LMFDB - Embedded newform 220.3.w.a.7.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,3,Mod(7,220)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("220.7"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 5, 14])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.20
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.14597 - 1.63913i) q^{2} +(1.96587 - 1.00166i) q^{3} +(-1.37351 + 3.75679i) q^{4} +(-3.42603 + 3.64175i) q^{5} +(-3.89468 - 2.07445i) q^{6} +(3.39399 - 6.66107i) q^{7} +(7.73187 - 2.05381i) q^{8} +(-2.42874 + 3.34288i) q^{9} +(9.89543 + 1.44238i) q^{10} +(-6.20602 - 9.08214i) q^{11} +(1.06290 + 8.76116i) q^{12} +(-3.80199 - 24.0048i) q^{13} +(-14.8078 + 2.07020i) q^{14} +(-3.08734 + 10.5909i) q^{15} +(-12.2270 - 10.3200i) q^{16} +(3.51456 - 22.1900i) q^{17} +(8.26268 + 0.150193i) q^{18} +(3.34228 + 1.08597i) q^{19} +(-8.97561 - 17.8728i) q^{20} -16.4944i q^{21} +(-7.77491 + 20.5803i) q^{22} +(-2.21098 - 2.21098i) q^{23} +(13.1426 - 11.7822i) q^{24} +(-1.52463 - 24.9535i) q^{25} +(-34.9901 + 33.7408i) q^{26} +(-4.53251 + 28.6171i) q^{27} +(20.3626 + 21.8995i) q^{28} +(8.27919 + 25.4807i) q^{29} +(20.8979 - 7.07633i) q^{30} +(17.9554 - 24.7134i) q^{31} +(-2.90404 + 31.8680i) q^{32} +(-21.2975 - 11.6380i) q^{33} +(-40.4000 + 19.6683i) q^{34} +(12.6300 + 35.1811i) q^{35} +(-9.22260 - 13.7157i) q^{36} +(-5.96306 + 11.7032i) q^{37} +(-2.05010 - 6.72293i) q^{38} +(-31.5189 - 43.3821i) q^{39} +(-19.0102 + 35.1939i) q^{40} +(-42.4154 - 13.7816i) q^{41} +(-27.0366 + 18.9021i) q^{42} +(-5.87291 + 5.87291i) q^{43} +(42.6437 - 10.8404i) q^{44} +(-3.85297 - 20.2977i) q^{45} +(-1.09037 + 6.15780i) q^{46} +(0.658485 + 1.29235i) q^{47} +(-34.3737 - 8.04043i) q^{48} +(-4.04927 - 5.57334i) q^{49} +(-39.1548 + 31.0950i) q^{50} +(-15.3177 - 47.1431i) q^{51} +(95.4032 + 18.6875i) q^{52} +(11.9588 - 1.89408i) q^{53} +(52.1013 - 25.3650i) q^{54} +(54.3369 + 8.51493i) q^{55} +(12.5613 - 58.4732i) q^{56} +(7.65827 - 1.21295i) q^{57} +(32.2786 - 42.7708i) q^{58} +(8.67104 + 26.6867i) q^{59} +(-35.5474 - 26.1452i) q^{60} +(-52.3876 - 72.1054i) q^{61} +(-61.0849 - 1.11035i) q^{62} +(14.0240 + 27.5237i) q^{63} +(55.5637 - 31.7596i) q^{64} +(100.445 + 68.3954i) q^{65} +(5.33007 + 48.2461i) q^{66} +(50.1111 - 50.1111i) q^{67} +(78.5360 + 43.6816i) q^{68} +(-6.56115 - 2.13185i) q^{69} +(43.1928 - 61.0187i) q^{70} +(66.1216 + 91.0085i) q^{71} +(-11.9131 + 30.8349i) q^{72} +(-27.8939 + 54.7449i) q^{73} +(26.0165 - 3.63723i) q^{74} +(-27.9922 - 47.5281i) q^{75} +(-8.67041 + 11.0647i) q^{76} +(-81.5600 + 10.5141i) q^{77} +(-34.9892 + 101.378i) q^{78} +(81.9076 - 112.736i) q^{79} +(79.4726 - 9.17101i) q^{80} +(8.26254 + 25.4295i) q^{81} +(26.0169 + 85.3176i) q^{82} +(-16.8053 + 106.104i) q^{83} +(61.9662 + 22.6552i) q^{84} +(68.7695 + 88.8228i) q^{85} +(16.3567 + 2.89630i) q^{86} +(41.7989 + 41.7989i) q^{87} +(-66.6372 - 57.4760i) q^{88} +60.9835i q^{89} +(-28.8552 + 29.5760i) q^{90} +(-172.802 - 56.1467i) q^{91} +(11.3430 - 5.26939i) q^{92} +(10.5434 - 66.5686i) q^{93} +(1.36373 - 2.56034i) q^{94} +(-15.4056 + 8.45116i) q^{95} +(26.2119 + 65.5572i) q^{96} +(-9.49650 - 59.9585i) q^{97} +(-4.49510 + 13.0242i) q^{98} +(45.4333 + 1.31221i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.14597	−	1.63913i	−0.572985	−	0.819566i
$2$	−1.14597	−	1.63913i	−0.572985	−	0.819566i
$3$	1.96587	−	1.00166i	0.655290	−	0.333887i	−0.0945363	−	0.995521i	$-0.530137\pi$
$3$	1.96587	−	1.00166i	0.655290	−	0.333887i	0.749827	+	0.661634i	$0.230137\pi$
$4$	−1.37351	+	3.75679i	−0.343377	+	0.939198i
$5$	−3.42603	+	3.64175i	−0.685206	+	0.728349i
$5$	−3.42603	+	3.64175i	−0.685206	+	0.728349i
$6$	−3.89468	−	2.07445i	−0.649114	−	0.345741i
$7$	3.39399	−	6.66107i	0.484855	−	0.951582i	−0.510909	−	0.859635i	$-0.670691\pi$
$7$	3.39399	−	6.66107i	0.484855	−	0.951582i	0.995764	−	0.0919469i	$-0.0293090\pi$
$8$	7.73187	−	2.05381i	0.966484	−	0.256726i
$9$	−2.42874	+	3.34288i	−0.269860	+	0.371431i
$10$	9.89543	+	1.44238i	0.989543	+	0.144238i
$11$	−6.20602	−	9.08214i	−0.564184	−	0.825649i
$11$	−6.20602	−	9.08214i	−0.564184	−	0.825649i
$12$	1.06290	+	8.76116i	0.0885747	+	0.730096i
$13$	−3.80199	−	24.0048i	−0.292461	−	1.84653i	−0.497106	−	0.867690i	$-0.665604\pi$
$13$	−3.80199	−	24.0048i	−0.292461	−	1.84653i	0.204645	−	0.978836i	$-0.434396\pi$
$14$	−14.8078	+	2.07020i	−1.05770	+	0.147871i
$15$	−3.08734	+	10.5909i	−0.205823	+	0.706062i
$16$	−12.2270	−	10.3200i	−0.764185	−	0.644997i
$17$	3.51456	−	22.1900i	0.206739	−	1.30530i	−0.637967	−	0.770064i	$-0.720224\pi$
$17$	3.51456	−	22.1900i	0.206739	−	1.30530i	0.844705	−	0.535232i	$-0.179776\pi$
$18$	8.26268	+	0.150193i	0.459038	+	0.00834405i
$19$	3.34228	+	1.08597i	0.175909	+	0.0571564i	0.395647	−	0.918402i	$-0.370520\pi$
$19$	3.34228	+	1.08597i	0.175909	+	0.0571564i	−0.219738	+	0.975559i	$0.570520\pi$
$20$	−8.97561	−	17.8728i	−0.448780	−	0.893642i
$21$		−	16.4944i		−	0.785449i
$22$	−7.77491	+	20.5803i	−0.353405	+	0.935470i
$23$	−2.21098	−	2.21098i	−0.0961295	−	0.0961295i	0.657407	−	0.753536i	$-0.271653\pi$
$23$	−2.21098	−	2.21098i	−0.0961295	−	0.0961295i	−0.753536	+	0.657407i	$0.771653\pi$
$24$	13.1426	−	11.7822i	0.547610	−	0.490927i
$25$	−1.52463	−	24.9535i	−0.0609852	−	0.998139i
$26$	−34.9901	+	33.7408i	−1.34577	+	1.29772i
$27$	−4.53251	+	28.6171i	−0.167871	+	1.05989i
$28$	20.3626	+	21.8995i	0.727236	+	0.782126i
$29$	8.27919	+	25.4807i	0.285489	+	0.878646i	0.986252	+	0.165251i	$0.0528434\pi$
$29$	8.27919	+	25.4807i	0.285489	+	0.878646i	−0.700762	+	0.713395i	$0.747157\pi$
$30$	20.8979	−	7.07633i	0.696597	−	0.235878i
$31$	17.9554	−	24.7134i	0.579205	−	0.797207i	−0.414403	−	0.910094i	$-0.636010\pi$
$31$	17.9554	−	24.7134i	0.579205	−	0.797207i	0.993608	+	0.112886i	$0.0360096\pi$
$32$	−2.90404	+	31.8680i	−0.0907512	+	0.995874i
$33$	−21.2975	−	11.6380i	−0.645378	−	0.352666i
$34$	−40.4000	+	19.6683i	−1.18823	+	0.578479i
$35$	12.6300	+	35.1811i	0.360858	+	1.00517i
$36$	−9.22260	−	13.7157i	−0.256183	−	0.380993i
$37$	−5.96306	+	11.7032i	−0.161164	+	0.316302i	−0.957440	−	0.288631i	$-0.906800\pi$
$37$	−5.96306	+	11.7032i	−0.161164	+	0.316302i	0.796277	+	0.604933i	$0.206800\pi$
$38$	−2.05010	−	6.72293i	−0.0539500	−	0.176919i
$39$	−31.5189	−	43.3821i	−0.808178	−	1.11236i
$40$	−19.0102	+	35.1939i	−0.475254	+	0.879848i
$41$	−42.4154	−	13.7816i	−1.03452	−	0.336136i	−0.257945	−	0.966160i	$-0.583045\pi$
$41$	−42.4154	−	13.7816i	−1.03452	−	0.336136i	−0.776576	+	0.630023i	$0.783045\pi$
$42$	−27.0366	+	18.9021i	−0.643728	+	0.450051i
$43$	−5.87291	+	5.87291i	−0.136579	+	0.136579i	−0.772091	−	0.635512i	$-0.780789\pi$
$43$	−5.87291	+	5.87291i	−0.136579	+	0.136579i	0.635512	+	0.772091i	$0.280789\pi$
$44$	42.6437	−	10.8404i	0.969175	−	0.246372i
$45$	−3.85297	−	20.2977i	−0.0856215	−	0.451059i
$46$	−1.09037	+	6.15780i	−0.0237037	+	0.133865i
$47$	0.658485	+	1.29235i	0.0140103	+	0.0274968i	0.897906	−	0.440188i	$-0.145088\pi$
$47$	0.658485	+	1.29235i	0.0140103	+	0.0274968i	−0.883895	+	0.467685i	$0.845088\pi$
$48$	−34.3737	−	8.04043i	−0.716119	−	0.167509i
$49$	−4.04927	−	5.57334i	−0.0826382	−	0.113742i
$50$	−39.1548	+	31.0950i	−0.783097	+	0.621900i
$51$	−15.3177	−	47.1431i	−0.300348	−	0.924375i
$52$	95.4032	+	18.6875i	1.83468	+	0.359375i
$53$	11.9588	−	1.89408i	0.225637	−	0.0357374i	−0.0425921	−	0.999093i	$-0.513562\pi$
$53$	11.9588	−	1.89408i	0.225637	−	0.0357374i	0.268229	+	0.963355i	$0.413562\pi$
$54$	52.1013	−	25.3650i	0.964840	−	0.469722i
$55$	54.3369	+	8.51493i	0.987943	+	0.154817i
$56$	12.5613	−	58.4732i	0.224309	−	1.04416i
$57$	7.65827	−	1.21295i	0.134356	−	0.0212798i
$58$	32.2786	−	42.7708i	0.556527	−	0.737428i
$59$	8.67104	+	26.6867i	0.146967	+	0.452317i	0.997259	−	0.0739942i	$-0.0235746\pi$
$59$	8.67104	+	26.6867i	0.146967	+	0.452317i	−0.850292	+	0.526311i	$0.823575\pi$
$60$	−35.5474	−	26.1452i	−0.592457	−	0.435753i
$61$	−52.3876	−	72.1054i	−0.858814	−	1.18206i	−0.981851	−	0.189654i	$-0.939264\pi$
$61$	−52.3876	−	72.1054i	−0.858814	−	1.18206i	0.123037	−	0.992402i	$-0.460736\pi$
$62$	−61.0849	−	1.11035i	−0.985240	−	0.0179089i
$63$	14.0240	+	27.5237i	0.222604	+	0.436884i
$64$	55.5637	−	31.7596i	0.868183	−	0.496244i
$65$	100.445	+	68.3954i	1.54531	+	1.05224i
$66$	5.33007	+	48.2461i	0.0807586	+	0.731002i
$67$	50.1111	−	50.1111i	0.747927	−	0.747927i	−0.226163	−	0.974090i	$-0.572618\pi$
$67$	50.1111	−	50.1111i	0.747927	−	0.747927i	0.974090	+	0.226163i	$0.0726181\pi$
$68$	78.5360	+	43.6816i	1.15494	+	0.642376i
$69$	−6.56115	−	2.13185i	−0.0950891	−	0.0308963i
$70$	43.1928	−	61.0187i	0.617040	−	0.871696i
$71$	66.1216	+	91.0085i	0.931289	+	1.28181i	0.959354	+	0.282204i	$0.0910655\pi$
$71$	66.1216	+	91.0085i	0.931289	+	1.28181i	−0.0280649	+	0.999606i	$0.508935\pi$
$72$	−11.9131	+	30.8349i	−0.165460	+	0.428262i
$73$	−27.8939	+	54.7449i	−0.382108	+	0.749930i	−0.999320	−	0.0368674i	$-0.988262\pi$
$73$	−27.8939	+	54.7449i	−0.382108	+	0.749930i	0.617212	+	0.786797i	$0.288262\pi$
$74$	26.0165	−	3.63723i	0.351574	−	0.0491517i
$75$	−27.9922	−	47.5281i	−0.373229	−	0.633709i
$76$	−8.67041	+	11.0647i	−0.114084	+	0.145588i
$77$	−81.5600	+	10.5141i	−1.05922	+	0.136547i
$78$	−34.9892	+	101.378i	−0.448580	+	1.29972i
$79$	81.9076	−	112.736i	1.03681	−	1.42704i	0.137092	−	0.990558i	$-0.456224\pi$
