LMFDB - Embedded newform 845.2.o.b.258.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(258,845)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(845, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 7])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.258"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			258.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.258
Dual form			845.2.o.b.357.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.366025 - 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(1.36603 - 0.366025i) q^{6} +(1.73205 + 1.00000i) q^{7} +3.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.23205 + 1.86603i) q^{10} +(-1.36603 - 0.366025i) q^{11} +(-1.00000 - 1.00000i) q^{12} +2.00000i q^{14} +(3.09808 - 0.633975i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.36603 + 0.366025i) q^{17} +1.00000i q^{18} +(1.83013 + 6.83013i) q^{19} +(2.23205 + 0.133975i) q^{20} +(2.00000 - 2.00000i) q^{21} +(-0.366025 - 1.36603i) q^{22} +(-4.09808 - 1.09808i) q^{23} +(1.09808 - 4.09808i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} +(1.73205 - 1.00000i) q^{28} +(2.09808 + 2.36603i) q^{30} +(-5.00000 - 5.00000i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 - 1.00000i) q^{34} +(-0.267949 + 4.46410i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-5.00000 + 5.00000i) q^{38} +(3.00000 + 6.00000i) q^{40} +(2.56218 - 9.56218i) q^{41} +(2.73205 + 0.732051i) q^{42} +(-0.366025 - 1.36603i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(-0.133975 + 2.23205i) q^{45} +(-1.09808 - 4.09808i) q^{46} +6.00000i q^{47} +(1.36603 - 0.366025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-4.96410 - 0.598076i) q^{50} +2.00000i q^{51} +(5.00000 + 5.00000i) q^{53} +(5.46410 + 1.46410i) q^{54} +(-0.633975 - 3.09808i) q^{55} +(5.19615 + 3.00000i) q^{56} +10.0000 q^{57} +(-9.56218 + 2.56218i) q^{59} +(1.00000 - 3.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(1.83013 - 6.83013i) q^{62} +(1.00000 + 1.73205i) q^{63} +7.00000 q^{64} -2.00000 q^{66} +(-2.00000 - 3.46410i) q^{67} +(-0.366025 + 1.36603i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(-4.00000 + 2.00000i) q^{70} +(1.36603 - 0.366025i) q^{71} +(2.59808 + 1.50000i) q^{72} +10.0000 q^{73} +(4.36603 + 5.56218i) q^{75} +(6.83013 + 1.83013i) q^{76} +(-2.00000 - 2.00000i) q^{77} +2.00000i q^{79} +(-1.23205 + 1.86603i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(9.56218 - 2.56218i) q^{82} -6.00000i q^{83} +(-0.732051 - 2.73205i) q^{84} +(-2.09808 - 2.36603i) q^{85} +(1.00000 - 1.00000i) q^{86} +(-4.09808 - 1.09808i) q^{88} +(-1.83013 + 6.83013i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(-3.00000 + 3.00000i) q^{92} +(-8.66025 + 5.00000i) q^{93} +(-5.19615 + 3.00000i) q^{94} +(-11.8301 + 10.4904i) q^{95} +(-5.00000 - 5.00000i) q^{96} +(1.00000 - 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 10 q^{19} + 2 q^{20} + 8 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 10 * q^19 + 2 * q^20 + 8 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 12 * q^25 + 16 * q^27 - 2 * q^30 - 20 * q^31 + 10 * q^32 - 4 * q^33 - 4 * q^34 - 8 * q^35 - 20 * q^38 + 12 * q^40 - 14 * q^41 + 4 * q^42 + 2 * q^43 - 4 * q^44 - 4 * q^45 + 6 * q^46 + 2 * q^48 - 6 * q^49 - 6 * q^50 + 20 * q^53 + 8 * q^54 - 6 * q^55 + 40 * q^57 - 14 * q^59 + 4 * q^60 + 28 * q^61 - 10 * q^62 + 4 * q^63 + 28 * q^64 - 8 * q^66 - 8 * q^67 + 2 * q^68 - 12 * q^69 - 16 * q^70 + 2 * q^71 + 40 * q^73 + 14 * q^75 + 10 * q^76 - 8 * q^77 + 2 * q^80 - 10 * q^81 + 14 * q^82 + 4 * q^84 + 2 * q^85 + 4 * q^86 - 6 * q^88 + 10 * q^89 - 8 * q^90 - 12 * q^92 - 30 * q^95 - 20 * q^96 + 4 * q^97 + 6 * q^98 - 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	0.366025	−	1.36603i	0.211325	−	0.788675i	−0.776103	−	0.630606i	$-0.782806\pi$
$3$	0.366025	−	1.36603i	0.211325	−	0.788675i	0.987428	−	0.158069i	$-0.0505269\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$5$	1.00000	+	2.00000i	0.447214	+	0.894427i
$6$	1.36603	−	0.366025i	0.557678	−	0.149429i
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$	3.00000			1.06066
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−1.23205	+	1.86603i	−0.389609	+	0.590089i
$11$	−1.36603	−	0.366025i	−0.411872	−	0.110361i	0.0469323	−	0.998898i	$-0.485055\pi$
$11$	−1.36603	−	0.366025i	−0.411872	−	0.110361i	−0.458804	+	0.888537i	$0.651722\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$		0			0
$13$		0			0
$14$			2.00000i			0.534522i
$15$	3.09808	−	0.633975i	0.799920	−	0.163692i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.36603	+	0.366025i	−0.331310	+	0.0887742i	−0.420639	−	0.907228i	$-0.638194\pi$
$17$	−1.36603	+	0.366025i	−0.331310	+	0.0887742i	0.0893296	+	0.996002i	$0.471528\pi$
$18$			1.00000i			0.235702i
$19$	1.83013	+	6.83013i	0.419860	+	1.56694i	0.774898	+	0.632087i	$0.217801\pi$
$19$	1.83013	+	6.83013i	0.419860	+	1.56694i	−0.355038	+	0.934852i	$0.615532\pi$
$20$	2.23205	+	0.133975i	0.499102	+	0.0299576i
$21$	2.00000	−	2.00000i	0.436436	−	0.436436i
$22$	−0.366025	−	1.36603i	−0.0780369	−	0.291238i
$23$	−4.09808	−	1.09808i	−0.854508	−	0.228965i	−0.195131	−	0.980777i	$-0.562513\pi$
$23$	−4.09808	−	1.09808i	−0.854508	−	0.228965i	−0.659377	+	0.751812i	$0.729180\pi$
$24$	1.09808	−	4.09808i	0.224144	−	0.836516i
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	2.09808	+	2.36603i	0.383055	+	0.431975i
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	0.0972349	−	0.995261i	$-0.469000\pi$
$31$	−5.00000	−	5.00000i	−0.898027	−	0.898027i	−0.995261	+	0.0972349i	$0.969000\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	−1.00000	−	1.00000i	−0.171499	−	0.171499i
$35$	−0.267949	+	4.46410i	−0.0452917	+	0.754571i
$36$	0.866025	−	0.500000i	0.144338	−	0.0833333i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	−5.00000	+	5.00000i	−0.811107	+	0.811107i
$39$		0			0
$40$	3.00000	+	6.00000i	0.474342	+	0.948683i
$41$	2.56218	−	9.56218i	0.400145	−	1.49336i	−0.412692	−	0.910870i	$-0.635412\pi$
$41$	2.56218	−	9.56218i	0.400145	−	1.49336i	0.812837	−	0.582491i	$-0.197922\pi$
$42$	2.73205	+	0.732051i	0.421565	+	0.112958i
$43$	−0.366025	−	1.36603i	−0.0558184	−	0.208317i	0.932384	−	0.361468i	$-0.117724\pi$
$43$	−0.366025	−	1.36603i	−0.0558184	−	0.208317i	−0.988203	+	0.153151i	$0.951058\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$	−0.133975	+	2.23205i	−0.0199718	+	0.332734i
$46$	−1.09808	−	4.09808i	−0.161903	−	0.604228i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	1.36603	−	0.366025i	0.197169	−	0.0528312i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−4.96410	−	0.598076i	−0.702030	−	0.0845807i
$51$			2.00000i			0.280056i
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$	5.46410	+	1.46410i	0.743570	+	0.199239i
$55$	−0.633975	−	3.09808i	−0.0854851	−	0.417745i
$56$	5.19615	+	3.00000i	0.694365	+	0.400892i
$57$	10.0000			1.32453
$58$		0			0
$59$	−9.56218	+	2.56218i	−1.24489	+	0.333567i	−0.820360	−	0.571847i	$-0.806227\pi$
$59$	−9.56218	+	2.56218i	−1.24489	+	0.333567i	−0.424529	+	0.905414i	$0.639560\pi$
$60$	1.00000	−	3.00000i	0.129099	−	0.387298i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$	1.83013	−	6.83013i	0.232426	−	0.867427i
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$	7.00000			0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	−0.366025	+	1.36603i	−0.0443871	+	0.165655i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	−4.00000	+	2.00000i	−0.478091	+	0.239046i
$71$	1.36603	−	0.366025i	0.162117	−	0.0434392i	−0.176847	−	0.984238i	$-0.556590\pi$
$71$	1.36603	−	0.366025i	0.162117	−	0.0434392i	0.338965	+	0.940799i	$0.389923\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$	4.36603	+	5.56218i	0.504145	+	0.642265i
$76$	6.83013	+	1.83013i	0.783469	+	0.209930i
$77$	−2.00000	−	2.00000i	−0.227921	−	0.227921i
$78$		0			0
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$	−1.23205	+	1.86603i	−0.137747	+	0.208628i
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$	9.56218	−	2.56218i	1.05597	−	0.282945i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	−0.732051	−	2.73205i	−0.0798733	−	0.298091i
