LMFDB - Embedded newform 378.2.z.a.41.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(41,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.41"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([17, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.3
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.984808 + 0.173648i) q^{2} +(-1.34465 + 1.09174i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.60134 - 2.18278i) q^{5} +(1.13465 - 1.30865i) q^{6} +(-0.615646 + 2.57313i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.616190 - 2.93604i) q^{9} +(2.94085 + 1.69790i) q^{10} +(0.604733 + 0.720693i) q^{11} +(-0.890163 + 1.48580i) q^{12} +(-0.436415 - 0.0769517i) q^{13} +(0.159475 - 2.64094i) q^{14} +(5.88094 + 0.0950914i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.11282 - 1.92746i) q^{17} +(-0.0969913 + 2.99843i) q^{18} +(6.85516 - 3.95783i) q^{19} +(-3.19101 - 1.16143i) q^{20} +(-1.98136 - 4.13209i) q^{21} +(-0.720693 - 0.604733i) q^{22} +(-0.171072 - 0.470016i) q^{23} +(0.618633 - 1.61781i) q^{24} +(1.13418 + 6.43225i) q^{25} +0.443147 q^{26} +(2.37684 + 4.62068i) q^{27} +(0.301543 + 2.62851i) q^{28} +(8.00322 - 1.41118i) q^{29} +(-5.80810 + 0.927567i) q^{30} +(2.68497 + 7.37690i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-1.59997 - 0.308869i) q^{33} +(-0.761215 + 2.09142i) q^{34} +(7.21807 - 5.34975i) q^{35} +(-0.425154 - 2.96972i) q^{36} +(-0.250369 + 0.433653i) q^{37} +(-6.06375 + 5.08809i) q^{38} +(0.670839 - 0.372980i) q^{39} +(3.34421 + 0.589675i) q^{40} +(1.16708 - 6.61885i) q^{41} +(2.66879 + 3.72526i) q^{42} +(3.79011 - 3.18028i) q^{43} +(0.814755 + 0.470399i) q^{44} +(-8.01164 + 6.29261i) q^{45} +(0.250090 + 0.433169i) q^{46} +(2.17304 + 0.790920i) q^{47} +(-0.328305 + 1.70065i) q^{48} +(-6.24196 - 3.16827i) q^{49} +(-2.23390 - 6.13758i) q^{50} +(0.607937 + 3.80669i) q^{51} +(-0.436415 + 0.0769517i) q^{52} +7.36731i q^{53} +(-3.14310 - 4.13774i) q^{54} -3.19476i q^{55} +(-0.753398 - 2.53622i) q^{56} +(-4.89689 + 12.8060i) q^{57} +(-7.63658 + 2.77949i) q^{58} +(-0.00253927 - 0.00213070i) q^{59} +(5.55879 - 1.92204i) q^{60} +(4.17042 - 11.4581i) q^{61} +(-3.92517 - 6.79859i) q^{62} +(7.17544 + 3.39309i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.967293 + 1.15278i) q^{65} +(1.62930 + 0.0263448i) q^{66} +(2.67026 - 15.1438i) q^{67} +(0.386479 - 2.19183i) q^{68} +(0.743170 + 0.445243i) q^{69} +(-6.17944 + 6.52188i) q^{70} +(-10.3605 - 5.98164i) q^{71} +(0.934382 + 2.85078i) q^{72} +(-3.87195 + 2.23547i) q^{73} +(0.171263 - 0.470541i) q^{74} +(-8.54745 - 7.41092i) q^{75} +(5.08809 - 6.06375i) q^{76} +(-2.22674 + 1.11236i) q^{77} +(-0.595880 + 0.483804i) q^{78} +(1.93918 + 10.9977i) q^{79} -3.39580 q^{80} +(-8.24062 - 3.61831i) q^{81} +6.72095i q^{82} +(-2.34318 - 13.2888i) q^{83} +(-3.27513 - 3.20523i) q^{84} +(-7.10206 + 2.58494i) q^{85} +(-3.18028 + 3.79011i) q^{86} +(-9.22091 + 10.6350i) q^{87} +(-0.884061 - 0.321772i) q^{88} +(4.96971 + 8.60779i) q^{89} +(6.79722 - 7.58822i) q^{90} +(0.466684 - 1.07558i) q^{91} +(-0.321510 - 0.383161i) q^{92} +(-11.6641 - 6.98808i) q^{93} +(-2.27736 - 0.401561i) q^{94} +(-26.4717 - 4.66767i) q^{95} +(0.0280026 - 1.73182i) q^{96} +(1.02275 + 1.21886i) q^{97} +(6.69729 + 2.03623i) q^{98} +(2.48861 - 1.33143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$2$	−0.984808	+	0.173648i	−0.696364	+	0.122788i
$3$	−1.34465	+	1.09174i	−0.776336	+	0.630319i
$3$	−1.34465	+	1.09174i	−0.776336	+	0.630319i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	−2.60134	−	2.18278i	−1.16335	−	0.976169i	−0.163407	−	0.986559i	$-0.552248\pi$
$5$	−2.60134	−	2.18278i	−1.16335	−	0.976169i	−0.999946	+	0.0103897i	$0.996693\pi$
$6$	1.13465	−	1.30865i	0.463218	−	0.534256i
$7$	−0.615646	+	2.57313i	−0.232692	+	0.972550i
$7$	−0.615646	+	2.57313i	−0.232692	+	0.972550i
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	0.616190	−	2.93604i	0.205397	−	0.978679i
$10$	2.94085	+	1.69790i	0.929979	+	0.536924i
$11$	0.604733	+	0.720693i	0.182334	+	0.217297i	0.849467	−	0.527641i	$-0.176923\pi$
$11$	0.604733	+	0.720693i	0.182334	+	0.217297i	−0.667134	+	0.744938i	$0.732479\pi$
$12$	−0.890163	+	1.48580i	−0.256968	+	0.428914i
$13$	−0.436415	−	0.0769517i	−0.121040	−	0.0213426i	0.112800	−	0.993618i	$-0.464018\pi$
$13$	−0.436415	−	0.0769517i	−0.121040	−	0.0213426i	−0.233840	+	0.972275i	$0.575129\pi$
$14$	0.159475	−	2.64094i	0.0426214	−	0.705821i
$15$	5.88094	+	0.0950914i	1.51845	+	0.0245525i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.11282	−	1.92746i	0.269899	−	0.467479i	−0.698936	−	0.715184i	$-0.746343\pi$
$17$	1.11282	−	1.92746i	0.269899	−	0.467479i	0.968836	+	0.247705i	$0.0796763\pi$
$18$	−0.0969913	+	2.99843i	−0.0228611	+	0.706737i
$19$	6.85516	−	3.95783i	1.57268	−	0.907988i	0.576843	−	0.816855i	$-0.304284\pi$
$19$	6.85516	−	3.95783i	1.57268	−	0.907988i	0.995839	−	0.0911335i	$-0.0290490\pi$
$20$	−3.19101	−	1.16143i	−0.713532	−	0.259704i
$21$	−1.98136	−	4.13209i	−0.432369	−	0.901697i
$22$	−0.720693	−	0.604733i	−0.153652	−	0.128930i
$23$	−0.171072	−	0.470016i	−0.0356710	−	0.0980051i	0.920579	−	0.390557i	$-0.127718\pi$
$23$	−0.171072	−	0.470016i	−0.0356710	−	0.0980051i	−0.956250	+	0.292552i	$0.905495\pi$
$24$	0.618633	−	1.61781i	0.126278	−	0.330233i
$25$	1.13418	+	6.43225i	0.226836	+	1.28645i
$26$	0.443147			0.0869084
$27$	2.37684	+	4.62068i	0.457423	+	0.889249i
$28$	0.301543	+	2.62851i	0.0569862	+	0.496742i
$29$	8.00322	−	1.41118i	1.48616	−	0.262050i	0.629123	−	0.777305i	$-0.283414\pi$
$29$	8.00322	−	1.41118i	1.48616	−	0.262050i	0.857037	+	0.515255i	$0.172303\pi$
$30$	−5.80810	+	0.927567i	−1.06041	+	0.169350i
$31$	2.68497	+	7.37690i	0.482236	+	1.32493i	0.907572	+	0.419896i	$0.137933\pi$
$31$	2.68497	+	7.37690i	0.482236	+	1.32493i	−0.425337	+	0.905035i	$0.639844\pi$
$32$	−0.642788	+	0.766044i	−0.113630	+	0.135419i
$33$	−1.59997	−	0.308869i	−0.278519	−	0.0537672i
$34$	−0.761215	+	2.09142i	−0.130547	+	0.358676i
$35$	7.21807	−	5.34975i	1.22008	−	0.904272i
$36$	−0.425154	−	2.96972i	−0.0708591	−	0.494954i
$37$	−0.250369	+	0.433653i	−0.0411605	+	0.0712920i	−0.885872	−	0.463930i	$-0.846439\pi$
$37$	−0.250369	+	0.433653i	−0.0411605	+	0.0712920i	0.844711	+	0.535222i	$0.179772\pi$
$38$	−6.06375	+	5.08809i	−0.983670	+	0.825397i
$39$	0.670839	−	0.372980i	0.107420	−	0.0597246i
$40$	3.34421	+	0.589675i	0.528767	+	0.0932358i
$41$	1.16708	−	6.61885i	0.182268	−	1.03369i	−0.747149	−	0.664657i	$-0.768578\pi$
$41$	1.16708	−	6.61885i	0.182268	−	1.03369i	0.929416	−	0.369033i	$-0.120311\pi$
$42$	2.66879	+	3.72526i	0.411804	+	0.574820i
$43$	3.79011	−	3.18028i	0.577987	−	0.484988i	−0.306299	−	0.951935i	$-0.599091\pi$
$43$	3.79011	−	3.18028i	0.577987	−	0.484988i	0.884285	+	0.466947i	$0.154646\pi$
$44$	0.814755	+	0.470399i	0.122829	+	0.0709153i
$45$	−8.01164	+	6.29261i	−1.19430	+	0.938047i
$46$	0.250090	+	0.433169i	0.0368738	+	0.0638673i
$47$	2.17304	+	0.790920i	0.316970	+	0.115368i	0.495606	−	0.868548i	$-0.334946\pi$
$47$	2.17304	+	0.790920i	0.316970	+	0.115368i	−0.178636	+	0.983915i	$0.557168\pi$
$48$	−0.328305	+	1.70065i	−0.0473868	+	0.245468i
$49$	−6.24196	−	3.16827i	−0.891708	−	0.452610i
$50$	−2.23390	−	6.13758i	−0.315921	−	0.867985i
$51$	0.607937	+	3.80669i	0.0851282	+	0.533043i
$52$	−0.436415	+	0.0769517i	−0.0605199	+	0.0106713i
$53$			7.36731i			1.01198i	0.862540	+	0.505989i	$0.168872\pi$
$53$			7.36731i			1.01198i	−0.862540	+	0.505989i	$0.831128\pi$
$54$	−3.14310	−	4.13774i	−0.427722	−	0.563076i
$55$		−	3.19476i		−	0.430782i
$56$	−0.753398	−	2.53622i	−0.100677	−	0.338916i
$57$	−4.89689	+	12.8060i	−0.648608	+	1.69620i
$58$	−7.63658	+	2.77949i	−1.00273	+	0.364965i
$59$	−0.00253927	−	0.00213070i	−0.000330585	−	0.000277394i	0.642622	−	0.766183i	$-0.277846\pi$
$59$	−0.00253927	−	0.00213070i	−0.000330585	−	0.000277394i	−0.642953	+	0.765906i	$0.722291\pi$
$60$	5.55879	−	1.92204i	0.717637	−	0.248135i
$61$	4.17042	−	11.4581i	0.533967	−	1.46706i	−0.320344	−	0.947301i	$-0.603798\pi$
$61$	4.17042	−	11.4581i	0.533967	−	1.46706i	0.854311	−	0.519762i	$-0.173979\pi$
$62$	−3.92517	−	6.79859i	−0.498497	−	0.863422i
$63$	7.17544	+	3.39309i	0.904020	+	0.427490i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	0.967293	+	1.15278i	0.119978	+	0.142984i
$66$	1.62930	+	0.0263448i	0.200553	+	0.00324282i
$67$	2.67026	−	15.1438i	0.326225	−	1.85011i	−0.174702	−	0.984621i	$-0.555896\pi$
$67$	2.67026	−	15.1438i	0.326225	−	1.85011i	0.500927	−	0.865490i	$-0.332993\pi$
$68$	0.386479	−	2.19183i	0.0468675	−	0.265799i
$69$	0.743170	+	0.445243i	0.0894671	+	0.0536009i
$70$	−6.17944	+	6.52188i	−0.738584	+	0.779513i
$71$	−10.3605	−	5.98164i	−1.22956	−	0.709889i	−0.262626	−	0.964898i	$-0.584588\pi$
$71$	−10.3605	−	5.98164i	−1.22956	−	0.709889i	−0.966939	+	0.255008i	$0.917922\pi$
$72$	0.934382	+	2.85078i	0.110118	+	0.335967i
$73$	−3.87195	+	2.23547i	−0.453177	+	0.261642i	−0.709171	−	0.705036i	$-0.750931\pi$
$73$	−3.87195	+	2.23547i	−0.453177	+	0.261642i	0.255994	+	0.966678i	$0.417597\pi$
$74$	0.171263	−	0.470541i	0.0199089	−	0.0546992i
$75$	−8.54745	−	7.41092i	−0.986975	−	0.855740i
$76$	5.08809	−	6.06375i	0.583644	−	0.695559i
$77$	−2.22674	+	1.11236i	−0.253760	+	0.126766i
$78$	−0.595880	+	0.483804i	−0.0674701	+	0.0547800i
