LMFDB - Embedded newform 845.2.t.a.418.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [845,2,Mod(188,845)] 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, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("845.188"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,0,-2,-2,-8,-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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.418
Dual form			845.2.t.a.657.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	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
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$5$	−2.00000	+	1.00000i	−0.894427	+	0.447214i
$6$	0.366025	+	1.36603i	0.149429	+	0.557678i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$		−	3.00000i		−	1.06066i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	1.23205	−	1.86603i	0.389609	−	0.590089i
$11$	−0.366025	+	1.36603i	−0.110361	+	0.411872i	−0.998898	−	0.0469323i	$-0.985055\pi$
$11$	−0.366025	+	1.36603i	−0.110361	+	0.411872i	0.888537	+	0.458804i	$0.151722\pi$
$12$	1.00000	+	1.00000i	0.288675	+	0.288675i
$13$		0			0
$13$		0			0
$14$			2.00000i			0.534522i
$15$	0.633975	+	3.09808i	0.163692	+	0.799920i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.36603	−	0.366025i	0.331310	−	0.0887742i	−0.0893296	−	0.996002i	$-0.528472\pi$
$17$	1.36603	−	0.366025i	0.331310	−	0.0887742i	0.420639	+	0.907228i	$0.361806\pi$
$18$	−1.00000			−0.235702
$19$	−6.83013	+	1.83013i	−1.56694	+	0.419860i	−0.934852	−	0.355038i	$-0.884468\pi$
$19$	−6.83013	+	1.83013i	−1.56694	+	0.419860i	−0.632087	+	0.774898i	$0.717801\pi$
$20$	0.133975	−	2.23205i	0.0299576	−	0.499102i
$21$	−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	0.659377	−	0.751812i	$-0.270820\pi$
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.195131	+	0.980777i	$0.437487\pi$
$24$	−4.09808	−	1.09808i	−0.836516	−	0.224144i
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$		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	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$	1.73205	+	1.00000i	0.301511	+	0.174078i
$34$	−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		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	5.00000	−	5.00000i	0.811107	−	0.811107i
$39$		0			0
$40$	3.00000	+	6.00000i	0.474342	+	0.948683i
$41$	9.56218	+	2.56218i	1.49336	+	0.400145i	0.910870	−	0.412692i	$-0.135412\pi$
$41$	9.56218	+	2.56218i	1.49336	+	0.400145i	0.582491	+	0.812837i	$0.302078\pi$
$42$	2.73205	+	0.732051i	0.421565	+	0.112958i
$43$	0.366025	+	1.36603i	0.0558184	+	0.208317i	0.988203	−	0.153151i	$-0.0489422\pi$
$43$	0.366025	+	1.36603i	0.0558184	+	0.208317i	−0.932384	+	0.361468i	$0.882276\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$	−2.23205	−	0.133975i	−0.332734	−	0.0199718i
$46$	−4.09808	+	1.09808i	−0.604228	+	0.161903i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	1.36603	−	0.366025i	0.197169	−	0.0528312i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−0.598076	+	4.96410i	−0.0845807	+	0.702030i
$51$		−	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	$0.588586\pi$
$54$	−1.46410	+	5.46410i	−0.199239	+	0.743570i
$55$	−0.633975	−	3.09808i	−0.0854851	−	0.417745i
$56$	−5.19615	−	3.00000i	−0.694365	−	0.400892i
$57$			10.0000i			1.32453i
$58$		0			0
$59$	2.56218	+	9.56218i	0.333567	+	1.24489i	0.905414	+	0.424529i	$0.139560\pi$
$59$	2.56218	+	9.56218i	0.333567	+	1.24489i	−0.571847	+	0.820360i	$0.693773\pi$
$60$	−3.00000	−	1.00000i	−0.387298	−	0.129099i
$61$	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
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	−0.273241	−	0.961946i	$-0.588096\pi$
$67$	3.46410	−	2.00000i	0.423207	−	0.244339i	0.696449	+	0.717607i	$0.254762\pi$
$68$	−0.366025	+	1.36603i	−0.0443871	+	0.165655i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	−2.00000	−	4.00000i	−0.239046	−	0.478091i
$71$	0.366025	+	1.36603i	0.0434392	+	0.162117i	0.984238	−	0.176847i	$-0.0565899\pi$
$71$	0.366025	+	1.36603i	0.0434392	+	0.162117i	−0.940799	+	0.338965i	$0.889923\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$		0			0
$75$	−4.36603	−	5.56218i	−0.504145	−	0.642265i
$76$	1.83013	−	6.83013i	0.209930	−	0.783469i
$77$	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	$0.964111\pi$
$80$	−1.86603	−	1.23205i	−0.208628	−	0.137747i
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$	−9.56218	+	2.56218i	−1.05597	+	0.282945i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	2.73205	−	0.732051i	0.298091	−	0.0798733i
$85$	−2.36603	+	2.09808i	−0.256631	+	0.227568i
$86$	−1.00000	−	1.00000i	−0.107833	−	0.107833i
$87$		0			0
$88$	4.09808	+	1.09808i	0.436856	+	0.117055i
$89$	6.83013	+	1.83013i	0.723992	+	0.193993i	0.601952	−	0.798532i	$-0.294390\pi$
$89$	6.83013	+	1.83013i	0.723992	+	0.193993i	0.122040	+	0.992525i	$0.461056\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$		0			0
$92$	−3.00000	+	3.00000i	−0.312772	+	0.312772i
$93$	−5.00000	−	8.66025i	−0.518476	−	0.898027i
$94$	−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
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	0.585348	−	0.810782i	$-0.300958\pi$
$97$	1.73205	+	1.00000i	0.175863	+	0.101535i	−0.409484	+	0.912317i	$0.634291\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$	−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	0.115924	−	0.993258i	$-0.463017\pi$
$101$	10.3923	−	6.00000i	1.03407	−	0.597022i	0.918149	+	0.396236i	$0.129684\pi$
$102$	1.00000	+	1.73205i	0.0990148	+	0.171499i
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	−0.962172	−	0.272442i	$-0.912169\pi$
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	0.272442	+	0.962172i	$0.412169\pi$
$104$		0			0
$105$	6.00000	+	2.00000i	0.585540	+	0.195180i
$106$	−6.83013	−	1.83013i	−0.663401	−	0.177758i
$107$	−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	0.129532	−	0.991575i	$-0.458653\pi$
$109$	−9.00000	−	9.00000i	−0.862044	−	0.862044i	−0.991575	+	0.129532i	$0.958653\pi$
$110$	2.09808	+	2.36603i	0.200044	+	0.225592i
$111$		0			0
$112$	2.00000			0.188982
$113$	−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
$115$	−9.29423	+	1.90192i	−0.866691	+	0.177355i
$116$		0			0
$117$		0			0
$118$	−7.00000	−	7.00000i	−0.644402	−	0.644402i
$119$	0.732051	−	2.73205i	0.0671070	−	0.250447i
$120$	9.29423	−	1.90192i	0.848443	−	0.173621i
$121$	7.79423	+	4.50000i	0.708566	+	0.409091i
$122$			14.0000i			1.26750i
