LMFDB - Embedded newform 378.2.bf.a.101.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (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			101.7
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.324716 - 1.70134i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.51689 + 2.11192i) q^{5} +(1.51203 + 0.844853i) q^{6} +(2.58943 - 0.542996i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.78912 + 1.10491i) q^{9} -3.28557i q^{10} +(2.31320 - 2.75676i) q^{11} +(-1.61911 + 0.615218i) q^{12} +(1.07488 - 2.95321i) q^{13} +(-1.24850 + 2.33265i) q^{14} +(4.41037 + 3.59631i) q^{15} +(-0.939693 + 0.342020i) q^{16} -5.93277 q^{17} +(0.946404 - 2.84681i) q^{18} -5.92479i q^{19} +(2.51689 + 2.11192i) q^{20} +(-1.76465 - 4.22918i) q^{21} +(0.624907 + 3.54402i) q^{22} +(2.31207 - 6.35235i) q^{23} +(0.569458 - 1.63576i) q^{24} +(1.00628 - 5.70690i) q^{25} +(1.57137 + 2.72170i) q^{26} +(2.78549 + 4.38646i) q^{27} +(-0.984397 - 2.45580i) q^{28} +(-1.66755 - 4.58155i) q^{29} +(-5.58987 + 1.06688i) q^{30} +(-5.71905 + 1.00842i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-5.44132 - 3.04037i) q^{33} +(3.81351 - 4.54476i) q^{34} +(-5.37055 + 6.83534i) q^{35} +(1.57245 + 2.55488i) q^{36} +(-0.378361 + 0.655341i) q^{37} +(4.53865 + 3.80838i) q^{38} +(-5.37345 - 0.869783i) q^{39} +(-3.23565 + 0.570532i) q^{40} +(0.362685 + 0.132007i) q^{41} +(4.37404 + 1.36667i) q^{42} +(0.563744 - 3.19715i) q^{43} +(-3.11656 - 1.79935i) q^{44} +(4.68643 - 8.67132i) q^{45} +(3.38002 + 5.85436i) q^{46} +(0.694267 - 3.93738i) q^{47} +(0.887026 + 1.48768i) q^{48} +(6.41031 - 2.81210i) q^{49} +(3.72492 + 4.43918i) q^{50} +(1.92647 + 10.0937i) q^{51} +(-3.09500 - 0.545732i) q^{52} +(7.08260 + 4.08914i) q^{53} +(-5.15070 - 0.685750i) q^{54} +11.8238i q^{55} +(2.51401 + 0.824467i) q^{56} +(-10.0801 + 1.92388i) q^{57} +(4.58155 + 1.66755i) q^{58} +(10.0710 + 3.66555i) q^{59} +(2.77582 - 4.96786i) q^{60} +(14.1733 + 2.49913i) q^{61} +(2.90364 - 5.02925i) q^{62} +(-6.62227 + 4.37556i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.53159 + 9.70297i) q^{65} +(5.82667 - 2.21398i) q^{66} +(-1.85767 + 1.55877i) q^{67} +(1.03021 + 5.84263i) q^{68} +(-11.5583 - 1.87090i) q^{69} +(-1.78405 - 8.50775i) q^{70} +(1.69873 - 0.980762i) q^{71} +(-2.96790 - 0.437683i) q^{72} +(-13.7210 + 7.92182i) q^{73} +(-0.258814 - 0.711086i) q^{74} +(-10.0361 + 0.141098i) q^{75} +(-5.83478 + 1.02883i) q^{76} +(4.49296 - 8.39450i) q^{77} +(4.12028 - 3.55722i) q^{78} +(0.103645 + 0.0869684i) q^{79} +(1.64278 - 2.84538i) q^{80} +(6.55837 - 6.16343i) q^{81} +(-0.334253 + 0.192981i) q^{82} +(-5.39571 + 1.96388i) q^{83} +(-3.85851 + 2.47223i) q^{84} +(14.9321 - 12.5295i) q^{85} +(2.08679 + 2.48694i) q^{86} +(-7.25329 + 4.32477i) q^{87} +(3.38167 - 1.23083i) q^{88} -14.2427 q^{89} +(3.63024 + 9.16383i) q^{90} +(1.17975 - 8.23080i) q^{91} +(-6.65733 - 1.17387i) q^{92} +(3.57274 + 9.40260i) q^{93} +(2.56994 + 3.06274i) q^{94} +(12.5127 + 14.9120i) q^{95} +(-1.70980 - 0.276759i) q^{96} +(-1.55558 - 0.274290i) q^{97} +(-1.96627 + 6.71817i) q^{98} +(-3.40582 + 10.2448i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	−0.324716	−	1.70134i	−0.187475	−	0.982269i
$3$	−0.324716	−	1.70134i	−0.187475	−	0.982269i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−2.51689	+	2.11192i	−1.12559	+	0.944480i	−0.998873	−	0.0474597i	$-0.984887\pi$
$5$	−2.51689	+	2.11192i	−1.12559	+	0.944480i	−0.126714	+	0.991939i	$0.540443\pi$
$6$	1.51203	+	0.844853i	0.617282	+	0.344910i
$7$	2.58943	−	0.542996i	0.978713	−	0.205233i
$7$	2.58943	−	0.542996i	0.978713	−	0.205233i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−2.78912	+	1.10491i	−0.929706	+	0.368302i
$10$		−	3.28557i		−	1.03899i
$11$	2.31320	−	2.75676i	0.697455	−	0.831195i	−0.294781	−	0.955565i	$-0.595247\pi$
$11$	2.31320	−	2.75676i	0.697455	−	0.831195i	0.992236	+	0.124370i	$0.0396910\pi$
$12$	−1.61911	+	0.615218i	−0.467396	+	0.177598i
$13$	1.07488	−	2.95321i	0.298118	−	0.819074i	−0.696696	−	0.717367i	$-0.745347\pi$
$13$	1.07488	−	2.95321i	0.298118	−	0.819074i	0.994814	−	0.101707i	$-0.0324305\pi$
$14$	−1.24850	+	2.33265i	−0.333674	+	0.623427i
$15$	4.41037	+	3.59631i	1.13875	+	0.928563i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−5.93277			−1.43891			−0.719453	−	0.694541i	$-0.755608\pi$
$17$	−5.93277			−1.43891			−0.719453	+	0.694541i	$0.755608\pi$
$18$	0.946404	−	2.84681i	0.223070	−	0.670999i
$19$		−	5.92479i		−	1.35924i	−0.733564	−	0.679620i	$-0.762145\pi$
$19$		−	5.92479i		−	1.35924i	0.733564	−	0.679620i	$-0.237855\pi$
$20$	2.51689	+	2.11192i	0.562794	+	0.472240i
$21$	−1.76465	−	4.22918i	−0.385079	−	0.922884i
$22$	0.624907	+	3.54402i	0.133231	+	0.755588i
$23$	2.31207	−	6.35235i	0.482099	−	1.32456i	−0.425591	−	0.904916i	$-0.639934\pi$
$23$	2.31207	−	6.35235i	0.482099	−	1.32456i	0.907690	−	0.419641i	$-0.137844\pi$
$24$	0.569458	−	1.63576i	0.116240	−	0.333899i
$25$	1.00628	−	5.70690i	0.201256	−	1.14138i
$26$	1.57137	+	2.72170i	0.308171	+	0.533768i
$27$	2.78549	+	4.38646i	0.536068	+	0.844175i
$28$	−0.984397	−	2.45580i	−0.186034	−	0.464103i
$29$	−1.66755	−	4.58155i	−0.309656	−	0.850772i	−0.992723	−	0.120417i	$-0.961577\pi$
$29$	−1.66755	−	4.58155i	−0.309656	−	0.850772i	0.683068	−	0.730355i	$-0.260645\pi$
$30$	−5.58987	+	1.06688i	−1.02057	+	0.194784i
$31$	−5.71905	+	1.00842i	−1.02717	+	0.181118i	−0.661751	−	0.749724i	$-0.730186\pi$
$31$	−5.71905	+	1.00842i	−1.02717	+	0.181118i	−0.365421	+	0.930842i	$0.619075\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	−5.44132	−	3.04037i	−0.947213	−	0.529261i
$34$	3.81351	−	4.54476i	0.654011	−	0.779420i
$35$	−5.37055	+	6.83534i	−0.907788	+	1.15538i
$36$	1.57245	+	2.55488i	0.262074	+	0.425813i
$37$	−0.378361	+	0.655341i	−0.0622022	+	0.107737i	−0.895449	−	0.445163i	$-0.853146\pi$
$37$	−0.378361	+	0.655341i	−0.0622022	+	0.107737i	0.833247	+	0.552900i	$0.186479\pi$
$38$	4.53865	+	3.80838i	0.736267	+	0.617801i
$39$	−5.37345	−	0.869783i	−0.860441	−	0.139277i
$40$	−3.23565	+	0.570532i	−0.511601	+	0.0902091i
$41$	0.362685	+	0.132007i	0.0566419	+	0.0206160i	0.370186	−	0.928958i	$-0.379294\pi$
$41$	0.362685	+	0.132007i	0.0566419	+	0.0206160i	−0.313544	+	0.949574i	$0.601516\pi$
$42$	4.37404	+	1.36667i	0.674929	+	0.210881i
$43$	0.563744	−	3.19715i	0.0859701	−	0.487561i	−0.911173	−	0.412024i	$-0.864822\pi$
$43$	0.563744	−	3.19715i	0.0859701	−	0.487561i	0.997143	−	0.0755366i	$-0.0240670\pi$
$44$	−3.11656	−	1.79935i	−0.469839	−	0.271262i
$45$	4.68643	−	8.67132i	0.698612	−	1.29264i
$46$	3.38002	+	5.85436i	0.498356	+	0.863178i
$47$	0.694267	−	3.93738i	0.101269	−	0.574326i	−0.891376	−	0.453265i	$-0.850259\pi$
$47$	0.694267	−	3.93738i	0.101269	−	0.574326i	0.992645	−	0.121061i	$-0.0386297\pi$
$48$	0.887026	+	1.48768i	0.128031	+	0.214728i
$49$	6.41031	−	2.81210i	0.915759	−	0.401729i
$50$	3.72492	+	4.43918i	0.526783	+	0.627795i
$51$	1.92647	+	10.0937i	0.269759	+	1.41339i
$52$	−3.09500	−	0.545732i	−0.429199	−	0.0756793i
$53$	7.08260	+	4.08914i	0.972870	+	0.561687i	0.900110	−	0.435663i	$-0.143486\pi$
$53$	7.08260	+	4.08914i	0.972870	+	0.561687i	0.0727599	+	0.997349i	$0.476819\pi$
$54$	−5.15070	−	0.685750i	−0.700922	−	0.0933188i
$55$			11.8238i			1.59431i
$56$	2.51401	+	0.824467i	0.335949	+	0.110174i
$57$	−10.0801	+	1.92388i	−1.33514	+	0.254824i
$58$	4.58155	+	1.66755i	0.601587	+	0.218960i
$59$	10.0710	+	3.66555i	1.31113	+	0.477214i	0.900607	−	0.434634i	$-0.143122\pi$
$59$	10.0710	+	3.66555i	1.31113	+	0.477214i	0.410528	+	0.911848i	$0.365345\pi$
$60$	2.77582	−	4.96786i	0.358357	−	0.641348i
$61$	14.1733	+	2.49913i	1.81470	+	0.319981i	0.974855	−	0.222839i	$-0.0715326\pi$
$61$	14.1733	+	2.49913i	1.81470	+	0.319981i	0.839849	+	0.542821i	$0.182644\pi$
$62$	2.90364	−	5.02925i	0.368762	−	0.638715i
$63$	−6.62227	+	4.37556i	−0.834328	+	0.551269i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	3.53159	+	9.70297i	0.438040	+	1.20351i
$66$	5.82667	−	2.21398i	0.717214	−	0.272522i
$67$	−1.85767	+	1.55877i	−0.226950	+	0.190434i	−0.749171	−	0.662376i	$-0.769548\pi$
$67$	−1.85767	+	1.55877i	−0.226950	+	0.190434i	0.522221	+	0.852810i	$0.325104\pi$
$68$	1.03021	+	5.84263i	0.124932	+	0.708523i
$69$	−11.5583	−	1.87090i	−1.39145	−	0.225230i
$70$	−1.78405	−	8.50775i	−0.213235	−	1.01687i
$71$	1.69873	−	0.980762i	0.201602	−	0.116395i	−0.395800	−	0.918337i	$-0.629533\pi$
$71$	1.69873	−	0.980762i	0.201602	−	0.116395i	0.597403	+	0.801941i	$0.296199\pi$
$72$	−2.96790	−	0.437683i	−0.349770	−	0.0515814i
$73$	−13.7210	+	7.92182i	−1.60592	+	0.927179i	−0.615651	+	0.788019i	$0.711107\pi$
$73$	−13.7210	+	7.92182i	−1.60592	+	0.927179i	−0.990270	+	0.139160i	$0.955560\pi$
$74$	−0.258814	−	0.711086i	−0.0300865	−	0.0826621i
$75$	−10.0361	+	0.141098i	−1.15887	+	0.0162925i
$76$	−5.83478	+	1.02883i	−0.669295	+	0.118015i
$77$	4.49296	−	8.39450i	0.512020	−	0.956642i
$78$	4.12028	−	3.55722i	0.466530	−	0.402775i
$79$	0.103645	+	0.0869684i	0.0116610	+	0.00978471i	0.648599	−	0.761130i	$-0.275355\pi$
$79$	0.103645	+	0.0869684i	0.0116610	+	0.00978471i	−0.636939	+	0.770915i	$0.719799\pi$
$80$	1.64278	−	2.84538i	0.183669	−	0.318123i
$81$	6.55837	−	6.16343i	0.728707	−	0.684825i
