LMFDB - Embedded newform 117.3.k.a.113.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(29,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 2]))

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

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

chi := DirichletCharacter("117.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.k (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:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$26$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			113.20
Character	$\chi$	$=$	117.113
Dual form			117.3.k.a.29.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.44466i q^{2} +(-2.12872 - 2.11389i) q^{3} -1.97636 q^{4} +(2.73246 + 1.57759i) q^{5} +(5.16775 - 5.20400i) q^{6} +(-3.82542 + 6.62581i) q^{7} +4.94710i q^{8} +(0.0628969 + 8.99978i) q^{9} +(-3.85666 + 6.67994i) q^{10} +6.15061i q^{11} +(4.20712 + 4.17782i) q^{12} +(-12.9012 - 1.59941i) q^{13} +(-16.1979 - 9.35184i) q^{14} +(-2.48179 - 9.13437i) q^{15} -19.9994 q^{16} +(18.6707 - 10.7795i) q^{17} +(-22.0014 + 0.153762i) q^{18} +(15.0726 + 26.1066i) q^{19} +(-5.40033 - 3.11788i) q^{20} +(22.1495 - 6.01798i) q^{21} -15.0362 q^{22} +(7.11157 - 4.10586i) q^{23} +(10.4577 - 10.5310i) q^{24} +(-7.52244 - 13.0293i) q^{25} +(3.91002 - 31.5391i) q^{26} +(18.8907 - 19.2910i) q^{27} +(7.56041 - 13.0950i) q^{28} +4.21916i q^{29} +(22.3304 - 6.06713i) q^{30} +(-25.9263 + 44.9057i) q^{31} -29.1034i q^{32} +(13.0017 - 13.0929i) q^{33} +(26.3523 + 45.6435i) q^{34} +(-20.9056 + 12.0698i) q^{35} +(-0.124307 - 17.7868i) q^{36} +(22.3585 - 38.7261i) q^{37} +(-63.8217 + 36.8475i) q^{38} +(24.0821 + 30.6766i) q^{39} +(-7.80448 + 13.5178i) q^{40} +(47.9389 - 27.6775i) q^{41} +(14.7119 + 54.1480i) q^{42} +(25.7507 - 44.6016i) q^{43} -12.1558i q^{44} +(-14.0261 + 24.6908i) q^{45} +(10.0374 + 17.3854i) q^{46} +(24.2699 - 14.0122i) q^{47} +(42.5732 + 42.2767i) q^{48} +(-4.76761 - 8.25775i) q^{49} +(31.8521 - 18.3898i) q^{50} +(-62.5314 - 16.5213i) q^{51} +(25.4975 + 3.16102i) q^{52} +0.382421i q^{53} +(47.1599 + 46.1813i) q^{54} +(-9.70312 + 16.8063i) q^{55} +(-32.7786 - 18.9247i) q^{56} +(23.1011 - 87.4356i) q^{57} -10.3144 q^{58} +47.9620i q^{59} +(4.90492 + 18.0528i) q^{60} +(25.6786 - 44.4766i) q^{61} +(-109.779 - 63.3811i) q^{62} +(-59.8715 - 34.0112i) q^{63} -8.84980 q^{64} +(-32.7289 - 24.7231i) q^{65} +(32.0078 + 31.7848i) q^{66} +(-12.9554 - 22.4394i) q^{67} +(-36.9001 + 21.3043i) q^{68} +(-23.8179 - 6.29287i) q^{69} +(-29.5067 - 51.1071i) q^{70} +(7.07732 - 4.08609i) q^{71} +(-44.5229 + 0.311158i) q^{72} -24.8357 q^{73} +(94.6722 + 54.6590i) q^{74} +(-11.5293 + 43.6373i) q^{75} +(-29.7890 - 51.5961i) q^{76} +(-40.7528 - 23.5286i) q^{77} +(-74.9938 + 58.8726i) q^{78} +(8.23711 + 14.2671i) q^{79} +(-54.6477 - 31.5508i) q^{80} +(-80.9921 + 1.13212i) q^{81} +(67.6622 + 117.194i) q^{82} +(-39.7129 + 22.9283i) q^{83} +(-43.7755 + 11.8937i) q^{84} +68.0225 q^{85} +(109.036 + 62.9518i) q^{86} +(8.91887 - 8.98142i) q^{87} -30.4277 q^{88} +(70.5240 + 40.7171i) q^{89} +(-60.3605 - 34.2890i) q^{90} +(59.9500 - 79.3628i) q^{91} +(-14.0550 + 8.11468i) q^{92} +(150.116 - 40.7862i) q^{93} +(34.2551 + 59.3316i) q^{94} +95.1136i q^{95} +(-61.5216 + 61.9530i) q^{96} +(-23.4733 + 40.6570i) q^{97} +(20.1874 - 11.6552i) q^{98} +(-55.3541 + 0.386854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) $ 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$			2.44466i			1.22233i	0.791503	+	0.611165i	$0.209299\pi$
$2$			2.44466i			1.22233i	−0.791503	+	0.611165i	$0.790701\pi$
$3$	−2.12872	−	2.11389i	−0.709573	−	0.704632i
$3$	−2.12872	−	2.11389i	−0.709573	−	0.704632i
$4$	−1.97636			−0.494091
$5$	2.73246	+	1.57759i	0.546492	+	0.315517i	0.747706	−	0.664030i	$-0.231155\pi$
$5$	2.73246	+	1.57759i	0.546492	+	0.315517i	−0.201214	+	0.979547i	$0.564489\pi$
$6$	5.16775	−	5.20400i	0.861292	−	0.867333i
$7$	−3.82542	+	6.62581i	−0.546488	+	0.946545i	0.452024	+	0.892006i	$0.350702\pi$
$7$	−3.82542	+	6.62581i	−0.546488	+	0.946545i	−0.998512	+	0.0545390i	$0.982631\pi$
$8$			4.94710i			0.618388i
$9$	0.0628969	+	8.99978i	0.00698855	+	0.999976i
$10$	−3.85666	+	6.67994i	−0.385666	+	0.667994i
$11$			6.15061i			0.559146i	0.960124	+	0.279573i	$0.0901930\pi$
$11$			6.15061i			0.559146i	−0.960124	+	0.279573i	$0.909807\pi$
$12$	4.20712	+	4.17782i	0.350594	+	0.348152i
$13$	−12.9012	−	1.59941i	−0.992403	−	0.123032i
$13$	−12.9012	−	1.59941i	−0.992403	−	0.123032i
$14$	−16.1979	−	9.35184i	−1.15699	−	0.667989i
$15$	−2.48179	−	9.13437i	−0.165453	−	0.608958i
$16$	−19.9994			−1.24997
$17$	18.6707	−	10.7795i	1.09828	−	0.634090i	0.162508	−	0.986707i	$-0.448042\pi$
$17$	18.6707	−	10.7795i	1.09828	−	0.634090i	0.935768	+	0.352617i	$0.114708\pi$
$18$	−22.0014	+	0.153762i	−1.22230	+	0.00854231i
$19$	15.0726	+	26.1066i	0.793297	+	1.37403i	0.923915	+	0.382598i	$0.124971\pi$
$19$	15.0726	+	26.1066i	0.793297	+	1.37403i	−0.130618	+	0.991433i	$0.541696\pi$
$20$	−5.40033	−	3.11788i	−0.270017	−	0.155894i
$21$	22.1495	−	6.01798i	1.05474	−	0.286570i
$22$	−15.0362			−0.683461
$23$	7.11157	−	4.10586i	0.309199	−	0.178516i	−0.337369	−	0.941372i	$-0.609537\pi$
$23$	7.11157	−	4.10586i	0.309199	−	0.178516i	0.646568	+	0.762857i	$0.276204\pi$
$24$	10.4577	−	10.5310i	0.435736	−	0.438792i
$25$	−7.52244	−	13.0293i	−0.300898	−	0.521170i
$26$	3.91002	−	31.5391i	0.150386	−	1.21304i
$27$	18.8907	−	19.2910i	0.699656	−	0.714480i
$28$	7.56041	−	13.0950i	0.270015	−	0.467679i
$29$			4.21916i			0.145488i	0.997351	+	0.0727442i	$0.0231757\pi$
$29$			4.21916i			0.145488i	−0.997351	+	0.0727442i	$0.976824\pi$
$30$	22.3304	−	6.06713i	0.744348	−	0.202238i
$31$	−25.9263	+	44.9057i	−0.836333	+	1.44857i	0.0566070	+	0.998397i	$0.481972\pi$
$31$	−25.9263	+	44.9057i	−0.836333	+	1.44857i	−0.892940	+	0.450175i	$0.851362\pi$
$32$		−	29.1034i		−	0.909482i
$33$	13.0017	−	13.0929i	0.393992	−	0.396755i
$34$	26.3523	+	45.6435i	0.775067	+	1.34246i
$35$	−20.9056	+	12.0698i	−0.597303	+	0.344853i
$36$	−0.124307	−	17.7868i	−0.00345298	−	0.494079i
$37$	22.3585	−	38.7261i	0.604285	−	1.04665i	−0.387879	−	0.921710i	$-0.626792\pi$
$37$	22.3585	−	38.7261i	0.604285	−	1.04665i	0.992164	−	0.124942i	$-0.0398744\pi$
$38$	−63.8217	+	36.8475i	−1.67952	+	0.969671i
$39$	24.0821	+	30.6766i	0.617490	+	0.786578i
$40$	−7.80448	+	13.5178i	−0.195112	+	0.337944i
$41$	47.9389	−	27.6775i	1.16924	−	0.675062i	0.215740	−	0.976451i	$-0.430784\pi$
$41$	47.9389	−	27.6775i	1.16924	−	0.675062i	0.953501	+	0.301389i	$0.0974502\pi$
$42$	14.7119	+	54.1480i	0.350284	+	1.28924i
$43$	25.7507	−	44.6016i	0.598854	−	1.03725i	−0.394137	−	0.919052i	$-0.628956\pi$
$43$	25.7507	−	44.6016i	0.598854	−	1.03725i	0.992991	−	0.118194i	$-0.0377103\pi$
$44$		−	12.1558i		−	0.276269i
$45$	−14.0261	+	24.6908i	−0.311690	+	0.548684i
$46$	10.0374	+	17.3854i	0.218205	+	0.377943i
$47$	24.2699	−	14.0122i	0.516380	−	0.298132i	−0.219072	−	0.975709i	$-0.570303\pi$
$47$	24.2699	−	14.0122i	0.516380	−	0.298132i	0.735452	+	0.677577i	$0.236970\pi$
$48$	42.5732	+	42.2767i	0.886942	+	0.880765i
$49$	−4.76761	−	8.25775i	−0.0972982	−	0.168525i
$50$	31.8521	−	18.3898i	0.637042	−	0.367796i
$51$	−62.5314	−	16.5213i	−1.22611	−	0.323947i
$52$	25.4975	+	3.16102i	0.490337	+	0.0607889i
$53$			0.382421i			0.00721549i	0.999993	+	0.00360774i	$0.00114838\pi$
$53$			0.382421i			0.00721549i	−0.999993	+	0.00360774i	$0.998852\pi$
$54$	47.1599	+	46.1813i	0.873331	+	0.855210i
$55$	−9.70312	+	16.8063i	−0.176420	+	0.305569i
$56$	−32.7786	−	18.9247i	−0.585332	−	0.337942i
$57$	23.1011	−	87.4356i	0.405283	−	1.53396i
$58$	−10.3144			−0.177835
$59$			47.9620i			0.812914i	0.913670	+	0.406457i	$0.133236\pi$
$59$			47.9620i			0.812914i	−0.913670	+	0.406457i	$0.866764\pi$
$60$	4.90492	+	18.0528i	0.0817486	+	0.300881i
$61$	25.6786	−	44.4766i	0.420960	−	0.729124i	−0.575074	−	0.818102i	$-0.695027\pi$
$61$	25.6786	−	44.4766i	0.420960	−	0.729124i	0.996034	+	0.0889776i	$0.0283600\pi$
$62$	−109.779	−	63.3811i	−1.77063	−	1.02228i
$63$	−59.8715	−	34.0112i	−0.950341	−	0.539860i
$64$	−8.84980			−0.138278
$65$	−32.7289	−	24.7231i	−0.503521	−	0.380356i
$66$	32.0078	+	31.7848i	0.484966	+	0.481589i
$67$	−12.9554	−	22.4394i	−0.193364	−	0.334916i	0.752999	−	0.658022i	$-0.228606\pi$
$67$	−12.9554	−	22.4394i	−0.193364	−	0.334916i	−0.946363	+	0.323105i	$0.895273\pi$
$68$	−36.9001	+	21.3043i	−0.542648	+	0.313298i
$69$	−23.8179	−	6.29287i	−0.345187	−	0.0912010i
$70$	−29.5067	−	51.1071i	−0.421524	−	0.730101i
$71$	7.07732	−	4.08609i	0.0996806	−	0.0575506i	−0.449331	−	0.893365i	$-0.648338\pi$
$71$	7.07732	−	4.08609i	0.0996806	−	0.0575506i	0.549012	+	0.835815i	$0.315004\pi$
$72$	−44.5229	+	0.311158i	−0.618373	+	0.00432163i
$73$	−24.8357			−0.340215			−0.170107	−	0.985426i	$-0.554411\pi$
$73$	−24.8357			−0.340215			−0.170107	+	0.985426i	$0.554411\pi$
$74$	94.6722	+	54.6590i	1.27935	+	0.738635i
$75$	−11.5293	+	43.6373i	−0.153724	+	0.581830i
