LMFDB - Embedded newform 165.2.p.b.101.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,2,Mod(41,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("165.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	165.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.31753163335$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			101.1
Character	$\chi$	$=$	165.101
Dual form			165.2.p.b.116.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.848632 + 2.61182i) q^{2} +(-0.139896 + 1.72639i) q^{3} +(-4.48340 - 3.25738i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-4.39031 - 1.83046i) q^{6} +(-0.0372155 + 0.0512227i) q^{7} +(7.86897 - 5.71714i) q^{8} +(-2.96086 - 0.483031i) q^{9} +O(q^{10})$	\(q+(-0.848632 + 2.61182i) q^{2} +(-0.139896 + 1.72639i) q^{3} +(-4.48340 - 3.25738i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-4.39031 - 1.83046i) q^{6} +(-0.0372155 + 0.0512227i) q^{7} +(7.86897 - 5.71714i) q^{8} +(-2.96086 - 0.483031i) q^{9} -2.74623i q^{10} +(-1.43771 + 2.98881i) q^{11} +(6.25073 - 7.28442i) q^{12} +(-1.24018 - 0.402959i) q^{13} +(-0.102202 - 0.140670i) q^{14} +(-0.400435 - 1.68513i) q^{15} +(4.82928 + 14.8630i) q^{16} +(0.915974 + 2.81908i) q^{17} +(3.77427 - 7.32332i) q^{18} +(-0.152082 - 0.209322i) q^{19} +(5.27056 + 1.71251i) q^{20} +(-0.0832242 - 0.0714144i) q^{21} +(-6.58616 - 6.29144i) q^{22} +5.90480i q^{23} +(8.76919 + 14.3847i) q^{24} +(0.809017 - 0.587785i) q^{25} +(2.10492 - 2.89717i) q^{26} +(1.24811 - 5.04403i) q^{27} +(0.333704 - 0.108427i) q^{28} +(-7.27305 - 5.28418i) q^{29} +(4.74107 + 0.384187i) q^{30} +(0.401111 - 1.23449i) q^{31} -23.4646 q^{32} +(-4.95873 - 2.90017i) q^{33} -8.14026 q^{34} +(0.0195653 - 0.0602159i) q^{35} +(11.7013 + 11.8103i) q^{36} +(4.16472 + 3.02584i) q^{37} +(0.675774 - 0.219572i) q^{38} +(0.869162 - 2.08467i) q^{39} +(-5.71714 + 7.86897i) q^{40} +(-4.06933 + 2.95654i) q^{41} +(0.257148 - 0.156762i) q^{42} +4.94107i q^{43} +(16.1815 - 8.71688i) q^{44} +(2.96521 - 0.455566i) q^{45} +(-15.4223 - 5.01101i) q^{46} +(4.62843 + 6.37049i) q^{47} +(-26.3349 + 6.25795i) q^{48} +(2.16188 + 6.65358i) q^{49} +(0.848632 + 2.61182i) q^{50} +(-4.99498 + 1.18695i) q^{51} +(4.24764 + 5.84637i) q^{52} +(-4.06872 - 1.32201i) q^{53} +(12.1149 + 7.54038i) q^{54} +(0.443749 - 3.28681i) q^{55} +0.615836i q^{56} +(0.382648 - 0.233269i) q^{57} +(19.9735 - 14.5116i) q^{58} +(1.85056 - 2.54708i) q^{59} +(-3.69379 + 8.85947i) q^{60} +(4.07249 - 1.32323i) q^{61} +(2.88388 + 2.09526i) q^{62} +(0.134932 - 0.133687i) q^{63} +(10.2543 - 31.5594i) q^{64} +1.30400 q^{65} +(11.7829 - 10.4901i) q^{66} +10.4211 q^{67} +(5.07614 - 15.6227i) q^{68} +(-10.1940 - 0.826059i) q^{69} +(0.140670 + 0.102202i) q^{70} +(8.12731 - 2.64072i) q^{71} +(-26.0605 + 13.1267i) q^{72} +(-7.99451 + 11.0035i) q^{73} +(-11.4373 + 8.30967i) q^{74} +(0.901569 + 1.47891i) q^{75} +1.43386i q^{76} +(-0.0995901 - 0.184873i) q^{77} +(4.70718 + 4.03921i) q^{78} +(7.16551 + 2.32822i) q^{79} +(-9.18583 - 12.6432i) q^{80} +(8.53336 + 2.86037i) q^{81} +(-4.26859 - 13.1374i) q^{82} +(-1.56621 - 4.82031i) q^{83} +(0.140504 + 0.591273i) q^{84} +(-1.74229 - 2.39805i) q^{85} +(-12.9052 - 4.19315i) q^{86} +(10.1400 - 11.8169i) q^{87} +(5.77417 + 31.7385i) q^{88} +10.2357i q^{89} +(-1.32652 + 8.13120i) q^{90} +(0.0667946 - 0.0485291i) q^{91} +(19.2342 - 26.4736i) q^{92} +(2.07510 + 0.865175i) q^{93} +(-20.5664 + 6.68243i) q^{94} +(0.209322 + 0.152082i) q^{95} +(3.28261 - 40.5091i) q^{96} +(0.276359 - 0.850545i) q^{97} -19.2126 q^{98} +(5.70054 - 8.15499i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	$ 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) $ 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/165\mathbb{Z}\right)^\times$.

$n$	$46$	$56$	$67$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.848632	+	2.61182i	−0.600074	+	1.84684i	−0.0724261	+	0.997374i	$0.523074\pi$
$2$	−0.848632	+	2.61182i	−0.600074	+	1.84684i	−0.527648	+	0.849463i	$0.676926\pi$
$3$	−0.139896	+	1.72639i	−0.0807691	+	0.996733i
$3$	−0.139896	+	1.72639i	−0.0807691	+	0.996733i
$4$	−4.48340	−	3.25738i	−2.24170	−	1.62869i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$5$	−0.951057	+	0.309017i	−0.425325	+	0.138197i
$6$	−4.39031	−	1.83046i	−1.79234	−	0.747281i
$7$	−0.0372155	+	0.0512227i	−0.0140661	+	0.0193604i	−0.815992	−	0.578063i	$-0.803809\pi$
$7$	−0.0372155	+	0.0512227i	−0.0140661	+	0.0193604i	0.801926	+	0.597423i	$0.203809\pi$
$8$	7.86897	−	5.71714i	2.78210	−	2.02131i
$9$	−2.96086	−	0.483031i	−0.986953	−	0.161010i
$10$		−	2.74623i		−	0.868435i
$11$	−1.43771	+	2.98881i	−0.433485	+	0.901161i
$11$	−1.43771	+	2.98881i	−0.433485	+	0.901161i
$12$	6.25073	−	7.28442i	1.80443	−	2.10283i
$13$	−1.24018	−	0.402959i	−0.343964	−	0.111761i	0.131940	−	0.991258i	$-0.457879\pi$
$13$	−1.24018	−	0.402959i	−0.343964	−	0.111761i	−0.475905	+	0.879497i	$0.657879\pi$
$14$	−0.102202	−	0.140670i	−0.0273147	−	0.0375955i
$15$	−0.400435	−	1.68513i	−0.103392	−	0.435098i
$16$	4.82928	+	14.8630i	1.20732	+	3.71575i
$17$	0.915974	+	2.81908i	0.222156	+	0.683727i	0.998568	+	0.0535006i	$0.0170379\pi$
$17$	0.915974	+	2.81908i	0.222156	+	0.683727i	−0.776411	+	0.630226i	$0.782962\pi$
$18$	3.77427	−	7.32332i	0.889604	−	1.72612i
$19$	−0.152082	−	0.209322i	−0.0348899	−	0.0480218i	0.791216	−	0.611537i	$-0.209449\pi$
$19$	−0.152082	−	0.209322i	−0.0348899	−	0.0480218i	−0.826106	+	0.563515i	$0.809449\pi$
$20$	5.27056	+	1.71251i	1.17853	+	0.382928i
$21$	−0.0832242	−	0.0714144i	−0.0181610	−	0.0155839i
$22$	−6.58616	−	6.29144i	−1.40417	−	1.34134i
$23$			5.90480i			1.23124i	0.788045	+	0.615618i	$0.211094\pi$
$23$			5.90480i			1.23124i	−0.788045	+	0.615618i	$0.788906\pi$
$24$	8.76919	+	14.3847i	1.79000	+	2.93627i
$25$	0.809017	−	0.587785i	0.161803	−	0.117557i
$26$	2.10492	−	2.89717i	0.412808	−	0.568181i
$27$	1.24811	−	5.04403i	0.240200	−	0.970724i
$28$	0.333704	−	0.108427i	0.0630642	−	0.0204908i
$29$	−7.27305	−	5.28418i	−1.35057	−	0.981248i	−0.998983	−	0.0450937i	$-0.985641\pi$
$29$	−7.27305	−	5.28418i	−1.35057	−	0.981248i	−0.351589	−	0.936154i	$-0.614359\pi$
$30$	4.74107	+	0.384187i	0.865598	+	0.0701427i
$31$	0.401111	−	1.23449i	0.0720416	−	0.221721i	−0.908552	−	0.417771i	$-0.862811\pi$
$31$	0.401111	−	1.23449i	0.0720416	−	0.221721i	0.980594	+	0.196050i	$0.0628114\pi$
$32$	−23.4646			−4.14799
$33$	−4.95873	−	2.90017i	−0.863204	−	0.504855i
$34$	−8.14026			−1.39604
$35$	0.0195653	−	0.0602159i	0.00330715	−	0.0101784i
$36$	11.7013	+	11.8103i	1.95022	+	1.96838i
$37$	4.16472	+	3.02584i	0.684675	+	0.497446i	0.874905	−	0.484294i	$-0.160923\pi$
$37$	4.16472	+	3.02584i	0.684675	+	0.497446i	−0.190230	+	0.981740i	$0.560923\pi$
$38$	0.675774	−	0.219572i	0.109625	−	0.0356193i
$39$	0.869162	−	2.08467i	0.139177	−	0.333814i
$40$	−5.71714	+	7.86897i	−0.903960	+	1.24419i
$41$	−4.06933	+	2.95654i	−0.635522	+	0.461734i	−0.858309	−	0.513134i	$-0.828485\pi$
$41$	−4.06933	+	2.95654i	−0.635522	+	0.461734i	0.222787	+	0.974867i	$0.428485\pi$
$42$	0.257148	−	0.156762i	0.0396789	−	0.0241889i
$43$			4.94107i			0.753506i	0.926314	+	0.376753i	$0.122959\pi$
$43$			4.94107i			0.753506i	−0.926314	+	0.376753i	$0.877041\pi$
$44$	16.1815	−	8.71688i	2.43946	−	1.31412i
$45$	2.96521	−	0.455566i	0.442027	−	0.0679117i
$46$	−15.4223	−	5.01101i	−2.27389	−	0.738832i
$47$	4.62843	+	6.37049i	0.675126	+	0.929231i	0.999863	−	0.0165736i	$-0.00527578\pi$
$47$	4.62843	+	6.37049i	0.675126	+	0.929231i	−0.324737	+	0.945804i	$0.605276\pi$
$48$	−26.3349	+	6.25795i	−3.80112	+	0.903258i
$49$	2.16188	+	6.65358i	0.308840	+	0.950512i
$50$	0.848632	+	2.61182i	0.120015	+	0.369367i
$51$	−4.99498	+	1.18695i	−0.699436	+	0.166207i
$52$	4.24764	+	5.84637i	0.589041	+	0.810746i
$53$	−4.06872	−	1.32201i	−0.558881	−	0.181591i	0.0159366	−	0.999873i	$-0.494927\pi$
$53$	−4.06872	−	1.32201i	−0.558881	−	0.181591i	−0.574818	+	0.818282i	$0.694927\pi$
$54$	12.1149	+	7.54038i	1.64863	+	1.02612i
$55$	0.443749	−	3.28681i	0.0598350	−	0.443193i
$56$			0.615836i			0.0822946i
$57$	0.382648	−	0.233269i	0.0506829	−	0.0308972i
$58$	19.9735	−	14.5116i	2.62265	−	1.90547i
$59$	1.85056	−	2.54708i	0.240922	−	0.331601i	−0.671384	−	0.741110i	$-0.734300\pi$
$59$	1.85056	−	2.54708i	0.240922	−	0.331601i	0.912306	+	0.409509i	$0.134300\pi$
$60$	−3.69379	+	8.85947i	−0.476866	+	1.14375i
$61$	4.07249	−	1.32323i	0.521429	−	0.169423i	−0.0364648	−	0.999335i	$-0.511610\pi$
$61$	4.07249	−	1.32323i	0.521429	−	0.169423i	0.557894	+	0.829912i	$0.311610\pi$
$62$	2.88388	+	2.09526i	0.366253	+	0.266098i
$63$	0.134932	−	0.133687i	0.0169998	−	0.0168430i
$64$	10.2543	−	31.5594i	1.28178	−	3.94492i
$65$	1.30400			0.161742
$66$	11.7829	−	10.4901i	1.45037	−	1.29125i
$67$	10.4211			1.27314			0.636572	−	0.771217i	$-0.280352\pi$
$67$	10.4211			1.27314			0.636572	+	0.771217i	$0.280352\pi$
$68$	5.07614	−	15.6227i	0.615572	−	1.89454i
$69$	−10.1940	−	0.826059i	−1.22721	−	0.0994458i
$70$	0.140670	+	0.102202i	0.0168132	+	0.0122155i
$71$	8.12731	−	2.64072i	0.964535	−	0.313396i	0.215927	−	0.976409i	$-0.430723\pi$
$71$	8.12731	−	2.64072i	0.964535	−	0.313396i	0.748608	+	0.663013i	$0.230723\pi$
$72$	−26.0605	+	13.1267i	−3.07126	+	1.54700i
$73$	−7.99451	+	11.0035i	−0.935686	+	1.28786i	0.0219135	+	0.999760i	$0.493024\pi$
$73$	−7.99451	+	11.0035i	−0.935686	+	1.28786i	−0.957600	+	0.288102i	$0.906976\pi$
$74$	−11.4373	+	8.30967i	−1.32956	+	0.965980i
