LMFDB - Embedded newform 144.3.w.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(5,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("144.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.w (of order $12$, degree $4$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$46$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	144.5
Dual form			144.3.w.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.98351 + 0.256277i) q^{2} +(-1.40595 - 2.65015i) q^{3} +(3.86864 - 1.01666i) q^{4} +(1.00259 + 3.74171i) q^{5} +(3.46789 + 4.89630i) q^{6} +(4.65369 - 2.68681i) q^{7} +(-7.41296 + 3.00800i) q^{8} +(-5.04662 + 7.45195i) q^{9} +O(q^{10})$	\(q+(-1.98351 + 0.256277i) q^{2} +(-1.40595 - 2.65015i) q^{3} +(3.86864 - 1.01666i) q^{4} +(1.00259 + 3.74171i) q^{5} +(3.46789 + 4.89630i) q^{6} +(4.65369 - 2.68681i) q^{7} +(-7.41296 + 3.00800i) q^{8} +(-5.04662 + 7.45195i) q^{9} +(-2.94756 - 7.16478i) q^{10} +(12.4933 + 3.34758i) q^{11} +(-8.13341 - 8.82313i) q^{12} +(-3.07587 - 11.4793i) q^{13} +(-8.54209 + 6.52195i) q^{14} +(8.50651 - 7.91765i) q^{15} +(13.9328 - 7.86617i) q^{16} -11.8846i q^{17} +(8.10028 - 16.0744i) q^{18} +(20.1387 - 20.1387i) q^{19} +(7.68268 + 13.4560i) q^{20} +(-13.6633 - 8.55548i) q^{21} +(-25.6386 - 3.43821i) q^{22} +(4.74003 - 8.20998i) q^{23} +(18.3939 + 15.4164i) q^{24} +(8.65545 - 4.99723i) q^{25} +(9.04291 + 21.9811i) q^{26} +(26.8441 + 2.89727i) q^{27} +(15.2719 - 15.1255i) q^{28} +(5.39392 - 20.1304i) q^{29} +(-14.8437 + 17.8848i) q^{30} +(-19.3613 + 33.5347i) q^{31} +(-25.6200 + 19.1733i) q^{32} +(-8.69337 - 37.8157i) q^{33} +(3.04574 + 23.5732i) q^{34} +(14.7190 + 14.7190i) q^{35} +(-11.9475 + 33.9596i) q^{36} +(9.65467 + 9.65467i) q^{37} +(-34.7843 + 45.1065i) q^{38} +(-26.0974 + 24.2908i) q^{39} +(-18.6872 - 24.7213i) q^{40} +(-11.7420 + 20.3377i) q^{41} +(29.2939 + 13.4683i) q^{42} +(19.5292 - 72.8841i) q^{43} +(51.7356 + 0.249158i) q^{44} +(-32.9427 - 11.4118i) q^{45} +(-7.29789 + 17.4994i) q^{46} +(-18.4560 + 10.6556i) q^{47} +(-40.4354 - 25.8647i) q^{48} +(-10.0621 + 17.4281i) q^{49} +(-15.8875 + 12.1303i) q^{50} +(-31.4959 + 16.7091i) q^{51} +(-23.5700 - 41.2822i) q^{52} +(-21.4244 + 21.4244i) q^{53} +(-53.9881 + 1.13275i) q^{54} +50.1026i q^{55} +(-26.4157 + 33.9155i) q^{56} +(-81.6846 - 25.0567i) q^{57} +(-5.53996 + 41.3112i) q^{58} +(-6.02423 - 22.4827i) q^{59} +(24.8591 - 39.2788i) q^{60} +(58.9293 + 15.7901i) q^{61} +(29.8091 - 71.4783i) q^{62} +(-3.46345 + 48.2384i) q^{63} +(45.9039 - 44.5963i) q^{64} +(39.8684 - 23.0180i) q^{65} +(26.9347 + 72.7801i) q^{66} +(24.1615 + 90.1720i) q^{67} +(-12.0825 - 45.9771i) q^{68} +(-28.4219 - 1.01902i) q^{69} +(-32.9674 - 25.4232i) q^{70} +124.525 q^{71} +(14.9950 - 70.4212i) q^{72} +86.4217i q^{73} +(-21.6244 - 16.6759i) q^{74} +(-25.4125 - 15.9124i) q^{75} +(57.4353 - 98.3836i) q^{76} +(67.1344 - 17.9886i) q^{77} +(45.5394 - 54.8693i) q^{78} +(46.4211 + 80.4037i) q^{79} +(43.4018 + 44.2460i) q^{80} +(-30.0632 - 75.2144i) q^{81} +(18.0783 - 43.3493i) q^{82} +(20.2421 - 75.5446i) q^{83} +(-61.5564 - 19.2072i) q^{84} +(44.4685 - 11.9153i) q^{85} +(-20.0580 + 149.571i) q^{86} +(-60.9322 + 14.0075i) q^{87} +(-102.682 + 12.7644i) q^{88} -164.215 q^{89} +(68.2668 + 14.1929i) q^{90} +(-45.1569 - 45.1569i) q^{91} +(9.99077 - 36.5805i) q^{92} +(116.093 + 4.16230i) q^{93} +(33.8770 - 25.8654i) q^{94} +(95.5439 + 55.1623i) q^{95} +(86.8326 + 40.9403i) q^{96} +(15.8533 + 27.4588i) q^{97} +(15.4919 - 37.1475i) q^{98} +(-87.9951 + 76.2057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	$ 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) $ 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	−1.98351	+	0.256277i	−0.991756	+	0.128138i
$2$	−1.98351	+	0.256277i	−0.991756	+	0.128138i
$3$	−1.40595	−	2.65015i	−0.468649	−	0.883384i
$3$	−1.40595	−	2.65015i	−0.468649	−	0.883384i
$4$	3.86864	−	1.01666i	0.967161	−	0.254164i
$5$	1.00259	+	3.74171i	0.200517	+	0.748341i	0.990769	+	0.135559i	$0.0432831\pi$
$5$	1.00259	+	3.74171i	0.200517	+	0.748341i	−0.790252	+	0.612782i	$0.790050\pi$
$6$	3.46789	+	4.89630i	0.577981	+	0.816050i
$7$	4.65369	−	2.68681i	0.664813	−	0.383830i	−0.129295	−	0.991606i	$-0.541272\pi$
$7$	4.65369	−	2.68681i	0.664813	−	0.383830i	0.794108	+	0.607776i	$0.207938\pi$
$8$	−7.41296	+	3.00800i	−0.926620	+	0.375999i
$9$	−5.04662	+	7.45195i	−0.560736	+	0.827995i
$10$	−2.94756	−	7.16478i	−0.294756	−	0.716478i
$11$	12.4933	+	3.34758i	1.13576	+	0.304325i	0.777244	−	0.629200i	$-0.216617\pi$
$11$	12.4933	+	3.34758i	1.13576	+	0.304325i	0.358513	+	0.933525i	$0.383284\pi$
$12$	−8.13341	−	8.82313i	−0.677784	−	0.735261i
$13$	−3.07587	−	11.4793i	−0.236605	−	0.883024i	−0.977419	−	0.211312i	$-0.932226\pi$
$13$	−3.07587	−	11.4793i	−0.236605	−	0.883024i	0.740813	−	0.671711i	$-0.234440\pi$
$14$	−8.54209	+	6.52195i	−0.610149	+	0.465854i
$15$	8.50651	−	7.91765i	0.567101	−	0.527843i
$16$	13.9328	−	7.86617i	0.870801	−	0.491635i
$17$		−	11.8846i		−	0.699092i	−0.936919	−	0.349546i	$-0.886336\pi$
$17$		−	11.8846i		−	0.699092i	0.936919	−	0.349546i	$-0.113664\pi$
$18$	8.10028	−	16.0744i	0.450015	−	0.893021i
$19$	20.1387	−	20.1387i	1.05993	−	1.05993i	0.0618460	−	0.998086i	$-0.480301\pi$
$19$	20.1387	−	20.1387i	1.05993	−	1.05993i	0.998086	−	0.0618460i	$-0.0196988\pi$
$20$	7.68268	+	13.4560i	0.384134	+	0.672802i
$21$	−13.6633	−	8.55548i	−0.650633	−	0.407404i
$22$	−25.6386	−	3.43821i	−1.16539	−	0.156282i
$23$	4.74003	−	8.20998i	0.206088	−	0.356955i	−0.744391	−	0.667744i	$-0.767260\pi$
$23$	4.74003	−	8.20998i	0.206088	−	0.356955i	0.950479	+	0.310789i	$0.100593\pi$
$24$	18.3939	+	15.4164i	0.766412	+	0.642350i
$25$	8.65545	−	4.99723i	0.346218	−	0.199889i
$26$	9.04291	+	21.9811i	0.347804	+	0.845426i
$27$	26.8441	+	2.89727i	0.994226	+	0.107306i
$28$	15.2719	−	15.1255i	0.545425	−	0.540197i
$29$	5.39392	−	20.1304i	0.185997	−	0.694151i	−0.808418	−	0.588609i	$-0.799676\pi$
$29$	5.39392	−	20.1304i	0.185997	−	0.694151i	0.994415	−	0.105542i	$-0.0336577\pi$
$30$	−14.8437	+	17.8848i	−0.494789	+	0.596160i
$31$	−19.3613	+	33.5347i	−0.624557	+	1.08176i	0.364069	+	0.931372i	$0.381387\pi$
$31$	−19.3613	+	33.5347i	−0.624557	+	1.08176i	−0.988626	+	0.150393i	$0.951946\pi$
$32$	−25.6200	+	19.1733i	−0.800625	+	0.599166i
$33$	−8.69337	−	37.8157i	−0.263435	−	1.14593i
$34$	3.04574	+	23.5732i	0.0895805	+	0.693329i
$35$	14.7190	+	14.7190i	0.420542	+	0.420542i
$36$	−11.9475	+	33.9596i	−0.331875	+	0.943323i
$37$	9.65467	+	9.65467i	0.260937	+	0.260937i	0.825435	−	0.564498i	$-0.190930\pi$
$37$	9.65467	+	9.65467i	0.260937	+	0.260937i	−0.564498	+	0.825435i	$0.690930\pi$
$38$	−34.7843	+	45.1065i	−0.915376	+	1.18701i
$39$	−26.0974	+	24.2908i	−0.669164	+	0.622842i
$40$	−18.6872	−	24.7213i	−0.467179	−	0.618033i
$41$	−11.7420	+	20.3377i	−0.286390	+	0.496042i	−0.972945	−	0.231036i	$-0.925789\pi$
$41$	−11.7420	+	20.3377i	−0.286390	+	0.496042i	0.686555	+	0.727077i	$0.259122\pi$
$42$	29.2939	+	13.4683i	0.697474	+	0.320674i
$43$	19.5292	−	72.8841i	0.454168	−	1.69498i	−0.236353	−	0.971667i	$-0.575952\pi$
$43$	19.5292	−	72.8841i	0.454168	−	1.69498i	0.690521	−	0.723312i	$-0.257381\pi$
$44$	51.7356	+	0.249158i	1.17581	+	0.00566269i
$45$	−32.9427	−	11.4118i	−0.732060	−	0.253594i
$46$	−7.29789	+	17.4994i	−0.158650	+	0.380421i
$47$	−18.4560	+	10.6556i	−0.392682	+	0.226715i	−0.683321	−	0.730118i	$-0.739465\pi$
$47$	−18.4560	+	10.6556i	−0.392682	+	0.226715i	0.290640	+	0.956833i	$0.406132\pi$
$48$	−40.4354	−	25.8647i	−0.842403	−	0.538848i
$49$	−10.0621	+	17.4281i	−0.205349	+	0.355675i
$50$	−15.8875	+	12.1303i	−0.317750	+	0.242605i
$51$	−31.4959	+	16.7091i	−0.617567	+	0.327629i
$52$	−23.5700	−	41.2822i	−0.453269	−	0.793889i
$53$	−21.4244	+	21.4244i	−0.404234	+	0.404234i	−0.879722	−	0.475488i	$-0.842271\pi$
$53$	−21.4244	+	21.4244i	−0.404234	+	0.404234i	0.475488	+	0.879722i	$0.342271\pi$
$54$	−53.9881	+	1.13275i	−0.999780	+	0.0209768i
$55$			50.1026i			0.910956i
$56$	−26.4157	+	33.9155i	−0.471709	+	0.605634i
$57$	−81.6846	−	25.0567i	−1.43306	−	0.439591i
$58$	−5.53996	+	41.3112i	−0.0955165	+	0.712262i
$59$	−6.02423	−	22.4827i	−0.102106	−	0.381063i	0.895895	−	0.444266i	$-0.146535\pi$
$59$	−6.02423	−	22.4827i	−0.102106	−	0.381063i	−0.998001	+	0.0632023i	$0.979869\pi$
$60$	24.8591	−	39.2788i	0.414319	−	0.654646i
$61$	58.9293	+	15.7901i	0.966054	+	0.258853i	0.707161	−	0.707053i	$-0.249976\pi$
$61$	58.9293	+	15.7901i	0.966054	+	0.258853i	0.258893	+	0.965906i	$0.416642\pi$
$62$	29.8091	−	71.4783i	0.480793	−	1.15288i
$63$	−3.46345	+	48.2384i	−0.0549754	+	0.765689i
$64$	45.9039	−	44.5963i	0.717249	−	0.696817i
$65$	39.8684	−	23.0180i	0.613359	−	0.354123i
$66$	26.9347	+	72.7801i	0.408102	+	1.10273i
$67$	24.1615	+	90.1720i	0.360620	+	1.34585i	0.873263	+	0.487249i	$0.162000\pi$
$67$	24.1615	+	90.1720i	0.360620	+	1.34585i	−0.512643	+	0.858602i	$0.671334\pi$
$68$	−12.0825	−	45.9771i	−0.177684	−	0.676134i
$69$	−28.4219	−	1.01902i	−0.411912	−	0.0147683i
$70$	−32.9674	−	25.4232i	−0.470963	−	0.363188i
$71$	124.525			1.75387			0.876935	−	0.480609i	$-0.159584\pi$
$71$	124.525			1.75387			0.876935	+	0.480609i	$0.159584\pi$
$72$	14.9950	−	70.4212i	0.208263	−	0.978073i
$73$			86.4217i			1.18386i	0.805990	+	0.591930i	$0.201634\pi$
$73$			86.4217i			1.18386i	−0.805990	+	0.591930i	$0.798366\pi$
$74$	−21.6244	−	16.6759i	−0.292222	−	0.225350i
$75$	−25.4125	−	15.9124i	−0.338834	−	0.212166i
$76$	57.4353	−	98.3836i	0.755728	−	1.29452i
$77$	67.1344	−	17.9886i	0.871875	−	0.233618i
