LMFDB - Embedded newform 220.3.w.a.7.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			7.3
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.98295 + 0.260620i) q^{2} +(-1.14015 + 0.580936i) q^{3} +(3.86415 - 1.03359i) q^{4} +(1.56915 - 4.74740i) q^{5} +(2.10946 - 1.44911i) q^{6} +(5.70983 - 11.2062i) q^{7} +(-7.39304 + 3.05663i) q^{8} +(-4.32761 + 5.95644i) q^{9} +(-1.87427 + 9.82278i) q^{10} +(-10.9222 - 1.30573i) q^{11} +(-3.80527 + 3.42328i) q^{12} +(2.16315 + 13.6576i) q^{13} +(-8.40175 + 23.7094i) q^{14} +(0.968868 + 6.32433i) q^{15} +(13.8634 - 7.98790i) q^{16} +(2.20685 - 13.9335i) q^{17} +(7.02905 - 12.9392i) q^{18} +(-8.78672 - 2.85498i) q^{19} +(1.15657 - 19.9665i) q^{20} +16.0938i q^{21} +(21.9985 - 0.257355i) q^{22} +(-29.9456 - 29.9456i) q^{23} +(6.65348 - 7.77990i) q^{24} +(-20.0755 - 14.8987i) q^{25} +(-7.84885 - 26.5185i) q^{26} +(3.27541 - 20.6801i) q^{27} +(10.4811 - 49.2040i) q^{28} +(7.25970 + 22.3431i) q^{29} +(-3.56946 - 12.2883i) q^{30} +(-11.6482 + 16.0323i) q^{31} +(-25.4086 + 19.4526i) q^{32} +(13.2115 - 4.85639i) q^{33} +(-0.744723 + 28.2045i) q^{34} +(-44.2406 - 44.6910i) q^{35} +(-10.5660 + 27.4896i) q^{36} +(12.5830 - 24.6955i) q^{37} +(18.1677 + 3.37128i) q^{38} +(-10.4005 - 14.3151i) q^{39} +(2.91024 + 39.8940i) q^{40} +(-12.0228 - 3.90645i) q^{41} +(-4.19436 - 31.9131i) q^{42} +(25.4909 - 25.4909i) q^{43} +(-43.5548 + 6.24356i) q^{44} +(21.4869 + 29.8914i) q^{45} +(67.1849 + 51.5761i) q^{46} +(-11.5996 - 22.7655i) q^{47} +(-11.1659 + 17.1612i) q^{48} +(-64.1748 - 88.3290i) q^{49} +(43.6916 + 24.3113i) q^{50} +(5.57833 + 17.1683i) q^{51} +(22.4751 + 50.5392i) q^{52} +(-7.11181 + 1.12640i) q^{53} +(-1.10532 + 41.8612i) q^{54} +(-23.3374 + 49.8033i) q^{55} +(-7.95992 + 100.301i) q^{56} +(11.6768 - 1.84942i) q^{57} +(-20.2186 - 42.4131i) q^{58} +(-15.9174 - 48.9888i) q^{59} +(10.2806 + 23.4368i) q^{60} +(7.37946 + 10.1570i) q^{61} +(18.9194 - 34.8270i) q^{62} +(42.0390 + 82.5063i) q^{63} +(45.3141 - 45.1955i) q^{64} +(68.2323 + 11.1615i) q^{65} +(-24.9321 + 13.0731i) q^{66} +(57.2536 - 57.2536i) q^{67} +(-5.87390 - 56.1221i) q^{68} +(51.5390 + 16.7460i) q^{69} +(99.3741 + 77.0899i) q^{70} +(18.6543 + 25.6754i) q^{71} +(13.7876 - 57.2641i) q^{72} +(-25.0092 + 49.0833i) q^{73} +(-18.5152 + 52.2492i) q^{74} +(31.5444 + 5.32421i) q^{75} +(-36.9041 - 1.95022i) q^{76} +(-76.9963 + 114.941i) q^{77} +(24.3544 + 25.6754i) q^{78} +(-36.7254 + 50.5482i) q^{79} +(-16.1680 - 78.3492i) q^{80} +(-12.1971 - 37.5387i) q^{81} +(24.8587 + 4.61290i) q^{82} +(-17.1464 + 108.258i) q^{83} +(16.6344 + 62.1889i) q^{84} +(-62.6849 - 32.3405i) q^{85} +(-43.9036 + 57.1905i) q^{86} +(-21.2570 - 21.2570i) q^{87} +(84.7396 - 23.7319i) q^{88} +42.5205i q^{89} +(-50.3977 - 53.6732i) q^{90} +(165.401 + 53.7419i) q^{91} +(-146.666 - 84.7629i) q^{92} +(3.96692 - 25.0461i) q^{93} +(28.9345 + 42.1196i) q^{94} +(-27.3414 + 37.2342i) q^{95} +(17.6689 - 36.9397i) q^{96} +(-2.69477 - 17.0141i) q^{97} +(150.275 + 158.427i) q^{98} +(55.0446 - 59.4069i) 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 $

$2$	−1.98295	+	0.260620i	−0.991473	+	0.130310i
$2$	−1.98295	+	0.260620i	−0.991473	+	0.130310i
$3$	−1.14015	+	0.580936i	−0.380051	+	0.193645i	−0.633571	−	0.773685i	$-0.718412\pi$
$3$	−1.14015	+	0.580936i	−0.380051	+	0.193645i	0.253520	+	0.967330i	$0.418412\pi$
$4$	3.86415	−	1.03359i	0.966039	−	0.258397i
$5$	1.56915	−	4.74740i	0.313830	−	0.949479i
$5$	1.56915	−	4.74740i	0.313830	−	0.949479i
$6$	2.10946	−	1.44911i	0.351576	−	0.241519i
$7$	5.70983	−	11.2062i	0.815691	−	1.60088i	0.0164553	−	0.999865i	$-0.494762\pi$
$7$	5.70983	−	11.2062i	0.815691	−	1.60088i	0.799235	−	0.601018i	$-0.205238\pi$
$8$	−7.39304	+	3.05663i	−0.924130	+	0.382078i
$9$	−4.32761	+	5.95644i	−0.480845	+	0.661827i
$10$	−1.87427	+	9.82278i	−0.187427	+	0.982278i
$11$	−10.9222	−	1.30573i	−0.992930	−	0.118703i
$11$	−10.9222	−	1.30573i	−0.992930	−	0.118703i
$12$	−3.80527	+	3.42328i	−0.317106	+	0.285273i
$13$	2.16315	+	13.6576i	0.166396	+	1.05058i	0.919617	+	0.392816i	$0.128499\pi$
$13$	2.16315	+	13.6576i	0.166396	+	1.05058i	−0.753221	+	0.657768i	$0.771501\pi$
$14$	−8.40175	+	23.7094i	−0.600125	+	1.69353i
$15$	0.968868	+	6.32433i	0.0645912	+	0.421622i
$16$	13.8634	−	7.98790i	0.866462	−	0.499244i
$17$	2.20685	−	13.9335i	0.129815	−	0.819617i	−0.833750	−	0.552142i	$-0.813811\pi$
$17$	2.20685	−	13.9335i	0.129815	−	0.819617i	0.963565	−	0.267475i	$-0.0861893\pi$
$18$	7.02905	−	12.9392i	0.390503	−	0.718843i
$19$	−8.78672	−	2.85498i	−0.462459	−	0.150262i	0.0685150	−	0.997650i	$-0.478174\pi$
$19$	−8.78672	−	2.85498i	−0.462459	−	0.150262i	−0.530974	+	0.847388i	$0.678174\pi$
$20$	1.15657	−	19.9665i	0.0578287	−	0.998327i
$21$			16.0938i			0.766371i
$22$	21.9985	−	0.257355i	0.999932	−	0.0116980i
$23$	−29.9456	−	29.9456i	−1.30198	−	1.30198i	−0.927054	−	0.374927i	$-0.877668\pi$
$23$	−29.9456	−	29.9456i	−1.30198	−	1.30198i	−0.374927	−	0.927054i	$-0.622332\pi$
$24$	6.65348	−	7.77990i	0.277228	−	0.324163i
$25$	−20.0755	−	14.8987i	−0.803022	−	0.595950i
$26$	−7.84885	−	26.5185i	−0.301879	−	1.01994i
$27$	3.27541	−	20.6801i	0.121311	−	0.765930i
$28$	10.4811	−	49.2040i	0.374325	−	1.75729i
$29$	7.25970	+	22.3431i	0.250334	+	0.770450i	0.994713	+	0.102692i	$0.0327458\pi$
$29$	7.25970	+	22.3431i	0.250334	+	0.770450i	−0.744379	+	0.667758i	$0.767254\pi$
$30$	−3.56946	−	12.2883i	−0.118982	−	0.409610i
$31$	−11.6482	+	16.0323i	−0.375747	+	0.517172i	−0.954452	−	0.298366i	$-0.903558\pi$
$31$	−11.6482	+	16.0323i	−0.375747	+	0.517172i	0.578704	+	0.815537i	$0.303558\pi$
$32$	−25.4086	+	19.4526i	−0.794017	+	0.607895i
$33$	13.2115	−	4.85639i	0.400350	−	0.147163i
$34$	−0.744723	+	28.2045i	−0.0219036	+	0.829545i
$35$	−44.2406	−	44.6910i	−1.26402	−	1.27689i
$36$	−10.5660	+	27.4896i	−0.293501	+	0.763600i
$37$	12.5830	−	24.6955i	0.340080	−	0.667445i	−0.656109	−	0.754666i	$-0.727799\pi$
$37$	12.5830	−	24.6955i	0.340080	−	0.667445i	0.996189	+	0.0872213i	$0.0277987\pi$
$38$	18.1677	+	3.37128i	0.478097	+	0.0887179i
$39$	−10.4005	−	14.3151i	−0.266680	−	0.367053i
$40$	2.91024	+	39.8940i	0.0727560	+	0.997350i
$41$	−12.0228	−	3.90645i	−0.293239	−	0.0952792i	0.158703	−	0.987326i	$-0.449269\pi$
$41$	−12.0228	−	3.90645i	−0.293239	−	0.0952792i	−0.451942	+	0.892047i	$0.649269\pi$
$42$	−4.19436	−	31.9131i	−0.0998656	−	0.759837i
$43$	25.4909	−	25.4909i	0.592811	−	0.592811i	−0.345579	−	0.938390i	$-0.612317\pi$
$43$	25.4909	−	25.4909i	0.592811	−	0.592811i	0.938390	+	0.345579i	$0.112317\pi$
$44$	−43.5548	+	6.24356i	−0.989881	+	0.141899i
$45$	21.4869	+	29.8914i	0.477487	+	0.664254i
$46$	67.1849	+	51.5761i	1.46054	+	1.12122i
$47$	−11.5996	−	22.7655i	−0.246800	−	0.484371i	0.734061	−	0.679084i	$-0.237623\pi$
$47$	−11.5996	−	22.7655i	−0.246800	−	0.484371i	−0.980860	+	0.194712i	$0.937623\pi$
$48$	−11.1659	+	17.1612i	−0.232623	+	0.357524i
$49$	−64.1748	−	88.3290i	−1.30969	−	1.80263i
$50$	43.6916	+	24.3113i	0.873833	+	0.486227i
$51$	5.57833	+	17.1683i	0.109379	+	0.336634i
$52$	22.4751	+	50.5392i	0.432213	+	0.971908i
$53$	−7.11181	+	1.12640i	−0.134185	+	0.0212528i	−0.223166	−	0.974781i	$-0.571639\pi$
$53$	−7.11181	+	1.12640i	−0.134185	+	0.0212528i	0.0889806	+	0.996033i	$0.471639\pi$
$54$	−1.10532	+	41.8612i	−0.0204689	+	0.775208i
