LMFDB - Embedded newform 570.2.s.a.521.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(221,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, 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("570.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.s (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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.8
Character	$\chi$	$=$	570.521
Dual form			570.2.s.a.221.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.691758 + 1.58791i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.72105 - 0.194877i) q^{6} -1.96058 q^{7} +1.00000 q^{8} +(-2.04294 + 2.19691i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.691758 + 1.58791i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.72105 - 0.194877i) q^{6} -1.96058 q^{7} +1.00000 q^{8} +(-2.04294 + 2.19691i) q^{9} +(0.866025 - 0.500000i) q^{10} +4.91222i q^{11} +(1.02929 - 1.39304i) q^{12} +(1.73616 - 1.00237i) q^{13} +(0.980288 - 1.69791i) q^{14} +(0.194877 - 1.72105i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.39530 - 1.96028i) q^{17} +(-0.881106 - 2.86769i) q^{18} +(-3.86720 - 2.01117i) q^{19} +1.00000i q^{20} +(-1.35624 - 3.11322i) q^{21} +(-4.25411 - 2.45611i) q^{22} +(-5.91161 + 3.41307i) q^{23} +(0.691758 + 1.58791i) q^{24} +(0.500000 + 0.866025i) q^{25} +2.00475i q^{26} +(-4.90172 - 1.72429i) q^{27} +(0.980288 + 1.69791i) q^{28} +(-2.51673 - 4.35910i) q^{29} +(1.39304 + 1.02929i) q^{30} +0.233588i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-7.80018 + 3.39807i) q^{33} +(3.39530 - 1.96028i) q^{34} +(1.69791 + 0.980288i) q^{35} +(2.92405 + 0.670786i) q^{36} +7.19430i q^{37} +(3.67532 - 2.34350i) q^{38} +(2.79269 + 2.06347i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(5.88249 - 10.1888i) q^{41} +(3.37425 + 0.382070i) q^{42} +(-2.94487 + 5.10067i) q^{43} +(4.25411 - 2.45611i) q^{44} +(2.86769 - 0.881106i) q^{45} -6.82614i q^{46} +(1.60922 - 0.929084i) q^{47} +(-1.72105 - 0.194877i) q^{48} -3.15615 q^{49} -1.00000 q^{50} +(0.764024 - 6.74748i) q^{51} +(-1.73616 - 1.00237i) q^{52} +(5.29044 + 9.16331i) q^{53} +(3.94413 - 3.38287i) q^{54} +(2.45611 - 4.25411i) q^{55} -1.96058 q^{56} +(0.518398 - 7.53202i) q^{57} +5.03345 q^{58} +(4.25879 - 7.37643i) q^{59} +(-1.58791 + 0.691758i) q^{60} +(3.91378 + 6.77887i) q^{61} +(-0.202293 - 0.116794i) q^{62} +(4.00534 - 4.30720i) q^{63} +1.00000 q^{64} -2.00475 q^{65} +(0.957276 - 8.45419i) q^{66} +(-13.7456 + 7.93605i) q^{67} +3.92055i q^{68} +(-9.50907 - 7.02611i) q^{69} +(-1.69791 + 0.980288i) q^{70} +(-2.26439 + 3.92204i) q^{71} +(-2.04294 + 2.19691i) q^{72} +(1.13889 - 1.97262i) q^{73} +(-6.23045 - 3.59715i) q^{74} +(-1.02929 + 1.39304i) q^{75} +(0.191874 + 4.35467i) q^{76} -9.63077i q^{77} +(-3.18336 + 1.38680i) q^{78} +(10.7900 + 6.22958i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.652788 - 8.97629i) q^{81} +(5.88249 + 10.1888i) q^{82} +13.7111i q^{83} +(-2.01801 + 2.73115i) q^{84} +(1.96028 + 3.39530i) q^{85} +(-2.94487 - 5.10067i) q^{86} +(5.18091 - 7.01179i) q^{87} +4.91222i q^{88} +(5.48139 + 9.49404i) q^{89} +(-0.670786 + 2.92405i) q^{90} +(-3.40387 + 1.96523i) q^{91} +(5.91161 + 3.41307i) q^{92} +(-0.370917 + 0.161586i) q^{93} +1.85817i q^{94} +(2.34350 + 3.67532i) q^{95} +(1.02929 - 1.39304i) q^{96} +(-13.3158 - 7.68789i) q^{97} +(1.57807 - 2.73330i) q^{98} +(-10.7917 - 10.0354i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	$ 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) $ 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9 - 2 * q^12 + 18 * q^13 + 6 * q^14 - 12 * q^16 + 12 * q^17 + 2 * q^18 + 6 * q^19 - 6 * q^21 + 18 * q^22 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 + 40 * q^39 + 6 * q^41 - 6 * q^42 - 22 * q^43 - 18 * q^44 + 8 * q^45 + 12 * q^47 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.691758	+	1.58791i	0.399387	+	0.916782i
$3$	0.691758	+	1.58791i	0.399387	+	0.916782i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	−1.72105	−	0.194877i	−0.702617	−	0.0795580i
$7$	−1.96058			−0.741028			−0.370514	−	0.928827i	$-0.620818\pi$
$7$	−1.96058			−0.741028			−0.370514	+	0.928827i	$0.620818\pi$
$8$	1.00000			0.353553
$9$	−2.04294	+	2.19691i	−0.680980	+	0.732302i
$10$	0.866025	−	0.500000i	0.273861	−	0.158114i
$11$			4.91222i			1.48109i	0.672007	+	0.740545i	$0.265432\pi$
$11$			4.91222i			1.48109i	−0.672007	+	0.740545i	$0.734568\pi$
$12$	1.02929	−	1.39304i	0.297132	−	0.402135i
$13$	1.73616	−	1.00237i	0.481524	−	0.278008i	−0.239527	−	0.970890i	$-0.576992\pi$
$13$	1.73616	−	1.00237i	0.481524	−	0.278008i	0.721051	+	0.692881i	$0.243659\pi$
$14$	0.980288	−	1.69791i	0.261993	−	0.453785i
$15$	0.194877	−	1.72105i	0.0503169	−	0.444374i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.39530	−	1.96028i	−0.823481	−	0.475437i	0.0281343	−	0.999604i	$-0.491043\pi$
$17$	−3.39530	−	1.96028i	−0.823481	−	0.475437i	−0.851615	+	0.524167i	$0.824377\pi$
$18$	−0.881106	−	2.86769i	−0.207679	−	0.675921i
$19$	−3.86720	−	2.01117i	−0.887195	−	0.461394i
$19$	−3.86720	−	2.01117i	−0.887195	−	0.461394i
$20$			1.00000i			0.223607i
$21$	−1.35624	−	3.11322i	−0.295957	−	0.679361i
$22$	−4.25411	−	2.45611i	−0.906978	−	0.523644i
$23$	−5.91161	+	3.41307i	−1.23266	+	0.711674i	−0.967583	−	0.252554i	$-0.918729\pi$
$23$	−5.91161	+	3.41307i	−1.23266	+	0.711674i	−0.265073	+	0.964228i	$0.585396\pi$
$24$	0.691758	+	1.58791i	0.141205	+	0.324132i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			2.00475i			0.393163i
$27$	−4.90172	−	1.72429i	−0.943336	−	0.331839i
$28$	0.980288	+	1.69791i	0.185257	+	0.320874i
$29$	−2.51673	−	4.35910i	−0.467344	−	0.809464i	0.531959	−	0.846770i	$-0.321456\pi$
$29$	−2.51673	−	4.35910i	−0.467344	−	0.809464i	−0.999304	+	0.0373055i	$0.988123\pi$
$30$	1.39304	+	1.02929i	0.254333	+	0.187923i
$31$			0.233588i			0.0419536i	0.999780	+	0.0209768i	$0.00667761\pi$
$31$			0.233588i			0.0419536i	−0.999780	+	0.0209768i	$0.993322\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−7.80018	+	3.39807i	−1.35784	+	0.591528i
$34$	3.39530	−	1.96028i	0.582289	−	0.336185i
$35$	1.69791	+	0.980288i	0.286999	+	0.165699i
$36$	2.92405	+	0.670786i	0.487341	+	0.111798i
$37$			7.19430i			1.18274i	0.806402	+	0.591368i	$0.201412\pi$
$37$			7.19430i			1.18274i	−0.806402	+	0.591368i	$0.798588\pi$
$38$	3.67532	−	2.34350i	0.596216	−	0.380167i
$39$	2.79269	+	2.06347i	0.447188	+	0.330420i
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	5.88249	−	10.1888i	0.918690	−	1.59122i	0.117282	−	0.993099i	$-0.462582\pi$
$41$	5.88249	−	10.1888i	0.918690	−	1.59122i	0.801407	−	0.598119i	$-0.204085\pi$
$42$	3.37425	+	0.382070i	0.520659	+	0.0589547i
$43$	−2.94487	+	5.10067i	−0.449089	+	0.777845i	−0.998327	−	0.0578212i	$-0.981585\pi$
$43$	−2.94487	+	5.10067i	−0.449089	+	0.777845i	0.549238	+	0.835666i	$0.314918\pi$
$44$	4.25411	−	2.45611i	0.641331	−	0.370272i
$45$	2.86769	−	0.881106i	0.427490	−	0.131347i
$46$		−	6.82614i		−	1.00646i
$47$	1.60922	−	0.929084i	0.234729	−	0.135521i	−0.378023	−	0.925796i	$-0.623396\pi$
$47$	1.60922	−	0.929084i	0.234729	−	0.135521i	0.612752	+	0.790275i	$0.290063\pi$
$48$	−1.72105	−	0.194877i	−0.248413	−	0.0281280i
$49$	−3.15615			−0.450878
$50$	−1.00000			−0.141421
$51$	0.764024	−	6.74748i	0.106985	−	0.944836i
$52$	−1.73616	−	1.00237i	−0.240762	−	0.139004i
$53$	5.29044	+	9.16331i	0.726698	+	1.25868i	0.958271	+	0.285861i	$0.0922794\pi$
$53$	5.29044	+	9.16331i	0.726698	+	1.25868i	−0.231573	+	0.972817i	$0.574387\pi$
$54$	3.94413	−	3.38287i	0.536729	−	0.460350i
$55$	2.45611	−	4.25411i	0.331182	−	0.573624i
$56$	−1.96058			−0.261993
$57$	0.518398	−	7.53202i	0.0686635	−	0.997640i
$58$	5.03345			0.660925
$59$	4.25879	−	7.37643i	0.554447	−	0.960330i	−0.443500	−	0.896274i	$-0.646263\pi$
$59$	4.25879	−	7.37643i	0.554447	−	0.960330i	0.997946	−	0.0640552i	$-0.0204034\pi$
$60$	−1.58791	+	0.691758i	−0.204999	+	0.0893056i
$61$	3.91378	+	6.77887i	0.501108	+	0.867945i	0.999999	+	0.00128020i	$0.000407502\pi$
$61$	3.91378	+	6.77887i	0.501108	+	0.867945i	−0.498891	+	0.866665i	$0.666259\pi$
$62$	−0.202293	−	0.116794i	−0.0256912	−	0.0148328i
$63$	4.00534	−	4.30720i	0.504625	−	0.542656i
$64$	1.00000			0.125000
$65$	−2.00475			−0.248658
$66$	0.957276	−	8.45419i	0.117833	−	1.04064i
$67$	−13.7456	+	7.93605i	−1.67930	+	0.969542i	−0.717186	+	0.696882i	$0.754570\pi$
$67$	−13.7456	+	7.93605i	−1.67930	+	0.969542i	−0.962110	+	0.272661i	$0.912096\pi$
$68$			3.92055i			0.475437i
$69$	−9.50907	−	7.02611i	−1.14476	−	0.845844i
$70$	−1.69791	+	0.980288i	−0.202939	+	0.117167i
$71$	−2.26439	+	3.92204i	−0.268734	+	0.465461i	−0.968535	−	0.248877i	$-0.919939\pi$
$71$	−2.26439	+	3.92204i	−0.268734	+	0.465461i	0.699801	+	0.714338i	$0.253272\pi$
$72$	−2.04294	+	2.19691i	−0.240763	+	0.258908i
$73$	1.13889	−	1.97262i	0.133297	−	0.230877i	−0.791649	−	0.610977i	$-0.790777\pi$
$73$	1.13889	−	1.97262i	0.133297	−	0.230877i	0.924946	+	0.380099i	$0.124110\pi$
$74$	−6.23045	−	3.59715i	−0.724275	−	0.418160i
