LMFDB - Embedded newform 220.2.r.a.171.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(51,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("220.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			171.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	220.171
Dual form			220.2.r.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.478148 - 1.33093i) q^{2} +(-0.295511 + 0.406737i) q^{3} +(-1.54275 + 1.27276i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.682636 + 0.198825i) q^{6} +(2.59618 - 1.88624i) q^{7} +(2.43162 + 1.44472i) q^{8} +(0.848943 + 2.61278i) q^{9} +(1.41355 - 0.0434654i) q^{10} +(0.569171 - 3.26742i) q^{11} +(-0.0617787 - 1.00361i) q^{12} +(3.70071 - 1.20243i) q^{13} +(-3.75181 - 2.55344i) q^{14} +(-0.295511 - 0.406737i) q^{15} +(0.760154 - 3.92711i) q^{16} +(2.89908 + 0.941970i) q^{17} +(3.07151 - 2.37918i) q^{18} +(0.0572103 + 0.0415657i) q^{19} +(-0.733733 - 1.86055i) q^{20} +1.61337i q^{21} +(-4.62086 + 0.804784i) q^{22} +5.67459i q^{23} +(-1.30619 + 0.562096i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-3.36984 - 4.35045i) q^{26} +(-2.74803 - 0.892888i) q^{27} +(-1.60453 + 6.21431i) q^{28} +(-2.43162 - 3.34684i) q^{29} +(-0.400040 + 0.587785i) q^{30} +(-0.894983 + 0.290798i) q^{31} +(-5.59017 + 0.866025i) q^{32} +(1.16078 + 1.19706i) q^{33} +(-0.132495 - 4.30888i) q^{34} +(0.991653 + 3.05199i) q^{35} +(-4.63515 - 2.95036i) q^{36} +(7.15701 - 5.19987i) q^{37} +(0.0279661 - 0.0960175i) q^{38} +(-0.604528 + 1.86055i) q^{39} +(-2.12543 + 1.86616i) q^{40} +(-4.98410 + 6.86002i) q^{41} +(2.14728 - 0.771427i) q^{42} +0.496387 q^{43} +(3.28056 + 5.76523i) q^{44} -2.74724 q^{45} +(7.55248 - 2.71329i) q^{46} +(-2.38052 + 3.27651i) q^{47} +(1.37266 + 1.46969i) q^{48} +(1.01915 - 3.13663i) q^{49} +(-0.395472 + 1.35779i) q^{50} +(-1.23985 + 0.900801i) q^{51} +(-4.17886 + 6.56518i) q^{52} +(2.43852 + 7.50500i) q^{53} +(0.125591 + 4.08437i) q^{54} +(2.93162 + 1.55100i) q^{55} +(9.03802 - 0.835843i) q^{56} +(-0.0338126 + 0.0109864i) q^{57} +(-3.29173 + 4.83660i) q^{58} +(-8.38521 - 11.5413i) q^{59} +(0.973579 + 0.251377i) q^{60} +(0.696830 + 0.226414i) q^{61} +(0.814966 + 1.05212i) q^{62} +(7.13233 + 5.18194i) q^{63} +(3.82555 + 7.02604i) q^{64} +3.89116i q^{65} +(1.03818 - 2.11729i) q^{66} +0.155688i q^{67} +(-5.67147 + 2.23662i) q^{68} +(-2.30806 - 1.67691i) q^{69} +(3.58783 - 2.77912i) q^{70} +(-14.2895 - 4.64294i) q^{71} +(-1.71044 + 7.57977i) q^{72} +(-7.84500 - 10.7977i) q^{73} +(-10.3428 - 7.03917i) q^{74} +(0.478148 - 0.155360i) q^{75} +(-0.141165 + 0.00868960i) q^{76} +(-4.68546 - 9.55641i) q^{77} +(2.76531 - 0.0850311i) q^{78} +(3.20955 + 9.87796i) q^{79} +(3.50000 + 1.93649i) q^{80} +(-5.49244 + 3.99049i) q^{81} +(11.5133 + 3.35338i) q^{82} +(1.52731 - 4.70059i) q^{83} +(-2.05343 - 2.48902i) q^{84} +(-1.79173 + 2.46611i) q^{85} +(-0.237346 - 0.660656i) q^{86} +2.07985 q^{87} +(6.10453 - 7.12283i) q^{88} +11.9625 q^{89} +(1.31359 + 3.65638i) q^{90} +(7.33964 - 10.1021i) q^{91} +(-7.22240 - 8.75447i) q^{92} +(0.146200 - 0.449957i) q^{93} +(5.49904 + 1.60165i) q^{94} +(-0.0572103 + 0.0415657i) q^{95} +(1.29972 - 2.52965i) q^{96} +(-2.04594 - 6.29675i) q^{97} +(-4.66194 + 0.143351i) q^{98} +(9.02024 - 1.28674i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 5 q^{2} - 5 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 3 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} - 10 q^{12} + 10 q^{13} - 15 q^{14} - 5 q^{15} + 7 q^{16} - 5 q^{17} + 10 q^{18} + 11 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) $ 8 * q + 5 * q^2 - 5 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 3 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 - 10 * q^12 + 10 * q^13 - 15 * q^14 - 5 * q^15 + 7 * q^16 - 5 * q^17 + 10 * q^18 + 11 * q^19 + q^20 - 16 * q^22 - 18 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 - 11 * q^28 - 5 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^33 - 14 * q^34 - 8 * q^35 + 9 * q^36 + 20 * q^37 + 15 * q^38 - 3 * q^39 + 5 * q^40 + 10 * q^41 + 4 * q^42 + 34 * q^43 + 8 * q^44 - 8 * q^45 + 25 * q^46 - 25 * q^48 - 23 * q^49 - 5 * q^50 - 9 * q^51 - 5 * q^52 - 7 * q^53 + 26 * q^54 + 9 * q^55 + 15 * q^56 + 5 * q^57 - 12 * q^58 + 5 * q^59 - 10 * q^61 - 39 * q^62 + 23 * q^63 + 11 * q^64 - 2 * q^66 - 30 * q^68 + 15 * q^69 - 5 * q^70 - 90 * q^71 + 30 * q^72 + 5 * q^73 - 5 * q^74 - 5 * q^75 + 18 * q^76 - 14 * q^77 + 21 * q^79 + 28 * q^80 - 10 * q^81 + 38 * q^82 - 19 * q^83 - 10 * q^84 + 35 * q^86 + 18 * q^87 + 47 * q^88 + 20 * q^89 + 5 * q^90 + 10 * q^91 + 11 * q^93 + 15 * q^94 - 11 * q^95 - 39 * q^96 - 44 * q^97 - 50 * q^98 + 6 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$

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 $

$2$	−0.478148	−	1.33093i	−0.338101	−	0.941110i
$2$	−0.478148	−	1.33093i	−0.338101	−	0.941110i
$3$	−0.295511	+	0.406737i	−0.170614	+	0.234830i	−0.885758	−	0.464147i	$-0.846361\pi$
$3$	−0.295511	+	0.406737i	−0.170614	+	0.234830i	0.715144	+	0.698977i	$0.246361\pi$
$4$	−1.54275	+	1.27276i	−0.771375	+	0.636381i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$5$	−0.309017	+	0.951057i	−0.138197	+	0.425325i
$6$	0.682636	+	0.198825i	0.278685	+	0.0811699i
$7$	2.59618	−	1.88624i	0.981264	−	0.712930i	0.0232736	−	0.999729i	$-0.492591\pi$
$7$	2.59618	−	1.88624i	0.981264	−	0.712930i	0.957991	+	0.286799i	$0.0925911\pi$
$8$	2.43162	+	1.44472i	0.859707	+	0.510787i
$9$	0.848943	+	2.61278i	0.282981	+	0.870926i
$10$	1.41355	−	0.0434654i	0.447002	−	0.0137450i
$11$	0.569171	−	3.26742i	0.171611	−	0.985165i
$11$	0.569171	−	3.26742i	0.171611	−	0.985165i
$12$	−0.0617787	−	1.00361i	−0.0178340	−	0.289717i
$13$	3.70071	−	1.20243i	1.02639	−	0.333495i	0.253029	−	0.967459i	$-0.418573\pi$
$13$	3.70071	−	1.20243i	1.02639	−	0.333495i	0.773363	+	0.633964i	$0.218573\pi$
$14$	−3.75181	−	2.55344i	−1.00271	−	0.682435i
$15$	−0.295511	−	0.406737i	−0.0763007	−	0.105019i
$16$	0.760154	−	3.92711i	0.190038	−	0.981777i
$17$	2.89908	+	0.941970i	0.703131	+	0.228461i	0.638694	−	0.769461i	$-0.279475\pi$
$17$	2.89908	+	0.941970i	0.703131	+	0.228461i	0.0644370	+	0.997922i	$0.479475\pi$
$18$	3.07151	−	2.37918i	0.723961	−	0.560778i
$19$	0.0572103	+	0.0415657i	0.0131249	+	0.00953583i	0.594328	−	0.804222i	$-0.297418\pi$
$19$	0.0572103	+	0.0415657i	0.0131249	+	0.00953583i	−0.581203	+	0.813758i	$0.697418\pi$
$20$	−0.733733	−	1.86055i	−0.164068	−	0.416031i
$21$			1.61337i			0.352065i
$22$	−4.62086	+	0.804784i	−0.985170	+	0.171580i
$23$			5.67459i			1.18323i	0.806220	+	0.591616i	$0.201510\pi$
$23$			5.67459i			1.18323i	−0.806220	+	0.591616i	$0.798490\pi$
$24$	−1.30619	+	0.562096i	−0.266626	+	0.114737i
$25$	−0.809017	−	0.587785i	−0.161803	−	0.117557i
$26$	−3.36984	−	4.35045i	−0.660880	−	0.853193i
$27$	−2.74803	−	0.892888i	−0.528858	−	0.171836i
$28$	−1.60453	+	6.21431i	−0.303227	+	1.17439i
$29$	−2.43162	−	3.34684i	−0.451540	−	0.621492i	0.521187	−	0.853442i	$-0.325489\pi$
$29$	−2.43162	−	3.34684i	−0.451540	−	0.621492i	−0.972728	+	0.231950i	$0.925489\pi$
$30$	−0.400040	+	0.587785i	−0.0730370	+	0.107314i
$31$	−0.894983	+	0.290798i	−0.160744	+	0.0522288i	−0.388283	−	0.921540i	$-0.626932\pi$
$31$	−0.894983	+	0.290798i	−0.160744	+	0.0522288i	0.227540	+	0.973769i	$0.426932\pi$
$32$	−5.59017	+	0.866025i	−0.988212	+	0.153093i
$33$	1.16078	+	1.19706i	0.202067	+	0.208382i
$34$	−0.132495	−	4.30888i	−0.0227226	−	0.738967i
$35$	0.991653	+	3.05199i	0.167620	+	0.515881i
$36$	−4.63515	−	2.95036i	−0.772525	−	0.491727i
$37$	7.15701	−	5.19987i	1.17660	−	0.854853i	0.184820	−	0.982772i	$-0.440830\pi$