$85$	−2.09808	−	2.36603i	−0.227568	−	0.256631i
$86$	1.00000	−	1.00000i	0.107833	−	0.107833i
$87$		0			0
$88$	−4.09808	−	1.09808i	−0.436856	−	0.117055i
$89$	−1.83013	+	6.83013i	−0.193993	+	0.723992i	0.798532	+	0.601952i	$0.205610\pi$
$89$	−1.83013	+	6.83013i	−0.193993	+	0.723992i	−0.992525	+	0.122040i	$0.961056\pi$
$90$	−2.00000	+	1.00000i	−0.210819	+	0.105409i
$91$		0			0
$92$	−3.00000	+	3.00000i	−0.312772	+	0.312772i
$93$	−8.66025	+	5.00000i	−0.898027	+	0.518476i
$94$	−5.19615	+	3.00000i	−0.535942	+	0.309426i
$95$	−11.8301	+	10.4904i	−1.21375	+	1.07629i
$96$	−5.00000	−	5.00000i	−0.510310	−	0.510310i
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$	−10.3923	+	6.00000i	−1.03407	+	0.597022i	−0.918149	−	0.396236i	$-0.870316\pi$
$101$	−10.3923	+	6.00000i	−1.03407	+	0.597022i	−0.115924	+	0.993258i	$0.536983\pi$
$102$	−1.73205	+	1.00000i	−0.171499	+	0.0990148i
$103$	7.00000	−	7.00000i	0.689730	−	0.689730i	−0.272442	−	0.962172i	$-0.587831\pi$
$103$	7.00000	−	7.00000i	0.689730	−	0.689730i	0.962172	+	0.272442i	$0.0878312\pi$
$104$		0			0
$105$	6.00000	+	2.00000i	0.585540	+	0.195180i
$106$	−1.83013	+	6.83013i	−0.177758	+	0.663401i
$107$	−9.56218	−	2.56218i	−0.924411	−	0.247695i	−0.234941	−	0.972010i	$-0.575490\pi$
$107$	−9.56218	−	2.56218i	−0.924411	−	0.247695i	−0.689470	+	0.724315i	$0.742156\pi$
$108$	−1.46410	−	5.46410i	−0.140883	−	0.525783i
$109$	−9.00000	+	9.00000i	−0.862044	+	0.862044i	−0.991575	−	0.129532i	$-0.958653\pi$
$109$	−9.00000	+	9.00000i	−0.862044	+	0.862044i	0.129532	+	0.991575i	$0.458653\pi$
$110$	2.36603	−	2.09808i	0.225592	−	0.200044i
$111$		0			0
$112$			2.00000i			0.188982i
$113$	−6.83013	+	1.83013i	−0.642524	+	0.172164i	−0.565347	−	0.824853i	$-0.691258\pi$
$113$	−6.83013	+	1.83013i	−0.642524	+	0.172164i	−0.0771777	+	0.997017i	$0.524591\pi$
$114$	5.00000	+	8.66025i	0.468293	+	0.811107i
$115$	−1.90192	−	9.29423i	−0.177355	−	0.866691i
$116$		0			0
$117$		0			0
$118$	−7.00000	−	7.00000i	−0.644402	−	0.644402i
$119$	−2.73205	−	0.732051i	−0.250447	−	0.0671070i
$120$	9.29423	−	1.90192i	0.848443	−	0.173621i
$121$	−7.79423	−	4.50000i	−0.708566	−	0.409091i
$122$	14.0000			1.26750
$123$	−12.1244	−	7.00000i	−1.09322	−	0.631169i
$124$	−6.83013	+	1.83013i	−0.613364	+	0.164350i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	3.29423	−	12.2942i	0.292316	−	1.09094i	−0.651010	−	0.759069i	$-0.725655\pi$
$127$	3.29423	−	12.2942i	0.292316	−	1.09094i	0.943326	−	0.331868i	$-0.107679\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$	−2.00000			−0.176090
$130$		0			0
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$	1.00000	+	1.73205i	0.0870388	+	0.150756i
$133$	−3.66025	+	13.6603i	−0.317384	+	1.18449i
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$	12.0000	+	4.00000i	1.03280	+	0.344265i
$136$	−4.09808	+	1.09808i	−0.351407	+	0.0941593i
$137$	13.8564	+	8.00000i	1.18383	+	0.683486i	0.956898	−	0.290424i	$-0.0937963\pi$
$137$	13.8564	+	8.00000i	1.18383	+	0.683486i	0.226935	+	0.973910i	$0.427130\pi$
$138$	−6.00000			−0.510754
$139$	−12.1244	−	7.00000i	−1.02837	−	0.593732i	−0.111856	−	0.993724i	$-0.535679\pi$
$139$	−12.1244	−	7.00000i	−1.02837	−	0.593732i	−0.916519	+	0.399992i	$0.869013\pi$
$140$	3.73205	+	2.46410i	0.315416	+	0.208255i
$141$	8.19615	+	2.19615i	0.690241	+	0.184949i
$142$	1.00000	+	1.00000i	0.0839181	+	0.0839181i
$143$		0			0
$144$			1.00000i			0.0833333i
$145$		0			0
$146$	5.00000	+	8.66025i	0.413803	+	0.716728i
$147$	−4.09808	+	1.09808i	−0.338004	+	0.0905678i
$148$		0			0
$149$	1.09808	+	4.09808i	0.0899579	+	0.335727i	0.996207	−	0.0870170i	$-0.0277334\pi$
$149$	1.09808	+	4.09808i	0.0899579	+	0.335727i	−0.906249	+	0.422744i	$0.861067\pi$
$150$	−2.63397	+	6.56218i	−0.215063	+	0.535800i
$151$	−7.00000	+	7.00000i	−0.569652	+	0.569652i	−0.932031	−	0.362379i	$-0.881965\pi$
$151$	−7.00000	+	7.00000i	−0.569652	+	0.569652i	0.362379	+	0.932031i	$0.381965\pi$
$152$	5.49038	+	20.4904i	0.445329	+	1.66199i
$153$	−1.36603	−	0.366025i	−0.110437	−	0.0295914i
$154$	0.732051	−	2.73205i	0.0589903	−	0.220155i
$155$	5.00000	−	15.0000i	0.401610	−	1.20483i
$156$		0			0
$157$	13.0000	−	13.0000i	1.03751	−	1.03751i	0.0382445	−	0.999268i	$-0.487823\pi$
$157$	13.0000	−	13.0000i	1.03751	−	1.03751i	0.999268	−	0.0382445i	$-0.0121766\pi$
$158$	−1.73205	+	1.00000i	−0.137795	+	0.0795557i
$159$	8.66025	−	5.00000i	0.686803	−	0.396526i
$160$	11.1603	+	0.669873i	0.882296	+	0.0529581i
$161$	−6.00000	−	6.00000i	−0.472866	−	0.472866i
$162$	2.50000	−	4.33013i	0.196419	−	0.340207i
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	−7.00000	−	7.00000i	−0.546608	−	0.546608i
$165$	−4.46410	−	0.267949i	−0.347530	−	0.0208598i
$166$	5.19615	−	3.00000i	0.403300	−	0.232845i
$167$	−15.5885	+	9.00000i	−1.20627	+	0.696441i	−0.961943	−	0.273252i	$-0.911901\pi$
$167$	−15.5885	+	9.00000i	−1.20627	+	0.696441i	−0.244328	+	0.969693i	$0.578568\pi$
$168$	6.00000	−	6.00000i	0.462910	−	0.462910i
$169$		0			0
$170$	1.00000	−	3.00000i	0.0766965	−	0.230089i
$171$	−1.83013	+	6.83013i	−0.139953	+	0.522313i
$172$	−1.36603	−	0.366025i	−0.104158	−	0.0279092i
$173$	−4.02628	−	15.0263i	−0.306112	−	1.14243i	−0.931984	−	0.362500i	$-0.881923\pi$
$173$	−4.02628	−	15.0263i	−0.306112	−	1.14243i	0.625871	−	0.779926i	$-0.284744\pi$
$174$		0			0
$175$	−9.19615	+	3.92820i	−0.695164	+	0.296944i
$176$	−0.366025	−	1.36603i	−0.0275902	−	0.102968i
$177$			14.0000i			1.05230i
$178$	−6.83013	+	1.83013i	−0.511940	+	0.137174i
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	0.949048	+	0.315130i	$0.102048\pi$
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	−0.201613	+	0.979465i	$0.564618\pi$
$180$	1.86603	+	1.23205i	0.139085	+	0.0918316i
$181$			8.00000i			0.594635i	0.954779	+	0.297318i	$0.0960920\pi$
$181$			8.00000i			0.594635i	−0.954779	+	0.297318i	$0.903908\pi$
$182$		0			0
$183$	−14.0000	−	14.0000i	−1.03491	−	1.03491i
$184$	−12.2942	−	3.29423i	−0.906343	−	0.242854i
$185$		0			0
$186$	−8.66025	−	5.00000i	−0.635001	−	0.366618i
$187$	2.00000			0.146254
$188$	5.19615	+	3.00000i	0.378968	+	0.218797i
$189$	10.9282	−	2.92820i	0.794910	−	0.212995i
$190$	−15.0000	−	5.00000i	−1.08821	−	0.362738i
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	2.56218	−	9.56218i	0.184909	−	0.690091i
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	0.366025	−	1.36603i	0.0260123	−	0.0970792i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	−9.00000	+	12.0000i	−0.636396	+	0.848528i
$201$	−5.46410	+	1.46410i	−0.385408	+	0.103270i
$202$	−10.3923	−	6.00000i	−0.731200	−	0.422159i
$203$		0			0
$204$	1.73205	+	1.00000i	0.121268	+	0.0700140i
$205$	21.6865	−	4.43782i	1.51465	−	0.309951i
$206$	9.56218	+	2.56218i	0.666228	+	0.178515i
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$		0			0
$209$		−	10.0000i		−	0.691714i
$210$	1.26795	+	6.19615i	0.0874968	+	0.427575i
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	0.788935	−	0.614477i	$-0.210633\pi$
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	−0.926620	+	0.375999i	$0.877300\pi$
$212$	6.83013	−	1.83013i	0.469095	−	0.125694i
$213$		−	2.00000i		−	0.137038i
$214$	−2.56218	−	9.56218i	−0.175147	−	0.653657i
$215$	2.36603	−	2.09808i	0.161362	−	0.143088i
$216$	12.0000	−	12.0000i	0.816497	−	0.816497i
$217$	−3.66025	−	13.6603i	−0.248474	−	0.927318i
$218$	−12.2942	−	3.29423i	−0.832670	−	0.223113i
$219$	3.66025	−	13.6603i	0.247337	−	0.923074i
$220$	−3.00000	−	1.00000i	−0.202260	−	0.0674200i
$221$		0			0
$222$		0			0
$223$	−1.73205	+	1.00000i	−0.115987	+	0.0669650i	−0.556871	−	0.830599i	$-0.687998\pi$
$223$	−1.73205	+	1.00000i	−0.115987	+	0.0669650i	0.440884	+	0.897564i	$0.354665\pi$
$224$	8.66025	−	5.00000i	0.578638	−	0.334077i
$225$	−4.59808	+	1.96410i	−0.306538	+	0.130940i
$226$	−5.00000	−	5.00000i	−0.332595	−	0.332595i
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$	5.00000	−	8.66025i	0.331133	−	0.573539i
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	0.799248	−	0.601002i	$-0.205232\pi$
$229$	3.00000	+	3.00000i	0.198246	+	0.198246i	−0.601002	+	0.799248i	$0.705232\pi$
$230$	7.09808	−	6.29423i	0.468033	−	0.415029i
