LMFDB - Embedded newform 845.2.t.a.427.1

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			427.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.427
Dual form			845.2.t.a.188.1

$q$-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} +(-1.36603 - 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 1.00000i) q^{5} +(-1.36603 + 0.366025i) q^{6} +(1.00000 - 1.73205i) q^{7} +3.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.23205 + 0.133975i) q^{10} +(1.36603 + 0.366025i) q^{11} +(1.00000 - 1.00000i) q^{12} -2.00000i q^{14} +(2.36603 + 2.09808i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.366025 - 1.36603i) q^{17} -1.00000 q^{18} +(1.83013 + 6.83013i) q^{19} +(1.86603 - 1.23205i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(1.36603 - 0.366025i) q^{22} +(-1.09808 + 4.09808i) q^{23} +(1.09808 - 4.09808i) q^{24} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +(1.00000 + 1.73205i) q^{28} +(3.09808 + 0.633975i) 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} +(-3.73205 + 2.46410i) 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} +(-0.732051 + 2.73205i) q^{42} +(-1.36603 + 0.366025i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.23205 + 1.86603i) q^{45} +(1.09808 + 4.09808i) q^{46} +6.00000 q^{47} +(-0.366025 - 1.36603i) q^{48} +(1.50000 + 2.59808i) q^{49} +(4.59808 + 1.96410i) q^{50} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(5.46410 + 1.46410i) q^{54} +(-2.36603 - 2.09808i) q^{55} +(5.19615 + 3.00000i) q^{56} -10.0000i q^{57} +(-9.56218 + 2.56218i) q^{59} +(-3.00000 + 1.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(6.83013 + 1.83013i) q^{62} +(-1.73205 + 1.00000i) q^{63} -7.00000 q^{64} -2.00000 q^{66} +(-3.46410 + 2.00000i) q^{67} +(1.36603 + 0.366025i) q^{68} +(3.00000 - 5.19615i) q^{69} +(-2.00000 + 4.00000i) q^{70} +(-1.36603 + 0.366025i) q^{71} +(1.50000 - 2.59808i) q^{72} +10.0000i q^{73} +(-2.63397 - 6.56218i) q^{75} +(-6.83013 - 1.83013i) q^{76} +(2.00000 - 2.00000i) q^{77} -2.00000i q^{79} +(-0.133975 - 2.23205i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(2.56218 + 9.56218i) q^{82} +6.00000 q^{83} +(-0.732051 - 2.73205i) q^{84} +(-0.633975 + 3.09808i) q^{85} +(-1.00000 + 1.00000i) q^{86} +(-1.09808 + 4.09808i) q^{88} +(-1.83013 + 6.83013i) 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} +(3.16987 - 15.4904i) 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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{4}\right)$

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	−0.161521	−	0.986869i	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$	−1.36603	−	0.366025i	−0.788675	−	0.211325i	−0.158069	−	0.987428i	$-0.550527\pi$
$3$	−1.36603	−	0.366025i	−0.788675	−	0.211325i	−0.630606	+	0.776103i	$0.717194\pi$
$4$	−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
$6$	−1.36603	+	0.366025i	−0.557678	+	0.149429i
$7$	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
$10$	−2.23205	+	0.133975i	−0.705836	+	0.0423665i
$11$	1.36603	+	0.366025i	0.411872	+	0.110361i	0.458804	−	0.888537i	$-0.348278\pi$
$11$	1.36603	+	0.366025i	0.411872	+	0.110361i	−0.0469323	+	0.998898i	$0.514945\pi$
$12$	1.00000	−	1.00000i	0.288675	−	0.288675i
$13$		0			0
$13$		0			0
$14$		−	2.00000i		−	0.534522i
$15$	2.36603	+	2.09808i	0.610905	+	0.541721i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.366025	−	1.36603i	−0.0887742	−	0.331310i	0.907228	−	0.420639i	$-0.138194\pi$
$17$	−0.366025	−	1.36603i	−0.0887742	−	0.331310i	−0.996002	+	0.0893296i	$0.971528\pi$
