LMFDB - Embedded newform 570.2.s.b.221.12

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			221.12
Character	$\chi$	$=$	570.221
Dual form			570.2.s.b.521.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.72105 + 0.194877i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.691758 + 1.58791i) q^{6} -1.96058 q^{7} -1.00000 q^{8} +(2.92405 + 0.670786i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.72105 + 0.194877i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.691758 + 1.58791i) q^{6} -1.96058 q^{7} -1.00000 q^{8} +(2.92405 + 0.670786i) 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} +(1.58791 - 0.691758i) 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} +(-3.37425 - 0.382070i) q^{21} +(-4.25411 + 2.45611i) q^{22} +(5.91161 + 3.41307i) q^{23} +(-1.72105 - 0.194877i) 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} +(-0.957276 + 8.45419i) q^{33} +(3.39530 + 1.96028i) q^{34} +(-1.69791 + 0.980288i) q^{35} +(-2.04294 + 2.19691i) 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} +(-1.35624 - 3.11322i) 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} +(-0.691758 - 1.58791i) q^{48} -3.15615 q^{49} +1.00000 q^{50} +(6.22550 - 2.71208i) q^{51} +(-1.73616 + 1.00237i) q^{52} +(-5.29044 + 9.16331i) q^{53} +(0.957584 + 5.10716i) q^{54} +(2.45611 + 4.25411i) q^{55} +1.96058 q^{56} +(-7.04758 + 2.70770i) q^{57} +5.03345 q^{58} +(-4.25879 - 7.37643i) q^{59} +(-0.194877 + 1.72105i) q^{60} +(3.91378 - 6.77887i) q^{61} +(0.202293 - 0.116794i) q^{62} +(-5.73281 - 1.31513i) q^{63} +1.00000 q^{64} +2.00475 q^{65} +(-7.80018 + 3.39807i) 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} +(-2.92405 - 0.670786i) 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} +(-0.390678 + 3.45027i) q^{78} +(10.7900 - 6.22958i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(8.10009 + 3.92282i) 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} +(2.19691 + 2.04294i) q^{90} +(-3.40387 - 1.96523i) q^{91} +(-5.91161 + 3.41307i) q^{92} +(0.0455208 - 0.402017i) 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} +(-3.29505 + 14.3636i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	$ 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 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} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 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} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * 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 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * 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 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.72105	+	0.194877i	0.993650	+	0.112512i
$3$	1.72105	+	0.194877i	0.993650	+	0.112512i
$4$	−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
$6$	0.691758	+	1.58791i	0.282409	+	0.648263i
$7$	−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
$9$	2.92405	+	0.670786i	0.974682	+	0.223595i
$10$	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	0.721051	−	0.692881i	$-0.243659\pi$
$13$	1.73616	+	1.00237i	0.481524	+	0.278008i	−0.239527	+	0.970890i	$0.576992\pi$
$14$	−0.980288	−	1.69791i	−0.261993	−	0.453785i
$15$	1.58791	−	0.691758i	0.409998	−	0.178611i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.39530	−	1.96028i	0.823481	−	0.475437i	−0.0281343	−	0.999604i	$-0.508957\pi$
$17$	3.39530	−	1.96028i	0.823481	−	0.475437i	0.851615	+	0.524167i	$0.175623\pi$
$18$	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
$21$	−3.37425	−	0.382070i	−0.736323	−	0.0833745i
$22$	−4.25411	+	2.45611i	−0.906978	+	0.523644i
$23$	5.91161	+	3.41307i	1.23266	+	0.711674i	0.967583	−	0.252554i	$-0.0812706\pi$
$23$	5.91161	+	3.41307i	1.23266	+	0.711674i	0.265073	+	0.964228i	$0.414604\pi$
$24$	−1.72105	−	0.194877i	−0.351308	−	0.0397790i
$25$	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	$-0.678544\pi$
$29$	2.51673	−	4.35910i	0.467344	−	0.809464i	0.999304	+	0.0373055i	$0.0118775\pi$
$30$	1.39304	+	1.02929i	0.254333	+	0.187923i
$31$		−	0.233588i		−	0.0419536i	−0.999780	−	0.0209768i	$-0.993322\pi$
$31$		−	0.233588i		−	0.0419536i	0.999780	−	0.0209768i	$-0.00667761\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−0.957276	+	8.45419i	−0.166640	+	1.47169i
$34$	3.39530	+	1.96028i	0.582289	+	0.336185i
$35$	−1.69791	+	0.980288i	−0.286999	+	0.165699i
$36$	−2.04294	+	2.19691i	−0.340490	+	0.366151i
$37$		−	7.19430i		−	1.18274i	−0.806402	−	0.591368i	$-0.798588\pi$
$37$		−	7.19430i		−	1.18274i	0.806402	−	0.591368i	$-0.201412\pi$
$38$	−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	−0.801407	−	0.598119i	$-0.795915\pi$
$41$	−5.88249	−	10.1888i	−0.918690	−	1.59122i	−0.117282	−	0.993099i	$-0.537418\pi$
$42$	−1.35624	−	3.11322i	−0.209273	−	0.480381i
$43$	−2.94487	−	5.10067i	−0.449089	−	0.777845i	0.549238	−	0.835666i	$-0.314918\pi$
$43$	−2.94487	−	5.10067i	−0.449089	−	0.777845i	−0.998327	+	0.0578212i	$0.981585\pi$
$44$	−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	$-0.376604\pi$
$47$	−1.60922	−	0.929084i	−0.234729	−	0.135521i	−0.612752	+	0.790275i	$0.709937\pi$
$48$	−0.691758	−	1.58791i	−0.0998467	−	0.229196i
$49$	−3.15615			−0.450878
$50$	1.00000			0.141421
$51$	6.22550	−	2.71208i	0.871745	−	0.379767i
$52$	−1.73616	+	1.00237i	−0.240762	+	0.139004i
$53$	−5.29044	+	9.16331i	−0.726698	+	1.25868i	0.231573	+	0.972817i	$0.425613\pi$
$53$	−5.29044	+	9.16331i	−0.726698	+	1.25868i	−0.958271	+	0.285861i	$0.907721\pi$
$54$	0.957584	+	5.10716i	0.130311	+	0.694996i
$55$	2.45611	+	4.25411i	0.331182	+	0.573624i
$56$	1.96058			0.261993
$57$	−7.04758	+	2.70770i	−0.933474	+	0.358644i
$58$	5.03345			0.660925
$59$	−4.25879	−	7.37643i	−0.554447	−	0.960330i	−0.997946	−	0.0640552i	$-0.979597\pi$
$59$	−4.25879	−	7.37643i	−0.554447	−	0.960330i	0.443500	−	0.896274i	$-0.353737\pi$
$60$	−0.194877	+	1.72105i	−0.0251584	+	0.222187i
$61$	3.91378	−	6.77887i	0.501108	−	0.867945i	−0.498891	−	0.866665i	$-0.666259\pi$
$61$	3.91378	−	6.77887i	0.501108	−	0.867945i	0.999999	−	0.00128020i	$-0.000407502\pi$
$62$	0.202293	−	0.116794i	0.0256912	−	0.0148328i
$63$	−5.73281	−	1.31513i	−0.722266	−	0.165690i
$64$	1.00000			0.125000
$65$	2.00475			0.248658
$66$	−7.80018	+	3.39807i	−0.960136	+	0.418273i
$67$	−13.7456	−	7.93605i	−1.67930	−	0.969542i	−0.962110	−	0.272661i	$-0.912096\pi$
$67$	−13.7456	−	7.93605i	−1.67930	−	0.969542i	−0.717186	−	0.696882i	$-0.754570\pi$
$68$			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	$-0.0800614\pi$
$71$	2.26439	+	3.92204i	0.268734	+	0.465461i	−0.699801	+	0.714338i	$0.746728\pi$
$72$	−2.92405	−	0.670786i	−0.344602	−	0.0790528i
$73$	1.13889	+	1.97262i	0.133297	+	0.230877i	0.924946	−	0.380099i	$-0.124110\pi$