$78$	45.5394	−	54.8693i	0.583838	−	0.703453i
$79$	46.4211	+	80.4037i	0.587609	+	1.01777i	0.994545	+	0.104311i	$0.0332639\pi$
$79$	46.4211	+	80.4037i	0.587609	+	1.01777i	−0.406936	+	0.913457i	$0.633403\pi$
$80$	43.4018	+	44.2460i	0.542522	+	0.553075i
$81$	−30.0632	−	75.2144i	−0.371150	−	0.928573i
$82$	18.0783	−	43.3493i	0.220467	−	0.528650i
$83$	20.2421	−	75.5446i	0.243881	−	0.910176i	−0.730062	−	0.683381i	$-0.760509\pi$
$83$	20.2421	−	75.5446i	0.243881	−	0.910176i	0.973943	−	0.226795i	$-0.0728247\pi$
$84$	−61.5564	−	19.2072i	−0.732815	−	0.228657i
$85$	44.4685	−	11.9153i	0.523159	−	0.140180i
$86$	−20.0580	+	149.571i	−0.233232	+	1.73920i
$87$	−60.9322	+	14.0075i	−0.700370	+	0.161006i
$88$	−102.682	+	12.7644i	−1.16684	+	0.145050i
$89$	−164.215			−1.84511			−0.922556	−	0.385863i	$-0.873904\pi$
$89$	−164.215			−1.84511			−0.922556	+	0.385863i	$0.873904\pi$
$90$	68.2668	+	14.1929i	0.758520	+	0.157699i
$91$	−45.1569	−	45.1569i	−0.496229	−	0.496229i
$92$	9.99077	−	36.5805i	0.108595	−	0.397614i
$93$	116.093	+	4.16230i	1.24831	+	0.0447559i
$94$	33.8770	−	25.8654i	0.360394	−	0.275164i
$95$	95.5439	+	55.1623i	1.00573	+	0.580656i
$96$	86.8326	+	40.9403i	0.904506	+	0.426461i
$97$	15.8533	+	27.4588i	0.163437	+	0.283080i	0.936099	−	0.351737i	$-0.114409\pi$
$97$	15.8533	+	27.4588i	0.163437	+	0.283080i	−0.772662	+	0.634817i	$0.781075\pi$
$98$	15.4919	−	37.1475i	0.158081	−	0.379056i
$99$	−87.9951	+	76.2057i	−0.888839	+	0.769755i
$100$	28.4044	−	28.1321i	0.284044	−	0.281321i
$101$	−120.067	−	32.1718i	−1.18878	−	0.318532i	−0.390376	−	0.920656i	$-0.627655\pi$
$101$	−120.067	−	32.1718i	−1.18878	−	0.318532i	−0.798403	+	0.602123i	$0.794322\pi$
$102$	58.1904	−	41.2143i	0.570494	−	0.404062i
$103$	−163.306	−	94.2846i	−1.58549	−	0.915384i	−0.994037	−	0.109046i	$-0.965220\pi$
$103$	−163.306	−	94.2846i	−1.58549	−	0.915384i	−0.591455	−	0.806338i	$-0.701446\pi$
$104$	57.3310	+	75.8434i	0.551260	+	0.729264i
$105$	18.3134	−	59.7017i	0.174414	−	0.568587i
$106$	37.0050	−	47.9862i	0.349104	−	0.452700i
$107$	96.3954	−	96.3954i	0.900891	−	0.900891i	−0.0946220	−	0.995513i	$-0.530164\pi$
$107$	96.3954	−	96.3954i	0.900891	−	0.900891i	0.995513	+	0.0946220i	$0.0301642\pi$
$108$	106.796	−	16.0827i	0.988850	−	0.148914i
$109$	−111.267	+	111.267i	−1.02079	+	1.02079i	−0.0210151	+	0.999779i	$0.506690\pi$
$109$	−111.267	+	111.267i	−1.02079	+	1.02079i	−0.999779	+	0.0210151i	$0.993310\pi$
$110$	−12.8401	−	99.3791i	−0.116729	−	0.903447i
$111$	12.0124	−	39.1603i	0.108220	−	0.352796i
$112$	43.7041	−	74.0415i	0.390215	−	0.661085i
$113$	−53.6807	−	30.9926i	−0.475051	−	0.274271i	0.243301	−	0.969951i	$-0.421770\pi$
$113$	−53.6807	−	30.9926i	−0.475051	−	0.274271i	−0.718352	+	0.695680i	$0.755103\pi$
$114$	168.444	+	28.7664i	1.47758	+	0.252337i
$115$	35.4716	+	9.50459i	0.308449	+	0.0826486i
$116$	0.401466	−	83.3611i	0.00346092	−	0.718630i
$117$	101.066	+	35.0105i	0.863812	+	0.299235i
$118$	17.7109	+	43.0509i	0.150093	+	0.364838i
$119$	−31.9316	−	55.3071i	−0.268332	−	0.464765i
$120$	−39.2421	+	84.2808i	−0.327018	+	0.702340i
$121$	40.0879	+	23.1447i	0.331305	+	0.191279i
$122$	−120.934	−	16.2176i	−0.991259	−	0.132931i
$123$	70.4067	+	2.52430i	0.572412	+	0.0205228i
$124$	−40.8086	+	149.418i	−0.329101	+	1.20498i
$125$	95.8540	+	95.8540i	0.766832	+	0.766832i
$126$	−5.49259	−	96.5691i	−0.0435920	−	0.766421i
$127$	−56.7743			−0.447041			−0.223521	−	0.974699i	$-0.571755\pi$
$127$	−56.7743			−0.447041			−0.223521	+	0.974699i	$0.571755\pi$
$128$	−79.6220	+	100.221i	−0.622047	+	0.782980i
$129$	−220.611	+	50.7158i	−1.71016	+	0.393145i
$130$	−73.1804	+	55.8739i	−0.562926	+	0.429799i
$131$	53.4982	−	14.3348i	0.408383	−	0.109426i	−0.0487784	−	0.998810i	$-0.515533\pi$
$131$	53.4982	−	14.3348i	0.408383	−	0.109426i	0.457161	+	0.889384i	$0.348866\pi$
$132$	−72.0772	−	137.457i	−0.546039	−	1.04134i
$133$	39.6104	−	147.828i	0.297823	−	1.11149i
$134$	−71.0337	−	172.665i	−0.530102	−	1.28855i
$135$	16.0728	+	103.348i	0.119058	+	0.765537i
$136$	35.7487	+	88.0998i	0.262858	+	0.647792i
$137$	−52.5810	−	91.0730i	−0.383803	−	0.664766i	0.607799	−	0.794091i	$-0.292052\pi$
$137$	−52.5810	−	91.0730i	−0.383803	−	0.664766i	−0.991602	+	0.129324i	$0.958719\pi$
$138$	56.6364	−	5.26265i	0.410409	−	0.0381352i
$139$	−97.9157	+	26.2364i	−0.704429	+	0.188751i	−0.593214	−	0.805045i	$-0.702141\pi$
$139$	−97.9157	+	26.2364i	−0.704429	+	0.188751i	−0.111216	+	0.993796i	$0.535474\pi$
$140$	71.9067	+	41.9784i	0.513619	+	0.299845i
$141$	54.1872	+	33.9301i	0.384306	+	0.240639i
$142$	−246.996	+	31.9128i	−1.73941	+	0.224738i
$143$		−	153.711i		−	1.07491i
$144$	−11.6954	+	143.524i	−0.0812179	+	0.996696i
$145$	80.7299			0.556758
$146$	−22.1479	−	171.419i	−0.151698	−	1.17410i
$147$	60.3339	+	2.16316i	0.410435	+	0.0147154i
$148$	47.1660	+	27.5350i	0.318689	+	0.186047i
$149$	54.4787	+	203.317i	0.365629	+	1.36454i	0.866566	+	0.499062i	$0.166322\pi$
$149$	54.4787	+	203.317i	0.365629	+	1.36454i	−0.500938	+	0.865483i	$0.667011\pi$
$150$	54.4840	+	25.0499i	0.363227	+	0.166999i
$151$	−126.469	+	73.0167i	−0.837541	+	0.483554i	−0.856428	−	0.516267i	$-0.827321\pi$
$151$	−126.469	+	73.0167i	−0.837541	+	0.483554i	0.0188867	+	0.999822i	$0.493988\pi$
$152$	−88.7102	+	209.865i	−0.583620	+	1.38069i
$153$	88.5632	+	59.9769i	0.578844	+	0.392006i
$154$	−128.552	+	52.8856i	−0.834752	+	0.343413i
$155$	−144.888	−	38.8227i	−0.934764	−	0.250469i
$156$	−76.2661	+	120.505i	−0.488886	+	0.772466i
$157$	27.0148	+	100.820i	0.172069	+	0.642168i	0.997032	+	0.0769830i	$0.0245287\pi$
$157$	27.0148	+	100.820i	0.172069	+	0.642168i	−0.824964	+	0.565185i	$0.808805\pi$
$158$	−112.682	−	147.585i	−0.713180	−	0.934083i
$159$	86.8995	+	26.6564i	0.546538	+	0.167650i
$160$	−97.4272	−	76.6396i	−0.608920	−	0.478998i
$161$		−	50.9423i		−	0.316412i
$162$	78.9064	+	141.484i	0.487077	+	0.873359i
$163$	33.4075	−	33.4075i	0.204954	−	0.204954i	−0.597165	−	0.802119i	$-0.703706\pi$
$163$	33.4075	−	33.4075i	0.204954	−	0.204954i	0.802119	+	0.597165i	$0.203706\pi$
$164$	−24.7491	+	90.6169i	−0.150909	+	0.552542i
$165$	132.780	−	70.4416i	0.804725	−	0.426919i
$166$	−20.7902	+	155.031i	−0.125242	+	0.933923i
$167$	−83.3490	+	144.365i	−0.499096	+	0.864459i	−0.999999	−	0.00104367i	$-0.999668\pi$
$167$	−83.3490	+	144.365i	−0.499096	+	0.864459i	0.500904	+	0.865503i	$0.333001\pi$
$168$	127.020	+	22.3223i	0.756073	+	0.132871i
$169$	24.0448	−	13.8823i	0.142277	−	0.0821437i
$170$	−85.1503	+	35.0304i	−0.500884	+	0.206061i
$171$	48.4402	+	251.705i	0.283276	+	1.47196i
$172$	1.45355	−	301.817i	0.00845087	−	1.75475i
$173$	−18.3433	+	68.4582i	−0.106031	+	0.395712i	−0.998460	−	0.0554750i	$-0.982333\pi$
$173$	−18.3433	+	68.4582i	−0.106031	+	0.395712i	0.892429	+	0.451187i	$0.148999\pi$
$174$	117.270	−	43.3997i	0.673965	−	0.249423i
$175$	26.8532	−	46.5111i	0.153447	−	0.265778i
$176$	200.400	−	51.6334i	1.13864	−	0.293372i
$177$	−51.1129	+	47.5747i	−0.288774	+	0.268783i
$178$	325.722	−	42.0845i	1.82990	−	0.236430i
$179$	−145.221	−	145.221i	−0.811290	−	0.811290i	0.173538	−	0.984827i	$-0.444480\pi$
$179$	−145.221	−	145.221i	−0.811290	−	0.811290i	−0.984827	+	0.173538i	$0.944480\pi$
$180$	−139.045	−	10.6566i	−0.772475	−	0.0592033i
$181$	84.5981	+	84.5981i	0.467393	+	0.467393i	0.901069	−	0.433676i	$-0.142784\pi$
$181$	84.5981	+	84.5981i	0.467393	+	0.467393i	−0.433676	+	0.901069i	$0.642784\pi$
$182$	101.142	+	77.9965i	0.555725	+	0.428552i
$183$	−41.0054	−	178.372i	−0.224073	−	0.974708i
$184$	−10.4421	+	75.1182i	−0.0567505	+	0.408251i
$185$	−26.4453	+	45.8046i	−0.142948	+	0.247592i
$186$	−231.339	+	21.4960i	−1.24376	+	0.115570i
$187$	39.7845	−	148.478i	0.212751	−	0.793998i
$188$	−60.5668	+	59.9862i	−0.322164	+	0.319075i
$189$	132.709	−	58.6420i	0.702162	−	0.310275i
$190$	−203.649	−	84.9294i	−1.07184	−	0.446997i
$191$	−9.02196	+	5.20883i	−0.0472354	+	0.0272714i	−0.523432	−	0.852068i	$-0.675348\pi$
$191$	−9.02196	+	5.20883i	−0.0472354	+	0.0272714i	0.476196	+	0.879339i	$0.342015\pi$
$192$	−182.726	−	58.9524i	−0.951695	−	0.307044i
$193$	81.1839	−	140.615i	0.420642	−	0.728573i	−0.575361	−	0.817900i	$-0.695138\pi$
$193$	81.1839	−	140.615i	0.420642	−	0.728573i	0.996002	+	0.0893270i	$0.0284716\pi$
$194$	−38.4824	−	50.4020i	−0.198363	−	0.259804i
$195$	−117.054	−	73.2952i	−0.600277	−	0.375873i
$196$	−21.2083	+	77.6528i	−0.108206	+	0.396188i
$197$	−158.587	+	158.587i	−0.805013	+	0.805013i	−0.983874	−	0.178862i	$-0.942759\pi$
$197$	−158.587	+	158.587i	−0.805013	+	0.805013i	0.178862	+	0.983874i	$0.442759\pi$
$198$	155.010	−	173.706i	0.782877	−	0.877304i
$199$			88.5298i			0.444874i	0.974947	+	0.222437i	$0.0714011\pi$
$199$			88.5298i			0.444874i	−0.974947	+	0.222437i	$0.928599\pi$
$200$	−49.1309	+	63.0798i	−0.245654	+	0.315399i
$201$	205.000	−	190.809i	1.01990	−	0.949298i
$202$	246.399	+	33.0428i	1.21980	+	0.163578i
$203$	−28.9849	−	108.173i	−0.142783	−	0.532872i
$204$	−104.859	+	96.6620i	−0.514015	+	0.473833i
$205$	−87.8701	−	23.5447i	−0.428635	−	0.114852i
$206$	348.082	+	145.163i	1.68972	+	0.704675i
$207$	37.2592	+	76.7551i	0.179996	+	0.370798i
$208$	−133.154	−	135.744i	−0.640162	−	0.652614i
$209$	319.015	−	184.184i	1.52639	−	0.881261i
$210$	−21.0248	+	123.112i	−0.100118	+	0.586249i
$211$	−75.6516	−	282.335i	−0.358538	−	1.33808i	−0.875973	−	0.482360i	$-0.839780\pi$
$211$	−75.6516	−	282.335i	−0.358538	−	1.33808i	0.517435	−	0.855723i	$-0.326887\pi$
$212$	−61.1021	+	104.665i	−0.288218	+	0.493701i
$213$	−175.075	−	330.010i	−0.821950	−	1.54934i
$214$	−166.498	+	215.905i	−0.778026	+	1.00890i
