LMFDB - Embedded newform 70.3.h.a.59.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [70,3,Mod(19,70)] 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("70.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(70, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	70.h (of order $6$, degree $2$, 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:	$1.90736185052$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 42x^{14} + 1322x^{12} + 17616x^{10} + 175407x^{8} + 205392x^{6} + 203018x^{4} + 23226x^{2} + 2401 $ x^16 + 42x^14 + 1322x^12 + 17616x^10 + 175407x^8 + 205392x^6 + 203018x^4 + 23226*x^2 + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.2
Root			$-0.518845 + 0.898665i$ of defining polynomial
Character	$\chi$	$=$	70.59
Dual form			70.3.h.a.19.2

$q$-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} +(-0.518845 + 0.898665i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.98086 + 4.59088i) q^{5} -1.46751i q^{6} +(-6.67941 + 2.09417i) q^{7} +2.82843i q^{8} +(3.96160 + 6.86169i) q^{9} +(-5.67229 - 4.22198i) q^{10} +(-6.23704 + 10.8029i) q^{11} +(1.03769 + 1.79733i) q^{12} +0.748223 q^{13} +(6.69977 - 7.28787i) q^{14} +(-5.15342 - 0.601827i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(5.77534 - 10.0032i) q^{17} +(-9.70390 - 5.60255i) q^{18} +(13.0948 - 7.56027i) q^{19} +(9.93250 + 1.15994i) q^{20} +(1.58362 - 7.08910i) q^{21} -17.6410i q^{22} +(31.4481 - 18.1566i) q^{23} +(-2.54181 - 1.46751i) q^{24} +(-17.1524 + 18.1878i) q^{25} +(-0.916382 + 0.529074i) q^{26} -17.5610 q^{27} +(-3.05220 + 13.6632i) q^{28} +50.5846 q^{29} +(6.73718 - 2.90694i) q^{30} +(-40.4989 - 23.3820i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-6.47211 - 11.2100i) q^{33} +16.3351i q^{34} +(-22.8450 - 26.5161i) q^{35} +15.8464 q^{36} +(-10.1657 + 5.86915i) q^{37} +(-10.6918 + 18.5188i) q^{38} +(-0.388211 + 0.672402i) q^{39} +(-12.9850 + 5.60271i) q^{40} +12.7397i q^{41} +(3.07322 + 9.80212i) q^{42} +26.2604i q^{43} +(12.4741 + 21.6057i) q^{44} +(-23.6539 + 31.7793i) q^{45} +(-25.6773 + 44.4743i) q^{46} +(20.2244 + 35.0296i) q^{47} +4.15076 q^{48} +(40.2289 - 27.9756i) q^{49} +(8.14664 - 34.4040i) q^{50} +(5.99301 + 10.3802i) q^{51} +(0.748223 - 1.29596i) q^{52} +(22.8390 + 13.1861i) q^{53} +(21.5078 - 12.4175i) q^{54} +(-61.9494 - 7.23458i) q^{55} +(-5.92320 - 18.8922i) q^{56} +15.6904i q^{57} +(-61.9532 + 35.7687i) q^{58} +(-68.4898 - 39.5426i) q^{59} +(-6.19582 + 8.32416i) q^{60} +(45.2611 - 26.1315i) q^{61} +66.1344 q^{62} +(-40.8307 - 37.5358i) q^{63} -8.00000 q^{64} +(1.48212 + 3.43500i) q^{65} +(15.8534 + 9.15294i) q^{66} +(30.0519 + 17.3504i) q^{67} +(-11.5507 - 20.0064i) q^{68} +37.6817i q^{69} +(46.7291 + 16.3216i) q^{70} +14.6636 q^{71} +(-19.4078 + 11.2051i) q^{72} +(50.5830 - 87.6124i) q^{73} +(8.30023 - 14.3764i) q^{74} +(-7.44528 - 24.8509i) q^{75} -30.2411i q^{76} +(19.0367 - 85.2182i) q^{77} -1.09803i q^{78} +(17.8625 + 30.9387i) q^{79} +(11.9416 - 16.0437i) q^{80} +(-26.5430 + 45.9738i) q^{81} +(-9.00833 - 15.6029i) q^{82} +80.8664 q^{83} +(-10.6951 - 9.83200i) q^{84} +(57.3636 + 6.69903i) q^{85} +(-18.5689 - 32.1623i) q^{86} +(-26.2455 + 45.4586i) q^{87} +(-30.5551 - 17.6410i) q^{88} +(-117.103 + 67.6093i) q^{89} +(6.49861 - 55.6473i) q^{90} +(-4.99769 + 1.56690i) q^{91} -72.6263i q^{92} +(42.0252 - 24.2633i) q^{93} +(-49.5394 - 28.6016i) q^{94} +(60.6472 + 45.1407i) q^{95} +(-5.08362 + 2.93503i) q^{96} -91.4185 q^{97} +(-29.4884 + 62.7091i) q^{98} -98.8347 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{4} - 6 q^{5} - 12 q^{9} + 24 q^{10} - 12 q^{11} + 32 q^{14} - 28 q^{15} - 32 q^{16} - 12 q^{19} - 8 q^{21} - 24 q^{24} - 42 q^{25} - 48 q^{26} - 136 q^{29} + 32 q^{30} + 84 q^{31} - 190 q^{35}+ \cdots + 176 q^{99}+O(q^{100}) $ 16 * q + 16 * q^4 - 6 * q^5 - 12 * q^9 + 24 * q^10 - 12 * q^11 + 32 * q^14 - 28 * q^15 - 32 * q^16 - 12 * q^19 - 8 * q^21 - 24 * q^24 - 42 * q^25 - 48 * q^26 - 136 * q^29 + 32 * q^30 + 84 * q^31 - 190 * q^35 - 48 * q^36 + 312 * q^39 + 48 * q^40 + 24 * q^44 + 384 * q^45 - 68 * q^46 + 296 * q^49 - 96 * q^50 - 76 * q^51 - 108 * q^54 + 56 * q^56 - 372 * q^59 - 28 * q^60 + 348 * q^61 - 128 * q^64 - 104 * q^65 + 480 * q^66 - 296 * q^70 - 384 * q^71 + 208 * q^74 - 150 * q^75 + 148 * q^79 + 24 * q^80 - 140 * q^81 + 256 * q^84 + 580 * q^85 - 188 * q^86 - 912 * q^89 - 616 * q^91 - 600 * q^94 - 310 * q^95 - 48 * q^96 + 176 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$2$	−1.22474	+	0.707107i	−0.612372	+	0.353553i
$3$	−0.518845	+	0.898665i	−0.172948	+	0.299555i	−0.939449	−	0.342688i	$-0.888663\pi$
$3$	−0.518845	+	0.898665i	−0.172948	+	0.299555i	0.766501	+	0.642243i	$0.221996\pi$
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$	1.98086	+	4.59088i	0.396171	+	0.918177i
$5$	1.98086	+	4.59088i	0.396171	+	0.918177i
$6$		−	1.46751i		−	0.244586i
$7$	−6.67941	+	2.09417i	−0.954201	+	0.299167i
$7$	−6.67941	+	2.09417i	−0.954201	+	0.299167i
$8$			2.82843i			0.353553i
$9$	3.96160	+	6.86169i	0.440178	+	0.762410i
$10$	−5.67229	−	4.22198i	−0.567229	−	0.422198i
$11$	−6.23704	+	10.8029i	−0.567004	+	0.982079i	0.429856	+	0.902897i	$0.358564\pi$
$11$	−6.23704	+	10.8029i	−0.567004	+	0.982079i	−0.996860	+	0.0791820i	$0.974769\pi$
$12$	1.03769	+	1.79733i	0.0864741	+	0.149778i
$13$	0.748223			0.0575556			0.0287778	−	0.999586i	$-0.490838\pi$
$13$	0.748223			0.0575556			0.0287778	+	0.999586i	$0.490838\pi$
$14$	6.69977	−	7.28787i	0.478555	−	0.520562i
$15$	−5.15342	−	0.601827i	−0.343562	−	0.0401218i
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	5.77534	−	10.0032i	0.339726	−	0.588422i	−0.644655	−	0.764473i	$-0.722999\pi$
$17$	5.77534	−	10.0032i	0.339726	−	0.588422i	0.984381	+	0.176051i	$0.0563324\pi$
$18$	−9.70390	−	5.60255i	−0.539106	−	0.311253i
$19$	13.0948	−	7.56027i	0.689198	−	0.397909i	−0.114113	−	0.993468i	$-0.536403\pi$
$19$	13.0948	−	7.56027i	0.689198	−	0.397909i	0.803312	+	0.595559i	$0.203069\pi$
$20$	9.93250	+	1.15994i	0.496625	+	0.0579969i
$21$	1.58362	−	7.08910i	0.0754104	−	0.337576i
$22$		−	17.6410i		−	0.801864i
$23$	31.4481	−	18.1566i	1.36731	−	0.789416i	0.376725	−	0.926325i	$-0.377050\pi$
$23$	31.4481	−	18.1566i	1.36731	−	0.789416i	0.990584	+	0.136909i	$0.0437169\pi$
$24$	−2.54181	−	1.46751i	−0.105909	−	0.0611464i
$25$	−17.1524	+	18.1878i	−0.686096	+	0.727511i
$26$	−0.916382	+	0.529074i	−0.0352455	+	0.0203490i
$27$	−17.5610			−0.650408
$28$	−3.05220	+	13.6632i	−0.109007	+	0.487973i
$29$	50.5846			1.74430			0.872148	−	0.489243i	$-0.162727\pi$
$29$	50.5846			1.74430			0.872148	+	0.489243i	$0.162727\pi$
$30$	6.73718	−	2.90694i	0.224573	−	0.0968978i
$31$	−40.4989	−	23.3820i	−1.30642	−	0.754259i	−0.324919	−	0.945742i	$-0.605337\pi$
$31$	−40.4989	−	23.3820i	−1.30642	−	0.754259i	−0.981496	+	0.191483i	$0.938670\pi$
$32$	4.89898	+	2.82843i	0.153093	+	0.0883883i
$33$	−6.47211	−	11.2100i	−0.196125	−	0.339698i
$34$			16.3351i			0.480445i
$35$	−22.8450	−	26.5161i	−0.652715	−	0.757603i
$36$	15.8464			0.440178
$37$	−10.1657	+	5.86915i	−0.274748	+	0.158626i	−0.631043	−	0.775748i	$-0.717373\pi$
$37$	−10.1657	+	5.86915i	−0.274748	+	0.158626i	0.356296	+	0.934373i	$0.384040\pi$
$38$	−10.6918	+	18.5188i	−0.281364	+	0.487337i
$39$	−0.388211	+	0.672402i	−0.00995414	+	0.0172411i
$40$	−12.9850	+	5.60271i	−0.324624	+	0.140068i
$41$			12.7397i			0.310724i	0.987858	+	0.155362i	$0.0496545\pi$
$41$			12.7397i			0.310724i	−0.987858	+	0.155362i	$0.950346\pi$
$42$	3.07322	+	9.80212i	0.0731719	+	0.233384i
$43$			26.2604i			0.610706i	0.952239	+	0.305353i	$0.0987745\pi$
$43$			26.2604i			0.610706i	−0.952239	+	0.305353i	$0.901226\pi$
$44$	12.4741	+	21.6057i	0.283502	+	0.491040i
$45$	−23.6539	+	31.7793i	−0.525641	+	0.706206i
$46$	−25.6773	+	44.4743i	−0.558201	+	0.966833i
$47$	20.2244	+	35.0296i	0.430305	+	0.745311i	0.996899	−	0.0786862i	$-0.0250725\pi$
$47$	20.2244	+	35.0296i	0.430305	+	0.745311i	−0.566594	+	0.823997i	$0.691739\pi$
$48$	4.15076			0.0864741
$49$	40.2289	−	27.9756i	0.820998	−	0.570930i
$50$	8.14664	−	34.4040i	0.162933	−	0.688079i
$51$	5.99301	+	10.3802i	0.117510	+	0.203533i
$52$	0.748223	−	1.29596i	0.0143889	−	0.0249223i
$53$	22.8390	+	13.1861i	0.430924	+	0.248794i	0.699740	−	0.714398i	$-0.253299\pi$
$53$	22.8390	+	13.1861i	0.430924	+	0.248794i	−0.268816	+	0.963191i	$0.586632\pi$
$54$	21.5078	−	12.4175i	0.398292	−	0.229954i
$55$	−61.9494	−	7.23458i	−1.12635	−	0.131538i
$56$	−5.92320	−	18.8922i	−0.105771	−	0.337361i
$57$			15.6904i			0.275270i
$58$	−61.9532	+	35.7687i	−1.06816	+	0.616702i
$59$	−68.4898	−	39.5426i	−1.16084	−	0.670214i	−0.209338	−	0.977843i	$-0.567131\pi$
$59$	−68.4898	−	39.5426i	−1.16084	−	0.670214i	−0.951506	+	0.307630i	$0.900464\pi$
$60$	−6.19582	+	8.32416i	−0.103264	+	0.138736i
$61$	45.2611	−	26.1315i	0.741985	−	0.428385i	−0.0808056	−	0.996730i	$-0.525749\pi$
$61$	45.2611	−	26.1315i	0.741985	−	0.428385i	0.822791	+	0.568345i	$0.192416\pi$
$62$	66.1344			1.06668
$63$	−40.8307	−	37.5358i	−0.648106	−	0.595806i
$64$	−8.00000			−0.125000
$65$	1.48212	+	3.43500i	0.0228019	+	0.0528462i
