LMFDB - Embedded newform 175.3.w.a.163.35

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,3,Mod(2,175)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("175.2"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([3, 20])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	175.w (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.76840462631$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$38$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			163.35
Character	$\chi$	$=$	175.163
Dual form			175.3.w.a.102.35

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22392 - 3.18843i) q^{2} +(-4.46346 + 0.233920i) q^{3} +(-5.69552 - 5.12827i) q^{4} +(-4.92516 - 0.861860i) q^{5} +(-4.71710 + 14.5177i) q^{6} +(6.16401 + 3.31738i) q^{7} +(-11.1499 + 5.68116i) q^{8} +(10.9170 - 1.14743i) q^{9} +(-8.77600 + 14.6487i) q^{10} +(-0.449650 + 4.27814i) q^{11} +(26.6213 + 21.5575i) q^{12} +(-7.40146 - 1.17228i) q^{13} +(18.1215 - 15.5933i) q^{14} +(22.1849 + 2.69478i) q^{15} +(1.26289 + 12.0156i) q^{16} +(-0.874796 + 1.34707i) q^{17} +(9.70314 - 36.2126i) q^{18} +(-22.9238 + 20.6407i) q^{19} +(23.6315 + 30.1663i) q^{20} +(-28.2888 - 13.3651i) q^{21} +(13.0902 + 6.66979i) q^{22} +(9.45191 + 3.62825i) q^{23} +(48.4382 - 27.9658i) q^{24} +(23.5144 + 8.48959i) q^{25} +(-12.7966 + 22.1643i) q^{26} +(-8.72837 + 1.38244i) q^{27} +(-18.0948 - 50.5049i) q^{28} +(-46.8737 + 15.2302i) q^{29} +(35.7447 - 67.4367i) q^{30} +(-49.7022 + 10.5645i) q^{31} +(-8.49302 - 2.27570i) q^{32} +(1.00625 - 19.2005i) q^{33} +(3.22435 + 4.43794i) q^{34} +(-27.4996 - 21.6511i) q^{35} +(-68.0626 - 49.4504i) q^{36} +(-2.05481 - 1.66395i) q^{37} +(37.7544 + 98.3535i) q^{38} +(33.3103 + 3.50106i) q^{39} +(59.8115 - 18.3710i) q^{40} +(2.42170 - 1.75947i) q^{41} +(-77.2370 + 73.8390i) q^{42} +(-23.5004 - 23.5004i) q^{43} +(24.5004 - 22.0603i) q^{44} +(-54.7571 - 3.75770i) q^{45} +(23.1368 - 25.6961i) q^{46} +(65.0093 - 42.2175i) q^{47} +(-8.44758 - 53.3359i) q^{48} +(26.9900 + 40.8967i) q^{49} +(55.8483 - 64.5834i) q^{50} +(3.58951 - 6.21722i) q^{51} +(36.1434 + 44.6334i) q^{52} +(-44.8902 + 2.35260i) q^{53} +(-6.27505 + 29.5218i) q^{54} +(5.90175 - 20.6830i) q^{55} +(-87.5747 - 1.96971i) q^{56} +(97.4911 - 97.4911i) q^{57} +(-8.80943 + 168.094i) q^{58} +(25.3265 - 56.8843i) q^{59} +(-112.535 - 129.118i) q^{60} +(-30.9698 + 13.7886i) q^{61} +(-27.1474 + 171.402i) q^{62} +(71.0992 + 29.1432i) q^{63} +(-46.0568 + 63.3917i) q^{64} +(35.4430 + 12.1527i) q^{65} +(-59.9878 - 26.7083i) q^{66} +(11.0227 - 16.9735i) q^{67} +(11.8906 - 3.18607i) q^{68} +(-43.0369 - 13.9835i) q^{69} +(-102.691 + 61.1813i) q^{70} +(-34.1676 - 105.157i) q^{71} +(-115.205 + 74.8152i) q^{72} +(-98.4134 + 79.6936i) q^{73} +(-7.82033 + 4.51507i) q^{74} +(-106.941 - 32.3925i) q^{75} +236.414 q^{76} +(-16.9638 + 24.8788i) q^{77} +(51.9322 - 101.923i) q^{78} +(-25.1734 + 118.431i) q^{79} +(4.13584 - 60.2674i) q^{80} +(-58.0004 + 12.3284i) q^{81} +(-2.64596 - 9.87486i) q^{82} +(101.280 - 51.6047i) q^{83} +(92.5797 + 221.194i) q^{84} +(5.46950 - 5.88058i) q^{85} +(-103.692 + 46.1668i) q^{86} +(205.656 - 78.9439i) q^{87} +(-19.2912 - 50.2554i) q^{88} +(-62.6959 - 140.817i) q^{89} +(-78.9997 + 169.990i) q^{90} +(-41.7338 - 31.7794i) q^{91} +(-35.2269 - 69.1367i) q^{92} +(219.372 - 58.7806i) q^{93} +(-55.0412 - 258.949i) q^{94} +(130.693 - 81.9015i) q^{95} +(38.4406 + 8.17080i) q^{96} +(-51.1064 - 26.0400i) q^{97} +(163.430 - 36.0014i) q^{98} +47.2206i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 24 q^{6} - 14 q^{7} - 4 q^{8} - 10 q^{9} - 24 q^{10} - 6 q^{11} + 36 q^{12} - 32 q^{13} - 20 q^{14} - 92 q^{15} - 262 q^{16} - 102 q^{17} - 6 q^{18} - 10 q^{19}+ \cdots - 262 q^{98}+O(q^{100}) $ 608 * q - 8 * q^2 - 8 * q^3 - 10 * q^4 - 6 * q^5 - 24 * q^6 - 14 * q^7 - 4 * q^8 - 10 * q^9 - 24 * q^10 - 6 * q^11 + 36 * q^12 - 32 * q^13 - 20 * q^14 - 92 * q^15 - 262 * q^16 - 102 * q^17 - 6 * q^18 - 10 * q^19 + 32 * q^20 - 12 * q^21 + 16 * q^22 + 56 * q^23 + 6 * q^25 - 16 * q^26 - 116 * q^27 + 34 * q^28 - 240 * q^29 + 166 * q^30 - 6 * q^31 - 140 * q^32 - 126 * q^33 - 40 * q^34 + 330 * q^35 - 568 * q^36 - 54 * q^37 + 304 * q^38 - 410 * q^39 + 148 * q^40 - 24 * q^41 + 350 * q^42 - 324 * q^43 - 10 * q^44 + 414 * q^45 - 6 * q^46 + 198 * q^47 - 68 * q^48 - 440 * q^50 - 16 * q^51 + 88 * q^52 + 382 * q^53 - 10 * q^54 - 248 * q^55 + 52 * q^56 + 584 * q^57 - 8 * q^58 - 410 * q^59 + 828 * q^60 - 6 * q^61 - 1656 * q^62 - 782 * q^63 + 860 * q^64 - 142 * q^65 + 138 * q^66 - 208 * q^67 + 378 * q^68 - 740 * q^69 - 140 * q^70 - 24 * q^71 - 498 * q^72 - 390 * q^73 + 360 * q^75 + 64 * q^76 + 692 * q^77 + 860 * q^78 - 10 * q^79 + 314 * q^80 - 402 * q^81 + 168 * q^82 + 400 * q^83 + 3580 * q^84 - 184 * q^85 - 6 * q^86 + 204 * q^87 - 1042 * q^88 - 760 * q^89 - 940 * q^90 - 12 * q^91 - 1412 * q^92 - 662 * q^93 - 10 * q^94 - 242 * q^95 - 54 * q^96 - 528 * q^97 - 262 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{20}\right)$

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 $

$2$	1.22392	−	3.18843i	0.611962	−	1.59422i	−0.180015	−	0.983664i	$-0.557614\pi$
$2$	1.22392	−	3.18843i	0.611962	−	1.59422i	0.791977	−	0.610552i	$-0.209052\pi$
$3$	−4.46346	+	0.233920i	−1.48782	+	0.0779733i	−0.778825	−	0.627241i	$-0.784184\pi$
$3$	−4.46346	+	0.233920i	−1.48782	+	0.0779733i	−0.708994	+	0.705214i	$0.750851\pi$
$4$	−5.69552	−	5.12827i	−1.42388	−	1.28207i
$5$	−4.92516	−	0.861860i	−0.985032	−	0.172372i
$5$	−4.92516	−	0.861860i	−0.985032	−	0.172372i
$6$	−4.71710	+	14.5177i	−0.786183	+	2.41962i
$7$	6.16401	+	3.31738i	0.880573	+	0.473911i
$7$	6.16401	+	3.31738i	0.880573	+	0.473911i
$8$	−11.1499	+	5.68116i	−1.39374	+	0.710145i
$9$	10.9170	−	1.14743i	1.21301	−	0.127492i
$10$	−8.77600	+	14.6487i	−0.877600	+	1.46487i
$11$	−0.449650	+	4.27814i	−0.0408773	+	0.388922i	0.954886	+	0.296972i	$0.0959767\pi$
$11$	−0.449650	+	4.27814i	−0.0408773	+	0.388922i	−0.995764	+	0.0919500i	$0.970690\pi$
$12$	26.6213	+	21.5575i	2.21844	+	1.79646i
$13$	−7.40146	−	1.17228i	−0.569343	−	0.0901751i	−0.134876	−	0.990863i	$-0.543063\pi$
$13$	−7.40146	−	1.17228i	−0.569343	−	0.0901751i	−0.434468	+	0.900687i	$0.643063\pi$
$14$	18.1215	−	15.5933i	1.29439	−	1.11381i
$15$	22.1849	+	2.69478i	1.47899	+	0.179652i
$16$	1.26289	+	12.0156i	0.0789309	+	0.750978i
$17$	−0.874796	+	1.34707i	−0.0514586	+	0.0792393i	−0.863464	−	0.504411i	$-0.831710\pi$
$17$	−0.874796	+	1.34707i	−0.0514586	+	0.0792393i	0.812005	+	0.583651i	$0.198376\pi$
$18$	9.70314	−	36.2126i	0.539063	−	2.01181i
$19$	−22.9238	+	20.6407i	−1.20652	+	1.08635i	−0.212494	+	0.977162i	$0.568159\pi$
$19$	−22.9238	+	20.6407i	−1.20652	+	1.08635i	−0.994021	+	0.109189i	$0.965175\pi$
$20$	23.6315	+	30.1663i	1.18158	+	1.50831i
$21$	−28.2888	−	13.3651i	−1.34709	−	0.636433i
$22$	13.0902	+	6.66979i	0.595009	+	0.303172i
$23$	9.45191	+	3.62825i	0.410953	+	0.157750i	0.555056	−	0.831813i	$-0.312697\pi$
$23$	9.45191	+	3.62825i	0.410953	+	0.157750i	−0.144104	+	0.989563i	$0.546030\pi$
$24$	48.4382	−	27.9658i	2.01826	−	1.16524i
$25$	23.5144	+	8.48959i	0.940576	+	0.339584i
$26$	−12.7966	+	22.1643i	−0.492175	+	0.852472i
$27$	−8.72837	+	1.38244i	−0.323273	+	0.0512014i
$28$	−18.0948	−	50.5049i	−0.646245	−	1.80375i
$29$	−46.8737	+	15.2302i	−1.61633	+	0.525178i	−0.971073	−	0.238784i	$-0.923251\pi$
$29$	−46.8737	+	15.2302i	−1.61633	+	0.525178i	−0.645261	+	0.763963i	$0.723251\pi$
$30$	35.7447	−	67.4367i	1.19149	−	2.24789i
$31$	−49.7022	+	10.5645i	−1.60330	+	0.340791i	−0.920781	−	0.390080i	$-0.872447\pi$
$31$	−49.7022	+	10.5645i	−1.60330	+	0.340791i	−0.682515	+	0.730871i	$0.739114\pi$
$32$	−8.49302	−	2.27570i	−0.265407	−	0.0711156i
$33$	1.00625	−	19.2005i	0.0304925	−	0.581832i
$34$	3.22435	+	4.43794i	0.0948338	+	0.130528i
$35$	−27.4996	−	21.6511i	−0.785703	−	0.618603i
$36$	−68.0626	−	49.4504i	−1.89063	−	1.37362i
$37$	−2.05481	−	1.66395i	−0.0555354	−	0.0449717i	0.601151	−	0.799136i	$-0.294709\pi$
$37$	−2.05481	−	1.66395i	−0.0555354	−	0.0449717i	−0.656686	+	0.754164i	$0.728042\pi$
$38$	37.7544	+	98.3535i	0.993536	+	2.58825i
$39$	33.3103	+	3.50106i	0.854111	+	0.0897707i
$40$	59.8115	−	18.3710i	1.49529	−	0.459274i
$41$	2.42170	−	1.75947i	0.0590658	−	0.0429138i	−0.557861	−	0.829935i	$-0.688378\pi$
$41$	2.42170	−	1.75947i	0.0590658	−	0.0429138i	0.616926	+	0.787021i	$0.288378\pi$
$42$	−77.2370	+	73.8390i	−1.83898	+	1.75807i
$43$	−23.5004	−	23.5004i	−0.546522	−	0.546522i	0.378911	−	0.925433i	$-0.376299\pi$
$43$	−23.5004	−	23.5004i	−0.546522	−	0.546522i	−0.925433	+	0.378911i	$0.876299\pi$
$44$	24.5004	−	22.0603i	0.556828	−	0.501370i
$45$	−54.7571	−	3.75770i	−1.21682	−	0.0835043i
$46$	23.1368	−	25.6961i	0.502975	−	0.558610i
$47$	65.0093	−	42.2175i	1.38318	−	0.898245i	0.383497	−	0.923542i	$-0.374720\pi$
$47$	65.0093	−	42.2175i	1.38318	−	0.898245i	0.999680	+	0.0252969i	$0.00805311\pi$
$48$	−8.44758	−	53.3359i	−0.175991	−	1.11116i
$49$	26.9900	+	40.8967i	0.550817	+	0.834626i
$50$	55.8483	−	64.5834i	1.11697	−	1.29167i
$51$	3.58951	−	6.21722i	0.0703826	−	0.121906i
$52$	36.1434	+	44.6334i	0.695066	+	0.858335i
$53$	−44.8902	+	2.35260i	−0.846986	+	0.0443886i	−0.470890	−	0.882192i	$-0.656067\pi$
$53$	−44.8902	+	2.35260i	−0.846986	+	0.0443886i	−0.376096	+	0.926581i	$0.622734\pi$
$54$	−6.27505	+	29.5218i	−0.116205	+	0.546700i
$55$	5.90175	−	20.6830i	0.107305	−	0.376054i
$56$	−87.5747	−	1.96971i	−1.56383	−	0.0351734i
$57$	97.4911	−	97.4911i	1.71037	−	1.71037i
$58$	−8.80943	+	168.094i	−0.151887	+	2.89817i
$59$	25.3265	−	56.8843i	0.429263	−	0.964140i	−0.561367	−	0.827567i	$-0.689724\pi$
$59$	25.3265	−	56.8843i	0.429263	−	0.964140i	0.990630	−	0.136573i	$-0.0436089\pi$
