LMFDB - Embedded newform 56.3.j.a.5.5

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			5.5
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33557 - 1.48871i) q^{2} +(1.70138 + 2.94687i) q^{3} +(-0.432496 + 3.97655i) q^{4} +(-2.15858 + 3.73877i) q^{5} +(2.11472 - 6.46862i) q^{6} +(-1.43197 + 6.85197i) q^{7} +(6.49755 - 4.66711i) q^{8} +(-1.28938 + 2.23327i) q^{9} +O(q^{10})$	\(q+(-1.33557 - 1.48871i) q^{2} +(1.70138 + 2.94687i) q^{3} +(-0.432496 + 3.97655i) 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} +(8.44888 - 1.77990i) q^{10} +(15.4899 - 8.94308i) q^{11} +(-12.4542 + 5.49111i) q^{12} -3.25607 q^{13} +(12.1131 - 7.01951i) q^{14} -14.6903 q^{15} +(-15.6259 - 3.43968i) q^{16} +(-13.6263 + 7.86717i) q^{17} +(5.04674 - 1.06319i) 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} +(24.8082 + 11.2069i) q^{24} +(3.18105 + 5.50975i) q^{25} +(4.34871 + 4.84733i) q^{26} +21.8499 q^{27} +(-26.6279 - 8.65775i) q^{28} -3.74374i q^{29} +(19.6199 + 21.8695i) q^{30} +(-0.0145172 + 0.00838150i) q^{31} +(15.7488 + 27.8563i) 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} +(3.04720 - 0.641947i) q^{38} +(-5.53981 - 9.59523i) q^{39} +(3.42377 + 34.3672i) q^{40} -70.3018i q^{41} +(41.2945 + 23.7528i) q^{42} +13.0380i q^{43} +(28.8633 + 65.4641i) q^{44} +(-5.56646 - 9.64139i) q^{45} +(-81.0487 + 17.0743i) 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} +(1.40824 - 12.9479i) q^{52} +(-39.7989 + 22.9779i) q^{53} +(-29.1821 - 32.5281i) q^{54} +77.2174i q^{55} +(22.6746 + 51.2041i) q^{56} -5.29824 q^{57} +(-5.57333 + 5.00004i) q^{58} +(34.3509 + 59.4974i) q^{59} +(6.35348 - 58.4165i) 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} +(-25.0926 - 119.110i) q^{66} +(-12.0808 + 6.97484i) q^{67} +(-25.3909 - 57.5883i) q^{68} +140.921 q^{69} +(0.0973128 + 60.4402i) q^{70} -75.7095 q^{71} +(2.04511 + 20.5284i) q^{72} +(-46.0282 + 26.5744i) q^{73} +(-0.555921 - 2.63886i) 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} +(46.5900 - 50.9968i) q^{80} +(48.7794 + 84.4884i) q^{81} +(-104.659 + 93.8931i) q^{82} -102.487 q^{83} +(-19.7908 - 93.1991i) q^{84} -67.9277i q^{85} +(19.4098 - 17.4132i) q^{86} +(11.0323 - 6.36952i) q^{87} +(58.9078 - 130.401i) 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} +(-14.7484 - 70.0080i) q^{94} +(-3.36100 - 5.82143i) q^{95} +(-55.2944 + 93.8040i) q^{96} +140.869i q^{97} +(30.7519 + 93.0501i) 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 $

$2$	−1.33557	−	1.48871i	−0.667786	−	0.744353i
$2$	−1.33557	−	1.48871i	−0.667786	−	0.744353i
$3$	1.70138	+	2.94687i	0.567126	+	0.982291i	0.996848	+	0.0793303i	$0.0252782\pi$
$3$	1.70138	+	2.94687i	0.567126	+	0.982291i	−0.429722	+	0.902961i	$0.641388\pi$
$4$	−0.432496	+	3.97655i	−0.108124	+	0.994137i
$5$	−2.15858	+	3.73877i	−0.431716	+	0.747754i	−0.997021	−	0.0771275i	$-0.975425\pi$
$5$	−2.15858	+	3.73877i	−0.431716	+	0.747754i	0.565305	+	0.824882i	$0.308758\pi$
$6$	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
$10$	8.44888	−	1.77990i	0.844888	−	0.177990i
$11$	15.4899	−	8.94308i	1.40817	−	0.813007i	0.412958	−	0.910750i	$-0.364496\pi$
$11$	15.4899	−	8.94308i	1.40817	−	0.813007i	0.995212	+	0.0977432i	$0.0311624\pi$
$12$	−12.4542	+	5.49111i	−1.03785	+	0.457592i
$13$	−3.25607			−0.250467			−0.125233	−	0.992127i	$-0.539968\pi$
$13$	−3.25607			−0.250467			−0.125233	+	0.992127i	$0.539968\pi$
$14$	12.1131	−	7.01951i	0.865219	−	0.501394i
$15$	−14.6903			−0.979350
$16$	−15.6259	−	3.43968i	−0.976618	−	0.214980i
$17$	−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	$0.486479\pi$
$18$	5.04674	−	1.06319i	0.280375	−	0.0590659i
$19$	−0.778522	+	1.34844i	−0.0409748	+	0.0709705i	−0.885786	−	0.464095i	$-0.846380\pi$
$19$	−0.778522	+	1.34844i	−0.0409748	+	0.0709705i	0.844811	+	0.535065i	$0.179713\pi$
$20$	−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	$-0.189987\pi$
$24$	24.8082	+	11.2069i	1.03367	+	0.466956i
$25$	3.18105	+	5.50975i	0.127242	+	0.220390i
$26$	4.34871	+	4.84733i	0.167258	+	0.186436i
$27$	21.8499			0.809257
$28$	−26.6279	−	8.65775i	−0.950995	−	0.309205i
$29$		−	3.74374i		−	0.129095i	−0.997915	−	0.0645473i	$-0.979440\pi$
$29$		−	3.74374i		−	0.129095i	0.997915	−	0.0645473i	$-0.0205603\pi$
$30$	19.6199	+	21.8695i	0.653996	+	0.728983i
$31$	−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	$0.333419\pi$
$32$	15.7488	+	27.8563i	0.492151	+	0.870510i
$33$	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	0.515697	−	0.856771i	$-0.327533\pi$
$37$	1.16774	+	0.674194i	0.0315605	+	0.0182215i	−0.484137	+	0.874992i	$0.660866\pi$
$38$	3.04720	−	0.641947i	0.0801895	−	0.0168933i
$39$	−5.53981	−	9.59523i	−0.142046	−	0.246031i
$40$	3.42377	+	34.3672i	0.0855944	+	0.859179i
$41$		−	70.3018i		−	1.71468i	−0.514753	−	0.857339i	$-0.672116\pi$
$41$		−	70.3018i		−	1.71468i	0.514753	−	0.857339i	$-0.327884\pi$
$42$	41.2945	+	23.7528i	0.983203	+	0.565544i
$43$			13.0380i			0.303210i	0.988441	+	0.151605i	$0.0484442\pi$
$43$			13.0380i			0.303210i	−0.988441	+	0.151605i	$0.951556\pi$
$44$	28.8633	+	65.4641i	0.655984	+	1.48782i
$45$	−5.56646	−	9.64139i	−0.123699	−	0.214253i
$46$	−81.0487	+	17.0743i	−1.76193	+	0.371181i
$47$	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
$52$	1.40824	−	12.9479i	0.0270815	−	0.248998i
$53$	−39.7989	+	22.9779i	−0.750923	+	0.433546i	−0.826027	−	0.563630i	$-0.809404\pi$
$53$	−39.7989	+	22.9779i	−0.750923	+	0.433546i	0.0751042	+	0.997176i	$0.476071\pi$
$54$	−29.1821	−	32.5281i	−0.540410	−	0.602373i
$55$			77.2174i			1.40395i
$56$	22.6746	+	51.2041i	0.404903	+	0.914360i
$57$	−5.29824			−0.0929516
$58$	−5.57333	+	5.00004i	−0.0960920	+	0.0862075i
$59$	34.3509	+	59.4974i	0.582218	+	1.00843i	0.995216	+	0.0976993i	$0.0311484\pi$
$59$	34.3509	+	59.4974i	0.582218	+	1.00843i	−0.412998	+	0.910732i	$0.635518\pi$
$60$	6.35348	−	58.4165i	0.105891	−	0.973609i
$61$	48.0386	−	83.2052i	0.787517	−	1.36402i	−0.139966	−	0.990156i	$-0.544699\pi$
$61$	48.0386	−	83.2052i	0.787517	−	1.36402i	0.927484	−	0.373864i	$-0.121967\pi$
$62$	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
$66$	−25.0926	−	119.110i	−0.380191	−	1.80470i
$67$	−12.0808	+	6.97484i	−0.180310	+	0.104102i	−0.587438	−	0.809269i	$-0.699864\pi$
$67$	−12.0808	+	6.97484i	−0.180310	+	0.104102i	0.407128	+	0.913371i	$0.366530\pi$
$68$	−25.3909	−	57.5883i	−0.373395	−	0.846887i
$69$	140.921			2.04234
$70$	0.0973128	+	60.4402i	0.00139018	+	0.863431i
$71$	−75.7095			−1.06633			−0.533166	−	0.846011i	$-0.678998\pi$
$71$	−75.7095			−1.06633			−0.533166	+	0.846011i	$0.678998\pi$
$72$	2.04511	+	20.5284i	0.0284044	+	0.285117i
