LMFDB - Embedded newform 378.2.z.a.41.10

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			41.10
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.984808 + 0.173648i) q^{2} +(1.34465 - 1.09174i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.60134 + 2.18278i) q^{5} +(-1.13465 + 1.30865i) q^{6} +(1.18236 - 2.36686i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.616190 - 2.93604i) q^{9} +O(q^{10})$	\(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} +(1.18236 - 2.36686i) 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} +(-0.753398 + 2.53622i) 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} +(-0.994137 - 4.47344i) 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} +(8.24205 - 3.57616i) 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} +(1.75584 + 4.23285i) 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} +(-4.20404 - 5.59697i) 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} +(0.159475 + 2.64094i) 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} +(-6.22063 - 4.92989i) 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} +(-7.49584 + 4.95305i) 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} +(2.42079 - 0.579199i) 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} +(-2.46419 - 3.86365i) 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} +(0.698134 - 0.941948i) 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} +(5.11208 + 4.78191i) 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 $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

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

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	0.999946	−	0.0103897i	$-0.00330721\pi$
$5$	2.60134	+	2.18278i	1.16335	+	0.976169i	0.163407	+	0.986559i	$0.447752\pi$
$6$	−1.13465	+	1.30865i	−0.463218	+	0.534256i
$7$	1.18236	−	2.36686i	0.446891	−	0.894589i
$7$	1.18236	−	2.36686i	0.446891	−	0.894589i
$8$	−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	0.233840	−	0.972275i	$-0.424871\pi$
$13$	0.436415	+	0.0769517i	0.121040	+	0.0213426i	−0.112800	+	0.993618i	$0.535982\pi$
$14$	−0.753398	+	2.53622i	−0.201354	+	0.677832i
$15$	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	$-0.920324\pi$
$17$	−1.11282	+	1.92746i	−0.269899	+	0.467479i	0.698936	+	0.715184i	$0.253657\pi$
$18$	−0.0969913	+	2.99843i	−0.0228611	+	0.706737i
$19$	−6.85516	+	3.95783i	−1.57268	+	0.907988i	−0.576843	+	0.816855i	$0.695716\pi$
$19$	−6.85516	+	3.95783i	−1.57268	+	0.907988i	−0.995839	+	0.0911335i	$0.970951\pi$
$20$	3.19101	+	1.16143i	0.713532	+	0.259704i
$21$	−0.994137	−	4.47344i	−0.216939	−	0.976185i
$22$	−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	$-0.862067\pi$
$31$	−2.68497	−	7.37690i	−0.482236	−	1.32493i	0.425337	−	0.905035i	$-0.360156\pi$
$32$	−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
$35$	8.24205	−	3.57616i	1.39316	−	0.604482i
$36$	−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	$0.231422\pi$
$41$	−1.16708	+	6.61885i	−0.182268	+	1.03369i	−0.929416	+	0.369033i	$0.879689\pi$
$42$	1.75584	+	4.23285i	0.270932	+	0.653143i
$43$	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	0.178636	−	0.983915i	$-0.442832\pi$
$47$	−2.17304	−	0.790920i	−0.316970	−	0.115368i	−0.495606	+	0.868548i	$0.665054\pi$
$48$	0.328305	−	1.70065i	0.0473868	−	0.245468i
$49$	−4.20404	−	5.59697i	−0.600578	−	0.799566i
$50$	−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
$56$	0.159475	+	2.64094i	0.0213107	+	0.352911i
