LMFDB - Embedded newform 804.2.j.a.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [804,2,Mod(499,804)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(804, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("804.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 804 = 2^{2} \cdot 3 \cdot 67 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	804.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.41997232251$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$34$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Character	$\chi$	$=$	804.499
Dual form			804.2.j.a.775.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39800 + 0.213516i) q^{2} -1.00000 q^{3} +(1.90882 - 0.596993i) q^{4} -1.98108i q^{5} +(1.39800 - 0.213516i) q^{6} +(-0.674999 + 1.16913i) q^{7} +(-2.54107 + 1.24216i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.39800 + 0.213516i) q^{2} -1.00000 q^{3} +(1.90882 - 0.596993i) q^{4} -1.98108i q^{5} +(1.39800 - 0.213516i) q^{6} +(-0.674999 + 1.16913i) q^{7} +(-2.54107 + 1.24216i) q^{8} +1.00000 q^{9} +(0.422992 + 2.76955i) q^{10} +(-0.665505 + 1.15269i) q^{11} +(-1.90882 + 0.596993i) q^{12} +(0.778626 - 0.449540i) q^{13} +(0.694021 - 1.77857i) q^{14} +1.98108i q^{15} +(3.28720 - 2.27910i) q^{16} +(-3.18636 - 5.51895i) q^{17} +(-1.39800 + 0.213516i) q^{18} +(1.97758 - 1.14175i) q^{19} +(-1.18269 - 3.78152i) q^{20} +(0.674999 - 1.16913i) q^{21} +(0.684260 - 1.75356i) q^{22} +(3.94074 - 2.27519i) q^{23} +(2.54107 - 1.24216i) q^{24} +1.07533 q^{25} +(-0.992537 + 0.794707i) q^{26} -1.00000 q^{27} +(-0.590489 + 2.63463i) q^{28} +(-2.25494 + 3.90567i) q^{29} +(-0.422992 - 2.76955i) q^{30} +(-4.24278 + 7.34872i) q^{31} +(-4.10889 + 3.88806i) q^{32} +(0.665505 - 1.15269i) q^{33} +(5.63293 + 7.03516i) q^{34} +(2.31614 + 1.33723i) q^{35} +(1.90882 - 0.596993i) q^{36} +(-3.71811 - 6.43996i) q^{37} +(-2.52087 + 2.01842i) q^{38} +(-0.778626 + 0.449540i) q^{39} +(2.46082 + 5.03406i) q^{40} +(-9.29294 - 5.36528i) q^{41} +(-0.694021 + 1.77857i) q^{42} -8.39986 q^{43} +(-0.582184 + 2.59758i) q^{44} -1.98108i q^{45} +(-5.02337 + 4.02213i) q^{46} +(-1.81688 - 1.04898i) q^{47} +(-3.28720 + 2.27910i) q^{48} +(2.58875 + 4.48385i) q^{49} +(-1.50332 + 0.229601i) q^{50} +(3.18636 + 5.51895i) q^{51} +(1.21789 - 1.32293i) q^{52} -8.69893i q^{53} +(1.39800 - 0.213516i) q^{54} +(2.28357 + 1.31842i) q^{55} +(0.262968 - 3.80930i) q^{56} +(-1.97758 + 1.14175i) q^{57} +(2.31848 - 5.94160i) q^{58} -3.00672i q^{59} +(1.18269 + 3.78152i) q^{60} +(4.31128 - 2.48912i) q^{61} +(4.36235 - 11.1794i) q^{62} +(-0.674999 + 1.16913i) q^{63} +(4.91407 - 6.31284i) q^{64} +(-0.890573 - 1.54252i) q^{65} +(-0.684260 + 1.75356i) q^{66} +(-0.750324 - 8.15089i) q^{67} +(-9.37697 - 8.63245i) q^{68} +(-3.94074 + 2.27519i) q^{69} +(-3.52349 - 1.37491i) q^{70} +(-8.55186 - 4.93742i) q^{71} +(-2.54107 + 1.24216i) q^{72} +(-2.61035 - 4.52126i) q^{73} +(6.57297 + 8.20921i) q^{74} -1.07533 q^{75} +(3.09322 - 3.36000i) q^{76} +(-0.898431 - 1.55613i) q^{77} +(0.992537 - 0.794707i) q^{78} +(-3.18040 + 5.50861i) q^{79} +(-4.51508 - 6.51220i) q^{80} +1.00000 q^{81} +(14.1371 + 5.51648i) q^{82} +(-6.27859 + 3.62494i) q^{83} +(0.590489 - 2.63463i) q^{84} +(-10.9335 + 6.31244i) q^{85} +(11.7430 - 1.79351i) q^{86} +(2.25494 - 3.90567i) q^{87} +(0.259269 - 3.75573i) q^{88} -10.7873 q^{89} +(0.422992 + 2.76955i) q^{90} +1.21376i q^{91} +(6.16389 - 6.69551i) q^{92} +(4.24278 - 7.34872i) q^{93} +(2.76398 + 1.07854i) q^{94} +(-2.26190 - 3.91773i) q^{95} +(4.10889 - 3.88806i) q^{96} +(-0.310273 + 0.179136i) q^{97} +(-4.57646 - 5.71569i) q^{98} +(-0.665505 + 1.15269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	$ 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) $ 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/804\mathbb{Z}\right)^\times$.

$n$	$269$	$337$	$403$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−1.39800	+	0.213516i	−0.988537	+	0.150979i
$2$	−1.39800	+	0.213516i	−0.988537	+	0.150979i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	1.90882	−	0.596993i	0.954411	−	0.298496i
$5$		−	1.98108i		−	0.885965i	−0.896530	−	0.442982i	$-0.853920\pi$
$5$		−	1.98108i		−	0.885965i	0.896530	−	0.442982i	$-0.146080\pi$
$6$	1.39800	−	0.213516i	0.570732	−	0.0871676i
$7$	−0.674999	+	1.16913i	−0.255126	+	0.441891i	−0.964930	−	0.262509i	$-0.915450\pi$
$7$	−0.674999	+	1.16913i	−0.255126	+	0.441891i	0.709804	+	0.704399i	$0.248783\pi$
$8$	−2.54107	+	1.24216i	−0.898404	+	0.439170i
$9$	1.00000			0.333333
$10$	0.422992	+	2.76955i	0.133762	+	0.875809i
$11$	−0.665505	+	1.15269i	−0.200657	+	0.347549i	−0.948740	−	0.316056i	$-0.897641\pi$
$11$	−0.665505	+	1.15269i	−0.200657	+	0.347549i	0.748083	+	0.663605i	$0.230974\pi$
$12$	−1.90882	+	0.596993i	−0.551029	+	0.172337i
$13$	0.778626	−	0.449540i	0.215952	−	0.124680i	−0.388123	−	0.921608i	$-0.626876\pi$
$13$	0.778626	−	0.449540i	0.215952	−	0.124680i	0.604074	+	0.796928i	$0.293543\pi$
$14$	0.694021	−	1.77857i	0.185485	−	0.475344i
$15$			1.98108i			0.511512i
$16$	3.28720	−	2.27910i	0.821800	−	0.569776i
$17$	−3.18636	−	5.51895i	−0.772807	−	1.33854i	−0.936019	−	0.351950i	$-0.885519\pi$
$17$	−3.18636	−	5.51895i	−0.772807	−	1.33854i	0.163212	−	0.986591i	$-0.447815\pi$
$18$	−1.39800	+	0.213516i	−0.329512	+	0.0503263i
$19$	1.97758	−	1.14175i	0.453687	−	0.261937i	−0.255699	−	0.966756i	$-0.582306\pi$
$19$	1.97758	−	1.14175i	0.453687	−	0.261937i	0.709386	+	0.704820i	$0.248972\pi$
$20$	−1.18269	−	3.78152i	−0.264457	−	0.845574i
$21$	0.674999	−	1.16913i	0.147297	−	0.255126i
$22$	0.684260	−	1.75356i	0.145885	−	0.373860i
$23$	3.94074	−	2.27519i	0.821700	−	0.474409i	−0.0293021	−	0.999571i	$-0.509328\pi$
$23$	3.94074	−	2.27519i	0.821700	−	0.474409i	0.851002	+	0.525162i	$0.175995\pi$
$24$	2.54107	−	1.24216i	0.518694	−	0.253555i
$25$	1.07533			0.215066
$26$	−0.992537	+	0.794707i	−0.194652	+	0.155855i
$27$	−1.00000			−0.192450
$28$	−0.590489	+	2.63463i	−0.111592	+	0.497899i
$29$	−2.25494	+	3.90567i	−0.418731	+	0.725264i	−0.995812	−	0.0914232i	$-0.970858\pi$
$29$	−2.25494	+	3.90567i	−0.418731	+	0.725264i	0.577081	+	0.816687i	$0.304192\pi$
$30$	−0.422992	−	2.76955i	−0.0772275	−	0.505649i
$31$	−4.24278	+	7.34872i	−0.762027	+	1.31987i	0.179778	+	0.983707i	$0.442462\pi$
$31$	−4.24278	+	7.34872i	−0.762027	+	1.31987i	−0.941804	+	0.336162i	$0.890871\pi$
$32$	−4.10889	+	3.88806i	−0.726356	+	0.687319i
$33$	0.665505	−	1.15269i	0.115850	−	0.200657i
$34$	5.63293	+	7.03516i	0.966040	+	1.20652i
$35$	2.31614	+	1.33723i	0.391500	+	0.226032i
$36$	1.90882	−	0.596993i	0.318137	−	0.0994988i
$37$	−3.71811	−	6.43996i	−0.611254	−	1.05872i	−0.991029	−	0.133645i	$-0.957332\pi$
$37$	−3.71811	−	6.43996i	−0.611254	−	1.05872i	0.379775	−	0.925079i	$-0.376001\pi$
$38$	−2.52087	+	2.01842i	−0.408940	+	0.327431i
$39$	−0.778626	+	0.449540i	−0.124680	+	0.0719840i
$40$	2.46082	+	5.03406i	0.389090	+	0.795954i
$41$	−9.29294	−	5.36528i	−1.45131	−	0.837916i	−0.452757	−	0.891634i	$-0.649560\pi$
$41$	−9.29294	−	5.36528i	−1.45131	−	0.837916i	−0.998556	+	0.0537176i	$0.982893\pi$
$42$	−0.694021	+	1.77857i	−0.107090	+	0.274440i
$43$	−8.39986			−1.28097			−0.640483	−	0.767972i	$-0.721266\pi$
$43$	−8.39986			−1.28097			−0.640483	+	0.767972i	$0.721266\pi$
$44$	−0.582184	+	2.59758i	−0.0877675	+	0.391600i
$45$		−	1.98108i		−	0.295322i
$46$	−5.02337	+	4.02213i	−0.740656	+	0.593030i
$47$	−1.81688	−	1.04898i	−0.265020	−	0.153009i	0.361602	−	0.932332i	$-0.382230\pi$
$47$	−1.81688	−	1.04898i	−0.265020	−	0.153009i	−0.626622	+	0.779323i	$0.715563\pi$
$48$	−3.28720	+	2.27910i	−0.474466	+	0.328960i
$49$	2.58875	+	4.48385i	0.369822	+	0.640550i
$50$	−1.50332	+	0.229601i	−0.212601	+	0.0324704i
$51$	3.18636	+	5.51895i	0.446180	+	0.772807i
$52$	1.21789	−	1.32293i	0.168890	−	0.183457i
$53$		−	8.69893i		−	1.19489i	−0.801910	−	0.597445i	$-0.796183\pi$
$53$		−	8.69893i		−	1.19489i	0.801910	−	0.597445i	$-0.203817\pi$
$54$	1.39800	−	0.213516i	0.190244	−	0.0290559i
$55$	2.28357	+	1.31842i	0.307916	+	0.177775i
$56$	0.262968	−	3.80930i	0.0351406	−	0.509040i
$57$	−1.97758	+	1.14175i	−0.261937	+	0.151229i
$58$	2.31848	−	5.94160i	0.304432	−	0.780170i
$59$		−	3.00672i		−	0.391442i	−0.980660	−	0.195721i	$-0.937295\pi$
$59$		−	3.00672i		−	0.391442i	0.980660	−	0.195721i	$-0.0627046\pi$
$60$	1.18269	+	3.78152i	0.152684	+	0.488193i
$61$	4.31128	−	2.48912i	0.552003	−	0.318699i	−0.197926	−	0.980217i	$-0.563421\pi$
$61$	4.31128	−	2.48912i	0.552003	−	0.318699i	0.749930	+	0.661518i	$0.230087\pi$
$62$	4.36235	−	11.1794i	0.554019	−	1.41979i
$63$	−0.674999	+	1.16913i	−0.0850419	+	0.147297i
$64$	4.91407	−	6.31284i	0.614259	−	0.789105i
$65$	−0.890573	−	1.54252i	−0.110462	−	0.191326i
$66$	−0.684260	+	1.75356i	−0.0842266	+	0.215848i
$67$	−0.750324	−	8.15089i	−0.0916667	−	0.995790i
$67$	−0.750324	−	8.15089i	−0.0916667	−	0.995790i
$68$	−9.37697	−	8.63245i	−1.13712	−	1.04684i
$69$	−3.94074	+	2.27519i	−0.474409	+	0.273900i
$70$	−3.52349	−	1.37491i	−0.421138	−	0.164333i
$71$	−8.55186	−	4.93742i	−1.01492	−	0.585964i	−0.102291	−	0.994755i	$-0.532617\pi$
$71$	−8.55186	−	4.93742i	−1.01492	−	0.585964i	−0.912628	+	0.408791i	$0.865951\pi$