$75$	0.901569	+	1.47891i	0.104104	+	0.170770i
$76$			1.43386i			0.164475i
$77$	−0.0995901	−	0.184873i	−0.0113493	−	0.0210683i
$78$	4.70718	+	4.03921i	0.532983	+	0.457351i
$79$	7.16551	+	2.32822i	0.806183	+	0.261945i	0.682980	−	0.730437i	$-0.260683\pi$
$79$	7.16551	+	2.32822i	0.806183	+	0.261945i	0.123203	+	0.992382i	$0.460683\pi$
$80$	−9.18583	−	12.6432i	−1.02701	−	1.41355i
$81$	8.53336	+	2.86037i	0.948151	+	0.317819i
$82$	−4.26859	−	13.1374i	−0.471387	−	1.45078i
$83$	−1.56621	−	4.82031i	−0.171914	−	0.529098i	0.827565	−	0.561370i	$-0.189726\pi$
$83$	−1.56621	−	4.82031i	−0.171914	−	0.529098i	−0.999479	+	0.0322723i	$0.989726\pi$
$84$	0.140504	+	0.591273i	0.0153302	+	0.0645131i
$85$	−1.74229	−	2.39805i	−0.188977	−	0.260105i
$86$	−12.9052	−	4.19315i	−1.39160	−	0.452159i
$87$	10.1400	−	11.8169i	1.08713	−	1.26691i
$88$	5.77417	+	31.7385i	0.615529	+	3.38333i
$89$			10.2357i			1.08498i	0.840061	+	0.542492i	$0.182519\pi$
$89$			10.2357i			1.08498i	−0.840061	+	0.542492i	$0.817481\pi$
$90$	−1.32652	+	8.13120i	−0.139827	+	0.857104i
$91$	0.0667946	−	0.0485291i	0.00700198	−	0.00508723i
$92$	19.2342	−	26.4736i	2.00530	−	2.76006i
$93$	2.07510	+	0.865175i	0.215178	+	0.0897145i
$94$	−20.5664	+	6.68243i	−2.12126	+	0.689240i
$95$	0.209322	+	0.152082i	0.0214760	+	0.0156032i
$96$	3.28261	−	40.5091i	0.335030	−	4.13444i
$97$	0.276359	−	0.850545i	0.0280600	−	0.0863597i	−0.936046	−	0.351878i	$-0.885543\pi$
$97$	0.276359	−	0.850545i	0.0280600	−	0.0863597i	0.964106	+	0.265518i	$0.0855431\pi$
$98$	−19.2126			−1.94077
$99$	5.70054	−	8.15499i	0.572926	−	0.819607i
$100$	−5.54179			−0.554179
$101$	2.99444	−	9.21594i	0.297958	−	0.917020i	−0.684254	−	0.729244i	$-0.739872\pi$
$101$	2.99444	−	9.21594i	0.297958	−	0.917020i	0.982212	−	0.187776i	$-0.0601280\pi$
$102$	1.13879	−	14.0533i	0.112757	−	1.39148i
$103$	2.11957	+	1.53996i	0.208847	+	0.151736i	0.687292	−	0.726381i	$-0.258799\pi$
$103$	2.11957	+	1.53996i	0.208847	+	0.151736i	−0.478445	+	0.878118i	$0.658799\pi$
$104$	−12.0627	+	3.91942i	−1.18285	+	0.384330i
$105$	0.101219	+	0.0422014i	0.00987798	+	0.00411844i
$106$	6.90569	−	9.50486i	0.670740	−	0.923194i
$107$	4.24517	−	3.08429i	0.410396	−	0.298170i	−0.363366	−	0.931646i	$-0.618373\pi$
$107$	4.24517	−	3.08429i	0.410396	−	0.298170i	0.773762	+	0.633476i	$0.218373\pi$
$108$	−22.0261	+	18.5488i	−2.11947	+	1.78486i
$109$		−	9.95491i		−	0.953507i	−0.879037	−	0.476754i	$-0.841813\pi$
$109$		−	9.95491i		−	0.953507i	0.879037	−	0.476754i	$-0.158187\pi$
$110$	8.20797	+	3.94828i	0.782599	+	0.376454i
$111$	−5.80642	+	6.76663i	−0.551121	+	0.642260i
$112$	−0.941047	−	0.305765i	−0.0889206	−	0.0288920i
$113$	5.05185	+	6.95327i	0.475238	+	0.654108i	0.977581	−	0.210560i	$-0.0675287\pi$
$113$	5.05185	+	6.95327i	0.475238	+	0.654108i	−0.502343	+	0.864668i	$0.667529\pi$
$114$	0.284530	+	1.19737i	0.0266486	+	0.112144i
$115$	−1.82468	−	5.61580i	−0.170153	−	0.523676i
$116$	15.3954	+	47.3822i	1.42943	+	4.39933i
$117$	3.47736	+	1.79215i	0.321482	+	0.165684i
$118$	5.08206	+	6.99486i	0.467842	+	0.643929i
$119$	−0.178489	−	0.0579947i	−0.0163621	−	0.00531637i
$120$	−12.7851	−	10.9709i	−1.16712	−	1.00150i
$121$	−6.86599	−	8.59408i	−0.624181	−	0.781280i
$122$			11.7596i			1.06466i
$123$	−4.53486	−	7.43886i	−0.408895	−	0.670739i
$124$	−5.81956	+	4.22816i	−0.522612	+	0.379700i
$125$	−0.587785	+	0.809017i	−0.0525731	+	0.0723607i
$126$	0.234659	+	0.465869i	0.0209051	+	0.0415029i
$127$	−3.16143	+	1.02721i	−0.280532	+	0.0911503i	−0.445904	−	0.895081i	$-0.647118\pi$
$127$	−3.16143	+	1.02721i	−0.280532	+	0.0911503i	0.165372	+	0.986231i	$0.447118\pi$
$128$	35.7589	+	25.9803i	3.16067	+	2.29636i
$129$	−8.53022	−	0.691237i	−0.751044	−	0.0608600i
$130$	−1.10662	+	3.40582i	−0.0970569	+	0.298711i
$131$	10.4486			0.912903			0.456451	−	0.889748i	$-0.349120\pi$
$131$	10.4486			0.912903			0.456451	+	0.889748i	$0.349120\pi$
$132$	12.7850	+	29.1551i	1.11279	+	2.53763i
$133$	0.0163818			0.00142049
$134$	−8.84372	+	27.2182i	−0.763981	+	2.35129i
$135$	0.371664	+	5.18284i	0.0319877	+	0.446068i
$136$	23.3248	+	16.9465i	2.00009	+	1.45315i
$137$	−4.83124	+	1.56976i	−0.412761	+	0.134114i	−0.508034	−	0.861337i	$-0.669628\pi$
$137$	−4.83124	+	1.56976i	−0.412761	+	0.134114i	0.0952732	+	0.995451i	$0.469628\pi$
$138$	10.8085	−	25.9239i	0.920079	−	2.20679i
$139$	−6.24680	+	8.59798i	−0.529846	+	0.729271i	−0.987107	−	0.160062i	$-0.948831\pi$
$139$	−6.24680	+	8.59798i	−0.529846	+	0.729271i	0.457261	+	0.889333i	$0.348831\pi$
$140$	−0.283866	+	0.206241i	−0.0239910	+	0.0174305i
$141$	−11.6455	+	7.09928i	−0.980724	+	0.597867i
$142$			23.4681i			1.96940i
$143$	2.98739	−	3.12733i	0.249818	−	0.261520i
$144$	−7.11952	−	46.3399i	−0.593294	−	3.86166i
$145$	8.54999	+	2.77806i	0.710038	+	0.230705i
$146$	−21.9548	−	30.2182i	−1.81699	−	2.50087i
$147$	−11.7891	+	2.80144i	−0.972351	+	0.231059i
$148$	−8.81577	−	27.1322i	−0.724652	−	2.23025i
$149$	−2.12753	−	6.54785i	−0.174294	−	0.536421i	0.825307	−	0.564685i	$-0.191002\pi$
$149$	−2.12753	−	6.54785i	−0.174294	−	0.536421i	−0.999601	+	0.0282637i	$0.991002\pi$
$150$	−4.62775	+	1.09969i	−0.377854	+	0.0897892i
$151$	−1.46205	−	2.01234i	−0.118980	−	0.163762i	0.745373	−	0.666648i	$-0.232272\pi$
$151$	−1.46205	−	2.01234i	−0.118980	−	0.163762i	−0.864353	+	0.502886i	$0.832272\pi$
$152$	−2.39345	−	0.777679i	−0.194134	−	0.0630781i
$153$	−1.35037	−	8.78933i	−0.109171	−	0.710576i
$154$	0.567372	−	0.103222i	0.0457201	−	0.00831786i
$155$			1.29802i			0.104260i
$156$	−10.6874	+	6.51520i	−0.855673	+	0.521634i
$157$	−7.42623	+	5.39548i	−0.592678	+	0.430606i	−0.843272	−	0.537486i	$-0.819374\pi$
$157$	−7.42623	+	5.39548i	−0.592678	+	0.430606i	0.250594	+	0.968092i	$0.419374\pi$
$158$	−12.1618	+	16.7392i	−0.967539	+	1.33170i
$159$	2.85150	−	6.83925i	0.226138	−	0.542388i
$160$	22.3162	−	7.25096i	1.76425	−	0.573239i
$161$	−0.302460	−	0.219750i	−0.0238372	−	0.0173187i
$162$	−14.7125	+	19.8602i	−1.15592	+	1.56037i
$163$	2.04528	−	6.29474i	0.160199	−	0.493042i	−0.838452	−	0.544976i	$-0.816539\pi$
$163$	2.04528	−	6.29474i	0.160199	−	0.493042i	0.998650	+	0.0519344i	$0.0165387\pi$
$164$	27.8750			2.17667
$165$	5.61223	+	1.22590i	0.436912	+	0.0954358i
$166$	13.9189			1.08032
$167$	4.10414	−	12.6313i	0.317588	−	0.977436i	−0.657088	−	0.753814i	$-0.728212\pi$
$167$	4.10414	−	12.6313i	0.317588	−	0.977436i	0.974676	−	0.223622i	$-0.0717881\pi$
$168$	−1.06318	−	0.0861531i	−0.0820257	−	0.00664686i
$169$	−9.14155	−	6.64172i	−0.703196	−	0.510902i
$170$	7.74184	−	2.51548i	0.593772	−	0.192928i
$171$	0.349183	+	0.693234i	0.0267027	+	0.0530129i
$172$	16.0950	−	22.1528i	1.22723	−	1.68914i
$173$	−1.82265	+	1.32423i	−0.138574	+	0.100680i	−0.654912	−	0.755705i	$-0.727295\pi$
$173$	−1.82265	+	1.32423i	−0.138574	+	0.100680i	0.516339	+	0.856384i	$0.327295\pi$
$174$	22.2585	+	36.5122i	1.68741	+	2.76798i
$175$			0.0633148i			0.00478615i
$176$	−51.3658	−	6.93485i	−3.87184	−	0.522734i
$177$	4.13837	+	3.55112i	0.311059	+	0.266918i
$178$	−26.7339	−	8.68636i	−2.00379	−	0.651070i
$179$	−5.66348	−	7.79511i	−0.423309	−	0.582634i	0.543093	−	0.839673i	$-0.317253\pi$
$179$	−5.66348	−	7.79511i	−0.423309	−	0.582634i	−0.966401	+	0.257039i	$0.917253\pi$
$180$	−14.7782	−	7.61634i	−1.10150	−	0.567688i
$181$	−0.784694	−	2.41504i	−0.0583258	−	0.179508i	0.917649	−	0.397392i	$-0.130085\pi$
$181$	−0.784694	−	2.41504i	−0.0583258	−	0.179508i	−0.975975	+	0.217884i	$0.930085\pi$
$182$	0.0700654	+	0.215639i	0.00519359	+	0.0159842i
$183$	1.71469	+	7.21583i	0.126754	+	0.533409i
$184$	33.7586	+	46.4647i	2.48872	+	3.42542i
$185$	−4.89592	−	1.59078i	−0.359955	−	0.116957i
$186$	−4.02068	+	4.68559i	−0.294811	+	0.343564i
$187$	−9.74260	−	1.31534i	−0.712449	−	0.0961871i
$188$		−	43.6380i		−	3.18263i
$189$	0.211920	+	0.251648i	0.0154149	+	0.0183047i
$190$	−0.574847	+	0.417651i	−0.0417038	+	0.0302996i
$191$	−11.1316	+	15.3213i	−0.805452	+	1.10861i	0.186557	+	0.982444i	$0.440267\pi$
$191$	−11.1316	+	15.3213i	−0.805452	+	1.10861i	−0.992009	+	0.126166i	$0.959733\pi$
$192$	53.0493	+	22.1179i	3.82851	+	1.59622i
$193$	0.0353572	−	0.0114883i	0.00254507	−	0.000826943i	−0.307744	−	0.951469i	$-0.599574\pi$
$193$	0.0353572	−	0.0114883i	0.00254507	−	0.000826943i	0.310289	+	0.950642i	$0.399574\pi$
$194$	1.98694	+	1.44360i	0.142654	+	0.103644i
$195$	−0.182425	+	2.25122i	−0.0130637	+	0.161213i
$196$	11.9807	−	36.8728i	0.855764	−	2.63377i
$197$	4.89464			0.348729			0.174364	−	0.984681i	$-0.444213\pi$
$197$	4.89464			0.348729			0.174364	+	0.984681i	$0.444213\pi$
$198$	16.4617	+	21.8094i	1.16988	+	1.54993i
$199$	24.7840			1.75689			0.878445	−	0.477844i	$-0.158581\pi$
$199$	24.7840			1.75689			0.878445	+	0.477844i	$0.158581\pi$
$200$	3.00568	−	9.25053i	0.212534	−	0.654111i
$201$	−1.45788	+	17.9910i	−0.102831	+	1.26899i
$202$	21.5292	+	15.6419i	1.51479	+	1.10056i
$203$	0.541341	−	0.175892i	0.0379947	−	0.0123452i
$204$	26.2608	+	10.9490i	1.83863	+	0.766581i
$205$	2.95654	−	4.06933i	0.206494	−	0.284214i
$206$	−5.82083	+	4.22908i	−0.405556	+	0.294654i
$207$	2.85220	−	17.4833i	0.198242	−	1.21517i
$208$		−	20.3788i		−	1.41302i
$209$	0.844274	−	0.153599i	0.0583996	−	0.0106246i
$210$	−0.196120	+	0.228553i	−0.0135336	+	0.0157717i
$211$	−8.72902	−	2.83623i	−0.600930	−	0.195254i	−0.00727497	−	0.999974i	$-0.502316\pi$
$211$	−8.72902	−	2.83623i	−0.600930	−	0.195254i	−0.593655	+	0.804719i	$0.702316\pi$
$212$	13.9354	+	19.1805i	0.957088	+	1.31732i
$213$	3.42195	+	14.4004i	0.234468	+	0.986696i
