LMFDB - Embedded newform 483.2.i.h.277.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.5
Root			$0.432430 - 0.748990i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.h.415.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.432430 - 0.748990i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.626009 - 1.08428i) q^{4} +(1.24779 + 2.16123i) q^{5} -0.864859 q^{6} +(-0.0271380 + 2.64561i) q^{7} -2.81254 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.432430 - 0.748990i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.626009 - 1.08428i) q^{4} +(1.24779 + 2.16123i) q^{5} -0.864859 q^{6} +(-0.0271380 + 2.64561i) q^{7} -2.81254 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.07916 - 1.86916i) q^{10} +(1.99155 - 3.44946i) q^{11} +(-0.626009 - 1.08428i) q^{12} +2.80699 q^{13} +(1.99327 - 1.12372i) q^{14} +2.49557 q^{15} +(-0.0357927 - 0.0619948i) q^{16} +(3.49385 - 6.05152i) q^{17} +(-0.432430 + 0.748990i) q^{18} +(2.99029 + 5.17933i) q^{19} +3.12450 q^{20} +(2.27760 + 1.34631i) q^{21} -3.44482 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.40627 + 2.43573i) q^{24} +(-0.613943 + 1.06338i) q^{25} +(-1.21382 - 2.10240i) q^{26} -1.00000 q^{27} +(2.85159 + 1.68560i) q^{28} -4.06198 q^{29} +(-1.07916 - 1.86916i) q^{30} +(1.72173 - 2.98212i) q^{31} +(-2.84349 + 4.92508i) q^{32} +(-1.99155 - 3.44946i) q^{33} -6.04338 q^{34} +(-5.75164 + 3.24251i) q^{35} -1.25202 q^{36} +(0.738463 + 1.27905i) q^{37} +(2.58618 - 4.47939i) q^{38} +(1.40349 - 2.43092i) q^{39} +(-3.50945 - 6.07854i) q^{40} -7.65339 q^{41} +(0.0234706 - 2.28808i) q^{42} +7.07993 q^{43} +(-2.49345 - 4.31879i) q^{44} +(1.24779 - 2.16123i) q^{45} +(-0.432430 + 0.748990i) q^{46} +(1.52265 + 2.63732i) q^{47} -0.0715855 q^{48} +(-6.99853 - 0.143593i) q^{49} +1.06195 q^{50} +(-3.49385 - 6.05152i) q^{51} +(1.75720 - 3.04356i) q^{52} +(-4.78552 + 8.28876i) q^{53} +(0.432430 + 0.748990i) q^{54} +9.94011 q^{55} +(0.0763267 - 7.44089i) q^{56} +5.98058 q^{57} +(1.75652 + 3.04238i) q^{58} +(4.15309 - 7.19336i) q^{59} +(1.56225 - 2.70590i) q^{60} +(1.85641 + 3.21539i) q^{61} -2.97811 q^{62} +(2.30474 - 1.29930i) q^{63} +4.77528 q^{64} +(3.50252 + 6.06654i) q^{65} +(-1.72241 + 2.98330i) q^{66} +(-2.23479 + 3.87076i) q^{67} +(-4.37436 - 7.57662i) q^{68} -1.00000 q^{69} +(4.91579 + 2.90576i) q^{70} -9.49028 q^{71} +(1.40627 + 2.43573i) q^{72} +(-6.45106 + 11.1736i) q^{73} +(0.638666 - 1.10620i) q^{74} +(0.613943 + 1.06338i) q^{75} +7.48779 q^{76} +(9.07190 + 5.36248i) q^{77} -2.42765 q^{78} +(-3.56152 - 6.16873i) q^{79} +(0.0893234 - 0.154713i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.30955 + 5.73232i) q^{82} +1.05716 q^{83} +(2.88557 - 1.62675i) q^{84} +17.4383 q^{85} +(-3.06157 - 5.30280i) q^{86} +(-2.03099 + 3.51778i) q^{87} +(-5.60131 + 9.70175i) q^{88} +(1.65027 + 2.85835i) q^{89} -2.15832 q^{90} +(-0.0761760 + 7.42619i) q^{91} -1.25202 q^{92} +(-1.72173 - 2.98212i) q^{93} +(1.31688 - 2.28091i) q^{94} +(-7.46248 + 12.9254i) q^{95} +(2.84349 + 4.92508i) q^{96} -15.9312 q^{97} +(2.91882 + 5.30392i) q^{98} -3.98310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.432430	−	0.748990i	−0.305774	−	0.529616i	0.671659	−	0.740860i	$-0.265582\pi$
$2$	−0.432430	−	0.748990i	−0.305774	−	0.529616i	−0.977433	+	0.211244i	$0.932249\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.626009	−	1.08428i	0.313005	−	0.542140i
$5$	1.24779	+	2.16123i	0.558027	+	0.966531i	0.997661	+	0.0683543i	$0.0217748\pi$
$5$	1.24779	+	2.16123i	0.558027	+	0.966531i	−0.439634	+	0.898177i	$0.644892\pi$
$6$	−0.864859			−0.353077
$7$	−0.0271380	+	2.64561i	−0.0102572	+	0.999947i
$7$	−0.0271380	+	2.64561i	−0.0102572	+	0.999947i
$8$	−2.81254			−0.994383
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.07916	−	1.86916i	0.341260	−	0.591080i
$11$	1.99155	−	3.44946i	0.600475	−	1.04005i	−0.392275	−	0.919848i	$-0.628312\pi$
$11$	1.99155	−	3.44946i	0.600475	−	1.04005i	0.992749	−	0.120204i	$-0.0383549\pi$
$12$	−0.626009	−	1.08428i	−0.180713	−	0.313005i
$13$	2.80699			0.778518			0.389259	−	0.921128i	$-0.372731\pi$
$13$	2.80699			0.778518			0.389259	+	0.921128i	$0.372731\pi$
$14$	1.99327	−	1.12372i	0.532725	−	0.300326i
$15$	2.49557			0.644354
$16$	−0.0357927	−	0.0619948i	−0.00894819	−	0.0154987i
$17$	3.49385	−	6.05152i	0.847383	−	1.46771i	−0.0361530	−	0.999346i	$-0.511510\pi$
$17$	3.49385	−	6.05152i	0.847383	−	1.46771i	0.883536	−	0.468364i	$-0.155156\pi$
$18$	−0.432430	+	0.748990i	−0.101925	+	0.176539i
$19$	2.99029	+	5.17933i	0.686019	+	1.18822i	0.973115	+	0.230318i	$0.0739767\pi$
$19$	2.99029	+	5.17933i	0.686019	+	1.18822i	−0.287096	+	0.957902i	$0.592690\pi$
$20$	3.12450			0.698660
$21$	2.27760	+	1.34631i	0.497013	+	0.293789i
$22$	−3.44482			−0.734438
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−1.40627	+	2.43573i	−0.287054	+	0.497191i
$25$	−0.613943	+	1.06338i	−0.122789	+	0.212676i
$26$	−1.21382	−	2.10240i	−0.238050	−	0.412315i
$27$	−1.00000			−0.192450
$28$	2.85159	+	1.68560i	0.538901	+	0.318549i
$29$	−4.06198			−0.754291			−0.377145	−	0.926154i	$-0.623094\pi$
$29$	−4.06198			−0.754291			−0.377145	+	0.926154i	$0.623094\pi$
$30$	−1.07916	−	1.86916i	−0.197027	−	0.341260i
$31$	1.72173	−	2.98212i	0.309232	−	0.535605i	−0.668963	−	0.743296i	$-0.733261\pi$
$31$	1.72173	−	2.98212i	0.309232	−	0.535605i	0.978195	+	0.207691i	$0.0665948\pi$
$32$	−2.84349	+	4.92508i	−0.502664	+	0.870639i
$33$	−1.99155	−	3.44946i	−0.346684	−	0.600475i
$34$	−6.04338			−1.03643
$35$	−5.75164	+	3.24251i	−0.972204	+	0.548084i
$36$	−1.25202			−0.208670
$37$	0.738463	+	1.27905i	0.121402	+	0.210275i	0.920321	−	0.391164i	$-0.127927\pi$
$37$	0.738463	+	1.27905i	0.121402	+	0.210275i	−0.798918	+	0.601439i	$0.794594\pi$
$38$	2.58618	−	4.47939i	0.419534	−	0.726654i
$39$	1.40349	−	2.43092i	0.224739	−	0.389259i
$40$	−3.50945	−	6.07854i	−0.554892	−	0.961102i
$41$	−7.65339			−1.19526			−0.597630	−	0.801772i	$-0.703891\pi$
$41$	−7.65339			−1.19526			−0.597630	+	0.801772i	$0.703891\pi$
$42$	0.0234706	−	2.28808i	0.00362159	−	0.353059i
$43$	7.07993			1.07968			0.539840	−	0.841768i	$-0.318485\pi$
$43$	7.07993			1.07968			0.539840	+	0.841768i	$0.318485\pi$
$44$	−2.49345	−	4.31879i	−0.375902	−	0.651082i
$45$	1.24779	−	2.16123i	0.186009	−	0.322177i
$46$	−0.432430	+	0.748990i	−0.0637583	+	0.110433i
$47$	1.52265	+	2.63732i	0.222102	+	0.384692i	0.955446	−	0.295166i	$-0.0953749\pi$
$47$	1.52265	+	2.63732i	0.222102	+	0.384692i	−0.733344	+	0.679858i	$0.762042\pi$
$48$	−0.0715855			−0.0103325
$49$	−6.99853	−	0.143593i	−0.999790	−	0.0205133i
$50$	1.06195			0.150182
$51$	−3.49385	−	6.05152i	−0.489237	−	0.847383i
$52$	1.75720	−	3.04356i	0.243680	−	0.422065i
$53$	−4.78552	+	8.28876i	−0.657342	+	1.13855i	0.323960	+	0.946071i	$0.394986\pi$
$53$	−4.78552	+	8.28876i	−0.657342	+	1.13855i	−0.981301	+	0.192478i	$0.938348\pi$
$54$	0.432430	+	0.748990i	0.0588462	+	0.101925i
$55$	9.94011			1.34032
$56$	0.0763267	−	7.44089i	0.0101996	−	0.994330i
$57$	5.98058			0.792147
$58$	1.75652	+	3.04238i	0.230643	+	0.399485i
$59$	4.15309	−	7.19336i	0.540686	−	0.936496i	−0.458179	−	0.888860i	$-0.651498\pi$
$59$	4.15309	−	7.19336i	0.540686	−	0.936496i	0.998865	−	0.0476357i	$-0.0151687\pi$
$60$	1.56225	−	2.70590i	0.201686	−	0.349330i
$61$	1.85641	+	3.21539i	0.237689	+	0.411689i	0.960051	−	0.279826i	$-0.0902769\pi$
$61$	1.85641	+	3.21539i	0.237689	+	0.411689i	−0.722362	+	0.691515i	$0.756944\pi$
$62$	−2.97811			−0.378220
$63$	2.30474	−	1.29930i	0.290369	−	0.163697i
$64$	4.77528			0.596909
$65$	3.50252	+	6.06654i	0.434434	+	0.752462i
$66$	−1.72241	+	2.98330i	−0.212014	+	0.367219i
$67$	−2.23479	+	3.87076i	−0.273023	+	0.472889i	−0.969634	−	0.244559i	$-0.921357\pi$
$67$	−2.23479	+	3.87076i	−0.273023	+	0.472889i	0.696612	+	0.717448i	$0.254690\pi$
$68$	−4.37436	−	7.57662i	−0.530469	−	0.918800i
$69$	−1.00000			−0.120386
$70$	4.91579	+	2.90576i	0.587549	+	0.347305i
$71$	−9.49028			−1.12629			−0.563144	−	0.826359i	$-0.690408\pi$
$71$	−9.49028			−1.12629			−0.563144	+	0.826359i	$0.690408\pi$
$72$	1.40627	+	2.43573i	0.165730	+	0.287054i
$73$	−6.45106	+	11.1736i	−0.755039	+	1.30777i	0.190316	+	0.981723i	$0.439049\pi$
$73$	−6.45106	+	11.1736i	−0.755039	+	1.30777i	−0.945355	+	0.326043i	$0.894285\pi$
$74$	0.638666	−	1.10620i	0.0742435	−	0.128593i
$75$	0.613943	+	1.06338i	0.0708920	+	0.122789i
$76$	7.48779			0.858908
$77$	9.07190	+	5.36248i	1.03384	+	0.611111i
$78$	−2.42765			−0.274877
