LMFDB - Embedded newform 126.2.m.a.83.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,2,Mod(41,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("126.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	126.m (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:	$1.00611506547$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			83.3
Root			$-1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	126.83
Dual form			126.2.m.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.40917 - 1.00709i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.17468 + 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} +(1.55364 + 2.14154i) q^{7} -1.00000i q^{8} +(0.971521 - 2.83834i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.40917 - 1.00709i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.17468 + 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} +(1.55364 + 2.14154i) q^{7} -1.00000i q^{8} +(0.971521 - 2.83834i) q^{9} -2.34936i q^{10} +(-4.91614 - 2.83834i) q^{11} +(1.57675 + 0.716830i) q^{12} +(1.48943 - 0.859925i) q^{13} +(-0.274725 - 2.63145i) q^{14} +(3.70436 + 1.68409i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.76883 q^{17} +(-2.26053 + 1.97231i) q^{18} -1.13932i q^{19} +(-1.17468 + 2.03460i) q^{20} +(4.34608 + 1.45313i) q^{21} +(2.83834 + 4.91614i) q^{22} +(-3.18272 + 1.83755i) q^{23} +(-1.00709 - 1.40917i) q^{24} +(-0.259741 + 0.449885i) q^{25} -1.71985 q^{26} +(-1.48943 - 4.97811i) q^{27} +(-1.07781 + 2.41626i) q^{28} +(3.59886 + 2.07781i) q^{29} +(-2.36603 - 3.31064i) q^{30} +(-7.24879 + 4.18509i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-9.78615 + 0.951321i) q^{33} +(1.53185 + 0.884414i) q^{34} +(-2.53215 + 5.67667i) q^{35} +(2.94383 - 0.577806i) q^{36} -9.19773 q^{37} +(-0.569660 + 0.986680i) q^{38} +(1.23284 - 2.71178i) q^{39} +(2.03460 - 1.17468i) q^{40} +(3.99709 + 6.92317i) q^{41} +(-3.03725 - 3.43149i) q^{42} +(1.76053 - 3.04933i) q^{43} -5.67667i q^{44} +(6.91611 - 1.35747i) q^{45} +3.67509 q^{46} +(5.90494 - 10.2277i) q^{47} +(0.167584 + 1.72392i) q^{48} +(-2.17238 + 6.65438i) q^{49} +(0.449885 - 0.259741i) q^{50} +(-2.49258 + 1.78138i) q^{51} +(1.48943 + 0.859925i) q^{52} +(-1.19917 + 5.05589i) q^{54} -13.3365i q^{55} +(2.14154 - 1.55364i) q^{56} +(-1.14740 - 1.60550i) q^{57} +(-2.07781 - 3.59886i) q^{58} +(1.11483 + 1.93094i) q^{59} +(0.393716 + 4.05012i) q^{60} +(7.79396 + 4.49985i) q^{61} +8.37019 q^{62} +(7.58780 - 2.32921i) q^{63} -1.00000 q^{64} +(3.49921 + 2.02027i) q^{65} +(8.95072 + 4.06921i) q^{66} +(-5.43562 - 9.41477i) q^{67} +(-0.884414 - 1.53185i) q^{68} +(-2.63442 + 5.79472i) q^{69} +(5.03124 - 3.65007i) q^{70} +4.52106i q^{71} +(-2.83834 - 0.971521i) q^{72} +5.34234i q^{73} +(7.96547 + 4.59886i) q^{74} +(0.0870571 + 0.895548i) q^{75} +(0.986680 - 0.569660i) q^{76} +(-1.55953 - 14.9379i) q^{77} +(-2.42356 + 1.73205i) q^{78} +(6.51422 - 11.2830i) q^{79} -2.34936 q^{80} +(-7.11229 - 5.51501i) q^{81} -7.99419i q^{82} +(-6.27298 + 10.8651i) q^{83} +(0.914596 + 4.49038i) q^{84} +(-2.07781 - 3.59886i) q^{85} +(-3.04933 + 1.76053i) q^{86} +(7.16396 - 0.696415i) q^{87} +(-2.83834 + 4.91614i) q^{88} -1.16106 q^{89} +(-6.66826 - 2.28245i) q^{90} +(4.15561 + 1.85366i) q^{91} +(-3.18272 - 1.83755i) q^{92} +(-6.00000 + 13.1977i) q^{93} +(-10.2277 + 5.90494i) q^{94} +(2.31806 - 1.33834i) q^{95} +(0.716830 - 1.57675i) q^{96} +(-3.97536 - 2.29517i) q^{97} +(5.20853 - 4.67667i) q^{98} +(-12.8323 + 11.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	$ 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	1.40917	−	1.00709i	0.813585	−	0.581446i
$3$	1.40917	−	1.00709i	0.813585	−	0.581446i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.17468	+	2.03460i	0.525332	+	0.909902i	0.999565	+	0.0295026i	$0.00939234\pi$
$5$	1.17468	+	2.03460i	0.525332	+	0.909902i	−0.474232	+	0.880400i	$0.657274\pi$
$6$	−1.72392	+	0.167584i	−0.703789	+	0.0684160i
$7$	1.55364	+	2.14154i	0.587222	+	0.809426i
$7$	1.55364	+	2.14154i	0.587222	+	0.809426i
$8$		−	1.00000i		−	0.353553i
$9$	0.971521	−	2.83834i	0.323840	−	0.946112i
$10$		−	2.34936i		−	0.742932i
$11$	−4.91614	−	2.83834i	−1.48227	−	0.855790i	−0.482475	−	0.875910i	$-0.660262\pi$
$11$	−4.91614	−	2.83834i	−1.48227	−	0.855790i	−0.999798	+	0.0201197i	$0.993595\pi$
$12$	1.57675	+	0.716830i	0.455170	+	0.206931i
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	−0.279024	−	0.960284i	$-0.590011\pi$
$13$	1.48943	−	0.859925i	0.413094	−	0.238500i	0.692118	+	0.721784i	$0.256678\pi$
$14$	−0.274725	−	2.63145i	−0.0734234	−	0.703284i
$15$	3.70436	+	1.68409i	0.956462	+	0.434830i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.76883			−0.429004			−0.214502	−	0.976724i	$-0.568813\pi$
$17$	−1.76883			−0.429004			−0.214502	+	0.976724i	$0.568813\pi$
$18$	−2.26053	+	1.97231i	−0.532812	+	0.464878i
$19$		−	1.13932i		−	0.261378i	−0.991423	−	0.130689i	$-0.958281\pi$
$19$		−	1.13932i		−	0.261378i	0.991423	−	0.130689i	$-0.0417189\pi$
$20$	−1.17468	+	2.03460i	−0.262666	+	0.454951i
$21$	4.34608	+	1.45313i	0.948393	+	0.317098i
$22$	2.83834	+	4.91614i	0.605135	+	1.04812i
$23$	−3.18272	+	1.83755i	−0.663644	+	0.383155i	−0.793664	−	0.608356i	$-0.791829\pi$
$23$	−3.18272	+	1.83755i	−0.663644	+	0.383155i	0.130020	+	0.991511i	$0.458496\pi$
$24$	−1.00709	−	1.40917i	−0.205572	−	0.287646i
$25$	−0.259741	+	0.449885i	−0.0519482	+	0.0899769i
$26$	−1.71985			−0.337290
$27$	−1.48943	−	4.97811i	−0.286642	−	0.958038i
$28$	−1.07781	+	2.41626i	−0.203686	+	0.456631i
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	0.795429	−	0.606046i	$-0.207245\pi$
$29$	3.59886	+	2.07781i	0.668292	+	0.385839i	−0.127137	+	0.991885i	$0.540579\pi$
$30$	−2.36603	−	3.31064i	−0.431975	−	0.604438i
$31$	−7.24879	+	4.18509i	−1.30192	+	0.751665i	−0.980734	−	0.195350i	$-0.937416\pi$
$31$	−7.24879	+	4.18509i	−1.30192	+	0.751665i	−0.321188	+	0.947015i	$0.604082\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−9.78615	+	0.951321i	−1.70355	+	0.165604i
$34$	1.53185	+	0.884414i	0.262710	+	0.151676i
$35$	−2.53215	+	5.67667i	−0.428012	+	0.959532i
$36$	2.94383	−	0.577806i	0.490638	−	0.0963009i
$37$	−9.19773			−1.51210			−0.756049	−	0.654515i	$-0.772873\pi$
$37$	−9.19773			−1.51210			−0.756049	+	0.654515i	$0.772873\pi$
$38$	−0.569660	+	0.986680i	−0.0924111	+	0.160061i
$39$	1.23284	−	2.71178i	0.197412	−	0.434232i
$40$	2.03460	−	1.17468i	0.321699	−	0.185733i
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	0.988687	+	0.149993i	$0.0479251\pi$
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	−0.364446	+	0.931225i	$0.618742\pi$
$42$	−3.03725	−	3.43149i	−0.468658	−	0.529490i
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	−0.699991	−	0.714152i	$-0.746813\pi$
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	0.968469	+	0.249134i	$0.0801459\pi$
$44$		−	5.67667i		−	0.855790i
$45$	6.91611	−	1.35747i	1.03099	−	0.202360i
$46$	3.67509			0.541863
$47$	5.90494	−	10.2277i	0.861324	−	1.49186i	−0.00932669	−	0.999957i	$-0.502969\pi$
$47$	5.90494	−	10.2277i	0.861324	−	1.49186i	0.870651	−	0.491901i	$-0.163698\pi$
$48$	0.167584	+	1.72392i	0.0241887	+	0.248827i
$49$	−2.17238	+	6.65438i	−0.310340	+	0.950626i
$50$	0.449885	−	0.259741i	0.0636233	−	0.0367329i
$51$	−2.49258	+	1.78138i	−0.349031	+	0.249443i
$52$	1.48943	+	0.859925i	0.206547	+	0.119250i
$53$		0			0		1.00000			$0$
$53$		0			0		−1.00000			$\pi$
$54$	−1.19917	+	5.05589i	−0.163186	+	0.688019i
$55$		−	13.3365i		−	1.79830i
$56$	2.14154	−	1.55364i	0.286175	−	0.207614i
$57$	−1.14740	−	1.60550i	−0.151977	−	0.212653i
$58$	−2.07781	−	3.59886i	−0.272829	−	0.472554i
$59$	1.11483	+	1.93094i	0.145139	+	0.251387i	0.929425	−	0.369012i	$-0.120304\pi$
$59$	1.11483	+	1.93094i	0.145139	+	0.251387i	−0.784286	+	0.620399i	$0.786971\pi$
$60$	0.393716	+	4.05012i	0.0508285	+	0.522868i
$61$	7.79396	+	4.49985i	0.997915	+	0.576146i	0.907631	−	0.419770i	$-0.137889\pi$
$61$	7.79396	+	4.49985i	0.997915	+	0.576146i	0.0902842	+	0.995916i	$0.471222\pi$
$62$	8.37019			1.06301
$63$	7.58780	−	2.32921i	0.955973	−	0.293453i
$64$	−1.00000			−0.125000
$65$	3.49921	+	2.02027i	0.434024	+	0.250584i
$66$	8.95072	+	4.06921i	1.10176	+	0.500885i
$67$	−5.43562	−	9.41477i	−0.664067	−	1.15020i	−0.979537	−	0.201262i	$-0.935496\pi$
$67$	−5.43562	−	9.41477i	−0.664067	−	1.15020i	0.315470	−	0.948935i	$-0.397838\pi$
$68$	−0.884414	−	1.53185i	−0.107251	−	0.185764i
$69$	−2.63442	+	5.79472i	−0.317147	+	0.697602i
$70$	5.03124	−	3.65007i	0.601348	−	0.436266i
$71$			4.52106i			0.536551i	0.963342	+	0.268276i	$0.0864538\pi$
$71$			4.52106i			0.536551i	−0.963342	+	0.268276i	$0.913546\pi$
$72$	−2.83834	−	0.971521i	−0.334501	−	0.114495i
$73$			5.34234i			0.625274i	0.949873	+	0.312637i	$0.101212\pi$
$73$			5.34234i			0.625274i	−0.949873	+	0.312637i	$0.898788\pi$
$74$	7.96547	+	4.59886i	0.925967	+	0.534607i
$75$	0.0870571	+	0.895548i	0.0100525	+	0.103409i
$76$	0.986680	−	0.569660i	0.113180	−	0.0653445i
$77$	−1.55953	−	14.9379i	−0.177724	−	1.70233i
$78$	−2.42356	+	1.73205i	−0.274414	+	0.196116i
$79$	6.51422	−	11.2830i	0.732907	−	1.26943i	−0.222729	−	0.974880i	$-0.571497\pi$
$79$	6.51422	−	11.2830i	0.732907	−	1.26943i	0.955636	−	0.294551i	$-0.0951701\pi$
