LMFDB - Embedded newform 56.3.j.a.5.14

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			5.14
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.95704 + 0.412286i) q^{2} +(-1.70138 - 2.94687i) q^{3} +(3.66004 + 1.61372i) q^{4} +(2.15858 - 3.73877i) q^{5} +(-2.11472 - 6.46862i) q^{6} +(-1.43197 + 6.85197i) q^{7} +(6.49755 + 4.66711i) q^{8} +(-1.28938 + 2.23327i) q^{9} +O(q^{10})$	\(q+(1.95704 + 0.412286i) q^{2} +(-1.70138 - 2.94687i) q^{3} +(3.66004 + 1.61372i) q^{4} +(2.15858 - 3.73877i) q^{5} +(-2.11472 - 6.46862i) q^{6} +(-1.43197 + 6.85197i) q^{7} +(6.49755 + 4.66711i) q^{8} +(-1.28938 + 2.23327i) q^{9} +(5.76588 - 6.42699i) q^{10} +(-15.4899 + 8.94308i) q^{11} +(-1.47168 - 13.5312i) q^{12} +3.25607 q^{13} +(-5.62740 + 12.8192i) q^{14} -14.6903 q^{15} +(10.7918 + 11.8126i) q^{16} +(-13.6263 + 7.86717i) q^{17} +(-3.44412 + 3.83902i) q^{18} +(0.778522 - 1.34844i) q^{19} +(13.9338 - 10.2007i) q^{20} +(22.6282 - 7.43796i) q^{21} +(-34.0014 + 11.1157i) q^{22} +(20.7069 - 35.8655i) q^{23} +(2.69860 - 27.0880i) q^{24} +(3.18105 + 5.50975i) q^{25} +(6.37227 + 1.34243i) q^{26} -21.8499 q^{27} +(-16.2982 + 22.7677i) q^{28} +3.74374i q^{29} +(-28.7495 - 6.05658i) q^{30} +(-0.0145172 + 0.00838150i) q^{31} +(16.2499 + 27.5670i) q^{32} +(52.7082 + 30.4311i) q^{33} +(-29.9109 + 9.77845i) q^{34} +(22.5269 + 20.1443i) q^{35} +(-8.32306 + 6.09316i) q^{36} +(-1.16774 - 0.674194i) q^{37} +(2.07954 - 2.31798i) q^{38} +(-5.53981 - 9.59523i) q^{39} +(31.4747 - 14.2185i) q^{40} -70.3018i q^{41} +(47.3510 - 5.22712i) q^{42} -13.0380i q^{43} +(-71.1252 + 7.73569i) q^{44} +(5.56646 + 9.64139i) q^{45} +(55.3112 - 61.6531i) q^{46} +(30.9797 + 17.8862i) q^{47} +(16.4493 - 51.8998i) q^{48} +(-44.8989 - 19.6236i) q^{49} +(3.95387 + 12.0943i) q^{50} +(46.3671 + 26.7701i) q^{51} +(11.9173 + 5.25439i) q^{52} +(39.7989 - 22.9779i) q^{53} +(-42.7613 - 9.00841i) q^{54} +77.2174i q^{55} +(-41.2832 + 37.8378i) q^{56} -5.29824 q^{57} +(-1.54349 + 7.32667i) q^{58} +(-34.3509 - 59.4974i) q^{59} +(-53.7669 - 23.7060i) q^{60} +(-48.0386 + 83.2052i) q^{61} +(-0.0318663 + 0.0104177i) q^{62} +(-13.4559 - 12.0328i) q^{63} +(20.4362 + 60.6495i) q^{64} +(7.02849 - 12.1737i) q^{65} +(90.6060 + 81.2859i) q^{66} +(12.0808 - 6.97484i) q^{67} +(-62.5684 + 6.80504i) q^{68} -140.921 q^{69} +(35.7810 + 48.7109i) q^{70} -75.7095 q^{71} +(-18.8007 + 8.49310i) q^{72} +(-46.0282 + 26.5744i) q^{73} +(-2.00736 - 1.80087i) q^{74} +(10.8244 - 18.7483i) q^{75} +(5.02543 - 3.67902i) q^{76} +(-39.0967 - 118.942i) q^{77} +(-6.88567 - 21.0623i) q^{78} +(11.6744 - 20.2206i) q^{79} +(67.4595 - 14.8497i) q^{80} +(48.7794 + 84.4884i) q^{81} +(28.9844 - 137.584i) q^{82} +102.487 q^{83} +(94.8230 + 9.29242i) q^{84} +67.9277i q^{85} +(5.37540 - 25.5160i) q^{86} +(11.0323 - 6.36952i) q^{87} +(-142.384 - 14.1848i) q^{88} +(-76.6985 - 44.2819i) q^{89} +(6.91880 + 21.1636i) q^{90} +(-4.66259 + 22.3105i) q^{91} +(133.665 - 97.8538i) q^{92} +(0.0493984 + 0.0285202i) q^{93} +(53.2545 + 47.7765i) q^{94} +(-3.36100 - 5.82143i) q^{95} +(53.5894 - 94.7883i) q^{96} +140.869i q^{97} +(-79.7786 - 56.9155i) q^{98} -46.1241i 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 $

$2$	1.95704	+	0.412286i	0.978522	+	0.206143i
$2$	1.95704	+	0.412286i	0.978522	+	0.206143i
$3$	−1.70138	−	2.94687i	−0.567126	−	0.982291i	−0.996848	−	0.0793303i	$-0.974722\pi$
$3$	−1.70138	−	2.94687i	−0.567126	−	0.982291i	0.429722	−	0.902961i	$-0.358612\pi$
$4$	3.66004	+	1.61372i	0.915010	+	0.403431i
$5$	2.15858	−	3.73877i	0.431716	−	0.747754i	−0.565305	−	0.824882i	$-0.691242\pi$
$5$	2.15858	−	3.73877i	0.431716	−	0.747754i	0.997021	+	0.0771275i	$0.0245748\pi$
$6$	−2.11472	−	6.46862i	−0.352453	−	1.07810i
$7$	−1.43197	+	6.85197i	−0.204567	+	0.978853i
$7$	−1.43197	+	6.85197i	−0.204567	+	0.978853i
$8$	6.49755	+	4.66711i	0.812193	+	0.583389i
$9$	−1.28938	+	2.23327i	−0.143264	+	0.248141i
$10$	5.76588	−	6.42699i	0.576588	−	0.642699i
$11$	−15.4899	+	8.94308i	−1.40817	+	0.813007i	−0.995212	−	0.0977432i	$-0.968838\pi$
$11$	−15.4899	+	8.94308i	−1.40817	+	0.813007i	−0.412958	+	0.910750i	$0.635504\pi$
$12$	−1.47168	−	13.5312i	−0.122640	−	1.12760i
$13$	3.25607			0.250467			0.125233	−	0.992127i	$-0.460032\pi$
$13$	3.25607			0.250467			0.125233	+	0.992127i	$0.460032\pi$
$14$	−5.62740	+	12.8192i	−0.401957	+	0.915659i
$15$	−14.6903			−0.979350
$16$	10.7918	+	11.8126i	0.674487	+	0.738286i
$17$	−13.6263	+	7.86717i	−0.801550	+	0.462775i	−0.844013	−	0.536323i	$-0.819813\pi$
$17$	−13.6263	+	7.86717i	−0.801550	+	0.462775i	0.0424631	+	0.999098i	$0.486479\pi$
$18$	−3.44412	+	3.83902i	−0.191340	+	0.213279i
$19$	0.778522	−	1.34844i	0.0409748	−	0.0709705i	−0.844811	−	0.535065i	$-0.820287\pi$
$19$	0.778522	−	1.34844i	0.0409748	−	0.0709705i	0.885786	+	0.464095i	$0.153620\pi$
$20$	13.9338	−	10.2007i	0.696692	−	0.510035i
$21$	22.6282	−	7.43796i	1.07753	−	0.354188i
$22$	−34.0014	+	11.1157i	−1.54552	+	0.505261i
$23$	20.7069	−	35.8655i	0.900301	−	1.55937i	0.0731984	−	0.997317i	$-0.476679\pi$
$23$	20.7069	−	35.8655i	0.900301	−	1.55937i	0.827103	−	0.562050i	$-0.189987\pi$
$24$	2.69860	−	27.0880i	0.112441	−	1.12867i
$25$	3.18105	+	5.50975i	0.127242	+	0.220390i
$26$	6.37227	+	1.34243i	0.245087	+	0.0516319i
$27$	−21.8499			−0.809257
$28$	−16.2982	+	22.7677i	−0.582080	+	0.813131i
$29$			3.74374i			0.129095i	0.997915	+	0.0645473i	$0.0205603\pi$
$29$			3.74374i			0.129095i	−0.997915	+	0.0645473i	$0.979440\pi$
$30$	−28.7495	−	6.05658i	−0.958316	−	0.201886i
$31$	−0.0145172	+	0.00838150i	−0.000468296	+	0.000270371i	−0.500234	−	0.865890i	$-0.666753\pi$
$31$	−0.0145172	+	0.00838150i	−0.000468296	+	0.000270371i	0.499766	+	0.866161i	$0.333419\pi$
$32$	16.2499	+	27.5670i	0.507808	+	0.861470i
$33$	52.7082	+	30.4311i	1.59722	+	0.922155i
$34$	−29.9109	+	9.77845i	−0.879732	+	0.287602i
$35$	22.5269	+	20.1443i	0.643626	+	0.575553i
$36$	−8.32306	+	6.09316i	−0.231196	+	0.169254i
$37$	−1.16774	−	0.674194i	−0.0315605	−	0.0182215i	0.484137	−	0.874992i	$-0.339134\pi$
$37$	−1.16774	−	0.674194i	−0.0315605	−	0.0182215i	−0.515697	+	0.856771i	$0.672467\pi$
$38$	2.07954	−	2.31798i	0.0547248	−	0.0609995i
$39$	−5.53981	−	9.59523i	−0.142046	−	0.246031i
$40$	31.4747	−	14.2185i	0.786868	−	0.355463i
$41$		−	70.3018i		−	1.71468i	−0.514753	−	0.857339i	$-0.672116\pi$
$41$		−	70.3018i		−	1.71468i	0.514753	−	0.857339i	$-0.327884\pi$
$42$	47.3510	−	5.22712i	1.12740	−	0.124455i
$43$		−	13.0380i		−	0.303210i	−0.988441	−	0.151605i	$-0.951556\pi$
$43$		−	13.0380i		−	0.303210i	0.988441	−	0.151605i	$-0.0484442\pi$
$44$	−71.1252	+	7.73569i	−1.61648	+	0.175811i
$45$	5.56646	+	9.64139i	0.123699	+	0.214253i
$46$	55.3112	−	61.6531i	1.20242	−	1.34028i
$47$	30.9797	+	17.8862i	0.659144	+	0.380557i	0.791951	−	0.610585i	$-0.209066\pi$
$47$	30.9797	+	17.8862i	0.659144	+	0.380557i	−0.132807	+	0.991142i	$0.542399\pi$
$48$	16.4493	−	51.8998i	0.342693	−	1.08124i
$49$	−44.8989	−	19.6236i	−0.916305	−	0.400482i
$50$	3.95387	+	12.0943i	0.0790774	+	0.241886i
$51$	46.3671	+	26.7701i	0.909160	+	0.524904i
$52$	11.9173	+	5.25439i	0.229180	+	0.101046i
$53$	39.7989	−	22.9779i	0.750923	−	0.433546i	−0.0751042	−	0.997176i	$-0.523929\pi$
$53$	39.7989	−	22.9779i	0.750923	−	0.433546i	0.826027	+	0.563630i	$0.190596\pi$
$54$	−42.7613	−	9.00841i	−0.791875	−	0.166822i
$55$			77.2174i			1.40395i
$56$	−41.2832	+	37.8378i	−0.737199	+	0.675675i
$57$	−5.29824			−0.0929516
$58$	−1.54349	+	7.32667i	−0.0266119	+	0.126322i
$59$	−34.3509	−	59.4974i	−0.582218	−	1.00843i	−0.995216	−	0.0976993i	$-0.968852\pi$
$59$	−34.3509	−	59.4974i	−0.582218	−	1.00843i	0.412998	−	0.910732i	$-0.364482\pi$
$60$	−53.7669	−	23.7060i	−0.896116	−	0.395100i
$61$	−48.0386	+	83.2052i	−0.787517	+	1.36402i	0.139966	+	0.990156i	$0.455301\pi$
$61$	−48.0386	+	83.2052i	−0.787517	+	1.36402i	−0.927484	+	0.373864i	$0.878033\pi$
$62$	−0.0318663	+	0.0104177i	−0.000513973	+	0.000168028i
$63$	−13.4559	−	12.0328i	−0.213586	−	0.190996i
$64$	20.4362	+	60.6495i	0.319316	+	0.947648i
$65$	7.02849	−	12.1737i	0.108131	−	0.187288i
$66$	90.6060	+	81.2859i	1.37282	+	1.23160i
$67$	12.0808	−	6.97484i	0.180310	−	0.104102i	−0.407128	−	0.913371i	$-0.633470\pi$
$67$	12.0808	−	6.97484i	0.180310	−	0.104102i	0.587438	+	0.809269i	$0.300136\pi$
$68$	−62.5684	+	6.80504i	−0.920124	+	0.100074i
$69$	−140.921			−2.04234
$70$	35.7810	+	48.7109i	0.511157	+	0.695870i
$71$	−75.7095			−1.06633			−0.533166	−	0.846011i	$-0.678998\pi$
$71$	−75.7095			−1.06633			−0.533166	+	0.846011i	$0.678998\pi$
$72$	−18.8007	+	8.49310i	−0.261121	+	0.117960i
$73$	−46.0282	+	26.5744i	−0.630523	+	0.364033i	−0.780955	−	0.624588i	$-0.785267\pi$
$73$	−46.0282	+	26.5744i	−0.630523	+	0.364033i	0.150432	+	0.988620i	$0.451934\pi$
$74$	−2.00736	−	1.80087i	−0.0271264	−	0.0243361i
$75$	10.8244	−	18.7483i	0.144325	−	0.249978i
$76$	5.02543	−	3.67902i	0.0661240	−	0.0484082i
$77$	−39.0967	−	118.942i	−0.507749	−	1.54470i
$78$	−6.88567	−	21.0623i	−0.0882778	−	0.270029i
$79$	11.6744	−	20.2206i	0.147777	−	0.255957i	−0.782628	−	0.622489i	$-0.786122\pi$
