LMFDB - Embedded newform 115.3.i.a.109.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [115,3,Mod(14,115)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(115, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([11, 21])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("115.14"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	115.i (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.13352304014$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$22$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			109.20
Character	$\chi$	$=$	115.109
Dual form			115.3.i.a.19.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.70071 + 1.23337i) q^{2} +(-0.857097 + 2.91901i) q^{3} +(3.15318 + 3.63896i) q^{4} +(-4.95118 - 0.696972i) q^{5} +(-5.91499 + 6.82626i) q^{6} +(-1.26402 + 8.79144i) q^{7} +(0.681750 + 2.32183i) q^{8} +(-0.214694 - 0.137975i) q^{9} +(-12.5121 - 7.98897i) q^{10} +(14.3361 - 6.54709i) q^{11} +(-13.3247 + 6.08520i) q^{12} +(17.5299 - 2.52042i) q^{13} +(-14.2569 + 22.1841i) q^{14} +(6.27811 - 13.8552i) q^{15} +(1.71853 - 11.9527i) q^{16} +(9.93564 - 11.4663i) q^{17} +(-0.409651 - 0.637429i) q^{18} +(-23.7302 + 20.5623i) q^{19} +(-13.0757 - 20.2148i) q^{20} +(-24.5789 - 11.2248i) q^{21} +46.7927 q^{22} +(-21.6053 - 7.88738i) q^{23} -7.36176 q^{24} +(24.0285 + 6.90168i) q^{25} +(50.4518 + 14.8140i) q^{26} +(-20.1058 + 17.4217i) q^{27} +(-35.9774 + 23.1213i) q^{28} +(15.6709 - 18.0852i) q^{29} +(34.0439 - 29.6755i) q^{30} +(1.65111 - 0.484811i) q^{31} +(24.6164 - 38.3039i) q^{32} +(6.82354 + 47.4587i) q^{33} +(40.9755 - 18.7129i) q^{34} +(12.3858 - 42.6470i) q^{35} +(-0.174881 - 1.21632i) q^{36} +(-42.6547 - 27.4125i) q^{37} +(-89.4494 + 26.2647i) q^{38} +(-7.66772 + 53.3301i) q^{39} +(-1.75722 - 11.9710i) q^{40} +(19.3888 - 12.4604i) q^{41} +(-52.5360 - 60.6298i) q^{42} +(4.66210 + 1.36891i) q^{43} +(69.0290 + 31.5245i) q^{44} +(0.966824 + 0.832777i) q^{45} +(-48.6216 - 47.9489i) q^{46} +17.5218i q^{47} +(33.4169 + 15.2610i) q^{48} +(-28.6765 - 8.42017i) q^{49} +(56.3815 + 48.2755i) q^{50} +(24.9545 + 38.8299i) q^{51} +(64.4466 + 55.8433i) q^{52} +(-4.26320 + 29.6512i) q^{53} +(-75.7873 + 22.2532i) q^{54} +(-75.5440 + 22.4240i) q^{55} +(-21.2740 + 3.05873i) q^{56} +(-39.6825 - 86.8925i) q^{57} +(64.6284 - 29.5148i) q^{58} +(4.40702 + 30.6515i) q^{59} +(70.2144 - 20.8420i) q^{60} +(-24.4297 - 83.2000i) q^{61} +(5.05713 + 0.727106i) q^{62} +(1.48438 - 1.71306i) q^{63} +(73.0903 - 46.9723i) q^{64} +(-88.5505 + 0.261204i) q^{65} +(-40.1059 + 136.588i) q^{66} +(22.2934 - 48.8157i) q^{67} +73.0544 q^{68} +(41.5411 - 56.3058i) q^{69} +(86.0501 - 99.9010i) q^{70} +(8.96525 - 19.6312i) q^{71} +(0.173988 - 0.592547i) q^{72} +(-3.46282 + 3.00055i) q^{73} +(-81.3881 - 126.642i) q^{74} +(-40.7408 + 64.2238i) q^{75} +(-149.651 - 21.5166i) q^{76} +(39.4372 + 134.311i) q^{77} +(-86.4842 + 134.572i) q^{78} +(45.2904 - 6.51178i) q^{79} +(-16.8395 + 57.9821i) q^{80} +(-34.5757 - 75.7102i) q^{81} +(67.7319 - 9.73837i) q^{82} +(-1.21776 - 0.782606i) q^{83} +(-36.6549 - 124.835i) q^{84} +(-57.1849 + 49.8471i) q^{85} +(10.9026 + 9.44714i) q^{86} +(39.3593 + 61.2443i) q^{87} +(24.9749 + 28.8226i) q^{88} +(-29.2249 + 99.5308i) q^{89} +(1.58399 + 3.44154i) q^{90} +157.299i q^{91} +(-39.4235 - 103.491i) q^{92} +5.23514i q^{93} +(-21.6110 + 47.3214i) q^{94} +(131.824 - 85.2687i) q^{95} +(90.7106 + 104.686i) q^{96} +(-116.921 + 75.1405i) q^{97} +(-67.0616 - 58.1092i) q^{98} +(-3.98122 - 0.572413i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30}+ \cdots + 1628 q^{99}+O(q^{100}) $ 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$-1$	$e\left(\frac{7}{22}\right)$

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 $

$2$	2.70071	+	1.23337i	1.35035	+	0.616686i	0.953555	−	0.301219i	$-0.0973936\pi$
$2$	2.70071	+	1.23337i	1.35035	+	0.616686i	0.396799	+	0.917905i	$0.370121\pi$
$3$	−0.857097	+	2.91901i	−0.285699	+	0.973002i	0.684159	+	0.729333i	$0.260169\pi$
$3$	−0.857097	+	2.91901i	−0.285699	+	0.973002i	−0.969858	+	0.243669i	$0.921649\pi$
$4$	3.15318	+	3.63896i	0.788294	+	0.909740i
$5$	−4.95118	−	0.696972i	−0.990237	−	0.139394i
$5$	−4.95118	−	0.696972i	−0.990237	−	0.139394i
$6$	−5.91499	+	6.82626i	−0.985832	+	1.13771i
$7$	−1.26402	+	8.79144i	−0.180574	+	1.25592i	0.674836	+	0.737968i	$0.264214\pi$
$7$	−1.26402	+	8.79144i	−0.180574	+	1.25592i	−0.855410	+	0.517952i	$0.826695\pi$
$8$	0.681750	+	2.32183i	0.0852188	+	0.290229i
$9$	−0.214694	−	0.137975i	−0.0238549	−	0.0153306i
$10$	−12.5121	−	7.98897i	−1.25121	−	0.798897i
$11$	14.3361	−	6.54709i	1.30328	−	0.595190i	0.361803	−	0.932255i	$-0.382161\pi$
$11$	14.3361	−	6.54709i	1.30328	−	0.595190i	0.941482	+	0.337064i	$0.109434\pi$
$12$	−13.3247	+	6.08520i	−1.11039	+	0.507100i
$13$	17.5299	−	2.52042i	1.34845	−	0.193878i	0.570034	−	0.821621i	$-0.306930\pi$
$13$	17.5299	−	2.52042i	1.34845	−	0.193878i	0.778421	+	0.627743i	$0.216021\pi$
$14$	−14.2569	+	22.1841i	−1.01835	+	1.58458i
$15$	6.27811	−	13.8552i	0.418541	−	0.923677i
$16$	1.71853	−	11.9527i	0.107408	−	0.747042i
$17$	9.93564	−	11.4663i	0.584449	−	0.674490i	−0.384106	−	0.923289i	$-0.625490\pi$
$17$	9.93564	−	11.4663i	0.584449	−	0.674490i	0.968555	+	0.248799i	$0.0800357\pi$
$18$	−0.409651	−	0.637429i	−0.0227584	−	0.0354127i
$19$	−23.7302	+	20.5623i	−1.24896	+	1.08223i	−0.255646	+	0.966770i	$0.582288\pi$
$19$	−23.7302	+	20.5623i	−1.24896	+	1.08223i	−0.993312	+	0.115458i	$0.963166\pi$
$20$	−13.0757	−	20.2148i	−0.653785	−	1.01074i
$21$	−24.5789	−	11.2248i	−1.17042	−	0.534514i
$22$	46.7927			2.12694
$23$	−21.6053	−	7.88738i	−0.939361	−	0.342929i
$23$	−21.6053	−	7.88738i	−0.939361	−	0.342929i
$24$	−7.36176			−0.306740
$25$	24.0285	+	6.90168i	0.961138	+	0.276067i
$26$	50.4518	+	14.8140i	1.94045	+	0.569769i
$27$	−20.1058	+	17.4217i	−0.744658	+	0.645250i
$28$	−35.9774	+	23.1213i	−1.28491	+	0.825759i
$29$	15.6709	−	18.0852i	0.540376	−	0.623628i	−0.418237	−	0.908338i	$-0.637352\pi$
$29$	15.6709	−	18.0852i	0.540376	−	0.623628i	0.958614	+	0.284710i	$0.0918974\pi$
$30$	34.0439	−	29.6755i	1.13480	−	0.989183i
$31$	1.65111	−	0.484811i	0.0532618	−	0.0156391i	−0.254993	−	0.966943i	$-0.582073\pi$
$31$	1.65111	−	0.484811i	0.0532618	−	0.0156391i	0.308255	+	0.951304i	$0.400255\pi$
$32$	24.6164	−	38.3039i	0.769263	−	1.19700i
$33$	6.82354	+	47.4587i	0.206774	+	1.43814i
$34$	40.9755	−	18.7129i	1.20516	−	0.550379i
$35$	12.3858	−	42.6470i	0.353879	−	1.21849i
$36$	−0.174881	−	1.21632i	−0.00485780	−	0.0337868i
$37$	−42.6547	−	27.4125i	−1.15283	−	0.740879i	−0.182629	−	0.983182i	$-0.558461\pi$
$37$	−42.6547	−	27.4125i	−1.15283	−	0.740879i	−0.970201	+	0.242303i	$0.922097\pi$
$38$	−89.4494	+	26.2647i	−2.35393	+	0.691177i
$39$	−7.66772	+	53.3301i	−0.196608	+	1.36744i
$40$	−1.75722	−	11.9710i	−0.0439305	−	0.299274i
$41$	19.3888	−	12.4604i	0.472898	−	0.303913i	−0.282398	−	0.959297i	$-0.591130\pi$
$41$	19.3888	−	12.4604i	0.472898	−	0.303913i	0.755295	+	0.655385i	$0.227493\pi$
$42$	−52.5360	−	60.6298i	−1.25086	−	1.44357i
$43$	4.66210	+	1.36891i	0.108421	+	0.0318352i	0.335493	−	0.942043i	$-0.391097\pi$
$43$	4.66210	+	1.36891i	0.108421	+	0.0318352i	−0.227072	+	0.973878i	$0.572915\pi$
$44$	69.0290	+	31.5245i	1.56884	+	0.716465i
$45$	0.966824	+	0.832777i	0.0214850	+	0.0185062i
$46$	−48.6216	−	47.9489i	−1.05699	−	1.04237i
$47$			17.5218i			0.372805i	0.982473	+	0.186403i	$0.0596829\pi$
$47$			17.5218i			0.372805i	−0.982473	+	0.186403i	$0.940317\pi$
$48$	33.4169	+	15.2610i	0.696186	+	0.317938i
$49$	−28.6765	−	8.42017i	−0.585234	−	0.171840i
$50$	56.3815	+	48.2755i	1.12763	+	0.965509i
$51$	24.9545	+	38.8299i	0.489304	+	0.761371i
$52$	64.4466	+	55.8433i	1.23936	+	1.07391i
$53$	−4.26320	+	29.6512i	−0.0804377	+	0.559457i	0.909254	+	0.416242i	$0.136653\pi$
$53$	−4.26320	+	29.6512i	−0.0804377	+	0.559457i	−0.989692	+	0.143215i	$0.954256\pi$
$54$	−75.7873	+	22.2532i	−1.40347	+	0.412096i
$55$	−75.5440	+	22.4240i	−1.37353	+	0.407709i
$56$	−21.2740	+	3.05873i	−0.379892	+	0.0546202i
$57$	−39.6825	−	86.8925i	−0.696184	−	1.52443i
$58$	64.6284	−	29.5148i	1.11428	−	0.508876i
$59$	4.40702	+	30.6515i	0.0746952	+	0.519516i	0.992477	+	0.122431i	$0.0390691\pi$
$59$	4.40702	+	30.6515i	0.0746952	+	0.519516i	−0.917782	+	0.397085i	$0.870022\pi$
$60$	70.2144	−	20.8420i	1.17024	−	0.347366i
$61$	−24.4297	−	83.2000i	−0.400488	−	1.36394i	−0.875186	−	0.483787i	$-0.839261\pi$
$61$	−24.4297	−	83.2000i	−0.400488	−	1.36394i	0.474698	−	0.880149i	$-0.342557\pi$
$62$	5.05713	+	0.727106i	0.0815667	+	0.0117275i
$63$	1.48438	−	1.71306i	0.0235616	−	0.0271915i
$64$	73.0903	−	46.9723i	1.14204	−	0.733942i
$65$	−88.5505	+	0.261204i	−1.36231	+	0.00401853i
$66$	−40.1059	+	136.588i	−0.607665	+	2.06952i
$67$	22.2934	−	48.8157i	0.332737	−	0.728592i	−0.667129	−	0.744942i	$-0.732477\pi$
$67$	22.2934	−	48.8157i	0.332737	−	0.728592i	0.999866	+	0.0163495i	$0.00520442\pi$
$68$	73.0544			1.07433
$69$	41.5411	−	56.3058i	0.602046	−	0.816025i
$70$	86.0501	−	99.9010i	1.22929	−	1.42716i
$71$	8.96525	−	19.6312i	0.126271	−	0.276495i	−0.835929	−	0.548837i	$-0.815071\pi$
$71$	8.96525	−	19.6312i	0.126271	−	0.276495i	0.962201	+	0.272342i	$0.0877981\pi$
$72$	0.173988	−	0.592547i	0.00241649	−	0.00822982i
$73$	−3.46282	+	3.00055i	−0.0474358	+	0.0411034i	−0.678256	−	0.734826i	$-0.737264\pi$
