LMFDB - Embedded newform 210.3.p.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,3,Mod(19,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("210.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	210.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.72208555157$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.4
Character	$\chi$	$=$	210.19
Dual form			210.3.p.a.199.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.84836 - 1.22205i) q^{5} +2.44949i q^{6} +(-1.07756 + 6.91657i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.84836 - 1.22205i) q^{5} +2.44949i q^{6} +(-1.07756 + 6.91657i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-6.80213 - 1.93160i) q^{10} +(8.06041 + 13.9610i) q^{11} +(1.73205 - 3.00000i) q^{12} +2.01172 q^{13} +(6.21048 - 7.70908i) q^{14} +(-6.03188 - 6.21421i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.22858 + 2.12797i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-8.06058 - 4.65378i) q^{19} +(6.96502 + 7.17555i) q^{20} +(11.3080 - 4.37359i) q^{21} -22.7983i q^{22} +(22.3935 + 12.9289i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(22.0132 - 11.8499i) q^{25} +(-2.46384 - 1.42250i) q^{26} +5.19615 q^{27} +(-13.0574 + 5.05018i) q^{28} +37.0708 q^{29} +(2.99341 + 11.8760i) q^{30} +(36.9509 - 21.3336i) q^{31} +(4.89898 - 2.82843i) q^{32} +(13.9610 - 24.1812i) q^{33} -3.47496i q^{34} +(3.22805 + 34.8508i) q^{35} -6.00000 q^{36} +(-24.4695 - 14.1275i) q^{37} +(6.58143 + 11.3994i) q^{38} +(-1.74220 - 3.01758i) q^{39} +(-3.45649 - 13.7132i) q^{40} -18.4211i q^{41} +(-16.9421 - 2.63946i) q^{42} +11.7122i q^{43} +(-16.1208 + 27.9221i) q^{44} +(-4.09755 + 14.4295i) q^{45} +(-18.2842 - 31.6692i) q^{46} +(-32.0864 + 55.5752i) q^{47} +6.92820 q^{48} +(-46.6777 - 14.9060i) q^{49} +(-35.3397 - 1.05253i) q^{50} +(2.12797 - 3.68575i) q^{51} +(2.01172 + 3.48440i) q^{52} +(-3.55634 + 2.05325i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(56.1409 + 57.8379i) q^{55} +(19.5630 + 3.04779i) q^{56} +16.1212i q^{57} +(-45.4023 - 26.2130i) q^{58} +(27.5105 - 15.8832i) q^{59} +(4.73144 - 16.6617i) q^{60} +(-80.8999 - 46.7076i) q^{61} -60.3405 q^{62} +(-16.3534 - 13.1744i) q^{63} -8.00000 q^{64} +(9.75354 - 2.45843i) q^{65} +(-34.1974 + 19.7439i) q^{66} +(-92.7821 + 53.5678i) q^{67} +(-2.45717 + 4.25594i) q^{68} -44.7871i q^{69} +(20.6897 - 44.9659i) q^{70} +98.9468 q^{71} +(7.34847 + 4.24264i) q^{72} +(27.6325 + 47.8610i) q^{73} +(19.9792 + 34.6051i) q^{74} +(-36.8388 - 22.7574i) q^{75} -18.6151i q^{76} +(-105.248 + 40.7066i) q^{77} +4.92769i q^{78} +(-59.3934 + 102.872i) q^{79} +(-5.46339 + 19.2393i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-13.0257 + 22.5612i) q^{82} +88.2727 q^{83} +(18.8833 + 15.2125i) q^{84} +(8.55711 + 8.81576i) q^{85} +(8.28175 - 14.3444i) q^{86} +(-32.1043 - 55.6062i) q^{87} +(39.4878 - 22.7983i) q^{88} +(-97.7203 - 56.4188i) q^{89} +(15.2216 - 14.7750i) q^{90} +(-2.16774 + 13.9142i) q^{91} +51.7156i q^{92} +(-64.0008 - 36.9509i) q^{93} +(78.5952 - 45.3770i) q^{94} +(-44.7677 - 12.7127i) q^{95} +(-8.48528 - 4.89898i) q^{96} +81.0963 q^{97} +(46.6282 + 51.2622i) q^{98} -48.3625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	$ 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$3$	−0.866025	−	1.50000i	−0.288675	−	0.500000i
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	4.84836	−	1.22205i	0.969672	−	0.244411i
$5$	4.84836	−	1.22205i	0.969672	−	0.244411i
$6$			2.44949i			0.408248i
$7$	−1.07756	+	6.91657i	−0.153937	+	0.988081i
$7$	−1.07756	+	6.91657i	−0.153937	+	0.988081i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	−6.80213	−	1.93160i	−0.680213	−	0.193160i
$11$	8.06041	+	13.9610i	0.732765	+	1.26919i	0.955697	+	0.294352i	$0.0951037\pi$
$11$	8.06041	+	13.9610i	0.732765	+	1.26919i	−0.222932	+	0.974834i	$0.571563\pi$
$12$	1.73205	−	3.00000i	0.144338	−	0.250000i
$13$	2.01172			0.154748			0.0773739	−	0.997002i	$-0.475346\pi$
$13$	2.01172			0.154748			0.0773739	+	0.997002i	$0.475346\pi$
$14$	6.21048	−	7.70908i	0.443606	−	0.550649i
$15$	−6.03188	−	6.21421i	−0.402126	−	0.414280i
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	1.22858	+	2.12797i	0.0722697	+	0.125175i	0.899896	−	0.436105i	$-0.143642\pi$
$17$	1.22858	+	2.12797i	0.0722697	+	0.125175i	−0.827626	+	0.561280i	$0.810309\pi$
$18$	3.67423	−	2.12132i	0.204124	−	0.117851i
$19$	−8.06058	−	4.65378i	−0.424241	−	0.244936i	0.272649	−	0.962114i	$-0.412100\pi$
$19$	−8.06058	−	4.65378i	−0.424241	−	0.244936i	−0.696890	+	0.717178i	$0.745433\pi$
$20$	6.96502	+	7.17555i	0.348251	+	0.358777i
$21$	11.3080	−	4.37359i	0.538478	−	0.208266i
$22$		−	22.7983i		−	1.03629i
$23$	22.3935	+	12.9289i	0.973632	+	0.562126i	0.900341	−	0.435184i	$-0.143317\pi$
$23$	22.3935	+	12.9289i	0.973632	+	0.562126i	0.0732901	+	0.997311i	$0.476650\pi$
$24$	−4.24264	+	2.44949i	−0.176777	+	0.102062i
$25$	22.0132	−	11.8499i	0.880527	−	0.473997i
$26$	−2.46384	−	1.42250i	−0.0947633	−	0.0547116i
$27$	5.19615			0.192450
$28$	−13.0574	+	5.05018i	−0.466336	+	0.180364i
$29$	37.0708			1.27830			0.639152	−	0.769080i	$-0.279285\pi$
$29$	37.0708			1.27830			0.639152	+	0.769080i	$0.279285\pi$
$30$	2.99341	+	11.8760i	0.0997804	+	0.395867i
$31$	36.9509	−	21.3336i	1.19196	−	0.688181i	0.233212	−	0.972426i	$-0.425076\pi$
$31$	36.9509	−	21.3336i	1.19196	−	0.688181i	0.958752	+	0.284245i	$0.0917430\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$	13.9610	−	24.1812i	0.423062	−	0.732765i
$34$		−	3.47496i		−	0.102205i
$35$	3.22805	+	34.8508i	0.0922299	+	0.995738i
$36$	−6.00000			−0.166667
$37$	−24.4695	−	14.1275i	−0.661337	−	0.381823i	0.131449	−	0.991323i	$-0.458037\pi$
$37$	−24.4695	−	14.1275i	−0.661337	−	0.381823i	−0.792786	+	0.609500i	$0.791370\pi$
$38$	6.58143	+	11.3994i	0.173196	+	0.299984i
$39$	−1.74220	−	3.01758i	−0.0446718	−	0.0773739i
$40$	−3.45649	−	13.7132i	−0.0864123	−	0.342831i
$41$		−	18.4211i		−	0.449295i	−0.974440	−	0.224648i	$-0.927877\pi$
$41$		−	18.4211i		−	0.449295i	0.974440	−	0.224648i	$-0.0721231\pi$
$42$	−16.9421	−	2.63946i	−0.403382	−	0.0628443i
$43$			11.7122i			0.272376i	0.990683	+	0.136188i	$0.0434851\pi$
$43$			11.7122i			0.272376i	−0.990683	+	0.136188i	$0.956515\pi$
$44$	−16.1208	+	27.9221i	−0.366382	+	0.634593i
$45$	−4.09755	+	14.4295i	−0.0910566	+	0.320655i
$46$	−18.2842	−	31.6692i	−0.397483	−	0.688461i
$47$	−32.0864	+	55.5752i	−0.682689	+	1.18245i	0.291469	+	0.956580i	$0.405856\pi$
$47$	−32.0864	+	55.5752i	−0.682689	+	1.18245i	−0.974157	+	0.225871i	$0.927477\pi$
$48$	6.92820			0.144338
$49$	−46.6777	−	14.9060i	−0.952607	−	0.304203i
$50$	−35.3397	−	1.05253i	−0.706793	−	0.0210505i
$51$	2.12797	−	3.68575i	0.0417249	−	0.0722697i
$52$	2.01172	+	3.48440i	0.0386869	+	0.0670077i
$53$	−3.55634	+	2.05325i	−0.0671007	+	0.0387406i	−0.533175	−	0.846005i	$-0.679001\pi$
$53$	−3.55634	+	2.05325i	−0.0671007	+	0.0387406i	0.466074	+	0.884746i	$0.345668\pi$
$54$	−6.36396	−	3.67423i	−0.117851	−	0.0680414i
$55$	56.1409	+	57.8379i	1.02074	+	1.05160i
$56$	19.5630	+	3.04779i	0.349339	+	0.0544248i
$57$			16.1212i			0.282827i
$58$	−45.4023	−	26.2130i	−0.782798	−	0.451949i
$59$	27.5105	−	15.8832i	0.466280	−	0.269207i	−0.248401	−	0.968657i	$-0.579905\pi$
$59$	27.5105	−	15.8832i	0.466280	−	0.269207i	0.714681	+	0.699451i	$0.246572\pi$
$60$	4.73144	−	16.6617i	0.0788573	−	0.277696i
$61$	−80.8999	−	46.7076i	−1.32623	−	0.765698i	−0.341514	−	0.939877i	$-0.610940\pi$
$61$	−80.8999	−	46.7076i	−1.32623	−	0.765698i	−0.984714	+	0.174179i	$0.944273\pi$
$62$	−60.3405			−0.973234
$63$	−16.3534	−	13.1744i	−0.259578	−	0.209118i
$64$	−8.00000			−0.125000
$65$	9.75354	−	2.45843i	0.150055	−	0.0378221i
$66$	−34.1974	+	19.7439i	−0.518143	+	0.299150i
$67$	−92.7821	+	53.5678i	−1.38481	+	0.799519i	−0.992724	−	0.120411i	$-0.961579\pi$
$67$	−92.7821	+	53.5678i	−1.38481	+	0.799519i	−0.392083	+	0.919930i	$0.628245\pi$
$68$	−2.45717	+	4.25594i	−0.0361348	+	0.0625874i
$69$		−	44.7871i		−	0.649088i
$70$	20.6897	−	44.9659i	0.295567	−	0.642371i
$71$	98.9468			1.39362			0.696808	−	0.717258i	$-0.254603\pi$
$71$	98.9468			1.39362			0.696808	+	0.717258i	$0.254603\pi$
$72$	7.34847	+	4.24264i	0.102062	+	0.0589256i
$73$	27.6325	+	47.8610i	0.378528	+	0.655630i	0.990848	−	0.134980i	$-0.0430971\pi$
$73$	27.6325	+	47.8610i	0.378528	+	0.655630i	−0.612320	+	0.790610i	$0.709764\pi$
$74$	19.9792	+	34.6051i	0.269990	+	0.467636i
$75$	−36.8388	−	22.7574i	−0.491185	−	0.303432i
$76$		−	18.6151i		−	0.244936i
$77$	−105.248	+	40.7066i	−1.36686	+	0.528657i
$78$			4.92769i			0.0631755i
$79$	−59.3934	+	102.872i	−0.751815	+	1.30218i	0.195128	+	0.980778i	$0.437488\pi$
$79$	−59.3934	+	102.872i	−0.751815	+	1.30218i	−0.946942	+	0.321404i	$0.895845\pi$
$80$	−5.46339	+	19.2393i	−0.0682924	+	0.240491i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−13.0257	+	22.5612i	−0.158850	+	0.275136i
$83$	88.2727			1.06353			0.531763	−	0.846893i	$-0.321530\pi$