$79$	11.6744	−	20.2206i	0.147777	−	0.255957i	0.930406	+	0.366532i	$0.119455\pi$
$80$	67.4595	−	14.8497i	0.843244	−	0.185621i
$81$	48.7794	+	84.4884i	0.602215	+	1.04307i
$82$	28.9844	−	137.584i	0.353469	−	1.67785i
$83$	102.487			1.23479			0.617393	−	0.786655i	$-0.288189\pi$
$83$	102.487			1.23479			0.617393	+	0.786655i	$0.288189\pi$
$84$	94.8230	+	9.29242i	1.12885	+	0.110624i
$85$			67.9277i			0.799150i
$86$	5.37540	−	25.5160i	0.0625047	−	0.296698i
$87$	11.0323	−	6.36952i	0.126808	−	0.0732129i
$88$	−142.384	−	14.1848i	−1.61800	−	0.161191i
$89$	−76.6985	−	44.2819i	−0.861781	−	0.497549i	0.00282755	−	0.999996i	$-0.499100\pi$
$89$	−76.6985	−	44.2819i	−0.861781	−	0.497549i	−0.864608	+	0.502447i	$0.832433\pi$
$90$	6.91880	+	21.1636i	0.0768755	+	0.235151i
$91$	−4.66259	+	22.3105i	−0.0512373	+	0.245170i
$92$	133.665	−	97.8538i	1.45288	−	1.06363i
$93$	0.0493984	+	0.0285202i	0.000531166	+	0.000306669i
$94$	53.2545	+	47.7765i	0.566537	+	0.508261i
$95$	−3.36100	−	5.82143i	−0.0353790	−	0.0612782i
$96$	53.5894	−	94.7883i	0.558223	−	0.987378i
$97$			140.869i			1.45226i	0.687558	+	0.726130i	$0.258683\pi$
$97$			140.869i			1.45226i	−0.687558	+	0.726130i	$0.741317\pi$
$98$	−79.7786	−	56.9155i	−0.814068	−	0.580770i
$99$		−	46.1241i		−	0.465900i
$100$	2.75159	+	25.2992i	0.0275159	+	0.252992i
$101$	17.6988	+	30.6553i	0.175236	+	0.303518i	0.940243	−	0.340504i	$-0.110598\pi$
$101$	17.6988	+	30.6553i	0.175236	+	0.303518i	−0.765007	+	0.644022i	$0.777265\pi$
$102$	79.7056	+	71.5067i	0.781427	+	0.701046i
$103$	87.1651	+	50.3248i	0.846263	+	0.488590i	0.859388	−	0.511324i	$-0.170845\pi$
$103$	87.1651	+	50.3248i	0.846263	+	0.488590i	−0.0131250	+	0.999914i	$0.504178\pi$
$104$	21.1565	+	15.1964i	0.203427	+	0.146119i
$105$	21.0360	−	100.657i	0.200343	−	0.958640i
$106$	87.3617	−	28.5603i	0.824167	−	0.269437i
$107$	92.6215	+	53.4751i	0.865622	+	0.499767i	0.865891	−	0.500233i	$-0.166752\pi$
$107$	92.6215	+	53.4751i	0.865622	+	0.499767i	−0.000269099		1.00000i	$0.500086\pi$
$108$	−79.9716	−	35.2597i	−0.740478	−	0.326479i
$109$	45.5799	−	26.3156i	0.418165	−	0.241427i	−0.276127	−	0.961121i	$-0.589051\pi$
$109$	45.5799	−	26.3156i	0.418165	−	0.241427i	0.694292	+	0.719694i	$0.255718\pi$
$110$	−31.8356	+	151.118i	−0.289415	+	1.37380i
$111$			4.58824i			0.0413355i
$112$	−96.3930	+	57.0298i	−0.860651	+	0.509195i
$113$	45.4346			0.402076			0.201038	−	0.979583i	$-0.435568\pi$
$113$	45.4346			0.402076			0.201038	+	0.979583i	$0.435568\pi$
$114$	−10.3689	−	2.18439i	−0.0909552	−	0.0191613i
$115$	−89.3952	−	154.837i	−0.777350	−	1.34641i
$116$	−6.04136	+	13.7022i	−0.0520807	+	0.118123i
$117$	−4.19831	+	7.27168i	−0.0358830	+	0.0621511i
$118$	−42.6962	−	130.601i	−0.361832	−	1.10679i
$119$	−34.3931	−	104.633i	−0.289018	−	0.879267i
$120$	−95.4506	−	68.5610i	−0.795422	−	0.571342i
$121$	99.4572	−	172.265i	0.821961	−	1.42368i
$122$	−128.318	+	143.031i	−1.05179	+	1.17238i
$123$	−207.171	+	119.610i	−1.68431	+	0.972439i
$124$	−0.0666589	+	0.00724992i	−0.000537571	+	5.84671e-5i
$125$	135.395			1.08316
$126$	−21.3729	−	29.0963i	−0.169626	−	0.230923i
$127$	125.695			0.989723			0.494861	−	0.868972i	$-0.335219\pi$
$127$	125.695			0.989723			0.494861	+	0.868972i	$0.335219\pi$
$128$	14.9896	+	127.119i	0.117106	+	0.993119i
$129$	−38.4215	+	22.1827i	−0.297841	+	0.171959i
$130$	18.7741	−	20.9267i	0.144416	−	0.160975i
$131$	−56.6504	+	98.1214i	−0.432446	+	0.749018i	−0.997083	−	0.0763210i	$-0.975683\pi$
$131$	−56.6504	+	98.1214i	−0.432446	+	0.749018i	0.564638	+	0.825339i	$0.309016\pi$
$132$	143.807	+	196.436i	1.08945	+	1.48815i
$133$	8.12464	+	7.26533i	0.0610875	+	0.0546265i
$134$	26.5182	−	8.66933i	0.197897	−	0.0646965i
$135$	−47.1648	+	81.6919i	−0.349369	+	0.605125i
$136$	−125.255	−	12.4783i	−0.920991	−	0.0917522i
$137$	−39.1679	−	67.8408i	−0.285897	−	0.495188i	0.686929	−	0.726724i	$-0.258958\pi$
$137$	−39.1679	−	67.8408i	−0.285897	−	0.495188i	−0.972826	+	0.231536i	$0.925625\pi$
$138$	−275.789	−	58.0999i	−1.99847	−	0.421013i
$139$	149.038			1.07222			0.536109	−	0.844149i	$-0.319894\pi$
$139$	149.038			1.07222			0.536109	+	0.844149i	$0.319894\pi$
$140$	49.9421	+	110.081i	0.356729	+	0.786295i
$141$		−	121.725i		−	0.863295i
$142$	−148.167	−	31.2140i	−1.04343	−	0.219817i
$143$	−50.4361	+	29.1193i	−0.352700	+	0.203631i
$144$	−40.2954	+	8.87011i	−0.279829	+	0.0615980i
$145$	13.9970	+	8.08117i	0.0965310	+	0.0557322i
$146$	−101.035	+	33.0305i	−0.692023	+	0.226236i
$147$	18.5617	+	165.699i	0.126270	+	1.12720i
$148$	−3.18601	−	4.35198i	−0.0215271	−	0.0294053i
$149$	73.8369	+	42.6298i	0.495550	+	0.286106i	0.726874	−	0.686771i	$-0.240972\pi$
$149$	73.8369	+	42.6298i	0.495550	+	0.286106i	−0.231324	+	0.972877i	$0.574306\pi$
$150$	28.9134	−	32.2286i	0.192756	−	0.214857i
$151$	−65.9012	−	114.144i	−0.436432	−	0.755922i	0.560979	−	0.827830i	$-0.310425\pi$
$151$	−65.9012	−	114.144i	−0.436432	−	0.755922i	−0.997411	+	0.0719076i	$0.977091\pi$
$152$	11.3518	−	5.12810i	0.0746828	−	0.0337375i
$153$		−	40.5751i		−	0.265197i
$154$	−27.4757	−	248.894i	−0.178413	−	1.61620i
$155$			0.0723686i			0.000466894i
$156$	−4.79189	−	44.0586i	−0.0307172	−	0.282427i
$157$	122.552	+	212.267i	0.780589	+	1.35202i	0.931599	+	0.363487i	$0.118414\pi$
$157$	122.552	+	212.267i	0.780589	+	1.35202i	−0.151010	+	0.988532i	$0.548253\pi$
$158$	31.1840	−	34.7595i	0.197367	−	0.219997i
$159$	−135.426	−	78.1883i	−0.851737	−	0.491750i
$160$	138.144	−	1.24885i	0.863397	−	0.00780534i
$161$	216.097	+	193.241i	1.34222	+	1.20026i
$162$	60.6301	+	185.459i	0.374260	+	1.14481i
$163$	−208.089	−	120.140i	−1.27662	−	0.737057i	−0.300395	−	0.953815i	$-0.597118\pi$
$163$	−208.089	−	120.140i	−1.27662	−	0.737057i	−0.976225	+	0.216758i	$0.930452\pi$
$164$	113.448	−	257.307i	0.691753	−	1.56895i
$165$	227.550	−	131.376i	1.37909	−	0.796219i
$166$	200.572	+	42.2540i	1.20827	+	0.254542i
$167$		−	73.1965i		−	0.438302i	−0.975691	−	0.219151i	$-0.929671\pi$
$167$		−	73.1965i		−	0.438302i	0.975691	−	0.219151i	$-0.0703288\pi$
$168$	181.742	+	57.2798i	1.08180	+	0.340951i
$169$	−158.398			−0.937266
$170$	−28.0056	+	132.938i	−0.164739	+	0.781986i
$171$	2.00762	+	3.47730i	0.0117405	+	0.0203351i
$172$	21.0398	−	47.7198i	0.122324	−	0.277441i
$173$	−18.5246	+	32.0855i	−0.107078	+	0.185465i	−0.914585	−	0.404393i	$-0.867483\pi$
$173$	−18.5246	+	32.0855i	−0.107078	+	0.185465i	0.807507	+	0.589858i	$0.200816\pi$
$174$	24.2168	−	7.91696i	0.139177	−	0.0454998i
$175$	−42.3078	+	13.9067i	−0.241759	+	0.0794668i
$176$	−272.804	−	86.4634i	−1.55002	−	0.491269i
$177$	−116.888	+	202.455i	−0.660382	+	1.14382i
$178$	−131.845	−	118.283i	−0.740705	−	0.664513i
$179$	−205.982	+	118.924i	−1.15074	+	0.664379i	−0.949067	−	0.315074i	$-0.897971\pi$
$179$	−205.982	+	118.924i	−1.15074	+	0.664379i	−0.201672	+	0.979453i	$0.564637\pi$
$180$	4.81494	+	44.2706i	0.0267497	+	0.245948i
$181$	−292.553			−1.61631			−0.808157	−	0.588966i	$-0.799535\pi$
$181$	−292.553			−1.61631			−0.808157	+	0.588966i	$0.799535\pi$
$182$	−18.3232	+	41.7403i	−0.100677	+	0.229342i
$183$	326.927			1.78649
$184$	301.932	−	136.396i	1.64094	−	0.741282i
$185$	−5.04132	+	2.91061i	−0.0272504	+	0.0157330i
$186$	0.0849164	+	0.0761815i	0.000456540	+	0.000409578i
$187$	140.713	−	243.723i	0.752478	−	1.30333i
$188$	84.5238	+	115.457i	0.449595	+	0.614132i
$189$	31.2884	−	149.715i	0.165547	−	0.792143i
$190$	−4.17754	−	12.7785i	−0.0219871	−	0.0672552i
$191$	−70.6135	+	122.306i	−0.369704	+	0.640346i	−0.989519	−	0.144402i	$-0.953874\pi$
$191$	−70.6135	+	122.306i	−0.369704	+	0.640346i	0.619815	+	0.784748i	$0.287208\pi$
$192$	143.957	−	163.411i	0.749775	−	0.851097i
$193$	32.9799	+	57.1229i	0.170880	+	0.295973i	0.938728	−	0.344659i	$-0.112006\pi$
$193$	32.9799	+	57.1229i	0.170880	+	0.295973i	−0.767848	+	0.640633i	$0.778672\pi$
$194$	−58.0783	+	275.687i	−0.299373	+	1.42107i
$195$	−47.8325			−0.245295
$196$	−132.665	−	144.278i	−0.676861	−	0.736111i
$197$		−	199.421i		−	1.01229i	−0.862448	−	0.506145i	$-0.831070\pi$
$197$		−	199.421i		−	1.01229i	0.862448	−	0.506145i	$-0.168930\pi$
$198$	19.0163	−	90.2668i	0.0960419	−	0.455893i
$199$	58.6230	−	33.8460i	0.294588	−	0.170080i	−0.345421	−	0.938448i	$-0.612264\pi$
$199$	58.6230	−	33.8460i	0.294588	−	0.170080i	0.640009	+	0.768367i	$0.278931\pi$
$200$	−5.04554	+	50.6462i	−0.0252277	+	0.253231i
$201$	−41.1079	−	23.7337i	−0.204517	−	0.118078i
$202$	21.9987	+	67.2907i	0.108904	+	0.333122i
$203$	−25.6520	−	5.36092i	−0.126365	−	0.0264085i
$204$	126.506	+	172.803i	0.620128	+	0.847075i
$205$	−262.842	−	151.752i	−1.28216	−	0.740254i
$206$	149.838	+	134.425i	0.727368	+	0.652548i
$207$	53.3982	+	92.4884i	0.257962	+	0.446804i
$208$	35.1388	+	38.4626i	0.168937	+	0.184916i
$209$			27.8495i			0.133251i
$210$	82.6679	−	188.318i	0.393657	−	0.896751i
$211$		−	62.1464i		−	0.294533i	−0.989097	−	0.147266i	$-0.952953\pi$
$211$		−	62.1464i		−	0.294533i	0.989097	−	0.147266i	$-0.0470475\pi$
$212$	182.746	−	19.8757i	0.862008	−	0.0937534i
$213$	128.811	+	223.106i	0.604744	+	1.04745i
$214$	159.217	+	142.840i	0.744006	+	0.667475i