$79$	−3.56152	−	6.16873i	−0.400702	−	0.694037i	0.593109	−	0.805123i	$-0.297901\pi$
$79$	−3.56152	−	6.16873i	−0.400702	−	0.694037i	−0.993811	+	0.111086i	$0.964567\pi$
$80$	0.0893234	−	0.154713i	0.00998666	−	0.0172974i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.30955	+	5.73232i	0.365479	+	0.633028i
$83$	1.05716			0.116038			0.0580192	−	0.998315i	$-0.481522\pi$
$83$	1.05716			0.116038			0.0580192	+	0.998315i	$0.481522\pi$
$84$	2.88557	−	1.62675i	0.314842	−	0.177493i
$85$	17.4383			1.89145
$86$	−3.06157	−	5.30280i	−0.330138	−	0.571816i
$87$	−2.03099	+	3.51778i	−0.217745	+	0.377145i
$88$	−5.60131	+	9.70175i	−0.597101	+	1.03421i
$89$	1.65027	+	2.85835i	0.174928	+	0.302984i	0.940136	−	0.340799i	$-0.110697\pi$
$89$	1.65027	+	2.85835i	0.174928	+	0.302984i	−0.765208	+	0.643783i	$0.777364\pi$
$90$	−2.15832			−0.227507
$91$	−0.0761760	+	7.42619i	−0.00798541	+	0.778477i
$92$	−1.25202			−0.130532
$93$	−1.72173	−	2.98212i	−0.178535	−	0.309232i
$94$	1.31688	−	2.28091i	0.135826	−	0.235258i
$95$	−7.46248	+	12.9254i	−0.765635	+	1.32612i
$96$	2.84349	+	4.92508i	0.290213	+	0.502664i
$97$	−15.9312			−1.61757			−0.808786	−	0.588103i	$-0.799875\pi$
$97$	−15.9312			−1.61757			−0.808786	+	0.588103i	$0.799875\pi$
$98$	2.91882	+	5.30392i	0.294845	+	0.535777i
$99$	−3.98310			−0.400316
$100$	0.768667	+	1.33137i	0.0768667	+	0.133137i
$101$	−3.48214	+	6.03125i	−0.346486	+	0.600132i	−0.985623	−	0.168962i	$-0.945959\pi$
$101$	−3.48214	+	6.03125i	−0.346486	+	0.600132i	0.639136	+	0.769093i	$0.279292\pi$
$102$	−3.02169	+	5.23372i	−0.299192	+	0.518215i
$103$	−3.00244	−	5.20038i	−0.295839	−	0.512408i	0.679341	−	0.733823i	$-0.262266\pi$
$103$	−3.00244	−	5.20038i	−0.295839	−	0.512408i	−0.975180	+	0.221415i	$0.928933\pi$
$104$	−7.89475			−0.774144
$105$	−0.0677249	+	6.60232i	−0.00660927	+	0.644320i
$106$	8.27760			0.803992
$107$	−2.85898	−	4.95191i	−0.276388	−	0.478719i	0.694096	−	0.719882i	$-0.255804\pi$
$107$	−2.85898	−	4.95191i	−0.276388	−	0.478719i	−0.970484	+	0.241164i	$0.922471\pi$
$108$	−0.626009	+	1.08428i	−0.0602377	+	0.104335i
$109$	−3.12793	+	5.41773i	−0.299601	+	0.518924i	−0.976045	−	0.217570i	$-0.930187\pi$
$109$	−3.12793	+	5.41773i	−0.299601	+	0.518924i	0.676444	+	0.736494i	$0.263520\pi$
$110$	−4.29840	−	7.44505i	−0.409836	−	0.709857i
$111$	1.47693			0.140184
$112$	0.164986	−	0.0930113i	0.0155897	−	0.00878874i
$113$	−3.79544			−0.357045			−0.178523	−	0.983936i	$-0.557132\pi$
$113$	−3.79544			−0.357045			−0.178523	+	0.983936i	$0.557132\pi$
$114$	−2.58618	−	4.47939i	−0.242218	−	0.419534i
$115$	1.24779	−	2.16123i	0.116357	−	0.201536i
$116$	−2.54284	+	4.40432i	−0.236096	+	0.408931i
$117$	−1.40349	−	2.43092i	−0.129753	−	0.224739i
$118$	−7.18368			−0.661311
$119$	15.9152	+	9.40759i	1.45894	+	0.862393i
$120$	−7.01890			−0.640735
$121$	−2.43253	−	4.21327i	−0.221139	−	0.383024i
$122$	1.60553	−	2.78086i	0.145358	−	0.251768i
$123$	−3.82670	+	6.62803i	−0.345042	+	0.597630i
$124$	−2.15564	−	3.73367i	−0.193582	−	0.335294i
$125$	9.41359			0.841977
$126$	−1.96980	−	1.16437i	−0.175484	−	0.103730i
$127$	20.8819			1.85297			0.926484	−	0.376333i	$-0.122815\pi$
$127$	20.8819			1.85297			0.926484	+	0.376333i	$0.122815\pi$
$128$	3.62202	+	6.27352i	0.320144	+	0.554506i
$129$	3.53997	−	6.13140i	0.311677	−	0.539840i
$130$	3.02919	−	5.24670i	0.265677	−	0.460166i
$131$	−6.07439	−	10.5212i	−0.530722	−	0.919237i	−0.999357	−	0.0358458i	$-0.988587\pi$
$131$	−6.07439	−	10.5212i	−0.530722	−	0.919237i	0.468635	−	0.883392i	$-0.344746\pi$
$132$	−4.98691			−0.434055
$133$	−13.7837	+	7.77059i	−1.19519	+	0.673795i
$134$	3.86555			0.333933
$135$	−1.24779	−	2.16123i	−0.107392	−	0.186009i
$136$	−9.82658	+	17.0201i	−0.842623	+	1.45947i
$137$	0.414316	−	0.717617i	0.0353974	−	0.0613102i	−0.847784	−	0.530342i	$-0.822064\pi$
$137$	0.414316	−	0.717617i	0.0353974	−	0.0613102i	0.883181	+	0.469032i	$0.155397\pi$
$138$	0.432430	+	0.748990i	0.0368109	+	0.0637583i
$139$	0.546099			0.0463195			0.0231598	−	0.999732i	$-0.492627\pi$
$139$	0.546099			0.0463195			0.0231598	+	0.999732i	$0.492627\pi$
$140$	−0.0847928	+	8.26622i	−0.00716630	+	0.698623i
$141$	3.04531			0.256461
$142$	4.10388	+	7.10812i	0.344390	+	0.596501i
$143$	5.59025	−	9.68259i	0.467480	−	0.809699i
$144$	−0.0357927	+	0.0619948i	−0.00298273	+	0.00516624i
$145$	−5.06849	−	8.77887i	−0.420915	−	0.729046i
$146$	11.1585			0.923485
$147$	−3.62362	+	5.98911i	−0.298871	+	0.493973i
$148$	1.84914			0.151998
$149$	9.27434	+	16.0636i	0.759783	+	1.31598i	0.942961	+	0.332903i	$0.108028\pi$
$149$	9.27434	+	16.0636i	0.759783	+	1.31598i	−0.183178	+	0.983080i	$0.558638\pi$
$150$	0.530974	−	0.919674i	0.0433538	−	0.0750911i
$151$	2.88625	−	4.99914i	0.234880	−	0.406824i	−0.724358	−	0.689424i	$-0.757864\pi$
$151$	2.88625	−	4.99914i	0.234880	−	0.406824i	0.959238	+	0.282600i	$0.0911969\pi$
$152$	−8.41030	−	14.5671i	−0.682166	−	1.18155i
$153$	−6.98770			−0.564922
$154$	0.0934855	−	9.11366i	0.00753328	−	0.734399i
$155$	8.59340			0.690239
$156$	−1.75720	−	3.04356i	−0.140688	−	0.243680i
$157$	−7.06448	+	12.2360i	−0.563807	+	0.976543i	0.433352	+	0.901225i	$0.357331\pi$
$157$	−7.06448	+	12.2360i	−0.563807	+	0.976543i	−0.997160	+	0.0753182i	$0.976003\pi$
$158$	−3.08021	+	5.33509i	−0.245049	+	0.424437i
$159$	4.78552	+	8.28876i	0.379516	+	0.657342i
$160$	−14.1923			−1.12200
$161$	2.30474	−	1.29930i	0.181639	−	0.102399i
$162$	0.864859			0.0679498
$163$	8.37481	+	14.5056i	0.655966	+	1.13617i	0.981651	+	0.190688i	$0.0610719\pi$
$163$	8.37481	+	14.5056i	0.655966	+	1.13617i	−0.325685	+	0.945478i	$0.605595\pi$
$164$	−4.79109	+	8.29842i	−0.374121	+	0.647997i
$165$	4.97006	−	8.60839i	0.386918	−	0.670162i
$166$	−0.457147	−	0.791803i	−0.0354815	−	0.0614558i
$167$	17.8518			1.38141			0.690707	−	0.723135i	$-0.257299\pi$
$167$	17.8518			1.38141			0.690707	+	0.723135i	$0.257299\pi$
$168$	−6.40583	−	3.78654i	−0.494221	−	0.292138i
$169$	−5.12084			−0.393910
$170$	−7.54084	−	13.0611i	−0.578356	−	1.00174i
$171$	2.99029	−	5.17933i	0.228673	−	0.396073i
$172$	4.43210	−	7.67663i	0.337945	−	0.585337i
$173$	−1.32680	−	2.29808i	−0.100874	−	0.174720i	0.811171	−	0.584809i	$-0.198831\pi$
$173$	−1.32680	−	2.29808i	−0.100874	−	0.174720i	−0.912045	+	0.410090i	$0.865497\pi$
$174$	3.51304			0.266323
$175$	−2.79663	−	1.65311i	−0.211405	−	0.124964i
$176$	−0.285132			−0.0214926
$177$	−4.15309	−	7.19336i	−0.312165	−	0.540686i
$178$	1.42725	−	2.47207i	0.106977	−	0.185289i
$179$	−5.73482	+	9.93299i	−0.428640	+	0.742427i	−0.996753	−	0.0805242i	$-0.974341\pi$
$179$	−5.73482	+	9.93299i	−0.428640	+	0.742427i	0.568112	+	0.822951i	$0.307674\pi$
$180$	−1.56225	−	2.70590i	−0.116443	−	0.201686i
$181$	−15.8393			−1.17732			−0.588662	−	0.808380i	$-0.700345\pi$
$181$	−15.8393			−1.17732			−0.588662	+	0.808380i	$0.700345\pi$
$182$	5.59509	−	3.15425i	0.414735	−	0.233809i
$183$	3.71282			0.274459
$184$	1.40627	+	2.43573i	0.103672	+	0.179564i
$185$	−1.84289	+	3.19197i	−0.135492	+	0.234679i
$186$	−1.48905	+	2.57912i	−0.109183	+	0.189110i
$187$	−13.9163	−	24.1038i	−1.01766	−	1.76264i
$188$	3.81278			0.278076
$189$	0.0271380	−	2.64561i	0.00197400	−	0.192440i
$190$	12.9080			0.936445
$191$	−10.8975	−	18.8751i	−0.788518	−	1.36575i	−0.926875	−	0.375370i	$-0.877515\pi$
$191$	−10.8975	−	18.8751i	−0.788518	−	1.36575i	0.138357	−	0.990382i	$-0.455818\pi$
$192$	2.38764	−	4.13551i	0.172313	−	0.298455i
$193$	−8.01667	+	13.8853i	−0.577053	+	0.999485i	0.418762	+	0.908096i	$0.362464\pi$
$193$	−8.01667	+	13.8853i	−0.577053	+	0.999485i	−0.995815	+	0.0913890i	$0.970869\pi$
$194$	6.88914	+	11.9323i	0.494612	+	0.856692i
$195$	7.00504			0.501641
$196$	−4.53684	+	7.49847i	−0.324060	+	0.535605i
$197$	10.6653			0.759870			0.379935	−	0.925013i	$-0.375946\pi$
$197$	10.6653			0.759870			0.379935	+	0.925013i	$0.375946\pi$
$198$	1.72241	+	2.98330i	0.122406	+	0.212014i
$199$	1.82952	−	3.16883i	0.129691	−	0.224632i	−0.793866	−	0.608093i	$-0.791935\pi$
$199$	1.82952	−	3.16883i	0.129691	−	0.224632i	0.923557	+	0.383461i	$0.125268\pi$
$200$	1.72674	−	2.99080i	0.122099	−	0.211481i
$201$	2.23479	+	3.87076i	0.157630	+	0.273023i
$202$	6.02313			0.423786
$203$	0.110234	−	10.7464i	0.00773691	−	0.754251i
$204$	−8.74872			−0.612533
$205$	−9.54980	−	16.5407i	−0.666987	−	1.15526i
$206$	−2.59669	+	4.49760i	−0.180920	+	0.313362i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	−0.100470	−	0.174019i	−0.00696632	−	0.0120660i
$209$	23.8212			1.64775
$210$	4.97436	−	2.80431i	0.343263	−	0.193516i
