LMFDB - Embedded newform 195.2.s.b.38.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [195,2,Mod(38,195)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(195, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("195.38");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 195 = 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	195.s (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.55708283941$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			38.8
Character	$\chi$	$=$	195.38
Dual form			195.2.s.b.77.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.299314 + 0.299314i) q^{2} +(1.72753 - 0.125002i) q^{3} +1.82082i q^{4} +(2.19735 - 0.414323i) q^{5} +(-0.479660 + 0.554490i) q^{6} +(-0.976029 - 0.976029i) q^{7} +(-1.14363 - 1.14363i) q^{8} +(2.96875 - 0.431892i) q^{9} +(-0.533684 + 0.781709i) q^{10} -1.78302 q^{11} +(0.227607 + 3.14553i) q^{12} +(-2.32186 + 2.75844i) q^{13} +0.584278 q^{14} +(3.74420 - 0.990431i) q^{15} -2.95704 q^{16} +(-3.26089 - 3.26089i) q^{17} +(-0.759317 + 1.01786i) q^{18} +6.18928 q^{19} +(0.754408 + 4.00098i) q^{20} +(-1.80813 - 1.56412i) q^{21} +(0.533684 - 0.533684i) q^{22} +(0.696530 - 0.696530i) q^{23} +(-2.11861 - 1.83270i) q^{24} +(4.65667 - 1.82082i) q^{25} +(-0.130675 - 1.52060i) q^{26} +(5.07463 - 1.11721i) q^{27} +(1.77718 - 1.77718i) q^{28} -7.33056 q^{29} +(-0.824242 + 1.41714i) q^{30} +6.61539i q^{31} +(3.17233 - 3.17233i) q^{32} +(-3.08024 + 0.222882i) q^{33} +1.95206 q^{34} +(-2.54907 - 1.74028i) q^{35} +(0.786399 + 5.40556i) q^{36} +(-5.21325 - 5.21325i) q^{37} +(-1.85254 + 1.85254i) q^{38} +(-3.66628 + 5.05553i) q^{39} +(-2.98677 - 2.03911i) q^{40} -6.45687 q^{41} +(1.00936 - 0.0730362i) q^{42} +(-1.78171 - 1.78171i) q^{43} -3.24657i q^{44} +(6.34443 - 2.17904i) q^{45} +0.416963i q^{46} +(5.69410 - 5.69410i) q^{47} +(-5.10838 + 0.369637i) q^{48} -5.09473i q^{49} +(-0.848810 + 1.93881i) q^{50} +(-6.04091 - 5.22568i) q^{51} +(-5.02263 - 4.22769i) q^{52} +(-1.74028 + 1.74028i) q^{53} +(-1.18451 + 1.85330i) q^{54} +(-3.91793 + 0.738748i) q^{55} +2.23242i q^{56} +(10.6922 - 0.773675i) q^{57} +(2.19414 - 2.19414i) q^{58} +9.15008i q^{59} +(1.80340 + 6.81753i) q^{60} +1.01503 q^{61} +(-1.98008 - 1.98008i) q^{62} +(-3.31913 - 2.47605i) q^{63} -4.01503i q^{64} +(-3.95904 + 7.02325i) q^{65} +(0.855246 - 0.988670i) q^{66} +(-3.72923 - 3.72923i) q^{67} +(5.93750 - 5.93750i) q^{68} +(1.11621 - 1.29035i) q^{69} +(1.28386 - 0.242080i) q^{70} +5.49755 q^{71} +(-3.88906 - 2.90121i) q^{72} +(1.35106 - 1.35106i) q^{73} +3.12079 q^{74} +(7.81696 - 3.72763i) q^{75} +11.2696i q^{76} +(1.74028 + 1.74028i) q^{77} +(-0.415824 - 2.61056i) q^{78} +10.2889i q^{79} +(-6.49764 + 1.22517i) q^{80} +(8.62694 - 2.56436i) q^{81} +(1.93263 - 1.93263i) q^{82} +(-7.93716 - 7.93716i) q^{83} +(2.84798 - 3.29228i) q^{84} +(-8.51636 - 5.81424i) q^{85} +1.06658 q^{86} +(-12.6638 + 0.916338i) q^{87} +(2.03911 + 2.03911i) q^{88} +3.75080i q^{89} +(-1.24676 + 2.55119i) q^{90} +(4.95852 - 0.426116i) q^{91} +(1.26826 + 1.26826i) q^{92} +(0.826940 + 11.4283i) q^{93} +3.40865i q^{94} +(13.6000 - 2.56436i) q^{95} +(5.08377 - 5.87686i) q^{96} +(6.92322 + 6.92322i) q^{97} +(1.52492 + 1.52492i) q^{98} +(-5.29335 + 0.770074i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{3} - 24 q^{10} - 24 q^{12} + 24 q^{16} + 24 q^{22} - 8 q^{25} - 16 q^{27} + 36 q^{30} - 8 q^{36} + 16 q^{40} + 12 q^{42} - 64 q^{43} - 20 q^{48} + 16 q^{51} - 72 q^{52} - 80 q^{55} + 8 q^{61}+ \cdots - 40 q^{91}+O(q^{100}) $ 32 * q - 4 * q^3 - 24 * q^10 - 24 * q^12 + 24 * q^16 + 24 * q^22 - 8 * q^25 - 16 * q^27 + 36 * q^30 - 8 * q^36 + 16 * q^40 + 12 * q^42 - 64 * q^43 - 20 * q^48 + 16 * q^51 - 72 * q^52 - 80 * q^55 + 8 * q^61 - 72 * q^66 + 44 * q^75 + 84 * q^78 + 112 * q^81 + 48 * q^82 + 20 * q^87 - 8 * q^88 + 44 * q^90 - 40 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/195\mathbb{Z}\right)^\times$.

$n$	$106$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.299314	+	0.299314i	−0.211647	+	0.211647i	−0.804967	−	0.593320i	$-0.797817\pi$
$2$	−0.299314	+	0.299314i	−0.211647	+	0.211647i	0.593320	+	0.804967i	$0.297817\pi$
$3$	1.72753	−	0.125002i	0.997392	−	0.0721702i
$3$	1.72753	−	0.125002i	0.997392	−	0.0721702i
$4$			1.82082i			0.910411i
$5$	2.19735	−	0.414323i	0.982684	−	0.185291i
$5$	2.19735	−	0.414323i	0.982684	−	0.185291i
$6$	−0.479660	+	0.554490i	−0.195820	+	0.226370i
$7$	−0.976029	−	0.976029i	−0.368904	−	0.368904i	0.498173	−	0.867078i	$-0.334004\pi$
$7$	−0.976029	−	0.976029i	−0.368904	−	0.368904i	−0.867078	+	0.498173i	$0.834004\pi$
$8$	−1.14363	−	1.14363i	−0.404333	−	0.404333i
$9$	2.96875	−	0.431892i	0.989583	−	0.143964i
$10$	−0.533684	+	0.781709i	−0.168766	+	0.247198i
$11$	−1.78302			−0.537602			−0.268801	−	0.963196i	$-0.586627\pi$
$11$	−1.78302			−0.537602			−0.268801	+	0.963196i	$0.586627\pi$
$12$	0.227607	+	3.14553i	0.0657045	+	0.908037i
$13$	−2.32186	+	2.75844i	−0.643967	+	0.765053i
$13$	−2.32186	+	2.75844i	−0.643967	+	0.765053i
$14$	0.584278			0.156155
$15$	3.74420	−	0.990431i	0.966749	−	0.255728i
$16$	−2.95704			−0.739260
$17$	−3.26089	−	3.26089i	−0.790882	−	0.790882i	0.190756	−	0.981637i	$-0.438906\pi$
$17$	−3.26089	−	3.26089i	−0.790882	−	0.790882i	−0.981637	+	0.190756i	$0.938906\pi$
$18$	−0.759317	+	1.01786i	−0.178973	+	0.239912i
$19$	6.18928			1.41992			0.709959	−	0.704243i	$-0.248714\pi$
$19$	6.18928			1.41992			0.709959	+	0.704243i	$0.248714\pi$
$20$	0.754408	+	4.00098i	0.168691	+	0.894646i
$21$	−1.80813	−	1.56412i	−0.394566	−	0.341319i
$22$	0.533684	−	0.533684i	0.113782	−	0.113782i
$23$	0.696530	−	0.696530i	0.145237	−	0.145237i	−0.630750	−	0.775986i	$-0.717253\pi$
$23$	0.696530	−	0.696530i	0.145237	−	0.145237i	0.775986	+	0.630750i	$0.217253\pi$
$24$	−2.11861	−	1.83270i	−0.432459	−	0.374098i
$25$	4.65667	−	1.82082i	0.931335	−	0.364164i
$26$	−0.130675	−	1.52060i	−0.0256274	−	0.298215i
$27$	5.07463	−	1.11721i	0.976613	−	0.215007i
$28$	1.77718	−	1.77718i	0.335855	−	0.335855i
$29$	−7.33056			−1.36125			−0.680625	−	0.732632i	$-0.738292\pi$
$29$	−7.33056			−1.36125			−0.680625	+	0.732632i	$0.738292\pi$
$30$	−0.824242	+	1.41714i	−0.150485	+	0.258733i
$31$			6.61539i			1.18816i	0.804406	+	0.594080i	$0.202484\pi$
$31$			6.61539i			1.18816i	−0.804406	+	0.594080i	$0.797516\pi$
$32$	3.17233	−	3.17233i	0.560795	−	0.560795i
$33$	−3.08024	+	0.222882i	−0.536200	+	0.0387989i
$34$	1.95206			0.334775
$35$	−2.54907	−	1.74028i	−0.430871	−	0.294162i
$36$	0.786399	+	5.40556i	0.131066	+	0.900927i
$37$	−5.21325	−	5.21325i	−0.857052	−	0.857052i	0.133937	−	0.990990i	$-0.457238\pi$
$37$	−5.21325	−	5.21325i	−0.857052	−	0.857052i	−0.990990	+	0.133937i	$0.957238\pi$
$38$	−1.85254	+	1.85254i	−0.300521	+	0.300521i
$39$	−3.66628	+	5.05553i	−0.587074	+	0.809533i
$40$	−2.98677	−	2.03911i	−0.472250	−	0.322412i
$41$	−6.45687			−1.00839			−0.504197	−	0.863589i	$-0.668211\pi$
$41$	−6.45687			−1.00839			−0.504197	+	0.863589i	$0.668211\pi$
$42$	1.00936	−	0.0730362i	0.155748	−	0.0112697i
$43$	−1.78171	−	1.78171i	−0.271708	−	0.271708i	0.558079	−	0.829788i	$-0.311538\pi$
$43$	−1.78171	−	1.78171i	−0.271708	−	0.271708i	−0.829788	+	0.558079i	$0.811538\pi$
$44$		−	3.24657i		−	0.489439i
$45$	6.34443	−	2.17904i	0.945772	−	0.324832i
$46$			0.416963i			0.0614778i
$47$	5.69410	−	5.69410i	0.830570	−	0.830570i	−0.157025	−	0.987595i	$-0.550190\pi$
$47$	5.69410	−	5.69410i	0.830570	−	0.830570i	0.987595	+	0.157025i	$0.0501902\pi$
$48$	−5.10838	+	0.369637i	−0.737332	+	0.0533525i
$49$		−	5.09473i		−	0.727819i
$50$	−0.848810	+	1.93881i	−0.120040	+	0.274188i
$51$	−6.04091	−	5.22568i	−0.845897	−	0.731741i
$52$	−5.02263	−	4.22769i	−0.696513	−	0.586275i
$53$	−1.74028	+	1.74028i	−0.239046	+	0.239046i	−0.816455	−	0.577409i	$-0.804064\pi$
$53$	−1.74028	+	1.74028i	−0.239046	+	0.239046i	0.577409	+	0.816455i	$0.304064\pi$
$54$	−1.18451	+	1.85330i	−0.161191	+	0.252203i
$55$	−3.91793	+	0.738748i	−0.528293	+	0.0996127i
$56$			2.23242i			0.298320i
$57$	10.6922	−	0.773675i	1.41621	−	0.102476i
$58$	2.19414	−	2.19414i	0.288105	−	0.288105i
$59$			9.15008i			1.19124i	0.803267	+	0.595620i	$0.203093\pi$
$59$			9.15008i			1.19124i	−0.803267	+	0.595620i	$0.796907\pi$
$60$	1.80340	+	6.81753i	0.232818	+	0.880139i
$61$	1.01503			0.129961			0.0649806	−	0.997887i	$-0.479301\pi$
$61$	1.01503			0.129961			0.0649806	+	0.997887i	$0.479301\pi$
$62$	−1.98008	−	1.98008i	−0.251470	−	0.251470i
$63$	−3.31913	−	2.47605i	−0.418170	−	0.311953i
$64$		−	4.01503i		−	0.501879i
$65$	−3.95904	+	7.02325i	−0.491059	+	0.871126i
$66$	0.855246	−	0.988670i	0.105274	−	0.121697i
$67$	−3.72923	−	3.72923i	−0.455599	−	0.455599i	0.441609	−	0.897208i	$-0.354408\pi$
$67$	−3.72923	−	3.72923i	−0.455599	−	0.455599i	−0.897208	+	0.441609i	$0.854408\pi$
$68$	5.93750	−	5.93750i	0.720027	−	0.720027i
$69$	1.11621	−	1.29035i	0.134376	−	0.155340i