$80$	−2.34936			−0.262666
$81$	−7.11229	−	5.51501i	−0.790255	−	0.612778i
$82$		−	7.99419i		−	0.882810i
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	0.283758	+	0.958896i	$0.408419\pi$
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	−0.972307	+	0.233707i	$0.924915\pi$
$84$	0.914596	+	4.49038i	0.0997906	+	0.489941i
$85$	−2.07781	−	3.59886i	−0.225370	−	0.390352i
$86$	−3.04933	+	1.76053i	−0.328817	+	0.189843i
$87$	7.16396	−	0.696415i	0.768057	−	0.0746636i
$88$	−2.83834	+	4.91614i	−0.302568	+	0.524062i
$89$	−1.16106			−0.123072			−0.0615360	−	0.998105i	$-0.519600\pi$
$89$	−1.16106			−0.123072			−0.0615360	+	0.998105i	$0.519600\pi$
$90$	−6.66826	−	2.28245i	−0.702897	−	0.240591i
$91$	4.15561	+	1.85366i	0.435626	+	0.194317i
$92$	−3.18272	−	1.83755i	−0.331822	−	0.191577i
$93$	−6.00000	+	13.1977i	−0.622171	+	1.36854i
$94$	−10.2277	+	5.90494i	−1.05490	+	0.609048i
$95$	2.31806	−	1.33834i	0.237828	−	0.137310i
$96$	0.716830	−	1.57675i	0.0731611	−	0.160927i
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	0.284416	−	0.958701i	$-0.408200\pi$
$97$	−3.97536	−	2.29517i	−0.403636	−	0.233039i	−0.688052	+	0.725662i	$0.741534\pi$
$98$	5.20853	−	4.67667i	0.526141	−	0.472415i
$99$	−12.8323	+	11.1962i	−1.28969	+	1.12526i
$100$	−0.519482			−0.0519482
$101$	3.31155	−	5.73577i	0.329511	−	0.570730i	−0.652904	−	0.757441i	$-0.726449\pi$
$101$	3.31155	−	5.73577i	0.329511	−	0.570730i	0.982415	+	0.186711i	$0.0597827\pi$
$102$	3.04933	−	0.296428i	0.301928	−	0.0293507i
$103$	−5.07471	+	2.92989i	−0.500026	+	0.288690i	−0.728724	−	0.684807i	$-0.759886\pi$
$103$	−5.07471	+	2.92989i	−0.500026	+	0.288690i	0.228698	+	0.973497i	$0.426553\pi$
$104$	−0.859925	−	1.48943i	−0.0843225	−	0.146051i
$105$	2.14871	+	10.5495i	0.209693	+	1.02953i
$106$		0			0
$107$		−	4.71563i		−	0.455878i	−0.973675	−	0.227939i	$-0.926801\pi$
$107$		−	4.71563i		−	0.455878i	0.973675	−	0.227939i	$-0.0731986\pi$
$108$	3.56645	−	3.77894i	0.343182	−	0.363629i
$109$	4.23669			0.405802			0.202901	−	0.979199i	$-0.434963\pi$
$109$	4.23669			0.405802			0.202901	+	0.979199i	$0.434963\pi$
$110$	−6.66826	+	11.5498i	−0.635794	+	1.10123i
$111$	−12.9612	+	9.26298i	−1.23022	+	0.879203i
$112$	−2.63145	+	0.274725i	−0.248649	+	0.0259591i
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	−0.195169	−	0.980770i	$-0.562526\pi$
$113$	5.91693	−	3.41614i	0.556618	−	0.321363i	0.751787	+	0.659406i	$0.229192\pi$
$114$	0.190932	+	1.96410i	0.0178824	+	0.183955i
$115$	−7.47736	−	4.31705i	−0.697267	−	0.402567i
$116$			4.15561i			0.385839i
$117$	−0.993738	−	5.06295i	−0.0918712	−	0.468069i
$118$		−	2.22966i		−	0.205257i
$119$	−2.74813	−	3.78802i	−0.251921	−	0.347247i
$120$	1.68409	−	3.70436i	0.153736	−	0.338160i
$121$	10.6123	+	18.3810i	0.964754	+	1.67100i
$122$	−4.49985	−	7.79396i	−0.407397	−	0.705632i
$123$	12.6049	+	5.73047i	1.13654	+	0.516699i
$124$	−7.24879	−	4.18509i	−0.650961	−	0.375832i
$125$	10.5263			0.941504
$126$	−7.73584	−	1.77675i	−0.689163	−	0.158285i
$127$	−6.67667			−0.592459			−0.296229	−	0.955117i	$-0.595729\pi$
$127$	−6.67667			−0.592459			−0.296229	+	0.955117i	$0.595729\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.590074	−	6.07004i	−0.0519532	−	0.534437i
$130$	−2.02027	−	3.49921i	−0.177189	−	0.306901i
$131$	3.73653	+	6.47185i	0.326462	+	0.565448i	0.981807	−	0.189881i	$-0.0608102\pi$
$131$	3.73653	+	6.47185i	0.326462	+	0.565448i	−0.655345	+	0.755329i	$0.727477\pi$
$132$	−5.71694	−	7.99939i	−0.497596	−	0.696258i
$133$	2.43990	−	1.77010i	0.211566	−	0.153487i
$134$			10.8712i			0.939133i
$135$	8.37888	−	8.87809i	0.721139	−	0.764104i
$136$			1.76883i			0.151676i
$137$	6.91772	+	3.99395i	0.591021	+	0.341226i	0.765501	−	0.643435i	$-0.222491\pi$
$137$	6.91772	+	3.99395i	0.591021	+	0.341226i	−0.174480	+	0.984661i	$0.555825\pi$
$138$	5.17883	−	3.70117i	0.440851	−	0.315064i
$139$	17.9792	−	10.3803i	1.52498	−	0.880446i	0.525415	−	0.850846i	$-0.323910\pi$
$139$	17.9792	−	10.3803i	1.52498	−	0.880446i	0.999562	−	0.0295993i	$-0.00942312\pi$
$140$	−6.18222	+	0.645428i	−0.522493	+	0.0545486i
$141$	−1.97915	−	20.3593i	−0.166675	−	1.71457i
$142$	2.26053	−	3.91535i	0.189699	−	0.328569i
$143$	−9.76302			−0.816425
$144$	1.97231	+	2.26053i	0.164359	+	0.188377i
$145$			9.76302i			0.810774i
$146$	2.67117	−	4.62660i	0.221068	−	0.382900i
$147$	3.64033	+	11.5649i	0.300250	+	0.953861i
$148$	−4.59886	−	7.96547i	−0.378024	−	0.654757i
$149$	−1.03726	+	0.598865i	−0.0849760	+	0.0490609i	−0.541886	−	0.840452i	$-0.682290\pi$
$149$	−1.03726	+	0.598865i	−0.0849760	+	0.0490609i	0.456910	+	0.889513i	$0.348956\pi$
$150$	0.372380	−	0.819096i	0.0304047	−	0.0668789i
$151$	−7.61229	+	13.1849i	−0.619480	+	1.07297i	0.370101	+	0.928991i	$0.379323\pi$
$151$	−7.61229	+	13.1849i	−0.619480	+	1.07297i	−0.989581	+	0.143979i	$0.954010\pi$
$152$	−1.13932			−0.0924111
$153$	−1.71845	+	5.02053i	−0.138929	+	0.405886i
$154$	−6.11835	+	13.7163i	−0.493030	+	1.10529i
$155$	−17.0300	−	9.83228i	−1.36788	−	0.789748i
$156$	2.96489	−	0.288220i	0.237381	−	0.0230761i
$157$	8.68358	−	5.01347i	0.693025	−	0.400118i	−0.111719	−	0.993740i	$-0.535636\pi$
$157$	8.68358	−	5.01347i	0.693025	−	0.400118i	0.804744	+	0.593621i	$0.202302\pi$
$158$	−11.2830	+	6.51422i	−0.897624	+	0.518243i
$159$		0			0
$160$	2.03460	+	1.17468i	0.160850	+	0.0928665i
$161$	−8.88000	−	3.96104i	−0.699842	−	0.312173i
$162$	3.40192	+	8.33228i	0.267280	+	0.654646i
$163$	12.0032			0.940160			0.470080	−	0.882624i	$-0.344225\pi$
$163$	12.0032			0.940160			0.470080	+	0.882624i	$0.344225\pi$
$164$	−3.99709	+	6.92317i	−0.312121	+	0.540609i
$165$	−13.4311	−	18.7934i	−1.04561	−	1.46307i
$166$	10.8651	−	6.27298i	0.843297	−	0.486878i
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	0.979681	+	0.200561i	$0.0642765\pi$
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	−0.316150	+	0.948709i	$0.602390\pi$
$168$	1.45313	−	4.34608i	0.112111	−	0.335307i
$169$	−5.02106	+	8.69673i	−0.386235	+	0.668979i
$170$			4.15561i			0.318721i
$171$	−3.23377	−	1.10687i	−0.247293	−	0.0846447i
$172$	3.52106			0.268478
$173$	0.993738	−	1.72121i	0.0755525	−	0.130861i	−0.825774	−	0.564001i	$-0.809261\pi$
$173$	0.993738	−	1.72121i	0.0755525	−	0.130861i	0.901326	+	0.433140i	$0.142595\pi$
$174$	−6.55238	−	2.97887i	−0.496735	−	0.225827i
$175$	−1.36699	+	0.142715i	−0.103335	+	0.0107882i
$176$	4.91614	−	2.83834i	0.370568	−	0.213948i
$177$	3.51563	+	1.59829i	0.264251	+	0.120135i
$178$	1.00551	+	0.580529i	0.0753659	+	0.0435125i
$179$		−	8.31122i		−	0.621210i	−0.950539	−	0.310605i	$-0.899468\pi$
$179$		−	8.31122i		−	0.621210i	0.950539	−	0.310605i	$-0.100532\pi$
$180$	4.63366	+	5.31079i	0.345373	+	0.395843i
$181$		−	15.4541i		−	1.14870i	−0.818611	−	0.574348i	$-0.805256\pi$
$181$		−	15.4541i		−	1.14870i	0.818611	−	0.574348i	$-0.194744\pi$
$182$	−2.67203	−	3.68312i	−0.198064	−	0.273011i
$183$	15.5148	−	1.50821i	1.14689	−	0.111490i
$184$	1.83755	+	3.18272i	0.135466	+	0.234634i
$185$	−10.8044	−	18.7137i	−0.794354	−	1.37586i
$186$	11.7950	−	8.42957i	0.864853	−	0.618086i
$187$	8.69581	+	5.02053i	0.635901	+	0.367137i
$188$	11.8099			0.861324
$189$	8.34677	−	10.9239i	0.607138	−	0.794596i
$190$	−2.67667			−0.194186
$191$	10.6851	+	6.16904i	0.773146	+	0.446376i	0.833996	−	0.551771i	$-0.186048\pi$
$191$	10.6851	+	6.16904i	0.773146	+	0.446376i	−0.0608498	+	0.998147i	$0.519381\pi$
$192$	−1.40917	+	1.00709i	−0.101698	+	0.0726808i
$193$	−2.19694	−	3.80521i	−0.158139	−	0.273905i	0.776058	−	0.630661i	$-0.217216\pi$
$193$	−2.19694	−	3.80521i	−0.158139	−	0.273905i	−0.934198	+	0.356756i	$0.883883\pi$
$194$	2.29517	+	3.97536i	0.164784	+	0.285414i
$195$	6.96559	−	0.677132i	0.498816	−	0.0484904i
$196$	−6.84905	+	1.44585i	−0.489218	+	0.103275i
$197$		−	10.8865i		−	0.775632i	−0.921737	−	0.387816i	$-0.873230\pi$
$197$		−	10.8865i		−	0.775632i	0.921737	−	0.387816i	$-0.126770\pi$
$198$	16.7112	−	3.28001i	1.18761	−	0.233100i
$199$			27.5665i			1.95414i	0.212926	+	0.977068i	$0.431701\pi$
$199$			27.5665i			1.95414i	−0.212926	+	0.977068i	$0.568299\pi$
$200$	0.449885	+	0.259741i	0.0318116	+	0.0183665i
$201$	−17.1413	−	7.79283i	−1.20905	−	0.549664i
$202$	−5.73577	+	3.31155i	−0.403567	+	0.233000i
$203$	1.14165	+	10.9353i	0.0801282	+	0.767506i
$204$	−2.78901	−	1.26795i	−0.195270	−	0.0887742i
$205$	−9.39060	+	16.2650i	−0.655868	+	1.13600i
$206$	5.85977			0.408270
$207$	2.12349	+	10.8189i	0.147593	+	0.751962i
$208$			1.71985i			0.119250i
$209$	−3.23377	+	5.60106i	−0.223685	+	0.387433i
$210$	3.41392	−	10.2105i	0.235583	−	0.704591i
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	0.987105	−	0.160071i	$-0.0511724\pi$
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	−0.632179	+	0.774823i	$0.717839\pi$
$212$		0			0
$213$	4.55313	+	6.37094i	0.311976	+	0.436530i
$214$	−2.35782	+	4.08386i	−0.161177	+	0.279167i
$215$	8.27223			0.564161
$216$	−4.97811	+	1.48943i	−0.338718	+	0.101343i
$217$	−20.2246	−	9.02143i	−1.37293	−	0.612415i
$218$	−3.66908	−	2.11835i	−0.248502	−	0.143473i
$219$	5.38024	+	7.52827i	0.363563	+	0.508713i
$220$	11.5498	−	6.66826i	0.778686	−	0.449574i
$221$	−2.63455	+	1.52106i	−0.177219	+	0.102318i
