LMFDB - Embedded newform 1155.2.q.j.331.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(331,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1155.331");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.q (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 13 x^{14} + 116 x^{12} + 545 x^{10} - 6 x^{9} + 1849 x^{8} + 78 x^{7} + 3192 x^{6} + 636 x^{5} + \cdots + 576 $ x^16 + 13x^14 + 116x^12 + 545x^10 - 6x^9 + 1849x^8 + 78x^7 + 3192x^6 + 636x^5 + 3912x^4 + 432x^3 + 1764x^2 - 144x + 576
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			331.1
Root			$-1.21150 - 2.09838i$ of defining polynomial
Character	$\chi$	$=$	1155.331
Dual form			1155.2.q.j.991.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.21150 + 2.09838i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.93546 - 3.35232i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.42300 q^{6} +(-0.185653 - 2.63923i) q^{7} +4.53326 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.21150 + 2.09838i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.93546 - 3.35232i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.42300 q^{6} +(-0.185653 - 2.63923i) q^{7} +4.53326 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.21150 + 2.09838i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.93546 + 3.35232i) q^{12} +6.70339 q^{13} +(5.76302 + 2.80786i) q^{14} -1.00000 q^{15} +(-1.62112 + 2.80786i) q^{16} +(-2.87093 - 4.97260i) q^{17} +(-1.21150 - 2.09838i) q^{18} +(0.919810 - 1.59316i) q^{19} -3.87093 q^{20} +(-2.19281 + 1.48039i) q^{21} -2.42300 q^{22} +(-3.66530 + 6.34849i) q^{23} +(-2.26663 - 3.92592i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-8.12116 + 14.0663i) q^{26} +1.00000 q^{27} +(-8.48823 + 5.73050i) q^{28} -6.84316 q^{29} +(1.21150 - 2.09838i) q^{30} +(-0.426183 - 0.738170i) q^{31} +(0.605295 + 1.04840i) q^{32} +(0.500000 - 0.866025i) q^{33} +13.9125 q^{34} +(-2.37847 - 1.15883i) q^{35} +3.87093 q^{36} +(2.08526 - 3.61177i) q^{37} +(2.22870 + 3.86022i) q^{38} +(-3.35170 - 5.80531i) q^{39} +(2.26663 - 3.92592i) q^{40} -0.963267 q^{41} +(-0.449836 - 6.39485i) q^{42} +1.36995 q^{43} +(1.93546 - 3.35232i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-8.88102 - 15.3824i) q^{46} +(6.48918 - 11.2396i) q^{47} +3.24223 q^{48} +(-6.93107 + 0.979959i) q^{49} +2.42300 q^{50} +(-2.87093 + 4.97260i) q^{51} +(-12.9742 - 22.4719i) q^{52} +(4.57386 + 7.92216i) q^{53} +(-1.21150 + 2.09838i) q^{54} +1.00000 q^{55} +(-0.841612 - 11.9643i) q^{56} -1.83962 q^{57} +(8.29049 - 14.3595i) q^{58} +(-6.56626 - 11.3731i) q^{59} +(1.93546 + 3.35232i) q^{60} +(-5.28954 + 9.16175i) q^{61} +2.06528 q^{62} +(2.37847 + 1.15883i) q^{63} -9.41773 q^{64} +(3.35170 - 5.80531i) q^{65} +(1.21150 + 2.09838i) q^{66} +(-6.57121 - 11.3817i) q^{67} +(-11.1132 + 19.2486i) q^{68} +7.33060 q^{69} +(5.31319 - 3.58700i) q^{70} -0.892317 q^{71} +(-2.26663 + 3.92592i) q^{72} +(-8.38665 - 14.5261i) q^{73} +(5.05258 + 8.75133i) q^{74} +(-0.500000 + 0.866025i) q^{75} -7.12104 q^{76} +(2.19281 - 1.48039i) q^{77} +16.2423 q^{78} +(0.364703 - 0.631684i) q^{79} +(1.62112 + 2.80786i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.16700 - 2.02130i) q^{82} +10.2026 q^{83} +(9.20687 + 4.48577i) q^{84} -5.74186 q^{85} +(-1.65970 + 2.87468i) q^{86} +(3.42158 + 5.92635i) q^{87} +(2.26663 + 3.92592i) q^{88} +(1.85414 - 3.21146i) q^{89} -2.42300 q^{90} +(-1.24450 - 17.6918i) q^{91} +28.3762 q^{92} +(-0.426183 + 0.738170i) q^{93} +(15.7233 + 27.2335i) q^{94} +(-0.919810 - 1.59316i) q^{95} +(0.605295 - 1.04840i) q^{96} +14.7928 q^{97} +(6.34066 - 15.7312i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	$ 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) $ 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.21150	+	2.09838i	−0.856660	+	1.48378i	0.0184367	+	0.999830i	$0.494131\pi$
$2$	−1.21150	+	2.09838i	−0.856660	+	1.48378i	−0.875097	+	0.483948i	$0.839202\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.93546	−	3.35232i	−0.967732	−	1.67616i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	2.42300			0.989186
$7$	−0.185653	−	2.63923i	−0.0701701	−	0.997535i
$7$	−0.185653	−	2.63923i	−0.0701701	−	0.997535i
$8$	4.53326			1.60275
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.21150	+	2.09838i	0.383110	+	0.663566i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	−1.93546	+	3.35232i	−0.558720	+	0.967732i
$13$	6.70339			1.85919			0.929593	−	0.368586i	$-0.120158\pi$
$13$	6.70339			1.85919			0.929593	+	0.368586i	$0.120158\pi$
$14$	5.76302	+	2.80786i	1.54023	+	0.750431i
$15$	−1.00000			−0.258199
$16$	−1.62112	+	2.80786i	−0.405279	+	0.701964i
$17$	−2.87093	−	4.97260i	−0.696303	−	1.20603i	−0.969740	−	0.244142i	$-0.921494\pi$
$17$	−2.87093	−	4.97260i	−0.696303	−	1.20603i	0.273437	−	0.961890i	$-0.411839\pi$
$18$	−1.21150	−	2.09838i	−0.285553	−	0.494593i
$19$	0.919810	−	1.59316i	0.211019	−	0.365495i	−0.741015	−	0.671489i	$-0.765655\pi$
$19$	0.919810	−	1.59316i	0.211019	−	0.365495i	0.952034	+	0.305993i	$0.0989885\pi$
$20$	−3.87093			−0.865566
$21$	−2.19281	+	1.48039i	−0.478511	+	0.323049i
$22$	−2.42300			−0.516585
$23$	−3.66530	+	6.34849i	−0.764268	+	1.32375i	0.176365	+	0.984325i	$0.443566\pi$
$23$	−3.66530	+	6.34849i	−0.764268	+	1.32375i	−0.940633	+	0.339426i	$0.889767\pi$
$24$	−2.26663	−	3.92592i	−0.462674	−	0.801375i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−8.12116	+	14.0663i	−1.59269	+	2.75862i
$27$	1.00000			0.192450
$28$	−8.48823	+	5.73050i	−1.60412	+	1.08296i
$29$	−6.84316			−1.27074			−0.635372	−	0.772207i	$-0.719153\pi$
$29$	−6.84316			−1.27074			−0.635372	+	0.772207i	$0.719153\pi$
$30$	1.21150	−	2.09838i	0.221189	−	0.383110i
$31$	−0.426183	−	0.738170i	−0.0765447	−	0.132579i	0.825212	−	0.564823i	$-0.191055\pi$
$31$	−0.426183	−	0.738170i	−0.0765447	−	0.132579i	−0.901757	+	0.432243i	$0.857722\pi$
$32$	0.605295	+	1.04840i	0.107002	+	0.185333i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	13.9125			2.38598
$35$	−2.37847	−	1.15883i	−0.402034	−	0.195879i
$36$	3.87093			0.645155
$37$	2.08526	−	3.61177i	0.342814	−	0.593772i	−0.642140	−	0.766587i	$-0.721953\pi$
$37$	2.08526	−	3.61177i	0.342814	−	0.593772i	0.984954	+	0.172816i	$0.0552865\pi$
$38$	2.22870	+	3.86022i	0.361543	+	0.626210i
$39$	−3.35170	−	5.80531i	−0.536701	−	0.929593i
$40$	2.26663	−	3.92592i	0.358386	−	0.620742i
$41$	−0.963267			−0.150437			−0.0752185	−	0.997167i	$-0.523965\pi$
$41$	−0.963267			−0.150437			−0.0752185	+	0.997167i	$0.523965\pi$
$42$	−0.449836	−	6.39485i	−0.0694112	−	0.986747i
$43$	1.36995			0.208916			0.104458	−	0.994529i	$-0.466689\pi$
$43$	1.36995			0.208916			0.104458	+	0.994529i	$0.466689\pi$
$44$	1.93546	−	3.35232i	0.291782	−	0.505382i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−8.88102	−	15.3824i	−1.30944	−	2.26801i
$47$	6.48918	−	11.2396i	0.946545	−	1.63946i	0.193916	−	0.981018i	$-0.437881\pi$
$47$	6.48918	−	11.2396i	0.946545	−	1.63946i	0.752629	−	0.658445i	$-0.228786\pi$
$48$	3.24223			0.467976
$49$	−6.93107	+	0.979959i	−0.990152	+	0.139994i
$50$	2.42300			0.342664
$51$	−2.87093	+	4.97260i	−0.402010	+	0.696303i
$52$	−12.9742	−	22.4719i	−1.79920	−	3.11630i
$53$	4.57386	+	7.92216i	0.628268	+	1.08819i	0.987899	+	0.155098i	$0.0495693\pi$
$53$	4.57386	+	7.92216i	0.628268	+	1.08819i	−0.359631	+	0.933095i	$0.617097\pi$
$54$	−1.21150	+	2.09838i	−0.164864	+	0.285553i
$55$	1.00000			0.134840
$56$	−0.841612	−	11.9643i	−0.112465	−	1.59880i
$57$	−1.83962			−0.243664
$58$	8.29049	−	14.3595i	1.08859	−	1.88550i
$59$	−6.56626	−	11.3731i	−0.854854	−	1.48065i	−0.876781	−	0.480891i	$-0.840313\pi$
$59$	−6.56626	−	11.3731i	−0.854854	−	1.48065i	0.0219268	−	0.999760i	$-0.493020\pi$
$60$	1.93546	+	3.35232i	0.249867	+	0.432783i
$61$	−5.28954	+	9.16175i	−0.677256	+	1.17304i	0.298548	+	0.954395i	$0.403498\pi$
$61$	−5.28954	+	9.16175i	−0.677256	+	1.17304i	−0.975804	+	0.218648i	$0.929836\pi$
$62$	2.06528			0.262291
$63$	2.37847	+	1.15883i	0.299659	+	0.145999i
$64$	−9.41773			−1.17722
$65$	3.35170	−	5.80531i	0.415727	−	0.720060i
$66$	1.21150	+	2.09838i	0.149125	+	0.258293i
$67$	−6.57121	−	11.3817i	−0.802801	−	1.39049i	−0.917765	−	0.397123i	$-0.870009\pi$
$67$	−6.57121	−	11.3817i	−0.802801	−	1.39049i	0.114964	−	0.993370i	$-0.463325\pi$
$68$	−11.1132	+	19.2486i	−1.34767	+	2.33423i
$69$	7.33060			0.882501
$70$	5.31319	−	3.58700i	0.635047	−	0.428728i
$71$	−0.892317			−0.105899			−0.0529493	−	0.998597i	$-0.516862\pi$
$71$	−0.892317			−0.105899			−0.0529493	+	0.998597i	$0.516862\pi$
$72$	−2.26663	+	3.92592i	−0.267125	+	0.462674i
$73$	−8.38665	−	14.5261i	−0.981584	−	1.70015i	−0.656231	−	0.754560i	$-0.727850\pi$
$73$	−8.38665	−	14.5261i	−0.981584	−	1.70015i	−0.325353	−	0.945593i	$-0.605483\pi$