$76$	−29.7890	−	51.5961i	−0.391961	−	0.678896i
$77$	−40.7528	−	23.5286i	−0.529257	−	0.305567i
$78$	−74.9938	+	58.8726i	−0.961458	+	0.754777i
$79$	8.23711	+	14.2671i	0.104267	+	0.180596i	0.913439	−	0.406977i	$-0.133417\pi$
$79$	8.23711	+	14.2671i	0.104267	+	0.180596i	−0.809171	+	0.587573i	$0.800084\pi$
$80$	−54.6477	−	31.5508i	−0.683096	−	0.394386i
$81$	−80.9921	+	1.13212i	−0.999902	+	0.0139768i
$82$	67.6622	+	117.194i	0.825149	+	1.42920i
$83$	−39.7129	+	22.9283i	−0.478469	+	0.276244i	−0.719778	−	0.694204i	$-0.755757\pi$
$83$	−39.7129	+	22.9283i	−0.478469	+	0.276244i	0.241309	+	0.970448i	$0.422423\pi$
$84$	−43.7755	+	11.8937i	−0.521137	+	0.141592i
$85$	68.0225			0.800265
$86$	109.036	+	62.9518i	1.26786	+	0.731997i
$87$	8.91887	−	8.98142i	0.102516	−	0.103235i
$88$	−30.4277			−0.345769
$89$	70.5240	+	40.7171i	0.792405	+	0.457495i	0.840809	−	0.541333i	$-0.182080\pi$
$89$	70.5240	+	40.7171i	0.792405	+	0.457495i	−0.0484035	+	0.998828i	$0.515413\pi$
$90$	−60.3605	−	34.2890i	−0.670672	−	0.380989i
$91$	59.9500	−	79.3628i	0.658791	−	0.872118i
$92$	−14.0550	+	8.11468i	−0.152772	+	0.0882030i
$93$	150.116	−	40.7862i	1.61415	−	0.438561i
$94$	34.2551	+	59.3316i	0.364416	+	0.631187i
$95$			95.1136i			1.00120i
$96$	−61.5216	+	61.9530i	−0.640850	+	0.645344i
$97$	−23.4733	+	40.6570i	−0.241993	+	0.419144i	−0.961282	−	0.275567i	$-0.911134\pi$
$97$	−23.4733	+	40.6570i	−0.241993	+	0.419144i	0.719289	+	0.694711i	$0.244468\pi$
$98$	20.1874	−	11.6552i	0.205994	−	0.118931i
$99$	−55.3541	+	0.386854i	−0.559133	+	0.00390762i
$100$	14.8671	+	25.7505i	0.148671	+	0.257505i
$101$			36.9184i			0.365529i	0.983157	+	0.182764i	$0.0585045\pi$
$101$			36.9184i			0.365529i	−0.983157	+	0.182764i	$0.941495\pi$
$102$	40.3889	−	152.868i	0.395970	−	1.49871i
$103$	−34.9957	+	60.6143i	−0.339764	+	0.588488i	−0.984388	−	0.176011i	$-0.943680\pi$
$103$	−34.9957	+	60.6143i	−0.339764	+	0.588488i	0.644624	+	0.764500i	$0.277014\pi$
$104$	7.91247	−	63.8238i	0.0760814	−	0.613690i
$105$	70.0165	+	18.4989i	0.666824	+	0.176180i
$106$	−0.934889			−0.00881971
$107$	97.4131	+	56.2415i	0.910403	+	0.525621i	0.880561	−	0.473933i	$-0.157166\pi$
$107$	97.4131	+	56.2415i	0.910403	+	0.525621i	0.0298423	+	0.999555i	$0.490500\pi$
$108$	−37.3349	+	38.1260i	−0.345693	+	0.353018i
$109$	−206.693			−1.89627			−0.948133	−	0.317875i	$-0.897031\pi$
$109$	−206.693			−1.89627			−0.948133	+	0.317875i	$0.897031\pi$
$110$	−41.0857	−	23.7208i	−0.373506	−	0.215644i
$111$	−129.458	+	35.1735i	−1.16629	+	0.316878i
$112$	76.5062	−	132.513i	0.683091	−	1.18315i
$113$			173.223i			1.53295i	0.642276	+	0.766473i	$0.277990\pi$
$113$			173.223i			1.53295i	−0.642276	+	0.766473i	$0.722010\pi$
$114$	213.750	+	56.4744i	1.87500	+	0.495390i
$115$	25.9094			0.225299
$116$		−	8.33860i		−	0.0718845i
$117$	13.5829	−	116.209i	0.116093	−	0.993238i
$118$	−117.251			−0.993650
$119$			164.945i			1.38609i
$120$	45.1887	−	12.2777i	0.376572	−	0.102314i
$121$	83.1700			0.687355
$122$	108.730	+	62.7753i	0.891230	+	0.514552i
$123$	−160.556	−	42.4201i	−1.30533	−	0.344879i
$124$	51.2398	−	88.7500i	0.413225	−	0.715726i
$125$		−	126.349i		−	1.01079i
$126$	83.1457	−	146.365i	0.659887	−	1.16163i
$127$	82.2784	−	142.510i	0.647862	−	1.12213i	−0.335771	−	0.941944i	$-0.608997\pi$
$127$	82.2784	−	142.510i	0.647862	−	1.12213i	0.983633	−	0.180186i	$-0.0576699\pi$
$128$		−	138.048i		−	1.07850i
$129$	−149.099	+	40.5099i	−1.15581	+	0.314030i
$130$	60.4397	−	80.0110i	0.464921	−	0.615469i
$131$	143.908	+	83.0856i	1.09854	+	0.634241i	0.935836	−	0.352435i	$-0.114646\pi$
$131$	143.908	+	83.0856i	1.09854	+	0.634241i	0.162701	+	0.986675i	$0.447979\pi$
$132$	−25.6962	+	25.8764i	−0.194668	+	0.196033i
$133$	−230.637			−1.73411
$134$	54.8567	−	31.6715i	0.409378	−	0.236355i
$135$	82.0512	−	22.9101i	0.607787	−	0.169704i
$136$	53.3274	+	92.3658i	0.392114	+	0.679161i
$137$	164.457	+	94.9496i	1.20042	+	0.693063i	0.960648	−	0.277767i	$-0.0895943\pi$
$137$	164.457	+	94.9496i	1.20042	+	0.693063i	0.239771	+	0.970829i	$0.422928\pi$
$138$	15.3839	−	58.2267i	0.111478	−	0.421932i
$139$	3.92118			0.0282099			0.0141050	−	0.999901i	$-0.495510\pi$
$139$	3.92118			0.0282099			0.0141050	+	0.999901i	$0.495510\pi$
$140$	41.3170	−	23.8544i	0.295122	−	0.170389i
$141$	−81.2841	−	21.4759i	−0.576483	−	0.152311i
$142$	9.98911	+	17.3016i	0.0703459	+	0.121843i
$143$	9.83737	−	79.3505i	0.0687928	−	0.554898i
$144$	−1.25790	−	179.991i	−0.00873544	−	1.24993i
$145$	−6.65610	+	11.5287i	−0.0459041	+	0.0795083i
$146$		−	60.7148i		−	0.415855i
$147$	−7.30710	+	27.6567i	−0.0497082	+	0.188141i
$148$	−44.1886	+	76.5369i	−0.298572	+	0.517141i
$149$		−	275.096i		−	1.84628i	−0.384462	−	0.923141i	$-0.625613\pi$
$149$		−	275.096i		−	1.84628i	0.384462	−	0.923141i	$-0.374387\pi$
$150$	−106.678	−	28.1852i	−0.711189	−	0.187901i
$151$	−10.8588	−	18.8080i	−0.0719127	−	0.124556i	0.827827	−	0.560984i	$-0.189577\pi$
$151$	−10.8588	−	18.8080i	−0.0719127	−	0.124556i	−0.899740	+	0.436427i	$0.856244\pi$
$152$	−129.152	+	74.5659i	−0.849684	+	0.490565i
$153$	98.1877	+	167.354i	0.641750	+	1.09382i
$154$	57.5195	−	99.6268i	0.373503	−	0.646927i
$155$	−141.685	+	81.8021i	−0.914099	+	0.527755i
$156$	−47.5950	−	60.6280i	−0.305096	−	0.388641i
$157$	31.9519	−	55.3422i	0.203515	−	0.352498i	−0.746144	−	0.665785i	$-0.768097\pi$
$157$	31.9519	−	55.3422i	0.203515	−	0.352498i	0.949659	+	0.313287i	$0.101430\pi$
$158$	−34.8782	+	20.1369i	−0.220748	+	0.127449i
$159$	0.808398	−	0.814067i	0.00508426	−	0.00511992i
$160$	45.9132	−	79.5239i	0.286957	−	0.497024i
$161$			62.8266i			0.390227i
$162$	−2.76764	−	197.998i	−0.0170842	−	1.22221i
$163$	−88.7596	−	153.736i	−0.544537	−	0.943166i	−0.998636	−	0.0522150i	$-0.983372\pi$
$163$	−88.7596	−	153.736i	−0.544537	−	0.943166i	0.454098	−	0.890952i	$-0.349961\pi$
$164$	−94.7447	+	54.7009i	−0.577712	+	0.333542i
$165$	56.1820	−	15.2645i	0.340497	−	0.0925123i
$166$	−56.0518	−	97.0846i	−0.337662	−	0.584847i
$167$	−55.2953	+	31.9247i	−0.331109	+	0.191166i	−0.656334	−	0.754471i	$-0.727894\pi$
$167$	−55.2953	+	31.9247i	−0.331109	+	0.191166i	0.325224	+	0.945637i	$0.394560\pi$
$168$	29.7716	+	109.576i	0.177212	+	0.652238i
$169$	163.884	+	41.2688i	0.969726	+	0.244194i
$170$			166.292i			0.978188i
$171$	−234.006	+	137.293i	−1.36845	+	0.802880i
$172$	−50.8928	+	88.1489i	−0.295888	+	0.512493i
$173$	212.899	+	122.917i	1.23063	+	0.710505i	0.967161	−	0.254163i	$-0.0818001\pi$
$173$	212.899	+	122.917i	1.23063	+	0.710505i	0.263469	+	0.964668i	$0.415133\pi$
$174$	21.9565	+	21.8036i	0.126187	+	0.125308i
$175$	115.106			0.657748
$176$		−	123.009i		−	0.698913i
$177$	101.387	−	102.098i	0.572805	−	0.576822i
$178$	−99.5394	+	172.407i	−0.559210	+	0.968580i
$179$	−101.540	−	58.6239i	−0.567260	−	0.327508i	0.188794	−	0.982017i	$-0.439542\pi$
$179$	−101.540	−	58.6239i	−0.567260	−	0.327508i	−0.756054	+	0.654509i	$0.772876\pi$
$180$	27.7206	−	48.7979i	0.154003	−	0.271100i
$181$	260.434			1.43886			0.719431	−	0.694564i	$-0.244403\pi$
$181$	260.434			1.43886			0.719431	+	0.694564i	$0.244403\pi$
$182$	194.015	+	146.557i	1.06602	+	0.805260i
$183$	−148.681	+	40.3964i	−0.812466	+	0.220745i
$184$	20.3121	+	35.1817i	0.110392	+	0.191205i
$185$	122.188	−	70.5450i	0.660473	−	0.381325i
$186$	99.7083	+	366.982i	0.536066	+	1.97302i
$187$	66.3007	+	114.836i	0.354549	+	0.614097i
$188$	−47.9661	+	27.6932i	−0.255139	+	0.147304i
$189$	55.5536	+	198.962i	0.293934	+	1.05271i
$190$	−232.520			−1.22379
$191$	−302.794	−	174.818i	−1.58531	−	0.915280i	−0.994065	−	0.108789i	$-0.965303\pi$
$191$	−302.794	−	174.818i	−1.58531	−	0.915280i	−0.591246	−	0.806491i	$-0.701364\pi$
$192$	18.8387	+	18.7075i	0.0981184	+	0.0974351i
$193$	148.706	+	257.567i	0.770499	+	1.33454i	0.937290	+	0.348551i	$0.113326\pi$
$193$	148.706	+	257.567i	0.770499	+	1.33454i	−0.166791	+	0.985992i	$0.553341\pi$
$194$	−99.3924	−	57.3843i	−0.512332	−	0.295795i
$195$	17.4085	+	121.814i	0.0892744	+	0.624688i
$196$	9.42254	+	16.3203i	0.0480742	+	0.0832669i
$197$	−301.201	−	173.899i	−1.52894	−	0.882734i	−0.999407	−	0.0344457i	$-0.989033\pi$
$197$	−301.201	−	173.899i	−1.52894	−	0.882734i	−0.529534	−	0.848289i	$-0.677633\pi$
$198$	−0.945728	−	135.322i	−0.00477640	−	0.683445i
$199$	32.5912	+	56.4496i	0.163775	+	0.283666i	0.936220	−	0.351416i	$-0.114300\pi$
$199$	32.5912	+	56.4496i	0.163775	+	0.283666i	−0.772445	+	0.635082i	$0.780966\pi$
$200$	64.4571	−	37.2143i	0.322285	−	0.186072i
$201$	−19.8561	+	75.1535i	−0.0987866	+	0.373898i
$202$	−90.2529			−0.446797
$203$	−27.9554	−	16.1401i	−0.137711	−	0.0795077i
$204$	123.585	+	32.6520i	0.605808	+	0.160059i
$205$	174.655			0.851975
$206$	−148.181	−	85.5525i	−0.719327	−	0.415304i
$207$	37.3992	+	63.7443i	0.180672	+	0.307943i
$208$	258.018	+	31.9874i	1.24047	+	0.153786i
$209$	−160.571	+	92.7060i	−0.768284	+	0.443569i
$210$	−45.2235	+	171.167i	−0.215350	+	0.815079i
$211$	46.6252	+	80.7573i	0.220973	+	0.382736i	0.955104	−	0.296272i	$-0.0957435\pi$