$231$	−3.46410	+	2.00000i	−0.227921	+	0.131590i
$232$		0			0
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	−0.673592	−	0.739104i	$-0.735249\pi$
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	0.739104	+	0.673592i	$0.235249\pi$
$234$		0			0
$235$	−12.0000	+	6.00000i	−0.782794	+	0.391397i
$236$	−2.56218	+	9.56218i	−0.166784	+	0.622445i
$237$	2.73205	+	0.732051i	0.177466	+	0.0475518i
$238$	−0.732051	−	2.73205i	−0.0474518	−	0.177093i
$239$	−3.00000	+	3.00000i	−0.194054	+	0.194054i	−0.797445	−	0.603391i	$-0.793816\pi$
$239$	−3.00000	+	3.00000i	−0.194054	+	0.194054i	0.603391	+	0.797445i	$0.293816\pi$
$240$	2.09808	+	2.36603i	0.135430	+	0.152726i
$241$	−6.22243	−	23.2224i	−0.400822	−	1.49589i	−0.811633	−	0.584168i	$-0.801421\pi$
$241$	−6.22243	−	23.2224i	−0.400822	−	1.49589i	0.410811	−	0.911721i	$-0.365246\pi$
$242$		−	9.00000i		−	0.578542i
$243$	9.56218	−	2.56218i	0.613414	−	0.164364i
$244$	−7.00000	−	12.1244i	−0.448129	−	0.776182i
$245$	3.69615	−	5.59808i	0.236139	−	0.357648i
$246$		−	14.0000i		−	0.892607i
$247$		0			0
$248$	−15.0000	−	15.0000i	−0.952501	−	0.952501i
$249$	−8.19615	−	2.19615i	−0.519410	−	0.139176i
$250$	−3.76795	−	10.5263i	−0.238306	−	0.665740i
$251$	1.73205	+	1.00000i	0.109326	+	0.0631194i	0.553666	−	0.832739i	$-0.313228\pi$
$251$	1.73205	+	1.00000i	0.109326	+	0.0631194i	−0.444340	+	0.895858i	$0.646562\pi$
$252$	2.00000			0.125988
$253$	5.19615	+	3.00000i	0.326679	+	0.188608i
$254$	12.2942	−	3.29423i	0.771409	−	0.206698i
$255$	−4.00000	+	2.00000i	−0.250490	+	0.125245i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−4.02628	+	15.0263i	−0.251152	+	0.937314i	0.719038	+	0.694971i	$0.244583\pi$
$257$	−4.02628	+	15.0263i	−0.251152	+	0.937314i	−0.970191	+	0.242343i	$0.922084\pi$
$258$	−1.00000	−	1.73205i	−0.0622573	−	0.107833i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−10.0000	−	17.3205i	−0.617802	−	1.07006i
$263$	0.366025	−	1.36603i	0.0225701	−	0.0842327i	−0.953722	−	0.300689i	$-0.902783\pi$
$263$	0.366025	−	1.36603i	0.0225701	−	0.0842327i	0.976292	+	0.216457i	$0.0694500\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$	−5.00000	+	15.0000i	−0.307148	+	0.921443i
$266$	−13.6603	+	3.66025i	−0.837564	+	0.224425i
$267$	8.66025	+	5.00000i	0.529999	+	0.305995i
$268$	−4.00000			−0.244339
$269$	10.3923	+	6.00000i	0.633630	+	0.365826i	0.782157	−	0.623082i	$-0.214120\pi$
$269$	10.3923	+	6.00000i	0.633630	+	0.365826i	−0.148527	+	0.988908i	$0.547453\pi$
$270$	2.53590	+	12.3923i	0.154330	+	0.754172i
$271$	−12.2942	−	3.29423i	−0.746821	−	0.200110i	−0.134714	−	0.990885i	$-0.543011\pi$
$271$	−12.2942	−	3.29423i	−0.746821	−	0.200110i	−0.612108	+	0.790774i	$0.709678\pi$
$272$	−1.00000	−	1.00000i	−0.0606339	−	0.0606339i
$273$		0			0
$274$			16.0000i			0.966595i
$275$	5.56218	−	4.36603i	0.335412	−	0.263281i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	20.4904	−	5.49038i	1.23115	−	0.329885i	0.416121	−	0.909309i	$-0.363389\pi$
$277$	20.4904	−	5.49038i	1.23115	−	0.329885i	0.815026	+	0.579424i	$0.196722\pi$
$278$		−	14.0000i		−	0.839664i
$279$	−1.83013	−	6.83013i	−0.109567	−	0.408909i
$280$	−0.803848	+	13.3923i	−0.0480391	+	0.800343i
$281$	−1.00000	+	1.00000i	−0.0596550	+	0.0596550i	−0.736305	−	0.676650i	$-0.763431\pi$
$281$	−1.00000	+	1.00000i	−0.0596550	+	0.0596550i	0.676650	+	0.736305i	$0.263431\pi$
$282$	2.19615	+	8.19615i	0.130779	+	0.488074i
$283$	12.2942	+	3.29423i	0.730816	+	0.195822i	0.604993	−	0.796231i	$-0.293176\pi$
$283$	12.2942	+	3.29423i	0.730816	+	0.195822i	0.125823	+	0.992053i	$0.459843\pi$
$284$	0.366025	−	1.36603i	0.0217196	−	0.0810587i
$285$	10.0000	+	20.0000i	0.592349	+	1.18470i
$286$		0			0
$287$	14.0000	−	14.0000i	0.826394	−	0.826394i
$288$	4.33013	−	2.50000i	0.255155	−	0.147314i
$289$	−12.9904	+	7.50000i	−0.764140	+	0.441176i
$290$		0			0
$291$	−2.00000	−	2.00000i	−0.117242	−	0.117242i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$	−3.00000	−	3.00000i	−0.174964	−	0.174964i
$295$	−14.6865	−	16.5622i	−0.855083	−	0.964287i
$296$		0			0
$297$	−6.92820	+	4.00000i	−0.402015	+	0.232104i
$298$	−3.00000	+	3.00000i	−0.173785	+	0.173785i
$299$		0			0
$300$	7.00000	−	1.00000i	0.404145	−	0.0577350i
$301$	0.732051	−	2.73205i	0.0421947	−	0.157473i
$302$	−9.56218	−	2.56218i	−0.550242	−	0.147437i
$303$	4.39230	+	16.3923i	0.252331	+	0.941713i
$304$	−5.00000	+	5.00000i	−0.286770	+	0.286770i
$305$	31.2487	+	1.87564i	1.78930	+	0.107399i
$306$	−0.366025	−	1.36603i	−0.0209243	−	0.0780905i
$307$			18.0000i			1.02731i	0.857996	+	0.513657i	$0.171710\pi$
$307$			18.0000i			1.02731i	−0.857996	+	0.513657i	$0.828290\pi$
$308$	−2.73205	+	0.732051i	−0.155673	+	0.0417125i
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$	15.4904	−	3.16987i	0.879795	−	0.180037i
$311$		−	6.00000i		−	0.340229i	−0.985424	−	0.170114i	$-0.945586\pi$
$311$		−	6.00000i		−	0.340229i	0.985424	−	0.170114i	$-0.0544137\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$	17.7583	+	4.75833i	1.00216	+	0.268528i
$315$	−2.46410	+	3.73205i	−0.138836	+	0.210277i
$316$	1.73205	+	1.00000i	0.0974355	+	0.0562544i
$317$	14.0000			0.786318			0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000			0.786318			0.393159	+	0.919470i	$0.371382\pi$
$318$	8.66025	+	5.00000i	0.485643	+	0.280386i
$319$		0			0
$320$	7.00000	+	14.0000i	0.391312	+	0.782624i
$321$	−7.00000	+	12.1244i	−0.390702	+	0.676716i
$322$	2.19615	−	8.19615i	0.122387	−	0.456754i
$323$	−5.00000	−	8.66025i	−0.278207	−	0.481869i
$324$	−5.00000			−0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$	9.00000	+	15.5885i	0.497701	+	0.862044i
$328$	7.68653	−	28.6865i	0.424418	−	1.58395i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	−2.00000	−	4.00000i	−0.110096	−	0.220193i
$331$	−4.09808	+	1.09808i	−0.225251	+	0.0603557i	−0.369679	−	0.929160i	$-0.620532\pi$
$331$	−4.09808	+	1.09808i	−0.225251	+	0.0603557i	0.144428	+	0.989515i	$0.453866\pi$
$332$	−5.19615	−	3.00000i	−0.285176	−	0.164646i
$333$		0			0
$334$	−15.5885	−	9.00000i	−0.852962	−	0.492458i
$335$	4.92820	−	7.46410i	0.269257	−	0.407807i
$336$	2.73205	+	0.732051i	0.149046	+	0.0399366i
$337$	13.0000	+	13.0000i	0.708155	+	0.708155i	0.966147	−	0.257992i	$-0.0830608\pi$
$337$	13.0000	+	13.0000i	0.708155	+	0.708155i	−0.257992	+	0.966147i	$0.583061\pi$
$338$		0			0
$339$			10.0000i			0.543125i
$340$	−3.09808	+	0.633975i	−0.168017	+	0.0343821i
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$	−6.83013	+	1.83013i	−0.369331	+	0.0989619i
$343$		−	20.0000i		−	1.07990i
$344$	−1.09808	−	4.09808i	−0.0592043	−	0.220953i
$345$	−13.3923	−	0.803848i	−0.721017	−	0.0432777i
$346$	11.0000	−	11.0000i	0.591364	−	0.591364i
$347$	1.09808	+	4.09808i	0.0589478	+	0.219996i	0.989116	−	0.147137i	$-0.0470059\pi$
$347$	1.09808	+	4.09808i	0.0589478	+	0.219996i	−0.930168	+	0.367133i	$0.880339\pi$
$348$		0			0
$349$	−3.29423	+	12.2942i	−0.176336	+	0.658095i	0.819984	+	0.572386i	$0.193982\pi$
$349$	−3.29423	+	12.2942i	−0.176336	+	0.658095i	−0.996320	+	0.0857088i	$0.972685\pi$
$350$	−8.00000	−	6.00000i	−0.427618	−	0.320713i
$351$		0			0
$352$	−5.00000	+	5.00000i	−0.266501	+	0.266501i
$353$	10.3923	−	6.00000i	0.553127	−	0.319348i	−0.197256	−	0.980352i	$-0.563203\pi$
$353$	10.3923	−	6.00000i	0.553127	−	0.319348i	0.750382	+	0.661004i	$0.229870\pi$
$354$	−12.1244	+	7.00000i	−0.644402	+	0.372046i
$355$	2.09808	+	2.36603i	0.111354	+	0.125576i
$356$	5.00000	+	5.00000i	0.264999	+	0.264999i
$357$	−2.00000	+	3.46410i	−0.105851	+	0.183340i
$358$	−10.0000	+	17.3205i	−0.528516	+	0.915417i
$359$	−1.00000	−	1.00000i	−0.0527780	−	0.0527780i	0.680225	−	0.733003i	$-0.261882\pi$
$359$	−1.00000	−	1.00000i	−0.0527780	−	0.0527780i	−0.733003	+	0.680225i	$0.761882\pi$
$360$	−0.401924	+	6.69615i	−0.0211832	+	0.352918i
$361$	−26.8468	+	15.5000i	−1.41299	+	0.815789i
$362$	−6.92820	+	4.00000i	−0.364138	+	0.210235i
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$		0			0
$365$	10.0000	+	20.0000i	0.523424	+	1.04685i
$366$	5.12436	−	19.1244i	0.267854	−	0.999646i
$367$	1.36603	+	0.366025i	0.0713059	+	0.0191064i	0.294296	−	0.955714i	$-0.404915\pi$
$367$	1.36603	+	0.366025i	0.0713059	+	0.0191064i	−0.222990	+	0.974821i	$0.571582\pi$