$73$	−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	$0.451934\pi$
$74$	−0.555921	−	2.63886i	−0.00751245	−	0.0356602i
$75$	−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	$0.119455\pi$
$80$	46.5900	−	50.9968i	0.582374	−	0.637460i
$81$	48.7794	+	84.4884i	0.602215	+	1.04307i
$82$	−104.659	+	93.8931i	−1.27633	+	1.14504i
$83$	−102.487			−1.23479			−0.617393	−	0.786655i	$-0.711811\pi$
$83$	−102.487			−1.23479			−0.617393	+	0.786655i	$0.711811\pi$
$84$	−19.7908	−	93.1991i	−0.235605	−	1.10951i
$85$		−	67.9277i		−	0.799150i
$86$	19.4098	−	17.4132i	0.225696	−	0.202480i
$87$	11.0323	−	6.36952i	0.126808	−	0.0732129i
$88$	58.9078	−	130.401i	0.669407	−	1.48183i
$89$	−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
$94$	−14.7484	−	70.0080i	−0.156898	−	0.744766i
$95$	−3.36100	−	5.82143i	−0.0353790	−	0.0612782i
$96$	−55.2944	+	93.8040i	−0.575983	+	0.977125i
$97$			140.869i			1.45226i	0.687558	+	0.726130i	$0.258683\pi$
$97$			140.869i			1.45226i	−0.687558	+	0.726130i	$0.741317\pi$
$98$	30.7519	+	93.0501i	0.313795	+	0.949491i
$99$			46.1241i			0.465900i
$100$	−23.2856	+	10.2667i	−0.232856	+	0.102667i
$101$	−17.6988	−	30.6553i	−0.175236	−	0.303518i	0.765007	−	0.644022i	$-0.222735\pi$
$101$	−17.6988	−	30.6553i	−0.175236	−	0.303518i	−0.940243	+	0.340504i	$0.889402\pi$
$102$	22.0738	+	104.780i	0.216410	+	1.02726i
$103$	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	0.000269099	−	1.00000i	$-0.499914\pi$
$107$	−92.6215	−	53.4751i	−0.865622	−	0.499767i	−0.865891	+	0.500233i	$0.833248\pi$
$108$	−9.45000	+	86.8873i	−0.0875000	+	0.804512i
$109$	−45.5799	+	26.3156i	−0.418165	+	0.241427i	−0.694292	−	0.719694i	$-0.744282\pi$
$109$	−45.5799	+	26.3156i	−0.418165	+	0.241427i	0.276127	+	0.961121i	$0.410949\pi$
$110$	114.954	−	103.129i	1.04504	−	0.937540i
$111$			4.58824i			0.0413355i
$112$	45.9444	−	102.143i	0.410218	−	0.911988i
$113$	45.4346			0.402076			0.201038	−	0.979583i	$-0.435568\pi$
$113$	45.4346			0.402076			0.201038	+	0.979583i	$0.435568\pi$
$114$	7.07618	+	7.88753i	0.0620718	+	0.0691888i
$115$	89.3952	+	154.837i	0.777350	+	1.34641i
$116$	14.8872	+	1.61915i	0.128338	+	0.0139582i
$117$	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
$122$	−188.027	+	39.6112i	−1.54121	+	0.324682i
$123$	207.171	−	119.610i	1.68431	−	0.972439i
$124$	−0.0270508	−	0.0613532i	−0.000218152	−	0.000494784i
$125$	−135.395			−1.08316
$126$	0.0581276	+	36.1026i	0.000461330	+	0.286528i
$127$	125.695			0.989723			0.494861	−	0.868972i	$-0.335219\pi$
$127$	125.695			0.989723			0.494861	+	0.868972i	$0.335219\pi$
$128$	−117.583	+	50.5782i	−0.918620	+	0.395143i
$129$	−38.4215	+	22.1827i	−0.297841	+	0.171959i
$130$	−27.5101	+	5.79549i	−0.211616	+	0.0445807i
$131$	56.6504	−	98.1214i	0.432446	−	0.749018i	−0.564638	−	0.825339i	$-0.690984\pi$
$131$	56.6504	−	98.1214i	0.432446	−	0.749018i	0.997083	+	0.0763210i	$0.0243174\pi$
$132$	−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
$136$	−51.8208	+	114.713i	−0.381036	+	0.843477i
$137$	−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	$0.925625\pi$
$138$	−188.211	−	209.791i	−1.36384	−	1.52022i
$139$	−149.038			−1.07222			−0.536109	−	0.844149i	$-0.680106\pi$
$139$	−149.038			−1.07222			−0.536109	+	0.844149i	$0.680106\pi$
$140$	89.8478	−	80.8671i	0.641770	−	0.577622i
$141$			121.725i			0.863295i
$142$	101.115	+	112.709i	0.712081	+	0.793727i
$143$	−50.4361	+	29.1193i	−0.352700	+	0.203631i
$144$	27.8294	−	30.4618i	0.193260	−	0.211540i
$145$	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	0.231324	−	0.972877i	$-0.425694\pi$
$149$	−73.8369	−	42.6298i	−0.495550	−	0.286106i	−0.726874	+	0.686771i	$0.759028\pi$
$150$	42.3675	−	8.92545i	0.282450	−	0.0595030i
$151$	−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	$0.977091\pi$
$152$	1.23483	+	12.3950i	0.00812389	+	0.0815460i
$153$		−	40.5751i		−	0.265197i
$154$	124.854	−	217.059i	0.810739	−	1.40948i
$155$		−	0.0723686i		−	0.000466894i
$156$	40.5518	−	17.8794i	0.259948	−	0.114612i
$157$	−122.552	−	212.267i	−0.780589	−	1.35202i	−0.931599	−	0.363487i	$-0.881586\pi$
$157$	−122.552	−	212.267i	−0.780589	−	1.35202i	0.151010	−	0.988532i	$-0.451747\pi$
$158$	−45.6946	+	9.62637i	−0.289206	+	0.0609264i
$159$	−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	0.976225	−	0.216758i	$-0.0695482\pi$
$163$	208.089	+	120.140i	1.27662	+	0.737057i	0.300395	+	0.953815i	$0.402882\pi$
$164$	279.559	+	30.4052i	1.70463	+	0.185398i
$165$	−227.550	+	131.376i	−1.37909	+	0.796219i
$166$	136.879	+	152.573i	0.824573	+	0.919117i
$167$		−	73.1965i		−	0.438302i	−0.975691	−	0.219151i	$-0.929671\pi$
$167$		−	73.1965i		−	0.438302i	0.975691	−	0.219151i	$-0.0703288\pi$
$168$	−112.314	+	153.937i	−0.668536	+	0.916290i
$169$	−158.398			−0.937266
$170$	−101.124	+	90.7224i	−0.594850	+	0.533661i
$171$	−2.00762	−	3.47730i	−0.0117405	−	0.0203351i
$172$	−51.8464	−	5.63890i	−0.301433	−	0.0327843i
$173$	18.5246	−	32.0855i	0.107078	−	0.185465i	−0.807507	−	0.589858i	$-0.799184\pi$
$173$	18.5246	−	32.0855i	0.107078	−	0.185465i	0.914585	+	0.404393i	$0.132517\pi$
$174$	−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
$178$	36.5136	+	173.323i	0.205132	+	0.973726i
$179$	205.982	−	118.924i	1.15074	−	0.664379i	0.201672	−	0.979453i	$-0.435363\pi$
$179$	205.982	−	118.924i	1.15074	−	0.664379i	0.949067	+	0.315074i	$0.102029\pi$
$180$	40.7469	−	17.9654i	0.226372	−	0.0998080i
$181$	292.553			1.61631			0.808157	−	0.588966i	$-0.200465\pi$
$181$	292.553			1.61631			0.808157	+	0.588966i	$0.200465\pi$
$182$	−39.4410	+	22.8560i	−0.216709	+	0.125582i
$183$	326.927			1.78649
$184$	−32.8437	−	329.679i	−0.178499	−	1.79173i
$185$	−5.04132	+	2.91061i	−0.0272504	+	0.0157330i
$186$	0.0235169	+	0.111631i	0.000126435	+	0.000600164i
$187$	−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	$0.287208\pi$
$192$	213.496	−	42.9648i	1.11196	−	0.223775i
$193$	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	$0.778672\pi$
$194$	209.713	−	188.141i	1.08099	−	0.969798i
$195$	47.8325			0.245295
$196$	97.4529	−	170.056i	0.497209	−	0.867631i
$197$			199.421i			1.01229i	0.862448	+	0.506145i	$0.168930\pi$
$197$			199.421i			1.01229i	−0.862448	+	0.506145i	$0.831070\pi$
$198$	68.6652	−	61.6020i	0.346794	−	0.311121i
$199$	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	$0.278931\pi$
$200$	46.3836	+	20.9535i	0.231918	+	0.104768i
$201$	−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
$206$	−41.4964	−	196.976i	−0.201439	−	0.956193i
$207$	53.3982	+	92.4884i	0.257962	+	0.446804i
$208$	50.8790	+	11.1998i	0.244611	+	0.0538454i