$123$	7.00000	−	12.1244i	0.631169	−	1.09322i
$124$	1.83013	+	6.83013i	0.164350	+	0.613364i
$125$	−2.00000	+	11.0000i	−0.178885	+	0.983870i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−3.29423	+	12.2942i	−0.292316	+	1.09094i	0.651010	+	0.759069i	$0.274345\pi$
$127$	−3.29423	+	12.2942i	−0.292316	+	1.09094i	−0.943326	+	0.331868i	$0.892321\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	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	$0.838289\pi$
$132$	−1.73205	+	1.00000i	−0.150756	+	0.0870388i
$133$	−3.66025	+	13.6603i	−0.317384	+	1.18449i
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$	−4.00000	+	12.0000i	−0.344265	+	1.03280i
$136$	−1.09808	−	4.09808i	−0.0941593	−	0.351407i
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	−0.290424	−	0.956898i	$-0.593796\pi$
$137$	8.00000	−	13.8564i	0.683486	−	1.18383i	0.973910	−	0.226935i	$-0.0728704\pi$
$138$			6.00000i			0.510754i
$139$	−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
$141$	2.19615	−	8.19615i	0.184949	−	0.690241i
$142$	−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
$149$	−4.09808	+	1.09808i	−0.335727	+	0.0899579i	−0.422744	−	0.906249i	$-0.638933\pi$
$149$	−4.09808	+	1.09808i	−0.335727	+	0.0899579i	0.0870170	+	0.996207i	$0.472267\pi$
$150$	6.56218	+	2.63397i	0.535800	+	0.215063i
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	0.932031	−	0.362379i	$-0.118035\pi$
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	−0.362379	+	0.932031i	$0.618035\pi$
$152$	5.49038	+	20.4904i	0.445329	+	1.66199i
$153$	1.36603	+	0.366025i	0.110437	+	0.0295914i
$154$	−2.73205	−	0.732051i	−0.220155	−	0.0589903i
$155$	−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	$-0.0121766\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	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
$162$	4.33013	+	2.50000i	0.340207	+	0.196419i
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	0.358162	−	0.933659i	$-0.383403\pi$
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	−0.629492	+	0.777007i	$0.716737\pi$
$164$	−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
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	0.969693	+	0.244328i	$0.0785675\pi$
$167$	9.00000	+	15.5885i	0.696441	+	1.20627i	−0.273252	+	0.961943i	$0.588099\pi$
$168$	−6.00000	+	6.00000i	−0.462910	+	0.462910i
$169$		0			0
$170$	1.00000	−	3.00000i	0.0766965	−	0.230089i
$171$	−6.83013	−	1.83013i	−0.522313	−	0.139953i
$172$	−1.36603	−	0.366025i	−0.104158	−	0.0279092i
$173$	4.02628	+	15.0263i	0.306112	+	1.14243i	0.931984	+	0.362500i	$0.118077\pi$
$173$	4.02628	+	15.0263i	0.306112	+	1.14243i	−0.625871	+	0.779926i	$0.715256\pi$
$174$		0			0
$175$	−3.92820	−	9.19615i	−0.296944	−	0.695164i
$176$	−1.36603	+	0.366025i	−0.102968	+	0.0275902i
$177$	14.0000			1.05230
$178$	−6.83013	+	1.83013i	−0.511940	+	0.137174i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	1.23205	−	1.86603i	0.0918316	−	0.139085i
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$		0			0
$183$	−14.0000	−	14.0000i	−1.03491	−	1.03491i
$184$	3.29423	−	12.2942i	0.242854	−	0.906343i
$185$		0			0
$186$	8.66025	+	5.00000i	0.635001	+	0.366618i
$187$			2.00000i			0.146254i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	−2.92820	−	10.9282i	−0.212995	−	0.794910i
$190$	−5.00000	+	15.0000i	−0.362738	+	1.08821i
$191$	−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
$193$	15.5885	−	9.00000i	1.12208	−	0.647834i	0.180150	−	0.983639i	$-0.442342\pi$
$193$	15.5885	−	9.00000i	1.12208	−	0.647834i	0.941932	+	0.335805i	$0.109008\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	0.366025	−	1.36603i	0.0260123	−	0.0970792i
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	−12.0000	−	9.00000i	−0.848528	−	0.636396i
$201$	−1.46410	−	5.46410i	−0.103270	−	0.385408i
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$		0			0
$204$	1.73205	+	1.00000i	0.121268	+	0.0700140i
$205$	−21.6865	+	4.43782i	−1.51465	+	0.309951i
$206$	2.56218	−	9.56218i	0.178515	−	0.666228i
$207$	3.00000	+	3.00000i	0.208514	+	0.208514i
$208$		0			0
$209$		−	10.0000i		−	0.691714i
$210$	−6.19615	+	1.26795i	−0.427575	+	0.0874968i
$211$	−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
$213$	2.00000			0.137038
$214$	9.56218	−	2.56218i	0.653657	−	0.175147i
$215$	−2.09808	−	2.36603i	−0.143088	−	0.161362i
$216$	−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
$219$	−13.6603	−	3.66025i	−0.923074	−	0.247337i
$220$	3.00000	+	1.00000i	0.202260	+	0.0674200i
$221$		0			0
$222$		0			0
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$	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
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	0.113761	−	0.993508i	$-0.463710\pi$
$227$	−10.3923	−	6.00000i	−0.689761	−	0.398234i	−0.803523	+	0.595274i	$0.797043\pi$
$228$	−8.66025	−	5.00000i	−0.573539	−	0.331133i
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	−0.601002	−	0.799248i	$-0.705232\pi$
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	0.799248	+	0.601002i	$0.205232\pi$
$230$	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	−0.739104	−	0.673592i	$-0.764751\pi$
$233$	−1.00000	+	1.00000i	−0.0655122	+	0.0655122i	0.673592	+	0.739104i	$0.264751\pi$
$234$		0			0
$235$	−12.0000	+	6.00000i	−0.782794	+	0.391397i
$236$	−9.56218	−	2.56218i	−0.622445	−	0.166784i
$237$	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	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$	−2.36603	+	2.09808i	−0.152726	+	0.135430i
$241$	−23.2224	+	6.22243i	−1.49589	+	0.400822i	−0.911721	−	0.410811i	$-0.865246\pi$
$241$	−23.2224	+	6.22243i	−1.49589	+	0.400822i	−0.584168	+	0.811633i	$0.698579\pi$
$242$	−9.00000			−0.578542
$243$	9.56218	−	2.56218i	0.613414	−	0.164364i
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$	−5.59808	−	3.69615i	−0.357648	−	0.236139i
$246$			14.0000i			0.892607i
$247$		0			0
$248$	−15.0000	−	15.0000i	−0.952501	−	0.952501i
$249$	2.19615	−	8.19615i	0.139176	−	0.519410i
$250$	−3.76795	−	10.5263i	−0.238306	−	0.665740i
$251$	−1.73205	−	1.00000i	−0.109326	−	0.0631194i	0.444340	−	0.895858i	$-0.353438\pi$
$251$	−1.73205	−	1.00000i	−0.109326	−	0.0631194i	−0.553666	+	0.832739i	$0.686772\pi$
$252$			2.00000i			0.125988i
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−3.29423	−	12.2942i	−0.206698	−	0.771409i
