0.891140	+	0.453728i	$0.850094\pi$
$632$	−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	−0.177787	−	0.984069i	$-0.556894\pi$
$643$	20.4452	−	20.4452i	0.806282	−	0.806282i	0.984069	+	0.177787i	$0.0568939\pi$
$644$	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	−0.987644	−	0.156716i	$-0.949909\pi$
$653$	−21.2334	+	21.2334i	−0.830928	+	0.830928i	0.156716	+	0.987644i	$0.449909\pi$
$654$	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	0.199869	−	0.979823i	$-0.435948\pi$
$659$	−20.0222	−	20.0222i	−0.779954	−	0.779954i	−0.979823	+	0.199869i	$0.935948\pi$
$660$	1.47924	+	2.17519i	0.0575795	+	0.0846691i
$661$	−19.9536	+	19.9536i	−0.776107	+	0.776107i	−0.979166	−	0.203059i	$-0.934912\pi$
$661$	−19.9536	+	19.9536i	−0.776107	+	0.776107i	0.203059	+	0.979166i	$0.434912\pi$
$662$	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	$0.0178739\pi$
$673$			2.91192i			0.112246i	−0.998424	+	0.0561231i	$0.982126\pi$
$674$	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	0.905401	+	0.424558i	$0.139570\pi$
$677$	34.6045	+	34.6045i	1.32996	+	1.32996i	0.424558	+	0.905401i	$0.360430\pi$
$678$	−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	0.998654	−	0.0518690i	$-0.0165178\pi$
$683$	24.7435	+	24.7435i	0.946785	+	0.946785i	−0.0518690	+	0.998654i	$0.516518\pi$
$684$	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	0.999422	−	0.0339907i	$-0.0108217\pi$
$691$	25.3782	+	25.3782i	0.965431	+	0.965431i	−0.0339907	+	0.999422i	$0.510822\pi$
$692$	−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	−0.966916	−	0.255094i	$-0.917894\pi$
$701$	−32.3544	−	32.3544i	−1.22201	−	1.22201i	−0.255094	−	0.966916i	$-0.582106\pi$
$702$	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	−0.571134	−	0.820857i	$-0.693496\pi$
$709$	6.64939	−	6.64939i	0.249723	−	0.249723i	0.820857	+	0.571134i	$0.193496\pi$
$710$	−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	−0.838596	−	0.544753i	$-0.816623\pi$
$733$	−7.95550	+	7.95550i	−0.293843	+	0.293843i	0.544753	+	0.838596i	$0.316623\pi$
$734$	−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	0.368249	−	0.929727i	$-0.379958\pi$
$739$	−15.2636	−	15.2636i	−0.561479	−	0.561479i	−0.929727	+	0.368249i	$0.879958\pi$
$740$	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	0.301422	−	0.953491i	$-0.402539\pi$
$757$	−17.9408	−	17.9408i	−0.652069	−	0.652069i	−0.953491	+	0.301422i	$0.902539\pi$
$758$	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	$0.0904295\pi$
$761$			15.4641i			0.560573i	−0.959916	+	0.280287i	$0.909570\pi$
$762$	−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	−0.977794	−	0.209566i	$-0.932795\pi$
$773$	−33.0120	−	33.0120i	−1.18736	−	1.18736i	−0.209566	−	0.977794i	$-0.567205\pi$
$774$	−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	0.0281690	−	0.999603i	$-0.491032\pi$
$787$	28.8326	−	28.8326i	1.02777	−	1.02777i	0.999603	−	0.0281690i	$-0.00896767\pi$
$788$	−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	−0.986139	−	0.165924i	$-0.946939\pi$
$797$	−23.1556	+	23.1556i	−0.820214	+	0.820214i	0.165924	+	0.986139i	$0.446939\pi$
$798$	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	$0.219714\pi$
$809$			36.2210i			1.27346i	−0.771086	+	0.636731i	$0.780286\pi$
$810$	24.1633	−	11.0070i	0.849012	−	0.386746i
$811$	9.17312	−	9.17312i	0.322112	−	0.322112i	−0.527465	−	0.849577i	$-0.676857\pi$
$811$	9.17312	−	9.17312i	0.322112	−	0.322112i	0.849577	+	0.527465i	$0.176857\pi$
$812$	−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	−0.568813	−	0.822467i	$-0.692597\pi$
$821$	7.26795	−	7.26795i	0.253653	−	0.253653i	0.822467	+	0.568813i	$0.192597\pi$
$822$	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	0.948494	−	0.316797i	$-0.102607\pi$
$827$	18.1661	+	18.1661i	0.631697	+	0.631697i	−0.316797	+	0.948494i	$0.602607\pi$
$828$	−0.262814	−	0.744032i	−0.00913341	−	0.0258569i
$829$	11.0865	+	11.0865i	0.385049	+	0.385049i	0.872917	−	0.487868i	$-0.162225\pi$
$829$	11.0865	+	11.0865i	0.385049	+	0.385049i	−0.487868	+	0.872917i	$0.662225\pi$
$830$	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	$-0.934093\pi$
$839$		−	11.9093i		−	0.411153i	0.978641	−	0.205577i	$-0.0659069\pi$
$840$	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	0.663992	−	0.747740i	$-0.268861\pi$
$853$	−2.44597	−	2.44597i	−0.0837485	−	0.0837485i	−0.747740	+	0.663992i	$0.768861\pi$