$37$	7.15701	−	5.19987i	1.17660	−	0.854853i	0.991785	+	0.127919i	$0.0408298\pi$
$38$	0.0279661	−	0.0960175i	0.00453670	−	0.0155761i
$39$	−0.604528	+	1.86055i	−0.0968020	+	0.297926i
$40$	−2.12543	+	1.86616i	−0.336059	+	0.295066i
$41$	−4.98410	+	6.86002i	−0.778385	+	1.07136i	0.217073	+	0.976155i	$0.430349\pi$
$41$	−4.98410	+	6.86002i	−0.778385	+	1.07136i	−0.995458	+	0.0951998i	$0.969651\pi$
$42$	2.14728	−	0.771427i	0.331332	−	0.119034i
$43$	0.496387			0.0756983			0.0378491	−	0.999283i	$-0.487949\pi$
$43$	0.496387			0.0756983			0.0378491	+	0.999283i	$0.487949\pi$
$44$	3.28056	+	5.76523i	0.494563	+	0.869142i
$45$	−2.74724			−0.409534
$46$	7.55248	−	2.71329i	1.11355	−	0.400053i
$47$	−2.38052	+	3.27651i	−0.347235	+	0.477928i	−0.946537	−	0.322595i	$-0.895445\pi$
$47$	−2.38052	+	3.27651i	−0.347235	+	0.477928i	0.599302	+	0.800523i	$0.295445\pi$
$48$	1.37266	+	1.46969i	0.198127	+	0.212131i
$49$	1.01915	−	3.13663i	0.145593	−	0.448090i
$50$	−0.395472	+	1.35779i	−0.0559281	+	0.192021i
$51$	−1.23985	+	0.900801i	−0.173613	+	0.126137i
$52$	−4.17886	+	6.56518i	−0.579503	+	0.910426i
$53$	2.43852	+	7.50500i	0.334957	+	1.03089i	0.966743	+	0.255749i	$0.0823220\pi$
$53$	2.43852	+	7.50500i	0.334957	+	1.03089i	−0.631786	+	0.775143i	$0.717678\pi$
$54$	0.125591	+	4.08437i	0.0170908	+	0.555812i
$55$	2.93162	+	1.55100i	0.395299	+	0.209137i
$56$	9.03802	−	0.835843i	1.20776	−	0.111694i
$57$	−0.0338126	+	0.0109864i	−0.00447859	+	0.00145518i
$58$	−3.29173	+	4.83660i	−0.432226	+	0.635076i
$59$	−8.38521	−	11.5413i	−1.09166	−	1.50254i	−0.845996	−	0.533189i	$-0.820993\pi$
$59$	−8.38521	−	11.5413i	−1.09166	−	1.50254i	−0.245666	−	0.969355i	$-0.579007\pi$
$60$	0.973579	+	0.251377i	0.125689	+	0.0324526i
$61$	0.696830	+	0.226414i	0.0892199	+	0.0289893i	0.353287	−	0.935515i	$-0.385064\pi$
$61$	0.696830	+	0.226414i	0.0892199	+	0.0289893i	−0.264067	+	0.964504i	$0.585064\pi$
$62$	0.814966	+	1.05212i	0.103501	+	0.133619i
$63$	7.13233	+	5.18194i	0.898589	+	0.652863i
$64$	3.82555	+	7.02604i	0.478193	+	0.878255i
$65$			3.89116i			0.482639i
$66$	1.03818	−	2.11729i	0.127791	−	0.260621i
$67$			0.155688i			0.0190203i	0.999955	+	0.00951016i	$0.00302722\pi$
$67$			0.155688i			0.0190203i	−0.999955	+	0.00951016i	$0.996973\pi$
$68$	−5.67147	+	2.23662i	−0.687766	+	0.271230i
$69$	−2.30806	−	1.67691i	−0.277858	−	0.201876i
$70$	3.58783	−	2.77912i	0.428828	−	0.332169i
$71$	−14.2895	−	4.64294i	−1.69585	−	0.551016i	−0.707972	−	0.706240i	$-0.750390\pi$
$71$	−14.2895	−	4.64294i	−1.69585	−	0.551016i	−0.987879	+	0.155224i	$0.950390\pi$
$72$	−1.71044	+	7.57977i	−0.201577	+	0.893285i
$73$	−7.84500	−	10.7977i	−0.918188	−	1.26378i	−0.964292	−	0.264840i	$-0.914681\pi$
$73$	−7.84500	−	10.7977i	−0.918188	−	1.26378i	0.0461045	−	0.998937i	$-0.485319\pi$
$74$	−10.3428	−	7.03917i	−1.20232	−	0.818287i
$75$	0.478148	−	0.155360i	0.0552117	−	0.0179394i
$76$	−0.141165	+	0.00868960i	−0.0161927	+	0.000996766i
$77$	−4.68546	−	9.55641i	−0.533958	−	1.08905i
$78$	2.76531	−	0.0850311i	0.313110	−	0.00962788i
$79$	3.20955	+	9.87796i	0.361102	+	1.11136i	0.952386	+	0.304894i	$0.0986212\pi$
$79$	3.20955	+	9.87796i	0.361102	+	1.11136i	−0.591284	+	0.806463i	$0.701379\pi$
$80$	3.50000	+	1.93649i	0.391312	+	0.216506i
$81$	−5.49244	+	3.99049i	−0.610271	+	0.443388i
$82$	11.5133	+	3.35338i	1.27144	+	0.370319i
$83$	1.52731	−	4.70059i	0.167644	−	0.515956i	−0.831577	−	0.555409i	$-0.812562\pi$
$83$	1.52731	−	4.70059i	0.167644	−	0.515956i	0.999221	+	0.0394531i	$0.0125616\pi$
$84$	−2.05343	−	2.48902i	−0.224048	−	0.271574i
$85$	−1.79173	+	2.46611i	−0.194341	+	0.267487i
$86$	−0.237346	−	0.660656i	−0.0255937	−	0.0712404i
$87$	2.07985			0.222984
$88$	6.10453	−	7.12283i	0.650745	−	0.759296i
$89$	11.9625			1.26803			0.634014	−	0.773322i	$-0.281406\pi$
$89$	11.9625			1.26803			0.634014	+	0.773322i	$0.281406\pi$
$90$	1.31359	+	3.65638i	0.138464	+	0.385417i
$91$	7.33964	−	10.1021i	0.769403	−	1.05899i
$92$	−7.22240	−	8.75447i	−0.752987	−	0.912716i
$93$	0.146200	−	0.449957i	0.0151602	−	0.0466583i
$94$	5.49904	+	1.60165i	0.567183	+	0.165198i
$95$	−0.0572103	+	0.0415657i	−0.00586966	+	0.00426455i
$96$	1.29972	−	2.52965i	0.132652	−	0.258181i
$97$	−2.04594	−	6.29675i	−0.207734	−	0.639338i	−0.999590	−	0.0286309i	$-0.990885\pi$
$97$	−2.04594	−	6.29675i	−0.207734	−	0.639338i	0.791857	−	0.610707i	$-0.209115\pi$
$98$	−4.66194	+	0.143351i	−0.470927	+	0.0144806i
$99$	9.02024	−	1.28674i	0.906569	−	0.129322i
$100$	1.99622	−	0.122881i	0.199622	−	0.0122881i
$101$	−18.7450	+	6.09061i	−1.86519	+	0.606039i	−0.872010	+	0.489488i	$0.837184\pi$
$101$	−18.7450	+	6.09061i	−1.86519	+	0.606039i	−0.993185	+	0.116551i	$0.962816\pi$
$102$	1.79173	+	1.21943i	0.177408	+	0.120742i
$103$	5.46885	+	7.52722i	0.538861	+	0.741679i	0.988448	−	0.151557i	$-0.0484289\pi$
$103$	5.46885	+	7.52722i	0.538861	+	0.741679i	−0.449587	+	0.893237i	$0.648429\pi$
$104$	10.7359	+	2.42264i	1.05274	+	0.237560i
$105$	−1.53440	−	0.498558i	−0.149742	−	0.0486543i
$106$	8.82266	−	6.83400i	0.856932	−	0.663777i
$107$	−3.16302	−	2.29807i	−0.305780	−	0.222162i	0.424303	−	0.905520i	$-0.360519\pi$
$107$	−3.16302	−	2.29807i	−0.305780	−	0.222162i	−0.730084	+	0.683358i	$0.760519\pi$
$108$	5.37595	−	2.12008i	0.517301	−	0.204005i
$109$		−	7.32285i		−	0.701402i	−0.936488	−	0.350701i	$-0.885943\pi$
$109$		−	7.32285i		−	0.701402i	0.936488	−	0.350701i	$-0.114057\pi$
$110$	0.662529	−	4.64339i	0.0631696	−	0.442730i
$111$			4.44764i			0.422151i
$112$	−5.43395	−	11.6293i	−0.513460	−	1.09887i
$113$	−10.6436	−	7.73303i	−1.00127	−	0.727462i	−0.0389066	−	0.999243i	$-0.512387\pi$
$113$	−10.6436	−	7.73303i	−1.00127	−	0.727462i	−0.962359	+	0.271781i	$0.912387\pi$
$114$	0.0307895	+	0.0397491i	0.00288370	+	0.00372285i
$115$	−5.39685	−	1.75354i	−0.503259	−	0.163519i
$116$	8.01111	+	2.06846i	0.743813	+	0.192052i
$117$	6.28339	+	8.64834i	0.580899	+	0.799539i
$118$	−11.3512	+	16.6786i	−1.04497	+	1.53539i
$119$	9.30333	−	3.02283i	0.852835	−	0.277103i
$120$	−0.130949	−	1.41596i	−0.0119540	−	0.129259i
$121$	−10.3521	−	3.71944i	−0.941099	−	0.338131i
$122$	−0.0318466	−	1.03569i	−0.00288326	−	0.0937670i
$123$	−1.31736	−	4.05443i	−0.118783	−	0.365576i
$124$	1.01062	−	1.58773i	0.0907563	−	0.142582i
$125$	0.809017	−	0.587785i	0.0723607	−	0.0525731i
$126$	3.48649	−	11.9704i	0.310602	−	1.06640i
$127$	3.52185	−	10.8391i	0.312514	−	0.961819i	−0.664252	−	0.747509i	$-0.731250\pi$
$127$	3.52185	−	10.8391i	0.312514	−	0.961819i	0.976766	−	0.214310i	$-0.0687503\pi$
$128$	7.52199	−	8.45102i	0.664856	−	0.746971i
$129$	−0.146688	+	0.201899i	−0.0129152	+	0.0177762i
$130$	5.17886	−	1.86055i	0.454216	−	0.163181i
$131$	2.64098			0.230743			0.115372	−	0.993322i	$-0.463194\pi$
$131$	2.64098			0.230743			0.115372	+	0.993322i	$0.463194\pi$
$132$	−3.31438	−	0.369367i	−0.288479	−	0.0321493i
$133$	0.226931			0.0196774
$134$	0.207210	−	0.0744419i	0.0179002	−	0.00643080i
$135$	1.69837	−	2.33761i	0.146173	−	0.201190i
$136$	5.68858	+	6.47889i	0.487792	+	0.555560i
$137$	4.87723	−	15.0106i	0.416690	−	1.28244i	−0.494040	−	0.869439i	$-0.664481\pi$
$137$	4.87723	−	15.0106i	0.416690	−	1.28244i	0.910730	−	0.413001i	$-0.135519\pi$
$138$	−1.12825	+	3.87368i	−0.0960430	+	0.329749i
$139$	−10.4351	+	7.58152i	−0.885091	+	0.643056i	−0.934593	−	0.355718i	$-0.884236\pi$
$139$	−10.4351	+	7.58152i	−0.885091	+	0.643056i	0.0495025	+	0.998774i	$0.484236\pi$
$140$	−5.41434	−	3.44633i	−0.457595	−	0.291268i
$141$	−0.629204	−	1.93649i	−0.0529886	−	0.163082i
$142$	0.653062	+	21.2383i	0.0548037	+	1.78228i
$143$	−1.82252	−	12.7762i	−0.152407	−	1.06840i