$57$	−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	$-0.277709\pi$
$59$	0.00253927	+	0.00213070i	0.000330585	+	0.000277394i	−0.642622	+	0.766183i	$0.722154\pi$
$60$	5.55879	−	1.92204i	0.717637	−	0.248135i
$61$	−4.17042	+	11.4581i	−0.533967	+	1.46706i	0.320344	+	0.947301i	$0.396202\pi$
$61$	−4.17042	+	11.4581i	−0.533967	+	1.46706i	−0.854311	+	0.519762i	$0.826021\pi$
$62$	3.92517	+	6.79859i	0.498497	+	0.863422i
$63$	−6.22063	−	4.92989i	−0.783725	−	0.621108i
$64$	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
$70$	−7.49584	+	4.95305i	−0.895925	+	0.592003i
$71$	−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	−0.255994	−	0.966678i	$-0.582403\pi$
$73$	3.87195	−	2.23547i	0.453177	−	0.261642i	0.709171	+	0.705036i	$0.249069\pi$
$74$	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
$77$	2.42079	−	0.579199i	0.275875	−	0.0660058i
$78$	−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	$0.209889\pi$
$83$	2.34318	+	13.2888i	0.257197	+	1.45864i	−0.533172	+	0.846007i	$0.679000\pi$
$84$	−2.46419	−	3.86365i	−0.268865	−	0.421558i
$85$	−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	$-0.990063\pi$
$89$	−4.96971	−	8.60779i	−0.526788	−	0.912424i	0.472724	−	0.881210i	$-0.343271\pi$
$90$	−6.79722	+	7.58822i	−0.716490	+	0.799868i
$91$	0.698134	−	0.941948i	0.0731843	−	0.0987430i
$92$	−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	$-0.247962\pi$
$97$	−1.02275	−	1.21886i	−0.103844	−	0.123757i	−0.815463	+	0.578809i	$0.803518\pi$
$98$	5.11208	+	4.78191i	0.516398	+	0.483046i
$99$	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	$-0.638233\pi$
$101$	−13.3280	−	4.85099i	−1.32619	−	0.482692i	−0.905435	+	0.424485i	$0.860455\pi$
$102$	−1.25973	−	3.64329i	−0.124731	−	0.360740i
$103$	−6.25058	+	7.44915i	−0.615888	+	0.733987i	−0.980358	−	0.197229i	$-0.936806\pi$
$103$	−6.25058	+	7.44915i	−0.615888	+	0.733987i	0.364470	+	0.931215i	$0.381250\pi$
$104$	−0.416422	+	0.151565i	−0.0408336	+	0.0148622i
$105$	7.17846	−	13.8069i	0.700546	−	1.34742i
$106$	−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
$112$	−0.615646	−	2.57313i	−0.0581731	−	0.243138i
$113$	−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
$119$	3.24628	+	4.91285i	0.297586	+	0.450361i
$120$	−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
$126$	6.98219	+	3.77479i	0.622023	+	0.336285i
$127$	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	−0.429874	−	0.902889i	$-0.641442\pi$
$131$	−2.04658	+	0.744896i	−0.178811	+	0.0650819i	0.251063	+	0.967971i	$0.419220\pi$
$132$	1.60912	−	0.256980i	0.140056	−	0.0223672i
$133$	1.26235	+	20.9048i	0.109459	+	1.81267i
$134$			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	0.999850	−	0.0173467i	$-0.00552191\pi$
$139$	2.62642	+	7.21603i	0.222770	+	0.612056i	−0.777079	+	0.629403i	$0.783300\pi$
$140$	6.52188	−	6.17944i	0.551199	−	0.522258i
$141$	−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
$147$	−11.7634	−	2.93624i	−0.970232	−	0.242177i
$148$	−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
$154$	−2.28344	+	0.990765i	−0.184005	+	0.0798381i
$155$	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	$-0.921887\pi$
$157$	−7.04611	+	8.39723i	−0.562341	+	0.670172i	0.407699	+	0.913116i	$0.366331\pi$
$158$	−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	$-0.510429\pi$
$167$	−13.2165	−	11.0900i	−1.02272	−	0.858168i	−0.989967	+	0.141295i	$0.954873\pi$
$168$	3.09767	+	3.37705i	0.238990	+	0.260545i
