LMFDB - Embedded newform 240.2.bk.b.11.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(11,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2, 0]))

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

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

chi := DirichletCharacter("240.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bk (of order $4$, degree $2$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.13
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.468379 - 1.33440i) q^{2} +(1.36262 + 1.06924i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.788576 - 2.31908i) q^{6} +1.05330 q^{7} +(2.39927 + 1.49784i) q^{8} +(0.713439 + 2.91393i) q^{9} +O(q^{10})$	\(q+(-0.468379 - 1.33440i) q^{2} +(1.36262 + 1.06924i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.788576 - 2.31908i) q^{6} +1.05330 q^{7} +(2.39927 + 1.49784i) q^{8} +(0.713439 + 2.91393i) q^{9} +(-1.27476 - 0.612368i) q^{10} +(0.562696 + 0.562696i) q^{11} +(-3.46394 + 0.0339362i) q^{12} +(1.89689 - 1.89689i) q^{13} +(-0.493345 - 1.40552i) q^{14} +(1.71958 - 0.207445i) q^{15} +(0.874950 - 3.90313i) q^{16} -1.69865i q^{17} +(3.55419 - 2.31684i) q^{18} +(2.43710 + 2.43710i) q^{19} +(-0.220074 + 1.98785i) q^{20} +(1.43524 + 1.12624i) q^{21} +(0.487306 - 1.01442i) q^{22} +3.79255i q^{23} +(1.66772 + 4.60638i) q^{24} -1.00000i q^{25} +(-3.41967 - 1.64274i) q^{26} +(-2.14356 + 4.73341i) q^{27} +(-1.64446 + 1.31664i) q^{28} +(-5.46614 - 5.46614i) q^{29} +(-1.08223 - 2.19745i) q^{30} -9.07008i q^{31} +(-5.61815 + 0.660616i) q^{32} +(0.165079 + 1.36840i) q^{33} +(-2.26668 + 0.795614i) q^{34} +(0.744797 - 0.744797i) q^{35} +(-4.75630 - 3.65755i) q^{36} +(1.25930 + 1.25930i) q^{37} +(2.11058 - 4.39355i) q^{38} +(4.61297 - 0.556495i) q^{39} +(2.75567 - 0.637404i) q^{40} -11.6541 q^{41} +(0.830608 - 2.44269i) q^{42} +(-6.90696 + 6.90696i) q^{43} +(-1.58188 - 0.175129i) q^{44} +(2.56494 + 1.55598i) q^{45} +(5.06078 - 1.77635i) q^{46} +7.75065 q^{47} +(5.36562 - 4.38294i) q^{48} -5.89056 q^{49} +(-1.33440 + 0.468379i) q^{50} +(1.81627 - 2.31461i) q^{51} +(-0.590372 + 5.33264i) q^{52} +(-6.77851 + 6.77851i) q^{53} +(7.32025 + 0.643331i) q^{54} +0.795773 q^{55} +(2.52715 + 1.57768i) q^{56} +(0.714978 + 5.92668i) q^{57} +(-4.73378 + 9.85424i) q^{58} +(0.908439 + 0.908439i) q^{59} +(-2.42538 + 2.47337i) q^{60} +(3.04034 - 3.04034i) q^{61} +(-12.1031 + 4.24824i) q^{62} +(0.751467 + 3.06925i) q^{63} +(3.51295 + 7.18743i) q^{64} -2.68261i q^{65} +(1.74867 - 0.861211i) q^{66} +(4.40764 + 4.40764i) q^{67} +(2.12333 + 2.65201i) q^{68} +(-4.05516 + 5.16779i) q^{69} +(-1.34270 - 0.645009i) q^{70} +5.47081i q^{71} +(-2.65287 + 8.05992i) q^{72} -7.69959i q^{73} +(1.09058 - 2.27024i) q^{74} +(1.06924 - 1.36262i) q^{75} +(-6.85130 - 0.758502i) q^{76} +(0.592689 + 0.592689i) q^{77} +(-2.90321 - 5.89489i) q^{78} -12.5927i q^{79} +(-2.14125 - 3.37862i) q^{80} +(-7.98201 + 4.15783i) q^{81} +(5.45855 + 15.5513i) q^{82} +(-1.73800 + 1.73800i) q^{83} +(-3.64857 + 0.0357450i) q^{84} +(-1.20113 - 1.20113i) q^{85} +(12.4517 + 5.98156i) q^{86} +(-1.60361 - 13.2929i) q^{87} +(0.507229 + 2.19289i) q^{88} -5.12144 q^{89} +(0.874938 - 4.15144i) q^{90} +(1.99800 - 1.99800i) q^{91} +(-4.74073 - 5.92109i) q^{92} +(9.69811 - 12.3590i) q^{93} +(-3.63024 - 10.3425i) q^{94} +3.44658 q^{95} +(-8.36173 - 5.10700i) q^{96} -6.76392 q^{97} +(2.75902 + 7.86035i) q^{98} +(-1.23821 + 2.04111i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	$ 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.468379	−	1.33440i	−0.331194	−	0.943563i
$2$	−0.468379	−	1.33440i	−0.331194	−	0.943563i
$3$	1.36262	+	1.06924i	0.786706	+	0.617328i
$3$	1.36262	+	1.06924i	0.786706	+	0.617328i
$4$	−1.56124	+	1.25001i	−0.780621	+	0.625005i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.788576	−	2.31908i	0.321935	−	0.946762i
$7$	1.05330			0.398111			0.199055	−	0.979988i	$-0.436213\pi$
$7$	1.05330			0.398111			0.199055	+	0.979988i	$0.436213\pi$
$8$	2.39927	+	1.49784i	0.848268	+	0.529566i
$9$	0.713439	+	2.91393i	0.237813	+	0.971311i
$10$	−1.27476	−	0.612368i	−0.403114	−	0.193648i
$11$	0.562696	+	0.562696i	0.169659	+	0.169659i	0.786830	−	0.617170i	$-0.211721\pi$
$11$	0.562696	+	0.562696i	0.169659	+	0.169659i	−0.617170	+	0.786830i	$0.711721\pi$
$12$	−3.46394	+	0.0339362i	−0.999952	+	0.00979653i
$13$	1.89689	−	1.89689i	0.526103	−	0.526103i	−0.393305	−	0.919408i	$-0.628668\pi$
$13$	1.89689	−	1.89689i	0.526103	−	0.526103i	0.919408	+	0.393305i	$0.128668\pi$
$14$	−0.493345	−	1.40552i	−0.131852	−	0.375642i
$15$	1.71958	−	0.207445i	0.443994	−	0.0535622i
$16$	0.874950	−	3.90313i	0.218737	−	0.975784i
$17$		−	1.69865i		−	0.411984i	−0.978554	−	0.205992i	$-0.933958\pi$
$17$		−	1.69865i		−	0.411984i	0.978554	−	0.205992i	$-0.0660421\pi$
$18$	3.55419	−	2.31684i	0.837730	−	0.546084i
$19$	2.43710	+	2.43710i	0.559109	+	0.559109i	0.929054	−	0.369945i	$-0.120623\pi$
$19$	2.43710	+	2.43710i	0.559109	+	0.559109i	−0.369945	+	0.929054i	$0.620623\pi$
$20$	−0.220074	+	1.98785i	−0.0492100	+	0.444498i
$21$	1.43524	+	1.12624i	0.313196	+	0.245765i
$22$	0.487306	−	1.01442i	0.103894	−	0.216274i
$23$			3.79255i			0.790802i	0.918509	+	0.395401i	$0.129394\pi$
$23$			3.79255i			0.790802i	−0.918509	+	0.395401i	$0.870606\pi$
$24$	1.66772	+	4.60638i	0.340422	+	0.940273i
$25$		−	1.00000i		−	0.200000i
$26$	−3.41967	−	1.64274i	−0.670653	−	0.322169i
$27$	−2.14356	+	4.73341i	−0.412528	+	0.910945i
$28$	−1.64446	+	1.31664i	−0.310773	+	0.248821i
$29$	−5.46614	−	5.46614i	−1.01504	−	1.01504i	−0.999885	−	0.0151515i	$-0.995177\pi$
$29$	−5.46614	−	5.46614i	−1.01504	−	1.01504i	−0.0151515	−	0.999885i	$-0.504823\pi$
$30$	−1.08223	−	2.19745i	−0.197588	−	0.401197i
$31$		−	9.07008i		−	1.62903i	−0.580140	−	0.814517i	$-0.697002\pi$
$31$		−	9.07008i		−	1.62903i	0.580140	−	0.814517i	$-0.302998\pi$
$32$	−5.61815	+	0.660616i	−0.993158	+	0.116781i
$33$	0.165079	+	1.36840i	0.0287366	+	0.238207i
$34$	−2.26668	+	0.795614i	−0.388732	+	0.136447i
$35$	0.744797	−	0.744797i	0.125894	−	0.125894i
$36$	−4.75630	−	3.65755i	−0.792716	−	0.609591i
$37$	1.25930	+	1.25930i	0.207028	+	0.207028i	0.803003	−	0.595975i	$-0.203234\pi$
$37$	1.25930	+	1.25930i	0.207028	+	0.207028i	−0.595975	+	0.803003i	$0.703234\pi$
$38$	2.11058	−	4.39355i	0.342381	−	0.712728i
$39$	4.61297	−	0.556495i	0.738666	−	0.0891105i
$40$	2.75567	−	0.637404i	0.435710	−	0.100782i
$41$	−11.6541			−1.82007			−0.910034	−	0.414533i	$-0.863945\pi$
$41$	−11.6541			−1.82007			−0.910034	+	0.414533i	$0.863945\pi$
$42$	0.830608	−	2.44269i	0.128166	−	0.376916i
$43$	−6.90696	+	6.90696i	−1.05330	+	1.05330i	−0.0548045	+	0.998497i	$0.517454\pi$
$43$	−6.90696	+	6.90696i	−1.05330	+	1.05330i	−0.998497	+	0.0548045i	$0.982546\pi$
$44$	−1.58188	−	0.175129i	−0.238477	−	0.0264017i
$45$	2.56494	+	1.55598i	0.382359	+	0.231952i
$46$	5.06078	−	1.77635i	0.746171	−	0.261909i
$47$	7.75065			1.13055			0.565274	−	0.824903i	$-0.308770\pi$
$47$	7.75065			1.13055			0.565274	+	0.824903i	$0.308770\pi$
$48$	5.36562	−	4.38294i	0.774460	−	0.632622i
$49$	−5.89056			−0.841508
$50$	−1.33440	+	0.468379i	−0.188713	+	0.0662389i
$51$	1.81627	−	2.31461i	0.254329	−	0.324110i
$52$	−0.590372	+	5.33264i	−0.0818699	+	0.739504i
$53$	−6.77851	+	6.77851i	−0.931101	+	0.931101i	−0.997775	−	0.0666742i	$-0.978761\pi$
$53$	−6.77851	+	6.77851i	−0.931101	+	0.931101i	0.0666742	+	0.997775i	$0.478761\pi$
$54$	7.32025	+	0.643331i	0.996160	+	0.0875463i
$55$	0.795773			0.107302
$56$	2.52715	+	1.57768i	0.337705	+	0.210826i
$57$	0.714978	+	5.92668i	0.0947011	+	0.785008i
$58$	−4.73378	+	9.85424i	−0.621576	+	1.29393i
$59$	0.908439	+	0.908439i	0.118269	+	0.118269i	0.763764	−	0.645495i	$-0.223349\pi$
$59$	0.908439	+	0.908439i	0.118269	+	0.118269i	−0.645495	+	0.763764i	$0.723349\pi$
$60$	−2.42538	+	2.47337i	−0.313115	+	0.319311i
$61$	3.04034	−	3.04034i	0.389276	−	0.389276i	−0.485153	−	0.874429i	$-0.661236\pi$
$61$	3.04034	−	3.04034i	0.389276	−	0.389276i	0.874429	+	0.485153i	$0.161236\pi$
$62$	−12.1031	+	4.24824i	−1.53710	+	0.539527i
$63$	0.751467	+	3.06925i	0.0946759	+	0.386689i
$64$	3.51295	+	7.18743i	0.439119	+	0.898429i
$65$		−	2.68261i		−	0.332737i
$66$	1.74867	−	0.861211i	0.215246	−	0.106008i
$67$	4.40764	+	4.40764i	0.538479	+	0.538479i	0.923082	−	0.384603i	$-0.125662\pi$
$67$	4.40764	+	4.40764i	0.538479	+	0.538479i	−0.384603	+	0.923082i	$0.625662\pi$
$68$	2.12333	+	2.65201i	0.257492	+	0.321603i
$69$	−4.05516	+	5.16779i	−0.488184	+	0.622129i
$70$	−1.34270	−	0.645009i	−0.160484	−	0.0770933i
$71$			5.47081i			0.649266i	0.945840	+	0.324633i	$0.105241\pi$
$71$			5.47081i			0.649266i	−0.945840	+	0.324633i	$0.894759\pi$
$72$	−2.65287	+	8.05992i	−0.312644	+	0.949870i
$73$		−	7.69959i		−	0.901169i	−0.892734	−	0.450584i	$-0.851216\pi$
$73$		−	7.69959i		−	0.901169i	0.892734	−	0.450584i	$-0.148784\pi$
$74$	1.09058	−	2.27024i	0.126777	−	0.263910i
$75$	1.06924	−	1.36262i	0.123466	−	0.157341i
$76$	−6.85130	−	0.758502i	−0.785899	−	0.0870062i
$77$	0.592689	+	0.592689i	0.0675432	+	0.0675432i
