LMFDB - Embedded newform 378.2.z.a.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
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			83.3
Character	$\chi$	$=$	378.83
Dual form			378.2.z.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 - 0.173648i) q^{2} +(-1.34465 - 1.09174i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.60134 + 2.18278i) q^{5} +(1.13465 + 1.30865i) q^{6} +(-0.615646 - 2.57313i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.616190 + 2.93604i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 144 * q - 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.999946	−	0.0103897i	$-0.996693\pi$
$5$	−2.60134	+	2.18278i	−1.16335	+	0.976169i	−0.163407	+	0.986559i	$0.552248\pi$
$6$	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	−0.667134	−	0.744938i	$-0.732479\pi$
$11$	0.604733	−	0.720693i	0.182334	−	0.217297i	0.849467	+	0.527641i	$0.176923\pi$
$12$	−0.890163	−	1.48580i	−0.256968	−	0.428914i
$13$	−0.436415	+	0.0769517i	−0.121040	+	0.0213426i	−0.233840	−	0.972275i	$-0.575129\pi$
$13$	−0.436415	+	0.0769517i	−0.121040	+	0.0213426i	0.112800	+	0.993618i	$0.464018\pi$
$14$	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	0.968836	−	0.247705i	$-0.0796763\pi$
$17$	1.11282	+	1.92746i	0.269899	+	0.467479i	−0.698936	+	0.715184i	$0.746343\pi$
$18$	−0.0969913	−	2.99843i	−0.0228611	−	0.706737i
$19$	6.85516	+	3.95783i	1.57268	+	0.907988i	0.995839	+	0.0911335i	$0.0290490\pi$
$19$	6.85516	+	3.95783i	1.57268	+	0.907988i	0.576843	+	0.816855i	$0.304284\pi$
$20$	−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	−0.956250	−	0.292552i	$-0.905495\pi$
$23$	−0.171072	+	0.470016i	−0.0356710	+	0.0980051i	0.920579	+	0.390557i	$0.127718\pi$
$24$	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	0.857037	−	0.515255i	$-0.172303\pi$
$29$	8.00322	+	1.41118i	1.48616	+	0.262050i	0.629123	+	0.777305i	$0.283414\pi$
$30$	−5.80810	−	0.927567i	−1.06041	−	0.169350i
$31$	2.68497	−	7.37690i	0.482236	−	1.32493i	−0.425337	−	0.905035i	$-0.639844\pi$
$31$	2.68497	−	7.37690i	0.482236	−	1.32493i	0.907572	−	0.419896i	$-0.137933\pi$
$32$	−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	0.844711	−	0.535222i	$-0.179772\pi$
$37$	−0.250369	−	0.433653i	−0.0411605	−	0.0712920i	−0.885872	+	0.463930i	$0.846439\pi$
$38$	−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	0.929416	+	0.369033i	$0.120311\pi$
$41$	1.16708	+	6.61885i	0.182268	+	1.03369i	−0.747149	+	0.664657i	$0.768578\pi$
$42$	2.66879	−	3.72526i	0.411804	−	0.574820i
$43$	3.79011	+	3.18028i	0.577987	+	0.484988i	0.884285	−	0.466947i	$-0.154646\pi$
$43$	3.79011	+	3.18028i	0.577987	+	0.484988i	−0.306299	+	0.951935i	$0.599091\pi$
$44$	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	−0.178636	−	0.983915i	$-0.557168\pi$
$47$	2.17304	−	0.790920i	0.316970	−	0.115368i	0.495606	+	0.868548i	$0.334946\pi$
$48$	−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	$-0.831128\pi$
$53$		−	7.36731i		−	1.01198i	0.862540	−	0.505989i	$-0.168872\pi$
$54$	−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	−0.642953	−	0.765906i	$-0.722291\pi$
$59$	−0.00253927	+	0.00213070i	−0.000330585	+	0.000277394i	0.642622	+	0.766183i	$0.277846\pi$
$60$	5.55879	+	1.92204i	0.717637	+	0.248135i
$61$	4.17042	+	11.4581i	0.533967	+	1.46706i	0.854311	+	0.519762i	$0.173979\pi$
$61$	4.17042	+	11.4581i	0.533967	+	1.46706i	−0.320344	+	0.947301i	$0.603798\pi$
$62$	−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	0.500927	+	0.865490i	$0.332993\pi$
$67$	2.67026	+	15.1438i	0.326225	+	1.85011i	−0.174702	+	0.984621i	$0.555896\pi$
$68$	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	−0.966939	−	0.255008i	$-0.917922\pi$
$71$	−10.3605	+	5.98164i	−1.22956	+	0.709889i	−0.262626	+	0.964898i	$0.584588\pi$
$72$	0.934382	−	2.85078i	0.110118	−	0.335967i