$209$			27.8495i			0.133251i
$210$	−177.944	+	103.118i	−0.847353	+	0.491040i
$211$			62.1464i			0.294533i	0.989097	+	0.147266i	$0.0470475\pi$
$211$			62.1464i			0.294533i	−0.989097	+	0.147266i	$0.952953\pi$
$212$	−74.1600	−	168.200i	−0.349811	−	0.793398i
$213$	−128.811	−	223.106i	−0.604744	−	1.04745i
$214$	44.0940	+	209.306i	0.206047	+	0.978066i
$215$	−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
$220$	−307.059	−	33.3962i	−1.39572	−	0.151801i
$221$	44.3683	−	25.6161i	0.200762	−	0.115910i
$222$	6.83054	−	6.12792i	0.0307682	−	0.0276033i
$223$		−	115.525i		−	0.518050i	−0.965871	−	0.259025i	$-0.916599\pi$
$223$		−	115.525i		−	0.518050i	0.965871	−	0.259025i	$-0.0834012\pi$
$224$	−213.422	+	68.0210i	−0.952779	+	0.303665i
$225$	−16.4063			−0.0729171
$226$	−60.6812	−	67.6388i	−0.268501	−	0.299287i
$227$	−28.2532	−	48.9360i	−0.124463	−	0.215577i	0.797060	−	0.603901i	$-0.206388\pi$
$227$	−28.2532	−	48.9360i	−0.124463	−	0.215577i	−0.921523	+	0.388324i	$0.873054\pi$
$228$	2.29147	−	21.0687i	0.0100503	−	0.0924067i
$229$	−59.1696	+	102.485i	−0.258383	+	0.447532i	−0.965809	−	0.259255i	$-0.916523\pi$
$229$	−59.1696	+	102.485i	−0.258383	+	0.447532i	0.707426	+	0.706787i	$0.249856\pi$
$230$	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	$0.149800\pi$
$234$	−16.4325	+	3.46180i	−0.0702245	+	0.0147940i
$235$	−133.745	+	77.2175i	−0.569126	+	0.328585i
$236$	−251.451	+	110.866i	−1.06547	+	0.469769i
$237$	79.4503			0.335233
$238$	−109.833	+	190.946i	−0.461484	+	0.802294i
$239$	−251.189			−1.05100			−0.525499	−	0.850794i	$-0.676121\pi$
$239$	−251.189			−1.05100			−0.525499	+	0.850794i	$0.676121\pi$
$240$	229.548	+	50.5298i	0.956452	+	0.210541i
$241$	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	$0.258386\pi$
$242$	−389.284	+	82.0096i	−1.60861	+	0.338883i
$243$	−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
$248$	−0.0552087	+	0.122212i	−0.000222616	+	0.000492792i
$249$	−174.370	−	302.017i	−0.700280	−	1.21292i
$250$	180.830	+	201.564i	0.723321	+	0.806256i
$251$	−121.248			−0.483059			−0.241529	−	0.970394i	$-0.577649\pi$
$251$	−121.248			−0.483059			−0.241529	+	0.970394i	$0.577649\pi$
$252$	53.6685	−	48.3041i	0.212970	−	0.191683i
$253$		−	740.735i		−	2.92781i
$254$	−167.874	−	187.123i	−0.660923	−	0.736704i
$255$	200.174	−	115.571i	0.784998	−	0.453219i
$256$	232.337	+	107.496i	0.907567	+	0.419907i
$257$	−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
$262$	−221.735	+	46.7123i	−0.846315	+	0.178291i
$263$	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	$0.769561\pi$
$264$	484.500	−	48.2675i	1.83523	−	0.182831i
$265$		−	198.399i		−	0.748675i
$266$	0.0350972	+	21.7986i	0.000131944	+	0.0819495i
$267$		−	301.361i		−	1.12869i
$268$	−22.5109	−	51.0564i	−0.0839959	−	0.190509i
$269$	152.466	+	264.079i	0.566789	+	0.981707i	0.996881	+	0.0789222i	$0.0251479\pi$
$269$	152.466	+	264.079i	0.566789	+	0.981707i	−0.430092	+	0.902785i	$0.641519\pi$
$270$	184.607	−	38.8908i	0.683731	−	0.144040i
$271$	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
$276$	−60.9479	+	560.381i	−0.220826	+	2.03036i
$277$	−14.4235	+	8.32739i	−0.0520703	+	0.0300628i	−0.525809	−	0.850603i	$-0.676237\pi$
$277$	−14.4235	+	8.32739i	−0.0520703	+	0.0300628i	0.473739	+	0.880665i	$0.342904\pi$
$278$	199.051	+	221.874i	0.716012	+	0.798109i
$279$		−	0.0432277i		−	0.000154938i
$280$	−240.386	−	25.7532i	−0.858520	−	0.0919756i
$281$	75.8291			0.269855			0.134927	−	0.990856i	$-0.456920\pi$
$281$	75.8291			0.269855			0.134927	+	0.990856i	$0.456920\pi$
$282$	181.212	−	162.572i	0.642596	−	0.576496i
$283$	−43.6656	−	75.6311i	−0.154296	−	0.267248i	0.778507	−	0.627636i	$-0.215977\pi$
$283$	−43.6656	−	75.6311i	−0.154296	−	0.267248i	−0.932802	+	0.360389i	$0.882644\pi$
$284$	32.7441	−	301.063i	0.115296	−	1.06008i
$285$	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
$290$	−6.66350	−	31.6304i	−0.0229776	−	0.109070i
$291$	−415.124	+	239.672i	−1.42654	+	0.823614i
$292$	−85.7673	−	194.527i	−0.293724	−	0.666187i
$293$	−27.5057			−0.0938760			−0.0469380	−	0.998898i	$-0.514946\pi$
$293$	−27.5057			−0.0938760			−0.0469380	+	0.998898i	$0.514946\pi$
$294$	−221.886	+	248.935i	−0.754715	+	0.846719i
$295$	−296.597			−1.00541
$296$	10.7340	−	1.06935i	0.0362634	−	0.00361268i
$297$	338.452	−	195.406i	1.13957	−	0.657931i
$298$	35.1513	+	166.857i	0.117957	+	0.559922i
$299$	−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
$304$	16.8033	−	18.3927i	0.0552740	−	0.0605023i
$305$	207.390	+	359.211i	0.679968	+	1.17774i
$306$	−60.4044	+	54.1909i	−0.197400	+	0.177095i
$307$	−247.996			−0.807805			−0.403902	−	0.914802i	$-0.632346\pi$
$307$	−247.996			−0.807805			−0.403902	+	0.914802i	$0.632346\pi$
$308$	−489.889	+	104.028i	−1.59055	+	0.337752i
$309$			342.486i			1.10837i
$310$	−0.107736	+	0.0966534i	−0.000347534	+	0.000311785i
$311$	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	$0.0853424\pi$
$312$	−80.7771	−	36.4905i	−0.258901	−	0.116957i
$313$	−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	0.795341	−	0.606162i	$-0.207292\pi$
$317$	211.775	+	122.268i	0.668059	+	0.385704i	−0.127282	+	0.991867i	$0.540625\pi$
$318$	64.4718	+	306.036i	0.202742	+	0.962377i
$319$	−33.4806	−	57.9900i	−0.104955	−	0.181787i
$320$	182.641	+	207.323i	0.570755	+	0.647885i
$321$		−	363.925i		−	1.13372i
$322$	−0.933506	−	579.793i	−0.00289909	−	1.80060i
$323$		−	24.4991i		−	0.0758485i
$324$	−357.069	+	157.433i	−1.10207	+	0.485904i
$325$	−10.3577	−	17.9401i	−0.0318699	−	0.0552004i
$326$	−99.0643	−	470.240i	−0.303878	−	1.44245i
$327$	−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	0.596785	−	0.802401i	$-0.296445\pi$
$331$	66.2919	+	38.2736i	0.200278	+	0.115630i	−0.396507	+	0.918032i	$0.629778\pi$
$332$	44.3253	−	407.546i	0.133510	−	1.22755i
$333$	−3.01132	+	1.73858i	−0.00904299	+	0.00522097i
$334$	−108.968	+	97.7592i	−0.326252	+	0.292692i
$335$		−	60.2230i		−	0.179770i
$336$	379.170	−	38.3909i	1.12848	−	0.114259i
$337$	−38.2520			−0.113507			−0.0567537	−	0.998388i	$-0.518075\pi$
$337$	−38.2520			−0.113507			−0.0567537	+	0.998388i	$0.518075\pi$
$338$	211.552	+	235.808i	0.625893	+	0.697657i
$339$	77.3015	+	133.890i	0.228028	+	0.394956i
$340$	270.118	+	29.3785i	0.794465	+	0.0864072i
$341$	−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
$346$	−72.5068	+	15.2748i	−0.209557	+	0.0441469i
$347$	208.395	−	120.317i	0.600561	−	0.346734i	−0.168701	−	0.985667i	$-0.553957\pi$
$347$	208.395	−	120.317i	0.600561	−	0.346734i	0.769262	+	0.638933i	$0.220624\pi$
$348$	20.5573	+	46.6254i	0.0590727	+	0.133981i
$349$	−430.367			−1.23314			−0.616572	−	0.787298i	$-0.711479\pi$