$78$	−2.90321	−	5.89489i	−0.328723	−	0.667465i
$79$		−	12.5927i		−	1.41679i	−0.705814	−	0.708397i	$-0.749419\pi$
$79$		−	12.5927i		−	1.41679i	0.705814	−	0.708397i	$-0.250581\pi$
$80$	−2.14125	−	3.37862i	−0.239399	−	0.377741i
$81$	−7.98201	+	4.15783i	−0.886890	+	0.461981i
$82$	5.45855	+	15.5513i	0.602796	+	1.71735i
$83$	−1.73800	+	1.73800i	−0.190770	+	0.190770i	−0.796029	−	0.605259i	$-0.793070\pi$
$83$	−1.73800	+	1.73800i	−0.190770	+	0.190770i	0.605259	+	0.796029i	$0.293070\pi$
$84$	−3.64857	+	0.0357450i	−0.398091	+	0.00390010i
$85$	−1.20113	−	1.20113i	−0.130281	−	0.130281i
$86$	12.4517	+	5.98156i	1.34270	+	0.645009i
$87$	−1.60361	−	13.2929i	−0.171925	−	1.42515i
$88$	0.507229	+	2.19289i	0.0540707	+	0.233762i
$89$	−5.12144			−0.542871			−0.271436	−	0.962457i	$-0.587498\pi$
$89$	−5.12144			−0.542871			−0.271436	+	0.962457i	$0.587498\pi$
$90$	0.874938	−	4.15144i	0.0922266	−	0.437601i
$91$	1.99800	−	1.99800i	0.209447	−	0.209447i
$92$	−4.74073	−	5.92109i	−0.494255	−	0.617317i
$93$	9.69811	−	12.3590i	1.00565	−	1.28157i
$94$	−3.63024	−	10.3425i	−0.374431	−	1.06674i
$95$	3.44658			0.353612
$96$	−8.36173	−	5.10700i	−0.853416	−	0.521231i
$97$	−6.76392			−0.686772			−0.343386	−	0.939194i	$-0.611574\pi$
$97$	−6.76392			−0.686772			−0.343386	+	0.939194i	$0.611574\pi$
$98$	2.75902	+	7.86035i	0.278703	+	0.794015i
$99$	−1.23821	+	2.04111i	−0.124445	+	0.205139i
$100$	1.25001	+	1.56124i	0.125001	+	0.156124i
$101$	10.5556	−	10.5556i	1.05032	−	1.05032i	0.0516563	−	0.998665i	$-0.483550\pi$
$101$	10.5556	−	10.5556i	1.05032	−	1.05032i	0.998665	−	0.0516563i	$-0.0164500\pi$
$102$	−3.93932	−	1.33952i	−0.390051	−	0.132632i
$103$	−17.0299			−1.67801			−0.839004	−	0.544126i	$-0.816861\pi$
$103$	−17.0299			−1.67801			−0.839004	+	0.544126i	$0.816861\pi$
$104$	7.39239	−	1.70991i	0.724883	−	0.167670i
$105$	1.81124	−	0.218503i	0.176759	−	0.0213237i
$106$	12.2202	+	5.87033i	1.18693	+	0.570177i
$107$	12.9830	+	12.9830i	1.25511	+	1.25511i	0.953399	+	0.301713i	$0.0975583\pi$
$107$	12.9830	+	12.9830i	1.25511	+	1.25511i	0.301713	+	0.953399i	$0.402442\pi$
$108$	−2.57020	−	10.0695i	−0.247317	−	0.968935i
$109$	−4.39564	+	4.39564i	−0.421026	+	0.421026i	−0.885557	−	0.464531i	$-0.846223\pi$
$109$	−4.39564	+	4.39564i	−0.421026	+	0.421026i	0.464531	+	0.885557i	$0.346223\pi$
$110$	−0.372723	−	1.06188i	−0.0355378	−	0.101246i
$111$	0.369444	+	3.06244i	0.0350661	+	0.290674i
$112$	0.921586	−	4.11118i	0.0870817	−	0.388470i
$113$		−	13.8967i		−	1.30729i	−0.756801	−	0.653646i	$-0.773239\pi$
$113$		−	13.8967i		−	1.30729i	0.756801	−	0.653646i	$-0.226761\pi$
$114$	7.57368	−	3.73000i	0.709340	−	0.349347i
$115$	2.68174	+	2.68174i	0.250074	+	0.250074i
$116$	15.3667	+	1.70123i	1.42676	+	0.157956i
$117$	6.88073	+	4.17410i	0.636124	+	0.385895i
$118$	0.786726	−	1.63771i	0.0724240	−	0.150764i
$119$		−	1.78919i		−	0.164015i
$120$	4.43646	+	2.07794i	0.404991	+	0.189689i
$121$		−	10.3667i		−	0.942431i
$122$	−5.48106	−	2.63300i	−0.496232	−	0.238380i
$123$	−15.8801	−	12.4611i	−1.43186	−	1.12358i
$124$	11.3377	+	14.1606i	1.01815	+	1.27166i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	3.74363	−	2.44033i	0.333509	−	0.217402i
$127$		−	7.70489i		−	0.683699i	−0.939755	−	0.341849i	$-0.888947\pi$
$127$		−	7.70489i		−	0.683699i	0.939755	−	0.341849i	$-0.111053\pi$
$128$	7.94551	−	8.05412i	0.702290	−	0.711891i
$129$	−16.7967	+	2.02631i	−1.47887	+	0.178407i
$130$	−3.57967	+	1.25648i	−0.313958	+	0.110200i
$131$	5.20937	−	5.20937i	0.455145	−	0.455145i	−0.441913	−	0.897058i	$-0.645700\pi$
$131$	5.20937	−	5.20937i	0.455145	−	0.455145i	0.897058	+	0.441913i	$0.145700\pi$
$132$	−1.96824	−	1.93005i	−0.171313	−	0.167989i
$133$	2.56700	+	2.56700i	0.222587	+	0.222587i
$134$	3.81710	−	7.94600i	0.329747	−	0.686430i
$135$	1.83130	+	4.86275i	0.157613	+	0.418519i
$136$	2.54431	−	4.07552i	0.218173	−	0.349473i
$137$	20.1712			1.72334			0.861672	−	0.507466i	$-0.169418\pi$
$137$	20.1712			1.72334			0.861672	+	0.507466i	$0.169418\pi$
$138$	8.79525	+	2.99072i	0.748701	+	0.254587i
$139$	5.81652	−	5.81652i	0.493351	−	0.493351i	−0.416010	−	0.909360i	$-0.636572\pi$
$139$	5.81652	−	5.81652i	0.493351	−	0.493351i	0.909360	+	0.416010i	$0.136572\pi$
$140$	−0.231804	+	2.09381i	−0.0195910	+	0.176959i
$141$	10.5611	+	8.28732i	0.889409	+	0.697918i
$142$	7.30025	−	2.56242i	0.612623	−	0.215033i
$143$	2.13475			0.178516
$144$	11.9977	−	0.235105i	0.999808	−	0.0195921i
$145$	−7.73029			−0.641966
$146$	−10.2743	+	3.60633i	−0.850309	+	0.298462i
$147$	−8.02656	−	6.29843i	−0.662019	−	0.519486i
$148$	−3.54021	−	0.391934i	−0.291004	−	0.0322168i
$149$	−0.935992	+	0.935992i	−0.0766795	+	0.0766795i	−0.744406	−	0.667727i	$-0.767267\pi$
$149$	−0.935992	+	0.935992i	−0.0766795	+	0.0766795i	0.667727	+	0.744406i	$0.267267\pi$
$150$	−2.31908	−	0.788576i	−0.189352	−	0.0643869i
$151$	−10.6218			−0.864389			−0.432195	−	0.901780i	$-0.642261\pi$
$151$	−10.6218			−0.864389			−0.432195	+	0.901780i	$0.642261\pi$
$152$	2.19686	+	9.49764i	0.178189	+	0.770360i
$153$	4.94976	−	1.21189i	0.400164	−	0.0979752i
$154$	0.513280	−	1.06849i	0.0413613	−	0.0861011i
$155$	−6.41351	−	6.41351i	−0.515146	−	0.515146i
$156$	−6.50634	+	6.63508i	−0.520924	+	0.531232i
$157$	−1.26925	+	1.26925i	−0.101297	+	0.101297i	−0.755939	−	0.654642i	$-0.772819\pi$
$157$	−1.26925	+	1.26925i	−0.101297	+	0.101297i	0.654642	+	0.755939i	$0.272819\pi$
$158$	−16.8037	+	5.89818i	−1.33683	+	0.469234i
$159$	−16.4844	+	1.98863i	−1.30730	+	0.157708i
$160$	−3.50550	+	4.43976i	−0.277134	+	0.350994i
$161$			3.99470i			0.314827i
$162$	9.28681	+	8.70374i	0.729641	+	0.683831i
$163$	3.55453	+	3.55453i	0.278412	+	0.278412i	0.832475	−	0.554063i	$-0.186923\pi$
$163$	3.55453	+	3.55453i	0.278412	+	0.278412i	−0.554063	+	0.832475i	$0.686923\pi$
$164$	18.1949	−	14.5678i	1.42078	−	1.13755i
$165$	1.08433	+	0.850874i	0.0844151	+	0.0662405i
$166$	3.13323	+	1.50514i	0.243185	+	0.116822i
$167$		−	3.54199i		−	0.274087i	−0.990565	−	0.137044i	$-0.956240\pi$
$167$		−	3.54199i		−	0.274087i	0.990565	−	0.137044i	$-0.0437601\pi$
$168$	1.75661	+	4.85190i	0.135526	+	0.374333i
$169$			5.80361i			0.446431i
$170$	−1.04020	+	2.16537i	−0.0797798	+	0.166076i
$171$	−5.36282	+	8.84027i	−0.410105	+	0.676033i
$172$	2.14966	−	19.4172i	0.163910	−	1.48055i
$173$	3.86212	+	3.86212i	0.293632	+	0.293632i	0.838513	−	0.544881i	$-0.183425\pi$
$173$	3.86212	+	3.86212i	0.293632	+	0.293632i	−0.544881	+	0.838513i	$0.683425\pi$
$174$	−16.9869	+	8.36597i	−1.28777	+	0.634223i
$175$		−	1.05330i		−	0.0796221i
$176$	2.68861	−	1.70395i	0.202662	−	0.128440i
$177$	0.266511	+	2.20920i	0.0200322	+	0.166053i
$178$	2.39877	+	6.83404i	0.179796	+	0.512233i
$179$	−16.2183	+	16.2183i	−1.21221	+	1.21221i	−0.241916	+	0.970297i	$0.577776\pi$
$179$	−16.2183	+	16.2183i	−1.21221	+	1.21221i	−0.970297	+	0.241916i	$0.922224\pi$
$180$	−5.94949	+	0.776934i	−0.443448	+	0.0579092i
$181$	12.5883	+	12.5883i	0.935681	+	0.935681i	0.998053	−	0.0623718i	$-0.0198665\pi$
$181$	12.5883	+	12.5883i	0.935681	+	0.935681i	−0.0623718	+	0.998053i	$0.519866\pi$
$182$	−3.60195	−	1.73031i	−0.266994	−	0.128259i
$183$	7.39368	−	0.891952i	0.546557	−	0.0659350i
$184$	−5.68064	+	9.09934i	−0.418782	+	0.670812i
$185$	1.78092			0.130936
$186$	−21.0343	−	7.15244i	−1.54231	−	0.524443i
$187$	0.955825	−	0.955825i	0.0698969	−	0.0698969i
$188$	−12.1006	+	9.68838i	−0.882529	+	0.706598i
$189$	−2.25781	+	4.98571i	−0.164232	+	0.362657i
$190$	−1.61431	−	4.59911i	−0.117114	−	0.333655i
$191$	−20.5110			−1.48412			−0.742060	−	0.670333i	$-0.766151\pi$
$191$	−20.5110			−1.48412			−0.742060	+	0.670333i	$0.766151\pi$
$192$	−2.89831	+	13.5499i	−0.209168	+	0.977880i
$193$	15.2783			1.09976			0.549878	−	0.835245i	$-0.314674\pi$
$193$	15.2783			1.09976			0.549878	+	0.835245i	$0.314674\pi$
$194$	3.16808	+	9.02577i	0.227455	+	0.648012i
$195$	2.86836	−	3.65536i	0.205408	−	0.261766i
$196$	9.19658	−	7.36325i	0.656899	−	0.525947i
$197$	7.06703	−	7.06703i	0.503505	−	0.503505i	−0.409020	−	0.912525i	$-0.634129\pi$
$197$	7.06703	−	7.06703i	0.503505	−	0.503505i	0.912525	+	0.409020i	$0.134129\pi$
$198$	3.30360	+	0.696252i	0.234777	+	0.0494805i
$199$	7.04107			0.499129			0.249564	−	0.968358i	$-0.419713\pi$
$199$	7.04107			0.499129			0.249564	+	0.968358i	$0.419713\pi$
$200$	1.49784	−	2.39927i	0.105913	−	0.169654i
$201$	1.29308	+	10.7188i	0.0912067	+	0.756042i
$202$	−19.0294	−	9.14135i	−1.33890	−	0.643183i
$203$	−5.75749	−	5.75749i	−0.404097	−	0.404097i
$204$	0.0576458	+	5.88402i	0.00403601	+	0.411964i
$205$	−8.24071	+	8.24071i	−0.575556	+	0.575556i
$206$	7.97646	+	22.7247i	0.555746	+	1.58331i
$207$	−11.0512	+	2.70576i	−0.768115	+	0.188063i
$208$	−5.74414	−	9.06351i	−0.398284	−	0.628441i
$209$			2.74269i			0.189716i
$210$	−1.13992	−	2.31457i	−0.0786617	−	0.159721i
$211$	8.80008	+	8.80008i	0.605823	+	0.605823i	0.941852	−	0.336029i	$-0.109084\pi$
$211$	8.80008	+	8.80008i	0.605823	+	0.605823i	−0.336029	+	0.941852i	$0.609084\pi$
$212$	2.10969	−	19.0561i	0.144894	−	1.30878i
$213$	−5.84963	+	7.45461i	−0.400810	+	0.510782i