$211$	−28.1857			−1.94039			−0.970193	−	0.242332i	$-0.922088\pi$
$211$	−28.1857			−1.94039			−0.970193	+	0.242332i	$0.922088\pi$
$212$	5.99156	+	10.3777i	0.411502	+	0.712742i
$213$	−4.74514	+	8.21882i	−0.325131	+	0.563144i
$214$	−2.47262	+	4.28270i	−0.169025	+	0.292759i
$215$	8.83424	+	15.3014i	0.602490	+	1.04354i
$216$	2.81254			0.191369
$217$	7.84282	+	4.63596i	0.532405	+	0.314709i
$218$	5.41044			0.366441
$219$	6.45106	+	11.1736i	0.435922	+	0.755039i
$220$	6.22260	−	10.7779i	0.419528	−	0.726643i
$221$	9.80718	−	16.9865i	0.659702	−	1.14264i
$222$	−0.638666	−	1.10620i	−0.0428645	−	0.0742435i
$223$	24.2280			1.62243			0.811215	−	0.584748i	$-0.198807\pi$
$223$	24.2280			1.62243			0.811215	+	0.584748i	$0.198807\pi$
$224$	−12.9527	−	7.65644i	−0.865437	−	0.511567i
$225$	1.22789			0.0818590
$226$	1.64126	+	2.84275i	0.109175	+	0.189097i
$227$	4.01827	−	6.95985i	0.266702	−	0.461942i	−0.701306	−	0.712860i	$-0.747399\pi$
$227$	4.01827	−	6.95985i	0.266702	−	0.461942i	0.968008	+	0.250919i	$0.0807327\pi$
$228$	3.74390	−	6.48462i	0.247946	−	0.429454i
$229$	−6.88950	−	11.9330i	−0.455271	−	0.788553i	0.543433	−	0.839453i	$-0.317124\pi$
$229$	−6.88950	−	11.9330i	−0.455271	−	0.788553i	−0.998704	+	0.0509000i	$0.983791\pi$
$230$	−2.15832			−0.142315
$231$	9.17999	−	5.17525i	0.603999	−	0.340507i
$232$	11.4245			0.750054
$233$	0.918005	+	1.59003i	0.0601405	+	0.104166i	0.894528	−	0.447012i	$-0.147512\pi$
$233$	0.918005	+	1.59003i	0.0601405	+	0.104166i	−0.834388	+	0.551178i	$0.814178\pi$
$234$	−1.21382	+	2.10240i	−0.0793501	+	0.137438i
$235$	−3.79990	+	6.58161i	−0.247878	+	0.429337i
$236$	−5.19974	−	9.00622i	−0.338474	−	0.586255i
$237$	−7.12304			−0.462691
$238$	0.164005	−	15.9884i	0.0106309	−	1.03638i
$239$	−4.42206			−0.286039			−0.143020	−	0.989720i	$-0.545681\pi$
$239$	−4.42206			−0.286039			−0.143020	+	0.989720i	$0.545681\pi$
$240$	−0.0893234	−	0.154713i	−0.00576580	−	0.00998666i
$241$	14.2294	−	24.6461i	0.916598	−	1.58759i	0.112053	−	0.993702i	$-0.464257\pi$
$241$	14.2294	−	24.6461i	0.916598	−	1.58759i	0.804545	−	0.593892i	$-0.202409\pi$
$242$	−2.10380	+	3.64389i	−0.135237	+	0.234238i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	4.64851			0.297591
$245$	−8.42233	−	15.3046i	−0.538083	−	0.977775i
$246$	6.61911			0.422019
$247$	8.39369	+	14.5383i	0.534078	+	0.925050i
$248$	−4.84243	+	8.38734i	−0.307495	+	0.532596i
$249$	0.528580	−	0.915528i	0.0334974	−	0.0580192i
$250$	−4.07072	−	7.05069i	−0.257455	−	0.445925i
$251$	−26.7064			−1.68569			−0.842846	−	0.538156i	$-0.819121\pi$
$251$	−26.7064			−1.68569			−0.842846	+	0.538156i	$0.819121\pi$
$252$	0.0339773	−	3.31235i	0.00214037	−	0.208659i
$253$	−3.98310			−0.250415
$254$	−9.02995	−	15.6403i	−0.566590	−	0.981362i
$255$	8.71915	−	15.1020i	0.546015	−	0.945725i
$256$	7.90781	−	13.6967i	0.494238	−	0.856046i
$257$	−2.18216	−	3.77961i	−0.136119	−	0.235766i	0.789905	−	0.613229i	$-0.210130\pi$
$257$	−2.18216	−	3.77961i	−0.136119	−	0.235766i	−0.926025	+	0.377463i	$0.876796\pi$
$258$	−6.12315			−0.381210
$259$	−3.40392	+	1.91897i	−0.211509	+	0.119239i
$260$	8.77043			0.543919
$261$	2.03099	+	3.51778i	0.125715	+	0.217745i
$262$	−5.25349	+	9.09932i	−0.324562	+	0.562158i
$263$	−0.774571	+	1.34160i	−0.0477621	+	0.0827264i	−0.888918	−	0.458066i	$-0.848542\pi$
$263$	−0.774571	+	1.34160i	−0.0477621	+	0.0827264i	0.841156	+	0.540793i	$0.181876\pi$
$264$	5.60131	+	9.70175i	0.344737	+	0.597101i
$265$	−23.8852			−1.46726
$266$	11.7806	+	6.96359i	0.722312	+	0.426965i
$267$	3.30053			0.201989
$268$	2.79799	+	4.84627i	0.170915	+	0.296033i
$269$	1.85766	−	3.21756i	0.113264	−	0.196178i	−0.803821	−	0.594872i	$-0.797203\pi$
$269$	1.85766	−	3.21756i	0.113264	−	0.196178i	0.917084	+	0.398693i	$0.130536\pi$
$270$	−1.07916	+	1.86916i	−0.0656756	+	0.113753i
$271$	−2.01004	−	3.48150i	−0.122101	−	0.211486i	0.798495	−	0.602002i	$-0.205630\pi$
$271$	−2.01004	−	3.48150i	−0.122101	−	0.211486i	−0.920596	+	0.390516i	$0.872297\pi$
$272$	−0.500218			−0.0303302
$273$	6.39318	+	3.77907i	0.386933	+	0.228720i
$274$	−0.716651			−0.0432945
$275$	2.44539	+	4.23554i	0.147463	+	0.255413i
$276$	−0.626009	+	1.08428i	−0.0376813	+	0.0652660i
$277$	5.69636	−	9.86639i	0.342261	−	0.592814i	−0.642591	−	0.766209i	$-0.722140\pi$
$277$	5.69636	−	9.86639i	0.342261	−	0.592814i	0.984852	+	0.173395i	$0.0554738\pi$
$278$	−0.236149	−	0.409023i	−0.0141633	−	0.0245316i
$279$	−3.44346			−0.206155
$280$	16.1767	−	9.11968i	0.966743	−	0.545005i
$281$	−27.9503			−1.66738			−0.833689	−	0.552235i	$-0.813775\pi$
$281$	−27.9503			−1.66738			−0.833689	+	0.552235i	$0.813775\pi$
$282$	−1.31688	−	2.28091i	−0.0784192	−	0.135826i
$283$	14.9877	−	25.9594i	0.890925	−	1.54313i	0.0521567	−	0.998639i	$-0.483390\pi$
$283$	14.9877	−	25.9594i	0.890925	−	1.54313i	0.838768	−	0.544488i	$-0.183276\pi$
$284$	−5.94100	+	10.2901i	−0.352533	+	0.610606i
$285$	7.46248	+	12.9254i	0.442039	+	0.765635i
$286$	−9.66956			−0.571773
$287$	0.207698	−	20.2479i	0.0122600	−	1.19520i
$288$	5.68699			0.335109
$289$	−15.9140	−	27.5638i	−0.936115	−	1.62140i
$290$	−4.38353	+	7.59249i	−0.257410	+	0.445847i
$291$	−7.96562	+	13.7969i	−0.466953	+	0.808786i
$292$	8.07684	+	13.9895i	0.472661	+	0.818673i
$293$	−4.87346			−0.284711			−0.142355	−	0.989816i	$-0.545468\pi$
$293$	−4.87346			−0.284711			−0.142355	+	0.989816i	$0.545468\pi$
$294$	6.05274	+	0.124188i	0.353003	+	0.00724279i
$295$	20.7287			1.20687
$296$	−2.07695	−	3.59739i	−0.120721	−	0.209094i
$297$	−1.99155	+	3.44946i	−0.115561	+	0.200158i
$298$	8.02100	−	13.8928i	0.464644	−	0.804787i
$299$	−1.40349	−	2.43092i	−0.0811661	−	0.140584i
$300$	1.53733			0.0887580
$301$	−0.192135	+	18.7308i	−0.0110745	+	1.07962i
$302$	−4.99241			−0.287281
$303$	3.48214	+	6.03125i	0.200044	+	0.346486i
$304$	0.214061	−	0.370765i	0.0122773	−	0.0212648i
$305$	−4.63280	+	8.02425i	−0.265273	+	0.459467i
$306$	3.02169	+	5.23372i	0.172738	+	0.299192i
$307$	−27.9064			−1.59270			−0.796351	−	0.604835i	$-0.793239\pi$
$307$	−27.9064			−1.59270			−0.796351	+	0.604835i	$0.793239\pi$
$308$	11.4935	−	6.47951i	0.654904	−	0.369204i
$309$	−6.00488			−0.341606
$310$	−3.71604	−	6.43638i	−0.211057	−	0.365562i
$311$	−13.5043	+	23.3901i	−0.765758	+	1.32633i	0.174087	+	0.984730i	$0.444303\pi$
$311$	−13.5043	+	23.3901i	−0.765758	+	1.32633i	−0.939845	+	0.341602i	$0.889031\pi$
$312$	−3.94738	+	6.83706i	−0.223476	+	0.387072i
$313$	−2.10701	−	3.64945i	−0.119095	−	0.206279i	0.800314	−	0.599581i	$-0.204666\pi$
$313$	−2.10701	−	3.64945i	−0.119095	−	0.206279i	−0.919409	+	0.393302i	$0.871333\pi$
$314$	12.2196			0.689590
$315$	5.68391	+	3.35981i	0.320252	+	0.189304i
$316$	−8.91818			−0.501687
$317$	3.99898	+	6.92643i	0.224605	+	0.389027i	0.956201	−	0.292711i	$-0.0945575\pi$
$317$	3.99898	+	6.92643i	0.224605	+	0.389027i	−0.731596	+	0.681738i	$0.761224\pi$
$318$	4.13880	−	7.16861i	0.232092	−	0.401996i
$319$	−8.08963	+	14.0117i	−0.452932	+	0.784502i
$320$	5.95852	+	10.3205i	0.333092	+	0.576932i
$321$	−5.71797			−0.319146
$322$	−1.96980	−	1.16437i	−0.109773	−	0.0648877i
$323$	41.7905			2.32528
$324$	0.626009	+	1.08428i	0.0347783	+	0.0602377i
$325$	−1.72333	+	2.98489i	−0.0955930	+	0.165572i
$326$	7.24304	−	12.5453i	0.401155	−	0.694820i
$327$	3.12793	+	5.41773i	0.172975	+	0.299601i
$328$	21.5255			1.18854
$329$	−7.01864	+	3.95678i	−0.386950	+	0.218145i
$330$	−8.59680			−0.473238
$331$	−12.0436	−	20.8601i	−0.661974	−	1.14657i	−0.980096	−	0.198523i	$-0.936385\pi$
$331$	−12.0436	−	20.8601i	−0.661974	−	1.14657i	0.318122	−	0.948050i	$-0.396948\pi$
$332$	0.661792	−	1.14626i	0.0363205	−	0.0629090i
$333$	0.738463	−	1.27905i	0.0404675	−	0.0700918i
$334$	−7.71965	−	13.3708i	−0.422401	−	0.731619i
$335$	−11.1541			−0.609416
$336$	0.00194269	−	0.189387i	0.000105982	−	0.0103319i
$337$	−6.91298			−0.376574			−0.188287	−	0.982114i	$-0.560294\pi$
$337$	−6.91298			−0.376574			−0.188287	+	0.982114i	$0.560294\pi$
$338$	2.21440	+	3.83546i	0.120448	+	0.208621i
$339$	−1.89772	+	3.28695i	−0.103070	+	0.178523i
$340$	10.9165	−	18.9080i	0.592032	−	1.02543i
$341$	−6.85782	−	11.8781i	−0.371372	−	0.643234i
$342$	−5.17236			−0.279689
$343$	0.569818	−	18.5115i	0.0307673	−	0.999527i
$344$	−19.9126			−1.07361
$345$	−1.24779	−	2.16123i	−0.0671786	−	0.116357i
$346$	−1.14749	+	1.98752i	−0.0616896	+	0.106850i
$347$	−6.09382	+	10.5548i	−0.327133	+	0.566611i	−0.981942	−	0.189183i	$-0.939416\pi$
$347$	−6.09382	+	10.5548i	−0.327133	+	0.566611i	0.654809	+	0.755795i	$0.272749\pi$