$215$	292.291			1.35949
$216$	−207.709	+	59.2696i	−0.961617	+	0.274396i
$217$			208.080i			0.958895i
$218$	192.184	−	249.214i	0.881576	−	1.14318i
$219$	229.031	−	121.504i	1.04580	−	0.554815i
$220$	50.9371	+	193.829i	0.231532	+	0.881042i
$221$	−136.427	+	36.5554i	−0.617315	+	0.165409i
$222$	−13.7909	+	80.7535i	−0.0621210	+	0.363754i
$223$	−39.5000	−	68.4160i	−0.177130	−	0.306798i	0.763766	−	0.645493i	$-0.223348\pi$
$223$	−39.5000	−	68.4160i	−0.177130	−	0.306798i	−0.940896	+	0.338695i	$0.890015\pi$
$224$	−67.7126	+	158.063i	−0.302288	+	0.705637i
$225$	−6.44170	+	89.7191i	−0.0286298	+	0.398752i
$226$	114.419	+	47.7170i	0.506279	+	0.211137i
$227$	−39.7756	+	148.445i	−0.175223	+	0.653941i	0.821290	+	0.570510i	$0.193255\pi$
$227$	−39.7756	+	148.445i	−0.175223	+	0.653941i	−0.996514	+	0.0834312i	$0.973412\pi$
$228$	−341.483	−	13.8902i	−1.49773	−	0.0609219i
$229$	142.591	−	38.2072i	0.622669	−	0.166844i	0.0663280	−	0.997798i	$-0.478872\pi$
$229$	142.591	−	38.2072i	0.622669	−	0.166844i	0.556341	+	0.830954i	$0.312205\pi$
$230$	−72.7942	−	9.76192i	−0.316497	−	0.0424431i
$231$	−142.060	−	152.625i	−0.614978	−	0.660716i
$232$	20.5672	+	165.451i	0.0886517	+	0.713149i
$233$	232.917			0.999644			0.499822	−	0.866128i	$-0.333399\pi$
$233$	232.917			0.999644			0.499822	+	0.866128i	$0.333399\pi$
$234$	−209.438	−	43.5429i	−0.895034	−	0.186081i
$235$	−58.3739	−	58.3739i	−0.248400	−	0.248400i
$236$	−46.1628	−	80.8531i	−0.195605	−	0.342598i
$237$	147.816	−	236.066i	0.623698	−	0.996061i
$238$	77.5106	+	101.519i	0.325675	+	0.426550i
$239$	−71.3891	−	41.2165i	−0.298699	−	0.172454i	0.343159	−	0.939277i	$-0.388503\pi$
$239$	−71.3891	−	41.2165i	−0.298699	−	0.172454i	−0.641858	+	0.766823i	$0.721836\pi$
$240$	56.2381	−	177.229i	0.234325	−	0.738454i
$241$	177.458	+	307.367i	0.736342	+	1.27538i	0.954132	+	0.299387i	$0.0967820\pi$
$241$	177.458	+	307.367i	0.736342	+	1.27538i	−0.217790	+	0.975996i	$0.569885\pi$
$242$	−85.4462	−	35.6343i	−0.353084	−	0.147249i
$243$	−157.062	+	185.420i	−0.646347	+	0.763043i
$244$	244.030	+	1.17524i	1.00012	+	0.00481658i
$245$	−75.2989	−	20.1763i	−0.307342	−	0.0823522i
$246$	−140.299	+	13.0366i	−0.570323	+	0.0529944i
$247$	−293.122	−	169.234i	−1.18673	−	0.685159i
$248$	42.6521	−	306.830i	0.171984	−	1.23722i
$249$	−228.664	+	52.5671i	−0.918330	+	0.211113i
$250$	−214.693	−	165.562i	−0.858771	−	0.662250i
$251$	−88.3235	+	88.3235i	−0.351886	+	0.351886i	−0.860811	−	0.508925i	$-0.830043\pi$
$251$	−88.3235	+	88.3235i	−0.351886	+	0.351886i	0.508925	+	0.860811i	$0.330043\pi$
$252$	35.6431	+	190.138i	0.141441	+	0.754517i
$253$	86.7023	−	86.7023i	0.342697	−	0.342697i
$254$	112.612	−	14.5499i	0.443356	−	0.0572832i
$255$	−94.0978	−	101.096i	−0.369011	−	0.396455i
$256$	132.247	−	219.196i	0.516589	−	0.856233i
$257$	−224.014	−	129.334i	−0.871649	−	0.503247i	−0.00375325	−	0.999993i	$-0.501195\pi$
$257$	−224.014	−	129.334i	−0.871649	−	0.503247i	−0.867896	+	0.496746i	$0.834528\pi$
$258$	424.588	−	157.133i	1.64569	−	0.609042i
$259$	70.8701	+	18.9896i	0.273630	+	0.0733189i
$260$	130.835	−	129.581i	0.503212	−	0.498388i
$261$	122.790	+	141.786i	0.470458	+	0.543240i
$262$	−102.441	+	42.1436i	−0.390995	+	0.160853i
$263$	217.325	+	376.418i	0.826331	+	1.43125i	0.900898	+	0.434031i	$0.142909\pi$
$263$	217.325	+	376.418i	0.826331	+	1.43125i	−0.0745671	+	0.997216i	$0.523757\pi$
$264$	178.193	+	254.177i	0.674974	+	0.962791i
$265$	−101.644	−	58.6840i	−0.383561	−	0.221449i
$266$	−40.6829	+	303.370i	−0.152943	+	1.14049i
$267$	230.878	+	435.195i	0.864710	+	1.62994i
$268$	185.146	+	324.279i	0.690844	+	1.21000i
$269$	6.46656	+	6.46656i	0.0240393	+	0.0240393i	0.719024	−	0.694985i	$-0.244589\pi$
$269$	6.46656	+	6.46656i	0.0240393	+	0.0240393i	−0.694985	+	0.719024i	$0.744589\pi$
$270$	−58.3662	−	200.872i	−0.216171	−	0.743970i
$271$	−162.021			−0.597863			−0.298932	−	0.954275i	$-0.596630\pi$
$271$	−162.021			−0.597863			−0.298932	+	0.954275i	$0.596630\pi$
$272$	−93.4859	−	165.585i	−0.343698	−	0.608770i
$273$	−56.1844	+	183.161i	−0.205804	+	0.670919i
$274$	127.635	+	167.169i	0.465821	+	0.610106i
$275$	124.864	−	33.4572i	0.454051	−	0.121663i
$276$	−110.990	+	24.9531i	−0.402139	+	0.0904099i
$277$	67.8658	−	253.279i	0.245003	−	0.914364i	−0.728379	−	0.685175i	$-0.759726\pi$
$277$	67.8658	−	253.279i	0.245003	−	0.914364i	0.973382	−	0.229189i	$-0.0736075\pi$
$278$	187.493	−	77.1338i	0.674436	−	0.277460i
$279$	−152.190	−	313.516i	−0.545484	−	1.12371i
$280$	−153.386	−	64.8366i	−0.547807	−	0.231559i
$281$	128.998	+	223.431i	0.459067	+	0.795127i	0.998912	−	0.0466376i	$-0.0148506\pi$
$281$	128.998	+	223.431i	0.459067	+	0.795127i	−0.539845	+	0.841764i	$0.681517\pi$
$282$	−116.176	−	53.4139i	−0.411973	−	0.189411i
$283$	−65.1839	+	17.4660i	−0.230332	+	0.0617172i	−0.372139	−	0.928177i	$-0.621375\pi$
$283$	−65.1839	+	17.4660i	−0.230332	+	0.0617172i	0.141807	+	0.989894i	$0.454709\pi$
$284$	481.742	−	126.599i	1.69628	−	0.445771i
$285$	11.8588	−	330.761i	0.0416099	−	1.16057i
$286$	39.3927	+	304.889i	0.137737	+	1.06604i
$287$			126.194i			0.439700i
$288$	−13.5840	−	287.679i	−0.0471667	−	0.998887i
$289$	147.757			0.511271
$290$	−160.129	+	20.6892i	−0.552168	+	0.0713421i
$291$	50.4811	−	80.6194i	0.173474	−	0.277043i
$292$	87.8612	+	334.335i	0.300895	+	1.14498i
$293$	−113.090	−	422.058i	−0.385973	−	1.44047i	−0.836628	−	0.547772i	$-0.815476\pi$
$293$	−113.090	−	422.058i	−0.385973	−	1.44047i	0.450655	−	0.892698i	$-0.351191\pi$
$294$	−120.227	+	11.1715i	−0.408937	+	0.0379984i
$295$	78.0840	−	45.0818i	0.264691	−	0.152820i
$296$	−100.611	−	42.5285i	−0.339902	−	0.143677i
$297$	325.673	+	126.059i	1.09654	+	0.424442i
$298$	−160.165	−	389.321i	−0.537465	−	1.30644i
$299$	−108.825	−	29.1595i	−0.363962	−	0.0975232i
$300$	−114.489	−	35.7237i	−0.381632	−	0.119079i
$301$	−104.943	−	391.652i	−0.348647	−	1.30117i
$302$	232.140	−	177.241i	0.768675	−	0.586889i
$303$	83.5473	+	363.427i	0.275734	+	1.19943i
$304$	122.174	−	439.003i	0.401890	−	1.44409i
$305$			236.327i			0.774843i
$306$	−191.037	−	96.2682i	−0.624304	−	0.314602i
$307$	281.005	−	281.005i	0.915324	−	0.915324i	−0.0813605	−	0.996685i	$-0.525927\pi$
$307$	281.005	−	281.005i	0.915324	−	0.915324i	0.996685	+	0.0813605i	$0.0259265\pi$
$308$	241.431	−	137.844i	0.783866	−	0.447546i
$309$	−20.2694	+	565.344i	−0.0655966	+	1.82959i
$310$	297.337	+	39.8738i	0.959152	+	0.128625i
$311$	93.6716	−	162.244i	0.301195	−	0.521685i	−0.675212	−	0.737624i	$-0.735948\pi$
$311$	93.6716	−	162.244i	0.301195	−	0.521685i	0.976407	+	0.215939i	$0.0692812\pi$
$312$	120.392	−	258.568i	0.385873	−	0.828743i
$313$	147.960	−	85.4249i	0.472716	−	0.272923i	−0.244660	−	0.969609i	$-0.578676\pi$
$313$	147.960	−	85.4249i	0.472716	−	0.272923i	0.717376	+	0.696686i	$0.245343\pi$
$314$	−79.4221	−	193.055i	−0.252937	−	0.614826i
$315$	−183.966	+	35.4040i	−0.584020	+	0.112394i
$316$	261.330	+	263.859i	0.826992	+	0.834997i
$317$	−148.256	+	553.300i	−0.467685	+	1.74543i	0.180144	+	0.983640i	$0.442344\pi$
$317$	−148.256	+	553.300i	−0.467685	+	1.74543i	−0.647829	+	0.761786i	$0.724323\pi$
$318$	−179.198	−	30.6029i	−0.563515	−	0.0962355i
$319$	134.776	−	233.439i	0.422495	−	0.731783i
$320$	212.889	+	127.047i	0.665278	+	0.397023i
$321$	−390.989	−	119.936i	−1.21804	−	0.373631i
$322$	13.0553	+	101.045i	0.0405445	+	0.313803i
$323$	−239.340	−	239.340i	−0.740990	−	0.740990i
$324$	−192.771	−	260.414i	−0.594972	−	0.803746i
$325$	−83.9877	−	83.9877i	−0.258424	−	0.258424i
$326$	−57.7027	+	74.8258i	−0.177002	+	0.229527i
$327$	451.308	+	138.438i	1.38015	+	0.423359i
$328$	25.8671	−	186.082i	0.0788631	−	0.567325i
$329$	−57.2591	+	99.1757i	−0.174040	+	0.301446i
$330$	−245.317	+	173.750i	−0.743386	+	0.526516i
$331$	−17.5294	+	65.4206i	−0.0529589	+	0.197645i	−0.987337	−	0.158638i	$-0.949290\pi$
$331$	−17.5294	+	65.4206i	−0.0529589	+	0.197645i	0.934378	+	0.356284i	$0.115956\pi$
$332$	1.50661	−	312.835i	0.00453798	−	0.942273i
$333$	−120.670	+	23.2227i	−0.362371	+	0.0697377i
$334$	128.326	−	307.710i	0.384211	−	0.921286i
$335$	−313.173	+	180.811i	−0.934845	+	0.539733i
$336$	−257.667	−	11.7241i	−0.766866	−	0.0348932i
$337$	−165.268	+	286.252i	−0.490409	+	0.849413i	−0.999939	−	0.0110397i	$-0.996486\pi$
$337$	−165.268	+	286.252i	−0.490409	+	0.849413i	0.509530	+	0.860453i	$0.329819\pi$
$338$	−44.1355	+	33.6978i	−0.130578	+	0.0996977i
$339$	−6.66281	+	185.836i	−0.0196543	+	0.548189i
$340$	159.919	−	91.3053i	0.470351	−	0.268545i
$341$	−354.147	+	354.147i	−1.03855	+	1.03855i
$342$	−160.588	−	486.846i	−0.469555	−	1.42353i
$343$			371.447i			1.08294i
$344$	74.4657	+	599.031i	0.216470	+	1.74137i
$345$	−24.6826	−	107.368i	−0.0715438	−	0.311212i
$346$	18.8400	−	140.489i	0.0544508	−	0.406037i
$347$	152.939	+	570.776i	0.440747	+	1.64489i	0.726928	+	0.686713i	$0.240947\pi$
$347$	152.939	+	570.776i	0.440747	+	1.64489i	−0.286182	+	0.958175i	$0.592386\pi$
$348$	−221.484	+	116.137i	−0.636448	+	0.333728i
$349$	−481.904	−	129.126i	−1.38081	−	0.369988i	−0.509396	−	0.860532i	$-0.670131\pi$
$349$	−481.904	−	129.126i	−1.38081	−	0.369988i	−0.871416	+	0.490544i	$0.836798\pi$
$350$	−41.3439	+	99.1372i	−0.118125	+	0.283249i
$351$	−49.3103	−	317.063i	−0.140485	−	0.903314i
$352$	−384.263	+	153.773i	−1.09166	+	0.436856i
$353$	100.398	−	57.9648i	0.284413	−	0.164206i	−0.351006	−	0.936373i	$-0.614160\pi$
$353$	100.398	−	57.9648i	0.284413	−	0.164206i	0.635420	+	0.772167i	$0.280827\pi$
$354$	89.1909	−	107.464i	0.251952	−	0.303571i
$355$	124.847	+	465.935i	0.351682	+	1.31249i
