LMFDB - Embedded newform 56.3.j.a.5.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [56,3,Mod(5,56)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(56, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("56.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 56 = 2^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	56.j (of order $6$, 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:	$1.52588948042$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.10
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.687752 + 1.87803i) q^{2} +(1.94818 + 3.37434i) q^{3} +(-3.05399 + 2.58324i) q^{4} +(4.42985 - 7.67272i) q^{5} +(-4.99725 + 5.97944i) q^{6} +(-6.92329 + 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 + 5.35338i) q^{9} +O(q^{10})$	\(q+(0.687752 + 1.87803i) q^{2} +(1.94818 + 3.37434i) q^{3} +(-3.05399 + 2.58324i) q^{4} +(4.42985 - 7.67272i) q^{5} +(-4.99725 + 5.97944i) q^{6} +(-6.92329 + 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 + 5.35338i) q^{9} +(17.4562 + 3.04246i) q^{10} +(3.15749 - 1.82298i) q^{11} +(-14.6664 - 5.27261i) q^{12} +7.79378 q^{13} +(-6.70239 - 12.2914i) q^{14} +34.5205 q^{15} +(2.65376 - 15.7784i) q^{16} +(-9.07152 + 5.23744i) q^{17} +(-12.1795 - 2.12277i) q^{18} +(-5.39264 + 9.34032i) q^{19} +(6.29174 + 34.8758i) q^{20} +(-16.9751 - 21.3482i) q^{21} +(5.59518 + 4.67610i) q^{22} +(6.45553 - 11.1813i) q^{23} +(-0.184759 - 31.1703i) q^{24} +(-26.7471 - 46.3273i) q^{25} +(5.36019 + 14.6370i) q^{26} +10.9817 q^{27} +(18.4740 - 21.0407i) q^{28} +17.2327i q^{29} +(23.7415 + 64.8305i) q^{30} +(-26.1797 + 15.1148i) q^{31} +(31.4574 - 5.86779i) q^{32} +(12.3027 + 7.10296i) q^{33} +(-16.0750 - 13.4345i) q^{34} +(-22.7396 + 57.6986i) q^{35} +(-4.38985 - 24.3334i) q^{36} +(-34.2810 - 19.7922i) q^{37} +(-21.2502 - 3.70371i) q^{38} +(15.1837 + 26.2989i) q^{39} +(-61.1706 + 35.8020i) q^{40} +73.6801i q^{41} +(28.4178 - 46.5619i) q^{42} -40.8501i q^{43} +(-4.93377 + 13.7239i) q^{44} +(27.3833 + 47.4293i) q^{45} +(25.4386 + 4.43371i) q^{46} +(-36.2025 - 20.9015i) q^{47} +(58.4116 - 21.7844i) q^{48} +(46.8639 - 14.3100i) q^{49} +(68.6087 - 82.0935i) q^{50} +(-35.3458 - 20.4069i) q^{51} +(-23.8022 + 20.1332i) q^{52} +(5.55272 - 3.20586i) q^{53} +(7.55266 + 20.6239i) q^{54} -32.3020i q^{55} +(52.2206 + 20.2239i) q^{56} -42.0232 q^{57} +(-32.3635 + 11.8518i) q^{58} +(7.95742 + 13.7827i) q^{59} +(-105.425 + 89.1746i) q^{60} +(6.07848 - 10.5282i) q^{61} +(-46.3912 - 38.7709i) q^{62} +(15.8658 - 40.2572i) q^{63} +(32.6548 + 55.0424i) q^{64} +(34.5253 - 59.7995i) q^{65} +(-4.87837 + 27.9899i) q^{66} +(-6.75274 + 3.89870i) q^{67} +(14.1748 - 39.4290i) q^{68} +50.3060 q^{69} +(-123.999 - 3.02333i) q^{70} -41.3627 q^{71} +(42.6797 - 24.9796i) q^{72} +(77.6038 - 44.8046i) q^{73} +(13.5934 - 77.9929i) q^{74} +(104.216 - 180.507i) q^{75} +(-7.65920 - 42.4557i) q^{76} +(-19.9762 + 15.8842i) q^{77} +(-38.9475 + 46.6025i) q^{78} +(-35.3975 + 61.3103i) q^{79} +(-109.307 - 90.2574i) q^{80} +(49.2112 + 85.2363i) q^{81} +(-138.373 + 50.6736i) q^{82} +60.8673 q^{83} +(106.989 + 21.3465i) q^{84} +92.8043i q^{85} +(76.7177 - 28.0947i) q^{86} +(-58.1489 + 33.5723i) q^{87} +(-29.1671 + 0.172886i) q^{88} +(-23.4004 - 13.5102i) q^{89} +(-70.2407 + 84.0463i) q^{90} +(-53.9586 + 8.05463i) q^{91} +(9.16883 + 50.8238i) q^{92} +(-102.005 - 58.8927i) q^{93} +(14.3553 - 82.3644i) q^{94} +(47.7771 + 82.7524i) q^{95} +(81.0845 + 94.7165i) q^{96} -3.26608i q^{97} +(59.1054 + 78.1701i) q^{98} +22.5377i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/56\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$29$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	0.687752	+	1.87803i	0.343876	+	0.939015i
$2$	0.687752	+	1.87803i	0.343876	+	0.939015i
$3$	1.94818	+	3.37434i	0.649392	+	1.12478i	0.983268	+	0.182163i	$0.0583098\pi$
$3$	1.94818	+	3.37434i	0.649392	+	1.12478i	−0.333876	+	0.942617i	$0.608357\pi$
$4$	−3.05399	+	2.58324i	−0.763498	+	0.645810i
$5$	4.42985	−	7.67272i	0.885969	−	1.53454i	0.0413705	−	0.999144i	$-0.486828\pi$
$5$	4.42985	−	7.67272i	0.885969	−	1.53454i	0.844599	−	0.535400i	$-0.179839\pi$
$6$	−4.99725	+	5.97944i	−0.832875	+	0.996574i
$7$	−6.92329	+	1.03347i	−0.989041	+	0.147638i
$7$	−6.92329	+	1.03347i	−0.989041	+	0.147638i
$8$	−6.95179	−	3.95886i	−0.868974	−	0.494858i
$9$	−3.09078	+	5.35338i	−0.343420	+	0.594820i
$10$	17.4562	+	3.04246i	1.74562	+	0.304246i
$11$	3.15749	−	1.82298i	0.287045	−	0.165725i	−0.349564	−	0.936913i	$-0.613670\pi$
$11$	3.15749	−	1.82298i	0.287045	−	0.165725i	0.636608	+	0.771187i	$0.280337\pi$
$12$	−14.6664	−	5.27261i	−1.22220	−	0.439384i
$13$	7.79378			0.599522			0.299761	−	0.954014i	$-0.403093\pi$
$13$	7.79378			0.599522			0.299761	+	0.954014i	$0.403093\pi$
$14$	−6.70239	−	12.2914i	−0.478742	−	0.877955i
$15$	34.5205			2.30136
$16$	2.65376	−	15.7784i	0.165860	−	0.986149i
$17$	−9.07152	+	5.23744i	−0.533619	+	0.308085i	−0.742489	−	0.669858i	$-0.766355\pi$
$17$	−9.07152	+	5.23744i	−0.533619	+	0.308085i	0.208870	+	0.977943i	$0.433021\pi$
$18$	−12.1795	−	2.12277i	−0.676639	−	0.117932i
$19$	−5.39264	+	9.34032i	−0.283823	+	0.491596i	−0.972323	−	0.233640i	$-0.924936\pi$
$19$	−5.39264	+	9.34032i	−0.283823	+	0.491596i	0.688500	+	0.725236i	$0.258269\pi$
$20$	6.29174	+	34.8758i	0.314587	+	1.74379i
$21$	−16.9751	−	21.3482i	−0.808336	−	1.01658i
$22$	5.59518	+	4.67610i	0.254326	+	0.212550i
$23$	6.45553	−	11.1813i	0.280675	−	0.486144i	−0.690876	−	0.722973i	$-0.742775\pi$
$23$	6.45553	−	11.1813i	0.280675	−	0.486144i	0.971551	+	0.236829i	$0.0761083\pi$
$24$	−0.184759	−	31.1703i	−0.00769831	−	1.29876i
$25$	−26.7471	−	46.3273i	−1.06988	−	1.85309i
$26$	5.36019	+	14.6370i	0.206161	+	0.562960i
$27$	10.9817			0.406728
$28$	18.4740	−	21.0407i	0.659785	−	0.751454i
$29$			17.2327i			0.594231i	0.954842	+	0.297115i	$0.0960246\pi$
$29$			17.2327i			0.594231i	−0.954842	+	0.297115i	$0.903975\pi$
$30$	23.7415	+	64.8305i	0.791384	+	2.16102i
$31$	−26.1797	+	15.1148i	−0.844505	+	0.487575i	−0.858793	−	0.512323i	$-0.828785\pi$
$31$	−26.1797	+	15.1148i	−0.844505	+	0.487575i	0.0142878	+	0.999898i	$0.495452\pi$
$32$	31.4574	−	5.86779i	0.983044	−	0.183368i
$33$	12.3027	+	7.10296i	0.372809	+	0.215241i
$34$	−16.0750	−	13.4345i	−0.472795	−	0.395133i
$35$	−22.7396	+	57.6986i	−0.649703	+	1.64853i
$36$	−4.38985	−	24.3334i	−0.121940	−	0.675928i
$37$	−34.2810	−	19.7922i	−0.926515	−	0.534924i	−0.0408071	−	0.999167i	$-0.512993\pi$
$37$	−34.2810	−	19.7922i	−0.926515	−	0.534924i	−0.885708	+	0.464244i	$0.846326\pi$
$38$	−21.2502	−	3.70371i	−0.559216	−	0.0974660i
$39$	15.1837	+	26.2989i	0.389324	+	0.674330i
$40$	−61.1706	+	35.8020i	−1.52927	+	0.895049i
$41$			73.6801i			1.79707i	0.438897	+	0.898537i	$0.355369\pi$
$41$			73.6801i			1.79707i	−0.438897	+	0.898537i	$0.644631\pi$
$42$	28.4178	−	46.5619i	0.676615	−	1.10862i
$43$		−	40.8501i		−	0.950002i	−0.879985	−	0.475001i	$-0.842448\pi$
$43$		−	40.8501i		−	0.950002i	0.879985	−	0.475001i	$-0.157552\pi$
$44$	−4.93377	+	13.7239i	−0.112131	+	0.311907i
$45$	27.3833	+	47.4293i	0.608518	+	1.05398i
$46$	25.4386	+	4.43371i	0.553014	+	0.0963851i
$47$	−36.2025	−	20.9015i	−0.770266	−	0.444713i	0.0627038	−	0.998032i	$-0.480028\pi$
$47$	−36.2025	−	20.9015i	−0.770266	−	0.444713i	−0.832969	+	0.553319i	$0.813361\pi$
$48$	58.4116	−	21.7844i	1.21691	−	0.453842i
$49$	46.8639	−	14.3100i	0.956406	−	0.292041i
$50$	68.6087	−	82.0935i	1.37217	−	1.64187i
$51$	−35.3458	−	20.4069i	−0.693055	−	0.400136i
$52$	−23.8022	+	20.1332i	−0.457734	+	0.387177i
$53$	5.55272	−	3.20586i	0.104768	−	0.0604880i	−0.446700	−	0.894684i	$-0.647401\pi$
$53$	5.55272	−	3.20586i	0.104768	−	0.0604880i	0.551469	+	0.834196i	$0.314068\pi$
$54$	7.55266	+	20.6239i	0.139864	+	0.381924i
$55$		−	32.3020i		−	0.587310i
$56$	52.2206	+	20.2239i	0.932511	+	0.361141i
$57$	−42.0232			−0.737249
$58$	−32.3635	+	11.8518i	−0.557991	+	0.204342i
$59$	7.95742	+	13.7827i	0.134871	+	0.233604i	0.925548	−	0.378629i	$-0.123605\pi$
$59$	7.95742	+	13.7827i	0.134871	+	0.233604i	−0.790677	+	0.612234i	$0.790271\pi$
$60$	−105.425	+	89.1746i	−1.75709	+	1.48624i
$61$	6.07848	−	10.5282i	0.0996472	−	0.172594i	−0.811891	−	0.583808i	$-0.801562\pi$
$61$	6.07848	−	10.5282i	0.0996472	−	0.172594i	0.911539	+	0.411214i	$0.134895\pi$
$62$	−46.3912	−	38.7709i	−0.748246	−	0.625338i
$63$	15.8658	−	40.2572i	0.251838	−	0.639004i
$64$	32.6548	+	55.0424i	0.510231	+	0.860037i
$65$	34.5253	−	59.7995i	0.531158	−	0.919992i
$66$	−4.87837	+	27.9899i	−0.0739147	+	0.424089i
$67$	−6.75274	+	3.89870i	−0.100787	+	0.0581895i	−0.549546	−	0.835463i	$-0.685199\pi$
$67$	−6.75274	+	3.89870i	−0.100787	+	0.0581895i	0.448759	+	0.893653i	$0.351866\pi$
$68$	14.1748	−	39.4290i	0.208453	−	0.579839i
$69$	50.3060			0.729073
$70$	−123.999	−	3.02333i	−1.77141	−	0.0431905i
$71$	−41.3627			−0.582574			−0.291287	−	0.956636i	$-0.594083\pi$
$71$	−41.3627			−0.582574			−0.291287	+	0.956636i	$0.594083\pi$
$72$	42.6797	−	24.9796i	0.592774	−	0.346939i
$73$	77.6038	−	44.8046i	1.06307	−	0.613761i	0.136787	−	0.990601i	$-0.456322\pi$
$73$	77.6038	−	44.8046i	1.06307	−	0.613761i	0.926279	+	0.376839i	$0.122989\pi$
$74$	13.5934	−	77.9929i	0.183695	−	1.05396i
$75$	104.216	−	180.507i	1.38955	−	2.40677i
$76$	−7.65920	−	42.4557i	−0.100779	−	0.558628i