$214$	11.2435	−	23.4054i	0.768591	−	1.59996i
$215$			9.76792i			0.666166i
$216$	−12.2329	+	8.14600i	−0.832340	+	0.554265i
$217$		−	9.55353i		−	0.648536i
$218$	7.92436	+	3.80671i	0.536705	+	0.257823i
$219$	8.23273	−	10.4916i	0.556316	−	0.708955i
$220$	−1.24239	+	0.994724i	−0.0837621	+	0.0670643i
$221$	−3.22216	−	3.22216i	−0.216746	−	0.216746i
$222$	3.91348	−	1.92737i	0.262656	−	0.129357i
$223$			7.13615i			0.477872i	0.971035	+	0.238936i	$0.0767986\pi$
$223$			7.13615i			0.477872i	−0.971035	+	0.238936i	$0.923201\pi$
$224$	−5.91760	+	0.695828i	−0.395387	+	0.0464919i
$225$	2.91393	−	0.713439i	0.194262	−	0.0475626i
$226$	−18.5437	+	6.50893i	−1.23351	+	0.432967i
$227$	4.09406	−	4.09406i	0.271732	−	0.271732i	−0.558065	−	0.829797i	$-0.688456\pi$
$227$	4.09406	−	4.09406i	0.271732	−	0.271732i	0.829797	+	0.558065i	$0.188456\pi$
$228$	−8.52467	−	8.35926i	−0.564560	−	0.553605i
$229$	2.75126	+	2.75126i	0.181808	+	0.181808i	0.792143	−	0.610335i	$-0.208965\pi$
$229$	2.75126	+	2.75126i	0.181808	+	0.181808i	−0.610335	+	0.792143i	$0.708965\pi$
$230$	2.32244	−	4.83458i	0.153137	−	0.318783i
$231$	0.173878	+	1.44133i	0.0114404	+	0.0948329i
$232$	−4.92732	−	21.3021i	−0.323494	−	1.39855i
$233$	21.9637			1.43889			0.719446	−	0.694549i	$-0.244396\pi$
$233$	21.9637			1.43889			0.719446	+	0.694549i	$0.244396\pi$
$234$	2.34712	−	11.1367i	0.153436	−	0.728029i
$235$	5.48053	−	5.48053i	0.357511	−	0.357511i
$236$	−2.55385	−	0.282735i	−0.166242	−	0.0184045i
$237$	13.4647	−	17.1591i	0.874626	−	1.11460i
$238$	−2.38750	+	0.838021i	−0.154759	+	0.0543209i
$239$	8.38950			0.542672			0.271336	−	0.962485i	$-0.412535\pi$
$239$	8.38950			0.542672			0.271336	+	0.962485i	$0.412535\pi$
$240$	0.694861	−	6.89327i	0.0448531	−	0.444959i
$241$	16.1062			1.03749			0.518745	−	0.854929i	$-0.326400\pi$
$241$	16.1062			1.03749			0.518745	+	0.854929i	$0.326400\pi$
$242$	−13.8334	+	4.85557i	−0.889243	+	0.312128i
$243$	−15.3221	−	2.86919i	−0.982915	−	0.184058i
$244$	−0.946250	+	8.54717i	−0.0605775	+	0.547176i
$245$	−4.16525	+	4.16525i	−0.266108	+	0.266108i
$246$	−9.19016	+	27.0269i	−0.585943	+	1.72317i
$247$	9.24583			0.588298
$248$	13.5855	−	21.7615i	0.862682	−	1.38186i
$249$	−4.22656	+	0.509880i	−0.267848	+	0.0323123i
$250$	−0.612368	+	1.27476i	−0.0387296	+	0.0806227i
$251$	−2.96030	−	2.96030i	−0.186852	−	0.186852i	0.607481	−	0.794334i	$-0.292180\pi$
$251$	−2.96030	−	2.96030i	−0.186852	−	0.186852i	−0.794334	+	0.607481i	$0.792180\pi$
$252$	−5.00981	−	3.85250i	−0.315589	−	0.242685i
$253$	−2.13406	+	2.13406i	−0.134167	+	0.134167i
$254$	−10.2814	+	3.60881i	−0.645113	+	0.226437i
$255$	−0.352378	−	2.92097i	−0.0220668	−	0.182919i
$256$	−14.4689	−	6.83009i	−0.904308	−	0.426881i
$257$			15.4344i			0.962768i	0.876510	+	0.481384i	$0.159866\pi$
$257$			15.4344i			0.962768i	−0.876510	+	0.481384i	$0.840134\pi$
$258$	10.5712	+	21.4645i	0.658131	+	1.33632i
$259$	1.32642	+	1.32642i	0.0824200	+	0.0824200i
$260$	3.35329	+	4.18820i	0.207962	+	0.259741i
$261$	12.0282	−	19.8277i	0.744527	−	1.22731i
$262$	−9.39135	−	4.51142i	−0.580199	−	0.278716i
$263$			9.33469i			0.575602i	0.957690	+	0.287801i	$0.0929241\pi$
$263$			9.33469i			0.575602i	−0.957690	+	0.287801i	$0.907076\pi$
$264$	−1.65357	+	3.53041i	−0.101770	+	0.217282i
$265$			9.58627i			0.588880i
$266$	2.22307	−	4.62774i	0.136305	−	0.283745i
$267$	−6.97855	−	5.47606i	−0.427080	−	0.335129i
$268$	−12.3910	−	1.37180i	−0.756900	−	0.0837958i
$269$	5.72888	+	5.72888i	0.349296	+	0.349296i	0.859847	−	0.510551i	$-0.170559\pi$
$269$	5.72888	+	5.72888i	0.349296	+	0.349296i	−0.510551	+	0.859847i	$0.670559\pi$
$270$	5.63111	−	4.72130i	0.342698	−	0.287329i
$271$			17.4361i			1.05917i	0.848258	+	0.529583i	$0.177651\pi$
$271$			17.4361i			1.05917i	−0.848258	+	0.529583i	$0.822349\pi$
$272$	−6.63007	−	1.48624i	−0.402007	−	0.0901163i
$273$	4.85885	−	0.586157i	0.294071	−	0.0354758i
$274$	−9.44779	−	26.9165i	−0.570762	−	1.62608i
$275$	0.562696	−	0.562696i	0.0339319	−	0.0339319i
$276$	−0.128705	−	13.1372i	−0.00774711	−	0.790764i
$277$	−15.5814	−	15.5814i	−0.936195	−	0.936195i	0.0618883	−	0.998083i	$-0.480288\pi$
$277$	−15.5814	−	15.5814i	−0.936195	−	0.936195i	−0.998083	+	0.0618883i	$0.980288\pi$
$278$	−10.4859	−	5.03722i	−0.628902	−	0.302112i
$279$	26.4296	−	6.47095i	1.58230	−	0.387406i
$280$	2.90255	−	0.671379i	0.173461	−	0.0401225i
$281$	−28.5603			−1.70376			−0.851882	−	0.523734i	$-0.824539\pi$
$281$	−28.5603			−1.70376			−0.851882	+	0.523734i	$0.824539\pi$
$282$	6.11197	−	17.9744i	0.363963	−	1.07036i
$283$	−7.06829	+	7.06829i	−0.420166	+	0.420166i	−0.885261	−	0.465095i	$-0.846020\pi$
$283$	−7.06829	+	7.06829i	−0.420166	+	0.420166i	0.465095	+	0.885261i	$0.346020\pi$
$284$	−6.83857	−	8.54126i	−0.405794	−	0.506830i
$285$	4.69636	+	3.68523i	0.278189	+	0.218294i
$286$	−0.999871	−	2.84860i	−0.0591236	−	0.168441i
$287$	−12.2753			−0.724589
$288$	−5.93320	−	15.8996i	−0.349617	−	0.936893i
$289$	14.1146			0.830269
$290$	3.62071	+	10.3153i	0.212615	+	0.605735i
$291$	−9.21662	−	7.23227i	−0.540288	−	0.423963i
$292$	9.62456	+	12.0209i	0.563235	+	0.703471i
$293$	−16.6326	+	16.6326i	−0.971689	+	0.971689i	−0.999610	−	0.0279210i	$-0.991111\pi$
$293$	−16.6326	+	16.6326i	−0.971689	+	0.971689i	0.0279210	+	0.999610i	$0.491111\pi$
$294$	−4.64515	+	13.6607i	−0.270911	+	0.796708i
$295$	1.28473			0.0747997
$296$	1.13517	+	4.90763i	0.0659802	+	0.285250i
$297$	−3.86964	+	1.45730i	−0.224539	+	0.0845610i
$298$	1.68739	+	0.810588i	0.0977477	+	0.0469561i
$299$	7.19406	+	7.19406i	0.416043	+	0.416043i
$300$	0.0339362	+	3.46394i	0.00195931	+	0.199990i
$301$	−7.27511	+	7.27511i	−0.419330	+	0.419330i
$302$	4.97503	+	14.1737i	0.286281	+	0.815606i
$303$	25.6697	−	3.09672i	1.47469	−	0.177902i
$304$	11.6447	−	7.37999i	0.667868	−	0.423272i
$305$		−	4.29969i		−	0.246200i
$306$	−3.93550	−	6.03733i	−0.224978	−	0.345131i
$307$	13.6581	+	13.6581i	0.779509	+	0.779509i	0.979747	−	0.200238i	$-0.0641715\pi$
$307$	13.6581	+	13.6581i	0.779509	+	0.779509i	−0.200238	+	0.979747i	$0.564172\pi$
$308$	−1.66620	−	0.184463i	−0.0949404	−	0.0105108i
$309$	−23.2052	−	18.2091i	−1.32010	−	1.03588i
$310$	−5.55423	+	11.5621i	−0.315459	+	0.656686i
$311$		−	27.8968i		−	1.58188i	−0.611891	−	0.790942i	$-0.709591\pi$
$311$		−	27.8968i		−	1.58188i	0.611891	−	0.790942i	$-0.290409\pi$
$312$	11.9013	+	5.57431i	0.673777	+	0.315583i
$313$			14.9837i			0.846926i	0.905913	+	0.423463i	$0.139186\pi$
$313$			14.9837i			0.846926i	−0.905913	+	0.423463i	$0.860814\pi$
$314$	2.28818	+	1.09920i	0.129130	+	0.0620314i
$315$	2.70165	+	1.63892i	0.152221	+	0.0923427i
$316$	15.7411	+	19.6603i	0.885504	+	1.10598i
$317$	−3.86121	−	3.86121i	−0.216867	−	0.216867i	0.590310	−	0.807177i	$-0.299006\pi$
$317$	−3.86121	−	3.86121i	−0.216867	−	0.216867i	−0.807177	+	0.590310i	$0.799006\pi$
$318$	10.3746	+	21.0653i	0.581777	+	1.18128i
$319$		−	6.15155i		−	0.344421i
$320$	7.56631	+	2.59825i	0.422970	+	0.145247i
$321$	3.80884	+	31.5727i	0.212589	+	1.76222i
$322$	5.33053	−	1.87104i	0.297059	−	0.104269i
$323$	4.13979	−	4.13979i	0.230344	−	0.230344i
$324$	7.26451	−	16.4690i	0.403584	−	0.914943i
$325$	−1.89689	−	1.89689i	−0.105221	−	0.105221i
$326$	3.07829	−	6.40803i	0.170491	−	0.354908i
$327$	−10.6896	+	1.28956i	−0.591134	+	0.0713127i
$328$	−27.9613	−	17.4560i	−1.54391	−	0.963847i
$329$	8.16377			0.450083
$330$	0.627527	−	1.84546i	0.0345442	−	0.101589i
$331$	−15.8003	+	15.8003i	−0.868461	+	0.868461i	−0.992302	−	0.123841i	$-0.960479\pi$
$331$	−15.8003	+	15.8003i	−0.868461	+	0.868461i	0.123841	+	0.992302i	$0.460479\pi$
$332$	0.540920	−	4.88595i	0.0296868	−	0.268151i
$333$	−2.77109	+	4.56796i	−0.151855	+	0.250322i
$334$	−4.72643	+	1.65899i	−0.258619	+	0.0907762i
$335$	6.23334			0.340564
$336$	5.65161	−	4.61655i	0.308321	−	0.251854i
$337$	18.5465			1.01029			0.505147	−	0.863033i	$-0.331438\pi$
$337$	18.5465			1.01029			0.505147	+	0.863033i	$0.331438\pi$
$338$	7.74433	−	2.71829i	0.421236	−	0.147856i
$339$	14.8589	−	18.9358i	0.807027	−	1.02845i
$340$	3.37668	+	0.373829i	0.183126	+	0.0202737i
$341$	5.10370	−	5.10370i	0.276381	−	0.276381i
$342$	14.3083	+	3.01555i	0.773704	+	0.163062i
$343$	−13.5776			−0.733124
$344$	−26.9172	+	6.22611i	−1.45128	+	0.335689i
$345$	0.786748	+	6.52161i	0.0423571	+	0.351112i
$346$	3.34468	−	6.96256i	0.179811	−	0.374309i
$347$	5.42722	+	5.42722i	0.291348	+	0.291348i	0.837613	−	0.546265i	$-0.183951\pi$
$347$	5.42722	+	5.42722i	0.291348	+	0.291348i	−0.546265	+	0.837613i	$0.683951\pi$
$348$	19.1199	+	18.7489i	1.02493	+	1.00504i
$349$	−20.2025	+	20.2025i	−1.08141	+	1.08141i	−0.0850368	+	0.996378i	$0.527101\pi$
$349$	−20.2025	+	20.2025i	−1.08141	+	1.08141i	−0.996378	+	0.0850368i	$0.972899\pi$
$350$	−1.40552	+	0.493345i	−0.0751284	+	0.0263704i
$351$	4.91266	+	13.0449i	0.262219	+	0.696283i
$352$	−3.53304	−	2.78958i	−0.188311	−	0.148685i
$353$		−	17.5628i		−	0.934771i	−0.884054	−	0.467385i	$-0.845196\pi$
$353$		−	17.5628i		−	0.934771i	0.884054	−	0.467385i	$-0.154804\pi$
$354$	2.82312	−	1.39037i	0.150047	−	0.0738975i
$355$	3.86845	+	3.86845i	0.205316	+	0.205316i