$55$	−23.3374	+	49.8033i	−0.424317	+	0.905514i
$56$	−7.95992	+	100.301i	−0.142141	+	1.79108i
$57$	11.6768	−	1.84942i	0.204855	−	0.0324459i
$58$	−20.2186	−	42.4131i	−0.348597	−	0.731260i
$59$	−15.9174	−	48.9888i	−0.269787	−	0.830318i	−0.990552	−	0.137139i	$-0.956209\pi$
$59$	−15.9174	−	48.9888i	−0.269787	−	0.830318i	0.720765	−	0.693179i	$-0.243791\pi$
$60$	10.2806	+	23.4368i	0.171344	+	0.390613i
$61$	7.37946	+	10.1570i	0.120975	+	0.166507i	0.865209	−	0.501411i	$-0.167186\pi$
$61$	7.37946	+	10.1570i	0.120975	+	0.166507i	−0.744235	+	0.667918i	$0.767186\pi$
$62$	18.9194	−	34.8270i	0.305151	−	0.561725i
$63$	42.0390	+	82.5063i	0.667286	+	1.30962i
$64$	45.3141	−	45.1955i	0.708032	−	0.706180i
$65$	68.2323	+	11.1615i	1.04973	+	0.171715i
$66$	−24.9321	+	13.0731i	−0.377759	+	0.198078i
$67$	57.2536	−	57.2536i	0.854532	−	0.854532i	−0.136156	−	0.990687i	$-0.543475\pi$
$67$	57.2536	−	57.2536i	0.854532	−	0.854532i	0.990687	+	0.136156i	$0.0434747\pi$
$68$	−5.87390	−	56.1221i	−0.0863809	−	0.825326i
$69$	51.5390	+	16.7460i	0.746942	+	0.242696i
$70$	99.3741	+	77.0899i	1.41963	+	1.10128i
$71$	18.6543	+	25.6754i	0.262736	+	0.361625i	0.919921	−	0.392104i	$-0.128253\pi$
$71$	18.6543	+	25.6754i	0.262736	+	0.361625i	−0.657185	+	0.753730i	$0.728253\pi$
$72$	13.7876	−	57.2641i	0.191494	−	0.795335i
$73$	−25.0092	+	49.0833i	−0.342592	+	0.672374i	−0.996445	−	0.0842474i	$-0.973151\pi$
$73$	−25.0092	+	49.0833i	−0.342592	+	0.672374i	0.653853	+	0.756621i	$0.273151\pi$
$74$	−18.5152	+	52.2492i	−0.250206	+	0.706070i
$75$	31.5444	+	5.32421i	0.420592	+	0.0709894i
$76$	−36.9041	−	1.95022i	−0.485581	−	0.0256608i
$77$	−76.9963	+	114.941i	−0.999953	+	1.49274i
$78$	24.3544	+	25.6754i	0.312236	+	0.329172i
$79$	−36.7254	+	50.5482i	−0.464878	+	0.639850i	−0.975511	−	0.219948i	$-0.929411\pi$
$79$	−36.7254	+	50.5482i	−0.464878	+	0.639850i	0.510633	+	0.859799i	$0.329411\pi$
$80$	−16.1680	−	78.3492i	−0.202100	−	0.979365i
$81$	−12.1971	−	37.5387i	−0.150581	−	0.463440i
$82$	24.8587	+	4.61290i	0.303155	+	0.0562548i
$83$	−17.1464	+	108.258i	−0.206583	+	1.30432i	0.638475	+	0.769642i	$0.279566\pi$
$83$	−17.1464	+	108.258i	−0.206583	+	1.30432i	−0.845059	+	0.534674i	$0.820434\pi$
$84$	16.6344	+	62.1889i	0.198028	+	0.740344i
$85$	−62.6849	−	32.3405i	−0.737470	−	0.380476i
$86$	−43.9036	+	57.1905i	−0.510507	+	0.665006i
$87$	−21.2570	−	21.2570i	−0.244334	−	0.244334i
$88$	84.7396	−	23.7319i	0.962950	−	0.269680i
$89$			42.5205i			0.477758i	0.971049	+	0.238879i	$0.0767799\pi$
$89$			42.5205i			0.477758i	−0.971049	+	0.238879i	$0.923220\pi$
$90$	−50.3977	−	53.6732i	−0.559975	−	0.596369i
$91$	165.401	+	53.7419i	1.81759	+	0.590571i
$92$	−146.666	−	84.7629i	−1.59419	−	0.921336i
$93$	3.96692	−	25.0461i	0.0426550	−	0.269313i
$94$	28.9345	+	42.1196i	0.307813	+	0.448081i
$95$	−27.3414	+	37.2342i	−0.287804	+	0.391939i
$96$	17.6689	−	36.9397i	0.184051	−	0.384789i
$97$	−2.69477	−	17.0141i	−0.0277811	−	0.175403i	0.969896	−	0.243518i	$-0.0783015\pi$
$97$	−2.69477	−	17.0141i	−0.0277811	−	0.175403i	−0.997677	+	0.0681150i	$0.978302\pi$
$98$	150.275	+	158.427i	1.53342	+	1.61660i
$99$	55.0446	−	59.4069i	0.556006	−	0.600070i
$100$	−92.9742	−	36.8212i	−0.929742	−	0.368212i
$101$	85.4230	−	117.575i	0.845772	−	1.16411i	−0.139007	−	0.990291i	$-0.544391\pi$
$101$	85.4230	−	117.575i	0.845772	−	1.16411i	0.984779	−	0.173814i	$-0.0556090\pi$
$102$	−15.5359	−	32.5901i	−0.152313	−	0.319510i
$103$	14.9480	−	29.3370i	0.145126	−	0.284825i	−0.806989	−	0.590567i	$-0.798904\pi$
$103$	14.9480	−	29.3370i	0.145126	−	0.284825i	0.952115	+	0.305741i	$0.0989043\pi$
$104$	−57.7384	−	94.3592i	−0.555177	−	0.907300i
$105$	76.4036	+	25.2536i	0.727654	+	0.240510i
$106$	13.8088	−	4.08707i	0.130271	−	0.0385572i
$107$	−85.0458	+	43.3330i	−0.794821	+	0.404981i	−0.803741	−	0.594979i	$-0.797160\pi$
$107$	−85.0458	+	43.3330i	−0.794821	+	0.404981i	0.00892073	+	0.999960i	$0.497160\pi$
$108$	−8.71806	−	83.2966i	−0.0807228	−	0.771265i
$109$	70.5708			0.647438			0.323719	−	0.946153i	$-0.395067\pi$
$109$	70.5708			0.647438			0.323719	+	0.946153i	$0.395067\pi$
$110$	33.2971	−	104.839i	0.302701	−	0.953085i
$111$			35.4665i			0.319518i
$112$	−10.3562	−	200.965i	−0.0924659	−	1.79433i
$113$	−50.8538	−	99.8062i	−0.450033	−	0.883240i	−0.998880	−	0.0473172i	$-0.984933\pi$
$113$	−50.8538	−	99.8062i	−0.450033	−	0.883240i	0.548846	−	0.835923i	$-0.315067\pi$
$114$	−22.6724	+	6.71049i	−0.198881	+	0.0588639i
$115$	−189.153	+	95.1745i	−1.64481	+	0.827604i
$116$	51.1461	+	78.8335i	0.440915	+	0.679599i
$117$	−90.7119	−	46.2200i	−0.775315	−	0.395043i
$118$	44.3308	+	92.9937i	0.375685	+	0.788082i
$119$	−143.540	−	104.288i	−1.20622	−	0.876372i
$120$	−26.4940	−	43.7945i	−0.220783	−	0.364954i
$121$	117.590	+	28.5229i	0.971819	+	0.235727i
$122$	−17.2802	−	18.2175i	−0.141641	−	0.149323i
$123$	15.9772	−	2.53054i	0.129896	−	0.0205735i
$124$	−28.4395	+	73.9908i	−0.229351	+	0.596700i
$125$	−102.232	+	71.9282i	−0.817854	+	0.575426i
$126$	−104.864	−	152.649i	−0.832253	−	1.21150i
$127$	189.532	+	30.0190i	1.49238	+	0.236370i	0.848680	−	0.528907i	$-0.177398\pi$
$127$	189.532	+	30.0190i	1.49238	+	0.236370i	0.643702	+	0.765277i	$0.277398\pi$
$128$	−78.0765	+	101.430i	−0.609973	+	0.792422i
$129$	−14.2549	+	43.8721i	−0.110503	+	0.340093i
$130$	−138.210	−	4.34990i	−1.06315	−	0.0334608i
$131$	203.551			1.55383			0.776913	−	0.629608i	$-0.216784\pi$
$131$	203.551			1.55383			0.776913	+	0.629608i	$0.216784\pi$
$132$	46.0319	−	32.4211i	0.348727	−	0.245615i
$133$	−82.1642	+	82.1642i	−0.617776	+	0.617776i
$134$	−98.6095	+	128.452i	−0.735892	+	0.958599i
$135$	−93.0371	−	47.9998i	−0.689164	−	0.355554i
$136$	26.2742	+	109.756i	0.193192	+	0.807032i
$137$	40.3614	+	6.39261i	0.294609	+	0.0466614i	0.301989	−	0.953311i	$-0.402349\pi$
$137$	40.3614	+	6.39261i	0.294609	+	0.0466614i	−0.00738061	+	0.999973i	$0.502349\pi$
$138$	−106.563	−	19.7744i	−0.772198	−	0.143293i
$139$	14.2923	−	4.64385i	0.102822	−	0.0334090i	−0.257154	−	0.966370i	$-0.582785\pi$
$139$	14.2923	−	4.64385i	0.102822	−	0.0334090i	0.359976	+	0.932961i	$0.382785\pi$
$140$	−217.145	−	126.966i	−1.55103	−	0.906903i
$141$	26.4506	+	19.2175i	0.187593	+	0.136294i
$142$	−43.6819	−	46.0513i	−0.307619	−	0.324305i
$143$	−5.79331	−	151.996i	−0.0405126	−	1.06291i
$144$	−12.4159	+	117.145i	−0.0862213	+	0.813507i
$145$	117.463	+	0.594900i	0.810089	+	0.00410276i
$146$	36.7998	−	103.847i	0.252054	−	0.711284i
$147$	124.483	+	63.4270i	0.846820	+	0.431476i
$148$	23.0976	−	108.433i	0.156065	−	0.732654i
$149$	48.3138	−	35.1020i	0.324254	−	0.235584i	−0.413735	−	0.910397i	$-0.635776\pi$
$149$	48.3138	−	35.1020i	0.324254	−	0.235584i	0.737988	+	0.674813i	$0.235776\pi$
$150$	−63.9384	−	2.33654i	−0.426256	−	0.0155769i
$151$	74.0712	−	227.968i	0.490538	−	1.50972i	−0.333259	−	0.942835i	$-0.608148\pi$
$151$	74.0712	−	227.968i	0.490538	−	1.50972i	0.823797	−	0.566885i	$-0.191852\pi$
$152$	73.6872	−	5.75076i	0.484784	−	0.0378339i
$153$	73.4437	+	73.4437i	0.480024	+	0.480024i
$154$	122.724	−	247.989i	0.796908	−	1.61032i
$155$	57.8341	+	80.4555i	0.373123	+	0.519068i
$156$	−54.9851	−	44.5658i	−0.352468	−	0.285678i
$157$	−26.0580	+	13.2772i	−0.165974	+	0.0845681i	−0.535004	−	0.844849i	$-0.679690\pi$
$157$	−26.0580	+	13.2772i	−0.165974	+	0.0845681i	0.369030	+	0.929418i	$0.379690\pi$
$158$	59.6507	−	109.806i	0.377536	−	0.694973i