$73$	1.13889	+	1.97262i	0.133297	+	0.230877i	−0.791649	+	0.610977i	$0.790777\pi$
$74$	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
$78$	−0.390678	+	3.45027i	−0.0442355	+	0.390666i
$79$	10.7900	−	6.22958i	1.21396	−	0.700883i	0.250344	−	0.968157i	$-0.419456\pi$
$79$	10.7900	−	6.22958i	1.21396	−	0.700883i	0.963621	+	0.267274i	$0.0861229\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	8.10009	+	3.92282i	0.900010	+	0.435868i
$82$	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	0.414332	+	0.910126i	$0.364015\pi$
$89$	−5.48139	+	9.49404i	−0.581026	+	1.00637i	−0.995358	+	0.0962408i	$0.969318\pi$
$90$	2.19691	+	2.04294i	0.231574	+	0.215345i
$91$	−3.40387	−	1.96523i	−0.356823	−	0.206012i
$92$	−5.91161	+	3.41307i	−0.616328	+	0.355837i
$93$	0.0455208	−	0.402017i	0.00472028	−	0.0416872i
$94$		−	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	−0.988532	−	0.151013i	$-0.951746\pi$
$97$	−13.3158	+	7.68789i	−1.35202	+	0.780587i	−0.363484	+	0.931600i	$0.618413\pi$
$98$	−1.57807	−	2.73330i	−0.159409	−	0.276105i
$99$	−3.29505	+	14.3636i	−0.331165	+	1.44359i
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−9.94449	−	5.74146i	−0.989514	−	0.571296i	−0.0843851	−	0.996433i	$-0.526893\pi$
$101$	−9.94449	−	5.74146i	−0.989514	−	0.571296i	−0.905129	+	0.425137i	$0.860226\pi$
$102$	5.46148	+	4.03541i	0.540767	+	0.399565i
$103$		−	1.76334i		−	0.173747i	−0.996219	−	0.0868736i	$-0.972312\pi$
$103$		−	1.76334i		−	0.173747i	0.996219	−	0.0868736i	$-0.0276876\pi$
$104$	−1.73616	−	1.00237i	−0.170245	−	0.0982907i
$105$	−3.11322	+	1.35624i	−0.303820	+	0.132356i
$106$	−10.5809			−1.02771
$107$	−3.01131			−0.291115			−0.145557	−	0.989350i	$-0.546498\pi$
$107$	−3.01131			−0.291115			−0.145557	+	0.989350i	$0.546498\pi$
$108$	−3.94413	+	3.38287i	−0.379524	+	0.325517i
$109$	9.05950	−	5.23051i	0.867743	−	0.500992i	0.00114554	−	0.999999i	$-0.499635\pi$
$109$	9.05950	−	5.23051i	0.867743	−	0.500992i	0.866598	+	0.499008i	$0.166302\pi$
$110$	−2.45611	+	4.25411i	−0.234181	+	0.405613i
$111$	1.40200	−	12.3818i	0.133072	−	1.17523i
$112$	0.980288	+	1.69791i	0.0926285	+	0.160437i
$113$	12.1589			1.14382			0.571909	−	0.820317i	$-0.306203\pi$
$113$	12.1589			1.14382			0.571909	+	0.820317i	$0.306203\pi$
$114$	−5.86873	−	4.74953i	−0.549657	−	0.444834i
$115$	6.82614			0.636541
$116$	2.51673	+	4.35910i	0.233672	+	0.404732i
$117$	4.40424	+	4.09558i	0.407172	+	0.378636i
$118$	4.25879	−	7.37643i	0.392053	−	0.679056i
$119$	−6.65674	+	3.84327i	−0.610222	+	0.352312i
$120$	−1.58791	+	0.691758i	−0.144956	+	0.0631486i
$121$	−13.1299			−1.19363
$122$	7.82756			0.708674
$123$	−8.13852	−	18.6818i	−0.733825	−	1.68448i
$124$	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	0.906633	−	0.421919i	$-0.138643\pi$
$127$	11.2081	+	6.47100i	0.994557	+	0.574208i	0.0879240	+	0.996127i	$0.471977\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−4.07428	−	9.35241i	−0.358720	−	0.823434i
$130$	1.00237	+	1.73616i	0.0879139	+	0.152271i
$131$	7.74381	−	4.47089i	0.676580	−	0.390624i	−0.121985	−	0.992532i	$-0.538926\pi$
$131$	7.74381	−	4.47089i	0.676580	−	0.390624i	0.798565	+	0.601908i	$0.205593\pi$
$132$	−6.84290	−	5.05612i	−0.595598	−	0.440079i
$133$	7.58193	−	3.94305i	0.657436	−	0.341906i
$134$		−	15.8721i		−	1.37114i
$135$	5.10716	−	0.957584i	0.439554	−	0.0824157i
$136$	−3.39530	+	1.96028i	−0.291145	+	0.168092i
$137$	3.55144	+	2.05042i	0.303420	+	0.175180i	0.643978	−	0.765044i	$-0.277283\pi$
$137$	3.55144	+	2.05042i	0.303420	+	0.175180i	−0.340558	+	0.940223i	$0.610616\pi$
$138$	−1.33025	+	11.7481i	−0.113239	+	1.00007i
$139$	6.74169	−	11.6770i	0.571823	−	0.990426i	−0.424556	−	0.905402i	$-0.639570\pi$
$139$	6.74169	−	11.6770i	0.571823	−	0.990426i	0.996379	−	0.0850246i	$-0.0270969\pi$
$140$		−	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
$147$	−5.43189	−	0.615059i	−0.448015	−	0.0507292i
$148$	6.23045	+	3.59715i	0.512140	+	0.295684i
$149$	3.99172	−	2.30462i	0.327014	−	0.188802i	−0.327500	−	0.944851i	$-0.606206\pi$
$149$	3.99172	−	2.30462i	0.327014	−	0.188802i	0.654515	+	0.756049i	$0.272873\pi$
$150$	1.72105	+	0.194877i	0.140523	+	0.0159116i
$151$		−	17.3564i		−	1.41245i	−0.707990	−	0.706223i	$-0.750398\pi$
$151$		−	17.3564i		−	1.41245i	0.707990	−	0.706223i	$-0.249602\pi$
$152$	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
$156$	−3.18336	+	1.38680i	−0.254873	+	0.111033i
$157$	0.833700	+	1.44401i	0.0665365	+	0.115245i	0.897375	−	0.441270i	$-0.145472\pi$
$157$	0.833700	+	1.44401i	0.0665365	+	0.115245i	−0.830838	+	0.556514i	$0.812138\pi$
$158$	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
$162$	0.652788	+	8.97629i	0.0512879	+	0.705244i
$163$	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
$165$	3.39807	+	7.80018i	0.264539	+	0.607243i
$166$	−11.8742	+	6.85554i	−0.921613	+	0.532093i
$167$	−4.84533	+	8.39236i	−0.374943	+	0.649420i	−0.990318	−	0.138814i	$-0.955671\pi$
$167$	−4.84533	+	8.39236i	−0.374943	+	0.649420i	0.615376	+	0.788234i	$0.289004\pi$
$168$	3.37425	+	0.382070i	0.260329	+	0.0294773i
$169$	−4.49050	−	7.77777i	−0.345423	−	0.598290i
$170$	3.92055			0.300693
$171$	−12.6569	+	3.28669i	−0.967899	+	0.251340i
$172$	5.88974			0.449089
$173$	5.22274	+	9.04605i	0.397078	+	0.687759i	0.993364	−	0.115013i	$-0.0366910\pi$
$173$	5.22274	+	9.04605i	0.397078	+	0.687759i	−0.596286	+	0.802772i	$0.703358\pi$
$174$	8.66284	+	0.980902i	0.656728	+	0.0743620i
$175$	−0.980288	+	1.69791i	−0.0741028	+	0.128350i
$176$	4.25411	−	2.45611i	0.320665	−	0.185136i
$177$	−5.89210	−	13.5252i	−0.442877	−	1.01661i
$178$	−10.9628			−0.821695
$179$	1.34670			0.100657			0.0503285	−	0.998733i	$-0.483973\pi$
$179$	1.34670			0.100657			0.0503285	+	0.998733i	$0.483973\pi$
$180$	−0.670786	+	2.92405i	−0.0499974	+	0.217946i
$181$	12.6588	+	7.30854i	0.940919	+	0.543240i	0.890248	−	0.455476i	$-0.150531\pi$
$181$	12.6588	+	7.30854i	0.940919	+	0.543240i	0.0506704	+	0.998715i	$0.483864\pi$
$182$		−	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
$186$	0.370917	−	0.161586i	0.0271970	−	0.0118481i
$187$	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	$0.929244\pi$
$192$	1.72105	+	0.194877i	0.124206	+	0.0140640i
$193$	2.59888	−	1.50046i	0.187071	−	0.108006i	−0.403540	−	0.914962i	$-0.632220\pi$
$193$	2.59888	−	1.50046i	0.187071	−	0.108006i	0.590611	+	0.806957i	$0.298887\pi$
$194$	−13.3158	−	7.68789i	−0.956020	−	0.551958i
$195$	3.45027	+	0.390678i	0.247079	+	0.0279770i
$196$	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	0.0555409	+	0.998456i	$0.482312\pi$
$199$	−11.8062	+	20.4489i	−0.836918	+	1.44958i	−0.892459	+	0.451128i	$0.851022\pi$
$200$	−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
$204$	−0.764024	+	6.74748i	−0.0534924	+	0.472418i
$205$	−10.1888	−	5.88249i	−0.711614	−	0.410851i
$206$	1.52710	−	0.881671i	0.106398	−	0.0614289i
