LMFDB - Embedded newform 855.2.i.d.286.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(286,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 0]))

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

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

chi := DirichletCharacter("855.286");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$46$
Relative dimension:	$23$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			286.18
Character	$\chi$	$=$	855.286
Dual form			855.2.i.d.571.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.949697 - 1.64492i) q^{2} +(1.57344 - 0.724068i) q^{3} +(-0.803848 - 1.39231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.303258 - 3.27584i) q^{6} +(2.16725 - 3.75380i) q^{7} +0.745138 q^{8} +(1.95145 - 2.27856i) q^{9} +O(q^{10})$	\(q+(0.949697 - 1.64492i) q^{2} +(1.57344 - 0.724068i) q^{3} +(-0.803848 - 1.39231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.303258 - 3.27584i) q^{6} +(2.16725 - 3.75380i) q^{7} +0.745138 q^{8} +(1.95145 - 2.27856i) q^{9} +1.89939 q^{10} +(-2.70926 + 4.69257i) q^{11} +(-2.27294 - 1.60867i) q^{12} +(0.848304 + 1.46931i) q^{13} +(-4.11647 - 7.12994i) q^{14} +(1.41378 + 1.00061i) q^{15} +(2.31535 - 4.01031i) q^{16} -5.99511 q^{17} +(-1.89477 - 5.37393i) q^{18} +1.00000 q^{19} +(0.803848 - 1.39231i) q^{20} +(0.692050 - 7.47563i) q^{21} +(5.14594 + 8.91304i) q^{22} +(2.89474 + 5.01385i) q^{23} +(1.17243 - 0.539531i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.22253 q^{26} +(1.42066 - 4.99817i) q^{27} -6.96858 q^{28} +(0.922912 - 1.59853i) q^{29} +(2.98859 - 1.37529i) q^{30} +(-1.33877 - 2.31882i) q^{31} +(-3.65263 - 6.32654i) q^{32} +(-0.865122 + 9.34518i) q^{33} +(-5.69354 + 9.86150i) q^{34} +4.33451 q^{35} +(-4.74113 - 0.885399i) q^{36} -10.5086 q^{37} +(0.949697 - 1.64492i) q^{38} +(2.39864 + 1.69764i) q^{39} +(0.372569 + 0.645308i) q^{40} +(5.21753 + 9.03702i) q^{41} +(-11.6396 - 8.23795i) q^{42} +(-2.72440 + 4.71880i) q^{43} +8.71133 q^{44} +(2.94902 + 0.550725i) q^{45} +10.9965 q^{46} +(1.48315 - 2.56889i) q^{47} +(0.739340 - 7.98647i) q^{48} +(-5.89399 - 10.2087i) q^{49} +(0.949697 + 1.64492i) q^{50} +(-9.43297 + 4.34087i) q^{51} +(1.36382 - 2.36220i) q^{52} -7.76809 q^{53} +(-6.87241 - 7.08363i) q^{54} -5.41851 q^{55} +(1.61490 - 2.79710i) q^{56} +(1.57344 - 0.724068i) q^{57} +(-1.75297 - 3.03624i) q^{58} +(-3.73704 - 6.47275i) q^{59} +(0.256686 - 2.77276i) q^{60} +(-0.736384 + 1.27546i) q^{61} -5.08570 q^{62} +(-4.32396 - 12.2636i) q^{63} -4.61415 q^{64} +(-0.848304 + 1.46931i) q^{65} +(14.5505 + 10.2981i) q^{66} +(-1.05258 - 1.82313i) q^{67} +(4.81916 + 8.34703i) q^{68} +(8.18508 + 5.79301i) q^{69} +(4.11647 - 7.12994i) q^{70} +9.51253 q^{71} +(1.45410 - 1.69784i) q^{72} -2.22539 q^{73} +(-9.97997 + 17.2858i) q^{74} +(-0.159660 + 1.72468i) q^{75} +(-0.803848 - 1.39231i) q^{76} +(11.7433 + 20.3400i) q^{77} +(5.07047 - 2.33333i) q^{78} +(3.20613 - 5.55319i) q^{79} +4.63070 q^{80} +(-1.38368 - 8.89300i) q^{81} +19.8203 q^{82} +(-7.55133 + 13.0793i) q^{83} +(-10.9647 + 5.04573i) q^{84} +(-2.99756 - 5.19192i) q^{85} +(5.17470 + 8.96285i) q^{86} +(0.294705 - 3.18345i) q^{87} +(-2.01877 + 3.49661i) q^{88} -3.09745 q^{89} +(3.70657 - 4.32788i) q^{90} +7.35397 q^{91} +(4.65387 - 8.06074i) q^{92} +(-3.78546 - 2.67917i) q^{93} +(-2.81709 - 4.87934i) q^{94} +(0.500000 + 0.866025i) q^{95} +(-10.3280 - 7.30970i) q^{96} +(-6.93187 + 12.0064i) q^{97} -22.3900 q^{98} +(5.40533 + 15.3305i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.949697	−	1.64492i	0.671537	−	1.16314i	−0.305931	−	0.952054i	$-0.598968\pi$
$2$	0.949697	−	1.64492i	0.671537	−	1.16314i	0.977468	−	0.211083i	$-0.0676990\pi$
$3$	1.57344	−	0.724068i	0.908428	−	0.418041i
$3$	1.57344	−	0.724068i	0.908428	−	0.418041i
$4$	−0.803848	−	1.39231i	−0.401924	−	0.696153i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	0.303258	−	3.27584i	0.123805	−	1.33736i
$7$	2.16725	−	3.75380i	0.819145	−	1.41880i	−0.0871675	−	0.996194i	$-0.527782\pi$
$7$	2.16725	−	3.75380i	0.819145	−	1.41880i	0.906313	−	0.422608i	$-0.138885\pi$
$8$	0.745138			0.263446
$9$	1.95145	−	2.27856i	0.650484	−	0.759520i
$10$	1.89939			0.600641
$11$	−2.70926	+	4.69257i	−0.816871	+	1.41486i	0.0911049	+	0.995841i	$0.470960\pi$
$11$	−2.70926	+	4.69257i	−0.816871	+	1.41486i	−0.907976	+	0.419021i	$0.862373\pi$
$12$	−2.27294	−	1.60867i	−0.656140	−	0.464384i
$13$	0.848304	+	1.46931i	0.235277	+	0.407512i	0.959353	−	0.282208i	$-0.0910668\pi$
$13$	0.848304	+	1.46931i	0.235277	+	0.407512i	−0.724076	+	0.689720i	$0.757734\pi$
$14$	−4.11647	−	7.12994i	−1.10017	−	1.90556i
$15$	1.41378	+	1.00061i	0.365037	+	0.258356i
$16$	2.31535	−	4.01031i	0.578838	−	1.00258i
$17$	−5.99511			−1.45403			−0.727014	−	0.686623i	$-0.759092\pi$
$17$	−5.99511			−1.45403			−0.727014	+	0.686623i	$0.759092\pi$
$18$	−1.89477	−	5.37393i	−0.446602	−	1.26665i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	0.803848	−	1.39231i	0.179746	−	0.311329i
$21$	0.692050	−	7.47563i	0.151018	−	1.63132i
$22$	5.14594	+	8.91304i	1.09712	+	1.90027i
$23$	2.89474	+	5.01385i	0.603596	+	1.04546i	0.992272	+	0.124084i	$0.0395993\pi$
$23$	2.89474	+	5.01385i	0.603596	+	1.04546i	−0.388676	+	0.921375i	$0.627067\pi$
$24$	1.17243	−	0.539531i	0.239322	−	0.110131i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.22253			0.631990
$27$	1.42066	−	4.99817i	0.273407	−	0.961898i
$28$	−6.96858			−1.31694
$29$	0.922912	−	1.59853i	0.171380	−	0.296840i	−0.767522	−	0.641022i	$-0.778511\pi$
$29$	0.922912	−	1.59853i	0.171380	−	0.296840i	0.938903	+	0.344183i	$0.111844\pi$
$30$	2.98859	−	1.37529i	0.545639	−	0.251093i
$31$	−1.33877	−	2.31882i	−0.240450	−	0.416471i	0.720393	−	0.693567i	$-0.243962\pi$
$31$	−1.33877	−	2.31882i	−0.240450	−	0.416471i	−0.960843	+	0.277095i	$0.910628\pi$
$32$	−3.65263	−	6.32654i	−0.645699	−	1.11838i
$33$	−0.865122	+	9.34518i	−0.150598	+	1.62679i
$34$	−5.69354	+	9.86150i	−0.976434	+	1.69123i
$35$	4.33451			0.732666
$36$	−4.74113	−	0.885399i	−0.790188	−	0.147567i
$37$	−10.5086			−1.72760			−0.863800	−	0.503834i	$-0.831922\pi$
$37$	−10.5086			−1.72760			−0.863800	+	0.503834i	$0.831922\pi$
$38$	0.949697	−	1.64492i	0.154061	−	0.266842i
$39$	2.39864	+	1.69764i	0.384089	+	0.271840i
$40$	0.372569	+	0.645308i	0.0589083	+	0.102032i
$41$	5.21753	+	9.03702i	0.814841	+	1.41135i	0.909442	+	0.415830i	$0.136509\pi$
$41$	5.21753	+	9.03702i	0.814841	+	1.41135i	−0.0946014	+	0.995515i	$0.530158\pi$
$42$	−11.6396	−	8.23795i	−1.79603	−	1.27114i
$43$	−2.72440	+	4.71880i	−0.415467	+	0.719610i	−0.995477	−	0.0949994i	$-0.969715\pi$
$43$	−2.72440	+	4.71880i	−0.415467	+	0.719610i	0.580011	+	0.814609i	$0.303048\pi$
$44$	8.71133			1.31328
$45$	2.94902	+	0.550725i	0.439614	+	0.0820973i
$46$	10.9965			1.62135
$47$	1.48315	−	2.56889i	0.216340	−	0.374712i	−0.737346	−	0.675515i	$-0.763921\pi$
$47$	1.48315	−	2.56889i	0.216340	−	0.374712i	0.953686	+	0.300803i	$0.0972547\pi$
$48$	0.739340	−	7.98647i	0.106715	−	1.15275i
$49$	−5.89399	−	10.2087i	−0.841998	−	1.45838i
$50$	0.949697	+	1.64492i	0.134307	+	0.232627i
$51$	−9.43297	+	4.34087i	−1.32088	+	0.607843i
$52$	1.36382	−	2.36220i	0.189127	−	0.327578i
$53$	−7.76809			−1.06703			−0.533514	−	0.845791i	$-0.679129\pi$
$53$	−7.76809			−1.06703			−0.533514	+	0.845791i	$0.679129\pi$
$54$	−6.87241	−	7.08363i	−0.935216	−	0.963960i
$55$	−5.41851			−0.730632
$56$	1.61490	−	2.79710i	0.215801	−	0.373778i
$57$	1.57344	−	0.724068i	0.208408	−	0.0959052i
$58$	−1.75297	−	3.03624i	−0.230177	−	0.398678i
$59$	−3.73704	−	6.47275i	−0.486522	−	0.842680i	0.513358	−	0.858174i	$-0.328401\pi$
$59$	−3.73704	−	6.47275i	−0.486522	−	0.842680i	−0.999880	+	0.0154941i	$0.995068\pi$
$60$	0.256686	−	2.77276i	0.0331380	−	0.357961i
$61$	−0.736384	+	1.27546i	−0.0942844	+	0.163305i	−0.909310	−	0.416120i	$-0.863390\pi$
$61$	−0.736384	+	1.27546i	−0.0942844	+	0.163305i	0.815025	+	0.579425i	$0.196723\pi$
$62$	−5.08570			−0.645884
$63$	−4.32396	−	12.2636i	−0.544768	−	1.54506i
$64$	−4.61415			−0.576769
$65$	−0.848304	+	1.46931i	−0.105219	+	0.182245i
$66$	14.5505	+	10.2981i	1.79104	+	1.26761i
$67$	−1.05258	−	1.82313i	−0.128593	−	0.222730i	0.794538	−	0.607214i	$-0.207713\pi$
$67$	−1.05258	−	1.82313i	−0.128593	−	0.222730i	−0.923132	+	0.384484i	$0.874380\pi$
$68$	4.81916	+	8.34703i	0.584409	+	1.01223i
$69$	8.18508	+	5.79301i	0.985368	+	0.697397i
$70$	4.11647	−	7.12994i	0.492012	−	0.852190i
$71$	9.51253			1.12893			0.564465	−	0.825457i	$-0.309083\pi$
$71$	9.51253			1.12893			0.564465	+	0.825457i	$0.309083\pi$
$72$	1.45410	−	1.69784i	0.171367	−	0.200093i
$73$	−2.22539			−0.260462			−0.130231	−	0.991484i	$-0.541572\pi$
$73$	−2.22539			−0.260462			−0.130231	+	0.991484i	$0.541572\pi$
$74$	−9.97997	+	17.2858i	−1.16015	+	2.00944i
$75$	−0.159660	+	1.72468i	−0.0184360	+	0.199148i
$76$	−0.803848	−	1.39231i	−0.0922077	−	0.159708i
$77$	11.7433	+	20.3400i	1.33827	+	2.31796i
$78$	5.07047	−	2.33333i	0.574117	−	0.264198i
