LMFDB - Embedded newform 112.2.w.a.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [112,2,Mod(37,112)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("112.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(112, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 112 = 2^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	112.w (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$0.894324502638$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	112.109
Dual form			112.2.w.a.37.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.86603 + 0.500000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-3.23205 - 0.866025i) q^{5} +(-1.36603 - 2.36603i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{9} -4.73205i q^{10} +(1.13397 + 4.23205i) q^{11} +(2.73205 - 2.73205i) q^{12} +(0.267949 + 0.267949i) q^{13} +(-2.09808 + 3.09808i) q^{14} +6.46410 q^{15} +(2.00000 - 3.46410i) q^{16} +(0.232051 - 0.401924i) q^{17} +(0.732051 + 0.732051i) q^{18} +(-1.13397 + 4.23205i) q^{19} +(6.46410 - 1.73205i) q^{20} +(-4.23205 - 2.86603i) q^{21} +(-5.36603 + 3.09808i) q^{22} +(-2.13397 + 1.23205i) q^{23} +(4.73205 + 2.73205i) q^{24} +(5.36603 + 3.09808i) q^{25} +(-0.267949 + 0.464102i) q^{26} +(3.09808 - 3.09808i) q^{27} +(-5.00000 - 1.73205i) q^{28} +(-3.73205 - 3.73205i) q^{29} +(2.36603 + 8.83013i) q^{30} +(-0.133975 + 0.232051i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-4.23205 - 7.33013i) q^{33} +(0.633975 + 0.169873i) q^{34} +(-3.86603 - 7.96410i) q^{35} +(-0.732051 + 1.26795i) q^{36} +(10.6962 + 2.86603i) q^{37} -6.19615 q^{38} +(-0.633975 - 0.366025i) q^{39} +(4.73205 + 8.19615i) q^{40} +8.92820i q^{41} +(2.36603 - 6.83013i) q^{42} +(-0.464102 + 0.464102i) q^{43} +(-6.19615 - 6.19615i) q^{44} +(-2.36603 + 0.633975i) q^{45} +(-2.46410 - 2.46410i) q^{46} +(-3.86603 - 6.69615i) q^{47} +(-2.00000 + 7.46410i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(-2.26795 + 8.46410i) q^{50} +(-0.232051 + 0.866025i) q^{51} +(-0.732051 - 0.196152i) q^{52} +(-2.96410 - 11.0622i) q^{53} +(5.36603 + 3.09808i) q^{54} -14.6603i q^{55} +(0.535898 - 7.46410i) q^{56} -8.46410i q^{57} +(3.73205 - 6.46410i) q^{58} +(2.66987 + 9.96410i) q^{59} +(-11.1962 + 6.46410i) q^{60} +(-0.0358984 + 0.133975i) q^{61} +(-0.366025 - 0.0980762i) q^{62} +(1.83013 + 0.633975i) q^{63} +8.00000i q^{64} +(-0.633975 - 1.09808i) q^{65} +(8.46410 - 8.46410i) q^{66} +(-7.33013 + 1.96410i) q^{67} +0.928203i q^{68} +(3.36603 - 3.36603i) q^{69} +(9.46410 - 8.19615i) q^{70} +7.46410i q^{71} +(-2.00000 - 0.535898i) q^{72} +(-2.76795 - 1.59808i) q^{73} +15.6603i q^{74} +(-11.5622 - 3.09808i) q^{75} +(-2.26795 - 8.46410i) q^{76} +(-6.50000 + 9.59808i) q^{77} +(0.267949 - 1.00000i) q^{78} +(-0.330127 - 0.571797i) q^{79} +(-9.46410 + 9.46410i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-12.1962 + 3.26795i) q^{82} +(8.46410 + 8.46410i) q^{83} +(10.1962 + 0.732051i) q^{84} +(-1.09808 + 1.09808i) q^{85} +(-0.803848 - 0.464102i) q^{86} +(8.83013 + 5.09808i) q^{87} +(6.19615 - 10.7321i) q^{88} +(4.50000 - 2.59808i) q^{89} +(-1.73205 - 3.00000i) q^{90} +(-0.0717968 + 1.00000i) q^{91} +(2.46410 - 4.26795i) q^{92} +(0.133975 - 0.500000i) q^{93} +(7.73205 - 7.73205i) q^{94} +(7.33013 - 12.6962i) q^{95} -10.9282 q^{96} +10.9282 q^{97} +(-9.83013 + 1.16987i) q^{98} +(2.26795 + 2.26795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} - 6 q^{5} - 2 q^{6} - 8 q^{8} + 6 q^{9} + 8 q^{11} + 4 q^{12} + 8 q^{13} + 2 q^{14} + 12 q^{15} + 8 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} + 12 q^{20} - 10 q^{21} - 18 q^{22} - 12 q^{23}+ \cdots + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 - 6 * q^5 - 2 * q^6 - 8 * q^8 + 6 * q^9 + 8 * q^11 + 4 * q^12 + 8 * q^13 + 2 * q^14 + 12 * q^15 + 8 * q^16 - 6 * q^17 - 4 * q^18 - 8 * q^19 + 12 * q^20 - 10 * q^21 - 18 * q^22 - 12 * q^23 + 12 * q^24 + 18 * q^25 - 8 * q^26 + 2 * q^27 - 20 * q^28 - 8 * q^29 + 6 * q^30 - 4 * q^31 + 8 * q^32 - 10 * q^33 + 6 * q^34 - 12 * q^35 + 4 * q^36 + 22 * q^37 - 4 * q^38 - 6 * q^39 + 12 * q^40 + 6 * q^42 + 12 * q^43 - 4 * q^44 - 6 * q^45 + 4 * q^46 - 12 * q^47 - 8 * q^48 - 4 * q^49 - 16 * q^50 + 6 * q^51 + 4 * q^52 + 2 * q^53 + 18 * q^54 + 16 * q^56 + 8 * q^58 + 28 * q^59 - 24 * q^60 - 14 * q^61 + 2 * q^62 - 10 * q^63 - 6 * q^65 + 20 * q^66 - 12 * q^67 + 10 * q^69 + 24 * q^70 - 8 * q^72 - 18 * q^73 - 22 * q^75 - 16 * q^76 - 26 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 - 4 * q^81 - 28 * q^82 + 20 * q^83 + 20 * q^84 + 6 * q^85 - 24 * q^86 + 18 * q^87 + 4 * q^88 + 18 * q^89 - 28 * q^91 - 4 * q^92 + 4 * q^93 + 24 * q^94 + 12 * q^95 - 16 * q^96 + 16 * q^97 - 22 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/112\mathbb{Z}\right)^\times$.

$n$	$15$	$17$	$85$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$	−1.86603	+	0.500000i	−1.07735	+	0.288675i	−0.753510	−	0.657437i	$-0.771641\pi$
$3$	−1.86603	+	0.500000i	−1.07735	+	0.288675i	−0.323840	+	0.946112i	$0.604974\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	−3.23205	−	0.866025i	−1.44542	−	0.387298i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	−3.23205	−	0.866025i	−1.44542	−	0.387298i	−0.894427	+	0.447214i	$0.852416\pi$
$6$	−1.36603	−	2.36603i	−0.557678	−	0.965926i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$7$	1.73205	+	2.00000i	0.654654	+	0.755929i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$	0.633975	−	0.366025i	0.211325	−	0.122008i
$10$		−	4.73205i		−	1.49641i
$11$	1.13397	+	4.23205i	0.341906	+	1.27601i	0.896185	+	0.443680i	$0.146327\pi$
$11$	1.13397	+	4.23205i	0.341906	+	1.27601i	−0.554279	+	0.832331i	$0.687006\pi$
$12$	2.73205	−	2.73205i	0.788675	−	0.788675i
$13$	0.267949	+	0.267949i	0.0743157	+	0.0743157i	0.743288	−	0.668972i	$-0.233265\pi$
$13$	0.267949	+	0.267949i	0.0743157	+	0.0743157i	−0.668972	+	0.743288i	$0.733265\pi$
$14$	−2.09808	+	3.09808i	−0.560734	+	0.827996i
$15$	6.46410			1.66902
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	−0.836512	−	0.547948i	$-0.815409\pi$
$17$	0.232051	−	0.401924i	0.0562806	−	0.0974808i	0.892793	+	0.450467i	$0.148743\pi$
$18$	0.732051	+	0.732051i	0.172546	+	0.172546i
$19$	−1.13397	+	4.23205i	−0.260152	+	0.970899i	0.705000	+	0.709207i	$0.250947\pi$
$19$	−1.13397	+	4.23205i	−0.260152	+	0.970899i	−0.965152	+	0.261692i	$0.915720\pi$
$20$	6.46410	−	1.73205i	1.44542	−	0.387298i
$21$	−4.23205	−	2.86603i	−0.923509	−	0.625418i
$22$	−5.36603	+	3.09808i	−1.14404	+	0.660512i
$23$	−2.13397	+	1.23205i	−0.444964	+	0.256900i	−0.705701	−	0.708510i	$-0.749368\pi$
$23$	−2.13397	+	1.23205i	−0.444964	+	0.256900i	0.260737	+	0.965410i	$0.416035\pi$
$24$	4.73205	+	2.73205i	0.965926	+	0.557678i
$25$	5.36603	+	3.09808i	1.07321	+	0.619615i
$26$	−0.267949	+	0.464102i	−0.0525492	+	0.0910178i
$27$	3.09808	−	3.09808i	0.596225	−	0.596225i
$28$	−5.00000	−	1.73205i	−0.944911	−	0.327327i
$29$	−3.73205	−	3.73205i	−0.693024	−	0.693024i	0.269872	−	0.962896i	$-0.413019\pi$
$29$	−3.73205	−	3.73205i	−0.693024	−	0.693024i	−0.962896	+	0.269872i	$0.913019\pi$
$30$	2.36603	+	8.83013i	0.431975	+	1.61215i
$31$	−0.133975	+	0.232051i	−0.0240625	+	0.0416776i	−0.877806	−	0.479016i	$-0.840993\pi$
$31$	−0.133975	+	0.232051i	−0.0240625	+	0.0416776i	0.853743	+	0.520694i	$0.174327\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$	−4.23205	−	7.33013i	−0.736705	−	1.27601i
$34$	0.633975	+	0.169873i	0.108726	+	0.0291330i
$35$	−3.86603	−	7.96410i	−0.653478	−	1.34618i
$36$	−0.732051	+	1.26795i	−0.122008	+	0.211325i
$37$	10.6962	+	2.86603i	1.75844	+	0.471172i	0.986394	−	0.164399i	$-0.0525685\pi$
$37$	10.6962	+	2.86603i	1.75844	+	0.471172i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−6.19615			−1.00515
$39$	−0.633975	−	0.366025i	−0.101517	−	0.0586110i
$40$	4.73205	+	8.19615i	0.748203	+	1.29593i
$41$			8.92820i			1.39435i	0.716900	+	0.697176i	$0.245560\pi$
$41$			8.92820i			1.39435i	−0.716900	+	0.697176i	$0.754440\pi$
$42$	2.36603	−	6.83013i	0.365086	−	1.05391i
$43$	−0.464102	+	0.464102i	−0.0707748	+	0.0707748i	−0.741608	−	0.670833i	$-0.765937\pi$
$43$	−0.464102	+	0.464102i	−0.0707748	+	0.0707748i	0.670833	+	0.741608i	$0.265937\pi$
$44$	−6.19615	−	6.19615i	−0.934105	−	0.934105i
$45$	−2.36603	+	0.633975i	−0.352706	+	0.0945074i
$46$	−2.46410	−	2.46410i	−0.363312	−	0.363312i
$47$	−3.86603	−	6.69615i	−0.563918	−	0.976734i	−0.997149	−	0.0754516i	$-0.975960\pi$
$47$	−3.86603	−	6.69615i	−0.563918	−	0.976734i	0.433232	−	0.901283i	$-0.357373\pi$
$48$	−2.00000	+	7.46410i	−0.288675	+	1.07735i
$49$	−1.00000	+	6.92820i	−0.142857	+	0.989743i
$50$	−2.26795	+	8.46410i	−0.320736	+	1.19700i
$51$	−0.232051	+	0.866025i	−0.0324936	+	0.121268i
$52$	−0.732051	−	0.196152i	−0.101517	−	0.0272014i
$53$	−2.96410	−	11.0622i	−0.407151	−	1.51951i	−0.800054	−	0.599927i	$-0.795196\pi$
$53$	−2.96410	−	11.0622i	−0.407151	−	1.51951i	0.392904	−	0.919580i	$-0.371471\pi$
$54$	5.36603	+	3.09808i	0.730224	+	0.421595i
$55$		−	14.6603i		−	1.97679i
$56$	0.535898	−	7.46410i	0.0716124	−	0.997433i
$57$		−	8.46410i		−	1.12110i
$58$	3.73205	−	6.46410i	0.490042	−	0.848778i
$59$	2.66987	+	9.96410i	0.347588	+	1.29722i	0.889560	+	0.456819i	$0.151011\pi$
$59$	2.66987	+	9.96410i	0.347588	+	1.29722i	−0.541972	+	0.840397i	$0.682322\pi$
$60$	−11.1962	+	6.46410i	−1.44542	+	0.834512i
$61$	−0.0358984	+	0.133975i	−0.00459632	+	0.0171537i	−0.968186	−	0.250232i	$-0.919493\pi$
$61$	−0.0358984	+	0.133975i	−0.00459632	+	0.0171537i	0.963590	+	0.267386i	$0.0861598\pi$