$368$	−1.09808	−	4.09808i	−0.0572412	−	0.213627i
$369$	7.00000	−	7.00000i	0.364405	−	0.364405i
$370$		0			0
$371$	3.66025	+	13.6603i	0.190031	+	0.709205i
$372$			10.0000i			0.518476i
$373$	20.4904	−	5.49038i	1.06095	−	0.284281i	0.314181	−	0.949363i	$-0.398270\pi$
$373$	20.4904	−	5.49038i	1.06095	−	0.284281i	0.746770	+	0.665082i	$0.231603\pi$
$374$	1.00000	+	1.73205i	0.0517088	+	0.0895622i
$375$	−6.75833	+	14.2942i	−0.348999	+	0.738151i
$376$			18.0000i			0.928279i
$377$		0			0
$378$	8.00000	+	8.00000i	0.411476	+	0.411476i
$379$	−1.36603	−	0.366025i	−0.0701680	−	0.0188015i	0.223564	−	0.974689i	$-0.428231\pi$
$379$	−1.36603	−	0.366025i	−0.0701680	−	0.0188015i	−0.293732	+	0.955888i	$0.594897\pi$
$380$	3.16987	+	15.4904i	0.162611	+	0.794640i
$381$	−15.5885	−	9.00000i	−0.798621	−	0.461084i
$382$	−8.00000			−0.409316
$383$	−25.9808	−	15.0000i	−1.32755	−	0.766464i	−0.342634	−	0.939469i	$-0.611319\pi$
$383$	−25.9808	−	15.0000i	−1.32755	−	0.766464i	−0.984921	+	0.173005i	$0.944652\pi$
$384$	−4.09808	+	1.09808i	−0.209129	+	0.0560360i
$385$	2.00000	−	6.00000i	0.101929	−	0.305788i
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$	0.366025	−	1.36603i	0.0186061	−	0.0694390i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$	−7.32051	+	27.3205i	−0.369271	+	1.37814i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−4.00000	+	2.00000i	−0.201262	+	0.100631i
$396$	−1.36603	+	0.366025i	−0.0686454	+	0.0183935i
$397$	−13.8564	−	8.00000i	−0.695433	−	0.401508i	0.110211	−	0.993908i	$-0.464847\pi$
$397$	−13.8564	−	8.00000i	−0.695433	−	0.401508i	−0.805644	+	0.592400i	$0.798181\pi$
$398$	8.00000			0.401004
$399$	17.3205	+	10.0000i	0.867110	+	0.500626i
$400$	−4.96410	−	0.598076i	−0.248205	−	0.0299038i
$401$	−15.0263	−	4.02628i	−0.750377	−	0.201063i	−0.136691	−	0.990614i	$-0.543647\pi$
$401$	−15.0263	−	4.02628i	−0.750377	−	0.201063i	−0.613685	+	0.789551i	$0.710314\pi$
$402$	−4.00000	−	4.00000i	−0.199502	−	0.199502i
$403$		0			0
$404$			12.0000i			0.597022i
$405$	6.16025	−	9.33013i	0.306105	−	0.463618i
$406$		0			0
$407$		0			0
$408$			6.00000i			0.297044i
$409$	2.56218	+	9.56218i	0.126692	+	0.472819i	0.999894	−	0.0145378i	$-0.00462769\pi$
$409$	2.56218	+	9.56218i	0.126692	+	0.472819i	−0.873203	+	0.487357i	$0.837961\pi$
$410$	14.6865	+	16.5622i	0.725316	+	0.817948i
$411$	16.0000	−	16.0000i	0.789222	−	0.789222i
$412$	−2.56218	−	9.56218i	−0.126229	−	0.471095i
$413$	−19.1244	−	5.12436i	−0.941048	−	0.252153i
$414$	1.09808	−	4.09808i	0.0539675	−	0.201409i
$415$	12.0000	−	6.00000i	0.589057	−	0.294528i
$416$		0			0
$417$	−14.0000	+	14.0000i	−0.685583	+	0.685583i
$418$	8.66025	−	5.00000i	0.423587	−	0.244558i
$419$	32.9090	−	19.0000i	1.60771	−	0.928211i	0.617827	−	0.786314i	$-0.288013\pi$
$419$	32.9090	−	19.0000i	1.60771	−	0.928211i	0.989882	−	0.141896i	$-0.0453200\pi$
$420$	4.73205	−	4.19615i	0.230900	−	0.204751i
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	0.922383	−	0.386276i	$-0.126239\pi$
$421$	11.0000	+	11.0000i	0.536107	+	0.536107i	−0.386276	+	0.922383i	$0.626239\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	15.0000	+	15.0000i	0.728464	+	0.728464i
$425$	2.63397	−	6.56218i	0.127767	−	0.318312i
$426$	1.73205	−	1.00000i	0.0839181	−	0.0484502i
$427$	24.2487	−	14.0000i	1.17348	−	0.677507i
$428$	−7.00000	+	7.00000i	−0.338358	+	0.338358i
$429$		0			0
$430$	3.00000	+	1.00000i	0.144673	+	0.0482243i
$431$	−4.75833	+	17.7583i	−0.229201	+	0.855389i	0.751477	+	0.659759i	$0.229342\pi$
$431$	−4.75833	+	17.7583i	−0.229201	+	0.855389i	−0.980678	+	0.195630i	$0.937325\pi$
$432$	5.46410	+	1.46410i	0.262892	+	0.0704416i
$433$	6.22243	+	23.2224i	0.299031	+	1.11600i	0.937963	+	0.346736i	$0.112710\pi$
$433$	6.22243	+	23.2224i	0.299031	+	1.11600i	−0.638932	+	0.769263i	$0.720623\pi$
$434$	10.0000	−	10.0000i	0.480015	−	0.480015i
$435$		0			0
$436$	3.29423	+	12.2942i	0.157765	+	0.588787i
$437$		−	30.0000i		−	1.43509i
$438$	13.6603	−	3.66025i	0.652712	−	0.174894i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−1.90192	−	9.29423i	−0.0906707	−	0.443085i
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.977678	+	0.210108i	$0.0673814\pi$
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.210108	+	0.977678i	$0.432619\pi$
$444$		0			0
$445$	−15.4904	+	3.16987i	−0.734314	+	0.150266i
$446$	−1.73205	−	1.00000i	−0.0820150	−	0.0473514i
$447$	6.00000			0.283790
$448$	12.1244	+	7.00000i	0.572822	+	0.330719i
$449$	−4.09808	+	1.09808i	−0.193400	+	0.0518214i	−0.354219	−	0.935163i	$-0.615253\pi$
$449$	−4.09808	+	1.09808i	−0.193400	+	0.0518214i	0.160819	+	0.986984i	$0.448587\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	−1.83013	+	6.83013i	−0.0860819	+	0.321262i
$453$	7.00000	+	12.1244i	0.328889	+	0.569652i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	0.888466	−	0.458942i	$-0.151771\pi$
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	−0.841688	+	0.539964i	$0.818438\pi$
$458$	−1.09808	+	4.09808i	−0.0513097	+	0.191491i
$459$	−4.00000	+	6.92820i	−0.186704	+	0.323381i
$460$	−9.00000	−	3.00000i	−0.419627	−	0.139876i
$461$	23.2224	−	6.22243i	1.08158	−	0.289808i	0.326335	−	0.945254i	$-0.394186\pi$
$461$	23.2224	−	6.22243i	1.08158	−	0.289808i	0.755241	+	0.655447i	$0.227520\pi$
$462$	−3.46410	−	2.00000i	−0.161165	−	0.0930484i
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	−18.6603	−	12.3205i	−0.865349	−	0.571350i
$466$	1.36603	+	0.366025i	0.0632799	+	0.0169558i
$467$	9.00000	+	9.00000i	0.416470	+	0.416470i	0.883985	−	0.467515i	$-0.154851\pi$
$467$	9.00000	+	9.00000i	0.416470	+	0.416470i	−0.467515	+	0.883985i	$0.654851\pi$
$468$		0			0
$469$		−	8.00000i		−	0.369406i
$470$	−11.1962	−	7.39230i	−0.516440	−	0.340982i
$471$	−13.0000	−	22.5167i	−0.599008	−	1.03751i
$472$	−28.6865	+	7.68653i	−1.32040	+	0.353801i
$473$			2.00000i			0.0919601i
$474$	0.732051	+	2.73205i	0.0336242	+	0.125487i
$475$	−32.8109	−	13.1699i	−1.50547	−	0.604275i
$476$	−2.00000	+	2.00000i	−0.0916698	+	0.0916698i
$477$	1.83013	+	6.83013i	0.0837958	+	0.312730i
$478$	−4.09808	−	1.09808i	−0.187442	−	0.0502248i
$479$	2.56218	−	9.56218i	0.117069	−	0.436907i	−0.882364	−	0.470567i	$-0.844050\pi$
$479$	2.56218	−	9.56218i	0.117069	−	0.436907i	0.999433	+	0.0336596i	$0.0107162\pi$
$480$	5.00000	−	15.0000i	0.228218	−	0.684653i
$481$		0			0
$482$	17.0000	−	17.0000i	0.774329	−	0.774329i
$483$	−10.3923	+	6.00000i	−0.472866	+	0.273009i
$484$	−7.79423	+	4.50000i	−0.354283	+	0.204545i
$485$	4.46410	+	0.267949i	0.202704	+	0.0121669i
$486$	7.00000	+	7.00000i	0.317526	+	0.317526i
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	21.0000	−	36.3731i	0.950625	−	1.64653i
$489$	−4.00000	−	4.00000i	−0.180886	−	0.180886i
$490$	6.69615	+	0.401924i	0.302501	+	0.0181571i
$491$	19.0526	−	11.0000i	0.859830	−	0.496423i	−0.00412539	−	0.999991i	$-0.501313\pi$
$491$	19.0526	−	11.0000i	0.859830	−	0.496423i	0.863955	+	0.503568i	$0.167980\pi$
$492$	−12.1244	+	7.00000i	−0.546608	+	0.315584i
$493$		0			0
$494$		0			0
$495$	1.00000	−	3.00000i	0.0449467	−	0.134840i
$496$	1.83013	−	6.83013i	0.0821751	−	0.306682i
$497$	2.73205	+	0.732051i	0.122549	+	0.0328370i
$498$	−2.19615	−	8.19615i	−0.0984119	−	0.367278i
$499$	−3.00000	+	3.00000i	−0.134298	+	0.134298i	−0.771060	−	0.636762i	$-0.780273\pi$
$499$	−3.00000	+	3.00000i	−0.134298	+	0.134298i	0.636762	+	0.771060i	$0.280273\pi$
$500$	−7.23205	+	8.52628i	−0.323427	+	0.381307i
$501$	6.58846	+	24.5885i	0.294351	+	1.09853i
$502$			2.00000i			0.0892644i
$503$	4.09808	−	1.09808i	0.182724	−	0.0489608i	−0.166297	−	0.986076i	$-0.553181\pi$
$503$	4.09808	−	1.09808i	0.182724	−	0.0489608i	0.349021	+	0.937115i	$0.386514\pi$
$504$	3.00000	+	5.19615i	0.133631	+	0.231455i
$505$	−22.3923	−	14.7846i	−0.996444	−	0.657906i
$506$			6.00000i			0.266733i
$507$		0			0
$508$	−9.00000	−	9.00000i	−0.399310	−	0.399310i
$509$	17.7583	+	4.75833i	0.787124	+	0.210909i	0.629923	−	0.776657i	$-0.283086\pi$
$509$	17.7583	+	4.75833i	0.787124	+	0.210909i	0.157201	+	0.987567i	$0.449753\pi$
$510$	−3.73205	−	2.46410i	−0.165258	−	0.109112i
$511$	17.3205	+	10.0000i	0.766214	+	0.442374i
$512$	11.0000			0.486136