$356$	−635.289	+	166.950i	−1.78452	+	0.468961i
$357$	−101.678	+	162.382i	−0.284813	+	0.454853i
$358$	325.264	+	250.831i	0.908559	+	0.700644i
$359$	598.738			1.66780			0.833898	−	0.551919i	$-0.186104\pi$
$359$	598.738			1.66780			0.833898	+	0.551919i	$0.186104\pi$
$360$	278.529	−	14.4967i	0.773693	−	0.0402685i
$361$		−	450.135i		−	1.24691i
$362$	−189.482	−	146.121i	−0.523431	−	0.403649i
$363$	4.97567	−	138.779i	0.0137071	−	0.382312i
$364$	−220.605	−	128.787i	−0.606057	−	0.353810i
$365$	−323.365	+	86.6453i	−0.885931	+	0.237384i
$366$	127.047	+	343.294i	0.347124	+	0.937961i
$367$	−30.0248	−	52.0045i	−0.0818115	−	0.141702i	0.822217	−	0.569175i	$-0.192737\pi$
$367$	−30.0248	−	52.0045i	−0.0818115	−	0.141702i	−0.904028	+	0.427473i	$0.859404\pi$
$368$	1.46096	−	151.674i	0.00396999	−	0.412158i
$369$	−92.2983	−	190.137i	−0.250131	−	0.515278i
$370$	40.7159	−	97.6313i	0.110043	−	0.263868i
$371$	−42.1393	+	157.266i	−0.113583	+	0.423897i
$372$	453.354	−	101.924i	1.21869	−	0.273990i
$373$	−599.280	+	160.577i	−1.60665	+	0.430500i	−0.947042	−	0.321111i	$-0.895944\pi$
$373$	−599.280	+	160.577i	−1.60665	+	0.430500i	−0.659607	+	0.751611i	$0.729277\pi$
$374$	−40.8616	+	304.703i	−0.109256	+	0.814715i
$375$	119.262	−	388.793i	0.318032	−	1.03678i
$376$	104.762	−	134.505i	0.278622	−	0.357727i
$377$	−247.674			−0.656960
$378$	−248.201	+	150.327i	−0.656615	+	0.397691i
$379$	−128.337	−	128.337i	−0.338620	−	0.338620i	0.517228	−	0.855848i	$-0.326964\pi$
$379$	−128.337	−	128.337i	−0.338620	−	0.338620i	−0.855848	+	0.517228i	$0.826964\pi$
$380$	425.707	+	116.268i	1.12028	+	0.305968i
$381$	79.8216	+	150.460i	0.209506	+	0.394909i
$382$	16.5603	−	12.6439i	0.0433515	−	0.0330992i
$383$	−56.1996	−	32.4468i	−0.146735	−	0.0847176i	0.424835	−	0.905271i	$-0.360332\pi$
$383$	−56.1996	−	32.4468i	−0.146735	−	0.0847176i	−0.571570	+	0.820553i	$0.693665\pi$
$384$	377.547	+	70.1045i	0.983194	+	0.182564i
$385$	134.616	+	233.162i	0.349652	+	0.605616i
$386$	−124.993	+	299.716i	−0.323816	+	0.776467i
$387$	444.572	+	513.350i	1.14877	+	1.32648i
$388$	89.2471	+	90.1109i	0.230018	+	0.232245i
$389$	399.684	+	107.095i	1.02747	+	0.275309i	0.732910	−	0.680326i	$-0.238162\pi$
$389$	399.684	+	107.095i	1.02747	+	0.275309i	0.294556	+	0.955634i	$0.404828\pi$
$390$	250.962	+	115.384i	0.643493	+	0.295855i
$391$	−97.5720	−	56.3332i	−0.249545	−	0.144075i
$392$	22.1664	−	159.460i	0.0565469	−	0.406787i
$393$	−113.205	−	121.624i	−0.288054	−	0.309477i
$394$	273.918	−	355.203i	0.695223	−	0.901529i
$395$	−254.306	+	254.306i	−0.643812	+	0.643812i
$396$	−262.947	+	384.274i	−0.664007	+	0.970388i
$397$	−396.576	+	396.576i	−0.998931	+	0.998931i	−0.999999	−	0.00106822i	$-0.999660\pi$
$397$	−396.576	+	396.576i	−0.998931	+	0.998931i	0.00106822	+	0.999999i	$0.499660\pi$
$398$	−22.6882	−	175.600i	−0.0570054	−	0.441206i
$399$	−447.457	+	102.865i	−1.12145	+	0.257807i
$400$	81.2858	−	137.711i	0.203214	−	0.344277i
$401$	75.9357	+	43.8415i	0.189366	+	0.109330i	0.591686	−	0.806169i	$-0.298463\pi$
$401$	75.9357	+	43.8415i	0.189366	+	0.109330i	−0.402320	+	0.915499i	$0.631796\pi$
$402$	−357.720	+	431.008i	−0.889850	+	1.07216i
$403$	444.508	+	119.106i	1.10300	+	0.295547i
$404$	−497.203	−	2.39453i	−1.23070	−	0.00592704i
$405$	251.289	−	187.897i	0.620467	−	0.463942i
$406$	85.2141	+	207.134i	0.209887	+	0.510183i
$407$	88.2992	+	152.939i	0.216951	+	0.375771i
$408$	183.217	−	218.603i	0.449061	−	0.535792i
$409$	54.0849	+	31.2259i	0.132237	+	0.0763470i	0.564659	−	0.825324i	$-0.309008\pi$
$409$	54.0849	+	31.2259i	0.132237	+	0.0763470i	−0.432422	+	0.901671i	$0.642341\pi$
$410$	180.325	+	24.1822i	0.439818	+	0.0589809i
$411$	−167.431	+	267.392i	−0.407375	+	0.650588i
$412$	−727.626	−	198.728i	−1.76608	−	0.482349i
$413$	−88.4417	−	88.4417i	−0.214145	−	0.214145i
$414$	−93.5747	−	142.696i	−0.226026	−	0.344677i
$415$	302.960			0.730025
$416$	298.900	+	235.125i	0.718510	+	0.565205i
$417$	207.195	+	222.605i	0.496870	+	0.533824i
$418$	−585.569	+	447.087i	−1.40088	+	1.06959i
$419$	−267.062	+	71.5590i	−0.637379	+	0.170785i	−0.563016	−	0.826446i	$-0.690359\pi$
$419$	−267.062	+	71.5590i	−0.637379	+	0.170785i	−0.0743629	+	0.997231i	$0.523692\pi$
$420$	10.1521	−	249.583i	0.0241716	−	0.594245i
$421$	158.502	−	591.536i	0.376488	−	1.40507i	−0.474670	−	0.880164i	$-0.657433\pi$
$421$	158.502	−	591.536i	0.376488	−	1.40507i	0.851158	−	0.524909i	$-0.175901\pi$
$422$	222.412	+	540.628i	0.527042	+	1.28111i
$423$	13.7357	−	191.308i	0.0324720	−	0.452266i
$424$	94.3737	−	223.263i	0.222580	−	0.526563i
$425$	−59.3898	−	102.866i	−0.139741	−	0.242038i
$426$	431.838	+	609.711i	1.01370	+	1.43125i
$427$	316.664	−	84.8498i	0.741601	−	0.198711i
$428$	274.918	−	470.920i	0.642333	−	1.10028i
$429$	−407.359	+	216.110i	−0.949554	+	0.503753i
$430$	−579.762	+	74.9074i	−1.34828	+	0.174203i
$431$		−	512.341i		−	1.18873i	−0.804196	−	0.594364i	$-0.797404\pi$
$431$		−	512.341i		−	1.18873i	0.804196	−	0.594364i	$-0.202596\pi$
$432$	396.804	−	170.793i	0.918529	−	0.395354i
$433$	92.4308			0.213466			0.106733	−	0.994288i	$-0.465961\pi$
$433$	92.4308			0.213466			0.106733	+	0.994288i	$0.465961\pi$
$434$	−53.3261	−	412.730i	−0.122871	−	0.950990i
$435$	−113.502	−	213.947i	−0.260924	−	0.491831i
$436$	−317.331	+	543.571i	−0.727823	+	1.24672i
$437$	−69.8802	−	260.796i	−0.159909	−	0.596788i
$438$	−423.147	+	299.701i	−0.966088	+	0.684249i
$439$	162.735	−	93.9551i	0.370695	−	0.214021i	−0.303067	−	0.952969i	$-0.598011\pi$
$439$	162.735	−	93.9551i	0.370695	−	0.214021i	0.673762	+	0.738949i	$0.264677\pi$
$440$	−150.708	−	371.409i	−0.342519	−	0.844110i
$441$	−79.0936	−	162.935i	−0.179350	−	0.369468i
$442$	261.235	−	107.471i	0.591030	−	0.243147i
$443$	−617.132	−	165.360i	−1.39307	−	0.373273i	−0.517222	−	0.855852i	$-0.673034\pi$
$443$	−617.132	−	165.360i	−1.39307	−	0.373273i	−0.875853	+	0.482578i	$0.839700\pi$
$444$	6.65909	−	163.710i	0.0149979	−	0.368716i
$445$	−164.640	−	614.444i	−0.369977	−	1.38077i
$446$	95.8822	+	125.581i	0.214982	+	0.281572i
$447$	462.228	−	430.230i	1.03407	−	0.962484i
$448$	93.8009	−	330.872i	0.209377	−	0.738555i
$449$		−	182.865i		−	0.407271i	−0.979047	−	0.203635i	$-0.934724\pi$
$449$		−	182.865i		−	0.407271i	0.979047	−	0.203635i	$-0.0652757\pi$
$450$	−10.2157	−	179.610i	−0.0227016	−	0.399133i
$451$	−214.778	+	214.778i	−0.476227	+	0.476227i
$452$	−239.180	−	65.3244i	−0.529160	−	0.144523i
$453$	371.314	+	232.504i	0.819677	+	0.513253i
$454$	40.8525	−	304.636i	0.0899836	−	0.671003i
$455$	123.690	−	214.237i	0.271846	−	0.470851i
$456$	680.895	−	59.9627i	1.49319	−	0.131497i
$457$	−408.786	+	236.013i	−0.894500	+	0.516440i	−0.875412	−	0.483378i	$-0.839410\pi$
$457$	−408.786	+	236.013i	−0.894500	+	0.516440i	−0.0190880	+	0.999818i	$0.506076\pi$
$458$	−273.040	+	112.327i	−0.596157	+	0.245256i
$459$	34.4328	−	319.030i	0.0750170	−	0.695055i
$460$	146.890	+	0.707421i	0.319326	+	0.00153787i
$461$	199.024	−	742.769i	0.431723	−	1.61121i	−0.317066	−	0.948403i	$-0.602698\pi$
$461$	199.024	−	742.769i	0.431723	−	1.61121i	0.748789	−	0.662808i	$-0.230636\pi$
$462$	320.892	+	266.328i	0.694572	+	0.576467i
$463$	−64.8072	+	112.249i	−0.139972	+	0.242439i	−0.927486	−	0.373858i	$-0.878035\pi$
$463$	−64.8072	+	112.249i	−0.139972	+	0.242439i	0.787514	+	0.616297i	$0.211368\pi$
$464$	−83.1965	−	322.902i	−0.179303	−	0.695910i
$465$	100.819	+	438.559i	0.216816	+	0.943138i
$466$	−461.994	+	59.6912i	−0.991403	+	0.128093i
$467$	−64.6941	−	64.6941i	−0.138531	−	0.138531i	0.634440	−	0.772972i	$-0.281231\pi$
$467$	−64.6941	−	64.6941i	−0.138531	−	0.138531i	−0.772972	+	0.634440i	$0.781231\pi$
$468$	426.582	+	32.6937i	0.911500	+	0.0698583i
$469$	354.715	+	354.715i	0.756323	+	0.756323i
$470$	130.745	+	100.826i	0.278181	+	0.214522i
$471$	229.208	−	213.342i	0.486642	−	0.452954i
$472$	112.285	+	148.543i	0.237893	+	0.314709i
$473$	487.970	−	845.189i	1.03165	−	1.78687i
$474$	−232.697	+	506.122i	−0.490923	+	1.06777i
$475$	73.6719	−	274.947i	0.155099	−	0.578836i
$476$	−179.760	−	181.500i	−0.377647	−	0.381302i
$477$	−51.5327	−	267.775i	−0.108035	−	0.561372i
$478$	152.164	+	63.4581i	0.318335	+	0.132757i
$479$	355.298	−	205.131i	0.741750	−	0.428249i	−0.0809554	−	0.996718i	$-0.525797\pi$
$479$	355.298	−	205.131i	0.741750	−	0.428249i	0.822705	+	0.568468i	$0.192464\pi$
$480$	−66.1293	+	365.948i	−0.137769	+	0.762392i
$481$	81.1324	−	140.525i	0.168674	−	0.292153i
$482$	−430.762	−	564.188i	−0.893698	−	1.17051i
$483$	−135.005	+	71.6221i	−0.279513	+	0.148286i
$484$	178.616	+	48.7832i	0.369041	+	0.100792i
$485$	−86.8484	+	86.8484i	−0.179069	+	0.179069i
$486$	264.017	−	408.033i	0.543244	−	0.839575i
$487$			869.101i			1.78460i	0.451442	+	0.892301i	$0.350910\pi$
$487$			869.101i			1.78460i	−0.451442	+	0.892301i	$0.649090\pi$
$488$	−484.337	+	60.2080i	−0.992494	+	0.123377i
$489$	−135.504	−	41.5658i	−0.277105	−	0.0850017i
$490$	154.527	+	20.7225i	0.315361	+	0.0422909i
$491$	104.814	+	391.173i	0.213471	+	0.796686i	0.986699	+	0.162558i	$0.0519744\pi$
$491$	104.814	+	391.173i	0.213471	+	0.796686i	−0.773228	+	0.634129i	$0.781359\pi$
$492$	274.945	−	61.8138i	0.558831	−	0.125638i
$493$	−239.241	−	64.1044i	−0.485275	−	0.130029i
$494$	624.783	+	260.558i	1.26474	+	0.527445i
$495$	−373.362	−	252.849i	−0.754267	−	0.510806i
$496$	−5.96746	+	619.532i	−0.0120312	+	1.24906i
$497$	579.500	−	334.574i	1.16600	−	0.673188i
$498$	440.087	−	162.869i	0.883708	−	0.327046i
$499$	59.9492	+	223.734i	0.120139	+	0.448364i	0.999620	−	0.0275699i	$-0.00877689\pi$
$499$	59.9492	+	223.734i	0.120139	+	0.448364i	−0.879481	+	0.475934i	$0.842110\pi$