$77$	−19.9762	+	15.8842i	−0.259432	+	0.206288i
$78$	−38.9475	+	46.6025i	−0.499326	+	0.597467i
$79$	−35.3975	+	61.3103i	−0.448070	+	0.776080i	−0.998260	−	0.0589594i	$-0.981222\pi$
$79$	−35.3975	+	61.3103i	−0.448070	+	0.776080i	0.550191	+	0.835039i	$0.314555\pi$
$80$	−109.307	−	90.2574i	−1.36634	−	1.12822i
$81$	49.2112	+	85.2363i	0.607546	+	1.05230i
$82$	−138.373	+	50.6736i	−1.68748	+	0.617971i
$83$	60.8673			0.733341			0.366671	−	0.930351i	$-0.380498\pi$
$83$	60.8673			0.733341			0.366671	+	0.930351i	$0.380498\pi$
$84$	106.989	+	21.3465i	1.27368	+	0.254125i
$85$			92.8043i			1.09182i
$86$	76.7177	−	28.0947i	0.892066	−	0.326683i
$87$	−58.1489	+	33.5723i	−0.668379	+	0.385889i
$88$	−29.1671	+	0.172886i	−0.331445	+	0.00196461i
$89$	−23.4004	−	13.5102i	−0.262926	−	0.151800i	0.362743	−	0.931889i	$-0.381840\pi$
$89$	−23.4004	−	13.5102i	−0.262926	−	0.151800i	−0.625668	+	0.780089i	$0.715174\pi$
$90$	−70.2407	+	84.0463i	−0.780453	+	0.933848i
$91$	−53.9586	+	8.05463i	−0.592952	+	0.0885124i
$92$	9.16883	+	50.8238i	0.0996612	+	0.552433i
$93$	−102.005	−	58.8927i	−1.09683	−	0.633255i
$94$	14.3553	−	82.3644i	0.152716	−	0.876217i
$95$	47.7771	+	82.7524i	0.502917	+	0.871078i
$96$	81.0845	+	94.7165i	0.844630	+	0.986630i
$97$		−	3.26608i		−	0.0336710i	−0.999858	−	0.0168355i	$-0.994641\pi$
$97$		−	3.26608i		−	0.0336710i	0.999858	−	0.0168355i	$-0.00535916\pi$
$98$	59.1054	+	78.1701i	0.603116	+	0.797654i
$99$			22.5377i			0.227653i
$100$	201.360	+	72.3892i	2.01360	+	0.723892i
$101$	68.8571	+	119.264i	0.681754	+	1.18083i	0.974445	+	0.224625i	$0.0721158\pi$
$101$	68.8571	+	119.264i	0.681754	+	1.18083i	−0.292691	+	0.956207i	$0.594551\pi$
$102$	14.0156	−	80.4154i	0.137408	−	0.788387i
$103$	86.3243	+	49.8393i	0.838100	+	0.483877i	0.856618	−	0.515952i	$-0.172562\pi$
$103$	86.3243	+	49.8393i	0.838100	+	0.483877i	−0.0185182	+	0.999829i	$0.505895\pi$
$104$	−54.1807	−	30.8545i	−0.520969	−	0.296678i
$105$	−238.995	+	35.6758i	−2.27615	+	0.339770i
$106$	9.83960	+	8.22333i	0.0928265	+	0.0775786i
$107$	81.4157	+	47.0054i	0.760894	+	0.439302i	0.829617	−	0.558333i	$-0.188559\pi$
$107$	81.4157	+	47.0054i	0.760894	+	0.439302i	−0.0687226	+	0.997636i	$0.521892\pi$
$108$	−33.5379	+	28.3682i	−0.310536	+	0.262669i
$109$	169.697	−	97.9745i	1.55685	−	0.898849i	0.559297	−	0.828967i	$-0.311071\pi$
$109$	169.697	−	97.9745i	1.55685	−	0.898849i	0.997555	−	0.0698815i	$-0.0222621\pi$
$110$	60.6642	−	22.2158i	0.551493	−	0.201962i
$111$		−	154.234i		−	1.38950i
$112$	−2.06626	+	111.981i	−0.0184487	+	0.999830i
$113$	101.873			0.901527			0.450763	−	0.892643i	$-0.351152\pi$
$113$	101.873			0.901527			0.450763	+	0.892643i	$0.351152\pi$
$114$	−28.9016	−	78.9209i	−0.253522	−	0.692288i
$115$	−57.1940	−	99.0629i	−0.497339	−	0.861417i
$116$	−44.5161	−	52.6285i	−0.383760	−	0.453694i
$117$	−24.0888	+	41.7231i	−0.205887	+	0.356608i
$118$	−20.4115	+	24.4233i	−0.172979	+	0.206977i
$119$	57.3920	−	45.6355i	0.482286	−	0.383491i
$120$	−239.979	−	136.662i	−1.99983	−	1.13885i
$121$	−53.8535	+	93.2770i	−0.445070	+	0.770884i
$122$	23.9528	+	4.17475i	0.196335	+	0.0342193i
$123$	−248.622	+	143.542i	−2.02131	+	1.16701i
$124$	40.9073	−	113.789i	0.329898	−	0.917653i
$125$	−252.449			−2.01960
$126$	86.5160	+	2.10943i	0.686635	+	0.0167415i
$127$	−139.079			−1.09511			−0.547554	−	0.836770i	$-0.684441\pi$
$127$	−139.079			−1.09511			−0.547554	+	0.836770i	$0.684441\pi$
$128$	−80.9129	+	99.1822i	−0.632132	+	0.774861i
$129$	137.842	−	79.5831i	1.06854	−	0.616924i
$130$	136.050	+	23.7122i	1.04654	+	0.182402i
$131$	−45.8526	+	79.4190i	−0.350020	+	0.606252i	−0.986252	−	0.165245i	$-0.947158\pi$
$131$	−45.8526	+	79.4190i	−0.350020	+	0.606252i	0.636233	+	0.771497i	$0.280492\pi$
$132$	−55.9210	+	10.0884i	−0.423644	+	0.0764272i
$133$	27.6819	−	70.2389i	0.208134	−	0.528112i
$134$	−11.9661	−	10.0005i	−0.0892991	−	0.0746307i
$135$	48.6471	−	84.2592i	0.360349	−	0.624142i
$136$	83.7976	−	0.496704i	0.616159	−	0.00365224i
$137$	−99.7904	−	172.842i	−0.728397	−	1.26162i	−0.957560	−	0.288233i	$-0.906932\pi$
$137$	−99.7904	−	172.842i	−0.728397	−	1.26162i	0.229163	−	0.973388i	$-0.426401\pi$
$138$	34.5981	+	94.4762i	0.250711	+	0.684610i
$139$	39.4768			0.284006			0.142003	−	0.989866i	$-0.454646\pi$
$139$	39.4768			0.284006			0.142003	+	0.989866i	$0.454646\pi$
$140$	−79.6026	−	234.953i	−0.568590	−	1.67823i
$141$		−	162.879i		−	1.15517i
$142$	−28.4473	−	77.6805i	−0.200333	−	0.547046i
$143$	24.6088	−	14.2079i	0.172089	−	0.0993559i
$144$	76.2656	+	62.9740i	0.529622	+	0.437320i
$145$	132.222	+	76.3382i	0.911873	+	0.526470i
$146$	137.516	+	114.928i	0.941894	+	0.787177i
$147$	139.586	+	130.256i	0.949564	+	0.886097i
$148$	155.822	−	28.1110i	1.05285	−	0.189939i
$149$	−82.0846	−	47.3916i	−0.550903	−	0.318064i	0.198583	−	0.980084i	$-0.436366\pi$
$149$	−82.0846	−	47.3916i	−0.550903	−	0.318064i	−0.749486	+	0.662020i	$0.769699\pi$
$150$	410.673	+	71.5764i	2.73782	+	0.477176i
$151$	−33.2843	−	57.6501i	−0.220426	−	0.381789i	0.734511	−	0.678596i	$-0.237411\pi$
$151$	−33.2843	−	57.6501i	−0.220426	−	0.381789i	−0.954937	+	0.296807i	$0.904078\pi$
$152$	74.4655	−	43.5832i	0.489905	−	0.286732i
$153$		−	64.7511i		−	0.423210i
$154$	−43.5696	−	26.5916i	−0.282920	−	0.172673i
$155$			267.826i			1.72791i
$156$	−114.307	−	41.0936i	−0.732737	−	0.263420i
$157$	12.7597	+	22.1004i	0.0812720	+	0.140767i	0.903797	−	0.427962i	$-0.140768\pi$
$157$	12.7597	+	22.1004i	0.0812720	+	0.140767i	−0.822525	+	0.568730i	$0.807435\pi$
$158$	−139.487	−	24.3113i	−0.882831	−	0.153869i
$159$	21.6353	+	12.4912i	0.136071	+	0.0785608i
$160$	94.3296	−	267.357i	0.589560	−	1.67098i
$161$	−33.1380	+	84.0830i	−0.205826	+	0.522255i
$162$	−126.231	+	151.042i	−0.779205	+	0.932355i
$163$	−166.364	−	96.0504i	−1.02064	−	0.589267i	−0.106350	−	0.994329i	$-0.533917\pi$
$163$	−166.364	−	96.0504i	−1.02064	−	0.589267i	−0.914289	+	0.405062i	$0.867250\pi$
$164$	−190.333	−	225.018i	−1.16057	−	1.37206i
$165$	108.998	−	62.9301i	0.660594	−	0.381394i
$166$	41.8616	+	114.311i	0.252179	+	0.688618i
$167$			184.150i			1.10269i	0.834276	+	0.551346i	$0.185886\pi$
$167$			184.150i			1.10269i	−0.834276	+	0.551346i	$0.814114\pi$
$168$	33.4926	+	215.610i	0.199361	+	1.28339i
$169$	−108.257			−0.640574
$170$	−174.289	+	63.8263i	−1.02523	+	0.375449i
$171$	−33.3349	−	57.7377i	−0.194941	−	0.337647i
$172$	105.526	+	124.756i	0.613521	+	0.725325i
$173$	34.9519	−	60.5384i	0.202034	−	0.349933i	−0.747150	−	0.664656i	$-0.768578\pi$
$173$	34.9519	−	60.5384i	0.202034	−	0.349933i	0.949184	+	0.314723i	$0.101912\pi$
$174$	−103.042	−	86.1160i	−0.592195	−	0.494920i
$175$	233.056	+	293.095i	1.33175	+	1.67483i
$176$	−20.3844	−	54.6578i	−0.115821	−	0.310556i
$177$	−31.0049	+	53.7021i	−0.175169	+	0.303401i
$178$	9.27893	−	53.2383i	0.0521288	−	0.299092i
$179$	207.251	−	119.657i	1.15783	−	0.668473i	0.207047	−	0.978331i	$-0.433615\pi$
$179$	207.251	−	119.657i	1.15783	−	0.668473i	0.950783	+	0.309858i	$0.100281\pi$
$180$	−206.150	−	74.1112i	−1.14528	−	0.411729i
$181$	−36.2834			−0.200461			−0.100230	−	0.994964i	$-0.531958\pi$
$181$	−36.2834			−0.200461			−0.100230	+	0.994964i	$0.531958\pi$
$182$	−52.2370	−	95.7963i	−0.287016	−	0.526353i
$183$	47.3678			0.258840
$184$	−89.1428	+	52.1735i	−0.484472	+	0.283552i
$185$	−303.720	+	175.353i	−1.64173	+	0.947852i
$186$	40.4480	−	232.072i	0.217462	−	1.24770i
$187$	−19.0955	+	33.0744i	−0.102115	+	0.176868i
$188$	164.556	−	29.6866i	0.875296	−	0.157907i
$189$	−76.0292	+	11.3492i	−0.402271	+	0.0600487i
$190$	−122.553	+	146.640i	−0.645014	+	0.771789i
$191$	162.622	−	281.669i	0.851422	−	1.47471i	−0.0285024	−	0.999594i	$-0.509074\pi$
$191$	162.622	−	281.669i	0.851422	−	1.47471i	0.879925	−	0.475113i	$-0.157593\pi$
$192$	−122.114	+	217.421i	−0.636013	+	1.13240i
$193$	−99.8198	−	172.893i	−0.517201	−	0.895818i	−0.999800	−	0.0199772i	$-0.993641\pi$
$193$	−99.8198	−	172.893i	−0.517201	−	0.895818i	0.482599	−	0.875841i	$-0.339693\pi$
$194$	6.13381	−	2.24626i	0.0316176	−	0.0115786i
$195$	269.045			1.37972
$196$	−106.156	+	164.763i	−0.541612	+	0.840629i
$197$			15.5053i			0.0787071i	0.999225	+	0.0393536i	$0.0125299\pi$
$197$			15.5053i			0.0787071i	−0.999225	+	0.0393536i	$0.987470\pi$
$198$	−42.3264	+	15.5003i	−0.213770	+	0.0782845i
$199$	−48.6375	+	28.0809i	−0.244409	+	0.141110i	−0.617202	−	0.786805i	$-0.711734\pi$
$199$	−48.6375	+	28.0809i	−0.244409	+	0.141110i	0.372792	+	0.927915i	$0.378400\pi$
$200$	2.53662	+	427.946i	0.0126831	+	2.13973i
$201$	−26.3110	−	15.1907i	−0.130901	−	0.0755756i
$202$	−176.625	+	211.340i	−0.874380	+	1.04624i
$203$	−17.8094	−	119.307i	−0.0877312	−	0.587719i
$204$	160.662	−	28.9841i	0.787558	−	0.142079i
$205$	565.326	+	326.391i	2.75769	+	1.59215i
$206$	−34.2301	+	196.397i	−0.166165	+	0.953382i
$207$	39.9052	+	69.1178i	0.192779	+	0.333903i
$208$	20.6828	−	122.973i	0.0994365	−	0.591218i
$209$			39.3226i			0.188147i
$210$	−231.370	−	424.304i	−1.10176	−	2.02050i
$211$		−	370.470i		−	1.75578i	−0.478859	−	0.877892i	$-0.658949\pi$
$211$		−	370.470i		−	1.75578i	0.478859	−	0.877892i	$-0.341051\pi$
$212$	−8.67646	+	24.1347i	−0.0409267	+	0.113843i
$213$	−80.5819	−	139.572i	−0.378319	−	0.655267i
$214$	−32.2837	+	185.229i	−0.150858	+	0.865556i
$215$	−313.431	−	180.960i	−1.45782	−	0.841673i
$216$	−76.3422	−	43.4749i	−0.353436	−	0.201273i
