LMFDB - Embedded newform 784.2.m.d.589.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(197,784)] 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("784.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [4,-2,-2,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$1$
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			589.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	784.589
Dual form			784.2.m.d.197.1

$q$-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} +(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} + 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}+ \cdots + 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

Character values

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

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	$-0.438307\pi$
$3$	−1.36603	−	1.36603i	−0.788675	−	0.788675i	−0.981277	+	0.192602i	$0.938307\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	−2.36603	+	2.36603i	−1.05812	+	1.05812i	−0.0599153	+	0.998203i	$0.519083\pi$
$5$	−2.36603	+	2.36603i	−1.05812	+	1.05812i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$	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	−0.0638541	−	0.997959i	$-0.520339\pi$
$11$	3.09808	−	3.09808i	0.934105	−	0.934105i	0.997959	+	0.0638541i	$0.0203392\pi$
$12$	−1.00000	−	3.73205i	−0.288675	−	1.07735i
$13$	−0.267949	−	0.267949i	−0.0743157	−	0.0743157i	0.668972	−	0.743288i	$-0.266735\pi$
$13$	−0.267949	−	0.267949i	−0.0743157	−	0.0743157i	−0.743288	+	0.668972i	$0.766735\pi$
$14$		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	$-0.482076\pi$
$17$	0.464102			0.112561			0.0562806	+	0.998415i	$0.482076\pi$
$18$	0.267949	−	1.00000i	0.0631562	−	0.235702i
$19$	3.09808	+	3.09808i	0.710747	+	0.710747i	0.966692	−	0.255944i	$-0.0823863\pi$
$19$	3.09808	+	3.09808i	0.710747	+	0.710747i	−0.255944	+	0.966692i	$0.582386\pi$
$20$	−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	$-0.917299\pi$
$23$		−	2.46410i		−	0.513801i	0.966438	−	0.256900i	$-0.0827012\pi$
$24$			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	0.269872	−	0.962896i	$-0.413019\pi$
$29$	−3.73205	−	3.73205i	−0.693024	−	0.693024i	−0.962896	+	0.269872i	$0.913019\pi$
$30$	−8.83013	−	2.36603i	−1.61215	−	0.431975i
$31$	−0.267949			−0.0481251			−0.0240625	−	0.999710i	$-0.507660\pi$
$31$	−0.267949			−0.0481251			−0.0240625	+	0.999710i	$0.507660\pi$
$32$	−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	−0.350823	+	0.936442i	$0.614098\pi$
$37$	−7.83013	+	7.83013i	−1.28726	+	1.28726i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	−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	−0.741608	−	0.670833i	$-0.765937\pi$
$43$	−0.464102	+	0.464102i	−0.0707748	+	0.0707748i	0.670833	+	0.741608i	$0.265937\pi$
$44$	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	$-0.690707\pi$
$47$	−7.73205			−1.12784			−0.563918	+	0.825831i	$0.690707\pi$
$48$	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	−0.119525	+	0.992831i	$0.538137\pi$
$53$	−8.09808	+	8.09808i	−1.11236	+	1.11236i	−0.992831	+	0.119525i	$0.961863\pi$
$54$	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	$-0.984345\pi$
$59$	−7.29423	+	7.29423i	−0.949628	+	0.949628i	0.0491631	+	0.998791i	$0.484345\pi$
$60$	11.1962	+	6.46410i	1.44542	+	0.834512i
$61$	0.0980762	+	0.0980762i	0.0125574	+	0.0125574i	0.713358	−	0.700800i	$-0.247174\pi$
$61$	0.0980762	+	0.0980762i	0.0125574	+	0.0125574i	−0.700800	+	0.713358i	$0.747174\pi$