$82$	−0.334253	+	0.192981i	−0.0369120	+	0.0213112i
$83$	−5.39571	+	1.96388i	−0.592256	+	0.215564i	−0.620722	−	0.784031i	$-0.713160\pi$
$83$	−5.39571	+	1.96388i	−0.592256	+	0.215564i	0.0284651	+	0.999595i	$0.490938\pi$
$84$	−3.85851	+	2.47223i	−0.420997	+	0.269743i
$85$	14.9321	−	12.5295i	1.61962	−	1.35902i
$86$	2.08679	+	2.48694i	0.225024	+	0.268174i
$87$	−7.25329	+	4.32477i	−0.777635	+	0.463664i
$88$	3.38167	−	1.23083i	0.360487	−	0.131207i
$89$	−14.2427			−1.50972			−0.754859	−	0.655887i	$-0.772295\pi$
$89$	−14.2427			−1.50972			−0.754859	+	0.655887i	$0.772295\pi$
$90$	3.63024	+	9.16383i	0.382661	+	0.965953i
$91$	1.17975	−	8.23080i	0.123671	−	0.862822i
$92$	−6.65733	−	1.17387i	−0.694075	−	0.122384i
$93$	3.57274	+	9.40260i	0.370476	+	0.975004i
$94$	2.56994	+	3.06274i	0.265069	+	0.315897i
$95$	12.5127	+	14.9120i	1.28377	+	1.52994i
$96$	−1.70980	−	0.276759i	−0.174505	−	0.0282466i
$97$	−1.55558	−	0.274290i	−0.157945	−	0.0278500i	0.0941165	−	0.995561i	$-0.469997\pi$
$97$	−1.55558	−	0.274290i	−0.157945	−	0.0278500i	−0.252061	+	0.967711i	$0.581109\pi$
$98$	−1.96627	+	6.71817i	−0.198624	+	0.678637i
$99$	−3.40582	+	10.2448i	−0.342298	+	1.02964i
$100$	−5.79494			−0.579494
$101$	−2.96745	+	1.08006i	−0.295272	+	0.107470i	−0.485409	−	0.874287i	$-0.661329\pi$
$101$	−2.96745	+	1.08006i	−0.295272	+	0.107470i	0.190136	+	0.981758i	$0.439107\pi$
$102$	−8.97050	−	5.01232i	−0.888211	−	0.496293i
$103$	−12.1541	−	14.4847i	−1.19758	−	1.42722i	−0.877328	−	0.479891i	$-0.840676\pi$
$103$	−12.1541	−	14.4847i	−1.19758	−	1.42722i	−0.320254	−	0.947332i	$-0.603768\pi$
$104$	2.40748	−	2.02012i	0.236073	−	0.198089i
$105$	13.3731	+	6.91758i	1.30508	+	0.675087i
$106$	−7.68507	+	2.79714i	−0.746440	+	0.271682i
$107$	−9.39646	+	5.42505i	−0.908390	+	0.524459i	−0.879913	−	0.475135i	$-0.842399\pi$
$107$	−9.39646	+	5.42505i	−0.908390	+	0.524459i	−0.0284774	+	0.999594i	$0.509066\pi$
$108$	3.83612	−	3.50488i	0.369131	−	0.337257i
$109$	0.897149	−	1.55391i	0.0859313	−	0.148837i	−0.819856	−	0.572569i	$-0.805947\pi$
$109$	0.897149	−	1.55391i	0.0859313	−	0.148837i	0.905788	+	0.423732i	$0.139280\pi$
$110$	−9.05752	−	7.60016i	−0.863601	−	0.724647i
$111$	1.23782	+	0.430921i	0.117488	+	0.0409012i
$112$	−2.24755	+	1.39589i	−0.212374	+	0.131899i
$113$	11.0887	−	1.95523i	1.04313	−	0.183933i	0.374272	−	0.927319i	$-0.377893\pi$
$113$	11.0887	−	1.95523i	1.04313	−	0.183933i	0.668862	+	0.743386i	$0.266781\pi$
$114$	5.00558	−	8.95844i	0.468816	−	0.839035i
$115$	7.59645	+	20.8711i	0.708372	+	1.94624i
$116$	−4.22238	+	2.43779i	−0.392038	+	0.226343i
$117$	0.265050	+	9.42450i	0.0245038	+	0.871296i
$118$	−9.28150	+	5.35868i	−0.854431	+	0.493306i
$119$	−15.3625	+	3.22147i	−1.40828	+	0.295312i
$120$	2.02134	+	5.31968i	0.184522	+	0.485618i
$121$	−0.338721	−	1.92098i	−0.0307928	−	0.174635i
$122$	−11.0249	+	9.25096i	−0.998144	+	0.837542i
$123$	0.106818	−	0.659916i	0.00963150	−	0.0595026i
$124$	1.98621	+	5.45706i	0.178367	+	0.490058i
$125$	1.30591	+	2.26191i	0.116804	+	0.202311i
$126$	0.904842	−	7.88551i	0.0806097	−	0.702497i
$127$	−0.518152	+	0.897465i	−0.0459785	+	0.0796371i	−0.888099	−	0.459653i	$-0.847974\pi$
$127$	−0.518152	+	0.897465i	−0.0459785	+	0.0796371i	0.842120	+	0.539290i	$0.181307\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	−5.62250	+	0.0790464i	−0.495033	+	0.00695965i
$130$	−9.70297	−	3.53159i	−0.851007	−	0.309741i
$131$	2.83791	+	1.03291i	0.247949	+	0.0902462i	0.463005	−	0.886356i	$-0.346771\pi$
$131$	2.83791	+	1.03291i	0.247949	+	0.0902462i	−0.215056	+	0.976602i	$0.568993\pi$
$132$	−2.04931	+	5.88661i	−0.178369	+	0.512364i
$133$	−3.21714	−	15.3418i	−0.278961	−	1.33031i
$134$		−	2.42501i		−	0.209489i
$135$	−16.2746	−	5.15749i	−1.40070	−	0.443886i
$136$	−5.13793	−	2.96638i	−0.440573	−	0.254365i
$137$	10.3397	+	1.82318i	0.883384	+	0.155764i	0.596895	−	0.802319i	$-0.296401\pi$
$137$	10.3397	+	1.82318i	0.883384	+	0.155764i	0.286489	+	0.958084i	$0.407512\pi$
$138$	8.86271	−	7.65156i	0.754444	−	0.651344i
$139$	8.31587	+	9.91047i	0.705343	+	0.840595i	0.993120	−	0.117102i	$-0.0373605\pi$
$139$	8.31587	+	9.91047i	0.705343	+	0.840595i	−0.287777	+	0.957698i	$0.592916\pi$
$140$	7.66408	+	4.10201i	0.647733	+	0.346683i
$141$	−6.92427	+	0.0973479i	−0.583128	+	0.00819817i
$142$	−0.340615	+	1.93172i	−0.0285838	+	0.162107i
$143$	−5.65489	−	9.79455i	−0.472886	−	0.819062i
$144$	2.24301	−	1.99221i	0.186918	−	0.166017i
$145$	13.8729	+	8.00952i	1.15208	+	0.665155i
$146$	2.75122	−	15.6029i	0.227692	−	1.29131i
$147$	−6.86588	−	9.99298i	−0.566288	−	0.824208i
$148$	0.711086	+	0.258814i	0.0584509	+	0.0212744i
$149$	1.42182	−	0.250705i	0.116480	−	0.0205386i	−0.115104	−	0.993353i	$-0.536720\pi$
$149$	1.42182	−	0.250705i	0.116480	−	0.0205386i	0.231584	+	0.972815i	$0.425609\pi$
$150$	6.34302	−	7.77882i	0.517905	−	0.635138i
$151$	3.10788	+	2.60782i	0.252916	+	0.212222i	0.760427	−	0.649424i	$-0.224990\pi$
$151$	3.10788	+	2.60782i	0.252916	+	0.212222i	−0.507511	+	0.861645i	$0.669434\pi$
$152$	2.96240	−	5.13102i	0.240282	−	0.416181i
$153$	16.5472	−	6.55515i	1.33776	−	0.529952i
$154$	3.54255	+	8.83769i	0.285466	+	0.712161i
$155$	12.2645	−	14.6163i	0.985109	−	1.17401i
$156$	0.0765208	+	5.44285i	0.00612656	+	0.435777i
$157$	−0.0993042	+	0.272836i	−0.00792534	+	0.0217747i	−0.943592	−	0.331110i	$-0.892577\pi$
$157$	−0.0993042	+	0.272836i	−0.00792534	+	0.0217747i	0.935667	+	0.352885i	$0.114799\pi$
$158$	−0.133243	+	0.0234944i	−0.0106003	+	0.00186911i
$159$	4.65719	−	13.3777i	0.369339	−	1.06092i
$160$	1.12373	+	3.08742i	0.0888386	+	0.244082i
$161$	2.53764	−	17.7044i	0.199994	−	1.39530i
$162$	0.505822	+	8.98577i	0.0397411	+	0.705989i
$163$	8.34897	+	14.4608i	0.653942	+	1.13266i	0.982158	+	0.188058i	$0.0602193\pi$
$163$	8.34897	+	14.4608i	0.653942	+	1.13266i	−0.328216	+	0.944603i	$0.606447\pi$
$164$	0.0670216	−	0.380098i	0.00523350	−	0.0296807i
$165$	20.1162	−	3.83936i	1.56605	−	0.298894i
$166$	1.96388	−	5.39571i	0.152427	−	0.418789i
$167$	−3.48153	−	19.7448i	−0.269409	−	1.52789i	−0.756179	−	0.654365i	$-0.772936\pi$
$167$	−3.48153	−	19.7448i	−0.269409	−	1.52789i	0.486770	−	0.873530i	$-0.338175\pi$
$168$	0.586359	−	4.54491i	0.0452386	−	0.350647i
$169$	2.39249	+	2.00753i	0.184037	+	0.154426i
$170$			19.4925i			1.49501i
$171$	6.54634	+	16.5249i	0.500611	+	1.26369i
$172$	−3.24647			−0.247541
$173$	5.44727	−	1.98264i	0.414148	−	0.150738i	−0.126538	−	0.991962i	$-0.540387\pi$
$173$	5.44727	−	1.98264i	0.414148	−	0.150738i	0.540687	+	0.841224i	$0.318164\pi$
$174$	1.34936	−	8.33625i	0.102295	−	0.631970i
$175$	−0.493131	−	15.3240i	−0.0372772	−	1.15839i
$176$	−1.23083	+	3.38167i	−0.0927771	+	0.254903i
$177$	2.96613	−	18.3245i	0.222948	−	1.37735i
$178$	9.15500	−	10.9105i	0.686196	−	0.817777i
$179$		−	5.38259i		−	0.402314i	−0.979559	−	0.201157i	$-0.935530\pi$
$179$		−	5.38259i		−	0.402314i	0.979559	−	0.201157i	$-0.0644701\pi$
$180$	−9.35338	−	3.10947i	−0.697159	−	0.231766i
$181$	5.96343	+	3.44299i	0.443258	+	0.255915i	0.704979	−	0.709228i	$-0.250957\pi$
$181$	5.96343	+	3.44299i	0.443258	+	0.255915i	−0.261721	+	0.965144i	$0.584290\pi$
$182$	5.54683	+	6.19439i	0.411158	+	0.459159i
$183$	−0.350421	−	24.9251i	−0.0259038	−	1.84252i
$184$	5.17848	−	4.34526i	0.381763	−	0.320337i
$185$	−0.431735	−	2.44849i	−0.0317418	−	0.180016i
$186$	−9.49932	−	3.30700i	−0.696524	−	0.242481i
$187$	−13.7237	+	16.3552i	−1.00357	+	1.19601i
$188$	−3.99812			−0.291593
$189$	9.59467	+	9.84592i	0.697910	+	0.716186i
$190$	−19.4663			−1.41223
$191$	0.658273	−	0.784499i	0.0476310	−	0.0567644i	−0.741703	−	0.670728i	$-0.765982\pi$
$191$	0.658273	−	0.784499i	0.0476310	−	0.0567644i	0.789334	+	0.613964i	$0.210426\pi$
$192$	1.31105	−	1.13188i	0.0946166	−	0.0816866i
$193$	0.332875	+	1.88783i	0.0239608	+	0.135889i	0.994442	−	0.105290i	$-0.0335771\pi$
$193$	0.332875	+	1.88783i	0.0239608	+	0.135889i	−0.970481	+	0.241179i	$0.922466\pi$
$194$	1.21002	−	1.01533i	0.0868747	−	0.0728965i
$195$	15.3613	−	9.15915i	1.10005	−	0.655901i
$196$	−3.88252	−	5.82461i	−0.277323	−	0.416043i
$197$	−10.8249	−	6.24979i	−0.771246	−	0.445279i	0.0620732	−	0.998072i	$-0.480229\pi$
$197$	−10.8249	−	6.24979i	−0.771246	−	0.445279i	−0.833319	+	0.552793i	$0.813562\pi$
$198$	−5.65875	−	9.19424i	−0.402150	−	0.653406i
$199$			13.3247i			0.944560i	0.881449	+	0.472280i	$0.156569\pi$
$199$			13.3247i			0.944560i	−0.881449	+	0.472280i	$0.843431\pi$
$200$	3.72492	−	4.43918i	0.263391	−	0.313898i
$201$	3.25521	+	2.65437i	0.229605	+	0.187225i
$202$	1.08006	−	2.96745i	0.0759930	−	0.208789i
$203$	−6.80576	−	10.9581i	−0.477671	−	0.769110i
$204$	9.60578	−	3.64994i	0.672539	−	0.255547i
$205$	−1.19163	+	0.433717i	−0.0832268	+	0.0302921i
$206$	18.9085			1.31742
$207$	0.570121	+	20.2721i	0.0396261	+	1.40901i
$208$			3.14274i			0.217910i
$209$	−16.3332	−	13.7052i	−1.12979	−	0.948009i
$210$	−13.8953	+	5.79788i	−0.958864	+	0.400092i
$211$	1.90492	+	10.8034i	0.131140	+	0.743734i	0.977470	+	0.211074i	$0.0676962\pi$
$211$	1.90492	+	10.8034i	0.131140	+	0.743734i	−0.846330	+	0.532659i	$0.821193\pi$
$212$	2.79714	−	7.68507i	0.192108	−	0.527813i
$213$	−2.22022	−	2.57165i	−0.152127	−	0.176207i