$79$	81.9076	−	112.736i	1.03681	−	1.42704i	0.899713	−	0.436482i	$-0.143776\pi$
$80$	79.4726	−	9.17101i	0.993407	−	0.114638i
$81$	8.26254	+	25.4295i	0.102007	+	0.313944i
$82$	26.0169	+	85.3176i	0.317279	+	1.04046i
$83$	−16.8053	+	106.104i	−0.202473	+	1.27837i	0.651740	+	0.758443i	$0.274040\pi$
$83$	−16.8053	+	106.104i	−0.202473	+	1.27837i	−0.854213	+	0.519923i	$0.825960\pi$
$84$	61.9662	+	22.6552i	0.737692	+	0.269705i
$85$	68.7695	+	88.8228i	0.809053	+	1.04497i
$86$	16.3567	+	2.89630i	0.190194	+	0.0336779i
$87$	41.7989	+	41.7989i	0.480447	+	0.480447i
$88$	−66.6372	−	57.4760i	−0.757241	−	0.653136i
$89$			60.9835i			0.685207i	0.939480	+	0.342604i	$0.111309\pi$
$89$			60.9835i			0.685207i	−0.939480	+	0.342604i	$0.888691\pi$
$90$	−28.8552	+	29.5760i	−0.320613	+	0.328623i
$91$	−172.802	−	56.1467i	−1.89892	−	0.616997i
$92$	11.3430	−	5.26939i	0.123293	−	0.0572760i
$93$	10.5434	−	66.5686i	0.113370	−	0.715791i
$94$	1.36373	−	2.56034i	0.0145077	−	0.0272376i
$95$	−15.4056	+	8.45116i	−0.162164	+	0.0889596i
$96$	26.2119	+	65.5572i	0.273041	+	0.682887i
$97$	−9.49650	−	59.9585i	−0.0979021	−	0.618129i	−0.987038	−	0.160486i	$-0.948694\pi$
$97$	−9.49650	−	59.9585i	−0.0979021	−	0.618129i	0.889136	−	0.457643i	$-0.151306\pi$
$98$	−4.49510	+	13.0242i	−0.0458684	+	0.132900i
$99$	45.4333	+	1.31221i	0.458922	+	0.0132546i
$100$	95.8391	+	28.5460i	0.958391	+	0.285460i
$101$	48.6366	−	66.9425i	0.481550	−	0.662797i	−0.497252	−	0.867606i	$-0.665657\pi$
$101$	48.6366	−	66.9425i	0.481550	−	0.662797i	0.978802	+	0.204809i	$0.0656574\pi$
$102$	−59.7202	+	79.1324i	−0.585492	+	0.775808i
$103$	55.9118	−	109.733i	0.542833	−	1.06537i	−0.442824	−	0.896609i	$-0.646023\pi$
$103$	55.9118	−	109.733i	0.542833	−	1.06537i	0.985657	−	0.168762i	$-0.0539768\pi$
$104$	−78.6979	−	177.794i	−0.756711	−	1.70956i
$105$	60.0686	+	56.5104i	0.572081	+	0.538195i
$106$	−16.8090	−	17.4314i	−0.158576	−	0.164447i
$107$	−52.8616	+	26.9343i	−0.494033	+	0.251723i	−0.683212	−	0.730220i	$-0.739418\pi$
$107$	−52.8616	+	26.9343i	−0.494033	+	0.251723i	0.189179	+	0.981943i	$0.439418\pi$
$108$	−101.283	−	56.3335i	−0.937806	−	0.521606i
$109$	76.1479			0.698604			0.349302	−	0.937010i	$-0.386419\pi$
$109$	76.1479			0.698604			0.349302	+	0.937010i	$0.386419\pi$
$110$	−48.3113	−	98.8232i	−0.439194	−	0.898392i
$111$			28.9799i			0.261080i
$112$	−110.240	+	46.4189i	−0.984287	+	0.414454i
$113$	−43.8155	−	85.9928i	−0.387748	−	0.760998i	0.611802	−	0.791011i	$-0.290445\pi$
$113$	−43.8155	−	85.9928i	−0.387748	−	0.760998i	−0.999550	+	0.0300131i	$0.990445\pi$
$114$	−10.7643	−	11.1629i	−0.0944239	−	0.0979202i
$115$	15.6267	−	0.476943i	0.135884	−	0.00414733i
$116$	−107.097	−	3.89476i	−0.923253	−	0.0335755i
$117$	89.4793	+	45.5920i	0.764780	+	0.389675i
$118$	33.8063	−	44.7951i	0.286494	−	0.379620i
$119$	−135.881	−	98.7234i	−1.14186	−	0.829608i
$120$	−2.11914	+	88.2285i	−0.0176595	+	0.735238i
$121$	−43.9706	+	112.728i	−0.363393	+	0.931636i
$122$	−58.1556	+	168.501i	−0.476685	+	1.38115i
$123$	−97.1876	+	15.3930i	−0.790143	+	0.125146i
$124$	68.1814	+	101.399i	0.549850	+	0.817730i
$125$	96.0976	+	79.9390i	0.768781	+	0.639512i
$126$	29.0439	−	54.5286i	0.230507	−	0.432767i
$127$	225.582	+	35.7286i	1.77623	+	0.281328i	0.956567	−	0.291513i	$-0.0941587\pi$
$127$	225.582	+	35.7286i	1.77623	+	0.281328i	0.819667	+	0.572841i	$0.194159\pi$
$128$	−115.733	−	54.6807i	−0.904160	−	0.427193i
$129$	−5.66272	+	17.4281i	−0.0438971	+	0.135101i
$130$	−2.99815	−	243.022i	−0.0230627	−	1.86940i
$131$	5.12951			0.0391566			0.0195783	−	0.999808i	$-0.493768\pi$
$131$	5.12951			0.0391566			0.0195783	+	0.999808i	$0.493768\pi$
$132$	72.9737	−	64.0253i	0.552831	−	0.485040i
$133$	18.5774	−	18.5774i	0.139680	−	0.139680i
$134$	−139.564	−	24.7129i	−1.04153	−	0.184425i
$135$	−88.6878	−	114.549i	−0.656946	−	0.848514i
$136$	−18.4000	−	178.789i	−0.135294	−	1.31462i
$137$	−85.0724	−	13.4741i	−0.620966	−	0.0983514i	−0.161979	−	0.986794i	$-0.551788\pi$
$137$	−85.0724	−	13.4741i	−0.620966	−	0.0983514i	−0.458987	+	0.888443i	$0.651788\pi$
$138$	4.02450	+	13.1976i	0.0291631	+	0.0956349i
$139$	−199.834	+	64.9299i	−1.43765	+	0.467122i	−0.921165	−	0.389172i	$-0.872761\pi$
$139$	−199.834	+	64.9299i	−1.43765	+	0.467122i	−0.516488	+	0.856294i	$0.672761\pi$
$140$	−149.515	−	0.873022i	−1.06797	−	0.00623587i
$141$	2.58899	+	1.88101i	0.0183617	+	0.0133405i
$142$	73.4016	−	212.675i	0.516913	−	1.49771i
$143$	−194.420	+	183.505i	−1.35958	+	1.28325i
$144$	64.1945	−	15.8087i	0.445795	−	0.109783i
$145$	−121.159	−	57.1470i	−0.835580	−	0.394118i
$146$	121.700	−	17.0142i	0.833559	−	0.116535i
$147$	−13.5430	−	6.90048i	−0.0921289	−	0.0469420i
$148$	−35.7760	−	38.4763i	−0.241730	−	0.259975i
$149$	1.65140	−	1.19981i	0.0110832	−	0.00805241i	−0.582230	−	0.813024i	$-0.697820\pi$
$149$	1.65140	−	1.19981i	0.0110832	−	0.00805241i	0.593313	+	0.804972i	$0.297820\pi$
$150$	−45.8267	+	100.349i	−0.305511	+	0.668991i
$151$	−17.4519	+	53.7115i	−0.115576	+	0.355705i	−0.992067	−	0.125713i	$-0.959878\pi$
$151$	−17.4519	+	53.7115i	−0.115576	+	0.355705i	0.876491	+	0.481418i	$0.159878\pi$
$152$	28.0725	+	1.53219i	0.184687	+	0.0100802i
$153$	65.6426	+	65.6426i	0.429037	+	0.429037i
$154$	110.699	+	121.639i	0.718826	+	0.789861i
$155$	28.4844	+	150.058i	0.183771	+	0.968115i
$156$	206.269	−	58.8245i	1.32224	−	0.377080i
$157$	−142.173	+	72.4407i	−0.905559	+	0.461406i	−0.843783	−	0.536685i	$-0.819677\pi$
$157$	−142.173	+	72.4407i	−0.905559	+	0.461406i	−0.0617763	+	0.998090i	$0.519677\pi$
$158$	−278.653	−	5.06515i	−1.76363	−	0.0320579i
$159$	21.6122	−	15.7022i	0.135926	−	0.0987557i
$160$	−106.106	−	119.756i	−0.663160	−	0.748477i
$161$	−22.2315	+	7.22346i	−0.138084	+	0.0448662i
$162$	32.2137	−	42.6848i	0.198850	−	0.263487i
$163$	19.2052	+	121.257i	0.117824	+	0.743909i	0.973886	+	0.227037i	$0.0729038\pi$
$163$	19.2052	+	121.257i	0.117824	+	0.743909i	−0.856063	+	0.516872i	$0.827096\pi$
$164$	110.032	−	140.417i	0.670929	−	0.856198i
$165$	115.348	−	37.6879i	0.699081	−	0.228412i
$166$	193.177	−	94.0464i	1.16372	−	0.566544i
$167$	−8.52467	−	53.8227i	−0.0510459	−	0.322291i	−0.999977	−	0.00680736i	$-0.997833\pi$
$167$	−8.52467	−	53.8227i	−0.0510459	−	0.322291i	0.948931	−	0.315484i	$-0.102167\pi$
$168$	−33.8765	−	127.533i	−0.201646	−	0.759124i
$169$	−401.048	+	130.309i	−2.37307	+	0.771056i
$170$	66.7846	−	214.511i	0.392851	−	1.26183i
$171$	−11.7478	+	8.53528i	−0.0687006	+	0.0499139i
$172$	−13.9968	−	30.1298i	−0.0813769	−	0.175173i
$173$	5.43173	−	2.76760i	0.0313973	−	0.0159977i	−0.438221	−	0.898867i	$-0.644391\pi$
$173$	5.43173	−	2.76760i	0.0313973	−	0.0159977i	0.469619	+	0.882869i	$0.344391\pi$
$174$	20.6136	−	116.414i	0.118469	−	0.669047i
$175$	−171.391	−	74.5360i	−0.979380	−	0.425920i
$176$	−17.8465	+	175.093i	−0.101400	+	0.994846i
$177$	43.7772	+	43.7772i	0.247329	+	0.247329i
$178$	99.9599	−	69.8852i	0.561573	−	0.392613i
$179$	−37.5449	+	115.551i	−0.209748	+	0.645538i	0.789737	+	0.613446i	$0.210217\pi$
$179$	−37.5449	+	115.551i	−0.209748	+	0.645538i	−0.999485	+	0.0320924i	$0.989783\pi$
$180$	81.5462	+	13.4042i	0.453034	+	0.0744677i
$181$	154.011	−	111.895i	0.850889	−	0.618207i	−0.0745021	−	0.997221i	$-0.523737\pi$
$181$	154.011	−	111.895i	0.850889	−	0.618207i	0.925391	+	0.379014i	$0.123737\pi$
$182$	105.994	+	347.588i	0.582384	+	1.90982i
$183$	−175.213	−	89.2752i	−0.957446	−	0.487843i
$184$	−21.6359	−	12.5541i	−0.117587	−	0.0682286i
$185$	−22.1903	−	61.8113i	−0.119948	−	0.334115i
$186$	−121.197	+	59.0035i	−0.651598	+	0.317223i
$187$	−223.344	+	105.792i	−1.19435	+	0.565733i
$188$	−5.75952	+	0.698741i	−0.0306358	+	0.00371670i
$189$	175.237	+	127.317i	0.927182	+	0.673637i
$190$	31.5069	+	15.5670i	0.165826	+	0.0819317i
$191$	269.193	−	87.4660i	1.40939	−	0.457937i	0.497172	−	0.867652i	$-0.334372\pi$
$191$	269.193	−	87.4660i	1.40939	−	0.457937i	0.912214	+	0.409715i	$0.134372\pi$
$192$	77.4187	−	118.091i	0.403223	−	0.615059i
$193$	355.018	+	56.2293i	1.83947	+	0.291344i	0.976757	−	0.214349i	$-0.0687631\pi$
$193$	355.018	+	56.2293i	1.83947	+	0.291344i	0.862714	+	0.505693i	$0.168763\pi$
$194$	−87.3973	+	84.2767i	−0.450501	+	0.434416i
$195$	265.971	+	33.8444i	1.36396	+	0.173561i
$196$	26.4996	−	7.55724i	0.135202	−	0.0385574i
$197$	−106.459	+	106.459i	−0.540399	+	0.540399i	−0.923646	−	0.383247i	$-0.874806\pi$
$197$	−106.459	+	106.459i	−0.540399	+	0.540399i	0.383247	+	0.923646i	$0.374806\pi$
$198$	−49.9143	−	75.9750i	−0.252093	−	0.383712i
$199$	63.6082			0.319639			0.159820	−	0.987146i	$-0.448909\pi$
$199$	63.6082			0.319639			0.159820	+	0.987146i	$0.448909\pi$
$200$	−63.0380	−	189.806i	−0.315190	−	0.949029i
$201$	48.3176	−	148.706i	0.240386	−	0.739832i
$202$	−165.464	−	3.00767i	−0.819127	−	0.0148895i
$203$	197.828	+	31.3329i	0.974524	+	0.154349i
$204$	198.146	+	7.20588i	0.971304	+	0.0353229i
$205$	195.505	−	107.250i	0.953684	−	0.523170i
$206$	−243.940	+	34.1040i	−1.18418	+	0.165553i
$207$	12.7609	−	2.02113i	0.0616470	−	0.00976393i
$208$	−201.242	+	332.743i	−0.967510	+	1.59972i
$209$	−10.8793	−	37.0946i	−0.0520541	−	0.177486i
$210$	23.7913	−	163.220i	0.113292	−	0.777236i
$211$	145.524	+	105.729i	0.689687	+	0.501087i	0.876557	−	0.481298i	$-0.159834\pi$
$211$	145.524	+	105.729i	0.689687	+	0.501087i	−0.186870	+	0.982385i	$0.559834\pi$