$255$	2.00000	+	4.00000i	0.125245	+	0.250490i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	4.02628	−	15.0263i	0.251152	−	0.937314i	−0.719038	−	0.694971i	$-0.755417\pi$
$257$	4.02628	−	15.0263i	0.251152	−	0.937314i	0.970191	−	0.242343i	$-0.0779159\pi$
$258$	−1.73205	+	1.00000i	−0.107833	+	0.0622573i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	17.3205	−	10.0000i	1.07006	−	0.617802i
$263$	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
$265$	−15.0000	−	5.00000i	−0.921443	−	0.307148i
$266$	−3.66025	−	13.6603i	−0.224425	−	0.837564i
$267$	5.00000	−	8.66025i	0.305995	−	0.529999i
$268$			4.00000i			0.244339i
$269$	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
$271$	−3.29423	+	12.2942i	−0.200110	+	0.746821i	0.790774	+	0.612108i	$0.209678\pi$
$271$	−3.29423	+	12.2942i	−0.200110	+	0.746821i	−0.990885	+	0.134714i	$0.956989\pi$
$272$	1.00000	+	1.00000i	0.0606339	+	0.0606339i
$273$		0			0
$274$			16.0000i			0.966595i
$275$	4.36603	+	5.56218i	0.263281	+	0.335412i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−20.4904	+	5.49038i	−1.23115	+	0.329885i	−0.815026	−	0.579424i	$-0.803278\pi$
$277$	−20.4904	+	5.49038i	−1.23115	+	0.329885i	−0.416121	+	0.909309i	$0.636611\pi$
$278$	14.0000			0.839664
$279$	6.83013	−	1.83013i	0.408909	−	0.109567i
$280$	13.3923	+	0.803848i	0.800343	+	0.0480391i
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	0.736305	−	0.676650i	$-0.236569\pi$
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	−0.676650	+	0.736305i	$0.736569\pi$
$282$	2.19615	+	8.19615i	0.130779	+	0.488074i
$283$	−12.2942	−	3.29423i	−0.730816	−	0.195822i	−0.125823	−	0.992053i	$-0.540157\pi$
$283$	−12.2942	−	3.29423i	−0.730816	−	0.195822i	−0.604993	+	0.796231i	$0.706824\pi$
$284$	−1.36603	−	0.366025i	−0.0810587	−	0.0217196i
$285$	−10.0000	−	20.0000i	−0.592349	−	1.18470i
$286$		0			0
$287$	14.0000	−	14.0000i	0.826394	−	0.826394i
$288$	2.50000	+	4.33013i	0.147314	+	0.255155i
$289$	−12.9904	+	7.50000i	−0.764140	+	0.441176i
$290$		0			0
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$	8.66025	+	5.00000i	0.506803	+	0.292603i
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	0.644042	−	0.764990i	$-0.277256\pi$
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	−0.340480	+	0.940252i	$0.610589\pi$
$294$	−3.00000	+	3.00000i	−0.174964	+	0.174964i
$295$	−14.6865	−	16.5622i	−0.855083	−	0.964287i
$296$		0			0
$297$	4.00000	+	6.92820i	0.232104	+	0.402015i
$298$	3.00000	−	3.00000i	0.173785	−	0.173785i
$299$		0			0
$300$	7.00000	−	1.00000i	0.404145	−	0.0577350i
$301$	2.73205	+	0.732051i	0.157473	+	0.0421947i
$302$	−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
$305$	−1.87564	+	31.2487i	−0.107399	+	1.78930i
$306$	−1.36603	+	0.366025i	−0.0780905	+	0.0209243i
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$	−2.73205	+	0.732051i	−0.155673	+	0.0417125i
$309$	7.00000	+	12.1244i	0.398216	+	0.689730i
$310$	−3.16987	−	15.4904i	−0.180037	−	0.879795i
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		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	$0.632875\pi$
$314$	−4.75833	+	17.7583i	−0.268528	+	1.00216i
$315$	−2.46410	+	3.73205i	−0.138836	+	0.210277i
$316$	−1.73205	−	1.00000i	−0.0974355	−	0.0562544i
$317$			14.0000i			0.786318i	0.919470	+	0.393159i	$0.128618\pi$
$317$			14.0000i			0.786318i	−0.919470	+	0.393159i	$0.871382\pi$
$318$	−5.00000	+	8.66025i	−0.280386	+	0.485643i
$319$		0			0
$320$	14.0000	−	7.00000i	0.782624	−	0.391312i
$321$	−7.00000	+	12.1244i	−0.390702	+	0.676716i
$322$	−2.19615	+	8.19615i	−0.122387	+	0.456754i
$323$	−8.66025	+	5.00000i	−0.481869	+	0.278207i
$324$	5.00000			0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$	−15.5885	+	9.00000i	−0.862044	+	0.497701i
$328$	7.68653	−	28.6865i	0.424418	−	1.58395i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	4.00000	−	2.00000i	0.220193	−	0.110096i
$331$	−1.09808	−	4.09808i	−0.0603557	−	0.225251i	0.929160	−	0.369679i	$-0.120532\pi$
$331$	−1.09808	−	4.09808i	−0.0603557	−	0.225251i	−0.989515	+	0.144428i	$0.953866\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$		0			0
$334$	−15.5885	−	9.00000i	−0.852962	−	0.492458i
$335$	−4.92820	+	7.46410i	−0.269257	+	0.407807i
$336$	0.732051	−	2.73205i	0.0399366	−	0.149046i
$337$	−13.0000	−	13.0000i	−0.708155	−	0.708155i	0.257992	−	0.966147i	$-0.416939\pi$
$337$	−13.0000	−	13.0000i	−0.708155	−	0.708155i	−0.966147	+	0.257992i	$0.916939\pi$
$338$		0			0
$339$			10.0000i			0.543125i
$340$	−0.633975	−	3.09808i	−0.0343821	−	0.168017i
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$	6.83013	−	1.83013i	0.369331	−	0.0989619i
$343$	20.0000			1.07990
$344$	4.09808	−	1.09808i	0.220953	−	0.0592043i
$345$	−0.803848	+	13.3923i	−0.0432777	+	0.721017i
$346$	−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
$349$	12.2942	+	3.29423i	0.658095	+	0.176336i	0.572386	−	0.819984i	$-0.306018\pi$
$349$	12.2942	+	3.29423i	0.658095	+	0.176336i	0.0857088	+	0.996320i	$0.472685\pi$
$350$	8.00000	+	6.00000i	0.427618	+	0.320713i
$351$		0			0
$352$	−5.00000	+	5.00000i	−0.266501	+	0.266501i
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	0.980352	−	0.197256i	$-0.0632029\pi$
$353$	6.00000	+	10.3923i	0.319348	+	0.553127i	−0.661004	+	0.750382i	$0.729870\pi$
$354$	−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
$357$	−3.46410	−	2.00000i	−0.183340	−	0.105851i
$358$	17.3205	+	10.0000i	0.915417	+	0.528516i
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	−0.733003	−	0.680225i	$-0.761882\pi$
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	0.680225	+	0.733003i	$0.261882\pi$
$360$	−0.401924	+	6.69615i	−0.0211832	+	0.352918i
$361$	26.8468	−	15.5000i	1.41299	−	0.815789i
$362$	4.00000	+	6.92820i	0.210235	+	0.364138i
$363$	9.00000	−	9.00000i	0.472377	−	0.472377i
$364$		0			0
$365$	10.0000	+	20.0000i	0.523424	+	1.04685i
$366$	19.1244	+	5.12436i	0.999646	+	0.267854i
$367$	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
$371$	13.6603	−	3.66025i	0.709205	−	0.190031i
$372$	10.0000			0.518476
$373$	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
$375$	14.2942	+	6.75833i	0.738151	+	0.348999i
$376$		−	18.0000i		−	0.928279i
$377$		0			0
$378$	8.00000	+	8.00000i	0.411476	+	0.411476i
$379$	0.366025	−	1.36603i	0.0188015	−	0.0701680i	−0.955888	−	0.293732i	$-0.905103\pi$
$379$	0.366025	−	1.36603i	0.0188015	−	0.0701680i	0.974689	+	0.223564i	$0.0717693\pi$
$380$	3.16987	+	15.4904i	0.162611	+	0.794640i
$381$	15.5885	+	9.00000i	0.798621	+	0.461084i