$62$	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	0.954327	−	0.298763i	$-0.0965740\pi$
$67$	5.36603	+	5.36603i	0.655564	+	0.655564i	−0.298763	+	0.954327i	$0.596574\pi$
$68$	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	$0.146055\pi$
$71$			7.46410i			0.885826i	−0.896565	+	0.442913i	$0.853945\pi$
$72$	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	$-0.478150\pi$
$83$	−8.46410	−	8.46410i	−0.929056	−	0.929056i	−0.997645	+	0.0685891i	$0.978150\pi$
$84$		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	$-0.687203\pi$
$97$	−10.9282			−1.10959			−0.554795	+	0.831987i	$0.687203\pi$
$98$		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	$-0.868504\pi$
$101$	−5.16987	+	5.16987i	−0.514422	+	0.514422i	0.401457	+	0.915878i	$0.368504\pi$
$102$	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	−0.737087	−	0.675798i	$-0.763799\pi$
$107$	−0.633975	+	0.633975i	−0.0612886	+	0.0612886i	0.675798	+	0.737087i	$0.263799\pi$
$108$	−8.46410	+	2.26795i	−0.814459	+	0.218234i
$109$	−10.5622	−	10.5622i	−1.01167	−	1.01167i	−0.999931	−	0.0117421i	$-0.996262\pi$
$109$	−10.5622	−	10.5622i	−1.01167	−	1.01167i	−0.0117421	−	0.999931i	$-0.503738\pi$
$110$	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	$-0.382872\pi$
$131$	−6.56218	−	6.56218i	−0.573340	−	0.573340i	−0.933060	+	0.359720i	$0.882872\pi$
$132$	−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	$0.197131\pi$
$137$			13.5885i			1.16094i	−0.814282	+	0.580470i	$0.802869\pi$
$138$	5.83013	−	3.36603i	0.496293	−	0.286535i
$139$	−1.92820	+	1.92820i	−0.163548	+	0.163548i	−0.784136	−	0.620588i	$-0.786894\pi$
$139$	−1.92820	+	1.92820i	−0.163548	+	0.163548i	0.620588	+	0.784136i	$0.286894\pi$
$140$		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	−0.922822	−	0.385227i	$-0.874123\pi$
$149$	−6.56218	+	6.56218i	−0.537595	+	0.537595i	0.385227	+	0.922822i	$0.374123\pi$
$150$	14.6603	−	8.46410i	1.19700	−	0.691091i
$151$			9.39230i			0.764335i	0.924093	+	0.382167i	$0.124822\pi$
$151$			9.39230i			0.764335i	−0.924093	+	0.382167i	$0.875178\pi$
$152$		−	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	$-0.477982\pi$
$157$	−11.6340	−	11.6340i	−0.928492	−	0.928492i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	−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	0.713728	−	0.700423i	$-0.247005\pi$
$163$	0.169873	+	0.169873i	0.0133055	+	0.0133055i	−0.700423	+	0.713728i	$0.747005\pi$
$164$	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	$-0.307920\pi$
$173$	−3.36603	−	3.36603i	−0.255914	−	0.255914i	−0.823390	+	0.567476i	$0.807920\pi$
$174$	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	0.883731	−	0.467995i	$-0.155023\pi$
$179$	5.56218	+	5.56218i	0.415737	+	0.415737i	−0.467995	+	0.883731i	$0.655023\pi$
$180$	−1.26795	−	4.73205i	−0.0945074	−	0.352706i
$181$	7.39230	−	7.39230i	0.549466	−	0.549466i	−0.376821	−	0.926286i	$-0.622983\pi$
$181$	7.39230	−	7.39230i	0.549466	−	0.549466i	0.926286	+	0.376821i	$0.122983\pi$
$182$		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	−0.683195	−	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
$199$			1.92820i			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	0.632187	−	0.774816i	$-0.282157\pi$
$211$	−2.07180	−	2.07180i	−0.142628	−	0.142628i	−0.774816	+	0.632187i	$0.782157\pi$
$212$	−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	$-0.296011\pi$
$223$	17.8564			1.19575			0.597877	+	0.801588i	$0.296011\pi$