$207$	14.9964	+	13.9454i	1.04232	+	0.969272i
$208$		−	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	−0.410625	−	0.911804i	$-0.634689\pi$
$211$	2.52326	−	1.45680i	0.173708	−	0.100290i	0.584333	+	0.811514i	$0.301356\pi$
$212$	−5.29044	−	9.16331i	−0.363349	−	0.629339i
$213$	3.13283	+	7.19132i	0.214658	+	0.492741i
$214$	−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
$219$	1.57567	+	3.61692i	0.106474	+	0.244409i
$220$	−4.91222			−0.331182
$221$	7.85971			0.528702
$222$	11.4239	−	4.97672i	0.766724	−	0.334015i
$223$	3.39391	−	1.95947i	0.227273	−	0.131216i	−0.382040	−	0.924146i	$-0.624778\pi$
$223$	3.39391	−	1.95947i	0.227273	−	0.131216i	0.609313	+	0.792930i	$0.291445\pi$
$224$	−0.980288	+	1.69791i	−0.0654982	+	0.113446i
$225$	2.04294	−	2.19691i	0.136196	−	0.146460i
$226$	6.07947	+	10.5300i	0.404400	+	0.700442i
$227$	0.316084			0.0209793			0.0104896	−	0.999945i	$-0.496661\pi$
$227$	0.316084			0.0209793			0.0104896	+	0.999945i	$0.496661\pi$
$228$	1.17885	−	7.45723i	0.0780712	−	0.493867i
$229$	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
$231$	1.87681	−	16.5751i	0.123485	−	1.09056i
$232$	−2.51673	+	4.35910i	−0.165231	+	0.286189i
$233$	9.37631	−	5.41341i	0.614262	−	0.354644i	−0.160369	−	0.987057i	$-0.551269\pi$
$233$	9.37631	−	5.41341i	0.614262	−	0.354644i	0.774632	+	0.632413i	$0.217935\pi$
$234$	−1.34475	+	5.86197i	−0.0879093	+	0.383209i
$235$	−1.85817			−0.121214
$236$	8.51757			0.554447
$237$	19.7841	−	8.61873i	1.28511	−	0.559847i
$238$	−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	−0.138119	−	0.990416i	$-0.544106\pi$
$241$	−16.5317	−	9.54461i	−1.06490	−	0.614822i	−0.926785	+	0.375593i	$0.877439\pi$
$242$	−6.56495	−	11.3708i	−0.422011	−	0.730944i
$243$	13.1762	+	8.32989i	0.845255	+	0.534363i
$244$	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
$249$	−2.67197	+	23.5975i	−0.169329	+	1.49543i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$	−10.0866	−	5.82352i	−0.636663	−	0.367578i	0.146665	−	0.989186i	$-0.453146\pi$
$251$	−10.0866	−	5.82352i	−0.636663	−	0.367578i	−0.783328	+	0.621609i	$0.786479\pi$
$252$	4.00534	−	4.30720i	0.252313	−	0.271328i
$253$	−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	0.220571	+	0.975371i	$0.429208\pi$
$257$	−11.7735	+	20.3923i	−0.734410	+	1.27204i	−0.954982	+	0.296665i	$0.904125\pi$
$258$	6.06228	−	8.20463i	0.377421	−	0.510798i
$259$			14.1050i			0.876440i
$260$	−1.00237	+	1.73616i	−0.0621645	+	0.107672i
$261$	10.2830	−	11.0580i	0.636505	−	0.684474i
$262$	7.74381	+	4.47089i	0.478414	+	0.276213i
$263$	−3.46036	+	1.99784i	−0.213375	+	0.123192i	−0.602879	−	0.797833i	$-0.705980\pi$
$263$	−3.46036	+	1.99784i	−0.213375	+	0.123192i	0.389504	+	0.921025i	$0.372646\pi$
$264$	0.957276	−	8.45419i	0.0589163	−	0.520319i
$265$			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	$-0.144840\pi$
$269$	1.12373	+	1.94636i	0.0685152	+	0.118672i	−0.829733	+	0.558161i	$0.811507\pi$
$270$	3.38287	+	3.94413i	0.205875	+	0.240032i
$271$	2.70149	+	4.67912i	0.164104	+	0.284236i	0.936337	−	0.351103i	$-0.114193\pi$
$271$	2.70149	+	4.67912i	0.164104	+	0.284236i	−0.772233	+	0.635340i	$0.780860\pi$
$272$	−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
$276$	−10.8393	+	4.72204i	−0.652450	+	0.284233i
$277$	−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
$279$	0.156687	−	0.683021i	0.00938062	−	0.0408914i
$280$	1.69791	−	0.980288i	0.101469	−	0.0585834i
$281$	9.35418	−	16.2019i	0.558023	−	0.966525i	−0.439638	−	0.898175i	$-0.644893\pi$
$281$	9.35418	−	16.2019i	0.558023	−	0.966525i	0.997661	−	0.0683499i	$-0.0217734\pi$
$282$	0.362113	−	3.19801i	0.0215635	−	0.190438i
$283$	10.5801	+	18.3252i	0.628919	+	1.08932i	0.987769	+	0.155924i	$0.0498355\pi$
$283$	10.5801	+	18.3252i	0.628919	+	1.08932i	−0.358850	+	0.933395i	$0.616831\pi$
$284$	−4.52879			−0.268734
$285$	−4.74953	+	5.86873i	−0.281338	+	0.347633i
$286$	−9.84775			−0.582310
$287$	11.5331	+	19.9758i	0.680775	+	1.17914i
$288$	2.04294	−	2.19691i	0.120381	−	0.129454i
$289$	−0.814625	+	1.41097i	−0.0479191	+	0.0829984i
$290$	4.35910	−	2.51673i	0.255975	−	0.147787i
$291$	−24.4154	+	10.6363i	−1.43126	+	0.623512i
$292$	−2.27778			−0.133297
$293$	12.3120			0.719275			0.359638	−	0.933092i	$-0.382900\pi$
$293$	12.3120			0.719275			0.359638	+	0.933092i	$0.382900\pi$
$294$	−2.18329	−	5.01169i	−0.127332	−	0.292287i
$295$	−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
$300$	0.691758	+	1.58791i	0.0399387	+	0.0916782i
$301$	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
$306$	8.61309	+	8.00946i	0.492377	+	0.457870i
$307$	−13.1520	+	7.59331i	−0.750624	+	0.433373i	−0.825919	−	0.563788i	$-0.809343\pi$
$307$	−13.1520	+	7.59331i	−0.750624	+	0.433373i	0.0752952	+	0.997161i	$0.476010\pi$
$308$	8.34049	+	4.81539i	0.475244	+	0.274382i
$309$	0.343634	−	3.03481i	0.0195487	−	0.172644i
$310$	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	−0.996189	−	0.0872234i	$-0.972201\pi$
$313$	−7.47579	+	12.9485i	−0.422557	+	0.731890i	0.573632	+	0.819113i	$0.305534\pi$
$314$	−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	−0.245771	−	0.969328i	$-0.579041\pi$
$317$	12.7583	−	22.0980i	0.716577	−	1.24115i	0.962348	−	0.271821i	$-0.0876257\pi$
$318$	−18.2103	−	2.06197i	−1.02118	−	0.115629i
$319$	21.4128	+	12.3627i	1.19889	+	0.692179i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	−5.18263	−	0.586834i	−0.289266	−	0.0327539i
$322$		−	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
$327$	16.6112	−	7.23650i	0.918601	−	0.400179i
$328$	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	$0.224950\pi$
$331$			23.6270i			1.29866i	−0.760508	+	0.649329i	$0.775050\pi$
$332$	−11.8742	−	6.85554i	−0.651679	−	0.376247i
$333$	4.82583	−	21.0365i	0.264454	−	1.15279i
$334$	−9.69066			−0.530249
$335$	−15.8721			−0.867185
$336$	1.35624	+	3.11322i	0.0739892	+	0.169840i
$337$	−1.65491	+	0.955464i	−0.0901489	+	0.0520475i	−0.544397	−	0.838828i	$-0.683241\pi$
$337$	−1.65491	+	0.955464i	−0.0901489	+	0.0520475i	0.454248	+	0.890875i	$0.349908\pi$
$338$	4.49050	−	7.77777i	0.244251	−	0.423055i
$339$	20.9262	+	2.36949i	1.13655	+	0.128693i
$340$	1.96028	+	3.39530i	0.106311	+	0.184136i
$341$	1.14743			0.0621370
$342$	−9.17482	−	9.31787i	−0.496117	−	0.503853i
$343$	19.9119			1.07514
$344$	2.94487	+	5.10067i	0.158777	+	0.275010i
$345$	11.7481	+	1.33025i	0.632499	+	0.0716185i
$346$	−5.22274	+	9.04605i	−0.280776	+	0.486319i
$347$	−13.6960	+	7.90736i	−0.735237	+	0.424489i	−0.820335	−	0.571883i	$-0.806213\pi$
$347$	−13.6960	+	7.90736i	−0.735237	+	0.424489i	0.0850978	+	0.996373i	$0.472880\pi$
$348$	3.48193	+	7.99269i	0.186651	+	0.428453i
$349$	−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
$351$	6.78179	+	7.90698i	0.361985	+	0.422044i
