LMFDB - Embedded newform 56.3.j.a.5.12

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			5.12
Character	$\chi$	$=$	56.5
Dual form			56.3.j.a.45.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54685 + 1.26777i) q^{2} +(0.126628 + 0.219326i) q^{3} +(0.785498 + 3.92212i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 + 0.499801i) q^{6} +(2.89466 - 6.37346i) q^{7} +(-3.75731 + 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +O(q^{10})$	\(q+(1.54685 + 1.26777i) q^{2} +(0.126628 + 0.219326i) q^{3} +(0.785498 + 3.92212i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 + 0.499801i) q^{6} +(2.89466 - 6.37346i) q^{7} +(-3.75731 + 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +(-6.68405 + 2.52070i) q^{10} +(6.82675 - 3.94142i) q^{11} +(-0.760757 + 0.668930i) q^{12} -18.1529 q^{13} +(12.5577 - 6.18902i) q^{14} -0.904575 q^{15} +(-14.7660 + 6.16163i) q^{16} +(-8.26180 + 4.76995i) q^{17} +(16.7221 - 6.30626i) q^{18} +(12.4094 - 21.4938i) q^{19} +(-13.5349 - 4.57472i) q^{20} +(1.76441 - 0.172184i) q^{21} +(15.5568 + 2.55798i) q^{22} +(2.14949 - 3.72303i) q^{23} +(-2.02483 + 0.0702677i) q^{24} +(6.12120 + 10.6022i) q^{25} +(-28.0798 - 23.0138i) q^{26} +4.54237 q^{27} +(27.2712 + 6.34684i) q^{28} +28.3630i q^{29} +(-1.39924 - 1.14680i) q^{30} +(-28.2372 + 16.3027i) q^{31} +(-30.6523 - 9.18881i) q^{32} +(1.72891 + 0.998189i) q^{33} +(-18.8270 - 3.09569i) q^{34} +(14.5452 + 20.3362i) q^{35} +(33.8616 + 11.4450i) q^{36} +(-25.9006 - 14.9537i) q^{37} +(46.4448 - 17.5153i) q^{38} +(-2.29867 - 3.98141i) q^{39} +(-15.1368 - 24.2356i) q^{40} +45.2606i q^{41} +(2.94757 + 1.97053i) q^{42} +24.9109i q^{43} +(20.8211 + 23.6793i) q^{44} +(15.9585 + 27.6409i) q^{45} +(8.04492 - 3.03391i) q^{46} +(44.0432 + 25.4284i) q^{47} +(-3.22119 - 2.45833i) q^{48} +(-32.2419 - 36.8979i) q^{49} +(-3.97264 + 24.1604i) q^{50} +(-2.09235 - 1.20802i) q^{51} +(-14.2591 - 71.1978i) q^{52} +(54.3930 - 31.4038i) q^{53} +(7.02636 + 5.75869i) q^{54} +28.1558i q^{55} +(34.1381 + 44.3913i) q^{56} +6.28554 q^{57} +(-35.9579 + 43.8733i) q^{58} +(-37.0048 - 64.0942i) q^{59} +(-0.710541 - 3.54785i) q^{60} +(25.2994 - 43.8198i) q^{61} +(-64.3469 - 10.5804i) q^{62} +(-36.3890 - 50.8770i) q^{63} +(-35.7653 - 53.0740i) q^{64} +(32.4191 - 56.1515i) q^{65} +(1.40890 + 3.73592i) q^{66} +(-108.673 + 62.7422i) q^{67} +(-25.1979 - 28.6569i) q^{68} +1.08875 q^{69} +(-3.28249 + 49.8971i) q^{70} -5.33822 q^{71} +(37.8691 + 60.6326i) q^{72} +(-23.6569 + 13.6583i) q^{73} +(-21.1065 - 55.9674i) q^{74} +(-1.55023 + 2.68508i) q^{75} +(94.0487 + 31.7880i) q^{76} +(-5.35941 - 54.9191i) q^{77} +(1.49183 - 9.07283i) q^{78} +(51.5380 - 89.2664i) q^{79} +(7.31096 - 56.6789i) q^{80} +(-39.6362 - 68.6519i) q^{81} +(-57.3802 + 70.0114i) q^{82} +51.5695 q^{83} +(2.06127 + 6.78497i) q^{84} -34.0744i q^{85} +(-31.5814 + 38.5334i) q^{86} +(-6.22075 + 3.59155i) q^{87} +(2.18715 + 63.0248i) q^{88} +(133.222 + 76.9158i) q^{89} +(-10.3570 + 62.9880i) q^{90} +(-52.5464 + 115.697i) q^{91} +(16.2906 + 5.50613i) q^{92} +(-7.15123 - 4.12877i) q^{93} +(35.8909 + 95.1708i) q^{94} +(44.3238 + 76.7711i) q^{95} +(-1.86610 - 7.88642i) q^{96} -47.0436i q^{97} +(-3.09519 - 97.9511i) q^{98} -70.4400i 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 $

$2$	1.54685	+	1.26777i	0.773426	+	0.633887i
$2$	1.54685	+	1.26777i	0.773426	+	0.633887i
$3$	0.126628	+	0.219326i	0.0422093	+	0.0731087i	0.886358	−	0.463000i	$-0.153227\pi$
$3$	0.126628	+	0.219326i	0.0422093	+	0.0731087i	−0.844149	+	0.536109i	$0.819894\pi$
$4$	0.785498	+	3.92212i	0.196374	+	0.980529i
$5$	−1.78589	+	3.09325i	−0.357178	+	0.618650i	−0.987488	−	0.157693i	$-0.949594\pi$
$5$	−1.78589	+	3.09325i	−0.357178	+	0.618650i	0.630310	+	0.776343i	$0.282928\pi$
$6$	−0.0821813	+	0.499801i	−0.0136969	+	0.0833001i
$7$	2.89466	−	6.37346i	0.413522	−	0.910494i
$7$	2.89466	−	6.37346i	0.413522	−	0.910494i
$8$	−3.75731	+	7.06276i	−0.469664	+	0.882845i
$9$	4.46793	−	7.73868i	0.496437	−	0.859854i
$10$	−6.68405	+	2.52070i	−0.668405	+	0.252070i
$11$	6.82675	−	3.94142i	0.620613	−	0.358311i	−0.156494	−	0.987679i	$-0.550019\pi$
$11$	6.82675	−	3.94142i	0.620613	−	0.358311i	0.777108	+	0.629368i	$0.216686\pi$
$12$	−0.760757	+	0.668930i	−0.0633964	+	0.0557442i
$13$	−18.1529			−1.39638			−0.698189	−	0.715914i	$-0.746010\pi$
$13$	−18.1529			−1.39638			−0.698189	+	0.715914i	$0.746010\pi$
$14$	12.5577	−	6.18902i	0.896979	−	0.442073i
$15$	−0.904575			−0.0603050
$16$	−14.7660	+	6.16163i	−0.922874	+	0.385102i
$17$	−8.26180	+	4.76995i	−0.485988	+	0.280585i	−0.722909	−	0.690944i	$-0.757195\pi$
$17$	−8.26180	+	4.76995i	−0.485988	+	0.280585i	0.236920	+	0.971529i	$0.423862\pi$
$18$	16.7221	−	6.30626i	0.929007	−	0.350348i
$19$	12.4094	−	21.4938i	0.653129	−	1.13125i	−0.329231	−	0.944250i	$-0.606789\pi$
$19$	12.4094	−	21.4938i	0.653129	−	1.13125i	0.982359	−	0.187003i	$-0.0598773\pi$
$20$	−13.5349	−	4.57472i	−0.676745	−	0.228736i
$21$	1.76441	−	0.172184i	0.0840196	−	0.00819925i
$22$	15.5568	+	2.55798i	0.707127	+	0.116272i
$23$	2.14949	−	3.72303i	0.0934563	−	0.161871i	−0.815507	−	0.578747i	$-0.803542\pi$
$23$	2.14949	−	3.72303i	0.0934563	−	0.161871i	0.908963	+	0.416876i	$0.136875\pi$
$24$	−2.02483	+	0.0702677i	−0.0843679	+	0.00292782i
$25$	6.12120	+	10.6022i	0.244848	+	0.424089i
$26$	−28.0798	−	23.0138i	−1.07999	−	0.885145i
$27$	4.54237			0.168236
$28$	27.2712	+	6.34684i	0.973971	+	0.226673i
$29$			28.3630i			0.978035i	0.872274	+	0.489017i	$0.162644\pi$
$29$			28.3630i			0.978035i	−0.872274	+	0.489017i	$0.837356\pi$
$30$	−1.39924	−	1.14680i	−0.0466414	−	0.0382265i
$31$	−28.2372	+	16.3027i	−0.910876	+	0.525895i	−0.880713	−	0.473650i	$-0.842936\pi$
$31$	−28.2372	+	16.3027i	−0.910876	+	0.525895i	−0.0301634	+	0.999545i	$0.509603\pi$
$32$	−30.6523	−	9.18881i	−0.957885	−	0.287150i
$33$	1.72891	+	0.998189i	0.0523914	+	0.0302482i
$34$	−18.8270	−	3.09569i	−0.553735	−	0.0910497i
$35$	14.5452	+	20.3362i	0.415576	+	0.581034i
$36$	33.8616	+	11.4450i	0.940599	+	0.317917i
$37$	−25.9006	−	14.9537i	−0.700017	−	0.404155i	0.107337	−	0.994223i	$-0.465768\pi$
$37$	−25.9006	−	14.9537i	−0.700017	−	0.404155i	−0.807354	+	0.590068i	$0.799101\pi$
$38$	46.4448	−	17.5153i	1.22223	−	0.460930i
$39$	−2.29867	−	3.98141i	−0.0589402	−	0.102087i
$40$	−15.1368	−	24.2356i	−0.378419	−	0.605890i
$41$			45.2606i			1.10392i	0.833872	+	0.551958i	$0.186119\pi$
$41$			45.2606i			1.10392i	−0.833872	+	0.551958i	$0.813881\pi$
$42$	2.94757	+	1.97053i	0.0701803	+	0.0469174i
$43$			24.9109i			0.579323i	0.957129	+	0.289661i	$0.0935427\pi$
$43$			24.9109i			0.579323i	−0.957129	+	0.289661i	$0.906457\pi$
$44$	20.8211	+	23.6793i	0.473207	+	0.538166i
$45$	15.9585	+	27.6409i	0.354632	+	0.614242i
$46$	8.04492	−	3.03391i	0.174889	−	0.0659545i
$47$	44.0432	+	25.4284i	0.937090	+	0.541029i	0.889047	−	0.457816i	$-0.151368\pi$
$47$	44.0432	+	25.4284i	0.937090	+	0.541029i	0.0480430	+	0.998845i	$0.484702\pi$
$48$	−3.22119	−	2.45833i	−0.0671082	−	0.0512153i
$49$	−32.2419	−	36.8979i	−0.657998	−	0.753019i
$50$	−3.97264	+	24.1604i	−0.0794529	+	0.483207i
$51$	−2.09235	−	1.20802i	−0.0410265	−	0.0236867i
$52$	−14.2591	−	71.1978i	−0.274213	−	1.36919i
$53$	54.3930	−	31.4038i	1.02628	−	0.592525i	0.110365	−	0.993891i	$-0.464798\pi$
$53$	54.3930	−	31.4038i	1.02628	−	0.592525i	0.915918	+	0.401366i	$0.131465\pi$
$54$	7.02636	+	5.75869i	0.130118	+	0.106642i
$55$			28.1558i			0.511924i
$56$	34.1381	+	44.3913i	0.609609	+	0.792702i
$57$	6.28554			0.110273
$58$	−35.9579	+	43.8733i	−0.619963	+	0.756437i
$59$	−37.0048	−	64.0942i	−0.627200	−	1.08634i	−0.988111	−	0.153741i	$-0.950868\pi$
$59$	−37.0048	−	64.0942i	−0.627200	−	1.08634i	0.360912	−	0.932600i	$-0.382466\pi$
$60$	−0.710541	−	3.54785i	−0.0118424	−	0.0591308i
$61$	25.2994	−	43.8198i	0.414743	−	0.718357i	−0.580658	−	0.814148i	$-0.697205\pi$
$61$	25.2994	−	43.8198i	0.414743	−	0.718357i	0.995401	+	0.0957908i	$0.0305380\pi$
$62$	−64.3469	−	10.5804i	−1.03785	−	0.170652i
$63$	−36.3890	−	50.8770i	−0.577604	−	0.807571i
$64$	−35.7653	−	53.0740i	−0.558832	−	0.829281i
$65$	32.4191	−	56.1515i	0.498755	−	0.863869i
$66$	1.40890	+	3.73592i	0.0213469	+	0.0566049i
$67$	−108.673	+	62.7422i	−1.62198	+	0.936451i	−0.635592	+	0.772025i	$0.719244\pi$
$67$	−108.673	+	62.7422i	−1.62198	+	0.936451i	−0.986389	+	0.164426i	$0.947423\pi$
$68$	−25.1979	−	28.6569i	−0.370558	−	0.421426i
$69$	1.08875			0.0157789
$70$	−3.28249	+	49.8971i	−0.0468927	+	0.712815i
$71$	−5.33822			−0.0751863			−0.0375931	−	0.999293i	$-0.511969\pi$
$71$	−5.33822			−0.0751863			−0.0375931	+	0.999293i	$0.511969\pi$
$72$	37.8691	+	60.6326i	0.525960	+	0.842119i
$73$	−23.6569	+	13.6583i	−0.324067	+	0.187100i	−0.653204	−	0.757182i	$-0.726576\pi$
$73$	−23.6569	+	13.6583i	−0.324067	+	0.187100i	0.329137	+	0.944282i	$0.393242\pi$
$74$	−21.1065	−	55.9674i	−0.285223	−	0.756316i
$75$	−1.55023	+	2.68508i	−0.0206697	+	0.0358010i
$76$	94.0487	+	31.7880i	1.23748	+	0.418263i
$77$	−5.35941	−	54.9191i	−0.0696027	−	0.713234i
$78$	1.49183	−	9.07283i	0.0191260	−	0.116318i
$79$	51.5380	−	89.2664i	0.652380	−	1.12995i	−0.330164	−	0.943924i	$-0.607104\pi$