$211$	46.6252	+	80.7573i	0.220973	+	0.382736i	−0.734131	+	0.679008i	$0.762410\pi$
$212$		−	0.755803i		−	0.00356511i
$213$	−23.7032	−	6.26257i	−0.111283	−	0.0294017i
$214$	−137.491	+	238.142i	−0.642483	+	1.11281i
$215$	140.726	−	81.2480i	0.654538	−	0.377898i
$216$	95.4344	+	93.4543i	0.441826	+	0.432659i
$217$	−198.358	−	343.566i	−0.914092	−	1.58325i
$218$		−	505.294i		−	2.31786i
$219$	52.8682	+	52.5000i	0.241407	+	0.239726i
$220$	19.1769	−	33.2153i	0.0871677	−	0.150979i
$221$	−258.116	+	109.207i	−1.16794	+	0.494150i
$222$	−85.9872	−	316.481i	−0.387330	−	1.42559i
$223$	−246.243			−1.10423			−0.552115	−	0.833768i	$-0.686179\pi$
$223$	−246.243			−1.10423			−0.552115	+	0.833768i	$0.686179\pi$
$224$	192.834	+	111.333i	0.860865	+	0.497021i
$225$	116.787	−	68.5198i	0.519055	−	0.304533i
$226$	−423.471			−1.87377
$227$	−164.409	−	94.9215i	−0.724268	−	0.418156i	0.0920534	−	0.995754i	$-0.470657\pi$
$227$	−164.409	−	94.9215i	−0.724268	−	0.418156i	−0.816322	+	0.577598i	$0.803990\pi$
$228$	−45.6562	+	172.804i	−0.200247	+	0.757914i
$229$	21.0010	−	36.3747i	0.0917072	−	0.158842i	−0.816522	−	0.577314i	$-0.804101\pi$
$229$	21.0010	−	36.3747i	0.0917072	−	0.158842i	0.908230	+	0.418472i	$0.137434\pi$
$230$			63.3397i			0.275390i
$231$	37.0142	+	136.233i	0.160235	+	0.589753i
$232$	−20.8726			−0.0899683
$233$		−	151.808i		−	0.651536i	−0.945450	−	0.325768i	$-0.894377\pi$
$233$		−	151.808i		−	0.651536i	0.945450	−	0.325768i	$-0.105623\pi$
$234$	284.091	+	33.2056i	1.21407	+	0.141904i
$235$	88.4219			0.376263
$236$		−	94.7902i		−	0.401654i
$237$	12.6246	−	47.7830i	0.0532685	−	0.201616i
$238$	−403.234			−1.69426
$239$	171.028	+	98.7429i	0.715597	+	0.413150i	0.813130	−	0.582082i	$-0.197762\pi$
$239$	171.028	+	98.7429i	0.715597	+	0.413150i	−0.0975330	+	0.995232i	$0.531095\pi$
$240$	49.6344	+	182.682i	0.206810	+	0.761176i
$241$	4.05145	−	7.01731i	0.0168110	−	0.0291175i	−0.857498	−	0.514488i	$-0.827982\pi$
$241$	4.05145	−	7.01731i	0.0168110	−	0.0291175i	0.874309	+	0.485371i	$0.161315\pi$
$242$			203.322i			0.840175i
$243$	174.803	+	168.799i	0.719352	+	0.694645i
$244$	−50.7502	+	87.9018i	−0.207992	+	0.360253i
$245$		−	30.0853i		−	0.122797i
$246$	103.703	−	392.505i	0.421556	−	1.59555i
$247$	−152.700	−	360.915i	−0.618221	−	1.46119i
$248$	−222.153	−	128.260i	−0.895779	−	0.517178i
$249$	133.006	+	35.1411i	0.534159	+	0.141129i
$250$	308.879			1.23552
$251$	95.8522	−	55.3403i	0.381881	−	0.220479i	−0.296755	−	0.954954i	$-0.595905\pi$
$251$	95.8522	−	55.3403i	0.381881	−	0.220479i	0.678636	+	0.734474i	$0.262571\pi$
$252$	118.328	+	67.2184i	0.469555	+	0.266740i
$253$	25.2536	+	43.7405i	0.0998165	+	0.172887i
$254$	348.390	+	201.143i	1.37161	+	0.791901i
$255$	−144.801	−	143.792i	−0.567847	−	0.563892i
$256$	302.082			1.18001
$257$	−435.380	+	251.367i	−1.69408	+	0.978080i	−0.742927	+	0.669372i	$0.766563\pi$
$257$	−435.380	+	251.367i	−1.69408	+	0.978080i	−0.951157	+	0.308708i	$0.900103\pi$
$258$	−99.0329	−	364.497i	−0.383849	−	1.41278i
$259$	171.061	+	296.287i	0.660469	+	1.14397i
$260$	64.6842	+	48.8619i	0.248785	+	0.187930i
$261$	−37.9716	+	0.265372i	−0.145485	+	0.00101675i
$262$	−203.116	+	351.807i	−0.775252	+	1.34278i
$263$		−	201.900i		−	0.767681i	−0.923399	−	0.383840i	$-0.874601\pi$
$263$		−	201.900i		−	0.767681i	0.923399	−	0.383840i	$-0.125399\pi$
$264$	64.7721	+	64.3210i	0.245349	+	0.243640i
$265$	−0.603302	+	1.04495i	−0.00227661	+	0.00394321i
$266$		−	563.828i		−	2.11965i
$267$	−64.0543	−	235.756i	−0.239904	−	0.882980i
$268$	25.6045	+	44.3484i	0.0955393	+	0.165479i
$269$	241.432	−	139.391i	0.897515	−	0.518180i	0.0211218	−	0.999777i	$-0.493276\pi$
$269$	241.432	−	139.391i	0.897515	−	0.518180i	0.876393	+	0.481596i	$0.159943\pi$
$270$	56.0074	+	200.587i	0.207435	+	0.742916i
$271$	−58.8505	+	101.932i	−0.217161	+	0.376133i	−0.953939	−	0.300001i	$-0.903013\pi$
$271$	−58.8505	+	101.932i	−0.217161	+	0.376133i	0.736778	+	0.676135i	$0.236346\pi$
$272$	−373.403	+	215.584i	−1.37281	+	0.792590i
$273$	−295.381	+	42.2131i	−1.08198	+	0.154627i
$274$	−232.119	+	402.043i	−0.847151	+	1.46731i
$275$	80.1379	−	46.2676i	0.291410	−	0.168246i
$276$	47.0728	+	12.4370i	0.170554	+	0.0450616i
$277$	−55.1523	+	95.5265i	−0.199106	+	0.344861i	−0.948239	−	0.317558i	$-0.897137\pi$
$277$	−55.1523	+	95.5265i	−0.199106	+	0.344861i	0.749133	+	0.662420i	$0.230470\pi$
$278$			9.58595i			0.0344818i
$279$	−405.772	−	230.507i	−1.45438	−	0.826189i
$280$	−59.7108	−	103.422i	−0.213253	−	0.369365i
$281$	−15.0724	+	8.70203i	−0.0536383	+	0.0309681i	−0.526579	−	0.850126i	$-0.676526\pi$
$281$	−15.0724	+	8.70203i	−0.0536383	+	0.0309681i	0.472941	+	0.881094i	$0.343192\pi$
$282$	52.5012	−	198.712i	0.186174	−	0.704652i
$283$	−246.465	−	426.889i	−0.870900	−	1.50844i	−0.861067	−	0.508491i	$-0.830203\pi$
$283$	−246.465	−	426.889i	−0.870900	−	1.50844i	−0.00983293	−	0.999952i	$-0.503130\pi$
$284$	−13.9874	+	8.07561i	−0.0492513	+	0.0284352i
$285$	201.060	−	202.470i	0.705474	−	0.710422i
$286$	193.985	+	24.0490i	0.678269	+	0.0840875i
$287$			423.512i			1.47565i
$288$	261.924	−	1.83052i	0.909460	−	0.00635596i
$289$	87.8963	−	152.241i	0.304140	−	0.526785i
$290$	−28.1837	−	16.2719i	−0.0971853	−	0.0561100i
$291$	135.913	−	36.9272i	0.467054	−	0.126898i
$292$	49.0843			0.168097
$293$		−	346.112i		−	1.18127i	−0.806938	−	0.590636i	$-0.798877\pi$
$293$		−	346.112i		−	1.18127i	0.806938	−	0.590636i	$-0.201123\pi$
$294$	−67.6112	−	17.8634i	−0.229970	−	0.0607598i
$295$	−75.6641	+	131.054i	−0.256489	+	0.444251i
$296$	191.582	+	110.610i	0.647237	+	0.373682i
$297$	118.651	+	116.189i	0.399499	+	0.391210i
$298$	672.516			2.25677
$299$	−98.3150	+	41.5964i	−0.328813	+	0.139118i
$300$	22.7861	−	86.2431i	0.0759536	−	0.287477i
$301$	197.014	+	341.239i	0.654533	+	1.13368i
$302$	45.9792	−	26.5461i	0.152249	−	0.0879011i
$303$	78.0416	−	78.5889i	0.257563	−	0.259369i
$304$	−301.444	−	522.117i	−0.991594	−	1.71749i
$305$	140.331	−	81.0203i	0.460102	−	0.265640i
$306$	−409.124	+	240.036i	−1.33701	+	0.784430i
$307$	446.987			1.45598			0.727992	−	0.685586i	$-0.240454\pi$
$307$	446.987			1.45598			0.727992	+	0.685586i	$0.240454\pi$
$308$	80.5423	+	46.5011i	0.261501	+	0.150978i
$309$	202.628	−	55.0537i	0.655755	−	0.178167i
$310$	−199.978	−	346.372i	−0.645091	−	1.11733i
$311$	76.2524	+	44.0243i	0.245184	+	0.141557i	0.617557	−	0.786526i	$-0.288122\pi$
$311$	76.2524	+	44.0243i	0.245184	+	0.141557i	−0.372373	+	0.928083i	$0.621456\pi$
$312$	−151.760	+	119.137i	−0.486411	+	0.381849i
$313$	−171.445	−	296.951i	−0.547747	−	0.948726i	−0.998428	−	0.0560413i	$-0.982152\pi$
$313$	−171.445	−	296.951i	−0.547747	−	0.948726i	0.450681	−	0.892685i	$-0.351181\pi$
$314$	135.293	+	78.1114i	0.430869	+	0.248763i
$315$	−109.941	−	187.387i	−0.349019	−	0.594878i
$316$	−16.2795	−	28.1969i	−0.0515174	−	0.0892308i
$317$	290.108	−	167.494i	0.915166	−	0.528371i	0.0330763	−	0.999453i	$-0.489470\pi$
$317$	290.108	−	167.494i	0.915166	−	0.528371i	0.882090	+	0.471081i	$0.156136\pi$
$318$	1.99012	+	1.97626i	0.00625823	+	0.00621465i
$319$	−25.9504			−0.0813493
$320$	−24.1817	−	13.9613i	−0.0755678	−	0.0436291i
$321$	−88.4767	−	325.644i	−0.275628	−	1.01447i
$322$	−153.590			−0.476986
$323$	562.833	+	324.952i	1.74252	+	1.00604i
$324$	160.070	−	2.23747i	0.494043	−	0.00690578i
$325$	76.2096	+	180.125i	0.234491	+	0.554231i
$326$	375.833	−	216.987i	1.15286	−	0.665604i
$327$	439.991	+	436.927i	1.34554	+	1.33617i
$328$	136.924	+	237.159i	0.417450	+	0.723045i
$329$			214.410i			0.651702i
$330$	37.3166	+	137.346i	0.113081	+	0.416199i
$331$	27.4099	−	47.4753i	0.0828092	−	0.143430i	−0.821646	−	0.569998i	$-0.806944\pi$
$331$	27.4099	−	47.4753i	0.0828092	−	0.143430i	0.904456	+	0.426568i	$0.140277\pi$
$332$	78.4872	−	45.3146i	0.236407	−	0.136490i
$333$	349.933	+	198.786i	1.05085	+	0.596955i
$334$	−78.0451	−	135.178i	−0.233668	−	0.404725i
$335$		−	81.7530i		−	0.244039i
$336$	−442.978	+	120.356i	−1.31839	+	0.358203i
$337$	−93.3550	+	161.696i	−0.277018	+	0.479809i	−0.970642	−	0.240528i	$-0.922679\pi$
$337$	−93.3550	+	161.696i	−0.277018	+	0.479809i	0.693624	+	0.720337i	$0.256013\pi$
$338$	−100.888	+	400.640i	−0.298486	+	1.18533i
$339$	366.175	−	368.743i	1.08016	−	1.08774i
$340$	−134.437			−0.395404
$341$	−276.198	−	159.463i	−0.809964	−	0.467633i
$342$	−335.634	−	572.064i	−0.981385	−	1.67270i
$343$	−301.938			−0.880287
$344$	220.649	+	127.391i	0.641420	+	0.370324i
$345$	−55.1539	−	54.7698i	−0.159866	−	0.158753i
$346$	−300.491	+	520.466i	−0.868471	+	1.50424i
$347$		−	156.844i		−	0.452000i	−0.974127	−	0.226000i	$-0.927435\pi$
$347$		−	156.844i		−	0.452000i	0.974127	−	0.226000i	$-0.0725650\pi$
$348$	−17.6269	+	17.7505i	−0.0506521	+	0.0510073i
$349$	−21.9346			−0.0628499			−0.0314250	−	0.999506i	$-0.510005\pi$
$349$	−21.9346			−0.0628499			−0.0314250	+	0.999506i	$0.510005\pi$
$350$			281.395i			0.803985i
$351$	−274.568	+	218.663i	−0.782244	+	0.622972i
$352$	179.004			0.508534