$217$	165.629	−	131.700i	0.763266	−	0.606914i
$218$	300.709	+	251.314i	1.37940	+	1.15281i
$219$	302.372	+	174.574i	1.38069	+	0.797143i
$220$	83.4439	+	98.6502i	0.379290	+	0.448410i
$221$	−70.7014	+	40.8195i	−0.319916	+	0.184704i
$222$	289.657	−	106.075i	1.30476	−	0.477816i
$223$			6.78533i			0.0304275i	0.999884	+	0.0152137i	$0.00484287\pi$
$223$			6.78533i			0.0304275i	−0.999884	+	0.0152137i	$0.995157\pi$
$224$	−211.725	+	73.1346i	−0.945199	+	0.326494i
$225$	330.677			1.46968
$226$	70.0631	+	191.320i	0.310014	+	0.846547i
$227$	−148.309	−	256.879i	−0.653344	−	1.13163i	−0.982306	−	0.187282i	$-0.940032\pi$
$227$	−148.309	−	256.879i	−0.653344	−	1.13163i	0.328962	−	0.944343i	$-0.393301\pi$
$228$	128.339	−	108.556i	0.562889	−	0.476123i
$229$	−89.0964	+	154.320i	−0.389067	+	0.673885i	−0.992324	−	0.123662i	$-0.960536\pi$
$229$	−89.0964	+	154.320i	−0.389067	+	0.673885i	0.603257	+	0.797547i	$0.293869\pi$
$230$	146.708	−	175.543i	0.637860	−	0.763230i
$231$	−92.5158	−	36.4614i	−0.400501	−	0.157842i
$232$	68.2219	−	119.798i	0.294060	−	0.516371i
$233$	−58.9011	+	102.020i	−0.252795	+	0.437853i	−0.964294	−	0.264833i	$-0.914683\pi$
$233$	−58.9011	+	102.020i	−0.252795	+	0.437853i	0.711500	+	0.702687i	$0.248016\pi$
$234$	−94.9244	−	16.5444i	−0.405660	−	0.0707026i
$235$	−320.743	+	185.181i	−1.36486	+	0.788004i
$236$	−59.9058	−	21.5362i	−0.253838	−	0.0912552i
$237$	−275.842			−1.16389
$238$	125.176	+	76.3980i	0.525951	+	0.321000i
$239$	46.3543			0.193951			0.0969755	−	0.995287i	$-0.469083\pi$
$239$	46.3543			0.193951			0.0969755	+	0.995287i	$0.469083\pi$
$240$	91.6089	−	544.677i	0.381704	−	2.26949i
$241$	317.501	−	183.309i	1.31743	−	0.760619i	0.334115	−	0.942532i	$-0.391562\pi$
$241$	317.501	−	183.309i	1.31743	−	0.760619i	0.983315	+	0.181914i	$0.0582291\pi$
$242$	−212.215	−	36.9870i	−0.876921	−	0.152839i
$243$	−142.327	+	246.517i	−0.585706	+	1.01447i
$244$	8.63331	+	47.8553i	0.0353824	+	0.196128i
$245$	97.8032	−	422.965i	0.399197	−	1.72639i
$246$	−440.566	−	368.198i	−1.79092	−	1.49674i
$247$	−42.0290	+	72.7964i	−0.170158	+	0.294722i
$248$	241.833	−	1.43345i	0.975134	−	0.00578003i
$249$	118.580	+	205.387i	0.476226	+	0.824847i
$250$	−173.623	−	474.108i	−0.694490	−	1.89643i
$251$	−129.896			−0.517513			−0.258756	−	0.965943i	$-0.583313\pi$
$251$	−129.896			−0.517513			−0.258756	+	0.965943i	$0.583313\pi$
$252$	55.5400	+	163.930i	0.220397	+	0.650518i
$253$		−	47.0732i		−	0.186060i
$254$	−95.6517	−	261.194i	−0.376582	−	1.02832i
$255$	−313.153	+	180.799i	−1.22805	+	0.709016i
$256$	−241.915	−	83.7440i	−0.944981	−	0.327125i
$257$	232.394	+	134.173i	0.904256	+	0.522073i	0.878579	−	0.477598i	$-0.158492\pi$
$257$	232.394	+	134.173i	0.904256	+	0.522073i	0.0256776	+	0.999670i	$0.491826\pi$
$258$	244.261	+	204.138i	0.946747	+	0.791233i
$259$	257.792	+	101.599i	0.995337	+	0.392272i
$260$	49.0365	+	271.814i	0.188602	+	1.04544i
$261$	−92.2532	−	53.2624i	−0.353460	−	0.204070i
$262$	−180.686	−	31.4919i	−0.689643	−	0.120198i
$263$	117.691	+	203.847i	0.447495	+	0.775085i	0.998222	−	0.0596008i	$-0.0189828\pi$
$263$	117.691	+	203.847i	0.447495	+	0.775085i	−0.550727	+	0.834685i	$0.685649\pi$
$264$	−57.4061	−	98.0830i	−0.217447	−	0.371526i
$265$		−	56.8059i		−	0.214362i
$266$	150.949	+	3.68043i	0.567477	+	0.0138362i
$267$		−	105.281i		−	0.394311i
$268$	10.5516	−	29.3505i	0.0393715	−	0.109517i
$269$	177.348	+	307.175i	0.659285	+	1.14192i	0.980801	+	0.195011i	$0.0624743\pi$
$269$	177.348	+	307.175i	0.659285	+	1.14192i	−0.321516	+	0.946904i	$0.604192\pi$
$270$	191.698	+	33.4112i	0.709994	+	0.123745i
$271$	−365.350	−	210.935i	−1.34816	−	0.778358i	−0.360168	−	0.932888i	$-0.617281\pi$
$271$	−365.350	−	210.935i	−1.34816	−	0.778358i	−0.987988	+	0.154529i	$0.950614\pi$
$272$	58.5648	+	157.033i	0.215312	+	0.577327i
$273$	−132.300	−	166.383i	−0.484615	−	0.609461i
$274$	255.972	−	306.282i	0.934203	−	1.11782i
$275$	−168.907	−	97.5186i	−0.614208	−	0.354613i
$276$	−153.634	+	129.952i	−0.556646	+	0.470842i
$277$	−319.155	+	184.264i	−1.15218	+	0.665214i	−0.949419	−	0.314013i	$-0.898326\pi$
$277$	−319.155	+	184.264i	−1.15218	+	0.665214i	−0.202766	+	0.979227i	$0.564993\pi$
$278$	27.1503	+	74.1386i	0.0976628	+	0.266686i
$279$		−	186.866i		−	0.669772i
$280$	386.502	−	311.085i	1.38036	−	1.11102i
$281$	−35.2868			−0.125576			−0.0627879	−	0.998027i	$-0.519999\pi$
$281$	−35.2868			−0.125576			−0.0627879	+	0.998027i	$0.519999\pi$
$282$	305.892	−	112.021i	1.08472	−	0.397236i
$283$	−98.3087	−	170.276i	−0.347380	−	0.601681i	0.638403	−	0.769702i	$-0.279595\pi$
$283$	−98.3087	−	170.276i	−0.347380	−	0.601681i	−0.985783	+	0.168022i	$0.946262\pi$
$284$	126.322	−	106.850i	0.444794	−	0.376232i
$285$	−186.156	+	322.432i	−0.653180	+	1.13134i
$286$	43.6076	+	36.4445i	0.152474	+	0.127428i
$287$	−76.1460	−	510.108i	−0.265317	−	1.77738i
$288$	−65.8153	+	186.540i	−0.228525	+	0.647707i
$289$	−89.6384	+	155.258i	−0.310167	+	0.537226i
$290$	−52.4297	+	300.818i	−0.180792	+	1.03730i
$291$	11.0209	−	6.36291i	0.0378724	−	0.0218657i
$292$	−121.261	+	337.302i	−0.415276	+	1.15514i
$293$	317.573			1.08387			0.541933	−	0.840421i	$-0.317693\pi$
$293$	317.573			1.08387			0.541933	+	0.840421i	$0.317693\pi$
$294$	−148.625	+	351.730i	−0.505526	+	1.19636i
$295$	141.001			0.477968
$296$	159.960	+	273.305i	0.540406	+	0.923328i
$297$	34.6745	−	20.0193i	0.116749	−	0.0674051i
$298$	32.5489	−	186.751i	0.109225	−	0.626681i
$299$	50.3130	−	87.1447i	0.168271	−	0.291454i
$300$	148.019	+	820.483i	0.493396	+	2.73494i
$301$	42.2173	+	282.817i	0.140257	+	0.939591i
$302$	85.3773	−	102.158i	0.282706	−	0.338271i
$303$	−268.292	+	464.695i	−0.885451	+	1.53365i
$304$	133.064	+	109.874i	0.437712	+	0.361428i
$305$	−53.8535	−	93.2769i	−0.176569	−	0.305826i
$306$	121.604	−	44.5327i	0.397400	−	0.145532i
$307$	−132.193			−0.430596			−0.215298	−	0.976548i	$-0.569072\pi$
$307$	−132.193			−0.430596			−0.215298	+	0.976548i	$0.569072\pi$
$308$	19.9747	−	100.114i	0.0648529	−	0.325044i
$309$			388.383i			1.25690i
$310$	−502.984	+	184.198i	−1.62253	+	0.594186i
$311$	400.453	−	231.202i	1.28763	−	0.743414i	0.309400	−	0.950932i	$-0.399872\pi$
$311$	400.453	−	231.202i	1.28763	−	0.743414i	0.978231	+	0.207518i	$0.0665385\pi$
$312$	−1.43997	−	242.934i	−0.00461530	−	0.778635i
$313$	−490.206	−	283.021i	−1.56615	−	0.904220i	−0.996611	−	0.0822589i	$-0.973787\pi$
$313$	−490.206	−	283.021i	−1.56615	−	0.904220i	−0.569544	−	0.821961i	$-0.692880\pi$
$314$	−32.7298	+	39.1627i	−0.104235	+	0.124722i
$315$	−238.599	−	300.067i	−0.757458	−	0.952594i
$316$	−50.2753	−	278.682i	−0.159099	−	0.881904i
$317$	−153.315	−	88.5163i	−0.483643	−	0.279231i	0.238291	−	0.971194i	$-0.423413\pi$
$317$	−153.315	−	88.5163i	−0.483643	−	0.279231i	−0.721933	+	0.691963i	$0.756746\pi$
$318$	−8.57904	+	49.2227i	−0.0269781	+	0.154788i
$319$	31.4148	+	54.4120i	0.0984790	+	0.170571i
$320$	566.980	−	6.72171i	1.77181	−	0.0210053i
$321$			366.299i			1.14112i
$322$	−180.701	−	4.40585i	−0.561184	−	0.0136828i
$323$		−	112.975i		−	0.349766i
$324$	−370.476	−	133.187i	−1.14345	−	0.411070i
$325$	−208.461	−	361.065i	−0.641418	−	1.11097i
$326$	65.9682	−	378.496i	0.202357	−	1.16103i
$327$	661.199	+	381.743i	2.02201	+	1.16741i
$328$	291.689	−	512.208i	0.889297	−	1.56161i
$329$	272.241	+	107.293i	0.827481	+	0.326119i
$330$	193.148	+	161.421i	0.585298	+	0.489156i
$331$	429.688	+	248.080i	1.29815	+	0.749487i	0.980084	−	0.198582i	$-0.0636335\pi$
$331$	429.688	+	248.080i	1.29815	+	0.749487i	0.318065	+	0.948069i	$0.396967\pi$
$332$	−185.888	+	157.235i	−0.559905	+	0.473599i
$333$	211.910	−	122.346i	0.636367	−	0.367406i
$334$	−345.839	+	126.649i	−1.03545	+	0.379190i
$335$			69.0825i			0.206216i
$336$	−381.887	+	211.186i	−1.13657	+	0.628531i
$337$	−206.191			−0.611843			−0.305922	−	0.952057i	$-0.598965\pi$
$337$	−206.191			−0.611843			−0.305922	+	0.952057i	$0.598965\pi$
$338$	−74.4540	−	203.310i	−0.220278	−	0.601508i
$339$	198.466	+	343.752i	0.585444	+	1.01402i
$340$	−239.736	−	283.424i	−0.705105	−	0.833599i
$341$	−55.1080	+	95.4499i	−0.161607	+	0.279912i
$342$	85.5070	−	102.313i	0.250020	−	0.299161i
$343$	−309.663	+	147.505i	−0.902809	+	0.430043i
$344$	−161.720	+	283.981i	−0.470116	+	0.825527i
$345$	222.848	−	385.984i	0.645936	−	1.11879i
$346$	137.731	+	24.0052i	0.398067	+	0.0693793i
$347$	524.976	−	303.095i	1.51290	−	0.873472i	0.513013	−	0.858381i	$-0.328529\pi$
$347$	524.976	−	303.095i	1.51290	−	0.873472i	0.999886	−	0.0150913i	$-0.00480389\pi$
$348$	90.8612	−	252.742i	0.261095	−	0.726271i
$349$	136.343			0.390669			0.195335	−	0.980737i	$-0.437421\pi$
$349$	136.343			0.390669			0.195335	+	0.980737i	$0.437421\pi$
$350$	−390.157	+	639.262i	−1.11473	+	1.82646i
$351$	85.5887			0.243842
$352$	88.6296	−	75.8737i	0.251789	−	0.215550i
$353$	−8.72457	+	5.03713i	−0.0247155	+	0.0142695i	−0.512307	−	0.858802i	$-0.671209\pi$
$353$	−8.72457	+	5.03713i	−0.0247155	+	0.0142695i	0.487591	+	0.873072i	$0.337876\pi$
$354$	−122.178	−	21.2944i	−0.345135	−	0.0601537i
$355$	−183.231	+	317.365i	−0.516143	+	0.893985i
$356$	106.365	−	19.1887i	0.298777	−	0.0539007i
$357$	265.799	+	104.754i	0.744536	+	0.293429i
$358$	367.257	+	306.930i	1.02586	+	0.857347i
$359$	−197.808	+	342.613i	−0.550997	+	0.954354i	0.447206	+	0.894431i	$0.352419\pi$