$500$	468.276	+	273.374i	0.936551	+	0.546749i
$501$	499.773	+	17.9184i	0.997551	+	0.0357653i
$502$	152.556	−	197.826i	0.303895	−	0.394076i
$503$	−543.851			−1.08121			−0.540607	−	0.841275i	$-0.681805\pi$
$503$	−543.851			−1.08121			−0.540607	+	0.841275i	$0.681805\pi$
$504$	−119.426	−	368.007i	−0.236957	−	0.730173i
$505$		−	481.509i		−	0.953484i
$506$	−149.755	+	194.195i	−0.295959	+	0.383784i
$507$	−70.5959	−	44.2047i	−0.139242	−	0.0871887i
$508$	−219.639	+	57.7199i	−0.432361	+	0.113622i
$509$	665.031	−	178.195i	1.30655	−	0.350088i	0.462624	−	0.886555i	$-0.346908\pi$
$509$	665.031	−	178.195i	1.30655	−	0.350088i	0.843921	+	0.536467i	$0.180241\pi$
$510$	212.553	+	176.410i	0.416770	+	0.345903i
$511$	232.199	+	402.180i	0.454401	+	0.787045i
$512$	−206.138	+	468.669i	−0.402614	+	0.915370i
$513$	598.953	−	482.258i	1.16755	−	0.940074i
$514$	477.480	+	199.127i	0.928949	+	0.387407i
$515$	189.057	−	705.570i	0.367101	−	1.37004i
$516$	−801.906	+	420.487i	−1.55408	+	0.814897i
$517$	−266.248	+	71.3409i	−0.514986	+	0.137990i
$518$	−145.438	−	19.5037i	−0.280769	−	0.0376520i
$519$	207.215	−	47.6361i	0.399257	−	0.0917843i
$520$	−226.304	+	290.555i	−0.435201	+	0.558760i
$521$	−51.1580			−0.0981920			−0.0490960	−	0.998794i	$-0.515634\pi$
$521$	−51.1580			−0.0981920			−0.0490960	+	0.998794i	$0.515634\pi$
$522$	−279.891	−	249.766i	−0.536190	−	0.478478i
$523$	628.440	+	628.440i	1.20161	+	1.20161i	0.973678	+	0.227929i	$0.0731955\pi$
$523$	628.440	+	628.440i	1.20161	+	1.20161i	0.227929	+	0.973678i	$0.426804\pi$
$524$	192.392	−	109.846i	0.367160	−	0.209629i
$525$	−161.016	−	5.77292i	−0.306697	−	0.0109960i
$526$	−527.534	−	690.934i	−1.00292	−	1.31356i
$527$	398.545	+	230.100i	0.756253	+	0.436623i
$528$	−418.588	−	458.496i	−0.792781	−	0.868364i
$529$	219.564	+	380.296i	0.415055	+	0.718897i
$530$	216.651	+	90.3515i	0.408775	+	0.170475i
$531$	197.942	+	68.5696i	0.372773	+	0.129133i
$532$	2.94818	−	612.165i	0.00554170	−	1.15069i
$533$	269.580	+	72.2336i	0.505778	+	0.135523i
$534$	−569.479	−	804.046i	−1.06644	−	1.50570i
$535$	457.328	+	264.038i	0.854819	+	0.493530i
$536$	−450.345	−	595.764i	−0.840197	−	1.11150i
$537$	−180.685	+	589.030i	−0.336470	+	1.09689i
$538$	−14.4837	−	11.1693i	−0.0269214	−	0.0207607i
$539$	−184.051	+	184.051i	−0.341468	+	0.341468i
$540$	167.249	+	383.474i	0.309720	+	0.710137i
$541$	138.038	−	138.038i	0.255154	−	0.255154i	−0.567926	−	0.823080i	$-0.692254\pi$
$541$	138.038	−	138.038i	0.255154	−	0.255154i	0.823080	+	0.567926i	$0.192254\pi$
$542$	321.371	−	41.5222i	0.592935	−	0.0766093i
$543$	105.257	−	343.138i	0.193844	−	0.631931i
$544$	227.866	+	304.482i	0.418872	+	0.559710i
$545$	−527.881	−	304.772i	−0.968590	−	0.559215i
$546$	64.5026	−	377.700i	0.118137	−	0.691759i
$547$	−655.476	−	175.634i	−1.19831	−	0.321086i	−0.396145	−	0.918188i	$-0.629652\pi$
$547$	−655.476	−	175.634i	−1.19831	−	0.321086i	−0.802165	+	0.597102i	$0.796319\pi$
$548$	−296.007	−	298.872i	−0.540159	−	0.545387i
$549$	−415.061	+	359.452i	−0.756030	+	0.654739i
$550$	−239.095	+	98.3625i	−0.434718	+	0.178841i
$551$	−296.773	−	514.026i	−0.538608	−	0.932897i
$552$	213.756	−	77.9391i	0.387239	−	0.141194i
$553$	432.059	+	249.449i	0.781300	+	0.451084i
$554$	−69.7033	+	519.774i	−0.125818	+	0.938220i
$555$	158.570	+	5.68523i	0.285712	+	0.0102437i
$556$	−352.128	+	201.046i	−0.633323	+	0.361594i
$557$	523.493	+	523.493i	0.939844	+	0.939844i	0.998291	−	0.0584463i	$-0.0186146\pi$
$557$	523.493	+	523.493i	0.939844	+	0.939844i	−0.0584463	+	0.998291i	$0.518615\pi$
$558$	382.218	+	582.861i	0.684978	+	1.04455i
$559$	−896.728			−1.60417
$560$	320.859	+	89.2949i	0.572962	+	0.159455i
$561$	−449.424	+	103.317i	−0.801111	+	0.184166i
$562$	−313.129	−	410.118i	−0.557168	−	0.729748i
$563$	535.008	−	143.355i	0.950281	−	0.254627i	0.249800	−	0.968298i	$-0.419635\pi$
$563$	535.008	−	143.355i	0.950281	−	0.254627i	0.700482	+	0.713670i	$0.252969\pi$
$564$	244.126	+	76.1738i	0.432848	+	0.135060i
$565$	62.1455	−	231.930i	0.109992	−	0.410496i
$566$	124.817	−	51.3491i	0.220525	−	0.0907228i
$567$	−341.992	−	269.250i	−0.603160	−	0.474869i
$568$	−923.097	+	374.570i	−1.62517	+	0.659454i
$569$	281.315	+	487.252i	0.494402	+	0.856330i	0.999979	−	0.00645162i	$-0.00205363\pi$
$569$	281.315	+	487.252i	0.494402	+	0.856330i	−0.505577	+	0.862782i	$0.668720\pi$
$570$	61.2443	+	659.108i	0.107446	+	1.15633i
$571$	93.7407	−	25.1177i	0.164169	−	0.0439890i	−0.175798	−	0.984426i	$-0.556251\pi$
$571$	93.7407	−	25.1177i	0.164169	−	0.0439890i	0.339967	+	0.940437i	$0.389584\pi$
$572$	−156.272	−	594.655i	−0.273202	−	1.03961i
$573$	26.4886	+	16.5862i	0.0462279	+	0.0289463i
$574$	−32.3406	−	250.307i	−0.0563425	−	0.436075i
$575$		−	94.7480i		−	0.164779i
$576$	100.670	+	567.135i	0.174774	+	0.984609i
$577$	−606.259			−1.05071			−0.525354	−	0.850884i	$-0.676067\pi$
$577$	−606.259			−1.05071			−0.525354	+	0.850884i	$0.676067\pi$
$578$	−293.078	+	37.8668i	−0.507056	+	0.0655134i
$579$	−486.790	−	17.4530i	−0.840743	−	0.0301433i
$580$	312.315	−	82.0746i	0.538474	−	0.141508i
$581$	−108.773	−	405.948i	−0.187218	−	0.698706i
$582$	−79.4689	+	172.847i	−0.136545	+	0.296988i
$583$	−339.382	+	195.942i	−0.582130	+	0.336093i
$584$	−259.956	−	640.641i	−0.445130	−	1.09699i
$585$	−29.6715	+	413.260i	−0.0507205	+	0.706428i
$586$	332.479	+	808.175i	0.567371	+	1.37914i
$587$	237.410	+	63.6138i	0.404446	+	0.108371i	0.455307	−	0.890335i	$-0.349530\pi$
$587$	237.410	+	63.6138i	0.404446	+	0.108371i	−0.0508604	+	0.998706i	$0.516196\pi$
$588$	235.610	−	52.9704i	0.400696	−	0.0900856i
$589$	285.435	+	1065.26i	0.484609	+	1.80858i
$590$	−143.327	+	109.431i	−0.242927	+	0.185477i
$591$	643.247	+	197.315i	1.08840	+	0.333867i
$592$	210.462	+	58.5715i	0.355510	+	0.0989384i
$593$		−	849.686i		−	1.43286i	−0.697659	−	0.716430i	$-0.745775\pi$
$593$		−	849.686i		−	1.43286i	0.697659	−	0.716430i	$-0.254225\pi$
$594$	−678.283	−	166.578i	−1.14189	−	0.280434i
$595$	174.929	−	174.929i	0.293998	−	0.293998i
$596$	417.462	+	731.176i	0.700440	+	1.22681i
$597$	234.618	−	124.468i	0.392994	−	0.208490i
$598$	223.328	+	29.9489i	0.373458	+	0.0500818i
$599$	−172.533	+	298.836i	−0.288035	+	0.498891i	−0.973341	−	0.229364i	$-0.926335\pi$
$599$	−172.533	+	298.836i	−0.288035	+	0.498891i	0.685306	+	0.728256i	$0.259669\pi$
$600$	236.246	+	41.5174i	0.393744	+	0.0691957i
$601$	−114.395	+	66.0458i	−0.190341	+	0.109893i	−0.592142	−	0.805834i	$-0.701718\pi$
$601$	−114.395	+	66.0458i	−0.190341	+	0.109893i	0.401801	+	0.915727i	$0.368384\pi$
$602$	308.526	+	749.951i	0.512502	+	1.24577i
$603$	−793.892	−	275.014i	−1.31657	−	0.456076i
$604$	−415.029	+	411.051i	−0.687135	+	0.680548i
$605$	−46.4092	+	173.202i	−0.0767095	+	0.286284i
$606$	−258.855	−	699.450i	−0.427154	−	1.15421i
$607$	399.074	−	691.216i	0.657453	−	1.13874i	−0.323820	−	0.946119i	$-0.604967\pi$
$607$	399.074	−	691.216i	0.657453	−	1.13874i	0.981273	−	0.192623i	$-0.0616993\pi$
$608$	−129.828	+	902.079i	−0.213533	+	1.48368i
$609$	−245.924	+	228.900i	−0.403816	+	0.375862i
$610$	−60.5652	−	468.758i	−0.0992871	−	0.768455i
$611$	179.087	+	179.087i	0.293105	+	0.293105i
$612$	403.595	+	141.991i	0.659470	+	0.232011i
$613$	−92.1791	−	92.1791i	−0.150374	−	0.150374i	0.627911	−	0.778285i	$-0.283910\pi$
$613$	−92.1791	−	92.1791i	−0.150374	−	0.150374i	−0.778285	+	0.627911i	$0.783910\pi$
$614$	−485.361	+	629.391i	−0.790490	+	1.02507i
$615$	61.1436	+	265.972i	0.0994205	+	0.432475i
$616$	−443.555	+	335.289i	−0.720056	+	0.544300i
$617$	39.3936	−	68.2317i	0.0638470	−	0.110586i	−0.832335	−	0.554273i	$-0.812996\pi$
$617$	39.3936	−	68.2317i	0.0638470	−	0.110586i	0.896182	+	0.443687i	$0.146330\pi$
$618$	−104.680	−	1126.56i	−0.169385	−	1.82292i
$619$	128.392	−	479.166i	0.207418	−	0.774096i	−0.781280	−	0.624180i	$-0.785433\pi$
$619$	128.392	−	479.166i	0.207418	−	0.774096i	0.988699	−	0.149916i	$-0.0479003\pi$
$620$	−599.991	−	2.88955i	−0.967727	−	0.00466057i
$621$	151.028	−	206.656i	0.243202	−	0.332780i
$622$	−144.219	+	345.819i	−0.231864	+	0.555979i
$623$	−764.206	+	441.214i	−1.22665	+	0.708209i
$624$	−172.535	+	543.726i	−0.276498	+	0.871356i
$625$	−137.625	+	238.373i	−0.220200	+	0.381397i
$626$	−271.588	+	207.360i	−0.433847	+	0.331246i
$627$	−936.633	−	586.487i	−1.49383	−	0.935386i
$628$	207.010	+	362.574i	0.329634	+	0.577347i
$629$	114.742	−	114.742i	0.182419	−	0.182419i
$630$	355.826	−	117.371i	0.564804	−	0.186303i
$631$		−	806.396i		−	1.27797i	−0.769221	−	0.638983i	$-0.779355\pi$
$631$		−	806.396i		−	1.27797i	0.769221	−	0.638983i	$-0.220645\pi$
$632$	−585.972	−	456.395i	−0.927170	−	0.722144i
$633$	−641.870	+	597.437i	−1.01401	+	0.943818i
$634$	152.270	−	1135.47i	0.240174	−	1.79097i
$635$	−56.9212	−	212.433i	−0.0896396	−	0.334540i
$636$	363.284	+	14.7770i	0.571201	+	0.0232343i
$637$	231.012	+	61.8995i	0.362656	+	0.0971734i
$638$	−207.505	+	497.569i	−0.325243	+	0.779889i
$639$	−628.430	+	927.953i	−0.983458	+	1.45220i
$640$	−454.827	−	197.441i	−0.710667	−	0.308502i
$641$	−103.969	+	60.0266i	−0.162198	+	0.0936453i	−0.578902	−	0.815397i	$-0.696519\pi$
$641$	−103.969	+	60.0266i	−0.162198	+	0.0936453i	0.416704	+	0.909042i	$0.363185\pi$
$642$	806.269	+	137.692i	1.25587	+	0.214474i
$643$	210.532	+	785.714i	0.327421	+	1.22195i	0.911856	+	0.410511i	$0.134649\pi$
$643$	210.532	+	785.714i	0.327421	+	1.22195i	−0.584435	+	0.811440i	$0.698684\pi$
$644$	−51.7908	−	197.077i	−0.0804205	−	0.306021i
$645$	−410.945	−	774.615i	−0.637125	−	1.20095i
$646$	536.070	+	413.396i	0.829830	+	0.639932i