$169$	−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	$-0.857806\pi$
$173$	−8.32627	+	6.98657i	−0.633035	+	0.531179i	0.268835	+	0.963186i	$0.413361\pi$
$174$	−7.23407	+	12.0746i	−0.548414	+	0.915376i
$175$	16.5652	+	4.92080i	1.25221	+	0.371978i
$176$	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	−0.218959	−	0.975734i	$-0.570266\pi$
$181$	6.94977	−	4.01245i	0.516572	−	0.298243i	0.735531	+	0.677491i	$0.236933\pi$
$182$	−0.523960	+	1.04887i	−0.0388385	+	0.0777472i
$183$	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
$189$	−13.7468	+	0.162332i	−0.999930	+	0.0118079i
$190$	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
$196$	−5.86478	−	3.82156i	−0.418913	−	0.272969i
$197$	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	−0.0778999	−	0.996961i	$-0.524821\pi$
$199$	−13.8280	−	7.98362i	−0.980244	−	0.565944i	−0.902344	+	0.431017i	$0.858155\pi$
$200$	−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
$203$	6.12262	−	20.6110i	0.429724	−	1.44661i
$204$	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
$210$	−4.67186	+	14.8437i	−0.322389	+	1.02431i
$211$	−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	$-0.717992\pi$
$223$	5.22456	−	14.3544i	0.349862	−	0.961238i	0.982413	−	0.186720i	$-0.0597856\pi$
$224$	1.05311	+	2.42713i	0.0703640	+	0.162169i
$225$	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	$-0.428297\pi$
$227$	18.4124	−	15.4498i	1.22207	−	1.02544i	0.998714	−	0.0507061i	$-0.0161472\pi$
$228$	−0.221659	+	13.7085i	−0.0146797	+	0.907870i
$229$	12.0270	+	2.12068i	0.794764	+	0.140138i	0.556265	−	0.831005i	$-0.312234\pi$
$229$	12.0270	+	2.12068i	0.794764	+	0.140138i	0.238498	+	0.971143i	$0.423345\pi$
$230$	−0.294944	+	1.67271i	−0.0194480	+	0.110295i
$231$	2.62279	−	3.42171i	0.172567	−	0.225132i
$232$	−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
$238$	−4.05007	−	4.27451i	−0.262527	−	0.277075i
$239$	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	0.436179	−	0.899860i	$-0.356332\pi$
$241$	17.9121	−	3.15839i	1.15382	−	0.203450i	0.717644	+	0.696410i	$0.245220\pi$
$242$			10.1149i			0.650210i
$243$	−15.0311	+	4.13127i	−0.964243	+	0.265021i
$244$			12.1935i			0.780608i
$245$	1.28081	−	23.7361i	0.0818282	−	1.51644i
$246$	−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	$-0.266729\pi$
$251$	−4.89870	−	8.48480i	−0.309203	−	0.535556i	−0.978188	+	0.207720i	$0.933396\pi$
$252$	−7.53160	−	2.50500i	−0.474446	−	0.157800i
$253$	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	$0.204701\pi$
$257$	−2.51430	+	14.2593i	−0.156838	+	0.889471i	−0.957086	+	0.289803i	$0.906410\pi$
$258$	−0.138547	+	8.56844i	−0.00862555	+	0.533448i
$259$	0.730367	+	1.10532i	0.0453828	+	0.0686814i
$260$	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
$266$	−4.87325	−	20.3680i	−0.298798	−	1.24884i
$267$	−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	$-0.539427\pi$
$269$	−4.05269			−0.247097			−0.123549	+	0.992339i	$0.539427\pi$
$270$	−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
$273$	−0.0896171	−	2.02878i	−0.00542388	−	0.122787i
$274$	−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
$280$	−5.34975	+	7.21807i	−0.319708	+	0.431362i
$281$	−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	0.618373	−	0.785885i	$-0.287792\pi$
$283$	15.6562	+	2.76061i	0.930665	+	0.164101i	0.312292	+	0.949986i	$0.398903\pi$
$284$	−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
$287$	14.2860	+	10.5882i	0.843274	+	0.625001i
$288$	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	$-0.720704\pi$