$212$	−9.30977	+	47.5281i	−0.0439140	+	0.224189i
$213$	221.146	+	112.680i	1.03824	+	0.529012i
$214$	104.727	+	55.7812i	0.489377	+	0.260660i
$215$	−1.26688	−	41.5084i	−0.00589247	−	0.193063i
$216$	23.7294	+	230.573i	0.109858	+	1.06747i
$217$	−103.678	−	203.479i	−0.477777	−	0.937691i
$218$	−87.2631	−	124.816i	−0.400290	−	0.572552i
$219$			135.562i			0.619003i
$220$	−106.621	+	192.437i	−0.484640	+	0.874714i
$221$	−546.030			−2.47073
$222$	47.5018	−	33.2101i	0.213972	−	0.149595i
$223$	361.802	−	184.347i	1.62243	−	0.826670i	0.623436	−	0.781875i	$-0.285736\pi$
$223$	361.802	−	184.347i	1.62243	−	0.826670i	0.998996	−	0.0447958i	$-0.0142637\pi$
$224$	202.419	+	127.503i	0.903654	+	0.569212i
$225$	87.1193	+	55.5089i	0.387197	+	0.246706i
$226$	−90.7423	+	170.365i	−0.401514	+	0.753825i
$227$	189.506	−	371.927i	0.834829	−	1.63844i	0.0670331	−	0.997751i	$-0.478647\pi$
$227$	189.506	−	371.927i	0.834829	−	1.63844i	0.767796	−	0.640694i	$-0.221353\pi$
$228$	−5.96188	+	30.4365i	−0.0261486	+	0.133493i
$229$	−227.018	+	312.463i	−0.991344	+	1.36447i	−0.0608562	+	0.998147i	$0.519383\pi$
$229$	−227.018	+	312.463i	−0.991344	+	1.36447i	−0.930488	+	0.366322i	$0.880617\pi$
$230$	−18.6895	−	25.0677i	−0.0812587	−	0.108990i
$231$	−149.805	+	102.365i	−0.648506	+	0.443138i
$232$	116.346	+	180.010i	0.501492	+	0.775905i
$233$	−21.7187	−	137.126i	−0.0932131	−	0.588524i	−0.989442	−	0.144932i	$-0.953704\pi$
$233$	−21.7187	−	137.126i	−0.0932131	−	0.588524i	0.896229	−	0.443593i	$-0.146296\pi$
$234$	−27.8093	−	198.915i	−0.118843	−	0.850066i
$235$	−6.96240	−	2.02959i	−0.0296272	−	0.00863657i
$236$	−112.166	−	4.07909i	−0.475280	−	0.0172843i
$237$	48.0964	−	303.669i	0.202938	−	1.28130i
$238$	−6.10503	+	335.861i	−0.0256514	+	1.41118i
$239$	−290.832	−	94.4969i	−1.21687	−	0.395384i	−0.370928	−	0.928662i	$-0.620960\pi$
$239$	−290.832	−	94.4969i	−1.21687	−	0.395384i	−0.845941	+	0.533277i	$0.820960\pi$
$240$	147.047	−	97.6336i	0.612694	−	0.406807i
$241$		−	118.046i		−	0.489817i	−0.969546	−	0.244909i	$-0.921242\pi$
$241$		−	118.046i		−	0.489817i	0.969546	−	0.244909i	$-0.0787579\pi$
$242$	235.165	−	57.1093i	0.971756	−	0.235989i
$243$	−142.673	−	142.673i	−0.587134	−	0.587134i
$244$	342.840	−	97.7722i	1.40508	−	0.400706i
$245$	34.1696	+	4.34803i	0.139468	+	0.0177471i
$246$	136.605	+	141.663i	0.555306	+	0.575867i
$247$	13.3613	−	84.3597i	0.0540942	−	0.341537i
$248$	88.0718	−	227.958i	0.355128	−	0.919185i
$249$	73.2437	+	225.421i	0.294151	+	0.905304i
$250$	20.9056	−	249.124i	0.0836225	−	0.996498i
$251$	56.7228	−	78.0722i	0.225987	−	0.311045i	−0.680934	−	0.732345i	$-0.738426\pi$
$251$	56.7228	−	78.0722i	0.225987	−	0.311045i	0.906921	+	0.421300i	$0.138426\pi$
$252$	−122.663	+	14.8814i	−0.486758	+	0.0590530i
$253$	−6.35903	+	33.8018i	−0.0251345	+	0.133604i
$254$	−199.946	−	410.702i	−0.787188	−	1.61694i
$255$	224.162	+	105.731i	0.879068	+	0.414629i
$256$	42.9971	+	252.363i	0.167957	+	0.985794i
$257$	138.639	−	272.095i	0.539452	−	1.05873i	−0.446977	−	0.894546i	$-0.647499\pi$
$257$	138.639	−	272.095i	0.539452	−	1.05873i	0.986429	−	0.164189i	$-0.0525007\pi$
$258$	35.0562	−	10.6901i	0.135877	−	0.0414344i
$259$	57.7171	+	79.4407i	0.222846	+	0.306721i
$260$	−394.909	+	283.410i	−1.51888	+	1.09004i
$261$	−105.287	−	34.2098i	−0.403398	−	0.131072i
$262$	−5.87827	−	8.40795i	−0.0224361	−	0.0320914i
$263$	199.993	−	199.993i	0.760428	−	0.760428i	−0.215972	−	0.976400i	$-0.569292\pi$
$263$	199.993	−	199.993i	0.760428	−	0.760428i	0.976400	+	0.215972i	$0.0692919\pi$
$264$	−188.572	−	46.2424i	−0.714286	−	0.175161i
$265$	−34.0733	+	50.0400i	−0.128579	+	0.188830i
$266$	−51.7399	−	9.16166i	−0.194511	−	0.0344423i
$267$	61.0848	+	119.886i	0.228782	+	0.449010i
$268$	119.429	+	257.085i	0.445631	+	0.959272i
$269$	60.1949	+	82.8512i	0.223773	+	0.307997i	0.906111	−	0.423040i	$-0.139037\pi$
$269$	60.1949	+	82.8512i	0.223773	+	0.307997i	−0.682338	+	0.731037i	$0.739037\pi$
$270$	−86.1280	+	276.641i	−0.318992	+	1.02460i
$271$	−149.787	−	460.998i	−0.552721	−	1.70110i	−0.701888	−	0.712287i	$-0.747659\pi$
$271$	−149.787	−	460.998i	−0.552721	−	1.70110i	0.149167	−	0.988812i	$-0.452341\pi$
$272$	−271.972	+	235.047i	−0.999899	+	0.864142i
$273$	−395.946	+	62.7117i	−1.45035	+	0.229713i
$274$	75.4045	+	154.886i	0.275199	+	0.565276i
$275$	−217.169	+	168.709i	−0.789705	+	0.613486i
$276$	17.0207	−	21.7208i	0.0616691	−	0.0786984i
$277$	74.3928	−	11.7827i	0.268566	−	0.0425367i	−0.0206989	−	0.999786i	$-0.506589\pi$
$277$	74.3928	−	11.7827i	0.268566	−	0.0425367i	0.289265	+	0.957249i	$0.406589\pi$
$278$	335.432	+	253.146i	1.20659	+	0.910598i
$279$	39.0050	+	120.045i	0.139803	+	0.430269i
$280$	169.909	+	246.076i	0.606818	+	0.878842i
$281$	177.226	+	243.931i	0.630698	+	0.868082i	0.998077	−	0.0619897i	$-0.0197446\pi$
$281$	177.226	+	243.931i	0.630698	+	0.868082i	−0.367378	+	0.930072i	$0.619745\pi$
$282$	0.116322	−	6.39929i	0.000412488	−	0.0226925i
$283$	101.087	+	198.394i	0.357197	+	0.701038i	0.997762	−	0.0668655i	$-0.0212998\pi$
$283$	101.087	+	198.394i	0.357197	+	0.701038i	−0.640565	+	0.767904i	$0.721300\pi$
$284$	−432.718	+	123.404i	−1.52366	+	0.434521i
$285$	−21.8202	+	32.0451i	−0.0765621	+	0.112439i
$286$	523.588	+	108.389i	1.83073	+	0.378983i
$287$	−235.757	+	235.757i	−0.821454	+	0.821454i
$288$	−99.4775	−	87.1069i	−0.345408	−	0.302455i
$289$	−205.190	−	66.6703i	−0.710000	−	0.230693i
$290$	45.1731	+	264.085i	0.155769	+	0.910636i
$291$	−78.7271	−	108.359i	−0.270540	−	0.372366i
$292$	−167.353	−	179.984i	−0.573125	−	0.616383i
$293$	9.60038	−	18.8418i	0.0327658	−	0.0643065i	−0.874043	−	0.485848i	$-0.838511\pi$
$293$	9.60038	−	18.8418i	0.0327658	−	0.0643065i	0.906809	+	0.421542i	$0.138511\pi$
$294$	4.20902	+	30.1064i	0.0143164	+	0.102403i
$295$	−126.893	−	59.8518i	−0.430147	−	0.202887i
$296$	−22.0695	+	102.734i	−0.0745592	+	0.347075i
$297$	288.033	−	136.434i	0.969810	−	0.459372i
$298$	−3.85909	−	1.33191i	−0.0129500	−	0.00446950i
$299$	−44.6680	+	61.4803i	−0.149391	+	0.205620i
$300$	217.001	−	39.8805i	0.723336	−	0.132935i
$301$	19.1873	+	59.0525i	0.0637452	+	0.196188i
$302$	108.040	−	32.9457i	0.357747	−	0.109092i
$303$	28.5595	−	180.318i	0.0942559	−	0.595108i
$304$	−29.6587	−	47.7703i	−0.0975616	−	0.157139i
$305$	442.071	+	56.2528i	1.44941	+	0.184435i
$306$	32.3724	−	182.821i	0.105792	−	0.597455i
$307$	29.1175	+	29.1175i	0.0948453	+	0.0948453i	0.752937	−	0.658092i	$-0.228636\pi$
$307$	29.1175	+	29.1175i	0.0948453	+	0.0948453i	−0.658092	+	0.752937i	$0.728636\pi$
$308$	72.5238	−	320.845i	0.235467	−	1.04170i
$309$		−	271.726i		−	0.879372i
$310$	213.322	−	218.651i	0.688136	−	0.705327i
$311$	−9.88022	−	3.21028i	−0.0317692	−	0.0103224i	0.293089	−	0.956085i	$-0.405317\pi$
$311$	−9.88022	−	3.21028i	−0.0317692	−	0.0103224i	−0.324858	+	0.945763i	$0.605317\pi$
$312$	−332.799	−	270.691i	−1.06666	−	0.867599i
$313$	−17.8548	+	112.731i	−0.0570442	+	0.360163i	0.942611	+	0.333894i	$0.108363\pi$
$313$	−17.8548	+	112.731i	−0.0570442	+	0.360163i	−0.999655	+	0.0262691i	$0.991637\pi$
$314$	281.666	+	150.025i	0.897024	+	0.477787i
$315$	−148.281	−	43.2251i	−0.470734	−	0.137223i
$316$	311.026	+	462.554i	0.984258	+	1.46378i
$317$	−43.0686	−	271.925i	−0.135863	−	0.857806i	−0.957634	−	0.287988i	$-0.907014\pi$
$317$	−43.0686	−	271.925i	−0.135863	−	0.857806i	0.821771	−	0.569818i	$-0.192986\pi$
$318$	−50.5048	−	17.4310i	−0.158820	−	0.0548144i
$319$	180.039	−	233.327i	0.564385	−	0.731432i
$320$	−74.7026	+	311.158i	−0.233445	+	0.972370i
$321$	−76.9400	+	105.899i	−0.239688	+	0.329903i
$322$	37.3168	+	28.1625i	0.115891	+	0.0874612i
$323$	35.8444	−	70.3486i	0.110973	−	0.217797i
$324$	−106.882	−	3.88692i	−0.329883	−	0.0119967i
$325$	−593.207	+	131.471i	−1.82525	+	0.404527i
$326$	176.748	−	170.437i	0.542171	−	0.522813i
$327$	149.697	−	76.2744i	0.457789	−	0.233255i
$328$	−356.255	−	19.4443i	−1.08614	−	0.0592815i
$329$	10.8433			0.0329584
$330$	−193.961	−	145.882i	−0.587761	−	0.442067i
$331$			138.206i			0.417541i	0.977965	+	0.208771i	$0.0669462\pi$
$331$			138.206i			0.417541i	−0.977965	+	0.208771i	$0.933054\pi$
$332$	−375.530	−	208.869i	−1.13111	−	0.629124i
$333$	−24.6395	−	48.3577i	−0.0739925	−	0.145218i
$334$	−78.4534	+	75.6522i	−0.234890	+	0.226504i
$335$	10.8098	+	354.174i	0.0322679	+	1.05724i
$336$	−170.222	+	201.677i	−0.506613	+	0.600229i
$337$	−46.3347	−	23.6087i	−0.137492	−	0.0700555i	0.383891	−	0.923378i	$-0.374584\pi$
$337$	−46.3347	−	23.6087i	−0.137492	−	0.0700555i	−0.521383	+	0.853323i	$0.674584\pi$
$338$	673.182	+	508.042i	1.99166	+	1.50308i
$339$	−172.271	−	125.162i	−0.508175	−	0.369211i
$340$	−428.144	+	136.354i	−1.25925	+	0.401041i
$341$	−335.882	−	9.70096i	−0.984992	−	0.0284486i
$342$	27.4531	+	9.47503i	0.0802722	+	0.0277048i
$343$	310.941	−	49.2483i	0.906534	−	0.143581i
$344$	−33.3468	+	57.4705i	−0.0969383	+	0.167065i
$345$	30.2423	−	16.5903i	0.0876590	−	0.0480877i
$346$	−10.7611	−	5.73173i	−0.0311013	−	0.0165657i
$347$	291.621	+	46.1882i	0.840406	+	0.133107i	0.561774	−	0.827291i	$-0.310119\pi$
$347$	291.621	+	46.1882i	0.840406	+	0.133107i	0.278632	+	0.960398i	$0.410119\pi$
$348$	−214.441	+	99.6186i	−0.616209	+	0.286260i
$349$	38.4443	−	118.319i	0.110156	−	0.339024i	−0.880750	−	0.473581i	$-0.842961\pi$
$349$	38.4443	−	118.319i	0.110156	−	0.339024i	0.990906	+	0.134557i	$0.0429612\pi$