$214$	1.88410	−	10.6853i	0.128794	−	0.730429i
$215$	5.33325	+	9.23745i	0.363724	+	0.629989i
$216$	0.219078	+	5.19153i	0.0149064	+	0.353239i
$217$	−14.2615	+	5.71667i	−0.968135	+	0.388073i
$218$	0.613686	+	1.68609i	0.0415641	+	0.114196i
$219$	17.9331	+	20.7717i	1.21181	+	1.40362i
$220$	11.6441	−	2.05317i	0.785047	−	0.138425i
$221$	−6.37702	+	17.5207i	−0.428965	+	1.17857i
$222$	−1.12576	+	0.671232i	−0.0755560	+	0.0450502i
$223$	−0.181176	+	0.215917i	−0.0121324	+	0.0144589i	−0.772077	−	0.635530i	$-0.780782\pi$
$223$	−0.181176	+	0.215917i	−0.0121324	+	0.0144589i	0.759944	+	0.649988i	$0.225226\pi$
$224$	0.375388	−	2.61899i	0.0250817	−	0.174988i
$225$	3.49895	+	17.0291i	0.233263	+	1.13527i
$226$	−5.62987	+	9.75121i	−0.374493	+	0.648641i
$227$	7.76814	+	6.51824i	0.515589	+	0.432631i	0.863091	−	0.505049i	$-0.168525\pi$
$227$	7.76814	+	6.51824i	0.515589	+	0.432631i	−0.347502	+	0.937679i	$0.612970\pi$
$228$	3.64504	+	9.59287i	0.241398	+	0.635303i
$229$	−15.6963	+	2.76769i	−1.03724	+	0.182894i	−0.666240	−	0.745738i	$-0.732097\pi$
$229$	−15.6963	+	2.76769i	−1.03724	+	0.182894i	−0.371003	+	0.928632i	$0.620986\pi$
$230$	−20.8711	−	7.59645i	−1.37620	−	0.500895i
$231$	−15.7408	−	4.91822i	−1.03567	−	0.323595i
$232$	0.846636	−	4.80151i	0.0555844	−	0.315235i
$233$	−23.2127	−	13.4019i	−1.52072	−	0.877986i	−0.999701	−	0.0244388i	$-0.992220\pi$
$233$	−23.2127	−	13.4019i	−1.52072	−	0.877986i	−0.521015	−	0.853547i	$-0.674447\pi$
$234$	−7.38996	−	5.85491i	−0.483097	−	0.382748i
$235$	6.56805	+	11.3762i	0.428452	+	0.742101i
$236$	1.86105	−	10.5545i	0.121144	−	0.687041i
$237$	0.114308	−	0.204575i	0.00742508	−	0.0132886i
$238$	7.40703	−	13.8391i	0.480126	−	0.897054i
$239$	13.3347	+	15.8917i	0.862552	+	1.02795i	0.999302	+	0.0373443i	$0.0118898\pi$
$239$	13.3347	+	15.8917i	0.862552	+	1.02795i	−0.136750	+	0.990606i	$0.543666\pi$
$240$	−5.37440	−	1.87099i	−0.346916	−	0.120772i
$241$	23.6617	+	4.17219i	1.52418	+	0.268754i	0.872075	−	0.489372i	$-0.162774\pi$
$241$	23.6617	+	4.17219i	1.52418	+	0.268754i	0.652107	+	0.758127i	$0.273885\pi$
$242$	1.68928	+	0.975308i	0.108591	+	0.0626952i
$243$	−12.6157	−	9.15665i	−0.809297	−	0.587399i
$244$		−	14.3919i		−	0.921349i
$245$	−10.1951	+	20.6158i	−0.651341	+	1.31710i
$246$	0.436863	+	0.506014i	0.0278534	+	0.0322622i
$247$	−17.4972	−	6.36845i	−1.11332	−	0.405215i
$248$	−5.45706	−	1.98621i	−0.346523	−	0.126124i
$249$	5.09330	+	8.54224i	0.322775	+	0.541343i
$250$	−2.57215	−	0.453539i	−0.162677	−	0.0286843i
$251$	14.9759	−	25.9391i	0.945273	−	1.63726i	0.190068	−	0.981771i	$-0.439129\pi$
$251$	14.9759	−	25.9391i	0.945273	−	1.63726i	0.755204	−	0.655489i	$-0.227538\pi$
$252$	5.45903	+	5.76186i	0.343887	+	0.362963i
$253$	−12.1636	−	21.0681i	−0.764722	−	1.32454i
$254$	−0.354437	−	0.973807i	−0.0222393	−	0.0611021i
$255$	−26.1657	−	21.3361i	−1.63856	−	1.33612i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	1.94308	+	11.0198i	0.121206	+	0.687394i	0.983489	+	0.180967i	$0.0579228\pi$
$257$	1.94308	+	11.0198i	0.121206	+	0.687394i	−0.862283	+	0.506427i	$0.830966\pi$
$258$	3.55352	−	4.35789i	0.221232	−	0.271311i
$259$	−0.623893	+	1.90241i	−0.0387668	+	0.118210i
$260$	8.94231	−	5.16284i	0.554578	−	0.320186i
$261$	9.71317	+	10.9360i	0.601230	+	0.676921i
$262$	−2.61543	+	1.51002i	−0.161582	+	0.0932894i
$263$	−5.57444	−	15.3157i	−0.343735	−	0.944404i	−0.984301	−	0.176500i	$-0.943522\pi$
$263$	−5.57444	−	15.3157i	−0.343735	−	0.944404i	0.640566	−	0.767903i	$-0.278700\pi$
$264$	−3.19214	−	5.35370i	−0.196463	−	0.329497i
$265$	−26.4621	+	4.66597i	−1.62555	+	0.286629i
$266$	13.8205	+	7.39707i	0.847387	+	0.453544i
$267$	4.62482	+	24.2316i	0.283034	+	1.48295i
$268$	1.85767	+	1.55877i	0.113475	+	0.0952169i
$269$	8.00969	−	13.8732i	0.488359	−	0.845863i	−0.511551	−	0.859253i	$-0.670929\pi$
$269$	8.00969	−	13.8732i	0.488359	−	0.845863i	0.999910	+	0.0133899i	$0.00426227\pi$
$270$	14.4120	−	9.15192i	0.877086	−	0.556968i
$271$	3.22979	−	1.86472i	0.196196	−	0.113274i	−0.398684	−	0.917088i	$-0.630533\pi$
$271$	3.22979	−	1.86472i	0.196196	−	0.113274i	0.594880	+	0.803815i	$0.297200\pi$
$272$	5.57498	−	2.02913i	0.338033	−	0.123034i
$273$	−14.3865	+	0.665519i	−0.870709	+	0.0402791i
$274$	−8.04289	+	6.74879i	−0.485889	+	0.407709i
$275$	−13.4048	−	15.9753i	−0.808342	−	0.963345i
$276$	0.164596	+	11.7076i	0.00990751	+	0.704712i
$277$	11.4251	−	4.15840i	0.686468	−	0.249854i	0.0248460	−	0.999691i	$-0.492090\pi$
$277$	11.4251	−	4.15840i	0.686468	−	0.249854i	0.661622	+	0.749837i	$0.269868\pi$
$278$	−12.9372			−0.775922
$279$	14.8369	−	9.13162i	0.888262	−	0.546696i
$280$	−8.06870	+	3.23430i	−0.482197	+	0.193286i
$281$	30.0504	+	5.29870i	1.79266	+	0.316094i	0.968266	−	0.249923i	$-0.0804053\pi$
$281$	30.0504	+	5.29870i	1.79266	+	0.316094i	0.824394	+	0.566017i	$0.191516\pi$
$282$	4.37626	−	5.36687i	0.260602	−	0.319592i
$283$	4.63819	+	5.52757i	0.275712	+	0.328580i	0.886076	−	0.463541i	$-0.153421\pi$
$283$	4.63819	+	5.52757i	0.275712	+	0.328580i	−0.610364	+	0.792121i	$0.708977\pi$
$284$	−1.26084	−	1.50262i	−0.0748173	−	0.0891638i
$285$	21.3074	−	26.1305i	1.26214	−	1.54784i
$286$	11.1380	+	1.96392i	0.658601	+	0.116129i
$287$	1.01083	+	0.144886i	0.0596673	+	0.00855232i
$288$	0.0843370	+	2.99881i	0.00496961	+	0.176707i
$289$	18.1977			1.07045
$290$	−15.0530	+	5.47883i	−0.883941	+	0.321728i
$291$	0.0384601	+	2.73563i	0.00225457	+	0.160366i
$292$	10.1841	+	12.1369i	0.595979	+	0.710260i
$293$	−15.4530	+	12.9666i	−0.902775	+	0.757518i	−0.970731	−	0.240170i	$-0.922797\pi$
$293$	−15.4530	+	12.9666i	−0.902775	+	0.757518i	0.0679558	+	0.997688i	$0.478352\pi$
$294$	12.0684	+	1.16380i	0.703842	+	0.0678742i
$295$	−33.0890	+	12.0434i	−1.92652	+	0.701194i
$296$	−0.655341	+	0.378361i	−0.0380909	+	0.0219918i
$297$	18.5358	+	2.46781i	1.07556	+	0.143197i
$298$	−0.721877	+	1.25033i	−0.0418172	+	0.0724296i
$299$	−16.2746	−	13.6560i	−0.941187	−	0.789749i
$300$	1.88171	+	9.85917i	0.108641	+	0.569219i
$301$	−0.276264	−	8.58491i	−0.0159236	−	0.494826i
$302$	−3.99542	+	0.704500i	−0.229910	+	0.0405394i
$303$	2.80114	+	4.69793i	0.160921	+	0.269889i
$304$	2.02640	+	5.56748i	0.116222	+	0.319317i
$305$	−40.9506	+	23.6428i	−2.34482	+	1.35378i
$306$	−5.61479	+	16.8894i	−0.320976	+	0.965505i
$307$	21.4952	−	12.4103i	1.22680	−	0.708292i	0.260439	−	0.965490i	$-0.416133\pi$
$307$	21.4952	−	12.4103i	1.22680	−	0.708292i	0.966359	+	0.257199i	$0.0827995\pi$
$308$	−9.04716	−	2.96701i	−0.515510	−	0.169061i
$309$	−20.6968	+	25.3817i	−1.17740	+	1.44392i
$310$	3.31324	+	18.7903i	0.188179	+	1.06722i
$311$	4.36005	−	3.65851i	0.247236	−	0.207455i	−0.510745	−	0.859732i	$-0.670630\pi$
$311$	4.36005	−	3.65851i	0.247236	−	0.207455i	0.757981	+	0.652277i	$0.226186\pi$
$312$	−4.21865	−	3.43998i	−0.238834	−	0.194750i
$313$	−1.15994	−	3.18690i	−0.0655634	−	0.180134i	0.902585	−	0.430513i	$-0.141667\pi$
$313$	−1.15994	−	3.18690i	−0.0655634	−	0.180134i	−0.968148	+	0.250378i	$0.919445\pi$
$314$	−0.145173	−	0.251447i	−0.00819259	−	0.0141900i
$315$	7.42669	−	24.9985i	0.418447	−	1.40851i
$316$	0.0676494	−	0.117172i	0.00380558	−	0.00659145i
$317$	12.5437	+	2.21179i	0.704523	+	0.124226i	0.514421	−	0.857538i	$-0.328007\pi$
$317$	12.5437	+	2.21179i	0.704523	+	0.124226i	0.190102	+	0.981764i	$0.439118\pi$
$318$	7.25435	+	12.1666i	0.406804	+	0.682272i
$319$	−16.4876	−	6.00100i	−0.923128	−	0.335991i
$320$	−3.08742	−	1.12373i	−0.172592	−	0.0628184i
$321$	12.2810	+	14.2250i	0.685461	+	0.793961i
$322$	11.9312	+	13.3241i	0.664900	+	0.742524i
$323$			35.1504i			1.95582i
$324$	−7.20864	−	5.38846i	−0.400480	−	0.299359i
$325$	−15.7721	−	9.10600i	−0.874876	−	0.505110i
$326$	−16.4443	−	2.89957i	−0.910764	−	0.160592i
$327$	−2.93504	−	1.02178i	−0.162308	−	0.0565044i
$328$	0.248091	+	0.295664i	0.0136986	+	0.0163253i
$329$	−0.340227	−	10.5726i	−0.0187573	−	0.582884i
$330$	−9.98934	+	17.8778i	−0.549895	+	0.984142i
$331$	−0.644422	+	3.65470i	−0.0354207	+	0.200881i	−0.997383	−	0.0723024i	$-0.976965\pi$
$331$	−0.644422	+	3.65470i	−0.0354207	+	0.200881i	0.961962	+	0.273183i	$0.0880764\pi$
$332$	2.87100	+	4.97272i	0.157567	+	0.272913i
$333$	0.331204	−	2.24588i	0.0181499	−	0.123073i
$334$	17.3632	+	10.0247i	0.950074	+	0.548526i
$335$	1.38355	−	7.84649i	0.0755913	−	0.428700i
$336$	3.10470	+	3.37059i	0.169375	+	0.183881i
$337$	−31.6420	−	11.5168i	−1.72365	−	0.627358i	−0.725506	−	0.688216i	$-0.758394\pi$
$337$	−31.6420	−	11.5168i	−1.72365	−	0.627358i	−0.998146	+	0.0608583i	$0.980616\pi$
$338$	−3.07572	+	0.542332i	−0.167297	+	0.0294990i
$339$	−6.92719	−	18.2307i	−0.376233	−	0.990156i
$340$	−14.9321	−	12.5295i	−0.809808	−	0.679509i
$341$	−10.4493	+	18.0987i	−0.565862	+	0.980102i
$342$	−16.8667	−	5.60725i	−0.912049	−	0.303205i
$343$	15.0721	−	10.7625i	0.813817	−	0.581122i
$344$	2.08679	−	2.48694i	0.112512	−	0.134087i
$345$	33.0421	−	19.7013i	1.77893	−	1.06068i
$346$	−1.98264	+	5.44727i	−0.106588	+	0.292847i
$347$	−30.7658	+	5.42484i	−1.65159	+	0.291221i	−0.920409	−	0.390957i	$-0.872144\pi$
$347$	−30.7658	+	5.42484i	−1.65159	+	0.291221i	−0.731186	+	0.682178i	$0.761033\pi$
$348$	5.51859	+	6.39211i	0.295827	+	0.342653i
$349$	−1.03957	−	2.85621i	−0.0556471	−	0.152889i	0.908754	−	0.417331i	$-0.137034\pi$