$214$	4.45304	+	13.7051i	0.304404	+	0.936858i
$215$	−1.52687	−	4.69924i	−0.104132	−	0.320485i
$216$	−19.0161	−	46.8269i	−1.29388	−	3.18617i
$217$	0.0483065	+	0.0664882i	0.00327926	+	0.00451352i
$218$	26.0004	+	8.44806i	1.76097	+	0.572175i
$219$	−17.8779	−	15.3410i	−1.20808	−	1.03665i
$220$	−12.6959	+	13.2906i	−0.855957	+	0.896053i
$221$		−	3.86527i		−	0.260006i
$222$	−12.7457	−	20.9077i	−0.855437	−	1.40323i
$223$	10.3346	−	7.50853i	0.692056	−	0.502808i	−0.185279	−	0.982686i	$-0.559319\pi$
$223$	10.3346	−	7.50853i	0.692056	−	0.502808i	0.877335	+	0.479878i	$0.159319\pi$
$224$	0.873247	−	1.20192i	0.0583463	−	0.0803067i
$225$	−2.67930	+	1.34957i	−0.178620	+	0.0899712i
$226$	−22.4479	+	7.29375i	−1.49321	+	0.485173i
$227$	−22.7399	−	16.5215i	−1.50930	−	1.09657i	−0.966487	−	0.256717i	$-0.917359\pi$
$227$	−22.7399	−	16.5215i	−1.50930	−	1.09657i	−0.542813	−	0.839853i	$-0.682641\pi$
$228$	−2.47541	−	0.200592i	−0.163938	−	0.0132845i
$229$	−4.01979	+	12.3716i	−0.265635	+	0.817540i	0.725912	+	0.687788i	$0.241418\pi$
$229$	−4.01979	+	12.3716i	−0.265635	+	0.817540i	−0.991546	+	0.129752i	$0.958582\pi$
$230$	16.2160			1.06925
$231$	0.333096	−	0.146068i	0.0219161	−	0.00961059i
$232$	−87.4419			−5.74084
$233$	1.41251	−	4.34726i	0.0925367	−	0.284799i	−0.894067	−	0.447933i	$-0.852160\pi$
$233$	1.41251	−	4.34726i	0.0925367	−	0.284799i	0.986604	+	0.163134i	$0.0521604\pi$
$234$	−7.63178	+	7.56136i	−0.498905	+	0.494302i
$235$	−6.37049	−	4.62843i	−0.415565	−	0.301925i
$236$	−16.5936	+	5.39159i	−1.08015	+	0.350963i
$237$	−5.02184	+	12.0448i	−0.326204	+	0.782392i
$238$	0.302944	−	0.416966i	0.0196369	−	0.0270279i
$239$	7.57328	−	5.50231i	0.489875	−	0.355915i	−0.315261	−	0.949005i	$-0.602092\pi$
$239$	7.57328	−	5.50231i	0.489875	−	0.355915i	0.805136	+	0.593090i	$0.202092\pi$
$240$	23.1122	−	14.0896i	1.49189	−	0.909481i
$241$		−	8.56042i		−	0.551425i	−0.961240	−	0.275712i	$-0.911086\pi$
$241$		−	8.56042i		−	0.551425i	0.961240	−	0.275712i	$-0.0889138\pi$
$242$	28.2729	−	10.6395i	1.81745	−	0.683935i
$243$	−6.13191	+	14.3318i	−0.393362	+	0.919384i
$244$	−22.5689	−	7.33308i	−1.44483	−	0.469452i
$245$	−4.11214	−	5.65988i	−0.262715	−	0.361596i
$246$	23.2774	−	5.53139i	1.48411	−	0.352669i
$247$	0.104260	+	0.320880i	0.00663392	+	0.0204171i
$248$	−3.90144	−	12.0074i	−0.247742	−	0.762470i
$249$	8.54085	−	2.02956i	0.541255	−	0.128618i
$250$	−1.61419	−	2.22175i	−0.102091	−	0.140516i
$251$	10.0937	+	3.27964i	0.637109	+	0.207009i	0.609722	−	0.792616i	$-0.291281\pi$
$251$	10.0937	+	3.27964i	0.637109	+	0.207009i	0.0273872	+	0.999625i	$0.491281\pi$
$252$	−1.04042	+	0.159848i	−0.0655406	+	0.0100695i
$253$	−17.6483	−	8.48938i	−1.10954	−	0.533723i
$254$		−	9.12883i		−	0.572793i
$255$	4.38372	−	2.67239i	0.274519	−	0.167352i
$256$	−44.5101	+	32.3385i	−2.78188	+	2.02116i
$257$	−9.37067	+	12.8976i	−0.584527	+	0.804532i	−0.994183	−	0.107708i	$-0.965649\pi$
$257$	−9.37067	+	12.8976i	−0.584527	+	0.804532i	0.409656	+	0.912240i	$0.365649\pi$
$258$	9.04441	−	21.6928i	0.563081	−	1.35054i
$259$	−0.309984	+	0.100720i	−0.0192615	+	0.00625843i
$260$	−5.84637	−	4.24764i	−0.362577	−	0.263427i
$261$	18.9821	+	19.1588i	1.17496	+	1.18590i
$262$	−8.86706	+	27.2900i	−0.547809	+	1.68598i
$263$	5.96276			0.367680			0.183840	−	0.982956i	$-0.441147\pi$
$263$	5.96276			0.367680			0.183840	+	0.982956i	$0.441147\pi$
$264$	−55.6008	+	5.52840i	−3.42199	+	0.340249i
$265$	4.27810			0.262802
$266$	−0.0139022	+	0.0427865i	−0.000852396	+	0.00262341i
$267$	−17.6708	−	1.43194i	−1.08144	−	0.0876331i
$268$	−46.7222	−	33.9457i	−2.85401	−	2.07356i
$269$	19.7510	−	6.41748i	1.20424	−	0.391281i	0.362920	−	0.931820i	$-0.381780\pi$
$269$	19.7510	−	6.41748i	1.20424	−	0.391281i	0.841319	+	0.540540i	$0.181780\pi$
$270$	−13.8521	−	3.42761i	−0.843010	−	0.208598i
$271$	−5.07017	+	6.97849i	−0.307991	+	0.423913i	−0.934753	−	0.355297i	$-0.884380\pi$
$271$	−5.07017	+	6.97849i	−0.307991	+	0.423913i	0.626762	+	0.779210i	$0.284380\pi$
$272$	−37.4764	+	27.2282i	−2.27234	+	1.65095i
$273$	0.0744360	+	0.122103i	0.00450507	+	0.00738999i
$274$		−	13.9505i		−	0.842780i
$275$	0.593649	+	3.26306i	0.0357984	+	0.196770i
$276$	43.0130	+	36.9093i	2.58908	+	2.22168i
$277$	20.7911	+	6.75543i	1.24922	+	0.405895i	0.857640	−	0.514251i	$-0.171930\pi$
$277$	20.7911	+	6.75543i	1.24922	+	0.405895i	0.391576	+	0.920146i	$0.371930\pi$
$278$	−17.1552	−	23.6120i	−1.02890	−	1.41616i
$279$	−1.78393	+	3.46141i	−0.106801	+	0.207229i
$280$	−0.190304	−	0.585695i	−0.0113728	−	0.0350020i
$281$	−9.11129	−	28.0417i	−0.543534	−	1.67283i	−0.724451	−	0.689327i	$-0.757906\pi$
$281$	−9.11129	−	28.0417i	−0.543534	−	1.67283i	0.180917	−	0.983498i	$-0.442094\pi$
$282$	−8.65934	−	36.4405i	−0.515656	−	2.17000i
$283$	12.8850	+	17.7347i	0.765934	+	1.05422i	0.996697	+	0.0812074i	$0.0258776\pi$
$283$	12.8850	+	17.7347i	0.765934	+	1.05422i	−0.230764	+	0.973010i	$0.574122\pi$
$284$	−45.0399	−	14.6343i	−2.67263	−	0.868389i
$285$	−0.291836	+	0.340097i	−0.0172869	+	0.0201456i
$286$	5.63283	+	10.4565i	0.333076	+	0.618304i
$287$		−	0.318471i		−	0.0187987i
$288$	69.4754	+	11.3341i	4.09387	+	0.667870i
$289$	6.64509	−	4.82794i	0.390888	−	0.283997i
$290$	−14.5116	+	19.9735i	−0.852150	+	1.17288i
$291$	1.42971	+	0.596091i	0.0838112	+	0.0349435i
$292$	71.6852	−	23.2919i	4.19506	−	1.36306i
$293$	25.0363	+	18.1899i	1.46264	+	1.06267i	0.982666	+	0.185383i	$0.0593525\pi$
$293$	25.0363	+	18.1899i	1.46264	+	1.06267i	0.479970	+	0.877285i	$0.340647\pi$
$294$	2.68777	−	33.1685i	0.156754	−	1.93443i
$295$	−0.972896	+	2.99427i	−0.0566442	+	0.174333i
$296$	50.0712			2.91033
$297$	13.2812	+	10.9822i	0.770655	+	0.637253i
$298$	18.9073			1.09527
$299$	2.37939	−	7.32302i	0.137604	−	0.423501i
$300$	0.775275	−	9.56730i	0.0447605	−	0.552369i
$301$	−0.253095	−	0.183884i	−0.0145882	−	0.0105989i
$302$	6.49662	−	2.11088i	0.373839	−	0.121468i
$303$	15.4914	+	6.45885i	0.889958	+	0.371051i
$304$	2.37671	−	3.27126i	0.136314	−	0.187620i
$305$	−3.46427	+	2.51694i	−0.198363	+	0.144119i
$306$	24.1021	+	3.93200i	1.37783	+	0.224777i
$307$			32.9033i			1.87789i	0.344066	+	0.938945i	$0.388195\pi$
$307$			32.9033i			1.87789i	−0.344066	+	0.938945i	$0.611805\pi$
$308$	−0.155701	+	1.15327i	−0.00887191	+	0.0657134i
$309$	−2.95509	+	3.44377i	−0.168109	+	0.195909i
$310$	−3.39020	−	1.10154i	−0.192551	−	0.0625635i
$311$	9.18476	+	12.6417i	0.520820	+	0.716847i	0.985697	−	0.168528i	$-0.0539014\pi$
$311$	9.18476	+	12.6417i	0.520820	+	0.716847i	−0.464877	+	0.885375i	$0.653901\pi$
$312$	−5.07892	−	21.3733i	−0.287537	−	1.21002i
$313$	6.78984	+	20.8970i	0.383785	+	1.18117i	0.937358	+	0.348367i	$0.113264\pi$
$313$	6.78984	+	20.8970i	0.383785	+	1.18117i	−0.553574	+	0.832800i	$0.686736\pi$
$314$	−7.78988	−	23.9748i	−0.439608	−	1.35298i
$315$	−0.0870164	+	0.168840i	−0.00490282	+	0.00951307i
$316$	−24.5420	−	33.7792i	−1.38059	−	1.90023i
$317$	−29.6596	−	9.63698i	−1.66585	−	0.541267i	−0.683762	−	0.729705i	$-0.739657\pi$
$317$	−29.6596	−	9.63698i	−1.66585	−	0.541267i	−0.982085	+	0.188438i	$0.939657\pi$
$318$	15.4430	+	13.2516i	0.866003	+	0.743114i
$319$	26.2500	−	14.1407i	1.46972	−	0.791726i
$320$			33.1835i			1.85501i
$321$	4.73082	+	7.76030i	0.264049	+	0.433138i
$322$	0.830625	−	0.603485i	0.0462889	−	0.0336309i
$323$	0.450793	−	0.620463i	0.0250828	−	0.0345235i
$324$	−28.9412	−	40.6206i	−1.60784	−	2.25670i
$325$	−1.24018	+	0.402959i	−0.0687928	+	0.0223522i
$326$	14.7050	+	10.6838i	0.814437	+	0.591723i
$327$	17.1861	+	1.39265i	0.950392	+	0.0770139i
$328$	−15.1185	+	46.5298i	−0.834777	+	2.56918i
$329$	−0.498563			−0.0274867
$330$	−7.96454	+	13.6178i	−0.438434	+	0.749637i
$331$	−7.79821			−0.428629			−0.214314	−	0.976765i	$-0.568752\pi$
$331$	−7.79821			−0.428629			−0.214314	+	0.976765i	$0.568752\pi$
$332$	−8.67963	+	26.7132i	−0.476357	+	1.46608i
$333$	−10.8696	−	10.9708i	−0.595648	−	0.601195i
$334$	29.5077	+	21.4386i	1.61459	+	1.17307i
$335$	−9.91109	+	3.22031i	−0.541501	+	0.175944i
$336$	0.659518	−	1.58184i	0.0359797	−	0.0862965i
$337$	−12.5507	+	17.2746i	−0.683682	+	0.941008i	−0.999971	−	0.00765519i	$-0.997563\pi$
$337$	−12.5507	+	17.2746i	−0.683682	+	0.941008i	0.316288	+	0.948663i	$0.397563\pi$
$338$	25.1048	−	18.2397i	1.36552	−	0.992110i
$339$	−12.7108	+	7.74873i	−0.690356	+	0.420853i
$340$			16.4267i			0.890864i
$341$	3.11298	+	2.97368i	0.168578	+	0.161034i
$342$	−2.10693	+	0.323702i	−0.113930	+	0.0175038i
$343$	−0.842782	−	0.273836i	−0.0455059	−	0.0147858i
$344$	28.2488	+	38.8811i	1.52307	+	2.09633i
$345$	9.95034	−	2.36449i	0.535708	−	0.127300i
$346$	−1.91190	−	5.88423i	−0.102784	−	0.316338i
$347$	−0.921655	−	2.83656i	−0.0494771	−	0.152275i	0.923265	−	0.384163i	$-0.125510\pi$
$347$	−0.921655	−	2.83656i	−0.0494771	−	0.152275i	−0.972743	+	0.231888i	$0.925510\pi$
$348$	−83.9541	+	19.9499i	−4.50041	+	1.06943i
$349$	−18.1548	−	24.9879i	−0.971803	−	1.33757i	−0.941131	−	0.338043i	$-0.890235\pi$
$349$	−18.1548	−	24.9879i	−0.971803	−	1.33757i	−0.0306727	−	0.999529i	$-0.509765\pi$
$350$	−0.165367	−	0.0537310i	−0.00883923	−	0.00287204i
$351$	−3.58042	+	5.75257i	−0.191109	+	0.307049i
$352$	33.7353	−	70.1313i	1.79810	−	3.73801i
$353$			5.82979i			0.310288i	0.987892	+	0.155144i	$0.0495842\pi$
$353$			5.82979i			0.310288i	−0.987892	+	0.155144i	$0.950416\pi$
$354$	−12.7868	+	7.79508i	−0.679613	+	0.414304i
$355$	−6.91351	+	5.02296i	−0.366931	+	0.266591i
$356$	33.3416	−	45.8908i	1.76710	−	2.43221i