$18$	−1.00000			−0.235702
$19$	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	$0.615532\pi$
$20$	1.86603	−	1.23205i	0.417256	−	0.275495i
$21$	−2.00000	+	2.00000i	−0.436436	+	0.436436i
$22$	1.36603	−	0.366025i	0.291238	−	0.0780369i
$23$	−1.09808	+	4.09808i	−0.228965	+	0.854508i	0.751812	+	0.659377i	$0.229180\pi$
$23$	−1.09808	+	4.09808i	−0.228965	+	0.854508i	−0.980777	+	0.195131i	$0.937487\pi$
$24$	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
$28$	1.00000	+	1.73205i	0.188982	+	0.327327i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	3.09808	+	0.633975i	0.565629	+	0.115747i
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	0.995261	−	0.0972349i	$-0.0309998\pi$
$31$	5.00000	+	5.00000i	0.898027	+	0.898027i	−0.0972349	+	0.995261i	$0.531000\pi$
$32$	−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
$35$	−3.73205	+	2.46410i	−0.630832	+	0.416509i
$36$	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
$41$	−2.56218	+	9.56218i	−0.400145	+	1.49336i	0.412692	+	0.910870i	$0.364588\pi$
$41$	−2.56218	+	9.56218i	−0.400145	+	1.49336i	−0.812837	+	0.582491i	$0.802078\pi$
$42$	−0.732051	+	2.73205i	−0.112958	+	0.421565i
$43$	−1.36603	+	0.366025i	−0.208317	+	0.0558184i	−0.361468	−	0.932384i	$-0.617724\pi$
$43$	−1.36603	+	0.366025i	−0.208317	+	0.0558184i	0.153151	+	0.988203i	$0.451058\pi$
$44$	−1.00000	+	1.00000i	−0.150756	+	0.150756i
$45$	1.23205	+	1.86603i	0.183663	+	0.278171i
$46$	1.09808	+	4.09808i	0.161903	+	0.604228i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$	−0.366025	−	1.36603i	−0.0528312	−	0.197169i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	4.59808	+	1.96410i	0.650266	+	0.277766i
$51$			2.00000i			0.280056i
$52$		0			0
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	−0.274721	−	0.961524i	$-0.588586\pi$
$53$	5.00000	−	5.00000i	0.686803	−	0.686803i	0.961524	+	0.274721i	$0.0885855\pi$
$54$	5.46410	+	1.46410i	0.743570	+	0.199239i
$55$	−2.36603	−	2.09808i	−0.319035	−	0.282905i
$56$	5.19615	+	3.00000i	0.694365	+	0.400892i
$57$		−	10.0000i		−	1.32453i
$58$		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	$0.639560\pi$
$60$	−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	$-0.187058\pi$
$62$	6.83013	+	1.83013i	0.867427	+	0.232426i
$63$	−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	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	1.36603	+	0.366025i	0.165655	+	0.0443871i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	−2.00000	+	4.00000i	−0.239046	+	0.478091i
$71$	−1.36603	+	0.366025i	−0.162117	+	0.0434392i	−0.338965	−	0.940799i	$-0.610077\pi$
$71$	−1.36603	+	0.366025i	−0.162117	+	0.0434392i	0.176847	+	0.984238i	$0.443410\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$		0			0
$75$	−2.63397	−	6.56218i	−0.304145	−	0.757735i
$76$	−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	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	−0.133975	−	2.23205i	−0.0149788	−	0.249551i
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$	2.56218	+	9.56218i	0.282945	+	1.05597i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−0.732051	−	2.73205i	−0.0798733	−	0.298091i
$85$	−0.633975	+	3.09808i	−0.0687642	+	0.336034i
$86$	−1.00000	+	1.00000i	−0.107833	+	0.107833i
$87$		0			0
$88$	−1.09808	+	4.09808i	−0.117055	+	0.436856i
$89$	−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
$93$	−5.00000	−	8.66025i	−0.518476	−	0.898027i
$94$	5.19615	−	3.00000i	0.535942	−	0.309426i
$95$	3.16987	−	15.4904i	0.325222	−	1.58928i