$79$	3.20613	−	5.55319i	0.360718	−	0.624782i	−0.627361	−	0.778729i	$-0.715865\pi$
$79$	3.20613	−	5.55319i	0.360718	−	0.624782i	0.988079	+	0.153946i	$0.0491982\pi$
$80$	4.63070			0.517728
$81$	−1.38368	−	8.89300i	−0.153742	−	0.988111i
$82$	19.8203			2.18878
$83$	−7.55133	+	13.0793i	−0.828866	+	1.43564i	0.0700629	+	0.997543i	$0.477680\pi$
$83$	−7.55133	+	13.0793i	−0.828866	+	1.43564i	−0.898929	+	0.438095i	$0.855653\pi$
$84$	−10.9647	+	5.04573i	−1.19634	+	0.550534i
$85$	−2.99756	−	5.19192i	−0.325131	−	0.563143i
$86$	5.17470	+	8.96285i	0.558003	+	0.966489i
$87$	0.294705	−	3.18345i	0.0315957	−	0.341302i
$88$	−2.01877	+	3.49661i	−0.215202	+	0.372740i
$89$	−3.09745			−0.328329			−0.164165	−	0.986433i	$-0.552493\pi$
$89$	−3.09745			−0.328329			−0.164165	+	0.986433i	$0.552493\pi$
$90$	3.70657	−	4.32788i	0.390707	−	0.456199i
$91$	7.35397			0.770905
$92$	4.65387	−	8.06074i	0.485200	−	0.840391i
$93$	−3.78546	−	2.67917i	−0.392534	−	0.277817i
$94$	−2.81709	−	4.87934i	−0.290561	−	0.503266i
$95$	0.500000	+	0.866025i	0.0512989	+	0.0888523i
$96$	−10.3280	−	7.30970i	−1.05410	−	0.746043i
$97$	−6.93187	+	12.0064i	−0.703825	+	1.21906i	0.263289	+	0.964717i	$0.415193\pi$
$97$	−6.93187	+	12.0064i	−0.703825	+	1.21906i	−0.967114	+	0.254344i	$0.918141\pi$
$98$	−22.3900			−2.26173
$99$	5.40533	+	15.3305i	0.543256	+	1.54078i
$100$	1.60770			0.160770
$101$	9.68113	−	16.7682i	0.963308	−	1.66850i	0.249214	−	0.968448i	$-0.419828\pi$
$101$	9.68113	−	16.7682i	0.963308	−	1.66850i	0.714094	−	0.700050i	$-0.246839\pi$
$102$	−1.81807	+	19.6390i	−0.180015	+	1.94455i
$103$	2.07821	+	3.59957i	0.204772	+	0.354676i	0.950060	−	0.312067i	$-0.101021\pi$
$103$	2.07821	+	3.59957i	0.204772	+	0.354676i	−0.745288	+	0.666743i	$0.767688\pi$
$104$	0.632104	+	1.09484i	0.0619829	+	0.107357i
$105$	6.82011	−	3.13848i	0.665574	−	0.306284i
$106$	−7.37733	+	12.7779i	−0.716549	+	1.24110i
$107$	−6.67313			−0.645116			−0.322558	−	0.946550i	$-0.604543\pi$
$107$	−6.67313			−0.645116			−0.322558	+	0.946550i	$0.604543\pi$
$108$	−8.10098	+	2.03977i	−0.779518	+	0.196277i
$109$	8.05306			0.771343			0.385671	−	0.922636i	$-0.373970\pi$
$109$	8.05306			0.771343			0.385671	+	0.922636i	$0.373970\pi$
$110$	−5.14594	+	8.91304i	−0.490647	+	0.849825i
$111$	−16.5347	+	7.60893i	−1.56940	+	0.722208i
$112$	−10.0359	−	17.3827i	−0.948305	−	1.64251i
$113$	7.06950	+	12.2447i	0.665043	+	1.15189i	0.979274	+	0.202542i	$0.0649201\pi$
$113$	7.06950	+	12.2447i	0.665043	+	1.15189i	−0.314231	+	0.949347i	$0.601747\pi$
$114$	0.303258	−	3.27584i	0.0284027	−	0.306810i
$115$	−2.89474	+	5.01385i	−0.269936	+	0.467543i
$116$	−2.96753			−0.275528
$117$	5.00333	+	0.934365i	0.462558	+	0.0863821i
$118$	−14.1962			−1.30687
$119$	−12.9929	+	22.5044i	−1.19106	+	2.06298i
$120$	1.05346	+	0.745591i	0.0961676	+	0.0680629i
$121$	−9.18014	−	15.9005i	−0.834558	−	1.44550i
$122$	1.39868	+	2.42259i	0.126631	+	0.219331i
$123$	14.7529	+	10.4414i	1.33022	+	0.941469i
$124$	−2.15233	+	3.72795i	−0.193285	+	0.334780i
$125$	−1.00000			−0.0894427
$126$	−24.2791	−	4.53409i	−2.16295	−	0.403929i
$127$	2.01867			0.179128			0.0895640	−	0.995981i	$-0.471453\pi$
$127$	2.01867			0.179128			0.0895640	+	0.995981i	$0.471453\pi$
$128$	2.92321	−	5.06315i	0.258378	−	0.447524i
$129$	−0.869957	+	9.39741i	−0.0765955	+	0.827396i
$130$	1.61126	+	2.79079i	0.141317	+	0.244769i
$131$	10.4319	+	18.0685i	0.911436	+	1.57865i	0.812038	+	0.583605i	$0.198358\pi$
$131$	10.4319	+	18.0685i	0.911436	+	1.57865i	0.0993980	+	0.995048i	$0.468308\pi$
$132$	13.7068	−	6.30759i	1.19302	−	0.549006i
$133$	2.16725	−	3.75380i	0.187925	−	0.325495i
$134$	−3.99854			−0.345421
$135$	5.03888	−	1.26875i	0.433677	−	0.109197i
$136$	−4.46719			−0.383058
$137$	9.74618	−	16.8809i	0.832672	−	1.44223i	−0.0632398	−	0.997998i	$-0.520143\pi$
$137$	9.74618	−	16.8809i	0.832672	−	1.44223i	0.895912	−	0.444232i	$-0.146523\pi$
$138$	17.3024	−	7.96223i	1.47288	−	0.677790i
$139$	0.697648	+	1.20836i	0.0591737	+	0.102492i	0.894095	−	0.447878i	$-0.147820\pi$
$139$	0.697648	+	1.20836i	0.0591737	+	0.102492i	−0.834921	+	0.550370i	$0.814487\pi$
$140$	−3.48429	−	6.03497i	−0.294476	−	0.510048i
$141$	0.473601	−	5.11591i	0.0398844	−	0.430838i
$142$	9.03402	−	15.6474i	0.758118	−	1.31310i
$143$	−9.19309			−0.768765
$144$	−4.61944	−	13.1016i	−0.384953	−	1.09180i
$145$	1.84582			0.153287
$146$	−2.11344	+	3.66059i	−0.174910	+	0.302952i
$147$	−16.6656	−	11.7951i	−1.37456	−	0.972847i
$148$	8.44731	+	14.6312i	0.694365	+	1.20267i
$149$	5.27020	+	9.12826i	0.431752	+	0.747816i	0.997024	−	0.0770880i	$-0.0245623\pi$
$149$	5.27020	+	9.12826i	0.431752	+	0.747816i	−0.565272	+	0.824904i	$0.691229\pi$
$150$	2.68533	+	1.90055i	0.219256	+	0.155179i
$151$	3.04685	−	5.27729i	0.247949	−	0.429460i	−0.715008	−	0.699117i	$-0.753577\pi$
$151$	3.04685	−	5.27729i	0.247949	−	0.429460i	0.962957	+	0.269657i	$0.0869102\pi$
$152$	0.745138			0.0604387
$153$	−11.6992	+	13.6602i	−0.945821	+	1.10436i
$154$	44.6103			3.59480
$155$	1.33877	−	2.31882i	0.107532	−	0.186252i
$156$	0.435495	−	4.70428i	0.0348675	−	0.376644i
$157$	9.37614	+	16.2399i	0.748297	+	1.29609i	0.948638	+	0.316363i	$0.102462\pi$
$157$	9.37614	+	16.2399i	0.748297	+	1.29609i	−0.200341	+	0.979726i	$0.564205\pi$
$158$	−6.08971	−	10.5477i	−0.484472	−	0.839129i
$159$	−12.2226	+	5.62462i	−0.969319	+	0.446062i
$160$	3.65263	−	6.32654i	0.288766	−	0.500157i
$161$	25.0946			1.97773
$162$	−15.9424	−	6.16960i	−1.25255	−	0.484730i
$163$	8.82139			0.690944			0.345472	−	0.938429i	$-0.387719\pi$
$163$	8.82139			0.690944			0.345472	+	0.938429i	$0.387719\pi$
$164$	8.38820	−	14.5288i	0.655009	−	1.13451i
$165$	−8.52572	+	3.92337i	−0.663727	+	0.305434i
$166$	14.3429	+	24.8427i	1.11323	+	1.92817i
$167$	−5.77956	−	10.0105i	−0.447236	−	0.774635i	0.550969	−	0.834525i	$-0.314258\pi$
$167$	−5.77956	−	10.0105i	−0.447236	−	0.774635i	−0.998205	+	0.0598908i	$0.980925\pi$
$168$	0.515673	−	5.57037i	0.0397850	−	0.429764i
$169$	5.06076	−	8.76549i	0.389289	−	0.674269i
$170$	−11.3871			−0.873349
$171$	1.95145	−	2.27856i	0.149231	−	0.174246i
$172$	8.76001			0.667945
$173$	4.68420	−	8.11328i	0.356133	−	0.616841i	−0.631178	−	0.775638i	$-0.717428\pi$
$173$	4.68420	−	8.11328i	0.356133	−	0.616841i	0.987311	+	0.158797i	$0.0507615\pi$
$174$	−4.95665	−	3.50808i	−0.375763	−	0.265947i
$175$	2.16725	+	3.75380i	0.163829	+	0.283760i
$176$	12.5458	+	21.7299i	0.945673	+	1.63795i
$177$	−10.5667	−	7.47863i	−0.794245	−	0.562129i
$178$	−2.94164	+	5.09507i	−0.220485	+	0.381892i
$179$	−9.72778			−0.727088			−0.363544	−	0.931577i	$-0.618433\pi$
$179$	−9.72778			−0.727088			−0.363544	+	0.931577i	$0.618433\pi$
$180$	−1.60378	−	4.54863i	−0.119539	−	0.339035i
$181$	−3.48706			−0.259191			−0.129595	−	0.991567i	$-0.541368\pi$
$181$	−3.48706			−0.259191			−0.129595	+	0.991567i	$0.541368\pi$
$182$	6.98404	−	12.0967i	0.517691	−	0.896668i
$183$	−0.235143	+	2.54005i	−0.0173823	+	0.187766i
$184$	2.15698	+	3.73601i	0.159015	+	0.275422i
$185$	−5.25429	−	9.10070i	−0.386303	−	0.669097i
$186$	−8.00206	+	3.68239i	−0.586739	+	0.270006i
$187$	16.2423	−	28.1325i	1.18775	−	2.05725i
$188$	−4.76892			−0.347809
$189$	−15.6832	−	16.1652i	−1.14078	−	1.17584i
$190$	1.89939			0.137797
$191$	0.253007	−	0.438220i	0.0183069	−	0.0317085i	−0.856727	−	0.515770i	$-0.827506\pi$
$191$	0.253007	−	0.438220i	0.0183069	−	0.0317085i	0.875034	+	0.484062i	$0.160839\pi$
$192$	−7.26010	+	3.34096i	−0.523953	+	0.241113i
$193$	−0.966019	−	1.67319i	−0.0695356	−	0.120439i	0.829161	−	0.559009i	$-0.188818\pi$
$193$	−0.966019	−	1.67319i	−0.0695356	−	0.120439i	−0.898697	+	0.438570i	$0.855485\pi$
$194$	13.1664	+	22.8048i	0.945289	+	1.63729i
$195$	−0.270881	+	2.92610i	−0.0193982	+	0.209542i
$196$	−9.47574	+	16.4125i	−0.676839	+	1.17232i
$197$	−1.68488			−0.120043			−0.0600214	−	0.998197i	$-0.519117\pi$
$197$	−1.68488			−0.120043			−0.0600214	+	0.998197i	$0.519117\pi$
$198$	30.3510	+	5.66800i	2.15695	+	0.402807i
$199$	14.1721			1.00463			0.502317	−	0.864684i	$-0.332481\pi$
$199$	14.1721			1.00463			0.502317	+	0.864684i	$0.332481\pi$
$200$	−0.372569	+	0.645308i	−0.0263446	+	0.0456302i
$201$	−2.97625	−	2.10645i	−0.209928	−	0.148577i
$202$	−18.3883	−	31.8494i	−1.29379	−	2.24092i
$203$	−4.00037	−	6.92885i	−0.280771	−	0.486310i
$204$	13.6265	+	9.64418i	0.954046	+	0.675228i
$205$	−5.21753	+	9.03702i	−0.364408	+	0.631173i
$206$	7.89468			0.550049
$207$	17.0733	+	3.18842i	1.18668	+	0.221610i
$208$	7.85649			0.544750
$209$	−2.70926	+	4.69257i	−0.187403	+	0.324592i
$210$	1.31447	−	14.1992i	0.0907074	−	0.979835i
$211$	−4.21280	−	7.29679i	−0.290021	−	0.502332i	0.683793	−	0.729676i	$-0.260329\pi$
$211$	−4.21280	−	7.29679i	−0.290021	−	0.502332i	−0.973814	+	0.227344i	$0.926996\pi$
$212$	6.24436	+	10.8156i	0.428865	+	0.742815i
$213$	14.9674	−	6.88772i	1.02555	−	0.471939i
$214$	−6.33745	+	10.9768i	−0.433219	+	0.750358i
$215$	−5.44880			−0.371605
$216$	1.05859	−	3.72433i	0.0720280	−	0.253408i