$357$	0.125092	−	0.300029i	0.00662055	−	0.0158792i
$358$	25.1657	−	8.17682i	1.33005	−	0.432158i
$359$	11.2457	+	8.17045i	0.593523	+	0.431220i	0.843574	−	0.537013i	$-0.180447\pi$
$359$	11.2457	+	8.17045i	0.593523	+	0.431220i	−0.250051	+	0.968233i	$0.580447\pi$
$360$	20.7286	−	20.5373i	1.09249	−	1.08241i
$361$	5.85064	−	18.0064i	0.307928	−	0.947706i
$362$	6.97357			0.366523
$363$	15.7973	−	10.6511i	0.829142	−	0.559038i
$364$	−0.457545			−0.0239819
$365$	4.20296	−	12.9354i	0.219993	−	0.677069i
$366$	−20.3016	−	1.64512i	−1.06118	−	0.0859916i
$367$	−5.80111	−	4.21475i	−0.302815	−	0.220008i	0.425992	−	0.904727i	$-0.359925\pi$
$367$	−5.80111	−	4.21475i	−0.302815	−	0.220008i	−0.728808	+	0.684719i	$0.759925\pi$
$368$	−87.7630	+	28.5159i	−4.57496	+	1.48650i
$369$	13.4768	−	6.78828i	0.701574	−	0.353384i
$370$	8.30967	−	11.4373i	0.431999	−	0.594596i
$371$	0.219136	−	0.159212i	0.0113770	−	0.00826586i
$372$	−6.48532	−	10.6383i	−0.336248	−	0.551572i
$373$		−	26.1267i		−	1.35279i	−0.736539	−	0.676395i	$-0.763541\pi$
$373$		−	26.1267i		−	1.35279i	0.736539	−	0.676395i	$-0.236459\pi$
$374$	11.7033	−	24.3297i	0.605164	−	1.25806i
$375$	−1.31445	−	1.12793i	−0.0678780	−	0.0582459i
$376$	72.8419	+	23.6678i	3.75654	+	1.22057i
$377$	6.89059	+	9.48408i	0.354883	+	0.488455i
$378$	−0.837101	+	0.339940i	−0.0430558	+	0.0174846i
$379$	9.85217	+	30.3219i	0.506072	+	1.55753i	0.798961	+	0.601383i	$0.205383\pi$
$379$	9.85217	+	30.3219i	0.506072	+	1.55753i	−0.292889	+	0.956146i	$0.594617\pi$
$380$	−0.443088	−	1.36369i	−0.0227300	−	0.0699556i
$381$	−1.33110	−	5.60158i	−0.0681942	−	0.286977i
$382$	−30.5699	−	42.0758i	−1.56409	−	2.15279i
$383$	7.75281	+	2.51904i	0.396150	+	0.128717i	0.500316	−	0.865843i	$-0.333217\pi$
$383$	7.75281	+	2.51904i	0.396150	+	0.128717i	−0.104166	+	0.994560i	$0.533217\pi$
$384$	−49.8548	+	58.0993i	−2.54414	+	2.96487i
$385$	0.151845	+	0.145050i	0.00773873	+	0.00739244i
$386$			0.102096i			0.00519656i
$387$	2.38669	−	14.6298i	0.121322	−	0.743675i
$388$	−4.00958	+	2.91313i	−0.203555	+	0.147892i
$389$	0.826360	−	1.13739i	0.0418981	−	0.0576678i	−0.787554	−	0.616246i	$-0.788653\pi$
$389$	0.826360	−	1.13739i	0.0418981	−	0.0576678i	0.829452	+	0.558578i	$0.188653\pi$
$390$	−5.72498	−	2.38692i	−0.289895	−	0.120866i
$391$	−16.6461	+	5.40864i	−0.841829	+	0.273527i
$392$	55.0513	+	39.9971i	2.78051	+	2.02016i
$393$	−1.46173	+	18.0385i	−0.0737343	+	0.909920i
$394$	−4.15375	+	12.7839i	−0.209263	+	0.644045i
$395$	−7.53427			−0.379090
$396$	−52.1217	+	17.9933i	−2.61922	+	0.904196i
$397$	−1.06068			−0.0532338			−0.0266169	−	0.999646i	$-0.508473\pi$
$397$	−1.06068			−0.0532338			−0.0266169	+	0.999646i	$0.508473\pi$
$398$	−21.0325	+	64.7313i	−1.05426	+	3.24469i
$399$	−0.00229176	+	0.0282815i	−0.000114731	+	0.00141585i
$400$	12.6432	+	9.18583i	0.632161	+	0.459292i
$401$	7.97991	−	2.59283i	0.398498	−	0.129480i	−0.102910	−	0.994691i	$-0.532816\pi$
$401$	7.97991	−	2.59283i	0.398498	−	0.129480i	0.501408	+	0.865211i	$0.332816\pi$
$402$	−45.7520	−	19.0754i	−2.28190	−	0.951396i
$403$	−0.994900	+	1.36936i	−0.0495595	+	0.0682128i
$404$	−43.4451	+	31.5647i	−2.16148	+	1.57040i
$405$	−8.99961	−	0.0834221i	−0.447194	−	0.00414528i
$406$			1.56315i			0.0775780i
$407$	−15.0313	+	8.09727i	−0.745075	+	0.401367i
$408$	−32.5193	+	37.8971i	−1.60995	+	1.87618i
$409$	−18.3678	−	5.96807i	−0.908231	−	0.295102i	−0.182601	−	0.983187i	$-0.558452\pi$
$409$	−18.3678	−	5.96807i	−0.908231	−	0.295102i	−0.725630	+	0.688085i	$0.758452\pi$
$410$	8.11934	+	11.1753i	0.400986	+	0.551909i
$411$	−2.03416	−	8.56022i	−0.100338	−	0.422244i
$412$	−4.48665	−	13.8085i	−0.221041	−	0.680296i
$413$	0.0615987	+	0.189581i	0.00303108	+	0.00932869i
$414$	43.2427	+	22.2863i	2.12526	+	1.09531i
$415$	2.97912	+	4.10040i	0.146239	+	0.201281i
$416$	29.1003	+	9.45528i	1.42676	+	0.463583i
$417$	−13.9696	−	11.9872i	−0.684093	−	0.587018i
$418$	−0.315306	+	2.33544i	−0.0154221	+	0.114230i
$419$			29.5609i			1.44414i	0.691818	+	0.722072i	$0.256810\pi$
$419$			29.5609i			1.44414i	−0.691818	+	0.722072i	$0.743190\pi$
$420$	−0.316340	−	0.518916i	−0.0154358	−	0.0253205i
$421$	23.4498	−	17.0373i	1.14287	−	0.830346i	0.155356	−	0.987859i	$-0.450347\pi$
$421$	23.4498	−	17.0373i	1.14287	−	0.830346i	0.987517	+	0.157513i	$0.0503475\pi$
$422$	14.8155	−	20.3917i	0.721205	−	0.992653i
$423$	−10.6270	−	21.0978i	−0.516701	−	1.02581i
$424$	−39.5747	+	12.8586i	−1.92192	+	0.624469i
$425$	2.39805	+	1.74229i	0.116323	+	0.0845133i
$426$	−40.5151	−	3.28310i	−1.96297	−	0.159067i
$427$	−0.0837801	+	0.257849i	−0.00405441	+	0.0124782i
$428$	−29.0795			−1.40561
$429$	4.98107	+	5.59490i	0.240488	+	0.270124i
$430$	13.5693			0.654371
$431$	−7.30102	+	22.4702i	−0.351678	+	1.08235i	0.606233	+	0.795287i	$0.292680\pi$
$431$	−7.30102	+	22.4702i	−0.351678	+	1.08235i	−0.957911	+	0.287066i	$0.907320\pi$
$432$	80.9968	−	5.80832i	3.89696	−	0.279453i
$433$	0.359462	+	0.261164i	0.0172746	+	0.0125508i	0.596389	−	0.802696i	$-0.296602\pi$
$433$	0.359462	+	0.261164i	0.0172746	+	0.0125508i	−0.579114	+	0.815246i	$0.696602\pi$
$434$	−0.214650	+	0.0697440i	−0.0103035	+	0.00334782i
$435$	−5.99213	+	14.3720i	−0.287301	+	0.689084i
$436$	−32.4269	+	44.6319i	−1.55297	+	2.13748i
$437$	1.23601	−	0.898011i	0.0591262	−	0.0429577i
$438$	55.2398	−	33.6751i	2.63946	−	1.60906i
$439$			12.2512i			0.584718i	0.956309	+	0.292359i	$0.0944402\pi$
$439$			12.2512i			0.584718i	−0.956309	+	0.292359i	$0.905560\pi$
$440$	−15.2993	−	28.4007i	−0.729365	−	1.35395i
$441$	−3.18713	−	20.7446i	−0.151768	−	0.987837i
$442$	10.0954	+	3.28019i	0.480189	+	0.156023i
$443$	−12.9228	−	17.7867i	−0.613981	−	0.845072i	0.382917	−	0.923783i	$-0.374920\pi$
$443$	−12.9228	−	17.7867i	−0.613981	−	0.845072i	−0.996897	+	0.0787110i	$0.974920\pi$
$444$	48.0740	−	11.4238i	2.28149	−	0.542149i
$445$	−3.16301	−	9.73474i	−0.149941	−	0.461471i
$446$	10.8407	+	33.3641i	0.513320	+	1.57984i
$447$	11.6018	−	2.75693i	0.548746	−	0.130398i
$448$	1.23494	+	1.69975i	0.0583455	+	0.0803056i
$449$	23.6737	+	7.69204i	1.11723	+	0.363010i	0.808710	−	0.588208i	$-0.200166\pi$
$449$	23.6737	+	7.69204i	1.11723	+	0.363010i	0.308520	+	0.951218i	$0.400166\pi$
$450$	−1.25109	−	8.14315i	−0.0589769	−	0.383872i
$451$	−2.98603	−	16.4131i	−0.140607	−	0.772862i
$452$		−	47.6301i		−	2.24033i
$453$	3.67863	−	2.24256i	0.172837	−	0.105364i
$454$	62.4490	−	45.3719i	2.93088	−	2.12941i
$455$	−0.0485291	+	0.0667946i	−0.00227508	+	0.00313138i
$456$	1.67741	−	4.02324i	0.0785521	−	0.188405i
$457$	−26.2033	+	8.51396i	−1.22574	+	0.398266i	−0.849168	−	0.528122i	$-0.822896\pi$
$457$	−26.2033	+	8.51396i	−1.22574	+	0.398266i	−0.376569	+	0.926389i	$0.622896\pi$
$458$	−28.9012	−	20.9979i	−1.35046	−	0.981169i
$459$	15.3627	−	1.10167i	0.717072	−	0.0514215i
$460$	−10.1120	+	31.1216i	−0.471475	+	1.45105i
$461$	−32.8483			−1.52990			−0.764948	−	0.644092i	$-0.777235\pi$
$461$	−32.8483			−1.52990			−0.764948	+	0.644092i	$0.777235\pi$
$462$	0.0988283	+	0.993947i	0.00459791	+	0.0462426i
$463$	−25.5399			−1.18694			−0.593470	−	0.804856i	$-0.702242\pi$
$463$	−25.5399			−1.18694			−0.593470	+	0.804856i	$0.702242\pi$
$464$	43.4152	−	133.618i	2.01550	−	6.20306i
$465$	−2.24089	−	0.181588i	−0.103919	−	0.00842095i
$466$	10.1556	+	7.37845i	0.470448	+	0.341800i
$467$	−38.2538	+	12.4294i	−1.77017	+	0.575165i	−0.998171	−	0.0604537i	$-0.980745\pi$
$467$	−38.2538	+	12.4294i	−1.77017	+	0.575165i	−0.772003	+	0.635618i	$0.780745\pi$
$468$	−9.75268	−	19.3620i	−0.450818	−	0.895010i
$469$	−0.387828	+	0.533799i	−0.0179082	+	0.0246486i
$470$	17.4948	−	12.7107i	0.806976	−	0.586303i
$471$	−8.27580	−	13.5754i	−0.381329	−	0.625521i
$472$		−	30.6228i		−	1.40953i
$473$	−14.7679	−	7.10382i	−0.679030	−	0.326634i
$474$	−27.1971	−	23.3377i	−1.24920	−	1.07194i
$475$	−0.246073	−	0.0799540i	−0.0112906	−	0.00366854i
$476$	0.611329	+	0.841422i	0.0280202	+	0.0385665i
$477$	11.4083	+	5.87959i	0.522351	+	0.269208i
$478$	7.94412	+	24.4495i	0.363356	+	1.11829i
$479$	4.44891	+	13.6923i	0.203276	+	0.625619i	0.999780	+	0.0209855i	$0.00668038\pi$
$479$	4.44891	+	13.6923i	0.203276	+	0.625619i	−0.796504	+	0.604633i	$0.793320\pi$
$480$	9.39606	+	39.5408i	0.428869	+	1.80478i
$481$	−3.94571	−	5.43081i	−0.179909	−	0.247623i
$482$	22.3583	+	7.26465i	1.01839	+	0.330896i
$483$	0.421688	−	0.491422i	0.0191875	−	0.0223605i
$484$	2.78878	+	60.8959i	0.126763	+	2.76799i
$485$			0.894315i			0.0406088i
$486$	−32.2283	−	28.1779i	−1.46191	−	1.27817i
$487$	9.30397	−	6.75973i	0.421603	−	0.306313i	−0.356679	−	0.934227i	$-0.616091\pi$
$487$	9.30397	−	6.75973i	0.421603	−	0.306313i	0.778283	+	0.627914i	$0.216091\pi$
$488$	24.4812	−	33.6955i	1.10821	−	1.52532i
$489$	10.5811	+	4.41157i	0.478492	+	0.199498i
$490$	18.2723	−	5.93703i	0.825458	−	0.268207i
$491$	1.05277	+	0.764883i	0.0475109	+	0.0345187i	0.611287	−	0.791409i	$-0.290652\pi$
$491$	1.05277	+	0.764883i	0.0475109	+	0.0345187i	−0.563776	+	0.825927i	$0.690652\pi$
$492$	−3.89960	+	48.1232i	−0.175808	+	2.16956i
$493$	8.23460	−	25.3435i	0.370868	−	1.14141i
$494$	−0.926560			−0.0416879
$495$	−2.90151	+	9.51742i	−0.130413	+	0.427776i
$496$	20.2853			0.910838
$497$	−0.167197	+	0.514579i	−0.00749981	+	0.0230820i
$498$	−1.94720	+	24.0295i	−0.0872563	+	1.07679i
$499$	−29.6423	−	21.5364i	−1.32697	−	0.964101i	−0.999817	−	0.0191303i	$-0.993910\pi$
$499$	−29.6423	−	21.5364i	−1.32697	−	0.964101i	−0.327154	−	0.944971i	$-0.606090\pi$
$500$	5.27056	−	1.71251i	0.235706	−	0.0765857i