$66$	15.8534	+	9.15294i	0.240202	+	0.138681i
$67$	30.0519	+	17.3504i	0.448535	+	0.258962i	0.707211	−	0.707002i	$-0.249953\pi$
$67$	30.0519	+	17.3504i	0.448535	+	0.258962i	−0.258676	+	0.965964i	$0.583286\pi$
$68$	−11.5507	−	20.0064i	−0.169863	−	0.294211i
$69$			37.6817i			0.546112i
$70$	46.7291	+	16.3216i	0.667558	+	0.233166i
$71$	14.6636			0.206530			0.103265	−	0.994654i	$-0.467071\pi$
$71$	14.6636			0.206530			0.103265	+	0.994654i	$0.467071\pi$
$72$	−19.4078	+	11.2051i	−0.269553	+	0.155626i
$73$	50.5830	−	87.6124i	0.692918	−	1.20017i	−0.277959	−	0.960593i	$-0.589658\pi$
$73$	50.5830	−	87.6124i	0.692918	−	1.20017i	0.970877	−	0.239577i	$-0.0770086\pi$
$74$	8.30023	−	14.3764i	0.112165	−	0.194276i
$75$	−7.44528	−	24.8509i	−0.0992703	−	0.331345i
$76$		−	30.2411i		−	0.397909i
$77$	19.0367	−	85.2182i	0.247230	−	1.10673i
$78$		−	1.09803i		−	0.0140773i
$79$	17.8625	+	30.9387i	0.226107	+	0.391629i	0.956651	−	0.291237i	$-0.0940667\pi$
$79$	17.8625	+	30.9387i	0.226107	+	0.391629i	−0.730544	+	0.682866i	$0.760733\pi$
$80$	11.9416	−	16.0437i	0.149270	−	0.200546i
$81$	−26.5430	+	45.9738i	−0.327691	+	0.567577i
$82$	−9.00833	−	15.6029i	−0.109858	−	0.190279i
$83$	80.8664			0.974293			0.487147	−	0.873320i	$-0.338038\pi$
$83$	80.8664			0.974293			0.487147	+	0.873320i	$0.338038\pi$
$84$	−10.6951	−	9.83200i	−0.127322	−	0.117048i
$85$	57.3636	+	6.69903i	0.674865	+	0.0788122i
$86$	−18.5689	−	32.1623i	−0.215917	−	0.373980i
$87$	−26.2455	+	45.4586i	−0.301673	+	0.522512i
$88$	−30.5551	−	17.6410i	−0.347217	−	0.200466i
$89$	−117.103	+	67.6093i	−1.31576	+	0.759655i	−0.983044	−	0.183372i	$-0.941299\pi$
$89$	−117.103	+	67.6093i	−1.31576	+	0.759655i	−0.332717	+	0.943027i	$0.607965\pi$
$90$	6.49861	−	55.6473i	0.0722068	−	0.618304i
$91$	−4.99769	+	1.56690i	−0.0549196	+	0.0172187i
$92$		−	72.6263i		−	0.789416i
$93$	42.0252	−	24.2633i	0.451884	−	0.260895i
$94$	−49.5394	−	28.6016i	−0.527014	−	0.304272i
$95$	60.6472	+	45.1407i	0.638391	+	0.475166i
$96$	−5.08362	+	2.93503i	−0.0529543	+	0.0305732i
$97$	−91.4185			−0.942459			−0.471230	−	0.882011i	$-0.656190\pi$
$97$	−91.4185			−0.942459			−0.471230	+	0.882011i	$0.656190\pi$
$98$	−29.4884	+	62.7091i	−0.300902	+	0.639889i
$99$	−98.8347			−0.998330
$100$	14.3497	+	47.8966i	0.143497	+	0.478966i
$101$	76.2197	+	44.0054i	0.754650	+	0.435698i	0.827372	−	0.561655i	$-0.189835\pi$
$101$	76.2197	+	44.0054i	0.754650	+	0.435698i	−0.0727215	+	0.997352i	$0.523168\pi$
$102$	−14.6798	−	8.47539i	−0.143920	−	0.0830921i
$103$	−56.2976	−	97.5104i	−0.546579	−	0.946703i	−0.998506	−	0.0546475i	$-0.982596\pi$
$103$	−56.2976	−	97.5104i	−0.546579	−	0.946703i	0.451927	−	0.892055i	$-0.350737\pi$
$104$			2.11629i			0.0203490i
$105$	35.6821	−	6.77228i	0.339830	−	0.0644979i
$106$	−37.2959			−0.351848
$107$	2.48799	−	1.43644i	0.0232523	−	0.0134247i	−0.488329	−	0.872660i	$-0.662393\pi$
$107$	2.48799	−	1.43644i	0.0232523	−	0.0134247i	0.511581	+	0.859235i	$0.329060\pi$
$108$	−17.5610	+	30.4166i	−0.162602	+	0.281635i
$109$	42.6084	−	73.8000i	0.390903	−	0.677064i	−0.601666	−	0.798748i	$-0.705496\pi$
$109$	42.6084	−	73.8000i	0.390903	−	0.677064i	0.992569	+	0.121684i	$0.0388294\pi$
$110$	80.9878	−	34.9443i	0.736253	−	0.317676i
$111$		−	12.1807i		−	0.109736i
$112$	20.6132	+	18.9498i	0.184047	+	0.169195i
$113$			211.525i			1.87190i	0.352132	+	0.935950i	$0.385457\pi$
$113$			211.525i			1.87190i	−0.352132	+	0.935950i	$0.614543\pi$
$114$	−11.0948	−	19.2168i	−0.0973228	−	0.168568i
$115$	145.649	+	108.409i	1.26651	+	0.942686i
$116$	50.5846	−	87.6150i	0.436074	−	0.755302i
$117$	2.96416	+	5.13408i	0.0253347	+	0.0438810i
$118$	111.843			0.947825
$119$	−17.6275	+	78.9098i	−0.148130	+	0.663108i
$120$	1.70223	−	14.5761i	0.0141852	−	0.121467i
$121$	−17.3014	−	29.9668i	−0.142986	−	0.247660i
$122$	−36.9555	+	64.0088i	−0.302914	+	0.524663i
$123$	−11.4487	−	6.60993i	−0.0930791	−	0.0537392i
$124$	−80.9977	+	46.7641i	−0.653208	+	0.377130i
$125$	−117.474	−	42.7173i	−0.939795	−	0.341739i
$126$	76.5490	+	17.1001i	0.607531	+	0.135715i
$127$			52.2434i			0.411366i	0.978619	+	0.205683i	$0.0659415\pi$
$127$			52.2434i			0.411366i	−0.978619	+	0.205683i	$0.934058\pi$
$128$	9.79796	−	5.65685i	0.0765466	−	0.0441942i
$129$	−23.5993	−	13.6250i	−0.182940	−	0.105621i
$130$	−4.24414	−	3.15899i	−0.0326472	−	0.0242999i
$131$	81.3342	−	46.9583i	0.620872	−	0.358461i	−0.156336	−	0.987704i	$-0.549968\pi$
$131$	81.3342	−	46.9583i	0.620872	−	0.358461i	0.777208	+	0.629243i	$0.216635\pi$
$132$	−25.8884			−0.196125
$133$	−71.6328	+	77.9207i	−0.538592	+	0.585870i
$134$	−49.0745			−0.366227
$135$	−34.7859	−	80.6206i	−0.257673	−	0.597190i
$136$	28.2933	+	16.3351i	0.208039	+	0.120111i
$137$	−101.185	−	58.4189i	−0.738573	−	0.426415i	0.0829771	−	0.996551i	$-0.473557\pi$
$137$	−101.185	−	58.4189i	−0.738573	−	0.426415i	−0.821550	+	0.570136i	$0.806891\pi$
$138$	−26.6450	−	46.1505i	−0.193080	−	0.334424i
$139$			67.8796i			0.488342i	0.969732	+	0.244171i	$0.0785159\pi$
$139$			67.8796i			0.488342i	−0.969732	+	0.244171i	$0.921484\pi$
$140$	−68.7723	+	13.0526i	−0.491231	+	0.0932330i
$141$	−41.9732			−0.297682
$142$	−17.9592	+	10.3687i	−0.126473	+	0.0730193i
$143$	−4.66670	+	8.08296i	−0.0326343	+	0.0565242i
$144$	15.8464	−	27.4468i	0.110044	−	0.190603i
$145$	100.201	+	232.228i	0.691040	+	1.60157i
$146$			143.070i			0.979934i
$147$	4.26813	+	50.6673i	0.0290349	+	0.344676i
$148$			23.4766i			0.158626i
$149$	−86.0779	−	149.091i	−0.577704	−	1.00061i	−0.995742	−	0.0921836i	$-0.970615\pi$
$149$	−86.0779	−	149.091i	−0.577704	−	1.00061i	0.418038	−	0.908430i	$-0.362718\pi$
$150$	26.6908	+	25.1714i	0.177939	+	0.167809i
$151$	55.1081	−	95.4500i	0.364954	−	0.632119i	−0.623815	−	0.781572i	$-0.714418\pi$
$151$	55.1081	−	95.4500i	0.364954	−	0.632119i	0.988769	+	0.149453i	$0.0477514\pi$
$152$	21.3837	+	37.0376i	0.140682	+	0.243668i
$153$	91.5184			0.598159
$154$	36.9432	+	117.831i	0.239891	+	0.765140i
$155$	27.1217	−	232.242i	0.174979	−	1.49834i
$156$	0.776423	+	1.34480i	0.00497707	+	0.00862054i
$157$	102.082	−	176.811i	0.650201	−	1.12618i	−0.332873	−	0.942972i	$-0.608018\pi$
$157$	102.082	−	176.811i	0.650201	−	1.12618i	0.983074	−	0.183210i	$-0.0586488\pi$
$158$	−43.7539	−	25.2613i	−0.276924	−	0.159882i
$159$	−23.6997	+	13.6830i	−0.149055	+	0.0860569i
$160$	−3.28080	+	28.0934i	−0.0205050	+	0.175583i
$161$	−172.032	+	187.133i	−1.06852	+	1.16231i
$162$		−	75.0748i		−	0.463425i
$163$	84.7593	−	48.9358i	0.519996	−	0.300220i	−0.216937	−	0.976186i	$-0.569607\pi$
$163$	84.7593	−	48.9358i	0.519996	−	0.300220i	0.736933	+	0.675966i	$0.236273\pi$
$164$	22.0658	+	12.7397i	0.134548	+	0.0776811i
$165$	38.6436	−	51.9181i	0.234203	−	0.314655i
$166$	−99.0407	+	57.1811i	−0.596630	+	0.344465i
$167$	−97.1736			−0.581878			−0.290939	−	0.956742i	$-0.593968\pi$
$167$	−97.1736			−0.581878			−0.290939	+	0.956742i	$0.593968\pi$
$168$	20.0510	+	4.47915i	0.119351	+	0.0266616i
$169$	−168.440			−0.996687
$170$	−74.9927	+	32.3576i	−0.441133	+	0.190339i
$171$	103.752	+	59.9015i	0.606740	+	0.350301i
$172$	45.4843	+	26.2604i	0.264444	+	0.152677i
$173$	−30.9286	−	53.5699i	−0.178778	−	0.309652i	0.762684	−	0.646771i	$-0.223881\pi$
$173$	−30.9286	−	53.5699i	−0.178778	−	0.309652i	−0.941462	+	0.337118i	$0.890548\pi$
$174$		−	74.2336i		−	0.426630i
$175$	76.4797	−	157.403i	0.437027	−	0.899449i
$176$	49.8963			0.283502
$177$	71.0711	−	41.0329i	0.401532	−	0.231824i
$178$	95.6140	−	165.608i	0.537157	−	0.930383i
$179$	112.111	−	194.181i	0.626316	−	1.08481i	−0.361968	−	0.932190i	$-0.617895\pi$
$179$	112.111	−	194.181i	0.626316	−	1.08481i	0.988285	−	0.152622i	$-0.0487715\pi$
$180$	31.3895	+	72.7490i	0.174386	+	0.404161i
$181$		−	329.246i		−	1.81904i	−0.415659	−	0.909520i	$-0.636449\pi$
$181$		−	329.246i		−	1.81904i	0.415659	−	0.909520i	$-0.363551\pi$
$182$	5.01292	−	5.45296i	0.0275435	−	0.0299613i
$183$			54.2327i			0.296354i
$184$	51.3545	+	88.9486i	0.279101	+	0.483416i
$185$	−47.0813	−	35.0434i	−0.254494	−	0.189424i
$186$	−34.3135	+	59.4327i	−0.184481	+	0.319530i
$187$	72.0421	+	124.781i	0.385252	+	0.667275i
$188$	80.8974			0.430305
$189$	117.297	−	36.7757i	0.620620	−	0.194581i
$190$	−106.197	−	12.4019i	−0.558930	−	0.0652730i
$191$	33.1175	+	57.3612i	0.173390	+	0.300320i	0.939603	−	0.342266i	$-0.111195\pi$
$191$	33.1175	+	57.3612i	0.173390	+	0.300320i	−0.766213	+	0.642587i	$0.777861\pi$
$192$	4.15076	−	7.18932i	0.0216185	−	0.0374444i
$193$	−219.500	−	126.728i	−1.13730	−	0.656623i	−0.191543	−	0.981484i	$-0.561349\pi$
$193$	−219.500	−	126.728i	−1.13730	−	0.656623i	−0.945762	+	0.324861i	$0.894682\pi$
$194$	111.964	−	64.6427i	0.577136	−	0.333210i
$195$	−3.85591	−	0.450301i	−0.0197739	−	0.00230924i
$196$	−8.22623	−	97.6541i	−0.0419706	−	0.498235i
$197$		−	191.330i		−	0.971217i	−0.874176	−	0.485608i	$-0.838598\pi$
$197$		−	191.330i		−	0.971217i	0.874176	−	0.485608i	$-0.161402\pi$
$198$	121.047	−	69.8867i	0.611350	−	0.352963i
$199$	195.609	+	112.935i	0.982960	+	0.567512i	0.903162	−	0.429299i	$-0.141239\pi$
$199$	195.609	+	112.935i	0.982960	+	0.567512i	0.0797973	+	0.996811i	$0.474573\pi$
$200$	−51.4428	−	48.5143i	−0.257214	−	0.242572i