$79$	51.5380	−	89.2664i	0.652380	−	1.12995i	0.982544	−	0.186031i	$-0.0595626\pi$
$80$	7.31096	−	56.6789i	0.0913870	−	0.708486i
$81$	−39.6362	−	68.6519i	−0.489336	−	0.847554i
$82$	−57.3802	+	70.0114i	−0.699758	+	0.853797i
$83$	51.5695			0.621319			0.310660	−	0.950521i	$-0.399450\pi$
$83$	51.5695			0.621319			0.310660	+	0.950521i	$0.399450\pi$
$84$	2.06127	+	6.78497i	0.0245389	+	0.0807735i
$85$		−	34.0744i		−	0.400876i
$86$	−31.5814	+	38.5334i	−0.367225	+	0.448063i
$87$	−6.22075	+	3.59155i	−0.0715029	+	0.0412822i
$88$	2.18715	+	63.0248i	0.0248540	+	0.716191i
$89$	133.222	+	76.9158i	1.49688	+	0.864222i	0.999994	−	0.00359545i	$-0.00114447\pi$
$89$	133.222	+	76.9158i	1.49688	+	0.864222i	0.496883	+	0.867818i	$0.334478\pi$
$90$	−10.3570	+	62.9880i	−0.115078	+	0.699867i
$91$	−52.5464	+	115.697i	−0.577433	+	1.27139i
$92$	16.2906	+	5.50613i	0.177072	+	0.0598493i
$93$	−7.15123	−	4.12877i	−0.0768950	−	0.0443953i
$94$	35.8909	+	95.1708i	0.381818	+	1.01245i
$95$	44.3238	+	76.7711i	0.466566	+	0.808117i
$96$	−1.86610	−	7.88642i	−0.0194385	−	0.0821502i
$97$		−	47.0436i		−	0.484986i	−0.970153	−	0.242493i	$-0.922035\pi$
$97$		−	47.0436i		−	0.484986i	0.970153	−	0.242493i	$-0.0779651\pi$
$98$	−3.09519	−	97.9511i	−0.0315836	−	0.999501i
$99$		−	70.4400i		−	0.711516i
$100$	−36.7750	+	32.3361i	−0.367750	+	0.323361i
$101$	74.6727	+	129.337i	0.739333	+	1.28056i	0.952796	+	0.303612i	$0.0981926\pi$
$101$	74.6727	+	129.337i	0.739333	+	1.28056i	−0.213462	+	0.976951i	$0.568474\pi$
$102$	−1.70506	−	4.52125i	−0.0167163	−	0.0443260i
$103$	−17.1847	−	9.92160i	−0.166842	−	0.0963262i	0.414254	−	0.910161i	$-0.364043\pi$
$103$	−17.1847	−	9.92160i	−0.166842	−	0.0963262i	−0.581096	+	0.813835i	$0.697376\pi$
$104$	68.2061	−	128.210i	0.655827	−	1.23279i
$105$	−2.61843	+	5.76527i	−0.0249375	+	0.0549073i
$106$	123.951	+	20.3810i	1.16935	+	0.192274i
$107$	−7.91877	−	4.57190i	−0.0740072	−	0.0427281i	0.462540	−	0.886599i	$-0.346938\pi$
$107$	−7.91877	−	4.57190i	−0.0740072	−	0.0427281i	−0.536547	+	0.843870i	$0.680272\pi$
$108$	3.56802	+	17.8157i	0.0330372	+	0.164960i
$109$	103.229	−	59.5992i	0.947053	−	0.546781i	0.0548888	−	0.998492i	$-0.482520\pi$
$109$	103.229	−	59.5992i	0.947053	−	0.546781i	0.892164	+	0.451711i	$0.149186\pi$
$110$	−35.6952	+	43.5528i	−0.324502	+	0.395935i
$111$		−	7.57425i		−	0.0682365i
$112$	−3.47160	+	111.946i	−0.0309965	+	0.999519i
$113$	−124.011			−1.09744			−0.548720	−	0.836006i	$-0.684885\pi$
$113$	−124.011			−1.09744			−0.548720	+	0.836006i	$0.684885\pi$
$114$	9.72279	+	7.96864i	0.0852876	+	0.0699003i
$115$	7.67752	+	13.2979i	0.0667611	+	0.115634i
$116$	−111.243	+	22.2791i	−0.958991	+	0.192061i
$117$	−81.1059	+	140.480i	−0.693213	+	1.20068i
$118$	24.0160	−	146.058i	0.203526	−	1.23778i
$119$	6.48601	+	66.4636i	0.0545043	+	0.558518i
$120$	3.39877	−	6.38880i	0.0283231	−	0.0532400i
$121$	−29.4303	+	50.9749i	−0.243226	+	0.421280i
$122$	94.6879	−	35.7088i	0.776130	−	0.292695i
$123$	−9.92683	+	5.73126i	−0.0807059	+	0.0465956i
$124$	−86.1215	−	97.9437i	−0.694528	−	0.789868i
$125$	−133.022			−1.06417
$126$	8.21211	−	124.832i	0.0651755	−	0.990732i
$127$	−57.6144			−0.453656			−0.226828	−	0.973935i	$-0.572836\pi$
$127$	−57.6144			−0.453656			−0.226828	+	0.973935i	$0.572836\pi$
$128$	11.9623	−	127.440i	0.0934551	−	0.995623i
$129$	−5.46361	+	3.15441i	−0.0423535	+	0.0244528i
$130$	121.335	−	45.7579i	0.933345	−	0.351984i
$131$	62.1497	−	107.646i	0.474425	−	0.821728i	−0.525146	−	0.851012i	$-0.675989\pi$
$131$	62.1497	−	107.646i	0.474425	−	0.821728i	0.999571	+	0.0292837i	$0.00932261\pi$
$132$	−2.55696	+	7.56508i	−0.0193709	+	0.0573112i
$133$	−101.069	−	141.308i	−0.759915	−	1.06247i
$134$	−247.644	−	40.7196i	−1.84809	−	0.303877i
$135$	−8.11216	+	14.0507i	−0.0600901	+	0.104079i
$136$	−2.64691	−	76.2733i	−0.0194626	−	0.560833i
$137$	84.7404	+	146.775i	0.618543	+	1.07135i	0.989752	+	0.142799i	$0.0456102\pi$
$137$	84.7404	+	146.775i	0.618543	+	1.07135i	−0.371208	+	0.928550i	$0.621056\pi$
$138$	1.68413	+	1.38028i	0.0122038	+	0.0100020i
$139$	266.497			1.91725			0.958624	−	0.284677i	$-0.0918862\pi$
$139$	266.497			1.91725			0.958624	+	0.284677i	$0.0918862\pi$
$140$	−68.3357	+	73.0219i	−0.488112	+	0.521585i
$141$			12.8798i			0.0913459i
$142$	−8.25744	−	6.76766i	−0.0581510	−	0.0476596i
$143$	−123.925	+	71.5483i	−0.866610	+	0.500338i
$144$	−18.2905	+	141.799i	−0.127018	+	0.984715i
$145$	−87.7339	−	50.6532i	−0.605061	−	0.349332i
$146$	−53.9093	−	8.86421i	−0.369242	−	0.0607138i
$147$	4.00996	−	11.7438i	0.0272786	−	0.0798899i
$148$	38.3054	−	113.331i	0.258820	−	0.765753i
$149$	−26.6902	−	15.4096i	−0.179129	−	0.103420i	0.407754	−	0.913092i	$-0.366312\pi$
$149$	−26.6902	−	15.4096i	−0.179129	−	0.103420i	−0.586883	+	0.809672i	$0.699645\pi$
$150$	−5.80205	+	2.18807i	−0.0386803	+	0.0145872i
$151$	−11.7448	−	20.3425i	−0.0777800	−	0.134719i	0.824512	−	0.565845i	$-0.191450\pi$
$151$	−11.7448	−	20.3425i	−0.0777800	−	0.134719i	−0.902292	+	0.431126i	$0.858116\pi$
$152$	105.179	+	168.404i	0.691970	+	1.10792i
$153$			85.2473i			0.557172i
$154$	61.3347	−	91.7461i	0.398278	−	0.595754i
$155$		−	116.460i		−	0.751352i
$156$	13.8099	−	12.1430i	0.0885253	−	0.0778399i
$157$	63.8147	+	110.530i	0.406463	+	0.704015i	0.994491	−	0.104826i	$-0.0334287\pi$
$157$	63.8147	+	110.530i	0.406463	+	0.704015i	−0.588028	+	0.808841i	$0.700095\pi$
$158$	192.891	−	72.7434i	1.22083	−	0.460401i
$159$	13.7754	+	7.95320i	0.0866374	+	0.0500202i
$160$	83.1650	−	78.4052i	0.519781	−	0.490032i
$161$	−17.5065	−	24.4766i	−0.108736	−	0.152029i
$162$	25.7238	−	156.444i	0.158789	−	0.965704i
$163$	138.291	+	79.8421i	0.848409	+	0.489829i	0.860114	−	0.510103i	$-0.170393\pi$
$163$	138.291	+	79.8421i	0.848409	+	0.489829i	−0.0117050	+	0.999931i	$0.503726\pi$
$164$	−177.517	+	35.5521i	−1.08242	+	0.216781i
$165$	−6.17530	+	3.56531i	−0.0374261	+	0.0216080i
$166$	79.7704	+	65.3785i	0.480544	+	0.393846i
$167$		−	142.792i		−	0.855042i	−0.904005	−	0.427521i	$-0.859387\pi$
$167$		−	142.792i		−	0.855042i	0.904005	−	0.427521i	$-0.140613\pi$
$168$	−5.41334	+	13.1086i	−0.0322223	+	0.0780272i
$169$	160.528			0.949869
$170$	43.1987	−	52.7081i	0.254110	−	0.310048i
$171$	−110.889	−	192.066i	−0.648474	−	1.12319i
$172$	−97.7033	+	19.5674i	−0.568043	+	0.113764i
$173$	−97.8898	+	169.550i	−0.565837	+	0.980059i	0.431134	+	0.902288i	$0.358114\pi$
$173$	−97.8898	+	169.550i	−0.565837	+	0.980059i	−0.996971	+	0.0777710i	$0.975220\pi$
$174$	−14.1758	−	2.33091i	−0.0814704	−	0.0133960i
$175$	85.2916	−	8.32338i	0.487380	−	0.0475622i
$176$	−76.5181	+	100.263i	−0.434762	+	0.569675i
$177$	9.37168	−	16.2322i	0.0529474	−	0.0917075i
$178$	108.563	+	287.873i	0.609904	+	1.61726i
$179$	−129.477	+	74.7535i	−0.723334	+	0.417617i	−0.815979	−	0.578082i	$-0.803801\pi$
$179$	−129.477	+	74.7535i	−0.723334	+	0.417617i	0.0926444	+	0.995699i	$0.470468\pi$
$180$	−95.8754	+	84.3028i	−0.532641	+	0.468349i
$181$	−91.2994			−0.504417			−0.252208	−	0.967673i	$-0.581157\pi$
$181$	−91.2994			−0.504417			−0.252208	+	0.967673i	$0.581157\pi$
$182$	−227.959	+	112.349i	−1.25252	+	0.617300i
$183$	12.8144			0.0700242
$184$	18.2186	+	29.1700i	0.0990141	+	0.158532i
$185$	92.5114	−	53.4115i	0.500062	−	0.288711i
$186$	−5.82755	−	15.4527i	−0.0313309	−	0.0830792i
$187$	−37.6008	+	65.1265i	−0.201074	+	0.348270i
$188$	−65.1372	+	192.717i	−0.346474	+	1.02509i
$189$	13.1486	−	28.9506i	0.0695693	−	0.153178i
$190$	−28.7661	+	174.946i	−0.151400	+	0.920769i
$191$	−13.9140	+	24.0997i	−0.0728480	+	0.126176i	−0.900148	−	0.435583i	$-0.856542\pi$
$191$	−13.9140	+	24.0997i	−0.0728480	+	0.126176i	0.827300	+	0.561760i	$0.189875\pi$
$192$	7.11162	−	14.5649i	0.0370397	−	0.0758589i
$193$	−121.192	−	209.911i	−0.627938	−	1.08762i	−0.987965	−	0.154678i	$-0.950566\pi$
$193$	−121.192	−	209.911i	−0.627938	−	1.08762i	0.360027	−	0.932942i	$-0.382767\pi$
$194$	59.6407	−	72.7695i	0.307426	−	0.375100i
$195$	16.4207			0.0842085
$196$	119.392	−	155.440i	0.609143	−	0.793060i
$197$			94.7050i			0.480736i	0.970682	+	0.240368i	$0.0772682\pi$
$197$			94.7050i			0.480736i	−0.970682	+	0.240368i	$0.922732\pi$
$198$	89.3021	−	108.960i	0.451021	−	0.550304i
$199$	267.738	−	154.579i	1.34542	−	0.776778i	0.357823	−	0.933790i	$-0.383519\pi$
$199$	267.738	−	154.579i	1.34542	−	0.776778i	0.987597	+	0.157011i	$0.0501859\pi$
$200$	−97.8802	+	3.39674i	−0.489401	+	0.0169837i
$201$	−27.5220	−	15.8899i	−0.136926	−	0.0790540i
$202$	−48.4624	+	294.733i	−0.239913	+	1.45907i
$203$	180.770	+	82.1012i	0.890494	+	0.404439i
$204$	3.09445	−	9.15534i	0.0151689	−	0.0448791i
$205$	−140.002	−	80.8304i	−0.682938	−	0.394295i
$206$	−14.0039	−	37.1336i	−0.0679799	−	0.180260i
$207$	−19.2076	−	33.2685i	−0.0927903	−	0.160717i
$208$	268.045	−	111.851i	1.28868	−	0.537747i
$209$		−	195.644i		−	0.936094i
$210$	−11.3594	+	5.59843i	−0.0540923	+	0.0266592i
$211$			125.864i			0.596514i	0.954486	+	0.298257i	$0.0964052\pi$
$211$			125.864i			0.596514i	−0.954486	+	0.298257i	$0.903595\pi$
$212$	165.895	+	188.668i	0.782523	+	0.889943i
$213$	−0.675969	−	1.17081i	−0.00317356	−	0.00549677i