$356$	7.99580	−	6.40185i	0.423776	−	0.339297i
$357$	1.91308	−	2.43798i	0.101251	−	0.129032i
$358$	29.2380	+	14.0454i	1.54528	+	0.742321i
$359$			1.82368i			0.0962504i	0.998841	+	0.0481252i	$0.0153246\pi$
$359$			1.82368i			0.0962504i	−0.998841	+	0.0481252i	$0.984675\pi$
$360$	3.82336	+	7.57509i	0.201509	+	0.399242i
$361$		−	7.12108i		−	0.374793i
$362$	10.9017	−	22.6939i	0.572982	−	1.19277i
$363$	11.0846	−	14.1259i	0.581789	−	0.741417i
$364$	−0.621840	+	5.61688i	−0.0325933	+	0.294404i
$365$	−5.44443	−	5.44443i	−0.284975	−	0.284975i
$366$	−4.65327	−	9.44835i	−0.243230	−	0.493873i
$367$			12.8599i			0.671282i	0.941990	+	0.335641i	$0.108953\pi$
$367$			12.8599i			0.671282i	−0.941990	+	0.335641i	$0.891047\pi$
$368$	14.8028	+	3.31829i	0.771652	+	0.172978i
$369$	−8.31451	−	33.9593i	−0.432836	−	1.76785i
$370$	−0.834147	−	2.37646i	−0.0433652	−	0.123546i
$371$	−7.13982	+	7.13982i	−0.370681	+	0.370681i
$372$	0.307804	+	31.4182i	0.0159589	+	1.62896i
$373$	−0.776365	−	0.776365i	−0.0401986	−	0.0401986i	0.686722	−	0.726920i	$-0.259049\pi$
$373$	−0.776365	−	0.776365i	−0.0401986	−	0.0401986i	−0.726920	+	0.686722i	$0.759049\pi$
$374$	−1.72314	−	0.827763i	−0.0891015	−	0.0428026i
$375$	−0.207445	−	1.71958i	−0.0107124	−	0.0887989i
$376$	18.5959	+	11.6092i	0.959008	+	0.598700i
$377$	−20.7373			−1.06803
$378$	7.71044	+	0.677622i	0.396582	+	0.0348531i
$379$	7.30192	−	7.30192i	0.375074	−	0.375074i	−0.494247	−	0.869321i	$-0.664556\pi$
$379$	7.30192	−	7.30192i	0.375074	−	0.375074i	0.869321	+	0.494247i	$0.164556\pi$
$380$	−5.38095	+	4.30826i	−0.276037	+	0.221009i
$381$	8.23840	−	10.4988i	0.422066	−	0.537870i
$382$	9.60691	+	27.3698i	0.491532	+	1.40036i
$383$	20.6284			1.05406			0.527030	−	0.849846i	$-0.323305\pi$
$383$	20.6284			1.05406			0.527030	+	0.849846i	$0.323305\pi$
$384$	19.4385	−	2.47899i	0.991966	−	0.126505i
$385$	0.838188			0.0427180
$386$	−7.15604	−	20.3874i	−0.364233	−	1.03769i
$387$	−25.0541	−	15.1987i	−1.27357	−	0.772594i
$388$	10.5601	−	8.45497i	0.536109	−	0.429236i
$389$	23.2975	−	23.2975i	1.18123	−	1.18123i	0.201806	−	0.979426i	$-0.435319\pi$
$389$	23.2975	−	23.2975i	1.18123	−	1.18123i	0.979426	−	0.201806i	$-0.0646810\pi$
$390$	−6.22119	−	2.11544i	−0.315022	−	0.107120i
$391$	6.44223			0.325798
$392$	−14.1330	−	8.82311i	−0.713825	−	0.445634i
$393$	12.6685	−	1.52829i	0.639039	−	0.0770918i
$394$	−12.7403	−	6.12019i	−0.641847	−	0.308331i
$395$	−8.90442	−	8.90442i	−0.448030	−	0.448030i
$396$	−0.618262	−	4.73444i	−0.0310689	−	0.237914i
$397$	−13.1882	+	13.1882i	−0.661895	+	0.661895i	−0.955826	−	0.293932i	$-0.905036\pi$
$397$	−13.1882	+	13.1882i	−0.661895	+	0.661895i	0.293932	+	0.955826i	$0.405036\pi$
$398$	−3.29789	−	9.39560i	−0.165309	−	0.470959i
$399$	0.753087	+	6.24259i	0.0377015	+	0.312520i
$400$	−3.90313	−	0.874950i	−0.195157	−	0.0437475i
$401$		−	7.82917i		−	0.390970i	−0.980707	−	0.195485i	$-0.937372\pi$
$401$		−	7.82917i		−	0.390970i	0.980707	−	0.195485i	$-0.0626281\pi$
$402$	13.6974	−	6.74593i	0.683166	−	0.336456i
$403$	−17.2049	−	17.2049i	−0.857039	−	0.857039i
$404$	−3.28523	+	29.6744i	−0.163446	+	1.47636i
$405$	−2.70410	+	8.58416i	−0.134368	+	0.426550i
$406$	−4.98610	+	10.3795i	−0.247456	+	0.515125i
$407$			1.41721i			0.0702484i
$408$	7.82463	−	2.83288i	0.387377	−	0.140248i
$409$		−	2.35956i		−	0.116673i	−0.998297	−	0.0583364i	$-0.981420\pi$
$409$		−	2.35956i		−	0.116673i	0.998297	−	0.0583364i	$-0.0185796\pi$
$410$	14.8562	+	7.13662i	0.733694	+	0.352452i
$411$	27.4856	+	21.5679i	1.35577	+	1.06387i
$412$	26.5878	−	21.2876i	1.30989	−	1.04876i
$413$	0.956861	+	0.956861i	0.0470840	+	0.0470840i
$414$	8.78674	+	13.4795i	0.431845	+	0.662479i
$415$			2.45790i			0.120654i
$416$	−9.40390	+	11.9101i	−0.461064	+	0.583942i
$417$	14.1449	−	1.70640i	0.692681	−	0.0835630i
$418$	3.65985	−	1.28462i	0.179009	−	0.0628329i
$419$	17.8346	−	17.8346i	0.871277	−	0.871277i	−0.121335	−	0.992612i	$-0.538717\pi$
$419$	17.8346	−	17.8346i	0.871277	−	0.871277i	0.992612	+	0.121335i	$0.0387174\pi$
$420$	−2.55465	+	2.60520i	−0.124654	+	0.127121i
$421$	−20.2623	−	20.2623i	−0.987526	−	0.987526i	0.0123969	−	0.999923i	$-0.496054\pi$
$421$	−20.2623	−	20.2623i	−0.987526	−	0.987526i	−0.999923	+	0.0123969i	$0.996054\pi$
$422$	7.62105	−	15.8646i	0.370987	−	0.772277i
$423$	5.52962	+	22.5849i	0.268859	+	1.09811i
$424$	−26.4166	+	6.11032i	−1.28290	+	0.296744i
$425$	−1.69865			−0.0823968
$426$	12.6873	+	4.31415i	0.614700	+	0.209021i
$427$	3.20240	−	3.20240i	0.154975	−	0.154975i
$428$	−36.4984	−	4.04071i	−1.76422	−	0.195315i
$429$	2.90884	+	2.28256i	0.140440	+	0.110203i
$430$	13.0343	−	4.57509i	0.628570	−	0.220630i
$431$	−32.0613			−1.54434			−0.772170	−	0.635416i	$-0.780829\pi$
$431$	−32.0613			−1.54434			−0.772170	+	0.635416i	$0.780829\pi$
$432$	16.5996	+	12.5081i	0.798650	+	0.601796i
$433$	23.0436			1.10740			0.553702	−	0.832715i	$-0.313215\pi$
$433$	23.0436			1.10740			0.553702	+	0.832715i	$0.313215\pi$
$434$	−12.7482	+	4.47467i	−0.611934	+	0.214791i
$435$	−10.5334	−	8.26556i	−0.505038	−	0.396303i
$436$	1.36806	−	12.3572i	0.0655182	−	0.591804i
$437$	−9.24284	+	9.24284i	−0.442145	+	0.442145i
$438$	−17.8560	−	6.07171i	−0.853192	−	0.290118i
$439$	−24.4096			−1.16501			−0.582504	−	0.812828i	$-0.697927\pi$
$439$	−24.4096			−1.16501			−0.582504	+	0.812828i	$0.697927\pi$
$440$	1.90927	+	1.19194i	0.0910209	+	0.0568235i
$441$	−4.20255	−	17.1647i	−0.200122	−	0.817366i
$442$	−2.79045	+	5.80884i	−0.132728	+	0.276298i
$443$	−20.8618	−	20.8618i	−0.991173	−	0.991173i	0.00878795	−	0.999961i	$-0.497203\pi$
$443$	−20.8618	−	20.8618i	−0.991173	−	0.991173i	−0.999961	+	0.00878795i	$0.997203\pi$
$444$	−4.40488	−	4.31940i	−0.209046	−	0.204990i
$445$	−3.62140	+	3.62140i	−0.171671	+	0.171671i
$446$	9.52247	−	3.34242i	0.450902	−	0.158268i
$447$	−2.27620	+	0.274594i	−0.107661	+	0.0129879i
$448$	3.70020	+	7.57053i	0.174818	+	0.357674i
$449$			36.3508i			1.71550i	0.514067	+	0.857750i	$0.328138\pi$
$449$			36.3508i			1.71550i	−0.514067	+	0.857750i	$0.671862\pi$
$450$	−2.31684	−	3.55419i	−0.109217	−	0.167546i
$451$	−6.55773	−	6.55773i	−0.308792	−	0.308792i
$452$	17.3710	+	21.6961i	0.817064	+	1.02050i
$453$	−14.4734	−	11.3573i	−0.680020	−	0.533612i
$454$	−7.38068	−	3.54553i	−0.346392	−	0.166400i
$455$		−	2.82560i		−	0.132466i
$456$	−7.16180	+	15.2906i	−0.335382	+	0.716048i
$457$		−	17.2582i		−	0.807303i	−0.914913	−	0.403651i	$-0.867741\pi$
$457$		−	17.2582i		−	0.807303i	0.914913	−	0.403651i	$-0.132259\pi$
$458$	2.38264	−	4.95990i	0.111334	−	0.231761i
$459$	8.04042	+	3.64116i	0.375295	+	0.169955i
$460$	−7.53905	−	0.834642i	−0.351510	−	0.0389154i
$461$	−5.19393	−	5.19393i	−0.241905	−	0.241905i	0.575733	−	0.817638i	$-0.304717\pi$
$461$	−5.19393	−	5.19393i	−0.241905	−	0.241905i	−0.817638	+	0.575733i	$0.804717\pi$
$462$	1.84187	−	0.907115i	0.0856918	−	0.0422028i
$463$		−	5.72585i		−	0.266103i	−0.991109	−	0.133051i	$-0.957522\pi$
$463$		−	5.72585i		−	0.266103i	0.991109	−	0.133051i	$-0.0424775\pi$
$464$	−26.1177	+	16.5525i	−1.21248	+	0.768430i
$465$	−1.88155	−	15.5968i	−0.0872546	−	0.723282i
$466$	−10.2874	−	29.3084i	−0.476552	−	1.35768i
$467$	−8.05288	+	8.05288i	−0.372643	+	0.372643i	−0.868439	−	0.495796i	$-0.834876\pi$
$467$	−8.05288	+	8.05288i	−0.372643	+	0.372643i	0.495796	+	0.868439i	$0.334876\pi$
$468$	−15.9601	+	2.08421i	−0.737758	+	0.0963426i
$469$	4.64257	+	4.64257i	0.214374	+	0.214374i
$470$	−9.88019	−	4.74625i	−0.455739	−	0.218928i
$471$	−3.08664	+	0.372364i	−0.142225	+	0.0171576i
$472$	0.818890	+	3.54028i	0.0376925	+	0.162955i
$473$	−7.77304			−0.357405
$474$	−29.2036	−	9.93033i	−1.34137	−	0.456115i
$475$	2.43710	−	2.43710i	0.111822	−	0.111822i
$476$	2.23651	+	2.79336i	0.102510	+	0.128034i
$477$	−24.5882	−	14.9161i	−1.12582	−	0.682960i
$478$	−3.92947	−	11.1949i	−0.179730	−	0.512045i
$479$	28.4148			1.29830			0.649152	−	0.760659i	$-0.275124\pi$
$479$	28.4148			1.29830			0.649152	+	0.760659i	$0.275124\pi$
$480$	−9.52383	+	2.30144i	−0.434701	+	0.105046i
$481$	4.77752			0.217836
$482$	−7.54379	−	21.4920i	−0.343610	−	0.978936i
$483$	−4.27131	+	5.44324i	−0.194351	+	0.247676i
$484$	12.9585	+	16.1850i	0.589024	+	0.735682i
$485$	−4.78281	+	4.78281i	−0.217176	+	0.217176i
$486$	3.34793	+	21.7897i	0.151865	+	0.988401i
$487$	2.38929			0.108269			0.0541345	−	0.998534i	$-0.482760\pi$
$487$	2.38929			0.108269			0.0541345	+	0.998534i	$0.482760\pi$
$488$	11.8485	−	2.74064i	0.536358	−	0.124063i
$489$	1.04280	+	8.64412i	0.0471571	+	0.390900i
$490$	7.50903	+	3.60719i	0.339223	+	0.162956i
$491$	28.6044	+	28.6044i	1.29090	+	1.29090i	0.934230	+	0.356670i	$0.116088\pi$
$491$	28.6044	+	28.6044i	1.29090	+	1.29090i	0.356670	+	0.934230i	$0.383912\pi$
$492$	40.3691	−	0.395496i	1.81998	−	0.0178303i
$493$	−9.28507	+	9.28507i	−0.418179	+	0.418179i
$494$	−4.33056	−	12.3376i	−0.194841	−	0.555096i
$495$	0.567735	+	2.31883i	0.0255178	+	0.104224i
$496$	−35.4017	−	7.93586i	−1.58958	−	0.356331i
$497$			5.76242i			0.258480i
$498$	2.66002	+	5.40111i	0.119198	+	0.242029i