$73$	−3.46282	+	3.00055i	−0.0474358	+	0.0411034i	0.630820	+	0.775929i	$0.282719\pi$
$74$	−81.3881	−	126.642i	−1.09984	−	1.71138i
$75$	−40.7408	+	64.2238i	−0.543210	+	0.856317i
$76$	−149.651	−	21.5166i	−1.96909	−	0.283113i
$77$	39.4372	+	134.311i	0.512172	+	1.74430i
$78$	−86.4842	+	134.572i	−1.10877	+	1.72528i
$79$	45.2904	−	6.51178i	0.573296	−	0.0824276i	0.150432	−	0.988620i	$-0.451934\pi$
$79$	45.2904	−	6.51178i	0.573296	−	0.0824276i	0.422865	+	0.906193i	$0.361025\pi$
$80$	−16.8395	+	57.9821i	−0.210493	+	0.724776i
$81$	−34.5757	−	75.7102i	−0.426861	−	0.934694i
$82$	67.7319	−	9.73837i	0.825998	−	0.118761i
$83$	−1.21776	−	0.782606i	−0.0146718	−	0.00942898i	0.533284	−	0.845936i	$-0.320958\pi$
$83$	−1.21776	−	0.782606i	−0.0146718	−	0.00942898i	−0.547956	+	0.836507i	$0.684594\pi$
$84$	−36.6549	−	124.835i	−0.436368	−	1.48613i
$85$	−57.1849	+	49.8471i	−0.672763	+	0.586436i
$86$	10.9026	+	9.44714i	0.126774	+	0.109850i
$87$	39.3593	+	61.2443i	0.452406	+	0.703957i
$88$	24.9749	+	28.8226i	0.283806	+	0.327529i
$89$	−29.2249	+	99.5308i	−0.328370	+	1.11832i	0.615536	+	0.788109i	$0.288940\pi$
$89$	−29.2249	+	99.5308i	−0.328370	+	1.11832i	−0.943906	+	0.330215i	$0.892879\pi$
$90$	1.58399	+	3.44154i	0.0175998	+	0.0382394i
$91$			157.299i			1.72856i
$92$	−39.4235	−	103.491i	−0.428516	−	1.12490i
$93$			5.23514i			0.0562919i
$94$	−21.6110	+	47.3214i	−0.229904	+	0.503419i
$95$	131.824	−	85.2687i	1.38762	−	0.897565i
$96$	90.7106	+	104.686i	0.944902	+	1.09048i
$97$	−116.921	+	75.1405i	−1.20537	+	0.774644i	−0.979877	−	0.199601i	$-0.936035\pi$
$97$	−116.921	+	75.1405i	−1.20537	+	0.774644i	−0.225492	+	0.974245i	$0.572399\pi$
$98$	−67.0616	−	58.1092i	−0.684302	−	0.592951i
$99$	−3.98122	−	0.572413i	−0.0402143	−	0.00578195i
$100$	50.6511	+	109.201i	0.506511	+	1.09201i
$101$	62.5621	+	40.2062i	0.619427	+	0.398081i	0.812382	−	0.583126i	$-0.198171\pi$
$101$	62.5621	+	40.2062i	0.619427	+	0.398081i	−0.192955	+	0.981208i	$0.561807\pi$
$102$	19.5030	+	135.647i	0.191206	+	1.32987i
$103$	−34.6389	−	75.8486i	−0.336300	−	0.736395i	0.663632	−	0.748059i	$-0.269014\pi$
$103$	−34.6389	−	75.8486i	−0.336300	−	0.736395i	−0.999932	+	0.0116648i	$0.996287\pi$
$104$	17.8030	+	38.9831i	0.171183	+	0.374838i
$105$	113.871	+	72.7068i	1.08449	+	0.692446i
$106$	−48.0846	+	74.8211i	−0.453629	+	0.705860i
$107$	−11.6631	+	3.42460i	−0.109001	+	0.0320056i	−0.335778	−	0.941941i	$-0.608999\pi$
$107$	−11.6631	+	3.42460i	−0.109001	+	0.0320056i	0.226777	+	0.973947i	$0.427181\pi$
$108$	−126.794	−	18.2302i	−1.17402	−	0.168798i
$109$	−99.0452	−	85.8231i	−0.908671	−	0.787368i	0.0689764	−	0.997618i	$-0.478027\pi$
$109$	−99.0452	−	85.8231i	−0.908671	−	0.787368i	−0.977648	+	0.210250i	$0.932572\pi$
$110$	−231.679	−	32.6132i	−2.10618	−	0.296484i
$111$	116.577	−	101.014i	1.05024	−	0.910037i
$112$	102.909	+	30.2168i	0.918829	+	0.269793i
$113$	−22.2316	+	48.6805i	−0.196740	+	0.430801i	−0.982131	−	0.188199i	$-0.939735\pi$
$113$	−22.2316	+	48.6805i	−0.196740	+	0.430801i	0.785391	+	0.619001i	$0.212462\pi$
$114$		−	283.615i		−	2.48785i
$115$	101.475	+	54.1102i	0.882388	+	0.470523i
$116$	115.224			0.993315
$117$	−4.11132	−	1.87758i	−0.0351395	−	0.0160477i
$118$	−25.9026	+	88.2162i	−0.219514	+	0.747595i
$119$	88.2468	+	101.842i	0.741569	+	0.855817i
$120$	36.4494	+	5.13094i	0.303745	+	0.0427578i
$121$	83.4221	−	96.2743i	0.689439	−	0.795655i
$122$	36.6390	−	254.830i	0.300320	−	2.08877i
$123$	19.7540	+	67.2758i	0.160601	+	0.546958i
$124$	6.97047	+	4.47965i	0.0562134	+	0.0361262i
$125$	−114.159	−	50.9187i	−0.913272	−	0.407349i
$126$	6.12172	−	2.79570i	0.0485851	−	0.0221881i
$127$	−73.1021	+	33.3846i	−0.575607	+	0.262871i	−0.681878	−	0.731466i	$-0.738836\pi$
$127$	−73.1021	+	33.3846i	−0.575607	+	0.262871i	0.106271	+	0.994337i	$0.466109\pi$
$128$	75.0559	−	10.7914i	0.586374	−	0.0843079i
$129$	−7.99174	+	12.4354i	−0.0619515	+	0.0963984i
$130$	−239.471	−	108.510i	−1.84209	−	0.834694i
$131$	28.2693	−	196.617i	0.215796	−	1.50090i	−0.537527	−	0.843246i	$-0.680641\pi$
$131$	28.2693	−	196.617i	0.215796	−	1.50090i	0.753324	−	0.657650i	$-0.228449\pi$
$132$	−151.185	+	174.476i	−1.14534	+	1.32179i
$133$	−150.777	−	234.614i	−1.13366	−	1.76401i
$134$	120.416	−	104.341i	0.898626	−	0.778664i
$135$	111.690	−	72.2451i	0.827332	−	0.535149i
$136$	33.3965	+	15.2517i	0.245562	+	0.112145i
$137$	111.692			0.815269			0.407634	−	0.913145i	$-0.366354\pi$
$137$	111.692			0.815269			0.407634	+	0.913145i	$0.366354\pi$
$138$	181.636	−	100.830i	1.31621	−	0.730650i
$139$	−119.573			−0.860239			−0.430120	−	0.902772i	$-0.641529\pi$
$139$	−119.573			−0.860239			−0.430120	+	0.902772i	$0.641529\pi$
$140$	194.245	−	89.4024i	1.38747	−	0.638588i
$141$	−51.1463	−	15.0179i	−0.362740	−	0.106510i
$142$	48.4251	−	41.9606i	0.341022	−	0.295497i
$143$	234.810	−	150.903i	1.64203	−	1.05527i
$144$	−2.01813	+	2.32905i	−0.0140148	+	0.0161740i
$145$	−90.1945	+	78.6210i	−0.622031	+	0.542214i
$146$	−13.0529	+	3.83266i	−0.0894031	+	0.0262511i
$147$	49.1571	−	76.4899i	0.334402	−	0.520339i
$148$	−34.7448	−	241.655i	−0.234762	−	1.63281i
$149$	158.705	−	72.4780i	1.06513	−	0.486430i	0.195793	−	0.980645i	$-0.437272\pi$
$149$	158.705	−	72.4780i	1.06513	−	0.486430i	0.869339	+	0.494215i	$0.164545\pi$
$150$	−189.241	+	123.201i	−1.26161	+	0.821341i
$151$	39.1149	+	272.050i	0.259039	+	1.80166i	0.539706	+	0.841853i	$0.318535\pi$
$151$	39.1149	+	272.050i	0.259039	+	1.80166i	−0.280667	+	0.959805i	$0.590556\pi$
$152$	−63.9203	−	41.0791i	−0.420528	−	0.270257i
$153$	−3.71519	+	1.09088i	−0.0242823	+	0.00712993i
$154$	−59.1468	+	411.375i	−0.384070	+	2.67127i
$155$	−8.51287	+	1.24961i	−0.0549218	+	0.00806198i
$156$	−218.244	+	140.257i	−1.39900	+	0.899083i
$157$	33.1913	+	38.3048i	0.211409	+	0.243979i	0.851544	−	0.524284i	$-0.175667\pi$
$157$	33.1913	+	38.3048i	0.211409	+	0.243979i	−0.640134	+	0.768263i	$0.721121\pi$
$158$	130.348	+	38.2735i	0.824985	+	0.242237i
$159$	−82.8980	−	37.8583i	−0.521371	−	0.238102i
$160$	−148.577	+	172.493i	−0.928608	+	1.07808i
$161$	96.6509	−	179.972i	0.600316	−	1.11784i
$162$		−	247.116i		−	1.52541i
$163$	98.0804	+	44.7918i	0.601720	+	0.274796i	0.692895	−	0.721039i	$-0.256335\pi$
$163$	98.0804	+	44.7918i	0.601720	+	0.274796i	−0.0911749	+	0.995835i	$0.529062\pi$
$164$	106.479	+	31.2652i	0.649264	+	0.190641i
$165$	−0.707158	−	239.733i	−0.00428581	−	1.45293i
$166$	−2.32357	−	3.61554i	−0.0139974	−	0.0217804i
$167$	−183.863	−	159.318i	−1.10098	−	0.954001i	−0.101809	−	0.994804i	$-0.532463\pi$
$167$	−183.863	−	159.318i	−1.10098	−	0.954001i	−0.999167	+	0.0408031i	$0.987008\pi$
$168$	9.30539	−	64.7204i	0.0553892	−	0.385241i
$169$	138.791	−	40.7527i	0.821248	−	0.241140i
$170$	−215.920	+	64.0922i	−1.27012	+	0.377013i
$171$	7.93183	−	1.14042i	0.0463850	−	0.00666915i
$172$	9.71899	+	21.2816i	0.0565057	+	0.123730i
$173$	21.1139	−	9.64239i	0.122046	−	0.0557364i	−0.353456	−	0.935451i	$-0.614994\pi$
$173$	21.1139	−	9.64239i	0.122046	−	0.0557364i	0.475502	+	0.879715i	$0.342266\pi$
$174$	30.7610	+	213.948i	0.176787	+	1.22958i
$175$	−91.0481	+	202.521i	−0.520275	+	1.15726i
$176$	−53.6181	−	182.606i	−0.304648	−	1.03754i
$177$	−93.2490	−	13.4072i	−0.526831	−	0.0757468i
$178$	−201.686	+	232.759i	−1.13307	+	1.30763i
$179$	14.3663	−	9.23264i	0.0802585	−	0.0515790i	−0.499896	−	0.866085i	$-0.666628\pi$
$179$	14.3663	−	9.23264i	0.0802585	−	0.0515790i	0.580155	+	0.814506i	$0.302992\pi$
$180$	0.0181238	+	6.14413i	0.000100688	+	0.0341341i
$181$	4.82436	−	16.4303i	0.0266539	−	0.0907749i	−0.945092	−	0.326805i	$-0.894028\pi$
$181$	4.82436	−	16.4303i	0.0266539	−	0.0907749i	0.971746	+	0.236030i	$0.0758463\pi$
$182$	−194.008	+	424.819i	−1.06598	+	2.33417i
$183$	263.800			1.44153
$184$	3.58371	−	55.5410i	0.0194767	−	0.301854i
$185$	192.086	+	165.454i	1.03830	+	0.894344i
$186$	−6.45688	+	14.1386i	−0.0347144	+	0.0760140i
$187$	67.3674	−	229.432i	0.360254	−	1.22691i
$188$	−63.7613	+	55.2495i	−0.339156	+	0.293880i
$189$	−127.748	−	198.780i	−0.675916	−	1.05175i
$190$	461.186	−	67.6977i	2.42730	−	0.356304i
$191$	−78.6732	−	11.3115i	−0.411902	−	0.0592225i	−0.0667507	−	0.997770i	$-0.521263\pi$
$191$	−78.6732	−	11.3115i	−0.411902	−	0.0592225i	−0.345151	+	0.938547i	$0.612172\pi$
$192$	74.4668	+	253.611i	0.387848	+	1.32089i
$193$	11.7434	−	18.2731i	0.0608465	−	0.0946791i	−0.809497	−	0.587124i	$-0.800260\pi$
$193$	11.7434	−	18.2731i	0.0608465	−	0.0946791i	0.870344	+	0.492445i	$0.163897\pi$
$194$	−408.445	+	58.7256i	−2.10539	+	0.302709i
$195$	75.1339	−	258.703i	0.385302	−	1.32668i
$196$	−59.7813	−	130.903i	−0.305007	−	0.667872i
$197$	−327.947	+	47.1517i	−1.66471	+	0.239349i	−0.909370	−	0.415989i	$-0.863436\pi$
$197$	−327.947	+	47.1517i	−1.66471	+	0.239349i	−0.755336	+	0.655337i	$0.772527\pi$
$198$	−10.0461	−	6.45624i	−0.0507379	−	0.0326073i
$199$	103.203	+	351.476i	0.518606	+	1.76621i	0.634473	+	0.772945i	$0.281217\pi$
$199$	103.203	+	351.476i	0.518606	+	1.76621i	−0.115867	+	0.993265i	$0.536964\pi$
$200$	0.356898	+	60.4952i	0.00178449	+	0.302476i
$201$	123.386	+	106.914i	0.613859	+	0.531912i
$202$	119.373	+	185.748i	0.590954	+	0.919543i
$203$	139.187	+	160.630i	0.685648	+	0.791280i
$204$	−62.6147	+	213.246i	−0.306935	+	1.04532i
$205$	−104.682	+	48.1804i	−0.510644	+	0.235026i
$206$		−	247.568i		−	1.20179i
$207$	3.55026	+	4.67437i	0.0171510	+	0.0225815i
$208$		−	213.861i		−	1.02818i