$144$	10.9060	−	1.34778i	0.908832	−	0.112315i
$145$	3.93444	−	1.27838i	0.326738	−	0.106164i
$146$	−10.6199	+	15.6040i	−0.878912	+	1.29140i
$147$	0.974611	+	1.34144i	0.0803845	+	0.110640i
$148$	−4.42327	+	17.1313i	−0.363591	+	1.40818i
$149$	12.2540	+	3.98156i	1.00388	+	0.326182i	0.764417	−	0.644722i	$-0.223027\pi$
$149$	12.2540	+	3.98156i	1.00388	+	0.326182i	0.239468	+	0.970904i	$0.423027\pi$
$150$	−0.435398	−	0.562096i	−0.0355501	−	0.0458950i
$151$	9.72065	+	7.06247i	0.791055	+	0.574735i	0.908276	−	0.418370i	$-0.137399\pi$
$151$	9.72065	+	7.06247i	0.791055	+	0.574735i	−0.117221	+	0.993106i	$0.537399\pi$
$152$	0.0790627	+	0.183725i	0.00641283	+	0.0149021i
$153$			8.37435i			0.677026i
$154$	−10.4786	+	10.8054i	−0.844387	+	0.870723i
$155$		−	0.941041i		−	0.0755862i
$156$	−1.43540	−	3.63978i	−0.114924	−	0.291416i
$157$	4.93977	+	3.58895i	0.394236	+	0.286429i	0.767189	−	0.641421i	$-0.221655\pi$
$157$	4.93977	+	3.58895i	0.394236	+	0.286429i	−0.372953	+	0.927850i	$0.621655\pi$
$158$	11.6122	−	8.99481i	0.923820	−	0.715588i
$159$	−3.77317	−	1.22598i	−0.299232	−	0.0972263i
$160$	0.903818	−	5.58418i	0.0714531	−	0.441469i
$161$	10.7036	+	14.7323i	0.843563	+	1.16106i
$162$	7.93727	+	5.40201i	0.623611	+	0.424422i
$163$	−22.5515	+	7.32742i	−1.76637	+	0.573928i	−0.997828	−	0.0658721i	$-0.979017\pi$
$163$	−22.5515	+	7.32742i	−1.76637	+	0.573928i	−0.768541	+	0.639800i	$0.779017\pi$
$164$	−1.04196	−	16.9269i	−0.0813634	−	1.32177i
$165$	−1.49718	+	0.734058i	−0.116555	+	0.0571463i
$166$	−6.98643	+	0.214827i	−0.542252	+	0.0166738i
$167$	4.45689	+	13.7169i	0.344884	+	1.06144i	0.961646	+	0.274294i	$0.0884442\pi$
$167$	4.45689	+	13.7169i	0.344884	+	1.06144i	−0.616762	+	0.787150i	$0.711556\pi$
$168$	−2.33087	+	3.92309i	−0.179830	+	0.302673i
$169$	1.73219	−	1.25851i	0.133245	−	0.0968083i
$170$	4.13893	+	1.20551i	0.317442	+	0.0924582i
$171$	−0.0600337	+	0.184765i	−0.00459090	+	0.0141293i
$172$	−0.765800	+	0.631782i	−0.0583917	+	0.0481729i
$173$	−5.53034	+	7.61185i	−0.420464	+	0.578719i	−0.965731	−	0.259543i	$-0.916428\pi$
$173$	−5.53034	+	7.61185i	−0.420464	+	0.578719i	0.545268	+	0.838262i	$0.316428\pi$
$174$	−0.994477	−	2.76814i	−0.0753911	−	0.209852i
$175$	−3.20906			−0.242582
$176$	−12.3989	−	4.71894i	−0.934599	−	0.355703i
$177$	7.17218			0.539094
$178$	−5.71986	−	15.9213i	−0.428722	−	1.19335i
$179$	2.33964	−	3.22024i	0.174873	−	0.240692i	−0.712579	−	0.701592i	$-0.752473\pi$
$179$	2.33964	−	3.22024i	0.174873	−	0.240692i	0.887452	+	0.460900i	$0.152473\pi$
$180$	4.23830	−	3.49658i	0.315904	−	0.260620i
$181$	−0.595756	+	1.83355i	−0.0442822	+	0.136287i	−0.970753	−	0.240079i	$-0.922827\pi$
$181$	−0.595756	+	1.83355i	−0.0442822	+	0.136287i	0.926471	+	0.376366i	$0.122827\pi$
$182$	−16.9547	−	4.93823i	−1.25677	−	0.366046i
$183$	−0.298012	+	0.216518i	−0.0220297	+	0.0160055i
$184$	−8.19821	+	13.7984i	−0.604380	+	1.01723i
$185$	2.73373	+	8.41356i	0.200988	+	0.618578i
$186$	−0.668766	+	0.0205640i	−0.0490363	+	0.00150783i
$187$	4.72789	−	8.93639i	0.345737	−	0.653494i
$188$	−0.497665	−	8.08467i	−0.0362959	−	0.589635i
$189$	−8.81858	+	2.86533i	−0.641457	+	0.208422i
$190$	0.0826761	+	0.0562684i	0.00599795	+	0.00408214i
$191$	10.5199	+	14.4795i	0.761196	+	1.04770i	0.997114	+	0.0759237i	$0.0241905\pi$
$191$	10.5199	+	14.4795i	0.761196	+	1.04770i	−0.235917	+	0.971773i	$0.575809\pi$
$192$	−3.98824	−	0.520285i	−0.287826	−	0.0375483i
$193$	6.55977	+	2.13140i	0.472182	+	0.153421i	0.535435	−	0.844576i	$-0.320148\pi$
$193$	6.55977	+	2.13140i	0.472182	+	0.153421i	−0.0632531	+	0.997998i	$0.520148\pi$
$194$	−7.40227	+	5.73378i	−0.531452	+	0.411661i
$195$	−1.58268	−	1.14988i	−0.113338	−	0.0823447i
$196$	2.41988	+	6.13617i	0.172849	+	0.438298i
$197$			5.15052i			0.366959i	0.983024	+	0.183480i	$0.0587361\pi$
$197$			5.15052i			0.366959i	−0.983024	+	0.183480i	$0.941264\pi$
$198$	−6.02557	−	11.3901i	−0.428218	−	0.809457i
$199$			18.1133i			1.28402i	0.766697	+	0.642009i	$0.221899\pi$
$199$			18.1133i			1.28402i	−0.766697	+	0.642009i	$0.778101\pi$
$200$	−1.11803	−	2.59808i	−0.0790569	−	0.183712i
$201$	−0.0633240	−	0.0460076i	−0.00446653	−	0.00324513i
$202$	17.0690	+	22.0360i	1.20097	+	1.55045i
$203$	−12.6259	−	4.10239i	−0.886161	−	0.287931i
$204$	0.766267	−	2.96774i	0.0536494	−	0.207783i
$205$	−4.98410	−	6.86002i	−0.348104	−	0.479125i
$206$	7.40329	−	10.8778i	0.515812	−	0.757890i
$207$	−14.8264	+	4.81740i	−1.03051	+	0.334833i
$208$	−1.90898	−	15.4471i	−0.132364	−	1.07106i
$209$	0.168375	−	0.163272i	0.0116468	−	0.0112938i
$210$	0.0701256	+	2.28057i	0.00483913	+	0.157374i
$211$	1.09365	+	3.36590i	0.0752897	+	0.231718i	0.981618	−	0.190856i	$-0.0611265\pi$
$211$	1.09365	+	3.36590i	0.0752897	+	0.231718i	−0.906328	+	0.422574i	$0.861126\pi$
$212$	−13.3141	−	8.47468i	−0.914417	−	0.582043i
$213$	6.11116	−	4.44002i	0.418730	−	0.304225i
$214$	−1.54618	+	5.30857i	−0.105694	+	0.362886i
$215$	−0.153392	+	0.472092i	−0.0104612	+	0.0321964i
$216$	−5.39218	−	6.14131i	−0.366891	−	0.417863i
$217$	−1.77503	+	2.44311i	−0.120497	+	0.165849i
$218$	−9.74620	+	3.50140i	−0.660096	+	0.237145i
$219$	6.71011			0.453427
$220$	−6.49681	+	1.33845i	−0.438015	+	0.0902380i
$221$	11.8613			0.797879
$222$	5.91949	−	2.12663i	0.397290	−	0.142730i
$223$	6.41560	−	8.83032i	0.429620	−	0.591322i	−0.538246	−	0.842788i	$-0.680913\pi$
$223$	6.41560	−	8.83032i	0.429620	−	0.591322i	0.967866	+	0.251466i	$0.0809128\pi$
$224$	−12.8796	+	12.7927i	−0.860552	+	0.854751i
$225$	0.848943	−	2.61278i	0.0565962	−	0.174185i
$226$	−5.20291	+	17.8634i	−0.346092	+	1.18826i
$227$	−6.15855	+	4.47445i	−0.408757	+	0.296980i	−0.773099	−	0.634286i	$-0.781294\pi$
$227$	−6.15855	+	4.47445i	−0.408757	+	0.296980i	0.364341	+	0.931266i	$0.381294\pi$
$228$	0.0381813	−	0.0599847i	0.00252862	−	0.00397258i
$229$	−2.00680	−	6.17630i	−0.132613	−	0.408141i	0.862598	−	0.505890i	$-0.168836\pi$
$229$	−2.00680	−	6.17630i	−0.132613	−	0.408141i	−0.995211	+	0.0977487i	$0.968836\pi$
$230$	0.246648	+	8.02128i	0.0162635	+	0.528908i
$231$	5.27155	+	0.918281i	0.346842	+	0.0604184i
$232$	−1.07752	−	11.6513i	−0.0707425	−	0.764942i
$233$	20.0082	−	6.50106i	1.31078	−	0.425899i	0.431462	−	0.902131i	$-0.357998\pi$
$233$	20.0082	−	6.50106i	1.31078	−	0.425899i	0.879320	+	0.476232i	$0.157998\pi$
$234$	8.50595	−	12.4979i	0.556051	−	0.817015i
$235$	−2.38052	−	3.27651i	−0.155288	−	0.213736i
$236$	27.6256	+	7.13289i	1.79827	+	0.464312i
$237$	−4.96619	−	1.61361i	−0.322589	−	0.104815i
$238$	−8.47155	−	10.9367i	−0.549129	−	0.708922i
$239$	−11.4476	−	8.31718i	−0.740485	−	0.537994i	0.152378	−	0.988322i	$-0.451307\pi$
$239$	−11.4476	−	8.31718i	−0.740485	−	0.537994i	−0.892863	+	0.450329i	$0.851307\pi$
$240$	−1.82193	+	0.851323i	−0.117605	+	0.0549526i
$241$		−	4.74712i		−	0.305789i	−0.988243	−	0.152895i	$-0.951141\pi$
$241$		−	4.74712i		−	0.305789i	0.988243	−	0.152895i	$-0.0488595\pi$
$242$	−0.000488196		15.5563i	−3.13824e−5		1.00000i
$243$		−	12.0816i		−	0.775032i
$244$	−1.36320	+	0.537599i	−0.0872702	+	0.0344162i
$245$	2.66818	+	1.93854i	0.170463	+	0.123849i
$246$	−4.76627	+	3.69193i	−0.303886	+	0.235389i
$247$	0.261699	+	0.0850311i	0.0166515	+	0.00541040i
$248$	−2.59638	−	0.585894i	−0.164870	−	0.0372043i
$249$	1.46056	+	2.01029i	0.0925593	+	0.127397i
$250$	−1.16913	−	0.795697i	−0.0739423	−	0.0503243i
$251$	−12.3766	+	4.02140i	−0.781204	+	0.253829i	−0.672354	−	0.740230i	$-0.734717\pi$
$251$	−12.3766	+	4.02140i	−0.781204	+	0.253829i	−0.108850	+	0.994058i	$0.534717\pi$
$252$	−17.5988	+	1.08332i	−1.10862	+	0.0682428i
$253$	18.5413	+	3.22981i	1.16568	+	0.203056i