$83$	88.2727			1.06353			0.531763	+	0.846893i	$0.321530\pi$
$84$	18.8833	+	15.2125i	0.224801	+	0.181101i
$85$	8.55711	+	8.81576i	0.100672	+	0.103715i
$86$	8.28175	−	14.3444i	0.0962994	−	0.166795i
$87$	−32.1043	−	55.6062i	−0.369015	−	0.639152i
$88$	39.4878	−	22.7983i	0.448725	−	0.259071i
$89$	−97.7203	−	56.4188i	−1.09798	−	0.633919i	−0.162291	−	0.986743i	$-0.551888\pi$
$89$	−97.7203	−	56.4188i	−1.09798	−	0.633919i	−0.935690	+	0.352824i	$0.885222\pi$
$90$	15.2216	−	14.7750i	0.169129	−	0.164167i
$91$	−2.16774	+	13.9142i	−0.0238213	+	0.152903i
$92$			51.7156i			0.562126i
$93$	−64.0008	−	36.9509i	−0.688181	−	0.397321i
$94$	78.5952	−	45.3770i	0.836119	−	0.482734i
$95$	−44.7677	−	12.7127i	−0.471239	−	0.133818i
$96$	−8.48528	−	4.89898i	−0.0883883	−	0.0510310i
$97$	81.0963			0.836045			0.418022	−	0.908437i	$-0.362723\pi$
$97$	81.0963			0.836045			0.418022	+	0.908437i	$0.362723\pi$
$98$	46.6282	+	51.2622i	0.475798	+	0.523083i
$99$	−48.3625			−0.488510
$100$	42.5378	+	26.2780i	0.425378	+	0.262780i
$101$	11.4135	−	6.58956i	0.113004	−	0.0652432i	−0.442432	−	0.896802i	$-0.645884\pi$
$101$	11.4135	−	6.58956i	0.113004	−	0.0652432i	0.555437	+	0.831559i	$0.312551\pi$
$102$	−5.21244	+	3.00940i	−0.0511024	+	0.0295040i
$103$	80.2268	−	138.957i	0.778901	−	1.34910i	−0.153675	−	0.988121i	$-0.549111\pi$
$103$	80.2268	−	138.957i	0.778901	−	1.34910i	0.932576	−	0.360974i	$-0.117556\pi$
$104$		−	5.69001i		−	0.0547116i
$105$	49.4807	−	35.0238i	0.471244	−	0.333560i
$106$	5.80747			0.0547875
$107$	−177.991	−	102.763i	−1.66347	−	0.960402i	−0.971041	−	0.238912i	$-0.923209\pi$
$107$	−177.991	−	102.763i	−1.66347	−	0.960402i	−0.692424	−	0.721491i	$-0.743457\pi$
$108$	5.19615	+	9.00000i	0.0481125	+	0.0833333i
$109$	−20.0475	−	34.7233i	−0.183922	−	0.318563i	0.759291	−	0.650752i	$-0.225546\pi$
$109$	−20.0475	−	34.7233i	−0.183922	−	0.318563i	−0.943213	+	0.332189i	$0.892213\pi$
$110$	−27.8608	−	110.534i	−0.253280	−	1.00486i
$111$			48.9389i			0.440891i
$112$	−21.8046	−	17.5659i	−0.194684	−	0.156838i
$113$			20.3263i			0.179879i	0.995947	+	0.0899396i	$0.0286674\pi$
$113$			20.3263i			0.179879i	−0.995947	+	0.0899396i	$0.971333\pi$
$114$	11.3994	−	19.7443i	0.0999945	−	0.173196i
$115$	124.372	+	35.3179i	1.08149	+	0.307112i
$116$	37.0708	+	64.2086i	0.319576	+	0.553522i
$117$	−3.01758	+	5.22660i	−0.0257913	+	0.0446718i
$118$	−44.9245			−0.380716
$119$	−16.0421	+	6.20458i	−0.134808	+	0.0521393i
$120$	−17.5764	+	17.0607i	−0.146470	+	0.142173i
$121$	−69.4405	+	120.274i	−0.573888	+	0.994004i
$122$	66.0545	+	114.410i	0.541430	+	0.937785i
$123$	−27.6317	+	15.9531i	−0.224648	+	0.129700i
$124$	73.9018	+	42.6672i	0.595982	+	0.344090i
$125$	92.2465	−	84.3540i	0.737972	−	0.674832i
$126$	10.7131	+	27.6989i	0.0850243	+	0.219833i
$127$			31.7188i			0.249754i	0.992172	+	0.124877i	$0.0398537\pi$
$127$			31.7188i			0.249754i	−0.992172	+	0.124877i	$0.960146\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$	17.5682	−	10.1430i	0.136188	−	0.0786281i
$130$	−13.6840	−	3.88584i	−0.105261	−	0.0298911i
$131$	37.6020	+	21.7095i	0.287038	+	0.165721i	0.636605	−	0.771190i	$-0.280338\pi$
$131$	37.6020	+	21.7095i	0.287038	+	0.165721i	−0.349567	+	0.936911i	$0.613671\pi$
$132$	55.8442			0.423062
$133$	40.8739	−	50.7368i	0.307322	−	0.381480i
$134$	151.513			1.13069
$135$	25.1928	−	6.34998i	0.186613	−	0.0470369i
$136$	6.01881	−	3.47496i	0.0442559	−	0.0255512i
$137$	152.127	−	87.8304i	1.11041	−	0.641098i	0.171478	−	0.985188i	$-0.445146\pi$
$137$	152.127	−	87.8304i	1.11041	−	0.641098i	0.938937	+	0.344090i	$0.111813\pi$
$138$	−31.6692	+	54.8527i	−0.229487	+	0.397483i
$139$			190.508i			1.37056i	0.728280	+	0.685280i	$0.240320\pi$
$139$			190.508i			1.37056i	−0.728280	+	0.685280i	$0.759680\pi$
$140$	−57.1353	+	40.4420i	−0.408110	+	0.288871i
$141$	111.150			0.788301
$142$	−121.185	−	69.9659i	−0.853412	−	0.492718i
$143$	16.2153	+	28.0857i	0.113394	+	0.196404i
$144$	−6.00000	−	10.3923i	−0.0416667	−	0.0721688i
$145$	179.733	−	45.3026i	1.23954	−	0.312432i
$146$		−	78.1566i		−	0.535319i
$147$	18.0652	+	82.9256i	0.122892	+	0.564120i
$148$		−	56.5098i		−	0.381823i
$149$	−67.5463	+	116.994i	−0.453331	+	0.785192i	−0.998591	−	0.0530753i	$-0.983098\pi$
$149$	−67.5463	+	116.994i	−0.453331	+	0.785192i	0.545260	+	0.838267i	$0.316431\pi$
$150$	29.0263	+	53.9210i	0.193508	+	0.359473i
$151$	−60.0363	−	103.986i	−0.397592	−	0.688649i	0.595837	−	0.803106i	$-0.296821\pi$
$151$	−60.0363	−	103.986i	−0.397592	−	0.688649i	−0.993428	+	0.114457i	$0.963487\pi$
$152$	−13.1629	+	22.7988i	−0.0865978	+	0.149992i
$153$	−7.37150			−0.0481798
$154$	157.686	+	24.5664i	1.02393	+	0.159522i
$155$	153.080	−	148.589i	0.987615	−	0.958638i
$156$	3.48440	−	6.03516i	0.0223359	−	0.0386869i
$157$	11.8343	+	20.4977i	0.0753779	+	0.130558i	0.901251	−	0.433298i	$-0.142650\pi$
$157$	11.8343	+	20.4977i	0.0753779	+	0.130558i	−0.825873	+	0.563857i	$0.809317\pi$
$158$	145.483	−	83.9949i	0.920781	−	0.531613i
$159$	6.15976	+	3.55634i	0.0387406	+	0.0223669i
$160$	20.2955	−	19.7001i	0.126847	−	0.123125i
$161$	−113.554	+	140.955i	−0.705304	+	0.875495i
$162$			12.7279i			0.0785674i
$163$	−18.1452	−	10.4762i	−0.111321	−	0.0642709i	0.443306	−	0.896370i	$-0.353806\pi$
$163$	−18.1452	−	10.4762i	−0.111321	−	0.0642709i	−0.554627	+	0.832099i	$0.687139\pi$
$164$	31.9063	−	18.4211i	0.194551	−	0.112324i
$165$	38.1373	−	134.300i	0.231135	−	0.813942i
$166$	−108.112	−	62.4182i	−0.651274	−	0.376013i
$167$	−157.271			−0.941741			−0.470871	−	0.882202i	$-0.656060\pi$
$167$	−157.271			−0.941741			−0.470871	+	0.882202i	$0.656060\pi$
$168$	−12.3704	−	31.9840i	−0.0736332	−	0.190381i
$169$	−164.953			−0.976053
$170$	−4.24659	−	16.8479i	−0.0249800	−	0.0991050i
$171$	24.1817	−	13.9613i	0.141414	−	0.0816452i
$172$	−20.2861	+	11.7122i	−0.117942	+	0.0680939i
$173$	161.711	−	280.092i	0.934747	−	1.61903i	0.159664	−	0.987171i	$-0.448959\pi$
$173$	161.711	−	280.092i	0.934747	−	1.61903i	0.775084	−	0.631859i	$-0.217708\pi$
$174$			90.8046i			0.521866i
$175$	58.2403	+	165.024i	0.332802	+	0.942997i
$176$	−64.4833			−0.366382
$177$	−47.6496	−	27.5105i	−0.269207	−	0.155427i
$178$	79.7883	+	138.197i	0.448249	+	0.776389i
$179$	−83.6585	−	144.901i	−0.467366	−	0.809502i	0.531939	−	0.846783i	$-0.321464\pi$
$179$	−83.6585	−	144.901i	−0.467366	−	0.809502i	−0.999305	+	0.0372812i	$0.988130\pi$
$180$	−29.0902	+	7.33233i	−0.161612	+	0.0407352i
$181$		−	170.969i		−	0.944583i	−0.881443	−	0.472291i	$-0.843427\pi$
$181$		−	170.969i		−	0.944583i	0.881443	−	0.472291i	$-0.156573\pi$
$182$	12.4938	−	15.5085i	0.0686470	−	0.0852116i
$183$			161.800i			0.884152i
$184$	36.5685	−	63.3385i	0.198742	−	0.344231i
$185$	−135.901	−	38.5919i	−0.734602	−	0.208605i
$186$	52.2564	+	90.5108i	0.280949	+	0.486617i
$187$	−19.8058	+	34.3046i	−0.105913	+	0.183447i
$188$	−128.345			−0.682689
$189$	−5.59914	+	35.9395i	−0.0296251	+	0.190156i
$190$	45.8398	+	47.2254i	0.241262	+	0.248555i
$191$	−137.400	+	237.984i	−0.719371	+	1.24599i	0.241878	+	0.970307i	$0.422237\pi$
$191$	−137.400	+	237.984i	−0.719371	+	1.24599i	−0.961249	+	0.275681i	$0.911097\pi$
$192$	6.92820	+	12.0000i	0.0360844	+	0.0625000i
$193$	−172.002	+	99.3052i	−0.891200	+	0.514535i	−0.874335	−	0.485323i	$-0.838702\pi$
$193$	−172.002	+	99.3052i	−0.891200	+	0.514535i	−0.0168653	+	0.999858i	$0.505369\pi$
$194$	−99.3223	−	57.3438i	−0.511971	−	0.295586i
$195$	−12.1345	−	12.5012i	−0.0622280	−	0.0641090i
$196$	−20.8598	−	95.7542i	−0.106428	−	0.488542i
$197$		−	335.747i		−	1.70430i	−0.523298	−	0.852150i	$-0.675299\pi$
$197$		−	335.747i		−	1.70430i	0.523298	−	0.852150i	$-0.324701\pi$
$198$	59.2317	+	34.1974i	0.299150	+	0.172714i
$199$	306.912	−	177.196i	1.54227	−	0.890431i	0.543578	−	0.839359i	$-0.317069\pi$
$199$	306.912	−	177.196i	1.54227	−	0.890431i	0.998695	−	0.0510725i	$-0.0162639\pi$
$200$	−33.5166	−	62.2626i	−0.167583	−	0.311313i
$201$	160.703	+	92.7821i	0.799519	+	0.461602i
$202$	−18.6381			−0.0922678
$203$	−39.9459	+	256.403i	−0.196778	+	1.26307i
$204$	8.51188			0.0417249
$205$	−22.5116	−	89.3121i	−0.109813	−	0.435669i
$206$	−196.515	+	113.458i	−0.953955	+	0.550766i
$207$	−67.1806	+	38.7867i	−0.324544	+	0.187375i
$208$	−4.02344	+	6.96880i	−0.0193435	+	0.0335039i
$209$		−	150.045i		−	0.717921i
$210$	−85.3667	+	7.90706i	−0.406508	+	0.0376527i
$211$	−115.978			−0.549660			−0.274830	−	0.961493i	$-0.588622\pi$
$211$	−115.978			−0.549660			−0.274830	+	0.961493i	$0.588622\pi$
$212$	−7.11267	−	4.10650i	−0.0335503	−	0.0193703i
$213$	−85.6904	−	148.420i	−0.402302	−	0.696808i
$214$	145.329	+	251.717i	0.679107	+	1.17625i
$215$	14.3129	+	56.7847i	0.0665716	+	0.264115i
$216$		−	14.6969i		−	0.0680414i
$217$	107.739	+	278.561i	0.496491	+	1.28369i
$218$			56.7030i			0.260105i
$219$	47.8610	−	82.8976i	0.218543	−	0.378528i
$220$	−44.0372	+	155.077i	−0.200169	+	0.704895i
$221$	2.47157	+	4.28088i	0.0111836	+	0.0193705i