$352$	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
$357$	−12.2056	+	5.31723i	−0.645987	+	0.281418i
$358$	0.673349	+	1.16628i	0.0355876	+	0.0616396i
$359$	−3.05773	+	1.76538i	−0.161381	+	0.0931733i	−0.578515	−	0.815671i	$-0.696368\pi$
$359$	−3.05773	+	1.76538i	−0.161381	+	0.0931733i	0.417135	+	0.908845i	$0.363034\pi$
$360$	−2.86769	+	0.881106i	−0.151141	+	0.0464384i
$361$	10.9104	−	15.5552i	0.574232	−	0.818693i
$362$			14.6171i			0.768257i
$363$	−22.5972	−	2.55871i	−1.18605	−	0.134297i
$364$	3.40387	−	1.96523i	0.178411	−	0.103006i
$365$	1.97262	+	1.13889i	0.103251	+	0.0596123i
$366$	13.4716	+	1.52541i	0.704174	+	0.0797343i
$367$	−1.33512	+	2.31249i	−0.0696925	+	0.120711i	−0.898766	−	0.438429i	$-0.855535\pi$
$367$	−1.33512	+	2.31249i	−0.0696925	+	0.120711i	0.829073	+	0.559140i	$0.188868\pi$
$368$		−	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	$0.0343848\pi$
$373$			4.16443i			0.215626i	−0.994171	+	0.107813i	$0.965615\pi$
$374$	−9.62931	+	16.6785i	−0.497920	+	0.862422i
$375$	0.194877	−	1.72105i	0.0100634	−	0.0888748i
$376$	1.60922	+	0.929084i	0.0829892	+	0.0479138i
$377$	8.73888	−	5.04540i	0.450075	−	0.259851i
$378$	−1.87742	−	10.0130i	−0.0965638	−	0.515011i
$379$			10.8219i			0.555884i	0.960598	+	0.277942i	$0.0896523\pi$
$379$			10.8219i			0.555884i	−0.960598	+	0.277942i	$0.910348\pi$
$380$	−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	$-0.305745\pi$
$383$	−8.28137	−	14.3437i	−0.423158	−	0.732931i	−0.996246	+	0.0865623i	$0.972412\pi$
$384$	0.691758	+	1.58791i	0.0353012	+	0.0810329i
$385$	−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	−0.978670	−	0.205440i	$-0.934138\pi$
$389$	−32.4626	−	18.7423i	−1.64592	−	0.950273i	−0.667251	−	0.744833i	$-0.732529\pi$
$390$	1.38680	+	3.18336i	0.0702233	+	0.161196i
$391$	26.7623			1.35343
$392$	3.15615			0.159409
$393$	14.1988	−	6.18555i	0.716234	−	0.312020i
$394$	2.14864	−	1.24052i	0.108247	−	0.0624965i
$395$	6.22958	−	10.7900i	0.313444	−	0.542902i
$396$	−10.7917	−	10.0354i	−0.542302	−	0.504296i
$397$	−2.65169	−	4.59286i	−0.133085	−	0.230509i	0.791780	−	0.610807i	$-0.209155\pi$
$397$	−2.65169	−	4.59286i	−0.133085	−	0.230509i	−0.924864	+	0.380298i	$0.875822\pi$
$398$	−23.6124			−1.18358
$399$	13.8173	−	5.30865i	0.691730	−	0.265765i
$400$	−1.00000			−0.0500000
$401$	3.00036	+	5.19678i	0.149831	+	0.259515i	0.931165	−	0.364598i	$-0.118794\pi$
$401$	3.00036	+	5.19678i	0.149831	+	0.259515i	−0.781334	+	0.624113i	$0.785460\pi$
$402$	3.09310	−	27.3167i	0.154270	−	1.36243i
$403$	0.234142	−	0.405546i	0.0116634	−	0.0202017i
$404$	9.94449	−	5.74146i	0.494757	−	0.285648i
$405$	8.97629	−	0.652788i	0.446036	−	0.0324373i
$406$	−9.86847			−0.489764
$407$	35.3400			1.75174
$408$	−6.22550	+	2.71208i	−0.308208	+	0.134268i
$409$	−23.6531	−	13.6561i	−1.16957	−	0.675253i	−0.215993	−	0.976395i	$-0.569299\pi$
$409$	−23.6531	−	13.6561i	−1.16957	−	0.675253i	−0.953579	+	0.301143i	$0.902632\pi$
$410$		−	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
$414$	−4.57888	+	19.9599i	−0.225039	+	0.980978i
$415$	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	$-0.0406878\pi$
$420$	0.382070	−	3.37425i	0.0186431	−	0.164647i
$421$	0.601100	−	0.347045i	0.0292958	−	0.0169139i	−0.485281	−	0.874358i	$-0.661283\pi$
$421$	0.601100	−	0.347045i	0.0292958	−	0.0169139i	0.514576	+	0.857445i	$0.327949\pi$
$422$	2.52326	+	1.45680i	0.122830	+	0.0709160i
$423$	−4.08222	−	3.79613i	−0.198484	−	0.184574i
$424$	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	$-0.964298\pi$
$431$	−8.30269	+	14.3807i	−0.399926	+	0.692693i	0.593790	+	0.804620i	$0.297631\pi$
$432$	−0.957584	−	5.10716i	−0.0460718	−	0.245718i
$433$	18.0716	+	10.4336i	0.868465	+	0.501409i	0.866838	−	0.498590i	$-0.166149\pi$
$433$	18.0716	+	10.4336i	0.868465	+	0.501409i	0.00162720	+	0.999999i	$0.499482\pi$
$434$	−0.396610	+	0.228983i	−0.0190379	+	0.0109915i
$435$	0.980902	−	8.66284i	0.0470306	−	0.415351i
$436$			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	−0.708648	−	0.705562i	$-0.750695\pi$
$439$	−9.46913	+	5.46701i	−0.451937	+	0.260926i	0.256711	+	0.966488i	$0.417361\pi$
$440$	−2.45611	−	4.25411i	−0.117090	−	0.202807i
$441$	−9.22871	−	2.11710i	−0.439463	−	0.100814i
$442$	3.92986	+	6.80671i	0.186924	+	0.323762i
$443$	−32.8931	−	18.9908i	−1.56280	−	0.902281i	−0.996972	−	0.0777559i	$-0.975225\pi$
$443$	−32.8931	−	18.9908i	−1.56280	−	0.902281i	−0.565825	−	0.824525i	$-0.691442\pi$
$444$	10.0219	+	7.40505i	0.475620	+	0.351428i
$445$			10.9628i			0.519685i
$446$	3.39391	+	1.95947i	0.160706	+	0.0927838i
$447$	7.31908	−	3.18848i	0.346180	−	0.150810i
$448$	−1.96058			−0.0926285
$449$	−37.0794			−1.74989			−0.874944	−	0.484225i	$-0.839102\pi$
$449$	−37.0794			−1.74989			−0.874944	+	0.484225i	$0.839102\pi$
$450$	2.92405	+	0.670786i	0.137841	+	0.0316211i
$451$	50.0494	−	28.8961i	2.35674	−	1.36066i
$452$	−6.07947	+	10.5300i	−0.285954	+	0.495287i
$453$	3.38236	−	29.8713i	0.158917	−	1.40348i
$454$	0.158042	+	0.273737i	0.00741729	+	0.0128471i
$455$	−3.93045			−0.184263
$456$	7.04758	−	2.70770i	0.330033	−	0.126800i
$457$	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
$459$	20.0229	−	3.75426i	0.934588	−	0.175234i
$460$	−3.41307	+	5.91161i	−0.159135	+	0.275630i
$461$	−4.14251	+	2.39168i	−0.192936	+	0.111392i	−0.593356	−	0.804940i	$-0.702197\pi$
$461$	−4.14251	+	2.39168i	−0.192936	+	0.111392i	0.400420	+	0.916332i	$0.368864\pi$
$462$	15.2928	−	6.66217i	0.711487	−	0.309952i
$463$	−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
$465$	−0.161586	−	0.370917i	−0.00749338	−	0.0172009i
$466$	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
$471$	1.15344	+	2.64769i	0.0531476	+	0.121999i
$472$	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
$477$	−21.6161	+	23.2452i	−0.989734	+	1.06432i
$478$	2.75990	−	1.59343i	0.126235	−	0.0728817i
$479$	22.9732	+	13.2636i	1.04967	+	0.606028i	0.922557	−	0.385860i	$-0.126095\pi$
$479$	22.9732	+	13.2636i	1.04967	+	0.606028i	0.127114	+	0.991888i	$0.459429\pi$
$480$	0.194877	−	1.72105i	0.00889485	−	0.0785550i
$481$	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	$-0.917464\pi$
$487$		−	11.3164i		−	0.512796i	0.966571	−	0.256398i	$-0.0825357\pi$
$488$	−3.91378	+	6.77887i	−0.177169	+	0.306865i
$489$	14.7312	+	1.66803i	0.666167	+	0.0754308i
$490$	−2.73330	−	1.57807i	−0.123478	−	0.0712900i
$491$	6.02160	−	3.47657i	0.271751	−	0.156896i	−0.357932	−	0.933748i	$-0.616518\pi$
$491$	6.02160	−	3.47657i	0.271751	−	0.156896i	0.629683	+	0.776852i	$0.283185\pi$
$492$	20.2481	+	2.29272i	0.912857	+	0.103364i
$493$		−	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
$498$	−21.7720	+	9.48476i	−0.975628	+	0.425022i
$499$	−17.0361	−	29.5074i	−0.762642	−	1.32093i	−0.941484	−	0.337057i	$-0.890569\pi$