$501$	21.2323	+	8.85242i	0.948591	+	0.395497i
$502$	−17.1317	+	23.5797i	−0.764625	+	1.05242i
$503$	−10.5773	+	7.68487i	−0.471619	+	0.342651i	−0.798072	−	0.602562i	$-0.794147\pi$
$503$	−10.5773	+	7.68487i	−0.471619	+	0.342651i	0.326453	+	0.945213i	$0.394147\pi$
$504$	0.297468	−	1.82340i	0.0132503	−	0.0812209i
$505$			9.69021i			0.431209i
$506$	37.1497	−	38.8899i	1.65151	−	1.72887i
$507$	12.7451	−	14.8527i	0.566029	−	0.659634i
$508$	17.5200	+	5.69259i	0.777324	+	0.252568i
$509$	20.8708	+	28.7261i	0.925080	+	1.27326i	0.961748	+	0.273936i	$0.0883257\pi$
$509$	20.8708	+	28.7261i	0.925080	+	1.27326i	−0.0366676	+	0.999328i	$0.511674\pi$
$510$	3.25965	+	13.7174i	0.144340	+	0.607415i
$511$	−0.266110	−	0.819001i	−0.0117720	−	0.0362305i
$512$	−19.3723	−	59.6219i	−0.856145	−	2.63494i
$513$	−1.24564	+	0.505845i	−0.0549964	+	0.0223336i
$514$	−25.7340	−	35.4199i	−1.13508	−	1.56230i
$515$	−2.49170	−	0.809603i	−0.109798	−	0.0356754i
$516$	35.9928	+	30.8853i	1.58450	+	1.35965i
$517$	−25.6945	+	4.67460i	−1.13004	+	0.205589i
$518$		−	0.895097i		−	0.0393283i
$519$	−2.03116	−	3.33187i	−0.0891582	−	0.146253i
$520$	10.2612	−	7.45517i	0.449982	−	0.326931i
$521$	1.60853	−	2.21395i	0.0704710	−	0.0969950i	−0.772327	−	0.635226i	$-0.780907\pi$
$521$	1.60853	−	2.21395i	0.0704710	−	0.0969950i	0.842798	+	0.538231i	$0.180907\pi$
$522$	−66.1482	+	33.3189i	−2.89523	+	1.45833i
$523$	−10.7371	+	3.48869i	−0.469500	+	0.152550i	−0.534206	−	0.845355i	$-0.679389\pi$
$523$	−10.7371	+	3.48869i	−0.469500	+	0.152550i	0.0647057	+	0.997904i	$0.479389\pi$
$524$	−46.8455	−	34.0353i	−2.04646	−	1.48684i
$525$	−0.109306	−	0.00885749i	−0.00477051	−	0.000386573i
$526$	−5.06019	+	15.5737i	−0.220635	+	0.679044i
$527$	3.84754			0.167601
$528$	19.1581	−	87.7073i	0.833751	−	3.81697i
$529$	−11.8667			−0.515942
$530$	−3.63053	+	11.1736i	−0.157700	+	0.485352i
$531$	−6.70956	+	6.64765i	−0.291170	+	0.288484i
$532$	−0.0734464	−	0.0533620i	−0.00318431	−	0.00231353i
$533$	6.23806	−	2.02687i	0.270200	−	0.0877935i
$534$	18.7360	−	44.9379i	0.810787	−	1.94465i
$535$	−3.08429	+	4.24517i	−0.133346	+	0.183535i
$536$	82.0037	−	59.5791i	3.54202	−	2.57343i
$537$	14.2497	−	8.68688i	0.614921	−	0.374867i
$538$			57.0321i			2.45883i
$539$	−22.9945	−	3.10446i	−0.990441	−	0.133719i
$540$	15.2162	−	24.4474i	0.654801	−	1.05205i
$541$	22.9369	+	7.45267i	0.986136	+	0.320415i	0.757312	−	0.653053i	$-0.226512\pi$
$541$	22.9369	+	7.45267i	0.986136	+	0.320415i	0.228824	+	0.973468i	$0.426512\pi$
$542$	−13.9239	−	19.1646i	−0.598081	−	0.823188i
$543$	4.27908	−	1.01683i	0.183633	−	0.0436365i
$544$	−21.4930	−	66.1486i	−0.921503	−	2.83610i
$545$	3.07624	+	9.46768i	0.131771	+	0.405551i
$546$	−0.382079	+	0.0907932i	−0.0163515	+	0.00388559i
$547$	16.5194	+	22.7370i	0.706318	+	0.972163i	0.999868	+	0.0162198i	$0.00516315\pi$
$547$	16.5194	+	22.7370i	0.706318	+	0.972163i	−0.293550	+	0.955944i	$0.594837\pi$
$548$	26.7737	+	8.69931i	1.14372	+	0.371616i
$549$	−12.6972	+	1.95076i	−0.541904	+	0.0832566i
$550$	−9.02633	−	1.21864i	−0.384884	−	0.0519628i
$551$			2.32604i			0.0990926i
$552$	−84.9390	+	51.7803i	−3.61524	+	2.20392i
$553$	−0.385926	+	0.280391i	−0.0164112	+	0.0119235i
$554$	−35.2880	+	48.5697i	−1.49924	+	2.06353i
$555$	3.43123	−	8.22973i	0.145648	−	0.349333i
$556$	56.0138	−	18.2000i	2.37552	−	0.771852i
$557$	−9.38569	−	6.81910i	−0.397684	−	0.288935i	0.370913	−	0.928668i	$-0.379045\pi$
$557$	−9.38569	−	6.81910i	−0.397684	−	0.288935i	−0.768597	+	0.639733i	$0.779045\pi$
$558$	−7.52668	−	7.59677i	−0.318630	−	0.321597i
$559$	1.99105	−	6.12782i	0.0842124	−	0.259179i
$560$	0.989475			0.0418130
$561$	3.63374	−	16.6355i	0.153417	−	0.702353i
$562$	80.9720			3.41560
$563$	−1.91518	+	5.89430i	−0.0807150	+	0.248415i	−0.983268	−	0.182163i	$-0.941690\pi$
$563$	−1.91518	+	5.89430i	−0.0807150	+	0.248415i	0.902553	+	0.430578i	$0.141690\pi$
$564$	75.3363	+	6.10479i	3.17223	+	0.257058i
$565$	−6.95327	−	5.05185i	−0.292526	−	0.212533i
$566$	−57.2545	+	18.6031i	−2.40658	+	0.781947i
$567$	−0.464089	+	0.330652i	−0.0194899	+	0.0138861i
$568$	48.8562	−	67.2448i	2.04996	−	2.82153i
$569$	−7.67029	+	5.57279i	−0.321555	+	0.233623i	−0.736839	−	0.676069i	$-0.763682\pi$
$569$	−7.67029	+	5.57279i	−0.321555	+	0.233623i	0.415284	+	0.909692i	$0.363682\pi$
$570$	−0.640611	−	1.05084i	−0.0268322	−	0.0440148i
$571$			32.5792i			1.36340i	0.731634	+	0.681698i	$0.238758\pi$
$571$			32.5792i			1.36340i	−0.731634	+	0.681698i	$0.761242\pi$
$572$	−23.5806	+	4.29001i	−0.985953	+	0.179374i
$573$	−24.8933	−	21.3608i	−1.03993	−	0.892362i
$574$	0.831790	+	0.270265i	0.0347182	+	0.0112806i
$575$	3.47075	+	4.77708i	0.144740	+	0.199218i
$576$	−45.6056	+	88.4897i	−1.90023	+	3.68707i
$577$	−12.3011	−	37.8590i	−0.512103	−	1.57609i	−0.788492	−	0.615045i	$-0.789138\pi$
$577$	−12.3011	−	37.8590i	−0.512103	−	1.57609i	0.276389	−	0.961046i	$-0.410862\pi$
$578$	6.97049	+	21.4530i	0.289934	+	0.892325i
$579$	0.0148869	+	0.0626476i	0.000618679	+	0.00260355i
$580$	−29.2838	−	40.3057i	−1.21595	−	1.67360i
$581$	0.305197	+	0.0991645i	0.0126617	+	0.00411404i
$582$	−2.77018	+	3.22829i	−0.114828	+	0.133817i
$583$	9.80085	−	10.2600i	0.405910	−	0.424924i
$584$			132.292i			5.47428i
$585$	−3.86097	−	0.629874i	−0.159631	−	0.0260421i
$586$	−68.7555	+	49.9538i	−2.84026	+	2.06357i
$587$	21.4347	−	29.5023i	0.884704	−	1.21769i	−0.0903914	−	0.995906i	$-0.528812\pi$
$587$	21.4347	−	29.5023i	0.884704	−	1.21769i	0.975096	−	0.221785i	$-0.0711882\pi$
$588$	61.9808	+	25.8417i	2.55605	+	1.06569i
$589$	−0.319408	+	0.103782i	−0.0131610	+	0.00427626i
$590$	−6.99486	−	5.08206i	−0.287974	−	0.209225i
$591$	−0.684741	+	8.45007i	−0.0281665	+	0.347589i
$592$	−24.8605	+	76.5128i	−1.02176	+	3.14466i
$593$	24.3804			1.00118			0.500591	−	0.865684i	$-0.333116\pi$
$593$	24.3804			1.00118			0.500591	+	0.865684i	$0.333116\pi$
$594$	−39.9545	+	25.3683i	−1.63935	+	1.04088i
$595$	0.187675			0.00769392
$596$	−11.7903	+	36.2868i	−0.482950	+	1.48637i
$597$	−3.46718	+	42.7869i	−0.141902	+	1.75115i
$598$	17.1072	+	12.4291i	0.699565	+	0.508264i
$599$	32.9061	−	10.6919i	1.34451	−	0.436857i	0.453667	−	0.891171i	$-0.350116\pi$
$599$	32.9061	−	10.6919i	1.34451	−	0.436857i	0.890842	+	0.454314i	$0.150116\pi$
$600$	15.5496	+	6.48309i	0.634808	+	0.264671i
$601$	15.6450	−	21.5335i	0.638172	−	0.878368i	−0.360345	−	0.932819i	$-0.617341\pi$
$601$	15.6450	−	21.5335i	0.638172	−	0.878368i	0.998516	+	0.0544511i	$0.0173409\pi$
$602$	0.695058	−	0.504989i	0.0283285	−	0.0205818i
$603$	−30.8555	−	5.03373i	−1.25653	−	0.204989i
$604$			13.7846i			0.560887i
$605$	9.18566	+	6.05175i	0.373450	+	0.246039i
$606$	−30.0159	+	34.9796i	−1.21931	+	1.42095i
$607$	31.1598	+	10.1244i	1.26474	+	0.410938i	0.863180	−	0.504897i	$-0.168469\pi$
$607$	31.1598	+	10.1244i	1.26474	+	0.410938i	0.401556	+	0.915834i	$0.368469\pi$
$608$	3.56853	+	4.91166i	0.144723	+	0.199194i
$609$	0.227927	+	0.959173i	0.00923609	+	0.0388676i
$610$	−3.63390	−	11.1840i	−0.147132	−	0.452827i
$611$	−3.17304	−	9.76562i	−0.128368	−	0.395075i
$612$	−22.5760	+	43.8048i	−0.912580	+	1.77070i
$613$	−25.9638	−	35.7361i	−1.04867	−	1.44337i	−0.889959	−	0.456040i	$-0.849267\pi$
$613$	−25.9638	−	35.7361i	−1.04867	−	1.44337i	−0.158707	−	0.987326i	$-0.550733\pi$
$614$	−85.9376	−	27.9228i	−3.46816	−	1.12687i
$615$	6.61164	+	5.67343i	0.266607	+	0.228775i
$616$	−1.84062	−	0.885393i	−0.0741607	−	0.0356735i
$617$		−	33.3457i		−	1.34245i	−0.741255	−	0.671223i	$-0.765769\pi$
$617$		−	33.3457i		−	1.34245i	0.741255	−	0.671223i	$-0.234231\pi$
$618$	−6.48674	−	10.6407i	−0.260935	−	0.428030i
$619$	−10.2316	+	7.43369i	−0.411242	+	0.298785i	−0.774105	−	0.633058i	$-0.781800\pi$
$619$	−10.2316	+	7.43369i	−0.411242	+	0.298785i	0.362862	+	0.931843i	$0.381800\pi$
$620$	4.22816	−	5.81956i	0.169807	−	0.233719i
$621$	29.7840	+	7.36986i	1.19519	+	0.295742i
$622$	−40.8125	+	13.2608i	−1.63643	+	0.531708i
$623$	−0.524301	−	0.380927i	−0.0210057	−	0.0152615i
$624$	35.1818	+	2.85091i	1.40840	+	0.114128i
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$	−60.3413			−2.41172
$627$	0.147061	+	1.47903i	0.00587304	+	0.0590670i
$628$	50.8699			2.02993
$629$	−4.71532	+	14.5123i	−0.188012	+	0.578642i
$630$	−0.367136	−	0.370555i	−0.0146270	−	0.0147632i
$631$	−16.0975	−	11.6955i	−0.640831	−	0.465591i	0.219305	−	0.975656i	$-0.429621\pi$
$631$	−16.0975	−	11.6955i	−0.640831	−	0.465591i	−0.860135	+	0.510066i	$0.829621\pi$
$632$	69.6960	−	22.6456i	2.77236	−	0.900793i
$633$	6.11760	−	14.6729i	0.243153	−	0.583196i
$634$	50.3401	−	69.2873i	1.99926	−	2.75175i
$635$	2.68928	−	1.95387i	0.106721	−	0.0775371i
$636$	−35.0625	+	21.3747i	−1.39032	+	0.847563i
$637$		−	9.12279i		−	0.361458i
$638$	14.6564	+	80.5604i	0.580250	+	3.18942i
$639$	−25.3394	+	3.89307i	−1.00241	+	0.154007i
$640$	−42.0371	−	13.6587i	−1.66166	−	0.539907i
$641$	−0.529085	−	0.728223i	−0.0208976	−	0.0287631i	0.798440	−	0.602074i	$-0.205659\pi$
$641$	−0.529085	−	0.728223i	−0.0208976	−	0.0287631i	−0.819338	+	0.573311i	$0.805659\pi$
$642$	−24.2833	+	5.77041i	−0.958384	+	0.227740i
$643$	10.3862	+	31.9655i	0.409593	+	1.26060i	0.916999	+	0.398890i	$0.130604\pi$
$643$	10.3862	+	31.9655i	0.409593	+	1.26060i	−0.507406	+	0.861707i	$0.669396\pi$
$644$	0.640240	+	1.97046i	0.0252290	+	0.0776469i
$645$	8.32633	−	1.97858i	0.327849	−	0.0779065i
$646$	1.23798	+	1.70394i	0.0487078	+	0.0670405i
$647$	19.0378	+	6.18576i	0.748454	+	0.243187i	0.658316	−	0.752742i	$-0.271269\pi$