$75$	−1.02929	+	1.39304i	−0.118853	+	0.160854i
$76$	0.191874	+	4.35467i	0.0220095	+	0.499515i
$77$		−	9.63077i		−	1.09753i
$78$	−3.18336	+	1.38680i	−0.360445	+	0.157024i
$79$	10.7900	+	6.22958i	1.21396	+	0.700883i	0.963621	−	0.267274i	$-0.0861229\pi$
$79$	10.7900	+	6.22958i	1.21396	+	0.700883i	0.250344	+	0.968157i	$0.419456\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−0.652788	−	8.97629i	−0.0725320	−	0.997366i
$82$	5.88249	+	10.1888i	0.649612	+	1.12516i
$83$			13.7111i			1.50499i	0.658599	+	0.752494i	$0.271149\pi$
$83$			13.7111i			1.50499i	−0.658599	+	0.752494i	$0.728851\pi$
$84$	−2.01801	+	2.73115i	−0.220183	+	0.297993i
$85$	1.96028	+	3.39530i	0.212622	+	0.368272i
$86$	−2.94487	−	5.10067i	−0.317554	−	0.550019i
$87$	5.18091	−	7.01179i	0.555451	−	0.751743i
$88$			4.91222i			0.523644i
$89$	5.48139	+	9.49404i	0.581026	+	1.00637i	0.995358	+	0.0962408i	$0.0306819\pi$
$89$	5.48139	+	9.49404i	0.581026	+	1.00637i	−0.414332	+	0.910126i	$0.635985\pi$
$90$	−0.670786	+	2.92405i	−0.0707070	+	0.308222i
$91$	−3.40387	+	1.96523i	−0.356823	+	0.206012i
$92$	5.91161	+	3.41307i	0.616328	+	0.355837i
$93$	−0.370917	+	0.161586i	−0.0384623	+	0.0167557i
$94$			1.85817i			0.191655i
$95$	2.34350	+	3.67532i	0.240439	+	0.377080i
$96$	1.02929	−	1.39304i	0.105052	−	0.142176i
$97$	−13.3158	−	7.68789i	−1.35202	−	0.780587i	−0.363484	−	0.931600i	$-0.618413\pi$
$97$	−13.3158	−	7.68789i	−1.35202	−	0.780587i	−0.988532	+	0.151013i	$0.951746\pi$
$98$	1.57807	−	2.73330i	0.159409	−	0.276105i
$99$	−10.7917	−	10.0354i	−1.08460	−	1.00859i
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	9.94449	−	5.74146i	0.989514	−	0.571296i	0.0843851	−	0.996433i	$-0.473107\pi$
$101$	9.94449	−	5.74146i	0.989514	−	0.571296i	0.905129	+	0.425137i	$0.139774\pi$
$102$	5.46148	+	4.03541i	0.540767	+	0.399565i
$103$			1.76334i			0.173747i	0.996219	+	0.0868736i	$0.0276876\pi$
$103$			1.76334i			0.173747i	−0.996219	+	0.0868736i	$0.972312\pi$
$104$	1.73616	−	1.00237i	0.170245	−	0.0982907i
$105$	−0.382070	+	3.37425i	−0.0372862	+	0.329293i
$106$	−10.5809			−1.02771
$107$	3.01131			0.291115			0.145557	−	0.989350i	$-0.453502\pi$
$107$	3.01131			0.291115			0.145557	+	0.989350i	$0.453502\pi$
$108$	0.957584	+	5.10716i	0.0921436	+	0.491436i
$109$	9.05950	+	5.23051i	0.867743	+	0.500992i	0.866598	−	0.499008i	$-0.166302\pi$
$109$	9.05950	+	5.23051i	0.867743	+	0.500992i	0.00114554	+	0.999999i	$0.499635\pi$
$110$	2.45611	+	4.25411i	0.234181	+	0.405613i
$111$	−11.4239	+	4.97672i	−1.08431	+	0.472369i
$112$	0.980288	−	1.69791i	0.0926285	−	0.160437i
$113$	−12.1589			−1.14382			−0.571909	−	0.820317i	$-0.693797\pi$
$113$	−12.1589			−1.14382			−0.571909	+	0.820317i	$0.693797\pi$
$114$	6.26372	+	4.21495i	0.586651	+	0.394767i
$115$	6.82614			0.636541
$116$	−2.51673	+	4.35910i	−0.233672	+	0.404732i
$117$	−1.34475	+	5.86197i	−0.124323	+	0.541939i
$118$	4.25879	+	7.37643i	0.392053	+	0.679056i
$119$	6.65674	+	3.84327i	0.610222	+	0.352312i
$120$	0.194877	−	1.72105i	0.0177897	−	0.157110i
$121$	−13.1299			−1.19363
$122$	−7.82756			−0.708674
$123$	20.2481	+	2.29272i	1.82571	+	0.206727i
$124$	0.202293	−	0.116794i	0.0181664	−	0.0104884i
$125$		−	1.00000i		−	0.0894427i
$126$	1.72747	+	5.62232i	0.153896	+	0.500876i
$127$	11.2081	−	6.47100i	0.994557	−	0.574208i	0.0879240	−	0.996127i	$-0.471977\pi$
$127$	11.2081	−	6.47100i	0.994557	−	0.574208i	0.906633	+	0.421919i	$0.138643\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−10.1366	−	1.14777i	−0.892475	−	0.101056i
$130$	1.00237	−	1.73616i	0.0879139	−	0.152271i
$131$	−7.74381	−	4.47089i	−0.676580	−	0.390624i	0.121985	−	0.992532i	$-0.461074\pi$
$131$	−7.74381	−	4.47089i	−0.676580	−	0.390624i	−0.798565	+	0.601908i	$0.794407\pi$
$132$	6.84290	+	5.05612i	0.595598	+	0.440079i
$133$	7.58193	+	3.94305i	0.657436	+	0.341906i
$134$		−	15.8721i		−	1.37114i
$135$	3.38287	+	3.94413i	0.291151	+	0.339457i
$136$	−3.39530	−	1.96028i	−0.291145	−	0.168092i
$137$	−3.55144	+	2.05042i	−0.303420	+	0.175180i	−0.643978	−	0.765044i	$-0.722717\pi$
$137$	−3.55144	+	2.05042i	−0.303420	+	0.175180i	0.340558	+	0.940223i	$0.389384\pi$
$138$	10.8393	−	4.72204i	0.922704	−	0.401967i
$139$	6.74169	+	11.6770i	0.571823	+	0.990426i	0.996379	+	0.0850246i	$0.0270969\pi$
$139$	6.74169	+	11.6770i	0.571823	+	0.990426i	−0.424556	+	0.905402i	$0.639570\pi$
$140$		−	1.96058i		−	0.165699i
$141$	2.58850	+	1.91260i	0.217991	+	0.161070i
$142$	−2.26439	−	3.92204i	−0.190024	−	0.329131i
$143$	4.92387	+	8.52840i	0.411755	+	0.713181i
$144$	−0.881106	−	2.86769i	−0.0734255	−	0.238974i
$145$			5.03345i			0.418006i
$146$	1.13889	+	1.97262i	0.0942553	+	0.163255i
$147$	−2.18329	−	5.01169i	−0.180075	−	0.413357i
$148$	6.23045	−	3.59715i	0.512140	−	0.295684i
$149$	−3.99172	−	2.30462i	−0.327014	−	0.188802i	0.327500	−	0.944851i	$-0.393794\pi$
$149$	−3.99172	−	2.30462i	−0.327014	−	0.188802i	−0.654515	+	0.756049i	$0.727127\pi$
$150$	−0.691758	−	1.58791i	−0.0564818	−	0.129653i
$151$			17.3564i			1.41245i	0.707990	+	0.706223i	$0.249602\pi$
$151$			17.3564i			1.41245i	−0.707990	+	0.706223i	$0.750398\pi$
$152$	−3.86720	−	2.01117i	−0.313671	−	0.163127i
$153$	11.2429	−	3.45442i	0.908938	−	0.279274i
$154$	8.34049	+	4.81539i	0.672096	+	0.388035i
$155$	0.116794	−	0.202293i	0.00938111	−	0.0162486i
$156$	0.390678	−	3.45027i	0.0312793	−	0.276243i
$157$	0.833700	−	1.44401i	0.0665365	−	0.115245i	−0.830838	−	0.556514i	$-0.812138\pi$
$157$	0.833700	−	1.44401i	0.0665365	−	0.115245i	0.897375	+	0.441270i	$0.145472\pi$
$158$	−10.7900	+	6.22958i	−0.858403	+	0.495599i
$159$	−10.8908	+	14.7396i	−0.863700	+	1.16892i
$160$			1.00000i			0.0790569i
$161$	11.5902	−	6.69158i	0.913432	−	0.527370i
$162$	8.10009	+	3.92282i	0.636403	+	0.308206i
$163$	8.55940			0.670424			0.335212	−	0.942143i	$-0.391192\pi$
$163$	8.55940			0.670424			0.335212	+	0.942143i	$0.391192\pi$
$164$	−11.7650			−0.918690
$165$	8.45419	+	0.957276i	0.658158	+	0.0745238i
$166$	−11.8742	−	6.85554i	−0.921613	−	0.532093i
$167$	4.84533	+	8.39236i	0.374943	+	0.649420i	0.990318	−	0.138814i	$-0.0443290\pi$
$167$	4.84533	+	8.39236i	0.374943	+	0.649420i	−0.615376	+	0.788234i	$0.710996\pi$
$168$	−1.35624	−	3.11322i	−0.104637	−	0.240190i
$169$	−4.49050	+	7.77777i	−0.345423	+	0.598290i
$170$	−3.92055			−0.300693
$171$	12.3188	−	4.38716i	0.942042	−	0.335495i
$172$	5.88974			0.449089
$173$	−5.22274	+	9.04605i	−0.397078	+	0.687759i	−0.993364	−	0.115013i	$-0.963309\pi$
$173$	−5.22274	+	9.04605i	−0.397078	+	0.687759i	0.596286	+	0.802772i	$0.296642\pi$
$174$	3.48193	+	7.99269i	0.263965	+	0.605924i
$175$	−0.980288	−	1.69791i	−0.0741028	−	0.128350i
$176$	−4.25411	−	2.45611i	−0.320665	−	0.185136i
$177$	14.6592	+	1.65987i	1.10185	+	0.124764i
$178$	−10.9628			−0.821695
$179$	−1.34670			−0.100657			−0.0503285	−	0.998733i	$-0.516027\pi$
$179$	−1.34670			−0.100657			−0.0503285	+	0.998733i	$0.516027\pi$
$180$	−2.19691	−	2.04294i	−0.163748	−	0.152272i
$181$	12.6588	−	7.30854i	0.940919	−	0.543240i	0.0506704	−	0.998715i	$-0.483864\pi$
$181$	12.6588	−	7.30854i	0.940919	−	0.543240i	0.890248	+	0.455476i	$0.150531\pi$
$182$		−	3.93045i		−	0.291345i
$183$	−8.05687	+	10.9041i	−0.595581	+	0.806053i
$184$	−5.91161	+	3.41307i	−0.435810	+	0.251615i
$185$	3.59715	−	6.23045i	0.264468	−	0.458072i
$186$	0.0455208	−	0.402017i	0.00333774	−	0.0294773i
$187$	9.62931	−	16.6785i	0.704165	−	1.21965i
$188$	−1.60922	−	0.929084i	−0.117364	−	0.0677604i
$189$	9.61019	+	3.38059i	0.699038	+	0.245902i
$190$	−4.35467	+	0.191874i	−0.315921	+	0.0139200i
$191$			6.09365i			0.440921i	0.975396	+	0.220461i	$0.0707560\pi$
$191$			6.09365i			0.440921i	−0.975396	+	0.220461i	$0.929244\pi$
$192$	0.691758	+	1.58791i	0.0499234	+	0.114598i
$193$	2.59888	+	1.50046i	0.187071	+	0.108006i	0.590611	−	0.806957i	$-0.298887\pi$
$193$	2.59888	+	1.50046i	0.187071	+	0.108006i	−0.403540	+	0.914962i	$0.632220\pi$
$194$	13.3158	−	7.68789i	0.956020	−	0.551958i
$195$	−1.38680	−	3.18336i	−0.0993108	−	0.227965i
$196$	1.57807	+	2.73330i	0.112719	+	0.195236i
$197$		−	2.48104i		−	0.176767i	−0.996087	−	0.0883833i	$-0.971830\pi$
$197$		−	2.48104i		−	0.176767i	0.996087	−	0.0883833i	$-0.0281700\pi$
$198$	14.0867	−	4.32818i	1.00110	−	0.307591i
$199$	−11.8062	−	20.4489i	−0.836918	−	1.44958i	−0.892459	−	0.451128i	$-0.851022\pi$
$199$	−11.8062	−	20.4489i	−0.836918	−	1.44958i	0.0555409	−	0.998456i	$-0.482312\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−22.1104	−	16.3371i	−1.55955	−	1.15233i
$202$			11.4829i			0.807935i
$203$	4.93423	+	8.54634i	0.346315	+	0.599836i
$204$	−6.22550	+	2.71208i	−0.435872	+	0.189883i
$205$	−10.1888	+	5.88249i	−0.711614	+	0.410851i
$206$	−1.52710	−	0.881671i	−0.106398	−	0.0614289i
$207$	4.57888	−	19.9599i	0.318254	−	1.38731i
$208$			2.00475i			0.139004i
$209$	9.87930	−	18.9965i	0.683366	−	1.31402i
$210$	−2.73115	−	2.01801i	−0.188468	−	0.139256i
$211$	2.52326	+	1.45680i	0.173708	+	0.100290i	0.584333	−	0.811514i	$-0.301356\pi$
$211$	2.52326	+	1.45680i	0.173708	+	0.100290i	−0.410625	+	0.911804i	$0.634689\pi$