$350$	74.2350	+	366.349i	0.212100	+	1.04671i
$351$	704.182			2.00622
$352$	307.452	−	171.398i	0.873443	−	0.486927i
$353$	27.2983	−	27.2983i	0.0773324	−	0.0773324i	−0.667383	−	0.744715i	$-0.732585\pi$
$353$	27.2983	−	27.2983i	0.0773324	−	0.0773324i	0.744715	+	0.667383i	$0.232585\pi$
$354$	21.5893	−	121.924i	0.0609866	−	0.344418i
$355$	−557.964	−	71.0000i	−1.57173	−	0.200000i
$356$	−229.102	−	83.7612i	−0.643545	−	0.235284i
$357$	−366.012	−	57.9706i	−1.02524	−	0.162383i
$358$	232.429	−	70.8773i	0.649244	−	0.197981i
$359$	1.11809	−	0.363291i	0.00311447	−	0.00101195i	−0.307459	−	0.951561i	$-0.599479\pi$
$359$	1.11809	−	0.363291i	0.00311447	−	0.00101195i	0.310574	+	0.950549i	$0.399479\pi$
$360$	−71.4782	−	149.026i	−0.198551	−	0.413960i
$361$	−282.064	−	204.931i	−0.781340	−	0.567677i
$362$	−359.903	−	124.215i	−0.994208	−	0.343136i
$363$	26.4748	+	265.652i	0.0729333	+	0.731824i
$364$	448.276	−	572.063i	1.23153	−	1.57160i
$365$	−103.802	−	289.140i	−0.284388	−	0.792164i
$366$	54.4544	+	389.503i	0.148782	+	1.06422i
$367$	64.4758	+	32.8521i	0.175683	+	0.0895151i	0.539621	−	0.841908i	$-0.318568\pi$
$367$	64.4758	+	32.8521i	0.175683	+	0.0895151i	−0.363937	+	0.931423i	$0.618568\pi$
$368$	4.21635	+	49.8507i	0.0114575	+	0.135464i
$369$	149.086	−	108.317i	0.404028	−	0.293543i
$370$	−75.8875	+	107.207i	−0.205101	+	0.289748i
$371$	27.9713	−	86.0867i	0.0753942	−	0.232040i
$372$	235.603	+	131.042i	0.633341	+	0.352263i
$373$	−254.086	−	254.086i	−0.681195	−	0.681195i	0.279074	−	0.960270i	$-0.409972\pi$
$373$	−254.086	−	254.086i	−0.681195	−	0.681195i	−0.960270	+	0.279074i	$0.909972\pi$
$374$	429.353	+	244.856i	1.14800	+	0.654696i
$375$	268.987	+	60.8925i	0.717300	+	0.162380i
$376$	7.74557	+	8.63988i	0.0205999	+	0.0229784i
$377$	580.183	−	295.618i	1.53895	−	0.784133i
$378$	7.87328	−	433.139i	0.0208288	−	1.14587i
$379$	149.015	−	108.266i	0.393180	−	0.285662i	−0.373577	−	0.927599i	$-0.621869\pi$
$379$	149.015	−	108.266i	0.393180	−	0.285662i	0.766757	+	0.641937i	$0.221869\pi$
$380$	−10.5896	−	69.4833i	−0.0278673	−	0.182851i
$381$	479.252	−	155.719i	1.25788	−	0.408710i
$382$	−451.855	−	341.009i	−1.18287	−	0.892693i
$383$	48.1389	+	303.937i	0.125689	+	0.793569i	0.967328	+	0.253528i	$0.0815910\pi$
$383$	48.1389	+	303.937i	0.125689	+	0.793569i	−0.841639	+	0.540040i	$0.818409\pi$
$384$	−282.287	+	8.42958i	−0.735122	+	0.0219520i
$385$	241.137	−	333.042i	0.626330	−	0.865045i
$386$	−314.672	−	646.358i	−0.815214	−	1.67450i
$387$	−5.36864	−	33.8962i	−0.0138724	−	0.0875872i
$388$	238.295	+	46.6771i	0.614163	+	0.120302i
$389$	−40.6797	+	13.2176i	−0.104575	+	0.0339785i	−0.360837	−	0.932629i	$-0.617509\pi$
$389$	−40.6797	+	13.2176i	−0.104575	+	0.0339785i	0.256262	+	0.966607i	$0.417509\pi$
$390$	−249.320	−	474.747i	−0.639282	−	1.21730i
$391$	−56.8323	+	41.2911i	−0.145351	+	0.105604i
$392$	−42.7550	−	34.7760i	−0.109069	−	0.0887142i
$393$	10.0840	−	5.13804i	0.0256589	−	0.0130739i
$394$	296.498	+	52.5014i	0.752534	+	0.133252i
$395$	129.939	+	684.524i	0.328958	+	1.73297i
$396$	−67.3327	+	168.881i	−0.170032	+	0.426468i
$397$	116.524	+	116.524i	0.293512	+	0.293512i	0.838466	−	0.544954i	$-0.183453\pi$
$397$	116.524	+	116.524i	0.293512	+	0.293512i	−0.544954	+	0.838466i	$0.683453\pi$
$398$	−72.8931	−	104.262i	−0.183149	−	0.261966i
$399$	17.9125	−	55.1290i	0.0448935	−	0.138168i
$400$	−238.877	+	320.839i	−0.597193	+	0.802098i
$401$	367.548	−	267.039i	0.916578	−	0.665933i	−0.0260920	−	0.999660i	$-0.508306\pi$
$401$	367.548	−	267.039i	0.916578	−	0.665933i	0.942670	+	0.333727i	$0.108306\pi$
$402$	−299.120	+	91.2140i	−0.744079	+	0.226901i
$403$	−661.508	−	337.055i	−1.64146	−	0.836365i
$404$	184.686	+	274.663i	0.457145	+	0.679860i
$405$	−120.915	−	57.0321i	−0.298557	−	0.140820i
$406$	−175.347	−	360.174i	−0.431888	−	0.887127i
$407$	143.297	−	18.4728i	0.352080	−	0.0453876i
$408$	−215.258	−	333.045i	−0.527593	−	0.816287i
$409$	−465.248	−	338.023i	−1.13753	−	0.826461i	−0.150753	−	0.988571i	$-0.548170\pi$
$409$	−465.248	−	338.023i	−1.13753	−	0.826461i	−0.986773	+	0.162111i	$0.948170\pi$
$410$	−399.840	−	197.554i	−0.975219	−	0.481839i
$411$	−180.738	+	58.7253i	−0.439751	+	0.142884i
$412$	335.449	+	360.768i	0.814197	+	0.875651i
$413$	207.191	+	32.8159i	0.501674	+	0.0794574i
$414$	−17.9365	−	18.6007i	−0.0433250	−	0.0449292i
$415$	−328.830	−	424.718i	−0.792361	−	1.02342i
$416$	776.026	−	51.4508i	1.86545	−	0.123680i
$417$	−327.810	+	327.810i	−0.786114	+	0.786114i
$418$	−48.3356	+	60.3419i	−0.115635	+	0.144359i
$419$	−91.7096			−0.218877			−0.109439	−	0.993994i	$-0.534905\pi$
$419$	−91.7096			−0.218877			−0.109439	+	0.993994i	$0.534905\pi$
$420$	−294.802	+	148.048i	−0.701911	+	0.352494i
$421$	−39.9193	+	122.859i	−0.0948201	+	0.291826i	−0.987207	−	0.159445i	$-0.949029\pi$
$421$	−39.9193	+	122.859i	−0.0948201	+	0.291826i	0.892387	+	0.451272i	$0.149029\pi$
$422$	6.53828	−	359.696i	0.0154935	−	0.852359i
$423$	−5.91946	−	0.937551i	−0.0139940	−	0.00221643i
$424$	88.5736	−	39.2058i	0.208900	−	0.0924666i
$425$	−559.077	−	53.8687i	−1.31547	−	0.126750i
$426$	−68.7301	−	491.615i	−0.161338	−	1.15403i
$427$	−658.102	+	104.233i	−1.54122	+	0.244106i
$428$	−28.5809	−	235.584i	−0.0667778	−	0.550431i
$429$	−198.395	+	555.490i	−0.462459	+	1.29485i
$430$	−66.5860	+	49.6440i	−0.154851	+	0.115451i
$431$	−514.937	−	374.123i	−1.19475	−	0.868036i	−0.200991	−	0.979593i	$-0.564416\pi$
$431$	−514.937	−	374.123i	−1.19475	−	0.868036i	−0.993758	+	0.111557i	$0.964416\pi$
$432$	350.746	−	303.125i	0.811912	−	0.701678i
$433$	334.013	+	170.188i	0.771392	+	0.393044i	0.794947	−	0.606679i	$-0.207498\pi$
$433$	334.013	+	170.188i	0.771392	+	0.393044i	−0.0235550	+	0.999723i	$0.507498\pi$
$434$	−214.717	+	403.122i	−0.494740	+	0.928853i
$435$	−295.425	+	9.01668i	−0.679138	+	0.0207280i
$436$	−104.590	+	286.072i	−0.239884	+	0.656127i
$437$	−4.98865	−	9.79077i	−0.0114157	−	0.0224045i
$438$	222.203	−	155.349i	0.507313	−	0.354679i
$439$			127.663i			0.290804i	0.989373	+	0.145402i	$0.0464476\pi$
$439$			127.663i			0.290804i	−0.989373	+	0.145402i	$0.953552\pi$
$440$	437.614	−	45.7613i	0.994577	−	0.104003i
$441$	28.4657			0.0645480
$442$	625.734	+	895.016i	1.41569	+	2.02492i
$443$	−414.379	+	211.137i	−0.935393	+	0.476606i	−0.854114	−	0.520085i	$-0.825900\pi$
$443$	−414.379	+	211.137i	−0.935393	+	0.476606i	−0.0812782	+	0.996691i	$0.525900\pi$
$444$	−108.871	−	39.8040i	−0.245206	−	0.0896487i
$445$	−222.086	−	208.931i	−0.499070	−	0.469508i
$446$	−716.784	−	381.785i	−1.60714	−	0.856020i
$447$	2.04463	−	4.01281i	0.00457411	−	0.00897720i
$448$	−22.9706	−	477.906i	−0.0512736	−	1.06675i
$449$	−100.112	+	137.793i	−0.222967	+	0.306888i	−0.905816	−	0.423672i	$-0.860741\pi$
$449$	−100.112	+	137.793i	−0.222967	+	0.306888i	0.682849	+	0.730560i	$0.260741\pi$
$450$	−8.84971	−	206.412i	−0.0196660	−	0.458692i
$451$	138.064	+	470.751i	0.306129	+	1.04379i
$452$	383.238	−	46.4941i	0.847871	−	0.102863i
$453$	19.4925	+	123.071i	0.0430298	+	0.271679i
$454$	−826.806	+	115.591i	−1.82116	+	0.254606i
$455$	796.497	−	436.940i	1.75054	−	0.960308i
$456$	56.7216	−	25.1070i	0.124389	−	0.0550592i
$457$	−112.778	+	712.054i	−0.246780	+	1.55811i	0.483739	+	0.875212i	$0.339278\pi$
$457$	−112.778	+	712.054i	−0.246780	+	1.55811i	−0.730518	+	0.682893i	$0.760722\pi$
$458$	772.324	+	14.0387i	1.68630	+	0.0306522i
$459$	619.085	+	201.153i	1.34877	+	0.438241i
$460$	−19.6716	+	59.3613i	−0.0427643	+	0.129046i
$461$			794.261i			1.72291i	0.507834	+	0.861455i	$0.330446\pi$
$461$			794.261i			1.72291i	−0.507834	+	0.861455i	$0.669554\pi$
$462$	339.461	+	128.243i	0.734765	+	0.277582i
$463$	460.952	+	460.952i	0.995577	+	0.995577i	0.999990	−	0.00441279i	$-0.00140464\pi$
$463$	460.952	+	460.952i	0.995577	+	0.995577i	−0.00441279	+	0.999990i	$0.501405\pi$
$464$	161.731	−	396.993i	0.348557	−	0.855588i
$465$	206.304	+	266.463i	0.443664	+	0.573038i
$466$	−199.879	+	192.742i	−0.428925	+	0.413610i
$467$	28.8788	−	182.333i	0.0618389	−	0.390435i	−0.937284	−	0.348566i	$-0.886669\pi$
$467$	28.8788	−	182.333i	0.0618389	−	0.390435i	0.999123	−	0.0418693i	$-0.0133313\pi$
$468$	−294.180	+	273.534i	−0.628590	+	0.584475i
$469$	−163.717	−	503.870i	−0.349077	−	1.07435i
$470$	4.65193	+	13.7382i	0.00989772	+	0.0292301i
$471$	−206.932	+	284.818i	−0.439347	+	0.604709i
$472$	121.853	+	188.530i	0.258163	+	0.399427i
$473$	89.7861	+	16.8912i	0.189823	+	0.0357108i
$474$	−552.870	+	269.159i	−1.16639	+	0.567845i
$475$	22.0030	−	85.0572i	0.0463222	−	0.179068i
$476$	557.517	−	374.880i	1.17125	−	0.787562i
$477$	−22.7131	+	44.5769i	−0.0476165	+	0.0934527i
$478$	178.391	+	585.002i	0.373203	+	1.22385i
$479$	−242.012	−	333.102i	−0.505245	−	0.695410i	0.477863	−	0.878434i	$-0.341411\pi$
$479$	−242.012	−	333.102i	−0.505245	−	0.695410i	−0.983108	+	0.183024i	$0.941411\pi$
$480$	−328.545	−	129.144i	−0.684470	−	0.269049i
$481$	303.604	+	98.6469i	0.631193	+	0.205087i
$482$	−193.493	+	135.277i	−0.401437	+	0.280658i
$483$	−36.4688	+	36.4688i	−0.0755048	+	0.0755048i
$484$	−363.102	−	320.021i	−0.750210	−	0.661200i
$485$	250.889	+	170.836i	0.517297	+	0.352239i
$486$	−70.3611	+	397.360i	−0.144776	+	0.817613i
$487$	−368.760	−	723.732i	−0.757208	−	1.48610i	−0.870302	−	0.492519i	$-0.836076\pi$