$349$	−1.03957	−	2.85621i	−0.0556471	−	0.152889i	−0.964402	+	0.264442i	$0.914812\pi$
$350$	12.0559	+	9.47234i	0.644413	+	0.506318i
$351$	15.9482	−	3.51123i	0.851253	−	0.187416i
$352$	−1.79935	−	3.11656i	−0.0959056	−	0.166113i
$353$	−0.0854082	+	0.484374i	−0.00454582	+	0.0257806i	−0.986996	−	0.160743i	$-0.948611\pi$
$353$	−0.0854082	+	0.484374i	−0.00454582	+	0.0257806i	0.982450	+	0.186524i	$0.0597221\pi$
$354$	12.1308	+	14.0509i	0.644744	+	0.746799i
$355$	−2.20422	+	6.05605i	−0.116988	+	0.321422i
$356$	2.47321	+	14.0263i	0.131080	+	0.743391i
$357$	10.4693	+	25.0908i	0.554092	+	1.32794i
$358$	4.12331	+	3.45986i	0.217923	+	0.182860i
$359$			22.3463i			1.17939i	0.807625	+	0.589697i	$0.200753\pi$
$359$			22.3463i			1.17939i	−0.807625	+	0.589697i	$0.799247\pi$
$360$	8.39423	−	5.16637i	0.442415	−	0.272292i
$361$	−16.1031			−0.847534
$362$	−6.47070	+	2.35514i	−0.340092	+	0.123784i
$363$	−3.15826	+	1.20005i	−0.165765	+	0.0629865i
$364$	−8.31061	+	0.267437i	−0.435595	+	0.0140175i
$365$	17.8040	−	48.9160i	0.931902	−	2.56038i
$366$	19.3190	+	15.7531i	1.00982	+	0.823428i
$367$	6.98984	−	8.33016i	0.364866	−	0.434831i	−0.552111	−	0.833771i	$-0.686177\pi$
$367$	6.98984	−	8.33016i	0.364866	−	0.434831i	0.916977	+	0.398940i	$0.130622\pi$
$368$			6.76003i			0.352391i
$369$	−1.15743	+	0.0325509i	−0.0602533	+	0.00169453i
$370$	2.15316	+	1.24313i	0.111938	+	0.0646273i
$371$	20.5603	+	6.74273i	1.06744	+	0.350065i
$372$	8.63936	−	5.15121i	0.447930	−	0.267078i
$373$	7.76621	−	6.51662i	0.402119	−	0.337418i	−0.419193	−	0.907897i	$-0.637687\pi$
$373$	7.76621	−	6.51662i	0.402119	−	0.337418i	0.821312	+	0.570479i	$0.193243\pi$
$374$	−3.70743	−	21.0259i	−0.191706	−	1.08722i
$375$	3.42422	−	2.95628i	0.176826	−	0.152662i
$376$	2.56994	−	3.06274i	0.132535	−	0.157949i
$377$	−15.3227			−0.789159
$378$	−13.7098	+	1.02111i	−0.705154	+	0.0525201i
$379$	9.75561			0.501112			0.250556	−	0.968102i	$-0.419387\pi$
$379$	9.75561			0.501112			0.250556	+	0.968102i	$0.419387\pi$
$380$	12.5127	−	14.9120i	0.641887	−	0.764972i
$381$	1.69515	+	0.590131i	0.0868449	+	0.0302333i
$382$	0.177832	+	1.00853i	0.00909865	+	0.0516010i
$383$	−5.78307	+	4.85257i	−0.295501	+	0.247955i	−0.778469	−	0.627683i	$-0.784003\pi$
$383$	−5.78307	+	4.85257i	−0.295501	+	0.247955i	0.482968	+	0.875638i	$0.339559\pi$
$384$	0.0243484	+	1.73188i	0.00124252	+	0.0883796i
$385$	6.42025	+	30.6168i	0.327206	+	1.56038i
$386$	−1.66013	−	0.958474i	−0.0844982	−	0.0487851i
$387$	1.96020	+	9.54011i	0.0996426	+	0.484951i
$388$			1.57957i			0.0801908i
$389$	3.51334	−	4.18703i	0.178133	−	0.212291i	−0.669588	−	0.742733i	$-0.733529\pi$
$389$	3.51334	−	4.18703i	0.178133	−	0.212291i	0.847722	+	0.530442i	$0.177974\pi$
$390$	−2.85773	+	17.6548i	−0.144707	+	0.893987i
$391$	−13.7169	+	37.6870i	−0.693696	+	1.90591i
$392$	6.95754	+	0.769803i	0.351409	+	0.0388809i
$393$	0.835824	−	5.16365i	0.0421617	−	0.260472i
$394$	11.7458	−	4.27511i	0.591743	−	0.215377i
$395$	−0.444533			−0.0223669
$396$	10.6806	+	1.57509i	0.536719	+	0.0791511i
$397$		−	31.1158i		−	1.56166i	−0.624745	−	0.780829i	$-0.714797\pi$
$397$		−	31.1158i		−	1.56166i	0.624745	−	0.780829i	$-0.285203\pi$
$398$	−10.2073	−	8.56493i	−0.511645	−	0.429321i
$399$	−25.0570	+	10.4552i	−1.25442	+	0.523414i
$400$	1.00628	+	5.70690i	0.0503140	+	0.285345i
$401$	−4.67699	+	12.8499i	−0.233558	+	0.641694i	−1.00000		0.000619001i	$-0.999803\pi$
$401$	−4.67699	+	12.8499i	−0.233558	+	0.641694i	0.766442	+	0.642313i	$0.222025\pi$
$402$	−4.12577	+	0.787441i	−0.205775	+	0.0392740i
$403$	−3.16921	+	17.9735i	−0.157870	+	0.895324i
$404$	1.57895	+	2.73482i	0.0785556	+	0.136062i
$405$	−3.49001	+	29.3634i	−0.173420	+	1.45908i
$406$	12.7691	+	1.83024i	0.633719	+	0.0908331i
$407$	0.931394	+	2.55898i	0.0461675	+	0.126844i
$408$	−3.37846	+	9.70459i	−0.167259	+	0.480449i
$409$	−15.6493	+	2.75939i	−0.773806	+	0.136443i	−0.546589	−	0.837401i	$-0.684074\pi$
$409$	−15.6493	+	2.75939i	−0.773806	+	0.136443i	−0.227217	+	0.973844i	$0.572963\pi$
$410$	0.433717	−	1.19163i	0.0214197	−	0.0588502i
$411$	−0.255640	−	18.1834i	−0.0126098	−	0.896923i
$412$	−12.1541	+	14.4847i	−0.598791	+	0.713611i
$413$	28.0686	+	4.02317i	1.38116	+	0.197967i
$414$	−15.8958	−	12.5939i	−0.781235	−	0.618956i
$415$	9.43286	−	16.3382i	0.463041	−	0.802010i
$416$	−2.40748	−	2.02012i	−0.118036	−	0.0990443i
$417$	14.1608	−	17.3662i	0.693457	−	0.850428i
$418$	20.9976	−	3.70244i	1.02703	−	0.181092i
$419$	19.8533	+	7.22602i	0.969898	+	0.353014i	0.777905	−	0.628382i	$-0.216283\pi$
$419$	19.8533	+	7.22602i	0.969898	+	0.353014i	0.191993	+	0.981396i	$0.438505\pi$
$420$	4.49027	−	14.3712i	0.219103	−	0.701242i
$421$	5.50568	−	31.2242i	0.268330	−	1.52178i	−0.491051	−	0.871131i	$-0.663387\pi$
$421$	5.50568	−	31.2242i	0.268330	−	1.52178i	0.759382	−	0.650646i	$-0.225502\pi$
$422$	−9.50031	−	5.48501i	−0.462468	−	0.267006i
$423$	2.41404	+	11.7489i	0.117375	+	0.571252i
$424$	4.08914	+	7.08260i	0.198586	+	0.343961i
$425$	−5.97003	+	33.8577i	−0.289589	+	1.64234i
$426$	3.39713	−	0.0477600i	0.164591	−	0.00231398i
$427$	38.0578	−	1.22471i	1.84175	−	0.0592677i
$428$	6.97431	+	8.31166i	0.337116	+	0.401759i
$429$	−14.8276	+	12.8013i	−0.715885	+	0.618055i
$430$	−10.5044	−	1.85222i	−0.506569	−	0.0893218i
$431$	14.1867	+	8.19067i	0.683347	+	0.394531i	0.801115	−	0.598511i	$-0.204241\pi$
$431$	14.1867	+	8.19067i	0.683347	+	0.394531i	−0.117768	+	0.993041i	$0.537574\pi$
$432$	−4.11776	−	3.16923i	−0.198116	−	0.152480i
$433$			20.4469i			0.982615i	0.870986	+	0.491307i	$0.163481\pi$
$433$			20.4469i			0.982615i	−0.870986	+	0.491307i	$0.836519\pi$
$434$	4.78791	−	14.5996i	0.229827	−	0.700801i
$435$	9.12217	−	26.2033i	0.437374	−	1.25635i
$436$	−1.68609	−	0.613686i	−0.0807490	−	0.0293902i
$437$	−37.6363	−	13.6985i	−1.80039	−	0.655289i
$438$	−27.4393	+	0.385767i	−1.31110	+	0.0184327i
$439$	38.4267	+	6.77566i	1.83400	+	0.323385i	0.980321	−	0.197408i	$-0.0632524\pi$
$439$	38.4267	+	6.77566i	1.83400	+	0.323385i	0.853683	+	0.520793i	$0.174364\pi$
$440$	−5.91188	+	10.2397i	−0.281838	+	0.488157i
$441$	−14.7720	+	14.9261i	−0.703429	+	0.710766i
$442$	−9.32258	−	16.1472i	−0.443430	−	0.768043i
$443$	−6.47072	−	17.7782i	−0.307433	−	0.844666i	−0.993155	−	0.116802i	$-0.962736\pi$
$443$	−6.47072	−	17.7782i	−0.307433	−	0.844666i	0.685722	−	0.727864i	$-0.259487\pi$
$444$	0.209430	−	1.29384i	0.00993910	−	0.0614030i
$445$	35.8472	−	30.0794i	1.69932	−	1.42590i
$446$	−0.0489445	−	0.277578i	−0.00231759	−	0.0131437i
$447$	−0.888224	−	2.33759i	−0.0420115	−	0.110564i
$448$	1.76496	+	1.97102i	0.0833867	+	0.0931217i
$449$	1.23187	−	0.711219i	0.0581354	−	0.0335645i	−0.470651	−	0.882320i	$-0.655981\pi$
$449$	1.23187	−	0.711219i	0.0581354	−	0.0335645i	0.528786	+	0.848755i	$0.322647\pi$
$450$	−15.2941	−	8.26572i	−0.720971	−	0.389650i
$451$	1.20287	−	0.694480i	0.0566411	−	0.0327018i
$452$	−3.85106	−	10.5807i	−0.181138	−	0.497674i
$453$	3.42762	−	6.13437i	0.161043	−	0.288218i
$454$	−9.98653	+	1.76089i	−0.468691	+	0.0826428i
$455$	14.4135	+	23.2075i	0.675715	+	1.08799i
$456$	−9.69155	−	3.37392i	−0.453848	−	0.157998i
$457$	−25.5772	−	21.4618i	−1.19645	−	1.00394i	−0.999724	−	0.0234833i	$-0.992524\pi$
$457$	−25.5772	−	21.4618i	−1.19645	−	1.00394i	−0.196727	−	0.980458i	$-0.563031\pi$
$458$	7.96924	−	13.8031i	0.372378	−	0.644978i
$459$	−16.5257	−	26.0238i	−0.771353	−	1.21469i
$460$	19.2349	−	11.1053i	0.896831	−	0.517785i
$461$	4.99360	−	1.81752i	0.232575	−	0.0846504i	−0.223104	−	0.974795i	$-0.571619\pi$
$461$	4.99360	−	1.81752i	0.232575	−	0.0846504i	0.455679	+	0.890144i	$0.349397\pi$
$462$	13.8856	−	8.89682i	0.646016	−	0.413917i
$463$	−17.6114	+	14.7777i	−0.818471	+	0.686779i	−0.952614	−	0.304183i	$-0.901617\pi$
$463$	−17.6114	+	14.7777i	−0.818471	+	0.686779i	0.134142	+	0.990962i	$0.457172\pi$
$464$	3.13396	+	3.73491i	0.145491	+	0.173389i
$465$	−28.8497	−	16.1200i	−1.33787	−	0.747545i
$466$	25.1873	−	9.16742i	1.16678	−	0.424673i
$467$	36.5062			1.68930			0.844652	−	0.535316i	$-0.179807\pi$
$467$	36.5062			1.68930			0.844652	+	0.535316i	$0.179807\pi$
$468$	9.23530	−	1.89757i	0.426902	−	0.0877152i
$469$	−3.96390	+	5.04503i	−0.183036	+	0.232958i
$470$	−12.9365	−	2.28106i	−0.596717	−	0.105217i
$471$	0.496433	+	0.0803560i	0.0228744	+	0.00370261i
$472$	6.88898	+	8.20997i	0.317091	+	0.377894i
$473$	−7.50973	−	8.94975i	−0.345298	−	0.411510i
$474$	0.0832382	+	0.219063i	0.00382326	+	0.0100619i
$475$	−33.8122	−	5.96200i	−1.55141	−	0.273555i
$476$	5.84020	+	14.5697i	0.267685	+	0.667801i
$477$	−24.2723	−	3.57949i	−1.11135	−	0.163894i
$478$	−20.7452			−0.948862
$479$	−13.3938	+	4.87496i	−0.611980	+	0.222742i	−0.629369	−	0.777106i	$-0.716687\pi$
$479$	−13.3938	+	4.87496i	−0.611980	+	0.222742i	0.0173895	+	0.999849i	$0.494464\pi$
$480$	4.88786	−	2.91438i	0.223099	−	0.133023i
$481$	1.52867	+	1.82179i	0.0697012	+	0.0830667i
$482$	−18.4055	+	15.4441i	−0.838348	+	0.703457i
$483$	−30.9453	+	1.43153i	−1.40806	+	0.0651369i
$484$	−1.83298	+	0.667150i	−0.0833173	+	0.0303250i
$485$	4.49450	−	2.59490i	0.204085	−	0.117828i
$486$	15.1236	−	3.77840i	0.686021	−	0.171392i
$487$	−3.73664	+	6.47205i	−0.169323	+	0.293276i	−0.938182	−	0.346142i	$-0.887492\pi$
