LMFDB - Embedded newform 220.2.v.a.3.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(3,220)] 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("220.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 16])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.v (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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$32$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			3.15
Character	$\chi$	$=$	220.3
Dual form			220.2.v.a.147.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.262448 + 1.38965i) q^{2} +(-1.70123 - 0.866818i) q^{3} +(-1.86224 - 0.729420i) q^{4} +(-1.70162 + 1.45068i) q^{5} +(1.65105 - 2.13661i) q^{6} +(3.08760 - 1.57321i) q^{7} +(1.50238 - 2.39643i) q^{8} +(0.379441 + 0.522256i) q^{9} +(-1.56935 - 2.74538i) q^{10} +(-0.129499 - 3.31410i) q^{11} +(2.53582 + 2.85513i) q^{12} +(0.762891 + 0.120830i) q^{13} +(1.37588 + 4.70357i) q^{14} +(4.15232 - 0.992945i) q^{15} +(2.93589 + 2.71671i) q^{16} +(6.61747 - 1.04810i) q^{17} +(-0.825336 + 0.390225i) q^{18} +(-2.49041 - 7.66469i) q^{19} +(4.22699 - 1.46033i) q^{20} -6.61640 q^{21} +(4.63941 + 0.689820i) q^{22} +(-2.99206 + 2.99206i) q^{23} +(-4.63315 + 2.77457i) q^{24} +(0.791033 - 4.93703i) q^{25} +(-0.368130 + 1.02844i) q^{26} +(0.703241 + 4.44009i) q^{27} +(-6.89740 + 0.677543i) q^{28} +(-3.00842 - 0.977496i) q^{29} +(0.290076 + 6.03086i) q^{30} +(-2.39730 - 3.29961i) q^{31} +(-4.54579 + 3.36686i) q^{32} +(-2.65241 + 5.75028i) q^{33} +(-0.280245 + 9.47103i) q^{34} +(-2.97170 + 7.15615i) q^{35} +(-0.325668 - 1.24934i) q^{36} +(-2.40476 - 4.71961i) q^{37} +(11.3048 - 1.44921i) q^{38} +(-1.19311 - 0.866847i) q^{39} +(0.919977 + 6.25729i) q^{40} +(-0.427127 - 1.31456i) q^{41} +(1.73646 - 9.19446i) q^{42} +(4.80560 - 4.80560i) q^{43} +(-2.17621 + 6.26611i) q^{44} +(-1.40329 - 0.338233i) q^{45} +(-3.37266 - 4.94318i) q^{46} +(-1.43672 + 2.81973i) q^{47} +(-2.63972 - 7.16663i) q^{48} +(2.94379 - 4.05179i) q^{49} +(6.65313 + 2.39497i) q^{50} +(-12.1663 - 3.95308i) q^{51} +(-1.33255 - 0.781483i) q^{52} +(2.68953 + 0.425980i) q^{53} +(-6.35472 - 0.188034i) q^{54} +(5.02806 + 5.45148i) q^{55} +(0.868661 - 9.76277i) q^{56} +(-2.40714 + 15.1981i) q^{57} +(2.14793 - 3.92411i) q^{58} +(-1.80173 + 5.54515i) q^{59} +(-8.45690 - 1.17968i) q^{60} +(8.40557 + 6.10701i) q^{61} +(5.21446 - 2.46543i) q^{62} +(1.99318 + 1.01558i) q^{63} +(-3.48572 - 7.20068i) q^{64} +(-1.47344 + 0.901107i) q^{65} +(-7.29474 - 5.19507i) q^{66} +(-5.81112 - 5.81112i) q^{67} +(-13.0878 - 2.87509i) q^{68} +(7.68375 - 2.49660i) q^{69} +(-9.16461 - 6.00773i) q^{70} +(-0.695455 + 0.957212i) q^{71} +(1.82161 - 0.124677i) q^{72} +(2.92976 - 1.49279i) q^{73} +(7.18971 - 2.10312i) q^{74} +(-5.62523 + 7.71332i) q^{75} +(-0.953035 + 16.0901i) q^{76} +(-5.61361 - 10.0289i) q^{77} +(1.51774 - 1.43050i) q^{78} +(5.82487 - 4.23201i) q^{79} +(-8.93687 - 0.363767i) q^{80} +(3.25083 - 10.0050i) q^{81} +(1.93888 - 0.248552i) q^{82} +(8.93934 - 1.41585i) q^{83} +(12.3213 + 4.82613i) q^{84} +(-9.73997 + 11.3833i) q^{85} +(5.41687 + 7.93931i) q^{86} +(4.27070 + 4.27070i) q^{87} +(-8.13654 - 4.66869i) q^{88} -2.39359i q^{89} +(0.838317 - 1.86132i) q^{90} +(2.54560 - 0.827114i) q^{91} +(7.75442 - 3.38948i) q^{92} +(1.21820 + 7.69140i) q^{93} +(-3.54137 - 2.73657i) q^{94} +(15.3568 + 9.42961i) q^{95} +(10.6519 - 1.78742i) q^{96} +(0.256492 - 1.61943i) q^{97} +(4.85796 + 5.15422i) q^{98} +(1.68167 - 1.32514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 32 q^{10} - 20 q^{12} - 12 q^{13} - 4 q^{16} - 12 q^{17} - 26 q^{18} - 52 q^{20} - 64 q^{21} - 10 q^{22} - 12 q^{25} - 36 q^{26} + 10 q^{28} - 10 q^{30}+ \cdots + 236 q^{98}+O(q^{100}) $ 256 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 32 * q^10 - 20 * q^12 - 12 * q^13 - 4 * q^16 - 12 * q^17 - 26 * q^18 - 52 * q^20 - 64 * q^21 - 10 * q^22 - 12 * q^25 - 36 * q^26 + 10 * q^28 - 10 * q^30 + 4 * q^32 - 20 * q^33 + 4 * q^36 - 12 * q^37 + 30 * q^38 - 42 * q^40 - 48 * q^41 - 30 * q^42 - 72 * q^45 + 60 * q^46 - 18 * q^48 + 14 * q^50 - 46 * q^52 - 36 * q^53 + 8 * q^56 + 12 * q^57 - 18 * q^58 + 70 * q^60 - 24 * q^61 - 124 * q^62 - 32 * q^65 - 20 * q^66 - 38 * q^68 - 26 * q^70 - 116 * q^72 + 12 * q^73 - 48 * q^76 - 20 * q^77 + 100 * q^78 - 26 * q^80 - 24 * q^81 - 2 * q^82 + 36 * q^85 + 28 * q^86 + 126 * q^88 + 8 * q^90 - 56 * q^92 + 36 * q^93 + 104 * q^96 - 92 * q^97 + 236 * q^98

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.262448	+	1.38965i	−0.185579	+	0.982629i
$2$	−0.262448	+	1.38965i	−0.185579	+	0.982629i
$3$	−1.70123	−	0.866818i	−0.982203	−	0.500458i	−0.112297	−	0.993675i	$-0.535821\pi$
$3$	−1.70123	−	0.866818i	−0.982203	−	0.500458i	−0.869906	+	0.493217i	$0.835821\pi$
$4$	−1.86224	−	0.729420i	−0.931121	−	0.364710i
$5$	−1.70162	+	1.45068i	−0.760988	+	0.648766i
$5$	−1.70162	+	1.45068i	−0.760988	+	0.648766i
$6$	1.65105	−	2.13661i	0.674040	−	0.872268i
$7$	3.08760	−	1.57321i	1.16700	−	0.594618i	0.240406	−	0.970672i	$-0.422719\pi$
$7$	3.08760	−	1.57321i	1.16700	−	0.594618i	0.926598	+	0.376054i	$0.122719\pi$
$8$	1.50238	−	2.39643i	0.531171	−	0.847265i
$9$	0.379441	+	0.522256i	0.126480	+	0.174085i
$10$	−1.56935	−	2.74538i	−0.496273	−	0.868167i
$11$	−0.129499	−	3.31410i	−0.0390453	−	0.999237i
$11$	−0.129499	−	3.31410i	−0.0390453	−	0.999237i
$12$	2.53582	+	2.85513i	0.732028	+	0.824206i
$13$	0.762891	+	0.120830i	0.211588	+	0.0335122i	0.261328	−	0.965250i	$-0.415839\pi$
$13$	0.762891	+	0.120830i	0.211588	+	0.0335122i	−0.0497405	+	0.998762i	$0.515839\pi$
$14$	1.37588	+	4.70357i	0.367718	+	1.25708i
$15$	4.15232	−	0.992945i	1.07213	−	0.256377i
$16$	2.93589	+	2.71671i	0.733973	+	0.679178i
$17$	6.61747	−	1.04810i	1.60497	−	0.254203i	0.711289	−	0.702900i	$-0.248112\pi$
$17$	6.61747	−	1.04810i	1.60497	−	0.254203i	0.893684	+	0.448697i	$0.148112\pi$
$18$	−0.825336	+	0.390225i	−0.194534	+	0.0919769i
$19$	−2.49041	−	7.66469i	−0.571339	−	1.75840i	−0.648320	−	0.761368i	$-0.724528\pi$
$19$	−2.49041	−	7.66469i	−0.571339	−	1.75840i	0.0769811	−	0.997033i	$-0.475472\pi$
$20$	4.22699	−	1.46033i	0.945184	−	0.326539i
$21$	−6.61640			−1.44382
$22$	4.63941	+	0.689820i	0.989126	+	0.147070i
$23$	−2.99206	+	2.99206i	−0.623889	+	0.623889i	−0.946523	−	0.322635i	$-0.895431\pi$
$23$	−2.99206	+	2.99206i	−0.623889	+	0.623889i	0.322635	+	0.946523i	$0.395431\pi$
$24$	−4.63315	+	2.77457i	−0.945738	+	0.566358i
$25$	0.791033	−	4.93703i	0.158207	−	0.987406i
$26$	−0.368130	+	1.02844i	−0.0721963	+	0.201693i
$27$	0.703241	+	4.44009i	0.135339	+	0.854495i
$28$	−6.89740	+	0.677543i	−1.30349	+	0.128043i
$29$	−3.00842	−	0.977496i	−0.558650	−	0.181516i	0.0160636	−	0.999871i	$-0.494887\pi$
$29$	−3.00842	−	0.977496i	−0.558650	−	0.181516i	−0.574714	+	0.818355i	$0.694887\pi$
$30$	0.290076	+	6.03086i	0.0529604	+	1.10108i
$31$	−2.39730	−	3.29961i	−0.430568	−	0.592627i	0.537515	−	0.843254i	$-0.319363\pi$
$31$	−2.39730	−	3.29961i	−0.430568	−	0.592627i	−0.968084	+	0.250627i	$0.919363\pi$
$32$	−4.54579	+	3.36686i	−0.803591	+	0.595183i
$33$	−2.65241	+	5.75028i	−0.461726	+	1.00099i
$34$	−0.280245	+	9.47103i	−0.0480616	+	1.62427i
$35$	−2.97170	+	7.15615i	−0.502309	+	1.20961i
$36$	−0.325668	−	1.24934i	−0.0542779	−	0.208223i
$37$	−2.40476	−	4.71961i	−0.395340	−	0.775898i	0.604445	−	0.796647i	$-0.293395\pi$
$37$	−2.40476	−	4.71961i	−0.395340	−	0.775898i	−0.999785	+	0.0207487i	$0.993395\pi$
$38$	11.3048	−	1.44921i	1.83388	−	0.235093i
$39$	−1.19311	−	0.866847i	−0.191051	−	0.138807i
$40$	0.919977	+	6.25729i	0.145461	+	0.989364i
$41$	−0.427127	−	1.31456i	−0.0667060	−	0.205300i	0.912148	−	0.409862i	$-0.134423\pi$
$41$	−0.427127	−	1.31456i	−0.0667060	−	0.205300i	−0.978854	+	0.204562i	$0.934423\pi$
$42$	1.73646	−	9.19446i	0.267941	−	1.41874i
$43$	4.80560	−	4.80560i	0.732847	−	0.732847i	−0.238336	−	0.971183i	$-0.576602\pi$
$43$	4.80560	−	4.80560i	0.732847	−	0.732847i	0.971183	+	0.238336i	$0.0766019\pi$
$44$	−2.17621	+	6.26611i	−0.328076	+	0.944651i
$45$	−1.40329	−	0.338233i	−0.209191	−	0.0504208i
$46$	−3.37266	−	4.94318i	−0.497271	−	0.728832i
$47$	−1.43672	+	2.81973i	−0.209568	+	0.411300i	−0.971733	−	0.236083i	$-0.924136\pi$
$47$	−1.43672	+	2.81973i	−0.209568	+	0.411300i	0.762165	+	0.647383i	$0.224136\pi$
$48$	−2.63972	−	7.16663i	−0.381011	−	1.03441i
$49$	2.94379	−	4.05179i	0.420542	−	0.578826i
$50$	6.65313	+	2.39497i	0.940894	+	0.338700i
$51$	−12.1663	−	3.95308i	−1.70363	−	0.553542i
$52$	−1.33255	−	0.781483i	−0.184792	−	0.108372i
$53$	2.68953	+	0.425980i	0.369435	+	0.0585128i	0.338392	−	0.941005i	$-0.390117\pi$
$53$	2.68953	+	0.425980i	0.369435	+	0.0585128i	0.0310432	+	0.999518i	$0.490117\pi$
$54$	−6.35472	−	0.188034i	−0.864768	−	0.0255882i
$55$	5.02806	+	5.45148i	0.677984	+	0.735077i
$56$	0.868661	−	9.76277i	0.116080	−	1.30461i
$57$	−2.40714	+	15.1981i	−0.318834	+	2.01304i
$58$	2.14793	−	3.92411i	0.282037	−	0.515260i
$59$	−1.80173	+	5.54515i	−0.234565	+	0.721918i	0.762614	+	0.646854i	$0.223916\pi$
$59$	−1.80173	+	5.54515i	−0.234565	+	0.721918i	−0.997179	+	0.0750632i	$0.976084\pi$
$60$	−8.45690	−	1.17968i	−1.09178	−	0.152296i
$61$	8.40557	+	6.10701i	1.07622	+	0.781922i	0.977021	−	0.213145i	$-0.0683707\pi$
$61$	8.40557	+	6.10701i	1.07622	+	0.781922i	0.0992030	+	0.995067i	$0.468371\pi$
$62$	5.21446	−	2.46543i	0.662237	−	0.313110i
$63$	1.99318	+	1.01558i	0.251118	+	0.127951i
$64$	−3.48572	−	7.20068i	−0.435715	−	0.900085i
$65$	−1.47344	+	0.901107i	−0.182758	+	0.111769i
$66$	−7.29474	−	5.19507i	−0.897921	−	0.639468i
$67$	−5.81112	−	5.81112i	−0.709941	−	0.709941i	0.256581	−	0.966523i	$-0.417404\pi$
