LMFDB - Embedded newform 240.2.bk.b.11.18

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			11.18
Character	$\chi$	$=$	240.11
Dual form			240.2.bk.b.131.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.468379 + 1.33440i) q^{2} +(1.06924 + 1.36262i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.31746 + 2.06502i) q^{6} +1.05330 q^{7} +(-2.39927 - 1.49784i) q^{8} +(-0.713439 + 2.91393i) q^{9} +O(q^{10})$	\(q+(0.468379 + 1.33440i) q^{2} +(1.06924 + 1.36262i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.31746 + 2.06502i) 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} +(-3.37263 - 0.790807i) 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} +(-4.22251 + 0.412813i) q^{18} +(2.43710 + 2.43710i) q^{19} +(0.220074 - 1.98785i) q^{20} +(1.12624 + 1.43524i) q^{21} +(0.487306 - 1.01442i) q^{22} -3.79255i q^{23} +(-0.524418 - 4.87083i) q^{24} -1.00000i q^{25} +(3.41967 + 1.64274i) q^{26} +(-4.73341 + 2.14356i) q^{27} +(-1.64446 + 1.31664i) q^{28} +(5.46614 + 5.46614i) q^{29} +(-0.528602 - 2.39177i) 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} +(-2.52859 - 5.44116i) 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} +(-1.38768 + 2.17509i) q^{42} +(-6.90696 + 6.90696i) q^{43} +(1.58188 + 0.175129i) q^{44} +(-1.55598 - 2.56494i) q^{45} +(5.06078 - 1.77635i) q^{46} -7.75065 q^{47} +(6.25400 - 2.98118i) q^{48} -5.89056 q^{49} +(1.33440 - 0.468379i) q^{50} +(-2.31461 + 1.81627i) q^{51} +(-0.590372 + 5.33264i) q^{52} +(6.77851 - 6.77851i) q^{53} +(-5.07739 - 5.31226i) 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} +(2.94399 - 1.82562i) 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} +(1.90331 - 0.420647i) q^{66} +(4.40764 + 4.40764i) q^{67} +(-2.12333 - 2.65201i) q^{68} +(5.16779 - 4.05516i) q^{69} +(-1.34270 - 0.645009i) q^{70} -5.47081i q^{71} +(6.07634 - 5.92268i) q^{72} -7.69959i q^{73} +(-1.09058 + 2.27024i) q^{74} +(1.36262 - 1.06924i) q^{75} +(-6.85130 - 0.758502i) q^{76} +(-0.592689 - 0.592689i) q^{77} +(1.41803 + 6.41619i) 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} +(-3.55240 - 0.832958i) 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} +(2.69386 - 3.27767i) q^{90} +(1.99800 - 1.99800i) q^{91} +(4.74073 + 5.92109i) q^{92} +(12.3590 - 9.69811i) q^{93} +(-3.63024 - 10.3425i) q^{94} -3.44658 q^{95} +(6.90733 + 6.94901i) q^{96} -6.76392 q^{97} +(-2.75902 - 7.86035i) q^{98} +(2.04111 - 1.23821i) 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
$3$	1.06924	+	1.36262i	0.617328	+	0.786706i
$3$	1.06924	+	1.36262i	0.617328	+	0.786706i
$4$	−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
$6$	−1.31746	+	2.06502i	−0.537851	+	0.843040i
$7$	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	0.617170	−	0.786830i	$-0.288279\pi$
$11$	−0.562696	−	0.562696i	−0.169659	−	0.169659i	−0.786830	+	0.617170i	$0.788279\pi$
$12$	−3.37263	−	0.790807i	−0.973594	−	0.228286i
$13$	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	$0.0660421\pi$
$17$			1.69865i			0.411984i	−0.978554	+	0.205992i	$0.933958\pi$
$18$	−4.22251	+	0.412813i	−0.995255	+	0.0973010i
$19$	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
$21$	1.12624	+	1.43524i	0.245765	+	0.313196i
$22$	0.487306	−	1.01442i	0.103894	−	0.216274i
$23$		−	3.79255i		−	0.790802i	−0.918509	−	0.395401i	$-0.870606\pi$
$23$		−	3.79255i		−	0.790802i	0.918509	−	0.395401i	$-0.129394\pi$
$24$	−0.524418	−	4.87083i	−0.107046	−	0.994254i
$25$		−	1.00000i		−	0.200000i
$26$	3.41967	+	1.64274i	0.670653	+	0.322169i
$27$	−4.73341	+	2.14356i	−0.910945	+	0.412528i
$28$	−1.64446	+	1.31664i	−0.310773	+	0.248821i
$29$	5.46614	+	5.46614i	1.01504	+	1.01504i	0.999885	+	0.0151515i	$0.00482306\pi$
$29$	5.46614	+	5.46614i	1.01504	+	1.01504i	0.0151515	+	0.999885i	$0.495177\pi$
$30$	−0.528602	−	2.39177i	−0.0965091	−	0.436676i
$31$		−	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
$36$	−2.52859	−	5.44116i	−0.421432	−	0.906860i
$37$	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	$-0.136055\pi$
$41$	11.6541			1.82007			0.910034	+	0.414533i	$0.136055\pi$
$42$	−1.38768	+	2.17509i	−0.214124	+	0.335623i
$43$	−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
$45$	−1.55598	−	2.56494i	−0.231952	−	0.382359i
$46$	5.06078	−	1.77635i	0.746171	−	0.261909i
$47$	−7.75065			−1.13055			−0.565274	−	0.824903i	$-0.691230\pi$
$47$	−7.75065			−1.13055			−0.565274	+	0.824903i	$0.691230\pi$
$48$	6.25400	−	2.98118i	0.902688	−	0.430296i
$49$	−5.89056			−0.841508
$50$	1.33440	−	0.468379i	0.188713	−	0.0662389i
$51$	−2.31461	+	1.81627i	−0.324110	+	0.254329i
$52$	−0.590372	+	5.33264i	−0.0818699	+	0.739504i
$53$	6.77851	−	6.77851i	0.931101	−	0.931101i	−0.0666742	−	0.997775i	$-0.521239\pi$
$53$	6.77851	−	6.77851i	0.931101	−	0.931101i	0.997775	+	0.0666742i	$0.0212388\pi$
$54$	−5.07739	−	5.31226i	−0.690946	−	0.722907i
$55$	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	0.645495	−	0.763764i	$-0.276651\pi$
$59$	−0.908439	−	0.908439i	−0.118269	−	0.118269i	−0.763764	+	0.645495i	$0.776651\pi$
$60$	2.94399	−	1.82562i	0.380068	−	0.235687i
$61$	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
$66$	1.90331	−	0.420647i	0.234281	−	0.0517781i
$67$	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
$69$	5.16779	−	4.05516i	0.622129	−	0.488184i
$70$	−1.34270	−	0.645009i	−0.160484	−	0.0770933i
$71$		−	5.47081i		−	0.649266i	−0.945840	−	0.324633i	$-0.894759\pi$
$71$		−	5.47081i		−	0.649266i	0.945840	−	0.324633i	$-0.105241\pi$
$72$	6.07634	−	5.92268i	0.716103	−	0.697995i
$73$		−	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