$647$	19.0378	+	6.18576i	0.748454	+	0.243187i	0.0901379	+	0.995929i	$0.471269\pi$
$648$	83.5019	−	26.2783i	3.28027	−	1.03231i
$649$	4.95217	+	9.19292i	0.194389	+	0.360854i
$650$		−	3.58110i		−	0.140462i
$651$	−0.121543	+	0.0740946i	−0.00476363	+	0.00290399i
$652$	−29.6742	+	21.5596i	−1.16213	+	0.844338i
$653$	9.04342	−	12.4472i	0.353896	−	0.487097i	−0.594539	−	0.804067i	$-0.702665\pi$
$653$	9.04342	−	12.4472i	0.353896	−	0.487097i	0.948436	+	0.316970i	$0.102665\pi$
$654$	−18.2220	+	43.7051i	−0.712537	+	1.70900i
$655$	−9.93725	+	3.22881i	−0.388281	+	0.126160i
$656$	−63.5949	−	46.2044i	−2.48296	−	1.80398i
$657$	28.9856	−	28.7182i	1.13084	−	1.12040i
$658$	0.423097	−	1.30216i	0.0164940	−	0.0507634i
$659$	−6.13649			−0.239044			−0.119522	−	0.992832i	$-0.538136\pi$
$659$	−6.13649			−0.239044			−0.119522	+	0.992832i	$0.538136\pi$
$660$	−21.1687	−	23.7774i	−0.823991	−	0.925533i
$661$	−2.13426			−0.0830130			−0.0415065	−	0.999138i	$-0.513216\pi$
$661$	−2.13426			−0.0830130			−0.0415065	+	0.999138i	$0.513216\pi$
$662$	6.61782	−	20.3675i	0.257209	−	0.791607i
$663$	6.67297	+	0.540736i	0.259156	+	0.0210004i
$664$	−39.8829	−	28.9766i	−1.54776	−	1.12451i
$665$	−0.0155801	+	0.00506227i	−0.000604169	+	0.000196306i
$666$	37.8780	−	19.0792i	1.46774	−	0.739304i
$667$	31.2020	−	42.9459i	1.20815	−	1.66287i
$668$	−59.5454	+	43.2623i	−2.30388	+	1.67387i
$669$	11.5169	+	18.8920i	0.445269	+	0.730406i
$670$		−	28.6189i		−	1.10564i
$671$	−1.90016	+	14.0743i	−0.0733549	+	0.543333i
$672$	1.95282	+	1.67571i	0.0753318	+	0.0646419i
$673$	33.6843	+	10.9447i	1.29843	+	0.421887i	0.875036	−	0.484058i	$-0.160837\pi$
$673$	33.6843	+	10.9447i	1.29843	+	0.421887i	0.423397	+	0.905944i	$0.360837\pi$
$674$	−34.4672	−	47.4401i	−1.32763	−	1.82732i
$675$	−1.95506	−	4.81433i	−0.0752503	−	0.185304i
$676$	19.3506	+	59.5551i	0.744254	+	2.29058i
$677$	12.2193	+	37.6071i	0.469625	+	1.44536i	0.853072	+	0.521794i	$0.174737\pi$
$677$	12.2193	+	37.6071i	0.469625	+	1.44536i	−0.383447	+	0.923563i	$0.625263\pi$
$678$	−9.45151	−	39.7742i	−0.362983	−	1.52752i
$679$	0.0332824	+	0.0458093i	0.00127726	+	0.00175800i
$680$	−27.4200	−	8.90930i	−1.05151	−	0.341656i
$681$	31.7038	−	36.9467i	1.21489	−	1.41580i
$682$	−10.4085	+	5.60700i	−0.398563	+	0.214703i
$683$		−	35.9157i		−	1.37427i	−0.726528	−	0.687137i	$-0.758867\pi$
$683$		−	35.9157i		−	1.37427i	0.726528	−	0.687137i	$-0.241133\pi$
$684$	0.692601	−	4.24547i	0.0264823	−	0.162330i
$685$	4.10970	−	2.98587i	0.157023	−	0.114084i
$686$	1.43042	−	1.96881i	0.0546138	−	0.0751695i
$687$	−20.7959	−	8.67047i	−0.793414	−	0.330799i
$688$	−73.4391	+	23.8618i	−2.79984	+	0.909723i
$689$	4.51323	+	3.27905i	0.171940	+	0.124922i
$690$	−2.26855	+	27.9951i	−0.0863622	+	1.06575i
$691$	−9.85758	+	30.3385i	−0.375000	+	1.15413i	0.568479	+	0.822698i	$0.307532\pi$
$691$	−9.85758	+	30.3385i	−0.375000	+	1.15413i	−0.943479	+	0.331433i	$0.892468\pi$
$692$	12.4852			0.474617
$693$	0.205572	+	0.595489i	0.00780905	+	0.0226208i
$694$	8.19075			0.310916
$695$	3.28414	−	10.1075i	0.124574	−	0.383400i
$696$	12.2328	−	150.959i	0.463682	−	5.72208i
$697$	−12.0621	−	8.76363i	−0.456885	−	0.331946i
$698$	80.6707	−	26.2115i	3.05343	−	0.992120i
$699$	7.30747	+	3.04671i	0.276394	+	0.115237i
$700$	0.206241	−	0.283866i	0.00779516	−	0.0107291i
$701$	17.3900	−	12.6345i	0.656810	−	0.477200i	−0.208774	−	0.977964i	$-0.566947\pi$
$701$	17.3900	−	12.6345i	0.656810	−	0.477200i	0.865584	+	0.500764i	$0.166947\pi$
$702$	−11.9862	−	14.2332i	−0.452391	−	0.537199i
$703$		−	1.33194i		−	0.0502352i
$704$	79.5824	+	76.0213i	2.99938	+	2.86516i
$705$	8.88169	−	10.3505i	0.334504	−	0.389821i
$706$	−15.2264	−	4.94735i	−0.573052	−	0.186196i
$707$	0.360626	+	0.496359i	0.0135627	+	0.0186675i
$708$	−6.98662	−	29.4013i	−0.262573	−	1.10497i
$709$	3.74651	+	11.5306i	0.140703	+	0.433040i	0.996433	−	0.0843822i	$-0.0268917\pi$
$709$	3.74651	+	11.5306i	0.140703	+	0.433040i	−0.855730	+	0.517422i	$0.826892\pi$
$710$	−7.25204	−	22.3195i	−0.272164	−	0.837636i
$711$	−20.0915	−	10.3547i	−0.753489	−	0.388331i
$712$	58.5190	+	80.5445i	2.19309	+	3.01853i
$713$	7.28943	+	2.36848i	0.272991	+	0.0887002i
$714$	0.677466	+	0.581331i	0.0253535	+	0.0217558i
$715$	−1.87478	+	3.89742i	−0.0701127	+	0.145755i
$716$			53.3968i			1.99553i
$717$	8.43967	+	13.8442i	0.315185	+	0.517021i
$718$	−30.8832	+	22.4379i	−1.15255	+	0.837377i
$719$	18.9700	−	26.1100i	0.707463	−	0.973739i	−0.292385	−	0.956301i	$-0.594449\pi$
$719$	18.9700	−	26.1100i	0.707463	−	0.973739i	0.999848	−	0.0174382i	$-0.00555103\pi$
$720$	21.0909	+	41.8718i	0.786011	+	1.56047i
$721$	−0.157762	+	0.0512598i	−0.00587535	+	0.00190902i
$722$	42.0645	+	30.5616i	1.56548	+	1.13739i
$723$	14.7786	+	1.19757i	0.549623	+	0.0445381i
$724$	−4.34861	+	13.3836i	−0.161615	+	0.497399i
$725$	−8.98999			−0.333880
$726$	14.4127	+	50.2985i	0.534906	+	1.86675i
$727$	9.40120			0.348671			0.174336	−	0.984686i	$-0.444222\pi$
$727$	9.40120			0.348671			0.174336	+	0.984686i	$0.444222\pi$
$728$	0.248157	−	0.763748i	0.00919731	−	0.0283064i
$729$	−23.8844	−	12.5910i	−0.884608	−	0.466335i
$730$	30.2182	+	21.9548i	1.11842	+	0.812583i
$731$	−13.9293	+	4.52589i	−0.515192	+	0.167396i
$732$	15.8171	−	37.9369i	0.584616	−	1.40219i
$733$	−6.42953	+	8.84949i	−0.237480	+	0.326863i	−0.911077	−	0.412235i	$-0.864748\pi$
$733$	−6.42953	+	8.84949i	−0.237480	+	0.326863i	0.673597	+	0.739099i	$0.264748\pi$
$734$	15.9312	−	11.5747i	0.588031	−	0.427229i
$735$	10.3464	−	6.30737i	0.381634	−	0.232651i
$736$		−	138.554i		−	5.10716i
$737$	−14.9826	+	31.1468i	−0.551890	+	1.14731i
$738$	6.29293	+	40.9597i	0.231646	+	1.50775i
$739$	−2.50713	−	0.814615i	−0.0922261	−	0.0299661i	0.262540	−	0.964921i	$-0.415440\pi$
$739$	−2.50713	−	0.814615i	−0.0922261	−	0.0299661i	−0.354767	+	0.934955i	$0.615440\pi$
$740$	16.7686	+	23.0800i	0.616426	+	0.848438i
$741$	−0.568550	+	0.135104i	−0.0208862	+	0.00496318i
$742$	0.229867	+	0.707456i	0.00843866	+	0.0259715i
$743$	−1.14494	−	3.52378i	−0.0420039	−	0.129275i	0.927856	−	0.372940i	$-0.121650\pi$
$743$	−1.14494	−	3.52378i	−0.0420039	−	0.129275i	−0.969859	+	0.243665i	$0.921650\pi$
$744$	21.2753	−	5.05562i	0.779989	−	0.185348i
$745$	4.04680	+	5.56994i	0.148263	+	0.204067i
$746$	68.2384	+	22.1720i	2.49838	+	0.811774i
$747$	2.30898	+	15.0288i	0.0844811	+	0.549875i
$748$	39.3954	+	37.6326i	1.44044	+	1.37598i
$749$			0.332233i			0.0121395i
$750$	4.06143	−	2.47592i	0.148302	−	0.0904078i
$751$	23.9244	−	17.3821i	0.873013	−	0.634281i	−0.0583807	−	0.998294i	$-0.518594\pi$
$751$	23.9244	−	17.3821i	0.873013	−	0.634281i	0.931394	+	0.364013i	$0.118594\pi$
$752$	−72.3325	+	99.5571i	−2.63769	+	3.63048i
$753$	−7.07402	+	16.9669i	−0.257792	+	0.618307i
$754$	−30.6183	+	9.94849i	−1.11505	+	0.362303i
$755$	2.01234	+	1.46205i	0.0732366	+	0.0532095i
$756$	−0.130408	−	1.81854i	−0.00474291	−	0.0661397i
$757$	5.16432	−	15.8942i	0.187701	−	0.577683i	−0.812284	−	0.583262i	$-0.801776\pi$
$757$	5.16432	−	15.8942i	0.187701	−	0.577683i	0.999984	+	0.00557933i	$0.00177597\pi$
$758$	−87.5562			−3.18018
$759$	17.1249	−	29.2803i	0.621596	−	1.06281i
$760$	2.51662			0.0912875
$761$	4.39513	−	13.5268i	0.159323	−	0.490347i	−0.839250	−	0.543746i	$-0.817005\pi$
$761$	4.39513	−	13.5268i	0.159323	−	0.490347i	0.998573	+	0.0533988i	$0.0170055\pi$
$762$	15.7599	+	1.27709i	0.570922	+	0.0462640i
$763$	0.509918	+	0.370477i	0.0184603	+	0.0134122i
$764$	99.8147	−	32.4317i	3.61117	−	1.17334i
$765$	4.00033	+	7.94187i	0.144632	+	0.287139i
$766$	−13.1586	+	18.1112i	−0.475439	+	0.654385i
$767$	−3.32140	+	2.41313i	−0.119929	+	0.0871332i
$768$	−49.6022	−	81.3660i	−1.78986	−	2.93604i
$769$			22.9193i			0.826492i	0.910619	+	0.413246i	$0.135605\pi$
$769$			22.9193i			0.826492i	−0.910619	+	0.413246i	$0.864395\pi$
$770$	−0.507705	+	0.273497i	−0.0182964	+	0.00985616i
$771$	−20.9554	−	17.9818i	−0.754692	−	0.647598i
$772$	−0.195942	−	0.0636656i	−0.00705212	−	0.00229137i
$773$	20.2090	+	27.8153i	0.726868	+	1.00045i	0.999268	+	0.0382640i	$0.0121828\pi$
$773$	20.2090	+	27.8153i	0.726868	+	1.00045i	−0.272399	+	0.962184i	$0.587817\pi$
$774$	36.1850	+	18.6489i	1.30064	+	0.670322i
$775$	−0.401111	−	1.23449i	−0.0144083	−	0.0443443i
$776$	−2.68803	−	8.27289i	−0.0964945	−	0.296980i
$777$	−0.130517	−	0.549244i	−0.00468225	−	0.0197040i
$778$	2.26938	+	3.12353i	0.0813611	+	0.111984i
$779$	1.23774	+	0.402166i	0.0443466	+	0.0144091i
$780$	8.15097	−	9.49890i	0.291852	−	0.340115i
$781$	−3.79208	+	28.0876i	−0.135691	+	1.00505i
$782$		−	48.0666i		−	1.71886i
$783$	−35.7312	+	30.0902i	−1.27693	+	1.07534i
$784$	−88.4518	+	64.2640i	−3.15899	+	2.29514i
$785$	5.39548	−	7.42623i	0.192573	−	0.265054i
$786$	−45.8728	−	19.1258i	−1.63623	−	0.682194i
$787$	17.0485	−	5.53941i	0.607715	−	0.197459i	0.0110366	−	0.999939i	$-0.496487\pi$
$787$	17.0485	−	5.53941i	0.607715	−	0.197459i	0.596678	+	0.802481i	$0.296487\pi$
$788$	−21.9447	−	15.9437i	−0.781746	−	0.567972i
$789$	−0.834167	+	10.2941i	−0.0296971	+	0.366478i
$790$	6.39382	−	19.6782i	0.227482	−	0.700118i
$791$	−0.544172			−0.0193485
$792$	−1.76585	−	96.7622i	−0.0627467	−	3.43829i
$793$	−5.58383			−0.198288
$794$	0.900124	−	2.77030i	0.0319442	−	0.0983141i
$795$	−0.598490	+	7.38568i	−0.0212262	+	0.261943i
$796$	−111.117	−	80.7309i	−3.93842	−	2.86143i
$797$	10.1962	−	3.31295i	0.361168	−	0.117351i	−0.122811	−	0.992430i	$-0.539191\pi$
$797$	10.1962	−	3.31295i	0.361168	−	0.117351i	0.483980	+	0.875079i	$0.339191\pi$