$222$	15.8562	−	1.54140i	1.06420	−	0.103452i
$223$	−6.24329	−	3.60456i	−0.418081	−	0.241379i	0.276175	−	0.961107i	$-0.410933\pi$
$223$	−6.24329	−	3.60456i	−0.418081	−	0.241379i	−0.694256	+	0.719728i	$0.744267\pi$
$224$	2.41626	+	1.07781i	0.161443	+	0.0720139i
$225$	1.02458	+	1.17430i	0.0683053	+	0.0782870i
$226$	−6.83228			−0.454477
$227$	6.37800	−	11.0470i	0.423323	−	0.733217i	−0.572939	−	0.819598i	$-0.694197\pi$
$227$	6.37800	−	11.0470i	0.423323	−	0.733217i	0.996262	+	0.0863812i	$0.0275303\pi$
$228$	0.816699	−	1.79643i	0.0540872	−	0.118971i
$229$	3.89208	−	2.24709i	0.257196	−	0.148492i	−0.365859	−	0.930670i	$-0.619225\pi$
$229$	3.89208	−	2.24709i	0.257196	−	0.148492i	0.623055	+	0.782178i	$0.285891\pi$
$230$	4.31705	+	7.47736i	0.284658	+	0.493042i
$231$	−17.2415	−	19.4794i	−1.13441	−	1.28165i
$232$	2.07781	−	3.59886i	0.136415	−	0.236277i
$233$		−	2.15403i		−	0.141115i	−0.997508	−	0.0705577i	$-0.977522\pi$
$233$		−	2.15403i		−	0.141115i	0.997508	−	0.0705577i	$-0.0224779\pi$
$234$	−1.67087	+	4.88151i	−0.109228	+	0.319114i
$235$	27.7456			1.80993
$236$	−1.11483	+	1.93094i	−0.0725693	+	0.125694i
$237$	−2.18336	−	22.4600i	−0.141825	−	1.45894i
$238$	0.485942	+	4.65458i	0.0314989	+	0.301712i
$239$	−8.78317	+	5.07096i	−0.568136	+	0.328013i	−0.756404	−	0.654104i	$-0.773046\pi$
$239$	−8.78317	+	5.07096i	−0.568136	+	0.328013i	0.188269	+	0.982118i	$0.439712\pi$
$240$	−3.31064	+	2.36603i	−0.213701	+	0.152726i
$241$	9.13490	+	5.27404i	0.588431	+	0.339731i	0.764477	−	0.644651i	$-0.222997\pi$
$241$	9.13490	+	5.27404i	0.588431	+	0.339731i	−0.176046	+	0.984382i	$0.556331\pi$
$242$		−	21.2246i		−	1.36437i
$243$	−15.5766	−	0.608830i	−0.999237	−	0.0390564i
$244$			8.99970i			0.576146i
$245$	−16.0909	+	3.39682i	−1.02801	+	0.217015i
$246$	−8.05090	−	11.2652i	−0.513307	−	0.718241i
$247$	−0.979729	−	1.69694i	−0.0623387	−	0.107974i
$248$	4.18509	+	7.24879i	0.265754	+	0.460299i
$249$	2.10251	+	21.6283i	0.133241	+	1.37064i
$250$	−9.11608	−	5.26317i	−0.576551	−	0.332872i
$251$	−29.3005			−1.84943			−0.924714	−	0.380662i	$-0.875696\pi$
$251$	−29.3005			−1.84943			−0.924714	+	0.380662i	$0.875696\pi$
$252$	5.81106	+	5.40663i	0.366062	+	0.340585i
$253$	20.8623			1.31160
$254$	5.78217	+	3.33834i	0.362805	+	0.209466i
$255$	−6.55238	−	2.97887i	−0.410326	−	0.186544i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.81430	−	6.60656i	−0.237930	−	0.412106i	0.722190	−	0.691694i	$-0.243135\pi$
$257$	−3.81430	−	6.60656i	−0.237930	−	0.412106i	−0.960120	+	0.279588i	$0.909802\pi$
$258$	−2.52400	+	5.55185i	−0.157137	+	0.345643i
$259$	−14.2900	−	19.6973i	−0.887937	−	1.22393i
$260$			4.04054i			0.250584i
$261$	9.39388	−	8.19615i	0.581467	−	0.507329i
$262$		−	7.47305i		−	0.461687i
$263$	−10.5531	−	6.09281i	−0.650729	−	0.375699i	0.138006	−	0.990431i	$-0.455931\pi$
$263$	−10.5531	−	6.09281i	−0.650729	−	0.375699i	−0.788736	+	0.614733i	$0.789264\pi$
$264$	0.951321	+	9.78615i	0.0585498	+	0.602296i
$265$		0			0
$266$	−2.99806	+	0.313000i	−0.183823	+	0.0191913i
$267$	−1.63613	+	1.16930i	−0.100129	+	0.0715597i
$268$	5.43562	−	9.41477i	0.332034	−	0.575099i
$269$	2.77433			0.169154			0.0845771	−	0.996417i	$-0.473046\pi$
$269$	2.77433			0.169154			0.0845771	+	0.996417i	$0.473046\pi$
$270$	−11.6954	+	3.49921i	−0.711757	+	0.212955i
$271$		−	3.20793i		−	0.194868i	−0.995242	−	0.0974338i	$-0.968937\pi$
$271$		−	3.20793i		−	0.194868i	0.995242	−	0.0974338i	$-0.0310634\pi$
$272$	0.884414	−	1.53185i	0.0536255	−	0.0928821i
$273$	7.72278	−	1.57297i	0.467404	−	0.0952003i
$274$	−3.99395	−	6.91772i	−0.241283	−	0.417915i
$275$	2.55385	−	1.47446i	0.154003	−	0.0889135i
$276$	−6.33558	+	0.615888i	−0.381357	+	0.0370721i
$277$	−5.04054	+	8.73047i	−0.302857	+	0.524563i	−0.976782	−	0.214236i	$-0.931274\pi$
$277$	−5.04054	+	8.73047i	−0.302857	+	0.524563i	0.673925	+	0.738800i	$0.264607\pi$
$278$	−20.7606			−1.24514
$279$	4.83634	+	24.6404i	0.289544	+	1.47518i
$280$	5.67667	+	2.53215i	0.339246	+	0.151325i
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	0.620562	−	0.784157i	$-0.286904\pi$
$281$	4.21999	+	2.43641i	0.251743	+	0.145344i	−0.368819	+	0.929501i	$0.620238\pi$
$282$	−8.46568	+	18.6213i	−0.504124	+	1.10888i
$283$	−2.44030	+	1.40891i	−0.145061	+	0.0837508i	−0.570774	−	0.821107i	$-0.693357\pi$
$283$	−2.44030	+	1.40891i	−0.145061	+	0.0837508i	0.425713	+	0.904858i	$0.360023\pi$
$284$	−3.91535	+	2.26053i	−0.232333	+	0.134138i
$285$	1.91872	−	4.22045i	0.113655	−	0.249998i
$286$	8.45502	+	4.88151i	0.499956	+	0.288650i
$287$	−8.61618	+	19.3161i	−0.508597	+	1.14019i
$288$	−0.577806	−	2.94383i	−0.0340475	−	0.173467i
$289$	−13.8712			−0.815956
$290$	4.88151	−	8.45502i	0.286652	−	0.496496i
$291$	−7.91341	+	0.769270i	−0.463892	+	0.0450954i
$292$	−4.62660	+	2.67117i	−0.270751	+	0.156318i
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	0.722846	−	0.691010i	$-0.242834\pi$
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	−0.959855	+	0.280498i	$0.909500\pi$
$294$	2.62985	−	11.8357i	0.153376	−	0.690272i
$295$	−2.61914	+	4.53648i	−0.152492	+	0.264124i
$296$			9.19773i			0.534607i
$297$	−6.80728	+	28.7006i	−0.394999	+	1.66538i
$298$	1.19773			0.0693826
$299$	−3.16030	+	5.47381i	−0.182765	+	0.316558i
$300$	−0.732039	+	0.523168i	−0.0422643	+	0.0302051i
$301$	9.26549	−	0.967324i	0.534054	−	0.0557556i
$302$	13.1849	−	7.61229i	0.758705	−	0.438038i
$303$	−1.10993	−	11.4177i	−0.0637637	−	0.655931i
$304$	0.986680	+	0.569660i	0.0565900	+	0.0326722i
$305$			21.1435i			1.21067i
$306$	3.99849	−	3.48868i	0.228578	−	0.199434i
$307$			10.8996i			0.622074i	0.950398	+	0.311037i	$0.100676\pi$
$307$			10.8996i			0.622074i	−0.950398	+	0.311037i	$0.899324\pi$
$308$	12.1568	−	8.81952i	0.692699	−	0.502539i
$309$	−4.20046	+	9.23943i	−0.238956	+	0.525613i
$310$	9.83228	+	17.0300i	0.558436	+	0.967240i
$311$	4.11819	+	7.13291i	0.233521	+	0.404470i	0.958842	−	0.283941i	$-0.0916419\pi$
$311$	4.11819	+	7.13291i	0.233521	+	0.404470i	−0.725321	+	0.688411i	$0.758309\pi$
$312$	−2.71178	−	1.23284i	−0.153524	−	0.0697958i
$313$	−29.2736	−	16.9011i	−1.65464	−	0.955308i	−0.975127	−	0.221648i	$-0.928857\pi$
$313$	−29.2736	−	16.9011i	−1.65464	−	0.955308i	−0.679516	−	0.733661i	$-0.737810\pi$
$314$	−10.0269			−0.565853
$315$	13.6523	+	12.7021i	0.769217	+	0.715682i
$316$	13.0284			0.732907
$317$	5.82913	+	3.36545i	0.327396	+	0.189022i	0.654685	−	0.755902i	$-0.272801\pi$
$317$	5.82913	+	3.36545i	0.327396	+	0.189022i	−0.327288	+	0.944925i	$0.606135\pi$
$318$		0			0
$319$	−11.7950	−	20.4296i	−0.660394	−	1.14384i
$320$	−1.17468	−	2.03460i	−0.0656665	−	0.113738i
$321$	−4.74909	−	6.64513i	−0.265068	−	0.370895i
$322$	5.70979	+	7.87036i	0.318194	+	0.438598i
$323$			2.01526i			0.112132i
$324$	1.21999	−	8.91693i	0.0677771	−	0.495385i
$325$			0.893431i			0.0495586i
$326$	−10.3950	−	6.00158i	−0.575728	−	0.332397i
$327$	5.97022	−	4.26675i	0.330154	−	0.235952i
$328$	6.92317	−	3.99709i	0.382268	−	0.220703i
$329$	31.0771	−	3.24447i	1.71334	−	0.178874i
$330$	2.23499	+	22.9912i	0.123032	+	1.26562i
$331$	16.0284	−	27.7621i	0.881002	−	1.52594i	0.0307744	−	0.999526i	$-0.490203\pi$
$331$	16.0284	−	27.7621i	0.881002	−	1.52594i	0.850228	−	0.526415i	$-0.176464\pi$
$332$	−12.5460			−0.688549
$333$	−8.93579	+	26.1062i	−0.489678	+	1.43061i
$334$		−	17.1494i		−	0.938375i
$335$	12.7702	−	22.1187i	0.697712	−	1.20847i
$336$	−3.43149	+	3.03725i	−0.187203	+	0.165696i
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	−0.980668	−	0.195681i	$-0.937308\pi$
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$338$	8.69673	−	5.02106i	0.473040	−	0.273110i
$339$	4.89758	−	10.7728i	0.266000	−	0.585100i
$340$	2.07781	−	3.59886i	0.112685	−	0.195176i
$341$	47.5148			2.57307
$342$	2.24709	+	2.57547i	0.121509	+	0.139265i
$343$	−17.6257	+	5.68629i	−0.951700	+	0.307031i
$344$	−3.04933	−	1.76053i	−0.164409	−	0.0949214i
$345$	−14.8846	+	1.44694i	−0.801357	+	0.0779007i
$346$	−1.72121	+	0.993738i	−0.0925326	+	0.0534237i
$347$	19.7453	−	11.3999i	1.05998	−	0.611981i	0.134554	−	0.990906i	$-0.457040\pi$
$347$	19.7453	−	11.3999i	1.05998	−	0.611981i	0.925427	+	0.378926i	$0.123706\pi$
$348$	4.18509	+	5.85596i	0.224345	+	0.313913i
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	0.432604	−	0.901584i	$-0.357595\pi$
$349$	−2.46389	−	1.42253i	−0.131889	−	0.0761461i	−0.564493	+	0.825438i	$0.690928\pi$
$350$	1.25521	+	0.559901i	0.0670936	+	0.0299279i
$351$	−6.49921	−	6.13376i	−0.346902	−	0.327396i
$352$	−5.67667			−0.302568
$353$	−3.57212	+	6.18709i	−0.190125	+	0.329306i	−0.945291	−	0.326227i	$-0.894223\pi$
$353$	−3.57212	+	6.18709i	−0.190125	+	0.329306i	0.755167	+	0.655533i	$0.227556\pi$
$354$	−2.24548	−	3.14197i	−0.119346	−	0.166994i
$355$	−9.19856	+	5.31079i	−0.488209	+	0.281868i
$356$	−0.580529	−	1.00551i	−0.0307680	−	0.0532917i
$357$	−7.68747	−	2.57033i	−0.406864	−	0.136036i
$358$	−4.15561	+	7.19773i	−0.219631	+	0.380412i
$359$		−	11.6037i		−	0.612421i	−0.951964	−	0.306210i	$-0.900939\pi$
$359$		−	11.6037i		−	0.612421i	0.951964	−	0.306210i	$-0.0990611\pi$
$360$	−1.35747	−	6.91611i	−0.0715451	−	0.364511i
$361$	17.7019			0.931682
$362$	−7.72706	+	13.3837i	−0.406125	+	0.703429i
$363$	33.4660	+	15.2144i	1.75651	+	0.798550i