$70$	1.28386	−	0.242080i	0.153451	−	0.0289341i
$71$	5.49755			0.652439			0.326220	−	0.945294i	$-0.394225\pi$
$71$	5.49755			0.652439			0.326220	+	0.945294i	$0.394225\pi$
$72$	−3.88906	−	2.90121i	−0.458330	−	0.341911i
$73$	1.35106	−	1.35106i	0.158130	−	0.158130i	−0.623608	−	0.781737i	$-0.714334\pi$
$73$	1.35106	−	1.35106i	0.158130	−	0.158130i	0.781737	+	0.623608i	$0.214334\pi$
$74$	3.12079			0.362785
$75$	7.81696	−	3.72763i	0.902624	−	0.430429i
$76$			11.2696i			1.29271i
$77$	1.74028	+	1.74028i	0.198324	+	0.198324i
$78$	−0.415824	−	2.61056i	−0.0470828	−	0.295588i
$79$			10.2889i			1.15760i	0.815471	+	0.578798i	$0.196478\pi$
$79$			10.2889i			1.15760i	−0.815471	+	0.578798i	$0.803522\pi$
$80$	−6.49764	+	1.22517i	−0.726458	+	0.136978i
$81$	8.62694	−	2.56436i	0.958549	−	0.284929i
$82$	1.93263	−	1.93263i	0.213423	−	0.213423i
$83$	−7.93716	−	7.93716i	−0.871217	−	0.871217i	0.121388	−	0.992605i	$-0.461265\pi$
$83$	−7.93716	−	7.93716i	−0.871217	−	0.871217i	−0.992605	+	0.121388i	$0.961265\pi$
$84$	2.84798	−	3.29228i	0.310740	−	0.359218i
$85$	−8.51636	−	5.81424i	−0.923729	−	0.630643i
$86$	1.06658			0.115012
$87$	−12.6638	+	0.916338i	−1.35770	+	0.0982417i
$88$	2.03911	+	2.03911i	0.217370	+	0.217370i
$89$			3.75080i			0.397584i	0.980042	+	0.198792i	$0.0637018\pi$
$89$			3.75080i			0.397584i	−0.980042	+	0.198792i	$0.936298\pi$
$90$	−1.24676	+	2.55119i	−0.131420	+	0.268919i
$91$	4.95852	−	0.426116i	0.519794	−	0.0446691i
$92$	1.26826	+	1.26826i	0.132225	+	0.132225i
$93$	0.826940	+	11.4283i	0.0857497	+	1.18506i
$94$			3.40865i			0.351575i
$95$	13.6000	−	2.56436i	1.39533	−	0.263098i
$96$	5.08377	−	5.87686i	0.518860	−	0.599805i
$97$	6.92322	+	6.92322i	0.702947	+	0.702947i	0.965042	−	0.262095i	$-0.0844134\pi$
$97$	6.92322	+	6.92322i	0.702947	+	0.702947i	−0.262095	+	0.965042i	$0.584413\pi$
$98$	1.52492	+	1.52492i	0.154041	+	0.154041i
$99$	−5.29335	+	0.770074i	−0.532002	+	0.0773954i
$100$	3.31539	+	8.47897i	0.331539	+	0.847897i
$101$			9.05829i			0.901334i	0.892692	+	0.450667i	$0.148814\pi$
$101$			9.05829i			0.901334i	−0.892692	+	0.450667i	$0.851186\pi$
$102$	3.37225	−	0.244012i	0.333902	−	0.0241608i
$103$	7.98677	+	7.98677i	0.786960	+	0.786960i	0.980995	−	0.194035i	$-0.0621574\pi$
$103$	7.98677	+	7.98677i	0.786960	+	0.786960i	−0.194035	+	0.980995i	$0.562157\pi$
$104$	5.80996	−	0.499285i	0.569713	−	0.0489589i
$105$	−4.62114	−	2.68776i	−0.450977	−	0.262299i
$106$		−	1.04178i		−	0.101187i
$107$	12.5715	+	12.5715i	1.21534	+	1.21534i	0.969248	+	0.246088i	$0.0791451\pi$
$107$	12.5715	+	12.5715i	1.21534	+	1.21534i	0.246088	+	0.969248i	$0.420855\pi$
$108$	2.03424	+	9.23999i	0.195745	+	0.889119i
$109$	17.1929			1.64679			0.823393	−	0.567472i	$-0.192079\pi$
$109$	17.1929			1.64679			0.823393	+	0.567472i	$0.192079\pi$
$110$	0.951572	−	1.39381i	0.0907289	−	0.132894i
$111$	−9.65773	−	8.35439i	−0.916671	−	0.792964i
$112$	2.88616	+	2.88616i	0.272716	+	0.272716i
$113$	3.70507	−	3.70507i	0.348544	−	0.348544i	−0.511023	−	0.859567i	$-0.670733\pi$
$113$	3.70507	−	3.70507i	0.348544	−	0.348544i	0.859567	+	0.511023i	$0.170733\pi$
$114$	−2.96875	+	3.43189i	−0.278049	+	0.321426i
$115$	1.24193	−	1.81911i	0.115811	−	0.169633i
$116$		−	13.3476i		−	1.23930i
$117$	−5.70166	+	9.19190i	−0.527119	+	0.849792i
$118$	−2.73875	−	2.73875i	−0.252122	−	0.252122i
$119$			6.36545i			0.583519i
$120$	−5.41465	−	3.14928i	−0.494287	−	0.287489i
$121$	−7.82082			−0.710984
$122$	−0.303812	+	0.303812i	−0.0275059	+	0.0275059i
$123$	−11.1545	+	0.807124i	−1.00576	+	0.0727760i
$124$	−12.0455			−1.08171
$125$	9.47792	−	5.93035i	0.847731	−	0.530426i
$126$	1.73458	−	0.252345i	0.154528	−	0.0224807i
$127$	−1.94381	+	1.94381i	−0.172485	+	0.172485i	−0.788070	−	0.615585i	$-0.788920\pi$
$127$	−1.94381	+	1.94381i	−0.172485	+	0.172485i	0.615585	+	0.788070i	$0.288920\pi$
$128$	7.54642	+	7.54642i	0.667016	+	0.667016i
$129$	−3.30068	−	2.85525i	−0.290609	−	0.251390i
$130$	−0.917159	−	3.28715i	−0.0804401	−	0.288302i
$131$		−	2.31201i		−	0.202001i	−0.994886	−	0.101001i	$-0.967796\pi$
$131$		−	2.31201i		−	0.202001i	0.994886	−	0.101001i	$-0.0322044\pi$
$132$	−0.405829	−	5.60856i	−0.0353229	−	0.488163i
$133$	−6.04091	−	6.04091i	−0.523814	−	0.523814i
$134$	2.23242			0.192852
$135$	10.6878	−	4.55743i	0.919862	−	0.392241i
$136$			7.45847i			0.639558i
$137$	−9.28076	+	9.28076i	−0.792909	+	0.792909i	−0.981966	−	0.189057i	$-0.939457\pi$
$137$	−9.28076	+	9.28076i	−0.792909	+	0.792909i	0.189057	+	0.981966i	$0.439457\pi$
$138$	0.0521213	+	0.720317i	0.00443686	+	0.0613175i
$139$		−	6.42368i		−	0.544849i	−0.962177	−	0.272425i	$-0.912174\pi$
$139$		−	6.42368i		−	0.544849i	0.962177	−	0.272425i	$-0.0878255\pi$
$140$	3.16875	−	4.64140i	0.267808	−	0.392270i
$141$	9.12498	−	10.5485i	0.768462	−	0.888347i
$142$	−1.64549	+	1.64549i	−0.138087	+	0.138087i
$143$	4.13993	−	4.91836i	0.346198	−	0.411294i
$144$	−8.77870	+	1.27712i	−0.731559	+	0.106427i
$145$	−16.1078	+	3.03722i	−1.33768	+	0.252227i
$146$			0.808782i			0.0669353i
$147$	−0.636854	−	8.80133i	−0.0525268	−	0.725921i
$148$	9.49239	−	9.49239i	0.780270	−	0.780270i
$149$		−	18.3935i		−	1.50685i	−0.657532	−	0.753427i	$-0.728400\pi$
$149$		−	18.3935i		−	1.50685i	0.657532	−	0.753427i	$-0.271600\pi$
$150$	−1.22399	+	3.45546i	−0.0999386	+	0.282137i
$151$			6.18928i			0.503676i	0.967769	+	0.251838i	$0.0810350\pi$
$151$			6.18928i			0.503676i	−0.967769	+	0.251838i	$0.918965\pi$
$152$	−7.07821	−	7.07821i	−0.574119	−	0.574119i
$153$	−11.0891	−	8.27241i	−0.896501	−	0.668784i
$154$	−1.04178			−0.0839493
$155$	2.74091	+	14.5363i	0.220155	+	1.16758i
$156$	−9.20523	−	6.67564i	−0.737008	−	0.534479i
$157$	−0.617238	+	0.617238i	−0.0492609	+	0.0492609i	−0.731308	−	0.682047i	$-0.761090\pi$
$157$	−0.617238	+	0.617238i	−0.0492609	+	0.0492609i	0.682047	+	0.731308i	$0.261090\pi$
$158$	−3.07962	−	3.07962i	−0.245002	−	0.245002i
$159$	−2.78886	+	3.22394i	−0.221171	+	0.255675i
$160$	5.65635	−	8.28509i	0.447174	−	0.654994i
$161$	−1.35967			−0.107157
$162$	−1.81462	+	3.34971i	−0.142570	+	0.263178i
$163$	1.40215	−	1.40215i	0.109824	−	0.109824i	−0.650059	−	0.759884i	$-0.725256\pi$
$163$	1.40215	−	1.40215i	0.109824	−	0.109824i	0.759884	+	0.650059i	$0.225256\pi$
$164$		−	11.7568i		−	0.918053i
$165$	−6.67601	+	1.76596i	−0.519726	+	0.137480i
$166$	4.75141			0.368781
$167$	−5.82972	+	5.82972i	−0.451117	+	0.451117i	−0.895725	−	0.444608i	$-0.853343\pi$
$167$	−5.82972	+	5.82972i	−0.451117	+	0.451117i	0.444608	+	0.895725i	$0.353343\pi$
$168$	0.279058	+	3.85659i	0.0215298	+	0.297542i
$169$	−2.21796	−	12.8094i	−0.170612	−	0.985338i
$170$	4.28935	−	0.808782i	0.328978	−	0.0620308i
$171$	18.3744	−	2.67310i	1.40513	−	0.204417i
$172$	3.24418	−	3.24418i	0.247366	−	0.247366i
$173$	−15.4525	+	15.4525i	−1.17483	+	1.17483i	−0.193791	+	0.981043i	$0.562078\pi$
$173$	−15.4525	+	15.4525i	−1.17483	+	1.17483i	−0.981043	+	0.193791i	$0.937922\pi$
$174$	3.51618	−	4.06472i	0.266561	−	0.308146i
$175$	−6.32223	−	2.76787i	−0.477915	−	0.209232i
$176$	5.27247			0.397428
$177$	1.14378	+	15.8071i	0.0859720	+	1.18813i
$178$	−1.12267	−	1.12267i	−0.0841474	−	0.0841474i
$179$	12.5389			0.937199			0.468599	−	0.883411i	$-0.344759\pi$
$179$	12.5389			0.937199			0.468599	+	0.883411i	$0.344759\pi$
$180$	3.96764	+	11.5521i	0.295730	+	0.861041i
$181$	−15.6411			−1.16259			−0.581296	−	0.813692i	$-0.697454\pi$
$181$	−15.6411			−1.16259			−0.581296	+	0.813692i	$0.697454\pi$
$182$	−1.35661	+	1.61170i	−0.100559	+	0.119467i
$183$	1.75350	−	0.126881i	0.129622	−	0.00937932i
$184$	−1.59314			−0.117448
$185$	−13.6153	−	9.29535i	−1.00102	−	0.683408i
$186$	−3.66817	−	3.17314i	−0.268963	−	0.232666i
$187$	5.81424	+	5.81424i	0.425180	+	0.425180i
$188$	10.3679	+	10.3679i	0.756160	+	0.756160i
$189$	−6.04341	−	3.86256i	−0.439594	−	0.280960i
$190$	−3.30312	+	4.83822i	−0.239633	+	0.351001i
$191$			21.3421i			1.54426i	0.635466	+	0.772129i	$0.280808\pi$
$191$			21.3421i			1.54426i	−0.635466	+	0.772129i	$0.719192\pi$
$192$	−0.501888	−	6.93610i	−0.0362207	−	0.500570i
$193$	11.1604	−	11.1604i	0.803346	−	0.803346i	−0.180271	−	0.983617i	$-0.557697\pi$
$193$	11.1604	−	11.1604i	0.803346	−	0.803346i	0.983617	+	0.180271i	$0.0576974\pi$
$194$	−4.14444			−0.297553
$195$	−5.96146	+	12.6278i	−0.426909	+	0.904295i
$196$	9.27660			0.662615
$197$	−13.0719	+	13.0719i	−0.931333	+	0.931333i	−0.997789	−	0.0664562i	$-0.978831\pi$
$197$	−13.0719	+	13.0719i	−0.931333	+	0.931333i	0.0664562	+	0.997789i	$0.478831\pi$
$198$	1.35388	−	1.81487i	0.0962161	−	0.128977i
$199$			11.8546i			0.840351i	0.907443	+	0.420175i	$0.138031\pi$
$199$			11.8546i			0.840351i	−0.907443	+	0.420175i	$0.861969\pi$
$200$	−7.40783	−	3.24315i	−0.523813	−	0.229325i
$201$	−6.90854	−	5.97622i	−0.487291	−	0.421530i
$202$	−2.71127	−	2.71127i	−0.190765	−	0.190765i
$203$	7.15484	+	7.15484i	0.502171	+	0.502171i