$215$	−48.7463	−	28.1437i	−0.226727	−	0.130901i
$216$	−141.971	−	101.976i	−0.657273	−	0.472111i
$217$	−0.0366416	−	0.111473i	−0.000168855	−	0.000513702i
$218$	100.051	−	32.7088i	0.458952	−	0.150040i
$219$	156.623	+	90.4261i	0.715172	+	0.412905i
$220$	−124.608	+	282.619i	−0.566398	+	1.28463i
$221$	−44.3683	+	25.6161i	−0.200762	+	0.115910i
$222$	−1.89167	+	8.97938i	−0.00852101	+	0.0404477i
$223$		−	115.525i		−	0.518050i	−0.965871	−	0.259025i	$-0.916599\pi$
$223$		−	115.525i		−	0.518050i	0.965871	−	0.259025i	$-0.0834012\pi$
$224$	−212.158	+	71.8684i	−0.947133	+	0.320841i
$225$	−16.4063			−0.0729171
$226$	88.9175	+	18.7320i	0.393440	+	0.0828851i
$227$	28.2532	+	48.9360i	0.124463	+	0.215577i	0.921523	−	0.388324i	$-0.126946\pi$
$227$	28.2532	+	48.9360i	0.124463	+	0.215577i	−0.797060	+	0.603901i	$0.793612\pi$
$228$	−19.3918	−	8.54989i	−0.0850517	−	0.0374995i
$229$	59.1696	−	102.485i	0.258383	−	0.447532i	−0.707426	−	0.706787i	$-0.750144\pi$
$229$	59.1696	−	102.485i	0.258383	−	0.447532i	0.965809	+	0.259255i	$0.0834771\pi$
$230$	−111.113	−	339.879i	−0.483101	−	1.47774i
$231$	−283.990	+	317.579i	−1.22939	+	1.37480i
$232$	−17.4724	+	24.3251i	−0.0753123	+	0.104850i
$233$	12.3403	−	21.3740i	0.0529625	−	0.0917337i	−0.838329	−	0.545165i	$-0.816467\pi$
$233$	12.3403	−	21.3740i	0.0529625	−	0.0917337i	0.891291	+	0.453431i	$0.149800\pi$
$234$	−11.2143	+	12.5001i	−0.0479243	+	0.0534192i
$235$	133.745	−	77.2175i	0.569126	−	0.328585i
$236$	−29.7132	−	273.196i	−0.125903	−	1.15761i
$237$	−79.4503			−0.335233
$238$	−24.1702	−	218.951i	−0.101555	−	0.919961i
$239$	−251.189			−1.05100			−0.525499	−	0.850794i	$-0.676121\pi$
$239$	−251.189			−1.05100			−0.525499	+	0.850794i	$0.676121\pi$
$240$	−158.534	−	173.530i	−0.660560	−	0.723041i
$241$	97.3782	−	56.2213i	0.404059	−	0.233283i	−0.284175	−	0.958772i	$-0.591720\pi$
$241$	97.3782	−	56.2213i	0.404059	−	0.233283i	0.688234	+	0.725489i	$0.258386\pi$
$242$	265.665	−	296.125i	1.09779	−	1.22366i
$243$	67.6598	−	117.190i	0.278436	−	0.482265i
$244$	−310.093	+	227.014i	−1.27087	+	0.930384i
$245$	−170.286	+	125.508i	−0.695046	+	0.512276i
$246$	−454.755	+	148.668i	−1.84860	+	0.604343i
$247$	2.53492	−	4.39061i	0.0102628	−	0.0177758i
$248$	−0.133443	−	0.0132941i	−0.000538078	−	5.36052e-5i
$249$	−174.370	−	302.017i	−0.700280	−	1.21292i
$250$	264.975	+	55.8216i	1.05990	+	0.223286i
$251$	121.248			0.483059			0.241529	−	0.970394i	$-0.422351\pi$
$251$	121.248			0.483059			0.241529	+	0.970394i	$0.422351\pi$
$252$	−29.8318	−	65.7546i	−0.118380	−	0.260931i
$253$			740.735i			2.92781i
$254$	245.990	+	51.8222i	0.968466	+	0.204024i
$255$	200.174	−	115.571i	0.784998	−	0.453219i
$256$	−23.0741	+	254.958i	−0.0901332	+	0.995930i
$257$	−90.7377	−	52.3874i	−0.353065	−	0.203842i	0.312969	−	0.949763i	$-0.398676\pi$
$257$	−90.7377	−	52.3874i	−0.353065	−	0.203842i	−0.666034	+	0.745921i	$0.732010\pi$
$258$	−84.3381	+	27.5718i	−0.326892	+	0.106867i
$259$	6.29172	−	7.03588i	0.0242924	−	0.0271656i
$260$	45.3695	−	33.2142i	0.174498	−	0.127747i
$261$	−8.36079	−	4.82710i	−0.0320337	−	0.0184946i
$262$	−151.321	+	168.672i	−0.577562	+	0.643785i
$263$	52.3392	+	90.6542i	0.199008	+	0.344693i	0.948207	−	0.317653i	$-0.102895\pi$
$263$	52.3392	+	90.6542i	0.199008	+	0.344693i	−0.749199	+	0.662345i	$0.769561\pi$
$264$	200.449	+	443.723i	0.759276	+	1.68077i
$265$		−	198.399i		−	0.748675i
$266$	12.9049	+	17.5682i	0.0485146	+	0.0660460i
$267$			301.361i			1.12869i
$268$	55.4716	−	6.03318i	0.206983	−	0.0225119i
$269$	−152.466	−	264.079i	−0.566789	−	0.981707i	−0.996881	−	0.0789222i	$-0.974852\pi$
$269$	−152.466	−	264.079i	−0.566789	−	0.981707i	0.430092	−	0.902785i	$-0.358481\pi$
$270$	−125.984	+	140.429i	−0.466608	+	0.520108i
$271$	88.8942	+	51.3231i	0.328023	+	0.189384i	0.654963	−	0.755661i	$-0.272684\pi$
$271$	88.8942	+	51.3231i	0.328023	+	0.189384i	−0.326940	+	0.945045i	$0.606018\pi$
$272$	−239.984	−	76.0613i	−0.882295	−	0.279637i
$273$	73.6790	−	24.2185i	0.269886	−	0.0887125i
$274$	−48.6835	−	148.916i	−0.177677	−	0.543488i
$275$	−98.5482	−	56.8968i	−0.358357	−	0.206898i
$276$	−515.778	−	227.408i	−1.86876	−	0.823942i
$277$	14.4235	−	8.32739i	0.0520703	−	0.0300628i	−0.473739	−	0.880665i	$-0.657096\pi$
$277$	14.4235	−	8.32739i	0.0520703	−	0.0300628i	0.525809	+	0.850603i	$0.323763\pi$
$278$	291.675	+	61.4464i	1.04919	+	0.221030i
$279$		−	0.0432277i		−	0.000154938i
$280$	52.3539	+	236.024i	0.186978	+	0.842944i
$281$	75.8291			0.269855			0.134927	−	0.990856i	$-0.456920\pi$
$281$	75.8291			0.269855			0.134927	+	0.990856i	$0.456920\pi$
$282$	50.1853	−	238.220i	0.177962	−	0.844753i
$283$	43.6656	+	75.6311i	0.154296	+	0.267248i	0.932802	−	0.360389i	$-0.117356\pi$
$283$	43.6656	+	75.6311i	0.154296	+	0.267248i	−0.778507	+	0.627636i	$0.784023\pi$
$284$	−277.100	−	122.174i	−0.975704	−	0.430191i
$285$	−11.4367	+	19.8089i	−0.0401287	+	0.0695050i
$286$	−110.711	+	36.1936i	−0.387102	+	0.126551i
$287$	481.706	+	100.670i	1.67842	+	0.350767i
$288$	−82.5169	+	0.745975i	−0.286517	+	0.00259019i
$289$	−20.7152	+	35.8798i	−0.0716789	+	0.124151i
$290$	24.0610	+	21.5860i	0.0829689	+	0.0744344i
$291$	415.124	−	239.672i	1.42654	−	0.823614i
$292$	−211.349	+	22.9866i	−0.723797	+	0.0787213i
$293$	27.5057			0.0938760			0.0469380	−	0.998898i	$-0.485054\pi$
$293$	27.5057			0.0938760			0.0469380	+	0.998898i	$0.485054\pi$
$294$	−31.9891	+	331.932i	−0.108806	+	1.12902i
$295$	−296.597			−1.00541
$296$	−4.44090	−	9.83057i	−0.0150030	−	0.0332114i
$297$	338.452	−	195.406i	1.13957	−	0.657931i
$298$	126.926	+	113.870i	0.425928	+	0.382115i
$299$	67.4232	−	116.780i	0.225496	−	0.390570i
$300$	69.8722	−	51.1522i	0.232907	−	0.170507i
$301$	89.3363	+	18.6701i	0.296798	+	0.0620269i
$302$	−81.9115	−	250.555i	−0.271230	−	0.829654i
$303$	60.2248	−	104.312i	0.198762	−	0.344266i
$304$	24.3302	−	5.35574i	0.0800335	−	0.0176175i
$305$	207.390	+	359.211i	0.679968	+	1.17774i
$306$	16.7285	−	79.4072i	0.0546684	−	0.259501i
$307$	247.996			0.807805			0.403902	−	0.914802i	$-0.367654\pi$
$307$	247.996			0.807805			0.403902	+	0.914802i	$0.367654\pi$
$308$	48.8444	−	498.425i	0.158586	−	1.61826i
$309$		−	342.486i		−	1.10837i
$310$	−0.0298365	+	0.141628i	−9.62468e−5	+	0.000456866i
$311$	378.484	−	218.518i	1.21699	−	0.702630i	0.252717	−	0.967540i	$-0.418676\pi$
$311$	378.484	−	218.518i	1.21699	−	0.702630i	0.964273	+	0.264910i	$0.0853424\pi$
$312$	8.78681	−	88.2003i	0.0281629	−	0.282693i
$313$	−71.7330	−	41.4151i	−0.229179	−	0.132317i	0.381014	−	0.924569i	$-0.375575\pi$
$313$	−71.7330	−	41.4151i	−0.229179	−	0.132317i	−0.610193	+	0.792253i	$0.708908\pi$
$314$	152.326	+	465.943i	0.485114	+	1.48389i
$315$	−74.0335	+	24.3350i	−0.235027	+	0.0772540i
$316$	75.3593	−	55.1691i	0.238479	−	0.174586i
$317$	−211.775	−	122.268i	−0.668059	−	0.385704i	0.127282	−	0.991867i	$-0.459375\pi$
$317$	−211.775	−	122.268i	−0.668059	−	0.385704i	−0.795341	+	0.606162i	$0.792708\pi$
$318$	−232.799	−	208.852i	−0.732072	−	0.656768i
$319$	−33.4806	−	57.9900i	−0.104955	−	0.181787i
$320$	270.868	+	54.5106i	0.846462	+	0.170345i
$321$		−	363.925i		−	1.13372i
$322$	343.241	+	467.276i	1.06597	+	1.45117i
$323$			24.4991i			0.0758485i
$324$	42.1938	+	387.948i	0.130228	+	1.19737i
$325$	10.3577	+	17.9401i	0.0318699	+	0.0552004i
$326$	−357.707	−	320.912i	−1.09726	−	0.984393i
$327$	−155.097	−	89.5456i	−0.474304	−	0.273840i
$328$	328.106	−	456.789i	1.00032	−	1.39265i
$329$	−166.917	+	186.660i	−0.507348	+	0.567355i
$330$	499.490	−	163.293i	1.51361	−	0.494828i
$331$	−66.2919	−	38.2736i	−0.200278	−	0.115630i	0.396507	−	0.918032i	$-0.370222\pi$
$331$	−66.2919	−	38.2736i	−0.200278	−	0.115630i	−0.596785	+	0.802401i	$0.703555\pi$
$332$	375.108	+	165.386i	1.12984	+	0.498151i
$333$	3.01132	−	1.73858i	0.00904299	−	0.00522097i
$334$	30.1779	−	143.249i	0.0903529	−	0.428888i
$335$		−	60.2230i		−	0.179770i
$336$	332.061	+	187.029i	0.988276	+	0.556633i
$337$	−38.2520			−0.113507			−0.0567537	−	0.998388i	$-0.518075\pi$
$337$	−38.2520			−0.113507			−0.0567537	+	0.998388i	$0.518075\pi$
$338$	−309.992	−	65.3052i	−0.917136	−	0.193211i
$339$	−77.3015	−	133.890i	−0.228028	−	0.394956i
$340$	−109.616	+	248.618i	−0.322401	+	0.731230i
$341$	0.149913	−	0.259656i	0.000439627	−	0.000761456i
$342$	2.49536	+	7.63294i	0.00729637	+	0.0223185i
$343$	198.754	−	279.546i	0.579459	−	0.815002i
$344$	60.8500	−	84.7153i	0.176889	−	0.246265i
$345$	−304.190	+	526.873i	−0.881711	+	1.52717i
$346$	−49.4818	+	55.1553i	−0.143011	+	0.159408i
$347$	−208.395	+	120.317i	−0.600561	+	0.346734i	−0.769262	−	0.638933i	$-0.779376\pi$
$347$	−208.395	+	120.317i	−0.600561	+	0.346734i	0.168701	+	0.985667i	$0.446043\pi$
$348$	50.6574	−	5.50958i	0.145567	−	0.0158321i
$349$	430.367			1.23314			0.616572	−	0.787298i	$-0.288521\pi$
$349$	430.367			1.23314			0.616572	+	0.787298i	$0.288521\pi$
$350$	−88.5317	+	9.77310i	−0.252948	+	0.0279232i
$351$	−71.1449			−0.202692
$352$	−498.242	−	281.686i	−1.41546	−	0.800244i
$353$	−265.950	+	153.546i	−0.753399	+	0.434975i	−0.826921	−	0.562318i	$-0.809910\pi$
$353$	−265.950	+	153.546i	−0.753399	+	0.434975i	0.0735214	+	0.997294i	$0.476576\pi$