$254$	−16.1101	+	0.495373i	−1.01084	+	0.0310825i
$255$	−0.473579	−	1.45753i	−0.0296567	−	0.0912739i
$256$	−14.8443	−	5.97041i	−0.927771	−	0.373151i
$257$	−10.5292	+	7.64990i	−0.656792	+	0.477188i	−0.865578	−	0.500774i	$-0.833049\pi$
$257$	−10.5292	+	7.64990i	−0.656792	+	0.477188i	0.208786	+	0.977961i	$0.433049\pi$
$258$	0.338851	+	0.0986941i	0.0210960	+	0.00614442i
$259$	8.77270	−	26.9996i	0.545109	−	1.67767i
$260$	−4.95252	−	6.00308i	−0.307142	−	0.372295i
$261$	6.68024	−	9.19456i	0.413496	−	0.569129i
$262$	−1.26278	−	3.51496i	−0.0780146	−	0.217155i
$263$	23.6461			1.45808			0.729040	−	0.684471i	$-0.239967\pi$
$263$	23.6461			1.45808			0.729040	+	0.684471i	$0.239967\pi$
$264$	1.09316	+	4.58781i	0.0672793	+	0.282360i
$265$	−7.89123			−0.484754
$266$	−0.108507	−	0.302030i	−0.00665297	−	0.0185186i
$267$	−3.53507	+	4.86561i	−0.216343	+	0.297770i
$268$	−0.198154	−	0.240188i	−0.0121042	−	0.0146718i
$269$	−4.01098	+	12.3445i	−0.244554	+	0.752660i	0.751155	+	0.660125i	$0.229497\pi$
$269$	−4.01098	+	12.3445i	−0.244554	+	0.752660i	−0.995709	+	0.0925345i	$0.970503\pi$
$270$	−3.92327	−	1.14269i	−0.238763	−	0.0695422i
$271$	−16.9252	+	12.2969i	−1.02813	+	0.746981i	−0.967934	−	0.251205i	$-0.919173\pi$
$271$	−16.9252	+	12.2969i	−1.02813	+	0.746981i	−0.0601974	+	0.998186i	$0.519173\pi$
$272$	5.90297	−	10.6690i	0.357920	−	0.646902i
$273$	1.93997	+	5.97060i	0.117412	+	0.361357i
$274$	−22.3101	+	0.686017i	−1.34780	+	0.0414438i
$275$	−2.38101	+	2.30885i	−0.143580	+	0.139229i
$276$	5.69506	−	0.350569i	0.342803	−	0.0211018i
$277$	13.2733	−	4.31275i	0.797514	−	0.259128i	0.118213	−	0.992988i	$-0.462283\pi$
$277$	13.2733	−	4.31275i	0.797514	−	0.259128i	0.679300	+	0.733860i	$0.262283\pi$
$278$	15.0800	+	10.2633i	0.904437	+	0.615549i
$279$	−1.51958	−	2.09152i	−0.0909749	−	0.125216i
$280$	−1.99797	+	8.85395i	−0.119401	+	0.529125i
$281$	10.5559	+	3.42982i	0.629712	+	0.204606i	0.606447	−	0.795124i	$-0.292594\pi$
$281$	10.5559	+	3.42982i	0.629712	+	0.204606i	0.0232643	+	0.999729i	$0.492594\pi$
$282$	−2.27648	+	1.76336i	−0.135563	+	0.105006i
$283$	−10.2954	−	7.48008i	−0.612001	−	0.444645i	0.238117	−	0.971236i	$-0.423470\pi$
$283$	−10.2954	−	7.48008i	−0.612001	−	0.444645i	−0.850118	+	0.526592i	$0.823470\pi$
$284$	27.9545	−	11.0242i	1.65879	−	0.654168i
$285$		−	0.0355527i		−	0.00210596i
$286$	−16.1328	+	8.53455i	−0.953950	+	0.504658i
$287$			27.2110i			1.60622i
$288$	−7.00847	−	13.8707i	−0.412978	−	0.817337i
$289$	−6.23590	−	4.53065i	−0.366818	−	0.266509i
$290$	−3.58268	−	4.62521i	−0.210382	−	0.271602i
$291$	3.16572	+	1.02860i	0.185578	+	0.0602978i
$292$	25.8458	+	6.67336i	1.51251	+	0.390529i
$293$	−17.0950	−	23.5292i	−0.998700	−	1.37459i	−0.926119	−	0.377231i	$-0.876876\pi$
$293$	−17.0950	−	23.5292i	−0.998700	−	1.37459i	−0.0725812	−	0.997363i	$-0.523124\pi$
$294$	1.31935	−	1.93854i	0.0769461	−	0.113058i
$295$	13.5676	−	4.40837i	0.789934	−	0.256665i
$296$	24.9155	−	2.30420i	1.44818	−	0.133929i
$297$	−4.48154	+	8.47076i	−0.260045	+	0.491523i
$298$	−0.560034	−	18.2130i	−0.0324419	−	1.05505i
$299$	6.82331	+	21.0000i	0.394602	+	1.21446i
$300$	−0.539926	+	0.848249i	−0.0311727	+	0.0489737i
$301$	1.28871	−	0.936303i	0.0742800	−	0.0539676i
$302$	4.75174	−	16.3144i	0.273432	−	0.938789i
$303$	3.06208	−	9.42411i	0.175912	−	0.541401i
$304$	0.206722	−	0.193075i	0.0118563	−	0.0110736i
$305$	−0.430664	+	0.592759i	−0.0246598	+	0.0339413i
$306$	11.1457	−	4.00417i	0.637156	−	0.228903i
$307$	29.1604			1.66427			0.832137	−	0.554570i	$-0.187117\pi$
$307$	29.1604			1.66427			0.832137	+	0.554570i	$0.187117\pi$
$308$	19.3915	+	8.77967i	1.10493	+	0.500268i
$309$	−4.67770			−0.266105
$310$	−1.25246	+	0.449957i	−0.0711349	+	0.0255558i
$311$	6.97622	−	9.60194i	0.395585	−	0.544476i	−0.564044	−	0.825745i	$-0.690755\pi$
$311$	6.97622	−	9.60194i	0.395585	−	0.544476i	0.959629	+	0.281269i	$0.0907552\pi$
$312$	−4.15796	+	3.65077i	−0.235398	+	0.206684i
$313$	−5.97282	+	18.3825i	−0.337604	+	1.03904i	0.627821	+	0.778358i	$0.283947\pi$
$313$	−5.97282	+	18.3825i	−0.337604	+	1.03904i	−0.965425	+	0.260681i	$0.916053\pi$
$314$	2.41470	−	8.29053i	0.136270	−	0.467862i
$315$	−7.13233	+	5.18194i	−0.401861	+	0.291969i
$316$	−17.5238	−	11.1542i	−0.985792	−	0.627475i
$317$	1.99819	+	6.14980i	0.112230	+	0.345407i	0.991359	−	0.131176i	$-0.0418752\pi$
$317$	1.99819	+	6.14980i	0.112230	+	0.345407i	−0.879130	+	0.476583i	$0.841875\pi$
$318$	0.172442	+	5.60802i	0.00967008	+	0.314482i
$319$	−12.3195	+	6.04021i	−0.689761	+	0.338187i
$320$	−7.86432	+	1.46715i	−0.439629	+	0.0820159i
$321$	1.86942	−	0.607410i	0.104341	−	0.0339023i
$322$	14.4897	−	21.2899i	0.807479	−	1.18644i
$323$	0.126704	+	0.174393i	0.00704999	+	0.00970349i
$324$	3.39452	−	13.1469i	0.188584	−	0.730384i
$325$	−3.70071	−	1.20243i	−0.205278	−	0.0666990i
$326$	20.5352	+	26.5109i	1.13734	+	1.46830i
$327$	2.97847	+	2.16399i	0.164710	+	0.119669i
$328$	−22.0303	+	9.48031i	−1.21642	+	0.523463i
$329$			12.9966i			0.716528i
$330$	1.69285	+	1.64165i	0.0931884	+	0.0903698i
$331$		−	23.7859i		−	1.30739i	−0.756757	−	0.653697i	$-0.773217\pi$
$331$		−	23.7859i		−	1.30739i	0.756757	−	0.653697i	$-0.226783\pi$
$332$	3.62647	+	9.19573i	0.199028	+	0.504681i
$333$	19.6620	+	14.2853i	1.07747	+	0.782828i
$334$	16.1252	−	12.4905i	0.882330	−	0.683450i
$335$	−0.148068	−	0.0481102i	−0.00808983	−	0.00262854i
$336$	6.33586	+	1.22641i	0.345650	+	0.0669060i
$337$	2.80658	+	3.86293i	0.152884	+	0.210427i	0.878588	−	0.477580i	$-0.158486\pi$
$337$	2.80658	+	3.86293i	0.152884	+	0.210427i	−0.725704	+	0.688007i	$0.758486\pi$
$338$	−2.50323	−	1.70367i	−0.136158	−	0.0926673i
$339$	6.29061	−	2.04394i	0.341659	−	0.111012i
$340$	−0.374574	−	6.08504i	−0.0203141	−	0.330008i
$341$	0.440761	+	3.08980i	0.0238685	+	0.167322i
$342$	0.274614	−	0.00844416i	0.0148494	−	0.000456608i
$343$	3.67105	+	11.2983i	0.198218	+	0.610053i
$344$	1.20702	+	0.717142i	0.0650783	+	0.0386657i
$345$	2.30806	−	1.67691i	0.124262	−	0.0902815i
$346$	12.7752	+	3.72090i	0.686797	+	0.200037i
$347$	6.31545	−	19.4370i	0.339031	−	1.04343i	−0.625671	−	0.780087i	$-0.715175\pi$
$347$	6.31545	−	19.4370i	0.339031	−	1.04343i	0.964702	−	0.263344i	$-0.0848254\pi$
$348$	−3.20869	+	2.64716i	−0.172004	+	0.141903i
$349$	1.38082	−	1.90054i	0.0739138	−	0.101734i	−0.770459	−	0.637489i	$-0.779973\pi$
$349$	1.38082	−	1.90054i	0.0739138	−	0.101734i	0.844373	+	0.535755i	$0.179973\pi$
$350$	1.53440	+	4.27103i	0.0820173	+	0.228296i
$351$	−11.2433			−0.600123
$352$	−0.352090	+	18.7584i	−0.0187664	+	0.999824i
$353$	−15.3669			−0.817897			−0.408949	−	0.912557i	$-0.634104\pi$
$353$	−15.3669			−0.817897			−0.408949	+	0.912557i	$0.634104\pi$
$354$	−3.42936	−	9.54567i	−0.182268	−	0.507347i
$355$	8.83140	−	12.1554i	0.468722	−	0.645140i
$356$	−18.4552	+	15.2255i	−0.978124	+	0.806949i
$357$	−1.51974	+	4.67729i	−0.0804333	+	0.247548i
$358$	−5.40461	−	1.57415i	−0.285642	−	0.0831964i
$359$	13.1667	−	9.56619i	0.694914	−	0.504884i	−0.183358	−	0.983046i	$-0.558697\pi$
$359$	13.1667	−	9.56619i	0.694914	−	0.504884i	0.878272	+	0.478162i	$0.158697\pi$
$360$	−6.68024	−	3.96900i	−0.352079	−	0.209185i
$361$	−5.86978	−	18.0653i	−0.308936	−	0.950806i
$362$	2.72519	−	0.0837973i	0.143233	−	0.00440429i
$363$	4.57199	−	3.11144i	0.239967	−	0.163308i
$364$	1.53440	+	24.9267i	0.0804246	+	1.30651i
$365$	12.6935	−	4.12436i	0.664407	−	0.215879i
$366$	0.430664	+	0.293105i	0.0225112	+	0.0153209i
$367$	−9.76265	−	13.4371i	−0.509606	−	0.701413i	0.474246	−	0.880392i	$-0.342721\pi$
$367$	−9.76265	−	13.4371i	−0.509606	−	0.701413i	−0.983853	+	0.178979i	$0.942721\pi$