$67$	−5.81112	−	5.81112i	−0.709941	−	0.709941i	−0.966523	+	0.256581i	$0.917404\pi$
$68$	−13.0878	−	2.87509i	−1.58713	−	0.348656i
$69$	7.68375	−	2.49660i	0.925015	−	0.300556i
$70$	−9.16461	−	6.00773i	−1.09538	−	0.718061i
$71$	−0.695455	+	0.957212i	−0.0825354	+	0.113600i	−0.848288	−	0.529535i	$-0.822367\pi$
$71$	−0.695455	+	0.957212i	−0.0825354	+	0.113600i	0.765753	+	0.643135i	$0.222367\pi$
$72$	1.82161	−	0.124677i	0.214679	−	0.0146933i
$73$	2.92976	−	1.49279i	0.342903	−	0.174718i	−0.274055	−	0.961714i	$-0.588365\pi$
$73$	2.92976	−	1.49279i	0.342903	−	0.174718i	0.616958	+	0.786996i	$0.288365\pi$
$74$	7.18971	−	2.10312i	0.835787	−	0.244483i
$75$	−5.62523	+	7.71332i	−0.649546	+	0.890658i
$76$	−0.953035	+	16.0901i	−0.109321	+	1.84566i
$77$	−5.61361	−	10.0289i	−0.639731	−	1.14290i
$78$	1.51774	−	1.43050i	0.171850	−	0.161973i
$79$	5.82487	−	4.23201i	0.655349	−	0.476139i	−0.209740	−	0.977757i	$-0.567262\pi$
$79$	5.82487	−	4.23201i	0.655349	−	0.476139i	0.865089	+	0.501618i	$0.167262\pi$
$80$	−8.93687	−	0.363767i	−0.999173	−	0.0406704i
$81$	3.25083	−	10.0050i	0.361203	−	1.11167i
$82$	1.93888	−	0.248552i	0.214113	−	0.0274480i
$83$	8.93934	−	1.41585i	0.981220	−	0.155410i	0.354839	−	0.934927i	$-0.384536\pi$
$83$	8.93934	−	1.41585i	0.981220	−	0.155410i	0.626381	+	0.779517i	$0.284536\pi$
$84$	12.3213	+	4.82613i	1.34437	+	0.526574i
$85$	−9.73997	+	11.3833i	−1.05645	+	1.23470i
$86$	5.41687	+	7.93931i	0.584116	+	0.856118i
$87$	4.27070	+	4.27070i	0.457867	+	0.457867i
$88$	−8.13654	−	4.66869i	−0.867358	−	0.497684i
$89$		−	2.39359i		−	0.253720i	−0.991921	−	0.126860i	$-0.959510\pi$
$89$		−	2.39359i		−	0.253720i	0.991921	−	0.126860i	$-0.0404900\pi$
$90$	0.838317	−	1.86132i	0.0883663	−	0.196200i
$91$	2.54560	−	0.827114i	0.266851	−	0.0867051i
$92$	7.75442	−	3.38948i	0.808454	−	0.353377i
$93$	1.21820	+	7.69140i	0.126321	+	0.797561i
$94$	−3.54137	−	2.73657i	−0.365264	−	0.282256i
$95$	15.3568	+	9.42961i	1.57557	+	0.967457i
$96$	10.6519	−	1.78742i	1.08715	−	0.182427i
$97$	0.256492	−	1.61943i	0.0260429	−	0.164428i	−0.971239	−	0.238106i	$-0.923474\pi$
$97$	0.256492	−	1.61943i	0.0260429	−	0.164428i	0.997282	+	0.0736775i	$0.0234736\pi$
$98$	4.85796	+	5.15422i	0.490728	+	0.520655i
$99$	1.68167	−	1.32514i	0.169014	−	0.133181i
$100$	−5.07426	+	8.61695i	−0.507426	+	0.861695i
$101$	0.403948	−	0.293485i	0.0401943	−	0.0292029i	−0.567507	−	0.823369i	$-0.692092\pi$
$101$	0.403948	−	0.293485i	0.0401943	−	0.0292029i	0.607701	+	0.794166i	$0.292092\pi$
$102$	8.68642	−	15.8694i	0.860084	−	1.57131i
$103$	4.38134	+	8.59885i	0.431706	+	0.847270i	0.999706	+	0.0242420i	$0.00771722\pi$
$103$	4.38134	+	8.59885i	0.431706	+	0.847270i	−0.568000	+	0.823028i	$0.692283\pi$
$104$	1.43571	−	1.64668i	0.140783	−	0.161470i
$105$	11.2586	−	9.59830i	1.09873	−	0.936698i
$106$	−1.29782	+	3.62570i	−0.126056	+	0.352159i
$107$	−6.77110	+	13.2890i	−0.654587	+	1.28470i	0.290185	+	0.956970i	$0.406283\pi$
$107$	−6.77110	+	13.2890i	−0.654587	+	1.28470i	−0.944772	+	0.327728i	$0.893717\pi$
$108$	1.92908	−	8.78148i	0.185626	−	0.844998i
$109$			12.6619i			1.21279i	0.795165	+	0.606394i	$0.207384\pi$
$109$			12.6619i			1.21279i	−0.795165	+	0.606394i	$0.792616\pi$
$110$	−8.89524	+	5.55651i	−0.848127	+	0.529792i
$111$			10.1136i			0.959941i
$112$	13.3388	+	3.76935i	1.26040	+	0.356170i
$113$	2.61186	−	5.12606i	0.245703	−	0.482219i	−0.734913	−	0.678162i	$-0.762777\pi$
$113$	2.61186	−	5.12606i	0.245703	−	0.482219i	0.980615	+	0.195943i	$0.0627768\pi$
$114$	−20.4883	−	7.33379i	−1.91890	−	0.686872i
$115$	0.750822	−	9.43190i	0.0700145	−	0.879529i
$116$	4.88941	+	4.01474i	0.453970	+	0.372759i
$117$	0.226368	+	0.444273i	0.0209278	+	0.0410730i
$118$	−7.23295	−	3.95908i	−0.665847	−	0.364463i
$119$	18.7832	−	13.6468i	1.72186	−	1.25100i
$120$	3.85884	−	11.4425i	0.352262	−	1.04455i
$121$	−10.9665	+	0.858342i	−0.996951	+	0.0780311i
$122$	−10.6926	+	10.0780i	−0.968064	+	0.912421i
$123$	−0.412846	+	2.60661i	−0.0372251	+	0.235030i
$124$	2.05756	+	7.89331i	0.184774	+	0.708840i
$125$	5.81603	+	9.54850i	0.520202	+	0.854043i
$126$	−1.93440	+	2.50329i	−0.172330	+	0.223011i
$127$	−0.214557	−	1.35466i	−0.0190388	−	0.120207i	0.976339	−	0.216248i	$-0.0693819\pi$
$127$	−0.214557	−	1.35466i	−0.0190388	−	0.120207i	−0.995377	+	0.0960413i	$0.969382\pi$
$128$	10.9212	−	2.95412i	0.965309	−	0.261110i
$129$	−12.3410	+	4.00983i	−1.08656	+	0.353046i
$130$	−0.865520	−	2.28405i	−0.0759112	−	0.200325i
$131$		−	0.155975i		−	0.0136276i	−0.999977	−	0.00681381i	$-0.997831\pi$
$131$		−	0.155975i		−	0.0136276i	0.999977	−	0.00681381i	$-0.00216892\pi$
$132$	9.13380	−	8.77369i	0.794995	−	0.763652i
$133$	−19.7476	−	19.7476i	−1.71233	−	1.71233i
$134$	9.60053	−	6.55030i	0.829359	−	0.565859i
$135$	−7.63782	−	6.53517i	−0.657358	−	0.562458i
$136$	7.43024	−	17.4329i	0.637138	−	1.49486i
$137$	−7.99186	+	1.26579i	−0.682791	+	0.108143i	−0.488188	−	0.872739i	$-0.662342\pi$
$137$	−7.99186	+	1.26579i	−0.682791	+	0.108143i	−0.194603	+	0.980882i	$0.562342\pi$
$138$	1.45281	+	11.3329i	0.123672	+	0.964724i
$139$	−2.08824	+	6.42693i	−0.177122	+	0.545125i	−0.999724	−	0.0234924i	$-0.992521\pi$
$139$	−2.08824	+	6.42693i	−0.177122	+	0.545125i	0.822602	+	0.568617i	$0.192521\pi$
$140$	10.7539	−	11.1589i	0.908867	−	0.943096i
$141$	4.88839	−	3.55162i	0.411676	−	0.299100i
$142$	−1.14767	−	1.21766i	−0.0963101	−	0.102183i
$143$	0.301649	−	2.54394i	0.0252252	−	0.212735i
$144$	−0.304822	+	2.56412i	−0.0254018	+	0.213677i
$145$	6.53723	−	2.70094i	0.542888	−	0.224301i
$146$	1.30554	+	4.46311i	0.108047	+	0.369370i
$147$	−8.52022	+	4.34127i	−0.702736	+	0.358062i
$148$	1.03567	+	10.5431i	0.0851315	+	0.866640i
$149$	5.49438	−	7.56236i	0.450117	−	0.619533i	−0.522306	−	0.852758i	$-0.674928\pi$
$149$	5.49438	−	7.56236i	0.450117	−	0.619533i	0.972423	+	0.233226i	$0.0749280\pi$
$150$	−9.24247	−	9.84144i	−0.754645	−	0.803550i
$151$	−7.04551	+	2.28923i	−0.573356	+	0.186295i	−0.581322	−	0.813674i	$-0.697464\pi$
$151$	−7.04551	+	2.28923i	−0.573356	+	0.186295i	0.00796617	+	0.999968i	$0.497464\pi$
$152$	−22.1094	−	5.54718i	−1.79331	−	0.449936i
$153$	3.05832	+	3.05832i	0.247251	+	0.247251i
$154$	15.4099	−	5.16889i	1.24176	−	0.416521i
$155$	8.86599	+	2.13695i	0.712133	+	0.171644i
$156$	1.58957	+	2.48456i	0.127267	+	0.198924i
$157$	11.6091	+	5.91512i	0.926505	+	0.472078i	0.851058	−	0.525072i	$-0.175962\pi$
$157$	11.6091	+	5.91512i	0.926505	+	0.472078i	0.0754472	+	0.997150i	$0.475962\pi$
$158$	4.35228	+	9.20519i	0.346249	+	0.732326i
$159$	−4.20625	−	3.05602i	−0.333577	−	0.242358i
$160$	2.85097	−	12.3236i	0.225389	−	0.974269i
$161$	−4.53115	+	13.9455i	−0.357105	+	1.09906i
$162$	13.0503	+	7.14331i	1.02533	+	0.561231i
$163$	−2.33364	+	14.7340i	−0.182785	+	1.15406i	0.710209	+	0.703991i	$0.248600\pi$
$163$	−2.33364	+	14.7340i	−0.182785	+	1.15406i	−0.892994	+	0.450068i	$0.851400\pi$
$164$	−0.163454	+	2.75959i	−0.0127636	+	0.215487i
$165$	−3.82843	−	13.6326i	−0.298043	−	1.06130i
$166$	−0.378574	+	12.7941i	−0.0293831	+	0.993016i
$167$	−7.53431	−	1.19332i	−0.583022	−	0.0923417i	−0.142045	−	0.989860i	$-0.545368\pi$
$167$	−7.53431	−	1.19332i	−0.583022	−	0.0923417i	−0.440977	+	0.897518i	$0.645368\pi$
$168$	−9.94033	+	15.8557i	−0.766913	+	1.22329i
$169$	−11.7963	−	3.83286i	−0.907410	−	0.294835i
$170$	−13.2626	−	16.5227i	−1.01719	−	1.26723i
$171$	3.05797	−	4.20893i	0.233849	−	0.321865i
$172$	−12.4545	+	5.44389i	−0.949646	+	0.415093i
$173$	3.57696	−	7.02019i	0.271952	−	0.533735i	−0.714127	−	0.700016i	$-0.753176\pi$
$173$	3.57696	−	7.02019i	0.271952	−	0.533735i	0.986078	+	0.166281i	$0.0531760\pi$
$174$	−7.05560	+	4.81393i	−0.534884	+	0.364943i
$175$	−5.32460	−	16.4880i	−0.402502	−	1.24638i
$176$	8.62326	−	10.0816i	0.650002	−	0.759932i
$177$	7.87179	−	7.87179i	0.591680	−	0.591680i
$178$	3.32625	+	0.628193i	0.249313	+	0.0470851i
$179$	−1.97080	−	6.06549i	−0.147304	−	0.453356i	0.849996	−	0.526789i	$-0.176604\pi$
$179$	−1.97080	−	6.06549i	−0.147304	−	0.453356i	−0.997300	+	0.0734334i	$0.976604\pi$
$180$	2.36656	+	1.65346i	0.176393	+	0.123242i
$181$	−1.17313	−	0.852329i	−0.0871981	−	0.0633531i	0.543332	−	0.839518i	$-0.317162\pi$
$181$	−1.17313	−	0.852329i	−0.0871981	−	0.0633531i	−0.630530	+	0.776165i	$0.717162\pi$
$182$	0.481311	+	3.75456i	0.0356772	+	0.278306i
$183$	−9.00612	−	17.6755i	−0.665752	−	1.30661i
$184$	2.67505	+	11.6655i	0.197207	+	0.859990i
$185$	10.9386	+	4.54244i	0.804225	+	0.333967i
$186$	−11.0081	−	0.325725i	−0.807150	−	0.0238833i
$187$	−4.33047	−	21.7952i	−0.316676	−	1.59382i
$188$	4.73230	−	4.20305i	0.345138	−	0.306539i
$189$	9.15653	+	12.6029i	0.666039	+	0.916725i
$190$	−17.1342	+	18.8657i	−1.24304	+	1.36866i
$191$	4.68918	+	1.52361i	0.339297	+	0.110244i	0.473709	−	0.880681i	$-0.342915\pi$
$191$	4.68918	+	1.52361i	0.339297	+	0.110244i	−0.134413	+	0.990925i	$0.542915\pi$
$192$	−0.311684	+	15.2715i	−0.0224939	+	1.10212i
$193$	−1.06773	−	6.74138i	−0.0768568	−	0.485255i	−0.995852	−	0.0909865i	$-0.970998\pi$
$193$	−1.06773	−	6.74138i	−0.0768568	−	0.485255i	0.918995	−	0.394269i	$-0.129002\pi$
$194$	2.18312	+	0.781450i	0.156739	+	0.0561048i
$195$	3.28775	−	0.255784i	0.235441	−	0.0183170i
$196$	−8.43751	+	5.39814i	−0.602679	+	0.385582i
$197$	1.58036	−	1.58036i	0.112596	−	0.112596i	−0.648564	−	0.761160i	$-0.724630\pi$
$197$	1.58036	−	1.58036i	0.112596	−	0.112596i	0.761160	+	0.648564i	$0.224630\pi$
$198$	1.40012	+	2.68471i	0.0995024	+	0.190794i
$199$	11.5373			0.817860			0.408930	−	0.912566i	$-0.365902\pi$
$199$	11.5373			0.817860			0.408930	+	0.912566i	$0.365902\pi$