$72$	−2.54107	+	1.24216i	−0.299468	+	0.146390i
$73$	−2.61035	−	4.52126i	−0.305518	−	0.529173i	0.671858	−	0.740680i	$-0.265496\pi$
$73$	−2.61035	−	4.52126i	−0.305518	−	0.529173i	−0.977377	+	0.211506i	$0.932163\pi$
$74$	6.57297	+	8.20921i	0.764092	+	0.954301i
$75$	−1.07533			−0.124169
$76$	3.09322	−	3.36000i	0.354817	−	0.385419i
$77$	−0.898431	−	1.55613i	−0.102386	−	0.177337i
$78$	0.992537	−	0.794707i	0.112383	−	0.0899829i
$79$	−3.18040	+	5.50861i	−0.357823	+	0.619767i	−0.987597	−	0.157011i	$-0.949814\pi$
$79$	−3.18040	+	5.50861i	−0.357823	+	0.619767i	0.629774	+	0.776778i	$0.283147\pi$
$80$	−4.51508	−	6.51220i	−0.504802	−	0.728086i
$81$	1.00000			0.111111
$82$	14.1371	+	5.51648i	1.56118	+	0.609194i
$83$	−6.27859	+	3.62494i	−0.689164	+	0.397889i	−0.803299	−	0.595576i	$-0.796924\pi$
$83$	−6.27859	+	3.62494i	−0.689164	+	0.397889i	0.114135	+	0.993465i	$0.463590\pi$
$84$	0.590489	−	2.63463i	0.0644277	−	0.287462i
$85$	−10.9335	+	6.31244i	−1.18590	+	0.684680i
$86$	11.7430	−	1.79351i	1.26628	−	0.193399i
$87$	2.25494	−	3.90567i	0.241755	−	0.418731i
$88$	0.259269	−	3.75573i	0.0276382	−	0.400362i
$89$	−10.7873			−1.14345			−0.571726	−	0.820445i	$-0.693726\pi$
$89$	−10.7873			−1.14345			−0.571726	+	0.820445i	$0.693726\pi$
$90$	0.422992	+	2.76955i	0.0445873	+	0.291936i
$91$			1.21376i			0.127236i
$92$	6.16389	−	6.69551i	0.642630	−	0.698055i
$93$	4.24278	−	7.34872i	0.439956	−	0.762027i
$94$	2.76398	+	1.07854i	0.285083	+	0.111243i
$95$	−2.26190	−	3.91773i	−0.232067	−	0.401951i
$96$	4.10889	−	3.88806i	0.419362	−	0.396824i
$97$	−0.310273	+	0.179136i	−0.0315034	+	0.0181885i	−0.515669	−	0.856788i	$-0.672457\pi$
$97$	−0.310273	+	0.179136i	−0.0315034	+	0.0181885i	0.484166	+	0.874976i	$0.339123\pi$
$98$	−4.57646	−	5.71569i	−0.462292	−	0.577372i
$99$	−0.665505	+	1.15269i	−0.0668858	+	0.115850i
$100$	2.05261	−	0.641964i	0.205261	−	0.0641964i
$101$	−1.65528	−	0.955675i	−0.164706	−	0.0950933i	0.415381	−	0.909648i	$-0.363648\pi$
$101$	−1.65528	−	0.955675i	−0.164706	−	0.0950933i	−0.580087	+	0.814554i	$0.696982\pi$
$102$	−5.63293	−	7.03516i	−0.557743	−	0.696585i
$103$	−10.3068	−	5.95066i	−1.01556	−	0.586336i	−0.102748	−	0.994707i	$-0.532763\pi$
$103$	−10.3068	−	5.95066i	−1.01556	−	0.586336i	−0.912816	+	0.408371i	$0.866097\pi$
$104$	−1.42014	+	2.10949i	−0.139256	+	0.206853i
$105$	−2.31614	−	1.33723i	−0.226032	−	0.130500i
$106$	1.85736	+	12.1611i	0.180403	+	1.18119i
$107$		−	11.4174i		−	1.10376i	−0.833924	−	0.551880i	$-0.813911\pi$
$107$		−	11.4174i		−	1.10376i	0.833924	−	0.551880i	$-0.186089\pi$
$108$	−1.90882	+	0.596993i	−0.183676	+	0.0574456i
$109$		−	10.4511i		−	1.00103i	−0.865727	−	0.500516i	$-0.833144\pi$
$109$		−	10.4511i		−	1.00103i	0.865727	−	0.500516i	$-0.166856\pi$
$110$	−3.47393	−	1.35557i	−0.331227	−	0.129249i
$111$	3.71811	+	6.43996i	0.352908	+	0.611254i
$112$	0.445719	+	5.38157i	0.0421164	+	0.508510i
$113$	6.36392	+	3.67421i	0.598667	+	0.345640i	0.768517	−	0.639829i	$-0.220995\pi$
$113$	6.36392	+	3.67421i	0.598667	+	0.345640i	−0.169850	+	0.985470i	$0.554328\pi$
$114$	2.52087	−	2.01842i	0.236102	−	0.189042i
$115$	−4.50732	−	7.80691i	−0.420310	−	0.727998i
$116$	−1.97262	+	8.80140i	−0.183153	+	0.817189i
$117$	0.778626	−	0.449540i	0.0719840	−	0.0415600i
$118$	0.641983	+	4.20340i	0.0590994	+	0.386954i
$119$	8.60317			0.788652
$120$	−2.46082	−	5.03406i	−0.224641	−	0.459544i
$121$	4.61421	+	7.99204i	0.419473	+	0.726549i
$122$	−5.49572	+	4.40032i	−0.497559	+	0.398387i
$123$	9.29294	+	5.36528i	0.837916	+	0.483771i
$124$	−3.71159	+	16.5603i	−0.333311	+	1.48716i
$125$		−	12.0357i		−	1.07651i
$126$	0.694021	−	1.77857i	0.0618283	−	0.158448i
$127$	−6.96529	−	4.02141i	−0.618069	−	0.356843i	0.158048	−	0.987432i	$-0.449480\pi$
$127$	−6.96529	−	4.02141i	−0.618069	−	0.356843i	−0.776117	+	0.630589i	$0.782813\pi$
$128$	−5.52199	+	9.87460i	−0.488079	+	0.872799i
$129$	8.39986			0.739566
$130$	1.57438	+	1.96629i	0.138082	+	0.172455i
$131$			6.35082i			0.554874i	0.960744	+	0.277437i	$0.0894849\pi$
$131$			6.35082i			0.554874i	−0.960744	+	0.277437i	$0.910515\pi$
$132$	0.582184	−	2.59758i	0.0506726	−	0.226090i
$133$			3.08273i			0.267307i
$134$	2.78930	+	11.2348i	0.240959	+	0.970535i
$135$			1.98108i			0.170504i
$136$	14.9522	+	10.0660i	1.28214	+	0.863156i
$137$			18.7146i			1.59890i	0.600735	+	0.799448i	$0.294875\pi$
$137$			18.7146i			1.59890i	−0.600735	+	0.799448i	$0.705125\pi$
$138$	5.02337	−	4.02213i	0.427618	−	0.342386i
$139$	−9.28148			−0.787245			−0.393622	−	0.919272i	$-0.628778\pi$
$139$	−9.28148			−0.787245			−0.393622	+	0.919272i	$0.628778\pi$
$140$	5.21942	+	1.16981i	0.441121	+	0.0988666i
$141$	1.81688	+	1.04898i	0.153009	+	0.0883399i
$142$	13.0097	+	5.07656i	1.09175	+	0.426016i
$143$			1.19668i			0.100072i
$144$	3.28720	−	2.27910i	0.273933	−	0.189925i
$145$	7.73743	+	4.46721i	0.642558	+	0.370981i
$146$	4.61464	+	5.76338i	0.381910	+	0.476981i
$147$	−2.58875	−	4.48385i	−0.213517	−	0.369822i
$148$	−10.9418	−	10.0731i	−0.899413	−	0.828000i
$149$	7.54238			0.617896			0.308948	−	0.951079i	$-0.400023\pi$
$149$	7.54238			0.617896			0.308948	+	0.951079i	$0.400023\pi$
$150$	1.50332	−	0.229601i	0.122745	−	0.0187468i
$151$	−1.61302	+	0.931279i	−0.131266	+	0.0757864i	−0.564195	−	0.825642i	$-0.690813\pi$
$151$	−1.61302	+	0.931279i	−0.131266	+	0.0757864i	0.432929	+	0.901428i	$0.357480\pi$
$152$	−3.60692	+	5.35775i	−0.292560	+	0.434571i
$153$	−3.18636	−	5.51895i	−0.257602	−	0.446180i
$154$	1.58827	+	1.98364i	0.127986	+	0.159846i
$155$	14.5584	+	8.40529i	1.16936	+	0.675129i
$156$	−1.21789	+	1.32293i	−0.0975089	+	0.105919i
$157$	−4.40978	−	7.63796i	−0.351939	−	0.609576i	0.634650	−	0.772799i	$-0.281144\pi$
$157$	−4.40978	−	7.63796i	−0.351939	−	0.609576i	−0.986589	+	0.163224i	$0.947811\pi$
$158$	3.27003	−	8.38012i	0.260149	−	0.666687i
$159$			8.69893i			0.689870i
$160$	7.70256	+	8.14003i	0.608941	+	0.643526i
$161$			6.14299i			0.484136i
$162$	−1.39800	+	0.213516i	−0.109837	+	0.0167754i
$163$	6.63190	+	3.82893i	0.519450	+	0.299905i	0.736710	−	0.676209i	$-0.236378\pi$
$163$	6.63190	+	3.82893i	0.519450	+	0.299905i	−0.217259	+	0.976114i	$0.569712\pi$
$164$	−20.9416	−	4.69355i	−1.63526	−	0.366505i
$165$	−2.28357	−	1.31842i	−0.177775	−	0.102639i
$166$	8.00349	−	6.40826i	0.621192	−	0.497377i
$167$	8.11423	+	4.68475i	0.627898	+	0.362517i	0.779938	−	0.625857i	$-0.215251\pi$
$167$	8.11423	+	4.68475i	0.627898	+	0.362517i	−0.152039	+	0.988374i	$0.548584\pi$
$168$	−0.262968	+	3.80930i	−0.0202884	+	0.293894i
$169$	−6.09583	+	10.5583i	−0.468910	+	0.812176i
$170$	13.9372	−	11.1593i	1.06893	−	0.855877i
$171$	1.97758	−	1.14175i	0.151229	−	0.0873122i
$172$	−16.0338	+	5.01465i	−1.22257	+	0.382364i
$173$	0.690590	+	1.19614i	0.0525046	+	0.0909406i	0.891083	−	0.453840i	$-0.149946\pi$
$173$	0.690590	+	1.19614i	0.0525046	+	0.0909406i	−0.838579	+	0.544781i	$0.816613\pi$
$174$	−2.31848	+	5.94160i	−0.175764	+	0.450431i
$175$	−0.725847	+	1.25720i	−0.0548689	+	0.0950357i
$176$	0.439449	+	5.30587i	0.0331248	+	0.399945i
$177$			3.00672i			0.225999i
$178$	15.0807	−	2.30326i	1.13034	−	0.172637i
$179$	6.96594			0.520659			0.260329	−	0.965520i	$-0.416169\pi$
$179$	6.96594			0.520659			0.260329	+	0.965520i	$0.416169\pi$
$180$	−1.18269	−	3.78152i	−0.0881524	−	0.281858i
$181$	8.09158	−	14.0150i	0.601442	−	1.04173i	−0.391161	−	0.920322i	$-0.627926\pi$
$181$	8.09158	−	14.0150i	0.601442	−	1.04173i	0.992603	−	0.121406i	$-0.0387403\pi$
$182$	−0.259157	−	1.69683i	−0.0192100	−	0.125778i
$183$	−4.31128	+	2.48912i	−0.318699	+	0.184001i
$184$	−7.18754	+	10.6764i	−0.529872	+	0.787077i
$185$	−12.7581	+	7.36587i	−0.937992	+	0.541550i
$186$	−4.36235	+	11.1794i	−0.319863	+	0.819716i
$187$	8.48217			0.620278
$188$	−4.09434	−	0.917647i	−0.298610	−	0.0669263i
$189$	0.674999	−	1.16913i	0.0490990	−	0.0850419i
$190$	3.99865	+	4.99405i	0.290092	+	0.362306i
$191$	3.06855	+	5.31488i	0.222032	+	0.384571i	0.955425	−	0.295234i	$-0.0953976\pi$
$191$	3.06855	+	5.31488i	0.222032	+	0.384571i	−0.733393	+	0.679805i	$0.762064\pi$
$192$	−4.91407	+	6.31284i	−0.354642	+	0.455590i
$193$	3.37238			0.242749			0.121375	−	0.992607i	$-0.461270\pi$
$193$	3.37238			0.242749			0.121375	+	0.992607i	$0.461270\pi$
$194$	0.395514	−	0.316681i	0.0283962	−	0.0227364i
$195$	0.890573	+	1.54252i	0.0637753	+	0.110462i
$196$	7.61829	+	7.01341i	0.544164	+	0.500958i
$197$	17.0373	+	9.83648i	1.21386	+	0.700820i	0.963597	−	0.267359i	$-0.0861509\pi$
$197$	17.0373	+	9.83648i	1.21386	+	0.700820i	0.250259	+	0.968179i	$0.419484\pi$
$198$	0.684260	−	1.75356i	0.0486282	−	0.124620i
$199$	19.0932	−	11.0235i	1.35348	−	0.781432i	0.364744	−	0.931108i	$-0.381156\pi$
$199$	19.0932	−	11.0235i	1.35348	−	0.781432i	0.988735	+	0.149676i	$0.0478230\pi$
$200$	−2.73249	+	1.33573i	−0.193216	+	0.0944507i
$201$	0.750324	+	8.15089i	0.0529238	+	0.574919i
$202$	2.51814	+	0.982608i	0.177175	+	0.0691360i
$203$	−3.04416	−	5.27264i	−0.213658	−	0.370067i
$204$	9.37697	+	8.63245i	0.656519	+	0.604392i
$205$	−10.6290	+	18.4100i	−0.742364	+	1.28581i
$206$	15.6796	+	6.11836i	1.09245	+	0.426286i
$207$	3.94074	−	2.27519i	0.273900	−	0.158136i
$208$	1.53495	−	3.25230i	0.106430	−	0.225506i
$209$			3.03937i			0.210238i
$210$	3.52349	+	1.37491i	0.243144	+	0.0948778i