$798$	−0.0719213	−	0.0299862i	−0.00254599	−	0.00106150i
$799$	−13.7194	+	18.8831i	−0.485357	+	0.668036i
$800$	−18.9833	+	13.7921i	−0.671160	+	0.487626i
$801$	4.94417	−	30.3065i	0.174693	−	1.07083i
$802$			23.0425i			0.813658i
$803$	−21.3936	−	39.7139i	−0.754964	−	1.40147i
$804$	65.1397	−	75.9119i	2.29730	−	2.67721i
$805$	0.355563	+	0.115529i	0.0125320	+	0.00407188i
$806$	−2.73223	−	3.76059i	−0.0962386	−	0.132461i
$807$	8.31600	+	34.9957i	0.292737	+	1.23191i
$808$	−29.1257	−	89.6396i	−1.02464	−	3.15351i
$809$	−12.7613	−	39.2753i	−0.448664	−	1.38085i	−0.878415	−	0.477898i	$-0.841399\pi$
$809$	−12.7613	−	39.2753i	−0.448664	−	1.38085i	0.429751	−	0.902947i	$-0.358601\pi$
$810$	7.85525	−	23.4346i	0.276005	−	0.823408i
$811$	11.2615	+	15.5001i	0.395445	+	0.544283i	0.959593	−	0.281390i	$-0.0907956\pi$
$811$	11.2615	+	15.5001i	0.395445	+	0.544283i	−0.564149	+	0.825673i	$0.690796\pi$
$812$	−3.00000	−	0.974758i	−0.105279	−	0.0342073i
$813$	−11.3383	−	9.72936i	−0.397652	−	0.341224i
$814$	−8.39256	−	46.1308i	−0.294159	−	1.61688i
$815$			6.61868i			0.231842i
$816$	−41.7638	−	68.5081i	−1.46202	−	2.39826i
$817$	1.03428	−	0.751445i	0.0361847	−	0.0262897i
$818$	31.1751	−	42.9088i	1.09001	−	1.50027i
$819$	−0.221210	+	0.111424i	−0.00772972	+	0.00389347i
$820$	−26.5107	+	8.61385i	−0.925794	+	0.300809i
$821$	17.6258	+	12.8059i	0.615146	+	0.446930i	0.851223	−	0.524805i	$-0.175862\pi$
$821$	17.6258	+	12.8059i	0.615146	+	0.446930i	−0.236077	+	0.971734i	$0.575862\pi$
$822$	24.0840	+	1.95162i	0.840027	+	0.0680705i
$823$	−5.73612	+	17.6540i	−0.199949	+	0.615378i	0.799935	+	0.600087i	$0.204868\pi$
$823$	−5.73612	+	17.6540i	−0.199949	+	0.615378i	−0.999883	+	0.0152911i	$0.995132\pi$
$824$	25.4830			0.887741
$825$	−5.71638	+	0.568380i	−0.199019	+	0.0197885i
$826$	−0.547428			−0.0190474
$827$	5.44156	−	16.7474i	0.189222	−	0.582365i	−0.810774	−	0.585360i	$-0.800953\pi$
$827$	5.44156	−	16.7474i	0.189222	−	0.582365i	0.999996	+	0.00299497i	$0.000953330\pi$
$828$	−69.7373	+	69.0939i	−2.42354	+	2.40118i
$829$	30.3264	+	22.0334i	1.05328	+	0.765253i	0.972833	−	0.231506i	$-0.0743654\pi$
$829$	30.3264	+	22.0334i	1.05328	+	0.765253i	0.0804465	+	0.996759i	$0.474365\pi$
$830$	−13.2377	+	4.30119i	−0.459487	+	0.149296i
$831$	−14.5711	+	34.9485i	−0.505466	+	1.21235i
$832$	−25.4343	+	35.0073i	−0.881775	+	1.21366i
$833$	−16.7767	+	12.1890i	−0.581280	+	0.422324i
$834$	43.1636	−	26.3133i	1.49463	−	0.911155i
$835$			13.2813i			0.459618i
$836$	−4.28555	−	2.06148i	−0.148219	−	0.0712977i
$837$	−5.72618	−	3.56400i	−0.197926	−	0.123190i
$838$	−77.2078	−	25.0863i	−2.66710	−	0.866593i
$839$	−27.6309	−	38.0307i	−0.953926	−	1.31297i	−0.949761	−	0.312975i	$-0.898674\pi$
$839$	−27.6309	−	38.0307i	−0.953926	−	1.31297i	−0.00416433	−	0.999991i	$-0.501326\pi$
$840$	1.03776	−	0.246603i	0.0358062	−	0.00850860i
$841$	16.0132	+	49.2836i	0.552180	+	1.69944i
$842$	24.5981	+	75.7051i	0.847706	+	2.60897i
$843$	49.6855	−	11.8067i	1.71126	−	0.406646i
$844$	29.8970	+	41.1497i	1.02910	+	1.41643i
$845$	10.7465	+	3.49176i	0.369692	+	0.120120i
$846$	64.1220	−	9.85152i	2.20456	−	0.338702i
$847$	0.695733	−	0.0318618i	0.0239057	−	0.00109478i
$848$		−	66.8576i		−	2.29590i
$849$	−32.4196	+	19.7635i	−1.11264	+	0.678283i
$850$	−6.58561	+	4.78472i	−0.225884	+	0.164115i
$851$	−17.8670	+	24.5918i	−0.612473	+	0.842997i
$852$	31.5655	−	75.7092i	1.08142	−	2.59375i
$853$	24.7446	−	8.04000i	0.847238	−	0.275284i	0.146949	−	0.989144i	$-0.453055\pi$
$853$	24.7446	−	8.04000i	0.847238	−	0.275284i	0.700289	+	0.713860i	$0.253055\pi$
$854$	−0.602357	−	0.437638i	−0.0206122	−	0.0149757i
$855$	−0.546313	−	0.551401i	−0.0186835	−	0.0188575i
$856$	15.7717	−	48.5404i	0.539067	−	1.65908i
$857$	21.8303			0.745710			0.372855	−	0.927890i	$-0.378379\pi$
$857$	21.8303			0.745710			0.372855	+	0.927890i	$0.378379\pi$
$858$	−18.8400	+	8.26166i	−0.643187	+	0.282048i
$859$	−49.8178			−1.69976			−0.849881	−	0.526974i	$-0.823326\pi$
$859$	−49.8178			−1.69976			−0.849881	+	0.526974i	$0.823326\pi$
$860$	−8.46162	+	26.0422i	−0.288539	+	0.888032i
$861$	0.549806	+	0.0445528i	0.0187373	+	0.00151836i
$862$	−52.4924	−	38.1379i	−1.78790	−	1.29898i
$863$	−46.1689	+	15.0012i	−1.57161	+	0.510646i	−0.959877	−	0.280421i	$-0.909526\pi$
$863$	−46.1689	+	15.0012i	−1.57161	+	0.510646i	−0.611730	+	0.791067i	$0.709526\pi$
$864$	−29.2865	+	118.356i	−0.996346	+	4.02656i
$865$	1.32423	−	1.82265i	0.0450253	−	0.0619720i
$866$	−0.987166	+	0.717218i	−0.0335453	+	0.0243721i
$867$	7.40530	+	12.1474i	0.251497	+	0.412549i
$868$		−	0.455446i		−	0.0154589i
$869$	−17.2605	+	18.0691i	−0.585523	+	0.612951i
$870$	−32.4520	−	27.8469i	−1.10022	−	0.944099i
$871$	−12.9241	−	4.19929i	−0.437916	−	0.142288i
$872$	−56.9136	−	78.3349i	−1.92734	−	2.65275i
$873$	−1.22910	+	2.38485i	−0.0415987	+	0.0807150i
$874$	1.29653	+	3.99031i	0.0438558	+	0.134974i
$875$	−0.0195653	−	0.0602159i	−0.000661429	−	0.00203567i
$876$	30.1825	+	127.015i	1.01977	+	4.29145i
$877$	−28.7564	−	39.5798i	−0.971034	−	1.33651i	−0.941523	−	0.336950i	$-0.890605\pi$
$877$	−28.7564	−	39.5798i	−0.971034	−	1.33651i	−0.0295119	−	0.999564i	$-0.509395\pi$
$878$	−31.9980	−	10.3968i	−1.07988	−	0.350874i
$879$	−34.9054	+	40.6778i	−1.17733	+	1.37203i
$880$	50.9947	−	9.27747i	1.71903	−	0.312743i
$881$		−	29.7595i		−	1.00262i	−0.865266	−	0.501312i	$-0.832851\pi$
$881$		−	29.7595i		−	1.00262i	0.865266	−	0.501312i	$-0.167149\pi$
$882$	56.8858	+	9.28029i	1.91545	+	0.312484i
$883$	10.5124	−	7.63769i	0.353770	−	0.257029i	−0.396679	−	0.917957i	$-0.629837\pi$
$883$	10.5124	−	7.63769i	0.353770	−	0.257029i	0.750449	+	0.660929i	$0.229837\pi$
$884$	−12.5907	+	17.3296i	−0.423470	+	0.582856i
$885$	−5.03317	−	2.09849i	−0.169188	−	0.0705399i
$886$	57.4224	−	18.6577i	1.92914	−	0.626817i
$887$	−9.04690	−	6.57296i	−0.303765	−	0.220698i	0.425451	−	0.904981i	$-0.360115\pi$
$887$	−9.04690	−	6.57296i	−0.303765	−	0.220698i	−0.729217	+	0.684283i	$0.760115\pi$
$888$	−7.00477	+	86.4426i	−0.235065	+	2.90082i
$889$	0.0650377	−	0.200165i	0.00218129	−	0.00671333i
$890$	28.1096			0.942237
$891$	−20.8176	+	21.3922i	−0.697416	+	0.716667i
$892$	−70.7923			−2.37030
$893$	0.629586	−	1.93767i	0.0210683	−	0.0648415i
$894$	−2.64506	+	32.6414i	−0.0884640	+	1.09169i
$895$	7.79511	+	5.66348i	0.260562	+	0.189309i
$896$	−2.66157	+	0.864796i	−0.0889168	+	0.0288908i
$897$	12.3095	+	5.13223i	0.411003	+	0.171360i
$898$	−40.1805	+	55.3037i	−1.34084	+	1.84551i
$899$	−9.44058	+	6.85898i	−0.314861	+	0.228760i
$900$	16.4085	+	2.67686i	0.546949	+	0.0892286i
$901$		−	12.6809i		−	0.422464i
$902$	45.4021	+	6.12970i	1.51172	+	0.204097i
$903$	0.352864	−	0.411217i	0.0117426	−	0.0136844i
$904$	79.5056	+	25.8329i	2.64432	+	0.859191i
$905$	1.49258	+	2.05435i	0.0496149	+	0.0682891i
$906$	2.73535	+	11.5110i	0.0908761	+	0.382428i
$907$	−11.6014	−	35.7054i	−0.385218	−	1.18558i	−0.936322	−	0.351142i	$-0.885794\pi$
$907$	−11.6014	−	35.7054i	−0.385218	−	1.18558i	0.551105	−	0.834436i	$-0.314206\pi$
$908$	48.1353	+	148.145i	1.59743	+	4.91637i
$909$	−13.3177	+	25.8407i	−0.441720	+	0.857081i
$910$	−0.133272	−	0.183433i	−0.00441793	−	0.00608076i
$911$	35.9244	+	11.6725i	1.19023	+	0.386728i	0.836157	−	0.548490i	$-0.184797\pi$
$911$	35.9244	+	11.6725i	1.19023	+	0.386728i	0.354071	+	0.935219i	$0.384797\pi$
$912$	5.31499	+	4.56077i	0.175997	+	0.151022i
$913$	16.6588	+	2.24908i	0.551325	+	0.0744338i
$914$		−	75.6635i		−	2.50273i
$915$	−3.86058	−	6.33279i	−0.127627	−	0.209356i
$916$	58.3215	−	42.3730i	1.92700	−	1.40004i
$917$	−0.388852	+	0.535208i	−0.0128410	+	0.0176741i
$918$	−10.1600	+	41.0597i	−0.335329	+	1.35517i
$919$	43.6417	−	14.1801i	1.43961	−	0.467757i	0.517833	−	0.855482i	$-0.326739\pi$
$919$	43.6417	−	14.1801i	1.43961	−	0.467757i	0.921775	+	0.387725i	$0.126739\pi$
$920$	−46.4647	−	33.7586i	−1.53190	−	1.11299i
$921$	−56.8040	−	4.60304i	−1.87176	−	0.151675i
$922$	27.8761	−	85.7938i	0.918051	−	2.82547i
$923$	−11.1434			−0.366791
$924$	−1.96921	−	0.430139i	−0.0647821	−	0.0141505i
$925$	5.14787			0.169261
$926$	21.6740	−	66.7057i	0.712252	−	2.19209i
$927$	−5.53189	−	5.58341i	−0.181691	−	0.183383i
$928$	170.659	+	123.991i	5.60217	+	4.07021i
$929$	−12.7551	+	4.14438i	−0.418481	+	0.135973i	−0.510686	−	0.859767i	$-0.670609\pi$
$929$	−12.7551	+	4.14438i	−0.418481	+	0.135973i	0.0922048	+	0.995740i	$0.470609\pi$
$930$	2.37597	−	5.69872i	0.0779112	−	0.186868i
$931$	1.06396	−	1.46442i	0.0348699	−	0.0479943i
$932$	−20.4936	+	14.8894i	−0.671289	+	0.487720i
$933$	−23.1095	+	14.0880i	−0.756571	+	0.461219i
$934$		−	110.460i		−	3.61437i
$935$	9.67222	−	1.75967i	0.316316	−	0.0575472i
$936$	37.6092	−	5.77817i	1.22930	−	0.188865i
$937$	3.27580	+	1.06437i	0.107016	+	0.0347716i	0.362035	−	0.932164i	$-0.382082\pi$
$937$	3.27580	+	1.06437i	0.107016	+	0.0347716i	−0.255020	+	0.966936i	$0.582082\pi$
$938$	−1.06507	−	1.46594i	−0.0347756	−	0.0478645i
$939$	−37.0263	+	8.79852i	−1.20831	+	0.287129i
$940$	13.4849	+	41.5022i	0.439829	+	1.35365i
$941$	−16.6975	−	51.3896i	−0.544323	−	1.67525i	−0.722594	−	0.691272i	$-0.757050\pi$
$941$	−16.6975	−	51.3896i	−0.544323	−	1.67525i	0.178271	−	0.983981i	$-0.442950\pi$
$942$	42.4796	−	10.0944i	1.38406	−	0.328893i
$943$	−17.4578	−	24.0286i	−0.568503	−	0.782477i
$944$	46.7940	+	15.2043i	1.52302	+	0.494858i
$945$	−0.279311	−	0.173844i	−0.00908599	−	0.00565516i
$946$	31.0865	−	32.5427i	1.01071	−	1.05805i
$947$			20.8212i			0.676598i	0.941039	+	0.338299i	$0.109852\pi$
