LMFDB - Embedded newform 784.2.m.e.197.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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:	$ 2 $
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	784.197
Dual form			784.2.m.e.589.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 + 0.366025i) q^{2} +(1.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-1.36603 + 2.36603i) q^{6} +(-2.00000 + 2.00000i) q^{8} -0.732051i q^{9} +O(q^{10})$	\(q+(-1.36603 + 0.366025i) q^{2} +(1.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-1.36603 + 2.36603i) q^{6} +(-2.00000 + 2.00000i) q^{8} -0.732051i q^{9} +(-4.09808 - 2.36603i) q^{10} +(3.09808 + 3.09808i) q^{11} +(1.00000 - 3.73205i) q^{12} +(0.267949 - 0.267949i) q^{13} +6.46410 q^{15} +(2.00000 - 3.46410i) q^{16} -0.464102 q^{17} +(0.267949 + 1.00000i) q^{18} +(-3.09808 + 3.09808i) q^{19} +(6.46410 + 1.73205i) q^{20} +(-5.36603 - 3.09808i) q^{22} +2.46410i q^{23} +5.46410i q^{24} +6.19615i q^{25} +(-0.267949 + 0.464102i) q^{26} +(3.09808 + 3.09808i) q^{27} +(-3.73205 + 3.73205i) q^{29} +(-8.83013 + 2.36603i) q^{30} +0.267949 q^{31} +(-1.46410 + 5.46410i) q^{32} +8.46410 q^{33} +(0.633975 - 0.169873i) q^{34} +(-0.732051 - 1.26795i) q^{36} +(-7.83013 - 7.83013i) q^{37} +(3.09808 - 5.36603i) q^{38} -0.732051i q^{39} -9.46410 q^{40} -8.92820i q^{41} +(-0.464102 - 0.464102i) q^{43} +(8.46410 + 2.26795i) q^{44} +(1.73205 - 1.73205i) q^{45} +(-0.901924 - 3.36603i) q^{46} +7.73205 q^{47} +(-2.00000 - 7.46410i) q^{48} +(-2.26795 - 8.46410i) q^{50} +(-0.633975 + 0.633975i) q^{51} +(0.196152 - 0.732051i) q^{52} +(-8.09808 - 8.09808i) q^{53} +(-5.36603 - 3.09808i) q^{54} +14.6603i q^{55} +8.46410i q^{57} +(3.73205 - 6.46410i) q^{58} +(7.29423 + 7.29423i) q^{59} +(11.1962 - 6.46410i) q^{60} +(-0.0980762 + 0.0980762i) q^{61} +(-0.366025 + 0.0980762i) q^{62} -8.00000i q^{64} +1.26795 q^{65} +(-11.5622 + 3.09808i) q^{66} +(5.36603 - 5.36603i) q^{67} +(-0.803848 + 0.464102i) q^{68} +(3.36603 + 3.36603i) q^{69} -7.46410i q^{71} +(1.46410 + 1.46410i) q^{72} -3.19615i q^{73} +(13.5622 + 7.83013i) q^{74} +(8.46410 + 8.46410i) q^{75} +(-2.26795 + 8.46410i) q^{76} +(0.267949 + 1.00000i) q^{78} +0.660254 q^{79} +(12.9282 - 3.46410i) q^{80} +10.6603 q^{81} +(3.26795 + 12.1962i) q^{82} +(8.46410 - 8.46410i) q^{83} +(-1.09808 - 1.09808i) q^{85} +(0.803848 + 0.464102i) q^{86} +10.1962i q^{87} -12.3923 q^{88} -5.19615i q^{89} +(-1.73205 + 3.00000i) q^{90} +(2.46410 + 4.26795i) q^{92} +(0.366025 - 0.366025i) q^{93} +(-10.5622 + 2.83013i) q^{94} -14.6603 q^{95} +(5.46410 + 9.46410i) q^{96} +10.9282 q^{97} +(2.26795 - 2.26795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} + 6 q^{5} - 2 q^{6} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 + 6 * q^5 - 2 * q^6 - 8 * q^8	$ 4 q - 2 q^{2} + 2 q^{3} + 6 q^{5} - 2 q^{6} - 8 q^{8} - 6 q^{10} + 2 q^{11} + 4 q^{12} + 8 q^{13} + 12 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{18} - 2 q^{19} + 12 q^{20} - 18 q^{22} - 8 q^{26} + 2 q^{27} - 8 q^{29} - 18 q^{30} + 8 q^{31} + 8 q^{32} + 20 q^{33} + 6 q^{34} + 4 q^{36} - 14 q^{37} + 2 q^{38} - 24 q^{40} + 12 q^{43} + 20 q^{44} - 14 q^{46} + 24 q^{47} - 8 q^{48} - 16 q^{50} - 6 q^{51} - 20 q^{52} - 22 q^{53} - 18 q^{54} + 8 q^{58} - 2 q^{59} + 24 q^{60} + 10 q^{61} + 2 q^{62} + 12 q^{65} - 22 q^{66} + 18 q^{67} - 24 q^{68} + 10 q^{69} - 8 q^{72} + 30 q^{74} + 20 q^{75} - 16 q^{76} + 8 q^{78} - 32 q^{79} + 24 q^{80} + 8 q^{81} + 20 q^{82} + 20 q^{83} + 6 q^{85} + 24 q^{86} - 8 q^{88} - 4 q^{92} - 2 q^{93} - 18 q^{94} - 24 q^{95} + 8 q^{96} + 16 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 + 6 * q^5 - 2 * q^6 - 8 * q^8 - 6 * q^10 + 2 * q^11 + 4 * q^12 + 8 * q^13 + 12 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^18 - 2 * q^19 + 12 * q^20 - 18 * q^22 - 8 * q^26 + 2 * q^27 - 8 * q^29 - 18 * q^30 + 8 * q^31 + 8 * q^32 + 20 * q^33 + 6 * q^34 + 4 * q^36 - 14 * q^37 + 2 * q^38 - 24 * q^40 + 12 * q^43 + 20 * q^44 - 14 * q^46 + 24 * q^47 - 8 * q^48 - 16 * q^50 - 6 * q^51 - 20 * q^52 - 22 * q^53 - 18 * q^54 + 8 * q^58 - 2 * q^59 + 24 * q^60 + 10 * q^61 + 2 * q^62 + 12 * q^65 - 22 * q^66 + 18 * q^67 - 24 * q^68 + 10 * q^69 - 8 * q^72 + 30 * q^74 + 20 * q^75 - 16 * q^76 + 8 * q^78 - 32 * q^79 + 24 * q^80 + 8 * q^81 + 20 * q^82 + 20 * q^83 + 6 * q^85 + 24 * q^86 - 8 * q^88 - 4 * q^92 - 2 * q^93 - 18 * q^94 - 24 * q^95 + 8 * q^96 + 16 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	1.36603	−	1.36603i	0.788675	−	0.788675i	−0.192602	−	0.981277i	$-0.561693\pi$
$3$	1.36603	−	1.36603i	0.788675	−	0.788675i	0.981277	+	0.192602i	$0.0616926\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$	2.36603	+	2.36603i	1.05812	+	1.05812i	0.998203	+	0.0599153i	$0.0190830\pi$
$5$	2.36603	+	2.36603i	1.05812	+	1.05812i	0.0599153	+	0.998203i	$0.480917\pi$
$6$	−1.36603	+	2.36603i	−0.557678	+	0.965926i
$7$		0			0
$7$		0			0
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		−	0.732051i		−	0.244017i
$10$	−4.09808	−	2.36603i	−1.29593	−	0.748203i
$11$	3.09808	+	3.09808i	0.934105	+	0.934105i	0.997959	−	0.0638541i	$-0.0203392\pi$
$11$	3.09808	+	3.09808i	0.934105	+	0.934105i	−0.0638541	+	0.997959i	$0.520339\pi$
$12$	1.00000	−	3.73205i	0.288675	−	1.07735i
$13$	0.267949	−	0.267949i	0.0743157	−	0.0743157i	−0.668972	−	0.743288i	$-0.733265\pi$
$13$	0.267949	−	0.267949i	0.0743157	−	0.0743157i	0.743288	+	0.668972i	$0.233265\pi$
$14$		0			0
$15$	6.46410			1.66902
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−0.464102			−0.112561			−0.0562806	−	0.998415i	$-0.517924\pi$
$17$	−0.464102			−0.112561			−0.0562806	+	0.998415i	$0.517924\pi$
$18$	0.267949	+	1.00000i	0.0631562	+	0.235702i
$19$	−3.09808	+	3.09808i	−0.710747	+	0.710747i	−0.966692	−	0.255944i	$-0.917614\pi$
$19$	−3.09808	+	3.09808i	−0.710747	+	0.710747i	0.255944	+	0.966692i	$0.417614\pi$
$20$	6.46410	+	1.73205i	1.44542	+	0.387298i
$21$		0			0
$22$	−5.36603	−	3.09808i	−1.14404	−	0.660512i
$23$			2.46410i			0.513801i	0.966438	+	0.256900i	$0.0827012\pi$
$23$			2.46410i			0.513801i	−0.966438	+	0.256900i	$0.917299\pi$
$24$			5.46410i			1.11536i
$25$			6.19615i			1.23923i
$26$	−0.267949	+	0.464102i	−0.0525492	+	0.0910178i
$27$	3.09808	+	3.09808i	0.596225	+	0.596225i
$28$		0			0
$29$	−3.73205	+	3.73205i	−0.693024	+	0.693024i	−0.962896	−	0.269872i	$-0.913019\pi$
$29$	−3.73205	+	3.73205i	−0.693024	+	0.693024i	0.269872	+	0.962896i	$0.413019\pi$
$30$	−8.83013	+	2.36603i	−1.61215	+	0.431975i
$31$	0.267949			0.0481251			0.0240625	−	0.999710i	$-0.492340\pi$
$31$	0.267949			0.0481251			0.0240625	+	0.999710i	$0.492340\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$	8.46410			1.47341
$34$	0.633975	−	0.169873i	0.108726	−	0.0291330i
$35$		0			0
$36$	−0.732051	−	1.26795i	−0.122008	−	0.211325i
$37$	−7.83013	−	7.83013i	−1.28726	−	1.28726i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−7.83013	−	7.83013i	−1.28726	−	1.28726i	−0.350823	−	0.936442i	$-0.614098\pi$
$38$	3.09808	−	5.36603i	0.502574	−	0.870484i
$39$		−	0.732051i		−	0.117222i
$40$	−9.46410			−1.49641
$41$		−	8.92820i		−	1.39435i	−0.716900	−	0.697176i	$-0.754440\pi$
$41$		−	8.92820i		−	1.39435i	0.716900	−	0.697176i	$-0.245560\pi$
$42$		0			0
$43$	−0.464102	−	0.464102i	−0.0707748	−	0.0707748i	0.670833	−	0.741608i	$-0.265937\pi$
$43$	−0.464102	−	0.464102i	−0.0707748	−	0.0707748i	−0.741608	+	0.670833i	$0.765937\pi$
$44$	8.46410	+	2.26795i	1.27601	+	0.341906i
$45$	1.73205	−	1.73205i	0.258199	−	0.258199i
$46$	−0.901924	−	3.36603i	−0.132981	−	0.496293i
$47$	7.73205			1.12784			0.563918	−	0.825831i	$-0.309293\pi$
$47$	7.73205			1.12784			0.563918	+	0.825831i	$0.309293\pi$
$48$	−2.00000	−	7.46410i	−0.288675	−	1.07735i
$49$		0			0
$50$	−2.26795	−	8.46410i	−0.320736	−	1.19700i
$51$	−0.633975	+	0.633975i	−0.0887742	+	0.0887742i
$52$	0.196152	−	0.732051i	0.0272014	−	0.101517i
$53$	−8.09808	−	8.09808i	−1.11236	−	1.11236i	−0.992831	−	0.119525i	$-0.961863\pi$
$53$	−8.09808	−	8.09808i	−1.11236	−	1.11236i	−0.119525	−	0.992831i	$-0.538137\pi$
$54$	−5.36603	−	3.09808i	−0.730224	−	0.421595i
$55$			14.6603i			1.97679i
$56$		0			0
$57$			8.46410i			1.12110i
$58$	3.73205	−	6.46410i	0.490042	−	0.848778i
$59$	7.29423	+	7.29423i	0.949628	+	0.949628i	0.998791	−	0.0491631i	$-0.0156554\pi$
$59$	7.29423	+	7.29423i	0.949628	+	0.949628i	−0.0491631	+	0.998791i	$0.515655\pi$
$60$	11.1962	−	6.46410i	1.44542	−	0.834512i