$499$	−12.3490	−	12.3490i	−0.552817	−	0.552817i	0.374436	−	0.927253i	$-0.377836\pi$
$499$	−12.3490	−	12.3490i	−0.552817	−	0.552817i	−0.927253	+	0.374436i	$0.877836\pi$
$500$	1.98785	+	0.220074i	0.0888996	+	0.00984200i
$501$	3.78725	−	4.82637i	0.169202	−	0.215626i
$502$	−2.56368	+	5.33676i	−0.114422	+	0.238191i
$503$			21.7749i			0.970893i	0.874266	+	0.485446i	$0.161343\pi$
$503$			21.7749i			0.970893i	−0.874266	+	0.485446i	$0.838657\pi$
$504$	−2.79428	+	8.48952i	−0.124467	+	0.378153i
$505$		−	14.9279i		−	0.664281i
$506$	3.84723	+	1.84813i	0.171030	+	0.0821596i
$507$	−6.20547	+	7.90808i	−0.275594	+	0.351210i
$508$	9.63119	+	12.0292i	0.427315	+	0.533709i
$509$	−12.5929	−	12.5929i	−0.558173	−	0.558173i	0.370614	−	0.928787i	$-0.379147\pi$
$509$	−12.5929	−	12.5929i	−0.558173	−	0.558173i	−0.928787	+	0.370614i	$0.879147\pi$
$510$	−3.73270	+	1.83834i	−0.165287	+	0.0814029i
$511$		−	8.10999i		−	0.358765i
$512$	−2.33712	+	22.5064i	−0.103287	+	0.994652i
$513$	−16.7599	+	6.31173i	−0.739966	+	0.278670i
$514$	20.5956	−	7.22913i	0.908432	−	0.318863i
$515$	−12.0420	+	12.0420i	−0.530633	+	0.530633i
$516$	23.6909	−	24.1597i	1.04293	−	1.06357i
$517$	4.36126	+	4.36126i	0.191808	+	0.191808i
$518$	1.14871	−	2.39125i	0.0504714	−	0.105065i
$519$	1.13304	+	9.39214i	0.0497349	+	0.412269i
$520$	4.01812	−	6.43629i	0.176206	−	0.282250i
$521$	21.1851			0.928136			0.464068	−	0.885800i	$-0.346389\pi$
$521$	21.1851			0.928136			0.464068	+	0.885800i	$0.346389\pi$
$522$	−32.0919	−	6.76353i	−1.40462	−	0.296032i
$523$	22.7910	−	22.7910i	0.996582	−	0.996582i	−0.00341189	−	0.999994i	$-0.501086\pi$
$523$	22.7910	−	22.7910i	0.996582	−	0.996582i	0.999994	+	0.00341189i	$0.00108604\pi$
$524$	−1.62132	+	14.6449i	−0.0708277	+	0.639764i
$525$	1.12624	−	1.43524i	0.0491529	−	0.0626392i
$526$	12.4562	−	4.37218i	0.543116	−	0.190636i
$527$	−15.4069			−0.671135
$528$	5.48547	+	0.552952i	0.238725	+	0.0240641i
$529$	8.61654			0.374632
$530$	12.7919	−	4.49001i	0.555645	−	0.195034i
$531$	−1.99901	+	3.29525i	−0.0867498	+	0.143002i
$532$	−7.21649	−	0.798932i	−0.312875	−	0.0346381i
$533$	−22.1066	+	22.1066i	−0.957543	+	0.957543i
$534$	−4.03864	+	11.8770i	−0.174769	+	0.513970i
$535$	18.3607			0.793802
$536$	3.97316	+	17.1770i	0.171614	+	0.741935i
$537$	−39.4406	+	4.75800i	−1.70199	+	0.205323i
$538$	4.96133	−	10.3279i	0.213898	−	0.445268i
$539$	−3.31459	−	3.31459i	−0.142770	−	0.142770i
$540$	−8.93759	−	5.30278i	−0.384613	−	0.228195i
$541$	3.91275	−	3.91275i	0.168222	−	0.168222i	−0.617975	−	0.786198i	$-0.712047\pi$
$541$	3.91275	−	3.91275i	0.168222	−	0.168222i	0.786198	+	0.617975i	$0.212047\pi$
$542$	23.2667	−	8.16669i	0.999389	−	0.350790i
$543$	3.69306	+	30.6130i	0.158484	+	1.31373i
$544$	1.12216	+	9.54328i	0.0481121	+	0.409165i
$545$			6.21637i			0.266280i
$546$	−3.05795	−	6.20910i	−0.130868	−	0.265725i
$547$	−4.84133	−	4.84133i	−0.207000	−	0.207000i	0.595991	−	0.802991i	$-0.296759\pi$
$547$	−4.84133	−	4.84133i	−0.207000	−	0.207000i	−0.802991	+	0.595991i	$0.796759\pi$
$548$	−31.4922	+	25.2142i	−1.34528	+	1.07710i
$549$	11.0285	+	6.69025i	0.470683	+	0.285533i
$550$	−1.01442	−	0.487306i	−0.0432549	−	0.0207788i
$551$		−	26.6431i		−	1.13503i
$552$	−17.4699	+	6.32492i	−0.743570	+	0.269206i
$553$		−	13.2640i		−	0.564041i
$554$	−13.4938	+	28.0898i	−0.573296	+	1.19342i
$555$	2.42671	+	1.90424i	0.103008	+	0.0808304i
$556$	−1.81028	+	16.3517i	−0.0767731	+	0.693466i
$557$	24.4160	+	24.4160i	1.03454	+	1.03454i	0.999382	+	0.0351576i	$0.0111933\pi$
$557$	24.4160	+	24.4160i	1.03454	+	1.03454i	0.0351576	+	0.999382i	$0.488807\pi$
$558$	−21.0139	−	32.2368i	−0.889590	−	1.36469i
$559$			26.2035i			1.10829i
$560$	−2.25538	−	3.55870i	−0.0953073	−	0.150383i
$561$	2.32443	−	0.280413i	0.0981376	−	0.0118390i
$562$	13.3771	+	38.1108i	0.564277	+	1.60761i
$563$	20.4783	−	20.4783i	0.863059	−	0.863059i	−0.128633	−	0.991692i	$-0.541059\pi$
$563$	20.4783	−	20.4783i	0.863059	−	0.863059i	0.991692	+	0.128633i	$0.0410589\pi$
$564$	−26.8477	+	0.263027i	−1.13049	+	0.0110754i
$565$	−9.82645	−	9.82645i	−0.413402	−	0.413402i
$566$	12.7426	+	6.12128i	0.535610	+	0.257297i
$567$	−8.40746	+	4.37945i	−0.353080	+	0.183920i
$568$	−8.19440	+	13.1259i	−0.343829	+	0.550752i
$569$	10.2571			0.430001			0.215000	−	0.976614i	$-0.431025\pi$
$569$	10.2571			0.430001			0.215000	+	0.976614i	$0.431025\pi$
$570$	2.71789	−	7.99291i	0.113840	−	0.334786i
$571$	14.1309	−	14.1309i	0.591360	−	0.591360i	−0.346638	−	0.937999i	$-0.612677\pi$
$571$	14.1309	−	14.1309i	0.591360	−	0.591360i	0.937999	+	0.346638i	$0.112677\pi$
$572$	−3.33286	+	2.66845i	−0.139354	+	0.111574i
$573$	−27.9485	−	21.9312i	−1.16757	−	0.916189i
$574$	5.74950	+	16.3802i	0.239980	+	0.683695i
$575$	3.79255			0.158160
$576$	−18.4374	+	15.3643i	−0.768226	+	0.640179i
$577$	−35.9679			−1.49736			−0.748682	−	0.662929i	$-0.769313\pi$
$577$	−35.9679			−1.49736			−0.748682	+	0.662929i	$0.769313\pi$
$578$	−6.61098	−	18.8345i	−0.274980	−	0.783411i
$579$	20.8184	+	16.3362i	0.865185	+	0.678910i
$580$	12.0688	−	9.66294i	0.501132	−	0.401232i
$581$	−1.83064	+	1.83064i	−0.0759476	+	0.0759476i
$582$	−5.33386	+	15.6861i	−0.221096	+	0.650210i
$583$	−7.62849			−0.315940
$584$	11.5328	−	18.4734i	0.477229	−	0.764433i
$585$	7.81694	−	1.91388i	0.323191	−	0.0791292i
$586$	29.9850	+	14.4042i	1.23867	+	0.595032i
$587$	−1.24605	−	1.24605i	−0.0514299	−	0.0514299i	0.680924	−	0.732354i	$-0.261578\pi$
$587$	−1.24605	−	1.24605i	−0.0514299	−	0.0514299i	−0.732354	+	0.680924i	$0.761578\pi$
$588$	20.4045	−	0.199903i	0.841468	−	0.00824386i
$589$	22.1047	−	22.1047i	0.910808	−	0.910808i
$590$	−0.601740	−	1.71434i	−0.0247732	−	0.0705782i
$591$	17.1860	−	2.07327i	0.706938	−	0.0852829i
$592$	6.01705	−	3.81340i	0.247299	−	0.156730i
$593$		−	39.3347i		−	1.61528i	−0.589674	−	0.807642i	$-0.700744\pi$
$593$		−	39.3347i		−	1.61528i	0.589674	−	0.807642i	$-0.299256\pi$
$594$	3.75708	+	4.48108i	0.154155	+	0.183861i
$595$	−1.26515	−	1.26515i	−0.0518661	−	0.0518661i
$596$	0.291310	−	2.63131i	0.0119325	−	0.107783i
$597$	9.59427	+	7.52862i	0.392667	+	0.308126i
$598$	6.23020	−	12.9693i	0.254772	−	0.530354i
$599$			6.93885i			0.283514i	0.989902	+	0.141757i	$0.0452751\pi$
$599$			6.93885i			0.283514i	−0.989902	+	0.141757i	$0.954725\pi$
$600$	4.60638	−	1.66772i	0.188055	−	0.0680844i
$601$			4.21999i			0.172137i	0.996289	+	0.0860686i	$0.0274304\pi$
$601$			4.21999i			0.172137i	−0.996289	+	0.0860686i	$0.972570\pi$
$602$	13.1154	+	6.30039i	0.534544	+	0.256785i
$603$	−9.69898	+	15.9881i	−0.394973	+	0.651088i
$604$	16.5832	−	13.2774i	0.674760	−	0.540248i
$605$	−7.33040	−	7.33040i	−0.298023	−	0.298023i
$606$	−16.1554	−	32.8032i	−0.656269	−	1.33254i
$607$			12.3619i			0.501756i	0.968019	+	0.250878i	$0.0807193\pi$
$607$			12.3619i			0.501756i	−0.968019	+	0.250878i	$0.919281\pi$
$608$	−15.3020	−	12.0820i	−0.620577	−	0.489990i
$609$	−1.68909	−	14.0014i	−0.0684453	−	0.567366i
$610$	−5.73751	+	2.01389i	−0.232305	+	0.0815399i
$611$	14.7021	−	14.7021i	0.594785	−	0.594785i
$612$	−6.21290	+	8.07930i	−0.251142	+	0.326586i
$613$	7.81288	+	7.81288i	0.315559	+	0.315559i	0.847059	−	0.531499i	$-0.178371\pi$
$613$	7.81288	+	7.81288i	0.315559	+	0.315559i	−0.531499	+	0.847059i	$0.678371\pi$
$614$	11.8282	−	24.6225i	0.477347	−	0.993685i
$615$	−20.0402	+	2.41760i	−0.808100	+	0.0974868i
$616$	0.534265	+	2.30977i	0.0215261	+	0.0930633i
$617$	−38.3142			−1.54247			−0.771236	−	0.636550i	$-0.780361\pi$
$617$	−38.3142			−1.54247			−0.771236	+	0.636550i	$0.780361\pi$
$618$	−13.4294	+	39.4938i	−0.540209	+	1.58867i
$619$	−17.9582	+	17.9582i	−0.721800	+	0.721800i	−0.968972	−	0.247172i	$-0.920499\pi$
$619$	−17.9582	+	17.9582i	−0.721800	+	0.721800i	0.247172	+	0.968972i	$0.420499\pi$
$620$	18.0300	+	1.99609i	0.724102	+	0.0801648i
$621$	−17.9517	−	8.12956i	−0.720377	−	0.326228i
$622$	−37.2255	+	13.0663i	−1.49261	+	0.523911i
$623$	−5.39442			−0.216123
$624$	1.86404	−	18.4919i	0.0746214	−	0.740270i
$625$	−1.00000			−0.0400000
$626$	19.9942	−	7.01804i	0.799128	−	0.280497i
$627$	−2.93261	+	3.73724i	−0.117117	+	0.149251i
$628$	0.395032	−	3.56819i	0.0157635	−	0.142386i
$629$	2.13912	−	2.13912i	0.0852922	−	0.0852922i
$630$	0.921574	−	4.37272i	0.0367164	−	0.174213i
$631$	−10.8167			−0.430606			−0.215303	−	0.976547i	$-0.569074\pi$
$631$	−10.8167			−0.430606			−0.215303	+	0.976547i	$0.569074\pi$
$632$	18.8619	−	30.2133i	0.750287	−	1.20182i
$633$	2.58170	+	21.4006i	0.102613	+	0.850596i
$634$	−3.34388	+	6.96090i	−0.132802	+	0.276453i
$635$	−5.44818	−	5.44818i	−0.216205	−	0.216205i
$636$	23.2503	−	23.7104i	0.921934	−	0.940177i
$637$	−11.1737	+	11.1737i	−0.442720	+	0.442720i
$638$	−8.20863	+	2.88126i	−0.324983	+	0.114070i
$639$	−15.9416	+	3.90309i	−0.630639	+	0.154404i
$640$	−0.0768010	−	11.3134i	−0.00303582	−	0.447203i
$641$			26.9453i			1.06427i	0.846658	+	0.532137i	$0.178611\pi$
$641$			26.9453i			1.06427i	−0.846658	+	0.532137i	$0.821389\pi$
$642$	40.3467	−	19.8705i	1.59236	−	0.784228i
$643$	15.6842	+	15.6842i	0.618523	+	0.618523i	0.945153	−	0.326629i	$-0.105913\pi$