$62$	−0.366025	−	0.0980762i	−0.0464853	−	0.0124557i
$63$	1.83013	+	0.633975i	0.230574	+	0.0798733i
$64$			8.00000i			1.00000i
$65$	−0.633975	−	1.09808i	−0.0786349	−	0.136200i
$66$	8.46410	−	8.46410i	1.04186	−	1.04186i
$67$	−7.33013	+	1.96410i	−0.895518	+	0.239953i	−0.677090	−	0.735900i	$-0.736759\pi$
$67$	−7.33013	+	1.96410i	−0.895518	+	0.239953i	−0.218427	+	0.975853i	$0.570093\pi$
$68$			0.928203i			0.112561i
$69$	3.36603	−	3.36603i	0.405222	−	0.405222i
$70$	9.46410	−	8.19615i	1.13118	−	0.979628i
$71$			7.46410i			0.885826i	0.896565	+	0.442913i	$0.146055\pi$
$71$			7.46410i			0.885826i	−0.896565	+	0.442913i	$0.853945\pi$
$72$	−2.00000	−	0.535898i	−0.235702	−	0.0631562i
$73$	−2.76795	−	1.59808i	−0.323964	−	0.187041i	0.329194	−	0.944262i	$-0.393223\pi$
$73$	−2.76795	−	1.59808i	−0.323964	−	0.187041i	−0.653158	+	0.757222i	$0.726556\pi$
$74$			15.6603i			1.82047i
$75$	−11.5622	−	3.09808i	−1.33509	−	0.357735i
$76$	−2.26795	−	8.46410i	−0.260152	−	0.970899i
$77$	−6.50000	+	9.59808i	−0.740744	+	1.09380i
$78$	0.267949	−	1.00000i	0.0303393	−	0.113228i
$79$	−0.330127	−	0.571797i	−0.0371422	−	0.0643322i	0.846857	−	0.531821i	$-0.178492\pi$
$79$	−0.330127	−	0.571797i	−0.0371422	−	0.0643322i	−0.883999	+	0.467489i	$0.845159\pi$
$80$	−9.46410	+	9.46410i	−1.05812	+	1.05812i
$81$	−5.33013	+	9.23205i	−0.592236	+	1.02578i
$82$	−12.1962	+	3.26795i	−1.34684	+	0.360885i
$83$	8.46410	+	8.46410i	0.929056	+	0.929056i	0.997645	−	0.0685891i	$-0.0218498\pi$
$83$	8.46410	+	8.46410i	0.929056	+	0.929056i	−0.0685891	+	0.997645i	$0.521850\pi$
$84$	10.1962	+	0.732051i	1.11249	+	0.0798733i
$85$	−1.09808	+	1.09808i	−0.119103	+	0.119103i
$86$	−0.803848	−	0.464102i	−0.0866811	−	0.0500454i
$87$	8.83013	+	5.09808i	0.946689	+	0.546571i
$88$	6.19615	−	10.7321i	0.660512	−	1.14404i
$89$	4.50000	−	2.59808i	0.476999	−	0.275396i	−0.242166	−	0.970235i	$-0.577858\pi$
$89$	4.50000	−	2.59808i	0.476999	−	0.275396i	0.719165	+	0.694839i	$0.244525\pi$
$90$	−1.73205	−	3.00000i	−0.182574	−	0.316228i
$91$	−0.0717968	+	1.00000i	−0.00752635	+	0.104828i
$92$	2.46410	−	4.26795i	0.256900	−	0.444964i
$93$	0.133975	−	0.500000i	0.0138925	−	0.0518476i
$94$	7.73205	−	7.73205i	0.797500	−	0.797500i
$95$	7.33013	−	12.6962i	0.752055	−	1.30260i
$96$	−10.9282			−1.11536
$97$	10.9282			1.10959			0.554795	−	0.831987i	$-0.312797\pi$
$97$	10.9282			1.10959			0.554795	+	0.831987i	$0.312797\pi$
$98$	−9.83013	+	1.16987i	−0.992993	+	0.118175i
$99$	2.26795	+	2.26795i	0.227937	+	0.227937i
$100$	−12.3923			−1.23923
$101$	1.89230	+	7.06218i	0.188291	+	0.702713i	0.993902	+	0.110268i	$0.0351708\pi$
$101$	1.89230	+	7.06218i	0.188291	+	0.702713i	−0.805611	+	0.592445i	$0.798163\pi$
$102$	−1.26795			−0.125546
$103$	0.401924	−	0.232051i	0.0396027	−	0.0228646i	−0.480068	−	0.877231i	$-0.659388\pi$
$103$	0.401924	−	0.232051i	0.0396027	−	0.0228646i	0.519671	+	0.854367i	$0.326055\pi$
$104$		−	1.07180i		−	0.105098i
$105$	11.1962	+	12.9282i	1.09263	+	1.26166i
$106$	14.0263	−	8.09808i	1.36235	−	0.786555i
$107$	0.866025	+	0.232051i	0.0837218	+	0.0224332i	0.300437	−	0.953802i	$-0.402868\pi$
$107$	0.866025	+	0.232051i	0.0837218	+	0.0224332i	−0.216715	+	0.976235i	$0.569534\pi$
$108$	−2.26795	+	8.46410i	−0.218234	+	0.814459i
$109$	14.4282	−	3.86603i	1.38197	−	0.370298i	0.510134	−	0.860095i	$-0.329596\pi$
$109$	14.4282	−	3.86603i	1.38197	−	0.370298i	0.871837	+	0.489797i	$0.162929\pi$
$110$	20.0263	−	5.36603i	1.90943	−	0.511630i
$111$	−21.3923			−2.03047
$112$	10.3923	−	2.00000i	0.981981	−	0.188982i
$113$	5.46410			0.514019			0.257010	−	0.966409i	$-0.417263\pi$
$113$	5.46410			0.514019			0.257010	+	0.966409i	$0.417263\pi$
$114$	11.5622	−	3.09808i	1.08290	−	0.290161i
$115$	7.96410	−	2.13397i	0.742656	−	0.198994i
$116$	10.1962	+	2.73205i	0.946689	+	0.253665i
$117$	0.267949	+	0.0717968i	0.0247719	+	0.00663761i
$118$	−12.6340	+	7.29423i	−1.16305	+	0.671488i
$119$	1.20577	−	0.232051i	0.110533	−	0.0212721i
$120$	−12.9282	−	12.9282i	−1.18018	−	1.18018i
$121$	−7.09808	+	4.09808i	−0.645280	+	0.372552i
$122$	−0.196152			−0.0177588
$123$	−4.46410	−	16.6603i	−0.402514	−	1.50220i
$124$		−	0.535898i		−	0.0481251i
$125$	−2.83013	−	2.83013i	−0.253134	−	0.253134i
$126$	−0.196152	+	2.73205i	−0.0174746	+	0.243390i
$127$	2.53590			0.225025			0.112512	−	0.993650i	$-0.464110\pi$
$127$	2.53590			0.225025			0.112512	+	0.993650i	$0.464110\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$	0.633975	−	1.09808i	0.0558184	−	0.0966802i
$130$	1.26795	−	1.26795i	0.111207	−	0.111207i
$131$	2.40192	−	8.96410i	0.209857	−	0.783197i	−0.778057	−	0.628194i	$-0.783794\pi$
$131$	2.40192	−	8.96410i	0.209857	−	0.783197i	0.987914	−	0.155003i	$-0.0495388\pi$
$132$	14.6603	+	8.46410i	1.27601	+	0.736705i
$133$	−10.4282	+	5.06218i	−0.904240	+	0.438946i
$134$	−5.36603	−	9.29423i	−0.463554	−	0.802899i
$135$	−12.6962	+	7.33013i	−1.09271	+	0.630877i
$136$	−1.26795	+	0.339746i	−0.108726	+	0.0291330i
$137$	−11.7679	−	6.79423i	−1.00540	−	0.580470i	−0.0955611	−	0.995424i	$-0.530465\pi$
$137$	−11.7679	−	6.79423i	−1.00540	−	0.580470i	−0.909843	+	0.414953i	$0.863798\pi$
$138$	5.83013	+	3.36603i	0.496293	+	0.286535i
$139$	1.92820	−	1.92820i	0.163548	−	0.163548i	−0.620588	−	0.784136i	$-0.713106\pi$
$139$	1.92820	−	1.92820i	0.163548	−	0.163548i	0.784136	+	0.620588i	$0.213106\pi$
$140$	14.6603	+	9.92820i	1.23902	+	0.839086i
$141$	10.5622	+	10.5622i	0.889496	+	0.889496i
$142$	−10.1962	+	2.73205i	−0.855642	+	0.229269i
$143$	−0.830127	+	1.43782i	−0.0694187	+	0.120237i
$144$		−	2.92820i		−	0.244017i
$145$	8.83013	+	15.2942i	0.733302	+	1.27012i
$146$	1.16987	−	4.36603i	0.0968194	−	0.361335i
$147$	−1.59808	−	13.4282i	−0.131807	−	1.10754i
$148$	−21.3923	+	5.73205i	−1.75844	+	0.471172i
$149$	8.96410	+	2.40192i	0.734368	+	0.196773i	0.606573	−	0.795027i	$-0.292544\pi$
$149$	8.96410	+	2.40192i	0.734368	+	0.196773i	0.127794	+	0.991801i	$0.459210\pi$
$150$		−	16.9282i		−	1.38218i
$151$	−8.13397	−	4.69615i	−0.661933	−	0.382167i	0.131080	−	0.991372i	$-0.458156\pi$
$151$	−8.13397	−	4.69615i	−0.661933	−	0.382167i	−0.793013	+	0.609204i	$0.791489\pi$
$152$	10.7321	−	6.19615i	0.870484	−	0.502574i
$153$		−	0.339746i		−	0.0274668i
$154$	−15.4904	−	5.36603i	−1.24825	−	0.432407i
$155$	0.633975	−	0.633975i	0.0509221	−	0.0509221i
$156$	1.46410			0.117222
$157$	−15.8923	+	4.25833i	−1.26834	+	0.339852i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$	−15.8923	+	4.25833i	−1.26834	+	0.339852i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	0.660254	−	0.660254i	0.0525270	−	0.0525270i
$159$	11.0622	+	19.1603i	0.877288	+	1.51951i
$160$	−16.3923	−	9.46410i	−1.29593	−	0.748203i
$161$	−6.16025	−	2.13397i	−0.485496	−	0.168181i
$162$	−14.5622	−	3.90192i	−1.14411	−	0.306564i
$163$	0.0621778	−	0.232051i	0.00487014	−	0.0181756i	−0.963448	−	0.267895i	$-0.913672\pi$
$163$	0.0621778	−	0.232051i	0.00487014	−	0.0181756i	0.968318	+	0.249720i	$0.0803385\pi$
$164$	−8.92820	−	15.4641i	−0.697176	−	1.20754i
$165$	7.33013	+	27.3564i	0.570650	+	2.12969i
$166$	−8.46410	+	14.6603i	−0.656942	+	1.13786i
$167$			5.85641i			0.453182i	0.973990	+	0.226591i	$0.0727581\pi$
$167$			5.85641i			0.453182i	−0.973990	+	0.226591i	$0.927242\pi$
$168$	2.73205	+	14.1962i	0.210782	+	1.09526i
$169$		−	12.8564i		−	0.988954i
$170$	−1.90192	−	1.09808i	−0.145871	−	0.0842186i
$171$	0.830127	+	3.09808i	0.0634814	+	0.236916i
$172$	0.339746	−	1.26795i	0.0259054	−	0.0966802i
$173$	1.23205	−	4.59808i	0.0936711	−	0.349585i	−0.903144	−	0.429339i	$-0.858747\pi$
$173$	1.23205	−	4.59808i	0.0936711	−	0.349585i	0.996815	+	0.0797535i	$0.0254133\pi$
$174$	−3.73205	+	13.9282i	−0.282926	+	1.05589i
$175$	3.09808	+	16.0981i	0.234193	+	1.21690i
$176$	16.9282	+	4.53590i	1.27601	+	0.341906i
$177$	−9.96410	−	17.2583i	−0.748948	−	1.29722i
$178$	5.19615	+	5.19615i	0.389468	+	0.389468i
$179$	−7.59808	+	2.03590i	−0.567907	+	0.152170i	−0.531336	−	0.847161i	$-0.678310\pi$
$179$	−7.59808	+	2.03590i	−0.567907	+	0.152170i	−0.0365704	+	0.999331i	$0.511643\pi$
$180$	3.46410	−	3.46410i	0.258199	−	0.258199i
$181$	−7.39230	+	7.39230i	−0.549466	+	0.549466i	−0.926286	−	0.376821i	$-0.877017\pi$
$181$	−7.39230	+	7.39230i	−0.549466	+	0.549466i	0.376821	+	0.926286i	$0.377017\pi$
$182$	−1.39230	+	0.267949i	−0.103205	+	0.0198617i
$183$		−	0.267949i		−	0.0198074i
$184$	6.73205	+	1.80385i	0.496293	+	0.132981i
$185$	−32.0885	−	18.5263i	−2.35919	−	1.36208i
$186$	0.732051			0.0536766
$187$	1.96410	+	0.526279i	0.143629	+	0.0384854i
$188$	13.3923	+	7.73205i	0.976734	+	0.563918i
$189$	11.5622	+	0.830127i	0.841025	+	0.0603829i
$190$	20.0263	+	5.36603i	1.45286	+	0.389292i
$191$	4.33013	+	7.50000i	0.313317	+	0.542681i	0.979078	−	0.203484i	$-0.0652264\pi$
$191$	4.33013	+	7.50000i	0.313317	+	0.542681i	−0.665761	+	0.746165i	$0.731893\pi$
$192$	−4.00000	−	14.9282i	−0.288675	−	1.07735i
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$	4.00000	+	14.9282i	0.287183	+	1.07178i
$195$	1.73205	+	1.73205i	0.124035	+	0.124035i
$196$	−5.19615	−	13.0000i	−0.371154	−	0.928571i
$197$	0.660254	−	0.660254i	0.0470412	−	0.0470412i	−0.683195	−	0.730236i	$-0.739410\pi$
$197$	0.660254	−	0.660254i	0.0470412	−	0.0470412i	0.730236	+	0.683195i	$0.239410\pi$
$198$	−2.26795	+	3.92820i	−0.161176	+	0.279165i
$199$	1.66987	+	0.964102i	0.118374	+	0.0683434i	0.558018	−	0.829829i	$-0.311562\pi$
$199$	1.66987	+	0.964102i	0.118374	+	0.0683434i	−0.439644	+	0.898172i	$0.644895\pi$