$61$	−0.0980762	+	0.0980762i	−0.0125574	+	0.0125574i	−0.713358	−	0.700800i	$-0.752826\pi$
$61$	−0.0980762	+	0.0980762i	−0.0125574	+	0.0125574i	0.700800	+	0.713358i	$0.252826\pi$
$62$	−0.366025	+	0.0980762i	−0.0464853	+	0.0124557i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	1.26795			0.157270
$66$	−11.5622	+	3.09808i	−1.42321	+	0.381347i
$67$	5.36603	−	5.36603i	0.655564	−	0.655564i	−0.298763	−	0.954327i	$-0.596574\pi$
$67$	5.36603	−	5.36603i	0.655564	−	0.655564i	0.954327	+	0.298763i	$0.0965740\pi$
$68$	−0.803848	+	0.464102i	−0.0974808	+	0.0562806i
$69$	3.36603	+	3.36603i	0.405222	+	0.405222i
$70$		0			0
$71$		−	7.46410i		−	0.885826i	−0.896565	−	0.442913i	$-0.853945\pi$
$71$		−	7.46410i		−	0.885826i	0.896565	−	0.442913i	$-0.146055\pi$
$72$	1.46410	+	1.46410i	0.172546	+	0.172546i
$73$		−	3.19615i		−	0.374081i	−0.982352	−	0.187041i	$-0.940110\pi$
$73$		−	3.19615i		−	0.374081i	0.982352	−	0.187041i	$-0.0598896\pi$
$74$	13.5622	+	7.83013i	1.57657	+	0.910234i
$75$	8.46410	+	8.46410i	0.977350	+	0.977350i
$76$	−2.26795	+	8.46410i	−0.260152	+	0.970899i
$77$		0			0
$78$	0.267949	+	1.00000i	0.0303393	+	0.113228i
$79$	0.660254			0.0742844			0.0371422	−	0.999310i	$-0.488175\pi$
$79$	0.660254			0.0742844			0.0371422	+	0.999310i	$0.488175\pi$
$80$	12.9282	−	3.46410i	1.44542	−	0.387298i
$81$	10.6603			1.18447
$82$	3.26795	+	12.1962i	0.360885	+	1.34684i
$83$	8.46410	−	8.46410i	0.929056	−	0.929056i	−0.0685891	−	0.997645i	$-0.521850\pi$
$83$	8.46410	−	8.46410i	0.929056	−	0.929056i	0.997645	+	0.0685891i	$0.0218498\pi$
$84$		0			0
$85$	−1.09808	−	1.09808i	−0.119103	−	0.119103i
$86$	0.803848	+	0.464102i	0.0866811	+	0.0500454i
$87$			10.1962i			1.09314i
$88$	−12.3923			−1.32102
$89$		−	5.19615i		−	0.550791i	−0.961331	−	0.275396i	$-0.911191\pi$
$89$		−	5.19615i		−	0.550791i	0.961331	−	0.275396i	$-0.0888088\pi$
$90$	−1.73205	+	3.00000i	−0.182574	+	0.316228i
$91$		0			0
$92$	2.46410	+	4.26795i	0.256900	+	0.444964i
$93$	0.366025	−	0.366025i	0.0379551	−	0.0379551i
$94$	−10.5622	+	2.83013i	−1.08941	+	0.291905i
$95$	−14.6603			−1.50411
$96$	5.46410	+	9.46410i	0.557678	+	0.965926i
$97$	10.9282			1.10959			0.554795	−	0.831987i	$-0.312797\pi$
$97$	10.9282			1.10959			0.554795	+	0.831987i	$0.312797\pi$
$98$		0			0
$99$	2.26795	−	2.26795i	0.227937	−	0.227937i
$100$	6.19615	+	10.7321i	0.619615	+	1.07321i
$101$	5.16987	+	5.16987i	0.514422	+	0.514422i	0.915878	−	0.401457i	$-0.131496\pi$
$101$	5.16987	+	5.16987i	0.514422	+	0.514422i	−0.401457	+	0.915878i	$0.631496\pi$
$102$	0.633975	−	1.09808i	0.0627728	−	0.108726i
$103$		−	0.464102i		−	0.0457293i	−0.999739	−	0.0228646i	$-0.992721\pi$
$103$		−	0.464102i		−	0.0457293i	0.999739	−	0.0228646i	$-0.00727868\pi$
$104$			1.07180i			0.105098i
$105$		0			0
$106$	14.0263	+	8.09808i	1.36235	+	0.786555i
$107$	−0.633975	−	0.633975i	−0.0612886	−	0.0612886i	0.675798	−	0.737087i	$-0.263799\pi$
$107$	−0.633975	−	0.633975i	−0.0612886	−	0.0612886i	−0.737087	+	0.675798i	$0.763799\pi$
$108$	8.46410	+	2.26795i	0.814459	+	0.218234i
$109$	−10.5622	+	10.5622i	−1.01167	+	1.01167i	−0.0117421	+	0.999931i	$0.503738\pi$
$109$	−10.5622	+	10.5622i	−1.01167	+	1.01167i	−0.999931	+	0.0117421i	$0.996262\pi$
$110$	−5.36603	−	20.0263i	−0.511630	−	1.90943i
$111$	−21.3923			−2.03047
$112$		0			0
$113$	5.46410			0.514019			0.257010	−	0.966409i	$-0.417263\pi$
$113$	5.46410			0.514019			0.257010	+	0.966409i	$0.417263\pi$
$114$	−3.09808	−	11.5622i	−0.290161	−	1.08290i
$115$	−5.83013	+	5.83013i	−0.543662	+	0.543662i
$116$	−2.73205	+	10.1962i	−0.253665	+	0.946689i
$117$	−0.196152	−	0.196152i	−0.0181343	−	0.0181343i
$118$	−12.6340	−	7.29423i	−1.16305	−	0.671488i
$119$		0			0
$120$	−12.9282	+	12.9282i	−1.18018	+	1.18018i
$121$			8.19615i			0.745105i
$122$	0.0980762	−	0.169873i	0.00887940	−	0.0153796i
$123$	−12.1962	−	12.1962i	−1.09969	−	1.09969i
$124$	0.464102	−	0.267949i	0.0416776	−	0.0240625i
$125$	−2.83013	+	2.83013i	−0.253134	+	0.253134i
$126$		0			0
$127$	2.53590			0.225025			0.112512	−	0.993650i	$-0.464110\pi$
$127$	2.53590			0.225025			0.112512	+	0.993650i	$0.464110\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	−1.26795			−0.111637
$130$	−1.73205	+	0.464102i	−0.151911	+	0.0407044i
$131$	6.56218	−	6.56218i	0.573340	−	0.573340i	−0.359720	−	0.933060i	$-0.617128\pi$
$131$	6.56218	−	6.56218i	0.573340	−	0.573340i	0.933060	+	0.359720i	$0.117128\pi$
$132$	14.6603	−	8.46410i	1.27601	−	0.736705i
$133$		0			0
$134$	−5.36603	+	9.29423i	−0.463554	+	0.802899i
$135$			14.6603i			1.26175i
$136$	0.928203	−	0.928203i	0.0795928	−	0.0795928i
$137$		−	13.5885i		−	1.16094i	−0.814282	−	0.580470i	$-0.802869\pi$
$137$		−	13.5885i		−	1.16094i	0.814282	−	0.580470i	$-0.197131\pi$
$138$	−5.83013	−	3.36603i	−0.496293	−	0.286535i
$139$	1.92820	+	1.92820i	0.163548	+	0.163548i	0.784136	−	0.620588i	$-0.213106\pi$
$139$	1.92820	+	1.92820i	0.163548	+	0.163548i	−0.620588	+	0.784136i	$0.713106\pi$
$140$		0			0
$141$	10.5622	−	10.5622i	0.889496	−	0.889496i
$142$	2.73205	+	10.1962i	0.229269	+	0.855642i
$143$	1.66025			0.138837
$144$	−2.53590	−	1.46410i	−0.211325	−	0.122008i
$145$	−17.6603			−1.46660
$146$	1.16987	+	4.36603i	0.0968194	+	0.361335i
$147$		0			0
$148$	−21.3923	−	5.73205i	−1.75844	−	0.471172i
$149$	−6.56218	−	6.56218i	−0.537595	−	0.537595i	0.385227	−	0.922822i	$-0.374123\pi$
$149$	−6.56218	−	6.56218i	−0.537595	−	0.537595i	−0.922822	+	0.385227i	$0.874123\pi$
$150$	−14.6603	−	8.46410i	−1.19700	−	0.691091i
$151$		−	9.39230i		−	0.764335i	−0.924093	−	0.382167i	$-0.875178\pi$
$151$		−	9.39230i		−	0.764335i	0.924093	−	0.382167i	$-0.124822\pi$
$152$		−	12.3923i		−	1.00515i
$153$			0.339746i			0.0274668i
$154$		0			0
$155$	0.633975	+	0.633975i	0.0509221	+	0.0509221i
$156$	−0.732051	−	1.26795i	−0.0586110	−	0.101517i
$157$	11.6340	−	11.6340i	0.928492	−	0.928492i	−0.0691164	−	0.997609i	$-0.522018\pi$
$157$	11.6340	−	11.6340i	0.928492	−	0.928492i	0.997609	+	0.0691164i	$0.0220180\pi$
$158$	−0.901924	+	0.241670i	−0.0717532	+	0.0192262i
$159$	−22.1244			−1.75458
$160$	−16.3923	+	9.46410i	−1.29593	+	0.748203i
$161$		0			0
$162$	−14.5622	+	3.90192i	−1.14411	+	0.306564i
$163$	0.169873	−	0.169873i	0.0133055	−	0.0133055i	−0.700423	−	0.713728i	$-0.747005\pi$
$163$	0.169873	−	0.169873i	0.0133055	−	0.0133055i	0.713728	+	0.700423i	$0.247005\pi$
$164$	−8.92820	−	15.4641i	−0.697176	−	1.20754i
$165$	20.0263	+	20.0263i	1.55904	+	1.55904i
$166$	−8.46410	+	14.6603i	−0.656942	+	1.13786i
$167$		−	5.85641i		−	0.453182i	−0.973990	−	0.226591i	$-0.927242\pi$
$167$		−	5.85641i		−	0.453182i	0.973990	−	0.226591i	$-0.0727581\pi$
$168$		0			0
$169$			12.8564i			0.988954i
$170$	1.90192	+	1.09808i	0.145871	+	0.0842186i
$171$	2.26795	+	2.26795i	0.173434	+	0.173434i
$172$	−1.26795	−	0.339746i	−0.0966802	−	0.0259054i
$173$	3.36603	−	3.36603i	0.255914	−	0.255914i	−0.567476	−	0.823390i	$-0.692080\pi$
$173$	3.36603	−	3.36603i	0.255914	−	0.255914i	0.823390	+	0.567476i	$0.192080\pi$
$174$	−3.73205	−	13.9282i	−0.282926	−	1.05589i
$175$		0			0
$176$	16.9282	−	4.53590i	1.27601	−	0.341906i
$177$	19.9282			1.49790
$178$	1.90192	+	7.09808i	0.142555	+	0.532023i
$179$	5.56218	−	5.56218i	0.415737	−	0.415737i	−0.467995	−	0.883731i	$-0.655023\pi$
$179$	5.56218	−	5.56218i	0.415737	−	0.415737i	0.883731	+	0.467995i	$0.155023\pi$
$180$	1.26795	−	4.73205i	0.0945074	−	0.352706i
$181$	−7.39230	−	7.39230i	−0.549466	−	0.549466i	0.376821	−	0.926286i	$-0.377017\pi$
$181$	−7.39230	−	7.39230i	−0.549466	−	0.549466i	−0.926286	+	0.376821i	$0.877017\pi$
$182$		0			0
$183$			0.267949i			0.0198074i
$184$	−4.92820	−	4.92820i	−0.363312	−	0.363312i
$185$		−	37.0526i		−	2.72416i
$186$	−0.366025	+	0.633975i	−0.0268383	+	0.0464853i
$187$	−1.43782	−	1.43782i	−0.105144	−	0.105144i
$188$	13.3923	−	7.73205i	0.976734	−	0.563918i
$189$		0			0
$190$	20.0263	−	5.36603i	1.45286	−	0.389292i
$191$	−8.66025			−0.626634			−0.313317	−	0.949649i	$-0.601440\pi$
$191$	−8.66025			−0.626634			−0.313317	+	0.949649i	$0.601440\pi$
$192$	−10.9282	−	10.9282i	−0.788675	−	0.788675i
$193$	−23.0000			−1.65558			−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−23.0000			−1.65558			−0.827788	+	0.561041i	$0.810401\pi$
$194$	−14.9282	+	4.00000i	−1.07178	+	0.287183i
$195$	1.73205	−	1.73205i	0.124035	−	0.124035i
$196$		0			0
$197$	0.660254	+	0.660254i	0.0470412	+	0.0470412i	0.730236	−	0.683195i	$-0.239410\pi$
