LMFDB - Embedded newform 117.3.k.a.29.7

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			29.7
Character	$\chi$	$=$	117.29
Dual form			117.3.k.a.113.20

$q$-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 $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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	$-0.790701\pi$
$2$		−	2.44466i		−	1.22233i	0.791503	−	0.611165i	$-0.209299\pi$
$3$	−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	−0.201214	−	0.979547i	$-0.564489\pi$
$5$	2.73246	−	1.57759i	0.546492	−	0.315517i	0.747706	+	0.664030i	$0.231155\pi$
$6$	5.16775	+	5.20400i	0.861292	+	0.867333i
$7$	−3.82542	−	6.62581i	−0.546488	−	0.946545i	−0.998512	−	0.0545390i	$-0.982631\pi$
$7$	−3.82542	−	6.62581i	−0.546488	−	0.946545i	0.452024	−	0.892006i	$-0.350702\pi$
$8$		−	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	$-0.909807\pi$
$11$		−	6.15061i		−	0.559146i	0.960124	−	0.279573i	$-0.0901930\pi$
$12$	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	0.935768	−	0.352617i	$-0.114708\pi$
$17$	18.6707	+	10.7795i	1.09828	+	0.634090i	0.162508	+	0.986707i	$0.448042\pi$
$18$	−22.0014	−	0.153762i	−1.22230	−	0.00854231i
$19$	15.0726	−	26.1066i	0.793297	−	1.37403i	−0.130618	−	0.991433i	$-0.541696\pi$
$19$	15.0726	−	26.1066i	0.793297	−	1.37403i	0.923915	−	0.382598i	$-0.124971\pi$
$20$	−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	0.646568	−	0.762857i	$-0.276204\pi$
$23$	7.11157	+	4.10586i	0.309199	+	0.178516i	−0.337369	+	0.941372i	$0.609537\pi$
$24$	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	$-0.976824\pi$
$29$		−	4.21916i		−	0.145488i	0.997351	−	0.0727442i	$-0.0231757\pi$
$30$	22.3304	+	6.06713i	0.744348	+	0.202238i
$31$	−25.9263	−	44.9057i	−0.836333	−	1.44857i	−0.892940	−	0.450175i	$-0.851362\pi$
$31$	−25.9263	−	44.9057i	−0.836333	−	1.44857i	0.0566070	−	0.998397i	$-0.481972\pi$
$32$			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	0.992164	+	0.124942i	$0.0398744\pi$
$37$	22.3585	+	38.7261i	0.604285	+	1.04665i	−0.387879	+	0.921710i	$0.626792\pi$
$38$	−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	0.953501	−	0.301389i	$-0.0974502\pi$
$41$	47.9389	+	27.6775i	1.16924	+	0.675062i	0.215740	+	0.976451i	$0.430784\pi$
$42$	14.7119	−	54.1480i	0.350284	−	1.28924i
$43$	25.7507	+	44.6016i	0.598854	+	1.03725i	0.992991	+	0.118194i	$0.0377103\pi$
$43$	25.7507	+	44.6016i	0.598854	+	1.03725i	−0.394137	+	0.919052i	$0.628956\pi$
$44$			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	0.735452	−	0.677577i	$-0.236970\pi$
$47$	24.2699	+	14.0122i	0.516380	+	0.298132i	−0.219072	+	0.975709i	$0.570303\pi$
$48$	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	$-0.998852\pi$
$53$		−	0.382421i		−	0.00721549i	0.999993	−	0.00360774i	$-0.00114838\pi$
$54$	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	$-0.866764\pi$
$59$		−	47.9620i		−	0.812914i	0.913670	−	0.406457i	$-0.133236\pi$
$60$	4.90492	−	18.0528i	0.0817486	−	0.300881i
$61$	25.6786	+	44.4766i	0.420960	+	0.729124i	0.996034	−	0.0889776i	$-0.0283600\pi$
$61$	25.6786	+	44.4766i	0.420960	+	0.729124i	−0.575074	+	0.818102i	$0.695027\pi$
$62$	−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	−0.946363	−	0.323105i	$-0.895273\pi$
$67$	−12.9554	+	22.4394i	−0.193364	+	0.334916i	0.752999	+	0.658022i	$0.228606\pi$
$68$	−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	0.549012	−	0.835815i	$-0.315004\pi$
$71$	7.07732	+	4.08609i	0.0996806	+	0.0575506i	−0.449331	+	0.893365i	$0.648338\pi$