$382$		−	8.00000i		−	0.409316i
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	−0.173005	−	0.984921i	$-0.555348\pi$
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	0.939469	−	0.342634i	$-0.111319\pi$
$384$	1.09808	+	4.09808i	0.0560360	+	0.209129i
$385$	−6.00000	−	2.00000i	−0.305788	−	0.101929i
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$	−0.366025	+	1.36603i	−0.0186061	+	0.0694390i
$388$	−1.73205	+	1.00000i	−0.0879316	+	0.0507673i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	7.79423	−	4.50000i	0.393668	−	0.227284i
$393$	−7.32051	+	27.3205i	−0.369271	+	1.37814i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−2.00000	−	4.00000i	−0.100631	−	0.201262i
$396$	−0.366025	−	1.36603i	−0.0183935	−	0.0686454i
$397$	−8.00000	+	13.8564i	−0.401508	+	0.695433i	−0.993908	−	0.110211i	$-0.964847\pi$
$397$	−8.00000	+	13.8564i	−0.401508	+	0.695433i	0.592400	+	0.805644i	$0.298181\pi$
$398$		−	8.00000i		−	0.401004i
$399$	17.3205	+	10.0000i	0.867110	+	0.500626i
$400$	4.96410	+	0.598076i	0.248205	+	0.0299038i
$401$	−4.02628	+	15.0263i	−0.201063	+	0.750377i	0.789551	+	0.613685i	$0.210314\pi$
$401$	−4.02628	+	15.0263i	−0.201063	+	0.750377i	−0.990614	+	0.136691i	$0.956353\pi$
$402$	4.00000	+	4.00000i	0.199502	+	0.199502i
$403$		0			0
$404$			12.0000i			0.597022i
$405$	9.33013	+	6.16025i	0.463618	+	0.306105i
$406$		0			0
$407$		0			0
$408$	−6.00000			−0.297044
$409$	−9.56218	+	2.56218i	−0.472819	+	0.126692i	−0.487357	−	0.873203i	$-0.662039\pi$
$409$	−9.56218	+	2.56218i	−0.472819	+	0.126692i	0.0145378	+	0.999894i	$0.495372\pi$
$410$	16.5622	−	14.6865i	0.817948	−	0.725316i
$411$	−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
$414$	−4.09808	−	1.09808i	−0.201409	−	0.0539675i
$415$	−12.0000	+	6.00000i	−0.589057	+	0.294528i
$416$		0			0
$417$	−14.0000	+	14.0000i	−0.685583	+	0.685583i
$418$	5.00000	+	8.66025i	0.244558	+	0.423587i
$419$	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	$-0.873761\pi$
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	0.386276	+	0.922383i	$0.373761\pi$
$422$	3.46410	+	2.00000i	0.168630	+	0.0973585i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$	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
$427$	−14.0000	−	24.2487i	−0.677507	−	1.17348i
$428$	7.00000	−	7.00000i	0.338358	−	0.338358i
$429$		0			0
$430$	3.00000	+	1.00000i	0.144673	+	0.0482243i
$431$	−17.7583	−	4.75833i	−0.855389	−	0.229201i	−0.195630	−	0.980678i	$-0.562675\pi$
$431$	−17.7583	−	4.75833i	−0.855389	−	0.229201i	−0.659759	+	0.751477i	$0.729342\pi$
$432$	5.46410	+	1.46410i	0.262892	+	0.0704416i
$433$	−6.22243	−	23.2224i	−0.299031	−	1.11600i	−0.937963	−	0.346736i	$-0.887290\pi$
$433$	−6.22243	−	23.2224i	−0.299031	−	1.11600i	0.638932	−	0.769263i	$-0.279377\pi$
$434$	10.0000	+	10.0000i	0.480015	+	0.480015i
$435$		0			0
$436$	12.2942	−	3.29423i	0.588787	−	0.157765i
$437$	−30.0000			−1.43509
$438$	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	$0.833333\pi$
$440$	−9.29423	+	1.90192i	−0.443085	+	0.0906707i
$441$			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
$447$			6.00000i			0.283790i
$448$	−7.00000	+	12.1244i	−0.330719	+	0.572822i
$449$	1.09808	+	4.09808i	0.0518214	+	0.193400i	0.986984	−	0.160819i	$-0.0514134\pi$
$449$	1.09808	+	4.09808i	0.0518214	+	0.193400i	−0.935163	+	0.354219i	$0.884747\pi$
$450$	−3.00000	+	4.00000i	−0.141421	+	0.188562i
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	1.83013	−	6.83013i	0.0860819	−	0.321262i
$453$	12.1244	−	7.00000i	0.569652	−	0.328889i
$454$	12.0000			0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$	−1.73205	+	1.00000i	−0.0810219	+	0.0467780i	−0.539964	−	0.841688i	$-0.681562\pi$
$457$	−1.73205	+	1.00000i	−0.0810219	+	0.0467780i	0.458942	+	0.888466i	$0.348229\pi$
$458$	−1.09808	+	4.09808i	−0.0513097	+	0.191491i
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$	3.00000	−	9.00000i	0.139876	−	0.419627i
$461$	6.22243	+	23.2224i	0.289808	+	1.08158i	0.945254	+	0.326335i	$0.105814\pi$
$461$	6.22243	+	23.2224i	0.289808	+	1.08158i	−0.655447	+	0.755241i	$0.727520\pi$
$462$	−2.00000	+	3.46410i	−0.0930484	+	0.161165i
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$		0			0
$465$	18.6603	+	12.3205i	0.865349	+	0.571350i
$466$	0.366025	−	1.36603i	0.0169558	−	0.0632799i
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	0.467515	−	0.883985i	$-0.345149\pi$
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	−0.883985	+	0.467515i	$0.845149\pi$
$468$		0			0
$469$		−	8.00000i		−	0.369406i
$470$	7.39230	−	11.1962i	0.340982	−	0.516440i
$471$	−13.0000	−	22.5167i	−0.599008	−	1.03751i
$472$	28.6865	−	7.68653i	1.32040	−	0.353801i
$473$	−2.00000			−0.0919601
$474$	−2.73205	+	0.732051i	−0.125487	+	0.0336242i
$475$	−13.1699	+	32.8109i	−0.604275	+	1.50547i
$476$	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
$479$	−9.56218	−	2.56218i	−0.436907	−	0.117069i	0.0336596	−	0.999433i	$-0.489284\pi$
$479$	−9.56218	−	2.56218i	−0.436907	−	0.117069i	−0.470567	+	0.882364i	$0.655950\pi$
$480$	−5.00000	+	15.0000i	−0.228218	+	0.684653i
$481$		0			0
$482$	17.0000	−	17.0000i	0.774329	−	0.774329i
$483$	−6.00000	−	10.3923i	−0.273009	−	0.472866i
$484$	−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
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	0.779936	−	0.625859i	$-0.215252\pi$
$487$	13.8564	+	8.00000i	0.627894	+	0.362515i	−0.152042	+	0.988374i	$0.548585\pi$
$488$	−36.3731	−	21.0000i	−1.64653	−	0.950625i
$489$	−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	−0.863955	−	0.503568i	$-0.832020\pi$
$491$	−19.0526	+	11.0000i	−0.859830	+	0.496423i	0.00412539	+	0.999991i	$0.498687\pi$
$492$	7.00000	+	12.1244i	0.315584	+	0.546608i
$493$		0			0
$494$		0			0
$495$	1.00000	−	3.00000i	0.0449467	−	0.134840i
$496$	6.83013	+	1.83013i	0.306682	+	0.0821751i
$497$	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	0.636762	−	0.771060i	$-0.280273\pi$
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	−0.771060	+	0.636762i	$0.780273\pi$
$500$	−8.52628	−	7.23205i	−0.381307	−	0.323427i
$501$	24.5885	−	6.58846i	1.09853	−	0.294351i
$502$	2.00000			0.0892644
$503$	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
$505$	−14.7846	+	22.3923i	−0.657906	+	0.996444i
$506$		−	6.00000i		−	0.266733i
$507$		0			0
$508$	−9.00000	−	9.00000i	−0.399310	−	0.399310i
$509$	−4.75833	+	17.7583i	−0.210909	+	0.787124i	0.776657	+	0.629923i	$0.216914\pi$