$222$	34.6051	−	59.9377i	0.155879	−	0.269990i
$223$	−219.848			−0.985865			−0.492932	−	0.870068i	$-0.664075\pi$
$223$	−219.848			−0.985865			−0.492932	+	0.870068i	$0.664075\pi$
$224$	14.2841	+	36.9319i	0.0637682	+	0.164875i
$225$	−2.23275	+	74.9668i	−0.00992331	+	0.333186i
$226$	14.3729	−	24.8946i	0.0635969	−	0.110153i
$227$	27.3586	+	47.3864i	0.120522	+	0.208751i	0.919974	−	0.391980i	$-0.128210\pi$
$227$	27.3586	+	47.3864i	0.120522	+	0.208751i	−0.799451	+	0.600731i	$0.794876\pi$
$228$	−27.9227	+	16.1212i	−0.122468	+	0.0707068i
$229$	−169.371	−	97.7862i	−0.739610	−	0.427014i	0.0823176	−	0.996606i	$-0.473768\pi$
$229$	−169.371	−	97.7862i	−0.739610	−	0.427014i	−0.821927	+	0.569592i	$0.807101\pi$
$230$	−127.350	−	131.199i	−0.553696	−	0.570432i
$231$	152.207	+	122.619i	0.658906	+	0.530819i
$232$		−	104.852i		−	0.451949i
$233$	138.492	+	79.9586i	0.594388	+	0.343170i	0.766831	−	0.641850i	$-0.221833\pi$
$233$	138.492	+	79.9586i	0.594388	+	0.343170i	−0.172443	+	0.985020i	$0.555166\pi$
$234$	7.39153	−	4.26750i	0.0315878	−	0.0182372i
$235$	−87.6502	+	308.660i	−0.372980	+	1.31345i
$236$	55.0210	+	31.7664i	0.233140	+	0.134603i
$237$	205.745			0.868121
$238$	24.0348	+	3.74446i	0.100987	+	0.0157330i
$239$	−457.640			−1.91481			−0.957406	−	0.288746i	$-0.906762\pi$
$239$	−457.640			−1.91481			−0.957406	+	0.288746i	$0.906762\pi$
$240$	33.5904	−	8.46665i	0.139960	−	0.0352777i
$241$	−69.7461	+	40.2679i	−0.289403	+	0.167087i	−0.637673	−	0.770308i	$-0.720103\pi$
$241$	−69.7461	+	40.2679i	−0.289403	+	0.167087i	0.348270	+	0.937394i	$0.386769\pi$
$242$	170.094	−	98.2037i	0.702867	−	0.405800i
$243$	−7.79423	+	13.5000i	−0.0320750	+	0.0555556i
$244$		−	186.830i		−	0.765698i
$245$	−244.526	−	15.2267i	−0.998067	−	0.0621499i
$246$	45.1223			0.183424
$247$	−16.2156	−	9.36210i	−0.0656503	−	0.0379032i
$248$	−60.3405	−	104.513i	−0.243309	−	0.421423i
$249$	−76.4464	−	132.409i	−0.307014	−	0.531763i
$250$	−172.626	+	38.0840i	−0.690503	+	0.152336i
$251$		−	270.813i		−	1.07894i	−0.842006	−	0.539468i	$-0.818625\pi$
$251$		−	270.813i		−	1.07894i	0.842006	−	0.539468i	$-0.181375\pi$
$252$	6.46534	−	41.4994i	0.0256561	−	0.164680i
$253$			416.849i			1.64763i
$254$	22.4286	−	38.8474i	0.0883014	−	0.152943i
$255$	5.81297	−	20.4703i	0.0227960	−	0.0802759i
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	37.6643	−	65.2365i	0.146554	−	0.253839i	−0.783398	−	0.621521i	$-0.786515\pi$
$257$	37.6643	−	65.2365i	0.146554	−	0.253839i	0.929952	+	0.367682i	$0.119849\pi$
$258$	−28.6888			−0.111197
$259$	124.081	−	154.022i	0.479076	−	0.594678i
$260$	14.0117	+	14.4352i	0.0538911	+	0.0555200i
$261$	−55.6062	+	96.3128i	−0.213051	+	0.369015i
$262$	−30.7019	−	53.1772i	−0.117183	−	0.202966i
$263$	−109.340	+	63.1274i	−0.415741	+	0.240028i	−0.693254	−	0.720694i	$-0.743823\pi$
$263$	−109.340	+	63.1274i	−0.415741	+	0.240028i	0.277512	+	0.960722i	$0.410490\pi$
$264$	−68.3949	−	39.4878i	−0.259071	−	0.149575i
$265$	−14.7332	+	14.3009i	−0.0555970	+	0.0539658i
$266$	−85.9364	+	33.2374i	−0.323069	+	0.124953i
$267$			195.441i			0.731987i
$268$	−185.564	−	107.136i	−0.692404	−	0.399759i
$269$	165.159	−	95.3546i	0.613974	−	0.354478i	−0.160545	−	0.987028i	$-0.551325\pi$
$269$	165.159	−	95.3546i	0.613974	−	0.354478i	0.774519	+	0.632550i	$0.217992\pi$
$270$	−35.3449	−	10.0369i	−0.130907	−	0.0371737i
$271$	−276.614	−	159.703i	−1.02071	−	0.589310i	−0.106404	−	0.994323i	$-0.533934\pi$
$271$	−276.614	−	159.703i	−1.02071	−	0.589310i	−0.914311	+	0.405013i	$0.867267\pi$
$272$	−9.82867			−0.0361348
$273$	22.7486	−	8.79844i	0.0833283	−	0.0322287i
$274$	−248.422			−0.906650
$275$	342.872	+	211.811i	1.24681	+	0.770224i
$276$	77.5734	−	44.7871i	0.281063	−	0.162272i
$277$	71.8095	−	41.4592i	0.259240	−	0.149672i	−0.364748	−	0.931106i	$-0.618845\pi$
$277$	71.8095	−	41.4592i	0.259240	−	0.149672i	0.623988	+	0.781434i	$0.285511\pi$
$278$	134.709	−	233.324i	0.484566	−	0.839293i
$279$			128.002i			0.458787i
$280$	98.5730	−	9.13029i	0.352046	−	0.0326082i
$281$	477.215			1.69828			0.849138	−	0.528171i	$-0.177122\pi$
$281$	477.215			1.69828			0.849138	+	0.528171i	$0.177122\pi$
$282$	−136.131	−	78.5952i	−0.482734	−	0.278706i
$283$	−80.2461	−	138.990i	−0.283555	−	0.491132i	0.688703	−	0.725044i	$-0.258181\pi$
$283$	−80.2461	−	138.990i	−0.283555	−	0.491132i	−0.972258	+	0.233912i	$0.924847\pi$
$284$	98.9468	+	171.381i	0.348404	+	0.603454i
$285$	19.7009	+	78.1611i	0.0691261	+	0.274250i
$286$		−	45.8638i		−	0.160363i
$287$	127.411	+	19.8498i	0.443940	+	0.0691630i
$288$			16.9706i			0.0589256i
$289$	141.481	−	245.053i	0.489554	−	0.847933i
$290$	−252.160	−	71.6061i	−0.869519	−	0.246917i
$291$	−70.2315	−	121.644i	−0.241345	−	0.418022i
$292$	−55.2651	+	95.7219i	−0.189264	+	0.327815i
$293$	−80.9312			−0.276216			−0.138108	−	0.990417i	$-0.544102\pi$
$293$	−80.9312			−0.276216			−0.138108	+	0.990417i	$0.544102\pi$
$294$	36.5120	−	114.337i	0.124191	−	0.388900i
$295$	113.971	−	110.627i	0.386341	−	0.375006i
$296$	−39.9585	+	69.2101i	−0.134995	+	0.233818i
$297$	41.8831	+	72.5437i	0.141021	+	0.244255i
$298$	165.454	−	95.5249i	0.555214	−	0.320553i
$299$	45.0495	+	26.0094i	0.150667	+	0.0869878i
$300$	2.57815	−	86.5642i	0.00859384	−	0.288547i
$301$	−81.0079	−	12.6205i	−0.269129	−	0.0419286i
$302$			169.808i			0.562279i
$303$	−19.7687	−	11.4135i	−0.0652432	−	0.0376682i
$304$	32.2423	−	18.6151i	0.106060	−	0.0612339i
$305$	−449.311	−	127.591i	−1.47315	−	0.418331i
$306$	9.02821	+	5.21244i	0.0295040	+	0.0170341i
$307$	490.744			1.59852			0.799258	−	0.600988i	$-0.205226\pi$
$307$	490.744			1.59852			0.799258	+	0.600988i	$0.205226\pi$
$308$	−175.754	−	141.588i	−0.570629	−	0.459702i
$309$	−277.914			−0.899397
$310$	−292.553	+	73.7394i	−0.943718	+	0.237869i
$311$	244.729	−	141.294i	0.786910	−	0.454323i	−0.0519634	−	0.998649i	$-0.516548\pi$
$311$	244.729	−	141.294i	0.786910	−	0.454323i	0.838874	+	0.544326i	$0.183215\pi$
$312$	−8.53501	+	4.92769i	−0.0273558	+	0.0157939i
$313$	−41.1702	+	71.3088i	−0.131534	+	0.227824i	−0.924268	−	0.381744i	$-0.875324\pi$
$313$	−41.1702	+	71.3088i	−0.131534	+	0.227824i	0.792734	+	0.609568i	$0.208657\pi$
$314$		−	33.4725i		−	0.106600i
$315$	−95.3872	−	43.8895i	−0.302816	−	0.139332i
$316$	−237.573			−0.751815
$317$	210.694	+	121.644i	0.664651	+	0.383736i	0.794047	−	0.607857i	$-0.207970\pi$
$317$	210.694	+	121.644i	0.664651	+	0.383736i	−0.129396	+	0.991593i	$0.541304\pi$
$318$	−5.02942	−	8.71121i	−0.0158158	−	0.0273937i
$319$	298.806	+	517.547i	0.936696	+	1.62241i
$320$	−38.7869	+	9.77644i	−0.121209	+	0.0305514i
$321$			355.982i			1.10898i
$322$	238.745	−	92.3388i	0.741443	−	0.286766i
$323$		−	22.8702i		−	0.0708056i
$324$	9.00000	−	15.5885i	0.0277778	−	0.0481125i
$325$	44.2843	−	23.8387i	0.136259	−	0.0733499i
$326$	14.8155	+	25.6613i	0.0454464	+	0.0787155i
$327$	−34.7233	+	60.1426i	−0.106188	+	0.183922i
$328$	−52.1028			−0.158850
$329$	−349.815	−	281.813i	−1.06327	−	0.856574i
$330$	−141.673	+	137.517i	−0.429313	+	0.416717i
$331$	290.559	−	503.264i	0.877823	−	1.52043i	0.0240980	−	0.999710i	$-0.492329\pi$
$331$	290.559	−	503.264i	0.877823	−	1.52043i	0.853725	−	0.520724i	$-0.174338\pi$
$332$	88.2727	+	152.893i	0.265882	+	0.460520i
$333$	73.4084	−	42.3824i	0.220446	−	0.127274i
$334$	192.617	+	111.207i	0.576696	+	0.332956i
$335$	−384.378	+	373.101i	−1.14740	+	1.11373i
$336$	−7.46553	+	47.9194i	−0.0222188	+	0.142617i
$337$		−	120.153i		−	0.356538i	−0.983982	−	0.178269i	$-0.942950\pi$
$337$		−	120.153i		−	0.356538i	0.983982	−	0.178269i	$-0.0570498\pi$
$338$	202.025	+	116.639i	0.597708	+	0.345087i
$339$	30.4895	−	17.6031i	0.0899396	−	0.0519266i
$340$	−6.71224	+	23.6371i	−0.0197419	+	0.0695209i
$341$	595.679	+	343.915i	1.74686	+	1.00855i
$342$	−39.4886			−0.115464
$343$	153.396	−	306.788i	0.447219	−	0.894425i
$344$	33.1270			0.0962994
$345$	−54.7322	−	217.144i	−0.158644	−	0.629402i
$346$	−396.110	+	228.694i	−1.14483	+	0.660966i
$347$	438.824	−	253.355i	1.26462	−	0.730130i	0.290657	−	0.956827i	$-0.406126\pi$
$347$	438.824	−	253.355i	1.26462	−	0.730130i	0.973965	+	0.226697i	$0.0727928\pi$
$348$	64.2086	−	111.212i	0.184507	−	0.319576i
$349$			521.456i			1.49414i	0.664743	+	0.747072i	$0.268541\pi$
$349$			521.456i			1.49414i	−0.664743	+	0.747072i	$0.731459\pi$
$350$	45.3603	−	243.295i	0.129601	−	0.695128i
$351$	10.4532			0.0297812
$352$	78.9756	+	45.5966i	0.224362	+	0.129536i
$353$	−166.483	−	288.357i	−0.471624	−	0.816877i	0.527849	−	0.849338i	$-0.322999\pi$
$353$	−166.483	−	288.357i	−0.471624	−	0.816877i	−0.999473	+	0.0324615i	$0.989665\pi$
$354$	38.9057	+	67.3867i	0.109903	+	0.190358i
$355$	479.729	−	120.918i	1.35135	−	0.340615i
$356$		−	225.675i		−	0.633919i
$357$	23.1997	+	18.6898i	0.0649853	+	0.0523525i
$358$			236.622i			0.660955i
$359$	−233.831	+	405.008i	−0.651341	+	1.12816i	0.331457	+	0.943470i	$0.392460\pi$
$359$	−233.831	+	405.008i	−0.651341	+	1.12816i	−0.982798	+	0.184685i	$0.940873\pi$