$201$	−31.1845	+	18.0044i	−0.155147	+	0.0895740i
$202$	−124.466			−0.616169
$203$	−337.875	+	105.933i	−1.66441	+	0.521835i
$204$	23.9720			0.117510
$205$	−58.4865	+	25.2355i	−0.285300	+	0.123100i
$206$	137.900	+	79.6169i	0.669420	+	0.386490i
$207$	249.170	+	143.858i	1.20372	+	0.694967i
$208$	−1.49645	−	2.59192i	−0.00719445	−	0.0124612i
$209$			188.615i			0.902463i
$210$	−38.9128	+	33.5254i	−0.185299	+	0.159645i
$211$	−186.816			−0.885386			−0.442693	−	0.896673i	$-0.645977\pi$
$211$	−186.816			−0.885386			−0.442693	+	0.896673i	$0.645977\pi$
$212$	45.6779	−	26.3722i	0.215462	−	0.124397i
$213$	−7.60814	+	13.1777i	−0.0357190	+	0.0618670i
$214$	−2.03144	+	3.51855i	−0.00949270	+	0.0164418i
$215$	−120.558	+	52.0180i	−0.560736	+	0.241944i
$216$		−	49.6701i		−	0.229954i
$217$	319.474	+	71.3667i	1.47223	+	0.328879i
$218$			120.515i			0.552821i
$219$	52.4894	+	90.9144i	0.239678	+	0.415134i
$220$	−74.4801	+	100.065i	−0.338546	+	0.454841i
$221$	4.32124	−	7.48461i	0.0195531	−	0.0338670i
$222$	8.61306	+	14.9183i	0.0387976	+	0.0671994i
$223$	194.106			0.870431			0.435215	−	0.900326i	$-0.356672\pi$
$223$	194.106			0.870431			0.435215	+	0.900326i	$0.356672\pi$
$224$	−38.6455	−	8.63293i	−0.172524	−	0.0385399i
$225$	−192.750	−	45.6419i	−0.856666	−	0.202853i
$226$	−149.571	−	259.064i	−0.661817	−	1.14630i
$227$	−175.878	+	304.630i	−0.774795	+	1.34198i	0.160115	+	0.987098i	$0.448814\pi$
$227$	−175.878	+	304.630i	−0.774795	+	1.34198i	−0.934910	+	0.354886i	$0.884520\pi$
$228$	27.1766	+	15.6904i	0.119196	+	0.0688176i
$229$	162.993	−	94.1041i	0.711760	−	0.410935i	−0.0999523	−	0.994992i	$-0.531869\pi$
$229$	162.993	−	94.1041i	0.711760	−	0.410935i	0.811712	+	0.584057i	$0.198536\pi$
$230$	−255.039	−	29.7840i	−1.10887	−	0.129496i
$231$	66.7055	+	61.3226i	0.288768	+	0.265466i
$232$			143.075i			0.616702i
$233$	−272.001	+	157.040i	−1.16739	+	0.673991i	−0.953063	−	0.302772i	$-0.902088\pi$
$233$	−272.001	+	157.040i	−1.16739	+	0.673991i	−0.214324	+	0.976763i	$0.568755\pi$
$234$	−7.26068	−	4.19196i	−0.0310286	−	0.0179143i
$235$	−120.755	+	162.236i	−0.513852	+	0.690367i
$236$	−136.980	+	79.0852i	−0.580422	+	0.335107i
$237$	−37.0714			−0.156419
$238$	−34.2085	−	109.109i	−0.143733	−	0.458441i
$239$	336.269			1.40699			0.703493	−	0.710703i	$-0.251623\pi$
$239$	336.269			1.40699			0.703493	+	0.710703i	$0.251623\pi$
$240$	8.22205	+	19.0556i	0.0342586	+	0.0793985i
$241$	−331.276	−	191.262i	−1.37459	−	0.793619i	−0.383086	−	0.923713i	$-0.625139\pi$
$241$	−331.276	−	191.262i	−1.37459	−	0.793619i	−0.991502	+	0.130094i	$0.958472\pi$
$242$	42.3795	+	24.4678i	0.175122	+	0.101107i
$243$	−106.568	−	184.581i	−0.438551	−	0.759593i
$244$		−	104.526i		−	0.428385i
$245$	208.120	+	129.271i	0.849471	+	0.527635i
$246$	18.6957			0.0759988
$247$	9.79781	−	5.65677i	0.0396672	−	0.0229019i
$248$	66.1344	−	114.548i	0.266671	−	0.461887i
$249$	−41.9571	+	72.6718i	−0.168502	+	0.291855i
$250$	174.082	−	30.7491i	0.696327	−	0.122996i
$251$			302.072i			1.20347i	0.798695	+	0.601736i	$0.205524\pi$
$251$			302.072i			1.20347i	−0.798695	+	0.601736i	$0.794476\pi$
$252$	−105.845	+	33.1850i	−0.420018	+	0.131687i
$253$			452.973i			1.79041i
$254$	−36.9417	−	63.9849i	−0.145440	−	0.251909i
$255$	−35.7830	+	48.0749i	−0.140325	+	0.188529i
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−102.339	−	177.257i	−0.398208	−	0.689717i	0.595297	−	0.803506i	$-0.297034\pi$
$257$	−102.339	−	177.257i	−0.398208	−	0.689717i	−0.993505	+	0.113789i	$0.963701\pi$
$258$	38.5375			0.149370
$259$	55.6096	−	60.4911i	0.214709	−	0.233556i
$260$	7.43173	+	0.867892i	0.0285836	+	0.00333805i
$261$	200.396	+	347.096i	0.767800	+	1.32987i
$262$	−66.4091	+	115.024i	−0.253470	+	0.439023i
$263$	84.3776	+	48.7155i	0.320828	+	0.185230i	0.651761	−	0.758424i	$-0.274030\pi$
$263$	84.3776	+	48.7155i	0.320828	+	0.185230i	−0.330934	+	0.943654i	$0.607364\pi$
$264$	31.7067	−	18.3059i	0.120101	−	0.0693405i
$265$	−15.2950	+	130.971i	−0.0577171	+	0.494229i
$266$	32.6336	−	146.085i	0.122683	−	0.549192i
$267$		−	140.315i		−	0.525524i
$268$	60.1037	−	34.7009i	0.224268	−	0.129481i
$269$	83.6084	+	48.2713i	0.310812	+	0.179447i	0.647290	−	0.762244i	$-0.275902\pi$
$269$	83.6084	+	48.2713i	0.310812	+	0.179447i	−0.336478	+	0.941691i	$0.609236\pi$
$270$	99.6112	+	74.1423i	0.368930	+	0.274601i
$271$	−72.4056	+	41.8034i	−0.267179	+	0.154256i	−0.627605	−	0.778532i	$-0.715965\pi$
$271$	−72.4056	+	41.8034i	−0.267179	+	0.154256i	0.360426	+	0.932788i	$0.382631\pi$
$272$	−46.2027			−0.169863
$273$	1.18490	−	5.30423i	0.00434029	−	0.0194294i
$274$	165.234			0.603043
$275$	−89.4998	−	298.733i	−0.325454	−	1.08630i
$276$	65.2667	+	37.6817i	0.236473	+	0.136528i
$277$	−334.055	−	192.867i	−1.20598	−	0.696271i	−0.244098	−	0.969750i	$-0.578492\pi$
$277$	−334.055	−	192.867i	−1.20598	−	0.696271i	−0.961878	+	0.273480i	$0.911825\pi$
$278$	−47.9981	−	83.1352i	−0.172655	−	0.299047i
$279$		−	370.521i		−	1.32803i
$280$	74.9989	−	64.6155i	0.267853	−	0.230770i
$281$	243.459			0.866402			0.433201	−	0.901297i	$-0.357384\pi$
$281$	243.459			0.866402			0.433201	+	0.901297i	$0.357384\pi$
$282$	51.4064	−	29.6795i	0.182292	−	0.105247i
$283$	51.4153	−	89.0540i	0.181680	−	0.314678i	−0.760773	−	0.649018i	$-0.775180\pi$
$283$	51.4153	−	89.0540i	0.181680	−	0.314678i	0.942453	+	0.334340i	$0.108513\pi$
$284$	14.6636	−	25.3981i	0.0516324	−	0.0894300i
$285$	−72.0329	+	31.0805i	−0.252747	+	0.109054i
$286$		−	13.1994i		−	0.0461518i
$287$	−26.6791	−	85.0936i	−0.0929585	−	0.296494i
$288$			44.8204i			0.155626i
$289$	77.7909	+	134.738i	0.269173	+	0.466221i
$290$	−286.930	−	213.567i	−0.989415	−	0.736438i
$291$	47.4320	−	82.1547i	0.162997	−	0.282318i
$292$	−101.166	−	175.225i	−0.346459	−	0.600085i
$293$	440.610			1.50379			0.751894	−	0.659284i	$-0.229141\pi$
$293$	440.610			1.50379			0.751894	+	0.659284i	$0.229141\pi$
$294$	−41.0546	−	59.0365i	−0.139641	−	0.200804i
$295$	45.8670	−	392.757i	0.155481	−	1.33138i
$296$	−16.6005	−	28.7528i	−0.0560827	−	0.0971380i
$297$	109.529	−	189.709i	0.368784	−	0.638752i
$298$	210.847	+	121.733i	0.707540	+	0.408499i
$299$	23.5302	−	13.5852i	0.0786963	−	0.0454353i
$300$	−50.4883	−	11.9553i	−0.168294	−	0.0398510i
$301$	−54.9936	−	175.404i	−0.182703	−	0.582736i
$302$			155.869i			0.516123i
$303$	−79.0923	+	45.6640i	−0.261031	+	0.150706i
$304$	−52.3791	−	30.2411i	−0.172300	−	0.0994772i
$305$	209.622	+	156.026i	0.687286	+	0.511559i
$306$	−112.087	+	64.7133i	−0.366296	+	0.211481i
$307$	247.192			0.805185			0.402592	−	0.915379i	$-0.368109\pi$
$307$	247.192			0.805185			0.402592	+	0.915379i	$0.368109\pi$
$308$	−128.566	−	118.191i	−0.417420	−	0.383736i
$309$	116.839			0.378119
$310$	131.003	+	303.615i	0.422589	+	0.979404i
$311$	−369.117	−	213.110i	−1.18687	−	0.685240i	−0.229276	−	0.973361i	$-0.573636\pi$
$311$	−369.117	−	213.110i	−1.18687	−	0.685240i	−0.957594	+	0.288121i	$0.906969\pi$
$312$	−1.90184	−	1.09803i	−0.00609564	−	0.00351932i
$313$	−66.9870	−	116.025i	−0.214016	−	0.370686i	0.738952	−	0.673758i	$-0.235321\pi$
$313$	−66.9870	−	116.025i	−0.214016	−	0.370686i	−0.952968	+	0.303072i	$0.901988\pi$
$314$			288.730i			0.919523i
$315$	91.4426	−	261.802i	0.290294	−	0.831117i
$316$	71.4499			0.226107
$317$	−278.831	+	160.983i	−0.879593	+	0.507833i	−0.870524	−	0.492126i	$-0.836220\pi$
$317$	−278.831	+	160.983i	−0.879593	+	0.507833i	−0.00906850	+	0.999959i	$0.502887\pi$
$318$	19.3508	−	33.5165i	0.0608514	−	0.105398i
$319$	−315.498	+	546.459i	−0.989022	+	1.71304i
$320$	−15.8469	−	36.7271i	−0.0495214	−	0.114772i
$321$			2.98116i			0.00928711i
$322$	78.3721	−	350.834i	0.243392	−	1.08955i
$323$		−	174.652i		−	0.540720i
$324$	53.0859	+	91.9475i	0.163845	+	0.283789i
$325$	−12.8338	+	13.6085i	−0.0394887	+	0.0418723i
$326$	−69.2057	+	119.868i	−0.212287	+	0.367693i
$327$	44.2143	+	76.5814i	0.135212	+	0.234194i
$328$	−36.0333			−0.109858
$329$	−208.445	−	191.624i	−0.633570	−	0.582443i
$330$	−10.6168	+	90.9116i	−0.0321723	+	0.275490i
$331$	117.402	+	203.347i	0.354690	+	0.614342i	0.987065	−	0.160321i	$-0.0512530\pi$
$331$	117.402	+	203.347i	0.354690	+	0.614342i	−0.632375	+	0.774663i	$0.717920\pi$
$332$	80.8664	−	140.065i	0.243573	−	0.421881i
$333$	−80.5446	−	46.5025i	−0.241876	−	0.139647i
$334$	119.013	−	68.7121i	0.356326	−	0.205725i
$335$	−20.1254	+	172.333i	−0.0600759	+	0.514428i
$336$	−27.7246	+	8.69238i	−0.0825136	+	0.0258702i
$337$		−	217.706i		−	0.646012i	−0.946397	−	0.323006i	$-0.895307\pi$
$337$		−	217.706i		−	0.646012i	0.946397	−	0.323006i	$-0.104693\pi$
$338$	206.296	−	119.105i	0.610344	−	0.352382i
$339$	−190.090	−	109.748i	−0.560737	−	0.323742i
$340$	68.9666	−	92.6576i	0.202843	−	0.272522i
$341$	505.186	−	291.669i	1.48148	−	0.855335i
$342$	−169.427			−0.495401
$343$	−210.120	+	271.106i	−0.612594	+	0.790398i
$344$	−74.2755			−0.215917
$345$	−172.992	+	74.6421i	−0.501427	+	0.216354i
$346$	75.7593	+	43.7396i	0.218957	+	0.126415i
$347$	161.281	+	93.1157i	0.464787	+	0.268345i	0.714055	−	0.700090i	$-0.246857\pi$
$347$	161.281	+	93.1157i	0.464787	+	0.268345i	−0.249268	+	0.968435i	$0.580190\pi$
$348$	52.4911	+	90.9172i	0.150836	+	0.261256i