$204$	9.51503	−	10.9994i	0.666185	−	0.770114i
$205$	−14.1880	+	2.67523i	−0.990932	+	0.186846i
$206$	−4.78111			−0.333115
$207$	1.76700	−	2.36865i	0.122815	−	0.164633i
$208$	6.86582	−	8.15681i	0.476059	−	0.565573i
$209$	−11.0356			−0.763351
$210$	2.18766	−	0.578687i	0.150963	−	0.0399332i
$211$	6.82795			0.470056			0.235028	−	0.971989i	$-0.424482\pi$
$211$	6.82795			0.470056			0.235028	+	0.971989i	$0.424482\pi$
$212$	−3.16875	−	3.16875i	−0.217631	−	0.217631i
$213$	9.49720	−	0.687207i	0.650738	−	0.0470867i
$214$	−7.52567			−0.514444
$215$	−4.65324	−	3.17683i	−0.317348	−	0.216658i
$216$	−7.08114	−	4.52580i	−0.481811	−	0.307942i
$217$	6.45682	−	6.45682i	0.438317	−	0.438317i
$218$	−5.14609	+	5.14609i	−0.348537	+	0.348537i
$219$	2.16512	−	2.50289i	0.146305	−	0.169130i
$220$	−1.34513	−	7.13385i	−0.0906885	−	0.480964i
$221$	16.5663	−	1.42364i	1.11437	−	0.0957645i
$222$	5.39128	−	0.390107i	0.361839	−	0.0261823i
$223$	−7.05618	+	7.05618i	−0.472516	+	0.472516i	−0.902728	−	0.430212i	$-0.858439\pi$
$223$	−7.05618	+	7.05618i	−0.472516	+	0.472516i	0.430212	+	0.902728i	$0.358439\pi$
$224$	−6.19258			−0.413759
$225$	13.0381	−	7.41674i	0.869206	−	0.494450i
$226$			2.21796i			0.147537i
$227$	9.96306	−	9.96306i	0.661272	−	0.661272i	−0.294408	−	0.955680i	$-0.595122\pi$
$227$	9.96306	−	9.96306i	0.661272	−	0.661272i	0.955680	+	0.294408i	$0.0951225\pi$
$228$	1.40872	+	19.4686i	0.0932950	+	1.28934i
$229$	6.60624			0.436552			0.218276	−	0.975887i	$-0.429957\pi$
$229$	6.60624			0.436552			0.218276	+	0.975887i	$0.429957\pi$
$230$	0.172757	+	0.916212i	0.0113913	+	0.0604132i
$231$	3.22394	+	2.78886i	0.212120	+	0.183494i
$232$	8.38341	+	8.38341i	0.550398	+	0.550398i
$233$	0.851914	−	0.851914i	0.0558108	−	0.0558108i	−0.678651	−	0.734461i	$-0.737435\pi$
$233$	0.851914	−	0.851914i	0.0558108	−	0.0558108i	0.734461	+	0.678651i	$0.237435\pi$
$234$	−1.04468	−	4.45785i	−0.0682927	−	0.291419i
$235$	10.1527	−	14.8711i	0.662291	−	0.970085i
$236$	−16.6607			−1.08452
$237$	1.28614	+	17.7745i	0.0835439	+	1.15458i
$238$	−1.90527	−	1.90527i	−0.123500	−	0.123500i
$239$		−	1.35859i		−	0.0878799i	−0.999034	−	0.0439399i	$-0.986009\pi$
$239$		−	1.35859i		−	0.0878799i	0.999034	−	0.0439399i	$-0.0139910\pi$
$240$	−11.0717	+	2.92874i	−0.714678	+	0.189049i
$241$		−	3.74390i		−	0.241166i	−0.992703	−	0.120583i	$-0.961524\pi$
$241$		−	3.74390i		−	0.241166i	0.992703	−	0.120583i	$-0.0384764\pi$
$242$	2.34088	−	2.34088i	0.150478	−	0.150478i
$243$	14.5828	−	5.50840i	0.935486	−	0.353364i
$244$			1.84819i			0.118318i
$245$	−2.11086	−	11.1949i	−0.134858	−	0.715216i
$246$	3.09710	−	3.58027i	0.197464	−	0.228270i
$247$	−14.3706	+	17.0727i	−0.914380	+	1.08631i
$248$	7.56553	−	7.56553i	0.480412	−	0.480412i
$249$	−14.7039	−	12.7196i	−0.931821	−	0.806069i
$250$	−1.06184	+	4.61191i	−0.0671566	+	0.291683i
$251$		−	7.63465i		−	0.481895i	−0.970538	−	0.240947i	$-0.922542\pi$
$251$		−	7.63465i		−	0.481895i	0.970538	−	0.240947i	$-0.0774581\pi$
$252$	4.50844	−	6.04354i	0.284005	−	0.380707i
$253$	−1.24193	+	1.24193i	−0.0780795	+	0.0780795i
$254$		−	1.16362i		−	0.0730120i
$255$	−15.4391	−	8.97974i	−0.966834	−	0.562333i
$256$	3.51256			0.219535
$257$	−16.8456	−	16.8456i	−1.05080	−	1.05080i	−0.998639	−	0.0521601i	$-0.983389\pi$
$257$	−16.8456	−	16.8456i	−1.05080	−	1.05080i	−0.0521601	−	0.998639i	$-0.516611\pi$
$258$	1.84256	−	0.133325i	0.114712	−	0.00830047i
$259$			10.1766i			0.632341i
$260$	−12.7881	−	7.20871i	−0.793083	−	0.447065i
$261$	−21.7626	+	3.16601i	−1.34707	+	0.195971i
$262$	0.692018	+	0.692018i	0.0427530	+	0.0427530i
$263$	3.24560	−	3.24560i	0.200132	−	0.200132i	−0.599925	−	0.800057i	$-0.704803\pi$
$263$	3.24560	−	3.24560i	0.200132	−	0.200132i	0.800057	+	0.599925i	$0.204803\pi$
$264$	3.77753	+	3.26774i	0.232491	+	0.201116i
$265$	−3.10297	+	4.54505i	−0.190614	+	0.279200i
$266$	3.61626			0.221727
$267$	0.468859	+	6.47963i	0.0286937	+	0.396547i
$268$	6.79027	−	6.79027i	0.414782	−	0.414782i
$269$	13.0130			0.793415			0.396707	−	0.917945i	$-0.370153\pi$
$269$	13.0130			0.793415			0.396707	+	0.917945i	$0.370153\pi$
$270$	−1.83492	+	4.56312i	−0.111669	+	0.277703i
$271$		−	12.1798i		−	0.739873i	−0.929057	−	0.369936i	$-0.879379\pi$
$271$		−	12.1798i		−	0.739873i	0.929057	−	0.369936i	$-0.120621\pi$
$272$	9.64257	+	9.64257i	0.584667	+	0.584667i
$273$	8.51274	−	1.35596i	0.515215	−	0.0820662i
$274$		−	5.55572i		−	0.335633i
$275$	−8.30296	+	3.24657i	−0.500688	+	0.195776i
$276$	2.34949	+	2.03242i	0.141423	+	0.122338i
$277$	0.122666	−	0.122666i	0.00737030	−	0.00737030i	−0.703412	−	0.710782i	$-0.748341\pi$
$277$	0.122666	−	0.122666i	0.00737030	−	0.00737030i	0.710782	+	0.703412i	$0.248341\pi$
$278$	1.92270	+	1.92270i	0.115316	+	0.115316i
$279$	2.85713	+	19.6394i	0.171052	+	1.17578i
$280$	0.924944	+	4.90541i	0.0552760	+	0.293154i
$281$	28.1225			1.67765			0.838824	−	0.544403i	$-0.183244\pi$
$281$	28.1225			1.67765			0.838824	+	0.544403i	$0.183244\pi$
$282$	0.426089	+	5.88856i	0.0253733	+	0.350658i
$283$	4.47421	+	4.47421i	0.265964	+	0.265964i	0.827472	−	0.561507i	$-0.189778\pi$
$283$	4.47421	+	4.47421i	0.265964	+	0.265964i	−0.561507	+	0.827472i	$0.689778\pi$
$284$			10.0101i			0.593988i
$285$	23.1739	−	6.13005i	1.37270	−	0.363113i
$286$	0.232996	+	2.71127i	0.0137774	+	0.160321i
$287$	6.30209	+	6.30209i	0.372001	+	0.372001i
$288$	8.04776	−	10.7880i	0.474219	−	0.635687i
$289$			4.26678i			0.250987i
$290$	3.91220	−	5.73037i	0.229733	−	0.336499i
$291$	12.8255	+	11.0947i	0.751846	+	0.650382i
$292$	2.46004	+	2.46004i	0.143963	+	0.143963i
$293$	−3.58558	−	3.58558i	−0.209472	−	0.209472i	0.594571	−	0.804043i	$-0.297322\pi$
$293$	−3.58558	−	3.58558i	−0.209472	−	0.209472i	−0.804043	+	0.594571i	$0.797322\pi$
$294$	2.82498	+	2.44374i	0.164756	+	0.142522i
$295$	3.79109	+	20.1059i	0.220726	+	1.17061i
$296$			11.9240i			0.693069i
$297$	−9.04819	+	1.99201i	−0.525029	+	0.115588i
$298$	5.50543	+	5.50543i	0.318921	+	0.318921i
$299$	0.304092	+	3.53858i	0.0175861	+	0.204641i
$300$	6.78735	+	14.2333i	0.391868	+	0.821759i
$301$			3.47800i			0.200469i
$302$	−1.85254	−	1.85254i	−0.106602	−	0.106602i
$303$	1.13231	+	15.6485i	0.0650494	+	0.898983i
$304$	−18.3019			−1.04969
$305$	2.23037	−	0.420550i	0.127711	−	0.0240806i
$306$	5.79517	−	0.843079i	0.331288	−	0.0481956i
$307$	−12.9376	−	12.9376i	−0.738389	−	0.738389i	0.233877	−	0.972266i	$-0.424859\pi$
$307$	−12.9376	−	12.9376i	−0.738389	−	0.738389i	−0.972266	+	0.233877i	$0.924859\pi$
$308$	−3.16875	+	3.16875i	−0.180556	+	0.180556i
$309$	14.7958	+	12.7991i	0.841703	+	0.728113i
$310$	−5.17131	−	3.53053i	−0.293711	−	0.200521i
$311$		−	33.1865i		−	1.88183i	−0.338639	−	0.940916i	$-0.609967\pi$
$311$		−	33.1865i		−	1.88183i	0.338639	−	0.940916i	$-0.390033\pi$
$312$	9.97448	−	1.58879i	0.564694	−	0.0899476i
$313$	10.6131	+	10.6131i	0.599890	+	0.599890i	0.940283	−	0.340393i	$-0.110560\pi$
$313$	10.6131	+	10.6131i	0.599890	+	0.599890i	−0.340393	+	0.940283i	$0.610560\pi$
$314$		−	0.369496i		−	0.0208519i
$315$	−8.31915	−	4.06555i	−0.468731	−	0.229068i
$316$	−18.7343			−1.05389
$317$	−19.8856	+	19.8856i	−1.11688	+	1.11688i	−0.124688	+	0.992196i	$0.539793\pi$
$317$	−19.8856	+	19.8856i	−1.11688	+	1.11688i	−0.992196	+	0.124688i	$0.960207\pi$
$318$	−0.130225	−	1.79972i	−0.00730268	−	0.100923i
$319$	13.0706			0.731811
$320$	−1.66352	−	8.82241i	−0.0929935	−	0.493188i
$321$	23.2892	+	20.1463i	1.29988	+	1.12446i
$322$	0.406968	−	0.406968i	0.0226794	−	0.0226794i
$323$	−20.1825	−	20.1825i	−1.12299	−	1.12299i
$324$	4.66924	+	15.7081i	0.259402	+	0.872673i
$325$	−5.78950	+	17.0728i	−0.321144	+	0.947030i
$326$			0.839363i			0.0464880i
$327$	29.7014	−	2.14916i	1.64249	−	0.118849i
$328$	7.38424	+	7.38424i	0.407727	+	0.407727i
$329$	−11.1152			−0.612802
$330$	1.46964	−	2.52680i	0.0809013	−	0.139096i
$331$		−	10.7854i		−	0.592820i	−0.955061	−	0.296410i	$-0.904211\pi$
$331$		−	10.7854i		−	0.592820i	0.955061	−	0.296410i	$-0.0957894\pi$
$332$	14.4522	−	14.4522i	0.793165	−	0.793165i
$333$	−17.7284	−	13.2253i	−0.971509	−	0.724740i
$334$		−	3.48983i		−	0.190955i
$335$	−9.73953	−	6.64932i	−0.532127	−	0.363291i
$336$	5.34671	+	4.62516i	0.291687	+	0.252323i
$337$	10.0688	−	10.0688i	0.548485	−	0.548485i	−0.377517	−	0.926002i	$-0.623222\pi$
$337$	10.0688	−	10.0688i	0.548485	−	0.548485i	0.926002	+	0.377517i	$0.123222\pi$
$338$	4.49790	+	3.17017i	0.244653	+	0.172434i
$339$	5.93750	−	6.86378i	0.322481	−	0.372790i
$340$	10.5867	−	15.5068i	0.574145	−	0.840974i
$341$		−	11.7954i		−	0.638757i
$342$	−4.69962	+	6.29981i	−0.254126	+	0.340655i
$343$	−11.8048	+	11.8048i	−0.637400	+	0.637400i
$344$			4.07522i			0.219721i
$345$	1.91809	−	3.29782i	0.103266	−	0.177548i
$346$		−	9.25031i		−	0.497300i
$347$	−10.4666	−	10.4666i	−0.561879	−	0.561879i	0.367962	−	0.929841i	$-0.380056\pi$
$347$	−10.4666	−	10.4666i	−0.561879	−	0.561879i	−0.929841	+	0.367962i	$0.880056\pi$