$200$	−10.6428	−	9.31294i	−0.752559	−	0.658524i
$201$	4.84885	+	14.9232i	0.342011	+	1.05260i
$202$	0.301826	+	0.638369i	0.0212364	+	0.0449155i
$203$	−10.8266	+	1.71477i	−0.759880	+	0.120353i
$204$	19.7732	+	16.2360i	1.38440	+	1.13674i
$205$	2.63382	+	1.61726i	0.183954	+	0.112954i
$206$	−13.0993	+	3.83176i	−0.912668	+	0.266972i
$207$	−2.69794	−	0.427311i	−0.187520	−	0.0297002i
$208$	1.91151	+	2.42730i	0.132539	+	0.168303i
$209$	−25.0790	+	9.24602i	−1.73475	+	0.639561i
$210$	10.3835	+	18.1646i	0.716527	+	1.25347i
$211$	−6.96111	−	9.58115i	−0.479223	−	0.659593i	0.499133	−	0.866526i	$-0.333652\pi$
$211$	−6.96111	−	9.58115i	−0.479223	−	0.659593i	−0.978355	+	0.206932i	$0.933652\pi$
$212$	−4.69784	−	2.75507i	−0.322649	−	0.189219i
$213$	2.01286	−	1.02560i	0.137919	−	0.0702730i
$214$	−16.6900	−	12.8971i	−1.14091	−	0.881629i
$215$	−1.20591	+	15.1487i	−0.0822422	+	1.03313i
$216$	11.6969	+	4.98543i	0.795872	+	0.339215i
$217$	−12.5929	−	6.41640i	−0.854862	−	0.435574i
$218$	−17.5955	−	3.32308i	−1.19172	−	0.225067i
$219$	−6.27816			−0.424239
$220$	−5.38706	−	13.8195i	−0.363195	−	0.931713i
$221$	5.17505			0.348112
$222$	−14.0544	−	2.65429i	−0.943266	−	0.178145i
$223$	5.89454	+	3.00342i	0.394727	+	0.201124i	0.640077	−	0.768311i	$-0.278903\pi$
$223$	5.89454	+	3.00342i	0.394727	+	0.201124i	−0.245349	+	0.969435i	$0.578903\pi$
$224$	−8.73882	+	17.5470i	−0.583887	+	1.17241i
$225$	2.87855	−	1.46019i	0.191903	−	0.0973461i
$226$	6.43794	+	4.97488i	0.428245	+	0.330924i
$227$	−5.32141	+	2.71139i	−0.353194	+	0.179962i	−0.621581	−	0.783350i	$-0.713509\pi$
$227$	−5.32141	+	2.71139i	−0.353194	+	0.179962i	0.268387	+	0.963311i	$0.413509\pi$
$228$	15.5685	−	26.5467i	1.03105	−	1.75810i
$229$	9.47300	+	13.0385i	0.625993	+	0.861606i	0.997772	−	0.0667153i	$-0.0212519\pi$
$229$	9.47300	+	13.0385i	0.625993	+	0.861606i	−0.371779	+	0.928321i	$0.621252\pi$
$230$	12.9100	+	3.51876i	0.851258	+	0.232020i
$231$	0.856814	+	21.9274i	0.0563742	+	1.44272i
$232$	−6.86229	+	5.74089i	−0.450531	+	0.376908i
$233$	10.6258	+	1.68296i	0.696119	+	0.110254i	0.494459	−	0.869201i	$-0.335366\pi$
$233$	10.6258	+	1.68296i	0.696119	+	0.110254i	0.201660	+	0.979456i	$0.435366\pi$
$234$	−0.676792	+	0.197974i	−0.0442433	+	0.0129419i
$235$	−1.64578	−	6.88235i	−0.107359	−	0.448955i
$236$	7.40000	−	9.01220i	0.481699	−	0.586644i
$237$	−13.5778	+	2.15051i	−0.881973	+	0.139691i
$238$	14.0347	+	29.6837i	0.909731	+	1.92411i
$239$	−4.45399	−	13.7080i	−0.288105	−	0.886695i	−0.985451	−	0.169960i	$-0.945636\pi$
$239$	−4.45399	−	13.7080i	−0.288105	−	0.886695i	0.697346	−	0.716734i	$-0.254364\pi$
$240$	14.8883	+	8.36549i	0.961037	+	0.539990i
$241$	13.1016			0.843946			0.421973	−	0.906608i	$-0.361338\pi$
$241$	13.1016			0.843946			0.421973	+	0.906608i	$0.361338\pi$
$242$	1.68533	−	15.4648i	0.108337	−	0.994114i
$243$	−4.66668	+	4.66668i	−0.299367	+	0.299367i
$244$	−11.1986	−	17.5039i	−0.716920	−	1.12057i
$245$	0.868635	+	11.1651i	0.0554951	+	0.713313i
$246$	−3.51391	−	1.25781i	−0.224039	−	0.0801950i
$247$	−0.973786	−	6.14824i	−0.0619605	−	0.391203i
$248$	−11.5089	+	0.787705i	−0.730817	+	0.0500193i
$249$	−16.4351	−	5.34010i	−1.04153	−	0.338415i
$250$	−14.7955	+	5.57625i	−0.935747	+	0.352673i
$251$	−5.31843	−	7.32020i	−0.335697	−	0.462047i	0.607482	−	0.794334i	$-0.292180\pi$
$251$	−5.31843	−	7.32020i	−0.335697	−	0.462047i	−0.943178	+	0.332287i	$0.892180\pi$
$252$	−2.97101	−	3.34512i	−0.187156	−	0.210723i
$253$	10.3035	+	9.52852i	0.647773	+	0.599053i
$254$	1.93881	+	0.0573688i	0.121652	+	0.00359964i
$255$	26.4372	−	10.9229i	1.65556	−	0.684016i
$256$	1.23893	+	15.9520i	0.0774331	+	0.996998i
$257$	9.50541	+	18.6554i	0.592931	+	1.16369i	0.971260	+	0.238021i	$0.0764989\pi$
$257$	9.50541	+	18.6554i	0.592931	+	1.16369i	−0.378329	+	0.925671i	$0.623501\pi$
$258$	−2.33339	−	18.2020i	−0.145270	−	1.13321i
$259$	−14.8499	−	10.7891i	−0.922727	−	0.670400i
$260$	3.40118	−	0.603324i	0.210933	−	0.0374165i
$261$	−0.631017	−	1.94207i	−0.0390590	−	0.120211i
$262$	0.216751	+	0.0409354i	0.0133909	+	0.00252899i
$263$	−15.0488	+	15.0488i	−0.927947	+	0.927947i	−0.997573	−	0.0696264i	$-0.977819\pi$
$263$	−15.0488	+	15.0488i	−0.927947	+	0.927947i	0.0696264	+	0.997573i	$0.477819\pi$
$264$	9.79519	+	14.9954i	0.602852	+	0.922903i
$265$	−5.19452	+	3.17680i	−0.319097	+	0.195149i
$266$	32.6249	−	22.2595i	2.00036	−	1.36482i
$267$	−2.07481	+	4.07204i	−0.126976	+	0.249205i
$268$	6.58297	+	15.0605i	0.402119	+	0.919964i
$269$	15.2344	−	20.9684i	0.928859	−	1.27847i	−0.0314437	−	0.999506i	$-0.510010\pi$
$269$	15.2344	−	20.9684i	0.928859	−	1.27847i	0.960303	−	0.278960i	$-0.0899895\pi$
$270$	11.0861	−	8.89873i	0.674679	−	0.541560i
$271$	20.4052	+	6.63006i	1.23953	+	0.402747i	0.854158	−	0.520014i	$-0.174073\pi$
$271$	20.4052	+	6.63006i	1.23953	+	0.402747i	0.385372	+	0.922761i	$0.374073\pi$
$272$	22.2756	+	14.9007i	1.35066	+	0.903485i
$273$	−5.04759	−	0.799460i	−0.305494	−	0.0483855i
$274$	0.338449	−	11.4381i	0.0204465	−	0.690999i
$275$	−16.4642	−	1.98222i	−0.992830	−	0.119532i
$276$	−16.1301	−	0.955405i	−0.970917	−	0.0575086i
$277$	−2.89155	+	18.2565i	−0.173736	+	1.09693i	0.734543	+	0.678563i	$0.237397\pi$
$277$	−2.89155	+	18.2565i	−0.173736	+	1.09693i	−0.908279	+	0.418365i	$0.862603\pi$
$278$	−8.38311	−	4.58864i	−0.502786	−	0.275209i
$279$	0.813603	−	2.50401i	0.0487092	−	0.149911i
$280$	12.6846	+	17.8727i	0.758048	+	1.06810i
$281$	−19.5715	−	14.2196i	−1.16754	−	0.848268i	−0.176828	−	0.984242i	$-0.556584\pi$
$281$	−19.5715	−	14.2196i	−1.16754	−	0.848268i	−0.990712	+	0.135974i	$0.956584\pi$
$282$	3.65256	+	7.72525i	0.217507	+	0.460032i
$283$	27.5473	+	14.0361i	1.63752	+	0.834358i	0.997838	+	0.0657181i	$0.0209338\pi$
$283$	27.5473	+	14.0361i	1.63752	+	0.834358i	0.639682	+	0.768640i	$0.279066\pi$
$284$	1.99332	−	1.27528i	0.118282	−	0.0756740i
$285$	−17.9516	−	29.3534i	−1.06336	−	1.73875i
$286$	3.45602	+	1.08684i	0.204359	+	0.0642661i
$287$	−3.38688	−	3.38688i	−0.199921	−	0.199921i
$288$	−3.48323	−	1.09654i	−0.205251	−	0.0646144i
$289$	26.5245	−	8.61832i	1.56026	−	0.506960i
$290$	2.03768	+	9.79331i	0.119656	+	0.575083i
$291$	−1.84010	+	2.53268i	−0.107869	+	0.148469i
$292$	−6.54479	+	0.642906i	−0.383005	+	0.0376232i
$293$	−17.1430	+	8.73478i	−1.00150	+	0.510291i	−0.876262	−	0.481835i	$-0.839970\pi$
$293$	−17.1430	+	8.73478i	−1.00150	+	0.510291i	−0.125241	+	0.992126i	$0.539970\pi$
$294$	−3.79672	−	12.9795i	−0.221429	−	0.756978i
$295$	−4.97840	−	12.0495i	−0.289854	−	0.701549i
$296$	−14.9230	−	1.32781i	−0.867384	−	0.0771772i
$297$	14.6238	−	2.90559i	0.848560	−	0.168600i
$298$	9.06703	+	9.61997i	0.525239	+	0.557270i
$299$	−2.64415	+	1.92109i	−0.152915	+	0.111099i
$300$	16.1018	−	10.2609i	0.929638	−	0.592415i
$301$	7.27755	−	22.3980i	0.419471	−	1.29100i
$302$	−1.33214	−	10.3916i	−0.0766559	−	0.597968i
$303$	−0.941604	+	0.149135i	−0.0540938	+	0.00856761i
$304$	13.5112	−	29.2684i	0.774920	−	1.67866i
$305$	−23.1624	+	1.80202i	−1.32628	+	0.103183i
$306$	−5.05264	+	3.44734i	−0.288840	+	0.197071i
$307$	18.0680	+	18.0680i	1.03120	+	1.03120i	0.999497	+	0.0316993i	$0.0100919\pi$
$307$	18.0680	+	18.0680i	1.03120	+	1.03120i	0.0316993	+	0.999497i	$0.489908\pi$
$308$	3.13864	+	22.7709i	0.178841	+	1.29749i
$309$		−	18.4264i		−	1.04824i
$310$	−5.29647	+	11.7598i	−0.300819	+	0.667910i
$311$	19.3086	−	6.27374i	1.09489	−	0.355751i	0.294756	−	0.955573i	$-0.404762\pi$
$311$	19.3086	−	6.27374i	1.09489	−	0.355751i	0.800134	+	0.599821i	$0.204762\pi$
$312$	−3.86984	+	1.55687i	−0.219087	+	0.0881406i
$313$	2.74917	+	17.3576i	0.155392	+	0.981109i	0.934950	+	0.354779i	$0.115444\pi$
$313$	2.74917	+	17.3576i	0.155392	+	0.981109i	−0.779558	+	0.626330i	$0.784556\pi$
$314$	−11.2667	+	14.5801i	−0.635817	+	0.822804i
$315$	−4.86493	+	1.16335i	−0.274108	+	0.0655474i
$316$	−13.9342	+	3.63226i	−0.783862	+	0.204331i
$317$	4.00874	−	25.3102i	0.225153	−	1.42156i	−0.573222	−	0.819400i	$-0.694307\pi$
$317$	4.00874	−	25.3102i	0.225153	−	1.42156i	0.798375	−	0.602161i	$-0.205693\pi$
$318$	5.35071	−	5.04316i	0.300053	−	0.282806i
$319$	−2.84993	+	10.0968i	−0.159565	+	0.565311i
$320$	16.3773	+	7.19616i	0.915518	+	0.402277i
$321$	23.0383	−	16.7383i	1.28587	−	0.934243i
$322$	−18.1901	−	9.95666i	−1.01369	−	0.554863i
$323$	−24.5136	−	48.1107i	−1.36397	−	2.67695i
$324$	−13.3517	+	16.2606i	−0.741761	+	0.903364i
$325$	1.20001	−	3.67084i	0.0665648	−	0.203621i
$326$	−19.8627	−	7.10986i	−1.10009	−	0.393779i
$327$	10.9755	−	21.5407i	0.606949	−	1.19120i
$328$	−3.79195	−	0.951390i	−0.209376	−	0.0525317i
$329$			10.9665i			0.604601i
$330$	19.9493	−	1.74233i	1.09817	−	0.0959120i
$331$		−	22.6923i		−	1.24728i	−0.781711	−	0.623641i	$-0.785653\pi$
$331$		−	22.6923i		−	1.24728i	0.781711	−	0.623641i	$-0.214347\pi$
$332$	−17.6800	−	3.88387i	−0.970314	−	0.213155i
$333$	1.55238	−	3.04671i	0.0850698	−	0.166959i
$334$	3.63565	−	10.1569i	0.198934	−	0.555758i
$335$	18.3184	+	1.45823i	1.00084	+	0.0796716i
$336$	−19.4250	−	17.9749i	−1.05972	−	0.980609i
$337$	0.432559	+	0.848946i	0.0235630	+	0.0462450i	0.902488	−	0.430715i	$-0.141739\pi$
$337$	0.432559	+	0.848946i	0.0235630	+	0.0462450i	−0.878925	+	0.476960i	$0.841739\pi$
$338$	8.42225	−	15.3868i	0.458110	−	0.836933i
$339$	−8.88672	+	6.45658i	−0.482660	+	0.350673i
$340$	26.4414	−	14.0940i	1.43399	−	0.764355i
$341$	−10.6248	+	8.37219i	−0.575363	+	0.453379i
$342$	5.04638	+	5.35412i	0.272877	+	0.289518i
$343$	−1.07969	+	6.81692i	−0.0582980	+	0.368079i
$344$	−4.29644	−	18.7361i	−0.231648	−	1.01018i
$345$	−9.45306	+	15.3950i	−0.508936	+	0.828838i
$346$	8.81682	+	6.81315i	0.473995	+	0.366277i
