LMFDB - Embedded newform 475.2.n.a.39.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(39,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([3, 0]))

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

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

chi := DirichletCharacter("475.39");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.n (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			39.19
Character	$\chi$	$=$	475.39
Dual form			475.2.n.a.134.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49224 + 2.05389i) q^{2} +(-0.805296 - 0.261657i) q^{3} +(-1.37366 + 4.22769i) q^{4} +(0.616846 + 2.14930i) q^{5} +(-0.664281 - 2.04445i) q^{6} +1.89983i q^{7} +(-5.90407 + 1.91835i) q^{8} +(-1.84701 - 1.34193i) q^{9} +O(q^{10})$	\(q+(1.49224 + 2.05389i) q^{2} +(-0.805296 - 0.261657i) q^{3} +(-1.37366 + 4.22769i) q^{4} +(0.616846 + 2.14930i) q^{5} +(-0.664281 - 2.04445i) q^{6} +1.89983i q^{7} +(-5.90407 + 1.91835i) q^{8} +(-1.84701 - 1.34193i) q^{9} +(-3.49395 + 4.47421i) q^{10} +(1.23208 - 0.895155i) q^{11} +(2.21241 - 3.04512i) q^{12} +(0.300809 - 0.414028i) q^{13} +(-3.90205 + 2.83501i) q^{14} +(0.0656351 - 1.89223i) q^{15} +(-5.55779 - 4.03797i) q^{16} +(1.69942 - 0.552175i) q^{17} -5.79606i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-9.93392 - 0.344575i) q^{20} +(0.497103 - 1.52993i) q^{21} +(3.67710 + 1.19476i) q^{22} +(0.852439 + 1.17328i) q^{23} +5.25647 q^{24} +(-4.23900 + 2.65158i) q^{25} +1.29925 q^{26} +(2.62937 + 3.61901i) q^{27} +(-8.03190 - 2.60972i) q^{28} +(-1.63440 + 5.03018i) q^{29} +(3.98437 - 2.68885i) q^{30} +(-0.155040 - 0.477163i) q^{31} -5.02492i q^{32} +(-1.22641 + 0.398484i) q^{33} +(3.67005 + 2.66645i) q^{34} +(-4.08331 + 1.17190i) q^{35} +(8.21045 - 5.96524i) q^{36} +(4.36579 - 6.00899i) q^{37} +(1.49224 - 2.05389i) q^{38} +(-0.350573 + 0.254706i) q^{39} +(-7.76501 - 11.5063i) q^{40} +(-0.150678 - 0.109474i) q^{41} +(3.88410 - 1.26202i) q^{42} +0.882567i q^{43} +(2.09199 + 6.43847i) q^{44} +(1.74490 - 4.79756i) q^{45} +(-1.13775 + 3.50164i) q^{46} +(-1.43354 - 0.465787i) q^{47} +(3.41910 + 4.70599i) q^{48} +3.39064 q^{49} +(-11.7717 - 4.74966i) q^{50} -1.51302 q^{51} +(1.33717 + 1.84046i) q^{52} +(10.8001 + 3.50915i) q^{53} +(-3.50942 + 10.8009i) q^{54} +(2.68396 + 2.09593i) q^{55} +(-3.64454 - 11.2167i) q^{56} +0.846738i q^{57} +(-12.7704 + 4.14934i) q^{58} +(-0.638073 - 0.463588i) q^{59} +(7.90959 + 2.87676i) q^{60} +(3.98304 - 2.89385i) q^{61} +(0.748686 - 1.03048i) q^{62} +(2.54945 - 3.50901i) q^{63} +(-0.794934 + 0.577554i) q^{64} +(1.07542 + 0.391138i) q^{65} +(-2.64854 - 1.92428i) q^{66} +(-4.39726 + 1.42876i) q^{67} +7.94312i q^{68} +(-0.379469 - 1.16789i) q^{69} +(-8.50025 - 6.63792i) q^{70} +(-1.36252 + 4.19341i) q^{71} +(13.4792 + 4.37965i) q^{72} +(9.69659 + 13.3462i) q^{73} +18.8566 q^{74} +(4.10745 - 1.02614i) q^{75} +4.44526 q^{76} +(1.70064 + 2.34074i) q^{77} +(-1.04628 - 0.339957i) q^{78} +(3.27969 - 10.0938i) q^{79} +(5.25051 - 14.4362i) q^{80} +(0.946008 + 2.91151i) q^{81} -0.472836i q^{82} +(9.57643 - 3.11157i) q^{83} +(5.78521 + 4.20320i) q^{84} +(2.23507 + 3.31196i) q^{85} +(-1.81270 + 1.31700i) q^{86} +(2.63236 - 3.62313i) q^{87} +(-5.55703 + 7.64860i) q^{88} +(-3.68623 + 2.67820i) q^{89} +(12.4575 - 3.57528i) q^{90} +(0.786583 + 0.571486i) q^{91} +(-6.13123 + 1.99216i) q^{92} +0.424825i q^{93} +(-1.18252 - 3.63941i) q^{94} +(1.85349 - 1.25083i) q^{95} +(-1.31480 + 4.04655i) q^{96} +(12.1536 + 3.94895i) q^{97} +(5.05965 + 6.96401i) q^{98} -3.47690 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	$ 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) $ 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

Coefficient data

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

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

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

$2$	1.49224	+	2.05389i	1.05517	+	1.45232i	0.884236	+	0.467040i	$0.154679\pi$
$2$	1.49224	+	2.05389i	1.05517	+	1.45232i	0.170937	+	0.985282i	$0.445321\pi$
$3$	−0.805296	−	0.261657i	−0.464938	−	0.151067i	0.0671744	−	0.997741i	$-0.478602\pi$
$3$	−0.805296	−	0.261657i	−0.464938	−	0.151067i	−0.532112	+	0.846674i	$0.678602\pi$
$4$	−1.37366	+	4.22769i	−0.686830	+	2.11385i
$5$	0.616846	+	2.14930i	0.275862	+	0.961197i
$5$	0.616846	+	2.14930i	0.275862	+	0.961197i
$6$	−0.664281	−	2.04445i	−0.271192	−	0.834642i
$7$			1.89983i			0.718069i	0.933324	+	0.359034i	$0.116894\pi$
$7$			1.89983i			0.718069i	−0.933324	+	0.359034i	$0.883106\pi$
$8$	−5.90407	+	1.91835i	−2.08740	+	0.678238i
$9$	−1.84701	−	1.34193i	−0.615671	−	0.447311i
$10$	−3.49395	+	4.47421i	−1.10489	+	1.41487i
$11$	1.23208	−	0.895155i	0.371485	−	0.269899i	−0.386342	−	0.922356i	$-0.626261\pi$
$11$	1.23208	−	0.895155i	0.371485	−	0.269899i	0.757826	+	0.652456i	$0.226261\pi$
$12$	2.21241	−	3.04512i	0.638667	−	0.879049i
$13$	0.300809	−	0.414028i	0.0834294	−	0.114831i	−0.765262	−	0.643718i	$-0.777391\pi$
$13$	0.300809	−	0.414028i	0.0834294	−	0.114831i	0.848692	+	0.528888i	$0.177391\pi$
$14$	−3.90205	+	2.83501i	−1.04287	+	0.757687i
$15$	0.0656351	−	1.89223i	0.0169469	−	0.488571i
$16$	−5.55779	−	4.03797i	−1.38945	−	1.00949i
$17$	1.69942	−	0.552175i	0.412170	−	0.133922i	−0.0955900	−	0.995421i	$-0.530474\pi$
$17$	1.69942	−	0.552175i	0.412170	−	0.133922i	0.507760	+	0.861499i	$0.330474\pi$
$18$		−	5.79606i		−	1.36614i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$19$	−0.309017	−	0.951057i	−0.0708934	−	0.218187i
$20$	−9.93392	−	0.344575i	−2.22129	−	0.0770493i
$21$	0.497103	−	1.52993i	0.108477	−	0.333857i
$22$	3.67710	+	1.19476i	0.783961	+	0.254724i
$23$	0.852439	+	1.17328i	0.177746	+	0.244646i	0.888589	−	0.458705i	$-0.151686\pi$
$23$	0.852439	+	1.17328i	0.177746	+	0.244646i	−0.710843	+	0.703351i	$0.751686\pi$
$24$	5.25647			1.07297
$25$	−4.23900	+	2.65158i	−0.847800	+	0.530316i
$26$	1.29925			0.254804
$27$	2.62937	+	3.61901i	0.506022	+	0.696480i
$28$	−8.03190	−	2.60972i	−1.51789	−	0.493191i
$29$	−1.63440	+	5.03018i	−0.303501	+	0.934080i	0.676731	+	0.736230i	$0.263396\pi$
$29$	−1.63440	+	5.03018i	−0.303501	+	0.934080i	−0.980232	+	0.197850i	$0.936604\pi$
$30$	3.98437	−	2.68885i	0.727444	−	0.490915i
$31$	−0.155040	−	0.477163i	−0.0278460	−	0.0857011i	0.936168	−	0.351554i	$-0.114347\pi$
$31$	−0.155040	−	0.477163i	−0.0278460	−	0.0857011i	−0.964014	+	0.265853i	$0.914347\pi$
$32$		−	5.02492i		−	0.888288i
$33$	−1.22641	+	0.398484i	−0.213490	+	0.0693672i
$34$	3.67005	+	2.66645i	0.629408	+	0.457292i
$35$	−4.08331	+	1.17190i	−0.690206	+	0.198088i
$36$	8.21045	−	5.96524i	1.36841	−	0.994207i
$37$	4.36579	−	6.00899i	0.717731	−	0.987872i	−0.281865	−	0.959454i	$-0.590953\pi$
$37$	4.36579	−	6.00899i	0.717731	−	0.987872i	0.999596	−	0.0284176i	$-0.00904682\pi$
$38$	1.49224	−	2.05389i	0.242073	−	0.333185i
$39$	−0.350573	+	0.254706i	−0.0561367	+	0.0407857i
$40$	−7.76501	−	11.5063i	−1.22776	−	1.81931i
$41$	−0.150678	−	0.109474i	−0.0235319	−	0.0170969i	0.575957	−	0.817480i	$-0.304630\pi$
$41$	−0.150678	−	0.109474i	−0.0235319	−	0.0170969i	−0.599489	+	0.800383i	$0.704630\pi$
$42$	3.88410	−	1.26202i	0.599330	−	0.194734i
$43$			0.882567i			0.134590i	0.997733	+	0.0672951i	$0.0214369\pi$
$43$			0.882567i			0.134590i	−0.997733	+	0.0672951i	$0.978563\pi$
$44$	2.09199	+	6.43847i	0.315379	+	0.970636i
$45$	1.74490	−	4.79756i	0.260114	−	0.715178i
$46$	−1.13775	+	3.50164i	−0.167752	+	0.516288i
$47$	−1.43354	−	0.465787i	−0.209104	−	0.0679420i	0.202592	−	0.979263i	$-0.435063\pi$
$47$	−1.43354	−	0.465787i	−0.209104	−	0.0679420i	−0.411696	+	0.911321i	$0.635063\pi$
$48$	3.41910	+	4.70599i	0.493505	+	0.679251i
$49$	3.39064			0.484377
$50$	−11.7717	−	4.74966i	−1.66477	−	0.671704i
$51$	−1.51302			−0.211865
$52$	1.33717	+	1.84046i	0.185433	+	0.255226i
$53$	10.8001	+	3.50915i	1.48350	+	0.482019i	0.935157	−	0.354232i	$-0.115258\pi$
$53$	10.8001	+	3.50915i	1.48350	+	0.482019i	0.548346	+	0.836252i	$0.315258\pi$
$54$	−3.50942	+	10.8009i	−0.477571	+	1.46981i
$55$	2.68396	+	2.09593i	0.361905	+	0.282615i
$56$	−3.64454	−	11.2167i	−0.487022	−	1.49890i
$57$			0.846738i			0.112153i
$58$	−12.7704	+	4.14934i	−1.67683	+	0.544835i
$59$	−0.638073	−	0.463588i	−0.0830701	−	0.0603540i	0.545475	−	0.838127i	$-0.316349\pi$
$59$	−0.638073	−	0.463588i	−0.0830701	−	0.0603540i	−0.628545	+	0.777773i	$0.716349\pi$
$60$	7.90959	+	2.87676i	1.02112	+	0.371388i
$61$	3.98304	−	2.89385i	0.509976	−	0.370519i	−0.302838	−	0.953042i	$-0.597934\pi$
$61$	3.98304	−	2.89385i	0.509976	−	0.370519i	0.812815	+	0.582522i	$0.197934\pi$
$62$	0.748686	−	1.03048i	0.0950832	−	0.130871i
$63$	2.54945	−	3.50901i	0.321200	−	0.442094i
$64$	−0.794934	+	0.577554i	−0.0993668	+	0.0721942i
$65$	1.07542	+	0.391138i	0.133390	+	0.0485147i
$66$	−2.64854	−	1.92428i	−0.326013	−	0.236862i
$67$	−4.39726	+	1.42876i	−0.537211	+	0.174550i	−0.565042	−	0.825062i	$-0.691140\pi$
$67$	−4.39726	+	1.42876i	−0.537211	+	0.174550i	0.0278311	+	0.999613i	$0.491140\pi$
$68$			7.94312i			0.963245i
$69$	−0.379469	−	1.16789i	−0.0456827	−	0.140597i
$70$	−8.50025	−	6.63792i	−1.01597	−	0.793384i
$71$	−1.36252	+	4.19341i	−0.161701	+	0.497666i	−0.998778	−	0.0494198i	$-0.984263\pi$
$71$	−1.36252	+	4.19341i	−0.161701	+	0.497666i	0.837077	+	0.547086i	$0.184263\pi$
