LMFDB - Embedded newform 392.3.j.e.117.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(117,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, 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("392.117");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.j (of order $6$, degree $2$, not 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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			117.12
Character	$\chi$	$=$	392.117
Dual form			392.3.j.e.325.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.54685 + 1.26777i) q^{2} +(-0.126628 - 0.219326i) q^{3} +(0.785498 + 3.92212i) q^{4} +(1.78589 - 3.09325i) q^{5} +(0.0821813 - 0.499801i) q^{6} +(-3.75731 + 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +O(q^{10})$	\(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} +(-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} -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} +(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} +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} +(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} +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} +(-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} +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} +(-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} -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} +(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} -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} +(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} -70.4400i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	$ 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 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} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 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} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 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 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 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 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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	0.844149	−	0.536109i	$-0.180106\pi$
$3$	−0.126628	−	0.219326i	−0.0422093	−	0.0731087i	−0.886358	+	0.463000i	$0.846773\pi$
$4$	0.785498	+	3.92212i	0.196374	+	0.980529i
$5$	1.78589	−	3.09325i	0.357178	−	0.618650i	−0.630310	−	0.776343i	$-0.717072\pi$
$5$	1.78589	−	3.09325i	0.357178	−	0.618650i	0.987488	+	0.157693i	$0.0504056\pi$
$6$	0.0821813	−	0.499801i	0.0136969	−	0.0833001i
$7$		0			0
$7$		0			0
$8$	−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	$-0.253990\pi$
$13$	18.1529			1.39638			0.698189	+	0.715914i	$0.253990\pi$
$14$		0			0
$15$	−0.904575			−0.0603050
$16$	−14.7660	+	6.16163i	−0.922874	+	0.385102i
$17$	8.26180	−	4.76995i	0.485988	−	0.280585i	−0.236920	−	0.971529i	$-0.576138\pi$
$17$	8.26180	−	4.76995i	0.485988	−	0.280585i	0.722909	+	0.690944i	$0.242805\pi$
$18$	16.7221	−	6.30626i	0.929007	−	0.350348i
$19$	−12.4094	+	21.4938i	−0.653129	+	1.13125i	0.329231	+	0.944250i	$0.393211\pi$
$19$	−12.4094	+	21.4938i	−0.653129	+	1.13125i	−0.982359	+	0.187003i	$0.940123\pi$
$20$	13.5349	+	4.57472i	0.676745	+	0.228736i
$21$		0			0
$22$	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
$28$		0			0
$29$			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	0.0301634	−	0.999545i	$-0.490397\pi$
$31$	28.2372	−	16.3027i	0.910876	−	0.525895i	0.880713	+	0.473650i	$0.157064\pi$
$32$	−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
$35$		0			0
$36$	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	$-0.813881\pi$
$41$		−	45.2606i		−	1.10392i	0.833872	−	0.551958i	$-0.186119\pi$
$42$		0			0
$43$			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	−0.0480430	−	0.998845i	$-0.515298\pi$