$359$	−197.808	+	342.613i	−0.550997	+	0.954354i	−0.998203	+	0.0599236i	$0.980914\pi$
$360$	−2.59696	−	438.126i	−0.00721377	−	1.21702i
$361$	122.339	+	211.897i	0.338889	+	0.586973i
$362$	−24.9540	−	68.1412i	−0.0689336	−	0.188235i
$363$	−419.664			−1.15610
$364$	143.982	−	163.987i	0.395556	−	0.450513i
$365$		−	793.909i		−	2.17509i
$366$	32.5773	+	88.9581i	0.0890090	+	0.243055i
$367$	164.486	−	94.9661i	0.448191	−	0.258763i	−0.258875	−	0.965911i	$-0.583352\pi$
$367$	164.486	−	94.9661i	0.448191	−	0.258763i	0.707066	+	0.707148i	$0.250018\pi$
$368$	−159.292	−	131.530i	−0.432858	−	0.357419i
$369$	−394.438	−	227.729i	−1.06894	−	0.617151i
$370$	−538.201	−	449.795i	−1.45460	−	1.21566i
$371$	−35.1299	+	27.9337i	−0.0946898	+	0.0752930i
$372$	463.657	−	83.6457i	1.24639	−	0.224854i
$373$	−311.859	−	180.052i	−0.836083	−	0.482713i	0.0198479	−	0.999803i	$-0.493682\pi$
$373$	−311.859	−	180.052i	−0.836083	−	0.482713i	−0.855931	+	0.517090i	$0.827015\pi$
$374$	−75.2476	−	13.1149i	−0.201197	−	0.0350667i
$375$	−491.816	−	851.850i	−1.31151	−	2.27160i
$376$	168.926	+	288.624i	0.449271	+	0.767616i
$377$			134.308i			0.356254i
$378$	−73.6034	−	134.980i	−0.194718	−	0.357089i
$379$			11.2929i			0.0297966i	0.999889	+	0.0148983i	$0.00474246\pi$
$379$			11.2929i			0.0297966i	−0.999889	+	0.0148983i	$0.995258\pi$
$380$	−359.680	−	129.306i	−0.946527	−	0.340278i
$381$	−270.950	−	469.299i	−0.711154	−	1.23176i
$382$	640.826	+	111.690i	1.67756	+	0.292382i
$383$	376.075	+	217.127i	0.981918	+	0.566910i	0.902849	−	0.429959i	$-0.141472\pi$
$383$	376.075	+	217.127i	0.981918	+	0.566910i	0.0790692	+	0.996869i	$0.474805\pi$
$384$	−492.307	−	79.8031i	−1.28205	−	0.207820i
$385$	33.3831	+	223.636i	0.0867095	+	0.580874i
$386$	256.047	−	306.372i	0.663334	−	0.793710i
$387$	218.686	+	126.258i	0.565080	+	0.326249i
$388$	8.43708	+	9.97460i	0.0217450	+	0.0257077i
$389$	37.3803	−	21.5816i	0.0960934	−	0.0554796i	−0.451183	−	0.892431i	$-0.648998\pi$
$389$	37.3803	−	21.5816i	0.0960934	−	0.0554796i	0.547277	+	0.836952i	$0.315665\pi$
$390$	185.036	+	505.275i	0.474452	+	1.29558i
$391$			135.242i			0.345887i
$392$	−382.439	−	86.0476i	−0.975610	−	0.219509i
$393$	−357.315			−0.909199
$394$	−29.1194	+	10.6638i	−0.0739072	+	0.0270655i
$395$	313.611	+	543.190i	0.793952	+	1.37517i
$396$	−58.2202	−	68.8299i	−0.147021	−	0.173813i
$397$	243.395	−	421.573i	0.613086	−	1.06190i	−0.377631	−	0.925956i	$-0.623261\pi$
$397$	243.395	−	421.573i	0.613086	−	1.06190i	0.990717	−	0.135940i	$-0.0434053\pi$
$398$	−86.1872	−	72.0300i	−0.216551	−	0.180980i
$399$	290.939	−	43.4297i	0.729170	−	0.108846i
$400$	−801.950	+	299.084i	−2.00488	+	0.747711i
$401$	273.457	−	473.641i	0.681938	−	1.18115i	−0.292451	−	0.956280i	$-0.594471\pi$
$401$	273.457	−	473.641i	0.681938	−	1.18115i	0.974389	−	0.224870i	$-0.0721958\pi$
$402$	10.4331	−	59.8604i	0.0259530	−	0.148906i
$403$	−204.039	+	117.802i	−0.506299	+	0.292312i
$404$	−518.377	−	186.357i	−1.28311	−	0.461280i
$405$	871.992			2.15307
$406$	211.813	−	115.500i	0.521708	−	0.284483i
$407$	−144.323			−0.354601
$408$	164.929	+	281.794i	0.404237	+	0.690671i
$409$	57.8217	−	33.3834i	0.141373	−	0.0816220i	−0.427645	−	0.903947i	$-0.640657\pi$
$409$	57.8217	−	33.3834i	0.141373	−	0.0816220i	0.569018	+	0.822325i	$0.307323\pi$
$410$	−224.168	+	1286.18i	−0.546752	+	3.13702i
$411$	388.819	−	673.453i	0.946030	−	1.63857i
$412$	−392.381	+	70.7871i	−0.952380	+	0.171813i
$413$	−69.3354	−	87.1976i	−0.167882	−	0.211132i
$414$	−102.360	+	122.479i	−0.247248	+	0.295843i
$415$	269.633	−	467.018i	0.649718	−	1.12534i
$416$	245.172	−	45.7323i	0.589356	−	0.109933i
$417$	76.9077	+	133.208i	0.184431	+	0.319444i
$418$	−73.8491	+	27.0442i	−0.176672	+	0.0646991i
$419$	−550.169			−1.31305			−0.656527	−	0.754303i	$-0.727975\pi$
$419$	−550.169			−1.31305			−0.656527	+	0.754303i	$0.727975\pi$
$420$	637.731	−	726.335i	1.51841	−	1.72937i
$421$			579.599i			1.37672i	0.725369	+	0.688360i	$0.241669\pi$
$421$			579.599i			1.37672i	−0.725369	+	0.688360i	$0.758331\pi$
$422$	695.755	−	254.792i	1.64871	−	0.603772i
$423$	223.788	−	129.204i	0.529049	−	0.305446i
$424$	−51.2929	+	0.304035i	−0.120974	+	0.000717064i
$425$	485.273	+	280.173i	1.14182	+	0.659230i
$426$	206.700	−	247.326i	0.485211	−	0.580578i
$427$	−31.2025	+	79.1719i	−0.0730737	+	0.185414i
$428$	−370.069	+	66.7620i	−0.864647	+	0.155986i
$429$	95.8845	+	55.3589i	0.223507	+	0.129042i
$430$	124.285	−	713.089i	0.289034	−	1.65835i
$431$	215.935	+	374.010i	0.501009	+	0.867773i	0.999999	+	0.00116534i	$0.000370939\pi$
$431$	215.935	+	374.010i	0.501009	+	0.867773i	−0.498990	+	0.866607i	$0.666296\pi$
$432$	29.1426	−	173.273i	0.0674598	−	0.401095i
$433$			0.143463i			0.000331322i	1.00000		0.000165661i	$5.27316e-5\pi$
$433$			0.143463i			0.000331322i	−1.00000		0.000165661i	$0.999947\pi$
$434$	361.248	+	220.479i	0.832370	+	0.508015i
$435$			594.881i			1.36754i
$436$	−265.162	+	737.581i	−0.608169	+	1.69170i
$437$	69.6247	+	120.593i	0.159324	+	0.275958i
$438$	−119.899	+	687.927i	−0.273742	+	1.57061i
$439$	−165.713	−	95.6744i	−0.377478	−	0.217937i	0.299242	−	0.954177i	$-0.403266\pi$
$439$	−165.713	−	95.6744i	−0.377478	−	0.217937i	−0.676721	+	0.736240i	$0.736599\pi$
$440$	−127.879	+	224.557i	−0.290635	+	0.510357i
$441$	−68.2389	+	295.109i	−0.154737	+	0.669182i
$442$	−125.285	−	104.706i	−0.283451	−	0.236891i
$443$	−340.782	−	196.751i	−0.769260	−	0.444133i	0.0633505	−	0.997991i	$-0.479821\pi$
$443$	−340.782	−	196.751i	−0.769260	−	0.444133i	−0.832611	+	0.553859i	$0.813155\pi$
$444$	398.425	+	471.031i	0.897352	+	1.06088i
$445$	−207.320	+	119.696i	−0.465888	+	0.268981i
$446$	−12.7431	+	4.66663i	−0.0285719	+	0.0104633i
$447$		−	369.308i		−	0.826193i
$448$	−282.963	−	347.327i	−0.631614	−	0.775283i
$449$	−725.831			−1.61655			−0.808275	−	0.588805i	$-0.799598\pi$
$449$	−725.831			−1.61655			−0.808275	+	0.588805i	$0.799598\pi$
$450$	227.424	+	621.021i	0.505386	+	1.38005i
$451$	134.317	+	232.644i	0.297821	+	0.515841i
$452$	−311.118	+	263.161i	−0.688314	+	0.582215i
$453$	129.687	−	224.625i	0.286286	−	0.495861i
$454$	380.427	−	455.198i	0.837944	−	1.00264i
$455$	−177.227	+	449.690i	−0.389511	+	0.988330i
$456$	292.137	+	166.364i	0.640650	+	0.364834i
$457$	34.6713	−	60.0525i	0.0758673	−	0.131406i	−0.825596	−	0.564262i	$-0.809161\pi$
$457$	34.6713	−	60.0525i	0.0758673	−	0.131406i	0.901463	+	0.432856i	$0.142494\pi$
$458$	−351.093	−	61.1922i	−0.766579	−	0.133607i
$459$	−99.6203	+	57.5158i	−0.217038	+	0.125307i
$460$	430.573	+	154.792i	0.936029	+	0.336504i
$461$	−768.006			−1.66596			−0.832978	−	0.553306i	$-0.813366\pi$
$461$	−768.006			−1.66596			−0.832978	+	0.553306i	$0.813366\pi$
$462$	4.84772	−	198.824i	0.0104929	−	0.430355i
$463$	215.717			0.465911			0.232956	−	0.972487i	$-0.425160\pi$
$463$	215.717			0.465911			0.232956	+	0.972487i	$0.425160\pi$
$464$	271.904	+	45.7314i	0.586000	+	0.0985589i
$465$	−903.734	+	521.771i	−1.94351	+	1.12209i
$466$	−232.106	−	40.4538i	−0.498081	−	0.0868107i
$467$	−14.4688	+	25.0607i	−0.0309824	+	0.0536631i	−0.881101	−	0.472928i	$-0.843197\pi$
$467$	−14.4688	+	25.0607i	−0.0309824	+	0.0536631i	0.850118	+	0.526592i	$0.176530\pi$
$468$	−34.2135	−	189.649i	−0.0731058	−	0.405233i
$469$	42.7220	−	33.9705i	0.0910917	−	0.0724319i
$470$	−568.367	−	475.006i	−1.20929	−	1.01065i
$471$	−49.7163	+	86.1111i	−0.105555	+	0.182826i
$472$	−0.754659	−	127.316i	−0.00159885	−	0.269738i
$473$	−74.4688	−	128.984i	−0.157439	−	0.272693i
$474$	−189.711	−	518.040i	−0.400235	−	1.09291i
$475$	576.949			1.21463
$476$	−57.3876	+	287.628i	−0.120562	+	0.604260i
$477$			39.6344i			0.0830911i
$478$	31.8803	+	87.0547i	0.0666951	+	0.182123i
$479$	−695.377	+	401.476i	−1.45173	+	0.838154i	−0.998580	−	0.0532818i	$-0.983032\pi$
$479$	−695.377	+	401.476i	−1.45173	+	0.838154i	−0.453146	+	0.891436i	$0.649698\pi$
$480$	1085.92	−	202.559i	2.26234	−	0.421998i
$481$	−267.179	−	154.256i	−0.555466	−	0.320698i
$482$	562.622	+	470.205i	1.16726	+	0.975528i
$483$	−348.283	+	51.9897i	−0.721083	+	0.107639i
$484$	−76.4885	−	423.984i	−0.158034	−	0.876000i
$485$	−25.0598	−	14.4683i	−0.0516696	−	0.0298315i
$486$	−560.852	−	97.7511i	−1.15402	−	0.201134i
$487$	−9.96197	−	17.2546i	−0.0204558	−	0.0354305i	0.855616	−	0.517611i	$-0.173178\pi$
$487$	−9.96197	−	17.2546i	−0.0204558	−	0.0354305i	−0.876072	+	0.482180i	$0.839845\pi$
$488$	−83.9362	+	49.1262i	−0.172000	+	0.100668i
$489$		−	748.493i		−	1.53066i
$490$	861.604	−	107.217i	1.75838	−	0.218811i
$491$			76.2017i			0.155197i	0.996985	+	0.0775985i	$0.0247252\pi$
$491$			76.2017i			0.155197i	−0.996985	+	0.0775985i	$0.975275\pi$
$492$	388.486	−	1080.62i	0.789606	−	2.19639i
$493$	−90.2552	−	156.327i	−0.183073	−	0.317093i
$494$	−165.619	−	28.8659i	−0.335262	−	0.0584330i
$495$	172.925	+	99.8384i	0.349344	+	0.201694i
$496$	169.013	+	453.184i	0.340753	+	0.913677i
$497$	286.366	−	42.7471i	0.576190	−	0.0860102i
$498$	−304.169	+	363.953i	−0.610781	+	0.730828i
$499$	−452.819	−	261.435i	−0.907454	−	0.523919i	−0.0278428	−	0.999612i	$-0.508864\pi$
$499$	−452.819	−	261.435i	−0.907454	−	0.523919i	−0.879611	+	0.475694i	$0.842197\pi$
$500$	770.979	−	652.137i	1.54196	−	1.30427i
$501$	−621.384	+	358.756i	−1.24029	+	0.716080i
$502$	−89.3361	−	243.948i	−0.177960	−	0.485952i
$503$			132.060i			0.262545i	0.991346	+	0.131273i	$0.0419064\pi$