$79$	1.93918	+	10.9977i	0.218175	+	1.23733i	0.875311	+	0.483561i	$0.160657\pi$
$79$	1.93918	+	10.9977i	0.218175	+	1.23733i	−0.657135	+	0.753773i	$0.728232\pi$
$80$	−3.39580			−0.379662
$81$	−8.24062	−	3.61831i	−0.915624	−	0.402035i
$82$			6.72095i			0.742205i
$83$	−2.34318	−	13.2888i	−0.257197	−	1.45864i	−0.790369	−	0.612631i	$-0.790111\pi$
$83$	−2.34318	−	13.2888i	−0.257197	−	1.45864i	0.533172	−	0.846007i	$-0.321000\pi$
$84$	−3.27513	−	3.20523i	−0.357346	−	0.349719i
$85$	−7.10206	+	2.58494i	−0.770326	+	0.280376i
$86$	−3.18028	+	3.79011i	−0.342939	+	0.408698i
$87$	−9.22091	+	10.6350i	−0.988585	+	1.14019i
$88$	−0.884061	−	0.321772i	−0.0942412	−	0.0343010i
$89$	4.96971	+	8.60779i	0.526788	+	0.912424i	0.999513	+	0.0312137i	$0.00993725\pi$
$89$	4.96971	+	8.60779i	0.526788	+	0.912424i	−0.472724	+	0.881210i	$0.656729\pi$
$90$	6.79722	−	7.58822i	0.716490	−	0.799868i
$91$	0.466684	−	1.07558i	0.0489218	−	0.112751i
$92$	−0.321510	−	0.383161i	−0.0335197	−	0.0399473i
$93$	−11.6641	−	6.98808i	−1.20951	−	0.724630i
$94$	−2.27736	−	0.401561i	−0.234892	−	0.0414178i
$95$	−26.4717	−	4.66767i	−2.71593	−	0.478893i
$96$	0.0280026	−	1.73182i	0.00285801	−	0.176754i
$97$	1.02275	+	1.21886i	0.103844	+	0.123757i	0.815463	−	0.578809i	$-0.196482\pi$
$97$	1.02275	+	1.21886i	0.103844	+	0.123757i	−0.711619	+	0.702565i	$0.752038\pi$
$98$	6.69729	+	2.03623i	0.676529	+	0.205691i
$99$	2.48861	−	1.33143i	0.250115	−	0.133814i
$100$	3.26574	+	5.65643i	0.326574	+	0.565643i
$101$	13.3280	+	4.85099i	1.32619	+	0.482692i	0.905435	−	0.424485i	$-0.139545\pi$
$101$	13.3280	+	4.85099i	1.32619	+	0.482692i	0.420750	+	0.907177i	$0.361767\pi$
$102$	−1.25973	−	3.64329i	−0.124731	−	0.360740i
$103$	6.25058	−	7.44915i	0.615888	−	0.733987i	−0.364470	−	0.931215i	$-0.618750\pi$
$103$	6.25058	−	7.44915i	0.615888	−	0.733987i	0.980358	+	0.197229i	$0.0631941\pi$
$104$	0.416422	−	0.151565i	0.0408336	−	0.0148622i
$105$	−3.86526	+	15.0738i	−0.377211	+	1.47106i
$106$	−1.27932	−	7.25539i	−0.124259	−	0.704705i
$107$			10.6751i			1.03200i	0.856588	+	0.516001i	$0.172580\pi$
$107$			10.6751i			1.03200i	−0.856588	+	0.516001i	$0.827420\pi$
$108$	3.81386	+	3.52909i	0.366989	+	0.339587i
$109$	−3.06313			−0.293395			−0.146697	−	0.989181i	$-0.546864\pi$
$109$	−3.06313			−0.293395			−0.146697	+	0.989181i	$0.546864\pi$
$110$	0.554765	+	3.14623i	0.0528948	+	0.299981i
$111$	−0.136777	−	0.856452i	−0.0129823	−	0.0812908i
$112$	1.18236	+	2.36686i	0.111723	+	0.223647i
$113$	−8.27791	+	9.86522i	−0.778720	+	0.928042i	−0.998875	−	0.0474227i	$-0.984899\pi$
$113$	−8.27791	+	9.86522i	−0.778720	+	0.928042i	0.220155	+	0.975465i	$0.429344\pi$
$114$	2.59875	−	13.4618i	0.243396	−	1.26081i
$115$	−0.580927	+	1.59608i	−0.0541717	+	0.148835i
$116$	7.03791	−	4.06334i	0.653454	−	0.377272i
$117$	−0.494848	+	1.23391i	−0.0457487	+	0.114075i
$118$	0.00287069	+	0.00165739i	0.000264268	+	0.000152575i
$119$	4.27451	+	4.05007i	0.391843	+	0.371269i
$120$	−5.14059	+	2.85812i	−0.469269	+	0.260909i
$121$	1.75643	−	9.96123i	0.159676	−	0.905567i
$122$	−2.11738	+	12.0082i	−0.191698	+	1.08717i
$123$	5.65677	+	10.1742i	0.510053	+	0.917378i
$124$	5.04610	+	6.01371i	0.453153	+	0.540047i
$125$	2.60030	−	4.50386i	0.232578	−	0.402837i
$126$	−7.65563	−	2.09554i	−0.682018	−	0.186686i
$127$	2.00102	+	3.46586i	0.177562	+	0.307546i	0.941045	−	0.338282i	$-0.109846\pi$
$127$	2.00102	+	3.46586i	0.177562	+	0.307546i	−0.763483	+	0.645828i	$0.776512\pi$
$128$	−0.342020	+	0.939693i	−0.0302306	+	0.0830579i
$129$	−1.62434	+	8.41421i	−0.143015	+	0.740830i
$130$	−1.15278	−	0.967293i	−0.101105	−	0.0848372i
$131$	2.04658	−	0.744896i	0.178811	−	0.0650819i	−0.251063	−	0.967971i	$-0.580780\pi$
$131$	2.04658	−	0.744896i	0.178811	−	0.0650819i	0.429874	+	0.902889i	$0.358558\pi$
$132$	−1.60912	+	0.256980i	−0.140056	+	0.0223672i
$133$	5.96364	+	20.0758i	0.517113	+	1.74079i
$134$			15.3774i			1.32841i
$135$	3.90297	−	17.2080i	0.335914	−	1.48103i
$136$			2.22564i			0.190847i
$137$	0.365105	−	0.0643778i	0.0311930	−	0.00550017i	−0.158030	−	0.987434i	$-0.550514\pi$
$137$	0.365105	−	0.0643778i	0.0311930	−	0.00550017i	0.189223	+	0.981934i	$0.439403\pi$
$138$	−0.809195	−	0.309428i	−0.0688833	−	0.0263403i
$139$	−2.62642	−	7.21603i	−0.222770	−	0.612056i	0.777079	−	0.629403i	$-0.216700\pi$
$139$	−2.62642	−	7.21603i	−0.222770	−	0.612056i	−0.999850	+	0.0173467i	$0.994478\pi$
$140$	4.95305	−	7.49584i	0.418609	−	0.633514i
$141$	−3.78546	+	1.30888i	−0.318794	+	0.110228i
$142$	11.2418	+	4.09168i	0.943391	+	0.343366i
$143$	−0.208456	−	0.361056i	−0.0174320	−	0.0301931i
$144$	−1.41522	−	2.64521i	−0.117935	−	0.220434i
$145$	−23.8994	−	13.7983i	−1.98473	−	1.14589i
$146$	3.42494	−	2.87387i	0.283450	−	0.237843i
$147$	11.8522	−	2.55439i	0.977555	−	0.210683i
$148$	−0.0869524	+	0.493131i	−0.00714744	+	0.0405352i
$149$	−1.33021	−	0.234552i	−0.108975	−	0.0192153i	0.118895	−	0.992907i	$-0.462065\pi$
$149$	−1.33021	−	0.234552i	−0.108975	−	0.0192153i	−0.227870	+	0.973692i	$0.573176\pi$
$150$	9.70449	+	5.81408i	0.792368	+	0.474718i
$151$	1.44238	−	1.21030i	0.117379	−	0.0984928i	−0.582209	−	0.813039i	$-0.697811\pi$
$151$	1.44238	−	1.21030i	0.117379	−	0.0984928i	0.699588	+	0.714547i	$0.253367\pi$
$152$	−3.95783	+	6.85516i	−0.321022	+	0.556027i
$153$	−4.97340	−	4.45497i	−0.402075	−	0.360163i
$154$	1.99975	−	1.48213i	0.161144	−	0.119434i
$155$	9.11764	−	25.0505i	0.732347	−	2.01211i
$156$	0.502816	−	0.579927i	0.0402575	−	0.0464313i
$157$	7.04611	−	8.39723i	0.562341	−	0.670172i	−0.407699	−	0.913116i	$-0.633669\pi$
$157$	7.04611	−	8.39723i	0.562341	−	0.670172i	0.970040	+	0.242944i	$0.0781132\pi$
$158$	−3.81945	−	10.4938i	−0.303859	−	0.834846i
$159$	−8.04322	−	9.90649i	−0.637869	−	0.785636i
$160$	3.34421	−	0.589675i	0.264383	−	0.0466179i
$161$	1.31473	−	0.150826i	0.103615	−	0.0118867i
$162$	8.74374	+	2.13237i	0.686973	+	0.167535i
$163$	18.9873			1.48720			0.743602	−	0.668623i	$-0.233116\pi$
$163$	18.9873			1.48720			0.743602	+	0.668623i	$0.233116\pi$
$164$	−1.16708	−	6.61885i	−0.0911338	−	0.516845i
$165$	3.48786	+	4.29585i	0.271530	+	0.334432i
$166$	4.61516	+	12.6801i	0.358206	+	0.984163i
$167$	13.2165	+	11.0900i	1.02272	+	0.858168i	0.989967	−	0.141295i	$-0.0451267\pi$
$167$	13.2165	+	11.0900i	1.02272	+	0.858168i	0.0327573	+	0.999463i	$0.489571\pi$
$168$	3.78196	+	2.58782i	0.291784	+	0.199654i
$169$	−12.0315	−	4.37910i	−0.925498	−	0.336854i
$170$	6.54529	−	3.77893i	0.502001	−	0.289830i
$171$	−7.39625	−	22.5658i	−0.565605	−	1.72565i
$172$	2.47382	−	4.28478i	0.188627	−	0.326711i
$173$	8.32627	−	6.98657i	0.633035	−	0.531179i	−0.268835	−	0.963186i	$-0.586639\pi$
$173$	8.32627	−	6.98657i	0.633035	−	0.531179i	0.901870	+	0.432007i	$0.142194\pi$
$174$	7.23407	−	12.0746i	0.548414	−	0.915376i
$175$	−17.2493	−	1.04161i	−1.30392	−	0.0787380i
$176$	0.926505	+	0.163368i	0.0698379	+	0.0123143i
$177$	0.00574062		9.28227e-5i	0.000431492		6.97698e-6i
$178$	−6.38894	−	7.61404i	−0.478871	−	0.570696i
$179$	7.43780	+	4.29421i	0.555927	+	0.320965i	0.751509	−	0.659723i	$-0.229326\pi$
$179$	7.43780	+	4.29421i	0.555927	+	0.320965i	−0.195582	+	0.980687i	$0.562660\pi$
$180$	−5.37628	+	8.65326i	−0.400724	+	0.644976i
$181$	−6.94977	+	4.01245i	−0.516572	+	0.298243i	−0.735531	−	0.677491i	$-0.763067\pi$
$181$	−6.94977	+	4.01245i	−0.516572	+	0.298243i	0.218959	+	0.975734i	$0.429734\pi$
$182$	−0.272822	+	1.14027i	−0.0202229	+	0.0845228i
$183$	6.90157	+	19.9603i	0.510179	+	1.47550i
$184$	0.383161	+	0.321510i	0.0282470	+	0.0237020i
$185$	1.59786	−	0.581575i	0.117477	−	0.0427582i
$186$	12.7003	+	4.85648i	0.931232	+	0.356094i
$187$	2.06207	−	0.363599i	0.150794	−	0.0265890i
$188$	2.31250			0.168656
$189$	−13.3529	+	3.27120i	−0.971279	+	0.237945i
$190$	26.8800			1.95008
$191$	21.8549	−	3.85361i	1.58136	−	0.278837i	0.687163	−	0.726503i	$-0.258856\pi$
$191$	21.8549	−	3.85361i	1.58136	−	0.278837i	0.894201	+	0.447666i	$0.147745\pi$
$192$	0.273151	+	1.71038i	0.0197130	+	0.123436i
$193$	23.8391	−	8.67673i	1.71598	−	0.624565i	0.718499	−	0.695528i	$-0.244830\pi$
$193$	23.8391	−	8.67673i	1.71598	−	0.624565i	0.997479	+	0.0709632i	$0.0226073\pi$
$194$	−1.21886	−	1.02275i	−0.0875091	−	0.0734289i
$195$	−2.55921	−	0.494048i	−0.183269	−	0.0353795i
$196$	−6.94914	−	0.842326i	−0.496367	−	0.0601661i
$197$	1.35235	−	0.780778i	0.0963507	−	0.0556281i	−0.451050	−	0.892498i	$-0.648951\pi$
$197$	1.35235	−	0.780778i	0.0963507	−	0.0556281i	0.547401	+	0.836870i	$0.315617\pi$
$198$	−2.21960	+	1.74335i	−0.157740	+	0.123894i
$199$	13.8280	+	7.98362i	0.980244	+	0.565944i	0.902344	−	0.431017i	$-0.141845\pi$
$199$	13.8280	+	7.98362i	0.980244	+	0.565944i	0.0778999	+	0.996961i	$0.475179\pi$
$200$	−4.19835	−	5.00340i	−0.296869	−	0.353794i
$201$	12.9426	+	23.2784i	0.912900	+	1.64193i
$202$	−13.9679	−	2.46291i	−0.982777	−	0.173290i
$203$	−1.29600	+	21.4621i	−0.0909613	+	1.50634i
$204$	1.87324	+	3.36919i	0.131153	+	0.235891i
$205$	−17.4835	+	14.6704i	−1.22110	+	1.02462i
$206$	−4.86209	+	8.42138i	−0.338758	+	0.586746i
$207$	−1.48540	+	0.212654i	−0.103242	+	0.0147805i
$208$	−0.383777	+	0.221574i	−0.0266101	+	0.0153634i
$209$	6.99792	+	2.54704i	0.484056	+	0.176182i
$210$	1.18899	−	15.5160i	0.0820482	−	1.07071i
$211$	−19.9260	−	16.7199i	−1.37176	−	1.15105i	−0.972149	−	0.234365i	$-0.924699\pi$