$348$	2.54284	+	4.40432i	0.136310	+	0.236096i
$349$	27.0701			1.44903			0.724515	−	0.689259i	$-0.242064\pi$
$349$	27.0701			1.44903			0.724515	+	0.689259i	$0.242064\pi$
$350$	−0.0288192	+	2.80950i	−0.00154045	+	0.150174i
$351$	−2.80699			−0.149826
$352$	11.3259	+	19.6171i	0.603673	+	1.04559i
$353$	14.2886	−	24.7486i	0.760505	−	1.31723i	−0.182085	−	0.983283i	$-0.558285\pi$
$353$	14.2886	−	24.7486i	0.760505	−	1.31723i	0.942590	−	0.333951i	$-0.108382\pi$
$354$	−3.59184	+	6.22125i	−0.190904	+	0.330656i
$355$	−11.8418	−	20.5107i	−0.628499	−	1.08859i
$356$	4.13233			0.219013
$357$	16.1048	−	9.07914i	0.852356	−	0.480519i
$358$	9.91962			0.524268
$359$	9.73136	+	16.8552i	0.513601	+	0.889584i	0.999876	+	0.0157775i	$0.00502233\pi$
$359$	9.73136	+	16.8552i	0.513601	+	0.889584i	−0.486274	+	0.873806i	$0.661644\pi$
$360$	−3.50945	+	6.07854i	−0.184964	+	0.320367i
$361$	−8.38365	+	14.5209i	−0.441245	+	0.764258i
$362$	6.84937	+	11.8635i	0.359995	+	0.623529i
$363$	−4.86506			−0.255350
$364$	8.00438	+	4.73146i	0.419544	+	0.247996i
$365$	−32.1982			−1.68533
$366$	−1.60553	−	2.78086i	−0.0839225	−	0.145358i
$367$	−2.40920	+	4.17286i	−0.125759	+	0.217821i	−0.922029	−	0.387120i	$-0.873470\pi$
$367$	−2.40920	+	4.17286i	−0.125759	+	0.217821i	0.796270	+	0.604941i	$0.206803\pi$
$368$	−0.0357927	+	0.0619948i	−0.00186583	+	0.00323170i
$369$	3.82670	+	6.62803i	0.199210	+	0.345042i
$370$	3.18768			0.165719
$371$	−21.7990	−	12.8856i	−1.13175	−	0.668985i
$372$	−4.31127			−0.223529
$373$	12.3176	+	21.3347i	0.637782	+	1.10467i	0.985918	+	0.167227i	$0.0534813\pi$
$373$	12.3176	+	21.3347i	0.637782	+	1.10467i	−0.348136	+	0.937444i	$0.613185\pi$
$374$	−12.0357	+	20.8464i	−0.622350	+	1.07794i
$375$	4.70679	−	8.15241i	0.243058	−	0.420988i
$376$	−4.28253	−	7.41755i	−0.220854	−	0.382531i
$377$	−11.4019			−0.587229
$378$	−1.99327	+	1.12372i	−0.102523	+	0.0577977i
$379$	31.7983			1.63337			0.816684	−	0.577085i	$-0.195810\pi$
$379$	31.7983			1.63337			0.816684	+	0.577085i	$0.195810\pi$
$380$	9.34316	+	16.1828i	0.479294	+	0.830162i
$381$	10.4409	−	18.0843i	0.534906	−	0.926484i
$382$	−9.42483	+	16.3243i	−0.482216	+	0.835223i
$383$	11.1827	+	19.3690i	0.571409	+	0.989709i	0.996422	+	0.0845218i	$0.0269363\pi$
$383$	11.1827	+	19.3690i	0.571409	+	0.989709i	−0.425013	+	0.905187i	$0.639730\pi$
$384$	7.24404			0.369671
$385$	−0.269755	+	26.2977i	−0.0137480	+	1.34025i
$386$	13.8666			0.705791
$387$	−3.53997	−	6.13140i	−0.179947	−	0.311677i
$388$	−9.97310	+	17.2739i	−0.506308	+	0.876950i
$389$	−9.95483	+	17.2423i	−0.504730	+	0.874218i	0.495255	+	0.868748i	$0.335075\pi$
$389$	−9.95483	+	17.2423i	−0.504730	+	0.874218i	−0.999985	+	0.00547015i	$0.998259\pi$
$390$	−3.02919	−	5.24670i	−0.153389	−	0.265677i
$391$	−6.98770			−0.353383
$392$	19.6836	+	0.403862i	0.994173	+	0.0203981i
$393$	−12.1488			−0.612825
$394$	−4.61198	−	7.98819i	−0.232348	−	0.402439i
$395$	8.88803	−	15.3945i	0.447206	−	0.774583i
$396$	−2.49345	+	4.31879i	−0.125301	+	0.217027i
$397$	−13.5533	−	23.4750i	−0.680222	−	1.17818i	−0.974913	−	0.222586i	$-0.928550\pi$
$397$	−13.5533	−	23.4750i	−0.680222	−	1.17818i	0.294691	−	0.955593i	$-0.404783\pi$
$398$	−3.16456			−0.158625
$399$	−0.162301	+	15.8223i	−0.00812521	+	0.792105i
$400$	0.0878987			0.00439494
$401$	17.0891	+	29.5992i	0.853390	+	1.47811i	0.878131	+	0.478420i	$0.158790\pi$
$401$	17.0891	+	29.5992i	0.853390	+	1.47811i	−0.0247414	+	0.999694i	$0.507876\pi$
$402$	1.93278	−	3.34767i	0.0963981	−	0.166966i
$403$	4.83287	−	8.37077i	0.240742	−	0.416978i
$404$	4.35971	+	7.55123i	0.216903	+	0.375688i
$405$	−2.49557			−0.124006
$406$	−8.09664	+	4.56451i	−0.401829	+	0.226533i
$407$	5.88274			0.291596
$408$	9.82658	+	17.0201i	0.486488	+	0.842623i
$409$	−7.57386	+	13.1183i	−0.374503	+	0.648659i	−0.990253	−	0.139284i	$-0.955520\pi$
$409$	−7.57386	+	13.1183i	−0.374503	+	0.648659i	0.615749	+	0.787942i	$0.288853\pi$
$410$	−8.25923	+	14.3054i	−0.407895	+	0.706494i
$411$	−0.414316	−	0.717617i	−0.0204367	−	0.0353974i
$412$	−7.51822			−0.370396
$413$	18.9181	+	11.1827i	0.930901	+	0.550264i
$414$	0.864859			0.0425055
$415$	1.31911	+	2.28477i	0.0647526	+	0.112155i
$416$	−7.98165	+	13.8246i	−0.391332	+	0.677808i
$417$	0.273050	−	0.472936i	0.0133713	−	0.0231598i
$418$	−10.3010	−	17.8419i	−0.503839	−	0.872674i
$419$	14.0504			0.686405			0.343202	−	0.939262i	$-0.388488\pi$
$419$	14.0504			0.686405			0.343202	+	0.939262i	$0.388488\pi$
$420$	7.11636	+	4.20654i	0.347243	+	0.205258i
$421$	−26.0914			−1.27161			−0.635807	−	0.771848i	$-0.719333\pi$
$421$	−26.0914			−1.27161			−0.635807	+	0.771848i	$0.719333\pi$
$422$	12.1884	+	21.1108i	0.593320	+	1.02766i
$423$	1.52265	−	2.63732i	0.0740340	−	0.128231i
$424$	13.4595	−	23.3125i	0.653649	−	1.13215i
$425$	4.29004	+	7.43058i	0.208098	+	0.360436i
$426$	8.20775			0.397667
$427$	−8.55706	+	4.82408i	−0.414105	+	0.233453i
$428$	−7.15900			−0.346043
$429$	−5.59025	−	9.68259i	−0.269900	−	0.467480i
$430$	7.64038	−	13.2335i	0.368452	−	0.638177i
$431$	−1.54723	+	2.67988i	−0.0745274	+	0.129085i	−0.900881	−	0.434067i	$-0.857078\pi$
$431$	−1.54723	+	2.67988i	−0.0745274	+	0.129085i	0.826353	+	0.563152i	$0.190411\pi$
$432$	0.0357927	+	0.0619948i	0.00172208	+	0.00298273i
$433$	18.9836			0.912293			0.456146	−	0.889905i	$-0.349229\pi$
$433$	18.9836			0.912293			0.456146	+	0.889905i	$0.349229\pi$
$434$	0.0808199	−	7.87892i	0.00387948	−	0.378200i
$435$	−10.1370			−0.486031
$436$	3.91622	+	6.78310i	0.187553	+	0.324851i
$437$	2.99029	−	5.17933i	0.143045	−	0.247761i
$438$	5.57926	−	9.66356i	0.266587	−	0.461743i
$439$	5.98560	+	10.3674i	0.285677	+	0.494808i	0.972773	−	0.231759i	$-0.0744481\pi$
$439$	5.98560	+	10.3674i	0.285677	+	0.494808i	−0.687096	+	0.726567i	$0.741115\pi$
$440$	−27.9569			−1.33280
$441$	3.37491	+	6.13270i	0.160710	+	0.292033i
$442$	−16.9637			−0.806879
$443$	−9.74098	−	16.8719i	−0.462808	−	0.801607i	0.536291	−	0.844033i	$-0.319825\pi$
$443$	−9.74098	−	16.8719i	−0.462808	−	0.801607i	−0.999100	+	0.0424256i	$0.986491\pi$
$444$	0.924569	−	1.60140i	0.0438781	−	0.0759991i
$445$	−4.11836	+	7.13321i	−0.195229	+	0.338147i
$446$	−10.4769	−	18.1466i	−0.496097	−	0.859265i
$447$	18.5487			0.877322
$448$	−0.129591	+	12.6335i	−0.00612262	+	0.596878i
$449$	−25.9358			−1.22399			−0.611993	−	0.790864i	$-0.709632\pi$
$449$	−25.9358			−1.22399			−0.611993	+	0.790864i	$0.709632\pi$
$450$	−0.530974	−	0.919674i	−0.0250304	−	0.0433538i
$451$	−15.2421	+	26.4001i	−0.717723	+	1.24313i
$452$	−2.37598	+	4.11532i	−0.111757	+	0.193568i
$453$	−2.88625	−	4.99914i	−0.135608	−	0.234880i
$454$	−6.95048			−0.326202
$455$	−16.1448	+	9.10167i	−0.756878	+	0.426693i
$456$	−16.8206			−0.787697
$457$	−2.30666	−	3.99525i	−0.107901	−	0.186890i	0.807019	−	0.590526i	$-0.201080\pi$
$457$	−2.30666	−	3.99525i	−0.107901	−	0.186890i	−0.914920	+	0.403636i	$0.867746\pi$
$458$	−5.95845	+	10.3203i	−0.278420	+	0.482238i
$459$	−3.49385	+	6.05152i	−0.163079	+	0.282461i
$460$	−1.56225	−	2.70590i	−0.0728403	−	0.126163i
$461$	13.8181			0.643571			0.321786	−	0.946813i	$-0.395717\pi$
$461$	13.8181			0.643571			0.321786	+	0.946813i	$0.395717\pi$
$462$	−7.84591	−	4.63779i	−0.365025	−	0.215769i
$463$	−34.1291			−1.58611			−0.793057	−	0.609147i	$-0.791512\pi$
$463$	−34.1291			−1.58611			−0.793057	+	0.609147i	$0.791512\pi$
$464$	0.145389	+	0.251822i	0.00674954	+	0.0116905i
$465$	4.29670	−	7.44211i	0.199255	−	0.345119i
$466$	0.793946	−	1.37515i	0.0367788	−	0.0637028i
$467$	13.9858	+	24.2241i	0.647185	+	1.12096i	0.983792	+	0.179312i	$0.0573871\pi$
$467$	13.9858	+	24.2241i	0.647185	+	1.12096i	−0.336608	+	0.941645i	$0.609280\pi$
$468$	−3.51440			−0.162453
$469$	−10.1799	−	6.01742i	−0.470064	−	0.277859i
$470$	6.57275			0.303179
$471$	7.06448	+	12.2360i	0.325514	+	0.563807i
$472$	−11.6807	+	20.2316i	−0.537649	+	0.931235i
$473$	14.1000	−	24.4220i	0.648320	−	1.12292i
$474$	3.08021	+	5.33509i	0.141479	+	0.245049i
$475$	−7.34346			−0.336941
$476$	20.1635	−	11.3673i	0.924193	−	0.521017i
$477$	9.57104			0.438228
$478$	1.91223	+	3.31208i	0.0874634	+	0.151491i
$479$	16.3134	−	28.2557i	0.745380	−	1.29104i	−0.204637	−	0.978838i	$-0.565601\pi$
$479$	16.3134	−	28.2557i	0.745380	−	1.29104i	0.950017	−	0.312199i	$-0.101065\pi$
$480$	−7.09615	+	12.2909i	−0.323893	+	0.561000i
$481$	2.07285	+	3.59029i	0.0945140	+	0.163703i
$482$	−24.6129			−1.12109
$483$	0.0271380	−	2.64561i	0.00123482	−	0.120380i
$484$	−6.09115			−0.276870
$485$	−19.8788	−	34.4311i	−0.902649	−	1.56343i