$224$		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	0.992171	+	0.124883i	$0.0398557\pi$
$227$	16.8301	+	16.8301i	1.11705	+	1.11705i	0.124883	+	0.992171i	$0.460144\pi$
$228$	8.46410	−	14.6603i	0.560549	−	0.970899i
$229$	−12.7583	+	12.7583i	−0.843094	+	0.843094i	−0.989260	−	0.146166i	$-0.953307\pi$
$229$	−12.7583	+	12.7583i	−0.843094	+	0.843094i	0.146166	+	0.989260i	$0.453307\pi$
$230$	−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	$0.119527\pi$
$233$			11.1962i			0.733484i	−0.930323	+	0.366742i	$0.880473\pi$
$234$	−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	$-0.500736\pi$
$241$	−0.0717968			−0.00462484			−0.00231242	+	0.999997i	$0.500736\pi$
$242$	−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	$-0.957420\pi$
$251$	−13.5885	+	13.5885i	−0.857696	+	0.857696i	0.133370	+	0.991066i	$0.457420\pi$
$252$		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	$-0.513827\pi$
$257$	−1.39230			−0.0868496			−0.0434248	+	0.999057i	$0.513827\pi$
$258$	−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	$-0.713751\pi$
$263$		−	25.3923i		−	1.56576i	0.622175	−	0.782878i	$-0.286249\pi$
$264$	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	$-0.0108991\pi$
$269$	15.8301	+	15.8301i	0.965180	+	0.965180i	−0.0342340	+	0.999414i	$0.510899\pi$
$270$	−5.36603	+	20.0263i	−0.326566	+	1.21876i
$271$	12.1244			0.736502			0.368251	−	0.929726i	$-0.379957\pi$
$271$	12.1244			0.736502			0.368251	+	0.929726i	$0.379957\pi$
$272$	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	−0.233636	−	0.972324i	$-0.575062\pi$
$277$	12.2942	−	12.2942i	0.738689	−	0.738689i	0.972324	+	0.233636i	$0.0750623\pi$
$278$	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	$0.126011\pi$
$281$			12.9282i			0.771232i	−0.922659	+	0.385616i	$0.873989\pi$
$282$	−10.5622	−	18.2942i	−0.628969	−	1.08941i
$283$	12.3660	−	12.3660i	0.735084	−	0.735084i	−0.236538	−	0.971622i	$-0.576013\pi$
$283$	12.3660	−	12.3660i	0.735084	−	0.735084i	0.971622	+	0.236538i	$0.0760129\pi$
$284$	−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	$-0.828752\pi$
$293$	−5.92820	+	5.92820i	−0.346329	+	0.346329i	0.512411	+	0.858740i	$0.328752\pi$
$294$		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	$-0.368319\pi$
$307$	−9.00000	−	9.00000i	−0.513657	−	0.513657i	−0.915645	+	0.401988i	$0.868319\pi$
$308$		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	0.421770	−	0.906703i	$-0.361409\pi$
$317$	−8.63397	−	8.63397i	−0.484932	−	0.484932i	−0.906703	+	0.421770i	$0.861409\pi$
$318$	−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	−0.268777	−	0.963203i	$-0.586619\pi$
$331$	12.6340	−	12.6340i	0.694426	−	0.694426i	0.963203	+	0.268777i	$0.0866193\pi$
$332$	−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	−0.298329	−	0.954463i	$-0.596429\pi$
$347$	12.2224	−	12.2224i	0.656135	−	0.656135i	0.954463	+	0.298329i	$0.0964292\pi$
$348$	−10.1962	+	17.6603i	−0.546571	+	0.946689i
$349$	18.1244	+	18.1244i	0.970175	+	0.970175i	0.999568	−	0.0293934i	$-0.00935756\pi$
$349$	18.1244	+	18.1244i	0.970175	+	0.970175i	−0.0293934	+	0.999568i	$0.509358\pi$
$350$		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	$-0.619560\pi$
$353$	−13.7846			−0.733681			−0.366840	+	0.930284i	$0.619560\pi$
$354$	−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	$0.0207128\pi$
$359$			2.46410i			0.130050i	−0.997884	+	0.0650252i	$0.979287\pi$
$360$			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	$-0.343156\pi$
$367$	18.1244			0.946084			0.473042	+	0.881040i	$0.343156\pi$