$96$	5.00000	+	5.00000i	0.510310	+	0.510310i
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$	−4.96410	+	0.598076i	−0.496410	+	0.0598076i
$101$	−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	$0.536983\pi$
$102$	1.00000	+	1.73205i	0.0990148	+	0.171499i
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	0.272442	−	0.962172i	$-0.412169\pi$
$103$	−7.00000	−	7.00000i	−0.689730	−	0.689730i	−0.962172	+	0.272442i	$0.912169\pi$
$104$		0			0
$105$	6.00000	−	2.00000i	0.585540	−	0.195180i
$106$	1.83013	−	6.83013i	0.177758	−	0.663401i
$107$	2.56218	−	9.56218i	0.247695	−	0.924411i	−0.724315	−	0.689470i	$-0.757844\pi$
$107$	2.56218	−	9.56218i	0.247695	−	0.924411i	0.972010	−	0.234941i	$-0.0754897\pi$
$108$	−5.46410	+	1.46410i	−0.525783	+	0.140883i
$109$	−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	$0.458653\pi$
$110$	−3.09808	−	0.633975i	−0.295390	−	0.0604471i
$111$		0			0
$112$	2.00000			0.188982
$113$	1.83013	+	6.83013i	0.172164	+	0.642524i	0.997017	+	0.0771777i	$0.0245909\pi$
$113$	1.83013	+	6.83013i	0.172164	+	0.642524i	−0.824853	+	0.565347i	$0.808742\pi$
$114$	−5.00000	−	8.66025i	−0.468293	−	0.811107i
$115$	6.29423	−	7.09808i	0.586940	−	0.661899i
$116$		0			0
$117$		0			0
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	−2.73205	−	0.732051i	−0.250447	−	0.0671070i
$120$	−6.29423	+	7.09808i	−0.574582	+	0.647963i
$121$	−7.79423	−	4.50000i	−0.708566	−	0.409091i
$122$		−	14.0000i		−	1.26750i
$123$	7.00000	−	12.1244i	0.631169	−	1.09322i
$124$	−6.83013	+	1.83013i	−0.613364	+	0.164350i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	12.2942	+	3.29423i	1.09094	+	0.292316i	0.759069	−	0.651010i	$-0.225655\pi$
$127$	12.2942	+	3.29423i	1.09094	+	0.292316i	0.331868	+	0.943326i	$0.392321\pi$
$128$	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
$133$	13.6603	+	3.66025i	1.18449	+	0.317384i
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$	−4.00000	−	12.0000i	−0.344265	−	1.03280i
$136$	4.09808	−	1.09808i	0.351407	−	0.0941593i
$137$	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	0.916519	−	0.399992i	$-0.130987\pi$
$139$	12.1244	+	7.00000i	1.02837	+	0.593732i	0.111856	+	0.993724i	$0.464321\pi$
$140$	−0.267949	−	4.46410i	−0.0226458	−	0.377285i
$141$	−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
$147$	−1.09808	−	4.09808i	−0.0905678	−	0.338004i
$148$		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	$0.861067\pi$
$150$	−5.56218	−	4.36603i	−0.454150	−	0.356484i
$151$	7.00000	−	7.00000i	0.569652	−	0.569652i	−0.362379	−	0.932031i	$-0.618035\pi$
$151$	7.00000	−	7.00000i	0.569652	−	0.569652i	0.932031	+	0.362379i	$0.118035\pi$
$152$	−20.4904	+	5.49038i	−1.66199	+	0.445329i
$153$	−0.366025	+	1.36603i	−0.0295914	+	0.110437i
$154$	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	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	−8.66025	+	5.00000i	−0.686803	+	0.396526i
$160$	6.16025	+	9.33013i	0.487011	+	0.737611i
$161$	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	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	−7.00000	−	7.00000i	−0.546608	−	0.546608i
$165$	2.46410	+	3.73205i	0.191830	+	0.290540i
$166$	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
$171$	1.83013	−	6.83013i	0.139953	−	0.522313i
$172$	0.366025	−	1.36603i	0.0279092	−	0.104158i
$173$	−15.0263	+	4.02628i	−1.14243	+	0.306112i	−0.779926	−	0.625871i	$-0.784744\pi$
$173$	−15.0263	+	4.02628i	−1.14243	+	0.306112i	−0.362500	+	0.931984i	$0.618077\pi$
$174$		0			0
$175$	9.92820	−	1.19615i	0.750502	−	0.0904206i