$47$	−44.0432	−	25.4284i	−0.937090	−	0.541029i	−0.889047	+	0.457816i	$0.848632\pi$
$48$	3.22119	+	2.45833i	0.0671082	+	0.0512153i
$49$		0			0
$50$	−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
$56$		0			0
$57$	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	$0.0491323\pi$
$59$	37.0048	+	64.0942i	0.627200	+	1.08634i	−0.360912	+	0.932600i	$0.617534\pi$
$60$	−0.710541	−	3.54785i	−0.0118424	−	0.0591308i
$61$	−25.2994	+	43.8198i	−0.414743	+	0.718357i	−0.995401	−	0.0957908i	$-0.969462\pi$
$61$	−25.2994	+	43.8198i	−0.414743	+	0.718357i	0.580658	+	0.814148i	$0.302795\pi$
$62$	64.3469	+	10.5804i	1.03785	+	0.170652i
$63$		0			0
$64$	−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
$70$		0			0
$71$	−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	−0.329137	−	0.944282i	$-0.606758\pi$
$73$	23.6569	−	13.6583i	0.324067	−	0.187100i	0.653204	+	0.757182i	$0.273424\pi$
$74$	−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
$77$		0			0
$78$	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	$-0.600550\pi$
$83$	−51.5695			−0.621319			−0.310660	+	0.950521i	$0.600550\pi$
$84$		0			0
$85$		−	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	−0.496883	−	0.867818i	$-0.665522\pi$
$89$	−133.222	−	76.9158i	−1.49688	−	0.864222i	−0.999994	+	0.00359545i	$0.998856\pi$
$90$	10.3570	−	62.9880i	0.115078	−	0.699867i
$91$		0			0
$92$	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	$0.0779651\pi$
$97$			47.0436i			0.484986i	−0.970153	+	0.242493i	$0.922035\pi$
$98$		0			0
$99$		−	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	$-0.901807\pi$
$101$	−74.6727	−	129.337i	−0.739333	−	1.28056i	0.213462	−	0.976951i	$-0.431526\pi$
$102$	−1.70506	−	4.52125i	−0.0167163	−	0.0443260i
$103$	17.1847	+	9.92160i	0.166842	+	0.0963262i	0.581096	−	0.813835i	$-0.302624\pi$
$103$	17.1847	+	9.92160i	0.166842	+	0.0963262i	−0.414254	+	0.910161i	$0.635957\pi$
$104$	−68.2061	+	128.210i	−0.655827	+	1.23279i
$105$		0			0
$106$	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
$112$		0			0
$113$	−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
$119$		0			0
$120$	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
$126$		0			0
$127$	−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	−0.999571	−	0.0292837i	$-0.990677\pi$
$131$	−62.1497	+	107.646i	−0.474425	+	0.821728i	0.525146	+	0.851012i	$0.324011\pi$
$132$	2.55696	−	7.56508i	0.0193709	−	0.0573112i
$133$		0			0
$134$	−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	$-0.908114\pi$
$139$	−266.497			−1.91725			−0.958624	+	0.284677i	$0.908114\pi$
$140$		0			0
$141$			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
$147$		0			0
$148$	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
$154$		0			0
$155$		−	116.460i		−	0.751352i
$156$	13.8099	−	12.1430i	0.0885253	−	0.0778399i
$157$	−63.8147	−	110.530i	−0.406463	−	0.704015i	0.588028	−	0.808841i	$-0.299905\pi$
$157$	−63.8147	−	110.530i	−0.406463	−	0.704015i	−0.994491	+	0.104826i	$0.966571\pi$
$158$	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
$161$		0			0
$162$	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	$0.140613\pi$
$167$			142.792i			0.855042i	−0.904005	+	0.427521i	$0.859387\pi$
$168$		0			0
$169$	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	$-0.641886\pi$
$173$	97.8898	−	169.550i	0.565837	−	0.980059i	0.996971	−	0.0777710i	$-0.0247803\pi$
$174$	14.1758	+	2.33091i	0.0814704	+	0.0133960i
$175$		0			0
$176$	−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	$-0.418843\pi$
$181$	91.2994			0.504417			0.252208	+	0.967673i	$0.418843\pi$
$182$		0			0
$183$	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
$189$		0			0
$190$	−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
$196$		0			0
$197$			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	−0.987597	−	0.157011i	$-0.949814\pi$