$354$	−312.224	+	348.023i	−0.881988	+	0.983116i
$355$	−163.425	+	283.061i	−0.460353	+	0.797354i
$356$	−209.261	−	285.844i	−0.587811	−	0.802931i
$357$	−249.824	+	279.372i	−0.699787	+	0.782555i
$358$	−452.147	+	147.816i	−1.26298	+	0.412893i
$359$	−230.880	+	399.896i	−0.643120	+	1.11392i	0.341613	+	0.939841i	$0.389027\pi$
$359$	−230.880	+	399.896i	−0.643120	+	1.11392i	−0.984732	+	0.174075i	$0.944306\pi$
$360$	−8.82909	+	88.6247i	−0.0245252	+	0.246180i
$361$	179.288	+	310.536i	0.496642	+	0.860209i
$362$	−572.539	−	120.615i	−1.58160	−	0.333192i
$363$	−676.858			−1.86462
$364$	−53.0682	+	74.1331i	−0.145792	+	0.203662i
$365$			229.452i			0.628635i
$366$	639.811	+	134.787i	1.74812	+	0.368272i
$367$	−542.949	+	313.471i	−1.47942	+	0.854146i	−0.999729	−	0.0232895i	$-0.992586\pi$
$367$	−542.949	+	313.471i	−1.47942	+	0.854146i	−0.479695	+	0.877435i	$0.659253\pi$
$368$	647.129	−	142.451i	1.75850	−	0.387094i
$369$	157.003	+	90.6457i	0.425482	+	0.245652i
$370$	−11.0661	+	3.61772i	−0.0299083	+	0.00977762i
$371$	100.453	+	305.605i	0.270763	+	0.823732i
$372$	0.134777	+	0.184100i	0.000362303	+	0.000494894i
$373$	357.317	+	206.297i	0.957953	+	0.553075i	0.895543	−	0.444976i	$-0.146788\pi$
$373$	357.317	+	206.297i	0.957953	+	0.553075i	0.0624108	+	0.998051i	$0.480121\pi$
$374$	375.866	−	418.962i	1.00499	−	1.12022i
$375$	−230.359	−	398.993i	−0.614290	−	1.06398i
$376$	117.816	+	260.802i	0.313340	+	0.693622i
$377$			12.1899i			0.0323339i
$378$	122.958	−	280.099i	0.325286	−	0.741003i
$379$		−	327.118i		−	0.863107i	−0.902087	−	0.431554i	$-0.857966\pi$
$379$		−	327.118i		−	0.863107i	0.902087	−	0.431554i	$-0.142034\pi$
$380$	−2.90724	−	26.7304i	−0.00765064	−	0.0703432i
$381$	−213.854	−	370.407i	−0.561298	−	0.972196i
$382$	−188.619	+	210.246i	−0.493766	+	0.550381i
$383$	−215.523	−	124.432i	−0.562724	−	0.324889i	0.191514	−	0.981490i	$-0.438660\pi$
$383$	−215.523	−	124.432i	−0.562724	−	0.324889i	−0.754238	+	0.656601i	$0.771994\pi$
$384$	349.102	−	260.451i	0.909119	−	0.678257i
$385$	−529.091	−	110.573i	−1.37426	−	0.287203i
$386$	40.9922	+	125.389i	0.106197	+	0.324842i
$387$	29.1175	+	16.8110i	0.0752390	+	0.0434392i
$388$	−227.324	+	515.587i	−0.585886	+	1.32883i
$389$	−326.728	+	188.637i	−0.839918	+	0.484927i	−0.857236	−	0.514923i	$-0.827821\pi$
$389$	−326.728	+	188.637i	−0.839918	+	0.484927i	0.0173181	+	0.999850i	$0.494487\pi$
$390$	−93.6103	−	19.7207i	−0.240026	−	0.0505658i
$391$			651.620i			1.66655i
$392$	−200.147	−	337.054i	−0.510580	−	0.859830i
$393$	385.535			0.981005
$394$	82.2186	−	390.276i	0.208677	−	0.990549i
$395$	−50.4003	−	87.2958i	−0.127596	−	0.221002i
$396$	74.4314	−	168.816i	0.187958	−	0.426303i
$397$	335.874	−	581.752i	0.846031	−	1.46537i	−0.0386913	−	0.999251i	$-0.512319\pi$
$397$	335.874	−	581.752i	0.846031	−	1.46537i	0.884723	−	0.466118i	$-0.154348\pi$
$398$	128.682	−	42.0687i	0.323322	−	0.105700i
$399$	7.58692	−	36.3034i	0.0190148	−	0.0909859i
$400$	−30.7550	+	97.0365i	−0.0768876	+	0.242591i
$401$	235.200	−	407.378i	0.586534	−	1.01591i	−0.408149	−	0.912915i	$-0.633826\pi$
$401$	235.200	−	407.378i	0.586534	−	1.01591i	0.994682	−	0.102991i	$-0.0328411\pi$
$402$	−70.6650	−	63.3961i	−0.175784	−	0.157702i
$403$	−0.0472689	+	0.0272907i	−0.000117293	+	6.77189e-5i
$404$	15.3093	+	140.761i	0.0378944	+	0.348417i
$405$	421.177			1.03994
$406$	−47.9918	−	21.0675i	−0.118207	−	0.0518904i
$407$	24.1175			0.0592567
$408$	176.334	+	390.340i	0.432191	+	0.956716i
$409$	−57.7400	+	33.3362i	−0.141174	+	0.0815067i	−0.568923	−	0.822391i	$-0.692640\pi$
$409$	−57.7400	+	33.3362i	−0.141174	+	0.0815067i	0.427750	+	0.903897i	$0.359307\pi$
$410$	−451.829	−	405.352i	−1.10202	−	0.988663i
$411$	−133.279	+	230.846i	−0.324279	+	0.561669i
$412$	237.818	+	324.851i	0.577227	+	0.788474i
$413$	456.864	−	150.172i	1.10621	−	0.363614i
$414$	66.3709	+	203.019i	0.160316	+	0.490384i
$415$	221.227	−	383.177i	0.533077	−	0.923317i
$416$	52.9107	+	89.7602i	0.127189	+	0.215770i
$417$	−253.571	−	439.197i	−0.608083	−	1.05323i
$418$	−11.4820	+	54.5027i	−0.0274688	+	0.130389i
$419$	−437.380			−1.04387			−0.521933	−	0.852986i	$-0.674789\pi$
$419$	−437.380			−1.04387			−0.521933	+	0.852986i	$0.674789\pi$
$420$	239.425	−	334.463i	0.570060	−	0.796341i
$421$		−	703.800i		−	1.67173i	−0.548933	−	0.835867i	$-0.684966\pi$
$421$		−	703.800i		−	1.67173i	0.548933	−	0.835867i	$-0.315034\pi$
$422$	25.6221	−	121.623i	0.0607158	−	0.288207i
$423$	−79.8893	+	46.1241i	−0.188864	+	0.109040i
$424$	365.836	+	36.4458i	0.862820	+	0.0859571i
$425$	−86.6923	−	50.0518i	−0.203982	−	0.117769i
$426$	160.104	+	489.736i	0.375832	+	1.14961i
$427$	−501.330	−	448.306i	−1.17407	−	1.04990i
$428$	252.705	+	345.186i	0.590431	+	0.806510i
$429$	171.622	+	99.0858i	0.400051	+	0.230969i
$430$	−83.7954	−	75.1758i	−0.194873	−	0.174827i
$431$	274.869	+	476.087i	0.637747	+	1.10461i	0.985926	+	0.167183i	$0.0534670\pi$
$431$	274.869	+	476.087i	0.637747	+	1.10461i	−0.348178	+	0.937428i	$0.613200\pi$
$432$	−235.800	−	258.104i	−0.545833	−	0.597463i
$433$			355.012i			0.819890i	0.912110	+	0.409945i	$0.134452\pi$
$433$			355.012i			0.819890i	−0.912110	+	0.409945i	$0.865548\pi$
$434$	−0.0257503	−	0.233265i	−5.93326e−5	−	0.000537477i
$435$		−	54.9965i		−	0.126429i
$436$	209.290	−	22.7628i	0.480024	−	0.0522082i
$437$	−32.2416	−	55.8441i	−0.0737794	−	0.127790i
$438$	269.236	+	241.541i	0.614694	+	0.551464i
$439$	477.032	+	275.415i	1.08663	+	0.627369i	0.932678	−	0.360709i	$-0.117465\pi$
$439$	477.032	+	275.415i	1.08663	+	0.627369i	0.153956	+	0.988078i	$0.450799\pi$
$440$	−360.382	+	501.724i	−0.819050	+	1.14028i
$441$	101.717	−	74.9692i	0.230650	−	0.169998i
$442$	−97.3919	+	31.8393i	−0.220344	+	0.0720347i
$443$	−234.027	−	135.116i	−0.528278	−	0.305001i	0.212037	−	0.977262i	$-0.431990\pi$
$443$	−234.027	−	135.116i	−0.528278	−	0.305001i	−0.740315	+	0.672260i	$0.765324\pi$
$444$	−7.40414	+	16.7931i	−0.0166760	+	0.0378224i
$445$	−331.120	+	191.172i	−0.744089	+	0.429600i
$446$	47.6294	−	226.088i	0.106792	−	0.506923i
$447$		−	290.117i		−	0.649032i
$448$	−444.832	+	53.1800i	−0.992930	+	0.118705i
$449$	455.397			1.01425			0.507124	−	0.861873i	$-0.330709\pi$
$449$	455.397			1.01425			0.507124	+	0.861873i	$0.330709\pi$
$450$	−32.1079	−	6.76410i	−0.0713509	−	0.0150313i
$451$	628.714	+	1088.96i	1.39404	+	2.41456i
$452$	166.293	+	73.3188i	0.367904	+	0.162210i
$453$	−224.246	+	388.405i	−0.495024	+	0.857406i
$454$	35.1171	+	107.418i	0.0773505	+	0.236604i
$455$	73.3492	+	65.5914i	0.161207	+	0.144157i
$456$	−34.4256	−	24.7275i	−0.0754947	−	0.0542269i
$457$	84.3172	−	146.042i	0.184501	−	0.319566i	−0.758907	−	0.651199i	$-0.774266\pi$
$457$	84.3172	−	146.042i	0.184501	−	0.319566i	0.943408	+	0.331633i	$0.107600\pi$
$458$	158.051	−	176.173i	0.345089	−	0.384656i
$459$	297.735	−	171.897i	0.648659	−	0.374504i
$460$	−77.3261	−	710.969i	−0.168100	−	1.54558i
$461$	265.062			0.574971			0.287485	−	0.957785i	$-0.407181\pi$
$461$	265.062			0.574971			0.287485	+	0.957785i	$0.407181\pi$
$462$	−686.713	+	504.431i	−1.48639	+	1.09184i
$463$	97.4735			0.210526			0.105263	−	0.994444i	$-0.466432\pi$
$463$	97.4735			0.210526			0.105263	+	0.994444i	$0.466432\pi$
$464$	−44.2232	+	40.4017i	−0.0953087	+	0.0870727i
$465$	0.213261	−	0.123126i	0.000458626	−	0.000264788i
$466$	32.9626	−	36.7421i	0.0707352	−	0.0788456i
$467$	−37.0997	+	64.2586i	−0.0794427	+	0.137599i	−0.903010	−	0.429620i	$-0.858647\pi$
$467$	−37.0997	+	64.2586i	−0.0794427	+	0.137599i	0.823567	+	0.567219i	$0.191981\pi$
$468$	−27.1005	+	19.8398i	−0.0579070	+	0.0423926i
$469$	30.4921	+	92.7648i	0.0650150	+	0.197793i
$470$	293.580	−	95.9770i	0.624638	−	0.204206i
$471$	417.016	−	722.293i	0.885385	−	1.53353i
$472$	54.4847	−	546.907i	0.115434	−	1.15870i
$473$	116.600	+	201.958i	0.246512	+	0.426972i
$474$	−155.488	−	32.7562i	−0.328033	−	0.0691059i
$475$	9.90608			0.0208549
$476$	42.9682	−	438.461i	0.0902692	−	0.921137i
$477$			118.509i			0.248447i
$478$	−491.587	−	103.561i	−1.02843	−	0.216656i
$479$	−475.220	+	274.368i	−0.992108	+	0.572794i	−0.905904	−	0.423484i	$-0.860807\pi$
$479$	−475.220	+	274.368i	−0.992108	+	0.572794i	−0.0862043	+	0.996277i	$0.527474\pi$
$480$	−238.715	−	404.967i	−0.497322	−	0.843681i
$481$	−3.80224	−	2.19522i	−0.00790486	−	0.00456387i
$482$	213.753	−	69.8799i	0.443470	−	0.144979i
$483$	201.795	−	965.588i	0.417795	−	1.99915i
$484$	642.006	−	470.001i	1.32646	−	0.971076i
$485$	526.678	+	304.078i	1.08593	+	0.626964i
$486$	180.729	−	201.451i	0.371871	−	0.414509i
$487$	−283.938	−	491.795i	−0.583034	−	1.00985i	−0.995117	−	0.0986990i	$-0.968532\pi$
$487$	−283.938	−	491.795i	−0.583034	−	1.00985i	0.412083	−	0.911146i	$-0.364801\pi$
$488$	−700.461	+	316.429i	−1.43537	+	0.648419i
$489$			817.617i			1.67202i
$490$	−385.003	+	175.417i	−0.785720	+	0.357995i
$491$			78.8005i			0.160490i	0.996775	+	0.0802449i	$0.0255702\pi$
$491$			78.8005i			0.160490i	−0.996775	+	0.0802449i	$0.974430\pi$
$492$	−951.270	+	103.462i	−1.93348	+	0.210288i
$493$	−29.4527	−	51.0135i	−0.0597417	−	0.103476i