$176$	0.366025	+	1.36603i	0.0275902	+	0.102968i
$177$	14.0000			1.05230
$178$	1.83013	+	6.83013i	0.137174	+	0.511940i
$179$	−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	$-0.435382\pi$
$180$	−2.23205	+	0.133975i	−0.166367	+	0.00998588i
$181$			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
$187$		−	2.00000i		−	0.146254i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	10.9282	−	2.92820i	0.794910	−	0.212995i
$190$	−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	$0.260132\pi$
$192$	9.56218	+	2.56218i	0.690091	+	0.184909i
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.941932	−	0.335805i	$-0.890992\pi$
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.180150	+	0.983639i	$0.557658\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	−0.303340	−	0.952882i	$-0.598102\pi$
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	0.673550	+	0.739141i	$0.264768\pi$
$198$	−1.36603	−	0.366025i	−0.0970792	−	0.0260123i
$199$	−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
$201$	5.46410	−	1.46410i	0.385408	−	0.103270i
$202$	−6.00000	+	10.3923i	−0.422159	+	0.731200i
$203$		0			0
$204$	−1.73205	−	1.00000i	−0.121268	−	0.0700140i
$205$	14.6865	−	16.5622i	1.02575	−	1.15675i
$206$	−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
$210$	4.19615	−	4.73205i	0.289562	−	0.326543i
$211$	−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	$0.877300\pi$
$212$	1.83013	+	6.83013i	0.125694	+	0.469095i
$213$	2.00000			0.137038
$214$	−2.56218	−	9.56218i	−0.175147	−	0.653657i
$215$	3.09808	+	0.633975i	0.211287	+	0.0432367i
$216$	−12.0000	+	12.0000i	−0.816497	+	0.816497i
$217$	13.6603	−	3.66025i	0.927318	−	0.248474i
$218$	−3.29423	+	12.2942i	−0.223113	+	0.832670i
$219$	3.66025	−	13.6603i	0.247337	−	0.923074i
$220$	3.00000	−	1.00000i	0.202260	−	0.0674200i
$221$		0			0
$222$		0			0
$223$	−1.00000	−	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
$225$	−0.598076	−	4.96410i	−0.0398717	−	0.330940i
$226$	5.00000	+	5.00000i	0.332595	+	0.332595i
$227$	10.3923	+	6.00000i	0.689761	+	0.398234i	0.803523	−	0.595274i	$-0.202957\pi$
$227$	10.3923	+	6.00000i	0.689761	+	0.398234i	−0.113761	+	0.993508i	$0.536290\pi$
$228$	8.66025	+	5.00000i	0.573539	+	0.331133i
$229$	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	$0.705232\pi$
$230$	1.90192	−	9.29423i	0.125409	−	0.612843i
$231$	−3.46410	+	2.00000i	−0.227921	+	0.131590i
$232$		0			0
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	0.673592	−	0.739104i	$-0.264751\pi$
$233$	−1.00000	−	1.00000i	−0.0655122	−	0.0655122i	−0.739104	+	0.673592i	$0.764751\pi$
$234$		0			0
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$	2.56218	−	9.56218i	0.166784	−	0.622445i
$237$	−0.732051	+	2.73205i	−0.0475518	+	0.177466i
$238$	−2.73205	+	0.732051i	−0.177093	+	0.0474518i
$239$	−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	$0.293816\pi$
$240$	−0.633975	+	3.09808i	−0.0409229	+	0.199980i
$241$	6.22243	+	23.2224i	0.400822	+	1.49589i	0.811633	+	0.584168i	$0.198579\pi$
$241$	6.22243	+	23.2224i	0.400822	+	1.49589i	−0.410811	+	0.911721i	$0.634754\pi$
$242$	−9.00000			−0.578542
$243$	−2.56218	−	9.56218i	−0.164364	−	0.613414i
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$	−0.401924	−	6.69615i	−0.0256780	−	0.427801i
$246$		−	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
$250$	−7.23205	−	8.52628i	−0.457395	−	0.539249i
$251$	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	$0.646562\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	12.2942	−	3.29423i	0.771409	−	0.206698i