$60$	−112.535	−	129.118i	−1.87558	−	2.15197i
$61$	−30.9698	+	13.7886i	−0.507701	+	0.226043i	−0.644569	−	0.764546i	$-0.722963\pi$
$61$	−30.9698	+	13.7886i	−0.507701	+	0.226043i	0.136868	+	0.990589i	$0.456296\pi$
$62$	−27.1474	+	171.402i	−0.437862	+	2.76455i
$63$	71.0992	+	29.1432i	1.12856	+	0.462590i
$64$	−46.0568	+	63.3917i	−0.719638	+	0.990496i
$65$	35.4430	+	12.1527i	0.545278	+	0.186964i
$66$	−59.9878	−	26.7083i	−0.908906	−	0.404671i
$67$	11.0227	−	16.9735i	0.164518	−	0.253335i	−0.746791	−	0.665059i	$-0.768406\pi$
$67$	11.0227	−	16.9735i	0.164518	−	0.253335i	0.911309	+	0.411724i	$0.135073\pi$
$68$	11.8906	−	3.18607i	0.174861	−	0.0468539i
$69$	−43.0369	−	13.9835i	−0.623723	−	0.202660i
$70$	−102.691	+	61.1813i	−1.46701	+	0.874019i
$71$	−34.1676	−	105.157i	−0.481234	−	1.48108i	−0.837363	−	0.546648i	$-0.815904\pi$
$71$	−34.1676	−	105.157i	−0.481234	−	1.48108i	0.356129	−	0.934437i	$-0.384096\pi$
$72$	−115.205	+	74.8152i	−1.60007	+	1.03910i
$73$	−98.4134	+	79.6936i	−1.34813	+	1.09169i	−0.360863	+	0.932619i	$0.617518\pi$
$73$	−98.4134	+	79.6936i	−1.34813	+	1.09169i	−0.987267	+	0.159075i	$0.949149\pi$
$74$	−7.82033	+	4.51507i	−0.105680	+	0.0610145i
$75$	−106.941	−	32.3925i	−1.42589	−	0.431899i
$76$	236.414			3.11071
$77$	−16.9638	+	24.8788i	−0.220310	+	0.323101i
$78$	51.9322	−	101.923i	0.665798	−	1.30670i
$79$	−25.1734	+	118.431i	−0.318650	+	1.49913i	0.469105	+	0.883142i	$0.344577\pi$
$79$	−25.1734	+	118.431i	−0.318650	+	1.49913i	−0.787755	+	0.615989i	$0.788757\pi$
$80$	4.13584	−	60.2674i	0.0516980	−	0.753342i
$81$	−58.0004	+	12.3284i	−0.716054	+	0.152202i
$82$	−2.64596	−	9.87486i	−0.0322678	−	0.120425i
$83$	101.280	−	51.6047i	1.22024	−	0.621743i	0.279263	−	0.960215i	$-0.409910\pi$
$83$	101.280	−	51.6047i	1.22024	−	0.621743i	0.940977	+	0.338472i	$0.109910\pi$
$84$	92.5797	+	221.194i	1.10214	+	2.63326i
$85$	5.46950	−	5.88058i	0.0643470	−	0.0691832i
$86$	−103.692	+	46.1668i	−1.20572	+	0.536823i
$87$	205.656	−	78.9439i	2.36386	−	0.907402i
$88$	−19.2912	−	50.2554i	−0.219219	−	0.571084i
$89$	−62.6959	−	140.817i	−0.704448	−	1.58222i	−0.809075	−	0.587706i	$-0.800031\pi$
$89$	−62.6959	−	140.817i	−0.704448	−	1.58222i	0.104626	−	0.994512i	$-0.466635\pi$
$90$	−78.9997	+	169.990i	−0.877774	+	1.88878i
$91$	−41.7338	−	31.7794i	−0.458613	−	0.349224i
$92$	−35.2269	−	69.1367i	−0.382901	−	0.751486i
$93$	219.372	−	58.7806i	2.35884	−	0.632050i
$94$	−55.0412	−	258.949i	−0.585545	−	2.75477i
$95$	130.693	−	81.9015i	1.37571	−	0.862121i
$96$	38.4406	+	8.17080i	0.400423	+	0.0851125i
$97$	−51.1064	−	26.0400i	−0.526870	−	0.268454i	0.170259	−	0.985399i	$-0.445540\pi$
$97$	−51.1064	−	26.0400i	−0.526870	−	0.268454i	−0.697129	+	0.716946i	$0.745540\pi$
$98$	163.430	−	36.0014i	1.66765	−	0.367361i
$99$			47.2206i			0.476975i
$100$	−90.3898	−	168.941i	−0.903898	−	1.68941i
$101$	62.4860	+	108.229i	0.618673	+	1.07157i	0.989728	+	0.142962i	$0.0456627\pi$
$101$	62.4860	+	108.229i	0.618673	+	1.07157i	−0.371055	+	0.928611i	$0.621004\pi$
$102$	−15.4299	−	19.0543i	−0.151273	−	0.186807i
$103$	37.6430	+	57.9651i	0.365466	+	0.562768i	0.972791	−	0.231685i	$-0.0744240\pi$
$103$	37.6430	+	57.9651i	0.365466	+	0.562768i	−0.607325	+	0.794454i	$0.707757\pi$
$104$	89.1855	−	28.9781i	0.857553	−	0.278636i
$105$	127.808	+	90.2062i	1.21722	+	0.859106i
$106$	−47.4411	+	146.009i	−0.447558	+	1.37744i
$107$	5.65879	+	21.1189i	0.0528859	+	0.197373i	0.987314	−	0.158778i	$-0.0507555\pi$
$107$	5.65879	+	21.1189i	0.0528859	+	0.197373i	−0.934428	+	0.356151i	$0.884089\pi$
$108$	56.8022	+	36.8878i	0.525946	+	0.341553i
$109$	8.84426	−	19.8645i	0.0811400	−	0.182243i	−0.868420	−	0.495830i	$-0.834864\pi$
$109$	8.84426	−	19.8645i	0.0811400	−	0.182243i	0.949560	+	0.313587i	$0.101531\pi$
$110$	−58.7229	−	44.1317i	−0.533845	−	0.401197i
$111$	9.56079	+	6.94632i	0.0861333	+	0.0625795i
$112$	−32.0759	+	78.2540i	−0.286392	+	0.698697i
$113$	11.8105	+	1.87060i	0.104518	+	0.0165540i	0.208474	−	0.978028i	$-0.433150\pi$
$113$	11.8105	+	1.87060i	0.104518	+	0.0165540i	−0.103957	+	0.994582i	$0.533150\pi$
$114$	−191.522	−	430.165i	−1.68002	−	3.77338i
$115$	−43.4251	−	26.0159i	−0.377610	−	0.226225i
$116$	345.075	+	153.637i	2.97478	+	1.32446i
$117$	−82.1472	−	4.30515i	−0.702113	−	0.0367962i
$118$	−150.374	−	150.374i	−1.27435	−	1.27435i
$119$	−9.86099	+	5.40131i	−0.0828654	+	0.0453892i
$120$	−262.669	+	95.9892i	−2.18890	+	0.799910i
$121$	100.256	+	21.3100i	0.828559	+	0.176116i
$122$	6.05945	+	115.621i	0.0496676	+	0.947715i
$123$	−10.3976	+	8.41978i	−0.0845331	+	0.0684535i
$124$	337.258	+	194.716i	2.71982	+	1.57029i
$125$	−108.495	−	62.0787i	−0.867963	−	0.496630i
$126$	179.941	−	191.026i	1.42810	−	1.51608i
$127$	33.8659	−	5.36383i	0.266660	−	0.0422349i	−0.0216724	−	0.999765i	$-0.506899\pi$
$127$	33.8659	−	5.36383i	0.266660	−	0.0422349i	0.288333	+	0.957530i	$0.406899\pi$
$128$	126.595	+	194.939i	0.989023	+	1.52296i
$129$	110.390	+	99.3960i	0.855740	+	0.770512i
$130$	82.1275	−	98.1338i	0.631750	−	0.754875i
$131$	11.7453	+	13.0444i	0.0896586	+	0.0995759i	0.786304	−	0.617839i	$-0.211992\pi$
$131$	11.7453	+	13.0444i	0.0896586	+	0.0995759i	−0.696646	+	0.717415i	$0.745325\pi$
$132$	−104.196	+	104.196i	−0.789366	+	0.789366i
$133$	−209.775	+	51.1825i	−1.57726	+	0.384831i
$134$	−40.6278	−	55.9193i	−0.303192	−	0.417308i
$135$	44.1801	+	0.713901i	0.327260	+	0.00528816i
$136$	2.10099	−	19.9896i	0.0154484	−	0.146982i
$137$	−124.671	+	47.8568i	−0.910009	+	0.349320i	−0.767929	−	0.640535i	$-0.778713\pi$
$137$	−124.671	+	47.8568i	−0.910009	+	0.349320i	−0.142081	+	0.989855i	$0.545379\pi$
$138$	−97.2595	+	120.105i	−0.704779	+	0.870329i
$139$	19.2566	−	26.5044i	0.138536	−	0.190679i	−0.734111	−	0.679029i	$-0.762401\pi$
$139$	19.2566	−	26.5044i	0.138536	−	0.190679i	0.872648	+	0.488350i	$0.162401\pi$
$140$	45.5919	+	264.340i	0.325656	+	1.88814i
$141$	−280.291	+	203.643i	−1.98788	+	1.44428i
$142$	−377.104	−	19.7632i	−2.65566	−	0.139177i
$143$	8.34323	−	31.1374i	0.0583443	−	0.217744i
$144$	27.5742	+	129.726i	0.191487	+	0.900877i
$145$	243.987	−	34.6125i	1.68267	−	0.238707i
$146$	133.647	+	411.323i	0.915391	+	2.81728i
$147$	−130.035	−	176.227i	−0.884595	−	1.19882i
$148$	3.17002	+	20.0147i	0.0214190	+	0.135235i
$149$	−49.5189	−	28.5898i	−0.332342	−	0.191878i	0.324539	−	0.945872i	$-0.394791\pi$
$149$	−49.5189	−	28.5898i	−0.332342	−	0.191878i	−0.656880	+	0.753995i	$0.728124\pi$
$150$	−234.169	+	301.329i	−1.56113	+	2.00886i
$151$	−68.1668	−	118.068i	−0.451436	−	0.781910i	0.547040	−	0.837107i	$-0.315755\pi$
$151$	−68.1668	−	118.068i	−0.451436	−	0.781910i	−0.998475	+	0.0551971i	$0.982421\pi$
$152$	138.335	−	360.375i	0.910100	−	2.37089i
$153$	−8.00453	+	15.7098i	−0.0523172	+	0.102678i
$154$	58.5619	+	84.5378i	0.380272	+	0.548947i
$155$	253.896	−	9.19567i	1.63804	−	0.0593269i
$156$	−171.765	−	190.765i	−1.10106	−	1.22285i
$157$	−143.892	−	38.5558i	−0.916511	−	0.245578i	−0.230418	−	0.973092i	$-0.574009\pi$
$157$	−143.892	−	38.5558i	−0.916511	−	0.245578i	−0.686093	+	0.727513i	$0.740676\pi$
$158$	346.800	+	225.214i	2.19494	+	1.42541i
$159$	199.815	−	21.0014i	1.25670	−	0.132085i
$160$	39.8682	+	18.5280i	0.249176	+	0.115800i
$161$	46.2254	+	53.7201i	0.287114	+	0.333665i
$162$	−31.6799	+	200.019i	−0.195555	+	1.23469i
$163$	18.5984	−	22.9672i	0.114101	−	0.140903i	−0.716896	−	0.697181i	$-0.754438\pi$
$163$	18.5984	−	22.9672i	0.114101	−	0.140903i	0.830996	+	0.556278i	$0.187771\pi$
$164$	−22.8158	−	2.39804i	−0.139121	−	0.0146222i
$165$	−21.5041	+	93.6981i	−0.130328	+	0.567867i
$166$	−40.5791	−	386.084i	−0.244452	−	2.32581i
$167$	−80.7001	−	158.383i	−0.483234	−	0.948401i	−0.995956	−	0.0898455i	$-0.971363\pi$
$167$	−80.7001	−	158.383i	−0.483234	−	0.948401i	0.512722	−	0.858555i	$-0.328637\pi$
$168$	391.347	−	11.6938i	2.32945	−	0.0696057i
$169$	−107.321	−	34.8707i	−0.635036	−	0.206336i
$170$	−12.0556	−	24.6365i	−0.0709151	−	0.144921i
$171$	−226.576	+	251.639i	−1.32501	+	1.47157i
$172$	13.3306	+	254.364i	0.0775038	+	1.47886i
$173$	−19.3400	−	7.42392i	−0.111792	−	0.0429129i	0.301829	−	0.953362i	$-0.402403\pi$
$173$	−19.3400	−	7.42392i	−0.111792	−	0.0429129i	−0.413621	+	0.910449i	$0.635736\pi$
$174$		−	752.341i		−	4.32380i
$175$	116.780	+	130.336i	0.667313	+	0.744777i
$176$	−51.9724			−0.295298
$177$	−99.7374	+	259.825i	−0.563488	+	1.46794i
$178$	−525.721	+	27.5519i	−2.95349	+	0.154786i
$179$	92.0001	+	82.8373i	0.513967	+	0.462778i	0.884833	−	0.465908i	$-0.154272\pi$
$179$	92.0001	+	82.8373i	0.513967	+	0.462778i	−0.370866	+	0.928686i	$0.620939\pi$
$180$	292.600	+	302.211i	1.62556	+	1.67895i
$181$	−7.83680	+	24.1192i	−0.0432973	+	0.133255i	−0.970368	−	0.241630i	$-0.922318\pi$
$181$	−7.83680	+	24.1192i	−0.0432973	+	0.133255i	0.927071	+	0.374885i	$0.122318\pi$
$182$	−152.405	+	94.1698i	−0.837392	+	0.517417i
$183$	135.007	−	68.7894i	0.737742	−	0.375899i
$184$	−126.001	+	13.2432i	−0.684786	+	0.0719739i
$185$	8.68618	+	9.96619i	0.0469523	+	0.0538713i
$186$	81.0771	−	771.397i	0.435898	−	4.14729i
$187$	−5.36959	−	4.34821i	−0.0287144	−	0.0232525i
$188$	−586.765	−	92.9344i	−3.12109	−	0.494332i
$189$	−58.3878	−	20.4339i	−0.308930	−	0.108116i
$190$	−101.179	−	516.946i	−0.532523	−	2.72077i
$191$	5.75832	+	54.7868i	0.0301483	+	0.286842i	0.999200	+	0.0399850i	$0.0127310\pi$
$191$	5.75832	+	54.7868i	0.0301483	+	0.286842i	−0.969052	+	0.246857i	$0.920602\pi$
$192$	190.744	−	293.720i	0.993458	−	1.52979i
$193$	−63.8836	+	238.417i	−0.331003	+	1.23532i	0.577134	+	0.816649i	$0.304171\pi$
$193$	−63.8836	+	238.417i	−0.331003	+	1.23532i	−0.908138	+	0.418672i	$0.862496\pi$
$194$	−145.577	+	131.078i	−0.750398	+	0.675661i
$195$	−161.041	−	45.9521i	−0.825853	−	0.235652i