$347$	−0.615732	−	3.88758i	−0.0330542	−	0.208696i	0.965634	−	0.259907i	$-0.0836919\pi$
$347$	−0.615732	−	3.88758i	−0.0330542	−	0.208696i	−0.998688	+	0.0512109i	$0.983692\pi$
$348$	−4.83794	−	11.0682i	−0.259341	−	0.593318i
$349$	0.703663	−	0.228634i	0.0376662	−	0.0122385i	−0.290123	−	0.956989i	$-0.593696\pi$
$349$	0.703663	−	0.228634i	0.0376662	−	0.0122385i	0.327789	+	0.944751i	$0.393696\pi$
$350$	24.3100	−	3.07207i	1.29942	−	0.164209i
$351$			3.47228i			0.185336i
$352$	11.7468	+	14.6292i	0.626105	+	0.779739i
$353$	−4.54635	−	4.54635i	−0.241978	−	0.241978i	0.575690	−	0.817668i	$-0.304734\pi$
$353$	−4.54635	−	4.54635i	−0.241978	−	0.241978i	−0.817668	+	0.575690i	$0.804734\pi$
$354$	8.87308	+	13.0049i	0.471599	+	0.691205i
$355$	−0.205210	−	2.63770i	−0.0108914	−	0.139995i
$356$	−1.74594	+	4.45745i	−0.0925344	+	0.236244i
$357$	−43.7838	+	6.93468i	−2.31729	+	0.367022i
$358$	8.94613	−	1.14684i	0.472818	−	0.0606123i
$359$	−0.871453	+	2.68206i	−0.0459935	+	0.141554i	−0.971416	−	0.237383i	$-0.923710\pi$
$359$	−0.871453	+	2.68206i	−0.0459935	+	0.141554i	0.925423	+	0.378937i	$0.123710\pi$
$360$	−2.91883	+	2.85474i	−0.153836	+	0.150458i
$361$	−37.1740	+	27.0085i	−1.95653	+	1.42150i
$362$	1.49232	−	1.40655i	0.0784348	−	0.0739264i
$363$	19.4005	+	8.04569i	1.01826	+	0.422289i
$364$	−5.34383	−	0.316522i	−0.280093	−	0.0165902i
$365$	−2.81978	+	6.79032i	−0.147594	+	0.355421i
$366$	26.9264	−	7.87644i	1.40746	−	0.411708i
$367$	6.90146	−	3.51647i	0.360253	−	0.183558i	−0.264490	−	0.964388i	$-0.585204\pi$
$367$	6.90146	−	3.51647i	0.360253	−	0.183558i	0.624743	+	0.780830i	$0.285204\pi$
$368$	−16.9130	+	0.655797i	−0.881649	+	0.0341858i
$369$	0.524468	−	0.721869i	0.0273027	−	0.0375790i
$370$	−9.18321	+	14.0087i	−0.477413	+	0.728278i
$371$	8.97435	−	2.91594i	0.465925	−	0.151388i
$372$	3.34168	−	15.2118i	0.173258	−	0.788697i
$373$	14.9204	+	14.9204i	0.772551	+	0.772551i	0.978552	−	0.206001i	$-0.0660450\pi$
$373$	14.9204	+	14.9204i	0.772551	+	0.772551i	−0.206001	+	0.978552i	$0.566045\pi$
$374$	31.4242	−	0.297727i	1.62491	−	0.0153951i
$375$	−1.61758	−	21.2856i	−0.0835313	−	1.09918i
$376$	4.59877	+	7.67931i	0.237164	+	0.396030i
$377$	−2.17699	−	1.10923i	−0.112121	−	0.0571283i
$378$	−19.9167	+	9.41675i	−1.02440	+	0.484345i
$379$	28.8655	+	20.9720i	1.48272	+	1.07726i	0.976667	+	0.214761i	$0.0688974\pi$
$379$	28.8655	+	20.9720i	1.48272	+	1.07726i	0.506057	+	0.862500i	$0.331103\pi$
$380$	−21.7199	−	28.7618i	−1.11421	−	1.47545i
$381$	−0.809233	+	2.49056i	−0.0414583	+	0.127595i
$382$	−3.34794	+	6.11644i	−0.171295	+	0.312944i
$383$	−3.96424	+	25.0292i	−0.202563	+	1.27893i	0.651454	+	0.758688i	$0.274159\pi$
$383$	−3.96424	+	25.0292i	−0.202563	+	1.27893i	−0.854017	+	0.520245i	$0.825841\pi$
$384$	−21.1402	−	4.44109i	−1.07880	−	0.226634i
$385$	24.1010	+	8.92178i	1.22830	+	0.454696i
$386$	9.64836	+	0.285492i	0.491089	+	0.0145312i
$387$	4.33320	+	0.686311i	0.220269	+	0.0348872i
$388$	−1.65890	+	2.82868i	−0.0842176	+	0.143604i
$389$	28.0975	+	9.12944i	1.42460	+	0.462881i	0.917061	−	0.398747i	$-0.130555\pi$
$389$	28.0975	+	9.12944i	1.42460	+	0.462881i	0.507540	+	0.861628i	$0.330555\pi$
$390$	−0.507413	+	4.63594i	−0.0256939	+	0.234750i
$391$	−16.6639	+	22.9359i	−0.842730	+	1.15992i
$392$	−5.28711	−	13.1419i	−0.267039	−	0.663766i
$393$	−0.135202	+	0.265349i	−0.00682004	+	0.0133851i
$394$	1.78139	+	2.61091i	0.0897450	+	0.131536i
$395$	−3.77241	+	15.6513i	−0.189810	+	0.787504i
$396$	−4.09826	+	1.24108i	−0.205945	+	0.0623667i
$397$	25.9429	−	25.9429i	1.30204	−	1.30204i	0.375021	−	0.927016i	$-0.377636\pi$
$397$	25.9429	−	25.9429i	1.30204	−	1.30204i	0.927016	−	0.375021i	$-0.122364\pi$
$398$	−3.02795	+	16.0328i	−0.151777	+	0.803653i
$399$	16.4775	+	50.7126i	0.824909	+	2.53881i
$400$	15.7349	−	12.3456i	0.786744	−	0.617279i
$401$	10.0464	+	7.29910i	0.501691	+	0.364500i	0.809663	−	0.586896i	$-0.199650\pi$
$401$	10.0464	+	7.29910i	0.501691	+	0.364500i	−0.307971	+	0.951396i	$0.599650\pi$
$402$	−22.0106	+	2.82162i	−1.09779	+	0.140730i
$403$	−1.43019	−	2.80691i	−0.0712428	−	0.139822i
$404$	−0.966322	+	0.251893i	−0.0480763	+	0.0125321i
$405$	8.98245	+	21.7407i	0.446341	+	1.08030i
$406$	0.458499	−	15.4952i	0.0227549	−	0.769015i
$407$	−15.3298	+	8.58078i	−0.759871	+	0.425334i
$408$	−27.7517	+	23.2167i	−1.37391	+	1.14940i
$409$	−17.7444	−	24.4231i	−0.877406	−	1.20765i	−0.977133	−	0.212631i	$-0.931797\pi$
$409$	−17.7444	−	24.4231i	−0.877406	−	1.20765i	0.0997266	−	0.995015i	$-0.468203\pi$
$410$	−2.93866	+	3.23564i	−0.145130	+	0.159797i
$411$	14.6932	+	4.77410i	0.724761	+	0.235489i
$412$	−1.88693	−	19.2090i	−0.0929624	−	0.946359i
$413$	3.16068	+	19.9557i	0.155527	+	0.981957i
$414$	1.30188	−	3.63704i	0.0639839	−	0.178751i
$415$	−13.1574	+	15.3774i	−0.645872	+	0.754847i
$416$	−3.87476	+	2.01928i	−0.189976	+	0.0990033i
$417$	9.12354	−	9.12354i	0.446782	−	0.446782i
$418$	−6.26678	−	37.2776i	−0.306518	−	1.82331i
$419$	−21.6999			−1.06011			−0.530055	−	0.847963i	$-0.677829\pi$
$419$	−21.6999			−1.06011			−0.530055	+	0.847963i	$0.677829\pi$
$420$	−27.9674	+	9.66211i	−1.36467	+	0.471463i
$421$	−6.81240	−	20.9664i	−0.332016	−	1.02184i	−0.968173	−	0.250281i	$-0.919477\pi$
$421$	−6.81240	−	20.9664i	−0.332016	−	1.02184i	0.636157	−	0.771559i	$-0.280523\pi$
$422$	15.1413	−	7.15894i	0.737069	−	0.348492i
$423$	−2.01777	+	0.319584i	−0.0981076	+	0.0155387i
$424$	5.06152	−	5.80527i	0.245809	−	0.281929i
$425$	0.0601121	−	33.4997i	0.00291587	−	1.62498i
$426$	0.896955	+	3.06633i	0.0434576	+	0.148564i
$427$	35.5607	+	5.63226i	1.72090	+	0.272564i
$428$	22.3027	−	19.8084i	1.07804	−	0.957476i
$429$	−2.71831	+	4.06635i	−0.131241	+	0.196325i
$430$	−20.7349	−	5.65153i	−0.999926	−	0.272541i
$431$	5.66689	+	7.79980i	0.272964	+	0.375703i	0.923388	−	0.383869i	$-0.125408\pi$
$431$	5.66689	+	7.79980i	0.272964	+	0.375703i	−0.650423	+	0.759572i	$0.725408\pi$
$432$	−9.99781	+	14.9461i	−0.481020	+	0.719096i
$433$	−14.5545	+	7.41590i	−0.699446	+	0.356385i	−0.767281	−	0.641311i	$-0.778391\pi$
$433$	−14.5545	+	7.41590i	−0.699446	+	0.356385i	0.0678351	+	0.997697i	$0.478391\pi$
$434$	12.2215	−	15.8157i	0.586652	−	0.759179i
$435$	−13.4625	−	1.07168i	−0.645479	−	0.0513831i
$436$	9.23582	−	23.5795i	0.442316	−	1.12925i
$437$	30.3847	+	15.4818i	1.45350	+	0.740594i
$438$	1.64769	−	8.72443i	0.0787297	−	0.416870i
$439$	−18.2148			−0.869343			−0.434671	−	0.900589i	$-0.643135\pi$
$439$	−18.2148			−0.869343			−0.434671	+	0.900589i	$0.643135\pi$
$440$	20.6181	−	3.85920i	0.982930	−	0.183980i
$441$	3.23307			0.153956
$442$	−1.35818	+	7.19150i	−0.0646021	+	0.342065i
$443$	−18.7505	−	9.55388i	−0.890865	−	0.453919i	−0.0522446	−	0.998634i	$-0.516638\pi$
$443$	−18.7505	−	9.55388i	−0.890865	−	0.453919i	−0.838621	+	0.544716i	$0.816638\pi$
$444$	7.37707	−	18.8340i	0.350100	−	0.893821i
$445$	3.47235	+	4.07299i	0.164605	+	0.193078i
$446$	−5.72070	+	7.40309i	−0.270883	+	0.350546i
$447$	−15.9024	+	8.10266i	−0.752156	+	0.383243i
$448$	−22.0907	−	16.7491i	−1.04369	−	0.791319i
$449$	21.0165	+	28.9267i	0.991830	+	1.36514i	0.930206	+	0.367037i	$0.119628\pi$
$449$	21.0165	+	28.9267i	0.991830	+	1.36514i	0.0616231	+	0.998099i	$0.480372\pi$
$450$	1.27368	+	4.38339i	0.0600421	+	0.206635i
$451$	−4.30127	+	1.58577i	−0.202539	+	0.0746711i
$452$	−8.60296	+	7.64082i	−0.404649	+	0.359394i
$453$	13.9704	+	2.21269i	0.656384	+	0.103961i
$454$	−2.37129	−	8.10649i	−0.111290	−	0.380456i
$455$	−3.13176	+	5.10029i	−0.146819	+	0.239105i
$456$	32.8047	+	28.6018i	1.53622	+	1.33940i
$457$	0.561552	−	0.0889411i	0.0262683	−	0.00416049i	−0.143286	−	0.989681i	$-0.545767\pi$
$457$	0.561552	−	0.0889411i	0.0262683	−	0.00416049i	0.169555	+	0.985521i	$0.445767\pi$
$458$	−20.6050	+	9.74222i	−0.962811	+	0.455224i
$459$	9.30736	+	28.6451i	0.434430	+	1.33704i
$460$	−8.27803	+	17.0168i	−0.385965	+	0.793413i
$461$	3.93828			0.183424			0.0917120	−	0.995786i	$-0.470766\pi$
$461$	3.93828			0.183424			0.0917120	+	0.995786i	$0.470766\pi$
$462$	−30.6962	−	4.56412i	−1.42812	−	0.212342i
$463$	17.7178	−	17.7178i	0.823417	−	0.823417i	−0.163179	−	0.986596i	$-0.552175\pi$
$463$	17.7178	−	17.7178i	0.823417	−	0.823417i	0.986596	+	0.163179i	$0.0521749\pi$
$464$	−6.17683	−	11.0428i	−0.286752	−	0.512651i
$465$	−13.2307	−	11.3206i	−0.613559	−	0.524982i
$466$	−5.12744	+	14.3244i	−0.237524	+	0.663566i
$467$	4.33568	+	27.3744i	0.200631	+	1.26674i	0.858190	+	0.513333i	$0.171589\pi$
$467$	4.33568	+	27.3744i	0.200631	+	1.26674i	−0.657558	+	0.753404i	$0.728411\pi$
$468$	−0.0974911	−	0.992461i	−0.00450653	−	0.0458765i
$469$	−27.0846	−	8.80031i	−1.25065	−	0.406360i
$470$	9.99597	−	0.480792i	0.461080	−	0.0221773i
$471$	−14.6223	−	20.1259i	−0.673761	−	0.927353i
$472$	10.5817	+	12.6486i	0.487061	+	0.582201i
$473$	−16.5485	−	15.3039i	−0.760902	−	0.703674i
$474$	0.575009	−	19.4328i	0.0264111	−	0.892576i
$475$	−39.8108	+	6.23220i	−1.82664	+	0.285953i
$476$	−44.9332	+	11.7128i	−2.05951	+	0.536856i
$477$	0.798048	+	1.56626i	0.0365401	+	0.0717140i
$478$	20.2182	−	2.59185i	0.924758	−	0.118548i
$479$	12.4104	+	9.01671i	0.567047	+	0.411984i	0.834031	−	0.551717i	$-0.186027\pi$
$479$	12.4104	+	9.01671i	0.567047	+	0.411984i	−0.266984	+	0.963701i	$0.586027\pi$
$480$	−15.5325	+	18.4940i	−0.708958	+	0.844133i
$481$	−1.26430	−	3.89111i	−0.0576471	−	0.177419i
$482$	−3.43848	+	18.2066i	−0.156618	+	0.829286i
$483$	19.7967	−	19.7967i	0.900781	−	0.900781i
$484$	21.0483	+	6.40072i	0.956741	+	0.290942i
$485$	1.91283	+	3.12774i	0.0868570	+	0.142024i
$486$	−5.26028	−	7.70979i	−0.238611	−	0.349723i
$487$	5.87161	−	11.5237i	0.266068	−	0.522188i	−0.718860	−	0.695155i	$-0.755336\pi$