$214$	−6.45302	−	17.1113i	−0.0301543	−	0.0799592i
$215$	−77.0556	−	44.4881i	−0.358398	−	0.206921i
$216$	−17.0671	+	32.0817i	−0.0790142	+	0.148526i
$217$	22.1679	+	227.159i	0.102156	+	1.04682i
$218$	235.238	+	38.6797i	1.07907	+	0.177430i
$219$	−5.99125	−	3.45905i	−0.0273573	−	0.0157947i
$220$	−110.430	+	22.1163i	−0.501956	+	0.100529i
$221$	149.976	−	86.5885i	0.678623	−	0.391803i
$222$	9.60244	−	11.7162i	0.0432542	−	0.0527759i
$223$			8.94619i			0.0401174i	0.999799	+	0.0200587i	$0.00638532\pi$
$223$			8.94619i			0.0401174i	−0.999799	+	0.0200587i	$0.993615\pi$
$224$	−147.293	+	168.763i	−0.657556	+	0.753406i
$225$	109.396			0.486206
$226$	−191.826	−	157.218i	−0.848788	−	0.695653i
$227$	−136.347	−	236.160i	−0.600647	−	1.04035i	−0.992723	−	0.120419i	$-0.961576\pi$
$227$	−136.347	−	236.160i	−0.600647	−	1.04035i	0.392076	−	0.919933i	$-0.371757\pi$
$228$	4.93727	+	24.6526i	0.0216547	+	0.108125i
$229$	165.611	−	286.846i	0.723191	−	1.25260i	−0.236523	−	0.971626i	$-0.576008\pi$
$229$	165.611	−	286.846i	0.723191	−	1.25260i	0.959714	−	0.280978i	$-0.0906588\pi$
$230$	−4.98269	+	30.3032i	−0.0216639	+	0.131753i
$231$	11.3665	−	8.12975i	0.0492058	−	0.0351937i
$232$	−200.321	−	106.569i	−0.863453	−	0.459347i
$233$	−79.1185	+	137.037i	−0.339564	+	0.588143i	−0.984351	−	0.176220i	$-0.943613\pi$
$233$	−79.1185	+	137.037i	−0.339564	+	0.588143i	0.644786	+	0.764363i	$0.276946\pi$
$234$	−303.555	+	114.477i	−1.29724	+	0.489218i
$235$	−157.313	+	90.8245i	−0.669416	+	0.386487i
$236$	222.318	−	195.483i	0.942023	−	0.828317i
$237$	26.1046			0.110146
$238$	−74.2279	+	111.032i	−0.311882	+	0.466521i
$239$	48.9981			0.205013			0.102507	−	0.994732i	$-0.467314\pi$
$239$	48.9981			0.205013			0.102507	+	0.994732i	$0.467314\pi$
$240$	13.3569	−	5.57365i	0.0556539	−	0.0232235i
$241$	170.914	−	98.6771i	0.709186	−	0.409449i	−0.101574	−	0.994828i	$-0.532388\pi$
$241$	170.914	−	98.6771i	0.709186	−	0.409449i	0.810759	+	0.585379i	$0.199054\pi$
$242$	−110.149	+	41.5395i	−0.455161	+	0.171651i
$243$	30.4787	−	52.7907i	0.125427	−	0.217246i
$244$	191.739	+	64.8067i	0.785815	+	0.265601i
$245$	171.715	−	33.8367i	0.700878	−	0.138109i
$246$	−22.6213	−	3.71957i	−0.0919564	−	0.0151202i
$247$	−225.267	+	390.175i	−0.912014	+	1.57965i
$248$	−9.04662	−	260.687i	−0.0364783	−	1.05116i
$249$	6.53014	+	11.3105i	0.0262255	+	0.0454239i
$250$	−205.765	−	168.641i	−0.823059	−	0.674565i
$251$	−315.497			−1.25696			−0.628480	−	0.777826i	$-0.716323\pi$
$251$	−315.497			−1.25696			−0.628480	+	0.777826i	$0.716323\pi$
$252$	170.962	−	182.686i	0.678421	−	0.724944i
$253$		−	33.8883i		−	0.133946i
$254$	−89.1209	−	73.0420i	−0.350870	−	0.287567i
$255$	7.47341	−	4.31478i	0.0293075	−	0.0169207i
$256$	180.069	−	181.965i	0.703393	−	0.710801i
$257$	−329.533	−	190.256i	−1.28223	−	0.740296i	−0.304974	−	0.952361i	$-0.598648\pi$
$257$	−329.533	−	190.256i	−1.28223	−	0.740296i	−0.977256	+	0.212065i	$0.931981\pi$
$258$	−12.4505	−	2.04721i	−0.0482576	−	0.00793492i
$259$	−170.281	+	121.791i	−0.657454	+	0.470234i
$260$	245.698	+	83.0445i	0.944991	+	0.319402i
$261$	219.492	+	126.724i	0.840967	+	0.485532i
$262$	232.608	−	87.7212i	0.887816	−	0.334814i
$263$	−98.1636	−	170.024i	−0.373246	−	0.646480i	0.616817	−	0.787106i	$-0.288422\pi$
$263$	−98.1636	−	170.024i	−0.373246	−	0.646480i	−0.990063	+	0.140626i	$0.955088\pi$
$264$	−13.5460	+	8.46041i	−0.0513108	+	0.0320470i
$265$			224.335i			0.846547i
$266$	22.8087	−	346.715i	0.0857471	−	1.30344i
$267$			38.9588i			0.145913i
$268$	−331.445	−	376.943i	−1.23673	−	1.40650i
$269$	−51.1557	−	88.6043i	−0.190170	−	0.329384i	0.755137	−	0.655568i	$-0.227571\pi$
$269$	−51.1557	−	88.6043i	−0.190170	−	0.329384i	−0.945306	+	0.326184i	$0.894237\pi$
$270$	−30.3614	+	11.4499i	−0.112450	+	0.0424071i
$271$	−221.981	−	128.161i	−0.819118	−	0.472918i	0.0309944	−	0.999520i	$-0.490133\pi$
$271$	−221.981	−	128.161i	−0.819118	−	0.472918i	−0.850112	+	0.526602i	$0.823466\pi$
$272$	92.6030	−	121.339i	0.340452	−	0.446100i
$273$	−32.0292	+	3.12564i	−0.117323	+	0.0114492i
$274$	−54.9964	+	334.470i	−0.200717	+	1.22070i
$275$	83.5757	+	48.2525i	0.303912	+	0.175464i
$276$	0.855207	+	4.27018i	0.00309858	+	0.0154717i
$277$	170.372	−	98.3646i	0.615063	−	0.355107i	−0.159881	−	0.987136i	$-0.551111\pi$
$277$	170.372	−	98.3646i	0.615063	−	0.355107i	0.774944	+	0.632029i	$0.217778\pi$
$278$	412.232	+	337.858i	1.48285	+	1.21532i
$279$			291.358i			1.04429i
$280$	−198.280	+	26.3197i	−0.708144	+	0.0939990i
$281$	−70.2923			−0.250151			−0.125075	−	0.992147i	$-0.539917\pi$
$281$	−70.2923			−0.250151			−0.125075	+	0.992147i	$0.539917\pi$
$282$	−16.3286	+	19.9231i	−0.0579030	+	0.0706493i
$283$	148.495	+	257.201i	0.524718	+	0.908838i	0.999586	+	0.0287807i	$0.00916244\pi$
$283$	148.495	+	257.201i	0.524718	+	0.908838i	−0.474868	+	0.880057i	$0.657504\pi$
$284$	−4.19316	−	20.9371i	−0.0147647	−	0.0737223i
$285$	−11.2253	+	19.4427i	−0.0393869	+	0.0682201i
$286$	−282.401	−	46.4347i	−0.987416	−	0.162359i
$287$	288.466	+	131.014i	1.00511	+	0.456494i
$288$	−208.062	+	196.154i	−0.722437	+	0.681089i
$289$	−98.9951	+	171.465i	−0.342544	+	0.593303i
$290$	−71.4945	−	189.580i	−0.246533	−	0.653723i
$291$	10.3179	−	5.95704i	0.0354567	−	0.0204709i
$292$	−72.1519	−	82.0565i	−0.247096	−	0.281015i
$293$	−135.561			−0.462665			−0.231333	−	0.972875i	$-0.574309\pi$
$293$	−135.561			−0.462665			−0.231333	+	0.972875i	$0.574309\pi$
$294$	21.0913	−	13.0822i	0.0717391	−	0.0444973i
$295$	264.346			0.896087
$296$	202.931	−	126.744i	0.685579	−	0.428190i
$297$	31.0096	−	17.9034i	0.104409	−	0.0602808i
$298$	−21.7499	−	57.6735i	−0.0729862	−	0.193535i
$299$	−39.0196	+	67.5839i	−0.130500	+	0.226033i
$300$	−11.7489	−	3.97106i	−0.0391630	−	0.0132369i
$301$	158.768	+	72.1084i	0.527470	+	0.239563i
$302$	7.62233	−	46.3566i	0.0252395	−	0.153499i
$303$	−18.9113	+	32.7553i	−0.0624136	+	0.108103i
$304$	−50.8010	+	393.839i	−0.167109	+	1.29552i
$305$	90.3637	+	156.515i	0.296274	+	0.513162i
$306$	−108.074	+	131.865i	−0.353184	+	0.430931i
$307$	−76.2052			−0.248225			−0.124113	−	0.992268i	$-0.539608\pi$
$307$	−76.2052			−0.248225			−0.124113	+	0.992268i	$0.539608\pi$
$308$	211.189	−	64.1590i	0.685679	−	0.208308i
$309$		−	5.02541i		−	0.0162635i
$310$	147.644	−	180.146i	0.476272	−	0.581115i
$311$	−171.554	+	99.0468i	−0.551621	+	0.318479i	−0.749776	−	0.661692i	$-0.769839\pi$
$311$	−171.554	+	99.0468i	−0.551621	+	0.318479i	0.198154	+	0.980171i	$0.436505\pi$
$312$	36.7565	−	1.27556i	0.117809	−	0.00408834i
$313$	−47.9693	−	27.6951i	−0.153257	−	0.0884827i	0.421411	−	0.906870i	$-0.361535\pi$
$313$	−47.9693	−	27.6951i	−0.153257	−	0.0884827i	−0.574667	+	0.818387i	$0.694868\pi$
$314$	−41.4156	+	251.877i	−0.131897	+	0.802155i
$315$	222.362	−	21.6997i	0.705912	−	0.0688881i
$316$	390.596	+	132.019i	1.23606	+	0.417783i
$317$	259.080	+	149.580i	0.817289	+	0.471862i	0.849481	−	0.527620i	$-0.176915\pi$
$317$	259.080	+	149.580i	0.817289	+	0.471862i	−0.0321920	+	0.999482i	$0.510249\pi$
$318$	11.2256	+	29.7665i	0.0353005	+	0.0936052i
$319$	111.791	+	193.627i	0.350441	+	0.606981i
$320$	228.044	−	15.8467i	0.712637	−	0.0495210i
$321$		−	2.31572i		−	0.00721409i
$322$	3.95080	−	60.0560i	0.0122696	−	0.186509i
$323$			236.770i			0.733034i
$324$	238.127	−	209.384i	0.734958	−	0.646246i
$325$	−111.117	−	192.461i	−0.341900	−	0.592188i
$326$	112.693	+	298.825i	0.345685	+	0.916642i
$327$	26.1433	+	15.0938i	0.0799490	+	0.0461586i
$328$	−319.665	−	170.058i	−0.974588	−	0.518469i
$329$	289.557	−	207.101i	0.880111	−	0.629487i
$330$	−14.0723	−	2.31388i	−0.0426433	−	0.00701176i
$331$	−325.087	−	187.689i	−0.982135	−	0.567036i	−0.0792209	−	0.996857i	$-0.525243\pi$
$331$	−325.087	−	187.689i	−0.982135	−	0.567036i	−0.902914	+	0.429821i	$0.858577\pi$
$332$	40.5077	+	202.262i	0.122011	+	0.609222i
$333$	−231.445	+	133.625i	−0.695029	+	0.401275i
$334$	181.028	−	220.878i	0.542000	−	0.661311i
$335$		−	448.203i		−	1.33792i
$336$	−24.9923	+	13.4141i	−0.0743819	+	0.0399229i
$337$	−4.99043			−0.0148084			−0.00740419	−	0.999973i	$-0.502357\pi$
$337$	−4.99043			−0.0148084			−0.00740419	+	0.999973i	$0.502357\pi$
$338$	248.313	+	203.513i	0.734653	+	0.602110i
$339$	−15.7032	−	27.1988i	−0.0463222	−	0.0802324i
$340$	133.644	−	26.7654i	0.393070	−	0.0787217i
$341$	−128.512	+	222.589i	−0.376868	+	0.652755i
$342$	71.9668	−	437.679i	0.210429	−	1.27976i
$343$	−328.497	+	98.6856i	−0.957717	+	0.287713i
$344$	−175.940	−	93.5978i	−0.511452	−	0.272087i
$345$	−1.94438	+	3.36776i	−0.00563588	+	0.00976163i
$346$	−366.372	+	138.167i	−1.05888	+	0.399326i
$347$	320.772	−	185.198i	0.924414	−	0.533711i	0.0393734	−	0.999225i	$-0.487464\pi$
$347$	320.772	−	185.198i	0.924414	−	0.533711i	0.885041	+	0.465514i	$0.154130\pi$
$348$	−18.9729	−	21.5773i	−0.0545197	−	0.0620039i
$349$	−25.6801			−0.0735821			−0.0367910	−	0.999323i	$-0.511714\pi$
$349$	−25.6801			−0.0735821			−0.0367910	+	0.999323i	$0.511714\pi$
$350$	142.486	+	95.2554i	0.407102	+	0.272158i
$351$	−82.4571			−0.234921
$352$	−245.473	+	58.0841i	−0.697366	+	0.165012i
$353$	−229.938	+	132.755i	−0.651383	+	0.376076i	−0.788986	−	0.614411i	$-0.789394\pi$