$217$	−11.6058			−0.787854
$218$	7.64796	−	13.2467i	0.517985	−	0.897177i
$219$	−3.50152	+	1.61133i	−0.236611	+	0.108884i
$220$	4.35566	+	7.54423i	0.293659	+	0.508632i
$221$	−5.08568	−	8.80865i	−0.342100	−	0.592534i
$222$	−3.18681	+	34.4244i	−0.213885	+	2.31042i
$223$	−5.62330	+	9.73984i	−0.376564	+	0.652228i	−0.990560	−	0.137081i	$-0.956228\pi$
$223$	−5.62330	+	9.73984i	−0.376564	+	0.652228i	0.613996	+	0.789309i	$0.289561\pi$
$224$	−31.6647			−2.11569
$225$	0.997567	+	2.82929i	0.0665044	+	0.188619i
$226$	26.8555			1.78640
$227$	−8.72547	+	15.1130i	−0.579130	+	1.00308i	0.416450	+	0.909159i	$0.363274\pi$
$227$	−8.72547	+	15.1130i	−0.579130	+	1.00308i	−0.995579	+	0.0939234i	$0.970059\pi$
$228$	−2.27294	−	1.60867i	−0.150529	−	0.106537i
$229$	−8.13819	−	14.0958i	−0.537787	−	0.931474i	−0.999023	−	0.0441967i	$-0.985927\pi$
$229$	−8.13819	−	14.0958i	−0.537787	−	0.931474i	0.461236	−	0.887278i	$-0.347406\pi$
$230$	5.49826	+	9.52327i	0.362545	+	0.627946i
$231$	33.2050	+	23.5009i	2.18473	+	1.54624i
$232$	0.687697	−	1.19113i	0.0451495	−	0.0782013i
$233$	4.76527			0.312183			0.156092	−	0.987743i	$-0.450111\pi$
$233$	4.76527			0.312183			0.156092	+	0.987743i	$0.450111\pi$
$234$	6.28860	−	7.34273i	0.411099	−	0.480009i
$235$	2.96630			0.193500
$236$	−6.00803	+	10.4062i	−0.391090	+	0.677387i
$237$	1.02379	−	11.0591i	0.0665020	−	0.718365i
$238$	24.6787	+	42.7448i	1.59968	+	2.77073i
$239$	5.53809	+	9.59226i	0.358229	+	0.620472i	0.987665	−	0.156581i	$-0.0500472\pi$
$239$	5.53809	+	9.59226i	0.358229	+	0.620472i	−0.629436	+	0.777053i	$0.716714\pi$
$240$	7.28615	−	3.35295i	0.470319	−	0.216432i
$241$	13.7263	−	23.7746i	0.884187	−	1.53146i	0.0375440	−	0.999295i	$-0.488047\pi$
$241$	13.7263	−	23.7746i	0.884187	−	1.53146i	0.846643	−	0.532162i	$-0.178620\pi$
$242$	−34.8734			−2.24175
$243$	−8.61628	−	12.9908i	−0.552735	−	0.833357i
$244$	2.36777			0.151581
$245$	5.89399	−	10.2087i	0.376553	−	0.652209i
$246$	31.1861	−	14.3512i	1.98835	−	0.915001i
$247$	0.848304	+	1.46931i	0.0539763	+	0.0934897i
$248$	−0.997567	−	1.72784i	−0.0633456	−	0.109718i
$249$	−2.41130	+	26.0472i	−0.152810	+	1.65067i
$250$	−0.949697	+	1.64492i	−0.0600641	+	0.104034i
$251$	−24.5383			−1.54884			−0.774422	−	0.632670i	$-0.781959\pi$
$251$	−24.5383			−1.54884			−0.774422	+	0.632670i	$0.781959\pi$
$252$	−13.5988	+	15.8783i	−0.856646	+	1.00024i
$253$	−31.3704			−1.97224
$254$	1.91712	−	3.32056i	0.120291	−	0.208350i
$255$	−8.47579	−	5.99876i	−0.530774	−	0.375657i
$256$	−10.1665	−	17.6089i	−0.635405	−	1.10055i
$257$	−6.13034	−	10.6181i	−0.382400	−	0.662336i	0.609005	−	0.793167i	$-0.291569\pi$
$257$	−6.13034	−	10.6181i	−0.382400	−	0.662336i	−0.991405	+	0.130830i	$0.958236\pi$
$258$	14.6318	+	10.3557i	0.910937	+	0.644718i
$259$	−22.7748	+	39.4471i	−1.41516	+	2.45112i
$260$	2.72763			0.169161
$261$	−1.84133	−	5.22237i	−0.113976	−	0.323256i
$262$	39.6284			2.44825
$263$	1.47837	−	2.56061i	0.0911602	−	0.157894i	−0.816839	−	0.576865i	$-0.804276\pi$
$263$	1.47837	−	2.56061i	0.0911602	−	0.157894i	0.908000	+	0.418971i	$0.137609\pi$
$264$	−0.644635	+	6.96345i	−0.0396746	+	0.428571i
$265$	−3.88404	−	6.72736i	−0.238595	−	0.413258i
$266$	−4.11647	−	7.12994i	−0.252397	−	0.437164i
$267$	−4.87367	+	2.24277i	−0.298264	+	0.137255i
$268$	−1.69223	+	2.93104i	−0.103370	+	0.179041i
$269$	1.46748			0.0894740			0.0447370	−	0.998999i	$-0.485755\pi$
$269$	1.46748			0.0894740			0.0447370	+	0.998999i	$0.485755\pi$
$270$	2.69840	−	9.49350i	0.164219	−	0.577756i
$271$	−26.5659			−1.61376			−0.806882	−	0.590713i	$-0.798847\pi$
$271$	−26.5659			−1.61376			−0.806882	+	0.590713i	$0.798847\pi$
$272$	−13.8808	+	24.0422i	−0.841647	+	1.45777i
$273$	11.5711	−	5.32477i	0.700312	−	0.322270i
$274$	−18.5118	−	32.0634i	−1.11834	−	1.93702i
$275$	−2.70926	−	4.69257i	−0.163374	−	0.282973i
$276$	1.48608	−	16.0528i	0.0894514	−	0.966268i
$277$	−6.81406	+	11.8023i	−0.409417	+	0.709132i	−0.994825	−	0.101608i	$-0.967601\pi$
$277$	−6.81406	+	11.8023i	−0.409417	+	0.709132i	0.585407	+	0.810739i	$0.300935\pi$
$278$	2.65022			0.158949
$279$	−7.89610	−	1.47459i	−0.472727	−	0.0882812i
$280$	3.22981			0.193018
$281$	−4.77273	+	8.26662i	−0.284717	+	0.493145i	−0.972541	−	0.232733i	$-0.925233\pi$
$281$	−4.77273	+	8.26662i	−0.284717	+	0.493145i	0.687823	+	0.725878i	$0.258566\pi$
$282$	−7.96551	−	5.63761i	−0.474339	−	0.335715i
$283$	−4.98545	−	8.63505i	−0.296354	−	0.513300i	0.678945	−	0.734189i	$-0.262438\pi$
$283$	−4.98545	−	8.63505i	−0.296354	−	0.513300i	−0.975299	+	0.220889i	$0.929104\pi$
$284$	−7.64663	−	13.2444i	−0.453744	−	0.785908i
$285$	1.41378	+	1.00061i	0.0837453	+	0.0592709i
$286$	−8.73065	+	15.1219i	−0.516254	+	0.894179i
$287$	45.2308			2.66989
$288$	−21.5433	−	4.02319i	−1.26945	−	0.237069i
$289$	18.9414			1.11420
$290$	1.75297	−	3.03624i	0.102938	−	0.178294i
$291$	−2.21349	+	23.9105i	−0.129757	+	1.40166i
$292$	1.78887	+	3.09842i	0.104686	+	0.181321i
$293$	−16.2356	−	28.1209i	−0.948495	−	1.64284i	−0.748597	−	0.663026i	$-0.769272\pi$
$293$	−16.2356	−	28.1209i	−0.948495	−	1.64284i	−0.199899	−	0.979817i	$-0.564061\pi$
$294$	−35.2294	+	16.2119i	−2.05462	+	0.945496i
$295$	3.73704	−	6.47275i	0.217579	−	0.376858i
$296$	−7.83035			−0.455130
$297$	19.6053	+	20.2079i	1.13762	+	1.17258i
$298$	20.0204			1.15975
$299$	−4.91125	+	8.50653i	−0.284025	+	0.491945i
$300$	2.52962	−	1.16408i	0.146048	−	0.0672083i
$301$	11.8089	+	20.4537i	0.680655	+	1.17893i
$302$	−5.78716	−	10.0237i	−0.333014	−	0.576797i
$303$	3.09139	−	33.3936i	0.177595	−	1.91841i
$304$	2.31535	−	4.01031i	0.132795	−	0.230007i
$305$	−1.47277			−0.0843305
$306$	11.3594	+	32.2173i	0.649372	+	1.84174i
$307$	20.5301			1.17171			0.585857	−	0.810414i	$-0.300758\pi$
$307$	20.5301			1.17171			0.585857	+	0.810414i	$0.300758\pi$
$308$	18.8797	−	32.7005i	1.07577	−	1.86329i
$309$	5.87628	+	4.15895i	0.334290	+	0.236594i
$310$	−2.54285	−	4.40434i	−0.144424	−	0.250150i
$311$	0.780909	+	1.35257i	0.0442813	+	0.0766974i	0.887317	−	0.461161i	$-0.152567\pi$
$311$	0.780909	+	1.35257i	0.0442813	+	0.0766974i	−0.843035	+	0.537858i	$0.819234\pi$
$312$	1.78732	+	1.26498i	0.101187	+	0.0716152i
$313$	3.69287	−	6.39625i	0.208734	−	0.361537i	−0.742582	−	0.669755i	$-0.766399\pi$
$313$	3.69287	−	6.39625i	0.208734	−	0.361537i	0.951316	+	0.308218i	$0.0997325\pi$
$314$	35.6180			2.01004
$315$	8.45858	−	9.87644i	0.476587	−	0.556475i
$316$	−10.3090			−0.579926
$317$	−3.07466	+	5.32547i	−0.172690	+	0.299108i	−0.939360	−	0.342934i	$-0.888579\pi$
$317$	−3.07466	+	5.32547i	−0.172690	+	0.299108i	0.766669	+	0.642042i	$0.221913\pi$
$318$	−2.35573	+	25.4470i	−0.132103	+	1.42700i
$319$	5.00081	+	8.66166i	0.279992	+	0.484960i
$320$	−2.30707	−	3.99597i	−0.128969	−	0.223381i
$321$	−10.4998	+	4.83180i	−0.586041	+	0.269685i
$322$	23.8323	−	41.2787i	1.32812	−	2.30037i
$323$	−5.99511			−0.333577
$324$	−11.2695	+	9.07513i	−0.626084	+	0.504174i
$325$	−1.69661			−0.0941109
$326$	8.37764	−	14.5105i	0.463995	−	0.803662i
$327$	12.6710	−	5.83096i	0.700710	−	0.322453i
$328$	3.88778	+	6.73383i	0.214667	+	0.371813i
$329$	−6.42874	−	11.1349i	−0.354428	−	0.613887i
$330$	−1.64321	+	17.7502i	−0.0904556	+	0.977115i
$331$	−0.676005	+	1.17088i	−0.0371566	+	0.0643572i	−0.884006	−	0.467476i	$-0.845163\pi$
$331$	−0.676005	+	1.17088i	−0.0371566	+	0.0643572i	0.846849	+	0.531833i	$0.178497\pi$
$332$	24.2805			1.33256
$333$	−20.5070	+	23.9445i	−1.12378	+	1.31215i
$334$	−21.9553			−1.20134
$335$	1.05258	−	1.82313i	0.0575087	−	0.0996081i
$336$	−28.3772	−	20.0840i	−1.54810	−	1.09567i
$337$	−2.78674	−	4.82678i	−0.151804	−	0.262931i	0.780087	−	0.625671i	$-0.215175\pi$
$337$	−2.78674	−	4.82678i	−0.151804	−	0.262931i	−0.931891	+	0.362740i	$0.881841\pi$
$338$	−9.61238	−	16.6491i	−0.522844	−	0.905593i
$339$	19.9895	+	14.1476i	1.08568	+	0.768393i
$340$	−4.81916	+	8.34703i	−0.261356	+	0.452681i
$341$	14.5083			0.785667
$342$	−1.89477	−	5.37393i	−0.102458	−	0.290589i
$343$	−20.7535			−1.12058
$344$	−2.03005	+	3.51615i	−0.109453	+	0.189578i
$345$	−0.924353	+	9.98500i	−0.0497655	+	0.537574i
$346$	−8.89715	−	15.4103i	−0.478314	−	0.828463i
$347$	2.94804	+	5.10615i	0.158259	+	0.274112i	0.934241	−	0.356643i	$-0.116079\pi$
$347$	2.94804	+	5.10615i	0.158259	+	0.274112i	−0.775982	+	0.630755i	$0.782745\pi$
$348$	−4.66924	+	2.14869i	−0.250297	+	0.115182i
$349$	2.63431	−	4.56276i	0.141011	−	0.244239i	−0.786866	−	0.617123i	$-0.788298\pi$
$349$	2.63431	−	4.56276i	0.141011	−	0.244239i	0.927878	+	0.372885i	$0.121631\pi$
$350$	8.23294			0.440069
$351$	8.54900	−	2.15258i	0.456312	−	0.114896i
$352$	39.5836			2.10981
$353$	2.66050	−	4.60813i	0.141604	−	0.245266i	−0.786497	−	0.617595i	$-0.788107\pi$
$353$	2.66050	−	4.60813i	0.141604	−	0.245266i	0.928101	+	0.372329i	$0.121441\pi$
$354$	−22.3370	+	10.2790i	−1.18720	+	0.546325i
$355$	4.75626	+	8.23809i	0.252436	+	0.437233i
$356$	2.48988	+	4.31260i	0.131964	+	0.228568i
$357$	−4.14891	+	44.8172i	−0.219584	+	2.37198i