$293$	−10.8584	+	3.95215i	−0.634357	+	0.230887i	0.00476955	+	0.999989i	$0.498482\pi$
$294$	12.0946	+	0.848936i	0.705371	+	0.0495109i
$295$	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
$301$	−3.04600	−	12.7309i	−0.175568	−	0.733797i
$302$	−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	$-0.431211\pi$
$307$	−9.18543	−	5.30321i	−0.524240	−	0.302670i	−0.738668	+	0.674070i	$0.764545\pi$
$308$	2.07670	−	1.37223i	0.118331	−	0.0781900i
$309$	−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	$0.212631\pi$
$311$	−2.90114	+	16.4532i	−0.164508	+	0.932974i	−0.949570	+	0.313556i	$0.898480\pi$
$312$	−0.394474	+	0.658430i	−0.0223327	+	0.0372762i
$313$	15.9842	+	19.0492i	0.903479	+	1.07672i	0.996708	+	0.0810793i	$0.0258367\pi$
$313$	15.9842	+	19.0492i	0.903479	+	1.07672i	−0.0932289	+	0.995645i	$0.529719\pi$
$314$	5.48090	−	9.49320i	0.309305	−	0.535732i
$315$	−5.42107	−	26.4026i	−0.305443	−	1.48762i
$316$	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
$322$	1.32095	−	0.0797661i	0.0736135	−	0.00444519i
$323$		−	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
$329$	−4.44131	+	4.20812i	−0.244857	+	0.232001i
$330$	−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
$336$	−3.63703	−	2.78784i	−0.198416	−	0.152089i
$337$	−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
$343$	−18.2179	+	3.33274i	−0.983676	+	0.179951i
$344$	−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	0.162902	−	0.986642i	$-0.447914\pi$
$349$	12.2071	−	2.15244i	0.653432	−	0.115218i	0.490530	+	0.871425i	$0.336803\pi$
$350$	−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	$0.0608197\pi$
$353$	2.33281	+	13.2300i	0.124163	+	0.704164i	−0.857638	+	0.514253i	$0.828069\pi$
$354$	−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
$357$	9.72870	+	3.06198i	0.514898	+	0.162057i
$358$	−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
$364$	0.333866	−	1.12392i	0.0174993	−	0.0589093i
$365$	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	$-0.125399\pi$
$367$	7.37637	+	8.79081i	0.385043	+	0.458877i	−0.538356	+	0.842717i	$0.680954\pi$
$368$	−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
$371$	17.4374	+	8.71083i	0.905304	+	0.452244i
$372$	−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
$378$	13.5097	−	2.54697i	0.694866	−	0.131002i
$379$	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	$0.00593319\pi$
$383$	23.3240	+	19.5711i	1.19180	+	1.00004i	0.191973	+	0.981400i	$0.438511\pi$
$384$	0.566005	+	1.63696i	0.0288838	+	0.0835358i
$385$	7.56156	+	3.77737i	0.385373	+	0.192512i
$386$	−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
$392$	6.43929	+	2.74509i	0.325233	+	0.138648i
$393$	−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	$-0.538490\pi$
$397$	13.5243	−	7.80827i	0.678766	−	0.391886i	0.799390	+	0.600813i	$0.205156\pi$
$398$	15.0043	+	5.46112i	0.752098	+	0.273741i
$399$	24.5201	+	26.7315i	1.22754	+	1.33825i
$400$	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	$-0.855360\pi$
$409$	−9.95715	−	27.3570i	−0.492349	−	1.35272i	0.406175	−	0.913795i	$-0.366862\pi$
$410$	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
$413$	0.00804541	−	0.00349084i	0.000395889	−	0.000171773i
$414$	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	$-0.604403\pi$
$419$	6.23009	−	35.3326i	0.304360	−	1.72611i	0.626502	−	0.779420i	$-0.284486\pi$
$420$	2.02330	−	15.4294i	0.0987270	−	0.752879i
$421$	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