$72$	−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	−0.809171	−	0.587573i	$-0.800084\pi$
$79$	8.23711	−	14.2671i	0.104267	−	0.180596i	0.913439	+	0.406977i	$0.133417\pi$
$80$	−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	0.241309	−	0.970448i	$-0.422423\pi$
$83$	−39.7129	−	22.9283i	−0.478469	−	0.276244i	−0.719778	+	0.694204i	$0.755757\pi$
$84$	−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	−0.0484035	−	0.998828i	$-0.515413\pi$
$89$	70.5240	−	40.7171i	0.792405	−	0.457495i	0.840809	+	0.541333i	$0.182080\pi$
$90$	−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	0.719289	−	0.694711i	$-0.244468\pi$
$97$	−23.4733	−	40.6570i	−0.241993	−	0.419144i	−0.961282	+	0.275567i	$0.911134\pi$
$98$	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	$-0.941495\pi$
$101$		−	36.9184i		−	0.365529i	0.983157	−	0.182764i	$-0.0585045\pi$
$102$	40.3889	+	152.868i	0.395970	+	1.49871i
$103$	−34.9957	−	60.6143i	−0.339764	−	0.588488i	0.644624	−	0.764500i	$-0.277014\pi$
$103$	−34.9957	−	60.6143i	−0.339764	−	0.588488i	−0.984388	+	0.176011i	$0.943680\pi$
$104$	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	0.0298423	−	0.999555i	$-0.490500\pi$
$107$	97.4131	−	56.2415i	0.910403	−	0.525621i	0.880561	+	0.473933i	$0.157166\pi$
$108$	−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	$-0.722010\pi$
$113$		−	173.223i		−	1.53295i	0.642276	−	0.766473i	$-0.277990\pi$
$114$	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	0.983633	+	0.180186i	$0.0576699\pi$
$127$	82.2784	+	142.510i	0.647862	+	1.12213i	−0.335771	+	0.941944i	$0.608997\pi$
$128$			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	0.162701	−	0.986675i	$-0.447979\pi$
$131$	143.908	−	83.0856i	1.09854	−	0.634241i	0.935836	+	0.352435i	$0.114646\pi$
$132$	−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	0.239771	−	0.970829i	$-0.422928\pi$
$137$	164.457	−	94.9496i	1.20042	−	0.693063i	0.960648	+	0.277767i	$0.0895943\pi$
$138$	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	$0.374387\pi$
$149$			275.096i			1.84628i	−0.384462	+	0.923141i	$0.625613\pi$
$150$	−106.678	+	28.1852i	−0.711189	+	0.187901i
$151$	−10.8588	+	18.8080i	−0.0719127	+	0.124556i	−0.899740	−	0.436427i	$-0.856244\pi$
$151$	−10.8588	+	18.8080i	−0.0719127	+	0.124556i	0.827827	+	0.560984i	$0.189577\pi$
$152$	−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	0.949659	−	0.313287i	$-0.101430\pi$
$157$	31.9519	+	55.3422i	0.203515	+	0.352498i	−0.746144	+	0.665785i	$0.768097\pi$
$158$	−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	0.454098	+	0.890952i	$0.349961\pi$
$163$	−88.7596	+	153.736i	−0.544537	+	0.943166i	−0.998636	+	0.0522150i	$0.983372\pi$
$164$	−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	0.325224	−	0.945637i	$-0.394560\pi$
$167$	−55.2953	−	31.9247i	−0.331109	−	0.191166i	−0.656334	+	0.754471i	$0.727894\pi$
$168$	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	0.263469	−	0.964668i	$-0.415133\pi$
$173$	212.899	−	122.917i	1.23063	−	0.710505i	0.967161	+	0.254163i	$0.0818001\pi$
$174$	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	−0.756054	−	0.654509i	$-0.772876\pi$
$179$	−101.540	+	58.6239i	−0.567260	+	0.327508i	0.188794	+	0.982017i	$0.439542\pi$
$180$	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	−0.591246	+	0.806491i	$0.701364\pi$
$191$	−302.794	+	174.818i	−1.58531	+	0.915280i	−0.994065	+	0.108789i	$0.965303\pi$
$192$	18.8387	−	18.7075i	0.0981184	−	0.0974351i
$193$	148.706	−	257.567i	0.770499	−	1.33454i	−0.166791	−	0.985992i	$-0.553341\pi$