$74$	5.05258	+	8.75133i	0.587351	+	1.01732i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−7.12104			−0.816839
$77$	2.19281	−	1.48039i	0.249894	−	0.168707i
$78$	16.2423			1.83908
$79$	0.364703	−	0.631684i	0.0410323	−	0.0710700i	−0.844780	−	0.535114i	$-0.820269\pi$
$79$	0.364703	−	0.631684i	0.0410323	−	0.0710700i	0.885812	+	0.464044i	$0.153602\pi$
$80$	1.62112	+	2.80786i	0.181246	+	0.313928i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.16700	−	2.02130i	0.128873	−	0.223215i
$83$	10.2026			1.11988			0.559941	−	0.828532i	$-0.310824\pi$
$83$	10.2026			1.11988			0.559941	+	0.828532i	$0.310824\pi$
$84$	9.20687	+	4.48577i	1.00455	+	0.489437i
$85$	−5.74186			−0.622792
$86$	−1.65970	+	2.87468i	−0.178970	+	0.309985i
$87$	3.42158	+	5.92635i	0.366832	+	0.635372i
$88$	2.26663	+	3.92592i	0.241624	+	0.418504i
$89$	1.85414	−	3.21146i	0.196538	−	0.340414i	−0.750866	−	0.660455i	$-0.770363\pi$
$89$	1.85414	−	3.21146i	0.196538	−	0.340414i	0.947404	+	0.320041i	$0.103697\pi$
$90$	−2.42300			−0.255407
$91$	−1.24450	−	17.6918i	−0.130459	−	1.85460i
$92$	28.3762			2.95843
$93$	−0.426183	+	0.738170i	−0.0441931	+	0.0765447i
$94$	15.7233	+	27.2335i	1.62173	+	2.80892i
$95$	−0.919810	−	1.59316i	−0.0943705	−	0.163454i
$96$	0.605295	−	1.04840i	0.0617776	−	0.107002i
$97$	14.7928			1.50199			0.750993	−	0.660310i	$-0.229575\pi$
$97$	14.7928			1.50199			0.750993	+	0.660310i	$0.229575\pi$
$98$	6.34066	−	15.7312i	0.640503	−	1.58909i
$99$	−1.00000			−0.100504
$100$	−1.93546	+	3.35232i	−0.193546	+	0.335232i
$101$	−0.0787597	−	0.136416i	−0.00783689	−	0.0135739i	0.862080	−	0.506772i	$-0.169161\pi$
$101$	−0.0787597	−	0.136416i	−0.00783689	−	0.0135739i	−0.869917	+	0.493198i	$0.835828\pi$
$102$	−6.95626	−	12.0486i	−0.688773	−	1.19299i
$103$	6.75387	−	11.6980i	0.665479	−	1.15264i	−0.313677	−	0.949530i	$-0.601561\pi$
$103$	6.75387	−	11.6980i	0.665479	−	1.15264i	0.979155	−	0.203113i	$-0.0651059\pi$
$104$	30.3882			2.97981
$105$	0.185653	+	2.63923i	0.0181178	+	0.257562i
$106$	−22.1649			−2.15285
$107$	−0.642230	+	1.11238i	−0.0620867	+	0.107537i	−0.895398	−	0.445267i	$-0.853109\pi$
$107$	−0.642230	+	1.11238i	−0.0620867	+	0.107537i	0.833311	+	0.552804i	$0.186442\pi$
$108$	−1.93546	−	3.35232i	−0.186240	−	0.322577i
$109$	6.78194	+	11.7467i	0.649592	+	1.12513i	0.983220	+	0.182421i	$0.0583934\pi$
$109$	6.78194	+	11.7467i	0.649592	+	1.12513i	−0.333629	+	0.942705i	$0.608273\pi$
$110$	−1.21150	+	2.09838i	−0.115512	+	0.200073i
$111$	−4.17052			−0.395848
$112$	7.71154	+	3.75721i	0.728672	+	0.355023i
$113$	−4.23830			−0.398706			−0.199353	−	0.979928i	$-0.563884\pi$
$113$	−4.23830			−0.398706			−0.199353	+	0.979928i	$0.563884\pi$
$114$	2.22870	−	3.86022i	0.208737	−	0.361543i
$115$	3.66530	+	6.34849i	0.341791	+	0.592000i
$116$	13.2447	+	22.9405i	1.22974	+	2.12997i
$117$	−3.35170	+	5.80531i	−0.309864	+	0.536701i
$118$	31.8201			2.92928
$119$	−12.5908	+	8.50022i	−1.15420	+	0.779214i
$120$	−4.53326			−0.413828
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	−12.8166	−	22.1989i	−1.16036	−	2.00980i
$123$	0.481633	+	0.834213i	0.0434274	+	0.0752185i
$124$	−1.64972	+	2.85741i	−0.148150	+	0.256603i
$125$	−1.00000			−0.0894427
$126$	−5.31319	+	3.58700i	−0.473336	+	0.319555i
$127$	−16.1560			−1.43361			−0.716807	−	0.697272i	$-0.754397\pi$
$127$	−16.1560			−1.43361			−0.716807	+	0.697272i	$0.754397\pi$
$128$	10.1990	−	17.6652i	0.901472	−	1.56139i
$129$	−0.684976	−	1.18641i	−0.0603088	−	0.104458i
$130$	8.12116	+	14.0663i	0.712273	+	1.23369i
$131$	−7.55969	+	13.0938i	−0.660493	+	1.14401i	0.319993	+	0.947420i	$0.396319\pi$
$131$	−7.55969	+	13.0938i	−0.660493	+	1.14401i	−0.980486	+	0.196587i	$0.937014\pi$
$132$	−3.87093			−0.336921
$133$	−4.37547	−	2.13182i	−0.379402	−	0.184852i
$134$	31.8441			2.75091
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−13.0147	−	22.5421i	−1.11600	−	1.93297i
$137$	−3.53003	−	6.11420i	−0.301591	−	0.522371i	0.674905	−	0.737904i	$-0.264184\pi$
$137$	−3.53003	−	6.11420i	−0.301591	−	0.522371i	−0.976497	+	0.215533i	$0.930851\pi$
$138$	−8.88102	+	15.3824i	−0.756003	+	1.30944i
$139$	−19.3700			−1.64294			−0.821472	−	0.570248i	$-0.806847\pi$
$139$	−19.3700			−1.64294			−0.821472	+	0.570248i	$0.806847\pi$
$140$	0.718648	+	10.2163i	0.0607368	+	0.863432i
$141$	−12.9784			−1.09298
$142$	1.08104	−	1.87242i	0.0907190	−	0.157130i
$143$	3.35170	+	5.80531i	0.280283	+	0.485464i
$144$	−1.62112	−	2.80786i	−0.135093	−	0.233988i
$145$	−3.42158	+	5.92635i	−0.284147	+	0.492157i
$146$	40.6417			3.36353
$147$	4.31420	+	5.51250i	0.355829	+	0.454663i
$148$	−16.1438			−1.32701
$149$	2.95104	−	5.11135i	0.241759	−	0.418738i	−0.719457	−	0.694537i	$-0.755609\pi$
$149$	2.95104	−	5.11135i	0.241759	−	0.418738i	0.961215	+	0.275799i	$0.0889424\pi$
$150$	−1.21150	−	2.09838i	−0.0989186	−	0.171332i
$151$	−5.38728	−	9.33104i	−0.438410	−	0.759349i	0.559157	−	0.829062i	$-0.311125\pi$
$151$	−5.38728	−	9.33104i	−0.438410	−	0.759349i	−0.997567	+	0.0697130i	$0.977792\pi$
$152$	4.16974	−	7.22220i	0.338210	−	0.585798i
$153$	5.74186			0.464202
$154$	0.449836	+	6.39485i	0.0362488	+	0.515312i
$155$	−0.852366			−0.0684637
$156$	−12.9742	+	22.4719i	−1.03877	+	1.79920i
$157$	4.09310	+	7.08946i	0.326665	+	0.565800i	0.981848	−	0.189670i	$-0.0607418\pi$
$157$	4.09310	+	7.08946i	0.326665	+	0.565800i	−0.655183	+	0.755470i	$0.727408\pi$
$158$	0.883676	+	1.53057i	0.0703015	+	0.121766i
$159$	4.57386	−	7.92216i	0.362731	−	0.628268i
$160$	1.21059			0.0957055
$161$	17.4356	+	8.49496i	1.37412	+	0.669497i
$162$	2.42300			0.190369
$163$	−0.757470	+	1.31198i	−0.0593296	+	0.102762i	−0.894165	−	0.447738i	$-0.852230\pi$
$163$	−0.757470	+	1.31198i	−0.0593296	+	0.102762i	0.834835	+	0.550500i	$0.185563\pi$
$164$	1.86437	+	3.22918i	0.145583	+	0.252157i
$165$	−0.500000	−	0.866025i	−0.0389249	−	0.0674200i
$166$	−12.3605	+	21.4090i	−0.959358	+	1.66166i
$167$	−17.2294			−1.33325			−0.666625	−	0.745393i	$-0.732262\pi$
$167$	−17.2294			−1.33325			−0.666625	+	0.745393i	$0.732262\pi$
$168$	−9.94060	+	6.71102i	−0.766934	+	0.517766i
$169$	31.9355			2.45658
$170$	6.95626	−	12.0486i	0.533521	−	0.924085i
$171$	0.919810	+	1.59316i	0.0703396	+	0.121832i
$172$	−2.65149	−	4.59252i	−0.202175	−	0.350177i
$173$	1.04296	−	1.80646i	0.0792948	−	0.137343i	−0.823651	−	0.567097i	$-0.808067\pi$
$173$	1.04296	−	1.80646i	0.0792948	−	0.137343i	0.902946	+	0.429754i	$0.141400\pi$
$174$	−16.5810			−1.25700
$175$	−2.19281	+	1.48039i	−0.165761	+	0.111907i
$176$	−3.24223			−0.244393
$177$	−6.56626	+	11.3731i	−0.493550	+	0.854854i
$178$	4.49257	+	7.78136i	0.336733	+	0.583238i
$179$	−7.34782	−	12.7268i	−0.549202	−	0.951245i	−0.998329	−	0.0577775i	$-0.981599\pi$
$179$	−7.34782	−	12.7268i	−0.549202	−	0.951245i	0.449128	−	0.893467i	$-0.351735\pi$
$180$	1.93546	−	3.35232i	0.144261	−	0.249867i
$181$	3.45265			0.256634			0.128317	−	0.991733i	$-0.459043\pi$
$181$	3.45265			0.256634			0.128317	+	0.991733i	$0.459043\pi$
$182$	38.6318	+	18.8222i	2.86358	+	1.39519i
$183$	10.5791			0.782028
$184$	−16.6158	+	28.7794i	−1.22493	+	2.12164i
$185$	−2.08526	−	3.61177i	−0.153311	−	0.265543i
$186$	−1.03264	−	1.78859i	−0.0757169	−	0.131146i
$187$	2.87093	−	4.97260i	0.209943	−	0.363632i
$188$	−50.2383			−3.66401
$189$	−0.185653	−	2.63923i	−0.0135042	−	0.191976i
$190$	4.45740			0.323374
$191$	−2.42061	+	4.19263i	−0.175150	+	0.303368i	−0.940213	−	0.340587i	$-0.889374\pi$
$191$	−2.42061	+	4.19263i	−0.175150	+	0.303368i	0.765063	+	0.643955i	$0.222708\pi$
$192$	4.70886	+	8.15599i	0.339833	+	0.588608i
$193$	−2.96050	−	5.12773i	−0.213101	−	0.369102i	0.739582	−	0.673066i	$-0.235023\pi$
$193$	−2.96050	−	5.12773i	−0.213101	−	0.369102i	−0.952683	+	0.303964i	$0.901690\pi$
$194$	−17.9215	+	31.0410i	−1.28669	+	2.22861i
$195$	−6.70339			−0.480040
$196$	16.7000	+	21.3385i	1.19286	+	1.52418i
$197$	13.7885			0.982391			0.491196	−	0.871049i	$-0.336560\pi$
$197$	13.7885			0.982391			0.491196	+	0.871049i	$0.336560\pi$
$198$	1.21150	−	2.09838i	0.0860976	−	0.149125i
$199$	−13.5196	−	23.4166i	−0.958376	−	1.65996i	−0.726445	−	0.687224i	$-0.758829\pi$
$199$	−13.5196	−	23.4166i	−0.958376	−	1.65996i	−0.231931	−	0.972732i	$-0.574504\pi$
$200$	−2.26663	−	3.92592i	−0.160275	−	0.277604i
$201$	−6.57121	+	11.3817i	−0.463498	+	0.802801i
$202$	0.381670			0.0268542
$203$	1.27045	+	18.0607i	0.0891681	+	1.26761i
$204$	22.2263			1.55615
$205$	−0.481633	+	0.834213i	−0.0336387	+	0.0582640i
$206$	16.3646	+	28.3444i	1.14018	+	1.97485i
$207$	−3.66530	−	6.34849i	−0.254756	−	0.441250i
$208$	−10.8670	+	18.8222i	−0.753490	+	1.30508i
$209$	1.83962			0.127249
$210$	−5.76302	−	2.80786i	−0.397686	−	0.193761i
$211$	−5.97392			−0.411261			−0.205631	−	0.978630i	$-0.565925\pi$