$211$	20.1483	−	11.6326i	1.38707	−	0.800824i	0.394084	−	0.919074i	$-0.371062\pi$
$211$	20.1483	−	11.6326i	1.38707	−	0.800824i	0.992984	+	0.118251i	$0.0377286\pi$
$212$	−5.19320	−	16.6047i	−0.356670	−	1.14042i
$213$	8.55186	+	4.93742i	0.585964	+	0.338306i
$214$	2.43780	+	15.9615i	0.166644	+	1.09111i
$215$			16.6408i			1.13489i
$216$	2.54107	−	1.24216i	0.172898	−	0.0845184i
$217$	−5.72775	−	9.92076i	−0.388825	−	0.673465i
$218$	2.23148	+	14.6106i	0.151135	+	0.989557i
$219$	2.61035	+	4.52126i	0.176391	+	0.305518i
$220$	5.14601	+	1.15335i	0.346944	+	0.0777590i
$221$	−4.96197	−	2.86480i	−0.333778	−	0.192707i
$222$	−6.57297	−	8.20921i	−0.441149	−	0.550966i
$223$		−	26.6186i		−	1.78251i	−0.453500	−	0.891256i	$-0.649825\pi$
$223$		−	26.6186i		−	1.78251i	0.453500	−	0.891256i	$-0.350175\pi$
$224$	−1.77217	−	7.42827i	−0.118408	−	0.496322i
$225$	1.07533			0.0716887
$226$	−9.68127	−	3.77775i	−0.643989	−	0.251292i
$227$	−18.8726	−	10.8961i	−1.25262	−	0.723199i	−0.280988	−	0.959711i	$-0.590662\pi$
$227$	−18.8726	−	10.8961i	−1.25262	−	0.723199i	−0.971628	+	0.236513i	$0.923996\pi$
$228$	−3.09322	+	3.36000i	−0.204854	+	0.222522i
$229$	−5.84003	+	3.37174i	−0.385920	+	0.222811i	−0.680391	−	0.732850i	$-0.738190\pi$
$229$	−5.84003	+	3.37174i	−0.385920	+	0.222811i	0.294471	+	0.955660i	$0.404857\pi$
$230$	7.96814	+	9.95169i	0.525404	+	0.656195i
$231$	0.898431	+	1.55613i	0.0591124	+	0.102386i
$232$	0.878485	−	12.7256i	0.0576754	−	0.835474i
$233$	1.15476	+	0.666702i	0.0756509	+	0.0436771i	0.537348	−	0.843360i	$-0.319426\pi$
$233$	1.15476	+	0.666702i	0.0756509	+	0.0436771i	−0.461697	+	0.887038i	$0.652759\pi$
$234$	−0.992537	+	0.794707i	−0.0648842	+	0.0519516i
$235$	−2.07811	+	3.59939i	−0.135561	+	0.234798i
$236$	−1.79499	−	5.73929i	−0.116844	−	0.373596i
$237$	3.18040	−	5.50861i	0.206589	−	0.357823i
$238$	−12.0273	+	1.83692i	−0.779611	+	0.119070i
$239$	1.58989	−	2.75377i	0.102841	−	0.178127i	−0.810013	−	0.586412i	$-0.800540\pi$
$239$	1.58989	−	2.75377i	0.102841	−	0.178127i	0.912854	+	0.408286i	$0.133873\pi$
$240$	4.51508	+	6.51220i	0.291447	+	0.420361i
$241$	−10.7931			−0.695244			−0.347622	−	0.937635i	$-0.613011\pi$
$241$	−10.7931			−0.695244			−0.347622	+	0.937635i	$0.613011\pi$
$242$	−8.15710	−	10.1877i	−0.524358	−	0.654889i
$243$	−1.00000			−0.0641500
$244$	6.74348	−	7.32509i	0.431707	−	0.468941i
$245$	8.88286	−	5.12852i	0.567505	−	0.327649i
$246$	−14.1371	−	5.51648i	−0.901350	−	0.351718i
$247$	1.02653	−	1.77800i	0.0653165	−	0.113131i
$248$	1.65292	−	23.9438i	0.104960	−	1.52043i
$249$	6.27859	−	3.62494i	0.397889	−	0.229721i
$250$	2.56982	+	16.8259i	0.162530	+	1.06417i
$251$	3.38730	+	5.86698i	0.213805	+	0.370321i	0.952902	−	0.303278i	$-0.0980810\pi$
$251$	3.38730	+	5.86698i	0.213805	+	0.370321i	−0.739097	+	0.673599i	$0.764748\pi$
$252$	−0.590489	+	2.63463i	−0.0371973	+	0.165966i
$253$			6.05659i			0.380775i
$254$	10.5961	+	4.13474i	0.664860	+	0.259437i
$255$	10.9335	−	6.31244i	0.684680	−	0.395300i
$256$	5.61137	−	14.9837i	0.350710	−	0.936484i
$257$	−12.6711	+	21.9470i	−0.790403	+	1.36902i	0.135315	+	0.990803i	$0.456795\pi$
$257$	−12.6711	+	21.9470i	−0.790403	+	1.36902i	−0.925718	+	0.378215i	$0.876538\pi$
$258$	−11.7430	+	1.79351i	−0.731089	+	0.111659i
$259$	10.0389			0.623786
$260$	−2.62082	−	2.41273i	−0.162536	−	0.149631i
$261$	−2.25494	+	3.90567i	−0.139577	+	0.241755i
$262$	−1.35600	−	8.87846i	−0.0837742	−	0.548513i
$263$			22.6729i			1.39807i	0.715087	+	0.699035i	$0.246387\pi$
$263$			22.6729i			1.39807i	−0.715087	+	0.699035i	$0.753613\pi$
$264$	−0.259269	+	3.75573i	−0.0159569	+	0.231149i
$265$	−17.2333			−1.05863
$266$	−0.658214	−	4.30967i	−0.0403577	−	0.264243i
$267$	10.7873			0.660172
$268$	−6.29826	−	15.1107i	−0.384727	−	0.923030i
$269$	17.6052			1.07341			0.536704	−	0.843770i	$-0.319669\pi$
$269$	17.6052			1.07341			0.536704	+	0.843770i	$0.319669\pi$
$270$	−0.422992	−	2.76955i	−0.0257425	−	0.168550i
$271$	−17.6983			−1.07510			−0.537549	−	0.843232i	$-0.680650\pi$
$271$	−17.6983			−1.07510			−0.537549	+	0.843232i	$0.680650\pi$
$272$	−23.0525	−	10.8798i	−1.39776	−	0.659686i
$273$		−	1.21376i		−	0.0734598i
$274$	−3.99587	−	26.1631i	−0.241400	−	1.58057i
$275$	−0.715638	+	1.23952i	−0.0431546	+	0.0747460i
$276$	−6.16389	+	6.69551i	−0.371023	+	0.403023i
$277$	27.9713			1.68063			0.840317	−	0.542096i	$-0.182369\pi$
$277$	27.9713			1.68063			0.840317	+	0.542096i	$0.182369\pi$
$278$	12.9755	−	1.98175i	0.778221	−	0.118857i
$279$	−4.24278	+	7.34872i	−0.254009	+	0.439956i
$280$	−7.54653	−	0.520960i	−0.450991	−	0.0311333i
$281$	22.2749	−	12.8604i	1.32881	−	0.767190i	0.343696	−	0.939081i	$-0.388321\pi$
$281$	22.2749	−	12.8604i	1.32881	−	0.767190i	0.985116	+	0.171891i	$0.0549878\pi$
$282$	−2.76398	−	1.07854i	−0.164593	−	0.0642261i
$283$		−	3.99127i		−	0.237257i	−0.992939	−	0.118628i	$-0.962150\pi$
$283$		−	3.99127i		−	0.237257i	0.992939	−	0.118628i	$-0.0378497\pi$
$284$	−19.2716	−	4.31925i	−1.14356	−	0.256301i
$285$	2.26190	+	3.91773i	0.133984	+	0.232067i
$286$	−0.255512	−	1.67297i	−0.0151087	−	0.0989246i
$287$	12.5455	−	7.24312i	0.740535	−	0.427548i
$288$	−4.10889	+	3.88806i	−0.242119	+	0.229106i
$289$	−11.8058	+	20.4483i	−0.694461	+	1.20284i
$290$	−11.7708	−	4.59310i	−0.691203	−	0.269716i
$291$	0.310273	−	0.179136i	0.0181885	−	0.0105011i
$292$	−7.68185	−	7.07192i	−0.449546	−	0.413853i
$293$	−10.0828			−0.589042			−0.294521	−	0.955645i	$-0.595160\pi$
$293$	−10.0828			−0.589042			−0.294521	+	0.955645i	$0.595160\pi$
$294$	4.57646	+	5.71569i	0.266904	+	0.333346i
$295$	−5.95654			−0.346803
$296$	17.4475	+	11.7459i	1.01411	+	0.682716i
$297$	0.665505	−	1.15269i	0.0386165	−	0.0668858i
$298$	−10.5443	+	1.61042i	−0.610813	+	0.0932892i
$299$	2.04557	−	3.54304i	0.118299	−	0.204899i
$300$	−2.05261	+	0.641964i	−0.118508	+	0.0370638i
$301$	5.66990	−	9.82055i	0.326807	−	0.566047i
$302$	2.05617	−	1.64634i	0.118319	−	0.0947361i
$303$	1.65528	+	0.955675i	0.0950933	+	0.0549021i
$304$	3.89851	−	8.26028i	0.223595	−	0.473760i
$305$	−4.93114	−	8.54098i	−0.282356	−	0.489055i
$306$	5.63293	+	7.03516i	0.322013	+	0.402173i
$307$	−8.52684	+	4.92297i	−0.486652	+	0.280969i	−0.723185	−	0.690655i	$-0.757322\pi$
$307$	−8.52684	+	4.92297i	−0.486652	+	0.280969i	0.236532	+	0.971624i	$0.423989\pi$
$308$	−2.64394	−	2.43401i	−0.150652	−	0.138691i
$309$	10.3068	+	5.95066i	0.586336	+	0.338521i
$310$	−22.1473	−	8.64216i	−1.25788	−	0.490842i
$311$	7.21137			0.408919			0.204460	−	0.978875i	$-0.434456\pi$
$311$	7.21137			0.408919			0.204460	+	0.978875i	$0.434456\pi$
$312$	1.42014	−	2.10949i	0.0803997	−	0.119426i
$313$			5.05347i			0.285639i	0.989749	+	0.142820i	$0.0456169\pi$
$313$			5.05347i			0.285639i	−0.989749	+	0.142820i	$0.954383\pi$
$314$	7.79571	+	9.73633i	0.439937	+	0.549453i
$315$	2.31614	+	1.33723i	0.130500	+	0.0753441i
$316$	−2.78221	+	12.4136i	−0.156512	+	0.698321i
$317$	12.5631	+	21.7600i	0.705616	+	1.22216i	0.966469	+	0.256784i	$0.0826629\pi$
$317$	12.5631	+	21.7600i	0.705616	+	1.22216i	−0.260853	+	0.965379i	$0.584004\pi$
$318$	−1.85736	−	12.1611i	−0.104156	−	0.681962i
$319$	−3.00134	−	5.19848i	−0.168043	−	0.291059i
$320$	−12.5062	−	9.73515i	−0.699119	−	0.544212i
$321$			11.4174i			0.637256i
$322$	−1.31163	−	8.58792i	−0.0730942	−	0.478586i
$323$	−12.6026	−	7.27609i	−0.701225	−	0.404853i
$324$	1.90882	−	0.596993i	0.106046	−	0.0331663i
$325$	0.837280	−	0.483404i	0.0464440	−	0.0268144i
$326$	−10.0889	−	3.93683i	−0.558775	−	0.218041i
$327$			10.4511i			0.577946i
$328$	30.2786	+	2.09022i	1.67185	+	0.115413i
$329$	2.45279	−	1.41612i	0.135227	−	0.0780732i
$330$	3.47393	+	1.35557i	0.191234	+	0.0746218i
$331$	13.2553	−	22.9588i	0.728576	−	1.26193i	−0.228910	−	0.973448i	$-0.573516\pi$
$331$	13.2553	−	22.9588i	0.728576	−	1.26193i	0.957485	−	0.288482i	$-0.0931507\pi$
$332$	−9.82064	+	10.6676i	−0.538977	+	0.585463i
$333$	−3.71811	−	6.43996i	−0.203751	−	0.352908i
$334$	−12.3440	−	4.81678i	−0.675433	−	0.263562i
$335$	−16.1475	+	1.48645i	−0.882235	+	0.0812135i
$336$	−0.445719	−	5.38157i	−0.0243159	−	0.293588i
$337$	9.11887	−	5.26478i	0.496737	−	0.286791i	−0.230628	−	0.973042i	$-0.574078\pi$
$337$	9.11887	−	5.26478i	0.496737	−	0.286791i	0.727365	+	0.686251i	$0.240745\pi$
$338$	6.26762	−	16.0621i	0.340913	−	0.873661i
$339$	−6.36392	−	3.67421i	−0.345640	−	0.199556i
$340$	−17.1015	+	18.5765i	−0.927462	+	1.00745i
$341$	−5.64719	−	9.78122i	−0.305812	−	0.529683i
$342$	−2.52087	+	2.01842i	−0.136313	+	0.109144i
$343$	−16.4396			−0.887655
$344$	21.3446	−	10.4340i	1.15083	−	0.562563i
$345$	4.50732	+	7.80691i	0.242666	+	0.420310i
$346$	−1.22084	−	1.52475i	−0.0656328	−	0.0819711i
$347$	−9.43468	+	16.3413i	−0.506480	+	0.877250i	0.493492	+	0.869751i	$0.335720\pi$
$347$	−9.43468	+	16.3413i	−0.506480	+	0.877250i	−0.999972	+	0.00749900i	$0.997613\pi$
$348$	1.97262	−	8.80140i	0.105743	−	0.471805i
$349$	−19.2298			−1.02935			−0.514673	−	0.857387i	$-0.672087\pi$
$349$	−19.2298			−1.02935			−0.514673	+	0.857387i	$0.672087\pi$
$350$	0.746303	−	1.91255i	0.0398916	−	0.102230i
$351$	−0.778626	+	0.449540i	−0.0415600	+	0.0239947i
$352$	−1.74724	−	7.32379i	−0.0931283	−	0.390360i
$353$	17.5882	−	10.1545i	0.936124	−	0.540472i	0.0473811	−	0.998877i	$-0.484912\pi$