$72$	13.4792	+	4.37965i	1.58854	+	0.516147i
$73$	9.69659	+	13.3462i	1.13490	+	1.56206i	0.778410	+	0.627756i	$0.216026\pi$
$73$	9.69659	+	13.3462i	1.13490	+	1.56206i	0.356489	+	0.934299i	$0.383974\pi$
$74$	18.8566			2.19204
$75$	4.10745	−	1.02614i	0.474288	−	0.118489i
$76$	4.44526			0.509906
$77$	1.70064	+	2.34074i	0.193806	+	0.266752i
$78$	−1.04628	−	0.339957i	−0.118468	−	0.0384925i
$79$	3.27969	−	10.0938i	0.368994	−	1.13565i	−0.578448	−	0.815719i	$-0.696342\pi$
$79$	3.27969	−	10.0938i	0.368994	−	1.13565i	0.947442	−	0.319927i	$-0.103658\pi$
$80$	5.25051	−	14.4362i	0.587025	−	1.61401i
$81$	0.946008	+	2.91151i	0.105112	+	0.323502i
$82$		−	0.472836i		−	0.0522160i
$83$	9.57643	−	3.11157i	1.05115	−	0.341539i	0.268030	−	0.963411i	$-0.413627\pi$
$83$	9.57643	−	3.11157i	1.05115	−	0.341539i	0.783119	+	0.621871i	$0.213627\pi$
$84$	5.78521	+	4.20320i	0.631218	+	0.458607i
$85$	2.23507	+	3.31196i	0.242428	+	0.359232i
$86$	−1.81270	+	1.31700i	−0.195468	+	0.142016i
$87$	2.63236	−	3.62313i	0.282218	−	0.388440i
$88$	−5.55703	+	7.64860i	−0.592382	+	0.815344i
$89$	−3.68623	+	2.67820i	−0.390740	+	0.283889i	−0.765759	−	0.643128i	$-0.777636\pi$
$89$	−3.68623	+	2.67820i	−0.390740	+	0.283889i	0.375019	+	0.927017i	$0.377636\pi$
$90$	12.4575	−	3.57528i	1.31313	−	0.376867i
$91$	0.786583	+	0.571486i	0.0824563	+	0.0599080i
$92$	−6.13123	+	1.99216i	−0.639225	+	0.207697i
$93$			0.424825i			0.0440523i
$94$	−1.18252	−	3.63941i	−0.121967	−	0.375377i
$95$	1.85349	−	1.25083i	0.190164	−	0.128332i
$96$	−1.31480	+	4.04655i	−0.134191	+	0.412999i
$97$	12.1536	+	3.94895i	1.23401	+	0.400955i	0.852167	−	0.523270i	$-0.175288\pi$
$97$	12.1536	+	3.94895i	1.23401	+	0.400955i	0.381847	+	0.924225i	$0.375288\pi$
$98$	5.05965	+	6.96401i	0.511102	+	0.703471i
$99$	−3.47690			−0.349441
$100$	−5.38711	−	21.5636i	−0.538711	−	2.15636i
$101$	−0.0583747			−0.00580850			−0.00290425	−	0.999996i	$-0.500924\pi$
$101$	−0.0583747			−0.00580850			−0.00290425	+	0.999996i	$0.500924\pi$
$102$	−2.25778	−	3.10757i	−0.223554	−	0.307696i
$103$	−17.5673	−	5.70795i	−1.73095	−	0.562421i	−0.737367	−	0.675492i	$-0.763931\pi$
$103$	−17.5673	−	5.70795i	−1.73095	−	0.562421i	−0.993587	+	0.113071i	$0.963931\pi$
$104$	−0.981746	+	3.02150i	−0.0962681	+	0.296283i
$105$	3.59491	+	0.124696i	0.350828	+	0.0121690i
$106$	8.90887	+	27.4187i	0.865306	+	2.66314i
$107$		−	16.8517i		−	1.62912i	−0.580080	−	0.814560i	$-0.696979\pi$
$107$		−	16.8517i		−	1.62912i	0.580080	−	0.814560i	$-0.303021\pi$
$108$	−18.9119	+	6.14486i	−1.81980	+	0.591289i
$109$	−11.7256	−	8.51915i	−1.12311	−	0.815986i	−0.138431	−	0.990372i	$-0.544206\pi$
$109$	−11.7256	−	8.51915i	−1.12311	−	0.815986i	−0.984677	+	0.174386i	$0.944206\pi$
$110$	−0.299700	+	8.64020i	−0.0285753	+	0.823810i
$111$	−5.08804	+	3.69668i	−0.482935	+	0.350873i
$112$	7.67146	−	10.5589i	0.724885	−	0.997718i
$113$	8.10575	−	11.1566i	0.762525	−	1.04953i	−0.234475	−	0.972122i	$-0.575337\pi$
$113$	8.10575	−	11.1566i	0.762525	−	1.04953i	0.997000	−	0.0774035i	$-0.0246630\pi$
$114$	−1.73911	+	1.26354i	−0.162883	+	0.118341i
$115$	−1.99591	+	2.55588i	−0.186120	+	0.238337i
$116$	−19.0209	−	13.8195i	−1.76605	−	1.28311i
$117$	−1.11120	+	0.361049i	−0.102730	+	0.0333790i
$118$		−	2.00232i		−	0.184328i
$119$	1.04904	+	3.22861i	0.0961653	+	0.295966i
$120$	3.24243	+	11.2977i	0.295992	+	1.03134i
$121$	−2.68248	+	8.25583i	−0.243862	+	0.750530i
$122$	11.8873	+	3.86242i	1.07623	+	0.349687i
$123$	0.0926955	+	0.127584i	0.00835807	+	0.0115039i
$124$	2.23027			0.200284
$125$	−8.31386	−	7.47528i	−0.743614	−	0.668609i
$126$	11.0115			0.980985
$127$	−7.63612	−	10.5102i	−0.677596	−	0.932631i	0.322306	−	0.946636i	$-0.395542\pi$
$127$	−7.63612	−	10.5102i	−0.677596	−	0.932631i	−0.999902	+	0.0140046i	$0.995542\pi$
$128$	−11.9304	−	3.87643i	−1.05451	−	0.342631i
$129$	0.230930	−	0.710728i	0.0203322	−	0.0625761i
$130$	0.801437	+	2.79248i	0.0702906	+	0.244916i
$131$	1.57975	+	4.86198i	0.138024	+	0.424794i	0.996048	−	0.0888155i	$-0.0283082\pi$
$131$	1.57975	+	4.86198i	0.138024	+	0.424794i	−0.858024	+	0.513609i	$0.828308\pi$
$132$		−	5.73226i		−	0.498929i
$133$	1.80685	−	0.587080i	0.156674	−	0.0509063i
$134$	−9.49628	−	6.89945i	−0.820354	−	0.596022i
$135$	−6.15644	+	7.88368i	−0.529862	+	0.678519i
$136$	−8.97422	+	6.52015i	−0.769533	+	0.559098i
$137$	10.6876	−	14.7103i	0.913107	−	1.25678i	−0.0529879	−	0.998595i	$-0.516874\pi$
$137$	10.6876	−	14.7103i	0.913107	−	1.25678i	0.966095	−	0.258188i	$-0.0831255\pi$
$138$	1.83245	−	2.52215i	0.155989	−	0.214700i
$139$	−14.7388	+	10.7084i	−1.25013	+	0.908270i	−0.998229	−	0.0594835i	$-0.981055\pi$
$139$	−14.7388	+	10.7084i	−1.25013	+	0.908270i	−0.251898	+	0.967754i	$0.581055\pi$
$140$	0.654635	−	18.8728i	0.0553267	−	1.59504i
$141$	1.03255	+	0.750193i	0.0869565	+	0.0631776i
$142$	−10.6460	+	3.45910i	−0.893394	+	0.290281i
$143$		−	0.779384i		−	0.0651754i
$144$	4.84662	+	14.9164i	0.403885	+	1.24303i
$145$	−11.8195	−	0.409981i	−0.981560	−	0.0340471i
$146$	−12.9420	+	39.8315i	−1.07109	+	3.29648i
$147$	−2.73047	−	0.887183i	−0.225205	−	0.0731736i
$148$	19.4070	+	26.7115i	1.59525	+	2.19567i
$149$	−1.88982			−0.154820			−0.0774098	−	0.996999i	$-0.524665\pi$
$149$	−1.88982			−0.154820			−0.0774098	+	0.996999i	$0.524665\pi$
$150$	8.23690	+	6.90502i	0.672540	+	0.563792i
$151$	5.09269			0.414437			0.207218	−	0.978295i	$-0.433559\pi$
$151$	5.09269			0.414437			0.207218	+	0.978295i	$0.433559\pi$
$152$	3.64891	+	5.02230i	0.295966	+	0.407362i
$153$	−3.87983	−	1.26063i	−0.313666	−	0.101916i
$154$	−2.26985	+	6.98588i	−0.182910	+	0.562938i
$155$	0.929933	−	0.627564i	0.0746940	−	0.0504071i
$156$	−0.595252	−	1.83200i	−0.0476583	−	0.146677i
$157$		−	11.9624i		−	0.954707i	−0.878711	−	0.477354i	$-0.841596\pi$
$157$		−	11.9624i		−	0.954707i	0.878711	−	0.477354i	$-0.158404\pi$
$158$	25.6258	−	8.32632i	2.03868	−	0.662406i
$159$	−7.77906	−	5.65182i	−0.616919	−	0.448218i
$160$	10.8001	−	3.09960i	0.853820	−	0.245045i
$161$	−2.22904	+	1.61949i	−0.175673	+	0.127634i
$162$	−4.56827	+	6.28768i	−0.358917	+	0.494007i
$163$	−4.16251	+	5.72921i	−0.326033	+	0.448746i	−0.940297	−	0.340354i	$-0.889453\pi$
$163$	−4.16251	+	5.72921i	−0.326033	+	0.448746i	0.614264	+	0.789101i	$0.289453\pi$
$164$	0.669800	−	0.486638i	0.0523026	−	0.0380001i
$165$	−1.61297	−	2.39012i	−0.125569	−	0.186070i
$166$	20.6812	+	15.0257i	1.60517	+	1.16622i
$167$	14.4259	−	4.68725i	1.11631	−	0.362710i	0.307950	−	0.951402i	$-0.400357\pi$
$167$	14.4259	−	4.68725i	1.11631	−	0.362710i	0.808357	+	0.588692i	$0.200357\pi$
$168$			9.98641i			0.770468i
$169$	3.93629	+	12.1146i	0.302791	+	0.931896i
$170$	−3.46715	+	9.53284i	−0.265918	+	0.731135i
$171$	−0.705496	+	2.17129i	−0.0539507	+	0.166043i
$172$	−3.73122	−	1.21235i	−0.284503	−	0.0924406i
$173$	1.71702	+	2.36327i	0.130542	+	0.179676i	0.869285	−	0.494312i	$-0.164580\pi$
$173$	1.71702	+	2.36327i	0.130542	+	0.179676i	−0.738742	+	0.673988i	$0.764580\pi$
$174$	11.3696			0.861929
$175$	−5.03755	−	8.05339i	−0.380803	−	0.608779i
$176$	−10.4622			−0.788619
$177$	0.392537	+	0.540281i	0.0295049	+	0.0406100i
$178$	−11.0015	−	3.57460i	−0.824596	−	0.267928i
$179$	6.74661	−	20.7639i	0.504265	−	1.55197i	−0.297737	−	0.954648i	$-0.596232\pi$
$179$	6.74661	−	20.7639i	0.504265	−	1.55197i	0.802002	−	0.597321i	$-0.203768\pi$
$180$	17.8857	+	13.9671i	1.33312	+	1.04105i
$181$	4.15092	+	12.7752i	0.308535	+	0.949573i	0.978334	+	0.207031i	$0.0663802\pi$
$181$	4.15092	+	12.7752i	0.308535	+	0.949573i	−0.669799	+	0.742542i	$0.733620\pi$
$182$			2.46835i			0.182966i
$183$	−3.96472	+	1.28822i	−0.293081	+	0.0952277i
$184$	−7.28362	−	5.29186i	−0.536955	−	0.390121i
$185$	15.6082	+	5.67677i	1.14753	+	0.417364i
$186$	−0.872545	+	0.633941i	−0.0639781	+	0.0464828i
$187$	1.59953	−	2.20156i	0.116969	−	0.160994i
$188$	3.93841	−	5.42075i	0.287238	−	0.395349i
$189$	−6.87552	+	4.99536i	−0.500120	+	0.363359i
$190$	5.33492	+	1.94034i	0.387036	+	0.140767i
$191$	−18.2689	−	13.2731i	−1.32189	−	0.960410i	−0.999907	−	0.0136656i	$-0.995650\pi$
$191$	−18.2689	−	13.2731i	−1.32189	−	0.960410i	−0.321985	−	0.946745i	$-0.604350\pi$
$192$	0.791278	−	0.257102i	0.0571056	−	0.0185547i
$193$		−	25.3707i		−	1.82622i	−0.407712	−	0.913111i	$-0.633673\pi$
$193$		−	25.3707i		−	1.82622i	0.407712	−	0.913111i	$-0.366327\pi$
$194$	10.0254	+	30.8550i	0.719783	+	2.21526i
$195$	−0.763691	−	0.596373i	−0.0546890	−	0.0427072i
$196$	−4.65759	+	14.3346i	−0.332685	+	1.02390i
$197$	−9.86047	−	3.20386i	−0.702530	−	0.228266i	−0.0640972	−	0.997944i	$-0.520417\pi$
$197$	−9.86047	−	3.20386i	−0.702530	−	0.228266i	−0.638432	+	0.769678i	$0.720417\pi$
$198$	−5.18837	−	7.14118i	−0.368721	−	0.507501i
$199$	−22.7011			−1.60924			−0.804621	−	0.593789i	$-0.797631\pi$
$199$	−22.7011			−1.60924			−0.804621	+	0.593789i	$0.797631\pi$
$200$	19.9407	−	23.7870i	1.41002	−	1.68199i
$201$	3.91494			0.276138
$202$	−0.0871091	−	0.119895i	−0.00612898	−	0.00843581i
$203$	−9.55649	−	3.10509i	−0.670734	−	0.217935i
$204$	2.07837	−	6.39656i	0.145515	−	0.447849i
$205$	0.142347	−	0.391380i	0.00994195	−	0.0273352i
$206$	−14.4911	−	44.5989i	−1.00964	−	3.10735i
$207$		−	3.31098i		−	0.230129i
$208$	−3.34366	+	1.08642i	−0.231841	+	0.0753298i
$209$	−1.23208	−	0.895155i	−0.0852244	−	0.0619192i
$210$	5.10836	+	7.56964i	0.352510	+	0.522355i