$211$	−19.9260	−	16.7199i	−1.37176	−	1.15105i	−0.399616	−	0.916683i	$-0.630857\pi$
$212$	2.51977	+	6.92301i	0.173058	+	0.475474i
$213$	20.4617	−	3.26778i	1.40201	−	0.223904i
$214$	−1.85371	−	10.5129i	−0.126717	−	0.718649i
$215$	−16.8012			−1.14583
$216$	−4.36874	−	2.81320i	−0.297255	−	0.191414i
$217$	−20.6347	+	2.36721i	−1.40077	+	0.160697i
$218$	3.01659	−	0.531907i	0.204310	−	0.0360253i
$219$	2.76587	−	7.23311i	0.186900	−	0.488768i
$220$	−1.09267	−	3.00210i	−0.0736680	−	0.202401i
$221$	−0.633974	+	0.755541i	−0.0426457	+	0.0508232i
$222$	0.283421	+	0.819689i	0.0190219	+	0.0550140i
$223$	−5.22456	+	14.3544i	−0.349862	+	0.961238i	0.632551	+	0.774519i	$0.282008\pi$
$223$	−5.22456	+	14.3544i	−0.349862	+	0.961238i	−0.982413	+	0.186720i	$0.940214\pi$
$224$	−1.57540	−	2.12559i	−0.105261	−	0.142022i
$225$	19.5842	+	0.633497i	1.30561	+	0.0422331i
$226$	6.43907	−	11.1528i	0.428320	−	0.741873i
$227$	−18.4124	+	15.4498i	−1.22207	+	1.02544i	−0.223361	+	0.974736i	$0.571703\pi$
$227$	−18.4124	+	15.4498i	−1.22207	+	1.02544i	−0.998714	+	0.0507061i	$0.983853\pi$
$228$	−0.221659	+	13.7085i	−0.0146797	+	0.907870i
$229$	−12.0270	−	2.12068i	−0.794764	−	0.140138i	−0.238498	−	0.971143i	$-0.576655\pi$
$229$	−12.0270	−	2.12068i	−0.794764	−	0.140138i	−0.556265	+	0.831005i	$0.687766\pi$
$230$	0.294944	−	1.67271i	0.0194480	−	0.110295i
$231$	1.77977	−	3.92677i	0.117101	−	0.258362i
$232$	−6.22540	+	5.22373i	−0.408717	+	0.342955i
$233$	−3.32396	−	1.91909i	−0.217760	−	0.125724i	0.387153	−	0.922016i	$-0.373459\pi$
$233$	−3.32396	−	1.91909i	−0.217760	−	0.125724i	−0.604913	+	0.796292i	$0.706792\pi$
$234$	0.273063	−	1.30110i	0.0178507	−	0.0850554i
$235$	−3.92639	−	6.80071i	−0.256130	−	0.443629i
$236$	−0.00311488	−	0.00113372i	−0.000202761	−	7.37991e-5i
$237$	−14.6142	−	12.6710i	−0.949292	−	0.823067i
$238$	−4.91285	−	3.24628i	−0.318453	−	0.210425i
$239$	5.85260	+	16.0799i	0.378573	+	1.04012i	0.971948	+	0.235196i	$0.0755731\pi$
$239$	5.85260	+	16.0799i	0.378573	+	1.04012i	−0.593375	+	0.804926i	$0.702205\pi$
$240$	4.56618	−	3.70735i	0.294746	−	0.239308i
$241$	−17.9121	+	3.15839i	−1.15382	+	0.203450i	−0.717644	−	0.696410i	$-0.754780\pi$
$241$	−17.9121	+	3.15839i	−1.15382	+	0.203450i	−0.436179	+	0.899860i	$0.643668\pi$
$242$			10.1149i			0.650210i
$243$	15.0311	−	4.13127i	0.964243	−	0.265021i
$244$		−	12.1935i		−	0.780608i
$245$	9.32179	+	21.8666i	0.595548	+	1.39700i
$246$	−7.33756	−	9.03736i	−0.467826	−	0.576201i
$247$	−3.29626	+	1.19974i	−0.209736	+	0.0763376i
$248$	−6.01371	−	5.04610i	−0.381871	−	0.320428i
$249$	17.6588	+	15.3107i	1.11908	+	0.970278i
$250$	−1.77871	+	4.88697i	−0.112496	+	0.309079i
$251$	4.89870	+	8.48480i	0.309203	+	0.535556i	0.978188	−	0.207720i	$-0.0666043\pi$
$251$	4.89870	+	8.48480i	0.309203	+	0.535556i	−0.668985	+	0.743276i	$0.733271\pi$
$252$	7.90321	+	0.734322i	0.497856	+	0.0462579i
$253$	0.235284	−	0.407525i	0.0147922	−	0.0256209i
$254$	−2.57246	−	3.06574i	−0.161410	−	0.192361i
$255$	6.72772	−	11.2295i	0.421306	−	0.703217i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	2.51430	−	14.2593i	0.156838	−	0.889471i	−0.800249	−	0.599668i	$-0.795299\pi$
$257$	2.51430	−	14.2593i	0.156838	−	0.889471i	0.957086	−	0.289803i	$-0.0935897\pi$
$258$	0.138547	−	8.56844i	0.00862555	−	0.533448i
$259$	−0.961704	−	0.911209i	−0.0597574	−	0.0566198i
$260$	1.30323	+	0.752421i	0.0808229	+	0.0466632i
$261$	0.788217	−	24.3673i	0.0487894	−	1.50830i
$262$	−1.88614	+	1.08896i	−0.116526	+	0.0672765i
$263$	−4.10344	+	11.2741i	−0.253029	+	0.695192i	0.746526	+	0.665356i	$0.231720\pi$
$263$	−4.10344	+	11.2741i	−0.253029	+	0.695192i	−0.999555	+	0.0298351i	$0.990502\pi$
$264$	1.54005	−	0.532496i	0.0947834	−	0.0327729i
$265$	16.0812	−	19.1649i	0.987862	−	1.17729i
$266$	−9.35917	−	18.7352i	−0.573847	−	1.14873i
$267$	−16.0800	−	6.14885i	−0.984083	−	0.376304i
$268$	−2.67026	−	15.1438i	−0.163112	−	0.925056i
$269$	4.05269			0.247097			0.123549	−	0.992339i	$-0.460573\pi$
$269$	4.05269			0.247097			0.123549	+	0.992339i	$0.460573\pi$
$270$	−0.855525	+	17.6244i	−0.0520656	+	1.07258i
$271$			20.4925i			1.24483i	0.782686	+	0.622416i	$0.213849\pi$
$271$			20.4925i			1.24483i	−0.782686	+	0.622416i	$0.786151\pi$
$272$	−0.386479	−	2.19183i	−0.0234337	−	0.132899i
$273$	0.546725	+	1.95578i	0.0330893	+	0.118369i
$274$	−0.348379	+	0.126800i	−0.0210463	+	0.00766024i
$275$	−3.94980	+	4.70719i	−0.238182	+	0.283854i
$276$	0.850633	+	0.164212i	0.0512021	+	0.00988440i
$277$	16.2030	+	5.89740i	0.973542	+	0.354340i	0.779326	−	0.626618i	$-0.215561\pi$
$277$	16.2030	+	5.89740i	0.973542	+	0.354340i	0.194216	+	0.980959i	$0.437784\pi$
$278$	3.83957	+	6.65033i	0.230282	+	0.398860i
$279$	23.3133	−	3.33761i	1.39573	−	0.199817i
$280$	−3.57616	+	8.24205i	−0.213717	+	0.492557i
$281$	−13.9815	−	16.6625i	−0.834067	−	0.994003i	−0.999969	−	0.00786044i	$-0.997498\pi$
$281$	−13.9815	−	16.6625i	−0.834067	−	0.994003i	0.165902	−	0.986142i	$-0.446947\pi$
$282$	3.50067	−	1.94634i	0.208462	−	0.115903i
$283$	−15.6562	−	2.76061i	−0.930665	−	0.164101i	−0.312292	−	0.949986i	$-0.601097\pi$
$283$	−15.6562	−	2.76061i	−0.930665	−	0.164101i	−0.618373	+	0.785885i	$0.712208\pi$
$284$	−11.7815	−	2.07740i	−0.699105	−	0.123271i
$285$	40.6911	−	22.6239i	2.41033	−	1.34012i
$286$	0.267986	+	0.319373i	0.0158463	+	0.0188849i
$287$	16.3126	+	7.07792i	0.962904	+	0.417796i
$288$	1.85306	+	2.35928i	0.109192	+	0.139022i
$289$	6.02325	+	10.4326i	0.354309	+	0.613681i
$290$	25.9323	+	9.43860i	1.52280	+	0.554253i
$291$	−2.70592	−	0.522370i	−0.158624	−	0.0306219i
$292$	−2.87387	+	3.42494i	−0.168180	+	0.200429i
$293$	10.8584	−	3.95215i	0.634357	−	0.230887i	−0.00476955	−	0.999989i	$-0.501518\pi$
$293$	10.8584	−	3.95215i	0.634357	−	0.230887i	0.639127	+	0.769102i	$0.279296\pi$
$294$	−11.2286	+	4.57370i	−0.654865	+	0.266744i
$295$	0.00195465	+	0.0110853i	0.000113804	+	0.000645414i
$296$		−	0.500739i		−	0.0291049i
$297$	−1.89274	+	4.50725i	−0.109828	+	0.261537i
$298$	1.35073			0.0782458
$299$	0.0384898	+	0.218286i	0.00222592	+	0.0126238i
$300$	−10.5667	−	4.04059i	−0.610067	−	0.233283i
$301$	5.84990	+	11.7104i	0.337182	+	0.674974i
$302$	−1.21030	+	1.44238i	−0.0696449	+	0.0829996i
$303$	−23.2176	+	8.02785i	−1.33382	+	0.461188i
$304$	2.70731	−	7.43829i	0.155275	−	0.426615i
$305$	−35.8592	+	20.7033i	−2.05329	+	1.18547i
$306$	5.67144	+	3.52367i	0.324215	+	0.201435i
$307$	9.18543	+	5.30321i	0.524240	+	0.302670i	0.738668	−	0.674070i	$-0.235455\pi$
$307$	9.18543	+	5.30321i	0.524240	+	0.302670i	−0.214428	+	0.976740i	$0.568789\pi$
$308$	−1.71200	+	1.80687i	−0.0975501	+	0.102956i
$309$	−0.272303	+	16.8406i	−0.0154908	+	0.958026i
$310$	−4.62915	+	26.2532i	−0.262918	+	1.49108i
$311$	2.90114	−	16.4532i	0.164508	−	0.932974i	−0.785061	−	0.619418i	$-0.787369\pi$
$311$	2.90114	−	16.4532i	0.164508	−	0.932974i	0.949570	−	0.313556i	$-0.101520\pi$
$312$	−0.394474	+	0.658430i	−0.0223327	+	0.0372762i
$313$	−15.9842	−	19.0492i	−0.903479	−	1.07672i	−0.996708	−	0.0810793i	$-0.974163\pi$
$313$	−15.9842	−	19.0492i	−0.903479	−	1.07672i	0.0932289	−	0.995645i	$-0.470281\pi$
$314$	−5.48090	+	9.49320i	−0.309305	+	0.535732i
$315$	−11.2593	−	24.4890i	−0.634392	−	1.37980i
$316$	5.58366	+	9.67118i	0.314105	+	0.544047i
$317$	6.00784	−	16.5064i	0.337434	−	0.927092i	−0.648686	−	0.761056i	$-0.724681\pi$
$317$	6.00784	−	16.5064i	0.337434	−	0.927092i	0.986120	−	0.166035i	$-0.0530966\pi$
$318$	9.64127	+	8.35930i	0.540655	+	0.468766i
$319$	5.85684	+	4.91447i	0.327920	+	0.275158i
$320$	−3.19101	+	1.16143i	−0.178383	+	0.0649261i
$321$	−11.6545	−	14.3543i	−0.650490	−	0.801180i
$322$	−1.26857	+	0.376835i	−0.0706944	+	0.0210002i
$323$		−	17.6174i		−	0.980261i
$324$	−8.98119	−	0.581644i	−0.498955	−	0.0323135i
$325$		−	2.89441i		−	0.160553i
$326$	−18.6989	+	3.29712i	−1.03564	+	0.182610i
$327$	4.11885	−	3.34415i	0.227773	−	0.184932i
$328$	2.29870	+	6.31563i	0.126925	+	0.348722i
$329$	−3.37296	+	5.10457i	−0.185957	+	0.281424i
$330$	−4.18084	−	3.62493i	−0.230148	−	0.199546i
$331$	−6.81196	−	2.47935i	−0.374419	−	0.136278i	0.147954	−	0.988994i	$-0.452731\pi$
$331$	−6.81196	−	2.47935i	−0.374419	−	0.136278i	−0.522374	+	0.852717i	$0.674953\pi$
$332$	−6.74692	−	11.6860i	−0.370285	−	0.641353i
$333$	1.11894	+	1.00231i	0.0613178	+	0.0549260i
$334$	−14.9415	−	8.62647i	−0.817562	−	0.472019i
$335$	−40.0019	+	33.5656i	−2.18554	+	1.83388i
$336$	−4.17387	−	1.89177i	−0.227703	−	0.103205i
$337$	−1.90759	+	10.8185i	−0.103913	+	0.589320i	0.887736	+	0.460353i	$0.152277\pi$
$337$	−1.90759	+	10.8185i	−0.103913	+	0.589320i	−0.991649	+	0.128967i	$0.958834\pi$
$338$	12.6091	+	2.22333i	0.685845	+	0.120933i
$339$	0.360622	−	22.3027i	0.0195863	−	1.21131i
$340$	−5.78965	+	4.85809i	−0.313988	+	0.263467i
$341$	−3.69279	+	6.39610i	−0.199976	+	0.346368i
$342$	11.2024	+	20.9386i	0.605756	+	1.13223i
$343$	11.9952	−	14.1108i	0.647680	−	0.761912i
$344$	−1.69219	+	4.64926i	−0.0912369	+	0.250671i
$345$	−0.961368	−	2.78040i	−0.0517583	−	0.149692i
$346$	−6.98657	+	8.32627i	−0.375601	+	0.447623i
$347$	−1.76874	−	4.85957i	−0.0949509	−	0.260875i	0.883120	−	0.469147i	$-0.155438\pi$
$347$	−1.76874	−	4.85957i	−0.0949509	−	0.260875i	−0.978071	+	0.208271i	$0.933216\pi$
$348$	−5.02743	+	13.1474i	−0.269499	+	0.704774i