$486$	0.432430	−	0.748990i	0.0196154	−	0.0339749i
$487$	12.9711	−	22.4665i	0.587775	−	1.01806i	−0.406748	−	0.913540i	$-0.633337\pi$
$487$	12.9711	−	22.4665i	0.587775	−	1.01806i	0.994523	−	0.104516i	$-0.0333293\pi$
$488$	−5.22122	−	9.04342i	−0.236354	−	0.409376i
$489$	16.7496			0.757444
$490$	−7.82093	+	12.9264i	−0.353314	+	0.583956i
$491$	26.0005			1.17339			0.586693	−	0.809810i	$-0.300430\pi$
$491$	26.0005			1.17339			0.586693	+	0.809810i	$0.300430\pi$
$492$	4.79109	+	8.29842i	0.215999	+	0.374121i
$493$	−14.1919	+	24.5812i	−0.639173	+	1.10708i
$494$	7.25937	−	12.5736i	0.326614	−	0.565713i
$495$	−4.97006	−	8.60839i	−0.223387	−	0.386918i
$496$	−0.246502			−0.0110683
$497$	0.257547	−	25.1076i	0.0115526	−	1.12623i
$498$	−0.914295			−0.0409705
$499$	11.6036	+	20.0980i	0.519448	+	0.899711i	0.999744	+	0.0226043i	$0.00719577\pi$
$499$	11.6036	+	20.0980i	0.519448	+	0.899711i	−0.480296	+	0.877106i	$0.659471\pi$
$500$	5.89299	−	10.2070i	0.263543	−	0.456469i
$501$	8.92590	−	15.4601i	0.398780	−	0.690707i
$502$	11.5486	+	20.0028i	0.515441	+	0.892769i
$503$	12.5204			0.558256			0.279128	−	0.960254i	$-0.409955\pi$
$503$	12.5204			0.558256			0.279128	+	0.960254i	$0.409955\pi$
$504$	−6.48216	+	3.65434i	−0.288738	+	0.162777i
$505$	−17.3799			−0.773395
$506$	1.72241	+	2.98330i	0.0765705	+	0.132624i
$507$	−2.56042	+	4.43477i	−0.113712	+	0.196955i
$508$	13.0723	−	22.6418i	0.579988	−	1.00457i
$509$	12.1059	+	20.9680i	0.536585	+	0.929392i	0.999085	+	0.0427725i	$0.0136191\pi$
$509$	12.1059	+	20.9680i	0.536585	+	0.929392i	−0.462500	+	0.886619i	$0.653048\pi$
$510$	−15.0817			−0.667828
$511$	−29.3858	−	17.3702i	−1.29995	−	0.768413i
$512$	0.809780			0.0357875
$513$	−2.99029	−	5.17933i	−0.132024	−	0.228673i
$514$	−1.88726	+	3.26883i	−0.0832436	+	0.144182i
$515$	7.49281	−	12.9779i	0.330172	−	0.571876i
$516$	−4.43210	−	7.67663i	−0.195112	−	0.337945i
$517$	12.1298			0.533466
$518$	2.90925	+	1.71968i	0.127825	+	0.0755586i
$519$	−2.65359			−0.116480
$520$	−9.85097	−	17.0624i	−0.431994	−	0.748235i
$521$	3.41410	−	5.91340i	0.149575	−	0.259071i	−0.781496	−	0.623911i	$-0.785543\pi$
$521$	3.41410	−	5.91340i	0.149575	−	0.259071i	0.931070	+	0.364840i	$0.118876\pi$
$522$	1.75652	−	3.04238i	0.0768809	−	0.133162i
$523$	4.77002	+	8.26192i	0.208579	+	0.361269i	0.951267	−	0.308369i	$-0.0997830\pi$
$523$	4.77002	+	8.26192i	0.208579	+	0.361269i	−0.742688	+	0.669637i	$0.766450\pi$
$524$	−15.2105			−0.664474
$525$	−2.82995	+	1.59540i	−0.123509	+	0.0696288i
$526$	1.33979			0.0584177
$527$	−12.0309	−	20.8382i	−0.524075	−	0.907725i
$528$	−0.142566	+	0.246932i	−0.00620439	+	0.0107463i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	10.3287	+	17.8898i	0.448649	+	0.777083i
$531$	−8.30618			−0.360457
$532$	−0.203204	+	19.8098i	−0.00881000	+	0.858863i
$533$	−21.4830			−0.930530
$534$	−1.42725	−	2.47207i	−0.0617631	−	0.106977i
$535$	7.13480	−	12.3578i	0.308464	−	0.534276i
$536$	6.28542	−	10.8867i	0.271489	−	0.470233i
$537$	5.73482	+	9.93299i	0.247476	+	0.428640i
$538$	−3.21323			−0.138532
$539$	−14.4332	+	23.8552i	−0.621683	+	1.02752i
$540$	−3.12450			−0.134457
$541$	−16.5874	−	28.7302i	−0.713147	−	1.23521i	−0.963670	−	0.267097i	$-0.913936\pi$
$541$	−16.5874	−	28.7302i	−0.713147	−	1.23521i	0.250522	−	0.968111i	$-0.419398\pi$
$542$	−1.73840	+	3.01100i	−0.0746709	+	0.129334i
$543$	−7.91963	+	13.7172i	−0.339864	+	0.588662i
$544$	19.8695	+	34.4149i	0.851897	+	1.47553i
$545$	−15.6119			−0.668742
$546$	0.0658815	−	6.42261i	0.00281947	−	0.274863i
$547$	17.2100			0.735848			0.367924	−	0.929856i	$-0.380069\pi$
$547$	17.2100			0.735848			0.367924	+	0.929856i	$0.380069\pi$
$548$	−0.518732	−	0.898470i	−0.0221591	−	0.0383807i
$549$	1.85641	−	3.21539i	0.0792296	−	0.137230i
$550$	2.11492	−	3.66315i	0.0901805	−	0.156197i
$551$	−12.1465	−	21.0383i	−0.517458	−	0.896264i
$552$	2.81254			0.119710
$553$	16.4167	−	9.25499i	0.698110	−	0.393562i
$554$	−9.85311			−0.418619
$555$	1.84289	+	3.19197i	0.0782262	+	0.135492i
$556$	0.341863	−	0.592124i	0.0144982	−	0.0251117i
$557$	−8.94619	+	15.4953i	−0.379062	+	0.656555i	−0.990926	−	0.134408i	$-0.957087\pi$
$557$	−8.94619	+	15.4953i	−0.379062	+	0.656555i	0.611864	+	0.790963i	$0.290420\pi$
$558$	1.48905	+	2.57912i	0.0630367	+	0.109183i
$559$	19.8733			0.840550
$560$	0.406886	+	0.240514i	0.0171941	+	0.0101636i
$561$	−27.8327			−1.17510
$562$	12.0866	+	20.9345i	0.509841	+	0.883070i
$563$	−8.20800	+	14.2167i	−0.345926	+	0.599161i	−0.985522	−	0.169550i	$-0.945768\pi$
$563$	−8.20800	+	14.2167i	−0.345926	+	0.599161i	0.639596	+	0.768712i	$0.279102\pi$
$564$	1.90639	−	3.30197i	0.0802736	−	0.139038i
$565$	−4.73590	−	8.20282i	−0.199241	−	0.345095i
$566$	−25.9245			−1.08969
$567$	−2.27760	−	1.34631i	−0.0956501	−	0.0565396i
$568$	26.6918			1.11996
$569$	−2.47067	−	4.27933i	−0.103576	−	0.179399i	0.809580	−	0.587010i	$-0.199695\pi$
$569$	−2.47067	−	4.27933i	−0.103576	−	0.179399i	−0.913155	+	0.407611i	$0.866362\pi$
$570$	6.45400	−	11.1787i	0.270328	−	0.468222i
$571$	21.4309	−	37.1194i	0.896855	−	1.55340i	0.0653629	−	0.997862i	$-0.479179\pi$
$571$	21.4309	−	37.1194i	0.896855	−	1.55340i	0.831492	−	0.555537i	$-0.187487\pi$
$572$	−6.99909	−	12.1228i	−0.292647	−	0.506879i
$573$	−21.7951			−0.910502
$574$	−15.2553	+	8.60023i	−0.636744	+	0.358967i
$575$	1.22789			0.0512063
$576$	−2.38764	−	4.13551i	−0.0994849	−	0.172313i
$577$	−6.90651	+	11.9624i	−0.287522	+	0.498002i	−0.973218	−	0.229886i	$-0.926165\pi$
$577$	−6.90651	+	11.9624i	−0.287522	+	0.498002i	0.685696	+	0.727888i	$0.259498\pi$
$578$	−13.7633	+	23.8388i	−0.572479	+	0.991563i
$579$	8.01667	+	13.8853i	0.333162	+	0.577053i
$580$	−12.6917			−0.526993
$581$	−0.0286892	+	2.79684i	−0.00119023	+	0.116032i
$582$	13.7783			0.571128
$583$	19.0612	+	33.0149i	0.789434	+	1.36734i
$584$	18.1438	−	31.4261i	0.750798	−	1.30042i
$585$	3.50252	−	6.06654i	0.144811	−	0.250821i
$586$	2.10743	+	3.65018i	0.0870572	+	0.150787i
$587$	19.9885			0.825012			0.412506	−	0.910955i	$-0.364654\pi$
$587$	19.9885			0.825012			0.412506	+	0.910955i	$0.364654\pi$
$588$	4.22545	+	7.67825i	0.174254	+	0.316646i
$589$	20.5939			0.848556
$590$	−8.96370	−	15.5256i	−0.369029	−	0.639178i
$591$	5.33264	−	9.23640i	0.219355	−	0.379935i
$592$	0.0528632	−	0.0915617i	0.00217266	−	0.00376316i
$593$	1.36034	+	2.35618i	0.0558625	+	0.0967566i	0.892604	−	0.450841i	$-0.148876\pi$
$593$	1.36034	+	2.35618i	0.0558625	+	0.0967566i	−0.836742	+	0.547598i	$0.815542\pi$
$594$	3.44482			0.141343
$595$	−0.473241	+	46.1350i	−0.0194010	+	1.89135i
$596$	23.2233			0.951262
$597$	−1.82952	−	3.16883i	−0.0748774	−	0.129691i
$598$	−1.21382	+	2.10240i	−0.0496369	+	0.0859737i
$599$	−8.73492	+	15.1293i	−0.356899	+	0.618168i	−0.987441	−	0.157988i	$-0.949499\pi$
$599$	−8.73492	+	15.1293i	−0.356899	+	0.618168i	0.630542	+	0.776155i	$0.282833\pi$
$600$	−1.72674	−	2.99080i	−0.0704937	−	0.122099i
$601$	27.6015			1.12589			0.562944	−	0.826495i	$-0.309669\pi$
$601$	27.6015			1.12589			0.562944	+	0.826495i	$0.309669\pi$
$602$	14.1122	−	7.95583i	0.575172	−	0.324255i
$603$	4.46957			0.182015
$604$	−3.61364	−	6.25901i	−0.147037	−	0.254676i
$605$	6.07056	−	10.5145i	0.246803	−	0.427476i
$606$	3.01156	−	5.21618i	0.122336	−	0.211893i
$607$	6.45863	+	11.1867i	0.262148	+	0.454053i	0.966812	−	0.255487i	$-0.0822359\pi$
$607$	6.45863	+	11.1867i	0.262148	+	0.454053i	−0.704665	+	0.709540i	$0.748903\pi$
$608$	−34.0115			−1.37935
$609$	−9.25156	−	5.46868i	−0.374892	−	0.221602i
$610$	8.01345			0.324455
$611$	4.27407	+	7.40291i	0.172910	+	0.299490i
$612$	−4.37436	+	7.57662i	−0.176823	+	0.306267i
$613$	19.4271	−	33.6486i	0.784651	−	1.35906i	−0.144556	−	0.989497i	$-0.546175\pi$
$613$	19.4271	−	33.6486i	0.784651	−	1.35906i	0.929207	−	0.369559i	$-0.120491\pi$
$614$	12.0675	+	20.9016i	0.487007	+	0.843520i
$615$	−19.0996			−0.770170
$616$	−25.5151	−	15.0822i	−1.02803	−	0.607678i
$617$	−25.3417			−1.02022			−0.510108	−	0.860110i	$-0.670395\pi$
$617$	−25.3417			−1.02022			−0.510108	+	0.860110i	$0.670395\pi$
$618$	2.59669	+	4.49760i	0.104454	+	0.180920i
$619$	−17.7926	+	30.8177i	−0.715145	+	1.23867i	0.247758	+	0.968822i	$0.420306\pi$
$619$	−17.7926	+	30.8177i	−0.715145	+	1.23867i	−0.962904	+	0.269846i	$0.913027\pi$
$620$	5.37955	−	9.31765i	0.216048	−	0.374206i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	23.3586			0.936596
$623$	−7.60686	+	4.28840i	−0.304762	+	0.171811i
$624$	−0.200939			−0.00804401
$625$	14.8159	+	25.6618i	0.592634	+	1.02647i