$494$	6.77114	−	7.54751i	0.0137068	−	0.0152784i
$495$	−172.447	−	99.5626i	−0.348379	−	0.201136i
$496$	−0.255674	−	0.0810339i	−0.000515471	−	0.000163375i
$497$	108.414	−	518.759i	0.218136	−	1.04378i
$498$	−216.732	−	662.951i	−0.435204	−	1.33123i
$499$	290.932	+	167.970i	0.583030	+	0.336612i	0.762337	−	0.647181i	$-0.224052\pi$
$499$	290.932	+	167.970i	0.583030	+	0.336612i	−0.179307	+	0.983793i	$0.557385\pi$
$500$	495.552	+	218.490i	0.991105	+	0.436981i
$501$	−215.701	+	124.535i	−0.430541	+	0.248573i
$502$	237.287	+	49.9887i	0.472684	+	0.0995791i
$503$		−	274.052i		−	0.544836i	−0.962179	−	0.272418i	$-0.912177\pi$
$503$		−	274.052i		−	0.544836i	0.962179	−	0.272418i	$-0.0878233\pi$
$504$	−31.2724	−	140.984i	−0.0620485	−	0.279730i
$505$	152.817			0.302609
$506$	−305.394	+	1449.65i	−0.603546	+	2.86492i
$507$	269.495	+	466.779i	0.531548	+	0.920669i
$508$	460.048	+	202.837i	0.905607	+	0.399285i
$509$	−168.009	+	291.000i	−0.330076	+	0.571709i	−0.982526	−	0.186123i	$-0.940408\pi$
$509$	−168.009	+	291.000i	−0.330076	+	0.571709i	0.652450	+	0.757831i	$0.273741\pi$
$510$	439.398	−	143.648i	0.861566	−	0.281663i
$511$	−116.176	−	353.437i	−0.227350	−	0.691658i
$512$	−150.273	+	489.451i	−0.293501	+	0.955959i
$513$	−17.0106	+	29.4633i	−0.0331591	+	0.0574333i
$514$	−155.979	−	139.934i	−0.303461	−	0.272246i
$515$	376.306	−	217.260i	0.730691	−	0.421865i
$516$	−176.421	+	19.1878i	−0.341901	+	0.0371857i
$517$	−639.829			−1.23758
$518$	15.2140	−	11.1755i	0.0293706	−	0.0215744i
$519$	126.069			0.242908
$520$	102.484	−	46.2965i	0.197084	−	0.0890316i
$521$	−547.572	+	316.141i	−1.05100	+	0.606796i	−0.922930	−	0.384969i	$-0.874212\pi$
$521$	−547.572	+	316.141i	−1.05100	+	0.606796i	−0.128072	+	0.991765i	$0.540879\pi$
$522$	−14.3723	−	12.8939i	−0.0275331	−	0.0247009i
$523$	−389.623	+	674.847i	−0.744977	+	1.29034i	0.205229	+	0.978714i	$0.434206\pi$
$523$	−389.623	+	674.847i	−0.744977	+	1.29034i	−0.950206	+	0.311624i	$0.899127\pi$
$524$	−365.683	+	267.710i	−0.697869	+	0.510897i
$525$	112.963	+	101.015i	0.215167	+	0.192410i
$526$	65.0547	+	198.993i	0.123678	+	0.378314i
$527$	0.131877	−	0.228418i	0.000250242	−	0.000433431i
$528$	209.347	+	951.027i	0.396490	+	1.80119i
$529$	−593.054	−	1027.20i	−1.12109	−	1.94178i
$530$	81.7970	−	388.275i	0.154334	−	0.732595i
$531$	177.165			0.333644
$532$	18.0123	+	39.7023i	0.0338577	+	0.0746284i
$533$		−	228.907i		−	0.429470i
$534$	−124.247	+	589.777i	−0.232672	+	1.10445i
$535$	399.862	−	230.861i	0.747406	−	0.431515i
$536$	111.048	+	11.0629i	0.207179	+	0.0206398i
$537$	700.908	+	404.669i	1.30523	+	0.753574i
$538$	−189.507	−	579.674i	−0.352243	−	1.07746i
$539$	870.974	−	97.5673i	1.61591	−	0.181015i
$540$	−304.453	+	222.885i	−0.563802	+	0.412750i
$541$	−583.617	−	336.952i	−1.07878	−	0.622831i	−0.148209	−	0.988956i	$-0.547351\pi$
$541$	−583.617	−	336.952i	−1.07878	−	0.622831i	−0.930566	+	0.366125i	$0.880684\pi$
$542$	152.810	+	137.091i	0.281937	+	0.252936i
$543$	497.743	+	862.117i	0.916655	+	1.58769i
$544$	−438.301	−	247.797i	−0.805700	−	0.455510i
$545$		−	227.217i		−	0.416913i
$546$	154.178	−	17.0199i	0.282377	−	0.0311719i
$547$		−	52.5329i		−	0.0960382i	−0.998846	−	0.0480191i	$-0.984709\pi$
$547$		−	52.5329i		−	0.0960382i	0.998846	−	0.0480191i	$-0.0152908\pi$
$548$	−33.8799	−	311.506i	−0.0618247	−	0.568442i
$549$	−123.880	−	214.566i	−0.225646	−	0.390831i
$550$	−169.405	−	151.980i	−0.308010	−	0.276326i
$551$	5.04821	+	2.91458i	0.00916190	+	0.00528963i
$552$	−915.643	−	657.695i	−1.65877	−	1.19148i
$553$	121.834	+	108.948i	0.220314	+	0.197012i
$554$	31.6606	−	10.3505i	0.0571491	−	0.0186832i
$555$	17.1544	+	9.90409i	0.0309088	+	0.0178452i
$556$	545.486	+	240.507i	0.981091	+	0.432566i
$557$	−678.123	+	391.515i	−1.21746	+	0.702899i	−0.964373	−	0.264546i	$-0.914778\pi$
$557$	−678.123	+	391.515i	−1.21746	+	0.702899i	−0.253083	+	0.967445i	$0.581445\pi$
$558$	0.0178222	−	0.0845985i	3.19394e−5	−	0.000151610i
$559$		−	42.4528i		−	0.0759441i
$560$	5.14945	+	483.495i	0.00919545	+	0.863384i
$561$	−957.628			−1.70700
$562$	148.401	+	31.2633i	0.264059	+	0.0556286i
$563$	−446.202	−	772.844i	−0.792543	−	1.37272i	−0.924388	−	0.381454i	$-0.875423\pi$
$563$	−446.202	−	772.844i	−0.792543	−	1.37272i	0.131845	−	0.991270i	$-0.457910\pi$
$564$	196.430	−	445.517i	0.348280	−	0.789924i
$565$	98.0743	−	169.870i	0.173583	−	0.300654i
$566$	54.2739	+	166.016i	0.0958903	+	0.293315i
$567$	−648.763	+	213.250i	−1.14420	+	0.376102i
$568$	−491.926	−	353.345i	−0.866067	−	0.622085i
$569$	148.722	−	257.593i	0.261373	−	0.452712i	−0.705234	−	0.708975i	$-0.749158\pi$
$569$	148.722	−	257.593i	0.261373	−	0.452712i	0.966607	+	0.256263i	$0.0824912\pi$
$570$	−30.5490	+	34.0517i	−0.0535948	+	0.0597399i
$571$	218.885	−	126.373i	0.383335	−	0.221319i	−0.295933	−	0.955209i	$-0.595631\pi$
$571$	218.885	−	126.373i	0.383335	−	0.221319i	0.679268	+	0.733890i	$0.262297\pi$
$572$	−231.588	+	25.1879i	−0.404875	+	0.0440348i
$573$	480.561			0.838676
$574$	901.214	+	395.616i	1.57006	+	0.689226i
$575$	263.479			0.458225
$576$	−161.797	−	32.5606i	−0.280897	−	0.0565289i
$577$	764.454	−	441.358i	1.32488	−	0.764918i	0.340375	−	0.940290i	$-0.389446\pi$
$577$	764.454	−	441.358i	1.32488	−	0.764918i	0.984502	+	0.175371i	$0.0561126\pi$
$578$	−55.3333	+	61.6777i	−0.0957323	+	0.106709i
$579$	112.223	−	194.375i	0.193821	−	0.335709i
$580$	38.1888	+	52.1647i	0.0658428	+	0.0899391i
$581$	−146.759	+	702.239i	−0.252597	+	1.20867i
$582$	911.229	−	297.899i	1.56568	−	0.511853i
$583$	−410.987	+	711.850i	−0.704951	+	1.22101i
$584$	−423.096	−	42.1502i	−0.724479	−	0.0721750i
$585$	18.1248	+	31.3930i	0.0309825	+	0.0536633i
$586$	53.8298	+	11.3402i	0.0918597	+	0.0193519i
$587$	66.7814			0.113767			0.0568836	−	0.998381i	$-0.481884\pi$
$587$	66.7814			0.113767			0.0568836	+	0.998381i	$0.481884\pi$
$588$	−199.455	+	636.418i	−0.339209	+	1.08234i
$589$			0.0261007i			4.43136e-5i
$590$	−580.452	−	122.283i	−0.983818	−	0.207259i
$591$	−587.670	+	339.291i	−0.994365	+	0.574097i
$592$	−4.63803	−	21.0698i	−0.00783451	−	0.0355908i
$593$	−311.911	−	180.082i	−0.525989	−	0.303680i	0.213393	−	0.976967i	$-0.431549\pi$
$593$	−311.911	−	180.082i	−0.525989	−	0.303680i	−0.739381	+	0.673287i	$0.764882\pi$
$594$	742.929	−	242.878i	1.25072	−	0.408886i
$595$	−465.439	−	97.2704i	−0.782250	−	0.163480i
$596$	201.454	+	275.179i	0.338009	+	0.461710i
$597$	−199.480	−	115.170i	−0.334137	−	0.192914i
$598$	180.097	−	200.747i	0.301166	−	0.335697i
$599$	99.0219	+	171.511i	0.165312	+	0.286329i	0.936766	−	0.349956i	$-0.113804\pi$
$599$	99.0219	+	171.511i	0.165312	+	0.286329i	−0.771454	+	0.636285i	$0.780470\pi$
$600$	157.832	−	71.2997i	0.263054	−	0.118833i
$601$			373.907i			0.622141i	0.950387	+	0.311071i	$0.100688\pi$
$601$			373.907i			0.622141i	−0.950387	+	0.311071i	$0.899312\pi$
$602$	167.138	+	73.3702i	0.277637	+	0.121877i
$603$			35.9728i			0.0596565i
$604$	−57.0040	−	524.119i	−0.0943775	−	0.867746i
$605$	−429.373	−	743.696i	−0.709708	−	1.22925i
$606$	160.869	−	179.314i	0.265461	−	0.295898i
$607$	200.164	+	115.565i	0.329760	+	0.190387i	0.655735	−	0.754992i	$-0.272359\pi$
$607$	200.164	+	115.565i	0.329760	+	0.190387i	−0.325975	+	0.945379i	$0.605692\pi$
$608$	49.8234	−	0.450416i	0.0819463	−	0.000740816i
$609$	27.8458	+	84.7142i	0.0457238	+	0.139104i
$610$	257.775	+	788.495i	0.422581	+	1.29261i
$611$	100.872	+	58.2386i	0.165094	+	0.0953168i
$612$	65.4769	−	148.506i	0.106988	−	0.242658i
$613$	444.718	−	256.758i	0.725479	−	0.418855i	−0.0912873	−	0.995825i	$-0.529098\pi$
$613$	444.718	−	256.758i	0.725479	−	0.418855i	0.816766	+	0.576969i	$0.195765\pi$
$614$	485.339	+	102.245i	0.790455	+	0.166523i
$615$			1032.75i			1.67927i
$616$	301.084	−	955.301i	0.488773	−	1.55081i
$617$	−1119.01			−1.81363			−0.906815	−	0.421529i	$-0.861493\pi$
$617$	−1119.01			−1.81363			−0.906815	+	0.421529i	$0.861493\pi$
$618$	141.202	−	670.261i	0.228482	−	1.08456i
$619$	−64.1019	−	111.028i	−0.103557	−	0.179366i	0.809591	−	0.586995i	$-0.199689\pi$
$619$	−64.1019	−	111.028i	−0.103557	−	0.179366i	−0.913148	+	0.407629i	$0.866356\pi$
$620$	−0.116783	+	0.264872i	−0.000188359	+	0.000427213i
$621$	−452.445	+	783.658i	−0.728575	+	1.26193i
$622$	830.802	−	271.605i	1.33569	−	0.436665i
$623$	413.248	−	462.125i	0.663319	−	0.741774i
$624$	53.5599	−	168.989i	0.0858332	−	0.270816i
$625$	212.735	−	368.469i	0.340377	−	0.589550i
$626$	−123.310	−	110.626i	−0.196980	−	0.176718i
$627$	82.0690	−	47.3826i	0.130892	−	0.0755703i
$628$	106.007	+	974.672i	0.168801	+	1.55203i
$629$	21.2160			0.0337297
$630$	−154.920	+	17.1018i	−0.245904	+	0.0271456i
$631$	313.995			0.497615			0.248808	−	0.968553i	$-0.419961\pi$
$631$	313.995			0.497615			0.248808	+	0.968553i	$0.419961\pi$
$632$	170.227	−	76.8989i	0.269346	−	0.121675i
$633$	−183.138	+	105.735i	−0.289317	+	0.167037i
$634$	−364.043	−	326.596i	−0.574200	−	0.515136i
$635$	271.322	−	469.944i	0.427279	−	0.740070i
$636$	−369.491	−	504.713i	−0.580961	−	0.793573i
$637$	−146.194	−	63.8959i	−0.229504	−	0.100307i
$638$	−41.6145	−	127.293i	−0.0652264	−	0.199518i