$353$	17.5882	−	10.1545i	0.936124	−	0.540472i	0.888743	+	0.458405i	$0.151579\pi$
$354$	−0.641983	−	4.20340i	−0.0341210	−	0.223408i
$355$	−9.78141	+	16.9419i	−0.519143	+	0.899183i
$356$	−20.5910	+	6.43994i	−1.09132	+	0.341316i
$357$	−8.60317			−0.455328
$358$	−9.73840	+	1.48734i	−0.514690	+	0.0786084i
$359$			1.45426i			0.0767530i	0.999263	+	0.0383765i	$0.0122186\pi$
$359$			1.45426i			0.0767530i	−0.999263	+	0.0383765i	$0.987781\pi$
$360$	2.46082	+	5.03406i	0.129697	+	0.265318i
$361$	−6.89279	+	11.9387i	−0.362779	+	0.628351i
$362$	−8.31961	+	21.3207i	−0.437269	+	1.12059i
$363$	−4.61421	−	7.99204i	−0.242183	−	0.419473i
$364$	0.724603	+	2.31684i	0.0379795	+	0.121436i
$365$	−8.95696	+	5.17131i	−0.468829	+	0.270679i
$366$	5.49572	−	4.40032i	0.287266	−	0.230009i
$367$	4.83904	−	8.38147i	0.252596	−	0.437509i	−0.711644	−	0.702540i	$-0.752049\pi$
$367$	4.83904	−	8.38147i	0.252596	−	0.437509i	0.964240	+	0.265031i	$0.0853823\pi$
$368$	7.76860	−	16.4603i	0.404966	−	0.858054i
$369$	−9.29294	−	5.36528i	−0.483771	−	0.279305i
$370$	16.2631	−	13.0216i	0.845477	−	0.676959i
$371$	10.1702	+	5.87177i	0.528011	+	0.304847i
$372$	3.71159	−	16.5603i	0.192437	−	0.858612i
$373$	−3.22896	−	1.86424i	−0.167189	−	0.0965267i	0.414071	−	0.910245i	$-0.364107\pi$
$373$	−3.22896	−	1.86424i	−0.167189	−	0.0965267i	−0.581260	+	0.813718i	$0.697440\pi$
$374$	−11.8581	+	1.81108i	−0.613167	+	0.0936488i
$375$			12.0357i			0.621521i
$376$	5.91983	+	0.408664i	0.305292	+	0.0210752i
$377$			4.05474i			0.208830i
$378$	−0.694021	+	1.77857i	−0.0356966	+	0.0914799i
$379$	5.08937	+	8.81505i	0.261424	+	0.452799i	0.966620	−	0.256213i	$-0.0824747\pi$
$379$	5.08937	+	8.81505i	0.261424	+	0.452799i	−0.705197	+	0.709012i	$0.749141\pi$
$380$	−6.65643	−	6.12792i	−0.341468	−	0.314355i
$381$	6.96529	+	4.02141i	0.356843	+	0.206023i
$382$	−5.42465	−	6.77503i	−0.277549	−	0.346641i
$383$	−1.28210	−	2.22066i	−0.0655122	−	0.113470i	0.831409	−	0.555661i	$-0.187535\pi$
$383$	−1.28210	−	2.22066i	−0.0655122	−	0.113470i	−0.896921	+	0.442191i	$0.854201\pi$
$384$	5.52199	−	9.87460i	0.281793	−	0.503911i
$385$	−3.08281	+	1.77986i	−0.157115	+	0.0907101i
$386$	−4.71460	+	0.720058i	−0.239967	+	0.0366500i
$387$	−8.39986			−0.426989
$388$	−0.485312	+	0.527169i	−0.0246380	+	0.0267630i
$389$	−4.22185	−	7.31246i	−0.214056	−	0.370756i	0.738924	−	0.673789i	$-0.235334\pi$
$389$	−4.22185	−	7.31246i	−0.214056	−	0.370756i	−0.952980	+	0.303033i	$0.902001\pi$
$390$	−1.57438	−	1.96629i	−0.0797217	−	0.0995671i
$391$	−25.1132	−	14.4991i	−1.27003	−	0.733253i
$392$	−12.1479	−	8.17813i	−0.613560	−	0.413058i
$393$		−	6.35082i		−	0.320357i
$394$	−25.9184	−	10.1137i	−1.30575	−	0.509520i
$395$	10.9130	+	6.30062i	0.549092	+	0.317018i
$396$	−0.582184	+	2.59758i	−0.0292558	+	0.130533i
$397$	33.6318			1.68793			0.843967	−	0.536395i	$-0.180214\pi$
$397$	33.6318			1.68793			0.843967	+	0.536395i	$0.180214\pi$
$398$	−24.3386	+	19.4875i	−1.21998	+	0.976821i
$399$		−	3.08273i		−	0.154330i
$400$	3.53483	−	2.45079i	0.176741	−	0.122540i
$401$		−	7.04872i		−	0.351996i	−0.984391	−	0.175998i	$-0.943685\pi$
$401$		−	7.04872i		−	0.351996i	0.984391	−	0.175998i	$-0.0563152\pi$
$402$	−2.78930	−	11.2348i	−0.139118	−	0.560339i
$403$			7.62920i			0.380038i
$404$	−3.73016	−	0.836025i	−0.185582	−	0.0415938i
$405$		−	1.98108i		−	0.0984405i
$406$	5.38154	+	6.72119i	0.267081	+	0.333567i
$407$	9.89770			0.490611
$408$	−14.9522	−	10.0660i	−0.740244	−	0.498344i
$409$	−3.58909	−	2.07216i	−0.177469	−	0.102462i	0.408634	−	0.912698i	$-0.366005\pi$
$409$	−3.58909	−	2.07216i	−0.177469	−	0.102462i	−0.586103	+	0.810237i	$0.699339\pi$
$410$	10.9286	−	28.0068i	0.539724	−	1.38315i
$411$		−	18.7146i		−	0.923123i
$412$	−23.2264	−	5.20564i	−1.14428	−	0.256463i
$413$	3.51525	+	2.02953i	0.172974	+	0.0998668i
$414$	−5.02337	+	4.02213i	−0.246885	+	0.197677i
$415$	7.18129	+	12.4384i	0.352516	+	0.610575i
$416$	−1.45145	+	4.87446i	−0.0711630	+	0.238990i
$417$	9.28148			0.454516
$418$	−0.648956	−	4.24905i	−0.0317415	−	0.207828i
$419$	16.3938	−	9.46496i	0.800889	−	0.462394i	−0.0428927	−	0.999080i	$-0.513657\pi$
$419$	16.3938	−	9.46496i	0.800889	−	0.462394i	0.843782	+	0.536686i	$0.180324\pi$
$420$	−5.21942	−	1.16981i	−0.254681	−	0.0570806i
$421$	−2.02661	−	3.51020i	−0.0987711	−	0.171077i	0.812405	−	0.583093i	$-0.198158\pi$
$421$	−2.02661	−	3.51020i	−0.0987711	−	0.171077i	−0.911176	+	0.412017i	$0.864825\pi$
$422$	−25.6836	+	20.5645i	−1.25026	+	1.00106i
$423$	−1.81688	−	1.04898i	−0.0883399	−	0.0510031i
$424$	10.8055	+	22.1046i	0.524760	+	1.07349i
$425$	−3.42640	−	5.93469i	−0.166205	−	0.287875i
$426$	−13.0097	−	5.07656i	−0.630324	−	0.245960i
$427$			6.72061i			0.325233i
$428$	−6.81609	−	21.7937i	−0.329468	−	1.05344i
$429$		−	1.19668i		−	0.0577765i
$430$	−3.55308	−	23.2638i	−0.171345	−	1.12188i
$431$	−20.9848	−	12.1156i	−1.01080	−	0.583588i	−0.0993771	−	0.995050i	$-0.531685\pi$
$431$	−20.9848	−	12.1156i	−1.01080	−	0.583588i	−0.911427	+	0.411462i	$0.865018\pi$
$432$	−3.28720	+	2.27910i	−0.158155	+	0.109653i
$433$	−6.08984	−	3.51597i	−0.292659	−	0.168967i	0.346481	−	0.938057i	$-0.387376\pi$
$433$	−6.08984	−	3.51597i	−0.292659	−	0.168967i	−0.639140	+	0.769090i	$0.720710\pi$
$434$	10.1257	+	12.6463i	0.486047	+	0.607040i
$435$	−7.73743	−	4.46721i	−0.370981	−	0.214186i
$436$	−6.23922	−	19.9493i	−0.298804	−	0.955396i
$437$	5.19541	−	8.99871i	0.248530	−	0.430467i
$438$	−4.61464	−	5.76338i	−0.220496	−	0.275385i
$439$	−12.0099	+	6.93391i	−0.573200	+	0.330937i	−0.758427	−	0.651758i	$-0.774032\pi$
$439$	−12.0099	+	6.93391i	−0.573200	+	0.330937i	0.185226	+	0.982696i	$0.440698\pi$
$440$	−7.44039	−	0.513633i	−0.354707	−	0.0244865i
$441$	2.58875	+	4.48385i	0.123274	+	0.213517i
$442$	7.54853	+	2.94553i	0.359047	+	0.140105i
$443$	−7.44185	+	12.8897i	−0.353573	+	0.612406i	−0.986873	−	0.161500i	$-0.948367\pi$
$443$	−7.44185	+	12.8897i	−0.353573	+	0.612406i	0.633300	+	0.773907i	$0.281700\pi$
$444$	10.9418	+	10.0731i	0.519276	+	0.478046i
$445$			21.3705i			1.01306i
$446$	5.68350	+	37.2128i	0.269122	+	1.76208i
$447$	−7.54238			−0.356742
$448$	4.06355	+	10.0064i	0.191985	+	0.472756i
$449$	15.9441	−	27.6160i	0.752448	−	1.30328i	−0.194186	−	0.980965i	$-0.562206\pi$
$449$	15.9441	−	27.6160i	0.752448	−	1.30328i	0.946633	−	0.322313i	$-0.104460\pi$
$450$	−1.50332	+	0.229601i	−0.0708670	+	0.0108235i
$451$	12.3690	−	7.14124i	0.582433	−	0.336268i
$452$	14.3411	+	3.21420i	0.674546	+	0.151183i
$453$	1.61302	−	0.931279i	0.0757864	−	0.0437553i
$454$	28.7104	+	11.2032i	1.34745	+	0.525790i
$455$	2.40454			0.112727
$456$	3.60692	−	5.35775i	0.168909	−	0.250900i
$457$	−4.28836	+	7.42765i	−0.200601	+	0.347451i	−0.948722	−	0.316111i	$-0.897623\pi$
$457$	−4.28836	+	7.42765i	−0.200601	+	0.347451i	0.748121	+	0.663562i	$0.230956\pi$
$458$	7.44445	−	5.96064i	0.347856	−	0.278522i
$459$	3.18636	+	5.51895i	0.148727	+	0.257602i
$460$	−13.2643	−	12.2112i	−0.618453	−	0.569348i
$461$	33.1023			1.54173			0.770864	−	0.637000i	$-0.219825\pi$
$461$	33.1023			1.54173			0.770864	+	0.637000i	$0.219825\pi$
$462$	−1.58827	−	1.98364i	−0.0738928	−	0.0922873i
$463$	−16.0497	−	27.7989i	−0.745893	−	1.29192i	−0.949777	−	0.312929i	$-0.898690\pi$
$463$	−16.0497	−	27.7989i	−0.745893	−	1.29192i	0.203884	−	0.978995i	$-0.434644\pi$
$464$	1.48899	+	17.9779i	0.0691247	+	0.834605i
$465$	−14.5584	−	8.40529i	−0.675129	−	0.389786i
$466$	−1.75671	−	0.685490i	−0.0813781	−	0.0317547i
$467$	−3.93096	+	2.26954i	−0.181903	+	0.105022i	−0.588187	−	0.808725i	$-0.700158\pi$
$467$	−3.93096	+	2.26954i	−0.181903	+	0.105022i	0.406283	+	0.913747i	$0.366825\pi$
$468$	1.21789	−	1.32293i	0.0562968	−	0.0611522i
$469$	10.0359	+	4.62461i	0.463417	+	0.213545i
$470$	2.13667	−	5.47566i	0.0985573	−	0.252574i
$471$	4.40978	+	7.63796i	0.203192	+	0.351939i
$472$	3.73483	+	7.64028i	0.171910	+	0.351673i
$473$	5.59015	−	9.68242i	0.257035	−	0.445198i
$474$	−3.27003	+	8.38012i	−0.150197	+	0.384912i
$475$	2.12655	−	1.22776i	0.0975728	−	0.0563337i
$476$	16.4219	−	5.13603i	0.752698	−	0.235410i
$477$		−	8.69893i		−	0.398297i
$478$	−1.63470	+	4.18925i	−0.0747693	+	0.191612i
$479$	20.6264	−	11.9087i	0.942446	−	0.544121i	0.0517196	−	0.998662i	$-0.483530\pi$
$479$	20.6264	−	11.9087i	0.942446	−	0.544121i	0.890726	+	0.454540i	$0.150196\pi$
$480$	−7.70256	−	8.14003i	−0.351572	−	0.371540i
$481$	−5.79004	−	3.34288i	−0.264003	−	0.152422i
$482$	15.0888	−	2.30450i	0.687274	−	0.104967i
$483$		−	6.14299i		−	0.279516i
$484$	13.5789	+	12.5007i	0.617222	+	0.568215i
$485$	0.354882	+	0.614674i	0.0161144	+	0.0279109i
$486$	1.39800	−	0.213516i	0.0634147	−	0.00968529i
$487$	−9.05716	−	15.6875i	−0.410419	−	0.710867i	0.584517	−	0.811382i	$-0.301284\pi$
$487$	−9.05716	−	15.6875i	−0.410419	−	0.710867i	−0.994936	+	0.100515i	$0.967951\pi$
$488$	−7.86338	+	11.6803i	−0.355958	+	0.528744i
$489$	−6.63190	−	3.82893i	−0.299905	−	0.173150i
$490$	−11.3232	+	9.06632i	−0.511532	+	0.409575i
$491$		−	24.7459i		−	1.11677i	−0.829584	−	0.558383i	$-0.811422\pi$
$491$		−	24.7459i		−	1.11677i	0.829584	−	0.558383i	$-0.188578\pi$
$492$	20.9416	+	4.69355i	0.944120	+	0.211602i
$493$	28.7402			1.29439
$494$	−1.05546	+	2.70483i	−0.0474873	+	0.121696i