$159$	7.45417	−	5.41577i	0.0468816	−	0.0340615i
$160$	52.4796	+	151.149i	0.327998	+	0.944679i
$161$	−506.560	+	164.591i	−3.14633	+	1.02231i
$162$	33.9694	+	71.2584i	0.209688	+	0.439867i
$163$	13.9140	+	87.8497i	0.0853621	+	0.538955i	0.992897	+	0.118978i	$0.0379619\pi$
$163$	13.9140	+	87.8497i	0.0853621	+	0.538955i	−0.907535	+	0.419977i	$0.862038\pi$
$164$	−50.4956	−	2.66847i	−0.307900	−	0.0162712i
$165$	−2.32434	−	70.3408i	−0.0140869	−	0.426308i
$166$	5.78623	−	219.139i	0.0348568	−	1.32011i
$167$	9.33352	+	58.9295i	0.0558893	+	0.352871i	0.999746	+	0.0225173i	$0.00716810\pi$
$167$	9.33352	+	58.9295i	0.0558893	+	0.352871i	−0.943857	+	0.330354i	$0.892832\pi$
$168$	−49.1927	−	118.982i	−0.292814	−	0.708227i
$169$	−21.1220	+	6.86296i	−0.124982	+	0.0406092i
$170$	132.729	+	47.7926i	0.780761	+	0.281133i
$171$	55.0310	−	39.9824i	0.321819	−	0.233815i
$172$	72.1536	−	124.848i	0.419498	−	0.725859i
$173$	254.328	−	129.587i	1.47010	−	0.749056i	0.478466	−	0.878106i	$-0.341193\pi$
$173$	254.328	−	129.587i	1.47010	−	0.749056i	0.991638	+	0.129050i	$0.0411928\pi$
$174$	47.6916	+	36.6116i	0.274090	+	0.210411i
$175$	−281.586	+	139.901i	−1.60906	+	0.799434i
$176$	−161.849	+	69.1438i	−0.919597	+	0.392863i
$177$	46.6076	+	46.6076i	0.263320	+	0.263320i
$178$	−11.0817	−	84.3158i	−0.0622565	−	0.473684i
$179$	30.4193	−	93.6208i	0.169940	−	0.523021i	−0.829426	−	0.558616i	$-0.811333\pi$
$179$	30.4193	−	93.6208i	0.169940	−	0.523021i	0.999366	+	0.0355947i	$0.0113325\pi$
$180$	113.924	+	93.2964i	0.632913	+	0.518313i
$181$	170.356	−	123.771i	0.941195	−	0.683819i	−0.00751269	−	0.999972i	$-0.502391\pi$
$181$	170.356	−	123.771i	0.941195	−	0.683819i	0.948708	+	0.316153i	$0.102391\pi$
$182$	−341.987	−	63.4607i	−1.87905	−	0.348685i
$183$	−14.3142	−	7.29347i	−0.0782199	−	0.0398550i
$184$	312.921	+	129.856i	1.70066	+	0.705741i
$185$	−97.4946	−	98.4872i	−0.526998	−	0.532363i
$186$	−1.33867	+	50.6990i	−0.00719717	+	0.272575i
$187$	−42.2971	+	149.303i	−0.226187	+	0.798413i
$188$	−68.3527	−	75.9800i	−0.363578	−	0.404149i
$189$	−213.043	−	154.785i	−1.12721	−	0.818968i
$190$	44.5126	−	80.9591i	0.234277	−	0.426100i
$191$	−171.039	+	55.5739i	−0.895491	+	0.290963i	−0.720375	−	0.693585i	$-0.756030\pi$
$191$	−171.039	+	55.5739i	−0.895491	+	0.290963i	−0.175116	+	0.984548i	$0.556030\pi$
$192$	−25.4092	+	77.8543i	−0.132340	+	0.405491i
$193$	−121.790	−	19.2896i	−0.631034	−	0.0999459i	−0.167279	−	0.985910i	$-0.553498\pi$
$193$	−121.790	−	19.2896i	−0.631034	−	0.0999459i	−0.463755	+	0.885964i	$0.653498\pi$
$194$	9.77779	+	33.0357i	0.0504010	+	0.170287i
$195$	−84.2793	+	26.9129i	−0.432201	+	0.138015i
$196$	−339.277	−	274.987i	−1.73101	−	1.40299i
$197$	207.848	−	207.848i	1.05506	−	1.05506i	0.0566714	−	0.998393i	$-0.481951\pi$
$197$	207.848	−	207.848i	1.05506	−	1.05506i	0.998393	−	0.0566714i	$-0.0180487\pi$
$198$	−93.6680	+	132.146i	−0.473070	+	0.667407i
$199$	−20.9279			−0.105166			−0.0525828	−	0.998617i	$-0.516745\pi$
$199$	−20.9279			−0.105166			−0.0525828	+	0.998617i	$0.516745\pi$
$200$	193.959	+	48.7835i	0.969796	+	0.243918i
$201$	−32.0171	+	98.5385i	−0.159289	+	0.490241i
$202$	−138.747	+	255.407i	−0.686866	+	1.26439i
$203$	291.832	+	46.2216i	1.43760	+	0.227693i
$204$	39.3005	+	60.5754i	0.192650	+	0.296938i
$205$	−37.4110	+	50.9472i	−0.182493	+	0.248523i
$206$	−21.9952	+	62.0694i	−0.106773	+	0.301308i
$207$	307.962	−	48.7764i	1.48774	−	0.235635i
$208$	139.084	+	172.061i	0.668673	+	0.827218i
$209$	92.2428	+	42.6558i	0.441353	+	0.204095i
$210$	−158.086	−	30.1642i	−0.752790	−	0.143639i
$211$	234.256	+	170.197i	1.11022	+	0.806621i	0.982698	−	0.185215i	$-0.0592982\pi$
$211$	234.256	+	170.197i	1.11022	+	0.806621i	0.127520	+	0.991836i	$0.459298\pi$
$212$	−26.3169	+	11.7033i	−0.124136	+	0.0552041i
$213$	−36.1845	−	18.4369i	−0.169880	−	0.0865582i
$214$	157.348	−	108.092i	0.735270	−	0.505101i
$215$	−81.0164	−	161.014i	−0.376820	−	0.748904i
$216$	38.9962	+	162.901i	0.180538	+	0.754170i
$217$	113.152	+	222.073i	0.521438	+	1.02338i
$218$	−139.938	+	18.3921i	−0.641918	+	0.0843675i
$219$		−	70.4912i		−	0.321877i
$220$	−38.7032	+	216.569i	−0.175924	+	0.984404i
$221$	195.072			0.882677
$222$	−9.24326	−	70.3281i	−0.0416363	−	0.316793i
$223$	−320.680	+	163.395i	−1.43803	+	0.732712i	−0.987138	−	0.159867i	$-0.948893\pi$
$223$	−320.680	+	163.395i	−1.43803	+	0.732712i	−0.450890	+	0.892580i	$0.648893\pi$
$224$	72.9112	+	395.804i	0.325496	+	1.76698i
$225$	175.623	−	55.1029i	0.780545	−	0.244902i
$226$	126.852	+	184.657i	0.561291	+	0.817066i
$227$	−131.133	+	257.362i	−0.577676	+	1.13375i	0.398580	+	0.917134i	$0.369503\pi$
$227$	−131.133	+	257.362i	−0.577676	+	1.13375i	−0.976256	+	0.216620i	$0.930497\pi$
$228$	43.2093	−	19.2154i	0.189514	−	0.0842781i
$229$	−96.6116	+	132.974i	−0.421885	+	0.580675i	−0.966067	−	0.258293i	$-0.916840\pi$
$229$	−96.6116	+	132.974i	−0.421885	+	0.580675i	0.544182	+	0.838967i	$0.316840\pi$
$230$	350.275	−	238.023i	1.52294	−	1.03488i
$231$	21.0141	−	175.780i	0.0909703	−	0.760953i
$232$	−121.966	−	142.993i	−0.525714	−	0.616349i
$233$	−33.7105	−	212.840i	−0.144680	−	0.913476i	−0.948079	−	0.318035i	$-0.896977\pi$
$233$	−33.7105	−	212.840i	−0.144680	−	0.913476i	0.803399	−	0.595442i	$-0.203023\pi$
$234$	191.923	+	68.0106i	0.820183	+	0.290643i
$235$	−126.278	+	19.3454i	−0.537354	+	0.0823209i
$236$	−112.142	−	172.848i	−0.475176	−	0.732407i
$237$	12.5073	−	78.9677i	0.0527732	−	0.333197i
$238$	311.813	+	169.389i	1.31014	+	0.711717i
$239$	219.393	+	71.2851i	0.917962	+	0.298264i	0.729631	−	0.683842i	$-0.239692\pi$
$239$	219.393	+	71.2851i	0.917962	+	0.298264i	0.188332	+	0.982106i	$0.439692\pi$
$240$	63.9499	+	79.9374i	0.266458	+	0.333072i
$241$			134.969i			0.560038i	0.959995	+	0.280019i	$0.0903407\pi$
$241$			134.969i			0.560038i	−0.959995	+	0.280019i	$0.909659\pi$
$242$	−240.609	−	25.9132i	−0.994250	−	0.107079i
$243$	168.962	+	168.962i	0.695317	+	0.695317i
$244$	39.0135	+	31.6207i	0.159891	+	0.129593i
$245$	−520.033	+	166.062i	−2.12258	+	0.677803i
$246$	−31.0225	+	9.18191i	−0.126108	+	0.0373248i
$247$	19.9851	−	126.181i	0.0809115	−	0.510855i
$248$	37.1105	−	154.132i	0.149639	−	0.621499i
$249$	−43.3416	−	133.392i	−0.174063	−	0.535710i
$250$	183.974	−	169.273i	0.735897	−	0.677094i
$251$	−99.4209	+	136.841i	−0.396099	+	0.545184i	−0.959760	−	0.280823i	$-0.909393\pi$
$251$	−99.4209	+	136.841i	−0.396099	+	0.545184i	0.563660	+	0.826007i	$0.309393\pi$
$252$	247.723	+	275.366i	0.983027	+	1.09272i
$253$	287.972	+	366.173i	1.13823	+	1.44733i
$254$	−383.656	−	10.1302i	−1.51046	−	0.0398827i
$255$	90.2581	+	0.457120i	0.353953	+	0.00179263i
$256$	128.387	−	221.479i	0.501512	−	0.865151i
$257$	218.027	−	427.902i	0.848354	−	1.66499i	0.106614	−	0.994301i	$-0.465999\pi$
$257$	218.027	−	427.902i	0.848354	−	1.66499i	0.741740	−	0.670688i	$-0.234001\pi$
$258$	16.8328	−	90.7110i	0.0652433	−	0.351593i
$259$	−204.895	−	282.014i	−0.791101	−	1.08886i
$260$	275.197	−	27.3946i	1.05845	−	0.105364i
$261$	−164.502	−	53.4500i	−0.630277	−	0.204789i
$262$	−403.631	+	53.0494i	−1.54058	+	0.202479i
$263$	−136.497	+	136.497i	−0.519002	+	0.519002i	−0.917269	−	0.398268i	$-0.869612\pi$
$263$	−136.497	+	136.497i	−0.519002	+	0.519002i	0.398268	+	0.917269i	$0.369612\pi$
$264$	−82.8293	+	76.2862i	−0.313747	+	0.288963i