$368$	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	−0.765703	−	0.643195i	$-0.777609\pi$
$373$	−2.36603	+	2.36603i	−0.122508	+	0.122508i	0.643195	+	0.765703i	$0.277609\pi$
$374$	−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	−0.278850	+	0.960335i	$0.589953\pi$
$379$	−24.1244	+	24.1244i	−1.23918	+	1.23918i	−0.960335	+	0.278850i	$0.910047\pi$
$380$	−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	$-0.376536\pi$
$383$	14.8038			0.756441			0.378221	+	0.925715i	$0.376536\pi$
$384$	−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	−0.230985	−	0.972957i	$-0.574195\pi$
$389$	14.6340	−	14.6340i	0.741972	−	0.741972i	0.972957	+	0.230985i	$0.0741949\pi$
$390$	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	$-0.207418\pi$
$397$	3.75833	+	3.75833i	0.188625	+	0.188625i	−0.606476	+	0.795102i	$0.707418\pi$
$398$	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	$-0.0221020\pi$
$419$	19.0000	+	19.0000i	0.928211	+	0.928211i	−0.0693796	+	0.997590i	$0.522102\pi$
$420$		0			0
$421$	−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
$423$		−	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	$-0.747297\pi$
$433$	−29.1769			−1.40215			−0.701077	+	0.713086i	$0.747297\pi$
$434$		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	−0.448693	−	0.893686i	$-0.648110\pi$
$443$	9.36603	−	9.36603i	0.444993	−	0.444993i	0.893686	+	0.448693i	$0.148110\pi$
$444$	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	$0.239268\pi$
$457$			29.1962i			1.36574i	−0.730541	+	0.682869i	$0.760732\pi$
$458$	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	$-0.264049\pi$
$461$	−1.33975	−	1.33975i	−0.0623982	−	0.0623982i	−0.737617	+	0.675219i	$0.764049\pi$
$462$		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	$-0.250274\pi$
$467$	−0.0262794	−	0.0262794i	−0.00121607	−	0.00121607i	−0.707715	+	0.706498i	$0.750274\pi$
$468$	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	$-0.384097\pi$
$479$	15.5885			0.712255			0.356127	+	0.934437i	$0.384097\pi$
$480$	−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	$0.168773\pi$
$487$			22.3205i			1.01144i	−0.862698	+	0.505719i	$0.831227\pi$
$488$		−	0.392305i		−	0.0177588i
$489$		−	0.464102i		−	0.0209874i
$490$		0			0
$491$	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	$-0.0927145\pi$
$492$	−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	0.765072	−	0.643945i	$-0.222703\pi$
$499$	2.70577	+	2.70577i	0.121127	+	0.121127i	−0.643945	+	0.765072i	$0.722703\pi$
$500$	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	$-0.373793\pi$
$509$	−12.0981	−	12.0981i	−0.536238	−	0.536238i	−0.922422	+	0.386184i	$0.873793\pi$
$510$	−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	−0.115920	+	0.993259i	$0.536982\pi$
$523$	−25.3660	+	25.3660i	−1.10918	+	1.10918i	−0.993259	+	0.115920i	$0.963018\pi$
$524$	−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	0.281931	−	0.959435i	$-0.409025\pi$
$541$	−15.7583	−	15.7583i	−0.677504	−	0.677504i	−0.959435	+	0.281931i	$0.909025\pi$
$542$	−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	0.951439	−	0.307838i	$-0.0996054\pi$
$547$	15.0526	+	15.0526i	0.643601	+	0.643601i	−0.307838	+	0.951439i	$0.599605\pi$
$548$	−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	0.783579	−	0.621292i	$-0.213392\pi$
$557$	3.83013	+	3.83013i	0.162288	+	0.162288i	−0.621292	+	0.783579i	$0.713392\pi$
$558$	−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	−0.917014	−	0.398854i	$-0.869408\pi$