$643$	15.6842	+	15.6842i	0.618523	+	0.618523i	−0.326629	+	0.945153i	$0.605913\pi$
$644$	−4.99342	−	6.23670i	−0.196768	−	0.245760i
$645$	−10.4443	+	13.3099i	−0.411243	+	0.524077i
$646$	−7.46312	−	3.58514i	−0.293633	−	0.141055i
$647$		−	2.13219i		−	0.0838250i	−0.999121	−	0.0419125i	$-0.986655\pi$
$647$		−	2.13219i		−	0.0838250i	0.999121	−	0.0419125i	$-0.0133451\pi$
$648$	−25.3787	−	1.98004i	−0.996970	−	0.0777832i
$649$			1.02235i			0.0401308i
$650$	−1.64274	+	3.41967i	−0.0644338	+	0.134131i
$651$	10.2150	−	13.0178i	0.400359	−	0.510207i
$652$	−9.99268	−	1.10628i	−0.391344	−	0.0433253i
$653$	24.6766	+	24.6766i	0.965670	+	0.965670i	0.999430	−	0.0337602i	$-0.0107483\pi$
$653$	24.6766	+	24.6766i	0.965670	+	0.965670i	−0.0337602	+	0.999430i	$0.510748\pi$
$654$	6.72756	+	13.6601i	0.263068	+	0.534154i
$655$		−	7.36717i		−	0.287859i
$656$	−10.1968	+	45.4876i	−0.398117	+	1.77599i
$657$	22.4361	−	5.49319i	0.875315	−	0.214310i
$658$	−3.82374	−	10.8937i	−0.149065	−	0.424682i
$659$	1.81555	−	1.81555i	0.0707239	−	0.0707239i	−0.670860	−	0.741584i	$-0.734075\pi$
$659$	1.81555	−	1.81555i	0.0707239	−	0.0707239i	0.741584	+	0.670860i	$0.234075\pi$
$660$	−2.75650	+	0.0270055i	−0.107297	+	0.00105119i
$661$	6.11318	+	6.11318i	0.237775	+	0.237775i	0.815928	−	0.578153i	$-0.196226\pi$
$661$	6.11318	+	6.11318i	0.237775	+	0.237775i	−0.578153	+	0.815928i	$0.696226\pi$
$662$	28.4844	+	13.6833i	1.10708	+	0.531818i
$663$	−0.945292	−	7.83583i	−0.0367121	−	0.304319i
$664$	−6.77316	+	1.56668i	−0.262850	+	0.0607988i
$665$	3.63029			0.140777
$666$	7.39340	+	1.55820i	0.286488	+	0.0603789i
$667$	20.7306	−	20.7306i	0.802693	−	0.802693i
$668$	4.42752	+	5.52990i	0.171306	+	0.213958i
$669$	−7.63028	+	9.72382i	−0.295004	+	0.375945i
$670$	−2.91957	−	8.31777i	−0.112793	−	0.321343i
$671$	3.42158			0.132089
$672$	−8.80743	−	5.37921i	−0.339754	−	0.207508i
$673$	−10.6352			−0.409957			−0.204978	−	0.978767i	$-0.565712\pi$
$673$	−10.6352			−0.409957			−0.204978	+	0.978767i	$0.565712\pi$
$674$	−8.68681	−	24.7485i	−0.334603	−	0.953275i
$675$	4.73341	+	2.14356i	0.182189	+	0.0825056i
$676$	−7.25457	−	9.06083i	−0.279022	−	0.348494i
$677$	19.5927	−	19.5927i	0.753009	−	0.753009i	−0.222031	−	0.975040i	$-0.571269\pi$
$677$	19.5927	−	19.5927i	0.753009	−	0.753009i	0.975040	+	0.222031i	$0.0712685\pi$
$678$	−32.2276	−	10.9586i	−1.23769	−	0.420862i
$679$	−7.12445			−0.273411
$680$	−1.08273	−	4.68093i	−0.0415207	−	0.179505i
$681$	9.95617	−	1.20108i	0.381521	−	0.0460256i
$682$	−9.20084	−	4.41990i	−0.352318	−	0.169247i
$683$	−3.73270	−	3.73270i	−0.142828	−	0.142828i	0.632077	−	0.774905i	$-0.282202\pi$
$683$	−3.73270	−	3.73270i	−0.142828	−	0.142828i	−0.774905	+	0.632077i	$0.782202\pi$
$684$	−2.67777	−	20.5054i	−0.102387	−	0.784043i
$685$	14.2632	−	14.2632i	0.544969	−	0.544969i
$686$	6.35949	+	18.1180i	0.242806	+	0.691748i
$687$	0.807142	+	6.69066i	0.0307944	+	0.255265i
$688$	20.9156	+	33.0020i	0.797398	+	1.25819i
$689$			25.7162i			0.979709i
$690$	8.33394	−	4.10442i	0.317268	−	0.156253i
$691$	−5.56010	−	5.56010i	−0.211516	−	0.211516i	0.593395	−	0.804911i	$-0.297787\pi$
$691$	−5.56010	−	5.56010i	−0.211516	−	0.211516i	−0.804911	+	0.593395i	$0.797787\pi$
$692$	−10.8574	−	1.20201i	−0.412737	−	0.0456937i
$693$	−1.30421	+	2.14990i	−0.0495428	+	0.0816680i
$694$	4.70007	−	9.78407i	0.178412	−	0.371398i
$695$		−	8.22580i		−	0.312022i
$696$	16.0631	−	34.2951i	0.608871	−	1.29995i
$697$			19.7963i			0.749839i
$698$	36.4206	+	17.4958i	1.37854	+	0.662224i
$699$	29.9281	+	23.4846i	1.13198	+	0.888267i
$700$	1.31664	+	1.64446i	0.0497642	+	0.0621547i
$701$	−3.06221	−	3.06221i	−0.115658	−	0.115658i	0.646909	−	0.762567i	$-0.276061\pi$
$701$	−3.06221	−	3.06221i	−0.115658	−	0.115658i	−0.762567	+	0.646909i	$0.776061\pi$
$702$	15.1061	−	12.6654i	0.570141	−	0.478025i
$703$			6.13809i			0.231503i
$704$	−2.06762	+	6.02106i	−0.0779263	+	0.226927i
$705$	13.3279	−	1.60784i	0.501957	−	0.0605546i
$706$	−23.4357	+	8.22603i	−0.882015	+	0.309591i
$707$	11.1182	−	11.1182i	0.418144	−	0.418144i
$708$	−3.17760	−	3.11595i	−0.119422	−	0.117104i
$709$	17.4095	+	17.4095i	0.653827	+	0.653827i	0.953912	−	0.300085i	$-0.0970151\pi$
$709$	17.4095	+	17.4095i	0.653827	+	0.653827i	−0.300085	+	0.953912i	$0.597015\pi$
$710$	3.35015	−	6.97396i	0.125729	−	0.261728i
$711$	36.6944	−	8.98416i	1.37615	−	0.336932i
$712$	−12.2877	−	7.67109i	−0.460500	−	0.287486i
$713$	34.3988			1.28824
$714$	−4.14929	−	1.41091i	−0.155283	−	0.0528022i
$715$	1.50949	−	1.50949i	0.0564519	−	0.0564519i
$716$	5.04765	−	45.5937i	0.188639	−	1.70392i
$717$	11.4317	+	8.97041i	0.426923	+	0.335006i
$718$	2.43352	−	0.854176i	0.0908182	−	0.0318776i
$719$	9.52559			0.355244			0.177622	−	0.984099i	$-0.443159\pi$
$719$	9.52559			0.355244			0.177622	+	0.984099i	$0.443159\pi$
$720$	8.31741	−	8.64990i	0.309971	−	0.322363i
$721$	−17.9376			−0.668032
$722$	−9.50236	+	3.33537i	−0.353641	+	0.124129i
$723$	21.9465	+	17.2214i	0.816199	+	0.640471i
$724$	−35.3889	−	3.91788i	−1.31522	−	0.145607i
$725$	−5.46614	+	5.46614i	−0.203007	+	0.203007i
$726$	−24.0413	−	8.17497i	−0.892258	−	0.303401i
$727$	8.04272			0.298288			0.149144	−	0.988815i	$-0.452348\pi$
$727$	8.04272			0.298288			0.149144	+	0.988815i	$0.452348\pi$
$728$	7.78641	−	1.80105i	0.288584	−	0.0667512i
$729$	−17.8103	−	20.2927i	−0.659641	−	0.751581i
$730$	−4.71498	+	9.81510i	−0.174509	+	0.363273i
$731$	11.7325	+	11.7325i	0.433943	+	0.433943i
$732$	−10.4284	+	10.6347i	−0.385444	+	0.393071i
$733$	24.1436	−	24.1436i	0.891766	−	0.891766i	−0.102924	−	0.994689i	$-0.532820\pi$
$733$	24.1436	−	24.1436i	0.891766	−	0.891766i	0.994689	+	0.102924i	$0.0328197\pi$
$734$	17.1603	−	6.02332i	0.633397	−	0.222325i
$735$	−10.1293	+	1.22197i	−0.373625	+	0.0450730i
$736$	−2.50542	−	21.3071i	−0.0923510	−	0.785391i
$737$			4.96032i			0.182716i
$738$	−41.4210	+	27.0007i	−1.52473	+	0.993911i
$739$	−11.0488	−	11.0488i	−0.406436	−	0.406436i	0.474058	−	0.880494i	$-0.342789\pi$
$739$	−11.0488	−	11.0488i	−0.406436	−	0.406436i	−0.880494	+	0.474058i	$0.842789\pi$
$740$	−2.78045	+	2.22617i	−0.102211	+	0.0818356i
$741$	12.5985	+	9.88604i	0.462818	+	0.363173i
$742$	12.8715	+	6.18322i	0.472528	+	0.226993i
$743$		−	7.30891i		−	0.268138i	−0.990972	−	0.134069i	$-0.957196\pi$
$743$		−	7.30891i		−	0.268138i	0.990972	−	0.134069i	$-0.0428044\pi$
$744$	41.7802	−	15.1264i	1.53174	−	0.554559i
$745$			1.32369i			0.0484964i
$746$	−0.672347	+	1.39961i	−0.0246164	+	0.0512435i
$747$	−6.30437	−	3.82445i	−0.230665	−	0.139929i
$748$	−0.297483	+	2.68707i	−0.0108771	+	0.0982488i
$749$	13.6750	+	13.6750i	0.499673	+	0.499673i
$750$	−2.19745	+	1.08223i	−0.0802394	+	0.0395175i
$751$		−	21.0774i		−	0.769127i	−0.923099	−	0.384563i	$-0.874352\pi$
$751$		−	21.0774i		−	0.769127i	0.923099	−	0.384563i	$-0.125648\pi$
$752$	6.78143	−	30.2518i	0.247293	−	1.10317i
$753$	−0.868469	−	7.19902i	−0.0316488	−	0.262347i
$754$	9.71295	+	27.6719i	0.353725	+	1.00775i
$755$	−7.51074	+	7.51074i	−0.273344	+	0.273344i
$756$	−2.70719	−	10.6062i	−0.0984596	−	0.385743i
$757$	−8.59274	−	8.59274i	−0.312309	−	0.312309i	0.533495	−	0.845803i	$-0.320878\pi$
$757$	−8.59274	−	8.59274i	−0.312309	−	0.312309i	−0.845803	+	0.533495i	$0.820878\pi$
$758$	−13.1637	−	6.32361i	−0.478129	−	0.229684i
$759$	−5.18972	+	0.626072i	−0.188375	+	0.0227250i
$760$	8.26926	+	5.16243i	0.299958	+	0.187261i
$761$	5.70368			0.206758			0.103379	−	0.994642i	$-0.467034\pi$
$761$	5.70368			0.206758			0.103379	+	0.994642i	$0.467034\pi$
$762$	−17.8683	−	6.07589i	−0.647300	−	0.220106i
$763$	−4.62993	+	4.62993i	−0.167615	+	0.167615i
$764$	32.0226	−	25.6389i	1.15854	−	0.927583i
$765$	2.64308	−	4.35694i	0.0955606	−	0.157526i
$766$	−9.66191	−	27.5265i	−0.349099	−	0.994572i
$767$	3.44642			0.124443
$768$	−12.4125	−	24.7776i	−0.447899	−	0.894084i
$769$	32.6273			1.17657			0.588286	−	0.808653i	$-0.299803\pi$
$769$	32.6273			1.17657			0.588286	+	0.808653i	$0.299803\pi$
$770$	−0.392590	−	1.11848i	−0.0141480	−	0.0403071i
$771$	−16.5031	+	21.0311i	−0.594344	+	0.757416i
$772$	−23.8531	+	19.0980i	−0.858493	+	0.687353i
$773$	10.1714	−	10.1714i	0.365841	−	0.365841i	−0.500117	−	0.865958i	$-0.666710\pi$
$773$	10.1714	−	10.1714i	0.365841	−	0.365841i	0.865958	+	0.500117i	$0.166710\pi$
$774$	−8.54633	+	40.5510i	−0.307191	+	1.45757i
$775$	−9.07008			−0.325807
$776$	−16.2284	−	10.1313i	−0.582567	−	0.363691i
$777$	0.389136	+	3.22568i	0.0139602	+	0.115720i
$778$	−42.0003	−	20.1761i	−1.50578	−	0.723349i
$779$	−28.4023	−	28.4023i	−1.01762	−	1.01762i
$780$	0.0910375	+	9.29238i	0.00325966	+	0.332721i
$781$	−3.07840	+	3.07840i	−0.110154	+	0.110154i
$782$	−3.01741	−	8.59651i	−0.107902	−	0.307410i
$783$	37.5905	−	14.1565i	1.34337	−	0.505911i
$784$	−5.15394	+	22.9916i	−0.184069	+	0.821130i
$785$			1.79500i			0.0640662i
$786$	−7.97299	−	16.1890i	−0.284387	−	0.577441i
$787$	26.4738	+	26.4738i	0.943688	+	0.943688i	0.998497	−	0.0548088i	$-0.0174549\pi$
$787$	26.4738	+	26.4738i	0.943688	+	0.943688i	−0.0548088	+	0.998497i	$0.517455\pi$
$788$	−2.19948	+	19.8672i	−0.0783533	+	0.707740i
$789$	−9.98105	+	12.7196i	−0.355335	+	0.452829i