$73$	−3.87195	−	2.23547i	−0.453177	−	0.261642i	0.255994	−	0.966678i	$-0.417597\pi$
$73$	−3.87195	−	2.23547i	−0.453177	−	0.261642i	−0.709171	+	0.705036i	$0.750931\pi$
$74$	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	−0.657135	−	0.753773i	$-0.728232\pi$
$79$	1.93918	−	10.9977i	0.218175	−	1.23733i	0.875311	−	0.483561i	$-0.160657\pi$
$80$	−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	0.533172	+	0.846007i	$0.321000\pi$
$83$	−2.34318	+	13.2888i	−0.257197	+	1.45864i	−0.790369	+	0.612631i	$0.790111\pi$
$84$	−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	−0.472724	−	0.881210i	$-0.656729\pi$
$89$	4.96971	−	8.60779i	0.526788	−	0.912424i	0.999513	−	0.0312137i	$-0.00993725\pi$
$90$	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	−0.711619	−	0.702565i	$-0.752038\pi$
$97$	1.02275	−	1.21886i	0.103844	−	0.123757i	0.815463	+	0.578809i	$0.196482\pi$
$98$	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	0.420750	−	0.907177i	$-0.361767\pi$
$101$	13.3280	−	4.85099i	1.32619	−	0.482692i	0.905435	+	0.424485i	$0.139545\pi$
$102$	−1.25973	+	3.64329i	−0.124731	+	0.360740i
$103$	6.25058	+	7.44915i	0.615888	+	0.733987i	0.980358	−	0.197229i	$-0.0631941\pi$
$103$	6.25058	+	7.44915i	0.615888	+	0.733987i	−0.364470	+	0.931215i	$0.618750\pi$
$104$	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	$-0.827420\pi$
$107$		−	10.6751i		−	1.03200i	0.856588	−	0.516001i	$-0.172580\pi$
$108$	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	0.220155	−	0.975465i	$-0.429344\pi$
$113$	−8.27791	−	9.86522i	−0.778720	−	0.928042i	−0.998875	+	0.0474227i	$0.984899\pi$
$114$	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	−0.763483	−	0.645828i	$-0.776512\pi$
$127$	2.00102	−	3.46586i	0.177562	−	0.307546i	0.941045	+	0.338282i	$0.109846\pi$
$128$	−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	0.429874	−	0.902889i	$-0.358558\pi$
$131$	2.04658	+	0.744896i	0.178811	+	0.0650819i	−0.251063	+	0.967971i	$0.580780\pi$
$132$	−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	0.189223	−	0.981934i	$-0.439403\pi$
$137$	0.365105	+	0.0643778i	0.0311930	+	0.00550017i	−0.158030	+	0.987434i	$0.550514\pi$
$138$	−0.809195	+	0.309428i	−0.0688833	+	0.0263403i
$139$	−2.62642	+	7.21603i	−0.222770	+	0.612056i	−0.999850	−	0.0173467i	$-0.994478\pi$
$139$	−2.62642	+	7.21603i	−0.222770	+	0.612056i	0.777079	+	0.629403i	$0.216700\pi$
$140$	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	−0.227870	−	0.973692i	$-0.573176\pi$
$149$	−1.33021	+	0.234552i	−0.108975	+	0.0192153i	0.118895	+	0.992907i	$0.462065\pi$
$150$	9.70449	−	5.81408i	0.792368	−	0.474718i
$151$	1.44238	+	1.21030i	0.117379	+	0.0984928i	0.699588	−	0.714547i	$-0.253367\pi$
$151$	1.44238	+	1.21030i	0.117379	+	0.0984928i	−0.582209	+	0.813039i	$0.697811\pi$
$152$	−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	0.970040	−	0.242944i	$-0.0781132\pi$
$157$	7.04611	+	8.39723i	0.562341	+	0.670172i	−0.407699	+	0.913116i	$0.633669\pi$
$158$	−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	0.0327573	−	0.999463i	$-0.489571\pi$
$167$	13.2165	−	11.0900i	1.02272	−	0.858168i	0.989967	+	0.141295i	$0.0451267\pi$
$168$	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	0.901870	−	0.432007i	$-0.142194\pi$
$173$	8.32627	+	6.98657i	0.633035	+	0.531179i	−0.268835	+	0.963186i	$0.586639\pi$
$174$	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	−0.195582	−	0.980687i	$-0.562660\pi$
$179$	7.43780	−	4.29421i	0.555927	−	0.320965i	0.751509	+	0.659723i	$0.229326\pi$
$180$	−5.37628	−	8.65326i	−0.400724	−	0.644976i
$181$	−6.94977	−	4.01245i	−0.516572	−	0.298243i	0.218959	−	0.975734i	$-0.429734\pi$
$181$	−6.94977	−	4.01245i	−0.516572	−	0.298243i	−0.735531	+	0.677491i	$0.763067\pi$