$211$	−5.59762	+	4.06691i	−0.385356	+	0.279978i	−0.763550	−	0.645749i	$-0.776545\pi$
$211$	−5.59762	+	4.06691i	−0.385356	+	0.279978i	0.378194	+	0.925726i	$0.376545\pi$
$212$	−29.6712	+	40.8390i	−2.03783	+	2.80483i
$213$	2.19446	−	3.02042i	0.150362	−	0.206956i
$214$	34.6117	−	25.1468i	2.36600	−	1.71900i
$215$	−1.89690	+	0.544408i	−0.129368	+	0.0371283i
$216$	−22.4665	−	16.3229i	−1.52865	−	1.11063i
$217$	0.906530	−	0.294550i	0.0615393	−	0.0199953i
$218$		−	36.7957i		−	2.49212i
$219$	−4.31650	−	13.2848i	−0.291682	−	0.897705i
$220$	−12.5478	+	8.46786i	−0.845972	+	0.570903i
$221$	0.282585	−	0.869706i	0.0190087	−	0.0585028i
$222$	−15.1852	−	4.93396i	−1.01916	−	0.331146i
$223$	−0.689271	−	0.948700i	−0.0461570	−	0.0635297i	0.785315	−	0.619097i	$-0.212501\pi$
$223$	−0.689271	−	0.948700i	−0.0461570	−	0.0635297i	−0.831472	+	0.555567i	$0.812501\pi$
$224$	9.54650			0.637852
$225$	11.3877	+	0.790958i	0.759182	+	0.0527305i
$226$	35.0102			2.32885
$227$	12.5707	+	17.3021i	0.834345	+	1.14838i	0.987099	+	0.160114i	$0.0511860\pi$
$227$	12.5707	+	17.3021i	0.834345	+	1.14838i	−0.152753	+	0.988264i	$0.548814\pi$
$228$	−3.57975	−	1.16313i	−0.237075	−	0.0770302i
$229$	5.44916	−	16.7708i	0.360091	−	1.10824i	−0.592908	−	0.805270i	$-0.702020\pi$
$229$	5.44916	−	16.7708i	0.360091	−	1.10824i	0.952999	−	0.302975i	$-0.0979797\pi$
$230$	−8.22789	−	0.285398i	−0.542531	−	0.0188186i
$231$	−0.757053	−	2.32997i	−0.0498104	−	0.153301i
$232$		−	32.8338i		−	2.15565i
$233$	2.48444	−	0.807244i	0.162761	−	0.0528843i	−0.226503	−	0.974010i	$-0.572729\pi$
$233$	2.48444	−	0.807244i	0.162761	−	0.0528843i	0.389264	+	0.921126i	$0.372729\pi$
$234$	−2.39973	−	1.74351i	−0.156875	−	0.113976i
$235$	0.116840	−	3.36844i	0.00762181	−	0.219733i
$236$	2.83640	−	2.06077i	0.184634	−	0.134144i
$237$	−5.28224	+	7.27038i	−0.343118	+	0.472262i
$238$	−5.06580	+	6.97248i	−0.328367	+	0.451959i
$239$	14.3067	−	10.3944i	0.925424	−	0.672360i	−0.0194443	−	0.999811i	$-0.506190\pi$
$239$	14.3067	−	10.3944i	0.925424	−	0.672360i	0.944868	+	0.327451i	$0.106190\pi$
$240$	−8.00554	+	10.2516i	−0.516755	+	0.661735i
$241$	20.9707	+	15.2361i	1.35084	+	0.981443i	0.998969	+	0.0453951i	$0.0144547\pi$
$241$	20.9707	+	15.2361i	1.35084	+	0.981443i	0.351872	+	0.936048i	$0.385545\pi$
$242$	−20.9595	+	6.81015i	−1.34733	+	0.437773i
$243$		−	16.0122i		−	1.02718i
$244$	6.76296	+	20.8142i	0.432954	+	1.33250i
$245$	2.09150	+	7.28751i	0.133621	+	0.465582i
$246$	−0.123721	+	0.380773i	−0.00788815	+	0.0242772i
$247$	−0.486719	−	0.158145i	−0.0309692	−	0.0100625i
$248$	1.83073	+	2.51978i	0.116251	+	0.160006i
$249$	−8.52602			−0.540315
$250$	2.94715	−	28.2307i	0.186394	−	1.78547i
$251$	−20.4831			−1.29288			−0.646441	−	0.762964i	$-0.723743\pi$
$251$	−20.4831			−1.29288			−0.646441	+	0.762964i	$0.723743\pi$
$252$	11.3330	+	15.5985i	0.713909	+	0.982612i
$253$	2.10054	+	0.682506i	0.132060	+	0.0429088i
$254$	10.1919	−	31.3675i	0.639499	−	1.96817i
$255$	−0.933298	−	3.25193i	−0.0584454	−	0.203644i
$256$	−9.23402	−	28.4194i	−0.577126	−	1.77621i
$257$			6.61075i			0.412367i	0.978513	+	0.206184i	$0.0661044\pi$
$257$			6.61075i			0.412367i	−0.978513	+	0.206184i	$0.933896\pi$
$258$	1.80436	−	0.586273i	0.112335	−	0.0364997i
$259$	11.4161	+	8.29426i	0.709360	+	0.515380i
$260$	−3.13088	+	4.00927i	−0.194169	+	0.248644i
$261$	9.76893	−	7.09754i	0.604681	−	0.439327i
$262$	−7.62862	+	10.4999i	−0.471298	+	0.648686i
$263$	9.68633	−	13.3321i	0.597285	−	0.822092i	−0.398171	−	0.917311i	$-0.630355\pi$
$263$	9.68633	−	13.3321i	0.597285	−	0.822092i	0.995456	+	0.0952188i	$0.0303551\pi$
$264$	6.47636	−	4.70535i	0.398593	−	0.289594i
$265$	−0.880252	+	25.3772i	−0.0540735	+	1.55891i
$266$	3.90205	+	2.83501i	0.239250	+	0.173825i
$267$	3.66928	−	1.19222i	0.224556	−	0.0729627i
$268$		−	20.5529i		−	1.25547i
$269$	−5.59596	−	17.2226i	−0.341192	−	1.05008i	−0.963591	−	0.267381i	$-0.913842\pi$
$269$	−5.59596	−	17.2226i	−0.341192	−	1.05008i	0.622399	−	0.782700i	$-0.286158\pi$
$270$	−25.3791	−	0.880318i	−1.54452	−	0.0535745i
$271$	0.158009	−	0.486301i	0.00959834	−	0.0295407i	−0.946143	−	0.323750i	$-0.895056\pi$
$271$	0.158009	−	0.486301i	0.00959834	−	0.0295407i	0.955741	+	0.294209i	$0.0950563\pi$
$272$	−11.6747	−	3.79333i	−0.707881	−	0.230005i
$273$	−0.483899	−	0.666030i	−0.0292869	−	0.0403100i
$274$	46.1619			2.78874
$275$	−2.84919	+	7.06151i	−0.171813	+	0.425825i
$276$	5.45872			0.328576
$277$	5.66966	+	7.80362i	0.340657	+	0.468874i	0.944633	−	0.328128i	$-0.106418\pi$
$277$	5.66966	+	7.80362i	0.340657	+	0.468874i	−0.603976	+	0.797002i	$0.706418\pi$
$278$	−43.9876	−	14.2924i	−2.63820	−	0.857204i
$279$	−0.353961	+	1.08938i	−0.0211911	+	0.0652195i
$280$	21.8600	−	14.7522i	1.30639	−	0.881613i
$281$	−5.26154	−	16.1934i	−0.313877	−	0.966015i	−0.976214	−	0.216809i	$-0.930435\pi$
$281$	−5.26154	−	16.1934i	−0.313877	−	0.966015i	0.662337	−	0.749206i	$-0.269565\pi$
$282$			3.24022i			0.192952i
$283$	−13.0864	+	4.25203i	−0.777906	+	0.252757i	−0.670946	−	0.741506i	$-0.734112\pi$
$283$	−13.0864	+	4.25203i	−0.777906	+	0.252757i	−0.106960	+	0.994263i	$0.534112\pi$
$284$	−15.8568	−	11.5206i	−0.940927	−	0.683624i
$285$	−1.81990	+	0.522307i	−0.107801	+	0.0309388i
$286$	1.60077	−	1.16303i	0.0946556	−	0.0687713i
$287$	0.207981	−	0.286262i	0.0122768	−	0.0168975i
$288$	−6.74310	+	9.28109i	−0.397341	+	0.546893i
$289$	−11.1702	+	8.11560i	−0.657068	+	0.477388i
$290$	−16.7955	−	24.8879i	−0.986268	−	1.46147i
$291$	−8.75400	−	6.36015i	−0.513169	−	0.372839i
$292$	−69.7435	+	22.6610i	−4.08143	+	1.32614i
$293$			13.8791i			0.810825i	0.914134	+	0.405413i	$0.132872\pi$
$293$			13.8791i			0.810825i	−0.914134	+	0.405413i	$0.867128\pi$
$294$	−2.25234	−	6.93198i	−0.131359	−	0.404281i
$295$	0.602796	−	1.65738i	0.0350962	−	0.0964961i
$296$	−14.2486	+	43.8525i	−0.828181	+	2.54888i
$297$	6.47916	+	2.10521i	0.375959	+	0.122156i
$298$	−2.82006	−	3.88148i	−0.163362	−	0.224848i
$299$	0.742192			0.0429221
$300$	−1.30403	+	18.7746i	−0.0752881	+	1.08395i
$301$	−1.67673			−0.0966451
$302$	7.59951	+	10.4598i	0.437303	+	0.601896i
$303$	0.0470089	+	0.0152741i	0.00270059	+	0.000877476i
$304$	−2.12289	+	6.53357i	−0.121756	+	0.374726i
$305$	8.67668	+	6.77570i	0.496825	+	0.387976i
$306$	−3.20044	−	9.84993i	−0.182957	−	0.563083i
$307$			11.1606i			0.636970i	0.947928	+	0.318485i	$0.103174\pi$
$307$			11.1606i			0.636970i	−0.947928	+	0.318485i	$0.896826\pi$
$308$	−12.2320	+	3.97442i	−0.696984	+	0.226464i
$309$	12.6533	+	9.19318i	0.719822	+	0.522982i
$310$	2.67663	+	0.973506i	0.152023	+	0.0552914i
$311$	8.70851	−	6.32710i	0.493814	−	0.358777i	−0.312835	−	0.949807i	$-0.601279\pi$
$311$	8.70851	−	6.32710i	0.493814	−	0.358777i	0.806649	+	0.591031i	$0.201279\pi$
$312$	1.58119	−	2.17632i	0.0895174	−	0.123210i
$313$	−4.85088	+	6.67667i	−0.274188	+	0.377388i	−0.923798	−	0.382880i	$-0.874932\pi$
$313$	−4.85088	+	6.67667i	−0.274188	+	0.377388i	0.649610	+	0.760268i	$0.274932\pi$
$314$	24.5696	−	17.8509i	1.38654	−	1.00738i
$315$	9.11455	+	3.31501i	0.513547	+	0.186780i
$316$	38.1685	+	27.7310i	2.14715	+	1.55999i
$317$	29.5885	−	9.61387i	1.66185	−	0.539969i	0.680594	−	0.732661i	$-0.261722\pi$
$317$	29.5885	−	9.61387i	1.66185	−	0.539969i	0.981259	+	0.192692i	$0.0617218\pi$
$318$		−	24.4112i		−	1.36891i
$319$	2.48908	+	7.66060i	0.139362	+	0.428911i
$320$	−1.73169	−	1.35229i	−0.0968044	−	0.0755954i
$321$	−4.40937	+	13.5706i	−0.246107	+	0.757439i
$322$	−6.65252	−	2.16153i	−0.370730	−	0.120458i
$323$	−1.05030	−	1.44561i	−0.0584402	−	0.0804360i
$324$	−13.6085			−0.756027
$325$	−0.177302	+	2.55268i	−0.00983493	+	0.141597i
$326$	−17.9787			−0.995746
$327$	7.21349	+	9.92851i	0.398907	+	0.549048i
$328$	1.09962	+	0.357288i	0.0607163	+	0.0197279i
$329$	0.884917	−	2.72349i	0.0487870	−	0.150151i
$330$	2.50211	−	6.87950i	0.137737	−	0.378704i
$331$	9.92170	+	30.5359i	0.545346	+	1.67840i	0.720165	+	0.693803i	$0.244066\pi$
$331$	9.92170	+	30.5359i	0.545346	+	1.67840i	−0.174819	+	0.984601i	$0.555934\pi$
$332$			44.7604i			2.45655i
$333$	−16.1273	+	5.24009i	−0.883772	+	0.287155i
$334$	31.1540	+	22.6347i	1.70467	+	1.23852i
$335$	−5.78326	−	8.56972i	−0.315973	−	0.468214i
$336$	−8.94059	+	6.49572i	−0.487749	+	0.354371i
$337$	−10.8782	+	14.9725i	−0.592572	+	0.815606i	−0.995003	−	0.0998447i	$-0.968165\pi$
$337$	−10.8782	+	14.9725i	−0.592572	+	0.815606i	0.402431	+	0.915450i	$0.368165\pi$
$338$	−19.0083	+	26.1627i	−1.03392	+	1.42306i
$339$	−9.44673	+	6.86345i	−0.513076	+	0.372772i
$340$	−17.0722	+	4.89969i	−0.925868	+	0.265723i
$341$	−0.618156	−	0.449116i	−0.0334750	−	0.0243210i
$342$	−5.51238	+	1.79108i	−0.298075	+	0.0968505i
$343$			19.7405i			1.06589i
$344$	−1.69307	−	5.21074i	−0.0912842	−	0.280944i
$345$	2.27606	−	1.53600i	0.122539	−	0.0826954i
$346$	−2.29170	+	7.05314i	−0.123203	+	0.379179i
$347$	−17.3204	−	5.62775i	−0.929810	−	0.302113i	−0.195325	−	0.980739i	$-0.562576\pi$
$347$	−17.3204	−	5.62775i	−0.929810	−	0.302113i	−0.734485	+	0.678625i	$0.762576\pi$
$348$	11.7015	+	16.1057i	0.627267	+	0.863358i
$349$	−6.84441			−0.366373			−0.183186	−	0.983078i	$-0.558641\pi$
$349$	−6.84441			−0.366373			−0.183186	+	0.983078i	$0.558641\pi$
$350$	9.02356	−	22.3642i	0.482329	−	1.19542i
$351$	2.28931			0.122194
$352$	−4.49808	−	6.19107i	−0.239748	−	0.329985i