$199$	−267.738	+	154.579i	−1.34542	+	0.776778i	−0.357823	+	0.933790i	$0.616481\pi$
$200$	−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
$203$		0			0
$204$	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
$210$		0			0
$211$			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
$217$		0			0
$218$	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	$-0.993615\pi$
$223$		−	8.94619i		−	0.0401174i	0.999799	−	0.0200587i	$-0.00638532\pi$
$224$		0			0
$225$	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	$0.0384237\pi$
$227$	136.347	+	236.160i	0.600647	+	1.04035i	−0.392076	+	0.919933i	$0.628243\pi$
$228$	4.93727	+	24.6526i	0.0216547	+	0.108125i
$229$	−165.611	+	286.846i	−0.723191	+	1.25260i	0.236523	+	0.971626i	$0.423992\pi$
$229$	−165.611	+	286.846i	−0.723191	+	1.25260i	−0.959714	+	0.280978i	$0.909341\pi$
$230$	4.98269	−	30.3032i	0.0216639	−	0.131753i
$231$		0			0
$232$	−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
$238$		0			0
$239$	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	−0.810759	−	0.585379i	$-0.800946\pi$
$241$	−170.914	+	98.6771i	−0.709186	+	0.409449i	0.101574	+	0.994828i	$0.467612\pi$
$242$	−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
$245$		0			0
$246$	−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	$-0.283677\pi$
$251$	315.497			1.25696			0.628480	+	0.777826i	$0.283677\pi$
$252$		0			0
$253$		−	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	0.977256	−	0.212065i	$-0.0680188\pi$
$257$	329.533	+	190.256i	1.28223	+	0.740296i	0.304974	+	0.952361i	$0.401352\pi$
$258$	12.4505	+	2.04721i	0.0482576	+	0.00793492i
$259$		0			0
$260$	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
$266$		0			0
$267$			38.9588i			0.145913i
$268$	−331.445	−	376.943i	−1.23673	−	1.40650i
$269$	51.1557	+	88.6043i	0.190170	+	0.329384i	0.945306	−	0.326184i	$-0.105763\pi$
$269$	51.1557	+	88.6043i	0.190170	+	0.329384i	−0.755137	+	0.655568i	$0.772429\pi$
$270$	−30.3614	+	11.4499i	−0.112450	+	0.0424071i
$271$	221.981	+	128.161i	0.819118	+	0.472918i	0.850112	−	0.526602i	$-0.176534\pi$
$271$	221.981	+	128.161i	0.819118	+	0.472918i	−0.0309944	+	0.999520i	$0.509867\pi$
$272$	−92.6030	+	121.339i	−0.340452	+	0.446100i
$273$		0			0
$274$	−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
$280$		0			0
$281$	−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	$-0.990838\pi$
$283$	−148.495	−	257.201i	−0.524718	−	0.908838i	0.474868	−	0.880057i	$-0.342496\pi$
$284$	−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
$287$		0			0
$288$	−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	$-0.425691\pi$
$293$	135.561			0.462665			0.231333	+	0.972875i	$0.425691\pi$
$294$		0			0
$295$	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
$301$		0			0
$302$	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	$-0.460392\pi$
$307$	76.2052			0.248225			0.124113	+	0.992268i	$0.460392\pi$
$308$		0			0
$309$		−	5.02541i		−	0.0162635i
$310$	147.644	−	180.146i	0.476272	−	0.581115i
$311$	171.554	−	99.0468i	0.551621	−	0.318479i	−0.198154	−	0.980171i	$-0.563495\pi$
$311$	171.554	−	99.0468i	0.551621	−	0.318479i	0.749776	+	0.661692i	$0.230161\pi$
$312$	36.7565	−	1.27556i	0.117809	−	0.00408834i
$313$	47.9693	+	27.6951i	0.153257	+	0.0884827i	0.574667	−	0.818387i	$-0.305132\pi$
$313$	47.9693	+	27.6951i	0.153257	+	0.0884827i	−0.421411	+	0.906870i	$0.638465\pi$
$314$	41.4156	−	251.877i	0.131897	−	0.802155i
$315$		0			0
$316$	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
$322$		0			0
$323$			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
$329$		0			0
$330$	−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
$336$		0			0
$337$	−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
$343$		0			0