$790$	−7.71140	+	16.0527i	−0.274359	+	0.571129i
$791$		−	14.6374i		−	0.520446i
$792$	−6.02805	+	3.04252i	−0.214197	+	0.108111i
$793$		−	11.5344i		−	0.409599i
$794$	23.7753	+	11.4212i	0.843755	+	0.405323i
$795$	−10.2500	+	13.0624i	−0.363532	+	0.463275i
$796$	−10.9928	+	8.80141i	−0.389630	+	0.311958i
$797$	1.74739	+	1.74739i	0.0618956	+	0.0618956i	0.737377	−	0.675481i	$-0.236064\pi$
$797$	1.74739	+	1.74739i	0.0618956	+	0.0618956i	−0.675481	+	0.737377i	$0.736064\pi$
$798$	7.97737	−	3.92882i	0.282396	−	0.139079i
$799$		−	13.1657i		−	0.465767i
$800$	0.660616	+	5.61815i	0.0233563	+	0.198632i
$801$	−3.65383	−	14.9235i	−0.129102	−	0.527297i
$802$	−10.4472	+	3.66702i	−0.368905	+	0.129487i
$803$	4.33253	−	4.33253i	0.152892	−	0.152892i
$804$	−15.4174	−	15.1182i	−0.543728	−	0.533178i
$805$	2.82468	+	2.82468i	0.0995569	+	0.0995569i
$806$	−14.8998	+	31.0167i	−0.524824	+	1.09252i
$807$	1.68070	+	13.9318i	0.0591633	+	0.490424i
$808$	41.1363	−	9.51508i	1.44717	−	0.334739i
$809$	11.1168			0.390846			0.195423	−	0.980719i	$-0.437392\pi$
$809$	11.1168			0.390846			0.195423	+	0.980719i	$0.437392\pi$
$810$	12.7212	−	0.412292i	0.446979	−	0.0144865i
$811$	2.65898	−	2.65898i	0.0933693	−	0.0933693i	−0.658879	−	0.752249i	$-0.728969\pi$
$811$	2.65898	−	2.65898i	0.0933693	−	0.0933693i	0.752249	+	0.658879i	$0.228969\pi$
$812$	16.1858	+	1.79191i	0.568009	+	0.0628838i
$813$	−18.6434	+	23.7586i	−0.653852	+	0.833252i
$814$	1.89112	−	0.663791i	0.0662838	−	0.0232659i
$815$	5.02687			0.176083
$816$	−7.44509	−	9.11432i	−0.260630	−	0.319065i
$817$	−33.6659			−1.17782
$818$	−3.14860	+	1.10517i	−0.110088	+	0.0386414i
$819$	7.24748	+	4.39658i	0.253248	+	0.153629i
$820$	2.56477	−	23.1667i	0.0895656	−	0.809017i
$821$	−16.0559	+	16.0559i	−0.560354	+	0.560354i	−0.929408	−	0.369054i	$-0.879682\pi$
$821$	−16.0559	+	16.0559i	−0.560354	+	0.560354i	0.369054	+	0.929408i	$0.379682\pi$
$822$	15.9065	−	46.7788i	0.554804	−	1.63160i
$823$	52.6100			1.83387			0.916934	−	0.399038i	$-0.130656\pi$
$823$	52.6100			1.83387			0.916934	+	0.399038i	$0.130656\pi$
$824$	−40.8593	−	25.5081i	−1.42340	−	0.888616i
$825$	1.36840	−	0.165079i	0.0476415	−	0.00574733i
$826$	0.828660	−	1.72501i	0.0288328	−	0.0600207i
$827$	−19.0003	−	19.0003i	−0.660706	−	0.660706i	0.294841	−	0.955546i	$-0.404733\pi$
$827$	−19.0003	−	19.0003i	−0.660706	−	0.660706i	−0.955546	+	0.294841i	$0.904733\pi$
$828$	13.8714	−	18.0385i	0.482066	−	0.626882i
$829$	18.6518	−	18.6518i	0.647804	−	0.647804i	−0.304658	−	0.952462i	$-0.598542\pi$
$829$	18.6518	−	18.6518i	0.647804	−	0.647804i	0.952462	+	0.304658i	$0.0985421\pi$
$830$	3.27982	−	1.15123i	0.113844	−	0.0399598i
$831$	−4.57115	−	37.8917i	−0.158571	−	1.31445i
$832$	20.2975	+	6.97009i	0.703688	+	0.241644i
$833$			10.0060i			0.346688i
$834$	−8.90222	−	18.0758i	−0.308259	−	0.625912i
$835$	−2.50456	−	2.50456i	−0.0866740	−	0.0866740i
$836$	−3.42840	−	4.28201i	−0.118574	−	0.148096i
$837$	42.9324	+	19.4422i	1.48396	+	0.672022i
$838$	−32.1518	−	15.4451i	−1.11067	−	0.533542i
$839$		−	20.1324i		−	0.695048i	−0.937671	−	0.347524i	$-0.887023\pi$
$839$		−	20.1324i		−	0.695048i	0.937671	−	0.347524i	$-0.112977\pi$
$840$	4.67293	+	2.18870i	0.161231	+	0.0755174i
$841$			30.7574i			1.06060i
$842$	−17.5476	+	36.5285i	−0.604730	+	1.25886i
$843$	−38.9167	−	30.5379i	−1.34036	−	1.05178i
$844$	−24.7392	−	2.73886i	−0.851560	−	0.0942755i
$845$	4.10377	+	4.10377i	0.141174	+	0.141174i
$846$	27.5473	−	17.9570i	0.947094	−	0.617374i
$847$		−	10.9193i		−	0.375192i
$848$	20.5266	+	32.3883i	0.704886	+	1.11222i
$849$	−17.1891	+	2.07364i	−0.589928	+	0.0711671i
$850$	0.795614	+	2.26668i	0.0272893	+	0.0777465i
$851$	−4.77597	+	4.77597i	−0.163718	+	0.163718i
$852$	−0.185658	−	18.9505i	−0.00636055	−	0.649235i
$853$	−1.43240	−	1.43240i	−0.0490446	−	0.0490446i	0.682159	−	0.731204i	$-0.261041\pi$
$853$	−1.43240	−	1.43240i	−0.0490446	−	0.0490446i	−0.731204	+	0.682159i	$0.761041\pi$
$854$	−5.77321	−	2.77334i	−0.197555	−	0.0949017i
$855$	2.45893	+	10.0431i	0.0840935	+	0.343467i
$856$	11.7032	+	50.5960i	0.400007	+	1.72934i
$857$	5.40711			0.184703			0.0923517	−	0.995726i	$-0.470562\pi$
$857$	5.40711			0.184703			0.0923517	+	0.995726i	$0.470562\pi$
$858$	1.68341	−	4.95066i	0.0574707	−	0.169013i
$859$	−26.6360	+	26.6360i	−0.908808	+	0.908808i	−0.996176	−	0.0873685i	$-0.972154\pi$
$859$	−26.6360	+	26.6360i	−0.908808	+	0.908808i	0.0873685	+	0.996176i	$0.472154\pi$
$860$	−12.2100	−	15.2501i	−0.416357	−	0.520023i
$861$	−16.7265	−	13.1253i	−0.570038	−	0.447309i
$862$	15.0169	+	42.7826i	0.511476	+	1.45718i
$863$	−22.2772			−0.758324			−0.379162	−	0.925330i	$-0.623788\pi$
$863$	−22.2772			−0.758324			−0.379162	+	0.925330i	$0.623788\pi$
$864$	8.91586	−	28.0091i	0.303324	−	0.952888i
$865$	5.46187			0.185709
$866$	−10.7931	−	30.7494i	−0.366766	−	1.04491i
$867$	19.2327	+	15.0919i	0.653178	+	0.512548i
$868$	11.9420	+	14.9154i	0.405338	+	0.506260i
$869$	7.08589	−	7.08589i	0.240372	−	0.240372i
$870$	−6.09592	+	17.9272i	−0.206671	+	0.607789i
$871$	16.7216			0.566591
$872$	−17.1303	+	3.96234i	−0.580104	+	0.134182i
$873$	−4.82565	−	19.7096i	−0.163323	−	0.667069i
$874$	16.6628	+	8.00448i	0.563627	+	0.270756i
$875$	−0.744797	−	0.744797i	−0.0251787	−	0.0251787i
$876$	0.261295	+	26.6709i	0.00882832	+	0.901126i
$877$	−0.146610	+	0.146610i	−0.00495067	+	0.00495067i	−0.709578	−	0.704627i	$-0.751114\pi$
$877$	−0.146610	+	0.146610i	−0.00495067	+	0.00495067i	0.704627	+	0.709578i	$0.251114\pi$
$878$	11.4330	+	32.5722i	0.385844	+	1.09926i
$879$	−40.4482	+	4.87955i	−1.36428	+	0.164583i
$880$	0.696261	−	3.10601i	0.0234710	−	0.104703i
$881$		−	19.8694i		−	0.669416i	−0.942322	−	0.334708i	$-0.891362\pi$
$881$		−	19.8694i		−	0.669416i	0.942322	−	0.334708i	$-0.108638\pi$
$882$	−20.9361	+	13.6475i	−0.704957	+	0.459534i
$883$	−8.91596	−	8.91596i	−0.300046	−	0.300046i	0.540986	−	0.841032i	$-0.318051\pi$
$883$	−8.91596	−	8.91596i	−0.300046	−	0.300046i	−0.841032	+	0.540986i	$0.818051\pi$
$884$	9.05830	+	1.00284i	0.304664	+	0.0337291i
$885$	1.75059	+	1.37369i	0.0588454	+	0.0461759i
$886$	−18.0667	+	37.6092i	−0.606963	+	1.26351i
$887$			18.7409i			0.629257i	0.949215	+	0.314629i	$0.101880\pi$
$887$			18.7409i			0.629257i	−0.949215	+	0.314629i	$0.898120\pi$
$888$	−3.70066	+	7.90098i	−0.124186	+	0.265140i
$889$		−	8.11558i		−	0.272188i
$890$	6.52859	+	3.13621i	0.218839	+	0.105126i
$891$	−6.83104	−	2.15185i	−0.228848	−	0.0720897i
$892$	−8.92026	−	11.1413i	−0.298672	−	0.373037i
$893$	18.8891	+	18.8891i	0.632100	+	0.632100i
$894$	1.43254	+	2.90875i	0.0479114	+	0.0972830i
$895$			22.9362i			0.766671i
$896$	8.36902	−	8.48342i	0.279589	−	0.283411i
$897$	2.11054	+	17.4949i	0.0704688	+	0.584139i
$898$	48.5065	−	17.0260i	1.61868	−	0.568164i
$899$	−49.5783	+	49.5783i	−1.65353	+	1.65353i
$900$	−3.65755	+	4.75630i	−0.121918	+	0.158543i
$901$	11.5143	+	11.5143i	0.383598	+	0.383598i
$902$	−5.67912	+	11.8221i	−0.189094	+	0.393634i
$903$	−17.6920	+	2.13432i	−0.588754	+	0.0710256i
$904$	20.8150	−	33.3419i	0.692298	−	1.10893i
$905$	17.8025			0.591777
$906$	−8.37609	+	24.6328i	−0.278277	+	0.818371i
$907$	−24.5854	+	24.5854i	−0.816344	+	0.816344i	−0.985576	−	0.169232i	$-0.945871\pi$
$907$	−24.5854	+	24.5854i	−0.816344	+	0.816344i	0.169232	+	0.985576i	$0.445871\pi$
$908$	−1.27420	+	11.5094i	−0.0422858	+	0.381954i
$909$	38.2891	+	23.2275i	1.26997	+	0.770408i
$910$	−3.77047	+	1.32345i	−0.124990	+	0.0438720i
$911$	−46.5631			−1.54270			−0.771352	−	0.636408i	$-0.780419\pi$
$911$	−46.5631			−1.54270			−0.771352	+	0.636408i	$0.780419\pi$
$912$	23.7582	+	2.39490i	0.786713	+	0.0793030i
$913$	−1.95593			−0.0647318
$914$	−23.0293	+	8.08337i	−0.761741	+	0.267374i
$915$	4.59742	−	5.85883i	0.151986	−	0.193687i
$916$	−7.73447	−	0.856277i	−0.255554	−	0.0282922i
$917$	5.48704	−	5.48704i	0.181198	−	0.181198i
$918$	1.09280	−	12.4346i	0.0360677	−	0.410402i
$919$	−41.9173			−1.38272			−0.691362	−	0.722508i	$-0.742989\pi$
$919$	−41.9173			−1.38272			−0.691362	+	0.722508i	$0.742989\pi$
$920$	2.41739	+	10.4510i	0.0796990	+	0.344560i
$921$	4.00691	+	33.2146i	0.132032	+	1.09446i
$922$	−4.49804	+	9.36350i	−0.148135	+	0.308371i
$923$	10.3775	+	10.3775i	0.341581	+	0.341581i
$924$	−2.07315	−	2.03292i	−0.0682016	−	0.0668782i
$925$	1.25930	−	1.25930i	0.0414056	−	0.0414056i
$926$	−7.64056	+	2.68187i	−0.251085	+	0.0881317i
$927$	−12.1498	−	49.6240i	−0.399052	−	1.62987i
$928$	34.3206	+	27.0986i	1.12663	+	0.889554i
$929$		−	4.67449i		−	0.153365i	−0.997056	−	0.0766825i	$-0.975567\pi$
$929$		−	4.67449i		−	0.153365i	0.997056	−	0.0766825i	$-0.0244328\pi$
$930$	−19.9310	+	9.81593i	−0.653564	+	0.321877i
$931$	−14.3559	−	14.3559i	−0.470495	−	0.470495i
$932$	−34.2907	+	27.4549i	−1.12323	+	0.899314i
$933$	29.8285	−	38.0126i	0.976541	−	1.24448i
$934$	14.5176	+	6.97395i	0.475029	+	0.228195i
$935$		−	1.35174i		−	0.0442067i
$936$	10.2566	+	20.3210i	0.335246	+	0.664213i
$937$		−	7.27403i		−	0.237632i	−0.992916	−	0.118816i	$-0.962090\pi$
$937$		−	7.27403i		−	0.237632i	0.992916	−	0.118816i	$-0.0379099\pi$