$200$	−4.53590	−	16.9282i	−0.320736	−	1.19700i
$201$	12.6962	−	7.33013i	0.895518	−	0.517027i
$202$	−8.95448	+	5.16987i	−0.630035	+	0.363751i
$203$	1.00000	−	13.9282i	0.0701862	−	0.977568i
$204$	−0.464102	−	1.73205i	−0.0324936	−	0.121268i
$205$	7.73205	−	28.8564i	0.540030	−	2.01542i
$206$	0.464102	+	0.464102i	0.0323355	+	0.0323355i
$207$	−0.901924	+	1.56218i	−0.0626880	+	0.108579i
$208$	1.46410	−	0.392305i	0.101517	−	0.0272014i
$209$	−19.1962			−1.32783
$210$	−13.5622	+	20.0263i	−0.935879	+	1.38194i
$211$	−2.07180	−	2.07180i	−0.142628	−	0.142628i	0.632187	−	0.774816i	$-0.282157\pi$
$211$	−2.07180	−	2.07180i	−0.142628	−	0.142628i	−0.774816	+	0.632187i	$0.782157\pi$
$212$	16.1962	+	16.1962i	1.11236	+	1.11236i
$213$	−3.73205	−	13.9282i	−0.255716	−	0.954345i
$214$			1.26795i			0.0866752i
$215$	1.90192	−	1.09808i	0.129710	−	0.0748882i
$216$	−12.3923			−0.843190
$217$	−0.696152	+	0.133975i	−0.0472579	+	0.00909479i
$218$	10.5622	+	18.2942i	0.715361	+	1.23904i
$219$	5.96410	+	1.59808i	0.403017	+	0.107988i
$220$	14.6603	+	25.3923i	0.988394	+	1.71195i
$221$	0.169873	−	0.0455173i	0.0114269	−	0.00306183i
$222$	−7.83013	−	29.2224i	−0.525524	−	1.96128i
$223$	−17.8564			−1.19575			−0.597877	−	0.801588i	$-0.703989\pi$
$223$	−17.8564			−1.19575			−0.597877	+	0.801588i	$0.703989\pi$
$224$	6.53590	+	13.4641i	0.436698	+	0.899608i
$225$	4.53590			0.302393
$226$	2.00000	+	7.46410i	0.133038	+	0.496505i
$227$	22.9904	−	6.16025i	1.52593	−	0.408870i	0.604238	−	0.796804i	$-0.293478\pi$
$227$	22.9904	−	6.16025i	1.52593	−	0.408870i	0.921687	+	0.387934i	$0.126811\pi$
$228$	8.46410	+	14.6603i	0.560549	+	0.970899i
$229$	−17.4282	−	4.66987i	−1.15169	−	0.308594i	−0.368047	−	0.929807i	$-0.619973\pi$
$229$	−17.4282	−	4.66987i	−1.15169	−	0.308594i	−0.783641	+	0.621213i	$0.786640\pi$
$230$	5.83013	+	10.0981i	0.384427	+	0.665847i
$231$	7.33013	−	21.1603i	0.482287	−	1.39224i
$232$			14.9282i			0.980085i
$233$	9.69615	−	5.59808i	0.635216	−	0.366742i	−0.147553	−	0.989054i	$-0.547140\pi$
$233$	9.69615	−	5.59808i	0.635216	−	0.366742i	0.782769	+	0.622312i	$0.213806\pi$
$234$			0.392305i			0.0256458i
$235$	6.69615	+	24.9904i	0.436809	+	1.63019i
$236$	−14.5885	−	14.5885i	−0.949628	−	0.949628i
$237$	0.901924	+	0.901924i	0.0585862	+	0.0585862i
$238$	0.758330	+	1.56218i	0.0491552	+	0.101261i
$239$	−15.4641			−1.00029			−0.500145	−	0.865942i	$-0.666720\pi$
$239$	−15.4641			−1.00029			−0.500145	+	0.865942i	$0.666720\pi$
$240$	12.9282	−	22.3923i	0.834512	−	1.44542i
$241$	−0.0358984	+	0.0621778i	−0.00231242	+	0.00400523i	−0.867179	−	0.497996i	$-0.834069\pi$
$241$	−0.0358984	+	0.0621778i	−0.00231242	+	0.00400523i	0.864867	+	0.502001i	$0.167403\pi$
$242$	−8.19615	−	8.19615i	−0.526869	−	0.526869i
$243$	1.92820	−	7.19615i	0.123694	−	0.461633i
$244$	−0.0717968	−	0.267949i	−0.00459632	−	0.0171537i
$245$	9.23205	−	21.5263i	0.589814	−	1.37526i
$246$	21.1244	−	12.1962i	1.34684	−	0.777598i
$247$	−1.43782	+	0.830127i	−0.0914864	+	0.0528197i
$248$	0.732051	−	0.196152i	0.0464853	−	0.0124557i
$249$	−20.0263	−	11.5622i	−1.26911	−	0.732723i
$250$	2.83013	−	4.90192i	0.178993	−	0.310025i
$251$	13.5885	−	13.5885i	0.857696	−	0.857696i	−0.133370	−	0.991066i	$-0.542580\pi$
$251$	13.5885	−	13.5885i	0.857696	−	0.857696i	0.991066	+	0.133370i	$0.0425800\pi$
$252$	−3.80385	+	0.732051i	−0.239620	+	0.0461149i
$253$	−7.63397	−	7.63397i	−0.479944	−	0.479944i
$254$	0.928203	+	3.46410i	0.0582407	+	0.217357i
$255$	1.50000	−	2.59808i	0.0939336	−	0.162698i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−0.696152	−	1.20577i	−0.0434248	−	0.0752140i	0.843496	−	0.537135i	$-0.180494\pi$
$257$	−0.696152	−	1.20577i	−0.0434248	−	0.0752140i	−0.886921	+	0.461921i	$0.847160\pi$
$258$	1.73205	+	0.464102i	0.107833	+	0.0288937i
$259$	12.7942	+	26.3564i	0.794995	+	1.63771i
$260$	2.19615	+	1.26795i	0.136200	+	0.0786349i
$261$	−3.73205	−	1.00000i	−0.231008	−	0.0618984i
$262$	13.1244			0.810825
$263$	21.9904	+	12.6962i	1.35598	+	0.782878i	0.989080	−	0.147380i	$-0.0470841\pi$
$263$	21.9904	+	12.6962i	1.35598	+	0.782878i	0.366905	+	0.930258i	$0.380417\pi$
$264$	−6.19615	+	23.1244i	−0.381347	+	1.42321i
$265$			38.3205i			2.35401i
$266$	−10.7321	−	12.3923i	−0.658024	−	0.759821i
$267$	−7.09808	+	7.09808i	−0.434395	+	0.434395i
$268$	10.7321	−	10.7321i	0.655564	−	0.655564i
$269$	21.6244	−	5.79423i	1.31846	−	0.353280i	0.470059	−	0.882635i	$-0.344232\pi$
$269$	21.6244	−	5.79423i	1.31846	−	0.353280i	0.848401	+	0.529354i	$0.177566\pi$
$270$	−14.6603	−	14.6603i	−0.892195	−	0.892195i
$271$	6.06218	+	10.5000i	0.368251	+	0.637830i	0.989292	−	0.145948i	$-0.0466233\pi$
$271$	6.06218	+	10.5000i	0.368251	+	0.637830i	−0.621041	+	0.783778i	$0.713290\pi$
$272$	−0.928203	−	1.60770i	−0.0562806	−	0.0974808i
$273$	−0.366025	−	1.90192i	−0.0221529	−	0.115110i
$274$	4.97372	−	18.5622i	0.300473	−	1.12138i
$275$	−7.02628	+	26.2224i	−0.423701	+	1.58127i
$276$	−2.46410	+	9.19615i	−0.148321	+	0.553543i
$277$	4.50000	+	16.7942i	0.270379	+	1.00907i	0.958875	+	0.283828i	$0.0916044\pi$
$277$	4.50000	+	16.7942i	0.270379	+	1.00907i	−0.688496	+	0.725240i	$0.741729\pi$
$278$	3.33975	+	1.92820i	0.200305	+	0.115646i
$279$			0.196152i			0.0117433i
$280$	−8.19615	+	23.6603i	−0.489814	+	1.41397i
$281$			12.9282i			0.771232i	0.922659	+	0.385616i	$0.126011\pi$
$281$			12.9282i			0.771232i	−0.922659	+	0.385616i	$0.873989\pi$
$282$	−10.5622	+	18.2942i	−0.628969	+	1.08941i
$283$	−4.52628	−	16.8923i	−0.269059	−	1.00414i	−0.959719	−	0.280963i	$-0.909346\pi$
$283$	−4.52628	−	16.8923i	−0.269059	−	1.00414i	0.690659	−	0.723180i	$-0.257320\pi$
$284$	−7.46410	−	12.9282i	−0.442913	−	0.767148i
$285$	−7.33013	+	27.3564i	−0.434199	+	1.62045i
$286$	−2.26795	−	0.607695i	−0.134107	−	0.0359338i
$287$	−17.8564	+	15.4641i	−1.05403	+	0.912817i
$288$	4.00000	−	1.07180i	0.235702	−	0.0631562i
$289$	8.39230	+	14.5359i	0.493665	+	0.855053i
$290$	−17.6603	+	17.6603i	−1.03705	+	1.03705i
$291$	−20.3923	+	5.46410i	−1.19542	+	0.320311i
$292$	6.39230			0.374081
$293$	5.92820	−	5.92820i	0.346329	−	0.346329i	−0.512411	−	0.858740i	$-0.671248\pi$
$293$	5.92820	−	5.92820i	0.346329	−	0.346329i	0.858740	+	0.512411i	$0.171248\pi$
$294$	17.7583	−	7.09808i	1.03569	−	0.413968i
$295$		−	34.5167i		−	2.00964i
$296$	−15.6603	−	27.1244i	−0.910234	−	1.57657i
$297$	16.6244	+	9.59808i	0.964643	+	0.556937i
$298$			13.1244i			0.760274i
$299$	−0.901924	−	0.241670i	−0.0521596	−	0.0139761i
$300$	23.1244	−	6.19615i	1.33509	−	0.357735i
$301$	−1.73205	−	0.124356i	−0.0998337	−	0.00716774i
$302$	3.43782	−	12.8301i	0.197824	−	0.738291i
$303$	−7.06218	−	12.2321i	−0.405712	−	0.702713i
$304$	12.3923	+	12.3923i	0.710747	+	0.710747i
$305$	0.232051	−	0.401924i	0.0132872	−	0.0230141i
$306$	0.464102	−	0.124356i	0.0265309	−	0.00710894i
$307$	9.00000	+	9.00000i	0.513657	+	0.513657i	0.915645	−	0.401988i	$-0.131681\pi$
$307$	9.00000	+	9.00000i	0.513657	+	0.513657i	−0.401988	+	0.915645i	$0.631681\pi$
$308$	1.66025	−	23.1244i	0.0946018	−	1.31763i
$309$	−0.633975	+	0.633975i	−0.0360656	+	0.0360656i
$310$	1.09808	+	0.633975i	0.0623665	+	0.0360073i
$311$	−0.401924	−	0.232051i	−0.0227910	−	0.0131584i	0.488561	−	0.872530i	$-0.337522\pi$
$311$	−0.401924	−	0.232051i	−0.0227910	−	0.0131584i	−0.511352	+	0.859371i	$0.670855\pi$
$312$	0.535898	+	2.00000i	0.0303393	+	0.113228i
$313$	8.30385	−	4.79423i	0.469361	−	0.270986i	−0.246611	−	0.969115i	$-0.579317\pi$
$313$	8.30385	−	4.79423i	0.469361	−	0.270986i	0.715972	+	0.698129i	$0.245984\pi$
$314$	−11.6340	−	20.1506i	−0.656543	−	1.13717i
$315$	−5.36603	−	3.63397i	−0.302341	−	0.204751i
$316$	1.14359	+	0.660254i	0.0643322	+	0.0371422i
$317$	−3.16025	+	11.7942i	−0.177498	+	0.662430i	0.818615	+	0.574342i	$0.194742\pi$
$317$	−3.16025	+	11.7942i	−0.177498	+	0.662430i	−0.996113	+	0.0880875i	$0.971924\pi$
$318$	−22.1244	+	22.1244i	−1.24067	+	1.24067i
$319$	11.5622	−	20.0263i	0.647358	−	1.12126i
$320$	6.92820	−	25.8564i	0.387298	−	1.44542i
$321$	−1.73205			−0.0966736
$322$	0.660254	−	9.19615i	0.0367945	−	0.512482i
$323$	1.43782	+	1.43782i	0.0800026	+	0.0800026i
$324$		−	21.3205i		−	1.18447i
$325$	0.607695	+	2.26795i	0.0337089	+	0.125803i
$326$	0.339746			0.0188168
$327$	−24.9904	+	14.4282i	−1.38197	+	0.797881i
$328$	17.8564	−	17.8564i	0.985955	−	0.985955i
$329$	6.69615	−	19.3301i	0.369171	−	1.06570i
$330$	−34.6865	+	20.0263i	−1.90943	+	1.10241i
$331$	−17.2583	−	4.62436i	−0.948604	−	0.254178i	−0.248834	−	0.968546i	$-0.580047\pi$
$331$	−17.2583	−	4.62436i	−0.948604	−	0.254178i	−0.699770	+	0.714369i	$0.746714\pi$
$332$	−23.1244	−	6.19615i	−1.26911	−	0.340058i
$333$	7.83013	−	2.09808i	0.429088	−	0.114974i
$334$	−8.00000	+	2.14359i	−0.437741	+	0.117292i
$335$	25.3923			1.38733
$336$	−18.3923	+	8.92820i	−1.00338	+	0.487073i
$337$	−33.8564			−1.84428			−0.922138	−	0.386861i	$-0.873559\pi$
$337$	−33.8564			−1.84428			−0.922138	+	0.386861i	$0.873559\pi$
$338$	17.5622	−	4.70577i	0.955257	−	0.255960i
$339$	−10.1962	+	2.73205i	−0.553779	+	0.148385i
$340$	0.803848	−	3.00000i	0.0435948	−	0.162698i
$341$	−1.13397	−	0.303848i	−0.0614082	−	0.0164543i
$342$	−3.92820	+	2.26795i	−0.212413	+	0.122637i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	1.85641			0.100091
$345$	−13.7942	+	7.96410i	−0.742656	+	0.428773i
$346$	6.73205			0.361917
$347$	4.47372	+	16.6962i	0.240162	+	0.896296i	0.975754	+	0.218871i	$0.0702375\pi$
$347$	4.47372	+	16.6962i	0.240162	+	0.896296i	−0.735592	+	0.677425i	$0.763096\pi$
$348$	−20.3923			−1.09314