$368$	22.2847	+	4.31356i	1.16167	+	0.224860i
$369$	−22.1549	−	7.19857i	−1.15334	−	0.374743i
$370$	9.89074	−	7.66133i	0.514195	−	0.398294i
$371$	20.4871	+	14.8847i	1.06363	+	0.772776i
$372$	0.347138	+	0.880248i	0.0179983	+	0.0456387i
$373$		−	11.8791i		−	0.615076i	−0.951536	−	0.307538i	$-0.900495\pi$
$373$		−	11.8791i		−	0.615076i	0.951536	−	0.307538i	$-0.0995051\pi$
$374$	−14.1543	−	2.01957i	−0.731903	−	0.104430i
$375$			0.502754i			0.0259621i
$376$	−10.5222	+	4.52802i	−0.542640	+	0.233515i
$377$	−13.0231	−	9.46181i	−0.670722	−	0.487308i
$378$	8.03014	+	10.3669i	0.413026	+	0.533214i
$379$	−20.1255	−	6.53916i	−1.03378	−	0.335894i	−0.257494	−	0.966280i	$-0.582897\pi$
$379$	−20.1255	−	6.53916i	−1.03378	−	0.335894i	−0.776282	+	0.630386i	$0.782897\pi$
$380$	0.0353579	−	0.136941i	0.00181382	−	0.00702491i
$381$	3.36793	+	4.63556i	0.172544	+	0.237487i
$382$	14.2411	−	20.9246i	0.728636	−	1.07060i
$383$	−1.39303	+	0.452624i	−0.0711807	+	0.0231280i	−0.344391	−	0.938826i	$-0.611915\pi$
$383$	−1.39303	+	0.452624i	−0.0711807	+	0.0231280i	0.273210	+	0.961954i	$0.411915\pi$
$384$	1.21450	+	5.55684i	0.0619774	+	0.283571i
$385$	10.5366	−	1.50304i	0.536993	−	0.0766022i
$386$	−0.299796	−	9.74971i	−0.0152592	−	0.496247i
$387$	0.421404	+	1.29695i	0.0214212	+	0.0659276i
$388$	11.1706	+	7.11032i	0.567103	+	0.360972i
$389$	−5.86718	+	4.26275i	−0.297478	+	0.216130i	−0.726505	−	0.687161i	$-0.758856\pi$
$389$	−5.86718	+	4.26275i	−0.297478	+	0.216130i	0.429027	+	0.903292i	$0.358856\pi$
$390$	−0.773659	+	2.65624i	−0.0391757	+	0.134504i
$391$	−5.34529	+	16.4511i	−0.270323	+	0.831968i
$392$	7.00975	−	6.15469i	0.354046	−	0.310859i
$393$	−0.780439	+	1.07418i	−0.0393680	+	0.0541853i
$394$	6.85498	−	2.46271i	0.345349	−	0.124069i
$395$	−10.3863			−0.522592
$396$	−12.2783	+	13.4657i	−0.617006	+	0.676679i
$397$	−37.7420			−1.89422			−0.947108	−	0.320915i	$-0.896010\pi$
$397$	−37.7420			−1.89422			−0.947108	+	0.320915i	$0.896010\pi$
$398$	24.1075	−	8.66083i	1.20840	−	0.434128i
$399$	−0.0670608	+	0.0923012i	−0.00335724	+	0.00462084i
$400$	−2.92327	+	2.73029i	−0.146164	+	0.136514i
$401$	10.3234	−	31.7723i	0.515528	−	1.58663i	−0.266790	−	0.963755i	$-0.585963\pi$
$401$	10.3234	−	31.7723i	0.515528	−	1.58663i	0.782318	−	0.622879i	$-0.214037\pi$
$402$	−0.0309547	+	0.106278i	−0.00154388	+	0.00530068i
$403$	−2.96241	+	2.15232i	−0.147568	+	0.107214i
$404$	21.1669	−	33.2542i	1.05309	−	1.65446i
$405$	−2.09793	−	6.45675i	−0.104247	−	0.320839i
$406$	0.577029	+	18.7657i	0.0286375	+	0.931325i
$407$	−12.9166	−	26.3446i	−0.640252	−	1.30585i
$408$	−4.31624	+	0.399170i	−0.213686	+	0.0197618i
$409$	−9.88229	+	3.21095i	−0.488648	+	0.158771i	−0.542970	−	0.839752i	$-0.682700\pi$
$409$	−9.88229	+	3.21095i	−0.488648	+	0.158771i	0.0543221	+	0.998523i	$0.482700\pi$
$410$	−6.74707	+	9.91359i	−0.333214	+	0.489597i
$411$	4.66407	+	6.41955i	0.230062	+	0.316653i
$412$	−18.0174	−	4.65208i	−0.887655	−	0.229191i
$413$	−43.5391	−	14.1467i	−2.14242	−	0.696114i
$414$	13.5009	+	17.4295i	0.663531	+	0.856614i
$415$	3.99856	+	2.90512i	0.196281	+	0.142607i
$416$	−19.6463	+	9.92672i	−0.963237	+	0.486697i
$417$		−	6.48475i		−	0.317560i
$418$	−0.297812	−	0.146027i	−0.0145665	−	0.00714243i
$419$			29.4844i			1.44041i	0.693762	+	0.720205i	$0.255952\pi$
$419$			29.4844i			1.44041i	−0.693762	+	0.720205i	$0.744048\pi$
$420$	3.00174	−	1.18378i	0.146470	−	0.0577625i
$421$	−7.51048	−	5.45668i	−0.366039	−	0.265943i	0.389528	−	0.921015i	$-0.372638\pi$
$421$	−7.51048	−	5.45668i	−0.366039	−	0.265943i	−0.755566	+	0.655072i	$0.772638\pi$
$422$	3.95685	−	3.06496i	0.192616	−	0.149200i
$423$	−10.5817	−	3.43821i	−0.514501	−	0.167171i
$424$	−4.91310	+	21.7723i	−0.238601	+	1.05736i
$425$	−1.79173	−	2.46611i	−0.0869118	−	0.119624i
$426$	−8.83140	−	6.01055i	−0.427883	−	0.291212i
$427$	2.23617	−	0.726574i	0.108216	−	0.0351614i
$428$	7.80464	−	0.480427i	0.377251	−	0.0232223i
$429$	5.73511	+	3.03422i	0.276894	+	0.146493i
$430$	0.701665	−	0.0215756i	0.0338373	−	0.00104047i
$431$	−9.30079	−	28.6249i	−0.448003	−	1.37881i	−0.879157	−	0.476533i	$-0.841893\pi$
$431$	−9.30079	−	28.6249i	−0.448003	−	1.37881i	0.431153	−	0.902279i	$-0.358107\pi$
$432$	−5.59539	+	10.1131i	−0.269208	+	0.486565i
$433$	7.90428	−	5.74279i	0.379855	−	0.275981i	−0.381430	−	0.924398i	$-0.624568\pi$
$433$	7.90428	−	5.74279i	0.379855	−	0.275981i	0.761286	+	0.648416i	$0.224568\pi$
$434$	4.10034	+	1.19427i	0.196823	+	0.0573266i
$435$	−0.642710	+	1.97806i	−0.0308156	+	0.0948406i
$436$	9.32024	+	11.2973i	0.446359	+	0.541044i
$437$	−0.235868	+	0.324645i	−0.0112831	+	0.0155299i
$438$	−3.20842	−	8.93069i	−0.153304	−	0.426725i
$439$	−10.3425			−0.493622			−0.246811	−	0.969064i	$-0.579383\pi$
$439$	−10.3425			−0.493622			−0.246811	+	0.969064i	$0.579383\pi$
$440$	4.88781	+	8.00683i	0.233017	+	0.381711i
$441$	9.06052			0.431453
$442$	−5.67147	−	15.7866i	−0.269764	−	0.750892i
$443$	−18.5086	+	25.4750i	−0.879372	+	1.21035i	0.0972223	+	0.995263i	$0.469004\pi$
$443$	−18.5086	+	25.4750i	−0.879372	+	1.21035i	−0.976594	+	0.215089i	$0.930996\pi$
$444$	−5.66078	−	6.86159i	−0.268649	−	0.325637i
$445$	−3.69663	+	11.3771i	−0.175237	+	0.539324i
$446$	−14.8201	−	4.31652i	−0.701754	−	0.204393i
$447$	−5.24064	+	3.80755i	−0.247874	+	0.180091i
$448$	23.1846	+	11.0250i	1.09537	+	0.520882i
$449$	−0.787165	−	2.42264i	−0.0371486	−	0.114332i	0.930763	−	0.365624i	$-0.119144\pi$
$449$	−0.787165	−	2.42264i	−0.0371486	−	0.114332i	−0.967911	+	0.251292i	$0.919144\pi$
$450$	−3.88335	+	0.119410i	−0.183063	+	0.00562903i
$451$	19.5778	+	20.1897i	0.921882	+	0.950694i
$452$	26.2627	−	1.61664i	1.23529	−	0.0760405i
$453$	−5.74513	+	1.86671i	−0.269930	+	0.0877055i
$454$	8.89987	+	6.05715i	0.417692	+	0.284276i
$455$	7.33964	+	10.1021i	0.344088	+	0.473596i
$456$	−0.0980917	−	0.0221352i	−0.00459356	−	0.00103658i
$457$	16.2280	+	5.27279i	0.759113	+	0.246651i	0.662898	−	0.748710i	$-0.269326\pi$
$457$	16.2280	+	5.27279i	0.759113	+	0.246651i	0.0962151	+	0.995361i	$0.469326\pi$
$458$	−7.26068	+	5.62410i	−0.339269	+	0.262797i
$459$	−7.12569	−	5.17712i	−0.332599	−	0.241647i
$460$	10.5578	−	4.16363i	0.492262	−	0.194130i
$461$		−	1.34620i		−	0.0626990i	−0.999508	−	0.0313495i	$-0.990020\pi$
$461$		−	1.34620i		−	0.0626990i	0.999508	−	0.0313495i	$-0.00998049\pi$
$462$	−1.29841	−	7.45514i	−0.0604076	−	0.346844i
$463$		−	4.36322i		−	0.202776i	−0.994847	−	0.101388i	$-0.967672\pi$
$463$		−	4.36322i		−	0.202776i	0.994847	−	0.101388i	$-0.0323284\pi$
$464$	−14.9918	+	7.00512i	−0.695976	+	0.325204i
$465$	0.382756	+	0.278088i	0.0177499	+	0.0128960i
$466$	−18.2193	−	23.5211i	−0.843995	−	1.08959i
$467$	17.9687	+	5.83839i	0.831493	+	0.270168i	0.693674	−	0.720289i	$-0.255991\pi$
$467$	17.9687	+	5.83839i	0.831493	+	0.270168i	0.137819	+	0.990457i	$0.455991\pi$
$468$	−20.7010	−	5.34497i	−0.956903	−	0.247071i
$469$	0.293664	+	0.404194i	0.0135602	+	0.0186640i
$470$	−3.22256	+	4.73496i	−0.148646	+	0.218408i
$471$	−2.91952	+	0.948608i	−0.134524	+	0.0437096i
$472$	−3.71572	−	40.1783i	−0.171030	−	1.84935i
$473$	0.282529	−	1.62190i	0.0129907	−	0.0745753i
$474$	0.226966	+	7.38119i	0.0104249	+	0.339029i
$475$	−0.0218524	−	0.0672548i	−0.00100266	−	0.00308586i
$476$	−10.5054	+	16.5044i	−0.481512	+	0.756478i
$477$	−17.5387	+	12.7426i	−0.803044	+	0.583446i
$478$	−5.59594	+	19.2128i	−0.255952	+	0.878774i
$479$	5.41103	−	16.6534i	0.247236	−	0.760915i	−0.748024	−	0.663671i	$-0.768997\pi$
$479$	5.41103	−	16.6534i	0.247236	−	0.760915i	0.995261	−	0.0972438i	$-0.0310027\pi$
$480$	2.00420	+	2.01781i	0.0914790	+	0.0920998i
$481$	20.2335	−	27.8490i	0.922568	−	1.26981i