$349$	−430.367			−1.23314			−0.616572	+	0.787298i	$0.711479\pi$
$350$	77.2081	+	44.4105i	0.220594	+	0.126887i
$351$	−71.1449			−0.202692
$352$	493.068	+	290.648i	1.40076	+	0.825703i
$353$	−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	$0.476576\pi$
$354$	457.509	−	96.3822i	1.29240	−	0.272266i
$355$	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	$0.944306\pi$
$360$	−81.1657	−	36.6661i	−0.225460	−	0.101850i
$361$	179.288	+	310.536i	0.496642	+	0.860209i
$362$	−390.726	−	435.526i	−1.07935	−	1.20311i
$363$	676.858			1.86462
$364$	86.7022	+	28.1902i	0.238193	+	0.0774457i
$365$		−	229.452i		−	0.628635i
$366$	−436.635	−	486.699i	−1.19299	−	1.32978i
$367$	−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	$0.659253\pi$
$368$	−446.930	+	489.205i	−1.21448	+	1.32936i
$369$	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	−0.0624108	−	0.998051i	$-0.519879\pi$
$373$	−357.317	−	206.297i	−0.957953	−	0.553075i	−0.895543	+	0.444976i	$0.853212\pi$
$374$	550.765	−	116.028i	1.47263	−	0.310236i
$375$	−230.359	−	398.993i	−0.614290	−	1.06398i
$376$	284.769	−	28.3697i	0.757364	−	0.0754512i
$377$			12.1899i			0.0323339i
$378$	264.670	−	153.376i	0.700184	−	0.405756i
$379$			327.118i			0.863107i	0.902087	+	0.431554i	$0.142034\pi$
$379$			327.118i			0.863107i	−0.902087	+	0.431554i	$0.857966\pi$
$380$	24.6028	−	10.8475i	0.0647443	−	0.0285459i
$381$	213.854	+	370.407i	0.561298	+	0.972196i
$382$	276.387	−	58.2259i	0.723527	−	0.152424i
$383$	−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
$388$	−560.173	−	60.9253i	−1.44375	−	0.157024i
$389$	326.728	−	188.637i	0.839918	−	0.484927i	−0.0173181	−	0.999850i	$-0.505513\pi$
$389$	326.728	−	188.637i	0.839918	−	0.484927i	0.857236	+	0.514923i	$0.172179\pi$
$390$	−63.8837	−	71.2086i	−0.163804	−	0.182586i
$391$			651.620i			1.66655i
$392$	−383.318	+	82.0428i	−0.977853	+	0.209293i
$393$	385.535			0.981005
$394$	296.880	−	266.341i	0.753502	−	0.675994i
$395$	50.4003	+	87.2958i	0.127596	+	0.221002i
$396$	−183.415	−	19.9485i	−0.463168	−	0.0503749i
$397$	−335.874	+	581.752i	−0.846031	+	1.46537i	0.0386913	+	0.999251i	$0.487681\pi$
$397$	−335.874	+	581.752i	−0.846031	+	1.46537i	−0.884723	+	0.466118i	$0.845652\pi$
$398$	−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	$-0.0328411\pi$
$402$	19.5701	+	92.8957i	0.0486819	+	0.231084i
$403$	0.0472689	−	0.0272907i	0.000117293	−	6.77189e-5i
$404$	129.557	−	57.1220i	0.320685	−	0.141391i
$405$	−421.177			−1.03994
$406$	−26.2792	−	45.3482i	−0.0647272	−	0.111695i
$407$	24.1175			0.0592567
$408$	−426.211	+	42.4606i	−1.04464	+	0.104070i
$409$	−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	$0.359307\pi$
$410$	−125.130	−	593.971i	−0.305196	−	1.44871i
$411$	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
$416$	−51.2793	−	90.7021i	−0.123267	−	0.218034i
$417$	−253.571	−	439.197i	−0.608083	−	1.05323i
$418$	41.4598	−	37.1950i	0.0991860	−	0.0889833i
$419$	437.380			1.04387			0.521933	−	0.852986i	$-0.325211\pi$
$419$	437.380			1.04387			0.521933	+	0.852986i	$0.325211\pi$
$420$	391.170	+	127.185i	0.931358	+	0.302820i
$421$			703.800i			1.67173i	0.548933	+	0.835867i	$0.315034\pi$
$421$			703.800i			1.67173i	−0.548933	+	0.835867i	$0.684966\pi$
$422$	92.5178	−	83.0010i	0.219236	−	0.196685i
$423$	−79.8893	+	46.1241i	−0.188864	+	0.109040i
$424$	−151.355	+	335.046i	−0.356969	+	0.790203i
$425$	−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
$430$	23.2065	+	110.157i	0.0539686	+	0.256179i
$431$	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	$0.613200\pi$
$432$	−341.425	−	75.1568i	−0.790335	−	0.173974i
$433$			355.012i			0.819890i	0.912110	+	0.409945i	$0.134452\pi$
$433$			355.012i			0.819890i	−0.912110	+	0.409945i	$0.865548\pi$
$434$	−0.117014	+	0.203429i	−0.000269616	+	0.000468731i
$435$			54.9965i			0.126429i
$436$	−84.9321	−	192.632i	−0.194798	−	0.441817i
$437$	32.2416	+	55.8441i	0.0737794	+	0.127790i
$438$	74.5628	+	353.936i	0.170235	+	0.808073i
$439$	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	0.740315	−	0.672260i	$-0.234676\pi$
$443$	234.027	+	135.116i	0.528278	+	0.305001i	−0.212037	+	0.977262i	$0.568010\pi$
$444$	−18.2454	−	1.98439i	−0.0410932	−	0.00446936i
$445$	331.120	−	191.172i	0.744089	−	0.429600i
$446$	−171.983	+	154.292i	−0.385612	+	0.345947i
$447$		−	290.117i		−	0.649032i
$448$	386.304	+	226.876i	0.862287	+	0.506421i
$449$	455.397			1.01425			0.507124	−	0.861873i	$-0.330709\pi$
$449$	455.397			1.01425			0.507124	+	0.861873i	$0.330709\pi$
$450$	21.9118	+	24.4242i	0.0486930	+	0.0542761i
$451$	−628.714	−	1088.96i	−1.39404	−	2.41456i
$452$	−19.6503	+	180.673i	−0.0434741	+	0.399719i
$453$	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	$0.107600\pi$
$458$	231.595	−	48.7896i	0.505666	−	0.106528i
$459$	−297.735	+	171.897i	−0.648659	+	0.374504i
$460$	−654.380	+	288.518i	−1.42257	+	0.627213i
$461$	−265.062			−0.574971			−0.287485	−	0.957785i	$-0.592819\pi$
$461$	−265.062			−0.574971			−0.287485	+	0.957785i	$0.592819\pi$
$462$	852.070	−	1.37189i	1.84431	−	0.00296946i
$463$	97.4735			0.210526			0.105263	−	0.994444i	$-0.466432\pi$
$463$	97.4735			0.210526			0.105263	+	0.994444i	$0.466432\pi$
$464$	−12.8773	+	58.4993i	−0.0277528	+	0.126076i
$465$	0.213261	−	0.123126i	0.000458626	−	0.000264788i
$466$	−48.3009	+	10.1754i	−0.103650	+	0.0218357i
$467$	37.0997	−	64.2586i	0.0794427	−	0.137599i	−0.823567	−	0.567219i	$-0.808019\pi$
$467$	37.0997	−	64.2586i	0.0794427	−	0.137599i	0.903010	+	0.429620i	$0.141353\pi$
$468$	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
$472$	500.877	+	226.268i	1.06118	+	0.479382i
$473$	116.600	+	201.958i	0.246512	+	0.426972i
$474$	−106.112	−	118.278i	−0.223864	−	0.249532i
$475$	−9.90608			−0.0208549
$476$	430.952	−	91.5126i	0.905362	−	0.192253i
$477$		−	118.509i		−	0.248447i
$478$	335.480	+	373.946i	0.701842	+	0.782314i
$479$	−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	$0.527474\pi$
$480$	−231.354	−	409.216i	−0.481988	−	0.852534i
$481$	−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
$486$	264.827	−	55.7904i	0.544911	−	0.114795i
$487$	−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	$-0.364801\pi$
$488$	−76.1951	−	764.831i	−0.156137	−	1.56728i
$489$			817.617i			1.67202i
$490$	−414.274	−	85.8818i	−0.845456	−	0.175269i
$491$		−	78.8005i		−	0.160490i	−0.996775	−	0.0802449i	$-0.974430\pi$
$491$		−	78.8005i		−	0.160490i	0.996775	−	0.0802449i	$-0.0255702\pi$
$492$	386.035	+	875.555i	0.784623	+	1.77958i
$493$	29.4527	+	51.0135i	0.0597417	+	0.103476i
$494$	−9.92190	+	2.09022i	−0.0200848	+	0.00423122i