$193$	148.706	−	257.567i	0.770499	−	1.33454i	0.937290	−	0.348551i	$-0.113326\pi$
$194$	−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	−0.529534	+	0.848289i	$0.677633\pi$
$197$	−301.201	+	173.899i	−1.52894	+	0.882734i	−0.999407	+	0.0344457i	$0.989033\pi$
$198$	−0.945728	+	135.322i	−0.00477640	+	0.683445i
$199$	32.5912	−	56.4496i	0.163775	−	0.283666i	−0.772445	−	0.635082i	$-0.780966\pi$
$199$	32.5912	−	56.4496i	0.163775	−	0.283666i	0.936220	+	0.351416i	$0.114300\pi$
$200$	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	−0.734131	−	0.679008i	$-0.762410\pi$
$211$	46.6252	−	80.7573i	0.220973	−	0.382736i	0.955104	+	0.296272i	$0.0957435\pi$
$212$			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	−0.816322	−	0.577598i	$-0.803990\pi$
$227$	−164.409	+	94.9215i	−0.724268	+	0.418156i	0.0920534	+	0.995754i	$0.470657\pi$
$228$	−45.6562	−	172.804i	−0.200247	−	0.757914i
$229$	21.0010	+	36.3747i	0.0917072	+	0.158842i	0.908230	−	0.418472i	$-0.137434\pi$
$229$	21.0010	+	36.3747i	0.0917072	+	0.158842i	−0.816522	+	0.577314i	$0.804101\pi$
$230$		−	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	$0.105623\pi$
$233$			151.808i			0.651536i	−0.945450	+	0.325768i	$0.894377\pi$
$234$	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	−0.0975330	−	0.995232i	$-0.531095\pi$
$239$	171.028	−	98.7429i	0.715597	−	0.413150i	0.813130	+	0.582082i	$0.197762\pi$
$240$	49.6344	−	182.682i	0.206810	−	0.761176i
$241$	4.05145	+	7.01731i	0.0168110	+	0.0291175i	0.874309	−	0.485371i	$-0.161315\pi$
$241$	4.05145	+	7.01731i	0.0168110	+	0.0291175i	−0.857498	+	0.514488i	$0.827982\pi$
$242$		−	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	0.678636	−	0.734474i	$-0.262571\pi$
$251$	95.8522	+	55.3403i	0.381881	+	0.220479i	−0.296755	+	0.954954i	$0.595905\pi$
$252$	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	−0.951157	−	0.308708i	$-0.900103\pi$
$257$	−435.380	−	251.367i	−1.69408	−	0.978080i	−0.742927	−	0.669372i	$-0.766563\pi$
$258$	−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	$0.125399\pi$
$263$			201.900i			0.767681i	−0.923399	+	0.383840i	$0.874601\pi$
$264$	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	0.876393	−	0.481596i	$-0.159943\pi$
$269$	241.432	+	139.391i	0.897515	+	0.518180i	0.0211218	+	0.999777i	$0.493276\pi$
$270$	56.0074	−	200.587i	0.207435	−	0.742916i
$271$	−58.8505	−	101.932i	−0.217161	−	0.376133i	0.736778	−	0.676135i	$-0.236346\pi$
$271$	−58.8505	−	101.932i	−0.217161	−	0.376133i	−0.953939	+	0.300001i	$0.903013\pi$
$272$	−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	0.749133	−	0.662420i	$-0.230470\pi$
$277$	−55.1523	−	95.5265i	−0.199106	−	0.344861i	−0.948239	+	0.317558i	$0.897137\pi$
$278$		−	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	0.472941	−	0.881094i	$-0.343192\pi$
$281$	−15.0724	−	8.70203i	−0.0536383	−	0.0309681i	−0.526579	+	0.850126i	$0.676526\pi$
$282$	52.5012	+	198.712i	0.186174	+	0.704652i
$283$	−246.465	+	426.889i	−0.870900	+	1.50844i	−0.00983293	+	0.999952i	$0.503130\pi$
$283$	−246.465	+	426.889i	−0.870900	+	1.50844i	−0.861067	+	0.508491i	$0.830203\pi$
$284$	−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	$0.201123\pi$
$293$			346.112i			1.18127i	−0.806938	+	0.590636i	$0.798877\pi$
$294$	−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	−0.372373	−	0.928083i	$-0.621456\pi$
$311$	76.2524	−	44.0243i	0.245184	−	0.141557i	0.617557	+	0.786526i	$0.288122\pi$
$312$	−151.760	−	119.137i	−0.486411	−	0.381849i