$209$	−205.576	+	450.148i	−0.983617	+	2.15382i
$210$	217.858	+	336.805i	1.03742	+	1.60384i
$211$	143.214	+	165.278i	0.678740	+	0.783307i	0.985717	−	0.168409i	$-0.0538631\pi$
$211$	143.214	+	165.278i	0.678740	+	0.783307i	−0.306977	+	0.951717i	$0.599318\pi$
$212$	−121.342	+	77.9819i	−0.572369	+	0.367839i
$213$	49.6194	+	42.9954i	0.232955	+	0.201857i
$214$	−35.7225	−	5.13612i	−0.166927	−	0.0240005i
$215$	−22.1288	−	10.0271i	−0.102925	−	0.0466377i
$216$	−54.1574	−	34.8049i	−0.250729	−	0.161134i
$217$	2.17515	+	15.1285i	0.0100237	+	0.0697165i
$218$	−161.640	−	353.943i	−0.741469	−	1.62359i
$219$	−5.79064	−	12.6797i	−0.0264413	−	0.0578984i
$220$	−319.804	−	204.195i	−1.45365	−	0.928158i
$221$	145.271	−	226.046i	0.657334	−	1.02283i
$222$	439.427	−	129.027i	1.97940	−	0.581205i
$223$	−36.2673	−	5.21446i	−0.162634	−	0.0233832i	0.0605168	−	0.998167i	$-0.480725\pi$
$223$	−36.2673	−	5.21446i	−0.162634	−	0.0233832i	−0.223151	+	0.974784i	$0.571634\pi$
$224$	305.631	+	264.831i	1.36442	+	1.18228i
$225$	−4.20650	−	4.79708i	−0.0186956	−	0.0213204i
$226$	−120.082	+	104.052i	−0.531338	+	0.460407i
$227$	295.684	+	86.8206i	1.30257	+	0.382469i	0.858173	−	0.513360i	$-0.171599\pi$
$227$	295.684	+	86.8206i	1.30257	+	0.382469i	0.444398	+	0.895829i	$0.353418\pi$
$228$	191.073	−	418.391i	0.838038	−	1.83505i
$229$		−	220.092i		−	0.961099i	−0.876968	−	0.480549i	$-0.840437\pi$
$229$		−	220.092i		−	0.961099i	0.876968	−	0.480549i	$-0.159563\pi$
$230$	207.315	+	271.292i	0.901371	+	1.17953i
$231$	−425.856			−1.84353
$232$	52.6744	+	24.0556i	0.227045	+	0.103688i
$233$	5.52422	−	18.8138i	0.0237091	−	0.0807458i	−0.946789	−	0.321856i	$-0.895693\pi$
$233$	5.52422	−	18.8138i	0.0237091	−	0.0807458i	0.970498	+	0.241110i	$0.0775115\pi$
$234$	−8.78773	−	10.1416i	−0.0375544	−	0.0433401i
$235$	12.2122	−	86.7539i	0.0519670	−	0.369165i
$236$	−97.6434	+	112.686i	−0.413743	+	0.477485i
$237$	−19.8104	+	137.784i	−0.0835881	+	0.581368i
$238$	112.719	+	383.887i	0.473611	+	1.61297i
$239$	−116.929	−	75.1458i	−0.489243	−	0.314417i	0.272658	−	0.962111i	$-0.412097\pi$
$239$	−116.929	−	75.1458i	−0.489243	−	0.314417i	−0.761901	+	0.647694i	$0.775734\pi$
$240$	−154.817	−	98.8507i	−0.645071	−	0.411878i
$241$	−329.221	+	150.350i	−1.36606	+	0.623861i	−0.957384	−	0.288817i	$-0.906738\pi$
$241$	−329.221	+	150.350i	−1.36606	+	0.623861i	−0.408680	+	0.912678i	$0.634011\pi$
$242$	344.041	−	157.118i	1.42166	−	0.649249i
$243$	13.6368	−	1.96068i	0.0561187	−	0.00806865i
$244$	225.730	−	351.243i	0.925125	−	1.43952i
$245$	136.114	+	61.6765i	0.555567	+	0.251741i
$246$	−29.6264	+	206.056i	−0.120433	+	0.837627i
$247$	−364.163	+	420.266i	−1.47434	+	1.70148i
$248$	2.25130	+	3.50309i	0.00907781	+	0.0141253i
$249$	3.32817	−	2.88387i	0.0133661	−	0.0115818i
$250$	−245.509	−	278.317i	−0.982035	−	1.11327i
$251$	193.156	+	88.2114i	0.769546	+	0.351440i	0.761193	−	0.648525i	$-0.224614\pi$
$251$	193.156	+	88.2114i	0.769546	+	0.351440i	0.00835278	+	0.999965i	$0.497341\pi$
$252$	10.9143			0.0433107
$253$	−361.376	+	28.3775i	−1.42836	+	0.112164i
$254$	−238.603			−0.939382
$255$	−96.4909	−	209.647i	−0.378396	−	0.822144i
$256$	−117.439	−	34.4832i	−0.458746	−	0.134700i
$257$	−109.160	+	94.5880i	−0.424748	+	0.368047i	−0.840847	−	0.541273i	$-0.817943\pi$
$257$	−109.160	+	94.5880i	−0.424748	+	0.368047i	0.416099	+	0.909320i	$0.363397\pi$
$258$	−36.9208	+	23.7276i	−0.143104	+	0.0919673i
$259$	294.912	−	340.346i	1.13866	−	1.31408i
$260$	−280.166	−	321.408i	−1.07756	−	1.23618i
$261$	−5.85976	+	1.72058i	−0.0224512	+	0.00659227i
$262$	318.850	−	496.140i	1.21698	−	1.89366i
$263$	−11.8836	−	82.6519i	−0.0451846	−	0.314266i	−0.999862	−	0.0166228i	$-0.994709\pi$
$263$	−11.8836	−	82.6519i	−0.0451846	−	0.314266i	0.954677	−	0.297643i	$-0.0962005\pi$
$264$	−105.539	+	48.1981i	−0.399769	+	0.182569i
$265$	41.7740	−	143.837i	0.157638	−	0.542782i
$266$	−117.839	−	819.588i	−0.443004	−	3.08116i
$267$	−265.482	−	170.615i	−0.994316	−	0.639008i
$268$	247.933	−	72.7998i	0.925125	−	0.271641i
$269$	9.72566	−	67.6435i	0.0361549	−	0.251463i	−0.963726	−	0.266893i	$-0.914003\pi$
$269$	9.72566	−	67.6435i	0.0361549	−	0.251463i	0.999881	+	0.0154307i	$0.00491194\pi$
$270$	390.747	−	57.3578i	1.44721	−	0.212436i
$271$	−424.294	+	272.677i	−1.56566	+	1.00619i	−0.584869	+	0.811127i	$0.698854\pi$
$271$	−424.294	+	272.677i	−1.56566	+	1.00619i	−0.980791	+	0.195061i	$0.937509\pi$
$272$	−119.979	−	138.463i	−0.441098	−	0.509054i
$273$	−459.156	−	134.820i	−1.68189	−	0.493848i
$274$	301.647	+	137.758i	1.10090	+	0.502765i
$275$	389.661	−	58.3732i	1.41695	−	0.212266i
$276$	335.881	−	26.3754i	1.21696	−	0.0955632i
$277$		−	158.309i		−	0.571513i	−0.958302	−	0.285756i	$-0.907755\pi$
$277$		−	158.309i		−	0.571513i	0.958302	−	0.285756i	$-0.0922449\pi$
$278$	−322.932	−	147.478i	−1.16163	−	0.530498i
$279$	−0.421376	−	0.123727i	−0.00151031	−	0.000443467i
$280$	107.463	−	0.316992i	0.383797	−	0.00113212i
$281$	219.367	+	341.341i	0.780664	+	1.21474i	0.972407	+	0.233292i	$0.0749498\pi$
$281$	219.367	+	341.341i	0.780664	+	1.21474i	−0.191742	+	0.981445i	$0.561414\pi$
$282$	−119.609	−	103.642i	−0.424144	−	0.367523i
$283$	21.2561	−	147.839i	0.0751099	−	0.522401i	−0.917181	−	0.398471i	$-0.869541\pi$
$283$	21.2561	−	147.839i	0.0751099	−	0.522401i	0.992291	−	0.123930i	$-0.0395498\pi$
$284$	99.7061	−	29.2764i	0.351078	−	0.103086i
$285$	135.914	+	457.879i	0.476890	+	1.60659i
$286$	820.272	−	117.937i	2.86808	−	0.412368i
$287$	85.0373	+	186.206i	0.296297	+	0.648800i
$288$	−10.5700	+	4.82715i	−0.0367014	+	0.0167610i
$289$	8.36900	+	58.2077i	0.0289585	+	0.201411i
$290$	−340.558	+	101.089i	−1.17434	+	0.348583i
$291$	−119.123	−	405.695i	−0.409357	−	1.39414i
$292$	−21.8378	−	3.13979i	−0.0747868	−	0.0107527i
$293$	171.622	−	198.063i	0.585741	−	0.675981i	−0.383088	−	0.923712i	$-0.625139\pi$
$293$	171.622	−	198.063i	0.585741	−	0.675981i	0.968829	+	0.247731i	$0.0796848\pi$
$294$	227.099	−	145.948i	0.772447	−	0.496421i
$295$	−0.456722	−	154.833i	−0.00154821	−	0.524856i
$296$	34.5673	−	117.725i	0.116781	−	0.397721i
$297$	−174.177	+	381.395i	−0.586455	+	1.28416i
$298$	518.008			1.73828
$299$	−398.619	−	83.8105i	−1.33317	−	0.280303i
$300$	−362.171	+	54.2550i	−1.20724	+	0.180850i
$301$	−17.9277	+	39.2562i	−0.0595605	+	0.130419i
$302$	−229.901	+	782.972i	−0.761263	+	2.59262i
$303$	−170.984	+	148.158i	−0.564304	+	0.488972i
$304$	204.994	+	318.976i	0.674321	+	1.04926i
$305$	62.9680	+	428.966i	0.206452	+	1.40644i
$306$	−11.3791	−	1.63607i	−0.0371866	−	0.00534663i
$307$	−59.7905	−	203.628i	−0.194757	−	0.663283i	−0.997735	−	0.0672730i	$-0.978570\pi$
$307$	−59.7905	−	203.628i	−0.194757	−	0.663283i	0.802977	−	0.596010i	$-0.203248\pi$
$308$	−364.399	+	567.016i	−1.18311	+	1.84096i
$309$	251.091	−	36.1015i	0.812594	−	0.116833i
$310$	−24.5320	−	7.12472i	−0.0791356	−	0.0229830i
$311$	128.438	+	281.240i	0.412984	+	0.904309i	0.995787	+	0.0916957i	$0.0292287\pi$
$311$	128.438	+	281.240i	0.412984	+	0.904309i	−0.582803	+	0.812614i	$0.698044\pi$
$312$	−129.051	+	18.5547i	−0.413625	+	0.0594703i
$313$	329.168	+	211.543i	1.05165	+	0.675857i	0.947842	−	0.318740i	$-0.103260\pi$
$313$	329.168	+	211.543i	1.05165	+	0.675857i	0.103812	+	0.994597i	$0.466896\pi$
$314$	42.3959	+	144.387i	0.135019	+	0.459832i
$315$	−8.54339	+	7.44713i	−0.0271219	+	0.0236417i
$316$	166.505	+	144.277i	0.526914	+	0.456574i
$317$	−143.062	−	222.609i	−0.451299	−	0.702235i	0.538827	−	0.842417i	$-0.318868\pi$
$317$	−143.062	−	222.609i	−0.451299	−	0.702235i	−0.990126	+	0.140181i	$0.955231\pi$
$318$	−177.190	−	204.488i	−0.557202	−	0.643045i
$319$	106.255	−	361.871i	0.333087	−	1.13439i
$320$	−394.622	+	181.626i	−1.23319	+	0.567583i
$321$		−	36.9799i		−	0.115202i
$322$	482.998	−	366.845i	1.49999	−	1.13927i
$323$			476.399i			1.47492i
$324$	166.483	−	364.548i	0.513837	−	1.12515i
$325$	438.612	+	60.4240i	1.34957	+	0.185920i
$326$	209.642	+	241.939i	0.643072	+	0.742145i
$327$	335.409	−	215.555i	1.02572	−	0.659188i
$328$	42.1493	+	36.5226i	0.128504	+	0.111349i
$329$	−154.042	−	22.1479i	−0.468213	−	0.0673189i
$330$	293.770	−	648.321i	0.890212	−	1.96461i
$331$	296.038	+	190.252i	0.894375	+	0.574780i	0.905117	−	0.425162i	$-0.139783\pi$
$331$	296.038	+	190.252i	0.894375	+	0.574780i	−0.0107420	+	0.999942i	$0.503419\pi$
$332$	−0.991936	−	6.89907i	−0.00298776	−	0.0207803i
$333$	5.37545	+	11.7706i	0.0161425	+	0.0353471i
$334$	−300.062	−	657.043i	−0.898388	−	1.96720i
$335$	−144.402	+	226.158i	−0.431050	+	0.675097i
$336$	−176.406	+	274.493i	−0.525017	+	0.816943i
$337$	195.228	−	57.3241i	0.579311	−	0.170101i	0.0210675	−	0.999778i	$-0.493294\pi$
$337$	195.228	−	57.3241i	0.579311	−	0.170101i	0.558244	+	0.829677i	$0.311475\pi$
$338$	425.097	+	61.1197i	1.25768	+	0.180828i
$339$	−123.044	−	106.618i	−0.362962	−	0.314508i
$340$	−361.706	−	50.9169i	−1.06384	−	0.149756i
$341$	20.4965	−	17.7603i	0.0601070	−	0.0520830i
$342$	22.8281	+	6.70294i	0.0667489	+	0.0195993i
$343$	−70.5199	+	154.417i	−0.205597	+	0.450195i
$344$			11.7578i			0.0341798i
$345$	−244.921	+	249.827i	−0.709917	+	0.724137i
$346$	68.9151			0.199177
$347$	52.6759	+	24.0563i	0.151804	+	0.0693264i	0.489868	−	0.871797i	$-0.337045\pi$
$347$	52.6759	+	24.0563i	0.151804	+	0.0693264i	−0.338064	+	0.941123i	$0.609772\pi$
$348$	−98.7586	+	336.341i	−0.283789	+	0.966497i