$360$	40.8128	+	11.5896i	0.113369	+	0.0321934i
$361$	−137.185	−	237.611i	−0.380013	−	0.658202i
$362$	−120.894	+	209.394i	−0.333960	+	0.578436i
$363$	240.549			0.662669
$364$	−26.2678	+	10.1596i	−0.0721644	+	0.0279109i
$365$	192.461	+	198.279i	0.527291	+	0.543229i
$366$	114.410	−	198.163i	0.312595	−	0.541430i
$367$	−257.049	−	445.222i	−0.700407	−	1.21314i	−0.968324	−	0.249698i	$-0.919669\pi$
$367$	−257.049	−	445.222i	−0.700407	−	1.21314i	0.267917	−	0.963442i	$-0.413665\pi$
$368$	−89.5741	+	51.7156i	−0.243408	+	0.140532i
$369$	47.8594	+	27.6317i	0.129700	+	0.0748826i
$370$	139.156	+	143.362i	0.376097	+	0.387465i
$371$	−10.3693	−	26.8101i	−0.0279496	−	0.0722645i
$372$		−	147.804i		−	0.397321i
$373$	−227.214	−	131.182i	−0.609152	−	0.351694i	0.163481	−	0.986546i	$-0.447728\pi$
$373$	−227.214	−	131.182i	−0.609152	−	0.351694i	−0.772634	+	0.634852i	$0.781061\pi$
$374$	48.5141	−	28.0096i	0.129717	−	0.0748920i
$375$	−206.419	−	65.3170i	−0.550450	−	0.174179i
$376$	157.190	+	90.7539i	0.418060	+	0.241367i
$377$	74.5761			0.197815
$378$	32.2706	−	40.0576i	0.0853720	−	0.105972i
$379$	101.259			0.267173			0.133587	−	0.991037i	$-0.457351\pi$
$379$	101.259			0.267173			0.133587	+	0.991037i	$0.457351\pi$
$380$	−22.7487	−	90.2527i	−0.0598649	−	0.237507i
$381$	47.5782	−	27.4693i	0.124877	−	0.0720978i
$382$	336.560	−	194.313i	0.881046	−	0.508672i
$383$	−285.977	+	495.327i	−0.746677	+	1.29328i	0.202731	+	0.979235i	$0.435018\pi$
$383$	−285.977	+	495.327i	−0.746677	+	1.29328i	−0.949407	+	0.314047i	$0.898315\pi$
$384$		−	19.5959i		−	0.0510310i
$385$	−460.534	+	325.979i	−1.19619	+	0.846698i
$386$	280.878			0.727662
$387$	−30.4291	−	17.5682i	−0.0786281	−	0.0453960i
$388$	81.0963	+	140.463i	0.209011	+	0.362018i
$389$	359.003	+	621.811i	0.922887	+	1.59849i	0.794925	+	0.606708i	$0.207510\pi$
$389$	359.003	+	621.811i	0.922887	+	1.59849i	0.127962	+	0.991779i	$0.459156\pi$
$390$	6.02191	+	23.8912i	0.0154408	+	0.0612595i
$391$			63.5370i			0.162499i
$392$	−42.1605	+	132.025i	−0.107552	+	0.336797i
$393$		−	75.2039i		−	0.191359i
$394$	−237.409	+	411.204i	−0.602561	+	1.04367i
$395$	−162.245	+	571.344i	−0.410746	+	1.44644i
$396$	−48.3625	−	83.7663i	−0.122127	−	0.211531i
$397$	−92.1713	+	159.645i	−0.232169	+	0.402129i	−0.958446	−	0.285273i	$-0.907916\pi$
$397$	−92.1713	+	159.645i	−0.232169	+	0.402129i	0.726277	+	0.687402i	$0.241249\pi$
$398$	−501.186			−1.25926
$399$	−111.503	−	17.3714i	−0.279456	−	0.0435375i
$400$	−2.97699	+	99.9557i	−0.00744248	+	0.249889i
$401$	54.6862	−	94.7192i	0.136375	−	0.236208i	−0.789747	−	0.613432i	$-0.789788\pi$
$401$	54.6862	−	94.7192i	0.136375	−	0.236208i	0.926122	+	0.377225i	$0.123122\pi$
$402$	−131.214	−	227.269i	−0.326402	−	0.565345i
$403$	74.3348	−	42.9172i	0.184454	−	0.106494i
$404$	22.8269	+	13.1791i	0.0565022	+	0.0326216i
$405$	−31.3426	−	32.2900i	−0.0773891	−	0.0797283i
$406$	230.228	−	285.782i	0.567063	−	0.703896i
$407$		−	455.492i		−	1.11915i
$408$	−10.4249	−	6.01881i	−0.0255512	−	0.0147520i
$409$	−88.1678	+	50.9037i	−0.215569	+	0.124459i	−0.603897	−	0.797062i	$-0.706386\pi$
$409$	−88.1678	+	50.9037i	−0.215569	+	0.124459i	0.388328	+	0.921521i	$0.373053\pi$
$410$	−35.5822	+	125.303i	−0.0867860	+	0.305616i
$411$	−263.491	−	152.127i	−0.641098	−	0.370138i
$412$	320.907			0.778901
$413$	80.2130	+	207.393i	0.194220	+	0.502163i
$414$	109.705			0.264989
$415$	427.978	−	107.874i	1.03127	−	0.259938i
$416$	9.85538	−	5.69001i	0.0236908	−	0.0136779i
$417$	285.762	−	164.985i	0.685280	−	0.395647i
$418$	−106.098	+	183.767i	−0.253823	+	0.439635i
$419$		−	288.226i		−	0.687891i	−0.938990	−	0.343946i	$-0.888236\pi$
$419$		−	288.226i		−	0.687891i	0.938990	−	0.343946i	$-0.111764\pi$
$420$	110.144	+	50.6793i	0.262247	+	0.120665i
$421$	−331.135			−0.786544			−0.393272	−	0.919422i	$-0.628657\pi$
$421$	−331.135			−0.786544			−0.393272	+	0.919422i	$0.628657\pi$
$422$	142.044	+	82.0091i	0.336597	+	0.194334i
$423$	−96.2591	−	166.726i	−0.227563	−	0.394150i
$424$	5.80747	+	10.0588i	0.0136969	+	0.0237237i
$425$	52.2613	+	32.2847i	0.122968	+	0.0759641i
$426$			242.369i			0.568941i
$427$	410.230	−	509.219i	0.960726	−	1.19255i
$428$		−	411.052i		−	0.960402i
$429$	28.0857	−	48.6459i	0.0654679	−	0.113394i
$430$	22.6232	−	79.6676i	0.0526122	−	0.185273i
$431$	−22.7734	−	39.4447i	−0.0528386	−	0.0915191i	0.838396	−	0.545061i	$-0.183494\pi$
$431$	−22.7734	−	39.4447i	−0.0528386	−	0.0915191i	−0.891235	+	0.453542i	$0.850160\pi$
$432$	−10.3923	+	18.0000i	−0.0240563	+	0.0416667i
$433$	439.384			1.01474			0.507372	−	0.861727i	$-0.330617\pi$
$433$	439.384			1.01474			0.507372	+	0.861727i	$0.330617\pi$
$434$	65.0203	−	417.349i	0.149816	−	0.961634i
$435$	−223.607	−	230.366i	−0.514039	−	0.529577i
$436$	40.0950	−	69.4466i	0.0919611	−	0.159281i
$437$	−120.336	−	208.429i	−0.275370	−	0.476954i
$438$	−117.235	+	67.6856i	−0.267660	+	0.154533i
$439$	−193.248	−	111.572i	−0.440201	−	0.254150i	0.263482	−	0.964664i	$-0.415129\pi$
$439$	−193.248	−	111.572i	−0.440201	−	0.254150i	−0.703683	+	0.710514i	$0.748462\pi$
$440$	163.590	−	158.791i	0.371796	−	0.360888i
$441$	108.743	−	98.9134i	0.246584	−	0.224293i
$442$		−	6.99065i		−	0.0158160i
$443$	210.380	+	121.463i	0.474899	+	0.274183i	0.718288	−	0.695746i	$-0.244926\pi$
$443$	210.380	+	121.463i	0.474899	+	0.274183i	−0.243390	+	0.969929i	$0.578259\pi$
$444$	−84.7647	+	48.9389i	−0.190912	+	0.110223i
$445$	−542.730	−	154.119i	−1.21962	−	0.346335i
$446$	269.258	+	155.456i	0.603716	+	0.348556i
$447$	233.987			0.523461
$448$	8.62045	−	55.3325i	0.0192421	−	0.123510i
$449$	519.036			1.15598			0.577991	−	0.816043i	$-0.303837\pi$
$449$	519.036			1.15598			0.577991	+	0.816043i	$0.303837\pi$
$450$	55.7440	−	90.2364i	0.123876	−	0.200525i
$451$	257.178	−	148.482i	0.570239	−	0.329228i
$452$	−35.2063	+	20.3263i	−0.0778900	+	0.0449698i
$453$	−103.986	+	180.109i	−0.229550	+	0.397592i
$454$		−	77.3817i		−	0.170444i
$455$	6.49393	+	70.1101i	0.0142724	+	0.154088i
$456$	45.5975			0.0999945
$457$	404.221	+	233.377i	0.884510	+	0.510672i	0.872143	−	0.489251i	$-0.162730\pi$
$457$	404.221	+	233.377i	0.884510	+	0.510672i	0.0123672	+	0.999924i	$0.496063\pi$
$458$	138.291	+	239.526i	0.301944	+	0.522983i
$459$	6.38391	+	11.0573i	0.0139083	+	0.0240899i
$460$	63.1993	+	250.736i	0.137390	+	0.545078i
$461$			328.092i			0.711696i	0.934544	+	0.355848i	$0.115808\pi$
$461$			328.092i			0.711696i	−0.934544	+	0.355848i	$0.884192\pi$
$462$	−99.7103	−	257.804i	−0.215823	−	0.558017i
$463$		−	292.689i		−	0.632157i	−0.948733	−	0.316079i	$-0.897634\pi$
$463$		−	292.689i		−	0.632157i	0.948733	−	0.316079i	$-0.102366\pi$
$464$	−74.1416	+	128.417i	−0.159788	+	0.276761i
$465$	−355.455	−	100.939i	−0.764419	−	0.217072i
$466$	−113.079	−	195.858i	−0.242658	−	0.420296i
$467$	−48.9058	+	84.7073i	−0.104723	+	0.181386i	−0.913625	−	0.406558i	$-0.866729\pi$
$467$	−48.9058	+	84.7073i	−0.104723	+	0.181386i	0.808902	+	0.587944i	$0.200062\pi$
$468$	−12.0703			−0.0257913
$469$	−270.527	−	699.456i	−0.576817	−	1.49138i
$470$	325.605	−	316.052i	0.692776	−	0.672450i
$471$	20.4977	−	35.5030i	0.0435194	−	0.0753779i
$472$	−44.9245	−	77.8114i	−0.0951789	−	0.164855i
$473$	−163.514	+	94.4048i	−0.345695	+	0.199587i
$474$	−251.985	−	145.483i	−0.531613	−	0.306927i
$475$	−232.586	−	6.92713i	−0.489654	−	0.0145834i
$476$	−26.7888	−	21.5812i	−0.0562789	−	0.0453386i
$477$		−	12.3195i		−	0.0258271i
$478$	560.492	+	323.600i	1.17258	+	0.676988i
$479$	38.4835	−	22.2184i	0.0803413	−	0.0463851i	−0.459291	−	0.888286i	$-0.651897\pi$
$479$	38.4835	−	22.2184i	0.0803413	−	0.0463851i	0.539632	+	0.841901i	$0.318563\pi$
$480$	−47.1265	−	13.3825i	−0.0981802	−	0.0278803i
$481$	−49.2257	−	28.4205i	−0.102340	−	0.0590863i
$482$	113.895			0.236297
$483$	309.773	+	48.2606i	0.641351	+	0.0999183i
$484$	−277.762			−0.573888
$485$	393.184	−	99.1042i	0.810689	−	0.204338i
$486$	19.0919	−	11.0227i	0.0392837	−	0.0226805i
$487$	−517.227	+	298.621i	−1.06207	+	0.613185i	−0.926004	−	0.377515i	$-0.876779\pi$
$487$	−517.227	+	298.621i	−1.06207	+	0.613185i	−0.136064	+	0.990700i	$0.543445\pi$
$488$	−132.109	+	228.819i	−0.270715	+	0.468892i
$489$			36.2905i			0.0742137i
$490$	288.716	+	191.555i	0.589215	+	0.390929i
$491$	−421.357			−0.858161			−0.429080	−	0.903266i	$-0.641162\pi$
$491$	−421.357			−0.858161			−0.429080	+	0.903266i	$0.641162\pi$
$492$	−55.2633	−	31.9063i	−0.112324	−	0.0648502i
$493$	45.5446	+	78.8856i	0.0923826	+	0.160011i
$494$	13.2400	+	22.9324i	0.0268016	+	0.0464218i
$495$	−234.479	+	59.1016i	−0.473694	+	0.119397i
$496$			170.669i			0.344090i
$497$	−106.621	+	684.372i	−0.214528	+	1.37701i
$498$			216.223i			0.434183i
$499$	−66.9673	+	115.991i	−0.134203	+	0.232446i	−0.925293	−	0.379254i	$-0.876181\pi$
$499$	−66.9673	+	115.991i	−0.134203	+	0.232446i	0.791090	+	0.611700i	$0.209514\pi$
$500$	238.352	+	75.4216i	0.476704	+	0.150843i
$501$	136.201	+	235.906i	0.271857	+	0.470871i
$502$	−191.494	+	331.677i	−0.381462	+	0.660711i