$487$	−368.760	−	723.732i	−0.757208	−	1.48610i	0.113094	−	0.993584i	$-0.463924\pi$
$488$	−553.145	−	449.915i	−1.13349	−	0.921958i
$489$	159.214	+	219.139i	0.325590	+	0.448137i
$490$	−32.0304	−	60.9912i	−0.0653681	−	0.124472i
$491$	−154.806	−	476.443i	−0.315287	−	0.970353i	−0.975636	−	0.219394i	$-0.929592\pi$
$491$	−154.806	−	476.443i	−0.315287	−	0.970353i	0.660350	−	0.750958i	$-0.270408\pi$
$492$	75.6595	−	386.256i	0.153779	−	0.785073i
$493$	594.516	−	94.1620i	1.20591	−	0.190998i
$494$	−153.588	+	74.7728i	−0.310908	+	0.151362i
$495$	−160.435	+	160.961i	−0.324110	+	0.325174i
$496$	−474.581	+	116.872i	−0.956816	+	0.235628i
$497$	830.630	−	131.559i	1.67129	−	0.264706i
$498$	285.559	−	378.381i	0.573412	−	0.759802i
$499$	23.9614	+	73.7457i	0.0480189	+	0.147787i	0.972191	−	0.234189i	$-0.0752436\pi$
$499$	23.9614	+	73.7457i	0.0480189	+	0.147787i	−0.924172	+	0.381976i	$0.875244\pi$
$500$	−432.305	+	251.222i	−0.864610	+	0.502444i
$501$	−70.6705	−	97.2696i	−0.141059	−	0.194151i
$502$	−192.973	−	3.50772i	−0.384409	−	0.00698750i
$503$	−159.293	−	312.630i	−0.316686	−	0.621531i	0.676712	−	0.736247i	$-0.263404\pi$
$503$	−159.293	−	312.630i	−0.316686	−	0.621531i	−0.993398	+	0.114716i	$0.963404\pi$
$504$	164.961	+	184.007i	0.327303	+	0.365094i
$505$	77.1572	+	406.469i	0.152787	+	0.804890i
$506$	62.6929	−	28.3125i	0.123899	−	0.0559536i
$507$	−657.885	+	657.885i	−1.29760	+	1.29760i
$508$	−444.063	+	798.390i	−0.874139	+	1.57163i
$509$	795.866	+	258.593i	1.56359	+	0.508041i	0.957763	−	0.287557i	$-0.0928432\pi$
$509$	795.866	+	258.593i	1.56359	+	0.508041i	0.605825	+	0.795598i	$0.292843\pi$
$510$	−83.5770	−	488.596i	−0.163877	−	0.958031i
$511$	269.988	+	371.607i	0.528352	+	0.727214i
$512$	364.383	−	359.679i	0.711686	−	0.702497i
$513$	−46.2263	+	90.7242i	−0.0901097	+	0.176850i
$514$	−604.876	+	84.5645i	−1.17680	+	0.164522i
$515$	208.065	+	579.566i	0.404009	+	1.12537i
$516$	−57.6958	−	45.2112i	−0.111814	−	0.0876186i
$517$	7.65073	−	14.0008i	0.0147983	−	0.0270809i
$518$	64.0718	−	185.643i	0.123691	−	0.358383i
$519$	7.90587	−	10.8815i	0.0152329	−	0.0209663i
$520$	917.101	+	322.529i	1.76366	+	0.620248i
$521$	82.1904	+	252.956i	0.157755	+	0.485520i	0.998430	−	0.0560205i	$-0.0178412\pi$
$521$	82.1904	+	252.956i	0.157755	+	0.485520i	−0.840675	+	0.541541i	$0.817841\pi$
$522$	64.5813	+	211.783i	0.123719	+	0.405714i
$523$	43.1088	−	272.178i	0.0824260	−	0.520417i	−0.911583	−	0.411117i	$-0.865139\pi$
$523$	43.1088	−	272.178i	0.0824260	−	0.520417i	0.994009	−	0.109301i	$-0.0348611\pi$
$524$	−7.04542	+	19.2705i	−0.0134455	+	0.0367758i
$525$	−411.593	+	25.1479i	−0.783987	+	0.0479008i
$526$	−557.000	−	98.6287i	−1.05893	−	0.187507i
$527$	−485.287	−	485.287i	−0.920847	−	0.920847i
$528$	140.300	+	362.086i	0.265719	+	0.685769i
$529$		−	519.223i		−	0.981518i
$530$	121.069	−	1.49362i	0.228432	−	0.00281815i
$531$	−110.270	−	35.8289i	−0.207665	−	0.0674745i
$532$	44.2752	+	95.3075i	0.0832241	+	0.179150i
$533$	−169.562	+	1070.57i	−0.318127	+	2.00858i
$534$	126.507	−	237.511i	0.236905	−	0.444778i
$535$	83.0174	−	284.786i	0.155173	−	0.532311i
$536$	284.534	−	490.371i	0.530847	−	0.914872i
$537$	41.9349	+	264.766i	0.0780910	+	0.493047i
$538$	66.8224	−	193.612i	0.124205	−	0.359874i
$539$	−25.4880	+	71.3644i	−0.0472876	+	0.132401i
$540$	552.151	−	175.847i	1.02250	−	0.325643i
$541$	−326.076	+	448.806i	−0.602729	+	0.829585i	−0.995955	−	0.0898569i	$-0.971359\pi$
$541$	−326.076	+	448.806i	−0.602729	+	0.829585i	0.393226	+	0.919442i	$0.371359\pi$
$542$	−583.985	+	773.811i	−1.07746	+	1.42770i
$543$	190.684	−	374.239i	0.351168	−	0.689206i
$544$	696.944	+	176.442i	1.28115	+	0.324343i
$545$	−260.885	+	277.311i	−0.478688	+	0.508828i
$546$	556.535	+	577.142i	1.01930	+	1.05704i
$547$	106.830	−	54.4328i	0.195302	−	0.0995115i	−0.353605	−	0.935395i	$-0.615044\pi$
$547$	106.830	−	54.4328i	0.195302	−	0.0995115i	0.548907	+	0.835884i	$0.315044\pi$
$548$	167.467	−	301.092i	0.305597	−	0.549438i
$549$	368.276			0.670812
$550$	525.405	+	162.634i	0.955282	+	0.295697i
$551$			94.1547i			0.170880i
$552$	−55.1084	−	3.00781i	−0.0998340	−	0.00544893i
$553$	−472.951	−	928.218i	−0.855245	−	1.67851i
$554$	−104.565	−	108.437i	−0.188746	−	0.195735i
$555$	−105.537	−	99.2859i	−0.190157	−	0.178894i
$556$	30.5448	−	839.916i	0.0549367	−	1.51064i
$557$	267.437	+	136.266i	0.480138	+	0.244643i	0.677270	−	0.735734i	$-0.263163\pi$
$557$	267.437	+	136.266i	0.480138	+	0.244643i	−0.197132	+	0.980377i	$0.563163\pi$
$558$	152.071	−	201.502i	0.272529	−	0.361116i
$559$	163.307	+	118.650i	0.292141	+	0.212253i
$560$	208.640	−	560.499i	0.372572	−	1.00089i
$561$	−333.098	+	431.689i	−0.593758	+	0.769499i
$562$	196.739	−	570.035i	0.350070	−	1.01430i
$563$	−148.417	+	23.5070i	−0.263618	+	0.0417530i	−0.286844	−	0.957977i	$-0.592606\pi$
$563$	−148.417	+	23.5070i	−0.263618	+	0.0417530i	0.0232260	+	0.999730i	$0.492606\pi$
$564$	−10.6226	+	7.14273i	−0.0188344	+	0.0126644i
$565$	463.277	+	135.049i	0.819960	+	0.239025i
$566$	209.351	−	393.048i	0.369879	−	0.694431i
$567$	197.431	+	31.2699i	0.348202	+	0.0551498i
$568$	698.158	+	567.865i	1.22915	+	0.999762i
$569$	31.6886	−	97.5274i	0.0556917	−	0.171401i	−0.919342	−	0.393461i	$-0.871278\pi$
$569$	31.6886	−	97.5274i	0.0556917	−	0.171401i	0.975033	+	0.222059i	$0.0712778\pi$
$570$	77.5314	−	0.956499i	0.136020	−	0.00167807i
$571$	680.148			1.19115			0.595576	−	0.803299i	$-0.296924\pi$
$571$	680.148			1.19115			0.595576	+	0.803299i	$0.296924\pi$
$572$	−422.352	−	982.441i	−0.738378	−	1.71755i
$573$	441.587	−	441.587i	0.770658	−	0.770658i
$574$	656.608	+	116.267i	1.14392	+	0.202555i
$575$	−51.8006	+	58.5425i	−0.0900881	+	0.101813i
$576$	−28.7815	+	262.879i	−0.0499679	+	0.456387i
$577$	−951.374	−	150.683i	−1.64883	−	0.261149i	−0.738263	−	0.674513i	$-0.764354\pi$
$577$	−951.374	−	150.683i	−1.64883	−	0.261149i	−0.910566	+	0.413364i	$0.864354\pi$
$578$	125.860	+	412.736i	0.217751	+	0.714075i
$579$	754.242	−	245.068i	1.30266	−	0.423261i
$580$	381.102	−	376.678i	0.657073	−	0.649444i
$581$	649.732	+	472.058i	1.11830	+	0.812492i
$582$	−87.3950	+	253.220i	−0.150163	+	0.435085i
$583$	−91.4187	−	96.8565i	−0.156807	−	0.166135i
$584$	−103.236	+	480.569i	−0.176775	+	0.822892i
$585$	−472.593	+	169.661i	−0.807852	+	0.290019i
$586$	−41.8860	+	5.85586i	−0.0714778	+	0.00999293i
$587$	−117.183	−	59.7076i	−0.199630	−	0.101717i	0.351318	−	0.936256i	$-0.385734\pi$
$587$	−117.183	−	59.7076i	−0.199630	−	0.101717i	−0.550948	+	0.834540i	$0.685734\pi$
$588$	44.5250	−	41.4002i	0.0757228	−	0.0704085i
$589$	86.8499	−	63.1002i	0.147453	−	0.107131i
$590$	47.3111	+	276.583i	0.0801884	+	0.468785i
$591$	−102.649	+	315.920i	−0.173686	+	0.534551i
$592$	193.686	−	81.5556i	0.327173	−	0.137763i
$593$	−247.701	−	247.701i	−0.417708	−	0.417708i	0.466705	−	0.884413i	$-0.345441\pi$
$593$	−247.701	−	247.701i	−0.417708	−	0.417708i	−0.884413	+	0.466705i	$0.845441\pi$
$594$	−553.710	−	315.776i	−0.932172	−	0.531609i
$595$	825.058	−	156.615i	1.38665	−	0.263219i
$596$	2.23923	+	7.85189i	0.00375710	+	0.0131743i
$597$	125.046	−	63.7139i	0.209457	−	0.106723i
$598$	151.963	+	2.76226i	0.254118	+	0.00461917i
$599$	90.6094	−	65.8316i	0.151268	−	0.109902i	−0.509577	−	0.860425i	$-0.670198\pi$
$599$	90.6094	−	65.8316i	0.151268	−	0.109902i	0.660845	+	0.750523i	$0.270198\pi$
$600$	−314.046	−	309.991i	−0.523409	−	0.516652i
$601$	652.420	−	211.984i	1.08556	−	0.352719i	0.289029	−	0.957320i	$-0.406668\pi$
$601$	652.420	−	211.984i	1.08556	−	0.352719i	0.796528	+	0.604602i	$0.206668\pi$
$602$	74.8067	−	99.1229i	0.124264	−	0.164656i
$603$	45.8083	+	289.222i	0.0759673	+	0.479639i
$604$	−177.812	−	139.336i	−0.294391	−	0.230689i
$605$	−259.882	−	546.339i	−0.429557	−	0.903040i
$606$	−328.293	+	159.826i	−0.541738	+	0.263739i
$607$	93.2153	+	588.538i	0.153567	+	0.969585i	0.937309	+	0.348498i	$0.113308\pi$
$607$	93.2153	+	588.538i	0.153567	+	0.969585i	−0.783742	+	0.621086i	$0.786692\pi$
$608$	−44.3138	+	103.358i	−0.0728846	+	0.169997i
$609$	420.290	−	136.561i	0.690132	−	0.224237i
$610$	−414.394	−	789.077i	−0.679335	−	1.29357i
$611$	28.5191	−	20.7203i	0.0466761	−	0.0339122i
$612$	−336.766	+	156.445i	−0.550271	+	0.255629i
$613$	−862.749	+	439.593i	−1.40742	+	0.717117i	−0.982176	−	0.187961i	$-0.939812\pi$
$613$	−862.749	+	439.593i	−1.40742	+	0.717117i	−0.425245	+	0.905078i	$0.639812\pi$
$614$	14.3596	−	81.0952i	0.0233870	−	0.132077i
$615$	276.910	−	406.669i	0.450261	−	0.661251i
$616$	−609.017	+	248.803i	−0.988664	+	0.403900i
$617$	362.297	+	362.297i	0.587191	+	0.587191i	0.936870	−	0.349679i	$-0.113709\pi$
$617$	362.297	+	362.297i	0.587191	+	0.587191i	−0.349679	+	0.936870i	$0.613709\pi$
$618$	−445.395	+	311.390i	−0.720703	+	0.503867i
$619$	−194.146	+	597.519i	−0.313644	+	0.965298i	0.662665	+	0.748916i	$0.269426\pi$
$619$	−194.146	+	597.519i	−0.313644	+	0.965298i	−0.976309	+	0.216382i	$0.930574\pi$
$620$	−602.859	−	99.0953i	−0.972354	−	0.159831i
$621$	73.2931	−	53.2505i	0.118024	−	0.0857497i
$622$	6.06037	+	19.8739i	0.00974336	+	0.0319516i
$623$	406.215	+	206.977i	0.652031	+	0.332226i
$624$	−62.3205	+	855.705i	−0.0998725	+	1.37132i
$625$	−620.351	+	76.0897i	−0.992562	+	0.121743i
$626$	205.242	−	99.9199i	0.327863	−	0.159616i
$627$	−58.5436	−	62.0259i	−0.0933709	−	0.0989248i
$628$	−76.8692	−	633.611i	−0.122403	−	1.00894i