$349$	−12.2071	+	2.15244i	−0.653432	+	0.115218i	−0.490530	−	0.871425i	$-0.663197\pi$
$349$	−12.2071	+	2.15244i	−0.653432	+	0.115218i	−0.162902	+	0.986642i	$0.552086\pi$
$350$	17.1681	−	1.96952i	0.917672	−	0.105275i
$351$	−0.681719	−	2.19943i	−0.0363874	−	0.117397i
$352$	−0.940798			−0.0501447
$353$	−2.33281	−	13.2300i	−0.124163	−	0.704164i	−0.981801	−	0.189910i	$-0.939180\pi$
$353$	−2.33281	−	13.2300i	−0.124163	−	0.704164i	0.857638	−	0.514253i	$-0.171931\pi$
$354$	−0.00566953		0.000905436i	−0.000301332		4.81234e-5i
$355$	13.8945	+	38.1749i	0.737446	+	2.02611i
$356$	7.61404	+	6.38894i	0.403543	+	0.338613i
$357$	−10.1694	−	0.779277i	−0.538220	−	0.0412437i
$358$	−8.07048	−	2.93742i	−0.426538	−	0.155247i
$359$	−12.5072	+	7.22101i	−0.660103	+	0.381110i	−0.792316	−	0.610111i	$-0.791125\pi$
$359$	−12.5072	+	7.22101i	−0.660103	+	0.381110i	0.132214	+	0.991221i	$0.457792\pi$
$360$	3.79198	−	9.45538i	0.199855	−	0.498342i
$361$	21.8288	−	37.8086i	1.14889	−	1.98993i
$362$	6.14743	−	5.15831i	0.323102	−	0.271115i
$363$	8.51332	+	15.3120i	0.446833	+	0.803671i
$364$	0.0706708	−	1.17033i	0.00370415	−	0.0613417i
$365$	14.9518	+	2.63640i	0.782612	+	0.137996i
$366$	−10.2628	−	18.4586i	−0.536444	−	0.964845i
$367$	−7.37637	−	8.79081i	−0.385043	−	0.458877i	0.538356	−	0.842717i	$-0.319046\pi$
$367$	−7.37637	−	8.79081i	−0.385043	−	0.458877i	−0.923399	+	0.383841i	$0.874601\pi$
$368$	−0.433169	−	0.250090i	−0.0225805	−	0.0130369i
$369$	−18.7140	−	7.50506i	−0.974214	−	0.390698i
$370$	−1.47260	+	0.850205i	−0.0765568	+	0.0442001i
$371$	−18.9570	−	4.53566i	−0.984200	−	0.235480i
$372$	−13.3507	−	2.57731i	−0.692201	−	0.133627i
$373$	0.595553	+	0.499728i	0.0308366	+	0.0258749i	0.658076	−	0.752952i	$-0.271371\pi$
$373$	0.595553	+	0.499728i	0.0308366	+	0.0258749i	−0.627239	+	0.778827i	$0.715815\pi$
$374$	−1.96760	+	0.716150i	−0.101742	+	0.0370312i
$375$	1.42055	+	8.89500i	0.0733569	+	0.459336i
$376$	−2.27736	+	0.401561i	−0.117446	+	0.0207089i
$377$	−3.60132			−0.185477
$378$	12.5820	−	5.54021i	0.647147	−	0.284958i
$379$	5.88815			0.302454			0.151227	−	0.988499i	$-0.451678\pi$
$379$	5.88815			0.302454			0.151227	+	0.988499i	$0.451678\pi$
$380$	−26.4717	+	4.66767i	−1.35797	+	0.239446i
$381$	−6.47451	−	2.47579i	−0.331699	−	0.126839i
$382$	−20.8537	+	7.59012i	−1.06697	+	0.388344i
$383$	−23.3240	−	19.5711i	−1.19180	−	1.00004i	−0.999826	−	0.0186386i	$-0.994067\pi$
$383$	−23.3240	−	19.5711i	−1.19180	−	1.00004i	−0.191973	−	0.981400i	$-0.561489\pi$
$384$	−0.566005	−	1.63696i	−0.0288838	−	0.0835358i
$385$	8.22053	+	1.96684i	0.418957	+	0.100240i
$386$	−21.9703	+	12.6845i	−1.11826	+	0.645626i
$387$	−7.00199	−	13.0876i	−0.355931	−	0.665278i
$388$	1.37794	+	0.795555i	0.0699544	+	0.0403882i
$389$	−4.97627	−	5.93049i	−0.252307	−	0.300688i	0.624993	−	0.780630i	$-0.285102\pi$
$389$	−4.97627	−	5.93049i	−0.252307	−	0.300688i	−0.877300	+	0.479943i	$0.840657\pi$
$390$	2.60612	+	0.0421395i	0.131966	+	0.00213382i
$391$	−1.09631	−	0.193309i	−0.0554429	−	0.00977608i
$392$	6.98983	−	0.377176i	0.353040	−	0.0190502i
$393$	−1.93871	+	3.23597i	−0.0977951	+	0.163233i
$394$	−1.19622	+	1.00375i	−0.0602647	+	0.0505681i
$395$	18.9610	−	32.8414i	0.954032	−	1.65243i
$396$	1.88315	−	2.10229i	0.0946319	−	0.105644i
$397$	−13.5243	+	7.80827i	−0.678766	+	0.391886i	−0.799390	−	0.600813i	$-0.794844\pi$
$397$	−13.5243	+	7.80827i	−0.678766	+	0.391886i	0.120624	+	0.992698i	$0.461510\pi$
$398$	−15.0043	−	5.46112i	−0.752098	−	0.273741i
$399$	−29.9367	−	20.4843i	−1.49871	−	1.02550i
$400$	5.00340	+	4.19835i	0.250170	+	0.209918i
$401$	0.945466	+	2.59765i	0.0472143	+	0.129720i	0.961059	−	0.276344i	$-0.0891230\pi$
$401$	0.945466	+	2.59765i	0.0472143	+	0.129720i	−0.913844	+	0.406065i	$0.866901\pi$
$402$	−16.7882	−	20.6773i	−0.837320	−	1.03129i
$403$	−0.604097	−	3.42601i	−0.0300922	−	0.170661i
$404$	14.1834			0.705648
$405$	13.5386	+	27.3999i	0.672741	+	1.36151i
$406$	−2.45054	−	21.3611i	−0.121618	−	1.06013i
$407$	−0.463937	+	0.0818046i	−0.0229965	+	0.00405490i
$408$	−2.42983	−	2.99272i	−0.120295	−	0.148162i
$409$	9.95715	+	27.3570i	0.492349	+	1.35272i	0.898525	+	0.438923i	$0.144640\pi$
$409$	9.95715	+	27.3570i	0.492349	+	1.35272i	−0.406175	+	0.913795i	$0.633138\pi$
$410$	14.6704	−	17.4835i	0.724518	−	0.863447i
$411$	−0.420656	+	0.485167i	−0.0207494	+	0.0239315i
$412$	3.32586	−	9.13774i	0.163854	−	0.450184i
$413$	0.00704586	−	0.00522211i	0.000346704	−	0.000256963i
$414$	1.42590	−	0.467360i	0.0700794	−	0.0229695i
$415$	−22.9112	+	39.6834i	−1.12467	+	1.94798i
$416$	0.339471	−	0.284850i	0.0166439	−	0.0139659i
$417$	11.4097	+	6.83569i	0.558735	+	0.334745i
$418$	−7.33390	−	1.29316i	−0.358713	−	0.0632507i
$419$	−6.23009	+	35.3326i	−0.304360	+	1.72611i	0.322142	+	0.946691i	$0.395597\pi$
$419$	−6.23009	+	35.3326i	−0.304360	+	1.72611i	−0.626502	+	0.779420i	$0.715514\pi$
$420$	1.52340	+	15.4868i	0.0743345	+	0.755677i
$421$	4.15270	−	3.48453i	0.202390	−	0.169825i	−0.535959	−	0.844244i	$-0.680050\pi$
$421$	4.15270	−	3.48453i	0.202390	−	0.169825i	0.738349	+	0.674418i	$0.235606\pi$
$422$	22.5267	+	13.0058i	1.09658	+	0.633112i
$423$	3.66117	−	5.89276i	0.178012	−	0.286516i
$424$	−3.68366	−	6.38028i	−0.178894	−	0.309854i
$425$	13.6601	+	4.97186i	0.662611	+	0.241171i
$426$	−19.5834	+	6.77127i	−0.948819	+	0.328069i
$427$	26.9157	+	17.7852i	1.30254	+	0.860685i
$428$	3.65110	+	10.0313i	0.176483	+	0.484882i
$429$	0.674482	+	0.257915i	0.0325643	+	0.0124523i
$430$	16.5460	−	2.91750i	0.797917	−	0.140694i
$431$		−	34.4253i		−	1.65821i	−0.559094	−	0.829104i	$-0.688851\pi$
$431$		−	34.4253i		−	1.65821i	0.559094	−	0.829104i	$-0.311149\pi$
$432$	4.79088	+	2.01184i	0.230501	+	0.0967947i
$433$		−	18.9403i		−	0.910213i	−0.890437	−	0.455107i	$-0.849601\pi$
$433$		−	18.9403i		−	0.910213i	0.890437	−	0.455107i	$-0.150399\pi$
$434$	19.9102	−	5.91443i	0.955718	−	0.283902i
$435$	47.2006	−	7.53804i	2.26310	−	0.361421i
$436$	−2.87840	+	1.04765i	−0.137850	+	0.0501734i
$437$	−3.03297	−	2.54496i	−0.145087	−	0.121742i
$438$	−1.46783	+	7.60351i	−0.0701358	+	0.363310i
$439$	1.13447	−	3.11693i	0.0541453	−	0.148763i	−0.909671	−	0.415329i	$-0.863667\pi$
$439$	1.13447	−	3.11693i	0.0541453	−	0.148763i	0.963817	+	0.266565i	$0.0858888\pi$
$440$	1.59738	+	2.76675i	0.0761522	+	0.131899i
$441$	−13.1484	+	16.3744i	−0.626114	+	0.779732i
$442$	0.493144	−	0.854151i	0.0234565	−	0.0406278i
$443$	15.9592	+	19.0194i	0.758245	+	0.903641i	0.997736	−	0.0672576i	$-0.0214249\pi$
$443$	15.9592	+	19.0194i	0.758245	+	0.903641i	−0.239491	+	0.970899i	$0.576980\pi$
$444$	−0.421452	−	0.758021i	−0.0200012	−	0.0359741i
$445$	5.86103	−	33.2395i	0.277839	−	1.57571i
$446$	2.65258	−	15.0435i	0.125603	−	0.712331i
$447$	2.04475	−	1.13686i	0.0967132	−	0.0537716i
$448$	1.92057	+	1.81973i	0.0907384	+	0.0859741i
$449$	2.44182	+	1.40979i	0.115237	+	0.0665320i	0.556511	−	0.830841i	$-0.312140\pi$
$449$	2.44182	+	1.40979i	0.115237	+	0.0665320i	−0.441274	+	0.897373i	$0.645473\pi$
$450$	−19.3967	+	2.77689i	−0.914368	+	0.130904i
$451$	5.47593	−	3.16153i	0.257851	−	0.148871i
$452$	−4.40458	+	12.1015i	−0.207174	+	0.569206i
$453$	−0.618164	+	3.20214i	−0.0290439	+	0.150450i
$454$	15.4498	−	18.4124i	0.725097	−	0.864137i
$455$	−3.56175	+	1.77927i	−0.166977	+	0.0834133i
$456$	−2.16217	−	13.5388i	−0.101253	−	0.634010i
$457$	−0.972923	−	5.51772i	−0.0455114	−	0.258108i	0.953560	−	0.301205i	$-0.0973887\pi$
$457$	−0.972923	−	5.51772i	−0.0455114	−	0.258108i	−0.999071	+	0.0430967i	$0.986278\pi$
$458$	12.2125			0.570652
$459$	11.5512	+	0.560720i	0.539163	+	0.0261722i
$460$			1.69852i			0.0791937i
$461$	−5.26328	−	29.8496i	−0.245136	−	1.39023i	−0.820178	−	0.572109i	$-0.806125\pi$
$461$	−5.26328	−	29.8496i	−0.245136	−	1.39023i	0.575042	−	0.818124i	$-0.304986\pi$
$462$	−1.07086	+	4.17617i	−0.0498209	+	0.194293i
$463$	−26.8268	+	9.76416i	−1.24675	+	0.453779i	−0.879301	−	0.476266i	$-0.841990\pi$
$463$	−26.8268	+	9.76416i	−1.24675	+	0.453779i	−0.367446	+	0.930045i	$0.619768\pi$
$464$	5.22373	−	6.22540i	0.242506	−	0.289007i
$465$	15.0887	+	43.6384i	0.699721	+	2.02368i
$466$	3.60671	+	1.31273i	0.167077	+	0.0608112i
$467$	−1.35485	−	2.34667i	−0.0626951	−	0.108591i	0.832974	−	0.553312i	$-0.186636\pi$
$467$	−1.35485	−	2.34667i	−0.0626951	−	0.108591i	−0.895669	+	0.444721i	$0.853303\pi$
$468$	−0.0429814	+	1.32875i	−0.00198682	+	0.0614214i
$469$	37.3230	+	16.1942i	1.72342	+	0.747777i
$470$	5.04767	+	6.01558i	0.232832	+	0.277478i
$471$	−0.306959	+	18.9839i	−0.0141439	+	0.874733i
$472$	0.00326442		0.000575606i	0.000150257		2.64944e-5i
$473$	4.58401	+	0.808285i	0.210773	+	0.0371650i
$474$	16.5924	+	9.94074i	0.762116	+	0.456593i
$475$	33.2327	+	39.6052i	1.52482	+	1.81721i
$476$	5.40193	+	2.34385i	0.247597	+	0.107430i
$477$	21.6307	+	4.53966i	0.990402	+	0.207857i
$478$	−8.55593	−	14.8193i	−0.391339	−	0.677820i
$479$	7.83328	+	2.85108i	0.357912	+	0.130269i	0.514717	−	0.857360i	$-0.327897\pi$
$479$	7.83328	+	2.85108i	0.357912	+	0.130269i	−0.156805	+	0.987630i	$0.550119\pi$
$480$	−3.85304	+	4.44393i	−0.175866	+	0.202837i
$481$	0.142635	−	0.169986i	0.00650361	−	0.00775070i
$482$	17.0916	−	6.22082i	0.778500	−	0.283351i
$483$	−1.60320	+	1.63816i	−0.0729479	+	0.0745388i
$484$	−1.75643	−	9.96123i	−0.0798379	−	0.452783i
$485$		−	5.40310i		−	0.245342i