$503$	−705.456			−1.40250			−0.701248	−	0.712917i	$-0.747374\pi$
$503$	−705.456			−1.40250			−0.701248	+	0.712917i	$0.747374\pi$
$504$	−37.2629	+	46.2545i	−0.0739343	+	0.0917748i
$505$	47.2837	−	45.8964i	0.0936311	−	0.0908840i
$506$	294.757	−	510.534i	0.582524	−	1.00896i
$507$	142.853	+	247.429i	0.281762	+	0.488027i
$508$	−54.9385	+	31.7188i	−0.108147	+	0.0624386i
$509$	349.959	+	202.049i	0.687542	+	0.396952i	0.802691	−	0.596396i	$-0.203401\pi$
$509$	349.959	+	202.049i	0.687542	+	0.396952i	−0.115149	+	0.993348i	$0.536734\pi$
$510$	−21.5941	+	20.9606i	−0.0423414	+	0.0410991i
$511$	−360.809	+	139.549i	−0.706084	+	0.273091i
$512$			22.6274i			0.0441942i
$513$	−41.8840	−	24.1817i	−0.0816452	−	0.0471379i
$514$	−92.2584	+	53.2654i	−0.179491	+	0.103629i
$515$	219.155	−	771.754i	0.425544	−	1.49855i
$516$	35.1365	+	20.2861i	0.0680939	+	0.0393141i
$517$	−1034.52			−2.00100
$518$	−260.877	+	100.899i	−0.503623	+	0.194785i
$519$	−560.184			−1.07935
$520$	−6.95350	−	27.5872i	−0.0133721	−	0.0530523i
$521$	−723.309	+	417.603i	−1.38831	+	0.801541i	−0.993125	−	0.117061i	$-0.962653\pi$
$521$	−723.309	+	417.603i	−1.38831	+	0.801541i	−0.395184	+	0.918602i	$0.629319\pi$
$522$	136.207	−	78.6391i	0.260933	−	0.150650i
$523$	135.274	−	234.301i	0.258649	−	0.447993i	−0.707231	−	0.706982i	$-0.750056\pi$
$523$	135.274	−	234.301i	0.258649	−	0.447993i	0.965880	+	0.258989i	$0.0833893\pi$
$524$			86.8380i			0.165721i
$525$	197.099	−	230.276i	0.375427	−	0.438621i
$526$	178.551			0.339451
$527$	90.7945	+	52.4202i	0.172286	+	0.0994691i
$528$	55.8442	+	96.7249i	0.105765	+	0.183191i
$529$	69.8133	+	120.920i	0.131972	+	0.228583i
$530$	28.1567	−	7.09705i	0.0531259	−	0.0133907i
$531$			95.2992i			0.179471i
$532$	128.753	+	20.0588i	0.242016	+	0.0377045i
$533$		−	37.0581i		−	0.0695274i
$534$	138.197	−	239.365i	0.258796	−	0.448249i
$535$	−988.545	−	280.718i	−1.84775	−	0.524706i
$536$	151.513	+	262.427i	0.282673	+	0.489603i
$537$	−144.901	+	250.975i	−0.269834	+	0.467366i
$538$	−269.703			−0.501308
$539$	−168.139	−	771.818i	−0.311946	−	1.43194i
$540$	36.1913	+	37.2852i	0.0670209	+	0.0690467i
$541$	175.091	−	303.266i	0.323643	−	0.560566i	−0.657594	−	0.753373i	$-0.728426\pi$
$541$	175.091	−	303.266i	0.323643	−	0.560566i	0.981237	+	0.192806i	$0.0617589\pi$
$542$	225.854	+	391.191i	0.416705	+	0.721754i
$543$	−256.454	+	148.064i	−0.472291	+	0.272678i
$544$	12.0376	+	6.94992i	0.0221280	+	0.0127756i
$545$	−139.631	−	143.852i	−0.256204	−	0.263949i
$546$	−34.0827	−	5.30986i	−0.0624225	−	0.00972502i
$547$		−	250.119i		−	0.457255i	−0.973514	−	0.228628i	$-0.926576\pi$
$547$		−	250.119i		−	0.457255i	0.973514	−	0.228628i	$-0.0734238\pi$
$548$	304.254	+	175.661i	0.555207	+	0.320549i
$549$	242.700	−	140.123i	0.442076	−	0.255233i
$550$	−270.158	−	501.862i	−0.491196	−	0.912477i
$551$	−298.812	−	172.519i	−0.542309	−	0.313102i
$552$	−126.677			−0.229487
$553$	−647.523	−	521.649i	−1.17093	−	0.943307i
$554$	−117.264			−0.211669
$555$	59.8061	+	237.274i	0.107759	+	0.427520i
$556$	−329.969	+	190.508i	−0.593470	+	0.342640i
$557$	−317.710	+	183.430i	−0.570395	+	0.329318i	−0.757307	−	0.653059i	$-0.773485\pi$
$557$	−317.710	+	183.430i	−0.570395	+	0.329318i	0.186912	+	0.982377i	$0.440152\pi$
$558$	90.5108	−	156.769i	0.162206	−	0.280949i
$559$			23.5616i			0.0421495i
$560$	−127.183	−	58.5194i	−0.227112	−	0.104499i
$561$	68.6093			0.122298
$562$	−584.467	−	337.442i	−1.03998	−	0.600431i
$563$	55.4530	+	96.0473i	0.0984955	+	0.170599i	0.911062	−	0.412269i	$-0.135264\pi$
$563$	55.4530	+	96.0473i	0.0984955	+	0.170599i	−0.812567	+	0.582868i	$0.801930\pi$
$564$	111.150	+	192.518i	0.197075	+	0.341344i
$565$	24.8399	+	98.5494i	0.0439645	+	0.174424i
$566$			226.970i			0.401008i
$567$	58.7583	−	22.7258i	0.103630	−	0.0400808i
$568$		−	279.864i		−	0.492718i
$569$	−7.08673	+	12.2746i	−0.0124547	+	0.0215722i	−0.872186	−	0.489175i	$-0.837298\pi$
$569$	−7.08673	+	12.2746i	−0.0124547	+	0.0215722i	0.859731	+	0.510747i	$0.170631\pi$
$570$	31.1396	−	109.658i	0.0546310	−	0.192383i
$571$	−532.592	−	922.477i	−0.932736	−	1.61555i	−0.778622	−	0.627493i	$-0.784081\pi$
$571$	−532.592	−	922.477i	−0.932736	−	1.61555i	−0.154114	−	0.988053i	$-0.549252\pi$
$572$	−32.4306	+	56.1714i	−0.0566968	+	0.0982018i
$573$	475.967			0.830658
$574$	−142.010	−	114.404i	−0.247404	−	0.199310i
$575$	646.159	+	19.2446i	1.12375	+	0.0334689i
$576$	12.0000	−	20.7846i	0.0208333	−	0.0360844i
$577$	201.337	+	348.725i	0.348937	+	0.604377i	0.986061	−	0.166385i	$-0.0532093\pi$
$577$	201.337	+	348.725i	0.348937	+	0.604377i	−0.637124	+	0.770761i	$0.719876\pi$
$578$	−346.557	+	200.085i	−0.599579	+	0.346167i
$579$	297.916	+	172.002i	0.514535	+	0.297067i
$580$	258.199	+	266.004i	0.445171	+	0.458627i
$581$	−95.1188	+	610.544i	−0.163716	+	1.05085i
$582$			198.645i			0.341314i
$583$	−57.3311	−	33.1001i	−0.0983380	−	0.0567755i
$584$	135.371	−	78.1566i	0.231800	−	0.133830i
$585$	−8.24312	+	29.0281i	−0.0140908	+	0.0496207i
$586$	99.1201	+	57.2270i	0.169147	+	0.0976570i
$587$	−218.363			−0.371999			−0.185999	−	0.982550i	$-0.559552\pi$
$587$	−218.363			−0.371999			−0.185999	+	0.982550i	$0.559552\pi$
$588$	−125.566	+	114.215i	−0.213548	+	0.194244i
$589$	−397.127			−0.674240
$590$	−217.810	+	54.9002i	−0.369169	+	0.0930511i
$591$	−503.620	+	290.765i	−0.852150	+	0.491989i
$592$	97.8779	−	56.5098i	0.165334	−	0.0954558i
$593$	−67.3842	+	116.713i	−0.113633	+	0.196818i	−0.917232	−	0.398353i	$-0.869582\pi$
$593$	−67.3842	+	116.713i	−0.113633	+	0.196818i	0.803600	+	0.595170i	$0.202915\pi$
$594$		−	118.463i		−	0.199433i
$595$	−70.1956	+	49.6863i	−0.117976	+	0.0835065i
$596$	−270.185			−0.453331
$597$	−531.588	−	306.912i	−0.890431	−	0.514091i
$598$	−36.7828	−	63.7096i	−0.0615097	−	0.106538i
$599$	397.982	+	689.325i	0.664411	+	1.15079i	0.979445	+	0.201713i	$0.0646507\pi$
$599$	397.982	+	689.325i	0.664411	+	1.15079i	−0.315034	+	0.949080i	$0.602016\pi$
$600$	−64.3677	+	104.196i	−0.107279	+	0.173660i
$601$			1083.37i			1.80262i	0.433175	+	0.901310i	$0.357393\pi$
$601$			1083.37i			1.80262i	−0.433175	+	0.901310i	$0.642607\pi$
$602$	90.2900	+	72.7381i	0.149983	+	0.120827i
$603$		−	321.407i		−	0.533013i
$604$	120.073	−	207.972i	0.198796	−	0.344324i
$605$	−189.690	+	667.994i	−0.313538	+	1.10412i
$606$	16.1411	+	27.9571i	0.0266354	+	0.0461339i
$607$	−500.755	+	867.333i	−0.824967	+	1.42888i	0.0769782	+	0.997033i	$0.475473\pi$
$607$	−500.755	+	867.333i	−0.824967	+	1.42888i	−0.901945	+	0.431851i	$0.857861\pi$
$608$	−52.6515			−0.0865978
$609$	419.198	−	162.132i	0.688339	−	0.266227i
$610$	460.071	+	473.977i	0.754214	+	0.777012i
$611$	−64.5488	+	111.802i	−0.105645	+	0.182982i
$612$	−7.37150	−	12.7678i	−0.0120449	−	0.0208625i
$613$	92.4983	−	53.4039i	0.150894	−	0.0871189i	−0.422652	−	0.906292i	$-0.638901\pi$
$613$	92.4983	−	53.4039i	0.150894	−	0.0871189i	0.573546	+	0.819173i	$0.305567\pi$
$614$	−601.037	−	347.009i	−0.978887	−	0.565161i
$615$	−114.473	+	111.114i	−0.186134	+	0.180673i
$616$	115.136	+	297.686i	0.186908	+	0.483257i
$617$		−	670.343i		−	1.08646i	−0.839585	−	0.543228i	$-0.817202\pi$
$617$		−	670.343i		−	1.08646i	0.839585	−	0.543228i	$-0.182798\pi$
$618$	340.373	+	196.515i	0.550766	+	0.317985i
$619$	853.129	−	492.554i	1.37824	−	0.795726i	0.386290	−	0.922377i	$-0.373756\pi$
$619$	853.129	−	492.554i	1.37824	−	0.795726i	0.991947	+	0.126652i	$0.0404230\pi$
$620$	410.444	+	116.554i	0.662006	+	0.187990i
$621$	116.360	+	67.1806i	0.187375	+	0.108181i
$622$	−399.641			−0.642510
$623$	495.524	−	615.094i	0.795383	−	0.987310i
$624$	13.9376			0.0223359
$625$	344.159	−	521.709i	0.550654	−	0.834734i
$626$	100.846	−	58.2234i	0.161096	−	0.0930087i
$627$	−225.068	+	129.943i	−0.358960	+	0.207246i
$628$	−23.6686	+	40.9953i	−0.0376889	+	0.0652791i
$629$		−	69.4271i		−	0.110377i
$630$	85.7904	+	121.202i	0.136175	+	0.192385i
$631$	1170.51			1.85500			0.927501	−	0.373820i	$-0.121952\pi$
$631$	1170.51			1.85500			0.927501	+	0.373820i	$0.121952\pi$
$632$	290.967	+	167.990i	0.460391	+	0.265807i
$633$	100.440	+	173.968i	0.158673	+	0.274830i
$634$	−172.031	−	297.967i	−0.271343	−	0.469979i
$635$	38.7621	+	153.784i	0.0610427	+	0.242180i
$636$			14.2253i			0.0223669i
$637$	−93.9026	−	29.9867i	−0.147414	−	0.0470748i
$638$		−	845.151i		−	1.32469i
$639$	−148.420	+	257.071i	−0.232269	+	0.402302i
$640$	54.4170	+	15.4528i	0.0850266	+	0.0241450i
$641$	−13.9729	−	24.2018i	−0.0217986	−	0.0377563i	0.854920	−	0.518759i	$-0.173606\pi$
$641$	−13.9729	−	24.2018i	−0.0217986	−	0.0377563i	−0.876719	+	0.481003i	$0.840273\pi$
$642$	251.717	−	435.987i	0.392083	−	0.679107i
$643$	1006.11			1.56472			0.782358	−	0.622829i	$-0.214017\pi$
$643$	1006.11			1.56472			0.782358	+	0.622829i	$0.214017\pi$
$644$	−357.695	−	55.7265i	−0.555426	−	0.0865318i
$645$	72.7818	−	70.6464i	0.112840	−	0.109529i
$646$	−16.1717	+	28.0102i	−0.0250336	+	0.0433594i