$197$	0.660254	+	0.660254i	0.0470412	+	0.0470412i	−0.683195	+	0.730236i	$0.739410\pi$
$198$	−2.26795	+	3.92820i	−0.161176	+	0.279165i
$199$			1.92820i			0.136687i	0.997662	+	0.0683434i	$0.0217713\pi$
$199$			1.92820i			0.136687i	−0.997662	+	0.0683434i	$0.978229\pi$
$200$	−12.3923	−	12.3923i	−0.876268	−	0.876268i
$201$		−	14.6603i		−	1.03405i
$202$	−8.95448	−	5.16987i	−0.630035	−	0.363751i
$203$		0			0
$204$	−0.464102	+	1.73205i	−0.0324936	+	0.121268i
$205$	21.1244	−	21.1244i	1.47539	−	1.47539i
$206$	0.169873	+	0.633975i	0.0118356	+	0.0441711i
$207$	1.80385			0.125376
$208$	−0.392305	−	1.46410i	−0.0272014	−	0.101517i
$209$	−19.1962			−1.32783
$210$		0			0
$211$	−2.07180	+	2.07180i	−0.142628	+	0.142628i	−0.774816	−	0.632187i	$-0.782157\pi$
$211$	−2.07180	+	2.07180i	−0.142628	+	0.142628i	0.632187	+	0.774816i	$0.282157\pi$
$212$	−22.1244	−	5.92820i	−1.51951	−	0.407151i
$213$	−10.1962	−	10.1962i	−0.698629	−	0.698629i
$214$	1.09808	+	0.633975i	0.0750629	+	0.0433376i
$215$		−	2.19615i		−	0.149776i
$216$	−12.3923			−0.843190
$217$		0			0
$218$	10.5622	−	18.2942i	0.715361	−	1.23904i
$219$	−4.36603	−	4.36603i	−0.295029	−	0.295029i
$220$	14.6603	+	25.3923i	0.988394	+	1.71195i
$221$	−0.124356	+	0.124356i	−0.00836507	+	0.00836507i
$222$	29.2224	−	7.83013i	1.96128	−	0.525524i
$223$	−17.8564			−1.19575			−0.597877	−	0.801588i	$-0.703989\pi$
$223$	−17.8564			−1.19575			−0.597877	+	0.801588i	$0.703989\pi$
$224$		0			0
$225$	4.53590			0.302393
$226$	−7.46410	+	2.00000i	−0.496505	+	0.133038i
$227$	−16.8301	+	16.8301i	−1.11705	+	1.11705i	−0.124883	+	0.992171i	$0.539856\pi$
$227$	−16.8301	+	16.8301i	−1.11705	+	1.11705i	−0.992171	+	0.124883i	$0.960144\pi$
$228$	8.46410	+	14.6603i	0.560549	+	0.970899i
$229$	12.7583	+	12.7583i	0.843094	+	0.843094i	0.989260	−	0.146166i	$-0.0466933\pi$
$229$	12.7583	+	12.7583i	0.843094	+	0.843094i	−0.146166	+	0.989260i	$0.546693\pi$
$230$	5.83013	−	10.0981i	0.384427	−	0.665847i
$231$		0			0
$232$		−	14.9282i		−	0.980085i
$233$		−	11.1962i		−	0.733484i	−0.930323	−	0.366742i	$-0.880473\pi$
$233$		−	11.1962i		−	0.733484i	0.930323	−	0.366742i	$-0.119527\pi$
$234$	0.339746	+	0.196152i	0.0222099	+	0.0128229i
$235$	18.2942	+	18.2942i	1.19338	+	1.19338i
$236$	19.9282	+	5.33975i	1.29722	+	0.347588i
$237$	0.901924	−	0.901924i	0.0585862	−	0.0585862i
$238$		0			0
$239$	−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
$241$	0.0717968			0.00462484			0.00231242	−	0.999997i	$-0.499264\pi$
$241$	0.0717968			0.00462484			0.00231242	+	0.999997i	$0.499264\pi$
$242$	−3.00000	−	11.1962i	−0.192847	−	0.719716i
$243$	5.26795	−	5.26795i	0.337939	−	0.337939i
$244$	−0.0717968	+	0.267949i	−0.00459632	+	0.0171537i
$245$		0			0
$246$	21.1244	+	12.1962i	1.34684	+	0.777598i
$247$			1.66025i			0.105639i
$248$	−0.535898	+	0.535898i	−0.0340296	+	0.0340296i
$249$		−	23.1244i		−	1.46545i
$250$	2.83013	−	4.90192i	0.178993	−	0.310025i
$251$	13.5885	+	13.5885i	0.857696	+	0.857696i	0.991066	−	0.133370i	$-0.0425800\pi$
$251$	13.5885	+	13.5885i	0.857696	+	0.857696i	−0.133370	+	0.991066i	$0.542580\pi$
$252$		0			0
$253$	−7.63397	+	7.63397i	−0.479944	+	0.479944i
$254$	−3.46410	+	0.928203i	−0.217357	+	0.0582407i
$255$	−3.00000			−0.187867
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	1.39230			0.0868496			0.0434248	−	0.999057i	$-0.486173\pi$
$257$	1.39230			0.0868496			0.0434248	+	0.999057i	$0.486173\pi$
$258$	1.73205	−	0.464102i	0.107833	−	0.0288937i
$259$		0			0
$260$	2.19615	−	1.26795i	0.136200	−	0.0786349i
$261$	2.73205	+	2.73205i	0.169110	+	0.169110i
$262$	−6.56218	+	11.3660i	−0.405413	+	0.702195i
$263$			25.3923i			1.56576i	0.622175	+	0.782878i	$0.286249\pi$
$263$			25.3923i			1.56576i	−0.622175	+	0.782878i	$0.713751\pi$
$264$	−16.9282	+	16.9282i	−1.04186	+	1.04186i
$265$		−	38.3205i		−	2.35401i
$266$		0			0
$267$	−7.09808	−	7.09808i	−0.434395	−	0.434395i
$268$	3.92820	−	14.6603i	0.239953	−	0.895518i
$269$	−15.8301	+	15.8301i	−0.965180	+	0.965180i	−0.999414	−	0.0342340i	$-0.989101\pi$
$269$	−15.8301	+	15.8301i	−0.965180	+	0.965180i	0.0342340	+	0.999414i	$0.489101\pi$
$270$	−5.36603	−	20.0263i	−0.326566	−	1.21876i
$271$	−12.1244			−0.736502			−0.368251	−	0.929726i	$-0.620043\pi$
$271$	−12.1244			−0.736502			−0.368251	+	0.929726i	$0.620043\pi$
$272$	−0.928203	+	1.60770i	−0.0562806	+	0.0974808i
$273$		0			0
$274$	4.97372	+	18.5622i	0.300473	+	1.12138i
$275$	−19.1962	+	19.1962i	−1.15757	+	1.15757i
$276$	9.19615	+	2.46410i	0.553543	+	0.148321i
$277$	12.2942	+	12.2942i	0.738689	+	0.738689i	0.972324	−	0.233636i	$-0.0750623\pi$
$277$	12.2942	+	12.2942i	0.738689	+	0.738689i	−0.233636	+	0.972324i	$0.575062\pi$
$278$	−3.33975	−	1.92820i	−0.200305	−	0.115646i
$279$		−	0.196152i		−	0.0117433i
$280$		0			0
$281$		−	12.9282i		−	0.771232i	−0.922659	−	0.385616i	$-0.873989\pi$
$281$		−	12.9282i		−	0.771232i	0.922659	−	0.385616i	$-0.126011\pi$
$282$	−10.5622	+	18.2942i	−0.628969	+	1.08941i
$283$	−12.3660	−	12.3660i	−0.735084	−	0.735084i	0.236538	−	0.971622i	$-0.423987\pi$
$283$	−12.3660	−	12.3660i	−0.735084	−	0.735084i	−0.971622	+	0.236538i	$0.923987\pi$
$284$	−7.46410	−	12.9282i	−0.442913	−	0.767148i
$285$	−20.0263	+	20.0263i	−1.18625	+	1.18625i
$286$	−2.26795	+	0.607695i	−0.134107	+	0.0359338i
$287$		0			0
$288$	4.00000	+	1.07180i	0.235702	+	0.0631562i
$289$	−16.7846			−0.987330
$290$	24.1244	−	6.46410i	1.41663	−	0.379585i
$291$	14.9282	−	14.9282i	0.875107	−	0.875107i
$292$	−3.19615	−	5.53590i	−0.187041	−	0.323964i
$293$	5.92820	+	5.92820i	0.346329	+	0.346329i	0.858740	−	0.512411i	$-0.171248\pi$
$293$	5.92820	+	5.92820i	0.346329	+	0.346329i	−0.512411	+	0.858740i	$0.671248\pi$
$294$		0			0
$295$			34.5167i			2.00964i
$296$	31.3205			1.82047
$297$			19.1962i			1.11387i
$298$	11.3660	+	6.56218i	0.658416	+	0.380137i
$299$	0.660254	+	0.660254i	0.0381835	+	0.0381835i
$300$	23.1244	+	6.19615i	1.33509	+	0.357735i
$301$		0			0
$302$	3.43782	+	12.8301i	0.197824	+	0.738291i
$303$	14.1244			0.811423
$304$	4.53590	+	16.9282i	0.260152	+	0.970899i
$305$	−0.464102			−0.0265744
$306$	−0.124356	−	0.464102i	−0.00710894	−	0.0265309i
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	−0.401988	−	0.915645i	$-0.631681\pi$
$307$	9.00000	−	9.00000i	0.513657	−	0.513657i	0.915645	+	0.401988i	$0.131681\pi$
$308$		0			0
$309$	−0.633975	−	0.633975i	−0.0360656	−	0.0360656i
$310$	−1.09808	−	0.633975i	−0.0623665	−	0.0360073i
$311$		−	0.464102i		−	0.0263168i	−0.999913	−	0.0131584i	$-0.995811\pi$
$311$		−	0.464102i		−	0.0263168i	0.999913	−	0.0131584i	$-0.00418857\pi$
$312$	1.46410	+	1.46410i	0.0828884	+	0.0828884i
$313$		−	9.58846i		−	0.541972i	−0.962583	−	0.270986i	$-0.912650\pi$
$313$		−	9.58846i		−	0.541972i	0.962583	−	0.270986i	$-0.0873497\pi$
$314$	−11.6340	+	20.1506i	−0.656543	+	1.13717i
$315$		0			0
$316$	1.14359	−	0.660254i	0.0643322	−	0.0371422i
$317$	−8.63397	+	8.63397i	−0.484932	+	0.484932i	−0.906703	−	0.421770i	$-0.861409\pi$
$317$	−8.63397	+	8.63397i	−0.484932	+	0.484932i	0.421770	+	0.906703i	$0.361409\pi$
$318$	30.2224	−	8.09808i	1.69479	−	0.454118i
$319$	−23.1244			−1.29472
$320$	18.9282	−	18.9282i	1.05812	−	1.05812i
$321$	−1.73205			−0.0966736
$322$		0			0
$323$	1.43782	−	1.43782i	0.0800026	−	0.0800026i
$324$	18.4641	−	10.6603i	1.02578	−	0.592236i
$325$	1.66025	+	1.66025i	0.0920943	+	0.0920943i
$326$	−0.169873	+	0.294229i	−0.00940839	+	0.0162958i
$327$			28.8564i			1.59576i
$328$	17.8564	+	17.8564i	0.985955	+	0.985955i
$329$		0			0
$330$	−34.6865	−	20.0263i	−1.90943	−	1.10241i
$331$	12.6340	+	12.6340i	0.694426	+	0.694426i	0.963203	−	0.268777i	$-0.0866193\pi$
$331$	12.6340	+	12.6340i	0.694426	+	0.694426i	−0.268777	+	0.963203i	$0.586619\pi$
$332$	6.19615	−	23.1244i	0.340058	−	1.26911i
$333$	−5.73205	+	5.73205i	−0.314114	+	0.314114i
$334$	2.14359	+	8.00000i	0.117292	+	0.437741i
$335$	25.3923			1.38733
$336$		0			0
$337$	−33.8564			−1.84428			−0.922138	−	0.386861i	$-0.873559\pi$
$337$	−33.8564			−1.84428			−0.922138	+	0.386861i	$0.873559\pi$
$338$	−4.70577	−	17.5622i	−0.255960	−	0.955257i
$339$	7.46410	−	7.46410i	0.405394	−	0.405394i
$340$	−3.00000	−	0.803848i	−0.162698	−	0.0435948i
$341$	0.830127	+	0.830127i	0.0449539	+	0.0449539i
$342$	−3.92820	−	2.26795i	−0.212413	−	0.122637i
$343$		0			0
$344$	1.85641			0.100091
$345$			15.9282i			0.857546i
$346$	−3.36603	+	5.83013i	−0.180959	+	0.313430i
$347$	12.2224	+	12.2224i	0.656135	+	0.656135i	0.954463	−	0.298329i	$-0.0964292\pi$