$265$	−5.81201	+	35.5300i	−0.0219321	+	0.134076i
$266$	141.514	−	184.341i	0.532006	−	0.693010i
$267$	−24.7017	−	48.4798i	−0.0925157	−	0.181572i
$268$	162.060	−	280.414i	0.604702	−	1.04632i
$269$	203.979	+	280.753i	0.758287	+	1.04369i	0.997355	+	0.0726892i	$0.0231581\pi$
$269$	203.979	+	280.753i	0.758287	+	1.04369i	−0.239068	+	0.971003i	$0.576842\pi$
$270$	196.997	+	70.9338i	0.729620	+	0.262718i
$271$	−105.639	−	325.122i	−0.389811	−	1.19971i	−0.932930	−	0.360058i	$-0.882757\pi$
$271$	−105.639	−	325.122i	−0.389811	−	1.19971i	0.543119	−	0.839656i	$-0.317243\pi$
$272$	−80.7049	−	210.793i	−0.296709	−	0.774976i
$273$	−219.802	+	34.8133i	−0.805137	+	0.127521i
$274$	−81.7005	−	2.15725i	−0.298177	−	0.00787318i
$275$	199.816	+	188.941i	0.726604	+	0.687057i
$276$	216.463	+	11.4391i	0.784286	+	0.0414461i
$277$	−271.666	+	43.0277i	−0.980744	+	0.155335i	−0.626164	−	0.779691i	$-0.715376\pi$
$277$	−271.666	+	43.0277i	−0.980744	+	0.155335i	−0.354580	+	0.935026i	$0.615376\pi$
$278$	−27.1306	+	12.9334i	−0.0975920	+	0.0465229i
$279$	−45.0869	−	138.763i	−0.161602	−	0.497359i
$280$	463.676	+	195.175i	1.65599	+	0.697055i
$281$	217.880	+	299.886i	0.775374	+	1.06721i	0.995777	+	0.0918017i	$0.0292626\pi$
$281$	217.880	+	299.886i	0.775374	+	1.06721i	−0.220404	+	0.975409i	$0.570737\pi$
$282$	−57.4585	−	31.2136i	−0.203753	−	0.110687i
$283$	−157.212	−	308.545i	−0.555518	−	1.09026i	−0.982545	−	0.186026i	$-0.940439\pi$
$283$	−157.212	−	308.545i	−0.555518	−	1.09026i	0.427027	−	0.904239i	$-0.359561\pi$
$284$	98.6208	+	79.9329i	0.347256	+	0.281454i
$285$	9.54265	−	58.3362i	0.0334830	−	0.204688i
$286$	51.1009	+	299.890i	0.178674	+	1.04857i
$287$	−112.425	+	112.425i	−0.391723	+	0.391723i
$288$	−5.91027	−	235.528i	−0.0205218	−	0.817806i
$289$	85.5834	+	27.8077i	0.296136	+	0.0962205i
$290$	−233.078	+	29.4335i	−0.803716	+	0.101495i
$291$	12.9566	+	17.8332i	0.0445242	+	0.0612824i
$292$	−45.9074	+	215.515i	−0.157217	+	0.738064i
$293$	−130.463	+	256.047i	−0.445265	+	0.873882i	0.553882	+	0.832595i	$0.313146\pi$
$293$	−130.463	+	256.047i	−0.445265	+	0.873882i	−0.999147	+	0.0412870i	$0.986854\pi$
$294$	−263.373	−	93.3298i	−0.895825	−	0.317448i
$295$	−257.546	−	1.30436i	−0.873037	−	0.00442157i
$296$	−17.5416	+	221.036i	−0.0592621	+	0.746743i
$297$	−62.7774	+	221.596i	−0.211372	+	0.746115i
$298$	−86.6554	+	82.1970i	−0.290790	+	0.275829i
$299$	344.208	−	473.761i	1.15120	−	1.58449i
$300$	127.395	−	12.0304i	0.424651	−	0.0401012i
$301$	−140.107	−	431.204i	−0.465471	−	1.43257i
$302$	−87.4664	+	471.352i	−0.289624	+	1.56077i
$303$	−29.0918	+	183.678i	−0.0960124	+	0.606199i
$304$	−144.619	+	30.6078i	−0.475721	+	0.100683i
$305$	59.7985	−	19.0954i	0.196061	−	0.0626080i
$306$	−164.776	−	126.494i	−0.538483	−	0.413379i
$307$	−250.280	−	250.280i	−0.815245	−	0.815245i	0.170170	−	0.985415i	$-0.445568\pi$
$307$	−250.280	−	250.280i	−0.815245	−	0.815245i	−0.985415	+	0.170170i	$0.945568\pi$
$308$	−178.724	+	523.732i	−0.580273	+	1.70043i
$309$			42.1324i			0.136351i
$310$	−135.650	−	144.466i	−0.437581	−	0.466020i
$311$	−257.788	−	83.7604i	−0.828901	−	0.269326i	−0.136318	−	0.990665i	$-0.543527\pi$
$311$	−257.788	−	83.7604i	−0.828901	−	0.269326i	−0.692582	+	0.721339i	$0.743527\pi$
$312$	120.647	+	74.0414i	0.386690	+	0.237312i
$313$	59.7559	−	377.284i	0.190913	−	1.20538i	−0.687035	−	0.726624i	$-0.741088\pi$
$313$	59.7559	−	377.284i	0.190913	−	1.20538i	0.877949	−	0.478755i	$-0.158912\pi$
$314$	48.2113	−	33.1192i	0.153539	−	0.105475i
$315$	457.655	−	70.1114i	1.45287	−	0.222576i
$316$	−89.6666	+	233.285i	−0.283755	+	0.738243i
$317$	64.8925	+	409.715i	0.204708	+	1.29248i	0.849284	+	0.527937i	$0.177034\pi$
$317$	64.8925	+	409.715i	0.204708	+	1.29248i	−0.644575	+	0.764541i	$0.722966\pi$
$318$	−13.3698	+	12.6819i	−0.0420433	+	0.0398802i
$319$	−50.1181	−	253.515i	−0.157110	−	0.794718i
$320$	−143.457	−	286.042i	−0.448302	−	0.893882i
$321$	71.7914	−	98.8124i	0.223649	−	0.307827i
$322$	961.585	−	458.395i	2.98629	−	1.42359i
$323$	−59.1708	+	116.129i	−0.183191	+	0.359533i
$324$	−85.9309	−	132.449i	−0.265219	−	0.408792i
$325$	160.054	−	306.412i	0.492475	−	0.942806i
$326$	−50.4861	−	170.575i	−0.154865	−	0.523236i
$327$	−80.4614	+	40.9971i	−0.246059	+	0.125373i
$328$	100.826	−	7.86871i	0.307395	−	0.0239900i
$329$	−321.345			−0.976734
$330$	22.9412	+	138.876i	0.0695189	+	0.420837i
$331$		−	214.985i		−	0.649500i	−0.945800	−	0.324750i	$-0.894720\pi$
$331$		−	214.985i		−	0.649500i	0.945800	−	0.324750i	$-0.105280\pi$
$332$	45.6381	+	436.049i	0.137464	+	1.31340i
$333$	92.6430	+	181.822i	0.278207	+	0.546012i
$334$	−33.8660	−	114.422i	−0.101395	−	0.342579i
$335$	−181.966	−	361.645i	−0.543183	−	1.07954i
$336$	128.556	+	223.114i	0.382606	+	0.664031i
$337$	−350.857	−	178.771i	−1.04112	−	0.530477i	−0.152109	−	0.988364i	$-0.548606\pi$
$337$	−350.857	−	178.771i	−1.04112	−	0.530477i	−0.889010	+	0.457887i	$0.848606\pi$
$338$	40.0952	−	19.1137i	0.118625	−	0.0565494i
$339$	115.962	+	84.2514i	0.342071	+	0.248529i
$340$	−275.651	−	60.1782i	−0.810738	−	0.176995i
$341$	148.158	−	159.899i	0.434480	−	0.468913i
$342$	−98.7034	+	93.6251i	−0.288606	+	0.273758i
$343$	−747.573	+	118.404i	−2.17951	+	0.345201i
$344$	−110.539	+	266.371i	−0.321334	+	0.774335i
$345$	160.372	−	218.399i	0.464847	−	0.633040i
$346$	−470.546	+	323.246i	−1.35996	+	0.934238i
$347$	461.418	+	73.0815i	1.32974	+	0.210609i	0.780551	−	0.625092i	$-0.214938\pi$
$347$	461.418	+	73.0815i	1.32974	+	0.210609i	0.549184	+	0.835701i	$0.314938\pi$
$348$	−104.112	−	60.1695i	−0.299171	−	0.172901i
$349$	11.3458	−	34.9188i	0.0325095	−	0.100054i	−0.933485	−	0.358616i	$-0.883249\pi$
$349$	11.3458	−	34.9188i	0.0325095	−	0.100054i	0.965995	+	0.258562i	$0.0832487\pi$
$350$	521.909	−	350.803i	1.49117	−	1.00229i
$351$	289.526			0.824860
$352$	302.918	−	179.290i	0.860562	−	0.509345i
$353$	459.925	−	459.925i	1.30290	−	1.30290i	0.376479	−	0.926425i	$-0.377135\pi$
$353$	459.925	−	459.925i	1.30290	−	1.30290i	0.926425	−	0.376479i	$-0.122865\pi$
$354$	−104.567	−	80.2736i	−0.295388	−	0.226761i
$355$	151.163	−	48.2707i	0.425810	−	0.135974i
$356$	43.9487	+	164.306i	0.123451	+	0.461533i
$357$	224.243	+	35.5166i	0.628131	+	0.0994862i
$358$	−35.9203	+	193.573i	−0.100336	+	0.540707i
$359$	−76.3153	+	24.7963i	−0.212577	+	0.0690706i	−0.413370	−	0.910563i	$-0.635648\pi$
$359$	−76.3153	+	24.7963i	−0.212577	+	0.0690706i	0.200792	+	0.979634i	$0.435648\pi$
$360$	−250.221	−	155.311i	−0.695057	−	0.431419i
$361$	−223.000	−	162.019i	−0.617727	−	0.448805i
$362$	−305.550	+	289.830i	−0.844062	+	0.800635i
$363$	−150.641	+	35.7919i	−0.414988	+	0.0986003i
$364$	694.681	+	36.7108i	1.90846	+	0.100854i
$365$	193.775	+	195.748i	0.530890	+	0.536295i
$366$	30.2852	+	10.7320i	0.0827464	+	0.0293224i
$367$	127.184	+	64.8033i	0.346550	+	0.176576i	0.618598	−	0.785708i	$-0.287701\pi$
$367$	127.184	+	64.8033i	0.346550	+	0.176576i	−0.272048	+	0.962284i	$0.587701\pi$
$368$	−654.349	−	175.945i	−1.77812	−	0.478111i
$369$	75.2985	−	54.7076i	0.204061	−	0.148259i
$370$	218.994	+	169.886i	0.591877	+	0.459151i
$371$	−27.9846	+	86.1277i	−0.0754302	+	0.232150i
$372$	−10.5586	−	100.882i	−0.0283834	−	0.271189i
$373$	−278.179	−	278.179i	−0.745788	−	0.745788i	0.227897	−	0.973685i	$-0.426815\pi$
$373$	−278.179	−	278.179i	−0.745788	−	0.745788i	−0.973685	+	0.227897i	$0.926815\pi$