$629$	238.736	+	173.452i	0.379548	+	0.275758i
$630$	99.0741	+	292.587i	0.157260	+	0.464424i
$631$	262.751	−	85.3730i	0.416404	−	0.135298i	−0.0933192	−	0.995636i	$-0.529748\pi$
$631$	262.751	−	85.3730i	0.416404	−	0.135298i	0.509723	+	0.860338i	$0.329748\pi$
$632$	401.761	−	1039.88i	0.635697	−	1.64539i
$633$	391.986	+	62.0846i	0.619252	+	0.0980799i
$634$	−396.365	+	382.213i	−0.625181	+	0.602859i
$635$	−902.964	+	699.104i	−1.42199	+	1.10095i
$636$	29.3053	+	102.759i	0.0460775	+	0.161571i
$637$	−118.392	+	118.392i	−0.185859	+	0.185859i
$638$	−588.772	−	27.7218i	−0.922840	−	0.0434510i
$639$	−464.823			−0.727422
$640$	595.636	−	234.131i	0.930682	−	0.365829i
$641$	−20.0396	+	61.6756i	−0.0312631	+	0.0962179i	−0.965470	−	0.260512i	$-0.916108\pi$
$641$	−20.0396	+	61.6756i	−0.0312631	+	0.0962179i	0.934207	+	0.356730i	$0.116108\pi$
$642$	261.753	+	4.75795i	0.407715	+	0.00741114i
$643$	−191.822	−	30.3816i	−0.298324	−	0.0472498i	0.00547840	−	0.999985i	$-0.498256\pi$
$643$	−191.822	−	30.3816i	−0.298324	−	0.0472498i	−0.303802	+	0.952735i	$0.598256\pi$
$644$	3.39811	−	93.4406i	0.00527657	−	0.145094i
$645$	−44.0679	−	80.3313i	−0.0683224	−	0.124545i
$646$	−156.387	+	21.8637i	−0.242085	+	0.0338447i
$647$	1220.56	−	193.317i	1.88649	−	0.298790i	0.896845	−	0.442346i	$-0.145854\pi$
$647$	1220.56	−	193.317i	1.88649	−	0.298790i	0.989642	+	0.143556i	$0.0458536\pi$
$648$	116.112	+	179.648i	0.179186	+	0.277234i
$649$	188.560	−	244.370i	0.290539	−	0.376533i
$650$	895.297	+	821.683i	1.37738	+	1.26413i
$651$	−407.634	−	296.163i	−0.626166	−	0.454936i
$652$	−481.916	−	94.3974i	−0.739136	−	0.144781i
$653$	−850.168	−	433.182i	−1.30194	−	0.663372i	−0.340984	−	0.940069i	$-0.610760\pi$
$653$	−850.168	−	433.182i	−1.30194	−	0.663372i	−0.960957	+	0.276697i	$0.910760\pi$
$654$	−296.572	−	157.965i	−0.453474	−	0.241536i
$655$	−17.5739	+	18.6804i	−0.0268303	+	0.0285197i
$656$	376.386	+	606.231i	0.573758	+	0.924133i
$657$	−115.258	−	226.207i	−0.175431	−	0.344303i
$658$	−12.4261	−	17.7736i	−0.0188847	−	0.0270116i
$659$		−	363.622i		−	0.551779i	−0.961189	−	0.275890i	$-0.911028\pi$
$659$		−	363.622i		−	0.551779i	0.961189	−	0.275890i	$-0.0889724\pi$
$660$	−16.8462	+	485.104i	−0.0255245	+	0.735007i
$661$	−264.611			−0.400319			−0.200159	−	0.979763i	$-0.564146\pi$
$661$	−264.611			−0.400319			−0.200159	+	0.979763i	$0.564146\pi$
$662$	226.538	−	158.380i	0.342203	−	0.239245i
$663$	−1073.43	+	546.938i	−1.61904	+	0.824943i
$664$	87.9820	+	854.901i	0.132503	+	1.28750i
$665$	4.00744	+	131.301i	0.00602622	+	0.197445i
$666$	−51.0286	+	95.8039i	−0.0766195	+	0.143850i
$667$	38.0322	−	74.6424i	0.0570198	−	0.111908i
$668$	213.909	+	41.9004i	0.320223	+	0.0627251i
$669$	526.603	−	724.807i	0.787149	−	1.08342i
$670$	568.150	−	423.591i	0.847985	−	0.632226i
$671$	−329.752	+	923.280i	−0.491434	+	1.37598i
$672$	525.644	+	47.9005i	0.782208	+	0.0712805i
$673$	149.072	+	941.205i	0.221504	+	1.39852i	0.808293	+	0.588781i	$0.200392\pi$
$673$	149.072	+	941.205i	0.221504	+	1.39852i	−0.586789	+	0.809740i	$0.699608\pi$
$674$	14.4004	+	103.004i	0.0213655	+	0.152824i
$675$	721.007	+	69.4712i	1.06816	+	0.102920i
$676$	61.3007	−	1685.63i	0.0906815	−	2.49354i
$677$	−52.8761	+	333.846i	−0.0781035	+	0.493126i	0.917366	+	0.398045i	$0.130311\pi$
$677$	−52.8761	+	333.846i	−0.0781035	+	0.493126i	−0.995470	+	0.0950813i	$0.969689\pi$
$678$	−7.74001	+	425.808i	−0.0114160	+	0.628035i
$679$	−431.619	−	140.242i	−0.635669	−	0.206541i
$680$	714.142	+	545.527i	1.05021	+	0.802246i
$681$		−	920.982i		−	1.35240i
$682$	369.010	+	561.672i	0.541070	+	0.823566i
$683$	−325.755	−	325.755i	−0.476948	−	0.476948i	0.427206	−	0.904154i	$-0.359498\pi$
$683$	−325.755	−	325.755i	−0.476948	−	0.476948i	−0.904154	+	0.427206i	$0.859498\pi$
$684$	−15.9296	−	55.8573i	−0.0232889	−	0.0816628i
$685$	340.530	−	263.649i	0.497124	−	0.384889i
$686$	−437.054	−	453.237i	−0.637105	−	0.660695i
$687$	−133.305	+	841.658i	−0.194040	+	1.22512i
$688$	132.416	−	11.1997i	0.192465	−	0.0162786i
$689$	−90.9343	−	279.867i	−0.131980	−	0.406193i
$690$	−61.8505	−	30.5592i	−0.0896383	−	0.0442888i
$691$	222.977	−	306.902i	0.322687	−	0.444141i	−0.616598	−	0.787278i	$-0.711490\pi$
$691$	222.977	−	306.902i	0.322687	−	0.444141i	0.939285	+	0.343137i	$0.111490\pi$
$692$	2.93679	+	24.2072i	0.00424392	+	0.0349815i
$693$	162.941	−	298.181i	0.235124	−	0.430276i
$694$	−258.480	−	530.936i	−0.372450	−	0.765037i
$695$	448.178	−	950.196i	0.644861	−	1.36719i
$696$	409.031	+	237.337i	0.587688	+	0.341001i
$697$	−454.885	+	892.762i	−0.652632	+	1.28086i
$698$	−237.997	+	72.5751i	−0.340970	+	0.103976i
$699$	−180.050	−	247.818i	−0.257582	−	0.354532i
$700$	515.424	−	541.506i	0.736319	−	0.773580i
$701$	558.942	+	181.611i	0.797349	+	0.259074i	0.679230	−	0.733925i	$-0.262314\pi$
$701$	558.942	+	181.611i	0.797349	+	0.259074i	0.118119	+	0.992999i	$0.462314\pi$
$702$	−806.971	−	1154.25i	−1.14953	−	1.64423i
$703$	−32.6395	+	32.6395i	−0.0464289	+	0.0464289i
$704$	−633.275	−	307.537i	−0.899538	−	0.436842i
$705$	−15.7202	+	2.98405i	−0.0222981	+	0.00423269i
$706$	−76.0287	−	13.4625i	−0.107689	−	0.0190687i
$707$	−280.837	−	551.174i	−0.397224	−	0.779595i
$708$	−224.590	+	104.334i	−0.317218	+	0.147364i
$709$	−300.528	−	413.641i	−0.423875	−	0.583414i	0.542659	−	0.839953i	$-0.317418\pi$
$709$	−300.528	−	413.641i	−0.423875	−	0.583414i	−0.966534	+	0.256539i	$0.917418\pi$
$710$	523.032	+	995.941i	0.736665	+	1.40273i
$711$	177.931	+	547.614i	0.250254	+	0.770203i
$712$	125.248	+	471.516i	0.175911	+	0.662242i
$713$	−94.3397	+	14.9419i	−0.132314	+	0.0209564i
$714$	324.417	+	666.375i	0.454366	+	0.933298i
$715$	−2.18892	−	1336.72i	−0.00306143	−	1.86954i
$716$	−382.534	−	299.759i	−0.534266	−	0.418658i
$717$	−666.391	+	105.546i	−0.929416	+	0.147205i
$718$	−1.87678	−	1.41638i	−0.00261390	−	0.00197268i
$719$	274.300	+	844.208i	0.381502	+	1.17414i	0.938986	+	0.343954i	$0.111766\pi$
$719$	274.300	+	844.208i	0.381502	+	1.17414i	−0.557485	+	0.830187i	$0.688234\pi$
$720$	−162.361	+	287.941i	−0.225501	+	0.399918i
$721$	−541.176	−	744.865i	−0.750591	−	1.03310i
$722$	−12.6729	+	697.184i	−0.0175525	+	0.965629i
$723$	−118.242	−	232.063i	−0.163544	−	0.320972i
$724$	208.833	+	732.276i	0.288443	+	1.01143i
$725$	623.210	−	245.443i	0.859600	−	0.338542i
$726$	405.100	−	347.825i	0.557989	−	0.479098i
$727$	−178.567	+	178.567i	−0.245621	+	0.245621i	−0.819171	−	0.573550i	$-0.805566\pi$
$727$	−178.567	+	178.567i	−0.245621	+	0.245621i	0.573550	+	0.819171i	$0.305566\pi$
$728$	−1451.40	−	79.2170i	−1.99368	−	0.108815i
$729$	−652.254	−	211.930i	−0.894724	−	0.290713i
$730$	−354.985	+	501.490i	−0.486281	+	0.686973i
$731$	109.679	+	150.961i	0.150040	+	0.206513i
$732$	576.044	−	535.617i	0.786945	−	0.731717i
$733$	89.0044	−	174.681i	0.121425	−	0.238310i	−0.822291	−	0.569067i	$-0.807304\pi$
$733$	89.0044	−	174.681i	0.121425	−	0.238310i	0.943716	+	0.330758i	$0.107304\pi$
$734$	−20.0385	−	143.332i	−0.0273004	−	0.195275i
$735$	71.5283	−	25.6787i	0.0973175	−	0.0349371i
$736$	76.8801	−	64.0386i	0.104457	−	0.0870089i
$737$	−766.107	−	144.125i	−1.03949	−	0.195557i
$738$	−348.395	−	120.243i	−0.472080	−	0.162931i
$739$	−698.721	+	961.707i	−0.945495	+	1.30136i	0.00800389	+	0.999968i	$0.497452\pi$
$739$	−698.721	+	961.707i	−0.945495	+	1.30136i	−0.953499	+	0.301395i	$0.902548\pi$
$740$	262.691	+	1.53385i	0.354988	+	0.00207278i
$741$	−58.2333	−	179.224i	−0.0785875	−	0.241868i
$742$	−173.162	+	52.8042i	−0.233371	+	0.0711646i
$743$	−19.8363	+	125.242i	−0.0266976	+	0.168562i	−0.997435	−	0.0715829i	$-0.977195\pi$
$743$	−19.8363	+	125.242i	−0.0266976	+	0.168562i	0.970737	+	0.240145i	$0.0771950\pi$
$744$	−55.1989	−	536.354i	−0.0741920	−	0.720906i
$745$	−1.28833	+	10.1245i	−0.00172930	+	0.0135900i
$746$	−125.305	+	707.655i	−0.167970	+	0.948599i
$747$	−313.878	−	313.878i	−0.420185	−	0.420185i
$748$	−90.6741	−	984.364i	−0.121222	−	1.31600i
$749$			443.530i			0.592162i
$750$	−208.441	−	510.687i	−0.277921	−	0.680916i
$751$	−150.708	−	48.9680i	−0.200676	−	0.0652037i	0.206954	−	0.978351i	$-0.433645\pi$
$751$	−150.708	−	48.9680i	−0.200676	−	0.0652037i	−0.407631	+	0.913147i	$0.633645\pi$
$752$	5.28572	−	22.5971i	0.00702889	−	0.0300493i
$753$	33.3078	−	210.297i	0.0442334	−	0.279279i
$754$	−1149.43	−	612.227i	−1.52444	−	0.811973i
$755$	−135.813	−	247.572i	−0.179884	−	0.327911i
$756$	−718.995	+	483.459i	−0.951051	+	0.639496i
$757$	60.3435	+	380.994i	0.0797140	+	0.503294i	0.994950	+	0.100375i	$0.0320044\pi$
$757$	60.3435	+	380.994i	0.0797140	+	0.503294i	−0.915236	+	0.402919i	$0.867996\pi$
$758$	−348.229	−	120.186i	−0.459405	−	0.158557i
$759$	21.3569	+	72.8196i	0.0281382	+	0.0959415i
$760$	−101.757	+	96.9834i	−0.133891	+	0.127610i
$761$	565.865	−	778.846i	0.743581	−	1.02345i	−0.254824	−	0.966988i	$-0.582017\pi$
$761$	565.865	−	778.846i	0.743581	−	1.02345i	0.998405	−	0.0564637i	$-0.0179825\pi$
$762$	−804.452	−	607.109i	−1.05571	−	0.796731i
$763$	258.445	−	507.226i	0.338722	−	0.664779i
$764$	−41.1464	+	1131.44i	−0.0538565	+	1.48094i
$765$	−463.947	+	14.1601i	−0.606467	+	0.0185100i
$766$	443.027	−	427.208i	0.578364	−	0.557713i
$767$	607.643	−	309.610i	0.792233	−	0.403663i
$768$	337.309	+	453.045i	0.439205	+	0.589903i
$769$	721.515			0.938251			0.469125	−	0.883132i	$-0.344569\pi$