$353$	−229.938	+	132.755i	−0.651383	+	0.376076i	0.137603	+	0.990487i	$0.456060\pi$
$354$	35.0754	−	13.2277i	0.0990831	−	0.0373663i
$355$	9.53348	−	16.5125i	0.0268549	−	0.0465140i
$356$	−197.027	+	582.929i	−0.553446	+	1.63744i
$357$	−13.7559	+	9.83871i	−0.0385319	+	0.0275594i
$358$	−295.052	−	48.5148i	−0.824167	−	0.135516i
$359$	275.228	−	476.709i	0.766651	−	1.32788i	−0.172718	−	0.984971i	$-0.555255\pi$
$359$	275.228	−	476.709i	0.766651	−	1.32788i	0.939369	−	0.342908i	$-0.111412\pi$
$360$	−255.182	+	8.85558i	−0.708838	+	0.0245988i
$361$	−127.489	−	220.817i	−0.353155	−	0.611682i
$362$	−141.227	−	115.747i	−0.390129	−	0.319743i
$363$	−14.9068			−0.0410656
$364$	−495.051	−	115.214i	−1.36003	−	0.316521i
$365$		−	97.5689i		−	0.267312i
$366$	19.8220	+	16.2458i	0.0541585	+	0.0443874i
$367$	180.099	−	103.980i	0.490732	−	0.283324i	−0.234146	−	0.972201i	$-0.575229\pi$
$367$	180.099	−	103.980i	0.490732	−	0.283324i	0.724878	+	0.688877i	$0.241896\pi$
$368$	−8.79946	+	68.2187i	−0.0239116	+	0.185377i
$369$	350.257	+	202.221i	0.949207	+	0.548025i
$370$	210.815	+	34.6639i	0.569770	+	0.0936863i
$371$	−42.7018	−	437.575i	−0.115099	−	1.17945i
$372$	10.5762	−	31.2911i	0.0284307	−	0.0841159i
$373$	−393.539	−	227.210i	−1.05507	−	0.609142i	−0.131002	−	0.991382i	$-0.541820\pi$
$373$	−393.539	−	227.210i	−1.05507	−	0.609142i	−0.924063	+	0.382240i	$0.875153\pi$
$374$	−140.729	+	53.0717i	−0.376280	+	0.141903i
$375$	−16.8443	−	29.1751i	−0.0449180	−	0.0778003i
$376$	−345.079	+	215.525i	−0.917762	+	0.573204i
$377$		−	514.871i		−	1.36570i
$378$	57.0417	−	28.1128i	0.150904	−	0.0743724i
$379$		−	373.244i		−	0.984813i	−0.870365	−	0.492406i	$-0.836117\pi$
$379$		−	373.244i		−	0.984813i	0.870365	−	0.492406i	$-0.163883\pi$
$380$	−266.289	+	234.147i	−0.700760	+	0.616175i
$381$	−7.29559	−	12.6363i	−0.0191485	−	0.0331662i
$382$	−52.0758	+	19.6389i	−0.136324	+	0.0514107i
$383$	−270.298	−	156.056i	−0.705738	−	0.407458i	0.103743	−	0.994604i	$-0.466918\pi$
$383$	−270.298	−	156.056i	−0.705738	−	0.407458i	−0.809481	+	0.587146i	$0.800251\pi$
$384$	29.4656	−	13.5138i	0.0767334	−	0.0351922i
$385$	179.450	+	81.5014i	0.466103	+	0.211692i
$386$	78.6533	−	478.345i	0.203765	−	1.23923i
$387$	192.777	+	111.300i	0.498133	+	0.287597i
$388$	184.511	−	36.9527i	0.475543	−	0.0952388i
$389$	−439.628	+	253.819i	−1.13015	+	0.652492i	−0.943973	−	0.330024i	$-0.892943\pi$
$389$	−439.628	+	253.819i	−1.13015	+	0.652492i	−0.186177	+	0.982516i	$0.559610\pi$
$390$	25.4003	+	20.8177i	0.0651290	+	0.0533787i
$391$			41.0120i			0.104890i
$392$	381.744	−	89.0801i	0.973838	−	0.227245i
$393$	31.4796			0.0801007
$394$	−120.065	+	146.495i	−0.304732	+	0.371814i
$395$	184.082	+	318.840i	0.466031	+	0.807190i
$396$	276.274	−	55.3305i	0.697662	−	0.139723i
$397$	95.6487	−	165.668i	0.240929	−	0.417301i	−0.720050	−	0.693922i	$-0.755881\pi$
$397$	95.6487	−	165.668i	0.240929	−	0.417301i	0.960979	+	0.276621i	$0.0892146\pi$
$398$	610.123	+	100.321i	1.53297	+	0.252064i
$399$	18.1945	−	40.0606i	0.0456002	−	0.100402i
$400$	−155.712	−	118.836i	−0.389281	−	0.297089i
$401$	61.2011	−	106.004i	0.152621	−	0.264348i	−0.779569	−	0.626316i	$-0.784562\pi$
$401$	61.2011	−	106.004i	0.152621	−	0.264348i	0.932190	+	0.361968i	$0.117895\pi$
$402$	−22.4277	−	59.4709i	−0.0557904	−	0.147938i
$403$	512.587	−	295.942i	1.27193	−	0.734347i
$404$	−448.619	+	394.469i	−1.11044	+	0.976408i
$405$	283.143			0.699120
$406$	175.539	+	356.174i	0.432362	+	0.877277i
$407$	−235.756			−0.579254
$408$	16.3936	−	10.2389i	0.0401803	−	0.0250953i
$409$	−4.57744	+	2.64279i	−0.0111918	+	0.00646158i	−0.505585	−	0.862777i	$-0.668723\pi$
$409$	−4.57744	+	2.64279i	−0.0111918	+	0.00646158i	0.494394	+	0.869238i	$0.335390\pi$
$410$	−114.088	−	302.524i	−0.278264	−	0.737863i
$411$	−21.4610	+	37.1716i	−0.0522166	+	0.0904418i
$412$	25.4151	−	75.1939i	0.0616872	−	0.182509i
$413$	−515.617	+	50.3178i	−1.24847	+	0.121835i
$414$	12.4657	−	75.8123i	0.0301103	−	0.183122i
$415$	−92.0975	+	159.517i	−0.221922	+	0.384379i
$416$	556.429	+	166.804i	1.33757	+	0.400970i
$417$	33.7460	+	58.4498i	0.0809257	+	0.140167i
$418$	248.032	−	302.632i	0.593378	−	0.723999i
$419$	34.7160			0.0828545			0.0414272	−	0.999142i	$-0.486810\pi$
$419$	34.7160			0.0828545			0.0414272	+	0.999142i	$0.486810\pi$
$420$	−24.6688	−	5.74119i	−0.0587353	−	0.0136695i
$421$			394.337i			0.936669i	0.883551	+	0.468334i	$0.155146\pi$
$421$			394.337i			0.936669i	−0.883551	+	0.468334i	$0.844854\pi$
$422$	−159.568	+	194.694i	−0.378122	+	0.461359i
$423$	393.564	−	227.224i	0.930412	−	0.537173i
$424$	17.4264	+	502.159i	0.0411000	+	1.18434i
$425$	−101.144	−	58.3956i	−0.237986	−	0.137401i
$426$	0.438702	−	2.66805i	0.00102982	−	0.00626302i
$427$	−206.050	−	288.088i	−0.482554	−	0.674678i
$428$	11.7114	−	34.6495i	0.0273630	−	0.0809569i
$429$	−31.3848	−	18.1200i	−0.0731581	−	0.0422378i
$430$	−62.7927	−	166.506i	−0.146030	−	0.387222i
$431$	215.872	+	373.901i	0.500862	+	0.867519i	1.00000		0.000995912i	$0.000317009\pi$
$431$	215.872	+	373.901i	0.500862	+	0.867519i	−0.499137	+	0.866523i	$0.666350\pi$
$432$	−67.0725	+	27.9884i	−0.155260	+	0.0647879i
$433$			318.535i			0.735647i	0.929896	+	0.367823i	$0.119897\pi$
$433$			318.535i			0.735647i	−0.929896	+	0.367823i	$0.880103\pi$
$434$	−253.696	+	379.485i	−0.584553	+	0.874390i
$435$		−	25.6565i		−	0.0589803i
$436$	314.841	+	358.060i	0.722112	+	0.821239i
$437$	−53.3481	−	92.4016i	−0.122078	−	0.211445i
$438$	−4.88228	−	12.9462i	−0.0111468	−	0.0295575i
$439$	532.799	+	307.612i	1.21366	+	0.700710i	0.963556	−	0.267508i	$-0.0862001\pi$
$439$	532.799	+	307.612i	1.21366	+	0.700710i	0.250109	+	0.968218i	$0.419533\pi$
$440$	−198.858	−	105.790i	−0.451949	−	0.240432i
$441$	−429.596	+	84.6525i	−0.974141	+	0.191956i
$442$	341.765	+	56.1957i	0.773223	+	0.127140i
$443$	86.4553	+	49.9150i	0.195159	+	0.112675i	0.594395	−	0.804173i	$-0.297391\pi$
$443$	86.4553	+	49.9150i	0.195159	+	0.112675i	−0.399237	+	0.916848i	$0.630725\pi$
$444$	29.7071	−	5.94956i	0.0669079	−	0.0133999i
$445$	−475.840	+	274.726i	−1.06930	+	0.617362i
$446$	−11.3417	+	13.8384i	−0.0254299	+	0.0310279i
$447$		−	7.80515i		−	0.0174612i
$448$	−441.793	+	74.3174i	−0.986145	+	0.165887i
$449$	−75.3168			−0.167743			−0.0838717	−	0.996477i	$-0.526729\pi$
$449$	−75.3168			−0.167743			−0.0838717	+	0.996477i	$0.526729\pi$
$450$	169.220	+	138.690i	0.376044	+	0.308200i
$451$	178.391	+	308.983i	0.395546	+	0.685105i
$452$	−97.4101	−	486.384i	−0.215509	−	1.07607i
$453$	2.97443	−	5.15187i	0.00656608	−	0.0113728i
$454$	88.4889	−	538.161i	0.194909	−	1.18538i
$455$	−264.037	−	369.161i	−0.580301	−	0.811343i
$456$	−23.6167	+	44.3932i	−0.0517910	+	0.0973536i
$457$	104.447	−	180.907i	0.228549	−	0.395858i	−0.728830	−	0.684695i	$-0.759935\pi$
$457$	104.447	−	180.907i	0.228549	−	0.395858i	0.957378	+	0.288837i	$0.0932687\pi$
$458$	619.832	−	233.752i	1.35334	−	0.510374i
$459$	−37.5281	+	21.6669i	−0.0817606	+	0.0472045i
$460$	−46.1251	+	40.5576i	−0.100272	+	0.0881686i
$461$	751.461			1.63007			0.815034	−	0.579413i	$-0.196718\pi$
$461$	751.461			1.63007			0.815034	+	0.579413i	$0.196718\pi$
$462$	27.8890	+	1.83468i	0.0603659	+	0.00397118i
$463$	−3.56075			−0.00769060			−0.00384530	−	0.999993i	$-0.501224\pi$
$463$	−3.56075			−0.00769060			−0.00384530	+	0.999993i	$0.501224\pi$
$464$	−174.762	−	418.808i	−0.376643	−	0.902603i
$465$	25.5426	−	14.7470i	0.0549304	−	0.0317141i
$466$	−296.117	+	111.672i	−0.635444	+	0.239639i
$467$	−206.945	+	358.440i	−0.443138	+	0.767537i	−0.997920	−	0.0644583i	$-0.979468\pi$
$467$	−206.945	+	358.440i	−0.443138	+	0.767537i	0.554783	+	0.831995i	$0.312801\pi$
$468$	−614.686	−	207.760i	−1.31343	−	0.443932i
$469$	85.3146	+	874.238i	0.181908	+	1.86405i
$470$	−358.484	−	58.9449i	−0.762733	−	0.125415i
$471$	−16.1615	+	27.9925i	−0.0343131	+	0.0594320i
$472$	591.720	−	20.5345i	1.25364	−	0.0435052i
$473$	98.1843	+	170.060i	0.207578	+	0.359535i
$474$	40.3800	+	33.0948i	0.0851898	+	0.0698202i
$475$	303.843			0.639669
$476$	−255.583	+	77.6459i	−0.536940	+	0.163122i
$477$		−	561.240i		−	1.17660i
$478$	75.7928	+	62.1186i	0.158562	+	0.129955i
$479$	−785.798	+	453.681i	−1.64050	+	0.947142i	−0.659841	+	0.751405i	$0.729376\pi$
$479$	−785.798	+	453.681i	−1.64050	+	0.947142i	−0.980657	+	0.195737i	$0.937290\pi$
$480$	27.7273	+	8.31197i	0.0577653	+	0.0173166i
$481$	470.172	+	271.454i	0.977488	+	0.564353i
$482$	389.478	+	64.0412i	0.808047	+	0.132866i
$483$	3.15154	−	6.93907i	0.00652494	−	0.0143666i
$484$	−223.047	−	75.3886i	−0.460840	−	0.155762i
$485$	145.518	+	84.0147i	0.300037	+	0.173226i
$486$	114.073	−	43.0193i	0.234718	−	0.0885170i
$487$	−421.452	−	729.977i	−0.865405	−	1.49893i	−0.866644	−	0.498926i	$-0.833728\pi$
$487$	−421.452	−	729.977i	−0.865405	−	1.49893i	0.00123943	−	0.999999i	$-0.499605\pi$
$488$	214.431	+	343.328i	0.439408	+	0.703540i
$489$			40.4410i			0.0827014i
$490$	308.515	+	165.356i	0.629623	+	0.337461i
$491$			144.126i			0.293535i	0.989171	+	0.146768i	$0.0468870\pi$
$491$			144.126i			0.293535i	−0.989171	+	0.146768i	$0.953113\pi$
$492$	−30.2762	−	34.4323i	−0.0615369	−	0.0699843i