$487$	5.87161	−	11.5237i	0.266068	−	0.522188i	0.984928	+	0.172968i	$0.0553356\pi$
$488$	27.2633	−	10.9683i	1.23415	−	0.496512i
$489$	16.7418	−	23.0431i	0.757090	−	1.04204i
$490$	−15.7436	−	1.72316i	−0.711221	−	0.0778446i
$491$	18.3140	+	5.95059i	0.826501	+	0.268546i	0.691571	−	0.722309i	$-0.256919\pi$
$491$	18.3140	+	5.95059i	0.826501	+	0.268546i	0.134930	+	0.990855i	$0.456919\pi$
$492$	2.67013	−	4.55300i	0.120379	−	0.205265i
$493$	−20.9327	−	3.31541i	−0.942760	−	0.149319i
$494$	8.79946	+	0.260373i	0.395906	+	0.0117147i
$495$	−0.939212	+	4.69445i	−0.0422144	+	0.211000i
$496$	1.92586	−	16.2001i	0.0864736	−	0.727405i
$497$	−0.641392	+	4.04959i	−0.0287704	+	0.181649i
$498$	11.7342	−	21.4375i	0.525823	−	0.960639i
$499$	−4.10123	+	12.6223i	−0.183596	+	0.565051i	−0.999921	−	0.0125415i	$-0.996008\pi$
$499$	−4.10123	+	12.6223i	−0.183596	+	0.565051i	0.816325	+	0.577593i	$0.196008\pi$
$500$	−3.86600	−	22.0239i	−0.172893	−	0.984941i
$501$	11.7832	+	8.56098i	0.526433	+	0.382476i
$502$	11.5683	−	5.46958i	0.516319	−	0.244119i
$503$	−19.6478	−	10.0110i	−0.876052	−	0.446371i	−0.0426833	−	0.999089i	$-0.513591\pi$
$503$	−19.6478	−	10.0110i	−0.876052	−	0.446371i	−0.833368	+	0.552718i	$0.813591\pi$
$504$	5.42827	−	3.25074i	0.241795	−	0.144799i
$505$	−0.261612	+	1.08540i	−0.0116416	+	0.0482997i
$506$	−15.9454	+	11.8174i	−0.708860	+	0.525349i
$507$	16.7458	+	16.7458i	0.743709	+	0.743709i
$508$	−0.588559	+	2.67921i	−0.0261131	+	0.118871i
$509$	−33.7798	+	10.9757i	−1.49726	+	0.486491i	−0.939219	−	0.343320i	$-0.888449\pi$
$509$	−33.7798	+	10.9757i	−1.49726	+	0.486491i	−0.558045	+	0.829810i	$0.688449\pi$
$510$	8.24055	+	39.6050i	0.364897	+	1.75374i
$511$	6.69746	−	9.21827i	0.296278	−	0.407792i
$512$	−22.4928	−	2.46488i	−0.994049	−	0.108933i
$513$	32.2805	−	16.4478i	1.42522	−	0.726186i
$514$	−28.4191	+	8.31310i	−1.25351	+	0.366675i
$515$	−19.9296	−	8.27607i	−0.878203	−	0.364687i
$516$	25.9068	+	1.53449i	1.14048	+	0.0675522i
$517$	9.53091	+	4.39629i	0.419169	+	0.193349i
$518$	18.8903	−	17.8045i	0.829993	−	0.782286i
$519$	−12.1704	+	8.84235i	−0.534223	+	0.388136i
$520$	−0.0542262	+	4.88479i	−0.00237798	+	0.214212i
$521$	5.38087	−	16.5606i	0.235740	−	0.725533i	−0.761282	−	0.648421i	$-0.775430\pi$
$521$	5.38087	−	16.5606i	0.235740	−	0.725533i	0.997022	−	0.0771128i	$-0.0245702\pi$
$522$	2.86440	−	0.367199i	0.125371	−	0.0160719i
$523$	27.7769	−	4.39943i	1.21460	−	0.192374i	0.483931	−	0.875106i	$-0.339209\pi$
$523$	27.7769	−	4.39943i	1.21460	−	0.192374i	0.730668	+	0.682733i	$0.239209\pi$
$524$	−0.113771	+	0.290464i	−0.00497013	+	0.0126890i
$525$	−5.23379	+	32.6654i	−0.228421	+	1.42563i
$526$	−16.9630	−	24.8620i	−0.739621	−	1.08403i
$527$	−19.3224	−	19.3224i	−0.841698	−	0.841698i
$528$	−23.4091	+	9.67636i	−1.01875	+	0.421109i
$529$			5.09510i			0.221526i
$530$	−3.05134	−	8.05230i	−0.132542	−	0.349770i
$531$	−3.57964	+	1.16310i	−0.155343	+	0.0504741i
$532$	22.3705	+	51.1790i	0.969884	+	2.21889i
$533$	−0.167013	−	1.05448i	−0.00723412	−	0.0456745i
$534$	−5.11418	−	3.95195i	−0.221312	−	0.171018i
$535$	−7.75633	−	32.4356i	−0.335335	−	1.40231i
$536$	−22.6564	+	5.19542i	−0.978609	+	0.224408i
$537$	−1.90490	+	12.0271i	−0.0822027	+	0.519007i
$538$	25.1404	+	26.6736i	1.08388	+	1.14998i
$539$	−13.8092	−	9.23132i	−0.594805	−	0.397621i
$540$	9.45658	+	17.7412i	0.406946	+	0.763462i
$541$	−25.7630	+	18.7179i	−1.10764	+	0.804747i	−0.982290	−	0.187365i	$-0.940005\pi$
$541$	−25.7630	+	18.7179i	−1.10764	+	0.804747i	−0.125349	+	0.992113i	$0.540005\pi$
$542$	−14.5688	+	26.6160i	−0.625782	+	1.14326i
$543$	1.25695	+	2.46690i	0.0539407	+	0.105865i
$544$	−26.5528	+	27.0446i	−1.13844	+	1.15953i
$545$	−18.3684	−	21.5457i	−0.786814	−	0.922917i
$546$	2.43570	−	6.80456i	0.104238	−	0.291208i
$547$	8.37994	−	16.4466i	0.358300	−	0.703204i	−0.639549	−	0.768750i	$-0.720879\pi$
$547$	8.37994	−	16.4466i	0.358300	−	0.703204i	0.997850	+	0.0655461i	$0.0208789\pi$
$548$	15.8061	+	3.47222i	0.675202	+	0.148326i
$549$			6.70712i			0.286253i
$550$	7.07559	−	22.3592i	0.301704	−	0.953402i
$551$			25.4930i			1.08604i
$552$	5.56098	−	22.1644i	0.236691	−	0.943379i
$553$	11.3270	−	22.2305i	0.481674	−	0.945338i
$554$	−24.6113	−	8.80962i	−1.04563	−	0.374285i
$555$	−14.6716	−	17.2095i	−0.622777	−	0.730504i
$556$	8.57673	−	10.4453i	0.363734	−	0.442979i
$557$	−1.86891	−	3.66795i	−0.0791883	−	0.155416i	0.848017	−	0.529969i	$-0.177796\pi$
$557$	−1.86891	−	3.66795i	−0.0791883	−	0.155416i	−0.927206	+	0.374553i	$0.877796\pi$
$558$	3.26617	+	1.78780i	0.138268	+	0.0756834i
$559$	4.24681	−	3.08549i	0.179621	−	0.130502i
$560$	−28.1658	+	12.9364i	−1.19022	+	0.546664i
$561$	−11.5254	+	40.8323i	−0.486601	+	1.72394i
$562$	24.8967	−	23.4657i	1.05020	−	0.989839i
$563$	4.54458	−	28.6934i	0.191531	−	1.20928i	−0.685220	−	0.728337i	$-0.740294\pi$
$563$	4.54458	−	28.6934i	0.191531	−	1.20928i	0.876751	−	0.480945i	$-0.159706\pi$
$564$	−11.6940	+	3.04829i	−0.492406	+	0.128356i
$565$	2.99190	+	12.5116i	0.125870	+	0.526366i
$566$	−26.7349	+	34.5974i	−1.12375	+	1.45424i
$567$	−5.70276	−	36.0058i	−0.239493	−	1.51210i
$568$	1.24905	+	3.10470i	0.0524090	+	0.130270i
$569$	4.08396	−	1.32696i	0.171208	−	0.0556290i	−0.222158	−	0.975011i	$-0.571310\pi$
$569$	4.08396	−	1.32696i	0.171208	−	0.0556290i	0.393367	+	0.919382i	$0.371310\pi$
$570$	45.5023	−	17.2427i	1.90588	−	0.722215i
$571$		−	4.73738i		−	0.198253i	−0.995075	−	0.0991267i	$-0.968395\pi$
$571$		−	4.73738i		−	0.198253i	0.995075	−	0.0991267i	$-0.0316049\pi$
$572$	−2.41735	+	4.51741i	−0.101074	+	0.188882i
$573$	−6.65666	−	6.65666i	−0.278086	−	0.278086i
$574$	5.59545	−	3.81769i	0.233550	−	0.159347i
$575$	12.4051	+	17.1387i	0.517328	+	0.714735i
$576$	2.43797	−	4.55267i	0.101582	−	0.189695i
$577$	−14.1283	+	2.23770i	−0.588167	+	0.0931565i	−0.443423	−	0.896313i	$-0.646236\pi$
$577$	−14.1283	+	2.23770i	−0.588167	+	0.0931565i	−0.144744	+	0.989469i	$0.546236\pi$
$578$	5.01514	+	39.1215i	0.208602	+	1.62724i
$579$	−4.02710	+	12.3941i	−0.167361	+	0.515083i
$580$	−14.1440	+	0.261418i	−0.587299	+	0.0108548i
$581$	25.3737	−	18.4351i	1.05268	−	0.764815i
$582$	−3.03661	−	3.22179i	−0.125871	−	0.133548i
$583$	1.06345	−	8.96852i	0.0440435	−	0.371438i
$584$	0.824254	−	9.26369i	0.0341079	−	0.383334i
$585$	−1.02969	−	0.427595i	−0.0425725	−	0.0176789i
$586$	−7.63913	−	26.1151i	−0.315570	−	1.07881i
$587$	24.0079	−	12.2326i	0.990910	−	0.504894i	0.118125	−	0.992999i	$-0.462312\pi$
$587$	24.0079	−	12.2326i	0.990910	−	0.504894i	0.872785	+	0.488105i	$0.162312\pi$
$588$	19.0333	−	1.86967i	0.784921	−	0.0771041i
$589$	−19.3202	+	26.5920i	−0.796074	+	1.09570i
$590$	18.0511	−	3.75586i	0.743153	−	0.154626i
$591$	−4.05845	+	1.31867i	−0.166942	+	0.0542428i
$592$	5.76170	−	20.3893i	0.236805	−	0.837995i
$593$	−23.1674	−	23.1674i	−0.951373	−	0.951373i	0.0474983	−	0.998871i	$-0.484875\pi$
$593$	−23.1674	−	23.1674i	−0.951373	−	0.951373i	−0.998871	+	0.0474983i	$0.984875\pi$
$594$	0.199764	+	21.0845i	0.00819642	+	0.865108i
$595$	−12.1647	+	50.4703i	−0.498706	+	2.06908i
$596$	−15.7480	+	10.0752i	−0.645063	+	0.412698i
$597$	−19.6276	−	10.0008i	−0.803305	−	0.409304i
$598$	−1.97568	−	4.17862i	−0.0807918	−	0.170877i
$599$	−20.2651	−	14.7235i	−0.828011	−	0.601585i	0.0909849	−	0.995852i	$-0.470998\pi$
$599$	−20.2651	−	14.7235i	−0.828011	−	0.601585i	−0.918996	+	0.394267i	$0.870998\pi$
$600$	10.0332	+	25.0688i	0.409603	+	1.02343i
$601$	5.59065	−	17.2063i	0.228047	−	0.701858i	−0.769921	−	0.638140i	$-0.779704\pi$
$601$	5.59065	−	17.2063i	0.228047	−	0.701858i	0.997968	−	0.0637180i	$-0.0202958\pi$
$602$	29.2154	+	15.9915i	1.19073	+	0.651767i
$603$	0.829915	−	5.23987i	0.0337967	−	0.213384i
$604$	14.7903	+	0.876046i	0.601807	+	0.0356458i
$605$	17.4156	−	17.3694i	0.708044	−	0.706168i
$606$	0.0398762	−	1.34764i	0.00161986	−	0.0547441i
$607$	13.6347	+	2.15953i	0.553416	+	0.0876525i	0.426878	−	0.904309i	$-0.359613\pi$
$607$	13.6347	+	2.15953i	0.553416	+	0.0876525i	0.126538	+	0.991962i	$0.459613\pi$
$608$	37.1268	+	26.4572i	1.50569	+	1.07298i
$609$	19.9049	+	6.46750i	0.806588	+	0.262076i
$610$	3.57477	−	32.6606i	0.144738	−	1.32239i
$611$	−1.43677	+	1.97755i	−0.0581256	+	0.0800030i
$612$	−3.46454	−	7.92614i	−0.140046	−	0.320395i
$613$	2.21426	−	4.34573i	0.0894332	−	0.175523i	−0.841957	−	0.539544i	$-0.818597\pi$
$613$	2.21426	−	4.34573i	0.0894332	−	0.175523i	0.931390	+	0.364022i	$0.118597\pi$
$614$	−29.8501	+	20.3663i	−1.20465	+	0.821916i
$615$	−3.07885	−	5.03437i	−0.124151	−	0.203005i
$616$	−32.4672	−	1.61456i	−1.30814	−	0.0650525i
$617$	6.51169	−	6.51169i	0.262151	−	0.262151i	−0.563776	−	0.825927i	$-0.690652\pi$
$617$	6.51169	−	6.51169i	0.262151	−	0.262151i	0.825927	+	0.563776i	$0.190652\pi$
$618$	25.6062	+	4.83597i	1.03003	+	0.194531i
$619$	−14.6449	−	45.0723i	−0.588628	−	1.81161i	−0.584187	−	0.811619i	$-0.698587\pi$
$619$	−14.6449	−	45.0723i	−0.588628	−	1.81161i	−0.00444060	−	0.999990i	$-0.501413\pi$
$620$	−14.9519	−	10.4465i	−0.600482	−	0.419543i
$621$	−15.3892	−	11.1809i	−0.617546	−	0.448674i
$622$	3.65080	+	28.4787i	0.146384	+	1.14189i
$623$	−3.76563	−	7.39046i	−0.150867	−	0.296093i
$624$	−1.14788	−	5.78632i	−0.0459518	−	0.231638i
$625$	−23.7485	−	7.81070i	−0.949941	−	0.312428i
$626$	−24.8425	−	0.735081i	−0.992904	−	0.0293797i
$627$	50.6797	+	6.00937i	2.02395	+	0.239991i
$628$	−17.3043	−	19.4833i	−0.690517	−	0.777467i
$629$	−20.8601	−	28.7114i	−0.831745	−	1.14480i
$630$	−0.339858	−	7.06585i	−0.0135403	−	0.281510i
$631$	−36.8610	−	11.9769i	−1.46741	−	0.476791i	−0.537087	−	0.843527i	$-0.680475\pi$