$364$	0.472486	+	4.52570i	0.0247650	+	0.237211i
$365$	−10.8695	+	6.27554i	−0.568938	+	0.328477i
$366$	−14.1903	−	6.45125i	−0.741739	−	0.337212i
$367$	6.78525	+	3.91747i	0.354187	+	0.204490i	0.666528	−	0.745480i	$-0.267780\pi$
$367$	6.78525	+	3.91747i	0.354187	+	0.204490i	−0.312341	+	0.949970i	$0.601113\pi$
$368$		−	3.67509i		−	0.191577i
$369$	23.5335	−	4.61909i	1.22511	−	0.240460i
$370$			21.6088i			1.12339i
$371$		0			0
$372$	−14.4296	+	1.40271i	−0.748138	+	0.0727272i
$373$	−12.8339	−	22.2289i	−0.664512	−	1.15097i	−0.979417	−	0.201845i	$-0.935306\pi$
$373$	−12.8339	−	22.2289i	−0.664512	−	1.15097i	0.314905	−	0.949123i	$-0.398027\pi$
$374$	−5.02053	−	8.69581i	−0.259605	−	0.449650i
$375$	14.8334	−	10.6010i	0.765994	−	0.547434i
$376$	−10.2277	−	5.90494i	−0.527451	−	0.304524i
$377$	7.14702			0.368091
$378$	−12.6905	+	5.28698i	−0.652727	+	0.271933i
$379$	−15.1045			−0.775868			−0.387934	−	0.921687i	$-0.626811\pi$
$379$	−15.1045			−0.775868			−0.387934	+	0.921687i	$0.626811\pi$
$380$	2.31806	+	1.33834i	0.118914	+	0.0686551i
$381$	−9.40856	+	6.72404i	−0.482015	+	0.344483i
$382$	−6.16904	−	10.6851i	−0.315636	−	0.546697i
$383$	0.763322	+	1.32211i	0.0390040	+	0.0675568i	0.884868	−	0.465841i	$-0.154248\pi$
$383$	0.763322	+	1.32211i	0.0390040	+	0.0675568i	−0.845864	+	0.533398i	$0.820915\pi$
$384$	1.72392	−	0.167584i	0.0879737	−	0.00855200i
$385$	28.5607	−	20.7202i	1.45559	−	1.05600i
$386$			4.39388i			0.223643i
$387$	−6.94462	−	7.95946i	−0.353015	−	0.404602i
$388$		−	4.59035i		−	0.233039i
$389$	12.8948	+	7.44483i	0.653794	+	0.377468i	0.789908	−	0.613225i	$-0.210128\pi$
$389$	12.8948	+	7.44483i	0.653794	+	0.377468i	−0.136115	+	0.990693i	$0.543462\pi$
$390$	−6.37094	−	2.89638i	−0.322605	−	0.146664i
$391$	5.62969	−	3.25030i	0.284706	−	0.164375i
$392$	6.65438	+	2.17238i	0.336097	+	0.109722i
$393$	11.7832	+	5.35691i	0.594382	+	0.270220i
$394$	−5.44325	+	9.42799i	−0.274227	+	0.474975i
$395$	30.6085			1.54008
$396$	−16.1123	−	5.51501i	−0.809673	−	0.277139i
$397$			28.7869i			1.44478i	0.691488	+	0.722388i	$0.256955\pi$
$397$			28.7869i			1.44478i	−0.691488	+	0.722388i	$0.743045\pi$
$398$	13.7832	−	23.8733i	0.690892	−	1.19666i
$399$	1.65558	−	4.95158i	0.0828825	−	0.247889i
$400$	−0.259741	−	0.449885i	−0.0129871	−	0.0224942i
$401$	−33.0592	+	19.0868i	−1.65090	+	0.953147i	−0.674196	+	0.738552i	$0.735510\pi$
$401$	−33.0592	+	19.0868i	−1.65090	+	0.953147i	−0.976703	+	0.214595i	$0.931157\pi$
$402$	10.9484	+	15.3194i	0.546055	+	0.764064i
$403$	−7.19773	+	12.4668i	−0.358544	+	0.621017i
$404$	6.62310			0.329511
$405$	2.86619	−	20.9491i	0.142422	−	1.04097i
$406$	4.47894	−	10.0411i	0.222286	−	0.498329i
$407$	45.2173	+	26.1062i	2.24134	+	1.29404i
$408$	1.78138	+	2.49258i	0.0881913	+	0.123401i
$409$	6.03355	−	3.48347i	0.298340	−	0.172247i	−0.343357	−	0.939205i	$-0.611564\pi$
$409$	6.03355	−	3.48347i	0.298340	−	0.172247i	0.641697	+	0.766958i	$0.278231\pi$
$410$	16.2650	−	9.39060i	0.803271	−	0.463769i
$411$	13.7705	−	1.33865i	0.679250	−	0.0660305i
$412$	−5.07471	−	2.92989i	−0.250013	−	0.144345i
$413$	−2.40314	+	5.38745i	−0.118251	+	0.265099i
$414$	3.57043	−	10.4311i	0.175477	−	0.512663i
$415$	−29.4750			−1.44687
$416$	0.859925	−	1.48943i	0.0421613	−	0.0730255i
$417$	14.8818	−	32.7344i	0.728766	−	1.60301i
$418$	5.60106	−	3.23377i	0.273957	−	0.158169i
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	−0.880146	−	0.474702i	$-0.842556\pi$
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	0.0289690	−	0.999580i	$-0.490778\pi$
$420$	−8.06179	+	7.13559i	−0.393375	+	0.348181i
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	−0.788302	−	0.615288i	$-0.789040\pi$
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	0.927006	+	0.375046i	$0.122373\pi$
$422$		−	10.3112i		−	0.501942i
$423$	−23.2928	−	26.6966i	−1.13253	−	1.29803i
$424$		0			0
$425$	0.459437	−	0.795769i	0.0222860	−	0.0386005i
$426$	−0.757659	−	7.79396i	−0.0367087	−	0.377619i
$427$	2.47244	+	23.6822i	0.119650	+	1.14606i
$428$	4.08386	−	2.35782i	0.197401	−	0.113969i
$429$	−13.7578	+	9.83228i	−0.664231	+	0.474707i
$430$	−7.16396	−	4.13611i	−0.345477	−	0.199461i
$431$			30.2936i			1.45919i	0.683880	+	0.729595i	$0.260291\pi$
$431$			30.2936i			1.45919i	−0.683880	+	0.729595i	$0.739709\pi$
$432$	5.05589	+	1.19917i	0.243251	+	0.0576950i
$433$			23.6094i			1.13459i	0.823513	+	0.567297i	$0.192011\pi$
$433$			23.6094i			1.13459i	−0.823513	+	0.567297i	$0.807989\pi$
$434$	13.0043	+	17.9251i	0.624226	+	0.860432i
$435$	9.83228	+	13.7578i	0.471422	+	0.659634i
$436$	2.11835	+	3.66908i	0.101450	+	0.175717i
$437$	2.09355	+	3.62614i	0.100148	+	0.173462i
$438$	−0.895293	−	9.20979i	−0.0427787	−	0.440061i
$439$	21.6681	+	12.5101i	1.03416	+	0.597075i	0.918175	−	0.396175i	$-0.129663\pi$
$439$	21.6681	+	12.5101i	1.03416	+	0.597075i	0.115989	+	0.993250i	$0.462996\pi$
$440$	−13.3365			−0.635794
$441$	16.7768	+	12.6308i	0.798897	+	0.601467i
$442$	3.04212			0.144699
$443$	−19.9446	−	11.5150i	−0.947595	−	0.547094i	−0.0552622	−	0.998472i	$-0.517599\pi$
$443$	−19.9446	−	11.5150i	−0.947595	−	0.547094i	−0.892333	+	0.451377i	$0.850933\pi$
$444$	−14.5026	−	6.59321i	−0.688261	−	0.312900i
$445$	−1.36387	−	2.36229i	−0.0646537	−	0.111983i
$446$	3.60456	+	6.24329i	0.170681	+	0.295628i
$447$	−0.858568	+	1.88853i	−0.0406089	+	0.0893242i
$448$	−1.55364	−	2.14154i	−0.0734028	−	0.101178i
$449$		−	15.9028i		−	0.750501i	−0.926923	−	0.375251i	$-0.877557\pi$
$449$		−	15.9028i		−	0.750501i	0.926923	−	0.375251i	$-0.122443\pi$
$450$	−0.300160	−	1.52927i	−0.0141497	−	0.0720904i
$451$		−	45.3804i		−	2.13688i
$452$	5.91693	+	3.41614i	0.278309	+	0.160682i
$453$	2.55140	+	26.2460i	0.119875	+	1.23315i
$454$	−11.0470	+	6.37800i	−0.518462	+	0.299334i
$455$	1.11004	+	10.6325i	0.0520394	+	0.498458i
$456$	−1.60550	+	1.14740i	−0.0751842	+	0.0537321i
$457$	2.83307	−	4.90702i	0.132525	−	0.229541i	−0.792124	−	0.610360i	$-0.791025\pi$
$457$	2.83307	−	4.90702i	0.132525	−	0.229541i	0.924649	+	0.380819i	$0.124358\pi$
$458$	−4.49418			−0.209999
$459$	2.63455	+	8.80542i	0.122970	+	0.411002i
$460$		−	8.63411i		−	0.402567i
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	0.223194	+	0.974774i	$0.428352\pi$
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	−0.955776	+	0.294095i	$0.904982\pi$
$462$	5.19186	+	25.4904i	0.241547	+	1.18592i
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	0.952192	−	0.305500i	$-0.0988236\pi$
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	−0.740667	+	0.671873i	$0.765490\pi$
$464$	−3.59886	+	2.07781i	−0.167073	+	0.0964597i
$465$	−33.9002	+	3.29547i	−1.57209	+	0.152824i
$466$	−1.07702	+	1.86545i	−0.0498918	+	0.0864152i
$467$	−30.3032			−1.40226			−0.701132	−	0.713032i	$-0.747322\pi$
$467$	−30.3032			−1.40226			−0.701132	+	0.713032i	$0.747322\pi$
$468$	3.88777	−	3.39208i	0.179712	−	0.156799i
$469$	11.7171	−	26.2678i	0.541045	−	1.21293i
$470$	−24.0284	−	13.8728i	−1.10835	−	0.639906i
$471$	7.18761	−	15.8100i	0.331188	−	0.728487i
$472$	1.93094	−	1.11483i	0.0888788	−	0.0513142i
$473$	−17.3100	+	9.99395i	−0.795916	+	0.459522i
$474$	−9.33917	+	20.5426i	−0.428962	+	0.943555i
$475$	0.512563	+	0.295928i	0.0235180	+	0.0135781i
$476$	1.90645	−	4.27396i	0.0873821	−	0.195897i
$477$		0			0
$478$	10.1419			0.463881
$479$	−2.33143	+	4.03816i	−0.106526	+	0.184508i	−0.914361	−	0.404901i	$-0.867306\pi$
$479$	−2.33143	+	4.03816i	−0.106526	+	0.184508i	0.807835	+	0.589409i	$0.200639\pi$
$480$	4.05012	−	0.393716i	0.184862	−	0.0179706i
$481$	−13.6994	+	7.90935i	−0.624639	+	0.360636i
$482$	−5.27404	−	9.13490i	−0.240226	−	0.416083i
$483$	−16.5026	+	3.36122i	−0.750893	+	0.152941i
$484$	−10.6123	+	18.3810i	−0.482377	+	0.835501i
$485$		−	10.7844i		−	0.489693i
$486$	13.1853	+	8.31554i	0.598097	+	0.377201i
$487$	−19.4821			−0.882818			−0.441409	−	0.897306i	$-0.645521\pi$
$487$	−19.4821			−0.882818			−0.441409	+	0.897306i	$0.645521\pi$
$488$	4.49985	−	7.79396i	0.203699	−	0.352816i
$489$	16.9145	−	12.0883i	0.764900	−	0.546652i
$490$	15.6335	+	5.10370i	0.706250	+	0.230562i
$491$	−17.7437	+	10.2443i	−0.800762	+	0.462320i	−0.843737	−	0.536756i	$-0.819649\pi$
$491$	−17.7437	+	10.2443i	−0.800762	+	0.462320i	0.0429758	+	0.999076i	$0.486316\pi$
$492$	1.33970	+	13.7814i	0.0603984	+	0.621312i
$493$	−6.36577	−	3.67528i	−0.286700	−	0.165526i
$494$			1.95946i			0.0881602i
$495$	−37.8535	−	12.9567i	−1.70139	−	0.582361i
$496$		−	8.37019i		−	0.375832i
$497$	−9.68203	+	7.02412i	−0.434298	+	0.315075i
$498$	8.99332	−	19.7819i	0.403000	−	0.886449i
$499$	5.12598	+	8.87845i	0.229470	+	0.397454i	0.957651	−	0.287931i	$-0.0929673\pi$
$499$	5.12598	+	8.87845i	0.229470	+	0.397454i	−0.728181	+	0.685385i	$0.759634\pi$
$500$	5.26317	+	9.11608i	0.235376	+	0.407683i
$501$	27.0405	+	12.2932i	1.20808	+	0.549221i
$502$	25.3749	+	14.6502i	1.13254	+	0.653872i
$503$	−14.5521			−0.648845			−0.324422	−	0.945912i	$-0.605170\pi$
$503$	−14.5521			−0.648845			−0.324422	+	0.945912i	$0.605170\pi$
$504$	−2.32921	−	7.58780i	−0.103751	−	0.337988i
$505$	15.5600			0.692412
$506$	−18.0673	−	10.4311i	−0.803188	−	0.463721i
$507$	1.68290	+	17.3119i	0.0747403	+	0.768846i
$508$	−3.33834	−	5.78217i	−0.148115	−	0.256542i