$348$	−1.66849	−	23.0585i	−0.0894403	−	1.23607i
$349$	−6.87214			−0.367857			−0.183929	−	0.982940i	$-0.558882\pi$
$349$	−6.87214			−0.367857			−0.183929	+	0.982940i	$0.558882\pi$
$350$	2.72079	−	1.06387i	0.145433	−	0.0568661i
$351$	−8.70081	+	16.5920i	−0.464415	+	0.885618i
$352$	−5.65635	+	5.65635i	−0.301484	+	0.301484i
$353$	6.26593	+	6.26593i	0.333502	+	0.333502i	0.853915	−	0.520413i	$-0.174222\pi$
$353$	6.26593	+	6.26593i	0.333502	+	0.333502i	−0.520413	+	0.853915i	$0.674222\pi$
$354$	−5.07363	−	4.38893i	−0.269660	−	0.233269i
$355$	12.0800	−	2.27776i	0.641141	−	0.120891i
$356$	−6.82954			−0.361965
$357$	0.795696	+	10.9965i	0.0421127	+	0.581998i
$358$	−3.75306	+	3.75306i	−0.198355	+	0.198355i
$359$			17.4323i			0.920040i	0.887909	+	0.460020i	$0.152158\pi$
$359$			17.4323i			0.920040i	−0.887909	+	0.460020i	$0.847842\pi$
$360$	−9.74766	−	4.76365i	−0.513747	−	0.251066i
$361$	19.3071			1.01616
$362$	4.68159	−	4.68159i	0.246059	−	0.246059i
$363$	−13.5107	+	0.977622i	−0.709130	+	0.0513118i
$364$	0.775881	+	9.02858i	0.0406672	+	0.473226i
$365$	2.40897	−	3.52852i	0.126091	−	0.184691i
$366$	−0.486869	+	0.562823i	−0.0254490	+	0.0294193i
$367$	20.1562	−	20.1562i	1.05215	−	1.05215i	0.0535819	−	0.998563i	$-0.482936\pi$
$367$	20.1562	−	20.1562i	1.05215	−	1.05215i	0.998563	−	0.0535819i	$-0.0170638\pi$
$368$	−2.05967	+	2.05967i	−0.107368	+	0.107368i
$369$	−19.1688	+	2.78867i	−0.997889	+	0.145172i
$370$	6.85747	−	1.29302i	0.356503	−	0.0672207i
$371$	3.39714			0.176371
$372$	−20.8089	+	1.50571i	−1.07889	+	0.0780675i
$373$	−26.0312	−	26.0312i	−1.34784	−	1.34784i	−0.888001	−	0.459842i	$-0.847906\pi$
$373$	−26.0312	−	26.0312i	−1.34784	−	1.34784i	−0.459842	−	0.888001i	$-0.652094\pi$
$374$	−3.48057			−0.179976
$375$	15.6321	−	11.4296i	0.807240	−	0.590224i
$376$	−13.0238			−0.671653
$377$	17.0205	−	20.2209i	0.876601	−	1.04143i
$378$	2.96500	−	0.652761i	0.152503	−	0.0335744i
$379$	28.6521			1.47176			0.735879	−	0.677113i	$-0.236769\pi$
$379$	28.6521			1.47176			0.735879	+	0.677113i	$0.236769\pi$
$380$	4.66924	+	24.7632i	0.239527	+	1.27032i
$381$	−3.11502	+	3.60098i	−0.159587	+	0.184484i
$382$	−6.38798	−	6.38798i	−0.326837	−	0.326837i
$383$	−2.84747	−	2.84747i	−0.145499	−	0.145499i	0.630605	−	0.776104i	$-0.282807\pi$
$383$	−2.84747	−	2.84747i	−0.145499	−	0.145499i	−0.776104	+	0.630605i	$0.782807\pi$
$384$	13.9800	+	12.0934i	0.713415	+	0.617138i
$385$	4.54505	+	3.10297i	0.231637	+	0.158142i
$386$			6.68095i			0.340052i
$387$	−6.05895	−	4.51994i	−0.307994	−	0.229762i
$388$	−12.6060	+	12.6060i	−0.639971	+	0.639971i
$389$	−19.7341			−1.00056			−0.500281	−	0.865863i	$-0.666770\pi$
$389$	−19.7341			−1.00056			−0.500281	+	0.865863i	$0.666770\pi$
$390$	−1.99532	−	5.56402i	−0.101037	−	0.281745i
$391$	−4.54262			−0.229730
$392$	−5.82647	+	5.82647i	−0.294281	+	0.294281i
$393$	−0.289007	−	3.99408i	−0.0145785	−	0.201475i
$394$		−	7.82520i		−	0.394228i
$395$	4.26294	+	22.6084i	0.214492	+	1.13755i
$396$	−1.40217	−	9.63825i	−0.0704616	−	0.484341i
$397$	5.15520	+	5.15520i	0.258732	+	0.258732i	0.824538	−	0.565806i	$-0.191435\pi$
$397$	5.15520	+	5.15520i	0.258732	+	0.258732i	−0.565806	+	0.824538i	$0.691435\pi$
$398$	−3.54825	−	3.54825i	−0.177858	−	0.177858i
$399$	−11.1910	−	9.68076i	−0.560252	−	0.484644i
$400$	−13.7700	+	5.38424i	−0.688498	+	0.269212i
$401$	−21.4787			−1.07260			−0.536298	−	0.844029i	$-0.680178\pi$
$401$	−21.4787			−1.07260			−0.536298	+	0.844029i	$0.680178\pi$
$402$	3.85659	−	0.279058i	0.192349	−	0.0139182i
$403$	−18.2481	−	15.3600i	−0.909005	−	0.765136i
$404$	−16.4935			−0.820584
$405$	17.8939	−	9.20912i	0.889156	−	0.457605i
$406$	−4.28309			−0.212566
$407$	9.29535	+	9.29535i	0.460753	+	0.460753i
$408$	0.932327	+	12.8848i	0.0461571	+	0.637891i
$409$	12.7208			0.629003			0.314502	−	0.949257i	$-0.398163\pi$
$409$	12.7208			0.629003			0.314502	+	0.949257i	$0.398163\pi$
$410$	3.44593	−	5.04740i	0.170182	−	0.249273i
$411$	−14.8727	+	17.1929i	−0.733617	+	0.848065i
$412$	−14.5425	+	14.5425i	−0.716457	+	0.716457i
$413$	8.93075	−	8.93075i	0.439453	−	0.439453i
$414$	0.180083	+	1.23786i	0.00885059	+	0.0608374i
$415$	−20.7292	−	14.1522i	−1.01756	−	0.694702i
$416$	1.38498	+	16.1164i	0.0679043	+	0.790171i
$417$	−0.802975	−	11.0971i	−0.0393219	−	0.543428i
$418$	3.30312	−	3.30312i	0.161561	−	0.161561i
$419$	17.7329			0.866309			0.433155	−	0.901320i	$-0.357400\pi$
$419$	17.7329			0.866309			0.433155	+	0.901320i	$0.357400\pi$
$420$	4.89394	−	8.41428i	0.238800	−	0.410575i
$421$		−	17.8269i		−	0.868831i	−0.900713	−	0.434415i	$-0.856955\pi$
$421$		−	17.8269i		−	0.868831i	0.900713	−	0.434415i	$-0.143045\pi$
$422$	−2.04370	+	2.04370i	−0.0994858	+	0.0994858i
$423$	14.4451	−	19.3636i	0.702346	−	0.941490i
$424$	3.98047			0.193309
$425$	−21.1224	−	9.24739i	−1.02459	−	0.448564i
$426$	−2.63696	+	3.04834i	−0.127761	+	0.147692i
$427$	−0.990698	−	0.990698i	−0.0479432	−	0.0479432i
$428$	−22.8905	+	22.8905i	−1.10645	+	1.10645i
$429$	6.53706	−	9.01414i	0.315612	−	0.435207i
$430$	2.34365	−	0.441909i	0.113021	−	0.0213107i
$431$	−0.0512892			−0.00247051			−0.00123526	−	0.999999i	$-0.500393\pi$
$431$	−0.0512892			−0.00247051			−0.00123526	+	0.999999i	$0.500393\pi$
$432$	−15.0059	+	3.30363i	−0.721970	+	0.158946i
$433$	5.73907	+	5.73907i	0.275802	+	0.275802i	0.831431	−	0.555629i	$-0.187522\pi$
$433$	5.73907	+	5.73907i	0.275802	+	0.275802i	−0.555629	+	0.831431i	$0.687522\pi$
$434$			3.86523i			0.185537i
$435$	−27.4471	+	7.26041i	−1.31599	+	0.348110i
$436$			31.3053i			1.49925i
$437$	4.31102	−	4.31102i	0.206224	−	0.206224i
$438$	0.101100	+	1.39720i	0.00483073	+	0.0667608i
$439$		−	35.7022i		−	1.70397i	−0.523563	−	0.851987i	$-0.675397\pi$
$439$		−	35.7022i		−	1.70397i	0.523563	−	0.851987i	$-0.324603\pi$
$440$	5.32549	+	3.63579i	0.253883	+	0.173329i
$441$	−2.20037	−	15.1250i	−0.104780	−	0.720237i
$442$	−4.53240	+	5.38463i	−0.215584	+	0.256121i
$443$	−15.3403	+	15.3403i	−0.728838	+	0.728838i	−0.970388	−	0.241550i	$-0.922344\pi$
$443$	−15.3403	+	15.3403i	−0.728838	+	0.728838i	0.241550	+	0.970388i	$0.422344\pi$
$444$	15.2119	−	17.5850i	0.721923	−	0.834548i
$445$	1.55404	+	8.24181i	0.0736686	+	0.390699i
$446$		−	4.22402i		−	0.200013i
$447$	−2.29923	−	31.7754i	−0.108750	−	1.50292i
$448$	−3.91879	+	3.91879i	−0.185145	+	0.185145i
$449$		−	31.6433i		−	1.49334i	−0.665195	−	0.746669i	$-0.731652\pi$
$449$		−	31.6433i		−	1.49334i	0.665195	−	0.746669i	$-0.268348\pi$
$450$	−1.68255	+	6.12242i	−0.0793161	+	0.288614i
$451$	11.5128			0.542115
$452$	6.74628	+	6.74628i	0.317318	+	0.317318i
$453$	0.773675	+	10.6922i	0.0363504	+	0.502363i
$454$			5.96417i			0.279912i
$455$	10.7190	−	2.99075i	0.502516	−	0.140209i
$456$	−13.1126	−	11.3431i	−0.614056	−	0.531188i
$457$	5.45533	+	5.45533i	0.255189	+	0.255189i	0.823094	−	0.567905i	$-0.192246\pi$
$457$	5.45533	+	5.45533i	0.255189	+	0.255189i	−0.567905	+	0.823094i	$0.692246\pi$
$458$	−1.97734	+	1.97734i	−0.0923950	+	0.0923950i
$459$	−20.1909	−	12.9047i	−0.942430	−	0.602340i
$460$	3.31227	+	2.26134i	0.154435	+	0.105435i
$461$	−13.0161			−0.606218			−0.303109	−	0.952956i	$-0.598025\pi$
$461$	−13.0161			−0.606218			−0.303109	+	0.952956i	$0.598025\pi$
$462$	−1.79972	+	0.130225i	−0.0837304	+	0.00605864i
$463$	−21.9129	+	21.9129i	−1.01838	+	1.01838i	−0.0185498	+	0.999828i	$0.505905\pi$
$463$	−21.9129	+	21.9129i	−1.01838	+	1.01838i	−0.999828	+	0.0185498i	$0.994095\pi$
$464$	21.6767			1.00632
$465$	6.55209	+	24.7694i	0.303846	+	1.14865i
$466$			0.509980i			0.0236244i
$467$	9.26751	+	9.26751i	0.428849	+	0.428849i	0.888236	−	0.459387i	$-0.151931\pi$
$467$	9.26751	+	9.26751i	0.428849	+	0.428849i	−0.459387	+	0.888236i	$0.651931\pi$
$468$	−16.7368	−	10.3817i	−0.773660	−	0.479895i
$469$			7.27969i			0.336145i
$470$	1.41228	+	7.48998i	0.0651436	+	0.345487i
$471$	−0.989143	+	1.14346i	−0.0455773	+	0.0526876i
$472$	10.4643	−	10.4643i	0.481657	−	0.481657i
$473$	3.17683	+	3.17683i	0.146071	+	0.146071i
$474$	−5.70512	−	4.93519i	−0.262045	−	0.226681i
$475$	28.8214	−	11.2696i	1.32242	−	0.517083i
$476$	−11.5903			−0.531243
$477$	−4.41485	+	5.91808i	−0.202142	+	0.270970i
$478$	0.406645	+	0.406645i	0.0185995	+	0.0185995i
$479$		−	9.43309i		−	0.431009i	−0.976503	−	0.215505i	$-0.930860\pi$
$479$		−	9.43309i		−	0.431009i	0.976503	−	0.215505i	$-0.0691396\pi$
$480$	8.73588	−	15.0198i	0.398737	−	0.685559i
$481$	26.4848	−	2.27600i	1.20760	−	0.103777i
$482$	1.12060	+	1.12060i	0.0510421	+	0.0510421i
$483$	−2.34887	+	0.169962i	−0.106877	+	0.00773353i
$484$		−	14.2403i		−	0.647288i
$485$	18.0812	+	12.3443i	0.821024	+	0.560525i
$486$	−2.71609	+	6.01357i	−0.123204	+	0.272781i
$487$	−25.8933	−	25.8933i	−1.17334	−	1.17334i	−0.981408	−	0.191931i	$-0.938525\pi$
$487$	−25.8933	−	25.8933i	−1.17334	−	1.17334i	−0.191931	−	0.981408i	$-0.561475\pi$
$488$	−1.16081	−	1.16081i	−0.0525475	−	0.0525475i