$427$	22.1888	+	23.4184i	1.07379	+	1.13330i
$428$	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	$0.150399\pi$
$433$			18.9403i			0.910213i	−0.890437	+	0.455107i	$0.849601\pi$
$434$	20.7323	−	1.25193i	0.995181	−	0.0600945i
$435$	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	$-0.914111\pi$
$439$	−1.13447	+	3.11693i	−0.0541453	+	0.148763i	0.909671	+	0.415329i	$0.136333\pi$
$440$	−1.59738	−	2.76675i	−0.0761522	−	0.131899i
$441$	−19.0234	+	8.89443i	−0.905875	+	0.423544i
$442$	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
$448$	−1.45858	−	2.20738i	−0.0689114	−	0.104289i
$449$	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
$455$	3.87215	−	0.926450i	0.181529	−	0.0434327i
$456$	−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	$0.193875\pi$
$461$	5.26328	+	29.8496i	0.245136	+	1.39023i	−0.575042	+	0.818124i	$0.695014\pi$
$462$	−1.98877	+	3.82517i	−0.0925260	+	0.177963i
$463$	−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	0.895669	−	0.444721i	$-0.146697\pi$
$467$	1.35485	+	2.34667i	0.0626951	+	0.108591i	−0.832974	+	0.553312i	$0.813364\pi$
$468$	0.0429814	−	1.32875i	0.00198682	−	0.0614214i
$469$	−32.6861	−	24.2256i	−1.50930	−	1.11863i
$470$	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
$476$	4.73080	+	3.50628i	0.216836	+	0.160710i
$477$	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	$-0.449881\pi$
$479$	−7.83328	−	2.85108i	−0.357912	−	0.130269i	−0.514717	+	0.857360i	$0.672103\pi$
$480$	−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
$483$	−1.93252	+	1.23254i	−0.0879328	+	0.0560826i
$484$	−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
$490$	2.86037	+	23.5979i	0.129218	+	1.06604i
$491$	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
$497$	−26.4075	+	17.4494i	−1.18454	+	0.782712i
$498$	−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	−0.707541	−	0.706673i	$-0.750195\pi$
$503$	5.79141	−	10.0310i	0.258226	−	0.447261i	0.965767	+	0.259412i	$0.0835287\pi$
$504$	7.85216	+	1.15910i	0.349763	+	0.0516303i
$505$	−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	$-0.456709\pi$
$509$	19.7703	−	7.19579i	0.876301	−	0.318948i	0.740716	+	0.671818i	$0.234486\pi$
$510$	4.67553	−	12.2271i	0.207036	−	0.541427i
$511$	−0.713002	−	11.8075i	−0.0315413	−	0.522333i
$512$			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
$518$	−0.911209	−	0.961704i	−0.0400362	−	0.0422548i
$519$	−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	$-0.218779\pi$
$521$	−3.72023	−	6.44363i	−0.162986	−	0.282301i	−0.935938	+	0.352164i	$0.885446\pi$
$522$	3.45509	+	24.1340i	0.151225	+	1.05632i
$523$	−0.241039	−	0.139164i	−0.0105399	−	0.00608521i	0.494721	−	0.869052i	$-0.335270\pi$
$523$	−0.241039	−	0.139164i	−0.0105399	−	0.00608521i	−0.505261	+	0.862967i	$0.668604\pi$
$524$	−1.66839	+	1.39995i	−0.0728840	+	0.0611569i
$525$	27.6468	−	11.4682i	1.20660	−	0.500515i
$526$	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
$532$	8.33608	+	19.2123i	0.361415	+	0.832960i
$533$	−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
$546$	0.440549	+	1.98239i	0.0188538	+	0.0848387i
$547$	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
$553$	28.3227	+	8.41343i	1.20441	+	0.357776i
$554$	−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
$560$	4.01507	−	8.03739i	0.169668	−	0.339642i
$561$	−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	$-0.487709\pi$
$563$	16.8581	−	6.13586i	0.710486	−	0.258596i	0.671881	+	0.740659i	$0.265486\pi$