$509$	−16.6617	−	28.8589i	−0.738517	−	1.27915i	−0.953163	−	0.302457i	$-0.902193\pi$
$509$	−16.6617	−	28.8589i	−0.738517	−	1.27915i	0.214646	−	0.976692i	$-0.431140\pi$
$510$	4.18509	+	5.85596i	0.185319	+	0.259306i
$511$	−11.4408	+	8.30010i	−0.506113	+	0.367175i
$512$			1.00000i			0.0441942i
$513$	−5.67166	+	1.69694i	−0.250410	+	0.0749218i
$514$			7.62860i			0.336483i
$515$	−11.9223	−	6.88335i	−0.525360	−	0.303317i
$516$	4.96177	−	3.54604i	0.218430	−	0.156106i
$517$	−58.0591	+	33.5204i	−2.55343	+	1.47423i
$518$	2.52685	+	24.2034i	0.111023	+	1.06343i
$519$	−0.333070	−	3.42626i	−0.0146202	−	0.150396i
$520$	2.02027	−	3.49921i	0.0885947	−	0.153451i
$521$	−6.53925			−0.286490			−0.143245	−	0.989687i	$-0.545754\pi$
$521$	−6.53925			−0.286490			−0.143245	+	0.989687i	$0.545754\pi$
$522$	−12.2334	+	2.40114i	−0.535442	+	0.105095i
$523$		−	0.786858i		−	0.0344069i	−0.999852	−	0.0172034i	$-0.994524\pi$
$523$		−	0.786858i		−	0.0344069i	0.999852	−	0.0172034i	$-0.00547630\pi$
$524$	−3.73653	+	6.47185i	−0.163231	+	0.282724i
$525$	−1.78260	+	1.57780i	−0.0777988	+	0.0688608i
$526$	6.09281	+	10.5531i	0.265659	+	0.460135i
$527$	12.8219	−	7.40271i	0.558530	−	0.322467i
$528$	4.06921	−	8.95072i	0.177090	−	0.389530i
$529$	−4.74685	+	8.22178i	−0.206385	+	0.357469i
$530$		0			0
$531$	6.56374	−	1.28831i	0.284842	−	0.0559079i
$532$	2.75290	+	1.22797i	0.119353	+	0.0532391i
$533$	11.9068	+	6.87440i	0.515741	+	0.297763i
$534$	2.00158	−	0.194575i	0.0866167	−	0.00842009i
$535$	9.59445	−	5.53936i	0.414804	−	0.239487i
$536$	−9.41477	+	5.43562i	−0.406656	+	0.234783i
$537$	−8.37019	−	11.7119i	−0.361200	−	0.505407i
$538$	−2.40264	−	1.38717i	−0.103585	−	0.0598050i
$539$	29.5671	−	26.5479i	1.27354	−	1.14350i
$540$	11.8781	+	2.81728i	0.511152	+	0.121236i
$541$	5.60454			0.240958			0.120479	−	0.992716i	$-0.461557\pi$
$541$	5.60454			0.240958			0.120479	+	0.992716i	$0.461557\pi$
$542$	−1.60396	+	2.77815i	−0.0688961	+	0.119332i
$543$	−15.5638	−	21.7775i	−0.667905	−	0.934561i
$544$	−1.53185	+	0.884414i	−0.0656775	+	0.0379189i
$545$	4.97675	+	8.61999i	0.213181	+	0.369240i
$546$	−7.47460	−	2.49916i	−0.319884	−	0.106954i
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	−0.975135	−	0.221612i	$-0.928868\pi$
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	0.679489	+	0.733685i	$0.262201\pi$
$548$			7.98789i			0.341226i
$549$	20.3441	−	17.7502i	0.868264	−	0.757559i
$550$	−2.94893			−0.125743
$551$	2.36729	−	4.10026i	0.100850	−	0.174677i
$552$	5.79472	+	2.63442i	0.246640	+	0.112128i
$553$	34.2837	−	3.57924i	1.45789	−	0.152205i
$554$	8.73047	−	5.04054i	0.370922	−	0.214152i
$555$	−34.0717	−	15.4898i	−1.44626	−	0.657506i
$556$	17.9792	+	10.3803i	0.762488	+	0.440223i
$557$		−	27.8233i		−	1.17891i	−0.807800	−	0.589456i	$-0.799342\pi$
$557$		−	27.8233i		−	1.17891i	0.807800	−	0.589456i	$-0.200658\pi$
$558$	8.13181	−	23.7574i	0.344247	−	1.00573i
$559$		−	6.05569i		−	0.256128i
$560$	−3.65007	−	5.03124i	−0.154243	−	0.212609i
$561$	17.3100	−	1.68272i	0.730830	−	0.0710447i
$562$	−2.43641	−	4.21999i	−0.102774	−	0.178009i
$563$	12.2650	+	21.2436i	0.516909	+	0.895312i	0.999807	+	0.0196359i	$0.00625069\pi$
$563$	12.2650	+	21.2436i	0.516909	+	0.895312i	−0.482898	+	0.875676i	$0.660416\pi$
$564$	16.6421	−	11.8937i	0.700760	−	0.500814i
$565$	13.9010	+	8.02574i	0.584819	+	0.337645i
$566$	2.81781			0.118441
$567$	0.760631	−	23.7996i	0.0319435	−	0.999490i
$568$	4.52106			0.189699
$569$	−23.4762	−	13.5540i	−0.984172	−	0.568212i	−0.0806449	−	0.996743i	$-0.525698\pi$
$569$	−23.4762	−	13.5540i	−0.984172	−	0.568212i	−0.903527	+	0.428531i	$0.859031\pi$
$570$	−3.77188	+	2.69566i	−0.157987	+	0.112909i
$571$	14.9177	+	25.8382i	0.624287	+	1.08130i	0.988678	+	0.150051i	$0.0479438\pi$
$571$	14.9177	+	25.8382i	0.624287	+	1.08130i	−0.364391	+	0.931246i	$0.618723\pi$
$572$	−4.88151	−	8.45502i	−0.204106	−	0.353522i
$573$	21.2699	−	2.06767i	0.888563	−	0.0863781i
$574$	17.1199	−	12.4201i	0.714570	−	0.518406i
$575$		−	1.90915i		−	0.0796169i
$576$	−0.971521	+	2.83834i	−0.0404800	+	0.118264i
$577$		−	28.1666i		−	1.17259i	−0.810097	−	0.586296i	$-0.800585\pi$
$577$		−	28.1666i		−	1.17259i	0.810097	−	0.586296i	$-0.199415\pi$
$578$	12.0129	+	6.93562i	0.499669	+	0.288484i
$579$	−6.92807	−	3.14967i	−0.287921	−	0.130896i
$580$	−8.45502	+	4.88151i	−0.351076	+	0.202694i
$581$	−33.0141	+	3.44670i	−1.36965	+	0.142993i
$582$	7.23785	+	3.29050i	0.300018	+	0.136395i
$583$		0			0
$584$	5.34234			0.221068
$585$	9.13376	−	7.96920i	0.377635	−	0.329486i
$586$			8.11389i			0.335182i
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	−0.745343	−	0.666681i	$-0.767714\pi$
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	0.950034	+	0.312145i	$0.101048\pi$
$588$	−8.19537	+	8.93509i	−0.337971	+	0.368477i
$589$	4.76816	+	8.25870i	0.196469	+	0.340294i
$590$	4.53648	−	2.61914i	0.186764	−	0.107828i
$591$	−10.9637	−	15.3409i	−0.450988	−	0.631042i
$592$	4.59886	−	7.96547i	0.189012	−	0.327379i
$593$	−4.69872			−0.192953			−0.0964766	−	0.995335i	$-0.530757\pi$
$593$	−4.69872			−0.192953			−0.0964766	+	0.995335i	$0.530757\pi$
$594$	20.2456	−	21.4518i	0.830686	−	0.880178i
$595$	4.47894	−	10.0411i	0.183619	−	0.411643i
$596$	−1.03726	−	0.598865i	−0.0424880	−	0.0245305i
$597$	27.7621	+	38.8459i	1.13623	+	1.58986i
$598$	5.47381	−	3.16030i	0.223841	−	0.129234i
$599$	12.7309	−	7.35019i	0.520170	−	0.300320i	−0.216834	−	0.976208i	$-0.569573\pi$
$599$	12.7309	−	7.35019i	0.520170	−	0.300320i	0.737004	+	0.675888i	$0.236240\pi$
$600$	0.895548	−	0.0870571i	0.0365606	−	0.00355409i
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	0.794018	−	0.607894i	$-0.207986\pi$
$601$	16.2923	+	9.40634i	0.664575	+	0.383693i	−0.129443	+	0.991587i	$0.541319\pi$
$602$	−8.50781	−	3.79502i	−0.346752	−	0.154673i
$603$	−32.0031	+	6.28147i	−1.30327	+	0.255801i
$604$	−15.2246			−0.619480
$605$	−24.9321	+	43.1836i	−1.01363	+	1.75566i
$606$	−4.74763	+	10.4430i	−0.192859	+	0.424218i
$607$	10.9051	−	6.29608i	0.442625	−	0.255550i	−0.262085	−	0.965045i	$-0.584410\pi$
$607$	10.9051	−	6.29608i	0.442625	−	0.255550i	0.704711	+	0.709495i	$0.251077\pi$
$608$	−0.569660	−	0.986680i	−0.0231028	−	0.0400152i
$609$	12.6216	+	14.2599i	0.511455	+	0.577841i
$610$	10.5718	−	18.3108i	0.428038	−	0.741383i
$611$		−	20.3112i		−	0.821704i
$612$	−5.20713	+	1.02204i	−0.210486	+	0.0413135i
$613$	−9.82017			−0.396633			−0.198317	−	0.980138i	$-0.563547\pi$
$613$	−9.82017			−0.396633			−0.198317	+	0.980138i	$0.563547\pi$
$614$	5.44981	−	9.43935i	0.219937	−	0.380941i
$615$	3.14744	+	32.3774i	0.126917	+	1.30558i
$616$	−14.9379	+	1.55953i	−0.601864	+	0.0628351i
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	−0.564022	−	0.825760i	$-0.690747\pi$
$617$	−3.25158	+	1.87730i	−0.130904	+	0.0755772i	0.433118	+	0.901337i	$0.357413\pi$
$618$	8.25742	−	5.90135i	0.332162	−	0.237387i
$619$	9.56902	+	5.52468i	0.384611	+	0.222055i	0.679823	−	0.733376i	$-0.262057\pi$
$619$	9.56902	+	5.52468i	0.384611	+	0.222055i	−0.295211	+	0.955432i	$0.595390\pi$
$620$		−	19.6646i		−	0.789748i
$621$	13.8880	+	13.1071i	0.557305	+	0.525968i
$622$		−	8.23637i		−	0.330248i
$623$	−1.80387	−	2.48645i	−0.0722706	−	0.0996176i
$624$	1.73205	+	2.42356i	0.0693375	+	0.0970201i
$625$	13.6638	+	23.6664i	0.546551	+	0.946654i
$626$	16.9011	+	29.2736i	0.675505	+	1.17001i
$627$	1.08386	+	11.1496i	0.0432852	+	0.445270i
$628$	8.68358	+	5.01347i	0.346513	+	0.200059i
$629$	16.2692			0.648696
$630$	−5.47215	−	17.8265i	−0.218016	−	0.710223i
$631$	19.4921			0.775969			0.387984	−	0.921666i	$-0.373171\pi$
$631$	19.4921			0.775969			0.387984	+	0.921666i	$0.373171\pi$
$632$	−11.2830	−	6.51422i	−0.448812	−	0.259122i
$633$	16.2583	+	7.39139i	0.646208	+	0.293781i
$634$	−3.36545	−	5.82913i	−0.133659	−	0.231504i
$635$	−7.84294	−	13.5844i	−0.311238	−	0.539080i
$636$		0			0
$637$	2.48665	+	11.7793i	0.0985245	+	0.466714i
$638$			23.5900i			0.933938i
$639$	12.8323	+	4.39230i	0.507637	+	0.173757i
$640$			2.34936i			0.0928665i
$641$	−22.6669	−	13.0868i	−0.895290	−	0.516896i	−0.0196208	−	0.999807i	$-0.506246\pi$
$641$	−22.6669	−	13.0868i	−0.895290	−	0.516896i	−0.875669	+	0.482912i	$0.839579\pi$
$642$	0.790267	+	8.12940i	0.0311893	+	0.320842i
$643$	9.50955	−	5.49034i	0.375020	−	0.216518i	−0.300629	−	0.953741i	$-0.597197\pi$
$643$	9.50955	−	5.49034i	0.375020	−	0.216518i	0.675649	+	0.737223i	$0.263863\pi$
$644$	−1.00964	−	9.67082i	−0.0397854	−	0.381084i
$645$	11.6570	−	8.33092i	0.458993	−	0.328029i
$646$	1.00763	−	1.74527i	0.0396447	−	0.0686666i
$647$	32.0126			1.25855			0.629273	−	0.777185i	$-0.283353\pi$
$647$	32.0126			1.25855			0.629273	+	0.777185i	$0.283353\pi$
$648$	−5.51501	+	7.11229i	−0.216650	+	0.279397i
$649$		−	12.6570i		−	0.496833i
$650$	0.446715	−	0.773734i	0.0175216	−	0.0303483i
$651$	−37.5853	+	7.65534i	−1.47308	+	0.300036i
$652$	6.00158	+	10.3950i	0.235040	+	0.407101i
$653$	19.3686	−	11.1825i	0.757952	−	0.437604i	−0.0706080	−	0.997504i	$-0.522494\pi$
$653$	19.3686	−	11.1825i	0.757952	−	0.437604i	0.828560	+	0.559900i	$0.189161\pi$
$654$	−7.30374	+	0.710004i	−0.285599	+	0.0277633i
$655$	−8.77843	+	15.2047i	−0.343002	+	0.594097i
$656$	−7.99419			−0.312121