$503$			132.060i			0.262545i	−0.991346	+	0.131273i	$0.958094\pi$
$504$	−269.669	+	217.049i	−0.535057	+	0.430653i
$505$	1220.11			2.41605
$506$	88.4048	−	32.3747i	0.174713	−	0.0639816i
$507$	−210.904	−	365.296i	−0.415983	−	0.720504i
$508$	424.746	−	359.274i	0.836113	−	0.707231i
$509$	155.079	−	268.604i	0.304673	−	0.527709i	−0.672515	−	0.740083i	$-0.734786\pi$
$509$	155.079	−	268.604i	0.304673	−	0.527709i	0.977189	+	0.212374i	$0.0681194\pi$
$510$	−554.918	−	463.766i	−1.08807	−	0.909345i
$511$	−490.969	+	390.396i	−0.960801	+	0.763984i
$512$	−9.10394	−	511.919i	−0.0177811	−	0.999842i
$513$	−59.2201	+	102.572i	−0.115439	+	0.199946i
$514$	−92.1509	+	528.720i	−0.179282	+	1.02864i
$515$	764.806	−	441.561i	1.48506	−	0.857400i
$516$	−215.387	+	599.125i	−0.417416	+	1.16110i
$517$	−152.412			−0.294801
$518$	−13.5080	+	554.016i	−0.0260772	+	1.06953i
$519$	272.369			0.524797
$520$	−476.750	+	279.033i	−0.916828	+	0.536601i
$521$	52.9121	−	30.5488i	0.101559	−	0.0586349i	−0.448360	−	0.893853i	$-0.647992\pi$
$521$	52.9121	−	30.5488i	0.101559	−	0.0586349i	0.549919	+	0.835218i	$0.314659\pi$
$522$	36.5810	−	209.886i	0.0700786	−	0.402080i
$523$	−256.923	+	445.004i	−0.491249	+	0.850868i	−0.999949	−	0.0100759i	$-0.996793\pi$
$523$	−256.923	+	445.004i	−0.491249	+	0.850868i	0.508701	+	0.860944i	$0.330126\pi$
$524$	−65.1247	−	360.993i	−0.124284	−	0.688918i
$525$	−534.969	+	1357.41i	−1.01899	+	2.58554i
$526$	−301.889	+	361.224i	−0.573933	+	0.686738i
$527$	158.326	−	274.229i	0.300429	−	0.520359i
$528$	144.722	−	175.267i	0.274094	−	0.331945i
$529$	181.152	+	313.765i	0.342443	+	0.593128i
$530$	106.683	−	39.0684i	0.201289	−	0.0737140i
$531$	−98.3784			−0.185270
$532$	96.9035	+	286.018i	0.182149	+	0.537628i
$533$			574.246i			1.07739i
$534$	197.721	−	72.4073i	0.370264	−	0.135594i
$535$	721.318	−	416.453i	1.34826	−	0.778417i
$536$	62.3780	−	0.369741i	0.116377	−	0.000689816i
$537$	807.525	+	466.225i	1.50377	+	0.868202i
$538$	−454.913	+	544.325i	−0.845563	+	1.01176i
$539$	121.885	−	130.616i	0.226133	−	0.242329i
$540$	69.0938	+	382.994i	0.127951	+	0.709248i
$541$	92.7322	+	53.5390i	0.171409	+	0.0989630i	0.583250	−	0.812293i	$-0.301781\pi$
$541$	92.7322	+	53.5390i	0.171409	+	0.0989630i	−0.411841	+	0.911256i	$0.635114\pi$
$542$	144.872	−	831.210i	0.267291	−	1.53360i
$543$	−70.6863	−	122.432i	−0.130177	−	0.225474i
$544$	−254.634	+	217.986i	−0.468078	+	0.400710i
$545$		−	1736.05i		−	3.18541i
$546$	221.482	−	362.893i	0.405645	−	0.664640i
$547$		−	43.3240i		−	0.0792030i	−0.999216	−	0.0396015i	$-0.987391\pi$
$547$		−	43.3240i		−	0.0792030i	0.999216	−	0.0396015i	$-0.0126088\pi$
$548$	751.252	+	270.076i	1.37090	+	0.492840i
$549$	37.5744	+	65.0808i	0.0684416	+	0.118544i
$550$	66.9766	−	384.282i	0.121776	−	0.698694i
$551$	−160.959	−	92.9296i	−0.292121	−	0.168656i
$552$	−349.717	−	199.155i	−0.633545	−	0.360788i
$553$	181.705	−	461.051i	0.328581	−	0.833727i
$554$	−565.553	−	472.655i	−1.02085	−	0.853167i
$555$	−1183.40	−	683.235i	−2.13225	−	1.23105i
$556$	−120.562	+	101.978i	−0.216838	+	0.183414i
$557$	62.7878	−	36.2506i	0.112725	−	0.0650818i	−0.442577	−	0.896730i	$-0.645936\pi$
$557$	62.7878	−	36.2506i	0.112725	−	0.0650818i	0.555302	+	0.831648i	$0.312603\pi$
$558$	350.941	−	128.518i	0.628926	−	0.230318i
$559$		−	318.377i		−	0.569547i
$560$	850.045	+	511.912i	1.51794	+	0.914129i
$561$	−148.805			−0.265250
$562$	−24.2686	−	66.2697i	−0.0431825	−	0.117918i
$563$	292.471	+	506.575i	0.519487	+	0.899779i	0.999743	+	0.0226503i	$0.00721043\pi$
$563$	292.471	+	506.575i	0.519487	+	0.899779i	−0.480256	+	0.877128i	$0.659456\pi$
$564$	420.756	+	497.432i	0.746021	+	0.881972i
$565$	451.280	−	781.639i	0.798725	−	1.38343i
$566$	252.171	−	301.734i	0.445531	−	0.533099i
$567$	−428.792	−	539.257i	−0.756247	−	0.951071i
$568$	287.545	+	163.749i	0.506241	+	0.288291i
$569$	−371.765	+	643.915i	−0.653365	+	1.13166i	0.328936	+	0.944352i	$0.393310\pi$
$569$	−371.765	+	643.915i	−0.653365	+	1.13166i	−0.982301	+	0.187309i	$0.940023\pi$
$570$	−733.567	−	127.854i	−1.28696	−	0.224305i
$571$	893.793	−	516.031i	1.56531	−	0.903733i	0.568607	−	0.822609i	$-0.307483\pi$
$571$	893.793	−	516.031i	1.56531	−	0.903733i	0.996704	−	0.0811234i	$-0.0258508\pi$
$572$	−38.4527	+	106.961i	−0.0672250	+	0.186995i
$573$	1267.26			2.21163
$574$	905.629	−	493.833i	1.57775	−	0.860336i
$575$	−690.666			−1.20116
$576$	−395.592	+	4.68985i	−0.686791	+	0.00814209i
$577$	−825.404	+	476.547i	−1.43051	+	0.825905i	−0.997159	−	0.0753213i	$-0.976002\pi$
$577$	−825.404	+	476.547i	−1.43051	+	0.825905i	−0.433350	+	0.901226i	$0.642668\pi$
$578$	−353.229	−	61.5644i	−0.611122	−	0.106513i
$579$	388.933	−	673.652i	0.671732	−	1.16347i
$580$	−601.004	+	108.424i	−1.03621	+	0.186937i
$581$	−421.402	+	62.9044i	−0.725305	+	0.108269i
$582$	19.5294	+	16.3214i	0.0335556	+	0.0280437i
$583$	11.6884	−	20.2450i	0.0200488	−	0.0347255i
$584$	−716.860	+	4.24914i	−1.22750	+	0.00727592i
$585$	213.420	+	369.654i	0.364820	+	0.631887i
$586$	218.411	+	596.412i	0.372716	+	1.01777i
$587$	−96.2876			−0.164033			−0.0820167	−	0.996631i	$-0.526136\pi$
$587$	−96.2876			−0.164033			−0.0820167	+	0.996631i	$0.526136\pi$
$588$	−762.777	−	37.2181i	−1.29724	−	0.0632962i
$589$		−	326.035i		−	0.553540i
$590$	96.9734	+	264.803i	0.164362	+	0.448819i
$591$	−52.3201	+	30.2071i	−0.0885282	+	0.0511118i
$592$	−403.262	+	488.376i	−0.681186	+	0.824960i
$593$	44.1840	+	25.5096i	0.0745092	+	0.0430179i	0.536792	−	0.843715i	$-0.319636\pi$
$593$	44.1840	+	25.5096i	0.0745092	+	0.0430179i	−0.462283	+	0.886733i	$0.652969\pi$
$594$	61.4443	+	51.3514i	0.103442	+	0.0864501i
$595$	−95.9103	−	642.511i	−0.161194	−	1.07985i
$596$	373.109	−	67.3105i	0.626023	−	0.112937i
$597$	−189.509	−	109.413i	−0.317435	−	0.183271i
$598$	198.263	+	34.5554i	0.331544	+	0.0577849i
$599$	−451.118	−	781.359i	−0.753119	−	1.30444i	−0.946304	−	0.323277i	$-0.895215\pi$
$599$	−451.118	−	781.359i	−0.753119	−	1.30444i	0.193186	−	0.981162i	$-0.438118\pi$
$600$	−1439.09	+	842.273i	−2.39849	+	1.40379i
$601$			903.595i			1.50349i	0.659456	+	0.751743i	$0.270787\pi$
$601$			903.595i			1.50349i	−0.659456	+	0.751743i	$0.729213\pi$
$602$	−502.104	+	273.793i	−0.834060	+	0.454806i
$603$		−	48.2000i		−	0.0799337i
$604$	250.574	+	90.0818i	0.414858	+	0.149142i
$605$	477.125	+	826.406i	0.788637	+	1.36596i
$606$	−1057.23	−	184.265i	−1.74460	−	0.304067i
$607$	−306.928	−	177.205i	−0.505648	−	0.291936i	0.225395	−	0.974267i	$-0.427633\pi$
$607$	−306.928	−	177.205i	−0.505648	−	0.291936i	−0.731043	+	0.682332i	$0.760966\pi$
$608$	−114.831	+	325.465i	−0.188867	+	0.535305i
$609$	367.886	−	292.526i	0.604082	−	0.480338i
$610$	138.139	−	165.290i	0.226457	−	0.270967i
$611$	−282.154	−	162.902i	−0.461791	−	0.266615i
$612$	167.267	+	197.749i	0.273313	+	0.323120i
$613$	−290.984	+	168.000i	−0.474688	+	0.274061i	−0.718200	−	0.695837i	$-0.755034\pi$
$613$	−290.984	+	168.000i	−0.474688	+	0.274061i	0.243512	+	0.969898i	$0.421700\pi$
$614$	−90.9160	−	248.262i	−0.148072	−	0.404336i
$615$			2543.47i			4.13573i
$616$	201.754	−	31.3402i	0.327522	−	0.0508770i
$617$	223.359			0.362008			0.181004	−	0.983482i	$-0.442065\pi$
$617$	223.359			0.362008			0.181004	+	0.983482i	$0.442065\pi$
$618$	−729.395	+	267.111i	−1.18025	+	0.432219i
$619$	363.026	+	628.780i	0.586472	+	1.01580i	0.994690	+	0.102915i	$0.0328170\pi$
$619$	363.026	+	628.780i	0.586472	+	1.01580i	−0.408218	+	0.912885i	$0.633850\pi$
$620$	−691.857	−	817.938i	−1.11590	−	1.31925i
$621$	70.8925	−	122.789i	0.114159	−	0.197728i
$622$	709.617	+	593.054i	1.14086	+	0.953463i
$623$	175.970	+	69.3516i	0.282456	+	0.111319i
$624$	455.247	−	169.783i	0.729563	−	0.272088i
$625$	−449.635	+	778.791i	−0.719416	+	1.24607i
$626$	194.381	−	1115.27i	0.310513	−	1.78158i
$627$	−132.688	+	76.6074i	−0.211623	+	0.122181i
$628$	−96.0588	−	34.5333i	−0.152960	−	0.0549893i
$629$	414.642			0.659208
$630$	399.438	−	654.469i	0.634028	−	1.03884i
$631$	−326.157			−0.516888			−0.258444	−	0.966026i	$-0.583210\pi$
$631$	−326.157			−0.516888			−0.258444	+	0.966026i	$0.583210\pi$
$632$	488.795	−	286.082i	0.773410	−	0.452662i
$633$	1250.09	−	721.741i	1.97487	−	1.14019i
$634$	60.7937	−	348.807i	0.0958892	−	0.550169i
$635$	−616.097	+	1067.11i	−0.970232	+	1.68049i
$636$	−98.3419	+	17.7413i	−0.154626	+	0.0278951i
$637$	365.247	−	111.529i	0.573386	−	0.175085i
$638$	−80.5818	+	96.4200i	−0.126304	+	0.151128i
$639$	127.843	−	221.431i	0.200067	−	0.346527i
$640$	402.566	+	1060.18i	0.629009	+	1.65654i
$641$	299.187	+	518.208i	0.466751	+	0.808436i	0.999279	−	0.0379764i	$-0.0120912\pi$
$641$	299.187	+	518.208i	0.466751	+	0.808436i	−0.532528	+	0.846413i	$0.678758\pi$
$642$	−687.920	+	251.923i	−1.07153	+	0.392403i
$643$	1008.20			1.56796			0.783979	−	0.620787i	$-0.213187\pi$
$643$	1008.20			1.56796			0.783979	+	0.620787i	$0.213187\pi$
$644$	−116.003	−	342.392i	−0.180129	−	0.531665i
$645$		−	1410.16i		−	2.18630i
$646$	212.170	−	77.6985i	0.328436	−	0.120276i
$647$	574.378	−	331.617i	0.887756	−	0.512546i	0.0145481	−	0.999894i	$-0.495369\pi$
$647$	574.378	−	331.617i	0.887756	−	0.512546i	0.873208	+	0.487348i	$0.162036\pi$
$648$	−4.66705	−	787.365i	−0.00720224	−	1.21507i
$649$	50.2509	+	29.0124i	0.0774283	+	0.0447032i
$650$	534.721	−	639.819i	0.822648	−	0.984337i
$651$	767.075	+	302.312i	1.17830	+	0.464381i