$212$	5.29044	−	9.16331i	0.363349	−	0.629339i
$213$	−7.79428	−	0.882554i	−0.534055	−	0.0604716i
$214$	−1.50566	+	2.60787i	−0.102925	+	0.178271i
$215$	5.10067	−	2.94487i	0.347863	−	0.200839i
$216$	−4.90172	−	1.72429i	−0.333520	−	0.117323i
$217$		−	0.457966i		−	0.0310888i
$218$	−9.05950	+	5.23051i	−0.613587	+	0.354255i
$219$	3.92018	+	0.443886i	0.264901	+	0.0299950i
$220$	−4.91222			−0.331182
$221$	−7.85971			−0.528702
$222$	1.40200	−	12.3818i	0.0940961	−	0.831010i
$223$	3.39391	+	1.95947i	0.227273	+	0.131216i	0.609313	−	0.792930i	$-0.291445\pi$
$223$	3.39391	+	1.95947i	0.227273	+	0.131216i	−0.382040	+	0.924146i	$0.624778\pi$
$224$	0.980288	+	1.69791i	0.0654982	+	0.113446i
$225$	−2.92405	−	0.670786i	−0.194936	−	0.0447190i
$226$	6.07947	−	10.5300i	0.404400	−	0.700442i
$227$	−0.316084			−0.0209793			−0.0104896	−	0.999945i	$-0.503339\pi$
$227$	−0.316084			−0.0209793			−0.0104896	+	0.999945i	$0.503339\pi$
$228$	−6.78212	+	3.31706i	−0.449157	+	0.219678i
$229$	6.13340			0.405306			0.202653	−	0.979251i	$-0.435044\pi$
$229$	6.13340			0.405306			0.202653	+	0.979251i	$0.435044\pi$
$230$	−3.41307	+	5.91161i	−0.225051	+	0.389800i
$231$	15.2928	−	6.66217i	1.00619	−	0.438339i
$232$	−2.51673	−	4.35910i	−0.165231	−	0.286189i
$233$	−9.37631	−	5.41341i	−0.614262	−	0.354644i	0.160369	−	0.987057i	$-0.448731\pi$
$233$	−9.37631	−	5.41341i	−0.614262	−	0.354644i	−0.774632	+	0.632413i	$0.782065\pi$
$234$	−4.40424	−	4.09558i	−0.287914	−	0.267736i
$235$	−1.85817			−0.121214
$236$	−8.51757			−0.554447
$237$	−2.42800	+	21.4429i	−0.157715	+	1.39287i
$238$	−6.65674	+	3.84327i	−0.431492	+	0.249122i
$239$		−	3.18686i		−	0.206141i	−0.994674	−	0.103070i	$-0.967133\pi$
$239$		−	3.18686i		−	0.206141i	0.994674	−	0.103070i	$-0.0328667\pi$
$240$	1.39304	+	1.02929i	0.0899202	+	0.0664407i
$241$	−16.5317	+	9.54461i	−1.06490	+	0.614822i	−0.926785	−	0.375593i	$-0.877439\pi$
$241$	−16.5317	+	9.54461i	−1.06490	+	0.614822i	−0.138119	+	0.990416i	$0.544106\pi$
$242$	6.56495	−	11.3708i	0.422011	−	0.730944i
$243$	13.8020	−	7.24600i	0.885399	−	0.464831i
$244$	3.91378	−	6.77887i	0.250554	−	0.433973i
$245$	2.73330	+	1.57807i	0.174624	+	0.100819i
$246$	−12.1096	+	16.3890i	−0.772081	+	1.04493i
$247$	−8.73001	+	0.384659i	−0.555477	+	0.0244753i
$248$			0.233588i			0.0148328i
$249$	−21.7720	+	9.48476i	−1.37975	+	0.601072i
$250$	0.866025	+	0.500000i	0.0547723	+	0.0316228i
$251$	10.0866	−	5.82352i	0.636663	−	0.367578i	−0.146665	−	0.989186i	$-0.546854\pi$
$251$	10.0866	−	5.82352i	0.636663	−	0.367578i	0.783328	+	0.621609i	$0.213521\pi$
$252$	−5.73281	−	1.31513i	−0.361133	−	0.0828451i
$253$	−16.7657	−	29.0391i	−1.05405	−	1.82567i
$254$			12.9420i			0.812053i
$255$	−4.03541	+	5.46148i	−0.252707	+	0.342011i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	11.7735	+	20.3923i	0.734410	+	1.27204i	0.954982	+	0.296665i	$0.0958746\pi$
$257$	11.7735	+	20.3923i	0.734410	+	1.27204i	−0.220571	+	0.975371i	$0.570792\pi$
$258$	6.06228	−	8.20463i	0.377421	−	0.510798i
$259$		−	14.1050i		−	0.876440i
$260$	1.00237	+	1.73616i	0.0621645	+	0.107672i
$261$	14.7181	+	3.37637i	0.911025	+	0.208992i
$262$	7.74381	−	4.47089i	0.478414	−	0.276213i
$263$	3.46036	+	1.99784i	0.213375	+	0.123192i	0.602879	−	0.797833i	$-0.294020\pi$
$263$	3.46036	+	1.99784i	0.213375	+	0.123192i	−0.389504	+	0.921025i	$0.627354\pi$
$264$	−7.80018	+	3.39807i	−0.480068	+	0.209137i
$265$		−	10.5809i		−	0.649979i
$266$	−7.20574	+	4.59462i	−0.441812	+	0.281714i
$267$	−11.2839	+	15.2716i	−0.690565	+	0.934604i
$268$	13.7456	+	7.93605i	0.839648	+	0.484771i
$269$	−1.12373	+	1.94636i	−0.0685152	+	0.118672i	−0.898248	−	0.439489i	$-0.855160\pi$
$269$	−1.12373	+	1.94636i	−0.0685152	+	0.118672i	0.829733	+	0.558161i	$0.188493\pi$
$270$	−5.10716	+	0.957584i	−0.310812	+	0.0582767i
$271$	2.70149	−	4.67912i	0.164104	−	0.284236i	−0.772233	−	0.635340i	$-0.780860\pi$
$271$	2.70149	−	4.67912i	0.164104	−	0.284236i	0.936337	+	0.351103i	$0.114193\pi$
$272$	3.39530	−	1.96028i	0.205870	−	0.118859i
$273$	−5.47527	−	4.04559i	−0.331378	−	0.244851i
$274$		−	4.10085i		−	0.247741i
$275$	−4.25411	+	2.45611i	−0.256532	+	0.148109i
$276$	−1.33025	+	11.7481i	−0.0800719	+	0.707155i
$277$	−20.1531			−1.21088			−0.605441	−	0.795890i	$-0.707003\pi$
$277$	−20.1531			−1.21088			−0.605441	+	0.795890i	$0.707003\pi$
$278$	−13.4834			−0.808680
$279$	−0.513170	−	0.477206i	−0.0307227	−	0.0285696i
$280$	1.69791	+	0.980288i	0.101469	+	0.0585834i
$281$	−9.35418	−	16.2019i	−0.558023	−	0.966525i	−0.997661	−	0.0683499i	$-0.978227\pi$
$281$	−9.35418	−	16.2019i	−0.558023	−	0.966525i	0.439638	−	0.898175i	$-0.355107\pi$
$282$	−2.95061	+	1.28540i	−0.175706	+	0.0765447i
$283$	10.5801	−	18.3252i	0.628919	−	1.08932i	−0.358850	−	0.933395i	$-0.616831\pi$
$283$	10.5801	−	18.3252i	0.628919	−	1.08932i	0.987769	−	0.155924i	$-0.0498355\pi$
$284$	4.52879			0.268734
$285$	−4.21495	+	6.26372i	−0.249672	+	0.371031i
$286$	−9.84775			−0.582310
$287$	−11.5331	+	19.9758i	−0.680775	+	1.17914i
$288$	2.92405	+	0.670786i	0.172301	+	0.0395264i
$289$	−0.814625	−	1.41097i	−0.0479191	−	0.0829984i
$290$	−4.35910	−	2.51673i	−0.255975	−	0.147787i
$291$	2.99638	−	26.4625i	0.175651	−	1.55126i
$292$	−2.27778			−0.133297
$293$	−12.3120			−0.719275			−0.359638	−	0.933092i	$-0.617100\pi$
$293$	−12.3120			−0.719275			−0.359638	+	0.933092i	$0.617100\pi$
$294$	5.43189	+	0.615059i	0.316794	+	0.0358709i
$295$	−7.37643	+	4.25879i	−0.429472	+	0.247956i
$296$			7.19430i			0.418160i
$297$	8.47007	−	24.0783i	0.491483	−	1.39717i
$298$	3.99172	−	2.30462i	0.231234	−	0.133503i
$299$	−6.84234	+	11.8513i	−0.395702	+	0.685377i
$300$	1.72105	+	0.194877i	0.0993650	+	0.0112512i
$301$	5.77364	−	10.0002i	0.332787	−	0.576405i
$302$	−15.0311	−	8.67821i	−0.864943	−	0.499375i
$303$	15.9961	+	11.8193i	0.918953	+	0.679001i
$304$	3.67532	−	2.34350i	0.210794	−	0.134409i
$305$		−	7.82756i		−	0.448205i
$306$	−2.62985	+	11.4639i	−0.150339	+	0.655347i
$307$	−13.1520	−	7.59331i	−0.750624	−	0.433373i	0.0752952	−	0.997161i	$-0.476010\pi$
$307$	−13.1520	−	7.59331i	−0.750624	−	0.433373i	−0.825919	+	0.563788i	$0.809343\pi$
$308$	−8.34049	+	4.81539i	−0.475244	+	0.274382i
$309$	−2.80004	+	1.21981i	−0.159288	+	0.0693924i
$310$	0.116794	+	0.202293i	0.00663344	+	0.0114895i
$311$			31.8839i			1.80797i	0.427563	+	0.903986i	$0.359372\pi$
$311$			31.8839i			1.80797i	−0.427563	+	0.903986i	$0.640628\pi$
$312$	2.79269	+	2.06347i	0.158105	+	0.116821i
$313$	−7.47579	−	12.9485i	−0.422557	−	0.731890i	0.573632	−	0.819113i	$-0.305534\pi$
$313$	−7.47579	−	12.9485i	−0.422557	−	0.731890i	−0.996189	+	0.0872234i	$0.972201\pi$
$314$	0.833700	+	1.44401i	0.0470484	+	0.0814902i
$315$	−5.62232	+	1.72747i	−0.316782	+	0.0973321i
$316$		−	12.4592i		−	0.700883i
$317$	−12.7583	−	22.0980i	−0.716577	−	1.24115i	−0.962348	−	0.271821i	$-0.912374\pi$
$317$	−12.7583	−	22.0980i	−0.716577	−	1.24115i	0.245771	−	0.969328i	$-0.420959\pi$
$318$	−7.31942	−	16.8015i	−0.410452	−	0.942183i
$319$	21.4128	−	12.3627i	1.19889	−	0.692179i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	2.08310	+	4.78171i	0.116267	+	0.266889i
$322$			13.3832i			0.745814i
$323$	9.18784	+	14.4093i	0.511225	+	0.801755i
$324$	−7.44731	+	5.05348i	−0.413739	+	0.280749i
$325$	1.73616	+	1.00237i	0.0963049	+	0.0556016i
$326$	−4.27970	+	7.41266i	−0.237031	+	0.410549i
$327$	−2.03861	+	18.0040i	−0.112735	+	0.995621i
$328$	5.88249	−	10.1888i	0.324806	−	0.562580i
$329$	−3.15500	+	1.82154i	−0.173941	+	0.100425i
$330$	−5.05612	+	6.84290i	−0.278330	+	0.376689i
$331$		−	23.6270i		−	1.29866i	−0.760508	−	0.649329i	$-0.775050\pi$
$331$		−	23.6270i		−	1.29866i	0.760508	−	0.649329i	$-0.224950\pi$
$332$	11.8742	−	6.85554i	0.651679	−	0.376247i
$333$	−15.8052	−	14.6975i	−0.866120	−	0.805420i
$334$	−9.69066			−0.530249
$335$	15.8721			0.867185
$336$	3.37425	+	0.382070i	0.184081	+	0.0208436i
$337$	−1.65491	−	0.955464i	−0.0901489	−	0.0520475i	0.454248	−	0.890875i	$-0.349908\pi$
$337$	−1.65491	−	0.955464i	−0.0901489	−	0.0520475i	−0.544397	+	0.838828i	$0.683241\pi$
$338$	−4.49050	−	7.77777i	−0.244251	−	0.423055i
$339$	−8.41105	−	19.3074i	−0.456826	−	1.04863i
$340$	1.96028	−	3.39530i	0.106311	−	0.184136i
$341$	−1.14743			−0.0621370
$342$	−2.36000	+	12.8620i	−0.127614	+	0.695496i
$343$	19.9119			1.07514
$344$	−2.94487	+	5.10067i	−0.158777	+	0.275010i
$345$	4.72204	+	10.8393i	0.254226	+	0.583569i
$346$	−5.22274	−	9.04605i	−0.280776	−	0.486319i
$347$	13.6960	+	7.90736i	0.735237	+	0.424489i	0.820335	−	0.571883i	$-0.193787\pi$
$347$	13.6960	+	7.90736i	0.735237	+	0.424489i	−0.0850978	+	0.996373i	$0.527120\pi$
$348$	−8.66284	−	0.980902i	−0.464377	−	0.0525819i
$349$	−29.7786			−1.59401			−0.797006	−	0.603972i	$-0.793584\pi$
$349$	−29.7786			−1.59401			−0.797006	+	0.603972i	$0.793584\pi$
$350$	1.96058			0.104797
$351$	−10.2385	+	1.91971i	−0.546493	+	0.102467i
$352$	4.25411	−	2.45611i	0.226745	−	0.130911i
$353$		−	2.45671i		−	0.130758i	−0.997861	−	0.0653788i	$-0.979174\pi$