$657$	15.1634	+	5.19020i	0.591579	+	0.202489i
$658$	−28.5358	−	12.7288i	−1.11244	−	0.496219i
$659$	−19.2546	−	11.1166i	−0.750053	−	0.433043i	0.0756603	−	0.997134i	$-0.475894\pi$
$659$	−19.2546	−	11.1166i	−0.750053	−	0.433043i	−0.825713	+	0.564091i	$0.809227\pi$
$660$	9.56002	−	21.0284i	0.372123	−	0.818531i
$661$	−9.13646	+	5.27494i	−0.355367	+	0.205171i	−0.667047	−	0.745016i	$-0.732442\pi$
$661$	−9.13646	+	5.27494i	−0.355367	+	0.205171i	0.311679	+	0.950187i	$0.399108\pi$
$662$	−27.7621	+	16.0284i	−1.07900	+	0.622963i
$663$	−2.18068	+	4.79667i	−0.0846907	+	0.186287i
$664$	10.8651	+	6.27298i	0.421649	+	0.243439i
$665$	6.46754	+	2.88493i	0.250801	+	0.111873i
$666$	20.7917	−	18.1408i	0.805664	−	0.702941i
$667$	−15.2723			−0.591344
$668$	−8.57472	+	14.8518i	−0.331766	+	0.574635i
$669$	−12.4280	+	1.20814i	−0.480494	+	0.0467093i
$670$	−22.1187	+	12.7702i	−0.854519	+	0.493357i
$671$	−25.5442	−	44.2438i	−0.986121	−	1.70801i
$672$	4.49038	−	0.914596i	0.173220	−	0.0352813i
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	−0.608498	−	0.793555i	$-0.708228\pi$
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	0.991488	+	0.130197i	$0.0415610\pi$
$674$			24.2246i			0.933096i
$675$	2.62644	+	0.622947i	0.101092	+	0.0239772i
$676$	−10.0421			−0.386235
$677$	−7.96449	+	13.7949i	−0.306100	+	0.530181i	−0.977506	−	0.210909i	$-0.932358\pi$
$677$	−7.96449	+	13.7949i	−0.306100	+	0.530181i	0.671405	+	0.741090i	$0.265691\pi$
$678$	−9.62785	+	6.88075i	−0.369755	+	0.264254i
$679$	−1.26108	−	12.0793i	−0.0483960	−	0.463560i
$680$	−3.59886	+	2.07781i	−0.138010	+	0.0796802i
$681$	−2.13771	−	21.9904i	−0.0819171	−	0.842673i
$682$	−41.1490	−	23.7574i	−1.57568	−	0.909718i
$683$			19.0269i			0.728042i	0.931391	+	0.364021i	$0.118596\pi$
$683$			19.0269i			0.728042i	−0.931391	+	0.364021i	$0.881404\pi$
$684$	−0.658305	−	3.35397i	−0.0251709	−	0.128242i
$685$			18.7664i			0.717028i
$686$	18.1075	+	3.88839i	0.691346	+	0.148459i
$687$	3.22157	−	7.08623i	0.122910	−	0.270356i
$688$	1.76053	+	3.04933i	0.0671196	+	0.116254i
$689$		0			0
$690$	13.6139	+	6.18919i	0.518271	+	0.235618i
$691$	0.139477	+	0.0805273i	0.00530597	+	0.00306340i	0.502651	−	0.864490i	$-0.332358\pi$
$691$	0.139477	+	0.0805273i	0.00530597	+	0.00306340i	−0.497345	+	0.867553i	$0.665692\pi$
$692$	1.98748			0.0755525
$693$	−43.9138	−	10.0860i	−1.66815	−	0.383136i
$694$	−22.7999			−0.865471
$695$	42.2396	+	24.3870i	1.60224	+	0.925053i
$696$	−0.696415	−	7.16396i	−0.0263976	−	0.271549i
$697$	−7.07017	−	12.2459i	−0.267802	−	0.463847i
$698$	1.42253	+	2.46389i	0.0538434	+	0.0932595i
$699$	−2.16932	−	3.03540i	−0.0820511	−	0.114809i
$700$	−0.807090	−	1.11249i	−0.0305051	−	0.0420482i
$701$		−	9.98234i		−	0.377028i	−0.982071	−	0.188514i	$-0.939633\pi$
$701$		−	9.98234i		−	0.377028i	0.982071	−	0.188514i	$-0.0603670\pi$
$702$	2.56160	+	8.56160i	0.0966814	+	0.323137i
$703$			10.4792i			0.395229i
$704$	4.91614	+	2.83834i	0.185284	+	0.106974i
$705$	39.0983	−	27.9425i	1.47253	−	1.05237i
$706$	6.18709	−	3.57212i	0.232854	−	0.134438i
$707$	17.4283	−	1.81953i	0.655460	−	0.0684306i
$708$	0.373656	+	3.84377i	0.0140429	+	0.144458i
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	−0.540821	−	0.841138i	$-0.681886\pi$
$709$	12.1962	−	21.1244i	0.458036	−	0.793342i	0.998857	+	0.0477959i	$0.0152197\pi$
$710$	10.6216			0.398621
$711$	−25.6961	−	29.4512i	−0.963679	−	1.10450i
$712$			1.16106i			0.0435125i
$713$	15.3806	−	26.6400i	0.576008	−	0.997676i
$714$	5.37238	+	6.06971i	0.201056	+	0.227153i
$715$	−11.4684	−	19.8639i	−0.428894	−	0.742867i
$716$	7.19773	−	4.15561i	0.268992	−	0.155302i
$717$	−7.27004	+	15.9913i	−0.271504	+	0.597207i
$718$	−5.80186	+	10.0491i	−0.216523	+	0.375030i
$719$	−16.2692			−0.606739			−0.303370	−	0.952873i	$-0.598112\pi$
$719$	−16.2692			−0.606739			−0.303370	+	0.952873i	$0.598112\pi$
$720$	−2.28245	+	6.66826i	−0.0850619	+	0.248512i
$721$	−14.1588	−	6.31570i	−0.527300	−	0.235209i
$722$	−15.3303	−	8.85097i	−0.570536	−	0.329399i
$723$	18.1841	−	1.76769i	0.676274	−	0.0657412i
$724$	13.3837	−	7.72706i	0.497400	−	0.287174i
$725$	−1.86955	+	1.07938i	−0.0694332	+	0.0400873i
$726$	−21.3752	−	29.9091i	−0.793307	−	1.11003i
$727$	20.6626	+	11.9296i	0.766335	+	0.442444i	0.831566	−	0.555427i	$-0.187445\pi$
$727$	20.6626	+	11.9296i	0.766335	+	0.442444i	−0.0652306	+	0.997870i	$0.520778\pi$
$728$	1.85366	−	4.15561i	0.0687013	−	0.154017i
$729$	−22.5632	+	14.8291i	−0.835673	+	0.549227i
$730$	12.5511			0.464536
$731$	−3.11408	+	5.39374i	−0.115178	+	0.199495i
$732$	9.06354	+	12.6821i	0.334998	+	0.468744i
$733$	10.6259	−	6.13486i	0.392476	−	0.226596i	−0.290756	−	0.956797i	$-0.593907\pi$
$733$	10.6259	−	6.13486i	0.392476	−	0.226596i	0.683233	+	0.730201i	$0.260574\pi$
$734$	−3.91747	−	6.78525i	−0.144596	−	0.250448i
$735$	−19.2539	+	20.9917i	−0.710189	+	0.774292i
$736$	−1.83755	+	3.18272i	−0.0677329	+	0.117317i
$737$			61.7125i			2.27321i
$738$	−22.6902	−	7.76652i	−0.835237	−	0.285890i
$739$	41.8891			1.54092			0.770459	−	0.637490i	$-0.220027\pi$
$739$	41.8891			1.54092			0.770459	+	0.637490i	$0.220027\pi$
$740$	10.8044	−	18.7137i	0.397177	−	0.687931i
$741$	−3.08959	−	1.40460i	−0.113499	−	0.0515992i
$742$		0			0
$743$	43.9160	−	25.3549i	1.61112	−	0.930182i	0.622011	−	0.783008i	$-0.286316\pi$
$743$	43.9160	−	25.3549i	1.61112	−	0.930182i	0.989111	−	0.147173i	$-0.0470176\pi$
$744$	13.1977	+	6.00000i	0.483852	+	0.219971i
$745$	−2.43690	−	1.40695i	−0.0892813	−	0.0515466i
$746$			25.6677i			0.939762i
$747$	24.7445	+	28.3605i	0.905355	+	1.03766i
$748$			10.0411i			0.367137i
$749$	10.0987	−	7.32642i	0.368999	−	0.267701i
$750$	−18.1466	+	1.76405i	−0.662621	+	0.0644140i
$751$	16.3683	+	28.3508i	0.597289	+	1.03454i	0.993219	+	0.116255i	$0.0370890\pi$
$751$	16.3683	+	28.3508i	0.597289	+	1.03454i	−0.395930	+	0.918281i	$0.629578\pi$
$752$	5.90494	+	10.2277i	0.215331	+	0.372964i
$753$	−41.2893	+	29.5083i	−1.50467	+	1.07534i
$754$	−6.18951	−	3.57351i	−0.225408	−	0.130140i
$755$	−35.7680			−1.30173
$756$	13.6338	+	1.76657i	0.495855	+	0.0642496i
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$	13.0809	+	7.55227i	0.475120	+	0.274311i
$759$	29.3985	−	21.0103i	1.06710	−	0.762626i
$760$	−1.33834	−	2.31806i	−0.0485465	−	0.0840850i
$761$	21.8509	+	37.8469i	0.792096	+	1.37195i	0.924667	+	0.380777i	$0.124343\pi$
$761$	21.8509	+	37.8469i	0.792096	+	1.37195i	−0.132571	+	0.991174i	$0.542323\pi$
$762$	11.5101	−	1.11891i	0.416966	−	0.0405337i
$763$	6.58231	+	9.07305i	0.238296	+	0.328466i
$764$			12.3381i			0.446376i
$765$	−12.2334	+	2.40114i	−0.442300	+	0.0868132i
$766$		−	1.52664i		−	0.0551599i
$767$	3.32093	+	1.91734i	0.119912	+	0.0692311i
$768$	−1.57675	−	0.716830i	−0.0568962	−	0.0258664i
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.986417	−	0.164262i	$-0.947476\pi$
$769$	−37.0864	+	21.4118i	−1.33737	+	0.772131i	−0.350953	+	0.936393i	$0.614142\pi$
$770$	−35.0944	+	3.66388i	−1.26471	+	0.132037i
$771$	−12.0284	−	5.46841i	−0.433193	−	0.196940i
$772$	2.19694	−	3.80521i	0.0790696	−	0.136953i
$773$	−21.6051			−0.777080			−0.388540	−	0.921432i	$-0.627020\pi$
$773$	−21.6051			−0.777080			−0.388540	+	0.921432i	$0.627020\pi$
$774$	2.03449	+	10.3654i	0.0731281	+	0.372577i
$775$		−	4.34816i		−	0.156191i
$776$	−2.29517	+	3.97536i	−0.0823919	+	0.142707i
$777$	−39.9741	−	13.3655i	−1.43406	−	0.479484i
$778$	−7.44483	−	12.8948i	−0.266910	−	0.462302i
$779$	7.88771	−	4.55397i	0.282606	−	0.163163i
$780$	4.06921	+	5.69381i	0.145701	+	0.203871i
$781$	12.8323	−	22.2262i	0.459175	−	0.795315i
$782$	−6.50061			−0.232461
$783$	4.98328	−	21.0103i	0.178088	−	0.750847i
$784$	−4.67667	−	5.20853i	−0.167024	−	0.186019i
$785$	20.4008	+	11.7784i	0.728137	+	0.420390i
$786$	−7.52607	−	10.5308i	−0.268446	−	0.375621i
$787$	−44.4307	+	25.6521i	−1.58378	+	0.914398i	−0.589484	+	0.807780i	$0.700669\pi$
$787$	−44.4307	+	25.6521i	−1.58378	+	0.914398i	−0.994300	+	0.106618i	$0.965998\pi$
$788$	9.42799	−	5.44325i	0.335858	−	0.193908i
$789$	−21.0071	+	2.04212i	−0.747872	+	0.0727014i
$790$	−26.5077	−	15.3042i	−0.943102	−	0.544500i
$791$	16.5086	+	7.36387i	0.586978	+	0.261829i
$792$	11.1962	+	12.8323i	0.397838	+	0.455975i
$793$	15.4781			0.549644
$794$	14.3935	−	24.9302i	0.510805	−	0.884740i
$795$		0			0
$796$	−23.8733	+	13.7832i	−0.846166	+	0.488534i
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	0.849662	−	0.527327i	$-0.176806\pi$
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	−0.881510	+	0.472166i	$0.843472\pi$
$798$	−3.90956	+	3.46040i	−0.138397	+	0.122497i
$799$	−10.4448	+	18.0910i	−0.369512	+	0.640013i
$800$			0.519482i			0.0183665i
$801$	−1.12799	+	3.29547i	−0.0398557	+	0.116440i
$802$	38.1735			1.34795
$803$	15.1634	−	26.2637i	0.535103	−	0.926826i
$804$	−1.82185	−	18.7412i	−0.0642517	−	0.660951i
$805$	−2.37201	−	22.7202i	−0.0836023	−	0.800783i
$806$	12.4668	−	7.19773i	0.439125	−	0.253529i
$807$	3.90951	−	2.79402i	0.137621	−	0.0983541i
$808$	−5.73577	−	3.31155i	−0.201784	−	0.116500i
$809$		−	40.6883i		−	1.43052i	−0.698857	−	0.715262i	$-0.746308\pi$
$809$		−	40.6883i		−	1.43052i	0.698857	−	0.715262i	$-0.253692\pi$
$810$	−12.9567	+	16.7093i	−0.455253	+	0.587106i