$495$	−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	0.179307	−	0.983793i	$-0.442615\pi$
$499$	−290.932	−	167.970i	−0.583030	−	0.336612i	−0.762337	+	0.647181i	$0.775948\pi$
$500$	58.5579	−	538.406i	0.117116	−	1.07681i
$501$	215.701	−	124.535i	0.430541	−	0.248573i
$502$	161.935	+	180.502i	0.322580	+	0.359566i
$503$		−	274.052i		−	0.544836i	−0.962179	−	0.272418i	$-0.912177\pi$
$503$		−	274.052i		−	0.544836i	0.962179	−	0.272418i	$-0.0878233\pi$
$504$	−143.589	−	15.3831i	−0.284898	−	0.0305220i
$505$	152.817			0.302609
$506$	−1102.74	+	989.304i	−2.17932	+	1.95515i
$507$	−269.495	−	466.779i	−0.531548	−	0.920669i
$508$	−54.3625	+	499.832i	−0.107013	+	0.983921i
$509$	168.009	−	291.000i	0.330076	−	0.571709i	−0.652450	−	0.757831i	$-0.726259\pi$
$509$	168.009	−	291.000i	0.330076	−	0.571709i	0.982526	+	0.186123i	$0.0595923\pi$
$510$	−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
$514$	43.1972	+	205.049i	0.0840412	+	0.398928i
$515$	−376.306	+	217.260i	−0.730691	+	0.421865i
$516$	−71.5933	−	162.379i	−0.138747	−	0.314688i
$517$	639.829			1.23758
$518$	18.8774	−	0.0303939i	0.0364429	−	5.86755e-5i
$519$	126.069			0.242908
$520$	−11.1480	−	111.902i	−0.0214385	−	0.215196i
$521$	−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	$0.540879\pi$
$522$	−3.98029	−	18.8937i	−0.00762508	−	0.0361948i
$523$	389.623	−	674.847i	0.744977	−	1.29034i	−0.205229	−	0.978714i	$-0.565794\pi$
$523$	389.623	−	674.847i	0.744977	−	1.29034i	0.950206	−	0.311624i	$-0.100873\pi$
$524$	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
$528$	−718.940	−	656.813i	−1.36163	−	1.24396i
$529$	−593.054	−	1027.20i	−1.12109	−	1.94178i
$530$	−295.358	+	264.976i	−0.557279	+	0.499955i
$531$	−177.165			−0.333644
$532$	32.4048	−	29.1658i	0.0609113	−	0.0548230i
$533$			228.907i			0.429470i
$534$	−448.638	+	402.489i	−0.840146	+	0.753725i
$535$	399.862	−	230.861i	0.747406	−	0.431515i
$536$	−45.9431	+	101.702i	−0.0857146	+	0.189742i
$537$	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	0.930566	−	0.366125i	$-0.119316\pi$
$541$	583.617	+	336.952i	1.07878	+	0.622831i	0.148209	+	0.988956i	$0.452649\pi$
$542$	−42.3195	−	200.883i	−0.0780803	−	0.370633i
$543$	497.743	+	862.117i	0.916655	+	1.58769i
$544$	−433.749	−	255.681i	−0.797333	−	0.470002i
$545$		−	227.217i		−	0.416913i
$546$	−134.458	−	77.3409i	−0.246260	−	0.141650i
$547$			52.5329i			0.0960382i	0.998846	+	0.0480191i	$0.0152908\pi$
$547$			52.5329i			0.0960382i	−0.998846	+	0.0480191i	$0.984709\pi$
$548$	286.712	−	126.412i	0.523198	−	0.230679i
$549$	123.880	+	214.566i	0.225646	+	0.390831i
$550$	−46.9155	−	222.699i	−0.0853009	−	0.404907i
$551$	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
$556$	64.4585	−	592.658i	0.115933	−	1.06593i
$557$	678.123	−	391.515i	1.21746	−	0.702899i	0.253083	−	0.967445i	$-0.418555\pi$
$557$	678.123	−	391.515i	1.21746	−	0.702899i	0.964373	+	0.264546i	$0.0852220\pi$
$558$	−0.0643534	+	0.0577337i	−0.000115329	+	0.000103465i
$559$		−	42.4528i		−	0.0759441i
$560$	282.713	+	392.259i	0.504845	+	0.700462i
$561$	−957.628			−1.70700
$562$	−101.275	−	112.887i	−0.180205	−	0.200867i
$563$	446.202	+	772.844i	0.792543	+	1.37272i	0.924388	+	0.381454i	$0.124577\pi$
$563$	446.202	+	772.844i	0.792543	+	1.37272i	−0.131845	+	0.991270i	$0.542090\pi$
$564$	−484.044	−	52.6454i	−0.858234	−	0.0933429i
$565$	−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	$0.0824912\pi$
$570$	−44.7642	+	9.43036i	−0.0785337	+	0.0165445i
$571$	−218.885	+	126.373i	−0.383335	+	0.221319i	−0.679268	−	0.733890i	$-0.737703\pi$
$571$	−218.885	+	126.373i	−0.383335	+	0.221319i	0.295933	+	0.955209i	$0.404369\pi$
$572$	−93.9808	−	213.155i	−0.164302	−	0.372649i
$573$	−480.561			−0.838676
$574$	−493.484	−	851.570i	−0.859728	−	1.48357i
$575$	263.479			0.458225
$576$	109.097	+	123.840i	0.189404	+	0.215000i
$577$	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	$0.0561126\pi$
$578$	81.0811	−	17.0812i	0.140279	−	0.0295522i
$579$	−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
$584$	−175.045	+	387.487i	−0.299734	+	0.663504i
$585$	18.1248	+	31.3930i	0.0309825	+	0.0536633i
$586$	36.7358	+	40.9479i	0.0626890	+	0.0698769i
$587$	−66.7814			−0.113767			−0.0568836	−	0.998381i	$-0.518116\pi$
$587$	−66.7814			−0.113767			−0.0568836	+	0.998381i	$0.518116\pi$
$588$	666.937	−	2.14763i	1.13425	−	0.00365244i
$589$		−	0.0261007i		−	4.43136e-5i
$590$	396.126	+	441.545i	0.671400	+	0.748382i
$591$	−587.670	+	339.291i	−0.994365	+	0.574097i
$592$	−15.9279	−	14.5515i	−0.0269053	−	0.0245803i
$593$	−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
$598$	263.900	−	55.5952i	0.441305	−	0.0929686i
$599$	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	$0.780470\pi$
$600$	17.1688	+	172.337i	0.0286146	+	0.287228i
$601$			373.907i			0.622141i	0.950387	+	0.311071i	$0.100688\pi$
$601$			373.907i			0.622141i	−0.950387	+	0.311071i	$0.899312\pi$
$602$	91.5207	+	157.931i	0.152028	+	0.262343i
$603$		−	35.9728i		−	0.0596565i
$604$	482.402	−	212.692i	0.798679	−	0.352140i
$605$	429.373	+	743.696i	0.709708	+	1.22925i
$606$	−235.725	+	49.6597i	−0.388986	+	0.0819466i
$607$	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
$612$	161.349	+	17.5486i	0.263642	+	0.0286741i
$613$	−444.718	+	256.758i	−0.725479	+	0.418855i	−0.816766	−	0.576969i	$-0.804235\pi$
$613$	−444.718	+	256.758i	−0.725479	+	0.418855i	0.0912873	+	0.995825i	$0.470902\pi$
$614$	331.217	+	369.193i	0.539441	+	0.601292i
$615$			1032.75i			1.67927i
$616$	809.149	+	590.364i	1.31355	+	0.958384i
$617$	−1119.01			−1.81363			−0.906815	−	0.421529i	$-0.861493\pi$
$617$	−1119.01			−1.81363			−0.906815	+	0.421529i	$0.861493\pi$
$618$	509.862	−	457.415i	0.825019	−	0.740154i
$619$	64.1019	+	111.028i	0.103557	+	0.179366i	0.913148	−	0.407629i	$-0.133644\pi$
$619$	64.1019	+	111.028i	0.103557	+	0.179366i	−0.809591	+	0.586995i	$0.800311\pi$
$620$	0.287777	+	0.0312991i	0.000464157	+	5.04824e-5i
$621$	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
$626$	34.1497	+	162.102i	0.0545522	+	0.258949i
$627$	−82.0690	+	47.3826i	−0.130892	+	0.0755703i
$628$	897.094	−	395.531i	1.42849	−	0.629827i
$629$	−21.2160			−0.0337297
$630$	−135.105	−	77.7130i	−0.214452	−	0.123354i
$631$	313.995			0.497615			0.248808	−	0.968553i	$-0.419961\pi$
$631$	313.995			0.497615			0.248808	+	0.968553i	$0.419961\pi$
$632$	−18.5170	−	185.870i	−0.0292991	−	0.294098i
$633$	−183.138	+	105.735i	−0.289317	+	0.167037i
$634$	−100.819	−	478.569i	−0.159020	−	0.754840i
$635$	−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
$640$	64.7127	−	548.795i	0.101114	−	0.857492i