$353$		−	535.408i		−	1.51674i	−0.651827	−	0.758368i	$-0.725997\pi$
$353$		−	535.408i		−	1.51674i	0.651827	−	0.758368i	$-0.274003\pi$
$354$	249.594	+	247.856i	0.705067	+	0.700157i
$355$	25.7847			0.0726329
$356$	−139.381	−	80.4717i	−0.391520	−	0.226044i
$357$	348.676	−	351.121i	0.976683	−	0.983532i
$358$	143.316	−	248.230i	0.400323	−	0.693380i
$359$		−	100.858i		−	0.280941i	−0.990085	−	0.140471i	$-0.955138\pi$
$359$		−	100.858i		−	0.280941i	0.990085	−	0.140471i	$-0.0448615\pi$
$360$	−122.148	−	69.3884i	−0.339299	−	0.192746i
$361$	−273.869	+	474.355i	−0.758641	+	1.31400i
$362$			636.673i			1.75876i
$363$	−177.046	−	175.813i	−0.487729	−	0.484332i
$364$	−118.483	+	156.850i	−0.325503	+	0.430906i
$365$	−67.8625	−	39.1804i	−0.185925	−	0.107344i
$366$	−98.7554	−	363.475i	−0.269824	−	0.993101i
$367$	−573.781			−1.56344			−0.781718	−	0.623632i	$-0.785656\pi$
$367$	−573.781			−1.56344			−0.781718	+	0.623632i	$0.785656\pi$
$368$	−142.227	+	82.1150i	−0.386487	+	0.223139i
$369$	252.107	+	429.699i	0.683217	+	1.16450i
$370$	172.459	+	298.707i	0.466104	+	0.807317i
$371$	−2.53385	−	1.46292i	−0.00682978	−	0.00394318i
$372$	−296.683	+	80.6083i	−0.797536	+	0.216689i
$373$	−292.915			−0.785294			−0.392647	−	0.919689i	$-0.628441\pi$
$373$	−292.915			−0.785294			−0.392647	+	0.919689i	$0.628441\pi$
$374$	−280.735	+	162.083i	−0.750629	+	0.433376i
$375$	−267.088	+	268.961i	−0.712233	+	0.717228i
$376$	69.3199	+	120.066i	0.184361	+	0.319323i
$377$	6.74819	−	54.4324i	0.0178997	−	0.144383i
$378$	−486.395	+	135.810i	−1.28676	+	0.359285i
$379$	111.262	−	192.712i	0.293568	−	0.508475i	−0.681082	−	0.732207i	$-0.738491\pi$
$379$	111.262	−	192.712i	0.293568	−	0.508475i	0.974651	+	0.223731i	$0.0718238\pi$
$380$		−	187.979i		−	0.494682i
$381$	−476.400	+	129.437i	−1.25039	+	0.339729i
$382$	427.372	−	740.230i	1.11877	−	1.93777i
$383$			567.525i			1.48179i	0.671622	+	0.740894i	$0.265598\pi$
$383$			567.525i			1.48179i	−0.671622	+	0.740894i	$0.734402\pi$
$384$	−291.820	+	293.866i	−0.759948	+	0.765277i
$385$	−74.2369	−	128.582i	−0.192823	−	0.333980i
$386$	−629.663	+	363.536i	−1.63125	+	0.941804i
$387$	403.024	+	228.946i	1.04141	+	0.591590i
$388$	46.3918	−	80.3529i	0.119566	−	0.207095i
$389$	192.834	−	111.333i	0.495718	−	0.286203i	−0.231225	−	0.972900i	$-0.574273\pi$
$389$	192.834	−	111.333i	0.495718	−	0.286203i	0.726944	+	0.686697i	$0.240940\pi$
$390$	−297.794	+	42.5579i	−0.763574	+	0.109123i
$391$	88.5185	−	153.319i	0.226390	−	0.392119i
$392$	40.8519	−	23.5859i	0.104214	−	0.0601681i
$393$	−130.707	−	481.073i	−0.332587	−	1.22410i
$394$	425.123	−	736.335i	1.07899	−	1.86887i
$395$			51.9790i			0.131592i
$396$	109.400	−	0.764565i	0.276262	−	0.00193072i
$397$	54.6826	+	94.7131i	0.137740	+	0.238572i	0.926641	−	0.375948i	$-0.122683\pi$
$397$	54.6826	+	94.7131i	0.137740	+	0.238572i	−0.788901	+	0.614520i	$0.789350\pi$
$398$	−138.000	+	79.6744i	−0.346734	+	0.200187i
$399$	490.961	+	487.541i	1.23048	+	1.22191i
$400$	150.445	+	260.578i	0.376112	+	0.651444i
$401$	143.236	−	82.6971i	0.357196	−	0.206227i	−0.310654	−	0.950523i	$-0.600548\pi$
$401$	143.236	−	82.6971i	0.357196	−	0.206227i	0.667850	+	0.744296i	$0.267215\pi$
$402$	−183.725	−	48.5415i	−0.457027	−	0.120750i
$403$	406.305	−	537.872i	1.00820	−	1.33467i
$404$		−	72.9641i		−	0.180604i
$405$	−223.094	−	124.679i	−0.550848	−	0.307848i
$406$	39.4570	−	68.3415i	0.0971846	−	0.168329i
$407$	238.189	+	137.519i	0.585232	+	0.337884i
$408$	81.7325	−	309.350i	0.200325	−	0.758210i
$409$	45.5352			0.111333			0.0556665	−	0.998449i	$-0.482272\pi$
$409$	45.5352			0.111333			0.0556665	+	0.998449i	$0.482272\pi$
$410$			426.972i			1.04139i
$411$	−149.370	−	549.767i	−0.363432	−	1.33763i
$412$	69.1642	−	119.796i	0.167874	−	0.290767i
$413$	−317.787	−	183.474i	−0.769460	−	0.444248i
$414$	−155.833	+	91.4283i	−0.376408	+	0.220841i
$415$	−144.685			−0.348639
$416$	−46.5484	+	375.470i	−0.111895	+	0.902572i
$417$	−8.34709	−	8.28896i	−0.0200170	−	0.0198776i
$418$	−226.635	−	392.543i	−0.542188	−	0.939097i
$419$	−339.027	+	195.737i	−0.809134	+	0.467154i	−0.846655	−	0.532142i	$-0.821387\pi$
$419$	−339.027	+	195.737i	−0.809134	+	0.467154i	0.0375209	+	0.999296i	$0.488054\pi$
$420$	−138.378	−	36.5605i	−0.329472	−	0.0870489i
$421$	111.844	+	193.719i	0.265662	+	0.460140i	0.967737	−	0.251963i	$-0.0810762\pi$
$421$	111.844	+	193.719i	0.265662	+	0.460140i	−0.702075	+	0.712103i	$0.747743\pi$
$422$	−197.424	+	113.983i	−0.467830	+	0.270102i
$423$	127.633	+	217.542i	0.301734	+	0.514284i
$424$	−1.89188			−0.00446197
$425$	−280.898	−	162.177i	−0.660937	−	0.381592i
$426$	15.3098	−	57.9463i	0.0359386	−	0.136024i
$427$	196.462	+	340.283i	0.460099	+	0.796915i
$428$	−192.524	−	111.154i	−0.449822	−	0.259705i
$429$	−188.680	+	148.120i	−0.439813	+	0.345268i
$430$	198.624	+	344.026i	0.461915	+	0.800061i
$431$	−210.330	−	121.434i	−0.488006	−	0.281750i	0.235741	−	0.971816i	$-0.424248\pi$
$431$	−210.330	−	121.434i	−0.488006	−	0.281750i	−0.723747	+	0.690066i	$0.757582\pi$
$432$	−377.803	+	385.809i	−0.874545	+	0.893075i
$433$	−31.9975	−	55.4212i	−0.0738972	−	0.127994i	0.826709	−	0.562630i	$-0.190210\pi$
$433$	−31.9975	−	55.4212i	−0.0738972	−	0.127994i	−0.900606	+	0.434636i	$0.856877\pi$
$434$	839.902	−	484.918i	1.93526	−	1.11732i
$435$	38.5394	−	10.4711i	0.0885964	−	0.0240714i
$436$	408.500			0.936927
$437$	214.380	+	123.772i	0.490573	+	0.283232i
$438$	−128.345	+	129.245i	−0.293024	+	0.295079i
$439$	−243.386			−0.554411			−0.277205	−	0.960811i	$-0.589408\pi$
$439$	−243.386			−0.554411			−0.277205	+	0.960811i	$0.589408\pi$
$440$	−83.1425	−	48.0023i	−0.188960	−	0.109096i
$441$	74.0181	−	43.4269i	0.167841	−	0.0984736i
$442$	−266.974	−	631.006i	−0.604014	−	1.42761i
$443$	−8.10700	+	4.68058i	−0.0183002	+	0.0105656i	−0.509122	−	0.860694i	$-0.670030\pi$
$443$	−8.10700	+	4.68058i	−0.0183002	+	0.0105656i	0.490822	+	0.871260i	$0.336697\pi$
$444$	255.856	−	69.5155i	0.576252	−	0.156567i
$445$	128.469	+	222.516i	0.288695	+	0.500035i
$446$		−	601.981i		−	1.34973i
$447$	−581.524	+	585.602i	−1.30095	+	1.31007i
$448$	33.8542	−	58.6371i	0.0755673	−	0.130886i
$449$	−351.048	+	202.678i	−0.781844	+	0.451398i	−0.837083	−	0.547075i	$-0.815741\pi$
$449$	−351.048	+	202.678i	−0.781844	+	0.451398i	0.0552392	+	0.998473i	$0.482408\pi$
$450$	167.508	+	285.505i	0.372239	+	0.634456i
$451$	170.234	+	294.854i	0.377459	+	0.653777i
$452$		−	342.352i		−	0.757415i
$453$	−16.6428	+	62.9914i	−0.0367391	+	0.139054i
$454$	232.051	−	401.924i	0.511125	−	0.885295i
$455$	289.013	−	122.279i	0.635193	−	0.268746i
$456$	432.553	+	114.284i	0.948581	+	0.250622i
$457$	9.69301			0.0212101			0.0106050	−	0.999944i	$-0.496624\pi$
$457$	9.69301			0.0212101			0.0106050	+	0.999944i	$0.496624\pi$
$458$	88.9238	+	51.3402i	0.194157	+	0.112097i
$459$	144.755	−	563.808i	0.315370	−	1.22834i
$460$	−51.2064			−0.111318
$461$	−295.284	−	170.483i	−0.640530	−	0.369810i	0.144289	−	0.989536i	$-0.453911\pi$
$461$	−295.284	−	170.483i	−0.640530	−	0.369810i	−0.784819	+	0.619725i	$0.787244\pi$
$462$	−333.043	+	90.4872i	−0.720873	+	0.195860i
$463$	235.726	−	408.289i	0.509127	−	0.881834i	−0.490817	−	0.871263i	$-0.663302\pi$
$463$	235.726	−	408.289i	0.509127	−	0.881834i	0.999944	−	0.0105715i	$-0.00336507\pi$
$464$		−	84.3809i		−	0.181855i
$465$	474.529	+	125.374i	1.02049	+	0.269622i
$466$	371.119			0.796392
$467$			766.744i			1.64185i	0.571036	+	0.820925i	$0.306542\pi$
$467$			766.744i			1.64185i	−0.571036	+	0.820925i	$0.693458\pi$
$468$	−26.8448	+	229.671i	−0.0573607	+	0.490750i
$469$	198.239			0.422684
$470$			216.161i			0.459918i
$471$	−185.004	+	50.2653i	−0.392790	+	0.106720i
$472$	−237.273			−0.502697
$473$	274.327	+	158.383i	0.579972	+	0.334847i
$474$	116.813	+	30.8629i	0.246441	+	0.0651117i
$475$	226.766	−	392.771i	0.477403	−	0.826885i
$476$		−	325.991i		−	0.684854i
$477$	−3.44170	+	0.0240531i	−0.00721531	+	5.04258e-5i
$478$	−241.393	+	418.105i	−0.505006	+	0.874696i
$479$		−	226.151i		−	0.472132i	−0.971737	−	0.236066i	$-0.924142\pi$
$479$		−	226.151i		−	0.472132i	0.971737	−	0.236066i	$-0.0758581\pi$
$480$	−265.841	+	72.2286i	−0.553836	+	0.150476i
$481$	−350.392	+	463.854i	−0.728465	+	0.964354i
$482$	17.1549	+	9.90441i	0.0355912	+	0.0205486i
$483$	132.809	−	133.740i	0.274966	−	0.276895i
$484$	−164.374			−0.339616
$485$	−128.280	+	74.0623i	−0.264494	+	0.152706i
$486$	−412.656	+	427.333i	−0.849086	+	0.879286i
$487$	313.254	+	542.572i	0.643232	+	1.11411i	0.984707	+	0.174220i	$0.0557403\pi$
$487$	313.254	+	542.572i	0.643232	+	1.11411i	−0.341475	+	0.939891i	$0.610926\pi$
$488$	220.030	+	127.035i	0.450882	+	0.260317i
$489$	−136.038	+	514.890i	−0.278196	+	1.05294i
$490$	73.5483			0.150099
$491$	336.641	−	194.360i	0.685623	−	0.395845i	−0.116347	−	0.993209i	$-0.537119\pi$
$491$	336.641	−	194.360i	0.685623	−	0.395845i	0.801970	+	0.597364i	$0.203785\pi$
$492$	317.317	+	83.8375i	0.644953	+	0.170401i
$493$	45.4806	+	78.7747i	0.0922527	+	0.159786i