$349$		−	81.7368i		−	0.234203i	−0.993120	−	0.117101i	$-0.962640\pi$
$349$		−	81.7368i		−	0.234203i	0.993120	−	0.117101i	$-0.0373603\pi$
$350$	17.6330	+	246.858i	0.0503800	+	0.705310i
$351$	−13.1396			−0.0374347
$352$	−61.1103	+	35.2820i	−0.173609	+	0.100233i
$353$	53.9682	−	93.4757i	0.152884	−	0.264804i	−0.779402	−	0.626524i	$-0.784477\pi$
$353$	53.9682	−	93.4757i	0.152884	−	0.264804i	0.932287	+	0.361720i	$0.117810\pi$
$354$	−58.0293	+	100.510i	−0.163925	+	0.283926i
$355$	29.0465	+	67.3189i	0.0818212	+	0.189631i
$356$			270.437i			0.759655i
$357$	−61.7676	−	56.7832i	−0.173018	−	0.159056i
$358$			317.097i			0.885745i
$359$	−301.930	−	522.957i	−0.841029	−	1.45671i	−0.889025	−	0.457858i	$-0.848617\pi$
$359$	−301.930	−	522.957i	−0.841029	−	1.45671i	0.0479959	−	0.998848i	$-0.484717\pi$
$360$	−89.8854	−	66.9032i	−0.249682	−	0.185842i
$361$	−66.1847	+	114.635i	−0.183337	+	0.317549i
$362$	232.812	+	403.243i	0.643128	+	1.11393i
$363$	35.9069			0.0989169
$364$	−2.28373	+	10.2232i	−0.00627398	+	0.0280856i
$365$	502.416	+	58.6732i	1.37648	+	0.160748i
$366$	−38.3483	−	66.4213i	−0.104777	−	0.181479i
$367$	−271.765	+	470.710i	−0.740503	+	1.28259i	0.211763	+	0.977321i	$0.432080\pi$
$367$	−271.765	+	470.710i	−0.740503	+	1.28259i	−0.952266	+	0.305268i	$0.901254\pi$
$368$	−125.792	−	72.6263i	−0.341827	−	0.197354i
$369$	−87.4159	+	50.4696i	−0.236900	+	0.136774i
$370$	82.4421	+	9.62775i	0.222816	+	0.0260210i
$371$	−180.165	−	40.2466i	−0.485619	−	0.108481i
$372$		−	97.0531i		−	0.260895i
$373$	72.1316	−	41.6452i	0.193382	−	0.111649i	−0.400183	−	0.916435i	$-0.631053\pi$
$373$	72.1316	−	41.6452i	0.193382	−	0.111649i	0.593565	+	0.804786i	$0.297720\pi$
$374$	−176.466	−	101.883i	−0.471835	−	0.272414i
$375$	99.3395	−	83.4065i	0.264905	−	0.222417i
$376$	−99.0787	+	57.2031i	−0.263507	+	0.152136i
$377$	37.8485			0.100394
$378$	−117.655	+	127.983i	−0.311256	+	0.338578i
$379$	−30.4409			−0.0803189			−0.0401595	−	0.999193i	$-0.512787\pi$
$379$	−30.4409			−0.0803189			−0.0401595	+	0.999193i	$0.512787\pi$
$380$	138.833	−	59.9032i	0.365351	−	0.157640i
$381$	−46.9493	−	27.1062i	−0.123227	−	0.0711449i
$382$	−81.1209	−	46.8352i	−0.212358	−	0.122605i
$383$	−147.759	−	255.925i	−0.385793	−	0.668213i	0.606086	−	0.795399i	$-0.292739\pi$
$383$	−147.759	−	255.925i	−0.385793	−	0.668213i	−0.991879	+	0.127186i	$0.959405\pi$
$384$			11.7401i			0.0305732i
$385$	428.936	−	81.4098i	1.11412	−	0.211454i
$386$	358.442			0.928605
$387$	−180.191	+	104.033i	−0.465609	+	0.268819i
$388$	−91.4185	+	158.342i	−0.235615	+	0.408097i
$389$	−214.388	+	371.330i	−0.551125	+	0.954577i	0.447069	+	0.894500i	$0.352468\pi$
$389$	−214.388	+	371.330i	−0.551125	+	0.954577i	−0.998194	+	0.0600771i	$0.980865\pi$
$390$	5.04092	−	2.17504i	0.0129254	−	0.00557702i
$391$		−	419.441i		−	1.07274i
$392$	79.1269	+	113.785i	0.201854	+	0.290267i
$393$			97.4563i			0.247980i
$394$	135.291	+	234.330i	0.343377	+	0.594746i
$395$	−106.653	+	143.290i	−0.270007	+	0.362759i
$396$	−98.8347	+	171.187i	−0.249582	+	0.432290i
$397$	160.392	+	277.807i	0.404009	+	0.699765i	0.994206	−	0.107495i	$-0.0342830\pi$
$397$	160.392	+	277.807i	0.404009	+	0.699765i	−0.590196	+	0.807260i	$0.700950\pi$
$398$	−319.428			−0.802583
$399$	−32.8584	−	104.803i	−0.0823518	−	0.262663i
$400$	97.3091	+	23.0422i	0.243273	+	0.0576054i
$401$	118.854	+	205.861i	0.296394	+	0.513370i	0.975308	−	0.220848i	$-0.0708824\pi$
$401$	118.854	+	205.861i	0.296394	+	0.513370i	−0.678914	+	0.734218i	$0.737549\pi$
$402$	25.4620	−	44.1015i	0.0633384	−	0.109705i
$403$	−30.3022	−	17.4950i	−0.0751915	−	0.0434119i
$404$	152.439	−	88.0109i	0.377325	−	0.217849i
$405$	−263.638	−	30.7882i	−0.650958	−	0.0760202i
$406$	338.905	−	368.654i	0.834741	−	0.908015i
$407$		−	146.425i		−	0.359765i
$408$	−29.3596	+	16.9508i	−0.0719598	+	0.0415460i
$409$	171.560	+	99.0500i	0.419461	+	0.242176i	0.694847	−	0.719158i	$-0.255472\pi$
$409$	171.560	+	99.0500i	0.419461	+	0.242176i	−0.275386	+	0.961334i	$0.588806\pi$
$410$	53.7868	−	72.2633i	0.131187	−	0.176252i
$411$	104.998	−	60.6207i	0.255470	−	0.147496i
$412$	−225.191			−0.546579
$413$	540.280	+	120.692i	1.30818	+	0.292232i
$414$	−406.892			−0.982831
$415$	160.185	+	371.248i	0.385987	+	0.894573i
$416$	3.66553	+	2.11629i	0.00881137	+	0.00508725i
$417$	−61.0010	−	35.2189i	−0.146285	−	0.0844579i
$418$	−133.371	−	231.005i	−0.319069	−	0.552644i
$419$		−	56.6448i		−	0.135190i	−0.997713	−	0.0675952i	$-0.978467\pi$
$419$		−	56.6448i		−	0.135190i	0.997713	−	0.0675952i	$-0.0215326\pi$
$420$	23.9522	−	68.5755i	0.0570290	−	0.163275i
$421$	−220.350			−0.523396			−0.261698	−	0.965150i	$-0.584282\pi$
$421$	−220.350			−0.523396			−0.261698	+	0.965150i	$0.584282\pi$
$422$	228.802	−	132.099i	0.542186	−	0.313031i
$423$	−160.242	+	277.547i	−0.378822	+	0.656139i
$424$	−37.2959	+	64.5983i	−0.0879619	+	0.152355i
$425$	82.8745	+	276.619i	0.194999	+	0.650869i
$426$		−	21.5191i		−	0.0505142i
$427$	−247.593	+	269.327i	−0.579844	+	0.630743i
$428$		−	5.74577i		−	0.0134247i
$429$	−4.84258	−	8.38760i	−0.0112881	−	0.0195515i
$430$	110.871	−	148.956i	0.257839	−	0.346410i
$431$	136.661	−	236.704i	0.317079	−	0.549197i	−0.662798	−	0.748798i	$-0.730631\pi$
$431$	136.661	−	236.704i	0.317079	−	0.549197i	0.979877	+	0.199601i	$0.0639646\pi$
$432$	35.1220	+	60.8332i	0.0813010	+	0.140818i
$433$	−201.926			−0.466342			−0.233171	−	0.972436i	$-0.574910\pi$
$433$	−201.926			−0.466342			−0.233171	+	0.972436i	$0.574910\pi$
$434$	−441.738	+	138.496i	−1.01783	+	0.319116i
$435$	−260.684	−	30.4432i	−0.599273	−	0.0699843i
$436$	−85.2169	−	147.600i	−0.195452	−	0.338532i
$437$	274.537	−	475.512i	0.628231	−	1.08813i
$438$	−128.572	−	74.2313i	−0.293544	−	0.169478i
$439$	−527.183	+	304.370i	−1.20087	+	0.693325i	−0.960749	−	0.277418i	$-0.910521\pi$
$439$	−527.183	+	304.370i	−1.20087	+	0.693325i	−0.240124	+	0.970742i	$0.577188\pi$
$440$	20.4625	−	175.219i	0.0465056	−	0.398226i
$441$	351.331	+	165.210i	0.796669	+	0.374627i
$442$			12.2223i			0.0276523i
$443$	674.954	−	389.685i	1.52360	−	0.879650i	0.523988	−	0.851726i	$-0.324444\pi$
$443$	674.954	−	389.685i	1.52360	−	0.879650i	0.999610	−	0.0279237i	$-0.00888954\pi$
$444$	−21.0976	−	12.1807i	−0.0475171	−	0.0274340i
$445$	−542.350	−	403.680i	−1.21876	−	0.907147i
$446$	−237.730	+	137.254i	−0.533028	+	0.307744i
$447$	178.644			0.399652
$448$	53.4352	−	16.7533i	0.119275	−	0.0373959i
$449$	−8.03323			−0.0178914			−0.00894569	−	0.999960i	$-0.502848\pi$
$449$	−8.03323			−0.0178914			−0.00894569	+	0.999960i	$0.502848\pi$
$450$	268.343	−	80.3950i	0.596318	−	0.178656i
$451$	−137.625	−	79.4580i	−0.305156	−	0.176182i
$452$	366.372	+	211.525i	0.810557	+	0.467975i
$453$	57.1850	+	99.0474i	0.126236	+	0.218648i
$454$		−	497.459i		−	1.09573i
$455$	−17.0932	−	19.8400i	−0.0375674	−	0.0436043i
$456$	−44.3792			−0.0973228
$457$	432.413	−	249.654i	0.946200	−	0.546289i	0.0543016	−	0.998525i	$-0.482707\pi$
$457$	432.413	−	249.654i	0.946200	−	0.546289i	0.891898	+	0.452236i	$0.149373\pi$
$458$	−133.083	+	230.507i	−0.290575	+	0.503290i
$459$	−101.421	+	175.666i	−0.220960	+	0.382715i
$460$	333.419	−	143.862i	0.724823	−	0.312744i
$461$			690.386i			1.49758i	0.662805	+	0.748792i	$0.269366\pi$
$461$			690.386i			1.49758i	−0.662805	+	0.748792i	$0.730634\pi$
$462$	−125.059	−	27.9366i	−0.270690	−	0.0604689i
$463$		−	615.045i		−	1.32839i	−0.747559	−	0.664195i	$-0.768774\pi$
$463$		−	615.045i		−	1.32839i	0.747559	−	0.664195i	$-0.231226\pi$
$464$	−101.169	−	175.230i	−0.218037	−	0.377651i
$465$	194.636	+	144.871i	0.418572	+	0.311550i
$466$	222.088	−	384.668i	0.476584	−	0.825467i
$467$	−23.9340	−	41.4549i	−0.0512506	−	0.0887686i	0.839262	−	0.543727i	$-0.182987\pi$
$467$	−23.9340	−	41.4549i	−0.0512506	−	0.0887686i	−0.890513	+	0.454959i	$0.849654\pi$
$468$	11.8566			0.0253347
$469$	−237.063	−	52.9570i	−0.505465	−	0.112915i
$470$	33.1760	−	284.085i	0.0705873	−	0.604436i
$471$	105.929	+	183.474i	0.224902	+	0.389542i
$472$	111.843	−	193.718i	0.236956	−	0.410420i
$473$	−283.687	−	163.787i	−0.599762	−	0.346273i
$474$	45.4030	−	26.2134i	0.0957869	−	0.0553026i
$475$	−87.1025	+	367.841i	−0.183374	+	0.774403i
$476$	119.048	+	109.442i	0.250102	+	0.229919i
$477$			208.952i			0.438054i
$478$	−411.844	+	237.778i	−0.861599	+	0.497444i
$479$	116.614	+	67.3269i	0.243452	+	0.140557i	0.616762	−	0.787149i	$-0.288444\pi$
$479$	116.614	+	67.3269i	0.243452	+	0.140557i	−0.373310	+	0.927707i	$0.621777\pi$
$480$	−23.5443	−	17.5244i	−0.0490506	−	0.0365092i
$481$	−7.60619	+	4.39143i	−0.0158133	+	0.00912980i
$482$	540.971			1.12235
$483$	−78.9119	−	251.692i	−0.163379	−	0.521101i
$484$	−69.2054			−0.142986
$485$	−181.087	−	419.692i	−0.373375	−	0.865344i
$486$	261.037	+	150.710i	0.537113	+	0.310103i
$487$	386.964	+	223.414i	0.794588	+	0.458755i	0.841575	−	0.540140i	$-0.181629\pi$
$487$	386.964	+	223.414i	0.794588	+	0.458755i	−0.0469875	+	0.998895i	$0.514962\pi$
$488$	73.9110	+	128.018i	0.151457	+	0.262331i
$489$			101.560i			0.207690i
$490$	−346.303	−	11.1602i	−0.706740	−	0.0227758i
$491$	−119.125			−0.242617			−0.121309	−	0.992615i	$-0.538709\pi$