$641$	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	$0.775615\pi$
$642$	−541.778	+	486.048i	−0.843891	+	0.757085i
$643$	637.869			0.992020			0.496010	−	0.868317i	$-0.334798\pi$
$643$	637.869			0.992020			0.496010	+	0.868317i	$0.334798\pi$
$644$	−861.896	+	775.745i	−1.33835	+	1.20457i
$645$		−	191.532i		−	0.296949i
$646$	−36.4719	+	32.7203i	−0.0564581	+	0.0506505i
$647$	−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	$0.508643\pi$
$648$	711.263	+	321.309i	1.09763	+	0.495847i
$649$	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	−0.408112	−	0.912932i	$-0.633813\pi$
$653$	−916.022	−	528.865i	−1.40279	−	0.809901i	−0.994678	+	0.103031i	$0.967146\pi$
$654$	73.8367	+	350.489i	0.112900	+	0.535916i
$655$	244.569	+	423.606i	0.373388	+	0.646726i
$656$	−241.816	+	1098.53i	−0.368622	+	1.67459i
$657$		−	137.058i		−	0.208612i
$658$	500.812	−	0.806341i	0.761112	−	0.00122544i
$659$		−	644.502i		−	0.978000i	−0.872284	−	0.489000i	$-0.837362\pi$
$659$		−	644.502i		−	0.978000i	0.872284	−	0.489000i	$-0.162638\pi$
$660$	−424.009	−	961.684i	−0.642438	−	1.45710i
$661$	560.069	+	970.068i	0.847306	+	1.46758i	0.883604	+	0.468236i	$0.155110\pi$
$661$	560.069	+	970.068i	0.847306	+	1.46758i	−0.0362979	+	0.999341i	$0.511557\pi$
$662$	−31.5593	−	149.806i	−0.0476727	−	0.226294i
$663$	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
$668$	291.070	+	31.6572i	0.435733	+	0.0473910i
$669$	340.438	−	196.552i	0.508876	−	0.293800i
$670$	−89.6544	+	80.4322i	−0.133813	+	0.120048i
$671$		−	1718.45i		−	2.56103i
$672$	−563.562	−	513.200i	−0.838634	−	0.763690i
$673$	−307.811			−0.457371			−0.228686	−	0.973500i	$-0.573443\pi$
$673$	−307.811			−0.457371			−0.228686	+	0.973500i	$0.573443\pi$
$674$	51.0883	+	56.9460i	0.0757987	+	0.0844897i
$675$	69.5058	+	120.388i	0.102972	+	0.178352i
$676$	68.5065	−	629.878i	0.101341	−	0.931772i
$677$	−507.773	+	879.488i	−0.750033	+	1.29910i	0.197773	+	0.980248i	$0.436629\pi$
$677$	−507.773	+	879.488i	−0.750033	+	1.29910i	−0.947806	+	0.318848i	$0.896704\pi$
$678$	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
$682$	0.586772	−	0.123614i	0.000860369	−	0.000181252i
$683$	−840.220	+	485.102i	−1.23019	+	0.710251i	−0.967070	−	0.254512i	$-0.918085\pi$
$683$	−840.220	+	485.102i	−1.23019	+	0.710251i	−0.263121	+	0.964763i	$0.584752\pi$
$684$	14.6959	−	6.47948i	0.0214853	−	0.00947293i
$685$	338.188			0.493706
$686$	−681.612	+	77.4663i	−0.993604	+	0.112925i
$687$	−402.680			−0.586143
$688$	44.8467	−	203.731i	0.0651842	−	0.296121i
$689$	129.588	−	74.8177i	0.188081	−	0.108589i
$690$	1190.63	−	250.827i	1.72555	−	0.363517i
$691$	274.581	−	475.588i	0.397367	−	0.688260i	−0.596033	−	0.802960i	$-0.703257\pi$
$691$	274.581	−	475.588i	0.397367	−	0.688260i	0.993400	+	0.114700i	$0.0365906\pi$
$692$	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
$696$	41.9559	−	92.8754i	0.0602814	−	0.133442i
$697$	553.076	+	957.956i	0.793510	+	1.37440i
$698$	574.786	+	640.691i	0.823476	+	0.917895i
$699$	83.9818			0.120146
$700$	−37.0027	−	174.254i	−0.0528610	−	0.248934i
$701$			452.665i			0.645742i	0.946443	+	0.322871i	$0.104648\pi$
$701$			452.665i			0.645742i	−0.946443	+	0.322871i	$0.895352\pi$
$702$	95.0191	+	105.914i	0.135355	+	0.150874i
$703$	−1.81822	+	1.04975i	−0.00258637	+	0.00149324i
$704$	−225.839	−	1122.21i	−0.320794	−	1.59406i
$705$	−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	0.00454321	−	0.999990i	$-0.498554\pi$
$709$	−609.174	−	351.707i	−0.859202	−	0.496060i	−0.863745	+	0.503929i	$0.831887\pi$
$710$	−639.660	+	134.756i	−0.900930	+	0.189797i
$711$	30.1054	+	52.1442i	0.0423424	+	0.0733392i
$712$	−705.020	+	70.2365i	−0.990197	+	0.0986468i
$713$			0.694220i			0.000973661i
$714$	−749.561	+	1.20684i	−1.04981	+	0.00169026i
$715$		−	251.425i		−	0.351644i
$716$	383.820	+	870.533i	0.536062	+	1.21583i
$717$	−427.367	−	740.221i	−0.596049	−	1.03239i
$718$	903.684	−	190.377i	1.25861	−	0.265149i
$719$	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
$724$	−126.528	+	1163.35i	−0.174762	+	1.60684i
$725$	20.6271	−	11.9090i	0.0284511	−	0.0164263i
$726$	−903.992	−	1007.64i	−1.24517	−	1.38794i
$727$		−	889.995i		−	1.22420i	−0.790779	−	0.612101i	$-0.790324\pi$
$727$		−	889.995i		−	1.22420i	0.790779	−	0.612101i	$-0.209676\pi$
$728$	−73.8300	−	166.724i	−0.101415	−	0.229017i
$729$	417.569			0.572797
$730$	−341.586	+	306.449i	−0.467927	+	0.419794i
$731$	−102.573	−	177.661i	−0.140318	−	0.243038i
$732$	−141.395	+	1300.04i	−0.193162	+	1.77601i
$733$	−456.127	+	790.035i	−0.622274	+	1.07781i	0.366787	+	0.930305i	$0.380458\pi$
$733$	−456.127	+	790.035i	−0.622274	+	1.07781i	−0.989061	+	0.147505i	$0.952876\pi$
$734$	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
$738$	−74.7438	−	354.795i	−0.101279	−	0.480752i
$739$	1081.52	−	624.415i	1.46349	−	0.844946i	0.464319	−	0.885668i	$-0.346299\pi$
$739$	1081.52	−	624.415i	1.46349	−	0.844946i	0.999171	+	0.0407224i	$0.0129659\pi$
$740$	−9.39382	−	21.3059i	−0.0126944	−	0.0287917i
$741$	17.2514			0.0232813
$742$	−320.793	+	557.702i	−0.432336	+	0.751620i
$743$	−305.880			−0.411682			−0.205841	−	0.978585i	$-0.565993\pi$
$743$	−305.880			−0.411682			−0.205841	+	0.978585i	$0.565993\pi$
$744$	−0.454075	+	0.0452365i	−0.000610316	+	6.08018e-5i
$745$	318.766	−	184.040i	0.427874	−	0.247033i
$746$	170.106	+	807.464i	0.228025	+	1.08239i
$747$	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	$0.278698\pi$
$752$	−422.564	−	386.048i	−0.561920	−	0.513362i
$753$	−206.288	−	357.302i	−0.273955	−	0.474504i
$754$	18.1472	−	16.2805i	0.0240678	−	0.0215921i
$755$	569.012			0.753659
$756$	−581.817	−	189.171i	−0.769599	−	0.250226i
$757$		−	939.898i		−	1.24161i	−0.783965	−	0.620804i	$-0.786806\pi$
$757$		−	939.898i		−	1.24161i	0.783965	−	0.620804i	$-0.213194\pi$
$758$	486.982	−	436.889i	0.642457	−	0.576371i
$759$	2182.85	−	1260.27i	2.87596	−	1.66044i
$760$	−49.0075	−	22.1388i	−0.0644836	−	0.0291301i
$761$	−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
$766$	102.603	+	487.039i	0.133947	+	0.635821i
$767$	−111.849	−	193.728i	−0.145826	−	0.252579i
$768$	78.5156	+	867.560i	0.102234	+	1.12964i
$769$		−	300.115i		−	0.390267i	−0.980777	−	0.195133i	$-0.937486\pi$
$769$		−	300.115i		−	0.390267i	0.980777	−	0.195133i	$-0.0625139\pi$
$770$	542.029	+	935.340i	0.703933	+	1.21473i
$771$		−	356.524i		−	0.462417i
$772$	−241.416	+	106.441i	−0.312714	+	0.137877i
$773$	−375.120	−	649.727i	−0.485278	−	0.840527i	0.514579	−	0.857443i	$-0.327948\pi$
$773$	−375.120	−	649.727i	−0.485278	−	0.840527i	−0.999857	+	0.0169165i	$0.994615\pi$
$774$	13.8619	+	65.7997i	0.0179094	+	0.0850125i