$647$	−825.493			−1.27588			−0.637939	−	0.770087i	$-0.720213\pi$
$647$	−825.493			−1.27588			−0.637939	+	0.770087i	$0.720213\pi$
$648$	449.102	+	467.131i	0.693058	+	0.720882i
$649$		−	301.051i		−	0.463869i
$650$	188.115	+	145.067i	0.289407	+	0.223179i
$651$	551.444	−	292.550i	0.847073	−	0.449385i
$652$	95.2778	−	163.206i	0.146132	−	0.250316i
$653$	−45.5134	+	12.1953i	−0.0696989	+	0.0186758i	−0.293500	−	0.955959i	$-0.594820\pi$
$653$	−45.5134	+	12.1953i	−0.0696989	+	0.0186758i	0.223801	+	0.974635i	$0.428153\pi$
$654$	−930.655	−	158.935i	−1.42302	−	0.243019i
$655$	107.273	+	185.803i	0.163776	+	0.283668i
$656$	−3.61907	+	375.726i	−0.00551688	+	0.572753i
$657$	−644.011	−	436.138i	−0.980229	−	0.663832i
$658$	88.1578	−	211.391i	0.133978	−	0.321262i
$659$	144.063	−	537.650i	0.218608	−	0.815857i	−0.766257	−	0.642534i	$-0.777883\pi$
$659$	144.063	−	537.650i	0.218608	−	0.815857i	0.984865	−	0.173323i	$-0.0554503\pi$
$660$	442.062	−	407.505i	0.669791	−	0.617432i
$661$	−908.098	+	243.324i	−1.37382	+	0.368115i	−0.868874	−	0.495033i	$-0.835156\pi$
$661$	−908.098	+	243.324i	−1.37382	+	0.368115i	−0.504950	+	0.863148i	$0.668489\pi$
$662$	18.0040	−	134.255i	0.0271964	−	0.202802i
$663$	288.686	+	310.156i	0.435424	+	0.467807i
$664$	77.1839	+	620.897i	0.116241	+	0.935086i
$665$	592.842			0.891492
$666$	233.398	−	76.9873i	0.350448	−	0.115597i
$667$	−139.703	−	139.703i	−0.209449	−	0.209449i
$668$	−175.678	+	643.233i	−0.262991	+	0.962924i
$669$	−125.778	+	200.870i	−0.188009	+	0.300255i
$670$	574.845	−	438.899i	0.857978	−	0.655073i
$671$	683.365	+	394.541i	1.01843	+	0.587989i
$672$	514.091	−	42.7792i	0.765016	−	0.0636595i
$673$	642.305	+	1112.50i	0.954390	+	1.65305i	0.735757	+	0.677246i	$0.236827\pi$
$673$	642.305	+	1112.50i	0.954390	+	1.65305i	0.218633	+	0.975807i	$0.429840\pi$
$674$	254.451	−	610.139i	0.377524	−	0.905251i
$675$	246.826	−	109.069i	0.365668	−	0.161583i
$676$	78.9073	−	78.1509i	0.116727	−	0.115608i
$677$	81.0177	+	21.7086i	0.119672	+	0.0320659i	0.318158	−	0.948038i	$-0.396936\pi$
$677$	81.0177	+	21.7086i	0.119672	+	0.0320659i	−0.198486	+	0.980104i	$0.563602\pi$
$678$	−34.4097	−	370.316i	−0.0507518	−	0.546188i
$679$	147.553	+	85.1898i	0.217309	+	0.125464i
$680$	−293.802	+	222.089i	−0.432062	+	0.326601i
$681$	449.324	−	103.294i	0.659800	−	0.151680i
$682$	611.695	−	793.214i	0.896913	−	1.16307i
$683$	422.773	−	422.773i	0.618994	−	0.618994i	−0.326280	−	0.945273i	$-0.605795\pi$
$683$	422.773	−	422.773i	0.618994	−	0.618994i	0.945273	+	0.326280i	$0.105795\pi$
$684$	443.296	+	924.510i	0.648093	+	1.35162i
$685$	288.051	−	288.051i	0.420513	−	0.420513i
$686$	−95.1933	−	736.770i	−0.138766	−	1.07401i
$687$	−301.731	−	324.171i	−0.439200	−	0.471865i
$688$	−301.221	−	1169.10i	−0.437822	−	1.69928i
$689$	311.836	+	180.039i	0.452592	+	0.261304i
$690$	76.4742	+	206.641i	0.110832	+	0.299479i
$691$	−504.924	−	135.294i	−0.730715	−	0.195795i	−0.125768	−	0.992060i	$-0.540139\pi$
$691$	−504.924	−	135.294i	−0.730715	−	0.195795i	−0.604948	+	0.796265i	$0.706806\pi$
$692$	−1.36528	+	283.489i	−0.00197295	+	0.409667i
$693$	−204.752	+	591.064i	−0.295457	+	0.852906i
$694$	−449.633	−	1092.95i	−0.647887	−	1.57485i
$695$	−196.338	−	340.067i	−0.282501	−	0.489306i
$696$	409.553	−	287.121i	0.588438	−	0.412530i
$697$	241.705	+	139.548i	0.346779	+	0.200213i
$698$	988.954	+	132.622i	1.41684	+	0.190002i
$699$	−327.469	−	617.266i	−0.468482	−	0.883070i
$700$	56.5996	−	207.235i	0.0808566	−	0.296050i
$701$	387.399	+	387.399i	0.552638	+	0.552638i	0.927201	−	0.374563i	$-0.122207\pi$
$701$	387.399	+	387.399i	0.552638	+	0.552638i	−0.374563	+	0.927201i	$0.622207\pi$
$702$	179.064	+	616.262i	0.255076	+	0.877866i
$703$	388.865			0.553151
$704$	722.782	−	403.489i	1.02668	−	0.573138i
$705$	−72.6292	+	236.770i	−0.103020	+	0.335845i
$706$	−184.286	+	140.704i	−0.261028	+	0.199297i
$707$	−645.192	+	172.879i	−0.912578	+	0.244524i
$708$	−149.371	+	236.014i	−0.210976	+	0.333353i
$709$	42.2947	−	157.846i	0.0596540	−	0.222632i	−0.929663	−	0.368410i	$-0.879902\pi$
$709$	42.2947	−	157.846i	0.0596540	−	0.222632i	0.989317	+	0.145779i	$0.0465688\pi$
$710$	−367.044	−	892.193i	−0.516963	−	1.25661i
$711$	−833.434	−	59.8394i	−1.17220	−	0.0841623i
$712$	1217.32	−	493.958i	1.70972	−	0.693761i
$713$	183.546	+	317.911i	0.257428	+	0.445878i
$714$	160.065	−	348.145i	0.224181	−	0.487598i
$715$	575.143	−	154.109i	0.804396	−	0.215537i
$716$	−709.448	−	414.168i	−0.990849	−	0.578447i
$717$	−8.86075	+	247.140i	−0.0123581	+	0.344686i
$718$	−1187.61	+	153.443i	−1.65405	+	0.213709i
$719$			480.946i			0.668909i	0.942412	+	0.334455i	$0.108552\pi$
$719$			480.946i			0.668909i	−0.942412	+	0.334455i	$0.891448\pi$
$720$	−548.751	+	100.135i	−0.762155	+	0.139076i
$721$	−1013.30			−1.40541
$722$	115.359	+	892.848i	0.159777	+	1.23663i
$723$	565.073	−	902.434i	0.781567	−	1.24818i
$724$	413.287	+	241.273i	0.570838	+	0.333249i
$725$	−53.9093	−	201.192i	−0.0743576	−	0.277506i
$726$	25.6966	+	276.546i	0.0353948	+	0.380917i
$727$	−45.9366	+	26.5215i	−0.0631865	+	0.0364807i	−0.531260	−	0.847209i	$-0.678281\pi$
$727$	−45.9366	+	26.5215i	−0.0631865	+	0.0364807i	0.468074	+	0.883689i	$0.344948\pi$
$728$	470.578	+	198.914i	0.646398	+	0.273234i
$729$	712.212	+	155.549i	0.976971	+	0.213374i
$730$	619.193	−	254.733i	0.848209	−	0.348949i
$731$	−866.196	−	232.096i	−1.18495	−	0.317505i
$732$	−339.978	−	648.368i	−0.464451	−	0.885749i
$733$	165.745	+	618.567i	0.226118	+	0.843884i	0.981953	+	0.189123i	$0.0605644\pi$
$733$	165.745	+	618.567i	0.226118	+	0.843884i	−0.755835	+	0.654762i	$0.772769\pi$
$734$	72.8822	+	95.4570i	0.0992945	+	0.130050i
$735$	52.3961	+	227.920i	0.0712872	+	0.310096i
$736$	35.9727	+	301.222i	0.0488760	+	0.409269i
$737$			1207.43i			1.63831i
$738$	231.803	+	353.486i	0.314096	+	0.478978i
$739$	726.916	−	726.916i	0.983648	−	0.983648i	−0.0162206	−	0.999868i	$-0.505163\pi$
$739$	726.916	−	726.916i	0.983648	−	0.983648i	0.999868	+	0.0162206i	$0.00516340\pi$
$740$	−55.7399	+	204.087i	−0.0753242	+	0.275794i
$741$	−36.3821	+	1014.75i	−0.0490986	+	1.36944i
$742$	43.2801	−	322.738i	0.0583290	−	0.434957i
$743$	−440.165	+	762.388i	−0.592415	+	1.02609i	0.401491	+	0.915863i	$0.368492\pi$
$743$	−440.165	+	762.388i	−0.592415	+	1.02609i	−0.993906	+	0.110230i	$0.964841\pi$
$744$	−873.113	+	318.352i	−1.17354	+	0.427893i
$745$	−706.134	+	407.686i	−0.947830	+	0.547230i
$746$	1147.53	−	472.087i	1.53824	−	0.632825i
$747$	460.801	+	532.089i	0.616868	+	0.712301i
$748$	2.96114	−	614.855i	0.00395874	−	0.821998i
$749$	189.598	−	707.590i	0.253135	−	0.944713i
$750$	−136.919	+	801.741i	−0.182559	+	1.06899i
$751$	−428.427	+	742.057i	−0.570475	+	0.988092i	0.426042	+	0.904703i	$0.359908\pi$
$751$	−428.427	+	742.057i	−0.570475	+	0.988092i	−0.996517	+	0.0833883i	$0.973426\pi$
$752$	−173.326	+	293.641i	−0.230487	+	0.390480i
$753$	358.249	+	109.893i	0.475762	+	0.145940i
$754$	491.264	−	63.4731i	0.651544	−	0.0841818i
$755$	−400.003	−	400.003i	−0.529805	−	0.529805i
$756$	453.783	−	361.784i	0.600243	−	0.478550i
$757$	−119.448	−	119.448i	−0.157791	−	0.157791i	0.623796	−	0.781587i	$-0.285590\pi$
$757$	−119.448	−	119.448i	−0.157791	−	0.157791i	−0.781587	+	0.623796i	$0.785590\pi$
$758$	287.448	+	221.668i	0.379219	+	0.292439i
$759$	−351.673	−	107.875i	−0.463338	−	0.142128i
$760$	−874.191	−	121.520i	−1.15025	−	0.159895i
$761$	−132.802	+	230.020i	−0.174510	+	0.302260i	−0.939992	−	0.341198i	$-0.889167\pi$
$761$	−132.802	+	230.020i	−0.174510	+	0.302260i	0.765482	+	0.643458i	$0.222501\pi$
$762$	−196.887	−	277.984i	−0.258382	−	0.364808i
$763$	−218.848	+	816.752i	−0.286826	+	1.07045i
$764$	−29.6072	+	29.3233i	−0.0387528	+	0.0383813i
$765$	−135.624	+	391.510i	−0.177286	+	0.511777i
$766$	119.788	+	49.9561i	0.156381	+	0.0652168i
$767$	−239.556	+	138.308i	−0.312329	+	0.180323i
$768$	−766.834	−	42.2966i	−0.998482	−	0.0550737i
$769$	750.091	−	1299.20i	0.975411	−	1.68946i	0.296838	−	0.954928i	$-0.404068\pi$
$769$	750.091	−	1299.20i	0.975411	−	1.68946i	0.678573	−	0.734533i	$-0.262599\pi$
$770$	−326.767	−	427.981i	−0.424373	−	0.555819i
$771$	−27.8044	+	775.508i	−0.0360628	+	1.00585i
$772$	171.115	−	626.524i	0.221651	−	0.811559i
$773$	572.185	−	572.185i	0.740213	−	0.740213i	−0.232406	−	0.972619i	$-0.574660\pi$
$773$	572.185	−	572.185i	0.740213	−	0.740213i	0.972619	+	0.232406i	$0.0746597\pi$
$774$	−1013.37	−	904.302i	−1.30927	−	1.16835i
$775$			387.010i			0.499368i
$776$	−200.116	−	155.864i	−0.257882	−	0.200856i
$777$	−49.3143	−	214.515i	−0.0634676	−	0.276081i
$778$	−820.225	−	109.995i	−1.05427	−	0.141381i
$779$	173.107	+	646.043i	0.222217	+	0.829324i
$780$	−527.357	−	164.549i	−0.676098	−	0.210960i
$781$	1555.73	+	416.856i	1.99197	+	0.533747i
$782$	207.972	+	86.7322i	0.265949	+	0.110911i
$783$	203.118	−	524.754i	0.259410	−	0.670184i
$784$	−3.10131	+	321.973i	−0.00395575	+	0.410679i
$785$	−350.156	+	202.163i	−0.446058	+	0.257532i
$786$	255.713	+	212.232i	0.325335	+	0.270015i
$787$	98.7267	+	368.453i	0.125447	+	0.468174i	0.999855	−	0.0170167i	$-0.00541686\pi$
$787$	98.7267	+	368.453i	0.125447	+	0.468174i	−0.874408	+	0.485191i	$0.838750\pi$
$788$	−452.290	+	774.748i	−0.573971	+	0.983182i
$789$	692.018	−	1105.17i	0.877082	−	1.40072i
$790$	439.246	−	569.591i	0.556008	−	0.721002i
$791$	−333.085			−0.421093
$792$	423.078	−	829.599i	0.534189	−	1.04747i
$793$		−	725.036i		−	0.914295i
$794$	684.980	−	888.246i	0.862695	−	1.11870i
$795$	−12.6159	+	351.878i	−0.0158691	+	0.442614i
$796$	90.0045	+	342.490i	0.113071	+	0.430264i