$513$	34.6410	+	20.0000i	1.52944	+	0.883022i
$514$	−15.0263	+	4.02628i	−0.662781	+	0.177592i
$515$	21.0000	+	7.00000i	0.925371	+	0.308457i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	2.19615	−	8.19615i	0.0965867	−	0.360466i
$518$		0			0
$519$	−22.0000			−0.965693
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	3.29423	−	12.2942i	0.144047	−	0.537589i	−0.855749	−	0.517390i	$-0.826903\pi$
$523$	3.29423	−	12.2942i	0.144047	−	0.537589i	0.999796	−	0.0201986i	$-0.00642985\pi$
$524$	−10.0000	+	17.3205i	−0.436852	+	0.756650i
$525$	2.00000	+	14.0000i	0.0872872	+	0.611010i
$526$	1.36603	−	0.366025i	0.0595615	−	0.0159595i
$527$	8.66025	+	5.00000i	0.377247	+	0.217803i
$528$	−2.00000			−0.0870388
$529$	−4.33013	−	2.50000i	−0.188266	−	0.108696i
$530$	−15.4904	+	3.16987i	−0.672859	+	0.137690i
$531$	−9.56218	−	2.56218i	−0.414963	−	0.111189i
$532$	10.0000	+	10.0000i	0.433555	+	0.433555i
$533$		0			0
$534$			10.0000i			0.432742i
$535$	−4.43782	−	21.6865i	−0.191864	−	0.937591i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	27.3205	−	7.32051i	1.17897	−	0.315903i
$538$			12.0000i			0.517357i
$539$	1.09808	+	4.09808i	0.0472975	+	0.176517i
$540$	9.46410	−	8.39230i	0.407270	−	0.361147i
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$	−3.29423	−	12.2942i	−0.141499	−	0.528082i
$543$	10.9282	+	2.92820i	0.468974	+	0.125661i
$544$	−1.83013	+	6.83013i	−0.0784660	+	0.292839i
$545$	−27.0000	−	9.00000i	−1.15655	−	0.385518i
$546$		0			0
$547$	−9.00000	+	9.00000i	−0.384812	+	0.384812i	−0.872832	−	0.488020i	$-0.837719\pi$
$547$	−9.00000	+	9.00000i	−0.384812	+	0.384812i	0.488020	+	0.872832i	$0.337719\pi$
$548$	13.8564	−	8.00000i	0.591916	−	0.341743i
$549$	12.1244	−	7.00000i	0.517455	−	0.298753i
$550$	6.56218	+	2.63397i	0.279812	+	0.112313i
$551$		0			0
$552$	−9.00000	+	15.5885i	−0.383065	+	0.663489i
$553$	−2.00000	+	3.46410i	−0.0850487	+	0.147309i
$554$	15.0000	+	15.0000i	0.637289	+	0.637289i
$555$		0			0
$556$	−12.1244	+	7.00000i	−0.514187	+	0.296866i
$557$	20.7846	−	12.0000i	0.880672	−	0.508456i	0.00979220	−	0.999952i	$-0.496883\pi$
$557$	20.7846	−	12.0000i	0.880672	−	0.508456i	0.870880	+	0.491496i	$0.163550\pi$
$558$	5.00000	−	5.00000i	0.211667	−	0.211667i
$559$		0			0
$560$	−4.00000	+	2.00000i	−0.169031	+	0.0845154i
$561$	0.732051	−	2.73205i	0.0309072	−	0.115347i
$562$	−1.36603	−	0.366025i	−0.0576223	−	0.0154398i
$563$	5.49038	+	20.4904i	0.231392	+	0.863567i	0.979742	+	0.200263i	$0.0641796\pi$
$563$	5.49038	+	20.4904i	0.231392	+	0.863567i	−0.748350	+	0.663304i	$0.769154\pi$
$564$	6.00000	−	6.00000i	0.252646	−	0.252646i
$565$	−10.4904	−	11.8301i	−0.441334	−	0.497697i
$566$	3.29423	+	12.2942i	0.138467	+	0.516765i
$567$		−	10.0000i		−	0.419961i
$568$	4.09808	−	1.09808i	0.171951	−	0.0460743i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	−12.3205	+	18.6603i	−0.516049	+	0.781592i
$571$			6.00000i			0.251092i	0.992088	+	0.125546i	$0.0400683\pi$
$571$			6.00000i			0.251092i	−0.992088	+	0.125546i	$0.959932\pi$
$572$		0			0
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$	19.1244	+	5.12436i	0.798235	+	0.213886i
$575$	16.6865	−	13.0981i	0.695877	−	0.546228i
$576$	6.06218	+	3.50000i	0.252591	+	0.145833i
$577$	−46.0000			−1.91501			−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−46.0000			−1.91501			−0.957503	+	0.288425i	$0.906868\pi$
$578$	−12.9904	−	7.50000i	−0.540329	−	0.311959i
$579$	24.5885	−	6.58846i	1.02186	−	0.273807i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	0.732051	−	2.73205i	0.0303445	−	0.113247i
$583$	−5.00000	−	8.66025i	−0.207079	−	0.358671i
$584$	30.0000			1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	0.821795	−	0.569783i	$-0.192973\pi$
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	−0.904344	+	0.426804i	$0.859639\pi$
$588$	−1.09808	+	4.09808i	−0.0452839	+	0.169002i
$589$	25.0000	−	43.3013i	1.03011	−	1.78420i
$590$	7.00000	−	21.0000i	0.288185	−	0.864556i
$591$	8.19615	−	2.19615i	0.337145	−	0.0903376i
$592$		0			0
$593$	−10.0000			−0.410651			−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000			−0.410651			−0.205325	+	0.978694i	$0.565825\pi$
$594$	−6.92820	−	4.00000i	−0.284268	−	0.164122i
$595$	−1.26795	−	6.19615i	−0.0519808	−	0.254017i
$596$	4.09808	+	1.09808i	0.167864	+	0.0449790i
$597$	−8.00000	−	8.00000i	−0.327418	−	0.327418i
$598$		0			0
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$	13.0981	+	16.6865i	0.534727	+	0.681225i
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$	2.73205	−	0.732051i	0.111350	−	0.0298362i
$603$		−	4.00000i		−	0.162893i
$604$	2.56218	+	9.56218i	0.104254	+	0.389079i
$605$	1.20577	−	20.0885i	0.0490216	−	0.816712i
$606$	−12.0000	+	12.0000i	−0.487467	+	0.487467i
$607$	−4.75833	−	17.7583i	−0.193135	−	0.720788i	−0.992742	−	0.120265i	$-0.961626\pi$
$607$	−4.75833	−	17.7583i	−0.193135	−	0.720788i	0.799607	−	0.600523i	$-0.205041\pi$
$608$	34.1506	+	9.15064i	1.38499	+	0.371107i
$609$		0			0
$610$	14.0000	+	28.0000i	0.566843	+	1.13369i
$611$		0			0
$612$	−1.00000	+	1.00000i	−0.0404226	+	0.0404226i
$613$	17.3205	−	10.0000i	0.699569	−	0.403896i	−0.107618	−	0.994192i	$-0.534322\pi$
$613$	17.3205	−	10.0000i	0.699569	−	0.403896i	0.807187	+	0.590296i	$0.200989\pi$
$614$	−15.5885	+	9.00000i	−0.629099	+	0.363210i
$615$	1.87564	−	31.2487i	0.0756333	−	1.26007i
$616$	−6.00000	−	6.00000i	−0.241747	−	0.241747i
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	−0.997899	−	0.0647859i	$-0.979364\pi$
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	0.555056	+	0.831813i	$0.312697\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	−25.0000	−	25.0000i	−1.00483	−	1.00483i	−0.999988	−	0.00484658i	$-0.998457\pi$
$619$	−25.0000	−	25.0000i	−1.00483	−	1.00483i	−0.00484658	−	0.999988i	$-0.501543\pi$
$620$	−10.4904	−	11.8301i	−0.421304	−	0.475109i
$621$	−20.7846	+	12.0000i	−0.834058	+	0.481543i
$622$	5.19615	−	3.00000i	0.208347	−	0.120289i
$623$	−10.0000	+	10.0000i	−0.400642	+	0.400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−3.29423	+	12.2942i	−0.131664	+	0.491376i
$627$	−13.6603	−	3.66025i	−0.545538	−	0.146176i
$628$	−4.75833	−	17.7583i	−0.189878	−	0.708635i
$629$		0			0
$630$	−4.46410	−	0.267949i	−0.177854	−	0.0106754i
$631$	−4.02628	−	15.0263i	−0.160284	−	0.598187i	−0.998595	−	0.0529946i	$-0.983123\pi$
$631$	−4.02628	−	15.0263i	−0.160284	−	0.598187i	0.838311	−	0.545192i	$-0.183543\pi$
$632$			6.00000i			0.238667i
$633$	−5.46410	+	1.46410i	−0.217179	+	0.0581928i
$634$	7.00000	+	12.1244i	0.278006	+	0.481520i
$635$	27.8827	−	5.70577i	1.10649	−	0.226427i
$636$		−	10.0000i		−	0.396526i
$637$		0			0
$638$		0			0
$639$	1.36603	+	0.366025i	0.0540391	+	0.0144797i
$640$	3.69615	−	5.59808i	0.146103	−	0.221283i
$641$	−20.7846	−	12.0000i	−0.820943	−	0.473972i	0.0297987	−	0.999556i	$-0.490513\pi$
$641$	−20.7846	−	12.0000i	−0.820943	−	0.473972i	−0.850741	+	0.525584i	$0.823847\pi$
$642$	−14.0000			−0.552536
$643$	−29.4449	−	17.0000i	−1.16119	−	0.670415i	−0.209603	−	0.977787i	$-0.567217\pi$
$643$	−29.4449	−	17.0000i	−1.16119	−	0.670415i	−0.951589	+	0.307372i	$0.900550\pi$
$644$	−8.19615	+	2.19615i	−0.322974	+	0.0865405i
$645$	−2.00000	−	4.00000i	−0.0787499	−	0.157500i
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	0.366025	−	1.36603i	0.0143899	−	0.0537040i	−0.958358	−	0.285571i	$-0.907817\pi$
$647$	0.366025	−	1.36603i	0.0143899	−	0.0537040i	0.972747	+	0.231867i	$0.0744834\pi$
$648$	−7.50000	−	12.9904i	−0.294628	−	0.510310i
$649$	14.0000			0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	4.75833	−	17.7583i	0.186208	−	0.694937i	−0.808161	−	0.588962i	$-0.799537\pi$
$653$	4.75833	−	17.7583i	0.186208	−	0.694937i	0.994369	−	0.105975i	$-0.0337965\pi$
$654$	−9.00000	+	15.5885i	−0.351928	+	0.609557i
$655$	−20.0000	−	40.0000i	−0.781465	−	1.56293i
$656$	9.56218	−	2.56218i	0.373340	−	0.100036i
$657$	8.66025	+	5.00000i	0.337869	+	0.195069i
$658$	−12.0000			−0.467809
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.869709	−	0.493564i	$-0.164306\pi$
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.00741531	+	0.999973i	$0.497640\pi$
$660$	−2.46410	+	3.73205i	−0.0959150	+	0.145270i