$494$	882.314	−	373.301i	1.78606	−	0.755670i
$495$	−151.863	−	86.2689i	−0.306794	−	0.174281i
$496$	518.512	−	898.089i	1.04539	−	1.81066i
$497$			62.5240i			0.125803i
$498$	−85.9080	+	325.154i	−0.172506	+	0.652919i
$499$	16.1707	−	28.0084i	0.0324062	−	0.0561291i	−0.849367	−	0.527802i	$-0.823016\pi$
$499$	16.1707	−	28.0084i	0.0324062	−	0.0561291i	0.881774	+	0.471673i	$0.156350\pi$
$500$			249.711i			0.499421i
$501$	185.194	+	48.9296i	0.369648	+	0.0976638i
$502$	135.288	+	234.326i	0.269498	+	0.466785i
$503$	431.726	−	249.257i	0.858302	−	0.495541i	−0.00514126	−	0.999987i	$-0.501637\pi$
$503$	431.726	−	249.257i	0.858302	−	0.495541i	0.863443	+	0.504446i	$0.168303\pi$
$504$	168.257	−	296.190i	0.333843	−	0.587680i
$505$	−58.2419	+	100.878i	−0.115331	+	0.199758i
$506$	−106.931	+	61.7364i	−0.211325	+	0.122009i
$507$	−261.625	−	434.283i	−0.516025	−	0.856574i
$508$	−162.612	+	281.652i	−0.320102	+	0.554434i
$509$	793.208	−	457.959i	1.55837	−	0.899723i	0.560952	−	0.827849i	$-0.310435\pi$
$509$	793.208	−	457.959i	1.55837	−	0.899723i	0.997414	−	0.0718741i	$-0.0228980\pi$
$510$	351.524	−	353.989i	0.689262	−	0.694096i
$511$	95.0068	−	164.557i	0.185923	−	0.322029i
$512$			186.295i			0.363857i
$513$	788.354	+	202.406i	1.53675	+	0.394553i
$514$	−614.506	−	1064.36i	−1.19554	−	2.07073i
$515$	−191.249	+	110.417i	−0.371356	+	0.214403i
$516$	294.674	−	80.0623i	0.571073	−	0.155159i
$517$	86.1836	+	149.274i	0.166699	+	0.288732i
$518$	−724.321	+	418.187i	−1.39830	+	0.807311i
$519$	−193.368	−	711.703i	−0.372578	−	1.37130i
$520$	122.308	−	161.913i	0.235208	−	0.311372i
$521$			62.7872i			0.120513i	0.998183	+	0.0602564i	$0.0191918\pi$
$521$			62.7872i			0.120513i	−0.998183	+	0.0602564i	$0.980808\pi$
$522$	−0.648746	−	92.8276i	−0.00124281	−	0.177831i
$523$	77.4887	−	134.214i	0.148162	−	0.256624i	−0.782386	−	0.622794i	$-0.785998\pi$
$523$	77.4887	−	134.214i	0.148162	−	0.256624i	0.930548	+	0.366169i	$0.119331\pi$
$524$	−284.415	−	164.207i	−0.542777	−	0.313373i
$525$	−245.028	−	243.322i	−0.466720	−	0.463470i
$526$	493.577			0.938359
$527$			1117.89i			2.12124i
$528$	−260.028	+	261.851i	−0.492477	+	0.495930i
$529$	−230.784	+	399.729i	−0.436264	+	0.755632i
$530$	−2.55455	−	1.47487i	−0.00481990	−	0.00278277i
$531$	−431.647	+	3.01666i	−0.812895	+	0.00568109i
$532$	455.822			0.856807
$533$	−662.739	+	280.400i	−1.24341	+	0.526079i
$534$	576.343	−	156.591i	1.07929	−	0.293242i
$535$	177.452	+	307.355i	0.331685	+	0.574496i
$536$	111.010	−	64.0916i	0.207108	−	0.119574i
$537$	92.2246	+	339.438i	0.171740	+	0.632101i
$538$	340.763	+	590.218i	0.633388	+	1.09706i
$539$	50.7902	−	29.3237i	0.0942304	−	0.0544040i
$540$	−162.163	+	45.2786i	−0.300302	+	0.0838493i
$541$	−849.273			−1.56982			−0.784910	−	0.619609i	$-0.787291\pi$
$541$	−849.273			−1.56982			−0.784910	+	0.619609i	$0.787291\pi$
$542$	−249.189	−	143.870i	−0.459759	−	0.265442i
$543$	−554.391	−	550.530i	−1.02098	−	1.01387i
$544$	−313.721	−	543.381i	−0.576693	−	0.998862i
$545$	−564.780	−	326.076i	−1.03629	−	0.598304i
$546$	−103.197	−	722.107i	−0.189005	−	1.32254i
$547$	−167.503	−	290.123i	−0.306221	−	0.530390i	0.671312	−	0.741175i	$-0.265731\pi$
$547$	−167.503	−	290.123i	−0.306221	−	0.530390i	−0.977532	+	0.210785i	$0.932398\pi$
$548$	−325.028	−	187.655i	−0.593116	−	0.342436i
$549$	401.894	+	228.304i	0.732048	+	0.415854i
$550$	113.109	+	195.910i	0.205652	+	0.356200i
$551$	−110.148	+	63.5940i	−0.199906	+	0.115416i
$552$	31.1315	−	117.830i	0.0563976	−	0.213459i
$553$	−126.041			−0.227923
$554$	−233.530	−	134.829i	−0.421534	−	0.243373i
$555$	−409.228	−	108.121i	−0.737348	−	0.194813i
$556$	−7.74967			−0.0139383
$557$	291.748	+	168.441i	0.523785	+	0.302407i	0.738482	−	0.674273i	$-0.235543\pi$
$557$	291.748	+	168.441i	0.523785	+	0.302407i	−0.214697	+	0.976681i	$0.568876\pi$
$558$	563.511	−	991.975i	1.00988	−	1.77773i
$559$	−403.552	+	534.229i	−0.721919	+	0.955687i
$560$	418.100	−	241.390i	0.746607	−	0.431054i
$561$	101.616	−	384.607i	0.181134	−	0.685573i
$562$	−21.2735	−	36.8468i	−0.0378532	−	0.0655637i
$563$		−	911.694i		−	1.61935i	−0.586878	−	0.809675i	$-0.699643\pi$
$563$		−	911.694i		−	1.61935i	0.586878	−	0.809675i	$-0.300357\pi$
$564$	160.647	+	42.4441i	0.284835	+	0.0752555i
$565$	−273.274	+	473.325i	−0.483671	+	0.837743i
$566$	1043.60	−	602.522i	1.84382	−	1.06453i
$567$	302.327	−	540.969i	0.533205	−	0.954091i
$568$	20.2143	+	35.0123i	0.0355886	+	0.0616413i
$569$		−	425.960i		−	0.748611i	−0.927305	−	0.374306i	$-0.877881\pi$
$569$		−	425.960i		−	0.748611i	0.927305	−	0.374306i	$-0.122119\pi$
$570$	494.971	+	491.524i	0.868370	+	0.862322i
$571$	383.824	−	664.803i	0.672196	−	1.16428i	−0.305084	−	0.952325i	$-0.598685\pi$
$571$	383.824	−	664.803i	0.672196	−	1.16428i	0.977280	−	0.211952i	$-0.0679822\pi$
$572$	−19.4422	+	156.825i	−0.0339899	+	0.274170i
$573$	275.017	+	1012.22i	0.479959	+	1.76652i
$574$	−1035.34			−1.80374
$575$	−106.993	−	61.7723i	−0.186074	−	0.107430i
$576$	−0.556625	−	79.6462i	−0.000966363	−	0.138275i
$577$	−535.973			−0.928895			−0.464448	−	0.885601i	$-0.653747\pi$
$577$	−535.973			−0.928895			−0.464448	+	0.885601i	$0.653747\pi$
$578$	372.177	+	214.877i	0.643905	+	0.371759i
$579$	227.915	−	862.637i	0.393636	−	1.48987i
$580$	13.1549	−	22.7849i	0.0226808	−	0.0392843i
$581$		−	350.841i		−	0.603856i
$582$	90.2744	+	332.260i	0.155111	+	0.570894i
$583$	−2.35212			−0.00403451
$584$		−	122.865i		−	0.210385i
$585$	220.444	−	296.108i	0.376828	−	0.506167i
$586$	846.127			1.44390
$587$			16.8090i			0.0286355i	0.999897	+	0.0143178i	$0.00455764\pi$
$587$			16.8090i			0.0286355i	−0.999897	+	0.0143178i	$0.995442\pi$
$588$	14.4415	−	54.6596i	0.0245603	−	0.0929585i
$589$	−1563.11			−2.65384
$590$	−320.383	−	184.973i	−0.543022	−	0.313514i
$591$	273.570	+	1006.89i	0.462893	+	1.70370i
$592$	−447.158	+	774.501i	−0.755335	+	1.30828i
$593$		−	363.547i		−	0.613065i	−0.951860	−	0.306532i	$-0.900831\pi$
$593$		−	363.547i		−	0.613065i	0.951860	−	0.306532i	$-0.0991688\pi$
$594$	−284.043	+	290.062i	−0.478188	+	0.488320i
$595$	−260.214	+	450.705i	−0.437335	+	0.757487i
$596$			543.690i			0.912231i
$597$	49.9510	−	189.060i	0.0836700	−	0.316683i
$598$	−101.689	−	240.347i	−0.170049	−	0.401918i
$599$	−808.916	−	467.028i	−1.35044	−	0.779679i	−0.362132	−	0.932127i	$-0.617951\pi$
$599$	−808.916	−	467.028i	−1.35044	−	0.779679i	−0.988312	+	0.152448i	$0.951284\pi$
$600$	−215.878	−	57.0366i	−0.359797	−	0.0950611i
$601$	−201.542			−0.335344			−0.167672	−	0.985843i	$-0.553625\pi$
$601$	−201.542			−0.335344			−0.167672	+	0.985843i	$0.553625\pi$
$602$	−834.213	+	481.633i	−1.38574	+	0.800055i
$603$	201.135	−	118.007i	0.333557	−	0.195700i
$604$	21.4610	+	37.1715i	0.0355314	+	0.0615422i
$605$	227.259	+	131.208i	0.375634	+	0.216872i
$606$	192.123	+	190.785i	0.317035	+	0.314827i
$607$	677.821			1.11667			0.558337	−	0.829614i	$-0.311440\pi$
$607$	677.821			1.11667			0.558337	+	0.829614i	$0.311440\pi$
$608$	759.791	−	438.665i	1.24966	−	0.721489i
$609$	25.3908	+	93.4525i	0.0416927	+	0.153452i
$610$	198.067	+	343.062i	0.324700	+	0.562397i
$611$	−335.522	+	141.957i	−0.549137	+	0.232336i
$612$	−194.055	−	330.752i	−0.317083	−	0.540445i
$613$	−314.267	+	544.326i	−0.512671	+	0.887971i	0.487222	+	0.873278i	$0.338010\pi$
$613$	−314.267	+	544.326i	−0.512671	+	0.887971i	−0.999892	+	0.0146930i	$0.995323\pi$
$614$			1092.73i			1.77969i
$615$	−371.791	−	369.202i	−0.604539	−	0.600328i
$616$	116.399	−	201.608i	0.188959	−	0.327286i
$617$			976.498i			1.58265i	0.611393	+	0.791327i	$0.290609\pi$
$617$			976.498i			1.58265i	−0.611393	+	0.791327i	$0.709391\pi$
$618$	134.587	+	495.357i	0.217779	+	0.801549i
$619$	337.425	+	584.436i	0.545112	+	0.944162i	0.998600	+	0.0528997i	$0.0168464\pi$
$619$	337.425	+	584.436i	0.545112	+	0.944162i	−0.453487	+	0.891263i	$0.649820\pi$
$620$	280.022	−	161.671i	0.451648	−	0.260759i
$621$	55.1364	−	214.752i	0.0887864	−	0.345816i
$622$	−107.625	+	186.411i	−0.173030	+	0.299696i
$623$	−539.568	+	311.520i	−0.866080	+	0.500031i
$624$	−481.629	−	613.514i	−0.771841	−	0.983196i
$625$	11.2646	−	19.5109i	0.0180234	−	0.0312175i
$626$	725.945	−	419.125i	1.15966	−	0.669528i
$627$	537.782	+	142.086i	0.857707	+	0.226613i
$628$	−63.1485	+	109.376i	−0.100555	+	0.174166i
$629$		−	964.058i		−	1.53268i
$630$	458.096	−	268.768i	0.727137	−	0.426616i
$631$	−425.578	−	737.123i	−0.674451	−	1.16818i	−0.976629	−	0.214932i	$-0.931047\pi$
$631$	−425.578	−	737.123i	−0.674451	−	1.16818i	0.302178	−	0.953251i	$-0.402286\pi$
$632$	−70.5808	+	40.7498i	−0.111678	+	0.0644776i
$633$	71.4603	−	270.471i	0.112892	−	0.427284i
$634$	409.465	+	709.215i	0.645844	+	1.11863i
$635$	449.645	−	259.603i	0.708102	−	0.408823i
$636$	−1.59769	+	1.60889i	−0.00251209	+	0.00252970i
$637$	48.3005	+	114.161i	0.0758250	+	0.179216i
$638$		−	63.4400i		−	0.0994357i
$639$	37.2191	+	63.4373i	0.0582458	+	0.0992760i
$640$	217.783	−	377.212i	0.340286	−	0.589393i
$641$	171.938	+	99.2685i	0.268234	+	0.154865i	0.628085	−	0.778145i	$-0.283839\pi$