$486$	−14.0853	+	6.67862i	−0.638923	+	0.302948i
$487$	8.68364			0.393493			0.196747	−	0.980454i	$-0.436962\pi$
$487$	8.68364			0.393493			0.196747	+	0.980454i	$0.436962\pi$
$488$	2.11738	+	12.0082i	0.0958491	+	0.543587i
$489$	−25.5314	+	20.7293i	−1.15457	+	0.937412i
$490$	−12.9773	−	19.9157i	−0.586253	−	0.899697i
$491$	20.0310	−	23.8720i	0.903988	−	1.07733i	−0.0926747	−	0.995696i	$-0.529542\pi$
$491$	20.0310	−	23.8720i	0.903988	−	1.07733i	0.996662	−	0.0816341i	$-0.0260139\pi$
$492$	8.79541	+	7.62591i	0.396528	+	0.343802i
$493$	6.18615	−	16.9963i	0.278610	−	0.765476i
$494$	3.03785	−	1.75390i	0.136679	−	0.0789118i
$495$	−9.37994	−	1.96858i	−0.421597	−	0.0884812i
$496$	6.79859	+	3.92517i	0.305266	+	0.176245i
$497$	21.7699	−	22.9763i	0.976514	−	1.03063i
$498$	−20.0492	−	12.0117i	−0.898425	−	0.538258i
$499$	−2.06289	+	11.6992i	−0.0923476	+	0.523729i	0.903180	+	0.429261i	$0.141226\pi$
$499$	−2.06289	+	11.6992i	−0.0923476	+	0.523729i	−0.995528	+	0.0944679i	$0.969885\pi$
$500$	0.903076	−	5.12160i	0.0403868	−	0.229045i
$501$	−29.8791	−	0.483128i	−1.33490	−	0.0215846i
$502$	−6.29765	−	7.50525i	−0.281078	−	0.334976i
$503$	−5.79141	+	10.0310i	−0.258226	+	0.447261i	−0.965767	−	0.259412i	$-0.916471\pi$
$503$	−5.79141	+	10.0310i	−0.258226	+	0.447261i	0.707541	+	0.706673i	$0.249805\pi$
$504$	−7.91066	+	0.649213i	−0.352369	+	0.0289182i
$505$	−24.0819	−	41.7112i	−1.07163	−	1.85612i
$506$	−0.160944	+	0.442190i	−0.00715484	+	0.0196577i
$507$	20.9590	−	7.24691i	0.930823	−	0.321847i
$508$	3.06574	+	2.57246i	0.136020	+	0.114134i
$509$	−19.7703	+	7.19579i	−0.876301	+	0.318948i	−0.740716	−	0.671818i	$-0.765514\pi$
$509$	−19.7703	+	7.19579i	−0.876301	+	0.318948i	−0.135585	+	0.990766i	$0.543291\pi$
$510$	−4.67553	+	12.2271i	−0.207036	+	0.541427i
$511$	−3.36840	−	11.3393i	−0.149009	−	0.501620i
$512$			1.00000i			0.0441942i
$513$	34.5815	+	22.2684i	1.52681	+	0.983172i
$514$			14.4793i			0.638654i
$515$	−32.5197	+	5.73410i	−1.43299	+	0.252675i
$516$	1.35145	+	8.46233i	0.0594944	+	0.372533i
$517$	0.744096	+	2.04439i	0.0327253	+	0.0899120i
$518$	1.10532	+	0.730367i	0.0485651	+	0.0320905i
$519$	−3.56841	+	18.4847i	−0.156636	+	0.811388i
$520$	−1.41409	−	0.514686i	−0.0620119	−	0.0225705i
$521$	3.72023	+	6.44363i	0.162986	+	0.282301i	0.935938	−	0.352164i	$-0.114554\pi$
$521$	3.72023	+	6.44363i	0.162986	+	0.282301i	−0.772952	+	0.634464i	$0.781221\pi$
$522$	3.45509	+	24.1340i	0.151225	+	1.05632i
$523$	0.241039	+	0.139164i	0.0105399	+	0.00608521i	0.505261	−	0.862967i	$-0.331396\pi$
$523$	0.241039	+	0.139164i	0.0105399	+	0.00608521i	−0.494721	+	0.869052i	$0.664730\pi$
$524$	1.66839	−	1.39995i	0.0728840	−	0.0611569i
$525$	24.3314	−	17.4312i	1.06191	−	0.760759i
$526$	2.08337	−	11.8154i	0.0908393	−	0.515175i
$527$	17.2066	+	3.03399i	0.749532	+	0.132163i
$528$	−1.42418	+	0.791833i	−0.0619797	+	0.0344601i
$529$	17.4274	−	14.6233i	0.757712	−	0.635796i
$530$	−12.5090	+	21.6662i	−0.543355	+	0.941119i
$531$	−0.00782049	+	0.00614248i	−0.000339380	+	0.000266561i
$532$	12.4703	+	16.8254i	0.540657	+	0.729474i
$533$	−1.01866	+	2.79876i	−0.0441232	+	0.121228i
$534$	16.9035	+	3.26317i	0.731486	+	0.141211i
$535$	23.3014	−	27.7695i	1.00741	−	1.20058i
$536$	5.25939	+	14.4501i	0.227171	+	0.624147i
$537$	−14.6894	+	2.34594i	−0.633896	+	0.101235i
$538$	−3.99112	+	0.703743i	−0.172070	+	0.0303405i
$539$	−1.49137	−	6.41449i	−0.0642378	−	0.276292i
$540$	−2.21791	−	17.5052i	−0.0954437	−	0.753302i
$541$	−34.8502			−1.49833			−0.749163	−	0.662385i	$-0.769544\pi$
$541$	−34.8502			−1.49833			−0.749163	+	0.662385i	$0.769544\pi$
$542$	−3.55849	−	20.1812i	−0.152850	−	0.866857i
$543$	4.96447	−	12.9827i	0.213046	−	0.557142i
$544$	0.761215	+	2.09142i	0.0326368	+	0.0896690i
$545$	7.96823	+	6.68614i	0.341322	+	0.286403i
$546$	−0.878036	−	1.83113i	−0.0375765	−	0.0783650i
$547$	10.6978	+	3.89368i	0.457405	+	0.166482i	0.560438	−	0.828196i	$-0.310633\pi$
$547$	10.6978	+	3.89368i	0.457405	+	0.166482i	−0.103034	+	0.994678i	$0.532855\pi$
$548$	0.321068	−	0.185369i	0.0137153	−	0.00791855i
$549$	−31.0717	−	19.3049i	−1.32611	−	0.823912i
$550$	3.07240	−	5.32155i	0.131008	−	0.226912i
$551$	49.2781	−	41.3493i	2.09932	−	1.76154i
$552$	−0.866225	−	0.0140064i	−0.0368690	−	0.000596151i
$553$	−29.4922	−	1.78090i	−1.25414	−	0.0757317i
$554$	−16.9809	−	2.99419i	−0.721449	−	0.127211i
$555$	−1.51364	+	2.52647i	−0.0642506	+	0.107243i
$556$	−4.93606	−	5.88256i	−0.209335	−	0.249476i
$557$	−24.9918	−	14.4290i	−1.05894	−	0.611378i	−0.133800	−	0.991008i	$-0.542718\pi$
$557$	−24.9918	−	14.4290i	−1.05894	−	0.611378i	−0.925138	+	0.379630i	$0.876051\pi$
$558$	−22.3796	+	7.33521i	−0.947402	+	0.310524i
$559$	−1.89879	+	1.09627i	−0.0803102	+	0.0463671i
$560$	2.09061	−	8.73783i	0.0883446	−	0.369241i
$561$	−2.37582	+	2.74017i	−0.100307	+	0.115690i
$562$	16.6625	+	13.9815i	0.702866	+	0.589775i
$563$	−16.8581	+	6.13586i	−0.710486	+	0.258596i	−0.671881	−	0.740659i	$-0.734514\pi$
$563$	−16.8581	+	6.13586i	−0.710486	+	0.258596i	−0.0386046	+	0.999255i	$0.512291\pi$
$564$	−3.10951	+	2.52465i	−0.130934	+	0.106307i
$565$	43.0672	−	7.59392i	1.81185	−	0.319478i
$566$	15.8977			0.668232
$567$	14.3837	−	18.9766i	0.604058	−	0.796940i
$568$	11.9633			0.501968
$569$	39.2969	−	6.92910i	1.64741	−	0.290483i	0.728529	−	0.685015i	$-0.240205\pi$
$569$	39.2969	−	6.92910i	1.64741	−	0.290483i	0.918882	+	0.394532i	$0.129093\pi$
$570$	−36.1443	+	29.3461i	−1.51392	+	1.22917i
$571$	1.84609	−	0.671920i	0.0772563	−	0.0281190i	−0.303103	−	0.952958i	$-0.598023\pi$
$571$	1.84609	−	0.671920i	0.0772563	−	0.0281190i	0.380359	+	0.924839i	$0.375800\pi$
$572$	−0.319373	−	0.267986i	−0.0133537	−	0.0112051i
$573$	−25.1801	+	29.0417i	−1.05191	+	1.21323i
$574$	−17.2939	−	4.13773i	−0.721832	−	0.172706i
$575$	2.82924	−	1.63346i	0.117987	−	0.0681200i
$576$	−2.23459	−	2.00165i	−0.0931078	−	0.0834023i
$577$	−21.6860	−	12.5204i	−0.902799	−	0.521231i	−0.0246916	−	0.999695i	$-0.507860\pi$
$577$	−21.6860	−	12.5204i	−0.902799	−	0.521231i	−0.878107	+	0.478464i	$0.841194\pi$
$578$	−7.74334	−	9.22816i	−0.322081	−	0.383841i
$579$	−22.5826	+	37.6934i	−0.938501	+	1.56649i
$580$	−27.1774	−	4.79210i	−1.12848	−	0.198981i
$581$	35.6364	+	2.15192i	1.47845	+	0.0892768i
$582$	2.75552	+	0.0445553i	0.114220	+	0.00184688i
$583$	−5.30957	+	4.45526i	−0.219900	+	0.184518i
$584$	2.23547	−	3.87195i	0.0925044	−	0.160222i
$585$	3.98063	−	2.12968i	0.164579	−	0.0880514i
$586$	−10.0072	+	5.77766i	−0.413393	+	0.238673i
$587$	−16.5825	−	6.03552i	−0.684431	−	0.249113i	−0.0236824	−	0.999720i	$-0.507539\pi$
$587$	−16.5825	−	6.03552i	−0.684431	−	0.249113i	−0.660749	+	0.750607i	$0.729761\pi$
$588$	10.2638	−	6.45404i	0.423272	−	0.266160i
$589$	47.6025	+	39.9432i	1.96143	+	1.64583i
$590$	−0.00384990	−	0.0105775i	−0.000158498	−	0.000435469i
$591$	−0.966029	+	2.52629i	−0.0397371	+	0.103918i
$592$	0.0869524	+	0.493131i	0.00357372	+	0.0202676i
$593$	−39.1523			−1.60779			−0.803897	−	0.594769i	$-0.797244\pi$
$593$	−39.1523			−1.60779			−0.803897	+	0.594769i	$0.797244\pi$
$594$	1.08131	−	4.76744i	0.0443665	−	0.195610i
$595$	−2.27902	−	19.8659i	−0.0934305	−	0.814423i
$596$	−1.33021	+	0.234552i	−0.0544876	+	0.00960763i
$597$	−27.3100	+	4.36147i	−1.11772	+	0.178503i
$598$	−0.0758101	−	0.208286i	−0.00310010	−	0.00851747i
$599$	−18.2649	+	21.7672i	−0.746283	+	0.889386i	−0.996898	−	0.0787012i	$-0.974923\pi$
$599$	−18.2649	+	21.7672i	−0.746283	+	0.889386i	0.250615	+	0.968087i	$0.419367\pi$
$600$	11.1078	+	2.14432i	0.453473	+	0.0875415i
$601$	−14.3707	+	39.4833i	−0.586195	+	1.61056i	0.191205	+	0.981550i	$0.438761\pi$
$601$	−14.3707	+	39.4833i	−0.586195	+	1.61056i	−0.777400	+	0.629007i	$0.783462\pi$
$602$	−7.79451	−	10.5166i	−0.317680	−	0.428626i
$603$	−42.8174	−	17.1715i	−1.74366	−	0.699276i
$604$	0.941446	−	1.63063i	0.0383069	−	0.0663495i
$605$	−26.3123	+	22.0786i	−1.06975	+	0.897623i
$606$	21.4708	−	11.9376i	0.872193	−	0.484931i
$607$	34.5554	+	6.09305i	1.40256	+	0.247309i	0.823195	−	0.567759i	$-0.192190\pi$
$607$	34.5554	+	6.09305i	1.40256	+	0.247309i	0.579365	+	0.815068i	$0.303301\pi$
$608$	−1.37454	+	7.79540i	−0.0557449	+	0.316145i
$609$	−21.6884	−	30.2740i	−0.878859	−	1.22676i
$610$	31.7194	−	26.6157i	1.28428	−	1.07764i
$611$	−0.887483	−	0.512388i	−0.0359037	−	0.0207290i
$612$	−6.19715	−	2.48530i	−0.250505	−	0.100462i
$613$	10.9144	+	18.9043i	0.440828	+	0.763536i	0.997751	−	0.0670280i	$-0.0213517\pi$
$613$	10.9144	+	18.9043i	0.440828	+	0.763536i	−0.556924	+	0.830564i	$0.688018\pi$
$614$	−9.96678	−	3.62761i	−0.402226	−	0.146398i
$615$	7.49293	−	38.8140i	0.302144	−	1.56513i
$616$	1.37223	−	2.07670i	0.0552886	−	0.0836727i
$617$	1.42517	+	3.91563i	0.0573753	+	0.157637i	0.965069	−	0.261996i	$-0.0843808\pi$
$617$	1.42517	+	3.91563i	0.0573753	+	0.157637i	−0.907694	+	0.419634i	$0.862159\pi$
$618$	−2.65617	−	16.6320i	−0.106847	−	0.669037i
$619$	24.0454	−	4.23985i	0.966465	−	0.170414i	0.331926	−	0.943305i	$-0.392301\pi$
$619$	24.0454	−	4.23985i	0.966465	−	0.170414i	0.634538	+	0.772891i	$0.281190\pi$
$620$		−	26.6582i		−	1.07062i
$621$	1.76518	−	1.90762i	0.0708343	−	0.0765502i
$622$			16.7070i			0.669889i
$623$	−25.2085	+	7.48834i	−1.00996	+	0.300014i
$624$	0.274145	−	0.716926i	0.0109746	−	0.0287000i