$255$	2.00000	−	4.00000i	0.125245	−	0.250490i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−15.0263	−	4.02628i	−0.937314	−	0.251152i	−0.242343	−	0.970191i	$-0.577916\pi$
$257$	−15.0263	−	4.02628i	−0.937314	−	0.251152i	−0.694971	+	0.719038i	$0.744583\pi$
$258$	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
$263$	−1.36603	−	0.366025i	−0.0842327	−	0.0225701i	0.216457	−	0.976292i	$-0.430550\pi$
$263$	−1.36603	−	0.366025i	−0.0842327	−	0.0225701i	−0.300689	+	0.953722i	$0.597217\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	−15.0000	+	5.00000i	−0.921443	+	0.307148i
$266$	13.6603	−	3.66025i	0.837564	−	0.224425i
$267$	5.00000	−	8.66025i	0.305995	−	0.529999i
$268$		−	4.00000i		−	0.244339i
$269$	−10.3923	−	6.00000i	−0.633630	−	0.365826i	0.148527	−	0.988908i	$-0.452547\pi$
$269$	−10.3923	−	6.00000i	−0.633630	−	0.365826i	−0.782157	+	0.623082i	$0.785880\pi$
$270$	−9.46410	−	8.39230i	−0.575967	−	0.510739i
$271$	12.2942	+	3.29423i	0.746821	+	0.200110i	0.612108	−	0.790774i	$-0.290322\pi$
$271$	12.2942	+	3.29423i	0.746821	+	0.200110i	0.134714	+	0.990885i	$0.456989\pi$
$272$	1.00000	−	1.00000i	0.0606339	−	0.0606339i
$273$		0			0
$274$		−	16.0000i		−	0.966595i
$275$	2.63397	+	6.56218i	0.158835	+	0.395714i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	5.49038	+	20.4904i	0.329885	+	1.23115i	0.909309	+	0.416121i	$0.136611\pi$
$277$	5.49038	+	20.4904i	0.329885	+	1.23115i	−0.579424	+	0.815026i	$0.696722\pi$
$278$	14.0000			0.839664
$279$	−1.83013	−	6.83013i	−0.109567	−	0.408909i
$280$	−7.39230	−	11.1962i	−0.441775	−	0.669098i
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	−0.676650	−	0.736305i	$-0.736569\pi$
$281$	1.00000	−	1.00000i	0.0596550	−	0.0596550i	0.736305	+	0.676650i	$0.236569\pi$
$282$	−8.19615	+	2.19615i	−0.488074	+	0.130779i
$283$	3.29423	−	12.2942i	0.195822	−	0.730816i	−0.796231	−	0.604993i	$-0.793176\pi$
$283$	3.29423	−	12.2942i	0.195822	−	0.730816i	0.992053	−	0.125823i	$-0.0401573\pi$
$284$	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
$288$	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	0.340480	−	0.940252i	$-0.389411\pi$
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	−0.644042	+	0.764990i	$0.722744\pi$
$294$	−3.00000	−	3.00000i	−0.174964	−	0.174964i
$295$	21.6865	+	4.43782i	1.26264	+	0.258380i
$296$		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
$301$	−0.732051	+	2.73205i	−0.0421947	+	0.157473i
$302$	2.56218	−	9.56218i	0.147437	−	0.550242i
$303$	16.3923	−	4.39230i	0.941713	−	0.252331i
$304$	−5.00000	+	5.00000i	−0.286770	+	0.286770i
$305$	−26.1244	+	17.2487i	−1.49588	+	0.987658i
$306$	0.366025	+	1.36603i	0.0209243	+	0.0780905i
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$	0.732051	+	2.73205i	0.0417125	+	0.155673i
$309$	7.00000	+	12.1244i	0.398216	+	0.689730i
$310$	−11.8301	−	10.4904i	−0.671906	−	0.595814i
$311$		−	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	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	17.7583	+	4.75833i	1.00216	+	0.268528i
$315$	4.46410	−	0.267949i	0.251524	−	0.0150972i
$316$	1.73205	+	1.00000i	0.0974355	+	0.0562544i
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786318i	0.919470	−	0.393159i	$-0.128618\pi$
$318$	−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
$322$	8.19615	+	2.19615i	0.456754	+	0.122387i
$323$	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
$328$	−28.6865	−	7.68653i	−1.58395	−	0.424418i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	4.00000	+	2.00000i	0.220193	+	0.110096i