$75$	1.36262	−	1.06924i	0.157341	−	0.123466i
$76$	−6.85130	−	0.758502i	−0.785899	−	0.0870062i
$77$	−0.592689	−	0.592689i	−0.0675432	−	0.0675432i
$78$	1.41803	+	6.41619i	0.160561	+	0.726491i
$79$		−	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	−0.605259	−	0.796029i	$-0.706930\pi$
$83$	1.73800	−	1.73800i	0.190770	−	0.190770i	0.796029	+	0.605259i	$0.206930\pi$
$84$	−3.55240	−	0.832958i	−0.387598	−	0.0908832i
$85$	−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	$-0.412502\pi$
$89$	5.12144			0.542871			0.271436	+	0.962457i	$0.412502\pi$
$90$	2.69386	−	3.27767i	0.283958	−	0.345497i
$91$	1.99800	−	1.99800i	0.209447	−	0.209447i
$92$	4.74073	+	5.92109i	0.494255	+	0.617317i
$93$	12.3590	−	9.69811i	1.28157	−	1.00565i
$94$	−3.63024	−	10.3425i	−0.374431	−	1.06674i
$95$	−3.44658			−0.353612
$96$	6.90733	+	6.94901i	0.704976	+	0.709231i
$97$	−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
$99$	2.04111	−	1.23821i	0.205139	−	0.124445i
$100$	1.25001	+	1.56124i	0.125001	+	0.156124i
$101$	−10.5556	+	10.5556i	−1.05032	+	1.05032i	−0.0516563	+	0.998665i	$0.516450\pi$
$101$	−10.5556	+	10.5556i	−1.05032	+	1.05032i	−0.998665	+	0.0516563i	$0.983550\pi$
$102$	−3.50775	−	2.23791i	−0.347319	−	0.221586i
$103$	−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	$-0.902442\pi$
$107$	−12.9830	−	12.9830i	−1.25511	−	1.25511i	−0.301713	−	0.953399i	$-0.597558\pi$
$108$	4.71052	−	9.26342i	0.453270	−	0.891373i
$109$	−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	$0.226761\pi$
$113$			13.8967i			1.30729i	−0.756801	+	0.653646i	$0.773239\pi$
$114$	−8.24344	+	1.82187i	−0.772069	+	0.170634i
$115$	2.68174	+	2.68174i	0.250074	+	0.250074i
$116$	−15.3667	−	1.70123i	−1.42676	−	0.157956i
$117$	4.17410	+	6.88073i	0.385895	+	0.636124i
$118$	0.786726	−	1.63771i	0.0724240	−	0.150764i
$119$			1.78919i			0.164015i
$120$	3.81502	+	3.07338i	0.348262	+	0.280560i
$121$		−	10.3667i		−	0.942431i
$122$	5.48106	+	2.63300i	0.496232	+	0.238380i
$123$	12.4611	+	15.8801i	1.12358	+	1.43186i
$124$	11.3377	+	14.1606i	1.01815	+	1.27166i
$125$	0.707107	+	0.707107i	0.0632456	+	0.0632456i
$126$	−4.44758	+	0.434817i	−0.396222	+	0.0387366i
$127$		−	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	−0.897058	−	0.441913i	$-0.854300\pi$
$131$	−5.20937	+	5.20937i	−0.455145	+	0.455145i	0.441913	+	0.897058i	$0.354300\pi$
$132$	1.45278	+	2.34275i	0.126448	+	0.203910i
$133$	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	$-0.830582\pi$
$137$	−20.1712			−1.72334			−0.861672	+	0.507466i	$0.830582\pi$
$138$	7.83169	+	4.99654i	0.666678	+	0.425334i
$139$	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
$141$	−8.28732	−	10.5611i	−0.697918	−	0.889409i
$142$	7.30025	−	2.56242i	0.612623	−	0.215033i
$143$	−2.13475			−0.178516
$144$	10.7492	+	5.33420i	0.895771	+	0.444516i
$145$	−7.73029			−0.641966
$146$	10.2743	−	3.60633i	0.850309	−	0.298462i
$147$	−6.29843	−	8.02656i	−0.519486	−	0.662019i
$148$	−3.54021	−	0.391934i	−0.291004	−	0.0322168i
$149$	0.935992	−	0.935992i	0.0766795	−	0.0766795i	−0.667727	−	0.744406i	$-0.732733\pi$
$149$	0.935992	−	0.935992i	0.0766795	−	0.0766795i	0.744406	+	0.667727i	$0.232733\pi$
$150$	2.06502	+	1.31746i	0.168608	+	0.107570i
$151$	−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
$156$	−7.89758	+	4.89744i	−0.632313	+	0.392109i
$157$	−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
$162$	1.80959	−	12.5986i	0.142175	−	0.989842i
$163$	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
$165$	0.850874	+	1.08433i	0.0662405	+	0.0844151i
$166$	3.13323	+	1.50514i	0.243185	+	0.116822i
$167$			3.54199i			0.274087i	0.990565	+	0.137044i	$0.0437601\pi$
$167$			3.54199i			0.274087i	−0.990565	+	0.137044i	$0.956240\pi$
$168$	−0.552370	−	5.13045i	−0.0426163	−	0.395823i
$169$			5.80361i			0.446431i
$170$	1.04020	−	2.16537i	0.0797798	−	0.166076i
$171$	−8.84027	+	5.36282i	−0.676033	+	0.410105i
$172$	2.14966	−	19.4172i	0.163910	−	1.48055i
$173$	−3.86212	−	3.86212i	−0.293632	−	0.293632i	0.544881	−	0.838513i	$-0.316575\pi$
$173$	−3.86212	−	3.86212i	−0.293632	−	0.293632i	−0.838513	+	0.544881i	$0.816575\pi$
$174$	−18.4891	+	4.08625i	−1.40166	+	0.309778i
$175$		−	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	$-0.422224\pi$
$179$	16.2183	−	16.2183i	1.21221	−	1.21221i	0.970297	−	0.241916i	$-0.0777759\pi$
$180$	5.63547	+	2.05949i	0.420043	+	0.153506i
$181$	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
$186$	18.7299	+	11.9495i	1.37334	+	0.876178i
$187$	0.955825	−	0.955825i	0.0698969	−	0.0698969i
$188$	12.1006	−	9.68838i	0.882529	−	0.706598i
$189$	−4.98571	+	2.25781i	−0.362657	+	0.164232i
$190$	−1.61431	−	4.59911i	−0.117114	−	0.333655i
$191$	20.5110			1.48412			0.742060	−	0.670333i	$-0.233849\pi$
$191$	20.5110			1.48412			0.742060	+	0.670333i	$0.233849\pi$
$192$	−6.03751	+	12.4719i	−0.435720	+	0.900083i
$193$	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
$195$	−3.65536	+	2.86836i	−0.261766	+	0.205408i
$196$	9.19658	−	7.36325i	0.656899	−	0.525947i
$197$	−7.06703	+	7.06703i	−0.503505	+	0.503505i	−0.912525	−	0.409020i	$-0.865871\pi$
$197$	−7.06703	+	7.06703i	−0.503505	+	0.503505i	0.409020	+	0.912525i	$0.365871\pi$
$198$	2.60828	+	2.14370i	0.185362	+	0.152346i
$199$	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
$204$	1.34331	−	5.72892i	0.0940502	−	0.401105i
$205$	−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
$210$	−0.556778	−	2.51926i	−0.0384213	−	0.173845i
$211$	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
$213$	7.45461	−	5.84963i	0.510782	−	0.400810i