$182$	−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	0.894201	−	0.447666i	$-0.147745\pi$
$191$	21.8549	+	3.85361i	1.58136	+	0.278837i	0.687163	+	0.726503i	$0.258856\pi$
$192$	0.273151	−	1.71038i	0.0197130	−	0.123436i
$193$	23.8391	+	8.67673i	1.71598	+	0.624565i	0.997479	−	0.0709632i	$-0.0226073\pi$
$193$	23.8391	+	8.67673i	1.71598	+	0.624565i	0.718499	+	0.695528i	$0.244830\pi$
$194$	−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	0.547401	−	0.836870i	$-0.315617\pi$
$197$	1.35235	+	0.780778i	0.0963507	+	0.0556281i	−0.451050	+	0.892498i	$0.648951\pi$
$198$	−2.21960	−	1.74335i	−0.157740	−	0.123894i
$199$	13.8280	−	7.98362i	0.980244	−	0.565944i	0.0778999	−	0.996961i	$-0.475179\pi$
$199$	13.8280	−	7.98362i	0.980244	−	0.565944i	0.902344	+	0.431017i	$0.141845\pi$
$200$	−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	−0.399616	+	0.916683i	$0.630857\pi$
$211$	−19.9260	+	16.7199i	−1.37176	+	1.15105i	−0.972149	+	0.234365i	$0.924699\pi$
$212$	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	−0.982413	−	0.186720i	$-0.940214\pi$
$223$	−5.22456	−	14.3544i	−0.349862	−	0.961238i	0.632551	−	0.774519i	$-0.282008\pi$
$224$	−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	−0.998714	−	0.0507061i	$-0.983853\pi$
$227$	−18.4124	−	15.4498i	−1.22207	−	1.02544i	−0.223361	−	0.974736i	$-0.571703\pi$
$228$	−0.221659	−	13.7085i	−0.0146797	−	0.907870i
$229$	−12.0270	+	2.12068i	−0.794764	+	0.140138i	−0.556265	−	0.831005i	$-0.687766\pi$
$229$	−12.0270	+	2.12068i	−0.794764	+	0.140138i	−0.238498	+	0.971143i	$0.576655\pi$
$230$	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	−0.604913	−	0.796292i	$-0.706792\pi$
$233$	−3.32396	+	1.91909i	−0.217760	+	0.125724i	0.387153	+	0.922016i	$0.373459\pi$
$234$	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	−0.593375	−	0.804926i	$-0.702205\pi$
$239$	5.85260	−	16.0799i	0.378573	−	1.04012i	0.971948	−	0.235196i	$-0.0755731\pi$
$240$	4.56618	+	3.70735i	0.294746	+	0.239308i
$241$	−17.9121	−	3.15839i	−1.15382	−	0.203450i	−0.436179	−	0.899860i	$-0.643668\pi$
$241$	−17.9121	−	3.15839i	−1.15382	−	0.203450i	−0.717644	+	0.696410i	$0.754780\pi$
$242$		−	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	−0.668985	−	0.743276i	$-0.733271\pi$
$251$	4.89870	−	8.48480i	0.309203	−	0.535556i	0.978188	+	0.207720i	$0.0666043\pi$
$252$	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	0.957086	+	0.289803i	$0.0935897\pi$
$257$	2.51430	+	14.2593i	0.156838	+	0.889471i	−0.800249	+	0.599668i	$0.795299\pi$
$258$	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	−0.999555	−	0.0298351i	$-0.990502\pi$
$263$	−4.10344	−	11.2741i	−0.253029	−	0.695192i	0.746526	−	0.665356i	$-0.231720\pi$
$264$	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	$-0.786151\pi$
$271$		−	20.4925i		−	1.24483i	0.782686	−	0.622416i	$-0.213849\pi$
$272$	−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	0.194216	−	0.980959i	$-0.437784\pi$
$277$	16.2030	−	5.89740i	0.973542	−	0.354340i	0.779326	+	0.626618i	$0.215561\pi$
$278$	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	0.165902	+	0.986142i	$0.446947\pi$
$281$	−13.9815	+	16.6625i	−0.834067	+	0.994003i	−0.999969	+	0.00786044i	$0.997498\pi$
$282$	3.50067	+	1.94634i	0.208462	+	0.115903i
$283$	−15.6562	+	2.76061i	−0.930665	+	0.164101i	−0.618373	−	0.785885i	$-0.712208\pi$
$283$	−15.6562	+	2.76061i	−0.930665	+	0.164101i	−0.312292	+	0.949986i	$0.601097\pi$
$284$	−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	0.639127	−	0.769102i	$-0.279296\pi$
$293$	10.8584	+	3.95215i	0.634357	+	0.230887i	−0.00476955	+	0.999989i	$0.501518\pi$
$294$	−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	−0.214428	−	0.976740i	$-0.568789\pi$
$307$	9.18543	−	5.30321i	0.524240	−	0.302670i	0.738668	+	0.674070i	$0.235455\pi$