$769$	721.515			0.938251			0.469125	+	0.883132i	$0.344569\pi$
$770$	−822.236	−	13.5992i	−1.06784	−	0.0176612i
$771$		−	673.773i		−	0.873895i
$772$	−698.861	+	1256.50i	−0.905260	+	1.62759i
$773$	−552.758	−	1084.85i	−0.715082	−	1.40343i	−0.906623	−	0.421943i	$-0.861348\pi$
$773$	−552.758	−	1084.85i	−0.715082	−	1.40343i	0.191541	−	0.981485i	$-0.438652\pi$
$774$	−49.4081	+	47.6440i	−0.0638347	+	0.0615555i
$775$	−644.061	−	410.369i	−0.831046	−	0.529509i
$776$	−196.569	−	444.088i	−0.253311	−	0.572278i
$777$	193.037	+	98.3573i	0.248439	+	0.126586i
$778$	68.2832	+	51.5324i	0.0877676	+	0.0662370i
$779$	−126.798	−	92.1238i	−0.162770	−	0.118259i
$780$	−492.460	+	952.714i	−0.631359	+	1.22143i
$781$	416.200	−	1165.33i	0.532907	−	1.49209i
$782$	132.810	+	45.8373i	0.169833	+	0.0586154i
$783$	−766.710	+	121.435i	−0.979196	+	0.155089i
$784$	−8.00637	+	109.933i	−0.0102122	+	0.140221i
$785$	223.278	−	765.941i	0.284430	−	0.975721i
$786$	−19.9778	−	10.6409i	−0.0254171	−	0.0135381i
$787$	621.983	+	98.5124i	0.790322	+	0.125175i	0.538529	−	0.842607i	$-0.318980\pi$
$787$	621.983	+	98.5124i	0.790322	+	0.125175i	0.251792	+	0.967781i	$0.418980\pi$
$788$	−253.721	−	546.165i	−0.321981	−	0.693102i
$789$	192.835	−	593.484i	0.244404	−	0.752198i
$790$	973.120	−	997.431i	1.23180	−	1.26257i
$791$	−721.513			−0.912154
$792$	353.980	−	83.1656i	0.446944	−	0.105007i
$793$	−1531.70	+	1531.70i	−1.93153	+	1.93153i
$794$	57.4654	−	324.532i	0.0723745	−	0.408730i
$795$	−16.8607	+	132.502i	−0.0212084	+	0.166669i
$796$	−87.3663	+	238.963i	−0.109757	+	0.300205i
$797$	550.191	+	87.1417i	0.690327	+	0.109337i	0.491735	−	0.870745i	$-0.336363\pi$
$797$	550.191	+	87.1417i	0.690327	+	0.109337i	0.198593	+	0.980082i	$0.436363\pi$
$798$	−110.891	+	33.8152i	−0.138961	+	0.0423750i
$799$	30.9916	−	10.0698i	0.0387880	−	0.0126030i
$800$	799.644	+	23.8790i	0.999554	+	0.0298487i
$801$	−203.860	−	148.113i	−0.254507	−	0.184910i
$802$	−858.911	−	296.440i	−1.07096	−	0.369627i
$803$	670.311	−	86.4115i	0.834758	−	0.107611i
$804$	492.294	+	385.768i	0.612306	+	0.479811i
$805$	49.8599	−	105.709i	0.0619377	−	0.131316i
$806$	205.590	+	1470.55i	0.255075	+	1.82451i
$807$	201.324	+	102.580i	0.249472	+	0.127113i
$808$	238.565	−	617.481i	0.295253	−	0.764210i
$809$	386.799	−	281.026i	0.478120	−	0.347375i	−0.322477	−	0.946577i	$-0.604516\pi$
$809$	386.799	−	281.026i	0.478120	−	0.347375i	0.800597	+	0.599203i	$0.204516\pi$
$810$	45.0823	+	263.554i	0.0556572	+	0.325375i
$811$	−238.204	+	733.118i	−0.293717	+	0.903967i	0.689933	+	0.723874i	$0.257640\pi$
$811$	−238.204	+	733.118i	−0.293717	+	0.903967i	−0.983649	+	0.180094i	$0.942360\pi$
$812$	−389.430	+	700.164i	−0.479594	+	0.862271i
$813$	−756.226	−	756.226i	−0.930168	−	0.930168i
$814$	−194.493	−	213.713i	−0.238935	−	0.262546i
$815$	−507.386	−	345.490i	−0.622559	−	0.423914i
$816$	−299.226	+	734.496i	−0.366698	+	0.900117i
$817$	−26.0067	+	13.2511i	−0.0318320	+	0.0162192i
$818$	−20.9032	+	1149.97i	−0.0255541	+	1.40583i
$819$	607.383	−	441.290i	0.741615	−	0.538815i
$820$	134.387	+	881.781i	0.163887	+	1.07534i
$821$	368.271	−	119.659i	0.448564	−	0.145747i	−0.0760193	−	0.997106i	$-0.524221\pi$
$821$	368.271	−	119.659i	0.448564	−	0.145747i	0.524583	+	0.851359i	$0.324221\pi$
$822$	303.379	+	228.956i	0.369074	+	0.278535i
$823$	54.9951	+	347.225i	0.0668227	+	0.421902i	0.998309	+	0.0581262i	$0.0185126\pi$
$823$	54.9951	+	347.225i	0.0668227	+	0.421902i	−0.931487	+	0.363776i	$0.881487\pi$
$824$	206.932	−	963.275i	0.251131	−	1.16902i
$825$	−257.937	+	549.189i	−0.312651	+	0.665684i
$826$	−183.646	−	377.220i	−0.222331	−	0.456683i
$827$	136.735	+	863.314i	0.165339	+	1.04391i	0.921175	+	0.389149i	$0.127231\pi$
$827$	136.735	+	863.314i	0.165339	+	1.04391i	−0.755836	+	0.654761i	$0.772769\pi$
$828$	−9.93425	+	50.7162i	−0.0119979	+	0.0612514i
$829$	−554.335	+	180.114i	−0.668679	+	0.217267i	−0.623632	−	0.781718i	$-0.714344\pi$
$829$	−554.335	+	180.114i	−0.668679	+	0.217267i	−0.0450468	+	0.998985i	$0.514344\pi$
$830$	−319.339	+	1025.71i	−0.384746	+	1.23579i
$831$	134.444	−	97.6796i	0.161786	−	0.117545i
$832$	−973.637	−	1213.05i	−1.17024	−	1.45799i
$833$	−137.904	+	70.2656i	−0.165551	+	0.0843525i
$834$	912.983	+	161.663i	1.09470	+	0.193841i
$835$	225.214	+	153.353i	0.269718	+	0.183657i
$836$	154.300	+	10.0784i	0.184569	+	0.0120555i
$837$	625.844	+	625.844i	0.747723	+	0.747723i
$838$	105.096	+	150.324i	0.125413	+	0.179384i
$839$	253.592	−	780.477i	0.302256	−	0.930247i	−0.678431	−	0.734664i	$-0.737340\pi$
$839$	253.592	−	780.477i	0.302256	−	0.930247i	0.980687	−	0.195583i	$-0.0626601\pi$
$840$	580.504	+	313.562i	0.691076	+	0.373288i
$841$	99.6608	−	72.4078i	0.118503	−	0.0860973i
$842$	247.128	−	75.3596i	0.293501	−	0.0895007i
$843$	592.740	+	302.016i	0.703132	+	0.358264i
$844$	−597.081	+	401.483i	−0.707442	+	0.475691i
$845$	899.454	−	1906.96i	1.06444	−	2.25675i
$846$	5.24675	+	10.7772i	0.00620184	+	0.0127390i
$847$	601.654	+	675.488i	0.710335	+	0.797507i
$848$	−165.766	−	100.255i	−0.195479	−	0.118225i
$849$	397.447	+	288.762i	0.468135	+	0.340120i
$850$	552.387	+	978.132i	0.649867	+	1.15074i
$851$	39.0596	−	12.6912i	0.0458985	−	0.0149133i
$852$	−727.059	+	676.034i	−0.853356	+	0.793467i
$853$	−382.422	−	60.5698i	−0.448326	−	0.0710079i	−0.0718109	−	0.997418i	$-0.522878\pi$
$853$	−382.422	−	60.5698i	−0.448326	−	0.0710079i	−0.376515	+	0.926410i	$0.622878\pi$
$854$	925.017	+	959.268i	1.08316	+	1.12326i
$855$	9.16502	−	72.0247i	0.0107193	−	0.0842394i
$856$	−353.401	+	316.820i	−0.412852	+	0.370117i
$857$	270.566	−	270.566i	0.315713	−	0.315713i	−0.531405	−	0.847118i	$-0.678336\pi$
$857$	270.566	−	270.566i	0.315713	−	0.315713i	0.847118	+	0.531405i	$0.178336\pi$
$858$	1137.88	−	311.379i	1.32620	−	0.362912i
$859$	1284.21			1.49501			0.747504	−	0.664257i	$-0.231252\pi$
$859$	1284.21			1.49501			0.747504	+	0.664257i	$0.231252\pi$
$860$	157.679	+	52.2527i	0.183347	+	0.0607590i
$861$	−227.319	+	699.617i	−0.264018	+	0.812564i
$862$	−23.1357	+	1272.78i	−0.0268396	+	1.47655i
$863$	−650.508	−	103.030i	−0.753775	−	0.119386i	−0.232290	−	0.972647i	$-0.574622\pi$
$863$	−650.508	−	103.030i	−0.753775	−	0.119386i	−0.521485	+	0.853260i	$0.674622\pi$
$864$	−898.806	−	227.547i	−1.04029	−	0.263364i
$865$	−8.53035	+	29.2629i	−0.00986168	+	0.0338299i
$866$	−103.808	−	742.521i	−0.119871	−	0.857415i
$867$	−470.158	+	74.4657i	−0.542282	+	0.0858890i
$868$	906.830	−	110.016i	1.04473	−	0.126746i
$869$	−1532.21	−	44.2533i	−1.76318	−	0.0509243i
$870$	353.328	+	473.908i	0.406124	+	0.544722i
$871$	−1393.43	−	1012.39i	−1.59981	−	1.16233i
$872$	588.766	−	156.393i	0.675190	−	0.179350i
$873$	223.499	+	113.878i	0.256012	+	0.130445i
$874$	−10.3315	+	19.3970i	−0.0118210	+	0.0221933i
$875$	858.634	−	368.801i	0.981296	−	0.421487i
$876$	−509.277	−	186.195i	−0.581366	−	0.212551i
$877$	181.609	+	356.429i	0.207080	+	0.406418i	0.971065	−	0.238817i	$-0.0767595\pi$
$877$	181.609	+	356.429i	0.207080	+	0.406418i	−0.763984	+	0.645235i	$0.776760\pi$
$878$	209.257	−	146.298i	0.238333	−	0.166626i
$879$		−	46.6569i		−	0.0530795i
$880$	−576.501	−	664.866i	−0.655115	−	0.755529i
$881$	−1517.58			−1.72256			−0.861282	−	0.508128i	$-0.830338\pi$
$881$	−1517.58			−1.72256			−0.861282	+	0.508128i	$0.830338\pi$
$882$	−32.6208	−	46.6590i	−0.0369850	−	0.0529013i
$883$	806.967	−	411.170i	0.913893	−	0.465651i	0.0672033	−	0.997739i	$-0.478592\pi$
$883$	806.967	−	411.170i	0.913893	−	0.465651i	0.846689	+	0.532088i	$0.178592\pi$
$884$	749.976	−	2051.32i	0.848389	−	2.32050i
$885$	−309.407	+	9.44343i	−0.349613	+	0.0106705i
$886$	820.946	+	437.266i	0.926576	+	0.493528i
$887$	193.183	−	379.143i	0.217794	−	0.427445i	−0.756098	−	0.654459i	$-0.772896\pi$
$887$	193.183	−	379.143i	0.217794	−	0.427445i	0.973891	+	0.227014i	$0.0728964\pi$
$888$	59.5192	+	224.069i	0.0670261	+	0.252330i
$889$	1003.61	−	1381.35i	1.12892	−	1.55383i
$890$	−87.9616	+	603.457i	−0.0988332	+	0.678042i
$891$	179.677	−	232.858i	0.201657	−	0.261344i
$892$	195.617	+	1612.42i	0.219302	+	1.80764i
$893$	0.797385	+	5.03449i	0.000892929	+	0.00563773i
$894$	−8.92061	+	1.24714i	−0.00997831	+	0.00139501i
$895$	−292.179	−	532.611i	−0.326457	−	0.595097i
$896$	−757.027	+	585.317i	−0.844896	+	0.653256i
$897$	−26.2292	+	165.605i	−0.0292410	+	0.184621i
$898$	340.586	+	6.19091i	0.379271	+	0.00689411i
$899$	778.372	+	252.908i	0.865820	+	0.281322i
$900$	−328.194	+	251.047i	−0.364660	+	0.278941i
$901$		−	272.022i		−	0.301911i
$902$	613.405	−	765.772i	0.680050	−	0.848971i
$903$	96.8704	+	96.8704i	0.107276	+	0.107276i
$904$	−515.389	−	574.897i	−0.570120	−	0.635947i
$905$	−120.151	+	944.226i	−0.132764	+	1.04334i
$906$	179.391	−	172.986i	0.198004	−	0.190934i
$907$	−45.0029	+	284.137i	−0.0496173	+	0.313271i	0.950380	+	0.311090i	$0.100694\pi$
$907$	−45.0029	+	284.137i	−0.0496173	+	0.313271i	−0.999998	+	0.00218092i	$0.999306\pi$
$908$	1136.96	+	1222.78i	1.25216	+	1.34667i
$909$	105.655	+	325.172i	0.116232	+	0.357725i
$910$	−1628.96	−	804.843i	−1.79007	−	0.884443i
$911$	−833.667	+	1147.44i	−0.915112	+	1.25954i	0.0502792	+	0.998735i	$0.483989\pi$
$911$	−833.667	+	1147.44i	−0.915112	+	1.25954i	−0.965391	+	0.260808i	$0.916011\pi$
$912$	−106.155	−	64.2023i	−0.116398	−	0.0703972i
$913$	1067.95	−	505.858i	1.16971	−	0.554062i
$914$	1296.39	−	631.134i	1.41837	−	0.690519i