$639$	97.6183	−	169.080i	0.152767	−	0.264601i
$640$	507.626	+	218.354i	0.793166	+	0.341179i
$641$	115.594	+	200.215i	0.180334	+	0.312348i	0.941994	−	0.335629i	$-0.108949\pi$
$641$	115.594	+	200.215i	0.180334	+	0.312348i	−0.761660	+	0.647977i	$0.775615\pi$
$642$	150.041	−	712.218i	0.233709	−	1.10937i
$643$	−637.869			−0.992020			−0.496010	−	0.868317i	$-0.665202\pi$
$643$	−637.869			−0.992020			−0.496010	+	0.868317i	$0.665202\pi$
$644$	479.087	+	1055.99i	0.743924	+	1.63974i
$645$			191.532i			0.296949i
$646$	−10.1006	+	47.9457i	−0.0156356	+	0.0742194i
$647$	−586.461	+	338.594i	−0.906432	+	0.523329i	−0.879281	−	0.476303i	$-0.841977\pi$
$647$	−586.461	+	338.594i	−0.906432	+	0.523329i	−0.0271505	+	0.999631i	$0.508643\pi$
$648$	−77.3701	+	776.626i	−0.119398	+	1.19850i
$649$	1064.18	+	614.405i	1.63972	+	0.946695i
$650$	12.8741	+	39.3799i	0.0198063	+	0.0605845i
$651$	−0.266157	+	0.297636i	−0.000408843	+	0.000457199i
$652$	−567.742	−	775.517i	−0.870769	−	1.18944i
$653$	916.022	+	528.865i	1.40279	+	0.809901i	0.994678	−	0.103031i	$-0.0328541\pi$
$653$	916.022	+	528.865i	1.40279	+	0.809901i	0.408112	+	0.912932i	$0.366187\pi$
$654$	−266.614	−	239.189i	−0.407667	−	0.365732i
$655$	244.569	+	423.606i	0.373388	+	0.646726i
$656$	830.445	−	758.683i	1.26592	−	1.15653i
$657$		−	137.058i		−	0.208612i
$658$	−403.622	+	296.484i	−0.613407	+	0.450583i
$659$			644.502i			0.978000i	0.872284	+	0.489000i	$0.162638\pi$
$659$			644.502i			0.978000i	−0.872284	+	0.489000i	$0.837362\pi$
$660$	1044.85	−	113.639i	1.58310	−	0.172181i
$661$	−560.069	−	970.068i	−0.847306	−	1.46758i	−0.883604	−	0.468236i	$-0.844890\pi$
$661$	−560.069	−	970.068i	−0.847306	−	1.46758i	0.0362979	−	0.999341i	$-0.488443\pi$
$662$	−113.956	−	102.234i	−0.172140	−	0.154433i
$663$	150.975	+	87.1652i	0.227714	+	0.131471i
$664$	665.916	+	478.319i	1.00289	+	0.720360i
$665$	44.7011	−	14.6934i	0.0672197	−	0.0220953i
$666$	6.61007	−	2.16096i	0.00992503	−	0.00324469i
$667$	134.271	+	77.5214i	0.201306	+	0.116224i
$668$	118.119	−	267.902i	0.176825	−	0.401051i
$669$	−340.438	+	196.552i	−0.508876	+	0.293800i
$670$	24.8291	−	117.859i	0.0370583	−	0.175909i
$671$		−	1718.45i		−	2.56103i
$672$	572.748	+	502.927i	0.852303	+	0.748403i
$673$	−307.811			−0.457371			−0.228686	−	0.973500i	$-0.573443\pi$
$673$	−307.811			−0.457371			−0.228686	+	0.973500i	$0.573443\pi$
$674$	−74.8609	−	15.7708i	−0.111070	−	0.0233987i
$675$	−69.5058	−	120.388i	−0.102972	−	0.178352i
$676$	−579.743	−	255.610i	−0.857608	−	0.378122i
$677$	507.773	−	879.488i	0.750033	−	1.29910i	−0.197773	−	0.980248i	$-0.563371\pi$
$677$	507.773	−	879.488i	0.750033	−	1.29910i	0.947806	−	0.318848i	$-0.103296\pi$
$678$	−96.0814	−	293.899i	−0.141713	−	0.433479i
$679$	−965.231	−	201.720i	−1.42155	−	0.297084i
$680$	−317.026	+	441.364i	−0.466215	+	0.649064i
$681$	96.1388	−	166.517i	0.141173	−	0.244519i
$682$	0.400438	−	0.446352i	0.000587153	−	0.000654475i
$683$	840.220	−	485.102i	1.23019	−	0.710251i	0.263121	−	0.964763i	$-0.415248\pi$
$683$	840.220	−	485.102i	1.23019	−	0.710251i	0.967070	+	0.254512i	$0.0819147\pi$
$684$	1.73657	+	15.9668i	0.00253885	+	0.0233433i
$685$	−338.188			−0.493706
$686$	504.224	−	465.139i	0.735020	−	0.678046i
$687$	−402.680			−0.586143
$688$	154.013	−	140.704i	0.223856	−	0.204512i
$689$	129.588	−	74.8177i	0.188081	−	0.108589i
$690$	−812.536	+	905.700i	−1.17759	+	1.31261i
$691$	−274.581	+	475.588i	−0.397367	+	0.688260i	−0.993400	−	0.114700i	$-0.963409\pi$
$691$	−274.581	+	475.588i	−0.397367	+	0.688260i	0.596033	+	0.802960i	$0.296743\pi$
$692$	−119.578	+	87.5407i	−0.172800	+	0.126504i
$693$	316.041	+	66.0483i	0.456047	+	0.0953078i
$694$	−457.442	+	149.547i	−0.659138	+	0.215485i
$695$	321.711	−	557.221i	0.462894	−	0.801756i
$696$	101.410	+	10.1028i	0.145705	+	0.0145156i
$697$	553.076	+	957.956i	0.793510	+	1.37440i
$698$	842.248	+	177.434i	1.20666	+	0.254204i
$699$	−83.9818			−0.120146
$700$	−177.290	−	17.3740i	−0.253271	−	0.0248200i
$701$		−	452.665i		−	0.645742i	−0.946443	−	0.322871i	$-0.895352\pi$
$701$		−	452.665i		−	0.645742i	0.946443	−	0.322871i	$-0.104648\pi$
$702$	−139.234	−	29.3320i	−0.198338	−	0.0417835i
$703$	−1.81822	+	1.04975i	−0.00258637	+	0.00149324i
$704$	−858.947	−	756.690i	−1.22010	−	1.07484i
$705$	−455.100	−	262.752i	−0.645533	−	0.372698i
$706$	−583.781	+	190.849i	−0.826885	+	0.270325i
$707$	−235.393	+	77.3744i	−0.332946	+	0.109440i
$708$	−754.520	+	552.371i	−1.06571	+	0.780185i
$709$	609.174	+	351.707i	0.859202	+	0.496060i	0.863745	−	0.503929i	$-0.168113\pi$
$709$	609.174	+	351.707i	0.859202	+	0.496060i	−0.00454321	+	0.999990i	$0.501446\pi$
$710$	−436.532	+	486.584i	−0.614834	+	0.685330i
$711$	30.1054	+	52.1442i	0.0423424	+	0.0733392i
$712$	−291.684	−	645.684i	−0.409668	−	0.906859i
$713$			0.694220i			0.000973661i
$714$	−604.098	+	443.745i	−0.846075	+	0.621491i
$715$			251.425i			0.351644i
$716$	−945.814	+	102.868i	−1.32097	+	0.143671i
$717$	427.367	+	740.221i	0.596049	+	1.03239i
$718$	−616.713	+	687.425i	−0.858932	+	0.957416i
$719$	54.1160	+	31.2439i	0.0752656	+	0.0434546i	0.537161	−	0.843480i	$-0.319497\pi$
$719$	54.1160	+	31.2439i	0.0752656	+	0.0434546i	−0.461895	+	0.886935i	$0.652830\pi$
$720$	−53.8176	+	169.802i	−0.0747467	+	0.235836i
$721$	−469.642	+	525.189i	−0.651376	+	0.728417i
$722$	222.845	+	681.650i	0.308649	+	0.944113i
$723$	−331.354	−	191.307i	−0.458305	−	0.264602i
$724$	−1070.76	−	472.099i	−1.47894	−	0.652071i
$725$	−20.6271	+	11.9090i	−0.0284511	+	0.0164263i
$726$	−1324.64	−	279.059i	−1.82457	−	0.384379i
$727$		−	889.995i		−	1.22420i	−0.790779	−	0.612101i	$-0.790324\pi$
$727$		−	889.995i		−	1.22420i	0.790779	−	0.612101i	$-0.209676\pi$
$728$	−134.421	+	123.203i	−0.184644	+	0.169234i
$729$	417.569			0.572797
$730$	−94.5997	+	449.047i	−0.129589	+	0.615133i
$731$	102.573	+	177.661i	0.140318	+	0.243038i
$732$	1196.57	+	527.570i	1.63465	+	0.720724i
$733$	456.127	−	790.035i	0.622274	−	1.07781i	−0.366787	−	0.930305i	$-0.619542\pi$
$733$	456.127	−	790.035i	0.622274	−	1.07781i	0.989061	−	0.147505i	$-0.0471243\pi$
$734$	−1191.81	+	389.628i	−1.62372	+	0.530828i
$735$	659.577	+	288.276i	0.897383	+	0.392212i
$736$	1325.19	−	11.9801i	1.80053	−	0.0162773i
$737$	−124.753	+	216.079i	−0.169271	+	0.293187i
$738$	269.890	+	242.128i	0.365704	+	0.328086i
$739$	−1081.52	+	624.415i	−1.46349	+	0.844946i	−0.999171	−	0.0407224i	$-0.987034\pi$
$739$	−1081.52	+	624.415i	−1.46349	+	0.844946i	−0.464319	+	0.885668i	$0.653701\pi$
$740$	−23.1483	+	2.51765i	−0.0312815	+	0.00340223i
$741$	−17.2514			−0.0232813
$742$	70.5947	+	639.497i	0.0951411	+	0.861856i
$743$	−305.880			−0.411682			−0.205841	−	0.978585i	$-0.565993\pi$
$743$	−305.880			−0.411682			−0.205841	+	0.978585i	$0.565993\pi$
$744$	0.187862	+	0.415859i	0.000252502	+	0.000558950i
$745$	318.766	−	184.040i	0.427874	−	0.247033i
$746$	614.231	+	551.048i	0.823366	+	0.738671i
$747$	−132.145	+	228.882i	−0.176901	+	0.306401i
$748$	908.318	−	664.963i	1.21433	−	0.888988i
$749$	−499.041	+	558.065i	−0.666276	+	0.745080i
$750$	−286.323	−	875.820i	−0.381764	−	1.16776i
$751$	−258.895	+	448.420i	−0.344734	+	0.597097i	−0.985305	−	0.170802i	$-0.945364\pi$
$751$	−258.895	+	448.420i	−0.344734	+	0.597097i	0.640571	+	0.767899i	$0.278698\pi$
$752$	123.045	+	558.975i	0.163624	+	0.743317i
$753$	−206.288	−	357.302i	−0.273955	−	0.474504i
$754$	−5.02571	+	23.8561i	−0.00666540	+	0.0316394i
$755$	−569.012			−0.753659
$756$	356.115	−	497.472i	0.471052	−	0.658032i
$757$			939.898i			1.24161i	0.783965	+	0.620804i	$0.213194\pi$
$757$			939.898i			1.24161i	−0.783965	+	0.620804i	$0.786806\pi$
$758$	134.866	−	640.184i	0.177923	−	0.844569i
$759$	2182.85	−	1260.27i	2.87596	−	1.66044i
$760$	5.33097	−	53.5112i	0.00701443	−	0.0704095i
$761$	−976.757	−	563.931i	−1.28352	−	0.741039i	−0.306028	−	0.952022i	$-0.599000\pi$
$761$	−976.757	−	563.931i	−1.28352	−	0.741039i	−0.977490	+	0.210983i	$0.932334\pi$
$762$	−265.809	−	813.072i	−0.348831	−	1.06702i
$763$	115.044	+	349.995i	0.150779	+	0.458710i
$764$	−455.816	+	333.695i	−0.596618	+	0.436773i
$765$	−151.701	−	87.5846i	−0.198302	−	0.114490i
$766$	−370.487	−	332.377i	−0.483664	−	0.433912i
$767$	−111.849	−	193.728i	−0.145826	−	0.252579i
$768$	790.587	−	365.784i	1.02941	−	0.476281i
$769$		−	300.115i		−	0.390267i	−0.980777	−	0.195133i	$-0.937486\pi$
$769$		−	300.115i		−	0.390267i	0.980777	−	0.195133i	$-0.0625139\pi$
$770$	−989.867	−	434.533i	−1.28554	−	0.564329i
$771$			356.524i			0.462417i
$772$	28.5273	+	262.292i	0.0369525	+	0.339757i
$773$	375.120	+	649.727i	0.485278	+	0.840527i	0.999857	−	0.0169165i	$-0.00538495\pi$
$773$	375.120	+	649.727i	0.485278	+	0.840527i	−0.514579	+	0.857443i	$0.672052\pi$
$774$	50.0533	+	44.9046i	0.0646683	+	0.0580162i
$775$	−0.0923598	−	0.0533240i	−0.000119174	−	6.88051e-5i
$776$	−657.452	+	915.304i	−0.847231	+	1.17952i
$777$	−31.4385	−	6.57022i	−0.0404613	−	0.00845588i
$778$	−717.194	+	234.465i	−0.921843	+	0.301369i
$779$	−94.7977	−	54.7315i	−0.121691	−	0.0702586i
$780$	−175.069	−	77.1884i	−0.224447	−	0.0989594i
$781$	1172.73	−	677.076i	1.50158	−	0.866935i