$344$	−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	$-0.488286\pi$
$349$	25.6801			0.0735821			0.0367910	+	0.999323i	$0.488286\pi$
$350$		0			0
$351$	−82.4571			−0.234921
$352$	−245.473	+	58.0841i	−0.697366	+	0.165012i
$353$	229.938	−	132.755i	0.651383	−	0.376076i	−0.137603	−	0.990487i	$-0.543940\pi$
$353$	229.938	−	132.755i	0.651383	−	0.376076i	0.788986	+	0.614411i	$0.210606\pi$
$354$	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
$357$		0			0
$358$	−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
$364$		0			0
$365$		−	97.5689i		−	0.267312i
$366$	19.8220	+	16.2458i	0.0541585	+	0.0443874i
$367$	−180.099	+	103.980i	−0.490732	+	0.283324i	−0.724878	−	0.688877i	$-0.758104\pi$
$367$	−180.099	+	103.980i	−0.490732	+	0.283324i	0.234146	+	0.972201i	$0.424771\pi$
$368$	−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
$371$		0			0
$372$	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
$378$		0			0
$379$		−	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	0.809481	−	0.587146i	$-0.199749\pi$
$383$	270.298	+	156.056i	0.705738	+	0.407458i	−0.103743	+	0.994604i	$0.533082\pi$
$384$	−29.4656	+	13.5138i	−0.0767334	+	0.0351922i
$385$		0			0
$386$	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
$392$		0			0
$393$	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	−0.960979	−	0.276621i	$-0.910785\pi$
$397$	−95.6487	+	165.668i	−0.240929	+	0.417301i	0.720050	+	0.693922i	$0.244119\pi$
$398$	−610.123	−	100.321i	−1.53297	−	0.252064i
$399$		0			0
$400$	−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
$406$		0			0
$407$	−235.756			−0.579254
$408$	16.3936	−	10.2389i	0.0401803	−	0.0250953i
$409$	4.57744	−	2.64279i	0.0111918	−	0.00646158i	−0.494394	−	0.869238i	$-0.664610\pi$
$409$	4.57744	−	2.64279i	0.0111918	−	0.00646158i	0.505585	+	0.862777i	$0.331277\pi$
$410$	−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
$413$		0			0
$414$	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	$-0.513190\pi$
$419$	−34.7160			−0.0828545			−0.0414272	+	0.999142i	$0.513190\pi$
$420$		0			0
$421$			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
$427$		0			0
$428$	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	$-0.880103\pi$
$433$		−	318.535i		−	0.735647i	0.929896	−	0.367823i	$-0.119897\pi$
$434$		0			0
$435$		−	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	−0.250109	−	0.968218i	$-0.580467\pi$
$439$	−532.799	−	307.612i	−1.21366	−	0.700710i	−0.963556	+	0.267508i	$0.913800\pi$
$440$	198.858	+	105.790i	0.451949	+	0.240432i
$441$		0			0
$442$	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
$448$		0			0
$449$	−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
$455$		0			0
$456$	−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	$-0.803282\pi$
$461$	−751.461			−1.63007			−0.815034	+	0.579413i	$0.803282\pi$
$462$		0			0
$463$	−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	−0.554783	−	0.831995i	$-0.687199\pi$
$467$	206.945	−	358.440i	0.443138	−	0.767537i	0.997920	+	0.0644583i	$0.0205320\pi$
$468$	614.686	+	207.760i	1.31343	+	0.443932i
$469$		0			0
$470$	−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
$476$		0			0
$477$		−	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	$-0.270624\pi$
$479$	785.798	−	453.681i	1.64050	−	0.947142i	0.980657	−	0.195737i	$-0.0627098\pi$
$480$	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
$483$		0			0
$484$	−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
$490$		0			0
$491$			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
$497$		0			0
$498$	−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	$-0.619074\pi$
$503$		−	936.429i		−	1.86169i	0.365418	−	0.930843i	$-0.380926\pi$
$504$		0			0
$505$	−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	−0.982365	−	0.186975i	$-0.940132\pi$