$214$	11.2435	−	23.4054i	0.768591	−	1.59996i
$215$		−	9.76792i		−	0.666166i
$216$	14.5674	+	1.94692i	0.991187	+	0.132471i
$217$		−	9.55353i		−	0.648536i
$218$	−7.92436	−	3.80671i	−0.536705	−	0.257823i
$219$	10.4916	−	8.23273i	0.708955	−	0.556316i
$220$	−1.24239	+	0.994724i	−0.0837621	+	0.0670643i
$221$	3.22216	+	3.22216i	0.216746	+	0.216746i
$222$	−4.25956	+	0.941399i	−0.285883	+	0.0631826i
$223$			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	−0.829797	−	0.558065i	$-0.811544\pi$
$227$	−4.09406	+	4.09406i	−0.271732	+	0.271732i	0.558065	+	0.829797i	$0.311544\pi$
$228$	−6.29216	−	10.1467i	−0.416709	−	0.671983i
$229$	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	$-0.755604\pi$
$233$	−21.9637			−1.43889			−0.719446	+	0.694549i	$0.755604\pi$
$234$	−7.22658	+	8.79270i	−0.472416	+	0.574797i
$235$	5.48053	−	5.48053i	0.357511	−	0.357511i
$236$	2.55385	+	0.282735i	0.166242	+	0.0184045i
$237$	17.1591	−	13.4647i	1.11460	−	0.874626i
$238$	−2.38750	+	0.838021i	−0.154759	+	0.0543209i
$239$	−8.38950			−0.542672			−0.271336	−	0.962485i	$-0.587465\pi$
$239$	−8.38950			−0.542672			−0.271336	+	0.962485i	$0.587465\pi$
$240$	−2.31424	+	6.53026i	−0.149383	+	0.421527i
$241$	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
$243$	−2.86919	−	15.3221i	−0.184058	−	0.982915i
$244$	−0.946250	+	8.54717i	−0.0605775	+	0.547176i
$245$	4.16525	−	4.16525i	0.266108	−	0.266108i
$246$	−15.3539	+	24.0660i	−0.978926	+	1.53439i
$247$	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	0.794334	−	0.607481i	$-0.207820\pi$
$251$	2.96030	+	2.96030i	0.186852	+	0.186852i	−0.607481	+	0.794334i	$0.707820\pi$
$252$	−2.66337	−	5.73118i	−0.167777	−	0.361030i
$253$	−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	$-0.840134\pi$
$257$		−	15.4344i		−	0.962768i	0.876510	−	0.481384i	$-0.159866\pi$
$258$	−5.16334	−	23.3626i	−0.321456	−	1.45449i
$259$	1.32642	+	1.32642i	0.0824200	+	0.0824200i
$260$	−3.35329	−	4.18820i	−0.207962	−	0.259741i
$261$	−19.8277	+	12.0282i	−1.22731	+	0.744527i
$262$	−9.39135	−	4.51142i	−0.580199	−	0.278716i
$263$		−	9.33469i		−	0.575602i	−0.957690	−	0.287801i	$-0.907076\pi$
$263$		−	9.33469i		−	0.575602i	0.957690	−	0.287801i	$-0.0929241\pi$
$264$	−2.44571	+	3.03589i	−0.150523	+	0.186846i
$265$			9.58627i			0.588880i
$266$	−2.22307	+	4.62774i	−0.136305	+	0.283745i
$267$	5.47606	+	6.97855i	0.335129	+	0.427080i
$268$	−12.3910	−	1.37180i	−0.756900	−	0.0837958i
$269$	−5.72888	−	5.72888i	−0.349296	−	0.349296i	0.510551	−	0.859847i	$-0.329441\pi$
$269$	−5.72888	−	5.72888i	−0.349296	−	0.349296i	−0.859847	+	0.510551i	$0.829441\pi$
$270$	7.34659	+	0.166074i	0.447099	+	0.0101069i
$271$			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
$276$	−2.99918	+	12.7909i	−0.180529	+	0.769920i
$277$	−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	$-0.175461\pi$
$281$	28.5603			1.70376			0.851882	+	0.523734i	$0.175461\pi$
$282$	10.2112	−	16.0052i	0.608066	−	0.953097i
$283$	−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
$285$	−3.68523	−	4.69636i	−0.218294	−	0.278189i
$286$	−0.999871	−	2.84860i	−0.0591236	−	0.168441i
$287$	12.2753			0.724589
$288$	−2.08322	+	16.8422i	−0.122755	+	0.992437i
$289$	14.1146			0.830269
$290$	−3.62071	−	10.3153i	−0.212615	−	0.605735i
$291$	−7.23227	−	9.21662i	−0.423963	−	0.540288i
$292$	9.62456	+	12.0209i	0.563235	+	0.703471i
$293$	16.6326	−	16.6326i	0.971689	−	0.971689i	−0.0279210	−	0.999610i	$-0.508889\pi$
$293$	16.6326	−	16.6326i	0.971689	−	0.971689i	0.999610	+	0.0279210i	$0.00888869\pi$
$294$	7.76058	−	12.1641i	0.452606	−	0.709425i
$295$	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
$300$	−0.790807	+	3.37263i	−0.0456573	+	0.194719i
$301$	−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
$306$	−0.701226	−	7.17258i	−0.0400864	−	0.410029i
$307$	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
$309$	−18.2091	−	23.2052i	−1.03588	−	1.32010i
$310$	−5.55423	+	11.5621i	−0.315459	+	0.656686i
$311$			27.8968i			1.58188i	0.611891	+	0.790942i	$0.290409\pi$
$311$			27.8968i			1.58188i	−0.611891	+	0.790942i	$0.709591\pi$
$312$	−10.2342	−	8.24467i	−0.579397	−	0.466763i
$313$			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
$315$	−1.63892	−	2.70165i	−0.0923427	−	0.152221i
$316$	15.7411	+	19.6603i	0.885504	+	1.10598i
$317$	3.86121	+	3.86121i	0.216867	+	0.216867i	0.807177	−	0.590310i	$-0.200994\pi$
$317$	3.86121	+	3.86121i	0.216867	+	0.216867i	−0.590310	+	0.807177i	$0.700994\pi$
$318$	5.06732	+	22.9282i	0.284161	+	1.28575i
$319$		−	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
$324$	17.6592	−	3.48622i	0.981065	−	0.193679i
$325$	−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
$330$	−1.04840	+	1.64328i	−0.0577125	+	0.0904598i
$331$	−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
$333$	−4.56796	+	2.77109i	−0.250322	+	0.151855i
$334$	−4.72643	+	1.65899i	−0.258619	+	0.0907762i
$335$	−6.23334			−0.340564
$336$	6.58735	−	3.14008i	0.359370	−	0.171305i
$337$	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
$339$	−18.9358	+	14.8589i	−1.02845	+	0.807027i
$340$	3.37668	+	0.373829i	0.183126	+	0.0202737i
$341$	−5.10370	+	5.10370i	−0.276381	+	0.276381i
$342$	−11.2968	−	9.28461i	−0.610858	−	0.502054i
$343$	−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	0.546265	−	0.837613i	$-0.316049\pi$
$347$	−5.42722	−	5.42722i	−0.291348	−	0.291348i	−0.837613	+	0.546265i	$0.816049\pi$
$348$	−14.1126	−	22.7579i	−0.756515	−	1.21995i
$349$	−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	$0.154804\pi$
$353$			17.5628i			0.934771i	−0.884054	+	0.467385i	$0.845196\pi$