$509$	−4.75833	+	17.7583i	−0.210909	+	0.787124i	−0.987567	+	0.157201i	$0.949753\pi$
$510$	−3.73205	−	2.46410i	−0.165258	−	0.109112i
$511$	−17.3205	−	10.0000i	−0.766214	−	0.442374i
$512$			11.0000i			0.486136i
$513$	−20.0000	+	34.6410i	−0.883022	+	1.52944i
$514$	4.02628	+	15.0263i	0.177592	+	0.662781i
$515$	7.00000	−	21.0000i	0.308457	−	0.925371i
$516$	−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
$525$	−14.0000	+	2.00000i	−0.611010	+	0.0872872i
$526$	0.366025	+	1.36603i	0.0159595	+	0.0595615i
$527$	5.00000	−	8.66025i	0.217803	−	0.377247i
$528$			2.00000i			0.0870388i
$529$	−4.33013	−	2.50000i	−0.188266	−	0.108696i
$530$	15.4904	−	3.16987i	0.672859	−	0.137690i
$531$	−2.56218	+	9.56218i	−0.111189	+	0.414963i
$532$	−10.0000	−	10.0000i	−0.433555	−	0.433555i
$533$		0			0
$534$			10.0000i			0.432742i
$535$	21.6865	−	4.43782i	0.937591	−	0.191864i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	−27.3205	+	7.32051i	−1.17897	+	0.315903i
$538$	−12.0000			−0.517357
$539$	−4.09808	+	1.09808i	−0.176517	+	0.0472975i
$540$	−8.39230	−	9.46410i	−0.361147	−	0.407270i
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	0.873595	−	0.486654i	$-0.161783\pi$
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	−0.486654	+	0.873595i	$0.661783\pi$
$542$	−3.29423	−	12.2942i	−0.141499	−	0.528082i
$543$	−10.9282	−	2.92820i	−0.468974	−	0.125661i
$544$	6.83013	+	1.83013i	0.292839	+	0.0784660i
$545$	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	$0.337719\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	12.1244	−	7.00000i	0.517455	−	0.298753i
$550$	−6.56218	−	2.63397i	−0.279812	−	0.112313i
$551$		0			0
$552$	−15.5885	−	9.00000i	−0.663489	−	0.383065i
$553$	3.46410	+	2.00000i	0.147309	+	0.0850487i
$554$	15.0000	−	15.0000i	0.637289	−	0.637289i
$555$		0			0
$556$	12.1244	−	7.00000i	0.514187	−	0.296866i
$557$	−12.0000	−	20.7846i	−0.508456	−	0.880672i	−0.999952	−	0.00979220i	$-0.996883\pi$
$557$	−12.0000	−	20.7846i	−0.508456	−	0.880672i	0.491496	−	0.870880i	$-0.336450\pi$
$558$	−5.00000	+	5.00000i	−0.211667	+	0.211667i
$559$		0			0
$560$	−4.00000	+	2.00000i	−0.169031	+	0.0845154i
$561$	2.73205	+	0.732051i	0.115347	+	0.0309072i
$562$	−1.36603	−	0.366025i	−0.0576223	−	0.0154398i
$563$	−5.49038	−	20.4904i	−0.231392	−	0.863567i	−0.979742	−	0.200263i	$-0.935820\pi$
$563$	−5.49038	−	20.4904i	−0.231392	−	0.863567i	0.748350	−	0.663304i	$-0.230846\pi$
$564$	6.00000	+	6.00000i	0.252646	+	0.252646i
$565$	11.8301	−	10.4904i	0.497697	−	0.441334i
$566$	12.2942	−	3.29423i	0.516765	−	0.138467i
$567$	−10.0000			−0.419961
$568$	4.09808	−	1.09808i	0.171951	−	0.0460743i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	18.6603	+	12.3205i	0.781592	+	0.516049i
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$		0			0
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$	−5.12436	+	19.1244i	−0.213886	+	0.798235i
$575$	16.6865	−	13.0981i	0.695877	−	0.546228i
$576$	−6.06218	−	3.50000i	−0.252591	−	0.145833i
$577$		−	46.0000i		−	1.91501i	−0.288425	−	0.957503i	$-0.593132\pi$
$577$		−	46.0000i		−	1.91501i	0.288425	−	0.957503i	$-0.406868\pi$
$578$	7.50000	−	12.9904i	0.311959	−	0.540329i
$579$	−6.58846	−	24.5885i	−0.273807	−	1.02186i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−0.732051	+	2.73205i	−0.0303445	+	0.113247i
$583$	−8.66025	+	5.00000i	−0.358671	+	0.207079i
$584$	−30.0000			−1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$	3.46410	−	2.00000i	0.142979	−	0.0825488i	−0.426804	−	0.904344i	$-0.640361\pi$
$587$	3.46410	−	2.00000i	0.142979	−	0.0825488i	0.569783	+	0.821795i	$0.307027\pi$
$588$	−1.09808	+	4.09808i	−0.0452839	+	0.169002i
$589$	−25.0000	+	43.3013i	−1.03011	+	1.78420i
$590$	21.0000	+	7.00000i	0.864556	+	0.288185i
$591$	2.19615	+	8.19615i	0.0903376	+	0.337145i
$592$		0			0
$593$			10.0000i			0.410651i	0.978694	+	0.205325i	$0.0658253\pi$
$593$			10.0000i			0.410651i	−0.978694	+	0.205325i	$0.934175\pi$
$594$	−6.92820	−	4.00000i	−0.284268	−	0.164122i
$595$	1.26795	+	6.19615i	0.0519808	+	0.254017i
$596$	1.09808	−	4.09808i	0.0449790	−	0.167864i
$597$	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	$-0.209990\pi$
$600$	−16.6865	+	13.0981i	−0.681225	+	0.534727i
$601$	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
$603$	4.00000			0.162893
$604$	−9.56218	+	2.56218i	−0.389079	+	0.104254i
$605$	−20.0885	−	1.20577i	−0.816712	−	0.0490216i
$606$	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
$613$	10.0000	+	17.3205i	0.403896	+	0.699569i	0.994192	−	0.107618i	$-0.0343224\pi$
$613$	10.0000	+	17.3205i	0.403896	+	0.699569i	−0.590296	+	0.807187i	$0.700989\pi$
$614$	−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
$617$	−19.0526	−	11.0000i	−0.767027	−	0.442843i	0.0647859	−	0.997899i	$-0.479364\pi$
$617$	−19.0526	−	11.0000i	−0.767027	−	0.442843i	−0.831813	+	0.555056i	$0.812697\pi$
$618$	−12.1244	−	7.00000i	−0.487713	−	0.281581i
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.00484658	+	0.999988i	$0.501543\pi$
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.999988	+	0.00484658i	$0.998457\pi$
$620$	−10.4904	−	11.8301i	−0.421304	−	0.475109i
$621$	20.7846	−	12.0000i	0.834058	−	0.481543i
$622$	−3.00000	−	5.19615i	−0.120289	−	0.208347i
$623$	10.0000	−	10.0000i	0.400642	−	0.400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	−12.2942	−	3.29423i	−0.491376	−	0.131664i
$627$	−13.6603	−	3.66025i	−0.545538	−	0.146176i
$628$	4.75833	+	17.7583i	0.189878	+	0.708635i
$629$		0			0
$630$	0.267949	−	4.46410i	0.0106754	−	0.177854i
$631$	−15.0263	+	4.02628i	−0.598187	+	0.160284i	−0.545192	−	0.838311i	$-0.683543\pi$
$631$	−15.0263	+	4.02628i	−0.598187	+	0.160284i	−0.0529946	+	0.998595i	$0.516877\pi$
$632$	6.00000			0.238667
$633$	−5.46410	+	1.46410i	−0.217179	+	0.0581928i
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$	−5.70577	−	27.8827i	−0.226427	−	1.10649i
$636$			10.0000i			0.396526i
$637$		0			0
$638$		0			0
$639$	−0.366025	+	1.36603i	−0.0144797	+	0.0540391i
$640$	3.69615	−	5.59808i	0.146103	−	0.221283i
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	0.850741	−	0.525584i	$-0.176153\pi$
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	−0.0297987	+	0.999556i	$0.509487\pi$
$642$		−	14.0000i		−	0.552536i
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	−0.307372	−	0.951589i	$-0.599450\pi$
$643$	17.0000	−	29.4449i	0.670415	−	1.16119i	0.977787	−	0.209603i	$-0.0672170\pi$