$353$	−2.41612	−	0.785046i	−0.128597	−	0.0417838i	0.244011	−	0.969772i	$-0.421537\pi$
$353$	−2.41612	−	0.785046i	−0.128597	−	0.0417838i	−0.372609	+	0.927989i	$0.621537\pi$
$354$	−0.523920	+	1.61246i	−0.0278460	+	0.0857012i
$355$	−9.85337	−	0.341781i	−0.522962	−	0.0181398i
$356$	−6.25899	−	19.2632i	−0.331726	−	1.02095i
$357$		−	2.87448i		−	0.152133i
$358$	52.7145	−	17.1280i	2.78605	−	0.905241i
$359$	−12.8405	−	9.32916i	−0.677695	−	0.492374i	0.194897	−	0.980824i	$-0.437563\pi$
$359$	−12.8405	−	9.32916i	−0.677695	−	0.492374i	−0.872592	+	0.488449i	$0.837563\pi$
$360$	−1.09861	+	31.6724i	−0.0579019	+	1.66928i
$361$	−0.809017	+	0.587785i	−0.0425798	+	0.0309361i
$362$	−20.0447	+	27.5892i	−1.05353	+	1.45006i
$363$	4.32038	−	5.94650i	0.226761	−	0.312110i
$364$	−3.49657	+	2.54040i	−0.183270	+	0.133153i
$365$	−22.7037	+	29.0735i	−1.18837	+	1.52177i
$366$	−8.56218	−	6.22079i	−0.447552	−	0.325166i
$367$	10.8033	−	3.51021i	0.563928	−	0.183231i	−0.0131599	−	0.999913i	$-0.504189\pi$
$367$	10.8033	−	3.51021i	0.563928	−	0.183231i	0.577088	+	0.816682i	$0.304189\pi$
$368$		−	9.96297i		−	0.519356i
$369$	0.131397	+	0.404398i	0.00684026	+	0.0210521i
$370$	11.6316	+	40.5286i	0.604700	+	2.10698i
$371$	−6.66680	+	20.5183i	−0.346123	+	1.06526i
$372$	−1.79603	−	0.583565i	−0.0931198	−	0.0302564i
$373$	3.00839	+	4.14069i	0.155768	+	0.214397i	0.879768	−	0.475404i	$-0.157698\pi$
$373$	3.00839	+	4.14069i	0.155768	+	0.214397i	−0.723999	+	0.689801i	$0.757698\pi$
$374$	6.90866			0.357238
$375$	4.73916	+	8.19519i	0.244729	+	0.423198i
$376$	9.35728			0.482565
$377$	1.59099	+	2.18981i	0.0819402	+	0.112781i
$378$	−20.5199	−	6.66731i	−1.05543	−	0.342929i
$379$	8.48871	−	26.1256i	0.436036	−	1.34198i	−0.455985	−	0.889987i	$-0.650713\pi$
$379$	8.48871	−	26.1256i	0.436036	−	1.34198i	0.892021	−	0.451993i	$-0.149287\pi$
$380$	2.74204	+	9.55420i	0.140664	+	0.490120i
$381$	3.39927	+	10.4619i	0.174150	+	0.535978i
$382$		−	57.3291i		−	2.93321i
$383$	−1.90160	+	0.617866i	−0.0971670	+	0.0315715i	−0.357197	−	0.934029i	$-0.616268\pi$
$383$	−1.90160	+	0.617866i	−0.0971670	+	0.0315715i	0.260030	+	0.965601i	$0.416268\pi$
$384$	8.59323	+	6.24335i	0.438521	+	0.318604i
$385$	−3.98191	+	5.09907i	−0.202937	+	0.259873i
$386$	52.1087	−	37.8592i	2.65226	−	1.92698i
$387$	1.18435	−	1.63011i	0.0602037	−	0.0828633i
$388$	−33.3899	+	45.9573i	−1.69512	+	2.33313i
$389$	−20.4966	+	14.8916i	−1.03922	+	0.755035i	−0.970132	−	0.242576i	$-0.922008\pi$
$389$	−20.4966	+	14.8916i	−1.03922	+	0.755035i	−0.0690843	+	0.997611i	$0.522008\pi$
$390$	0.0852763	−	2.45847i	0.00431813	−	0.124490i
$391$	2.09651	+	1.52320i	0.106025	+	0.0770316i
$392$	−20.0186	+	6.50442i	−1.01109	+	0.328523i
$393$		−	4.32869i		−	0.218354i
$394$	−8.13381	−	25.0333i	−0.409775	−	1.26116i
$395$	23.7178	+	0.822692i	1.19337	+	0.0413941i
$396$	4.77608	−	14.6993i	0.240007	−	0.738665i
$397$	−19.0706	−	6.19642i	−0.957127	−	0.310989i	−0.211519	−	0.977374i	$-0.567841\pi$
$397$	−19.0706	−	6.19642i	−0.957127	−	0.310989i	−0.745608	+	0.666385i	$0.767841\pi$
$398$	−33.8756	−	46.6257i	−1.69803	−	2.33714i
$399$	−1.60866			−0.0805338
$400$	34.2665	+	2.38004i	1.71332	+	0.119002i
$401$	25.5967			1.27824			0.639118	−	0.769109i	$-0.279300\pi$
$401$	25.5967			1.27824			0.639118	+	0.769109i	$0.279300\pi$
$402$	5.84203	+	8.04086i	0.291374	+	0.401042i
$403$	−0.244196	−	0.0793442i	−0.0121643	−	0.00395242i
$404$	0.0801870	−	0.246790i	0.00398945	−	0.0122783i
$405$	−5.67418	+	3.82921i	−0.281952	+	0.190275i
$406$	−7.88305	−	24.2615i	−0.391229	−	1.20408i
$407$		−	11.3116i		−	0.560694i
$408$	8.93294	−	2.90249i	0.442247	−	0.143695i
$409$	12.0796	+	8.77636i	0.597299	+	0.433963i	0.844919	−	0.534894i	$-0.179648\pi$
$409$	12.0796	+	8.77636i	0.597299	+	0.433963i	−0.247620	+	0.968857i	$0.579648\pi$
$410$	1.01627	−	0.291667i	0.0501899	−	0.0144044i
$411$	−12.4558	+	9.04963i	−0.614397	+	0.446386i
$412$	48.2629	−	66.4282i	2.37774	−	3.27268i
$413$	0.880738	−	1.21223i	0.0433383	−	0.0596501i
$414$	6.80040	−	4.94078i	0.334222	−	0.242826i
$415$	12.5949	+	18.6633i	0.618259	+	0.916144i
$416$	−2.08046	−	1.51154i	−0.102003	−	0.0741093i
$417$	14.6710	−	4.76689i	0.718442	−	0.233436i
$418$		−	3.86634i		−	0.189109i
$419$	6.33011	+	19.4821i	0.309246	+	0.951762i	0.978058	+	0.208331i	$0.0668030\pi$
$419$	6.33011	+	19.4821i	0.309246	+	0.951762i	−0.668812	+	0.743431i	$0.733197\pi$
$420$	−5.46536	+	15.0269i	−0.266682	+	0.733237i
$421$	3.71161	−	11.4232i	0.180893	−	0.556731i	−0.818961	−	0.573850i	$-0.805449\pi$
$421$	3.71161	−	11.4232i	0.180893	−	0.556731i	0.999853	+	0.0171186i	$0.00544930\pi$
$422$	−16.7060	−	5.42811i	−0.813235	−	0.264236i
$423$	2.02272	+	2.78404i	0.0983481	+	0.135365i
$424$	−70.4961			−3.42359
$425$	−5.73971	+	6.84681i	−0.278417	+	0.332119i
$426$	9.47829			0.459225
$427$	5.49783	+	7.56711i	0.266059	+	0.366198i
$428$	71.2440	+	23.1486i	3.44371	+	1.11893i
$429$	−0.203931	+	0.627635i	−0.00984588	+	0.0303025i
$430$	−3.94879	−	3.08365i	−0.190428	−	0.148707i
$431$	−7.25157	−	22.3180i	−0.349296	−	1.07502i	−0.959244	−	0.282580i	$-0.908810\pi$
$431$	−7.25157	−	22.3180i	−0.349296	−	1.07502i	0.609948	−	0.792442i	$-0.291190\pi$
$432$		−	30.7310i		−	1.47855i
$433$	13.1100	−	4.25969i	0.630025	−	0.204707i	0.0234386	−	0.999725i	$-0.492539\pi$
$433$	13.1100	−	4.25969i	0.630025	−	0.204707i	0.606586	+	0.795018i	$0.292539\pi$
$434$	1.95773	+	1.42238i	0.0939743	+	0.0682763i
$435$	9.41096	+	3.42282i	0.451221	+	0.164112i
$436$	52.1233	−	37.8698i	2.49625	−	1.81363i
$437$	0.852439	−	1.17328i	0.0407777	−	0.0561257i
$438$	20.8443	−	28.6898i	0.995981	−	1.37085i
$439$	−9.25599	+	6.72487i	−0.441765	+	0.320961i	−0.786336	−	0.617799i	$-0.788024\pi$
$439$	−9.25599	+	6.72487i	−0.441765	+	0.320961i	0.344571	+	0.938760i	$0.388024\pi$
$440$	−19.8670	−	7.22573i	−0.947122	−	0.344473i
$441$	−6.26256	−	4.55001i	−0.298217	−	0.216667i
$442$	2.20797	−	0.717412i	0.105022	−	0.0341238i
$443$			7.92865i			0.376702i	0.982102	+	0.188351i	$0.0603142\pi$
$443$			7.92865i			0.376702i	−0.982102	+	0.188351i	$0.939686\pi$
$444$	−8.63917	−	26.5886i	−0.409997	−	1.26184i
$445$	−8.03011	−	6.27079i	−0.380664	−	0.297264i
$446$	0.919970	−	2.83138i	0.0435619	−	0.134070i
$447$	1.52186	+	0.494483i	0.0719815	+	0.0233882i
$448$	−1.09725	−	1.51024i	−0.0518404	−	0.0713522i
$449$	−24.0265			−1.13388			−0.566939	−	0.823760i	$-0.691873\pi$
$449$	−24.0265			−1.13388			−0.566939	+	0.823760i	$0.691873\pi$
$450$	15.3687	+	24.5695i	0.724487	+	1.15822i
$451$	−0.283642			−0.0133562
$452$	36.0322	+	49.5940i	1.69481	+	2.33271i
$453$	−4.10112	−	1.33253i	−0.192687	−	0.0626079i
$454$	−16.7781	+	51.6377i	−0.787435	+	2.42348i
$455$	−0.743096	+	2.04312i	−0.0348369	+	0.0957832i
$456$	−1.62434	−	4.99920i	−0.0760666	−	0.234109i
$457$		−	5.35005i		−	0.250265i	−0.992140	−	0.125132i	$-0.960064\pi$
$457$		−	5.35005i		−	0.250265i	0.992140	−	0.125132i	$-0.0399356\pi$
$458$	42.5769	−	13.8341i	1.98949	−	0.646423i
$459$	6.46673	+	4.69835i	0.301841	+	0.219300i
$460$	−8.06378	−	11.9490i	−0.375976	−	0.557126i
$461$	−4.55251	+	3.30760i	−0.212032	+	0.154050i	−0.688732	−	0.725016i	$-0.741833\pi$
$461$	−4.55251	+	3.30760i	−0.212032	+	0.154050i	0.476701	+	0.879066i	$0.341833\pi$
$462$	3.65580	−	5.03178i	0.170083	−	0.234100i
$463$	−15.5520	+	21.4054i	−0.722761	+	0.994795i	0.276667	+	0.960966i	$0.410770\pi$
$463$	−15.5520	+	21.4054i	−0.722761	+	0.994795i	−0.999428	+	0.0338289i	$0.989230\pi$
$464$	29.3954	−	21.3570i	1.36465	−	0.991473i
$465$	−0.913077	+	0.262052i	−0.0423429	+	0.0121524i
$466$	5.36538	+	3.89818i	0.248546	+	0.180580i
$467$	19.1891	−	6.23492i	0.887967	−	0.288518i	0.170705	−	0.985322i	$-0.445395\pi$
$467$	19.1891	−	6.23492i	0.887967	−	0.288518i	0.717261	+	0.696804i	$0.245395\pi$
$468$		−	5.19375i		−	0.240081i
$469$	−2.71440	−	8.35405i	−0.125339	−	0.385754i
$470$	7.09277	−	4.78655i	0.327165	−	0.220787i
$471$	−3.13005	+	9.63331i	−0.144225	+	0.443880i
$472$	4.65655	+	1.51300i	0.214335	+	0.0696417i
$473$	0.790034	+	1.08739i	0.0363258	+	0.0499982i
$474$	−22.8150			−1.04793
$475$	3.83172	+	3.21215i	0.175812	+	0.147383i
$476$	−15.0906			−0.691676
$477$	−15.2388	−	20.9744i	−0.697737	−	0.960353i
$478$	42.6981	+	13.8735i	1.95297	+	0.634557i
$479$	1.96912	−	6.06033i	0.0899714	−	0.276904i	−0.895939	−	0.444177i	$-0.853496\pi$
$479$	1.96912	−	6.06033i	0.0899714	−	0.276904i	0.985911	+	0.167273i	$0.0534962\pi$
$480$	−9.50828	−	0.329811i	−0.433992	−	0.0150537i
$481$	−1.17462	−	3.61511i	−0.0535581	−	0.164835i
$482$			65.8075i			2.99745i
$483$	2.21879	−	0.720927i	0.100958	−	0.0328033i
$484$	−31.2183	−	22.6814i	−1.41901	−	1.03097i
$485$	−0.990573	+	28.5577i	−0.0449796	+	1.29674i
$486$	32.8874	−	23.8941i	1.49180	−	1.08386i
$487$	11.5319	−	15.8723i	0.522562	−	0.719244i	−0.463413	−	0.886143i	$-0.653375\pi$
$487$	11.5319	−	15.8723i	0.522562	−	0.719244i	0.985974	+	0.166898i	$0.0533752\pi$
$488$	−17.9647	+	24.7263i	−0.813225	+	1.11931i
$489$	4.85114	−	3.52456i	0.219376	−	0.159386i
$490$	−11.8467	+	15.1704i	−0.535181	+	0.685331i
$491$	−9.06137	−	6.58347i	−0.408934	−	0.297108i	0.364236	−	0.931307i	$-0.381330\pi$
$491$	−9.06137	−	6.58347i	−0.408934	−	0.297108i	−0.773170	+	0.634199i	$0.781330\pi$
$492$	−0.666720	+	0.216630i	−0.0300580	+	0.00976645i
$493$			9.45085i			0.425645i
$494$	−0.401490	−	1.23566i	−0.0180639	−	0.0555949i