$915$	925.401	−	332.220i	1.01137	−	0.363082i
$916$	−862.049	−	1282.03i	−0.941101	−	1.39960i
$917$	17.4095	−	34.1681i	0.0189853	−	0.0372607i
$918$	−379.736	−	1245.28i	−0.413656	−	1.35651i
$919$	−220.782	−	303.880i	−0.240242	−	0.330664i	0.671822	−	0.740712i	$-0.265512\pi$
$919$	−220.782	−	303.880i	−0.240242	−	0.330664i	−0.912064	+	0.410048i	$0.865512\pi$
$920$	119.844	−	35.7819i	0.130265	−	0.0388934i
$921$	86.4071	+	28.0754i	0.0938188	+	0.0304836i
$922$	1301.90	−	910.200i	1.41204	−	0.987201i
$923$	1933.25	−	1933.25i	2.09453	−	2.09453i
$924$	−178.806	−	703.384i	−0.193512	−	0.761238i
$925$	301.126	+	130.956i	0.325541	+	0.141574i
$926$	227.324	−	1283.80i	0.245491	−	1.38639i
$927$	231.029	+	453.420i	0.249222	+	0.489126i
$928$	−836.062	+	189.844i	−0.900929	+	0.204573i
$929$	−115.696	−	159.242i	−0.124539	−	0.171413i	0.742195	−	0.670184i	$-0.233785\pi$
$929$	−115.696	−	159.242i	−0.124539	−	0.171413i	−0.866734	+	0.498771i	$0.833785\pi$
$930$	200.349	−	643.517i	0.215429	−	0.691954i
$931$	−7.48130	−	23.0251i	−0.00803577	−	0.0247315i
$932$	544.985	+	106.751i	0.584748	+	0.114540i
$933$	−22.6389	+	3.58564i	−0.0242646	+	0.00384313i
$934$	−331.963	+	161.612i	−0.355420	+	0.173033i
$935$	379.916	−	1175.81i	0.406328	−	1.25755i
$936$	785.480	+	168.738i	0.839188	+	0.180275i
$937$	932.143	−	147.637i	0.994817	−	0.157563i	0.362260	−	0.932077i	$-0.382005\pi$
$937$	932.143	−	147.637i	0.994817	−	0.157563i	0.632557	+	0.774514i	$0.282005\pi$
$938$	−638.294	+	845.774i	−0.680484	+	0.901678i
$939$	77.8180	+	239.499i	0.0828732	+	0.255058i
$940$	17.1877	−	23.3686i	0.0182848	−	0.0248602i
$941$	630.205	+	867.402i	0.669718	+	0.921788i	0.999754	−	0.0221806i	$-0.00706088\pi$
$941$	630.205	+	867.402i	0.669718	+	0.921788i	−0.330036	+	0.943968i	$0.607061\pi$
$942$	703.993	+	12.7967i	0.747338	+	0.0135846i
$943$	63.3086	+	124.250i	0.0671354	+	0.131761i
$944$	169.385	−	415.782i	0.179433	−	0.440447i
$945$	−1064.03	+	201.977i	−1.12595	+	0.213732i
$946$	−75.2052	−	166.528i	−0.0794981	−	0.176034i
$947$	−706.093	+	706.093i	−0.745610	+	0.745610i	−0.973651	−	0.228041i	$-0.926768\pi$
$947$	−706.093	+	706.093i	−0.745610	+	0.745610i	0.228041	+	0.973651i	$0.426768\pi$
$948$	1074.76	+	597.779i	1.13371	+	0.630568i
$949$	1420.19	+	461.449i	1.49652	+	0.486248i
$950$	−164.635	+	61.4071i	−0.173300	+	0.0646390i
$951$	−357.044	−	491.429i	−0.375440	−	0.516749i
$952$	−1253.37	−	484.242i	−1.31657	−	0.508658i
$953$	154.221	−	302.677i	0.161827	−	0.317604i	−0.795827	−	0.605524i	$-0.792964\pi$
$953$	154.221	−	302.677i	0.161827	−	0.317604i	0.957655	+	0.287920i	$0.0929637\pi$
$954$	99.0960	−	13.8541i	0.103874	−	0.0145221i
$955$	−603.733	+	1279.99i	−0.632181	+	1.34031i
$956$	754.464	−	962.801i	0.789188	−	1.00711i
$957$	120.219	−	639.028i	0.125620	−	0.667741i
$958$	−268.658	+	778.415i	−0.280437	+	0.812541i
$959$	−378.487	+	520.942i	−0.394668	+	0.543214i
$960$	164.820	+	686.524i	0.171687	+	0.715129i
$961$	8.60670	+	26.4887i	0.00895598	+	0.0275637i
$962$	−186.226	−	610.693i	−0.193582	−	0.634816i
$963$	38.3490	−	242.126i	0.0398225	−	0.251429i
$964$	443.474	+	162.137i	0.460035	+	0.168192i
$965$	−1421.07	+	1100.24i	−1.47262	+	1.14015i
$966$	101.569	+	17.9850i	0.105144	+	0.0186181i
$967$	1084.86	+	1084.86i	1.12188	+	1.12188i	0.991459	+	0.130419i	$0.0416324\pi$
$967$	1084.86	+	1084.86i	1.12188	+	1.12188i	0.130419	+	0.991459i	$0.458368\pi$
$968$	−108.453	+	961.905i	−0.112038	+	0.993704i
$969$		−	174.200i		−	0.179773i
$970$	−7.48868	−	607.013i	−0.00772029	−	0.625787i
$971$	1212.76	+	394.049i	1.24898	+	0.405818i	0.857555	−	0.514393i	$-0.171983\pi$
$971$	1212.76	+	394.049i	1.24898	+	0.405818i	0.391424	+	0.920211i	$0.371983\pi$
$972$	731.957	−	340.032i	0.753043	−	0.349827i
$973$	−245.730	+	1551.48i	−0.252549	+	1.59453i
$974$	−763.705	+	1433.82i	−0.784091	+	1.47210i
$975$	−1034.48	+	852.649i	−1.06100	+	0.874511i
$976$	−103.583	+	1422.27i	−0.106130	+	1.45724i
$977$	211.905	+	1337.92i	0.216894	+	1.36942i	0.820278	+	0.571964i	$0.193818\pi$
$977$	211.905	+	1337.92i	0.216894	+	1.36942i	−0.603384	+	0.797451i	$0.706182\pi$
$978$	176.743	−	512.099i	0.180719	−	0.523618i
$979$	553.860	−	378.465i	0.565741	−	0.386583i
$980$	−63.2668	+	122.396i	−0.0645580	+	0.124894i
$981$	−184.944	+	254.553i	−0.188526	+	0.259483i
$982$	−603.551	+	799.737i	−0.614614	+	0.814396i
$983$	−646.980	+	1269.77i	−0.658169	+	1.29173i	0.284717	+	0.958612i	$0.408100\pi$
$983$	−646.980	+	1269.77i	−0.658169	+	1.29173i	−0.942885	+	0.333117i	$0.891900\pi$
$984$	−719.828	+	318.622i	−0.731532	+	0.323803i
$985$	−22.9648	−	752.426i	−0.0233145	−	0.763885i
$986$	−835.641	−	866.583i	−0.847506	−	0.878887i
$987$	21.3166	−	10.8613i	0.0215974	−	0.0110044i
$988$	298.570	+	166.064i	0.302196	+	0.168081i
$989$	25.9698			0.0262586
$990$	447.690	+	78.5172i	0.452212	+	0.0793103i
$991$			477.644i			0.481982i	0.970527	+	0.240991i	$0.0774725\pi$
$991$			477.644i			0.481982i	−0.970527	+	0.240991i	$0.922528\pi$
$992$	735.423	+	643.969i	0.741354	+	0.649162i
$993$	138.436	+	271.696i	0.139412	+	0.273611i
$994$	−1167.52	−	1210.75i	−1.17457	−	1.21806i
$995$	−217.924	+	231.645i	−0.219019	+	0.232809i
$996$	−947.460	−	34.4558i	−0.951265	−	0.0345942i
$997$	−1330.49	−	677.919i	−1.33449	−	0.679959i	−0.366380	−	0.930465i	$-0.619403\pi$
$997$	−1330.49	−	677.919i	−1.33449	−	0.679959i	−0.968115	+	0.250506i	$0.919403\pi$
$998$	93.4199	−	123.786i	0.0936071	−	0.124034i
$999$	−307.883	−	223.690i	−0.308191	−	0.223914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.w.a.7.20	✓	544
4.3	odd	2	inner	220.3.w.a.7.29	yes	544
5.3	odd	4	inner	220.3.w.a.183.15	yes	544
11.8	odd	10	inner	220.3.w.a.107.61	yes	544
20.3	even	4	inner	220.3.w.a.183.61	yes	544
44.19	even	10	inner	220.3.w.a.107.15	yes	544
55.8	even	20	inner	220.3.w.a.63.29	yes	544
220.63	odd	20	inner	220.3.w.a.63.20	yes	544

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.w.a.7.20	✓	544	1.1	even	1	trivial
220.3.w.a.7.29	yes	544	4.3	odd	2	inner
220.3.w.a.63.20	yes	544	220.63	odd	20	inner
220.3.w.a.63.29	yes	544	55.8	even	20	inner
220.3.w.a.107.15	yes	544	44.19	even	10	inner
220.3.w.a.107.61	yes	544	11.8	odd	10	inner
220.3.w.a.183.15	yes	544	5.3	odd	4	inner
220.3.w.a.183.61	yes	544	20.3	even	4	inner

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.14597 - 1.63913i) q^{2} +(1.96587 - 1.00166i) q^{3} +(-1.37351 + 3.75679i) q^{4} +(-3.42603 + 3.64175i) q^{5} +(-3.89468 - 2.07445i) q^{6} +(3.39399 - 6.66107i) q^{7} +(7.73187 - 2.05381i) q^{8} +(-2.42874 + 3.34288i) q^{9} +(9.89543 + 1.44238i) q^{10} +(-6.20602 - 9.08214i) q^{11} +(1.06290 + 8.76116i) q^{12} +(-3.80199 - 24.0048i) q^{13} +(-14.8078 + 2.07020i) q^{14} +(-3.08734 + 10.5909i) q^{15} +(-12.2270 - 10.3200i) q^{16} +(3.51456 - 22.1900i) q^{17} +(8.26268 + 0.150193i) q^{18} +(3.34228 + 1.08597i) q^{19} +(-8.97561 - 17.8728i) q^{20} -16.4944i q^{21} +(-7.77491 + 20.5803i) q^{22} +(-2.21098 - 2.21098i) q^{23} +(13.1426 - 11.7822i) q^{24} +(-1.52463 - 24.9535i) q^{25} +(-34.9901 + 33.7408i) q^{26} +(-4.53251 + 28.6171i) q^{27} +(20.3626 + 21.8995i) q^{28} +(8.27919 + 25.4807i) q^{29} +(20.8979 - 7.07633i) q^{30} +(17.9554 - 24.7134i) q^{31} +(-2.90404 + 31.8680i) q^{32} +(-21.2975 - 11.6380i) q^{33} +(-40.4000 + 19.6683i) q^{34} +(12.6300 + 35.1811i) q^{35} +(-9.22260 - 13.7157i) q^{36} +(-5.96306 + 11.7032i) q^{37} +(-2.05010 - 6.72293i) q^{38} +(-31.5189 - 43.3821i) q^{39} +(-19.0102 + 35.1939i) q^{40} +(-42.4154 - 13.7816i) q^{41} +(-27.0366 + 18.9021i) q^{42} +(-5.87291 + 5.87291i) q^{43} +(42.6437 - 10.8404i) q^{44} +(-3.85297 - 20.2977i) q^{45} +(-1.09037 + 6.15780i) q^{46} +(0.658485 + 1.29235i) q^{47} +(-34.3737 - 8.04043i) q^{48} +(-4.04927 - 5.57334i) q^{49} +(-39.1548 + 31.0950i) q^{50} +(-15.3177 - 47.1431i) q^{51} +(95.4032 + 18.6875i) q^{52} +(11.9588 - 1.89408i) q^{53} +(52.1013 - 25.3650i) q^{54} +(54.3369 + 8.51493i) q^{55} +(12.5613 - 58.4732i) q^{56} +(7.65827 - 1.21295i) q^{57} +(32.2786 - 42.7708i) q^{58} +(8.67104 + 26.6867i) q^{59} +(-35.5474 - 26.1452i) q^{60} +(-52.3876 - 72.1054i) q^{61} +(-61.0849 - 1.11035i) q^{62} +(14.0240 + 27.5237i) q^{63} +(55.5637 - 31.7596i) q^{64} +(100.445 + 68.3954i) q^{65} +(5.33007 + 48.2461i) q^{66} +(50.1111 - 50.1111i) q^{67} +(78.5360 + 43.6816i) q^{68} +(-6.56115 - 2.13185i) q^{69} +(43.1928 - 61.0187i) q^{70} +(66.1216 + 91.0085i) q^{71} +(-11.9131 + 30.8349i) q^{72} +(-27.8939 + 54.7449i) q^{73} +(26.0165 - 3.63723i) q^{74} +(-27.9922 - 47.5281i) q^{75} +(-8.67041 + 11.0647i) q^{76} +(-81.5600 + 10.5141i) q^{77} +(-34.9892 + 101.378i) q^{78} +(81.9076 - 112.736i) q^{79} +(79.4726 - 9.17101i) q^{80} +(8.26254 + 25.4295i) q^{81} +(26.0169 + 85.3176i) q^{82} +(-16.8053 + 106.104i) q^{83} +(61.9662 + 22.6552i) q^{84} +(68.7695 + 88.8228i) q^{85} +(16.3567 + 2.89630i) q^{86} +(41.7989 + 41.7989i) q^{87} +(-66.6372 - 57.4760i) q^{88} +60.9835i q^{89} +(-28.8552 + 29.5760i) q^{90} +(-172.802 - 56.1467i) q^{91} +(11.3430 - 5.26939i) q^{92} +(10.5434 - 66.5686i) q^{93} +(1.36373 - 2.56034i) q^{94} +(-15.4056 + 8.45116i) q^{95} +(26.2119 + 65.5572i) q^{96} +(-9.49650 - 59.9585i) q^{97} +(-4.49510 + 13.0242i) q^{98} +(45.4333 + 1.31221i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

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