$487$	−3.73664	+	6.47205i	−0.169323	+	0.293276i	0.768859	+	0.639419i	$0.220825\pi$
$488$	11.0249	+	9.25096i	0.499072	+	0.418771i
$489$	21.8918	−	18.9001i	0.989980	−	0.854693i
$490$	−9.23935	−	21.0615i	−0.417391	−	0.951461i
$491$	16.4226	−	2.89575i	0.741143	−	0.130683i	0.209686	−	0.977769i	$-0.432756\pi$
$491$	16.4226	−	2.89575i	0.741143	−	0.130683i	0.531457	+	0.847085i	$0.321645\pi$
$492$	−0.668439	+	0.00939755i	−0.0301356	+	0.000423674i
$493$	9.89317	+	27.1812i	0.445566	+	1.22418i
$494$	16.1255	−	9.31005i	0.725519	−	0.418879i
$495$	−13.0641	−	32.9778i	−0.587189	−	1.48224i
$496$	5.02925	−	2.90364i	0.225820	−	0.130377i
$497$	3.86620	−	3.46202i	0.173423	−	0.155293i
$498$	−9.81765	−	1.58915i	−0.439939	−	0.0712116i
$499$	1.39403	+	7.90591i	0.0624051	+	0.353917i	0.999981	+	0.00613676i	$0.00195340\pi$
$499$	1.39403	+	7.90591i	0.0624051	+	0.353917i	−0.937576	+	0.347780i	$0.886935\pi$
$500$	2.00078	−	1.67885i	0.0894774	−	0.0750804i
$501$	−32.4620	+	12.3347i	−1.45030	+	0.551074i
$502$	10.2441	+	28.1456i	0.457219	+	1.25620i
$503$	−0.766281	−	1.32724i	−0.0341668	−	0.0591786i	0.848436	−	0.529297i	$-0.177544\pi$
$503$	−0.766281	−	1.32724i	−0.0341668	−	0.0591786i	−0.882603	+	0.470119i	$0.844211\pi$
$504$	−7.92284	+	0.478209i	−0.352911	+	0.0213011i
$505$	5.18774	−	8.98542i	0.230851	−	0.399846i
$506$	23.9577	+	4.22439i	1.06505	+	0.187797i
$507$	2.63862	−	4.72231i	0.117185	−	0.209725i
$508$	0.973807	+	0.354437i	0.0432057	+	0.0157256i
$509$	10.3589	+	3.77032i	0.459149	+	0.167116i	0.561230	−	0.827660i	$-0.310328\pi$
$509$	10.3589	+	3.77032i	0.459149	+	0.167116i	−0.102082	+	0.994776i	$0.532550\pi$
$510$	33.1634	−	6.32953i	1.46850	−	0.280276i
$511$	−31.2281	+	27.9635i	−1.38145	+	1.23703i
$512$			1.00000i			0.0441942i
$513$	25.9889	−	16.5035i	1.14744	−	0.728646i
$514$	−9.69061	−	5.59488i	−0.427435	−	0.246780i
$515$	61.1812	+	10.7879i	2.69597	+	0.475371i
$516$	1.05418	+	5.52335i	0.0464078	+	0.243152i
$517$	−9.24845	−	11.0219i	−0.406746	−	0.484741i
$518$	−1.05630	−	1.70077i	−0.0464111	−	0.0747277i
$519$	−5.14197	−	8.62386i	−0.225707	−	0.378546i
$520$	−1.79304	+	10.1688i	−0.0786299	+	0.445932i
$521$	6.32917	+	10.9624i	0.277286	+	0.480273i	0.970709	−	0.240257i	$-0.0772317\pi$
$521$	6.32917	+	10.9624i	0.277286	+	0.480273i	−0.693423	+	0.720530i	$0.743898\pi$
$522$	−14.6210	+	0.411192i	−0.639942	+	0.0179974i
$523$	−4.54862	−	2.62615i	−0.198897	−	0.114833i	0.397244	−	0.917713i	$-0.369967\pi$
$523$	−4.54862	−	2.62615i	−0.198897	−	0.114833i	−0.596141	+	0.802880i	$0.703300\pi$
$524$	0.524424	−	2.97416i	0.0229096	−	0.129927i
$525$	−25.9113	+	5.81495i	−1.13086	+	0.253785i
$526$	15.3157	+	5.57444i	0.667794	+	0.243057i
$527$	33.9298	−	5.98274i	1.47800	−	0.260612i
$528$	6.15304	+	0.995973i	0.267777	+	0.0433441i
$529$	−17.3877	−	14.5900i	−0.755986	−	0.634348i
$530$	13.4351	−	23.2703i	0.583585	−	1.01080i
$531$	−32.1393	+	0.903869i	−1.39473	+	0.0392246i
$532$	−14.5501	+	5.83235i	−0.630827	+	0.252864i
$533$	0.779688	−	0.929195i	0.0337720	−	0.0402479i
$534$	−21.5353	−	12.0330i	−0.931922	−	0.520717i
$535$	12.1926	−	33.4988i	0.527131	−	1.44828i
$536$	−2.38817	+	0.421099i	−0.103153	+	0.0181887i
$537$	−9.15762	+	1.74782i	−0.395181	+	0.0754238i
$538$	5.47895	+	15.0533i	0.236214	+	0.648993i
$539$	7.07602	−	24.1766i	0.304786	−	1.04136i
$540$	−2.25308	+	16.9230i	−0.0969570	+	0.728249i
$541$	−14.7793	−	25.5986i	−0.635414	−	1.10057i	−0.986427	−	0.164199i	$-0.947496\pi$
$541$	−14.7793	−	25.5986i	−0.635414	−	1.10057i	0.351013	−	0.936370i	$-0.385837\pi$
$542$	−0.647611	+	3.67278i	−0.0278173	+	0.157760i
$543$	3.92127	−	11.2638i	0.168278	−	0.483377i
$544$	−2.02913	+	5.57498i	−0.0869980	+	0.239025i
$545$	1.02371	+	5.80572i	0.0438507	+	0.248690i
$546$	8.73763	−	11.4485i	0.373936	−	0.489949i
$547$	−30.7531	−	25.8049i	−1.31491	−	1.10334i	−0.987359	−	0.158503i	$-0.949333\pi$
$547$	−30.7531	−	25.8049i	−1.31491	−	1.10334i	−0.327548	−	0.944835i	$-0.606222\pi$
$548$		−	10.4993i		−	0.448506i
$549$	−42.2923	+	8.68977i	−1.80499	+	0.370870i
$550$	20.8542			0.889227
$551$	−27.1447	+	9.87987i	−1.15640	+	0.420897i
$552$	−9.07431	−	7.39939i	−0.386228	−	0.314939i
$553$	0.315605	+	0.168920i	0.0134209	+	0.00718321i
$554$	−4.15840	+	11.4251i	−0.176673	+	0.485406i
$555$	−4.02552	+	1.52959i	−0.170874	+	0.0649275i
$556$	8.31587	−	9.91047i	0.352672	−	0.420298i
$557$		−	18.5445i		−	0.785756i	−0.919591	−	0.392878i	$-0.871479\pi$
$557$		−	18.5445i		−	0.785756i	0.919591	−	0.392878i	$-0.128521\pi$
$558$	−2.54175	+	17.2354i	−0.107601	+	0.729634i
$559$	−8.83590	−	5.10141i	−0.373719	−	0.215767i
$560$	2.70884	−	8.25995i	0.114469	−	0.349047i
$561$	32.2821	+	18.0378i	1.36295	+	0.761557i
$562$	−23.3751	+	19.6140i	−0.986019	+	0.827368i
$563$	5.22122	+	29.6110i	0.220048	+	1.24796i	0.871928	+	0.489634i	$0.162870\pi$
$563$	5.22122	+	29.6110i	0.220048	+	1.24796i	−0.651880	+	0.758322i	$0.726019\pi$
$564$	1.29826	+	6.80217i	0.0546664	+	0.286423i
$565$	−23.7797	+	28.3395i	−1.00042	+	1.19225i
$566$	−7.21574			−0.303300
$567$	13.6357	−	19.5209i	0.572647	−	0.819802i
$568$	1.96152			0.0823038
$569$	−4.79220	+	5.71112i	−0.200900	+	0.239423i	−0.857083	−	0.515179i	$-0.827725\pi$
$569$	−4.79220	+	5.71112i	−0.200900	+	0.239423i	0.656183	+	0.754602i	$0.272170\pi$
$570$	6.32102	+	33.1188i	0.264758	+	1.38719i
$571$	−4.05675	−	23.0070i	−0.169770	−	0.962812i	−0.944009	−	0.329919i	$-0.892979\pi$
$571$	−4.05675	−	23.0070i	−0.169770	−	0.962812i	0.774239	−	0.632893i	$-0.218133\pi$
$572$	−8.66379	+	7.26978i	−0.362251	+	0.303965i
$573$	−1.54845	−	0.865207i	−0.0646875	−	0.0361445i
$574$	−0.760737	+	0.681209i	−0.0317525	+	0.0284331i
$575$	−33.9257	−	19.5870i	−1.41480	−	0.816834i
$576$	−2.35144	−	1.86299i	−0.0979765	−	0.0776248i
$577$			35.4895i			1.47745i	0.674009	+	0.738723i	$0.264571\pi$
$577$			35.4895i			1.47745i	−0.674009	+	0.738723i	$0.735429\pi$
$578$	−11.6973	+	13.9403i	−0.486542	+	0.579838i
$579$	3.10375	−	1.17934i	0.128987	−	0.0490117i
$580$	5.47883	−	15.0530i	0.227496	−	0.625041i
$581$	−12.9055	+	8.01518i	−0.535408	+	0.332526i
$582$	−2.12034	−	1.72897i	−0.0878909	−	0.0716681i
$583$	27.6562	−	10.0660i	1.14540	−	0.416893i
$584$	−15.8436			−0.655614
$585$	−20.5709	−	23.1607i	−0.850502	−	0.957576i
$586$		−	20.1725i		−	0.833318i
$587$	14.4979	+	12.1652i	0.598393	+	0.502111i	0.890929	−	0.454144i	$-0.150055\pi$
$587$	14.4979	+	12.1652i	0.598393	+	0.502111i	−0.292536	+	0.956255i	$0.594499\pi$
$588$	−8.64892	+	8.49683i	−0.356676	+	0.350403i
$589$	5.97470	+	33.8842i	0.246183	+	1.39617i
$590$	12.0434	−	33.0890i	0.495819	−	1.36225i
$591$	−7.11798	+	20.4463i	−0.292794	+	0.841050i
$592$	0.131403	−	0.745226i	0.00540065	−	0.0306286i
$593$	13.5580	+	23.4831i	0.556759	+	0.964335i	0.997764	+	0.0668307i	$0.0212887\pi$
$593$	13.5580	+	23.4831i	0.556759	+	0.964335i	−0.441005	+	0.897505i	$0.645378\pi$
$594$	−13.8050	+	12.6130i	−0.566428	+	0.517517i
$595$	31.8622	−	40.5524i	1.30622	−	1.66249i
$596$	−0.493793	−	1.35669i	−0.0202266	−	0.0555720i
$597$	22.6698	−	4.32673i	0.927813	−	0.177081i
$598$	20.9223	−	3.68916i	0.855575	−	0.150861i
$599$	−6.10131	+	16.7632i	−0.249293	+	0.684926i	0.750420	+	0.660961i	$0.229851\pi$
$599$	−6.10131	+	16.7632i	−0.249293	+	0.684926i	−0.999713	+	0.0239649i	$0.992371\pi$
$600$	−8.76210	−	4.89588i	−0.357711	−	0.199873i
$601$	−0.667624	+	0.795644i	−0.0272330	+	0.0324550i	−0.779489	−	0.626416i	$-0.784521\pi$
$601$	−0.667624	+	0.795644i	−0.0272330	+	0.0324550i	0.752256	+	0.658871i	$0.228966\pi$
$602$	6.75400	+	5.30664i	0.275273	+	0.216283i
$603$	3.45896	−	6.40013i	0.140860	−	0.260634i
$604$	2.02853	−	3.51351i	0.0825396	−	0.142963i
$605$	4.90949	+	4.11955i	0.199599	+	0.167483i
$606$	−5.39936	−	0.873977i	−0.219334	−	0.0355029i
$607$	31.9491	−	5.63348i	1.29677	−	0.228656i	0.517685	−	0.855571i	$-0.326794\pi$
$607$	31.9491	−	5.63348i	1.29677	−	0.228656i	0.779088	+	0.626915i	$0.215683\pi$
$608$	−5.56748	−	2.02640i	−0.225791	−	0.0821813i
$609$	−16.4336	+	15.1372i	−0.665922	+	0.613390i
$610$	8.21107	−	46.5673i	0.332456	−	1.88545i
$611$	−10.8817	−	6.28253i	−0.440225	−	0.254164i
$612$	−9.32895	−	15.1575i	−0.377100	−	0.612706i
$613$	17.7854	+	30.8051i	0.718344	+	1.24421i	0.961656	+	0.274260i	$0.0884327\pi$
$613$	17.7854	+	30.8051i	0.718344	+	1.24421i	−0.243312	+	0.969948i	$0.578234\pi$
$614$	−4.31004	+	24.4435i	−0.173939	+	0.986458i
$615$	1.12484	+	1.88653i	0.0453579	+	0.0760721i
$616$	8.08826	−	5.02337i	0.325885	−	0.202398i
$617$	−18.5665	−	22.1267i	−0.747458	−	0.890786i	0.249528	−	0.968368i	$-0.419724\pi$
$617$	−18.5665	−	22.1267i	−0.747458	−	0.890786i	−0.996986	+	0.0775820i	$0.975280\pi$
$618$	−6.13989	−	32.1697i	−0.246982	−	1.29406i
$619$	−6.77747	−	1.19505i	−0.272409	−	0.0480331i	0.0357747	−	0.999360i	$-0.488610\pi$
$619$	−6.77747	−	1.19505i	−0.272409	−	0.0480331i	−0.308184	+	0.951327i	$0.599721\pi$
$620$	−16.5239	−	9.54009i	−0.663617	−	0.383139i
$621$	34.3046	−	7.55264i	1.37660	−	0.303077i
$622$			5.69164i			0.228214i
$623$	−36.8804	+	7.73371i	−1.47758	+	0.309844i
$624$	5.34688	−	1.02050i	0.214046	−	0.0408527i
$625$	19.1635	+	6.97494i	0.766540	+	0.278998i
$626$	3.18690	+	1.15994i	0.127374	+	0.0463603i