$313$	−171.445	+	296.951i	−0.547747	+	0.948726i	0.450681	+	0.892685i	$0.351181\pi$
$313$	−171.445	+	296.951i	−0.547747	+	0.948726i	−0.998428	+	0.0560413i	$0.982152\pi$
$314$	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	0.882090	−	0.471081i	$-0.156136\pi$
$317$	290.108	+	167.494i	0.915166	+	0.528371i	0.0330763	+	0.999453i	$0.489470\pi$
$318$	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	0.904456	−	0.426568i	$-0.140277\pi$
$331$	27.4099	+	47.4753i	0.0828092	+	0.143430i	−0.821646	+	0.569998i	$0.806944\pi$
$332$	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	0.693624	−	0.720337i	$-0.256013\pi$
$337$	−93.3550	−	161.696i	−0.277018	−	0.479809i	−0.970642	+	0.240528i	$0.922679\pi$
$338$	−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	$0.0725650\pi$
$347$			156.844i			0.452000i	−0.974127	+	0.226000i	$0.927435\pi$
$348$	−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	$0.274003\pi$
$353$			535.408i			1.51674i	−0.651827	+	0.758368i	$0.725997\pi$
$354$	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	$0.0448615\pi$
$359$			100.858i			0.280941i	−0.990085	+	0.140471i	$0.955138\pi$
$360$	−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	0.974651	−	0.223731i	$-0.0718238\pi$
$379$	111.262	+	192.712i	0.293568	+	0.508475i	−0.681082	+	0.732207i	$0.738491\pi$
$380$			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	$-0.734402\pi$
$383$		−	567.525i		−	1.48179i	0.671622	−	0.740894i	$-0.265598\pi$
$384$	−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	0.726944	−	0.686697i	$-0.240940\pi$
$389$	192.834	+	111.333i	0.495718	+	0.286203i	−0.231225	+	0.972900i	$0.574273\pi$
$390$	−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	−0.788901	−	0.614520i	$-0.789350\pi$
$397$	54.6826	−	94.7131i	0.137740	−	0.238572i	0.926641	+	0.375948i	$0.122683\pi$
$398$	−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	0.667850	−	0.744296i	$-0.267215\pi$
$401$	143.236	+	82.6971i	0.357196	+	0.206227i	−0.310654	+	0.950523i	$0.600548\pi$
$402$	−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	0.0375209	−	0.999296i	$-0.488054\pi$
$419$	−339.027	−	195.737i	−0.809134	−	0.467154i	−0.846655	+	0.532142i	$0.821387\pi$
$420$	−138.378	+	36.5605i	−0.329472	+	0.0870489i
$421$	111.844	−	193.719i	0.265662	−	0.460140i	−0.702075	−	0.712103i	$-0.747743\pi$
$421$	111.844	−	193.719i	0.265662	−	0.460140i	0.967737	+	0.251963i	$0.0810762\pi$
$422$	−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	−0.723747	−	0.690066i	$-0.757582\pi$
$431$	−210.330	+	121.434i	−0.488006	+	0.281750i	0.235741	+	0.971816i	$0.424248\pi$
$432$	−377.803	−	385.809i	−0.874545	−	0.893075i
$433$	−31.9975	+	55.4212i	−0.0738972	+	0.127994i	−0.900606	−	0.434636i	$-0.856877\pi$
$433$	−31.9975	+	55.4212i	−0.0738972	+	0.127994i	0.826709	+	0.562630i	$0.190210\pi$
$434$	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	0.490822	−	0.871260i	$-0.336697\pi$
$443$	−8.10700	−	4.68058i	−0.0183002	−	0.0105656i	−0.509122	+	0.860694i	$0.670030\pi$
$444$	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	0.0552392	−	0.998473i	$-0.482408\pi$
$449$	−351.048	−	202.678i	−0.781844	−	0.451398i	−0.837083	+	0.547075i	$0.815741\pi$
$450$	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	−0.784819	−	0.619725i	$-0.787244\pi$
$461$	−295.284	+	170.483i	−0.640530	+	0.369810i	0.144289	+	0.989536i	$0.453911\pi$
$462$	−333.043	−	90.4872i	−0.720873	−	0.195860i
$463$	235.726	+	408.289i	0.509127	+	0.881834i	0.999944	+	0.0105715i	$0.00336507\pi$