$661$	23.2224	+	6.22243i	0.903248	+	0.242025i	0.680411	−	0.732831i	$-0.261801\pi$
$661$	23.2224	+	6.22243i	0.903248	+	0.242025i	0.222837	+	0.974856i	$0.428468\pi$
$662$	−3.00000	−	3.00000i	−0.116598	−	0.116598i
$663$		0			0
$664$		−	18.0000i		−	0.698535i
$665$	−30.9808	+	6.33975i	−1.20138	+	0.245845i
$666$		0			0
$667$		0			0
$668$			18.0000i			0.696441i
$669$	0.732051	+	2.73205i	0.0283027	+	0.105627i
$670$	8.92820	+	0.535898i	0.344927	+	0.0207036i
$671$	−14.0000	+	14.0000i	−0.540464	+	0.540464i
$672$	−3.66025	−	13.6603i	−0.141197	−	0.526956i
$673$	20.4904	+	5.49038i	0.789846	+	0.211639i	0.631121	−	0.775684i	$-0.282595\pi$
$673$	20.4904	+	5.49038i	0.789846	+	0.211639i	0.158725	+	0.987323i	$0.449262\pi$
$674$	−4.75833	+	17.7583i	−0.183284	+	0.684025i
$675$	4.00000	+	28.0000i	0.153960	+	1.07772i
$676$		0			0
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	−0.993935	−	0.109973i	$-0.964924\pi$
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	0.109973	+	0.993935i	$0.464924\pi$
$678$	−8.66025	+	5.00000i	−0.332595	+	0.192024i
$679$	3.46410	−	2.00000i	0.132940	−	0.0767530i
$680$	−6.29423	−	7.09808i	−0.241373	−	0.272199i
$681$	12.0000	+	12.0000i	0.459841	+	0.459841i
$682$	−5.00000	+	8.66025i	−0.191460	+	0.331618i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	5.00000	+	5.00000i	0.191180	+	0.191180i
$685$	−2.14359	+	35.7128i	−0.0819025	+	1.36452i
$686$	17.3205	−	10.0000i	0.661300	−	0.381802i
$687$	5.19615	−	3.00000i	0.198246	−	0.114457i
$688$	1.00000	−	1.00000i	0.0381246	−	0.0381246i
$689$		0			0
$690$	−6.00000	−	12.0000i	−0.228416	−	0.456832i
$691$	1.09808	−	4.09808i	0.0417728	−	0.155898i	−0.941889	−	0.335924i	$-0.890951\pi$
$691$	1.09808	−	4.09808i	0.0417728	−	0.155898i	0.983662	+	0.180026i	$0.0576181\pi$
$692$	−15.0263	−	4.02628i	−0.571213	−	0.153056i
$693$	−0.732051	−	2.73205i	−0.0278083	−	0.103782i
$694$	−3.00000	+	3.00000i	−0.113878	+	0.113878i
$695$	1.87564	−	31.2487i	0.0711472	−	1.18533i
$696$		0			0
$697$			14.0000i			0.530288i
$698$	−12.2942	+	3.29423i	−0.465343	+	0.124688i
$699$	−1.00000	−	1.73205i	−0.0378235	−	0.0655122i
$700$	−1.19615	+	9.92820i	−0.0452103	+	0.375251i
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$		0			0
$703$		0			0
$704$	−9.56218	−	2.56218i	−0.360388	−	0.0965657i
$705$	3.80385	+	18.5885i	0.143261	+	0.700082i
$706$	10.3923	+	6.00000i	0.391120	+	0.225813i
$707$	−24.0000			−0.902613
$708$	12.1244	+	7.00000i	0.455661	+	0.263076i
$709$	39.6147	−	10.6147i	1.48776	−	0.398645i	0.578782	−	0.815482i	$-0.303528\pi$
$709$	39.6147	−	10.6147i	1.48776	−	0.398645i	0.908981	+	0.416838i	$0.136862\pi$
$710$	−1.00000	+	3.00000i	−0.0375293	+	0.112588i
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$	−5.49038	+	20.4904i	−0.205761	+	0.767909i
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	0.366025	−	1.36603i	0.0136599	−	0.0509796i
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	−0.781748	−	0.623595i	$-0.785672\pi$
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	0.930923	+	0.365216i	$0.119005\pi$
$720$	−2.00000	+	1.00000i	−0.0745356	+	0.0372678i
$721$	19.1244	−	5.12436i	0.712228	−	0.190841i
$722$	−26.8468	−	15.5000i	−0.999134	−	0.576850i
$723$	−34.0000			−1.26447
$724$	6.92820	+	4.00000i	0.257485	+	0.148659i
$725$		0			0
$726$	−12.2942	−	3.29423i	−0.456282	−	0.122260i
$727$	−35.0000	−	35.0000i	−1.29808	−	1.29808i	−0.929660	−	0.368418i	$-0.879900\pi$
$727$	−35.0000	−	35.0000i	−1.29808	−	1.29808i	−0.368418	−	0.929660i	$-0.620100\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$	−12.3205	+	18.6603i	−0.456002	+	0.690647i
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$	−19.1244	+	5.12436i	−0.706857	+	0.189402i
$733$			4.00000i			0.147743i	0.997268	+	0.0738717i	$0.0235355\pi$
$733$			4.00000i			0.147743i	−0.997268	+	0.0738717i	$0.976464\pi$
$734$	0.366025	+	1.36603i	0.0135102	+	0.0504209i
$735$	−6.29423	−	7.09808i	−0.232166	−	0.261816i
$736$	−15.0000	+	15.0000i	−0.552907	+	0.552907i
$737$	1.46410	+	5.46410i	0.0539309	+	0.201273i
$738$	9.56218	+	2.56218i	0.351989	+	0.0943151i
$739$	1.09808	−	4.09808i	0.0403934	−	0.150750i	−0.942784	−	0.333405i	$-0.891802\pi$
$739$	1.09808	−	4.09808i	0.0403934	−	0.150750i	0.983177	+	0.182655i	$0.0584691\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	+	10.0000i	−0.367112	+	0.367112i
$743$	−29.4449	+	17.0000i	−1.08023	+	0.623670i	−0.930958	−	0.365127i	$-0.881026\pi$
$743$	−29.4449	+	17.0000i	−1.08023	+	0.623670i	−0.149270	+	0.988797i	$0.547692\pi$
$744$	−25.9808	+	15.0000i	−0.952501	+	0.549927i
$745$	−7.09808	+	6.29423i	−0.260053	+	0.230603i
$746$	15.0000	+	15.0000i	0.549189	+	0.549189i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	1.00000	−	1.73205i	0.0365636	−	0.0633300i
$749$	−14.0000	−	14.0000i	−0.511549	−	0.511549i
$750$	−15.7583	+	1.29423i	−0.575413	+	0.0472585i
$751$	43.3013	−	25.0000i	1.58009	−	0.912263i	0.585240	−	0.810860i	$-0.301000\pi$
$751$	43.3013	−	25.0000i	1.58009	−	0.912263i	0.994845	−	0.101403i	$-0.0323332\pi$
$752$	−5.19615	+	3.00000i	−0.189484	+	0.109399i
$753$	2.00000	−	2.00000i	0.0728841	−	0.0728841i
$754$		0			0
$755$	−21.0000	−	7.00000i	−0.764268	−	0.254756i
$756$	2.92820	−	10.9282i	0.106498	−	0.397455i
$757$	47.8109	+	12.8109i	1.73772	+	0.465620i	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	47.8109	+	12.8109i	1.73772	+	0.465620i	0.755779	+	0.654827i	$0.227258\pi$
$758$	−0.366025	−	1.36603i	−0.0132946	−	0.0496163i
$759$	6.00000	−	6.00000i	0.217786	−	0.217786i
$760$	−35.4904	+	31.4711i	−1.28737	+	1.14158i
$761$	2.56218	+	9.56218i	0.0928789	+	0.346629i	0.996689	−	0.0813044i	$-0.0259086\pi$
$761$	2.56218	+	9.56218i	0.0928789	+	0.346629i	−0.903810	+	0.427933i	$0.859242\pi$
$762$		−	18.0000i		−	0.652071i
$763$	−24.5885	+	6.58846i	−0.890162	+	0.238518i
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$	−0.633975	−	3.09808i	−0.0229214	−	0.112011i
$766$		−	30.0000i		−	1.08394i
$767$		0			0
$768$	−17.0000	−	17.0000i	−0.613435	−	0.613435i
$769$	−20.4904	−	5.49038i	−0.738902	−	0.197988i	−0.130312	−	0.991473i	$-0.541598\pi$
$769$	−20.4904	−	5.49038i	−0.738902	−	0.197988i	−0.608590	+	0.793485i	$0.708265\pi$
$770$	6.19615	−	1.26795i	0.223294	−	0.0456937i
$771$	19.0526	+	11.0000i	0.686161	+	0.396155i
$772$	18.0000			0.647834
$773$	−27.7128	−	16.0000i	−0.996761	−	0.575480i	−0.0894724	−	0.995989i	$-0.528518\pi$
$773$	−27.7128	−	16.0000i	−0.996761	−	0.575480i	−0.907288	+	0.420509i	$0.861851\pi$
$774$	1.36603	−	0.366025i	0.0491008	−	0.0131565i
$775$	35.0000	−	5.00000i	1.25724	−	0.179605i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$		0			0
$778$	−9.00000	−	15.5885i	−0.322666	−	0.558873i
$779$	70.0000			2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	3.00000	+	5.19615i	0.107280	+	0.185814i
$783$		0			0
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	39.0000	+	13.0000i	1.39197	+	0.463990i
$786$	−27.3205	+	7.32051i	−0.974490	+	0.261114i
$787$	19.0526	+	11.0000i	0.679150	+	0.392108i	0.799535	−	0.600620i	$-0.205079\pi$
$787$	19.0526	+	11.0000i	0.679150	+	0.392108i	−0.120384	+	0.992727i	$0.538413\pi$
$788$	6.00000			0.213741
$789$	−1.73205	−	1.00000i	−0.0616626	−	0.0356009i
$790$	−3.73205	−	2.46410i	−0.132780	−	0.0876688i
$791$	−13.6603	−	3.66025i	−0.485703	−	0.130144i
$792$	−3.00000	−	3.00000i	−0.106600	−	0.106600i
$793$		0			0
$794$		−	16.0000i		−	0.567819i
$795$	18.6603	+	12.3205i	0.661811	+	0.436963i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−23.2224	+	6.22243i	−0.822581	+	0.220410i	−0.645474	−	0.763782i	$-0.723340\pi$
$797$	−23.2224	+	6.22243i	−0.822581	+	0.220410i	−0.177106	+	0.984192i	$0.556674\pi$
$798$			20.0000i			0.707992i
$799$	−2.19615	−	8.19615i	−0.0776943	−	0.289959i
$800$	9.82051	+	22.9904i	0.347207	+	0.812833i
$801$	−5.00000	+	5.00000i	−0.176666	+	0.176666i
$802$	−4.02628	−	15.0263i	−0.142173	−	0.530596i
$803$	−13.6603	−	3.66025i	−0.482060	−	0.129168i
$804$	−1.46410	+	5.46410i	−0.0516349	+	0.192704i
$805$	6.00000	−	18.0000i	0.211472	−	0.634417i
$806$		0			0
$807$	12.0000	−	12.0000i	0.422420	−	0.422420i
$808$	−31.1769	+	18.0000i	−1.09680	+	0.633238i