$482$	−6.31809	+	2.26983i	−0.287781	+	0.103388i
$483$	−9.15519			−0.416575
$484$	20.7046	−	7.43758i	0.941120	−	0.338072i
$485$	6.62079			0.300635
$486$	−16.0797	+	5.77677i	−0.729390	+	0.262040i
$487$	−6.32403	+	8.70428i	−0.286569	+	0.394429i	−0.927896	−	0.372839i	$-0.878384\pi$
$487$	−6.32403	+	8.70428i	−0.286569	+	0.394429i	0.641327	+	0.767268i	$0.278384\pi$
$488$	1.36732	+	1.55728i	0.0618956	+	0.0704947i
$489$	3.68389	−	11.3379i	0.166591	−	0.512716i
$490$	1.30428	−	4.47806i	0.0589215	−	0.202298i
$491$	18.8359	−	13.6851i	0.850051	−	0.617598i	−0.0751094	−	0.997175i	$-0.523931\pi$
$491$	18.8359	−	13.6851i	0.850051	−	0.617598i	0.925160	+	0.379577i	$0.123931\pi$
$492$	7.19269	+	4.57828i	0.324271	+	0.206405i
$493$	−3.89685	−	11.9933i	−0.175505	−	0.540150i
$494$	−0.0119602	−	0.388960i	−0.000538115	−	0.0175002i
$495$	−1.56365	+	8.97639i	−0.0702807	+	0.403459i
$496$	0.461669	+	3.73575i	0.0207295	+	0.167740i
$497$	−45.8558	+	14.8995i	−2.05691	+	0.668332i
$498$	1.97719	−	2.90512i	0.0886001	−	0.130182i
$499$	8.36834	+	11.5180i	0.374618	+	0.515618i	0.954149	−	0.299333i	$-0.0967641\pi$
$499$	8.36834	+	11.5180i	0.374618	+	0.515618i	−0.579531	+	0.814951i	$0.696764\pi$
$500$	−0.500000	+	1.93649i	−0.0223607	+	0.0866025i
$501$	−6.89622	−	2.24072i	−0.308100	−	0.100108i
$502$	11.2700	+	14.5496i	0.503007	+	0.649379i
$503$	23.5444	+	17.1060i	1.04979	+	0.762718i	0.972173	−	0.234265i	$-0.0752683\pi$
$503$	23.5444	+	17.1060i	1.04979	+	0.762718i	0.0776187	+	0.996983i	$0.475268\pi$
$504$	9.85664	+	22.9048i	0.439050	+	1.02026i
$505$		−	19.7096i		−	0.877067i
$506$	−4.56681	−	26.2215i	−0.203020	−	1.16569i
$507$			1.07645i			0.0478067i
$508$	8.36232	+	21.2046i	0.371018	+	0.940801i
$509$	28.7673	+	20.9006i	1.27509	+	0.926404i	0.999393	−	0.0348414i	$-0.0110926\pi$
$509$	28.7673	+	20.9006i	1.27509	+	0.926404i	0.275693	+	0.961246i	$0.411093\pi$
$510$	−1.71343	+	1.32721i	−0.0758718	+	0.0587700i
$511$	−40.7341	−	13.2353i	−1.80197	−	0.585496i
$512$	−0.848413	+	22.6115i	−0.0374949	+	0.999297i
$513$	−0.120102	−	0.165306i	−0.00530263	−	0.00729845i
$514$	15.2160	+	10.3558i	0.671148	+	0.456776i
$515$	−8.84878	+	2.87514i	−0.389924	+	0.126694i
$516$	−0.0306661	−	0.498178i	−0.00135000	−	0.0219311i
$517$	9.35081	+	9.64306i	0.411248	+	0.424101i
$518$	−40.1292	+	1.23394i	−1.76318	+	0.0542163i
$519$	−1.46174	−	4.49878i	−0.0641634	−	0.197475i
$520$	−5.62165	+	9.46181i	−0.246526	+	0.414928i
$521$	−15.9186	+	11.5655i	−0.697406	+	0.506695i	−0.879086	−	0.476662i	$-0.841846\pi$
$521$	−15.9186	+	11.5655i	−0.697406	+	0.506695i	0.181680	+	0.983358i	$0.441846\pi$
$522$	−15.4315	−	4.49457i	−0.675416	−	0.196722i
$523$	−12.2934	+	37.8352i	−0.537554	+	1.65442i	0.200513	+	0.979691i	$0.435739\pi$
$523$	−12.2934	+	37.8352i	−0.537554	+	1.65442i	−0.738066	+	0.674728i	$0.764261\pi$
$524$	−4.07437	+	3.36134i	−0.177990	+	0.146841i
$525$	0.948313	−	1.30524i	0.0413878	−	0.0569654i
$526$	−11.3063	−	31.4713i	−0.492979	−	1.37221i
$527$	−2.86856			−0.124956
$528$	5.58337	−	3.64857i	0.242985	−	0.158784i
$529$	−9.20092			−0.400040
$530$	3.77317	+	10.5027i	0.163896	+	0.456207i
$531$	23.0362	−	31.7066i	0.999685	−	1.37595i
$532$	−0.350098	+	0.288829i	−0.0151787	+	0.0125223i
$533$	−10.1960	+	31.3800i	−0.441637	+	1.35922i
$534$	8.16607	+	2.37845i	0.353380	+	0.102926i
$535$	3.16302	−	2.29807i	0.136749	−	0.0993541i
$536$	−0.224926	+	0.378574i	−0.00971533	+	0.0163519i
$537$	0.618399	+	1.90324i	0.0266859	+	0.0821307i
$538$	18.3476	−	0.564173i	0.791019	−	0.0243232i
$539$	−9.66862	−	5.11528i	−0.416457	−	0.220331i
$540$	0.355057	+	5.76798i	0.0152792	+	0.248214i
$541$	29.0963	−	9.45397i	1.25095	−	0.406458i	0.392688	−	0.919672i	$-0.371545\pi$
$541$	29.0963	−	9.45397i	1.25095	−	0.406458i	0.858261	+	0.513214i	$0.171545\pi$
$542$	24.4590	+	16.6465i	1.05060	+	0.715029i
$543$	−0.569719	−	0.784151i	−0.0244490	−	0.0336511i
$544$	−17.0221	−	2.75509i	−0.729819	−	0.118124i
$545$	6.96444	+	2.26288i	0.298324	+	0.0969313i
$546$	7.01886	−	5.43679i	0.300380	−	0.232673i
$547$	−6.79763	−	4.93876i	−0.290645	−	0.211166i	0.432902	−	0.901441i	$-0.357490\pi$
$547$	−6.79763	−	4.93876i	−0.290645	−	0.211166i	−0.723547	+	0.690275i	$0.757490\pi$
$548$	11.5805	+	29.3651i	0.494696	+	1.25442i
$549$			2.01287i			0.0859074i
$550$	4.21139	+	2.06499i	0.179574	+	0.0880514i
$551$		−	0.292546i		−	0.0124629i
$552$	−3.18966	−	7.41211i	−0.135761	−	0.315480i
$553$	26.9647	+	19.5910i	1.14666	+	0.833095i
$554$	−12.0865	−	15.6037i	−0.513508	−	0.662936i
$555$	−4.22995	−	1.37440i	−0.179552	−	0.0583398i
$556$	6.44923	−	24.9777i	0.273508	−	1.05929i
$557$	12.3439	+	16.9899i	0.523027	+	0.719885i	0.986048	−	0.166463i	$-0.0532345\pi$
$557$	12.3439	+	16.9899i	0.523027	+	0.719885i	−0.463021	+	0.886347i	$0.653234\pi$
$558$	−2.05709	+	3.02251i	−0.0870834	+	0.127953i
$559$	1.83698	−	0.596872i	0.0776961	−	0.0252450i
$560$	12.7393	−	1.57434i	0.538334	−	0.0665281i
$561$	2.23761	+	4.56381i	0.0944721	+	0.192684i
$562$	−0.482427	−	15.6891i	−0.0203500	−	0.661805i
$563$	−1.36983	−	4.21590i	−0.0577313	−	0.177679i	0.918032	−	0.396505i	$-0.129777\pi$
$563$	−1.36983	−	4.21590i	−0.0577313	−	0.177679i	−0.975764	+	0.218826i	$0.929777\pi$
$564$	3.43540	+	2.18669i	0.144656	+	0.0920765i
$565$	10.6436	−	7.73303i	0.447780	−	0.325331i
$566$	−5.03272	+	17.2791i	−0.211541	+	0.726295i
$567$	−6.73237	+	20.7201i	−0.282733	+	0.870162i
$568$	−28.0389	−	31.9342i	−1.17648	−	1.33993i
$569$	12.7625	−	17.5661i	0.535033	−	0.736410i	−0.452854	−	0.891585i	$-0.649594\pi$
$569$	12.7625	−	17.5661i	0.535033	−	0.736410i	0.987887	+	0.155175i	$0.0495941\pi$
$570$	−0.0473181	+	0.0169994i	−0.00198194	+	0.000712028i
$571$	−33.8605			−1.41702			−0.708508	−	0.705702i	$-0.750632\pi$
$571$	−33.8605			−1.41702			−0.708508	+	0.705702i	$0.750632\pi$
$572$	19.0727	+	17.3908i	0.797471	+	0.727146i
$573$	−8.99809			−0.375901
$574$	36.2160	−	13.0109i	1.51163	−	0.543064i
$575$	3.33544	−	4.59084i	0.139097	−	0.191451i
$576$	−15.1098	+	15.9600i	−0.629575	+	0.665001i
$577$	−8.75266	+	26.9379i	−0.364378	+	1.12144i	0.585992	+	0.810317i	$0.300705\pi$
$577$	−8.75266	+	26.9379i	−0.364378	+	1.12144i	−0.950370	+	0.311123i	$0.899295\pi$
$578$	−3.04829	+	10.4659i	−0.126792	+	0.435323i
$579$	−2.80540	+	2.03825i	−0.116589	+	0.0847066i
$580$	−4.44279	+	6.97983i	−0.184477	+	0.289822i
$581$	−4.90123	−	15.0844i	−0.203337	−	0.625808i
$582$	−0.144680	−	4.70517i	−0.00599719	−	0.195036i
$583$	25.9099	−	3.69606i	1.07308	−	0.153075i
$584$	−3.47634	−	37.5898i	−0.143852	−	1.55548i
$585$	−10.1667	+	3.30337i	−0.420343	+	0.136578i
$586$	−23.1418	+	34.0027i	−0.955981	+	1.40464i
$587$	−15.8943	−	21.8766i	−0.656027	−	0.902944i	0.343314	−	0.939221i	$-0.388450\pi$
$587$	−15.8943	−	21.8766i	−0.656027	−	0.902944i	−0.999342	+	0.0362762i	$0.988450\pi$
$588$	−3.21091	−	0.829053i	−0.132416	−	0.0341896i
$589$	−0.0632895	−	0.0205640i	−0.00260780	−	0.000847325i
$590$	−12.3545	−	15.9496i	−0.508628	−	0.656636i
$591$	−2.09490	−	1.52204i	−0.0861728	−	0.0626082i
$592$	−14.9800	−	32.0590i	−0.615675	−	1.31762i
$593$			3.03259i			0.124534i	0.998060	+	0.0622668i	$0.0198330\pi$
$593$			3.03259i			0.124534i	−0.998060	+	0.0622668i	$0.980167\pi$
$594$	13.4168	+	1.91434i	0.550499	+	0.0785464i
$595$			9.78210i			0.401027i
$596$	−23.9724	+	9.45385i	−0.981948	+	0.387245i
$597$	−7.36734	−	5.35269i	−0.301525	−	0.219071i
$598$	24.6870	−	19.1224i	1.00953	−	0.781975i
$599$	31.2756	+	10.1621i	1.27789	+	0.415211i	0.867835	−	0.496852i	$-0.165511\pi$
$599$	31.2756	+	10.1621i	1.27789	+	0.415211i	0.410051	+	0.912062i	$0.365511\pi$
$600$	1.38712	+	0.313016i	0.0566291	+	0.0127788i