$489$	2.24698	−	2.59753i	0.101612	−	0.117464i
$490$	3.98260	+	2.71898i	0.179916	+	0.122831i
$491$			16.5241i			0.745723i	0.927887	+	0.372862i	$0.121623\pi$
$491$			16.5241i			0.745723i	−0.927887	+	0.372862i	$0.878377\pi$
$492$	−1.46963	−	20.3103i	−0.0662560	−	0.915659i
$493$	23.9041	+	23.9041i	1.07659	+	1.07659i
$494$	−0.808782	−	9.41143i	−0.0363888	−	0.423440i
$495$	−11.3123	+	3.88528i	−0.508449	+	0.174630i
$496$		−	19.5620i		−	0.878358i
$497$	−5.36577	−	5.36577i	−0.240688	−	0.240688i
$498$	8.20822	−	0.593937i	0.367819	−	0.0266150i
$499$	−32.5487			−1.45708			−0.728539	−	0.685004i	$-0.759800\pi$
$499$	−32.5487			−1.45708			−0.728539	+	0.685004i	$0.759800\pi$
$500$	10.7981	+	17.2576i	0.482906	+	0.771784i
$501$	−9.34231	+	10.7998i	−0.417383	+	0.482498i
$502$	2.28516	+	2.28516i	0.101992	+	0.101992i
$503$	18.6730	−	18.6730i	0.832589	−	0.832589i	−0.155281	−	0.987870i	$-0.549628\pi$
$503$	18.6730	−	18.6730i	0.832589	−	0.832589i	0.987870	+	0.155281i	$0.0496284\pi$
$504$	0.964166	+	6.62751i	0.0429474	+	0.295213i
$505$	3.75306	+	19.9042i	0.167009	+	0.885726i
$506$		−	0.743455i		−	0.0330506i
$507$	−5.43281	−	21.8514i	−0.241279	−	0.970456i
$508$	−3.53933	−	3.53933i	−0.157033	−	0.157033i
$509$			17.1048i			0.758157i	0.925364	+	0.379079i	$0.123759\pi$
$509$			17.1048i			0.758157i	−0.925364	+	0.379079i	$0.876241\pi$
$510$	7.30890	−	1.93338i	0.323644	−	0.0856114i
$511$	−2.63735			−0.116669
$512$	−16.1442	+	16.1442i	−0.713480	+	0.713480i
$513$	31.4083	−	6.91471i	1.38671	−	0.305292i
$514$	10.0842			0.444797
$515$	20.8588	+	14.2406i	0.919149	+	0.627516i
$516$	5.19890	−	6.00996i	0.228869	−	0.264574i
$517$	−10.1527	+	10.1527i	−0.446516	+	0.446516i
$518$	−3.04599	−	3.04599i	−0.133833	−	0.133833i
$519$	−24.7632	+	28.6264i	−1.08698	+	1.25656i
$520$	12.5596	−	3.50430i	0.550776	−	0.153674i
$521$		−	31.7138i		−	1.38941i	−0.719296	−	0.694704i	$-0.755535\pi$
$521$		−	31.7138i		−	1.38941i	0.719296	−	0.694704i	$-0.244465\pi$
$522$	5.56622	−	7.46148i	0.243627	−	0.326580i
$523$	−1.96609	−	1.96609i	−0.0859713	−	0.0859713i	0.662813	−	0.748785i	$-0.269362\pi$
$523$	−1.96609	−	1.96609i	−0.0859713	−	0.0859713i	−0.748785	+	0.662813i	$0.769362\pi$
$524$	4.20976			0.183904
$525$	−11.2679	−	3.99130i	−0.491769	−	0.174195i
$526$			1.94291i			0.0847147i
$527$	21.5720	−	21.5720i	0.939693	−	0.939693i
$528$	9.10838	−	0.659072i	0.396391	−	0.0286824i
$529$			22.0297i			0.957813i
$530$	−0.431634	−	2.28916i	−0.0187490	−	0.0994347i
$531$	3.95185	+	27.1643i	0.171496	+	1.17883i
$532$	10.9994	−	10.9994i	0.476886	−	0.476886i
$533$	14.9919	−	17.8109i	0.649372	−	0.771475i
$534$	−2.07978	−	1.79911i	−0.0900009	−	0.0778550i
$535$	32.8327	+	22.4153i	1.41948	+	0.969100i
$536$			8.52970i			0.368427i
$537$	21.6613	−	1.56739i	0.934755	−	0.0676378i
$538$	−3.89496	+	3.89496i	−0.167924	+	0.167924i
$539$			9.08404i			0.391277i
$540$	8.29827	+	19.4606i	0.357101	+	0.837453i
$541$			2.13410i			0.0917520i	0.998947	+	0.0458760i	$0.0146079\pi$
$541$			2.13410i			0.0917520i	−0.998947	+	0.0458760i	$0.985392\pi$
$542$	3.64560	+	3.64560i	0.156592	+	0.156592i
$543$	−27.0205	+	1.95517i	−1.15956	+	0.0839045i
$544$	−20.6893			−0.887044
$545$	37.7789	−	7.12343i	1.61827	−	0.305134i
$546$	−2.14213	+	2.95384i	−0.0916745	+	0.126413i
$547$	−16.7725	+	16.7725i	−0.717142	+	0.717142i	−0.968019	−	0.250877i	$-0.919281\pi$
$547$	−16.7725	+	16.7725i	−0.717142	+	0.717142i	0.250877	+	0.968019i	$0.419281\pi$
$548$	−16.8986	−	16.8986i	−0.721873	−	0.721873i
$549$	3.01337	−	0.438383i	0.128607	−	0.0187097i
$550$	1.51345	−	3.45694i	0.0645337	−	0.147404i
$551$	−45.3708			−1.93286
$552$	−2.75220	+	0.199146i	−0.117142	+	0.00847623i
$553$	10.0423	−	10.0423i	0.427042	−	0.427042i
$554$			0.0734314i			0.00311980i
$555$	−24.6828	−	14.3561i	−1.04773	−	0.609382i
$556$	11.6964			0.496037
$557$	−1.09774	+	1.09774i	−0.0465129	+	0.0465129i	−0.729981	−	0.683468i	$-0.760471\pi$
$557$	−1.09774	+	1.09774i	−0.0465129	+	0.0465129i	0.683468	+	0.729981i	$0.260471\pi$
$558$	−6.73354	−	5.02318i	−0.285053	−	0.212648i
$559$	9.05161	−	0.777861i	0.382842	−	0.0329000i
$560$	7.53769	+	5.14609i	0.318525	+	0.217462i
$561$	10.7711	+	9.31751i	0.454756	+	0.393386i
$562$	−8.41746	+	8.41746i	−0.355069	+	0.355069i
$563$	6.40952	−	6.40952i	0.270129	−	0.270129i	−0.559023	−	0.829152i	$-0.688824\pi$
$563$	6.40952	−	6.40952i	0.270129	−	0.270129i	0.829152	+	0.559023i	$0.188824\pi$
$564$	19.2070	+	16.6150i	0.808761	+	0.699616i
$565$	6.60624	−	9.67643i	0.277927	−	0.407090i
$566$	−2.67839			−0.112581
$567$	−10.9230	−	5.91726i	−0.458724	−	0.248501i
$568$	−6.28714	−	6.28714i	−0.263802	−	0.263802i
$569$	22.1203			0.927330			0.463665	−	0.886011i	$-0.346534\pi$
$569$	22.1203			0.927330			0.463665	+	0.886011i	$0.346534\pi$
$570$	−5.10146	+	8.77108i	−0.213677	+	0.367380i
$571$	−27.4675			−1.14948			−0.574741	−	0.818336i	$-0.694897\pi$
$571$	−27.4675			−1.14948			−0.574741	+	0.818336i	$0.694897\pi$
$572$	8.95547	+	7.53807i	0.374447	+	0.315183i
$573$	2.66781	+	36.8692i	0.111449	+	1.54023i
$574$	−3.77261			−0.157466
$575$	1.97526	−	4.51177i	0.0823739	−	0.188154i
$576$	−1.73406	−	11.9196i	−0.0722524	−	0.496650i
$577$	−27.1625	−	27.1625i	−1.13079	−	1.13079i	−0.990046	−	0.140745i	$-0.955050\pi$
$577$	−27.1625	−	27.1625i	−1.13079	−	1.13079i	−0.140745	−	0.990046i	$-0.544950\pi$
$578$	−1.27711	−	1.27711i	−0.0531207	−	0.0531207i
$579$	17.8850	−	20.6751i	0.743274	−	0.859229i
$580$	−5.53023	−	29.3294i	−0.229630	−	1.21784i
$581$			15.4938i			0.642791i
$582$	−7.15965	+	0.518065i	−0.296777	+	0.0214745i
$583$	3.10297	−	3.10297i	0.128512	−	0.128512i
$584$	−3.09021			−0.127874
$585$	−8.72012	+	22.5601i	−0.360533	+	0.932747i
$586$	2.14643			0.0886681
$587$	18.4092	−	18.4092i	0.759827	−	0.759827i	−0.216464	−	0.976291i	$-0.569452\pi$
$587$	18.4092	−	18.4092i	0.759827	−	0.759827i	0.976291	+	0.216464i	$0.0694522\pi$
$588$	16.0257	−	1.15960i	0.660887	−	0.0478210i
$589$			40.9445i			1.68709i
$590$	−7.15271	−	4.88326i	−0.294472	−	0.201040i
$591$	−20.9481	+	24.2161i	−0.861690	+	0.996119i
$592$	15.4158	+	15.4158i	0.633584	+	0.633584i
$593$	26.8585	+	26.8585i	1.10294	+	1.10294i	0.994054	+	0.108891i	$0.0347300\pi$
$593$	26.8585	+	26.8585i	1.10294	+	1.10294i	0.108891	+	0.994054i	$0.465270\pi$
$594$	2.11201	−	3.30449i	0.0866569	−	0.135585i
$595$	2.63735	+	13.9871i	0.108121	+	0.573415i
$596$	33.4913			1.37186
$597$	1.48185	+	20.4792i	0.0606483	+	0.838159i
$598$	−1.15017	−	0.968128i	−0.0470338	−	0.0395897i
$599$	36.5079			1.49167			0.745836	−	0.666130i	$-0.232050\pi$
$599$	36.5079			1.49167			0.745836	+	0.666130i	$0.232050\pi$
$600$	−13.2027	−	4.67666i	−0.538997	−	0.190924i
$601$	−19.6210			−0.800359			−0.400180	−	0.916437i	$-0.631052\pi$
$601$	−19.6210			−0.800359			−0.400180	+	0.916437i	$0.631052\pi$
$602$	−1.04101	−	1.04101i	−0.0424286	−	0.0424286i
$603$	−12.6818	−	9.46053i	−0.516442	−	0.385263i
$604$	−11.2696			−0.458552
$605$	−17.1851	+	3.24034i	−0.698672	+	0.131739i
$606$	−5.02273	−	4.34490i	−0.204035	−	0.176500i
$607$	14.2907	−	14.2907i	0.580043	−	0.580043i	−0.354872	−	0.934915i	$-0.615475\pi$
$607$	14.2907	−	14.2907i	0.580043	−	0.580043i	0.934915	+	0.354872i	$0.115475\pi$
$608$	19.6344	−	19.6344i	0.796282	−	0.796282i
$609$	13.2546	+	11.4659i	0.537104	+	0.464620i
$610$	−0.541705	+	0.793458i	−0.0219330	+	0.0321262i
$611$	2.48594	+	28.9277i	0.100570	+	1.17029i
$612$	15.0626	−	20.1913i	0.608869	−	0.816185i
$613$	−18.2600	+	18.2600i	−0.737514	+	0.737514i	−0.972096	−	0.234582i	$-0.924628\pi$
$613$	−18.2600	+	18.2600i	−0.737514	+	0.737514i	0.234582	+	0.972096i	$0.424628\pi$
$614$	7.74482			0.312555
$615$	−24.1758	+	6.39508i	−0.974863	+	0.257875i
$616$		−	3.98047i		−	0.160378i
$617$	−6.13543	+	6.13543i	−0.247003	+	0.247003i	−0.819740	−	0.572737i	$-0.805882\pi$
$617$	−6.13543	+	6.13543i	−0.247003	+	0.247003i	0.572737	+	0.819740i	$0.305882\pi$
$618$	−8.25952	+	0.597650i	−0.332247	+	0.0240410i
$619$	−34.5846			−1.39007			−0.695036	−	0.718975i	$-0.744612\pi$
$619$	−34.5846			−1.39007			−0.695036	+	0.718975i	$0.744612\pi$
$620$	−26.4680	+	4.99070i	−1.06298	+	0.200432i
$621$	2.75646	−	4.31280i	0.110613	−	0.173067i
$622$	9.93318	+	9.93318i	0.398284	+	0.398284i
$623$	3.66089	−	3.66089i	0.146670	−	0.146670i
$624$	10.8413	−	14.9494i	0.434000	−	0.598455i
$625$	18.3692	−	16.9579i	0.734768	−	0.678318i
$626$	−6.35332			−0.253930
$627$	−19.0644	+	1.37948i	−0.761360	+	0.0550912i
$628$	−1.12388	−	1.12388i	−0.0448477	−	0.0448477i
$629$			33.9996i			1.35565i
$630$	3.70691	−	1.27316i	0.147687	−	0.0507241i
$631$		−	34.2929i		−	1.36518i	−0.730803	−	0.682589i	$-0.760854\pi$
$631$		−	34.2929i		−	1.36518i	0.730803	−	0.682589i	$-0.239146\pi$
$632$	11.7667	−	11.7667i	0.468054	−	0.468054i
$633$	11.7955	−	0.853511i	0.468830	−	0.0339240i
$634$		−	11.9041i		−	0.472770i
$635$	−3.46586	+	5.07659i	−0.137539	+	0.201459i