$499$	−17.0361	−	29.5074i	−0.762642	−	1.32093i	0.178843	−	0.983878i	$-0.442765\pi$
$500$	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	$-0.365968\pi$
$503$	−3.97574	−	2.29540i	−0.177270	−	0.102347i	−0.586009	+	0.810304i	$0.699302\pi$
$504$	5.73281	+	1.31513i	0.255360	+	0.0585803i
$505$	−11.4829			−0.510983
$506$	−33.5315			−1.49066
$507$	−6.21268	−	14.2610i	−0.275915	−	0.633355i
$508$	−11.2081	+	6.47100i	−0.497279	+	0.287104i
$509$	10.1206	−	17.5295i	0.448590	−	0.776980i	−0.549705	−	0.835359i	$-0.685260\pi$
$509$	10.1206	−	17.5295i	0.448590	−	0.776980i	0.998294	+	0.0583790i	$0.0185932\pi$
$510$	6.74748	+	0.764024i	0.298784	+	0.0338316i
$511$	−2.23288	−	3.86746i	−0.0987769	−	0.171087i
$512$	−1.00000			−0.0441942
$513$	−22.4237	+	3.19003i	−0.990032	+	0.140843i
$514$	−23.5470			−1.03861
$515$	−0.881671	−	1.52710i	−0.0388511	−	0.0672920i
$516$	10.1366	+	1.14777i	0.446237	+	0.0505279i
$517$	4.56386	−	7.90484i	0.200718	−	0.347655i
$518$	−12.2153	+	7.05248i	−0.536708	+	0.309868i
$519$	7.22575	+	16.5865i	0.317175	+	0.728068i
$520$	−2.00475			−0.0879139
$521$	19.3708			0.848650			0.424325	−	0.905510i	$-0.360511\pi$
$521$	19.3708			0.848650			0.424325	+	0.905510i	$0.360511\pi$
$522$	14.7181	+	3.37637i	0.644192	+	0.147780i
$523$	−35.0535	−	20.2382i	−1.53278	−	0.884954i	−0.999232	−	0.0391867i	$-0.987523\pi$
$523$	−35.0535	−	20.2382i	−1.53278	−	0.884954i	−0.533553	−	0.845767i	$-0.679143\pi$
$524$			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
$528$	7.80018	−	3.39807i	0.339459	−	0.147882i
$529$	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
$534$	−18.8675	−	2.13639i	−0.816477	−	0.0924505i
$535$	−2.60787	+	1.50566i	−0.112748	+	0.0650952i
$536$	13.7456	+	7.93605i	0.593721	+	0.342785i
$537$	2.31774	+	0.262440i	0.100018	+	0.0113251i
$538$	−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	−0.354082	−	0.935215i	$-0.615206\pi$
$541$	14.7204	−	25.4965i	0.632879	−	1.09618i	0.986960	−	0.160964i	$-0.0514602\pi$
$542$	−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
$546$	0.765953	−	6.76452i	0.0327798	−	0.289495i
$547$	10.3833	+	5.99478i	0.443956	+	0.256318i	0.705274	−	0.708935i	$-0.250824\pi$
$547$	10.3833	+	5.99478i	0.443956	+	0.256318i	−0.261318	+	0.965253i	$0.584157\pi$
$548$	−3.55144	+	2.05042i	−0.151710	+	0.0875898i
$549$	15.9912	−	17.1964i	0.682490	−	0.733925i
$550$			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
$555$	−4.97672	−	11.4239i	−0.211250	−	0.484919i
$556$	6.74169	+	11.6770i	0.285911	+	0.495213i
$557$	24.0375	+	13.8780i	1.01850	+	0.588031i	0.913669	−	0.406459i	$-0.133237\pi$
$557$	24.0375	+	13.8780i	1.01850	+	0.588031i	0.104831	+	0.994490i	$0.466570\pi$
$558$	0.669857	−	0.205815i	0.0283573	−	0.00871286i
$559$		−	11.8074i		−	0.499401i
$560$	1.69791	+	0.980288i	0.0717497	+	0.0414247i
$561$	13.3223	+	30.5810i	0.562469	+	1.29113i
$562$	18.7084			0.789164
$563$	17.1980			0.724809			0.362404	−	0.932021i	$-0.381956\pi$
$563$	17.1980			0.724809			0.362404	+	0.932021i	$0.381956\pi$
$564$	2.95061	−	1.28540i	0.124243	−	0.0541252i
$565$	10.5300	−	6.07947i	0.442998	−	0.255765i
$566$	−10.5801	+	18.3252i	−0.444713	+	0.770265i
$567$	−15.8808	−	7.69098i	−0.666933	−	0.322991i
$568$	−2.26439	−	3.92204i	−0.0950118	−	0.164565i
$569$	−26.3732			−1.10562			−0.552812	−	0.833306i	$-0.686445\pi$
$569$	−26.3732			−1.10562			−0.552812	+	0.833306i	$0.686445\pi$
$570$	−7.45723	−	1.17885i	−0.312349	−	0.0493766i
$571$	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
$573$	−1.18751	+	10.4875i	−0.0496089	+	0.438122i
$574$	−11.5331	+	19.9758i	−0.481380	+	0.833775i
$575$	5.91161	−	3.41307i	0.246531	−	0.142335i
$576$	2.92405	+	0.670786i	0.121835	+	0.0279494i
$577$	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
$579$	4.76521	−	2.07591i	0.198035	−	0.0862721i
$580$	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
$585$	5.86197	+	1.34475i	0.242363	+	0.0555987i
$586$	6.15600	+	10.6625i	0.254302	+	0.440464i
$587$	−29.3043	+	16.9188i	−1.20952	+	0.698315i	−0.962654	−	0.270736i	$-0.912733\pi$
$587$	−29.3043	+	16.9188i	−1.20952	+	0.698315i	−0.246863	+	0.969050i	$0.579400\pi$
$588$	3.24860	−	4.39663i	0.133970	−	0.181314i
$589$	0.469784	+	0.903329i	0.0193571	+	0.0372210i
$590$		−	8.51757i		−	0.350663i
$591$	0.483496	−	4.27000i	0.0198884	−	0.175644i
$592$	−6.23045	+	3.59715i	−0.256070	+	0.147842i
$593$	25.1953	+	14.5465i	1.03465	+	0.597354i	0.918312	−	0.395856i	$-0.129552\pi$
$593$	25.1953	+	14.5465i	1.03465	+	0.597354i	0.116335	+	0.993210i	$0.462886\pi$
$594$	−25.0875	+	4.70386i	−1.02935	+	0.193002i
$595$	−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	−0.434691	−	0.900580i	$-0.643142\pi$
$599$	13.7688	−	23.8483i	0.562580	−	0.974416i	0.997270	−	0.0738365i	$-0.0235243\pi$
$600$	−1.02929	+	1.39304i	−0.0420208	+	0.0568705i
$601$		−	14.9379i		−	0.609330i	−0.952460	−	0.304665i	$-0.901455\pi$
$601$		−	14.9379i		−	0.609330i	0.952460	−	0.304665i	$-0.0985445\pi$
$602$	−5.77364	+	10.0002i	−0.235316	+	0.407580i
$603$	−34.8695	−	32.4257i	−1.42000	−	1.32048i
$604$	15.0311	+	8.67821i	0.611607	+	0.353111i
$605$	−11.3708	+	6.56495i	−0.462290	+	0.266903i
$606$	2.23775	−	19.7627i	0.0909024	−	0.802805i
$607$		−	42.6299i		−	1.73030i	−0.501517	−	0.865148i	$-0.667225\pi$
$607$		−	42.6299i		−	1.73030i	0.501517	−	0.865148i	$-0.332775\pi$
$608$	−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
$612$	−2.62985	+	11.4639i	−0.106305	+	0.463400i
$613$	8.76635	+	15.1838i	0.354069	+	0.613266i	0.986958	−	0.160976i	$-0.0514643\pi$
$613$	8.76635	+	15.1838i	0.354069	+	0.613266i	−0.632889	+	0.774243i	$0.718131\pi$
$614$	−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	0.998903	+	0.0468313i	$0.0149123\pi$
$617$	38.2258	+	22.0697i	1.53891	+	0.888491i	0.540008	+	0.841660i	$0.318421\pi$
$618$	2.80004	−	1.21981i	0.112634	−	0.0490678i
$619$	−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
$621$	23.0919	+	26.9232i	0.926648	+	1.08039i
$622$	−27.6123	+	15.9420i	−1.10715	+	0.639214i
$623$	10.7467	−	18.6138i	0.430556	−	0.745746i
$624$	0.390678	−	3.45027i	0.0156396	−	0.138121i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−14.9516			−0.597585
$627$	−13.3008	−	34.6192i	−0.531184	−	1.38256i
$628$	−1.66740			−0.0665365
$629$	−14.1028	−	24.4268i	−0.562316	−	0.973961i
$630$	−4.30720	−	4.00534i	−0.171603	−	0.159577i
$631$	−17.6187	+	30.5165i	−0.701391	+	1.21484i	0.266588	+	0.963811i	$0.414104\pi$
$631$	−17.6187	+	30.5165i	−0.701391	+	1.21484i	−0.967978	+	0.251033i	$0.919230\pi$
$632$	−10.7900	+	6.22958i	−0.429201	+	0.247800i
$633$	4.62655	−	2.01551i	0.183889	−	0.0801094i
$634$	25.5166			1.01339
$635$	12.9420			0.513587
$636$	−7.31942	−	16.8015i	−0.290234	−	0.666224i
$637$	−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	$-0.00793168\pi$