$493$	−135.290	−	234.329i	−0.274422	−	0.475313i
$494$	−843.109	+	317.954i	−1.70670	+	0.643632i
$495$	217.889	+	125.798i	0.440179	+	0.254138i
$496$	316.498	−	414.713i	0.638101	−	0.836115i
$497$	−15.4523	+	34.0229i	−0.0310912	+	0.0684566i
$498$	−4.23805	+	25.7745i	−0.00851014	+	0.0517560i
$499$	−330.101	−	190.584i	−0.661526	−	0.381932i	0.131332	−	0.991338i	$-0.458074\pi$
$499$	−330.101	−	190.584i	−0.661526	−	0.381932i	−0.792858	+	0.609406i	$0.791408\pi$
$500$	−104.488	−	521.726i	−0.208976	−	1.04345i
$501$	31.3180	−	18.0815i	0.0625110	−	0.0360908i
$502$	−488.027	−	399.979i	−0.972165	−	0.796771i
$503$			936.429i			1.86169i	0.365418	+	0.930843i	$0.380926\pi$
$503$			936.429i			1.86169i	−0.365418	+	0.930843i	$0.619074\pi$
$504$	496.057	−	65.8466i	0.984240	−	0.130648i
$505$	−533.429			−1.05629
$506$	42.9627	−	52.4201i	0.0849065	−	0.103597i
$507$	20.3273	+	35.2080i	0.0400933	+	0.0694437i
$508$	−45.2560	−	225.970i	−0.0890865	−	0.444823i
$509$	167.592	−	290.278i	0.329258	−	0.570291i	−0.653107	−	0.757265i	$-0.726535\pi$
$509$	167.592	−	290.278i	0.329258	−	0.570291i	0.982365	+	0.186975i	$0.0598682\pi$
$510$	17.0304	+	2.80028i	0.0333930	+	0.00549075i
$511$	18.5721	+	190.312i	0.0363446	+	0.372431i
$512$	509.230	−	53.1863i	0.994590	−	0.103880i
$513$	56.3682	−	97.6327i	0.109880	−	0.190317i
$514$	−268.537	−	712.071i	−0.522446	−	1.38535i
$515$	61.3800	−	35.4378i	0.119185	−	0.0688112i
$516$	−16.6636	−	18.9511i	−0.0322939	−	0.0367270i
$517$	400.896			0.775427
$518$	−417.802	−	27.4852i	−0.806567	−	0.0530602i
$519$	−49.5824			−0.0955345
$520$	274.776	+	439.947i	0.528416	+	0.846051i
$521$	−421.675	+	243.454i	−0.809357	+	0.467283i	−0.846733	−	0.532019i	$-0.821434\pi$
$521$	−421.675	+	243.454i	−0.809357	+	0.467283i	0.0373754	+	0.999301i	$0.488100\pi$
$522$	178.865	+	474.290i	0.342652	+	0.908601i
$523$	−86.3132	+	149.499i	−0.165035	+	0.285849i	−0.936668	−	0.350220i	$-0.886107\pi$
$523$	−86.3132	+	149.499i	−0.165035	+	0.285849i	0.771633	+	0.636068i	$0.219440\pi$
$524$	471.020	+	159.202i	0.898894	+	0.303821i
$525$	12.6258	+	17.6527i	0.0240492	+	0.0336242i
$526$	63.7080	−	387.452i	0.121118	−	0.736600i
$527$	155.527	−	269.380i	0.295117	−	0.511157i
$528$	−31.6796	−	4.08632i	−0.0599993	−	0.00773925i
$529$	255.259	+	442.122i	0.482532	+	0.835770i
$530$	−284.406	+	347.013i	−0.536615	+	0.654741i
$531$	−661.339			−1.24546
$532$	474.838	−	507.400i	0.892553	−	0.953760i
$533$		−	821.611i		−	1.54148i
$534$	−49.3909	+	60.2634i	−0.0924923	+	0.112853i
$535$	28.2841	−	16.3298i	0.0528675	−	0.0305230i
$536$	−34.8166	−	1003.27i	−0.0649563	−	1.87178i
$537$	−32.7908	−	18.9318i	−0.0610629	−	0.0352547i
$538$	33.1999	−	201.912i	0.0617099	−	0.375300i
$539$	−365.538	−	124.814i	−0.678178	−	0.231566i
$540$	−61.4805	−	20.7801i	−0.113853	−	0.0384816i
$541$	500.736	+	289.100i	0.925574	+	0.534381i	0.885409	−	0.464812i	$-0.153878\pi$
$541$	500.736	+	289.100i	0.925574	+	0.534381i	0.0401652	+	0.999193i	$0.487212\pi$
$542$	−180.893	−	479.667i	−0.333750	−	0.884995i
$543$	−11.5611	−	20.0244i	−0.0212911	−	0.0368773i
$544$	297.074	−	70.2940i	0.546091	−	0.129217i
$545$			425.750i			0.781193i
$546$	−53.5070	−	35.7708i	−0.0979981	−	0.0655144i
$547$		−	454.579i		−	0.831040i	−0.909584	−	0.415520i	$-0.863600\pi$
$547$		−	454.579i		−	0.831040i	0.909584	−	0.415520i	$-0.136400\pi$
$548$	−509.104	+	447.653i	−0.929022	+	0.816885i
$549$	−226.071	−	391.567i	−0.411788	−	0.713237i
$550$	68.1060	+	180.595i	0.123829	+	0.328354i
$551$	609.629	+	351.969i	1.10640	+	0.638783i
$552$	−4.09075	+	7.68955i	−0.00741078	+	0.0139303i
$553$	−419.751	−	586.871i	−0.759043	−	1.06125i
$554$	388.245	+	63.8384i	0.700803	+	0.115232i
$555$	23.4291	+	13.5268i	0.0422145	+	0.0243726i
$556$	209.333	+	1045.23i	0.376498	+	1.87992i
$557$	25.2401	−	14.5724i	0.0453143	−	0.0261622i	−0.477172	−	0.878810i	$-0.658338\pi$
$557$	25.2401	−	14.5724i	0.0453143	−	0.0261622i	0.522486	+	0.852648i	$0.325005\pi$
$558$	−369.376	+	450.687i	−0.661964	+	0.807684i
$559$		−	452.205i		−	0.808953i
$560$	−340.078	−	210.662i	−0.607282	−	0.376182i
$561$	−19.0453			−0.0339488
$562$	−108.732	−	89.1148i	−0.193473	−	0.158567i
$563$	514.005	+	890.283i	0.912975	+	1.58132i	0.809839	+	0.586652i	$0.199554\pi$
$563$	514.005	+	890.283i	0.912975	+	1.58132i	0.103136	+	0.994667i	$0.467112\pi$
$564$	−50.5160	+	10.1170i	−0.0895673	+	0.0179380i
$565$	221.469	−	383.596i	0.391981	−	0.678931i
$566$	−96.3730	+	586.110i	−0.170270	+	1.03553i
$567$	−552.283	+	53.8959i	−0.974044	+	0.0950544i
$568$	20.0574	−	37.7026i	0.0353122	−	0.0663778i
$569$	409.852	−	709.885i	0.720303	−	1.24760i	−0.240576	−	0.970630i	$-0.577336\pi$
$569$	409.852	−	709.885i	0.720303	−	1.24760i	0.960878	−	0.276971i	$-0.0893305\pi$
$570$	−42.0128	+	15.8439i	−0.0737067	+	0.0277964i
$571$	140.820	−	81.3023i	0.246620	−	0.142386i	−0.371596	−	0.928395i	$-0.621189\pi$
$571$	140.820	−	81.3023i	0.246620	−	0.142386i	0.618215	+	0.786009i	$0.287856\pi$
$572$	−377.964	−	429.848i	−0.660776	−	0.751483i
$573$	−7.04760			−0.0122995
$574$	280.119	+	568.369i	0.488012	+	0.990190i
$575$	52.6299			0.0915303
$576$	−570.519	+	39.6452i	−0.990485	+	0.0688285i
$577$	131.878	−	76.1400i	0.228559	−	0.131958i	−0.381348	−	0.924431i	$-0.624540\pi$
$577$	131.878	−	76.1400i	0.228559	−	0.131958i	0.609907	+	0.792473i	$0.291207\pi$
$578$	−370.509	+	139.727i	−0.641019	+	0.241742i
$579$	30.6926	−	53.1611i	0.0530097	−	0.0918154i
$580$	129.753	−	383.890i	0.223712	−	0.661880i
$581$	149.276	−	328.676i	0.256930	−	0.565708i
$582$	23.5124	+	3.86611i	0.0403994	+	0.00664279i
$583$	247.551	−	428.772i	0.424617	−	0.735457i
$584$	−7.57919	−	218.401i	−0.0129781	−	0.373975i
$585$	−289.692	−	501.762i	−0.495201	−	0.857713i
$586$	−209.693	−	171.861i	−0.357837	−	0.293278i
$587$	−894.404			−1.52369			−0.761843	−	0.647761i	$-0.775705\pi$
$587$	−894.404			−1.52369			−0.761843	+	0.647761i	$0.775705\pi$
$588$	49.2104	+	6.50277i	0.0836911	+	0.0110591i
$589$			809.232i			1.37391i
$590$	408.904	+	335.131i	0.693057	+	0.568018i
$591$	−20.7713	+	11.9923i	−0.0351460	+	0.0202916i
$592$	474.588	+	61.2167i	0.801669	+	0.103407i
$593$	164.729	+	95.1064i	0.277789	+	0.160382i	0.632422	−	0.774624i	$-0.282061\pi$
$593$	164.729	+	95.1064i	0.277789	+	0.160382i	−0.354633	+	0.935006i	$0.615394\pi$
$594$	70.6647	+	11.6193i	0.118964	+	0.0195610i
$595$	−217.172	−	98.6338i	−0.364995	−	0.165771i
$596$	39.4731	−	116.786i	0.0662301	−	0.195950i
$597$	67.8064	+	39.1480i	0.113579	+	0.0655746i
$598$	−146.039	+	55.0742i	−0.244212	+	0.0920973i
$599$	146.832	+	254.320i	0.245128	+	0.424574i	0.962168	−	0.272458i	$-0.0878366\pi$
$599$	146.832	+	254.320i	0.245128	+	0.424574i	−0.717040	+	0.697033i	$0.754503\pi$
$600$	−13.1394	−	21.0376i	−0.0218990	−	0.0350626i
$601$		−	597.574i		−	0.994299i	−0.867665	−	0.497150i	$-0.834380\pi$
$601$		−	597.574i		−	0.994299i	0.867665	−	0.497150i	$-0.165620\pi$
$602$	154.174	+	312.824i	0.256103	+	0.519640i
$603$			1121.31i			1.85956i
$604$	70.5603	−	62.0434i	0.116822	−	0.102721i
$605$	−105.119	−	182.071i	−0.173750	−	0.300944i
$606$	−70.7794	+	26.6924i	−0.116798	+	0.0440468i
$607$	−10.6620	−	6.15569i	−0.0175650	−	0.0101412i	0.491192	−	0.871051i	$-0.336561\pi$
$607$	−10.6620	−	6.15569i	−0.0175650	−	0.0101412i	−0.508757	+	0.860910i	$0.669895\pi$
$608$	−577.881	+	544.807i	−0.950462	+	0.896064i
$609$	4.88366	+	50.0440i	0.00801915	+	0.0821740i
$610$	−58.6458	+	356.665i	−0.0961407	+	0.584697i
$611$	−799.512	−	461.599i	−1.30853	−	0.755481i
$612$	−334.350	+	66.9615i	−0.546323	+	0.109414i
$613$	−118.897	+	68.6451i	−0.193959	+	0.111982i	−0.593835	−	0.804587i	$-0.702387\pi$
$613$	−118.897	+	68.6451i	−0.193959	+	0.111982i	0.399876	+	0.916569i	$0.369053\pi$
$614$	−117.878	−	96.6110i	−0.191984	−	0.157347i
$615$		−	40.9416i		−	0.0665717i
$616$	408.017	+	168.496i	0.662366	+	0.273532i
$617$	290.516			0.470853			0.235427	−	0.971892i	$-0.424351\pi$
$617$	290.516			0.470853			0.235427	+	0.971892i	$0.424351\pi$
$618$	6.37109	−	7.77356i	0.0103092	−	0.0125786i
$619$	−51.1586	−	88.6092i	−0.0826471	−	0.143149i	0.821739	−	0.569864i	$-0.193004\pi$
$619$	−51.1586	−	88.6092i	−0.0826471	−	0.143149i	−0.904386	+	0.426715i	$0.859671\pi$
$620$	456.768	−	91.4787i	0.736722	−	0.147546i
$621$	9.76379	−	16.9114i	0.0157227	−	0.0272325i
$622$	−390.938	−	64.2812i	−0.628517	−	0.103346i
$623$	875.851	−	626.440i	1.40586	−	1.00552i
$624$	58.4740	+	44.6259i	0.0937083	+	0.0715158i
$625$	84.5320	−	146.414i	0.135251	−	0.234262i
$626$	−39.0903	−	103.654i	−0.0624445	−	0.165582i
$627$	42.9098	−	24.7740i	0.0684366	−	0.0395119i
$628$	−383.386	+	337.110i	−0.610488	+	0.536799i
$629$	285.315			0.453600
$630$	371.472	+	248.339i	0.589637	+	0.394188i
$631$	−562.739			−0.891820			−0.445910	−	0.895078i	$-0.647120\pi$
$631$	−562.739			−0.891820			−0.445910	+	0.895078i	$0.647120\pi$
$632$	436.824	+	699.402i	0.691177	+	1.10665i
$633$	−27.6054	+	15.9380i	−0.0436104	+	0.0251785i
$634$	211.125	+	559.834i	0.333005	+	0.883019i
$635$	102.893	−	178.216i	0.162036	−	0.280655i
$636$	−20.3729	+	60.2758i	−0.0320328	+	0.0947732i
$637$	585.284	+	669.805i	0.918814	+	1.05150i
$638$	−72.5519	+	441.237i	−0.113718	+	0.691595i