$358$	−9.23844	+	16.0014i	−0.488267	+	0.845703i
$359$	−14.5787			−0.769435			−0.384717	−	0.923034i	$-0.625701\pi$
$359$	−14.5787			−0.769435			−0.384717	+	0.923034i	$0.625701\pi$
$360$	2.19742	+	0.410366i	0.115814	+	0.0216282i
$361$	1.00000			0.0526316
$362$	−3.31165	+	5.73594i	−0.174056	+	0.301474i
$363$	−25.9574	−	18.3714i	−1.36241	−	0.964250i
$364$	−5.91147	−	10.2390i	−0.309845	−	0.536668i
$365$	−1.11269	−	1.92724i	−0.0582410	−	0.100876i
$366$	3.95487	+	2.79907i	0.206724	+	0.146310i
$367$	−3.49717	+	6.05728i	−0.182551	+	0.316187i	−0.942748	−	0.333505i	$-0.891769\pi$
$367$	−3.49717	+	6.05728i	−0.182551	+	0.316187i	0.760198	+	0.649692i	$0.225102\pi$
$368$	26.8094			1.39754
$369$	30.7732	+	5.74685i	1.60199	+	0.299169i
$370$	−19.9599			−1.03767
$371$	−16.8354	+	29.1598i	−0.874052	+	1.51390i
$372$	−0.687285	+	7.42416i	−0.0356341	+	0.384925i
$373$	−1.19790	−	2.07483i	−0.0620250	−	0.107431i	0.833345	−	0.552753i	$-0.186423\pi$
$373$	−1.19790	−	2.07483i	−0.0620250	−	0.107431i	−0.895370	+	0.445322i	$0.853089\pi$
$374$	−30.8505	−	53.4346i	−1.59524	−	2.76304i
$375$	−1.57344	+	0.724068i	−0.0812523	+	0.0373907i
$376$	1.10515	−	1.91418i	0.0569939	−	0.0987163i
$377$	3.13164			0.161288
$378$	−41.4848	+	10.4456i	−2.13375	+	0.537263i
$379$	0.796935			0.0409358			0.0204679	−	0.999791i	$-0.493484\pi$
$379$	0.796935			0.0409358			0.0204679	+	0.999791i	$0.493484\pi$
$380$	0.803848	−	1.39231i	0.0412366	−	0.0714238i
$381$	3.17626	−	1.46165i	0.162725	−	0.0748828i
$382$	−0.480559	−	0.832353i	−0.0245875	−	0.0425869i
$383$	−8.97942	−	15.5528i	−0.458827	−	0.794712i	0.540072	−	0.841619i	$-0.318397\pi$
$383$	−8.97942	−	15.5528i	−0.458827	−	0.794712i	−0.998899	+	0.0469068i	$0.985064\pi$
$384$	0.933443	−	10.0832i	0.0476346	−	0.514556i
$385$	−11.7433	+	20.3400i	−0.598494	+	1.03662i
$386$	−3.66970			−0.186783
$387$	5.43554	+	15.4162i	0.276304	+	0.783650i
$388$	22.2887			1.13154
$389$	−15.8785	+	27.5023i	−0.805071	+	1.39442i	0.111172	+	0.993801i	$0.464539\pi$
$389$	−15.8785	+	27.5023i	−0.805071	+	1.39442i	−0.916243	+	0.400623i	$0.868794\pi$
$390$	4.55596	+	3.22449i	0.230700	+	0.163278i
$391$	−17.3543	−	30.0586i	−0.877646	−	1.52013i
$392$	−4.39183	−	7.60688i	−0.221821	−	0.384205i
$393$	29.4968	+	20.8764i	1.48792	+	1.05308i
$394$	−1.60013	+	2.77150i	−0.0806132	+	0.139626i
$395$	6.41227			0.322636
$396$	16.9997	−	19.8493i	0.854268	−	0.997464i
$397$	1.39867			0.0701972			0.0350986	−	0.999384i	$-0.488825\pi$
$397$	1.39867			0.0701972			0.0350986	+	0.999384i	$0.488825\pi$
$398$	13.4592	−	23.3120i	0.674649	−	1.16853i
$399$	0.692050	−	7.47563i	0.0346458	−	0.374249i
$400$	2.31535	+	4.01031i	0.115768	+	0.200515i
$401$	7.80159	+	13.5127i	0.389593	+	0.674794i	0.992395	−	0.123097i	$-0.0392825\pi$
$401$	7.80159	+	13.5127i	0.389593	+	0.674794i	−0.602802	+	0.797891i	$0.705949\pi$
$402$	−6.29148	+	2.89521i	−0.313790	+	0.144400i
$403$	2.27137	−	3.93412i	0.113145	−	0.195973i
$404$	−31.1286			−1.54871
$405$	7.00972	−	5.64480i	0.348316	−	0.280492i
$406$	−15.1966			−0.754193
$407$	28.4704	−	49.3123i	1.41123	−	2.44432i
$408$	−7.02886	+	3.23455i	−0.347981	+	0.160134i
$409$	−7.30287	−	12.6489i	−0.361104	−	0.625450i	0.627039	−	0.778988i	$-0.284267\pi$
$409$	−7.30287	−	12.6489i	−0.361104	−	0.625450i	−0.988143	+	0.153538i	$0.950933\pi$
$410$	9.91014	+	17.1649i	0.489427	+	0.847712i
$411$	3.11216	−	33.6180i	0.153511	−	1.65825i
$412$	3.34113	−	5.78701i	0.164606	−	0.285106i
$413$	−32.3965			−1.59413
$414$	21.4592	−	25.0562i	1.05466	−	1.23145i
$415$	−15.1027			−0.741360
$416$	6.19708	−	10.7337i	0.303837	−	0.526261i
$417$	1.97265	+	1.39614i	0.0966009	+	0.0683695i
$418$	5.14594	+	8.91304i	0.251696	+	0.435951i
$419$	−18.1479	−	31.4330i	−0.886582	−	1.53560i	−0.843890	−	0.536516i	$-0.819740\pi$
$419$	−18.1479	−	31.4330i	−0.886582	−	1.53560i	−0.0426916	−	0.999088i	$-0.513593\pi$
$420$	−9.85206	−	6.97282i	−0.480731	−	0.340239i
$421$	8.14047	−	14.0997i	0.396742	−	0.687178i	−0.596579	−	0.802554i	$-0.703474\pi$
$421$	8.14047	−	14.0997i	0.396742	−	0.687178i	0.993322	+	0.115376i	$0.0368073\pi$
$422$	−16.0036			−0.779041
$423$	−2.95909	−	8.39252i	−0.143876	−	0.408058i
$424$	−5.78830			−0.281105
$425$	2.99756	−	5.19192i	0.145403	−	0.251845i
$426$	2.88475	−	31.1615i	0.139767	−	1.50978i
$427$	3.19186	+	5.52847i	0.154465	+	0.267542i
$428$	5.36419	+	9.29104i	0.259288	+	0.449099i
$429$	−14.4648	+	6.65643i	−0.698368	+	0.321375i
$430$	−5.17470	+	8.96285i	−0.249546	+	0.432227i
$431$	6.47370			0.311827			0.155914	−	0.987771i	$-0.450168\pi$
$431$	6.47370			0.311827			0.155914	+	0.987771i	$0.450168\pi$
$432$	−16.7549	−	17.2698i	−0.806119	−	0.830895i
$433$	28.9568			1.39158			0.695788	−	0.718247i	$-0.255055\pi$
$433$	28.9568			1.39158			0.695788	+	0.718247i	$0.255055\pi$
$434$	−11.0220	+	19.0907i	−0.529073	+	0.916381i
$435$	2.90430	−	1.33650i	0.139251	−	0.0640804i
$436$	−6.47344	−	11.2123i	−0.310021	−	0.536973i
$437$	2.89474	+	5.01385i	0.138474	+	0.239845i
$438$	−0.674866	+	7.29001i	−0.0322464	+	0.348330i
$439$	6.56744	−	11.3751i	0.313447	−	0.542906i	−0.665659	−	0.746256i	$-0.731850\pi$
$439$	6.56744	−	11.3751i	0.313447	−	0.542906i	0.979106	+	0.203350i	$0.0651830\pi$
$440$	−4.03754			−0.192482
$441$	−34.7629	−	6.49193i	−1.65538	−	0.309140i
$442$	−19.3194			−0.918931
$443$	−7.43784	+	12.8827i	−0.353382	+	0.612076i	−0.986840	−	0.161702i	$-0.948302\pi$
$443$	−7.43784	+	12.8827i	−0.353382	+	0.612076i	0.633457	+	0.773777i	$0.281635\pi$
$444$	23.8853	+	16.9049i	1.13355	+	0.802271i
$445$	−1.54873	−	2.68247i	−0.0734167	−	0.127161i
$446$	10.6809	+	18.4998i	0.505753	+	0.875990i
$447$	14.9019	+	10.5468i	0.704833	+	0.498847i
$448$	−10.0000	+	17.3206i	−0.472457	+	0.818320i
$449$	25.8078			1.21794			0.608972	−	0.793192i	$-0.291582\pi$
$449$	25.8078			1.21794			0.608972	+	0.793192i	$0.291582\pi$
$450$	5.60134	+	1.04604i	0.264050	+	0.0493110i
$451$	−56.5425			−2.66248
$452$	11.3656	−	19.6858i	0.534594	−	0.925944i
$453$	0.972922	−	10.5096i	0.0457118	−	0.493786i
$454$	16.5731	+	28.7055i	0.777814	+	1.34721i
$455$	3.67698	+	6.36872i	0.172380	+	0.298570i
$456$	1.17243	−	0.539531i	0.0549042	−	0.0252658i
$457$	0.564801	−	0.978263i	0.0264203	−	0.0457612i	−0.852513	−	0.522706i	$-0.824923\pi$
$457$	0.564801	−	0.978263i	0.0264203	−	0.0457612i	0.878933	+	0.476945i	$0.158256\pi$
$458$	−30.9153			−1.44458
$459$	−8.51704	+	29.9646i	−0.397541	+	1.39863i
$460$	9.30774			0.433976
$461$	−20.7486	+	35.9376i	−0.966358	+	1.67378i	−0.260437	+	0.965491i	$0.583867\pi$
$461$	−20.7486	+	35.9376i	−0.966358	+	1.67378i	−0.705921	+	0.708290i	$0.749467\pi$
$462$	70.1918	−	32.3009i	3.26562	−	1.50277i
$463$	1.25244	+	2.16928i	0.0582057	+	0.100815i	0.893660	−	0.448745i	$-0.148129\pi$
$463$	1.25244	+	2.16928i	0.0582057	+	0.100815i	−0.835454	+	0.549560i	$0.814795\pi$
$464$	−4.27373	−	7.40232i	−0.198403	−	0.343644i
$465$	0.427497	−	4.61788i	0.0198247	−	0.214149i
$466$	4.52556	−	7.83850i	0.209643	−	0.363112i
$467$	0.0803212			0.00371682			0.00185841	−	0.999998i	$-0.499408\pi$
$467$	0.0803212			0.00371682			0.00185841	+	0.999998i	$0.499408\pi$
$468$	−2.72099	−	7.71725i	−0.125778	−	0.356730i
$469$	−9.12486			−0.421347
$470$	2.81709	−	4.87934i	0.129943	−	0.225067i
$471$	26.5117	+	18.7637i	1.22159	+	0.864585i
$472$	−2.78461	−	4.82309i	−0.128172	−	0.222001i
$473$	−14.7622	−	25.5688i	−0.678766	−	1.17566i
$474$	−17.2191	−	12.1868i	−0.790898	−	0.559760i
$475$	−0.500000	+	0.866025i	−0.0229416	+	0.0397360i
$476$	41.7774			1.91486
$477$	−15.1590	+	17.7001i	−0.694085	+	0.810430i
$478$	21.0380			0.962257
$479$	13.5059	−	23.3928i	0.617099	−	1.06885i	−0.372914	−	0.927866i	$-0.621641\pi$
$479$	13.5059	−	23.3928i	0.617099	−	1.06885i	0.990012	−	0.140980i	$-0.0450253\pi$
$480$	1.16636	−	12.5992i	0.0532368	−	0.575072i
$481$	−8.91448	−	15.4403i	−0.406465	−	0.704018i
$482$	−26.0716	−	45.1573i	−1.18753	−	2.05686i
$483$	39.4849	−	18.1702i	1.79663	−	0.826773i
$484$	−14.7589	+	25.5631i	−0.670858	+	1.16196i
$485$	−13.8637			−0.629520
$486$	−29.5517	+	1.83584i	−1.34049	+	0.0832756i
$487$	−15.9386			−0.722248			−0.361124	−	0.932518i	$-0.617607\pi$
$487$	−15.9386			−0.722248			−0.361124	+	0.932518i	$0.617607\pi$
$488$	−0.548708	+	0.950390i	−0.0248388	+	0.0430221i
$489$	13.8800	−	6.38728i	0.627673	−	0.288843i
$490$	−11.1950	−	19.3903i	−0.505739	−	0.875965i
$491$	−19.0478	−	32.9917i	−0.859613	−	1.48889i	−0.872298	−	0.488974i	$-0.837371\pi$
$491$	−19.0478	−	32.9917i	−0.859613	−	1.48889i	0.0126848	−	0.999920i	$-0.495962\pi$
$492$	2.67853	−	28.9339i	0.120757	−	1.30444i
$493$	−5.53296	+	9.58337i	−0.249192	+	0.431613i
$494$	3.22253			0.144988
$495$	−10.5740	+	12.3464i	−0.475264	+	0.554930i
$496$	−12.3989			−0.556726
$497$	20.6161	−	35.7081i	0.924757	−	1.60173i
$498$	40.5556	+	28.7033i	1.81734	+	1.28623i
$499$	−8.80891	−	15.2575i	−0.394341	−	0.683018i	0.598676	−	0.800991i	$-0.295694\pi$
$499$	−8.80891	−	15.2575i	−0.394341	−	0.683018i	−0.993017	+	0.117973i	$0.962360\pi$
$500$	0.803848	+	1.39231i	0.0359492	+	0.0622658i