$211$	−5.97392			−0.411261			−0.205631	+	0.978630i	$0.565925\pi$
$212$	17.7051	−	30.6661i	1.21599	−	2.10616i
$213$	0.446158	+	0.772769i	0.0305703	+	0.0529493i
$214$	−1.55612	−	2.69529i	−0.106374	−	0.184246i
$215$	0.684976	−	1.18641i	0.0467150	−	0.0809127i
$216$	4.53326			0.308449
$217$	−1.86908	+	1.26184i	−0.126881	+	0.0856591i
$218$	−32.8653			−2.22592
$219$	−8.38665	+	14.5261i	−0.566718	+	0.981584i
$220$	−1.93546	−	3.35232i	−0.130489	−	0.226014i
$221$	−19.2450	−	33.3333i	−1.29456	−	2.24224i
$222$	5.05258	−	8.75133i	0.339107	−	0.587351i
$223$	8.03255			0.537899			0.268950	−	0.963154i	$-0.413323\pi$
$223$	8.03255			0.537899			0.268950	+	0.963154i	$0.413323\pi$
$224$	2.65460	−	1.79215i	0.177368	−	0.119743i
$225$	1.00000			0.0666667
$226$	5.13470	−	8.89356i	0.341555	−	0.591591i
$227$	4.34697	+	7.52918i	0.288519	+	0.499729i	0.973456	−	0.228873i	$-0.0735039\pi$
$227$	4.34697	+	7.52918i	0.288519	+	0.499729i	−0.684938	+	0.728602i	$0.740171\pi$
$228$	3.56052	+	6.16700i	0.235801	+	0.408419i
$229$	0.0924026	−	0.160046i	0.00610614	−	0.0105761i	−0.862956	−	0.505279i	$-0.831390\pi$
$229$	0.0924026	−	0.160046i	0.00610614	−	0.0105761i	0.869062	+	0.494703i	$0.164723\pi$
$230$	−17.7620			−1.17119
$231$	−2.37847	−	1.15883i	−0.156492	−	0.0762457i
$232$	−31.0218			−2.03668
$233$	8.34236	−	14.4494i	0.546526	−	0.946612i	−0.451983	−	0.892027i	$-0.649283\pi$
$233$	8.34236	−	14.4494i	0.546526	−	0.946612i	0.998509	−	0.0545849i	$-0.0173835\pi$
$234$	−8.12116	−	14.0663i	−0.530897	−	0.919540i
$235$	−6.48918	−	11.2396i	−0.423308	−	0.733190i
$236$	−25.4175	+	44.0244i	−1.65454	+	2.86575i
$237$	−0.729406			−0.0473800
$238$	−2.58290	−	36.7183i	−0.167424	−	2.38010i
$239$	−13.1335			−0.849536			−0.424768	−	0.905302i	$-0.639644\pi$
$239$	−13.1335			−0.849536			−0.424768	+	0.905302i	$0.639644\pi$
$240$	1.62112	−	2.80786i	0.104643	−	0.181246i
$241$	6.10161	+	10.5683i	0.393039	+	0.680764i	0.992849	−	0.119379i	$-0.0380904\pi$
$241$	6.10161	+	10.5683i	0.393039	+	0.680764i	−0.599810	+	0.800143i	$0.704757\pi$
$242$	−1.21150	−	2.09838i	−0.0778782	−	0.134889i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	40.9509			2.62161
$245$	−2.61686	+	6.49246i	−0.167185	+	0.414788i
$246$	−2.33400			−0.148810
$247$	6.16585	−	10.6796i	0.392323	−	0.679524i
$248$	−1.93200	−	3.34632i	−0.122682	−	0.212492i
$249$	−5.10131	−	8.83572i	−0.323282	−	0.559941i
$250$	1.21150	−	2.09838i	0.0766220	−	0.132713i
$251$	14.6619			0.925449			0.462724	−	0.886502i	$-0.346872\pi$
$251$	14.6619			0.925449			0.462724	+	0.886502i	$0.346872\pi$
$252$	−0.718648	−	10.2163i	−0.0452706	−	0.643565i
$253$	−7.33060			−0.460871
$254$	19.5730	−	33.9014i	1.22812	−	2.12716i
$255$	2.87093	+	4.97260i	0.179785	+	0.311396i
$256$	15.2944	+	26.4907i	0.955901	+	1.65567i
$257$	5.25862	−	9.10819i	0.328023	−	0.568153i	−0.654096	−	0.756411i	$-0.726951\pi$
$257$	5.25862	−	9.10819i	0.328023	−	0.568153i	0.982120	+	0.188258i	$0.0602842\pi$
$258$	3.31939			0.206656
$259$	−9.91943	−	4.83294i	−0.616363	−	0.300304i
$260$	−25.9484			−1.60925
$261$	3.42158	−	5.92635i	0.211791	−	0.366832i
$262$	−18.3171	−	31.7262i	−1.13164	−	1.96005i
$263$	−4.95413	−	8.58081i	−0.305485	−	0.529115i	0.671884	−	0.740656i	$-0.265485\pi$
$263$	−4.95413	−	8.58081i	−0.305485	−	0.529115i	−0.977369	+	0.211541i	$0.932152\pi$
$264$	2.26663	−	3.92592i	0.139501	−	0.241624i
$265$	9.14772			0.561940
$266$	9.77424	−	6.59871i	0.599297	−	0.404593i
$267$	−3.70827			−0.226943
$268$	−25.4367	+	44.0577i	−1.55379	+	2.69125i
$269$	3.83907	+	6.64946i	0.234072	+	0.405424i	0.959003	−	0.283397i	$-0.0914615\pi$
$269$	3.83907	+	6.64946i	0.234072	+	0.405424i	−0.724931	+	0.688822i	$0.758128\pi$
$270$	1.21150	+	2.09838i	0.0737295	+	0.127703i
$271$	−3.22152	+	5.57983i	−0.195693	+	0.338951i	−0.947128	−	0.320857i	$-0.896029\pi$
$271$	−3.22152	+	5.57983i	−0.195693	+	0.338951i	0.751434	+	0.659808i	$0.229362\pi$
$272$	18.6164			1.12879
$273$	−14.6993	+	9.92367i	−0.889642	+	0.600608i
$274$	17.1065			1.03344
$275$	0.500000	−	0.866025i	0.0301511	−	0.0522233i
$276$	−14.1881	−	24.5745i	−0.854025	−	1.47921i
$277$	8.97453	+	15.5443i	0.539227	+	0.933969i	0.998946	+	0.0459044i	$0.0146170\pi$
$277$	8.97453	+	15.5443i	0.539227	+	0.933969i	−0.459719	+	0.888065i	$0.652050\pi$
$278$	23.4668	−	40.6457i	1.40744	−	2.43777i
$279$	0.852366			0.0510298
$280$	−10.7822	−	5.25330i	−0.644360	−	0.313945i
$281$	−9.30756			−0.555243			−0.277621	−	0.960691i	$-0.589546\pi$
$281$	−9.30756			−0.555243			−0.277621	+	0.960691i	$0.589546\pi$
$282$	15.7233	−	27.2335i	0.936308	−	1.62173i
$283$	1.37239	+	2.37704i	0.0815799	+	0.141300i	0.903929	−	0.427683i	$-0.140670\pi$
$283$	1.37239	+	2.37704i	0.0815799	+	0.141300i	−0.822349	+	0.568984i	$0.807337\pi$
$284$	1.72705	+	2.99133i	0.102481	+	0.177503i
$285$	−0.919810	+	1.59316i	−0.0544848	+	0.0943705i
$286$	−16.2423			−0.960429
$287$	0.178833	+	2.54228i	0.0105562	+	0.150066i
$288$	−1.21059			−0.0713346
$289$	−7.98447	+	13.8295i	−0.469675	+	0.813500i
$290$	−8.29049	−	14.3595i	−0.486834	−	0.843222i
$291$	−7.39642	−	12.8110i	−0.433586	−	0.750993i
$292$	−32.4641	+	56.2296i	−1.89982	+	3.29059i
$293$	−25.0642			−1.46427			−0.732134	−	0.681161i	$-0.761476\pi$
$293$	−25.0642			−1.46427			−0.732134	+	0.681161i	$0.761476\pi$
$294$	−16.7940	+	2.37444i	−0.979444	+	0.138480i
$295$	−13.1325			−0.764604
$296$	9.45302	−	16.3731i	0.549446	−	0.951668i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	7.15037	+	12.3848i	0.414210	+	0.717433i
$299$	−24.5700	+	42.5564i	−1.42092	+	2.46110i
$300$	3.87093			0.223488
$301$	−0.254335	−	3.61562i	−0.0146596	−	0.208401i
$302$	26.1067			1.50227
$303$	−0.0787597	+	0.136416i	−0.00452463	+	0.00783689i
$304$	2.98224	+	5.16539i	0.171043	+	0.296255i
$305$	5.28954	+	9.16175i	0.302878	+	0.524600i
$306$	−6.95626	+	12.0486i	−0.397663	+	0.688773i
$307$	−13.8291			−0.789267			−0.394633	−	0.918839i	$-0.629128\pi$
$307$	−13.8291			−0.789267			−0.394633	+	0.918839i	$0.629128\pi$
$308$	−9.20687	−	4.48577i	−0.524610	−	0.255600i
$309$	−13.5077			−0.768429
$310$	1.03264	−	1.78859i	0.0586501	−	0.101585i
$311$	2.60354	+	4.50947i	0.147633	+	0.255709i	0.930352	−	0.366667i	$-0.119501\pi$
$311$	2.60354	+	4.50947i	0.147633	+	0.255709i	−0.782719	+	0.622375i	$0.786168\pi$
$312$	−15.1941	−	26.3170i	−0.860198	−	1.48991i
$313$	0.00168382	−	0.00291645i	9.51749e−5	−	0.000164848i	−0.865978	−	0.500082i	$-0.833303\pi$
$313$	0.00168382	−	0.00291645i	9.51749e−5	−	0.000164848i	0.866073	+	0.499918i	$0.166636\pi$
$314$	−19.8352			−1.11936
$315$	2.19281	−	1.48039i	0.123551	−	0.0834108i
$316$	−2.82348			−0.158833
$317$	1.96998	−	3.41210i	0.110645	−	0.191643i	−0.805386	−	0.592751i	$-0.798042\pi$
$317$	1.96998	−	3.41210i	0.110645	−	0.191643i	0.916030	+	0.401109i	$0.131375\pi$
$318$	11.0825	+	19.1954i	0.621474	+	1.07642i
$319$	−3.42158	−	5.92635i	−0.191572	−	0.331812i
$320$	−4.70886	+	8.15599i	−0.263233	+	0.455934i
$321$	1.28446			0.0716916
$322$	−38.9489	+	26.2948i	−2.17054	+	1.46535i
$323$	−10.5628			−0.587732
$324$	−1.93546	+	3.35232i	−0.107526	+	0.186240i
$325$	−3.35170	−	5.80531i	−0.185919	−	0.322021i
$326$	−1.83535	−	3.17892i	−0.101651	−	0.176064i
$327$	6.78194	−	11.7467i	0.375042	−	0.649592i
$328$	−4.36674			−0.241113
$329$	−30.8686	−	15.0398i	−1.70184	−	0.829170i
$330$	2.42300			0.133382
$331$	17.1712	−	29.7413i	0.943813	−	1.63473i	0.185703	−	0.982606i	$-0.440544\pi$
$331$	17.1712	−	29.7413i	0.943813	−	1.63473i	0.758110	−	0.652126i	$-0.226123\pi$
$332$	−19.7468	−	34.2025i	−1.08375	−	1.87710i
$333$	2.08526	+	3.61177i	0.114271	+	0.197924i
$334$	20.8734	−	36.1538i	1.14214	−	1.97825i
$335$	−13.1424			−0.718047
$336$	−0.601929	−	8.55700i	−0.0328379	−	0.466823i
$337$	13.0016			0.708241			0.354120	−	0.935200i	$-0.384780\pi$
$337$	13.0016			0.708241			0.354120	+	0.935200i	$0.384780\pi$
$338$	−38.6898	+	67.0128i	−2.10445	+	3.64501i
$339$	2.11915	+	3.67047i	0.115096	+	0.199353i
$340$	11.1132	+	19.2486i	0.602696	+	1.04390i
$341$	0.426183	−	0.738170i	0.0230791	−	0.0399742i
$342$	−4.45740			−0.241028
$343$	3.87311	+	18.1107i	0.209128	+	0.977888i
$344$	6.21035			0.334840
$345$	3.66530	−	6.34849i	0.197333	−	0.341791i
$346$	2.52709	+	4.37705i	0.135857	+	0.235312i
$347$	3.91131	+	6.77459i	0.209970	+	0.363679i	0.951705	−	0.307014i	$-0.0993300\pi$
$347$	3.91131	+	6.77459i	0.209970	+	0.363679i	−0.741735	+	0.670693i	$0.765997\pi$
$348$	13.2447	−	22.9405i	0.709990	−	1.22974i
$349$	14.8262			0.793629			0.396814	−	0.917899i	$-0.370116\pi$
$349$	14.8262			0.793629			0.396814	+	0.917899i	$0.370116\pi$
$350$	−0.449836	−	6.39485i	−0.0240448	−	0.341819i
$351$	6.70339			0.357801
$352$	−0.605295	+	1.04840i	−0.0322623	+	0.0558800i
$353$	7.34633	+	12.7242i	0.391006	+	0.677242i	0.992582	−	0.121573i	$-0.0387939\pi$