$636$	−5.87022	−	5.07802i	−0.232770	−	0.201357i
$637$	14.0535	+	11.8292i	0.556820	+	0.468692i
$638$	−3.91220	+	3.91220i	−0.154886	+	0.154886i
$639$	16.3208	−	2.37435i	0.645643	−	0.0939277i
$640$	19.7088	+	13.4555i	0.779057	+	0.531874i
$641$		−	42.5250i		−	1.67964i	−0.542869	−	0.839818i	$-0.682662\pi$
$641$		−	42.5250i		−	1.67964i	0.542869	−	0.839818i	$-0.317338\pi$
$642$	−13.0008	+	0.940727i	−0.513102	+	0.0371275i
$643$	−18.9190	+	18.9190i	−0.746094	+	0.746094i	−0.973743	−	0.227649i	$-0.926896\pi$
$643$	−18.9190	+	18.9190i	−0.746094	+	0.746094i	0.227649	+	0.973743i	$0.426896\pi$
$644$		−	2.47571i		−	0.0975568i
$645$	−8.43574	−	4.90642i	−0.332157	−	0.193190i
$646$	12.0818			0.475353
$647$	12.3644	+	12.3644i	0.486095	+	0.486095i	0.907071	−	0.420977i	$-0.138313\pi$
$647$	12.3644	+	12.3644i	0.486095	+	0.486095i	−0.420977	+	0.907071i	$0.638313\pi$
$648$	−12.7987	−	6.93332i	−0.502779	−	0.272367i
$649$		−	16.3148i		−	0.640413i
$650$	−3.37726	−	6.84302i	−0.132467	−	0.268405i
$651$	10.3473	−	11.9615i	0.405541	−	0.468808i
$652$	2.55306	+	2.55306i	0.0999854	+	0.0999854i
$653$	−15.7250	+	15.7250i	−0.615366	+	0.615366i	−0.944339	−	0.328973i	$-0.893297\pi$
$653$	−15.7250	+	15.7250i	−0.615366	+	0.615366i	0.328973	+	0.944339i	$0.393297\pi$
$654$	−8.24677	+	9.53332i	−0.322474	+	0.372782i
$655$	−0.957919	−	5.08029i	−0.0374290	−	0.198504i
$656$	19.0932			0.745465
$657$	3.42745	−	4.59447i	0.133717	−	0.179247i
$658$	3.32694	−	3.32694i	0.129698	−	0.129698i
$659$	−9.53240			−0.371330			−0.185665	−	0.982613i	$-0.559444\pi$
$659$	−9.53240			−0.371330			−0.185665	+	0.982613i	$0.559444\pi$
$660$	−3.21550	−	12.1558i	−0.125163	−	0.473165i
$661$			1.70798i			0.0664328i	0.999448	+	0.0332164i	$0.0105750\pi$
$661$			1.70798i			0.0664328i	−0.999448	+	0.0332164i	$0.989425\pi$
$662$	3.22822	+	3.22822i	0.125468	+	0.125468i
$663$	28.4408	−	4.53021i	1.10455	−	0.175939i
$664$			18.1543i			0.704523i
$665$	−15.7769	−	10.7711i	−0.611801	−	0.417685i
$666$	9.26486	−	1.34785i	0.359006	−	0.0522280i
$667$	−5.10596	+	5.10596i	−0.197703	+	0.197703i
$668$	−10.6149	−	10.6149i	−0.410702	−	0.410702i
$669$	−11.3077	+	13.0718i	−0.437183	+	0.505386i
$670$	4.90541	−	0.924944i	0.189513	−	0.0357337i
$671$	−1.80982			−0.0698674
$672$	−10.6979	+	0.774088i	−0.412680	+	0.0298611i
$673$	21.7199	+	21.7199i	0.837239	+	0.837239i	0.988495	−	0.151255i	$-0.0483315\pi$
$673$	21.7199	+	21.7199i	0.837239	+	0.837239i	−0.151255	+	0.988495i	$0.548332\pi$
$674$			6.02749i			0.232170i
$675$	21.5966	−	14.4425i	0.831255	−	0.555891i
$676$	23.3236	−	4.03851i	0.897063	−	0.155327i
$677$	2.10006	+	2.10006i	0.0807118	+	0.0807118i	0.746310	−	0.665598i	$-0.231824\pi$
$677$	2.10006	+	2.10006i	0.0807118	+	0.0807118i	−0.665598	+	0.746310i	$0.731824\pi$
$678$	0.277250	+	3.83160i	0.0106477	+	0.147152i
$679$		−	13.5145i		−	0.518641i
$680$	3.09021	+	16.3889i	0.118504	+	0.628484i
$681$	15.9661	−	18.4569i	0.611823	−	0.707271i
$682$	3.53053	+	3.53053i	0.135191	+	0.135191i
$683$	−13.0377	−	13.0377i	−0.498875	−	0.498875i	0.412212	−	0.911088i	$-0.364756\pi$
$683$	−13.0377	−	13.0377i	−0.498875	−	0.498875i	−0.911088	+	0.412212i	$0.864756\pi$
$684$	4.86724	+	33.4565i	0.186103	+	1.27924i
$685$	−16.5478	+	24.2383i	−0.632260	+	0.926097i
$686$		−	7.06669i		−	0.269808i
$687$	11.4125	−	0.825796i	0.435414	−	0.0315061i
$688$	5.26858	+	5.26858i	0.200863	+	0.200863i
$689$	−0.759775	−	8.84116i	−0.0289451	−	0.336821i
$690$	0.412973	+	1.56119i	0.0157216	+	0.0594336i
$691$			18.1095i			0.688917i	0.938801	+	0.344459i	$0.111938\pi$
$691$			18.1095i			0.688917i	−0.938801	+	0.344459i	$0.888062\pi$
$692$	−28.1363	−	28.1363i	−1.06958	−	1.06958i
$693$	5.91808	+	4.41485i	0.224809	+	0.167706i
$694$	6.26563			0.237840
$695$	−2.66148	−	14.1151i	−0.100956	−	0.535414i
$696$	15.5306	+	13.4347i	0.588685	+	0.509240i
$697$	21.0551	+	21.0551i	0.797520	+	0.797520i
$698$	2.05693	−	2.05693i	0.0778559	−	0.0778559i
$699$	1.36522	−	1.57820i	0.0516373	−	0.0596931i
$700$	5.03981	−	11.5117i	0.190487	−	0.435099i
$701$			30.8016i			1.16336i	0.813418	+	0.581679i	$0.197604\pi$
$701$			30.8016i			1.16336i	−0.813418	+	0.581679i	$0.802396\pi$
$702$	−2.36196	−	7.57050i	−0.0891464	−	0.285730i
$703$	−32.2662	−	32.2662i	−1.21694	−	1.21694i
$704$			7.15890i			0.269811i
$705$	15.6803	−	26.9595i	0.590552	−	1.01535i
$706$	−3.75096			−0.141169
$707$	8.84116	−	8.84116i	0.332506	−	0.332506i
$708$	−28.7819	+	2.08263i	−1.08169	+	0.0782698i
$709$	−2.35235			−0.0883445			−0.0441723	−	0.999024i	$-0.514065\pi$
$709$	−2.35235			−0.0883445			−0.0441723	+	0.999024i	$0.514065\pi$
$710$	−2.93396	+	4.29749i	−0.110109	+	0.161282i
$711$	4.44371	+	30.5453i	0.166652	+	1.14554i
$712$	4.28951	−	4.28951i	0.160756	−	0.160756i
$713$	4.60782	+	4.60782i	0.172564	+	0.172564i
$714$	−3.52958	−	3.05325i	−0.132091	−	0.114265i
$715$	7.05907	−	12.5226i	0.263994	−	0.468319i
$716$			22.8310i			0.853236i
$717$	−0.169827	−	2.34701i	−0.00634231	−	0.0876507i
$718$	−5.21772	−	5.21772i	−0.194724	−	0.194724i
$719$	−38.5954			−1.43936			−0.719682	−	0.694303i	$-0.755713\pi$
$719$	−38.5954			−1.43936			−0.719682	+	0.694303i	$0.755713\pi$
$720$	−18.7607	+	6.44350i	−0.699171	+	0.240135i
$721$		−	15.5907i		−	0.580626i
$722$	−5.77889	+	5.77889i	−0.215068	+	0.215068i
$723$	−0.467997	−	6.46772i	−0.0174050	−	0.240537i
$724$		−	28.4796i		−	1.05844i
$725$	−34.1360	+	13.3476i	−1.26778	+	0.495719i
$726$	3.75134	−	4.33657i	0.139225	−	0.160945i
$727$	23.0427	−	23.0427i	0.854607	−	0.854607i	−0.136090	−	0.990697i	$-0.543453\pi$
$727$	23.0427	−	23.0427i	0.854607	−	0.854607i	0.990697	+	0.136090i	$0.0434535\pi$
$728$	−6.15800	−	5.18337i	−0.228231	−	0.192108i
$729$	24.5037	−	11.3388i	0.907544	−	0.419957i
$730$	0.335097	+	1.77718i	0.0124025	+	0.0657762i
$731$			11.6199i			0.429778i
$732$	0.231028	+	3.19281i	0.00853904	+	0.118010i
$733$	13.9647	−	13.9647i	0.515799	−	0.515799i	−0.400498	−	0.916297i	$-0.631163\pi$
$733$	13.9647	−	13.9647i	0.515799	−	0.515799i	0.916297	+	0.400498i	$0.131163\pi$
$734$			12.0661i			0.445367i
$735$	−5.04598	−	19.0757i	−0.186124	−	0.703618i
$736$		−	4.41925i		−	0.162896i
$737$	6.64932	+	6.64932i	0.244931	+	0.244931i
$738$	4.90281	−	6.57219i	0.180475	−	0.241925i
$739$	38.8310			1.42842			0.714210	−	0.699931i	$-0.246786\pi$
$739$	38.8310			1.42842			0.714210	+	0.699931i	$0.246786\pi$
$740$	16.9252	−	24.7910i	0.622182	−	0.911335i
$741$	−22.6916	+	31.2901i	−0.833596	+	1.14947i
$742$	−1.01681	+	1.01681i	−0.0373283	+	0.0373283i
$743$	3.86986	+	3.86986i	0.141971	+	0.141971i	0.774520	−	0.632549i	$-0.217991\pi$
$743$	3.86986	+	3.86986i	0.141971	+	0.141971i	−0.632549	+	0.774520i	$0.717991\pi$
$744$	12.1240	−	14.0154i	0.444487	−	0.513830i
$745$	−7.62084	−	40.4169i	−0.279206	−	1.48076i
$746$	15.5830			0.570534
$747$	−26.9914	−	20.1354i	−0.987565	−	0.736717i
$748$	−10.5867	+	10.5867i	−0.387088	+	0.387088i
$749$		−	24.5404i		−	0.896685i
$750$	−1.25786	+	8.09996i	−0.0459307	+	0.295769i
$751$	−23.4223			−0.854693			−0.427347	−	0.904088i	$-0.640552\pi$
$751$	−23.4223			−0.854693			−0.427347	+	0.904088i	$0.640552\pi$
$752$	−16.8377	+	16.8377i	−0.614007	+	0.614007i
$753$	−0.954350	−	13.1891i	−0.0347784	−	0.480638i
$754$	0.957919	+	11.1469i	0.0348854	+	0.405945i
$755$	2.56436	+	13.6000i	0.0933265	+	0.494954i
$756$	7.03303	−	11.0040i	0.255789	−	0.400211i
$757$	−20.8912	+	20.8912i	−0.759305	+	0.759305i	−0.976196	−	0.216891i	$-0.930408\pi$
$757$	−20.8912	+	20.8912i	−0.759305	+	0.759305i	0.216891	+	0.976196i	$0.430408\pi$
$758$	−8.57596	+	8.57596i	−0.311493	+	0.311493i
$759$	−1.99023	+	2.30072i	−0.0722409	+	0.0835109i
$760$	−18.4860	−	12.6206i	−0.670556	−	0.457798i
$761$	15.8155			0.573310			0.286655	−	0.958034i	$-0.407457\pi$
$761$	15.8155			0.573310			0.286655	+	0.958034i	$0.407457\pi$
$762$	−0.145455	−	2.01019i	−0.00526929	−	0.0728216i
$763$	−16.7808	−	16.7808i	−0.607506	−	0.607506i
$764$	−38.8601			−1.40591
$765$	−27.7941	−	13.5829i	−1.00490	−	0.491090i
$766$	1.70458			0.0615888
$767$	−25.2399	−	21.2452i	−0.911361	−	0.767119i
$768$	6.06806	−	0.439078i	0.218962	−	0.0158439i
$769$	−45.2098			−1.63031			−0.815153	−	0.579245i	$-0.803347\pi$
$769$	−45.2098			−1.63031			−0.815153	+	0.579245i	$0.803347\pi$
$770$	−2.28916	+	0.431634i	−0.0824956	+	0.0155550i
$771$	−31.2071	−	26.9956i	−1.12390	−	0.972222i
$772$	20.3212	+	20.3212i	0.731375	+	0.731375i
$773$	7.73848	+	7.73848i	0.278334	+	0.278334i	0.832444	−	0.554110i	$-0.186941\pi$
$773$	7.73848	+	7.73848i	0.278334	+	0.278334i	−0.554110	+	0.832444i	$0.686941\pi$
$774$	3.16641	−	0.460648i	0.113814	−	0.0165576i
$775$	12.0455	+	30.8057i	0.432685	+	1.10657i
$776$		−	15.8352i		−	0.568449i
$777$	1.27210	+	17.5804i	0.0456362	+	0.630692i
$778$	5.90671	−	5.90671i	0.211766	−	0.211766i
$779$	−39.9633			−1.43184
$780$	−22.9930	−	10.8548i	−0.823280	−	0.388663i
$781$	−9.80227			−0.350753
$782$	1.35967	−	1.35967i	0.0486216	−	0.0486216i