$501$	−16.3421	−	11.5661i	−0.730110	−	0.516737i
$502$	−23.3039	+	40.3636i	−1.04011	+	1.80152i
$503$	−13.9527			−0.622119			−0.311060	−	0.950390i	$-0.600684\pi$
$503$	−13.9527			−0.622119			−0.311060	+	0.950390i	$0.600684\pi$
$504$	−3.22195	−	9.13805i	−0.143517	−	0.407041i
$505$	19.3623			0.861609
$506$	−29.7924	+	51.6019i	−1.32443	+	2.29399i
$507$	1.61601	−	17.4563i	0.0717694	−	0.775264i
$508$	−1.62270	−	2.81061i	−0.0719959	−	0.124701i
$509$	−1.02390	−	1.77344i	−0.0453835	−	0.0786065i	0.842441	−	0.538788i	$-0.181118\pi$
$509$	−1.02390	−	1.77344i	−0.0453835	−	0.0786065i	−0.887825	+	0.460182i	$0.847784\pi$
$510$	−17.9169	+	8.24502i	−0.793375	+	0.365096i
$511$	−4.82298	+	8.35364i	−0.213356	+	0.369543i
$512$	−26.9275			−1.19004
$513$	1.42066	−	4.99817i	0.0627239	−	0.220675i
$514$	−23.2878			−1.02718
$515$	−2.07821	+	3.59957i	−0.0915769	+	0.158616i
$516$	13.7834	−	6.34285i	0.606780	−	0.279228i
$517$	8.03648	+	13.9196i	0.353444	+	0.612183i
$518$	43.2583	+	74.9255i	1.90066	+	3.29204i
$519$	1.49576	−	16.1575i	0.0656568	−	0.709234i
$520$	−0.632104	+	1.09484i	−0.0277196	+	0.0480117i
$521$	20.0525			0.878514			0.439257	−	0.898361i	$-0.355242\pi$
$521$	20.0525			0.878514			0.439257	+	0.898361i	$0.355242\pi$
$522$	−10.3391	−	1.93081i	−0.452530	−	0.0845094i
$523$	−37.7841			−1.65218			−0.826092	−	0.563535i	$-0.809441\pi$
$523$	−37.7841			−1.65218			−0.826092	+	0.563535i	$0.809441\pi$
$524$	16.7713	−	29.0487i	0.732656	−	1.26900i
$525$	6.12806	+	4.33715i	0.267450	+	0.189289i
$526$	−2.80801	−	4.86361i	−0.122435	−	0.212063i
$527$	8.02607	+	13.9016i	0.349621	+	0.605561i
$528$	35.4740	+	25.1068i	1.54381	+	1.09263i
$529$	−5.25910	+	9.10902i	−0.228656	+	0.396044i
$530$	−14.7547			−0.640901
$531$	−22.0412	−	4.11617i	−0.956507	−	0.178626i
$532$	−6.96858			−0.302126
$533$	−8.85210	+	15.3323i	−0.383427	+	0.664115i
$534$	−0.939328	+	10.1468i	−0.0406487	+	0.439093i
$535$	−3.33657	−	5.77910i	−0.144252	−	0.249852i
$536$	−0.784319	−	1.35848i	−0.0338774	−	0.0586774i
$537$	−15.3061	+	7.04357i	−0.660507	+	0.303953i
$538$	1.39366	−	2.41390i	0.0600851	−	0.104070i
$539$	63.8733			2.75122
$540$	−5.81699	−	5.99577i	−0.250323	−	0.258017i
$541$	−32.1574			−1.38255			−0.691277	−	0.722590i	$-0.742952\pi$
$541$	−32.1574			−1.38255			−0.691277	+	0.722590i	$0.742952\pi$
$542$	−25.2296	+	43.6989i	−1.08370	+	1.87703i
$543$	−5.48669	+	2.52487i	−0.235456	+	0.108352i
$544$	21.8979	+	37.9283i	0.938865	+	1.62616i
$545$	4.02653	+	6.97415i	0.172477	+	0.298740i
$546$	2.23015	−	24.0904i	0.0954416	−	1.03097i
$547$	5.77382	−	10.0005i	0.246871	−	0.427593i	−0.715785	−	0.698320i	$-0.753931\pi$
$547$	5.77382	−	10.0005i	0.246871	−	0.427593i	0.962656	+	0.270728i	$0.0872644\pi$
$548$	−31.3378			−1.33868
$549$	1.46918	+	4.16688i	0.0627033	+	0.177838i
$550$	−10.2919			−0.438848
$551$	0.922912	−	1.59853i	0.0393174	−	0.0680997i
$552$	6.09902	+	4.31659i	0.259591	+	0.183726i
$553$	−13.8970	−	24.0703i	−0.590961	−	1.02358i
$554$	12.9426	+	22.4172i	0.549878	+	0.952417i
$555$	−14.8569	−	10.5150i	−0.630639	−	0.446336i
$556$	1.12161	−	1.94268i	0.0475667	−	0.0823880i
$557$	−3.71819			−0.157545			−0.0787724	−	0.996893i	$-0.525100\pi$
$557$	−3.71819			−0.157545			−0.0787724	+	0.996893i	$0.525100\pi$
$558$	−9.92449	+	11.5881i	−0.420137	+	0.490562i
$559$	−9.24447			−0.391000
$560$	10.0359	−	17.3827i	0.424095	−	0.734554i
$561$	5.18650	−	56.0254i	0.218974	−	2.36539i
$562$	9.06530	+	15.7016i	0.382397	+	0.662330i
$563$	4.93215	+	8.54274i	0.207866	+	0.360034i	0.951042	−	0.309062i	$-0.100015\pi$
$563$	4.93215	+	8.54274i	0.207866	+	0.360034i	−0.743176	+	0.669096i	$0.766682\pi$
$564$	−7.50362	+	3.45302i	−0.315960	+	0.145398i
$565$	−7.06950	+	12.2447i	−0.297416	+	0.515140i
$566$	−18.9387			−0.796051
$567$	−36.3813	−	14.0793i	−1.52787	−	0.591277i
$568$	7.08815			0.297412
$569$	16.3762	−	28.3645i	0.686527	−	1.18910i	−0.286427	−	0.958102i	$-0.592468\pi$
$569$	16.3762	−	28.3645i	0.686527	−	1.18910i	0.972954	−	0.230998i	$-0.0741991\pi$
$570$	2.98859	−	1.37529i	0.125178	−	0.0576046i
$571$	−12.9907	−	22.5005i	−0.543643	−	0.941618i	−0.998691	−	0.0511507i	$-0.983711\pi$
$571$	−12.9907	−	22.5005i	−0.543643	−	0.941618i	0.455048	−	0.890467i	$-0.349622\pi$
$572$	7.38985	+	12.7996i	0.308985	+	0.535178i
$573$	0.0807903	−	0.872709i	0.00337506	−	0.0364579i
$574$	42.9556	−	74.4013i	1.79293	−	3.10545i
$575$	−5.78949			−0.241438
$576$	−9.00428	+	10.5136i	−0.375178	+	0.438067i
$577$	0.804688			0.0334996			0.0167498	−	0.999860i	$-0.494668\pi$
$577$	0.804688			0.0334996			0.0167498	+	0.999860i	$0.494668\pi$
$578$	17.9885	−	31.1571i	0.748225	−	1.29596i
$579$	−2.73148	−	1.93321i	−0.113517	−	0.0803416i
$580$	−1.48376	−	2.56995i	−0.0616099	−	0.106711i
$581$	32.7313	+	56.6923i	1.35792	+	2.35199i
$582$	37.2287	+	26.3487i	1.54318	+	1.09219i
$583$	21.0457	−	36.4523i	0.871625	−	1.50970i
$584$	−1.65822			−0.0686176
$585$	1.69248	+	4.80019i	0.0699754	+	0.198463i
$586$	−61.6757			−2.54780
$587$	−16.4688	+	28.5248i	−0.679740	+	1.17734i	0.295320	+	0.955399i	$0.404574\pi$
$587$	−16.4688	+	28.5248i	−0.679740	+	1.17734i	−0.975059	+	0.221945i	$0.928759\pi$
$588$	−3.02580	+	32.6852i	−0.124782	+	1.34791i
$589$	−1.33877	−	2.31882i	−0.0551630	−	0.0955451i
$590$	−7.09812	−	12.2943i	−0.292225	−	0.506148i
$591$	−2.65107	+	1.21997i	−0.109050	+	0.0501828i
$592$	−24.3311	+	42.1427i	−1.00000	+	1.73205i
$593$	−24.5653			−1.00878			−0.504388	−	0.863477i	$-0.668282\pi$
$593$	−24.5653			−1.00878			−0.504388	+	0.863477i	$0.668282\pi$
$594$	51.8595	−	13.0579i	2.12782	−	0.535771i
$595$	−25.9859			−1.06532
$596$	8.47289	−	14.6755i	0.347063	−	0.601131i
$597$	22.2990	−	10.2616i	0.912638	−	0.419978i
$598$	9.32840	+	16.1573i	0.381466	+	0.660719i
$599$	21.0238	+	36.4142i	0.859008	+	1.48785i	0.872876	+	0.487942i	$0.162252\pi$
$599$	21.0238	+	36.4142i	0.859008	+	1.48785i	−0.0138682	+	0.999904i	$0.504415\pi$
$600$	−0.118969	+	1.28512i	−0.00485689	+	0.0524649i
$601$	13.0003	−	22.5172i	0.530295	−	0.918498i	−0.469080	−	0.883155i	$-0.655415\pi$
$601$	13.0003	−	22.5172i	0.530295	−	0.918498i	0.999375	−	0.0353422i	$-0.0112521\pi$
$602$	44.8596			1.82834
$603$	−6.20817	−	1.15937i	−0.252816	−	0.0472131i
$604$	−9.79681			−0.398627
$605$	9.18014	−	15.9005i	0.373226	−	0.646446i
$606$	−51.9941	−	36.7989i	−2.11211	−	1.49485i
$607$	−3.64494	−	6.31323i	−0.147944	−	0.256246i	0.782524	−	0.622621i	$-0.213932\pi$
$607$	−3.64494	−	6.31323i	−0.147944	−	0.256246i	−0.930467	+	0.366375i	$0.880599\pi$
$608$	−3.65263	−	6.32654i	−0.148134	−	0.256575i
$609$	−11.3113	−	8.00561i	−0.458358	−	0.324404i
$610$	−1.39868	+	2.42259i	−0.0566311	+	0.0980879i
$611$	5.03266			0.203599
$612$	28.4236	+	5.30807i	1.14895	+	0.214566i
$613$	38.0526			1.53693			0.768466	−	0.639891i	$-0.221020\pi$
$613$	38.0526			1.53693			0.768466	+	0.639891i	$0.221020\pi$
$614$	19.4974	−	33.7704i	0.786850	−	1.36286i
$615$	−1.66607	+	17.9971i	−0.0671822	+	0.725713i
$616$	8.75038	+	15.1561i	0.352563	+	0.610656i
$617$	21.1085	+	36.5610i	0.849796	+	1.47189i	0.881390	+	0.472390i	$0.156609\pi$
$617$	21.1085	+	36.5610i	0.849796	+	1.47189i	−0.0315932	+	0.999501i	$0.510058\pi$
$618$	12.4218	−	5.71629i	0.499680	−	0.229943i
$619$	−15.2486	+	26.4114i	−0.612895	+	1.06156i	0.377855	+	0.925865i	$0.376662\pi$
$619$	−15.2486	+	26.4114i	−0.612895	+	1.06156i	−0.990750	+	0.135700i	$0.956672\pi$
$620$	−4.30467			−0.172880
$621$	29.1725	−	7.34544i	1.17065	−	0.294762i
$622$	2.96651			0.118946
$623$	−6.71297	+	11.6272i	−0.268949	+	0.465834i
$624$	12.3617	−	5.68864i	0.494866	−	0.227728i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−7.01422	−	12.1490i	−0.280345	−	0.485571i
$627$	−0.865122	+	9.34518i	−0.0345496	+	0.373211i
$628$	15.0740	−	26.1089i	0.601518	−	1.04186i
$629$	63.0001			2.51198
$630$	−8.21291	−	23.2933i	−0.327210	−	0.928029i
$631$	28.0867			1.11811			0.559057	−	0.829129i	$-0.311163\pi$
$631$	28.0867			1.11811			0.559057	+	0.829129i	$0.311163\pi$
$632$	2.38901	−	4.13789i	0.0950298	−	0.164596i
$633$	−11.9120	−	8.43073i	−0.473459	−	0.335092i
$634$	5.83999	+	10.1152i	0.231936	+	0.401725i
$635$	1.00934	+	1.74822i	0.0400542	+	0.0693760i
$636$	17.6564	+	12.4963i	0.700120	+	0.495511i
$637$	9.99979	−	17.3201i	0.396206	−	0.686249i
$638$	18.9970			0.752099
$639$	18.5632	−	21.6749i	0.734350	−	0.857445i
$640$	5.84643			0.231100
$641$	18.1940	−	31.5129i	0.718618	−	1.24468i	−0.242929	−	0.970044i	$-0.578108\pi$
$641$	18.1940	−	31.5129i	0.718618	−	1.24468i	0.961547	−	0.274640i	$-0.0885585\pi$
$642$	−2.02368	+	21.8601i	−0.0798683	+	0.862750i
$643$	−15.3651	−	26.6132i	−0.605942	−	1.04952i	−0.991902	−	0.127006i	$-0.959463\pi$
$643$	−15.3651	−	26.6132i	−0.605942	−	1.04952i	0.385960	−	0.922515i	$-0.373870\pi$
$644$	−20.1723	−	34.9394i	−0.794898	−	1.37680i
$645$	−8.57337	+	3.94530i	−0.337576	+	0.155346i
$646$	−5.69354	+	9.86150i	−0.224009	+	0.387995i
$647$	−24.6759			−0.970111			−0.485056	−	0.874483i	$-0.661201\pi$