$644$	2.19615	+	8.19615i	0.0865405	+	0.322974i
$645$	−4.00000	+	2.00000i	−0.157500	+	0.0787499i
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	−0.366025	+	1.36603i	−0.0143899	+	0.0537040i	−0.972747	−	0.231867i	$-0.925517\pi$
$647$	−0.366025	+	1.36603i	−0.0143899	+	0.0537040i	0.958358	+	0.285571i	$0.0921832\pi$
$648$	−12.9904	+	7.50000i	−0.510310	+	0.294628i
$649$	−14.0000			−0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$	3.46410	−	2.00000i	0.135665	−	0.0783260i
$653$	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
$655$	40.0000	−	20.0000i	1.56293	−	0.781465i
$656$	2.56218	+	9.56218i	0.100036	+	0.373340i
$657$	5.00000	−	8.66025i	0.195069	−	0.337869i
$658$			12.0000i			0.467809i
$659$	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
$661$	6.22243	−	23.2224i	0.242025	−	0.903248i	−0.732831	−	0.680411i	$-0.761801\pi$
$661$	6.22243	−	23.2224i	0.242025	−	0.903248i	0.974856	−	0.222837i	$-0.0715319\pi$
$662$	3.00000	+	3.00000i	0.116598	+	0.116598i
$663$		0			0
$664$		−	18.0000i		−	0.698535i
$665$	−6.33975	−	30.9808i	−0.245845	−	1.20138i
$666$		0			0
$667$		0			0
$668$	−18.0000			−0.696441
$669$	−2.73205	+	0.732051i	−0.105627	+	0.0283027i
$670$	0.535898	−	8.92820i	0.0207036	−	0.344927i
$671$	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	−0.158725	−	0.987323i	$-0.550738\pi$
$673$	−20.4904	−	5.49038i	−0.789846	−	0.211639i	−0.631121	+	0.775684i	$0.717405\pi$
$674$	17.7583	+	4.75833i	0.684025	+	0.183284i
$675$	−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	$0.464924\pi$
$678$	−5.00000	−	8.66025i	−0.192024	−	0.332595i
$679$	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
$682$	−8.66025	−	5.00000i	−0.331618	−	0.191460i
$683$	10.3923	+	6.00000i	0.397650	+	0.229584i	0.685470	−	0.728101i	$-0.259597\pi$
$683$	10.3923	+	6.00000i	0.397650	+	0.229584i	−0.287819	+	0.957685i	$0.592930\pi$
$684$	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
$687$	−3.00000	−	5.19615i	−0.114457	−	0.198246i
$688$	−1.00000	+	1.00000i	−0.0381246	+	0.0381246i
$689$		0			0
$690$	−6.00000	−	12.0000i	−0.228416	−	0.456832i
$691$	4.09808	+	1.09808i	0.155898	+	0.0417728i	0.335924	−	0.941889i	$-0.390951\pi$
$691$	4.09808	+	1.09808i	0.155898	+	0.0417728i	−0.180026	+	0.983662i	$0.557618\pi$
$692$	−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
$695$	31.2487	+	1.87564i	1.18533	+	0.0711472i
$696$		0			0
$697$	14.0000			0.530288
$698$	−12.2942	+	3.29423i	−0.465343	+	0.124688i
$699$	1.00000	+	1.73205i	0.0378235	+	0.0655122i
$700$	9.92820	+	1.19615i	0.375251	+	0.0452103i
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$		0			0
$703$		0			0
$704$	2.56218	−	9.56218i	0.0965657	−	0.360388i
$705$	3.80385	+	18.5885i	0.143261	+	0.700082i
$706$	−10.3923	−	6.00000i	−0.391120	−	0.225813i
$707$		−	24.0000i		−	0.902613i
$708$	−7.00000	+	12.1244i	−0.263076	+	0.455661i
$709$	−10.6147	−	39.6147i	−0.398645	−	1.48776i	−0.815482	−	0.578782i	$-0.803528\pi$
$709$	−10.6147	−	39.6147i	−0.398645	−	1.48776i	0.416838	−	0.908981i	$-0.363138\pi$
$710$	3.00000	+	1.00000i	0.112588	+	0.0375293i
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$	5.49038	−	20.4904i	0.205761	−	0.767909i
$713$	25.9808	−	15.0000i	0.972987	−	0.561754i
$714$	4.00000			0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$	−5.19615	+	3.00000i	−0.194054	+	0.112037i
$718$	0.366025	−	1.36603i	0.0136599	−	0.0509796i
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	−0.930923	−	0.365216i	$-0.880995\pi$
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	0.781748	+	0.623595i	$0.214328\pi$
$720$	−1.00000	−	2.00000i	−0.0372678	−	0.0745356i
$721$	5.12436	+	19.1244i	0.190841	+	0.712228i
$722$	−15.5000	+	26.8468i	−0.576850	+	0.999134i
$723$			34.0000i			1.26447i
$724$	6.92820	+	4.00000i	0.257485	+	0.148659i
$725$		0			0
$726$	−3.29423	+	12.2942i	−0.122260	+	0.456282i
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.929660	+	0.368418i	$0.120100\pi$
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.368418	+	0.929660i	$0.379900\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$	−18.6603	−	12.3205i	−0.690647	−	0.456002i
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$	19.1244	−	5.12436i	0.706857	−	0.189402i
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$	−1.36603	+	0.366025i	−0.0504209	+	0.0135102i
$735$	−7.09808	+	6.29423i	−0.261816	+	0.232166i
$736$	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
$739$	−4.09808	−	1.09808i	−0.150750	−	0.0403934i	0.182655	−	0.983177i	$-0.441531\pi$
$739$	−4.09808	−	1.09808i	−0.150750	−	0.0403934i	−0.333405	+	0.942784i	$0.608198\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	+	10.0000i	−0.367112	+	0.367112i
$743$	−17.0000	−	29.4449i	−0.623670	−	1.08023i	−0.988797	−	0.149270i	$-0.952308\pi$
$743$	−17.0000	−	29.4449i	−0.623670	−	1.08023i	0.365127	−	0.930958i	$-0.381026\pi$
$744$	−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
$747$	5.19615	+	3.00000i	0.190117	+	0.109764i
$748$	−1.73205	−	1.00000i	−0.0633300	−	0.0365636i
$749$	−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	$0.699000\pi$
$751$	−43.3013	+	25.0000i	−1.58009	+	0.912263i	−0.994845	+	0.101403i	$0.967667\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	−2.00000	+	2.00000i	−0.0728841	+	0.0728841i
$754$		0			0
$755$	−21.0000	−	7.00000i	−0.764268	−	0.254756i
$756$	10.9282	+	2.92820i	0.397455	+	0.106498i
$757$	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
$760$	−31.4711	−	35.4904i	−1.14158	−	1.28737i
$761$	9.56218	−	2.56218i	0.346629	−	0.0928789i	−0.0813044	−	0.996689i	$-0.525909\pi$
$761$	9.56218	−	2.56218i	0.346629	−	0.0928789i	0.427933	+	0.903810i	$0.359242\pi$
$762$	−18.0000			−0.652071
$763$	−24.5885	+	6.58846i	−0.890162	+	0.238518i
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$	−3.09808	+	0.633975i	−0.112011	+	0.0229214i
$766$			30.0000i			1.08394i
$767$		0			0
$768$	−17.0000	−	17.0000i	−0.613435	−	0.613435i
$769$	5.49038	−	20.4904i	0.197988	−	0.738902i	−0.793485	−	0.608590i	$-0.791735\pi$
$769$	5.49038	−	20.4904i	0.197988	−	0.738902i	0.991473	−	0.130312i	$-0.0415979\pi$
$770$	6.19615	−	1.26795i	0.223294	−	0.0456937i
$771$	−19.0526	−	11.0000i	−0.686161	−	0.396155i
$772$			18.0000i			0.647834i
$773$	16.0000	−	27.7128i	0.575480	−	0.996761i	−0.420509	−	0.907288i	$-0.638149\pi$
$773$	16.0000	−	27.7128i	0.575480	−	0.996761i	0.995989	−	0.0894724i	$-0.0285181\pi$