$495$	−2.14471	−	7.47290i	−0.0963976	−	0.335882i
$496$	−1.06509	+	3.27802i	−0.0478241	+	0.147187i
$497$	−7.96677	−	2.58856i	−0.357358	−	0.116113i
$498$	−12.7229	−	17.5115i	−0.570126	−	0.784711i
$499$	6.50535			0.291219			0.145610	−	0.989342i	$-0.453486\pi$
$499$	6.50535			0.291219			0.145610	+	0.989342i	$0.453486\pi$
$500$	43.0236	−	24.8799i	1.92407	−	1.11266i
$501$	−12.8436			−0.573808
$502$	−30.5657	−	42.0701i	−1.36421	−	1.87768i
$503$	19.9027	+	6.46677i	0.887417	+	0.288339i	0.717034	−	0.697039i	$-0.245499\pi$
$503$	19.9027	+	6.46677i	0.887417	+	0.288339i	0.170383	+	0.985378i	$0.445499\pi$
$504$	−8.32060	+	25.6082i	−0.370629	+	1.14068i
$505$	−0.0360082	−	0.125465i	−0.00160235	−	0.00558312i
$506$	1.73271	+	5.33274i	0.0770285	+	0.237069i
$507$		−	10.7858i		−	0.479016i
$508$	54.9234	−	17.8457i	2.43683	−	0.791775i
$509$	0.511527	+	0.371646i	0.0226730	+	0.0164729i	0.599064	−	0.800701i	$-0.295539\pi$
$509$	0.511527	+	0.371646i	0.0226730	+	0.0164729i	−0.576391	+	0.817174i	$0.695539\pi$
$510$	5.28641	−	6.76955i	0.234086	−	0.299761i
$511$	−25.3555	+	18.4219i	−1.12166	+	0.814936i
$512$	29.8442	−	41.0770i	1.31894	−	1.81536i
$513$	2.62937	−	3.61901i	0.116089	−	0.159783i
$514$	−13.5778	+	9.86483i	−0.598890	+	0.435119i
$515$	1.43181	−	41.2783i	0.0630930	−	1.81894i
$516$	2.68752	+	1.95260i	0.118311	+	0.0859583i
$517$	−2.18319	+	0.709360i	−0.0960164	+	0.0311976i
$518$			35.8244i			1.57403i
$519$	−0.764342	−	2.35240i	−0.0335509	−	0.103259i
$520$	−7.09971	−	0.246266i	−0.311343	−	0.0107995i
$521$	−10.2695	+	31.6062i	−0.449913	+	1.38469i	0.427091	+	0.904209i	$0.359538\pi$
$521$	−10.2695	+	31.6062i	−0.449913	+	1.38469i	−0.877004	+	0.480482i	$0.840462\pi$
$522$	29.1552	+	9.47309i	1.27609	+	0.414626i
$523$	−13.1370	−	18.0815i	−0.574440	−	0.790649i	0.418632	−	0.908156i	$-0.362510\pi$
$523$	−13.1370	−	18.0815i	−0.574440	−	0.790649i	−0.993072	+	0.117507i	$0.962510\pi$
$524$	−22.7250			−0.992747
$525$	1.94950	+	7.80347i	0.0850831	+	0.340571i
$526$	41.8370			1.82418
$527$	−0.526955	−	0.725292i	−0.0229545	−	0.0315942i
$528$	8.42518	+	2.73751i	0.366659	+	0.119135i
$529$	6.45745	−	19.8740i	0.280759	−	0.864087i
$530$	−53.4356	+	36.0610i	−2.32110	+	1.56639i
$531$	0.556427	+	1.71250i	0.0241469	+	0.0743164i
$532$			8.44524i			0.366148i
$533$	−0.0906503	+	0.0294541i	−0.00392650	+	0.00127580i
$534$	7.92414	+	5.75722i	0.342911	+	0.249139i
$535$	36.2195	−	10.3949i	1.56590	−	0.449412i
$536$	23.2209	−	16.8709i	1.00299	−	0.728713i
$537$	−10.8660	+	14.9558i	−0.468904	+	0.645391i
$538$	27.0229	−	37.1938i	1.16504	−	1.60354i
$539$	4.17752	−	3.03515i	0.179939	−	0.130733i
$540$	−24.8729	−	36.8570i	−1.07036	−	1.58607i
$541$	6.00499	+	4.36288i	0.258175	+	0.187575i	0.709342	−	0.704864i	$-0.248992\pi$
$541$	6.00499	+	4.36288i	0.258175	+	0.187575i	−0.451167	+	0.892439i	$0.648992\pi$
$542$	1.23460	−	0.401145i	0.0530305	−	0.0172306i
$543$		−	11.3739i		−	0.488102i
$544$	−2.77463	−	8.53944i	−0.118961	−	0.366125i
$545$	11.0773	−	30.4569i	0.474501	−	1.30463i
$546$	0.645861	−	1.98775i	0.0276403	−	0.0850681i
$547$	−15.9456	−	5.18103i	−0.681783	−	0.221525i	−0.0524072	−	0.998626i	$-0.516689\pi$
$547$	−15.9456	−	5.18103i	−0.681783	−	0.221525i	−0.629376	+	0.777101i	$0.716689\pi$
$548$	47.5093	+	65.3910i	2.02950	+	2.79336i
$549$	−11.2401			−0.479715
$550$	−18.7553	+	4.68553i	−0.799727	+	0.199792i
$551$	5.28904			0.225321
$552$	4.48082	+	6.16732i	0.190716	+	0.262498i
$553$	19.1766	+	6.23086i	0.815472	+	0.264963i
$554$	−7.56730	+	23.2898i	−0.321504	+	0.989487i
$555$	−11.0838	−	8.65546i	−0.470482	−	0.367404i
$556$	−25.0255	−	77.0206i	−1.06132	−	3.26640i
$557$			7.28195i			0.308546i	0.988028	+	0.154273i	$0.0493036\pi$
$557$			7.28195i			0.308546i	−0.988028	+	0.154273i	$0.950696\pi$
$558$	−2.76567	+	0.898619i	−0.117080	+	0.0380416i
$559$	0.365408	+	0.265484i	0.0154551	+	0.0112288i
$560$	27.4263	+	9.97509i	1.15897	+	0.421525i
$561$	−1.86415	+	1.35438i	−0.0787044	+	0.0571821i
$562$	25.4079	−	34.9710i	1.07177	−	1.47516i
$563$	−16.1288	+	22.1994i	−0.679749	+	0.935594i	−0.999931	−	0.0117621i	$-0.996256\pi$
$563$	−16.1288	+	22.1994i	−0.679749	+	0.935594i	0.320182	+	0.947356i	$0.396256\pi$
$564$	−4.58996	+	3.33480i	−0.193272	+	0.140420i
$565$	28.9789	+	10.5398i	1.21915	+	0.443413i
$566$	−28.2613	−	20.5330i	−1.18791	−	0.863067i
$567$	−5.53139	+	1.79726i	−0.232296	+	0.0754777i
$568$		−	27.3719i		−	1.14850i
$569$	−2.81912	−	8.67636i	−0.118184	−	0.363732i	0.874414	−	0.485180i	$-0.161246\pi$
$569$	−2.81912	−	8.67636i	−0.118184	−	0.363732i	−0.992598	+	0.121448i	$0.961246\pi$
$570$	−3.78849	−	2.95846i	−0.158682	−	0.123916i
$571$	7.04599	−	21.6853i	0.294866	−	0.907503i	−0.688401	−	0.725330i	$-0.741687\pi$
$571$	7.04599	−	21.6853i	0.294866	−	0.907503i	0.983267	−	0.182173i	$-0.0583130\pi$
$572$	3.29500	+	1.07061i	0.137771	+	0.0447644i
$573$	11.2389	+	15.4690i	0.469511	+	0.646226i
$574$	0.898310			0.0374947
$575$	−6.72454	−	2.71323i	−0.280433	−	0.113150i
$576$	2.24329			0.0934705
$577$	19.4472	+	26.7667i	0.809597	+	1.11431i	0.991385	+	0.130977i	$0.0418113\pi$
$577$	19.4472	+	26.7667i	0.809597	+	1.11431i	−0.181789	+	0.983338i	$0.558189\pi$
$578$	−33.3371	−	10.8319i	−1.38664	−	0.450547i
$579$	−6.63840	+	20.4309i	−0.275883	+	0.849080i
$580$	17.9693	−	49.4062i	0.746135	−	2.05148i
$581$	5.91146	+	18.1936i	0.245249	+	0.754798i
$582$		−	27.4707i		−	1.13870i
$583$	16.4477	−	5.34419i	0.681195	−	0.221334i
$584$	−82.8519	−	60.1955i	−3.42844	−	2.49091i
$585$	−1.46144	−	2.16558i	−0.0604232	−	0.0895359i
$586$	−28.5062	+	20.7109i	−1.17758	+	0.855561i
$587$	−15.9517	+	21.9556i	−0.658396	+	0.906204i	−0.999427	−	0.0338481i	$-0.989224\pi$
$587$	−15.9517	+	21.9556i	−0.658396	+	0.906204i	0.341031	+	0.940052i	$0.389224\pi$
$588$	7.50147	−	10.3249i	0.309355	−	0.425791i
$589$	−0.405899	+	0.294903i	−0.0167248	+	0.0121513i
$590$	4.30359	−	1.23512i	0.177176	−	0.0508492i
$591$	7.10229	+	5.16011i	0.292149	+	0.212259i
$592$	−48.5282	+	15.7678i	−1.99450	+	0.648051i
$593$			34.0979i			1.40023i	0.714029	+	0.700116i	$0.246869\pi$
$593$			34.0979i			1.40023i	−0.714029	+	0.700116i	$0.753131\pi$
$594$	5.34459	+	16.4490i	0.219291	+	0.674909i
$595$	−6.29216	+	4.24626i	−0.257954	+	0.174080i
$596$	2.59596	−	7.98956i	0.106335	−	0.327265i
$597$	18.2811	+	5.93990i	0.748197	+	0.243104i
$598$	1.10753	+	1.52438i	0.0452903	+	0.0623367i
$599$	23.3138			0.952575			0.476288	−	0.879290i	$-0.341982\pi$
$599$	23.3138			0.952575			0.476288	+	0.879290i	$0.341982\pi$
$600$	−22.2822	+	13.9379i	−0.909666	+	0.569014i
$601$	14.2553			0.581485			0.290743	−	0.956801i	$-0.406098\pi$
$601$	14.2553			0.581485			0.290743	+	0.956801i	$0.406098\pi$
$602$	−2.50208	−	3.44382i	−0.101977	−	0.140360i
$603$	10.0391	+	3.26190i	0.408823	+	0.132835i
$604$	−6.99562	+	21.5303i	−0.284648	+	0.876056i
$605$	−19.3989	−	0.672885i	−0.788679	−	0.0273567i
$606$	0.0387772	+	0.119344i	0.00157522	+	0.00484802i
$607$		−	24.8603i		−	1.00905i	−0.863398	−	0.504524i	$-0.831668\pi$
$607$		−	24.8603i		−	1.00905i	0.863398	−	0.504524i	$-0.168332\pi$
$608$	−4.77898	+	1.55278i	−0.193813	+	0.0629737i
$609$	6.88333	+	5.00104i	0.278927	+	0.202652i
$610$	−0.968867	+	27.9320i	−0.0392283	+	1.13093i
$611$	−0.624072	+	0.453415i	−0.0252472	+	0.0183432i
$612$	10.6591	−	14.6711i	0.430870	−	0.593042i
$613$	−24.2060	+	33.3166i	−0.977670	+	1.34565i	−0.0395942	+	0.999216i	$0.512607\pi$
$613$	−24.2060	+	33.3166i	−0.977670	+	1.34565i	−0.938075	+	0.346431i	$0.887393\pi$
$614$	−22.9227	+	16.6543i	−0.925085	+	0.672114i
$615$	−0.217039	+	0.277931i	−0.00875184	+	0.0112072i
$616$	−14.5311	−	10.5574i	−0.585473	−	0.425371i
$617$	−0.106090	+	0.0344707i	−0.00427102	+	0.00138774i	−0.311152	−	0.950360i	$-0.600715\pi$
$617$	−0.106090	+	0.0344707i	−0.00427102	+	0.00138774i	0.306881	+	0.951748i	$0.400715\pi$
$618$			39.7070i			1.59725i
$619$	−3.09213	−	9.51661i	−0.124283	−	0.382505i	0.869486	−	0.493957i	$-0.164450\pi$
$619$	−3.09213	−	9.51661i	−0.124283	−	0.382505i	−0.993770	+	0.111452i	$0.964450\pi$
$620$	1.37573	+	4.79353i	0.0552508	+	0.192513i
$621$	−2.00475	+	6.16998i	−0.0804477	+	0.247593i
$622$	25.9904	+	8.44478i	1.04212	+	0.338605i
$623$	−5.08814	−	7.00322i	−0.203852	−	0.280578i
$624$	2.97691			0.119172
$625$	10.9383	−	22.4801i	0.437530	−	0.899204i
$626$	−20.9518			−0.837404
$627$	0.757962	+	1.04325i	0.0302701	+	0.0416632i
$628$	50.5735	+	16.4323i	2.01810	+	0.655722i
$629$	4.10129	−	12.6225i	0.163529	−	0.503291i
$630$	6.79242	+	23.6671i	0.270617	+	0.942920i
$631$	7.84044	+	24.1304i	0.312123	+	0.960616i	0.976923	+	0.213594i	$0.0685170\pi$
$631$	7.84044	+	24.1304i	0.312123	+	0.960616i	−0.664799	+	0.747022i	$0.731483\pi$
$632$			65.8863i			2.62082i
$633$	5.57188	−	1.81041i	0.221462	−	0.0719574i
$634$	63.8990	+	46.4253i	2.53775	+	1.84378i
$635$	17.8793	−	22.8955i	0.709519	−	0.908581i
$636$	34.5799	−	25.1238i	1.37118	−	0.996223i
$637$	1.01993	−	1.40382i	0.0404113	−	0.0556213i
$638$	−12.0197	+	16.5438i	−0.475866	+	0.654974i
$639$	8.14387	−	5.91687i	0.322166	−	0.234068i
$640$	0.972381	−	28.0333i	0.0384367	−	1.10811i
$641$	−18.7816	−	13.6456i	−0.741828	−	0.538969i	0.151455	−	0.988464i	$-0.451604\pi$
$641$	−18.7816	−	13.6456i	−0.741828	−	0.538969i	−0.893283	+	0.449495i	$0.851604\pi$
$642$	−34.4525	+	11.1943i	−1.35973	+	0.441803i