$491$	−119.125			−0.242617			−0.121309	+	0.992615i	$0.538709\pi$
$492$	−22.8975	+	13.2199i	−0.0465395	+	0.0268696i
$493$	292.143	−	506.007i	0.592582	−	1.02638i
$494$	−7.99988	+	13.8562i	−0.0161941	+	0.0280490i
$495$	−195.777	−	453.738i	−0.395510	−	0.916643i
$496$			187.056i			0.377130i
$497$	−97.9442	+	30.7081i	−0.197071	+	0.0617869i
$498$		−	118.673i		−	0.238298i
$499$	−42.1210	−	72.9558i	−0.0844109	−	0.146204i	0.820729	−	0.571318i	$-0.193568\pi$
$499$	−42.1210	−	72.9558i	−0.0844109	−	0.146204i	−0.905140	+	0.425114i	$0.860234\pi$
$500$	−191.463	+	160.754i	−0.382926	+	0.321508i
$501$	50.4180	−	87.3265i	0.100635	−	0.174304i
$502$	−213.597	−	369.961i	−0.425492	−	0.736973i
$503$	388.428			0.772223			0.386111	−	0.922452i	$-0.373818\pi$
$503$	388.428			0.772223			0.386111	+	0.922452i	$0.373818\pi$
$504$	106.167	−	115.487i	0.210649	−	0.229140i
$505$	−51.0436	+	437.084i	−0.101076	+	0.865513i
$506$	−320.300	−	554.776i	−0.633004	−	1.09640i
$507$	87.3943	−	151.371i	0.172375	−	0.298563i
$508$	90.4883	+	52.2434i	0.178127	+	0.102841i
$509$	68.8518	−	39.7516i	0.135269	−	0.0780975i	−0.430838	−	0.902429i	$-0.641782\pi$
$509$	68.8518	−	39.7516i	0.135269	−	0.0780975i	0.566107	+	0.824332i	$0.308449\pi$
$510$	9.83093	−	84.1818i	0.0192763	−	0.165062i
$511$	−154.390	+	691.128i	−0.302132	+	1.35250i
$512$		−	22.6274i		−	0.0441942i
$513$	−229.957	+	132.766i	−0.448260	+	0.258803i
$514$	250.680	+	144.730i	0.487703	+	0.281576i
$515$	336.141	−	451.610i	0.652701	−	0.876913i
$516$	−47.1986	+	27.2501i	−0.0914701	+	0.0528103i
$517$	−504.561			−0.975939
$518$	−25.3340	+	113.408i	−0.0489073	+	0.218934i
$519$	64.1885			0.123677
$520$	−9.71566	+	4.19208i	−0.0186840	+	0.00806169i
$521$	69.7252	+	40.2559i	0.133830	+	0.0772666i	0.565420	−	0.824803i	$-0.308714\pi$
$521$	69.7252	+	40.2559i	0.133830	+	0.0772666i	−0.431590	+	0.902070i	$0.642047\pi$
$522$	−490.868	−	283.403i	−0.940359	−	0.542917i
$523$	406.182	+	703.527i	0.776638	+	1.34518i	0.933869	+	0.357615i	$0.116410\pi$
$523$	406.182	+	703.527i	0.776638	+	1.34518i	−0.157231	+	0.987562i	$0.550257\pi$
$524$		−	187.833i		−	0.358461i
$525$	101.772	+	150.398i	0.193851	+	0.286472i
$526$	−137.788			−0.261955
$527$	−467.789	+	270.078i	−0.887646	+	0.512483i
$528$	−25.8884	+	44.8401i	−0.0490311	+	0.0849244i
$529$	394.822	−	683.851i	0.746355	−	1.29272i
$530$	−73.8778	−	171.221i	−0.139392	−	0.323058i
$531$		−	626.608i		−	1.18005i
$532$	63.3299	+	201.992i	0.119041	+	0.379685i
$533$			9.53214i			0.0178839i
$534$	99.2176	+	171.850i	0.185801	+	0.321816i
$535$	11.5229	+	8.57669i	0.0215381	+	0.0160312i
$536$	−49.0745	+	84.9995i	−0.0915569	+	0.158581i
$537$	116.336	+	201.500i	0.216641	+	0.375233i
$538$	−136.532			−0.253777
$539$	51.3073	+	609.073i	0.0951898	+	1.13001i
$540$	−174.425	−	20.3697i	−0.323009	−	0.0377217i
$541$	−141.664	−	245.370i	−0.261857	−	0.453549i	0.704879	−	0.709328i	$-0.251001\pi$
$541$	−141.664	−	245.370i	−0.261857	−	0.453549i	−0.966735	+	0.255779i	$0.917668\pi$
$542$	59.1190	−	102.397i	0.109076	−	0.188924i
$543$	295.882	+	170.828i	0.544903	+	0.314600i
$544$	56.5865	−	32.6703i	0.104019	−	0.0600556i
$545$	423.208	+	49.4231i	0.776529	+	0.0906847i
$546$	2.29945	+	7.33417i	0.00421146	+	0.0134326i
$547$			51.6110i			0.0943529i	0.998887	+	0.0471764i	$0.0150223\pi$
$547$			51.6110i			0.0943529i	−0.998887	+	0.0471764i	$0.984978\pi$
$548$	−202.369	+	116.838i	−0.369287	+	0.213208i
$549$	358.613	+	207.045i	0.653211	+	0.377131i
$550$	320.851	+	302.586i	0.583365	+	0.550156i
$551$	662.393	−	382.433i	1.20217	−	0.694070i
$552$	−106.580			−0.193080
$553$	−184.101	−	169.245i	−0.332914	−	0.306049i
$554$	545.510			0.984675
$555$	55.9202	−	24.1282i	0.100757	−	0.0434743i
$556$	117.571	+	67.8796i	0.211458	+	0.122086i
$557$	−204.171	−	117.878i	−0.366555	−	0.211631i	0.305397	−	0.952225i	$-0.401211\pi$
$557$	−204.171	−	117.878i	−0.366555	−	0.211631i	−0.671953	+	0.740594i	$0.734544\pi$
$558$	261.998	+	453.794i	0.469530	+	0.813251i
$559$			19.6486i			0.0351496i
$560$	−46.1645	+	132.170i	−0.0824366	+	0.236017i
$561$	−149.515			−0.266514
$562$	−298.175	+	172.151i	−0.530561	+	0.306319i
$563$	−132.816	+	230.044i	−0.235907	+	0.408604i	−0.959536	−	0.281586i	$-0.909140\pi$
$563$	−132.816	+	230.044i	−0.235907	+	0.408604i	0.723629	+	0.690190i	$0.242473\pi$
$564$	−41.9732	+	72.6997i	−0.0744205	+	0.128900i
$565$	−971.085	+	419.000i	−1.71874	+	0.741593i
$566$			145.425i			0.256934i
$567$	81.0145	−	362.663i	0.142883	−	0.639617i
$568$			41.4750i			0.0730193i
$569$	13.0381	+	22.5826i	0.0229141	+	0.0396883i	0.877255	−	0.480025i	$-0.159372\pi$
$569$	13.0381	+	22.5826i	0.0229141	+	0.0396883i	−0.854341	+	0.519713i	$0.826039\pi$
$570$	66.2447	−	89.0006i	0.116219	−	0.156141i
$571$	−147.312	+	255.152i	−0.257989	+	0.446851i	−0.965703	−	0.259649i	$-0.916393\pi$
$571$	−147.312	+	255.152i	−0.257989	+	0.446851i	0.707714	+	0.706499i	$0.249727\pi$
$572$	9.33340	+	16.1659i	0.0163171	+	0.0282621i
$573$	−68.7313			−0.119950
$574$	92.8454	+	85.3530i	0.161751	+	0.148699i
$575$	−209.183	+	883.399i	−0.363797	+	1.53635i
$576$	−31.6928	−	54.8935i	−0.0550222	−	0.0953013i
$577$	−287.549	+	498.049i	−0.498351	+	0.863170i	−0.999998	−	0.00190285i	$-0.999394\pi$
$577$	−287.549	+	498.049i	−0.498351	+	0.863170i	0.501647	+	0.865072i	$0.332728\pi$
$578$	−190.548	−	110.013i	−0.329668	−	0.190334i
$579$	227.773	−	131.505i	0.393389	−	0.227124i
$580$	502.431	+	58.6750i	0.866261	+	0.101164i
$581$	−540.139	+	169.348i	−0.929672	+	0.291476i
$582$			134.158i			0.230512i
$583$	−284.895	+	164.484i	−0.488671	+	0.282134i
$584$	247.805	+	143.070i	0.424324	+	0.244984i
$585$	−17.6984	+	23.7780i	−0.0302536	+	0.0406461i
$586$	−539.635	+	311.558i	−0.920878	+	0.531669i
$587$	−509.360			−0.867734			−0.433867	−	0.900977i	$-0.642851\pi$
$587$	−509.360			−0.867734			−0.433867	+	0.900977i	$0.642851\pi$
$588$	92.0265	+	43.2747i	0.156508	+	0.0735964i
$589$	−707.098			−1.20051
$590$	221.546	+	513.460i	0.375501	+	0.870271i
$591$	171.941	+	99.2704i	0.290933	+	0.167970i
$592$	40.6627	+	23.4766i	0.0686869	+	0.0396564i
$593$	−107.373	−	185.975i	−0.181067	−	0.313618i	0.761177	−	0.648544i	$-0.224622\pi$
$593$	−107.373	−	185.975i	−0.181067	−	0.313618i	−0.942244	+	0.334926i	$0.891289\pi$
$594$			309.794i			0.521539i
$595$	−397.183	+	75.3833i	−0.667535	+	0.126695i
$596$	−344.312			−0.577704
$597$	−202.981	+	117.191i	−0.340002	+	0.196300i
$598$	−19.2123	+	33.2767i	−0.0321276	+	0.0556467i
$599$	477.250	−	826.621i	0.796744	−	1.38000i	−0.124982	−	0.992159i	$-0.539887\pi$
$599$	477.250	−	826.621i	0.796744	−	1.38000i	0.921726	−	0.387842i	$-0.126779\pi$
$600$	70.2889	−	21.0584i	0.117148	−	0.0350974i
$601$		−	851.298i		−	1.41647i	−0.705977	−	0.708234i	$-0.749492\pi$
$601$		−	851.298i		−	1.41647i	0.705977	−	0.708234i	$-0.250508\pi$
$602$	191.382	+	175.938i	0.317911	+	0.292256i
$603$			274.942i			0.455957i
$604$	−110.216	−	190.900i	−0.182477	−	0.316059i
$605$	103.303	−	138.788i	0.170748	−	0.229402i
$606$	64.5786	−	111.853i	0.106565	−	0.184577i
$607$	−525.284	−	909.818i	−0.865377	−	1.49888i	−0.866673	−	0.498877i	$-0.833746\pi$
$607$	−525.284	−	909.818i	−0.865377	−	1.49888i	0.00129613	−	0.999999i	$-0.499587\pi$
$608$	85.5347			0.140682
$609$	80.1066	−	358.599i	0.131538	−	0.588832i
$610$	−367.061	−	42.8661i	−0.601739	−	0.0702723i
$611$	15.1323	+	26.2100i	0.0247665	+	0.0428968i
$612$	91.5184	−	158.514i	0.149540	−	0.259011i
$613$	876.517	+	506.057i	1.42988	+	0.825542i	0.997111	−	0.0759624i	$-0.0242029\pi$
$613$	876.517	+	506.057i	1.42988	+	0.825542i	0.432770	+	0.901504i	$0.357536\pi$
$614$	−302.747	+	174.791i	−0.493073	+	0.284676i
$615$	7.66710	−	65.6531i	0.0124668	−	0.106753i
$616$	241.033	+	53.8439i	0.391288	+	0.0874090i
$617$			706.409i			1.14491i	0.819937	+	0.572454i	$0.194009\pi$
$617$			706.409i			1.14491i	−0.819937	+	0.572454i	$0.805991\pi$
$618$	−143.098	+	82.6176i	−0.231550	+	0.133685i
$619$	681.409	+	393.412i	1.10082	+	0.635560i	0.936437	−	0.350836i	$-0.114103\pi$
$619$	681.409	+	393.412i	1.10082	+	0.635560i	0.164385	+	0.986396i	$0.447436\pi$
$620$	−375.133	−	279.218i	−0.605054	−	0.450352i
$621$	−552.261	+	318.848i	−0.889309	+	0.513443i
$622$	602.765			0.969076
$623$	640.591	−	696.823i	1.02824	−	1.11850i
$624$	3.10569			0.00497707
$625$	−36.5896	−	623.928i	−0.0585434	−	0.998285i
$626$	164.084	+	94.7339i	0.262115	+	0.151332i
$627$	−169.502	−	97.8617i	−0.270337	−	0.156079i
$628$	−204.163	−	353.621i	−0.325101	−	0.563091i
$629$			135.585i			0.215557i
$630$	73.1280	+	385.300i	0.116076	+	0.611588i
$631$	−218.755			−0.346680			−0.173340	−	0.984862i	$-0.555456\pi$
$631$	−218.755			−0.346680			−0.173340	+	0.984862i	$0.555456\pi$
$632$	−87.5079	+	50.5227i	−0.138462	+	0.0799410i
$633$	96.9287	−	167.885i	0.153126	−	0.265222i
$634$	227.664	−	394.326i	0.359092	−	0.621966i
$635$	−239.843	+	103.487i	−0.377706	+	0.162971i
$636$			54.7322i			0.0860569i
$637$	30.1002	−	20.9320i	0.0472531	−	0.0328603i
$638$		−	892.363i		−	1.39869i
$639$	58.0914	+	100.617i	0.0909098	+	0.157460i
$640$	45.3783	+	33.7759i	0.0709036	+	0.0527748i
$641$	304.336	−	527.125i	0.474783	−	0.822348i	−0.524800	−	0.851225i	$-0.675860\pi$