$196$	56.0070	−	371.340i	0.285750	−	1.89459i
$197$	156.601	+	79.7922i	0.794929	+	0.405037i	0.803782	−	0.594924i	$-0.202818\pi$
$197$	156.601	+	79.7922i	0.794929	+	0.405037i	−0.00885272	+	0.999961i	$0.502818\pi$
$198$	150.559	+	57.7944i	0.760401	+	0.291891i
$199$	12.5447	−	7.24269i	0.0630387	−	0.0363954i	−0.468149	−	0.883649i	$-0.655079\pi$
$199$	12.5447	−	7.24269i	0.0630387	−	0.0363954i	0.531188	+	0.847254i	$0.321746\pi$
$200$	−310.414	+	38.9309i	−1.55207	+	0.194655i
$201$	−45.2289	+	78.3388i	−0.225019	+	0.389745i
$202$	421.558	−	66.7683i	2.08692	−	0.330536i
$203$	−339.454	−	61.6186i	−1.67219	−	0.303540i
$204$	−52.3277	+	17.0023i	−0.256508	+	0.0833446i
$205$	−13.4437	+	6.57849i	−0.0655788	+	0.0320902i
$206$	230.890	−	49.0772i	1.12082	−	0.238239i
$207$	107.350	+	28.7644i	0.518599	+	0.138958i
$208$	4.73839	−	90.4138i	0.0227807	−	0.434682i
$209$	−77.9959	−	107.352i	−0.373186	−	0.513647i
$210$	444.043	−	297.102i	2.11449	−	1.41477i
$211$	129.661	+	94.2044i	0.614508	+	0.446466i	0.850999	−	0.525167i	$-0.175997\pi$
$211$	129.661	+	94.2044i	0.614508	+	0.446466i	−0.236491	+	0.971634i	$0.575997\pi$
$212$	267.738	+	216.810i	1.26292	+	1.02269i
$213$	177.104	+	461.371i	0.831474	+	2.16606i
$214$	74.2620	+	7.80525i	0.347019	+	0.0364731i
$215$	95.4893	+	135.997i	0.444136	+	0.632546i
$216$	89.4667	−	65.0014i	0.414198	−	0.300932i
$217$	−341.411	−	99.7610i	−1.57332	−	0.459728i
$218$	−52.5120	−	52.5120i	−0.240881	−	0.240881i
$219$	420.622	−	378.730i	1.92065	−	1.72936i
$220$	−139.681	+	87.5345i	−0.634916	+	0.397884i
$221$	8.05391	−	8.94477i	0.0364430	−	0.0404741i
$222$	33.8496	−	21.9822i	0.152475	−	0.0990187i
$223$	−62.5350	−	394.830i	−0.280426	−	1.77054i	−0.578191	−	0.815901i	$-0.696241\pi$
$223$	−62.5350	−	394.830i	−0.280426	−	1.77054i	0.297765	−	0.954639i	$-0.403759\pi$
$224$	−44.8017	−	42.2020i	−0.200008	−	0.188402i
$225$	266.449	+	65.7002i	1.18422	+	0.292001i
$226$	20.4194	−	35.3675i	0.0903514	−	0.156493i
$227$	104.090	+	128.541i	0.458548	+	0.566259i	0.953010	−	0.302940i	$-0.0979682\pi$
$227$	104.090	+	128.541i	0.458548	+	0.566259i	−0.494462	+	0.869199i	$0.664635\pi$
$228$	−1055.22	+	55.3019i	−4.62817	+	0.242552i
$229$	11.0404	−	51.9412i	0.0482116	−	0.226818i	−0.947445	−	0.319918i	$-0.896345\pi$
$229$	11.0404	−	51.9412i	0.0482116	−	0.226818i	0.995657	+	0.0931007i	$0.0296779\pi$
$230$	−136.099	+	106.616i	−0.591735	+	0.463550i
$231$	69.8977	−	115.014i	0.302588	−	0.497895i
$232$	436.112	−	436.112i	1.87979	−	1.87979i
$233$	4.73483	−	90.3459i	0.0203212	−	0.387751i	−0.969469	−	0.245216i	$-0.921141\pi$
$233$	4.73483	−	90.3459i	0.0203212	−	0.387751i	0.989790	−	0.142535i	$-0.0455254\pi$
$234$	−114.269	+	256.652i	−0.488327	+	1.09680i
$235$	−356.567	+	151.899i	−1.51731	+	0.646380i
$236$	−435.966	+	194.104i	−1.84731	+	0.822476i
$237$	84.6568	−	534.502i	0.357202	−	2.25528i
$238$	5.15262	+	38.0519i	0.0216496	+	0.159882i
$239$	−192.281	+	264.651i	−0.804521	+	1.10733i	0.187625	+	0.982241i	$0.439921\pi$
$239$	−192.281	+	264.651i	−0.804521	+	1.10733i	−0.992146	+	0.125087i	$0.960079\pi$
$240$	−4.36239	+	269.968i	−0.0181766	+	1.12487i
$241$	96.9959	+	43.1854i	0.402473	+	0.179192i	0.597982	−	0.801509i	$-0.295969\pi$
$241$	96.9959	+	43.1854i	0.402473	+	0.179192i	−0.195510	+	0.980702i	$0.562636\pi$
$242$	190.651	−	293.576i	0.787813	−	1.21312i
$243$	332.823	−	89.1796i	1.36964	−	0.366994i
$244$	247.101	+	80.2879i	1.01271	+	0.329049i
$245$	−97.6830	−	224.684i	−0.398706	−	0.917079i
$246$	14.1201	+	43.4571i	0.0573986	+	0.176655i
$247$	193.866	−	125.898i	0.784883	−	0.509709i
$248$	494.156	−	400.160i	1.99256	−	1.61355i
$249$	−439.987	+	254.027i	−1.76702	+	1.02019i
$250$	−330.724	+	269.950i	−1.32289	+	1.07980i
$251$	−364.849			−1.45358			−0.726791	−	0.686859i	$-0.758989\pi$
$251$	−364.849			−1.45358			−0.726791	+	0.686859i	$0.758989\pi$
$252$	−255.493	−	530.602i	−1.01386	−	2.10556i
$253$	−19.7722	+	38.8051i	−0.0781510	+	0.153380i
$254$	24.3471	−	114.544i	0.0958546	−	0.450960i
$255$	−23.0373	+	27.5271i	−0.0903423	+	0.107950i
$256$	469.916	−	99.8837i	1.83561	−	0.390171i
$257$	−119.974	−	447.749i	−0.466825	−	1.74222i	−0.650766	−	0.759279i	$-0.725552\pi$
$257$	−119.974	−	447.749i	−0.466825	−	1.74222i	0.183940	−	0.982937i	$-0.441115\pi$
$258$	452.027	−	230.319i	1.75204	−	0.892710i
$259$	−7.14591	−	17.0732i	−0.0275904	−	0.0659197i
$260$	−139.544	−	250.977i	−0.536710	−	0.965298i
$261$	−494.246	+	220.053i	−1.89366	+	0.843114i
$262$	55.9666	−	21.4836i	0.213613	−	0.0819984i
$263$	−21.1000	−	54.9674i	−0.0802282	−	0.209002i	0.887599	−	0.460617i	$-0.152372\pi$
$263$	−21.1000	−	54.9674i	−0.0802282	−	0.209002i	−0.967827	+	0.251615i	$0.919038\pi$
$264$	97.8613	+	219.800i	0.370687	+	0.832576i
$265$	223.119	+	27.1022i	0.841959	+	0.102272i
$266$	−93.5573	+	731.498i	−0.351719	+	2.74999i
$267$	312.781	+	613.866i	1.17146	+	2.29913i
$268$	−149.825	+	40.1454i	−0.559047	+	0.149796i
$269$	10.9784	+	51.6492i	0.0408118	+	0.192005i	0.993831	−	0.110906i	$-0.0353751\pi$
$269$	10.9784	+	51.6492i	0.0408118	+	0.192005i	−0.953019	+	0.302910i	$0.902042\pi$
$270$	56.3493	−	139.991i	0.208701	−	0.518487i
$271$	377.884	+	80.3217i	1.39441	+	0.296390i	0.843030	−	0.537867i	$-0.180770\pi$
$271$	377.884	+	80.3217i	1.39441	+	0.296390i	0.551376	+	0.834257i	$0.314103\pi$
$272$	−17.2907	−	8.81003i	−0.0635686	−	0.0323898i
$273$	193.711	+	132.083i	0.709564	+	0.483822i
$274$			456.079i			1.66452i
$275$	−46.8929	+	96.7805i	−0.170520	+	0.351929i
$276$	173.406	+	300.349i	0.628284	+	1.08822i
$277$	−65.9933	−	81.4949i	−0.238243	−	0.294205i	0.643975	−	0.765046i	$-0.277284\pi$
$277$	−65.9933	−	81.4949i	−0.238243	−	0.294205i	−0.882218	+	0.470841i	$0.843951\pi$
$278$	−60.9388	−	93.8376i	−0.219204	−	0.337545i
$279$	−530.479	+	172.363i	−1.90136	+	0.617789i
$280$	429.622	+	85.1782i	1.53436	+	0.304208i
$281$	−12.9517	+	39.8612i	−0.0460915	+	0.141855i	−0.971454	−	0.237229i	$-0.923761\pi$
$281$	−12.9517	+	39.8612i	−0.0460915	+	0.141855i	0.925362	+	0.379084i	$0.123761\pi$
$282$	306.248	+	1142.93i	1.08598	+	4.05295i
$283$	−98.1777	−	63.7573i	−0.346917	−	0.225291i	0.359404	−	0.933182i	$-0.382980\pi$
$283$	−98.1777	−	63.7573i	−0.346917	−	0.225291i	−0.706321	+	0.707891i	$0.749647\pi$
$284$	−344.671	+	774.145i	−1.21363	+	2.72586i
$285$	−564.183	+	396.136i	−1.97959	+	1.38995i
$286$	−89.0678	−	64.7116i	−0.311426	−	0.226264i
$287$	20.7642	−	2.81168i	0.0723490	−	0.00979680i
$288$	−95.3299	−	15.0988i	−0.331007	−	0.0524263i
$289$	116.498	+	261.658i	0.403106	+	0.905390i
$290$	188.261	−	820.297i	0.649177	−	2.82861i
$291$	234.203	+	104.274i	0.804820	+	0.358329i
$292$	969.207	+	50.7940i	3.31920	+	0.173952i
$293$	237.403	+	237.403i	0.810249	+	0.810249i	0.984671	−	0.174422i	$-0.0558058\pi$
$293$	237.403	+	237.403i	0.810249	+	0.810249i	−0.174422	+	0.984671i	$0.555806\pi$
$294$	−721.042	+	198.920i	−2.45252	+	0.676600i
$295$	−173.763	+	258.336i	−0.589028	+	0.875716i
$296$	32.3641	+	6.87921i	0.109338	+	0.0232406i
$297$	−1.98955	−	37.9628i	−0.00669881	−	0.127821i
$298$	−151.764	+	122.896i	−0.509275	+	0.412403i
$299$	−65.7046	−	37.9346i	−0.219748	−	0.126872i
$300$	442.970	+	732.917i	1.47657	+	2.44306i
$301$	−66.8971	−	222.817i	−0.222250	−	0.740255i
$302$	−459.884	+	72.8384i	−1.52279	+	0.241187i
$303$	−304.220	−	468.458i	−1.00403	−	1.54607i
$304$	−276.961	−	249.377i	−0.911057	−	0.820319i
$305$	164.415	−	41.2196i	0.539065	−	0.135146i
$306$	40.2926	+	44.7495i	0.131675	+	0.146240i
$307$	−204.815	+	204.815i	−0.667149	+	0.667149i	−0.957055	−	0.289906i	$-0.906376\pi$
$307$	−204.815	+	204.815i	−0.667149	+	0.667149i	0.289906	+	0.957055i	$0.406376\pi$
$308$	224.203	−	54.7027i	0.727933	−	0.177606i
$309$	−181.577	−	249.919i	−0.587628	−	0.808801i
$310$	281.430	−	820.786i	0.907839	−	2.64770i
$311$	−10.0218	+	95.3506i	−0.0322243	+	0.306594i	0.966524	+	0.256576i	$0.0825944\pi$
$311$	−10.0218	+	95.3506i	−0.0322243	+	0.306594i	−0.998748	+	0.0500176i	$0.984072\pi$
$312$	−391.297	+	150.205i	−1.25416	+	0.481426i
$313$	198.752	−	245.439i	0.634991	−	0.784149i	−0.353499	−	0.935435i	$-0.615008\pi$
$313$	198.752	−	245.439i	0.634991	−	0.784149i	0.988490	+	0.151286i	$0.0483415\pi$
$314$	−299.046	+	411.601i	−0.952375	+	1.31083i
$315$	−325.058	−	204.812i	−1.03193	−	0.650198i
$316$	750.724	−	545.433i	2.37571	−	1.72605i
$317$	102.044	+	5.34789i	0.321905	+	0.0168703i	0.212604	−	0.977138i	$-0.431806\pi$
$317$	102.044	+	5.34789i	0.321905	+	0.0168703i	0.109301	+	0.994009i	$0.465139\pi$
$318$	177.597	−	662.802i	0.558482	−	2.08428i
$319$	−44.0800	−	207.380i	−0.138182	−	0.650095i
$320$	281.472	−	272.520i	0.879600	−	0.851625i
$321$	−30.1979	−	92.9395i	−0.0940744	−	0.289531i
$322$	227.859	−	81.6371i	0.707637	−	0.253532i
$323$	−7.75075	−	48.9363i	−0.0239961	−	0.151506i
$324$	393.566	+	227.225i	1.21471	+	0.701312i
$325$	−164.089	−	90.4008i	−0.504889	−	0.278156i
$326$	−50.4661	−	87.4099i	−0.154804	−	0.268128i
$327$	−34.8293	+	90.7334i	−0.106512	+	0.277472i
$328$	−17.0059	+	33.3759i	−0.0518472	+	0.101756i
$329$	540.769	−	44.5689i	1.64368	−	0.135468i
$330$	272.431	+	183.244i	0.825547	+	0.555284i
$331$	−332.335	−	369.096i	−1.00403	−	1.11509i	−0.993348	−	0.115149i	$-0.963265\pi$
$331$	−332.335	−	369.096i	−1.00403	−	1.11509i	−0.0106853	−	0.999943i	$-0.503401\pi$
$332$	−841.484	−	225.475i	−2.53459	−	0.679142i
$333$	−24.3417	−	15.8077i	−0.0730983	−	0.0474706i
$334$	−603.764	+	63.4581i	−1.80768	+	0.189994i
$335$	−68.9173	+	74.0970i	−0.205723	+	0.221185i
$336$	124.864	−	356.787i	0.371620	−	1.06187i
$337$	20.4403	−	129.055i	0.0606539	−	0.382953i	−0.938624	−	0.344943i	$-0.887898\pi$
$337$	20.4403	−	129.055i	0.0606539	−	0.382953i	0.999277	−	0.0380100i	$-0.0121019\pi$
$338$	−242.536	+	299.507i	−0.717562	+	0.886115i