$354$	3.07278	−	0.679110i	0.163316	−	0.0360943i
$355$	3.86845	+	3.86845i	0.205316	+	0.205316i
$356$	−7.99580	+	6.40185i	−0.423776	+	0.339297i
$357$	−2.43798	+	1.91308i	−0.129032	+	0.101251i
$358$	29.2380	+	14.0454i	1.54528	+	0.742321i
$359$		−	1.82368i		−	0.0962504i	−0.998841	−	0.0481252i	$-0.984675\pi$
$359$		−	1.82368i		−	0.0962504i	0.998841	−	0.0481252i	$-0.0153246\pi$
$360$	−0.108651	+	8.48459i	−0.00572642	+	0.447177i
$361$		−	7.12108i		−	0.374793i
$362$	−10.9017	+	22.6939i	−0.572982	+	1.19277i
$363$	14.1259	−	11.0846i	0.741417	−	0.581789i
$364$	−0.621840	+	5.61688i	−0.0325933	+	0.294404i
$365$	5.44443	+	5.44443i	0.284975	+	0.284975i
$366$	2.27283	+	10.2839i	0.118803	+	0.537548i
$367$			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
$372$	−7.17268	+	30.5900i	−0.371886	+	1.58602i
$373$	−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
$378$	−5.34803	−	5.59541i	−0.275073	−	0.287797i
$379$	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
$381$	10.4988	−	8.23840i	0.537870	−	0.422066i
$382$	9.60691	+	27.3698i	0.491532	+	1.40036i
$383$	−20.6284			−1.05406			−0.527030	−	0.849846i	$-0.676695\pi$
$383$	−20.6284			−1.05406			−0.527030	+	0.849846i	$0.676695\pi$
$384$	−19.4703	−	2.21486i	−0.993592	−	0.113026i
$385$	0.838188			0.0427180
$386$	7.15604	+	20.3874i	0.364233	+	1.03769i
$387$	−15.1987	−	25.0541i	−0.772594	−	1.27357i
$388$	10.5601	−	8.45497i	0.536109	−	0.429236i
$389$	−23.2975	+	23.2975i	−1.18123	+	1.18123i	−0.201806	+	0.979426i	$0.564681\pi$
$389$	−23.2975	+	23.2975i	−1.18123	+	1.18123i	−0.979426	+	0.201806i	$0.935319\pi$
$390$	−5.53963	−	3.53423i	−0.280510	−	0.178963i
$391$	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
$396$	−1.63889	+	4.48455i	−0.0823573	+	0.225357i
$397$	−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	$0.0626281\pi$
$401$			7.82917i			0.390970i	−0.980707	+	0.195485i	$0.937372\pi$
$402$	−14.9087	+	3.29496i	−0.743580	+	0.164338i
$403$	−17.2049	−	17.2049i	−0.857039	−	0.857039i
$404$	3.28523	−	29.6744i	0.163446	−	1.47636i
$405$	8.58416	−	2.70410i	0.426550	−	0.134368i
$406$	−4.98610	+	10.3795i	−0.247456	+	0.515125i
$407$		−	1.41721i		−	0.0702484i
$408$	8.27385	−	0.890804i	0.409617	−	0.0441014i
$409$		−	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
$411$	−21.5679	−	27.4856i	−1.06387	−	1.35577i
$412$	26.5878	−	21.2876i	1.30989	−	1.04876i
$413$	−0.956861	−	0.956861i	−0.0470840	−	0.0470840i
$414$	1.56562	+	16.0141i	0.0769458	+	0.787050i
$415$			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	−0.992612	−	0.121335i	$-0.961283\pi$
$419$	−17.8346	+	17.8346i	−0.871277	+	0.871277i	0.121335	+	0.992612i	$0.461283\pi$
$420$	3.10091	−	1.92293i	0.151309	−	0.0938295i
$421$	−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
$426$	11.2973	+	7.20758i	0.547357	+	0.349208i
$427$	3.20240	−	3.20240i	0.154975	−	0.154975i
$428$	36.4984	+	4.04071i	1.76422	+	0.195315i
$429$	−2.28256	−	2.90884i	−0.110203	−	0.140440i
$430$	13.0343	−	4.57509i	0.628570	−	0.220630i
$431$	32.0613			1.54434			0.772170	−	0.635416i	$-0.219171\pi$
$431$	32.0613			1.54434			0.772170	+	0.635416i	$0.219171\pi$
$432$	4.22510	+	20.3506i	0.203280	+	0.979121i
$433$	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
$435$	−8.26556	−	10.5334i	−0.396303	−	0.505038i
$436$	1.36806	−	12.3572i	0.0655182	−	0.591804i
$437$	9.24284	−	9.24284i	0.442145	−	0.442145i
$438$	15.8998	+	10.1439i	0.759721	+	0.484695i
$439$	−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	0.999961	−	0.00878795i	$-0.00279733\pi$
$443$	20.8618	+	20.8618i	0.991173	+	0.991173i	−0.00878795	+	0.999961i	$0.502797\pi$
$444$	−3.25129	−	5.24302i	−0.154300	−	0.248823i
$445$	−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	$-0.671862\pi$
$449$		−	36.3508i		−	1.71550i	0.514067	−	0.857750i	$-0.328138\pi$
$450$	0.412813	+	4.22251i	0.0194602	+	0.199051i
$451$	−6.55773	−	6.55773i	−0.308792	−	0.308792i
$452$	−17.3710	−	21.6961i	−0.817064	−	1.02050i
$453$	−11.3573	−	14.4734i	−0.533612	−	0.680020i
$454$	−7.38068	−	3.54553i	−0.346392	−	0.166400i
$455$			2.82560i			0.132466i
$456$	10.5926	−	13.1488i	0.496046	−	0.615747i
$457$		−	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
$459$	−3.64116	−	8.04042i	−0.169955	−	0.375295i
$460$	−7.53905	−	0.834642i	−0.351510	−	0.0389154i
$461$	5.19393	+	5.19393i	0.241905	+	0.241905i	0.817638	−	0.575733i	$-0.195283\pi$
$461$	5.19393	+	5.19393i	0.241905	+	0.241905i	−0.575733	+	0.817638i	$0.695283\pi$
$462$	2.00476	−	0.443068i	0.0932697	−	0.0206134i
$463$		−	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	−0.495796	−	0.868439i	$-0.665124\pi$
$467$	8.05288	−	8.05288i	0.372643	−	0.372643i	0.868439	+	0.495796i	$0.165124\pi$
$468$	−15.1178	−	5.52482i	−0.698818	−	0.255385i
$469$	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
$474$	26.0042	+	16.5904i	1.19441	+	0.762025i
$475$	2.43710	−	2.43710i	0.111822	−	0.111822i
$476$	−2.23651	−	2.79336i	−0.102510	−	0.128034i
$477$	14.9161	+	24.5882i	0.682960	+	1.12582i
$478$	−3.92947	−	11.1949i	−0.179730	−	0.512045i
$479$	−28.4148			−1.29830			−0.649152	−	0.760659i	$-0.724876\pi$
$479$	−28.4148			−1.29830			−0.649152	+	0.760659i	$0.724876\pi$
$480$	−9.79791	−	0.0294754i	−0.447212	−	0.00134536i
$481$	4.77752			0.217836
$482$	7.54379	+	21.4920i	0.343610	+	0.978936i
$483$	5.44324	−	4.27131i	0.247676	−	0.194351i
$484$	12.9585	+	16.1850i	0.589024	+	0.735682i
$485$	4.78281	−	4.78281i	0.217176	−	0.217176i
$486$	19.1020	−	11.0052i	0.866483	−	0.499206i
$487$	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	$-0.883912\pi$