$495$	2.28357	+	1.31842i	0.102639	+	0.0592585i
$496$	2.80162	+	33.8265i	0.125796	+	1.51885i
$497$	11.5450	−	6.66551i	0.517864	−	0.298989i
$498$	−8.00349	+	6.40826i	−0.358645	+	0.287161i
$499$	−2.19295	−	3.79829i	−0.0981697	−	0.170035i	0.812757	−	0.582602i	$-0.197965\pi$
$499$	−2.19295	−	3.79829i	−0.0981697	−	0.170035i	−0.910927	+	0.412567i	$0.864632\pi$
$500$	−7.18522	−	22.9740i	−0.321333	−	1.02743i
$501$	−8.11423	−	4.68475i	−0.362517	−	0.209299i
$502$	−5.98815	−	7.47881i	−0.267264	−	0.333796i
$503$	−2.06918	+	3.58393i	−0.0922602	+	0.159799i	−0.908462	−	0.417968i	$-0.862742\pi$
$503$	−2.06918	+	3.58393i	−0.0922602	+	0.159799i	0.816202	+	0.577767i	$0.196076\pi$
$504$	0.262968	−	3.80930i	0.0117135	−	0.169680i
$505$	−1.89327	+	3.27924i	−0.0842493	+	0.145924i
$506$	−1.29318	−	8.46713i	−0.0574889	−	0.376410i
$507$	6.09583	−	10.5583i	0.270725	−	0.468910i
$508$	−15.6962	−	3.51793i	−0.696408	−	0.156083i
$509$	9.34555			0.414234			0.207117	−	0.978316i	$-0.433592\pi$
$509$	9.34555			0.414234			0.207117	+	0.978316i	$0.433592\pi$
$510$	−13.9372	+	11.1593i	−0.617149	+	0.494141i
$511$	7.04793			0.311782
$512$	−4.64543	+	22.1454i	−0.205301	+	0.978699i
$513$	−1.97758	+	1.14175i	−0.0873122	+	0.0504097i
$514$	13.0282	−	33.3875i	0.574650	−	1.47266i
$515$	−11.7887	+	20.4187i	−0.519473	+	0.899754i
$516$	16.0338	−	5.01465i	0.705850	−	0.220758i
$517$	2.41829	−	1.39620i	0.106356	−	0.0614049i
$518$	−14.0344	+	2.14347i	−0.616636	+	0.0941785i
$519$	−0.690590	−	1.19614i	−0.0303135	−	0.0525046i
$520$	4.17907	+	2.81341i	0.183264	+	0.123376i
$521$			42.9979i			1.88377i	0.335934	+	0.941886i	$0.390948\pi$
$521$			42.9979i			1.88377i	−0.335934	+	0.941886i	$0.609052\pi$
$522$	2.31848	−	5.94160i	0.101477	−	0.260057i
$523$	−16.7976	+	9.69808i	−0.734506	+	0.424067i	−0.820068	−	0.572265i	$-0.806065\pi$
$523$	−16.7976	+	9.69808i	−0.734506	+	0.424067i	0.0855622	+	0.996333i	$0.472731\pi$
$524$	3.79139	+	12.1226i	0.165628	+	0.529578i
$525$	0.725847	−	1.25720i	0.0316786	−	0.0548689i
$526$	−4.84103	−	31.6967i	−0.211079	−	1.38204i
$527$	54.0762			2.35560
$528$	−0.439449	−	5.30587i	−0.0191246	−	0.230909i
$529$	−1.14706	+	1.98677i	−0.0498724	+	0.0863815i
$530$	24.0921	−	3.67958i	1.04650	−	0.159831i
$531$		−	3.00672i		−	0.130481i
$532$	1.84037	+	5.88439i	0.0797901	+	0.255121i
$533$	−9.64763			−0.417885
$534$	−15.0807	+	2.30326i	−0.652604	+	0.0996719i
$535$	−22.6187			−0.977892
$536$	12.0313	+	19.7800i	0.519675	+	0.854364i
$537$	−6.96594			−0.300602
$538$	−24.6121	+	3.75900i	−1.06110	+	0.162062i
$539$	−6.89131			−0.296830
$540$	1.18269	+	3.78152i	0.0508948	+	0.162731i
$541$			23.2746i			1.00066i	0.865836	+	0.500328i	$0.166787\pi$
$541$			23.2746i			1.00066i	−0.865836	+	0.500328i	$0.833213\pi$
$542$	24.7423	−	3.77889i	1.06277	−	0.162317i
$543$	−8.09158	+	14.0150i	−0.347243	+	0.601442i
$544$	34.5504	+	10.2879i	1.48134	+	0.441092i
$545$	−20.7044			−0.886879
$546$	0.259157	+	1.69683i	0.0110909	+	0.0726178i
$547$	2.36701	−	4.09977i	0.101206	−	0.175294i	−0.810976	−	0.585080i	$-0.801063\pi$
$547$	2.36701	−	4.09977i	0.101206	−	0.175294i	0.912182	+	0.409786i	$0.134397\pi$
$548$	11.1725	+	35.7228i	0.477265	+	1.52600i
$549$	4.31128	−	2.48912i	0.184001	−	0.106233i
$550$	0.735806	−	1.88565i	0.0313749	−	0.0804046i
$551$			10.2983i			0.438724i
$552$	7.18754	−	10.6764i	0.305922	−	0.454419i
$553$	−4.29353	−	7.43662i	−0.182580	−	0.316237i
$554$	−39.1040	+	5.97233i	−1.66137	+	0.253740i
$555$	12.7581	−	7.36587i	0.541550	−	0.312664i
$556$	−17.7167	+	5.54097i	−0.751355	+	0.234990i
$557$	2.96497	−	5.13549i	0.125630	−	0.217597i	−0.796349	−	0.604837i	$-0.793238\pi$
$557$	2.96497	−	5.13549i	0.125630	−	0.217597i	0.921979	+	0.387240i	$0.126571\pi$
$558$	4.36235	−	11.1794i	0.184673	−	0.473263i
$559$	−6.54035	+	3.77607i	−0.276627	+	0.159711i
$560$	10.6613	−	0.883003i	0.450522	−	0.0373137i
$561$	−8.48217			−0.358117
$562$	−28.3945	+	22.7350i	−1.19775	+	0.959018i
$563$	−37.9180			−1.59805			−0.799026	−	0.601297i	$-0.794651\pi$
$563$	−37.9180			−1.59805			−0.799026	+	0.601297i	$0.794651\pi$
$564$	4.09434	+	0.917647i	0.172403	+	0.0386399i
$565$	7.27889	−	12.6074i	0.306225	−	0.530398i
$566$	0.852202	+	5.57981i	0.0358207	+	0.234537i
$567$	−0.674999	+	1.16913i	−0.0283473	+	0.0490990i
$568$	27.8639	+	1.92353i	1.16915	+	0.0807097i
$569$	−5.08045	+	8.79960i	−0.212984	+	0.368898i	−0.952647	−	0.304079i	$-0.901651\pi$
$569$	−5.08045	+	8.79960i	−0.212984	+	0.368898i	0.739663	+	0.672977i	$0.234985\pi$
$570$	−3.99865	−	4.99405i	−0.167485	−	0.209178i
$571$	−29.5894	−	17.0834i	−1.23828	−	0.714919i	−0.269535	−	0.962991i	$-0.586870\pi$
$571$	−29.5894	−	17.0834i	−1.23828	−	0.714919i	−0.968742	+	0.248071i	$0.920203\pi$
$572$	0.714412	+	2.28426i	0.0298710	+	0.0955096i
$573$	−3.06855	−	5.31488i	−0.128190	−	0.222032i
$574$	−15.9920	+	12.8046i	−0.667495	+	0.534452i
$575$	4.23760	−	2.44658i	0.176720	−	0.102029i
$576$	4.91407	−	6.31284i	0.204753	−	0.263035i
$577$	−4.64887	−	2.68402i	−0.193535	−	0.111737i	0.400101	−	0.916471i	$-0.368975\pi$
$577$	−4.64887	−	2.68402i	−0.193535	−	0.111737i	−0.593636	+	0.804733i	$0.702308\pi$
$578$	12.1385	−	31.1075i	0.504897	−	1.29390i
$579$	−3.37238			−0.140151
$580$	17.4363	+	3.90791i	0.724001	+	0.162267i
$581$		−	9.78733i		−	0.406047i
$582$	−0.395514	+	0.316681i	−0.0163946	+	0.0131268i
$583$	10.0272	+	5.78918i	0.415282	+	0.239763i
$584$	12.2492	+	8.24636i	0.506876	+	0.341237i
$585$	−0.890573	−	1.54252i	−0.0368207	−	0.0637753i
$586$	14.0957	−	2.15284i	0.582290	−	0.0889329i
$587$	22.6747	+	39.2737i	0.935885	+	1.62100i	0.773048	+	0.634347i	$0.218731\pi$
$587$	22.6747	+	39.2737i	0.935885	+	1.62100i	0.162837	+	0.986653i	$0.447936\pi$
$588$	−7.61829	−	7.01341i	−0.314173	−	0.289228i
$589$			19.3769i			0.798410i
$590$	8.32726	−	1.27182i	0.342828	−	0.0523600i
$591$	−17.0373	−	9.83648i	−0.700820	−	0.404619i
$592$	−26.8995	−	12.6955i	−1.10556	−	0.521781i
$593$	−30.0452	+	17.3466i	−1.23381	+	0.712339i	−0.967821	−	0.251638i	$-0.919031\pi$
$593$	−30.0452	+	17.3466i	−1.23381	+	0.712339i	−0.265985	+	0.963977i	$0.585697\pi$
$594$	−0.684260	+	1.75356i	−0.0280755	+	0.0719493i
$595$		−	17.0436i		−	0.698718i
$596$	14.3971	−	4.50275i	0.589727	−	0.184440i
$597$	−19.0932	+	11.0235i	−0.781432	+	0.451160i
$598$	−2.10322	+	5.38994i	−0.0860071	+	0.220411i
$599$	5.62464	−	9.74216i	0.229816	−	0.398054i	−0.727937	−	0.685644i	$-0.759521\pi$
$599$	5.62464	−	9.74216i	0.229816	−	0.398054i	0.957754	+	0.287590i	$0.0928541\pi$
$600$	2.73249	−	1.33573i	0.111553	−	0.0545311i
$601$	−8.37140	−	14.4997i	−0.341477	−	0.591455i	0.643231	−	0.765673i	$-0.277594\pi$
$601$	−8.37140	−	14.4997i	−0.341477	−	0.591455i	−0.984707	+	0.174218i	$0.944260\pi$
$602$	−5.82968	+	14.9398i	−0.237600	+	0.608899i
$603$	−0.750324	−	8.15089i	−0.0305556	−	0.331930i
$604$	−2.52301	+	2.74061i	−0.102660	+	0.111514i
$605$	15.8329	−	9.14110i	0.643697	−	0.371639i
$606$	−2.51814	−	0.982608i	−0.102292	−	0.0399157i
$607$	40.9324	+	23.6323i	1.66140	+	0.959207i	0.972050	+	0.234774i	$0.0754351\pi$
$607$	40.9324	+	23.6323i	1.66140	+	0.959207i	0.689345	+	0.724433i	$0.257898\pi$
$608$	−3.68643	+	12.3803i	−0.149504	+	0.502087i
$609$	3.04416	+	5.27264i	0.123356	+	0.213658i
$610$	8.71738	+	10.8874i	0.352957	+	0.440820i
$611$	−1.88623			−0.0763087
$612$	−9.37697	−	8.63245i	−0.379042	−	0.348946i
$613$	−18.4191	−	31.9028i	−0.743940	−	1.28854i	−0.950688	−	0.310148i	$-0.899621\pi$
$613$	−18.4191	−	31.9028i	−0.743940	−	1.28854i	0.206748	−	0.978394i	$-0.433712\pi$
$614$	10.8694	−	8.70295i	0.438654	−	0.351222i
$615$	10.6290	−	18.4100i	0.428604	−	0.742364i
$616$	4.21594	+	2.83823i	0.169865	+	0.114356i
$617$	−25.2032			−1.01464			−0.507321	−	0.861757i	$-0.669364\pi$
$617$	−25.2032			−1.01464			−0.507321	+	0.861757i	$0.669364\pi$
$618$	−15.6796	−	6.11836i	−0.630724	−	0.246116i
$619$	27.7991	−	16.0498i	1.11734	−	0.645098i	0.176621	−	0.984279i	$-0.443483\pi$
$619$	27.7991	−	16.0498i	1.11734	−	0.645098i	0.940721	+	0.339181i	$0.110150\pi$
$620$	32.8072	+	7.35295i	1.31757	+	0.295301i
$621$	−3.94074	+	2.27519i	−0.158136	+	0.0913000i
$622$	−10.0815	+	1.53974i	−0.404232	+	0.0617381i
$623$	7.28141	−	12.6118i	0.291724	−	0.505280i
$624$	−1.53495	+	3.25230i	−0.0614472	+	0.130196i
$625$	−18.4670			−0.738680
$626$	−1.07900	−	7.06477i	−0.0431255	−	0.282365i
$627$		−	3.03937i		−	0.121381i
$628$	−12.9773	−	11.9469i	−0.517850	−	0.476733i
$629$	−23.6945	+	41.0401i	−0.944763	+	1.63638i
$630$	−3.52349	−	1.37491i	−0.140379	−	0.0547777i
$631$	18.1781	+	31.4854i	0.723658	+	1.25341i	0.959524	+	0.281627i	$0.0908742\pi$
$631$	18.1781	+	31.4854i	0.723658	+	1.25341i	−0.235865	+	0.971786i	$0.575792\pi$
$632$	1.23903	−	17.9483i	0.0492859	−	0.713947i
$633$	−20.1483	+	11.6326i	−0.800824	+	0.462356i
$634$	−22.2094	−	27.7381i	−0.882048	−	1.10162i
$635$	−7.96673	+	13.7988i	−0.316150	+	0.547588i
$636$	5.19320	+	16.6047i	0.205924	+	0.658419i
$637$	4.03134	+	2.32750i	0.159728	+	0.0922187i
$638$	5.30585	+	6.62665i	0.210060	+	0.262352i
$639$	−8.55186	−	4.93742i	−0.338306	−	0.195321i
$640$	19.5623	+	10.9395i	0.773269	+	0.432421i
$641$	−15.4302	−	8.90862i	−0.609456	−	0.351869i	0.163297	−	0.986577i	$-0.447787\pi$