$782$	−268.654	+	1275.25i	−0.343547	+	1.63075i
$783$		−	81.8005i		−	0.104471i
$784$	−252.735	−	742.146i	−0.322366	−	0.946615i
$785$	1058.16			1.34797
$786$	754.509	+	158.951i	0.959935	+	0.202227i
$787$	144.776	+	250.760i	0.183960	+	0.318627i	0.943225	−	0.332153i	$-0.107775\pi$
$787$	144.776	+	250.760i	0.183960	+	0.318627i	−0.759266	+	0.650781i	$0.774442\pi$
$788$	321.811	−	729.890i	0.408389	−	0.926256i
$789$	178.098	−	308.474i	0.225726	−	0.390969i
$790$	−62.6447	−	191.621i	−0.0792971	−	0.242558i
$791$	−65.0610	+	311.316i	−0.0822516	+	0.393573i
$792$	215.266	−	299.693i	0.271801	−	0.378401i
$793$	−156.417	+	270.922i	−0.197247	+	0.341642i
$794$	897.169	−	1000.04i	1.12994	−	1.25949i
$795$	−584.657	+	337.552i	−0.735417	+	0.424593i
$796$	269.181	−	29.2765i	0.338167	−	0.0367795i
$797$	1086.57			1.36332			0.681659	−	0.731670i	$-0.261259\pi$
$797$	1086.57			1.36332			0.681659	+	0.731670i	$0.261259\pi$
$798$	29.8153	−	67.9193i	0.0373625	−	0.0851119i
$799$	−562.854			−0.704448
$800$	−100.196	+	177.225i	−0.125245	+	0.221531i
$801$	197.787	−	114.192i	0.246925	−	0.142562i
$802$	628.253	−	700.288i	0.783358	−	0.873177i
$803$	475.313	−	823.267i	0.591922	−	1.02524i
$804$	−112.157	−	153.203i	−0.139499	−	0.190551i
$805$	1188.95	−	390.811i	1.47696	−	0.485480i
$806$	−0.103759	+	0.0339208i	−0.000128733	+	4.20854e-5i
$807$	−518.806	+	898.598i	−0.642882	+	1.11350i
$808$	−28.0725	+	281.786i	−0.0347432	+	0.348746i
$809$	−90.9745	−	157.572i	−0.112453	−	0.194774i	0.804306	−	0.594216i	$-0.202537\pi$
$809$	−90.9745	−	157.572i	−0.112453	−	0.194774i	−0.916759	+	0.399441i	$0.869204\pi$
$810$	824.262	+	173.645i	1.01761	+	0.214377i
$811$	1005.31			1.23960			0.619799	−	0.784760i	$-0.287214\pi$
$811$	1005.31			1.23960			0.619799	+	0.784760i	$0.287214\pi$
$812$	−85.2363	−	61.0164i	−0.104971	−	0.0751434i
$813$		−	349.280i		−	0.429619i
$814$	47.1990	+	9.94329i	0.0579840	+	0.0122153i
$815$	−898.355	+	518.665i	−1.10228	+	0.636399i
$816$	184.161	+	836.613i	0.225688	+	1.02526i
$817$	−17.5810	−	10.1504i	−0.0215190	−	0.0124240i
$818$	−126.744	+	41.4351i	−0.154944	+	0.0506541i
$819$	−43.8135	−	39.1795i	−0.0534963	−	0.0478382i
$820$	−717.128	−	979.573i	−0.874546	−	1.19460i
$821$	−851.009	−	491.330i	−1.03655	−	0.598453i	−0.117697	−	0.993050i	$-0.537551\pi$
$821$	−851.009	−	491.330i	−1.03655	−	0.598453i	−0.918855	+	0.394596i	$0.870885\pi$
$822$	−356.007	+	396.826i	−0.433099	+	0.482757i
$823$	−742.505	−	1286.06i	−0.902194	−	1.56265i	−0.824641	−	0.565657i	$-0.808623\pi$
$823$	−742.505	−	1286.06i	−0.902194	−	1.56265i	−0.0775532	−	0.996988i	$-0.524711\pi$
$824$	331.488	+	733.797i	0.402291	+	0.890530i
$825$			387.212i			0.469348i
$826$	956.017	−	105.536i	1.15741	−	0.127767i
$827$		−	708.113i		−	0.856243i	−0.903721	−	0.428121i	$-0.859176\pi$
$827$		−	708.113i		−	0.856243i	0.903721	−	0.428121i	$-0.140824\pi$
$828$	46.1890	+	424.681i	0.0557838	+	0.512900i
$829$	75.0164	+	129.932i	0.0904902	+	0.156734i	0.907718	−	0.419582i	$-0.137823\pi$
$829$	75.0164	+	129.932i	0.0904902	+	0.156734i	−0.817227	+	0.576316i	$0.804490\pi$
$830$	590.929	−	658.685i	0.711963	−	0.793596i
$831$	−49.0796	−	28.3361i	−0.0590609	−	0.0340988i
$832$	66.5417	+	197.479i	0.0799780	+	0.237354i
$833$	766.191	−	85.8294i	0.919797	−	0.103037i
$834$	−315.174	−	964.072i	−0.377907	−	1.15596i
$835$	−273.665	−	158.001i	−0.327743	−	0.189222i
$836$	−44.9414	+	101.930i	−0.0537576	+	0.121926i
$837$	0.317199	−	0.183135i	0.000378972	−	0.000218799i
$838$	−855.972	−	180.325i	−1.02145	−	0.215186i
$839$			1106.41i			1.31873i	0.751824	+	0.659364i	$0.229174\pi$
$839$			1106.41i			1.31873i	−0.751824	+	0.659364i	$0.770826\pi$
$840$	606.460	−	555.847i	0.721977	−	0.661723i
$841$	826.984			0.983335
$842$	290.167	−	1377.37i	0.344616	−	1.63583i
$843$	−129.014	−	223.459i	−0.153042	−	0.265076i
$844$	100.287	−	227.458i	0.118824	−	0.269501i
$845$	−341.915	+	592.214i	−0.404633	+	0.700845i
$846$	−175.363	+	57.3297i	−0.207285	+	0.0677656i
$847$	1037.93	+	928.156i	1.22542	+	1.09582i
$848$	700.931	+	222.155i	0.826569	+	0.261975i
$849$	148.584	−	257.354i	0.175010	−	0.303126i
$850$	−149.025	−	133.696i	−0.175323	−	0.157289i
$851$	−48.3606	+	27.9210i	−0.0568279	+	0.0328096i
$852$	111.420	+	1024.44i	0.130775	+	1.20240i
$853$	−1243.82			−1.45817			−0.729086	−	0.684423i	$-0.760054\pi$
$853$	−1243.82			−1.45817			−0.729086	+	0.684423i	$0.760054\pi$
$854$	−796.294	−	1084.05i	−0.932429	−	1.26937i
$855$	17.3344			0.0202742
$856$	352.239	+	779.731i	0.411494	+	0.910901i
$857$	245.650	−	141.826i	0.286639	−	0.165491i	−0.349786	−	0.936830i	$-0.613746\pi$
$857$	245.650	−	141.826i	0.286639	−	0.165491i	0.636425	+	0.771339i	$0.280412\pi$
$858$	295.019	+	264.672i	0.343846	+	0.308476i
$859$	−455.900	+	789.641i	−0.530733	+	0.919256i	0.468624	+	0.883398i	$0.344750\pi$
$859$	−455.900	+	789.641i	−0.530733	+	0.919256i	−0.999357	+	0.0358586i	$0.988583\pi$
$860$	−132.997	−	181.670i	−0.154648	−	0.211244i
$861$	−522.902	−	1590.80i	−0.607319	−	1.84762i
$862$	341.647	+	1045.05i	0.396342	+	1.21235i
$863$	436.908	−	756.747i	0.506266	−	0.876879i	−0.493707	−	0.869628i	$-0.664359\pi$
$863$	436.908	−	756.747i	0.506266	−	0.876879i	0.999974	−	0.00725099i	$-0.00230808\pi$
$864$	−355.058	−	602.338i	−0.410947	−	0.697150i
$865$	79.9735	+	138.518i	0.0924550	+	0.160137i
$866$	−146.367	+	694.775i	−0.169014	+	0.802280i
$867$	140.978			0.162604
$868$	0.0457772	−	0.467126i	5.27387e−5	−	0.000538164i
$869$			417.620i			0.480575i
$870$	22.6743	−	107.631i	0.0260624	−	0.123713i
$871$	39.3358	−	22.7105i	0.0451617	−	0.0260741i
$872$	418.975	+	41.7397i	0.480476	+	0.0478667i
$873$	−314.599	−	181.634i	−0.360365	−	0.208057i
$874$	−40.0745	−	122.582i	−0.0458518	−	0.140254i
$875$	−193.882	+	927.724i	−0.221579	+	1.06026i
$876$	427.323	+	583.709i	0.487811	+	0.666334i
$877$	−549.476	−	317.240i	−0.626540	−	0.361733i	0.152871	−	0.988246i	$-0.451148\pi$
$877$	−549.476	−	317.240i	−0.626540	−	0.361733i	−0.779411	+	0.626513i	$0.784482\pi$
$878$	820.024	+	735.672i	0.933968	+	0.837896i
$879$	−46.7975	−	81.0557i	−0.0532395	−	0.0922136i
$880$	−912.137	+	833.315i	−1.03652	+	0.946949i
$881$		−	670.044i		−	0.760549i	−0.924874	−	0.380274i	$-0.875830\pi$
$881$		−	670.044i		−	0.760549i	0.924874	−	0.380274i	$-0.124170\pi$
$882$	229.973	−	104.782i	0.260740	−	0.118800i
$883$		−	875.514i		−	0.991522i	−0.868459	−	0.495761i	$-0.834889\pi$
$883$		−	875.514i		−	0.991522i	0.868459	−	0.495761i	$-0.165111\pi$
$884$	−203.727	+	22.1577i	−0.230460	+	0.0250652i
$885$	504.623	+	874.033i	0.570196	+	0.987608i
$886$	−402.295	−	360.913i	−0.454057	−	0.407351i
$887$	854.152	+	493.145i	0.962967	+	0.555969i	0.897085	−	0.441858i	$-0.145681\pi$
$887$	854.152	+	493.145i	0.962967	+	0.555969i	0.0658820	+	0.997827i	$0.479014\pi$
$888$	−21.4138	+	29.8123i	−0.0241146	+	0.0335724i
$889$	−179.991	+	861.257i	−0.202465	+	0.968793i
$890$	−726.833	+	237.616i	−0.816667	+	0.266985i
$891$	−1511.17	−	872.476i	−1.69604	−	0.979210i
$892$	186.426	−	422.827i	0.208997	−	0.474021i
$893$	48.2368	−	27.8495i	0.0540166	−	0.0311865i
$894$	119.611	−	567.773i	0.133793	−	0.635092i
$895$			1026.83i			1.14729i
$896$	−892.482	−	79.3225i	−0.996074	−	0.0885296i
$897$	−458.850			−0.511538
$898$	891.233	+	187.754i	0.992464	+	0.209080i
$899$	−0.0313782	−	0.0543486i	−3.49034e−5	−	6.04545e-5i
$900$	−60.0479	−	26.4753i	−0.0667199	−	0.0294170i
$901$	−361.543	+	626.210i	−0.401268	+	0.695017i
$902$	781.457	+	2390.36i	0.866360	+	2.65007i
$903$	−96.9764	−	295.028i	−0.107394	−	0.326719i
$904$	295.213	+	212.048i	0.326564	+	0.234567i
$905$	−631.499	+	1093.79i	−0.697789	+	1.20861i
$906$	−598.993	+	667.673i	−0.661140	+	0.736945i
$907$	750.592	−	433.355i	0.827555	−	0.477789i	−0.0254599	−	0.999676i	$-0.508105\pi$
$907$	750.592	−	433.355i	0.827555	−	0.477789i	0.853015	+	0.521887i	$0.174772\pi$
$908$	24.4388	+	224.700i	0.0269150	+	0.247467i
$909$	−91.2820			−0.100420
$910$	116.505	+	158.606i	0.128028	+	0.174292i
$911$	−128.713			−0.141288			−0.0706438	−	0.997502i	$-0.522505\pi$
$911$	−128.713			−0.141288			−0.0706438	+	0.997502i	$0.522505\pi$
$912$	−57.1776	−	62.5859i	−0.0626947	−	0.0686249i
$913$	−1587.51	+	916.552i	−1.73879	+	1.00389i
$914$	225.223	−	251.047i	0.246415	−	0.274669i
$915$	705.699	−	1222.31i	0.771256	−	1.33585i
$916$	381.945	−	279.615i	0.416971	−	0.305257i
$917$	−591.203	−	528.673i	−0.644714	−	0.576525i
$918$	653.550	−	213.659i	0.711929	−	0.232743i
$919$	−430.087	+	744.933i	−0.467995	+	0.810591i	−0.999331	−	0.0365701i	$-0.988357\pi$
$919$	−430.087	+	744.933i	−0.467995	+	0.810591i	0.531336	+	0.847161i	$0.321690\pi$
$920$	141.792	−	1423.28i	0.154121	−	1.54704i
$921$	−421.935	−	730.813i	−0.458127	−	0.793500i
$922$	518.737	+	109.281i	0.562622	+	0.118526i
$923$	−246.515			−0.267081
$924$	−1551.90	+	704.071i	−1.67954	+	0.761981i
$925$		−	8.57859i		−	0.00927415i
$926$	190.760	+	40.1869i	0.206004	+	0.0433984i
$927$	−224.778	+	129.776i	−0.242479	+	0.139995i
$928$	−103.204	+	60.8353i	−0.111211	+	0.0655553i
$929$	202.025	+	116.639i	0.217465	+	0.125554i	0.604776	−	0.796396i	$-0.293263\pi$