$353$	7.34633	+	12.7242i	0.391006	+	0.677242i	−0.601577	+	0.798815i	$0.705461\pi$
$354$	−15.9100	−	27.5570i	−0.845609	−	1.46464i
$355$	−0.446158	+	0.772769i	−0.0236796	+	0.0410143i
$356$	−14.3545			−0.760785
$357$	13.6568	+	6.65387i	0.722795	+	0.352160i
$358$	35.6075			1.88192
$359$	12.3161	−	21.3321i	0.650020	−	1.12587i	−0.333098	−	0.942892i	$-0.608094\pi$
$359$	12.3161	−	21.3321i	0.650020	−	1.12587i	0.983118	−	0.182975i	$-0.0585727\pi$
$360$	2.26663	+	3.92592i	0.119462	+	0.206914i
$361$	7.80790	+	13.5237i	0.410942	+	0.711773i
$362$	−4.18289	+	7.24498i	−0.219848	+	0.380788i
$363$	1.00000			0.0524864
$364$	−56.8999	+	38.4138i	−2.98237	+	2.01343i
$365$	−16.7733			−0.877955
$366$	−12.8166	+	22.1989i	−0.669932	+	1.16036i
$367$	17.6133	+	30.5072i	0.919409	+	1.59246i	0.800314	+	0.599581i	$0.204666\pi$
$367$	17.6133	+	30.5072i	0.919409	+	1.59246i	0.119095	+	0.992883i	$0.462001\pi$
$368$	−11.8838	−	20.5833i	−0.619484	−	1.07298i
$369$	0.481633	−	0.834213i	0.0250728	−	0.0434274i
$370$	10.1052			0.525342
$371$	20.0593	−	13.5422i	1.04142	−	0.703078i
$372$	3.29945			0.171068
$373$	−4.33339	+	7.50566i	−0.224375	+	0.388628i	−0.956132	−	0.292937i	$-0.905367\pi$
$373$	−4.33339	+	7.50566i	−0.224375	+	0.388628i	0.731757	+	0.681566i	$0.238701\pi$
$374$	6.95626	+	12.0486i	0.359700	+	0.623018i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	29.4172	−	50.9520i	1.51707	−	2.62765i
$377$	−45.8724			−2.36255
$378$	5.76302	+	2.80786i	0.296418	+	0.144421i
$379$	0.328188			0.0168579			0.00842893	−	0.999964i	$-0.497317\pi$
$379$	0.328188			0.0168579			0.00842893	+	0.999964i	$0.497317\pi$
$380$	−3.56052	+	6.16700i	−0.182651	+	0.316360i
$381$	8.07800	+	13.9915i	0.413849	+	0.716807i
$382$	−5.86515	−	10.1587i	−0.300087	−	0.519766i
$383$	6.23684	−	10.8025i	0.318687	−	0.551983i	−0.661527	−	0.749921i	$-0.730091\pi$
$383$	6.23684	−	10.8025i	0.318687	−	0.551983i	0.980214	+	0.197939i	$0.0634247\pi$
$384$	−20.3980			−1.04093
$385$	−0.185653	−	2.63923i	−0.00946173	−	0.134508i
$386$	14.3466			0.730221
$387$	−0.684976	+	1.18641i	−0.0348193	+	0.0603088i
$388$	−28.6310	−	49.5904i	−1.45352	−	2.51757i
$389$	8.96302	+	15.5244i	0.454443	+	0.787119i	0.998656	−	0.0518284i	$-0.0165049\pi$
$389$	8.96302	+	15.5244i	0.454443	+	0.787119i	−0.544213	+	0.838947i	$0.683172\pi$
$390$	8.12116	−	14.0663i	0.411231	−	0.712273i
$391$	42.0913			2.12865
$392$	−31.4203	+	4.44241i	−1.58697	+	0.224376i
$393$	15.1194			0.762672
$394$	−16.7048	+	28.9335i	−0.841575	+	1.45765i
$395$	−0.364703	−	0.631684i	−0.0183502	−	0.0317835i
$396$	1.93546	+	3.35232i	0.0972608	+	0.168461i
$397$	5.58369	−	9.67124i	0.280237	−	0.485385i	−0.691206	−	0.722658i	$-0.742920\pi$
$397$	5.58369	−	9.67124i	0.280237	−	0.485385i	0.971443	+	0.237273i	$0.0762535\pi$
$398$	65.5158			3.28401
$399$	0.341530	+	4.85518i	0.0170979	+	0.243063i
$400$	3.24223			0.162112
$401$	10.0611	−	17.4264i	0.502428	−	0.870231i	−0.497568	−	0.867425i	$-0.665774\pi$
$401$	10.0611	−	17.4264i	0.502428	−	0.870231i	0.999996	−	0.00280595i	$-0.000893164\pi$
$402$	−15.9220	−	27.5778i	−0.794120	−	1.37546i
$403$	−2.85687	−	4.94825i	−0.142311	−	0.246490i
$404$	−0.304873	+	0.528056i	−0.0151680	+	0.0262718i
$405$	−1.00000			−0.0496904
$406$	−39.4373	−	19.2146i	−1.95724	−	0.953605i
$407$	4.17052			0.206725
$408$	−13.0147	+	22.5421i	−0.644322	+	1.11600i
$409$	11.3447	+	19.6496i	0.560960	+	0.971611i	0.997413	+	0.0718843i	$0.0229012\pi$
$409$	11.3447	+	19.6496i	0.560960	+	0.971611i	−0.436453	+	0.899727i	$0.643765\pi$
$410$	−1.16700	−	2.02130i	−0.0576339	−	0.0998248i
$411$	−3.53003	+	6.11420i	−0.174124	+	0.301591i
$412$	−52.2875			−2.57602
$413$	−28.7972	+	19.4413i	−1.41702	+	0.956644i
$414$	17.7620			0.872957
$415$	5.10131	−	8.83572i	0.250413	−	0.433729i
$416$	4.05753	+	7.02784i	0.198937	+	0.344568i
$417$	9.68502	+	16.7749i	0.474277	+	0.821472i
$418$	−2.22870	+	3.86022i	−0.109009	+	0.188810i
$419$	9.26131			0.452444			0.226222	−	0.974076i	$-0.427362\pi$
$419$	9.26131			0.452444			0.226222	+	0.974076i	$0.427362\pi$
$420$	8.48823	−	5.73050i	0.414183	−	0.279620i
$421$	−2.89826			−0.141253			−0.0706264	−	0.997503i	$-0.522500\pi$
$421$	−2.89826			−0.141253			−0.0706264	+	0.997503i	$0.522500\pi$
$422$	7.23740	−	12.5355i	0.352311	−	0.610221i
$423$	6.48918	+	11.2396i	0.315515	+	0.546488i
$424$	20.7345	+	35.9132i	1.00696	+	1.74410i
$425$	−2.87093	+	4.97260i	−0.139261	+	0.241206i
$426$	−2.16208			−0.104753
$427$	25.1620	+	12.2594i	1.21767	+	0.593274i
$428$	4.97206			0.240333
$429$	3.35170	−	5.80531i	0.161821	−	0.280283i
$430$	1.65970	+	2.87468i	0.0800377	+	0.138629i
$431$	−2.67034	−	4.62517i	−0.128626	−	0.222787i	0.794519	−	0.607240i	$-0.207723\pi$
$431$	−2.67034	−	4.62517i	−0.128626	−	0.222787i	−0.923144	+	0.384453i	$0.874390\pi$
$432$	−1.62112	+	2.80786i	−0.0779960	+	0.135093i
$433$	−15.0092			−0.721298			−0.360649	−	0.932702i	$-0.617445\pi$
$433$	−15.0092			−0.721298			−0.360649	+	0.932702i	$0.617445\pi$
$434$	−0.383425	−	5.45075i	−0.0184050	−	0.261645i
$435$	6.84316			0.328104
$436$	26.2524	−	45.4705i	1.25726	−	2.17764i
$437$	6.74276	+	11.6788i	0.322550	+	0.558673i
$438$	−20.3209	−	35.1968i	−0.970968	−	1.68177i
$439$	−3.73534	+	6.46980i	−0.178278	+	0.308787i	−0.941291	−	0.337597i	$-0.890386\pi$
$439$	−3.73534	+	6.46980i	−0.178278	+	0.308787i	0.763013	+	0.646383i	$0.223719\pi$
$440$	4.53326			0.216115
$441$	2.61686	−	6.49246i	0.124613	−	0.309165i
$442$	93.2611			4.43598
$443$	7.60748	−	13.1765i	0.361442	−	0.626036i	−0.626756	−	0.779215i	$-0.715618\pi$
$443$	7.60748	−	13.1765i	0.361442	−	0.626036i	0.988198	+	0.153179i	$0.0489512\pi$
$444$	8.07189	+	13.9809i	0.383075	+	0.663505i
$445$	−1.85414	−	3.21146i	−0.0878945	−	0.152238i
$446$	−9.73144	+	16.8553i	−0.460797	+	0.798124i
$447$	−5.90208			−0.279159
$448$	1.74842	+	24.8555i	0.0826053	+	1.17431i
$449$	11.7899			0.556399			0.278200	−	0.960523i	$-0.410262\pi$
$449$	11.7899			0.556399			0.278200	+	0.960523i	$0.410262\pi$
$450$	−1.21150	+	2.09838i	−0.0571107	+	0.0989186i
$451$	−0.481633	−	0.834213i	−0.0226792	−	0.0392816i
$452$	8.20308	+	14.2081i	0.385840	+	0.668295i
$453$	−5.38728	+	9.33104i	−0.253116	+	0.438410i
$454$	−21.0654			−0.988649
$455$	−15.9438	−	7.76813i	−0.747457	−	0.364175i
$456$	−8.33948			−0.390532
$457$	2.07012	−	3.58556i	0.0968363	−	0.167725i	−0.813537	−	0.581513i	$-0.802461\pi$
$457$	2.07012	−	3.58556i	0.0968363	−	0.167725i	0.910374	+	0.413787i	$0.135794\pi$
$458$	0.223892	+	0.387791i	0.0104618	+	0.0181203i
$459$	−2.87093	−	4.97260i	−0.134003	−	0.232101i
$460$	14.1881	−	24.5745i	0.661525	−	1.14579i
$461$	27.6014			1.28552			0.642762	−	0.766066i	$-0.277788\pi$
$461$	27.6014			1.28552			0.642762	+	0.766066i	$0.277788\pi$
$462$	5.31319	−	3.58700i	0.247192	−	0.166882i
$463$	28.8597			1.34123			0.670613	−	0.741807i	$-0.266031\pi$
$463$	28.8597			1.34123			0.670613	+	0.741807i	$0.266031\pi$
$464$	11.0936	−	19.2146i	0.515006	−	0.892016i
$465$	0.426183	+	0.738170i	0.0197638	+	0.0342318i
$466$	20.2135	+	35.0109i	0.936375	+	1.62185i
$467$	−12.0969	+	20.9524i	−0.559777	+	0.969562i	0.437738	+	0.899103i	$0.355780\pi$
$467$	−12.0969	+	20.9524i	−0.559777	+	0.969562i	−0.997515	+	0.0704594i	$0.977553\pi$
$468$	25.9484			1.19946
$469$	−28.8189	+	19.4560i	−1.33073	+	0.898394i
$470$	31.4466			1.45052
$471$	4.09310	−	7.08946i	0.188600	−	0.326665i
$472$	−29.7666	−	51.5572i	−1.37012	−	2.37311i
$473$	0.684976	+	1.18641i	0.0314952	+	0.0545513i
$474$	0.883676	−	1.53057i	0.0405886	−	0.0703015i
$475$	−1.83962			−0.0844075
$476$	52.8646	+	25.7566i	2.42304	+	1.18055i
$477$	−9.14772			−0.418845
$478$	15.9112	−	27.5591i	0.727763	−	1.26052i
$479$	0.132493	+	0.229484i	0.00605374	+	0.0104854i	0.869036	−	0.494748i	$-0.164740\pi$
$479$	0.132493	+	0.229484i	0.00605374	+	0.0104854i	−0.862983	+	0.505234i	$0.831406\pi$
$480$	−0.605295	−	1.04840i	−0.0276278	−	0.0478527i
$481$	13.9783	−	24.2111i	0.637356	−	1.10393i
$482$	−29.5684			−1.34680
$483$	−1.36095	−	19.3471i	−0.0619251	−	0.880325i
$484$	3.87093			0.175951
$485$	7.39642	−	12.8110i	0.335854	−	0.581717i
$486$	−1.21150	−	2.09838i	−0.0549548	−	0.0951844i
$487$	1.78083	+	3.08449i	0.0806972	+	0.139772i	0.903550	−	0.428484i	$-0.140952\pi$
$487$	1.78083	+	3.08449i	0.0806972	+	0.139772i	−0.822852	+	0.568255i	$0.807619\pi$
$488$	−23.9789	+	41.5326i	−1.08547	+	1.88009i
$489$	1.51494			0.0685080
$490$	−10.4533	−	13.3568i	−0.472233	−	0.603398i
$491$	9.44476			0.426236			0.213118	−	0.977026i	$-0.431638\pi$
$491$	9.44476			0.426236			0.213118	+	0.977026i	$0.431638\pi$
$492$	1.86437	−	3.22918i	0.0840522	−	0.145583i
$493$	19.6462	+	34.0283i	0.884822	+	1.53256i
$494$	14.9398	+	25.8766i	0.672175	+	1.16424i
$495$	−0.500000	+	0.866025i	−0.0224733	+	0.0389249i
$496$	2.76357			0.124088