$349$	−18.1244	−	18.1244i	−0.970175	−	0.970175i	0.0293934	−	0.999568i	$-0.490642\pi$
$349$	−18.1244	−	18.1244i	−0.970175	−	0.970175i	−0.999568	+	0.0293934i	$0.990642\pi$
$350$	−20.8564	+	10.1244i	−1.11482	+	0.541170i
$351$	1.66025			0.0886178
$352$			24.7846i			1.32102i
$353$	−6.89230	+	11.9378i	−0.366840	+	0.635386i	−0.989070	−	0.147449i	$-0.952894\pi$
$353$	−6.89230	+	11.9378i	−0.366840	+	0.635386i	0.622229	+	0.782835i	$0.286227\pi$
$354$	19.9282	−	19.9282i	1.05917	−	1.05917i
$355$	6.46410	−	24.1244i	0.343079	−	1.28039i
$356$	−5.19615	+	9.00000i	−0.275396	+	0.476999i
$357$	−2.13397	+	1.03590i	−0.112942	+	0.0548256i
$358$	−5.56218	−	9.63397i	−0.293970	−	0.509171i
$359$	2.13397	−	1.23205i	0.112627	−	0.0650252i	−0.442628	−	0.896705i	$-0.645954\pi$
$359$	2.13397	−	1.23205i	0.112627	−	0.0650252i	0.555255	+	0.831680i	$0.312621\pi$
$360$	6.00000	+	3.46410i	0.316228	+	0.182574i
$361$	−0.169873	−	0.0980762i	−0.00894068	−	0.00516191i
$362$	−12.8038	−	7.39230i	−0.672955	−	0.388531i
$363$	11.1962	−	11.1962i	0.587646	−	0.587646i
$364$	−0.875644	−	1.80385i	−0.0458962	−	0.0945473i
$365$	7.56218	+	7.56218i	0.395822	+	0.395822i
$366$	0.366025	−	0.0980762i	0.0191325	−	0.00512653i
$367$	9.06218	−	15.6962i	0.473042	−	0.819332i	−0.526482	−	0.850186i	$-0.676489\pi$
$367$	9.06218	−	15.6962i	0.473042	−	0.819332i	0.999524	+	0.0308537i	$0.00982261\pi$
$368$			9.85641i			0.513801i
$369$	3.26795	+	5.66025i	0.170123	+	0.294661i
$370$	13.5622	−	50.6147i	0.705064	−	2.63133i
$371$	16.9904	−	25.0885i	0.882097	−	1.30253i
$372$	0.267949	+	1.00000i	0.0138925	+	0.0518476i
$373$	3.23205	+	0.866025i	0.167349	+	0.0448411i	0.341521	−	0.939874i	$-0.389058\pi$
$373$	3.23205	+	0.866025i	0.167349	+	0.0448411i	−0.174171	+	0.984715i	$0.555725\pi$
$374$			2.87564i			0.148696i
$375$	6.69615	+	3.86603i	0.345788	+	0.199641i
$376$	−5.66025	+	21.1244i	−0.291905	+	1.08941i
$377$		−	2.00000i		−	0.103005i
$378$	3.09808	+	16.0981i	0.159348	+	0.827996i
$379$	−24.1244	+	24.1244i	−1.23918	+	1.23918i	−0.278850	+	0.960335i	$0.589953\pi$
$379$	−24.1244	+	24.1244i	−1.23918	+	1.23918i	−0.960335	+	0.278850i	$0.910047\pi$
$380$			29.3205i			1.50411i
$381$	−4.73205	+	1.26795i	−0.242430	+	0.0649590i
$382$	−8.66025	+	8.66025i	−0.443097	+	0.443097i
$383$	7.40192	+	12.8205i	0.378221	+	0.655097i	0.990803	−	0.135309i	$-0.0432027\pi$
$383$	7.40192	+	12.8205i	0.378221	+	0.655097i	−0.612583	+	0.790406i	$0.709869\pi$
$384$	18.9282	−	10.9282i	0.965926	−	0.557678i
$385$	29.3205	−	25.3923i	1.49431	−	1.29411i
$386$	31.4186	+	8.41858i	1.59916	+	0.428495i
$387$	−0.124356	+	0.464102i	−0.00632135	+	0.0235916i
$388$	−18.9282	+	10.9282i	−0.960934	+	0.554795i
$389$	5.35641	+	19.9904i	0.271581	+	1.01355i	0.958098	+	0.286440i	$0.0924717\pi$
$389$	5.35641	+	19.9904i	0.271581	+	1.01355i	−0.686518	+	0.727113i	$0.740862\pi$
$390$	−1.73205	+	3.00000i	−0.0877058	+	0.151911i
$391$			1.14359i			0.0578340i
$392$	15.8564	−	11.8564i	0.800869	−	0.598839i
$393$			17.9282i			0.904358i
$394$	1.14359	+	0.660254i	0.0576134	+	0.0332631i
$395$	0.571797	+	2.13397i	0.0287702	+	0.107372i
$396$	−6.19615	−	1.66025i	−0.311368	−	0.0834309i
$397$	−1.37564	+	5.13397i	−0.0690416	+	0.257667i	−0.991816	−	0.127673i	$-0.959249\pi$
$397$	−1.37564	+	5.13397i	−0.0690416	+	0.257667i	0.922775	+	0.385340i	$0.125916\pi$
$398$	−0.705771	+	2.63397i	−0.0353771	+	0.132029i
$399$	16.9282	−	14.6603i	0.847470	−	0.733931i
$400$	21.4641	−	12.3923i	1.07321	−	0.619615i
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$	14.6603	+	14.6603i	0.731187	+	0.731187i
$403$	−0.0980762	+	0.0262794i	−0.00488552	+	0.00130907i
$404$	−10.3397	−	10.3397i	−0.514422	−	0.514422i
$405$	25.2224	−	25.2224i	1.25331	−	1.25331i
$406$	19.3923	−	3.73205i	0.962424	−	0.185219i
$407$			48.5167i			2.40488i
$408$	2.19615	−	1.26795i	0.108726	−	0.0627728i
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$	42.2487			2.08652
$411$	25.3564	+	6.79423i	1.25074	+	0.335135i
$412$	−0.464102	+	0.803848i	−0.0228646	+	0.0396027i
$413$	−15.3038	+	22.5981i	−0.753053	+	1.11198i
$414$	−2.46410	−	0.660254i	−0.121104	−	0.0324497i
$415$	−20.0263	−	34.6865i	−0.983051	−	1.70269i
$416$	1.07180	+	1.85641i	0.0525492	+	0.0910178i
$417$	−2.63397	+	4.56218i	−0.128986	+	0.223411i
$418$	−7.02628	−	26.2224i	−0.343667	−	1.28258i
$419$	−19.0000	−	19.0000i	−0.928211	−	0.928211i	0.0693796	−	0.997590i	$-0.477898\pi$
$419$	−19.0000	−	19.0000i	−0.928211	−	0.928211i	−0.997590	+	0.0693796i	$0.977898\pi$
$420$	−32.3205	−	11.1962i	−1.57708	−	0.546316i
$421$	−8.66025	+	8.66025i	−0.422075	+	0.422075i	−0.885918	−	0.463843i	$-0.846470\pi$
$421$	−8.66025	+	8.66025i	−0.422075	+	0.422075i	0.463843	+	0.885918i	$0.346470\pi$
$422$	2.07180	−	3.58846i	0.100853	−	0.174683i
$423$	−4.90192	−	2.83013i	−0.238340	−	0.137605i
$424$	−16.1962	+	28.0526i	−0.786555	+	1.36235i
$425$	2.49038	−	1.43782i	0.120801	−	0.0697446i
$426$	17.6603	−	10.1962i	0.855642	−	0.494005i
$427$	−0.330127	+	0.160254i	−0.0159760	+	0.00775524i
$428$	−1.73205	+	0.464102i	−0.0837218	+	0.0224332i
$429$	0.830127	−	3.09808i	0.0400789	−	0.149577i
$430$	2.19615	+	2.19615i	0.105908	+	0.105908i
$431$	−6.66987	+	11.5526i	−0.321276	+	0.556467i	−0.980752	−	0.195259i	$-0.937445\pi$
$431$	−6.66987	+	11.5526i	−0.321276	+	0.556467i	0.659475	+	0.751726i	$0.270779\pi$
$432$	−4.53590	−	16.9282i	−0.218234	−	0.814459i
$433$	29.1769			1.40215			0.701077	−	0.713086i	$-0.252703\pi$
$433$	29.1769			1.40215			0.701077	+	0.713086i	$0.252703\pi$
$434$	−0.437822	−	0.901924i	−0.0210161	−	0.0432937i
$435$	−24.1244	−	24.1244i	−1.15667	−	1.15667i
$436$	−21.1244	+	21.1244i	−1.01167	+	1.01167i
$437$	−2.79423	−	10.4282i	−0.133666	−	0.498849i
$438$			8.73205i			0.417234i
$439$	12.5263	−	7.23205i	0.597847	−	0.345167i	−0.170347	−	0.985384i	$-0.554489\pi$
$439$	12.5263	−	7.23205i	0.597847	−	0.345167i	0.768194	+	0.640217i	$0.221156\pi$
$440$	−29.3205	+	29.3205i	−1.39780	+	1.39780i
$441$	1.90192	+	4.75833i	0.0905678	+	0.226587i
$442$	0.124356	+	0.215390i	0.00591500	+	0.0102451i
$443$	−12.7942	−	3.42820i	−0.607872	−	0.162879i	−0.0582637	−	0.998301i	$-0.518556\pi$
$443$	−12.7942	−	3.42820i	−0.607872	−	0.162879i	−0.549608	+	0.835422i	$0.685223\pi$
$444$	37.0526	−	21.3923i	1.75844	−	1.01523i
$445$	−16.7942	+	4.50000i	−0.796123	+	0.213320i
$446$	−6.53590	−	24.3923i	−0.309484	−	1.15501i
$447$	−17.9282			−0.847975
$448$	−16.0000	+	13.8564i	−0.755929	+	0.654654i
$449$	11.3205			0.534248			0.267124	−	0.963662i	$-0.413927\pi$
$449$	11.3205			0.534248			0.267124	+	0.963662i	$0.413927\pi$
$450$	1.66025	+	6.19615i	0.0782651	+	0.292089i
$451$	−37.7846	+	10.1244i	−1.77921	+	0.476737i
$452$	−9.46410	+	5.46410i	−0.445154	+	0.257010i
$453$	17.5263	+	4.69615i	0.823456	+	0.220644i
$454$	16.8301	+	29.1506i	0.789877	+	1.36811i
$455$	1.09808	−	3.16987i	0.0514786	−	0.148606i
$456$	−16.9282	+	16.9282i	−0.792736	+	0.792736i
$457$	25.2846	−	14.5981i	1.18276	−	0.682869i	0.226112	−	0.974101i	$-0.427399\pi$
$457$	25.2846	−	14.5981i	1.18276	−	0.682869i	0.956652	+	0.291232i	$0.0940652\pi$
$458$		−	25.5167i		−	1.19232i
$459$	−0.526279	−	1.96410i	−0.0245646	−	0.0916764i
$460$	−11.6603	+	11.6603i	−0.543662	+	0.543662i
$461$	1.33975	+	1.33975i	0.0623982	+	0.0623982i	0.737617	−	0.675219i	$-0.235951\pi$
$461$	1.33975	+	1.33975i	0.0623982	+	0.0623982i	−0.675219	+	0.737617i	$0.735951\pi$
$462$	31.5885	+	2.26795i	1.46963	+	0.105515i
$463$	29.8564			1.38754			0.693772	−	0.720194i	$-0.255947\pi$
$463$	29.8564			1.38754			0.693772	+	0.720194i	$0.255947\pi$
$464$	−20.3923	+	5.46410i	−0.946689	+	0.253665i
$465$	−0.866025	+	1.50000i	−0.0401610	+	0.0695608i
$466$	11.1962	+	11.1962i	0.518652	+	0.518652i
$467$	0.00961894	−	0.0358984i	0.000445112	−	0.00166118i	−0.965703	−	0.259650i	$-0.916393\pi$
$467$	0.00961894	−	0.0358984i	0.000445112	−	0.00166118i	0.966148	+	0.257988i	$0.0830596\pi$
$468$	−0.535898	+	0.143594i	−0.0247719	+	0.00663761i
$469$	−16.6244	−	11.2583i	−0.767641	−	0.519861i
$470$	−31.6865	+	18.2942i	−1.46159	+	0.843850i
$471$	27.5263	−	15.8923i	1.26834	−	0.732279i
$472$	14.5885	−	25.2679i	0.671488	−	1.16305i
$473$	−2.49038	−	1.43782i	−0.114508	−	0.0661111i
$474$	−0.901924	+	1.56218i	−0.0414267	+	0.0717532i
$475$	−19.1962	+	19.1962i	−0.880780	+	0.880780i
$476$	−1.85641	+	1.60770i	−0.0850883	+	0.0736886i
$477$	−5.92820	−	5.92820i	−0.271434	−	0.271434i
$478$	−5.66025	−	21.1244i	−0.258894	−	0.966206i
$479$	7.79423	−	13.5000i	0.356127	−	0.616831i	−0.631183	−	0.775634i	$-0.717430\pi$
$479$	7.79423	−	13.5000i	0.356127	−	0.616831i	0.987310	+	0.158803i	$0.0507636\pi$
$480$	35.3205	+	9.46410i	1.61215	+	0.431975i
$481$	2.09808	+	3.63397i	0.0956640	+	0.165695i
$482$	−0.0980762	−	0.0262794i	−0.00446725	−	0.00119700i
$483$	12.5622	+	0.901924i	0.571599	+	0.0410390i
$484$	8.19615	−	14.1962i	0.372552	−	0.645280i
$485$	−35.3205	−	9.46410i	−1.60382	−	0.429743i
$486$	10.5359			0.477918
$487$	−19.3301	−	11.1603i	−0.875932	−	0.505719i	−0.00661681	−	0.999978i	$-0.502106\pi$
$487$	−19.3301	−	11.1603i	−0.875932	−	0.505719i	−0.869315	+	0.494259i	$0.835440\pi$
$488$	0.339746	−	0.196152i	0.0153796	−	0.00887940i
$489$			0.464102i			0.0209874i
$490$	32.7846	+	4.73205i	1.48106	+	0.213772i
$491$	27.5885	−	27.5885i	1.24505	−	1.24505i	0.287170	−	0.957880i	$-0.407286\pi$
$491$	27.5885	−	27.5885i	1.24505	−	1.24505i	0.957880	−	0.287170i	$-0.0927145\pi$
$492$	24.3923	+	24.3923i	1.09969	+	1.09969i
$493$	−2.36603	+	0.633975i	−0.106560	+	0.0285528i
$494$	−1.66025	−	1.66025i	−0.0746984	−	0.0746984i