$563$	−31.2224	−	31.2224i	−1.31587	−	1.31587i	−0.398854	−	0.917014i	$-0.630592\pi$
$564$	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	$-0.782464\pi$
$569$		−	30.1244i		−	1.26288i	0.775425	−	0.631439i	$-0.217536\pi$
$570$	−20.0263	−	34.6865i	−0.838809	−	1.45286i
$571$	−7.43782	+	7.43782i	−0.311263	+	0.311263i	−0.845399	−	0.534136i	$-0.820637\pi$
$571$	−7.43782	+	7.43782i	−0.311263	+	0.311263i	0.534136	+	0.845399i	$0.320637\pi$
$572$	−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	$-0.237786\pi$
$577$	35.2487			1.46742			0.733712	+	0.679461i	$0.237786\pi$
$578$	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	$-0.825699\pi$
$587$	−8.07180	+	8.07180i	−0.333159	+	0.333159i	0.520626	+	0.853785i	$0.325699\pi$
$588$		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	$-0.561772\pi$
$593$	−9.39230			−0.385696			−0.192848	+	0.981229i	$0.561772\pi$
$594$	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	$0.203853\pi$
$599$			29.2487i			1.19507i	−0.801843	+	0.597535i	$0.796147\pi$
$600$	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	$-0.359483\pi$
$607$	21.0526			0.854497			0.427249	+	0.904134i	$0.359483\pi$
$608$	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	−0.949684	−	0.313211i	$-0.898595\pi$
$613$	−15.7583	+	15.7583i	−0.636473	+	0.636473i	0.313211	+	0.949684i	$0.398595\pi$
$614$	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	$0.0480068\pi$
$617$			7.46410i			0.300493i	−0.988649	+	0.150247i	$0.951993\pi$
$618$	1.09808	−	0.633975i	0.0441711	−	0.0255022i
$619$	18.9545	−	18.9545i	0.761845	−	0.761845i	−0.214811	−	0.976656i	$-0.568913\pi$
$619$	18.9545	−	18.9545i	0.761845	−	0.761845i	0.976656	+	0.214811i	$0.0689135\pi$
$620$	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	$-0.895165\pi$
$631$		−	16.2487i		−	0.646851i	0.946254	−	0.323425i	$-0.104835\pi$
$632$	−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	$-0.391213\pi$
$643$	−15.3923	−	15.3923i	−0.607013	−	0.607013i	−0.942164	+	0.335151i	$0.891213\pi$
$644$		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	0.344971	−	0.938614i	$-0.387889\pi$
$653$	−15.1699	−	15.1699i	−0.593643	−	0.593643i	−0.938614	+	0.344971i	$0.887889\pi$
$654$	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	0.513245	−	0.858242i	$-0.328443\pi$
$659$	−8.85641	−	8.85641i	−0.344997	−	0.344997i	−0.858242	+	0.513245i	$0.828443\pi$
$660$	54.7128	−	14.6603i	2.12969	−	0.570650i
$661$	−13.2224	+	13.2224i	−0.514293	+	0.514293i	−0.915839	−	0.401546i	$-0.868473\pi$
$661$	−13.2224	+	13.2224i	−0.514293	+	0.514293i	0.401546	+	0.915839i	$0.368473\pi$
$662$	−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	0.578427	−	0.815734i	$-0.303667\pi$
$677$	36.2750	−	36.2750i	1.39416	−	1.39416i	0.815734	−	0.578427i	$-0.196333\pi$
$678$	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	0.239558	−	0.970882i	$-0.422997\pi$
$683$	31.6340	−	31.6340i	1.21044	−	1.21044i	0.970882	−	0.239558i	$-0.0770027\pi$
$684$	−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	$-0.320530\pi$
$691$	−8.16987	−	8.16987i	−0.310797	−	0.310797i	−0.845218	+	0.534421i	$0.820530\pi$
$692$	−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	0.832791	−	0.553588i	$-0.186742\pi$
$701$	7.39230	+	7.39230i	0.279204	+	0.279204i	−0.553588	+	0.832791i	$0.686742\pi$
$702$	−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	−0.576232	−	0.817287i	$-0.695477\pi$
$709$	6.41858	−	6.41858i	0.241055	−	0.241055i	0.817287	+	0.576232i	$0.195477\pi$