$626$	−1.82227	+	3.15626i	−0.0728324	+	0.126149i
$627$	11.9106	−	20.6298i	0.475664	−	0.823874i
$628$	8.84486	+	15.3198i	0.352948	+	0.611325i
$629$	10.3203			0.411498
$630$	0.0585725	−	5.71008i	0.00233358	−	0.227495i
$631$	−12.5559			−0.499842			−0.249921	−	0.968266i	$-0.580405\pi$
$631$	−12.5559			−0.499842			−0.249921	+	0.968266i	$0.580405\pi$
$632$	10.0169	+	17.3498i	0.398451	+	0.690138i
$633$	−14.0929	+	24.4096i	−0.560141	+	0.970193i
$634$	3.45855	−	5.99039i	0.137357	−	0.237909i
$635$	26.0562	+	45.1306i	1.03401	+	1.79095i
$636$	11.9831			0.475161
$637$	−19.6448	−	0.403064i	−0.778354	−	0.0159700i
$638$	13.9928			0.553980
$639$	4.74514	+	8.21882i	0.187715	+	0.325131i
$640$	−9.03901	+	15.6560i	−0.357298	+	0.618859i
$641$	22.0244	−	38.1474i	0.869912	−	1.50673i	0.00782674	−	0.999969i	$-0.497509\pi$
$641$	22.0244	−	38.1474i	0.869912	−	1.50673i	0.862086	−	0.506763i	$-0.169158\pi$
$642$	2.47262	+	4.28270i	0.0975865	+	0.169025i
$643$	27.1797			1.07186			0.535931	−	0.844262i	$-0.319961\pi$
$643$	27.1797			1.07186			0.535931	+	0.844262i	$0.319961\pi$
$644$	0.0339773	−	3.31235i	0.00133889	−	0.130525i
$645$	17.6685			0.695696
$646$	−18.0714	−	31.3006i	−0.711011	−	1.23151i
$647$	−16.8824	+	29.2412i	−0.663716	+	1.14959i	0.315916	+	0.948787i	$0.397688\pi$
$647$	−16.8824	+	29.2412i	−0.663716	+	1.14959i	−0.979632	+	0.200803i	$0.935645\pi$
$648$	1.40627	−	2.43573i	0.0552435	−	0.0956845i
$649$	−16.5422	−	28.6519i	−0.649336	−	1.12468i
$650$	2.98087			0.116919
$651$	7.93627	−	4.47410i	0.311047	−	0.175354i
$652$	20.9708			0.821281
$653$	−15.9665	−	27.6548i	−0.624817	−	1.08221i	−0.988576	−	0.150722i	$-0.951840\pi$
$653$	−15.9665	−	27.6548i	−0.624817	−	1.08221i	0.363759	−	0.931493i	$-0.381493\pi$
$654$	2.70522	−	4.68558i	0.105782	−	0.183220i
$655$	15.1591	−	26.2563i	0.592315	−	1.02592i
$656$	0.273936	+	0.474471i	0.0106954	+	0.0185250i
$657$	12.9021			0.503359
$658$	5.99866	+	3.54586i	0.233852	+	0.138232i
$659$	47.4986			1.85028			0.925142	−	0.379622i	$-0.123946\pi$
$659$	47.4986			1.85028			0.925142	+	0.379622i	$0.123946\pi$
$660$	−6.22260	−	10.7779i	−0.242214	−	0.419528i
$661$	14.7146	−	25.4865i	0.572332	−	0.991308i	−0.423994	−	0.905665i	$-0.639372\pi$
$661$	14.7146	−	25.4865i	0.572332	−	0.991308i	0.996326	−	0.0856431i	$-0.0272945\pi$
$662$	−10.4160	+	18.0410i	−0.404829	+	0.701184i
$663$	−9.80718	−	16.9865i	−0.380879	−	0.659702i
$664$	−2.97330			−0.115387
$665$	−33.9931	−	20.0936i	−1.31820	−	0.779197i
$666$	−1.27733			−0.0494956
$667$	2.03099	+	3.51778i	0.0786403	+	0.136209i
$668$	11.1754	−	19.3563i	0.432389	−	0.748920i
$669$	12.1140	−	20.9821i	0.468355	−	0.811215i
$670$	4.82338	+	8.35435i	0.186344	+	0.322757i
$671$	14.7885			0.570904
$672$	−13.1070	+	7.38913i	−0.505614	+	0.285042i
$673$	−21.8311			−0.841528			−0.420764	−	0.907170i	$-0.638238\pi$
$673$	−21.8311			−0.841528			−0.420764	+	0.907170i	$0.638238\pi$
$674$	2.98938	+	5.17776i	0.115147	+	0.199440i
$675$	0.613943	−	1.06338i	0.0236307	−	0.0409295i
$676$	−3.20569	+	5.55242i	−0.123296	+	0.213554i
$677$	−15.9797	−	27.6776i	−0.614148	−	1.06374i	−0.990533	−	0.137272i	$-0.956167\pi$
$677$	−15.9797	−	27.6776i	−0.614148	−	1.06374i	0.376385	−	0.926463i	$-0.377167\pi$
$678$	3.28252			0.126065
$679$	0.432342	−	42.1479i	0.0165918	−	1.61749i
$680$	−49.0459			−1.88083
$681$	−4.01827	−	6.95985i	−0.153981	−	0.266702i
$682$	−5.93105	+	10.2729i	−0.227112	+	0.393369i
$683$	−2.90119	+	5.02502i	−0.111011	+	0.192277i	−0.916178	−	0.400771i	$-0.868742\pi$
$683$	−2.90119	+	5.02502i	−0.111011	+	0.192277i	0.805167	+	0.593048i	$0.202076\pi$
$684$	−3.74390	−	6.48462i	−0.143151	−	0.247946i
$685$	2.06791			0.0790109
$686$	−14.1113	+	7.57813i	−0.538773	+	0.289334i
$687$	−13.7790			−0.525702
$688$	−0.253410	−	0.438919i	−0.00966117	−	0.0167336i
$689$	−13.4329	+	23.2664i	−0.511752	+	0.886380i
$690$	−1.07916	+	1.86916i	−0.0410829	+	0.0711577i
$691$	−25.2129	−	43.6701i	−0.959145	−	1.66129i	−0.724585	−	0.689185i	$-0.757969\pi$
$691$	−25.2129	−	43.6701i	−0.959145	−	1.66129i	−0.234559	−	0.972102i	$-0.575365\pi$
$692$	−3.32235			−0.126297
$693$	0.108093	−	10.5377i	0.00410613	−	0.400295i
$694$	10.5406			0.400115
$695$	0.681415	+	1.18025i	0.0258475	+	0.0447693i
$696$	5.71224	−	9.89389i	0.216522	−	0.375027i
$697$	−26.7398	+	46.3147i	−1.01284	+	1.75429i
$698$	−11.7059	−	20.2752i	−0.443076	−	0.767430i
$699$	1.83601			0.0694443
$700$	−3.54315	+	1.99746i	−0.133918	+	0.0754971i
$701$	28.8283			1.08883			0.544414	−	0.838817i	$-0.316752\pi$
$701$	28.8283			1.08883			0.544414	+	0.838817i	$0.316752\pi$
$702$	1.21382	+	2.10240i	0.0458128	+	0.0793501i
$703$	−4.41643	+	7.64948i	−0.166569	+	0.288506i
$704$	9.51019	−	16.4721i	0.358429	−	0.620817i
$705$	3.79990	+	6.58161i	0.143112	+	0.247878i
$706$	−24.7153			−0.930171
$707$	−15.8618	−	9.37608i	−0.596546	−	0.352624i
$708$	−10.3995			−0.390837
$709$	−16.2278	−	28.1074i	−0.609447	−	1.05559i	−0.991332	−	0.131384i	$-0.958058\pi$
$709$	−16.2278	−	28.1074i	−0.609447	−	1.05559i	0.381884	−	0.924210i	$-0.375275\pi$
$710$	−10.2415	+	17.7388i	−0.384358	+	0.665727i
$711$	−3.56152	+	6.16873i	−0.133567	+	0.231346i
$712$	−4.64144	−	8.03921i	−0.173945	−	0.301282i
$713$	−3.44346			−0.128959
$714$	−13.7644	−	8.13625i	−0.515119	−	0.304491i
$715$	27.9017			1.04347
$716$	7.18009	+	12.4363i	0.268333	+	0.464766i
$717$	−2.21103	+	3.82962i	−0.0825725	+	0.143020i
$718$	8.41626	−	14.5774i	0.314092	−	0.544023i
$719$	8.01756	+	13.8868i	0.299004	+	0.517891i	0.975908	−	0.218180i	$-0.0700121\pi$
$719$	8.01756	+	13.8868i	0.299004	+	0.517891i	−0.676904	+	0.736071i	$0.736679\pi$
$720$	−0.178647			−0.00665777
$721$	13.8397	−	7.80216i	0.515416	−	0.290568i
$722$	14.5014			0.539685
$723$	−14.2294	−	24.6461i	−0.529198	−	0.916598i
$724$	−9.91552	+	17.1742i	−0.368508	+	0.638274i
$725$	2.49382	−	4.31943i	0.0926183	−	0.160420i
$726$	2.10380	+	3.64389i	0.0780793	+	0.135237i
$727$	40.6150			1.50633			0.753164	−	0.657833i	$-0.228527\pi$
$727$	40.6150			1.50633			0.753164	+	0.657833i	$0.228527\pi$
$728$	0.214248	−	20.8865i	0.00794055	−	0.774104i
$729$	1.00000			0.0370370
$730$	13.9234	+	24.1161i	0.515330	+	0.892577i
$731$	24.7362	−	42.8444i	0.914902	−	1.58466i
$732$	2.32426	−	4.02573i	0.0859070	−	0.148795i
$733$	1.20729	+	2.09108i	0.0445922	+	0.0772359i	0.887460	−	0.460885i	$-0.152468\pi$
$733$	1.20729	+	2.09108i	0.0445922	+	0.0772359i	−0.842868	+	0.538121i	$0.819134\pi$
$734$	4.16724			0.153816
$735$	−17.4653	−	0.358348i	−0.644219	−	0.0132178i
$736$	5.68699			0.209625
$737$	8.90137	+	15.4176i	0.327886	+	0.567916i
$738$	3.30955	−	5.73232i	0.121826	−	0.211009i
$739$	−1.39817	+	2.42171i	−0.0514327	+	0.0890840i	−0.890596	−	0.454796i	$-0.849712\pi$
$739$	−1.39817	+	2.42171i	−0.0514327	+	0.0890840i	0.839163	+	0.543880i	$0.183045\pi$
$740$	2.30733	+	3.99641i	0.0848191	+	0.146911i
$741$	16.7874			0.616700
$742$	−0.224638	+	21.8993i	−0.00824671	+	0.803950i
$743$	3.56515			0.130793			0.0653964	−	0.997859i	$-0.479169\pi$
$743$	3.56515			0.130793			0.0653964	+	0.997859i	$0.479169\pi$
$744$	4.84243	+	8.38734i	0.177532	+	0.307495i
$745$	−23.1448	+	40.0879i	−0.847959	+	1.46871i
$746$	10.6530	−	18.4516i	0.390034	−	0.675559i
$747$	−0.528580	−	0.915528i	−0.0193397	−	0.0334974i
$748$	−34.8470			−1.27413
$749$	13.1784	−	7.42938i	0.481529	−	0.271464i
$750$	−8.14143			−0.297283
$751$	1.89657	+	3.28495i	0.0692067	+	0.119870i	0.898552	−	0.438866i	$-0.144620\pi$
$751$	1.89657	+	3.28495i	0.0692067	+	0.119870i	−0.829346	+	0.558736i	$0.811287\pi$
$752$	0.109000	−	0.188794i	0.00397482	−	0.00688459i
$753$	−13.3532	+	23.1284i	−0.486617	+	0.842846i
$754$	4.93053	+	8.53993i	0.179559	+	0.311006i
$755$	14.4057			0.524278
$756$	−2.85159	−	1.68560i	−0.103711	−	0.0613048i
$757$	−6.45659			−0.234669			−0.117334	−	0.993092i	$-0.537435\pi$
$757$	−6.45659			−0.234669			−0.117334	+	0.993092i	$0.537435\pi$
$758$	−13.7505	−	23.8166i	−0.499441	−	0.865058i
$759$	−1.99155	+	3.44946i	−0.0722886	+	0.125208i
$760$	20.9885	−	36.3532i	0.761334	−	1.31867i
$761$	11.2002	+	19.3993i	0.406007	+	0.703225i	0.994438	−	0.105322i	$-0.0335875\pi$
$761$	11.2002	+	19.3993i	0.406007	+	0.703225i	−0.588431	+	0.808547i	$0.700254\pi$
$762$	−18.0599			−0.654241
$763$	−14.2483	−	8.42231i	−0.515824	−	0.304908i
$764$	−27.2878			−0.987239
$765$	−8.71915	−	15.1020i	−0.315242	−	0.546015i
$766$	9.67146	−	16.7515i	0.349444	−	0.605255i
$767$	11.6577	−	20.1917i	0.420934	−	0.729078i
$768$	−7.90781	−	13.6967i	−0.285349	−	0.494238i