$349$	−204.293	−	235.767i	−0.585367	−	0.675550i	0.383383	−	0.923590i	$-0.374759\pi$
$349$	−204.293	−	235.767i	−0.585367	−	0.675550i	−0.968750	+	0.248040i	$0.920214\pi$
$350$	−495.678	+	434.654i	−1.41622	+	1.24187i
$351$	−308.542	+	356.076i	−0.879037	+	1.01446i
$352$	102.125	−	710.296i	0.290128	−	2.01789i
$353$	−125.739	−	428.226i	−0.356200	−	1.21310i	−0.921552	−	0.388255i	$-0.873078\pi$
$353$	−125.739	−	428.226i	−0.356200	−	1.21310i	0.565352	−	0.824850i	$-0.308740\pi$
$354$	−235.302	−	151.220i	−0.664696	−	0.427174i
$355$	−58.0710	+	90.9490i	−0.163580	+	0.256194i
$356$	−454.340	+	207.490i	−1.27624	+	0.582837i
$357$	−372.914	+	170.304i	−1.04458	+	0.477042i
$358$	50.1864	−	7.21571i	0.140185	−	0.0201556i
$359$	−83.1864	+	129.440i	−0.231717	+	0.360558i	−0.937568	−	0.347802i	$-0.886928\pi$
$359$	−83.1864	+	129.440i	−0.231717	+	0.360558i	0.705851	+	0.708360i	$0.250565\pi$
$360$	−1.27443	+	2.81255i	−0.00354009	+	0.00781263i
$361$	88.9372	−	618.572i	0.246364	−	1.71350i
$362$	33.2938	−	38.4231i	0.0919718	−	0.106141i
$363$	209.524	+	326.026i	0.577202	+	0.898143i
$364$	−572.405	+	495.991i	−1.57254	+	1.36261i
$365$	19.2363	−	12.4428i	0.0527023	−	0.0340898i
$366$	712.447	+	325.364i	1.94658	+	0.888972i
$367$	−565.736			−1.54152			−0.770758	−	0.637128i	$-0.780122\pi$
$367$	−565.736			−1.54152			−0.770758	+	0.637128i	$0.780122\pi$
$368$	−131.405	+	244.686i	−0.357078	+	0.664908i
$369$	−5.88189			−0.0159401
$370$	314.701	+	683.755i	0.850544	+	1.84799i
$371$	−255.288	−	74.9593i	−0.688108	−	0.202047i
$372$	−19.0505	+	16.5073i	−0.0512110	+	0.0443746i
$373$	−105.073	+	67.5261i	−0.281696	+	0.181035i	−0.673857	−	0.738861i	$-0.735364\pi$
$373$	−105.073	+	67.5261i	−0.281696	+	0.181035i	0.392161	+	0.919896i	$0.371727\pi$
$374$	464.916	−	536.541i	1.24309	−	1.43460i
$375$	246.477	−	289.589i	0.657273	−	0.772236i
$376$	−40.6827	+	11.9455i	−0.108199	+	0.0317700i
$377$	229.127	−	356.529i	0.607765	−	0.945701i
$378$	−99.8408	−	694.408i	−0.264129	−	1.83706i
$379$	82.2020	−	37.5404i	0.216892	−	0.0990512i	−0.304006	−	0.952670i	$-0.598324\pi$
$379$	82.2020	−	37.5404i	0.216892	−	0.0990512i	0.520898	+	0.853619i	$0.325597\pi$
$380$	725.954	+	210.835i	1.91041	+	0.554830i
$381$	−34.7942	−	241.999i	−0.0913234	−	0.635169i
$382$	−198.522	−	127.582i	−0.519692	−	0.333986i
$383$	492.071	−	144.485i	1.28478	−	0.377246i	0.433118	−	0.901337i	$-0.357413\pi$
$383$	492.071	−	144.485i	1.28478	−	0.377246i	0.851662	+	0.524091i	$0.175595\pi$
$384$	−32.8300	+	228.338i	−0.0854949	+	0.594630i
$385$	−101.650	−	692.485i	−0.264026	−	1.79866i
$386$	54.2529	−	34.8663i	0.140552	−	0.0903271i
$387$	−0.812047	−	0.937152i	−0.00209831	−	0.00242158i
$388$	−642.106	−	188.539i	−1.65491	−	0.485926i
$389$	−469.307	−	214.325i	−1.20644	−	0.550965i	−0.292290	−	0.956330i	$-0.594417\pi$
$389$	−469.307	−	214.325i	−1.20644	−	0.550965i	−0.914155	+	0.405365i	$0.867144\pi$
$390$	521.992	−	606.014i	1.33844	−	1.55388i
$391$	−305.102	+	169.368i	−0.780312	+	0.433165i
$392$		−	72.3223i		−	0.184496i
$393$	549.698	+	251.039i	1.39872	+	0.638775i
$394$	−943.845	−	277.138i	−2.39555	−	0.703396i
$395$	−228.780	+	0.674849i	−0.579189	+	0.00170848i
$396$	−10.4705	−	16.2924i	−0.0264407	−	0.0411425i
$397$	260.358	+	225.601i	0.655814	+	0.568266i	0.917916	−	0.396774i	$-0.129870\pi$
$397$	260.358	+	225.601i	0.655814	+	0.568266i	−0.262103	+	0.965040i	$0.584416\pi$
$398$	−154.780	+	1076.52i	−0.388895	+	2.70483i
$399$	814.070	−	239.032i	2.04028	−	0.599079i
$400$	123.787	−	275.343i	0.309468	−	0.688358i
$401$	−372.167	+	53.5095i	−0.928097	+	0.133440i	−0.589754	−	0.807583i	$-0.700775\pi$
$401$	−372.167	+	53.5095i	−0.928097	+	0.133440i	−0.338343	+	0.941023i	$0.609866\pi$
$402$	201.364	+	440.925i	0.500905	+	1.09683i
$403$	27.7220	−	12.6602i	0.0687890	−	0.0314149i
$404$	50.9606	+	354.438i	0.126140	+	0.877323i
$405$	118.423	+	398.954i	0.292402	+	0.985071i
$406$	177.786	+	605.483i	0.437896	+	1.49134i
$407$	−790.976	−	113.725i	−1.94343	−	0.279423i
$408$	−73.1437	+	84.4124i	−0.179274	+	0.206893i
$409$	−189.522	+	121.799i	−0.463380	+	0.297796i	−0.751422	−	0.659822i	$-0.770632\pi$
$409$	−189.522	+	121.799i	−0.463380	+	0.297796i	0.288043	+	0.957618i	$0.406996\pi$
$410$	−342.140	+	1.00924i	−0.834489	+	0.00246156i
$411$	−95.7307	+	326.029i	−0.232921	+	0.793258i
$412$	166.788	−	365.214i	0.404824	−	0.886441i
$413$	−275.041			−0.665959
$414$	3.82299	+	17.0029i	0.00923427	+	0.0410698i
$415$	5.48389	+	4.72357i	0.0132142	+	0.0113821i
$416$	334.982	−	733.508i	0.805244	−	1.76324i
$417$	102.486	−	349.035i	0.245770	−	0.837014i
$418$	−1110.40	+	962.168i	−2.65646	+	2.30184i
$419$	−19.1032	−	29.7252i	−0.0455924	−	0.0709432i	0.817709	−	0.575632i	$-0.195244\pi$
$419$	−19.1032	−	29.7252i	−0.0455924	−	0.0709432i	−0.863302	+	0.504688i	$0.831607\pi$
$420$	94.4787	+	643.630i	0.224949	+	1.53245i
$421$	−587.786	−	84.5109i	−1.39617	−	0.200739i	−0.597190	−	0.802100i	$-0.703716\pi$
$421$	−587.786	−	84.5109i	−1.39617	−	0.200739i	−0.798977	+	0.601361i	$0.794625\pi$
$422$	182.930	+	623.004i	0.433484	+	1.47631i
$423$	2.41758	−	3.76183i	0.00571533	−	0.00889322i
$424$	−71.7514	+	10.3163i	−0.169225	+	0.0243309i
$425$	317.875	−	206.946i	0.747941	−	0.486931i
$426$	80.9781	+	177.317i	0.190090	+	0.416238i
$427$	762.328	−	109.606i	1.78531	−	0.256689i
$428$	−49.2379	−	31.6432i	−0.115042	−	0.0739328i
$429$	239.232	+	814.749i	0.557650	+	1.89918i
$430$	−47.3963	−	54.3733i	−0.110224	−	0.126450i
$431$	60.7723	+	52.6595i	0.141003	+	0.122180i	0.722507	−	0.691364i	$-0.242990\pi$
$431$	60.7723	+	52.6595i	0.141003	+	0.122180i	−0.581504	+	0.813544i	$0.697535\pi$
$432$	173.684	+	270.257i	0.402046	+	0.625596i
$433$	85.4017	+	98.5588i	0.197233	+	0.227619i	0.845747	−	0.533583i	$-0.179155\pi$
$433$	85.4017	+	98.5588i	0.197233	+	0.227619i	−0.648515	+	0.761202i	$0.724610\pi$
$434$	−12.7846	+	43.5404i	−0.0294576	+	0.100323i
$435$	−152.190	−	330.664i	−0.349861	−	0.760147i
$436$		−	631.037i		−	1.44733i
$437$	674.881	−	257.087i	1.54435	−	0.588299i
$438$		−	41.3863i		−	0.0944893i
$439$	233.391	−	511.055i	0.531643	−	1.16414i	−0.433198	−	0.901299i	$-0.642615\pi$
$439$	233.391	−	511.055i	0.531643	−	1.16414i	0.964840	−	0.262836i	$-0.0846579\pi$
$440$	−103.567	−	160.113i	−0.235379	−	0.363892i
$441$	4.99489	+	5.76441i	0.0113263	+	0.0130712i
$442$	671.133	−	431.311i	1.51840	−	0.975816i
$443$	−232.287	−	201.278i	−0.524349	−	0.454351i	0.352019	−	0.935993i	$-0.385495\pi$
$443$	−232.287	−	201.278i	−0.524349	−	0.454351i	−0.876368	+	0.481642i	$0.840041\pi$
$444$	735.173	+	105.702i	1.65579	+	0.238067i
$445$	214.068	−	472.427i	0.481052	−	1.06163i
$446$	−91.5162	−	58.8139i	−0.205193	−	0.131870i
$447$	75.5384	+	525.381i	0.168990	+	1.17535i
$448$	320.566	+	701.942i	0.715550	+	1.56684i
$449$	−19.0566	−	41.7281i	−0.0424422	−	0.0929355i	0.887223	−	0.461340i	$-0.152631\pi$
$449$	−19.0566	−	41.7281i	−0.0424422	−	0.0929355i	−0.929665	+	0.368405i	$0.879904\pi$
$450$	−5.44395	−	18.1437i	−0.0120977	−	0.0403194i
$451$	196.381	−	305.575i	0.435434	−	0.677549i
$452$	−247.247	+	72.5982i	−0.547006	+	0.160616i
$453$	−827.642	−	118.997i	−1.82702	−	0.262686i
$454$	691.473	+	599.165i	1.52307	+	1.31975i
$455$	109.633	−	778.816i	0.240952	−	1.71168i
$456$	174.696	−	151.375i	0.383105	−	0.331963i
$457$	491.633	+	144.356i	1.07578	+	0.315879i	0.771191	−	0.636604i	$-0.219661\pi$
$457$	491.633	+	144.356i	1.07578	+	0.315879i	0.304593	+	0.952483i	$0.401480\pi$
$458$	271.455	−	594.403i	0.592696	−	1.29782i
$459$			403.636i			0.879380i
$460$	123.063	+	539.881i	0.267527	+	1.17365i
$461$	−23.7601			−0.0515404			−0.0257702	−	0.999668i	$-0.508204\pi$
$461$	−23.7601			−0.0515404			−0.0257702	+	0.999668i	$0.508204\pi$
$462$	−1150.11	−	525.239i	−2.48942	−	1.13688i
$463$	−100.096	+	340.897i	−0.216191	+	0.736279i	0.777963	+	0.628310i	$0.216253\pi$
$463$	−100.096	+	340.897i	−0.216191	+	0.736279i	−0.994154	+	0.107969i	$0.965565\pi$
$464$	−189.235	−	218.389i	−0.407835	−	0.470666i
$465$	3.64875	−	25.9202i	0.00784677	−	0.0557423i
$466$	38.1237	−	43.9971i	0.0818105	−	0.0944144i
$467$	−55.9653	+	389.247i	−0.119840	+	0.833506i	0.837890	+	0.545839i	$0.183789\pi$
$467$	−55.9653	+	389.247i	−0.119840	+	0.833506i	−0.957730	+	0.287667i	$0.907120\pi$
$468$	−6.13129	−	20.8813i	−0.0131011	−	0.0446181i
$469$	400.981	+	257.695i	0.854970	+	0.549456i
$470$	139.982	−	219.235i	0.297833	−	0.466457i
$471$	−140.260	+	64.0546i	−0.297792	+	0.135997i
$472$	−68.1630	+	31.1290i	−0.144413	+	0.0659512i
$473$	75.7988	−	10.8982i	0.160251	−	0.0230407i
$474$	−223.441	+	347.681i	−0.471395	+	0.733505i
$475$	−712.115	+	330.303i	−1.49919	+	0.695375i
$476$	−92.3420	+	642.253i	−0.193996	+	1.34927i
$477$	5.00642	−	5.77772i	0.0104956	−	0.0121126i
$478$	−223.109	−	347.164i	−0.466755	−	0.726284i
$479$	388.735	−	336.841i	0.811556	−	0.703217i	−0.146684	−	0.989183i	$-0.546860\pi$
$479$	388.735	−	336.841i	0.811556	−	0.703217i	0.958240	+	0.285966i	$0.0923145\pi$
$480$	−376.162	−	581.541i	−0.783671	−	1.21154i
$481$	−816.824	−	373.031i	−1.69818	−	0.775532i
$482$	−1074.57			−2.22940
$483$	442.500	+	436.378i	0.916149	+	0.903474i
$484$	613.383			1.26732
$485$	631.268	−	290.544i	1.30158	−	0.599059i
$486$	39.2474	+	11.5241i	0.0807559	+	0.0237121i
$487$	−83.7145	+	72.5390i	−0.171898	+	0.148951i	−0.736561	−	0.676371i	$-0.763552\pi$
$487$	−83.7145	+	72.5390i	−0.171898	+	0.148951i	0.564663	+	0.825322i	$0.309006\pi$