$509$	−167.592	+	290.278i	−0.329258	+	0.570291i	0.653107	+	0.757265i	$0.273465\pi$
$510$	−17.0304	−	2.80028i	−0.0333930	−	0.00549075i
$511$		0			0
$512$	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
$518$		0			0
$519$	−49.5824			−0.0955345
$520$	274.776	+	439.947i	0.528416	+	0.846051i
$521$	421.675	−	243.454i	0.809357	−	0.467283i	−0.0373754	−	0.999301i	$-0.511900\pi$
$521$	421.675	−	243.454i	0.809357	−	0.467283i	0.846733	+	0.532019i	$0.178566\pi$
$522$	178.865	+	474.290i	0.342652	+	0.908601i
$523$	86.3132	−	149.499i	0.165035	−	0.285849i	−0.771633	−	0.636068i	$-0.780560\pi$
$523$	86.3132	−	149.499i	0.165035	−	0.285849i	0.936668	+	0.350220i	$0.113893\pi$
$524$	−471.020	−	159.202i	−0.898894	−	0.303821i
$525$		0			0
$526$	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
$532$		0			0
$533$		−	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
$539$		0			0
$540$	−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
$546$		0			0
$547$		−	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
$553$		0			0
$554$	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
$560$		0			0
$561$	−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	$-0.800446\pi$
$563$	−514.005	−	890.283i	−0.912975	−	1.58132i	−0.103136	−	0.994667i	$-0.532888\pi$
$564$	−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
$567$		0			0
$568$	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
$574$		0			0
$575$	52.6299			0.0915303
$576$	−570.519	+	39.6452i	−0.990485	+	0.0688285i
$577$	−131.878	+	76.1400i	−0.228559	+	0.131958i	−0.609907	−	0.792473i	$-0.708793\pi$
$577$	−131.878	+	76.1400i	−0.228559	+	0.131958i	0.381348	+	0.924431i	$0.375460\pi$
$578$	−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
$581$		0			0
$582$	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	$-0.224295\pi$
$587$	894.404			1.52369			0.761843	+	0.647761i	$0.224295\pi$
$588$		0			0
$589$			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	0.354633	−	0.935006i	$-0.384606\pi$
$593$	−164.729	−	95.1064i	−0.277789	−	0.160382i	−0.632422	+	0.774624i	$0.717939\pi$
$594$	−70.6647	−	11.6193i	−0.118964	−	0.0195610i
$595$		0			0
$596$	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	$0.165620\pi$
$601$			597.574i			0.994299i	−0.867665	+	0.497150i	$0.834380\pi$
$602$		0			0
$603$			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	0.508757	−	0.860910i	$-0.330105\pi$
$607$	10.6620	+	6.15569i	0.0175650	+	0.0101412i	−0.491192	+	0.871051i	$0.663439\pi$
$608$	577.881	−	544.807i	0.950462	−	0.896064i
$609$		0			0
$610$	−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
$616$		0			0
$617$	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	0.904386	−	0.426715i	$-0.140329\pi$
$619$	51.1586	+	88.6092i	0.0826471	+	0.143149i	−0.821739	+	0.569864i	$0.806996\pi$
$620$	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
$623$		0			0
$624$	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
$630$		0			0
$631$	−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
$637$		0			0
$638$	−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	$-0.563070\pi$
$643$	−253.143			−0.393690			−0.196845	+	0.980435i	$0.563070\pi$
$644$		0			0
$645$		−	22.5337i		−	0.0349360i
$646$	−300.171	+	366.248i	−0.464661	+	0.566947i
$647$	−485.492	+	280.299i	−0.750374	+	0.433229i	−0.825829	−	0.563921i	$-0.809292\pi$
$647$	−485.492	+	280.299i	−0.750374	+	0.433229i	0.0754551	+	0.997149i	$0.475959\pi$
$648$	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
$651$		0			0
$652$	−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
$658$		0			0
$659$			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	0.877524	−	0.479533i	$-0.159194\pi$
$661$	15.5168	+	26.8758i	0.0234747	+	0.0406593i	−0.854049	+	0.520192i	$0.825860\pi$
$662$	−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