$641$	171.938	+	99.2685i	0.268234	+	0.154865i	−0.359851	+	0.933010i	$0.617172\pi$
$642$	796.088	−	216.295i	1.24001	−	0.336909i
$643$	−1201.46			−1.86853			−0.934263	−	0.356585i	$-0.883941\pi$
$643$	−1201.46			−1.86853			−0.934263	+	0.356585i	$0.883941\pi$
$644$		−	124.168i		−	0.192808i
$645$	−471.315	−	124.525i	−0.730721	−	0.193062i
$646$	−794.397	+	1375.94i	−1.22972	+	2.12993i
$647$	951.412	+	549.298i	1.47050	+	0.848993i	0.999452	−	0.0331157i	$-0.0105430\pi$
$647$	951.412	+	549.298i	1.47050	+	0.848993i	0.471047	+	0.882108i	$0.343876\pi$
$648$	−5.60070	−	400.676i	−0.00864306	−	0.618328i
$649$	−294.995			−0.454538
$650$	−440.344	+	186.307i	−0.677453	+	0.286626i
$651$	−304.014	+	1150.66i	−0.466995	+	1.76753i
$652$	175.421	+	303.838i	0.269051	+	0.466010i
$653$	80.1614	−	46.2812i	0.122759	−	0.0708747i	−0.437363	−	0.899285i	$-0.644088\pi$
$653$	80.1614	−	46.2812i	0.122759	−	0.0708747i	0.560122	+	0.828410i	$0.310754\pi$
$654$	−1068.14	+	1075.63i	−1.63324	+	1.64469i
$655$	262.149	+	454.056i	0.400228	+	0.693215i
$656$	−958.751	+	553.535i	−1.46151	+	0.843804i
$657$	−1.56209	−	223.516i	−0.00237761	−	0.340206i
$658$	−524.160			−0.796595
$659$	529.611	+	305.771i	0.803659	+	0.463993i	0.844749	−	0.535163i	$-0.179750\pi$
$659$	529.611	+	305.771i	0.803659	+	0.463993i	−0.0410900	+	0.999155i	$0.513083\pi$
$660$	−111.036	+	30.1682i	−0.168236	+	0.0457095i
$661$	292.415	+	506.478i	0.442383	+	0.766229i	0.997866	−	0.0652985i	$-0.0208000\pi$
$661$	292.415	+	506.478i	0.442383	+	0.766229i	−0.555483	+	0.831528i	$0.687467\pi$
$662$	116.061	+	67.0078i	0.175319	+	0.101220i
$663$	780.309	+	313.159i	1.17694	+	0.472336i
$664$	−113.429	−	196.464i	−0.170826	−	0.295879i
$665$	−630.205	−	363.849i	−0.947677	−	0.547141i
$666$	−485.965	+	855.467i	−0.729677	+	1.28448i
$667$	17.3233	+	30.0049i	0.0259720	+	0.0449848i
$668$	109.284	−	63.0949i	0.163598	−	0.0944534i
$669$	524.183	+	520.532i	0.783532	+	0.778075i
$670$	199.858			0.298296
$671$	273.558	+	157.939i	0.407687	+	0.235378i
$672$	−175.144	−	644.627i	−0.260631	−	0.959266i
$673$	−289.120			−0.429598			−0.214799	−	0.976658i	$-0.568910\pi$
$673$	−289.120			−0.429598			−0.214799	+	0.976658i	$0.568910\pi$
$674$	−395.291	−	228.221i	−0.586485	−	0.338607i
$675$	−393.451	−	101.016i	−0.582891	−	0.149654i
$676$	−323.894	−	81.5622i	−0.479133	−	0.120654i
$677$	−963.176	+	556.090i	−1.42271	+	0.821403i	−0.996530	−	0.0832338i	$-0.973475\pi$
$677$	−963.176	+	556.090i	−1.42271	+	0.821403i	−0.426182	+	0.904637i	$0.640142\pi$
$678$	901.452	+	895.174i	1.32958	+	1.32032i
$679$	−179.590	−	311.060i	−0.264492	−	0.458114i
$680$			336.515i			0.494874i
$681$	149.326	+	549.604i	0.219275	+	0.807055i
$682$	389.832	−	675.209i	0.571602	−	0.990043i
$683$	943.198	−	544.556i	1.38096	−	0.797300i	0.388690	−	0.921369i	$-0.372928\pi$
$683$	943.198	−	544.556i	1.38096	−	0.797300i	0.992274	+	0.124069i	$0.0395944\pi$
$684$	462.480	−	271.340i	0.676140	−	0.396696i
$685$	299.582	+	518.892i	0.437346	+	0.757506i
$686$		−	738.137i		−	1.07600i
$687$	−121.598	+	33.0378i	−0.176998	+	0.0480899i
$688$	−515.000	+	892.006i	−0.748547	+	1.29652i
$689$	0.611649	−	4.93370i	0.000887735	−	0.00716067i
$690$	133.894	−	134.833i	0.194049	−	0.195409i
$691$	−133.449			−0.193124			−0.0965621	−	0.995327i	$-0.530785\pi$
$691$	−133.449			−0.193124			−0.0965621	+	0.995327i	$0.530785\pi$
$692$	−420.766	−	242.929i	−0.608043	−	0.351054i
$693$	209.189	−	368.246i	0.301861	−	0.531380i
$694$	383.430			0.552493
$695$	10.7145	+	6.18600i	0.0154165	+	0.00890072i
$696$	44.4320	+	44.1226i	0.0638391	+	0.0633945i
$697$	596.702	−	1033.52i	0.856100	−	1.48281i
$698$		−	53.6227i		−	0.0768234i
$699$	−320.906	+	323.156i	−0.459093	+	0.462313i
$700$	−227.491			−0.324987
$701$		−	693.561i		−	0.989388i	−0.869067	−	0.494694i	$-0.835280\pi$
$701$		−	693.561i		−	0.989388i	0.869067	−	0.494694i	$-0.164720\pi$
$702$	−534.557	−	671.224i	−0.761478	−	0.956160i
$703$	1348.01			1.91751
$704$		−	54.4317i		−	0.0773177i
$705$	−188.225	−	186.915i	−0.266986	−	0.265127i
$706$	1308.89			1.85395
$707$	−244.614	−	141.228i	−0.345989	−	0.199757i
$708$	−200.377	+	201.782i	−0.283018	+	0.285003i
$709$	−78.2712	+	135.570i	−0.110397	+	0.191212i	−0.915930	−	0.401338i	$-0.868545\pi$
$709$	−78.2712	+	135.570i	−0.110397	+	0.191212i	0.805534	+	0.592550i	$0.201879\pi$
$710$			63.0347i			0.0887813i
$711$	−127.883	+	75.0295i	−0.179863	+	0.105527i
$712$	−201.432	+	348.890i	−0.282910	+	0.490014i
$713$			425.800i			0.597195i
$714$	858.372	+	852.394i	1.20220	+	1.19383i
$715$	152.062	−	201.303i	0.212675	−	0.281542i
$716$	200.679	+	115.862i	0.280278	+	0.161819i
$717$	−155.338	−	571.730i	−0.216650	−	0.797393i
$718$	246.563			0.343403
$719$	−105.238	+	60.7593i	−0.146367	+	0.0845053i	−0.571395	−	0.820675i	$-0.693598\pi$
$719$	−105.238	+	60.7593i	−0.146367	+	0.0845053i	0.425028	+	0.905180i	$0.360264\pi$
$720$	280.514	−	493.801i	0.389602	−	0.685835i
$721$	−267.746	−	463.750i	−0.371354	−	0.643204i
$722$	−1159.64	−	669.517i	−1.60615	−	0.927309i
$723$	−23.4582	+	6.37356i	−0.0324457	+	0.00881543i
$724$	−514.712			−0.710929
$725$	54.9726	−	31.7384i	0.0758242	−	0.0437771i
$726$	429.802	−	432.816i	0.592014	−	0.596166i
$727$	343.562	+	595.068i	0.472576	+	0.818525i	0.999507	−	0.0313826i	$-0.00999103\pi$
$727$	343.562	+	595.068i	0.472576	+	0.818525i	−0.526932	+	0.849908i	$0.676658\pi$
$728$	392.616	+	296.579i	0.539308	+	0.407389i
$729$	−15.2830	−	728.840i	−0.0209643	−	0.999780i
$730$	95.7828	−	165.901i	0.131209	−	0.227261i
$731$		−	1110.32i		−	1.51891i
$732$	293.848	−	79.8379i	0.401432	−	0.109068i
$733$	−17.5857	+	30.4593i	−0.0239914	+	0.0415542i	−0.877772	−	0.479079i	$-0.840971\pi$
$733$	−17.5857	+	30.4593i	−0.0239914	+	0.0415542i	0.853780	+	0.520633i	$0.174304\pi$
$734$		−	1402.70i		−	1.91103i
$735$	−63.5971	+	64.0432i	−0.0865267	+	0.0871335i
$736$	−119.495	−	206.971i	−0.162357	−	0.281210i
$737$	138.016	−	79.6835i	0.187267	−	0.108119i
$738$	−1050.47	+	616.316i	−1.42340	+	0.835116i
$739$	700.539	−	1213.37i	0.947956	−	1.64191i	0.198234	−	0.980155i	$-0.436479\pi$
$739$	700.539	−	1213.37i	0.947956	−	1.64191i	0.749722	−	0.661753i	$-0.230187\pi$
$740$	−241.487	+	139.423i	−0.326334	+	0.188409i
$741$	−437.879	+	1091.08i	−0.590930	+	1.47244i
$742$	3.57634	−	6.19440i	0.00481987	−	0.00834825i
$743$	−719.045	+	415.141i	−0.967759	+	0.558736i	−0.898552	−	0.438866i	$-0.855380\pi$
$743$	−719.045	+	415.141i	−0.967759	+	0.558736i	−0.0692068	+	0.997602i	$0.522047\pi$
$744$	201.773	+	742.639i	0.271201	+	0.998171i
$745$	433.988	−	751.689i	0.582534	−	1.00898i
$746$		−	716.077i		−	0.959889i
$747$	−208.847	−	355.965i	−0.279581	−	0.476527i
$748$	−131.034	−	226.958i	−0.175179	−	0.303420i
$749$	−745.291	+	430.294i	−0.995049	+	0.574492i
$750$	−657.517	−	652.938i	−0.876690	−	0.870584i
$751$	−362.979	−	628.698i	−0.483327	−	0.837147i	0.516489	−	0.856294i	$-0.327239\pi$
$751$	−362.979	−	628.698i	−0.483327	−	0.837147i	−0.999817	+	0.0191462i	$0.993905\pi$
$752$	−485.384	+	280.236i	−0.645457	+	0.372655i
$753$	−321.026	−	84.8175i	−0.426329	−	0.112639i
$754$	133.069	+	16.4970i	0.176484	+	0.0218794i
$755$		−	68.5229i		−	0.0907588i
$756$	−109.794	−	393.222i	−0.145230	−	0.520134i
$757$	455.691	−	789.279i	0.601969	−	1.04264i	−0.390554	−	0.920580i	$-0.627716\pi$
$757$	455.691	−	789.279i	0.601969	−	1.04264i	0.992523	−	0.122061i	$-0.0389503\pi$
$758$	471.116	+	271.999i	0.621525	+	0.358837i
$759$	38.7050	−	146.495i	0.0509947	−	0.193010i
$760$	−470.537			−0.619127
$761$			1155.39i			1.51825i	0.650943	+	0.759126i	$0.274374\pi$
$761$			1155.39i			1.51825i	−0.650943	+	0.759126i	$0.725626\pi$
$762$	−316.429	−	1164.64i	−0.415261	−	1.52839i
$763$	790.686	−	1369.51i	1.03629	−	1.79490i
$764$	598.432	+	345.505i	0.783288	+	0.452231i
$765$	4.27841	+	612.188i	0.00559269	+	0.800246i
$766$	−1387.40			−1.81123
$767$	76.7110	−	618.768i	0.100014	−	0.806739i
$768$	−643.049	−	638.570i	−0.837303	−	0.831472i
$769$	275.054	+	476.408i	0.357678	+	0.619516i	0.987572	−	0.157165i	$-0.0502353\pi$
$769$	275.054	+	476.408i	0.357678	+	0.619516i	−0.629895	+	0.776681i	$0.716902\pi$
$770$	314.340	−	181.484i	0.408233	−	0.235694i
$771$	1458.16	+	385.258i	1.89126	+	0.499686i
$772$	−293.898	−	509.045i	−0.380696	−	0.659385i
$773$	−507.118	+	292.785i	−0.656039	+	0.378764i	−0.790766	−	0.612118i	$-0.790318\pi$
$773$	−507.118	+	292.785i	−0.656039	+	0.378764i	0.134727	+	0.990883i	$0.456984\pi$
$774$	−559.694	+	985.256i	−0.723119	+	1.27294i
$775$	780.117			1.00660
$776$	−201.134	−	116.125i	−0.259194	−	0.149645i
$777$	262.178	−	992.318i	0.337423	−	1.27711i
$778$	272.171	+	471.415i	0.349835	+	0.605931i
$779$	1445.13	+	834.348i	1.85511	+	1.07105i
$780$	−34.4055	−	240.749i	−0.0441097	−	0.308652i
$781$	25.1320	+	43.5299i	0.0321792	+	0.0557360i
$782$	374.812	+	216.398i	0.479299	+	0.276723i
$783$	81.3918	+	79.7030i	0.103949	+	0.101792i
$784$	95.3496	+	165.150i	0.121619	+	0.210651i