$641$	−15.4302	−	8.90862i	−0.609456	−	0.351869i	−0.772752	+	0.634708i	$0.781121\pi$
$642$	−2.43780	−	15.9615i	−0.0962121	−	0.629951i
$643$			9.73121i			0.383761i	0.981418	+	0.191881i	$0.0614587\pi$
$643$			9.73121i			0.383761i	−0.981418	+	0.191881i	$0.938541\pi$
$644$	3.66732	+	11.7259i	0.144513	+	0.462064i
$645$		−	16.6408i		−	0.655230i
$646$	19.1720	+	7.48115i	0.754312	+	0.294342i
$647$	−16.8905	−	29.2551i	−0.664033	−	1.15014i	−0.979547	−	0.201217i	$-0.935510\pi$
$647$	−16.8905	−	29.2551i	−0.664033	−	1.15014i	0.315514	−	0.948921i	$-0.397823\pi$
$648$	−2.54107	+	1.24216i	−0.0998226	+	0.0487967i
$649$	3.46581	+	2.00099i	0.136045	+	0.0785456i
$650$	−1.06731	+	0.854573i	−0.0418632	+	0.0335191i
$651$	5.72775	+	9.92076i	0.224488	+	0.388825i
$652$	14.9450	+	3.34955i	0.585289	+	0.131178i
$653$	27.8279	−	16.0664i	1.08899	−	0.628729i	0.155682	−	0.987807i	$-0.450242\pi$
$653$	27.8279	−	16.0664i	1.08899	−	0.628729i	0.933307	+	0.359079i	$0.116909\pi$
$654$	−2.23148	−	14.6106i	−0.0872576	−	0.571321i
$655$	12.5815			0.491599
$656$	−42.7758	+	3.54283i	−1.67011	+	0.138324i
$657$	−2.61035	−	4.52126i	−0.101839	−	0.176391i
$658$	−3.12664	+	2.50345i	−0.121889	+	0.0975946i
$659$	−9.68776	−	5.59323i	−0.377382	−	0.217881i	0.299297	−	0.954160i	$-0.403248\pi$
$659$	−9.68776	−	5.59323i	−0.377382	−	0.217881i	−0.676678	+	0.736279i	$0.736581\pi$
$660$	−5.14601	−	1.15335i	−0.200308	−	0.0448942i
$661$		−	43.2836i		−	1.68354i	−0.539838	−	0.841769i	$-0.681515\pi$
$661$		−	43.2836i		−	1.68354i	0.539838	−	0.841769i	$-0.318485\pi$
$662$	−13.6288	+	34.9267i	−0.529699	+	1.35746i
$663$	4.96197	+	2.86480i	0.192707	+	0.111259i
$664$	11.4516	−	17.0103i	0.444407	−	0.660126i
$665$	6.10713			0.236825
$666$	6.57297	+	8.20921i	0.254697	+	0.318100i
$667$			20.5216i			0.794599i
$668$	18.2854	+	4.09822i	0.707483	+	0.158565i
$669$			26.6186i			1.02913i
$670$	22.2569	−	5.52583i	0.859860	−	0.213481i
$671$			6.62609i			0.255797i
$672$	1.77217	+	7.42827i	0.0683628	+	0.286552i
$673$		−	17.5584i		−	0.676827i	−0.940998	−	0.338414i	$-0.890110\pi$
$673$		−	17.5584i		−	0.676827i	0.940998	−	0.338414i	$-0.109890\pi$
$674$	−11.6241	+	9.30721i	−0.447743	+	0.358500i
$675$	−1.07533			−0.0413895
$676$	−5.33263	+	23.7930i	−0.205101	+	0.915117i
$677$	14.3752	+	8.29952i	0.552483	+	0.318976i	0.750123	−	0.661298i	$-0.229994\pi$
$677$	14.3752	+	8.29952i	0.552483	+	0.318976i	−0.197640	+	0.980275i	$0.563328\pi$
$678$	9.68127	+	3.77775i	0.371807	+	0.145084i
$679$		−	0.483667i		−	0.0185614i
$680$	19.9416	−	29.6215i	0.764726	−	1.13593i
$681$	18.8726	+	10.8961i	0.723199	+	0.417539i
$682$	9.98323	+	12.4684i	0.382278	+	0.477440i
$683$	−19.8637	−	34.4049i	−0.760062	−	1.31647i	−0.942818	−	0.333307i	$-0.891835\pi$
$683$	−19.8637	−	34.4049i	−0.760062	−	1.31647i	0.182756	−	0.983158i	$-0.441498\pi$
$684$	3.09322	−	3.36000i	0.118272	−	0.128473i
$685$	37.0751			1.41657
$686$	22.9826	−	3.51012i	0.877480	−	0.134017i
$687$	5.84003	−	3.37174i	0.222811	−	0.128640i
$688$	−27.6120	+	19.1442i	−1.05270	+	0.729864i
$689$	−3.91052	−	6.77321i	−0.148979	−	0.258039i
$690$	−7.96814	−	9.95169i	−0.303342	−	0.378854i
$691$	29.4400	+	16.9972i	1.11995	+	0.646603i	0.941388	−	0.337325i	$-0.109522\pi$
$691$	29.4400	+	16.9972i	1.11995	+	0.646603i	0.178562	+	0.983929i	$0.442856\pi$
$692$	2.03230	+	1.87093i	0.0772564	+	0.0711223i
$693$	−0.898431	−	1.55613i	−0.0341286	−	0.0591124i
$694$	9.70056	−	24.8597i	0.368228	−	0.943661i
$695$			18.3873i			0.697471i
$696$	−0.878485	+	12.7256i	−0.0332989	+	0.482361i
$697$			68.3830i			2.59019i
$698$	26.8832	−	4.10587i	1.01755	−	0.155409i
$699$	−1.15476	−	0.666702i	−0.0436771	−	0.0252170i
$700$	−0.634971	+	2.83310i	−0.0239997	+	0.107081i
$701$	−2.22770	−	1.28616i	−0.0841390	−	0.0485777i	0.457340	−	0.889292i	$-0.348802\pi$
$701$	−2.22770	−	1.28616i	−0.0841390	−	0.0485777i	−0.541479	+	0.840714i	$0.682136\pi$
$702$	0.992537	−	0.794707i	0.0374609	−	0.0299943i
$703$	−14.7057	−	8.49035i	−0.554637	−	0.320220i
$704$	4.00640	+	9.86562i	0.150997	+	0.371824i
$705$	2.07811	−	3.59939i	0.0782661	−	0.135561i
$706$	−22.4202	+	17.9514i	−0.843794	+	0.675611i
$707$	2.23462	−	1.29016i	0.0840416	−	0.0485215i
$708$	1.79499	+	5.73929i	0.0674598	+	0.215696i
$709$	−9.00921	−	15.6044i	−0.338348	−	0.586036i	0.645774	−	0.763528i	$-0.276535\pi$
$709$	−9.00921	−	15.6044i	−0.338348	−	0.586036i	−0.984122	+	0.177493i	$0.943201\pi$
$710$	10.0571	−	25.7733i	0.377435	−	0.967255i
$711$	−3.18040	+	5.50861i	−0.119274	+	0.206589i
$712$	27.4113	−	13.3996i	1.02728	−	0.502170i
$713$			38.6125i			1.44605i
$714$	12.0273	−	1.83692i	0.450109	−	0.0687449i
$715$	2.37072			0.0886601
$716$	13.2967	−	4.15861i	0.496922	−	0.155415i
$717$	−1.58989	+	2.75377i	−0.0593756	+	0.102841i
$718$	−0.310509	−	2.03306i	−0.0115881	−	0.0758732i
$719$	20.9198	−	12.0780i	0.780176	−	0.450435i	−0.0563167	−	0.998413i	$-0.517936\pi$
$719$	20.9198	−	12.0780i	0.780176	−	0.450435i	0.836493	+	0.547978i	$0.184602\pi$
$720$	−4.51508	−	6.51220i	−0.168267	−	0.242695i
$721$	13.9142	−	8.03338i	0.518193	−	0.299179i
$722$	7.08704	−	18.1620i	0.263752	−	0.675920i
$723$	10.7931			0.401399
$724$	7.07851	−	31.5828i	0.263071	−	1.17376i
$725$	−2.42480	+	4.19988i	−0.0900549	+	0.155980i
$726$	8.15710	+	10.1877i	0.302738	+	0.378100i
$727$	−2.71931	−	4.70999i	−0.100854	−	0.174684i	0.811183	−	0.584793i	$-0.198824\pi$
$727$	−2.71931	−	4.70999i	−0.100854	−	0.174684i	−0.912037	+	0.410109i	$0.865491\pi$
$728$	−1.50768	−	3.08424i	−0.0558784	−	0.114309i
$729$	1.00000			0.0370370
$730$	11.4177	−	9.14196i	0.422588	−	0.338359i
$731$	26.7650	+	46.3584i	0.989940	+	1.71463i
$732$	−6.74348	+	7.32509i	−0.249246	+	0.270743i
$733$	−43.3909	−	25.0518i	−1.60268	−	0.925308i	−0.990949	−	0.134242i	$-0.957140\pi$
$733$	−43.3909	−	25.0518i	−1.60268	−	0.925308i	−0.611731	−	0.791066i	$-0.709527\pi$
$734$	−4.97541	+	12.7505i	−0.183646	+	0.470630i
$735$	−8.88286	+	5.12852i	−0.327649	+	0.189168i
$736$	−7.34598	+	24.6703i	−0.270776	+	0.909360i
$737$	9.89478	+	4.55957i	0.364479	+	0.167954i
$738$	14.1371	+	5.51648i	0.520395	+	0.203065i
$739$	23.2088	+	40.1987i	0.853748	+	1.47873i	0.877802	+	0.479024i	$0.159009\pi$
$739$	23.2088	+	40.1987i	0.853748	+	1.47873i	−0.0240540	+	0.999711i	$0.507657\pi$
$740$	−19.9555	+	21.6766i	−0.733579	+	0.796848i
$741$	−1.02653	+	1.77800i	−0.0377105	+	0.0653165i
$742$	−15.4717	−	6.03724i	−0.567983	−	0.221634i
$743$	−20.2722	+	11.7042i	−0.743715	+	0.429384i	−0.823419	−	0.567434i	$-0.807936\pi$
$743$	−20.2722	+	11.7042i	−0.743715	+	0.429384i	0.0797032	+	0.996819i	$0.474603\pi$
$744$	−1.65292	+	23.9438i	−0.0605989	+	0.877823i
$745$		−	14.9420i		−	0.547434i
$746$	4.91214	+	1.91678i	0.179846	+	0.0701782i
$747$	−6.27859	+	3.62494i	−0.229721	+	0.132630i
$748$	16.1909	−	5.06379i	0.592000	−	0.185151i
$749$	13.3484	+	7.70672i	0.487741	+	0.281597i
$750$	−2.56982	−	16.8259i	−0.0938365	−	0.614397i
$751$			20.4752i			0.747151i	0.927600	+	0.373576i	$0.121868\pi$
$751$			20.4752i			0.747151i	−0.927600	+	0.373576i	$0.878132\pi$
$752$	−8.36319	+	0.692666i	−0.304974	+	0.0252589i
$753$	−3.38730	−	5.86698i	−0.123440	−	0.213805i
$754$	−0.865752	−	5.66853i	−0.0315288	−	0.206436i
$755$	1.84494	+	3.19552i	0.0671441	+	0.116297i
$756$	0.590489	−	2.63463i	0.0214759	−	0.0958207i
$757$	14.8740	+	8.58751i	0.540605	+	0.312119i	0.745324	−	0.666702i	$-0.232295\pi$
$757$	14.8740	+	8.58751i	0.540605	+	0.312119i	−0.204719	+	0.978821i	$0.565628\pi$
$758$	−8.99711	−	11.2368i	−0.326790	−	0.408139i
$759$		−	6.05659i		−	0.219840i
$760$	10.6141	+	7.14558i	0.385014	+	0.259198i
$761$	−39.7805			−1.44204			−0.721021	−	0.692913i	$-0.756327\pi$
$761$	−39.7805			−1.44204			−0.721021	+	0.692913i	$0.756327\pi$
$762$	−10.5961	−	4.13474i	−0.383857	−	0.149786i
$763$	12.2187	+	7.05447i	0.442347	+	0.255389i
$764$	9.03025	+	8.31326i	0.326703	+	0.300763i
$765$	−10.9335	+	6.31244i	−0.395300	+	0.228227i
$766$	2.26652	+	2.83074i	0.0818929	+	0.102279i
$767$	−1.35164	−	2.34111i	−0.0488049	−	0.0845326i
$768$	−5.61137	+	14.9837i	−0.202483	+	0.540679i
$769$	3.80483	+	2.19672i	0.137206	+	0.0792157i	0.567032	−	0.823696i	$-0.308092\pi$
$769$	3.80483	+	2.19672i	0.137206	+	0.0792157i	−0.429826	+	0.902912i	$0.641425\pi$
$770$	3.92975	−	3.14648i	0.141618	−	0.113391i
$771$	12.6711	−	21.9470i	0.456339	−	0.790403i
$772$	6.43728	−	2.01329i	0.231683	−	0.0724598i
$773$	14.5656	−	25.2283i	0.523886	−	0.907398i	−0.475727	−	0.879593i	$-0.657815\pi$
$773$	14.5656	−	25.2283i	0.523886	−	0.907398i	0.999613	−	0.0278049i	$-0.00885171\pi$
$774$	11.7430	−	1.79351i	0.422094	−	0.0644663i
$775$	−4.56240	+	7.90230i	−0.163886	+	0.283859i
$776$	0.565909	−	0.840606i	0.0203149	−	0.0301760i
$777$	−10.0389			−0.360143
$778$	7.46348	+	9.32140i	0.267579	+	0.334188i
$779$	−24.5033			−0.877923
$780$	2.62082	+	2.41273i	0.0938403	+	0.0863895i
$781$	11.3826	−	6.57175i	0.407302	−	0.235156i
$782$	38.2042	+	14.9077i	1.36618	+	0.533100i
$783$	2.25494	−	3.90567i	0.0805849	−	0.139577i
$784$	18.7289	+	8.83928i	0.668890	+	0.315688i
$785$	−15.1314	+	8.73612i	−0.540063	+	0.311805i
$786$	1.35600	+	8.87846i	0.0483670	+	0.316684i
$787$	8.78108	+	15.2093i	0.313012	+	0.542152i	0.979013	−	0.203799i	$-0.0653288\pi$
$787$	8.78108	+	15.2093i	0.313012	+	0.542152i	−0.666001	+	0.745951i	$0.731995\pi$