$811$		−	0.378710i		−	0.0132983i	−0.999978	−	0.00664916i	$-0.997883\pi$
$811$		−	0.378710i		−	0.0132983i	0.999978	−	0.00664916i	$-0.00211651\pi$
$812$	−8.89940	+	6.45634i	−0.312308	+	0.226573i
$813$	−3.23068	−	4.52051i	−0.113305	−	0.158541i
$814$	−26.1062	−	45.2173i	−0.915023	−	1.58487i
$815$	14.0999	+	24.4217i	0.493896	+	0.855453i
$816$	−0.296428	−	3.04933i	−0.0103771	−	0.106748i
$817$	−3.47416	−	2.00581i	−0.121545	−	0.0701743i
$818$	−6.96694			−0.243593
$819$	9.29858	−	9.99414i	0.324919	−	0.349224i
$820$	−18.7812			−0.655868
$821$	11.4968	+	6.63771i	0.401243	+	0.231658i	0.687020	−	0.726638i	$-0.258918\pi$
$821$	11.4968	+	6.63771i	0.401243	+	0.231658i	−0.285777	+	0.958296i	$0.592252\pi$
$822$	−12.5949	−	5.72596i	−0.439299	−	0.199716i
$823$	−13.8711	−	24.0255i	−0.483517	−	0.837476i	0.516304	−	0.856405i	$-0.327308\pi$
$823$	−13.8711	−	24.0255i	−0.483517	−	0.837476i	−0.999821	+	0.0189295i	$0.993974\pi$
$824$	2.92989	+	5.07471i	0.102067	+	0.176786i
$825$	2.11388	−	4.64974i	0.0735959	−	0.161883i
$826$	4.77491	−	3.46410i	0.166140	−	0.120531i
$827$		−	27.7183i		−	0.963859i	−0.876210	−	0.481929i	$-0.839936\pi$
$827$		−	27.7183i		−	0.963859i	0.876210	−	0.481929i	$-0.160064\pi$
$828$	−8.30766	+	7.24842i	−0.288711	+	0.251900i
$829$		−	42.7361i		−	1.48429i	−0.670242	−	0.742143i	$-0.733810\pi$
$829$		−	42.7361i		−	1.48429i	0.670242	−	0.742143i	$-0.266190\pi$
$830$	25.5261	+	14.7375i	0.886023	+	0.511545i
$831$	1.68943	+	17.3790i	0.0586057	+	0.602872i
$832$	−1.48943	+	0.859925i	−0.0516368	+	0.0298125i
$833$	3.84257	−	11.7705i	0.133137	−	0.407822i
$834$	−29.2552	+	20.9079i	−1.01303	+	0.723981i
$835$	−20.1451	+	34.8923i	−0.697149	+	1.20750i
$836$	−6.46754			−0.223685
$837$	31.6305	+	29.8519i	1.09331	+	1.03183i
$838$			34.8463i			1.20375i
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	−0.897331	−	0.441359i	$-0.854496\pi$
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	0.830894	+	0.556431i	$0.187830\pi$
$840$	10.5495	−	2.14871i	0.363993	−	0.0741376i
$841$	−5.86545	−	10.1593i	−0.202257	−	0.350319i
$842$	−4.92936	+	2.84597i	−0.169877	+	0.0980785i
$843$	8.40038	−	0.816609i	0.289324	−	0.0281255i
$844$	−5.15561	+	8.92978i	−0.177463	+	0.307376i
$845$	−23.5925			−0.811608
$846$	6.82382	+	34.7663i	0.234608	+	1.19529i
$847$	−22.8760	+	51.2842i	−0.786028	+	1.76215i
$848$		0			0
$849$	−2.01989	+	4.44300i	−0.0693225	+	0.152483i
$850$	−0.795769	+	0.459437i	−0.0272946	+	0.0157586i
$851$	29.2738	−	16.9013i	1.00349	−	0.579368i
$852$	−3.24083	+	7.12860i	−0.111029	+	0.244222i
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.0242213	−	0.999707i	$-0.507711\pi$
$853$	−26.3470	−	15.2114i	−0.902103	−	0.520830i	−0.877882	+	0.478877i	$0.841044\pi$
$854$	9.69992	−	21.7456i	0.331924	−	0.744121i
$855$	−1.54660	−	7.87967i	−0.0528924	−	0.269479i
$856$	−4.71563			−0.161177
$857$	19.4657	−	33.7156i	0.664937	−	1.15170i	−0.314366	−	0.949302i	$-0.601792\pi$
$857$	19.4657	−	33.7156i	0.664937	−	1.15170i	0.979303	−	0.202402i	$-0.0648748\pi$
$858$	16.8307	−	1.63613i	0.574591	−	0.0558565i
$859$	11.5922	−	6.69275i	0.395520	−	0.228354i	−0.289029	−	0.957320i	$-0.593332\pi$
$859$	11.5922	−	6.69275i	0.395520	−	0.228354i	0.684549	+	0.728967i	$0.259999\pi$
$860$	4.13611	+	7.16396i	0.141040	+	0.244289i
$861$	7.31145	+	35.8969i	0.249174	+	1.22336i
$862$	15.1468	−	26.2350i	0.515901	−	0.893567i
$863$			21.7219i			0.739424i	0.929146	+	0.369712i	$0.120544\pi$
$863$			21.7219i			0.739424i	−0.929146	+	0.369712i	$0.879456\pi$
$864$	−3.77894	−	3.56645i	−0.128562	−	0.121333i
$865$	4.66929			0.158761
$866$	11.8047	−	20.4463i	0.401139	−	0.694794i
$867$	−19.5469	+	13.9697i	−0.663849	+	0.474434i
$868$	−2.29950	−	22.0257i	−0.0780502	−	0.747602i
$869$	−64.0496	+	36.9791i	−2.17273	+	1.25443i
$870$	−1.63613	−	16.8307i	−0.0554700	−	0.570614i
$871$	−16.1920	−	9.34845i	−0.548645	−	0.316760i
$872$		−	4.23669i		−	0.143473i
$873$	−10.3766	+	9.05358i	−0.351195	+	0.306417i
$874$		−	4.18711i		−	0.141631i
$875$	16.3542	+	22.5426i	0.552872	+	0.762078i
$876$	−3.82955	+	8.42356i	−0.129388	+	0.284606i
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	0.862695	−	0.505725i	$-0.168775\pi$
$877$	−0.196152	−	0.339746i	−0.00662360	−	0.0114724i	−0.869318	+	0.494253i	$0.835442\pi$
$878$	−12.5101	−	21.6681i	−0.422196	−	0.731265i
$879$	−12.7936	−	5.81628i	−0.431518	−	0.196178i
$880$	11.5498	+	6.66826i	0.389343	+	0.224787i
$881$	43.3363			1.46004			0.730018	−	0.683427i	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$	−8.21376	−	19.3270i	−0.276572	−	0.650775i
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	2.17403			0.0731618			0.0365809	+	0.999331i	$0.488353\pi$
$884$	−2.63455	−	1.52106i	−0.0886096	−	0.0511588i
$885$	0.877852	+	9.03038i	0.0295087	+	0.303553i
$886$	11.5150	+	19.9446i	0.386854	+	0.670051i
$887$	−5.72215	−	9.91105i	−0.192131	−	0.332781i	0.753825	−	0.657075i	$-0.228207\pi$
$887$	−5.72215	−	9.91105i	−0.192131	−	0.332781i	−0.945956	+	0.324294i	$0.894873\pi$
$888$	9.26298	+	12.9612i	0.310845	+	0.434948i
$889$	−10.3732	−	14.2984i	−0.347905	−	0.479551i
$890$			2.72774i			0.0914341i
$891$	19.3116	+	47.2996i	0.646963	+	1.58460i
$892$		−	7.20913i		−	0.241379i
$893$	−11.6526	−	6.72762i	−0.389939	−	0.225131i
$894$	1.68780	−	1.20623i	0.0564486	−	0.0403423i
$895$	16.9100	−	9.76302i	0.565240	−	0.326342i
$896$	0.274725	+	2.63145i	0.00917793	+	0.0879106i
$897$	1.05923	+	10.8962i	0.0353668	+	0.363815i
$898$	−7.95142	+	13.7723i	−0.265342	+	0.459586i
$899$	−34.7832			−1.16009
$900$	−0.504688	+	1.47446i	−0.0168229	+	0.0491488i
$901$		0			0
$902$	−22.6902	+	39.3006i	−0.755501	+	1.30857i
$903$	12.0825	−	10.6943i	0.402079	−	0.355886i
$904$	−3.41614	−	5.91693i	−0.113619	−	0.196794i
$905$	31.4430	−	18.1536i	1.04520	−	0.603447i
$906$	10.9134	−	24.0054i	0.362575	−	0.797527i
$907$	26.9446	−	46.6694i	0.894680	−	1.54963i	0.0604797	−	0.998169i	$-0.480737\pi$
$907$	26.9446	−	46.6694i	0.894680	−	1.54963i	0.834200	−	0.551462i	$-0.185930\pi$
$908$	12.7560			0.423323
$909$	−13.0628	−	14.9717i	−0.433266	−	0.496580i
$910$	4.35492	−	9.76302i	0.144364	−	0.323641i
$911$	−7.00460	−	4.04411i	−0.232073	−	0.133987i	0.379455	−	0.925210i	$-0.376111\pi$
$911$	−7.00460	−	4.04411i	−0.232073	−	0.133987i	−0.611528	+	0.791223i	$0.709445\pi$
$912$	1.96410	−	0.190932i	0.0650379	−	0.00632240i
$913$	61.6777	−	35.6097i	2.04124	−	1.17851i
$914$	−4.90702	+	2.83307i	−0.162310	+	0.0937096i
$915$	21.2935	+	29.7948i	0.703942	+	0.984986i
$916$	3.89208	+	2.24709i	0.128598	+	0.0742460i
$917$	−8.05450	+	18.0569i	−0.265983	+	0.596290i
$918$	2.12112	−	8.94300i	0.0700075	−	0.295163i
$919$	25.6751			0.846943			0.423472	−	0.905909i	$-0.360811\pi$
$919$	25.6751			0.846943			0.423472	+	0.905909i	$0.360811\pi$
$920$	−4.31705	+	7.47736i	−0.142329	+	0.246521i
$921$	10.9770	+	15.3594i	0.361703	+	0.506110i
$922$	27.2438	−	15.7292i	0.897226	−	0.518014i
$923$	3.88777	+	6.73382i	0.127968	+	0.221646i
$924$	8.24892	−	24.6713i	0.271370	−	0.811625i
$925$	2.38903	−	4.13792i	0.0785507	−	0.136054i
$926$		−	9.10296i		−	0.299142i
$927$	3.38581	+	17.2502i	0.111205	+	0.566570i
$928$	4.15561			0.136415
$929$	5.42618	−	9.39842i	0.178027	−	0.308352i	−0.763177	−	0.646189i	$-0.776362\pi$
$929$	5.42618	−	9.39842i	0.178027	−	0.308352i	0.941205	+	0.337837i	$0.109695\pi$
$930$	31.0062	+	14.0961i	1.01673	+	0.462231i
$931$	7.58147	+	2.47504i	0.248473	+	0.0811161i
$932$	1.86545	−	1.07702i	0.0611048	−	0.0352789i
$933$	12.9867	+	5.90408i	0.425167	+	0.193291i
$934$	26.2433	+	15.1516i	0.858708	+	0.495775i
$935$			23.5900i			0.771477i
$936$	−5.06295	+	0.993738i	−0.165488	+	0.0324814i
$937$		−	0.458120i		−	0.0149661i	−0.999972	−	0.00748306i	$-0.997618\pi$
$937$		−	0.458120i		−	0.0149661i	0.999972	−	0.00748306i	$-0.00238195\pi$
$938$	−23.2812	+	16.8900i	−0.760158	+	0.551479i
$939$	−58.2725	+	5.66473i	−1.90165	+	0.184861i
$940$	13.8728	+	24.0284i	0.452482	+	0.783721i
$941$	−3.68890	−	6.38937i	−0.120255	−	0.208287i	0.799613	−	0.600515i	$-0.205038\pi$
$941$	−3.68890	−	6.38937i	−0.120255	−	0.208287i	−0.919868	+	0.392228i	$0.871704\pi$
$942$	−14.1297	+	10.0981i	−0.460369	+	0.329013i
$943$	−25.4433	−	14.6897i	−0.828548	−	0.478362i
$944$	−2.22966			−0.0725693
$945$	32.0306	+	4.15031i	1.04195	+	0.135009i
$946$	19.9879			0.649862
$947$	−10.3846	−	5.99552i	−0.337453	−	0.194828i	0.321692	−	0.946844i	$-0.395748\pi$
$947$	−10.3846	−	5.99552i	−0.337453	−	0.194828i	−0.659145	+	0.752016i	$0.729082\pi$
$948$	18.3593	−	13.1209i	0.596282	−	0.426146i
$949$	4.59401	+	7.95706i	0.149128	+	0.258297i
$950$	−0.295928	−	0.512563i	−0.00960118	−	0.0166297i
$951$	11.6036	−	1.12799i	0.376271	−	0.0365777i
$952$	−3.78802	+	2.74813i	−0.122770	+	0.0890674i
$953$		−	58.6883i		−	1.90110i	−0.310572	−	0.950550i	$-0.600521\pi$
$953$		−	58.6883i		−	1.90110i	0.310572	−	0.950550i	$-0.399479\pi$
$954$		0			0
$955$			28.9866i			0.937983i
$956$	−8.78317	−	5.07096i	−0.284068	−	0.164007i
$957$	−37.1957	−	16.9100i	−1.20237	−	0.546624i
$958$	4.03816	−	2.33143i	0.130467	−	0.0753251i
$959$	2.19448	+	21.0197i	0.0708633	+	0.678763i
$960$	−3.70436	−	1.68409i	−0.119558	−	0.0543538i
$961$	19.5300	−	33.8270i	0.630000	−	1.09119i
$962$	15.8187			0.510016