$710$	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	$-0.700488\pi$
$719$	−31.5885			−1.17805			−0.589025	+	0.808115i	$0.700488\pi$
$720$	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	−0.966993	−	0.254801i	$-0.917990\pi$
$733$	−33.0788	−	33.0788i	−1.22179	−	1.22179i	−0.254801	−	0.966993i	$-0.582010\pi$
$734$	−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	−0.880182	−	0.474636i	$-0.842580\pi$
$739$	−36.8301	−	36.8301i	−1.35482	−	1.35482i	−0.474636	−	0.880182i	$-0.657420\pi$
$740$	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	$-0.848830\pi$
$743$		−	24.9282i		−	0.914527i	0.889331	−	0.457264i	$-0.151170\pi$
$744$		−	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	−0.731034	−	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
$759$			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	$-0.395659\pi$
$769$	17.8564			0.643918			0.321959	+	0.946754i	$0.395659\pi$
$770$		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	$-0.840477\pi$
$773$	−11.0263	+	11.0263i	−0.396588	+	0.396588i	0.480440	+	0.877028i	$0.340477\pi$
$774$	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	$-0.342488\pi$
$787$	−11.3660	−	11.3660i	−0.405155	−	0.405155i	−0.880045	+	0.474890i	$0.842488\pi$
$788$	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	0.995932	+	0.0901101i	$0.0287219\pi$
$797$	30.6603	+	30.6603i	1.08604	+	1.08604i	0.0901101	+	0.995932i	$0.471278\pi$
$798$		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	$-0.897632\pi$
$809$		−	17.9808i		−	0.632170i	0.948731	−	0.316085i	$-0.102368\pi$
$810$	43.6865	−	25.2224i	1.53499	−	0.886226i
$811$	10.3205	−	10.3205i	0.362402	−	0.362402i	−0.502295	−	0.864697i	$-0.667511\pi$
$811$	10.3205	−	10.3205i	0.362402	−	0.362402i	0.864697	+	0.502295i	$0.167511\pi$
$812$		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	−0.891481	−	0.453058i	$-0.850333\pi$
$821$	−12.5622	+	12.5622i	−0.438423	+	0.438423i	0.453058	+	0.891481i	$0.350333\pi$
$822$	−32.1506	+	18.5622i	−1.12138	+	0.647430i
$823$		−	31.2487i		−	1.08926i	−0.838676	−	0.544631i	$-0.816670\pi$
$823$		−	31.2487i		−	1.08926i	0.838676	−	0.544631i	$-0.183330\pi$
$824$	−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	0.395383	−	0.918516i	$-0.370612\pi$
$827$	37.7846	−	37.7846i	1.31390	−	1.31390i	0.918516	−	0.395383i	$-0.129388\pi$
$828$	3.12436	+	1.80385i	0.108579	+	0.0626880i
$829$	−24.7583	−	24.7583i	−0.859892	−	0.859892i	0.131433	−	0.991325i	$-0.458042\pi$
$829$	−24.7583	−	24.7583i	−0.859892	−	0.859892i	−0.991325	+	0.131433i	$0.958042\pi$
$830$	−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	0.275603	−	0.961272i	$-0.411123\pi$
$853$	36.1244	−	36.1244i	1.23687	−	1.23687i	0.961272	−	0.275603i	$-0.0888774\pi$
$854$		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	$-0.503053\pi$
$859$	29.0263	−	29.0263i	0.990364	−	0.990364i	0.999954	+	0.00959014i	$0.00305268\pi$
$860$	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	0.963710	−	0.266950i	$-0.0860160\pi$
$877$	20.6340	+	20.6340i	0.696760	+	0.696760i	−0.266950	+	0.963710i	$0.586016\pi$
$878$	−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	$-0.818782\pi$
$881$	−50.0000			−1.68454			−0.842271	+	0.539054i	$0.818782\pi$
$882$		0			0
$883$	−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	$0.787963\pi$
$884$	−0.0910347	−	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	−0.572757	−	0.819725i	$-0.694126\pi$
$907$	7.43782	−	7.43782i	0.246969	−	0.246969i	0.819725	+	0.572757i	$0.194126\pi$