$339$	−53.1532	−	5.58663i	−0.156794	−	0.0164797i
$340$	−61.3088	+	5.44389i	−0.180320	+	0.0160114i
$341$	−22.8479	−	217.383i	−0.0670026	−	0.637487i
$342$	525.020	+	1030.41i	1.53515	+	3.01289i
$343$	30.6971	+	341.624i	0.0894958	+	0.995987i
$344$	395.538	+	128.518i	1.14982	+	0.373599i
$345$	199.912	+	105.963i	0.579455	+	0.307139i
$346$	−47.3413	+	52.5779i	−0.136825	+	0.151959i
$347$	−13.5515	−	258.578i	−0.0390533	−	0.745182i	−0.946045	−	0.324034i	$-0.894961\pi$
$347$	−13.5515	−	258.578i	−0.0390533	−	0.745182i	0.906992	−	0.421148i	$-0.138373\pi$
$348$	−1576.16	−	605.033i	−4.52921	−	1.73860i
$349$			280.236i			0.802967i	0.915866	+	0.401484i	$0.131505\pi$
$349$			280.236i			0.802967i	−0.915866	+	0.401484i	$0.868495\pi$
$350$	558.497	−	212.823i	1.59571	−	0.608065i
$351$	66.2233			0.188670
$352$	13.5546	−	35.3110i	0.0385075	−	0.100315i
$353$	419.991	−	22.0108i	1.18978	−	0.0623536i	0.552852	−	0.833279i	$-0.313539\pi$
$353$	419.991	−	22.0108i	1.18978	−	0.0623536i	0.636925	+	0.770926i	$0.280206\pi$
$354$	706.363	+	636.012i	1.99537	+	1.79664i
$355$	77.6502	+	547.363i	0.218733	+	1.54187i
$356$	−365.064	+	1123.55i	−1.02546	+	3.15604i
$357$	42.7506	−	26.4152i	0.119750	−	0.0739922i
$358$	376.722	−	191.950i	1.05230	−	0.536172i
$359$	287.432	−	30.2103i	0.800645	−	0.0841512i	0.304636	−	0.952469i	$-0.401465\pi$
$359$	287.432	−	30.2103i	0.800645	−	0.0841512i	0.496009	+	0.868318i	$0.334798\pi$
$360$	631.885	−	269.186i	1.75524	−	0.747739i
$361$	61.7280	−	587.302i	0.170992	−	1.62688i
$362$	67.3108	+	54.5072i	0.185941	+	0.150572i
$363$	−452.472	−	71.6644i	−1.24648	−	0.197423i
$364$	74.7226	+	395.022i	0.205282	+	1.08523i
$365$	553.387	−	307.685i	1.51613	−	0.842974i
$366$	−54.0922	−	514.653i	−0.147793	−	1.40616i
$367$	−71.7219	+	110.442i	−0.195428	+	0.300932i	−0.922776	−	0.385336i	$-0.874086\pi$
$367$	−71.7219	+	110.442i	−0.195428	+	0.300932i	0.727349	+	0.686268i	$0.240752\pi$
$368$	−31.6590	+	118.153i	−0.0860298	+	0.321067i
$369$	24.4189	−	21.9869i	0.0661759	−	0.0595851i
$370$	42.4077	−	15.4974i	0.114616	−	0.0418849i
$371$	−284.508	−	134.416i	−0.766869	−	0.362308i
$372$	−1550.88	−	790.215i	−4.16904	−	2.12423i
$373$	199.069	+	76.4152i	0.533696	+	0.204867i	0.610265	−	0.792198i	$-0.291063\pi$
$373$	199.069	+	76.4152i	0.533696	+	0.204867i	−0.0765688	+	0.997064i	$0.524396\pi$
$374$	−20.4359	+	11.7987i	−0.0546415	+	0.0315473i
$375$	498.786	+	251.706i	1.33010	+	0.671217i
$376$	−485.003	+	840.050i	−1.28990	+	2.23418i
$377$	364.788	−	57.7767i	0.967606	−	0.153254i
$378$	−136.614	+	161.156i	−0.361414	+	0.426339i
$379$	−163.022	+	52.9690i	−0.430136	+	0.139760i	−0.516080	−	0.856540i	$-0.672609\pi$
$379$	−163.022	+	52.9690i	−0.430136	+	0.139760i	0.0859440	+	0.996300i	$0.472609\pi$
$380$	−1164.38	−	203.756i	−3.06415	−	0.536199i
$381$	−149.904	+	31.8631i	−0.393449	+	0.0836302i
$382$	181.732	+	48.6948i	0.475737	+	0.127473i
$383$	−29.8634	+	569.828i	−0.0779724	+	1.48780i	0.627251	+	0.778817i	$0.284180\pi$
$383$	−29.8634	+	569.828i	−0.0779724	+	1.48780i	−0.705224	+	0.708985i	$0.749153\pi$
$384$	−610.652	−	840.490i	−1.59024	−	2.18878i
$385$	104.992	−	107.912i	0.272706	−	0.280290i
$386$	681.987	+	495.493i	1.76681	+	1.28366i
$387$	−283.520	−	229.590i	−0.732611	−	0.593257i
$388$	157.537	+	410.399i	0.406024	+	1.05773i
$389$	132.147	+	13.8892i	0.339710	+	0.0357050i	0.272848	−	0.962057i	$-0.412035\pi$
$389$	132.147	+	13.8892i	0.339710	+	0.0357050i	0.0668623	+	0.997762i	$0.478701\pi$
$390$	−343.617	+	457.227i	−0.881070	+	1.17238i
$391$	−13.1560	+	9.55839i	−0.0336470	+	0.0244460i
$392$	−533.277	−	302.660i	−1.36040	−	0.772091i
$393$	−55.4759	−	55.4759i	−0.141160	−	0.141160i
$394$	446.080	−	401.652i	1.13218	−	1.01942i
$395$	226.054	−	561.597i	0.572289	−	1.42177i
$396$	242.160	−	268.946i	0.611515	−	0.679156i
$397$	89.7704	−	58.2976i	0.226122	−	0.146845i	−0.426606	−	0.904437i	$-0.640291\pi$
$397$	89.7704	−	58.2976i	0.226122	−	0.146845i	0.652728	+	0.757592i	$0.273624\pi$
$398$	−7.73904	−	48.8624i	−0.0194448	−	0.122770i
$399$	924.351	−	277.521i	2.31667	−	0.695542i
$400$	−72.3117	+	293.262i	−0.180779	+	0.733155i
$401$	−9.89135	+	17.1323i	−0.0246667	+	0.0427240i	−0.878095	−	0.478486i	$-0.841186\pi$
$401$	−9.89135	+	17.1323i	−0.0246667	+	0.0427240i	0.853429	+	0.521210i	$0.174519\pi$
$402$	194.421	+	240.090i	0.483634	+	0.597239i
$403$	380.253	−	19.9282i	0.943557	−	0.0494497i
$404$	199.137	−	936.865i	0.492913	−	2.31897i
$405$	296.286	−	10.7310i	0.731571	−	0.0264962i
$406$	−611.933	+	1006.91i	−1.50722	+	2.48007i
$407$	8.04256	−	8.04256i	0.0197606	−	0.0197606i
$408$	−4.70171	+	89.7140i	−0.0115238	+	0.219887i
$409$	11.0666	−	24.8560i	0.0270578	−	0.0607727i	−0.899511	−	0.436898i	$-0.856077\pi$
$409$	11.0666	−	24.8560i	0.0270578	−	0.0607727i	0.926569	+	0.376125i	$0.122744\pi$
$410$	4.52104	+	50.9157i	0.0110269	+	0.124185i
$411$	545.270	−	242.770i	1.32669	−	0.590681i
$412$	82.8644	−	523.185i	0.201127	−	1.26987i
$413$	344.819	−	266.618i	0.834914	−	0.645563i
$414$	223.102	−	307.073i	0.538893	−	0.741722i
$415$	−543.295	+	166.872i	−1.30915	+	0.402102i
$416$	60.1931	+	26.7997i	0.144695	+	0.0644223i
$417$	−79.7510	+	122.806i	−0.191249	+	0.294498i
$418$	−437.746	+	117.294i	−1.04724	+	0.280607i
$419$	628.714	+	204.281i	1.50051	+	0.487545i	0.940167	−	0.340715i	$-0.110669\pi$
$419$	628.714	+	204.281i	1.50051	+	0.487545i	0.560344	+	0.828260i	$0.310669\pi$
$420$	−265.332	−	1169.21i	−0.631742	−	2.78382i
$421$	−179.111	−	551.248i	−0.425443	−	1.30938i	−0.902570	−	0.430544i	$-0.858322\pi$
$421$	−179.111	−	551.248i	−0.425443	−	1.30938i	0.477127	−	0.878834i	$-0.341678\pi$
$422$	459.060	−	298.117i	1.08782	−	0.706438i
$423$	661.268	−	535.484i	1.56328	−	1.26592i
$424$	487.157	−	281.260i	1.14895	−	0.663349i
$425$	−32.0064	+	24.2488i	−0.0753091	+	0.0570561i
$426$	1687.81			3.96200
$427$	−236.640	−	17.7451i	−0.554192	−	0.0415577i
$428$	76.0736	−	149.303i	0.177742	−	0.348838i
$429$	−29.9560	+	140.932i	−0.0698275	+	0.328513i
$430$	550.490	−	138.011i	1.28021	−	0.320955i
$431$	69.9157	−	14.8610i	0.162217	−	0.0344804i	−0.126087	−	0.992019i	$-0.540242\pi$
$431$	69.9157	−	14.8610i	0.162217	−	0.0344804i	0.288304	+	0.957539i	$0.406909\pi$
$432$	−27.6339	−	103.131i	−0.0639674	−	0.238729i
$433$	−402.247	+	204.955i	−0.928977	+	0.473338i	−0.851910	−	0.523688i	$-0.824556\pi$
$433$	−402.247	+	204.955i	−0.928977	+	0.473338i	−0.0770674	+	0.997026i	$0.524556\pi$
$434$	−735.942	+	966.466i	−1.69572	+	2.22688i
$435$	−1080.93	+	211.565i	−2.48489	+	0.486356i
$436$	−152.243	+	67.7832i	−0.349182	+	0.155466i
$437$	−291.563	+	111.921i	−0.667192	+	0.256111i
$438$	−692.745	−	1804.66i	−1.58161	−	4.12023i
$439$	25.3436	+	56.9227i	0.0577303	+	0.129664i	0.940107	−	0.340879i	$-0.110725\pi$
$439$	25.3436	+	56.9227i	0.0577303	+	0.129664i	−0.882377	+	0.470543i	$0.844058\pi$
$440$	51.6993	+	264.142i	0.117498	+	0.600323i
$441$	341.577	+	415.502i	0.774552	+	0.942181i
$442$	−18.6624	−	36.6271i	−0.0422227	−	0.0828667i
$443$	−308.721	+	82.7215i	−0.696887	+	0.186730i	−0.589836	−	0.807523i	$-0.700807\pi$
$443$	−308.721	+	82.7215i	−0.696887	+	0.186730i	−0.107051	+	0.994254i	$0.534141\pi$
$444$	−18.8311	−	88.5933i	−0.0424124	−	0.199534i
$445$	187.423	+	747.583i	0.421174	+	1.67996i
$446$	−1335.43	−	283.854i	−2.99423	−	0.636444i
$447$	227.713	+	116.026i	0.509426	+	0.259565i
$448$	−494.189	+	237.960i	−1.10310	+	0.531160i
$449$			164.422i			0.366196i	0.983095	+	0.183098i	$0.0586125\pi$
$449$			164.422i			0.366196i	−0.983095	+	0.183098i	$0.941388\pi$
$450$	535.594	−	769.142i	1.19021	−	1.70920i
$451$	6.43832	+	11.1515i	0.0142756	+	0.0247261i
$452$	−57.6740	−	71.2215i	−0.127597	−	0.157570i
$453$	331.878	+	511.048i	0.732623	+	1.12814i
$454$	537.242	−	174.561i	1.18335	−	0.384495i
$455$	178.156	+	192.487i	0.391552	+	0.423049i
$456$	−533.154	+	1640.88i	−1.16920	+	3.59842i
$457$	−36.7109	−	137.007i	−0.0803302	−	0.299796i	0.914059	−	0.405582i	$-0.132931\pi$
$457$	−36.7109	−	137.007i	−0.0803302	−	0.299796i	−0.994389	+	0.105785i	$0.966264\pi$
$458$	−152.098	−	98.7738i	−0.332092	−	0.215663i
$459$	5.77331	−	12.9671i	0.0125780	−	0.0282507i
$460$	113.912	+	370.870i	0.247635	+	0.806239i
$461$	−571.084	−	414.917i	−1.23879	−	0.900037i	−0.241277	−	0.970456i	$-0.577566\pi$
$461$	−571.084	−	414.917i	−1.23879	−	0.900037i	−0.997517	+	0.0704191i	$0.977566\pi$
$462$	−281.164	−	363.632i	−0.608580	−	0.787083i
$463$	467.160	+	73.9908i	1.00898	+	0.159807i	0.638981	−	0.769223i	$-0.279356\pi$
$463$	467.160	+	73.9908i	1.00898	+	0.159807i	0.370004	+	0.929030i	$0.379356\pi$
$464$	−242.197	−	543.983i	−0.521976	−	1.17238i
$465$	−1131.10	+	100.436i	−2.43248	+	0.215991i
$466$	−282.267	−	125.673i	−0.605722	−	0.269685i
$467$	−403.754	−	21.1599i	−0.864570	−	0.0453102i	−0.385106	−	0.922872i	$-0.625835\pi$
$467$	−403.754	−	21.1599i	−0.864570	−	0.0453102i	−0.479463	+	0.877562i	$0.659169\pi$
$468$	445.793	+	445.793i	0.952550	+	0.952550i
$469$	124.251	−	68.0582i	0.264928	−	0.145113i
$470$	47.9095	+	1322.80i	0.101935	+	2.81447i
$471$	651.276	+	138.433i	1.38275	+	0.293913i
$472$	40.7805	+	778.138i	0.0863994	+	1.64860i
$473$	111.105	−	89.9711i	0.234894	−	0.190214i
$474$	−1600.61	−	924.112i	−3.37681	−	1.94960i
$475$	−714.270	+	290.739i	−1.50373	+	0.612083i
$476$	83.8629	+	19.8065i	0.176183	+	0.0416103i
$477$	−487.369	+	77.1917i	−1.02174	+	0.161828i
$478$	608.486	+	936.986i	1.27298	+	1.96022i
$479$	99.9681	+	90.0116i	0.208702	+	0.187916i	0.766852	−	0.641824i	$-0.221822\pi$
$479$	99.9681	+	90.0116i	0.208702	+	0.187916i	−0.558150	+	0.829740i	$0.688489\pi$
$480$	−182.284	−	73.3729i	−0.379758	−	0.152860i
$481$	13.2580	+	14.7245i	0.0275634	+	0.0306123i
$482$	256.409	−	256.409i	0.531969	−	0.531969i