$495$	−5.36603	−	9.29423i	−0.241185	−	0.417745i
$496$	0.535898	+	0.928203i	0.0240625	+	0.0416776i
$497$	−14.9282	+	12.9282i	−0.669621	+	0.579909i
$498$	8.46410	−	31.5885i	0.379285	−	1.41551i
$499$	0.990381	−	3.69615i	0.0443355	−	0.165463i	−0.940209	−	0.340599i	$-0.889370\pi$
$499$	0.990381	−	3.69615i	0.0443355	−	0.165463i	0.984544	+	0.175137i	$0.0560367\pi$
$500$	7.73205	+	2.07180i	0.345788	+	0.0926536i
$501$	−2.92820	−	10.9282i	−0.130822	−	0.488236i
$502$	23.5359	+	13.5885i	1.05046	+	0.606483i
$503$		−	4.14359i		−	0.184754i	−0.995724	−	0.0923769i	$-0.970554\pi$
$503$		−	4.14359i		−	0.184754i	0.995724	−	0.0923769i	$-0.0294464\pi$
$504$	−2.39230	−	4.92820i	−0.106562	−	0.219520i
$505$		−	24.4641i		−	1.08864i
$506$	7.63397	−	13.2224i	0.339372	−	0.587809i
$507$	6.42820	+	23.9904i	0.285487	+	1.06545i
$508$	−4.39230	+	2.53590i	−0.194877	+	0.112512i
$509$	4.42820	−	16.5263i	0.196277	−	0.732514i	−0.795656	−	0.605749i	$-0.792874\pi$
$509$	4.42820	−	16.5263i	0.196277	−	0.732514i	0.991933	−	0.126766i	$-0.0404597\pi$
$510$	4.09808	+	1.09808i	0.181466	+	0.0486236i
$511$	−1.59808	−	8.30385i	−0.0706947	−	0.367341i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$	9.59808	+	16.6244i	0.423765	+	0.733983i
$514$	1.39230	−	1.39230i	0.0614119	−	0.0614119i
$515$	−1.50000	+	0.401924i	−0.0660979	+	0.0177109i
$516$			2.53590i			0.111637i
$517$	23.9545	−	23.9545i	1.05352	−	1.05352i
$518$	−31.3205	+	27.1244i	−1.37614	+	1.19178i
$519$			9.19615i			0.403666i
$520$	−0.928203	+	3.46410i	−0.0407044	+	0.151911i
$521$	37.6244	+	21.7224i	1.64835	+	0.951677i	0.977727	+	0.209881i	$0.0673078\pi$
$521$	37.6244	+	21.7224i	1.64835	+	0.951677i	0.670626	+	0.741796i	$0.266026\pi$
$522$		−	5.46410i		−	0.239157i
$523$	−34.6506	−	9.28461i	−1.51517	−	0.405988i	−0.597019	−	0.802227i	$-0.703648\pi$
$523$	−34.6506	−	9.28461i	−1.51517	−	0.405988i	−0.918147	+	0.396239i	$0.870315\pi$
$524$	4.80385	+	17.9282i	0.209857	+	0.783197i
$525$	−13.8301	−	28.4904i	−0.603596	−	1.24342i
$526$	−9.29423	+	34.6865i	−0.405248	+	1.51240i
$527$	0.0621778	+	0.107695i	0.00270851	+	0.00469127i
$528$	−33.8564			−1.47341
$529$	−8.46410	+	14.6603i	−0.368004	+	0.637402i
$530$	−52.3468	+	14.0263i	−2.27380	+	0.609263i
$531$	5.33975	+	5.33975i	0.231725	+	0.231725i
$532$	13.0000	−	19.1962i	0.563621	−	0.832259i
$533$	−2.39230	+	2.39230i	−0.103622	+	0.103622i
$534$	−12.2942	−	7.09808i	−0.532023	−	0.307164i
$535$	−2.59808	−	1.50000i	−0.112325	−	0.0648507i
$536$	18.5885	+	10.7321i	0.802899	+	0.463554i
$537$	13.1603	−	7.59808i	0.567907	−	0.327881i
$538$	15.8301	+	27.4186i	0.682485	+	1.18210i
$539$	−30.4545	+	3.62436i	−1.31177	+	0.156112i
$540$	14.6603	−	25.3923i	0.630877	−	1.09271i
$541$	−5.76795	+	21.5263i	−0.247984	+	0.925487i	0.723877	+	0.689929i	$0.242358\pi$
$541$	−5.76795	+	21.5263i	−0.247984	+	0.925487i	−0.971860	+	0.235558i	$0.924308\pi$
$542$	−12.1244	+	12.1244i	−0.520786	+	0.520786i
$543$	10.0981	−	17.4904i	0.433350	−	0.750584i
$544$	1.85641	−	1.85641i	0.0795928	−	0.0795928i
$545$	−49.9808			−2.14094
$546$	2.46410	−	1.19615i	0.105454	−	0.0511906i
$547$	15.0526	+	15.0526i	0.643601	+	0.643601i	0.951439	−	0.307838i	$-0.0996054\pi$
$547$	15.0526	+	15.0526i	0.643601	+	0.643601i	−0.307838	+	0.951439i	$0.599605\pi$
$548$	27.1769			1.16094
$549$	0.0262794	+	0.0980762i	0.00112158	+	0.00418579i
$550$	−38.3923			−1.63705
$551$	20.0263	−	11.5622i	0.853148	−	0.492565i
$552$	−13.4641			−0.573070
$553$	0.571797	−	1.65064i	0.0243153	−	0.0701921i
$554$	−21.2942	+	12.2942i	−0.904705	+	0.522332i
$555$	69.1410	+	18.5263i	2.93487	+	0.786397i
$556$	−1.41154	+	5.26795i	−0.0598627	+	0.223411i
$557$	−5.23205	+	1.40192i	−0.221689	+	0.0594014i	−0.367954	−	0.929844i	$-0.619942\pi$
$557$	−5.23205	+	1.40192i	−0.221689	+	0.0594014i	0.146265	+	0.989245i	$0.453275\pi$
$558$	−0.267949	+	0.0717968i	−0.0113432	+	0.00303940i
$559$	−0.248711			−0.0105194
$560$	−35.3205	−	2.53590i	−1.49256	−	0.107161i
$561$	−3.92820			−0.165849
$562$	−17.6603	+	4.73205i	−0.744953	+	0.199610i
$563$	−42.6506	+	11.4282i	−1.79751	+	0.481641i	−0.993585	−	0.113089i	$-0.963925\pi$
$563$	−42.6506	+	11.4282i	−1.79751	+	0.481641i	−0.803925	+	0.594731i	$0.797259\pi$
$564$	−28.8564	−	7.73205i	−1.21507	−	0.325578i
$565$	−17.6603	−	4.73205i	−0.742972	−	0.199079i
$566$	21.4186	−	12.3660i	0.900290	−	0.519783i
$567$	−27.6962	+	5.33013i	−1.16313	+	0.223844i
$568$	14.9282	−	14.9282i	0.626373	−	0.626373i
$569$	−26.0885	+	15.0622i	−1.09369	+	0.631439i	−0.934555	−	0.355818i	$-0.884202\pi$
$569$	−26.0885	+	15.0622i	−1.09369	+	0.631439i	−0.159130	+	0.987258i	$0.550869\pi$
$570$	−40.0526			−1.67762
$571$	−2.72243	−	10.1603i	−0.113930	−	0.425193i	0.885274	−	0.465069i	$-0.153970\pi$
$571$	−2.72243	−	10.1603i	−0.113930	−	0.425193i	−0.999205	+	0.0398756i	$0.987304\pi$
$572$		−	3.32051i		−	0.138837i
$573$	−11.8301	−	11.8301i	−0.494211	−	0.494211i
$574$	−27.6603	−	18.7321i	−1.15452	−	0.781861i
$575$	−15.2679			−0.636717
$576$	2.92820	+	5.07180i	0.122008	+	0.211325i
$577$	17.6244	−	30.5263i	0.733712	−	1.27083i	−0.221575	−	0.975143i	$-0.571120\pi$
$577$	17.6244	−	30.5263i	0.733712	−	1.27083i	0.955286	−	0.295682i	$-0.0955470\pi$
$578$	−16.7846	+	16.7846i	−0.698148	+	0.698148i
$579$	−11.5000	+	42.9186i	−0.477924	+	1.78364i
$580$	−30.5885	−	17.6603i	−1.27012	−	0.733302i
$581$	−2.26795	+	31.5885i	−0.0940904	+	1.31051i
$582$	−14.9282	−	25.8564i	−0.618794	−	1.07178i
$583$	43.4545	−	25.0885i	1.79970	−	1.03906i
$584$	2.33975	+	8.73205i	0.0968194	+	0.361335i
$585$	−0.803848	−	0.464102i	−0.0332350	−	0.0191882i
$586$	10.2679	+	5.92820i	0.424165	+	0.244892i
$587$	8.07180	−	8.07180i	0.333159	−	0.333159i	−0.520626	−	0.853785i	$-0.674301\pi$
$587$	8.07180	−	8.07180i	0.333159	−	0.333159i	0.853785	+	0.520626i	$0.174301\pi$
$588$	16.1962	+	21.6603i	0.667918	+	0.893254i
$589$	−0.830127	−	0.830127i	−0.0342048	−	0.0342048i
$590$	47.1506	−	12.6340i	1.94116	−	0.520133i
$591$	−0.901924	+	1.56218i	−0.0371002	+	0.0642594i
$592$	31.3205	−	31.3205i	1.28726	−	1.28726i
$593$	−4.69615	−	8.13397i	−0.192848	−	0.334022i	0.753345	−	0.657625i	$-0.228439\pi$
$593$	−4.69615	−	8.13397i	−0.192848	−	0.334022i	−0.946193	+	0.323603i	$0.895106\pi$
$594$	−7.02628	+	26.2224i	−0.288292	+	1.07592i
$595$	−4.09808	−	0.294229i	−0.168005	−	0.0120622i
$596$	−17.9282	+	4.80385i	−0.734368	+	0.196773i
$597$	−3.59808	−	0.964102i	−0.147259	−	0.0394581i
$598$		−	1.32051i		−	0.0539996i
$599$	−25.3301	−	14.6244i	−1.03496	−	0.597535i	−0.116559	−	0.993184i	$-0.537186\pi$
$599$	−25.3301	−	14.6244i	−1.03496	−	0.597535i	−0.918402	+	0.395649i	$0.870520\pi$
$600$	16.9282	+	29.3205i	0.691091	+	1.19700i
$601$			10.0000i			0.407909i	0.978980	+	0.203954i	$0.0653794\pi$
$601$			10.0000i			0.407909i	−0.978980	+	0.203954i	$0.934621\pi$
$602$	−0.464102	−	2.41154i	−0.0189154	−	0.0982871i
$603$	−3.92820	+	3.92820i	−0.159969	+	0.159969i
$604$	18.7846			0.764335
$605$	26.4904	−	7.09808i	1.07699	−	0.288578i
$606$	14.1244	−	14.1244i	0.573763	−	0.573763i
$607$	10.5263	+	18.2321i	0.427249	+	0.740016i	0.996627	−	0.0820591i	$-0.0261496\pi$
$607$	10.5263	+	18.2321i	0.427249	+	0.740016i	−0.569379	+	0.822075i	$0.692816\pi$
$608$	−12.3923	+	21.4641i	−0.502574	+	0.870484i
$609$	5.09808	+	26.4904i	0.206584	+	1.07344i
$610$	0.633975	+	0.169873i	0.0256689	+	0.00687796i
$611$	0.758330	−	2.83013i	0.0306788	−	0.114495i
$612$	0.339746	+	0.588457i	0.0137334	+	0.0237870i
$613$	−5.76795	−	21.5263i	−0.232965	−	0.869438i	−0.979056	−	0.203593i	$-0.934738\pi$
$613$	−5.76795	−	21.5263i	−0.232965	−	0.869438i	0.746090	−	0.665845i	$-0.231929\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$			57.7128i			2.32721i
$616$	32.1962	−	6.19615i	1.29722	−	0.249650i
$617$			7.46410i			0.300493i	0.988649	+	0.150247i	$0.0480068\pi$
$617$			7.46410i			0.300493i	−0.988649	+	0.150247i	$0.951993\pi$
$618$	−1.09808	−	0.633975i	−0.0441711	−	0.0255022i
$619$	−6.93782	−	25.8923i	−0.278855	−	1.04070i	−0.953214	−	0.302296i	$-0.902247\pi$
$619$	−6.93782	−	25.8923i	−0.278855	−	1.04070i	0.674359	−	0.738403i	$-0.264420\pi$
$620$	−0.464102	+	1.73205i	−0.0186388	+	0.0695608i
$621$	−2.79423	+	10.4282i	−0.112129	+	0.418469i
$622$	0.169873	−	0.633975i	0.00681129	−	0.0254201i
$623$	12.9904	+	4.50000i	0.520449	+	0.180289i
$624$	−2.53590	+	1.46410i	−0.101517	+	0.0586110i
$625$	−8.79423	−	15.2321i	−0.351769	−	0.609282i
$626$	9.58846	+	9.58846i	0.383232	+	0.383232i
$627$	35.8205	−	9.59808i	1.43053	−	0.383310i
$628$	23.2679	−	23.2679i	0.928492	−	0.928492i
$629$	3.63397	−	3.63397i	0.144896	−	0.144896i
$630$	3.00000	−	8.66025i	0.119523	−	0.345033i
$631$		−	16.2487i		−	0.646851i	−0.946254	−	0.323425i	$-0.895165\pi$
$631$		−	16.2487i		−	0.646851i	0.946254	−	0.323425i	$-0.104835\pi$
$632$	−0.483340	+	1.80385i	−0.0192262	+	0.0717532i
$633$	4.90192	+	2.83013i	0.194834	+	0.112487i
$634$	−17.2679			−0.685798
$635$	−8.19615	−	2.19615i	−0.325254	−	0.0871517i
$636$	−38.3205	−	22.1244i	−1.51951	−	0.877288i
$637$	−2.12436	+	1.58846i	−0.0841700	+	0.0629370i
$638$	31.5885	+	8.46410i	1.25060	+	0.335097i
$639$	2.73205	+	4.73205i	0.108078	+	0.187197i
$640$	37.8564			1.49641
$641$	19.4282	−	33.6506i	0.767368	−	1.32912i	−0.171618	−	0.985164i	$-0.554899\pi$
$641$	19.4282	−	33.6506i	0.767368	−	1.32912i	0.938986	−	0.343957i	$-0.111767\pi$
$642$	−0.633975	−	2.36603i	−0.0250210	−	0.0933796i
$643$	15.3923	+	15.3923i	0.607013	+	0.607013i	0.942164	−	0.335151i	$-0.108787\pi$
$643$	15.3923	+	15.3923i	0.607013	+	0.607013i	−0.335151	+	0.942164i	$0.608787\pi$