$769$	53.5732			1.93190			0.965950	−	0.258731i	$-0.0833042\pi$
$769$	53.5732			1.93190			0.965950	+	0.258731i	$0.0833042\pi$
$770$	19.8134	−	11.1699i	0.714024	−	0.402534i
$771$	−4.36432			−0.157177
$772$	10.0370	+	17.3846i	0.361240	+	0.625687i
$773$	22.2622	−	38.5592i	0.800715	−	1.38688i	−0.118431	−	0.992962i	$-0.537786\pi$
$773$	22.2622	−	38.5592i	0.800715	−	1.38688i	0.919146	−	0.393917i	$-0.128880\pi$
$774$	−3.06157	+	5.30280i	−0.110046	+	0.190605i
$775$	2.11409	+	3.66170i	0.0759402	+	0.131532i
$776$	44.8072			1.60849
$777$	−0.0400808	+	3.90737i	−0.00143789	+	0.140176i
$778$	17.2191			0.617333
$779$	−22.8858	−	39.6395i	−0.819971	−	1.42023i
$780$	4.38522	−	7.59542i	0.157016	−	0.271960i
$781$	−18.9003	+	32.7364i	−0.676308	+	1.17140i
$782$	3.02169	+	5.23372i	0.108055	+	0.187157i
$783$	4.06198			0.145163
$784$	0.241594	+	0.439012i	0.00862837	+	0.0156790i
$785$	−35.2599			−1.25848
$786$	5.25349	+	9.09932i	0.187386	+	0.324562i
$787$	7.63566	−	13.2253i	0.272182	−	0.471433i	−0.697238	−	0.716839i	$-0.745588\pi$
$787$	7.63566	−	13.2253i	0.272182	−	0.471433i	0.969420	+	0.245407i	$0.0789215\pi$
$788$	6.67656	−	11.5641i	0.237843	−	0.411956i
$789$	0.774571	+	1.34160i	0.0275755	+	0.0477621i
$790$	−15.3738			−0.546975
$791$	0.103001	−	10.0413i	0.00366228	−	0.357026i
$792$	11.2026			0.398068
$793$	5.21091	+	9.02556i	0.185045	+	0.320507i
$794$	−11.7217	+	20.3026i	−0.415988	+	0.720513i
$795$	−11.9426	+	20.6852i	−0.423561	+	0.733629i
$796$	−2.29060	−	3.96743i	−0.0811880	−	0.140622i
$797$	38.5369			1.36505			0.682524	−	0.730863i	$-0.260882\pi$
$797$	38.5369			1.36505			0.682524	+	0.730863i	$0.260882\pi$
$798$	11.9209	−	6.72047i	0.421996	−	0.237902i
$799$	21.2797			0.752822
$800$	−3.49148	−	6.04743i	−0.123443	−	0.213809i
$801$	1.65027	−	2.85835i	0.0583093	−	0.100995i
$802$	14.7797	−	25.5992i	0.521889	−	0.903938i
$803$	25.6952	+	44.5054i	0.906763	+	1.57056i
$804$	5.59599			0.197355
$805$	5.68391	+	3.35981i	0.200332	+	0.118418i
$806$	−8.35951			−0.294451
$807$	−1.85766	−	3.21756i	−0.0653928	−	0.113264i
$808$	9.79366	−	16.9631i	0.344540	−	0.596761i
$809$	18.1759	−	31.4816i	0.639031	−	1.10683i	−0.346615	−	0.938007i	$-0.612669\pi$
$809$	18.1759	−	31.4816i	0.639031	−	1.10683i	0.985646	−	0.168826i	$-0.0539976\pi$
$810$	1.07916	+	1.86916i	0.0379178	+	0.0656756i
$811$	−21.9469			−0.770661			−0.385330	−	0.922779i	$-0.625912\pi$
$811$	−21.9469			−0.770661			−0.385330	+	0.922779i	$0.625912\pi$
$812$	−11.5831	−	6.84688i	−0.406488	−	0.240279i
$813$	−4.02009			−0.140991
$814$	−2.54387	−	4.40611i	−0.0891626	−	0.154434i
$815$	−20.9000	+	36.1998i	−0.732094	+	1.26802i
$816$	−0.250109	+	0.433201i	−0.00875556	+	0.0151651i
$817$	21.1710	+	36.6693i	0.740681	+	1.28290i
$818$	13.1006			0.458053
$819$	6.46936	−	3.64713i	0.226058	−	0.127441i
$820$	−23.9130			−0.835080
$821$	6.53980	+	11.3273i	0.228241	+	0.395325i	0.957287	−	0.289140i	$-0.0933693\pi$
$821$	6.53980	+	11.3273i	0.228241	+	0.395325i	−0.729046	+	0.684465i	$0.760036\pi$
$822$	−0.358325	+	0.620638i	−0.0124980	+	0.0216472i
$823$	−15.8026	+	27.3710i	−0.550845	+	0.954091i	0.447369	+	0.894349i	$0.352361\pi$
$823$	−15.8026	+	27.3710i	−0.550845	+	0.954091i	−0.998214	+	0.0597419i	$0.980972\pi$
$824$	8.44448	+	14.6263i	0.294177	+	0.509530i
$825$	4.89079			0.170275
$826$	0.194951	−	19.0052i	0.00678320	−	0.661276i
$827$	21.5412			0.749060			0.374530	−	0.927215i	$-0.377804\pi$
$827$	21.5412			0.749060			0.374530	+	0.927215i	$0.377804\pi$
$828$	0.626009	+	1.08428i	0.0217553	+	0.0376813i
$829$	−16.6569	+	28.8507i	−0.578519	+	1.00203i	0.417130	+	0.908847i	$0.363036\pi$
$829$	−16.6569	+	28.8507i	−0.578519	+	1.00203i	−0.995649	+	0.0931782i	$0.970297\pi$
$830$	1.14084	−	1.97600i	0.0395993	−	0.0685880i
$831$	−5.69636	−	9.86639i	−0.197605	−	0.342261i
$832$	13.4041			0.464704
$833$	−25.3208	+	41.8501i	−0.877312	+	1.45002i
$834$	−0.472299			−0.0163544
$835$	22.2752	+	38.5819i	0.770867	+	1.33518i
$836$	14.9123	−	25.8289i	0.515753	−	0.893310i
$837$	−1.72173	+	2.98212i	−0.0595117	+	0.103077i
$838$	−6.07579	−	10.5236i	−0.209885	−	0.363531i
$839$	4.75994			0.164331			0.0821656	−	0.996619i	$-0.473816\pi$
$839$	4.75994			0.164331			0.0821656	+	0.996619i	$0.473816\pi$
$840$	0.190479	−	18.5693i	0.00657214	−	0.640701i
$841$	−12.5003			−0.431045
$842$	11.2827	+	19.5422i	0.388827	+	0.673468i
$843$	−13.9752	+	24.2057i	−0.481330	+	0.833689i
$844$	−17.6445	+	30.5612i	−0.607350	+	1.05196i
$845$	−6.38971	−	11.0673i	−0.219813	−	0.380727i
$846$	−2.63377			−0.0905507
$847$	11.2127	−	6.32120i	0.385273	−	0.217199i
$848$	0.685147			0.0235281
$849$	−14.9877	−	25.9594i	−0.514376	−	0.890925i
$850$	3.71029	−	6.42640i	0.127262	−	0.220424i
$851$	0.738463	−	1.27905i	0.0253142	−	0.0438454i
$852$	5.94100	+	10.2901i	0.203535	+	0.352533i
$853$	34.8330			1.19266			0.596330	−	0.802740i	$-0.296625\pi$
$853$	34.8330			1.19266			0.596330	+	0.802740i	$0.296625\pi$
$854$	7.31351	+	4.32308i	0.250263	+	0.147933i
$855$	14.9250			0.510423
$856$	8.04100	+	13.9274i	0.274836	+	0.476030i
$857$	−9.92880	+	17.1972i	−0.339161	+	0.587445i	−0.984275	−	0.176642i	$-0.943477\pi$
$857$	−9.92880	+	17.1972i	−0.339161	+	0.587445i	0.645114	+	0.764086i	$0.276810\pi$
$858$	−4.83478	+	8.37408i	−0.165057	+	0.285886i
$859$	−16.8998	−	29.2714i	−0.576615	−	0.998727i	−0.995864	−	0.0908555i	$-0.971040\pi$
$859$	−16.8998	−	29.2714i	−0.576615	−	0.998727i	0.419249	−	0.907871i	$-0.362293\pi$
$860$	22.1213			0.754329
$861$	−17.4314	−	10.3038i	−0.594059	−	0.351153i
$862$	2.67627			0.0911541
$863$	−17.8000	−	30.8306i	−0.605921	−	1.04949i	−0.991905	−	0.126980i	$-0.959472\pi$
$863$	−17.8000	−	30.8306i	−0.605921	−	1.04949i	0.385985	−	0.922505i	$-0.373862\pi$
$864$	2.84349	−	4.92508i	0.0967376	−	0.167555i
$865$	3.31112	−	5.73502i	0.112581	−	0.194997i
$866$	−8.20907	−	14.2185i	−0.278955	−	0.483165i
$867$	−31.8279			−1.08093
$868$	9.93635	−	5.60165i	0.337262	−	0.190133i
$869$	−28.3718			−0.962446
$870$	4.38353	+	7.59249i	0.148616	+	0.257410i
$871$	−6.27301	+	10.8652i	−0.212553	+	0.368152i
$872$	8.79742	−	15.2376i	0.297918	−	0.516009i
$873$	7.96562	+	13.7969i	0.269595	+	0.466953i
$874$	−5.17236			−0.174958
$875$	−0.255466	+	24.9047i	−0.00863633	+	0.841933i
$876$	16.1537			0.545782
$877$	−7.44012	−	12.8867i	−0.251235	−	0.435152i	0.712631	−	0.701539i	$-0.247503\pi$
$877$	−7.44012	−	12.8867i	−0.251235	−	0.435152i	−0.963866	+	0.266387i	$0.914170\pi$
$878$	5.17671	−	8.96632i	0.174705	−	0.302599i
$879$	−2.43673	+	4.22054i	−0.0821889	+	0.142355i
$880$	−0.355784	−	0.616236i	−0.0119935	−	0.0207733i
$881$	−25.2288			−0.849980			−0.424990	−	0.905198i	$-0.639722\pi$
$881$	−25.2288			−0.849980			−0.424990	+	0.905198i	$0.639722\pi$
$882$	3.13392	−	5.17973i	0.105525	−	0.174411i
$883$	−5.13080			−0.172665			−0.0863325	−	0.996266i	$-0.527515\pi$
$883$	−5.13080			−0.172665			−0.0863325	+	0.996266i	$0.527515\pi$
$884$	−12.2788	−	21.2675i	−0.412980	−	0.715302i
$885$	10.3643	−	17.9516i	0.348393	−	0.603435i
$886$	−8.42458	+	14.5918i	−0.283029	+	0.490221i
$887$	2.13610	+	3.69983i	0.0717231	+	0.124228i	0.899657	−	0.436598i	$-0.143817\pi$
$887$	2.13610	+	3.69983i	0.0717231	+	0.124228i	−0.827933	+	0.560826i	$0.810484\pi$
$888$	−4.15391			−0.139396
$889$	−0.566693	+	55.2454i	−0.0190063	+	1.85287i
$890$	7.12361			0.238784
$891$	1.99155	+	3.44946i	0.0667194	+	0.115561i
$892$	15.1670	−	26.2700i	0.507828	−	0.879584i
$893$	−9.10635	+	15.7727i	−0.304733	+	0.527812i
$894$	−8.02100	−	13.8928i	−0.268262	−	0.464644i
$895$	−28.6233			−0.956772
$896$	−16.6956	+	9.41220i	−0.557761	+	0.314440i
$897$	−2.80699			−0.0937225
$898$	11.2154	+	19.4256i	0.374263	+	0.648242i
$899$	−6.99363	+	12.1133i	−0.233251	+	0.404002i
$900$	0.768667	−	1.33137i	0.0256222	−	0.0443790i
$901$	33.4398	+	57.9194i	1.11404	+	1.92957i
$902$	26.3646			0.877844
$903$	16.1252	+	9.53177i	0.536614	+	0.317198i
$904$	10.6748			0.355039
$905$	−19.7640	−	34.2323i	−0.656978	−	1.13792i
$906$	−2.49620	+	4.32355i	−0.0829308	+	0.143640i
$907$	14.6117	−	25.3082i	0.485173	−	0.840344i	−0.514682	−	0.857381i	$-0.672090\pi$
$907$	14.6117	−	25.3082i	0.485173	−	0.840344i	0.999855	+	0.0170370i	$0.00542330\pi$
$908$	−5.03095	−	8.71386i	−0.166958	−	0.289180i
$909$	6.96429			0.230991
$910$	13.7985	+	8.15644i	0.457417	+	0.270383i
$911$	−48.3422			−1.60165			−0.800824	−	0.598900i	$-0.795605\pi$
$911$	−48.3422			−1.60165			−0.800824	+	0.598900i	$0.795605\pi$
$912$	−0.214061	−	0.370765i	−0.00708828	−	0.0122773i