$491$	−28.6044	−	28.6044i	−1.29090	−	1.29090i	−0.356670	−	0.934230i	$-0.616088\pi$
$492$	−39.3050	−	9.21616i	−1.77201	−	0.415497i
$493$	−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
$498$	1.29925	+	5.87874i	0.0582209	+	0.263433i
$499$	−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
$501$	−4.82637	+	3.78725i	−0.215626	+	0.169202i
$502$	−2.56368	+	5.33676i	−0.114422	+	0.238191i
$503$		−	21.7749i		−	0.970893i	−0.874266	−	0.485446i	$-0.838657\pi$
$503$		−	21.7749i		−	0.970893i	0.874266	−	0.485446i	$-0.161343\pi$
$504$	6.40021	−	6.23837i	0.285088	−	0.277879i
$505$		−	14.9279i		−	0.664281i
$506$	−3.84723	−	1.84813i	−0.171030	−	0.0821596i
$507$	−7.90808	+	6.20547i	−0.351210	+	0.275594i
$508$	9.63119	+	12.0292i	0.427315	+	0.533709i
$509$	12.5929	+	12.5929i	0.558173	+	0.558173i	0.928787	−	0.370614i	$-0.120853\pi$
$509$	12.5929	+	12.5929i	0.558173	+	0.558173i	−0.370614	+	0.928787i	$0.620853\pi$
$510$	4.06279	−	0.897912i	0.179903	−	0.0397602i
$511$		−	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
$516$	28.7567	−	17.8325i	1.26594	−	0.785034i
$517$	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	$-0.653611\pi$
$521$	−21.1851			−0.928136			−0.464068	+	0.885800i	$0.653611\pi$
$522$	−25.3373	−	20.8243i	−1.10898	−	0.911456i
$523$	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
$525$	1.43524	−	1.12624i	0.0626392	−	0.0491529i
$526$	12.4562	−	4.37218i	0.543116	−	0.190636i
$527$	15.4069			0.671135
$528$	−5.19660	−	1.84161i	−0.226153	−	0.0801456i
$529$	8.61654			0.374632
$530$	−12.7919	+	4.49001i	−0.555645	+	0.195034i
$531$	3.29525	−	1.99901i	0.143002	−	0.0867498i
$532$	−7.21649	−	0.798932i	−0.312875	−	0.0346381i
$533$	22.1066	−	22.1066i	0.957543	−	0.957543i
$534$	−6.74729	+	10.5759i	−0.291984	+	0.457662i
$535$	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
$540$	3.21938	+	9.88107i	0.138540	+	0.425214i
$541$	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
$546$	1.49362	+	6.75819i	0.0639209	+	0.289224i
$547$	−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
$549$	6.69025	+	11.0285i	0.285533	+	0.470683i
$550$	−1.01442	−	0.487306i	−0.0432549	−	0.0207788i
$551$			26.6431i			1.13503i
$552$	−18.4729	+	1.98888i	−0.786258	+	0.0846525i
$553$		−	13.2640i		−	0.564041i
$554$	13.4938	−	28.0898i	0.573296	−	1.19342i
$555$	−1.90424	−	2.42671i	−0.0808304	−	0.103008i
$556$	−1.81028	+	16.3517i	−0.0767731	+	0.693466i
$557$	−24.4160	−	24.4160i	−1.03454	−	1.03454i	−0.999382	−	0.0351576i	$-0.988807\pi$
$557$	−24.4160	−	24.4160i	−1.03454	−	1.03454i	−0.0351576	−	0.999382i	$-0.511193\pi$
$558$	3.74425	+	38.2985i	0.158507	+	1.62130i
$559$			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	−0.991692	−	0.128633i	$-0.958941\pi$
$563$	−20.4783	+	20.4783i	−0.863059	+	0.863059i	0.128633	+	0.991692i	$0.458941\pi$
$564$	26.1401	+	6.12926i	1.10069	+	0.258089i
$565$	−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	$-0.568975\pi$
$569$	−10.2571			−0.430001			−0.215000	+	0.976614i	$0.568975\pi$
$570$	4.54074	−	7.11725i	0.190191	−	0.298109i
$571$	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
$573$	21.9312	+	27.9485i	0.916189	+	1.16757i
$574$	5.74950	+	16.3802i	0.239980	+	0.683695i
$575$	−3.79255			−0.158160
$576$	−23.4500	+	5.10870i	−0.977082	+	0.212863i
$577$	−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
$579$	16.3362	+	20.8184i	0.678910	+	0.865185i
$580$	12.0688	−	9.66294i	0.501132	−	0.401232i
$581$	1.83064	−	1.83064i	0.0759476	−	0.0759476i
$582$	8.91120	−	13.9676i	0.369381	−	0.578976i
$583$	−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	0.732354	−	0.680924i	$-0.238422\pi$
$587$	1.24605	+	1.24605i	0.0514299	+	0.0514299i	−0.680924	+	0.732354i	$0.738422\pi$
$588$	19.8667	+	4.65829i	0.819287	+	0.192105i
$589$	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	$0.299256\pi$
$593$			39.3347i			1.61528i	−0.589674	+	0.807642i	$0.700744\pi$
$594$	−0.132157	+	5.84622i	−0.00542246	+	0.239873i
$595$	−1.26515	−	1.26515i	−0.0518661	−	0.0518661i
$596$	−0.291310	+	2.63131i	−0.0119325	+	0.107783i
$597$	7.52862	+	9.59427i	0.308126	+	0.392667i
$598$	6.23020	−	12.9693i	0.254772	−	0.530354i
$599$		−	6.93885i		−	0.283514i	−0.989902	−	0.141757i	$-0.954725\pi$
$599$		−	6.93885i		−	0.283514i	0.989902	−	0.141757i	$-0.0452751\pi$
$600$	−4.87083	+	0.524418i	−0.198851	+	0.0214093i
$601$			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
$603$	−15.9881	+	9.69898i	−0.651088	+	0.394973i
$604$	16.5832	−	13.2774i	0.674760	−	0.540248i
$605$	7.33040	+	7.33040i	0.298023	+	0.298023i
$606$	−7.89091	−	35.7041i	−0.320546	−	1.45038i
$607$			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
$612$	9.24264	−	4.29520i	0.373612	−	0.173623i
$613$	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	$-0.219639\pi$
$617$	38.3142			1.54247			0.771236	+	0.636550i	$0.219639\pi$
$618$	22.4362	−	35.1671i	0.902518	−	1.41463i
$619$	−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
$621$	8.12956	+	17.9517i	0.326228	+	0.720377i
$622$	−37.2255	+	13.0663i	−1.49261	+	0.523911i
$623$	5.39442			0.216123
$624$	6.20819	−	17.5181i	0.248527	−	0.701287i
$625$	−1.00000			−0.0400000
$626$	−19.9942	+	7.01804i	−0.799128	+	0.280497i
$627$	3.73724	−	2.93261i	0.149251	−	0.117117i
$628$	0.395032	−	3.56819i	0.0157635	−	0.142386i
$629$	−2.13912	+	2.13912i	−0.0852922	+	0.0852922i
$630$	2.83745	−	3.45237i	0.113047	−	0.137546i
$631$	−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
$636$	−28.2219	+	17.5009i	−1.11907	+	0.693957i
$637$	−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	$-0.821389\pi$