$644$	12.8038	−	2.46410i	0.504542	−	0.0970992i
$645$	−3.00000	+	3.00000i	−0.118125	+	0.118125i
$646$	−1.43782	+	2.49038i	−0.0565704	+	0.0979827i
$647$	−29.1340	−	16.8205i	−1.14537	−	0.661282i	−0.197619	−	0.980279i	$-0.563321\pi$
$647$	−29.1340	−	16.8205i	−1.14537	−	0.661282i	−0.947756	+	0.318997i	$0.896654\pi$
$648$	29.1244	−	7.80385i	1.14411	−	0.306564i
$649$	−39.1410	+	22.5981i	−1.53642	+	0.887052i
$650$	−2.87564	+	1.66025i	−0.112792	+	0.0651205i
$651$	1.23205	−	0.598076i	0.0482879	−	0.0234405i
$652$	0.124356	+	0.464102i	0.00487014	+	0.0181756i
$653$	−5.55256	+	20.7224i	−0.217288	+	0.810931i	0.768060	+	0.640378i	$0.221222\pi$
$653$	−5.55256	+	20.7224i	−0.217288	+	0.810931i	−0.985348	+	0.170554i	$0.945444\pi$
$654$	−28.8564	−	28.8564i	−1.12837	−	1.12837i
$655$	−15.5263	+	26.8923i	−0.606662	+	1.05077i
$656$	30.9282	+	17.8564i	1.20754	+	0.697176i
$657$	−2.33975			−0.0912822
$658$	28.8564	+	2.07180i	1.12494	+	0.0807670i
$659$	−8.85641	−	8.85641i	−0.344997	−	0.344997i	0.513245	−	0.858242i	$-0.328443\pi$
$659$	−8.85641	−	8.85641i	−0.344997	−	0.344997i	−0.858242	+	0.513245i	$0.828443\pi$
$660$	−40.0526	−	40.0526i	−1.55904	−	1.55904i
$661$	4.83975	+	18.0622i	0.188244	+	0.702537i	0.993913	+	0.110170i	$0.0351397\pi$
$661$	4.83975	+	18.0622i	0.188244	+	0.702537i	−0.805668	+	0.592367i	$0.798194\pi$
$662$		−	25.2679i		−	0.982067i
$663$	−0.294229	+	0.169873i	−0.0114269	+	0.00659732i
$664$		−	33.8564i		−	1.31388i
$665$	38.0885	−	7.33013i	1.47701	−	0.284250i
$666$	5.73205	+	9.92820i	0.222112	+	0.384710i
$667$	12.5622	+	3.36603i	0.486409	+	0.130333i
$668$	−5.85641	−	10.1436i	−0.226591	−	0.392467i
$669$	33.3205	−	8.92820i	1.28825	−	0.345184i
$670$	9.29423	+	34.6865i	0.359067	+	1.34006i
$671$	−0.607695			−0.0234598
$672$	−18.9282	−	21.8564i	−0.730171	−	0.843129i
$673$	−0.784610			−0.0302445			−0.0151222	−	0.999886i	$-0.504814\pi$
$673$	−0.784610			−0.0302445			−0.0151222	+	0.999886i	$0.504814\pi$
$674$	−12.3923	−	46.2487i	−0.477334	−	1.78143i
$675$	26.2224	−	7.02628i	1.00930	−	0.270442i
$676$	12.8564	+	22.2679i	0.494477	+	0.856460i
$677$	49.5526	+	13.2776i	1.90446	+	0.510298i	0.995660	+	0.0930654i	$0.0296666\pi$
$677$	49.5526	+	13.2776i	1.90446	+	0.510298i	0.908800	+	0.417233i	$0.137000\pi$
$678$	−7.46410	−	12.9282i	−0.286657	−	0.496505i
$679$	18.9282	+	21.8564i	0.726398	+	0.838772i
$680$	4.39230			0.168437
$681$	−39.8205	+	22.9904i	−1.52593	+	0.880993i
$682$		−	1.66025i		−	0.0635744i
$683$	11.5788	+	43.2128i	0.443052	+	1.65349i	0.721029	+	0.692905i	$0.243669\pi$
$683$	11.5788	+	43.2128i	0.443052	+	1.65349i	−0.277977	+	0.960588i	$0.589664\pi$
$684$	−4.53590	−	4.53590i	−0.173434	−	0.173434i
$685$	32.1506	+	32.1506i	1.22841	+	1.22841i
$686$	−19.3660	−	17.6340i	−0.739398	−	0.673268i
$687$	34.8564			1.32985
$688$	0.679492	+	2.53590i	0.0259054	+	0.0966802i
$689$	2.16987	−	3.75833i	0.0826656	−	0.143181i
$690$	−15.9282	−	15.9282i	−0.606376	−	0.606376i
$691$	2.99038	−	11.1603i	0.113759	−	0.424556i	−0.885432	−	0.464770i	$-0.846137\pi$
$691$	2.99038	−	11.1603i	0.113759	−	0.424556i	0.999191	+	0.0402135i	$0.0128038\pi$
$692$	2.46410	+	9.19615i	0.0936711	+	0.349585i
$693$	−0.607695	+	8.46410i	−0.0230844	+	0.321525i
$694$	−21.1699	+	12.2224i	−0.803597	+	0.463957i
$695$	−7.90192	+	4.56218i	−0.299737	+	0.173053i
$696$	−7.46410	−	27.8564i	−0.282926	−	1.05589i
$697$	3.58846	+	2.07180i	0.135923	+	0.0784749i
$698$	18.1244	−	31.3923i	0.686017	−	1.18822i
$699$	−15.2942	+	15.2942i	−0.578481	+	0.578481i
$700$	−21.4641	−	24.7846i	−0.811267	−	0.936770i
$701$	7.39230	+	7.39230i	0.279204	+	0.279204i	0.832791	−	0.553588i	$-0.186742\pi$
$701$	7.39230	+	7.39230i	0.279204	+	0.279204i	−0.553588	+	0.832791i	$0.686742\pi$
$702$	0.607695	+	2.26795i	0.0229360	+	0.0855982i
$703$	−24.2583	+	42.0167i	−0.914920	+	1.58469i
$704$	−33.8564	+	9.07180i	−1.27601	+	0.341906i
$705$	−24.9904	−	43.2846i	−0.941192	−	1.63019i
$706$	−18.8301	−	5.04552i	−0.708681	−	0.189891i
$707$	−10.8468	+	16.0167i	−0.407935	+	0.602369i
$708$	34.5167	+	19.9282i	1.29722	+	0.748948i
$709$	−8.76795	−	2.34936i	−0.329287	−	0.0882323i	0.0903879	−	0.995907i	$-0.471189\pi$
$709$	−8.76795	−	2.34936i	−0.329287	−	0.0882323i	−0.419675	+	0.907674i	$0.637856\pi$
$710$	35.3205			1.32556
$711$	−0.418584	−	0.241670i	−0.0156981	−	0.00906332i
$712$	−14.1962	−	3.80385i	−0.532023	−	0.142555i
$713$		−	0.660254i		−	0.0247267i
$714$	−2.19615	−	2.53590i	−0.0821889	−	0.0949036i
$715$	3.92820	−	3.92820i	0.146906	−	0.146906i
$716$	11.1244	−	11.1244i	0.415737	−	0.415737i
$717$	28.8564	−	7.73205i	1.07766	−	0.288759i
$718$	2.46410	+	2.46410i	0.0919595	+	0.0919595i
$719$	−15.7942	−	27.3564i	−0.589025	−	1.02022i	−0.994360	−	0.106054i	$-0.966178\pi$
$719$	−15.7942	−	27.3564i	−0.589025	−	1.02022i	0.405335	−	0.914168i	$-0.367155\pi$
$720$	−2.53590	+	9.46410i	−0.0945074	+	0.352706i
$721$	1.16025	+	0.401924i	0.0432101	+	0.0149684i
$722$	0.0717968	−	0.267949i	0.00267200	−	0.00997204i
$723$	0.0358984	−	0.133975i	0.00133508	−	0.00498257i
$724$	5.41154	−	20.1962i	0.201118	−	0.750584i
$725$	−8.46410	−	31.5885i	−0.314349	−	1.17317i
$726$	19.3923	+	11.1962i	0.719716	+	0.415528i
$727$		−	6.67949i		−	0.247729i	−0.992299	−	0.123864i	$-0.960471\pi$
$727$		−	6.67949i		−	0.247729i	0.992299	−	0.123864i	$-0.0395288\pi$
$728$	2.14359	−	1.85641i	0.0794469	−	0.0688030i
$729$		−	17.5885i		−	0.651424i
$730$	−7.56218	+	13.0981i	−0.279889	+	0.484782i
$731$	0.0788383	+	0.294229i	0.00291594	+	0.0108824i
$732$	0.267949	+	0.464102i	0.00990369	+	0.0171537i
$733$	12.1077	−	45.1865i	0.447208	−	1.66900i	−0.262832	−	0.964842i	$-0.584657\pi$
$733$	12.1077	−	45.1865i	0.447208	−	1.66900i	0.710040	−	0.704161i	$-0.248677\pi$
$734$	24.7583	+	6.63397i	0.913847	+	0.244864i
$735$	−6.46410	+	44.7846i	−0.238432	+	1.65191i
$736$	−13.4641	+	3.60770i	−0.496293	+	0.132981i
$737$	−16.6244	−	28.7942i	−0.612366	−	1.06065i
$738$	−6.53590	+	6.53590i	−0.240590	+	0.240590i
$739$	50.3109	−	13.4808i	1.85072	−	0.495898i	0.851138	−	0.524942i	$-0.175913\pi$
$739$	50.3109	−	13.4808i	1.85072	−	0.495898i	0.999578	+	0.0290444i	$0.00924642\pi$
$740$	74.1051			2.72416
$741$	2.26795	−	2.26795i	0.0833152	−	0.0833152i
$742$	40.4904	+	14.0263i	1.48645	+	0.514921i
$743$		−	24.9282i		−	0.914527i	−0.889331	−	0.457264i	$-0.848830\pi$
$743$		−	24.9282i		−	0.914527i	0.889331	−	0.457264i	$-0.151170\pi$
$744$	−1.26795	+	0.732051i	−0.0464853	+	0.0268383i
$745$	−26.8923	−	15.5263i	−0.985258	−	0.568839i
$746$			4.73205i			0.173253i
$747$	8.46410	+	2.26795i	0.309685	+	0.0829799i
$748$	−3.92820	+	1.05256i	−0.143629	+	0.0384854i
$749$	1.03590	+	2.13397i	0.0378509	+	0.0779737i
$750$	−2.83013	+	10.5622i	−0.103342	+	0.385676i
$751$	12.5263	+	21.6962i	0.457090	+	0.791704i	0.998806	−	0.0488582i	$-0.0155582\pi$
$751$	12.5263	+	21.6962i	0.457090	+	0.791704i	−0.541715	+	0.840562i	$0.682225\pi$
$752$	−30.9282			−1.12784
$753$	−18.5622	+	32.1506i	−0.676443	+	1.17163i
$754$	2.73205	−	0.732051i	0.0994954	−	0.0266597i
$755$	22.2224	+	22.2224i	0.808757	+	0.808757i
$756$	−20.8564	+	10.1244i	−0.758540	+	0.368219i
$757$	−1.33975	+	1.33975i	−0.0486939	+	0.0486939i	−0.731034	−	0.682341i	$-0.760962\pi$
$757$	−1.33975	+	1.33975i	−0.0486939	+	0.0486939i	0.682341	+	0.731034i	$0.260962\pi$
$758$	−41.7846	−	24.1244i	−1.51769	−	0.876236i
$759$	18.0622	+	10.4282i	0.655616	+	0.378520i
$760$	−40.0526	+	10.7321i	−1.45286	+	0.389292i
$761$	−15.2321	+	8.79423i	−0.552161	+	0.318791i	−0.749993	−	0.661445i	$-0.769943\pi$
$761$	−15.2321	+	8.79423i	−0.552161	+	0.318791i	0.197832	+	0.980236i	$0.436610\pi$
$762$	−3.46410	−	6.00000i	−0.125491	−	0.217357i
$763$	32.7224	+	22.1603i	1.18463	+	0.802255i
$764$	−15.0000	−	8.66025i	−0.542681	−	0.313317i
$765$	−0.294229	+	1.09808i	−0.0106379	+	0.0397010i
$766$	−14.8038	+	14.8038i	−0.534885	+	0.534885i
$767$	−1.95448	+	3.38526i	−0.0705723	+	0.122235i
$768$	21.8564	+	21.8564i	0.788675	+	0.788675i
$769$	−17.8564			−0.643918			−0.321959	−	0.946754i	$-0.604341\pi$
$769$	−17.8564			−0.643918			−0.321959	+	0.946754i	$0.604341\pi$
$770$	45.4186	+	30.7583i	1.63677	+	1.10845i
$771$	1.90192	+	1.90192i	0.0684961	+	0.0684961i
$772$			46.0000i			1.65558i
$773$	4.03590	+	15.0622i	0.145161	+	0.541749i	0.999748	+	0.0224406i	$0.00714368\pi$
$773$	4.03590	+	15.0622i	0.145161	+	0.541749i	−0.854587	+	0.519308i	$0.826190\pi$
$774$	−0.679492			−0.0244238
$775$	−1.43782	+	0.830127i	−0.0516481	+	0.0298190i
$776$	−21.8564	−	21.8564i	−0.784599	−	0.784599i
$777$	−37.0526	−	42.7846i	−1.32925	−	1.53489i
$778$	−25.3468	+	14.6340i	−0.908726	+	0.524653i
$779$	−37.7846	−	10.1244i	−1.35377	−	0.362743i
$780$	−4.73205	−	1.26795i	−0.169435	−	0.0453999i
$781$	−31.5885	+	8.46410i	−1.13032	+	0.302869i
$782$	−1.56218	+	0.418584i	−0.0558634	+	0.0149685i
$783$	−23.1244			−0.826397
$784$	22.0000	+	17.3205i	0.785714	+	0.618590i
$785$	55.0526			1.96491
$786$	−24.4904	+	6.56218i	−0.873543	+	0.234065i
$787$	−15.5263	+	4.16025i	−0.553452	+	0.148297i	−0.524696	−	0.851289i	$-0.675821\pi$
$787$	−15.5263	+	4.16025i	−0.553452	+	0.148297i	−0.0287557	+	0.999586i	$0.509154\pi$
$788$	−0.483340	+	1.80385i	−0.0172183	+	0.0642594i
$789$	−47.3827	−	12.6962i	−1.68687	−	0.451995i
$790$	−2.70577	+	1.56218i	−0.0962670	+	0.0555798i
$791$	9.46410	+	10.9282i	0.336505	+	0.388562i
$792$		−	9.07180i		−	0.322352i
$793$	−0.0455173	+	0.0262794i	−0.00161637	+	0.000933210i
$794$	−7.51666			−0.266756
$795$	−19.1603	−	71.5070i	−0.679544	−	2.53609i