$647$	−24.6759			−0.970111			−0.485056	+	0.874483i	$0.661201\pi$
$648$	−1.03103	−	6.62651i	−0.0405028	−	0.260314i
$649$	40.4984			1.58970
$650$	−1.61126	+	2.79079i	−0.0631990	+	0.109464i
$651$	−18.2611	+	8.40340i	−0.715708	+	0.329355i
$652$	−7.09106	−	12.2821i	−0.277707	−	0.481003i
$653$	−6.54100	−	11.3293i	−0.255969	−	0.443352i	0.709189	−	0.705018i	$-0.249061\pi$
$653$	−6.54100	−	11.3293i	−0.255969	−	0.443352i	−0.965158	+	0.261667i	$0.915728\pi$
$654$	2.44215	−	26.3805i	0.0954958	−	1.03156i
$655$	−10.4319	+	18.0685i	−0.407606	+	0.705995i
$656$	48.3216			1.88664
$657$	−4.34273	+	5.07068i	−0.169426	+	0.197826i
$658$	−24.4214			−0.952045
$659$	−15.1989	+	26.3253i	−0.592066	+	1.02549i	0.401888	+	0.915689i	$0.368354\pi$
$659$	−15.1989	+	26.3253i	−0.592066	+	1.02549i	−0.993954	+	0.109799i	$0.964979\pi$
$660$	12.3159	+	8.71662i	0.479397	+	0.339294i
$661$	13.3771	+	23.1698i	0.520308	+	0.901200i	0.999721	+	0.0236106i	$0.00751619\pi$
$661$	13.3771	+	23.1698i	0.520308	+	0.901200i	−0.479413	+	0.877589i	$0.659150\pi$
$662$	1.28400	+	2.22395i	0.0499041	+	0.0864364i
$663$	−14.3801	−	10.1775i	−0.558477	−	0.395263i
$664$	−5.62678	+	9.74587i	−0.218361	+	0.378213i
$665$	4.33451			0.168085
$666$	19.9114	+	56.4724i	0.771550	+	2.18826i
$667$	10.6864			0.413778
$668$	−9.29178	+	16.0938i	−0.359510	+	0.622689i
$669$	−1.79564	+	19.3967i	−0.0694233	+	0.749921i
$670$	−1.99927	−	3.46284i	−0.0772385	−	0.133781i
$671$	−3.99011	−	6.91107i	−0.154036	−	0.266799i
$672$	−49.8226	+	22.9274i	−1.92195	+	0.884444i
$673$	−18.7647	+	32.5014i	−0.723325	+	1.25284i	0.236335	+	0.971672i	$0.424054\pi$
$673$	−18.7647	+	32.5014i	−0.723325	+	1.25284i	−0.959660	+	0.281163i	$0.909280\pi$
$674$	−10.5862			−0.407767
$675$	3.61821	+	3.72942i	0.139265	+	0.143545i
$676$	−16.2723			−0.625859
$677$	15.1967	−	26.3215i	0.584058	−	1.01162i	−0.410934	−	0.911665i	$-0.634797\pi$
$677$	15.1967	−	26.3215i	0.584058	−	1.01162i	0.994992	−	0.0999533i	$-0.0318694\pi$
$678$	42.2557	−	19.4452i	1.62282	−	0.746790i
$679$	30.0463	+	52.0417i	1.15307	+	1.99718i
$680$	−2.23359	−	3.86870i	−0.0856544	−	0.148358i
$681$	−2.78622	+	30.0972i	−0.106768	+	1.15333i
$682$	13.7785	−	23.8650i	0.527604	−	0.913838i
$683$	30.5071			1.16732			0.583660	−	0.811998i	$-0.301620\pi$
$683$	30.5071			1.16732			0.583660	+	0.811998i	$0.301620\pi$
$684$	−4.74113	−	0.885399i	−0.181281	−	0.0338541i
$685$	19.4924			0.744764
$686$	−19.7095	+	34.1379i	−0.752514	+	1.30339i
$687$	−23.0113	−	16.2863i	−0.877935	−	0.621360i
$688$	12.6159	+	21.8513i	0.480976	+	0.833075i
$689$	−6.58970	−	11.4137i	−0.251048	−	0.434827i
$690$	15.5467	+	11.0032i	0.591853	+	0.418885i
$691$	−4.74113	+	8.21187i	−0.180361	+	0.312394i	−0.942003	−	0.335603i	$-0.891060\pi$
$691$	−4.74113	+	8.21187i	−0.180361	+	0.312394i	0.761643	+	0.647997i	$0.224393\pi$
$692$	−15.0616			−0.572555
$693$	69.2624	+	12.9347i	2.63106	+	0.491347i
$694$	11.1990			0.425107
$695$	−0.697648	+	1.20836i	−0.0264633	+	0.0458358i
$696$	0.219596	−	2.37211i	0.00832376	−	0.0899146i
$697$	−31.2797	−	54.1779i	−1.18480	−	2.05214i
$698$	−5.00359	−	8.66647i	−0.189389	−	0.328031i
$699$	7.49788	−	3.45038i	0.283596	−	0.130505i
$700$	3.48429	−	6.03497i	0.131694	−	0.228100i
$701$	−4.91494			−0.185635			−0.0928173	−	0.995683i	$-0.529587\pi$
$701$	−4.91494			−0.185635			−0.0928173	+	0.995683i	$0.529587\pi$
$702$	4.57813	−	16.1067i	0.172790	−	0.607910i
$703$	−10.5086			−0.396339
$704$	12.5009	−	21.6522i	0.471146	−	0.816048i
$705$	4.66731	−	2.14781i	0.175781	−	0.0808911i
$706$	−5.05335	−	8.75265i	−0.190185	−	0.329410i
$707$	−41.9629	−	72.6819i	−1.57818	−	2.73349i
$708$	−1.91849	+	20.7238i	−0.0721013	+	0.778849i
$709$	1.68955	−	2.92639i	0.0634524	−	0.109903i	−0.832554	−	0.553944i	$-0.813122\pi$
$709$	1.68955	−	2.92639i	0.0634524	−	0.109903i	0.896006	+	0.444041i	$0.146456\pi$
$710$	18.0680			0.678081
$711$	−6.39667	−	18.1421i	−0.239894	−	0.680384i
$712$	−2.30803			−0.0864971
$713$	7.75079	−	13.4248i	0.290269	−	0.502761i
$714$	69.7807	+	49.3874i	2.61148	+	1.84828i
$715$	−4.59655	−	7.96145i	−0.171901	−	0.297741i
$716$	7.81966	+	13.5440i	0.292234	+	0.506165i
$717$	15.6593	+	11.0829i	0.584808	+	0.413899i
$718$	−13.8454	+	23.9809i	−0.516704	+	0.894957i
$719$	4.11473			0.153453			0.0767267	−	0.997052i	$-0.475553\pi$
$719$	4.11473			0.153453			0.0767267	+	0.997052i	$0.475553\pi$
$720$	9.03659	−	10.5513i	0.336774	−	0.393225i
$721$	18.0161			0.670953
$722$	0.949697	−	1.64492i	0.0353441	−	0.0612177i
$723$	4.38309	−	47.3467i	0.163009	−	1.76084i
$724$	2.80307	+	4.85505i	0.104175	+	0.180437i
$725$	0.922912	+	1.59853i	0.0342761	+	0.0593679i
$726$	−54.8713	+	25.2507i	−2.03647	+	0.937142i
$727$	−22.2835	+	38.5961i	−0.826448	+	1.43145i	0.0743603	+	0.997231i	$0.476309\pi$
$727$	−22.2835	+	38.5961i	−0.826448	+	1.43145i	−0.900808	+	0.434218i	$0.857025\pi$
$728$	5.47972			0.203092
$729$	−22.9634	−	14.2014i	−0.850497	−	0.525979i
$730$	−4.22688			−0.156444
$731$	16.3331	−	28.2897i	0.604100	−	1.04633i
$732$	3.72555	−	1.71442i	0.137700	−	0.0633669i
$733$	−15.9046	−	27.5475i	−0.587449	−	1.01749i	−0.994565	−	0.104115i	$-0.966799\pi$
$733$	−15.9046	−	27.5475i	−0.587449	−	1.01749i	0.407116	−	0.913376i	$-0.366534\pi$
$734$	6.64250	+	11.5052i	0.245179	+	0.424663i
$735$	1.88207	−	20.3304i	0.0694213	−	0.749899i
$736$	21.1469	−	36.6274i	0.779483	−	1.35010i
$737$	11.4069			0.420177
$738$	38.6783	−	45.1617i	1.42377	−	1.66243i
$739$	34.4288			1.26648			0.633241	−	0.773954i	$-0.281724\pi$
$739$	34.4288			1.26648			0.633241	+	0.773954i	$0.281724\pi$
$740$	−8.44731	+	14.6312i	−0.310529	+	0.537852i
$741$	2.39864	+	1.69764i	0.0881161	+	0.0623644i
$742$	31.9771	+	55.3860i	1.17392	+	2.03328i
$743$	−5.15652	−	8.93135i	−0.189174	−	0.327659i	0.755801	−	0.654801i	$-0.227248\pi$
$743$	−5.15652	−	8.93135i	−0.189174	−	0.327659i	−0.944975	+	0.327142i	$0.893914\pi$
$744$	−2.82069	−	1.99635i	−0.103411	−	0.0731897i
$745$	−5.27020	+	9.12826i	−0.193085	+	0.334434i
$746$	−4.55058			−0.166608
$747$	15.0659	+	42.7297i	0.551232	+	1.56340i
$748$	−52.2254			−1.90955
$749$	−14.4624	+	25.0496i	−0.528444	+	0.915291i
$750$	−0.303258	+	3.27584i	−0.0110734	+	0.119617i
$751$	10.1242	+	17.5356i	0.369436	+	0.639883i	0.989478	−	0.144687i	$-0.0462174\pi$
$751$	10.1242	+	17.5356i	0.369436	+	0.639883i	−0.620041	+	0.784569i	$0.712884\pi$
$752$	−6.86804	−	11.8958i	−0.250452	−	0.433795i
$753$	−38.6096	+	17.7674i	−1.40701	+	0.647480i
$754$	2.97411	−	5.15131i	0.108311	−	0.187600i
$755$	6.09369			0.221772
$756$	−9.90001	+	34.8301i	−0.360060	+	1.26676i
$757$	41.7177			1.51625			0.758127	−	0.652107i	$-0.226115\pi$
$757$	41.7177			1.51625			0.758127	+	0.652107i	$0.226115\pi$
$758$	0.756847	−	1.31090i	0.0274899	−	0.0476139i
$759$	−49.3596	+	22.7143i	−1.79164	+	0.824478i
$760$	0.372569	+	0.645308i	0.0135145	+	0.0234078i
$761$	−17.8768	−	30.9636i	−0.648035	−	1.12243i	−0.983592	−	0.180409i	$-0.942258\pi$
$761$	−17.8768	−	30.9636i	−0.648035	−	1.12243i	0.335557	−	0.942020i	$-0.391076\pi$
$762$	0.612178	−	6.61284i	0.0221769	−	0.239558i
$763$	17.4530	−	30.2295i	0.631842	−	1.09438i
$764$	−0.813516			−0.0294320
$765$	−17.6797	−	3.30166i	−0.639210	−	0.119372i
$766$	−34.1109			−1.23248
$767$	6.34030	−	10.9817i	0.228935	−	0.396527i
$768$	−28.7464	−	20.3453i	−1.03730	−	0.734149i
$769$	−7.84615	−	13.5899i	−0.282939	−	0.490065i	0.689168	−	0.724602i	$-0.257976\pi$
$769$	−7.84615	−	13.5899i	−0.282939	−	0.490065i	−0.972107	+	0.234536i	$0.924643\pi$
$770$	22.3051	+	38.6336i	0.803822	+	1.39226i
$771$	−17.3339	−	12.2681i	−0.624266	−	0.441826i
$772$	−1.55307	+	2.68999i	−0.0558961	+	0.0968148i
$773$	40.4599			1.45524			0.727621	−	0.685979i	$-0.240626\pi$
$773$	40.4599			1.45524			0.727621	+	0.685979i	$0.240626\pi$
$774$	30.5206	+	5.69968i	1.09704	+	0.204871i
$775$	2.67754			0.0961800
$776$	−5.16520	+	8.94639i	−0.185420	+	0.321157i
$777$	−7.27246	+	78.5582i	−0.260898	+	2.81826i
$778$	30.1595	+	52.2378i	1.08127	+	1.87281i
$779$	5.21753	+	9.03702i	0.186937	+	0.323785i
$780$	4.29178	−	1.97499i	0.153670	−	0.0707160i
$781$	−25.7719	+	44.6382i	−0.922190	+	1.59728i
$782$	−65.9254			−2.35749
$783$	−6.67858	−	6.88385i	−0.238673	−	0.246009i
$784$	−54.5866			−1.94952
$785$	−9.37614	+	16.2399i	−0.334649	+	0.579629i
$786$	62.3531	−	28.6937i	2.22406	−	1.02347i
$787$	−21.9376	−	37.9971i	−0.781992	−	1.35445i	−0.930780	−	0.365580i	$-0.880871\pi$
$787$	−21.9376	−	37.9971i	−0.781992	−	1.35445i	0.148788	−	0.988869i	$-0.452463\pi$
$788$	1.35439	+	2.34587i	0.0482481	+	0.0835682i
$789$	0.472074	−	5.09942i	0.0168063	−	0.181544i
$790$	6.08971	−	10.5477i	0.216662	−	0.375270i
$791$	61.2857			2.17907
$792$	4.02771	+	11.4234i	0.143119	+	0.405911i
$793$	−2.49871			−0.0887319
$794$	1.32831	−	2.30070i	0.0471400	−	0.0816489i
$795$	−10.9824	−	7.77281i	−0.389505	−	0.275673i
$796$	−11.3922	−	19.7319i	−0.403787	−	0.699379i
$797$	14.2905	+	24.7519i	0.506196	+	0.876758i	0.999974	+	0.00716981i	$0.00228224\pi$
$797$	14.2905	+	24.7519i	0.506196	+	0.876758i	−0.493778	+	0.869588i	$0.664384\pi$