$783$	−37.1999	+	8.18977i	−1.32941	+	0.292678i
$784$			15.0653i			0.538047i
$785$	−1.10055	+	1.61202i	−0.0392803	+	0.0575355i
$786$	1.28199	+	1.10898i	0.0457270	+	0.0395560i
$787$	5.17131	+	5.17131i	0.184337	+	0.184337i	0.793243	−	0.608905i	$-0.208391\pi$
$787$	5.17131	+	5.17131i	0.184337	+	0.184337i	−0.608905	+	0.793243i	$0.708391\pi$
$788$	−23.8016	−	23.8016i	−0.847896	−	0.847896i
$789$	5.20117	−	6.01259i	0.185167	−	0.214054i
$790$	−8.04296	−	5.49105i	−0.286156	−	0.195363i
$791$	−7.23252			−0.257159
$792$	6.93429	+	5.17294i	0.246399	+	0.183812i
$793$	−2.35675	+	2.79989i	−0.0836907	+	0.0994271i
$794$	−3.08605			−0.109520
$795$	−4.79235	+	8.23961i	−0.169967	+	0.292229i
$796$	−21.5851			−0.765065
$797$	16.4636	+	16.4636i	0.583171	+	0.583171i	0.935773	−	0.352602i	$-0.114703\pi$
$797$	16.4636	+	16.4636i	0.583171	+	0.583171i	−0.352602	+	0.935773i	$0.614703\pi$
$798$	6.24721	−	0.452041i	0.221149	−	0.0160021i
$799$	−37.1357			−1.31376
$800$	8.99627	−	20.5488i	0.318066	−	0.726509i
$801$	1.61994	+	11.1352i	0.0572377	+	0.393442i
$802$	6.42888	−	6.42888i	0.227012	−	0.227012i
$803$	−2.40897	+	2.40897i	−0.0850108	+	0.0850108i
$804$	10.8816	−	12.5792i	0.383765	−	0.443635i
$805$	−2.98766	+	0.563342i	−0.105301	+	0.0198552i
$806$	10.0594	−	0.864465i	0.354327	−	0.0304495i
$807$	22.4804	−	1.62665i	0.791346	−	0.0572609i
$808$	10.3593	−	10.3593i	0.364439	−	0.364439i
$809$	21.0782			0.741070			0.370535	−	0.928818i	$-0.379174\pi$
$809$	21.0782			0.741070			0.370535	+	0.928818i	$0.379174\pi$
$810$	−2.59948	+	8.11232i	−0.0913364	+	0.285038i
$811$		−	14.9877i		−	0.526288i	−0.964757	−	0.263144i	$-0.915241\pi$
$811$		−	14.9877i		−	0.526288i	0.964757	−	0.263144i	$-0.0847594\pi$
$812$	−13.0277	+	13.0277i	−0.457182	+	0.457182i
$813$	−1.52251	−	21.0411i	−0.0533968	−	0.737944i
$814$	−5.56445			−0.195034
$815$	2.50006	−	3.66194i	0.0875733	−	0.128272i
$816$	17.8632	+	15.4525i	0.625338	+	0.540947i
$817$	−11.0275	−	11.0275i	−0.385803	−	0.385803i
$818$	−3.80751	+	3.80751i	−0.133127	+	0.133127i
$819$	14.5366	−	3.40657i	0.507948	−	0.119035i
$820$	−4.87111	−	25.8338i	−0.170107	−	0.902156i
$821$	14.4263			0.503480			0.251740	−	0.967795i	$-0.418997\pi$
$821$	14.4263			0.503480			0.251740	+	0.967795i	$0.418997\pi$
$822$	−0.694479	−	9.59770i	−0.0242227	−	0.334758i
$823$	1.29844	+	1.29844i	0.0452607	+	0.0452607i	0.729375	−	0.684114i	$-0.239811\pi$
$823$	1.29844	+	1.29844i	0.0452607	+	0.0452607i	−0.684114	+	0.729375i	$0.739811\pi$
$824$		−	18.2678i		−	0.636387i
$825$	−13.9378	+	6.64645i	−0.485253	+	0.231400i
$826$			5.34620i			0.186018i
$827$	−18.9853	+	18.9853i	−0.660182	+	0.660182i	−0.955423	−	0.295241i	$-0.904600\pi$
$827$	−18.9853	+	18.9853i	−0.660182	+	0.660182i	0.295241	+	0.955423i	$0.404600\pi$
$828$	4.31289	+	3.21739i	0.149883	+	0.111812i
$829$		−	38.1543i		−	1.32515i	−0.748994	−	0.662576i	$-0.769463\pi$
$829$		−	38.1543i		−	1.32515i	0.748994	−	0.662576i	$-0.230537\pi$
$830$	10.4405	−	1.96862i	0.362395	−	0.0683317i
$831$	0.196576	−	0.227244i	0.00681916	−	0.00788299i
$832$	11.0752	+	9.32232i	0.383964	+	0.323193i
$833$	−16.6134	+	16.6134i	−0.575619	+	0.575619i
$834$	3.56187	+	3.08118i	0.123337	+	0.106693i
$835$	−10.3945	+	15.2253i	−0.359718	+	0.526893i
$836$		−	20.0939i		−	0.694963i
$837$	7.39077	+	33.5706i	0.255463	+	1.16037i
$838$	−5.30771	+	5.30771i	−0.183352	+	0.183352i
$839$			46.7269i			1.61319i	0.591104	+	0.806595i	$0.298692\pi$
$839$			46.7269i			1.61319i	−0.591104	+	0.806595i	$0.701308\pi$
$840$	2.21106	+	8.35865i	0.0762889	+	0.288401i
$841$	24.7371			0.853003
$842$	5.33585	+	5.33585i	0.183885	+	0.183885i
$843$	48.5826	−	3.51538i	1.67327	−	0.121076i
$844$			12.4325i			0.427944i
$845$	−10.1809	−	27.2277i	−0.350232	−	0.936663i
$846$	1.47217	+	10.1194i	0.0506142	+	0.347913i
$847$	7.63335	+	7.63335i	0.262285	+	0.262285i
$848$	5.14609	−	5.14609i	0.176717	−	0.176717i
$849$	8.28865	+	7.17007i	0.284466	+	0.246076i
$850$	9.09010	−	3.55435i	0.311788	−	0.121913i
$851$	−7.26237			−0.248951
$852$	1.25128	+	17.2927i	0.0428682	+	0.592439i
$853$	16.6339	−	16.6339i	0.569533	−	0.569533i	−0.362464	−	0.931998i	$-0.618065\pi$
$853$	16.6339	−	16.6339i	0.569533	−	0.569533i	0.931998	+	0.362464i	$0.118065\pi$
$854$	0.593059			0.0202941
$855$	39.2674	−	13.4867i	1.34292	−	0.461234i
$856$		−	28.7542i		−	0.982800i
$857$	−22.0097	−	22.0097i	−0.751837	−	0.751837i	0.222985	−	0.974822i	$-0.428420\pi$
$857$	−22.0097	−	22.0097i	−0.751837	−	0.751837i	−0.974822	+	0.222985i	$0.928420\pi$
$858$	0.741425	+	4.65469i	0.0253118	+	0.158909i
$859$			0.648432i			0.0221242i	0.999939	+	0.0110621i	$0.00352125\pi$
$859$			0.648432i			0.0221242i	−0.999939	+	0.0110621i	$0.996479\pi$
$860$	5.78445	−	8.47272i	0.197248	−	0.288917i
$861$	11.6749	+	10.0993i	0.397878	+	0.344183i
$862$	0.0153516	−	0.0153516i	0.000522877	−	0.000522877i
$863$	32.6225	+	32.6225i	1.11048	+	1.11048i	0.993085	+	0.117397i	$0.0374549\pi$
$863$	32.6225	+	32.6225i	1.11048	+	1.11048i	0.117397	+	0.993085i	$0.462545\pi$
$864$	12.5543	−	19.6426i	0.427104	−	0.668254i
$865$	−27.5522	+	40.3569i	−0.936804	+	1.37218i
$866$	−3.43557			−0.116745
$867$	0.533358	+	7.37101i	0.0181138	+	0.250333i
$868$	11.7567	+	11.7567i	0.399049	+	0.399049i
$869$		−	18.3454i		−	0.622326i
$870$	6.04216	−	10.3884i	0.204848	−	0.352201i
$871$	18.9456	−	1.62811i	0.641948	−	0.0551665i
$872$	−19.6623	−	19.6623i	−0.665849	−	0.665849i
$873$	23.5434	+	17.5632i	0.796823	+	0.594425i
$874$			2.58070i			0.0872934i
$875$	−15.0389	−	3.46254i	−0.508408	−	0.117055i
$876$	4.55731	+	3.94229i	0.153977	+	0.133198i
$877$	12.0455	+	12.0455i	0.406746	+	0.406746i	0.880602	−	0.473856i	$-0.157138\pi$
$877$	12.0455	+	12.0455i	0.406746	+	0.406746i	−0.473856	+	0.880602i	$0.657138\pi$
$878$	10.6862	+	10.6862i	0.360641	+	0.360641i
$879$	−6.64241	−	5.74600i	−0.224043	−	0.193808i
$880$	11.5855	−	2.18451i	0.390546	−	0.0736397i
$881$		−	17.6186i		−	0.593585i	−0.954942	−	0.296792i	$-0.904083\pi$
$881$		−	17.6186i		−	0.593585i	0.954942	−	0.296792i	$-0.0959169\pi$
$882$	5.18572	+	3.86852i	0.174612	+	0.130260i
$883$	31.1721	+	31.1721i	1.04902	+	1.04902i	0.998735	+	0.0502889i	$0.0160142\pi$
$883$	31.1721	+	31.1721i	1.04902	+	1.04902i	0.0502889	+	0.998735i	$0.483986\pi$
$884$	2.59220	+	30.1642i	0.0871851	+	1.01453i
$885$	9.06252	+	34.2598i	0.304633	+	1.15163i
$886$		−	9.18312i		−	0.308513i
$887$	−12.6195	−	12.6195i	−0.423721	−	0.423721i	0.462762	−	0.886483i	$-0.346858\pi$
$887$	−12.6195	−	12.6195i	−0.423721	−	0.423721i	−0.886483	+	0.462762i	$0.846858\pi$
$888$	1.49053	+	20.5991i	0.0500189	+	0.691261i
$889$	3.79443			0.127261
$890$	−2.93203	−	2.00174i	−0.0982820	−	0.0670985i
$891$	−15.3820	+	4.57231i	−0.515318	+	0.153178i
$892$	−12.8480	−	12.8480i	−0.430184	−	0.430184i
$893$	35.2424	−	35.2424i	1.17934	−	1.17934i
$894$	10.1990	+	8.82262i	0.341106	+	0.295073i
$895$	27.5522	−	5.19514i	0.920970	−	0.173654i
$896$		−	14.7311i		−	0.492130i
$897$	0.967660	+	6.07501i	0.0323092	+	0.202839i
$898$	9.47128	+	9.47128i	0.316061	+	0.316061i
$899$		−	48.4945i		−	1.61738i
$900$	13.5046	+	23.7401i	0.450152	+	0.791335i
$901$	11.3497			0.378115
$902$	−3.44593	+	3.44593i	−0.114737	+	0.114737i
$903$	0.434759	+	6.00837i	0.0144679	+	0.199946i
$904$	−8.47443			−0.281855
$905$	−34.3689	+	6.48045i	−1.14246	+	0.215418i
$906$	−3.43189	−	2.96875i	−0.114017	−	0.0986301i
$907$	−15.3949	+	15.3949i	−0.511178	+	0.511178i	−0.914887	−	0.403710i	$-0.867721\pi$
$907$	−15.3949	+	15.3949i	−0.511178	+	0.511178i	0.403710	+	0.914887i	$0.367721\pi$
$908$	18.1410	+	18.1410i	0.602029	+	0.602029i
$909$	3.91220	+	26.8918i	0.129760	+	0.891945i
$910$	−2.31318	+	4.10353i	−0.0766813	+	0.136031i
$911$		−	26.3116i		−	0.871742i	−0.900009	−	0.435871i	$-0.856440\pi$
$911$		−	26.3116i		−	0.871742i	0.900009	−	0.435871i	$-0.143560\pi$
$912$	−31.6172	+	2.28779i	−1.04695	+	0.0757561i
$913$	14.1522	+	14.1522i	0.468368	+	0.468368i
$914$	−3.26571			−0.108020
$915$	3.80047	−	1.00532i	0.125640	−	0.0332347i
$916$			12.0288i			0.397442i
$917$	−2.25659	+	2.25659i	−0.0745192	+	0.0745192i
$918$	9.90597	−	2.18086i	0.326946	−	0.0719790i
$919$			7.78633i			0.256847i	0.991719	+	0.128424i	$0.0409917\pi$
$919$			7.78633i			0.256847i	−0.991719	+	0.128424i	$0.959008\pi$
$920$	−3.50068	+	0.660074i	−0.115414	+	0.0217620i
$921$	−23.9674	−	20.7329i	−0.789753	−	0.683174i
$922$	3.89589	−	3.89589i	0.128304	−	0.128304i
$923$	−12.7645	+	15.1646i	−0.420149	+	0.499151i
$924$	−5.07802	+	5.87022i	−0.167055	+	0.193116i
$925$	−33.7688	−	14.7840i	−1.11031	−	0.486095i
$926$		−	13.1177i		−	0.431073i
$927$	27.1601	+	20.2613i	0.892056	+	0.665468i
$928$	−23.2550	+	23.2550i	−0.763382	+	0.763382i
$929$		−	39.7057i		−	1.30270i	−0.758777	−	0.651350i	$-0.774203\pi$
$929$		−	39.7057i		−	1.30270i	0.758777	−	0.651350i	$-0.225797\pi$
$930$	−9.37495	−	5.45268i	−0.307417	−	0.178801i
$931$		−	31.5327i		−	1.03344i