$347$	12.2224	+	12.2224i	0.656135	+	0.656135i	−0.298329	+	0.954463i	$0.596429\pi$
$348$	10.1962	+	17.6603i	0.546571	+	0.946689i
$349$	−18.1244	+	18.1244i	−0.970175	+	0.970175i	−0.999568	−	0.0293934i	$-0.990642\pi$
$349$	−18.1244	+	18.1244i	−0.970175	+	0.970175i	0.0293934	+	0.999568i	$0.490642\pi$
$350$		0			0
$351$	1.66025			0.0886178
$352$	−21.4641	+	12.3923i	−1.14404	+	0.660512i
$353$	13.7846			0.733681			0.366840	−	0.930284i	$-0.380440\pi$
$353$	13.7846			0.733681			0.366840	+	0.930284i	$0.380440\pi$
$354$	−27.2224	+	7.29423i	−1.44686	+	0.387684i
$355$	17.6603	−	17.6603i	0.937309	−	0.937309i
$356$	−5.19615	−	9.00000i	−0.275396	−	0.476999i
$357$		0			0
$358$	−5.56218	+	9.63397i	−0.293970	+	0.509171i
$359$		−	2.46410i		−	0.130050i	−0.997884	−	0.0650252i	$-0.979287\pi$
$359$		−	2.46410i		−	0.130050i	0.997884	−	0.0650252i	$-0.0207128\pi$
$360$			6.92820i			0.365148i
$361$		−	0.196152i		−	0.0103238i
$362$	12.8038	+	7.39230i	0.672955	+	0.388531i
$363$	11.1962	+	11.1962i	0.587646	+	0.587646i
$364$		0			0
$365$	7.56218	−	7.56218i	0.395822	−	0.395822i
$366$	−0.0980762	−	0.366025i	−0.00512653	−	0.0191325i
$367$	−18.1244			−0.946084			−0.473042	−	0.881040i	$-0.656844\pi$
$367$	−18.1244			−0.946084			−0.473042	+	0.881040i	$0.656844\pi$
$368$	8.53590	+	4.92820i	0.444964	+	0.256900i
$369$	−6.53590			−0.340245
$370$	13.5622	+	50.6147i	0.705064	+	2.63133i
$371$		0			0
$372$	0.267949	−	1.00000i	0.0138925	−	0.0518476i
$373$	−2.36603	−	2.36603i	−0.122508	−	0.122508i	0.643195	−	0.765703i	$-0.277609\pi$
$373$	−2.36603	−	2.36603i	−0.122508	−	0.122508i	−0.765703	+	0.643195i	$0.777609\pi$
$374$	2.49038	+	1.43782i	0.128775	+	0.0743480i
$375$			7.73205i			0.399281i
$376$	−15.4641	+	15.4641i	−0.797500	+	0.797500i
$377$			2.00000i			0.103005i
$378$		0			0
$379$	−24.1244	−	24.1244i	−1.23918	−	1.23918i	−0.960335	−	0.278850i	$-0.910047\pi$
$379$	−24.1244	−	24.1244i	−1.23918	−	1.23918i	−0.278850	−	0.960335i	$-0.589953\pi$
$380$	−25.3923	+	14.6603i	−1.30260	+	0.752055i
$381$	3.46410	−	3.46410i	0.177471	−	0.177471i
$382$	11.8301	−	3.16987i	0.605282	−	0.162185i
$383$	−14.8038			−0.756441			−0.378221	−	0.925715i	$-0.623464\pi$
$383$	−14.8038			−0.756441			−0.378221	+	0.925715i	$0.623464\pi$
$384$	18.9282	+	10.9282i	0.965926	+	0.557678i
$385$		0			0
$386$	31.4186	−	8.41858i	1.59916	−	0.428495i
$387$	−0.339746	+	0.339746i	−0.0172703	+	0.0172703i
$388$	18.9282	−	10.9282i	0.960934	−	0.554795i
$389$	14.6340	+	14.6340i	0.741972	+	0.741972i	0.972957	−	0.230985i	$-0.0741949\pi$
$389$	14.6340	+	14.6340i	0.741972	+	0.741972i	−0.230985	+	0.972957i	$0.574195\pi$
$390$	−1.73205	+	3.00000i	−0.0877058	+	0.151911i
$391$		−	1.14359i		−	0.0578340i
$392$		0			0
$393$		−	17.9282i		−	0.904358i
$394$	−1.14359	−	0.660254i	−0.0576134	−	0.0332631i
$395$	1.56218	+	1.56218i	0.0786017	+	0.0786017i
$396$	1.66025	−	6.19615i	0.0834309	−	0.311368i
$397$	−3.75833	+	3.75833i	−0.188625	+	0.188625i	−0.795102	−	0.606476i	$-0.792582\pi$
$397$	−3.75833	+	3.75833i	−0.188625	+	0.188625i	0.606476	+	0.795102i	$0.292582\pi$
$398$	−0.705771	−	2.63397i	−0.0353771	−	0.132029i
$399$		0			0
$400$	21.4641	+	12.3923i	1.07321	+	0.619615i
$401$	−15.0000			−0.749064			−0.374532	−	0.927214i	$-0.622197\pi$
$401$	−15.0000			−0.749064			−0.374532	+	0.927214i	$0.622197\pi$
$402$	5.36603	+	20.0263i	0.267633	+	0.998820i
$403$	0.0717968	−	0.0717968i	0.00357645	−	0.00357645i
$404$	14.1244	+	3.78461i	0.702713	+	0.188291i
$405$	25.2224	+	25.2224i	1.25331	+	1.25331i
$406$		0			0
$407$		−	48.5167i		−	2.40488i
$408$		−	2.53590i		−	0.125546i
$409$			8.66025i			0.428222i	0.976809	+	0.214111i	$0.0686854\pi$
$409$			8.66025i			0.428222i	−0.976809	+	0.214111i	$0.931315\pi$
$410$	−21.1244	+	36.5885i	−1.04326	+	1.80698i
$411$	−18.5622	−	18.5622i	−0.915605	−	0.915605i
$412$	−0.464102	−	0.803848i	−0.0228646	−	0.0396027i
$413$		0			0
$414$	−2.46410	+	0.660254i	−0.121104	+	0.0324497i
$415$	40.0526			1.96610
$416$	1.07180	+	1.85641i	0.0525492	+	0.0910178i
$417$	5.26795			0.257973
$418$	26.2224	−	7.02628i	1.28258	−	0.343667i
$419$	−19.0000	+	19.0000i	−0.928211	+	0.928211i	−0.997590	−	0.0693796i	$-0.977898\pi$
$419$	−19.0000	+	19.0000i	−0.928211	+	0.928211i	0.0693796	+	0.997590i	$0.477898\pi$
$420$		0			0
$421$	−8.66025	−	8.66025i	−0.422075	−	0.422075i	0.463843	−	0.885918i	$-0.346470\pi$
$421$	−8.66025	−	8.66025i	−0.422075	−	0.422075i	−0.885918	+	0.463843i	$0.846470\pi$
$422$	2.07180	−	3.58846i	0.100853	−	0.174683i
$423$		−	5.66025i		−	0.275211i
$424$	32.3923			1.57311
$425$		−	2.87564i		−	0.139489i
$426$	17.6603	+	10.1962i	0.855642	+	0.494005i
$427$		0			0
$428$	−1.73205	−	0.464102i	−0.0837218	−	0.0224332i
$429$	2.26795	−	2.26795i	0.109498	−	0.109498i
$430$	0.803848	+	3.00000i	0.0387650	+	0.144673i
$431$	13.3397			0.642553			0.321276	−	0.946985i	$-0.395888\pi$
$431$	13.3397			0.642553			0.321276	+	0.946985i	$0.395888\pi$
$432$	16.9282	−	4.53590i	0.814459	−	0.218234i
$433$	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			0
$435$	−24.1244	+	24.1244i	−1.15667	+	1.15667i
$436$	−7.73205	+	28.8564i	−0.370298	+	1.38197i
$437$	−7.63397	−	7.63397i	−0.365183	−	0.365183i
$438$	7.56218	+	4.36603i	0.361335	+	0.208617i
$439$		−	14.4641i		−	0.690334i	−0.938541	−	0.345167i	$-0.887822\pi$
$439$		−	14.4641i		−	0.690334i	0.938541	−	0.345167i	$-0.112178\pi$
$440$	−29.3205	−	29.3205i	−1.39780	−	1.39780i
$441$		0			0
$442$	0.124356	−	0.215390i	0.00591500	−	0.0102451i
$443$	9.36603	+	9.36603i	0.444993	+	0.444993i	0.893686	−	0.448693i	$-0.148110\pi$
$443$	9.36603	+	9.36603i	0.444993	+	0.444993i	−0.448693	+	0.893686i	$0.648110\pi$
$444$	−37.0526	+	21.3923i	−1.75844	+	1.01523i
$445$	12.2942	−	12.2942i	0.582802	−	0.582802i
$446$	24.3923	−	6.53590i	1.15501	−	0.309484i
$447$	−17.9282			−0.847975
$448$		0			0
$449$	11.3205			0.534248			0.267124	−	0.963662i	$-0.413927\pi$
$449$	11.3205			0.534248			0.267124	+	0.963662i	$0.413927\pi$
$450$	−6.19615	+	1.66025i	−0.292089	+	0.0782651i
$451$	27.6603	−	27.6603i	1.30247	−	1.30247i
$452$	9.46410	−	5.46410i	0.445154	−	0.257010i
$453$	−12.8301	−	12.8301i	−0.602812	−	0.602812i
$454$	16.8301	−	29.1506i	0.789877	−	1.36811i
$455$		0			0
$456$	−16.9282	−	16.9282i	−0.792736	−	0.792736i
$457$		−	29.1962i		−	1.36574i	−0.730541	−	0.682869i	$-0.760732\pi$
$457$		−	29.1962i		−	1.36574i	0.730541	−	0.682869i	$-0.239268\pi$
$458$	−22.0981	−	12.7583i	−1.03258	−	0.596158i
$459$	−1.43782	−	1.43782i	−0.0671118	−	0.0671118i
$460$	−4.26795	+	15.9282i	−0.198994	+	0.742656i
$461$	1.33975	−	1.33975i	0.0623982	−	0.0623982i	−0.675219	−	0.737617i	$-0.735951\pi$
$461$	1.33975	−	1.33975i	0.0623982	−	0.0623982i	0.737617	+	0.675219i	$0.235951\pi$
$462$		0			0
$463$	29.8564			1.38754			0.693772	−	0.720194i	$-0.255947\pi$
$463$	29.8564			1.38754			0.693772	+	0.720194i	$0.255947\pi$
$464$	5.46410	+	20.3923i	0.253665	+	0.946689i
$465$	1.73205			0.0803219
$466$	4.09808	+	15.2942i	0.189840	+	0.708491i
$467$	0.0262794	−	0.0262794i	0.00121607	−	0.00121607i	−0.706498	−	0.707715i	$-0.749726\pi$
$467$	0.0262794	−	0.0262794i	0.00121607	−	0.00121607i	0.707715	+	0.706498i	$0.249726\pi$
$468$	−0.535898	−	0.143594i	−0.0247719	−	0.00663761i
$469$		0			0
$470$	−31.6865	−	18.2942i	−1.46159	−	0.843850i
$471$		−	31.7846i		−	1.46456i
$472$	−29.1769			−1.34298
$473$		−	2.87564i		−	0.132222i
$474$	−0.901924	+	1.56218i	−0.0414267	+	0.0717532i
$475$	−19.1962	−	19.1962i	−0.880780	−	0.880780i
$476$		0			0
$477$	−5.92820	+	5.92820i	−0.271434	+	0.271434i
$478$	21.1244	−	5.66025i	0.966206	−	0.258894i
$479$	−15.5885			−0.712255			−0.356127	−	0.934437i	$-0.615903\pi$
$479$	−15.5885			−0.712255			−0.356127	+	0.934437i	$0.615903\pi$
$480$	−9.46410	+	35.3205i	−0.431975	+	1.61215i
$481$	−4.19615			−0.191328
$482$	−0.0980762	+	0.0262794i	−0.00446725	+	0.00119700i
$483$		0			0
$484$	8.19615	+	14.1962i	0.372552	+	0.645280i
$485$	25.8564	+	25.8564i	1.17408	+	1.17408i
$486$	−5.26795	+	9.12436i	−0.238959	+	0.413889i
$487$		−	22.3205i		−	1.01144i	−0.862698	−	0.505719i	$-0.831227\pi$
$487$		−	22.3205i		−	1.01144i	0.862698	−	0.505719i	$-0.168773\pi$
$488$		−	0.392305i		−	0.0177588i
$489$		−	0.464102i		−	0.0209874i
$490$		0			0
$491$	27.5885	+	27.5885i	1.24505	+	1.24505i	0.957880	+	0.287170i	$0.0927145\pi$
$491$	27.5885	+	27.5885i	1.24505	+	1.24505i	0.287170	+	0.957880i	$0.407286\pi$
$492$	−33.3205	−	8.92820i	−1.50220	−	0.402514i