$809$	−24.2487	+	14.0000i	−0.852539	+	0.492214i	−0.861507	−	0.507746i	$-0.830479\pi$
$809$	−24.2487	+	14.0000i	−0.852539	+	0.492214i	0.00896753	+	0.999960i	$0.497146\pi$
$810$	11.1603	+	0.669873i	0.392131	+	0.0235369i
$811$	27.0000	+	27.0000i	0.948098	+	0.948098i	0.998718	−	0.0506198i	$-0.0161197\pi$
$811$	27.0000	+	27.0000i	0.948098	+	0.948098i	−0.0506198	+	0.998718i	$0.516120\pi$
$812$		0			0
$813$	−9.00000	+	15.5885i	−0.315644	+	0.546711i
$814$		0			0
$815$	8.92820	+	0.535898i	0.312741	+	0.0187717i
$816$	−1.73205	+	1.00000i	−0.0606339	+	0.0350070i
$817$	8.66025	−	5.00000i	0.302984	−	0.174928i
$818$	−7.00000	+	7.00000i	−0.244749	+	0.244749i
$819$		0			0
$820$	7.00000	−	21.0000i	0.244451	−	0.733352i
$821$	−3.29423	+	12.2942i	−0.114969	+	0.429072i	−0.999285	−	0.0378188i	$-0.987959\pi$
$821$	−3.29423	+	12.2942i	−0.114969	+	0.429072i	0.884315	+	0.466890i	$0.154626\pi$
$822$	21.8564	+	5.85641i	0.762330	+	0.204266i
$823$	−3.29423	−	12.2942i	−0.114830	−	0.428550i	0.884445	−	0.466645i	$-0.154538\pi$
$823$	−3.29423	−	12.2942i	−0.114830	−	0.428550i	−0.999274	+	0.0380955i	$0.987871\pi$
$824$	21.0000	−	21.0000i	0.731570	−	0.731570i
$825$	−3.92820	−	9.19615i	−0.136762	−	0.320169i
$826$	−5.12436	−	19.1244i	−0.178299	−	0.665421i
$827$		−	46.0000i		−	1.59958i	−0.600282	−	0.799788i	$-0.704945\pi$
$827$		−	46.0000i		−	1.59958i	0.600282	−	0.799788i	$-0.295055\pi$
$828$	−4.09808	+	1.09808i	−0.142418	+	0.0381608i
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$	11.1962	+	7.39230i	0.388624	+	0.256591i
$831$		−	30.0000i		−	1.04069i
$832$		0			0
$833$	3.00000	+	3.00000i	0.103944	+	0.103944i
$834$	−19.1244	−	5.12436i	−0.662222	−	0.177442i
$835$	−33.5885	−	22.1769i	−1.16238	−	0.767464i
$836$	−8.66025	−	5.00000i	−0.299521	−	0.172929i
$837$	−40.0000			−1.38260
$838$	32.9090	+	19.0000i	1.13682	+	0.656344i
$839$	−47.8109	+	12.8109i	−1.65062	+	0.442281i	−0.959785	−	0.280736i	$-0.909421\pi$
$839$	−47.8109	+	12.8109i	−1.65062	+	0.442281i	−0.690830	+	0.723017i	$0.742755\pi$
$840$	18.0000	+	6.00000i	0.621059	+	0.207020i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$	−4.02628	+	15.0263i	−0.138755	+	0.517840i
$843$	1.00000	+	1.73205i	0.0344418	+	0.0596550i
$844$	−4.00000			−0.137686
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−9.00000	−	15.5885i	−0.309244	−	0.535626i
$848$	−1.83013	+	6.83013i	−0.0628468	+	0.234548i
$849$	9.00000	−	15.5885i	0.308879	−	0.534994i
$850$	7.00000	−	1.00000i	0.240098	−	0.0342997i
$851$		0			0
$852$	−1.73205	−	1.00000i	−0.0593391	−	0.0342594i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	24.2487	+	14.0000i	0.829774	+	0.479070i
$855$	−15.4904	+	3.16987i	−0.529760	+	0.108407i
$856$	−28.6865	−	7.68653i	−0.980486	−	0.262720i
$857$	−3.00000	−	3.00000i	−0.102478	−	0.102478i	0.654009	−	0.756487i	$-0.273086\pi$
$857$	−3.00000	−	3.00000i	−0.102478	−	0.102478i	−0.756487	+	0.654009i	$0.773086\pi$
$858$		0			0
$859$			30.0000i			1.02359i	0.859109	+	0.511793i	$0.171019\pi$
$859$			30.0000i			1.02359i	−0.859109	+	0.511793i	$0.828981\pi$
$860$	−0.633975	−	3.09808i	−0.0216184	−	0.105644i
$861$	−14.0000	−	24.2487i	−0.477119	−	0.826394i
$862$	−17.7583	+	4.75833i	−0.604851	+	0.162069i
$863$			30.0000i			1.02121i	0.859815	+	0.510606i	$0.170579\pi$
$863$			30.0000i			1.02121i	−0.859815	+	0.510606i	$0.829421\pi$
$864$	−7.32051	−	27.3205i	−0.249049	−	0.929463i
$865$	26.0263	−	23.0788i	0.884920	−	0.784704i
$866$	−17.0000	+	17.0000i	−0.577684	+	0.577684i
$867$	5.49038	+	20.4904i	0.186463	+	0.695890i
$868$	−13.6603	−	3.66025i	−0.463659	−	0.124237i
$869$	0.732051	−	2.73205i	0.0248331	−	0.0926785i
$870$		0			0
$871$		0			0
$872$	−27.0000	+	27.0000i	−0.914335	+	0.914335i
$873$	1.73205	−	1.00000i	0.0586210	−	0.0338449i
$874$	25.9808	−	15.0000i	0.878812	−	0.507383i
$875$	−17.0526	−	14.4641i	−0.576482	−	0.488976i
$876$	−10.0000	−	10.0000i	−0.337869	−	0.337869i
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$		0			0
$879$	6.00000	+	6.00000i	0.202375	+	0.202375i
$880$	2.36603	−	2.09808i	0.0797587	−	0.0707261i
$881$	45.0333	−	26.0000i	1.51721	−	0.875962i	0.517416	−	0.855734i	$-0.326894\pi$
$881$	45.0333	−	26.0000i	1.51721	−	0.875962i	0.999795	−	0.0202281i	$-0.00643924\pi$
$882$	2.59808	−	1.50000i	0.0874818	−	0.0505076i
$883$	39.0000	−	39.0000i	1.31245	−	1.31245i	0.392853	−	0.919601i	$-0.371488\pi$
$883$	39.0000	−	39.0000i	1.31245	−	1.31245i	0.919601	−	0.392853i	$-0.128512\pi$
$884$		0			0
$885$	−28.0000	+	14.0000i	−0.941210	+	0.470605i
$886$	−9.15064	+	34.1506i	−0.307422	+	1.14731i
$887$	1.36603	+	0.366025i	0.0458666	+	0.0122899i	0.281679	−	0.959509i	$-0.409109\pi$
$887$	1.36603	+	0.366025i	0.0458666	+	0.0122899i	−0.235813	+	0.971799i	$0.575775\pi$
$888$		0			0
$889$	18.0000	−	18.0000i	0.603701	−	0.603701i
$890$	−10.4904	−	11.8301i	−0.351638	−	0.396547i
$891$	1.83013	+	6.83013i	0.0613116	+	0.228818i
$892$			2.00000i			0.0669650i
$893$	−40.9808	+	10.9808i	−1.37137	+	0.367457i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$	−24.6410	+	37.3205i	−0.823658	+	1.24749i
$896$		−	6.00000i		−	0.200446i
$897$		0			0
$898$	−3.00000	−	3.00000i	−0.100111	−	0.100111i
$899$		0			0
$900$	−0.598076	+	4.96410i	−0.0199359	+	0.165470i
$901$	−8.66025	−	5.00000i	−0.288515	−	0.166574i
$902$	−14.0000			−0.466149
$903$	−3.46410	−	2.00000i	−0.115278	−	0.0665558i
$904$	−20.4904	+	5.49038i	−0.681500	+	0.182607i
$905$	−16.0000	+	8.00000i	−0.531858	+	0.265929i
$906$	−7.00000	+	12.1244i	−0.232559	+	0.402805i
$907$	−14.2750	+	53.2750i	−0.473993	+	1.76897i	0.151206	+	0.988502i	$0.451684\pi$
$907$	−14.2750	+	53.2750i	−0.473993	+	1.76897i	−0.625200	+	0.780465i	$0.714982\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	5.00000	+	8.66025i	0.165567	+	0.286770i
$913$	−2.19615	+	8.19615i	−0.0726820	+	0.271253i
$914$	−1.00000	+	1.73205i	−0.0330771	+	0.0572911i
$915$	14.0000	−	42.0000i	0.462826	−	1.38848i
$916$	4.09808	−	1.09808i	0.135404	−	0.0362815i
$917$	−34.6410	−	20.0000i	−1.14395	−	0.660458i
$918$	−8.00000			−0.264039
$919$	−8.66025	−	5.00000i	−0.285675	−	0.164935i	0.350315	−	0.936632i	$-0.386075\pi$
$919$	−8.66025	−	5.00000i	−0.285675	−	0.164935i	−0.635990	+	0.771697i	$0.719408\pi$
$920$	−5.70577	−	27.8827i	−0.188114	−	0.919265i
$921$	24.5885	+	6.58846i	0.810217	+	0.217097i
$922$	17.0000	+	17.0000i	0.559865	+	0.559865i
$923$		0			0
$924$			4.00000i			0.131590i
$925$		0			0
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	9.56218	−	2.56218i	0.314063	−	0.0841530i
$928$		0			0
$929$	6.95448	+	25.9545i	0.228169	+	0.851539i	0.981110	+	0.193451i	$0.0619680\pi$
$929$	6.95448	+	25.9545i	0.228169	+	0.851539i	−0.752941	+	0.658088i	$0.771365\pi$
$930$	1.33975	−	22.3205i	0.0439320	−	0.731918i
$931$	15.0000	−	15.0000i	0.491605	−	0.491605i
$932$	−0.366025	−	1.36603i	−0.0119896	−	0.0447456i
$933$	−8.19615	−	2.19615i	−0.268330	−	0.0718988i
$934$	−3.29423	+	12.2942i	−0.107790	+	0.402279i
$935$	2.00000	+	4.00000i	0.0654070	+	0.130814i
$936$		0			0
$937$	−7.00000	+	7.00000i	−0.228680	+	0.228680i	−0.812141	−	0.583461i	$-0.801698\pi$
$937$	−7.00000	+	7.00000i	−0.228680	+	0.228680i	0.583461	+	0.812141i	$0.301698\pi$
$938$	6.92820	−	4.00000i	0.226214	−	0.130605i
$939$	15.5885	−	9.00000i	0.508710	−	0.293704i
$940$	−0.803848	+	13.3923i	−0.0262186	+	0.436809i
$941$	−21.0000	−	21.0000i	−0.684580	−	0.684580i	0.276448	−	0.961029i	$-0.410843\pi$
$941$	−21.0000	−	21.0000i	−0.684580	−	0.684580i	−0.961029	+	0.276448i	$0.910843\pi$
$942$	13.0000	−	22.5167i	0.423563	−	0.733632i
$943$	−21.0000	+	36.3731i	−0.683854	+	1.18447i
$944$	−7.00000	−	7.00000i	−0.227831	−	0.227831i
$945$	16.7846	+	18.9282i	0.546003	+	0.615734i
$946$	−1.73205	+	1.00000i	−0.0563138	+	0.0325128i
$947$	15.5885	−	9.00000i	0.506557	−	0.292461i	−0.224860	−	0.974391i	$-0.572193\pi$
$947$	15.5885	−	9.00000i	0.506557	−	0.292461i	0.731417	+	0.681930i	$0.238859\pi$
$948$	2.00000	−	2.00000i	0.0649570	−	0.0649570i
$949$		0			0
$950$	−5.00000	−	35.0000i	−0.162221	−	1.13555i
$951$	5.12436	−	19.1244i	0.166169	−	0.620150i
$952$	−8.19615	−	2.19615i	−0.265639	−	0.0711777i
$953$	4.75833	+	17.7583i	0.154137	+	0.575249i	0.999178	+	0.0405460i	$0.0129097\pi$