$374$	44.9615	−	307.084i	0.120218	−	0.821080i
$375$	74.7739	−	141.399i	0.199397	−	0.377065i
$376$	155.342	+	132.850i	0.413143	+	0.353325i
$377$	−289.448	+	147.481i	−0.767768	+	0.391197i
$378$	462.793	+	251.407i	1.22432	+	0.665098i
$379$	−495.949	+	360.328i	−1.30857	+	0.950734i	−1.00000		0.000466071i	$-0.999852\pi$
$379$	−495.949	+	360.328i	−1.30857	+	0.950734i	−0.308574	+	0.951200i	$0.599852\pi$
$380$	−67.1665	+	172.138i	−0.176754	+	0.452996i
$381$	−233.535	+	75.8801i	−0.612952	+	0.199160i
$382$	324.677	−	154.776i	0.849940	−	0.405173i
$383$	−44.8932	−	283.445i	−0.117215	−	0.740064i	−0.974361	−	0.224991i	$-0.927765\pi$
$383$	−44.8932	−	283.445i	−0.117215	−	0.740064i	0.857146	−	0.515073i	$-0.172235\pi$
$384$	30.0947	−	161.003i	0.0783717	−	0.419279i
$385$	424.852	+	545.892i	1.10351	+	1.41790i
$386$	246.529	+	6.50945i	0.638677	+	0.0168639i
$387$	41.5204	+	262.150i	0.107288	+	0.677389i
$388$	−27.9986	−	62.9598i	−0.0721613	−	0.162268i
$389$	443.797	−	144.198i	1.14087	−	0.370690i	0.323170	−	0.946341i	$-0.395251\pi$
$389$	443.797	−	144.198i	1.14087	−	0.370690i	0.817695	+	0.575651i	$0.195251\pi$
$390$	160.107	−	75.3316i	0.410531	−	0.193158i
$391$	−483.332	+	351.161i	−1.23614	+	0.898110i
$392$	744.436	+	456.862i	1.89907	+	1.16546i
$393$	−232.079	+	118.250i	−0.590533	+	0.300891i
$394$	−357.982	+	466.320i	−0.908583	+	1.18355i
$395$	182.345	+	253.668i	0.461632	+	0.642196i
$396$	151.299	−	286.451i	0.382067	−	0.723361i
$397$	−250.793	−	250.793i	−0.631720	−	0.631720i	0.316779	−	0.948499i	$-0.397399\pi$
$397$	−250.793	−	250.793i	−0.631720	−	0.631720i	−0.948499	+	0.316779i	$0.897399\pi$
$398$	41.4990	−	5.45423i	0.104269	−	0.0137041i
$399$	45.9475	−	141.412i	0.115157	−	0.354415i
$400$	−397.325	−	46.1856i	−0.993312	−	0.115464i
$401$	−243.162	+	176.668i	−0.606390	+	0.440568i	−0.848141	−	0.529770i	$-0.822278\pi$
$401$	−243.162	+	176.668i	−0.606390	+	0.440568i	0.241751	+	0.970338i	$0.422278\pi$
$402$	37.8072	−	203.741i	0.0940477	−	0.506818i
$403$	−244.160	−	124.406i	−0.605855	−	0.308699i
$404$	208.564	−	542.619i	0.516247	−	1.34312i
$405$	−197.350	−	0.999495i	−0.487284	−	0.00246789i
$406$	−590.733	−	15.5979i	−1.45501	−	0.0384186i
$407$	−169.680	+	253.300i	−0.416903	+	0.622358i
$408$	−93.7180	−	109.875i	−0.229701	−	0.269302i
$409$	19.9686	+	14.5081i	0.0488230	+	0.0354720i	0.611929	−	0.790913i	$-0.290394\pi$
$409$	19.9686	+	14.5081i	0.0488230	+	0.0354720i	−0.563106	+	0.826385i	$0.690394\pi$
$410$	60.9062	−	110.776i	0.148552	−	0.270185i
$411$	−49.7318	+	16.1588i	−0.121002	+	0.0393159i
$412$	27.4388	−	128.813i	0.0665990	−	0.312652i
$413$	−639.863	−	101.344i	−1.54930	−	0.245386i
$414$	−597.960	+	176.982i	−1.44435	+	0.427492i
$415$	487.040	+	251.274i	1.17359	+	0.605480i
$416$	−320.639	−	304.941i	−0.770766	−	0.733030i
$417$	−13.5976	+	13.5976i	−0.0326082	+	0.0326082i
$418$	−194.029	−	60.5440i	−0.464185	−	0.144842i
$419$	−18.9614			−0.0452539			−0.0226269	−	0.999744i	$-0.507203\pi$
$419$	−18.9614			−0.0452539			−0.0226269	+	0.999744i	$0.507203\pi$
$420$	321.337	+	18.6137i	0.765089	+	0.0443183i
$421$	−132.572	+	408.015i	−0.314898	+	0.969157i	0.660898	+	0.750475i	$0.270175\pi$
$421$	−132.572	+	408.015i	−0.314898	+	0.969157i	−0.975796	+	0.218681i	$0.929825\pi$
$422$	−508.874	−	276.440i	−1.20586	−	0.655071i
$423$	185.800	+	29.4278i	0.439242	+	0.0695692i
$424$	49.1349	−	30.0656i	0.115884	−	0.0709095i
$425$	−251.895	+	246.843i	−0.592694	+	0.580808i
$426$	76.5569	+	27.1290i	0.179711	+	0.0636832i
$427$	155.956	−	24.7010i	0.365237	−	0.0578478i
$428$	−283.842	+	255.348i	−0.663181	+	0.596607i
$429$	94.9051	+	169.933i	0.221224	+	0.396114i
$430$	202.615	+	298.168i	0.471197	+	0.693415i
$431$	−513.594	−	373.148i	−1.19163	−	0.865772i	−0.198197	−	0.980162i	$-0.563508\pi$
$431$	−513.594	−	373.148i	−1.19163	−	0.865772i	−0.993436	+	0.114391i	$0.963508\pi$
$432$	−119.782	−	312.860i	−0.277274	−	0.724213i
$433$	344.698	+	175.633i	0.796070	+	0.405618i	0.804207	−	0.594349i	$-0.202590\pi$
$433$	344.698	+	175.633i	0.796070	+	0.405618i	−0.00813710	+	0.999967i	$0.502590\pi$
$434$	−282.251	−	410.870i	−0.650348	−	0.946705i
$435$	−134.271	+	67.5602i	−0.308669	+	0.155311i
$436$	272.696	−	72.9412i	0.625450	−	0.167296i
$437$	177.630	+	348.618i	0.406475	+	0.797752i
$438$	18.3714	+	139.780i	0.0419438	+	0.319133i
$439$		−	23.8521i		−	0.0543328i	−0.999631	−	0.0271664i	$-0.991352\pi$
$439$		−	23.8521i		−	0.0543328i	0.999631	−	0.0271664i	$-0.00864840\pi$
$440$	20.3044	−	439.531i	0.0461464	−	0.998935i
$441$	803.850			1.82279
$442$	−386.817	+	50.8395i	−0.875151	+	0.115021i
$443$	605.407	−	308.470i	1.36661	−	0.696322i	0.391943	−	0.919990i	$-0.371803\pi$
$443$	605.407	−	308.470i	1.36661	−	0.696322i	0.974665	+	0.223668i	$0.0718032\pi$
$444$	36.6578	+	137.048i	0.0825626	+	0.308667i
$445$	201.862	+	66.7209i	0.453621	+	0.149935i
$446$	593.308	−	407.579i	1.33029	−	0.913854i
$447$	−34.6930	+	68.0889i	−0.0776130	+	0.152324i
$448$	−247.733	−	765.857i	−0.552976	−	1.70950i
$449$	−37.5024	+	51.6176i	−0.0835243	+	0.114961i	−0.848735	−	0.528819i	$-0.822635\pi$
$449$	−37.5024	+	51.6176i	−0.0835243	+	0.114961i	0.765210	+	0.643780i	$0.222635\pi$
$450$	−333.889	+	155.037i	−0.741976	+	0.344526i
$451$	126.215	+	58.3656i	0.279856	+	0.129414i
$452$	−299.665	−	333.105i	−0.662977	−	0.736957i
$453$	47.9823	+	302.948i	0.105921	+	0.668760i
$454$	192.955	−	544.511i	0.425011	−	1.19936i
$455$	514.672	−	700.893i	1.13115	−	1.54043i
$456$	−80.6738	+	49.3643i	−0.176916	+	0.108255i
$457$	45.1170	−	284.857i	0.0987242	−	0.623320i	−0.887866	−	0.460102i	$-0.847813\pi$
$457$	45.1170	−	284.857i	0.0987242	−	0.623320i	0.986590	−	0.163218i	$-0.0521873\pi$
$458$	156.920	−	288.860i	0.342620	−	0.630699i
$459$	−280.918	−	91.2758i	−0.612022	−	0.198858i
$460$	−632.544	+	563.275i	−1.37509	+	1.22451i
$461$		−	210.778i		−	0.457219i	−0.973518	−	0.228610i	$-0.926582\pi$
$461$		−	210.778i		−	0.457219i	0.973518	−	0.228610i	$-0.0734179\pi$
$462$	4.14182	+	354.039i	0.00896498	+	0.766319i
$463$	−425.161	−	425.161i	−0.918275	−	0.918275i	0.0786294	−	0.996904i	$-0.474946\pi$
$463$	−425.161	−	425.161i	−0.918275	−	0.918275i	−0.996904	+	0.0786294i	$0.974946\pi$
$464$	279.118	+	251.761i	0.601547	+	0.542588i
$465$	−112.679	−	58.1336i	−0.242321	−	0.125018i
$466$	122.316	+	413.265i	0.262482	+	0.886834i
$467$	71.3695	−	450.609i	0.152826	−	0.964902i	−0.785428	−	0.618953i	$-0.787557\pi$
$467$	71.3695	−	450.609i	0.152826	−	0.964902i	0.938253	−	0.345949i	$-0.112443\pi$
$468$	−398.297	−	84.8425i	−0.851063	−	0.181287i
$469$	−314.686	−	968.503i	−0.670972	−	2.06504i
$470$	245.361	−	71.2715i	0.522044	−	0.151641i
$471$	21.9968	−	30.2760i	0.0467024	−	0.0642803i
$472$	267.418	+	313.522i	0.566564	+	0.664242i
$473$	−311.701	+	245.133i	−0.658988	+	0.518252i
$474$	−4.22070	+	159.848i	−0.00890442	+	0.337233i
$475$	133.863	+	188.226i	0.281816	+	0.396266i
$476$	−662.454	−	254.624i	−1.39171	−	0.534925i
$477$	24.0678	−	47.2357i	0.0504566	−	0.0990266i
$478$	−453.623	−	84.1764i	−0.949002	−	0.176101i
$479$	67.9061	+	93.4647i	0.141766	+	0.195125i	0.873996	−	0.485933i	$-0.161520\pi$
$479$	67.9061	+	93.4647i	0.141766	+	0.195125i	−0.732230	+	0.681058i	$0.761520\pi$
$480$	−147.642	−	141.845i	−0.307588	−	0.295510i
$481$	364.499	+	118.433i	0.757795	+	0.246223i
$482$	−35.1756	−	267.636i	−0.0729784	−	0.555262i