$308$	−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	0.949570	+	0.313556i	$0.101520\pi$
$311$	2.90114	+	16.4532i	0.164508	+	0.932974i	−0.785061	+	0.619418i	$0.787369\pi$
$312$	−0.394474	−	0.658430i	−0.0223327	−	0.0372762i
$313$	−15.9842	+	19.0492i	−0.903479	+	1.07672i	0.0932289	+	0.995645i	$0.470281\pi$
$313$	−15.9842	+	19.0492i	−0.903479	+	1.07672i	−0.996708	+	0.0810793i	$0.974163\pi$
$314$	−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	0.986120	+	0.166035i	$0.0530966\pi$
$317$	6.00784	+	16.5064i	0.337434	+	0.927092i	−0.648686	+	0.761056i	$0.724681\pi$
$318$	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	−0.522374	−	0.852717i	$-0.674953\pi$
$331$	−6.81196	+	2.47935i	−0.374419	+	0.136278i	0.147954	+	0.988994i	$0.452731\pi$
$332$	−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	−0.991649	−	0.128967i	$-0.958834\pi$
$337$	−1.90759	−	10.8185i	−0.103913	−	0.589320i	0.887736	−	0.460353i	$-0.152277\pi$
$338$	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	−0.978071	−	0.208271i	$-0.933216\pi$
$347$	−1.76874	+	4.85957i	−0.0949509	+	0.260875i	0.883120	+	0.469147i	$0.155438\pi$
$348$	−5.02743	−	13.1474i	−0.269499	−	0.704774i
$349$	−12.2071	−	2.15244i	−0.653432	−	0.115218i	−0.162902	−	0.986642i	$-0.552086\pi$
$349$	−12.2071	−	2.15244i	−0.653432	−	0.115218i	−0.490530	+	0.871425i	$0.663197\pi$
$350$	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	0.857638	+	0.514253i	$0.171931\pi$
$353$	−2.33281	+	13.2300i	−0.124163	+	0.704164i	−0.981801	+	0.189910i	$0.939180\pi$
$354$	−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	0.132214	−	0.991221i	$-0.457792\pi$
$359$	−12.5072	−	7.22101i	−0.660103	−	0.381110i	−0.792316	+	0.610111i	$0.791125\pi$
$360$	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	−0.923399	−	0.383841i	$-0.874601\pi$
$367$	−7.37637	+	8.79081i	−0.385043	+	0.458877i	0.538356	+	0.842717i	$0.319046\pi$
$368$	−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	−0.627239	−	0.778827i	$-0.715815\pi$
$373$	0.595553	−	0.499728i	0.0308366	−	0.0258749i	0.658076	+	0.752952i	$0.271371\pi$
$374$	−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	−0.191973	+	0.981400i	$0.561489\pi$
$383$	−23.3240	+	19.5711i	−1.19180	+	1.00004i	−0.999826	+	0.0186386i	$0.994067\pi$
$384$	−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	−0.877300	−	0.479943i	$-0.840657\pi$
$389$	−4.97627	+	5.93049i	−0.252307	+	0.300688i	0.624993	+	0.780630i	$0.285102\pi$
$390$	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	0.120624	−	0.992698i	$-0.461510\pi$
$397$	−13.5243	−	7.80827i	−0.678766	−	0.391886i	−0.799390	+	0.600813i	$0.794844\pi$
$398$	−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	−0.913844	−	0.406065i	$-0.866901\pi$
$401$	0.945466	−	2.59765i	0.0472143	−	0.129720i	0.961059	+	0.276344i	$0.0891230\pi$
$402$	−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	−0.406175	−	0.913795i	$-0.633138\pi$
$409$	9.95715	−	27.3570i	0.492349	−	1.35272i	0.898525	−	0.438923i	$-0.144640\pi$
$410$	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	−0.626502	−	0.779420i	$-0.715514\pi$
$419$	−6.23009	−	35.3326i	−0.304360	−	1.72611i	0.322142	−	0.946691i	$-0.395597\pi$
$420$	1.52340	−	15.4868i	0.0743345	−	0.755677i
$421$	4.15270	+	3.48453i	0.202390	+	0.169825i	0.738349	−	0.674418i	$-0.235606\pi$
$421$	4.15270	+	3.48453i	0.202390	+	0.169825i	−0.535959	+	0.844244i	$0.680050\pi$
$422$	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	$0.311149\pi$
$431$			34.4253i			1.65821i	−0.559094	+	0.829104i	$0.688851\pi$
$432$	4.79088	−	2.01184i	0.230501	−	0.0967947i
$433$			18.9403i			0.910213i	0.890437	+	0.455107i	$0.150399\pi$
$433$			18.9403i			0.910213i	−0.890437	+	0.455107i	$0.849601\pi$
$434$	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	0.963817	−	0.266565i	$-0.0858888\pi$