$497$	0.165661	+	2.35503i	0.00743091	+	0.105637i
$498$	24.7209			1.10777
$499$	−7.70437	+	13.3444i	−0.344895	+	0.597376i	−0.985335	−	0.170633i	$-0.945419\pi$
$499$	−7.70437	+	13.3444i	−0.344895	+	0.597376i	0.640440	+	0.768008i	$0.278752\pi$
$500$	1.93546	+	3.35232i	0.0865566	+	0.149920i
$501$	8.61469	+	14.9211i	0.384876	+	0.666625i
$502$	−17.7629	+	30.7662i	−0.792795	+	1.37316i
$503$	−37.2660			−1.66161			−0.830804	−	0.556566i	$-0.812119\pi$
$503$	−37.2660			−1.66161			−0.830804	+	0.556566i	$0.812119\pi$
$504$	10.7822	+	5.25330i	0.480278	+	0.234001i
$505$	−0.157519			−0.00700952
$506$	8.88102	−	15.3824i	0.394810	−	0.683830i
$507$	−15.9677	−	27.6569i	−0.709152	−	1.22829i
$508$	31.2694	+	54.1601i	1.38735	+	2.40297i
$509$	6.83530	−	11.8391i	0.302969	−	0.524758i	−0.673838	−	0.738879i	$-0.735355\pi$
$509$	6.83530	−	11.8391i	0.302969	−	0.524758i	0.976807	+	0.214121i	$0.0686887\pi$
$510$	−13.9125			−0.616057
$511$	−36.7807	+	24.8311i	−1.62708	+	1.09846i
$512$	−33.3208			−1.47259
$513$	0.919810	−	1.59316i	0.0406106	−	0.0703396i
$514$	12.7416	+	22.0691i	0.562009	+	0.973428i
$515$	−6.75387	−	11.6980i	−0.297611	−	0.515478i
$516$	−2.65149	+	4.59252i	−0.116726	+	0.202175i
$517$	12.9784			0.570788
$518$	22.1587	−	14.9596i	0.973599	−	0.657288i
$519$	−2.08592			−0.0915617
$520$	15.1941	−	26.3170i	0.666306	−	1.15408i
$521$	20.4751	+	35.4639i	0.897029	+	1.55370i	0.831273	+	0.555864i	$0.187612\pi$
$521$	20.4751	+	35.4639i	0.897029	+	1.55370i	0.0657557	+	0.997836i	$0.479054\pi$
$522$	8.29049	+	14.3595i	0.362865	+	0.628500i
$523$	0.727649	−	1.26033i	0.0318179	−	0.0551102i	−0.849678	−	0.527302i	$-0.823204\pi$
$523$	0.727649	−	1.26033i	0.0318179	−	0.0551102i	0.881496	+	0.472192i	$0.156537\pi$
$524$	58.5260			2.55672
$525$	2.37847	+	1.15883i	0.103805	+	0.0505757i
$526$	24.0077			1.04679
$527$	−2.44708	+	4.23847i	−0.106597	+	0.184631i
$528$	1.62112	+	2.80786i	0.0705501	+	0.122196i
$529$	−15.3689	−	26.6197i	−0.668212	−	1.15738i
$530$	−11.0825	+	19.1954i	−0.481392	+	0.833795i
$531$	13.1325			0.569903
$532$	1.32204	+	18.7940i	0.0573176	+	0.814825i
$533$	−6.45716			−0.279690
$534$	4.49257	−	7.78136i	0.194413	−	0.336733i
$535$	0.642230	+	1.11238i	0.0277660	+	0.0480922i
$536$	−29.7890	−	51.5961i	−1.28669	−	2.22861i
$537$	−7.34782	+	12.7268i	−0.317082	+	0.549202i
$538$	−18.6041			−0.802080
$539$	−4.31420	−	5.51250i	−0.185826	−	0.237440i
$540$	−3.87093			−0.166578
$541$	15.4706	−	26.7959i	0.665133	−	1.15204i	−0.314116	−	0.949385i	$-0.601708\pi$
$541$	15.4706	−	26.7959i	0.665133	−	1.15204i	0.979249	−	0.202660i	$-0.0649585\pi$
$542$	−7.80574	−	13.5199i	−0.335285	−	0.580731i
$543$	−1.72633	−	2.99009i	−0.0740838	−	0.128317i
$544$	3.47552	−	6.01977i	0.149012	−	0.258095i
$545$	13.5639			0.581012
$546$	−3.01543	−	42.8672i	−0.129048	−	1.83455i
$547$	−7.86909			−0.336458			−0.168229	−	0.985748i	$-0.553805\pi$
$547$	−7.86909			−0.336458			−0.168229	+	0.985748i	$0.553805\pi$
$548$	−13.6645	+	23.6676i	−0.583719	+	1.01103i
$549$	−5.28954	−	9.16175i	−0.225752	−	0.391014i
$550$	1.21150	+	2.09838i	0.0516585	+	0.0894752i
$551$	−6.29441	+	10.9022i	−0.268151	+	0.464451i
$552$	33.2315			1.41443
$553$	−1.73487	−	0.845262i	−0.0737741	−	0.0359442i
$554$	−43.4906			−1.84774
$555$	−2.08526	+	3.61177i	−0.0885143	+	0.153311i
$556$	37.4900	+	64.9346i	1.58993	+	2.75384i
$557$	7.97806	+	13.8184i	0.338041	+	0.585504i	0.984064	−	0.177813i	$-0.0569024\pi$
$557$	7.97806	+	13.8184i	0.338041	+	0.585504i	−0.646023	+	0.763318i	$0.723569\pi$
$558$	−1.03264	+	1.78859i	−0.0437152	+	0.0757169i
$559$	9.18333			0.388413
$560$	7.10962	−	4.79979i	0.300436	−	0.202828i
$561$	−5.74186			−0.242421
$562$	11.2761	−	19.5308i	0.475654	−	0.823857i
$563$	−9.83985	−	17.0431i	−0.414700	−	0.718282i	0.580697	−	0.814120i	$-0.302780\pi$
$563$	−9.83985	−	17.0431i	−0.414700	−	0.718282i	−0.995397	+	0.0958382i	$0.969447\pi$
$564$	25.1192	+	43.5077i	1.05771	+	1.83200i
$565$	−2.11915	+	3.67047i	−0.0891533	+	0.154418i
$566$	−6.65058			−0.279545
$567$	−2.19281	+	1.48039i	−0.0920895	+	0.0621707i
$568$	−4.04511			−0.169729
$569$	−14.2751	+	24.7252i	−0.598445	+	1.03654i	0.394606	+	0.918850i	$0.370881\pi$
$569$	−14.2751	+	24.7252i	−0.598445	+	1.03654i	−0.993051	+	0.117686i	$0.962452\pi$
$570$	−2.22870	−	3.86022i	−0.0933499	−	0.161687i
$571$	10.5423	+	18.2598i	0.441182	+	0.764149i	0.997777	−	0.0666345i	$-0.0212261\pi$
$571$	10.5423	+	18.2598i	0.441182	+	0.764149i	−0.556596	+	0.830783i	$0.687893\pi$
$572$	12.9742	−	22.4719i	0.542478	−	0.939599i
$573$	4.84123			0.202245
$574$	−5.55133	−	2.70472i	−0.231708	−	0.112893i
$575$	7.33060			0.305707
$576$	4.70886	−	8.15599i	0.196203	−	0.339833i
$577$	4.33548	+	7.50928i	0.180489	+	0.312615i	0.942047	−	0.335481i	$-0.108899\pi$
$577$	4.33548	+	7.50928i	0.180489	+	0.312615i	−0.761558	+	0.648096i	$0.775565\pi$
$578$	−19.3464	−	33.5089i	−0.804703	−	1.39379i
$579$	−2.96050	+	5.12773i	−0.123034	+	0.213101i
$580$	26.4894			1.09991
$581$	−1.89414	−	26.9270i	−0.0785822	−	1.11712i
$582$	35.8431			1.48574
$583$	−4.57386	+	7.92216i	−0.189430	+	0.328102i
$584$	−38.0189	−	65.8507i	−1.57323	−	2.72492i
$585$	3.35170	+	5.80531i	0.138576	+	0.240020i
$586$	30.3653	−	52.5943i	1.25438	−	2.17265i
$587$	−29.7026			−1.22596			−0.612980	−	0.790099i	$-0.710029\pi$
$587$	−29.7026			−1.22596			−0.612980	+	0.790099i	$0.710029\pi$
$588$	10.1297	−	25.1318i	0.417741	−	1.03642i
$589$	−1.56803			−0.0646095
$590$	15.9100	−	27.5570i	0.655006	−	1.13450i
$591$	−6.89426	−	11.9412i	−0.283592	−	0.491196i
$592$	6.76089	+	11.7102i	0.277871	+	0.481287i
$593$	3.99933	−	6.92705i	0.164233	−	0.284460i	−0.772150	−	0.635441i	$-0.780818\pi$
$593$	3.99933	−	6.92705i	0.164233	−	0.284460i	0.936383	+	0.350981i	$0.114152\pi$
$594$	−2.42300			−0.0994169
$595$	1.06599	+	15.1541i	0.0437014	+	0.621257i
$596$	−22.8465			−0.935831
$597$	−13.5196	+	23.4166i	−0.553319	+	0.958376i
$598$	−59.5330	−	103.114i	−2.43449	−	4.21665i
$599$	4.35451	+	7.54224i	0.177921	+	0.308167i	0.941168	−	0.337939i	$-0.109730\pi$
$599$	4.35451	+	7.54224i	0.177921	+	0.308167i	−0.763248	+	0.646106i	$0.776396\pi$
$600$	−2.26663	+	3.92592i	−0.0925348	+	0.160275i
$601$	9.78565			0.399165			0.199583	−	0.979881i	$-0.436041\pi$
$601$	9.78565			0.399165			0.199583	+	0.979881i	$0.436041\pi$
$602$	7.89507	+	3.84663i	0.321779	+	0.156777i
$603$	13.1424			0.535201
$604$	−20.8538	+	36.1198i	−0.848528	+	1.46969i
$605$	0.500000	+	0.866025i	0.0203279	+	0.0352089i
$606$	−0.190835	−	0.330536i	−0.00775214	−	0.0134271i
$607$	1.32980	−	2.30329i	0.0539751	−	0.0934875i	−0.837775	−	0.546015i	$-0.816144\pi$
$607$	1.32980	−	2.30329i	0.0539751	−	0.0934875i	0.891751	+	0.452527i	$0.149478\pi$
$608$	2.22702			0.0903177
$609$	15.0058	−	10.1306i	0.608065	−	0.410512i
$610$	−25.6331			−1.03785
$611$	43.4995	−	75.3434i	1.75980	−	3.04807i
$612$	−11.1132	−	19.2486i	−0.449223	−	0.778077i
$613$	23.5897	+	40.8586i	0.952781	+	1.65026i	0.739367	+	0.673303i	$0.235125\pi$
$613$	23.5897	+	40.8586i	0.952781	+	1.65026i	0.213414	+	0.976962i	$0.431542\pi$
$614$	16.7539	−	29.0186i	0.676133	−	1.17110i
$615$	0.963267			0.0388427
$616$	9.94060	−	6.71102i	0.400518	−	0.270395i
$617$	−26.2666			−1.05745			−0.528727	−	0.848792i	$-0.677330\pi$
$617$	−26.2666			−1.05745			−0.528727	+	0.848792i	$0.677330\pi$
$618$	16.3646	−	28.3444i	0.658282	−	1.14018i
$619$	6.12560	+	10.6098i	0.246208	+	0.426446i	0.962471	−	0.271386i	$-0.0874819\pi$
$619$	6.12560	+	10.6098i	0.246208	+	0.426446i	−0.716262	+	0.697831i	$0.754149\pi$
$620$	1.64972	+	2.85741i	0.0662545	+	0.114756i
$621$	−3.66530	+	6.34849i	−0.147083	+	0.254756i
$622$	−12.6168			−0.505887
$623$	−8.82000	−	4.29728i	−0.353366	−	0.172167i
$624$	21.7340			0.870055
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	0.00407988	+	0.00706657i	0.000163065	+	0.000282437i
$627$	−0.919810	−	1.59316i	−0.0367337	−	0.0636246i
$628$	15.8441	−	27.4428i	0.632248	−	1.09509i
$629$	−23.9465			−0.954810
$630$	0.449836	+	6.39485i	0.0179219	+	0.254777i
$631$	17.3737			0.691635			0.345818	−	0.938302i	$-0.387602\pi$
$631$	17.3737			0.691635			0.345818	+	0.938302i	$0.387602\pi$
$632$	1.65329	−	2.86359i	0.0657645	−	0.113908i
$633$	2.98696	+	5.17356i	0.118721	+	0.205631i
$634$	4.77325	+	8.26752i	0.189570	+	0.328345i
$635$	−8.07800	+	13.9915i	−0.320566	+	0.555236i
$636$	−35.4102			−1.40411
$637$	−46.4617	+	6.56905i	−1.84088	+	0.260275i
$638$	16.5810			0.656447
$639$	0.446158	−	0.772769i	0.0176498	−	0.0305703i
$640$	−10.1990	−	17.6652i	−0.403150	−	0.698277i
$641$	1.24387	+	2.15445i	0.0491299	+	0.0850955i	0.889545	−	0.456848i	$-0.151022\pi$
$641$	1.24387	+	2.15445i	0.0491299	+	0.0850955i	−0.840415	+	0.541944i	$0.817689\pi$
$642$	−1.55612	+	2.69529i	−0.0614153	+	0.106374i