$627$	−18.0136	+	32.2387i	−0.719392	+	1.28749i
$628$	0.285935	+	0.0504181i	0.0114100	+	0.00201190i
$629$	2.24473	−	3.88798i	0.0895031	−	0.155024i
$630$	14.3762	+	21.7579i	0.572761	+	0.866856i
$631$	8.22286	+	14.2424i	0.327347	+	0.566982i	0.981985	−	0.188961i	$-0.0605121\pi$
$631$	8.22286	+	14.2424i	0.327347	+	0.566982i	−0.654638	+	0.755943i	$0.727179\pi$
$632$	0.0462749	+	0.127139i	0.00184072	+	0.00505733i
$633$	17.7616	−	6.74895i	0.705961	−	0.268247i
$634$	−9.75725	+	8.18730i	−0.387510	+	0.325159i
$635$	−0.591245	−	3.35312i	−0.0234628	−	0.133064i
$636$	−13.9832	−	2.26341i	−0.554470	−	0.0897502i
$637$	−1.41441	−	21.9537i	−0.0560411	−	0.869837i
$638$	15.1951	−	8.77287i	0.601578	−	0.347321i
$639$	−3.65431	+	4.61240i	−0.144562	+	0.182464i
$640$	2.84538	−	1.64278i	0.112474	−	0.0649367i
$641$	11.4189	+	31.3733i	0.451021	+	1.23917i	0.932006	+	0.362442i	$0.118057\pi$
$641$	11.4189	+	31.3733i	0.451021	+	1.23917i	−0.480985	+	0.876729i	$0.659721\pi$
$642$	−18.7911	+	0.264183i	−0.741624	+	0.0104265i
$643$	17.2520	−	3.04199i	0.680352	−	0.119964i	0.177216	−	0.984172i	$-0.443291\pi$
$643$	17.2520	−	3.04199i	0.680352	−	0.119964i	0.503135	+	0.864208i	$0.332180\pi$
$644$	−17.8761	+	0.575257i	−0.704417	+	0.0226683i
$645$	13.9843	−	12.0732i	0.550630	−	0.475382i
$646$	−26.9268	−	22.5942i	−1.05942	−	0.888958i
$647$	12.0992	−	20.9565i	0.475670	−	0.823884i	−0.523942	−	0.851754i	$-0.675539\pi$
$647$	12.0992	−	20.9565i	0.475670	−	0.823884i	0.999612	+	0.0278698i	$0.00887240\pi$
$648$	8.76143	−	2.05850i	0.344181	−	0.0808656i
$649$	33.4013	−	19.2842i	1.31112	−	0.756973i
$650$	17.1137	−	6.22887i	0.671254	−	0.244316i
$651$	14.3569	+	22.4074i	0.562693	+	0.878216i
$652$	12.7914	−	10.7332i	0.500949	−	0.420346i
$653$	−1.69858	−	2.02429i	−0.0664706	−	0.0792166i	0.731784	−	0.681536i	$-0.238688\pi$
$653$	−1.69858	−	2.02429i	−0.0664706	−	0.0792166i	−0.798255	+	0.602320i	$0.794243\pi$
$654$	2.66934	−	1.59159i	0.104379	−	0.0622361i
$655$	−9.32414	+	3.39371i	−0.364324	+	0.132603i
$656$	−0.385962			−0.0150693
$657$	29.5166	−	37.2553i	1.15155	−	1.45347i
$658$	8.31775	+	6.53528i	0.324260	+	0.254772i
$659$	−18.3488	−	3.23539i	−0.714769	−	0.126033i	−0.195574	−	0.980689i	$-0.562657\pi$
$659$	−18.3488	−	3.23539i	−0.714769	−	0.126033i	−0.519195	+	0.854656i	$0.673768\pi$
$660$	−7.27418	−	19.1439i	−0.283147	−	0.745176i
$661$	−27.1142	−	32.3135i	−1.05462	−	1.25685i	−0.965383	−	0.260838i	$-0.916001\pi$
$661$	−27.1142	−	32.3135i	−1.05462	−	1.25685i	−0.0892379	−	0.996010i	$-0.528443\pi$
$662$	−2.38544	−	2.84285i	−0.0927126	−	0.110491i
$663$	31.8794	+	5.16022i	1.23809	+	0.200406i
$664$	−5.65476	−	0.997088i	−0.219447	−	0.0386945i
$665$	40.4979	+	31.8194i	1.57044	+	1.23390i
$666$	1.50755	+	1.69734i	0.0584163	+	0.0657705i
$667$	−32.9591			−1.27618
$668$	−18.8402	+	6.85728i	−0.728950	+	0.265316i
$669$	0.426179	+	0.238130i	0.0164771	+	0.00920665i
$670$	5.12143	+	6.10349i	0.197858	+	0.235798i
$671$	39.6751	−	33.2914i	1.53164	−	1.28520i
$672$	−4.57768	+	0.211764i	−0.176588	+	0.00816897i
$673$	1.49663	−	0.544729i	0.0576908	−	0.0209977i	−0.313014	−	0.949749i	$-0.601339\pi$
$673$	1.49663	−	0.544729i	0.0576908	−	0.0209977i	0.370704	+	0.928751i	$0.379116\pi$
$674$	29.1615	−	16.8364i	1.12326	−	0.648513i
$675$	27.8361	−	11.4825i	1.07141	−	0.441963i
$676$	1.56158	−	2.70474i	0.0600609	−	0.104029i
$677$	11.6428	+	9.76946i	0.447469	+	0.375471i	0.838495	−	0.544909i	$-0.183436\pi$
$677$	11.6428	+	9.76946i	0.447469	+	0.375471i	−0.391027	+	0.920379i	$0.627880\pi$
$678$	18.4182	+	6.41194i	0.707348	+	0.246249i
$679$	−4.17700	+	0.134417i	−0.160299	+	0.00515844i
$680$	19.1964	−	3.38484i	0.736147	−	0.129803i
$681$	8.56731	−	15.3328i	0.328300	−	0.587555i
$682$	−7.14775	−	19.6383i	−0.273702	−	0.751989i
$683$	23.8221	−	13.7537i	0.911528	−	0.526271i	0.0306055	−	0.999532i	$-0.490256\pi$
$683$	23.8221	−	13.7537i	0.911528	−	0.526271i	0.880922	+	0.473261i	$0.156923\pi$
$684$	15.1371	−	9.31641i	0.578783	−	0.356222i
$685$	−29.8744	+	17.2480i	−1.14144	+	0.659012i
$686$	−1.44359	+	18.4639i	−0.0551165	+	0.704955i
$687$	9.80563	+	25.8061i	0.374108	+	0.984564i
$688$	0.563744	+	3.19715i	0.0214925	+	0.121890i
$689$	19.6891	−	16.5211i	0.750093	−	0.629403i
$690$	−6.14697	+	37.9755i	−0.234011	+	1.44570i
$691$	−4.91735	−	13.5103i	−0.187065	−	0.513957i	0.810339	−	0.585961i	$-0.199283\pi$
$691$	−4.91735	−	13.5103i	−0.187065	−	0.513957i	−0.997404	+	0.0720041i	$0.977061\pi$
$692$	−2.89843	−	5.02023i	−0.110182	−	0.190841i
$693$	−3.25625	+	28.3776i	−0.123695	+	1.07797i
$694$	15.6202	−	27.0550i	0.592935	−	1.02699i
$695$	−41.8603	−	7.38109i	−1.58785	−	0.279981i
$696$	−8.44392	+	0.118713i	−0.320066	+	0.00449979i
$697$	−2.15173	−	0.783165i	−0.0815025	−	0.0296645i
$698$	2.85621	+	1.03957i	0.108109	+	0.0393484i
$699$	−15.2636	+	43.8446i	−0.577323	+	1.65835i
$700$	−15.0056	+	3.14663i	−0.567158	+	0.118931i
$701$			33.8191i			1.27733i	0.769485	+	0.638664i	$0.220513\pi$
$701$			33.8191i			1.27733i	−0.769485	+	0.638664i	$0.779487\pi$
$702$	−7.56156	+	14.4740i	−0.285393	+	0.546287i
$703$	3.88276	+	2.24171i	0.146441	+	0.0845477i
$704$	3.54402	+	0.624907i	0.133570	+	0.0235521i
$705$	17.2220	−	14.8685i	0.648619	−	0.559981i
$706$	−0.316152	−	0.376776i	−0.0118986	−	0.0141801i
$707$	−7.09754	+	4.40807i	−0.266931	+	0.165782i
$708$	−18.5612	+	0.260950i	−0.697571	+	0.00980712i
$709$	4.20359	−	23.8398i	0.157869	−	0.895321i	−0.798246	−	0.602331i	$-0.794239\pi$
$709$	4.20359	−	23.8398i	0.157869	−	0.895321i	0.956116	−	0.292990i	$-0.0946503\pi$
$710$	−3.22236	−	5.58129i	−0.120933	−	0.209462i
$711$	−0.385170	−	0.128047i	−0.0144450	−	0.00480215i
$712$	−12.3345	−	7.12133i	−0.462255	−	0.266883i
$713$	−6.81697	+	38.6610i	−0.255298	+	1.44786i
$714$	−25.9502	−	8.10811i	−0.971160	−	0.303438i
$715$	34.9180	+	12.7091i	1.30586	+	0.475295i
$716$	−5.30082	+	0.934677i	−0.198101	+	0.0349305i
$717$	22.7072	−	27.8472i	0.848017	−	1.03997i
$718$	−17.1183	−	14.3639i	−0.638849	−	0.536058i
$719$	1.89246	−	3.27783i	0.0705767	−	0.122242i	−0.828577	−	0.559874i	$-0.810849\pi$
$719$	1.89246	−	3.27783i	0.0705767	−	0.122242i	0.899154	+	0.437632i	$0.144183\pi$
$720$	−1.43804	+	9.75123i	−0.0535924	+	0.363407i
$721$	−39.3374	−	30.9076i	−1.46500	−	1.15106i
$722$	10.3509	−	12.3357i	0.385221	−	0.459088i
$723$	−0.585011	−	41.6113i	−0.0217568	−	1.54754i
$724$	2.35514	−	6.47070i	0.0875282	−	0.240482i
$725$	−27.8245	+	4.90620i	−1.03337	+	0.182212i
$726$	1.11079	−	3.19074i	0.0412254	−	0.118420i
$727$	−10.8547	−	29.8232i	−0.402580	−	1.10608i	−0.961007	−	0.276526i	$-0.910817\pi$
$727$	−10.8547	−	29.8232i	−0.402580	−	1.10608i	0.558426	−	0.829554i	$-0.311405\pi$
$728$	5.13709	−	6.53820i	0.190393	−	0.242322i
$729$	−11.4821	+	24.4369i	−0.425261	+	0.905071i
$730$	26.0277	+	45.0812i	0.963327	+	1.66853i
$731$	−3.34456	+	18.9679i	−0.123703	+	0.701555i
$732$	−24.4856	+	4.67330i	−0.905013	+	0.172730i
$733$	−15.6683	+	43.0484i	−0.578724	+	1.59003i	0.211611	+	0.977354i	$0.432129\pi$
$733$	−15.6683	+	43.0484i	−0.578724	+	1.59003i	−0.790334	+	0.612676i	$0.790093\pi$
$734$	1.88829	+	10.7090i	0.0696982	+	0.395278i
$735$	38.3850	+	10.6510i	1.41585	+	0.392870i
$736$	−5.17848	−	4.34526i	−0.190881	−	0.160169i
$737$			8.72688i			0.321459i
$738$	0.719045	−	0.907564i	0.0264684	−	0.0334079i
$739$	5.63850			0.207415			0.103708	−	0.994608i	$-0.466929\pi$
$739$	5.63850			0.207415			0.103708	+	0.994608i	$0.466929\pi$
$740$	−2.33632	+	0.850351i	−0.0858848	+	0.0312595i
$741$	−5.15328	+	31.8366i	−0.189311	+	1.16955i
$742$	−18.3811	+	11.4160i	−0.674792	+	0.419093i
$743$	−6.33835	+	17.4145i	−0.232532	+	0.638875i	−0.999998	−	0.00221452i	$-0.999295\pi$
$743$	−6.33835	+	17.4145i	−0.232532	+	0.638875i	0.767466	+	0.641090i	$0.221517\pi$
$744$	−1.60722	+	9.92926i	−0.0589235	+	0.364024i
$745$	−3.04910	+	3.63377i	−0.111710	+	0.133131i
$746$			10.1381i			0.371181i
$747$	12.8794	−	11.4392i	0.471232	−	0.418540i
$748$	18.4898	+	10.6751i	0.676055	+	0.390321i
$749$	−21.3857	+	19.1500i	−0.781417	+	0.699727i
$750$	0.0635938	+	4.52337i	0.00232212	+	0.165170i
$751$	4.86527	−	4.08245i	0.177536	−	0.148971i	−0.549689	−	0.835369i	$-0.685254\pi$
$751$	4.86527	−	4.08245i	0.177536	−	0.148971i	0.727226	+	0.686399i	$0.240809\pi$
$752$	0.694267	+	3.93738i	0.0253173	+	0.143582i
$753$	−48.9941	−	17.0563i	−1.78545	−	0.621567i
$754$	9.84924	−	11.7379i	0.358688	−	0.427468i
$755$	−13.3297			−0.485118
$756$	8.03025	−	11.1586i	0.292057	−	0.405836i
$757$	22.7132			0.825525			0.412763	−	0.910839i	$-0.364564\pi$
$757$	22.7132			0.825525			0.412763	+	0.910839i	$0.364564\pi$
$758$	−6.27079	+	7.47323i	−0.227765	+	0.271440i
$759$	−31.8942	+	27.5356i	−1.15769	+	0.999481i
$760$	3.38029	+	19.1706i	0.122616	+	0.695389i
$761$	30.1453	−	25.2949i	1.09277	−	0.916941i	0.0958501	−	0.995396i	$-0.469443\pi$
$761$	30.1453	−	25.2949i	1.09277	−	0.916941i	0.996918	+	0.0784548i	$0.0249986\pi$
$762$	−1.54169	+	0.919228i	−0.0558494	+	0.0333001i
$763$	1.47934	−	4.51088i	0.0535557	−	0.163305i
$764$	−0.886889	−	0.512046i	−0.0320865	−	0.0185252i
$765$	−27.8035	+	51.4449i	−1.00524	+	1.86000i
$766$		−	7.54926i		−	0.272766i
$767$	21.6503	−	25.8018i	0.781747	−	0.931650i
$768$	−1.34235	−	1.09458i	−0.0484378	−	0.0394972i