$913$	2.10539	−	3.64664i	0.0696781	−	0.120686i
$914$	−1.99494	+	3.45533i	−0.0659866	+	0.114292i
$915$	4.63280	+	8.02425i	0.153156	+	0.265273i
$916$	−17.2516			−0.570008
$917$	27.9997	−	15.7850i	0.924633	−	0.521265i
$918$	6.04338			0.199461
$919$	−15.3964	−	26.6674i	−0.507881	−	0.879676i	−0.999958	−	0.00912440i	$-0.997096\pi$
$919$	−15.3964	−	26.6674i	−0.507881	−	0.879676i	0.492077	−	0.870552i	$-0.336238\pi$
$920$	−3.50945	+	6.07854i	−0.115703	+	0.200404i
$921$	−13.9532	+	24.1676i	−0.459773	+	0.796351i
$922$	−5.97534	−	10.3496i	−0.196787	−	0.340846i
$923$	−26.6391			−0.876835
$924$	0.135335	−	13.1934i	0.00445219	−	0.434032i
$925$	−1.81349			−0.0596273
$926$	14.7584	+	25.5624i	0.484992	+	0.840032i
$927$	−3.00244	+	5.20038i	−0.0986130	+	0.170803i
$928$	11.5502	−	20.0056i	0.379155	−	0.656715i
$929$	12.3286	+	21.3537i	0.404487	+	0.700593i	0.994262	−	0.106976i	$-0.0341166\pi$
$929$	12.3286	+	21.3537i	0.404487	+	0.700593i	−0.589774	+	0.807568i	$0.700783\pi$
$930$	−7.43209			−0.243708
$931$	−20.1839	−	36.6771i	−0.661500	−	1.20204i
$932$	2.29872			0.0752970
$933$	13.5043	+	23.3901i	0.442111	+	0.765758i
$934$	12.0957	−	20.9504i	0.395785	−	0.685519i
$935$	34.7292	−	60.1528i	1.13577	−	1.96721i
$936$	3.94738	+	6.83706i	0.129024	+	0.223476i
$937$	35.2046			1.15008			0.575042	−	0.818124i	$-0.304986\pi$
$937$	35.2046			1.15008			0.575042	+	0.818124i	$0.304986\pi$
$938$	−0.104903	+	10.2268i	−0.00342522	+	0.333915i
$939$	−4.21402			−0.137519
$940$	4.75754	+	8.24030i	0.155174	+	0.268769i
$941$	11.0415	−	19.1244i	0.359942	−	0.623438i	−0.628009	−	0.778206i	$-0.716130\pi$
$941$	11.0415	−	19.1244i	0.359942	−	0.623438i	0.987951	+	0.154768i	$0.0494630\pi$
$942$	6.10979	−	10.5825i	0.199068	−	0.344795i
$943$	3.82670	+	6.62803i	0.124614	+	0.215838i
$944$	−0.594602			−0.0193526
$945$	5.75164	−	3.24251i	0.187101	−	0.105479i
$946$	−24.3891			−0.792958
$947$	−2.92876	−	5.07277i	−0.0951720	−	0.164843i	0.814508	−	0.580152i	$-0.197007\pi$
$947$	−2.92876	−	5.07277i	−0.0951720	−	0.164843i	−0.909680	+	0.415309i	$0.863673\pi$
$948$	−4.45909	+	7.72337i	−0.144824	+	0.250843i
$949$	−18.1080	+	31.3640i	−0.587811	+	1.01812i
$950$	3.17553	+	5.50018i	0.103028	+	0.178449i
$951$	7.99795			0.259351
$952$	−44.7620	−	26.4592i	−1.45075	−	0.857548i
$953$	−48.8701			−1.58306			−0.791530	−	0.611131i	$-0.790715\pi$
$953$	−48.8701			−1.58306			−0.791530	+	0.611131i	$0.790715\pi$
$954$	−4.13880	−	7.16861i	−0.133999	−	0.232092i
$955$	27.1956	−	47.1041i	0.880029	−	1.52425i
$956$	−2.76825	+	4.79475i	−0.0895317	+	0.155073i
$957$	8.08963	+	14.0117i	0.261501	+	0.452932i
$958$	−28.2177			−0.911672
$959$	1.88729	+	1.11560i	0.0609439	+	0.0360244i
$960$	11.9170			0.384621
$961$	9.57129	+	16.5780i	0.308751	+	0.534773i
$962$	1.79273	−	3.10509i	0.0577998	−	0.100112i
$963$	−2.85898	+	4.95191i	−0.0921295	+	0.159573i
$964$	−17.8155	−	30.8574i	−0.573799	−	0.993848i
$965$	−40.0124			−1.28804
$966$	−1.99327	+	1.12372i	−0.0641325	+	0.0361549i
$967$	11.7300			0.377213			0.188606	−	0.982053i	$-0.439603\pi$
$967$	11.7300			0.377213			0.188606	+	0.982053i	$0.439603\pi$
$968$	6.84159	+	11.8500i	0.219897	+	0.380873i
$969$	20.8952	−	36.1916i	0.671251	−	1.16264i
$970$	−17.1924	+	29.7780i	−0.552013	+	0.956115i
$971$	12.1764	+	21.0901i	0.390758	+	0.676813i	0.992550	−	0.121840i	$-0.0388795\pi$
$971$	12.1764	+	21.0901i	0.390758	+	0.676813i	−0.601792	+	0.798653i	$0.705546\pi$
$972$	1.25202			0.0401585
$973$	−0.0148200	+	1.44477i	−0.000475109	+	0.0463171i
$974$	−22.4363			−0.718905
$975$	1.72333	+	2.98489i	0.0551907	+	0.0955930i
$976$	0.132892	−	0.230175i	0.00425377	−	0.00736774i
$977$	−25.4547	+	44.0889i	−0.814368	+	1.41053i	0.0954122	+	0.995438i	$0.469583\pi$
$977$	−25.4547	+	44.0889i	−0.814368	+	1.41053i	−0.909781	+	0.415090i	$0.863750\pi$
$978$	−7.24304	−	12.5453i	−0.231607	−	0.401155i
$979$	13.1463			0.420159
$980$	−21.8669	−	0.448658i	−0.698513	−	0.0143318i
$981$	6.25586			0.199734
$982$	−11.2434	−	19.4741i	−0.358791	−	0.621444i
$983$	16.7979	−	29.0948i	0.535770	−	0.927980i	−0.463356	−	0.886172i	$-0.653355\pi$
$983$	16.7979	−	29.0948i	0.535770	−	0.927980i	0.999126	−	0.0418082i	$-0.0133118\pi$
$984$	10.7627	−	18.6416i	0.343103	−	0.594272i
$985$	13.3080	+	23.0501i	0.424028	+	0.734438i
$986$	24.5481			0.781770
$987$	−0.0826436	+	8.05671i	−0.00263058	+	0.256448i
$988$	21.0181			0.668675
$989$	−3.53997	−	6.13140i	−0.112564	−	0.194967i
$990$	−4.29840	+	7.44505i	−0.136612	+	0.236619i
$991$	−5.21752	+	9.03702i	−0.165740	+	0.287070i	−0.936918	−	0.349550i	$-0.886335\pi$
$991$	−5.21752	+	9.03702i	−0.165740	+	0.287070i	0.771178	+	0.636620i	$0.219668\pi$
$992$	9.79146	+	16.9593i	0.310879	+	0.538458i
$993$	−24.0871			−0.764382
$994$	−18.9167	+	10.6644i	−0.600002	+	0.338253i
$995$	9.13142			0.289485
$996$	−0.661792	−	1.14626i	−0.0209697	−	0.0363205i
$997$	−7.58681	+	13.1407i	−0.240277	+	0.416171i	−0.960793	−	0.277267i	$-0.910572\pi$
$997$	−7.58681	+	13.1407i	−0.240277	+	0.416171i	0.720516	+	0.693438i	$0.243905\pi$
$998$	10.0355	−	17.3820i	0.317667	−	0.550216i
$999$	−0.738463	−	1.27905i	−0.0233639	−	0.0404675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.277.5	✓	20
7.2	even	3	inner	483.2.i.h.415.5	yes	20
7.3	odd	6		3381.2.a.bj.1.6		10
7.4	even	3		3381.2.a.bi.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.5	✓	20	1.1	even	1	trivial
483.2.i.h.415.5	yes	20	7.2	even	3	inner
3381.2.a.bi.1.6		10	7.4	even	3
3381.2.a.bj.1.6		10	7.3	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.432430 - 0.748990i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.626009 - 1.08428i) q^{4} +(1.24779 + 2.16123i) q^{5} -0.864859 q^{6} +(-0.0271380 + 2.64561i) q^{7} -2.81254 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.432430 - 0.748990i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.626009 - 1.08428i) q^{4} +(1.24779 + 2.16123i) q^{5} -0.864859 q^{6} +(-0.0271380 + 2.64561i) q^{7} -2.81254 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.07916 - 1.86916i) q^{10} +(1.99155 - 3.44946i) q^{11} +(-0.626009 - 1.08428i) q^{12} +2.80699 q^{13} +(1.99327 - 1.12372i) q^{14} +2.49557 q^{15} +(-0.0357927 - 0.0619948i) q^{16} +(3.49385 - 6.05152i) q^{17} +(-0.432430 + 0.748990i) q^{18} +(2.99029 + 5.17933i) q^{19} +3.12450 q^{20} +(2.27760 + 1.34631i) q^{21} -3.44482 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-1.40627 + 2.43573i) q^{24} +(-0.613943 + 1.06338i) q^{25} +(-1.21382 - 2.10240i) q^{26} -1.00000 q^{27} +(2.85159 + 1.68560i) q^{28} -4.06198 q^{29} +(-1.07916 - 1.86916i) q^{30} +(1.72173 - 2.98212i) q^{31} +(-2.84349 + 4.92508i) q^{32} +(-1.99155 - 3.44946i) q^{33} -6.04338 q^{34} +(-5.75164 + 3.24251i) q^{35} -1.25202 q^{36} +(0.738463 + 1.27905i) q^{37} +(2.58618 - 4.47939i) q^{38} +(1.40349 - 2.43092i) q^{39} +(-3.50945 - 6.07854i) q^{40} -7.65339 q^{41} +(0.0234706 - 2.28808i) q^{42} +7.07993 q^{43} +(-2.49345 - 4.31879i) q^{44} +(1.24779 - 2.16123i) q^{45} +(-0.432430 + 0.748990i) q^{46} +(1.52265 + 2.63732i) q^{47} -0.0715855 q^{48} +(-6.99853 - 0.143593i) q^{49} +1.06195 q^{50} +(-3.49385 - 6.05152i) q^{51} +(1.75720 - 3.04356i) q^{52} +(-4.78552 + 8.28876i) q^{53} +(0.432430 + 0.748990i) q^{54} +9.94011 q^{55} +(0.0763267 - 7.44089i) q^{56} +5.98058 q^{57} +(1.75652 + 3.04238i) q^{58} +(4.15309 - 7.19336i) q^{59} +(1.56225 - 2.70590i) q^{60} +(1.85641 + 3.21539i) q^{61} -2.97811 q^{62} +(2.30474 - 1.29930i) q^{63} +4.77528 q^{64} +(3.50252 + 6.06654i) q^{65} +(-1.72241 + 2.98330i) q^{66} +(-2.23479 + 3.87076i) q^{67} +(-4.37436 - 7.57662i) q^{68} -1.00000 q^{69} +(4.91579 + 2.90576i) q^{70} -9.49028 q^{71} +(1.40627 + 2.43573i) q^{72} +(-6.45106 + 11.1736i) q^{73} +(0.638666 - 1.10620i) q^{74} +(0.613943 + 1.06338i) q^{75} +7.48779 q^{76} +(9.07190 + 5.36248i) q^{77} -2.42765 q^{78} +(-3.56152 - 6.16873i) q^{79} +(0.0893234 - 0.154713i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.30955 + 5.73232i) q^{82} +1.05716 q^{83} +(2.88557 - 1.62675i) q^{84} +17.4383 q^{85} +(-3.06157 - 5.30280i) q^{86} +(-2.03099 + 3.51778i) q^{87} +(-5.60131 + 9.70175i) q^{88} +(1.65027 + 2.85835i) q^{89} -2.15832 q^{90} +(-0.0761760 + 7.42619i) q^{91} -1.25202 q^{92} +(-1.72173 - 2.98212i) q^{93} +(1.31688 - 2.28091i) q^{94} +(-7.46248 + 12.9254i) q^{95} +(2.84349 + 4.92508i) q^{96} -15.9312 q^{97} +(2.91882 + 5.30392i) q^{98} -3.98310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

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