$797$	−796.594	+	213.447i	−0.999491	+	0.267813i	−0.721232	−	0.692693i	$-0.756424\pi$
$797$	−796.594	+	213.447i	−0.999491	+	0.267813i	−0.278259	+	0.960506i	$0.589757\pi$
$798$	861.176	−	318.707i	1.07917	−	0.399382i
$799$	126.637	+	219.342i	0.158495	+	0.274521i
$800$	−125.939	+	293.982i	−0.157424	+	0.367478i
$801$	828.731	−	1223.72i	1.03462	−	1.52774i
$802$	−161.855	−	67.4996i	−0.201814	−	0.0841641i
$803$	−289.303	+	1079.69i	−0.360278	+	1.34458i
$804$	599.084	−	946.586i	0.745130	−	1.17735i
$805$	190.611	−	51.0741i	0.236784	−	0.0634460i
$806$	−912.211	−	122.330i	−1.13178	−	0.151774i
$807$	8.04573	−	26.2290i	0.00996992	−	0.0325019i
$808$	986.822	−	122.672i	1.22131	−	0.151822i
$809$	−371.253			−0.458904			−0.229452	−	0.973320i	$-0.573693\pi$
$809$	−371.253			−0.458904			−0.229452	+	0.973320i	$0.573693\pi$
$810$	−450.282	+	437.095i	−0.555903	+	0.539623i
$811$	−682.431	−	682.431i	−0.841468	−	0.841468i	0.147582	−	0.989050i	$-0.452851\pi$
$811$	−682.431	−	682.431i	−0.841468	−	0.841468i	−0.989050	+	0.147582i	$0.952851\pi$
$812$	−222.107	−	389.015i	−0.273531	−	0.479083i
$813$	227.793	+	429.380i	0.280188	+	0.528143i
$814$	−214.337	−	280.727i	−0.263314	−	0.344873i
$815$	158.495	+	91.5072i	0.194473	+	0.112279i
$816$	−307.390	+	480.556i	−0.376704	+	0.588917i
$817$	−1074.50	−	1861.09i	−1.31518	−	2.27795i
$818$	−115.281	−	48.0763i	−0.140930	−	0.0587730i
$819$	564.396	−	108.617i	0.689129	−	0.132622i
$820$	−363.875	−	1.75242i	−0.443750	−	0.00213710i
$821$	−124.780	−	33.4347i	−0.151986	−	0.0407244i	0.182024	−	0.983294i	$-0.441735\pi$
$821$	−124.780	−	33.4347i	−0.151986	−	0.0407244i	−0.334010	+	0.942570i	$0.608402\pi$
$822$	263.576	−	573.283i	0.320652	−	0.697425i
$823$	−364.270	−	210.311i	−0.442613	−	0.255543i	0.262093	−	0.965043i	$-0.415587\pi$
$823$	−364.270	−	210.311i	−0.442613	−	0.255543i	−0.704705	+	0.709500i	$0.748921\pi$
$824$	1494.19	+	207.705i	1.81333	+	0.252069i
$825$	−264.219	−	283.870i	−0.320265	−	0.344084i
$826$	198.091	+	152.760i	0.239819	+	0.184939i
$827$	646.935	−	646.935i	0.782268	−	0.782268i	−0.197945	−	0.980213i	$-0.563427\pi$
$827$	646.935	−	646.935i	0.782268	−	0.782268i	0.980213	+	0.197945i	$0.0634269\pi$
$828$	222.176	+	259.059i	0.268329	+	0.312873i
$829$	626.764	−	626.764i	0.756048	−	0.756048i	−0.219553	−	0.975601i	$-0.570460\pi$
$829$	626.764	−	626.764i	0.756048	−	0.756048i	0.975601	+	0.219553i	$0.0704598\pi$
$830$	−600.926	+	77.6417i	−0.724007	+	0.0935442i
$831$	−766.643	+	176.242i	−0.922555	+	0.212084i
$832$	−653.129	−	389.773i	−0.785011	−	0.468477i
$833$	207.125	+	119.584i	0.248650	+	0.143558i
$834$	−468.022	−	388.440i	−0.561177	−	0.465755i
$835$	−623.735	−	167.129i	−0.746988	−	0.200155i
$836$	1046.91	−	1036.87i	1.25228	−	1.24027i
$837$	−616.895	+	844.114i	−0.737031	+	1.00850i
$838$	511.381	−	210.380i	0.610240	−	0.251050i
$839$	441.149	+	764.093i	0.525804	+	0.910719i	0.999548	+	0.0300564i	$0.00956870\pi$
$839$	441.149	+	764.093i	0.525804	+	0.910719i	−0.473744	+	0.880662i	$0.657098\pi$
$840$	43.8256	+	497.653i	0.0521733	+	0.592444i
$841$	352.189	+	203.337i	0.418775	+	0.241780i
$842$	−162.793	+	1213.94i	−0.193341	+	1.44173i
$843$	410.761	−	655.995i	0.487261	−	0.778168i
$844$	−579.707	−	1015.34i	−0.686857	−	1.20301i
$845$	76.0504	+	76.0504i	0.0900005	+	0.0900005i
$846$	21.7830	+	382.983i	0.0257483	+	0.452698i
$847$	248.742			0.293674
$848$	−129.974	+	467.030i	−0.153272	+	0.550743i
$849$	137.933	+	148.191i	0.162465	+	0.174548i
$850$	144.163	+	188.816i	0.169603	+	0.222137i
$851$	125.028	−	33.5012i	0.146919	−	0.0393668i
$852$	−1012.81	−	1098.70i	−1.18875	−	1.28955i
$853$	−191.702	+	715.440i	−0.224738	+	0.838734i	0.757771	+	0.652520i	$0.226288\pi$
$853$	−191.702	+	715.440i	−0.224738	+	0.838734i	−0.982509	+	0.186214i	$0.940378\pi$
$854$	−606.361	+	249.454i	−0.710025	+	0.292101i
$855$	−893.241	+	433.605i	−1.04473	+	0.507141i
$856$	−424.618	+	1004.53i	−0.496049	+	1.17352i
$857$	−454.964	−	788.022i	−0.530880	−	0.919512i	−0.999351	−	0.0360325i	$-0.988528\pi$
$857$	−454.964	−	788.022i	−0.530880	−	0.919512i	0.468470	−	0.883479i	$-0.344805\pi$
$858$	752.617	−	533.054i	0.877176	−	0.621275i
$859$	−133.228	+	35.6983i	−0.155097	+	0.0415580i	−0.335532	−	0.942029i	$-0.608916\pi$
$859$	−133.228	+	35.6983i	−0.155097	+	0.0415580i	0.180435	+	0.983587i	$0.442249\pi$
$860$	1130.77	−	297.159i	1.31485	−	0.345534i
$861$	334.433	−	177.422i	0.388424	−	0.206065i
$862$	131.301	+	1016.24i	0.152322	+	1.17893i
$863$		−	512.214i		−	0.593527i	−0.954951	−	0.296764i	$-0.904093\pi$
$863$		−	512.214i		−	0.593527i	0.954951	−	0.296764i	$-0.0959073\pi$
$864$	−743.296	+	440.462i	−0.860297	+	0.509794i
$865$	−274.541			−0.317389
$866$	−183.338	+	23.6879i	−0.211706	+	0.0273532i
$867$	−207.739	−	391.579i	−0.239607	−	0.451648i
$868$	211.546	+	804.988i	0.243717	+	0.927406i
$869$	310.796	+	1159.91i	0.357648	+	1.33476i
$870$	279.962	+	395.278i	0.321796	+	0.454342i
$871$	960.794	−	554.715i	1.10309	−	0.636871i
$872$	490.125	−	1159.50i	0.562070	−	1.32971i
$873$	−284.628	−	20.4358i	−0.326034	−	0.0234088i
$874$	205.444	+	499.384i	0.235062	+	0.571378i
$875$	703.616	+	188.533i	0.804133	+	0.215467i
$876$	762.511	−	702.903i	0.870446	−	0.802401i
$877$	−259.253	−	967.546i	−0.295614	−	1.10325i	−0.940729	−	0.339160i	$-0.889857\pi$
$877$	−259.253	−	967.546i	−0.295614	−	1.10325i	0.645115	−	0.764085i	$-0.276809\pi$
$878$	−298.708	+	228.066i	−0.340215	+	0.259757i
$879$	−959.519	+	893.097i	−1.09160	+	1.01604i
$880$	394.115	+	698.070i	0.447858	+	0.793262i
$881$		−	18.4946i		−	0.0209928i	−0.999945	−	0.0104964i	$-0.996659\pi$
$881$		−	18.4946i		−	0.0209928i	0.999945	−	0.0104964i	$-0.00334117\pi$
$882$	198.640	+	302.914i	0.225215	+	0.343440i
$883$	162.276	−	162.276i	0.183778	−	0.183778i	−0.609222	−	0.793000i	$-0.708518\pi$
$883$	162.276	−	162.276i	0.183778	−	0.183778i	0.793000	+	0.609222i	$0.208518\pi$
$884$	−490.621	+	280.119i	−0.555002	+	0.316876i
$885$	−229.256	−	143.552i	−0.259046	−	0.162205i
$886$	1266.47	+	169.837i	1.42942	+	0.191690i
$887$	252.776	−	437.820i	0.284978	−	0.493596i	−0.687626	−	0.726065i	$-0.741347\pi$
$887$	252.776	−	437.820i	0.284978	−	0.493596i	0.972604	+	0.232469i	$0.0746804\pi$
$888$	28.7467	+	326.427i	0.0323724	+	0.367598i
$889$	−264.210	+	152.542i	−0.297199	+	0.171588i
$890$	484.033	+	1176.56i	0.543857	+	1.32198i
$891$	−123.803	−	1040.32i	−0.138949	−	1.16758i
$892$	−222.367	−	224.519i	−0.249290	−	0.251703i
$893$	−157.091	+	586.271i	−0.175913	+	0.656518i
$894$	−806.576	+	971.825i	−0.902210	+	1.08705i
$895$	397.777	−	688.970i	0.444444	−	0.769799i
$896$	−101.260	+	680.329i	−0.113014	+	0.759295i
$897$	75.7246	+	329.398i	0.0844198	+	0.367222i
$898$	46.8640	+	362.714i	0.0521871	+	0.403913i
$899$	570.633	+	570.633i	0.634742	+	0.634742i
$900$	66.2929	+	353.640i	0.0736588	+	0.392934i
$901$	254.620	+	254.620i	0.282597	+	0.282597i
$902$	370.973	−	481.059i	0.411278	−	0.533324i
$903$	−890.393	+	828.756i	−0.986038	+	0.917780i
$904$	491.159	+	68.2753i	0.543317	+	0.0755258i
$905$	−231.724	+	401.358i	−0.256049	+	0.443490i
$906$	−796.091	−	366.015i	−0.878688	−	0.403990i
$907$	−258.798	+	965.847i	−0.285334	+	1.06488i	0.663261	+	0.748388i	$0.269172\pi$
$907$	−258.798	+	965.847i	−0.285334	+	1.06488i	−0.948595	+	0.316493i	$0.897495\pi$
$908$	−2.96048	+	614.718i	−0.00326044	+	0.677002i
$909$	845.674	−	732.372i	0.930334	−	0.805690i
$910$	−190.437	+	456.641i	−0.209271	+	0.501804i
$911$	452.086	−	261.012i	0.496252	−	0.286512i	−0.230912	−	0.972975i	$-0.574171\pi$
$911$	452.086	−	261.012i	0.496252	−	0.286512i	0.727165	+	0.686463i	$0.240838\pi$
$912$	−1335.20	+	293.434i	−1.46403	+	0.321748i
$913$	505.783	−	876.042i	0.553979	−	0.959520i
$914$	750.348	−	572.897i	0.820950	−	0.626802i
$915$	626.303	−	332.263i	0.684484	−	0.363129i
$916$	512.791	−	292.776i	0.559815	−	0.319625i
$917$	210.449	−	210.449i	0.229497	−	0.229497i
$918$	13.4622	+	641.625i	0.0146647	+	0.698938i
$919$		−	495.997i		−	0.539713i	−0.962901	−	0.269857i	$-0.913024\pi$
$919$		−	495.997i		−	0.539713i	0.962901	−	0.269857i	$-0.0869763\pi$
$920$	−291.539	+	36.2413i	−0.316891	+	0.0393927i
$921$	−1139.78	−	349.627i	−1.23755	−	0.379617i
$922$	−204.413	+	1524.30i	−0.221706	+	1.65325i
$923$	−383.022	−	1429.46i	−0.414975	−	1.54871i
$924$	−704.747	−	446.027i	−0.762713	−	0.482713i
$925$	131.812	+	35.3189i	0.142500	+	0.0381826i
$926$	99.7789	−	239.257i	0.107753	−	0.258376i
$927$	1526.75	−	741.127i	1.64698	−	0.799490i
$928$	247.774	+	619.160i	0.266997	+	0.667198i
$929$	−1037.03	+	598.731i	−1.11629	+	0.644490i	−0.940451	−	0.339929i	$-0.889597\pi$
$929$	−1037.03	+	598.731i	−1.11629	+	0.644490i	−0.175838	+	0.984419i	$0.556264\pi$
$930$	−312.369	−	844.050i	−0.335880	−	0.907580i
$931$	148.341	+	553.617i	0.159335	+	0.594647i
$932$	901.073	−	236.797i	0.966816	−	0.254074i
$933$	−561.669	−	20.1376i	−0.602003	−	0.0215837i
$934$	144.901	+	111.742i	0.155140	+	0.119638i
$935$	595.447			0.636842
$936$	−854.510	+	44.4748i	−0.912938	+	0.0475158i
$937$			219.908i			0.234694i	0.993091	+	0.117347i	$0.0374390\pi$
$937$			219.908i			0.234694i	−0.993091	+	0.117347i	$0.962561\pi$
$938$	−794.488	−	612.677i	−0.847002	−	0.653174i
$939$	−434.413	−	272.014i	−0.462634	−	0.289685i
$940$	−285.174	−	166.482i	−0.303377	−	0.177108i
$941$	7.40638	−	1.98453i	0.00787075	−	0.00210896i	−0.254882	−	0.966972i	$-0.582036\pi$
$941$	7.40638	−	1.98453i	0.00787075	−	0.00210896i	0.262752	+	0.964863i	$0.415370\pi$
$942$	−399.963	+	481.906i	−0.424589	+	0.511578i
$943$	111.315	+	192.803i	0.118043	+	0.204457i
$944$	−260.787	−	265.860i	−0.276258	−	0.281632i