$641$	304.336	−	527.125i	0.474783	−	0.822348i	0.999583	+	0.0288778i	$0.00919336\pi$
$642$	−2.10800	−	3.65116i	−0.00328349	−	0.00568717i
$643$	−1184.38			−1.84196			−0.920978	−	0.389614i	$-0.872608\pi$
$643$	−1184.38			−1.84196			−0.920978	+	0.389614i	$0.872608\pi$
$644$	152.092	+	485.100i	0.236167	+	0.753261i
$645$	15.8042	−	135.331i	0.0245027	−	0.209815i
$646$	123.498	+	213.905i	0.191173	+	0.331122i
$647$	113.802	−	197.111i	0.175892	−	0.304653i	−0.764578	−	0.644531i	$-0.777052\pi$
$647$	113.802	−	197.111i	0.175892	−	0.304653i	0.940470	+	0.339878i	$0.110386\pi$
$648$	−130.033	−	75.0748i	−0.200669	−	0.115856i
$649$	854.347	−	493.258i	1.31641	−	0.760027i
$650$	6.09550	−	25.7418i	0.00937769	−	0.0396028i
$651$	−229.892	+	250.072i	−0.353137	+	0.384135i
$652$		−	195.743i		−	0.300220i
$653$	−199.761	+	115.332i	−0.305912	+	0.176619i	−0.645096	−	0.764102i	$-0.723183\pi$
$653$	−199.761	+	115.332i	−0.305912	+	0.176619i	0.339183	+	0.940720i	$0.389849\pi$
$654$	−108.303	−	62.5285i	−0.165600	−	0.0956093i
$655$	376.692	+	280.378i	0.575102	+	0.428058i
$656$	44.1316	−	25.4794i	0.0672738	−	0.0388406i
$657$	801.559			1.22003
$658$	390.790	+	87.2977i	0.593906	+	0.132671i
$659$	726.539			1.10249			0.551244	−	0.834344i	$-0.314153\pi$
$659$	726.539			1.10249			0.551244	+	0.834344i	$0.314153\pi$
$660$	−51.2813	−	118.851i	−0.0776989	−	0.180077i
$661$	−214.930	−	124.090i	−0.325159	−	0.187731i	0.328531	−	0.944493i	$-0.393447\pi$
$661$	−214.930	−	124.090i	−0.325159	−	0.187731i	−0.653690	+	0.756763i	$0.726780\pi$
$662$	−287.576	−	166.032i	−0.434405	−	0.250804i
$663$	4.48411	+	7.76670i	0.00676336	+	0.0117145i
$664$			228.725i			0.344465i
$665$	−499.619	−	174.508i	−0.751307	−	0.262418i
$666$	131.529			0.197491
$667$	1590.79	−	918.442i	2.38499	−	1.37697i
$668$	−97.1736	+	168.310i	−0.145469	+	0.251960i
$669$	−100.711	+	174.436i	−0.150539	+	0.260742i
$670$	−97.2095	−	225.295i	−0.145089	−	0.336261i
$671$			651.933i			0.971584i
$672$	27.8091	−	30.2502i	0.0413826	−	0.0450152i
$673$		−	835.990i		−	1.24218i	−0.783738	−	0.621092i	$-0.786689\pi$
$673$		−	835.990i		−	1.24218i	0.783738	−	0.621092i	$-0.213311\pi$
$674$	153.941	+	266.634i	0.228400	+	0.395600i
$675$	301.214	−	319.396i	0.446243	−	0.473179i
$676$	−168.440	+	291.747i	−0.249172	+	0.431578i
$677$	−189.063	−	327.468i	−0.279267	−	0.483704i	0.691936	−	0.721959i	$-0.256758\pi$
$677$	−189.063	−	327.468i	−0.279267	−	0.483704i	−0.971203	+	0.238255i	$0.923425\pi$
$678$	310.416			0.457840
$679$	610.622	−	191.446i	0.899295	−	0.281953i
$680$	−18.9477	+	162.249i	−0.0278643	+	0.238601i
$681$	−182.507	−	316.112i	−0.267999	−	0.464188i
$682$	−412.483	+	714.441i	−0.604813	+	1.04757i
$683$	−167.429	−	96.6649i	−0.245137	−	0.141530i	0.372399	−	0.928073i	$-0.378535\pi$
$683$	−167.429	−	96.6649i	−0.245137	−	0.141530i	−0.617535	+	0.786543i	$0.711869\pi$
$684$	207.505	−	119.803i	0.303370	−	0.175151i
$685$	67.7623	−	580.246i	0.0989231	−	0.847074i
$686$	65.6418	−	480.613i	0.0956878	−	0.700602i
$687$			195.302i			0.284282i
$688$	90.9686	−	52.5207i	0.132222	−	0.0763383i
$689$	17.0886	+	9.86613i	0.0248021	+	0.0143195i
$690$	159.092	−	213.742i	0.230568	−	0.309771i
$691$	501.502	−	289.542i	0.725763	−	0.419019i	−0.0911074	−	0.995841i	$-0.529041\pi$
$691$	501.502	−	289.542i	0.725763	−	0.419019i	0.816870	+	0.576822i	$0.195707\pi$
$692$	−123.714			−0.178778
$693$	660.157	−	206.976i	0.952607	−	0.298667i
$694$	−263.371			−0.379497
$695$	−311.627	+	134.460i	−0.448384	+	0.193467i
$696$	−128.576	−	74.2336i	−0.184736	−	0.106657i
$697$	127.438	+	73.5761i	0.182837	+	0.105561i
$698$	57.7966	+	100.107i	0.0828032	+	0.143419i
$699$		−	325.917i		−	0.466262i
$700$	−196.151	−	289.870i	−0.280216	−	0.414100i
$701$	−516.871			−0.737334			−0.368667	−	0.929562i	$-0.620186\pi$
$701$	−516.871			−0.737334			−0.368667	+	0.929562i	$0.620186\pi$
$702$	16.0926	−	9.29107i	0.0229239	−	0.0132351i
$703$	−88.7447	+	153.710i	−0.126237	+	0.218649i
$704$	49.8963	−	86.4230i	0.0708755	−	0.122760i
$705$	−83.1429	−	192.694i	−0.117933	−	0.273325i
$706$			152.645i			0.216211i
$707$	−601.257	−	134.313i	−0.850434	−	0.189977i
$708$		−	164.132i		−	0.231824i
$709$	−29.9375	−	51.8533i	−0.0422250	−	0.0731359i	0.844141	−	0.536122i	$-0.180111\pi$
$709$	−29.9375	−	51.8533i	−0.0422250	−	0.0731359i	−0.886366	+	0.462986i	$0.846778\pi$
$710$	−83.1763	−	61.9095i	−0.117150	−	0.0871965i
$711$	−141.528	+	245.134i	−0.199055	+	0.344773i
$712$	−191.228	−	331.216i	−0.268579	−	0.465192i
$713$	−1698.15			−2.38170
$714$	115.801	+	25.8686i	0.162187	+	0.0362305i
$715$	−46.3520	−	5.41308i	−0.0648279	−	0.00757074i
$716$	−224.221	−	388.363i	−0.313158	−	0.542406i
$717$	−174.472	+	302.194i	−0.243336	+	0.421470i
$718$	739.573	+	426.993i	1.03005	+	0.594698i
$719$	−1072.53	+	619.228i	−1.49170	+	0.861235i	−0.999955	−	0.00950279i	$-0.996975\pi$
$719$	−1072.53	+	619.228i	−1.49170	+	0.861235i	−0.491748	+	0.870738i	$0.663642\pi$
$720$	157.394	+	18.3808i	0.218603	+	0.0255289i
$721$	580.238	+	533.415i	0.804768	+	0.739826i
$722$		−	187.199i		−	0.259278i
$723$	343.761	−	198.471i	0.475465	−	0.274510i
$724$	−570.271	−	329.246i	−0.787668	−	0.454760i
$725$	−867.647	+	920.020i	−1.19675	+	1.26899i
$726$	−43.9767	+	25.3900i	−0.0605740	+	0.0349724i
$727$	387.549			0.533080			0.266540	−	0.963824i	$-0.414120\pi$
$727$	387.549			0.533080			0.266540	+	0.963824i	$0.414120\pi$
$728$	−4.43188	−	14.1356i	−0.00608774	−	0.0194170i
$729$	−256.605			−0.351995
$730$	−656.819	+	283.402i	−0.899753	+	0.388222i
$731$	262.687	+	151.663i	0.359353	+	0.207473i
$732$	93.9339	+	54.2327i	0.128325	+	0.0740884i
$733$	526.551	+	912.012i	0.718350	+	1.24422i	0.961653	+	0.274269i	$0.0884357\pi$
$733$	526.551	+	912.012i	0.718350	+	1.24422i	−0.243303	+	0.969950i	$0.578231\pi$
$734$		−	768.667i		−	1.04723i
$735$	−224.153	+	119.959i	−0.304970	+	0.163210i
$736$	205.418			0.279101
$737$	−374.869	+	216.431i	−0.508642	+	0.293665i
$738$	71.3748	−	123.625i	0.0967138	−	0.167513i
$739$	−123.560	+	214.013i	−0.167199	+	0.289598i	−0.937434	−	0.348163i	$-0.886806\pi$
$739$	−123.560	+	214.013i	−0.167199	+	0.289598i	0.770235	+	0.637760i	$0.220139\pi$
$740$	−107.778	+	46.5038i	−0.145646	+	0.0628430i
$741$			11.7399i			0.0158434i
$742$	249.114	−	78.1038i	0.335733	−	0.105261i
$743$			189.686i			0.255298i	0.991819	+	0.127649i	$0.0407431\pi$
$743$			189.686i			0.255298i	−0.991819	+	0.127649i	$0.959257\pi$
$744$	68.6269	+	118.865i	0.0922405	+	0.159765i
$745$	513.953	−	690.502i	0.689870	−	0.926849i
$746$	−58.8952	+	102.010i	−0.0789480	+	0.136742i
$747$	320.360	+	554.880i	0.428862	+	0.742811i
$748$	288.168			0.385252
$749$	−13.6102	+	14.8049i	−0.0181711	+	0.0197662i
$750$	−62.6883	+	172.395i	−0.0835844	+	0.229860i
$751$	400.319	+	693.373i	0.533048	+	0.923267i	0.999255	+	0.0385908i	$0.0122869\pi$
$751$	400.319	+	693.373i	0.533048	+	0.923267i	−0.466207	+	0.884676i	$0.654380\pi$
$752$	80.8974	−	140.118i	0.107576	−	0.186328i
$753$	−271.461	−	156.728i	−0.360506	−	0.208138i
$754$	−46.3548	+	26.7630i	−0.0614785	+	0.0354946i
$755$	547.361	+	63.9219i	0.724981	+	0.0846648i
$756$	53.5998	−	239.940i	0.0708992	−	0.317382i
$757$			809.069i			1.06878i	0.845237	+	0.534392i	$0.179459\pi$
$757$			809.069i			1.06878i	−0.845237	+	0.534392i	$0.820541\pi$
$758$	37.2823	−	21.5249i	0.0491851	−	0.0283970i
$759$	−407.071	−	235.023i	−0.536325	−	0.309648i
$760$	−127.677	+	171.536i	−0.167996	+	0.225705i
$761$	−213.647	+	123.349i	−0.280745	+	0.162088i	−0.633761	−	0.773529i	$-0.718490\pi$
$761$	−213.647	+	123.349i	−0.280745	+	0.162088i	0.353016	+	0.935617i	$0.385156\pi$
$762$	76.6680			0.100614
$763$	−130.050	+	582.169i	−0.170445	+	0.763000i
$764$	132.470			0.173390
$765$	181.285	+	420.150i	0.236974	+	0.549216i
$766$	361.933	+	208.962i	0.472498	+	0.272797i
$767$	−51.2456	−	29.5867i	−0.0668131	−	0.0385746i
$768$	−8.30151	−	14.3786i	−0.0108093	−	0.0187222i
$769$			851.221i			1.10692i	0.832876	+	0.553460i	$0.186693\pi$
$769$			851.221i			1.10692i	−0.832876	+	0.553460i	$0.813307\pi$
$770$	−467.771	+	403.009i	−0.607495	+	0.523389i
$771$	212.393			0.275478
$772$	−439.000	+	253.457i	−0.568652	+	0.328312i
$773$	−445.532	+	771.684i	−0.576368	+	0.998298i	0.419524	+	0.907744i	$0.362197\pi$
$773$	−445.532	+	771.684i	−0.576368	+	0.998298i	−0.995892	+	0.0905537i	$0.971136\pi$
$774$	147.125	−	254.828i	0.190084	−	0.329235i
$775$	1119.92	−	335.526i	1.44506	−	0.432936i
$776$		−	258.571i		−	0.333210i
$777$	25.5084	+	81.3599i	0.0328294	+	0.104710i
$778$		−	606.380i		−	0.779409i
$779$	96.3156	+	166.823i	0.123640	+	0.214151i
$780$	−4.63585	+	6.22833i	−0.00594340	+	0.00798504i
$781$	−91.4576	+	158.409i	−0.117103	+	0.202829i
$782$	296.590	+	513.709i	0.379271	+	0.656916i
$783$	−888.317			−1.13450
$784$	−177.368	−	83.4059i	−0.226235	−	0.106385i
$785$	1013.93	+	118.408i	1.29162	+	0.150839i
$786$	−68.9120	−	119.359i	−0.0876743	−	0.151856i
$787$	245.676	−	425.522i	0.312167	−	0.540689i	−0.666664	−	0.745358i	$-0.732278\pi$
$787$	245.676	−	425.522i	0.312167	−	0.540689i	0.978831	+	0.204669i	$0.0656118\pi$
$788$	−331.393	−	191.330i	−0.420549	−	0.242804i