$493$	1.73205	−	1.73205i	0.0780076	−	0.0780076i
$494$	−0.607695	−	2.26795i	−0.0273415	−	0.102040i
$495$	10.7321			0.482370
$496$	0.535898	−	0.928203i	0.0240625	−	0.0416776i
$497$		0			0
$498$	8.46410	+	31.5885i	0.379285	+	1.41551i
$499$	2.70577	−	2.70577i	0.121127	−	0.121127i	−0.643945	−	0.765072i	$-0.722703\pi$
$499$	2.70577	−	2.70577i	0.121127	−	0.121127i	0.765072	+	0.643945i	$0.222703\pi$
$500$	−2.07180	+	7.73205i	−0.0926536	+	0.345788i
$501$	−8.00000	−	8.00000i	−0.357414	−	0.357414i
$502$	−23.5359	−	13.5885i	−1.05046	−	0.606483i
$503$			4.14359i			0.184754i	0.995724	+	0.0923769i	$0.0294464\pi$
$503$			4.14359i			0.184754i	−0.995724	+	0.0923769i	$0.970554\pi$
$504$		0			0
$505$			24.4641i			1.08864i
$506$	7.63397	−	13.2224i	0.339372	−	0.587809i
$507$	17.5622	+	17.5622i	0.779964	+	0.779964i
$508$	4.39230	−	2.53590i	0.194877	−	0.112512i
$509$	12.0981	−	12.0981i	0.536238	−	0.536238i	−0.386184	−	0.922422i	$-0.626207\pi$
$509$	12.0981	−	12.0981i	0.536238	−	0.536238i	0.922422	+	0.386184i	$0.126207\pi$
$510$	4.09808	−	1.09808i	0.181466	−	0.0486236i
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	−19.1962			−0.847531
$514$	−1.90192	+	0.509619i	−0.0838903	+	0.0224783i
$515$	1.09808	−	1.09808i	0.0483870	−	0.0483870i
$516$	−2.19615	+	1.26795i	−0.0966802	+	0.0558184i
$517$	23.9545	+	23.9545i	1.05352	+	1.05352i
$518$		0			0
$519$		−	9.19615i		−	0.403666i
$520$	−2.53590	+	2.53590i	−0.111207	+	0.111207i
$521$			43.4449i			1.90335i	0.307101	+	0.951677i	$0.400641\pi$
$521$			43.4449i			1.90335i	−0.307101	+	0.951677i	$0.599359\pi$
$522$	−4.73205	−	2.73205i	−0.207116	−	0.119579i
$523$	25.3660	+	25.3660i	1.10918	+	1.10918i	0.993259	+	0.115920i	$0.0369817\pi$
$523$	25.3660	+	25.3660i	1.10918	+	1.10918i	0.115920	+	0.993259i	$0.463018\pi$
$524$	4.80385	−	17.9282i	0.209857	−	0.783197i
$525$		0			0
$526$	−9.29423	−	34.6865i	−0.405248	−	1.51240i
$527$	−0.124356			−0.00541702
$528$	16.9282	−	29.3205i	0.736705	−	1.27601i
$529$	16.9282			0.736009
$530$	14.0263	+	52.3468i	0.609263	+	2.27380i
$531$	5.33975	−	5.33975i	0.231725	−	0.231725i
$532$		0			0
$533$	−2.39230	−	2.39230i	−0.103622	−	0.103622i
$534$	12.2942	+	7.09808i	0.532023	+	0.307164i
$535$		−	3.00000i		−	0.129701i
$536$			21.4641i			0.927108i
$537$		−	15.1962i		−	0.655762i
$538$	15.8301	−	27.4186i	0.682485	−	1.18210i
$539$		0			0
$540$	14.6603	+	25.3923i	0.630877	+	1.09271i
$541$	−15.7583	+	15.7583i	−0.677504	+	0.677504i	−0.959435	−	0.281931i	$-0.909025\pi$
$541$	−15.7583	+	15.7583i	−0.677504	+	0.677504i	0.281931	+	0.959435i	$0.409025\pi$
$542$	16.5622	−	4.43782i	0.711406	−	0.190621i
$543$	−20.1962			−0.866700
$544$	0.679492	−	2.53590i	0.0291330	−	0.108726i
$545$	−49.9808			−2.14094
$546$		0			0
$547$	15.0526	−	15.0526i	0.643601	−	0.643601i	−0.307838	−	0.951439i	$-0.599605\pi$
$547$	15.0526	−	15.0526i	0.643601	−	0.643601i	0.951439	+	0.307838i	$0.0996054\pi$
$548$	−13.5885	−	23.5359i	−0.580470	−	1.00540i
$549$	0.0717968	+	0.0717968i	0.00306421	+	0.00306421i
$550$	19.1962	−	33.2487i	0.818527	−	1.41773i
$551$		−	23.1244i		−	0.985131i
$552$	−13.4641			−0.573070
$553$		0			0
$554$	−21.2942	−	12.2942i	−0.904705	−	0.522332i
$555$	−50.6147	−	50.6147i	−2.14848	−	2.14848i
$556$	5.26795	+	1.41154i	0.223411	+	0.0598627i
$557$	3.83013	−	3.83013i	0.162288	−	0.162288i	−0.621292	−	0.783579i	$-0.713392\pi$
$557$	3.83013	−	3.83013i	0.162288	−	0.162288i	0.783579	+	0.621292i	$0.213392\pi$
$558$	0.0717968	+	0.267949i	0.00303940	+	0.0113432i
$559$	−0.248711			−0.0105194
$560$		0			0
$561$	−3.92820			−0.165849
$562$	4.73205	+	17.6603i	0.199610	+	0.744953i
$563$	31.2224	−	31.2224i	1.31587	−	1.31587i	0.398854	−	0.917014i	$-0.369408\pi$
$563$	31.2224	−	31.2224i	1.31587	−	1.31587i	0.917014	−	0.398854i	$-0.130592\pi$
$564$	7.73205	−	28.8564i	0.325578	−	1.21507i
$565$	12.9282	+	12.9282i	0.543894	+	0.543894i
$566$	21.4186	+	12.3660i	0.900290	+	0.519783i
$567$		0			0
$568$	14.9282	+	14.9282i	0.626373	+	0.626373i
$569$			30.1244i			1.26288i	0.775425	+	0.631439i	$0.217536\pi$
$569$			30.1244i			1.26288i	−0.775425	+	0.631439i	$0.782464\pi$
$570$	20.0263	−	34.6865i	0.838809	−	1.45286i
$571$	−7.43782	−	7.43782i	−0.311263	−	0.311263i	0.534136	−	0.845399i	$-0.320637\pi$
$571$	−7.43782	−	7.43782i	−0.311263	−	0.311263i	−0.845399	+	0.534136i	$0.820637\pi$
$572$	2.87564	−	1.66025i	0.120237	−	0.0694187i
$573$	−11.8301	+	11.8301i	−0.494211	+	0.494211i
$574$		0			0
$575$	−15.2679			−0.636717
$576$	−5.85641			−0.244017
$577$	−35.2487			−1.46742			−0.733712	−	0.679461i	$-0.762214\pi$
$577$	−35.2487			−1.46742			−0.733712	+	0.679461i	$0.762214\pi$
$578$	22.9282	−	6.14359i	0.953688	−	0.255540i
$579$	−31.4186	+	31.4186i	−1.30571	+	1.30571i
$580$	−30.5885	+	17.6603i	−1.27012	+	0.733302i
$581$		0			0
$582$	−14.9282	+	25.8564i	−0.618794	+	1.07178i
$583$		−	50.1769i		−	2.07812i
$584$	6.39230	+	6.39230i	0.264515	+	0.264515i
$585$		−	0.928203i		−	0.0383765i
$586$	−10.2679	−	5.92820i	−0.424165	−	0.244892i
$587$	8.07180	+	8.07180i	0.333159	+	0.333159i	0.853785	−	0.520626i	$-0.174301\pi$
$587$	8.07180	+	8.07180i	0.333159	+	0.333159i	−0.520626	+	0.853785i	$0.674301\pi$
$588$		0			0
$589$	−0.830127	+	0.830127i	−0.0342048	+	0.0342048i
$590$	−12.6340	−	47.1506i	−0.520133	−	1.94116i
$591$	1.80385			0.0742004
$592$	−42.7846	+	11.4641i	−1.75844	+	0.471172i
$593$	9.39230			0.385696			0.192848	−	0.981229i	$-0.438228\pi$
$593$	9.39230			0.385696			0.192848	+	0.981229i	$0.438228\pi$
$594$	−7.02628	−	26.2224i	−0.288292	−	1.07592i
$595$		0			0
$596$	−17.9282	−	4.80385i	−0.734368	−	0.196773i
$597$	2.63397	+	2.63397i	0.107801	+	0.107801i
$598$	−1.14359	−	0.660254i	−0.0467650	−	0.0269998i
$599$		−	29.2487i		−	1.19507i	−0.801843	−	0.597535i	$-0.796147\pi$
$599$		−	29.2487i		−	1.19507i	0.801843	−	0.597535i	$-0.203853\pi$
$600$	−33.8564			−1.38218
$601$		−	10.0000i		−	0.407909i	−0.978980	−	0.203954i	$-0.934621\pi$
$601$		−	10.0000i		−	0.407909i	0.978980	−	0.203954i	$-0.0653794\pi$
$602$		0			0
$603$	−3.92820	−	3.92820i	−0.159969	−	0.159969i
$604$	−9.39230	−	16.2679i	−0.382167	−	0.661933i
$605$	−19.3923	+	19.3923i	−0.788409	+	0.788409i
$606$	−19.2942	+	5.16987i	−0.783774	+	0.210012i
$607$	−21.0526			−0.854497			−0.427249	−	0.904134i	$-0.640517\pi$
$607$	−21.0526			−0.854497			−0.427249	+	0.904134i	$0.640517\pi$
$608$	−12.3923	−	21.4641i	−0.502574	−	0.870484i
$609$		0			0
$610$	0.633975	−	0.169873i	0.0256689	−	0.00687796i
$611$	2.07180	−	2.07180i	0.0838159	−	0.0838159i
$612$	0.339746	+	0.588457i	0.0137334	+	0.0237870i
$613$	−15.7583	−	15.7583i	−0.636473	−	0.636473i	0.313211	−	0.949684i	$-0.398595\pi$
$613$	−15.7583	−	15.7583i	−0.636473	−	0.636473i	−0.949684	+	0.313211i	$0.898595\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$		−	57.7128i		−	2.32721i
$616$		0			0
$617$		−	7.46410i		−	0.300493i	−0.988649	−	0.150247i	$-0.951993\pi$
$617$		−	7.46410i		−	0.300493i	0.988649	−	0.150247i	$-0.0480068\pi$
$618$	1.09808	+	0.633975i	0.0441711	+	0.0255022i
$619$	−18.9545	−	18.9545i	−0.761845	−	0.761845i	0.214811	−	0.976656i	$-0.431087\pi$
$619$	−18.9545	−	18.9545i	−0.761845	−	0.761845i	−0.976656	+	0.214811i	$0.931087\pi$
$620$	1.73205	+	0.464102i	0.0695608	+	0.0186388i
$621$	−7.63397	+	7.63397i	−0.306341	+	0.306341i
$622$	0.169873	+	0.633975i	0.00681129	+	0.0254201i
$623$		0			0
$624$	−2.53590	−	1.46410i	−0.101517	−	0.0586110i
$625$	17.5885			0.703538
$626$	3.50962	+	13.0981i	0.140273	+	0.523504i
$627$	−26.2224	+	26.2224i	−1.04722	+	1.04722i
$628$	8.51666	−	31.7846i	0.339852	−	1.26834i
$629$	3.63397	+	3.63397i	0.144896	+	0.144896i
$630$		0			0
$631$			16.2487i			0.646851i	0.946254	+	0.323425i	$0.104835\pi$
$631$			16.2487i			0.646851i	−0.946254	+	0.323425i	$0.895165\pi$
$632$	−1.32051	+	1.32051i	−0.0525270	+	0.0525270i
$633$			5.66025i			0.224975i
$634$	8.63397	−	14.9545i	0.342899	−	0.593918i
$635$	6.00000	+	6.00000i	0.238103	+	0.238103i
$636$	−38.3205	+	22.1244i	−1.51951	+	0.877288i
$637$		0			0
$638$	31.5885	−	8.46410i	1.25060	−	0.335097i
$639$	−5.46410			−0.216157
$640$	−18.9282	+	32.7846i	−0.748203	+	1.29593i
$641$	−38.8564			−1.53474			−0.767368	−	0.641207i	$-0.778434\pi$
$641$	−38.8564			−1.53474			−0.767368	+	0.641207i	$0.778434\pi$
$642$	2.36603	−	0.633975i	0.0933796	−	0.0250210i
$643$	15.3923	−	15.3923i	0.607013	−	0.607013i	−0.335151	−	0.942164i	$-0.608787\pi$
$643$	15.3923	−	15.3923i	0.607013	−	0.607013i	0.942164	+	0.335151i	$0.108787\pi$