$652$	756.197	−	136.421i	1.15981	−	0.209235i
$653$	857.892	+	495.304i	1.31377	+	0.758506i	0.982718	−	0.185107i	$-0.0592631\pi$
$653$	857.892	+	495.304i	1.31377	+	0.758506i	0.331052	+	0.943612i	$0.392596\pi$
$654$	−262.184	+	1504.30i	−0.400894	+	2.30015i
$655$	406.240	+	703.628i	0.620213	+	1.07424i
$656$	1162.55	+	195.529i	1.77218	+	0.298062i
$657$			553.924i			0.843110i
$658$	−14.2651	+	585.068i	−0.0216795	+	0.889162i
$659$			82.2318i			0.124783i	0.998052	+	0.0623914i	$0.0198727\pi$
$659$			82.2318i			0.124783i	−0.998052	+	0.0623914i	$0.980127\pi$
$660$	−170.316	+	473.756i	−0.258055	+	0.717812i
$661$	−313.110	−	542.322i	−0.473691	−	0.820457i	0.525855	−	0.850574i	$-0.323745\pi$
$661$	−313.110	−	542.322i	−0.473691	−	0.820457i	−0.999546	+	0.0301171i	$0.990412\pi$
$662$	−170.384	+	977.584i	−0.257377	+	1.47671i
$663$	−275.478	−	159.047i	−0.415502	−	0.239890i
$664$	−423.137	−	240.965i	−0.637254	−	0.362900i
$665$	−416.297	−	523.543i	−0.626010	−	0.787282i
$666$	375.512	+	313.830i	0.563831	+	0.471216i
$667$	192.684	+	111.246i	0.288882	+	0.166786i
$668$	−475.703	−	562.392i	−0.712130	−	0.841904i
$669$	−22.8960	+	13.2190i	−0.0342242	+	0.0197594i
$670$	−129.739	+	47.5116i	−0.193640	+	0.0709129i
$671$		−	44.3237i		−	0.0660562i
$672$	−659.258	−	571.952i	−0.981039	−	0.851118i
$673$	−150.211			−0.223196			−0.111598	−	0.993753i	$-0.535597\pi$
$673$	−150.211			−0.223196			−0.111598	+	0.993753i	$0.535597\pi$
$674$	−141.808	−	387.233i	−0.210398	−	0.574530i
$675$	−293.727	−	508.751i	−0.435152	−	0.753705i
$676$	330.616	−	279.654i	0.489077	−	0.413689i
$677$	−278.207	+	481.869i	−0.410941	+	0.711771i	−0.994993	−	0.0999455i	$-0.968133\pi$
$677$	−278.207	+	481.869i	−0.410941	+	0.711771i	0.584052	+	0.811716i	$0.301467\pi$
$678$	−509.082	+	609.141i	−0.750859	+	0.898438i
$679$	3.37540	+	22.6121i	0.00497113	+	0.0333020i
$680$	367.400	−	645.156i	0.540293	−	0.948759i
$681$	577.865	−	1000.89i	0.848553	−	1.46974i
$682$	−217.158	−	37.8486i	−0.318414	−	0.0554965i
$683$	−685.334	+	395.678i	−1.00342	+	0.579323i	−0.909258	−	0.416234i	$-0.863350\pi$
$683$	−685.334	+	395.678i	−1.00342	+	0.579323i	−0.0941597	+	0.995557i	$0.530016\pi$
$684$	250.955	+	90.2186i	0.366893	+	0.131899i
$685$	−1768.22			−2.58135
$686$	−489.990	−	480.110i	−0.714271	−	0.699869i
$687$	−694.302			−1.01063
$688$	−644.549	−	108.406i	−0.936844	−	0.157567i
$689$	43.2767	−	24.9858i	0.0628109	−	0.0362639i
$690$	878.154	+	153.054i	1.27269	+	0.221817i
$691$	488.267	−	845.703i	0.706609	−	1.22388i	−0.259499	−	0.965743i	$-0.583557\pi$
$691$	488.267	−	845.703i	0.706609	−	1.22388i	0.966108	−	0.258139i	$-0.0831093\pi$
$692$	49.6424	+	275.173i	0.0717375	+	0.397649i
$693$	−23.2920	−	156.035i	−0.0336103	−	0.225158i
$694$	930.275	+	777.466i	1.34045	+	1.12027i
$695$	174.876	−	302.894i	0.251620	−	0.435819i
$696$	537.147	−	3.18390i	0.771763	−	0.00457457i
$697$	−385.895	−	668.390i	−0.553652	−	0.958953i
$698$	93.7705	+	256.057i	0.134342	+	0.366844i
$699$	−458.999			−0.656651
$700$	−1468.88	−	293.072i	−2.09841	−	0.418675i
$701$			855.098i			1.21983i	0.792468	+	0.609913i	$0.208796\pi$
$701$			855.098i			1.21983i	−0.792468	+	0.609913i	$0.791204\pi$
$702$	58.8638	+	160.738i	0.0838516	+	0.228972i
$703$	369.730	−	213.464i	0.525932	−	0.303647i
$704$	203.448	+	114.267i	0.288989	+	0.162311i
$705$	−1249.73	−	721.530i	−1.77266	−	1.02345i
$706$	−15.4602	−	12.9207i	−0.0218983	−	0.0183013i
$707$	−599.974	−	754.538i	−0.848619	−	1.06724i
$708$	−44.0365	−	244.099i	−0.0621984	−	0.344772i
$709$	−288.794	−	166.735i	−0.407326	−	0.235170i	0.282314	−	0.959322i	$-0.408898\pi$
$709$	−288.794	−	166.735i	−0.407326	−	0.235170i	−0.689640	+	0.724152i	$0.742231\pi$
$710$	−722.038	−	125.844i	−1.01695	−	0.177245i
$711$	−218.812	−	378.993i	−0.307752	−	0.533042i
$712$	109.189	+	186.559i	0.153356	+	0.262021i
$713$			390.297i			0.547401i
$714$	−13.9276	+	571.224i	−0.0195064	+	0.800034i
$715$		−	251.755i		−	0.352105i
$716$	−323.843	+	900.811i	−0.452295	+	1.25812i
$717$	90.3063	+	156.415i	0.125950	+	0.218152i
$718$	−779.481	−	135.856i	−1.08563	−	0.189215i
$719$	−34.4877	−	19.9115i	−0.0479662	−	0.0276933i	0.475825	−	0.879540i	$-0.342150\pi$
$719$	−34.4877	−	19.9115i	−0.0479662	−	0.0276933i	−0.523791	+	0.851847i	$0.675483\pi$
$720$	821.027	−	306.199i	1.14032	−	0.425276i
$721$	−649.155	−	255.839i	−0.900354	−	0.354839i
$722$	−313.811	+	375.489i	−0.434641	+	0.520068i
$723$	1237.09	+	714.237i	1.71106	+	0.987879i
$724$	110.809	−	93.7286i	0.153051	−	0.129459i
$725$	798.344	−	460.924i	1.10116	−	0.635757i
$726$	−288.625	−	788.142i	−0.397555	−	1.08560i
$727$		−	489.402i		−	0.673180i	−0.941651	−	0.336590i	$-0.890726\pi$
$727$		−	489.402i		−	0.673180i	0.941651	−	0.336590i	$-0.109274\pi$
$728$	406.996	+	157.621i	0.559061	+	0.216512i
$729$	−223.307			−0.306320
$730$	1490.99	−	546.013i	2.04245	−	0.747963i
$731$	213.950	+	370.572i	0.292681	+	0.506939i
$732$	−144.661	+	122.362i	−0.197624	+	0.167162i
$733$	89.1592	−	154.428i	0.121636	−	0.210680i	−0.798777	−	0.601627i	$-0.794519\pi$
$733$	89.1592	−	154.428i	0.121636	−	0.210680i	0.920413	+	0.390948i	$0.127853\pi$
$734$	291.475	+	243.597i	0.397105	+	0.331876i
$735$	1617.76	−	493.988i	2.20104	−	0.672093i
$736$	137.465	−	389.615i	0.186773	−	0.529368i
$737$	−14.2145	+	24.6202i	−0.0192869	+	0.0334060i
$738$	156.406	−	897.386i	0.211932	−	1.21597i
$739$	−764.182	+	441.200i	−1.03408	+	0.597024i	−0.918149	−	0.396234i	$-0.870317\pi$
$739$	−764.182	+	441.200i	−1.03408	+	0.597024i	−0.115926	+	0.993258i	$0.536983\pi$
$740$	474.580	−	1320.11i	0.641324	−	1.78393i
$741$	−327.520			−0.441997
$742$	−76.6210	−	46.7636i	−0.103263	−	0.0630237i
$743$	1404.00			1.88964			0.944819	−	0.327591i	$-0.106237\pi$
$743$	1404.00			1.88964			0.944819	+	0.327591i	$0.106237\pi$
$744$	475.970	+	813.234i	0.639745	+	1.09306i
$745$	−727.244	+	419.875i	−0.976167	+	0.563590i
$746$	123.661	−	709.512i	0.165766	−	0.951088i
$747$	−188.127	+	325.846i	−0.251844	+	0.436206i
$748$	−27.1215	−	150.337i	−0.0362586	−	0.200985i
$749$	−612.243	−	241.291i	−0.817414	−	0.322151i
$750$	1261.55	−	1509.51i	1.68207	−	2.01268i
$751$	−102.840	+	178.124i	−0.136938	+	0.237183i	−0.926336	−	0.376698i	$-0.877059\pi$
$751$	−102.840	+	178.124i	−0.136938	+	0.237183i	0.789398	+	0.613881i	$0.210393\pi$
$752$	−425.865	+	515.749i	−0.566310	+	0.685837i
$753$	−253.060	−	438.312i	−0.336069	−	0.582088i
$754$	−252.234	+	92.3705i	−0.334528	+	0.122507i
$755$	−589.777			−0.781162
$756$	202.875	−	231.062i	0.268353	−	0.305638i
$757$			15.0345i			0.0198606i	0.999951	+	0.00993032i	$0.00316097\pi$
$757$			15.0345i			0.0198606i	−0.999951	+	0.00993032i	$0.996839\pi$
$758$	−21.2085	+	7.76673i	−0.0279795	+	0.0102464i
$759$	158.841	−	91.7068i	0.209276	−	0.120826i
$760$	−4.53105	−	764.420i	−0.00596190	−	1.00582i
$761$	−544.290	−	314.246i	−0.715229	−	0.412938i	0.0977649	−	0.995210i	$-0.468831\pi$
$761$	−544.290	−	314.246i	−0.715229	−	0.412938i	−0.812994	+	0.582272i	$0.802164\pi$
$762$	695.011	−	831.613i	0.912088	−	1.09136i
$763$	−1073.61	+	853.682i	−1.40709	+	1.11885i
$764$	230.973	+	1280.31i	0.302320	+	1.67579i
$765$	−496.817	−	286.837i	−0.649434	−	0.374951i
$766$	−149.124	+	855.609i	−0.194679	+	1.11698i
$767$	62.0184	+	107.419i	0.0808584	+	0.140051i
$768$	−188.713	−	979.452i	−0.245719	−	1.27533i
$769$			442.918i			0.575967i	0.957635	+	0.287983i	$0.0929848\pi$
$769$			442.918i			0.575967i	−0.957635	+	0.287983i	$0.907015\pi$
$770$	−397.037	+	216.501i	−0.515632	+	0.281170i
$771$			1045.57i			1.35612i
$772$	751.473	+	270.156i	0.973410	+	0.349943i
$773$	−84.5990	−	146.530i	−0.109442	−	0.189560i	0.806102	−	0.591777i	$-0.201573\pi$
$773$	−84.5990	−	146.530i	−0.109442	−	0.189560i	−0.915545	+	0.402217i	$0.868240\pi$
$774$	−86.7154	+	497.534i	−0.112035	+	0.642808i
$775$	1400.46	+	808.555i	1.80704	+	1.04330i
$776$	−12.9300	+	22.7051i	−0.0166624	+	0.0292592i
$777$	159.396	+	1067.81i	0.205143	+	1.37427i
$778$	66.2392	+	55.3586i	0.0851404	+	0.0711551i
$779$	−688.196	−	397.330i	−0.883435	−	0.510051i
$780$	−821.662	+	695.007i	−1.05341	+	0.891035i
$781$	−130.602	+	75.4034i	−0.167225	+	0.0965472i
$782$	−253.988	+	93.0129i	−0.324793	+	0.118942i
$783$			189.244i			0.241690i
$784$	−101.423	−	777.412i	−0.129367	−	0.991597i
$785$	226.094			0.288018
$786$	−245.744	−	671.049i	−0.312652	−	0.853752i
$787$	−23.2437	−	40.2593i	−0.0295346	−	0.0511554i	0.850880	−	0.525360i	$-0.176069\pi$
$787$	−23.2437	−	40.2593i	−0.0295346	−	0.0511554i	−0.880415	+	0.474204i	$0.842736\pi$
$788$	−40.0539	−	47.3531i	−0.0508298	−	0.0600928i
$789$	−458.567	+	794.261i	−0.581200	+	1.00667i
$790$	−804.441	+	962.551i	−1.01828	+	1.21842i
$791$	−705.293	+	105.282i	−0.891647	+	0.133100i
$792$	89.2236	−	156.677i	0.112656	−	0.197825i
$793$	47.3743	−	82.0548i	0.0597407	−	0.103474i
$794$	959.122	+	167.166i	1.20796	+	0.210536i
$795$	191.683	−	110.668i	0.241110	−	0.139205i
$796$	75.9990	−	211.401i	0.0954761	−	0.265579i
$797$	1351.86			1.69618			0.848092	−	0.529850i	$-0.177752\pi$
$797$	1351.86			1.69618			0.848092	+	0.529850i	$0.177752\pi$
$798$	281.656	+	516.523i	0.352952	+	0.647272i
$799$	437.882			0.548038
$800$	−1113.23	−	1300.39i	−1.39154	−	1.62549i
$801$	144.651	−	83.5141i	0.180588	−	0.104262i
$802$	1077.58	+	187.813i	1.34362	+	0.234180i
$803$	163.355	−	282.940i	0.203431	−	0.352354i