$775$	−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
$780$	−20.6874	+	190.208i	−0.0265222	+	0.243857i
$781$	−1172.73	+	677.076i	−1.50158	+	0.866935i
$782$	970.071	−	870.285i	1.24050	−	1.11290i
$783$		−	81.8005i		−	0.104471i
$784$	634.087	+	461.075i	0.808784	+	0.588105i
$785$	1058.16			1.34797
$786$	−514.910	−	573.949i	−0.655102	−	0.730215i
$787$	−144.776	−	250.760i	−0.183960	−	0.318627i	0.759266	−	0.650781i	$-0.225558\pi$
$787$	−144.776	−	250.760i	−0.183960	−	0.318627i	−0.943225	+	0.332153i	$0.892225\pi$
$788$	−793.009	−	86.2489i	−1.00636	−	0.109453i
$789$	−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
$794$	1314.64	−	276.952i	1.65572	−	0.348807i
$795$	584.657	−	337.552i	0.735417	−	0.424593i
$796$	109.236	+	247.756i	0.137231	+	0.311251i
$797$	−1086.57			−1.36332			−0.681659	−	0.731670i	$-0.738741\pi$
$797$	−1086.57			−1.36332			−0.681659	+	0.731670i	$0.738741\pi$
$798$	−64.1780	+	37.1911i	−0.0804235	+	0.0466053i
$799$	−562.854			−0.704448
$800$	−103.383	+	175.384i	−0.129229	+	0.219231i
$801$	197.787	−	114.192i	0.246925	−	0.142562i
$802$	−920.593	+	193.939i	−1.14787	+	0.241819i
$803$	−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
$808$	−258.070	−	116.582i	−0.319394	−	0.144284i
$809$	−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	$0.869204\pi$
$810$	562.513	+	627.010i	0.694460	+	0.774086i
$811$	−1005.31			−1.23960			−0.619799	−	0.784760i	$-0.712786\pi$
$811$	−1005.31			−1.23960			−0.619799	+	0.784760i	$0.712786\pi$
$812$	−32.4124	+	99.6879i	−0.0399167	+	0.122768i
$813$			349.280i			0.429619i
$814$	−32.2106	−	35.9039i	−0.0395708	−	0.0441079i
$815$	−898.355	+	518.665i	−1.10228	+	0.636399i
$816$	632.447	+	577.795i	0.775058	+	0.708082i
$817$	−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	0.918855	−	0.394596i	$-0.129115\pi$
$821$	851.009	+	491.330i	1.03655	+	0.598453i	0.117697	+	0.993050i	$0.462449\pi$
$822$	−521.665	+	109.898i	−0.634629	+	0.133696i
$823$	−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	$-0.524711\pi$
$824$	801.231	−	79.8213i	0.972367	−	0.0968705i
$825$			387.212i			0.469348i
$826$	833.737	+	479.570i	1.00937	+	0.580594i
$827$			708.113i			0.856243i	0.903721	+	0.428121i	$0.140824\pi$
$827$			708.113i			0.856243i	−0.903721	+	0.428121i	$0.859176\pi$
$828$	−390.879	+	172.340i	−0.472076	+	0.208140i
$829$	−75.0164	−	129.932i	−0.0904902	−	0.156734i	0.817227	−	0.576316i	$-0.195510\pi$
$829$	−75.0164	−	129.932i	−0.0904902	−	0.156734i	−0.907718	+	0.419582i	$0.862177\pi$
$830$	−865.902	+	182.418i	−1.04326	+	0.219780i
$831$	−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
$836$	−110.745	−	12.0448i	−0.132470	−	0.0144077i
$837$	−0.317199	+	0.183135i	−0.000378972	+	0.000218799i
$838$	−584.152	−	651.130i	−0.697079	−	0.777005i
$839$			1106.41i			1.31873i	0.751824	+	0.659364i	$0.229174\pi$
$839$			1106.41i			1.31873i	−0.751824	+	0.659364i	$0.770826\pi$
$840$	−333.095	−	752.202i	−0.396542	−	0.895478i
$841$	826.984			0.983335
$842$	1047.75	−	939.975i	1.24436	−	1.11636i
$843$	129.014	+	223.459i	0.153042	+	0.265076i
$844$	−247.128	−	26.8781i	−0.292806	−	0.0318461i
$845$	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
$850$	41.2713	+	195.907i	0.0485544	+	0.230479i
$851$	48.3606	−	27.9210i	0.0568279	−	0.0328096i
$852$	942.904	−	415.729i	1.10669	−	0.487945i
$853$	1243.82			1.45817			0.729086	−	0.684423i	$-0.239946\pi$
$853$	1243.82			1.45817			0.729086	+	0.684423i	$0.239946\pi$
$854$	−2.16567	−	1345.08i	−0.00253591	−	1.57503i
$855$	17.3344			0.0202742
$856$	−851.386	+	84.8180i	−0.994610	+	0.0990864i
$857$	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	$0.280412\pi$
$858$	81.7033	+	387.831i	0.0952253	+	0.452017i
$859$	455.900	−	789.641i	0.530733	−	0.919256i	−0.468624	−	0.883398i	$-0.655250\pi$
$859$	455.900	−	789.641i	0.530733	−	0.919256i	0.999357	−	0.0358586i	$-0.0114166\pi$
$860$	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	$-0.00230808\pi$
$864$	344.111	+	608.659i	0.398276	+	0.704466i
$865$	79.9735	+	138.518i	0.0924550	+	0.160137i
$866$	528.509	−	474.145i	0.610288	−	0.547511i
$867$	−140.978			−0.162604
$868$	0.459126	−	0.0974953i	0.000528947	−	0.000112322i
$869$		−	417.620i		−	0.480575i
$870$	81.8737	−	73.4518i	0.0941077	−	0.0844274i
$871$	39.3358	−	22.7105i	0.0451617	−	0.0260741i
$872$	−173.340	+	383.713i	−0.198784	+	0.440038i
$873$	−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	0.779411	−	0.626513i	$-0.215518\pi$
$877$	549.476	+	317.240i	0.626540	+	0.361733i	−0.152871	+	0.988246i	$0.548852\pi$
$878$	−227.099	−	1078.00i	−0.258655	−	1.22779i
$879$	−46.7975	−	81.0557i	−0.0532395	−	0.0922136i
$880$	265.603	−	1206.59i	0.301822	−	1.37113i
$881$		−	670.044i		−	0.760549i	−0.924874	−	0.380274i	$-0.875830\pi$
$881$		−	670.044i		−	0.760549i	0.924874	−	0.380274i	$-0.124170\pi$
$882$	−247.457	−	51.2995i	−0.280563	−	0.0581627i
$883$			875.514i			0.991522i	0.868459	+	0.495761i	$0.165111\pi$
$883$			875.514i			0.991522i	−0.868459	+	0.495761i	$0.834889\pi$
$884$	82.6744	+	187.512i	0.0935231	+	0.212117i
$885$	−504.623	−	874.033i	−0.570196	−	0.987608i
$886$	−111.412	−	528.854i	−0.125748	−	0.596901i
$887$	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
$892$	459.392	+	49.9642i	0.515013	+	0.0560136i
$893$	−48.2368	+	27.8495i	−0.0540166	+	0.0311865i
$894$	−431.900	+	387.473i	−0.483109	+	0.433415i
$895$			1026.83i			1.14729i
$896$	−178.185	−	878.104i	−0.198867	−	0.980027i
$897$	−458.850			−0.511538
$898$	−608.216	−	677.953i	−0.677301	−	0.754959i
$899$	0.0313782	+	0.0543486i	3.49034e−5	+	6.04545e-5i
$900$	7.09567	−	65.2406i	0.00788408	−	0.0724896i
$901$	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
$906$	−877.718	+	184.907i	−0.968783	+	0.204091i
$907$	−750.592	+	433.355i	−0.827555	+	0.477789i	−0.853015	−	0.521887i	$-0.825228\pi$
$907$	−750.592	+	433.355i	−0.827555	+	0.477789i	0.0254599	+	0.999676i	$0.491895\pi$
$908$	206.816	−	91.1856i	0.227771	−	0.100425i
$909$	91.2820			0.100420
$910$	−0.316857	−	196.797i	−0.000348195	−	0.216261i
$911$	−128.713			−0.141288			−0.0706438	−	0.997502i	$-0.522505\pi$
$911$	−128.713			−0.141288			−0.0706438	+	0.997502i	$0.522505\pi$
$912$	82.7898	+	18.2243i	0.0907782	+	0.0199827i
$913$	−1587.51	+	916.552i	−1.73879	+	1.00389i
$914$	−330.025	+	69.5255i	−0.361077	+	0.0760673i
$915$	−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	$0.321690\pi$
$920$	1303.49	+	588.844i	1.41684	+	0.640047i
$921$	−421.935	−	730.813i	−0.458127	−	0.793500i
$922$	354.009	+	394.599i	0.383957	+	0.427982i
$923$	246.515			0.267081
$924$	−1140.04	−	1266.65i	−1.23381	−	1.37083i