$353$		−	2.45671i		−	0.130758i	0.997861	−	0.0653788i	$-0.0208256\pi$
$354$	−8.76709	+	11.8653i	−0.465965	+	0.630633i
$355$	3.92204	−	2.26439i	0.208160	−	0.120182i
$356$	5.48139	−	9.49404i	0.290513	−	0.503183i
$357$	−1.49793	+	13.2289i	−0.0792787	+	0.700150i
$358$	0.673349	−	1.16628i	0.0355876	−	0.0616396i
$359$	3.05773	+	1.76538i	0.161381	+	0.0931733i	0.578515	−	0.815671i	$-0.303632\pi$
$359$	3.05773	+	1.76538i	0.161381	+	0.0931733i	−0.417135	+	0.908845i	$0.636966\pi$
$360$	2.86769	−	0.881106i	0.151141	−	0.0464384i
$361$	10.9104	+	15.5552i	0.574232	+	0.818693i
$362$			14.6171i			0.768257i
$363$	−9.08271	−	20.8491i	−0.476719	−	1.09430i
$364$	3.40387	+	1.96523i	0.178411	+	0.103006i
$365$	−1.97262	+	1.13889i	−0.103251	+	0.0596123i
$366$	−5.41478	−	12.4295i	−0.283035	−	0.649700i
$367$	−1.33512	−	2.31249i	−0.0696925	−	0.120711i	0.829073	−	0.559140i	$-0.188868\pi$
$367$	−1.33512	−	2.31249i	−0.0696925	−	0.120711i	−0.898766	+	0.438429i	$0.855535\pi$
$368$		−	6.82614i		−	0.355837i
$369$	10.3662	+	33.7383i	0.539642	+	1.75635i
$370$	3.59715	+	6.23045i	0.187007	+	0.323906i
$371$	−10.3723	−	17.9654i	−0.538503	−	0.932715i
$372$	0.325396	+	0.240431i	0.0168710	+	0.0124657i
$373$		−	4.16443i		−	0.215626i	−0.994171	−	0.107813i	$-0.965615\pi$
$373$		−	4.16443i		−	0.215626i	0.994171	−	0.107813i	$-0.0343848\pi$
$374$	9.62931	+	16.6785i	0.497920	+	0.862422i
$375$	1.58791	−	0.691758i	0.0819995	−	0.0357223i
$376$	1.60922	−	0.929084i	0.0829892	−	0.0479138i
$377$	−8.73888	−	5.04540i	−0.450075	−	0.259851i
$378$	−7.73277	+	6.63237i	−0.397731	+	0.341132i
$379$		−	10.8219i		−	0.555884i	−0.960598	−	0.277942i	$-0.910348\pi$
$379$		−	10.8219i		−	0.555884i	0.960598	−	0.277942i	$-0.0896523\pi$
$380$	2.01117	−	3.86720i	0.103171	−	0.198383i
$381$	18.0287	+	13.3211i	0.923637	+	0.682462i
$382$	−5.27726	−	3.04683i	−0.270008	−	0.155889i
$383$	8.28137	−	14.3437i	0.423158	−	0.732931i	−0.573088	−	0.819494i	$-0.694255\pi$
$383$	8.28137	−	14.3437i	0.423158	−	0.732931i	0.996246	+	0.0865623i	$0.0275882\pi$
$384$	−1.72105	−	0.194877i	−0.0878271	−	0.00994475i
$385$	−4.81539	+	8.34049i	−0.245415	+	0.425071i
$386$	−2.59888	+	1.50046i	−0.132279	+	0.0763715i
$387$	−5.18949	−	16.8900i	−0.263797	−	0.858565i
$388$			15.3758i			0.780587i
$389$	32.4626	−	18.7423i	1.64592	−	0.950273i	0.667251	−	0.744833i	$-0.267471\pi$
$389$	32.4626	−	18.7423i	1.64592	−	0.950273i	0.978670	−	0.205440i	$-0.0658625\pi$
$390$	3.45027	+	0.390678i	0.174711	+	0.0197827i
$391$	26.7623			1.35343
$392$	−3.15615			−0.159409
$393$	1.74254	−	15.3893i	0.0878997	−	0.776286i
$394$	2.14864	+	1.24052i	0.108247	+	0.0624965i
$395$	−6.22958	−	10.7900i	−0.313444	−	0.542902i
$396$	−3.29505	+	14.3636i	−0.165582	+	0.721796i
$397$	−2.65169	+	4.59286i	−0.133085	+	0.230509i	−0.924864	−	0.380298i	$-0.875822\pi$
$397$	−2.65169	+	4.59286i	−0.133085	+	0.230509i	0.791780	+	0.610807i	$0.209155\pi$
$398$	23.6124			1.18358
$399$	−1.01636	+	14.7671i	−0.0508815	+	0.739279i
$400$	−1.00000			−0.0500000
$401$	−3.00036	+	5.19678i	−0.149831	+	0.259515i	−0.931165	−	0.364598i	$-0.881206\pi$
$401$	−3.00036	+	5.19678i	−0.149831	+	0.259515i	0.781334	+	0.624113i	$0.214540\pi$
$402$	25.2035	−	10.9797i	1.25704	−	0.547615i
$403$	0.234142	+	0.405546i	0.0116634	+	0.0202017i
$404$	−9.94449	−	5.74146i	−0.494757	−	0.285648i
$405$	−3.92282	+	8.10009i	−0.194926	+	0.402497i
$406$	−9.86847			−0.489764
$407$	−35.3400			−1.75174
$408$	0.764024	−	6.74748i	0.0378248	−	0.334050i
$409$	−23.6531	+	13.6561i	−1.16957	+	0.675253i	−0.953579	−	0.301143i	$-0.902632\pi$
$409$	−23.6531	+	13.6561i	−1.16957	+	0.675253i	−0.215993	+	0.976395i	$0.569299\pi$
$410$		−	11.7650i		−	0.581030i
$411$	−5.71263	−	4.22098i	−0.281783	−	0.208206i
$412$	1.52710	−	0.881671i	0.0752348	−	0.0434368i
$413$	−8.34967	+	14.4620i	−0.410860	+	0.711631i
$414$	14.9964	+	13.9454i	0.737032	+	0.685379i
$415$	6.85554	−	11.8742i	0.336525	−	0.582879i
$416$	−1.73616	−	1.00237i	−0.0851223	−	0.0491454i
$417$	−13.8784	+	18.7829i	−0.679627	+	0.919801i
$418$	11.5118	+	18.0540i	0.563061	+	0.883049i
$419$		−	5.21876i		−	0.254953i	−0.991842	−	0.127477i	$-0.959312\pi$
$419$		−	5.21876i		−	0.254953i	0.991842	−	0.127477i	$-0.0406878\pi$
$420$	3.11322	−	1.35624i	0.151910	−	0.0661780i
$421$	0.601100	+	0.347045i	0.0292958	+	0.0169139i	0.514576	−	0.857445i	$-0.327949\pi$
$421$	0.601100	+	0.347045i	0.0292958	+	0.0169139i	−0.485281	+	0.874358i	$0.661283\pi$
$422$	−2.52326	+	1.45680i	−0.122830	+	0.0709160i
$423$	−1.24643	+	5.43337i	−0.0606036	+	0.264179i
$424$	5.29044	+	9.16331i	0.256927	+	0.445010i
$425$		−	3.92055i		−	0.190175i
$426$	4.66145	−	6.30877i	0.225848	−	0.305661i
$427$	−7.67326	−	13.2905i	−0.371335	−	0.643171i
$428$	−1.50566	−	2.60787i	−0.0727787	−	0.126056i
$429$	−10.1362	+	13.7183i	−0.489382	+	0.662325i
$430$			5.88974i			0.284029i
$431$	8.30269	+	14.3807i	0.399926	+	0.692693i	0.993716	−	0.111927i	$-0.0357024\pi$
$431$	8.30269	+	14.3807i	0.399926	+	0.692693i	−0.593790	+	0.804620i	$0.702369\pi$
$432$	3.94413	−	3.38287i	0.189762	−	0.162758i
$433$	18.0716	−	10.4336i	0.868465	−	0.501409i	0.00162720	−	0.999999i	$-0.499482\pi$
$433$	18.0716	−	10.4336i	0.868465	−	0.501409i	0.866838	+	0.498590i	$0.166149\pi$
$434$	0.396610	+	0.228983i	0.0190379	+	0.0109915i
$435$	−7.99269	+	3.48193i	−0.383220	+	0.166946i
$436$		−	10.4610i		−	0.500992i
$437$	29.7256	−	1.30976i	1.42197	−	0.0626543i
$438$	−2.34451	+	3.17304i	−0.112025	+	0.151613i
$439$	−9.46913	−	5.46701i	−0.451937	−	0.260926i	0.256711	−	0.966488i	$-0.417361\pi$
$439$	−9.46913	−	5.46701i	−0.451937	−	0.260926i	−0.708648	+	0.705562i	$0.750695\pi$
$440$	2.45611	−	4.25411i	0.117090	−	0.202807i
$441$	6.44782	−	6.93375i	0.307039	−	0.330179i
$442$	3.92986	−	6.80671i	0.186924	−	0.323762i
$443$	32.8931	−	18.9908i	1.56280	−	0.902281i	0.565825	−	0.824525i	$-0.308558\pi$
$443$	32.8931	−	18.9908i	1.56280	−	0.902281i	0.996972	−	0.0777559i	$-0.0247755\pi$
$444$	10.0219	+	7.40505i	0.475620	+	0.351428i
$445$		−	10.9628i		−	0.519685i
$446$	−3.39391	+	1.95947i	−0.160706	+	0.0927838i
$447$	0.898233	−	7.93275i	0.0424849	−	0.375206i
$448$	−1.96058			−0.0926285
$449$	37.0794			1.74989			0.874944	−	0.484225i	$-0.160898\pi$
$449$	37.0794			1.74989			0.874944	+	0.484225i	$0.160898\pi$
$450$	2.04294	−	2.19691i	0.0963051	−	0.103563i
$451$	50.0494	+	28.8961i	2.35674	+	1.36066i
$452$	6.07947	+	10.5300i	0.285954	+	0.495287i
$453$	−27.5605	+	12.0065i	−1.29491	+	0.564112i
$454$	0.158042	−	0.273737i	0.00741729	−	0.0128471i
$455$	3.93045			0.184263
$456$	0.518398	−	7.53202i	0.0242762	−	0.352719i
$457$	24.8264			1.16133			0.580665	−	0.814142i	$-0.302793\pi$
$457$	24.8264			1.16133			0.580665	+	0.814142i	$0.302793\pi$
$458$	−3.06670	+	5.31168i	−0.143297	+	0.248198i
$459$	13.2627	+	15.4632i	0.619051	+	0.721760i
$460$	−3.41307	−	5.91161i	−0.159135	−	0.275630i
$461$	4.14251	+	2.39168i	0.192936	+	0.111392i	0.593356	−	0.804940i	$-0.297803\pi$
$461$	4.14251	+	2.39168i	0.192936	+	0.111392i	−0.400420	+	0.916332i	$0.631136\pi$
$462$	−1.87681	+	16.5751i	−0.0873172	+	0.771142i
$463$	−19.1590			−0.890394			−0.445197	−	0.895433i	$-0.646866\pi$
$463$	−19.1590			−0.890394			−0.445197	+	0.895433i	$0.646866\pi$
$464$	5.03345			0.233672
$465$	0.402017	+	0.0455208i	0.0186431	+	0.00211097i
$466$	9.37631	−	5.41341i	0.434349	−	0.250772i
$467$			18.5479i			0.858296i	0.903234	+	0.429148i	$0.141186\pi$
$467$			18.5479i			0.858296i	−0.903234	+	0.429148i	$0.858814\pi$
$468$	5.74899	−	1.76639i	0.265747	−	0.0816515i
$469$	26.9493	−	15.5592i	1.24441	−	0.718458i
$470$	0.929084	−	1.60922i	0.0428554	−	0.0742278i
$471$	2.86968	+	0.324937i	0.132228	+	0.0149723i
$472$	4.25879	−	7.37643i	0.196026	−	0.339528i
$473$	−25.0556	−	14.4659i	−1.15206	−	0.665141i
$474$	−17.3561	−	12.8242i	−0.797191	−	0.589033i
$475$	−0.191874	−	4.35467i	−0.00880380	−	0.199806i
$476$		−	7.68654i		−	0.352312i
$477$	−30.9390	−	7.09750i	−1.41660	−	0.324972i
$478$	2.75990	+	1.59343i	0.126235	+	0.0728817i
$479$	−22.9732	+	13.2636i	−1.04967	+	0.606028i	−0.922557	−	0.385860i	$-0.873905\pi$
$479$	−22.9732	+	13.2636i	−1.04967	+	0.606028i	−0.127114	+	0.991888i	$0.540571\pi$
$480$	−1.58791	+	0.691758i	−0.0724780	+	0.0315743i
$481$	7.21137	+	12.4905i	0.328810	+	0.569516i
$482$		−	19.0892i		−	0.869490i
$483$	18.6432	+	13.7752i	0.848297	+	0.626794i
$484$	6.56495	+	11.3708i	0.298407	+	0.516855i
$485$	7.68789	+	13.3158i	0.349089	+	0.604640i
$486$	−0.625786	+	15.5759i	−0.0283862	+	0.706537i
$487$			11.3164i			0.512796i	0.966571	+	0.256398i	$0.0825357\pi$
$487$			11.3164i			0.512796i	−0.966571	+	0.256398i	$0.917464\pi$
$488$	3.91378	+	6.77887i	0.177169	+	0.306865i
$489$	5.92104	+	13.5916i	0.267759	+	0.614633i
$490$	−2.73330	+	1.57807i	−0.123478	+	0.0712900i
$491$	−6.02160	−	3.47657i	−0.271751	−	0.156896i	0.357932	−	0.933748i	$-0.383482\pi$
$491$	−6.02160	−	3.47657i	−0.271751	−	0.156896i	−0.629683	+	0.776852i	$0.716815\pi$
$492$	−8.13852	−	18.6818i	−0.366913	−	0.842239i
$493$			19.7339i			0.888772i
$494$	4.03188	−	7.75274i	0.181403	−	0.348812i