$641$	12.1088	+	20.9730i	0.478267	+	0.828383i	−0.521422	+	0.853299i	$0.674598\pi$
$642$	−2.08310	−	4.78171i	−0.0822135	−	0.188719i
$643$	−8.96485	−	15.5276i	−0.353539	−	0.612348i	0.633328	−	0.773884i	$-0.281689\pi$
$643$	−8.96485	−	15.5276i	−0.353539	−	0.612348i	−0.986867	+	0.161536i	$0.948355\pi$
$644$	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	$0.896663\pi$
$648$	−8.10009	−	3.92282i	−0.318202	−	0.154103i
$649$	36.2346	−	20.9201i	1.42233	−	0.821185i
$650$	1.73616	+	1.00237i	0.0680978	+	0.0393163i
$651$	−0.0892469	+	0.788184i	−0.00349786	+	0.0308914i
$652$	−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	−0.328792	−	0.944402i	$-0.606642\pi$
$659$	16.7755	−	29.0560i	0.653480	−	1.13186i	0.982272	−	0.187459i	$-0.0600252\pi$
$660$	−8.45419	−	0.957276i	−0.329079	−	0.0372619i
$661$	13.8780	+	8.01246i	0.539791	+	0.311649i	0.744994	−	0.667071i	$-0.232452\pi$
$661$	13.8780	+	8.01246i	0.539791	+	0.311649i	−0.205203	+	0.978719i	$0.565785\pi$
$662$	−20.4616	+	11.8135i	−0.795262	+	0.459145i
$663$	13.5270	+	1.53167i	0.525345	+	0.0594853i
$664$		−	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
$669$	6.22295	−	2.71097i	0.240593	−	0.104812i
$670$	−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	$0.211330\pi$
$673$			31.9714i			1.23241i	−0.787586	+	0.616204i	$0.788670\pi$
$674$	−1.65491	−	0.955464i	−0.0637449	−	0.0368031i
$675$	3.94413	−	3.38287i	0.151810	−	0.130207i
$676$	8.98100			0.345423
$677$	−25.2864			−0.971835			−0.485918	−	0.874005i	$-0.661514\pi$
$677$	−25.2864			−0.971835			−0.485918	+	0.874005i	$0.661514\pi$
$678$	8.41105	+	19.3074i	0.323024	+	0.741494i
$679$	26.1067	−	15.0727i	1.00188	−	0.578437i
$680$	−1.96028	+	3.39530i	−0.0751732	+	0.130204i
$681$	0.543998	+	0.0615974i	0.0208460	+	0.00236042i
$682$	0.573717	+	0.993707i	0.0219688	+	0.0380510i
$683$	8.39063			0.321059			0.160529	−	0.987031i	$-0.448680\pi$
$683$	8.39063			0.321059			0.160529	+	0.987031i	$0.448680\pi$
$684$	3.48210	−	12.6046i	0.133141	−	0.481947i
$685$	4.10085			0.156685
$686$	9.95594	+	17.2442i	0.380120	+	0.658387i
$687$	10.5559	+	1.19526i	0.402733	+	0.0456018i
$688$	−2.94487	+	5.10067i	−0.112272	+	0.194461i
$689$	−18.3701	+	10.6060i	−0.699846	+	0.404056i
$690$	4.72204	+	10.8393i	0.179765	+	0.412646i
$691$	−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
$693$	6.46018	−	28.1608i	0.245402	−	1.06974i
$694$	−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
$699$	17.1921	−	7.48955i	0.650264	−	0.283281i
$700$	−0.980288	−	1.69791i	−0.0370514	−	0.0641749i
$701$	−29.1351	+	16.8212i	−1.10042	+	0.635327i	−0.936331	−	0.351119i	$-0.885801\pi$
$701$	−29.1351	+	16.8212i	−1.10042	+	0.635327i	−0.164087	+	0.986446i	$0.552468\pi$
$702$	−3.45675	+	9.82670i	−0.130467	+	0.370885i
$703$	14.4690	+	27.8218i	0.545707	+	1.04932i
$704$			4.91222i			0.185136i
$705$	−3.19801	−	0.362113i	−0.120444	−	0.0136380i
$706$	2.12758	−	1.22836i	0.0800724	−	0.0462298i
$707$	19.4969	+	11.2566i	0.733257	+	0.423346i
$708$	14.6592	+	1.65987i	0.550926	+	0.0623819i
$709$	22.1508	−	38.3664i	0.831892	−	1.44088i	−0.0646434	−	0.997908i	$-0.520591\pi$
$709$	22.1508	−	38.3664i	0.831892	−	1.44088i	0.896536	−	0.442971i	$-0.146076\pi$
$710$			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
$717$	0.621044	−	5.48475i	0.0231933	−	0.204832i
$718$	−3.05773	−	1.76538i	−0.114113	−	0.0658834i
$719$	12.8018	−	7.39114i	0.477428	−	0.275643i	−0.241916	−	0.970297i	$-0.577776\pi$
$719$	12.8018	−	7.39114i	0.477428	−	0.275643i	0.719344	+	0.694654i	$0.244443\pi$
$720$	−2.19691	−	2.04294i	−0.0818738	−	0.0761359i
$721$			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
$726$	−9.08271	−	20.8491i	−0.337091	−	0.773784i
$727$	2.63804	+	4.56923i	0.0978397	+	0.169463i	0.910790	−	0.412869i	$-0.135473\pi$
$727$	2.63804	+	4.56923i	0.0978397	+	0.169463i	−0.812951	+	0.582333i	$0.802140\pi$
$728$	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
$732$	5.41478	+	12.4295i	0.200136	+	0.459407i
$733$	−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
$735$	−5.01169	+	2.18329i	−0.184859	+	0.0805319i
$736$	5.91161	−	3.41307i	0.217905	−	0.125807i
$737$	38.9836	−	67.5216i	1.43598	−	2.48719i
$738$	24.0351	−	25.8465i	0.884746	−	0.951424i
$739$	23.4208	+	40.5660i	0.861548	+	1.49224i	0.870435	+	0.492284i	$0.163838\pi$
$739$	23.4208	+	40.5660i	0.861548	+	1.49224i	−0.00888687	+	0.999961i	$0.502829\pi$
$740$	7.19430			0.264468
$741$	−14.9499	−	2.36329i	−0.549197	−	0.0868177i
$742$	20.7446			0.761559
$743$	−3.70160	−	6.41135i	−0.135798	−	0.235210i	0.790104	−	0.612973i	$-0.210027\pi$
$743$	−3.70160	−	6.41135i	−0.135798	−	0.235210i	−0.925902	+	0.377763i	$0.876693\pi$
$744$	−0.0455208	+	0.402017i	−0.00166887	+	0.0147386i
$745$	2.30462	−	3.99172i	0.0844347	−	0.146245i
$746$	−3.60651	+	2.08222i	−0.132044	+	0.0762354i
$747$	−9.19720	+	40.0919i	−0.336508	+	1.46688i
$748$	−19.2586			−0.704165
$749$	5.90391			0.215724
$750$	1.58791	−	0.691758i	0.0579824	−	0.0252594i
$751$	−36.7844	−	21.2375i	−1.34228	−	0.774966i	−0.355139	−	0.934814i	$-0.615566\pi$
$751$	−36.7844	−	21.2375i	−1.34228	−	0.774966i	−0.987142	+	0.159848i	$0.948900\pi$
$752$			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
$756$	7.73277	−	6.63237i	0.281238	−	0.241217i
$757$	24.8985	+	43.1254i	0.904950	+	1.56742i	0.820984	+	0.570951i	$0.193425\pi$
$757$	24.8985	+	43.1254i	0.904950	+	1.56742i	0.0839656	+	0.996469i	$0.473241\pi$
$758$	−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	$0.802497\pi$
$762$	−2.52209	+	22.2739i	−0.0913657	+	0.806896i
$763$	−17.7618	+	10.2548i	−0.643022	+	0.371249i
$764$	−5.27726	−	3.04683i	−0.190924	−	0.110230i
$765$	8.00946	−	8.61309i	0.289583	−	0.311407i
$766$	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	0.236475	+	0.971638i	$0.424008\pi$
$769$	−20.0557	+	34.7374i	−0.723225	+	1.25266i	−0.959700	+	0.281026i	$0.909325\pi$
$770$	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	$-0.786472\pi$
$773$	4.07839	−	7.06397i	0.146689	−	0.254074i	0.930002	+	0.367555i	$0.119805\pi$
$774$	12.0324	−	12.9392i	0.432496	−	0.465090i
$775$	−0.202293	−	0.116794i	−0.00726657	−	0.00419536i
$776$	13.3158	−	7.68789i	0.478010	−	0.275979i
$777$	−2.74873	+	24.2754i	−0.0986100	+	0.870875i
$778$		−	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
$783$	19.8526	−	17.0275i	0.709475	−	0.608514i
$784$	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	$-0.738513\pi$
$787$		−	41.0793i		−	1.46432i	0.681134	−	0.732159i	$-0.261487\pi$
$788$	2.14864	+	1.24052i	0.0765422	+	0.0441917i
$789$	−6.34479	+	2.76404i	−0.225881	+	0.0984026i
$790$	12.4592			0.443277
$791$	−23.8385			−0.847600
$792$	3.29505	−	14.3636i	0.117084	−	0.510387i
$793$	13.5899	−	7.84613i	0.482592	−	0.278624i
$794$	2.65169	−	4.59286i	0.0941050	−	0.162995i