$643$	22.4097			0.883751			0.441875	−	0.897076i	$-0.354313\pi$
$643$	22.4097			0.883751			0.441875	+	0.897076i	$0.354313\pi$
$644$	−5.26812	−	74.8914i	−0.207593	−	2.95114i
$645$	−1.36995			−0.0539418
$646$	12.7969	−	22.1648i	0.503486	−	0.872064i
$647$	−4.59584	−	7.96024i	−0.180681	−	0.312949i	0.761431	−	0.648245i	$-0.224497\pi$
$647$	−4.59584	−	7.96024i	−0.180681	−	0.312949i	−0.942113	+	0.335296i	$0.891164\pi$
$648$	−2.26663	−	3.92592i	−0.0890417	−	0.154225i
$649$	6.56626	−	11.3731i	0.257748	−	0.446433i
$650$	16.2423			0.637076
$651$	2.02732	+	0.987751i	0.0794571	+	0.0387130i
$652$	5.86423			0.229661
$653$	16.9397	−	29.3404i	0.662902	−	1.14818i	−0.316948	−	0.948443i	$-0.602658\pi$
$653$	16.9397	−	29.3404i	0.662902	−	1.14818i	0.979850	−	0.199737i	$-0.0640087\pi$
$654$	16.4326	+	28.4622i	0.642567	+	1.11296i
$655$	7.55969	+	13.0938i	0.295381	+	0.511616i
$656$	1.56157	−	2.70472i	0.0609690	−	0.105601i
$657$	16.7733			0.654389
$658$	68.9565	−	46.5533i	2.68820	−	1.81484i
$659$	40.9449			1.59499			0.797494	−	0.603327i	$-0.206159\pi$
$659$	40.9449			1.59499			0.797494	+	0.603327i	$0.206159\pi$
$660$	−1.93546	+	3.35232i	−0.0753379	+	0.130489i
$661$	0.965322	+	1.67199i	0.0375467	+	0.0650328i	0.884188	−	0.467131i	$-0.154712\pi$
$661$	0.965322	+	1.67199i	0.0375467	+	0.0650328i	−0.846641	+	0.532164i	$0.821379\pi$
$662$	41.6058	+	72.0633i	1.61705	+	2.80082i
$663$	−19.2450	+	33.3333i	−0.747413	+	1.29456i
$664$	46.2511			1.79489
$665$	−4.03394	+	2.72336i	−0.156430	+	0.105607i
$666$	−10.1052			−0.391567
$667$	25.0822	−	43.4437i	0.971188	−	1.68215i
$668$	33.3469	+	57.7585i	1.29023	+	2.23474i
$669$	−4.01628	−	6.95639i	−0.155278	−	0.268950i
$670$	15.9220	−	27.5778i	0.615122	−	1.06542i
$671$	−10.5791			−0.408401
$672$	−2.87935	−	1.40287i	−0.111073	−	0.0541170i
$673$	27.6877			1.06728			0.533641	−	0.845711i	$-0.320824\pi$
$673$	27.6877			1.06728			0.533641	+	0.845711i	$0.320824\pi$
$674$	−15.7514	+	27.2822i	−0.606721	+	1.05087i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−61.8100	−	107.058i	−2.37731	−	4.11762i
$677$	7.54025	−	13.0601i	0.289795	−	0.501940i	−0.683965	−	0.729514i	$-0.739746\pi$
$677$	7.54025	−	13.0601i	0.289795	−	0.501940i	0.973761	+	0.227574i	$0.0730794\pi$
$678$	−10.2694			−0.394394
$679$	−2.74633	−	39.0417i	−0.105394	−	1.49828i
$680$	−26.0293			−0.998180
$681$	4.34697	−	7.52918i	0.166576	−	0.288519i
$682$	1.03264	+	1.78859i	0.0395419	+	0.0684885i
$683$	19.0040	+	32.9158i	0.727167	+	1.25949i	0.958076	+	0.286514i	$0.0924965\pi$
$683$	19.0040	+	32.9158i	0.727167	+	1.25949i	−0.230909	+	0.972975i	$0.574170\pi$
$684$	3.56052	−	6.16700i	0.136140	−	0.235801i
$685$	−7.06007			−0.269751
$686$	−42.6955	−	13.8139i	−1.63012	−	0.527418i
$687$	−0.184805			−0.00705076
$688$	−2.22085	+	3.84663i	−0.0846692	+	0.146651i
$689$	30.6604	+	53.1054i	1.16807	+	2.02315i
$690$	8.88102	+	15.3824i	0.338095	+	0.585597i
$691$	1.02113	−	1.76865i	0.0388456	−	0.0672826i	−0.845949	−	0.533264i	$-0.820965\pi$
$691$	1.02113	−	1.76865i	0.0388456	−	0.0672826i	0.884795	+	0.465981i	$0.154299\pi$
$692$	−8.07445			−0.306944
$693$	0.185653	+	2.63923i	0.00705236	+	0.100256i
$694$	−18.9542			−0.719492
$695$	−9.68502	+	16.7749i	−0.367374	+	0.636310i
$696$	15.5109	+	26.8657i	0.587940	+	1.01834i
$697$	2.76547	+	4.78993i	0.104750	+	0.181432i
$698$	−17.9620	+	31.1110i	−0.679870	+	1.17757i
$699$	−16.6847			−0.631074
$700$	9.20687	+	4.48577i	0.347987	+	0.169546i
$701$	−14.9641			−0.565185			−0.282592	−	0.959240i	$-0.591194\pi$
$701$	−14.9641			−0.565185			−0.282592	+	0.959240i	$0.591194\pi$
$702$	−8.12116	+	14.0663i	−0.306513	+	0.530897i
$703$	−3.83608	−	6.64429i	−0.144681	−	0.250594i
$704$	−4.70886	−	8.15599i	−0.177472	−	0.307390i
$705$	−6.48918	+	11.2396i	−0.244397	+	0.423308i
$706$	−35.6003			−1.33984
$707$	−0.345411	+	0.233191i	−0.0129905	+	0.00877005i
$708$	50.8350			1.91050
$709$	−19.8643	+	34.4060i	−0.746020	+	1.29214i	0.203697	+	0.979034i	$0.434704\pi$
$709$	−19.8643	+	34.4060i	−0.746020	+	1.29214i	−0.949717	+	0.313110i	$0.898629\pi$
$710$	−1.08104	−	1.87242i	−0.0405708	−	0.0702707i
$711$	0.364703	+	0.631684i	0.0136774	+	0.0236900i
$712$	8.40529	−	14.5584i	0.315001	−	0.545598i
$713$	6.24836			0.234003
$714$	−30.5076	+	20.5960i	−1.14172	+	0.770787i
$715$	6.70339			0.250693
$716$	−28.4429	+	49.2645i	−1.06296	+	1.84110i
$717$	6.56675	+	11.3739i	0.245240	+	0.424768i
$718$	29.8419	+	51.6878i	1.11369	+	1.92897i
$719$	8.92041	−	15.4506i	0.332675	−	0.576211i	−0.650360	−	0.759626i	$-0.725382\pi$
$719$	8.92041	−	15.4506i	0.332675	−	0.576211i	0.983035	+	0.183415i	$0.0587154\pi$
$720$	−3.24223			−0.120831
$721$	−32.1277	−	15.6532i	−1.19650	−	0.582957i
$722$	−37.8371			−1.40815
$723$	6.10161	−	10.5683i	0.226921	−	0.393039i
$724$	−6.68249	−	11.5744i	−0.248353	−	0.430160i
$725$	3.42158	+	5.92635i	0.127074	+	0.220099i
$726$	−1.21150	+	2.09838i	−0.0449630	+	0.0778782i
$727$	30.7133			1.13909			0.569547	−	0.821959i	$-0.307119\pi$
$727$	30.7133			1.13909			0.569547	+	0.821959i	$0.307119\pi$
$728$	−5.64165	−	80.2015i	−0.209094	−	2.97247i
$729$	1.00000			0.0370370
$730$	20.3209	−	35.1968i	0.752109	−	1.30269i
$731$	−3.93304	−	6.81222i	−0.145469	−	0.251959i
$732$	−20.4754	−	35.4645i	−0.756794	−	1.31081i
$733$	−0.918305	+	1.59055i	−0.0339184	+	0.0587483i	−0.882486	−	0.470338i	$-0.844132\pi$
$733$	−0.918305	+	1.59055i	−0.0339184	+	0.0587483i	0.848568	+	0.529086i	$0.177465\pi$
$734$	−85.3543			−3.15048
$735$	6.93107	−	0.979959i	0.255656	−	0.0361463i
$736$	−8.87435			−0.327113
$737$	6.57121	−	11.3817i	0.242054	−	0.419249i
$738$	1.16700	+	2.02130i	0.0429578	+	0.0744050i
$739$	−8.84431	−	15.3188i	−0.325343	−	0.563511i	0.656238	−	0.754554i	$-0.272147\pi$
$739$	−8.84431	−	15.3188i	−0.325343	−	0.563511i	−0.981582	+	0.191042i	$0.938813\pi$
$740$	−8.07189	+	13.9809i	−0.296728	+	0.513949i
$741$	−12.3317			−0.453016
$742$	4.11498	+	58.4984i	0.151066	+	2.14754i
$743$	10.6519			0.390780			0.195390	−	0.980726i	$-0.437403\pi$
$743$	10.6519			0.390780			0.195390	+	0.980726i	$0.437403\pi$
$744$	−1.93200	+	3.34632i	−0.0708305	+	0.122682i
$745$	−2.95104	−	5.11135i	−0.108118	−	0.187266i
$746$	−10.4998	−	18.1862i	−0.384425	−	0.665844i
$747$	−5.10131	+	8.83572i	−0.186647	+	0.323282i
$748$	−22.2263			−0.812675
$749$	3.05505	+	1.48848i	0.111629	+	0.0543878i
$750$	−2.42300			−0.0884755
$751$	−24.1504	+	41.8298i	−0.881261	+	1.52639i	−0.0313219	+	0.999509i	$0.509972\pi$
$751$	−24.1504	+	41.8298i	−0.881261	+	1.52639i	−0.849940	+	0.526880i	$0.823362\pi$
$752$	21.0394	+	36.4414i	0.767230	+	1.32888i
$753$	−7.33093	−	12.6975i	−0.267154	−	0.462724i
$754$	55.5744	−	96.2577i	2.02390	−	3.50550i
$755$	−10.7746			−0.392126
$756$	−8.48823	+	5.73050i	−0.308714	+	0.208416i
$757$	6.18279			0.224717			0.112359	−	0.993668i	$-0.464159\pi$
$757$	6.18279			0.224717			0.112359	+	0.993668i	$0.464159\pi$
$758$	−0.397599	+	0.688662i	−0.0144415	+	0.0250133i
$759$	3.66530	+	6.34849i	0.133042	+	0.230436i
$760$	−4.16974	−	7.22220i	−0.151252	−	0.261977i
$761$	−18.7900	+	32.5452i	−0.681137	+	1.17976i	0.293497	+	0.955960i	$0.405181\pi$
$761$	−18.7900	+	32.5452i	−0.681137	+	1.17976i	−0.974634	+	0.223804i	$0.928152\pi$
$762$	−39.1460			−1.41811
$763$	29.7430	−	20.0799i	1.07677	−	0.726941i
$764$	18.7401			0.677991
$765$	2.87093	−	4.97260i	0.103799	−	0.179785i
$766$	15.1119	+	26.1745i	0.546013	+	0.945723i
$767$	−44.0162	−	76.2383i	−1.58933	−	2.75281i
$768$	15.2944	−	26.4907i	0.551890	−	0.955901i
$769$	−14.9021			−0.537383			−0.268692	−	0.963226i	$-0.586591\pi$
$769$	−14.9021			−0.537383			−0.268692	+	0.963226i	$0.586591\pi$
$770$	5.76302	+	2.80786i	0.207685	+	0.101188i
$771$	−10.5172			−0.378769
$772$	−11.4599	+	19.8491i	−0.412450	+	0.714384i
$773$	10.9454	+	18.9580i	0.393679	+	0.681872i	0.992932	−	0.118688i	$-0.0378689\pi$
$773$	10.9454	+	18.9580i	0.393679	+	0.681872i	−0.599253	+	0.800560i	$0.704536\pi$
$774$	−1.65970	−	2.87468i	−0.0596566	−	0.103328i
$775$	−0.426183	+	0.738170i	−0.0153089	+	0.0265159i
$776$	67.0598			2.40731
$777$	0.774267	+	11.0069i	0.0277767	+	0.394872i
$778$	−43.4348			−1.55721
$779$	−0.886022	+	1.53464i	−0.0317450	+	0.0549840i
$780$	12.9742	+	22.4719i	0.464550	+	0.804625i
$781$	−0.446158	−	0.772769i	−0.0159648	−	0.0276519i
$782$	−50.9936	+	88.3235i	−1.82353	+	3.15844i
$783$	−6.84316			−0.244555
$784$	8.48448	−	21.0501i	0.303017	−	0.751788i
$785$	8.18620			0.292178
$786$	−18.3171	+	31.7262i	−0.653350	+	1.13164i
$787$	−9.66231	−	16.7356i	−0.344424	−	0.596560i	0.640825	−	0.767687i	$-0.278592\pi$
$787$	−9.66231	−	16.7356i	−0.344424	−	0.596560i	−0.985249	+	0.171127i	$0.945259\pi$
$788$	−26.6872	−	46.2236i	−0.950692	−	1.64665i
$789$	−4.95413	+	8.58081i	−0.176372	+	0.305485i
$790$	1.76735			0.0628795
$791$	0.786851	+	11.1858i	0.0279772	+	0.397723i