$643$			26.8886i			1.06038i	0.847878	+	0.530192i	$0.177880\pi$
$643$			26.8886i			1.06038i	−0.847878	+	0.530192i	$0.822120\pi$
$644$	−3.78477	−	11.6483i	−0.149141	−	0.459008i
$645$	1.67002	+	0.0579274i	0.0657569	+	0.00228089i
$646$	1.40183	−	4.31440i	0.0551544	−	0.169748i
$647$	34.6864	+	11.2703i	1.36366	+	0.443080i	0.897264	−	0.441495i	$-0.145552\pi$
$647$	34.6864	+	11.2703i	1.36366	+	0.443080i	0.466398	+	0.884575i	$0.345552\pi$
$648$	−11.1706	−	15.3750i	−0.438822	−	0.603987i
$649$	−1.20114			−0.0471488
$650$	−5.50751	+	3.44506i	−0.216022	+	0.135126i
$651$	−0.807096			−0.0316326
$652$	−18.5035	−	25.4678i	−0.724651	−	0.997397i
$653$	32.7071	+	10.6272i	1.27993	+	0.415874i	0.868555	−	0.495593i	$-0.165049\pi$
$653$	32.7071	+	10.6272i	1.27993	+	0.415874i	0.411373	+	0.911467i	$0.365049\pi$
$654$	−9.62785	+	29.6315i	−0.376479	+	1.15868i
$655$	−9.47541	+	6.39447i	−0.370235	+	0.249853i
$656$	0.395382	+	1.21686i	0.0154371	+	0.0475105i
$657$		−	37.6628i		−	1.46937i
$658$	6.91427	−	2.24658i	0.269546	−	0.0875809i
$659$	14.5798	+	10.5929i	0.567950	+	0.412640i	0.834360	−	0.551220i	$-0.185838\pi$
$659$	14.5798	+	10.5929i	0.567950	+	0.412640i	−0.266410	+	0.963860i	$0.585838\pi$
$660$	12.3204	−	3.53592i	0.479569	−	0.137636i
$661$	−3.07632	+	2.23508i	−0.119655	+	0.0869345i	−0.646003	−	0.763335i	$-0.723561\pi$
$661$	−3.07632	+	2.23508i	−0.119655	+	0.0869345i	0.526348	+	0.850269i	$0.323561\pi$
$662$	−47.9118	+	65.9450i	−1.86215	+	2.56302i
$663$	−0.455129	+	0.626431i	−0.0176757	+	0.0243286i
$664$	−50.5708	+	36.7418i	−1.96253	+	1.42586i
$665$	2.37636	+	3.52132i	0.0921513	+	0.136551i
$666$	−34.8284	−	25.3043i	−1.34957	−	0.980523i
$667$	−7.29504	+	2.37030i	−0.282465	+	0.0917785i
$668$			67.4268i			2.60882i
$669$	0.306834	+	0.944337i	0.0118629	+	0.0365102i
$670$	8.97126	−	24.6663i	0.346590	−	0.952941i
$671$	2.31696	−	7.13088i	0.0894454	−	0.275285i
$672$	−7.68775	−	2.49790i	−0.296562	−	0.0963587i
$673$	25.2554	+	34.7611i	0.973524	+	1.33994i	0.940246	+	0.340495i	$0.110595\pi$
$673$	25.2554	+	34.7611i	0.973524	+	1.33994i	0.0332776	+	0.999446i	$0.489405\pi$
$674$	−46.9848			−1.80979
$675$	−20.7420	−	8.36903i	−0.798360	−	0.322124i
$676$	−56.6241			−2.17785
$677$	−19.2300	−	26.4679i	−0.739070	−	1.01724i	−0.998672	−	0.0515269i	$-0.983591\pi$
$677$	−19.2300	−	26.4679i	−0.739070	−	1.01724i	0.259602	−	0.965716i	$-0.416409\pi$
$678$	−28.1936	−	9.16065i	−1.08277	−	0.351813i
$679$	−7.50235	+	23.0899i	−0.287914	+	0.886107i
$680$	−19.5495	−	15.2664i	−0.749689	−	0.585439i
$681$	−5.59592	−	17.2225i	−0.214436	−	0.659967i
$682$		−	1.93982i		−	0.0742794i
$683$	0.529915	−	0.172180i	0.0202766	−	0.00658828i	−0.298861	−	0.954297i	$-0.596607\pi$
$683$	0.529915	−	0.172180i	0.0202766	−	0.00658828i	0.319138	+	0.947708i	$0.396607\pi$
$684$	−8.21045	−	5.96524i	−0.313934	−	0.228087i
$685$	38.2095	+	13.8970i	1.45991	+	0.530977i
$686$	−40.5448	+	29.4575i	−1.54801	+	1.12469i
$687$	−8.77637	+	12.0796i	−0.334839	+	0.460867i
$688$	3.56378	−	4.90512i	0.135868	−	0.187006i
$689$	4.70164	−	3.41594i	0.179118	−	0.130137i
$690$	6.55121	+	2.38271i	0.249400	+	0.0907083i
$691$	−28.7989	−	20.9237i	−1.09556	−	0.795973i	−0.115233	−	0.993338i	$-0.536762\pi$
$691$	−28.7989	−	20.9237i	−1.09556	−	0.795973i	−0.980330	+	0.197365i	$0.936762\pi$
$692$	−12.3498	+	4.01269i	−0.469468	+	0.152540i
$693$		−	6.60552i		−	0.250923i
$694$	−14.2875	−	43.9723i	−0.542344	−	1.66916i
$695$	−32.1070	−	25.0727i	−1.21789	−	0.951061i
$696$	−8.59119	+	26.4410i	−0.325648	+	1.00224i
$697$	−0.316513	−	0.102841i	−0.0119888	−	0.00389539i
$698$	−10.2135	−	14.0577i	−0.386587	−	0.532091i
$699$	−2.21193			−0.0836630
$700$	40.9671	−	10.2346i	1.54841	−	0.386832i
$701$	−10.8011			−0.407951			−0.203976	−	0.978976i	$-0.565386\pi$
$701$	−10.8011			−0.407951			−0.203976	+	0.978976i	$0.565386\pi$
$702$	3.41620	+	4.70200i	0.128936	+	0.177465i
$703$	−7.06399	−	2.29523i	−0.266423	−	0.0865662i
$704$	−0.462419	+	1.42318i	−0.0174281	+	0.0536381i
$705$	−0.975465	+	2.68202i	−0.0367381	+	0.101011i
$706$	−1.99304	−	6.13393i	−0.0750089	−	0.230854i
$707$		−	0.110902i		−	0.00417090i
$708$	−2.82336	+	0.917364i	−0.106108	+	0.0344766i
$709$	−19.5612	−	14.2120i	−0.734636	−	0.533745i	0.156390	−	0.987695i	$-0.450014\pi$
$709$	−19.5612	−	14.2120i	−0.734636	−	0.533745i	−0.891027	+	0.453951i	$0.850014\pi$
$710$	−14.0016	−	20.7478i	−0.525471	−	0.778650i
$711$	−19.6029	+	14.2423i	−0.735166	+	0.534130i
$712$	16.6260	−	22.8838i	0.623087	−	0.857605i
$713$	0.427685	−	0.588658i	0.0160169	−	0.0220454i
$714$	5.90387	−	4.28941i	0.220947	−	0.160527i
$715$	1.67513	−	0.480760i	0.0626464	−	0.0179794i
$716$	78.5159	+	57.0452i	2.93428	+	2.13188i
$717$	−14.2409	+	4.62715i	−0.531836	+	0.172804i
$718$		−	40.2943i		−	1.50377i
$719$	−2.20921	−	6.79924i	−0.0823896	−	0.253569i	0.901373	−	0.433043i	$-0.142560\pi$
$719$	−2.20921	−	6.79924i	−0.0823896	−	0.253569i	−0.983763	+	0.179474i	$0.942560\pi$
$720$	−29.0702	+	19.6180i	−1.08338	+	0.731118i
$721$	10.8441	−	33.3748i	0.403857	−	1.24294i
$722$	−2.41450	−	0.784517i	−0.0898582	−	0.0291967i
$723$	−12.9010	−	17.7567i	−0.479793	−	0.660378i
$724$	−59.7116			−2.21916
$725$	−6.40967	−	25.6567i	−0.238049	−	0.952865i
$726$	18.6605			0.692557
$727$	7.86596	+	10.8266i	0.291732	+	0.401535i	0.929576	−	0.368631i	$-0.120173\pi$
$727$	7.86596	+	10.8266i	0.291732	+	0.401535i	−0.637844	+	0.770166i	$0.720173\pi$
$728$	−5.74035	−	1.86515i	−0.212751	−	0.0691271i
$729$	−1.35167	+	4.16002i	−0.0500620	+	0.154075i
$730$	−93.5932	−	3.24644i	−3.46404	−	0.120156i
$731$	0.487331	+	1.49985i	0.0180246	+	0.0554740i
$732$		−	18.5312i		−	0.684933i
$733$	−48.3623	+	15.7139i	−1.78630	+	0.580405i	−0.999331	−	0.0365836i	$-0.988352\pi$
$733$	−48.3623	+	15.7139i	−1.78630	+	0.580405i	−0.786972	+	0.616989i	$0.788352\pi$
$734$	23.3307	+	16.9508i	0.861152	+	0.625664i
$735$	0.222545	−	6.41586i	0.00820869	−	0.236652i
$736$	5.89564	−	4.28343i	0.217316	−	0.157889i
$737$	−4.13879	+	5.69656i	−0.152454	+	0.209836i
$738$	−0.634515	+	0.873335i	−0.0233568	+	0.0321479i
$739$	−32.7299	+	23.7796i	−1.20399	+	0.874748i	−0.994671	−	0.103100i	$-0.967124\pi$
$739$	−32.7299	+	23.7796i	−1.20399	+	0.874748i	−0.209316	+	0.977848i	$0.567124\pi$
$740$	−45.4399	+	58.1885i	−1.67041	+	2.13905i
$741$	0.350573	+	0.254706i	0.0128786	+	0.00935687i
$742$	−52.0909	+	16.9254i	−1.91232	+	0.621349i
$743$		−	29.4159i		−	1.07916i	−0.841933	−	0.539582i	$-0.818582\pi$
$743$		−	29.4159i		−	1.07916i	0.841933	−	0.539582i	$-0.181418\pi$
$744$	−0.814962	−	2.50819i	−0.0298779	−	0.0919549i
$745$	−1.16573	−	4.06178i	−0.0427089	−	0.148812i
$746$	−4.01530	+	12.3578i	−0.147010	+	0.452452i
$747$	−21.8633	−	7.10382i	−0.799937	−	0.259915i
$748$	7.11032	+	9.78652i	0.259979	+	0.357831i
$749$	32.0155			1.16982
$750$	−9.76007	+	21.9629i	−0.356387	+	0.801972i
$751$	−25.0770			−0.915074			−0.457537	−	0.889191i	$-0.651268\pi$
$751$	−25.0770			−0.915074			−0.457537	+	0.889191i	$0.651268\pi$
$752$	6.08650	+	8.37735i	0.221952	+	0.305491i
$753$	16.4950	+	5.35954i	0.601110	+	0.195312i
$754$	−2.12350	+	6.53545i	−0.0773331	+	0.238007i
$755$	3.14141	+	10.9457i	0.114327	+	0.398356i
$756$	−11.6742	−	35.9295i	−0.424587	−	1.30674i
$757$			1.50743i			0.0547886i	0.999625	+	0.0273943i	$0.00872097\pi$
$757$			1.50743i			0.0547886i	−0.999625	+	0.0273943i	$0.991279\pi$
$758$	66.3263	−	21.5507i	2.40908	−	0.782758i
$759$	−1.51297	−	1.09924i	−0.0549174	−	0.0398998i
$760$	−8.54362	+	10.9406i	−0.309910	+	0.396857i
$761$	42.4154	−	30.8166i	1.53756	−	1.11710i	0.585713	−	0.810518i	$-0.300815\pi$
$761$	42.4154	−	30.8166i	1.53756	−	1.11710i	0.951844	−	0.306582i	$-0.0991855\pi$
$762$	−16.4150	+	22.5934i	−0.594654	+	0.818472i
$763$	16.1849	−	22.2767i	0.585934	−	0.806469i
$764$	81.2100	−	59.0025i	2.93807	−	2.13464i
$765$	0.316223	−	9.11655i	0.0114331	−	0.329610i
$766$	−4.10667	−	2.98367i	−0.148380	−	0.107804i
$767$	−0.383876	+	0.124729i	−0.0138610	+	0.00450370i
$768$			25.3022i			0.913013i
$769$	−6.87912	−	21.1718i	−0.248068	−	0.763474i	−0.995117	−	0.0987048i	$-0.968530\pi$
$769$	−6.87912	−	21.1718i	−0.248068	−	0.763474i	0.747049	−	0.664769i	$-0.231470\pi$
$770$	−16.4149	−	0.569379i	−0.591553	−	0.0205190i
$771$	1.72975	−	5.32361i	0.0622953	−	0.191725i
$772$	107.259	+	34.8507i	3.86035	+	1.25430i
$773$	8.17851	+	11.2568i	0.294161	+	0.404877i	0.930360	−	0.366647i	$-0.119494\pi$
$773$	8.17851	+	11.2568i	0.294161	+	0.404877i	−0.636199	+	0.771525i	$0.719494\pi$
$774$	5.11541			0.183870
$775$	1.92245	+	1.61160i	0.0690564	+	0.0578902i
$776$	−79.3313			−2.84783
$777$	−7.02307	−	9.66642i	−0.251951	−	0.346781i
$778$	−61.1716	−	19.8759i	−2.19311	−	0.712584i
$779$	−0.0575537	+	0.177132i	−0.00206207	+	0.00634641i
$780$	3.57033	−	2.40944i	0.127838	−	0.0862716i
$781$	2.07502	+	6.38626i	0.0742501	+	0.228518i
$782$			6.57899i			0.235264i
$783$	−22.5017	+	7.31125i	−0.804146	+	0.261283i
$784$	−18.8445	−	13.6913i	−0.673016	−	0.488975i
$785$	25.7109	−	7.37899i	0.917662	−	0.263368i
$786$	8.89067	−	6.45945i	0.317120	−	0.230401i
$787$	−14.6998	+	20.2325i	−0.523990	+	0.721210i	−0.986200	−	0.165561i	$-0.947057\pi$
$787$	−14.6998	+	20.2325i	−0.523990	+	0.721210i	0.462210	+	0.886770i	$0.347057\pi$
$788$	27.0899	−	37.2860i	0.965037	−	1.32826i
$789$	−11.2888	+	8.20179i	−0.401892	+	0.291991i
$790$	33.7029	+	49.9415i	1.19910	+	1.77684i