$644$		0			0
$645$	−3.00000	−	3.00000i	−0.118125	−	0.118125i
$646$	−1.43782	+	2.49038i	−0.0565704	+	0.0979827i
$647$		−	33.6410i		−	1.32256i	−0.750137	−	0.661282i	$-0.770012\pi$
$647$		−	33.6410i		−	1.32256i	0.750137	−	0.661282i	$-0.229988\pi$
$648$	−21.3205	+	21.3205i	−0.837549	+	0.837549i
$649$			45.1962i			1.77410i
$650$	−2.87564	−	1.66025i	−0.112792	−	0.0651205i
$651$		0			0
$652$	0.124356	−	0.464102i	0.00487014	−	0.0181756i
$653$	−15.1699	+	15.1699i	−0.593643	+	0.593643i	−0.938614	−	0.344971i	$-0.887889\pi$
$653$	−15.1699	+	15.1699i	−0.593643	+	0.593643i	0.344971	+	0.938614i	$0.387889\pi$
$654$	−10.5622	−	39.4186i	−0.413014	−	1.54139i
$655$	31.0526			1.21332
$656$	−30.9282	−	17.8564i	−1.20754	−	0.697176i
$657$	−2.33975			−0.0912822
$658$		0			0
$659$	−8.85641	+	8.85641i	−0.344997	+	0.344997i	−0.858242	−	0.513245i	$-0.828443\pi$
$659$	−8.85641	+	8.85641i	−0.344997	+	0.344997i	0.513245	+	0.858242i	$0.328443\pi$
$660$	54.7128	+	14.6603i	2.12969	+	0.570650i
$661$	13.2224	+	13.2224i	0.514293	+	0.514293i	0.915839	−	0.401546i	$-0.131527\pi$
$661$	13.2224	+	13.2224i	0.514293	+	0.514293i	−0.401546	+	0.915839i	$0.631527\pi$
$662$	−21.8827	−	12.6340i	−0.850495	−	0.491033i
$663$			0.339746i			0.0131946i
$664$			33.8564i			1.31388i
$665$		0			0
$666$	5.73205	−	9.92820i	0.222112	−	0.384710i
$667$	−9.19615	−	9.19615i	−0.356076	−	0.356076i
$668$	−5.85641	−	10.1436i	−0.226591	−	0.392467i
$669$	−24.3923	+	24.3923i	−0.943061	+	0.943061i
$670$	−34.6865	+	9.29423i	−1.34006	+	0.359067i
$671$	−0.607695			−0.0234598
$672$		0			0
$673$	−0.784610			−0.0302445			−0.0151222	−	0.999886i	$-0.504814\pi$
$673$	−0.784610			−0.0302445			−0.0151222	+	0.999886i	$0.504814\pi$
$674$	46.2487	−	12.3923i	1.78143	−	0.477334i
$675$	−19.1962	+	19.1962i	−0.738860	+	0.738860i
$676$	12.8564	+	22.2679i	0.494477	+	0.856460i
$677$	−36.2750	−	36.2750i	−1.39416	−	1.39416i	−0.815734	−	0.578427i	$-0.803667\pi$
$677$	−36.2750	−	36.2750i	−1.39416	−	1.39416i	−0.578427	−	0.815734i	$-0.696333\pi$
$678$	−7.46410	+	12.9282i	−0.286657	+	0.496505i
$679$		0			0
$680$	4.39230			0.168437
$681$			45.9808i			1.76199i
$682$	−1.43782	−	0.830127i	−0.0550571	−	0.0317872i
$683$	31.6340	+	31.6340i	1.21044	+	1.21044i	0.970882	+	0.239558i	$0.0770027\pi$
$683$	31.6340	+	31.6340i	1.21044	+	1.21044i	0.239558	+	0.970882i	$0.422997\pi$
$684$	6.19615	+	1.66025i	0.236916	+	0.0634814i
$685$	32.1506	−	32.1506i	1.22841	−	1.22841i
$686$		0			0
$687$	34.8564			1.32985
$688$	−2.53590	+	0.679492i	−0.0966802	+	0.0259054i
$689$	−4.33975			−0.165331
$690$	−5.83013	−	21.7583i	−0.221949	−	0.828325i
$691$	8.16987	−	8.16987i	0.310797	−	0.310797i	−0.534421	−	0.845218i	$-0.679470\pi$
$691$	8.16987	−	8.16987i	0.310797	−	0.310797i	0.845218	+	0.534421i	$0.179470\pi$
$692$	2.46410	−	9.19615i	0.0936711	−	0.349585i
$693$		0			0
$694$	−21.1699	−	12.2224i	−0.803597	−	0.463957i
$695$			9.12436i			0.346107i
$696$	−20.3923	−	20.3923i	−0.772968	−	0.772968i
$697$			4.14359i			0.156950i
$698$	18.1244	−	31.3923i	0.686017	−	1.18822i
$699$	−15.2942	−	15.2942i	−0.578481	−	0.578481i
$700$		0			0
$701$	7.39230	−	7.39230i	0.279204	−	0.279204i	−0.553588	−	0.832791i	$-0.686742\pi$
$701$	7.39230	−	7.39230i	0.279204	−	0.279204i	0.832791	+	0.553588i	$0.186742\pi$
$702$	−2.26795	+	0.607695i	−0.0855982	+	0.0229360i
$703$	48.5167			1.82984
$704$	24.7846	−	24.7846i	0.934105	−	0.934105i
$705$	49.9808			1.88238
$706$	−18.8301	+	5.04552i	−0.708681	+	0.189891i
$707$		0			0
$708$	34.5167	−	19.9282i	1.29722	−	0.748948i
$709$	6.41858	+	6.41858i	0.241055	+	0.241055i	0.817287	−	0.576232i	$-0.195477\pi$
$709$	6.41858	+	6.41858i	0.241055	+	0.241055i	−0.576232	+	0.817287i	$0.695477\pi$
$710$	−17.6603	+	30.5885i	−0.662778	+	1.14796i
$711$		−	0.483340i		−	0.0181266i
$712$	10.3923	+	10.3923i	0.389468	+	0.389468i
$713$			0.660254i			0.0247267i
$714$		0			0
$715$	3.92820	+	3.92820i	0.146906	+	0.146906i
$716$	4.07180	−	15.1962i	0.152170	−	0.567907i
$717$	−21.1244	+	21.1244i	−0.788904	+	0.788904i
$718$	0.901924	+	3.36603i	0.0336595	+	0.125619i
$719$	31.5885			1.17805			0.589025	−	0.808115i	$-0.299512\pi$
$719$	31.5885			1.17805			0.589025	+	0.808115i	$0.299512\pi$
$720$	−2.53590	−	9.46410i	−0.0945074	−	0.352706i
$721$		0			0
$722$	0.0717968	+	0.267949i	0.00267200	+	0.00997204i
$723$	0.0980762	−	0.0980762i	0.00364749	−	0.00364749i
$724$	−20.1962	−	5.41154i	−0.750584	−	0.201118i
$725$	−23.1244	−	23.1244i	−0.858817	−	0.858817i
$726$	−19.3923	−	11.1962i	−0.719716	−	0.415528i
$727$			6.67949i			0.247729i	0.992299	+	0.123864i	$0.0395288\pi$
$727$			6.67949i			0.247729i	−0.992299	+	0.123864i	$0.960471\pi$
$728$		0			0
$729$			17.5885i			0.651424i
$730$	−7.56218	+	13.0981i	−0.279889	+	0.484782i
$731$	0.215390	+	0.215390i	0.00796650	+	0.00796650i
$732$	0.267949	+	0.464102i	0.00990369	+	0.0171537i
$733$	33.0788	−	33.0788i	1.22179	−	1.22179i	0.254801	−	0.966993i	$-0.417990\pi$
$733$	33.0788	−	33.0788i	1.22179	−	1.22179i	0.966993	−	0.254801i	$-0.0820101\pi$
$734$	24.7583	−	6.63397i	0.913847	−	0.244864i
$735$		0			0
$736$	−13.4641	−	3.60770i	−0.496293	−	0.132981i
$737$	33.2487			1.22473
$738$	8.92820	−	2.39230i	0.328652	−	0.0880620i
$739$	−36.8301	+	36.8301i	−1.35482	+	1.35482i	−0.474636	+	0.880182i	$0.657420\pi$
$739$	−36.8301	+	36.8301i	−1.35482	+	1.35482i	−0.880182	+	0.474636i	$0.842580\pi$
$740$	−37.0526	−	64.1769i	−1.36208	−	2.35919i
$741$	2.26795	+	2.26795i	0.0833152	+	0.0833152i
$742$		0			0
$743$			24.9282i			0.914527i	0.889331	+	0.457264i	$0.151170\pi$
$743$			24.9282i			0.914527i	−0.889331	+	0.457264i	$0.848830\pi$
$744$			1.46410i			0.0536766i
$745$		−	31.0526i		−	1.13768i
$746$	4.09808	+	2.36603i	0.150041	+	0.0866263i
$747$	−6.19615	−	6.19615i	−0.226705	−	0.226705i
$748$	−3.92820	−	1.05256i	−0.143629	−	0.0384854i
$749$		0			0
$750$	−2.83013	−	10.5622i	−0.103342	−	0.385676i
$751$	−25.0526			−0.914181			−0.457090	−	0.889420i	$-0.651108\pi$
$751$	−25.0526			−0.914181			−0.457090	+	0.889420i	$0.651108\pi$
$752$	15.4641	−	26.7846i	0.563918	−	0.976734i
$753$	37.1244			1.35289
$754$	−0.732051	−	2.73205i	−0.0266597	−	0.0994954i
$755$	22.2224	−	22.2224i	0.808757	−	0.808757i
$756$		0			0
$757$	−1.33975	−	1.33975i	−0.0486939	−	0.0486939i	0.682341	−	0.731034i	$-0.260962\pi$
$757$	−1.33975	−	1.33975i	−0.0486939	−	0.0486939i	−0.731034	+	0.682341i	$0.760962\pi$
$758$	41.7846	+	24.1244i	1.51769	+	0.876236i
$759$			20.8564i			0.757040i
$760$	29.3205	−	29.3205i	1.06357	−	1.06357i
$761$			17.5885i			0.637581i	0.947825	+	0.318791i	$0.103277\pi$
$761$			17.5885i			0.637581i	−0.947825	+	0.318791i	$0.896723\pi$
$762$	−3.46410	+	6.00000i	−0.125491	+	0.217357i
$763$		0			0
$764$	−15.0000	+	8.66025i	−0.542681	+	0.313317i
$765$	−0.803848	+	0.803848i	−0.0290632	+	0.0290632i
$766$	20.2224	−	5.41858i	0.730666	−	0.195781i
$767$	3.90897			0.141145
$768$	−29.8564	−	8.00000i	−1.07735	−	0.288675i
$769$	−17.8564			−0.643918			−0.321959	−	0.946754i	$-0.604341\pi$
$769$	−17.8564			−0.643918			−0.321959	+	0.946754i	$0.604341\pi$
$770$		0			0
$771$	1.90192	−	1.90192i	0.0684961	−	0.0684961i
$772$	−39.8372	+	23.0000i	−1.43377	+	0.827788i
$773$	11.0263	+	11.0263i	0.396588	+	0.396588i	0.877028	−	0.480440i	$-0.159523\pi$
$773$	11.0263	+	11.0263i	0.396588	+	0.396588i	−0.480440	+	0.877028i	$0.659523\pi$
$774$	0.339746	−	0.588457i	0.0122119	−	0.0211517i
$775$			1.66025i			0.0596381i
$776$	−21.8564	+	21.8564i	−0.784599	+	0.784599i
$777$		0			0
$778$	−25.3468	−	14.6340i	−0.908726	−	0.524653i
$779$	27.6603	+	27.6603i	0.991031	+	0.991031i
$780$	1.26795	−	4.73205i	0.0453999	−	0.169435i
$781$	23.1244	−	23.1244i	0.827455	−	0.827455i
$782$	0.418584	+	1.56218i	0.0149685	+	0.0558634i
$783$	−23.1244			−0.826397
$784$		0			0
$785$	55.0526			1.96491
$786$	6.56218	+	24.4904i	0.234065	+	0.873543i
$787$	11.3660	−	11.3660i	0.405155	−	0.405155i	−0.474890	−	0.880045i	$-0.657512\pi$
$787$	11.3660	−	11.3660i	0.405155	−	0.405155i	0.880045	+	0.474890i	$0.157512\pi$
$788$	1.80385	+	0.483340i	0.0642594	+	0.0172183i
$789$	34.6865	+	34.6865i	1.23487	+	1.23487i
$790$	−2.70577	−	1.56218i	−0.0962670	−	0.0555798i
$791$		0			0
$792$			9.07180i			0.322352i
$793$			0.0525589i			0.00186642i
$794$	3.75833	−	6.50962i	0.133378	−	0.231018i
$795$	−52.3468	−	52.3468i	−1.85655	−	1.85655i
$796$	1.92820	+	3.33975i	0.0683434	+	0.118374i
$797$	−30.6603	+	30.6603i	−1.08604	+	1.08604i	−0.0901101	+	0.995932i	$0.528722\pi$