$483$	−218.891	−	228.964i	−0.453191	−	0.474046i
$484$	−461.725	−	635.509i	−0.953977	−	1.31304i
$485$	229.264	+	172.298i	0.472710	+	0.355253i
$486$	123.007	−	1170.33i	0.253100	−	2.40809i
$487$	−86.6533	+	33.2631i	−0.177933	+	0.0683020i	−0.445703	−	0.895181i	$-0.647046\pi$
$487$	−86.6533	+	33.2631i	−0.177933	+	0.0683020i	0.267771	+	0.963483i	$0.413713\pi$
$488$	266.975	−	329.686i	0.547079	−	0.675587i
$489$	−77.6409	+	106.863i	−0.158775	+	0.218535i
$490$	−835.947	+	36.4590i	−1.70601	+	0.0744061i
$491$	679.662	−	493.803i	1.38424	−	1.00571i	0.387771	−	0.921756i	$-0.373245\pi$
$491$	679.662	−	493.803i	1.38424	−	1.00571i	0.996470	−	0.0839538i	$-0.0267548\pi$
$492$	102.399	+	5.36648i	0.208127	+	0.0109075i
$493$	20.4888	−	76.4653i	0.0415595	−	0.155102i
$494$	−164.140	−	772.219i	−0.332267	−	1.56320i
$495$	40.6975	−	232.569i	0.0822171	−	0.469836i
$496$	−189.708	−	583.862i	−0.382476	−	1.17714i
$497$	138.236	−	761.535i	0.278141	−	1.53226i
$498$	271.436	+	1713.78i	0.545052	+	3.44132i
$499$	47.2611	+	27.2862i	0.0947115	+	0.0546817i	0.546608	−	0.837389i	$-0.315919\pi$
$499$	47.2611	+	27.2862i	0.0947115	+	0.0546817i	−0.451896	+	0.892071i	$0.649252\pi$
$500$	299.581	+	909.964i	0.599162	+	1.81993i
$501$	397.251	+	688.058i	0.792915	+	1.37337i
$502$	−446.547	+	1163.30i	−0.889536	+	2.31732i
$503$	158.041	−	310.173i	0.314197	−	0.616646i	−0.678862	−	0.734266i	$-0.737527\pi$
$503$	158.041	−	310.173i	0.314197	−	0.616646i	0.993059	+	0.117620i	$0.0375266\pi$
$504$	−958.317	+	78.9823i	−1.90142	+	0.156711i
$505$	−214.475	−	586.899i	−0.424703	−	1.16218i
$506$	99.5278	+	110.537i	0.196695	+	0.218452i
$507$	487.180	+	130.540i	0.960908	+	0.257475i
$508$	−220.391	−	143.124i	−0.433841	−	0.281739i
$509$	−458.842	+	48.2262i	−0.901458	+	0.0947470i	−0.543906	−	0.839146i	$-0.683055\pi$
$509$	−458.842	+	48.2262i	−0.901458	+	0.0947470i	−0.357552	+	0.933893i	$0.616388\pi$
$510$	59.5725	+	107.144i	0.116809	+	0.210086i
$511$	−870.995	+	164.758i	−1.70449	+	0.322422i
$512$	111.223	−	702.237i	0.217233	−	1.37156i
$513$	171.553	−	211.850i	0.334411	−	0.412963i
$514$	−1574.46	−	165.482i	−3.06315	−	0.321950i
$515$	−135.440	−	317.930i	−0.262990	−	0.617341i
$516$	−119.002	−	1132.22i	−0.230623	−	2.19423i
$517$	151.381	+	297.102i	0.292806	+	0.574665i
$518$	−63.1828	+	1.88795i	−0.121974	+	0.00364470i
$519$	88.0598	+	28.6124i	0.169672	+	0.0551298i
$520$	−464.228	+	65.8566i	−0.892746	+	0.126647i
$521$	−398.985	+	443.117i	−0.765806	+	0.850513i	−0.992346	−	0.123488i	$-0.960592\pi$
$521$	−398.985	+	443.117i	−0.765806	+	0.850513i	0.226540	+	0.974002i	$0.427258\pi$
$522$	96.7027	+	1845.20i	0.185254	+	3.53486i
$523$	−293.349	−	112.606i	−0.560897	−	0.215308i	0.0613674	−	0.998115i	$-0.480454\pi$
$523$	−293.349	−	112.606i	−0.560897	−	0.215308i	−0.622265	+	0.782807i	$0.713787\pi$
$524$		−	134.528i		−	0.256733i
$525$	−551.730	−	554.432i	−1.05091	−	1.05606i
$526$	−201.085			−0.382290
$527$	29.2482	−	76.1940i	0.0554993	−	0.144581i
$528$	231.977	−	12.1574i	0.439350	−	0.0230253i
$529$	−316.949	−	285.382i	−0.599148	−	0.539475i
$530$	359.494	−	678.229i	0.678291	−	1.27968i
$531$	211.220	−	650.068i	0.397778	−	1.22423i
$532$	1457.26	+	784.274i	2.73921	+	1.47420i
$533$	−19.9867	+	10.1837i	−0.0374985	+	0.0191064i
$534$	2340.09	−	245.953i	4.38219	−	0.460587i
$535$	−9.66892	−	108.891i	−0.0180727	−	0.203534i
$536$	−26.4731	+	251.874i	−0.0493900	+	0.469915i
$537$	−430.016	−	348.220i	−0.800775	−	0.648455i
$538$	178.117	+	28.2109i	0.331072	+	0.0524367i
$539$	−187.098	+	97.0778i	−0.347120	+	0.180107i
$540$	−247.968	−	230.634i	−0.459199	−	0.427099i
$541$	88.8125	+	844.995i	0.164164	+	1.56191i	0.697859	+	0.716235i	$0.254136\pi$
$541$	88.8125	+	844.995i	0.164164	+	1.56191i	−0.533695	+	0.845677i	$0.679197\pi$
$542$	718.601	−	1106.55i	1.32583	−	2.04160i
$543$	29.3373	−	109.488i	0.0540281	−	0.201636i
$544$	10.4952	−	9.44991i	0.0192926	−	0.0173712i
$545$	−60.6799	+	90.2135i	−0.111339	+	0.165529i
$546$	658.227	−	455.974i	1.20554	−	0.835117i
$547$	695.729	+	354.492i	1.27190	+	0.648065i	0.953928	−	0.300035i	$-0.0969983\pi$
$547$	695.729	+	354.492i	1.27190	+	0.648065i	0.317972	+	0.948100i	$0.396998\pi$
$548$	955.491	+	366.779i	1.74360	+	0.669304i
$549$	−322.277	+	186.067i	−0.587025	+	0.338919i
$550$	251.184	+	267.967i	0.456699	+	0.487212i
$551$	760.161	−	1316.64i	1.37960	−	2.38954i
$552$	559.301	−	88.5845i	1.01323	−	0.160479i
$553$	−548.050	+	646.502i	−0.991049	+	1.16908i
$554$	−340.612	+	110.671i	−0.614823	+	0.199768i
$555$	−41.1017	−	42.4518i	−0.0740571	−	0.0764898i
$556$	−245.598	+	52.2034i	−0.441723	+	0.0938911i
$557$	−875.705	−	234.645i	−1.57218	−	0.421265i	−0.635687	−	0.771947i	$-0.719283\pi$
$557$	−875.705	−	234.645i	−1.57218	−	0.421265i	−0.936495	+	0.350682i	$0.885950\pi$
$558$	−99.6982	+	1902.35i	−0.178671	+	3.40924i
$559$	146.389	+	201.487i	0.261876	+	0.360441i
$560$	225.423	−	357.769i	0.402541	−	0.638873i
$561$	24.9841	+	18.1520i	0.0445349	+	0.0323565i
$562$	111.243	+	90.0828i	0.197941	+	0.160290i
$563$	205.576	+	535.544i	0.365144	+	0.951233i	0.985916	+	0.167242i	$0.0534861\pi$
$563$	205.576	+	535.544i	0.365144	+	0.951233i	−0.620772	+	0.783991i	$0.713181\pi$
$564$	2640.74	+	277.553i	4.68216	+	0.492115i
$565$	−56.5564	−	19.3920i	−0.100100	−	0.0343221i
$566$	−323.448	+	234.999i	−0.571462	+	0.415192i
$567$	−398.413	−	116.417i	−0.702668	−	0.205321i
$568$	978.380	+	978.380i	1.72250	+	1.72250i
$569$	−672.175	+	605.229i	−1.18133	+	1.06367i	−0.184602	+	0.982813i	$0.559100\pi$
$569$	−672.175	+	605.229i	−1.18133	+	1.06367i	−0.996726	+	0.0808585i	$0.974234\pi$
$570$	572.534	+	2283.70i	1.00445	+	4.00649i
$571$	435.354	−	483.510i	0.762442	−	0.846778i	−0.229521	−	0.973304i	$-0.573716\pi$
$571$	435.354	−	483.510i	0.762442	−	0.846778i	0.991963	+	0.126526i	$0.0403827\pi$
$572$	−207.200	+	134.557i	−0.362238	+	0.235240i
$573$	−38.5177	−	243.191i	−0.0672212	−	0.424418i
$574$	16.4489	−	69.6464i	0.0286566	−	0.121335i
$575$	191.454	+	165.559i	0.332963	+	0.287929i
$576$	−430.067	+	744.897i	−0.746644	+	1.29322i
$577$	229.192	+	283.029i	0.397213	+	0.490518i	0.936037	−	0.351901i	$-0.114465\pi$
$577$	229.192	+	283.029i	0.397213	+	0.490518i	−0.538824	+	0.842418i	$0.681131\pi$
$578$	976.862	−	51.1952i	1.69007	−	0.0885730i
$579$	229.371	−	1079.11i	0.396151	−	1.86374i
$580$	−1567.13	−	1054.09i	−2.70195	−	1.81740i
$581$	795.482	+	17.8918i	1.36916	+	0.0307948i
$582$	619.116	−	619.116i	1.06377	−	1.06377i
$583$	10.1202	−	193.104i	0.0173588	−	0.331225i
$584$	644.549	−	1447.68i	1.10368	−	2.47890i
$585$	400.878	+	92.0029i	0.685261	+	0.157270i
$586$	1047.51	−	466.380i	1.78755	−	0.795870i
$587$	64.2469	−	405.639i	0.109450	−	0.691038i	−0.870556	−	0.492069i	$-0.836241\pi$
$587$	64.2469	−	405.639i	0.109450	−	0.691038i	0.980006	−	0.198969i	$-0.0637592\pi$
$588$	−163.121	+	1670.56i	−0.277417	+	2.84109i
$589$	921.303	−	1268.07i	1.56418	−	2.15291i
$590$	611.014	+	870.216i	1.03562	+	1.47494i
$591$	−717.647	−	319.517i	−1.21429	−	0.540638i
$592$	17.3985	−	26.7913i	0.0293893	−	0.0452555i
$593$	−57.8969	+	15.5134i	−0.0976338	+	0.0261609i	−0.307305	−	0.951611i	$-0.599427\pi$
$593$	−57.8969	+	15.5134i	−0.0976338	+	0.0261609i	0.209671	+	0.977772i	$0.432761\pi$
$594$	−123.477	−	40.1200i	−0.207873	−	0.0675421i
$595$	53.2221	−	18.1035i	0.0894489	−	0.0304261i
$596$	135.420	+	416.780i	0.227215	+	0.699295i
$597$	−54.2985	+	35.2619i	−0.0909523	+	0.0590651i
$598$	−201.369	+	163.066i	−0.336738	+	0.272685i
$599$	−311.227	+	179.687i	−0.519578	+	0.299978i	−0.736762	−	0.676152i	$-0.763646\pi$
$599$	−311.227	+	179.687i	−0.519578	+	0.299978i	0.217184	+	0.976131i	$0.430313\pi$
$600$	1376.41	−	246.379i	2.29402	−	0.410631i
$601$	156.732			0.260786			0.130393	−	0.991462i	$-0.458376\pi$
$601$	156.732			0.260786			0.130393	+	0.991462i	$0.458376\pi$
$602$	−792.313	−	59.4139i	−1.31613	−	0.0986942i
$603$	100.859	−	197.948i	0.167263	−	0.328272i
$604$	−217.241	+	1022.04i	−0.359671	+	1.69212i
$605$	−475.409	−	191.361i	−0.785799	−	0.316300i
$606$	−1865.99	+	396.628i	−3.07919	+	0.654502i
$607$	69.2733	+	258.532i	0.114124	+	0.425917i	0.999220	−	0.0394919i	$-0.0125739\pi$
$607$	69.2733	+	258.532i	0.114124	+	0.425917i	−0.885096	+	0.465409i	$0.845907\pi$
$608$	241.664	−	123.134i	0.397474	−	0.202523i
$609$	1529.55	+	195.627i	2.51158	+	0.321227i
$610$	69.8055	−	574.675i	0.114435	−	0.942091i
$611$	−530.655	+	236.263i	−0.868502	+	0.386682i
$612$	126.154	−	48.4260i	0.206134	−	0.0791274i
$613$	−65.0538	−	169.471i	−0.106124	−	0.276462i	0.870228	−	0.492649i	$-0.163971\pi$
$613$	−65.0538	−	169.471i	−0.106124	−	0.276462i	−0.976352	+	0.216187i	$0.930638\pi$
$614$	402.360	+	903.715i	0.655309	+	1.47185i
$615$	58.4663	−	32.5075i	0.0950672	−	0.0528578i
$616$	47.8047	−	373.771i	0.0776050	−	0.606771i
$617$	217.485	+	426.838i	0.352487	+	0.691795i	0.997369	−	0.0724869i	$-0.0230936\pi$
$617$	217.485	+	426.838i	0.352487	+	0.691795i	−0.644882	+	0.764282i	$0.723094\pi$
$618$	−1019.09	+	273.064i	−1.64901	+	0.441851i
$619$	122.739	+	577.440i	0.198286	+	0.932860i	0.958919	+	0.283679i	$0.0915550\pi$
$619$	122.739	+	577.440i	0.198286	+	0.932860i	−0.760634	+	0.649181i	$0.775112\pi$
$620$	−1493.23	−	1249.68i	−2.40844	−	2.01560i
$621$	−87.5156	−	18.6020i	−0.140927	−	0.0299549i
$622$	291.753	+	148.656i	0.469056	+	0.238996i
$623$	80.6859	−	1075.99i	0.129512	−	1.72710i
$624$			404.667i			0.648504i
$625$	480.854	+	399.255i	0.769366	+	0.638808i
$626$	−539.306	−	934.106i	−0.861512	−	1.49218i
$627$	373.243	+	460.917i	0.595285	+	0.735115i
$628$	621.817	+	957.514i	0.990154	+	1.52470i
$629$	4.03900	−	1.31235i	0.00642130	−	0.00208641i
$630$	−1050.88	+	785.749i	−1.66806	+	1.24722i