$488$	176.521	−	113.443i	0.361724	−	0.232466i
$489$	−214.812	+	247.906i	−0.439288	+	0.506966i
$490$	291.534	+	334.449i	0.594967	+	0.682550i
$491$	647.446	−	190.107i	1.31863	−	0.387184i	0.454630	−	0.890680i	$-0.349771\pi$
$491$	647.446	−	190.107i	1.31863	−	0.387184i	0.863997	+	0.503496i	$0.167953\pi$
$492$	−182.526	+	284.016i	−0.370988	+	0.577269i
$493$	−51.6705	−	359.376i	−0.104808	−	0.728957i
$494$	−1501.84	+	685.868i	−3.04017	+	1.38840i
$495$	19.3128	+	5.60892i	0.0390157	+	0.0113312i
$496$	−2.95729	−	20.5684i	−0.00596227	−	0.0414685i
$497$	161.254	+	103.632i	0.324455	+	0.208514i
$498$	12.5453	−	3.68363i	0.0251914	−	0.00739685i
$499$	−105.078	+	730.835i	−0.210577	+	1.46460i	0.560657	+	0.828048i	$0.310548\pi$
$499$	−105.078	+	730.835i	−0.210577	+	1.46460i	−0.771235	+	0.636551i	$0.780361\pi$
$500$	−174.673	−	575.976i	−0.349346	−	1.15195i
$501$	622.639	−	400.146i	1.24279	−	0.798694i
$502$	412.861	+	476.467i	0.822432	+	0.949137i
$503$	−659.229	−	193.567i	−1.31059	−	0.384825i	−0.449504	−	0.893278i	$-0.648399\pi$
$503$	−659.229	−	193.567i	−1.31059	−	0.384825i	−0.861090	+	0.508453i	$0.830218\pi$
$504$	4.98942	+	2.27859i	0.00989964	+	0.00452101i
$505$	−281.734	−	242.673i	−0.557889	−	0.480540i
$506$	−1010.97	−	369.072i	−1.99797	−	0.729391i
$507$			440.060i			0.867969i
$508$	−351.989	−	160.748i	−0.692892	−	0.316433i
$509$	611.523	+	179.559i	1.20142	+	0.352769i	0.820396	−	0.571796i	$-0.193753\pi$
$509$	611.523	+	179.559i	1.20142	+	0.352769i	0.381025	+	0.924565i	$0.375571\pi$
$510$	−2.02120	−	685.204i	−0.00396314	−	1.34354i
$511$	−22.0021	−	34.2359i	−0.0430569	−	0.0669978i
$512$	−503.865	−	436.601i	−0.984111	−	0.852737i
$513$	118.882	−	826.843i	0.231739	−	1.61178i
$514$	−411.472	+	120.819i	−0.800530	+	0.235057i
$515$	118.639	+	399.683i	0.230367	+	0.776083i
$516$	−70.4513	+	10.1294i	−0.136533	+	0.0196305i
$517$	114.717	+	251.195i	0.221890	+	0.485871i
$518$	1216.24	−	555.440i	2.34796	−	1.07228i
$519$	10.0495	+	69.8960i	0.0193633	+	0.134674i
$520$	−60.9758	−	205.421i	−0.117261	−	0.395040i
$521$	98.0872	+	334.054i	0.188267	+	0.641179i	0.998484	+	0.0550485i	$0.0175313\pi$
$521$	98.0872	+	334.054i	0.188267	+	0.641179i	−0.810216	+	0.586131i	$0.800650\pi$
$522$	−17.9476	−	2.58048i	−0.0343824	−	0.00494345i
$523$	118.118	−	136.315i	0.225846	−	0.260641i	−0.631505	−	0.775371i	$-0.717563\pi$
$523$	118.118	−	136.315i	0.225846	−	0.260641i	0.857352	+	0.514731i	$0.172108\pi$
$524$	804.621	−	517.099i	1.53554	−	0.986830i
$525$	−513.122	−	439.350i	−0.977376	−	0.836857i
$526$	69.8466	−	237.876i	0.132788	−	0.452235i
$527$	10.8459	−	23.7491i	0.0205804	−	0.0450648i
$528$	578.985			1.09656
$529$	404.579	+	340.818i	0.764799	+	0.644269i
$530$	290.224	−	336.940i	0.547593	−	0.635735i
$531$	3.28299	−	7.18874i	0.00618265	−	0.0135381i
$532$	378.323	−	1288.45i	0.711134	−	2.42190i
$533$	308.478	−	267.298i	0.578759	−	0.501497i
$534$	−506.559	−	788.221i	−0.948612	−	1.47607i
$535$	60.1331	−	8.82696i	0.112398	−	0.0164990i
$536$	128.540	+	18.4813i	0.239814	+	0.0344800i
$537$	14.6368	+	49.8485i	0.0272567	+	0.0928277i
$538$	109.696	−	170.690i	0.203895	−	0.317267i
$539$	−466.237	+	67.0348i	−0.865004	+	0.124369i
$540$	615.075	+	178.633i	1.13903	+	0.330802i
$541$	297.633	+	651.725i	0.550153	+	1.20467i	0.956710	+	0.291042i	$0.0940019\pi$
$541$	297.633	+	651.725i	0.550153	+	1.20467i	−0.406557	+	0.913625i	$0.633271\pi$
$542$	−1482.21	+	213.109i	−2.73470	+	0.393190i
$543$	43.8250	+	28.1646i	0.0807091	+	0.0518686i
$544$	−194.626	−	662.834i	−0.357768	−	1.21844i
$545$	430.575	+	493.958i	0.790045	+	0.906345i
$546$	−1073.76	−	930.422i	−1.96660	−	1.70407i
$547$	−396.779	−	617.401i	−0.725374	−	1.12870i	−0.986558	−	0.163414i	$-0.947749\pi$
$547$	−396.779	−	617.401i	−0.725374	−	1.12870i	0.261184	−	0.965289i	$-0.415887\pi$
$548$	352.184	+	406.442i	0.642672	+	0.741683i
$549$	−6.23464	+	21.2332i	−0.0113564	+	0.0386762i
$550$	1124.36	+	322.948i	2.04429	+	0.587179i
$551$			751.396i			1.36370i
$552$	159.053	+	58.0650i	0.288140	+	0.105190i
$553$			406.399i			0.734898i
$554$	195.254	−	427.547i	0.352444	−	0.771745i
$555$	−647.596	+	418.889i	−1.16684	+	0.754755i
$556$	−377.036	−	435.122i	−0.678122	−	0.782594i
$557$	599.178	−	385.068i	1.07572	−	0.691325i	0.122158	−	0.992511i	$-0.461019\pi$
$557$	599.178	−	385.068i	1.07572	−	0.691325i	0.953566	+	0.301185i	$0.0973823\pi$
$558$	−0.985413	−	0.853865i	−0.00176597	−	0.00153022i
$559$	85.1764	+	12.2465i	0.152373	+	0.0219079i
$560$	−488.460	−	221.333i	−0.872251	−	0.395238i
$561$	611.974	+	393.292i	1.09086	+	0.701055i
$562$	171.445	+	1192.42i	0.305062	+	2.12175i
$563$	−160.235	−	350.865i	−0.284609	−	0.623206i	0.712291	−	0.701884i	$-0.247657\pi$
$563$	−160.235	−	350.865i	−0.284609	−	0.623206i	−0.996900	+	0.0786779i	$0.974930\pi$
$564$	−106.624	−	233.474i	−0.189049	−	0.413960i
$565$	144.002	−	225.531i	0.254871	−	0.399171i
$566$	239.748	−	373.054i	0.423582	−	0.659107i
$567$	709.306	−	208.271i	1.25098	−	0.367321i
$568$	51.6923	+	7.43223i	0.0910075	+	0.0130849i
$569$	286.327	+	248.103i	0.503210	+	0.436034i	0.869109	−	0.494621i	$-0.164693\pi$
$569$	286.327	+	248.103i	0.503210	+	0.436034i	−0.365899	+	0.930655i	$0.619238\pi$
$570$	−197.672	+	1404.23i	−0.346792	+	2.46356i
$571$	288.091	−	249.632i	0.504537	−	0.437184i	−0.365032	−	0.930995i	$-0.618942\pi$
$571$	288.091	−	249.632i	0.504537	−	0.437184i	0.869569	+	0.493811i	$0.164396\pi$
$572$	1289.53	+	378.639i	2.25442	+	0.661957i
$573$	100.449	−	219.953i	0.175304	−	0.383861i
$574$			607.770i			1.05883i
$575$	−464.706	−	338.634i	−0.808185	−	0.588929i
$576$	−22.1731			−0.0384949
$577$	544.231	+	248.542i	0.943208	+	0.430749i	0.826827	−	0.562456i	$-0.190143\pi$
$577$	544.231	+	248.542i	0.943208	+	0.430749i	0.116381	+	0.993205i	$0.462871\pi$
$578$	−49.1895	+	167.524i	−0.0851030	+	0.289834i
$579$	43.2739	+	49.9408i	0.0747391	+	0.0862535i
$580$	−570.498	−	80.3083i	−0.983617	−	0.138463i
$581$	8.41950	−	9.71662i	0.0144914	−	0.0167240i
$582$	178.657	−	1242.59i	0.306971	−	2.13503i
$583$	133.011	+	452.995i	0.228150	+	0.777007i
$584$	−9.32753	−	5.99444i	−0.0159718	−	0.0102645i
$585$	19.0473	+	12.1617i	0.0325595	+	0.0207892i
$586$	707.786	−	323.235i	1.20783	−	0.551596i
$587$	−457.022	+	208.715i	−0.778572	+	0.355562i	−0.764737	−	0.644343i	$-0.777131\pi$
$587$	−457.022	+	208.715i	−0.778572	+	0.355562i	−0.0138346	+	0.999904i	$0.504404\pi$
$588$	433.345	−	62.3055i	0.736981	−	0.105962i
$589$	−29.2125	+	45.4555i	−0.0495967	+	0.0771740i
$590$	189.733	−	418.721i	0.321581	−	0.709697i
$591$	143.447	−	997.693i	0.242718	−	1.68814i
$592$	−400.956	+	462.728i	−0.677291	+	0.781635i
$593$	−175.624	−	273.276i	−0.296162	−	0.460836i	0.661002	−	0.750384i	$-0.270131\pi$
$593$	−175.624	−	273.276i	−0.296162	−	0.460836i	−0.957164	+	0.289548i	$0.906495\pi$
$594$	−940.803	+	815.211i	−1.58384	+	1.37241i
$595$	−365.945	−	565.745i	−0.615033	−	0.950832i
$596$	764.169	+	348.984i	1.28216	+	0.585544i
$597$	−1114.41			−1.86669
$598$	−973.183	−	717.993i	−1.62740	−	1.20066i
$599$	232.660			0.388414			0.194207	−	0.980961i	$-0.437787\pi$
$599$	232.660			0.388414			0.194207	+	0.980961i	$0.437787\pi$
$600$	−176.892	−	50.8085i	−0.294819	−	0.0846808i
$601$	−350.338	−	102.869i	−0.582926	−	0.171162i	−0.0230432	−	0.999734i	$-0.507336\pi$
$601$	−350.338	−	102.869i	−0.582926	−	0.171162i	−0.559882	+	0.828572i	$0.689154\pi$
$602$	−96.8350	+	83.9080i	−0.160855	+	0.139382i
$603$	−11.5216	+	7.40449i	−0.0191072	+	0.0122794i
$604$	−866.645	+	1000.16i	−1.43484	+	1.65590i
$605$	−480.139	+	418.529i	−0.793618	+	0.691783i
$606$	−644.513	+	189.246i	−1.06355	+	0.312287i
$607$	462.733	−	720.026i	0.762327	−	1.18620i	−0.215441	−	0.976517i	$-0.569119\pi$
$607$	462.733	−	720.026i	0.762327	−	1.18620i	0.977768	−	0.209688i	$-0.0672447\pi$
$608$	203.465	+	1415.13i	0.334647	+	2.32752i
$609$	−588.176	+	268.611i	−0.965806	+	0.441069i
$610$	−359.016	+	1236.17i	−0.588551	+	2.02652i
$611$	44.1624	+	307.156i	0.0722789	+	0.502711i
$612$	−15.6843	−	10.0797i	−0.0256280	−	0.0164701i
$613$	−863.089	+	253.426i	−1.40797	+	0.413419i	−0.895415	−	0.445233i	$-0.853121\pi$
$613$	−863.089	+	253.426i	−1.40797	+	0.413419i	−0.512560	+	0.858651i	$0.671303\pi$
$614$	89.6721	−	623.683i	0.146046	−	1.01577i
$615$	−50.9161	−	346.863i	−0.0827904	−	0.564005i
$616$	−284.960	+	183.133i	−0.462598	+	0.297294i
$617$	607.324	+	700.890i	0.984318	+	1.13596i	0.990711	+	0.135984i	$0.0434197\pi$
$617$	607.324	+	700.890i	0.984318	+	1.13596i	−0.00639263	+	0.999980i	$0.502035\pi$
$618$	722.652	+	212.190i	1.16934	+	0.343349i
$619$	−810.104	−	369.962i	−1.30873	−	0.597677i	−0.365808	−	0.930691i	$-0.619207\pi$
$619$	−810.104	−	369.962i	−1.30873	−	0.597677i	−0.942922	+	0.333014i	$0.891934\pi$
$620$	−31.3899	−	27.0378i	−0.0506288	−	0.0436093i
$621$	571.803	−	217.820i	0.920778	−	0.350757i
$622$			917.960i			1.47582i
$623$	−838.078	−	382.738i	−1.34523	−	0.614346i
$624$	624.260	+	183.299i	1.00042	+	0.293749i
$625$	529.734	+	331.673i	0.847574	+	0.530677i
$626$	628.075	+	977.303i	1.00331	+	1.56119i
$627$	−1137.79	−	985.898i	−1.81465	−	1.57241i
$628$	−34.7316	+	241.563i	−0.0553051	+	0.384655i
$629$	−738.123	+	216.732i	−1.17349	+	0.344567i
$630$	−32.2583	+	9.57534i	−0.0512036	+	0.0151990i
$631$	−205.527	+	29.5503i	−0.325716	+	0.0468309i	−0.303233	−	0.952916i	$-0.598066\pi$