$938$	4.02056	−	8.36953i	0.131276	−	0.273275i
$939$	−16.0212	+	20.4170i	−0.522831	+	0.666282i
$940$	−1.70571	+	15.4072i	−0.0556343	+	0.502526i
$941$	19.2764	+	19.2764i	0.628393	+	0.628393i	0.947664	−	0.319271i	$-0.103438\pi$
$941$	19.2764	+	19.2764i	0.628393	+	0.628393i	−0.319271	+	0.947664i	$0.603438\pi$
$942$	1.94260	+	3.94441i	0.0632934	+	0.128516i
$943$		−	44.1989i		−	1.43931i
$944$	4.34060	−	2.75092i	0.141274	−	0.0895349i
$945$	1.92891	+	5.12194i	0.0627475	+	0.166617i
$946$	3.64073	+	10.3723i	0.118370	+	0.337234i
$947$	−3.44878	+	3.44878i	−0.112070	+	0.112070i	−0.760918	−	0.648848i	$-0.775251\pi$
$947$	−3.44878	+	3.44878i	−0.112070	+	0.112070i	0.648848	+	0.760918i	$0.275251\pi$
$948$	0.427349	+	43.6205i	0.0138797	+	1.41673i
$949$	−14.6053	−	14.6053i	−0.474108	−	0.474108i
$950$	−4.39355	−	2.11058i	−0.142546	−	0.0684762i
$951$	−1.13277	−	9.38991i	−0.0367326	−	0.304489i
$952$	2.67993	−	4.29275i	0.0868569	−	0.139129i
$953$	8.40732			0.272340			0.136170	−	0.990686i	$-0.456521\pi$
$953$	8.40732			0.272340			0.136170	+	0.990686i	$0.456521\pi$
$954$	−8.38739	+	39.7968i	−0.271552	+	1.28847i
$955$	−14.5034	+	14.5034i	−0.469320	+	0.469320i
$956$	−13.0980	+	10.4870i	−0.423621	+	0.339173i
$957$	6.57750	−	8.38220i	0.212620	−	0.270958i
$958$	−13.3089	−	37.9166i	−0.429991	−	1.22503i
$959$	21.2464			0.686082
$960$	7.53181	+	11.6306i	0.243088	+	0.375377i
$961$	−51.2663			−1.65375
$962$	−2.23769	−	6.37511i	−0.0721460	−	0.205542i
$963$	−28.5689	+	47.0941i	−0.920622	+	1.51759i
$964$	−25.1456	+	20.1329i	−0.809885	+	0.648436i
$965$	10.8034	−	10.8034i	0.347773	−	0.347773i
$966$	9.26405	+	3.15013i	0.298066	+	0.101354i
$967$	31.1168			1.00065			0.500325	−	0.865838i	$-0.333214\pi$
$967$	31.1168			1.00065			0.500325	+	0.865838i	$0.333214\pi$
$968$	15.5277	−	24.8726i	0.499080	−	0.799435i
$969$	10.0674	−	1.21450i	0.323411	−	0.0390153i
$970$	8.62235	+	4.14201i	0.276847	+	0.132992i
$971$	3.65433	+	3.65433i	0.117273	+	0.117273i	0.763308	−	0.646035i	$-0.223574\pi$
$971$	3.65433	+	3.65433i	0.117273	+	0.117273i	−0.646035	+	0.763308i	$0.723574\pi$
$972$	27.5081	−	14.6733i	0.882321	−	0.470647i
$973$	6.12655	−	6.12655i	0.196408	−	0.196408i
$974$	−1.11909	−	3.18826i	−0.0358581	−	0.102159i
$975$	−0.556495	−	4.61297i	−0.0178221	−	0.147733i
$976$	−9.20672	−	14.5270i	−0.294700	−	0.464998i
$977$		−	11.2604i		−	0.360251i	−0.983644	−	0.180126i	$-0.942350\pi$
$977$		−	11.2604i		−	0.360251i	0.983644	−	0.180126i	$-0.0576504\pi$
$978$	11.0463	−	5.44024i	0.353221	−	0.173960i
$979$	−2.88181	−	2.88181i	−0.0921031	−	0.0921031i
$980$	1.29636	−	11.7096i	0.0414106	−	0.374049i
$981$	−15.9446	−	9.67257i	−0.509072	−	0.308821i
$982$	24.7720	−	51.5675i	0.790507	−	1.64558i
$983$			33.0752i			1.05494i	0.849575	+	0.527468i	$0.176858\pi$
$983$			33.0752i			1.05494i	−0.849575	+	0.527468i	$0.823142\pi$
$984$	−19.4358	−	53.6833i	−0.619591	−	1.71136i
$985$		−	9.99429i		−	0.318445i
$986$	16.7389	+	8.04106i	0.533076	+	0.256079i
$987$	11.1241	+	8.72905i	0.354083	+	0.277849i
$988$	−14.4350	+	11.5574i	−0.459238	+	0.367689i
$989$	−26.1950	−	26.1950i	−0.832953	−	0.832953i
$990$	2.82833	−	1.84368i	0.0898901	−	0.0585959i
$991$		−	17.1909i		−	0.546086i	−0.962002	−	0.273043i	$-0.911970\pi$
$991$		−	17.1909i		−	0.546086i	0.962002	−	0.273043i	$-0.0880302\pi$
$992$	5.99184	+	50.9570i	0.190241	+	1.61789i
$993$	−38.4240	+	4.63536i	−1.21935	+	0.147099i
$994$	7.68936	−	2.69900i	0.243892	−	0.0856070i
$995$	4.97879	−	4.97879i	0.157838	−	0.157838i
$996$	5.96133	−	6.07929i	0.188892	−	0.192630i
$997$	−24.3023	−	24.3023i	−0.769662	−	0.769662i	0.208385	−	0.978047i	$-0.433179\pi$
$997$	−24.3023	−	24.3023i	−0.769662	−	0.769662i	−0.978047	+	0.208385i	$0.933179\pi$
$998$	−10.6945	+	22.2625i	−0.338527	+	0.704707i
$999$	−8.66018	+	3.26140i	−0.273996	+	0.103186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bk.b.11.13	✓	60
3.2	odd	2	inner	240.2.bk.b.11.18	yes	60
4.3	odd	2		960.2.bk.b.911.7		60
12.11	even	2		960.2.bk.b.911.9		60
16.3	odd	4	inner	240.2.bk.b.131.18	yes	60
16.13	even	4		960.2.bk.b.431.9		60
48.29	odd	4		960.2.bk.b.431.7		60
48.35	even	4	inner	240.2.bk.b.131.13	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bk.b.11.13	✓	60	1.1	even	1	trivial
240.2.bk.b.11.18	yes	60	3.2	odd	2	inner
240.2.bk.b.131.13	yes	60	48.35	even	4	inner
240.2.bk.b.131.18	yes	60	16.3	odd	4	inner
960.2.bk.b.431.7		60	48.29	odd	4
960.2.bk.b.431.9		60	16.13	even	4
960.2.bk.b.911.7		60	4.3	odd	2
960.2.bk.b.911.9		60	12.11	even	2

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bk (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.468379 - 1.33440i) q^{2} +(1.36262 + 1.06924i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.788576 - 2.31908i) q^{6} +1.05330 q^{7} +(2.39927 + 1.49784i) q^{8} +(0.713439 + 2.91393i) q^{9} +O(q^{10})\)	\(q+(-0.468379 - 1.33440i) q^{2} +(1.36262 + 1.06924i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.788576 - 2.31908i) q^{6} +1.05330 q^{7} +(2.39927 + 1.49784i) q^{8} +(0.713439 + 2.91393i) q^{9} +(-1.27476 - 0.612368i) q^{10} +(0.562696 + 0.562696i) q^{11} +(-3.46394 + 0.0339362i) q^{12} +(1.89689 - 1.89689i) q^{13} +(-0.493345 - 1.40552i) q^{14} +(1.71958 - 0.207445i) q^{15} +(0.874950 - 3.90313i) q^{16} -1.69865i q^{17} +(3.55419 - 2.31684i) q^{18} +(2.43710 + 2.43710i) q^{19} +(-0.220074 + 1.98785i) q^{20} +(1.43524 + 1.12624i) q^{21} +(0.487306 - 1.01442i) q^{22} +3.79255i q^{23} +(1.66772 + 4.60638i) q^{24} -1.00000i q^{25} +(-3.41967 - 1.64274i) q^{26} +(-2.14356 + 4.73341i) q^{27} +(-1.64446 + 1.31664i) q^{28} +(-5.46614 - 5.46614i) q^{29} +(-1.08223 - 2.19745i) q^{30} -9.07008i q^{31} +(-5.61815 + 0.660616i) q^{32} +(0.165079 + 1.36840i) q^{33} +(-2.26668 + 0.795614i) q^{34} +(0.744797 - 0.744797i) q^{35} +(-4.75630 - 3.65755i) q^{36} +(1.25930 + 1.25930i) q^{37} +(2.11058 - 4.39355i) q^{38} +(4.61297 - 0.556495i) q^{39} +(2.75567 - 0.637404i) q^{40} -11.6541 q^{41} +(0.830608 - 2.44269i) q^{42} +(-6.90696 + 6.90696i) q^{43} +(-1.58188 - 0.175129i) q^{44} +(2.56494 + 1.55598i) q^{45} +(5.06078 - 1.77635i) q^{46} +7.75065 q^{47} +(5.36562 - 4.38294i) q^{48} -5.89056 q^{49} +(-1.33440 + 0.468379i) q^{50} +(1.81627 - 2.31461i) q^{51} +(-0.590372 + 5.33264i) q^{52} +(-6.77851 + 6.77851i) q^{53} +(7.32025 + 0.643331i) q^{54} +0.795773 q^{55} +(2.52715 + 1.57768i) q^{56} +(0.714978 + 5.92668i) q^{57} +(-4.73378 + 9.85424i) q^{58} +(0.908439 + 0.908439i) q^{59} +(-2.42538 + 2.47337i) q^{60} +(3.04034 - 3.04034i) q^{61} +(-12.1031 + 4.24824i) q^{62} +(0.751467 + 3.06925i) q^{63} +(3.51295 + 7.18743i) q^{64} -2.68261i q^{65} +(1.74867 - 0.861211i) q^{66} +(4.40764 + 4.40764i) q^{67} +(2.12333 + 2.65201i) q^{68} +(-4.05516 + 5.16779i) q^{69} +(-1.34270 - 0.645009i) q^{70} +5.47081i q^{71} +(-2.65287 + 8.05992i) q^{72} -7.69959i q^{73} +(1.09058 - 2.27024i) q^{74} +(1.06924 - 1.36262i) q^{75} +(-6.85130 - 0.758502i) q^{76} +(0.592689 + 0.592689i) q^{77} +(-2.90321 - 5.89489i) q^{78} -12.5927i q^{79} +(-2.14125 - 3.37862i) q^{80} +(-7.98201 + 4.15783i) q^{81} +(5.45855 + 15.5513i) q^{82} +(-1.73800 + 1.73800i) q^{83} +(-3.64857 + 0.0357450i) q^{84} +(-1.20113 - 1.20113i) q^{85} +(12.4517 + 5.98156i) q^{86} +(-1.60361 - 13.2929i) q^{87} +(0.507229 + 2.19289i) q^{88} -5.12144 q^{89} +(0.874938 - 4.15144i) q^{90} +(1.99800 - 1.99800i) q^{91} +(-4.74073 - 5.92109i) q^{92} +(9.69811 - 12.3590i) q^{93} +(-3.63024 - 10.3425i) q^{94} +3.44658 q^{95} +(-8.36173 - 5.10700i) q^{96} -6.76392 q^{97} +(2.75902 + 7.86035i) q^{98} +(-1.23821 + 2.04111i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7}+O(q^{10}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7	\( 60 q + 4 q^{3} + 8 q^{4} + 8 q^{6} + 16 q^{7} + 4 q^{12} + 16 q^{13} - 52 q^{16} - 20 q^{18} + 20 q^{19} - 16 q^{21} - 24 q^{22} - 28 q^{24} - 20 q^{27} - 56 q^{28} - 12 q^{34} + 12 q^{36} + 24 q^{37} - 80 q^{39} - 8 q^{40} + 36 q^{42} - 8 q^{45} + 36 q^{46} + 56 q^{48} + 28 q^{49} - 36 q^{51} - 24 q^{52} + 92 q^{54} - 80 q^{58} + 28 q^{60} + 20 q^{61} - 64 q^{64} + 24 q^{66} - 40 q^{67} + 12 q^{69} - 16 q^{70} - 56 q^{72} + 4 q^{75} - 20 q^{76} - 8 q^{78} - 28 q^{81} - 32 q^{82} + 16 q^{84} - 20 q^{85} - 24 q^{87} + 8 q^{88} + 32 q^{90} - 16 q^{91} - 48 q^{93} + 28 q^{94} + 72 q^{96} - 8 q^{97} + 32 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 + 8 * q^4 + 8 * q^6 + 16 * q^7 + 4 * q^12 + 16 * q^13 - 52 * q^16 - 20 * q^18 + 20 * q^19 - 16 * q^21 - 24 * q^22 - 28 * q^24 - 20 * q^27 - 56 * q^28 - 12 * q^34 + 12 * q^36 + 24 * q^37 - 80 * q^39 - 8 * q^40 + 36 * q^42 - 8 * q^45 + 36 * q^46 + 56 * q^48 + 28 * q^49 - 36 * q^51 - 24 * q^52 + 92 * q^54 - 80 * q^58 + 28 * q^60 + 20 * q^61 - 64 * q^64 + 24 * q^66 - 40 * q^67 + 12 * q^69 - 16 * q^70 - 56 * q^72 + 4 * q^75 - 20 * q^76 - 8 * q^78 - 28 * q^81 - 32 * q^82 + 16 * q^84 - 20 * q^85 - 24 * q^87 + 8 * q^88 + 32 * q^90 - 16 * q^91 - 48 * q^93 + 28 * q^94 + 72 * q^96 - 8 * q^97 + 32 * q^99

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