$631$	−203.668	+	626.825i	−0.322770	+	0.993383i	0.649668	+	0.760218i	$0.274908\pi$
$631$	−203.668	+	626.825i	−0.322770	+	0.993383i	−0.972437	+	0.233165i	$0.925092\pi$
$632$	−392.147	−	1463.51i	−0.620486	−	2.31568i
$633$	−600.774	−	390.147i	−0.949090	−	0.616346i
$634$	141.945	−	318.814i	0.223888	−	0.502861i
$635$	−171.418	−	2.76992i	−0.269949	−	0.00436208i
$636$	−1245.75	−	905.093i	−1.95873	−	1.42310i
$637$	−151.823	−	334.335i	−0.238341	−	0.524859i
$638$	−715.168	−	113.271i	−1.12095	−	0.177542i
$639$	−493.669	−	1108.80i	−0.772565	−	1.73521i
$640$	−455.490	−	1069.21i	−0.711704	−	1.67065i
$641$	−482.502	−	214.824i	−0.752734	−	0.335139i	−0.00575211	−	0.999983i	$-0.501831\pi$
$641$	−482.502	−	214.824i	−0.752734	−	0.335139i	−0.746981	+	0.664845i	$0.768498\pi$
$642$	−333.291	−	17.4671i	−0.519145	−	0.0272072i
$643$	−278.918	−	278.918i	−0.433776	−	0.433776i	0.456134	−	0.889911i	$-0.349234\pi$
$643$	−278.918	−	278.918i	−0.433776	−	0.433776i	−0.889911	+	0.456134i	$0.849234\pi$
$644$	12.2135	−	543.020i	0.0189650	−	0.843199i
$645$	−458.025	−	584.682i	−0.710117	−	0.906484i
$646$	−165.516	−	35.1816i	−0.256217	−	0.0544607i
$647$	43.8553	+	836.810i	0.0677826	+	1.29337i	0.794851	+	0.606804i	$0.207549\pi$
$647$	43.8553	+	836.810i	0.0677826	+	1.29337i	−0.727069	+	0.686565i	$0.759118\pi$
$648$	576.660	−	466.970i	0.889907	−	0.720632i
$649$	231.971	+	133.928i	0.357428	+	0.206361i
$650$	−489.069	+	412.542i	−0.752414	+	0.634680i
$651$	1547.21	+	365.416i	2.37667	+	0.561315i
$652$	−223.710	+	35.4321i	−0.343113	+	0.0543438i
$653$	−557.113	−	857.880i	−0.853160	−	1.31375i	−0.948004	−	0.318259i	$-0.896902\pi$
$653$	−557.113	−	857.880i	−0.853160	−	1.31375i	0.0948438	−	0.995492i	$-0.469765\pi$
$654$	246.669	+	222.102i	0.377169	+	0.339605i
$655$	−46.6049	−	74.3687i	−0.0711525	−	0.113540i
$656$	24.1995	+	26.8762i	0.0368894	+	0.0409698i
$657$	−982.941	+	982.941i	−1.49611	+	1.49611i
$658$	519.756	−	1778.75i	0.789902	−	2.70327i
$659$	−246.602	−	339.418i	−0.374206	−	0.515050i	0.579832	−	0.814736i	$-0.303118\pi$
$659$	−246.602	−	339.418i	−0.374206	−	0.515050i	−0.954038	+	0.299686i	$0.903118\pi$
$660$	602.986	−	423.381i	0.913616	−	0.641486i
$661$	81.3214	−	773.721i	0.123028	−	1.17053i	−0.742562	−	0.669777i	$-0.766389\pi$
$661$	81.3214	−	773.721i	0.123028	−	1.17053i	0.865590	−	0.500754i	$-0.166944\pi$
$662$	−1583.59	+	607.883i	−2.39213	+	0.918252i
$663$	−33.8559	+	41.8086i	−0.0510648	+	0.0630597i
$664$	−836.087	+	1150.77i	−1.25917	+	1.73309i
$665$	1077.29	−	71.2849i	1.61998	−	0.107195i
$666$	−80.1942	+	58.2645i	−0.120412	+	0.0874842i
$667$	−498.304	−	26.1150i	−0.747083	−	0.0391530i
$668$	−352.601	+	1315.93i	−0.527846	+	1.96995i
$669$	371.481	+	1747.68i	0.555278	+	2.61238i
$670$	151.904	+	310.427i	0.226722	+	0.463324i
$671$	−45.0641	−	138.693i	−0.0671596	−	0.206696i
$672$	209.843	+	177.887i	0.312266	+	0.264713i
$673$	51.1187	+	322.751i	0.0759564	+	0.479570i	0.996118	+	0.0880307i	$0.0280574\pi$
$673$	51.1187	+	322.751i	0.0759564	+	0.479570i	−0.920161	+	0.391539i	$0.871943\pi$
$674$	−386.466	−	223.126i	−0.573392	−	0.331048i
$675$	−216.979	−	41.5931i	−0.321450	−	0.0616194i
$676$	432.423	+	748.979i	0.639679	+	1.10796i
$677$	−218.383	+	568.907i	−0.322575	+	0.840335i	0.672398	+	0.740190i	$0.265264\pi$
$677$	−218.383	+	568.907i	−0.322575	+	0.840335i	−0.994973	+	0.100146i	$0.968069\pi$
$678$	−82.8681	+	162.638i	−0.122224	+	0.239879i
$679$	−228.636	−	330.050i	−0.336724	−	0.486083i
$680$	−27.5759	+	96.6410i	−0.0405528	+	0.142119i
$681$	−494.671	−	549.388i	−0.726389	−	0.806737i
$682$	−721.075	−	193.211i	−1.05729	−	0.283301i
$683$	−556.915	−	361.665i	−0.815395	−	0.529524i	0.0682572	−	0.997668i	$-0.478256\pi$
$683$	−556.915	−	361.665i	−0.815395	−	0.529524i	−0.883652	+	0.468144i	$0.844923\pi$
$684$	2580.94	−	271.268i	3.77331	−	0.396591i
$685$	655.272	−	128.253i	0.956601	−	0.187231i
$686$	1126.81	+	320.246i	1.64259	+	0.466831i
$687$	−37.1285	+	234.420i	−0.0540444	+	0.341223i
$688$	252.694	−	312.051i	0.367288	−	0.453563i
$689$	335.011	+	35.2111i	0.486228	+	0.0511047i
$690$	582.532	−	507.715i	0.844250	−	0.735818i
$691$	57.0458	+	542.755i	0.0825555	+	0.785463i	0.954971	+	0.296698i	$0.0958856\pi$
$691$	57.0458	+	542.755i	0.0825555	+	0.785463i	−0.872416	+	0.488764i	$0.837448\pi$
$692$	72.0794	+	141.464i	0.104161	+	0.204427i
$693$	−156.648	+	291.068i	−0.226044	+	0.420011i
$694$	−841.044	−	273.272i	−1.21188	−	0.393763i
$695$	−117.685	+	113.942i	−0.169330	+	0.163945i
$696$	−1844.55	+	2048.58i	−2.65022	+	2.94337i
$697$	0.251629	+	4.80136i	0.000361017	+	0.00688862i
$698$	893.512	+	342.987i	1.28010	+	0.491386i
$699$			404.363i			0.578488i
$700$	3.27664	−	1341.21i	0.00468092	−	1.91601i
$701$	−161.866			−0.230908			−0.115454	−	0.993313i	$-0.536832\pi$
$701$	−161.866			−0.230908			−0.115454	+	0.993313i	$0.536832\pi$
$702$	81.0523	−	211.148i	0.115459	−	0.300781i
$703$	81.4492	−	4.26857i	0.115859	−	0.00607193i
$704$	−250.489	−	225.541i	−0.355808	−	0.320371i
$705$	1555.99	−	761.404i	2.20708	−	1.08001i
$706$	443.857	−	1366.05i	0.628693	−	1.93492i
$707$	26.1282	+	874.413i	0.0369564	+	1.23679i
$708$	1900.51	−	968.358i	2.68434	−	1.36774i
$709$	−1073.72	+	112.853i	−1.51442	+	0.159171i	−0.824974	−	0.565170i	$-0.808810\pi$
$709$	−1073.72	+	112.853i	−1.51442	+	0.159171i	−0.689441	+	0.724342i	$0.742144\pi$
$710$	1840.27	+	422.348i	2.59192	+	0.594856i
$711$	−138.927	+	1321.81i	−0.195397	+	1.85908i
$712$	1499.06	+	1213.91i	2.10542	+	1.70494i
$713$	−508.111	−	80.4769i	−0.712638	−	0.112871i
$714$	−31.8996	−	168.638i	−0.0446773	−	0.236187i
$715$	−67.9278	+	146.166i	−0.0950039	+	0.204428i
$716$	−99.1767	−	943.603i	−0.138515	−	1.31788i
$717$	796.329	−	1226.24i	1.11064	−	1.71024i
$718$	255.471	−	953.431i	0.355809	−	1.32790i
$719$	−483.083	+	434.970i	−0.671882	+	0.604965i	−0.932800	−	0.360396i	$-0.882642\pi$
$719$	−483.083	+	434.970i	−0.671882	+	0.604965i	0.260917	+	0.965361i	$0.415975\pi$
$720$	−24.0014	−	662.687i	−0.0333352	−	0.920399i
$721$	39.7396	+	482.173i	0.0551173	+	0.668757i
$722$	−1797.02	−	915.629i	−2.48895	−	1.26818i
$723$	−443.039	−	170.067i	−0.612779	−	0.235224i
$724$	168.325	−	97.1822i	0.232492	−	0.134230i
$725$	−1231.50	−	39.8099i	−1.69863	−	0.0549101i
$726$	−782.288	+	1354.96i	−1.07753	+	1.86634i
$727$	−753.233	+	119.300i	−1.03608	+	0.164099i	−0.651232	−	0.758879i	$-0.725747\pi$
$727$	−753.233	+	119.300i	−1.03608	+	0.164099i	−0.384852	+	0.922978i	$0.625747\pi$
$728$	645.872	+	117.241i	0.887187	+	0.161045i
$729$	−957.134	+	310.992i	−1.31294	+	0.426601i
$730$	−303.730	−	2141.02i	−0.416069	−	2.93290i
$731$	52.2148	−	11.0986i	0.0714293	−	0.0151828i
$732$	−1121.71	−	300.560i	−1.53238	−	0.410601i
$733$	−5.71806	+	109.107i	−0.00780090	+	0.148850i	0.991952	+	0.126615i	$0.0404114\pi$
$733$	−5.71806	+	109.107i	−0.00780090	+	0.148850i	−0.999753	+	0.0222346i	$0.992922\pi$
$734$	264.355	+	363.853i	0.360156	+	0.495713i
$735$	488.562	+	980.019i	0.664710	+	1.33336i
$736$	−72.0185	−	52.3245i	−0.0978512	−	0.0710931i
$737$	67.6584	+	54.7887i	0.0918025	+	0.0743402i
$738$	−40.2168	−	104.768i	−0.0544943	−	0.141962i
$739$	788.981	+	82.9252i	1.06763	+	0.112213i	0.622011	−	0.783008i	$-0.286316\pi$
$739$	788.981	+	82.9252i	1.06763	+	0.112213i	0.445622	+	0.895221i	$0.352983\pi$
$740$	1.63702	−	101.308i	0.00221219	−	0.136902i
$741$	−835.863	+	607.290i	−1.12802	+	0.819555i
$742$	−776.794	+	742.620i	−1.04689	+	1.00084i
$743$	−710.650	−	710.650i	−0.956461	−	0.956461i	0.0426302	−	0.999091i	$-0.486426\pi$
$743$	−710.650	−	710.650i	−0.956461	−	0.956461i	−0.999091	+	0.0426302i	$0.986426\pi$
$744$	−2112.04	+	1901.69i	−2.83876	+	2.55603i
$745$	219.248	+	183.487i	0.294293	+	0.246292i
$746$	487.289	−	541.190i	0.653203	−	0.725456i
$747$	1046.46	−	679.582i	1.40089	−	0.909748i
$748$	8.28383	+	52.3020i	0.0110746	+	0.0699225i
$749$	−35.1785	+	148.949i	−0.0469672	+	0.198864i
$750$	1413.02	−	1282.27i	1.88403	−	1.70970i
$751$	−632.288	+	1095.15i	−0.841927	+	1.45826i	0.0463356	+	0.998926i	$0.485246\pi$
$751$	−632.288	+	1095.15i	−0.841927	+	1.45826i	−0.888263	+	0.459335i	$0.848088\pi$
$752$	589.371	+	727.812i	0.783738	+	0.967835i
$753$	1628.49	−	85.3454i	2.16267	−	0.113341i
$754$	262.255	−	1233.81i	0.347819	−	1.63636i
$755$	233.974	+	640.256i	0.309899	+	0.848021i
$756$	227.758	+	415.811i	0.301268	+	0.550014i
$757$	−344.858	+	344.858i	−0.455559	+	0.455559i	−0.897195	−	0.441635i	$-0.854398\pi$
$757$	−344.858	+	344.858i	−0.455559	+	0.455559i	0.441635	+	0.897195i	$0.354398\pi$
$758$	−30.6383	+	584.613i	−0.0404199	+	0.771258i
$759$	79.1751	−	177.830i	0.104315	−	0.234295i
$760$	−991.916	+	1655.68i	−1.30515	+	2.17853i
$761$	−1158.81	+	515.935i	−1.52275	+	0.677970i	−0.986148	−	0.165867i	$-0.946958\pi$
$761$	−1158.81	+	515.935i	−1.52275	+	0.677970i	−0.536598	+	0.843838i	$0.680291\pi$
$762$	−81.8780	+	516.957i	−0.107451	+	0.678422i
$763$	120.414	−	93.1055i	0.157817	−	0.122026i
$764$	248.165	−	341.569i	0.324823	−	0.447080i
$765$	52.9632	−	70.4744i	0.0692329	−	0.0921234i
$766$	1780.31	+	792.644i	2.32416	+	1.03478i
$767$	−254.137	+	391.337i	−0.331339	+	0.510218i
$768$	−2074.08	+	555.749i	−2.70063	+	0.723632i
$769$	1191.02	+	386.987i	1.54880	+	0.503234i	0.953787	−	0.300484i	$-0.0971482\pi$
$769$	1191.02	+	386.987i	1.54880	+	0.503234i	0.595010	+	0.803719i	$0.297148\pi$
$770$	−215.567	−	466.834i	−0.279957	−	0.606278i
$771$	640.237	+	1970.45i	0.830398	+	2.55570i
$772$	1586.52	−	1030.30i	2.05507	−	1.33458i
$773$	−91.1600	+	73.8199i	−0.117930	+	0.0954980i	−0.686471	−	0.727157i	$-0.740841\pi$
$773$	−91.1600	+	73.8199i	−0.117930	+	0.0954980i	0.568541	+	0.822655i	$0.307508\pi$
$774$	−1079.04	+	622.984i	−1.39411	+	0.804889i
$775$	−1258.41	−	173.533i	−1.62375	−	0.223913i