$774$	−0.366025	−	1.36603i	−0.0131565	−	0.0491008i
$775$	−5.00000	−	35.0000i	−0.179605	−	1.25724i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$		0			0
$778$	−15.5885	+	9.00000i	−0.558873	+	0.322666i
$779$	−70.0000			−2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	−5.19615	+	3.00000i	−0.185814	+	0.107280i
$783$		0			0
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$	−13.0000	+	39.0000i	−0.463990	+	1.39197i
$786$	−7.32051	−	27.3205i	−0.261114	−	0.974490i
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	−0.600620	−	0.799535i	$-0.705079\pi$
$787$	11.0000	−	19.0526i	0.392108	−	0.679150i	0.992727	+	0.120384i	$0.0384127\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−1.73205	−	1.00000i	−0.0616626	−	0.0356009i
$790$	3.73205	+	2.46410i	0.132780	+	0.0876688i
$791$	−3.66025	+	13.6603i	−0.130144	+	0.485703i
$792$	3.00000	+	3.00000i	0.106600	+	0.106600i
$793$		0			0
$794$		−	16.0000i		−	0.567819i
$795$	−12.3205	+	18.6603i	−0.436963	+	0.661811i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	23.2224	−	6.22243i	0.822581	−	0.220410i	0.177106	−	0.984192i	$-0.443326\pi$
$797$	23.2224	−	6.22243i	0.822581	−	0.220410i	0.645474	+	0.763782i	$0.276660\pi$
$798$	−20.0000			−0.707992
$799$	8.19615	−	2.19615i	0.289959	−	0.0776943i
$800$	22.9904	−	9.82051i	0.812833	−	0.347207i
$801$	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
$804$	5.46410	+	1.46410i	0.192704	+	0.0516349i
$805$	−6.00000	+	18.0000i	−0.211472	+	0.634417i
$806$		0			0
$807$	12.0000	−	12.0000i	0.422420	−	0.422420i
$808$	−18.0000	−	31.1769i	−0.633238	−	1.09680i
$809$	−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	$-0.983880\pi$
$811$	−27.0000	+	27.0000i	−0.948098	+	0.948098i	0.0506198	+	0.998718i	$0.483880\pi$
$812$		0			0
$813$	15.5885	+	9.00000i	0.546711	+	0.315644i
$814$		0			0
$815$	8.92820	+	0.535898i	0.312741	+	0.0187717i
$816$	1.73205	−	1.00000i	0.0606339	−	0.0350070i
$817$	−5.00000	−	8.66025i	−0.174928	−	0.302984i
$818$	7.00000	−	7.00000i	0.244749	−	0.244749i
$819$		0			0
$820$	7.00000	−	21.0000i	0.244451	−	0.733352i
$821$	−12.2942	−	3.29423i	−0.429072	−	0.114969i	0.0378188	−	0.999285i	$-0.487959\pi$
$821$	−12.2942	−	3.29423i	−0.429072	−	0.114969i	−0.466890	+	0.884315i	$0.654626\pi$
$822$	21.8564	+	5.85641i	0.762330	+	0.204266i
$823$	3.29423	+	12.2942i	0.114830	+	0.428550i	0.999274	−	0.0380955i	$-0.0121291\pi$
$823$	3.29423	+	12.2942i	0.114830	+	0.428550i	−0.884445	+	0.466645i	$0.845462\pi$
$824$	21.0000	+	21.0000i	0.731570	+	0.731570i
$825$	9.19615	−	3.92820i	0.320169	−	0.136762i
$826$	−19.1244	+	5.12436i	−0.665421	+	0.178299i
$827$	−46.0000			−1.59958			−0.799788	−	0.600282i	$-0.795055\pi$
$827$	−46.0000			−1.59958			−0.799788	+	0.600282i	$0.795055\pi$
$828$	−4.09808	+	1.09808i	−0.142418	+	0.0381608i
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	0.994174	+	0.107788i	$0.0343769\pi$
$829$	17.0000	+	29.4449i	0.590434	+	1.02266i	−0.403739	+	0.914874i	$0.632290\pi$
$830$	7.39230	−	11.1962i	0.256591	−	0.388624i
$831$			30.0000i			1.04069i
$832$		0			0
$833$	3.00000	+	3.00000i	0.103944	+	0.103944i
$834$	5.12436	−	19.1244i	0.177442	−	0.662222i
$835$	−33.5885	−	22.1769i	−1.16238	−	0.767464i
$836$	8.66025	+	5.00000i	0.299521	+	0.172929i
$837$		−	40.0000i		−	1.38260i
$838$	−19.0000	+	32.9090i	−0.656344	+	1.13682i
$839$	12.8109	+	47.8109i	0.442281	+	1.65062i	0.723017	+	0.690830i	$0.242755\pi$
$839$	12.8109	+	47.8109i	0.442281	+	1.65062i	−0.280736	+	0.959785i	$0.590579\pi$
$840$	6.00000	−	18.0000i	0.207020	−	0.621059i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$	4.02628	−	15.0263i	0.138755	−	0.517840i
$843$	1.73205	−	1.00000i	0.0596550	−	0.0344418i
$844$	4.00000			0.137686
$845$		0			0
$846$	−6.00000			−0.206284
$847$	15.5885	−	9.00000i	0.535626	−	0.309244i
$848$	−1.83013	+	6.83013i	−0.0628468	+	0.234548i
$849$	−9.00000	+	15.5885i	−0.308879	+	0.534994i
$850$	1.00000	+	7.00000i	0.0342997	+	0.240098i
$851$		0			0
$852$	−1.00000	+	1.73205i	−0.0342594	+	0.0593391i
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$	24.2487	+	14.0000i	0.829774	+	0.479070i
$855$	15.4904	−	3.16987i	0.529760	−	0.108407i
$856$	−7.68653	+	28.6865i	−0.262720	+	0.980486i
$857$	3.00000	+	3.00000i	0.102478	+	0.102478i	0.756487	−	0.654009i	$-0.226914\pi$
$857$	3.00000	+	3.00000i	0.102478	+	0.102478i	−0.654009	+	0.756487i	$0.726914\pi$
$858$		0			0
$859$			30.0000i			1.02359i	0.859109	+	0.511793i	$0.171019\pi$
$859$			30.0000i			1.02359i	−0.859109	+	0.511793i	$0.828981\pi$
$860$	3.09808	−	0.633975i	0.105644	−	0.0216184i
$861$	−14.0000	−	24.2487i	−0.477119	−	0.826394i
$862$	17.7583	−	4.75833i	0.604851	−	0.162069i
$863$	−30.0000			−1.02121			−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000			−1.02121			−0.510606	+	0.859815i	$0.670579\pi$
$864$	27.3205	−	7.32051i	0.929463	−	0.249049i
$865$	−23.0788	−	26.0263i	−0.784704	−	0.884920i
$866$	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
$869$	−2.73205	−	0.732051i	−0.0926785	−	0.0248331i
$870$		0			0
$871$		0			0
$872$	−27.0000	+	27.0000i	−0.914335	+	0.914335i
$873$	1.00000	+	1.73205i	0.0338449	+	0.0586210i
$874$	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
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.939155	−	0.343495i	$-0.111611\pi$
$877$	32.9090	+	19.0000i	1.11126	+	0.641584i	0.172102	+	0.985079i	$0.444944\pi$
$878$		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	$0.673106\pi$
$881$	−45.0333	+	26.0000i	−1.51721	+	0.875962i	−0.999795	+	0.0202281i	$0.993561\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	−39.0000	+	39.0000i	−1.31245	+	1.31245i	−0.392853	+	0.919601i	$0.628512\pi$
$883$	−39.0000	+	39.0000i	−1.31245	+	1.31245i	−0.919601	+	0.392853i	$0.871488\pi$
$884$		0			0
$885$	−28.0000	+	14.0000i	−0.941210	+	0.470605i
$886$	−34.1506	−	9.15064i	−1.14731	−	0.307422i
$887$	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
$890$	11.8301	−	10.4904i	0.396547	−	0.351638i
$891$	6.83013	−	1.83013i	0.228818	−	0.0613116i
$892$	2.00000			0.0669650
$893$	−40.9808	+	10.9808i	−1.37137	+	0.367457i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	37.3205	+	24.6410i	1.24749	+	0.823658i
$896$			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
$902$		−	14.0000i		−	0.466149i
$903$	2.00000	−	3.46410i	0.0665558	−	0.115278i
$904$	5.49038	+	20.4904i	0.182607	+	0.681500i
$905$	8.00000	+	16.0000i	0.265929	+	0.531858i