$601$	25.8004	+	35.5112i	1.05242	+	1.44853i	0.886693	+	0.462358i	$0.152997\pi$
$601$	25.8004	+	35.5112i	1.05242	+	1.44853i	0.165726	+	0.986172i	$0.447003\pi$
$602$	−1.86235	−	1.26749i	−0.0759036	−	0.0516591i
$603$	−0.406778	+	0.132170i	−0.0165653	+	0.00538239i
$604$	−23.9854	+	1.47646i	−0.975951	+	0.0600762i
$605$	6.73637	−	8.69605i	0.273872	−	0.353545i
$606$	−14.0070	+	0.430703i	−0.568994	+	0.0174961i
$607$	1.04888	+	3.22811i	0.0425726	+	0.131025i	0.970084	−	0.242771i	$-0.0780562\pi$
$607$	1.04888	+	3.22811i	0.0425726	+	0.131025i	−0.927511	+	0.373795i	$0.878056\pi$
$608$	−0.355812	−	0.182814i	−0.0144301	−	0.00741408i
$609$	5.39968	−	3.92309i	0.218806	−	0.158972i
$610$	0.994841	+	0.289758i	0.0402799	+	0.0117320i
$611$	−4.86984	+	14.9878i	−0.197013	+	0.606343i
$612$	−10.6586	−	12.9195i	−0.430846	−	0.522241i
$613$	−17.4987	+	24.0849i	−0.706765	+	0.972779i	0.293096	+	0.956083i	$0.405315\pi$
$613$	−17.4987	+	24.0849i	−0.706765	+	0.972779i	−0.999861	+	0.0166955i	$0.994685\pi$
$614$	−13.9430	−	38.8105i	−0.562693	−	1.56626i
$615$	4.26308			0.171904
$616$	2.41312	−	30.0067i	0.0972274	−	1.20901i
$617$	27.3655			1.10169			0.550846	−	0.834607i	$-0.314305\pi$
$617$	27.3655			1.10169			0.550846	+	0.834607i	$0.314305\pi$
$618$	2.23663	+	6.22570i	0.0899706	+	0.250434i
$619$	−7.16184	+	9.85743i	−0.287859	+	0.396203i	−0.928317	−	0.371789i	$-0.878744\pi$
$619$	−7.16184	+	9.85743i	−0.287859	+	0.396203i	0.640458	+	0.767993i	$0.278744\pi$
$620$	1.19772	+	1.45179i	0.0481017	+	0.0583053i
$621$	5.06677	−	15.5939i	0.203323	−	0.625763i
$622$	−16.1152	−	4.69371i	−0.646159	−	0.188201i
$623$	31.0569	−	22.5642i	1.24427	−	0.904015i
$624$	6.84703	+	3.78835i	0.274101	+	0.151655i
$625$	0.309017	+	0.951057i	0.0123607	+	0.0380423i
$626$	27.3217	−	0.840119i	1.09199	−	0.0335779i
$627$	0.0166520	+	0.116733i	0.000665017	+	0.00466187i
$628$	−12.1887	+	0.750295i	−0.486382	+	0.0299400i
$629$	25.6469	−	8.33318i	1.02261	−	0.332266i
$630$	10.3071	+	7.01490i	0.410645	+	0.279480i
$631$	−16.9524	−	23.3330i	−0.674865	−	0.928873i	0.324993	−	0.945717i	$-0.394638\pi$
$631$	−16.9524	−	23.3330i	−0.674865	−	0.928873i	−0.999858	+	0.0168439i	$0.994638\pi$
$632$	−6.46654	+	28.6564i	−0.257225	+	1.13989i
$633$	−1.69222	−	0.549835i	−0.0672597	−	0.0218540i
$634$	7.22953	−	5.59997i	0.287121	−	0.222403i
$635$	9.22033	+	6.69896i	0.365898	+	0.265840i
$636$	7.38144	−	2.91097i	0.292693	−	0.115428i
$637$		−	12.8332i		−	0.508471i
$638$	13.9296	+	13.5083i	0.551480	+	0.534800i
$639$		−	41.2769i		−	1.63289i
$640$	5.71297	+	9.76534i	0.225825	+	0.386009i
$641$	−5.74895	−	4.17686i	−0.227070	−	0.164976i	0.468434	−	0.883499i	$-0.344819\pi$
$641$	−5.74895	−	4.17686i	−0.227070	−	0.164976i	−0.695503	+	0.718523i	$0.744819\pi$
$642$	−1.70228	−	2.19763i	−0.0671835	−	0.0867335i
$643$	27.4095	+	8.90590i	1.08093	+	0.351214i	0.794734	−	0.606958i	$-0.207610\pi$
$643$	27.4095	+	8.90590i	1.08093	+	0.351214i	0.286193	+	0.958172i	$0.407610\pi$
$644$	−35.2636	−	9.10503i	−1.38958	−	0.358789i
$645$	−0.146688	−	0.201899i	−0.00577583	−	0.00794975i
$646$	0.171522	−	0.252020i	0.00674843	−	0.00991558i
$647$	20.3988	−	6.62796i	0.801959	−	0.260572i	0.120770	−	0.992680i	$-0.461464\pi$
$647$	20.3988	−	6.62796i	0.801959	−	0.260572i	0.681188	+	0.732108i	$0.261464\pi$
$648$	−19.1207	+	1.76830i	−0.751132	+	0.0694653i
$649$	−42.4828	+	20.8291i	−1.66759	+	0.817613i
$650$	0.169131	+	5.50033i	0.00663385	+	0.215741i
$651$	−0.469163	−	1.44394i	−0.0183880	−	0.0565923i
$652$	25.4652	−	40.0071i	0.997296	−	1.56680i
$653$	24.2792	−	17.6399i	0.950118	−	0.690301i	−0.000716986	−	1.00000i	$-0.500228\pi$
$653$	24.2792	−	17.6399i	0.950118	−	0.690301i	0.950835	+	0.309699i	$0.100228\pi$
$654$	1.45596	−	4.99884i	0.0569327	−	0.195470i
$655$	−0.816107	+	2.51172i	−0.0318879	+	0.0981410i
$656$	23.1514	+	24.7877i	0.903908	+	0.967799i
$657$	21.5521	−	29.6639i	0.840827	−	1.15730i
$658$	17.2976	−	6.21431i	0.674331	−	0.242259i
$659$	25.4932			0.993075			0.496537	−	0.868015i	$-0.334605\pi$
$659$	25.4932			0.993075			0.496537	+	0.868015i	$0.334605\pi$
$660$	1.37549	−	3.03802i	0.0535408	−	0.118255i
$661$	0.531397			0.0206689			0.0103345	−	0.999947i	$-0.496710\pi$
$661$	0.531397			0.0206689			0.0103345	+	0.999947i	$0.496710\pi$
$662$	−31.6574	+	11.3732i	−1.23040	+	0.442032i
$663$	−3.50516	+	4.82444i	−0.136129	+	0.187366i
$664$	10.5049	−	9.22349i	0.407669	−	0.357941i
$665$	−0.0701256	+	0.215824i	−0.00271935	+	0.00836931i
$666$	9.61137	−	32.9992i	0.372433	−	1.27869i
$667$	18.9919	−	13.7984i	0.735370	−	0.534277i
$668$	−24.3342	−	15.4892i	−0.941518	−	0.599294i
$669$	1.69573	+	5.21892i	0.0655607	+	0.201775i
$670$	0.00676704	+	0.220072i	0.000261434	+	0.00850213i
$671$	1.13640	−	2.14797i	0.0438704	−	0.0829214i
$672$	−1.39722	−	9.01899i	−0.0538988	−	0.347915i
$673$	−8.51337	+	2.76616i	−0.328166	+	0.106628i	−0.468466	−	0.883481i	$-0.655193\pi$
$673$	−8.51337	+	2.76616i	−0.328166	+	0.106628i	0.140300	+	0.990109i	$0.455193\pi$
$674$	3.79932	−	5.58241i	0.146345	−	0.215026i
$675$	1.69837	+	2.33761i	0.0653705	+	0.0899747i
$676$	−1.07055	+	4.14623i	−0.0411750	+	0.159470i
$677$	−1.77141	−	0.575567i	−0.0680809	−	0.0221208i	0.274779	−	0.961508i	$-0.411395\pi$
$677$	−1.77141	−	0.575567i	−0.0680809	−	0.0221208i	−0.342859	+	0.939387i	$0.611395\pi$
$678$	−5.72819	−	7.39506i	−0.219990	−	0.284006i
$679$	−17.1888	−	12.4884i	−0.659645	−	0.479260i
$680$	−7.91966	+	3.40808i	−0.303705	+	0.130694i
$681$		−	3.82716i		−	0.146657i
$682$	3.90156	−	2.06400i	0.149398	−	0.0790348i
$683$			18.0214i			0.689571i	0.938681	+	0.344786i	$0.112048\pi$
$683$			18.0214i			0.689571i	−0.938681	+	0.344786i	$0.887952\pi$
$684$	−0.142545	−	0.361455i	−0.00545033	−	0.0138206i
$685$	12.7688	+	9.27705i	0.487869	+	0.354458i
$686$	13.2820	−	10.2882i	0.507109	−	0.392805i
$687$	3.10516	+	1.00893i	0.118469	+	0.0384930i
$688$	0.377330	−	1.94936i	0.0143856	−	0.0743188i
$689$	18.0485	+	24.8417i	0.687594	+	0.946392i
$690$	−3.33544	−	2.27006i	−0.126978	−	0.0864197i
$691$	35.3967	−	11.5011i	1.34655	−	0.437521i	0.455021	−	0.890481i	$-0.349632\pi$
$691$	35.3967	−	11.5011i	1.34655	−	0.437521i	0.891531	+	0.452959i	$0.149632\pi$
$692$	−1.15616	−	18.7820i	−0.0439504	−	0.713984i
$693$	20.9911	−	20.3549i	0.797386	−	0.773219i
$694$	−28.8890	+	0.888312i	−1.09661	+	0.0337199i
$695$	−3.98584	−	12.2672i	−0.151192	−	0.465320i
$696$	5.05741	+	3.00481i	0.191701	+	0.113897i
$697$	−20.9112	+	15.1929i	−0.792070	+	0.575473i
$698$	−3.18973	−	0.929041i	−0.120733	−	0.0351647i
$699$	−3.26844	+	10.0592i	−0.123624	+	0.380474i
$700$	4.95077	−	4.08437i	0.187122	−	0.154375i
$701$	22.3855	−	30.8110i	0.845489	−	1.16372i	−0.139349	−	0.990243i	$-0.544501\pi$
$701$	22.3855	−	30.8110i	0.845489	−	1.16372i	0.984839	−	0.173473i	$-0.0554989\pi$
$702$	5.37595	+	14.9640i	0.202902	+	0.564781i
$703$	0.625591			0.0235946
$704$	25.1344	−	8.50066i	0.947289	−	0.320381i
$705$	2.03615			0.0766858
$706$	7.34764	+	20.4523i	0.276532	+	0.769731i
$707$	−37.1770	+	51.1698i	−1.39819	+	1.92444i
$708$	−11.0649	+	9.12848i	−0.415844	+	0.343069i
$709$	−0.133182	+	0.409893i	−0.00500177	+	0.0153939i	−0.953526	−	0.301310i	$-0.902576\pi$
$709$	−0.133182	+	0.409893i	−0.00500177	+	0.0153939i	0.948524	+	0.316704i	$0.102576\pi$
$710$	−20.4007	−	5.94191i	−0.765623	−	0.222996i
$711$	−23.0842	+	16.7717i	−0.865726	+	0.628987i
$712$	29.0884	+	17.2826i	1.09013	+	0.647692i
$713$	−1.65016	−	5.07866i	−0.0617988	−	0.190197i
$714$	6.95180	−	0.213762i	0.260165	−	0.00799985i
$715$	12.7141	+	2.21473i	0.475479	+	0.0828263i
$716$	0.489118	+	7.94583i	0.0182792	+	0.296950i