$776$	717.769			0.924961
$777$	35.8893	+	74.5340i	0.0461895	+	0.0959253i
$778$	206.023	−	404.343i	0.264811	−	0.519721i
$779$	−19.1979	+	90.3191i	−0.0246443	+	0.115942i
$780$	681.560	+	1087.58i	0.873794	+	1.39434i
$781$	465.239	−	98.8897i	0.595697	−	0.126619i
$782$	14.3743	+	53.6457i	0.0183815	+	0.0686007i
$783$	388.076	−	197.735i	0.495627	−	0.252535i
$784$	−457.314	+	375.951i	−0.583309	+	0.479529i
$785$	675.462	+	313.908i	0.860462	+	0.399883i
$786$	−244.779	+	108.983i	−0.311424	+	0.138655i
$787$	300.624	−	115.399i	0.381987	−	0.146631i	−0.159795	−	0.987150i	$-0.551083\pi$
$787$	300.624	−	115.399i	0.381987	−	0.146631i	0.541782	+	0.840519i	$0.317750\pi$
$788$	−482.729	−	1257.55i	−0.612600	−	1.59588i
$789$	107.037	+	240.409i	0.135662	+	0.304701i
$790$	−1513.94	−	1408.11i	−1.91638	−	1.78242i
$791$	66.5945	+	50.7102i	0.0841903	+	0.0641090i
$792$	−268.268	−	526.505i	−0.338722	−	0.664779i
$793$	245.386	−	65.7509i	0.309440	−	0.0829141i
$794$	−76.0056	−	357.578i	−0.0957250	−	0.450351i
$795$	−1002.22	−	68.7773i	−1.26066	−	0.0865124i
$796$	−108.591	−	23.0817i	−0.136421	−	0.0289972i
$797$	586.501	+	298.837i	0.735886	+	0.374953i	0.781416	−	0.624010i	$-0.214498\pi$
$797$	586.501	+	298.837i	0.735886	+	0.374953i	−0.0455301	+	0.998963i	$0.514498\pi$
$798$	246.477	−	3286.89i	0.308869	−	4.11892i
$799$			124.504i			0.155824i
$800$	−180.389	−	125.614i	−0.225486	−	0.157017i
$801$	−846.032	−	1465.37i	−1.05622	−	1.82943i
$802$	42.5190	+	52.5065i	0.0530162	+	0.0654695i
$803$	−296.689	−	456.860i	−0.369475	−	0.568942i
$804$	659.345	−	214.234i	0.820081	−	0.266460i
$805$	−181.368	−	304.420i	−0.225302	−	0.378161i
$806$	401.861	−	1236.80i	0.498587	−	1.53449i
$807$	−61.0834	−	227.966i	−0.0756919	−	0.282486i
$808$	−1311.58	−	851.749i	−1.62324	−	1.05414i
$809$	190.394	−	427.633i	0.235345	−	0.528594i	−0.756806	−	0.653640i	$-0.773241\pi$
$809$	190.394	−	427.633i	0.235345	−	0.528594i	0.992151	+	0.125046i	$0.0399078\pi$
$810$	328.417	−	957.823i	0.405453	−	1.18250i
$811$	825.741	+	599.936i	1.01818	+	0.739748i	0.965908	−	0.258885i	$-0.0833551\pi$
$811$	825.741	+	599.936i	1.01818	+	0.739748i	0.0522678	+	0.998633i	$0.483355\pi$
$812$	1617.37	+	2091.76i	1.99184	+	2.57606i
$813$	−1705.46	−	270.118i	−2.09773	−	0.332248i
$814$	−15.7997	−	35.4867i	−0.0194099	−	0.0435954i
$815$	−111.395	+	97.0877i	−0.136681	+	0.119126i
$816$	79.2370	+	35.2786i	0.0971042	+	0.0432336i
$817$	1023.78	+	53.6542i	1.25310	+	0.0656723i
$818$	−65.7071	−	65.7071i	−0.0803265	−	0.0803265i
$819$	−492.074	−	299.050i	−0.600823	−	0.365141i
$820$	110.305	+	31.4748i	0.134518	+	0.0383839i
$821$	214.849	+	45.6676i	0.261692	+	0.0556244i	0.336889	−	0.941544i	$-0.390625\pi$
$821$	214.849	+	45.6676i	0.261692	+	0.0556244i	−0.0751971	+	0.997169i	$0.523959\pi$
$822$	−106.686	−	2035.69i	−0.129788	−	2.47651i
$823$	−748.946	+	606.485i	−0.910020	+	0.736920i	−0.965188	−	0.261557i	$-0.915764\pi$
$823$	−748.946	+	606.485i	−0.910020	+	0.736920i	0.0551679	+	0.998477i	$0.482431\pi$
$824$	−749.025	−	432.450i	−0.909011	−	0.524818i
$825$	186.666	−	442.945i	0.226261	−	0.536903i
$826$	−428.059	−	1425.75i	−0.518231	−	1.72609i
$827$	−538.018	+	85.2137i	−0.650566	+	0.103040i	−0.472990	−	0.881068i	$-0.656825\pi$
$827$	−538.018	+	85.2137i	−0.650566	+	0.103040i	−0.177576	+	0.984107i	$0.556825\pi$
$828$	−463.903	−	714.348i	−0.560270	−	0.862740i
$829$	−220.859	−	198.862i	−0.266416	−	0.239882i	0.525085	−	0.851050i	$-0.324033\pi$
$829$	−220.859	−	198.862i	−0.266416	−	0.239882i	−0.791501	+	0.611168i	$0.790700\pi$
$830$	−132.892	+	1936.50i	−0.160111	+	2.33313i
$831$	313.622	+	348.312i	0.377403	+	0.419148i
$832$	415.200	−	415.200i	0.499039	−	0.499039i
$833$	−78.7014	+	0.581138i	−0.0944795	+	0.000697645i
$834$	293.948	+	404.585i	0.352456	+	0.485114i
$835$	260.957	+	849.613i	0.312524	+	1.01750i
$836$	−106.304	+	1011.41i	−0.127157	+	1.20982i
$837$	419.214	−	160.921i	0.500853	−	0.192260i
$838$	1420.84	−	1754.59i	1.69551	−	2.09378i
$839$	92.3106	−	127.055i	0.110025	−	0.151436i	−0.750454	−	0.660923i	$-0.770165\pi$
$839$	92.3106	−	127.055i	0.110025	−	0.151436i	0.860478	+	0.509487i	$0.170165\pi$
$840$	−1937.52	−	279.692i	−2.30658	−	0.332967i
$841$	1284.80	−	933.461i	1.52770	−	1.10994i
$842$	−1976.84	−	103.602i	−2.34779	−	0.123042i
$843$	48.4851	−	180.949i	0.0575149	−	0.214649i
$844$	−255.383	−	1201.48i	−0.302586	−	1.42356i
$845$	498.520	+	264.240i	0.589965	+	0.312710i
$846$	−898.013	−	2763.80i	−1.06148	−	3.26690i
$847$	547.283	+	463.940i	0.646143	+	0.547746i
$848$	−84.9596	−	536.414i	−0.100188	−	0.632564i
$849$	453.126	+	261.612i	0.533717	+	0.308142i
$850$	38.1424	+	131.729i	0.0448734	+	0.154975i
$851$	−13.3846	−	23.1829i	−0.0157281	−	0.0272419i
$852$	1357.34	−	3535.99i	1.59312	−	4.15022i
$853$	−189.468	+	371.852i	−0.222120	+	0.435935i	−0.974994	−	0.222229i	$-0.928667\pi$
$853$	−189.468	+	371.852i	−0.222120	+	0.435935i	0.752875	+	0.658164i	$0.228667\pi$
$854$	−346.209	+	732.792i	−0.405396	+	0.858070i
$855$	1332.80	−	1044.08i	1.55883	−	1.22115i
$856$	−183.075	−	203.325i	−0.213872	−	0.237529i
$857$	−83.7589	−	22.4431i	−0.0977351	−	0.0261880i	0.209620	−	0.977783i	$-0.432777\pi$
$857$	−83.7589	−	22.4431i	−0.0977351	−	0.0261880i	−0.307355	+	0.951595i	$0.599444\pi$
$858$	412.688	+	268.003i	0.480988	+	0.312357i
$859$	−251.475	+	26.4311i	−0.292754	+	0.0307696i	−0.249767	−	0.968306i	$-0.580354\pi$
$859$	−251.475	+	26.4311i	−0.292754	+	0.0307696i	−0.0429867	+	0.999076i	$0.513687\pi$
$860$	153.570	−	1264.27i	0.178570	−	1.47008i
$861$	−92.0223	+	17.4070i	−0.106878	+	0.0202172i
$862$	38.1881	−	241.110i	0.0443017	−	0.279710i
$863$	625.187	−	772.041i	0.724434	−	0.894602i	−0.273297	−	0.961930i	$-0.588114\pi$
$863$	625.187	−	772.041i	0.724434	−	0.894602i	0.997731	+	0.0673279i	$0.0214474\pi$
$864$	77.2763	+	8.12207i	0.0894401	+	0.00940054i
$865$	88.8541	+	53.2324i	0.102722	+	0.0615403i
$866$	161.165	+	1533.39i	0.186103	+	1.77065i
$867$	−581.189	−	1140.65i	−0.670345	−	1.31563i
$868$	1432.91	+	2319.04i	1.65082	+	2.67171i
$869$	−495.346	−	160.948i	−0.570019	−	0.185210i
$870$	−648.413	+	3705.40i	−0.745302	+	4.25908i
$871$	−101.482	+	112.707i	−0.116512	+	0.129399i
$872$	14.2410	+	271.734i	0.0163314	+	0.311621i
$873$	−587.810	−	225.639i	−0.673322	−	0.258464i
$874$			1066.61i			1.22038i
$875$	−462.828	−	742.574i	−0.528946	−	0.848655i
$876$	−4337.90			−4.95194
$877$	−153.163	+	399.004i	−0.174645	+	0.454965i	−0.992764	−	0.120084i	$-0.961684\pi$
$877$	−153.163	+	399.004i	−0.174645	+	0.454965i	0.818119	+	0.575049i	$0.195017\pi$
$878$	212.513	−	11.1373i	0.242042	−	0.0126849i
$879$	−1115.17	−	1004.10i	−1.26868	−	1.14233i
$880$	255.972	+	44.7929i	0.290878	+	0.0509010i
$881$	237.487	−	730.910i	0.269565	−	0.829636i	−0.721041	−	0.692892i	$-0.756336\pi$
$881$	237.487	−	730.910i	0.269565	−	0.829636i	0.990606	−	0.136744i	$-0.0436638\pi$
$882$	1742.86	−	580.553i	1.97604	−	0.658223i
$883$	−250.938	+	127.859i	−0.284187	+	0.144801i	−0.590274	−	0.807203i	$-0.700980\pi$
$883$	−250.938	+	127.859i	−0.284187	+	0.144801i	0.306087	+	0.952004i	$0.400980\pi$
$884$	−91.7425	+	9.64252i	−0.103781	+	0.0109078i
$885$	715.155	−	1193.72i	0.808085	−	1.34884i
$886$	−114.099	+	1085.58i	−0.128780	+	1.22526i
$887$	1070.61	+	866.962i	1.20700	+	0.977409i	1.00000		0.000931336i	$-0.000296453\pi$
$887$	1070.61	+	866.962i	1.20700	+	0.977409i	0.207001	+	0.978341i	$0.433630\pi$
$888$	−146.065	−	23.1345i	−0.164488	−	0.0260523i
$889$	226.543	+	79.2832i	0.254829	+	0.0891824i
$890$	2613.01	+	317.401i	2.93596	+	0.356630i
$891$	−26.6625	−	253.677i	−0.0299243	−	0.284710i
$892$	−1668.63	+	2569.46i	−1.87066	+	2.88056i
$893$	−618.861	+	2309.62i	−0.693014	+	2.58636i
$894$	648.644	−	584.042i	0.725552	−	0.653290i
$895$	−381.721	−	487.278i	−0.426504	−	0.544445i
$896$	133.646	+	1621.57i	0.149158	+	1.80979i
$897$	302.144	+	153.950i	0.336838	+	0.171627i
$898$	524.248	+	201.240i	0.583795	+	0.224098i
$899$	2168.82	−	1252.17i	2.41248	−	1.39285i
$900$	−1180.64	−	1740.62i	−1.31182	−	1.93402i
$901$	36.1007	−	62.5283i	0.0400674	−	0.0693987i
$902$	43.4358	−	6.87955i	0.0481550	−	0.00762700i
$903$	350.714	+	978.885i	0.388387	+	1.08404i
$904$	−142.313	+	46.2403i	−0.157426	+	0.0511508i
$905$	59.3849	−	112.037i	0.0656186	−	0.123797i
$906$	2035.63	−	432.687i	2.24684	−	0.477580i
$907$	1579.78	+	423.301i	1.74176	+	0.466705i	0.982838	−	0.184471i	$-0.0590572\pi$
$907$	1579.78	+	423.301i	1.74176	+	0.466705i	0.758927	+	0.651176i	$0.225724\pi$
$908$	66.3436	−	1265.91i	0.0730656	−	1.39417i
$909$	806.347	+	1109.84i	0.887070	+	1.22095i
$910$	831.782	−	332.449i	0.914046	−	0.365329i
$911$	−757.259	−	550.181i	−0.831239	−	0.603930i	0.0886706	−	0.996061i	$-0.471738\pi$
$911$	−757.259	−	550.181i	−0.831239	−	0.603930i	−0.919910	+	0.392131i	$0.871738\pi$
$912$	1294.54	+	1048.30i	1.41945	+	1.14945i
$913$	175.231	+	456.493i	0.191929	+	0.499992i
$914$	−481.769	−	50.6359i	−0.527099	−	0.0554004i
$915$	−724.217	+	222.442i	−0.791494	+	0.243106i
$916$	−329.250	+	239.214i	−0.359443	+	0.261151i
$917$	29.1246	+	119.370i	0.0317608	+	0.130174i
$918$	−34.2785	−	34.2785i	−0.0373404	−	0.0373404i
$919$	−883.040	+	795.093i	−0.960871	+	0.865172i	−0.990930	−	0.134376i	$-0.957097\pi$
$919$	−883.040	+	795.093i	−0.960871	+	0.865172i	0.0300595	+	0.999548i	$0.490430\pi$
$920$	631.987	+	43.3700i	0.686942	+	0.0471413i
$921$	866.271	−	962.092i	0.940577	−	1.04462i
$922$	−2021.90	+	1313.04i	−2.19295	+	1.42412i
$923$	129.617	+	818.369i	0.140430	+	0.886641i
$924$	−987.926	+	296.609i	−1.06918	+	0.321005i
$925$	−34.1914	−	56.5714i	−0.0369636	−	0.0611582i
$926$	807.683	−	1398.95i	0.872227	−	1.51074i
$927$	477.461	+	589.615i	0.515060	+	0.636047i
$928$	432.758	−	22.6799i	0.466335	−	0.0244396i