$769$	2.42858	−	6.67247i	0.0875768	−	0.240615i	−0.888171	−	0.459513i	$-0.848024\pi$
$769$	2.42858	−	6.67247i	0.0875768	−	0.240615i	0.975748	+	0.218898i	$0.0702461\pi$
$770$	−27.5807	−	14.7619i	−0.993939	−	0.531982i
$771$	18.1174	−	6.88414i	0.652483	−	0.247926i
$772$	1.80134	−	0.655635i	0.0648317	−	0.0235968i
$773$	−1.65044			−0.0593622			−0.0296811	−	0.999559i	$-0.509449\pi$
$773$	−1.65044			−0.0593622			−0.0296811	+	0.999559i	$0.509449\pi$
$774$	−8.56814	−	4.63067i	−0.307976	−	0.166446i
$775$			33.6528i			1.20885i
$776$	−1.21002	−	1.01533i	−0.0434373	−	0.0364483i
$777$	3.43923	+	0.443711i	0.123382	+	0.0159180i
$778$	0.949123	+	5.38275i	0.0340277	+	0.192981i
$779$	0.782112	−	2.14884i	0.0280221	−	0.0769900i
$780$	−11.6875	−	13.5374i	−0.418478	−	0.484718i
$781$	1.22577	−	6.95169i	0.0438615	−	0.248751i
$782$	−20.0528	−	34.7325i	−0.717088	−	1.24203i
$783$	15.4518	−	20.0765i	0.552204	−	0.717476i
$784$	−5.06193	+	4.83497i	−0.180783	+	0.172677i
$785$	−0.326270	−	0.896421i	−0.0116451	−	0.0319946i
$786$	3.41833	+	3.95941i	0.121928	+	0.141228i
$787$	23.4455	−	4.13407i	0.835741	−	0.147364i	0.260630	−	0.965439i	$-0.416070\pi$
$787$	23.4455	−	4.13407i	0.835741	−	0.147364i	0.575111	+	0.818075i	$0.304959\pi$
$788$	−4.27511	+	11.7458i	−0.152294	+	0.418425i
$789$	−24.2470	+	14.4573i	−0.863217	+	0.514692i
$790$	0.285740	−	0.340532i	0.0101662	−	0.0121156i
$791$	27.6517	−	11.0840i	0.983180	−	0.394103i
$792$	−8.07193	+	7.16935i	−0.286823	+	0.254752i
$793$	22.6151	−	39.1705i	0.803085	−	1.39098i
$794$	23.8361	+	20.0009i	0.845911	+	0.709804i
$795$	16.5311	+	43.5059i	0.586297	+	1.54299i
$796$	13.1222	−	2.31380i	0.465105	−	0.0820106i
$797$	19.0250	+	6.92454i	0.673901	+	0.245280i	0.656226	−	0.754564i	$-0.272152\pi$
$797$	19.0250	+	6.92454i	0.673901	+	0.245280i	0.0176742	+	0.999844i	$0.494374\pi$
$798$	8.09721	−	25.9153i	0.286638	−	0.917391i
$799$	−4.11892	+	23.3596i	−0.145717	+	0.826402i
$800$	−5.01857	−	2.89747i	−0.177433	−	0.102441i
$801$	39.7244	−	15.7368i	1.40359	−	0.556032i
$802$	−6.83730	−	11.8425i	−0.241433	−	0.418175i
$803$	−9.90080	+	56.1502i	−0.349392	+	1.98150i
$804$	2.04878	−	3.66668i	0.0722549	−	0.129314i
$805$	31.0034	+	49.9193i	1.09273	+	1.75943i
$806$	−11.7314	−	13.9809i	−0.413220	−	0.492456i
$807$	−26.2039	−	9.12235i	−0.922420	−	0.321122i
$808$	−3.10992	−	0.548363i	−0.109407	−	0.0192913i
$809$	−33.5775	−	19.3860i	−1.18052	−	0.681575i	−0.224388	−	0.974500i	$-0.572038\pi$
$809$	−33.5775	−	19.3860i	−1.18052	−	0.681575i	−0.956136	+	0.292925i	$0.905372\pi$
$810$	−20.2503	−	21.5479i	−0.711524	−	0.757118i
$811$			21.7970i			0.765396i	0.923873	+	0.382698i	$0.125005\pi$
$811$			21.7970i			0.765396i	−0.923873	+	0.382698i	$0.874995\pi$
$812$	−9.60985	+	8.60523i	−0.337239	+	0.301984i
$813$	−4.22129	−	4.88947i	−0.148047	−	0.171481i
$814$	−2.55898	−	0.931394i	−0.0896923	−	0.0326453i
$815$	−51.5536	−	18.7640i	−1.80584	−	0.657273i
$816$	−5.26252	−	8.82604i	−0.184225	−	0.308973i
$817$	−18.9424	−	3.34006i	−0.662712	−	0.116854i
$818$	7.94533	−	13.7617i	0.277802	−	0.481167i
$819$	5.80380	+	24.2602i	0.202801	+	0.847719i
$820$	0.634051	+	1.09821i	0.0221420	+	0.0383511i
$821$	−1.15335	−	3.16880i	−0.0402522	−	0.110592i	0.917938	−	0.396723i	$-0.129853\pi$
$821$	−1.15335	−	3.16880i	−0.0402522	−	0.110592i	−0.958190	+	0.286131i	$0.907631\pi$
$822$	14.0936	+	11.4923i	0.491572	+	0.400839i
$823$	−29.0512	+	24.3769i	−1.01266	+	0.849725i	−0.988688	−	0.149988i	$-0.952077\pi$
$823$	−29.0512	+	24.3769i	−1.01266	+	0.849725i	−0.0239749	+	0.999713i	$0.507632\pi$
$824$	−3.28342	−	18.6212i	−0.114383	−	0.648700i
$825$	−22.8266	+	27.9936i	−0.794720	+	0.974613i
$826$	−21.1241	+	18.9157i	−0.735000	+	0.658163i
$827$	32.4938	−	18.7603i	1.12992	−	0.652360i	0.186006	−	0.982549i	$-0.440446\pi$
$827$	32.4938	−	18.7603i	1.12992	−	0.652360i	0.943915	+	0.330188i	$0.107112\pi$
$828$	19.8651	−	4.08167i	0.690360	−	0.141848i
$829$	5.12381	−	2.95824i	0.177957	−	0.102744i	−0.408375	−	0.912814i	$-0.633904\pi$
$829$	5.12381	−	2.95824i	0.177957	−	0.102744i	0.586333	+	0.810070i	$0.300571\pi$
$830$	6.45245	+	17.7280i	0.223968	+	0.615347i
$831$	−10.7848	−	18.0877i	−0.374120	−	0.627455i
$832$	3.09500	−	0.545732i	0.107300	−	0.0189198i
$833$	−38.0309	+	16.6835i	−1.31769	+	0.578051i
$834$	4.20092	+	22.0106i	0.145466	+	0.762164i
$835$	50.4620	+	42.3426i	1.74631	+	1.46533i
$836$	−10.6608	+	18.4650i	−0.368710	+	0.638625i
$837$	−20.3538	−	22.2774i	−0.703530	−	0.770021i
$838$	−18.2969	+	10.5637i	−0.632057	+	0.364918i
$839$	3.44126	−	1.25252i	0.118806	−	0.0432417i	−0.281933	−	0.959434i	$-0.590976\pi$
$839$	3.44126	−	1.25252i	0.118806	−	0.0432417i	0.400739	+	0.916192i	$0.368753\pi$
$840$	8.12268	+	12.6774i	0.280259	+	0.437411i
$841$	4.00542	−	3.36095i	0.138118	−	0.115895i
$842$	20.3802	+	24.2881i	0.702347	+	0.837025i
$843$	−0.742968	−	52.8466i	−0.0255892	−	1.82013i
$844$	10.3084	−	3.75197i	0.354831	−	0.129148i
$845$	−10.2614			−0.353002
$846$	−10.5519	−	5.70280i	−0.362782	−	0.196066i
$847$	−1.92018	−	4.79033i	−0.0659782	−	0.164598i
$848$	−8.05403	−	1.42014i	−0.276577	−	0.0487679i
$849$	7.89819	−	9.68603i	0.271065	−	0.332424i
$850$	−22.0991	−	26.3366i	−0.757991	−	0.903339i
$851$	3.28816	+	3.91867i	0.112717	+	0.134330i
$852$	−2.14704	+	2.63305i	−0.0735565	+	0.0902067i
$853$	15.8877	+	2.80143i	0.543984	+	0.0959191i	0.438886	−	0.898543i	$-0.355373\pi$
$853$	15.8877	+	2.80143i	0.543984	+	0.0959191i	0.105098	+	0.994462i	$0.466484\pi$
$854$	−23.5249	+	29.9412i	−0.805005	+	1.02457i
$855$	−51.3758	−	27.7661i	−1.75701	−	0.949581i
$856$	−10.8501			−0.370849
$857$	10.2777	−	3.74077i	0.351079	−	0.127782i	−0.160460	−	0.987042i	$-0.551298\pi$
$857$	10.2777	−	3.74077i	0.351079	−	0.127782i	0.511539	+	0.859260i	$0.329076\pi$
$858$	−0.275375	−	19.5872i	−0.00940115	−	0.668695i
$859$	−21.5981	−	25.7397i	−0.736919	−	0.878226i	0.259238	−	0.965813i	$-0.416529\pi$
$859$	−21.5981	−	25.7397i	−0.736919	−	0.878226i	−0.996157	+	0.0875877i	$0.972084\pi$
$860$	8.17101	−	6.85629i	0.278629	−	0.233798i
$861$	−0.0817328	−	1.76681i	−0.00278545	−	0.0602127i
$862$	−15.3934	+	5.60275i	−0.524302	+	0.190830i
$863$	−35.0893	+	20.2588i	−1.19445	+	0.689617i	−0.959313	−	0.282344i	$-0.908888\pi$
$863$	−35.0893	+	20.2588i	−1.19445	+	0.689617i	−0.235139	+	0.971962i	$0.575555\pi$
$864$	5.07462	−	1.11725i	0.172642	−	0.0380096i
$865$	−9.52299	+	16.4943i	−0.323791	+	0.560823i
$866$	−15.6632	−	13.1430i	−0.532258	−	0.446618i
$867$	−5.90909	−	30.9605i	−0.200683	−	1.05147i
$868$	8.10630	+	13.0522i	0.275146	+	0.443019i
$869$	0.479502	−	0.0845492i	0.0162660	−	0.00286814i
$870$	14.2093	+	23.8312i	0.481741	+	0.807952i
$871$	2.60660	+	7.16157i	0.0883213	+	0.242661i
$872$	1.55391	−	0.897149i	0.0526219	−	0.0303813i
$873$	4.64176	−	0.953738i	0.157100	−	0.0322792i
$874$	34.6858	−	20.0259i	1.17327	−	0.677386i
$875$	4.60978	+	5.14795i	0.155839	+	0.174032i
$876$	17.3421	−	21.2677i	0.585936	−	0.718568i
$877$	6.62852	+	37.5922i	0.223829	+	1.26940i	0.864911	+	0.501926i	$0.167375\pi$
$877$	6.62852	+	37.5922i	0.223829	+	1.26940i	−0.641082	+	0.767473i	$0.721514\pi$
$878$	−29.8906	+	25.0812i	−1.00876	+	0.846450i
$879$	27.0785	+	22.0804i	0.913335	+	0.744752i
$880$	−4.04396	−	11.1107i	−0.136322	−	0.374541i
$881$	8.28919	+	14.3573i	0.279270	+	0.483709i	0.971203	−	0.238252i	$-0.0765743\pi$
$881$	8.28919	+	14.3573i	0.279270	+	0.483709i	−0.691934	+	0.721961i	$0.743241\pi$
$882$	−1.93877	−	20.9103i	−0.0652819	−	0.704087i
$883$	11.1658	−	19.3397i	0.375758	−	0.650832i	−0.614682	−	0.788775i	$-0.710716\pi$
$883$	11.1658	−	19.3397i	0.375758	−	0.650832i	0.990440	+	0.137943i	$0.0440490\pi$
$884$	18.3619	+	3.23770i	0.617577	+	0.108896i
$885$	31.2345	+	52.3849i	1.04994	+	1.76090i
$886$	17.7782	+	6.47072i	0.597269	+	0.217388i
$887$	−12.9256	−	4.70453i	−0.433999	−	0.157963i	0.115776	−	0.993275i	$-0.463064\pi$
$887$	−12.9256	−	4.70453i	−0.433999	−	0.157963i	−0.549775	+	0.835313i	$0.685287\pi$
$888$	0.856521	+	0.992098i	0.0287430	+	0.0332926i
$889$	−0.854398	+	2.60528i	−0.0286556	+	0.0873782i
$890$			46.7952i			1.56858i
$891$	−1.82030	−	32.3371i	−0.0609823	−	1.08333i
$892$	0.244098	+	0.140930i	0.00817300	+	0.00471868i
$893$	−23.3282	−	4.11338i	−0.780647	−	0.137649i
$894$	2.36164	+	0.822157i	0.0789851	+	0.0274971i
$895$	11.3676	+	13.5474i	0.379977	+	0.452839i
$896$	−2.64438	+	0.0850968i	−0.0883426	+	0.00284288i
$897$	−17.9489	+	32.1230i	−0.599298	+	1.07256i
$898$	−0.247004	+	1.40083i	−0.00824262	+	0.0467462i
$899$	14.1569	+	24.5205i	0.472160	+	0.817805i
$900$	16.1628	−	6.40286i	0.538759	−	0.213429i
$901$	−42.0194	−	24.2599i	−1.39987	−	0.808215i
$902$	−0.241190	+	1.36786i	−0.00803076	+	0.0455447i
$903$	−14.5161	+	3.25768i	−0.483067	+	0.108409i
$904$	10.5807	+	3.85106i	0.351908	+	0.128084i
$905$	−22.2806	+	3.92867i	−0.740632	+	0.130593i
$906$	2.49597	+	6.56880i	0.0829231	+	0.218234i
$907$	27.6469	+	23.1985i	0.918001	+	0.770295i	0.973624	−	0.228157i	$-0.0732700\pi$
$907$	27.6469	+	23.1985i	0.918001	+	0.770295i	−0.0556230	+	0.998452i	$0.517714\pi$
$908$	5.07029	−	8.78200i	0.168264	−	0.291441i
$909$	7.08321	−	6.29118i	0.234935	−	0.208665i
$910$	−27.0428	−	3.87614i	−0.896461	−	0.128493i