$791$	21.1957	+	15.3996i	0.753632	+	0.547546i
$792$	20.5278	−	6.66990i	0.729425	−	0.237004i
$793$		−	2.51959i		−	0.0894731i
$794$	−15.7312	−	48.4156i	−0.558278	−	1.71820i
$795$	7.34898	−	20.2059i	0.260641	−	0.716628i
$796$	31.1837	−	95.9734i	1.10528	−	3.40169i
$797$	−1.86373	−	0.605562i	−0.0660167	−	0.0214501i	0.275822	−	0.961209i	$-0.411050\pi$
$797$	−1.86373	−	0.605562i	−0.0660167	−	0.0214501i	−0.341839	+	0.939758i	$0.611050\pi$
$798$	−2.40051	−	3.30402i	−0.0849771	−	0.116961i
$799$	−2.69339			−0.0952853
$800$	13.3240	+	21.3006i	0.471073	+	0.753091i
$801$	10.4025			0.367554
$802$	38.1964	+	52.5728i	1.34876	+	1.85641i
$803$	23.8938	+	7.76358i	0.843195	+	0.273971i
$804$	−5.37780	+	16.5512i	−0.189660	+	0.583714i
$805$	−4.85575	−	3.79190i	−0.171143	−	0.133647i
$806$	−0.201435	−	0.619954i	−0.00709525	−	0.0218369i
$807$			15.3335i			0.539765i
$808$	0.344648	−	0.111983i	0.0121247	−	0.00393955i
$809$	7.91941	+	5.75379i	0.278432	+	0.202292i	0.718233	−	0.695803i	$-0.244951\pi$
$809$	7.91941	+	5.75379i	0.278432	+	0.202292i	−0.439801	+	0.898095i	$0.644951\pi$
$810$	−16.3320	−	5.94005i	−0.573849	−	0.208712i
$811$	−15.1729	+	11.0238i	−0.532793	+	0.387097i	−0.821401	−	0.570351i	$-0.806807\pi$
$811$	−15.1729	+	11.0238i	−0.532793	+	0.387097i	0.288609	+	0.957447i	$0.406807\pi$
$812$	26.2547	−	36.1365i	0.921361	−	1.26814i
$813$	−0.254488	+	0.350272i	−0.00892527	+	0.0122846i
$814$	23.2328	−	16.8796i	0.814308	−	0.591630i
$815$	−14.8814	−	5.41246i	−0.521274	−	0.189590i
$816$	8.40902	+	6.10951i	0.294375	+	0.213876i
$817$	0.839371	−	0.272728i	0.0293659	−	0.00954156i
$818$			37.9067i			1.32538i
$819$	−0.685933	−	2.11109i	−0.0239684	−	0.0737673i
$820$	1.45910	+	1.13942i	0.0509539	+	0.0397904i
$821$	1.14370	−	3.51994i	0.0399154	−	0.122847i	−0.929113	−	0.369795i	$-0.879428\pi$
$821$	1.14370	−	3.51994i	0.0399154	−	0.122847i	0.969029	+	0.246948i	$0.0794278\pi$
$822$	−37.1740	−	12.0786i	−1.29659	−	0.421288i
$823$	−18.3517	−	25.2590i	−0.639701	−	0.880473i	0.358899	−	0.933376i	$-0.383152\pi$
$823$	−18.3517	−	25.2590i	−0.639701	−	0.880473i	−0.998600	+	0.0529038i	$0.983152\pi$
$824$	114.668			3.99465
$825$	4.14213	−	4.94109i	0.144211	−	0.172027i
$826$	3.80407			0.132360
$827$	−11.3841	−	15.6689i	−0.395865	−	0.544861i	0.563835	−	0.825887i	$-0.309325\pi$
$827$	−11.3841	−	15.6689i	−0.395865	−	0.544861i	−0.959700	+	0.281026i	$0.909325\pi$
$828$	13.9978	+	4.54817i	0.486458	+	0.158060i
$829$	2.35214	−	7.23913i	0.0816931	−	0.251426i	−0.901865	−	0.432018i	$-0.857802\pi$
$829$	2.35214	−	7.23913i	0.0816931	−	0.251426i	0.983558	+	0.180593i	$0.0578016\pi$
$830$	−19.5378	+	53.7187i	−0.678166	+	1.86460i
$831$	−2.52389	−	7.76773i	−0.0875528	−	0.269460i
$832$			0.502858i			0.0174335i
$833$	5.76212	−	1.87223i	0.199646	−	0.0648688i
$834$	31.6833	+	23.0193i	1.09710	+	0.797093i
$835$	18.9729	+	28.1143i	0.656583	+	0.972934i
$836$	5.47689	−	3.97919i	0.189422	−	0.137623i
$837$	1.31920	−	1.81573i	0.0455984	−	0.0627608i
$838$	−30.5681	+	42.0733i	−1.05596	+	1.45340i
$839$	−7.52862	+	5.46987i	−0.259917	+	0.188841i	−0.710110	−	0.704090i	$-0.751355\pi$
$839$	−7.52862	+	5.46987i	−0.259917	+	0.188841i	0.450193	+	0.892931i	$0.351355\pi$
$840$	−21.4638	+	6.16008i	−0.740572	+	0.212543i
$841$	0.830095	+	0.603100i	0.0286240	+	0.0207965i
$842$	29.0006	−	9.42286i	0.999426	−	0.324733i
$843$			14.4172i			0.496554i
$844$	−9.50441	−	29.2516i	−0.327155	−	1.00688i
$845$	−23.6100	+	15.9331i	−0.812207	+	0.548117i
$846$	−2.69973	+	8.30891i	−0.0928185	+	0.285666i
$847$	−15.6847	−	5.09626i	−0.538932	−	0.175110i
$848$	−45.8546	−	63.1135i	−1.57465	−	2.16733i
$849$	11.6510			0.399861
$850$	−22.6276	−	1.57165i	−0.776122	−	0.0539071i
$851$	10.7718			0.369252
$852$	9.75496	+	13.4266i	0.334199	+	0.459986i
$853$	−30.0224	−	9.75486i	−1.02795	−	0.334000i	−0.253968	−	0.967213i	$-0.581736\pi$
$853$	−30.0224	−	9.75486i	−1.02795	−	0.334000i	−0.773978	+	0.633212i	$0.781736\pi$
$854$	−7.33795	+	22.5839i	−0.251100	+	0.772805i
$855$	−5.10195	−	0.176970i	−0.174483	−	0.00605224i
$856$	32.3275	+	99.4938i	1.10493	+	3.40063i
$857$		−	10.8057i		−	0.369116i	−0.982822	−	0.184558i	$-0.940915\pi$
$857$		−	10.8057i		−	0.369116i	0.982822	−	0.184558i	$-0.0590853\pi$
$858$	−1.59341	+	0.517730i	−0.0543981	+	0.0176750i
$859$	7.15831	+	5.20081i	0.244238	+	0.177449i	0.703169	−	0.711022i	$-0.251768\pi$
$859$	7.15831	+	5.20081i	0.244238	+	0.177449i	−0.458931	+	0.888472i	$0.651768\pi$
$860$	0.304111	−	8.76736i	0.0103701	−	0.298964i
$861$	−0.242389	+	0.176106i	−0.00826059	+	0.00600167i
$862$	35.0178	−	48.1978i	1.19271	−	1.64162i
$863$	−3.86291	+	5.31683i	−0.131495	+	0.180987i	−0.869687	−	0.493603i	$-0.835680\pi$
$863$	−3.86291	+	5.31683i	−0.131495	+	0.180987i	0.738193	+	0.674590i	$0.235680\pi$
$864$	18.1852	−	13.2124i	0.618675	−	0.449493i
$865$	−4.02025	+	5.14817i	−0.136693	+	0.175043i
$866$	28.3122	+	20.5700i	0.962086	+	0.698997i
$867$	11.1188	−	3.61271i	0.377614	−	0.122694i
$868$			4.23714i			0.143818i
$869$	−4.99473	−	15.3722i	−0.169435	−	0.521466i
$870$	7.01331	+	24.4368i	0.237774	+	0.828484i
$871$	−0.731190	+	2.25037i	−0.0247754	+	0.0762509i
$872$	85.5714	+	27.8038i	2.89781	+	0.941556i
$873$	−17.1487	−	23.6031i	−0.580395	−	0.798845i
$874$	3.68184			0.124540
$875$	14.2018	−	15.7949i	0.480108	−	0.533966i
$876$	62.0935			2.09795
$877$	−17.0221	−	23.4289i	−0.574795	−	0.791138i	0.418318	−	0.908301i	$-0.362620\pi$
$877$	−17.0221	−	23.4289i	−0.574795	−	0.791138i	−0.993113	+	0.117163i	$0.962620\pi$
$878$	−27.6243	−	8.97569i	−0.932276	−	0.302915i
$879$	3.63156	−	11.1768i	0.122489	−	0.376983i
$880$	−6.45358	−	22.4865i	−0.217550	−	0.758019i
$881$	−18.1469	−	55.8504i	−0.611384	−	1.88165i	−0.444829	−	0.895616i	$-0.646735\pi$
$881$	−18.1469	−	55.8504i	−0.611384	−	1.88165i	−0.166556	−	0.986032i	$-0.553265\pi$
$882$		−	19.6523i		−	0.661729i
$883$	−2.95688	+	0.960750i	−0.0995071	+	0.0323318i	−0.358347	−	0.933588i	$-0.616660\pi$
$883$	−2.95688	+	0.960750i	−0.0995071	+	0.0323318i	0.258840	+	0.965920i	$0.416660\pi$
$884$	3.28867	+	2.38936i	0.110610	+	0.0803629i
$885$	−0.919093	+	1.17695i	−0.0308950	+	0.0395628i
$886$	−16.2846	+	11.8315i	−0.547092	+	0.397486i
$887$	26.2466	−	36.1253i	0.881274	−	1.21297i	−0.0947923	−	0.995497i	$-0.530219\pi$
$887$	26.2466	−	36.1253i	0.881274	−	1.21297i	0.976066	−	0.217473i	$-0.0697813\pi$
$888$	22.9486	−	31.5861i	0.770105	−	1.05996i
$889$	19.9676	−	14.5073i	0.669693	−	0.486561i
$890$	0.896669	−	25.8505i	0.0300564	−	0.866511i
$891$	3.77181	+	2.74038i	0.126360	+	0.0918062i
$892$	4.95764	−	1.61083i	0.165994	−	0.0539347i
$893$			1.50732i			0.0504405i
$894$	1.25537	+	3.86363i	0.0419858	+	0.129219i
$895$	48.7896	+	1.69235i	1.63086	+	0.0565690i
$896$	7.36456	−	22.6658i	0.246033	−	0.757211i
$897$	−0.597685	−	0.194200i	−0.0199561	−	0.00648413i
$898$	−35.8533	−	49.3478i	−1.19644	−	1.64676i
$899$	2.65361			0.0885030
$900$	−18.9868	+	47.0573i	−0.632893	+	1.56858i
$901$	20.2915			0.676008
$902$	−0.423262	−	0.582570i	−0.0140931	−	0.0193975i
$903$	1.35026	+	0.438727i	0.0449340	+	0.0145999i
$904$	−26.4546	+	81.4190i	−0.879868	+	2.70796i
$905$	−24.8973	+	16.8019i	−0.827614	+	0.558514i
$906$	−3.38297	−	10.4117i	−0.112392	−	0.345906i
$907$			30.4598i			1.01140i	0.862709	+	0.505701i	$0.168766\pi$
$907$			30.4598i			1.01140i	−0.862709	+	0.505701i	$0.831234\pi$
$908$	−90.4156	+	29.3778i	−3.00055	+	0.974937i
$909$	0.107819	+	0.0783350i	0.00357613	+	0.00259821i
$910$	−5.30524	+	1.52259i	−0.175867	+	0.0504735i
$911$	21.2440	−	15.4347i	0.703846	−	0.511374i	−0.177337	−	0.984150i	$-0.556748\pi$
$911$	21.2440	−	15.4347i	0.703846	−	0.511374i	0.881182	+	0.472776i	$0.156748\pi$
$912$	3.41910	−	4.70599i	0.113218	−	0.155831i
$913$	9.01354	−	12.4061i	0.298305	−	0.410581i
$914$	10.9884	−	7.98356i	0.363465	−	0.264073i
$915$	−5.21439	−	7.72676i	−0.172382	−	0.255439i
$916$	63.4164	+	46.0747i	2.09534	+	1.52235i
$917$	−9.23695	+	3.00127i	−0.305031	+	0.0991106i
$918$			20.2930i			0.669770i
$919$	9.47248	+	29.1533i	0.312468	+	0.961678i	0.976784	+	0.214226i	$0.0687229\pi$
$919$	9.47248	+	29.1533i	0.312468	+	0.961678i	−0.664316	+	0.747452i	$0.731277\pi$
$920$	6.88093	−	18.9190i	0.226857	−	0.623739i
$921$	2.92025	−	8.98760i	0.0962254	−	0.296151i
$922$	−13.5869	−	4.41465i	−0.447461	−	0.145389i
$923$	1.32633	+	1.82554i	0.0436567	+	0.0600882i
$924$	10.8903			0.358265
$925$	−2.57326	+	37.0483i	−0.0846084	+	1.21814i
$926$	−67.1717			−2.20740
$927$	24.7873	+	34.1168i	0.814121	+	1.12054i
$928$	25.2762	+	8.21274i	0.829732	+	0.269596i
$929$	13.4796	−	41.4860i	0.442252	−	1.36111i	−0.443217	−	0.896414i	$-0.646163\pi$
$929$	13.4796	−	41.4860i	0.442252	−	1.36111i	0.885469	−	0.464698i	$-0.153837\pi$
$930$	−1.90076	−	1.48432i	−0.0623283	−	0.0486727i
$931$	−1.04777	−	3.22469i	−0.0343391	−	0.105685i
$932$			11.6123i			0.380375i
$933$	−8.66845	+	2.81655i	−0.283792	+	0.0922097i
$934$	41.4407	+	30.1084i	1.35598	+	0.985177i
$935$	5.71849	+	2.07985i	0.187015	+	0.0680183i
$936$	5.86796	−	4.26332i	0.191800	−	0.139351i
$937$	−21.6192	+	29.7563i	−0.706269	+	0.972096i	0.293601	+	0.955928i	$0.405146\pi$
$937$	−21.6192	+	29.7563i	−0.706269	+	0.972096i	−0.999869	+	0.0161674i	$0.994854\pi$
$938$	13.1078	−	18.0413i	0.427985	−	0.589070i
$939$	5.65339	−	4.10743i	0.184491	−	0.134041i