$641$		−	26.9453i		−	1.06427i	0.846658	−	0.532137i	$-0.178611\pi$
$642$	43.9146	−	9.70551i	1.73317	−	0.383046i
$643$	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
$645$	13.3099	−	10.4443i	0.524077	−	0.411243i
$646$	−7.46312	−	3.58514i	−0.293633	−	0.141055i
$647$			2.13219i			0.0838250i	0.999121	+	0.0419125i	$0.0133451\pi$
$647$			2.13219i			0.0838250i	−0.999121	+	0.0419125i	$0.986655\pi$
$648$	12.9232	+	21.9315i	0.507671	+	0.861551i
$649$			1.02235i			0.0401308i
$650$	1.64274	−	3.41967i	0.0644338	−	0.134131i
$651$	13.0178	−	10.2150i	0.510207	−	0.400359i
$652$	−9.99268	−	1.10628i	−0.391344	−	0.0433253i
$653$	−24.6766	−	24.6766i	−0.965670	−	0.965670i	0.0337602	−	0.999430i	$-0.489252\pi$
$653$	−24.6766	−	24.6766i	−0.965670	−	0.965670i	−0.999430	+	0.0337602i	$0.989252\pi$
$654$	−3.28599	−	14.8681i	−0.128492	−	0.581390i
$655$		−	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	−0.741584	−	0.670860i	$-0.765925\pi$
$659$	−1.81555	+	1.81555i	−0.0707239	+	0.0707239i	0.670860	+	0.741584i	$0.265925\pi$
$660$	−2.68385	−	0.629302i	−0.104469	−	0.0244956i
$661$	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
$666$	−5.83727	−	4.79756i	−0.226190	−	0.185902i
$667$	20.7306	−	20.7306i	0.802693	−	0.802693i
$668$	−4.42752	−	5.52990i	−0.171306	−	0.213958i
$669$	−9.72382	+	7.63028i	−0.375945	+	0.295004i
$670$	−2.91957	−	8.31777i	−0.112793	−	0.321343i
$671$	−3.42158			−0.132089
$672$	7.27550	+	7.31941i	0.280659	+	0.282352i
$673$	−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
$675$	2.14356	+	4.73341i	0.0825056	+	0.182189i
$676$	−7.25457	−	9.06083i	−0.279022	−	0.348494i
$677$	−19.5927	+	19.5927i	−0.753009	+	0.753009i	−0.975040	−	0.222031i	$-0.928731\pi$
$677$	−19.5927	+	19.5927i	−0.753009	+	0.753009i	0.222031	+	0.975040i	$0.428731\pi$
$678$	−28.6969	−	18.3084i	−1.10210	−	0.703128i
$679$	−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	0.774905	−	0.632077i	$-0.217798\pi$
$683$	3.73270	+	3.73270i	0.142828	+	0.142828i	−0.632077	+	0.774905i	$0.717798\pi$
$684$	7.09822	−	19.4231i	0.271407	−	0.742661i
$685$	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
$690$	−9.07093	+	2.00475i	−0.345324	+	0.0763196i
$691$	−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
$693$	2.14990	−	1.30421i	0.0816680	−	0.0495428i
$694$	4.70007	−	9.78407i	0.178412	−	0.371398i
$695$			8.22580i			0.312022i
$696$	23.7581	−	29.4912i	0.900548	−	1.11786i
$697$			19.7963i			0.749839i
$698$	−36.4206	−	17.4958i	−1.37854	−	0.662224i
$699$	−23.4846	−	29.9281i	−0.888267	−	1.13198i
$700$	1.31664	+	1.64446i	0.0497642	+	0.0621547i
$701$	3.06221	+	3.06221i	0.115658	+	0.115658i	0.762567	−	0.646909i	$-0.223939\pi$
$701$	3.06221	+	3.06221i	0.115658	+	0.115658i	−0.646909	+	0.762567i	$0.723939\pi$
$702$	−19.7080	−	0.445511i	−0.743832	−	0.0168147i
$703$			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
$708$	2.34543	+	3.78223i	0.0881466	+	0.142145i
$709$	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
$714$	−3.69472	−	2.35719i	−0.138271	−	0.0882157i
$715$	1.50949	−	1.50949i	0.0564519	−	0.0564519i
$716$	−5.04765	+	45.5937i	−0.188639	+	1.70392i
$717$	−8.97041	−	11.4317i	−0.335006	−	0.426923i
$718$	2.43352	−	0.854176i	0.0908182	−	0.0318776i
$719$	−9.52559			−0.355244			−0.177622	−	0.984099i	$-0.556841\pi$
$719$	−9.52559			−0.355244			−0.177622	+	0.984099i	$0.556841\pi$
$720$	−11.3727	+	3.82902i	−0.423836	+	0.142699i
$721$	−17.9376			−0.668032
$722$	9.50236	−	3.33537i	0.353641	−	0.124129i
$723$	17.2214	+	21.9465i	0.640471	+	0.816199i
$724$	−35.3889	−	3.91788i	−1.31522	−	0.145607i
$725$	5.46614	−	5.46614i	0.203007	−	0.203007i
$726$	21.4075	+	13.6578i	0.794507	+	0.506888i
$727$	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
$732$	−12.6583	+	7.84962i	−0.467863	+	0.290130i
$733$	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
$738$	−49.2097	+	4.81098i	−1.81143	+	0.177095i
$739$	−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
$741$	9.88604	+	12.5985i	0.363173	+	0.462818i
$742$	12.8715	+	6.18322i	0.472528	+	0.226993i
$743$			7.30891i			0.268138i	0.990972	+	0.134069i	$0.0428044\pi$
$743$			7.30891i			0.268138i	−0.990972	+	0.134069i	$0.957196\pi$
$744$	−44.1788	+	4.75651i	−1.61967	+	0.174382i
$745$			1.32369i			0.0484964i
$746$	0.672347	−	1.39961i	0.0246164	−	0.0512435i
$747$	3.82445	+	6.30437i	0.139929	+	0.230665i
$748$	−0.297483	+	2.68707i	−0.0108771	+	0.0982488i
$749$	−13.6750	−	13.6750i	−0.499673	−	0.499673i
$750$	−2.39177	+	0.528602i	−0.0873352	+	0.0193018i
$751$		−	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
$756$	4.96160	−	9.75718i	0.180452	−	0.354865i
$757$	−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	$-0.532966\pi$
$761$	−5.70368			−0.206758			−0.103379	+	0.994642i	$0.532966\pi$
$762$	15.9107	+	10.1509i	0.576385	+	0.367728i
$763$	−4.62993	+	4.62993i	−0.167615	+	0.167615i
$764$	−32.0226	+	25.6389i	−1.15854	+	0.927583i
$765$	4.35694	−	2.64308i	0.157526	−	0.0955606i
$766$	−9.66191	−	27.5265i	−0.349099	−	0.994572i
$767$	−3.44642			−0.124443
$768$	−6.16401	−	27.0186i	−0.222424	−	0.974950i
$769$	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
$771$	21.0311	−	16.5031i	0.757416	−	0.594344i
$772$	−23.8531	+	19.0980i	−0.858493	+	0.687353i
$773$	−10.1714	+	10.1714i	−0.365841	+	0.365841i	−0.865958	−	0.500117i	$-0.833290\pi$
$773$	−10.1714	+	10.1714i	−0.365841	+	0.365841i	0.500117	+	0.865958i	$0.333290\pi$
$774$	26.3134	−	32.0160i	0.945816	−	1.15079i
$775$	−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
$780$	2.12143	−	9.04744i	0.0759592	−	0.323950i