$854$	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	0.135416	−	0.990789i	$-0.456763\pi$
$859$	33.0076	−	33.0076i	1.12620	−	1.12620i	0.990789	−	0.135416i	$-0.0432371\pi$
$860$	−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	$0.131277\pi$
$863$			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
$870$	−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	0.169836	−	0.985472i	$-0.445676\pi$
$877$	34.2135	−	34.2135i	1.15531	−	1.15531i	0.985472	−	0.169836i	$-0.0543237\pi$
$878$	−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	0.234415	−	0.972137i	$-0.424682\pi$
$883$	35.8531	−	35.8531i	1.20655	−	1.20655i	0.972137	−	0.234415i	$-0.0753176\pi$
$884$	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	0.994053	+	0.108899i	$0.0347327\pi$
$907$	33.2170	+	33.2170i	1.10295	+	1.10295i	0.108899	+	0.994053i	$0.465267\pi$
$908$	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	$-0.683250\pi$
$919$		−	50.8572i		−	1.67763i	0.544420	−	0.838813i	$-0.316750\pi$
$920$	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	0.0391593	−	0.999233i	$-0.487532\pi$
$941$	−29.4510	−	29.4510i	−0.960074	−	0.960074i	−0.999233	+	0.0391593i	$0.987532\pi$
$942$	−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	$-0.719837\pi$
$947$	4.11783	−	4.11783i	0.133811	−	0.133811i	0.770840	+	0.637029i	$0.219837\pi$
$948$	−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	−0.733986	−	0.679164i	$-0.762342\pi$
$971$	−1.70830	+	1.70830i	−0.0548220	+	0.0548220i	0.679164	+	0.733986i	$0.262342\pi$
$972$	−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
$980$	−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	0.444555	−	0.895752i	$-0.353362\pi$
$997$	−14.2467	−	14.2467i	−0.451197	−	0.451197i	−0.895752	+	0.444555i	$0.853362\pi$
$998$	−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.29.8	yes	16
3.2	odd	2		720.2.bm.f.109.1		16
4.3	odd	2		320.2.q.c.209.4		16
5.2	odd	4		400.2.l.i.301.5		16
5.3	odd	4		400.2.l.i.301.4		16
5.4	even	2	inner	80.2.q.c.29.1	✓	16
8.3	odd	2		640.2.q.f.289.5		16
8.5	even	2		640.2.q.e.289.4		16
15.14	odd	2		720.2.bm.f.109.8		16
16.3	odd	4		640.2.q.f.609.4		16
16.5	even	4	inner	80.2.q.c.69.1	yes	16
16.11	odd	4		320.2.q.c.49.5		16
16.13	even	4		640.2.q.e.609.5		16
20.3	even	4		1600.2.l.h.401.4		16
20.7	even	4		1600.2.l.h.401.5		16
20.19	odd	2		320.2.q.c.209.5		16
40.19	odd	2		640.2.q.f.289.4		16
40.29	even	2		640.2.q.e.289.5		16
48.5	odd	4		720.2.bm.f.469.8		16
80.19	odd	4		640.2.q.f.609.5		16
80.27	even	4		1600.2.l.h.1201.5		16
80.29	even	4		640.2.q.e.609.4		16
80.37	odd	4		400.2.l.i.101.5		16
80.43	even	4		1600.2.l.h.1201.4		16
80.53	odd	4		400.2.l.i.101.4		16
80.59	odd	4		320.2.q.c.49.4		16
80.69	even	4	inner	80.2.q.c.69.8	yes	16
240.149	odd	4		720.2.bm.f.469.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.1	✓	16	5.4	even	2	inner
80.2.q.c.29.8	yes	16	1.1	even	1	trivial
80.2.q.c.69.1	yes	16	16.5	even	4	inner
80.2.q.c.69.8	yes	16	80.69	even	4	inner
320.2.q.c.49.4		16	80.59	odd	4
320.2.q.c.49.5		16	16.11	odd	4
320.2.q.c.209.4		16	4.3	odd	2
320.2.q.c.209.5		16	20.19	odd	2
400.2.l.i.101.4		16	80.53	odd	4
400.2.l.i.101.5		16	80.37	odd	4
400.2.l.i.301.4		16	5.3	odd	4
400.2.l.i.301.5		16	5.2	odd	4
640.2.q.e.289.4		16	8.5	even	2
640.2.q.e.289.5		16	40.29	even	2
640.2.q.e.609.4		16	80.29	even	4
640.2.q.e.609.5		16	16.13	even	4
640.2.q.f.289.4		16	40.19	odd	2
640.2.q.f.289.5		16	8.3	odd	2
640.2.q.f.609.4		16	16.3	odd	4
640.2.q.f.609.5		16	80.19	odd	4
720.2.bm.f.109.1		16	3.2	odd	2
720.2.bm.f.109.8		16	15.14	odd	2
720.2.bm.f.469.1		16	240.149	odd	4
720.2.bm.f.469.8		16	48.5	odd	4
1600.2.l.h.401.4		16	20.3	even	4
1600.2.l.h.401.5		16	20.7	even	4
1600.2.l.h.1201.4		16	80.43	even	4
1600.2.l.h.1201.5		16	80.27	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 $\F_{q}$
Belyi maps

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} +(-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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 8 q^{5} - 4 q^{6} - 12 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 4 q^{20} - 16 q^{21} - 32 q^{24} + 32 q^{26} - 16 q^{29} - 36 q^{30} + 16 q^{31} + 48 q^{34} - 24 q^{35} + 60 q^{36}+ \cdots + 88 q^{99}+O(q^{100}) \) 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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