$789$	−87.5578	+	50.5515i	−0.110973	+	0.0640703i
$790$	29.3016	−	250.908i	0.0370906	−	0.317605i
$791$	−442.968	−	1412.86i	−0.560011	−	1.78617i
$792$		−	279.547i		−	0.352963i
$793$	33.8654	−	19.5522i	0.0427054	−	0.0246560i
$794$	−392.878	−	226.828i	−0.494808	−	0.285678i
$795$	−109.763	−	81.6986i	−0.138067	−	0.102765i
$796$	391.218	−	225.870i	0.491480	−	0.283756i
$797$	68.9206			0.0864751			0.0432375	−	0.999065i	$-0.486233\pi$
$797$	68.9206			0.0864751			0.0432375	+	0.999065i	$0.486233\pi$
$798$	114.350	+	105.122i	0.143295	+	0.131732i
$799$	467.210			0.584744
$800$	−135.472	+	40.5871i	−0.169340	+	0.0507339i
$801$	−927.828	−	535.682i	−1.15834	−	0.668766i
$802$	−291.132	−	168.085i	−0.363007	−	0.209582i
$803$	630.977	+	1092.88i	0.785774	+	1.36100i
$804$			72.0175i			0.0895740i
$805$	−1199.87	−	419.094i	−1.49053	−	0.520614i
$806$	49.4833			0.0613936
$807$	−86.7595	+	50.0906i	−0.107509	+	0.0620702i
$808$	−124.466	+	215.582i	−0.154042	+	0.266809i
$809$	19.0763	−	33.0411i	0.0235801	−	0.0408419i	−0.853995	−	0.520282i	$-0.825827\pi$
$809$	19.0763	−	33.0411i	0.0235801	−	0.0408419i	0.877575	+	0.479440i	$0.159160\pi$
$810$	344.660	−	148.713i	0.425506	−	0.183596i
$811$			763.676i			0.941648i	0.882227	+	0.470824i	$0.156043\pi$
$811$			763.676i			0.941648i	−0.882227	+	0.470824i	$0.843957\pi$
$812$	−154.394	+	691.149i	−0.190141	+	0.851169i
$813$		−	86.7579i		−	0.106713i
$814$	103.538	+	179.333i	0.127196	+	0.220310i
$815$	392.555	+	292.185i	0.481662	+	0.358509i
$816$	23.9720	−	41.5208i	0.0293775	−	0.0508833i
$817$	198.535	+	343.873i	0.243005	+	0.420898i
$818$	−280.156			−0.342489
$819$	−30.5505	−	28.0851i	−0.0373021	−	0.0342920i
$820$	−14.7773	+	126.537i	−0.0180211	+	0.154314i
$821$	204.439	+	354.099i	0.249013	+	0.431302i	0.963252	−	0.268599i	$-0.0865606\pi$
$821$	204.439	+	354.099i	0.249013	+	0.431302i	−0.714240	+	0.699901i	$0.753227\pi$
$822$	−85.7306	+	148.490i	−0.104295	+	0.180644i
$823$	−133.113	−	76.8529i	−0.161741	−	0.0933814i	0.416945	−	0.908932i	$-0.363101\pi$
$823$	−133.113	−	76.8529i	−0.161741	−	0.0933814i	−0.578686	+	0.815551i	$0.696434\pi$
$824$	275.801	−	159.234i	0.334710	−	0.193245i
$825$	314.898	+	74.5657i	0.381694	+	0.0903827i
$826$	−747.047	+	234.219i	−0.904416	+	0.283558i
$827$		−	571.706i		−	0.691301i	−0.938363	−	0.345650i	$-0.887658\pi$
$827$		−	571.706i		−	0.691301i	0.938363	−	0.345650i	$-0.112342\pi$
$828$	498.339	−	287.716i	0.601859	−	0.347483i
$829$	−1099.69	−	634.905i	−1.32652	−	0.765869i	−0.341763	−	0.939786i	$-0.611024\pi$
$829$	−1099.69	−	634.905i	−1.32652	−	0.765869i	−0.984760	+	0.173918i	$0.944357\pi$
$830$	−458.697	−	341.416i	−0.552647	−	0.411345i
$831$	346.646	−	200.136i	0.417143	−	0.240838i
$832$	−5.98578			−0.00719445
$833$	−47.5093	−	563.986i	−0.0570339	−	0.677054i
$834$	99.6142			0.119442
$835$	−192.487	−	446.112i	−0.230523	−	0.534266i
$836$	326.690	+	188.615i	0.390778	+	0.225616i
$837$	711.202	+	410.612i	0.849703	+	0.490576i
$838$	40.0539	+	69.3754i	0.0477970	+	0.0827869i
$839$			732.075i			0.872556i	0.899812	+	0.436278i	$0.143704\pi$
$839$			732.075i			0.872556i	−0.899812	+	0.436278i	$0.856296\pi$
$840$	19.1549	+	100.924i	0.0228035	+	0.120148i
$841$	1717.80			2.04257
$842$	269.872	−	155.811i	0.320513	−	0.185048i
$843$	−126.317	+	218.788i	−0.149843	+	0.259535i
$844$	−186.816	+	323.575i	−0.221346	+	0.383383i
$845$	−333.656	−	773.289i	−0.394859	−	0.915135i
$846$		−	453.232i		−	0.535735i
$847$	178.318	+	163.929i	0.210529	+	0.193540i
$848$		−	105.489i		−	0.124397i
$849$	53.3531	+	92.4103i	0.0628423	+	0.108846i
$850$	−297.099	−	280.187i	−0.349529	−	0.329632i
$851$	−213.127	+	369.147i	−0.250443	+	0.433780i
$852$	15.2163	+	26.3554i	0.0178595	+	0.0309335i
$853$	193.304			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$853$	193.304			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$854$	112.796	−	504.932i	0.132079	−	0.591255i
$855$	−69.4820	+	594.972i	−0.0812655	+	0.695873i
$856$	4.06287	+	7.03710i	0.00474635	+	0.00822092i
$857$	236.907	−	410.336i	0.276438	−	0.478805i	−0.694059	−	0.719918i	$-0.744179\pi$
$857$	236.907	−	410.336i	0.276438	−	0.478805i	0.970497	+	0.241113i	$0.0775126\pi$
$858$	11.8619	+	6.84844i	0.0138250	+	0.00798187i
$859$	−760.044	+	438.811i	−0.884801	+	0.510840i	−0.872238	−	0.489081i	$-0.837332\pi$
$859$	−760.044	+	438.811i	−0.884801	+	0.510840i	−0.0125624	+	0.999921i	$0.503999\pi$
$860$	−30.4604	+	260.831i	−0.0354191	+	0.303292i
$861$	90.3130	+	20.1748i	0.104893	+	0.0234318i
$862$			386.536i			0.448417i
$863$	−782.535	+	451.797i	−0.906761	+	0.523519i	−0.879388	−	0.476106i	$-0.842048\pi$
$863$	−782.535	+	451.797i	−0.906761	+	0.523519i	−0.0273737	+	0.999625i	$0.508714\pi$
$864$	−86.0311	−	49.6701i	−0.0995730	−	0.0574885i
$865$	184.668	−	248.104i	0.213489	−	0.286825i
$866$	247.308	−	142.783i	0.285575	−	0.164877i
$867$	−161.446			−0.186212
$868$	443.085	−	481.979i	0.510467	−	0.555275i
$869$	−445.636			−0.512814
$870$	340.798	−	147.046i	0.391721	−	0.169018i
$871$	22.4855	+	12.9820i	0.0258157	+	0.0149047i
$872$	208.738	+	120.515i	0.239378	+	0.138205i
$873$	−362.164	−	627.286i	−0.414850	−	0.718541i
$874$			776.508i			0.888453i
$875$	874.116	+	39.3154i	0.998990	+	0.0449319i
$876$	209.958			0.239678
$877$	1129.07	−	651.867i	1.28742	−	0.743292i	0.309226	−	0.950988i	$-0.399930\pi$
$877$	1129.07	−	651.867i	1.28742	−	0.743292i	0.978193	+	0.207696i	$0.0665966\pi$
$878$	430.443	−	745.550i	0.490255	−	0.849146i
$879$	−228.608	+	395.961i	−0.260077	+	0.450467i
$880$	98.8375	+	229.068i	0.112315	+	0.260305i
$881$		−	796.338i		−	0.903902i	−0.892043	−	0.451951i	$-0.850728\pi$
$881$		−	796.338i		−	0.903902i	0.892043	−	0.451951i	$-0.149272\pi$
$882$	−547.112	+	46.0879i	−0.620308	+	0.0522538i
$883$		−	1253.73i		−	1.41985i	−0.704276	−	0.709927i	$-0.748728\pi$
$883$		−	1253.73i		−	1.41985i	0.704276	−	0.709927i	$-0.251272\pi$
$884$	−8.64249	−	14.9692i	−0.00977657	−	0.0169335i
$885$	329.159	+	244.999i	0.371931	+	0.276835i
$886$	−551.097	+	954.529i	−0.622006	+	1.07735i
$887$	−489.613	−	848.034i	−0.551987	−	0.956070i	−0.998131	−	0.0611090i	$-0.980536\pi$
$887$	−489.613	−	848.034i	−0.551987	−	0.956070i	0.446144	−	0.894961i	$-0.352797\pi$
$888$	34.4522			0.0387976
$889$	−109.407	−	348.955i	−0.123067	−	0.392525i
$890$	949.686	+	110.906i	1.06706	+	0.124614i
$891$	−331.099	−	573.480i	−0.371604	−	0.643637i
$892$	194.106	−	336.202i	0.217608	−	0.376908i
$893$	529.666	+	305.803i	0.593132	+	0.342445i
$894$	−218.794	+	126.321i	−0.244736	+	0.141298i
$895$	1113.54	+	130.041i	1.24418	+	0.145298i
$896$	−53.5981	+	58.3030i	−0.0598194	+	0.0650703i
$897$			28.1943i			0.0314318i
$898$	9.83866	−	5.68035i	0.0109562	−	0.00632556i
$899$	−2048.62	−	1182.77i	−2.27877	−	1.31565i
$900$	−271.804	+	288.211i	−0.302004	+	0.320234i
$901$	263.805	−	152.308i	0.292792	−	0.169043i
$902$	224.741			0.249159
$903$	186.162	+	41.5864i	0.206160	+	0.0460536i
$904$	−598.282			−0.661817
$905$	1511.53	−	652.190i	1.67020	−	0.720652i
$906$	−140.074	−	80.8718i	−0.154607	−	0.0892625i
$907$	−1429.61	−	825.386i	−1.57620	−	0.910017i	−0.995383	−	0.0959807i	$-0.969401\pi$
$907$	−1429.61	−	825.386i	−1.57620	−	0.910017i	−0.580813	−	0.814037i	$-0.697265\pi$
$908$	351.757	+	609.261i	0.387398	+	0.670992i
$909$			697.328i			0.767138i
$910$	34.9638	+	12.2122i	0.0384217	+	0.0134200i
$911$	−736.949			−0.808945			−0.404472	−	0.914550i	$-0.632545\pi$
$911$	−736.949			−0.808945			−0.404472	+	0.914550i	$0.632545\pi$
$912$	54.3532	−	31.3808i	0.0595978	−	0.0344088i
$913$	−504.367	+	873.589i	−0.552428	+	0.956833i
$914$	−353.064	+	611.525i	−0.386285	+	0.669064i
$915$	−248.976	+	107.427i	−0.272105	+	0.117407i
$916$		−	376.416i		−	0.410935i
$917$	−444.926	+	483.981i	−0.485197	+	0.527788i
$918$		−	286.862i		−	0.312485i
$919$	−432.226	−	748.637i	−0.470322	−	0.814621i	0.529102	−	0.848558i	$-0.322529\pi$
$919$	−432.226	−	748.637i	−0.470322	−	0.814621i	−0.999424	+	0.0339368i	$0.989196\pi$
$920$	−306.627	+	411.957i	−0.333290	+	0.447779i
$921$	−128.254	+	222.143i	−0.139255	+	0.241197i
$922$	−488.177	−	845.547i	−0.529476	−	0.917080i
$923$	10.9717			0.0118870
$924$	172.919	−	54.2147i	0.187142	−	0.0586740i
$925$	67.6190	−	285.561i	0.0731016	−	0.308714i
$926$	434.902	+	753.273i	0.469657	+	0.813470i
$927$	446.058	−	772.594i	0.481184	−	0.833435i
$928$	247.813	+	143.075i	0.267040	+	0.154175i
$929$	515.059	−	297.370i	0.554423	−	0.320096i	−0.196481	−	0.980508i	$-0.562951\pi$
$929$	515.059	−	297.370i	0.554423	−	0.320096i	0.750904	+	0.660411i	$0.229618\pi$
$930$	−340.818	−	39.8015i	−0.366471	−	0.0427973i
$931$	315.285	−	670.475i	0.338652	−	0.720167i
$932$			628.160i			0.673991i
$933$	383.028	−	221.142i	0.410534	−	0.237022i
$934$	58.6261	+	33.8478i	0.0627689	+	0.0362396i
$935$	−430.148	+	577.909i	−0.460051	+	0.618084i
$936$	−14.5214	+	8.38391i	−0.0155143	+	0.00895717i
$937$	−312.979			−0.334022			−0.167011	−	0.985955i	$-0.553412\pi$
$937$	−312.979			−0.334022			−0.167011	+	0.985955i	$0.553412\pi$
$938$	327.788	−	102.770i	0.349455	−	0.109563i
$939$	139.023			0.148055
$940$	160.246	+	371.391i	0.170475	+	0.395096i