$798$	−11.6396	−	8.23795i	−0.412037	−	0.291620i
$799$	−8.89166	+	15.4008i	−0.314564	+	0.544841i
$800$	7.30526			0.258280
$801$	−6.04453	+	7.05774i	−0.213573	+	0.249373i
$802$	29.6366			1.04650
$803$	6.02914	−	10.4428i	0.212764	−	0.368518i
$804$	−0.540366	+	5.83711i	−0.0190572	+	0.205859i
$805$	12.5473	+	21.7326i	0.442234	+	0.765972i
$806$	−4.31422	−	7.47245i	−0.151962	−	0.263206i
$807$	2.30900	−	1.06256i	0.0812807	−	0.0374038i
$808$	7.21377	−	12.4946i	0.253780	−	0.439559i
$809$	7.61579			0.267757			0.133878	−	0.990998i	$-0.457257\pi$
$809$	7.61579			0.267757			0.133878	+	0.990998i	$0.457257\pi$
$810$	−2.62816	−	16.8913i	−0.0923440	−	0.593500i
$811$	7.41277			0.260298			0.130149	−	0.991494i	$-0.458454\pi$
$811$	7.41277			0.260298			0.130149	+	0.991494i	$0.458454\pi$
$812$	−6.43139	+	11.1395i	−0.225697	+	0.390919i
$813$	−41.7999	+	19.2355i	−1.46599	+	0.674619i
$814$	−54.0766	−	93.6634i	−1.89538	−	3.28290i
$815$	4.41069	+	7.63954i	0.154500	+	0.267602i
$816$	−4.43243	+	47.8798i	−0.155166	+	1.67613i
$817$	−2.72440	+	4.71880i	−0.0953146	+	0.165090i
$818$	−27.7420			−0.969978
$819$	14.3509	−	16.7565i	0.501461	−	0.585518i
$820$	16.7764			0.585857
$821$	−20.9937	+	36.3621i	−0.732685	+	1.26905i	0.223047	+	0.974808i	$0.428400\pi$
$821$	−20.9937	+	36.3621i	−0.732685	+	1.26905i	−0.955732	+	0.294240i	$0.904934\pi$
$822$	−52.3434	−	37.0462i	−1.82569	−	1.29213i
$823$	10.4322	+	18.0691i	0.363643	+	0.629848i	0.988557	−	0.150845i	$-0.0481995\pi$
$823$	10.4322	+	18.0691i	0.363643	+	0.629848i	−0.624914	+	0.780693i	$0.714866\pi$
$824$	1.54855	+	2.68217i	0.0539464	+	0.0934380i
$825$	−7.66060	−	5.42181i	−0.266708	−	0.188763i
$826$	−30.7669	+	53.2898i	−1.07052	+	1.85419i
$827$	−23.3270			−0.811160			−0.405580	−	0.914060i	$-0.632930\pi$
$827$	−23.3270			−0.811160			−0.405580	+	0.914060i	$0.632930\pi$
$828$	−9.28509	−	26.3343i	−0.322679	−	0.915179i
$829$	48.6836			1.69085			0.845425	−	0.534094i	$-0.179347\pi$
$829$	48.6836			1.69085			0.845425	+	0.534094i	$0.179347\pi$
$830$	−14.3429	+	24.8427i	−0.497851	+	0.862303i
$831$	−2.17587	+	23.5041i	−0.0754802	+	0.815348i
$832$	−3.91420	−	6.77960i	−0.135701	−	0.235040i
$833$	35.3351	+	61.2022i	1.22429	+	2.12053i
$834$	4.16997	−	1.91894i	0.144394	−	0.0664474i
$835$	5.77956	−	10.0105i	0.200010	−	0.346427i
$836$	8.71133			0.301287
$837$	−13.4918	+	3.39714i	−0.466344	+	0.117422i
$838$	−68.9399			−2.38149
$839$	−14.6638	+	25.3985i	−0.506252	+	0.876854i	0.493722	+	0.869620i	$0.335636\pi$
$839$	−14.6638	+	25.3985i	−0.506252	+	0.876854i	−0.999974	+	0.00723448i	$0.997697\pi$
$840$	5.08192	−	2.33860i	0.175343	−	0.0806894i
$841$	12.7965	+	22.1641i	0.441257	+	0.764280i
$842$	−15.4620	−	26.7809i	−0.532855	−	0.922931i
$843$	−1.52403	+	16.4628i	−0.0524905	+	0.567010i
$844$	−6.77291	+	11.7310i	−0.233133	+	0.403799i
$845$	10.1215			0.348191
$846$	−16.6153	−	3.10288i	−0.571245	−	0.106679i
$847$	−79.5828			−2.73450
$848$	−17.9859	+	31.1524i	−0.617637	+	1.06978i
$849$	−14.0967	−	9.97696i	−0.483797	−	0.342408i
$850$	−5.69354	−	9.86150i	−0.195287	−	0.338247i
$851$	−30.4197	−	52.6884i	−1.04277	−	1.80614i
$852$	−21.6214	−	15.3026i	−0.740736	−	0.524257i
$853$	−10.9070	+	18.8916i	−0.373450	+	0.646835i	−0.990094	−	0.140408i	$-0.955159\pi$
$853$	−10.9070	+	18.8916i	−0.373450	+	0.646835i	0.616644	+	0.787242i	$0.288492\pi$
$854$	12.1252			0.414916
$855$	2.94902	+	0.550725i	0.100854	+	0.0188344i
$856$	−4.97240			−0.169953
$857$	−6.55083	+	11.3464i	−0.223772	+	0.387585i	−0.955950	−	0.293528i	$-0.905171\pi$
$857$	−6.55083	+	11.3464i	−0.223772	+	0.387585i	0.732178	+	0.681113i	$0.238504\pi$
$858$	−2.78788	+	30.1151i	−0.0951766	+	1.02811i
$859$	−6.71435	−	11.6296i	−0.229091	−	0.396797i	0.728448	−	0.685101i	$-0.240242\pi$
$859$	−6.71435	−	11.6296i	−0.229091	−	0.396797i	−0.957539	+	0.288304i	$0.906909\pi$
$860$	4.38001	+	7.58639i	0.149357	+	0.258694i
$861$	71.1682	−	32.7502i	2.42541	−	1.11612i
$862$	6.14805	−	10.6487i	0.209403	−	0.362697i
$863$	−15.0821			−0.513400			−0.256700	−	0.966491i	$-0.582635\pi$
$863$	−15.0821			−0.513400			−0.256700	+	0.966491i	$0.582635\pi$
$864$	−36.8103	+	9.26857i	−1.25231	+	0.315323i
$865$	9.36841			0.318535
$866$	27.5002	−	47.6317i	0.934495	−	1.61859i
$867$	29.8032	−	13.7148i	1.01217	−	0.465780i
$868$	9.32931	+	16.1588i	0.316657	+	0.548467i
$869$	17.3725	+	30.0900i	0.589321	+	1.02073i
$870$	0.559761	−	6.04662i	0.0189777	−	0.205000i
$871$	1.78582	−	3.09313i	0.0605102	−	0.104807i
$872$	6.00064			0.203207
$873$	13.8300	+	39.2245i	0.468075	+	1.32755i
$874$	10.9965			0.371963
$875$	−2.16725	+	3.75380i	−0.0732666	+	0.126901i
$876$	5.05816	+	3.57992i	0.170899	+	0.120954i
$877$	−3.47319	−	6.01574i	−0.117281	−	0.203137i	0.801408	−	0.598118i	$-0.204085\pi$
$877$	−3.47319	−	6.01574i	−0.117281	−	0.203137i	−0.918689	+	0.394981i	$0.870751\pi$
$878$	−12.4742	−	21.6059i	−0.420982	−	0.729163i
$879$	−45.9073	−	32.4910i	−1.54842	−	1.09589i
$880$	−12.5458	+	21.7299i	−0.422918	+	0.732515i
$881$	17.9889			0.606062			0.303031	−	0.952981i	$-0.402001\pi$
$881$	17.9889			0.606062			0.303031	+	0.952981i	$0.402001\pi$
$882$	−43.6930	+	51.0170i	−1.47122	+	1.71783i
$883$	−7.06736			−0.237836			−0.118918	−	0.992904i	$-0.537943\pi$
$883$	−7.06736			−0.237836			−0.118918	+	0.992904i	$0.537943\pi$
$884$	−8.17623	+	14.1616i	−0.274996	+	0.476308i
$885$	1.19332	−	12.8904i	0.0401129	−	0.433305i
$886$	14.1274	+	24.4693i	0.474619	+	0.822063i
$887$	−11.3580	−	19.6726i	−0.381365	−	0.660543i	0.609893	−	0.792484i	$-0.291212\pi$
$887$	−11.3580	−	19.6726i	−0.381365	−	0.660543i	−0.991258	+	0.131941i	$0.957879\pi$
$888$	−12.3206	+	5.66970i	−0.413453	+	0.190263i
$889$	4.37497	−	7.57767i	0.146732	−	0.254147i
$890$	−5.88328			−0.197208
$891$	45.4798	+	17.6004i	1.52363	+	0.589635i
$892$	18.0811			0.605401
$893$	1.48315	−	2.56889i	0.0496318	−	0.0859648i
$894$	31.5010	−	14.4961i	1.05355	−	0.484823i
$895$	−4.86389	−	8.42450i	−0.162582	−	0.281600i
$896$	−12.6707	−	21.9463i	−0.423298	−	0.733174i
$897$	−1.56826	+	16.9406i	−0.0523628	+	0.565631i
$898$	24.5096	−	42.4518i	0.817894	−	1.41663i
$899$	−4.94226			−0.164834
$900$	3.13734	−	3.66324i	0.104578	−	0.122108i
$901$	46.5705			1.55149
$902$	−53.6982	+	93.0080i	−1.78795	+	3.09683i
$903$	33.3905	+	23.6322i	1.11117	+	0.786431i
$904$	5.26776	+	9.12402i	0.175203	+	0.303460i
$905$	−1.74353	−	3.01988i	−0.0579569	−	0.100384i
$906$	−16.3636	−	11.5814i	−0.543644	−	0.384765i
$907$	−3.80233	+	6.58582i	−0.126254	+	0.218679i	−0.922222	−	0.386660i	$-0.873629\pi$
$907$	−3.80233	+	6.58582i	−0.126254	+	0.218679i	0.795968	+	0.605338i	$0.206962\pi$
$908$	28.0558			0.931065
$909$	−19.3151	−	54.7814i	−0.640643	−	1.81698i
$910$	13.9681			0.463037
$911$	6.49292	−	11.2461i	0.215120	−	0.372599i	−0.738190	−	0.674593i	$-0.764319\pi$
$911$	6.49292	−	11.2461i	0.215120	−	0.372599i	0.953310	+	0.301994i	$0.0976523\pi$
$912$	0.739340	−	7.98647i	0.0244820	−	0.264458i
$913$	−40.9170	−	70.8702i	−1.35415	−	2.34546i
$914$	−1.07278	−	1.85811i	−0.0354844	−	0.0614607i
$915$	−2.31732	+	1.06638i	−0.0766082	+	0.0352536i
$916$	−13.0837	+	22.6617i	−0.432299	+	0.748764i
$917$	90.4340			2.98639
$918$	41.2008	+	42.4672i	1.35983	+	1.40163i
$919$	23.9505			0.790055			0.395027	−	0.918669i	$-0.370735\pi$
$919$	23.9505			0.790055			0.395027	+	0.918669i	$0.370735\pi$
$920$	−2.15698	+	3.73601i	−0.0711137	+	0.123172i
$921$	32.3029	−	14.8652i	1.06442	−	0.489825i
$922$	39.4097	+	68.2597i	1.29789	+	2.24801i
$923$	8.06952	+	13.9768i	0.265611	+	0.460053i
$924$	6.02867	−	65.1226i	0.198329	−	2.14238i
$925$	5.25429	−	9.10070i	0.172760	−	0.299229i
$926$	4.75774			0.156349
$927$	12.2574	+	2.28905i	0.402585	+	0.0751822i
$928$	−13.4842			−0.442641
$929$	23.5735	−	40.8305i	0.773421	−	1.33961i	−0.162256	−	0.986749i	$-0.551877\pi$
$929$	23.5735	−	40.8305i	0.773421	−	1.33961i	0.935677	−	0.352856i	$-0.114790\pi$
$930$	−7.19007	−	5.08879i	−0.235772	−	0.166868i
$931$	−5.89399	−	10.2087i	−0.193168	−	0.334576i
$932$	−3.83055	−	6.63471i	−0.125474	−	0.217327i
$933$	2.20807	+	1.56277i	0.0722890	+	0.0511627i
$934$	0.0762808	−	0.132122i	0.00249598	−	0.00432317i
$935$	32.4846			1.06236
$936$	3.72817	+	0.696231i	0.121859	+	0.0227570i
$937$	−25.2046			−0.823397			−0.411698	−	0.911320i	$-0.635064\pi$
$937$	−25.2046			−0.823397			−0.411698	+	0.911320i	$0.635064\pi$
$938$	−8.66585	+	15.0097i	−0.282950	+	0.490084i
$939$	1.17921	−	12.7380i	0.0384821	−	0.415690i
$940$	−2.38446	−	4.13000i	−0.0777725	−	0.134706i
$941$	9.42663	+	16.3274i	0.307299	+	0.532258i	0.977771	−	0.209677i	$-0.0672414\pi$
$941$	9.42663	+	16.3274i	0.307299	+	0.532258i	−0.670471	+	0.741935i	$0.733908\pi$
$942$	56.0429	−	25.7898i	1.82597	−	0.840278i
$943$	−30.2068	+	52.3197i	−0.983669	+	1.70377i
$944$	−34.6103			−1.12647
$945$	6.15788	−	21.6646i	0.200316	−	0.704750i
$946$	−56.0784			−1.82327
$947$	−6.74066	+	11.6752i	−0.219042	+	0.379392i	−0.954515	−	0.298162i	$-0.903627\pi$