$439$	1.13447	+	3.11693i	0.0541453	+	0.148763i	−0.909671	+	0.415329i	$0.863667\pi$
$440$	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	−0.239491	−	0.970899i	$-0.576980\pi$
$443$	15.9592	−	19.0194i	0.758245	−	0.903641i	0.997736	+	0.0672576i	$0.0214249\pi$
$444$	−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	−0.441274	−	0.897373i	$-0.645473\pi$
$449$	2.44182	−	1.40979i	0.115237	−	0.0665320i	0.556511	+	0.830841i	$0.312140\pi$
$450$	−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	−0.999071	−	0.0430967i	$-0.986278\pi$
$457$	−0.972923	+	5.51772i	−0.0455114	+	0.258108i	0.953560	+	0.301205i	$0.0973887\pi$
$458$	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	0.575042	+	0.818124i	$0.304986\pi$
$461$	−5.26328	+	29.8496i	−0.245136	+	1.39023i	−0.820178	+	0.572109i	$0.806125\pi$
$462$	−1.07086	−	4.17617i	−0.0498209	−	0.194293i
$463$	−26.8268	−	9.76416i	−1.24675	−	0.453779i	−0.367446	−	0.930045i	$-0.619768\pi$
$463$	−26.8268	−	9.76416i	−1.24675	−	0.453779i	−0.879301	+	0.476266i	$0.841990\pi$
$464$	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	−0.895669	−	0.444721i	$-0.853303\pi$
$467$	−1.35485	+	2.34667i	−0.0626951	+	0.108591i	0.832974	+	0.553312i	$0.186636\pi$
$468$	−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	−0.156805	−	0.987630i	$-0.550119\pi$
$479$	7.83328	−	2.85108i	0.357912	−	0.130269i	0.514717	+	0.857360i	$0.327897\pi$
$480$	−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	0.996662	+	0.0816341i	$0.0260139\pi$
$491$	20.0310	+	23.8720i	0.903988	+	1.07733i	−0.0926747	+	0.995696i	$0.529542\pi$
$492$	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	−0.995528	−	0.0944679i	$-0.969885\pi$
$499$	−2.06289	−	11.6992i	−0.0923476	−	0.523729i	0.903180	−	0.429261i	$-0.141226\pi$
$500$	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	0.707541	−	0.706673i	$-0.249805\pi$
$503$	−5.79141	−	10.0310i	−0.258226	−	0.447261i	−0.965767	+	0.259412i	$0.916471\pi$
$504$	−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	−0.135585	−	0.990766i	$-0.543291\pi$
$509$	−19.7703	−	7.19579i	−0.876301	−	0.318948i	−0.740716	+	0.671818i	$0.765514\pi$
$510$	−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	−0.772952	−	0.634464i	$-0.781221\pi$
$521$	3.72023	−	6.44363i	0.162986	−	0.282301i	0.935938	+	0.352164i	$0.114554\pi$
$522$	3.45509	−	24.1340i	0.151225	−	1.05632i
$523$	0.241039	−	0.139164i	0.0105399	−	0.00608521i	−0.494721	−	0.869052i	$-0.664730\pi$
$523$	0.241039	−	0.139164i	0.0105399	−	0.00608521i	0.505261	+	0.862967i	$0.331396\pi$
$524$	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	−0.103034	−	0.994678i	$-0.532855\pi$
$547$	10.6978	−	3.89368i	0.457405	−	0.166482i	0.560438	+	0.828196i	$0.310633\pi$
$548$	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	−0.925138	−	0.379630i	$-0.876051\pi$
$557$	−24.9918	+	14.4290i	−1.05894	+	0.611378i	−0.133800	+	0.991008i	$0.542718\pi$
$558$	−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	−0.0386046	−	0.999255i	$-0.512291\pi$
$563$	−16.8581	−	6.13586i	−0.710486	−	0.258596i	−0.671881	+	0.740659i	$0.734514\pi$
$564$	−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	0.918882	−	0.394532i	$-0.129093\pi$
$569$	39.2969	+	6.92910i	1.64741	+	0.290483i	0.728529	+	0.685015i	$0.240205\pi$
$570$	−36.1443	−	29.3461i	−1.51392	−	1.22917i
$571$	1.84609	+	0.671920i	0.0772563	+	0.0281190i	0.380359	−	0.924839i	$-0.375800\pi$
$571$	1.84609	+	0.671920i	0.0772563	+	0.0281190i	−0.303103	+	0.952958i	$0.598023\pi$
$572$	−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	−0.878107	−	0.478464i	$-0.841194\pi$
$577$	−21.6860	+	12.5204i	−0.902799	+	0.521231i	−0.0246916	+	0.999695i	$0.507860\pi$
$578$	−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	−0.660749	−	0.750607i	$-0.729761\pi$