$797$	−30.6603	+	30.6603i	−1.08604	+	1.08604i	−0.995932	+	0.0901101i	$0.971278\pi$
$798$		0			0
$799$	−3.58846			−0.126950
$800$	−33.8564	−	9.07180i	−1.19700	−	0.320736i
$801$	−3.80385			−0.134402
$802$	20.4904	−	5.49038i	0.723541	−	0.193872i
$803$	9.90192	−	9.90192i	0.349431	−	0.349431i
$804$	−14.6603	−	25.3923i	−0.517027	−	0.895518i
$805$		0			0
$806$	−0.0717968	+	0.124356i	−0.00252893	+	0.00438024i
$807$			43.2487i			1.52243i
$808$	−20.6795			−0.727502
$809$			17.9808i			0.632170i	0.948731	+	0.316085i	$0.102368\pi$
$809$			17.9808i			0.632170i	−0.948731	+	0.316085i	$0.897632\pi$
$810$	−43.6865	−	25.2224i	−1.53499	−	0.886226i
$811$	−10.3205	−	10.3205i	−0.362402	−	0.362402i	0.502295	−	0.864697i	$-0.332489\pi$
$811$	−10.3205	−	10.3205i	−0.362402	−	0.362402i	−0.864697	+	0.502295i	$0.832489\pi$
$812$		0			0
$813$	−16.5622	+	16.5622i	−0.580861	+	0.580861i
$814$	17.7583	+	66.2750i	0.622429	+	2.32294i
$815$	0.803848			0.0281576
$816$	0.928203	+	3.46410i	0.0324936	+	0.121268i
$817$	2.87564			0.100606
$818$	−3.16987	−	11.8301i	−0.110832	−	0.413631i
$819$		0			0
$820$	15.4641	−	57.7128i	0.540030	−	2.01542i
$821$	−12.5622	−	12.5622i	−0.438423	−	0.438423i	0.453058	−	0.891481i	$-0.350333\pi$
$821$	−12.5622	−	12.5622i	−0.438423	−	0.438423i	−0.891481	+	0.453058i	$0.850333\pi$
$822$	32.1506	+	18.5622i	1.12138	+	0.647430i
$823$			31.2487i			1.08926i	0.838676	+	0.544631i	$0.183330\pi$
$823$			31.2487i			1.08926i	−0.838676	+	0.544631i	$0.816670\pi$
$824$	0.928203	+	0.928203i	0.0323355	+	0.0323355i
$825$			52.4449i			1.82590i
$826$		0			0
$827$	37.7846	+	37.7846i	1.31390	+	1.31390i	0.918516	+	0.395383i	$0.129388\pi$
$827$	37.7846	+	37.7846i	1.31390	+	1.31390i	0.395383	+	0.918516i	$0.370612\pi$
$828$	3.12436	−	1.80385i	0.108579	−	0.0626880i
$829$	24.7583	−	24.7583i	0.859892	−	0.859892i	−0.131433	−	0.991325i	$-0.541958\pi$
$829$	24.7583	−	24.7583i	0.859892	−	0.859892i	0.991325	+	0.131433i	$0.0419577\pi$
$830$	−54.7128	+	14.6603i	−1.89911	+	0.508865i
$831$	33.5885			1.16517
$832$	−2.14359	−	2.14359i	−0.0743157	−	0.0743157i
$833$		0			0
$834$	−7.19615	+	1.92820i	−0.249182	+	0.0667682i
$835$	13.8564	−	13.8564i	0.479521	−	0.479521i
$836$	−33.2487	+	19.1962i	−1.14993	+	0.663913i
$837$	0.830127	+	0.830127i	0.0286934	+	0.0286934i
$838$	19.0000	−	32.9090i	0.656344	−	1.13682i
$839$			37.7128i			1.30199i	0.759082	+	0.650995i	$0.225648\pi$
$839$			37.7128i			1.30199i	−0.759082	+	0.650995i	$0.774352\pi$
$840$		0			0
$841$			1.14359i			0.0394343i
$842$	15.0000	+	8.66025i	0.516934	+	0.298452i
$843$	−17.6603	−	17.6603i	−0.608251	−	0.608251i
$844$	−1.51666	+	5.66025i	−0.0522056	+	0.194834i
$845$	−30.4186	+	30.4186i	−1.04643	+	1.04643i
$846$	2.07180	+	7.73205i	0.0712298	+	0.265833i
$847$		0			0
$848$	−44.2487	+	11.8564i	−1.51951	+	0.407151i
$849$	−33.7846			−1.15948
$850$	1.05256	+	3.92820i	0.0361025	+	0.134736i
$851$	19.2942	−	19.2942i	0.661398	−	0.661398i
$852$	−27.8564	−	7.46410i	−0.954345	−	0.255716i
$853$	−36.1244	−	36.1244i	−1.23687	−	1.23687i	−0.961272	−	0.275603i	$-0.911123\pi$
$853$	−36.1244	−	36.1244i	−1.23687	−	1.23687i	−0.275603	−	0.961272i	$-0.588877\pi$
$854$		0			0
$855$			10.7321i			0.367028i
$856$	2.53590			0.0866752
$857$			10.2679i			0.350746i	0.984502	+	0.175373i	$0.0561132\pi$
$857$			10.2679i			0.350746i	−0.984502	+	0.175373i	$0.943887\pi$
$858$	−2.26795	+	3.92820i	−0.0774265	+	0.134107i
$859$	−29.0263	−	29.0263i	−0.990364	−	0.990364i	0.00959014	−	0.999954i	$-0.496947\pi$
$859$	−29.0263	−	29.0263i	−0.990364	−	0.990364i	−0.999954	+	0.00959014i	$0.996947\pi$
$860$	−2.19615	−	3.80385i	−0.0748882	−	0.129710i
$861$		0			0
$862$	−18.2224	+	4.88269i	−0.620658	+	0.166305i
$863$	−15.3397			−0.522171			−0.261086	−	0.965316i	$-0.584080\pi$
$863$	−15.3397			−0.522171			−0.261086	+	0.965316i	$0.584080\pi$
$864$	−21.4641	+	12.3923i	−0.730224	+	0.421595i
$865$	15.9282			0.541575
$866$	−39.8564	+	10.6795i	−1.35438	+	0.362904i
$867$	−22.9282	+	22.9282i	−0.778683	+	0.778683i
$868$		0			0
$869$	2.04552	+	2.04552i	0.0693894	+	0.0693894i
$870$	24.1244	−	41.7846i	0.817892	−	1.41663i
$871$		−	2.87564i		−	0.0974375i
$872$		−	42.2487i		−	1.43072i
$873$		−	8.00000i		−	0.270759i
$874$	13.2224	+	7.63397i	0.447255	+	0.258223i
$875$		0			0
$876$	−11.9282	−	3.19615i	−0.403017	−	0.107988i
$877$	20.6340	−	20.6340i	0.696760	−	0.696760i	−0.266950	−	0.963710i	$-0.586016\pi$
$877$	20.6340	−	20.6340i	0.696760	−	0.696760i	0.963710	+	0.266950i	$0.0860160\pi$
$878$	5.29423	+	19.7583i	0.178672	+	0.666811i
$879$	16.1962			0.546283
$880$	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	$0.181218\pi$
$882$		0			0
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	−0.786216	−	0.617952i	$-0.787963\pi$
$883$	−5.00000	+	5.00000i	−0.168263	+	0.168263i	0.617952	+	0.786216i	$0.287963\pi$
$884$	−0.0910347	+	0.339746i	−0.00306183	+	0.0114269i
$885$	47.1506	+	47.1506i	1.58495	+	1.58495i
$886$	−16.2224	−	9.36603i	−0.545003	−	0.314658i
$887$			32.0718i			1.07687i	0.842668	+	0.538433i	$0.180983\pi$
$887$			32.0718i			1.07687i	−0.842668	+	0.538433i	$0.819017\pi$
$888$	42.7846	−	42.7846i	1.43576	−	1.43576i
$889$		0			0
$890$	−12.2942	+	21.2942i	−0.412103	+	0.713784i
$891$	33.0263	+	33.0263i	1.10642	+	1.10642i
$892$	−30.9282	+	17.8564i	−1.03555	+	0.597877i
$893$	−23.9545	+	23.9545i	−0.801606	+	0.801606i
$894$	24.4904	−	6.56218i	0.819081	−	0.219472i
$895$	26.3205			0.879798
$896$		0			0
$897$	1.80385			0.0602287
$898$	−15.4641	+	4.14359i	−0.516044	+	0.138274i
$899$	−1.00000	+	1.00000i	−0.0333519	+	0.0333519i
$900$	7.85641	−	4.53590i	0.261880	−	0.151197i
$901$	3.75833	+	3.75833i	0.125208	+	0.125208i
$902$	−27.6603	+	47.9090i	−0.920986	+	1.59519i
$903$		0			0
$904$	−10.9282	+	10.9282i	−0.363467	+	0.363467i
$905$		−	34.9808i		−	1.16280i
$906$	22.2224	+	12.8301i	0.738291	+	0.426252i
$907$	7.43782	+	7.43782i	0.246969	+	0.246969i	0.819725	−	0.572757i	$-0.194126\pi$
$907$	7.43782	+	7.43782i	0.246969	+	0.246969i	−0.572757	+	0.819725i	$0.694126\pi$
$908$	−12.3205	+	45.9808i	−0.408870	+	1.52593i
$909$	3.78461	−	3.78461i	0.125528	−	0.125528i
$910$		0			0
$911$	−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
$913$	52.4449			1.73567
$914$	10.6865	+	39.8827i	0.353479	+	1.31920i
$915$	−0.633975	+	0.633975i	−0.0209586	+	0.0209586i
$916$	34.8564	+	9.33975i	1.15169	+	0.308594i
$917$		0			0
$918$	2.49038	+	1.43782i	0.0821948	+	0.0474552i
$919$		−	16.3205i		−	0.538364i	−0.963089	−	0.269182i	$-0.913247\pi$
$919$		−	16.3205i		−	0.538364i	0.963089	−	0.269182i	$-0.0867533\pi$
$920$		−	23.3205i		−	0.768854i
$921$		−	24.5885i		−	0.810217i
$922$	−1.33975	+	2.32051i	−0.0441222	+	0.0764219i
$923$	−2.00000	−	2.00000i	−0.0658308	−	0.0658308i
$924$		0			0
$925$	48.5167	−	48.5167i	1.59522	−	1.59522i
$926$	−40.7846	+	10.9282i	−1.34027	+	0.359123i
$927$	−0.339746			−0.0111587
$928$	−14.9282	−	25.8564i	−0.490042	−	0.848778i
$929$	−40.0333			−1.31345			−0.656725	−	0.754130i	$-0.728059\pi$
$929$	−40.0333			−1.31345			−0.656725	+	0.754130i	$0.728059\pi$
$930$	−2.36603	+	0.633975i	−0.0775850	+	0.0207888i
$931$		0			0
$932$	−11.1962	−	19.3923i	−0.366742	−	0.635216i
$933$	−0.633975	−	0.633975i	−0.0207554	−	0.0207554i
$934$	−0.0262794	+	0.0455173i	−0.000859890	+	0.00148937i
$935$		−	6.80385i		−	0.222510i
$936$	0.784610			0.0256458
$937$			42.9282i			1.40240i	0.712963	+	0.701202i	$0.247353\pi$
$937$			42.9282i			1.40240i	−0.712963	+	0.701202i	$0.752647\pi$
$938$		0			0
$939$	−13.0981	−	13.0981i	−0.427440	−	0.427440i
$940$	49.9808	+	13.3923i	1.63019	+	0.436809i
$941$	−12.2224	+	12.2224i	−0.398440	+	0.398440i	−0.877682	−	0.479243i	$-0.840911\pi$
$941$	−12.2224	+	12.2224i	−0.398440	+	0.398440i	0.479243	+	0.877682i	$0.340911\pi$
$942$	11.6340	+	43.4186i	0.379055	+	1.41465i
$943$	22.0000			0.716419
$944$	39.8564	−	10.6795i	1.29722	−	0.347588i
$945$		0			0
$946$	1.05256	+	3.92820i	0.0342216	+	0.127717i
$947$	28.9545	−	28.9545i	0.940894	−	0.940894i	−0.0574539	−	0.998348i	$-0.518298\pi$
$947$	28.9545	−	28.9545i	0.940894	−	0.940894i	0.998348	+	0.0574539i	$0.0182982\pi$
$948$	0.660254	−	2.46410i	0.0214441	−	0.0800303i
$949$	−0.856406	−	0.856406i	−0.0278001	−	0.0278001i
$950$	33.2487	+	19.1962i	1.07873	+	0.622805i
$951$			23.5885i			0.764908i
$952$		0			0
$953$		−	23.4641i		−	0.760077i	−0.924971	−	0.380038i	$-0.875911\pi$
$953$		−	23.4641i		−	0.760077i	0.924971	−	0.380038i	$-0.124089\pi$