$331$	4.09808	−	1.09808i	0.225251	−	0.0603557i	−0.144428	−	0.989515i	$-0.546134\pi$
$331$	4.09808	−	1.09808i	0.225251	−	0.0603557i	0.369679	+	0.929160i	$0.379468\pi$
$332$	−3.00000	+	5.19615i	−0.164646	+	0.285176i
$333$		0			0
$334$	15.5885	+	9.00000i	0.852962	+	0.492458i
$335$	8.92820	−	0.535898i	0.487800	−	0.0292793i
$336$	−2.73205	−	0.732051i	−0.149046	−	0.0399366i
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	−0.966147	−	0.257992i	$-0.916939\pi$
$337$	−13.0000	+	13.0000i	−0.708155	+	0.708155i	0.257992	+	0.966147i	$0.416939\pi$
$338$		0			0
$339$		−	10.0000i		−	0.543125i
$340$	−2.36603	−	2.09808i	−0.128316	−	0.113784i
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$	−1.83013	−	6.83013i	−0.0989619	−	0.369331i
$343$	20.0000			1.07990
$344$	−1.09808	−	4.09808i	−0.0592043	−	0.220953i
$345$	−11.1962	+	7.39230i	−0.602781	+	0.397988i
$346$	−11.0000	+	11.0000i	−0.591364	+	0.591364i
$347$	−4.09808	+	1.09808i	−0.219996	+	0.0589478i	−0.367133	−	0.930168i	$-0.619661\pi$
$347$	−4.09808	+	1.09808i	−0.219996	+	0.0589478i	0.147137	+	0.989116i	$0.452994\pi$
$348$		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
$353$	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
$355$	3.09808	+	0.633975i	0.164429	+	0.0336479i
$356$	−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	0.680225	−	0.733003i	$-0.261882\pi$
$359$	−1.00000	−	1.00000i	−0.0527780	−	0.0527780i	−0.733003	+	0.680225i	$0.761882\pi$
$360$	−5.59808	+	3.69615i	−0.295045	+	0.194804i
$361$	−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
$366$	−5.12436	+	19.1244i	−0.267854	+	0.999646i
$367$	−0.366025	+	1.36603i	−0.0191064	+	0.0713059i	−0.974821	−	0.222990i	$-0.928418\pi$
$367$	−0.366025	+	1.36603i	−0.0191064	+	0.0713059i	0.955714	+	0.294296i	$0.0950850\pi$
$368$	−4.09808	+	1.09808i	−0.213627	+	0.0572412i
$369$	7.00000	−	7.00000i	0.364405	−	0.364405i
$370$		0			0
$371$	−3.66025	−	13.6603i	−0.190031	−	0.709205i
$372$	10.0000			0.518476
$373$	−5.49038	−	20.4904i	−0.284281	−	1.06095i	−0.949363	−	0.314181i	$-0.898270\pi$
$373$	−5.49038	−	20.4904i	−0.284281	−	1.06095i	0.665082	−	0.746770i	$-0.268397\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$	−1.29423	+	15.7583i	−0.0668337	+	0.813757i
$376$			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	$0.594897\pi$
$380$	11.8301	+	10.4904i	0.606873	+	0.538145i
$381$	−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	$-0.111319\pi$
$384$	−4.09808	+	1.09808i	−0.209129	+	0.0560360i
$385$	−6.00000	+	2.00000i	−0.305788	+	0.101929i
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$	1.36603	+	0.366025i	0.0694390	+	0.0186061i
$388$	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
$393$	27.3205	+	7.32051i	1.37814	+	0.369271i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	−2.00000	+	4.00000i	−0.100631	+	0.201262i
$396$	1.36603	−	0.366025i	0.0686454	−	0.0183935i
$397$	−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
$400$	−1.96410	+	4.59808i	−0.0982051	+	0.229904i
$401$	15.0263	+	4.02628i	0.750377	+	0.201063i	0.613685	−	0.789551i	$-0.289686\pi$
$401$	15.0263	+	4.02628i	0.750377	+	0.201063i	0.136691	+	0.990614i	$0.456353\pi$
$402$	4.00000	−	4.00000i	0.199502	−	0.199502i
$403$		0			0
$404$		−	12.0000i		−	0.597022i
$405$	0.669873	+	11.1603i	0.0332863	+	0.554557i
$406$		0			0
$407$		0			0
$408$	−6.00000			−0.297044
$409$	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	$0.837961\pi$
$410$	4.43782	−	21.6865i	0.219168	−	1.07102i