$908$	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	$0.0867533\pi$
$919$			16.3205i			0.538364i	−0.963089	+	0.269182i	$0.913247\pi$
$920$		−	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	$-0.271941\pi$
$929$	40.0333			1.31345			0.656725	+	0.754130i	$0.271941\pi$
$930$	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	$-0.159089\pi$
$941$	12.2224	+	12.2224i	0.398440	+	0.398440i	−0.479243	+	0.877682i	$0.659089\pi$
$942$	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	0.998348	−	0.0574539i	$-0.0182982\pi$
$947$	28.9545	+	28.9545i	0.940894	+	0.940894i	−0.0574539	+	0.998348i	$0.518298\pi$
$948$	−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	$0.124089\pi$
$953$			23.4641i			0.760077i	−0.924971	+	0.380038i	$0.875911\pi$
$954$	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	$-0.939492\pi$
$967$		−	11.7513i		−	0.377896i	0.981987	−	0.188948i	$-0.0605078\pi$
$968$	−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	−0.194797	+	0.980844i	$0.562405\pi$
$971$	−36.6340	+	36.6340i	−1.17564	+	1.17564i	−0.980844	+	0.194797i	$0.937595\pi$
$972$	−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	$-0.720746\pi$
$997$	4.09808	−	4.09808i	0.129787	−	0.129787i	0.769016	+	0.639229i	$0.220746\pi$
$998$	−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.d.589.1		4
7.2	even	3		784.2.x.a.557.1		4
7.3	odd	6		112.2.w.b.93.1	yes	4
7.4	even	3		784.2.x.h.765.1		4
7.5	odd	6		112.2.w.a.109.1	yes	4
7.6	odd	2		784.2.m.e.589.1		4
16.5	even	4	inner	784.2.m.d.197.1		4
28.3	even	6		448.2.ba.a.401.1		4
28.19	even	6		448.2.ba.b.81.1		4
56.3	even	6		896.2.ba.c.289.1		4
56.5	odd	6		896.2.ba.d.417.1		4
56.19	even	6		896.2.ba.a.417.1		4
56.45	odd	6		896.2.ba.b.289.1		4
112.3	even	12		896.2.ba.a.737.1		4
112.5	odd	12		112.2.w.b.53.1	yes	4
112.19	even	12		896.2.ba.c.865.1		4
112.37	even	12		784.2.x.h.165.1		4
112.45	odd	12		896.2.ba.d.737.1		4
112.53	even	12		784.2.x.a.373.1		4
112.59	even	12		448.2.ba.b.177.1		4
112.61	odd	12		896.2.ba.b.865.1		4
112.69	odd	4		784.2.m.e.197.1		4
112.75	even	12		448.2.ba.a.305.1		4
112.101	odd	12		112.2.w.a.37.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.a.37.1	✓	4	112.101	odd	12
112.2.w.a.109.1	yes	4	7.5	odd	6
112.2.w.b.53.1	yes	4	112.5	odd	12
112.2.w.b.93.1	yes	4	7.3	odd	6
448.2.ba.a.305.1		4	112.75	even	12
448.2.ba.a.401.1		4	28.3	even	6
448.2.ba.b.81.1		4	28.19	even	6
448.2.ba.b.177.1		4	112.59	even	12
784.2.m.d.197.1		4	16.5	even	4	inner
784.2.m.d.589.1		4	1.1	even	1	trivial
784.2.m.e.197.1		4	112.69	odd	4
784.2.m.e.589.1		4	7.6	odd	2
784.2.x.a.373.1		4	112.53	even	12
784.2.x.a.557.1		4	7.2	even	3
784.2.x.h.165.1		4	112.37	even	12
784.2.x.h.765.1		4	7.4	even	3
896.2.ba.a.417.1		4	56.19	even	6
896.2.ba.a.737.1		4	112.3	even	12
896.2.ba.b.289.1		4	56.45	odd	6
896.2.ba.b.865.1		4	112.61	odd	12
896.2.ba.c.289.1		4	56.3	even	6
896.2.ba.c.865.1		4	112.19	even	12
896.2.ba.d.417.1		4	56.5	odd	6
896.2.ba.d.737.1		4	112.45	odd	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
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} +(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 6 q^{5} + 2 q^{6} - 8 q^{8} + 6 q^{10} + 2 q^{11} - 4 q^{12} - 8 q^{13} + 12 q^{15} + 8 q^{16} - 12 q^{17} + 8 q^{18} + 2 q^{19} - 12 q^{20} - 18 q^{22} + 8 q^{26} - 2 q^{27} - 8 q^{29}+ \cdots + 16 q^{99}+O(q^{100}) \) 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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