$795$	−2.06197	+	18.2103i	−0.0731304	+	0.645851i
$796$	−11.8062	−	20.4489i	−0.418459	−	0.724792i
$797$	−39.4937			−1.39894			−0.699469	−	0.714663i	$-0.746580\pi$
$797$	−39.4937			−1.39894			−0.699469	+	0.714663i	$0.746580\pi$
$798$	11.5061	+	9.31181i	0.407311	+	0.329634i
$799$	−7.28505			−0.257727
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−22.3963	+	24.0842i	−0.791334	+	0.850973i
$802$	−3.00036	+	5.19678i	−0.105946	+	0.183505i
$803$	−9.68993	+	5.59448i	−0.341950	+	0.197425i
$804$	25.2035	−	10.9797i	0.888859	−	0.387223i
$805$	−13.3832			−0.471694
$806$	0.468284			0.0164946
$807$	1.55470	+	3.56878i	0.0547282	+	0.125627i
$808$	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	−0.499563	−	0.866277i	$-0.666506\pi$
$811$	−42.7046	−	24.6555i	−1.49956	−	0.865773i	−1.00000		0.000504396i	$0.999839\pi$
$812$	−4.93423	−	8.54634i	−0.173158	−	0.299918i
$813$	3.73756	+	8.57947i	0.131082	+	0.300895i
$814$	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
$819$	−8.63484	−	8.02968i	−0.301726	−	0.280580i
$820$	10.1888	−	5.88249i	0.355807	−	0.205425i
$821$	27.3273	+	15.7774i	0.953730	+	0.550636i	0.894238	−	0.447593i	$-0.147719\pi$
$821$	27.3273	+	15.7774i	0.953730	+	0.550636i	0.0594922	+	0.998229i	$0.481052\pi$
$822$	−0.799159	+	7.05778i	−0.0278739	+	0.246168i
$823$	−1.24210	+	2.15138i	−0.0432968	+	0.0749923i	−0.886862	−	0.462035i	$-0.847119\pi$
$823$	−1.24210	+	2.15138i	−0.0432968	+	0.0749923i	0.843565	+	0.537027i	$0.180453\pi$
$824$			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	0.432734	+	0.901522i	$0.357549\pi$
$827$	−16.2300	+	28.1113i	−0.564374	+	0.977524i	−0.997108	+	0.0760023i	$0.975784\pi$
$828$	−19.5753	+	6.01455i	−0.680287	+	0.209020i
$829$		−	30.4181i		−	1.05647i	−0.849100	−	0.528233i	$-0.822855\pi$
$829$		−	30.4181i		−	1.05647i	0.849100	−	0.528233i	$-0.177145\pi$
$830$	−6.85554	+	11.8742i	−0.237959	+	0.412158i
$831$	−34.6846	−	3.92737i	−1.20319	−	0.136239i
$832$	1.73616	+	1.00237i	0.0601905	+	0.0347510i
$833$	−10.7161	+	6.18692i	−0.371289	+	0.214364i
$834$	23.2056	+	2.62760i	0.803545	+	0.0909862i
$835$			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	$-0.132256\pi$
$839$	3.12520	+	5.41300i	0.107894	+	0.186878i	−0.807023	+	0.590520i	$0.798923\pi$
$840$	3.11322	−	1.35624i	0.107416	−	0.0467949i
$841$	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
$846$	1.24643	−	5.43337i	0.0428532	−	0.186803i
$847$	25.7421			0.884510
$848$	10.5809			0.363349
$849$	14.6377	+	33.6004i	0.502364	+	1.15316i
$850$	3.39530	−	1.96028i	0.116458	−	0.0672370i
$851$	24.5546	−	42.5299i	0.841722	−	1.45791i
$852$	−7.79428	−	0.882554i	−0.267028	−	0.0302358i
$853$	24.9526	+	43.2191i	0.854360	+	1.47979i	0.877238	+	0.480056i	$0.159384\pi$
$853$	24.9526	+	43.2191i	0.854360	+	1.47979i	−0.0228782	+	0.999738i	$0.507283\pi$
$854$	−15.3465			−0.525147
$855$	−9.31787	+	9.17482i	−0.318664	+	0.313772i
$856$	3.01131			0.102925
$857$	14.9335	+	25.8655i	0.510118	+	0.883550i	0.999931	+	0.0117228i	$0.00373156\pi$
$857$	14.9335	+	25.8655i	0.510118	+	0.883550i	−0.489813	+	0.871827i	$0.662935\pi$
$858$	−16.9485	−	1.91909i	−0.578612	−	0.0655168i
$859$	−12.1997	+	21.1305i	−0.416249	+	0.720964i	−0.995559	−	0.0941433i	$-0.969989\pi$
$859$	−12.1997	+	21.1305i	−0.416249	+	0.720964i	0.579310	+	0.815107i	$0.303322\pi$
$860$	5.10067	−	2.94487i	0.173931	−	0.100419i
$861$	15.9562	+	36.6270i	0.543785	+	1.24824i
$862$	−16.6054			−0.565581
$863$	23.3653			0.795363			0.397682	−	0.917523i	$-0.369815\pi$
$863$	23.3653			0.795363			0.397682	+	0.917523i	$0.369815\pi$
$864$	3.94413	−	3.38287i	0.134182	−	0.115088i
$865$	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
$870$	7.99269	−	3.48193i	0.270978	−	0.118049i
$871$	−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
$876$	−3.92018	−	0.443886i	−0.132451	−	0.0149975i
$877$	36.6106	−	21.1372i	1.23625	−	0.713751i	0.267927	−	0.963439i	$-0.413661\pi$
$877$	36.6106	−	21.1372i	1.23625	−	0.713751i	0.968326	+	0.249688i	$0.0803281\pi$
$878$	−9.46913	−	5.46701i	−0.319568	−	0.184503i
$879$	21.1896	+	2.39932i	0.714708	+	0.0809271i
$880$	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	−0.806889	−	0.590703i	$-0.798850\pi$
$883$	3.21281	−	5.56474i	0.108120	−	0.187268i	0.915008	+	0.403435i	$0.132184\pi$
$884$	−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	$-0.895522\pi$
$887$	−5.78172	+	10.0142i	−0.194131	+	0.336245i	0.752484	+	0.658610i	$0.228855\pi$
$888$	−1.40200	+	12.3818i	−0.0470480	+	0.415505i
$889$	−21.9743	−	12.6869i	−0.736995	−	0.425504i
$890$	−9.49404	+	5.48139i	−0.318241	+	0.183737i
$891$	−19.2697	+	39.7894i	−0.645560	+	1.33300i
$892$			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
$897$	9.46649	+	21.7301i	0.316077	+	0.725546i
$898$	−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
$903$	7.98793	+	18.3361i	0.265822	+	0.610187i
$904$	−12.1589			−0.404400
$905$	14.6171			0.485888
$906$	27.5605	−	12.0065i	0.915637	−	0.398888i
$907$	−33.9003	+	19.5724i	−1.12564	+	0.649890i	−0.942835	−	0.333259i	$-0.891852\pi$
$907$	−33.9003	+	19.5724i	−1.12564	+	0.649890i	−0.182807	+	0.983149i	$0.558518\pi$
$908$	−0.158042	+	0.273737i	−0.00524481	+	0.00908428i
$909$	−25.2269	−	23.4589i	−0.836723	−	0.778083i
$910$	−1.96523	−	3.40387i	−0.0651466	−	0.112837i
$911$	27.0371			0.895778			0.447889	−	0.894089i	$-0.352176\pi$
$911$	27.0371			0.895778			0.447889	+	0.894089i	$0.352176\pi$
$912$	5.86873	+	4.74953i	0.194333	+	0.157273i
$913$	−67.3519			−2.22902
$914$	12.4132	+	21.5003i	0.410592	+	0.711167i
$915$	1.52541	−	13.4716i	0.0504284	−	0.445359i
$916$	−3.06670	+	5.31168i	−0.101327	+	0.175503i
$917$	−15.1823	+	8.76552i	−0.501364	+	0.289463i
$918$	13.2627	+	15.4632i	0.437735	+	0.510361i
$919$	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
$921$	−24.1150	+	10.5055i	−0.794618	+	0.346167i
$922$	−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
$927$	1.18282	−	5.15609i	0.0388491	−	0.169348i
$928$	−2.51673	−	4.35910i	−0.0826156	−	0.143094i
$929$	10.5812	−	6.10909i	0.347160	−	0.200433i	−0.316274	−	0.948668i	$-0.602432\pi$
$929$	10.5812	−	6.10909i	0.347160	−	0.200433i	0.663434	+	0.748235i	$0.269099\pi$
$930$	0.240431	−	0.325396i	0.00788403	−	0.0106702i
$931$	12.2054	−	6.34754i	0.400017	−	0.208032i
$932$			10.8268i			0.354644i
$933$	−6.21343	+	54.8739i	−0.203418	+	1.79649i
$934$	−16.0630	+	9.27397i	−0.525597	+	0.303454i
$935$	16.6785	+	9.62931i	0.545444	+	0.314912i
$936$	−4.40424	−	4.09558i	−0.143957	−	0.133868i
$937$	15.9162	−	27.5678i	0.519961	−	0.900599i	−0.479770	−	0.877395i	$-0.659280\pi$
$937$	15.9162	−	27.5678i	0.519961	−	0.900599i	0.999731	−	0.0232047i	$-0.00738695\pi$
$938$			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	$-0.768920\pi$
$941$	6.16530	−	10.6786i	0.200983	−	0.348113i	0.948845	+	0.315741i	$0.102253\pi$