$631$	−205.527	+	29.5503i	−0.325716	+	0.0468309i	−0.0224827	+	0.999747i	$0.507157\pi$
$632$	45.9960	+	100.717i	0.0727785	+	0.159363i
$633$	−605.195	+	276.383i	−0.956075	+	0.436625i
$634$	−111.809	−	777.649i	−0.176355	−	1.22658i
$635$	385.210	−	114.343i	0.606630	−	0.180068i
$636$	−123.627	−	421.037i	−0.194383	−	0.662007i
$637$	−523.918	−	75.3281i	−0.822478	−	0.118254i
$638$	733.285	−	846.256i	1.14935	−	1.32642i
$639$	−4.63340	+	2.97771i	−0.00725102	+	0.00465995i
$640$	−379.137	+	1.11837i	−0.592402	+	0.00174745i
$641$	−279.522	+	951.963i	−0.436071	+	1.48512i	0.389608	+	0.920981i	$0.372611\pi$
$641$	−279.522	+	951.963i	−0.436071	+	1.48512i	−0.825679	+	0.564141i	$0.809208\pi$
$642$	45.6100	−	99.8720i	0.0710436	−	0.155564i
$643$	111.507			0.173417			0.0867085	−	0.996234i	$-0.472365\pi$
$643$	111.507			0.173417			0.0867085	+	0.996234i	$0.472365\pi$
$644$	959.668	−	215.775i	1.49017	−	0.335054i
$645$	48.2357	−	55.9999i	0.0747840	−	0.0868215i
$646$	−587.577	+	1286.61i	−0.909562	+	1.99166i
$647$	295.682	−	1007.00i	0.457004	−	1.55641i	−0.332765	−	0.943010i	$-0.607982\pi$
$647$	295.682	−	1007.00i	0.457004	−	1.55641i	0.789769	−	0.613404i	$-0.210200\pi$
$648$	152.214	−	131.894i	0.234898	−	0.203541i
$649$	263.858	+	410.570i	0.406560	+	0.632620i
$650$	1110.04	+	704.159i	1.70775	+	1.08332i
$651$	−46.0244	−	6.61731i	−0.0706980	−	0.0101648i
$652$	146.269	+	498.147i	0.224339	+	0.764029i
$653$	109.206	−	169.928i	0.167238	−	0.260227i	−0.747512	−	0.664249i	$-0.768752\pi$
$653$	109.206	−	169.928i	0.167238	−	0.260227i	0.914749	+	0.404022i	$0.132388\pi$
$654$	1171.70	−	168.465i	1.79159	−	0.257592i
$655$	−277.004	+	953.786i	−0.422906	+	1.45616i
$656$	−115.615	−	253.162i	−0.176242	−	0.385917i
$657$	1.15745	−	0.166416i	0.00176172	−	0.000253297i
$658$	−388.706	−	249.806i	−0.590739	−	0.379645i
$659$	−63.0974	−	214.890i	−0.0957472	−	0.326085i	0.897665	−	0.440678i	$-0.145262\pi$
$659$	−63.0974	−	214.890i	−0.0957472	−	0.326085i	−0.993413	+	0.114593i	$0.963444\pi$
$660$	870.149	−	758.493i	1.31841	−	1.14923i
$661$	780.042	+	675.910i	1.18009	+	1.02256i	0.999237	+	0.0390472i	$0.0124323\pi$
$661$	780.042	+	675.910i	1.18009	+	1.02256i	0.180856	+	0.983510i	$0.442113\pi$
$662$	564.861	+	878.941i	0.853265	+	1.32771i
$663$	535.318	+	617.790i	0.807417	+	0.931809i
$664$	0.986869	−	3.36097i	0.00148625	−	0.00506170i
$665$	583.006	+	1266.70i	0.876701	+	1.90482i
$666$			38.4189i			0.0576860i
$667$	−481.220	+	267.134i	−0.721469	+	0.400501i
$668$		−	1171.43i		−	1.75364i
$669$	46.3057	−	101.395i	0.0692163	−	0.151562i
$670$	−668.924	+	432.685i	−0.998394	+	0.645798i
$671$	−894.946	−	1032.82i	−1.33375	−	1.53923i
$672$	−1035.00	+	665.152i	−1.54017	+	0.989810i
$673$	788.816	+	683.513i	1.17209	+	1.01562i	0.999531	+	0.0306220i	$0.00974880\pi$
$673$	788.816	+	683.513i	1.17209	+	1.01562i	0.172558	+	0.984999i	$0.444797\pi$
$674$	597.956	+	85.9731i	0.887175	+	0.127556i
$675$	−603.350	+	279.854i	−0.893851	+	0.414599i
$676$	585.930	+	376.554i	0.866760	+	0.557033i
$677$	−30.1759	−	209.878i	−0.0445730	−	0.310012i	−0.999896	−	0.0144471i	$-0.995401\pi$
$677$	−30.1759	−	209.878i	−0.0445730	−	0.310012i	0.955323	−	0.295565i	$-0.0955079\pi$
$678$	−200.806	−	439.704i	−0.296174	−	0.648531i
$679$	−512.803	−	1122.88i	−0.755232	−	1.65373i
$680$	−154.722	−	98.7903i	−0.227533	−	0.145280i
$681$	−506.859	+	788.689i	−0.744287	+	1.15813i
$682$	77.2602	−	22.6856i	0.113285	−	0.0332634i
$683$	286.899	+	41.2498i	0.420057	+	0.0603950i	0.349103	−	0.937085i	$-0.386486\pi$
$683$	286.899	+	41.2498i	0.420057	+	0.0603950i	0.0709542	+	0.997480i	$0.477396\pi$
$684$	29.1604	+	25.2677i	0.0426322	+	0.0369410i
$685$	−553.007	−	77.8461i	−0.807309	−	0.113644i
$686$	−380.907	+	330.058i	−0.555258	+	0.481134i
$687$	642.449	+	188.640i	0.935151	+	0.274585i
$688$	24.3742	−	53.3719i	0.0354275	−	0.0775755i
$689$			530.528i			0.769997i
$690$	−969.591	+	372.631i	−1.40520	+	0.540045i
$691$	78.2916			0.113302			0.0566510	−	0.998394i	$-0.481958\pi$
$691$	78.2916			0.113302			0.0566510	+	0.998394i	$0.481958\pi$
$692$	101.664	+	46.4285i	0.146914	+	0.0670931i
$693$	10.0647	−	34.2771i	0.0145233	−	0.0494619i
$694$	112.592	+	129.938i	0.162236	+	0.187230i
$695$	592.029	+	83.3392i	0.851840	+	0.119913i
$696$	−115.365	+	133.139i	−0.165755	+	0.191291i
$697$	49.7647	−	346.121i	0.0713984	−	0.496587i
$698$	−260.948	−	888.707i	−0.373851	−	1.27322i
$699$	50.1827	+	32.2505i	0.0717921	+	0.0461380i
$700$	−1024.06	+	307.264i	−1.46294	+	0.438948i
$701$	1245.31	−	568.714i	1.77648	−	0.811289i	0.798671	−	0.601768i	$-0.205537\pi$
$701$	1245.31	−	568.714i	1.77648	−	0.811289i	0.977804	−	0.209521i	$-0.0671904\pi$
$702$	−1272.46	+	581.112i	−1.81262	+	0.827794i
$703$	1575.87	−	226.576i	2.24164	−	0.322299i
$704$	740.300	−	1151.93i	1.05156	−	1.63626i
$705$	242.768	+	110.004i	0.344352	+	0.156034i
$706$	188.579	−	1311.60i	0.267109	−	1.85778i
$707$	−432.550	+	499.190i	−0.611811	+	0.706067i
$708$	−245.243	−	381.605i	−0.346388	−	0.538990i
$709$	839.475	−	727.409i	1.18403	−	1.02597i	0.184961	−	0.982746i	$-0.440784\pi$
$709$	839.475	−	727.409i	1.18403	−	1.02597i	0.999066	−	0.0432192i	$-0.0137614\pi$
$710$	−269.007	+	174.004i	−0.378883	+	0.245076i
$711$	−10.6220	−	4.85092i	−0.0149396	−	0.00682268i
$712$	−251.018			−0.352553
$713$	−39.4967	−	2.54847i	−0.0553951	−	0.00357430i
$714$	−1217.18			−1.70473
$715$	−1267.76	+	583.493i	−1.77309	+	0.816074i
$716$	78.8966	+	23.1661i	0.110191	+	0.0323549i
$717$	319.570	−	276.909i	0.445705	−	0.386206i
$718$	−384.310	+	246.981i	−0.535251	+	0.343985i
$719$	−76.2745	+	88.0254i	−0.106084	+	0.122428i	−0.806308	−	0.591495i	$-0.798538\pi$
$719$	−76.2745	+	88.0254i	−0.106084	+	0.122428i	0.700224	+	0.713923i	$0.253083\pi$
$720$	11.6154	−	10.1250i	0.0161325	−	0.0140625i
$721$	710.603	−	208.652i	0.985579	−	0.289392i
$722$	1003.12	−	1560.89i	1.38937	−	2.16190i
$723$	−156.699	−	1089.86i	−0.216734	−	1.50742i
$724$	75.0011	−	34.2518i	0.103593	−	0.0473092i
$725$	501.366	−	326.404i	0.691539	−	0.450212i
$726$	163.752	+	1138.92i	0.225554	+	1.56876i
$727$	422.049	+	271.235i	0.580536	+	0.373088i	0.797706	−	0.603046i	$-0.206046\pi$
$727$	422.049	+	271.235i	0.580536	+	0.373088i	−0.217171	+	0.976134i	$0.569683\pi$
$728$	−365.221	+	107.239i	−0.501677	+	0.147306i
$729$	100.641	−	699.974i	0.138054	−	0.960184i
$730$	67.2983	−	9.87875i	0.0921895	−	0.0135325i
$731$	62.0173	−	39.8561i	0.0848390	−	0.0545227i
$732$	831.808	+	959.958i	1.13635	+	1.31142i
$733$	172.489	+	50.6474i	0.235320	+	0.0690961i	0.397266	−	0.917703i	$-0.369959\pi$
$733$	172.489	+	50.6474i	0.235320	+	0.0690961i	−0.161947	+	0.986800i	$0.551777\pi$
$734$	−1527.89	−	697.764i	−2.08159	−	0.950632i
$735$	−296.697	+	344.454i	−0.403669	+	0.468645i
$736$	−833.963	+	633.409i	−1.13310	+	0.860609i
$737$		−	845.785i		−	1.14761i
$738$	−15.8853	−	7.25456i	−0.0215248	−	0.00983003i
$739$	−81.5909	−	23.9573i	−0.110407	−	0.0324185i	0.226062	−	0.974113i	$-0.427415\pi$
$739$	−81.5909	−	23.9573i	−0.110407	−	0.0324185i	−0.336469	+	0.941694i	$0.609233\pi$
$740$	3.60078	+	1220.70i	0.00486592	+	1.64959i
$741$	−914.636	−	1423.20i	−1.23433	−	1.92065i
$742$	−597.006	−	517.308i	−0.804590	−	0.697181i
$743$	−141.301	+	982.773i	−0.190177	+	1.32271i	0.641360	+	0.767240i	$0.278370\pi$
$743$	−141.301	+	982.773i	−0.190177	+	1.32271i	−0.831537	+	0.555469i	$0.812539\pi$
$744$	−12.1551	+	3.56906i	−0.0163375	+	0.00479712i
$745$	−836.292	+	248.239i	−1.12254	+	0.333207i
$746$	−367.055	+	52.7746i	−0.492031	+	0.0707434i
$747$	0.153465	+	0.336041i	0.000205442	+	0.000449854i
$748$	1047.32	−	478.294i	1.40016	−	0.639430i
$749$	−15.3648	−	106.864i	−0.0205137	−	0.142676i
$750$	1022.83	−	478.096i	1.36378	−	0.637462i
$751$	−161.783	−	550.981i	−0.215423	−	0.733664i	−0.994312	−	0.106502i	$-0.966035\pi$
$751$	−161.783	−	550.981i	−0.215423	−	0.733664i	0.778889	−	0.627161i	$-0.215783\pi$
$752$	209.433	+	30.1119i	0.278501	+	0.0400424i
$753$	−423.043	+	488.218i	−0.561810	+	0.648363i
$754$	1058.54	−	680.282i	1.40390	−	0.902231i
$755$	−4.05368	−	1374.23i	−0.00536912	−	1.82018i
$756$	320.540	−	1091.66i	0.423995	−	1.44399i
$757$	−88.0087	+	192.712i	−0.116260	+	0.254573i	−0.958812	−	0.284041i	$-0.908325\pi$
$757$	−88.0087	+	192.712i	−0.116260	+	0.254573i	0.842552	+	0.538615i	$0.181052\pi$
$758$	268.305			0.353964
$759$	226.900	−	1079.18i	0.298946	−	1.42185i
$760$	287.850	+	247.941i	0.378750	+	0.326238i
$761$	−219.835	+	481.371i	−0.288876	+	0.632551i	−0.997316	−	0.0732206i	$-0.976672\pi$
$761$	−219.835	+	481.371i	−0.288876	+	0.632551i	0.708439	+	0.705772i	$0.249400\pi$
$762$	204.506	−	696.484i	0.268381	−	0.914020i
$763$	879.703	−	762.267i	1.15295	−	0.999040i
$764$	−206.909	−	321.956i	−0.270823	−	0.421408i
$765$	19.1549	−	2.81176i	0.0250391	−	0.00367550i
$766$	1507.14	+	216.695i	1.96755	+	0.282891i
$767$	154.509	+	526.210i	0.201446	+	0.686062i
$768$	201.313	−	313.249i	0.262127	−	0.407877i
$769$	491.956	−	70.7326i	0.639735	−	0.0919800i	0.185189	−	0.982703i	$-0.440710\pi$
$769$	491.956	−	70.7326i	0.639735	−	0.0919800i	0.454547	+	0.890723i	$0.349801\pi$
$770$	579.564	−	1995.57i	0.752681	−	2.59165i
$771$	−182.542	−	399.711i	−0.236760	−	0.518431i
$772$	103.524	−	14.8845i	0.134098	−	0.0192804i
$773$	304.132	+	195.454i	0.393444	+	0.252851i	0.722373	−	0.691503i	$-0.243051\pi$
$773$	304.132	+	195.454i	0.393444	+	0.252851i	−0.328929	+	0.944355i	$0.606688\pi$