$781$	−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
$786$	−3.89430	−	17.6206i	−0.138905	−	0.628506i
$787$	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
$789$	12.7196	−	9.98105i	0.452829	−	0.355335i
$790$	−7.71140	+	16.0527i	−0.274359	+	0.571129i
$791$			14.6374i			0.520446i
$792$	−6.75180	−	0.0864616i	−0.239915	−	0.00307228i
$793$		−	11.5344i		−	0.409599i
$794$	−23.7753	−	11.4212i	−0.843755	−	0.405323i
$795$	−13.0624	+	10.2500i	−0.463275	+	0.363532i
$796$	−10.9928	+	8.80141i	−0.389630	+	0.311958i
$797$	−1.74739	−	1.74739i	−0.0618956	−	0.0618956i	0.675481	−	0.737377i	$-0.263936\pi$
$797$	−1.74739	−	1.74739i	−0.0618956	−	0.0618956i	−0.737377	+	0.675481i	$0.763936\pi$
$798$	−8.68283	+	1.91898i	−0.307369	+	0.0679311i
$799$		−	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
$804$	−11.3797	−	18.3509i	−0.401332	−	0.647187i
$805$	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	$-0.562608\pi$
$809$	−11.1168			−0.390846			−0.195423	+	0.980719i	$0.562608\pi$
$810$	7.62900	+	10.1882i	0.268056	+	0.357975i
$811$	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
$813$	−23.7586	+	18.6434i	−0.833252	+	0.653852i
$814$	1.89112	−	0.663791i	0.0662838	−	0.0232659i
$815$	−5.02687			−0.176083
$816$	5.06399	+	10.6234i	0.177275	+	0.371893i
$817$	−33.6659			−1.17782
$818$	3.14860	−	1.10517i	0.110088	−	0.0386414i
$819$	4.39658	+	7.24748i	0.153629	+	0.253248i
$820$	2.56477	−	23.1667i	0.0895656	−	0.809017i
$821$	16.0559	−	16.0559i	0.560354	−	0.560354i	−0.369054	−	0.929408i	$-0.620318\pi$
$821$	16.0559	−	16.0559i	0.560354	−	0.560354i	0.929408	+	0.369054i	$0.120318\pi$
$822$	26.5748	−	41.6539i	0.926903	−	1.45285i
$823$	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	0.955546	−	0.294841i	$-0.0952666\pi$
$827$	19.0003	+	19.0003i	0.660706	+	0.660706i	−0.294841	+	0.955546i	$0.595267\pi$
$828$	−20.6359	+	9.58983i	−0.717147	+	0.333270i
$829$	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
$834$	4.34818	+	19.6742i	0.150565	+	0.681263i
$835$	−2.50456	−	2.50456i	−0.0866740	−	0.0866740i
$836$	3.42840	+	4.28201i	0.118574	+	0.148096i
$837$	19.4422	+	42.9324i	0.672022	+	1.48396i
$838$	−32.1518	−	15.4451i	−1.11067	−	0.533542i
$839$			20.1324i			0.695048i	0.937671	+	0.347524i	$0.112977\pi$
$839$			20.1324i			0.695048i	−0.937671	+	0.347524i	$0.887023\pi$
$840$	4.01836	+	3.23719i	0.138647	+	0.111694i
$841$			30.7574i			1.06060i
$842$	17.5476	−	36.5285i	0.604730	−	1.25886i
$843$	30.5379	+	38.9167i	1.05178	+	1.34036i
$844$	−24.7392	−	2.73886i	−0.851560	−	0.0942755i
$845$	−4.10377	−	4.10377i	−0.141174	−	0.141174i
$846$	32.7272	−	3.19957i	1.12518	−	0.110003i
$847$		−	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
$852$	−4.32636	+	18.4510i	−0.148218	+	0.632121i
$853$	−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	$-0.529438\pi$
$857$	−5.40711			−0.184703			−0.0923517	+	0.995726i	$0.529438\pi$
$858$	2.81245	−	4.40829i	0.0960153	−	0.150497i
$859$	−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
$861$	13.1253	+	16.7265i	0.447309	+	0.570038i
$862$	15.0169	+	42.7826i	0.511476	+	1.45718i
$863$	22.2772			0.758324			0.379162	−	0.925330i	$-0.376212\pi$
$863$	22.2772			0.758324			0.379162	+	0.925330i	$0.376212\pi$
$864$	−25.1769	+	15.1698i	−0.856536	+	0.516087i
$865$	5.46187			0.185709
$866$	10.7931	+	30.7494i	0.366766	+	1.04491i
$867$	15.0919	+	19.2327i	0.512548	+	0.653178i
$868$	11.9420	+	14.9154i	0.405338	+	0.506260i
$869$	−7.08589	+	7.08589i	−0.240372	+	0.240372i
$870$	10.1844	−	15.9632i	0.345282	−	0.541203i
$871$	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
$876$	−6.08889	+	25.9679i	−0.205724	+	0.877373i
$877$	−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	$0.108638\pi$
$881$			19.8694i			0.669416i	−0.942322	+	0.334708i	$0.891362\pi$
$882$	24.8729	−	2.43170i	0.837515	−	0.0818796i
$883$	−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
$885$	1.37369	+	1.75059i	0.0461759	+	0.0588454i
$886$	−18.0667	+	37.6092i	−0.606963	+	1.26351i
$887$		−	18.7409i		−	0.629257i	−0.949215	−	0.314629i	$-0.898120\pi$
$887$		−	18.7409i		−	0.629257i	0.949215	−	0.314629i	$-0.101880\pi$
$888$	5.47345	−	6.79425i	0.183677	−	0.228000i
$889$		−	8.11558i		−	0.272188i
$890$	−6.52859	−	3.13621i	−0.218839	−	0.105126i
$891$	2.15185	+	6.83104i	0.0720897	+	0.228848i
$892$	−8.92026	−	11.1413i	−0.298672	−	0.373037i
$893$	−18.8891	−	18.8891i	−0.632100	−	0.632100i
$894$	0.699707	+	3.16597i	0.0234017	+	0.105886i
$895$			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
$900$	−5.44116	+	2.52859i	−0.181372	+	0.0842865i
$901$	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
$906$	13.9938	−	21.9342i	0.464913	−	0.728715i
$907$	−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
$909$	−23.2275	−	38.2891i	−0.770408	−	1.26997i
$910$	−3.77047	+	1.32345i	−0.124990	+	0.0438720i
$911$	46.5631			1.54270			0.771352	−	0.636408i	$-0.219581\pi$
$911$	46.5631			1.54270			0.771352	+	0.636408i	$0.219581\pi$
$912$	22.5071	+	7.97621i	0.745284	+	0.264119i
$913$	−1.95593			−0.0647318
$914$	23.0293	−	8.08337i	0.761741	−	0.267374i
$915$	−5.85883	+	4.59742i	−0.193687	+	0.151986i
$916$	−7.73447	−	0.856277i	−0.255554	−	0.0282922i
$917$	−5.48704	+	5.48704i	−0.181198	+	0.181198i
$918$	9.02368	−	8.62473i	0.297826	−	0.284658i
$919$	−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
$924$	1.53022	+	2.46762i	0.0503404	+	0.0811788i
$925$	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	$0.0244328\pi$
$929$			4.67449i			0.153365i	−0.997056	+	0.0766825i	$0.975567\pi$
$930$	−21.6936	+	4.79446i	−0.711360	+	0.157217i