$564$	−3.10951	+	2.52465i	−0.130934	+	0.106307i
$565$	−43.0672	+	7.59392i	−1.81185	+	0.319478i
$566$	−15.8977			−0.668232
$567$	−18.3074	+	15.2262i	−0.768840	+	0.639442i
$568$	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
$574$	−15.9076	−	7.94660i	−0.663968	−	0.331685i
$575$	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	$-0.158806\pi$
$577$	21.6860	+	12.5204i	0.902799	+	0.521231i	0.0246916	+	0.999695i	$0.492140\pi$
$578$	−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
$581$	34.2233	+	10.1662i	1.41982	+	0.421766i
$582$	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	$-0.270239\pi$
$587$	16.5825	+	6.03552i	0.684431	+	0.249113i	0.0236824	+	0.999720i	$0.492461\pi$
$588$	−12.0583	+	1.26417i	−0.497275	+	0.0521334i
$589$	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	$-0.202756\pi$
$593$	39.1523			1.60779			0.803897	+	0.594769i	$0.202756\pi$
$594$	−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	$-0.561239\pi$
$601$	14.3707	−	39.4833i	0.586195	−	1.61056i	0.777400	−	0.629007i	$-0.216538\pi$
$602$	5.21042	+	12.0086i	0.212361	+	0.489432i
$603$	−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	$-0.696699\pi$
$607$	−34.5554	−	6.09305i	−1.40256	−	0.247309i	−0.823195	+	0.567759i	$0.807810\pi$
$608$	1.37454	−	7.79540i	0.0557449	−	0.316145i
$609$	−14.2691	−	34.3990i	−0.578215	−	1.39392i
$610$	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
$616$	−1.80687	+	1.71200i	−0.0728008	+	0.0689783i
$617$	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	−0.634538	−	0.772891i	$-0.718810\pi$
$619$	−24.0454	+	4.23985i	−0.966465	+	0.170414i	−0.331926	+	0.943305i	$0.607699\pi$
$620$		−	26.6582i		−	1.07062i
$621$	−1.76518	+	1.90762i	−0.0708343	+	0.0765502i
$622$		−	16.7070i		−	0.669889i
$623$	−26.2494	+	1.58509i	−1.05166	+	0.0635051i
$624$	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
$630$	9.92347	+	25.0601i	0.395360	+	0.998418i
$631$	−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
$637$	−1.40401	−	2.76611i	−0.0556290	−	0.109597i
$638$	−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	−0.706104	−	0.708108i	$-0.749549\pi$
$643$	2.88719	−	3.44082i	0.113860	−	0.135693i	0.819964	+	0.572415i	$0.193993\pi$
$644$	−1.28703	+	0.307934i	−0.0507160	+	0.0121343i
$645$	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	$-0.297334\pi$
$647$	30.2456			1.18908			0.594539	+	0.804067i	$0.297334\pi$
$648$	8.94574	−	0.986759i	0.351422	−	0.0387636i
$649$			0.00311854i			0.000122413i
$650$	−0.502609	−	2.85044i	−0.0197139	−	0.111803i
$651$	−30.3309	+	19.3447i	−1.18876	+	0.758180i
$652$	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
$658$	3.64311	−	4.91541i	0.142023	−	0.191623i
$659$	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	0.447804	−	0.894132i	$-0.352206\pi$
$661$	14.4693	+	2.55133i	0.562790	+	0.0992351i	0.114987	+	0.993367i	$0.463318\pi$
$662$	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
$665$	−42.3468	+	57.1358i	−1.64214	+	2.21563i
$666$	−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
$672$	4.06588	+	2.11392i	0.156845	+	0.0815463i
$673$	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	$-0.988853\pi$
$677$	−1.87976	−	10.6606i	−0.0722450	−	0.409722i	0.927142	−	0.374710i	$-0.122258\pi$
$678$	−3.51767	−	22.0265i	−0.135095	−	0.845921i
$679$	−4.09413	+	0.979561i	−0.157118	+	0.0375921i
$680$	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
$686$	17.3624	−	6.44562i	0.662901	−	0.246095i