$587$	−16.5825	+	6.03552i	−0.684431	+	0.249113i	−0.0236824	+	0.999720i	$0.507539\pi$
$588$	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	0.250615	−	0.968087i	$-0.419367\pi$
$599$	−18.2649	−	21.7672i	−0.746283	−	0.889386i	−0.996898	+	0.0787012i	$0.974923\pi$
$600$	11.1078	−	2.14432i	0.453473	−	0.0875415i
$601$	−14.3707	−	39.4833i	−0.586195	−	1.61056i	−0.777400	−	0.629007i	$-0.783462\pi$
$601$	−14.3707	−	39.4833i	−0.586195	−	1.61056i	0.191205	−	0.981550i	$-0.438761\pi$
$602$	−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	0.579365	−	0.815068i	$-0.303301\pi$
$607$	34.5554	−	6.09305i	1.40256	−	0.247309i	0.823195	+	0.567759i	$0.192190\pi$
$608$	−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	−0.556924	−	0.830564i	$-0.688018\pi$
$613$	10.9144	−	18.9043i	0.440828	−	0.763536i	0.997751	+	0.0670280i	$0.0213517\pi$
$614$	−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	−0.907694	−	0.419634i	$-0.862159\pi$
$617$	1.42517	−	3.91563i	0.0573753	−	0.157637i	0.965069	+	0.261996i	$0.0843808\pi$
$618$	−2.65617	+	16.6320i	−0.106847	+	0.669037i
$619$	24.0454	+	4.23985i	0.966465	+	0.170414i	0.634538	−	0.772891i	$-0.281190\pi$
$619$	24.0454	+	4.23985i	0.966465	+	0.170414i	0.331926	+	0.943305i	$0.392301\pi$
$620$			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	−0.986427	−	0.164199i	$-0.947496\pi$
$631$	−15.9614	−	27.6460i	−0.635414	−	1.10057i	0.351013	−	0.936370i	$-0.385837\pi$
$632$	−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	0.796552	−	0.604570i	$-0.206655\pi$
$641$	−5.12063	−	14.0688i	−0.202253	−	0.555685i	−0.998804	+	0.0488858i	$0.984433\pi$
$642$	13.9700	−	12.1125i	0.551353	−	0.478041i
$643$	−2.88719	−	3.44082i	−0.113860	−	0.135693i	0.706104	−	0.708108i	$-0.250451\pi$
$643$	−2.88719	−	3.44082i	−0.113860	−	0.135693i	−0.819964	+	0.572415i	$0.806007\pi$
$644$	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	0.986427	−	0.164198i	$-0.0525036\pi$
$653$	16.6977	+	19.8996i	0.653433	+	0.778731i	−0.332995	+	0.942929i	$0.608059\pi$
$654$	−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	−0.237413	−	0.971409i	$-0.576299\pi$
$659$	19.5219	−	23.2653i	0.760465	−	0.906286i	0.997877	+	0.0651225i	$0.0207438\pi$
$660$	4.74679	−	2.84386i	0.184769	−	0.110697i
$661$	−14.4693	+	2.55133i	−0.562790	+	0.0992351i	−0.447804	−	0.894132i	$-0.647794\pi$
$661$	−14.4693	+	2.55133i	−0.562790	+	0.0992351i	−0.114987	+	0.993367i	$0.536682\pi$
$662$	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	−0.944962	−	0.327180i	$-0.893902\pi$
$673$	1.42459	−	8.07926i	0.0549140	−	0.311433i	0.999876	+	0.0157474i	$0.00501276\pi$
$674$			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	−0.927142	−	0.374710i	$-0.877742\pi$
$677$	1.87976	−	10.6606i	0.0722450	−	0.409722i	0.999387	−	0.0350113i	$-0.0111467\pi$
$678$	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	0.843787	−	0.536678i	$-0.180321\pi$
$683$	20.9310	+	12.0845i	0.800904	+	0.462402i	−0.0428831	+	0.999080i	$0.513654\pi$
$684$	−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	−0.470184	−	0.882568i	$-0.655813\pi$
$691$	12.6341	−	15.0567i	0.480622	−	0.572783i	0.950807	+	0.309785i	$0.100257\pi$
$692$	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	$0.110486\pi$
$701$			18.0132i			0.680350i	−0.940362	+	0.340175i	$0.889514\pi$
$702$	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	−0.263916	−	0.964546i	$-0.585014\pi$
$709$	4.09818	−	1.49162i	0.153910	−	0.0560188i	0.417827	+	0.908527i	$0.362792\pi$
$710$	−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	−0.992498	−	0.122260i	$-0.960986\pi$
$719$	−16.1456	−	27.9650i	−0.602130	−	1.04292i	0.390368	−	0.920659i	$-0.372348\pi$
$720$	−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	0.0309014	−	0.999522i	$-0.490162\pi$