$788$	38.3934	+	8.60495i	1.36771	+	0.306539i
$789$		−	22.6729i		−	0.807176i
$790$	−16.6017	−	6.47818i	−0.590661	−	0.230483i
$791$	−8.59127	+	4.96017i	−0.305471	+	0.176363i
$792$	0.259269	−	3.75573i	0.00921274	−	0.133454i
$793$	2.23792	−	3.87619i	0.0794708	−	0.137647i
$794$	−47.0174	+	7.18095i	−1.66859	+	0.254842i
$795$	17.2333			0.611201
$796$	29.8646	−	32.4403i	1.05852	−	1.14982i
$797$	5.90369	−	10.2255i	0.209120	−	0.362206i	−0.742318	−	0.670048i	$-0.766274\pi$
$797$	5.90369	−	10.2255i	0.209120	−	0.362206i	0.951437	+	0.307842i	$0.0996069\pi$
$798$	0.658214	+	4.30967i	0.0233005	+	0.152561i
$799$			13.3697i			0.472986i
$800$	−4.41841	+	4.18096i	−0.156215	+	0.147819i
$801$	−10.7873			−0.381150
$802$	1.50502	+	9.85412i	0.0531439	+	0.347961i
$803$	6.94880			0.245218
$804$	6.29826	+	15.1107i	0.222122	+	0.532912i
$805$	12.1697			0.428927
$806$	−1.62896	−	10.6656i	−0.0573776	−	0.375681i
$807$	−17.6052			−0.619733
$808$	5.39328	+	0.372315i	0.189735	+	0.0130980i
$809$			52.7395i			1.85422i	0.374787	+	0.927111i	$0.377716\pi$
$809$			52.7395i			1.85422i	−0.374787	+	0.927111i	$0.622284\pi$
$810$	0.422992	+	2.76955i	0.0148624	+	0.0973121i
$811$	−13.4530	+	23.3012i	−0.472398	+	0.818217i	−0.999501	−	0.0315840i	$-0.989945\pi$
$811$	−13.4530	+	23.3012i	−0.472398	+	0.818217i	0.527103	+	0.849801i	$0.323278\pi$
$812$	−8.95849	−	8.24719i	−0.314381	−	0.289420i
$813$	17.6983			0.620708
$814$	−13.8370	+	2.11332i	−0.484987	+	0.0740718i
$815$	7.58540	−	13.1383i	0.265705	−	0.460215i
$816$	23.0525	+	10.8798i	0.806998	+	0.380870i
$817$	−16.6114	+	9.59058i	−0.581158	+	0.335532i
$818$	5.46000	+	2.13056i	0.190904	+	0.0744933i
$819$			1.21376i			0.0424121i
$820$	−9.29829	+	41.4869i	−0.324710	+	1.44879i
$821$	−21.3581	−	36.9934i	−0.745404	−	1.29108i	−0.950006	−	0.312233i	$-0.898923\pi$
$821$	−21.3581	−	36.9934i	−0.745404	−	1.29108i	0.204602	−	0.978845i	$-0.434410\pi$
$822$	3.99587	+	26.1631i	0.139372	+	0.912542i
$823$	24.7243	−	14.2746i	0.861834	−	0.497580i	−0.00279207	−	0.999996i	$-0.500889\pi$
$823$	24.7243	−	14.2746i	0.861834	−	0.497580i	0.864626	+	0.502416i	$0.167555\pi$
$824$	33.5821	+	2.31828i	1.16989	+	0.0807610i
$825$	0.715638	−	1.23952i	0.0249153	−	0.0431546i
$826$	−5.34767	−	2.08673i	−0.186069	−	0.0726065i
$827$	−12.3034	+	7.10335i	−0.427830	+	0.247008i	−0.698422	−	0.715686i	$-0.746114\pi$
$827$	−12.3034	+	7.10335i	−0.427830	+	0.247008i	0.270592	+	0.962694i	$0.412781\pi$
$828$	6.16389	−	6.69551i	0.214210	−	0.232685i
$829$	35.3948			1.22931			0.614657	−	0.788795i	$-0.289295\pi$
$829$	35.3948			1.22931			0.614657	+	0.788795i	$0.289295\pi$
$830$	−12.6953	−	15.8555i	−0.440659	−	0.550354i
$831$	−27.9713			−0.970314
$832$	0.988350	−	7.12441i	0.0342649	−	0.246994i
$833$	16.4974	−	28.5744i	0.571602	−	0.990043i
$834$	−12.9755	+	1.98175i	−0.449306	+	0.0686223i
$835$	9.28086	−	16.0749i	0.321178	−	0.556296i
$836$	1.81448	+	5.80162i	0.0627552	+	0.200653i
$837$	4.24278	−	7.34872i	0.146652	−	0.254009i
$838$	−20.8976	+	16.7324i	−0.721897	+	0.578011i
$839$	29.0290	+	16.7599i	1.00219	+	0.578617i	0.908897	−	0.417021i	$-0.136926\pi$
$839$	29.0290	+	16.7599i	1.00219	+	0.578617i	0.0932971	+	0.995638i	$0.470259\pi$
$840$	7.54653	+	0.520960i	0.260380	+	0.0179748i
$841$	4.33052	+	7.50068i	0.149328	+	0.258644i
$842$	3.58270	+	4.47455i	0.123468	+	0.154203i
$843$	−22.2749	+	12.8604i	−0.767190	+	0.442937i
$844$	31.5150	−	34.2330i	1.08479	−	1.17835i
$845$	20.9168	+	12.0763i	0.719559	+	0.415438i
$846$	2.76398	+	1.07854i	0.0950277	+	0.0370810i
$847$	−12.4583			−0.428074
$848$	−19.8258	−	28.5951i	−0.680820	−	0.981960i
$849$			3.99127i			0.136980i
$850$	6.05726	+	7.56512i	0.207762	+	0.259482i
$851$	−29.3042	−	16.9188i	−1.00454	−	0.579969i
$852$	19.2716	+	4.31925i	0.660233	+	0.147975i
$853$	−7.28485	−	12.6177i	−0.249429	−	0.432023i	0.713939	−	0.700208i	$-0.246909\pi$
$853$	−7.28485	−	12.6177i	−0.249429	−	0.432023i	−0.963367	+	0.268185i	$0.913576\pi$
$854$	−1.43496	−	9.39543i	−0.0491033	−	0.321505i
$855$	−2.26190	−	3.91773i	−0.0773555	−	0.133984i
$856$	14.1822	+	29.0123i	0.484738	+	0.991622i
$857$		−	51.8046i		−	1.76961i	−0.465960	−	0.884806i	$-0.654291\pi$
$857$		−	51.8046i		−	1.76961i	0.465960	−	0.884806i	$-0.345709\pi$
$858$	0.255512	+	1.67297i	0.00872302	+	0.0571142i
$859$	−10.7018	−	6.17869i	−0.365141	−	0.210814i	0.306193	−	0.951970i	$-0.400945\pi$
$859$	−10.7018	−	6.17869i	−0.365141	−	0.210814i	−0.671333	+	0.741155i	$0.734278\pi$
$860$	9.93442	+	31.7643i	0.338761	+	1.08315i
$861$	−12.5455	+	7.24312i	−0.427548	+	0.246845i
$862$	31.9237	+	12.4570i	1.08733	+	0.424288i
$863$			49.4755i			1.68417i	0.539348	+	0.842083i	$0.318671\pi$
$863$			49.4755i			1.68417i	−0.539348	+	0.842083i	$0.681329\pi$
$864$	4.10889	−	3.88806i	0.139787	−	0.132275i
$865$	2.36964	−	1.36811i	0.0805702	−	0.0465172i
$866$	9.26433	+	3.61506i	0.314815	+	0.122845i
$867$	11.8058	−	20.4483i	0.400947	−	0.694461i
$868$	−16.8559	−	15.5175i	−0.572126	−	0.526699i
$869$	−4.23314	−	7.33202i	−0.143600	−	0.248722i
$870$	11.7708	+	4.59310i	0.399066	+	0.155721i
$871$	−4.24837	−	6.00919i	−0.143951	−	0.203614i
$872$	12.9819	+	26.5569i	0.439624	+	0.899331i
$873$	−0.310273	+	0.179136i	−0.0105011	+	0.00606284i
$874$	−5.34182	+	13.6895i	−0.180690	+	0.463055i
$875$	14.0713	+	8.12409i	0.475698	+	0.274644i
$876$	7.68185	+	7.07192i	0.259546	+	0.238938i
$877$	4.63797	+	8.03320i	0.156613	+	0.271262i	0.933645	−	0.358199i	$-0.116609\pi$
$877$	4.63797	+	8.03320i	0.156613	+	0.271262i	−0.777032	+	0.629461i	$0.783276\pi$
$878$	15.3093	−	12.2579i	0.516665	−	0.413685i
$879$	10.0828			0.340084
$880$	10.5113	−	0.870584i	0.354337	−	0.0293474i
$881$	−21.6959	−	37.5784i	−0.730954	−	1.26605i	−0.956476	−	0.291811i	$-0.905742\pi$
$881$	−21.6959	−	37.5784i	−0.730954	−	1.26605i	0.225523	−	0.974238i	$-0.427591\pi$
$882$	−4.57646	−	5.71569i	−0.154097	−	0.192457i
$883$	0.515475	−	0.892828i	0.0173471	−	0.0300461i	−0.857222	−	0.514948i	$-0.827811\pi$
$883$	0.515475	−	0.892828i	0.0173471	−	0.0300461i	0.874569	+	0.484902i	$0.161145\pi$
$884$	−11.1818	−	2.50612i	−0.376084	−	0.0842901i
$885$	5.95654			0.200227
$886$	7.65157	−	19.6087i	0.257060	−	0.658768i
$887$	26.9738	−	15.5733i	0.905693	−	0.522902i	0.0266498	−	0.999645i	$-0.491516\pi$
$887$	26.9738	−	15.5733i	0.905693	−	0.522902i	0.879043	+	0.476743i	$0.158183\pi$
$888$	−17.4475	−	11.7459i	−0.585498	−	0.394166i
$889$	9.40313	−	5.42890i	0.315371	−	0.182079i
$890$	−4.56294	−	29.8760i	−0.152950	−	1.00144i
$891$	−0.665505	+	1.15269i	−0.0222953	+	0.0386165i
$892$	−15.8911	−	50.8101i	−0.532073	−	1.70125i
$893$	−4.79071			−0.160315
$894$	10.5443	−	1.61042i	0.352653	−	0.0538605i
$895$		−	13.8001i		−	0.461285i
$896$	−7.81738	−	13.1213i	−0.261160	−	0.438351i
$897$	−2.04557	+	3.54304i	−0.0682997	+	0.118299i
$898$	−16.3934	+	42.0115i	−0.547055	+	1.40194i
$899$	−19.1344	−	33.1418i	−0.638169	−	1.10534i
$900$	2.05261	−	0.641964i	0.0684205	−	0.0213988i
$901$	−48.0089	+	27.7180i	−1.59941	+	0.923419i
$902$	−15.7671	+	12.6245i	−0.524988	+	0.420349i
$903$	−5.66990	+	9.82055i	−0.188682	+	0.326807i
$904$	−20.7351	−	1.43141i	−0.689640	−	0.0476080i
$905$	−27.7648	−	16.0300i	−0.922935	−	0.532857i
$906$	−2.05617	+	1.64634i	−0.0683116	+	0.0546959i
$907$	−28.4058	−	16.4001i	−0.943198	−	0.544556i	−0.0522367	−	0.998635i	$-0.516635\pi$
$907$	−28.4058	−	16.4001i	−0.943198	−	0.544556i	−0.890961	+	0.454079i	$0.849968\pi$
$908$	−42.5293	−	9.53190i	−1.41138	−	0.316327i
$909$	−1.65528	−	0.955675i	−0.0549021	−	0.0316978i
$910$	−3.36156	+	0.513409i	−0.111435	+	0.0170194i
$911$		−	44.3407i		−	1.46907i	−0.678569	−	0.734537i	$-0.737400\pi$
$911$		−	44.3407i		−	1.46907i	0.678569	−	0.734537i	$-0.262600\pi$
$912$	−3.89851	+	8.26028i	−0.129093	+	0.273525i
$913$		−	9.64967i		−	0.319358i
$914$	4.40921	−	11.2995i	0.145844	−	0.373755i
$915$	4.93114	+	8.54098i	0.163018	+	0.282356i
$916$	−9.13466	+	9.92250i	−0.301818	+	0.327849i
$917$	−7.42495	−	4.28680i	−0.245193	−	0.141563i
$918$	−5.63293	−	7.03516i	−0.185914	−	0.232195i
$919$	0.298257	+	0.516596i	0.00983859	+	0.0170409i	0.870903	−	0.491455i	$-0.163535\pi$
$919$	0.298257	+	0.516596i	0.00983859	+	0.0170409i	−0.861064	+	0.508496i	$0.830202\pi$
$920$	21.1508	+	14.2391i	0.697323	+	0.469448i
$921$	8.52684	−	4.92297i	0.280969	−	0.162217i
$922$	−46.2771	+	7.06788i	−1.52405	+	0.232768i
$923$	−8.87827			−0.292232
$924$	2.64394	+	2.43401i	0.0869792	+	0.0800732i
$925$	−3.99820	−	6.92509i	−0.131460	−	0.227696i
$926$	28.3730	+	35.4360i	0.932396	+	1.16450i
$927$	−10.3068	−	5.95066i	−0.338521	−	0.195445i
$928$	−5.92019	−	24.8153i	−0.194340	−	0.814601i
$929$		−	16.1728i		−	0.530613i	−0.964164	−	0.265307i	$-0.914527\pi$
$929$		−	16.1728i		−	0.530613i	0.964164	−	0.265307i	$-0.0854732\pi$
$930$	22.1473	+	8.64216i	0.726239	+	0.283388i
$931$	10.2389	+	5.91144i	0.335567	+	0.193740i
$932$	2.60225	+	0.583231i	0.0852395	+	0.0191044i
$933$	−7.21137			−0.236090
$934$	5.01091	−	4.01215i	0.163962	−	0.131281i
$935$		−	16.8038i		−	0.549544i
$936$	−1.42014	+	2.10949i	−0.0464188	+	0.0689509i
$937$			20.7250i			0.677056i	0.940956	+	0.338528i	$0.109929\pi$
$937$			20.7250i			0.677056i	−0.940956	+	0.338528i	$0.890071\pi$