$495$	4.32818	+	14.0867i	0.194537	+	0.633151i
$496$	−0.202293	−	0.116794i	−0.00908322	−	0.00524420i
$497$	4.43951	−	7.68946i	0.199139	−	0.344920i
$498$	2.67197	−	23.5975i	0.119734	−	1.05743i
$499$	−17.0361	+	29.5074i	−0.762642	+	1.32093i	0.178843	+	0.983878i	$0.442765\pi$
$499$	−17.0361	+	29.5074i	−0.762642	+	1.32093i	−0.941484	+	0.337057i	$0.890569\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−9.97454	+	13.4995i	−0.445630	+	0.603111i
$502$			11.6470i			0.519833i
$503$	3.97574	−	2.29540i	0.177270	−	0.102347i	−0.408740	−	0.912651i	$-0.634032\pi$
$503$	3.97574	−	2.29540i	0.177270	−	0.102347i	0.586009	+	0.810304i	$0.300698\pi$
$504$	4.00534	−	4.30720i	0.178412	−	0.191858i
$505$	−11.4829			−0.510983
$506$	33.5315			1.49066
$507$	−15.4568	−	1.75019i	−0.686459	−	0.0777284i
$508$	−11.2081	−	6.47100i	−0.497279	−	0.287104i
$509$	−10.1206	−	17.5295i	−0.448590	−	0.776980i	0.549705	−	0.835359i	$-0.314740\pi$
$509$	−10.1206	−	17.5295i	−0.448590	−	0.776980i	−0.998294	+	0.0583790i	$0.981407\pi$
$510$	−2.71208	−	6.22550i	−0.120093	−	0.275670i
$511$	−2.23288	+	3.86746i	−0.0987769	+	0.171087i
$512$	1.00000			0.0441942
$513$	15.4881	+	16.5263i	0.683815	+	0.729655i
$514$	−23.5470			−1.03861
$515$	0.881671	−	1.52710i	0.0388511	−	0.0672920i
$516$	4.07428	+	9.35241i	0.179360	+	0.411717i
$517$	4.56386	+	7.90484i	0.200718	+	0.347655i
$518$	12.2153	+	7.05248i	0.536708	+	0.309868i
$519$	−17.9772	−	2.03558i	−0.789113	−	0.0893520i
$520$	−2.00475			−0.0879139
$521$	−19.3708			−0.848650			−0.424325	−	0.905510i	$-0.639489\pi$
$521$	−19.3708			−0.848650			−0.424325	+	0.905510i	$0.639489\pi$
$522$	−10.2830	+	11.0580i	−0.450077	+	0.483997i
$523$	−35.0535	+	20.2382i	−1.53278	+	0.884954i	−0.533553	+	0.845767i	$0.679143\pi$
$523$	−35.0535	+	20.2382i	−1.53278	+	0.884954i	−0.999232	+	0.0391867i	$0.987523\pi$
$524$			8.94178i			0.390624i
$525$	2.01801	−	2.73115i	0.0880731	−	0.119197i
$526$	−3.46036	+	1.99784i	−0.150879	+	0.0871099i
$527$	0.457897	−	0.793100i	0.0199463	−	0.0345480i
$528$	0.957276	−	8.45419i	0.0416601	−	0.367921i
$529$	11.7981	−	20.4349i	0.512960	−	0.888473i
$530$	9.16331	+	5.29044i	0.398029	+	0.229802i
$531$	7.50488	+	24.4258i	0.325684	+	1.05999i
$532$	−0.376184	−	8.53767i	−0.0163096	−	0.370155i
$533$		−	23.5858i		−	1.02161i
$534$	−7.58359	−	17.4079i	−0.328174	−	0.753315i
$535$	−2.60787	−	1.50566i	−0.112748	−	0.0650952i
$536$	−13.7456	+	7.93605i	−0.593721	+	0.342785i
$537$	−0.931590	−	2.13844i	−0.0402011	−	0.0922806i
$538$	−1.12373	−	1.94636i	−0.0484476	−	0.0839137i
$539$		−	15.5037i		−	0.667791i
$540$	1.72429	−	4.90172i	0.0742014	−	0.210936i
$541$	14.7204	+	25.4965i	0.632879	+	1.09618i	0.986960	+	0.160964i	$0.0514602\pi$
$541$	14.7204	+	25.4965i	0.632879	+	1.09618i	−0.354082	+	0.935215i	$0.615206\pi$
$542$	2.70149	+	4.67912i	0.116039	+	0.200985i
$543$	20.3621	+	15.0453i	0.873823	+	0.645655i
$544$			3.92055i			0.168092i
$545$	−5.23051	−	9.05950i	−0.224050	−	0.388067i
$546$	6.24122	−	2.71892i	0.267100	−	0.116359i
$547$	10.3833	−	5.99478i	0.443956	−	0.256318i	−0.261318	−	0.965253i	$-0.584157\pi$
$547$	10.3833	−	5.99478i	0.443956	−	0.256318i	0.705274	+	0.708935i	$0.250824\pi$
$548$	3.55144	+	2.05042i	0.151710	+	0.0875898i
$549$	−22.8882	−	5.25062i	−0.976843	−	0.224091i
$550$		−	4.91222i		−	0.209458i
$551$	0.965790	+	21.9191i	0.0411441	+	0.933783i
$552$	−9.50907	−	7.02611i	−0.404733	−	0.299051i
$553$	−21.1545	−	12.2136i	−0.899582	−	0.519374i
$554$	10.0766	−	17.4531i	0.428112	−	0.741511i
$555$	12.3818	+	1.40200i	0.525577	+	0.0595116i
$556$	6.74169	−	11.6770i	0.285911	−	0.495213i
$557$	−24.0375	+	13.8780i	−1.01850	+	0.588031i	−0.913669	−	0.406459i	$-0.866763\pi$
$557$	−24.0375	+	13.8780i	−1.01850	+	0.588031i	−0.104831	+	0.994490i	$0.533430\pi$
$558$	0.669857	−	0.205815i	0.0283573	−	0.00871286i
$559$			11.8074i			0.499401i
$560$	−1.69791	+	0.980288i	−0.0717497	+	0.0414247i
$561$	33.1451	+	3.75305i	1.39939	+	0.158454i
$562$	18.7084			0.789164
$563$	−17.1980			−0.724809			−0.362404	−	0.932021i	$-0.618044\pi$
$563$	−17.1980			−0.724809			−0.362404	+	0.932021i	$0.618044\pi$
$564$	0.362113	−	3.19801i	0.0152477	−	0.134660i
$565$	10.5300	+	6.07947i	0.442998	+	0.255765i
$566$	10.5801	+	18.3252i	0.444713	+	0.770265i
$567$	1.27984	+	17.5987i	0.0537483	+	0.739076i
$568$	−2.26439	+	3.92204i	−0.0950118	+	0.164565i
$569$	26.3732			1.10562			0.552812	−	0.833306i	$-0.313555\pi$
$569$	26.3732			1.10562			0.552812	+	0.833306i	$0.313555\pi$
$570$	−3.31706	−	6.78212i	−0.138936	−	0.284072i
$571$	6.53285			0.273391			0.136696	−	0.990613i	$-0.456352\pi$
$571$	6.53285			0.273391			0.136696	+	0.990613i	$0.456352\pi$
$572$	4.92387	−	8.52840i	0.205878	−	0.356590i
$573$	−9.67619	+	4.21534i	−0.404229	+	0.176098i
$574$	−11.5331	−	19.9758i	−0.481380	−	0.833775i
$575$	−5.91161	−	3.41307i	−0.246531	−	0.142335i
$576$	−2.04294	+	2.19691i	−0.0851225	+	0.0915377i
$577$	6.44640			0.268367			0.134184	−	0.990956i	$-0.457159\pi$
$577$	6.44640			0.268367			0.134184	+	0.990956i	$0.457159\pi$
$578$	1.62925			0.0677679
$579$	−0.584810	+	5.16475i	−0.0243039	+	0.214640i
$580$	4.35910	−	2.51673i	0.181002	−	0.104501i
$581$		−	26.8816i		−	1.11524i
$582$	21.4190	+	15.8262i	0.887847	+	0.656017i
$583$	−45.0122	+	25.9878i	−1.86421	+	1.07630i
$584$	1.13889	−	1.97262i	0.0471276	−	0.0816275i
$585$	4.09558	−	4.40424i	0.169331	−	0.182093i
$586$	6.15600	−	10.6625i	0.254302	−	0.440464i
$587$	29.3043	+	16.9188i	1.20952	+	0.698315i	0.962654	−	0.270736i	$-0.0872670\pi$
$587$	29.3043	+	16.9188i	1.20952	+	0.698315i	0.246863	+	0.969050i	$0.420600\pi$
$588$	−3.24860	+	4.39663i	−0.133970	+	0.181314i
$589$	0.469784	−	0.903329i	0.0193571	−	0.0372210i
$590$		−	8.51757i		−	0.350663i
$591$	3.93968	−	1.71628i	0.162057	−	0.0705983i
$592$	−6.23045	−	3.59715i	−0.256070	−	0.147842i
$593$	−25.1953	+	14.5465i	−1.03465	+	0.597354i	−0.918312	−	0.395856i	$-0.870448\pi$
$593$	−25.1953	+	14.5465i	−1.03465	+	0.597354i	−0.116335	+	0.993210i	$0.537114\pi$
$594$	16.6174	+	19.3744i	0.681820	+	0.794943i
$595$	−3.84327	−	6.65674i	−0.157559	−	0.272900i
$596$			4.60924i			0.188802i
$597$	24.3041	−	32.8929i	0.994700	−	1.34622i
$598$	−6.84234	−	11.8513i	−0.279804	−	0.484635i
$599$	−13.7688	−	23.8483i	−0.562580	−	0.974416i	−0.997270	−	0.0738365i	$-0.976476\pi$
$599$	−13.7688	−	23.8483i	−0.562580	−	0.974416i	0.434691	−	0.900580i	$-0.356858\pi$
$600$	−1.02929	+	1.39304i	−0.0420208	+	0.0568705i
$601$			14.9379i			0.609330i	0.952460	+	0.304665i	$0.0985445\pi$
$601$			14.9379i			0.609330i	−0.952460	+	0.304665i	$0.901455\pi$
$602$	5.77364	+	10.0002i	0.235316	+	0.407580i
$603$	10.6468	−	46.4107i	0.433570	−	1.88999i
$604$	15.0311	−	8.67821i	0.611607	−	0.353111i
$605$	11.3708	+	6.56495i	0.462290	+	0.266903i
$606$	−18.2339	+	7.94340i	−0.740701	+	0.322679i
$607$			42.6299i			1.73030i	0.501517	+	0.865148i	$0.332775\pi$
$607$			42.6299i			1.73030i	−0.501517	+	0.865148i	$0.667225\pi$
$608$	0.191874	+	4.35467i	0.00778153	+	0.176605i
$609$	−10.1576	+	13.7471i	−0.411605	+	0.557062i
$610$	6.77887	+	3.91378i	0.274468	+	0.158464i
$611$	1.86258	−	3.22608i	0.0753518	−	0.130513i
$612$	−8.61309	−	8.00946i	−0.348163	−	0.323763i
$613$	8.76635	−	15.1838i	0.354069	−	0.613266i	−0.632889	−	0.774243i	$-0.718131\pi$
$613$	8.76635	−	15.1838i	0.354069	−	0.613266i	0.986958	+	0.160976i	$0.0514643\pi$
$614$	13.1520	−	7.59331i	0.530771	−	0.306441i
$615$	−16.3890	−	12.1096i	−0.660870	−	0.488307i
$616$		−	9.63077i		−	0.388035i
$617$	−38.2258	+	22.0697i	−1.53891	+	0.888491i	−0.540008	+	0.841660i	$0.681579\pi$
$617$	−38.2258	+	22.0697i	−1.53891	+	0.888491i	−0.998903	+	0.0468313i	$0.985088\pi$
$618$	0.343634	−	3.03481i	0.0138230	−	0.122078i
$619$	−42.3600			−1.70259			−0.851296	−	0.524685i	$-0.824183\pi$
$619$	−42.3600			−1.70259			−0.851296	+	0.524685i	$0.824183\pi$
$620$	−0.233588			−0.00938111
$621$	34.8622	−	6.53660i	1.39897	−	0.262305i
$622$	−27.6123	−	15.9420i	−1.10715	−	0.639214i
$623$	−10.7467	−	18.6138i	−0.430556	−	0.745746i
$624$	−3.18336	+	1.38680i	−0.127437	+	0.0555164i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	14.9516			0.597585
$627$	36.9989	+	2.54648i	1.47759	+	0.101697i
$628$	−1.66740			−0.0665365
$629$	14.1028	−	24.4268i	0.562316	−	0.973961i
$630$	1.31513	−	5.73281i	0.0523959	−	0.228401i
$631$	−17.6187	−	30.5165i	−0.701391	−	1.21484i	−0.967978	−	0.251033i	$-0.919230\pi$
$631$	−17.6187	−	30.5165i	−0.701391	−	1.21484i	0.266588	−	0.963811i	$-0.414104\pi$
$632$	10.7900	+	6.22958i	0.429201	+	0.247800i
$633$	−0.567793	+	5.01447i	−0.0225678	+	0.199307i
$634$	25.5166			1.01339
$635$	−12.9420			−0.513587
$636$	18.2103	+	2.06197i	0.722084	+	0.0817623i
$637$	−5.47957	+	3.16363i	−0.217109	+	0.125348i
$638$			24.7254i			0.978889i
$639$	−3.99034	−	12.9872i	−0.157855	−	0.513764i
$640$	0.866025	−	0.500000i	0.0342327	−	0.0197642i
$641$	−12.1088	+	20.9730i	−0.478267	+	0.828383i	−0.999690	−	0.0249155i	$-0.992068\pi$
$641$	−12.1088	+	20.9730i	−0.478267	+	0.828383i	0.521422	+	0.853299i	$0.325402\pi$