$727$	−7.60133	−	1.34032i	−0.281918	−	0.0497097i	−0.312819	+	0.949813i	$0.601273\pi$
$728$	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	−0.875054	−	0.484026i	$-0.839174\pi$
$733$	2.88073	−	7.91475i	0.106402	−	0.292338i	0.981456	+	0.191688i	$0.0613962\pi$
$734$	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	0.640189	−	0.768217i	$-0.278856\pi$
$739$	−9.38414	−	16.2538i	−0.345201	−	0.597906i	−0.985390	+	0.170311i	$0.945523\pi$
$740$	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	−0.589247	−	0.807953i	$-0.700576\pi$
$743$	−23.6224	+	4.16527i	−0.866623	+	0.152809i	−0.277375	+	0.960762i	$0.589465\pi$
$744$	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	−0.937174	−	0.348863i	$-0.886568\pi$
$751$	−20.7273	+	17.3923i	−0.756349	+	0.634653i	0.180824	+	0.983515i	$0.442123\pi$
$752$	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	−0.183318	−	0.983054i	$-0.558684\pi$
$761$	20.7716	−	17.4294i	0.752968	−	0.631815i	0.936286	+	0.351238i	$0.114239\pi$
$762$	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	−0.433417	−	0.901193i	$-0.642692\pi$
$769$	−14.7658	+	2.60362i	−0.532470	+	0.0938889i	−0.0990528	+	0.995082i	$0.531581\pi$
$770$	−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	−0.903868	−	0.427812i	$-0.859285\pi$
$773$	−22.8659	−	39.6049i	−0.822430	−	1.42449i	0.0814382	−	0.996678i	$-0.474049\pi$
$774$	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	−0.618163	−	0.786050i	$-0.712123\pi$
$787$	10.1172	−	27.7969i	0.360640	−	0.990851i	0.978804	−	0.204801i	$-0.0656548\pi$
$788$	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	0.980054	+	0.198734i	$0.0636828\pi$
$797$	3.58749	+	20.3457i	0.127075	+	0.720680i	−0.852978	+	0.521947i	$0.825206\pi$
$798$	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	$-0.907994\pi$
$809$		−	16.2146i		−	0.570074i	0.958517	−	0.285037i	$-0.0920059\pi$
$810$	−18.0909	+	24.6327i	−0.635650	+	0.865504i
$811$		−	14.3508i		−	0.503924i	−0.967737	−	0.251962i	$-0.918924\pi$
$811$		−	14.3508i		−	0.503924i	0.967737	−	0.251962i	$-0.0810757\pi$
$812$	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	−0.980759	−	0.195220i	$-0.937458\pi$
$821$	−17.7133	+	21.1099i	−0.618198	+	0.736740i	0.362561	+	0.931960i	$0.381902\pi$
$822$	0.330017	+	0.550842i	0.0115106	+	0.0192128i
$823$	−6.80471	−	38.5914i	−0.237197	−	1.34521i	−0.837937	−	0.545767i	$-0.816238\pi$
$823$	−6.80471	−	38.5914i	−0.237197	−	1.34521i	0.600739	−	0.799445i	$-0.294873\pi$
$824$	−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	−0.791127	−	0.611653i	$-0.790505\pi$
$827$	−18.8933	+	10.9080i	−0.656983	+	0.379309i	0.134143	+	0.990962i	$0.457172\pi$
$828$	−1.32309	−	0.707865i	−0.0459804	−	0.0246000i
$829$	24.1551	+	13.9460i	0.838943	+	0.484364i	0.856905	−	0.515475i	$-0.172384\pi$
$829$	24.1551	+	13.9460i	0.838943	+	0.484364i	−0.0179619	+	0.999839i	$0.505718\pi$
$830$	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	−0.950537	−	0.310610i	$-0.899467\pi$
$839$	1.41672	−	8.03460i	0.0489105	−	0.277385i	0.999448	+	0.0332250i	$0.0105778\pi$
$840$	−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	−0.768379	−	0.639995i	$-0.778936\pi$
$853$	−0.136644	+	0.162846i	−0.00467861	+	0.00557576i	0.763700	+	0.645571i	$0.223381\pi$
$854$	−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	0.584993	−	0.811038i	$-0.301097\pi$
$857$	45.5058	−	16.5628i	1.55445	−	0.565773i	0.969456	+	0.245265i	$0.0788750\pi$
$858$	−0.709022	+	0.136874i	−0.0242056	+	0.00467282i
$859$	−4.91863	−	5.86180i	−0.167822	−	0.200002i	0.675578	−	0.737288i	$-0.263894\pi$
$859$	−4.91863	−	5.86180i	−0.167822	−	0.200002i	−0.843400	+	0.537286i	$0.819450\pi$
$860$	−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	$0.156567\pi$
$863$			27.7478i			0.944547i	−0.881452	+	0.472274i	$0.843433\pi$