$929$	202.025	+	116.639i	0.217465	+	0.125554i	−0.387311	+	0.921949i	$0.626596\pi$
$930$	0.468124	−	0.153039i	0.000503360	−	0.000164558i
$931$	−61.4160	+	45.2661i	−0.0659678	+	0.0486209i
$932$	79.6575	−	58.3158i	0.0854694	−	0.0625706i
$933$	−1287.89	−	743.563i	−1.38037	−	0.796960i
$934$	−99.0987	+	110.461i	−0.106101	+	0.118267i
$935$	−607.483	−	1052.19i	−0.649714	−	1.12534i
$936$	−61.2164	+	27.6541i	−0.0654022	+	0.0295450i
$937$		−	1426.29i		−	1.52219i	−0.648641	−	0.761095i	$-0.724662\pi$
$937$		−	1426.29i		−	1.52219i	0.648641	−	0.761095i	$-0.275338\pi$
$938$	21.4287	+	194.116i	0.0228451	+	0.206947i
$939$			281.851i			0.300161i
$940$	614.118	−	66.7925i	0.653317	−	0.0710558i
$941$	635.425	+	1100.59i	0.675265	+	1.16959i	0.976391	+	0.216010i	$0.0693043\pi$
$941$	635.425	+	1100.59i	0.675265	+	1.16959i	−0.301126	+	0.953584i	$0.597362\pi$
$942$	1113.91	−	1241.63i	1.18249	−	1.31808i
$943$	−2521.41	−	1455.73i	−2.67381	−	1.54373i
$944$	332.111	−	1047.86i	0.351812	−	1.11002i
$945$	−492.212	−	440.152i	−0.520859	−	0.465770i
$946$	144.928	+	443.312i	0.153200	+	0.468618i
$947$	1413.50	+	816.086i	1.49261	+	0.861759i	0.999964	−	0.00847064i	$-0.00269632\pi$
$947$	1413.50	+	816.086i	1.49261	+	0.861759i	0.492646	+	0.870230i	$0.336030\pi$
$948$	−290.791	−	128.211i	−0.306742	−	0.135243i
$949$	−149.871	+	86.5280i	−0.157925	+	0.0911781i
$950$	19.3866	+	4.08413i	0.0204070	+	0.00429909i
$951$			832.098i			0.874972i
$952$	264.862	−	840.373i	0.278216	−	0.882745i
$953$	95.9158			0.100646			0.0503231	−	0.998733i	$-0.483975\pi$
$953$	95.9158			0.100646			0.0503231	+	0.998733i	$0.483975\pi$
$954$	−48.8596	+	231.927i	−0.0512155	+	0.243110i
$955$	304.850	+	528.015i	0.319215	+	0.552896i
$956$	−919.361	−	405.349i	−0.961674	−	0.424005i
$957$	−113.926	+	197.326i	−0.119045	+	0.206192i
$958$	−1043.14	+	341.024i	−1.08888	+	0.355975i
$959$	520.930	−	171.231i	0.543201	−	0.178552i
$960$	−300.213	−	890.957i	−0.312722	−	0.928080i
$961$	−480.500	+	832.250i	−0.500000	+	0.866025i
$962$	−6.53609	−	5.86376i	−0.00679427	−	0.00609538i
$963$	−238.849	+	137.899i	−0.248025	+	0.143198i
$964$	447.134	−	48.6310i	0.463832	−	0.0504471i
$965$	284.759			0.295087
$966$	793.020	−	1806.50i	0.820932	−	1.87008i
$967$	1419.97			1.46843			0.734216	−	0.678916i	$-0.237550\pi$
$967$	1419.97			1.46843			0.734216	+	0.678916i	$0.237550\pi$
$968$	1450.21	−	655.122i	1.49815	−	0.676779i
$969$	72.1956	−	41.6822i	0.0745053	−	0.0430157i
$970$	905.365	+	812.235i	0.933366	+	0.837355i
$971$	329.817	−	571.261i	0.339668	−	0.588322i	−0.644702	−	0.764434i	$-0.723019\pi$
$971$	329.817	−	571.261i	0.339668	−	0.588322i	0.984370	+	0.176112i	$0.0563520\pi$
$972$	436.750	−	319.737i	0.449332	−	0.328948i
$973$	−213.418	+	1021.21i	−0.219341	+	1.04954i
$974$	−352.919	−	1079.53i	−0.362340	−	1.10834i
$975$	35.2448	−	61.0459i	0.0361486	−	0.0626111i
$976$	−1501.29	+	330.475i	−1.53821	+	0.338601i
$977$	957.151	+	1657.83i	0.979683	+	1.69686i	0.663523	+	0.748156i	$0.269060\pi$
$977$	957.151	+	1657.83i	0.979683	+	1.69686i	0.316160	+	0.948706i	$0.397606\pi$
$978$	−337.092	+	1600.11i	−0.344675	+	1.63611i
$979$	1584.07			1.61804
$980$	−825.789	+	184.569i	−0.842642	+	0.188335i
$981$			135.723i			0.138352i
$982$	−32.4883	+	154.216i	−0.0330838	+	0.157043i
$983$	193.655	−	111.806i	0.197004	−	0.113740i	−0.398253	−	0.917275i	$-0.630384\pi$
$983$	193.655	−	111.806i	0.197004	−	0.113740i	0.595257	+	0.803535i	$0.297050\pi$
$984$	−1904.33	−	189.716i	−1.93530	−	0.192801i
$985$	−745.591	−	430.467i	−0.756945	−	0.437022i
$986$	−36.6080	−	111.979i	−0.0371278	−	0.113569i
$987$	834.053	+	174.306i	0.845038	+	0.176602i
$988$	16.3631	−	11.9792i	0.0165619	−	0.0121247i
$989$	−467.616	−	269.978i	−0.472816	−	0.272981i
$990$	−296.439	−	265.946i	−0.299433	−	0.268632i
$991$	736.371	+	1275.43i	0.743058	+	1.28701i	0.951096	+	0.308894i	$0.0999589\pi$
$991$	736.371	+	1275.43i	0.743058	+	1.28701i	−0.208038	+	0.978121i	$0.566708\pi$
$992$	−0.466955	−	0.263997i	−0.000470721	−	0.000266126i
$993$			260.472i			0.262308i
$994$	426.047	−	970.537i	0.428619	−	0.976395i
$995$		−	292.237i		−	0.293706i
$996$	−150.828	−	1386.78i	−0.151434	−	1.39235i
$997$	53.4480	+	92.5746i	0.0536088	+	0.0928532i	0.891584	−	0.452854i	$-0.149594\pi$
$997$	53.4480	+	92.5746i	0.0536088	+	0.0928532i	−0.837976	+	0.545708i	$0.816261\pi$
$998$	500.115	+	448.671i	0.501117	+	0.449570i
$999$	25.5150	+	14.7311i	0.0255405	+	0.0147458i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.5.14	yes	28
4.3	odd	2		224.3.n.a.145.11		28
7.2	even	3		392.3.h.a.293.10		28
7.3	odd	6	inner	56.3.j.a.45.5	yes	28
7.4	even	3		392.3.j.e.325.5		28
7.5	odd	6		392.3.h.a.293.9		28
7.6	odd	2		392.3.j.e.117.14		28
8.3	odd	2		224.3.n.a.145.4		28
8.5	even	2	inner	56.3.j.a.5.5	✓	28
28.3	even	6		224.3.n.a.17.4		28
28.19	even	6		1568.3.h.a.881.22		28
28.23	odd	6		1568.3.h.a.881.8		28
56.3	even	6		224.3.n.a.17.11		28
56.5	odd	6		392.3.h.a.293.12		28
56.13	odd	2		392.3.j.e.117.5		28
56.19	even	6		1568.3.h.a.881.7		28
56.37	even	6		392.3.h.a.293.11		28
56.45	odd	6	inner	56.3.j.a.45.14	yes	28
56.51	odd	6		1568.3.h.a.881.21		28
56.53	even	6		392.3.j.e.325.14		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.5	✓	28	8.5	even	2	inner
56.3.j.a.5.14	yes	28	1.1	even	1	trivial
56.3.j.a.45.5	yes	28	7.3	odd	6	inner
56.3.j.a.45.14	yes	28	56.45	odd	6	inner
224.3.n.a.17.4		28	28.3	even	6
224.3.n.a.17.11		28	56.3	even	6
224.3.n.a.145.4		28	8.3	odd	2
224.3.n.a.145.11		28	4.3	odd	2
392.3.h.a.293.9		28	7.5	odd	6
392.3.h.a.293.10		28	7.2	even	3
392.3.h.a.293.11		28	56.37	even	6
392.3.h.a.293.12		28	56.5	odd	6
392.3.j.e.117.5		28	56.13	odd	2
392.3.j.e.117.14		28	7.6	odd	2
392.3.j.e.325.5		28	7.4	even	3
392.3.j.e.325.14		28	56.53	even	6
1568.3.h.a.881.7		28	56.19	even	6
1568.3.h.a.881.8		28	28.23	odd	6
1568.3.h.a.881.21		28	56.51	odd	6
1568.3.h.a.881.22		28	28.19	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)

\(f(q)\)	\(=\)	\(q+(1.95704 + 0.412286i) q^{2} +(-1.70138 - 2.94687i) q^{3} +(3.66004 + 1.61372i) q^{4} +(2.15858 - 3.73877i) q^{5} +(-2.11472 - 6.46862i) q^{6} +(-1.43197 + 6.85197i) q^{7} +(6.49755 + 4.66711i) q^{8} +(-1.28938 + 2.23327i) q^{9} +O(q^{10})\)	\(q+(1.95704 + 0.412286i) q^{2} +(-1.70138 - 2.94687i) q^{3} +(3.66004 + 1.61372i) q^{4} +(2.15858 - 3.73877i) q^{5} +(-2.11472 - 6.46862i) q^{6} +(-1.43197 + 6.85197i) q^{7} +(6.49755 + 4.66711i) q^{8} +(-1.28938 + 2.23327i) q^{9} +(5.76588 - 6.42699i) q^{10} +(-15.4899 + 8.94308i) q^{11} +(-1.47168 - 13.5312i) q^{12} +3.25607 q^{13} +(-5.62740 + 12.8192i) q^{14} -14.6903 q^{15} +(10.7918 + 11.8126i) q^{16} +(-13.6263 + 7.86717i) q^{17} +(-3.44412 + 3.83902i) q^{18} +(0.778522 - 1.34844i) q^{19} +(13.9338 - 10.2007i) q^{20} +(22.6282 - 7.43796i) q^{21} +(-34.0014 + 11.1157i) q^{22} +(20.7069 - 35.8655i) q^{23} +(2.69860 - 27.0880i) q^{24} +(3.18105 + 5.50975i) q^{25} +(6.37227 + 1.34243i) q^{26} -21.8499 q^{27} +(-16.2982 + 22.7677i) q^{28} +3.74374i q^{29} +(-28.7495 - 6.05658i) q^{30} +(-0.0145172 + 0.00838150i) q^{31} +(16.2499 + 27.5670i) q^{32} +(52.7082 + 30.4311i) q^{33} +(-29.9109 + 9.77845i) q^{34} +(22.5269 + 20.1443i) q^{35} +(-8.32306 + 6.09316i) q^{36} +(-1.16774 - 0.674194i) q^{37} +(2.07954 - 2.31798i) q^{38} +(-5.53981 - 9.59523i) q^{39} +(31.4747 - 14.2185i) q^{40} -70.3018i q^{41} +(47.3510 - 5.22712i) q^{42} -13.0380i q^{43} +(-71.1252 + 7.73569i) q^{44} +(5.56646 + 9.64139i) q^{45} +(55.3112 - 61.6531i) q^{46} +(30.9797 + 17.8862i) q^{47} +(16.4493 - 51.8998i) q^{48} +(-44.8989 - 19.6236i) q^{49} +(3.95387 + 12.0943i) q^{50} +(46.3671 + 26.7701i) q^{51} +(11.9173 + 5.25439i) q^{52} +(39.7989 - 22.9779i) q^{53} +(-42.7613 - 9.00841i) q^{54} +77.2174i q^{55} +(-41.2832 + 37.8378i) q^{56} -5.29824 q^{57} +(-1.54349 + 7.32667i) q^{58} +(-34.3509 - 59.4974i) q^{59} +(-53.7669 - 23.7060i) q^{60} +(-48.0386 + 83.2052i) q^{61} +(-0.0318663 + 0.0104177i) q^{62} +(-13.4559 - 12.0328i) q^{63} +(20.4362 + 60.6495i) q^{64} +(7.02849 - 12.1737i) q^{65} +(90.6060 + 81.2859i) q^{66} +(12.0808 - 6.97484i) q^{67} +(-62.5684 + 6.80504i) q^{68} -140.921 q^{69} +(35.7810 + 48.7109i) q^{70} -75.7095 q^{71} +(-18.8007 + 8.49310i) q^{72} +(-46.0282 + 26.5744i) q^{73} +(-2.00736 - 1.80087i) q^{74} +(10.8244 - 18.7483i) q^{75} +(5.02543 - 3.67902i) q^{76} +(-39.0967 - 118.942i) q^{77} +(-6.88567 - 21.0623i) q^{78} +(11.6744 - 20.2206i) q^{79} +(67.4595 - 14.8497i) q^{80} +(48.7794 + 84.4884i) q^{81} +(28.9844 - 137.584i) q^{82} +102.487 q^{83} +(94.8230 + 9.29242i) q^{84} +67.9277i q^{85} +(5.37540 - 25.5160i) q^{86} +(11.0323 - 6.36952i) q^{87} +(-142.384 - 14.1848i) q^{88} +(-76.6985 - 44.2819i) q^{89} +(6.91880 + 21.1636i) q^{90} +(-4.66259 + 22.3105i) q^{91} +(133.665 - 97.8538i) q^{92} +(0.0493984 + 0.0285202i) q^{93} +(53.2545 + 47.7765i) q^{94} +(-3.36100 - 5.82143i) q^{95} +(53.5894 - 94.7883i) q^{96} +140.869i q^{97} +(-79.7786 - 56.9155i) q^{98} -46.1241i 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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