$796$	−3.85641			−0.136687
$797$	−30.6603	−	30.6603i	−1.08604	−	1.08604i	−0.995932	−	0.0901101i	$-0.971278\pi$
$797$	−30.6603	−	30.6603i	−1.08604	−	1.08604i	−0.0901101	−	0.995932i	$-0.528722\pi$
$798$	26.2224	+	17.7583i	0.928264	+	0.628638i
$799$	−3.58846			−0.126950
$800$	24.7846	+	24.7846i	0.876268	+	0.876268i
$801$	1.90192	−	3.29423i	0.0672012	−	0.116396i
$802$	−15.0000	+	15.0000i	−0.529668	+	0.529668i
$803$	3.62436	−	13.5263i	0.127901	−	0.477332i
$804$	−14.6603	+	25.3923i	−0.517027	+	0.895518i
$805$	18.0622	+	12.2321i	0.636608	+	0.431123i
$806$	−0.0717968	−	0.124356i	−0.00252893	−	0.00438024i
$807$	−37.4545	+	21.6244i	−1.31846	+	0.761213i
$808$	10.3397	−	17.9090i	0.363751	−	0.630035i
$809$	15.5718	+	8.99038i	0.547475	+	0.316085i	0.748103	−	0.663583i	$-0.230965\pi$
$809$	15.5718	+	8.99038i	0.547475	+	0.316085i	−0.200628	+	0.979668i	$0.564298\pi$
$810$	43.6865	+	25.2224i	1.53499	+	0.886226i
$811$	−10.3205	+	10.3205i	−0.362402	+	0.362402i	−0.864697	−	0.502295i	$-0.832489\pi$
$811$	−10.3205	+	10.3205i	−0.362402	+	0.362402i	0.502295	+	0.864697i	$0.332489\pi$
$812$	12.1962	+	25.1244i	0.428001	+	0.881692i
$813$	−16.5622	−	16.5622i	−0.580861	−	0.580861i
$814$	−66.2750	+	17.7583i	−2.32294	+	0.622429i
$815$	−0.401924	+	0.696152i	−0.0140788	+	0.0243852i
$816$	2.53590	+	2.53590i	0.0887742	+	0.0887742i
$817$	−1.43782	−	2.49038i	−0.0503030	−	0.0871274i
$818$	−3.16987	+	11.8301i	−0.110832	+	0.413631i
$819$	0.320508	+	0.660254i	0.0111995	+	0.0230711i
$820$	15.4641	+	57.7128i	0.540030	+	2.01542i
$821$	17.1603	+	4.59808i	0.598897	+	0.160474i	0.545516	−	0.838100i	$-0.316334\pi$
$821$	17.1603	+	4.59808i	0.598897	+	0.160474i	0.0533808	+	0.998574i	$0.483000\pi$
$822$			37.1244i			1.29486i
$823$	27.0622	+	15.6244i	0.943328	+	0.544631i	0.891002	−	0.453999i	$-0.150003\pi$
$823$	27.0622	+	15.6244i	0.943328	+	0.544631i	0.0523262	+	0.998630i	$0.483336\pi$
$824$	−1.26795	−	0.339746i	−0.0441711	−	0.0118356i
$825$		−	52.4449i		−	1.82590i
$826$	−36.4711	−	12.6340i	−1.26899	−	0.439592i
$827$	37.7846	−	37.7846i	1.31390	−	1.31390i	0.395383	−	0.918516i	$-0.370612\pi$
$827$	37.7846	−	37.7846i	1.31390	−	1.31390i	0.918516	−	0.395383i	$-0.129388\pi$
$828$		−	3.60770i		−	0.125376i
$829$	−33.8205	+	9.06218i	−1.17463	+	0.314742i	−0.792796	−	0.609487i	$-0.791376\pi$
$829$	−33.8205	+	9.06218i	−1.17463	+	0.314742i	−0.381838	+	0.924229i	$0.624709\pi$
$830$	40.0526	−	40.0526i	1.39024	−	1.39024i
$831$	−16.7942	−	29.0885i	−0.582585	−	1.00907i
$832$	−2.14359	+	2.14359i	−0.0743157	+	0.0743157i
$833$	2.55256	+	2.00962i	0.0884409	+	0.0696292i
$834$	−7.19615	−	1.92820i	−0.249182	−	0.0667682i
$835$	5.07180	−	18.9282i	0.175517	−	0.655037i
$836$	33.2487	−	19.1962i	1.14993	−	0.663913i
$837$	0.303848	+	1.13397i	0.0105025	+	0.0391959i
$838$	19.0000	−	32.9090i	0.656344	−	1.13682i
$839$		−	37.7128i		−	1.30199i	−0.759082	−	0.650995i	$-0.774352\pi$
$839$		−	37.7128i		−	1.30199i	0.759082	−	0.650995i	$-0.225648\pi$
$840$	3.46410	−	48.2487i	0.119523	−	1.66474i
$841$		−	1.14359i		−	0.0394343i
$842$	−15.0000	−	8.66025i	−0.516934	−	0.298452i
$843$	−6.46410	−	24.1244i	−0.222635	−	0.830887i
$844$	5.66025	+	1.51666i	0.194834	+	0.0522056i
$845$	−11.1340	+	41.5526i	−0.383020	+	1.42945i
$846$	2.07180	−	7.73205i	0.0712298	−	0.265833i
$847$	−20.4904	−	7.09808i	−0.704058	−	0.243893i
$848$	−44.2487	−	11.8564i	−1.51951	−	0.407151i
$849$	16.8923	+	29.2583i	0.579742	+	1.00414i
$850$	2.87564	+	2.87564i	0.0986338	+	0.0986338i
$851$	−26.3564	+	7.06218i	−0.903486	+	0.242088i
$852$	20.3923	+	20.3923i	0.698629	+	0.698629i
$853$	−36.1244	+	36.1244i	−1.23687	+	1.23687i	−0.275603	+	0.961272i	$0.588877\pi$
$853$	−36.1244	+	36.1244i	−1.23687	+	1.23687i	−0.961272	+	0.275603i	$0.911123\pi$
$854$	−0.339746	−	0.392305i	−0.0116259	−	0.0134244i
$855$		−	10.7321i		−	0.367028i
$856$	−1.26795	−	2.19615i	−0.0433376	−	0.0750629i
$857$	8.89230	+	5.13397i	0.303755	+	0.175373i	0.644129	−	0.764917i	$-0.277220\pi$
$857$	8.89230	+	5.13397i	0.303755	+	0.175373i	−0.340373	+	0.940290i	$0.610553\pi$
$858$	4.53590			0.154853
$859$	39.6506	+	10.6244i	1.35286	+	0.362498i	0.861191	−	0.508282i	$-0.169719\pi$
$859$	39.6506	+	10.6244i	1.35286	+	0.362498i	0.491672	+	0.870781i	$0.336386\pi$
$860$	−2.19615	+	3.80385i	−0.0748882	+	0.129710i
$861$	25.5885	−	37.7846i	0.872052	−	1.28770i
$862$	−18.2224	−	4.88269i	−0.620658	−	0.166305i
$863$	7.66987	+	13.2846i	0.261086	+	0.452213i	0.966531	−	0.256551i	$-0.0825862\pi$
$863$	7.66987	+	13.2846i	0.261086	+	0.452213i	−0.705445	+	0.708765i	$0.749253\pi$
$864$	21.4641	−	12.3923i	0.730224	−	0.421595i
$865$	−7.96410	+	13.7942i	−0.270788	+	0.469018i
$866$	10.6795	+	39.8564i	0.362904	+	1.35438i
$867$	−22.9282	−	22.9282i	−0.778683	−	0.778683i
$868$	1.07180	−	0.928203i	0.0363792	−	0.0315053i
$869$	2.04552	−	2.04552i	0.0693894	−	0.0693894i
$870$	24.1244	−	41.7846i	0.817892	−	1.41663i
$871$	−2.49038	−	1.43782i	−0.0843833	−	0.0487187i
$872$	−36.5885	−	21.1244i	−1.23904	−	0.715361i
$873$	6.92820	−	4.00000i	0.234484	−	0.135379i
$874$	13.2224	−	7.63397i	0.447255	−	0.258223i
$875$	0.758330	−	10.5622i	0.0256362	−	0.357067i
$876$	−11.9282	+	3.19615i	−0.403017	+	0.107988i
$877$	7.55256	−	28.1865i	0.255032	−	0.951792i	−0.713041	−	0.701122i	$-0.752683\pi$
$877$	7.55256	−	28.1865i	0.255032	−	0.951792i	0.968073	−	0.250669i	$-0.0806507\pi$
$878$	14.4641	+	14.4641i	0.488140	+	0.488140i
$879$	−8.09808	+	14.0263i	−0.273141	+	0.473095i
$880$	−50.7846	−	29.3205i	−1.71195	−	0.988394i
$881$	50.0000			1.68454			0.842271	−	0.539054i	$-0.181218\pi$
$881$	50.0000			1.68454			0.842271	+	0.539054i	$0.181218\pi$
$882$	−5.80385	+	4.33975i	−0.195426	+	0.146127i
$883$	−5.00000	−	5.00000i	−0.168263	−	0.168263i	0.617952	−	0.786216i	$-0.287963\pi$
$883$	−5.00000	−	5.00000i	−0.168263	−	0.168263i	−0.786216	+	0.617952i	$0.787963\pi$
$884$	−0.248711	+	0.248711i	−0.00836507	+	0.00836507i
$885$	17.2583	+	64.4090i	0.580132	+	2.16508i
$886$		−	18.7321i		−	0.629316i
$887$	−27.7750	+	16.0359i	−0.932593	+	0.538433i	−0.887631	−	0.460556i	$-0.847650\pi$
$887$	−27.7750	+	16.0359i	−0.932593	+	0.538433i	−0.0449622	+	0.998989i	$0.514317\pi$
$888$	42.7846	+	42.7846i	1.43576	+	1.43576i
$889$	4.39230	+	5.07180i	0.147313	+	0.170103i
$890$	−12.2942	−	21.2942i	−0.412103	−	0.713784i
$891$	−45.1147	−	12.0885i	−1.51140	−	0.404979i
$892$	30.9282	−	17.8564i	1.03555	−	0.597877i
$893$	32.7224	−	8.76795i	1.09501	−	0.293408i
$894$	−6.56218	−	24.4904i	−0.219472	−	0.819081i
$895$	26.3205			0.879798
$896$	−24.7846	−	16.7846i	−0.827996	−	0.560734i
$897$	1.80385			0.0602287
$898$	4.14359	+	15.4641i	0.138274	+	0.516044i
$899$	1.36603	−	0.366025i	0.0455595	−	0.0122076i
$900$	−7.85641	+	4.53590i	−0.261880	+	0.151197i
$901$	−5.13397	−	1.37564i	−0.171037	−	0.0458294i
$902$	−27.6603	−	47.9090i	−0.920986	−	1.59519i
$903$	3.29423	−	0.633975i	0.109625	−	0.0210974i
$904$	−10.9282	−	10.9282i	−0.363467	−	0.363467i
$905$	30.2942	−	17.4904i	1.00701	−	0.581400i
$906$			25.6603i			0.852505i
$907$	2.72243	+	10.1603i	0.0903969	+	0.337366i	0.996281	−	0.0861591i	$-0.0274593\pi$
$907$	2.72243	+	10.1603i	0.0903969	+	0.337366i	−0.905885	+	0.423525i	$0.860793\pi$
$908$	−33.6603	+	33.6603i	−1.11705	+	1.11705i
$909$	3.78461	+	3.78461i	0.125528	+	0.125528i
$910$	4.73205	+	0.339746i	0.156866	+	0.0112625i
$911$	−27.3205			−0.905169			−0.452584	−	0.891722i	$-0.649498\pi$
$911$	−27.3205			−0.905169			−0.452584	+	0.891722i	$0.649498\pi$
$912$	−29.3205	−	16.9282i	−0.970899	−	0.560549i
$913$	−26.2224	+	45.4186i	−0.867836	+	1.50314i
$914$	29.1962	+	29.1962i	0.965723	+	0.965723i
$915$	−0.232051	+	0.866025i	−0.00767136	+	0.0286299i
$916$	34.8564	−	9.33975i	1.15169	−	0.308594i
$917$	22.0885	−	10.7224i	0.729425	−	0.354086i
$918$	2.49038	−	1.43782i	0.0821948	−	0.0474552i
$919$	14.1340	−	8.16025i	0.466237	−	0.269182i	−0.248426	−	0.968651i	$-0.579913\pi$
$919$	14.1340	−	8.16025i	0.466237	−	0.269182i	0.714663	+	0.699469i	$0.246580\pi$
$920$	−20.1962	−	11.6603i	−0.665847	−	0.384427i
$921$	−21.2942	−	12.2942i	−0.701669	−	0.405109i
$922$	−1.33975	+	2.32051i	−0.0441222	+	0.0764219i
$923$	−2.00000	+	2.00000i	−0.0658308	+	0.0658308i
$924$	8.46410	+	43.9808i	0.278449	+	1.44686i
$925$	48.5167	+	48.5167i	1.59522	+	1.59522i
$926$	10.9282	+	40.7846i	0.359123	+	1.34027i
$927$	0.169873	−	0.294229i	0.00557936	−	0.00966374i
$928$	−14.9282	−	25.8564i	−0.490042	−	0.848778i
$929$	20.0167	+	34.6699i	0.656725	+	1.13748i	0.981458	+	0.191676i	$0.0613922\pi$
$929$	20.0167	+	34.6699i	0.656725	+	1.13748i	−0.324733	+	0.945806i	$0.605274\pi$
$930$	−2.36603	−	0.633975i	−0.0775850	−	0.0207888i
$931$	−28.1865	−	12.0885i	−0.923776	−	0.396183i
$932$	−11.1962	+	19.3923i	−0.366742	+	0.635216i
$933$	0.866025	+	0.232051i	0.0283524	+	0.00759700i
$934$	0.0525589			0.00171978
$935$	−5.89230	−	3.40192i	−0.192699	−	0.111255i
$936$	−0.392305	−	0.679492i	−0.0128229	−	0.0222099i
$937$		−	42.9282i		−	1.40240i	−0.712963	−	0.701202i	$-0.752647\pi$
$937$		−	42.9282i		−	1.40240i	0.712963	−	0.701202i	$-0.247353\pi$
$938$	9.29423	−	26.8301i	0.303467	−	0.876035i
$939$	−13.0981	+	13.0981i	−0.427440	+	0.427440i
$940$	−36.5885	−	36.5885i	−1.19338	−	1.19338i
$941$	16.6962	−	4.47372i	0.544279	−	0.145839i	0.0238050	−	0.999717i	$-0.492422\pi$
$941$	16.6962	−	4.47372i	0.544279	−	0.145839i	0.520474	+	0.853877i	$0.325755\pi$
$942$	31.7846	+	31.7846i	1.03560	+	1.03560i
$943$	−11.0000	−	19.0526i	−0.358209	−	0.620437i
$944$	39.8564	+	10.6795i	1.29722	+	0.347588i