$483$	481.938	−	481.938i	0.997801	−	0.997801i
$484$	483.868	−	11.3229i	0.999726	−	0.0233943i
$485$	−85.0012	−	13.9045i	−0.175260	−	0.0286691i
$486$	−379.078	−	291.008i	−0.779995	−	0.598782i
$487$	310.925	+	610.224i	0.638449	+	1.25303i	0.952765	+	0.303708i	$0.0982249\pi$
$487$	310.925	+	610.224i	0.638449	+	1.25303i	−0.314316	+	0.949318i	$0.601775\pi$
$488$	−85.6026	−	52.5345i	−0.175415	−	0.107653i
$489$	−66.8992	−	92.0788i	−0.136808	−	0.188300i
$490$	987.918	−	464.822i	2.01616	−	0.948617i
$491$	101.745	+	313.138i	0.207220	+	0.637756i	0.999615	+	0.0277483i	$0.00883370\pi$
$491$	101.745	+	313.138i	0.207220	+	0.637756i	−0.792395	+	0.610008i	$0.791166\pi$
$492$	59.1229	−	26.2923i	0.120168	−	0.0534396i
$493$	327.338	−	51.8452i	0.663971	−	0.105163i
$494$	−6.74418	+	255.419i	−0.0136522	+	0.517043i
$495$	−195.655	−	354.537i	−0.395263	−	0.716236i
$496$	−33.4185	+	315.307i	−0.0673759	+	0.635699i
$497$	394.236	−	62.4408i	0.793231	−	0.125635i
$498$	120.709	+	253.213i	0.242387	+	0.508460i
$499$	119.220	+	366.921i	0.238918	+	0.735313i	0.996578	+	0.0826633i	$0.0263426\pi$
$499$	119.220	+	366.921i	0.238918	+	0.735313i	−0.757660	+	0.652650i	$0.773657\pi$
$500$	−320.695	+	383.608i	−0.641390	+	0.767215i
$501$	−44.8759	−	61.7664i	−0.0895727	−	0.123286i
$502$	161.483	−	297.260i	0.321679	−	0.592151i
$503$	181.255	+	355.732i	0.360347	+	0.707221i	0.998007	−	0.0630966i	$-0.0200976\pi$
$503$	181.255	+	355.732i	0.360347	+	0.707221i	−0.637660	+	0.770318i	$0.720098\pi$
$504$	−562.987	−	481.474i	−1.11704	−	0.955306i
$505$	−424.132	−	590.029i	−0.839865	−	1.16837i
$506$	−666.464	−	651.051i	−1.31712	−	1.28666i
$507$	20.0954	−	20.0954i	0.0396358	−	0.0396358i
$508$	763.410	−	79.9007i	1.50278	−	0.157285i
$509$	−245.184	−	79.6652i	−0.481698	−	0.156513i	0.0580947	−	0.998311i	$-0.481497\pi$
$509$	−245.184	−	79.6652i	−0.481698	−	0.156513i	−0.539793	+	0.841798i	$0.681497\pi$
$510$	−179.096	+	22.6166i	−0.351169	+	0.0443462i
$511$	407.238	+	560.515i	0.796943	+	1.09690i
$512$	−196.863	+	472.640i	−0.384498	+	0.923126i
$513$	−87.8215	+	172.359i	−0.171192	+	0.335983i
$514$	−320.816	+	905.329i	−0.624156	+	1.76134i
$515$	−115.819	−	116.998i	−0.224891	−	0.227181i
$516$	−9.73744	+	184.262i	−0.0188710	+	0.357097i
$517$	96.9677	+	263.795i	0.187558	+	0.510242i
$518$	479.795	+	505.819i	0.926244	+	0.976485i
$519$	−214.691	+	295.497i	−0.413663	+	0.569358i
$520$	−538.560	+	126.044i	−1.03569	+	0.242391i
$521$	−253.411	−	779.918i	−0.486393	−	1.49696i	−0.829953	−	0.557833i	$-0.811633\pi$
$521$	−253.411	−	779.918i	−0.486393	−	1.49696i	0.343561	−	0.939131i	$-0.388367\pi$
$522$	340.129	+	63.1160i	0.651589	+	0.120912i
$523$	11.9863	−	75.6784i	0.0229183	−	0.144701i	−0.973576	−	0.228364i	$-0.926662\pi$
$523$	11.9863	−	75.6784i	0.0229183	−	0.144701i	0.996494	+	0.0836639i	$0.0266622\pi$
$524$	786.554	−	210.388i	1.50106	−	0.401505i
$525$	239.777	−	323.092i	0.456719	−	0.615413i
$526$	235.093	−	306.241i	0.446945	−	0.582207i
$527$	197.680	+	197.680i	0.375105	+	0.375105i
$528$	144.364	−	172.858i	0.273417	−	0.327383i
$529$			1264.48i			2.39031i
$530$	2.26509	−	71.9689i	0.00427375	−	0.135790i
$531$	360.683	+	117.193i	0.679252	+	0.220703i
$532$	−232.571	+	402.419i	−0.437164	+	0.756427i
$533$	27.3455	−	172.653i	0.0513049	−	0.323926i
$534$	61.6169	+	89.6951i	0.115387	+	0.167968i
$535$	72.2695	+	471.742i	0.135083	+	0.881761i
$536$	−248.275	+	598.281i	−0.463200	+	1.11620i
$537$	19.7052	+	124.414i	0.0366949	+	0.231683i
$538$	−477.649	−	503.558i	−0.887824	−	0.935981i
$539$	585.598	+	1048.54i	1.08645	+	1.94535i
$540$	−409.122	−	89.3167i	−0.757633	−	0.165401i
$541$	−92.3756	+	127.144i	−0.170750	+	0.235017i	−0.885812	−	0.464044i	$-0.846398\pi$
$541$	−92.3756	+	127.144i	−0.170750	+	0.235017i	0.715063	+	0.699060i	$0.246398\pi$
$542$	294.209	+	617.169i	0.542821	+	1.13869i
$543$	−122.329	+	240.084i	−0.225284	+	0.442144i
$544$	214.970	+	396.959i	0.395166	+	0.729704i
$545$	110.736	−	335.027i	0.203185	−	0.614729i
$546$	426.784	−	126.318i	0.781655	−	0.231351i
$547$	−681.405	+	347.193i	−1.24571	+	0.634723i	−0.947494	−	0.319775i	$-0.896393\pi$
$547$	−681.405	+	347.193i	−1.24571	+	0.634723i	−0.298220	+	0.954497i	$0.596393\pi$
$548$	162.570	−	17.0150i	0.296660	−	0.0310493i
$549$	−92.4347			−0.168369
$550$	−445.466	−	322.583i	−0.809938	−	0.586515i
$551$		−	217.049i		−	0.393918i
$552$	−432.216	+	33.7313i	−0.783000	+	0.0611075i
$553$	356.756	+	700.173i	0.645128	+	1.26614i
$554$	527.485	−	156.123i	0.952139	−	0.281810i
$555$	168.373	+	55.6522i	0.303376	+	0.100274i
$556$	50.4278	−	32.7169i	0.0906975	−	0.0588434i
$557$	−170.997	−	87.1273i	−0.306996	−	0.156422i	0.293705	−	0.955896i	$-0.405112\pi$
$557$	−170.997	−	87.1273i	−0.306996	−	0.156422i	−0.600701	+	0.799474i	$0.705112\pi$
$558$	125.569	+	263.410i	0.225035	+	0.472060i
$559$	403.285	+	293.003i	0.721439	+	0.524156i
$560$	−970.312	−	266.179i	−1.73270	−	0.475320i
$561$	−38.5106	−	194.800i	−0.0686463	−	0.347237i
$562$	−510.201	−	537.874i	−0.907830	−	0.957072i
$563$	853.232	−	135.139i	1.51551	−	0.240033i	0.657416	−	0.753528i	$-0.271649\pi$
$563$	853.232	−	135.139i	1.51551	−	0.240033i	0.858093	+	0.513495i	$0.171649\pi$
$564$	122.072	+	46.9202i	0.216440	+	0.0831918i
$565$	−553.617	+	84.8124i	−0.979852	+	0.150110i
$566$	392.155	+	570.856i	0.692853	+	1.00858i
$567$	−490.308	−	77.6572i	−0.864741	−	0.136962i
$568$	−216.392	−	132.800i	−0.380972	−	0.233803i
$569$	202.545	−	623.371i	0.355967	−	1.09556i	−0.599479	−	0.800391i	$-0.704625\pi$
$569$	202.545	−	623.371i	0.355967	−	1.09556i	0.955446	−	0.295165i	$-0.0953745\pi$
$570$	−3.71901	+	118.165i	−0.00652459	+	0.207306i
$571$	−135.907			−0.238016			−0.119008	−	0.992893i	$-0.537971\pi$
$571$	−135.907			−0.238016			−0.119008	+	0.992893i	$0.537971\pi$
$572$	−179.487	−	581.347i	−0.313789	−	1.01634i
$573$	162.725	−	162.725i	0.283988	−	0.283988i
$574$	193.632	−	252.232i	0.337338	−	0.439428i
$575$	155.022	+	1047.33i	0.269604	+	1.82144i
$576$	73.1029	+	465.499i	0.126915	+	0.808158i
$577$	142.991	+	22.6475i	0.247818	+	0.0392505i	0.279108	−	0.960260i	$-0.409961\pi$
$577$	142.991	+	22.6475i	0.247818	+	0.0392505i	−0.0312896	+	0.999510i	$0.509961\pi$
$578$	−176.954	−	32.8365i	−0.306150	−	0.0568106i
$579$	150.065	−	48.7589i	0.259179	−	0.0842123i
$580$	454.510	−	119.110i	0.783637	−	0.205361i
$581$	1115.26	+	810.283i	1.91955	+	1.39463i
$582$	−30.3398	−	31.9855i	−0.0521303	−	0.0549579i
$583$	79.1475	−	3.01670i	0.135759	−	0.00517444i
$584$	34.8646	−	439.319i	0.0596997	−	0.752258i
$585$	−361.765	+	358.119i	−0.618402	+	0.612170i
$586$	191.970	−	541.730i	0.327593	−	0.924453i
$587$	−27.7181	−	14.1231i	−0.0472199	−	0.0240597i	0.430221	−	0.902724i	$-0.358436\pi$
$587$	−27.7181	−	14.1231i	−0.0472199	−	0.0240597i	−0.477441	+	0.878664i	$0.658436\pi$
$588$	546.577	+	116.428i	0.929553	+	0.198007i
$589$	148.121	−	107.616i	0.251479	−	0.182710i
$590$	511.040	−	64.5350i	0.866169	−	0.109381i
$591$	−116.232	+	357.724i	−0.196669	+	0.605286i
$592$	−22.8223	−	442.874i	−0.0385512	−	0.748099i
$593$	407.789	+	407.789i	0.687671	+	0.687671i	0.961717	−	0.274046i	$-0.0883621\pi$
$593$	407.789	+	407.789i	0.687671	+	0.687671i	−0.274046	+	0.961717i	$0.588362\pi$
$594$	66.7319	−	455.774i	0.112343	−	0.767297i
$595$	−720.334	+	517.800i	−1.21065	+	0.870252i
$596$	150.411	−	185.576i	0.252367	−	0.311370i