$647$	−383.652	−	664.505i	−0.592971	−	1.02706i	−0.993830	−	0.110916i	$-0.964621\pi$
$647$	−383.652	−	664.505i	−0.592971	−	1.02706i	0.400859	−	0.916140i	$-0.368712\pi$
$648$	−22.0454	+	12.7279i	−0.0340207	+	0.0196419i
$649$	443.492	+	256.050i	0.683347	+	0.394530i
$650$	−71.0935	−	2.11739i	−0.109375	−	0.00325752i
$651$	324.538	−	402.849i	0.498522	−	0.618816i
$652$		−	41.9047i		−	0.0642709i
$653$	−234.927	−	135.635i	−0.359766	−	0.207711i	0.309212	−	0.950993i	$-0.399935\pi$
$653$	−234.927	−	135.635i	−0.359766	−	0.207711i	−0.668978	+	0.743282i	$0.733268\pi$
$654$	85.0544	−	49.1062i	0.130053	−	0.0750859i
$655$	208.838	+	59.3038i	0.318837	+	0.0905402i
$656$	63.8126	+	36.8422i	0.0972753	+	0.0561619i
$657$	−165.795			−0.252352
$658$	229.162	+	592.505i	0.348271	+	0.900464i
$659$	309.291			0.469333			0.234667	−	0.972076i	$-0.424600\pi$
$659$	309.291			0.469333			0.234667	+	0.972076i	$0.424600\pi$
$660$	270.753	−	68.2446i	0.410231	−	0.103401i
$661$	−654.692	+	377.986i	−0.990457	+	0.571840i	−0.905411	−	0.424537i	$-0.860437\pi$
$661$	−654.692	+	377.986i	−0.990457	+	0.571840i	−0.0850458	+	0.996377i	$0.527104\pi$
$662$	−711.722	+	410.913i	−1.07511	+	0.620715i
$663$	4.28088	−	7.41470i	0.00645683	−	0.0111836i
$664$		−	249.673i		−	0.376013i
$665$	136.168	−	295.940i	0.204764	−	0.445023i
$666$	−119.875			−0.179993
$667$	830.146	+	479.285i	1.24460	+	0.718569i
$668$	−157.271	−	272.401i	−0.235435	−	0.407786i
$669$	190.394	+	329.772i	0.284595	+	0.492932i
$670$	734.587	−	185.157i	1.09640	−	0.276353i
$671$		−	1505.93i		−	2.24431i
$672$	43.0275	−	53.4101i	0.0640290	−	0.0794793i
$673$			846.409i			1.25767i	0.777541	+	0.628833i	$0.216467\pi$
$673$			846.409i			1.25767i	−0.777541	+	0.628833i	$0.783533\pi$
$674$	−84.9613	+	147.157i	−0.126055	+	0.218334i
$675$	114.384	−	61.5740i	0.169457	−	0.0912207i
$676$	−164.953	−	285.707i	−0.244013	−	0.422643i
$677$	456.036	−	789.878i	0.673613	−	1.16673i	−0.303259	−	0.952908i	$-0.598075\pi$
$677$	456.036	−	789.878i	0.673613	−	1.16673i	0.976872	−	0.213824i	$-0.0685919\pi$
$678$	−49.7892			−0.0734354
$679$	−87.3858	+	560.908i	−0.128698	+	0.826079i
$680$	24.9347	−	24.2032i	0.0366687	−	0.0355929i
$681$	47.3864	−	82.0757i	0.0695836	−	0.120522i
$682$	−486.370	−	842.417i	−0.713152	−	1.23522i
$683$	77.0163	−	44.4654i	0.112762	−	0.0651030i	−0.442558	−	0.896740i	$-0.645929\pi$
$683$	77.0163	−	44.4654i	0.112762	−	0.0651030i	0.555320	+	0.831637i	$0.312596\pi$
$684$	48.3635	+	27.9227i	0.0707068	+	0.0408226i
$685$	630.232	−	611.741i	0.920046	−	0.893052i
$686$	−404.803	+	267.269i	−0.590091	+	0.389605i
$687$			338.741i			0.493073i
$688$	−40.5721	−	23.4243i	−0.0589711	−	0.0340470i
$689$	−7.15436	+	4.13057i	−0.0103837	+	0.00599502i
$690$	−86.5107	+	304.647i	−0.125378	+	0.441518i
$691$	−427.475	−	246.803i	−0.618632	−	0.357167i	0.157704	−	0.987486i	$-0.449591\pi$
$691$	−427.475	−	246.803i	−0.618632	−	0.357167i	−0.776336	+	0.630319i	$0.782924\pi$
$692$	646.845			0.934747
$693$	52.1133	−	334.502i	0.0751995	−	0.482687i
$694$	−716.596			−1.03256
$695$	232.811	+	923.651i	0.334980	+	1.32899i
$696$	−157.278	+	90.8046i	−0.225974	+	0.130466i
$697$	39.1996	−	22.6319i	0.0562404	−	0.0324704i
$698$	368.725	−	638.651i	0.528260	−	0.914973i
$699$		−	276.985i		−	0.396258i
$700$	−227.590	+	265.900i	−0.325129	+	0.379857i
$701$	−631.538			−0.900910			−0.450455	−	0.892799i	$-0.648738\pi$
$701$	−631.538			−0.900910			−0.450455	+	0.892799i	$0.648738\pi$
$702$	−12.8025	−	7.39153i	−0.0182372	−	0.0105293i
$703$	131.492	+	227.751i	0.187044	+	0.323970i
$704$	−64.4833	−	111.688i	−0.0915956	−	0.158648i
$705$	538.897	−	135.832i	0.764393	−	0.192669i
$706$			470.886i			0.666977i
$707$	33.2785	+	86.0425i	0.0470700	+	0.121701i
$708$		−	110.042i		−	0.155427i
$709$	420.275	−	727.937i	0.592771	−	1.02671i	−0.401086	−	0.916040i	$-0.631367\pi$
$709$	420.275	−	727.937i	0.592771	−	1.02671i	0.993857	−	0.110669i	$-0.0352994\pi$
$710$	−673.048	−	191.126i	−0.947955	−	0.269191i
$711$	−178.180	−	308.617i	−0.250605	−	0.434060i
$712$	−159.577	+	276.395i	−0.224124	+	0.388195i
$713$	1103.28			1.54738
$714$	−15.1980	−	39.2950i	−0.0212858	−	0.0550350i
$715$	112.940	+	116.354i	0.157958	+	0.162732i
$716$	167.317	−	289.802i	0.233683	−	0.404751i
$717$	396.328	+	686.460i	0.552759	+	0.957406i
$718$	572.768	−	330.688i	0.797727	−	0.460568i
$719$	−375.726	−	216.925i	−0.522567	−	0.301704i	0.215417	−	0.976522i	$-0.430889\pi$
$719$	−375.726	−	216.925i	−0.522567	−	0.301704i	−0.737984	+	0.674818i	$0.764222\pi$
$720$	−41.7901	−	43.0533i	−0.0580418	−	0.0597962i
$721$	874.655	+	704.628i	1.21311	+	0.977292i
$722$			388.017i			0.537420i
$723$	120.804	+	69.7461i	0.167087	+	0.0964677i
$724$	296.128	−	170.969i	0.409016	−	0.236146i
$725$	816.046	−	439.286i	1.12558	−	0.605912i
$726$	−294.611	−	170.094i	−0.405800	−	0.234289i
$727$	119.222			0.163992			0.0819959	−	0.996633i	$-0.473871\pi$
$727$	119.222			0.163992			0.0819959	+	0.996633i	$0.473871\pi$
$728$	39.3553	+	6.13130i	0.0540595	+	0.00842211i
$729$	27.0000			0.0370370
$730$	−95.5117	−	378.931i	−0.130838	−	0.519084i
$731$	−24.9231	+	14.3894i	−0.0340946	+	0.0196845i
$732$	−280.245	+	161.800i	−0.382849	+	0.221038i
$733$	−11.4496	+	19.8313i	−0.0156202	+	0.0270549i	−0.873730	−	0.486412i	$-0.838306\pi$
$733$	−11.4496	+	19.8313i	−0.0156202	+	0.0270549i	0.858110	+	0.513466i	$0.171639\pi$
$734$			727.045i			0.990525i
$735$	188.926	+	379.976i	0.257042	+	0.516975i
$736$	146.274			0.198742
$737$	−1495.72	−	863.557i	−2.02948	−	1.17172i
$738$	−39.0771	−	67.6835i	−0.0529500	−	0.0917120i
$739$	387.414	+	671.021i	0.524241	+	0.908012i	0.999602	+	0.0282213i	$0.00898432\pi$
$739$	387.414	+	671.021i	0.524241	+	0.908012i	−0.475360	+	0.879791i	$0.657682\pi$
$740$	−69.0581	−	273.980i	−0.0933218	−	0.370243i
$741$			32.4313i			0.0437669i
$742$	−6.25788	+	40.1678i	−0.00843380	+	0.0541345i
$743$		−	236.167i		−	0.317856i	−0.987290	−	0.158928i	$-0.949196\pi$
$743$		−	236.167i		−	0.317856i	0.987290	−	0.158928i	$-0.0508037\pi$
$744$	−104.513	+	181.022i	−0.140474	+	0.243309i
$745$	−184.516	+	649.772i	−0.247672	+	0.872177i
$746$	185.519	+	321.329i	0.248685	+	0.430736i
$747$	−132.409	+	229.339i	−0.177254	+	0.307014i
$748$	−79.2231			−0.105913
$749$	902.562	−	1120.35i	1.20502	−	1.49580i
$750$	206.624	+	225.957i	0.275499	+	0.301276i
$751$	−295.853	+	512.433i	−0.393946	+	0.682334i	−0.992966	−	0.118400i	$-0.962224\pi$
$751$	−295.853	+	512.433i	−0.393946	+	0.682334i	0.599020	+	0.800734i	$0.295557\pi$
$752$	−128.345	−	222.301i	−0.170672	−	0.295613i
$753$	−406.220	+	234.531i	−0.539468	+	0.311462i
$754$	−91.3368	−	52.7333i	−0.121136	−	0.0699381i
$755$	−418.154	−	430.794i	−0.553847	−	0.570588i
$756$	−67.8482	+	26.2415i	−0.0897463	+	0.0347110i
$757$			1265.71i			1.67201i	0.548722	+	0.836005i	$0.315114\pi$
$757$			1265.71i			1.67201i	−0.548722	+	0.836005i	$0.684886\pi$
$758$	−124.016	−	71.6007i	−0.163610	−	0.0944601i
$759$	625.274	−	361.002i	0.823813	−	0.475629i
$760$	−35.9570	+	126.622i	−0.0473118	+	0.166608i
$761$	719.924	+	415.649i	0.946024	+	0.546187i	0.891844	−	0.452344i	$-0.149412\pi$
$761$	719.924	+	415.649i	0.946024	+	0.546187i	0.0541806	+	0.998531i	$0.482745\pi$
$762$	−77.6948			−0.101962
$763$	261.768	−	101.244i	0.343078	−	0.132692i
$764$	−549.600			−0.719371
$765$	−35.7397	+	9.00838i	−0.0467186	+	0.0117757i
$766$	700.498	−	404.433i	0.914488	−	0.527980i
$767$	55.3434	−	31.9525i	0.0721557	−	0.0416591i
$768$	−13.8564	+	24.0000i	−0.0180422	+	0.0312500i
$769$			641.313i			0.833957i	0.908916	+	0.416979i	$0.136911\pi$
$769$			641.313i			0.833957i	−0.908916	+	0.416979i	$0.863089\pi$
$770$	794.539	−	73.5939i	1.03187	−	0.0955765i
$771$	−130.473			−0.169226
$772$	−344.003	−	198.610i	−0.445600	−	0.257267i
$773$	−54.9910	−	95.2472i	−0.0711397	−	0.123218i	0.828261	−	0.560342i	$-0.189330\pi$
$773$	−54.9910	−	95.2472i	−0.0711397	−	0.123218i	−0.899401	+	0.437124i	$0.855997\pi$
$774$	24.8452	+	43.0332i	0.0320998	+	0.0555985i
$775$	560.604	−	907.485i	0.723360	−	1.17095i
$776$		−	229.375i		−	0.295586i
$777$	−338.489	−	52.7345i	−0.435636	−	0.0678693i
$778$		−	1015.41i		−	1.30516i
$779$	−85.7277	+	148.485i	−0.110048	+	0.190609i
$780$	9.51833	−	33.5188i	0.0122030	−	0.0429728i
$781$	797.552	+	1381.40i	1.02119	+	1.76876i
$782$	44.9274	−	77.8166i	0.0574520	−	0.0995097i
$783$	192.626			0.246010
$784$	144.991	−	131.885i	0.184938	−	0.168220i
$785$	82.4263	+	84.9178i	0.105002	+	0.108176i
$786$	−53.1772	+	92.1057i	−0.0676555	+	0.117183i
$787$	−334.261	−	578.957i	−0.424728	−	0.735651i	0.571667	−	0.820486i	$-0.306297\pi$
$787$	−334.261	−	578.957i	−0.424728	−	0.735651i	−0.996395	+	0.0848352i	$0.972964\pi$
$788$	581.531	−	335.747i	0.737983	−	0.426075i
$789$	189.382	+	109.340i	0.240028	+	0.138580i
$790$	602.710	−	585.026i	0.762923	−	0.740539i
$791$	−140.589	−	21.9028i	−0.177735	−	0.0276900i
$792$			136.790i			0.172714i
$793$	−162.748	−	93.9626i	−0.205231	−	0.118490i
$794$	225.773	−	130.350i	0.284348	−	0.164169i