$954$	5.92820	−	10.2679i	0.191933	−	0.332437i
$955$	−20.4904	−	20.4904i	−0.663053	−	0.663053i
$956$	−26.7846	+	15.4641i	−0.866276	+	0.500145i
$957$	−31.5885	+	31.5885i	−1.02111	+	1.02111i
$958$	21.2942	−	5.70577i	0.687985	−	0.184345i
$959$		0			0
$960$		−	51.7128i		−	1.66902i
$961$	−30.9282			−0.997684
$962$	5.73205	−	1.53590i	0.184809	−	0.0495194i
$963$	−0.464102	+	0.464102i	−0.0149555	+	0.0149555i
$964$	0.124356	−	0.0717968i	0.00400523	−	0.00231242i
$965$	−54.4186	−	54.4186i	−1.75180	−	1.75180i
$966$		0			0
$967$			11.7513i			0.377896i	0.981987	+	0.188948i	$0.0605078\pi$
$967$			11.7513i			0.377896i	−0.981987	+	0.188948i	$0.939492\pi$
$968$	−16.3923	−	16.3923i	−0.526869	−	0.526869i
$969$		−	3.92820i		−	0.126192i
$970$	−44.7846	−	25.8564i	−1.43795	−	0.830199i
$971$	36.6340	+	36.6340i	1.17564	+	1.17564i	0.980844	+	0.194797i	$0.0624046\pi$
$971$	36.6340	+	36.6340i	1.17564	+	1.17564i	0.194797	+	0.980844i	$0.437595\pi$
$972$	3.85641	−	14.3923i	0.123694	−	0.461633i
$973$		0			0
$974$	8.16987	+	30.4904i	0.261780	+	0.976975i
$975$	4.53590			0.145265
$976$	0.143594	+	0.535898i	0.00459632	+	0.0171537i
$977$	−44.8564			−1.43508			−0.717542	−	0.696515i	$-0.754733\pi$
$977$	−44.8564			−1.43508			−0.717542	+	0.696515i	$0.754733\pi$
$978$	0.169873	+	0.633975i	0.00543194	+	0.0202723i
$979$	16.0981	−	16.0981i	0.514497	−	0.514497i
$980$		0			0
$981$	7.73205	+	7.73205i	0.246865	+	0.246865i
$982$	−47.7846	−	27.5885i	−1.52487	−	0.880383i
$983$		−	21.7846i		−	0.694821i	−0.937713	−	0.347411i	$-0.887061\pi$
$983$		−	21.7846i		−	0.694821i	0.937713	−	0.347411i	$-0.112939\pi$
$984$	48.7846			1.55520
$985$			3.12436i			0.0995502i
$986$	−1.73205	+	3.00000i	−0.0551597	+	0.0955395i
$987$		0			0
$988$	1.66025	+	2.87564i	0.0528197	+	0.0914864i
$989$	1.14359	−	1.14359i	0.0363642	−	0.0363642i
$990$	−14.6603	+	3.92820i	−0.465933	+	0.124846i
$991$	−39.5885			−1.25757			−0.628784	−	0.777580i	$-0.716447\pi$
$991$	−39.5885			−1.25757			−0.628784	+	0.777580i	$0.716447\pi$
$992$	−0.392305	+	1.46410i	−0.0124557	+	0.0464853i
$993$	34.5167			1.09535
$994$		0			0
$995$	−4.56218	+	4.56218i	−0.144631	+	0.144631i
$996$	−23.1244	−	40.0526i	−0.732723	−	1.26911i
$997$	−4.09808	−	4.09808i	−0.129787	−	0.129787i	0.639229	−	0.769016i	$-0.279254\pi$
$997$	−4.09808	−	4.09808i	−0.129787	−	0.129787i	−0.769016	+	0.639229i	$0.779254\pi$
$998$	−2.70577	+	4.68653i	−0.0856497	+	0.148350i
$999$		−	48.5167i		−	1.53500i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.e.197.1		4
7.2	even	3		112.2.w.b.53.1	yes	4
7.3	odd	6		784.2.x.a.373.1		4
7.4	even	3		112.2.w.a.37.1	✓	4
7.5	odd	6		784.2.x.h.165.1		4
7.6	odd	2		784.2.m.d.197.1		4
16.13	even	4	inner	784.2.m.e.589.1		4
28.11	odd	6		448.2.ba.b.177.1		4
28.23	odd	6		448.2.ba.a.305.1		4
56.11	odd	6		896.2.ba.a.737.1		4
56.37	even	6		896.2.ba.b.865.1		4
56.51	odd	6		896.2.ba.c.865.1		4
56.53	even	6		896.2.ba.d.737.1		4
112.11	odd	12		896.2.ba.c.289.1		4
112.13	odd	4		784.2.m.d.589.1		4
112.37	even	12		896.2.ba.d.417.1		4
112.45	odd	12		784.2.x.h.765.1		4
112.51	odd	12		448.2.ba.b.81.1		4
112.53	even	12		896.2.ba.b.289.1		4
112.61	odd	12		784.2.x.a.557.1		4
112.67	odd	12		448.2.ba.a.401.1		4
112.93	even	12		112.2.w.a.109.1	yes	4
112.107	odd	12		896.2.ba.a.417.1		4
112.109	even	12		112.2.w.b.93.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.37.1	✓	4	7.4	even	3
112.2.w.a.109.1	yes	4	112.93	even	12
112.2.w.b.53.1	yes	4	7.2	even	3
112.2.w.b.93.1	yes	4	112.109	even	12
448.2.ba.a.305.1		4	28.23	odd	6
448.2.ba.a.401.1		4	112.67	odd	12
448.2.ba.b.81.1		4	112.51	odd	12
448.2.ba.b.177.1		4	28.11	odd	6
784.2.m.d.197.1		4	7.6	odd	2
784.2.m.d.589.1		4	112.13	odd	4
784.2.m.e.197.1		4	1.1	even	1	trivial
784.2.m.e.589.1		4	16.13	even	4	inner
784.2.x.a.373.1		4	7.3	odd	6
784.2.x.a.557.1		4	112.61	odd	12
784.2.x.h.165.1		4	7.5	odd	6
784.2.x.h.765.1		4	112.45	odd	12
896.2.ba.a.417.1		4	112.107	odd	12
896.2.ba.a.737.1		4	56.11	odd	6
896.2.ba.b.289.1		4	112.53	even	12
896.2.ba.b.865.1		4	56.37	even	6
896.2.ba.c.289.1		4	112.11	odd	12
896.2.ba.c.865.1		4	56.51	odd	6
896.2.ba.d.417.1		4	112.37	even	12
896.2.ba.d.737.1		4	56.53	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-1.36603 + 2.36603i) q^{6} +(-2.00000 + 2.00000i) q^{8} -0.732051i q^{9} +O(q^{10})\)	\(q+(-1.36603 + 0.366025i) q^{2} +(1.36603 - 1.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.36603 + 2.36603i) q^{5} +(-1.36603 + 2.36603i) q^{6} +(-2.00000 + 2.00000i) q^{8} -0.732051i q^{9} +(-4.09808 - 2.36603i) q^{10} +(3.09808 + 3.09808i) q^{11} +(1.00000 - 3.73205i) q^{12} +(0.267949 - 0.267949i) q^{13} +6.46410 q^{15} +(2.00000 - 3.46410i) q^{16} -0.464102 q^{17} +(0.267949 + 1.00000i) q^{18} +(-3.09808 + 3.09808i) q^{19} +(6.46410 + 1.73205i) q^{20} +(-5.36603 - 3.09808i) q^{22} +2.46410i q^{23} +5.46410i q^{24} +6.19615i q^{25} +(-0.267949 + 0.464102i) q^{26} +(3.09808 + 3.09808i) q^{27} +(-3.73205 + 3.73205i) q^{29} +(-8.83013 + 2.36603i) q^{30} +0.267949 q^{31} +(-1.46410 + 5.46410i) q^{32} +8.46410 q^{33} +(0.633975 - 0.169873i) q^{34} +(-0.732051 - 1.26795i) q^{36} +(-7.83013 - 7.83013i) q^{37} +(3.09808 - 5.36603i) q^{38} -0.732051i q^{39} -9.46410 q^{40} -8.92820i q^{41} +(-0.464102 - 0.464102i) q^{43} +(8.46410 + 2.26795i) q^{44} +(1.73205 - 1.73205i) q^{45} +(-0.901924 - 3.36603i) q^{46} +7.73205 q^{47} +(-2.00000 - 7.46410i) q^{48} +(-2.26795 - 8.46410i) q^{50} +(-0.633975 + 0.633975i) q^{51} +(0.196152 - 0.732051i) q^{52} +(-8.09808 - 8.09808i) q^{53} +(-5.36603 - 3.09808i) q^{54} +14.6603i q^{55} +8.46410i q^{57} +(3.73205 - 6.46410i) q^{58} +(7.29423 + 7.29423i) q^{59} +(11.1962 - 6.46410i) q^{60} +(-0.0980762 + 0.0980762i) q^{61} +(-0.366025 + 0.0980762i) q^{62} -8.00000i q^{64} +1.26795 q^{65} +(-11.5622 + 3.09808i) q^{66} +(5.36603 - 5.36603i) q^{67} +(-0.803848 + 0.464102i) q^{68} +(3.36603 + 3.36603i) q^{69} -7.46410i q^{71} +(1.46410 + 1.46410i) q^{72} -3.19615i q^{73} +(13.5622 + 7.83013i) q^{74} +(8.46410 + 8.46410i) q^{75} +(-2.26795 + 8.46410i) q^{76} +(0.267949 + 1.00000i) q^{78} +0.660254 q^{79} +(12.9282 - 3.46410i) q^{80} +10.6603 q^{81} +(3.26795 + 12.1962i) q^{82} +(8.46410 - 8.46410i) q^{83} +(-1.09808 - 1.09808i) q^{85} +(0.803848 + 0.464102i) q^{86} +10.1962i q^{87} -12.3923 q^{88} -5.19615i q^{89} +(-1.73205 + 3.00000i) q^{90} +(2.46410 + 4.26795i) q^{92} +(0.366025 - 0.366025i) q^{93} +(-10.5622 + 2.83013i) q^{94} -14.6603 q^{95} +(5.46410 + 9.46410i) q^{96} +10.9282 q^{97} +(2.26795 - 2.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} + 6 q^{5} - 2 q^{6} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 + 6 * q^5 - 2 * q^6 - 8 * q^8	\( 4 q - 2 q^{2} + 2 q^{3} + 6 q^{5} - 2 q^{6} - 8 q^{8} - 6 q^{10} + 2 q^{11} + 4 q^{12} + 8 q^{13} + 12 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{18} - 2 q^{19} + 12 q^{20} - 18 q^{22} - 8 q^{26} + 2 q^{27} - 8 q^{29} - 18 q^{30} + 8 q^{31} + 8 q^{32} + 20 q^{33} + 6 q^{34} + 4 q^{36} - 14 q^{37} + 2 q^{38} - 24 q^{40} + 12 q^{43} + 20 q^{44} - 14 q^{46} + 24 q^{47} - 8 q^{48} - 16 q^{50} - 6 q^{51} - 20 q^{52} - 22 q^{53} - 18 q^{54} + 8 q^{58} - 2 q^{59} + 24 q^{60} + 10 q^{61} + 2 q^{62} + 12 q^{65} - 22 q^{66} + 18 q^{67} - 24 q^{68} + 10 q^{69} - 8 q^{72} + 30 q^{74} + 20 q^{75} - 16 q^{76} + 8 q^{78} - 32 q^{79} + 24 q^{80} + 8 q^{81} + 20 q^{82} + 20 q^{83} + 6 q^{85} + 24 q^{86} - 8 q^{88} - 4 q^{92} - 2 q^{93} - 18 q^{94} - 24 q^{95} + 8 q^{96} + 16 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 + 6 * q^5 - 2 * q^6 - 8 * q^8 - 6 * q^10 + 2 * q^11 + 4 * q^12 + 8 * q^13 + 12 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^18 - 2 * q^19 + 12 * q^20 - 18 * q^22 - 8 * q^26 + 2 * q^27 - 8 * q^29 - 18 * q^30 + 8 * q^31 + 8 * q^32 + 20 * q^33 + 6 * q^34 + 4 * q^36 - 14 * q^37 + 2 * q^38 - 24 * q^40 + 12 * q^43 + 20 * q^44 - 14 * q^46 + 24 * q^47 - 8 * q^48 - 16 * q^50 - 6 * q^51 - 20 * q^52 - 22 * q^53 - 18 * q^54 + 8 * q^58 - 2 * q^59 + 24 * q^60 + 10 * q^61 + 2 * q^62 + 12 * q^65 - 22 * q^66 + 18 * q^67 - 24 * q^68 + 10 * q^69 - 8 * q^72 + 30 * q^74 + 20 * q^75 - 16 * q^76 + 8 * q^78 - 32 * q^79 + 24 * q^80 + 8 * q^81 + 20 * q^82 + 20 * q^83 + 6 * q^85 + 24 * q^86 - 8 * q^88 - 4 * q^92 - 2 * q^93 - 18 * q^94 - 24 * q^95 + 8 * q^96 + 16 * q^97 + 16 * q^99

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