$864$	−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	0.977748	−	0.209783i	$-0.0672756\pi$
$877$	−0.378601	−	2.14715i	−0.0127844	−	0.0725042i	−0.990533	+	0.137278i	$0.956165\pi$
$878$	−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	0.697763	+	0.716328i	$0.254179\pi$
$881$	28.7686	+	49.8288i	0.969240	+	1.67877i	0.271477	+	0.962445i	$0.412488\pi$
$882$	10.1053	+	18.4088i	0.340262	+	0.619856i
$883$	−26.2109	+	45.3986i	−0.882067	+	1.52778i	−0.0330272	+	0.999454i	$0.510515\pi$
$883$	−26.2109	+	45.3986i	−0.882067	+	1.52778i	−0.849039	+	0.528330i	$0.822819\pi$
$884$	−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	0.672126	−	0.740437i	$-0.265381\pi$
$887$	21.1772	+	7.70787i	0.711060	+	0.258805i	0.0389345	+	0.999242i	$0.487604\pi$
$888$	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	0.744063	−	0.668110i	$-0.232896\pi$
$907$	6.48432	+	5.44099i	0.215308	+	0.180665i	−0.528755	+	0.848775i	$0.677341\pi$
$908$	−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	−0.848013	−	0.529975i	$-0.822201\pi$
$911$	−16.2703	−	44.7023i	−0.539059	−	1.48105i	0.308954	−	0.951077i	$-0.400021\pi$
$912$	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	0.873642	−	0.486569i	$-0.161752\pi$
$929$	16.6470	+	13.9685i	0.546171	+	0.458292i	−0.327471	+	0.944861i	$0.606196\pi$
$930$	−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	0.882129	−	0.471008i	$-0.156110\pi$
$937$	28.0174	+	16.1758i	0.915288	+	0.528442i	0.0331591	+	0.999450i	$0.489443\pi$
$938$	−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	0.222811	−	0.974862i	$-0.428477\pi$
$941$	−7.15158	−	2.60296i	−0.233135	−	0.0848542i	−0.455946	+	0.890007i	$0.650699\pi$
$942$	−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	−0.225196	−	0.974314i	$-0.572302\pi$
$947$	−23.6969	−	4.17840i	−0.770046	−	0.135780i	−0.544850	+	0.838534i	$0.683413\pi$
$948$	−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	0.990465	−	0.137768i	$-0.0439927\pi$
$953$	42.1813	+	24.3534i	1.36639	+	0.788884i	0.375922	+	0.926651i	$0.377326\pi$
$954$	−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	−0.959862	−	0.280471i	$-0.909509\pi$
$967$	−26.4424	+	22.1878i	−0.850330	+	0.713512i	0.109532	+	0.993983i	$0.465065\pi$
$968$	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	0.886682	+	0.462379i	$0.153004\pi$
$977$	37.1354	+	44.2562i	1.18807	+	1.41588i	0.301384	+	0.953503i	$0.402551\pi$
$978$	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	0.559215	−	0.829022i	$-0.311102\pi$
$983$	−5.01976	−	4.21208i	−0.160106	−	0.134345i	−0.719321	+	0.694678i	$0.755547\pi$
$984$	−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	−0.183010	−	0.983111i	$-0.558584\pi$
$991$	23.9216	−	41.4334i	0.759894	−	1.31618i	0.942904	−	0.333064i	$-0.108083\pi$
$992$	−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	−0.348424	−	0.937337i	$-0.613283\pi$
$997$	−31.4624	−	5.54767i	−0.996423	−	0.175696i	−0.648000	+	0.761641i	$0.724394\pi$
$998$			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.83.3	yes	144
7.6	odd	2	inner	378.2.z.a.83.10	yes	144
27.14	odd	18	inner	378.2.z.a.41.10	yes	144
189.41	even	18	inner	378.2.z.a.41.3	✓	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.z.a.41.3	✓	144	189.41	even	18	inner
378.2.z.a.41.10	yes	144	27.14	odd	18	inner
378.2.z.a.83.3	yes	144	1.1	even	1	trivial
378.2.z.a.83.10	yes	144	7.6	odd	2	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.984808 - 0.173648i) q^{2} +(-1.34465 - 1.09174i) q^{3} +(0.939693 + 0.342020i) q^{4} +(-2.60134 + 2.18278i) q^{5} +(1.13465 + 1.30865i) q^{6} +(-0.615646 - 2.57313i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(0.616190 + 2.93604i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 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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