$625$	14.0927	−	5.12933i	0.563709	−	0.205173i
$626$	19.0492	+	15.9842i	0.761359	+	0.638856i
$627$	−12.1905	+	4.21506i	−0.486842	+	0.168333i
$628$	3.74916	−	10.3007i	0.149608	−	0.411044i
$629$	0.557233	+	0.965156i	0.0222183	+	0.0384833i
$630$	15.3408	+	22.1618i	0.611190	+	0.882946i
$631$	−15.9614	+	27.6460i	−0.635414	+	1.10057i	0.351013	+	0.936370i	$0.385837\pi$
$631$	−15.9614	+	27.6460i	−0.635414	+	1.10057i	−0.986427	+	0.164199i	$0.947496\pi$
$632$	−7.17821	−	8.55466i	−0.285534	−	0.340286i
$633$	45.0475	+	0.728393i	1.79048	+	0.0289510i
$634$	−3.05026	+	17.2989i	−0.121141	+	0.687026i
$635$	2.35990	−	13.3837i	0.0936498	−	0.531114i
$636$	−10.9464	−	6.55811i	−0.434052	−	0.260046i
$637$	2.48028	+	1.86301i	0.0982723	+	0.0738152i
$638$	−6.62125	−	3.82278i	−0.262138	−	0.151345i
$639$	−23.9463	+	26.7330i	−0.947302	+	1.05754i
$640$	2.94085	−	1.69790i	0.116247	−	0.0671155i
$641$	−5.12063	+	14.0688i	−0.202253	+	0.555685i	−0.998804	−	0.0488858i	$-0.984433\pi$
$641$	−5.12063	+	14.0688i	−0.202253	+	0.555685i	0.796552	+	0.604570i	$0.206655\pi$
$642$	13.9700	+	12.1125i	0.551353	+	0.478041i
$643$	−2.88719	+	3.44082i	−0.113860	+	0.135693i	−0.819964	−	0.572415i	$-0.806007\pi$
$643$	−2.88719	+	3.44082i	−0.113860	+	0.135693i	0.706104	+	0.708108i	$0.250451\pi$
$644$	1.18386	−	0.591394i	0.0466505	−	0.0233042i
$645$	22.5918	−	18.3426i	0.889552	−	0.722240i
$646$	3.05924	+	17.3498i	0.120364	+	0.682619i
$647$	−30.2456			−1.18908			−0.594539	−	0.804067i	$-0.702666\pi$
$647$	−30.2456			−1.18908			−0.594539	+	0.804067i	$0.702666\pi$
$648$	8.94574	−	0.986759i	0.351422	−	0.0387636i
$649$		−	0.00311854i		−	0.000122413i
$650$	0.502609	+	2.85044i	0.0197139	+	0.111803i
$651$	25.1622	−	25.7109i	0.986182	−	1.00769i
$652$	17.8423	−	6.49405i	0.698757	−	0.254327i
$653$	16.6977	−	19.8996i	0.653433	−	0.778731i	−0.332995	−	0.942929i	$-0.608059\pi$
$653$	16.6977	−	19.8996i	0.653433	−	0.778731i	0.986427	+	0.164198i	$0.0525036\pi$
$654$	−3.47557	+	4.00858i	−0.135906	+	0.156748i
$655$	−6.94980	−	2.52952i	−0.271551	−	0.0988365i
$656$	−3.36048	−	5.82052i	−0.131205	−	0.227253i
$657$	4.17757	+	12.7457i	0.162982	+	0.497255i
$658$	2.43532	−	5.61273i	0.0949386	−	0.218807i
$659$	19.5219	+	23.2653i	0.760465	+	0.906286i	0.997877	−	0.0651225i	$-0.0207438\pi$
$659$	19.5219	+	23.2653i	0.760465	+	0.906286i	−0.237413	+	0.971409i	$0.576299\pi$
$660$	4.74679	+	2.84386i	0.184769	+	0.110697i
$661$	−14.4693	−	2.55133i	−0.562790	−	0.0992351i	−0.114987	−	0.993367i	$-0.536682\pi$
$661$	−14.4693	−	2.55133i	−0.562790	−	0.0992351i	−0.447804	+	0.894132i	$0.647794\pi$
$662$	7.13901	+	1.25880i	0.277466	+	0.0489247i
$663$	0.0276187	−	1.70808i	0.00107262	−	0.0663363i
$664$	8.67367	+	10.3369i	0.336604	+	0.401148i
$665$	28.3077	−	65.2413i	1.09772	−	2.52995i
$666$	−1.27599	−	0.792776i	−0.0494438	−	0.0307194i
$667$	−2.03240	−	3.52023i	−0.0786950	−	0.136304i
$668$	16.2125	+	5.90085i	0.627279	+	0.228311i
$669$	−8.64606	−	25.0055i	−0.334276	−	0.966769i
$670$	33.5656	−	40.0019i	1.29675	−	1.54541i
$671$	10.7798	−	3.92352i	0.416149	−	0.151466i
$672$	4.43896	+	1.13825i	0.171237	+	0.0439088i
$673$	1.42459	+	8.07926i	0.0549140	+	0.311433i	0.999876	−	0.0157474i	$-0.00501276\pi$
$673$	1.42459	+	8.07926i	0.0549140	+	0.311433i	−0.944962	+	0.327180i	$0.893902\pi$
$674$		−	10.9854i		−	0.423140i
$675$	−27.0256	+	20.5291i	−1.04022	+	0.790165i
$676$	−12.8036			−0.492447
$677$	1.87976	+	10.6606i	0.0722450	+	0.409722i	0.999387	+	0.0350113i	$0.0111467\pi$
$677$	1.87976	+	10.6606i	0.0722450	+	0.409722i	−0.927142	+	0.374710i	$0.877742\pi$
$678$	3.51767	+	22.0265i	0.135095	+	0.845921i
$679$	−3.76593	+	1.88127i	−0.144523	+	0.0721964i
$680$	4.85809	−	5.78965i	0.186299	−	0.222023i
$681$	7.89104	−	40.8763i	0.302385	−	1.56638i
$682$	2.52602	−	6.94017i	0.0967262	−	0.265753i
$683$	20.9310	−	12.0845i	0.800904	−	0.462402i	−0.0428831	−	0.999080i	$-0.513654\pi$
$683$	20.9310	−	12.0845i	0.800904	−	0.462402i	0.843787	+	0.536678i	$0.180321\pi$
$684$	−14.6682	−	18.6752i	−0.560851	−	0.714065i
$685$	−1.09028	−	0.629475i	−0.0416576	−	0.0240510i
$686$	−9.36265	+	15.9794i	−0.357468	+	0.610096i
$687$	18.4873	−	10.2788i	0.705336	−	0.392160i
$688$	0.859148	−	4.87247i	0.0327547	−	0.185761i
$689$	0.566928	−	3.21521i	0.0215982	−	0.122490i
$690$	1.42957	+	2.57122i	0.0544230	+	0.0978847i
$691$	12.6341	+	15.0567i	0.480622	+	0.572783i	0.950807	−	0.309785i	$-0.100257\pi$
$691$	12.6341	+	15.0567i	0.480622	+	0.572783i	−0.470184	+	0.882568i	$0.655813\pi$
$692$	5.43459	−	9.41298i	0.206592	−	0.357828i
$693$	1.89385	+	7.22320i	0.0719412	+	0.274387i
$694$	2.58572	+	4.47860i	0.0981527	+	0.170005i
$695$	−8.91881	+	24.5042i	−0.338310	+	0.929498i
$696$	2.66803	−	13.8207i	0.101132	−	0.523870i
$697$	−11.4588	−	9.61511i	−0.434035	−	0.364198i
$698$	11.6479	−	4.23949i	0.440879	−	0.160467i
$699$	6.56473	−	1.04840i	0.248301	−	0.0396542i
$700$	−16.5652	+	4.92080i	−0.626107	+	0.185989i
$701$		−	18.0132i		−	0.680350i	−0.940362	−	0.340175i	$-0.889514\pi$
$701$		−	18.0132i		−	0.680350i	0.940362	−	0.340175i	$-0.110486\pi$
$702$	1.05329	+	2.04764i	0.0397538	+	0.0772832i
$703$			3.96368i			0.149493i
$704$	0.926505	−	0.163368i	0.0349190	−	0.00615716i
$705$	12.7043	+	4.85799i	0.478471	+	0.182962i
$706$	4.59474	+	12.6239i	0.172925	+	0.475109i
$707$	−20.6876	+	31.3081i	−0.778036	+	1.17746i
$708$	0.00542617	−	0.00187618i	0.000203928	−	7.05113e-5i
$709$	4.09818	+	1.49162i	0.153910	+	0.0560188i	0.417827	−	0.908527i	$-0.362792\pi$
$709$	4.09818	+	1.49162i	0.153910	+	0.0560188i	−0.263916	+	0.964546i	$0.585014\pi$
$710$	−20.3125	−	35.1822i	−0.762313	−	1.32036i
$711$	33.4844	+	1.08313i	1.25576	+	0.0406206i
$712$	−8.60779	−	4.96971i	−0.322591	−	0.186248i
$713$	3.00794	−	2.52396i	0.112648	−	0.0945231i
$714$	10.1502	−	0.998455i	0.379862	−	0.0373662i
$715$	−0.245843	+	1.39424i	−0.00919399	+	0.0521417i
$716$	8.45795	+	1.49136i	0.316088	+	0.0557349i
$717$	−25.4249	−	15.2324i	−0.949509	−	0.568863i
$718$	11.0632	−	9.28315i	0.412876	−	0.346444i
$719$	−16.1456	+	27.9650i	−0.602130	+	1.04292i	0.390368	+	0.920659i	$0.372348\pi$
$719$	−16.1456	+	27.9650i	−0.602130	+	1.04292i	−0.992498	+	0.122260i	$0.960986\pi$
$720$	−2.09246	+	9.97020i	−0.0779814	+	0.371568i
$721$	15.3195	+	20.6696i	0.570527	+	0.769775i
$722$	−14.9318	+	41.0248i	−0.555704	+	1.52678i
$723$	20.6375	−	23.8024i	0.767516	−	0.885222i
$724$	−5.15831	+	6.14743i	−0.191707	+	0.228468i
$725$	18.1542	+	49.8782i	0.674229	+	1.85243i
$726$	−11.0429	−	13.6010i	−0.409840	−	0.504782i
$727$	−7.60133	+	1.34032i	−0.281918	+	0.0497097i	−0.312819	−	0.949813i	$-0.601273\pi$
$727$	−7.60133	+	1.34032i	−0.281918	+	0.0497097i	0.0309014	+	0.999522i	$0.490162\pi$
$728$	0.133628	+	1.16482i	0.00495258	+	0.0431710i
$729$	−15.7013	+	21.9652i	−0.581529	+	0.813526i
$730$	−15.1824			−0.561927
$731$	−1.91216	−	10.8444i	−0.0707238	−	0.401094i
$732$	13.3122	+	16.3960i	0.492032	+	0.606014i
$733$	2.88073	+	7.91475i	0.106402	+	0.292338i	0.981456	−	0.191688i	$-0.0613962\pi$
$733$	2.88073	+	7.91475i	0.106402	+	0.292338i	−0.875054	+	0.484026i	$0.839174\pi$
$734$	8.79081	+	7.37637i	0.324475	+	0.272267i
$735$	−36.4073	−	19.2260i	−1.34290	−	0.709160i
$736$	0.470016	+	0.171072i	0.0173250	+	0.00630579i
$737$	12.5288	−	7.23353i	0.461506	−	0.266450i
$738$	19.7330	+	4.14138i	0.726381	+	0.152446i
$739$	−9.38414	+	16.2538i	−0.345201	+	0.597906i	−0.985390	−	0.170311i	$-0.945523\pi$
$739$	−9.38414	+	16.2538i	−0.345201	+	0.597906i	0.640189	+	0.768217i	$0.278856\pi$
$740$	1.30259	−	1.09300i	0.0478842	−	0.0401796i
$741$	3.12252	−	5.21190i	0.114709	−	0.191464i
$742$	19.4566	+	1.17490i	0.714276	+	0.0431319i
$743$	−23.6224	−	4.16527i	−0.866623	−	0.152809i	−0.277375	−	0.960762i	$-0.589465\pi$
$743$	−23.6224	−	4.16527i	−0.866623	−	0.152809i	−0.589247	+	0.807953i	$0.700576\pi$
$744$	13.5954	+	0.219830i	0.498432	+	0.00805936i
$745$	2.94835	+	3.51371i	0.108019	+	0.128732i
$746$	−0.673282	−	0.388719i	−0.0246506	−	0.0142320i
$747$	−40.4603	−	1.30878i	−1.48037	−	0.0478859i
$748$	1.81335	−	1.04694i	0.0663028	−	0.0382799i
$749$	−27.4684	−	6.57209i	−1.00367	−	0.240139i
$750$	−2.94357	−	8.51319i	−0.107484	−	0.310858i
$751$	−20.7273	−	17.3923i	−0.756349	−	0.634653i	0.180824	−	0.983515i	$-0.442123\pi$
$751$	−20.7273	−	17.3923i	−0.756349	−	0.634653i	−0.937174	+	0.348863i	$0.886568\pi$
$752$	2.17304	−	0.790920i	0.0792425	−	0.0288419i
$753$	−15.8503	−	6.06099i	−0.577617	−	0.220875i
$754$	3.54661	−	0.625362i	0.129160	−	0.0227743i
$755$	−6.39393			−0.232699
$756$	−11.4288	+	7.64088i	−0.415661	+	0.277896i
$757$	−43.5505			−1.58287			−0.791435	−	0.611253i	$-0.790666\pi$
$757$	−43.5505			−1.58287			−0.791435	+	0.611253i	$0.790666\pi$
$758$	−5.79870	+	1.02247i	−0.210618	+	0.0371377i
$759$	0.128536	+	0.804850i	0.00466557	+	0.0292142i
$760$	25.2590	−	9.19351i	0.916239	−	0.333484i
$761$	20.7716	+	17.4294i	0.752968	+	0.631815i	0.936286	−	0.351238i	$-0.114239\pi$
$761$	20.7716	+	17.4294i	0.752968	+	0.631815i	−0.183318	+	0.983054i	$0.558684\pi$
$762$	6.80607	+	1.31389i	0.246558	+	0.0475972i
$763$	1.88580	−	7.88182i	0.0682707	−	0.285341i
$764$	19.2189	−	11.0960i	0.695314	−	0.401440i
$765$	3.21325	+	22.4447i	0.116175	+	0.811490i
$766$	26.3681	+	15.2236i	0.952719	+	0.550053i
$767$	0.000944215		0.00112527i	3.40936e−5		4.06312e-5i