$931$	−14.3559	−	14.3559i	−0.470495	−	0.470495i
$932$	34.2907	−	27.4549i	1.12323	−	0.899314i
$933$	−38.0126	+	29.8285i	−1.24448	+	0.976541i
$934$	14.5176	+	6.97395i	0.475029	+	0.228195i
$935$			1.35174i			0.0442067i
$936$	0.291468	−	22.7608i	0.00952694	−	0.743961i
$937$		−	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
$939$	−20.4170	+	16.0212i	−0.666282	+	0.522831i
$940$	−1.70571	+	15.4072i	−0.0556343	+	0.502526i
$941$	−19.2764	−	19.2764i	−0.628393	−	0.628393i	0.319271	−	0.947664i	$-0.396562\pi$
$941$	−19.2764	−	19.2764i	−0.628393	−	0.628393i	−0.947664	+	0.319271i	$0.896562\pi$
$942$	−0.948839	−	4.29322i	−0.0309148	−	0.139881i
$943$		−	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	−0.648848	−	0.760918i	$-0.724749\pi$
$947$	3.44878	−	3.44878i	0.112070	−	0.112070i	0.760918	+	0.648848i	$0.224749\pi$
$948$	−9.95843	+	42.4707i	−0.323435	+	1.37938i
$949$	−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	$-0.543479\pi$
$953$	−8.40732			−0.272340			−0.136170	+	0.990686i	$0.543479\pi$
$954$	−25.8241	+	31.4206i	−0.836085	+	1.01728i
$955$	−14.5034	+	14.5034i	−0.469320	+	0.469320i
$956$	13.0980	−	10.4870i	0.423621	−	0.339173i
$957$	8.38220	−	6.57750i	0.270958	−	0.212620i
$958$	−13.3089	−	37.9166i	−0.429991	−	1.22503i
$959$	−21.2464			−0.686082
$960$	−4.54981	−	13.0881i	−0.146844	−	0.422418i
$961$	−51.2663			−1.65375
$962$	2.23769	+	6.37511i	0.0721460	+	0.205542i
$963$	47.0941	−	28.5689i	1.51759	−	0.920622i
$964$	−25.1456	+	20.1329i	−0.809885	+	0.648436i
$965$	−10.8034	+	10.8034i	−0.347773	+	0.347773i
$966$	8.24913	+	5.26286i	0.265411	+	0.169330i
$967$	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	0.646035	−	0.763308i	$-0.276426\pi$
$971$	−3.65433	−	3.65433i	−0.117273	−	0.117273i	−0.763308	+	0.646035i	$0.776426\pi$
$972$	23.6323	+	20.3350i	0.758007	+	0.652247i
$973$	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	$0.0576504\pi$
$977$			11.2604i			0.360251i	−0.983644	+	0.180126i	$0.942350\pi$
$978$	−12.0231	+	2.65721i	−0.384457	+	0.0849683i
$979$	−2.88181	−	2.88181i	−0.0921031	−	0.0921031i
$980$	−1.29636	+	11.7096i	−0.0414106	+	0.374049i
$981$	−9.67257	−	15.9446i	−0.308821	−	0.509072i
$982$	24.7720	−	51.5675i	0.790507	−	1.64558i
$983$		−	33.0752i		−	1.05494i	−0.849575	−	0.527468i	$-0.823142\pi$
$983$		−	33.0752i		−	1.05494i	0.849575	−	0.527468i	$-0.176858\pi$
$984$	−6.11163	−	56.7653i	−0.194832	−	1.80961i
$985$		−	9.99429i		−	0.318445i
$986$	−16.7389	−	8.04106i	−0.533076	−	0.256079i
$987$	−8.72905	−	11.1241i	−0.277849	−	0.354083i
$988$	−14.4350	+	11.5574i	−0.459238	+	0.367689i
$989$	26.1950	+	26.1950i	0.832953	+	0.832953i
$990$	−3.36016	+	0.328505i	−0.106793	+	0.0104406i
$991$		−	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
$996$	−7.23604	+	4.48720i	−0.229283	+	0.142182i
$997$	−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.11.18	yes	60
3.2	odd	2	inner	240.2.bk.b.11.13	✓	60
4.3	odd	2		960.2.bk.b.911.9		60
12.11	even	2		960.2.bk.b.911.7		60
16.3	odd	4	inner	240.2.bk.b.131.13	yes	60
16.13	even	4		960.2.bk.b.431.7		60
48.29	odd	4		960.2.bk.b.431.9		60
48.35	even	4	inner	240.2.bk.b.131.18	yes	60

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

\(f(q)\)	\(=\)	\(q+(0.468379 + 1.33440i) q^{2} +(1.06924 + 1.36262i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.31746 + 2.06502i) q^{6} +1.05330 q^{7} +(-2.39927 - 1.49784i) q^{8} +(-0.713439 + 2.91393i) q^{9} +O(q^{10})\)	\(q+(0.468379 + 1.33440i) q^{2} +(1.06924 + 1.36262i) q^{3} +(-1.56124 + 1.25001i) q^{4} +(-0.707107 + 0.707107i) q^{5} +(-1.31746 + 2.06502i) 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} +(-3.37263 - 0.790807i) 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} +(-4.22251 + 0.412813i) q^{18} +(2.43710 + 2.43710i) q^{19} +(0.220074 - 1.98785i) q^{20} +(1.12624 + 1.43524i) q^{21} +(0.487306 - 1.01442i) q^{22} -3.79255i q^{23} +(-0.524418 - 4.87083i) q^{24} -1.00000i q^{25} +(3.41967 + 1.64274i) q^{26} +(-4.73341 + 2.14356i) q^{27} +(-1.64446 + 1.31664i) q^{28} +(5.46614 + 5.46614i) q^{29} +(-0.528602 - 2.39177i) 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} +(-2.52859 - 5.44116i) 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} +(-1.38768 + 2.17509i) q^{42} +(-6.90696 + 6.90696i) q^{43} +(1.58188 + 0.175129i) q^{44} +(-1.55598 - 2.56494i) q^{45} +(5.06078 - 1.77635i) q^{46} -7.75065 q^{47} +(6.25400 - 2.98118i) q^{48} -5.89056 q^{49} +(1.33440 - 0.468379i) q^{50} +(-2.31461 + 1.81627i) q^{51} +(-0.590372 + 5.33264i) q^{52} +(6.77851 - 6.77851i) q^{53} +(-5.07739 - 5.31226i) 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} +(2.94399 - 1.82562i) 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} +(1.90331 - 0.420647i) q^{66} +(4.40764 + 4.40764i) q^{67} +(-2.12333 - 2.65201i) q^{68} +(5.16779 - 4.05516i) q^{69} +(-1.34270 - 0.645009i) q^{70} -5.47081i q^{71} +(6.07634 - 5.92268i) q^{72} -7.69959i q^{73} +(-1.09058 + 2.27024i) q^{74} +(1.36262 - 1.06924i) q^{75} +(-6.85130 - 0.758502i) q^{76} +(-0.592689 - 0.592689i) q^{77} +(1.41803 + 6.41619i) 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} +(-3.55240 - 0.832958i) 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} +(2.69386 - 3.27767i) q^{90} +(1.99800 - 1.99800i) q^{91} +(4.74073 + 5.92109i) q^{92} +(12.3590 - 9.69811i) q^{93} +(-3.63024 - 10.3425i) q^{94} -3.44658 q^{95} +(6.90733 + 6.94901i) q^{96} -6.76392 q^{97} +(-2.75902 - 7.86035i) q^{98} +(2.04111 - 1.23821i) 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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