$642$	−5.18263	−	0.586834i	−0.204542	−	0.0231605i
$643$	−8.96485	+	15.5276i	−0.353539	+	0.612348i	−0.986867	−	0.161536i	$-0.948355\pi$
$643$	−8.96485	+	15.5276i	−0.353539	+	0.612348i	0.633328	+	0.773884i	$0.281689\pi$
$644$	−11.5902	−	6.69158i	−0.456716	−	0.263685i
$645$	8.20463	+	6.06228i	0.323057	+	0.238702i
$646$	−17.0727	+	0.752254i	−0.671718	+	0.0295970i
$647$			16.2268i			0.637940i	0.947765	+	0.318970i	$0.103337\pi$
$647$			16.2268i			0.637940i	−0.947765	+	0.318970i	$0.896663\pi$
$648$	−0.652788	−	8.97629i	−0.0256439	−	0.352622i
$649$	36.2346	+	20.9201i	1.42233	+	0.821185i
$650$	−1.73616	+	1.00237i	−0.0680978	+	0.0393163i
$651$	0.727211	−	0.316802i	0.0285016	−	0.0124164i
$652$	−4.27970	−	7.41266i	−0.167606	−	0.290302i
$653$		−	13.0356i		−	0.510121i	−0.966925	−	0.255060i	$-0.917905\pi$
$653$		−	13.0356i		−	0.510121i	0.966925	−	0.255060i	$-0.0820953\pi$
$654$	−14.5726	−	10.7675i	−0.569833	−	0.421041i
$655$	4.47089	+	7.74381i	0.174692	+	0.302576i
$656$	5.88249	+	10.1888i	0.229672	+	0.397804i
$657$	2.00697	+	6.53197i	0.0782992	+	0.254837i
$658$		−	3.64308i		−	0.142022i
$659$	−16.7755	−	29.0560i	−0.653480	−	1.13186i	−0.982272	−	0.187459i	$-0.939975\pi$
$659$	−16.7755	−	29.0560i	−0.653480	−	1.13186i	0.328792	−	0.944402i	$-0.393358\pi$
$660$	−3.39807	−	7.80018i	−0.132270	−	0.303622i
$661$	13.8780	−	8.01246i	0.539791	−	0.311649i	−0.205203	−	0.978719i	$-0.565785\pi$
$661$	13.8780	−	8.01246i	0.539791	−	0.311649i	0.744994	+	0.667071i	$0.232452\pi$
$662$	20.4616	+	11.8135i	0.795262	+	0.459145i
$663$	−5.43702	−	12.4805i	−0.211156	−	0.484704i
$664$			13.7111i			0.532093i
$665$	−4.59462	−	7.20574i	−0.178172	−	0.279427i
$666$	20.6310	−	6.33894i	0.799436	−	0.245629i
$667$	29.7558	+	17.1795i	1.15215	+	0.665194i
$668$	4.84533	−	8.39236i	0.187471	−	0.324710i
$669$	−0.763711	+	6.74472i	−0.0295268	+	0.260766i
$670$	−7.93605	+	13.7456i	−0.306596	+	0.531040i
$671$	−33.2993	+	19.2253i	−1.28550	+	0.742186i
$672$	−2.01801	+	2.73115i	−0.0778464	+	0.105357i
$673$		−	31.9714i		−	1.23241i	−0.787586	−	0.616204i	$-0.788670\pi$
$673$		−	31.9714i		−	1.23241i	0.787586	−	0.616204i	$-0.211330\pi$
$674$	1.65491	−	0.955464i	0.0637449	−	0.0368031i
$675$	−0.957584	−	5.10716i	−0.0368574	−	0.196574i
$676$	8.98100			0.345423
$677$	25.2864			0.971835			0.485918	−	0.874005i	$-0.338486\pi$
$677$	25.2864			0.971835			0.485918	+	0.874005i	$0.338486\pi$
$678$	20.9262	+	2.36949i	0.803665	+	0.0909998i
$679$	26.1067	+	15.0727i	1.00188	+	0.578437i
$680$	1.96028	+	3.39530i	0.0751732	+	0.130204i
$681$	−0.218654	−	0.501915i	−0.00837884	−	0.0192334i
$682$	0.573717	−	0.993707i	0.0219688	−	0.0380510i
$683$	−8.39063			−0.321059			−0.160529	−	0.987031i	$-0.551320\pi$
$683$	−8.39063			−0.321059			−0.160529	+	0.987031i	$0.551320\pi$
$684$	−9.95880	−	8.47481i	−0.380784	−	0.324042i
$685$	4.10085			0.156685
$686$	−9.95594	+	17.2442i	−0.380120	+	0.658387i
$687$	4.24283	+	9.73931i	0.161874	+	0.371578i
$688$	−2.94487	−	5.10067i	−0.112272	−	0.194461i
$689$	18.3701	+	10.6060i	0.699846	+	0.404056i
$690$	−11.7481	−	1.33025i	−0.447244	−	0.0506419i
$691$	−10.0647			−0.382881			−0.191440	−	0.981504i	$-0.561316\pi$
$691$	−10.0647			−0.382881			−0.191440	+	0.981504i	$0.561316\pi$
$692$	10.4455			0.397078
$693$	21.1579	+	19.6751i	0.803722	+	0.747395i
$694$	−13.6960	+	7.90736i	−0.519891	+	0.300159i
$695$		−	13.4834i		−	0.511454i
$696$	5.18091	−	7.01179i	0.196382	−	0.265781i
$697$	−39.9456	+	23.0626i	−1.51305	+	0.873558i
$698$	14.8893	−	25.7890i	0.563568	−	0.976129i
$699$	2.10989	−	18.6335i	0.0798035	−	0.704785i
$700$	−0.980288	+	1.69791i	−0.0370514	+	0.0641749i
$701$	29.1351	+	16.8212i	1.10042	+	0.635327i	0.936331	−	0.351119i	$-0.114199\pi$
$701$	29.1351	+	16.8212i	1.10042	+	0.635327i	0.164087	+	0.986446i	$0.447532\pi$
$702$	3.45675	−	9.82670i	0.130467	−	0.370885i
$703$	14.4690	−	27.8218i	0.545707	−	1.04932i
$704$			4.91222i			0.185136i
$705$	−1.28540	−	2.95061i	−0.0484111	−	0.111126i
$706$	2.12758	+	1.22836i	0.0800724	+	0.0462298i
$707$	−19.4969	+	11.2566i	−0.733257	+	0.423346i
$708$	−5.89210	−	13.5252i	−0.221439	−	0.508307i
$709$	22.1508	+	38.3664i	0.831892	+	1.44088i	0.896536	+	0.442971i	$0.146076\pi$
$709$	22.1508	+	38.3664i	0.831892	+	1.44088i	−0.0646434	+	0.997908i	$0.520591\pi$
$710$			4.52879i			0.169962i
$711$	−35.7290	+	10.9778i	−1.33994	+	0.411701i
$712$	5.48139	+	9.49404i	0.205424	+	0.355804i
$713$	−0.797251	−	1.38088i	−0.0298573	−	0.0517143i
$714$	−10.7076	−	7.91172i	−0.400723	−	0.296089i
$715$		−	9.84775i		−	0.368285i
$716$	0.673349	+	1.16628i	0.0251642	+	0.0435858i
$717$	5.06045	−	2.20454i	0.188986	−	0.0823299i
$718$	−3.05773	+	1.76538i	−0.114113	+	0.0658834i
$719$	−12.8018	−	7.39114i	−0.477428	−	0.275643i	0.241916	−	0.970297i	$-0.422224\pi$
$719$	−12.8018	−	7.39114i	−0.477428	−	0.275643i	−0.719344	+	0.694654i	$0.755557\pi$
$720$	−0.670786	+	2.92405i	−0.0249987	+	0.108973i
$721$		−	3.45717i		−	0.128752i
$722$	−18.9264	+	1.67110i	−0.704367	+	0.0621919i
$723$	−26.5920	−	19.6484i	−0.988967	−	0.730733i
$724$	−12.6588	−	7.30854i	−0.470459	−	0.271620i
$725$	2.51673	−	4.35910i	0.0934689	−	0.161893i
$726$	22.5972	+	2.55871i	0.838662	+	0.0949625i
$727$	2.63804	−	4.56923i	0.0978397	−	0.169463i	−0.812951	−	0.582333i	$-0.802140\pi$
$727$	2.63804	−	4.56923i	0.0978397	−	0.169463i	0.910790	+	0.412869i	$0.135473\pi$
$728$	−3.40387	+	1.96523i	−0.126156	+	0.0728362i
$729$	21.0537	+	16.9039i	0.779766	+	0.626071i
$730$		−	2.27778i		−	0.0843045i
$731$	19.9975	−	11.5455i	0.739632	−	0.427027i
$732$	13.4716	+	1.52541i	0.497926	+	0.0563807i
$733$	−12.3735			−0.457025			−0.228513	−	0.973541i	$-0.573386\pi$
$733$	−12.3735			−0.457025			−0.228513	+	0.973541i	$0.573386\pi$
$734$	2.67023			0.0985601
$735$	−0.615059	+	5.43189i	−0.0226868	+	0.200358i
$736$	5.91161	+	3.41307i	0.217905	+	0.125807i
$737$	−38.9836	−	67.5216i	−1.43598	−	2.48719i
$738$	−34.4013	−	7.89177i	−1.26633	−	0.290500i
$739$	23.4208	−	40.5660i	0.861548	−	1.49224i	−0.00888687	−	0.999961i	$-0.502829\pi$
$739$	23.4208	−	40.5660i	0.861548	−	1.49224i	0.870435	−	0.492284i	$-0.163838\pi$
$740$	−7.19430			−0.264468
$741$	−6.64987	−	13.5964i	−0.244289	−	0.499477i
$742$	20.7446			0.761559
$743$	3.70160	−	6.41135i	0.135798	−	0.235210i	−0.790104	−	0.612973i	$-0.789973\pi$
$743$	3.70160	−	6.41135i	0.135798	−	0.235210i	0.925902	+	0.377763i	$0.123307\pi$
$744$	−0.370917	+	0.161586i	−0.0135985	+	0.00592404i
$745$	2.30462	+	3.99172i	0.0844347	+	0.146245i
$746$	3.60651	+	2.08222i	0.132044	+	0.0762354i
$747$	−30.1220	−	28.0109i	−1.10211	−	1.02487i
$748$	−19.2586			−0.704165
$749$	−5.90391			−0.215724
$750$	−0.194877	+	1.72105i	−0.00711588	+	0.0628440i
$751$	−36.7844	+	21.2375i	−1.34228	+	0.774966i	−0.987142	−	0.159848i	$-0.948900\pi$
$751$	−36.7844	+	21.2375i	−1.34228	+	0.774966i	−0.355139	+	0.934814i	$0.615566\pi$
$752$			1.85817i			0.0677604i
$753$	16.2248	+	11.9882i	0.591264	+	0.436876i
$754$	8.73888	−	5.04540i	0.318251	−	0.183743i
$755$	8.67821	−	15.0311i	0.315833	−	0.547038i
$756$	−1.87742	−	10.0130i	−0.0682809	−	0.364168i
$757$	24.8985	−	43.1254i	0.904950	−	1.56742i	0.0839656	−	0.996469i	$-0.473241\pi$
$757$	24.8985	−	43.1254i	0.904950	−	1.56742i	0.820984	−	0.570951i	$-0.193425\pi$
$758$	9.37204	+	5.41095i	0.340408	+	0.196535i
$759$	34.5138	−	46.7106i	1.25277	−	1.69549i
$760$	2.34350	+	3.67532i	0.0850079	+	0.133318i
$761$			32.0785i			1.16284i	0.813602	+	0.581422i	$0.197503\pi$
$761$			32.0785i			1.16284i	−0.813602	+	0.581422i	$0.802497\pi$
$762$	−20.5508	+	8.95273i	−0.744476	+	0.324323i
$763$	−17.7618	−	10.2548i	−0.643022	−	0.371249i
$764$	5.27726	−	3.04683i	0.190924	−	0.110230i
$765$	−11.4639	−	2.62985i	−0.414478	−	0.0950825i
$766$	8.28137	+	14.3437i	0.299218	+	0.518261i
$767$		−	17.0756i		−	0.616563i
$768$	1.02929	−	1.39304i	0.0371415	−	0.0502669i
$769$	−20.0557	−	34.7374i	−0.723225	−	1.25266i	−0.959700	−	0.281026i	$-0.909325\pi$
$769$	−20.0557	−	34.7374i	−0.723225	−	1.25266i	0.236475	−	0.971638i	$-0.424008\pi$
$770$	−4.81539	−	8.34049i	−0.173534	−	0.300571i
$771$	−24.2368	+	32.8018i	−0.872867	+	1.18133i
$772$		−	3.00092i		−	0.108006i
$773$	−4.07839	−	7.06397i	−0.146689	−	0.254074i	0.783313	−	0.621628i	$-0.213528\pi$
$773$	−4.07839	−	7.06397i	−0.146689	−	0.254074i	−0.930002	+	0.367555i	$0.880195\pi$
$774$	17.2219	+	3.95076i	0.619028	+	0.142007i
$775$	−0.202293	+	0.116794i	−0.00726657	+	0.00419536i
$776$	−13.3158	−	7.68789i	−0.478010	−	0.275979i
$777$	22.3975	−	9.75723i	0.803505	−	0.350039i
$778$			37.4846i			1.34389i
$779$	−43.2400	+	27.5713i	−1.54924	+	0.987843i
$780$	−2.06347	+	2.79269i	−0.0738842	+	0.0999942i
$781$	−19.2659	−	11.1232i	−0.689389	−	0.398019i
$782$	−13.3811	+	23.1768i	−0.478508	+	0.828800i
$783$	4.81996	+	25.7066i	0.172251	+	0.918680i
$784$	1.57807	−	2.73330i	0.0563597	−	0.0976179i
$785$	−1.44401	+	0.833700i	−0.0515389	+	0.0297560i
$786$	12.4562	+	9.20373i	0.444299	+	0.328286i
$787$			41.0793i			1.46432i	0.681134	+	0.732159i	$0.261487\pi$
$787$			41.0793i			1.46432i	−0.681134	+	0.732159i	$0.738513\pi$