$768$	0.841661	+	1.51381i	0.0303708	+	0.0546247i
$769$	−14.7658	−	2.60362i	−0.532470	−	0.0938889i	−0.0990528	−	0.995082i	$-0.531581\pi$
$769$	−14.7658	−	2.60362i	−0.532470	−	0.0938889i	−0.433417	+	0.901193i	$0.642692\pi$
$770$	−8.43718	−	0.509484i	−0.304055	−	0.0183605i
$771$	12.1867	+	21.9188i	0.438892	+	0.789387i
$772$	19.4338	−	16.3069i	0.699439	−	0.586899i
$773$	−22.8659	+	39.6049i	−0.822430	+	1.42449i	0.0814382	+	0.996678i	$0.474049\pi$
$773$	−22.8659	+	39.6049i	−0.822430	+	1.42449i	−0.903868	+	0.427812i	$0.859285\pi$
$774$	9.16825	+	11.6728i	0.329546	+	0.419572i
$775$	−44.4049	+	25.6372i	−1.59507	+	0.920914i
$776$	−1.49515	−	0.544192i	−0.0536729	−	0.0195353i
$777$	2.28797	+	0.175326i	0.0820803	+	0.00628980i
$778$	5.93049	+	4.97627i	0.212618	+	0.178408i
$779$	−18.1957	−	49.9924i	−0.651930	−	1.79116i
$780$	−2.57385	+	0.411049i	−0.0921585	+	0.0147179i
$781$	−1.95441	−	11.0840i	−0.0699344	−	0.396618i
$782$	1.11322			0.0398088
$783$	25.5430	+	33.6261i	0.912831	+	1.20170i
$784$	−6.81814	+	1.58522i	−0.243505	+	0.0566149i
$785$	−36.6586	+	6.46390i	−1.30840	+	0.230707i
$786$	1.34734	−	3.52347i	0.0480580	−	0.125678i
$787$	10.1172	+	27.7969i	0.360640	+	0.990851i	0.978804	+	0.204801i	$0.0656548\pi$
$787$	10.1172	+	27.7969i	0.360640	+	0.990851i	−0.618163	+	0.786050i	$0.712123\pi$
$788$	1.00375	−	1.19622i	0.0357571	−	0.0426136i
$789$	−6.79073	−	19.6397i	−0.241757	−	0.699191i
$790$	−12.9701	+	35.6350i	−0.461455	+	1.26784i
$791$	−20.2882	−	27.3736i	−0.721366	−	0.973293i
$792$	−1.48948	+	2.39736i	−0.0529265	+	0.0851865i
$793$	−2.70176	+	4.67958i	−0.0959422	+	0.166177i
$794$	11.9630	−	10.0381i	0.424549	−	0.356239i
$795$	−0.700568	+	43.3267i	−0.0248466	+	1.53664i
$796$	15.7247	+	2.77268i	0.557346	+	0.0982751i
$797$	3.58749	−	20.3457i	0.127075	−	0.720680i	−0.852978	−	0.521947i	$-0.825206\pi$
$797$	3.58749	−	20.3457i	0.127075	−	0.720680i	0.980054	−	0.198734i	$-0.0636828\pi$
$798$	33.0389	+	14.9746i	1.16957	+	0.530096i
$799$	3.94267	−	3.30830i	0.139482	−	0.117039i
$800$	−5.65643	−	3.26574i	−0.199985	−	0.115461i
$801$	28.3351	−	9.28722i	1.00117	−	0.328148i
$802$	−1.38218	−	2.39400i	−0.0488064	−	0.0845352i
$803$	−3.95258	−	1.43862i	−0.139484	−	0.0507679i
$804$	20.1237	+	17.4479i	0.709710	+	0.615342i
$805$	−3.74928	−	2.47742i	−0.132145	−	0.0873176i
$806$	1.18984	+	3.26906i	0.0419103	+	0.115148i
$807$	−5.44947	+	4.42450i	−0.191830	+	0.155750i
$808$	−13.9679	+	2.46291i	−0.491388	+	0.0866450i
$809$			16.2146i			0.570074i	0.958517	+	0.285037i	$0.0920059\pi$
$809$			16.2146i			0.570074i	−0.958517	+	0.285037i	$0.907994\pi$
$810$	−18.0909	−	24.6327i	−0.635650	−	0.865504i
$811$			14.3508i			0.503924i	0.967737	+	0.251962i	$0.0810757\pi$
$811$			14.3508i			0.503924i	−0.967737	+	0.251962i	$0.918924\pi$
$812$	6.12262	+	20.6110i	0.214862	+	0.723305i
$813$	−22.3726	−	27.5554i	−0.784642	−	0.966409i
$814$	0.442683	−	0.161124i	0.0155160	−	0.00564738i
$815$	−49.3925	−	41.4452i	−1.73014	−	1.45176i
$816$	2.91260	+	2.52532i	0.101961	+	0.0884039i
$817$	13.3948	−	36.8020i	0.468625	−	1.28754i
$818$	−14.5564	−	25.2124i	−0.508952	−	0.881530i
$819$	−2.87036	−	2.03296i	−0.100299	−	0.0710374i
$820$	−11.4115	+	19.7653i	−0.398508	+	0.690235i
$821$	−17.7133	−	21.1099i	−0.618198	−	0.736740i	0.362561	−	0.931960i	$-0.381902\pi$
$821$	−17.7133	−	21.1099i	−0.618198	−	0.736740i	−0.980759	+	0.195220i	$0.937458\pi$
$822$	0.330017	−	0.550842i	0.0115106	−	0.0192128i
$823$	−6.80471	+	38.5914i	−0.237197	+	1.34521i	0.600739	+	0.799445i	$0.294873\pi$
$823$	−6.80471	+	38.5914i	−0.237197	+	1.34521i	−0.837937	+	0.545767i	$0.816238\pi$
$824$	−1.68859	+	9.57644i	−0.0588247	+	0.333611i
$825$	0.172071	−	10.6417i	0.00599073	−	0.370497i
$826$	−0.00603201	+	0.00636627i	−0.000209880	+	0.000221511i
$827$	−18.8933	−	10.9080i	−0.656983	−	0.379309i	0.134143	−	0.990962i	$-0.457172\pi$
$827$	−18.8933	−	10.9080i	−0.656983	−	0.379309i	−0.791127	+	0.611653i	$0.790505\pi$
$828$	−1.32309	+	0.707865i	−0.0459804	+	0.0246000i
$829$	24.1551	−	13.9460i	0.838943	−	0.484364i	−0.0179619	−	0.999839i	$-0.505718\pi$
$829$	24.1551	−	13.9460i	0.838943	−	0.484364i	0.856905	+	0.515475i	$0.172384\pi$
$830$	15.6722	−	43.0590i	0.543989	−	1.49460i
$831$	−28.2259	+	9.75954i	−0.979144	+	0.338555i
$832$	−0.284850	+	0.339471i	−0.00987538	+	0.0117690i
$833$	−13.0529	+	8.50543i	−0.452257	+	0.294696i
$834$	−12.4234	−	4.75057i	−0.430186	−	0.164499i
$835$	−10.1736	−	57.6975i	−0.352073	−	1.99670i
$836$	7.44703			0.257561
$837$	−27.7045	+	29.9401i	−0.957609	+	1.03488i
$838$		−	35.8777i		−	1.23937i
$839$	1.41672	+	8.03460i	0.0489105	+	0.277385i	0.999448	−	0.0332250i	$-0.0105778\pi$
$839$	1.41672	+	8.03460i	0.0489105	+	0.277385i	−0.950537	+	0.310610i	$0.899467\pi$
$840$	−4.18951	−	14.9870i	−0.144552	−	0.517099i
$841$	34.8090	−	12.6694i	1.20031	−	0.436877i
$842$	−3.48453	+	4.15270i	−0.120085	+	0.143111i
$843$	36.9915	+	7.14109i	1.27406	+	0.245952i
$844$	−24.4429	−	8.89649i	−0.841359	−	0.306230i
$845$	21.7393	+	37.6536i	0.747854	+	1.29532i
$846$	−2.58229	+	6.43899i	−0.0887808	+	0.221377i
$847$	24.5502	+	10.6521i	0.843554	+	0.366011i
$848$	4.73562	+	5.64369i	0.162622	+	0.193805i
$849$	24.0661	−	13.3805i	0.825946	−	0.459218i
$850$	−14.3159	−	2.52428i	−0.491032	−	0.0865821i
$851$	0.246655	+	0.0434919i	0.00845522	+	0.00149088i
$852$	18.1101	−	10.0690i	0.620440	−	0.344959i
$853$	−0.136644	−	0.162846i	−0.00467861	−	0.00557576i	0.763700	−	0.645571i	$-0.223381\pi$
$853$	−0.136644	−	0.162846i	−0.00467861	−	0.00557576i	−0.768379	+	0.639995i	$0.778936\pi$
$854$	−29.5952	−	12.8411i	−1.01273	−	0.439414i
$855$	−30.0160	+	74.8456i	−1.02653	+	2.55966i
$856$	−5.33755	−	9.24491i	−0.182434	−	0.315985i
$857$	45.5058	+	16.5628i	1.55445	+	0.565773i	0.969456	−	0.245265i	$-0.0788750\pi$
$857$	45.5058	+	16.5628i	1.55445	+	0.565773i	0.584993	+	0.811038i	$0.301097\pi$
$858$	−0.709022	−	0.136874i	−0.0242056	−	0.00467282i
$859$	−4.91863	+	5.86180i	−0.167822	+	0.200002i	−0.843400	−	0.537286i	$-0.819450\pi$
$859$	−4.91863	+	5.86180i	−0.167822	+	0.200002i	0.675578	+	0.737288i	$0.263894\pi$
$860$	−15.7880	+	5.74635i	−0.538365	+	0.195949i
$861$	−29.6621	+	8.29186i	−1.01088	+	0.282586i
$862$	5.97789	+	33.9023i	0.203608	+	1.15472i
$863$		−	27.7478i		−	0.944547i	−0.881452	−	0.472274i	$-0.843433\pi$
$863$		−	27.7478i		−	0.944547i	0.881452	−	0.472274i	$-0.156567\pi$
$864$	−5.06744	−	1.14935i	−0.172398	−	0.0391017i
$865$	−36.9096			−1.25496
$866$	3.28895	+	18.6526i	0.111763	+	0.633840i
$867$	−19.4889	−	7.45236i	−0.661878	−	0.253095i
$868$	−18.5806	+	9.28194i	−0.630668	+	0.315049i
$869$	−6.75325	+	8.04821i	−0.229088	+	0.273017i
$870$	−45.1745	+	15.6198i	−1.53156	+	0.529561i
$871$	−2.33069	+	6.40351i	−0.0789723	+	0.216974i
$872$	2.65275	−	1.53156i	0.0898334	−	0.0518653i
$873$	4.20883	−	2.25177i	0.142447	−	0.0762108i
$874$	3.42882	+	1.97963i	0.115982	+	0.0669620i
$875$	9.98813	+	9.46369i	0.337660	+	0.319931i
$876$	0.125198	−	7.74289i	0.00423005	−	0.261608i
$877$	−0.378601	+	2.14715i	−0.0127844	+	0.0725042i	−0.990533	−	0.137278i	$-0.956165\pi$
$877$	−0.378601	+	2.14715i	−0.0127844	+	0.0725042i	0.977748	+	0.209783i	$0.0672756\pi$
$878$	−0.575986	+	3.26658i	−0.0194386	+	0.110242i
$879$	−10.2861	+	17.1689i	−0.346942	+	0.579093i
$880$	−2.05355	−	2.44733i	−0.0692253	−	0.0824995i
$881$	28.7686	−	49.8288i	0.969240	−	1.67877i	0.271477	−	0.962445i	$-0.412488\pi$
$881$	28.7686	−	49.8288i	0.969240	−	1.67877i	0.697763	−	0.716328i	$-0.254179\pi$
$882$	10.1053	−	18.4088i	0.340262	−	0.619856i
$883$	−26.2109	−	45.3986i	−0.882067	−	1.52778i	−0.849039	−	0.528330i	$-0.822819\pi$
$883$	−26.2109	−	45.3986i	−0.882067	−	1.52778i	−0.0330272	−	0.999454i	$-0.510515\pi$
$884$	−0.337331	+	0.926808i	−0.0113457	+	0.0311719i
$885$	−0.0147307	−	0.0127720i	−0.000495166	−	0.000429326i
$886$	−19.0194	−	15.9592i	−0.638971	−	0.536160i
$887$	21.1772	−	7.70787i	0.711060	−	0.258805i	0.0389345	−	0.999242i	$-0.487604\pi$
$887$	21.1772	−	7.70787i	0.711060	−	0.258805i	0.672126	+	0.740437i	$0.265381\pi$
$888$	0.546679	+	0.673321i	0.0183453	+	0.0225952i
$889$	−10.1500	+	3.01512i	−0.340421	+	0.101124i
$890$			33.7523i			1.13138i
$891$	−2.37568	−	8.12707i	−0.0795884	−	0.272267i
$892$			15.2756i			0.511464i
$893$	18.0268	−	3.17862i	0.603245	−	0.106368i
$894$	−1.81627	+	1.47465i	−0.0607451	+	0.0493198i
$895$	−9.97489	−	27.4058i	−0.333424	−	0.916074i
$896$	−2.20738	−	1.45858i	−0.0737435	−	0.0487277i
$897$	−0.290068	−	0.251499i	−0.00968510	−	0.00839730i
$898$	−2.64953	−	0.964351i	−0.0884161	−	0.0321808i
$899$	31.8986	+	55.2500i	1.06388	+	1.84269i
$900$	18.6198	−	6.10290i	0.620660	−	0.203430i
$901$	14.2002	+	8.19851i	0.473078	+	0.273132i
$902$	−4.84374	+	4.06438i	−0.161279	+	0.135329i
$903$	−20.6508	−	9.35980i	−0.687216	−	0.311475i
$904$	2.23626	−	12.6825i	0.0743771	−	0.421813i
$905$	26.8370	+	4.73209i	0.892092	+	0.157300i
$906$	0.0527259	−	3.26084i	0.00175170	−	0.108334i
$907$	6.48432	−	5.44099i	0.215308	−	0.180665i	−0.528755	−	0.848775i	$-0.677341\pi$
$907$	6.48432	−	5.44099i	0.215308	−	0.180665i	0.744063	+	0.668110i	$0.232896\pi$
$908$	−12.0178	+	20.8155i	−0.398826	+	0.690787i
$909$	22.4553	−	36.1424i	0.744794	−	1.19877i
$910$	3.19867	−	2.37073i	0.106035	−	0.0785888i
$911$	−16.2703	+	44.7023i	−0.539059	+	1.48105i	0.308954	+	0.951077i	$0.400021\pi$