$631$	−36.8610	−	11.9769i	−1.46741	−	0.476791i	−0.930325	+	0.366736i	$0.880475\pi$
$632$	−1.39055	−	20.3169i	−0.0553132	−	0.808165i
$633$	3.53731	+	22.3337i	0.140596	+	0.887686i
$634$	34.1202	+	12.2133i	1.35508	+	0.485054i
$635$	2.33028	+	1.99386i	0.0924742	+	0.0791240i
$636$	5.60393	+	8.75917i	0.222210	+	0.347324i
$637$	2.73537	−	2.73537i	0.108379	−	0.108379i
$638$	−13.2830	−	6.61028i	−0.525880	−	0.261703i
$639$	−0.763795			−0.0302152
$640$	−14.2983	+	20.8700i	−0.565190	+	0.824961i
$641$	8.45017	+	26.0070i	0.333762	+	1.02721i	0.967329	+	0.253525i	$0.0815901\pi$
$641$	8.45017	+	26.0070i	0.333762	+	1.02721i	−0.633567	+	0.773688i	$0.718410\pi$
$642$	17.2140	+	36.4081i	0.679383	+	1.43691i
$643$	−30.5118	+	4.83260i	−1.20327	+	0.190579i	−0.725697	−	0.688014i	$-0.758483\pi$
$643$	−30.5118	+	4.83260i	−1.20327	+	0.190579i	−0.477571	+	0.878593i	$0.658483\pi$
$644$	18.6102	−	22.6647i	0.733345	−	0.893114i
$645$	15.1827	−	24.7261i	0.597818	−	0.973589i
$646$	73.2904	−	21.4387i	2.88357	−	0.843496i
$647$	18.7934	+	2.97658i	0.738845	+	0.117022i	0.514503	−	0.857489i	$-0.327977\pi$
$647$	18.7934	+	2.97658i	0.738845	+	0.117022i	0.224343	+	0.974510i	$0.427977\pi$
$648$	−19.0923	−	22.8217i	−0.750017	−	0.896521i
$649$	18.6105	+	5.25302i	0.730526	+	0.206199i
$650$	4.78623	+	2.63100i	0.187731	+	0.103196i
$651$	15.8615	+	21.8315i	0.621662	+	0.855644i
$652$	15.0931	−	25.7361i	0.591092	−	1.00791i
$653$	−20.3839	+	10.3861i	−0.797683	+	0.406440i	−0.804808	−	0.593535i	$-0.797732\pi$
$653$	−20.3839	+	10.3861i	−0.797683	+	0.406440i	0.00712551	+	0.999975i	$0.497732\pi$
$654$	27.0535	+	20.9054i	1.05787	+	0.817467i
$655$	0.226271	+	0.265411i	0.00884113	+	0.0103705i
$656$	2.31729	−	5.01979i	0.0904749	−	0.195990i
$657$	1.89129	+	0.963661i	0.0737863	+	0.0375960i
$658$	−15.2395	−	2.87813i	−0.594099	−	0.112201i
$659$	41.2462			1.60673			0.803363	−	0.595490i	$-0.203042\pi$
$659$	41.2462			1.60673			0.803363	+	0.595490i	$0.203042\pi$
$660$	−2.81443	+	28.1798i	−0.109551	+	1.09690i
$661$	20.3285			0.790689			0.395344	−	0.918533i	$-0.370625\pi$
$661$	20.3285			0.790689			0.395344	+	0.918533i	$0.370625\pi$
$662$	31.5343	+	5.95555i	1.22562	+	0.231469i
$663$	−8.80394	−	4.48583i	−0.341917	−	0.174215i
$664$	10.0373	−	23.5496i	0.389522	−	0.913902i
$665$	62.2504	+	4.95541i	2.41397	+	0.192163i
$666$	3.82644	+	2.95686i	0.148272	+	0.114576i
$667$	11.9261	−	6.07666i	0.461781	−	0.235289i
$668$	13.1603	+	7.71792i	0.509186	+	0.298615i
$669$	−7.42452	−	10.2190i	−0.287049	−	0.395089i
$670$	−6.83406	+	25.0735i	−0.264023	+	0.968672i
$671$	19.1507	−	28.6477i	0.739304	−	1.10593i
$672$	30.0768	−	22.2765i	1.16024	−	0.859334i
$673$	12.6909	+	2.01004i	0.489197	+	0.0774812i	0.396160	−	0.918181i	$-0.370343\pi$
$673$	12.6909	+	2.01004i	0.489197	+	0.0774812i	0.0930368	+	0.995663i	$0.470343\pi$
$674$	−1.29326	+	0.378301i	−0.0498145	+	0.0145716i
$675$	22.4771	+	0.0403331i	0.865145	+	0.00155242i
$676$	19.1719	+	15.7422i	0.737379	+	0.605469i
$677$	−29.6215	+	4.69158i	−1.13845	+	0.180312i	−0.697065	−	0.717008i	$-0.745511\pi$
$677$	−29.6215	+	4.69158i	−1.13845	+	0.180312i	−0.441380	+	0.897320i	$0.645511\pi$
$678$	−6.64007	−	14.0439i	−0.255010	−	0.539353i
$679$	−1.75576	−	5.40367i	−0.0673798	−	0.207374i
$680$	12.6462	+	40.4432i	0.484960	+	1.55093i
$681$	11.4032			0.436972
$682$	−8.84595	−	16.9619i	−0.338729	−	0.649506i
$683$	13.3523	−	13.3523i	0.510912	−	0.510912i	−0.403894	−	0.914806i	$-0.632343\pi$
$683$	13.3523	−	13.3523i	0.510912	−	0.510912i	0.914806	+	0.403894i	$0.132343\pi$
$684$	−8.76476	+	5.60751i	−0.335129	+	0.214408i
$685$	11.7629	−	13.7476i	0.449436	−	0.525267i
$686$	−9.18975	−	3.28948i	−0.350866	−	0.125593i
$687$	−4.81374	−	30.3927i	−0.183656	−	1.15956i
$688$	27.1642	−	1.05328i	1.03562	−	0.0401561i
$689$	2.00035	+	0.649952i	0.0762071	+	0.0247612i
$690$	−18.9127	−	17.1768i	−0.719993	−	0.653910i
$691$	21.9644	+	30.2314i	0.835566	+	1.15006i	0.986861	+	0.161570i	$0.0516557\pi$
$691$	21.9644	+	30.2314i	0.835566	+	1.15006i	−0.151295	+	0.988489i	$0.548344\pi$
$692$	−11.7818	+	10.4642i	−0.447878	+	0.397788i
$693$	3.10761	−	6.73712i	0.118048	−	0.255922i
$694$	5.56396	+	0.164636i	0.211205	+	0.00624950i
$695$	−5.77005	−	13.9656i	−0.218871	−	0.529744i
$696$	16.6506	−	3.81821i	0.631140	−	0.144729i
$697$	−4.20430	−	8.25140i	−0.159249	−	0.312544i
$698$	0.133046	+	1.03785i	0.00503586	+	0.0392831i
$699$	−16.6181	−	12.0737i	−0.628553	−	0.456670i
$700$	−2.11102	+	34.5886i	−0.0797889	+	1.30733i
$701$	−14.1715	−	43.6155i	−0.535252	−	1.64734i	−0.743105	−	0.669175i	$-0.766647\pi$
$701$	−14.1715	−	43.6155i	−0.535252	−	1.64734i	0.207853	−	0.978160i	$-0.433353\pi$
$702$	−4.82524	−	0.911292i	−0.182117	−	0.0343945i
$703$	−30.1855	+	30.1855i	−1.13847	+	1.13847i
$704$	−23.4123	+	12.4845i	−0.882386	+	0.470527i
$705$	−3.16591	+	13.1350i	−0.119235	+	0.494693i
$706$	7.51101	−	5.12465i	0.282681	−	0.192869i
$707$	0.785515	−	1.54166i	0.0295423	−	0.0579801i
$708$	−20.4010	+	8.91734i	−0.766717	+	0.335134i
$709$	−2.23017	+	3.06957i	−0.0837559	+	0.115280i	−0.848839	−	0.528651i	$-0.822698\pi$
$709$	−2.23017	+	3.06957i	−0.0837559	+	0.115280i	0.765083	+	0.643932i	$0.222698\pi$
$710$	3.71933	+	0.407088i	0.139584	+	0.0152777i
$711$	4.42039	+	1.43627i	0.165778	+	0.0538644i
$712$	−5.73607	−	3.59608i	−0.214968	−	0.134769i
$713$	17.0455	+	2.69975i	0.638360	+	0.101106i
$714$	1.85421	−	62.6641i	0.0693921	−	2.34515i
$715$	3.17716	+	4.76642i	0.118819	+	0.178254i
$716$	−0.754189	+	12.7330i	−0.0281854	+	0.475853i
$717$	−4.30507	+	27.1812i	−0.160776	+	1.01510i
$718$	−3.49840	−	1.91491i	−0.130559	−	0.0714639i
$719$	−10.9197	+	33.6075i	−0.407237	+	1.25335i	0.511775	+	0.859119i	$0.328988\pi$
$719$	−10.9197	+	33.6075i	−0.407237	+	1.25335i	−0.919013	+	0.394228i	$0.871012\pi$
$720$	−3.20104	−	4.80537i	−0.119296	−	0.179085i
$721$	27.0556	+	19.6571i	1.00760	+	0.732068i
$722$	−27.7761	−	58.7471i	−1.03372	−	2.18634i
$723$	−22.2887	−	11.3567i	−0.828927	−	0.422359i
$724$	1.56295	+	2.44295i	0.0580865	+	0.0907915i
$725$	−7.20569	+	14.0794i	−0.267612	+	0.522897i
$726$	−16.2723	+	24.8482i	−0.603921	+	0.922204i
$727$	−1.35919	−	1.35919i	−0.0504095	−	0.0504095i	0.681453	−	0.731862i	$-0.261349\pi$
$727$	−1.35919	−	1.35919i	−0.0504095	−	0.0504095i	−0.731862	+	0.681453i	$0.761349\pi$
$728$	1.84233	−	7.34297i	0.0682813	−	0.272149i
$729$	−18.0308	+	5.85858i	−0.667809	+	0.216984i
$730$	−8.69610	−	5.70061i	−0.321857	−	0.210989i
$731$	26.7642	−	36.8377i	0.989908	−	1.36249i
$732$	3.87871	+	39.4853i	0.143361	+	1.45942i
$733$	8.25048	−	4.20383i	0.304739	−	0.155272i	−0.294934	−	0.955518i	$-0.595298\pi$
$733$	8.25048	−	4.20383i	0.304739	−	0.155272i	0.599672	+	0.800246i	$0.295298\pi$
$734$	3.07538	+	10.5135i	0.113514	+	0.388060i
$735$	8.20038	−	19.7473i	0.302476	−	0.728392i
$736$	3.52744	−	23.6752i	0.130023	−	0.872679i
$737$	−18.5061	+	20.0111i	−0.681680	+	0.737120i
$738$	0.865497	+	0.918279i	0.0318594	+	0.0338023i
$739$	5.45965	−	3.96667i	0.200837	−	0.145916i	−0.482821	−	0.875719i	$-0.660388\pi$
$739$	5.45965	−	3.96667i	0.200837	−	0.145916i	0.683658	+	0.729802i	$0.260388\pi$
$740$	−17.0571	−	16.4380i	−0.627030	−	0.604272i
$741$	−3.67278	+	11.3036i	−0.134923	+	0.415250i
$742$	1.69684	+	13.2365i	0.0622928	+	0.485926i
$743$	−0.273958	+	0.0433908i	−0.0100506	+	0.00159185i	−0.161458	−	0.986880i	$-0.551620\pi$
$743$	−0.273958	+	0.0433908i	−0.0100506	+	0.00159185i	0.151407	+	0.988471i	$0.451620\pi$
$744$	20.2621	+	8.63607i	0.742844	+	0.316614i
$745$	1.62124	+	20.8389i	0.0593978	+	0.763478i
$746$	−24.6500	+	16.8183i	−0.902500	+	0.615762i
$747$	4.13139	+	4.13139i	0.151160	+	0.151160i
$748$	−7.83348	+	43.7467i	−0.286420	+	1.59954i
$749$			51.6836i			1.88848i
$750$	30.0040	+	3.33849i	1.09559	+	0.121905i
$751$	−40.5685	+	13.1815i	−1.48037	+	0.481000i	−0.934222	−	0.356692i	$-0.883905\pi$
$751$	−40.5685	+	13.1815i	−1.48037	+	0.481000i	−0.546143	+	0.837692i	$0.683905\pi$
$752$	−11.8785	+	4.37526i	−0.433163	+	0.159549i
$753$	2.70258	+	17.0634i	0.0984875	+	0.621826i
$754$	2.11279	−	2.73413i	0.0769431	−	0.0995712i
$755$	8.66785	−	14.1162i	0.315455	−	0.513741i
$756$	−7.85888	−	30.1486i	−0.285825	−	1.09649i
$757$	5.44805	−	34.3976i	0.198013	−	1.25020i	−0.665701	−	0.746219i	$-0.731867\pi$
$757$	5.44805	−	34.3976i	0.198013	−	1.25020i	0.863713	−	0.503984i	$-0.168133\pi$
$758$	−36.7195	+	34.6089i	−1.33371	+	1.25705i
$759$	−9.26902	−	25.1414i	−0.336444	−	0.912575i
$760$	45.6690	−	22.6345i	1.65659	−	0.821041i
$761$	4.52503	−	3.28762i	0.164032	−	0.119176i	−0.502741	−	0.864437i	$-0.667675\pi$
$761$	4.52503	−	3.28762i	0.164032	−	0.119176i	0.666773	+	0.745261i	$0.267675\pi$
$762$	−3.24862	−	1.77819i	−0.117685	−	0.0644171i
$763$	19.9198	+	39.0948i	0.721145	+	1.41533i
$764$	−7.62103	−	6.25770i	−0.275719	−	0.226396i
$765$	−9.64077	−	0.767449i	−0.348563	−	0.0277472i
$766$	−33.7414	−	12.0778i	−1.21913	−	0.436387i
$767$	−2.04455	+	4.01265i	−0.0738243	+	0.144888i
$768$	11.7197	−	28.2118i	0.422900	−	1.01801i
$769$			4.12098i			0.148606i	0.997236	+	0.0743031i	$0.0236732\pi$
$769$			4.12098i			0.148606i	−0.997236	+	0.0743031i	$0.976327\pi$
$770$	−18.7234	+	31.1504i	−0.674744	+	1.12258i
$771$		−	39.9765i		−	1.43972i
$772$	−2.92893	+	13.3329i	−0.105414	+	0.479862i
$773$	−8.08645	+	15.8706i	−0.290849	+	0.570824i	−0.989482	−	0.144656i	$-0.953792\pi$
$773$	−8.08645	+	15.8706i	−0.290849	+	0.570824i	0.698632	+	0.715481i	$0.253792\pi$
$774$	−2.09097	+	5.84150i	−0.0751583	+	0.209968i
$775$	−18.1866	+	9.22546i	−0.653282	+	0.331388i
$776$	−3.49549	−	3.04766i	−0.125481	−	0.109405i
$777$	15.9108	+	31.2268i	0.570798	+	1.12025i