$597$	23.8610	−	12.1578i	0.0399682	−	0.0203648i
$598$	−559.074	+	1029.15i	−0.934906	+	1.72099i
$599$	411.162	−	298.727i	0.686414	−	0.498709i	−0.189065	−	0.981964i	$-0.560546\pi$
$599$	411.162	−	298.727i	0.686414	−	0.498709i	0.875479	+	0.483256i	$0.160546\pi$
$600$	−249.483	+	57.0573i	−0.415805	+	0.0950955i
$601$	−521.114	+	169.320i	−0.867078	+	0.281731i	−0.708582	−	0.705629i	$-0.750665\pi$
$601$	−521.114	+	169.320i	−0.867078	+	0.281731i	−0.158496	+	0.987360i	$0.550665\pi$
$602$	390.204	+	818.540i	0.648180	+	1.35970i
$603$	93.2566	+	588.799i	0.154654	+	0.976450i
$604$	50.5976	−	957.462i	0.0837709	−	1.58520i
$605$	319.926	−	513.490i	0.528803	−	0.848744i
$606$	9.81730	−	371.806i	0.0162002	−	0.613541i
$607$	−62.2856	−	393.256i	−0.102612	−	0.647868i	−0.984363	−	0.176152i	$-0.943635\pi$
$607$	−62.2856	−	393.256i	−0.102612	−	0.647868i	0.881751	−	0.471716i	$-0.156365\pi$
$608$	278.795	−	98.3841i	0.458544	−	0.161816i
$609$	−359.584	+	116.836i	−0.590451	+	0.191849i
$610$	−113.601	+	53.4499i	−0.186231	+	0.0876228i
$611$	285.830	−	207.667i	0.467806	−	0.339881i
$612$	359.708	+	207.887i	0.587759	+	0.339685i
$613$	−391.518	+	199.488i	−0.638692	+	0.325430i	−0.743175	−	0.669097i	$-0.766681\pi$
$613$	−391.518	+	199.488i	−0.638692	+	0.325430i	0.104483	+	0.994527i	$0.466681\pi$
$614$	561.520	+	431.065i	0.914528	+	0.702059i
$615$	13.0571	−	79.8210i	0.0212311	−	0.129790i
$616$	217.905	−	1085.11i	0.353743	−	1.76155i
$617$	−597.836	−	597.836i	−0.968941	−	0.968941i	0.0305913	−	0.999532i	$-0.490261\pi$
$617$	−597.836	−	597.836i	−0.968941	−	0.968941i	−0.999532	+	0.0305913i	$0.990261\pi$
$618$	−10.9805	−	83.5464i	−0.0177679	−	0.135188i
$619$	−30.6391	+	94.2974i	−0.0494977	+	0.152338i	−0.972750	−	0.231855i	$-0.925520\pi$
$619$	−30.6391	+	94.2974i	−0.0494977	+	0.152338i	0.923253	+	0.384193i	$0.125520\pi$
$620$	306.638	+	251.116i	0.494577	+	0.405026i
$621$	−717.362	+	521.194i	−1.15517	+	0.839282i
$622$	533.010	+	98.9079i	0.856929	+	0.159016i
$623$	476.492	+	242.785i	0.764835	+	0.389703i
$624$	−258.534	−	115.377i	−0.414317	−	0.184899i
$625$	181.055	+	598.201i	0.289688	+	0.957121i
$626$	−20.1652	+	763.707i	−0.0322128	+	1.21998i
$627$	−129.951	+	4.95307i	−0.207258	+	0.00789964i
$628$	−86.9689	+	78.2384i	−0.138485	+	0.124583i
$629$	−316.325	−	229.824i	−0.502902	−	0.365380i
$630$	−889.234	+	258.301i	−1.41148	+	0.410002i
$631$	136.339	−	44.2994i	0.216069	−	0.0702050i	−0.198982	−	0.980003i	$-0.563764\pi$
$631$	136.339	−	44.2994i	0.216069	−	0.0702050i	0.415051	+	0.909798i	$0.363764\pi$
$632$	117.005	−	485.960i	0.185135	−	0.768925i
$633$	−365.961	−	57.9625i	−0.578137	−	0.0915680i
$634$	−235.458	−	795.531i	−0.371385	−	1.25478i
$635$	439.917	−	852.681i	0.692782	−	1.34281i
$636$	23.2064	−	28.6319i	0.0364880	−	0.0450188i
$637$	1067.54	−	1067.54i	1.67589	−	1.67589i
$638$	165.453	+	489.645i	0.259330	+	0.767469i
$639$	−233.662			−0.365669
$640$	359.015	+	529.819i	0.560961	+	0.827842i
$641$	−124.564	+	383.368i	−0.194327	+	0.598078i	0.805656	+	0.592383i	$0.201813\pi$
$641$	−124.564	+	383.368i	−0.194327	+	0.598078i	−0.999984	+	0.00569511i	$0.998187\pi$
$642$	−116.606	+	214.650i	−0.181629	+	0.334346i
$643$	−311.199	−	49.2891i	−0.483980	−	0.0766548i	−0.0903232	−	0.995913i	$-0.528790\pi$
$643$	−311.199	−	49.2891i	−0.483980	−	0.0766548i	−0.393656	+	0.919258i	$0.628790\pi$
$644$	−1787.31	+	1159.58i	−2.77532	+	1.80059i
$645$	185.910	+	136.515i	0.288233	+	0.211652i
$646$	87.0670	−	245.699i	0.134779	−	0.380339i
$647$	−935.119	+	148.108i	−1.44532	+	0.228915i	−0.829293	−	0.558814i	$-0.811257\pi$
$647$	−935.119	+	148.108i	−1.44532	+	0.228915i	−0.616022	+	0.787729i	$0.711257\pi$
$648$	204.915	+	240.243i	0.316227	+	0.370746i
$649$	109.888	+	555.850i	0.169318	+	0.856472i
$650$	−237.523	+	649.312i	−0.365419	+	0.998941i
$651$	−258.021	−	187.463i	−0.396345	−	0.287962i
$652$	144.566	+	325.083i	0.221728	+	0.498594i
$653$	27.7207	+	14.1244i	0.0424513	+	0.0216300i	0.475087	−	0.879939i	$-0.342416\pi$
$653$	27.7207	+	14.1244i	0.0424513	+	0.0216300i	−0.432636	+	0.901569i	$0.642416\pi$
$654$	148.866	−	102.265i	0.227624	−	0.156368i
$655$	319.402	−	966.339i	0.487637	−	1.47533i
$656$	−197.881	+	41.8804i	−0.301648	+	0.0638420i
$657$	−184.132	−	361.379i	−0.280262	−	0.550044i
$658$	637.211	−	83.7489i	0.968405	−	0.127278i
$659$			495.499i			0.751895i	0.926641	+	0.375948i	$0.122683\pi$
$659$			495.499i			0.751895i	−0.926641	+	0.375948i	$0.877317\pi$
$660$	−81.6851	−	269.405i	−0.123765	−	0.408190i
$661$	278.241			0.420940			0.210470	−	0.977600i	$-0.432501\pi$
$661$	278.241			0.420940			0.210470	+	0.977600i	$0.432501\pi$
$662$	56.0292	+	426.303i	0.0846362	+	0.643962i
$663$	−222.411	+	113.324i	−0.335462	+	0.170926i
$664$	−204.141	−	852.768i	−0.307441	−	1.28429i
$665$	261.138	+	518.994i	0.392689	+	0.780441i
$666$	−231.092	−	336.399i	−0.346986	−	0.505103i
$667$	451.680	−	886.471i	0.677181	−	1.32904i
$668$	96.9750	+	218.066i	0.145172	+	0.326446i
$669$	270.702	−	372.590i	0.404637	−	0.556935i
$670$	455.081	+	669.699i	0.679226	+	0.999551i
$671$	−67.3379	−	120.572i	−0.100355	−	0.179690i
$672$	−313.067	−	408.920i	−0.465873	−	0.608512i
$673$	−104.338	−	658.765i	−0.155034	−	0.978849i	−0.935417	−	0.353547i	$-0.884976\pi$
$673$	−104.338	−	658.765i	−0.155034	−	0.978849i	0.780383	−	0.625302i	$-0.215024\pi$
$674$	742.322	+	263.052i	1.10137	+	0.390285i
$675$	−373.863	+	366.365i	−0.553872	+	0.542763i
$676$	−74.5252	+	48.3510i	−0.110244	+	0.0715252i
$677$	−59.2079	+	373.824i	−0.0874563	+	0.552178i	0.904588	+	0.426287i	$0.140179\pi$
$677$	−59.2079	+	373.824i	−0.0874563	+	0.552178i	−0.992044	+	0.125890i	$0.959821\pi$
$678$	−251.904	−	136.844i	−0.371540	−	0.201835i
$679$	−206.050	−	66.9496i	−0.303461	−	0.0986003i
$680$	562.285	+	47.4902i	0.826890	+	0.0698385i
$681$		−	369.611i		−	0.542748i
$682$	−252.116	+	355.685i	−0.369672	+	0.521532i
$683$	271.543	+	271.543i	0.397573	+	0.397573i	0.877376	−	0.479803i	$-0.159292\pi$
$683$	271.543	+	271.543i	0.397573	+	0.397573i	−0.479803	+	0.877376i	$0.659292\pi$
$684$	171.323	−	211.378i	0.250472	−	0.309032i
$685$	93.6813	−	181.580i	0.136761	−	0.265081i
$686$	1451.54	−	429.621i	2.11595	−	0.626270i
$687$	32.9022	−	207.736i	0.0478926	−	0.302382i
$688$	149.771	−	557.009i	0.217691	−	0.809605i
$689$	−30.7678	−	94.6936i	−0.0446557	−	0.137436i
$690$	−261.091	+	474.870i	−0.378392	+	0.688217i
$691$	295.402	−	406.585i	0.427499	−	0.588402i	−0.539878	−	0.841743i	$-0.681530\pi$
$691$	295.402	−	406.585i	0.427499	−	0.588402i	0.967377	+	0.253342i	$0.0815297\pi$
$692$	848.824	−	763.614i	1.22662	−	1.10349i
$693$	−351.429	−	956.044i	−0.507113	−	1.37957i
$694$	−934.014	−	24.6621i	−1.34584	−	0.0355361i
$695$	0.380543	−	75.1381i	0.000547544	−	0.108112i
$696$	222.129	+	92.1793i	0.319151	+	0.132442i
$697$	−80.9629	+	158.899i	−0.116159	+	0.227975i
$698$	−13.3976	+	72.1991i	−0.0191943	+	0.103437i
$699$	162.082	+	223.086i	0.231876	+	0.319150i
$700$	−943.492	+	831.643i	−1.34785	+	1.18806i
$701$	−812.067	−	263.857i	−1.15844	−	0.376400i	−0.334124	−	0.942529i	$-0.608441\pi$
$701$	−812.067	−	263.857i	−1.15844	−	0.376400i	−0.824317	+	0.566129i	$0.808441\pi$
$702$	−574.114	+	75.4561i	−0.817827	+	0.107487i
$703$	−181.068	+	181.068i	−0.257565	+	0.257565i
$704$	−553.944	+	434.468i	−0.786852	+	0.617142i
$705$	132.738	−	95.4162i	0.188280	−	0.135342i