$804$	119.595	−	21.5754i	0.148750	−	0.0268351i
$805$	498.349	+	626.733i	0.619067	+	0.778551i
$806$	−361.563	−	302.172i	−0.448590	−	0.374903i
$807$	−691.009	+	1196.86i	−0.856269	+	1.48310i
$808$	−6.53022	−	1101.69i	−0.00808195	−	1.36348i
$809$	701.563	+	1215.14i	0.867198	+	1.50203i	0.864848	+	0.502034i	$0.167415\pi$
$809$	701.563	+	1215.14i	0.867198	+	1.50203i	0.00235012	+	0.999997i	$0.499252\pi$
$810$	599.714	+	1637.63i	0.740388	+	2.02176i
$811$	689.037			0.849614			0.424807	−	0.905284i	$-0.360342\pi$
$811$	689.037			0.849614			0.424807	+	0.905284i	$0.360342\pi$
$812$	362.588	+	318.356i	0.446537	+	0.392065i
$813$		−	1643.75i		−	2.02184i
$814$	−99.2583	−	271.042i	−0.121939	−	0.332976i
$815$	−1473.94	+	850.977i	−1.80851	+	1.04414i
$816$	−415.788	+	503.545i	−0.509544	+	0.617090i
$817$	381.553	+	220.290i	0.467017	+	0.269632i
$818$	102.462	+	85.6314i	0.125259	+	0.104684i
$819$	123.655	−	313.756i	0.150982	−	0.383097i
$820$	−2569.65	+	463.576i	−3.13372	+	0.565336i
$821$	−19.3490	−	11.1711i	−0.0235675	−	0.0136067i	0.488170	−	0.872749i	$-0.337665\pi$
$821$	−19.3490	−	11.1711i	−0.0235675	−	0.0136067i	−0.511737	+	0.859142i	$0.670998\pi$
$822$	1532.18	+	267.044i	1.86396	+	0.324871i
$823$	−512.111	−	887.003i	−0.622249	−	1.07777i	−0.989066	−	0.147474i	$-0.952886\pi$
$823$	−512.111	−	887.003i	−0.622249	−	1.07777i	0.366816	−	0.930293i	$-0.380448\pi$
$824$	−402.801	−	688.219i	−0.488836	−	0.835217i
$825$		−	759.934i		−	0.921132i
$826$	116.074	−	190.184i	0.140525	−	0.230247i
$827$			466.377i			0.563938i	0.959424	+	0.281969i	$0.0909875\pi$
$827$			466.377i			0.563938i	−0.959424	+	0.281969i	$0.909012\pi$
$828$	−300.418	−	108.001i	−0.362824	−	0.130436i
$829$	−750.350	−	1299.64i	−0.905126	−	1.56773i	−0.820747	−	0.571291i	$-0.806443\pi$
$829$	−750.350	−	1299.64i	−0.905126	−	1.56773i	−0.0843791	−	0.996434i	$-0.526891\pi$
$830$	1062.51	+	185.186i	1.28014	+	0.223116i
$831$	−1243.54	−	717.958i	−1.49644	−	0.863969i
$832$	254.504	+	428.988i	0.305895	+	0.515611i
$833$	−350.179	+	375.260i	−0.420383	+	0.450493i
$834$	−197.275	+	236.049i	−0.236541	+	0.283033i
$835$	1412.93	+	815.755i	1.69213	+	0.976952i
$836$	−101.580	−	120.091i	−0.121507	−	0.143650i
$837$	−287.496	+	165.986i	−0.343484	+	0.198311i
$838$	−378.380	−	1033.23i	−0.451528	−	1.23298i
$839$		−	1068.18i		−	1.27316i	−0.771212	−	0.636579i	$-0.780349\pi$
$839$		−	1068.18i		−	1.27316i	0.771212	−	0.636579i	$-0.219651\pi$
$840$	1802.68	+	698.139i	2.14605	+	0.831118i
$841$	544.034			0.646890
$842$	−1088.50	+	398.620i	−1.29276	+	0.473421i
$843$	−68.7449	−	119.070i	−0.0815479	−	0.141245i
$844$	957.014	+	1131.41i	1.13390	+	1.34054i
$845$	−479.562	+	830.625i	−0.567529	+	0.982988i
$846$	396.559	+	331.420i	0.468746	+	0.391749i
$847$	276.445	−	701.440i	0.326381	−	0.828146i
$848$	−35.8478	−	96.1206i	−0.0422734	−	0.113350i
$849$	383.045	−	663.453i	0.451172	−	0.781453i
$850$	−192.425	+	1104.05i	−0.226382	+	1.29888i
$851$	−442.605	+	255.538i	−0.520100	+	0.300280i
$852$	606.644	+	218.090i	0.712024	+	0.255974i
$853$	918.640			1.07695			0.538476	−	0.842641i	$-0.319000\pi$
$853$	918.640			1.07695			0.538476	+	0.842641i	$0.319000\pi$
$854$	−170.147	−	4.14851i	−0.199235	−	0.00485775i
$855$	−590.673			−0.690846
$856$	−379.897	−	649.085i	−0.443805	−	0.758277i
$857$	−438.167	+	252.976i	−0.511280	+	0.295188i	−0.733360	−	0.679841i	$-0.762049\pi$
$857$	−438.167	+	252.976i	−0.511280	+	0.295188i	0.222080	+	0.975029i	$0.428716\pi$
$858$	−38.0210	+	218.147i	−0.0443135	+	0.254251i
$859$	−688.516	+	1192.54i	−0.801532	+	1.38829i	0.117075	+	0.993123i	$0.462648\pi$
$859$	−688.516	+	1192.54i	−0.801532	+	1.38829i	−0.918607	+	0.395171i	$0.870685\pi$
$860$	1424.68	−	257.018i	1.65660	−	0.298858i
$861$	1572.93	−	1250.72i	1.82687	−	1.45264i
$862$	−553.893	+	662.758i	−0.642567	+	0.768861i
$863$	−458.817	+	794.695i	−0.531654	+	0.920852i	0.467663	+	0.883907i	$0.345096\pi$
$863$	−458.817	+	794.695i	−0.531654	+	0.920852i	−0.999317	+	0.0369450i	$0.988237\pi$
$864$	345.455	−	64.4381i	0.399832	−	0.0745811i
$865$	−309.663	−	536.352i	−0.357992	−	0.620060i
$866$	−0.269427	+	0.0986667i	−0.000311117	+	0.000113934i
$867$	−698.525			−0.805681
$868$	−165.616	+	830.070i	−0.190802	+	0.956302i
$869$			258.116i			0.297026i
$870$	−1117.20	+	409.130i	−1.28414	+	0.470265i
$871$	−52.6294	+	30.3856i	−0.0604241	+	0.0348859i
$872$	−1567.57	+	9.29163i	−1.79767	+	0.0106555i
$873$	17.4846	+	10.0947i	0.0200282	+	0.0115633i
$874$	−178.594	+	213.696i	−0.204341	+	0.244503i
$875$	1747.78	−	260.898i	1.99746	−	0.298170i
$876$	−1374.41	+	247.949i	−1.56896	+	0.283047i
$877$	−606.173	−	349.974i	−0.691189	−	0.399058i	0.112868	−	0.993610i	$-0.463996\pi$
$877$	−606.173	−	349.974i	−0.691189	−	0.399058i	−0.804057	+	0.594552i	$0.797329\pi$
$878$	65.7100	−	377.014i	0.0748405	−	0.429401i
$879$	618.688	+	1071.60i	0.703854	+	1.21911i
$880$	−509.674	−	85.7217i	−0.579175	−	0.0974111i
$881$		−	6.37652i		−	0.00723783i	−0.999993	−	0.00361891i	$-0.998848\pi$
$881$		−	6.37652i		−	0.00723783i	0.999993	−	0.00361891i	$-0.00115194\pi$
$882$	−601.156	+	74.8074i	−0.681582	+	0.0848156i
$883$		−	1548.35i		−	1.75351i	−0.480935	−	0.876756i	$-0.659703\pi$
$883$		−	1548.35i		−	1.75351i	0.480935	−	0.876756i	$-0.340297\pi$
$884$	110.475	−	307.301i	0.124972	−	0.347626i
$885$	274.694	+	475.784i	0.310389	+	0.537609i
$886$	135.130	−	775.315i	0.152517	−	0.875073i
$887$	634.250	+	366.185i	0.715051	+	0.412835i	0.812928	−	0.582364i	$-0.197872\pi$
$887$	634.250	+	366.185i	0.715051	+	0.412835i	−0.0978774	+	0.995198i	$0.531205\pi$
$888$	−610.593	+	1072.21i	−0.687605	+	1.20744i
$889$	962.882	−	143.733i	1.08311	−	0.161680i
$890$	−367.378	−	307.032i	−0.412785	−	0.344980i
$891$	310.768	+	179.422i	0.348785	+	0.201371i
$892$	−17.5281	−	20.7224i	−0.0196504	−	0.0232313i
$893$	390.454	−	225.429i	0.437238	−	0.252440i
$894$	693.572	−	253.993i	0.775808	−	0.284108i
$895$		−	2120.24i		−	2.36899i
$896$	457.681	−	770.288i	0.510805	−	0.859696i
$897$	392.074			0.437095
$898$	−499.192	−	1363.13i	−0.555893	−	1.51796i
$899$	−260.469	−	451.146i	−0.289732	−	0.501831i
$900$	−1009.89	+	854.217i	−1.12209	+	0.949130i
$901$	−33.5811	+	58.1641i	−0.0372709	+	0.0645551i
$902$	−344.536	+	412.253i	−0.381969	+	0.457043i
$903$	−872.074	+	693.433i	−0.965752	+	0.767921i
$904$	−708.197	−	403.299i	−0.783403	−	0.446128i
$905$	−160.730	+	278.392i	−0.177602	+	0.307615i
$906$	511.045	+	89.0703i	0.564068	+	0.0983116i
$907$	626.862	−	361.919i	0.691138	−	0.399029i	−0.112900	−	0.993606i	$-0.536014\pi$
$907$	626.862	−	361.919i	0.691138	−	0.399029i	0.804038	+	0.594578i	$0.202681\pi$
$908$	1116.51	+	401.389i	1.22964	+	0.442058i
$909$	−851.288			−0.936511
$910$	−966.420	−	23.5632i	−1.06200	−	0.0258936i
$911$	1600.04			1.75636			0.878179	−	0.478332i	$-0.158758\pi$
$911$	1600.04			1.75636			0.878179	+	0.478332i	$0.158758\pi$
$912$	−111.519	+	663.059i	−0.122280	+	0.727038i
$913$	192.188	−	110.960i	0.210502	−	0.121533i
$914$	136.626	+	23.8126i	0.149481	+	0.0260531i
$915$	209.832	−	363.440i	0.229325	−	0.397202i
$916$	−126.544	−	701.448i	−0.138149	−	0.765773i
$917$	235.374	−	597.228i	0.256678	−	0.651284i
$918$	−176.531	−	147.533i	−0.192299	−	0.160712i
$919$	262.042	−	453.871i	0.285139	−	0.493875i	−0.687504	−	0.726180i	$-0.741294\pi$
$919$	262.042	−	453.871i	0.285139	−	0.493875i	0.972643	+	0.232306i	$0.0746270\pi$
$920$	5.42412	+	915.088i	0.00589578	+	0.994661i
$921$	−257.535	−	446.064i	−0.279626	−	0.484326i
$922$	−528.198	−	1442.34i	−0.572883	−	1.56436i
$923$	−322.372			−0.349266
$924$	376.731	−	127.637i	0.407718	−	0.138136i
$925$			2117.53i			2.28922i
$926$	148.360	+	405.123i	0.160216	+	0.437498i
$927$	−533.618	+	308.084i	−0.575640	+	0.332346i
$928$	101.118	+	542.096i	0.108963	+	0.584155i
$929$	551.791	+	318.577i	0.593962	+	0.342924i	0.766663	−	0.642050i	$-0.221916\pi$
$929$	551.791	+	318.577i	0.593962	+	0.342924i	−0.172700	+	0.984974i	$0.555249\pi$
$930$	−1601.45	−	1338.39i	−1.72199	−	1.43913i
$931$	−119.060	+	514.892i	−0.127884	+	0.553053i
$932$	−83.6577	−	463.723i	−0.0897615	−	0.497557i
$933$	1560.31	+	900.844i	1.67235	+	0.965534i
$934$	−57.0157	−	9.93728i	−0.0610446	−	0.0106395i
$935$	169.180	+	293.029i	0.180941	+	0.313400i
$936$	332.637	−	194.686i	0.355381	−	0.207998i
$937$		−	383.587i		−	0.409378i	−0.978827	−	0.204689i	$-0.934382\pi$
$937$		−	383.587i		−	0.409378i	0.978827	−	0.204689i	$-0.0656182\pi$
$938$	93.1799	+	56.8699i	0.0993389	+	0.0606289i
$939$		−	2205.50i		−	2.34877i
$940$	501.180	−	1394.10i	0.533170	−	1.48308i
$941$	−130.295	−	225.678i	−0.138465	−	0.239828i	0.788451	−	0.615098i	$-0.210883\pi$
$941$	−130.295	−	225.678i	−0.138465	−	0.239828i	−0.926916	+	0.375270i	$0.877550\pi$
$942$	−195.912	−	34.1455i	−0.207974	−	0.0362479i
$943$	823.840	+	475.644i	0.873637	+	0.504394i
$944$	238.585	−	88.9794i	0.252738	−	0.0942579i
$945$	−249.719	+	633.626i	−0.264252	+	0.670504i
$946$	191.019	−	228.564i	0.201923	−	0.241610i
$947$	851.444	+	491.581i	0.899096	+	0.519093i	0.876907	−	0.480660i	$-0.159603\pi$
$947$	851.444	+	491.581i	0.899096	+	0.519093i	0.0221894	+	0.999754i	$0.492936\pi$
$948$	842.421	−	712.567i	0.888629	−	0.751652i
$949$	604.827	−	349.197i	0.637331	−	0.367963i
$950$	396.798	+	1083.53i	0.417682	+	1.14056i
$951$		−	689.781i		−	0.725322i
$952$	−579.642	+	90.0410i	−0.608868	+	0.0945809i