$947$			20.8212i			0.676598i	−0.941039	+	0.338299i	$0.890148\pi$
$948$	61.7494	−	37.6435i	2.00553	−	1.22260i
$949$	14.3486	−	10.4249i	0.465775	−	0.338405i
$950$	0.417651	−	0.574847i	0.0135504	−	0.0186505i
$951$	20.7865	−	49.8559i	0.674047	−	1.61669i
$952$	−1.73609	+	0.564090i	−0.0562670	+	0.0182823i
$953$	21.3059	+	15.4796i	0.690166	+	0.501435i	0.876715	−	0.481011i	$-0.159730\pi$
$953$	21.3059	+	15.4796i	0.690166	+	0.501435i	−0.186549	+	0.982446i	$0.559730\pi$
$954$	−25.0379	+	24.8069i	−0.810632	+	0.803153i
$955$	5.85221	−	18.0113i	0.189373	−	0.582831i
$956$	−51.8772			−1.67783
$957$	20.7401	+	47.2959i	0.670431	+	1.52886i
$958$	−39.5374			−1.27740
$959$	0.0993893	−	0.305889i	0.00320945	−	0.00987767i
$960$	−57.2877	−	4.64224i	−1.84895	−	0.149828i
$961$	23.7164	+	17.2310i	0.765047	+	0.555839i
$962$	17.5328	−	5.69674i	0.565279	−	0.183670i
$963$	−14.0591	+	7.08161i	−0.453050	+	0.228202i
$964$	−27.8846	+	38.3798i	−0.898101	+	1.23613i
$965$	−0.0300767	+	0.0218520i	−0.000968202	+	0.000703440i
$966$	0.925650	+	1.51841i	0.0297823	+	0.0488540i
$967$			17.2563i			0.554924i	0.960737	+	0.277462i	$0.0894932\pi$
$967$			17.2563i			0.554924i	−0.960737	+	0.277462i	$0.910507\pi$
$968$	−103.162	−	28.3727i	−3.31575	−	0.911934i
$969$	1.00810	+	0.865046i	0.0323848	+	0.0277893i
$970$	−2.33579	−	0.758945i	−0.0749978	−	0.0243683i
$971$	−7.90692	−	10.8829i	−0.253745	−	0.349250i	0.663073	−	0.748554i	$-0.269252\pi$
$971$	−7.90692	−	10.8829i	−0.253745	−	0.349250i	−0.916818	+	0.399304i	$0.869252\pi$
$972$	74.1759	−	44.2811i	2.37919	−	1.42032i
$973$	−0.207934	−	0.639956i	−0.00666607	−	0.0205160i
$974$	9.75956	+	30.0368i	0.312717	+	0.962443i
$975$	−0.522169	−	2.19741i	−0.0167228	−	0.0703735i
$976$	39.3344	+	54.1391i	1.25906	+	1.73295i
$977$	−9.76288	−	3.17215i	−0.312342	−	0.101486i	0.148651	−	0.988890i	$-0.452507\pi$
$977$	−9.76288	−	3.17215i	−0.312342	−	0.101486i	−0.460993	+	0.887404i	$0.652507\pi$
$978$	−20.5017	+	23.8920i	−0.655571	+	0.763983i
$979$	−30.5926	−	14.7160i	−0.977744	−	0.470324i
$980$			38.7703i			1.23847i
$981$	−4.80853	+	29.4751i	−0.153524	+	0.941066i
$982$	−2.89115	+	2.10055i	−0.0922604	+	0.0670311i
$983$	2.02497	−	2.78714i	0.0645866	−	0.0888959i	−0.775502	−	0.631345i	$-0.782503\pi$
$983$	2.02497	−	2.78714i	0.0645866	−	0.0888959i	0.840088	+	0.542450i	$0.182503\pi$
$984$	−78.2137	−	32.6097i	−2.49336	−	1.03956i
$985$	−4.65508	+	1.51253i	−0.148323	+	0.0481931i
$986$	59.2045	+	43.0146i	1.88546	+	1.36986i
$987$	0.0697470	−	0.860715i	0.00222007	−	0.0273969i
$988$	0.577789	−	1.77825i	0.0183819	−	0.0565737i
$989$	−29.1760			−0.927744
$990$	−22.3955	−	15.6550i	−0.711776	−	0.497549i
$991$	−18.1676			−0.577113			−0.288556	−	0.957463i	$-0.593175\pi$
$991$	−18.1676			−0.577113			−0.288556	+	0.957463i	$0.593175\pi$
$992$	−9.41191	+	28.9669i	−0.298828	+	0.919699i
$993$	1.09094	−	13.4628i	0.0346199	−	0.427228i
$994$	−1.20210	−	0.873377i	−0.0381283	−	0.0277018i
$995$	−23.5710	+	7.65867i	−0.747250	+	0.242796i
$996$	−44.9031	−	18.7215i	−1.42281	−	0.593214i
$997$	21.4771	−	29.5607i	0.680186	−	0.936195i	−0.319750	−	0.947502i	$-0.603599\pi$
$997$	21.4771	−	29.5607i	0.680186	−	0.936195i	0.999936	+	0.0113065i	$0.00359905\pi$
$998$	81.4046	−	59.1439i	2.57682	−	1.87217i
$999$	20.4605	−	17.2304i	0.647341	−	0.545144i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.2.p.b.101.1	✓	48
3.2	odd	2	inner	165.2.p.b.101.12	yes	48
5.2	odd	4		825.2.bs.g.299.2		48
5.3	odd	4		825.2.bs.h.299.11		48
5.4	even	2		825.2.bi.e.101.12		48
11.6	odd	10	inner	165.2.p.b.116.12	yes	48
15.2	even	4		825.2.bs.h.299.12		48
15.8	even	4		825.2.bs.g.299.1		48
15.14	odd	2		825.2.bi.e.101.1		48
33.17	even	10	inner	165.2.p.b.116.1	yes	48
55.17	even	20		825.2.bs.g.149.1		48
55.28	even	20		825.2.bs.h.149.12		48
55.39	odd	10		825.2.bi.e.776.1		48
165.17	odd	20		825.2.bs.h.149.11		48
165.83	odd	20		825.2.bs.g.149.2		48
165.149	even	10		825.2.bi.e.776.12		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.p.b.101.1	✓	48	1.1	even	1	trivial
165.2.p.b.101.12	yes	48	3.2	odd	2	inner
165.2.p.b.116.1	yes	48	33.17	even	10	inner
165.2.p.b.116.12	yes	48	11.6	odd	10	inner
825.2.bi.e.101.1		48	15.14	odd	2
825.2.bi.e.101.12		48	5.4	even	2
825.2.bi.e.776.1		48	55.39	odd	10
825.2.bi.e.776.12		48	165.149	even	10
825.2.bs.g.149.1		48	55.17	even	20
825.2.bs.g.149.2		48	165.83	odd	20
825.2.bs.g.299.1		48	15.8	even	4
825.2.bs.g.299.2		48	5.2	odd	4
825.2.bs.h.149.11		48	165.17	odd	20
825.2.bs.h.149.12		48	55.28	even	20
825.2.bs.h.299.11		48	5.3	odd	4
825.2.bs.h.299.12		48	15.2	even	4

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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	165.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.848632 + 2.61182i) q^{2} +(-0.139896 + 1.72639i) q^{3} +(-4.48340 - 3.25738i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-4.39031 - 1.83046i) q^{6} +(-0.0372155 + 0.0512227i) q^{7} +(7.86897 - 5.71714i) q^{8} +(-2.96086 - 0.483031i) q^{9} +O(q^{10})\)	\(q+(-0.848632 + 2.61182i) q^{2} +(-0.139896 + 1.72639i) q^{3} +(-4.48340 - 3.25738i) q^{4} +(-0.951057 + 0.309017i) q^{5} +(-4.39031 - 1.83046i) q^{6} +(-0.0372155 + 0.0512227i) q^{7} +(7.86897 - 5.71714i) q^{8} +(-2.96086 - 0.483031i) q^{9} -2.74623i q^{10} +(-1.43771 + 2.98881i) q^{11} +(6.25073 - 7.28442i) q^{12} +(-1.24018 - 0.402959i) q^{13} +(-0.102202 - 0.140670i) q^{14} +(-0.400435 - 1.68513i) q^{15} +(4.82928 + 14.8630i) q^{16} +(0.915974 + 2.81908i) q^{17} +(3.77427 - 7.32332i) q^{18} +(-0.152082 - 0.209322i) q^{19} +(5.27056 + 1.71251i) q^{20} +(-0.0832242 - 0.0714144i) q^{21} +(-6.58616 - 6.29144i) q^{22} +5.90480i q^{23} +(8.76919 + 14.3847i) q^{24} +(0.809017 - 0.587785i) q^{25} +(2.10492 - 2.89717i) q^{26} +(1.24811 - 5.04403i) q^{27} +(0.333704 - 0.108427i) q^{28} +(-7.27305 - 5.28418i) q^{29} +(4.74107 + 0.384187i) q^{30} +(0.401111 - 1.23449i) q^{31} -23.4646 q^{32} +(-4.95873 - 2.90017i) q^{33} -8.14026 q^{34} +(0.0195653 - 0.0602159i) q^{35} +(11.7013 + 11.8103i) q^{36} +(4.16472 + 3.02584i) q^{37} +(0.675774 - 0.219572i) q^{38} +(0.869162 - 2.08467i) q^{39} +(-5.71714 + 7.86897i) q^{40} +(-4.06933 + 2.95654i) q^{41} +(0.257148 - 0.156762i) q^{42} +4.94107i q^{43} +(16.1815 - 8.71688i) q^{44} +(2.96521 - 0.455566i) q^{45} +(-15.4223 - 5.01101i) q^{46} +(4.62843 + 6.37049i) q^{47} +(-26.3349 + 6.25795i) q^{48} +(2.16188 + 6.65358i) q^{49} +(0.848632 + 2.61182i) q^{50} +(-4.99498 + 1.18695i) q^{51} +(4.24764 + 5.84637i) q^{52} +(-4.06872 - 1.32201i) q^{53} +(12.1149 + 7.54038i) q^{54} +(0.443749 - 3.28681i) q^{55} +0.615836i q^{56} +(0.382648 - 0.233269i) q^{57} +(19.9735 - 14.5116i) q^{58} +(1.85056 - 2.54708i) q^{59} +(-3.69379 + 8.85947i) q^{60} +(4.07249 - 1.32323i) q^{61} +(2.88388 + 2.09526i) q^{62} +(0.134932 - 0.133687i) q^{63} +(10.2543 - 31.5594i) q^{64} +1.30400 q^{65} +(11.7829 - 10.4901i) q^{66} +10.4211 q^{67} +(5.07614 - 15.6227i) q^{68} +(-10.1940 - 0.826059i) q^{69} +(0.140670 + 0.102202i) q^{70} +(8.12731 - 2.64072i) q^{71} +(-26.0605 + 13.1267i) q^{72} +(-7.99451 + 11.0035i) q^{73} +(-11.4373 + 8.30967i) q^{74} +(0.901569 + 1.47891i) q^{75} +1.43386i q^{76} +(-0.0995901 - 0.184873i) q^{77} +(4.70718 + 4.03921i) q^{78} +(7.16551 + 2.32822i) q^{79} +(-9.18583 - 12.6432i) q^{80} +(8.53336 + 2.86037i) q^{81} +(-4.26859 - 13.1374i) q^{82} +(-1.56621 - 4.82031i) q^{83} +(0.140504 + 0.591273i) q^{84} +(-1.74229 - 2.39805i) q^{85} +(-12.9052 - 4.19315i) q^{86} +(10.1400 - 11.8169i) q^{87} +(5.77417 + 31.7385i) q^{88} +10.2357i q^{89} +(-1.32652 + 8.13120i) q^{90} +(0.0667946 - 0.0485291i) q^{91} +(19.2342 - 26.4736i) q^{92} +(2.07510 + 0.865175i) q^{93} +(-20.5664 + 6.68243i) q^{94} +(0.209322 + 0.152082i) q^{95} +(3.28261 - 40.5091i) q^{96} +(0.276359 - 0.850545i) q^{97} -19.2126 q^{98} +(5.70054 - 8.15499i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9}+O(q^{10}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9	\( 48 q - 4 q^{3} - 4 q^{4} - 20 q^{6} + 10 q^{7} + 2 q^{9} + 8 q^{12} + 6 q^{15} + 32 q^{16} - 30 q^{18} - 100 q^{19} - 82 q^{22} + 100 q^{24} + 12 q^{25} + 14 q^{27} + 30 q^{28} + 10 q^{30} + 10 q^{31} - 46 q^{33} - 28 q^{34} + 14 q^{36} + 6 q^{37} - 50 q^{40} - 52 q^{42} + 32 q^{45} + 20 q^{46} - 80 q^{48} - 26 q^{49} - 30 q^{51} + 40 q^{52} + 6 q^{55} - 70 q^{57} + 92 q^{58} + 44 q^{60} + 70 q^{61} - 20 q^{63} + 18 q^{64} + 76 q^{66} + 20 q^{67} + 42 q^{69} - 4 q^{70} - 80 q^{72} + 90 q^{73} - 6 q^{75} - 108 q^{78} - 100 q^{79} + 38 q^{81} - 34 q^{82} + 70 q^{84} + 20 q^{85} + 74 q^{88} + 20 q^{90} - 86 q^{91} + 76 q^{93} + 10 q^{94} - 30 q^{96} + 6 q^{97} - 28 q^{99}+O(q^{100}) \) 48 * q - 4 * q^3 - 4 * q^4 - 20 * q^6 + 10 * q^7 + 2 * q^9 + 8 * q^12 + 6 * q^15 + 32 * q^16 - 30 * q^18 - 100 * q^19 - 82 * q^22 + 100 * q^24 + 12 * q^25 + 14 * q^27 + 30 * q^28 + 10 * q^30 + 10 * q^31 - 46 * q^33 - 28 * q^34 + 14 * q^36 + 6 * q^37 - 50 * q^40 - 52 * q^42 + 32 * q^45 + 20 * q^46 - 80 * q^48 - 26 * q^49 - 30 * q^51 + 40 * q^52 + 6 * q^55 - 70 * q^57 + 92 * q^58 + 44 * q^60 + 70 * q^61 - 20 * q^63 + 18 * q^64 + 76 * q^66 + 20 * q^67 + 42 * q^69 - 4 * q^70 - 80 * q^72 + 90 * q^73 - 6 * q^75 - 108 * q^78 - 100 * q^79 + 38 * q^81 - 34 * q^82 + 70 * q^84 + 20 * q^85 + 74 * q^88 + 20 * q^90 - 86 * q^91 + 76 * q^93 + 10 * q^94 - 30 * q^96 + 6 * q^97 - 28 * q^99

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