$463$	235.726	+	408.289i	0.509127	+	0.881834i	−0.490817	+	0.871263i	$0.663302\pi$
$464$			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	$-0.693458\pi$
$467$		−	766.744i		−	1.64185i	0.571036	−	0.820925i	$-0.306542\pi$
$468$	−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	$0.0758581\pi$
$479$			226.151i			0.472132i	−0.971737	+	0.236066i	$0.924142\pi$
$480$	−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	−0.341475	−	0.939891i	$-0.610926\pi$
$487$	313.254	−	542.572i	0.643232	−	1.11411i	0.984707	−	0.174220i	$-0.0557403\pi$
$488$	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	0.801970	−	0.597364i	$-0.203785\pi$
$491$	336.641	+	194.360i	0.685623	+	0.395845i	−0.116347	+	0.993209i	$0.537119\pi$
$492$	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	0.881774	−	0.471673i	$-0.156350\pi$
$499$	16.1707	+	28.0084i	0.0324062	+	0.0561291i	−0.849367	+	0.527802i	$0.823016\pi$
$500$		−	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	0.863443	−	0.504446i	$-0.168303\pi$
$503$	431.726	+	249.257i	0.858302	+	0.495541i	−0.00514126	+	0.999987i	$0.501637\pi$
$504$	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	0.997414	+	0.0718741i	$0.0228980\pi$
$509$	793.208	+	457.959i	1.55837	+	0.899723i	0.560952	+	0.827849i	$0.310435\pi$
$510$	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	$-0.980808\pi$
$521$		−	62.7872i		−	0.120513i	0.998183	−	0.0602564i	$-0.0191918\pi$
$522$	−0.648746	+	92.8276i	−0.00124281	+	0.177831i
$523$	77.4887	+	134.214i	0.148162	+	0.256624i	0.930548	−	0.366169i	$-0.119331\pi$
$523$	77.4887	+	134.214i	0.148162	+	0.256624i	−0.782386	+	0.622794i	$0.785998\pi$
$524$	−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	−0.977532	−	0.210785i	$-0.932398\pi$
$547$	−167.503	+	290.123i	−0.306221	+	0.530390i	0.671312	+	0.741175i	$0.265731\pi$
$548$	−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	−0.214697	−	0.976681i	$-0.568876\pi$
$557$	291.748	−	168.441i	0.523785	−	0.302407i	0.738482	+	0.674273i	$0.235543\pi$
$558$	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	$0.300357\pi$
$563$			911.694i			1.61935i	−0.586878	+	0.809675i	$0.699643\pi$
$564$	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	$0.122119\pi$
$569$			425.960i			0.748611i	−0.927305	+	0.374306i	$0.877881\pi$
$570$	494.971	−	491.524i	0.868370	−	0.862322i
$571$	383.824	+	664.803i	0.672196	+	1.16428i	0.977280	+	0.211952i	$0.0679822\pi$
$571$	383.824	+	664.803i	0.672196	+	1.16428i	−0.305084	+	0.952325i	$0.598685\pi$
$572$	−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	$-0.995442\pi$
$587$		−	16.8090i		−	0.0286355i	0.999897	−	0.0143178i	$-0.00455764\pi$
$588$	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	$0.0991688\pi$
$593$			363.547i			0.613065i	−0.951860	+	0.306532i	$0.900831\pi$
$594$	−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	−0.988312	−	0.152448i	$-0.951284\pi$
$599$	−808.916	+	467.028i	−1.35044	+	0.779679i	−0.362132	+	0.932127i	$0.617951\pi$
$600$	−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	−0.999892	−	0.0146930i	$-0.995323\pi$
$613$	−314.267	−	544.326i	−0.512671	−	0.887971i	0.487222	−	0.873278i	$-0.338010\pi$
$614$		−	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	$-0.709391\pi$
$617$		−	976.498i		−	1.58265i	0.611393	−	0.791327i	$-0.290609\pi$
$618$	134.587	−	495.357i	0.217779	−	0.801549i
$619$	337.425	−	584.436i	0.545112	−	0.944162i	−0.453487	−	0.891263i	$-0.649820\pi$
$619$	337.425	−	584.436i	0.545112	−	0.944162i	0.998600	−	0.0528997i	$-0.0168464\pi$