$911$	−16.2703	+	44.7023i	−0.539059	+	1.48105i	−0.848013	+	0.529975i	$0.822201\pi$
$912$	4.48030	+	12.9576i	0.148358	+	0.429070i
$913$	8.16017	−	9.72491i	0.270062	−	0.321847i
$914$	1.91628	+	5.26495i	0.0633850	+	0.174149i
$915$	25.6155	−	66.9879i	0.846823	−	2.21455i
$916$	−12.0270	+	2.12068i	−0.397382	+	0.0700691i
$917$	0.656739	+	5.72471i	0.0216874	+	0.189047i
$918$	−11.4731	+	1.45364i	−0.378668	+	0.0479773i
$919$	5.43170			0.179175			0.0895877	−	0.995979i	$-0.471445\pi$
$919$	5.43170			0.179175			0.0895877	+	0.995979i	$0.471445\pi$
$920$	−0.294944	−	1.67271i	−0.00972402	−	0.0551477i
$921$	−18.1410	+	2.89715i	−0.597766	+	0.0954645i
$922$	10.3666	+	28.4821i	0.341407	+	0.938009i
$923$	4.06118	+	3.40773i	0.133675	+	0.112167i
$924$	0.329406	−	4.29867i	0.0108367	−	0.141416i
$925$	−3.07333	−	1.11860i	−0.101050	−	0.0367793i
$926$	24.7237	−	14.2742i	0.812472	−	0.469081i
$927$	−18.0194	−	22.9420i	−0.591836	−	0.753515i
$928$	−4.06334	+	7.03791i	−0.133386	+	0.231031i
$929$	16.6470	−	13.9685i	0.546171	−	0.458292i	−0.327471	−	0.944861i	$-0.606196\pi$
$929$	16.6470	−	13.9685i	0.546171	−	0.458292i	0.873642	+	0.486569i	$0.161752\pi$
$930$	−22.4372	−	40.3553i	−0.735744	−	1.32330i
$931$	−55.3291	+	2.98559i	−1.81334	+	0.0978489i
$932$	−3.77987	−	0.666492i	−0.123814	−	0.0218317i
$933$	14.0616	+	25.2911i	0.460357	+	0.827994i
$934$	1.74177	+	2.07576i	0.0569923	+	0.0679208i
$935$	−6.15780	−	3.55520i	−0.201381	−	0.116268i
$936$	−0.188406	−	1.31602i	−0.00615825	−	0.0430156i
$937$	28.0174	−	16.1758i	0.915288	−	0.528442i	0.0331591	−	0.999450i	$-0.489443\pi$
$937$	28.0174	−	16.1758i	0.915288	−	0.528442i	0.882129	+	0.471008i	$0.156110\pi$
$938$	−39.5681	−	9.46706i	−1.29194	−	0.309110i
$939$	42.2900	+	8.16395i	1.38008	+	0.266421i
$940$	−6.01558	−	5.04767i	−0.196207	−	0.164637i
$941$	−7.15158	+	2.60296i	−0.233135	+	0.0848542i	−0.455946	−	0.890007i	$-0.650699\pi$
$941$	−7.15158	+	2.60296i	−0.233135	+	0.0848542i	0.222811	+	0.974862i	$0.428477\pi$
$942$	−2.99423	−	18.7488i	−0.0975572	−	0.610869i
$943$	−3.31062	+	0.583752i	−0.107809	+	0.0190096i
$944$	−0.00331478			−0.000107887
$945$	41.8756	+	20.6369i	1.36221	+	0.671318i
$946$	−4.65473			−0.151338
$947$	−23.6969	+	4.17840i	−0.770046	+	0.135780i	−0.544850	−	0.838534i	$-0.683413\pi$
$947$	−23.6969	+	4.17840i	−0.770046	+	0.135780i	−0.225196	+	0.974314i	$0.572302\pi$
$948$	−18.0665	−	6.90847i	−0.586774	−	0.224377i
$949$	1.86180	−	0.677640i	0.0604366	−	0.0219971i
$950$	−39.6052	−	33.2327i	−1.28496	−	1.07821i
$951$	9.94230	+	28.7544i	0.322401	+	0.932426i
$952$	−5.72687	−	1.37021i	−0.185609	−	0.0444088i
$953$	42.1813	−	24.3534i	1.36639	−	0.788884i	0.375922	−	0.926651i	$-0.377326\pi$
$953$	42.1813	−	24.3534i	1.36639	−	0.788884i	0.990465	+	0.137768i	$0.0439927\pi$
$954$	−22.0904	−	0.714565i	−0.715203	−	0.0231349i
$955$	−65.2635	−	37.6799i	−2.11188	−	1.21929i
$956$	10.9993	+	13.1085i	0.355743	+	0.423958i
$957$	−13.2408	−	0.214096i	−0.428013	−	0.00692074i
$958$	−8.20936	−	1.44753i	−0.265232	−	0.0467676i
$959$	−0.0591232	+	0.979095i	−0.00190919	+	0.0316166i
$960$	3.02282	−	5.04549i	0.0975611	−	0.162843i
$961$	−23.4623	+	19.6872i	−0.756847	+	0.635070i
$962$	−0.110951	+	0.192172i	−0.00357719	+	0.00619587i
$963$	31.3425	+	6.57789i	1.01000	+	0.211970i
$964$	−15.7517	+	9.09423i	−0.507327	+	0.292906i
$965$	−80.9530	−	29.4645i	−2.60597	−	0.948495i
$966$	1.29438	−	1.89166i	0.0416459	−	0.0608633i
$967$	−26.4424	−	22.1878i	−0.850330	−	0.713512i	0.109532	−	0.993983i	$-0.465065\pi$
$967$	−26.4424	−	22.1878i	−0.850330	−	0.713512i	−0.959862	+	0.280471i	$0.909509\pi$
$968$	3.45950	+	9.50490i	0.111193	+	0.305499i
$969$	19.2337	+	23.6894i	0.617877	+	0.761012i
$970$	0.938238	+	5.32101i	0.0301250	+	0.170847i
$971$	16.4000			0.526302			0.263151	−	0.964755i	$-0.415238\pi$
$971$	16.4000			0.526302			0.263151	+	0.964755i	$0.415238\pi$
$972$	12.7116	−	9.02305i	0.407725	−	0.289414i
$973$	20.1847	−	2.31559i	0.647092	−	0.0742344i
$974$	−8.55172	+	1.50790i	−0.274015	+	0.0483162i
$975$	3.15995	+	3.89198i	0.101199	+	0.124643i
$976$	−4.17042	−	11.4581i	−0.133492	−	0.366766i
$977$	37.1354	−	44.2562i	1.18807	−	1.41588i	0.301384	−	0.953503i	$-0.402551\pi$
$977$	37.1354	−	44.2562i	1.18807	−	1.41588i	0.886682	−	0.462379i	$-0.153004\pi$
$978$	21.5439	−	24.8479i	0.688899	−	0.794547i
$979$	−3.19822	+	8.78705i	−0.102216	+	0.280835i
$980$	16.2384	+	17.3596i	0.518718	+	0.554532i
$981$	−1.88747	+	8.99346i	−0.0602623	+	0.287139i
$982$	−15.5814	+	26.9877i	−0.497222	+	0.861213i
$983$	−5.01976	+	4.21208i	−0.160106	+	0.134345i	−0.719321	−	0.694678i	$-0.755547\pi$
$983$	−5.01976	+	4.21208i	−0.160106	+	0.134345i	0.559215	+	0.829022i	$0.311102\pi$
$984$	−9.98601	−	5.98275i	−0.318342	−	0.190723i
$985$	−5.22218	−	0.920810i	−0.166392	−	0.0293395i
$986$	−3.14079	+	17.8123i	−0.100023	+	0.567260i
$987$	−1.03742	−	10.5463i	−0.0330214	−	0.335692i
$988$	−2.68713	+	2.25477i	−0.0854891	+	0.0717339i
$989$	−2.14316	−	1.23736i	−0.0681487	−	0.0393457i
$990$	9.57928	+	0.309864i	0.304450	+	0.00984813i
$991$	23.9216	+	41.4334i	0.759894	+	1.31618i	0.942904	+	0.333064i	$0.108083\pi$
$991$	23.9216	+	41.4334i	0.759894	+	1.31618i	−0.183010	+	0.983111i	$0.558584\pi$
$992$	−7.37690	−	2.68497i	−0.234217	−	0.0852480i
$993$	11.8666	−	4.10305i	0.376574	−	0.130206i
$994$	−17.4494	+	26.4075i	−0.553461	+	0.837596i
$995$	−18.5449	−	50.9517i	−0.587912	−	1.61528i
$996$	21.8304	+	8.34772i	0.691722	+	0.264508i
$997$	−31.4624	+	5.54767i	−0.996423	+	0.175696i	−0.648000	−	0.761641i	$-0.724394\pi$
$997$	−31.4624	+	5.54767i	−0.996423	+	0.175696i	−0.348424	+	0.937337i	$0.613283\pi$
$998$		−	11.8797i		−	0.376045i
$999$	−2.59885	−	0.126154i	−0.0822241	−	0.00399134i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.z.a.41.3	✓	144
7.6	odd	2	inner	378.2.z.a.41.10	yes	144
27.2	odd	18	inner	378.2.z.a.83.10	yes	144
189.83	even	18	inner	378.2.z.a.83.3	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.3	✓	144	1.1	even	1	trivial
378.2.z.a.41.10	yes	144	7.6	odd	2	inner
378.2.z.a.83.3	yes	144	189.83	even	18	inner
378.2.z.a.83.10	yes	144	27.2	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(-1.34465 + 1.09174i) q^{3} +(0.939693 - 0.342020i) q^{4} +(-2.60134 - 2.18278i) q^{5} +(1.13465 - 1.30865i) q^{6} +(-0.615646 + 2.57313i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.616190 - 2.93604i) q^{9} +(2.94085 + 1.69790i) q^{10} +(0.604733 + 0.720693i) q^{11} +(-0.890163 + 1.48580i) q^{12} +(-0.436415 - 0.0769517i) q^{13} +(0.159475 - 2.64094i) q^{14} +(5.88094 + 0.0950914i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.11282 - 1.92746i) q^{17} +(-0.0969913 + 2.99843i) q^{18} +(6.85516 - 3.95783i) q^{19} +(-3.19101 - 1.16143i) q^{20} +(-1.98136 - 4.13209i) q^{21} +(-0.720693 - 0.604733i) q^{22} +(-0.171072 - 0.470016i) q^{23} +(0.618633 - 1.61781i) q^{24} +(1.13418 + 6.43225i) q^{25} +0.443147 q^{26} +(2.37684 + 4.62068i) q^{27} +(0.301543 + 2.62851i) q^{28} +(8.00322 - 1.41118i) q^{29} +(-5.80810 + 0.927567i) q^{30} +(2.68497 + 7.37690i) q^{31} +(-0.642788 + 0.766044i) q^{32} +(-1.59997 - 0.308869i) q^{33} +(-0.761215 + 2.09142i) q^{34} +(7.21807 - 5.34975i) q^{35} +(-0.425154 - 2.96972i) q^{36} +(-0.250369 + 0.433653i) q^{37} +(-6.06375 + 5.08809i) q^{38} +(0.670839 - 0.372980i) q^{39} +(3.34421 + 0.589675i) q^{40} +(1.16708 - 6.61885i) q^{41} +(2.66879 + 3.72526i) q^{42} +(3.79011 - 3.18028i) q^{43} +(0.814755 + 0.470399i) q^{44} +(-8.01164 + 6.29261i) q^{45} +(0.250090 + 0.433169i) q^{46} +(2.17304 + 0.790920i) q^{47} +(-0.328305 + 1.70065i) q^{48} +(-6.24196 - 3.16827i) q^{49} +(-2.23390 - 6.13758i) q^{50} +(0.607937 + 3.80669i) q^{51} +(-0.436415 + 0.0769517i) q^{52} +7.36731i q^{53} +(-3.14310 - 4.13774i) q^{54} -3.19476i q^{55} +(-0.753398 - 2.53622i) q^{56} +(-4.89689 + 12.8060i) q^{57} +(-7.63658 + 2.77949i) q^{58} +(-0.00253927 - 0.00213070i) q^{59} +(5.55879 - 1.92204i) q^{60} +(4.17042 - 11.4581i) q^{61} +(-3.92517 - 6.79859i) q^{62} +(7.17544 + 3.39309i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.967293 + 1.15278i) q^{65} +(1.62930 + 0.0263448i) q^{66} +(2.67026 - 15.1438i) q^{67} +(0.386479 - 2.19183i) q^{68} +(0.743170 + 0.445243i) q^{69} +(-6.17944 + 6.52188i) q^{70} +(-10.3605 - 5.98164i) q^{71} +(0.934382 + 2.85078i) q^{72} +(-3.87195 + 2.23547i) q^{73} +(0.171263 - 0.470541i) q^{74} +(-8.54745 - 7.41092i) q^{75} +(5.08809 - 6.06375i) q^{76} +(-2.22674 + 1.11236i) q^{77} +(-0.595880 + 0.483804i) q^{78} +(1.93918 + 10.9977i) q^{79} -3.39580 q^{80} +(-8.24062 - 3.61831i) q^{81} +6.72095i q^{82} +(-2.34318 - 13.2888i) q^{83} +(-3.27513 - 3.20523i) q^{84} +(-7.10206 + 2.58494i) q^{85} +(-3.18028 + 3.79011i) q^{86} +(-9.22091 + 10.6350i) q^{87} +(-0.884061 - 0.321772i) q^{88} +(4.96971 + 8.60779i) q^{89} +(6.79722 - 7.58822i) q^{90} +(0.466684 - 1.07558i) q^{91} +(-0.321510 - 0.383161i) q^{92} +(-11.6641 - 6.98808i) q^{93} +(-2.27736 - 0.401561i) q^{94} +(-26.4717 - 4.66767i) q^{95} +(0.0280026 - 1.73182i) q^{96} +(1.02275 + 1.21886i) q^{97} +(6.69729 + 2.03623i) q^{98} +(2.48861 - 1.33143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57}+ \cdots + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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