$932$	1.55118	+	1.55118i	0.0508107	+	0.0508107i
$933$	−4.14839	−	57.3308i	−0.135812	−	1.87693i
$934$	−5.54779			−0.181529
$935$	15.1849	+	10.3669i	0.496599	+	0.339035i
$936$	17.0327	−	3.99153i	0.556730	−	0.130467i
$937$	−10.9400	+	10.9400i	−0.357393	+	0.357393i	−0.862851	−	0.505458i	$-0.831324\pi$
$937$	−10.9400	+	10.9400i	−0.357393	+	0.357393i	0.505458	+	0.862851i	$0.331324\pi$
$938$	−2.17891	−	2.17891i	−0.0711440	−	0.0711440i
$939$	19.6612	+	17.0079i	0.641620	+	0.555032i
$940$	27.0777	+	18.4863i	0.883176	+	0.602957i
$941$	17.6417			0.575103			0.287552	−	0.957765i	$-0.407159\pi$
$941$	17.6417			0.575103			0.287552	+	0.957765i	$0.407159\pi$
$942$	−0.0461879	−	0.638317i	−0.00150488	−	0.0207975i
$943$	−4.49741	+	4.49741i	−0.146456	+	0.146456i
$944$		−	27.0571i		−	0.880635i
$945$	−14.8798	−	5.98346i	−0.484041	−	0.194642i
$946$	−1.90174			−0.0618309
$947$	4.36211	−	4.36211i	0.141750	−	0.141750i	−0.632671	−	0.774421i	$-0.718041\pi$
$947$	4.36211	−	4.36211i	0.141750	−	0.141750i	0.774421	+	0.632671i	$0.218041\pi$
$948$	−32.3642	+	2.34184i	−1.05114	+	0.0760593i
$949$	0.589847	+	6.86378i	0.0191473	+	0.222808i
$950$	−5.25352	+	11.9998i	−0.170447	+	0.389325i
$951$	−31.8672	+	36.8387i	−1.03337	+	1.19458i
$952$	7.27969	−	7.27969i	0.235936	−	0.235936i
$953$	3.66862	−	3.66862i	0.118838	−	0.118838i	−0.645187	−	0.764025i	$-0.723220\pi$
$953$	3.66862	−	3.66862i	0.118838	−	0.118838i	0.764025	+	0.645187i	$0.223220\pi$
$954$	−0.449938	−	3.09279i	−0.0145673	−	0.100133i
$955$	8.84250	+	46.8959i	0.286137	+	1.51752i
$956$	2.47375			0.0800068
$957$	22.5799	−	1.63385i	0.729903	−	0.0528150i
$958$	2.82346	+	2.82346i	0.0912218	+	0.0912218i
$959$	18.1166			0.585015
$960$	−3.97661	−	15.0331i	−0.128344	−	0.485191i
$961$	−12.7634			−0.411723
$962$	−7.24604	+	8.60852i	−0.233622	+	0.277550i
$963$	42.7512	+	31.8922i	1.37764	+	1.02771i
$964$	6.81698			0.219560
$965$	19.8993	−	29.1474i	0.640583	−	0.938288i
$966$	0.652179	−	0.753923i	0.0209835	−	0.0242571i
$967$	20.9698	+	20.9698i	0.674344	+	0.674344i	0.958714	−	0.284370i	$-0.0917846\pi$
$967$	20.9698	+	20.9698i	0.674344	+	0.674344i	−0.284370	+	0.958714i	$0.591785\pi$
$968$	8.94409	+	8.94409i	0.287474	+	0.287474i
$969$	−37.3889	−	32.3432i	−1.20110	−	1.03901i
$970$	−9.10677	+	1.71713i	−0.292401	+	0.0551339i
$971$			47.6286i			1.52847i	0.644936	+	0.764237i	$0.276884\pi$
$971$			47.6286i			1.52847i	−0.644936	+	0.764237i	$0.723116\pi$
$972$	10.0298	+	26.5527i	0.321707	+	0.851677i
$973$	−6.26970	+	6.26970i	−0.200997	+	0.200997i
$974$	15.5005			0.496667
$975$	−7.86742	+	30.2176i	−0.251959	+	0.967738i
$976$	−3.00148			−0.0960750
$977$	−23.4308	+	23.4308i	−0.749619	+	0.749619i	−0.974408	−	0.224789i	$-0.927831\pi$
$977$	−23.4308	+	23.4308i	−0.749619	+	0.749619i	0.224789	+	0.974408i	$0.427831\pi$
$978$	0.104922	+	1.45003i	0.00335505	+	0.0463668i
$979$		−	6.68777i		−	0.213742i
$980$	20.3839	−	3.84351i	0.651141	−	0.122776i
$981$	51.0415	−	7.42549i	1.62963	−	0.237078i
$982$	−4.94590	−	4.94590i	−0.157830	−	0.157830i
$983$	6.58757	+	6.58757i	0.210111	+	0.210111i	0.804315	−	0.594204i	$-0.202533\pi$
$983$	6.58757	+	6.58757i	0.210111	+	0.210111i	−0.594204	+	0.804315i	$0.702533\pi$
$984$	13.6796	+	11.8335i	0.436089	+	0.377238i
$985$	−23.3075	+	34.1395i	−0.742639	+	1.08777i
$986$	−14.3097			−0.455713
$987$	−19.2019	+	1.38943i	−0.611204	+	0.0442260i
$988$	−31.0864	−	26.1663i	−0.988990	−	0.832462i
$989$	−2.48203			−0.0789240
$990$	2.22301	−	4.54884i	0.0706517	−	0.144572i
$991$	18.9007			0.600401			0.300201	−	0.953876i	$-0.402946\pi$
$991$	18.9007			0.600401			0.300201	+	0.953876i	$0.402946\pi$
$992$	20.9862	+	20.9862i	0.666313	+	0.666313i
$993$	−1.34820	−	18.6322i	−0.0427839	−	0.591274i
$994$	3.21210			0.101882
$995$	4.91163	+	26.0487i	0.155709	+	0.825799i
$996$	23.1600	−	26.7732i	0.733854	−	0.848340i
$997$	−13.8173	+	13.8173i	−0.437598	+	0.437598i	−0.891203	−	0.453605i	$-0.850138\pi$
$997$	−13.8173	+	13.8173i	−0.437598	+	0.437598i	0.453605	+	0.891203i	$0.350138\pi$
$998$	9.74227	−	9.74227i	0.308386	−	0.308386i
$999$	−32.2796	−	20.6310i	−1.02128	−	0.652736i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	195.2.s.b.38.8	yes	32
3.2	odd	2	inner	195.2.s.b.38.9	yes	32
5.2	odd	4	inner	195.2.s.b.77.7	yes	32
5.3	odd	4		975.2.s.e.857.10		32
5.4	even	2		975.2.s.e.818.9		32
13.12	even	2	inner	195.2.s.b.38.10	yes	32
15.2	even	4	inner	195.2.s.b.77.10	yes	32
15.8	even	4		975.2.s.e.857.7		32
15.14	odd	2		975.2.s.e.818.8		32
39.38	odd	2	inner	195.2.s.b.38.7	✓	32
65.12	odd	4	inner	195.2.s.b.77.9	yes	32
65.38	odd	4		975.2.s.e.857.8		32
65.64	even	2		975.2.s.e.818.7		32
195.38	even	4		975.2.s.e.857.9		32
195.77	even	4	inner	195.2.s.b.77.8	yes	32
195.194	odd	2		975.2.s.e.818.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.s.b.38.7	✓	32	39.38	odd	2	inner
195.2.s.b.38.8	yes	32	1.1	even	1	trivial
195.2.s.b.38.9	yes	32	3.2	odd	2	inner
195.2.s.b.38.10	yes	32	13.12	even	2	inner
195.2.s.b.77.7	yes	32	5.2	odd	4	inner
195.2.s.b.77.8	yes	32	195.77	even	4	inner
195.2.s.b.77.9	yes	32	65.12	odd	4	inner
195.2.s.b.77.10	yes	32	15.2	even	4	inner
975.2.s.e.818.7		32	65.64	even	2
975.2.s.e.818.8		32	15.14	odd	2
975.2.s.e.818.9		32	5.4	even	2
975.2.s.e.818.10		32	195.194	odd	2
975.2.s.e.857.7		32	15.8	even	4
975.2.s.e.857.8		32	65.38	odd	4
975.2.s.e.857.9		32	195.38	even	4
975.2.s.e.857.10		32	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	195.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.299314 + 0.299314i) q^{2} +(1.72753 - 0.125002i) q^{3} +1.82082i q^{4} +(2.19735 - 0.414323i) q^{5} +(-0.479660 + 0.554490i) q^{6} +(-0.976029 - 0.976029i) q^{7} +(-1.14363 - 1.14363i) q^{8} +(2.96875 - 0.431892i) q^{9} +(-0.533684 + 0.781709i) q^{10} -1.78302 q^{11} +(0.227607 + 3.14553i) q^{12} +(-2.32186 + 2.75844i) q^{13} +0.584278 q^{14} +(3.74420 - 0.990431i) q^{15} -2.95704 q^{16} +(-3.26089 - 3.26089i) q^{17} +(-0.759317 + 1.01786i) q^{18} +6.18928 q^{19} +(0.754408 + 4.00098i) q^{20} +(-1.80813 - 1.56412i) q^{21} +(0.533684 - 0.533684i) q^{22} +(0.696530 - 0.696530i) q^{23} +(-2.11861 - 1.83270i) q^{24} +(4.65667 - 1.82082i) q^{25} +(-0.130675 - 1.52060i) q^{26} +(5.07463 - 1.11721i) q^{27} +(1.77718 - 1.77718i) q^{28} -7.33056 q^{29} +(-0.824242 + 1.41714i) q^{30} +6.61539i q^{31} +(3.17233 - 3.17233i) q^{32} +(-3.08024 + 0.222882i) q^{33} +1.95206 q^{34} +(-2.54907 - 1.74028i) q^{35} +(0.786399 + 5.40556i) q^{36} +(-5.21325 - 5.21325i) q^{37} +(-1.85254 + 1.85254i) q^{38} +(-3.66628 + 5.05553i) q^{39} +(-2.98677 - 2.03911i) q^{40} -6.45687 q^{41} +(1.00936 - 0.0730362i) q^{42} +(-1.78171 - 1.78171i) q^{43} -3.24657i q^{44} +(6.34443 - 2.17904i) q^{45} +0.416963i q^{46} +(5.69410 - 5.69410i) q^{47} +(-5.10838 + 0.369637i) q^{48} -5.09473i q^{49} +(-0.848810 + 1.93881i) q^{50} +(-6.04091 - 5.22568i) q^{51} +(-5.02263 - 4.22769i) q^{52} +(-1.74028 + 1.74028i) q^{53} +(-1.18451 + 1.85330i) q^{54} +(-3.91793 + 0.738748i) q^{55} +2.23242i q^{56} +(10.6922 - 0.773675i) q^{57} +(2.19414 - 2.19414i) q^{58} +9.15008i q^{59} +(1.80340 + 6.81753i) q^{60} +1.01503 q^{61} +(-1.98008 - 1.98008i) q^{62} +(-3.31913 - 2.47605i) q^{63} -4.01503i q^{64} +(-3.95904 + 7.02325i) q^{65} +(0.855246 - 0.988670i) q^{66} +(-3.72923 - 3.72923i) q^{67} +(5.93750 - 5.93750i) q^{68} +(1.11621 - 1.29035i) q^{69} +(1.28386 - 0.242080i) q^{70} +5.49755 q^{71} +(-3.88906 - 2.90121i) q^{72} +(1.35106 - 1.35106i) q^{73} +3.12079 q^{74} +(7.81696 - 3.72763i) q^{75} +11.2696i q^{76} +(1.74028 + 1.74028i) q^{77} +(-0.415824 - 2.61056i) q^{78} +10.2889i q^{79} +(-6.49764 + 1.22517i) q^{80} +(8.62694 - 2.56436i) q^{81} +(1.93263 - 1.93263i) q^{82} +(-7.93716 - 7.93716i) q^{83} +(2.84798 - 3.29228i) q^{84} +(-8.51636 - 5.81424i) q^{85} +1.06658 q^{86} +(-12.6638 + 0.916338i) q^{87} +(2.03911 + 2.03911i) q^{88} +3.75080i q^{89} +(-1.24676 + 2.55119i) q^{90} +(4.95852 - 0.426116i) q^{91} +(1.26826 + 1.26826i) q^{92} +(0.826940 + 11.4283i) q^{93} +3.40865i q^{94} +(13.6000 - 2.56436i) q^{95} +(5.08377 - 5.87686i) q^{96} +(6.92322 + 6.92322i) q^{97} +(1.52492 + 1.52492i) q^{98} +(-5.29335 + 0.770074i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{3} - 24 q^{10} - 24 q^{12} + 24 q^{16} + 24 q^{22} - 8 q^{25} - 16 q^{27} + 36 q^{30} - 8 q^{36} + 16 q^{40} + 12 q^{42} - 64 q^{43} - 20 q^{48} + 16 q^{51} - 72 q^{52} - 80 q^{55} + 8 q^{61}+ \cdots - 40 q^{91}+O(q^{100}) \) 32 * q - 4 * q^3 - 24 * q^10 - 24 * q^12 + 24 * q^16 + 24 * q^22 - 8 * q^25 - 16 * q^27 + 36 * q^30 - 8 * q^36 + 16 * q^40 + 12 * q^42 - 64 * q^43 - 20 * q^48 + 16 * q^51 - 72 * q^52 - 80 * q^55 + 8 * q^61 - 72 * q^66 + 44 * q^75 + 84 * q^78 + 112 * q^81 + 48 * q^82 + 20 * q^87 - 8 * q^88 + 44 * q^90 - 40 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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