$774$	−1.03724	−	3.53253i	−0.00134011	−	0.00456399i
$775$	43.0198	−	0.253800i	0.0555094	−	0.000327483i
$776$	−254.174	−	220.243i	−0.327544	−	0.283819i
$777$	740.705	+	1152.56i	0.953288	+	1.48334i
$778$	−1003.12	−	1157.66i	−1.28936	−	1.48800i
$779$	−203.885	+	694.368i	−0.261726	+	0.891358i
$780$	1178.32	−	542.328i	1.51067	−	0.695292i
$781$		−	340.131i		−	0.435508i
$782$	−1032.88	+	81.1084i	−1.32082	+	0.103719i
$783$			636.631i			0.813067i
$784$	−149.925	+	328.290i	−0.191231	+	0.418737i
$785$	−137.639	−	212.787i	−0.175336	−	0.271067i
$786$	1174.95	+	1355.96i	1.49485	+	1.72514i
$787$	125.792	−	80.8413i	0.159837	−	0.102721i	−0.458277	−	0.888809i	$-0.651533\pi$
$787$	125.792	−	80.8413i	0.159837	−	0.102721i	0.618114	+	0.786088i	$0.287897\pi$
$788$	−1205.66	−	1044.71i	−1.53002	−	1.32577i
$789$	251.447	+	36.1526i	0.318690	+	0.0458208i
$790$	−618.700	−	280.348i	−0.783164	−	0.354871i
$791$	−399.871	−	256.981i	−0.505525	−	0.324881i
$792$	−1.38515	−	9.63395i	−0.00174893	−	0.0121641i
$793$	−637.950	−	1396.92i	−0.804477	−	1.76156i
$794$	424.900	+	930.402i	0.535139	+	1.17179i
$795$	384.057	+	245.221i	0.483091	+	0.308454i
$796$	−953.591	+	1483.82i	−1.19798	+	1.86409i
$797$	−355.479	+	104.378i	−0.446021	+	0.130964i	−0.497028	−	0.867735i	$-0.665575\pi$
$797$	−355.479	+	104.378i	−0.446021	+	0.130964i	0.0510065	+	0.998698i	$0.483757\pi$
$798$	2493.38	+	358.494i	3.12454	+	0.449241i
$799$	200.911	+	174.091i	0.251453	+	0.217886i
$800$	855.856	−	750.489i	1.06982	−	0.938111i
$801$	20.0072	−	17.3363i	0.0249778	−	0.0216434i
$802$	−1071.11	−	314.507i	−1.33555	−	0.392153i
$803$	−29.9985	+	65.6876i	−0.0373581	+	0.0818028i
$804$			786.115i			0.977755i
$805$	−603.972	+	823.711i	−0.750276	+	1.02324i
$806$	90.4837			0.112263
$807$	189.116	+	86.3663i	0.234344	+	0.107021i
$808$	−50.7002	+	172.669i	−0.0627478	+	0.213699i
$809$	−955.649	−	1102.88i	−1.18127	−	1.36326i	−0.917037	−	0.398802i	$-0.869426\pi$
$809$	−955.649	−	1102.88i	−1.18127	−	1.36326i	−0.264235	−	0.964458i	$-0.585119\pi$
$810$	−172.233	+	1223.52i	−0.212633	+	1.51052i
$811$	932.771	−	1076.47i	1.15015	−	1.32734i	0.213553	−	0.976932i	$-0.431497\pi$
$811$	932.771	−	1076.47i	1.15015	−	1.32734i	0.936596	−	0.350411i	$-0.113958\pi$
$812$	−145.646	+	1012.99i	−0.179367	+	1.24752i
$813$	−432.285	−	1472.23i	−0.531716	−	1.81086i
$814$	−1995.93	−	1282.71i	−2.45200	−	1.57581i
$815$	−454.395	−	290.132i	−0.557540	−	0.355990i
$816$	507.006	−	231.542i	0.621331	−	0.283753i
$817$	−138.781	+	63.3790i	−0.169866	+	0.0775753i
$818$	−662.068	+	95.1910i	−0.809374	+	0.116370i
$819$	21.7034	−	33.7711i	0.0264999	−	0.0412346i
$820$	−505.408	−	229.013i	−0.616351	−	0.279284i
$821$	−145.583	+	1012.55i	−0.177324	+	1.23332i	0.685598	+	0.727981i	$0.259541\pi$
$821$	−145.583	+	1012.55i	−0.177324	+	1.23332i	−0.862922	+	0.505337i	$0.831368\pi$
$822$	−660.656	+	762.438i	−0.803718	+	0.927540i
$823$	737.850	+	1148.12i	0.896537	+	1.39504i	0.918560	+	0.395282i	$0.129353\pi$
$823$	737.850	+	1148.12i	0.896537	+	1.39504i	−0.0220223	+	0.999757i	$0.507010\pi$
$824$	152.492	−	132.135i	0.185064	−	0.160359i
$825$	−163.586	+	1187.45i	−0.198286	+	1.43934i
$826$	−742.806	−	339.228i	−0.899280	−	0.410688i
$827$	878.550			1.06233			0.531167	−	0.847267i	$-0.321754\pi$
$827$	878.550			1.06233			0.531167	+	0.847267i	$0.321754\pi$
$828$	−5.81525	+	27.6584i	−0.00702324	+	0.0334039i
$829$	−463.431			−0.559024			−0.279512	−	0.960142i	$-0.590173\pi$
$829$	−463.431			−0.559024			−0.279512	+	0.960142i	$0.590173\pi$
$830$	8.98447	+	19.5207i	0.0108247	+	0.0235189i
$831$	462.105	+	135.686i	0.556083	+	0.163281i
$832$	1162.88	−	1007.64i	1.39769	−	1.21110i
$833$	−381.468	+	245.154i	−0.457944	+	0.294303i
$834$	707.275	−	816.238i	0.848051	−	0.978703i
$835$	799.299	+	916.961i	0.957244	+	1.09816i
$836$	−2286.29	+	671.315i	−2.73480	+	0.803009i
$837$	−24.7507	+	38.5128i	−0.0295707	+	0.0460129i
$838$	−14.9300	−	103.840i	−0.0178162	−	0.123915i
$839$	−511.186	+	233.451i	−0.609281	+	0.278249i	−0.696066	−	0.717978i	$-0.745068\pi$
$839$	−511.186	+	233.451i	−0.609281	+	0.278249i	0.0867853	+	0.996227i	$0.472341\pi$
$840$	−91.1811	+	313.957i	−0.108549	+	0.373759i
$841$	38.1899	+	265.617i	0.0454101	+	0.315834i
$842$	−1483.21	−	953.199i	−1.76153	−	1.13207i
$843$	−1184.40	+	347.770i	−1.40498	+	0.412538i
$844$	−149.860	+	1042.30i	−0.177560	+	1.23495i
$845$	−715.583	+	105.041i	−0.846843	+	0.124308i
$846$	11.1689	−	7.17783i	0.0132020	−	0.00848444i
$847$	740.942	+	855.093i	0.874784	+	1.00955i
$848$	347.084	+	101.913i	0.409298	+	0.120181i
$849$	413.325	+	188.759i	0.486838	+	0.222331i
$850$	1113.73	−	166.842i	1.31027	−	0.196285i
$851$	705.355	+	928.690i	0.828855	+	1.09129i
$852$			316.135i			0.371051i
$853$	112.921	+	51.5692i	0.132381	+	0.0604563i	0.480504	−	0.876992i	$-0.340454\pi$
$853$	112.921	+	51.5692i	0.132381	+	0.0604563i	−0.348123	+	0.937449i	$0.613181\pi$
$854$	2194.01	+	644.220i	2.56910	+	0.754355i
$855$	−40.0668	+	0.118188i	−0.0468618	+	0.000138232i
$856$	−15.9027	−	24.7450i	−0.0185779	−	0.0289077i
$857$	232.652	+	201.594i	0.271473	+	0.235233i	0.779948	−	0.625844i	$-0.215245\pi$
$857$	232.652	+	201.594i	0.271473	+	0.235233i	−0.508475	+	0.861076i	$0.669791\pi$
$858$	−358.793	+	2495.46i	−0.418174	+	2.90846i
$859$	−1473.24	+	432.582i	−1.71506	+	0.503588i	−0.983916	−	0.178633i	$-0.942833\pi$
$859$	−1473.24	+	432.582i	−1.71506	+	0.503588i	−0.731147	+	0.682220i	$0.761014\pi$
$860$	−33.2878	−	112.143i	−0.0387068	−	0.130399i
$861$	−616.420	+	88.6279i	−0.715935	+	0.102936i
$862$	99.1796	+	217.173i	0.115058	+	0.251941i
$863$	−811.111	+	370.422i	−0.939874	+	0.429226i	−0.825621	−	0.564226i	$-0.809175\pi$
$863$	−811.111	+	370.422i	−0.939874	+	0.429226i	−0.114253	+	0.993452i	$0.536447\pi$
$864$	172.389	+	1198.99i	0.199524	+	1.38772i
$865$	−111.259	+	33.0255i	−0.128623	+	0.0381797i
$866$	109.085	+	371.511i	0.125965	+	0.428996i
$867$	−177.082	−	25.4605i	−0.204246	−	0.0293662i
$868$	−48.1933	+	55.6181i	−0.0555223	+	0.0640761i
$869$	606.656	−	389.874i	0.698108	−	0.448647i
$870$	−3.18792	−	1080.73i	−0.00366428	−	1.24222i
$871$	267.765	−	911.923i	0.307422	−	1.04698i
$872$	131.743	−	288.476i	0.151081	−	0.330821i
$873$	35.4697			0.0406297
$874$	2139.74	+	138.064i	2.44822	+	0.157968i
$875$	591.947	−	939.260i	0.676511	−	1.07344i
$876$	27.8822	−	61.0534i	0.0318289	−	0.0696957i
$877$	−140.452	+	478.334i	−0.160150	+	0.545421i	0.839847	+	0.542824i	$0.182645\pi$
$877$	−140.452	+	478.334i	−0.160150	+	0.545421i	−0.999997	+	0.00259697i	$0.999173\pi$
$878$	1260.64	−	1092.35i	1.43581	−	1.24414i
$879$	431.049	+	670.725i	0.490385	+	0.763054i
$880$	138.201	+	941.488i	0.157047	+	1.06987i
$881$	−358.100	−	51.4870i	−0.406470	−	0.0584415i	−0.0639521	−	0.997953i	$-0.520370\pi$
$881$	−358.100	−	51.4870i	−0.406470	−	0.0584415i	−0.342517	+	0.939511i	$0.611280\pi$
$882$	6.38008	+	21.7285i	0.00723365	+	0.0246355i
$883$	−691.269	+	1075.64i	−0.782864	+	1.21816i	0.188851	+	0.982006i	$0.439524\pi$
$883$	−691.269	+	1075.64i	−0.782864	+	1.21816i	−0.971715	+	0.236155i	$0.924113\pi$
$884$	1280.64	−	184.128i	1.44868	−	0.208289i
$885$	452.349	+	131.373i	0.511129	+	0.148445i
$886$	−379.089	−	830.088i	−0.427865	−	0.936894i
$887$	−1517.33	+	218.159i	−1.71063	+	0.245952i	−0.926943	−	0.375202i	$-0.877573\pi$
$887$	−1517.33	+	218.159i	−1.71063	+	0.245952i	−0.783689	+	0.621154i	$0.786664\pi$
$888$	314.014	+	201.804i	0.353619	+	0.227257i
$889$	−201.096	−	684.871i	−0.226205	−	0.770384i
$890$	1160.81	−	1011.86i	1.30428	−	1.13692i
$891$	−991.364	−	859.022i	−1.11264	−	0.964110i
$892$	−95.3822	−	148.418i	−0.106931	−	0.166387i
$893$	−360.290	−	415.797i	−0.403460	−	0.465618i
$894$	−443.983	+	1512.07i	−0.496625	+	1.69135i
$895$	−77.5649	+	35.6996i	−0.0866647	+	0.0398878i
$896$			673.490i			0.751663i
$897$	586.298	−	1091.74i	0.653621	−	1.21710i
$898$		−	136.199i		−	0.151669i
$899$	17.1066	−	37.4582i	0.0190284	−	0.0416665i
$900$	4.19255	−	30.4334i	0.00465839	−	0.0338148i
$901$	297.633	+	343.487i	0.330336	+	0.381228i
$902$	907.255	−	583.057i	1.00583	−	0.646405i
$903$	−99.2232	−	85.9774i	−0.109882	−	0.0952131i
$904$	−128.184	−	18.4301i	−0.141797	−	0.0203873i
$905$	−35.3377	+	77.9868i	−0.0390472	+	0.0861732i
$906$	−2088.45	−	1342.17i	−2.30514	−	1.48142i
$907$	68.1202	+	473.787i	0.0751050	+	0.522367i	0.992293	+	0.123912i	$0.0395442\pi$
$907$	68.1202	+	473.787i	0.0751050	+	0.522367i	−0.917188	+	0.398454i	$0.869547\pi$
$908$	616.407	+	1349.74i	0.678862	+	1.48650i
$909$	−7.88423	−	17.2641i	−0.00867352	−	0.0189924i
$910$	1256.66	−	1968.14i	1.38094	−	2.16279i
$911$	659.673	−	1026.47i	0.724119	−	1.12675i	−0.262692	−	0.964880i	$-0.584610\pi$
$911$	659.673	−	1026.47i	0.724119	−	1.12675i	0.986812	−	0.161872i	$-0.0517532\pi$
$912$	−1106.79	+	324.984i	−1.21359	+	0.356342i
$913$	−22.5817	−	3.24676i	−0.0247336	−	0.00355615i
$914$	1149.71	+	996.231i	1.25789	+	1.08997i
$915$	−1306.12	−	183.861i	−1.42746	−	0.200941i
$916$	800.905	−	693.988i	0.874350	−	0.757629i
$917$	1692.82	+	497.056i	1.84604	+	0.542046i
$918$	−497.833	+	1090.10i	−0.542302	+	1.18747i
$919$			309.678i			0.336972i	0.985704	+	0.168486i	$0.0538879\pi$
$919$			309.678i			0.336972i	−0.985704	+	0.168486i	$0.946112\pi$
$920$	−56.4542	+	272.496i	−0.0613633	+	0.296192i
$921$	645.637			0.701017
$922$	−64.1692	−	29.3051i	−0.0695978	−	0.0317842i
$923$	107.681	−	366.729i	0.116664	−	0.397323i