$911$	28.8281	−	34.3560i	0.955117	−	1.13826i	−0.0351922	−	0.999381i	$-0.511204\pi$
$911$	28.8281	−	34.3560i	0.955117	−	1.13826i	0.990309	−	0.138883i	$-0.0443512\pi$
$912$	8.81418	−	5.25544i	0.291867	−	0.174025i
$913$	−7.06740	+	19.4175i	−0.233897	+	0.642627i
$914$	32.8814	−	5.79788i	1.08762	−	0.191777i
$915$	53.5218	+	61.9937i	1.76938	+	2.04945i
$916$	5.45128	+	14.9773i	0.180115	+	0.494863i
$917$	7.90944	+	1.13369i	0.261193	+	0.0374377i
$918$	30.5579	+	4.06840i	1.00856	+	0.134277i
$919$	−19.3065	−	33.4398i	−0.636862	−	1.10308i	−0.986117	−	0.166050i	$-0.946899\pi$
$919$	−19.3065	−	33.4398i	−0.636862	−	1.10308i	0.349255	−	0.937028i	$-0.386435\pi$
$920$	−3.85682	+	21.8731i	−0.127155	+	0.721135i
$921$	−28.0940	−	32.5409i	−0.925727	−	1.07226i
$922$	−1.81752	+	4.99360i	−0.0598568	+	0.164455i
$923$	−1.07047	−	6.07091i	−0.0352348	−	0.199827i
$924$	−2.11013	+	16.3557i	−0.0694181	+	0.538064i
$925$	3.35923	+	2.81873i	0.110451	+	0.0926791i
$926$		−	22.9901i		−	0.755500i
$927$	49.9036	+	26.9705i	1.63905	+	0.885826i
$928$	−4.87558			−0.160049
$929$	20.9045	−	7.60862i	0.685855	−	0.249631i	0.0244956	−	0.999700i	$-0.492202\pi$
$929$	20.9045	−	7.60862i	0.685855	−	0.249631i	0.661359	+	0.750069i	$0.269980\pi$
$930$	30.8929	−	11.7385i	1.01302	−	0.384920i
$931$	−16.6611	−	37.9797i	−0.546046	−	1.24474i
$932$	−9.16742	+	25.1873i	−0.300289	+	0.825037i
$933$	−7.64016	−	6.22995i	−0.250128	−	0.203959i
$934$	−23.4657	+	27.9653i	−0.767822	+	0.915054i
$935$		−	70.1476i		−	2.29407i
$936$	−4.48271	+	8.29438i	−0.146522	+	0.271110i
$937$	−36.0663	−	20.8229i	−1.17824	−	0.680255i	−0.222630	−	0.974903i	$-0.571464\pi$
$937$	−36.0663	−	20.8229i	−1.17824	−	0.680255i	−0.955606	+	0.294648i	$0.904798\pi$
$938$	−1.31677	−	6.27940i	−0.0429941	−	0.205030i
$939$	−5.04535	+	3.00828i	−0.164649	+	0.0981716i
$940$	10.0628	−	8.44372i	0.328213	−	0.275404i
$941$	−5.83857	−	33.1122i	−0.190332	−	1.07943i	−0.918911	−	0.394464i	$-0.870930\pi$
$941$	−5.83857	−	33.1122i	−0.190332	−	1.07943i	0.728579	−	0.684961i	$-0.240181\pi$
$942$	−0.380657	+	0.328638i	−0.0124025	+	0.0107076i
$943$	1.67711	−	1.99870i	0.0546141	−	0.0650865i
$944$	−10.7174			−0.348820
$945$	−44.9425	−	4.51791i	−1.46198	−	0.146968i
$946$	11.6831			0.379849
$947$	−0.519822	+	0.619500i	−0.0168919	+	0.0201310i	−0.774424	−	0.632667i	$-0.781960\pi$
$947$	−0.519822	+	0.619500i	−0.0168919	+	0.0201310i	0.757532	+	0.652798i	$0.226405\pi$
$948$	−0.221317	−	0.0770470i	−0.00718803	−	0.00250237i
$949$	8.64637	+	49.0360i	0.280673	+	1.59178i
$950$	26.3012	−	22.0693i	0.853324	−	0.716024i
$951$	−0.310130	−	22.0593i	−0.0100567	−	0.715321i
$952$	−14.9150	−	4.89137i	−0.483399	−	0.158530i
$953$	26.1971	+	15.1249i	0.848606	+	0.489943i	0.860180	−	0.509990i	$-0.170351\pi$
$953$	26.1971	+	15.1249i	0.848606	+	0.489943i	−0.0115741	+	0.999933i	$0.503684\pi$
$954$	18.3440	−	16.2928i	0.593909	−	0.527500i
$955$			3.36472i			0.108880i
$956$	13.3347	−	15.8917i	0.431276	−	0.513975i
$957$	−4.85595	+	29.9996i	−0.156970	+	0.969751i
$958$	4.87496	−	13.3938i	0.157503	−	0.432735i
$959$	27.7640	−	0.893453i	0.896548	−	0.0288511i
$960$	−0.909311	+	5.61765i	−0.0293479	+	0.181309i
$961$	2.56016	−	0.931822i	0.0825858	−	0.0300588i
$962$	−2.37818			−0.0766757
$963$	20.2137	−	25.5133i	0.651377	−	0.822155i
$964$		−	24.0267i		−	0.773847i
$965$	−4.82475	−	4.04844i	−0.155314	−	0.130324i
$966$	18.7946	−	24.6256i	0.604707	−	0.792316i
$967$	−5.06837	−	28.7441i	−0.162988	−	0.924349i	−0.951115	−	0.308837i	$-0.900060\pi$
$967$	−5.06837	−	28.7441i	−0.162988	−	0.924349i	0.788127	−	0.615512i	$-0.211051\pi$
$968$	0.667150	−	1.83298i	0.0214430	−	0.0589142i
$969$	59.8028	−	11.4139i	1.92114	−	0.366667i
$970$	−0.901199	+	5.11095i	−0.0289357	+	0.164103i
$971$	−23.8211	−	41.2593i	−0.764454	−	1.32407i	−0.940535	−	0.339697i	$-0.889675\pi$
$971$	−23.8211	−	41.2593i	−0.764454	−	1.32407i	0.176081	−	0.984376i	$-0.443658\pi$
$972$	−6.82685	+	14.0141i	−0.218971	+	0.449502i
$973$	26.9147	+	21.1470i	0.862847	+	0.677942i
$974$	−2.55601	−	7.02258i	−0.0818999	−	0.225018i
$975$	−10.3710	+	29.7905i	−0.332137	+	0.954060i
$976$	−14.1733	+	2.49913i	−0.453676	+	0.0799953i
$977$	−6.77212	+	18.6062i	−0.216659	+	0.595266i	−0.999641	−	0.0267779i	$-0.991475\pi$
$977$	−6.77212	+	18.6062i	−0.216659	+	0.595266i	0.782982	+	0.622044i	$0.213698\pi$
$978$	0.406568	+	28.9188i	0.0130006	+	0.924722i
$979$	−32.9461	+	39.2636i	−1.05296	+	1.25487i
$980$	22.0730	+	6.46032i	0.705095	+	0.206367i
$981$	−0.785333	+	5.32530i	−0.0250738	+	0.170024i
$982$	−8.33799	+	14.4418i	−0.266076	+	0.460857i
$983$	20.7795	+	17.4360i	0.662762	+	0.556124i	0.910913	−	0.412598i	$-0.135378\pi$
$983$	20.7795	+	17.4360i	0.662762	+	0.556124i	−0.248151	+	0.968721i	$0.579823\pi$
$984$	0.422466	−	0.518095i	0.0134677	−	0.0165163i
$985$	40.4442	−	7.13141i	1.28866	−	0.227226i
$986$	−27.1812	−	9.89317i	−0.865627	−	0.315063i
$987$	−17.8771	+	4.01193i	−0.569033	+	0.127701i
$988$	−3.23335	+	18.3372i	−0.102866	+	0.583384i
$989$	−19.0060	−	10.9731i	−0.604356	−	0.348925i
$990$	33.6600	+	11.1900i	1.06978	+	0.355643i
$991$	12.7338	+	22.0557i	0.404504	+	0.700621i	0.994264	−	0.106958i	$-0.0341109\pi$
$991$	12.7338	+	22.0557i	0.404504	+	0.700621i	−0.589760	+	0.807579i	$0.700778\pi$
$992$	−1.00842	+	5.71905i	−0.0320175	+	0.181580i
$993$	6.42714	−	0.0903589i	0.203959	−	0.00286745i
$994$	0.166919	+	5.18702i	0.00529436	+	0.164522i
$995$	−28.1406	−	33.5367i	−0.892118	−	1.06318i
$996$	7.52802	−	6.49927i	0.238535	−	0.205937i
$997$	26.6548	+	4.69997i	0.844167	+	0.148849i	0.578974	−	0.815346i	$-0.303453\pi$
$997$	26.6548	+	4.69997i	0.844167	+	0.148849i	0.265193	+	0.964195i	$0.414564\pi$
$998$	−6.95234	−	4.01394i	−0.220072	−	0.127059i
$999$	−3.92855	+	0.165781i	−0.124294	+	0.00524508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.7	yes	144
7.5	odd	6		378.2.ba.a.47.14	✓	144
27.23	odd	18		378.2.ba.a.185.14	yes	144
189.131	even	18	inner	378.2.bf.a.131.7	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.14	✓	144	7.5	odd	6
378.2.ba.a.185.14	yes	144	27.23	odd	18
378.2.bf.a.101.7	yes	144	1.1	even	1	trivial
378.2.bf.a.131.7	yes	144	189.131	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(-0.324716 - 1.70134i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-2.51689 + 2.11192i) q^{5} +(1.51203 + 0.844853i) q^{6} +(2.58943 - 0.542996i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-2.78912 + 1.10491i) q^{9} -3.28557i q^{10} +(2.31320 - 2.75676i) q^{11} +(-1.61911 + 0.615218i) q^{12} +(1.07488 - 2.95321i) q^{13} +(-1.24850 + 2.33265i) q^{14} +(4.41037 + 3.59631i) q^{15} +(-0.939693 + 0.342020i) q^{16} -5.93277 q^{17} +(0.946404 - 2.84681i) q^{18} -5.92479i q^{19} +(2.51689 + 2.11192i) q^{20} +(-1.76465 - 4.22918i) q^{21} +(0.624907 + 3.54402i) q^{22} +(2.31207 - 6.35235i) q^{23} +(0.569458 - 1.63576i) q^{24} +(1.00628 - 5.70690i) q^{25} +(1.57137 + 2.72170i) q^{26} +(2.78549 + 4.38646i) q^{27} +(-0.984397 - 2.45580i) q^{28} +(-1.66755 - 4.58155i) q^{29} +(-5.58987 + 1.06688i) q^{30} +(-5.71905 + 1.00842i) q^{31} +(0.342020 - 0.939693i) q^{32} +(-5.44132 - 3.04037i) q^{33} +(3.81351 - 4.54476i) q^{34} +(-5.37055 + 6.83534i) q^{35} +(1.57245 + 2.55488i) q^{36} +(-0.378361 + 0.655341i) q^{37} +(4.53865 + 3.80838i) q^{38} +(-5.37345 - 0.869783i) q^{39} +(-3.23565 + 0.570532i) q^{40} +(0.362685 + 0.132007i) q^{41} +(4.37404 + 1.36667i) q^{42} +(0.563744 - 3.19715i) q^{43} +(-3.11656 - 1.79935i) q^{44} +(4.68643 - 8.67132i) q^{45} +(3.38002 + 5.85436i) q^{46} +(0.694267 - 3.93738i) q^{47} +(0.887026 + 1.48768i) q^{48} +(6.41031 - 2.81210i) q^{49} +(3.72492 + 4.43918i) q^{50} +(1.92647 + 10.0937i) q^{51} +(-3.09500 - 0.545732i) q^{52} +(7.08260 + 4.08914i) q^{53} +(-5.15070 - 0.685750i) q^{54} +11.8238i q^{55} +(2.51401 + 0.824467i) q^{56} +(-10.0801 + 1.92388i) q^{57} +(4.58155 + 1.66755i) q^{58} +(10.0710 + 3.66555i) q^{59} +(2.77582 - 4.96786i) q^{60} +(14.1733 + 2.49913i) q^{61} +(2.90364 - 5.02925i) q^{62} +(-6.62227 + 4.37556i) q^{63} +(0.500000 + 0.866025i) q^{64} +(3.53159 + 9.70297i) q^{65} +(5.82667 - 2.21398i) q^{66} +(-1.85767 + 1.55877i) q^{67} +(1.03021 + 5.84263i) q^{68} +(-11.5583 - 1.87090i) q^{69} +(-1.78405 - 8.50775i) q^{70} +(1.69873 - 0.980762i) q^{71} +(-2.96790 - 0.437683i) q^{72} +(-13.7210 + 7.92182i) q^{73} +(-0.258814 - 0.711086i) q^{74} +(-10.0361 + 0.141098i) q^{75} +(-5.83478 + 1.02883i) q^{76} +(4.49296 - 8.39450i) q^{77} +(4.12028 - 3.55722i) q^{78} +(0.103645 + 0.0869684i) q^{79} +(1.64278 - 2.84538i) q^{80} +(6.55837 - 6.16343i) q^{81} +(-0.334253 + 0.192981i) q^{82} +(-5.39571 + 1.96388i) q^{83} +(-3.85851 + 2.47223i) q^{84} +(14.9321 - 12.5295i) q^{85} +(2.08679 + 2.48694i) q^{86} +(-7.25329 + 4.32477i) q^{87} +(3.38167 - 1.23083i) q^{88} -14.2427 q^{89} +(3.63024 + 9.16383i) q^{90} +(1.17975 - 8.23080i) q^{91} +(-6.65733 - 1.17387i) q^{92} +(3.57274 + 9.40260i) q^{93} +(2.56994 + 3.06274i) q^{94} +(12.5127 + 14.9120i) q^{95} +(-1.70980 - 0.276759i) q^{96} +(-1.55558 - 0.274290i) q^{97} +(-1.96627 + 6.71817i) q^{98} +(-3.40582 + 10.2448i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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