$639$	−23.8508	+	41.3108i	−0.0373252	+	0.0646492i
$640$	372.840	+	264.596i	0.582563	+	0.413431i
$641$	376.275	+	651.727i	0.587012	+	1.01673i	0.994621	+	0.103578i	$0.0330291\pi$
$641$	376.275	+	651.727i	0.587012	+	1.01673i	−0.407610	+	0.913156i	$0.633638\pi$
$642$	2.93582	−	3.58208i	0.00457292	−	0.00557957i
$643$	253.143			0.393690			0.196845	−	0.980435i	$-0.436930\pi$
$643$	253.143			0.393690			0.196845	+	0.980435i	$0.436930\pi$
$644$	82.2488	−	87.8890i	0.127716	−	0.136474i
$645$		−	22.5337i		−	0.0349360i
$646$	−300.171	+	366.248i	−0.464661	+	0.566947i
$647$	485.492	−	280.299i	0.750374	−	0.433229i	−0.0754551	−	0.997149i	$-0.524041\pi$
$647$	485.492	−	280.299i	0.750374	−	0.433229i	0.825829	+	0.563921i	$0.190708\pi$
$648$	633.797	−	21.9947i	0.978082	−	0.0339424i
$649$	−505.244	−	291.703i	−0.778497	−	0.449465i
$650$	72.1150	−	438.581i	0.110946	−	0.674739i
$651$	−47.0149	+	33.6267i	−0.0722195	+	0.0516539i
$652$	−204.523	+	605.108i	−0.313686	+	0.928079i
$653$	−602.396	−	347.793i	−0.922505	−	0.532609i	−0.0380717	−	0.999275i	$-0.512122\pi$
$653$	−602.396	−	347.793i	−0.922505	−	0.532609i	−0.884433	+	0.466666i	$0.845455\pi$
$654$	21.3042	+	56.4918i	0.0325753	+	0.0863788i
$655$	221.985	+	384.489i	0.338908	+	0.587007i
$656$	−278.879	−	668.317i	−0.425120	−	1.01878i
$657$			244.097i			0.371533i
$658$	710.459	+	46.7377i	1.07972	+	0.0710299i
$659$			323.387i			0.490724i	0.969432	+	0.245362i	$0.0789068\pi$
$659$			323.387i			0.490724i	−0.969432	+	0.245362i	$0.921093\pi$
$660$	−18.8343	−	21.4197i	−0.0285368	−	0.0324541i
$661$	−15.5168	−	26.8758i	−0.0234747	−	0.0406593i	0.854049	−	0.520192i	$-0.174140\pi$
$661$	−15.5168	−	26.8758i	−0.0234747	−	0.0406593i	−0.877524	+	0.479533i	$0.840806\pi$
$662$	−264.914	−	702.463i	−0.400172	−	1.06112i
$663$	37.9822	+	21.9291i	0.0572884	+	0.0330755i
$664$	−193.763	+	364.223i	−0.291811	+	0.548529i
$665$	617.600	−	60.2699i	0.928721	−	0.0906315i
$666$	−527.416	−	86.7221i	−0.791916	−	0.130213i
$667$	105.596	+	60.9661i	0.158315	+	0.0914035i
$668$	560.047	−	112.163i	0.838393	−	0.167908i
$669$	−1.96213	+	1.13284i	−0.00293293	+	0.00169333i
$670$	568.220	−	693.303i	0.848089	−	1.03478i
$671$		−	398.862i		−	0.594429i
$672$	−55.6655	−	10.9350i	−0.0828355	−	0.0162723i
$673$	1011.75			1.50334			0.751670	−	0.659539i	$-0.229249\pi$
$673$	1011.75			1.50334			0.751670	+	0.659539i	$0.229249\pi$
$674$	−7.71945	−	6.32673i	−0.0114532	−	0.00938684i
$675$	27.8047	+	48.1592i	0.0411922	+	0.0713469i
$676$	126.094	+	629.609i	0.186530	+	0.931374i
$677$	34.7377	−	60.1674i	0.0513112	−	0.0888736i	−0.839229	−	0.543778i	$-0.816993\pi$
$677$	34.7377	−	60.1674i	0.0513112	−	0.0888736i	0.890540	+	0.454905i	$0.150327\pi$
$678$	10.1914	−	61.9806i	0.0150315	−	0.0914169i
$679$	−299.831	−	136.175i	−0.441577	−	0.200553i
$680$	240.660	+	128.028i	0.353911	+	0.188277i
$681$	34.5307	−	59.8089i	0.0507058	−	0.0878251i
$682$	−480.982	+	181.388i	−0.705252	+	0.265965i
$683$	824.530	−	476.042i	1.20722	−	0.696987i	0.245067	−	0.969506i	$-0.421190\pi$
$683$	824.530	−	476.042i	1.20722	−	0.696987i	0.962150	+	0.272519i	$0.0878567\pi$
$684$	666.200	−	585.787i	0.973977	−	0.856414i
$685$	−605.348			−0.883720
$686$	−633.247	−	263.808i	−0.923100	−	0.384560i
$687$	83.8839			0.122102
$688$	−153.492	−	367.834i	−0.223098	−	0.534642i
$689$	−987.391	+	570.070i	−1.43308	+	0.827388i
$690$	−7.27723	+	2.74439i	−0.0105467	+	0.00397738i
$691$	34.0754	−	59.0204i	0.0493132	−	0.0854130i	−0.840315	−	0.542098i	$-0.817630\pi$
$691$	34.0754	−	59.0204i	0.0493132	−	0.0854130i	0.889628	+	0.456685i	$0.150963\pi$
$692$	−741.888	−	250.754i	−1.07209	−	0.362361i
$693$	−448.947	−	203.900i	−0.647831	−	0.294228i
$694$	730.975	+	120.193i	1.05328	+	0.173189i
$695$	−475.935	+	824.343i	−0.684798	+	1.18611i
$696$	−1.99300	−	57.4302i	−0.00286351	−	0.0825147i
$697$	−215.891	−	373.934i	−0.309743	−	0.536490i
$698$	−39.7234	−	32.5566i	−0.0569103	−	0.0466427i
$699$	−40.0745			−0.0573311
$700$	99.6416	+	327.985i	0.142345	+	0.468551i
$701$		−	1.67276i		−	0.00238625i	−0.999999	−	0.00119312i	$-0.999620\pi$
$701$		−	1.67276i		−	0.00238625i	0.999999	−	0.00119312i	$-0.000379783\pi$
$702$	−127.549	−	104.537i	−0.181694	−	0.148913i
$703$	−642.825	+	371.135i	−0.914403	+	0.527931i
$704$	−453.347	−	221.356i	−0.643959	−	0.314427i
$705$	−39.8404	−	23.0019i	−0.0565112	−	0.0326267i
$706$	−523.984	−	86.1577i	−0.742186	−	0.122036i
$707$	1040.47	−	101.537i	1.47168	−	0.143617i
$708$	71.0261	+	24.0064i	0.100319	+	0.0339074i
$709$	−45.7969	−	26.4408i	−0.0645936	−	0.0372931i	0.467355	−	0.884070i	$-0.345207\pi$
$709$	−45.7969	−	26.4408i	−0.0645936	−	0.0372931i	−0.531949	+	0.846776i	$0.678540\pi$
$710$	35.6810	−	13.4560i	0.0502549	−	0.0189522i
$711$	−460.536	−	797.673i	−0.647731	−	1.12190i
$712$	−1043.79	+	651.919i	−1.46600	+	0.915617i
$713$			140.171i			0.196593i
$714$	−33.7516	−	2.22035i	−0.0472711	−	0.00310974i
$715$		−	511.109i		−	0.714838i
$716$	−394.896	−	449.104i	−0.551530	−	0.627241i
$717$	6.20454	+	10.7466i	0.00865347	+	0.0149882i
$718$	1030.10	−	388.471i	1.43467	−	0.541045i
$719$	−824.178	−	475.840i	−1.14628	−	0.661808i	−0.198305	−	0.980140i	$-0.563544\pi$
$719$	−824.178	−	475.840i	−1.14628	−	0.661808i	−0.947979	+	0.318333i	$0.896877\pi$
$720$	−405.955	−	309.815i	−0.563827	−	0.430298i
$721$	−112.979	+	80.8064i	−0.156697	+	0.112075i
$722$	82.7399	−	503.198i	0.114598	−	0.696950i
$723$	43.2849	+	24.9906i	0.0598685	+	0.0345651i
$724$	−71.7155	−	358.087i	−0.0990545	−	0.494595i
$725$	−300.711	+	173.615i	−0.414774	+	0.239470i
$726$	−23.0586	−	18.8985i	−0.0317612	−	0.0260310i
$727$			1061.98i			1.46078i	0.683032	+	0.730388i	$0.260661\pi$
$727$			1061.98i			1.46078i	−0.683032	+	0.730388i	$0.739339\pi$
$728$	−619.706	−	805.831i	−0.851244	−	1.10691i
$729$	−698.013			−0.957494
$730$	123.695	−	150.925i	0.169446	−	0.206746i
$731$	−118.824	−	205.809i	−0.162550	−	0.281544i
$732$	10.0657	+	50.2597i	0.0137510	+	0.0686607i
$733$	0.148102	−	0.256519i	0.000202048	−	0.000349958i	−0.865924	−	0.500175i	$-0.833269\pi$
$733$	0.148102	−	0.256519i	0.000202048	−	0.000349958i	0.866126	+	0.499825i	$0.166602\pi$
$734$	410.409	+	67.4828i	0.559140	+	0.0919384i
$735$	29.1652	+	33.3769i	0.0396806	+	0.0454108i
$736$	−100.097	+	94.3684i	−0.136002	+	0.128218i
$737$	−494.588	+	856.651i	−0.671082	+	1.16235i
$738$	285.425	+	756.853i	0.386755	+	1.02555i
$739$	−176.276	+	101.773i	−0.238533	+	0.137717i	−0.614502	−	0.788915i	$-0.710643\pi$
$739$	−176.276	+	101.773i	−0.238533	+	0.137717i	0.375969	+	0.926632i	$0.377310\pi$
$740$	282.153	+	320.886i	0.381288	+	0.433629i
$741$	−114.101			−0.153982
$742$	488.693	−	730.999i	0.658615	−	0.985174i
$743$	1142.13			1.53718			0.768592	−	0.639739i	$-0.220958\pi$
$743$	1142.13			1.53718			0.768592	+	0.639739i	$0.220958\pi$
$744$	56.0299	−	34.9944i	0.0753090	−	0.0470355i
$745$	95.3315	−	55.0397i	0.127962	−	0.0738788i
$746$	−320.696	−	850.379i	−0.429887	−	1.13992i
$747$	230.409	−	399.080i	0.308446	−	0.534244i
$748$	−284.969	−	96.3180i	−0.380975	−	0.128767i
$749$	−52.0610	+	37.2358i	−0.0695073	+	0.0497141i
$750$	10.9319	−	66.4843i	0.0145759	−	0.0886457i
$751$	396.068	−	686.010i	0.527387	−	0.913462i	−0.472103	−	0.881543i	$-0.656505\pi$
$751$	396.068	−	686.010i	0.527387	−	0.913462i	0.999490	−	0.0319185i	$-0.0101617\pi$
$752$	−807.022	−	104.097i	−1.07317	−	0.138427i
$753$	−39.9508	−	69.1967i	−0.0530554	−	0.0918947i
$754$	652.740	−	796.428i	0.865703	−	1.05627i
$755$	83.8995			0.111125
$756$	123.876	+	28.8297i	0.163857	+	0.0381345i
$757$			1179.34i			1.55792i	0.627076	+	0.778958i	$0.284252\pi$
$757$			1179.34i			1.55792i	−0.627076	+	0.778958i	$0.715748\pi$
$758$	473.189	−	577.353i	0.624260	−	0.761679i
$759$	7.43259	−	4.29121i	0.00979260	−	0.00565376i
$760$	−708.754	+	24.5959i	−0.932571	+	0.0323630i
$761$	197.869	+	114.240i	0.260011	+	0.150118i	0.624340	−	0.781153i	$-0.285368\pi$
$761$	197.869	+	114.240i	0.260011	+	0.150118i	−0.364328	+	0.931271i	$0.618701\pi$
$762$	4.73482	−	28.7957i	0.00621368	−	0.0377896i
$763$	−81.0408	−	830.443i	−0.106213	−	1.08839i
$764$	−105.451	−	35.6420i	−0.138025	−	0.0466518i
$765$	−263.691	−	152.242i	−0.344694	−	0.199009i
$766$	−220.266	−	584.073i	−0.287554	−	0.762497i
$767$	671.744	+	1163.49i	0.875807	+	1.51694i
$768$	62.7114	+	16.4519i	0.0816555	+	0.0214218i
$769$			83.4232i			0.108483i	0.998528	+	0.0542414i	$0.0172740\pi$
$769$			83.4232i			0.108483i	−0.998528	+	0.0542414i	$0.982726\pi$
$770$	174.257	+	353.572i	0.226307	+	0.459185i
$771$		−	96.3670i		−	0.124990i
$772$	728.098	−	640.213i	0.943132	−	0.829292i
$773$	285.318	+	494.186i	0.369105	+	0.639309i	0.989426	−	0.145039i	$-0.0463309\pi$
$773$	285.318	+	494.186i	0.369105	+	0.639309i	−0.620321	+	0.784348i	$0.712998\pi$
$774$	157.095	+	416.563i	0.202965	+	0.538195i
$775$	−345.691	−	199.585i	−0.446052	−	0.257528i
$776$	332.258	+	176.757i	0.428168	+	0.227780i
$777$	−48.2742	−	21.9249i	−0.0621289	−	0.0282173i
$778$	−1001.83	−	164.728i	−1.28769	−	0.211733i
$779$	972.822	+	561.659i	1.24881	+	0.721000i
$780$	12.8984	+	64.4037i	0.0165364	+	0.0825689i
$781$	−36.4427	+	21.0402i	−0.0466616	+	0.0269401i