$945$	−36.6506	−	12.6962i	−1.19225	−	0.413006i
$946$	1.05256	−	3.92820i	0.0342216	−	0.127717i
$947$	10.5981	−	39.5526i	0.344391	−	1.28529i	−0.548931	−	0.835868i	$-0.684965\pi$
$947$	10.5981	−	39.5526i	0.344391	−	1.28529i	0.893322	−	0.449418i	$-0.148368\pi$
$948$	−2.46410	−	0.660254i	−0.0800303	−	0.0214441i
$949$	−0.313467	−	1.16987i	−0.0101756	−	0.0379757i
$950$	−33.2487	−	19.1962i	−1.07873	−	0.622805i
$951$		−	23.5885i		−	0.764908i
$952$	−2.87564	−	1.94744i	−0.0932002	−	0.0631169i
$953$			23.4641i			0.760077i	0.924971	+	0.380038i	$0.124089\pi$
$953$			23.4641i			0.760077i	−0.924971	+	0.380038i	$0.875911\pi$
$954$	5.92820	−	10.2679i	0.191933	−	0.332437i
$955$	−7.50000	−	27.9904i	−0.242694	−	0.905747i
$956$	26.7846	−	15.4641i	0.866276	−	0.500145i
$957$	−11.5622	+	43.1506i	−0.373752	+	1.39486i
$958$	21.2942	+	5.70577i	0.687985	+	0.184345i
$959$	−6.79423	−	35.3038i	−0.219397	−	1.14002i
$960$			51.7128i			1.66902i
$961$	15.4641	+	26.7846i	0.498842	+	0.864020i
$962$	−4.19615	+	4.19615i	−0.135289	+	0.135289i
$963$	0.633975	−	0.169873i	0.0204295	−	0.00547408i
$964$		−	0.143594i		−	0.00462484i
$965$	−54.4186	+	54.4186i	−1.75180	+	1.75180i
$966$	3.36603	+	17.4904i	0.108300	+	0.562744i
$967$		−	11.7513i		−	0.377896i	−0.981987	−	0.188948i	$-0.939492\pi$
$967$		−	11.7513i		−	0.377896i	0.981987	−	0.188948i	$-0.0605078\pi$
$968$	22.3923	+	6.00000i	0.719716	+	0.192847i
$969$	−3.40192	−	1.96410i	−0.109286	−	0.0630960i
$970$		−	51.7128i		−	1.66040i
$971$	−50.0429	−	13.4090i	−1.60595	−	0.430314i	−0.659121	−	0.752037i	$-0.729071\pi$
$971$	−50.0429	−	13.4090i	−1.60595	−	0.430314i	−0.946834	+	0.321723i	$0.895738\pi$
$972$	3.85641	+	14.3923i	0.123694	+	0.461633i
$973$	7.19615	+	0.516660i	0.230698	+	0.0165634i
$974$	8.16987	−	30.4904i	0.261780	−	0.976975i
$975$	−2.26795	−	3.92820i	−0.0726325	−	0.125803i
$976$	0.392305	+	0.392305i	0.0125574	+	0.0125574i
$977$	22.4282	−	38.8468i	0.717542	−	1.24282i	−0.244429	−	0.969667i	$-0.578601\pi$
$977$	22.4282	−	38.8468i	0.717542	−	1.24282i	0.961971	−	0.273152i	$-0.0880661\pi$
$978$	−0.633975	+	0.169873i	−0.0202723	+	0.00543194i
$979$	16.0981	+	16.0981i	0.514497	+	0.514497i
$980$	5.53590	+	46.5167i	0.176838	+	1.48592i
$981$	7.73205	−	7.73205i	0.246865	−	0.246865i
$982$	47.7846	+	27.5885i	1.52487	+	0.880383i
$983$	−18.8660	−	10.8923i	−0.601733	−	0.347411i	0.167990	−	0.985789i	$-0.446272\pi$
$983$	−18.8660	−	10.8923i	−0.601733	−	0.347411i	−0.769723	+	0.638378i	$0.779606\pi$
$984$	−24.3923	+	42.2487i	−0.777598	+	1.34684i
$985$	−2.70577	+	1.56218i	−0.0862130	+	0.0497751i
$986$	−1.73205	−	3.00000i	−0.0551597	−	0.0955395i
$987$	−2.83013	+	39.4186i	−0.0900839	+	1.25471i
$988$	1.66025	−	2.87564i	0.0528197	−	0.0914864i
$989$	0.418584	−	1.56218i	0.0133102	−	0.0496744i
$990$	10.7321	−	10.7321i	0.341087	−	0.341087i
$991$	19.7942	−	34.2846i	0.628784	−	1.08909i	−0.359012	−	0.933333i	$-0.616886\pi$
$991$	19.7942	−	34.2846i	0.628784	−	1.08909i	0.987796	−	0.155753i	$-0.0497805\pi$
$992$	−1.07180	+	1.07180i	−0.0340296	+	0.0340296i
$993$	34.5167			1.09535
$994$	−23.1244	−	15.6603i	−0.733460	−	0.496713i
$995$	−4.56218	−	4.56218i	−0.144631	−	0.144631i
$996$	46.2487			1.46545
$997$	−1.50000	−	5.59808i	−0.0475055	−	0.177293i	0.938097	−	0.346373i	$-0.112587\pi$
$997$	−1.50000	−	5.59808i	−0.0475055	−	0.177293i	−0.985602	+	0.169080i	$0.945920\pi$
$998$	5.41154			0.171299
$999$	42.0167	−	24.2583i	1.32935	−	0.767500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	112.2.w.a.109.1	yes	4
4.3	odd	2		448.2.ba.b.81.1		4
7.2	even	3		112.2.w.b.93.1	yes	4
7.3	odd	6		784.2.m.d.589.1		4
7.4	even	3		784.2.m.e.589.1		4
7.5	odd	6		784.2.x.h.765.1		4
7.6	odd	2		784.2.x.a.557.1		4
8.3	odd	2		896.2.ba.a.417.1		4
8.5	even	2		896.2.ba.d.417.1		4
16.3	odd	4		896.2.ba.c.865.1		4
16.5	even	4		112.2.w.b.53.1	yes	4
16.11	odd	4		448.2.ba.a.305.1		4
16.13	even	4		896.2.ba.b.865.1		4
28.23	odd	6		448.2.ba.a.401.1		4
56.37	even	6		896.2.ba.b.289.1		4
56.51	odd	6		896.2.ba.c.289.1		4
112.5	odd	12		784.2.x.a.373.1		4
112.37	even	12	inner	112.2.w.a.37.1	✓	4
112.51	odd	12		896.2.ba.a.737.1		4
112.53	even	12		784.2.m.e.197.1		4
112.69	odd	4		784.2.x.h.165.1		4
112.93	even	12		896.2.ba.d.737.1		4
112.101	odd	12		784.2.m.d.197.1		4
112.107	odd	12		448.2.ba.b.177.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.37.1	✓	4	112.37	even	12	inner
112.2.w.a.109.1	yes	4	1.1	even	1	trivial
112.2.w.b.53.1	yes	4	16.5	even	4
112.2.w.b.93.1	yes	4	7.2	even	3
448.2.ba.a.305.1		4	16.11	odd	4
448.2.ba.a.401.1		4	28.23	odd	6
448.2.ba.b.81.1		4	4.3	odd	2
448.2.ba.b.177.1		4	112.107	odd	12
784.2.m.d.197.1		4	112.101	odd	12
784.2.m.d.589.1		4	7.3	odd	6
784.2.m.e.197.1		4	112.53	even	12
784.2.m.e.589.1		4	7.4	even	3
784.2.x.a.373.1		4	112.5	odd	12
784.2.x.a.557.1		4	7.6	odd	2
784.2.x.h.165.1		4	112.69	odd	4
784.2.x.h.765.1		4	7.5	odd	6
896.2.ba.a.417.1		4	8.3	odd	2
896.2.ba.a.737.1		4	112.51	odd	12
896.2.ba.b.289.1		4	56.37	even	6
896.2.ba.b.865.1		4	16.13	even	4
896.2.ba.c.289.1		4	56.51	odd	6
896.2.ba.c.865.1		4	16.3	odd	4
896.2.ba.d.417.1		4	8.5	even	2
896.2.ba.d.737.1		4	112.93	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 112 = 2^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	112.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.86603 + 0.500000i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(-3.23205 - 0.866025i) q^{5} +(-1.36603 - 2.36603i) q^{6} +(1.73205 + 2.00000i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(0.633975 - 0.366025i) q^{9} -4.73205i q^{10} +(1.13397 + 4.23205i) q^{11} +(2.73205 - 2.73205i) q^{12} +(0.267949 + 0.267949i) q^{13} +(-2.09808 + 3.09808i) q^{14} +6.46410 q^{15} +(2.00000 - 3.46410i) q^{16} +(0.232051 - 0.401924i) q^{17} +(0.732051 + 0.732051i) q^{18} +(-1.13397 + 4.23205i) q^{19} +(6.46410 - 1.73205i) q^{20} +(-4.23205 - 2.86603i) q^{21} +(-5.36603 + 3.09808i) q^{22} +(-2.13397 + 1.23205i) q^{23} +(4.73205 + 2.73205i) q^{24} +(5.36603 + 3.09808i) q^{25} +(-0.267949 + 0.464102i) q^{26} +(3.09808 - 3.09808i) q^{27} +(-5.00000 - 1.73205i) q^{28} +(-3.73205 - 3.73205i) q^{29} +(2.36603 + 8.83013i) q^{30} +(-0.133975 + 0.232051i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-4.23205 - 7.33013i) q^{33} +(0.633975 + 0.169873i) q^{34} +(-3.86603 - 7.96410i) q^{35} +(-0.732051 + 1.26795i) q^{36} +(10.6962 + 2.86603i) q^{37} -6.19615 q^{38} +(-0.633975 - 0.366025i) q^{39} +(4.73205 + 8.19615i) q^{40} +8.92820i q^{41} +(2.36603 - 6.83013i) q^{42} +(-0.464102 + 0.464102i) q^{43} +(-6.19615 - 6.19615i) q^{44} +(-2.36603 + 0.633975i) q^{45} +(-2.46410 - 2.46410i) q^{46} +(-3.86603 - 6.69615i) q^{47} +(-2.00000 + 7.46410i) q^{48} +(-1.00000 + 6.92820i) q^{49} +(-2.26795 + 8.46410i) q^{50} +(-0.232051 + 0.866025i) q^{51} +(-0.732051 - 0.196152i) q^{52} +(-2.96410 - 11.0622i) q^{53} +(5.36603 + 3.09808i) q^{54} -14.6603i q^{55} +(0.535898 - 7.46410i) q^{56} -8.46410i q^{57} +(3.73205 - 6.46410i) q^{58} +(2.66987 + 9.96410i) q^{59} +(-11.1962 + 6.46410i) q^{60} +(-0.0358984 + 0.133975i) q^{61} +(-0.366025 - 0.0980762i) q^{62} +(1.83013 + 0.633975i) q^{63} +8.00000i q^{64} +(-0.633975 - 1.09808i) q^{65} +(8.46410 - 8.46410i) q^{66} +(-7.33013 + 1.96410i) q^{67} +0.928203i q^{68} +(3.36603 - 3.36603i) q^{69} +(9.46410 - 8.19615i) q^{70} +7.46410i q^{71} +(-2.00000 - 0.535898i) q^{72} +(-2.76795 - 1.59808i) q^{73} +15.6603i q^{74} +(-11.5622 - 3.09808i) q^{75} +(-2.26795 - 8.46410i) q^{76} +(-6.50000 + 9.59808i) q^{77} +(0.267949 - 1.00000i) q^{78} +(-0.330127 - 0.571797i) q^{79} +(-9.46410 + 9.46410i) q^{80} +(-5.33013 + 9.23205i) q^{81} +(-12.1962 + 3.26795i) q^{82} +(8.46410 + 8.46410i) q^{83} +(10.1962 + 0.732051i) q^{84} +(-1.09808 + 1.09808i) q^{85} +(-0.803848 - 0.464102i) q^{86} +(8.83013 + 5.09808i) q^{87} +(6.19615 - 10.7321i) q^{88} +(4.50000 - 2.59808i) q^{89} +(-1.73205 - 3.00000i) q^{90} +(-0.0717968 + 1.00000i) q^{91} +(2.46410 - 4.26795i) q^{92} +(0.133975 - 0.500000i) q^{93} +(7.73205 - 7.73205i) q^{94} +(7.33013 - 12.6962i) q^{95} -10.9282 q^{96} +10.9282 q^{97} +(-9.83013 + 1.16987i) q^{98} +(2.26795 + 2.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} - 6 q^{5} - 2 q^{6} - 8 q^{8} + 6 q^{9} + 8 q^{11} + 4 q^{12} + 8 q^{13} + 2 q^{14} + 12 q^{15} + 8 q^{16} - 6 q^{17} - 4 q^{18} - 8 q^{19} + 12 q^{20} - 10 q^{21} - 18 q^{22} - 12 q^{23}+ \cdots + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 - 6 * q^5 - 2 * q^6 - 8 * q^8 + 6 * q^9 + 8 * q^11 + 4 * q^12 + 8 * q^13 + 2 * q^14 + 12 * q^15 + 8 * q^16 - 6 * q^17 - 4 * q^18 - 8 * q^19 + 12 * q^20 - 10 * q^21 - 18 * q^22 - 12 * q^23 + 12 * q^24 + 18 * q^25 - 8 * q^26 + 2 * q^27 - 20 * q^28 - 8 * q^29 + 6 * q^30 - 4 * q^31 + 8 * q^32 - 10 * q^33 + 6 * q^34 - 12 * q^35 + 4 * q^36 + 22 * q^37 - 4 * q^38 - 6 * q^39 + 12 * q^40 + 6 * q^42 + 12 * q^43 - 4 * q^44 - 6 * q^45 + 4 * q^46 - 12 * q^47 - 8 * q^48 - 4 * q^49 - 16 * q^50 + 6 * q^51 + 4 * q^52 + 2 * q^53 + 18 * q^54 + 16 * q^56 + 8 * q^58 + 28 * q^59 - 24 * q^60 - 14 * q^61 + 2 * q^62 - 10 * q^63 - 6 * q^65 + 20 * q^66 - 12 * q^67 + 10 * q^69 + 24 * q^70 - 8 * q^72 - 18 * q^73 - 22 * q^75 - 16 * q^76 - 26 * q^77 + 8 * q^78 + 16 * q^79 - 24 * q^80 - 4 * q^81 - 28 * q^82 + 20 * q^83 + 20 * q^84 + 6 * q^85 - 24 * q^86 + 18 * q^87 + 4 * q^88 + 18 * q^89 - 28 * q^91 - 4 * q^92 + 4 * q^93 + 24 * q^94 + 12 * q^95 - 16 * q^96 + 16 * q^97 - 22 * q^98 + 16 * q^99

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