$947$	−6.74066	+	11.6752i	−0.219042	+	0.379392i	0.735473	+	0.677554i	$0.236960\pi$
$948$	−16.2206	+	7.46441i	−0.526821	+	0.242433i
$949$	−1.88780	−	3.26977i	−0.0612807	−	0.106141i
$950$	0.949697	+	1.64492i	0.0308122	+	0.0533684i
$951$	−0.981804	+	10.6056i	−0.0318372	+	0.343910i
$952$	−9.68153	+	16.7689i	−0.313780	+	0.543483i
$953$	−15.3177			−0.496190			−0.248095	−	0.968736i	$-0.579805\pi$
$953$	−15.3177			−0.496190			−0.248095	+	0.968736i	$0.579805\pi$
$954$	14.7188	+	41.7451i	0.476537	+	1.35155i
$955$	0.506013			0.0163742
$956$	8.90357	−	15.4214i	0.287962	−	0.498765i
$957$	14.1401	+	10.0077i	0.457085	+	0.323503i
$958$	−25.6529	−	44.4322i	−0.828809	−	1.43554i
$959$	−42.2449	−	73.1703i	−1.36416	−	2.36279i
$960$	−6.52341	−	4.61695i	−0.210542	−	0.149012i
$961$	11.9154	−	20.6381i	0.384368	−	0.665744i
$962$	−33.8642			−1.09183
$963$	−13.0223	+	15.2051i	−0.419637	+	0.489979i
$964$	−44.1354			−1.42150
$965$	0.966019	−	1.67319i	0.0310973	−	0.0538620i
$966$	7.61014	−	82.2059i	0.244852	−	2.64493i
$967$	17.2832	+	29.9354i	0.555791	+	0.962658i	0.997842	+	0.0656677i	$0.0209177\pi$
$967$	17.2832	+	29.9354i	0.555791	+	0.962658i	−0.442051	+	0.896990i	$0.645749\pi$
$968$	−6.84047	−	11.8480i	−0.219861	−	0.380810i
$969$	−9.43297	+	4.34087i	−0.303031	+	0.139449i
$970$	−13.1664	+	22.8048i	−0.422746	+	0.732218i
$971$	16.7081			0.536188			0.268094	−	0.963393i	$-0.413606\pi$
$971$	16.7081			0.536188			0.268094	+	0.963393i	$0.413606\pi$
$972$	−11.1609	+	22.4391i	−0.357987	+	0.719735i
$973$	6.04792			0.193888
$974$	−15.1369	+	26.2178i	−0.485016	+	0.840073i
$975$	−2.66952	+	1.22846i	−0.0854930	+	0.0393422i
$976$	3.40998	+	5.90626i	0.109151	+	0.189055i
$977$	14.0725	+	24.3743i	0.450220	+	0.779804i	0.998399	−	0.0565568i	$-0.0180122\pi$
$977$	14.0725	+	24.3743i	0.450220	+	0.779804i	−0.548179	+	0.836361i	$0.684679\pi$
$978$	2.67516	−	28.8974i	0.0855421	−	0.924038i
$979$	8.39179	−	14.5350i	0.268203	−	0.464541i
$980$	−18.9515			−0.605383
$981$	15.7151	−	18.3494i	0.501746	−	0.585851i
$982$	−72.3584			−2.30905
$983$	20.0007	−	34.6423i	0.637924	−	1.10492i	−0.347964	−	0.937508i	$-0.613127\pi$
$983$	20.0007	−	34.6423i	0.637924	−	1.10492i	0.985888	−	0.167409i	$-0.0535399\pi$
$984$	10.9929	+	7.78028i	0.350442	+	0.248026i
$985$	−0.842441	−	1.45915i	−0.0268424	−	0.0464924i
$986$	10.5093	+	18.2026i	0.334683	+	0.579689i
$987$	−18.1777	−	12.8653i	−0.578602	−	0.409507i
$988$	1.36382	−	2.36220i	0.0433888	−	0.0751516i
$989$	−31.5457			−1.00310
$990$	10.2668	+	29.1187i	0.326302	+	0.925453i
$991$	49.6297			1.57654			0.788270	−	0.615329i	$-0.210977\pi$
$991$	49.6297			1.57654			0.788270	+	0.615329i	$0.210977\pi$
$992$	−9.78005	+	16.9395i	−0.310517	+	0.537831i
$993$	−0.215863	+	2.33178i	−0.00685020	+	0.0739968i
$994$	−39.1580	−	67.8237i	−1.24202	−	2.15124i
$995$	7.08605	+	12.2734i	0.224643	+	0.389093i
$996$	38.2040	−	17.5807i	1.21054	−	0.557067i
$997$	4.45059	−	7.70864i	0.140952	−	0.244135i	−0.786904	−	0.617076i	$-0.788317\pi$
$997$	4.45059	−	7.70864i	0.140952	−	0.244135i	0.927855	+	0.372941i	$0.121650\pi$
$998$	−33.4632			−1.05926
$999$	−14.9292	+	52.5237i	−0.472338	+	1.66178i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.i.d.286.18	✓	46
9.2	odd	6		7695.2.a.x.1.18		23
9.4	even	3	inner	855.2.i.d.571.18	yes	46
9.7	even	3		7695.2.a.w.1.6		23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.i.d.286.18	✓	46	1.1	even	1	trivial
855.2.i.d.571.18	yes	46	9.4	even	3	inner
7695.2.a.w.1.6		23	9.7	even	3
7695.2.a.x.1.18		23	9.2	odd	6

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.949697 - 1.64492i) q^{2} +(1.57344 - 0.724068i) q^{3} +(-0.803848 - 1.39231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.303258 - 3.27584i) q^{6} +(2.16725 - 3.75380i) q^{7} +0.745138 q^{8} +(1.95145 - 2.27856i) q^{9} +O(q^{10})\)	\(q+(0.949697 - 1.64492i) q^{2} +(1.57344 - 0.724068i) q^{3} +(-0.803848 - 1.39231i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.303258 - 3.27584i) q^{6} +(2.16725 - 3.75380i) q^{7} +0.745138 q^{8} +(1.95145 - 2.27856i) q^{9} +1.89939 q^{10} +(-2.70926 + 4.69257i) q^{11} +(-2.27294 - 1.60867i) q^{12} +(0.848304 + 1.46931i) q^{13} +(-4.11647 - 7.12994i) q^{14} +(1.41378 + 1.00061i) q^{15} +(2.31535 - 4.01031i) q^{16} -5.99511 q^{17} +(-1.89477 - 5.37393i) q^{18} +1.00000 q^{19} +(0.803848 - 1.39231i) q^{20} +(0.692050 - 7.47563i) q^{21} +(5.14594 + 8.91304i) q^{22} +(2.89474 + 5.01385i) q^{23} +(1.17243 - 0.539531i) q^{24} +(-0.500000 + 0.866025i) q^{25} +3.22253 q^{26} +(1.42066 - 4.99817i) q^{27} -6.96858 q^{28} +(0.922912 - 1.59853i) q^{29} +(2.98859 - 1.37529i) q^{30} +(-1.33877 - 2.31882i) q^{31} +(-3.65263 - 6.32654i) q^{32} +(-0.865122 + 9.34518i) q^{33} +(-5.69354 + 9.86150i) q^{34} +4.33451 q^{35} +(-4.74113 - 0.885399i) q^{36} -10.5086 q^{37} +(0.949697 - 1.64492i) q^{38} +(2.39864 + 1.69764i) q^{39} +(0.372569 + 0.645308i) q^{40} +(5.21753 + 9.03702i) q^{41} +(-11.6396 - 8.23795i) q^{42} +(-2.72440 + 4.71880i) q^{43} +8.71133 q^{44} +(2.94902 + 0.550725i) q^{45} +10.9965 q^{46} +(1.48315 - 2.56889i) q^{47} +(0.739340 - 7.98647i) q^{48} +(-5.89399 - 10.2087i) q^{49} +(0.949697 + 1.64492i) q^{50} +(-9.43297 + 4.34087i) q^{51} +(1.36382 - 2.36220i) q^{52} -7.76809 q^{53} +(-6.87241 - 7.08363i) q^{54} -5.41851 q^{55} +(1.61490 - 2.79710i) q^{56} +(1.57344 - 0.724068i) q^{57} +(-1.75297 - 3.03624i) q^{58} +(-3.73704 - 6.47275i) q^{59} +(0.256686 - 2.77276i) q^{60} +(-0.736384 + 1.27546i) q^{61} -5.08570 q^{62} +(-4.32396 - 12.2636i) q^{63} -4.61415 q^{64} +(-0.848304 + 1.46931i) q^{65} +(14.5505 + 10.2981i) q^{66} +(-1.05258 - 1.82313i) q^{67} +(4.81916 + 8.34703i) q^{68} +(8.18508 + 5.79301i) q^{69} +(4.11647 - 7.12994i) q^{70} +9.51253 q^{71} +(1.45410 - 1.69784i) q^{72} -2.22539 q^{73} +(-9.97997 + 17.2858i) q^{74} +(-0.159660 + 1.72468i) q^{75} +(-0.803848 - 1.39231i) q^{76} +(11.7433 + 20.3400i) q^{77} +(5.07047 - 2.33333i) q^{78} +(3.20613 - 5.55319i) q^{79} +4.63070 q^{80} +(-1.38368 - 8.89300i) q^{81} +19.8203 q^{82} +(-7.55133 + 13.0793i) q^{83} +(-10.9647 + 5.04573i) q^{84} +(-2.99756 - 5.19192i) q^{85} +(5.17470 + 8.96285i) q^{86} +(0.294705 - 3.18345i) q^{87} +(-2.01877 + 3.49661i) q^{88} -3.09745 q^{89} +(3.70657 - 4.32788i) q^{90} +7.35397 q^{91} +(4.65387 - 8.06074i) q^{92} +(-3.78546 - 2.67917i) q^{93} +(-2.81709 - 4.87934i) q^{94} +(0.500000 + 0.866025i) q^{95} +(-10.3280 - 7.30970i) q^{96} +(-6.93187 + 12.0064i) q^{97} -22.3900 q^{98} +(5.40533 + 15.3305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9	\( 46 q + 3 q^{2} + 2 q^{3} - 29 q^{4} + 23 q^{5} + 3 q^{6} - 10 q^{7} - 12 q^{8} - 8 q^{9} + 6 q^{10} - q^{11} + 9 q^{12} - 11 q^{13} - 3 q^{14} + q^{15} - 45 q^{16} - 30 q^{17} - 18 q^{18} + 46 q^{19} + 29 q^{20} - 2 q^{21} - 5 q^{22} + 13 q^{23} - 6 q^{24} - 23 q^{25} - 12 q^{26} + 23 q^{27} + 56 q^{28} + 2 q^{29} + 6 q^{30} - 16 q^{31} + 25 q^{32} + 19 q^{33} - 18 q^{34} - 20 q^{35} - 5 q^{36} + 58 q^{37} + 3 q^{38} + 32 q^{39} - 6 q^{40} + 14 q^{41} - 67 q^{42} - 34 q^{43} + 64 q^{44} - 7 q^{45} - 4 q^{46} + 22 q^{47} + 89 q^{48} - 61 q^{49} + 3 q^{50} - 38 q^{51} - 20 q^{52} - 70 q^{53} - 91 q^{54} - 2 q^{55} - 26 q^{56} + 2 q^{57} - 23 q^{58} - 15 q^{59} + 3 q^{60} - 32 q^{61} + 6 q^{62} - 31 q^{63} + 164 q^{64} + 11 q^{65} + 54 q^{66} - 16 q^{67} + 26 q^{68} - 19 q^{69} + 3 q^{70} + 50 q^{71} + 22 q^{72} + 82 q^{73} + 9 q^{74} - q^{75} - 29 q^{76} + 18 q^{77} - 41 q^{78} - 11 q^{79} - 90 q^{80} + 8 q^{81} + 60 q^{82} + 26 q^{83} + 123 q^{84} - 15 q^{85} - 15 q^{86} - 26 q^{87} - 22 q^{88} + 40 q^{89} - 12 q^{90} + 116 q^{91} + 2 q^{92} + 42 q^{93} - 36 q^{94} + 23 q^{95} - 48 q^{96} - 50 q^{97} - 24 q^{98} - 29 q^{99}+O(q^{100}) \) 46 * q + 3 * q^2 + 2 * q^3 - 29 * q^4 + 23 * q^5 + 3 * q^6 - 10 * q^7 - 12 * q^8 - 8 * q^9 + 6 * q^10 - q^11 + 9 * q^12 - 11 * q^13 - 3 * q^14 + q^15 - 45 * q^16 - 30 * q^17 - 18 * q^18 + 46 * q^19 + 29 * q^20 - 2 * q^21 - 5 * q^22 + 13 * q^23 - 6 * q^24 - 23 * q^25 - 12 * q^26 + 23 * q^27 + 56 * q^28 + 2 * q^29 + 6 * q^30 - 16 * q^31 + 25 * q^32 + 19 * q^33 - 18 * q^34 - 20 * q^35 - 5 * q^36 + 58 * q^37 + 3 * q^38 + 32 * q^39 - 6 * q^40 + 14 * q^41 - 67 * q^42 - 34 * q^43 + 64 * q^44 - 7 * q^45 - 4 * q^46 + 22 * q^47 + 89 * q^48 - 61 * q^49 + 3 * q^50 - 38 * q^51 - 20 * q^52 - 70 * q^53 - 91 * q^54 - 2 * q^55 - 26 * q^56 + 2 * q^57 - 23 * q^58 - 15 * q^59 + 3 * q^60 - 32 * q^61 + 6 * q^62 - 31 * q^63 + 164 * q^64 + 11 * q^65 + 54 * q^66 - 16 * q^67 + 26 * q^68 - 19 * q^69 + 3 * q^70 + 50 * q^71 + 22 * q^72 + 82 * q^73 + 9 * q^74 - q^75 - 29 * q^76 + 18 * q^77 - 41 * q^78 - 11 * q^79 - 90 * q^80 + 8 * q^81 + 60 * q^82 + 26 * q^83 + 123 * q^84 - 15 * q^85 - 15 * q^86 - 26 * q^87 - 22 * q^88 + 40 * q^89 - 12 * q^90 + 116 * q^91 + 2 * q^92 + 42 * q^93 - 36 * q^94 + 23 * q^95 - 48 * q^96 - 50 * q^97 - 24 * q^98 - 29 * q^99

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