$782$	−51.9939	+	63.4394i	−0.0664883	+	0.0811245i
$783$			128.835i			0.164540i
$784$	703.435	+	346.172i	0.897239	+	0.441546i
$785$	−455.864			−0.580718
$786$	48.6942	+	39.9090i	0.0619519	+	0.0507748i
$787$	−382.719	−	662.888i	−0.486301	−	0.842298i	0.513575	−	0.858045i	$-0.328321\pi$
$787$	−382.719	−	662.888i	−0.486301	−	0.842298i	−0.999876	+	0.0157470i	$0.994987\pi$
$788$	−371.444	+	74.3906i	−0.471376	+	0.0944043i
$789$	24.8605	−	43.0597i	0.0315089	−	0.0545750i
$790$	−119.469	+	726.573i	−0.151227	+	0.919713i
$791$	−358.968	+	790.377i	−0.453816	+	0.999212i
$792$	497.501	+	264.665i	0.628158	+	0.334173i
$793$	−459.257	+	795.456i	−0.579138	+	1.00310i
$794$	357.985	−	135.004i	0.450862	−	0.170030i
$795$	−49.2025	+	28.4071i	−0.0618900	+	0.0357322i
$796$	816.584	+	928.680i	1.02586	+	1.16668i
$797$	−577.729			−0.724880			−0.362440	−	0.932007i	$-0.618056\pi$
$797$	−577.729			−0.724880			−0.362440	+	0.932007i	$0.618056\pi$
$798$	78.9319	−	38.9013i	0.0989122	−	0.0487485i
$799$	−485.168			−0.607220
$800$	−90.2071	−	381.229i	−0.112759	−	0.476537i
$801$	1190.45	−	687.309i	1.48621	−	0.858063i
$802$	229.058	−	86.3824i	0.285608	−	0.107709i
$803$	−107.666	+	186.484i	−0.134080	+	0.232234i
$804$	40.7033	−	120.426i	0.0506260	−	0.149784i
$805$	106.977	−	10.4396i	0.132891	−	0.0129685i
$806$	1168.08	+	192.066i	1.44923	+	0.238295i
$807$	12.9555	−	22.4396i	0.0160539	−	0.0278062i
$808$	−1194.04	+	41.4369i	−1.47778	+	0.0512833i
$809$	41.4824	+	71.8496i	0.0512761	+	0.0888128i	0.890524	−	0.454936i	$-0.150338\pi$
$809$	41.4824	+	71.8496i	0.0512761	+	0.0888128i	−0.839248	+	0.543749i	$0.817004\pi$
$810$	437.981	+	358.962i	0.540717	+	0.443163i
$811$	525.164			0.647552			0.323776	−	0.946134i	$-0.395048\pi$
$811$	525.164			0.647552			0.323776	+	0.946134i	$0.395048\pi$
$812$	−180.016	+	773.493i	−0.221694	+	0.952577i
$813$		−	64.9150i		−	0.0798462i
$814$	−364.680	−	298.886i	−0.448010	−	0.367181i
$815$	−493.944	+	285.178i	−0.606066	+	0.349912i
$816$	38.3390	+	4.94531i	0.0469840	+	0.00606043i
$817$	535.429	+	309.130i	0.655360	+	0.378372i
$818$	−10.4311	−	1.71516i	−0.0127519	−	0.00209677i
$819$	660.567	+	923.565i	0.806553	+	1.12767i
$820$	207.055	−	612.598i	0.252506	−	0.747070i
$821$	506.369	+	292.352i	0.616771	+	0.356093i	0.775611	−	0.631211i	$-0.217442\pi$
$821$	506.369	+	292.352i	0.616771	+	0.356093i	−0.158840	+	0.987304i	$0.550775\pi$
$822$	−80.3222	+	30.2912i	−0.0977156	+	0.0368506i
$823$	−590.484	−	1022.75i	−0.717478	−	1.24271i	−0.961996	−	0.273063i	$-0.911963\pi$
$823$	−590.484	−	1022.75i	−0.717478	−	1.24271i	0.244518	−	0.969645i	$-0.421370\pi$
$824$	134.642	−	84.0931i	0.163401	−	0.102055i
$825$			24.4405i			0.0296248i
$826$	−861.375	−	575.852i	−1.04283	−	0.697158i
$827$			336.806i			0.407262i	0.979048	+	0.203631i	$0.0652743\pi$
$827$			336.806i			0.407262i	−0.979048	+	0.203631i	$0.934726\pi$
$828$	115.395	−	101.467i	0.139367	−	0.122544i
$829$	−184.145	−	318.949i	−0.222130	−	0.384740i	0.733325	−	0.679878i	$-0.237967\pi$
$829$	−184.145	−	318.949i	−0.222130	−	0.384740i	−0.955454	+	0.295139i	$0.904634\pi$
$830$	−344.693	+	129.991i	−0.415293	+	0.156616i
$831$	43.1479	+	24.9114i	0.0519228	+	0.0299777i
$832$	649.243	+	963.446i	0.780340	+	1.15799i
$833$	442.378	+	151.051i	0.531066	+	0.181334i
$834$	−21.9011	+	133.196i	−0.0262603	+	0.159707i
$835$	441.692	+	255.011i	0.528972	+	0.305402i
$836$	767.337	−	153.678i	0.917867	−	0.183825i
$837$	−128.264	+	74.0530i	−0.153242	+	0.0884743i
$838$	53.7005	+	44.0121i	0.0640818	+	0.0525204i
$839$		−	709.889i		−	0.846113i	−0.906103	−	0.423056i	$-0.860957\pi$
$839$		−	709.889i		−	0.846113i	0.906103	−	0.423056i	$-0.139043\pi$
$840$	−30.8805	−	40.1553i	−0.0367625	−	0.0478039i
$841$	36.5402			0.0434485
$842$	−499.931	+	609.981i	−0.593742	+	0.724443i
$843$	−8.90098	−	15.4169i	−0.0105587	−	0.0182882i
$844$	−493.655	+	98.8662i	−0.584899	+	0.117140i
$845$	−286.685	+	496.553i	−0.339272	+	0.587637i
$846$	896.854	+	147.468i	1.06011	+	0.174312i
$847$	239.695	+	335.128i	0.282993	+	0.395664i
$848$	−609.668	+	798.858i	−0.718948	+	0.942049i
$849$	−37.6073	+	65.1377i	−0.0442960	+	0.0767229i
$850$	−82.4226	−	218.557i	−0.0969677	−	0.257126i
$851$	−111.347	+	64.2860i	−0.130842	+	0.0755417i
$852$	4.06109	−	3.57090i	0.00476654	−	0.00419119i
$853$	−1136.65			−1.33253			−0.666267	−	0.745713i	$-0.732109\pi$
$853$	−1136.65			−1.33253			−0.666267	+	0.745713i	$0.732109\pi$
$854$	46.5005	−	706.854i	0.0544503	−	0.827698i
$855$	792.143			0.926483
$856$	62.0435	−	38.7503i	0.0724808	−	0.0452691i
$857$	578.645	−	334.081i	0.675198	−	0.389826i	−0.122845	−	0.992426i	$-0.539202\pi$
$857$	578.645	−	334.081i	0.675198	−	0.389826i	0.798043	+	0.602600i	$0.205869\pi$
$858$	−25.5755	−	67.8179i	−0.0298083	−	0.0790418i
$859$	−100.378	+	173.859i	−0.116854	+	0.202397i	−0.918519	−	0.395376i	$-0.870614\pi$
$859$	−100.378	+	173.859i	−0.116854	+	0.202397i	0.801665	+	0.597773i	$0.203948\pi$
$860$	113.960	−	337.166i	0.132512	−	0.392054i
$861$	7.79316	+	79.8582i	0.00905129	+	0.0927506i
$862$	−140.100	+	852.045i	−0.162529	+	0.988451i
$863$	−21.7855	+	37.7337i	−0.0252440	+	0.0437238i	−0.878371	−	0.477979i	$-0.841370\pi$
$863$	−21.7855	+	37.7337i	−0.0252440	+	0.0437238i	0.853127	+	0.521703i	$0.174703\pi$
$864$	−139.234	−	41.7390i	−0.161151	−	0.0483090i
$865$	−349.641	−	605.596i	−0.404209	−	0.700111i
$866$	−403.830	+	492.726i	−0.466317	+	0.568968i
$867$	−50.1422			−0.0578342
$868$	−873.532	+	265.378i	−1.00637	+	0.305735i
$869$		−	812.533i		−	0.935020i
$870$	32.5266	−	39.6867i	0.0373869	−	0.0456169i
$871$	1972.73	−	1138.95i	2.26490	−	1.30764i
$872$	33.0724	+	953.013i	0.0379271	+	1.09290i
$873$	−364.056	−	210.188i	−0.417017	−	0.240765i
$874$	34.6228	−	210.565i	0.0396142	−	0.240921i
$875$	−385.052	+	847.808i	−0.440059	+	0.968923i
$876$	8.86068	−	26.2154i	0.0101149	−	0.0299263i
$877$	129.242	+	74.6180i	0.147368	+	0.0850832i	0.571871	−	0.820343i	$-0.306218\pi$
$877$	129.242	+	74.6180i	0.147368	+	0.0850832i	−0.424503	+	0.905427i	$0.639551\pi$
$878$	434.179	+	1151.30i	0.494509	+	1.31127i
$879$	−17.1658	−	29.7321i	−0.0195288	−	0.0338249i
$880$	−173.485	−	415.748i	−0.197143	−	0.472441i
$881$		−	865.257i		−	0.982130i	−0.871123	−	0.491065i	$-0.836608\pi$
$881$		−	865.257i		−	0.982130i	0.871123	−	0.491065i	$-0.163392\pi$
$882$	−771.842	−	413.686i	−0.875104	−	0.469032i
$883$		−	1476.24i		−	1.67184i	−0.548850	−	0.835921i	$-0.684934\pi$
$883$		−	1476.24i		−	1.67184i	0.548850	−	0.835921i	$-0.315066\pi$
$884$	457.416	+	520.207i	0.517438	+	0.588469i
$885$	33.4736	+	57.9779i	0.0378233	+	0.0655118i
$886$	70.4526	+	186.817i	0.0795176	+	0.210854i
$887$	−518.166	−	299.163i	−0.584178	−	0.337275i	0.178614	−	0.983919i	$-0.442839\pi$
$887$	−518.166	−	299.163i	−0.584178	−	0.337275i	−0.762792	+	0.646644i	$0.776172\pi$
$888$	53.4951	+	28.4588i	0.0602423	+	0.0320482i
$889$	−166.774	+	367.203i	−0.187597	+	0.413051i
$890$	−1084.34	−	178.297i	−1.21836	−	0.200333i
$891$	−541.172	−	312.446i	−0.607376	−	0.350669i
$892$	−35.0880	+	7.02721i	−0.0393363	+	0.00787804i
$893$	1093.10	−	631.104i	1.22408	−	0.706723i
$894$	9.89516	−	12.0734i	0.0110684	−	0.0135049i
$895$		−	534.006i		−	0.596655i
$896$	−777.606	−	445.135i	−0.867863	−	0.496803i
$897$	−19.7639			−0.0220333
$898$	−116.504	−	95.4847i	−0.129737	−	0.106330i
$899$	−462.395	−	800.891i	−0.514343	−	0.890869i
$900$	85.9306	+	429.065i	0.0954784	+	0.476739i
$901$	−299.589	+	518.904i	−0.332508	+	0.575920i
$902$	−115.775	+	704.110i	−0.128354	+	0.780609i
$903$	4.28926	+	43.9530i	0.00475001	+	0.0486744i
$904$	465.946	−	875.858i	0.515428	−	0.968870i
$905$	163.051	−	282.412i	0.180167	−	0.312058i
$906$	11.1324	−	4.19827i	0.0122874	−	0.00463385i
$907$	−1463.00	+	844.666i	−1.61301	+	0.931274i	−0.624348	+	0.781146i	$0.714635\pi$
$907$	−1463.00	+	844.666i	−1.61301	+	0.931274i	−0.988667	+	0.150128i	$0.952031\pi$
$908$	819.146	−	720.271i	0.902143	−	0.793250i
$909$	1334.53			1.46813
$910$	59.5867	−	905.776i	0.0654799	−	0.995359i
$911$	−813.339			−0.892798			−0.446399	−	0.894834i	$-0.647294\pi$
$911$	−813.339			−0.892798			−0.446399	+	0.894834i	$0.647294\pi$
$912$	−92.8121	+	38.7291i	−0.101768	+	0.0424661i
$913$	352.052	−	203.257i	0.385599	−	0.222626i
$914$	390.913	−	147.421i	0.427694	−	0.161293i
$915$	−22.8852	+	39.6382i	−0.0250111	+	0.0433205i
$916$	1255.13	+	424.228i	1.37023	+	0.463131i
$917$	−506.178	−	707.708i	−0.551993	−	0.771764i
$918$	−85.5191	−	14.0617i	−0.0931581	−	0.0153178i
$919$	−751.489	+	1301.62i	−0.817724	+	1.41634i	0.0896310	+	0.995975i	$0.471431\pi$
$919$	−751.489	+	1301.62i	−0.817724	+	1.41634i	−0.907355	+	0.420365i	$0.861902\pi$
$920$	−122.766	+	4.26037i	−0.133442	+	0.00463083i
$921$	−9.64971	−	16.7138i	−0.0104774	−	0.0181474i
$922$	1162.40	+	952.683i	1.26074	+	1.03328i
$923$	96.9043			0.104988
$924$	40.8142	+	38.1950i	0.0441712	+	0.0413365i
$925$		−	366.139i		−	0.395826i
$926$	−5.50795	−	4.51422i	−0.00594810	−	0.00487497i
$927$	−153.560	+	88.6581i	−0.165653	+	0.0956398i
$928$	260.622	−	869.392i	0.280843	−	0.936845i
$929$	−1301.71	−	751.543i	−1.40120	−	0.808981i	−0.406681	−	0.913570i	$-0.633314\pi$