$953$	−1137.60			−1.19370			−0.596851	−	0.802352i	$-0.703582\pi$
$953$	−1137.60			−1.19370			−0.596851	+	0.802352i	$0.703582\pi$
$954$	−74.4347	+	27.2587i	−0.0780238	+	0.0285730i
$955$	−1440.78	−	2495.50i	−1.50867	−	2.61309i
$956$	−141.566	+	119.744i	−0.148081	+	0.125255i
$957$	−122.403	+	212.008i	−0.127903	+	0.221534i
$958$	−1232.23	−	1029.82i	−1.28625	−	1.07497i
$959$	869.505	+	1093.51i	0.906679	+	1.14026i
$960$	1127.26	+	1900.09i	1.17423	+	1.97926i
$961$	−23.5835	+	40.8479i	−0.0245406	+	0.0425056i
$962$	105.944	−	607.860i	0.110129	−	0.631871i
$963$	−503.275	+	290.566i	−0.522612	+	0.301730i
$964$	−496.114	+	1380.00i	−0.514641	+	1.43154i
$965$	−1768.75			−1.83290
$966$	−337.171	−	618.330i	−0.349038	−	0.640094i
$967$	−1296.35			−1.34059			−0.670297	−	0.742093i	$-0.733833\pi$
$967$	−1296.35			−1.34059			−0.670297	+	0.742093i	$0.733833\pi$
$968$	743.649	−	435.244i	0.768233	−	0.449632i
$969$	381.214	−	220.094i	0.393410	−	0.227135i
$970$	9.93692	−	57.0135i	0.0102442	−	0.0587768i
$971$	665.237	−	1152.22i	0.685105	−	1.18664i	−0.288299	−	0.957540i	$-0.593090\pi$
$971$	665.237	−	1152.22i	0.685105	−	1.18664i	0.973404	−	0.229096i	$-0.0735768\pi$
$972$	−202.147	−	1120.52i	−0.207971	−	1.15280i
$973$	−273.309	+	40.7980i	−0.280893	+	0.0419301i
$974$	25.5534	−	30.5758i	0.0262355	−	0.0313920i
$975$	812.237	−	1406.84i	0.833063	−	1.44291i
$976$	−149.988	−	123.848i	−0.153676	−	0.126893i
$977$	−693.081	−	1200.45i	−0.709397	−	1.22871i	−0.965081	−	0.261952i	$-0.915634\pi$
$977$	−693.081	−	1200.45i	−0.709397	−	1.22871i	0.255684	−	0.966760i	$-0.417699\pi$
$978$	1405.69	−	514.777i	1.43731	−	0.526357i
$979$	−98.5153			−0.100629
$980$	793.928	+	1544.38i	0.810131	+	1.57590i
$981$			1211.27i			1.23473i
$982$	−143.109	+	52.4079i	−0.145732	+	0.0533685i
$983$	−601.161	+	347.081i	−0.611558	+	0.353083i	−0.773575	−	0.633705i	$-0.781533\pi$
$983$	−601.161	+	347.081i	−0.611558	+	0.353083i	0.162017	+	0.986788i	$0.448200\pi$
$984$	2296.63	−	13.6131i	2.33397	−	0.0138344i
$985$	118.968	+	68.6861i	0.120780	+	0.0697321i
$986$	231.513	−	277.016i	0.234800	−	0.280949i
$987$	168.331	+	1127.66i	0.170548	+	1.14251i
$988$	−59.6941	−	330.891i	−0.0604192	−	0.334910i
$989$	−456.757	−	263.709i	−0.461838	−	0.266642i
$990$	−68.5698	+	393.423i	−0.0692625	+	0.397397i
$991$	467.257	+	809.312i	0.471500	+	0.816662i	0.999468	−	0.0326018i	$-0.0103793\pi$
$991$	467.257	+	809.312i	0.471500	+	0.816662i	−0.527968	+	0.849264i	$0.677046\pi$
$992$	−734.854	+	629.090i	−0.740780	+	0.634164i
$993$			1933.22i			1.94684i
$994$	277.229	+	508.405i	0.278903	+	0.511474i
$995$			497.576i			0.500076i
$996$	−892.707	−	320.930i	−0.896292	−	0.322218i
$997$	769.103	+	1332.12i	0.771417	+	1.33613i	0.936786	+	0.349902i	$0.113785\pi$
$997$	769.103	+	1332.12i	0.771417	+	1.33613i	−0.165370	+	0.986232i	$0.552882\pi$
$998$	179.556	−	1030.21i	0.179916	−	1.03228i
$999$	−376.463	−	217.351i	−0.376840	−	0.217568i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.5.10	yes	28
4.3	odd	2		224.3.n.a.145.2		28
7.2	even	3		392.3.h.a.293.17		28
7.3	odd	6	inner	56.3.j.a.45.1	yes	28
7.4	even	3		392.3.j.e.325.1		28
7.5	odd	6		392.3.h.a.293.18		28
7.6	odd	2		392.3.j.e.117.10		28
8.3	odd	2		224.3.n.a.145.13		28
8.5	even	2	inner	56.3.j.a.5.1	✓	28
28.3	even	6		224.3.n.a.17.13		28
28.19	even	6		1568.3.h.a.881.3		28
28.23	odd	6		1568.3.h.a.881.25		28
56.3	even	6		224.3.n.a.17.2		28
56.5	odd	6		392.3.h.a.293.19		28
56.13	odd	2		392.3.j.e.117.1		28
56.19	even	6		1568.3.h.a.881.26		28
56.37	even	6		392.3.h.a.293.20		28
56.45	odd	6	inner	56.3.j.a.45.10	yes	28
56.51	odd	6		1568.3.h.a.881.4		28
56.53	even	6		392.3.j.e.325.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.1	✓	28	8.5	even	2	inner
56.3.j.a.5.10	yes	28	1.1	even	1	trivial
56.3.j.a.45.1	yes	28	7.3	odd	6	inner
56.3.j.a.45.10	yes	28	56.45	odd	6	inner
224.3.n.a.17.2		28	56.3	even	6
224.3.n.a.17.13		28	28.3	even	6
224.3.n.a.145.2		28	4.3	odd	2
224.3.n.a.145.13		28	8.3	odd	2
392.3.h.a.293.17		28	7.2	even	3
392.3.h.a.293.18		28	7.5	odd	6
392.3.h.a.293.19		28	56.5	odd	6
392.3.h.a.293.20		28	56.37	even	6
392.3.j.e.117.1		28	56.13	odd	2
392.3.j.e.117.10		28	7.6	odd	2
392.3.j.e.325.1		28	7.4	even	3
392.3.j.e.325.10		28	56.53	even	6
1568.3.h.a.881.3		28	28.19	even	6
1568.3.h.a.881.4		28	56.51	odd	6
1568.3.h.a.881.25		28	28.23	odd	6
1568.3.h.a.881.26		28	56.19	even	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:	\( N \)	\(=\)	\( 56 = 2^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	56.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.687752 + 1.87803i) q^{2} +(1.94818 + 3.37434i) q^{3} +(-3.05399 + 2.58324i) q^{4} +(4.42985 - 7.67272i) q^{5} +(-4.99725 + 5.97944i) q^{6} +(-6.92329 + 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 + 5.35338i) q^{9} +O(q^{10})\)	\(q+(0.687752 + 1.87803i) q^{2} +(1.94818 + 3.37434i) q^{3} +(-3.05399 + 2.58324i) q^{4} +(4.42985 - 7.67272i) q^{5} +(-4.99725 + 5.97944i) q^{6} +(-6.92329 + 1.03347i) q^{7} +(-6.95179 - 3.95886i) q^{8} +(-3.09078 + 5.35338i) q^{9} +(17.4562 + 3.04246i) q^{10} +(3.15749 - 1.82298i) q^{11} +(-14.6664 - 5.27261i) q^{12} +7.79378 q^{13} +(-6.70239 - 12.2914i) q^{14} +34.5205 q^{15} +(2.65376 - 15.7784i) q^{16} +(-9.07152 + 5.23744i) q^{17} +(-12.1795 - 2.12277i) q^{18} +(-5.39264 + 9.34032i) q^{19} +(6.29174 + 34.8758i) q^{20} +(-16.9751 - 21.3482i) q^{21} +(5.59518 + 4.67610i) q^{22} +(6.45553 - 11.1813i) q^{23} +(-0.184759 - 31.1703i) q^{24} +(-26.7471 - 46.3273i) q^{25} +(5.36019 + 14.6370i) q^{26} +10.9817 q^{27} +(18.4740 - 21.0407i) q^{28} +17.2327i q^{29} +(23.7415 + 64.8305i) q^{30} +(-26.1797 + 15.1148i) q^{31} +(31.4574 - 5.86779i) q^{32} +(12.3027 + 7.10296i) q^{33} +(-16.0750 - 13.4345i) q^{34} +(-22.7396 + 57.6986i) q^{35} +(-4.38985 - 24.3334i) q^{36} +(-34.2810 - 19.7922i) q^{37} +(-21.2502 - 3.70371i) q^{38} +(15.1837 + 26.2989i) q^{39} +(-61.1706 + 35.8020i) q^{40} +73.6801i q^{41} +(28.4178 - 46.5619i) q^{42} -40.8501i q^{43} +(-4.93377 + 13.7239i) q^{44} +(27.3833 + 47.4293i) q^{45} +(25.4386 + 4.43371i) q^{46} +(-36.2025 - 20.9015i) q^{47} +(58.4116 - 21.7844i) q^{48} +(46.8639 - 14.3100i) q^{49} +(68.6087 - 82.0935i) q^{50} +(-35.3458 - 20.4069i) q^{51} +(-23.8022 + 20.1332i) q^{52} +(5.55272 - 3.20586i) q^{53} +(7.55266 + 20.6239i) q^{54} -32.3020i q^{55} +(52.2206 + 20.2239i) q^{56} -42.0232 q^{57} +(-32.3635 + 11.8518i) q^{58} +(7.95742 + 13.7827i) q^{59} +(-105.425 + 89.1746i) q^{60} +(6.07848 - 10.5282i) q^{61} +(-46.3912 - 38.7709i) q^{62} +(15.8658 - 40.2572i) q^{63} +(32.6548 + 55.0424i) q^{64} +(34.5253 - 59.7995i) q^{65} +(-4.87837 + 27.9899i) q^{66} +(-6.75274 + 3.89870i) q^{67} +(14.1748 - 39.4290i) q^{68} +50.3060 q^{69} +(-123.999 - 3.02333i) q^{70} -41.3627 q^{71} +(42.6797 - 24.9796i) q^{72} +(77.6038 - 44.8046i) q^{73} +(13.5934 - 77.9929i) q^{74} +(104.216 - 180.507i) q^{75} +(-7.65920 - 42.4557i) q^{76} +(-19.9762 + 15.8842i) q^{77} +(-38.9475 + 46.6025i) q^{78} +(-35.3975 + 61.3103i) q^{79} +(-109.307 - 90.2574i) q^{80} +(49.2112 + 85.2363i) q^{81} +(-138.373 + 50.6736i) q^{82} +60.8673 q^{83} +(106.989 + 21.3465i) q^{84} +92.8043i q^{85} +(76.7177 - 28.0947i) q^{86} +(-58.1489 + 33.5723i) q^{87} +(-29.1671 + 0.172886i) q^{88} +(-23.4004 - 13.5102i) q^{89} +(-70.2407 + 84.0463i) q^{90} +(-53.9586 + 8.05463i) q^{91} +(9.16883 + 50.8238i) q^{92} +(-102.005 - 58.8927i) q^{93} +(14.3553 - 82.3644i) q^{94} +(47.7771 + 82.7524i) q^{95} +(81.0845 + 94.7165i) q^{96} -3.26608i q^{97} +(59.1054 + 78.1701i) q^{98} +22.5377i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 4 q^{7} - 20 q^{8} - 32 q^{9} + 24 q^{10} - 18 q^{12} + 24 q^{14} + 28 q^{15} + 16 q^{16} - 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} - 30 q^{24} - 32 q^{25} - 30 q^{26} - 42 q^{28} + 22 q^{30} - 6 q^{31} + 88 q^{32} - 6 q^{33} + 256 q^{36} + 6 q^{38} - 20 q^{39} + 102 q^{40} + 18 q^{42} - 42 q^{44} + 68 q^{46} - 294 q^{47} - 20 q^{49} + 400 q^{50} - 168 q^{52} + 330 q^{54} - 96 q^{56} + 124 q^{57} - 22 q^{58} - 62 q^{60} + 432 q^{63} - 520 q^{64} - 52 q^{65} - 306 q^{66} - 456 q^{68} - 324 q^{70} - 136 q^{71} + 96 q^{72} + 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} + 276 q^{80} - 18 q^{81} - 642 q^{82} + 504 q^{84} + 168 q^{86} + 48 q^{87} + 50 q^{88} - 150 q^{89} + 1020 q^{92} + 618 q^{94} + 290 q^{95} + 1044 q^{96} + 424 q^{98}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 4 * q^7 - 20 * q^8 - 32 * q^9 + 24 * q^10 - 18 * q^12 + 24 * q^14 + 28 * q^15 + 16 * q^16 - 6 * q^17 - 42 * q^18 - 92 * q^22 + 30 * q^23 - 30 * q^24 - 32 * q^25 - 30 * q^26 - 42 * q^28 + 22 * q^30 - 6 * q^31 + 88 * q^32 - 6 * q^33 + 256 * q^36 + 6 * q^38 - 20 * q^39 + 102 * q^40 + 18 * q^42 - 42 * q^44 + 68 * q^46 - 294 * q^47 - 20 * q^49 + 400 * q^50 - 168 * q^52 + 330 * q^54 - 96 * q^56 + 124 * q^57 - 22 * q^58 - 62 * q^60 + 432 * q^63 - 520 * q^64 - 52 * q^65 - 306 * q^66 - 456 * q^68 - 324 * q^70 - 136 * q^71 + 96 * q^72 + 234 * q^73 - 138 * q^74 - 956 * q^78 - 162 * q^79 + 276 * q^80 - 18 * q^81 - 642 * q^82 + 504 * q^84 + 168 * q^86 + 48 * q^87 + 50 * q^88 - 150 * q^89 + 1020 * q^92 + 618 * q^94 + 290 * q^95 + 1044 * q^96 + 424 * q^98

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