$717$	6.76580	−	2.19834i	0.252674	−	0.0820986i
$718$	−19.0276	−	12.9499i	−0.710103	−	0.483288i
$719$	−4.70131	−	6.47080i	−0.175329	−	0.241320i	0.712304	−	0.701871i	$-0.247652\pi$
$719$	−4.70131	−	6.47080i	−0.175329	−	0.241320i	−0.887633	+	0.460551i	$0.847652\pi$
$720$	−2.08832	+	10.7887i	−0.0778272	+	0.402071i
$721$	28.3962	+	9.22650i	1.05753	+	0.343613i
$722$	−21.2371	+	16.4502i	−0.790361	+	0.612211i
$723$	1.93083	+	1.40283i	0.0718083	+	0.0521718i
$724$	−1.41457	−	3.58696i	−0.0525721	−	0.133308i
$725$			4.13692i			0.153641i
$726$	−6.32719	−	4.59728i	−0.234824	−	0.170621i
$727$		−	29.1784i		−	1.08217i	−0.840969	−	0.541084i	$-0.818014\pi$
$727$		−	29.1784i		−	1.08217i	0.840969	−	0.541084i	$-0.181986\pi$
$728$	32.4420	−	13.9608i	1.20238	−	0.517423i
$729$	−11.5633	−	8.40124i	−0.428271	−	0.311157i
$730$	−11.5586	−	14.9221i	−0.427803	−	0.552291i
$731$	1.43907	+	0.467581i	0.0532258	+	0.0172941i
$732$	0.184181	−	0.713332i	0.00680754	−	0.0263655i
$733$	1.46872	+	2.02152i	0.0542485	+	0.0746666i	0.835279	−	0.549826i	$-0.185306\pi$
$733$	1.46872	+	2.02152i	0.0542485	+	0.0746666i	−0.781031	+	0.624492i	$0.785306\pi$
$734$	−13.2159	+	19.4183i	−0.487808	+	0.716744i
$735$	−1.57695	+	0.512383i	−0.0581668	+	0.0188995i
$736$	−4.91434	−	31.7219i	−0.181145	−	1.16928i
$737$	0.508698	+	0.0886130i	0.0187381	+	0.00326410i
$738$	1.01253	+	32.9286i	0.0372717	+	1.21212i
$739$	0.554914	+	1.70785i	0.0204128	+	0.0628243i	0.960744	−	0.277436i	$-0.0894847\pi$
$739$	0.554914	+	1.70785i	0.0204128	+	0.0628243i	−0.940331	+	0.340261i	$0.889485\pi$
$740$	−14.9259	−	9.50063i	−0.548688	−	0.349250i
$741$	−0.111920	+	0.0813148i	−0.00411149	+	0.00298718i
$742$	10.0147	−	34.3839i	0.367651	−	1.26227i
$743$	6.36470	−	19.5885i	0.233498	−	0.718633i	−0.763819	−	0.645430i	$-0.776678\pi$
$743$	6.36470	−	19.5885i	0.233498	−	0.718633i	0.997317	−	0.0732026i	$-0.0233220\pi$
$744$	1.00557	−	0.882905i	0.0368658	−	0.0323689i
$745$	−7.57337	+	10.4239i	−0.277467	+	0.381901i
$746$	−15.8102	+	5.67996i	−0.578854	+	0.207958i
$747$	13.5782			0.496800
$748$	4.07995	+	19.8041i	0.149178	+	0.724109i
$749$	−12.5465			−0.458438
$750$	0.669131	−	0.240391i	0.0244332	−	0.00877783i
$751$	8.42266	−	11.5928i	0.307347	−	0.423027i	−0.627204	−	0.778855i	$-0.715801\pi$
$751$	8.42266	−	11.5928i	0.307347	−	0.423027i	0.934552	+	0.355827i	$0.115801\pi$
$752$	11.0576	+	11.8392i	0.403230	+	0.431732i
$753$	2.02178	−	6.22239i	0.0736776	−	0.226756i
$754$	−6.36606	+	21.8569i	−0.231838	+	0.795983i
$755$	−9.72065	+	7.06247i	−0.353771	+	0.257030i
$756$	9.95798	−	15.6444i	0.362168	−	0.568983i
$757$	3.43599	+	10.5749i	0.124883	+	0.384351i	0.993880	−	0.110467i	$-0.0352347\pi$
$757$	3.43599	+	10.5749i	0.124883	+	0.384351i	−0.868997	+	0.494818i	$0.835235\pi$
$758$	0.919778	+	29.9123i	0.0334078	+	1.08646i
$759$	−6.79284	+	6.58697i	−0.246564	+	0.239092i
$760$	−0.199165	+	0.0184189i	−0.00722446	+	0.000668124i
$761$	−19.2163	+	6.24374i	−0.696589	+	0.226336i	−0.635844	−	0.771818i	$-0.719348\pi$
$761$	−19.2163	+	6.24374i	−0.696589	+	0.226336i	−0.0607453	+	0.998153i	$0.519348\pi$
$762$	4.55924	−	6.69896i	0.165164	−	0.242678i
$763$	−13.8126	−	19.0114i	−0.500050	−	0.688260i
$764$	−34.6585	−	8.94880i	−1.25390	−	0.323756i
$765$	−7.96448	−	2.58782i	−0.287956	−	0.0935627i

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.478148 - 1.33093i) q^{2} +(-0.295511 + 0.406737i) q^{3} +(-1.54275 + 1.27276i) q^{4} +(-0.309017 + 0.951057i) q^{5} +(0.682636 + 0.198825i) q^{6} +(2.59618 - 1.88624i) q^{7} +(2.43162 + 1.44472i) q^{8} +(0.848943 + 2.61278i) q^{9} +(1.41355 - 0.0434654i) q^{10} +(0.569171 - 3.26742i) q^{11} +(-0.0617787 - 1.00361i) q^{12} +(3.70071 - 1.20243i) q^{13} +(-3.75181 - 2.55344i) q^{14} +(-0.295511 - 0.406737i) q^{15} +(0.760154 - 3.92711i) q^{16} +(2.89908 + 0.941970i) q^{17} +(3.07151 - 2.37918i) q^{18} +(0.0572103 + 0.0415657i) q^{19} +(-0.733733 - 1.86055i) q^{20} +1.61337i q^{21} +(-4.62086 + 0.804784i) q^{22} +5.67459i q^{23} +(-1.30619 + 0.562096i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-3.36984 - 4.35045i) q^{26} +(-2.74803 - 0.892888i) q^{27} +(-1.60453 + 6.21431i) q^{28} +(-2.43162 - 3.34684i) q^{29} +(-0.400040 + 0.587785i) q^{30} +(-0.894983 + 0.290798i) q^{31} +(-5.59017 + 0.866025i) q^{32} +(1.16078 + 1.19706i) q^{33} +(-0.132495 - 4.30888i) q^{34} +(0.991653 + 3.05199i) q^{35} +(-4.63515 - 2.95036i) q^{36} +(7.15701 - 5.19987i) q^{37} +(0.0279661 - 0.0960175i) q^{38} +(-0.604528 + 1.86055i) q^{39} +(-2.12543 + 1.86616i) q^{40} +(-4.98410 + 6.86002i) q^{41} +(2.14728 - 0.771427i) q^{42} +0.496387 q^{43} +(3.28056 + 5.76523i) q^{44} -2.74724 q^{45} +(7.55248 - 2.71329i) q^{46} +(-2.38052 + 3.27651i) q^{47} +(1.37266 + 1.46969i) q^{48} +(1.01915 - 3.13663i) q^{49} +(-0.395472 + 1.35779i) q^{50} +(-1.23985 + 0.900801i) q^{51} +(-4.17886 + 6.56518i) q^{52} +(2.43852 + 7.50500i) q^{53} +(0.125591 + 4.08437i) q^{54} +(2.93162 + 1.55100i) q^{55} +(9.03802 - 0.835843i) q^{56} +(-0.0338126 + 0.0109864i) q^{57} +(-3.29173 + 4.83660i) q^{58} +(-8.38521 - 11.5413i) q^{59} +(0.973579 + 0.251377i) q^{60} +(0.696830 + 0.226414i) q^{61} +(0.814966 + 1.05212i) q^{62} +(7.13233 + 5.18194i) q^{63} +(3.82555 + 7.02604i) q^{64} +3.89116i q^{65} +(1.03818 - 2.11729i) q^{66} +0.155688i q^{67} +(-5.67147 + 2.23662i) q^{68} +(-2.30806 - 1.67691i) q^{69} +(3.58783 - 2.77912i) q^{70} +(-14.2895 - 4.64294i) q^{71} +(-1.71044 + 7.57977i) q^{72} +(-7.84500 - 10.7977i) q^{73} +(-10.3428 - 7.03917i) q^{74} +(0.478148 - 0.155360i) q^{75} +(-0.141165 + 0.00868960i) q^{76} +(-4.68546 - 9.55641i) q^{77} +(2.76531 - 0.0850311i) q^{78} +(3.20955 + 9.87796i) q^{79} +(3.50000 + 1.93649i) q^{80} +(-5.49244 + 3.99049i) q^{81} +(11.5133 + 3.35338i) q^{82} +(1.52731 - 4.70059i) q^{83} +(-2.05343 - 2.48902i) q^{84} +(-1.79173 + 2.46611i) q^{85} +(-0.237346 - 0.660656i) q^{86} +2.07985 q^{87} +(6.10453 - 7.12283i) q^{88} +11.9625 q^{89} +(1.31359 + 3.65638i) q^{90} +(7.33964 - 10.1021i) q^{91} +(-7.22240 - 8.75447i) q^{92} +(0.146200 - 0.449957i) q^{93} +(5.49904 + 1.60165i) q^{94} +(-0.0572103 + 0.0415657i) q^{95} +(1.29972 - 2.52965i) q^{96} +(-2.04594 - 6.29675i) q^{97} +(-4.66194 + 0.143351i) q^{98} +(9.02024 - 1.28674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 5 q^{2} - 5 q^{3} - q^{4} + 2 q^{5} - 6 q^{6} + 3 q^{7} + 5 q^{8} + 3 q^{9} + 5 q^{10} + q^{11} - 10 q^{12} + 10 q^{13} - 15 q^{14} - 5 q^{15} + 7 q^{16} - 5 q^{17} + 10 q^{18} + 11 q^{19} + q^{20}+ \cdots + 6 q^{99}+O(q^{100}) \) 8 * q + 5 * q^2 - 5 * q^3 - q^4 + 2 * q^5 - 6 * q^6 + 3 * q^7 + 5 * q^8 + 3 * q^9 + 5 * q^10 + q^11 - 10 * q^12 + 10 * q^13 - 15 * q^14 - 5 * q^15 + 7 * q^16 - 5 * q^17 + 10 * q^18 + 11 * q^19 + q^20 - 16 * q^22 - 18 * q^24 - 2 * q^25 - 3 * q^26 + 10 * q^27 - 11 * q^28 - 5 * q^29 - 4 * q^30 - 10 * q^31 - 11 * q^33 - 14 * q^34 - 8 * q^35 + 9 * q^36 + 20 * q^37 + 15 * q^38 - 3 * q^39 + 5 * q^40 + 10 * q^41 + 4 * q^42 + 34 * q^43 + 8 * q^44 - 8 * q^45 + 25 * q^46 - 25 * q^48 - 23 * q^49 - 5 * q^50 - 9 * q^51 - 5 * q^52 - 7 * q^53 + 26 * q^54 + 9 * q^55 + 15 * q^56 + 5 * q^57 - 12 * q^58 + 5 * q^59 - 10 * q^61 - 39 * q^62 + 23 * q^63 + 11 * q^64 - 2 * q^66 - 30 * q^68 + 15 * q^69 - 5 * q^70 - 90 * q^71 + 30 * q^72 + 5 * q^73 - 5 * q^74 - 5 * q^75 + 18 * q^76 - 14 * q^77 + 21 * q^79 + 28 * q^80 - 10 * q^81 + 38 * q^82 - 19 * q^83 - 10 * q^84 + 35 * q^86 + 18 * q^87 + 47 * q^88 + 20 * q^89 + 5 * q^90 + 10 * q^91 + 11 * q^93 + 15 * q^94 - 11 * q^95 - 39 * q^96 - 44 * q^97 - 50 * q^98 + 6 * q^99

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