$945$	352.473	+	437.763i	0.372987	+	0.463241i
$946$	−751.293	+	1801.50i	−0.794178	+	1.90433i
$947$	−206.974	+	772.438i	−0.218558	+	0.815668i	0.766326	+	0.642452i	$0.222083\pi$
$947$	−206.974	+	772.438i	−0.218558	+	0.815668i	−0.984884	+	0.173217i	$0.944584\pi$
$948$	331.851	−	1063.54i	0.350054	−	1.12187i
$949$	992.062	−	265.822i	1.04538	−	0.280108i
$950$	−75.6665	+	564.242i	−0.0796489	+	0.593938i
$951$	1674.77	−	385.009i	1.76106	−	0.404846i
$952$	403.071	+	313.939i	0.423394	+	0.329768i
$953$	11.2506			0.0118054			0.00590272	−	0.999983i	$-0.498121\pi$
$953$	11.2506			0.0118054			0.00590272	+	0.999983i	$0.498121\pi$
$954$	170.840	+	517.928i	0.179078	+	0.542901i
$955$	−28.5352	−	28.5352i	−0.0298798	−	0.0298798i
$956$	−318.082	−	86.8738i	−0.332722	−	0.0908722i
$957$	−808.137	−	28.9742i	−0.844448	−	0.0302761i
$958$	−652.168	+	497.936i	−0.680760	+	0.519766i
$959$	−489.391	−	282.550i	−0.510314	−	0.294630i
$960$	37.3842	−	742.810i	0.0389419	−	0.773761i
$961$	−269.217	−	466.298i	−0.280143	−	0.485222i
$962$	−124.914	+	299.526i	−0.129848	+	0.311358i
$963$	231.863	+	1204.80i	0.240771	+	1.25110i
$964$	999.011	+	1008.68i	1.03632	+	1.04635i
$965$	607.532	+	162.788i	0.629567	+	0.168692i
$966$	249.429	−	176.662i	0.258208	−	0.182880i
$967$	206.224	+	119.064i	0.213262	+	0.123127i	0.602826	−	0.797872i	$-0.294041\pi$
$967$	206.224	+	119.064i	0.213262	+	0.123127i	−0.389564	+	0.920999i	$0.627374\pi$
$968$	−366.789	−	50.9869i	−0.378914	−	0.0526724i
$969$	−297.788	+	970.786i	−0.307314	+	1.00184i
$970$	150.008	−	194.522i	0.154647	−	0.200538i
$971$	956.820	−	956.820i	0.985396	−	0.985396i	−0.0144987	−	0.999895i	$-0.504615\pi$
$971$	956.820	−	956.820i	0.985396	−	0.985396i	0.999895	+	0.0144987i	$0.00461525\pi$
$972$	−419.111	+	877.001i	−0.431184	+	0.902264i
$973$	−385.177	+	385.177i	−0.395865	+	0.395865i
$974$	−222.730	−	1723.87i	−0.228676	−	1.76989i
$975$	−104.498	+	340.663i	−0.107177	+	0.349398i
$976$	945.258	−	243.548i	0.968502	−	0.249537i
$977$	25.8436	+	14.9208i	0.0264520	+	0.0152720i	0.513168	−	0.858288i	$-0.328472\pi$
$977$	25.8436	+	14.9208i	0.0264520	+	0.0152720i	−0.486716	+	0.873560i	$0.661805\pi$
$978$	279.427	+	47.7197i	0.285712	+	0.0487932i
$979$	−2051.59	−	549.722i	−2.09560	−	0.561514i
$980$	−311.817	−	1.50171i	−0.318181	−	0.00153236i
$981$	−267.633	−	1390.67i	−0.272816	−	1.41761i
$982$	−308.149	−	749.035i	−0.313798	−	0.762765i
$983$	−626.105	−	1084.45i	−0.636933	−	1.10320i	−0.986102	−	0.166141i	$-0.946869\pi$
$983$	−626.105	−	1084.45i	−0.636933	−	1.10320i	0.349169	−	0.937060i	$-0.386464\pi$
$984$	−529.515	+	193.070i	−0.538125	+	0.196210i
$985$	−752.386	−	434.390i	−0.763843	−	0.441005i
$986$	490.966	+	65.8400i	0.497937	+	0.0667748i
$987$	343.334	+	12.3096i	0.347856	+	0.0124717i
$988$	−1306.04	−	356.702i	−1.32190	−	0.361035i
$989$	−505.808	−	505.808i	−0.511433	−	0.511433i
$990$	805.368	+	405.845i	0.813503	+	0.409944i
$991$	−702.277			−0.708655			−0.354328	−	0.935121i	$-0.615290\pi$
$991$	−702.277			−0.708655			−0.354328	+	0.935121i	$0.615290\pi$
$992$	−146.935	−	1230.38i	−0.148120	−	1.24030i
$993$	198.020	−	45.5223i	0.199416	−	0.0458432i
$994$	−1063.70	+	812.145i	−1.07012	+	0.817047i
$995$	−331.253	+	88.7589i	−0.332917	+	0.0892049i
$996$	−831.178	+	435.836i	−0.834516	+	0.437587i
$997$	−210.524	+	785.686i	−0.211157	+	0.788050i	0.776327	+	0.630331i	$0.217081\pi$
$997$	−210.524	+	785.686i	−0.211157	+	0.788050i	−0.987484	+	0.157719i	$0.949586\pi$
$998$	−176.248	−	428.415i	−0.176601	−	0.429273i
$999$	231.199	+	287.143i	0.231430	+	0.287431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.w.a.5.3	✓	184
3.2	odd	2		432.3.x.a.341.44		184
9.2	odd	6	inner	144.3.w.a.101.14	yes	184
9.7	even	3		432.3.x.a.197.33		184
16.13	even	4	inner	144.3.w.a.77.14	yes	184
48.29	odd	4		432.3.x.a.125.33		184
144.29	odd	12	inner	144.3.w.a.29.3	yes	184
144.61	even	12		432.3.x.a.413.44		184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.w.a.5.3	✓	184	1.1	even	1	trivial
144.3.w.a.29.3	yes	184	144.29	odd	12	inner
144.3.w.a.77.14	yes	184	16.13	even	4	inner
144.3.w.a.101.14	yes	184	9.2	odd	6	inner
432.3.x.a.125.33		184	48.29	odd	4
432.3.x.a.197.33		184	9.7	even	3
432.3.x.a.341.44		184	3.2	odd	2
432.3.x.a.413.44		184	144.61	even	12

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.98351 + 0.256277i) q^{2} +(-1.40595 - 2.65015i) q^{3} +(3.86864 - 1.01666i) q^{4} +(1.00259 + 3.74171i) q^{5} +(3.46789 + 4.89630i) q^{6} +(4.65369 - 2.68681i) q^{7} +(-7.41296 + 3.00800i) q^{8} +(-5.04662 + 7.45195i) q^{9} +O(q^{10})\)	\(q+(-1.98351 + 0.256277i) q^{2} +(-1.40595 - 2.65015i) q^{3} +(3.86864 - 1.01666i) q^{4} +(1.00259 + 3.74171i) q^{5} +(3.46789 + 4.89630i) q^{6} +(4.65369 - 2.68681i) q^{7} +(-7.41296 + 3.00800i) q^{8} +(-5.04662 + 7.45195i) q^{9} +(-2.94756 - 7.16478i) q^{10} +(12.4933 + 3.34758i) q^{11} +(-8.13341 - 8.82313i) q^{12} +(-3.07587 - 11.4793i) q^{13} +(-8.54209 + 6.52195i) q^{14} +(8.50651 - 7.91765i) q^{15} +(13.9328 - 7.86617i) q^{16} -11.8846i q^{17} +(8.10028 - 16.0744i) q^{18} +(20.1387 - 20.1387i) q^{19} +(7.68268 + 13.4560i) q^{20} +(-13.6633 - 8.55548i) q^{21} +(-25.6386 - 3.43821i) q^{22} +(4.74003 - 8.20998i) q^{23} +(18.3939 + 15.4164i) q^{24} +(8.65545 - 4.99723i) q^{25} +(9.04291 + 21.9811i) q^{26} +(26.8441 + 2.89727i) q^{27} +(15.2719 - 15.1255i) q^{28} +(5.39392 - 20.1304i) q^{29} +(-14.8437 + 17.8848i) q^{30} +(-19.3613 + 33.5347i) q^{31} +(-25.6200 + 19.1733i) q^{32} +(-8.69337 - 37.8157i) q^{33} +(3.04574 + 23.5732i) q^{34} +(14.7190 + 14.7190i) q^{35} +(-11.9475 + 33.9596i) q^{36} +(9.65467 + 9.65467i) q^{37} +(-34.7843 + 45.1065i) q^{38} +(-26.0974 + 24.2908i) q^{39} +(-18.6872 - 24.7213i) q^{40} +(-11.7420 + 20.3377i) q^{41} +(29.2939 + 13.4683i) q^{42} +(19.5292 - 72.8841i) q^{43} +(51.7356 + 0.249158i) q^{44} +(-32.9427 - 11.4118i) q^{45} +(-7.29789 + 17.4994i) q^{46} +(-18.4560 + 10.6556i) q^{47} +(-40.4354 - 25.8647i) q^{48} +(-10.0621 + 17.4281i) q^{49} +(-15.8875 + 12.1303i) q^{50} +(-31.4959 + 16.7091i) q^{51} +(-23.5700 - 41.2822i) q^{52} +(-21.4244 + 21.4244i) q^{53} +(-53.9881 + 1.13275i) q^{54} +50.1026i q^{55} +(-26.4157 + 33.9155i) q^{56} +(-81.6846 - 25.0567i) q^{57} +(-5.53996 + 41.3112i) q^{58} +(-6.02423 - 22.4827i) q^{59} +(24.8591 - 39.2788i) q^{60} +(58.9293 + 15.7901i) q^{61} +(29.8091 - 71.4783i) q^{62} +(-3.46345 + 48.2384i) q^{63} +(45.9039 - 44.5963i) q^{64} +(39.8684 - 23.0180i) q^{65} +(26.9347 + 72.7801i) q^{66} +(24.1615 + 90.1720i) q^{67} +(-12.0825 - 45.9771i) q^{68} +(-28.4219 - 1.01902i) q^{69} +(-32.9674 - 25.4232i) q^{70} +124.525 q^{71} +(14.9950 - 70.4212i) q^{72} +86.4217i q^{73} +(-21.6244 - 16.6759i) q^{74} +(-25.4125 - 15.9124i) q^{75} +(57.4353 - 98.3836i) q^{76} +(67.1344 - 17.9886i) q^{77} +(45.5394 - 54.8693i) q^{78} +(46.4211 + 80.4037i) q^{79} +(43.4018 + 44.2460i) q^{80} +(-30.0632 - 75.2144i) q^{81} +(18.0783 - 43.3493i) q^{82} +(20.2421 - 75.5446i) q^{83} +(-61.5564 - 19.2072i) q^{84} +(44.4685 - 11.9153i) q^{85} +(-20.0580 + 149.571i) q^{86} +(-60.9322 + 14.0075i) q^{87} +(-102.682 + 12.7644i) q^{88} -164.215 q^{89} +(68.2668 + 14.1929i) q^{90} +(-45.1569 - 45.1569i) q^{91} +(9.99077 - 36.5805i) q^{92} +(116.093 + 4.16230i) q^{93} +(33.8770 - 25.8654i) q^{94} +(95.5439 + 55.1623i) q^{95} +(86.8326 + 40.9403i) q^{96} +(15.8533 + 27.4588i) q^{97} +(15.4919 - 37.1475i) q^{98} +(-87.9951 + 76.2057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6}+O(q^{10}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6	\( 184 q - 6 q^{2} - 4 q^{3} - 2 q^{4} - 6 q^{5} - 10 q^{6} - 8 q^{10} - 6 q^{11} - 64 q^{12} - 2 q^{13} - 6 q^{14} - 8 q^{15} - 2 q^{16} + 54 q^{18} - 8 q^{19} + 120 q^{20} - 22 q^{21} - 2 q^{22} - 160 q^{24} + 44 q^{27} - 72 q^{28} - 6 q^{29} - 90 q^{30} - 4 q^{31} - 6 q^{32} - 8 q^{33} + 6 q^{34} - 202 q^{36} - 8 q^{37} - 6 q^{38} - 2 q^{40} + 44 q^{42} - 2 q^{43} + 46 q^{45} - 160 q^{46} - 12 q^{47} - 118 q^{48} + 472 q^{49} + 228 q^{50} - 48 q^{51} - 2 q^{52} + 206 q^{54} - 300 q^{56} - 92 q^{58} - 438 q^{59} - 90 q^{60} - 2 q^{61} - 204 q^{63} + 244 q^{64} - 12 q^{65} - 508 q^{66} - 2 q^{67} - 144 q^{68} + 14 q^{69} + 96 q^{70} + 6 q^{72} + 246 q^{74} + 152 q^{75} - 158 q^{76} - 6 q^{77} + 304 q^{78} - 4 q^{79} - 8 q^{81} - 388 q^{82} - 726 q^{83} + 542 q^{84} + 48 q^{85} + 894 q^{86} + 22 q^{88} - 528 q^{90} - 204 q^{91} - 348 q^{92} + 62 q^{93} - 18 q^{94} - 12 q^{95} + 262 q^{96} - 4 q^{97} + 286 q^{99}+O(q^{100}) \) 184 * q - 6 * q^2 - 4 * q^3 - 2 * q^4 - 6 * q^5 - 10 * q^6 - 8 * q^10 - 6 * q^11 - 64 * q^12 - 2 * q^13 - 6 * q^14 - 8 * q^15 - 2 * q^16 + 54 * q^18 - 8 * q^19 + 120 * q^20 - 22 * q^21 - 2 * q^22 - 160 * q^24 + 44 * q^27 - 72 * q^28 - 6 * q^29 - 90 * q^30 - 4 * q^31 - 6 * q^32 - 8 * q^33 + 6 * q^34 - 202 * q^36 - 8 * q^37 - 6 * q^38 - 2 * q^40 + 44 * q^42 - 2 * q^43 + 46 * q^45 - 160 * q^46 - 12 * q^47 - 118 * q^48 + 472 * q^49 + 228 * q^50 - 48 * q^51 - 2 * q^52 + 206 * q^54 - 300 * q^56 - 92 * q^58 - 438 * q^59 - 90 * q^60 - 2 * q^61 - 204 * q^63 + 244 * q^64 - 12 * q^65 - 508 * q^66 - 2 * q^67 - 144 * q^68 + 14 * q^69 + 96 * q^70 + 6 * q^72 + 246 * q^74 + 152 * q^75 - 158 * q^76 - 6 * q^77 + 304 * q^78 - 4 * q^79 - 8 * q^81 - 388 * q^82 - 726 * q^83 + 542 * q^84 + 48 * q^85 + 894 * q^86 + 22 * q^88 - 528 * q^90 - 204 * q^91 - 348 * q^92 + 62 * q^93 - 18 * q^94 - 12 * q^95 + 262 * q^96 - 4 * q^97 + 286 * q^99

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