$925$			8.57859i			0.00927415i
$926$	−130.183	−	145.109i	−0.140586	−	0.156706i
$927$	−224.778	+	129.776i	−0.242479	+	0.139995i
$928$	104.287	−	58.9595i	0.112378	−	0.0635340i
$929$	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
$934$	−145.212	+	30.5914i	−0.155473	+	0.0327531i
$935$	−607.483	−	1052.19i	−0.649714	−	1.12534i
$936$	−6.65903	−	66.8420i	−0.00711435	−	0.0714124i
$937$		−	1426.29i		−	1.52219i	−0.648641	−	0.761095i	$-0.724662\pi$
$937$		−	1426.29i		−	1.52219i	0.648641	−	0.761095i	$-0.275338\pi$
$938$	−97.3753	+	169.288i	−0.103812	+	0.180477i
$939$		−	281.851i		−	0.300161i
$940$	−249.215	−	565.238i	−0.265123	−	0.601317i
$941$	−635.425	−	1100.59i	−0.675265	−	1.16959i	−0.976391	−	0.216010i	$-0.930696\pi$
$941$	−635.425	−	1100.59i	−0.675265	−	1.16959i	0.301126	−	0.953584i	$-0.402638\pi$
$942$	−1632.24	+	343.860i	−1.73274	+	0.365031i
$943$	−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	−0.492646	−	0.870230i	$-0.663970\pi$
$947$	−1413.50	−	816.086i	−1.49261	−	0.861759i	−0.999964	+	0.00847064i	$0.997304\pi$
$948$	−34.3619	+	315.938i	−0.0362467	+	0.333268i
$949$	149.871	−	86.5280i	0.157925	−	0.0911781i
$950$	13.2303	+	14.7472i	0.0139266	+	0.0155234i
$951$			832.098i			0.874972i
$952$	−711.803	−	519.340i	−0.747693	−	0.545525i
$953$	95.9158			0.100646			0.0503231	−	0.998733i	$-0.483975\pi$
$953$	95.9158			0.100646			0.0503231	+	0.998733i	$0.483975\pi$
$954$	−176.425	+	158.277i	−0.184932	+	0.165909i
$955$	−304.850	−	528.015i	−0.319215	−	0.552896i
$956$	108.638	−	998.864i	0.113638	−	1.04484i
$957$	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
$962$	1.81012	+	8.59229i	0.00188162	+	0.00893170i
$963$	238.849	−	137.899i	0.248025	−	0.143198i
$964$	181.451	+	411.545i	0.188227	+	0.426914i
$965$	−284.759			−0.295087
$966$	1706.99	−	989.199i	1.76707	−	1.02402i
$967$	1419.97			1.46843			0.734216	−	0.678916i	$-0.237550\pi$
$967$	1419.97			1.46843			0.734216	+	0.678916i	$0.237550\pi$
$968$	−157.751	−	1583.48i	−0.162966	−	1.63582i
$969$	72.1956	−	41.6822i	0.0745053	−	0.0430157i
$970$	250.734	+	1190.19i	0.258488	+	1.22700i
$971$	−329.817	+	571.261i	−0.339668	+	0.588322i	−0.984370	−	0.176112i	$-0.943648\pi$
$971$	−329.817	+	571.261i	−0.339668	+	0.588322i	0.644702	+	0.764434i	$0.276981\pi$
$972$	−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
$976$	−1036.85	+	1134.92i	−1.06234	+	1.16283i
$977$	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	$0.397606\pi$
$978$	1217.19	−	1091.99i	1.24457	−	1.11655i
$979$	−1584.07			−1.61804
$980$	425.439	+	731.433i	0.434122	+	0.746360i
$981$		−	135.723i		−	0.138352i
$982$	−117.311	+	105.244i	−0.119461	+	0.107173i
$983$	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	$0.297050\pi$
$984$	787.867	−	1744.06i	0.800678	−	1.77242i
$985$	−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
$990$	82.0964	+	389.697i	0.0829257	+	0.393633i
$991$	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	$0.566708\pi$
$992$	−0.462106	−	0.272396i	−0.000465833	−	0.000274593i
$993$			260.472i			0.262308i
$994$	−917.075	+	531.444i	−0.922610	+	0.534652i
$995$			292.237i			0.293706i
$996$	1276.40	−	562.768i	1.28153	−	0.565029i
$997$	−53.4480	−	92.5746i	−0.0536088	−	0.0928532i	0.837976	−	0.545708i	$-0.183739\pi$
$997$	−53.4480	−	92.5746i	−0.0536088	−	0.0928532i	−0.891584	+	0.452854i	$0.850406\pi$
$998$	138.503	+	657.448i	0.138781	+	0.658765i
$999$	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.5.5	✓	28
4.3	odd	2		224.3.n.a.145.4		28
7.2	even	3		392.3.h.a.293.11		28
7.3	odd	6	inner	56.3.j.a.45.14	yes	28
7.4	even	3		392.3.j.e.325.14		28
7.5	odd	6		392.3.h.a.293.12		28
7.6	odd	2		392.3.j.e.117.5		28
8.3	odd	2		224.3.n.a.145.11		28
8.5	even	2	inner	56.3.j.a.5.14	yes	28
28.3	even	6		224.3.n.a.17.11		28
28.19	even	6		1568.3.h.a.881.7		28
28.23	odd	6		1568.3.h.a.881.21		28
56.3	even	6		224.3.n.a.17.4		28
56.5	odd	6		392.3.h.a.293.9		28
56.13	odd	2		392.3.j.e.117.14		28
56.19	even	6		1568.3.h.a.881.22		28
56.37	even	6		392.3.h.a.293.10		28
56.45	odd	6	inner	56.3.j.a.45.5	yes	28
56.51	odd	6		1568.3.h.a.881.8		28
56.53	even	6		392.3.j.e.325.5		28

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

\(f(q)\)	\(=\)	\(q+(-1.33557 - 1.48871i) q^{2} +(1.70138 + 2.94687i) q^{3} +(-0.432496 + 3.97655i) q^{4} +(-2.15858 + 3.73877i) q^{5} +(2.11472 - 6.46862i) q^{6} +(-1.43197 + 6.85197i) q^{7} +(6.49755 - 4.66711i) q^{8} +(-1.28938 + 2.23327i) q^{9} +O(q^{10})\)	\(q+(-1.33557 - 1.48871i) q^{2} +(1.70138 + 2.94687i) q^{3} +(-0.432496 + 3.97655i) 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} +(8.44888 - 1.77990i) q^{10} +(15.4899 - 8.94308i) q^{11} +(-12.4542 + 5.49111i) q^{12} -3.25607 q^{13} +(12.1131 - 7.01951i) q^{14} -14.6903 q^{15} +(-15.6259 - 3.43968i) q^{16} +(-13.6263 + 7.86717i) q^{17} +(5.04674 - 1.06319i) 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} +(24.8082 + 11.2069i) q^{24} +(3.18105 + 5.50975i) q^{25} +(4.34871 + 4.84733i) q^{26} +21.8499 q^{27} +(-26.6279 - 8.65775i) q^{28} -3.74374i q^{29} +(19.6199 + 21.8695i) q^{30} +(-0.0145172 + 0.00838150i) q^{31} +(15.7488 + 27.8563i) 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} +(3.04720 - 0.641947i) q^{38} +(-5.53981 - 9.59523i) q^{39} +(3.42377 + 34.3672i) q^{40} -70.3018i q^{41} +(41.2945 + 23.7528i) q^{42} +13.0380i q^{43} +(28.8633 + 65.4641i) q^{44} +(-5.56646 - 9.64139i) q^{45} +(-81.0487 + 17.0743i) 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} +(1.40824 - 12.9479i) q^{52} +(-39.7989 + 22.9779i) q^{53} +(-29.1821 - 32.5281i) q^{54} +77.2174i q^{55} +(22.6746 + 51.2041i) q^{56} -5.29824 q^{57} +(-5.57333 + 5.00004i) q^{58} +(34.3509 + 59.4974i) q^{59} +(6.35348 - 58.4165i) 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} +(-25.0926 - 119.110i) q^{66} +(-12.0808 + 6.97484i) q^{67} +(-25.3909 - 57.5883i) q^{68} +140.921 q^{69} +(0.0973128 + 60.4402i) q^{70} -75.7095 q^{71} +(2.04511 + 20.5284i) q^{72} +(-46.0282 + 26.5744i) q^{73} +(-0.555921 - 2.63886i) 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} +(46.5900 - 50.9968i) q^{80} +(48.7794 + 84.4884i) q^{81} +(-104.659 + 93.8931i) q^{82} -102.487 q^{83} +(-19.7908 - 93.1991i) q^{84} -67.9277i q^{85} +(19.4098 - 17.4132i) q^{86} +(11.0323 - 6.36952i) q^{87} +(58.9078 - 130.401i) 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} +(-14.7484 - 70.0080i) q^{94} +(-3.36100 - 5.82143i) q^{95} +(-55.2944 + 93.8040i) q^{96} +140.869i q^{97} +(30.7519 + 93.0501i) 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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