$940$	14.0802	+	5.12106i	0.459246	+	0.167030i
$941$	4.06388	+	2.95258i	0.132479	+	0.0962515i	0.652051	−	0.758175i	$-0.273909\pi$
$941$	4.06388	+	2.95258i	0.132479	+	0.0962515i	−0.519572	+	0.854426i	$0.673909\pi$
$942$	−24.4566	+	7.94643i	−0.796839	+	0.258909i
$943$		−	0.270107i		−	0.00879588i
$944$	1.67432	+	5.15304i	0.0544946	+	0.167717i
$945$	−14.9777	−	11.6962i	−0.487224	−	0.380477i
$946$	−1.05446	+	3.24529i	−0.0342834	+	0.105514i
$947$	−31.0649	−	10.0936i	−1.00947	−	0.327998i	−0.242829	−	0.970069i	$-0.578075\pi$
$947$	−31.0649	−	10.0936i	−1.00947	−	0.327998i	−0.766645	+	0.642071i	$0.778075\pi$
$948$	−23.4809	−	32.3187i	−0.762625	−	1.04966i
$949$	8.44252			0.274056
$950$	−0.879551	+	12.6632i	−0.0285364	+	0.410850i
$951$	−26.3430			−0.854230
$952$	−12.3872	−	17.0495i	−0.401471	−	0.552578i
$953$	−2.96847	−	0.964514i	−0.0961581	−	0.0312437i	0.260543	−	0.965462i	$-0.416098\pi$
$953$	−2.96847	−	0.964514i	−0.0961581	−	0.0312437i	−0.356701	+	0.934219i	$0.616098\pi$
$954$	20.3393	−	62.5978i	0.658508	−	2.02668i
$955$	17.2589	−	47.4529i	0.558484	−	1.53554i
$956$	24.2919	+	74.7628i	0.785656	+	2.41800i
$957$		−	6.82033i		−	0.220470i
$958$	15.3857	−	4.99911i	0.497088	−	0.161514i
$959$	27.9470	+	20.3047i	0.902457	+	0.655674i
$960$	1.04069	+	1.54210i	0.0335880	+	0.0497712i
$961$	24.8759	−	18.0734i	0.802448	−	0.583012i
$962$	5.67224	−	7.80717i	0.182880	−	0.251713i
$963$	−22.6139	+	31.1254i	−0.728723	+	1.00300i
$964$	−93.2201	+	67.7284i	−3.00242	+	2.18138i
$965$	54.5293	−	15.6498i	1.75536	−	0.503785i
$966$	4.79167	+	3.48135i	0.154169	+	0.112011i
$967$	−5.04147	+	1.63807i	−0.162123	+	0.0526769i	−0.388954	−	0.921257i	$-0.627163\pi$
$967$	−5.04147	+	1.63807i	−0.162123	+	0.0526769i	0.226831	+	0.973934i	$0.427163\pi$
$968$		−	53.8889i		−	1.73205i
$969$	0.467548	+	1.43896i	0.0150198	+	0.0462262i
$970$	−60.1327	+	40.5805i	−1.93074	+	1.30296i
$971$	7.31291	−	22.5068i	0.234682	−	0.722278i	−0.762481	−	0.647011i	$-0.776019\pi$
$971$	7.31291	−	22.5068i	0.234682	−	0.722278i	0.997163	−	0.0752674i	$-0.0239810\pi$
$972$	67.6947	+	21.9953i	2.17131	+	0.705500i
$973$	−20.3441	−	28.0012i	−0.652201	−	0.897677i
$974$	49.8085			1.59597
$975$	0.810707	−	2.00927i	0.0259634	−	0.0643483i
$976$	−33.8222			−1.08262
$977$	−16.5071	−	22.7200i	−0.528108	−	0.726879i	0.458732	−	0.888574i	$-0.348304\pi$
$977$	−16.5071	−	22.7200i	−0.528108	−	0.726879i	−0.986841	+	0.161696i	$0.948304\pi$
$978$	14.4781	+	4.70423i	0.462960	+	0.150425i
$979$	−2.14431	+	6.59950i	−0.0685323	+	0.210921i
$980$	−33.6824	−	1.16833i	−1.07594	−	0.0373209i
$981$	10.2252	+	31.4700i	0.326466	+	1.00476i
$982$		−	28.4352i		−	0.907404i
$983$	−9.68294	+	3.14618i	−0.308838	+	0.100347i	−0.459335	−	0.888263i	$-0.651912\pi$
$983$	−9.68294	+	3.14618i	−0.308838	+	0.100347i	0.150498	+	0.988610i	$0.451912\pi$
$984$	−0.792032	−	0.575445i	−0.0252490	−	0.0183445i
$985$	0.803671	−	23.1694i	0.0256071	−	0.738239i
$986$	−19.4110	+	14.1029i	−0.618174	+	0.449129i
$987$	−1.42524	+	1.96167i	−0.0453659	+	0.0624408i
$988$	1.33717	−	1.84046i	0.0425411	−	0.0585529i
$989$	−1.03550	+	0.752335i	−0.0329270	+	0.0239229i
$990$	12.1481	−	15.5564i	0.386093	−	0.494414i
$991$	−26.6106	−	19.3338i	−0.845315	−	0.614157i	0.0785355	−	0.996911i	$-0.474976\pi$
$991$	−26.6106	−	19.3338i	−0.845315	−	0.614157i	−0.923850	+	0.382754i	$0.874976\pi$
$992$	−2.39771	+	0.779062i	−0.0761272	+	0.0247352i
$993$		−	27.1865i		−	0.862737i
$994$	−6.57171	−	20.2256i	−0.208442	−	0.641518i
$995$	−14.0031	−	48.7916i	−0.443929	−	1.54680i
$996$	11.7119	−	36.0454i	0.371104	−	1.14214i
$997$	12.1159	+	3.93668i	0.383713	+	0.124676i	0.494521	−	0.869166i	$-0.335344\pi$
$997$	12.1159	+	3.93668i	0.383713	+	0.124676i	−0.110807	+	0.993842i	$0.535344\pi$
$998$	9.70754	+	13.3613i	0.307287	+	0.422944i
$999$	33.2259			1.05122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.n.a.39.19	✓	80
25.9	even	10	inner	475.2.n.a.134.19	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
475.2.n.a.39.19	✓	80	1.1	even	1	trivial
475.2.n.a.134.19	yes	80	25.9	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.n (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.49224 + 2.05389i) q^{2} +(-0.805296 - 0.261657i) q^{3} +(-1.37366 + 4.22769i) q^{4} +(0.616846 + 2.14930i) q^{5} +(-0.664281 - 2.04445i) q^{6} +1.89983i q^{7} +(-5.90407 + 1.91835i) q^{8} +(-1.84701 - 1.34193i) q^{9} +O(q^{10})\)	\(q+(1.49224 + 2.05389i) q^{2} +(-0.805296 - 0.261657i) q^{3} +(-1.37366 + 4.22769i) q^{4} +(0.616846 + 2.14930i) q^{5} +(-0.664281 - 2.04445i) q^{6} +1.89983i q^{7} +(-5.90407 + 1.91835i) q^{8} +(-1.84701 - 1.34193i) q^{9} +(-3.49395 + 4.47421i) q^{10} +(1.23208 - 0.895155i) q^{11} +(2.21241 - 3.04512i) q^{12} +(0.300809 - 0.414028i) q^{13} +(-3.90205 + 2.83501i) q^{14} +(0.0656351 - 1.89223i) q^{15} +(-5.55779 - 4.03797i) q^{16} +(1.69942 - 0.552175i) q^{17} -5.79606i q^{18} +(-0.309017 - 0.951057i) q^{19} +(-9.93392 - 0.344575i) q^{20} +(0.497103 - 1.52993i) q^{21} +(3.67710 + 1.19476i) q^{22} +(0.852439 + 1.17328i) q^{23} +5.25647 q^{24} +(-4.23900 + 2.65158i) q^{25} +1.29925 q^{26} +(2.62937 + 3.61901i) q^{27} +(-8.03190 - 2.60972i) q^{28} +(-1.63440 + 5.03018i) q^{29} +(3.98437 - 2.68885i) q^{30} +(-0.155040 - 0.477163i) q^{31} -5.02492i q^{32} +(-1.22641 + 0.398484i) q^{33} +(3.67005 + 2.66645i) q^{34} +(-4.08331 + 1.17190i) q^{35} +(8.21045 - 5.96524i) q^{36} +(4.36579 - 6.00899i) q^{37} +(1.49224 - 2.05389i) q^{38} +(-0.350573 + 0.254706i) q^{39} +(-7.76501 - 11.5063i) q^{40} +(-0.150678 - 0.109474i) q^{41} +(3.88410 - 1.26202i) q^{42} +0.882567i q^{43} +(2.09199 + 6.43847i) q^{44} +(1.74490 - 4.79756i) q^{45} +(-1.13775 + 3.50164i) q^{46} +(-1.43354 - 0.465787i) q^{47} +(3.41910 + 4.70599i) q^{48} +3.39064 q^{49} +(-11.7717 - 4.74966i) q^{50} -1.51302 q^{51} +(1.33717 + 1.84046i) q^{52} +(10.8001 + 3.50915i) q^{53} +(-3.50942 + 10.8009i) q^{54} +(2.68396 + 2.09593i) q^{55} +(-3.64454 - 11.2167i) q^{56} +0.846738i q^{57} +(-12.7704 + 4.14934i) q^{58} +(-0.638073 - 0.463588i) q^{59} +(7.90959 + 2.87676i) q^{60} +(3.98304 - 2.89385i) q^{61} +(0.748686 - 1.03048i) q^{62} +(2.54945 - 3.50901i) q^{63} +(-0.794934 + 0.577554i) q^{64} +(1.07542 + 0.391138i) q^{65} +(-2.64854 - 1.92428i) q^{66} +(-4.39726 + 1.42876i) q^{67} +7.94312i q^{68} +(-0.379469 - 1.16789i) q^{69} +(-8.50025 - 6.63792i) q^{70} +(-1.36252 + 4.19341i) q^{71} +(13.4792 + 4.37965i) q^{72} +(9.69659 + 13.3462i) q^{73} +18.8566 q^{74} +(4.10745 - 1.02614i) q^{75} +4.44526 q^{76} +(1.70064 + 2.34074i) q^{77} +(-1.04628 - 0.339957i) q^{78} +(3.27969 - 10.0938i) q^{79} +(5.25051 - 14.4362i) q^{80} +(0.946008 + 2.91151i) q^{81} -0.472836i q^{82} +(9.57643 - 3.11157i) q^{83} +(5.78521 + 4.20320i) q^{84} +(2.23507 + 3.31196i) q^{85} +(-1.81270 + 1.31700i) q^{86} +(2.63236 - 3.62313i) q^{87} +(-5.55703 + 7.64860i) q^{88} +(-3.68623 + 2.67820i) q^{89} +(12.4575 - 3.57528i) q^{90} +(0.786583 + 0.571486i) q^{91} +(-6.13123 + 1.99216i) q^{92} +0.424825i q^{93} +(-1.18252 - 3.63941i) q^{94} +(1.85349 - 1.25083i) q^{95} +(-1.31480 + 4.04655i) q^{96} +(12.1536 + 3.94895i) q^{97} +(5.05965 + 6.96401i) q^{98} -3.47690 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9}+O(q^{10}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9	\( 80 q + 16 q^{4} - 3 q^{5} + 6 q^{6} + 8 q^{9} - 36 q^{10} + 20 q^{11} + 45 q^{12} - 10 q^{14} - 20 q^{16} - 15 q^{17} + 20 q^{19} + 12 q^{20} + 16 q^{21} + 15 q^{23} + 72 q^{24} + 41 q^{25} - 84 q^{26} + 15 q^{27} + 30 q^{28} - 24 q^{29} - 40 q^{30} + 8 q^{31} - 75 q^{33} - 24 q^{34} - 33 q^{35} - 32 q^{36} - 15 q^{37} - 30 q^{39} - 28 q^{40} + 13 q^{41} - 130 q^{42} - 24 q^{44} + 6 q^{45} + 30 q^{46} + 145 q^{48} - 28 q^{49} + 77 q^{50} - 36 q^{51} - 5 q^{52} - 10 q^{53} + 15 q^{54} - 8 q^{55} + 48 q^{56} - 60 q^{58} - 19 q^{59} - 110 q^{60} + 8 q^{61} + 110 q^{62} + 55 q^{63} + 16 q^{64} - 43 q^{65} - 17 q^{66} - 65 q^{67} - 42 q^{69} + 4 q^{70} + 18 q^{71} + 100 q^{73} + 22 q^{74} + 115 q^{75} + 64 q^{76} - 145 q^{78} - 16 q^{79} - 97 q^{80} + q^{81} - 70 q^{83} - 46 q^{84} - 16 q^{85} + 64 q^{86} + 10 q^{87} + 30 q^{88} + 4 q^{89} - 8 q^{90} + 16 q^{91} - 135 q^{92} + 38 q^{94} - 2 q^{95} + 50 q^{96} + 150 q^{97} + 130 q^{98} + 178 q^{99}+O(q^{100}) \) 80 * q + 16 * q^4 - 3 * q^5 + 6 * q^6 + 8 * q^9 - 36 * q^10 + 20 * q^11 + 45 * q^12 - 10 * q^14 - 20 * q^16 - 15 * q^17 + 20 * q^19 + 12 * q^20 + 16 * q^21 + 15 * q^23 + 72 * q^24 + 41 * q^25 - 84 * q^26 + 15 * q^27 + 30 * q^28 - 24 * q^29 - 40 * q^30 + 8 * q^31 - 75 * q^33 - 24 * q^34 - 33 * q^35 - 32 * q^36 - 15 * q^37 - 30 * q^39 - 28 * q^40 + 13 * q^41 - 130 * q^42 - 24 * q^44 + 6 * q^45 + 30 * q^46 + 145 * q^48 - 28 * q^49 + 77 * q^50 - 36 * q^51 - 5 * q^52 - 10 * q^53 + 15 * q^54 - 8 * q^55 + 48 * q^56 - 60 * q^58 - 19 * q^59 - 110 * q^60 + 8 * q^61 + 110 * q^62 + 55 * q^63 + 16 * q^64 - 43 * q^65 - 17 * q^66 - 65 * q^67 - 42 * q^69 + 4 * q^70 + 18 * q^71 + 100 * q^73 + 22 * q^74 + 115 * q^75 + 64 * q^76 - 145 * q^78 - 16 * q^79 - 97 * q^80 + q^81 - 70 * q^83 - 46 * q^84 - 16 * q^85 + 64 * q^86 + 10 * q^87 + 30 * q^88 + 4 * q^89 - 8 * q^90 + 16 * q^91 - 135 * q^92 + 38 * q^94 - 2 * q^95 + 50 * q^96 + 150 * q^97 + 130 * q^98 + 178 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more