$792$	−4.53326			−0.161082
$793$	−35.4579	+	61.4148i	−1.25915	+	2.18090i
$794$	13.5293	+	23.4334i	0.480136	+	0.831620i
$795$	−4.57386	−	7.92216i	−0.162218	−	0.280970i
$796$	−52.3333	+	90.6439i	−1.85490	+	3.21279i
$797$	36.0075			1.27545			0.637725	−	0.770264i	$-0.279876\pi$
$797$	36.0075			1.27545			0.637725	+	0.770264i	$0.279876\pi$
$798$	−10.6018	−	5.16539i	−0.375299	−	0.182853i
$799$	−74.5199			−2.63633
$800$	0.605295	−	1.04840i	0.0214004	−	0.0370666i
$801$	1.85414	+	3.21146i	0.0655127	+	0.113471i
$802$	24.3781	+	42.2241i	0.860820	+	1.49098i
$803$	8.38665	−	14.5261i	0.295959	−	0.512615i
$804$	50.8734			1.79417
$805$	16.0746	−	10.8522i	0.566557	−	0.382489i
$806$	13.8444			0.487648
$807$	3.83907	−	6.64946i	0.135141	−	0.234072i
$808$	−0.357038	−	0.618409i	−0.0125606	−	0.0217555i
$809$	10.3431	+	17.9148i	0.363644	+	0.629851i	0.988558	−	0.150844i	$-0.0481990\pi$
$809$	10.3431	+	17.9148i	0.363644	+	0.629851i	−0.624913	+	0.780694i	$0.714866\pi$
$810$	1.21150	−	2.09838i	0.0425678	−	0.0737295i
$811$	7.43118			0.260944			0.130472	−	0.991452i	$-0.458351\pi$
$811$	7.43118			0.260944			0.130472	+	0.991452i	$0.458351\pi$
$812$	58.0863	−	39.2148i	2.03843	−	1.37617i
$813$	6.44304			0.225967
$814$	−5.05258	+	8.75133i	−0.177093	+	0.306734i
$815$	0.757470	+	1.31198i	0.0265330	+	0.0459565i
$816$	−9.30822	−	16.1223i	−0.325853	−	0.564394i
$817$	1.26010	−	2.18255i	0.0440852	−	0.0763577i
$818$	−54.9765			−1.92221
$819$	15.9438	+	7.76813i	0.557121	+	0.271440i
$820$	3.72874			0.130213
$821$	3.05271	−	5.28745i	0.106540	−	0.184533i	−0.807826	−	0.589421i	$-0.799356\pi$
$821$	3.05271	−	5.28745i	0.106540	−	0.184533i	0.914366	+	0.404888i	$0.132689\pi$
$822$	−8.55327	−	14.8147i	−0.298330	−	0.516722i
$823$	−13.7636	−	23.8392i	−0.479768	−	0.830983i	0.519962	−	0.854189i	$-0.325946\pi$
$823$	−13.7636	−	23.8392i	−0.479768	−	0.830983i	−0.999731	+	0.0232060i	$0.992613\pi$
$824$	30.6171	−	53.0303i	1.06660	−	1.84740i
$825$	−1.00000			−0.0348155
$826$	−5.90748	−	83.9805i	−0.205547	−	2.92206i
$827$	7.09637			0.246765			0.123383	−	0.992359i	$-0.460626\pi$
$827$	7.09637			0.246765			0.123383	+	0.992359i	$0.460626\pi$
$828$	−14.1881	+	24.5745i	−0.493071	+	0.854025i
$829$	−6.93300	−	12.0083i	−0.240793	−	0.417066i	0.720147	−	0.693821i	$-0.244074\pi$
$829$	−6.93300	−	12.0083i	−0.240793	−	0.417066i	−0.960940	+	0.276755i	$0.910741\pi$
$830$	12.3605	+	21.4090i	0.429038	+	0.743116i
$831$	8.97453	−	15.5443i	0.311323	−	0.539227i
$832$	−63.1307			−2.18866
$833$	24.7715	+	31.6520i	0.858283	+	1.09668i
$834$	−46.9336			−1.62518
$835$	−8.61469	+	14.9211i	−0.298124	+	0.516366i
$836$	−3.56052	−	6.16700i	−0.123143	−	0.213290i
$837$	−0.426183	−	0.738170i	−0.0147310	−	0.0255149i
$838$	−11.2201	+	19.4337i	−0.387591	+	0.671327i
$839$	41.5223			1.43351			0.716755	−	0.697325i	$-0.245626\pi$
$839$	41.5223			1.43351			0.716755	+	0.697325i	$0.245626\pi$
$840$	0.841612	+	11.9643i	0.0290384	+	0.412808i
$841$	17.8288			0.614788
$842$	3.51125	−	6.08166i	0.121006	−	0.209588i
$843$	4.65378	+	8.06059i	0.160285	+	0.277621i
$844$	11.5623	+	20.0265i	0.397991	+	0.689340i
$845$	15.9677	−	27.6569i	0.549307	−	0.951428i
$846$	−31.4466			−1.08116
$847$	2.37847	+	1.15883i	0.0817251	+	0.0398180i
$848$	−29.6591			−1.01850
$849$	1.37239	−	2.37704i	0.0471002	−	0.0815799i
$850$	−6.95626	−	12.0486i	−0.238598	−	0.413264i
$851$	15.2862	+	26.4765i	0.524004	+	0.907602i
$852$	1.72705	−	2.99133i	0.0591677	−	0.102481i
$853$	48.7251			1.66832			0.834158	−	0.551526i	$-0.185954\pi$
$853$	48.7251			1.66832			0.834158	+	0.551526i	$0.185954\pi$
$854$	−56.2086	+	37.9471i	−1.92342	+	1.29852i
$855$	1.83962			0.0629137
$856$	−2.91140	+	5.04269i	−0.0995095	+	0.172356i
$857$	−11.2127	−	19.4209i	−0.383017	−	0.663406i	0.608475	−	0.793573i	$-0.291782\pi$
$857$	−11.2127	−	19.4209i	−0.383017	−	0.663406i	−0.991492	+	0.130168i	$0.958448\pi$
$858$	8.12116	+	14.0663i	0.277252	+	0.480214i
$859$	0.575366	−	0.996563i	0.0196312	−	0.0340023i	−0.856043	−	0.516905i	$-0.827084\pi$
$859$	0.575366	−	0.996563i	0.0196312	−	0.0340023i	0.875674	+	0.482903i	$0.160417\pi$
$860$	−5.30299			−0.180830
$861$	2.11226	−	1.42601i	0.0719858	−	0.0485985i
$862$	12.9405			0.440755
$863$	−9.38388	+	16.2534i	−0.319431	+	0.553270i	−0.980369	−	0.197170i	$-0.936825\pi$
$863$	−9.38388	+	16.2534i	−0.319431	+	0.553270i	0.660939	+	0.750440i	$0.270158\pi$
$864$	0.605295	+	1.04840i	0.0205925	+	0.0356673i
$865$	−1.04296	−	1.80646i	−0.0354617	−	0.0614215i
$866$	18.1837	−	31.4951i	0.617907	−	1.07025i
$867$	15.9689			0.542334
$868$	7.84763	+	3.82352i	0.266366	+	0.129779i
$869$	0.729406			0.0247434
$870$	−8.29049	+	14.3595i	−0.281074	+	0.486834i
$871$	−44.0494	−	76.2958i	−1.49256	−	2.58519i
$872$	30.7443	+	53.2507i	1.04113	+	1.80330i
$873$	−7.39642	+	12.8110i	−0.250331	+	0.433586i
$874$	−32.6754			−1.10526
$875$	0.185653	+	2.63923i	0.00627620	+	0.0892222i
$876$	64.9283			2.19372
$877$	−12.2457	+	21.2102i	−0.413509	+	0.716219i	−0.995271	−	0.0971404i	$-0.969030\pi$
$877$	−12.2457	+	21.2102i	−0.413509	+	0.716219i	0.581761	+	0.813359i	$0.302364\pi$
$878$	−9.05073	−	15.6763i	−0.305447	−	0.529051i
$879$	12.5321	+	21.7063i	0.422698	+	0.732134i
$880$	−1.62112	+	2.80786i	−0.0546478	+	0.0946528i
$881$	−1.63864			−0.0552071			−0.0276035	−	0.999619i	$-0.508788\pi$
$881$	−1.63864			−0.0552071			−0.0276035	+	0.999619i	$0.508788\pi$
$882$	10.4533	+	13.3568i	0.351981	+	0.449746i
$883$	18.8173			0.633252			0.316626	−	0.948550i	$-0.397450\pi$
$883$	18.8173			0.633252			0.316626	+	0.948550i	$0.397450\pi$
$884$	−74.4959	+	129.031i	−2.50557	+	4.33977i
$885$	6.56626	+	11.3731i	0.220722	+	0.382302i
$886$	18.4329	+	31.9267i	0.619266	+	1.07260i
$887$	22.6540	−	39.2379i	0.760647	−	1.31748i	−0.181871	−	0.983322i	$-0.558215\pi$
$887$	22.6540	−	39.2379i	0.760647	−	1.31748i	0.942518	−	0.334156i	$-0.108451\pi$
$888$	−18.9060			−0.634445
$889$	2.99940	+	42.6394i	0.100597	+	1.43008i
$890$	8.98515			0.301183
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	−15.5467	−	26.9277i	−0.520543	−	0.901606i
$893$	−11.9376	−	20.6766i	−0.399477	−	0.691915i
$894$	7.15037	−	12.3848i	0.239144	−	0.414210i
$895$	−14.6956			−0.491221
$896$	−48.5159	−	23.6379i	−1.62080	−	0.789686i
$897$	49.1399			1.64073
$898$	−14.2834	+	24.7397i	−0.476645	+	0.825573i
$899$	2.91644	+	5.05142i	0.0972687	+	0.168474i
$900$	−1.93546	−	3.35232i	−0.0645155	−	0.111744i
$901$	26.2625	−	45.4879i	0.874930	−	1.51542i
$902$	2.33400			0.0777135
$903$	−3.00405	+	2.02807i	−0.0999685	+	0.0674899i
$904$	−19.2133			−0.639025
$905$	1.72633	−	2.99009i	0.0573851	−	0.0993938i
$906$	−13.0534	−	22.6091i	−0.433669	−	0.751137i
$907$	−15.9918	−	27.6986i	−0.530998	−	0.919715i	−0.999346	−	0.0361712i	$-0.988484\pi$
$907$	−15.9918	−	27.6986i	−0.530998	−	0.919715i	0.468348	−	0.883544i	$-0.344849\pi$
$908$	16.8268	−	29.1449i	0.558418	−	0.967208i
$909$	0.157519			0.00522459
$910$	35.6164	−	24.0450i	1.18067	−	0.797086i
$911$	−53.7406			−1.78051			−0.890253	−	0.455467i	$-0.849472\pi$
$911$	−53.7406			−1.78051			−0.890253	+	0.455467i	$0.849472\pi$
$912$	2.98224	−	5.16539i	0.0987518	−	0.171043i
$913$	5.10131	+	8.83572i	0.168829	+	0.292420i
$914$	5.01591	+	8.68781i	0.165912	+	0.287367i
$915$	5.28954	−	9.16175i	0.174867	−	0.302878i
$916$	−0.715368			−0.0236364
$917$	35.9609	+	17.5209i	1.18753	+	0.578590i
$918$	13.9125			0.459182
$919$	2.94798	−	5.10606i	0.0972450	−	0.168433i	−0.813298	−	0.581847i	$-0.802330\pi$
$919$	2.94798	−	5.10606i	0.0972450	−	0.168433i	0.910543	+	0.413414i	$0.135664\pi$
$920$	16.6158	+	28.7794i	0.547806	+	0.948827i
$921$	6.91453	+	11.9763i	0.227842	+	0.394633i
$922$	−33.4391	+	57.9182i	−1.10126	+	1.90743i
$923$	−5.98155			−0.196885
$924$	0.718648	+	10.2163i	0.0236418	+	0.336091i
$925$	−4.17052			−0.137126
$926$	−34.9636	+	60.5587i	−1.14897	+	1.99008i
$927$	6.75387	+	11.6980i	0.221826	+	0.384214i
$928$	−4.14213	−	7.17438i	−0.135972	−	0.235510i
$929$	25.8091	−	44.7026i	0.846768	−	1.46665i	−0.0373089	−	0.999304i	$-0.511879\pi$
$929$	25.8091	−	44.7026i	0.846768	−	1.46665i	0.884077	−	0.467341i	$-0.154788\pi$
$930$	−2.06528			−0.0677233
$931$	−4.81403	+	11.9437i	−0.157774	+	0.391437i
$932$	−64.5854			−2.11557
$933$	2.60354	−	4.50947i	0.0852362	−	0.147633i
$934$	−29.3107	−	50.7677i	−0.959077	−	1.66117i
$935$	−2.87093	−	4.97260i	−0.0938894	−	0.162621i
$936$	−15.1941	+	26.3170i	−0.496635	+	0.860198i
$937$	−13.1633			−0.430025			−0.215012	−	0.976611i	$-0.568979\pi$
$937$	−13.1633			−0.430025			−0.215012	+	0.976611i	$0.568979\pi$
$938$	−5.91194	−	84.0439i	−0.193032	−	2.74413i
$939$	−0.00336763			−0.000109898
$940$	−25.1192	+	43.5077i	−0.819297	+	1.41906i
$941$	−25.6042	−	44.3477i	−0.834672	−	1.44569i	−0.894297	−	0.447474i	$-0.852324\pi$