$778$	−20.0608	+	36.6497i	−0.719216	+	1.31395i
$779$	−9.01198	+	6.54759i	−0.322888	+	0.234592i
$780$	−6.30916	−	1.92182i	−0.225904	−	0.0688121i
$781$	3.26235	+	2.18085i	0.116736	+	0.0780369i
$782$	−27.4994	−	29.1764i	−0.983377	−	1.04335i
$783$	2.22452	−	14.0451i	0.0794979	−	0.501930i
$784$	19.6502	−	3.89816i	0.701793	−	0.139220i
$785$	−28.3352	+	6.77580i	−1.01133	+	0.241839i
$786$	−0.333258	−	0.257524i	−0.0118869	−	0.00918556i
$787$	6.29372	+	39.7370i	0.224347	+	1.41647i	0.800600	+	0.599199i	$0.204514\pi$
$787$	6.29372	+	39.7370i	0.224347	+	1.41647i	−0.576253	+	0.817271i	$0.695486\pi$
$788$	−4.09577	+	1.79027i	−0.145906	+	0.0637758i
$789$	38.6459	−	12.5568i	1.37583	−	0.447034i
$790$	−20.7598	−	9.34997i	−0.738599	−	0.332657i
$791$		−	19.9362i		−	0.708850i
$792$	−0.649087	−	6.02086i	−0.0230643	−	0.213942i
$793$	5.67463	+	5.67463i	0.201512	+	0.201512i
$794$	29.2428	+	42.8602i	1.03779	+	1.52105i
$795$	11.5908	−	0.901750i	0.411082	−	0.0319818i
$796$	−21.4853	−	8.41557i	−0.761527	−	0.298282i
$797$	−31.6596	+	5.01439i	−1.12144	+	0.177619i	−0.689502	−	0.724284i	$-0.742171\pi$
$797$	−31.6596	+	5.01439i	−1.12144	+	0.177619i	−0.431939	+	0.901903i	$0.642171\pi$
$798$	−74.7972	+	9.58855i	−2.64779	+	0.339431i
$799$	−6.55211	+	20.1653i	−0.231797	+	0.713398i
$800$	13.0264	+	25.1060i	0.460554	+	0.887632i
$801$	1.25007	−	0.908229i	0.0441690	−	0.0320907i
$802$	−12.7798	+	12.0453i	−0.451271	+	0.425333i
$803$	−5.32664	−	9.51619i	−0.187973	−	0.335819i
$804$	1.85557	−	31.3275i	0.0654408	−	1.10484i
$805$	−12.5201	−	30.3032i	−0.441277	−	1.06805i
$806$	4.27596	−	1.25079i	0.150614	−	0.0440573i
$807$	−44.0930	+	22.4665i	−1.55215	+	0.790858i
$808$	−0.0964332	−	1.40896i	−0.00339251	−	0.0495669i
$809$	7.43771	−	10.2371i	0.261496	−	0.359918i	−0.658000	−	0.753018i	$-0.728597\pi$
$809$	7.43771	−	10.2371i	0.261496	−	0.359918i	0.919496	+	0.393100i	$0.128597\pi$
$810$	−32.5693	+	6.77664i	−1.14437	+	0.238107i
$811$	−39.0561	+	12.6901i	−1.37144	+	0.445609i	−0.899848	−	0.436205i	$-0.856322\pi$
$811$	−39.0561	+	12.6901i	−1.37144	+	0.445609i	−0.471597	+	0.881814i	$0.656322\pi$
$812$	21.4126	+	4.70384i	0.751434	+	0.165072i
$813$	−28.9669	−	28.9669i	−1.01591	−	1.01591i
$814$	−7.90099	−	23.5550i	−0.276930	−	0.825604i
$815$	−17.4035	−	28.4571i	−0.609617	−	0.996810i
$816$	−24.9797	−	44.6583i	−0.874463	−	1.56335i
$817$	−48.8013	−	24.8655i	−1.70734	−	0.869935i
$818$	38.5965	−	18.2487i	1.34950	−	0.638052i
$819$	1.39787	+	1.01561i	0.0488455	+	0.0354884i
$820$	−3.72515	−	4.93289i	−0.130088	−	0.172264i
$821$	−13.8910	+	42.7520i	−0.484799	+	1.49206i	0.347474	+	0.937690i	$0.387040\pi$
$821$	−13.8910	+	42.7520i	−0.484799	+	1.49206i	−0.832272	+	0.554367i	$0.812960\pi$
$822$	−10.4905	+	19.1654i	−0.365899	+	0.668469i
$823$	1.53307	−	9.67944i	0.0534395	−	0.337404i	−0.946454	−	0.322838i	$-0.895363\pi$
$823$	1.53307	−	9.67944i	0.0534395	−	0.337404i	0.999894	−	0.0145664i	$-0.00463678\pi$
$824$	27.1889	+	2.41919i	0.947172	+	0.0842764i
$825$	26.2912	+	17.6437i	0.915340	+	0.614275i
$826$	−28.5610	−	0.845110i	−0.993763	−	0.0294051i
$827$	−0.673931	−	0.106740i	−0.0234349	−	0.00371172i	0.144706	−	0.989475i	$-0.453776\pi$
$827$	−0.673931	−	0.106740i	−0.0234349	−	0.00371172i	−0.168141	+	0.985763i	$0.553776\pi$
$828$	4.71252	+	2.76369i	0.163772	+	0.0960448i
$829$	19.1491	+	6.22191i	0.665074	+	0.216096i	0.622049	−	0.782978i	$-0.286300\pi$
$829$	19.1491	+	6.22191i	0.665074	+	0.216096i	0.0430251	+	0.999074i	$0.486300\pi$
$830$	−17.9160	−	22.3199i	−0.621875	−	0.774737i
$831$	20.7443	−	28.5520i	0.719610	−	0.990459i
$832$	−1.78916	−	5.91451i	−0.0620281	−	0.205049i
$833$	15.2338	−	29.8980i	0.527819	−	1.03590i
$834$	10.2841	+	15.0730i	0.356108	+	0.521934i
$835$	14.5517	−	8.89933i	0.503581	−	0.307974i
$836$	53.4474	+	1.07481i	1.84852	+	0.0371730i
$837$	12.9647	−	12.9647i	0.448124	−	0.448124i
$838$	5.69509	−	30.1552i	0.196734	−	1.04170i
$839$	−6.90083	−	21.2386i	−0.238243	−	0.733237i	−0.996675	−	0.0814843i	$-0.974034\pi$
$839$	−6.90083	−	21.2386i	−0.238243	−	0.733237i	0.758431	−	0.651753i	$-0.225966\pi$
$840$	−6.08693	−	41.4007i	−0.210019	−	1.42846i
$841$	−15.3664	−	11.1643i	−0.529875	−	0.384977i
$842$	30.9238	−	3.96425i	1.06570	−	0.136617i
$843$	20.9699	+	41.1557i	0.722240	+	1.41748i
$844$	5.97459	+	22.9200i	0.205654	+	0.788939i
$845$	25.6332	−	10.5907i	0.881808	−	0.364330i
$846$	0.0854512	−	2.88787i	0.00293787	−	0.0992870i
$847$	−32.5097	+	19.9028i	−1.11705	+	0.683868i
$848$	6.73890	+	8.55731i	0.231415	+	0.293859i
$849$	−34.6975	−	47.7571i	−1.19082	−	1.63902i
$850$	46.5371	+	8.87547i	1.59621	+	0.304426i
$851$	21.3166	+	6.92617i	0.730722	+	0.237426i
$852$	−4.49652	+	0.441700i	−0.154048	+	0.0151324i
$853$	−2.43734	−	15.3888i	−0.0834530	−	0.526901i	−0.993631	−	0.112684i	$-0.964055\pi$
$853$	−2.43734	−	15.3888i	−0.0834530	−	0.526901i	0.910178	−	0.414218i	$-0.135945\pi$
$854$	−17.1597	+	47.9387i	−0.587192	+	1.64043i
$855$	0.902325	+	11.5982i	0.0308589	+	0.396649i
$856$	21.6734	+	36.1916i	0.740782	+	1.23700i
$857$	22.8723	−	22.8723i	0.781301	−	0.781301i	−0.198749	−	0.980050i	$-0.563688\pi$
$857$	22.8723	−	22.8723i	0.781301	−	0.781301i	0.980050	+	0.198749i	$0.0636878\pi$
$858$	−4.93737	−	4.84469i	−0.168559	−	0.165395i
$859$	−4.16692			−0.142174			−0.0710868	−	0.997470i	$-0.522647\pi$
$859$	−4.16692			−0.142174			−0.0710868	+	0.997470i	$0.522647\pi$
$860$	13.2955	−	27.3310i	0.453372	−	0.931978i
$861$	2.82604	+	8.69766i	0.0963112	+	0.296415i
$862$	−12.3262	+	5.82794i	−0.419834	+	0.198500i
$863$	5.12999	−	0.812510i	0.174627	−	0.0276582i	−0.0685086	−	0.997651i	$-0.521824\pi$
$863$	5.12999	−	0.812510i	0.174627	−	0.0276582i	0.243135	+	0.969992i	$0.421824\pi$
$864$	−18.1460	−	17.8160i	−0.617338	−	0.606113i
$865$	4.09743	+	17.1347i	0.139317	+	0.582599i
$866$	−6.48569	−	22.1720i	−0.220393	−	0.753434i
$867$	−52.5946	−	8.33017i	−1.78621	−	0.282907i
$868$	18.7708	+	21.1344i	0.637122	+	0.717349i
$869$	−14.7796	−	18.7561i	−0.501364	−	0.636258i
$870$	5.02247	−	18.4269i	0.170278	−	0.624731i
$871$	−3.73109	−	5.13541i	−0.126423	−	0.174007i
$872$	30.3432	+	19.0229i	1.02755	+	0.644197i
$873$	0.943081	−	0.480524i	0.0319185	−	0.0162633i
$874$	−29.4886	+	38.1609i	−0.997468	+	1.29081i
$875$	32.9794	+	20.3321i	1.11491	+	0.687351i
$876$	11.6915	+	4.57942i	0.395018	+	0.154724i
$877$	49.9661	+	25.4590i	1.68723	+	0.859689i	0.989703	+	0.143134i	$0.0457181\pi$
$877$	49.9661	+	25.4590i	1.68723	+	0.859689i	0.697531	+	0.716554i	$0.254282\pi$
$878$	4.78042	−	25.3121i	0.161331	−	0.854242i
$879$	36.7355			1.23906
$880$	−0.0482474	+	29.6648i	−0.00162642	+	0.999999i
$881$	−14.7796			−0.497938			−0.248969	−	0.968512i	$-0.580092\pi$
$881$	−14.7796			−0.497938			−0.248969	+	0.968512i	$0.580092\pi$
$882$	−0.848512	+	4.49283i	−0.0285709	+	0.151281i
$883$	4.42317	+	2.25372i	0.148852	+	0.0758436i	0.526830	−	0.849971i	$-0.323381\pi$
$883$	4.42317	+	2.25372i	0.148852	+	0.0758436i	−0.377978	+	0.925815i	$0.623381\pi$
$884$	−9.63721	−	3.77479i	−0.324134	−	0.126960i
$885$	−1.97533	+	24.8143i	−0.0664000	+	0.834123i
$886$	18.1976	−	23.5493i	0.611359	−	0.791153i
$887$	−30.4374	+	15.5086i	−1.02199	+	0.520729i	−0.882905	−	0.469552i	$-0.844415\pi$
$887$	−30.4374	+	15.5086i	−1.02199	+	0.520729i	−0.139083	+	0.990281i	$0.544415\pi$
$888$	24.2365	+	15.1945i	0.813324	+	0.509893i
$889$	−2.79363	−	3.84510i	−0.0936954	−	0.128961i
$890$	−6.57133	+	3.75639i	−0.220272	+	0.125915i
$891$	−33.5786	−	9.47792i	−1.12492	−	0.317522i
$892$	−8.78630	−	9.89268i	−0.294187	−	0.331231i
$893$	25.1904	+	3.98977i	0.842964	+	0.133512i
$894$	−7.08630	−	24.2252i	−0.237001	−	0.810213i
$895$	12.1527	+	7.46217i	0.406219	+	0.249433i
$896$	29.0730	−	26.3025i	0.971259	−	0.878706i
$897$	6.16353	−	0.976208i	0.205794	−	0.0325946i
$898$	−45.7137	+	21.6138i	−1.52549	+	0.721261i
$899$	3.98675	+	12.2700i	0.132966	+	0.409226i
$900$	−6.42564	+	0.619562i	−0.214188	+	0.0206521i
$901$	18.2444			0.607808
$902$	−1.07481	−	6.39343i	−0.0357872	−	0.212878i
$903$	−31.7958	+	31.7958i	−1.05810	+	1.05810i
$904$	−8.36022	−	13.9604i	−0.278057	−	0.464316i
$905$	3.23268	−	0.251500i	0.107458	−	0.00836013i
$906$	−6.74134	+	18.8332i	−0.223966	+	0.625690i
$907$	6.24990	+	39.4603i	0.207525	+	1.31026i	0.842906	+	0.538061i	$0.180843\pi$
$907$	6.24990	+	39.4603i	0.207525	+	1.31026i	−0.635381	+	0.772199i	$0.719157\pi$
$908$	11.8875	−	1.16773i	0.394501	−	0.0387524i
$909$	0.306549	+	0.0996038i	0.0101676	+	0.00330365i
$910$	−6.26568	−	5.69060i	−0.207705	−	0.188642i
$911$	20.7925	+	28.6185i	0.688888	+	0.948173i	0.999998	−	0.00220127i	$-0.000700686\pi$
$911$	20.7925	+	28.6185i	0.688888	+	0.948173i	−0.311110	+	0.950374i	$0.600701\pi$
$912$	−48.3560	+	38.0805i	−1.60123	+	1.26097i
$913$	−5.84990	−	29.4425i	−0.193603	−	0.974404i
$914$	−0.0237813	+	0.803702i	−0.000786615	+	0.0265841i
$915$	40.9666	+	17.0120i	1.35431	+	0.562399i
$916$	−8.13050	−	31.1906i	−0.268639	−	1.03057i
$917$	−0.245382	−	0.481589i	−0.00810323	−	0.0159035i
$918$	−42.2493	+	5.41610i	−1.39443	+	0.178758i
$919$	36.8272	+	26.7565i	1.21482	+	0.882616i	0.995659	−	0.0930741i	$-0.0296693\pi$
$919$	36.8272	+	26.7565i	1.21482	+	0.882616i	0.219157	+	0.975690i	$0.429669\pi$
$920$	−21.4748	−	15.9696i	−0.708004	−	0.526501i
$921$	−15.0761	−	46.3995i	−0.496775	−	1.52892i
$922$	−1.03359	+	5.47282i	−0.0340396	+	0.180238i
$923$	−0.646217	+	0.646217i	−0.0212705	+	0.0212705i
$924$	14.3987	−	41.4591i	0.473682	−	1.36390i
$925$	−25.2031	+	8.13901i	−0.828672	+	0.267609i
$926$	19.9715	+	29.2715i	0.656305	+	0.961923i
$927$	−2.82835	+	5.55094i	−0.0928951	+	0.182317i