$788$	−2.14864	+	1.24052i	−0.0765422	+	0.0441917i
$789$	−0.778664	+	6.87677i	−0.0277212	+	0.244820i
$790$	12.4592			0.443277
$791$	23.8385			0.847600
$792$	−10.7917	−	10.0354i	−0.383466	−	0.356591i
$793$	13.5899	+	7.84613i	0.482592	+	0.278624i
$794$	−2.65169	−	4.59286i	−0.0941050	−	0.162995i
$795$	16.8015	−	7.31942i	0.595889	−	0.259593i
$796$	−11.8062	+	20.4489i	−0.418459	+	0.724792i
$797$	39.4937			1.39894			0.699469	−	0.714663i	$-0.253420\pi$
$797$	39.4937			1.39894			0.699469	+	0.714663i	$0.253420\pi$
$798$	−12.2805	−	8.26373i	−0.434725	−	0.292533i
$799$	−7.28505			−0.257727
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−32.0557	−	7.35367i	−1.13263	−	0.259829i
$802$	−3.00036	−	5.19678i	−0.105946	−	0.183505i
$803$	9.68993	+	5.59448i	0.341950	+	0.197425i
$804$	−3.09310	+	27.3167i	−0.109085	+	0.963386i
$805$	−13.3832			−0.471694
$806$	−0.468284			−0.0164946
$807$	−3.86801	−	0.437978i	−0.136160	−	0.0154176i
$808$	9.94449	−	5.74146i	0.349846	−	0.201984i
$809$			16.4184i			0.577240i	0.957444	+	0.288620i	$0.0931964\pi$
$809$			16.4184i			0.577240i	−0.957444	+	0.288620i	$0.906804\pi$
$810$	−5.05348	−	7.44731i	−0.177561	−	0.261672i
$811$	−42.7046	+	24.6555i	−1.49956	+	0.865773i	−1.00000		0.000504396i	$-0.999839\pi$
$811$	−42.7046	+	24.6555i	−1.49956	+	0.865773i	−0.499563	+	0.866277i	$0.666506\pi$
$812$	4.93423	−	8.54634i	0.173158	−	0.299918i
$813$	9.29881	+	1.05291i	0.326124	+	0.0369273i
$814$	17.6700	−	30.6053i	0.619333	−	1.07272i
$815$	−7.41266	−	4.27970i	−0.259654	−	0.149911i
$816$	5.46148	+	4.03541i	0.191190	+	0.141267i
$817$	21.6467	−	13.8026i	0.757322	−	0.482893i
$818$		−	27.3123i		−	0.954951i
$819$	2.63649	−	11.4928i	0.0921265	−	0.401592i
$820$	10.1888	+	5.88249i	0.355807	+	0.205425i
$821$	−27.3273	+	15.7774i	−0.953730	+	0.550636i	−0.894238	−	0.447593i	$-0.852281\pi$
$821$	−27.3273	+	15.7774i	−0.953730	+	0.550636i	−0.0594922	+	0.998229i	$0.518948\pi$
$822$	6.51179	−	2.83680i	0.227125	−	0.0989446i
$823$	−1.24210	−	2.15138i	−0.0432968	−	0.0749923i	0.843565	−	0.537027i	$-0.180453\pi$
$823$	−1.24210	−	2.15138i	−0.0432968	−	0.0749923i	−0.886862	+	0.462035i	$0.847119\pi$
$824$			1.76334i			0.0614289i
$825$	−6.84290	−	5.05612i	−0.238239	−	0.176031i
$826$	−8.34967	−	14.4620i	−0.290522	−	0.503199i
$827$	16.2300	+	28.1113i	0.564374	+	0.977524i	0.997108	+	0.0760023i	$0.0242156\pi$
$827$	16.2300	+	28.1113i	0.564374	+	0.977524i	−0.432734	+	0.901522i	$0.642451\pi$
$828$	−19.5753	+	6.01455i	−0.680287	+	0.209020i
$829$			30.4181i			1.05647i	0.849100	+	0.528233i	$0.177145\pi$
$829$			30.4181i			1.05647i	−0.849100	+	0.528233i	$0.822855\pi$
$830$	6.85554	+	11.8742i	0.237959	+	0.412158i
$831$	−13.9411	−	32.0014i	−0.483611	−	1.11012i
$832$	1.73616	−	1.00237i	0.0601905	−	0.0347510i
$833$	10.7161	+	6.18692i	0.371289	+	0.214364i
$834$	−9.32725	−	21.4105i	−0.322976	−	0.741383i
$835$		−	9.69066i		−	0.335359i
$836$	−21.3911	+	0.942528i	−0.739827	+	0.0325980i
$837$	0.402772	−	1.14498i	0.0139218	−	0.0395763i
$838$	4.51958	+	2.60938i	0.156126	+	0.0901396i
$839$	−3.12520	+	5.41300i	−0.107894	+	0.186878i	−0.914917	−	0.403642i	$-0.867744\pi$
$839$	−3.12520	+	5.41300i	−0.107894	+	0.186878i	0.807023	+	0.590520i	$0.201077\pi$
$840$	−0.382070	+	3.37425i	−0.0131827	+	0.116423i
$841$	1.83217	−	3.17341i	0.0631783	−	0.109428i
$842$	−0.601100	+	0.347045i	−0.0207153	+	0.0119600i
$843$	19.2564	−	26.0614i	0.663226	−	0.897604i
$844$		−	2.91361i		−	0.100290i
$845$	7.77777	−	4.49050i	0.267563	−	0.154478i
$846$	−4.08222	−	3.79613i	−0.140350	−	0.130514i
$847$	25.7421			0.884510
$848$	−10.5809			−0.363349
$849$	36.4177	+	4.12361i	1.24985	+	0.141522i
$850$	3.39530	+	1.96028i	0.116458	+	0.0672370i
$851$	−24.5546	−	42.5299i	−0.841722	−	1.45791i
$852$	3.13283	+	7.19132i	0.107329	+	0.246371i
$853$	24.9526	−	43.2191i	0.854360	−	1.47979i	−0.0228782	−	0.999738i	$-0.507283\pi$
$853$	24.9526	−	43.2191i	0.854360	−	1.47979i	0.877238	−	0.480056i	$-0.159384\pi$
$854$	15.3465			0.525147
$855$	−12.8620	−	2.36000i	−0.439870	−	0.0807104i
$856$	3.01131			0.102925
$857$	−14.9335	+	25.8655i	−0.510118	+	0.883550i	0.489813	+	0.871827i	$0.337065\pi$
$857$	−14.9335	+	25.8655i	−0.510118	+	0.883550i	−0.999931	+	0.0117228i	$0.996268\pi$
$858$	−6.81226	−	15.6374i	−0.232567	−	0.533851i
$859$	−12.1997	−	21.1305i	−0.416249	−	0.720964i	0.579310	−	0.815107i	$-0.303322\pi$
$859$	−12.1997	−	21.1305i	−0.416249	−	0.720964i	−0.995559	+	0.0941433i	$0.969989\pi$
$860$	−5.10067	−	2.94487i	−0.173931	−	0.100419i
$861$	−39.6980	−	4.49504i	−1.35290	−	0.153191i
$862$	−16.6054			−0.565581
$863$	−23.3653			−0.795363			−0.397682	−	0.917523i	$-0.630185\pi$
$863$	−23.3653			−0.795363			−0.397682	+	0.917523i	$0.630185\pi$
$864$	0.957584	+	5.10716i	0.0325777	+	0.173749i
$865$	9.04605	−	5.22274i	0.307575	−	0.177579i
$866$			20.8673i			0.709099i
$867$	1.67698	−	2.26961i	0.0569532	−	0.0770799i
$868$	−0.396610	+	0.228983i	−0.0134618	+	0.00777219i
$869$	−30.6011	+	53.0026i	−1.03807	+	1.79799i
$870$	0.980902	−	8.66284i	0.0332557	−	0.293698i
$871$	−15.9098	+	27.5565i	−0.539081	+	0.933716i
$872$	9.05950	+	5.23051i	0.306794	+	0.177127i
$873$	44.0930	−	13.5477i	1.49232	−	0.458520i
$874$	−13.7285	+	26.3980i	−0.464374	+	0.892926i
$875$			1.96058i			0.0662795i
$876$	−1.57567	−	3.61692i	−0.0532371	−	0.122204i
$877$	36.6106	+	21.1372i	1.23625	+	0.713751i	0.968326	−	0.249688i	$-0.0803281\pi$
$877$	36.6106	+	21.1372i	1.23625	+	0.713751i	0.267927	+	0.963439i	$0.413661\pi$
$878$	9.46913	−	5.46701i	0.319568	−	0.184503i
$879$	−8.51694	−	19.5504i	−0.287269	−	0.659419i
$880$	2.45611	+	4.25411i	0.0827954	+	0.143406i
$881$			17.5330i			0.590703i	0.955389	+	0.295351i	$0.0954367\pi$
$881$			17.5330i			0.590703i	−0.955389	+	0.295351i	$0.904563\pi$
$882$	2.78090	+	9.05085i	0.0936377	+	0.304758i
$883$	3.21281	+	5.56474i	0.108120	+	0.187268i	0.915008	−	0.403435i	$-0.132184\pi$
$883$	3.21281	+	5.56474i	0.108120	+	0.187268i	−0.806889	+	0.590703i	$0.798850\pi$
$884$	3.92986	+	6.80671i	0.132175	+	0.228934i
$885$	−11.8653	−	8.76709i	−0.398847	−	0.294702i
$886$			37.9817i			1.27602i
$887$	5.78172	+	10.0142i	0.194131	+	0.336245i	0.946615	−	0.322365i	$-0.104478\pi$
$887$	5.78172	+	10.0142i	0.194131	+	0.336245i	−0.752484	+	0.658610i	$0.771145\pi$
$888$	−11.4239	+	4.97672i	−0.383362	+	0.167008i
$889$	−21.9743	+	12.6869i	−0.736995	+	0.425504i
$890$	9.49404	+	5.48139i	0.318241	+	0.183737i
$891$	44.0935	−	3.20664i	1.47719	−	0.107426i
$892$		−	3.91895i		−	0.131216i
$893$	−8.09172	+	0.356535i	−0.270779	+	0.0119310i
$894$	6.42084	+	4.74427i	0.214745	+	0.158672i
$895$	1.16628	+	0.673349i	0.0389843	+	0.0225076i
$896$	0.980288	−	1.69791i	0.0327491	−	0.0567231i
$897$	−23.5520	−	2.66682i	−0.786380	−	0.0890426i
$898$	−18.5397	+	32.1117i	−0.618678	+	1.07158i
$899$	1.01823	−	0.587876i	0.0339599	−	0.0196068i
$900$	0.881106	+	2.86769i	0.0293702	+	0.0955897i
$901$		−	41.4829i		−	1.38200i
$902$	−50.0494	+	28.8961i	−1.66646	+	0.962133i
$903$	19.8735	+	2.25030i	0.661348	+	0.0748851i
$904$	−12.1589			−0.404400
$905$	−14.6171			−0.485888
$906$	3.38236	−	29.8713i	0.112371	−	0.992408i
$907$	−33.9003	−	19.5724i	−1.12564	−	0.649890i	−0.182807	−	0.983149i	$-0.558518\pi$
$907$	−33.9003	−	19.5724i	−1.12564	−	0.649890i	−0.942835	+	0.333259i	$0.891852\pi$
$908$	0.158042	+	0.273737i	0.00524481	+	0.00908428i
$909$	−7.70257	+	33.5766i	−0.255478	+	1.11366i
$910$	−1.96523	+	3.40387i	−0.0651466	+	0.112837i
$911$	−27.0371			−0.895778			−0.447889	−	0.894089i	$-0.647824\pi$
$911$	−27.0371			−0.895778			−0.447889	+	0.894089i	$0.647824\pi$
$912$	6.26372	+	4.21495i	0.207412	+	0.139571i
$913$	−67.3519			−2.22902
$914$	−12.4132	+	21.5003i	−0.410592	+	0.711167i
$915$	12.4295	−	5.41478i	0.410906	−	0.179007i
$916$	−3.06670	−	5.31168i	−0.101327	−	0.175503i
$917$	15.1823	+	8.76552i	0.501364	+	0.289463i
$918$	−20.0229	+	3.75426i	−0.660854	+	0.123909i
$919$	36.3996			1.20071			0.600356	−	0.799733i	$-0.295025\pi$
$919$	36.3996			1.20071			0.600356	+	0.799733i	$0.295025\pi$
$920$	6.82614			0.225051
$921$	2.95952	−	26.1370i	0.0975193	−	0.861243i
$922$	−4.14251	+	2.39168i	−0.136426	+	0.0787658i
$923$			9.07906i			0.298841i
$924$	−13.4160	−	9.91290i	−0.441355	−	0.326111i
$925$	−6.23045	+	3.59715i	−0.204856	+	0.118274i
$926$	9.57949	−	16.5922i	0.314802	−	0.545253i
$927$	−3.87390	−	3.60240i	−0.127235	−	0.118318i
$928$	−2.51673	+	4.35910i	−0.0826156	+	0.143094i
$929$	−10.5812	−	6.10909i	−0.347160	−	0.200433i	0.316274	−	0.948668i	$-0.397568\pi$
$929$	−10.5812	−	6.10909i	−0.347160	−	0.200433i	−0.663434	+	0.748235i	$0.730901\pi$
$930$	−0.240431	+	0.325396i	−0.00788403	+	0.0106702i
$931$	12.2054	+	6.34754i	0.400017	+	0.208032i
$932$			10.8268i			0.354644i
$933$	−50.6289	+	22.0560i	−1.65752	+	0.722080i
$934$	−16.0630	−	9.27397i	−0.525597	−	0.303454i
$935$	−16.6785	+	9.62931i	−0.545444	+	0.314912i
$936$	−1.34475	+	5.86197i	−0.0439547	+	0.191604i
$937$	15.9162	+	27.5678i	0.519961	+	0.900599i	0.999731	+	0.0232047i	$0.00738695\pi$