$953$	4.75833	+	17.7583i	0.154137	+	0.575249i	−0.845040	+	0.534703i	$0.820424\pi$
$954$	−5.00000	+	5.00000i	−0.161881	+	0.161881i
$955$	−17.8564	−	1.07180i	−0.577820	−	0.0346825i
$956$	1.09808	+	4.09808i	0.0355143	+	0.132541i
$957$		0			0
$958$	9.56218	−	2.56218i	0.308940	−	0.0827802i
$959$	16.0000	+	27.7128i	0.516667	+	0.894893i
$960$	21.6865	−	4.43782i	0.699930	−	0.143230i
$961$			19.0000i			0.612903i
$962$		0			0
$963$	−7.00000	−	7.00000i	−0.225572	−	0.225572i
$964$	−23.2224	−	6.22243i	−0.747944	−	0.200411i
$965$	−22.1769	+	33.5885i	−0.713900	+	1.08125i
$966$	−10.3923	−	6.00000i	−0.334367	−	0.193047i
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	−23.3827	−	13.5000i	−0.751548	−	0.433906i
$969$	−13.6603	+	3.66025i	−0.438831	+	0.117584i
$970$	2.00000	+	4.00000i	0.0642161	+	0.128432i
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.247193	−	0.968966i	$-0.420492\pi$
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.715553	−	0.698558i	$-0.246175\pi$
$972$	2.56218	−	9.56218i	0.0821819	−	0.306707i
$973$	−14.0000	−	24.2487i	−0.448819	−	0.777378i
$974$	16.0000			0.512673
$975$		0			0
$976$	14.0000			0.448129
$977$	31.0000	+	53.6936i	0.991778	+	1.71781i	0.606715	+	0.794919i	$0.292487\pi$
$977$	31.0000	+	53.6936i	0.991778	+	1.71781i	0.385063	+	0.922890i	$0.374180\pi$
$978$	1.46410	−	5.46410i	0.0468168	−	0.174723i
$979$	5.00000	−	8.66025i	0.159801	−	0.276783i
$980$	−3.00000	−	6.00000i	−0.0958315	−	0.191663i
$981$	−12.2942	+	3.29423i	−0.392525	+	0.105177i
$982$	19.0526	+	11.0000i	0.607992	+	0.351024i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$	−36.3731	−	21.0000i	−1.15953	−	0.669456i
$985$	−7.39230	+	11.1962i	−0.235538	+	0.356739i
$986$		0			0
$987$	12.0000	+	12.0000i	0.381964	+	0.381964i
$988$		0			0
$989$			6.00000i			0.190789i
$990$	3.09808	−	0.633975i	0.0984633	−	0.0201490i
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$	−34.1506	+	9.15064i	−1.08428	+	0.290533i
$993$			6.00000i			0.190404i
$994$	0.732051	+	2.73205i	0.0232192	+	0.0866554i
$995$	17.8564	+	1.07180i	0.566086	+	0.0339782i
$996$	−6.00000	+	6.00000i	−0.190117	+	0.190117i
$997$	3.29423	+	12.2942i	0.104329	+	0.389362i	0.998268	−	0.0588266i	$-0.0187359\pi$
$997$	3.29423	+	12.2942i	0.104329	+	0.389362i	−0.893939	+	0.448189i	$0.852069\pi$
$998$	−4.09808	−	1.09808i	−0.129722	−	0.0347590i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.b.258.1		4
5.2	odd	4		845.2.t.b.427.1		4
13.2	odd	12		845.2.f.a.408.1		2
13.3	even	3		845.2.k.a.268.1		2
13.4	even	6		845.2.o.a.488.1		4
13.5	odd	4		845.2.t.b.418.1		4
13.6	odd	12		845.2.t.b.188.1		4
13.7	odd	12		845.2.t.a.188.1		4
13.8	odd	4		845.2.t.a.418.1		4
13.9	even	3	inner	845.2.o.b.488.1		4
13.10	even	6		65.2.k.a.8.1	yes	2
13.11	odd	12		65.2.f.a.18.1	✓	2
13.12	even	2		845.2.o.a.258.1		4
39.11	even	12		585.2.n.c.343.1		2
39.23	odd	6		585.2.w.b.73.1		2
52.11	even	12		1040.2.cd.b.993.1		2
52.23	odd	6		1040.2.bg.a.593.1		2
65.2	even	12		845.2.k.a.577.1		2
65.7	even	12		845.2.o.a.357.1		4
65.12	odd	4		845.2.t.a.427.1		4
65.17	odd	12		845.2.t.a.657.1		4
65.22	odd	12		845.2.t.b.657.1		4
65.23	odd	12		325.2.f.a.307.1		2
65.24	odd	12		325.2.f.a.18.1		2
65.32	even	12	inner	845.2.o.b.357.1		4
65.37	even	12		65.2.k.a.57.1	yes	2
65.42	odd	12		845.2.f.a.437.1		2
65.47	even	4		845.2.o.a.587.1		4
65.49	even	6		325.2.k.a.268.1		2
65.57	even	4	inner	845.2.o.b.587.1		4
65.62	odd	12		65.2.f.a.47.1	yes	2
65.63	even	12		325.2.k.a.57.1		2
195.62	even	12		585.2.n.c.307.1		2
195.167	odd	12		585.2.w.b.577.1		2
260.127	even	12		1040.2.cd.b.177.1		2
260.167	odd	12		1040.2.bg.a.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	13.11	odd	12
65.2.f.a.47.1	yes	2	65.62	odd	12
65.2.k.a.8.1	yes	2	13.10	even	6
65.2.k.a.57.1	yes	2	65.37	even	12
325.2.f.a.18.1		2	65.24	odd	12
325.2.f.a.307.1		2	65.23	odd	12
325.2.k.a.57.1		2	65.63	even	12
325.2.k.a.268.1		2	65.49	even	6
585.2.n.c.307.1		2	195.62	even	12
585.2.n.c.343.1		2	39.11	even	12
585.2.w.b.73.1		2	39.23	odd	6
585.2.w.b.577.1		2	195.167	odd	12
845.2.f.a.408.1		2	13.2	odd	12
845.2.f.a.437.1		2	65.42	odd	12
845.2.k.a.268.1		2	13.3	even	3
845.2.k.a.577.1		2	65.2	even	12
845.2.o.a.258.1		4	13.12	even	2
845.2.o.a.357.1		4	65.7	even	12
845.2.o.a.488.1		4	13.4	even	6
845.2.o.a.587.1		4	65.47	even	4
845.2.o.b.258.1		4	1.1	even	1	trivial
845.2.o.b.357.1		4	65.32	even	12	inner
845.2.o.b.488.1		4	13.9	even	3	inner
845.2.o.b.587.1		4	65.57	even	4	inner
845.2.t.a.188.1		4	13.7	odd	12
845.2.t.a.418.1		4	13.8	odd	4
845.2.t.a.427.1		4	65.12	odd	4
845.2.t.a.657.1		4	65.17	odd	12
845.2.t.b.188.1		4	13.6	odd	12
845.2.t.b.418.1		4	13.5	odd	4
845.2.t.b.427.1		4	5.2	odd	4
845.2.t.b.657.1		4	65.22	odd	12
1040.2.bg.a.577.1		2	260.167	odd	12
1040.2.bg.a.593.1		2	52.23	odd	6
1040.2.cd.b.177.1		2	260.127	even	12
1040.2.cd.b.993.1		2	52.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.366025 - 1.36603i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 + 2.00000i) q^{5} +(1.36603 - 0.366025i) q^{6} +(1.73205 + 1.00000i) q^{7} +3.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.23205 + 1.86603i) q^{10} +(-1.36603 - 0.366025i) q^{11} +(-1.00000 - 1.00000i) q^{12} +2.00000i q^{14} +(3.09808 - 0.633975i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-1.36603 + 0.366025i) q^{17} +1.00000i q^{18} +(1.83013 + 6.83013i) q^{19} +(2.23205 + 0.133975i) q^{20} +(2.00000 - 2.00000i) q^{21} +(-0.366025 - 1.36603i) q^{22} +(-4.09808 - 1.09808i) q^{23} +(1.09808 - 4.09808i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} +(1.73205 - 1.00000i) q^{28} +(2.09808 + 2.36603i) q^{30} +(-5.00000 - 5.00000i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 - 1.00000i) q^{34} +(-0.267949 + 4.46410i) q^{35} +(0.866025 - 0.500000i) q^{36} +(-5.00000 + 5.00000i) q^{38} +(3.00000 + 6.00000i) q^{40} +(2.56218 - 9.56218i) q^{41} +(2.73205 + 0.732051i) q^{42} +(-0.366025 - 1.36603i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(-0.133975 + 2.23205i) q^{45} +(-1.09808 - 4.09808i) q^{46} +6.00000i q^{47} +(1.36603 - 0.366025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-4.96410 - 0.598076i) q^{50} +2.00000i q^{51} +(5.00000 + 5.00000i) q^{53} +(5.46410 + 1.46410i) q^{54} +(-0.633975 - 3.09808i) q^{55} +(5.19615 + 3.00000i) q^{56} +10.0000 q^{57} +(-9.56218 + 2.56218i) q^{59} +(1.00000 - 3.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(1.83013 - 6.83013i) q^{62} +(1.00000 + 1.73205i) q^{63} +7.00000 q^{64} -2.00000 q^{66} +(-2.00000 - 3.46410i) q^{67} +(-0.366025 + 1.36603i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(-4.00000 + 2.00000i) q^{70} +(1.36603 - 0.366025i) q^{71} +(2.59808 + 1.50000i) q^{72} +10.0000 q^{73} +(4.36603 + 5.56218i) q^{75} +(6.83013 + 1.83013i) q^{76} +(-2.00000 - 2.00000i) q^{77} +2.00000i q^{79} +(-1.23205 + 1.86603i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(9.56218 - 2.56218i) q^{82} -6.00000i q^{83} +(-0.732051 - 2.73205i) q^{84} +(-2.09808 - 2.36603i) q^{85} +(1.00000 - 1.00000i) q^{86} +(-4.09808 - 1.09808i) q^{88} +(-1.83013 + 6.83013i) q^{89} +(-2.00000 + 1.00000i) q^{90} +(-3.00000 + 3.00000i) q^{92} +(-8.66025 + 5.00000i) q^{93} +(-5.19615 + 3.00000i) q^{94} +(-11.8301 + 10.4904i) q^{95} +(-5.00000 - 5.00000i) q^{96} +(1.00000 - 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 10 q^{19} + 2 q^{20} + 8 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 10 * q^19 + 2 * q^20 + 8 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 12 * q^25 + 16 * q^27 - 2 * q^30 - 20 * q^31 + 10 * q^32 - 4 * q^33 - 4 * q^34 - 8 * q^35 - 20 * q^38 + 12 * q^40 - 14 * q^41 + 4 * q^42 + 2 * q^43 - 4 * q^44 - 4 * q^45 + 6 * q^46 + 2 * q^48 - 6 * q^49 - 6 * q^50 + 20 * q^53 + 8 * q^54 - 6 * q^55 + 40 * q^57 - 14 * q^59 + 4 * q^60 + 28 * q^61 - 10 * q^62 + 4 * q^63 + 28 * q^64 - 8 * q^66 - 8 * q^67 + 2 * q^68 - 12 * q^69 - 16 * q^70 + 2 * q^71 + 40 * q^73 + 14 * q^75 + 10 * q^76 - 8 * q^77 + 2 * q^80 - 10 * q^81 + 14 * q^82 + 4 * q^84 + 2 * q^85 + 4 * q^86 - 6 * q^88 + 10 * q^89 - 8 * q^90 - 12 * q^92 - 30 * q^95 - 20 * q^96 + 4 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more