$795$	34.2107	+	9.71483i	0.0430324	+	0.0122199i
$796$	613.824	+	354.392i	0.771136	+	0.445216i
$797$	−780.422			−0.979199			−0.489600	−	0.871947i	$-0.662857\pi$
$797$	−780.422			−0.979199			−0.489600	+	0.871947i	$0.662857\pi$
$798$	124.279	+	100.120i	0.155738	+	0.125464i
$799$	−157.683			−0.197351
$800$	74.3254	−	120.315i	0.0929067	−	0.150394i
$801$	293.161	−	169.256i	0.365994	−	0.211306i
$802$	−133.953	+	77.3379i	−0.167024	+	0.0964313i
$803$	−445.459	+	771.558i	−0.554744	+	0.960844i
$804$			371.128i			0.461602i
$805$	−378.296	+	822.168i	−0.469933	+	1.02133i
$806$	−121.388			−0.150606
$807$	−286.064	−	165.159i	−0.354478	−	0.204658i
$808$	−18.6381	−	32.2821i	−0.0230669	−	0.0399531i
$809$	203.761	+	352.925i	0.251868	+	0.436249i	0.964040	−	0.265756i	$-0.0856217\pi$
$809$	203.761	+	352.925i	0.251868	+	0.436249i	−0.712172	+	0.702005i	$0.752288\pi$
$810$	15.5542	+	61.7095i	0.0192027	+	0.0761846i
$811$		−	639.782i		−	0.788880i	−0.918922	−	0.394440i	$-0.870939\pi$
$811$		−	639.782i		−	0.788880i	0.918922	−	0.394440i	$-0.129061\pi$
$812$	−484.049	+	187.214i	−0.596119	+	0.230560i
$813$			553.227i			0.680476i
$814$	−322.082	+	557.862i	−0.395678	+	0.685334i
$815$	−100.777	−	28.6177i	−0.123653	−	0.0351137i
$816$	8.51188	+	14.7430i	0.0104312	+	0.0180674i
$817$	54.5058	−	94.4067i	0.0667145	−	0.115553i
$818$	143.977			0.176011
$819$	−32.8985	−	26.5033i	−0.0401691	−	0.0323605i
$820$	132.182	−	128.303i	0.161197	−	0.156468i
$821$	−183.586	+	317.981i	−0.223613	+	0.387309i	−0.955902	−	0.293684i	$-0.905119\pi$
$821$	−183.586	+	317.981i	−0.223613	+	0.387309i	0.732289	+	0.680994i	$0.238452\pi$
$822$	215.140	+	372.633i	0.261727	+	0.453325i
$823$	−353.835	+	204.287i	−0.429933	+	0.248222i	−0.699318	−	0.714811i	$-0.746513\pi$
$823$	−353.835	+	204.287i	−0.429933	+	0.248222i	0.269385	+	0.963032i	$0.413180\pi$
$824$	−393.029	−	226.916i	−0.476977	−	0.275383i
$825$	20.7810	−	697.743i	0.0251891	−	0.845749i
$826$	48.4086	−	310.723i	0.0586061	−	0.376178i
$827$			655.960i			0.793181i	0.917996	+	0.396590i	$0.129807\pi$
$827$			655.960i			0.793181i	−0.917996	+	0.396590i	$0.870193\pi$
$828$	−134.361	−	77.5734i	−0.162272	−	0.0936877i
$829$	634.890	−	366.554i	0.765850	−	0.442164i	−0.0655421	−	0.997850i	$-0.520878\pi$
$829$	634.890	−	366.554i	0.765850	−	0.442164i	0.831392	+	0.555686i	$0.187544\pi$
$830$	−600.442	−	170.508i	−0.723424	−	0.205431i
$831$	−124.378	−	71.8095i	−0.149672	−	0.0864134i
$832$	−16.0938			−0.0193435
$833$	−25.6281	−	117.642i	−0.0307660	−	0.141227i
$834$	−466.647			−0.559529
$835$	−762.505	+	192.194i	−0.913180	+	0.230172i
$836$	259.886	−	150.045i	0.310869	−	0.179480i
$837$	192.002	−	110.853i	0.229394	−	0.132440i
$838$	−203.807	+	353.004i	−0.243206	+	0.421246i
$839$			998.770i			1.19043i	0.803567	+	0.595215i	$0.202933\pi$
$839$			998.770i			1.19043i	−0.803567	+	0.595215i	$0.797067\pi$
$840$	−99.0622	−	139.952i	−0.117931	−	0.166610i
$841$	533.246			0.634062
$842$	405.556	+	234.148i	0.481658	+	0.278085i
$843$	−413.281	−	715.823i	−0.490250	−	0.849138i
$844$	−115.978	−	200.880i	−0.137415	−	0.238010i
$845$	−799.751	+	201.582i	−0.946451	+	0.238558i
$846$			272.262i			0.321823i
$847$	−757.060	−	609.892i	−0.893813	−	0.720061i
$848$		−	16.4260i		−	0.0193703i
$849$	−138.990	+	240.738i	−0.163711	+	0.283555i
$850$	−41.1780	−	76.4949i	−0.0484447	−	0.0899940i
$851$	−365.305	−	632.727i	−0.429266	−	0.743510i
$852$	171.381	−	296.840i	0.201151	−	0.348404i
$853$	−600.268			−0.703714			−0.351857	−	0.936054i	$-0.614450\pi$
$853$	−600.268			−0.703714			−0.351857	+	0.936054i	$0.614450\pi$
$854$	−862.500	+	333.587i	−1.00995	+	0.390617i
$855$	100.180	−	97.2409i	0.117170	−	0.113732i
$856$	−290.658	+	503.434i	−0.339553	+	0.588124i
$857$	287.436	+	497.853i	0.335397	+	0.580925i	0.983561	−	0.180576i	$-0.0577961\pi$
$857$	287.436	+	497.853i	0.335397	+	0.580925i	−0.648164	+	0.761501i	$0.724463\pi$
$858$	−68.7957	+	39.7192i	−0.0801814	+	0.0462928i
$859$	−447.571	−	258.405i	−0.521038	−	0.300821i	0.216321	−	0.976322i	$-0.430594\pi$
$859$	−447.571	−	258.405i	−0.521038	−	0.300821i	−0.737359	+	0.675501i	$0.763927\pi$
$860$	−84.0412	+	81.5754i	−0.0977223	+	0.0948551i
$861$	−80.5663	−	208.307i	−0.0935730	−	0.241936i
$862$			64.4130i			0.0747250i
$863$	−400.292	−	231.109i	−0.463838	−	0.267797i	0.249819	−	0.968293i	$-0.419629\pi$
$863$	−400.292	−	231.109i	−0.463838	−	0.267797i	−0.713657	+	0.700496i	$0.752962\pi$
$864$	25.4558	−	14.6969i	0.0294628	−	0.0170103i
$865$	441.746	−	1555.61i	0.510689	−	1.79839i
$866$	−538.134	−	310.692i	−0.621401	−	0.358766i
$867$	−490.105			−0.565288
$868$	−374.744	+	465.170i	−0.431732	+	0.535910i
$869$	−1914.94			−2.20361
$870$	110.968	+	440.253i	0.127550	+	0.506038i
$871$	−186.652	+	107.763i	−0.214296	+	0.123724i
$872$	−98.2124	+	56.7030i	−0.112629	+	0.0650263i
$873$	−121.644	+	210.694i	−0.139341	+	0.241345i
$874$			340.363i			0.389431i
$875$	484.039	+	728.925i	0.553187	+	0.833057i
$876$	191.444			0.218543
$877$	679.369	+	392.234i	0.774651	+	0.447245i	0.834531	−	0.550960i	$-0.185738\pi$
$877$	679.369	+	392.234i	0.774651	+	0.447245i	−0.0598800	+	0.998206i	$0.519072\pi$
$878$	157.787	+	273.294i	0.179711	+	0.311269i
$879$	70.0885	+	121.397i	0.0797366	+	0.138108i
$880$	−312.638	+	78.8021i	−0.355271	+	0.0895479i
$881$		−	909.512i		−	1.03236i	−0.856479	−	0.516181i	$-0.827353\pi$
$881$		−	909.512i		−	1.03236i	0.856479	−	0.516181i	$-0.172647\pi$
$882$	−203.125	+	44.2504i	−0.230301	+	0.0501705i
$883$			993.966i			1.12567i	0.826570	+	0.562834i	$0.190289\pi$
$883$			993.966i			1.12567i	−0.826570	+	0.562834i	$0.809711\pi$
$884$	−4.94314	+	8.56176i	−0.00559178	+	0.00968525i
$885$	−264.642	−	75.1504i	−0.299030	−	0.0849157i
$886$	−171.775	−	297.522i	−0.193877	−	0.335804i
$887$	331.797	−	574.690i	0.374067	−	0.647903i	−0.616120	−	0.787652i	$-0.711296\pi$
$887$	331.797	−	574.690i	0.374067	−	0.647903i	0.990187	+	0.139750i	$0.0446297\pi$
$888$	138.420			0.155879
$889$	−219.385	−	34.1788i	−0.246777	−	0.0384463i
$890$	555.727	+	572.525i	0.624412	+	0.643286i
$891$	72.5437	−	125.649i	0.0814183	−	0.141021i
$892$	−219.848	−	380.788i	−0.246466	−	0.426892i
$893$	517.269	−	298.646i	0.579249	−	0.334429i
$894$	−286.575	−	165.454i	−0.320553	−	0.185071i
$895$	−582.683	−	600.296i	−0.651043	−	0.670721i
$896$	−49.6838	+	61.6726i	−0.0554507	+	0.0688311i
$897$		−	90.0990i		−	0.100445i
$898$	−635.687	−	367.014i	−0.707892	−	0.408701i
$899$	1369.80	−	790.854i	1.52369	−	0.879704i
$900$	−132.079	+	71.0995i	−0.146754	+	0.0789995i
$901$	−8.73852	−	5.04518i	−0.00969869	−	0.00559954i
$902$	−419.970			−0.465598
$903$	51.2241	+	132.442i	0.0567266	+	0.146668i
$904$	57.4916			0.0635969
$905$	−208.934	−	828.921i	−0.230866	−	0.915935i
$906$	254.713	−	147.058i	0.281140	−	0.162316i
$907$	647.717	−	373.960i	0.714131	−	0.412304i	−0.0984576	−	0.995141i	$-0.531391\pi$
$907$	647.717	−	373.960i	0.714131	−	0.412304i	0.812589	+	0.582837i	$0.198058\pi$
$908$	−54.7171	+	94.7728i	−0.0602611	+	0.104375i
$909$			39.5374i			0.0434954i
$910$	41.6219	−	90.4589i	0.0457384	−	0.0994054i
$911$	−709.142			−0.778421			−0.389211	−	0.921149i	$-0.627252\pi$
$911$	−709.142			−0.778421			−0.389211	+	0.921149i	$0.627252\pi$
$912$	−55.8453	−	32.2423i	−0.0612339	−	0.0353534i
$913$	711.514	+	1232.38i	0.779315	+	1.34981i
$914$	−330.045	−	571.655i	−0.361100	−	0.625443i
$915$	197.728	+	784.463i	0.216096	+	0.857337i
$916$		−	391.145i		−	0.427014i
$917$	−190.673	+	236.683i	−0.207932	+	0.258106i
$918$		−	18.0564i		−	0.0196693i
$919$	−628.282	+	1088.22i	−0.683658	+	1.18413i	0.290198	+	0.956967i	$0.406279\pi$
$919$	−628.282	+	1088.22i	−0.683658	+	1.18413i	−0.973856	+	0.227165i	$0.927054\pi$
$920$	99.8940	−	351.776i	0.108580	−	0.382365i
$921$	−424.997	−	736.117i	−0.461452	−	0.799258i
$922$	231.996	−	401.829i	0.251623	−	0.435823i
$923$	199.053			0.215659
$924$	−60.1752	+	386.250i	−0.0651247	+	0.418019i
$925$	−706.060	−	21.0287i	−0.763308	−	0.0227337i
$926$	−206.962	+	358.469i	−0.223501	+	0.387116i
$927$	240.680	+	416.871i	0.259634	+	0.449699i
$928$	181.609	−	104.852i	0.195700	−	0.112987i
$929$	−461.207	−	266.278i	−0.496455	−	0.286629i	0.230793	−	0.973003i	$-0.425868\pi$
$929$	−461.207	−	266.278i	−0.496455	−	0.286629i	−0.727249	+	0.686374i	$0.759201\pi$
$930$	363.967	+	374.969i	0.391362	+	0.403192i
$931$	306.880	+	337.378i	0.329625	+	0.362383i
$932$			319.834i			0.343170i
$933$	−423.883	−	244.729i	−0.454323	−	0.262303i
$934$	119.794	−	69.1632i	0.128259	−	0.0740506i
$935$	−54.1034	+	190.525i	−0.0578646	+	0.203770i
$936$	14.7831	+	8.53501i	0.0157939	+	0.00911860i
$937$	−1021.89			−1.09059			−0.545297	−	0.838243i	$-0.683583\pi$
$937$	−1021.89			−1.09059			−0.545297	+	0.838243i	$0.683583\pi$
$938$	−163.263	+	1047.95i	−0.174055	+	1.11721i
$939$	142.618			0.151883
$940$	−622.265	+	156.845i	−0.661984	+	0.166857i
$941$	1093.74	−	631.469i	1.16231	−	0.671061i	0.210455	−	0.977604i	$-0.432505\pi$