$963$	−13.3846	−	4.58134i	−0.431311	−	0.147632i
$964$			10.5481i			0.339731i
$965$	5.16140	−	8.93981i	0.166151	−	0.287783i
$966$	15.9723	+	5.34038i	0.513899	+	0.171824i
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	0.806632	−	0.591054i	$-0.201288\pi$
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	−0.915184	+	0.403037i	$0.867955\pi$
$968$	18.3810	−	10.6123i	0.590789	−	0.341092i
$969$	2.02956	+	2.83985i	0.0651988	+	0.0912290i
$970$	−5.39218	+	9.33953i	−0.173133	+	0.299874i
$971$	−6.40724			−0.205618			−0.102809	−	0.994701i	$-0.532783\pi$
$971$	−6.40724			−0.205618			−0.102809	+	0.994701i	$0.532783\pi$
$972$	−7.26102	−	13.7941i	−0.232897	−	0.442446i
$973$	50.1631	+	22.3759i	1.60816	+	0.717338i
$974$	16.8720	+	9.74105i	0.540613	+	0.312123i
$975$	0.899769	+	1.25900i	0.0288157	+	0.0403201i
$976$	−7.79396	+	4.49985i	−0.249479	+	0.144037i
$977$	11.7769	−	6.79937i	0.376775	−	0.217531i	−0.299639	−	0.954053i	$-0.596866\pi$
$977$	11.7769	−	6.79937i	0.376775	−	0.217531i	0.676414	+	0.736521i	$0.263533\pi$
$978$	−20.6925	+	2.01154i	−0.661674	+	0.0643220i
$979$	5.70793	+	3.29547i	0.182426	+	0.105324i
$980$	−10.9872	−	12.2367i	−0.350972	−	0.390887i
$981$	4.11604	−	12.0252i	0.131415	−	0.383934i
$982$	20.4886			0.653819
$983$	11.3849	−	19.7192i	0.363122	−	0.628946i	−0.625351	−	0.780344i	$-0.715044\pi$
$983$	11.3849	−	19.7192i	0.363122	−	0.628946i	0.988473	+	0.151398i	$0.0483774\pi$
$984$	5.73047	−	12.6049i	0.182681	−	0.401829i
$985$	22.1497	−	12.7882i	0.705749	−	0.407464i
$986$	3.67528	+	6.36577i	0.117045	+	0.202728i
$987$	40.5255	−	35.8696i	1.28994	−	1.14174i
$988$	0.979729	−	1.69694i	0.0311693	−	0.0539869i
$989$			12.9402i			0.411475i
$990$	26.3038	+	30.1476i	0.835989	+	0.958154i
$991$	−26.9905			−0.857383			−0.428691	−	0.903451i	$-0.641025\pi$
$991$	−26.9905			−0.857383			−0.428691	+	0.903451i	$0.641025\pi$
$992$	−4.18509	+	7.24879i	−0.132877	+	0.230149i
$993$	−5.37223	−	55.2636i	−0.170483	−	1.75374i
$994$	11.8969	−	1.24205i	0.377348	−	0.0393954i
$995$	−56.0869	+	32.3818i	−1.77807	+	1.02657i
$996$	−17.6794	+	12.6350i	−0.560193	+	0.400354i
$997$	−16.7263	−	9.65694i	−0.529728	−	0.305838i	0.211178	−	0.977448i	$-0.432270\pi$
$997$	−16.7263	−	9.65694i	−0.529728	−	0.305838i	−0.740906	+	0.671609i	$0.765603\pi$
$998$		−	10.2520i		−	0.324520i
$999$	13.6994	+	45.7873i	0.433430	+	1.44865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.2.m.a.83.3	yes	16
3.2	odd	2		378.2.m.a.251.6		16
4.3	odd	2		1008.2.cc.b.209.3		16
7.2	even	3		882.2.l.a.227.7		16
7.3	odd	6		882.2.t.b.803.8		16
7.4	even	3		882.2.t.b.803.5		16
7.5	odd	6		882.2.l.a.227.6		16
7.6	odd	2	inner	126.2.m.a.83.2	yes	16
9.2	odd	6		1134.2.d.a.1133.7		16
9.4	even	3		378.2.m.a.125.7		16
9.5	odd	6	inner	126.2.m.a.41.2	✓	16
9.7	even	3		1134.2.d.a.1133.10		16
12.11	even	2		3024.2.cc.b.2897.2		16
21.2	odd	6		2646.2.l.b.521.2		16
21.5	even	6		2646.2.l.b.521.3		16
21.11	odd	6		2646.2.t.a.1979.3		16
21.17	even	6		2646.2.t.a.1979.2		16
21.20	even	2		378.2.m.a.251.7		16
28.27	even	2		1008.2.cc.b.209.6		16
36.23	even	6		1008.2.cc.b.545.6		16
36.31	odd	6		3024.2.cc.b.881.7		16
63.4	even	3		2646.2.l.b.1097.7		16
63.5	even	6		882.2.t.b.815.5		16
63.13	odd	6		378.2.m.a.125.6		16
63.20	even	6		1134.2.d.a.1133.2		16
63.23	odd	6		882.2.t.b.815.8		16
63.31	odd	6		2646.2.l.b.1097.6		16
63.32	odd	6		882.2.l.a.509.2		16
63.34	odd	6		1134.2.d.a.1133.15		16
63.40	odd	6		2646.2.t.a.2285.3		16
63.41	even	6	inner	126.2.m.a.41.3	yes	16
63.58	even	3		2646.2.t.a.2285.2		16
63.59	even	6		882.2.l.a.509.3		16
84.83	odd	2		3024.2.cc.b.2897.7		16
252.139	even	6		3024.2.cc.b.881.2		16
252.167	odd	6		1008.2.cc.b.545.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	9.5	odd	6	inner
126.2.m.a.41.3	yes	16	63.41	even	6	inner
126.2.m.a.83.2	yes	16	7.6	odd	2	inner
126.2.m.a.83.3	yes	16	1.1	even	1	trivial
378.2.m.a.125.6		16	63.13	odd	6
378.2.m.a.125.7		16	9.4	even	3
378.2.m.a.251.6		16	3.2	odd	2
378.2.m.a.251.7		16	21.20	even	2
882.2.l.a.227.6		16	7.5	odd	6
882.2.l.a.227.7		16	7.2	even	3
882.2.l.a.509.2		16	63.32	odd	6
882.2.l.a.509.3		16	63.59	even	6
882.2.t.b.803.5		16	7.4	even	3
882.2.t.b.803.8		16	7.3	odd	6
882.2.t.b.815.5		16	63.5	even	6
882.2.t.b.815.8		16	63.23	odd	6
1008.2.cc.b.209.3		16	4.3	odd	2
1008.2.cc.b.209.6		16	28.27	even	2
1008.2.cc.b.545.3		16	252.167	odd	6
1008.2.cc.b.545.6		16	36.23	even	6
1134.2.d.a.1133.2		16	63.20	even	6
1134.2.d.a.1133.7		16	9.2	odd	6
1134.2.d.a.1133.10		16	9.7	even	3
1134.2.d.a.1133.15		16	63.34	odd	6
2646.2.l.b.521.2		16	21.2	odd	6
2646.2.l.b.521.3		16	21.5	even	6
2646.2.l.b.1097.6		16	63.31	odd	6
2646.2.l.b.1097.7		16	63.4	even	3
2646.2.t.a.1979.2		16	21.17	even	6
2646.2.t.a.1979.3		16	21.11	odd	6
2646.2.t.a.2285.2		16	63.58	even	3
2646.2.t.a.2285.3		16	63.40	odd	6
3024.2.cc.b.881.2		16	252.139	even	6
3024.2.cc.b.881.7		16	36.31	odd	6
3024.2.cc.b.2897.2		16	12.11	even	2
3024.2.cc.b.2897.7		16	84.83	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	126.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.40917 - 1.00709i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.17468 + 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} +(1.55364 + 2.14154i) q^{7} -1.00000i q^{8} +(0.971521 - 2.83834i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.40917 - 1.00709i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.17468 + 2.03460i) q^{5} +(-1.72392 + 0.167584i) q^{6} +(1.55364 + 2.14154i) q^{7} -1.00000i q^{8} +(0.971521 - 2.83834i) q^{9} -2.34936i q^{10} +(-4.91614 - 2.83834i) q^{11} +(1.57675 + 0.716830i) q^{12} +(1.48943 - 0.859925i) q^{13} +(-0.274725 - 2.63145i) q^{14} +(3.70436 + 1.68409i) q^{15} +(-0.500000 + 0.866025i) q^{16} -1.76883 q^{17} +(-2.26053 + 1.97231i) q^{18} -1.13932i q^{19} +(-1.17468 + 2.03460i) q^{20} +(4.34608 + 1.45313i) q^{21} +(2.83834 + 4.91614i) q^{22} +(-3.18272 + 1.83755i) q^{23} +(-1.00709 - 1.40917i) q^{24} +(-0.259741 + 0.449885i) q^{25} -1.71985 q^{26} +(-1.48943 - 4.97811i) q^{27} +(-1.07781 + 2.41626i) q^{28} +(3.59886 + 2.07781i) q^{29} +(-2.36603 - 3.31064i) q^{30} +(-7.24879 + 4.18509i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-9.78615 + 0.951321i) q^{33} +(1.53185 + 0.884414i) q^{34} +(-2.53215 + 5.67667i) q^{35} +(2.94383 - 0.577806i) q^{36} -9.19773 q^{37} +(-0.569660 + 0.986680i) q^{38} +(1.23284 - 2.71178i) q^{39} +(2.03460 - 1.17468i) q^{40} +(3.99709 + 6.92317i) q^{41} +(-3.03725 - 3.43149i) q^{42} +(1.76053 - 3.04933i) q^{43} -5.67667i q^{44} +(6.91611 - 1.35747i) q^{45} +3.67509 q^{46} +(5.90494 - 10.2277i) q^{47} +(0.167584 + 1.72392i) q^{48} +(-2.17238 + 6.65438i) q^{49} +(0.449885 - 0.259741i) q^{50} +(-2.49258 + 1.78138i) q^{51} +(1.48943 + 0.859925i) q^{52} +(-1.19917 + 5.05589i) q^{54} -13.3365i q^{55} +(2.14154 - 1.55364i) q^{56} +(-1.14740 - 1.60550i) q^{57} +(-2.07781 - 3.59886i) q^{58} +(1.11483 + 1.93094i) q^{59} +(0.393716 + 4.05012i) q^{60} +(7.79396 + 4.49985i) q^{61} +8.37019 q^{62} +(7.58780 - 2.32921i) q^{63} -1.00000 q^{64} +(3.49921 + 2.02027i) q^{65} +(8.95072 + 4.06921i) q^{66} +(-5.43562 - 9.41477i) q^{67} +(-0.884414 - 1.53185i) q^{68} +(-2.63442 + 5.79472i) q^{69} +(5.03124 - 3.65007i) q^{70} +4.52106i q^{71} +(-2.83834 - 0.971521i) q^{72} +5.34234i q^{73} +(7.96547 + 4.59886i) q^{74} +(0.0870571 + 0.895548i) q^{75} +(0.986680 - 0.569660i) q^{76} +(-1.55953 - 14.9379i) q^{77} +(-2.42356 + 1.73205i) q^{78} +(6.51422 - 11.2830i) q^{79} -2.34936 q^{80} +(-7.11229 - 5.51501i) q^{81} -7.99419i q^{82} +(-6.27298 + 10.8651i) q^{83} +(0.914596 + 4.49038i) q^{84} +(-2.07781 - 3.59886i) q^{85} +(-3.04933 + 1.76053i) q^{86} +(7.16396 - 0.696415i) q^{87} +(-2.83834 + 4.91614i) q^{88} -1.16106 q^{89} +(-6.66826 - 2.28245i) q^{90} +(4.15561 + 1.85366i) q^{91} +(-3.18272 - 1.83755i) q^{92} +(-6.00000 + 13.1977i) q^{93} +(-10.2277 + 5.90494i) q^{94} +(2.31806 - 1.33834i) q^{95} +(0.716830 - 1.57675i) q^{96} +(-3.97536 - 2.29517i) q^{97} +(5.20853 - 4.67667i) q^{98} +(-12.8323 + 11.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9	\( 16 q + 8 q^{4} + 2 q^{7} + 12 q^{9} - 12 q^{11} - 6 q^{14} - 8 q^{16} - 12 q^{18} + 18 q^{21} - 48 q^{23} - 8 q^{25} + 4 q^{28} - 12 q^{29} - 24 q^{30} + 12 q^{36} - 8 q^{37} - 36 q^{39} - 12 q^{42} + 4 q^{43} + 24 q^{46} - 8 q^{49} + 60 q^{50} + 12 q^{51} - 6 q^{56} + 48 q^{57} - 12 q^{58} + 24 q^{60} + 24 q^{63} - 16 q^{64} + 84 q^{65} - 28 q^{67} + 36 q^{74} + 78 q^{77} - 24 q^{78} - 4 q^{79} + 36 q^{81} + 18 q^{84} - 12 q^{85} - 24 q^{86} + 24 q^{91} - 48 q^{92} - 96 q^{93} + 12 q^{95} - 72 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 2 * q^7 + 12 * q^9 - 12 * q^11 - 6 * q^14 - 8 * q^16 - 12 * q^18 + 18 * q^21 - 48 * q^23 - 8 * q^25 + 4 * q^28 - 12 * q^29 - 24 * q^30 + 12 * q^36 - 8 * q^37 - 36 * q^39 - 12 * q^42 + 4 * q^43 + 24 * q^46 - 8 * q^49 + 60 * q^50 + 12 * q^51 - 6 * q^56 + 48 * q^57 - 12 * q^58 + 24 * q^60 + 24 * q^63 - 16 * q^64 + 84 * q^65 - 28 * q^67 + 36 * q^74 + 78 * q^77 - 24 * q^78 - 4 * q^79 + 36 * q^81 + 18 * q^84 - 12 * q^85 - 24 * q^86 + 24 * q^91 - 48 * q^92 - 96 * q^93 + 12 * q^95 - 72 * q^99

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