$687$	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	$-0.344187\pi$
$691$	−12.6341	−	15.0567i	−0.480622	−	0.572783i	−0.950807	+	0.309785i	$0.899743\pi$
$692$	−5.43459	+	9.41298i	−0.206592	+	0.357828i
$693$	−0.208881	−	7.46443i	−0.00793474	−	0.283550i
$694$	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
$700$	17.2493	−	1.04161i	0.651960	−	0.0393690i
$701$		−	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
$707$	−27.2401	+	25.8099i	−1.02447	+	0.970680i
$708$	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
$714$	−10.1126	−	1.32609i	−0.378455	−	0.0496278i
$715$	−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	$-0.627652\pi$
$719$	16.1456	−	27.9650i	0.602130	−	1.04292i	0.992498	−	0.122260i	$-0.0390143\pi$
$720$	2.09246	−	9.97020i	0.0779814	−	0.371568i
$721$	10.2406	+	23.6018i	0.381382	+	0.878978i
$722$	−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	$-0.509838\pi$
$727$	7.60133	−	1.34032i	0.281918	−	0.0497097i	0.312819	+	0.949813i	$0.398727\pi$
$728$	−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	$-0.160826\pi$
$733$	−2.88073	−	7.91475i	−0.106402	−	0.292338i	−0.981456	+	0.191688i	$0.938604\pi$
$734$	−8.79081	−	7.37637i	−0.324475	−	0.272267i
$735$	−24.1915	−	33.3152i	−0.892316	−	1.22885i
$736$	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
$742$	−18.6851	−	5.55052i	−0.685951	−	0.203766i
$743$	−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
$749$	25.2665	+	12.6218i	0.923217	+	0.461192i
$750$	−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
$756$	−12.8622	+	4.85421i	−0.467794	+	0.176546i
$757$	−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	$-0.441316\pi$
$761$	−20.7716	−	17.4294i	−0.752968	−	0.631815i	−0.936286	+	0.351238i	$0.885761\pi$
$762$	−6.80607	−	1.31389i	−0.246558	−	0.0475972i
$763$	−3.62173	+	7.25000i	−0.131115	+	0.262468i
$764$	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	$-0.357308\pi$
$769$	14.7658	+	2.60362i	0.532470	+	0.0938889i	0.0990528	+	0.995082i	\(0.468419\pi

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)

\(f(q)\)	\(=\)	\(q+(-0.984808 + 0.173648i) q^{2} +(1.34465 - 1.09174i) q^{3} +(0.939693 - 0.342020i) q^{4} +(2.60134 + 2.18278i) q^{5} +(-1.13465 + 1.30865i) q^{6} +(1.18236 - 2.36686i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(0.616190 - 2.93604i) q^{9} +O(q^{10})\)	\(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} +(1.18236 - 2.36686i) 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} +(-0.753398 + 2.53622i) 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} +(-0.994137 - 4.47344i) 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} +(8.24205 - 3.57616i) 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} +(1.75584 + 4.23285i) 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} +(-4.20404 - 5.59697i) 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} +(0.159475 + 2.64094i) 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} +(-6.22063 - 4.92989i) 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} +(-7.49584 + 4.95305i) 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} +(2.42079 - 0.579199i) 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} +(-2.46419 - 3.86365i) 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} +(0.698134 - 0.941948i) 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} +(5.11208 + 4.78191i) 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

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