$929$	−1301.71	−	751.543i	−1.40120	−	0.808981i	−0.994515	+	0.104589i	$0.966647\pi$
$930$	58.2066	+	9.57080i	0.0625877	+	0.0102912i
$931$	−1193.18	+	235.118i	−1.28161	+	0.252543i
$932$	−599.623	−	202.669i	−0.643373	−	0.217456i
$933$	−43.4471	−	25.0842i	−0.0465671	−	0.0268855i
$934$	−774.534	+	292.093i	−0.829266	+	0.312734i
$935$	−134.302	−	232.618i	−0.143638	−	0.248789i
$936$	−687.434	−	1100.66i	−0.734438	−	1.17592i
$937$			419.349i			0.447545i	0.974641	+	0.223772i	$0.0718372\pi$
$937$			419.349i			0.447545i	−0.974641	+	0.223772i	$0.928163\pi$
$938$	−976.368	+	1460.48i	−1.04090	+	1.55701i
$939$		−	14.0279i		−	0.0149392i
$940$	−479.793	−	545.656i	−0.510418	−	0.580485i
$941$	261.680	+	453.243i	0.278087	+	0.481661i	0.970909	−	0.239448i	$-0.0769664\pi$
$941$	261.680	+	453.243i	0.278087	+	0.481661i	−0.692822	+	0.721108i	$0.743633\pi$
$942$	−60.4875	+	22.8111i	−0.0642118	+	0.0242156i
$943$	168.507	+	97.2874i	0.178692	+	0.103168i
$944$	941.336	+	718.404i	0.997178	+	0.761021i
$945$	66.0695	+	92.3744i	0.0699148	+	0.0977507i
$946$	−63.7214	+	387.533i	−0.0673588	+	0.409655i
$947$	−311.949	−	180.104i	−0.329408	−	0.190184i	0.326170	−	0.945311i	$-0.394242\pi$
$947$	−311.949	−	180.104i	−0.329408	−	0.190184i	−0.655578	+	0.755127i	$0.727575\pi$
$948$	20.5051	+	102.385i	0.0216299	+	0.108001i
$949$	429.441	−	247.938i	0.452520	−	0.261262i
$950$	469.999	+	385.204i	0.494736	+	0.405478i
$951$			75.7642i			0.0796679i
$952$	−493.787	−	203.915i	−0.518683	−	0.214197i
$953$	1242.81			1.30410			0.652051	−	0.758175i	$-0.273909\pi$
$953$	1242.81			1.30410			0.652051	+	0.758175i	$0.273909\pi$
$954$	711.526	−	868.155i	0.745834	−	0.910016i
$955$	−49.6976	−	86.0789i	−0.0520394	−	0.0901349i
$956$	38.4879	+	192.176i	0.0402593	+	0.201021i
$957$	−28.3116	+	49.0372i	−0.0295838	+	0.0512406i
$958$	−1790.68	−	294.438i	−1.86918	−	0.307346i
$959$	1180.76	−	115.227i	1.23124	−	0.120153i
$960$	32.3524	+	48.0094i	0.0337004	+	0.0500098i
$961$	51.0585	−	88.4359i	0.0531306	−	0.0920248i
$962$	383.144	+	1015.97i	0.398278	+	1.05610i
$963$	−70.7610	+	40.8539i	−0.0734798	+	0.0424236i
$964$	521.275	+	592.833i	0.540742	+	0.614972i
$965$	865.742			0.897142
$966$	13.6721	−	6.73826i	0.0141534	−	0.00697543i
$967$	81.8793			0.0846735			0.0423368	−	0.999103i	$-0.486520\pi$
$967$	81.8793			0.0846735			0.0423368	+	0.999103i	$0.486520\pi$
$968$	−249.444	−	399.388i	−0.257691	−	0.412591i
$969$	−51.9298	+	29.9817i	−0.0535912	+	0.0309409i
$970$	118.583	+	314.442i	0.122250	+	0.324167i
$971$	409.052	−	708.499i	0.421269	−	0.729660i	−0.574795	−	0.818298i	$-0.694918\pi$
$971$	409.052	−	708.499i	0.421269	−	0.729660i	0.996064	+	0.0886380i	$0.0282514\pi$
$972$	230.992	+	78.0742i	0.237646	+	0.0803232i
$973$	771.419	−	1698.51i	0.792825	−	1.74564i
$974$	273.522	−	1663.47i	0.280823	−	1.70788i
$975$	28.1412	−	48.7419i	0.0288627	−	0.0499917i
$976$	−103.569	+	802.927i	−0.106116	+	0.822671i
$977$	−448.155	−	776.227i	−0.458705	−	0.794500i	0.540188	−	0.841544i	$-0.318353\pi$
$977$	−448.155	−	776.227i	−0.458705	−	0.794500i	−0.998893	+	0.0470441i	$0.985020\pi$
$978$	−51.2700	+	62.5562i	−0.0524234	+	0.0639634i
$979$	1212.63			1.23864
$980$	267.593	+	646.908i	0.273054	+	0.660110i
$981$		−	1065.14i		−	1.08577i
$982$	−182.719	+	222.941i	−0.186068	+	0.227028i
$983$	852.404	−	492.136i	0.867146	−	0.500647i	0.000746983	−	1.00000i	$-0.499762\pi$
$983$	852.404	−	492.136i	0.867146	−	0.500647i	0.866399	+	0.499353i	$0.166429\pi$
$984$	−3.18036	−	91.6450i	−0.00323207	−	0.0931351i
$985$	−292.947	−	169.133i	−0.297408	−	0.171708i
$986$	87.8030	−	533.990i	0.0890497	−	0.541572i
$987$	82.0887	+	37.2825i	0.0831699	+	0.0377736i
$988$	−1707.26	−	577.044i	−1.72799	−	0.584052i
$989$	92.7440	+	53.5458i	0.0937756	+	0.0541414i
$990$	177.558	+	470.825i	0.179351	+	0.475581i
$991$	612.037	+	1060.08i	0.617596	+	1.06971i	0.989923	+	0.141606i	$0.0452265\pi$
$991$	612.037	+	1060.08i	0.617596	+	1.06971i	−0.372327	+	0.928101i	$0.621440\pi$
$992$	1015.34	−	240.251i	1.02353	−	0.242188i
$993$		−	95.0667i		−	0.0957368i
$994$	−67.0359	+	33.0384i	−0.0674405	+	0.0332378i
$995$			1104.24i			1.10979i
$996$	−39.2318	+	34.4964i	−0.0393894	+	0.0346349i
$997$	186.825	+	323.590i	0.187387	+	0.324563i	0.944378	−	0.328861i	$-0.106665\pi$
$997$	186.825	+	323.590i	0.187387	+	0.324563i	−0.756991	+	0.653425i	$0.773332\pi$
$998$	−269.000	−	713.299i	−0.269539	−	0.714728i
$999$	−117.650	−	67.9254i	−0.117768	−	0.0679934i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	56.3.j.a.5.12	yes	28
4.3	odd	2		224.3.n.a.145.7		28
7.2	even	3		392.3.h.a.293.13		28
7.3	odd	6	inner	56.3.j.a.45.2	yes	28
7.4	even	3		392.3.j.e.325.2		28
7.5	odd	6		392.3.h.a.293.14		28
7.6	odd	2		392.3.j.e.117.12		28
8.3	odd	2		224.3.n.a.145.8		28
8.5	even	2	inner	56.3.j.a.5.2	✓	28
28.3	even	6		224.3.n.a.17.8		28
28.19	even	6		1568.3.h.a.881.13		28
28.23	odd	6		1568.3.h.a.881.15		28
56.3	even	6		224.3.n.a.17.7		28
56.5	odd	6		392.3.h.a.293.15		28
56.13	odd	2		392.3.j.e.117.2		28
56.19	even	6		1568.3.h.a.881.16		28
56.37	even	6		392.3.h.a.293.16		28
56.45	odd	6	inner	56.3.j.a.45.12	yes	28
56.51	odd	6		1568.3.h.a.881.14		28
56.53	even	6		392.3.j.e.325.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.2	✓	28	8.5	even	2	inner
56.3.j.a.5.12	yes	28	1.1	even	1	trivial
56.3.j.a.45.2	yes	28	7.3	odd	6	inner
56.3.j.a.45.12	yes	28	56.45	odd	6	inner
224.3.n.a.17.7		28	56.3	even	6
224.3.n.a.17.8		28	28.3	even	6
224.3.n.a.145.7		28	4.3	odd	2
224.3.n.a.145.8		28	8.3	odd	2
392.3.h.a.293.13		28	7.2	even	3
392.3.h.a.293.14		28	7.5	odd	6
392.3.h.a.293.15		28	56.5	odd	6
392.3.h.a.293.16		28	56.37	even	6
392.3.j.e.117.2		28	56.13	odd	2
392.3.j.e.117.12		28	7.6	odd	2
392.3.j.e.325.2		28	7.4	even	3
392.3.j.e.325.12		28	56.53	even	6
1568.3.h.a.881.13		28	28.19	even	6
1568.3.h.a.881.14		28	56.51	odd	6
1568.3.h.a.881.15		28	28.23	odd	6
1568.3.h.a.881.16		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)

\(f(q)\)	\(=\)	\(q+(1.54685 + 1.26777i) q^{2} +(0.126628 + 0.219326i) q^{3} +(0.785498 + 3.92212i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 + 0.499801i) q^{6} +(2.89466 - 6.37346i) q^{7} +(-3.75731 + 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +O(q^{10})\)	\(q+(1.54685 + 1.26777i) q^{2} +(0.126628 + 0.219326i) q^{3} +(0.785498 + 3.92212i) q^{4} +(-1.78589 + 3.09325i) q^{5} +(-0.0821813 + 0.499801i) q^{6} +(2.89466 - 6.37346i) q^{7} +(-3.75731 + 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +(-6.68405 + 2.52070i) q^{10} +(6.82675 - 3.94142i) q^{11} +(-0.760757 + 0.668930i) q^{12} -18.1529 q^{13} +(12.5577 - 6.18902i) q^{14} -0.904575 q^{15} +(-14.7660 + 6.16163i) q^{16} +(-8.26180 + 4.76995i) q^{17} +(16.7221 - 6.30626i) q^{18} +(12.4094 - 21.4938i) q^{19} +(-13.5349 - 4.57472i) q^{20} +(1.76441 - 0.172184i) q^{21} +(15.5568 + 2.55798i) q^{22} +(2.14949 - 3.72303i) q^{23} +(-2.02483 + 0.0702677i) q^{24} +(6.12120 + 10.6022i) q^{25} +(-28.0798 - 23.0138i) q^{26} +4.54237 q^{27} +(27.2712 + 6.34684i) q^{28} +28.3630i q^{29} +(-1.39924 - 1.14680i) q^{30} +(-28.2372 + 16.3027i) q^{31} +(-30.6523 - 9.18881i) q^{32} +(1.72891 + 0.998189i) q^{33} +(-18.8270 - 3.09569i) q^{34} +(14.5452 + 20.3362i) q^{35} +(33.8616 + 11.4450i) q^{36} +(-25.9006 - 14.9537i) q^{37} +(46.4448 - 17.5153i) q^{38} +(-2.29867 - 3.98141i) q^{39} +(-15.1368 - 24.2356i) q^{40} +45.2606i q^{41} +(2.94757 + 1.97053i) q^{42} +24.9109i q^{43} +(20.8211 + 23.6793i) q^{44} +(15.9585 + 27.6409i) q^{45} +(8.04492 - 3.03391i) q^{46} +(44.0432 + 25.4284i) q^{47} +(-3.22119 - 2.45833i) q^{48} +(-32.2419 - 36.8979i) q^{49} +(-3.97264 + 24.1604i) q^{50} +(-2.09235 - 1.20802i) q^{51} +(-14.2591 - 71.1978i) q^{52} +(54.3930 - 31.4038i) q^{53} +(7.02636 + 5.75869i) q^{54} +28.1558i q^{55} +(34.1381 + 44.3913i) q^{56} +6.28554 q^{57} +(-35.9579 + 43.8733i) q^{58} +(-37.0048 - 64.0942i) q^{59} +(-0.710541 - 3.54785i) q^{60} +(25.2994 - 43.8198i) q^{61} +(-64.3469 - 10.5804i) q^{62} +(-36.3890 - 50.8770i) q^{63} +(-35.7653 - 53.0740i) q^{64} +(32.4191 - 56.1515i) q^{65} +(1.40890 + 3.73592i) q^{66} +(-108.673 + 62.7422i) q^{67} +(-25.1979 - 28.6569i) q^{68} +1.08875 q^{69} +(-3.28249 + 49.8971i) q^{70} -5.33822 q^{71} +(37.8691 + 60.6326i) q^{72} +(-23.6569 + 13.6583i) q^{73} +(-21.1065 - 55.9674i) q^{74} +(-1.55023 + 2.68508i) q^{75} +(94.0487 + 31.7880i) q^{76} +(-5.35941 - 54.9191i) q^{77} +(1.49183 - 9.07283i) q^{78} +(51.5380 - 89.2664i) q^{79} +(7.31096 - 56.6789i) q^{80} +(-39.6362 - 68.6519i) q^{81} +(-57.3802 + 70.0114i) q^{82} +51.5695 q^{83} +(2.06127 + 6.78497i) q^{84} -34.0744i q^{85} +(-31.5814 + 38.5334i) q^{86} +(-6.22075 + 3.59155i) q^{87} +(2.18715 + 63.0248i) q^{88} +(133.222 + 76.9158i) q^{89} +(-10.3570 + 62.9880i) q^{90} +(-52.5464 + 115.697i) q^{91} +(16.2906 + 5.50613i) q^{92} +(-7.15123 - 4.12877i) q^{93} +(35.8909 + 95.1708i) q^{94} +(44.3238 + 76.7711i) q^{95} +(-1.86610 - 7.88642i) q^{96} -47.0436i q^{97} +(-3.09519 - 97.9511i) q^{98} -70.4400i 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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