$941$	1093.74	−	631.469i	1.16231	−	0.671061i	0.951857	+	0.306542i	$0.0991721\pi$
$942$	−50.2088	+	28.9881i	−0.0533002	+	0.0307729i
$943$	238.165	−	412.514i	0.252561	−	0.437448i
$944$			127.066i			0.134603i
$945$	16.7734	+	181.090i	0.0177496	+	0.191630i
$946$	267.017			0.282259
$947$	−354.270	−	204.538i	−0.374097	−	0.215985i	0.301150	−	0.953577i	$-0.402630\pi$
$947$	−354.270	−	204.538i	−0.374097	−	0.215985i	−0.675247	+	0.737592i	$0.735963\pi$
$948$	205.745	+	356.360i	0.217030	+	0.375907i
$949$	55.5889	+	96.2829i	0.0585763	+	0.101457i
$950$	279.960	+	172.947i	0.294695	+	0.182049i
$951$		−	421.389i		−	0.443101i
$952$	17.5492	+	45.3739i	0.0184340	+	0.0476617i
$953$			982.653i			1.03111i	0.856855	+	0.515557i	$0.172415\pi$
$953$			982.653i			1.03111i	−0.856855	+	0.515557i	$0.827585\pi$
$954$	−8.71121	+	15.0883i	−0.00913125	+	0.0158158i
$955$	−375.335	+	1321.74i	−0.393021	+	1.38402i
$956$	−457.640	−	792.656i	−0.478703	−	0.829138i
$957$	517.547	−	896.418i	0.540802	−	0.936696i
$958$	−62.8432			−0.0655984
$959$	443.560	+	1146.84i	0.462523	+	1.19587i
$960$	48.2551	+	49.7137i	0.0502657	+	0.0517851i
$961$	429.745	−	744.340i	0.447185	−	0.774547i
$962$	40.1927	+	69.6157i	0.0417803	+	0.0723656i
$963$	533.972	−	308.289i	0.554488	−	0.320134i
$964$	−139.492	−	80.5359i	−0.144701	−	0.0835434i
$965$	−712.569	+	691.663i	−0.738414	+	0.716749i
$966$	−345.267	−	278.149i	−0.357419	−	0.287939i
$967$			682.676i			0.705973i	0.935628	+	0.352986i	$0.114834\pi$
$967$			682.676i			0.705973i	−0.935628	+	0.352986i	$0.885166\pi$
$968$	340.187	+	196.407i	0.351433	+	0.202900i
$969$	−34.3053	+	19.8062i	−0.0354028	+	0.0204398i
$970$	−551.627	−	156.646i	−0.568688	−	0.161491i
$971$	−770.617	−	444.916i	−0.793632	−	0.458204i	0.0476075	−	0.998866i	$-0.484840\pi$
$971$	−770.617	−	444.916i	−0.793632	−	0.458204i	−0.841240	+	0.540662i	$0.818174\pi$
$972$	−31.1769			−0.0320750
$973$	−1317.66	−	205.283i	−1.35422	−	0.210979i
$974$	844.628			0.867175
$975$	−74.1095	−	45.7816i	−0.0760097	−	0.0469554i
$976$	323.600	−	186.830i	0.331557	−	0.191424i
$977$	−43.1756	+	24.9274i	−0.0441920	+	0.0255143i	−0.521933	−	0.852986i	$-0.674789\pi$
$977$	−43.1756	+	24.9274i	−0.0441920	+	0.0255143i	0.477741	+	0.878501i	$0.341456\pi$
$978$	25.6613	−	44.4466i	0.0262385	−	0.0454464i
$979$		−	1819.04i		−	1.85805i
$980$	−218.153	−	438.759i	−0.222605	−	0.447713i
$981$	120.285			0.122615
$982$	516.055	+	297.944i	0.525514	+	0.303406i
$983$	576.066	+	997.775i	0.586028	+	1.01503i	0.994746	+	0.102370i	$0.0326426\pi$
$983$	576.066	+	997.775i	0.586028	+	1.01503i	−0.408718	+	0.912661i	$0.634024\pi$
$984$	45.1223	+	78.1541i	0.0458560	+	0.0794249i
$985$	−410.301	−	1627.82i	−0.416550	−	1.65261i
$986$		−	128.820i		−	0.130649i
$987$	−119.771	+	768.779i	−0.121348	+	0.778905i
$988$		−	37.4484i		−	0.0379032i
$989$	−151.425	+	262.277i	−0.153110	+	0.265194i
$990$	328.968	+	93.4170i	0.332291	+	0.0943606i
$991$	166.565	+	288.499i	0.168078	+	0.291120i	0.937744	−	0.347327i	$-0.112911\pi$
$991$	166.565	+	288.499i	0.168078	+	0.291120i	−0.769666	+	0.638447i	$0.779577\pi$
$992$	120.681	−	209.026i	0.121654	−	0.210711i
$993$	−1006.53			−1.01362
$994$	614.507	−	762.788i	0.618216	−	0.767393i
$995$	1271.48	−	1234.17i	1.27787	−	1.24037i
$996$	152.893	−	264.818i	0.153507	−	0.265882i
$997$	24.8674	+	43.0716i	0.0249422	+	0.0432012i	0.878227	−	0.478244i	$-0.158726\pi$
$997$	24.8674	+	43.0716i	0.0249422	+	0.0432012i	−0.853285	+	0.521445i	$0.825393\pi$
$998$	164.036	−	94.7060i	0.164364	−	0.0948958i
$999$	−127.147	−	73.4084i	−0.127274	−	0.0734819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.3.p.a.19.4	✓	32
3.2	odd	2		630.3.bc.b.19.16		32
5.2	odd	4		1050.3.p.g.901.5		16
5.3	odd	4		1050.3.p.h.901.4		16
5.4	even	2	inner	210.3.p.a.19.15	yes	32
7.2	even	3		1470.3.h.a.979.10		32
7.3	odd	6	inner	210.3.p.a.199.15	yes	32
7.5	odd	6		1470.3.h.a.979.20		32
15.14	odd	2		630.3.bc.b.19.7		32
21.17	even	6		630.3.bc.b.199.7		32
35.3	even	12		1050.3.p.h.451.4		16
35.9	even	6		1470.3.h.a.979.19		32
35.17	even	12		1050.3.p.g.451.5		16
35.19	odd	6		1470.3.h.a.979.9		32
35.24	odd	6	inner	210.3.p.a.199.4	yes	32
105.59	even	6		630.3.bc.b.199.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.3.p.a.19.4	✓	32	1.1	even	1	trivial
210.3.p.a.19.15	yes	32	5.4	even	2	inner
210.3.p.a.199.4	yes	32	35.24	odd	6	inner
210.3.p.a.199.15	yes	32	7.3	odd	6	inner
630.3.bc.b.19.7		32	15.14	odd	2
630.3.bc.b.19.16		32	3.2	odd	2
630.3.bc.b.199.7		32	21.17	even	6
630.3.bc.b.199.16		32	105.59	even	6
1050.3.p.g.451.5		16	35.17	even	12
1050.3.p.g.901.5		16	5.2	odd	4
1050.3.p.h.451.4		16	35.3	even	12
1050.3.p.h.901.4		16	5.3	odd	4
1470.3.h.a.979.9		32	35.19	odd	6
1470.3.h.a.979.10		32	7.2	even	3
1470.3.h.a.979.19		32	35.9	even	6
1470.3.h.a.979.20		32	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	210.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.84836 - 1.22205i) q^{5} +2.44949i q^{6} +(-1.07756 + 6.91657i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.00000 + 1.73205i) q^{4} +(4.84836 - 1.22205i) q^{5} +2.44949i q^{6} +(-1.07756 + 6.91657i) q^{7} -2.82843i q^{8} +(-1.50000 + 2.59808i) q^{9} +(-6.80213 - 1.93160i) q^{10} +(8.06041 + 13.9610i) q^{11} +(1.73205 - 3.00000i) q^{12} +2.01172 q^{13} +(6.21048 - 7.70908i) q^{14} +(-6.03188 - 6.21421i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.22858 + 2.12797i) q^{17} +(3.67423 - 2.12132i) q^{18} +(-8.06058 - 4.65378i) q^{19} +(6.96502 + 7.17555i) q^{20} +(11.3080 - 4.37359i) q^{21} -22.7983i q^{22} +(22.3935 + 12.9289i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(22.0132 - 11.8499i) q^{25} +(-2.46384 - 1.42250i) q^{26} +5.19615 q^{27} +(-13.0574 + 5.05018i) q^{28} +37.0708 q^{29} +(2.99341 + 11.8760i) q^{30} +(36.9509 - 21.3336i) q^{31} +(4.89898 - 2.82843i) q^{32} +(13.9610 - 24.1812i) q^{33} -3.47496i q^{34} +(3.22805 + 34.8508i) q^{35} -6.00000 q^{36} +(-24.4695 - 14.1275i) q^{37} +(6.58143 + 11.3994i) q^{38} +(-1.74220 - 3.01758i) q^{39} +(-3.45649 - 13.7132i) q^{40} -18.4211i q^{41} +(-16.9421 - 2.63946i) q^{42} +11.7122i q^{43} +(-16.1208 + 27.9221i) q^{44} +(-4.09755 + 14.4295i) q^{45} +(-18.2842 - 31.6692i) q^{46} +(-32.0864 + 55.5752i) q^{47} +6.92820 q^{48} +(-46.6777 - 14.9060i) q^{49} +(-35.3397 - 1.05253i) q^{50} +(2.12797 - 3.68575i) q^{51} +(2.01172 + 3.48440i) q^{52} +(-3.55634 + 2.05325i) q^{53} +(-6.36396 - 3.67423i) q^{54} +(56.1409 + 57.8379i) q^{55} +(19.5630 + 3.04779i) q^{56} +16.1212i q^{57} +(-45.4023 - 26.2130i) q^{58} +(27.5105 - 15.8832i) q^{59} +(4.73144 - 16.6617i) q^{60} +(-80.8999 - 46.7076i) q^{61} -60.3405 q^{62} +(-16.3534 - 13.1744i) q^{63} -8.00000 q^{64} +(9.75354 - 2.45843i) q^{65} +(-34.1974 + 19.7439i) q^{66} +(-92.7821 + 53.5678i) q^{67} +(-2.45717 + 4.25594i) q^{68} -44.7871i q^{69} +(20.6897 - 44.9659i) q^{70} +98.9468 q^{71} +(7.34847 + 4.24264i) q^{72} +(27.6325 + 47.8610i) q^{73} +(19.9792 + 34.6051i) q^{74} +(-36.8388 - 22.7574i) q^{75} -18.6151i q^{76} +(-105.248 + 40.7066i) q^{77} +4.92769i q^{78} +(-59.3934 + 102.872i) q^{79} +(-5.46339 + 19.2393i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-13.0257 + 22.5612i) q^{82} +88.2727 q^{83} +(18.8833 + 15.2125i) q^{84} +(8.55711 + 8.81576i) q^{85} +(8.28175 - 14.3444i) q^{86} +(-32.1043 - 55.6062i) q^{87} +(39.4878 - 22.7983i) q^{88} +(-97.7203 - 56.4188i) q^{89} +(15.2216 - 14.7750i) q^{90} +(-2.16774 + 13.9142i) q^{91} +51.7156i q^{92} +(-64.0008 - 36.9509i) q^{93} +(78.5952 - 45.3770i) q^{94} +(-44.7677 - 12.7127i) q^{95} +(-8.48528 - 4.89898i) q^{96} +81.0963 q^{97} +(46.6282 + 51.2622i) q^{98} -48.3625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9	\( 32 q + 32 q^{4} + 12 q^{5} - 48 q^{9} - 24 q^{10} + 48 q^{11} - 16 q^{14} + 24 q^{15} - 64 q^{16} + 48 q^{19} - 24 q^{21} + 72 q^{25} + 96 q^{26} + 176 q^{29} - 24 q^{30} - 48 q^{31} + 68 q^{35} - 192 q^{36} - 72 q^{39} - 48 q^{40} - 96 q^{44} - 36 q^{45} + 32 q^{46} - 272 q^{49} + 192 q^{50} - 24 q^{51} - 64 q^{56} + 744 q^{59} + 24 q^{60} - 672 q^{61} - 256 q^{64} + 172 q^{65} + 320 q^{70} - 144 q^{71} - 416 q^{74} - 144 q^{75} + 128 q^{79} - 48 q^{80} - 144 q^{81} - 96 q^{84} - 736 q^{85} + 304 q^{86} - 48 q^{89} + 976 q^{91} + 528 q^{94} + 236 q^{95} - 288 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 + 12 * q^5 - 48 * q^9 - 24 * q^10 + 48 * q^11 - 16 * q^14 + 24 * q^15 - 64 * q^16 + 48 * q^19 - 24 * q^21 + 72 * q^25 + 96 * q^26 + 176 * q^29 - 24 * q^30 - 48 * q^31 + 68 * q^35 - 192 * q^36 - 72 * q^39 - 48 * q^40 - 96 * q^44 - 36 * q^45 + 32 * q^46 - 272 * q^49 + 192 * q^50 - 24 * q^51 - 64 * q^56 + 744 * q^59 + 24 * q^60 - 672 * q^61 - 256 * q^64 + 172 * q^65 + 320 * q^70 - 144 * q^71 - 416 * q^74 - 144 * q^75 + 128 * q^79 - 48 * q^80 - 144 * q^81 - 96 * q^84 - 736 * q^85 + 304 * q^86 - 48 * q^89 + 976 * q^91 + 528 * q^94 + 236 * q^95 - 288 * q^99

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