$942$	−1.71625	+	2.32275i	−0.0559183	+	0.0756793i
$943$		−	80.3093i		−	2.61523i
$944$	−4.25879	+	7.37643i	−0.138612	+	0.240082i
$945$	−10.0130	+	1.87742i	−0.325722	+	0.0610723i
$946$	25.0556	+	14.4659i	0.814628	+	0.470326i
$947$	39.3773	−	22.7345i	1.27959	−	0.738773i	0.302818	−	0.953048i	$-0.402072\pi$
$947$	39.3773	−	22.7345i	1.27959	−	0.738773i	0.976773	+	0.214276i	$0.0687391\pi$
$948$	−2.42800	+	21.4429i	−0.0788577	+	0.696433i
$949$			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	0.986104	+	0.166128i	$0.0531265\pi$
$953$	19.6623	+	34.0560i	0.636923	+	1.10318i	−0.349181	+	0.937055i	$0.613540\pi$
$954$	−30.9390	−	7.09750i	−1.00169	−	0.229790i
$955$	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
$960$	1.58791	−	0.691758i	0.0512497	−	0.0223264i
$961$	30.9454			0.998240
$962$	14.4227			0.465008
$963$	−8.80522	−	2.01995i	−0.283744	−	0.0650918i
$964$	16.5317	−	9.54461i	0.532452	−	0.307411i
$965$	1.50046	−	2.59888i	0.0483016	−	0.0836608i
$966$	2.60806	−	23.0331i	0.0839131	−	0.741079i
$967$	28.8842	+	50.0289i	0.928854	+	1.60882i	0.785243	+	0.619188i	$0.212538\pi$
$967$	28.8842	+	50.0289i	0.928854	+	1.60882i	0.143611	+	0.989634i	$0.454129\pi$
$968$	13.1299			0.422011
$969$	−18.6208	+	23.0087i	−0.598186	+	0.739145i
$970$	−15.3758			−0.493686
$971$	0.428825	+	0.742746i	0.0137616	+	0.0238358i	0.872824	−	0.488035i	$-0.162286\pi$
$971$	0.428825	+	0.742746i	0.0137616	+	0.0238358i	−0.859063	+	0.511871i	$0.828953\pi$
$972$	−13.8020	+	7.24600i	−0.442700	+	0.232416i
$973$	−13.2176	+	22.8935i	−0.423737	+	0.733933i
$974$	9.80030	−	5.65821i	0.314022	−	0.181301i
$975$	3.18336	−	1.38680i	0.101949	−	0.0444131i
$976$	−7.82756			−0.250554
$977$	3.12960			0.100125			0.0500625	−	0.998746i	$-0.484058\pi$
$977$	3.12960			0.100125			0.0500625	+	0.998746i	$0.484058\pi$
$978$	5.92104	+	13.5916i	0.189334	+	0.434611i
$979$	−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	0.999505	+	0.0314664i	$0.0100177\pi$
$983$	16.5230	+	28.6187i	0.527003	+	0.912796i	−0.472502	+	0.881330i	$0.656649\pi$
$984$	8.13852	+	18.6818i	0.259446	+	0.595553i
$985$	−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
$990$	−10.0354	+	10.7917i	−0.318945	+	0.342982i
$991$	3.55980	−	2.05525i	0.113081	−	0.0652873i	−0.442393	−	0.896821i	$-0.645870\pi$
$991$	3.55980	−	2.05525i	0.113081	−	0.0652873i	0.555474	+	0.831534i	$0.312537\pi$
$992$	−0.202293	−	0.116794i	−0.00642280	−	0.00370821i
$993$	−4.60435	+	40.6633i	−0.146115	+	1.29041i
$994$	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	−0.909229	−	0.416296i	$-0.863328\pi$
$997$	−2.97096	+	5.14586i	−0.0940914	+	0.162971i	0.815138	+	0.579267i	$0.196661\pi$
$998$	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.b.221.12	yes	24
3.2	odd	2		570.2.s.a.221.8	✓	24
19.8	odd	6		570.2.s.a.521.8	yes	24
57.8	even	6	inner	570.2.s.b.521.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.s.a.221.8	✓	24	3.2	odd	2
570.2.s.a.521.8	yes	24	19.8	odd	6
570.2.s.b.221.12	yes	24	1.1	even	1	trivial
570.2.s.b.521.12	yes	24	57.8	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.72105 + 0.194877i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.691758 + 1.58791i) q^{6} -1.96058 q^{7} -1.00000 q^{8} +(2.92405 + 0.670786i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.72105 + 0.194877i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 - 0.500000i) q^{5} +(0.691758 + 1.58791i) q^{6} -1.96058 q^{7} -1.00000 q^{8} +(2.92405 + 0.670786i) 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} +(1.58791 - 0.691758i) 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} +(-3.37425 - 0.382070i) q^{21} +(-4.25411 + 2.45611i) q^{22} +(5.91161 + 3.41307i) q^{23} +(-1.72105 - 0.194877i) 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} +(-0.957276 + 8.45419i) q^{33} +(3.39530 + 1.96028i) q^{34} +(-1.69791 + 0.980288i) q^{35} +(-2.04294 + 2.19691i) 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} +(-1.35624 - 3.11322i) 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} +(-0.691758 - 1.58791i) q^{48} -3.15615 q^{49} +1.00000 q^{50} +(6.22550 - 2.71208i) q^{51} +(-1.73616 + 1.00237i) q^{52} +(-5.29044 + 9.16331i) q^{53} +(0.957584 + 5.10716i) q^{54} +(2.45611 + 4.25411i) q^{55} +1.96058 q^{56} +(-7.04758 + 2.70770i) q^{57} +5.03345 q^{58} +(-4.25879 - 7.37643i) q^{59} +(-0.194877 + 1.72105i) q^{60} +(3.91378 - 6.77887i) q^{61} +(0.202293 - 0.116794i) q^{62} +(-5.73281 - 1.31513i) q^{63} +1.00000 q^{64} +2.00475 q^{65} +(-7.80018 + 3.39807i) 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} +(-2.92405 - 0.670786i) 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} +(-0.390678 + 3.45027i) q^{78} +(10.7900 - 6.22958i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(8.10009 + 3.92282i) 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} +(2.19691 + 2.04294i) q^{90} +(-3.40387 - 1.96523i) q^{91} +(-5.91161 + 3.41307i) q^{92} +(0.0455208 - 0.402017i) 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} +(-3.29505 + 14.3636i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * q^9	\( 24 q + 12 q^{2} + 2 q^{3} - 12 q^{4} + 4 q^{6} - 12 q^{7} - 24 q^{8} + 2 q^{9} + 2 q^{12} + 18 q^{13} - 6 q^{14} - 12 q^{16} - 12 q^{17} - 2 q^{18} + 6 q^{19} + 6 q^{21} + 18 q^{22} - 2 q^{24} + 12 q^{25} - 28 q^{27} + 6 q^{28} + 12 q^{32} - 8 q^{33} - 12 q^{34} - 4 q^{36} - 6 q^{38} + 40 q^{39} - 6 q^{41} - 6 q^{42} - 22 q^{43} + 18 q^{44} + 8 q^{45} - 12 q^{47} - 4 q^{48} + 12 q^{49} + 24 q^{50} - 4 q^{51} - 18 q^{52} - 8 q^{53} - 32 q^{54} + 12 q^{56} - 20 q^{57} - 26 q^{59} + 22 q^{61} + 18 q^{62} + 30 q^{63} + 24 q^{64} - 8 q^{65} - 22 q^{66} - 48 q^{67} + 64 q^{69} - 24 q^{71} - 2 q^{72} - 8 q^{73} - 30 q^{74} - 2 q^{75} - 12 q^{76} + 2 q^{78} + 18 q^{79} - 6 q^{81} + 6 q^{82} - 12 q^{84} + 22 q^{86} - 24 q^{87} - 28 q^{89} + 16 q^{90} + 18 q^{91} + 14 q^{93} - 2 q^{96} + 6 q^{97} + 6 q^{98} - 52 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 + 2 * q^3 - 12 * q^4 + 4 * q^6 - 12 * q^7 - 24 * q^8 + 2 * 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 - 2 * q^24 + 12 * q^25 - 28 * q^27 + 6 * q^28 + 12 * q^32 - 8 * q^33 - 12 * q^34 - 4 * 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 - 4 * q^48 + 12 * q^49 + 24 * q^50 - 4 * q^51 - 18 * q^52 - 8 * q^53 - 32 * q^54 + 12 * q^56 - 20 * q^57 - 26 * q^59 + 22 * q^61 + 18 * q^62 + 30 * q^63 + 24 * q^64 - 8 * q^65 - 22 * q^66 - 48 * q^67 + 64 * q^69 - 24 * q^71 - 2 * q^72 - 8 * q^73 - 30 * q^74 - 2 * q^75 - 12 * q^76 + 2 * q^78 + 18 * q^79 - 6 * q^81 + 6 * q^82 - 12 * q^84 + 22 * q^86 - 24 * q^87 - 28 * q^89 + 16 * q^90 + 18 * q^91 + 14 * q^93 - 2 * q^96 + 6 * q^97 + 6 * q^98 - 52 * q^99

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