$665$		0			0
$666$	−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
$672$		0			0
$673$	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	−0.890540	−	0.454905i	$-0.849673\pi$
$677$	−34.7377	+	60.1674i	−0.0513112	+	0.0888736i	0.839229	+	0.543778i	$0.183007\pi$
$678$	−10.1914	+	61.9806i	−0.0150315	+	0.0914169i
$679$		0			0
$680$	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
$686$		0			0
$687$	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	−0.889628	−	0.456685i	$-0.849037\pi$
$691$	−34.0754	+	59.0204i	−0.0493132	+	0.0854130i	0.840315	+	0.542098i	$0.182370\pi$
$692$	741.888	+	250.754i	1.07209	+	0.362361i
$693$		0			0
$694$	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
$700$		0			0
$701$		−	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
$707$		0			0
$708$	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
$714$		0			0
$715$		−	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	0.947979	−	0.318333i	$-0.103123\pi$
$719$	824.178	+	475.840i	1.14628	+	0.661808i	0.198305	+	0.980140i	$0.436456\pi$
$720$	405.955	+	309.815i	0.563827	+	0.430298i
$721$		0			0
$722$	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	$-0.739339\pi$
$727$		−	1061.98i		−	1.46078i	0.683032	−	0.730388i	$-0.260661\pi$
$728$		0			0
$729$	−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	−0.866126	−	0.499825i	$-0.833398\pi$
$733$	−0.148102	+	0.256519i	−0.000202048	+	0.000349958i	0.865924	+	0.500175i	$0.166731\pi$
$734$	−410.409	−	67.4828i	−0.559140	−	0.0919384i
$735$		0			0
$736$	−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
$742$		0			0
$743$	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
$749$		0			0
$750$	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
$756$		0			0
$757$			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	0.364328	−	0.931271i	$-0.381299\pi$
$761$	−197.869	−	114.240i	−0.260011	−	0.150118i	−0.624340	+	0.781153i	$0.714632\pi$
$762$	−4.73482	+	28.7957i	−0.00621368	+	0.0377896i
$763$		0			0
$764$	−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	$-0.982726\pi$
$769$		−	83.4232i		−	0.108483i	0.998528	−	0.0542414i	$-0.0172740\pi$
$770$		0			0
$771$		−	96.3670i		−	0.124990i
$772$	728.098	−	640.213i	0.943132	−	0.829292i
$773$	−285.318	−	494.186i	−0.369105	−	0.639309i	0.620321	−	0.784348i	$-0.287002\pi$
$773$	−285.318	−	494.186i	−0.369105	−	0.639309i	−0.989426	+	0.145039i	$0.953669\pi$
$774$	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
$777$		0			0
$778$	−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
$784$		0			0
$785$	−455.864			−0.580718
$786$	48.6942	+	39.9090i	0.0619519	+	0.0507748i
$787$	382.719	+	662.888i	0.486301	+	0.842298i	0.999876	−	0.0157470i	$-0.00501262\pi$
$787$	382.719	+	662.888i	0.486301	+	0.842298i	−0.513575	+	0.858045i	$0.671679\pi$
$788$	−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
$791$		0			0
$792$	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	$-0.381944\pi$
$797$	577.729			0.724880			0.362440	+	0.932007i	$0.381944\pi$
$798$		0			0
$799$	−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
$805$		0			0
$806$	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	$-0.604952\pi$
$811$	−525.164			−0.647552			−0.323776	+	0.946134i	$0.604952\pi$
$812$		0			0
$813$		−	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
$819$		0			0
$820$	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
$826$		0			0
$827$			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	0.955454	−	0.295139i	$-0.0953658\pi$
$829$	184.145	+	318.949i	0.222130	+	0.384740i	−0.733325	+	0.679878i	$0.762033\pi$
$830$	−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
$833$		0			0
$834$	−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	$0.139043\pi$
$839$			709.889i			0.846113i	−0.906103	+	0.423056i	$0.860957\pi$