$706$	−792.142	+	1031.87i	−1.12201	+	1.46158i
$707$	−829.811	−	1628.60i	−1.17371	−	2.30353i
$708$	228.272	+	131.926i	0.322418	+	0.186336i
$709$	−93.5263	−	128.728i	−0.131913	−	0.181563i	0.737951	−	0.674854i	$-0.235794\pi$
$709$	−93.5263	−	128.728i	−0.131913	−	0.181563i	−0.869864	+	0.493292i	$0.835794\pi$
$710$	−287.167	+	135.114i	−0.404461	+	0.190302i
$711$	−142.154	−	437.505i	−0.199935	−	0.615338i
$712$	−129.969	−	314.355i	−0.182541	−	0.441511i
$713$	828.908	−	131.286i	1.16256	−	0.184132i
$714$	−453.918	−	11.9854i	−0.635739	−	0.0167863i
$715$	−730.675	−	211.001i	−1.02192	−	0.295106i
$716$	20.7792	−	393.206i	0.0290213	−	0.549171i
$717$	−291.553	+	46.1775i	−0.406629	+	0.0644038i
$718$	144.867	−	69.0591i	0.201764	−	0.0961825i
$719$	215.325	+	662.701i	0.299478	+	0.921698i	0.981680	+	0.190535i	$0.0610222\pi$
$719$	215.325	+	662.701i	0.299478	+	0.921698i	−0.682203	+	0.731163i	$0.738978\pi$
$720$	536.651	+	242.761i	0.745349	+	0.337168i
$721$	−243.405	−	335.019i	−0.337594	−	0.464659i
$722$	484.421	+	263.156i	0.670944	+	0.364482i
$723$	−78.4084	−	153.885i	−0.108449	−	0.212843i
$724$	530.355	−	654.349i	0.732534	−	0.903798i
$725$	187.141	−	556.709i	0.258125	−	0.767875i
$726$	289.384	−	110.233i	0.398601	−	0.151837i
$727$	200.970	−	200.970i	0.276437	−	0.276437i	−0.555248	−	0.831685i	$-0.687377\pi$
$727$	200.970	−	200.970i	0.276437	−	0.276437i	0.831685	+	0.555248i	$0.187377\pi$
$728$	−1387.08	+	108.252i	−1.90533	+	0.148698i
$729$	47.0496	+	15.2873i	0.0645399	+	0.0209703i
$730$	−435.261	−	337.655i	−0.596247	−	0.462542i
$731$	−298.922	−	411.432i	−0.408923	−	0.562834i
$732$	−62.8509	−	13.3881i	−0.0858619	−	0.0182897i
$733$	327.790	−	643.323i	0.447189	−	0.877658i	−0.551855	−	0.833940i	$-0.686080\pi$
$733$	327.790	−	643.323i	0.447189	−	0.877658i	0.999044	−	0.0437176i	$-0.0139202\pi$
$734$	−269.088	−	95.3550i	−0.366604	−	0.129911i
$735$	496.445	−	491.442i	0.675435	−	0.668628i
$736$	1343.39	+	178.353i	1.82526	+	0.242328i
$737$	−700.095	+	550.580i	−0.949925	+	0.747055i
$738$	−135.055	+	128.106i	−0.183001	+	0.173586i
$739$	−191.895	+	264.121i	−0.259669	+	0.357403i	−0.918868	−	0.394565i	$-0.870895\pi$
$739$	−191.895	+	264.121i	−0.259669	+	0.357403i	0.659199	+	0.751968i	$0.270895\pi$
$740$	−478.530	−	279.800i	−0.646662	−	0.378109i
$741$	50.5172	+	155.476i	0.0681743	+	0.209819i
$742$	33.0454	−	178.080i	0.0445356	−	0.240000i
$743$	20.0681	−	126.705i	0.0270096	−	0.170532i	−0.970496	−	0.241116i	$-0.922486\pi$
$743$	20.0681	−	126.705i	0.0270096	−	0.170532i	0.997506	+	0.0705845i	$0.0224865\pi$
$744$	47.2291	+	197.292i	0.0634799	+	0.265178i
$745$	−90.8317	−	284.445i	−0.121922	−	0.381805i
$746$	624.113	+	479.115i	0.836612	+	0.642246i
$747$	−570.631	−	570.631i	−0.763897	−	0.763897i
$748$	−9.12420	+	620.649i	−0.0121981	+	0.829744i
$749$			1200.46i			1.60275i
$750$	−111.421	+	299.875i	−0.148562	+	0.399833i
$751$	−946.021	−	307.381i	−1.25968	−	0.409295i	−0.398300	−	0.917255i	$-0.630400\pi$
$751$	−946.021	−	307.381i	−1.25968	−	0.409295i	−0.861381	+	0.507960i	$0.830400\pi$
$752$	−342.658	−	222.950i	−0.455662	−	0.296476i
$753$	33.8589	−	213.777i	0.0449654	−	0.283900i
$754$	535.524	−	367.884i	0.710244	−	0.487909i
$755$	−966.024	−	709.361i	−1.27950	−	0.939550i
$756$	−983.216	−	377.914i	−1.30055	−	0.499886i
$757$	229.595	+	1449.61i	0.303296	+	1.91494i	0.394102	+	0.919067i	$0.371056\pi$
$757$	229.595	+	1449.61i	0.303296	+	1.91494i	−0.0908056	+	0.995869i	$0.528944\pi$
$758$	889.533	−	843.766i	1.17353	−	1.11315i
$759$	−541.055	−	250.200i	−0.712852	−	0.329644i
$760$	88.3251	−	358.846i	0.116217	−	0.472166i
$761$	401.804	−	553.035i	0.527994	−	0.726722i	−0.458829	−	0.888525i	$-0.651731\pi$
$761$	401.804	−	553.035i	0.527994	−	0.726722i	0.986823	+	0.161803i	$0.0517309\pi$
$762$	443.311	−	211.330i	0.581773	−	0.277336i
$763$	402.947	−	790.829i	0.528109	−	1.03647i
$764$	−603.480	+	391.530i	−0.789895	+	0.512474i
$765$	463.910	−	233.422i	0.606418	−	0.305127i
$766$	162.892	+	550.356i	0.212653	+	0.718480i
$767$	634.637	−	323.364i	0.827427	−	0.421595i
$768$	−17.7157	+	327.104i	−0.0230673	+	0.425916i
$769$	951.979			1.23794			0.618972	−	0.785413i	$-0.287549\pi$
$769$	951.979			1.23794

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.98295 + 0.260620i) q^{2} +(-1.14015 + 0.580936i) q^{3} +(3.86415 - 1.03359i) q^{4} +(1.56915 - 4.74740i) q^{5} +(2.10946 - 1.44911i) q^{6} +(5.70983 - 11.2062i) q^{7} +(-7.39304 + 3.05663i) q^{8} +(-4.32761 + 5.95644i) q^{9} +(-1.87427 + 9.82278i) q^{10} +(-10.9222 - 1.30573i) q^{11} +(-3.80527 + 3.42328i) q^{12} +(2.16315 + 13.6576i) q^{13} +(-8.40175 + 23.7094i) q^{14} +(0.968868 + 6.32433i) q^{15} +(13.8634 - 7.98790i) q^{16} +(2.20685 - 13.9335i) q^{17} +(7.02905 - 12.9392i) q^{18} +(-8.78672 - 2.85498i) q^{19} +(1.15657 - 19.9665i) q^{20} +16.0938i q^{21} +(21.9985 - 0.257355i) q^{22} +(-29.9456 - 29.9456i) q^{23} +(6.65348 - 7.77990i) q^{24} +(-20.0755 - 14.8987i) q^{25} +(-7.84885 - 26.5185i) q^{26} +(3.27541 - 20.6801i) q^{27} +(10.4811 - 49.2040i) q^{28} +(7.25970 + 22.3431i) q^{29} +(-3.56946 - 12.2883i) q^{30} +(-11.6482 + 16.0323i) q^{31} +(-25.4086 + 19.4526i) q^{32} +(13.2115 - 4.85639i) q^{33} +(-0.744723 + 28.2045i) q^{34} +(-44.2406 - 44.6910i) q^{35} +(-10.5660 + 27.4896i) q^{36} +(12.5830 - 24.6955i) q^{37} +(18.1677 + 3.37128i) q^{38} +(-10.4005 - 14.3151i) q^{39} +(2.91024 + 39.8940i) q^{40} +(-12.0228 - 3.90645i) q^{41} +(-4.19436 - 31.9131i) q^{42} +(25.4909 - 25.4909i) q^{43} +(-43.5548 + 6.24356i) q^{44} +(21.4869 + 29.8914i) q^{45} +(67.1849 + 51.5761i) q^{46} +(-11.5996 - 22.7655i) q^{47} +(-11.1659 + 17.1612i) q^{48} +(-64.1748 - 88.3290i) q^{49} +(43.6916 + 24.3113i) q^{50} +(5.57833 + 17.1683i) q^{51} +(22.4751 + 50.5392i) q^{52} +(-7.11181 + 1.12640i) q^{53} +(-1.10532 + 41.8612i) q^{54} +(-23.3374 + 49.8033i) q^{55} +(-7.95992 + 100.301i) q^{56} +(11.6768 - 1.84942i) q^{57} +(-20.2186 - 42.4131i) q^{58} +(-15.9174 - 48.9888i) q^{59} +(10.2806 + 23.4368i) q^{60} +(7.37946 + 10.1570i) q^{61} +(18.9194 - 34.8270i) q^{62} +(42.0390 + 82.5063i) q^{63} +(45.3141 - 45.1955i) q^{64} +(68.2323 + 11.1615i) q^{65} +(-24.9321 + 13.0731i) q^{66} +(57.2536 - 57.2536i) q^{67} +(-5.87390 - 56.1221i) q^{68} +(51.5390 + 16.7460i) q^{69} +(99.3741 + 77.0899i) q^{70} +(18.6543 + 25.6754i) q^{71} +(13.7876 - 57.2641i) q^{72} +(-25.0092 + 49.0833i) q^{73} +(-18.5152 + 52.2492i) q^{74} +(31.5444 + 5.32421i) q^{75} +(-36.9041 - 1.95022i) q^{76} +(-76.9963 + 114.941i) q^{77} +(24.3544 + 25.6754i) q^{78} +(-36.7254 + 50.5482i) q^{79} +(-16.1680 - 78.3492i) q^{80} +(-12.1971 - 37.5387i) q^{81} +(24.8587 + 4.61290i) q^{82} +(-17.1464 + 108.258i) q^{83} +(16.6344 + 62.1889i) q^{84} +(-62.6849 - 32.3405i) q^{85} +(-43.9036 + 57.1905i) q^{86} +(-21.2570 - 21.2570i) q^{87} +(84.7396 - 23.7319i) q^{88} +42.5205i q^{89} +(-50.3977 - 53.6732i) q^{90} +(165.401 + 53.7419i) q^{91} +(-146.666 - 84.7629i) q^{92} +(3.96692 - 25.0461i) q^{93} +(28.9345 + 42.1196i) q^{94} +(-27.3414 + 37.2342i) q^{95} +(17.6689 - 36.9397i) q^{96} +(-2.69477 - 17.0141i) q^{97} +(150.275 + 158.427i) q^{98} +(55.0446 - 59.4069i) 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

Introduction

L-functions

Modular forms

Varieties

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