$937$	15.9162	+	27.5678i	0.519961	+	0.900599i	−0.479770	+	0.877395i	$0.659280\pi$
$938$			31.1184i			1.01605i
$939$	15.3896	−	20.8281i	0.502220	−	0.679700i
$940$	0.929084	+	1.60922i	0.0303034	+	0.0524870i
$941$	−6.16530	−	10.6786i	−0.200983	−	0.348113i	0.747862	−	0.663854i	$-0.231080\pi$
$941$	−6.16530	−	10.6786i	−0.200983	−	0.348113i	−0.948845	+	0.315741i	$0.897747\pi$
$942$	−1.71625	+	2.32275i	−0.0559183	+	0.0756793i
$943$			80.3093i			2.61523i
$944$	4.25879	+	7.37643i	0.138612	+	0.240082i
$945$	−6.63237	−	7.73277i	−0.215751	−	0.251547i
$946$	25.0556	−	14.4659i	0.814628	−	0.470326i
$947$	−39.3773	−	22.7345i	−1.27959	−	0.738773i	−0.302818	−	0.953048i	$-0.597928\pi$
$947$	−39.3773	−	22.7345i	−1.27959	−	0.738773i	−0.976773	+	0.214276i	$0.931261\pi$
$948$	19.7841	−	8.61873i	0.642557	−	0.279923i
$949$		−	4.56637i		−	0.148231i
$950$	3.86720	+	2.01117i	0.125468	+	0.0652509i
$951$	26.2641	−	35.5456i	0.851672	−	1.15264i
$952$	6.65674	+	3.84327i	0.215746	+	0.124561i
$953$	−19.6623	+	34.0560i	−0.636923	+	1.10318i	0.349181	+	0.937055i	$0.386460\pi$
$953$	−19.6623	+	34.0560i	−0.636923	+	1.10318i	−0.986104	+	0.166128i	$0.946874\pi$
$954$	21.6161	−	23.2452i	0.699848	−	0.752591i
$955$	3.04683	−	5.27726i	0.0985930	−	0.170768i
$956$	−2.75990	+	1.59343i	−0.0892615	+	0.0515352i
$957$	34.4434	+	25.4497i	1.11340	+	0.822673i
$958$		−	26.5271i		−	0.857053i
$959$	6.96286	−	4.02001i	0.224843	−	0.129813i
$960$	0.194877	−	1.72105i	0.00628961	−	0.0555467i
$961$	30.9454			0.998240
$962$	−14.4227			−0.465008
$963$	−6.15193	+	6.61557i	−0.198243	+	0.213184i
$964$	16.5317	+	9.54461i	0.532452	+	0.307411i
$965$	−1.50046	−	2.59888i	−0.0483016	−	0.0836608i
$966$	−21.2513	+	9.25791i	−0.683749	+	0.297868i
$967$	28.8842	−	50.0289i	0.928854	−	1.60882i	0.143611	−	0.989634i	$-0.454129\pi$
$967$	28.8842	−	50.0289i	0.928854	−	1.60882i	0.785243	−	0.619188i	$-0.212538\pi$
$968$	−13.1299			−0.422011
$969$	−16.5250	+	24.5572i	−0.530858	+	0.788893i
$970$	−15.3758			−0.493686
$971$	−0.428825	+	0.742746i	−0.0137616	+	0.0238358i	−0.872824	−	0.488035i	$-0.837714\pi$
$971$	−0.428825	+	0.742746i	−0.0137616	+	0.0238358i	0.859063	+	0.511871i	$0.171047\pi$
$972$	−13.1762	−	8.32989i	−0.422628	−	0.267181i
$973$	−13.2176	−	22.8935i	−0.423737	−	0.733933i
$974$	−9.80030	−	5.65821i	−0.314022	−	0.181301i
$975$	−0.390678	+	3.45027i	−0.0125117	+	0.110497i
$976$	−7.82756			−0.250554
$977$	−3.12960			−0.100125			−0.0500625	−	0.998746i	$-0.515942\pi$
$977$	−3.12960			−0.100125			−0.0500625	+	0.998746i	$0.515942\pi$
$978$	−14.7312	−	1.66803i	−0.471051	−	0.0533376i
$979$	−46.6368	+	26.9258i	−1.49052	+	0.860552i
$980$		−	3.15615i		−	0.100819i
$981$	−29.9990	+	9.21726i	−0.957793	+	0.294284i
$982$	6.02160	−	3.47657i	0.192157	−	0.110942i
$983$	−16.5230	+	28.6187i	−0.527003	+	0.912796i	0.472502	+	0.881330i	$0.343351\pi$
$983$	−16.5230	+	28.6187i	−0.527003	+	0.912796i	−0.999505	+	0.0314664i	$0.989982\pi$
$984$	20.2481	+	2.29272i	0.645487	+	0.0730891i
$985$	−1.24052	+	2.14864i	−0.0395262	+	0.0684614i
$986$	−17.0901	−	9.86697i	−0.544259	−	0.314228i
$987$	−5.07494	−	3.74980i	−0.161537	−	0.119357i
$988$	4.69813	+	7.36808i	0.149467	+	0.234410i
$989$		−	40.2042i		−	1.27842i
$990$	−14.3636	−	3.29505i	−0.456504	−	0.104723i
$991$	3.55980	+	2.05525i	0.113081	+	0.0652873i	0.555474	−	0.831534i	$-0.312537\pi$
$991$	3.55980	+	2.05525i	0.113081	+	0.0652873i	−0.442393	+	0.896821i	$0.645870\pi$
$992$	0.202293	−	0.116794i	0.00642280	−	0.00370821i
$993$	37.5177	−	16.3442i	1.19059	−	0.518667i
$994$	4.43951	+	7.68946i	0.140813	+	0.243895i
$995$			23.6124i			0.748562i
$996$	19.1001	+	14.1127i	0.605208	+	0.447179i
$997$	−2.97096	−	5.14586i	−0.0940914	−	0.162971i	0.815138	−	0.579267i	$-0.196661\pi$
$997$	−2.97096	−	5.14586i	−0.0940914	−	0.162971i	−0.909229	+	0.416296i	$0.863328\pi$
$998$	−17.0361	−	29.5074i	−0.539269	−	0.934042i
$999$	12.4050	−	35.2644i	0.392478	−	1.11572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.s.a.521.8	yes	24
3.2	odd	2		570.2.s.b.521.12	yes	24
19.12	odd	6		570.2.s.b.221.12	yes	24
57.50	even	6	inner	570.2.s.a.221.8	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.8	✓	24	57.50	even	6	inner
570.2.s.a.521.8	yes	24	1.1	even	1	trivial
570.2.s.b.221.12	yes	24	19.12	odd	6
570.2.s.b.521.12	yes	24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.691758 + 1.58791i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.72105 - 0.194877i) q^{6} -1.96058 q^{7} +1.00000 q^{8} +(-2.04294 + 2.19691i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.691758 + 1.58791i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(-1.72105 - 0.194877i) q^{6} -1.96058 q^{7} +1.00000 q^{8} +(-2.04294 + 2.19691i) q^{9} +(0.866025 - 0.500000i) q^{10} +4.91222i q^{11} +(1.02929 - 1.39304i) q^{12} +(1.73616 - 1.00237i) q^{13} +(0.980288 - 1.69791i) q^{14} +(0.194877 - 1.72105i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.39530 - 1.96028i) q^{17} +(-0.881106 - 2.86769i) q^{18} +(-3.86720 - 2.01117i) q^{19} +1.00000i q^{20} +(-1.35624 - 3.11322i) q^{21} +(-4.25411 - 2.45611i) q^{22} +(-5.91161 + 3.41307i) q^{23} +(0.691758 + 1.58791i) q^{24} +(0.500000 + 0.866025i) q^{25} +2.00475i q^{26} +(-4.90172 - 1.72429i) q^{27} +(0.980288 + 1.69791i) q^{28} +(-2.51673 - 4.35910i) q^{29} +(1.39304 + 1.02929i) q^{30} +0.233588i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-7.80018 + 3.39807i) q^{33} +(3.39530 - 1.96028i) q^{34} +(1.69791 + 0.980288i) q^{35} +(2.92405 + 0.670786i) q^{36} +7.19430i q^{37} +(3.67532 - 2.34350i) q^{38} +(2.79269 + 2.06347i) q^{39} +(-0.866025 - 0.500000i) q^{40} +(5.88249 - 10.1888i) q^{41} +(3.37425 + 0.382070i) q^{42} +(-2.94487 + 5.10067i) q^{43} +(4.25411 - 2.45611i) q^{44} +(2.86769 - 0.881106i) q^{45} -6.82614i q^{46} +(1.60922 - 0.929084i) q^{47} +(-1.72105 - 0.194877i) q^{48} -3.15615 q^{49} -1.00000 q^{50} +(0.764024 - 6.74748i) q^{51} +(-1.73616 - 1.00237i) q^{52} +(5.29044 + 9.16331i) q^{53} +(3.94413 - 3.38287i) q^{54} +(2.45611 - 4.25411i) q^{55} -1.96058 q^{56} +(0.518398 - 7.53202i) q^{57} +5.03345 q^{58} +(4.25879 - 7.37643i) q^{59} +(-1.58791 + 0.691758i) q^{60} +(3.91378 + 6.77887i) q^{61} +(-0.202293 - 0.116794i) q^{62} +(4.00534 - 4.30720i) q^{63} +1.00000 q^{64} -2.00475 q^{65} +(0.957276 - 8.45419i) q^{66} +(-13.7456 + 7.93605i) q^{67} +3.92055i q^{68} +(-9.50907 - 7.02611i) q^{69} +(-1.69791 + 0.980288i) q^{70} +(-2.26439 + 3.92204i) q^{71} +(-2.04294 + 2.19691i) q^{72} +(1.13889 - 1.97262i) q^{73} +(-6.23045 - 3.59715i) q^{74} +(-1.02929 + 1.39304i) q^{75} +(0.191874 + 4.35467i) q^{76} -9.63077i q^{77} +(-3.18336 + 1.38680i) q^{78} +(10.7900 + 6.22958i) q^{79} +(0.866025 - 0.500000i) q^{80} +(-0.652788 - 8.97629i) q^{81} +(5.88249 + 10.1888i) q^{82} +13.7111i q^{83} +(-2.01801 + 2.73115i) q^{84} +(1.96028 + 3.39530i) q^{85} +(-2.94487 - 5.10067i) q^{86} +(5.18091 - 7.01179i) q^{87} +4.91222i q^{88} +(5.48139 + 9.49404i) q^{89} +(-0.670786 + 2.92405i) q^{90} +(-3.40387 + 1.96523i) q^{91} +(5.91161 + 3.41307i) q^{92} +(-0.370917 + 0.161586i) q^{93} +1.85817i q^{94} +(2.34350 + 3.67532i) q^{95} +(1.02929 - 1.39304i) q^{96} +(-13.3158 - 7.68789i) q^{97} +(1.57807 - 2.73330i) q^{98} +(-10.7917 - 10.0354i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9	\( 24 q - 12 q^{2} + 4 q^{3} - 12 q^{4} - 2 q^{6} - 12 q^{7} + 24 q^{8} - 4 q^{9} - 2 q^{12} + 18 q^{13} + 6 q^{14} - 12 q^{16} + 12 q^{17} + 2 q^{18} + 6 q^{19} - 6 q^{21} + 18 q^{22} + 4 q^{24} + 12 q^{25} + 28 q^{27} + 6 q^{28} - 12 q^{32} - 22 q^{33} - 12 q^{34} + 2 q^{36} + 6 q^{38} + 40 q^{39} + 6 q^{41} - 6 q^{42} - 22 q^{43} - 18 q^{44} + 8 q^{45} + 12 q^{47} - 2 q^{48} + 12 q^{49} - 24 q^{50} - 20 q^{51} - 18 q^{52} + 8 q^{53} + 4 q^{54} - 12 q^{56} + 26 q^{59} + 22 q^{61} - 18 q^{62} + 6 q^{63} + 24 q^{64} + 8 q^{65} + 8 q^{66} - 48 q^{67} - 64 q^{69} + 24 q^{71} - 4 q^{72} - 8 q^{73} + 30 q^{74} + 2 q^{75} - 12 q^{76} - 38 q^{78} + 18 q^{79} - 12 q^{81} + 6 q^{82} + 12 q^{84} - 22 q^{86} - 24 q^{87} + 28 q^{89} + 8 q^{90} + 18 q^{91} + 2 q^{93} - 2 q^{96} + 6 q^{97} - 6 q^{98} + 2 q^{99}+O(q^{100}) \) 24 * q - 12 * q^2 + 4 * q^3 - 12 * q^4 - 2 * q^6 - 12 * q^7 + 24 * q^8 - 4 * q^9 - 2 * q^12 + 18 * q^13 + 6 * q^14 - 12 * q^16 + 12 * q^17 + 2 * q^18 + 6 * q^19 - 6 * q^21 + 18 * q^22 + 4 * q^24 + 12 * q^25 + 28 * q^27 + 6 * q^28 - 12 * q^32 - 22 * q^33 - 12 * q^34 + 2 * q^36 + 6 * q^38 + 40 * q^39 + 6 * q^41 - 6 * q^42 - 22 * q^43 - 18 * q^44 + 8 * q^45 + 12 * q^47 - 2 * q^48 + 12 * q^49 - 24 * q^50 - 20 * q^51 - 18 * q^52 + 8 * q^53 + 4 * q^54 - 12 * q^56 + 26 * q^59 + 22 * q^61 - 18 * q^62 + 6 * q^63 + 24 * q^64 + 8 * q^65 + 8 * q^66 - 48 * q^67 - 64 * q^69 + 24 * q^71 - 4 * q^72 - 8 * q^73 + 30 * q^74 + 2 * q^75 - 12 * q^76 - 38 * q^78 + 18 * q^79 - 12 * q^81 + 6 * q^82 + 12 * q^84 - 22 * q^86 - 24 * q^87 + 28 * q^89 + 8 * q^90 + 18 * q^91 + 2 * q^93 - 2 * q^96 + 6 * q^97 - 6 * q^98 + 2 * q^99

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