$906$	−7.00000	+	12.1244i	−0.232559	+	0.402805i
$907$	14.2750	−	53.2750i	0.473993	−	1.76897i	−0.151206	−	0.988502i	$-0.548316\pi$
$907$	14.2750	−	53.2750i	0.473993	−	1.76897i	0.625200	−	0.780465i	$-0.285018\pi$
$908$	10.3923	−	6.00000i	0.344881	−	0.199117i
$909$	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	$0.369851\pi$
$912$	−8.66025	+	5.00000i	−0.286770	+	0.165567i
$913$	−2.19615	+	8.19615i	−0.0726820	+	0.271253i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$	42.0000	+	14.0000i	1.38848	+	0.462826i
$916$	1.09808	+	4.09808i	0.0362815	+	0.135404i
$917$	−20.0000	+	34.6410i	−0.660458	+	1.14395i
$918$			8.00000i			0.264039i
$919$	−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
$921$	6.58846	−	24.5885i	0.217097	−	0.810217i
$922$	−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
$929$	−25.9545	+	6.95448i	−0.851539	+	0.228169i	−0.658088	−	0.752941i	$-0.728635\pi$
$929$	−25.9545	+	6.95448i	−0.851539	+	0.228169i	−0.193451	+	0.981110i	$0.561968\pi$
$930$	−22.3205	−	1.33975i	−0.731918	−	0.0439320i
$931$	−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
$934$	12.2942	+	3.29423i	0.402279	+	0.107790i
$935$	−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	$0.301698\pi$
$938$	4.00000	+	6.92820i	0.130605	+	0.226214i
$939$	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	$-0.589157\pi$
$941$	21.0000	−	21.0000i	0.684580	−	0.684580i	0.961029	+	0.276448i	$0.0891575\pi$
$942$	22.5167	+	13.0000i	0.733632	+	0.423563i
$943$	36.3731	+	21.0000i	1.18447	+	0.683854i
$944$	−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
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$	−2.00000	+	2.00000i	−0.0649570	+	0.0649570i
$949$		0			0
$950$	−5.00000	−	35.0000i	−0.162221	−	1.13555i
$951$	19.1244	+	5.12436i	0.620150	+	0.166169i
$952$	−8.19615	−	2.19615i	−0.265639	−	0.0711777i
$953$	−4.75833	−	17.7583i	−0.154137	−	0.575249i	−0.999178	−	0.0405460i	$-0.987090\pi$
$953$	−4.75833	−	17.7583i	−0.154137	−	0.575249i	0.845040	−	0.534703i	$-0.179576\pi$
$954$	−5.00000	−	5.00000i	−0.161881	−	0.161881i
$955$	1.07180	−	17.8564i	0.0346825	−	0.577820i
$956$	4.09808	−	1.09808i	0.132541	−	0.0355143i
$957$		0			0
$958$	9.56218	−	2.56218i	0.308940	−	0.0827802i
$959$	−16.0000	−	27.7128i	−0.516667	−	0.894893i
$960$	−4.43782	−	21.6865i	−0.143230	−	0.699930i
$961$		−	19.0000i		−	0.612903i
$962$		0			0
$963$	−7.00000	−	7.00000i	−0.225572	−	0.225572i
$964$	6.22243	−	23.2224i	0.200411	−	0.747944i
$965$	−22.1769	+	33.5885i	−0.713900	+	1.08125i
$966$	10.3923	+	6.00000i	0.334367	+	0.193047i
$967$		0			0		1.00000			$0$
$967$		0			0		−1.00000			$\pi$
$968$	13.5000	−	23.3827i	0.433906	−	0.751548i
$969$	3.66025	+	13.6603i	0.117584	+	0.438831i
$970$	4.00000	−	2.00000i	0.128432	−	0.0642161i
$971$	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
$973$	−24.2487	+	14.0000i	−0.777378	+	0.448819i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	14.0000			0.448129
$977$	−53.6936	+	31.0000i	−1.71781	+	0.991778i	−0.794919	+	0.606715i	$0.792487\pi$
$977$	−53.6936	+	31.0000i	−1.71781	+	0.991778i	−0.922890	+	0.385063i	$0.874180\pi$
$978$	1.46410	−	5.46410i	0.0468168	−	0.174723i
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	6.00000	−	3.00000i	0.191663	−	0.0958315i
$981$	−3.29423	−	12.2942i	−0.105177	−	0.392525i
$982$	11.0000	−	19.0526i	0.351024	−	0.607992i
$983$		−	24.0000i		−	0.765481i	−0.923856	−	0.382741i	$-0.874980\pi$
$983$		−	24.0000i		−	0.765481i	0.923856	−	0.382741i	$-0.125020\pi$
$984$	−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
$990$	0.633975	+	3.09808i	0.0201490	+	0.0984633i
$991$		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
$993$	−6.00000			−0.190404
$994$	−2.73205	+	0.732051i	−0.0866554	+	0.0232192i
$995$	1.07180	−	17.8564i	0.0339782	−	0.566086i
$996$	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.t.a.418.1		4
5.2	odd	4		845.2.o.a.587.1		4
13.2	odd	12		845.2.k.a.268.1		2
13.3	even	3		65.2.f.a.18.1	✓	2
13.4	even	6		845.2.t.b.188.1		4
13.5	odd	4		845.2.o.b.258.1		4
13.6	odd	12		845.2.o.b.488.1		4
13.7	odd	12		845.2.o.a.488.1		4
13.8	odd	4		845.2.o.a.258.1		4
13.9	even	3	inner	845.2.t.a.188.1		4
13.10	even	6		845.2.f.a.408.1		2
13.11	odd	12		65.2.k.a.8.1	yes	2
13.12	even	2		845.2.t.b.418.1		4
39.11	even	12		585.2.w.b.73.1		2
39.29	odd	6		585.2.n.c.343.1		2
52.3	odd	6		1040.2.cd.b.993.1		2
52.11	even	12		1040.2.bg.a.593.1		2
65.2	even	12		845.2.f.a.437.1		2
65.3	odd	12		325.2.k.a.57.1		2
65.7	even	12	inner	845.2.t.a.657.1		4
65.12	odd	4		845.2.o.b.587.1		4
65.17	odd	12		845.2.o.b.357.1		4
65.22	odd	12		845.2.o.a.357.1		4
65.24	odd	12		325.2.k.a.268.1		2
65.29	even	6		325.2.f.a.18.1		2
65.32	even	12		845.2.t.b.657.1		4
65.37	even	12		65.2.f.a.47.1	yes	2
65.42	odd	12		65.2.k.a.57.1	yes	2
65.47	even	4	inner	845.2.t.a.427.1		4
65.57	even	4		845.2.t.b.427.1		4
65.62	odd	12		845.2.k.a.577.1		2
65.63	even	12		325.2.f.a.307.1		2
195.107	even	12		585.2.w.b.577.1		2
195.167	odd	12		585.2.n.c.307.1		2
260.107	even	12		1040.2.bg.a.577.1		2
260.167	odd	12		1040.2.cd.b.177.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	13.3	even	3
65.2.f.a.47.1	yes	2	65.37	even	12
65.2.k.a.8.1	yes	2	13.11	odd	12
65.2.k.a.57.1	yes	2	65.42	odd	12
325.2.f.a.18.1		2	65.29	even	6
325.2.f.a.307.1		2	65.63	even	12
325.2.k.a.57.1		2	65.3	odd	12
325.2.k.a.268.1		2	65.24	odd	12
585.2.n.c.307.1		2	195.167	odd	12
585.2.n.c.343.1		2	39.29	odd	6
585.2.w.b.73.1		2	39.11	even	12
585.2.w.b.577.1		2	195.107	even	12
845.2.f.a.408.1		2	13.10	even	6
845.2.f.a.437.1		2	65.2	even	12
845.2.k.a.268.1		2	13.2	odd	12
845.2.k.a.577.1		2	65.62	odd	12
845.2.o.a.258.1		4	13.8	odd	4
845.2.o.a.357.1		4	65.22	odd	12
845.2.o.a.488.1		4	13.7	odd	12
845.2.o.a.587.1		4	5.2	odd	4
845.2.o.b.258.1		4	13.5	odd	4
845.2.o.b.357.1		4	65.17	odd	12
845.2.o.b.488.1		4	13.6	odd	12
845.2.o.b.587.1		4	65.12	odd	4
845.2.t.a.188.1		4	13.9	even	3	inner
845.2.t.a.418.1		4	1.1	even	1	trivial
845.2.t.a.427.1		4	65.47	even	4	inner
845.2.t.a.657.1		4	65.7	even	12	inner
845.2.t.b.188.1		4	13.4	even	6
845.2.t.b.418.1		4	13.12	even	2
845.2.t.b.427.1		4	65.57	even	4
845.2.t.b.657.1		4	65.32	even	12
1040.2.bg.a.577.1		2	260.107	even	12
1040.2.bg.a.593.1		2	52.11	even	12
1040.2.cd.b.177.1		2	260.167	odd	12
1040.2.cd.b.993.1		2	52.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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