$840$		0			0
$841$	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
$847$		0			0
$848$	−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	$-0.267891\pi$
$853$	1136.65			1.33253			0.666267	+	0.745713i	$0.267891\pi$
$854$		0			0
$855$	792.143			0.926483
$856$	62.0435	−	38.7503i	0.0724808	−	0.0452691i
$857$	−578.645	+	334.081i	−0.675198	+	0.389826i	−0.798043	−	0.602600i	$-0.794131\pi$
$857$	−578.645	+	334.081i	−0.675198	+	0.389826i	0.122845	+	0.992426i	$0.460798\pi$
$858$	−25.5755	−	67.8179i	−0.0298083	−	0.0790418i
$859$	100.378	−	173.859i	0.116854	−	0.202397i	−0.801665	−	0.597773i	$-0.796052\pi$
$859$	100.378	−	173.859i	0.116854	−	0.202397i	0.918519	+	0.395376i	$0.129386\pi$
$860$	−113.960	+	337.166i	−0.132512	+	0.392054i
$861$		0			0
$862$	−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
$868$		0			0
$869$		−	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
$875$		0			0
$876$	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	$0.163392\pi$
$881$			865.257i			0.982130i	−0.871123	+	0.491065i	$0.836608\pi$
$882$		0			0
$883$		−	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	0.762792	−	0.646644i	$-0.223828\pi$
$887$	518.166	+	299.163i	0.584178	+	0.337275i	−0.178614	+	0.983919i	$0.557161\pi$
$888$	−53.4951	−	28.4588i	−0.0602423	−	0.0320482i
$889$		0			0
$890$	−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
$896$		0			0
$897$	−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
$903$		0			0
$904$	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
$910$		0			0
$911$	−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
$917$		0			0
$918$	−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
$924$		0			0
$925$		−	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	0.994515	−	0.104589i	$-0.0333528\pi$
$929$	1301.71	+	751.543i	1.40120	+	0.808981i	0.406681	+	0.913570i	$0.366686\pi$
$930$	−58.2066	−	9.57080i	−0.0625877	−	0.0102912i
$931$		0			0
$932$	−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	$-0.928163\pi$
$937$		−	419.349i		−	0.447545i	0.974641	−	0.223772i	$-0.0718372\pi$
$938$		0			0
$939$		−	14.0279i		−	0.0149392i
$940$	−479.793	−	545.656i	−0.510418	−	0.580485i
$941$	−261.680	−	453.243i	−0.278087	−	0.481661i	0.692822	−	0.721108i	$-0.256367\pi$
$941$	−261.680	−	453.243i	−0.278087	−	0.481661i	−0.970909	+	0.239448i	$0.923034\pi$
$942$	−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
$945$		0			0
$946$	−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
$952$		0			0
$953$	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
$959$		0			0
$960$	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
$966$		0			0
$967$	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	−0.996064	−	0.0886380i	$-0.971749\pi$
$971$	−409.052	+	708.499i	−0.421269	+	0.729660i	0.574795	+	0.818298i	$0.305082\pi$
$972$	−230.992	−	78.0742i	−0.237646	−	0.0803232i
$973$		0			0
$974$	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
$980$		0			0
$981$		−	1065.14i		−	1.08577i
$982$	−182.719	+	222.941i	−0.186068	+	0.227028i
$983$	−852.404	+	492.136i	−0.867146	+	0.500647i	−0.866399	−	0.499353i	$-0.833571\pi$
$983$	−852.404	+	492.136i	−0.867146	+	0.500647i	−0.000746983		1.00000i	$0.500238\pi$
$984$	−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
$987$		0			0
$988$	−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
$994$		0			0
$995$			1104.24i			1.10979i
$996$	−39.2318	+	34.4964i	−0.0393894	+	0.0346349i
$997$	−186.825	−	323.590i	−0.187387	−	0.324563i	0.756991	−	0.653425i	$-0.226668\pi$
$997$	−186.825	−	323.590i	−0.187387	−	0.324563i	−0.944378	+	0.328861i	$0.893335\pi$
$998$	−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	392.3.j.e.117.12		28
7.2	even	3		392.3.h.a.293.14		28
7.3	odd	6	inner	392.3.j.e.325.2		28
7.4	even	3		56.3.j.a.45.2	yes	28