$785$	174.614	−	100.814i	0.222439	−	0.128425i
$786$	1176.06	−	319.533i	1.49626	−	0.406531i
$787$	399.078			0.507087			0.253544	−	0.967324i	$-0.418404\pi$
$787$	399.078			0.507087			0.253544	+	0.967324i	$0.418404\pi$
$788$	595.283	+	343.687i	0.755436	+	0.436151i
$789$	−426.795	+	429.789i	−0.540932	+	0.544726i
$790$	−127.071			−0.160849
$791$	−1147.74	−	662.650i	−1.45100	−	0.837737i
$792$	−1.91381	−	273.843i	−0.00241643	−	0.345761i
$793$	−402.422	+	532.732i	−0.507467	+	0.671793i
$794$	−231.541	+	133.680i	−0.291614	+	0.168363i
$795$	3.49317	−	0.949088i	0.00439393	−	0.00119382i
$796$	−64.4120	−	111.565i	−0.0809196	−	0.140157i
$797$		−	482.781i		−	0.605748i	−0.953031	−	0.302874i	$-0.902054\pi$
$797$		−	482.781i		−	0.605748i	0.953031	−	0.302874i	$-0.0979462\pi$
$798$	−1191.87	+	1200.23i	−1.49358	+	1.50405i
$799$	302.090	−	523.235i	0.378085	−	0.654862i
$800$	−379.196	+	218.929i	−0.473995	+	0.273661i
$801$	−362.009	+	637.262i	−0.451946	+	0.795583i
$802$	202.166	+	350.162i	0.252078	+	0.436611i
$803$		−	152.755i		−	0.190230i
$804$	39.2429	−	148.531i	0.0488096	−	0.184740i
$805$	−99.1143	+	171.671i	−0.123123	+	0.213256i
$806$	1314.92	+	993.277i	1.63141	+	1.23235i
$807$	−808.597	−	213.637i	−1.00198	−	0.264730i
$808$	−182.639			−0.226039
$809$	−1069.07	−	617.227i	−1.32147	−	0.762950i	−0.337505	−	0.941324i	$-0.609583\pi$
$809$	−1069.07	−	617.227i	−1.32147	−	0.762950i	−0.983963	+	0.178374i	$0.942916\pi$
$810$	304.797	−	545.388i	0.376292	−	0.673319i
$811$	−169.669			−0.209209			−0.104605	−	0.994514i	$-0.533358\pi$
$811$	−169.669			−0.209209			−0.104605	+	0.994514i	$0.533358\pi$
$812$	55.2500	+	31.8986i	0.0680419	+	0.0392840i
$813$	340.750	−	92.5810i	0.419127	−	0.113876i
$814$	−336.186	+	582.292i	−0.413005	+	0.715346i
$815$		−	560.104i		−	0.687244i
$816$	1250.59	+	330.416i	1.53259	+	0.404922i
$817$	1552.53			1.90028
$818$			111.318i			0.136086i
$819$	718.018	+	534.545i	0.876701	+	0.652680i
$820$	−345.181			−0.420953
$821$			871.420i			1.06141i	0.847556	+	0.530706i	$0.178073\pi$
$821$			871.420i			1.06141i	−0.847556	+	0.530706i	$0.821927\pi$
$822$	1343.99	−	365.160i	1.63503	−	0.444234i
$823$	−454.811			−0.552625			−0.276313	−	0.961068i	$-0.589113\pi$
$823$	−454.811			−0.552625			−0.276313	+	0.961068i	$0.589113\pi$
$824$	−299.865	−	173.127i	−0.363914	−	0.210106i
$825$	−268.396	−	70.9122i	−0.325328	−	0.0859542i
$826$	448.533	−	776.881i	0.543018	−	0.940534i
$827$		−	58.1961i		−	0.0703702i	−0.999381	−	0.0351851i	$-0.988798\pi$
$827$		−	58.1961i		−	0.0703702i	0.999381	−	0.0351851i	$-0.0112021\pi$
$828$	−73.9144	−	125.982i	−0.0892685	−	0.152152i
$829$	184.684	−	319.882i	0.222779	−	0.385865i	−0.732872	−	0.680367i	$-0.761820\pi$
$829$	184.684	−	319.882i	0.222779	−	0.385865i	0.955651	+	0.294502i	$0.0951537\pi$
$830$		−	353.706i		−	0.426152i
$831$	319.337	−	86.7631i	0.384280	−	0.104408i
$832$	114.173	+	14.1545i	0.137228	+	0.0170126i
$833$	−178.029	−	102.785i	−0.213721	−	0.123392i
$834$	20.2637	−	20.4058i	0.0242970	−	0.0244674i
$835$	−201.456			−0.241265
$836$	317.347	−	183.221i	0.379602	−	0.219163i
$837$	376.508	+	1348.44i	0.449831	+	1.61104i
$838$	−478.512	−	828.806i	−0.571016	−	0.989029i
$839$	377.989	+	218.232i	0.450523	+	0.260109i	0.708051	−	0.706161i	$-0.249575\pi$
$839$	377.989	+	218.232i	0.450523	+	0.260109i	−0.257528	+	0.966271i	$0.582908\pi$
$840$	−91.5160	+	346.379i	−0.108948	+	0.412356i
$841$	823.199			0.978833
$842$	−473.577	+	273.420i	−0.562443	+	0.324727i
$843$	50.4800	+	13.3372i	0.0598814	+	0.0158211i
$844$	−92.1484	−	159.606i	−0.109181	−	0.189106i
$845$	382.701	+	371.306i	0.452900	+	0.439416i
$846$	−531.816	+	312.020i	−0.628625	+	0.368818i
$847$	−318.160	+	551.069i	−0.375631	+	0.650613i
$848$		−	7.64820i		−	0.00901911i
$849$	−377.745	+	1429.73i	−0.444929	+	1.68401i
$850$	396.467	−	686.701i	0.466432	−	0.807883i
$851$		−	367.204i		−	0.431498i
$852$	46.8462	+	12.3771i	0.0549837	+	0.0145271i
$853$	4.91575	+	8.51433i	0.00576290	+	0.00998163i	0.868892	−	0.495001i	$-0.164832\pi$
$853$	4.91575	+	8.51433i	0.00576290	+	0.00998163i	−0.863130	+	0.504983i	$0.831499\pi$
$854$	−831.876	+	480.284i	−0.974093	+	0.562393i
$855$	−856.001	+	5.98235i	−1.00117	+	0.00699690i
$856$	−278.233	+	481.913i	−0.325038	+	0.562982i
$857$	1224.81	−	707.143i	1.42918	−	0.825138i	0.432125	−	0.901814i	$-0.357764\pi$
$857$	1224.81	−	707.143i	1.42918	−	0.825138i	0.997056	+	0.0766755i	$0.0244305\pi$
$858$	−362.102	−	461.257i	−0.422031	−	0.537596i
$859$	97.9732	−	169.694i	0.114055	−	0.197549i	−0.803347	−	0.595512i	$-0.796949\pi$
$859$	97.9732	−	169.694i	0.114055	−	0.197549i	0.917402	+	0.397963i	$0.130283\pi$
$860$	−278.125	+	160.575i	−0.323401	+	0.186716i
$861$	895.261	−	901.539i	1.03979	−	1.04708i
$862$	296.866	−	514.186i	0.344392	−	0.596504i
$863$			414.684i			0.480514i	0.970709	+	0.240257i	$0.0772318\pi$
$863$			414.684i			0.480514i	−0.970709	+	0.240257i	$0.922768\pi$
$864$	−561.433	−	549.784i	−0.649807	−	0.636324i
$865$	387.825	+	671.733i	0.448353	+	0.776570i
$866$	135.486	−	78.2229i	0.156450	−	0.0903267i
$867$	−508.928	+	138.275i	−0.586999	+	0.159486i
$868$	392.027	+	679.011i	0.451645	+	0.782271i
$869$	−87.7513	+	50.6632i	−0.100980	+	0.0583006i
$870$	25.5982	+	94.2158i	0.0294233	+	0.108294i
$871$	131.251	+	310.217i	0.150690	+	0.356162i
$872$		−	1022.53i		−	1.17263i
$873$	−367.380	−	208.697i	−0.420825	−	0.239058i
$874$	−302.582	+	524.087i	−0.346203	+	0.599642i
$875$	837.162	+	483.336i	0.956756	+	0.552384i
$876$	−104.487	−	103.759i	−0.119277	−	0.118446i
$877$	−471.095			−0.537166			−0.268583	−	0.963257i	$-0.586555\pi$
$877$	−471.095			−0.537166			−0.268583	+	0.963257i	$0.586555\pi$
$878$		−	594.997i		−	0.677673i
$879$	−731.645	+	736.776i	−0.832361	+	0.838198i
$880$	194.057	−	336.117i	0.220519	−	0.381951i
$881$	1476.32	+	852.355i	1.67574	+	0.967486i	0.964329	+	0.264705i	$0.0852747\pi$
$881$	1476.32	+	852.355i	1.67574	+	0.967486i	0.711406	+	0.702781i	$0.248059\pi$
$882$	106.164	+	180.949i	0.120367	+	0.205158i
$883$	650.040			0.736172			0.368086	−	0.929792i	$-0.380013\pi$
$883$	650.040			0.736172			0.368086	+	0.929792i	$0.380013\pi$
$884$	510.131	−	215.833i	0.577071	−	0.244155i
$885$	438.102	−	119.031i	0.495031	−	0.134499i
$886$	−11.4424	−	19.8189i	−0.0129147	−	0.0223689i
$887$	−293.506	+	169.456i	−0.330898	+	0.191044i	−0.656240	−	0.754553i	$-0.727854\pi$
$887$	−293.506	+	169.456i	−0.330898	+	0.191044i	0.325342	+	0.945596i	$0.394521\pi$
$888$	−174.007	−	640.442i	−0.195954	−	0.721219i
$889$	629.498	+	1090.32i	0.708097	+	1.22646i
$890$	−543.975	+	314.064i	−0.611208	+	0.352881i
$891$	−6.96321	−	498.151i	−0.00781505	−	0.559092i
$892$	486.666			0.545590
$893$	731.622	+	422.402i	0.819285	+	0.473015i
$894$	−1431.60	−	1421.63i	−1.60134	−	1.59019i
$895$	−184.969	−	320.375i	−0.206669	−	0.357961i
$896$	914.683	+	528.093i	1.02085	+	0.589389i
$897$	297.215	+	119.280i	0.331344	+	0.132977i
$898$	−495.478	−	858.193i	−0.551757	−	0.955672i
$899$	−189.465	−	109.387i	−0.210750	−	0.121677i
$900$	−230.814	+	135.420i	−0.256460	+	0.150467i
$901$	4.12232	+	7.14006i	0.00457527	+	0.00792460i
$902$	−720.817	+	416.164i	−0.799132	+	0.461379i
$903$	301.955	−	1142.87i	0.334391	−	1.26564i
$904$	−856.952			−0.947956
$905$	711.626	+	410.857i	0.786327	+	0.453986i
$906$	−153.993	−	40.6860i	−0.169970	−	0.0449073i
$907$	−1091.67			−1.20361			−0.601803	−	0.798645i	$-0.705551\pi$
$907$	−1091.67			−1.20361			−0.601803	+	0.798645i	$0.705551\pi$
$908$	324.932	+	187.599i	0.357854	+	0.206607i
$909$	−332.257	+	2.32205i	−0.365520	+	0.00255451i
$910$	298.931	+	706.538i	0.328496	+	0.776415i
$911$	−680.446	+	392.856i	−0.746922	+	0.431236i	−0.824581	−	0.565744i	$-0.808589\pi$
$911$	−680.446	+	392.856i	−0.746922	+	0.431236i	0.0776587	+	0.996980i	$0.475256\pi$
$912$	−462.010	+	1748.66i	−0.506590	+	1.91739i
$913$	−141.023	−	244.259i	−0.154461	−	0.267534i
$914$			23.6961i			0.0259257i
$915$	−469.994	−	124.176i	−0.513655	−	0.135711i
$916$	−41.5055	+	71.8897i	−0.0453117	+	0.0784822i
$917$	−1101.02	+	635.674i	−1.20068	+	0.693210i
$918$	1378.32	+	353.876i	1.50144	+	0.385486i
$919$	0.983854	+	1.70409i	0.00107057	+	0.00185428i	0.866560	−	0.499073i	$-0.166326\pi$
$919$	0.983854	+	1.70409i	0.00107057	+	0.00185428i	−0.865490	+	0.500927i	$0.832993\pi$
$920$			128.177i			0.139322i
$921$	−951.510	−	944.883i	−1.03313	−	1.02593i
$922$	416.772	−	721.870i	0.452030	−	0.782939i
$923$	−97.8416	+	41.3961i	−0.106004	+	0.0448495i
$924$	−73.1536	−	269.246i	−0.0791705	−	0.291392i
$925$	−672.763			−0.727312
$926$	998.128	+	576.270i	1.07789	+	0.622322i
$927$	−547.716	−	311.141i	−0.590848	−	0.335643i
$928$	122.792			0.132319
$929$	472.351	+	272.712i	0.508451	+	0.293555i	0.732197	−	0.681093i	$-0.238495\pi$
$929$	472.351	+	272.712i	0.508451	+	0.293555i	−0.223745	+	0.974648i	$0.571828\pi$
$930$	−306.497	+	1160.06i	−0.329567	+	1.24738i
$931$	143.721	−	248.932i	0.154373	−	0.267382i
$932$			300.028i			0.321918i
$933$	−69.2571	−	254.905i	−0.0742306	−	0.273210i