$929$	−169.578	+	797.804i	−0.182539	+	0.858777i	0.787593	+	0.616196i	$0.211327\pi$
$929$	−169.578	+	797.804i	−0.182539	+	0.858777i	−0.970131	+	0.242581i	$0.922006\pi$
$930$	−1064.15	+	3729.37i	−1.14425	+	4.01008i
$931$	−1462.85	−	380.415i	−1.57127	−	0.408609i
$932$	−490.286	+	490.286i	−0.526058	+	0.526058i
$933$	22.4273	−	427.938i	0.0240378	−	0.458669i
$934$	−561.631	+	1261.44i	−0.601318	+	1.35058i
$935$	22.6985	+	26.0435i	0.0242765	+	0.0278540i
$936$	940.392	−	418.690i	1.00469	−	0.447318i
$937$	122.689	−	774.628i	0.130938	−	0.826710i	−0.831563	−	0.555431i	$-0.812553\pi$
$937$	122.689	−	774.628i	0.130938	−	0.826710i	0.962501	−	0.271279i	$-0.0874467\pi$
$938$	−64.9245	−	479.465i	−0.0692159	−	0.511157i
$939$	−829.709	+	1142.00i	−0.883610	+	1.21618i
$940$	2809.81	+	963.426i	2.98916	+	1.02492i
$941$	−714.566	−	318.145i	−0.759369	−	0.338093i	−0.00974107	−	0.999953i	$-0.503101\pi$
$941$	−714.566	−	318.145i	−0.759369	−	0.338093i	−0.749628	+	0.661860i	$0.769767\pi$
$942$	1238.50	−	1907.12i	1.31475	−	2.02454i
$943$	29.2734	−	7.84379i	0.0310429	−	0.00831791i
$944$	715.486	+	232.475i	0.757930	+	0.246266i
$945$	269.958	+	150.963i	0.285670	+	0.159749i
$946$	−150.882	−	464.369i	−0.159495	−	0.490876i
$947$	562.863	−	365.528i	0.594364	−	0.385985i	−0.212117	−	0.977244i	$-0.568036\pi$
$947$	562.863	−	365.528i	0.594364	−	0.385985i	0.806481	+	0.591260i	$0.201369\pi$
$948$	−3223.24	+	2610.13i	−3.40004	+	2.75330i
$949$	821.826	−	474.482i	0.865992	−	0.499981i
$950$	52.7902	+	2633.24i	0.0555687	+	2.77184i
$951$	−456.719			−0.480251
$952$	79.2634	−	116.246i	0.0832599	−	0.122107i
$953$	−521.626	+	1023.75i	−0.547351	+	1.07424i	0.437237	+	0.899346i	$0.355957\pi$
$953$	−521.626	+	1023.75i	−0.547351	+	1.07424i	−0.984588	+	0.174891i	$0.944043\pi$
$954$	−350.383	+	1648.42i	−0.367277	+	1.72790i
$955$	18.8578	−	274.796i	0.0197464	−	0.287745i
$956$	2452.34	−	521.261i	2.56521	−	0.545253i
$957$	245.260	+	915.322i	0.256280	+	0.956449i
$958$	409.349	−	208.574i	0.427296	−	0.217718i
$959$	−927.234	−	118.592i	−0.966876	−	0.123662i
$960$	−1192.59	+	1282.22i	−1.24228	+	1.33565i
$961$	1480.78	−	659.286i	1.54087	−	0.686041i
$962$	63.1748	−	24.2505i	0.0656703	−	0.0252085i
$963$	86.0096	+	224.063i	0.0893143	+	0.232672i
$964$	−330.976	−	743.384i	−0.343336	−	0.771146i
$965$	520.119	−	1119.18i	0.538983	−	1.15977i
$966$	−997.943	+	417.685i	−1.03307	+	0.432386i
$967$	438.359	+	860.327i	0.453318	+	0.889687i	0.998674	+	0.0514823i	$0.0163946\pi$
$967$	438.359	+	860.327i	0.453318	+	0.889687i	−0.545356	+	0.838205i	$0.683605\pi$
$968$	−1238.91	+	331.964i	−1.27986	+	0.342938i
$969$	46.0423	+	216.612i	0.0475153	+	0.223542i
$970$	829.962	−	520.114i	0.855631	−	0.536200i
$971$	−151.094	−	32.1160i	−0.155606	−	0.0330752i	0.129450	−	0.991586i	$-0.458679\pi$
$971$	−151.094	−	32.1160i	−0.155606	−	0.0330752i	−0.285056	+	0.958511i	$0.592012\pi$
$972$	−2352.94	−	1198.88i	−2.42072	−	1.23342i
$973$	206.623	−	99.4920i	0.212356	−	0.102253i
$974$			317.000i			0.325462i
$975$	753.550	+	365.116i	0.772872	+	0.374478i
$976$	−204.791	−	354.708i	−0.209827	−	0.363430i
$977$	−133.577	−	164.954i	−0.136721	−	0.168837i	0.704187	−	0.710015i	$-0.251312\pi$
$977$	−133.577	−	164.954i	−0.136721	−	0.168837i	−0.840908	+	0.541178i	$0.817978\pi$
$978$	245.700	+	378.345i	0.251227	+	0.386856i
$979$	630.627	−	204.903i	0.644154	−	0.209298i
$980$	−595.886	+	1780.64i	−0.608047	+	1.81698i
$981$	73.7601	−	227.010i	0.0751887	−	0.231407i
$982$	−742.603	−	2771.43i	−0.756215	−	2.82223i
$983$	896.145	+	581.963i	0.911643	+	0.592028i	0.912995	−	0.407971i	$-0.133764\pi$
$983$	896.145	+	581.963i	0.911643	+	0.592028i	−0.00135182	+	0.999999i	$0.500430\pi$
$984$	68.0978	−	152.950i	0.0692051	−	0.155437i
$985$	−702.515	−	527.957i	−0.713214	−	0.535997i
$986$	−218.728	−	158.915i	−0.221833	−	0.161171i
$987$	−2403.28	+	325.428i	−2.43493	+	0.329715i
$988$	−1749.81	−	277.143i	−1.77106	−	0.280509i
$989$	−136.859	−	307.389i	−0.138381	−	0.310808i
$990$	−691.719	−	414.408i	−0.698706	−	0.418594i
$991$	−863.089	−	384.272i	−0.870928	−	0.387762i	−0.0779099	−	0.996960i	$-0.524825\pi$
$991$	−863.089	−	384.272i	−0.870928	−	0.387762i	−0.793018	+	0.609198i	$0.791491\pi$
$992$	446.163	+	23.3824i	0.449762	+	0.0235710i
$993$	1569.70	+	1569.70i	1.58077	+	1.58077i
$994$	−2258.91	−	1372.82i	−2.27255	−	1.38110i
$995$	−68.0268	+	24.8596i	−0.0683687	+	0.0249845i
$996$	3808.67	+	809.559i	3.82397	+	0.812810i
$997$	−42.2324	−	805.842i	−0.0423595	−	0.808267i	−0.934381	−	0.356275i	$-0.884047\pi$
$997$	−42.2324	−	805.842i	−0.0423595	−	0.808267i	0.892022	−	0.451992i	$-0.149287\pi$
$998$	144.844	−	117.292i	0.145134	−	0.117527i
$999$	20.2355	+	11.6830i	0.0202557	+	0.0116946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.3.w.a.163.35	yes	608
7.4	even	3	inner	175.3.w.a.88.35	yes	608
25.2	odd	20	inner	175.3.w.a.2.35	✓	608
175.102	odd	60	inner	175.3.w.a.102.35	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.3.w.a.2.35	✓	608	25.2	odd	20	inner
175.3.w.a.88.35	yes	608	7.4	even	3	inner
175.3.w.a.102.35	yes	608	175.102	odd	60	inner
175.3.w.a.163.35	yes	608	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	175.w (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22392 - 3.18843i) q^{2} +(-4.46346 + 0.233920i) q^{3} +(-5.69552 - 5.12827i) q^{4} +(-4.92516 - 0.861860i) q^{5} +(-4.71710 + 14.5177i) q^{6} +(6.16401 + 3.31738i) q^{7} +(-11.1499 + 5.68116i) q^{8} +(10.9170 - 1.14743i) q^{9} +(-8.77600 + 14.6487i) q^{10} +(-0.449650 + 4.27814i) q^{11} +(26.6213 + 21.5575i) q^{12} +(-7.40146 - 1.17228i) q^{13} +(18.1215 - 15.5933i) q^{14} +(22.1849 + 2.69478i) q^{15} +(1.26289 + 12.0156i) q^{16} +(-0.874796 + 1.34707i) q^{17} +(9.70314 - 36.2126i) q^{18} +(-22.9238 + 20.6407i) q^{19} +(23.6315 + 30.1663i) q^{20} +(-28.2888 - 13.3651i) q^{21} +(13.0902 + 6.66979i) q^{22} +(9.45191 + 3.62825i) q^{23} +(48.4382 - 27.9658i) q^{24} +(23.5144 + 8.48959i) q^{25} +(-12.7966 + 22.1643i) q^{26} +(-8.72837 + 1.38244i) q^{27} +(-18.0948 - 50.5049i) q^{28} +(-46.8737 + 15.2302i) q^{29} +(35.7447 - 67.4367i) q^{30} +(-49.7022 + 10.5645i) q^{31} +(-8.49302 - 2.27570i) q^{32} +(1.00625 - 19.2005i) q^{33} +(3.22435 + 4.43794i) q^{34} +(-27.4996 - 21.6511i) q^{35} +(-68.0626 - 49.4504i) q^{36} +(-2.05481 - 1.66395i) q^{37} +(37.7544 + 98.3535i) q^{38} +(33.3103 + 3.50106i) q^{39} +(59.8115 - 18.3710i) q^{40} +(2.42170 - 1.75947i) q^{41} +(-77.2370 + 73.8390i) q^{42} +(-23.5004 - 23.5004i) q^{43} +(24.5004 - 22.0603i) q^{44} +(-54.7571 - 3.75770i) q^{45} +(23.1368 - 25.6961i) q^{46} +(65.0093 - 42.2175i) q^{47} +(-8.44758 - 53.3359i) q^{48} +(26.9900 + 40.8967i) q^{49} +(55.8483 - 64.5834i) q^{50} +(3.58951 - 6.21722i) q^{51} +(36.1434 + 44.6334i) q^{52} +(-44.8902 + 2.35260i) q^{53} +(-6.27505 + 29.5218i) q^{54} +(5.90175 - 20.6830i) q^{55} +(-87.5747 - 1.96971i) q^{56} +(97.4911 - 97.4911i) q^{57} +(-8.80943 + 168.094i) q^{58} +(25.3265 - 56.8843i) q^{59} +(-112.535 - 129.118i) q^{60} +(-30.9698 + 13.7886i) q^{61} +(-27.1474 + 171.402i) q^{62} +(71.0992 + 29.1432i) q^{63} +(-46.0568 + 63.3917i) q^{64} +(35.4430 + 12.1527i) q^{65} +(-59.9878 - 26.7083i) q^{66} +(11.0227 - 16.9735i) q^{67} +(11.8906 - 3.18607i) q^{68} +(-43.0369 - 13.9835i) q^{69} +(-102.691 + 61.1813i) q^{70} +(-34.1676 - 105.157i) q^{71} +(-115.205 + 74.8152i) q^{72} +(-98.4134 + 79.6936i) q^{73} +(-7.82033 + 4.51507i) q^{74} +(-106.941 - 32.3925i) q^{75} +236.414 q^{76} +(-16.9638 + 24.8788i) q^{77} +(51.9322 - 101.923i) q^{78} +(-25.1734 + 118.431i) q^{79} +(4.13584 - 60.2674i) q^{80} +(-58.0004 + 12.3284i) q^{81} +(-2.64596 - 9.87486i) q^{82} +(101.280 - 51.6047i) q^{83} +(92.5797 + 221.194i) q^{84} +(5.46950 - 5.88058i) q^{85} +(-103.692 + 46.1668i) q^{86} +(205.656 - 78.9439i) q^{87} +(-19.2912 - 50.2554i) q^{88} +(-62.6959 - 140.817i) q^{89} +(-78.9997 + 169.990i) q^{90} +(-41.7338 - 31.7794i) q^{91} +(-35.2269 - 69.1367i) q^{92} +(219.372 - 58.7806i) q^{93} +(-55.0412 - 258.949i) q^{94} +(130.693 - 81.9015i) q^{95} +(38.4406 + 8.17080i) q^{96} +(-51.1064 - 26.0400i) q^{97} +(163.430 - 36.0014i) q^{98} +47.2206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 8 q^{2} - 8 q^{3} - 10 q^{4} - 6 q^{5} - 24 q^{6} - 14 q^{7} - 4 q^{8} - 10 q^{9} - 24 q^{10} - 6 q^{11} + 36 q^{12} - 32 q^{13} - 20 q^{14} - 92 q^{15} - 262 q^{16} - 102 q^{17} - 6 q^{18} - 10 q^{19}+ \cdots - 262 q^{98}+O(q^{100}) \) 608 * q - 8 * q^2 - 8 * q^3 - 10 * q^4 - 6 * q^5 - 24 * q^6 - 14 * q^7 - 4 * q^8 - 10 * q^9 - 24 * q^10 - 6 * q^11 + 36 * q^12 - 32 * q^13 - 20 * q^14 - 92 * q^15 - 262 * q^16 - 102 * q^17 - 6 * q^18 - 10 * q^19 + 32 * q^20 - 12 * q^21 + 16 * q^22 + 56 * q^23 + 6 * q^25 - 16 * q^26 - 116 * q^27 + 34 * q^28 - 240 * q^29 + 166 * q^30 - 6 * q^31 - 140 * q^32 - 126 * q^33 - 40 * q^34 + 330 * q^35 - 568 * q^36 - 54 * q^37 + 304 * q^38 - 410 * q^39 + 148 * q^40 - 24 * q^41 + 350 * q^42 - 324 * q^43 - 10 * q^44 + 414 * q^45 - 6 * q^46 + 198 * q^47 - 68 * q^48 - 440 * q^50 - 16 * q^51 + 88 * q^52 + 382 * q^53 - 10 * q^54 - 248 * q^55 + 52 * q^56 + 584 * q^57 - 8 * q^58 - 410 * q^59 + 828 * q^60 - 6 * q^61 - 1656 * q^62 - 782 * q^63 + 860 * q^64 - 142 * q^65 + 138 * q^66 - 208 * q^67 + 378 * q^68 - 740 * q^69 - 140 * q^70 - 24 * q^71 - 498 * q^72 - 390 * q^73 + 360 * q^75 + 64 * q^76 + 692 * q^77 + 860 * q^78 - 10 * q^79 + 314 * q^80 - 402 * q^81 + 168 * q^82 + 400 * q^83 + 3580 * q^84 - 184 * q^85 - 6 * q^86 + 204 * q^87 - 1042 * q^88 - 760 * q^89 - 940 * q^90 - 12 * q^91 - 1412 * q^92 - 662 * q^93 - 10 * q^94 - 242 * q^95 - 54 * q^96 - 528 * q^97 - 262 * q^98

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