$924$	−1342.80	−	1549.67i	−1.45325	−	1.67713i
$925$	−835.735	−	953.070i	−0.903497	−	1.03035i
$926$	−690.784	+	797.207i	−0.745987	+	0.860915i
$927$	−3.02848	+	21.0636i	−0.00326697	+	0.0227223i
$928$	−306.972	−	1045.45i	−0.330789	−	1.12656i
$929$	−388.095	−	249.414i	−0.417756	−	0.268476i	0.314833	−	0.949147i	$-0.398052\pi$
$929$	−388.095	−	249.414i	−0.417756	−	0.268476i	−0.732589	+	0.680672i	$0.761688\pi$
$930$	41.8234	−	65.5025i	0.0449714	−	0.0704328i
$931$	853.637	−	389.843i	0.916904	−	0.418736i
$932$	85.8814	−	39.2207i	0.0921474	−	0.0420823i
$933$	−931.026	+	133.861i	−0.997884	+	0.143474i
$934$	−631.233	+	982.218i	−0.675838	+	1.05162i
$935$	−493.457	+	1089.01i	−0.527761	+	1.16472i
$936$	1.55652	−	10.8258i	0.00166295	−	0.0115660i
$937$	906.197	−	1045.81i	0.967126	−	1.11612i	−0.0260690	−	0.999660i	$-0.508299\pi$
$937$	906.197	−	1045.81i	0.967126	−	1.11612i	0.993195	−	0.116463i	$-0.0371556\pi$
$938$	765.099	+	1190.52i	0.815671	+	1.26921i
$939$	−899.625	+	779.529i	−0.958067	+	0.830170i
$940$	354.201	−	229.110i	0.376810	−	0.243735i
$941$	−820.882	−	374.884i	−0.872350	−	0.398389i	−0.0716328	−	0.997431i	$-0.522821\pi$
$941$	−820.882	−	374.884i	−0.872350	−	0.398389i	−0.800718	+	0.599042i	$0.795548\pi$
$942$	−457.804			−0.485992
$943$	−517.181	+	116.285i	−0.548442	+	0.123313i
$944$	373.940			0.396123
$945$	493.960	+	1073.23i	0.522709	+	1.13570i
$946$	218.152	+	64.0553i	0.230605	+	0.0677117i
$947$	158.287	−	137.156i	0.167145	−	0.144832i	−0.567272	−	0.823531i	$-0.692001\pi$
$947$	158.287	−	137.156i	0.167145	−	0.144832i	0.734417	+	0.678698i	$0.237456\pi$
$948$	−563.857	+	362.369i	−0.594786	+	0.382246i
$949$	−53.1402	+	61.3271i	−0.0559960	+	0.0646228i
$950$	−2330.60	+	13.7496i	−2.45327	+	0.0144733i
$951$	772.413	−	226.801i	0.812212	−	0.238487i
$952$	−176.298	+	274.325i	−0.185187	+	0.288156i
$953$	134.864	+	937.999i	0.141515	+	0.984259i	0.929568	+	0.368651i	$0.120180\pi$
$953$	134.864	+	937.999i	0.141515	+	0.984259i	−0.788053	+	0.615608i	$0.788911\pi$
$954$	20.6470	−	9.42915i	0.0216425	−	0.00988380i
$955$	381.642	+	110.838i	0.399625	+	0.116061i
$956$	−95.2457	−	662.448i	−0.0996294	−	0.692938i
$957$	965.232	+	620.317i	1.00860	+	0.648189i
$958$	1465.31	−	430.254i	1.52955	−	0.449117i
$959$	−141.180	+	981.931i	−0.147216	+	1.02391i
$960$	−191.939	−	1307.57i	−0.199937	−	1.36206i
$961$	−805.954	+	517.955i	−0.838661	+	0.538975i
$962$	−1745.92	−	2014.90i	−1.81488	−	2.09449i
$963$	2.97651	+	0.873982i	0.00309087	+	0.000907562i
$964$	−1585.21	−	723.942i	−1.64441	−	0.750978i
$965$	−70.8795	+	82.2885i	−0.0734502	+	0.0852730i
$966$	656.847	+	1724.30i	0.679965	+	1.78499i
$967$		−	1540.82i		−	1.59341i	−0.604370	−	0.796704i	$-0.706575\pi$
$967$		−	1540.82i		−	1.59341i	0.604370	−	0.796704i	$-0.293425\pi$
$968$	280.405	+	128.057i	0.289675	+	0.132290i
$969$	−1390.61	−	408.320i	−1.43510	−	0.421383i
$970$	2063.22	−	6.08604i	2.12703	−	0.00627426i
$971$	−347.049	−	540.019i	−0.357414	−	0.556148i	0.615259	−	0.788325i	$-0.289051\pi$
$971$	−347.049	−	540.019i	−0.357414	−	0.556148i	−0.972673	+	0.232177i	$0.925415\pi$
$972$	50.1342	+	43.4415i	0.0515784	+	0.0446929i
$973$	151.143	−	1051.22i	0.155337	−	1.08039i
$974$	−315.556	+	92.6556i	−0.323979	+	0.0951290i
$975$	−552.311	+	1228.52i	−0.566473	+	1.26002i
$976$	−1036.45	+	149.018i	−1.06193	+	0.152683i
$977$	−143.631	−	314.509i	−0.147013	−	0.321913i	0.821772	−	0.569816i	$-0.192986\pi$
$977$	−143.631	−	314.509i	−0.147013	−	0.321913i	−0.968785	+	0.247903i	$0.920258\pi$
$978$	−885.905	+	404.579i	−0.905833	+	0.413680i
$979$	232.666	+	1618.23i	0.237656	+	1.65294i
$980$	204.753	+	689.790i	0.208931	+	0.703868i
$981$	9.42291	+	32.0915i	0.00960542	+	0.0327130i
$982$	1983.04	+	285.118i	2.01939	+	0.290344i
$983$	892.720	−	1030.25i	0.908159	−	1.04807i	−0.0904792	−	0.995898i	$-0.528840\pi$
$983$	892.720	−	1030.25i	0.908159	−	1.04807i	0.998638	−	0.0521729i	$-0.0166147\pi$
$984$	−142.736	+	91.7306i	−0.145057	+	0.0932222i
$985$	1656.59	−	4.88657i	1.68182	−	0.00496099i
$986$	303.697	−	1034.30i	0.308010	−	1.04898i
$987$	196.679	−	430.667i	0.199269	−	0.436339i
$988$	−2677.60			−2.71012
$989$	−89.9289	−	66.3475i	−0.0909291	−	0.0670855i
$990$	45.2403	+	38.9679i	0.0456973	+	0.0393615i
$991$	−67.7361	+	148.321i	−0.0683512	+	0.149668i	−0.940724	−	0.339173i	$-0.889853\pi$
$991$	−67.7361	+	148.321i	−0.0683512	+	0.149668i	0.872373	+	0.488841i	$0.162580\pi$
$992$	22.0744	−	75.1785i	0.0222524	−	0.0757847i
$993$	−809.081	+	701.072i	−0.814784	+	0.706014i
$994$	307.684	+	478.765i	0.309541	+	0.481655i
$995$	−266.006	−	1812.15i	−0.267343	−	1.82126i
$996$	20.9886	+	3.01771i	0.0210729	+	0.00302982i
$997$	296.417	+	1009.50i	0.297309	+	1.01254i	0.963711	+	0.266949i	$0.0860155\pi$
$997$	296.417	+	1009.50i	0.297309	+	1.01254i	−0.666401	+	0.745593i	$0.732166\pi$
$998$	−1185.18	+	1844.17i	−1.18755	+	1.84787i
$999$	1335.18	−	191.970i	1.33652	−	0.192162i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.3.i.a.109.20	yes	220
5.4	even	2	inner	115.3.i.a.109.3	yes	220
23.19	odd	22	inner	115.3.i.a.19.3	✓	220
115.19	odd	22	inner	115.3.i.a.19.20	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.3.i.a.19.3	✓	220	23.19	odd	22	inner
115.3.i.a.19.20	yes	220	115.19	odd	22	inner
115.3.i.a.109.3	yes	220	5.4	even	2	inner
115.3.i.a.109.20	yes	220	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(2.70071 + 1.23337i) q^{2} +(-0.857097 + 2.91901i) q^{3} +(3.15318 + 3.63896i) q^{4} +(-4.95118 - 0.696972i) q^{5} +(-5.91499 + 6.82626i) q^{6} +(-1.26402 + 8.79144i) q^{7} +(0.681750 + 2.32183i) q^{8} +(-0.214694 - 0.137975i) q^{9} +(-12.5121 - 7.98897i) q^{10} +(14.3361 - 6.54709i) q^{11} +(-13.3247 + 6.08520i) q^{12} +(17.5299 - 2.52042i) q^{13} +(-14.2569 + 22.1841i) q^{14} +(6.27811 - 13.8552i) q^{15} +(1.71853 - 11.9527i) q^{16} +(9.93564 - 11.4663i) q^{17} +(-0.409651 - 0.637429i) q^{18} +(-23.7302 + 20.5623i) q^{19} +(-13.0757 - 20.2148i) q^{20} +(-24.5789 - 11.2248i) q^{21} +46.7927 q^{22} +(-21.6053 - 7.88738i) q^{23} -7.36176 q^{24} +(24.0285 + 6.90168i) q^{25} +(50.4518 + 14.8140i) q^{26} +(-20.1058 + 17.4217i) q^{27} +(-35.9774 + 23.1213i) q^{28} +(15.6709 - 18.0852i) q^{29} +(34.0439 - 29.6755i) q^{30} +(1.65111 - 0.484811i) q^{31} +(24.6164 - 38.3039i) q^{32} +(6.82354 + 47.4587i) q^{33} +(40.9755 - 18.7129i) q^{34} +(12.3858 - 42.6470i) q^{35} +(-0.174881 - 1.21632i) q^{36} +(-42.6547 - 27.4125i) q^{37} +(-89.4494 + 26.2647i) q^{38} +(-7.66772 + 53.3301i) q^{39} +(-1.75722 - 11.9710i) q^{40} +(19.3888 - 12.4604i) q^{41} +(-52.5360 - 60.6298i) q^{42} +(4.66210 + 1.36891i) q^{43} +(69.0290 + 31.5245i) q^{44} +(0.966824 + 0.832777i) q^{45} +(-48.6216 - 47.9489i) q^{46} +17.5218i q^{47} +(33.4169 + 15.2610i) q^{48} +(-28.6765 - 8.42017i) q^{49} +(56.3815 + 48.2755i) q^{50} +(24.9545 + 38.8299i) q^{51} +(64.4466 + 55.8433i) q^{52} +(-4.26320 + 29.6512i) q^{53} +(-75.7873 + 22.2532i) q^{54} +(-75.5440 + 22.4240i) q^{55} +(-21.2740 + 3.05873i) q^{56} +(-39.6825 - 86.8925i) q^{57} +(64.6284 - 29.5148i) q^{58} +(4.40702 + 30.6515i) q^{59} +(70.2144 - 20.8420i) q^{60} +(-24.4297 - 83.2000i) q^{61} +(5.05713 + 0.727106i) q^{62} +(1.48438 - 1.71306i) q^{63} +(73.0903 - 46.9723i) q^{64} +(-88.5505 + 0.261204i) q^{65} +(-40.1059 + 136.588i) q^{66} +(22.2934 - 48.8157i) q^{67} +73.0544 q^{68} +(41.5411 - 56.3058i) q^{69} +(86.0501 - 99.9010i) q^{70} +(8.96525 - 19.6312i) q^{71} +(0.173988 - 0.592547i) q^{72} +(-3.46282 + 3.00055i) q^{73} +(-81.3881 - 126.642i) q^{74} +(-40.7408 + 64.2238i) q^{75} +(-149.651 - 21.5166i) q^{76} +(39.4372 + 134.311i) q^{77} +(-86.4842 + 134.572i) q^{78} +(45.2904 - 6.51178i) q^{79} +(-16.8395 + 57.9821i) q^{80} +(-34.5757 - 75.7102i) q^{81} +(67.7319 - 9.73837i) q^{82} +(-1.21776 - 0.782606i) q^{83} +(-36.6549 - 124.835i) q^{84} +(-57.1849 + 49.8471i) q^{85} +(10.9026 + 9.44714i) q^{86} +(39.3593 + 61.2443i) q^{87} +(24.9749 + 28.8226i) q^{88} +(-29.2249 + 99.5308i) q^{89} +(1.58399 + 3.44154i) q^{90} +157.299i q^{91} +(-39.4235 - 103.491i) q^{92} +5.23514i q^{93} +(-21.6110 + 47.3214i) q^{94} +(131.824 - 85.2687i) q^{95} +(90.7106 + 104.686i) q^{96} +(-116.921 + 75.1405i) q^{97} +(-67.0616 - 58.1092i) q^{98} +(-3.98122 - 0.572413i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q + 26 q^{4} - 11 q^{5} - 14 q^{6} + 32 q^{9} - 11 q^{10} - 22 q^{11} - 22 q^{14} - 88 q^{15} - 142 q^{16} - 22 q^{19} - 99 q^{20} - 22 q^{21} - 88 q^{24} + 17 q^{25} + 34 q^{26} + 92 q^{29} + 341 q^{30}+ \cdots + 1628 q^{99}+O(q^{100}) \) 220 * q + 26 * q^4 - 11 * q^5 - 14 * q^6 + 32 * q^9 - 11 * q^10 - 22 * q^11 - 22 * q^14 - 88 * q^15 - 142 * q^16 - 22 * q^19 - 99 * q^20 - 22 * q^21 - 88 * q^24 + 17 * q^25 + 34 * q^26 + 92 * q^29 + 341 * q^30 - 152 * q^31 - 264 * q^34 - 13 * q^35 - 62 * q^36 - 118 * q^39 - 11 * q^40 - 80 * q^41 - 242 * q^44 + 226 * q^46 + 90 * q^49 - 211 * q^50 - 22 * q^51 + 658 * q^54 - 565 * q^55 + 770 * q^56 - 172 * q^59 - 891 * q^60 + 286 * q^61 - 474 * q^64 - 242 * q^65 - 44 * q^66 - 288 * q^69 + 790 * q^70 - 210 * q^71 + 506 * q^74 + 804 * q^75 - 2376 * q^76 + 462 * q^79 + 2398 * q^80 - 2408 * q^81 + 1034 * q^84 + 1197 * q^85 - 1518 * q^86 - 22 * q^89 + 154 * q^90 - 210 * q^94 - 338 * q^95 + 2772 * q^96 + 1628 * q^99

Introduction

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