$934$	−1874.43			−2.00688
$935$			418.380i			0.447465i
$936$	574.897	+	67.1962i	0.614207	+	0.0717908i
$937$	1697.45			1.81158			0.905790	−	0.423726i	$-0.139278\pi$
$937$	1697.45			1.81158			0.905790	+	0.423726i	$0.139278\pi$
$938$			484.627i			0.516660i
$939$	−262.766	+	994.543i	−0.279836	+	1.05915i
$940$	−174.754			−0.185908
$941$	−886.312	−	511.713i	−0.941884	−	0.543797i	−0.0513333	−	0.998682i	$-0.516347\pi$
$941$	−886.312	−	511.713i	−0.941884	−	0.543797i	−0.890550	+	0.454885i	$0.849680\pi$
$942$	−122.881	−	452.272i	−0.130447	−	0.480119i
$943$	227.280	−	393.661i	0.241019	−	0.417456i
$944$		−	959.212i		−	1.01611i
$945$	−162.082	+	631.297i	−0.171516	+	0.668039i
$946$	−387.192	+	670.636i	−0.409294	+	0.708917i
$947$		−	427.519i		−	0.451445i	−0.974192	−	0.225723i	$-0.927526\pi$
$947$		−	427.519i		−	0.451445i	0.974192	−	0.225723i	$-0.0724743\pi$
$948$	−24.9508	+	94.4366i	−0.0263195	+	0.0996166i
$949$	320.411	+	39.7225i	0.337630	+	0.0418572i
$950$	960.191	+	554.366i	1.01073	+	0.583543i
$951$	−971.622	−	256.710i	−1.02168	−	0.269937i
$952$	−815.999			−0.857141
$953$	124.120	−	71.6609i	0.130242	−	0.0751951i	−0.433464	−	0.901171i	$-0.642709\pi$
$953$	124.120	−	71.6609i	0.130242	−	0.0751951i	0.563705	+	0.825976i	$0.309375\pi$
$954$	−0.0588016	−	8.41380i	−6.16369e−5	−	0.00881949i
$955$	−551.582	−	955.369i	−0.577573	−	1.00039i
$956$	−338.013	−	195.152i	−0.353570	−	0.204134i
$957$	55.2412	+	54.8565i	0.0577233	+	0.0573213i
$958$	552.862			0.577101
$959$	−1258.24	+	726.443i	−1.31203	+	0.757501i
$960$	21.9633	+	80.8373i	0.0228785	+	0.0842056i
$961$	−863.849	−	1496.23i	−0.898907	−	1.55695i
$962$	−1133.97	−	856.589i	−1.17876	−	0.890425i
$963$	−500.034	+	880.234i	−0.519246	+	0.914054i
$964$	−8.00713	+	13.8687i	−0.00830615	+	0.0143867i
$965$			938.388i			0.972422i
$966$	326.949	+	324.672i	0.338457	+	0.336100i
$967$	208.251	−	360.702i	0.215358	−	0.373011i	−0.738025	−	0.674773i	$-0.764242\pi$
$967$	208.251	−	360.702i	0.215358	−	0.373011i	0.953383	+	0.301762i	$0.0975748\pi$
$968$			411.451i			0.425052i
$969$	−511.200	−	1881.50i	−0.527554	−	1.94169i
$970$	−181.057	−	313.600i	−0.186657	−	0.323299i
$971$	940.061	−	542.744i	0.968136	−	0.558954i	0.0694689	−	0.997584i	$-0.477870\pi$
$971$	940.061	−	542.744i	0.968136	−	0.558954i	0.898668	+	0.438630i	$0.144536\pi$
$972$	−345.474	−	333.608i	−0.355425	−	0.343218i
$973$	−15.0001	+	25.9810i	−0.0154164	+	0.0267020i
$974$	−1326.40	+	765.800i	−1.36181	+	0.786242i
$975$	218.536	−	544.535i	0.224140	−	0.558497i
$976$	−513.557	+	889.506i	−0.526185	+	0.911380i
$977$	707.037	−	408.208i	0.723682	−	0.417818i	−0.0924244	−	0.995720i	$-0.529462\pi$
$977$	707.037	−	408.208i	0.723682	−	0.417818i	0.816106	+	0.577902i	$0.196128\pi$
$978$	−1258.73	−	332.566i	−1.28705	−	0.340047i
$979$	−250.435	+	433.766i	−0.255807	+	0.443070i
$980$			59.4595i			0.0606729i
$981$	−13.0003	−	1860.19i	−0.0132521	−	1.89622i
$982$	475.144	+	822.973i	0.483853	+	0.838058i
$983$	−492.034	+	284.076i	−0.500543	+	0.288989i	−0.728938	−	0.684580i	$-0.759986\pi$
$983$	−492.034	+	284.076i	−0.500543	+	0.288989i	0.228395	+	0.973569i	$0.426652\pi$
$984$	209.857	−	794.287i	0.213269	−	0.807202i
$985$	−548.680	−	950.342i	−0.557036	−	0.964814i
$986$	−192.577	+	111.185i	−0.195312	+	0.112763i
$987$	453.240	−	456.419i	0.459210	−	0.462431i
$988$	301.792	+	713.298i	0.305457	+	0.721962i
$989$		−	422.916i		−	0.427620i
$990$	210.898	−	371.254i	0.213028	−	0.375004i
$991$	−110.273	+	190.998i	−0.111274	+	0.192732i	−0.916284	−	0.400529i	$-0.868826\pi$
$991$	−110.273	+	190.998i	−0.111274	+	0.192732i	0.805010	+	0.593261i	$0.202160\pi$
$992$	1306.91	+	754.545i	1.31745	+	0.760630i
$993$	−158.706	+	43.1200i	−0.159824	+	0.0434239i
$994$	−152.850			−0.153773
$995$			205.662i			0.206695i
$996$	−262.867	−	69.4515i	−0.263923	−	0.0697305i
$997$	305.126	−	528.493i	0.306044	−	0.530083i	−0.671449	−	0.741050i	$-0.734328\pi$
$997$	305.126	−	528.493i	0.306044	−	0.530083i	0.977493	+	0.210967i	$0.0676613\pi$
$998$	68.4711	+	39.5318i	0.0686083	+	0.0396110i
$999$	−324.696	−	1162.88i	−0.325021	−	1.16405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.k.a.113.20	yes	52
3.2	odd	2		351.3.k.a.152.7		52
9.2	odd	6		117.3.u.a.74.7	yes	52
9.7	even	3		351.3.u.a.35.20		52
13.3	even	3		117.3.u.a.68.7	yes	52
39.29	odd	6		351.3.u.a.341.20		52
117.16	even	3		351.3.k.a.224.20		52
117.29	odd	6	inner	117.3.k.a.29.7	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.k.a.29.7	✓	52	117.29	odd	6	inner
117.3.k.a.113.20	yes	52	1.1	even	1	trivial
117.3.u.a.68.7	yes	52	13.3	even	3
117.3.u.a.74.7	yes	52	9.2	odd	6
351.3.k.a.152.7		52	3.2	odd	2
351.3.k.a.224.20		52	117.16	even	3
351.3.u.a.35.20		52	9.7	even	3
351.3.u.a.341.20		52	39.29	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.44466i q^{2} +(-2.12872 - 2.11389i) q^{3} -1.97636 q^{4} +(2.73246 + 1.57759i) q^{5} +(5.16775 - 5.20400i) q^{6} +(-3.82542 + 6.62581i) q^{7} +4.94710i q^{8} +(0.0628969 + 8.99978i) q^{9} +(-3.85666 + 6.67994i) q^{10} +6.15061i q^{11} +(4.20712 + 4.17782i) q^{12} +(-12.9012 - 1.59941i) q^{13} +(-16.1979 - 9.35184i) q^{14} +(-2.48179 - 9.13437i) q^{15} -19.9994 q^{16} +(18.6707 - 10.7795i) q^{17} +(-22.0014 + 0.153762i) q^{18} +(15.0726 + 26.1066i) q^{19} +(-5.40033 - 3.11788i) q^{20} +(22.1495 - 6.01798i) q^{21} -15.0362 q^{22} +(7.11157 - 4.10586i) q^{23} +(10.4577 - 10.5310i) q^{24} +(-7.52244 - 13.0293i) q^{25} +(3.91002 - 31.5391i) q^{26} +(18.8907 - 19.2910i) q^{27} +(7.56041 - 13.0950i) q^{28} +4.21916i q^{29} +(22.3304 - 6.06713i) q^{30} +(-25.9263 + 44.9057i) q^{31} -29.1034i q^{32} +(13.0017 - 13.0929i) q^{33} +(26.3523 + 45.6435i) q^{34} +(-20.9056 + 12.0698i) q^{35} +(-0.124307 - 17.7868i) q^{36} +(22.3585 - 38.7261i) q^{37} +(-63.8217 + 36.8475i) q^{38} +(24.0821 + 30.6766i) q^{39} +(-7.80448 + 13.5178i) q^{40} +(47.9389 - 27.6775i) q^{41} +(14.7119 + 54.1480i) q^{42} +(25.7507 - 44.6016i) q^{43} -12.1558i q^{44} +(-14.0261 + 24.6908i) q^{45} +(10.0374 + 17.3854i) q^{46} +(24.2699 - 14.0122i) q^{47} +(42.5732 + 42.2767i) q^{48} +(-4.76761 - 8.25775i) q^{49} +(31.8521 - 18.3898i) q^{50} +(-62.5314 - 16.5213i) q^{51} +(25.4975 + 3.16102i) q^{52} +0.382421i q^{53} +(47.1599 + 46.1813i) q^{54} +(-9.70312 + 16.8063i) q^{55} +(-32.7786 - 18.9247i) q^{56} +(23.1011 - 87.4356i) q^{57} -10.3144 q^{58} +47.9620i q^{59} +(4.90492 + 18.0528i) q^{60} +(25.6786 - 44.4766i) q^{61} +(-109.779 - 63.3811i) q^{62} +(-59.8715 - 34.0112i) q^{63} -8.84980 q^{64} +(-32.7289 - 24.7231i) q^{65} +(32.0078 + 31.7848i) q^{66} +(-12.9554 - 22.4394i) q^{67} +(-36.9001 + 21.3043i) q^{68} +(-23.8179 - 6.29287i) q^{69} +(-29.5067 - 51.1071i) q^{70} +(7.07732 - 4.08609i) q^{71} +(-44.5229 + 0.311158i) q^{72} -24.8357 q^{73} +(94.6722 + 54.6590i) q^{74} +(-11.5293 + 43.6373i) q^{75} +(-29.7890 - 51.5961i) q^{76} +(-40.7528 - 23.5286i) q^{77} +(-74.9938 + 58.8726i) q^{78} +(8.23711 + 14.2671i) q^{79} +(-54.6477 - 31.5508i) q^{80} +(-80.9921 + 1.13212i) q^{81} +(67.6622 + 117.194i) q^{82} +(-39.7129 + 22.9283i) q^{83} +(-43.7755 + 11.8937i) q^{84} +68.0225 q^{85} +(109.036 + 62.9518i) q^{86} +(8.91887 - 8.98142i) q^{87} -30.4277 q^{88} +(70.5240 + 40.7171i) q^{89} +(-60.3605 - 34.2890i) q^{90} +(59.9500 - 79.3628i) q^{91} +(-14.0550 + 8.11468i) q^{92} +(150.116 - 40.7862i) q^{93} +(34.2551 + 59.3316i) q^{94} +95.1136i q^{95} +(-61.5216 + 61.9530i) q^{96} +(-23.4733 + 40.6570i) q^{97} +(20.1874 - 11.6552i) q^{98} +(-55.3541 + 0.386854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - q^{3} - 98 q^{4} - 6 q^{5} + 12 q^{6} - q^{7} - 3 q^{9} - 6 q^{10} - 39 q^{12} + 4 q^{13} - 6 q^{14} - 25 q^{15} + 166 q^{16} + 34 q^{18} + 5 q^{19} + 21 q^{20} - 91 q^{21} + 30 q^{22} - 75 q^{23}+ \cdots + 522 q^{99}+O(q^{100}) \) 52 * q - q^3 - 98 * q^4 - 6 * q^5 + 12 * q^6 - q^7 - 3 * q^9 - 6 * q^10 - 39 * q^12 + 4 * q^13 - 6 * q^14 - 25 * q^15 + 166 * q^16 + 34 * q^18 + 5 * q^19 + 21 * q^20 - 91 * q^21 + 30 * q^22 - 75 * q^23 - 24 * q^24 + 88 * q^25 - 132 * q^26 - 34 * q^27 - 22 * q^28 + 70 * q^30 + 14 * q^31 + 95 * q^33 - 6 * q^34 + 228 * q^35 - 58 * q^36 - 13 * q^37 - 192 * q^38 - 111 * q^39 + 72 * q^40 + 33 * q^41 + 159 * q^42 - 31 * q^43 - 47 * q^45 + 6 * q^46 - 69 * q^47 + 293 * q^48 - 123 * q^49 - 168 * q^50 + 235 * q^51 - 92 * q^52 - 339 * q^54 - 27 * q^55 + 168 * q^56 + 189 * q^57 + 210 * q^58 + 213 * q^60 + 8 * q^61 + 471 * q^62 + 169 * q^63 - 98 * q^64 - 246 * q^65 - 576 * q^66 - 34 * q^67 + 18 * q^68 - 193 * q^69 - 57 * q^70 + 144 * q^71 + 36 * q^72 - 106 * q^73 - 465 * q^74 - 58 * q^75 - 79 * q^76 + 282 * q^77 - 76 * q^78 - 25 * q^79 - 1050 * q^80 - 279 * q^81 + 81 * q^82 + 219 * q^83 + 395 * q^84 - 108 * q^85 - 24 * q^86 - 518 * q^87 + 30 * q^88 + 99 * q^89 + 183 * q^90 + 2 * q^91 + 888 * q^92 + 582 * q^93 + 303 * q^94 - 439 * q^96 + 212 * q^97 - 405 * q^98 + 522 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more