$941$	45.2375	+	26.1179i	0.0480738	+	0.0277554i	0.523844	−	0.851814i	$-0.324497\pi$
$941$	45.2375	+	26.1179i	0.0480738	+	0.0277554i	−0.475770	+	0.879569i	$0.657831\pi$
$942$	−259.472	−	149.806i	−0.275448	−	0.159030i
$943$	231.309	+	400.639i	0.245291	+	0.424856i
$944$			316.341i			0.335107i
$945$	401.182	+	465.650i	0.424531	+	0.492752i
$946$	463.260			0.489704
$947$	−487.134	+	281.247i	−0.514397	+	0.296987i	−0.734639	−	0.678458i	$-0.762649\pi$
$947$	−487.134	+	281.247i	−0.514397	+	0.296987i	0.220242	+	0.975445i	$0.429315\pi$
$948$	−37.0714	+	64.2095i	−0.0391048	+	0.0677315i
$949$	37.8474	−	65.5536i	0.0398813	−	0.0690765i
$950$	−153.425	−	512.103i	−0.161500	−	0.539055i
$951$		−	334.101i		−	0.351315i
$952$	−223.191	−	49.8581i	−0.234444	−	0.0523719i
$953$		−	786.616i		−	0.825411i	−0.910865	−	0.412705i	$-0.864584\pi$
$953$		−	786.616i		−	0.825411i	0.910865	−	0.412705i	$-0.135416\pi$
$954$	−147.751	−	255.913i	−0.154876	−	0.268252i
$955$	−197.737	+	265.663i	−0.207055	+	0.278181i
$956$	336.269	−	582.436i	0.351746	−	0.609243i
$957$	−327.389	−	567.054i	−0.342099	−	0.592533i
$958$	−190.429			−0.198778
$959$	798.192	+	178.306i	0.832317	+	0.185929i
$960$	41.2274	+	4.81462i	0.0429452	+	0.00501523i
$961$	612.939	+	1061.64i	0.637814	+	1.10473i
$962$	6.21043	−	10.7568i	0.00645574	−	0.0111817i
$963$	19.7129	+	11.3812i	0.0204703	+	0.0118185i
$964$	−662.551	+	382.524i	−0.687294	+	0.396809i
$965$	146.997	−	1258.73i	0.152328	−	1.30438i
$966$	274.620	+	252.459i	0.284285	+	0.261345i
$967$			372.034i			0.384730i	0.981323	+	0.192365i	$0.0616157\pi$
$967$			372.034i			0.384730i	−0.981323	+	0.192365i	$0.938384\pi$
$968$	84.7590	−	48.9356i	0.0875609	−	0.0505533i
$969$	156.954	+	90.6175i	0.161975	+	0.0935165i
$970$	518.552	+	385.968i	0.534590	+	0.397905i
$971$	−463.408	+	267.549i	−0.477248	+	0.275539i	−0.719269	−	0.694732i	$-0.755523\pi$
$971$	−463.408	+	267.549i	−0.477248	+	0.275539i	0.242021	+	0.970271i	$0.422190\pi$
$972$	−426.272			−0.438551
$973$	−142.151	−	453.395i	−0.146096	−	0.465977i
$974$	−631.910			−0.648778
$975$	−5.57073	−	18.5940i	−0.00571357	−	0.0190708i
$976$	−181.044	−	104.526i	−0.185496	−	0.107096i
$977$	696.209	+	401.956i	0.712599	+	0.411419i	0.812023	−	0.583626i	$-0.198367\pi$
$977$	696.209	+	401.956i	0.712599	+	0.411419i	−0.0994238	+	0.995045i	$0.531700\pi$
$978$	−71.8140	−	124.385i	−0.0734294	−	0.127184i
$979$		−	1686.73i		−	1.72291i
$980$	432.024	−	231.205i	0.440840	−	0.235923i
$981$	675.191			0.688268
$982$	145.898	−	84.2342i	0.148572	−	0.0857782i
$983$	118.542	−	205.321i	0.120592	−	0.208872i	−0.799409	−	0.600787i	$-0.794854\pi$
$983$	118.542	−	205.321i	0.120592	−	0.208872i	0.920001	+	0.391915i	$0.128187\pi$
$984$	18.6957	−	32.3819i	0.0189997	−	0.0329084i
$985$	878.372	−	378.997i	0.891749	−	0.384768i
$986$			826.305i			0.838038i
$987$	280.356	−	87.8989i	0.284049	−	0.0890566i
$988$		−	22.6271i		−	0.0229019i
$989$	476.798	+	825.838i	0.482101	+	0.835024i
$990$	560.619	+	417.278i	0.566282	+	0.421493i
$991$	211.092	−	365.622i	0.213009	−	0.368942i	−0.739646	−	0.672996i	$-0.765007\pi$
$991$	211.092	−	365.622i	0.213009	−	0.368942i	0.952655	+	0.304054i	$0.0983403\pi$
$992$	−132.269	−	229.096i	−0.133335	−	0.230944i
$993$	−243.655			−0.245372
$994$	98.2428	−	106.867i	0.0988358	−	0.107512i
$995$	−130.997	+	1121.73i	−0.131656	+	1.12736i
$996$	83.9141	+	145.344i	0.0842511	+	0.145927i
$997$	−776.469	+	1344.88i	−0.778806	+	1.34893i	0.153825	+	0.988098i	$0.450841\pi$
$997$	−776.469	+	1344.88i	−0.778806	+	1.34893i	−0.932630	+	0.360833i	$0.882492\pi$
$998$	103.175	+	59.5681i	0.103382	+	0.0596875i
$999$	178.519	−	103.068i	0.178698	−	0.103171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.3.h.a.59.2	yes	16
3.2	odd	2		630.3.bc.a.199.6		16
4.3	odd	2		560.3.br.b.129.6		16
5.2	odd	4		350.3.k.e.101.3		16
5.3	odd	4		350.3.k.e.101.6		16
5.4	even	2	inner	70.3.h.a.59.7	yes	16
7.2	even	3		490.3.h.b.19.6		16
7.3	odd	6		490.3.d.a.489.3		16
7.4	even	3		490.3.d.a.489.6		16
7.5	odd	6	inner	70.3.h.a.19.7	yes	16
7.6	odd	2		490.3.h.b.129.3		16
15.14	odd	2		630.3.bc.a.199.4		16
20.19	odd	2		560.3.br.b.129.3		16
21.5	even	6		630.3.bc.a.19.4		16
28.19	even	6		560.3.br.b.369.3		16
35.4	even	6		490.3.d.a.489.11		16
35.9	even	6		490.3.h.b.19.3		16
35.12	even	12		350.3.k.e.201.3		16
35.19	odd	6	inner	70.3.h.a.19.2	✓	16
35.24	odd	6		490.3.d.a.489.14		16
35.33	even	12		350.3.k.e.201.6		16
35.34	odd	2		490.3.h.b.129.6		16
105.89	even	6		630.3.bc.a.19.6		16
140.19	even	6		560.3.br.b.369.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.3.h.a.19.2	✓	16	35.19	odd	6	inner
70.3.h.a.19.7	yes	16	7.5	odd	6	inner
70.3.h.a.59.2	yes	16	1.1	even	1	trivial
70.3.h.a.59.7	yes	16	5.4	even	2	inner
350.3.k.e.101.3		16	5.2	odd	4
350.3.k.e.101.6		16	5.3	odd	4
350.3.k.e.201.3		16	35.12	even	12
350.3.k.e.201.6		16	35.33	even	12
490.3.d.a.489.3		16	7.3	odd	6
490.3.d.a.489.6		16	7.4	even	3
490.3.d.a.489.11		16	35.4	even	6
490.3.d.a.489.14		16	35.24	odd	6
490.3.h.b.19.3		16	35.9	even	6
490.3.h.b.19.6		16	7.2	even	3
490.3.h.b.129.3		16	7.6	odd	2
490.3.h.b.129.6		16	35.34	odd	2
560.3.br.b.129.3		16	20.19	odd	2
560.3.br.b.129.6		16	4.3	odd	2
560.3.br.b.369.3		16	28.19	even	6
560.3.br.b.369.6		16	140.19	even	6
630.3.bc.a.19.4		16	21.5	even	6
630.3.bc.a.19.6		16	105.89	even	6
630.3.bc.a.199.4		16	15.14	odd	2
630.3.bc.a.199.6		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	70.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 0.707107i) q^{2} +(-0.518845 + 0.898665i) q^{3} +(1.00000 - 1.73205i) q^{4} +(1.98086 + 4.59088i) q^{5} -1.46751i q^{6} +(-6.67941 + 2.09417i) q^{7} +2.82843i q^{8} +(3.96160 + 6.86169i) q^{9} +(-5.67229 - 4.22198i) q^{10} +(-6.23704 + 10.8029i) q^{11} +(1.03769 + 1.79733i) q^{12} +0.748223 q^{13} +(6.69977 - 7.28787i) q^{14} +(-5.15342 - 0.601827i) q^{15} +(-2.00000 - 3.46410i) q^{16} +(5.77534 - 10.0032i) q^{17} +(-9.70390 - 5.60255i) q^{18} +(13.0948 - 7.56027i) q^{19} +(9.93250 + 1.15994i) q^{20} +(1.58362 - 7.08910i) q^{21} -17.6410i q^{22} +(31.4481 - 18.1566i) q^{23} +(-2.54181 - 1.46751i) q^{24} +(-17.1524 + 18.1878i) q^{25} +(-0.916382 + 0.529074i) q^{26} -17.5610 q^{27} +(-3.05220 + 13.6632i) q^{28} +50.5846 q^{29} +(6.73718 - 2.90694i) q^{30} +(-40.4989 - 23.3820i) q^{31} +(4.89898 + 2.82843i) q^{32} +(-6.47211 - 11.2100i) q^{33} +16.3351i q^{34} +(-22.8450 - 26.5161i) q^{35} +15.8464 q^{36} +(-10.1657 + 5.86915i) q^{37} +(-10.6918 + 18.5188i) q^{38} +(-0.388211 + 0.672402i) q^{39} +(-12.9850 + 5.60271i) q^{40} +12.7397i q^{41} +(3.07322 + 9.80212i) q^{42} +26.2604i q^{43} +(12.4741 + 21.6057i) q^{44} +(-23.6539 + 31.7793i) q^{45} +(-25.6773 + 44.4743i) q^{46} +(20.2244 + 35.0296i) q^{47} +4.15076 q^{48} +(40.2289 - 27.9756i) q^{49} +(8.14664 - 34.4040i) q^{50} +(5.99301 + 10.3802i) q^{51} +(0.748223 - 1.29596i) q^{52} +(22.8390 + 13.1861i) q^{53} +(21.5078 - 12.4175i) q^{54} +(-61.9494 - 7.23458i) q^{55} +(-5.92320 - 18.8922i) q^{56} +15.6904i q^{57} +(-61.9532 + 35.7687i) q^{58} +(-68.4898 - 39.5426i) q^{59} +(-6.19582 + 8.32416i) q^{60} +(45.2611 - 26.1315i) q^{61} +66.1344 q^{62} +(-40.8307 - 37.5358i) q^{63} -8.00000 q^{64} +(1.48212 + 3.43500i) q^{65} +(15.8534 + 9.15294i) q^{66} +(30.0519 + 17.3504i) q^{67} +(-11.5507 - 20.0064i) q^{68} +37.6817i q^{69} +(46.7291 + 16.3216i) q^{70} +14.6636 q^{71} +(-19.4078 + 11.2051i) q^{72} +(50.5830 - 87.6124i) q^{73} +(8.30023 - 14.3764i) q^{74} +(-7.44528 - 24.8509i) q^{75} -30.2411i q^{76} +(19.0367 - 85.2182i) q^{77} -1.09803i q^{78} +(17.8625 + 30.9387i) q^{79} +(11.9416 - 16.0437i) q^{80} +(-26.5430 + 45.9738i) q^{81} +(-9.00833 - 15.6029i) q^{82} +80.8664 q^{83} +(-10.6951 - 9.83200i) q^{84} +(57.3636 + 6.69903i) q^{85} +(-18.5689 - 32.1623i) q^{86} +(-26.2455 + 45.4586i) q^{87} +(-30.5551 - 17.6410i) q^{88} +(-117.103 + 67.6093i) q^{89} +(6.49861 - 55.6473i) q^{90} +(-4.99769 + 1.56690i) q^{91} -72.6263i q^{92} +(42.0252 - 24.2633i) q^{93} +(-49.5394 - 28.6016i) q^{94} +(60.6472 + 45.1407i) q^{95} +(-5.08362 + 2.93503i) q^{96} -91.4185 q^{97} +(-29.4884 + 62.7091i) q^{98} -98.8347 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{4} - 6 q^{5} - 12 q^{9} + 24 q^{10} - 12 q^{11} + 32 q^{14} - 28 q^{15} - 32 q^{16} - 12 q^{19} - 8 q^{21} - 24 q^{24} - 42 q^{25} - 48 q^{26} - 136 q^{29} + 32 q^{30} + 84 q^{31} - 190 q^{35}+ \cdots + 176 q^{99}+O(q^{100}) \) 16 * q + 16 * q^4 - 6 * q^5 - 12 * q^9 + 24 * q^10 - 12 * q^11 + 32 * q^14 - 28 * q^15 - 32 * q^16 - 12 * q^19 - 8 * q^21 - 24 * q^24 - 42 * q^25 - 48 * q^26 - 136 * q^29 + 32 * q^30 + 84 * q^31 - 190 * q^35 - 48 * q^36 + 312 * q^39 + 48 * q^40 + 24 * q^44 + 384 * q^45 - 68 * q^46 + 296 * q^49 - 96 * q^50 - 76 * q^51 - 108 * q^54 + 56 * q^56 - 372 * q^59 - 28 * q^60 + 348 * q^61 - 128 * q^64 - 104 * q^65 + 480 * q^66 - 296 * q^70 - 384 * q^71 + 208 * q^74 - 150 * q^75 + 148 * q^79 + 24 * q^80 - 140 * q^81 + 256 * q^84 + 580 * q^85 - 188 * q^86 - 912 * q^89 - 616 * q^91 - 600 * q^94 - 310 * q^95 - 48 * q^96 + 176 * q^99

Introduction

L-functions

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