$620$	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	0.302178	+	0.953251i	$0.402286\pi$
$631$	−425.578	+	737.123i	−0.674451	+	1.16818i	−0.976629	+	0.214932i	$0.931047\pi$
$632$	−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	−0.359851	−	0.933010i	$-0.617172\pi$
$641$	171.938	−	99.2685i	0.268234	−	0.154865i	0.628085	+	0.778145i	$0.283839\pi$
$642$	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	0.471047	−	0.882108i	$-0.343876\pi$
$647$	951.412	−	549.298i	1.47050	−	0.848993i	0.999452	+	0.0331157i	$0.0105430\pi$
$648$	−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	0.560122	−	0.828410i	$-0.310754\pi$
$653$	80.1614	+	46.2812i	0.122759	+	0.0708747i	−0.437363	+	0.899285i	$0.644088\pi$
$654$	−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	−0.0410900	−	0.999155i	$-0.513083\pi$
$659$	529.611	−	305.771i	0.803659	−	0.463993i	0.844749	+	0.535163i	$0.179750\pi$
$660$	−111.036	−	30.1682i	−0.168236	−	0.0457095i
$661$	292.415	−	506.478i	0.442383	−	0.766229i	−0.555483	−	0.831528i	$-0.687467\pi$
$661$	292.415	−	506.478i	0.442383	−	0.766229i	0.997866	+	0.0652985i	$0.0208000\pi$
$662$	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	−0.426182	−	0.904637i	$-0.640142\pi$
$677$	−963.176	−	556.090i	−1.42271	−	0.821403i	−0.996530	+	0.0832338i	$0.973475\pi$
$678$	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	0.992274	−	0.124069i	$-0.0395944\pi$
$683$	943.198	+	544.556i	1.38096	+	0.797300i	0.388690	+	0.921369i	$0.372928\pi$
$684$	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	$0.164720\pi$
$701$			693.561i			0.989388i	−0.869067	+	0.494694i	$0.835280\pi$
$702$	−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	0.805534	−	0.592550i	$-0.201879\pi$
$709$	−78.2712	−	135.570i	−0.110397	−	0.191212i	−0.915930	+	0.401338i	$0.868545\pi$
$710$		−	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	0.425028	−	0.905180i	$-0.360264\pi$
$719$	−105.238	−	60.7593i	−0.146367	−	0.0845053i	−0.571395	+	0.820675i	$0.693598\pi$
$720$	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	−0.526932	−	0.849908i	$-0.676658\pi$
$727$	343.562	−	595.068i	0.472576	−	0.818525i	0.999507	+	0.0313826i	$0.00999103\pi$
$728$	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	0.853780	−	0.520633i	$-0.174304\pi$
$733$	−17.5857	−	30.4593i	−0.0239914	−	0.0415542i	−0.877772	+	0.479079i	$0.840971\pi$
$734$			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	0.749722	+	0.661753i	$0.230187\pi$
$739$	700.539	+	1213.37i	0.947956	+	1.64191i	0.198234	+	0.980155i	$0.436479\pi$
$740$	−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	−0.0692068	−	0.997602i	$-0.522047\pi$
$743$	−719.045	−	415.141i	−0.967759	−	0.558736i	−0.898552	+	0.438866i	$0.855380\pi$
$744$	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	−0.999817	−	0.0191462i	$-0.993905\pi$
$751$	−362.979	+	628.698i	−0.483327	+	0.837147i	0.516489	+	0.856294i	$0.327239\pi$
$752$	−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	0.992523	+	0.122061i	$0.0389503\pi$
$757$	455.691	+	789.279i	0.601969	+	1.04264i	−0.390554	+	0.920580i	$0.627716\pi$
$758$	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	$-0.725626\pi$
$761$		−	1155.39i		−	1.51825i	0.650943	−	0.759126i	$-0.274374\pi$
$762$	−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	−0.629895	−	0.776681i	$-0.716902\pi$
$769$	275.054	−	476.408i	0.357678	−	0.619516i	0.987572	+	0.157165i	$0.0502353\pi$
$770$

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