$928$	16.9668	−	5.68545i	0.556961	−	0.186634i
$929$	30.7589	−	42.3360i	1.00917	−	1.38900i	0.0896382	−	0.995974i	$-0.471429\pi$
$929$	30.7589	−	42.3360i	1.00917	−	1.38900i	0.919528	−	0.393024i	$-0.128571\pi$
$930$	19.2041	−	15.4149i	0.629726	−	0.505476i
$931$	−38.3869	−	12.4727i	−1.25808	−	0.408775i
$932$	−18.5602	−	10.8847i	−0.607960	−	0.356542i
$933$	−38.2865	−	6.06398i	−1.25344	−	0.198526i
$934$	−39.1787	−	1.15929i	−1.28197	−	0.0379330i
$935$	38.9868	+	30.8051i	1.27500	+	1.00743i
$936$	1.40476	+	0.124991i	0.0459159	+	0.00408546i
$937$	1.52867	−	9.65166i	0.0499396	−	0.315306i	−0.950055	−	0.312082i	$-0.898974\pi$
$937$	1.52867	−	9.65166i	0.0499396	−	0.315306i	0.999995	−	0.00322429i	$-0.00102632\pi$
$938$	19.3376	−	35.3284i	0.631395	−	1.15351i
$939$	10.3689	−	31.9122i	0.338377	−	1.04142i
$940$	−1.95529	+	14.0171i	−0.0637745	+	0.457186i
$941$	−37.1792	−	27.0123i	−1.21201	−	0.880575i	−0.216595	−	0.976261i	$-0.569495\pi$
$941$	−37.1792	−	27.0123i	−1.21201	−	0.880575i	−0.995411	+	0.0956870i	$0.969495\pi$
$942$	31.8055	−	15.0379i	1.03628	−	0.489961i
$943$	5.21124	+	2.65526i	0.169701	+	0.0864672i
$944$	−20.3543	+	11.3852i	−0.662475	+	0.370556i
$945$	−33.8637	−	8.16211i	−1.10159	−	0.265513i
$946$	25.6102	−	18.9802i	0.832658	−	0.617098i
$947$	21.6981	+	21.6981i	0.705094	+	0.705094i	0.965499	−	0.260405i	$-0.0838562\pi$
$947$	21.6981	+	21.6981i	0.705094	+	0.705094i	−0.260405	+	0.965499i	$0.583856\pi$
$948$	26.8538	+	5.89915i	0.872170	+	0.191595i
$949$	2.41546	−	0.784831i	0.0784092	−	0.0254767i
$950$	1.78769	−	56.9586i	0.0580003	−	1.84798i
$951$	−28.7591	+	39.5835i	−0.932578	+	1.28358i
$952$	−4.48407	−	65.5153i	−0.145329	−	2.12336i
$953$	−33.0860	+	16.8581i	−1.07176	+	0.546089i	−0.898584	−	0.438802i	$-0.855403\pi$
$953$	−33.0860	+	16.8581i	−1.07176	+	0.546089i	−0.173176	+	0.984891i	$0.555403\pi$
$954$	−2.38599	+	0.697945i	−0.0772494	+	0.0225968i
$955$	−10.1895	+	4.20991i	−0.329724	+	0.136230i
$956$	−1.70446	+	28.7764i	−0.0551262	+	0.930695i
$957$	13.6004	−	14.7065i	0.439640	−	0.475395i
$958$	−15.7871	+	14.8797i	−0.510059	+	0.480742i
$959$	−22.6843	+	16.4811i	−0.732515	+	0.532204i
$960$	−21.6237	−	26.4384i	−0.697902	−	0.853296i
$961$	4.43920	−	13.6624i	0.143200	−	0.440724i
$962$	5.73909	−	0.735717i	0.185036	−	0.0237205i
$963$	−9.50951	+	1.50616i	−0.306440	+	0.0485353i
$964$	−24.3983	−	9.55655i	−0.785816	−	0.307796i
$965$	11.5965	+	9.92234i	0.373304	+	0.319411i
$966$	22.3148	+	32.7060i	0.717968	+	1.05230i
$967$	−42.4902	−	42.4902i	−1.36639	−	1.36639i	−0.865521	−	0.500873i	$-0.833012\pi$
$967$	−42.4902	−	42.4902i	−1.36639	−	1.36639i	−0.500873	−	0.865521i	$-0.666988\pi$
$968$	−14.4188	+	27.5699i	−0.463439	+	0.886129i
$969$			103.096i			3.31192i
$970$	−4.84848	+	1.83729i	−0.155675	+	0.0589917i
$971$	12.3221	−	4.00368i	0.395434	−	0.128484i	−0.104549	−	0.994520i	$-0.533340\pi$
$971$	12.3221	−	4.00368i	0.395434	−	0.128484i	0.499982	+	0.866036i	$0.333340\pi$
$972$	12.0944	−	5.28651i	0.387930	−	0.169565i
$973$	3.66328	+	23.1290i	0.117439	+	0.741483i
$974$	14.4729	+	11.1838i	0.463741	+	0.358353i
$975$	−5.22344	+	5.20473i	−0.167284	+	0.166685i
$976$	8.08687	+	40.7651i	0.258854	+	1.30486i
$977$	3.93507	−	24.8451i	0.125894	−	0.794864i	−0.841252	−	0.540643i	$-0.818181\pi$
$977$	3.93507	−	24.8451i	0.125894	−	0.794864i	0.967146	−	0.254221i	$-0.0818190\pi$
$978$	27.6279	+	29.3128i	0.883444	+	0.937320i
$979$	−7.93260	+	0.309967i	−0.253527	+	0.00990659i
$980$	6.52645	−	21.4258i	0.208480	−	0.684421i
$981$	−6.61274	+	4.80444i	−0.211129	+	0.153394i
$982$	−13.0757	+	23.8883i	−0.417263	+	0.762308i
$983$	25.2655	+	49.5863i	0.805843	+	1.58156i	0.813485	+	0.581585i	$0.197567\pi$
$983$	25.2655	+	49.5863i	0.805843	+	1.58156i	−0.00764235	+	0.999971i	$0.502433\pi$
$984$	5.62629	+	4.90546i	0.179360	+	0.156381i
$985$	−0.396573	+	4.98179i	−0.0126359	+	0.158733i
$986$	10.1010	−	28.2189i	0.321681	−	0.898674i
$987$	9.50594	−	18.6565i	0.302577	−	0.593842i
$988$	−2.67123	+	12.1598i	−0.0849830	+	0.386855i
$989$			28.7573i			0.914430i
$990$	−6.27714	−	2.53722i	−0.199501	−	0.0806382i
$991$			43.8588i			1.39322i	0.717450	+	0.696610i	$0.245309\pi$
$991$			43.8588i			1.39322i	−0.717450	+	0.696610i	$0.754691\pi$
$992$	22.0070	+	6.92794i	0.698722	+	0.219962i
$993$	−19.6701	+	38.6048i	−0.624212	+	1.22508i
$994$	−5.45917	−	1.95411i	−0.173154	−	0.0619807i
$995$	−19.6322	+	16.7370i	−0.622382	+	0.530599i
$996$	26.7110	+	21.9327i	0.846371	+	0.694963i
$997$	16.2470	+	31.8866i	0.514548	+	1.00986i	0.991399	+	0.130873i	$0.0417781\pi$
$997$	16.2470	+	31.8866i	0.514548	+	1.00986i	−0.476851	+	0.878984i	$0.658222\pi$
$998$	−16.4642	−	9.01196i	−0.521164	−	0.285269i
$999$	19.2643	−	13.9964i	0.609497	−	0.442825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.v.a.3.15	✓	256
4.3	odd	2	inner	220.2.v.a.3.16	yes	256
5.2	odd	4	inner	220.2.v.a.47.3	yes	256
11.4	even	5	inner	220.2.v.a.103.2	yes	256
20.7	even	4	inner	220.2.v.a.47.2	yes	256
44.15	odd	10	inner	220.2.v.a.103.3	yes	256
55.37	odd	20	inner	220.2.v.a.147.16	yes	256
220.147	even	20	inner	220.2.v.a.147.15	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.v.a.3.15	✓	256	1.1	even	1	trivial
220.2.v.a.3.16	yes	256	4.3	odd	2	inner
220.2.v.a.47.2	yes	256	20.7	even	4	inner
220.2.v.a.47.3	yes	256	5.2	odd	4	inner
220.2.v.a.103.2	yes	256	11.4	even	5	inner
220.2.v.a.103.3	yes	256	44.15	odd	10	inner
220.2.v.a.147.15	yes	256	220.147	even	20	inner
220.2.v.a.147.16	yes	256	55.37	odd	20	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.v (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.262448 + 1.38965i) q^{2} +(-1.70123 - 0.866818i) q^{3} +(-1.86224 - 0.729420i) q^{4} +(-1.70162 + 1.45068i) q^{5} +(1.65105 - 2.13661i) q^{6} +(3.08760 - 1.57321i) q^{7} +(1.50238 - 2.39643i) q^{8} +(0.379441 + 0.522256i) q^{9} +(-1.56935 - 2.74538i) q^{10} +(-0.129499 - 3.31410i) q^{11} +(2.53582 + 2.85513i) q^{12} +(0.762891 + 0.120830i) q^{13} +(1.37588 + 4.70357i) q^{14} +(4.15232 - 0.992945i) q^{15} +(2.93589 + 2.71671i) q^{16} +(6.61747 - 1.04810i) q^{17} +(-0.825336 + 0.390225i) q^{18} +(-2.49041 - 7.66469i) q^{19} +(4.22699 - 1.46033i) q^{20} -6.61640 q^{21} +(4.63941 + 0.689820i) q^{22} +(-2.99206 + 2.99206i) q^{23} +(-4.63315 + 2.77457i) q^{24} +(0.791033 - 4.93703i) q^{25} +(-0.368130 + 1.02844i) q^{26} +(0.703241 + 4.44009i) q^{27} +(-6.89740 + 0.677543i) q^{28} +(-3.00842 - 0.977496i) q^{29} +(0.290076 + 6.03086i) q^{30} +(-2.39730 - 3.29961i) q^{31} +(-4.54579 + 3.36686i) q^{32} +(-2.65241 + 5.75028i) q^{33} +(-0.280245 + 9.47103i) q^{34} +(-2.97170 + 7.15615i) q^{35} +(-0.325668 - 1.24934i) q^{36} +(-2.40476 - 4.71961i) q^{37} +(11.3048 - 1.44921i) q^{38} +(-1.19311 - 0.866847i) q^{39} +(0.919977 + 6.25729i) q^{40} +(-0.427127 - 1.31456i) q^{41} +(1.73646 - 9.19446i) q^{42} +(4.80560 - 4.80560i) q^{43} +(-2.17621 + 6.26611i) q^{44} +(-1.40329 - 0.338233i) q^{45} +(-3.37266 - 4.94318i) q^{46} +(-1.43672 + 2.81973i) q^{47} +(-2.63972 - 7.16663i) q^{48} +(2.94379 - 4.05179i) q^{49} +(6.65313 + 2.39497i) q^{50} +(-12.1663 - 3.95308i) q^{51} +(-1.33255 - 0.781483i) q^{52} +(2.68953 + 0.425980i) q^{53} +(-6.35472 - 0.188034i) q^{54} +(5.02806 + 5.45148i) q^{55} +(0.868661 - 9.76277i) q^{56} +(-2.40714 + 15.1981i) q^{57} +(2.14793 - 3.92411i) q^{58} +(-1.80173 + 5.54515i) q^{59} +(-8.45690 - 1.17968i) q^{60} +(8.40557 + 6.10701i) q^{61} +(5.21446 - 2.46543i) q^{62} +(1.99318 + 1.01558i) q^{63} +(-3.48572 - 7.20068i) q^{64} +(-1.47344 + 0.901107i) q^{65} +(-7.29474 - 5.19507i) q^{66} +(-5.81112 - 5.81112i) q^{67} +(-13.0878 - 2.87509i) q^{68} +(7.68375 - 2.49660i) q^{69} +(-9.16461 - 6.00773i) q^{70} +(-0.695455 + 0.957212i) q^{71} +(1.82161 - 0.124677i) q^{72} +(2.92976 - 1.49279i) q^{73} +(7.18971 - 2.10312i) q^{74} +(-5.62523 + 7.71332i) q^{75} +(-0.953035 + 16.0901i) q^{76} +(-5.61361 - 10.0289i) q^{77} +(1.51774 - 1.43050i) q^{78} +(5.82487 - 4.23201i) q^{79} +(-8.93687 - 0.363767i) q^{80} +(3.25083 - 10.0050i) q^{81} +(1.93888 - 0.248552i) q^{82} +(8.93934 - 1.41585i) q^{83} +(12.3213 + 4.82613i) q^{84} +(-9.73997 + 11.3833i) q^{85} +(5.41687 + 7.93931i) q^{86} +(4.27070 + 4.27070i) q^{87} +(-8.13654 - 4.66869i) q^{88} -2.39359i q^{89} +(0.838317 - 1.86132i) q^{90} +(2.54560 - 0.827114i) q^{91} +(7.75442 - 3.38948i) q^{92} +(1.21820 + 7.69140i) q^{93} +(-3.54137 - 2.73657i) q^{94} +(15.3568 + 9.42961i) q^{95} +(10.6519 - 1.78742i) q^{96} +(0.256492 - 1.61943i) q^{97} +(4.85796 + 5.15422i) q^{98} +(1.68167 - 1.32514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 6 q^{8} - 32 q^{10} - 20 q^{12} - 12 q^{13} - 4 q^{16} - 12 q^{17} - 26 q^{18} - 52 q^{20} - 64 q^{21} - 10 q^{22} - 12 q^{25} - 36 q^{26} + 10 q^{28} - 10 q^{30}+ \cdots + 236 q^{98}+O(q^{100}) \) 256 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 6 * q^8 - 32 * q^10 - 20 * q^12 - 12 * q^13 - 4 * q^16 - 12 * q^17 - 26 * q^18 - 52 * q^20 - 64 * q^21 - 10 * q^22 - 12 * q^25 - 36 * q^26 + 10 * q^28 - 10 * q^30 + 4 * q^32 - 20 * q^33 + 4 * q^36 - 12 * q^37 + 30 * q^38 - 42 * q^40 - 48 * q^41 - 30 * q^42 - 72 * q^45 + 60 * q^46 - 18 * q^48 + 14 * q^50 - 46 * q^52 - 36 * q^53 + 8 * q^56 + 12 * q^57 - 18 * q^58 + 70 * q^60 - 24 * q^61 - 124 * q^62 - 32 * q^65 - 20 * q^66 - 38 * q^68 - 26 * q^70 - 116 * q^72 + 12 * q^73 - 48 * q^76 - 20 * q^77 + 100 * q^78 - 26 * q^80 - 24 * q^81 - 2 * q^82 + 36 * q^85 + 28 * q^86 + 126 * q^88 + 8 * q^90 - 56 * q^92 + 36 * q^93 + 104 * q^96 - 92 * q^97 + 236 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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