7.5	odd	6		392.3.h.a.293.13		28
7.6	odd	2		56.3.j.a.5.12	yes	28
8.5	even	2	inner	392.3.j.e.117.2		28
28.11	odd	6		224.3.n.a.17.8		28
28.19	even	6		1568.3.h.a.881.15		28
28.23	odd	6		1568.3.h.a.881.13		28
28.27	even	2		224.3.n.a.145.7		28
56.5	odd	6		392.3.h.a.293.16		28
56.11	odd	6		224.3.n.a.17.7		28
56.13	odd	2		56.3.j.a.5.2	✓	28
56.19	even	6		1568.3.h.a.881.14		28
56.27	even	2		224.3.n.a.145.8		28
56.37	even	6		392.3.h.a.293.15		28
56.45	odd	6	inner	392.3.j.e.325.12		28
56.51	odd	6		1568.3.h.a.881.16		28
56.53	even	6		56.3.j.a.45.12	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.2	✓	28	56.13	odd	2
56.3.j.a.5.12	yes	28	7.6	odd	2
56.3.j.a.45.2	yes	28	7.4	even	3
56.3.j.a.45.12	yes	28	56.53	even	6
224.3.n.a.17.7		28	56.11	odd	6
224.3.n.a.17.8		28	28.11	odd	6
224.3.n.a.145.7		28	28.27	even	2
224.3.n.a.145.8		28	56.27	even	2
392.3.h.a.293.13		28	7.5	odd	6
392.3.h.a.293.14		28	7.2	even	3
392.3.h.a.293.15		28	56.37	even	6
392.3.h.a.293.16		28	56.5	odd	6
392.3.j.e.117.2		28	8.5	even	2	inner
392.3.j.e.117.12		28	1.1	even	1	trivial
392.3.j.e.325.2		28	7.3	odd	6	inner
392.3.j.e.325.12		28	56.45	odd	6	inner
1568.3.h.a.881.13		28	28.23	odd	6
1568.3.h.a.881.14		28	56.19	even	6
1568.3.h.a.881.15		28	28.19	even	6
1568.3.h.a.881.16		28	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.54685 + 1.26777i) q^{2} +(-0.126628 - 0.219326i) q^{3} +(0.785498 + 3.92212i) q^{4} +(1.78589 - 3.09325i) q^{5} +(0.0821813 - 0.499801i) q^{6} +(-3.75731 + 7.06276i) q^{8} +(4.46793 - 7.73868i) q^{9} +O(q^{10})\)	\(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} +(-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} -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} +(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} +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} +(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} +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} +(-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} +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} +(-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} -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} +(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} -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} +(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} -70.4400i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9}+O(q^{10}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9	\( 28 q - 2 q^{2} - 4 q^{4} - 20 q^{8} - 32 q^{9} - 24 q^{10} + 18 q^{12} + 28 q^{15} + 16 q^{16} + 6 q^{17} - 42 q^{18} - 92 q^{22} + 30 q^{23} + 30 q^{24} - 32 q^{25} + 30 q^{26} + 22 q^{30} + 6 q^{31} + 88 q^{32} + 6 q^{33} + 256 q^{36} - 6 q^{38} - 20 q^{39} - 102 q^{40} - 42 q^{44} + 68 q^{46} + 294 q^{47} + 400 q^{50} + 168 q^{52} - 330 q^{54} + 124 q^{57} - 22 q^{58} - 62 q^{60} - 520 q^{64} - 52 q^{65} + 306 q^{66} + 456 q^{68} - 136 q^{71} + 96 q^{72} - 234 q^{73} - 138 q^{74} - 956 q^{78} - 162 q^{79} - 276 q^{80} - 18 q^{81} + 642 q^{82} + 168 q^{86} - 48 q^{87} + 50 q^{88} + 150 q^{89} + 1020 q^{92} - 618 q^{94} + 290 q^{95} - 1044 q^{96}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^4 - 20 * q^8 - 32 * q^9 - 24 * q^10 + 18 * q^12 + 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 + 22 * q^30 + 6 * q^31 + 88 * q^32 + 6 * q^33 + 256 * q^36 - 6 * q^38 - 20 * q^39 - 102 * q^40 - 42 * q^44 + 68 * q^46 + 294 * q^47 + 400 * q^50 + 168 * q^52 - 330 * q^54 + 124 * q^57 - 22 * q^58 - 62 * q^60 - 520 * q^64 - 52 * q^65 + 306 * q^66 + 456 * q^68 - 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 + 168 * q^86 - 48 * q^87 + 50 * q^88 + 150 * q^89 + 1020 * q^92 - 618 * q^94 + 290 * q^95 - 1044 * q^96

Introduction

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