$941$	−25.6042	−	44.3477i	−0.834672	−	1.44569i	0.0596249	−	0.998221i	$-0.481010\pi$
$942$	9.91758	+	17.1778i	0.323132	+	0.559682i
$943$	3.53066	−	6.11529i	0.114974	−	0.199141i
$944$	42.5787			1.38582
$945$	−2.37847	−	1.15883i	−0.0773715	−	0.0376969i
$946$	−3.31939			−0.107923
$947$	17.7797	−	30.7953i	0.577762	−	1.00071i	−0.417973	−	0.908459i	$-0.637259\pi$
$947$	17.7797	−	30.7953i	0.577762	−	1.00071i	0.995735	−	0.0922541i	$-0.0294072\pi$
$948$	1.41174	+	2.44521i	0.0458512	+	0.0794166i
$949$	−56.2190	−	97.3743i	−1.82495	−	3.16090i
$950$	2.22870	−	3.86022i	0.0723085	−	0.125242i
$951$	−3.93995			−0.127762
$952$	−57.0775	+	38.5337i	−1.84989	+	1.24888i
$953$	−1.31891			−0.0427236			−0.0213618	−	0.999772i	$-0.506800\pi$
$953$	−1.31891			−0.0427236			−0.0213618	+	0.999772i	$0.506800\pi$
$954$	11.0825	−	19.1954i	0.358808	−	0.621474i
$955$	2.42061	+	4.19263i	0.0783293	+	0.135670i
$956$	25.4194	+	44.0277i	0.822123	+	1.42396i
$957$	−3.42158	+	5.92635i	−0.110604	+	0.191572i
$958$	−0.642059			−0.0207440
$959$	−15.4814	+	10.4517i	−0.499921	+	0.337503i
$960$	9.41773			0.303956
$961$	15.1367	−	26.2176i	0.488282	−	0.845729i
$962$	33.8694	+	58.6636i	1.09199	+	1.89139i
$963$	−0.642230	−	1.11238i	−0.0206956	−	0.0358458i
$964$	23.6189	−	40.9091i	0.760713	−	1.31759i
$965$	−5.92099			−0.190603
$966$	42.2464	+	20.5833i	1.35926	+	0.662256i
$967$	−41.3797			−1.33068			−0.665340	−	0.746540i	$-0.731714\pi$
$967$	−41.3797			−1.33068			−0.665340	+	0.746540i	$0.731714\pi$
$968$	−2.26663	+	3.92592i	−0.0728523	+	0.126184i
$969$	5.28142	+	9.14768i	0.169664	+	0.293866i
$970$	17.9215	+	31.0410i	0.575426	+	0.996667i
$971$	8.26138	−	14.3091i	0.265120	−	0.459202i	−0.702475	−	0.711709i	$-0.747922\pi$
$971$	8.26138	−	14.3091i	0.265120	−	0.459202i	0.967595	+	0.252507i	$0.0812550\pi$
$972$	3.87093			0.124160
$973$	3.59610	+	51.1220i	0.115286	+	1.63889i
$974$	−8.62991			−0.276520
$975$	−3.35170	+	5.80531i	−0.107340	+	0.185919i
$976$	−17.1499	−	29.7046i	−0.548956	−	0.950819i
$977$	21.4131	+	37.0885i	0.685065	+	1.18657i	0.973417	+	0.229042i	$0.0735593\pi$
$977$	21.4131	+	37.0885i	0.685065	+	1.18657i	−0.288352	+	0.957524i	$0.593107\pi$
$978$	−1.83535	+	3.17892i	−0.0586880	+	0.101651i
$979$	3.70827			0.118517
$980$	26.8297	−	3.79335i	0.857042	−	0.121174i
$981$	−13.5639			−0.433061
$982$	−11.4423	+	19.8187i	−0.365139	+	0.632440i
$983$	−3.41746	−	5.91922i	−0.109000	−	0.188794i	0.806365	−	0.591418i	$-0.201432\pi$
$983$	−3.41746	−	5.91922i	−0.109000	−	0.188794i	−0.915365	+	0.402624i	$0.868098\pi$
$984$	2.18337	+	3.78171i	0.0696033	+	0.120556i
$985$	6.89426	−	11.9412i	0.219669	−	0.380479i
$986$	−95.2056			−3.03196
$987$	2.40947	+	34.2529i	0.0766942	+	1.09028i
$988$	−47.7351			−1.51866
$989$	−5.02129	+	8.69713i	−0.159668	+	0.276552i
$990$	−1.21150	−	2.09838i	−0.0385040	−	0.0666909i
$991$	6.09325	+	10.5538i	0.193558	+	0.335253i	0.946427	−	0.322918i	$-0.104664\pi$
$991$	6.09325	+	10.5538i	0.193558	+	0.335253i	−0.752869	+	0.658171i	$0.771330\pi$
$992$	0.515932	−	0.893621i	0.0163809	−	0.0283725i
$993$	−34.3423			−1.08982
$994$	−5.14244	−	2.50550i	−0.163108	−	0.0794696i
$995$	−27.0391			−0.857198
$996$	−19.7468	+	34.2025i	−0.625701	+	1.08375i
$997$	10.8288	+	18.7560i	0.342951	+	0.594008i	0.984979	−	0.172672i	$-0.0552402\pi$
$997$	10.8288	+	18.7560i	0.342951	+	0.594008i	−0.642028	+	0.766681i	$0.721907\pi$
$998$	−18.6677	−	32.3334i	−0.590915	−	1.02350i
$999$	2.08526	−	3.61177i	0.0659746	−	0.114271i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.q.j.331.1	✓	16
7.2	even	3		8085.2.a.cf.1.8		8
7.4	even	3	inner	1155.2.q.j.991.1	yes	16
7.5	odd	6		8085.2.a.ce.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.j.331.1	✓	16	1.1	even	1	trivial
1155.2.q.j.991.1	yes	16	7.4	even	3	inner
8085.2.a.ce.1.8		8	7.5	odd	6
8085.2.a.cf.1.8		8	7.2	even	3

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.21150 + 2.09838i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.93546 - 3.35232i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.42300 q^{6} +(-0.185653 - 2.63923i) q^{7} +4.53326 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.21150 + 2.09838i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.93546 - 3.35232i) q^{4} +(0.500000 - 0.866025i) q^{5} +2.42300 q^{6} +(-0.185653 - 2.63923i) q^{7} +4.53326 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.21150 + 2.09838i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-1.93546 + 3.35232i) q^{12} +6.70339 q^{13} +(5.76302 + 2.80786i) q^{14} -1.00000 q^{15} +(-1.62112 + 2.80786i) q^{16} +(-2.87093 - 4.97260i) q^{17} +(-1.21150 - 2.09838i) q^{18} +(0.919810 - 1.59316i) q^{19} -3.87093 q^{20} +(-2.19281 + 1.48039i) q^{21} -2.42300 q^{22} +(-3.66530 + 6.34849i) q^{23} +(-2.26663 - 3.92592i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-8.12116 + 14.0663i) q^{26} +1.00000 q^{27} +(-8.48823 + 5.73050i) q^{28} -6.84316 q^{29} +(1.21150 - 2.09838i) q^{30} +(-0.426183 - 0.738170i) q^{31} +(0.605295 + 1.04840i) q^{32} +(0.500000 - 0.866025i) q^{33} +13.9125 q^{34} +(-2.37847 - 1.15883i) q^{35} +3.87093 q^{36} +(2.08526 - 3.61177i) q^{37} +(2.22870 + 3.86022i) q^{38} +(-3.35170 - 5.80531i) q^{39} +(2.26663 - 3.92592i) q^{40} -0.963267 q^{41} +(-0.449836 - 6.39485i) q^{42} +1.36995 q^{43} +(1.93546 - 3.35232i) q^{44} +(0.500000 + 0.866025i) q^{45} +(-8.88102 - 15.3824i) q^{46} +(6.48918 - 11.2396i) q^{47} +3.24223 q^{48} +(-6.93107 + 0.979959i) q^{49} +2.42300 q^{50} +(-2.87093 + 4.97260i) q^{51} +(-12.9742 - 22.4719i) q^{52} +(4.57386 + 7.92216i) q^{53} +(-1.21150 + 2.09838i) q^{54} +1.00000 q^{55} +(-0.841612 - 11.9643i) q^{56} -1.83962 q^{57} +(8.29049 - 14.3595i) q^{58} +(-6.56626 - 11.3731i) q^{59} +(1.93546 + 3.35232i) q^{60} +(-5.28954 + 9.16175i) q^{61} +2.06528 q^{62} +(2.37847 + 1.15883i) q^{63} -9.41773 q^{64} +(3.35170 - 5.80531i) q^{65} +(1.21150 + 2.09838i) q^{66} +(-6.57121 - 11.3817i) q^{67} +(-11.1132 + 19.2486i) q^{68} +7.33060 q^{69} +(5.31319 - 3.58700i) q^{70} -0.892317 q^{71} +(-2.26663 + 3.92592i) q^{72} +(-8.38665 - 14.5261i) q^{73} +(5.05258 + 8.75133i) q^{74} +(-0.500000 + 0.866025i) q^{75} -7.12104 q^{76} +(2.19281 - 1.48039i) q^{77} +16.2423 q^{78} +(0.364703 - 0.631684i) q^{79} +(1.62112 + 2.80786i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.16700 - 2.02130i) q^{82} +10.2026 q^{83} +(9.20687 + 4.48577i) q^{84} -5.74186 q^{85} +(-1.65970 + 2.87468i) q^{86} +(3.42158 + 5.92635i) q^{87} +(2.26663 + 3.92592i) q^{88} +(1.85414 - 3.21146i) q^{89} -2.42300 q^{90} +(-1.24450 - 17.6918i) q^{91} +28.3762 q^{92} +(-0.426183 + 0.738170i) q^{93} +(15.7233 + 27.2335i) q^{94} +(-0.919810 - 1.59316i) q^{95} +(0.605295 - 1.04840i) q^{96} +14.7928 q^{97} +(6.34066 - 15.7312i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9}+O(q^{10}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9	\( 16 q - 8 q^{3} - 10 q^{4} + 8 q^{5} - 8 q^{9} + 8 q^{11} - 10 q^{12} + 8 q^{13} + 6 q^{14} - 16 q^{15} - 2 q^{16} - 4 q^{17} - 9 q^{19} - 20 q^{20} + 3 q^{21} + 5 q^{23} - 8 q^{25} - 32 q^{26} + 16 q^{27} + 2 q^{28} - 10 q^{29} - 5 q^{31} + 8 q^{33} + 3 q^{35} + 20 q^{36} - 7 q^{37} + 8 q^{38} - 4 q^{39} + 18 q^{41} + 28 q^{43} + 10 q^{44} + 8 q^{45} - 18 q^{46} + 5 q^{47} + 4 q^{48} - 20 q^{49} - 4 q^{51} - 8 q^{52} + q^{53} + 16 q^{55} + 42 q^{56} + 18 q^{57} - 10 q^{58} - 16 q^{59} + 10 q^{60} - 26 q^{61} - 32 q^{62} - 3 q^{63} - 16 q^{64} + 4 q^{65} - 3 q^{67} - 88 q^{68} - 10 q^{69} + 6 q^{70} - 60 q^{71} - 15 q^{73} + 18 q^{74} - 8 q^{75} + 44 q^{76} - 3 q^{77} + 64 q^{78} - 11 q^{79} + 2 q^{80} - 8 q^{81} - 42 q^{82} + 24 q^{83} - 10 q^{84} - 8 q^{85} + 48 q^{86} + 5 q^{87} + 6 q^{91} + 56 q^{92} - 5 q^{93} - 24 q^{94} + 9 q^{95} + 88 q^{97} - 24 q^{98} - 16 q^{99}+O(q^{100}) \) 16 * q - 8 * q^3 - 10 * q^4 + 8 * q^5 - 8 * q^9 + 8 * q^11 - 10 * q^12 + 8 * q^13 + 6 * q^14 - 16 * q^15 - 2 * q^16 - 4 * q^17 - 9 * q^19 - 20 * q^20 + 3 * q^21 + 5 * q^23 - 8 * q^25 - 32 * q^26 + 16 * q^27 + 2 * q^28 - 10 * q^29 - 5 * q^31 + 8 * q^33 + 3 * q^35 + 20 * q^36 - 7 * q^37 + 8 * q^38 - 4 * q^39 + 18 * q^41 + 28 * q^43 + 10 * q^44 + 8 * q^45 - 18 * q^46 + 5 * q^47 + 4 * q^48 - 20 * q^49 - 4 * q^51 - 8 * q^52 + q^53 + 16 * q^55 + 42 * q^56 + 18 * q^57 - 10 * q^58 - 16 * q^59 + 10 * q^60 - 26 * q^61 - 32 * q^62 - 3 * q^63 - 16 * q^64 + 4 * q^65 - 3 * q^67 - 88 * q^68 - 10 * q^69 + 6 * q^70 - 60 * q^71 - 15 * q^73 + 18 * q^74 - 8 * q^75 + 44 * q^76 - 3 * q^77 + 64 * q^78 - 11 * q^79 + 2 * q^80 - 8 * q^81 - 42 * q^82 + 24 * q^83 - 10 * q^84 - 8 * q^85 + 48 * q^86 + 5 * q^87 + 6 * q^91 + 56 * q^92 - 5 * q^93 - 24 * q^94 + 9 * q^95 + 88 * q^97 - 24 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more