$938$	−15.0177	−	4.32239i	−0.490345	−	0.141131i
$939$		−	5.05347i		−	0.164914i
$940$	−1.81793	+	8.11121i	−0.0592943	+	0.264558i
$941$		−	27.8155i		−	0.906759i	−0.891318	−	0.453380i	$-0.850218\pi$
$941$		−	27.8155i		−	0.906759i	0.891318	−	0.453380i	$-0.149782\pi$
$942$	−7.79571	−	9.73633i	−0.253998	−	0.317227i
$943$	−48.8280			−1.59006
$944$	−6.85263	−	9.88369i	−0.223034	−	0.321687i
$945$	−2.31614	−	1.33723i	−0.0753441	−	0.0434999i
$946$	−5.74769	+	14.7296i	−0.186873	+	0.478902i
$947$			28.8938i			0.938922i	0.882953	+	0.469461i	$0.155552\pi$
$947$			28.8938i			0.938922i	−0.882953	+	0.469461i	$0.844448\pi$
$948$	2.78221	−	12.4136i	0.0903621	−	0.403176i
$949$	−4.06497	−	2.34691i	−0.131955	−	0.0761840i
$950$	−2.71077	+	2.17047i	−0.0879491	+	0.0704194i
$951$	−12.5631	−	21.7600i	−0.407388	−	0.705616i
$952$	−21.8613	+	10.6865i	−0.708527	+	0.346352i
$953$	7.90689			0.256129			0.128065	−	0.991766i	$-0.459123\pi$
$953$	7.90689			0.256129			0.128065	+	0.991766i	$0.459123\pi$
$954$	1.85736	+	12.1611i	0.0601343	+	0.393731i
$955$	10.5292	−	6.07903i	0.340717	−	0.196713i
$956$	1.39084	−	6.20561i	0.0449829	−	0.200704i
$957$	3.00134	+	5.19848i	0.0970197	+	0.168043i
$958$	−26.2931	+	21.0524i	−0.849492	+	0.680173i
$959$	−21.8799	−	12.6323i	−0.706537	−	0.407920i
$960$	12.5062	+	9.73515i	0.403637	+	0.314201i
$961$	−20.5024	−	35.5113i	−0.661369	−	1.14552i
$962$	8.80825	+	3.43709i	0.283989	+	0.110816i
$963$		−	11.4174i		−	0.367920i
$964$	−20.6021	+	6.44339i	−0.663548	+	0.207528i
$965$		−	6.68095i		−	0.215067i
$966$	1.31163	+	8.58792i	0.0422010	+	0.276312i
$967$	42.4190	+	24.4906i	1.36410	+	0.787565i	0.990167	−	0.139889i	$-0.0446747\pi$
$967$	42.4190	+	24.4906i	1.36410	+	0.787565i	0.373936	+	0.927455i	$0.378008\pi$
$968$	−21.6524	−	14.5767i	−0.695935	−	0.468514i
$969$	12.6026	+	7.27609i	0.404853	+	0.233742i
$970$	−0.627370	−	0.783543i	−0.0201436	−	0.0251581i
$971$	−8.56307	−	4.94389i	−0.274802	−	0.158657i	0.356266	−	0.934385i	$-0.384050\pi$
$971$	−8.56307	−	4.94389i	−0.274802	−	0.158657i	−0.631068	+	0.775728i	$0.717383\pi$
$972$	−1.90882	+	0.596993i	−0.0612255	+	0.0191485i
$973$	6.26499	−	10.8513i	0.200846	−	0.347876i
$974$	16.0115	+	19.9973i	0.513040	+	0.640753i
$975$	−0.837280	+	0.483404i	−0.0268144	+	0.0154813i
$976$	8.49908	−	18.0081i	0.272049	−	0.576425i
$977$	30.6034	+	53.0066i	0.979088	+	1.69583i	0.665725	+	0.746197i	$0.268123\pi$
$977$	30.6034	+	53.0066i	0.979088	+	1.69583i	0.313364	+	0.949633i	$0.398544\pi$
$978$	10.0889	+	3.93683i	0.322609	+	0.125886i
$979$	7.17900	−	12.4344i	0.229442	−	0.397405i
$980$	13.8941	−	15.0924i	0.443831	−	0.482110i
$981$		−	10.4511i		−	0.333677i
$982$	5.28364	+	34.5948i	0.168608	+	1.10396i
$983$	−33.4843			−1.06798			−0.533991	−	0.845490i	$-0.679308\pi$
$983$	−33.4843			−1.06798			−0.533991	+	0.845490i	$0.679308\pi$
$984$	−30.2786	−	2.09022i	−0.965245	−	0.0666338i
$985$	19.4868	−	33.7522i	0.620902	−	1.07543i
$986$	−40.1789	+	6.13650i	−1.27956	+	0.195426i
$987$	−2.45279	+	1.41612i	−0.0780732	+	0.0450756i
$988$	0.898007	−	4.00671i	0.0285694	−	0.127471i
$989$	−33.1016	+	19.1112i	−1.05257	+	0.607702i
$990$	−3.47393	−	1.35557i	−0.110409	−	0.0430829i
$991$	55.8330			1.77359			0.886797	−	0.462159i	$-0.152925\pi$
$991$	55.8330			1.77359			0.886797	+	0.462159i	$0.152925\pi$
$992$	−11.1392	−	46.6913i	−0.353669	−	1.48245i
$993$	−13.2553	+	22.9588i	−0.420643	+	0.728576i
$994$	−14.7167	+	11.7834i	−0.466786	+	0.373748i
$995$	−21.8383	−	37.8251i	−0.692321	−	1.19914i
$996$	9.82064	−	10.6676i	0.311179	−	0.338017i
$997$	24.4850			0.775447			0.387723	−	0.921776i	$-0.373262\pi$
$997$	24.4850			0.775447			0.387723	+	0.921776i	$0.373262\pi$
$998$	3.87674	+	4.84179i	0.122716	+	0.153264i
$999$	3.71811	+	6.43996i	0.117636	+	0.203751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	804.2.j.a.499.1	✓	68
4.3	odd	2		804.2.j.b.499.11	yes	68
67.38	odd	6		804.2.j.b.775.11	yes	68
268.239	even	6	inner	804.2.j.a.775.1	yes	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
804.2.j.a.499.1	✓	68	1.1	even	1	trivial
804.2.j.a.775.1	yes	68	268.239	even	6	inner
804.2.j.b.499.11	yes	68	4.3	odd	2
804.2.j.b.775.11	yes	68	67.38	odd	6

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:	\( N \)	\(=\)	\( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	804.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39800 + 0.213516i) q^{2} -1.00000 q^{3} +(1.90882 - 0.596993i) q^{4} -1.98108i q^{5} +(1.39800 - 0.213516i) q^{6} +(-0.674999 + 1.16913i) q^{7} +(-2.54107 + 1.24216i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.39800 + 0.213516i) q^{2} -1.00000 q^{3} +(1.90882 - 0.596993i) q^{4} -1.98108i q^{5} +(1.39800 - 0.213516i) q^{6} +(-0.674999 + 1.16913i) q^{7} +(-2.54107 + 1.24216i) q^{8} +1.00000 q^{9} +(0.422992 + 2.76955i) q^{10} +(-0.665505 + 1.15269i) q^{11} +(-1.90882 + 0.596993i) q^{12} +(0.778626 - 0.449540i) q^{13} +(0.694021 - 1.77857i) q^{14} +1.98108i q^{15} +(3.28720 - 2.27910i) q^{16} +(-3.18636 - 5.51895i) q^{17} +(-1.39800 + 0.213516i) q^{18} +(1.97758 - 1.14175i) q^{19} +(-1.18269 - 3.78152i) q^{20} +(0.674999 - 1.16913i) q^{21} +(0.684260 - 1.75356i) q^{22} +(3.94074 - 2.27519i) q^{23} +(2.54107 - 1.24216i) q^{24} +1.07533 q^{25} +(-0.992537 + 0.794707i) q^{26} -1.00000 q^{27} +(-0.590489 + 2.63463i) q^{28} +(-2.25494 + 3.90567i) q^{29} +(-0.422992 - 2.76955i) q^{30} +(-4.24278 + 7.34872i) q^{31} +(-4.10889 + 3.88806i) q^{32} +(0.665505 - 1.15269i) q^{33} +(5.63293 + 7.03516i) q^{34} +(2.31614 + 1.33723i) q^{35} +(1.90882 - 0.596993i) q^{36} +(-3.71811 - 6.43996i) q^{37} +(-2.52087 + 2.01842i) q^{38} +(-0.778626 + 0.449540i) q^{39} +(2.46082 + 5.03406i) q^{40} +(-9.29294 - 5.36528i) q^{41} +(-0.694021 + 1.77857i) q^{42} -8.39986 q^{43} +(-0.582184 + 2.59758i) q^{44} -1.98108i q^{45} +(-5.02337 + 4.02213i) q^{46} +(-1.81688 - 1.04898i) q^{47} +(-3.28720 + 2.27910i) q^{48} +(2.58875 + 4.48385i) q^{49} +(-1.50332 + 0.229601i) q^{50} +(3.18636 + 5.51895i) q^{51} +(1.21789 - 1.32293i) q^{52} -8.69893i q^{53} +(1.39800 - 0.213516i) q^{54} +(2.28357 + 1.31842i) q^{55} +(0.262968 - 3.80930i) q^{56} +(-1.97758 + 1.14175i) q^{57} +(2.31848 - 5.94160i) q^{58} -3.00672i q^{59} +(1.18269 + 3.78152i) q^{60} +(4.31128 - 2.48912i) q^{61} +(4.36235 - 11.1794i) q^{62} +(-0.674999 + 1.16913i) q^{63} +(4.91407 - 6.31284i) q^{64} +(-0.890573 - 1.54252i) q^{65} +(-0.684260 + 1.75356i) q^{66} +(-0.750324 - 8.15089i) q^{67} +(-9.37697 - 8.63245i) q^{68} +(-3.94074 + 2.27519i) q^{69} +(-3.52349 - 1.37491i) q^{70} +(-8.55186 - 4.93742i) q^{71} +(-2.54107 + 1.24216i) q^{72} +(-2.61035 - 4.52126i) q^{73} +(6.57297 + 8.20921i) q^{74} -1.07533 q^{75} +(3.09322 - 3.36000i) q^{76} +(-0.898431 - 1.55613i) q^{77} +(0.992537 - 0.794707i) q^{78} +(-3.18040 + 5.50861i) q^{79} +(-4.51508 - 6.51220i) q^{80} +1.00000 q^{81} +(14.1371 + 5.51648i) q^{82} +(-6.27859 + 3.62494i) q^{83} +(0.590489 - 2.63463i) q^{84} +(-10.9335 + 6.31244i) q^{85} +(11.7430 - 1.79351i) q^{86} +(2.25494 - 3.90567i) q^{87} +(0.259269 - 3.75573i) q^{88} -10.7873 q^{89} +(0.422992 + 2.76955i) q^{90} +1.21376i q^{91} +(6.16389 - 6.69551i) q^{92} +(4.24278 - 7.34872i) q^{93} +(2.76398 + 1.07854i) q^{94} +(-2.26190 - 3.91773i) q^{95} +(4.10889 - 3.88806i) q^{96} +(-0.310273 + 0.179136i) q^{97} +(-4.57646 - 5.71569i) q^{98} +(-0.665505 + 1.15269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9}+O(q^{10}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9	\( 68 q - 68 q^{3} - 2 q^{4} + 4 q^{7} - 6 q^{8} + 68 q^{9} + 18 q^{10} + 2 q^{12} + 6 q^{13} + 10 q^{14} - 2 q^{16} - 36 q^{20} - 4 q^{21} - 22 q^{22} + 6 q^{24} - 68 q^{25} - q^{26} - 68 q^{27} + q^{28} - 8 q^{29} - 18 q^{30} + 2 q^{31} + 15 q^{32} - 2 q^{36} + 12 q^{37} - 22 q^{38} - 6 q^{39} + 18 q^{40} - 10 q^{42} - 4 q^{43} - 31 q^{44} + 32 q^{46} + 2 q^{48} - 46 q^{49} - 9 q^{50} - 28 q^{52} - 11 q^{56} + 4 q^{58} + 36 q^{60} + 6 q^{61} - 34 q^{62} + 4 q^{63} + 16 q^{64} + 22 q^{66} - 18 q^{67} + 34 q^{68} + 56 q^{70} - 36 q^{71} - 6 q^{72} + 6 q^{73} - 53 q^{74} + 68 q^{75} + 14 q^{76} - 4 q^{77} + q^{78} + 6 q^{79} + 55 q^{80} + 68 q^{81} - 26 q^{82} + 12 q^{83} - q^{84} - 21 q^{86} + 8 q^{87} - 50 q^{88} + 18 q^{90} + 10 q^{92} - 2 q^{93} - 16 q^{94} + 20 q^{95} - 15 q^{96} + 18 q^{97} - 70 q^{98}+O(q^{100}) \) 68 * q - 68 * q^3 - 2 * q^4 + 4 * q^7 - 6 * q^8 + 68 * q^9 + 18 * q^10 + 2 * q^12 + 6 * q^13 + 10 * q^14 - 2 * q^16 - 36 * q^20 - 4 * q^21 - 22 * q^22 + 6 * q^24 - 68 * q^25 - q^26 - 68 * q^27 + q^28 - 8 * q^29 - 18 * q^30 + 2 * q^31 + 15 * q^32 - 2 * q^36 + 12 * q^37 - 22 * q^38 - 6 * q^39 + 18 * q^40 - 10 * q^42 - 4 * q^43 - 31 * q^44 + 32 * q^46 + 2 * q^48 - 46 * q^49 - 9 * q^50 - 28 * q^52 - 11 * q^56 + 4 * q^58 + 36 * q^60 + 6 * q^61 - 34 * q^62 + 4 * q^63 + 16 * q^64 + 22 * q^66 - 18 * q^67 + 34 * q^68 + 56 * q^70 - 36 * q^71 - 6 * q^72 + 6 * q^73 - 53 * q^74 + 68 * q^75 + 14 * q^76 - 4 * q^77 + q^78 + 6 * q^79 + 55 * q^80 + 68 * q^81 - 26 * q^82 + 12 * q^83 - q^84 - 21 * q^86 + 8 * q^87 - 50 * q^88 + 18 * q^90 + 10 * q^92 - 2 * q^93 - 16 * q^94 + 20 * q^95 - 15 * q^96 + 18 * q^97 - 70 * q^98

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