$411$	−16.0000	+	16.0000i	−0.789222	+	0.789222i
$412$	9.56218	−	2.56218i	0.471095	−	0.126229i
$413$	−5.12436	+	19.1244i	−0.252153	+	0.941048i
$414$	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
$418$	5.00000	+	8.66025i	0.244558	+	0.423587i
$419$	−32.9090	+	19.0000i	−1.60771	+	0.928211i	−0.617827	+	0.786314i	$0.711987\pi$
$419$	−32.9090	+	19.0000i	−1.60771	+	0.928211i	−0.989882	+	0.141896i	$0.954680\pi$
$420$	−1.26795	+	6.19615i	−0.0618696	+	0.302341i
$421$	−11.0000	−	11.0000i	−0.536107	−	0.536107i	0.386276	−	0.922383i	$-0.373761\pi$
$421$	−11.0000	−	11.0000i	−0.536107	−	0.536107i	−0.922383	+	0.386276i	$0.873761\pi$
$422$	−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
$425$	4.36603	−	5.56218i	0.211783	−	0.269805i
$426$	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
$431$	4.75833	−	17.7583i	0.229201	−	0.855389i	−0.751477	−	0.659759i	$-0.770658\pi$
$431$	4.75833	−	17.7583i	0.229201	−	0.855389i	0.980678	−	0.195630i	$-0.0626750\pi$
$432$	−1.46410	+	5.46410i	−0.0704416	+	0.262892i
$433$	23.2224	−	6.22243i	1.11600	−	0.299031i	0.346736	−	0.937963i	$-0.387290\pi$
$433$	23.2224	−	6.22243i	1.11600	−	0.299031i	0.769263	+	0.638932i	$0.220623\pi$
$434$	10.0000	−	10.0000i	0.480015	−	0.480015i
$435$		0			0
$436$	−3.29423	−	12.2942i	−0.157765	−	0.588787i
$437$	−30.0000			−1.43509
$438$	−3.66025	−	13.6603i	−0.174894	−	0.652712i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	6.29423	−	7.09808i	0.300066	−	0.338388i
$441$		−	3.00000i		−	0.142857i
$442$		0			0
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.210108	−	0.977678i	$-0.432619\pi$
$443$	25.0000	−	25.0000i	1.18779	−	1.18779i	0.977678	−	0.210108i	$-0.0673814\pi$
$444$		0			0
$445$	10.4904	−	11.8301i	0.497292	−	0.560802i
$446$	−1.73205	−	1.00000i	−0.0820150	−	0.0473514i
$447$		−	6.00000i		−	0.283790i
$448$	−7.00000	+	12.1244i	−0.330719	+	0.572822i
$449$	−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	$0.448587\pi$
$450$	−3.00000	−	4.00000i	−0.141421	−	0.188562i
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	−6.83013	−	1.83013i	−0.321262	−	0.0860819i
$453$	−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	−0.458942	−	0.888466i	$-0.651771\pi$
$457$	1.73205	−	1.00000i	0.0810219	−	0.0467780i	0.539964	+	0.841688i	$0.318438\pi$
$458$	4.09808	+	1.09808i	0.191491	+	0.0513097i
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$	3.00000	+	9.00000i	0.139876	+	0.419627i
$461$	−23.2224	+	6.22243i	−1.08158	+	0.289808i	−0.755241	−	0.655447i	$-0.772480\pi$
$461$	−23.2224	+	6.22243i	−1.08158	+	0.289808i	−0.326335	+	0.945254i	$0.605814\pi$
$462$	−2.00000	+	3.46410i	−0.0930484	+	0.161165i
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$	1.33975	+	22.3205i	0.0621292	+	1.03509i
$466$	−1.36603	−	0.366025i	−0.0632799	−	0.0169558i
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	−0.883985	−	0.467515i	$-0.845149\pi$
$467$	−9.00000	+	9.00000i	−0.416470	+	0.416470i	0.467515	+	0.883985i	$0.345149\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$	−13.3923	+	0.803848i	−0.617741	+	0.0370787i
$471$	−13.0000	−	22.5167i	−0.599008	−	1.03751i
$472$	−7.68653	−	28.6865i	−0.353801	−	1.32040i
$473$	−2.00000			−0.0919601
$474$	0.732051	+	2.73205i	0.0336242	+	0.125487i
$475$	−21.8301	+	27.8109i	−1.00163	+	1.27605i
$476$	2.00000	−	2.00000i	0.0916698	−	0.0916698i
$477$	−6.83013	+	1.83013i	−0.312730	+	0.0837958i
$478$	−1.09808	+	4.09808i	−0.0502248	+	0.187442i
$479$	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
$483$	−6.00000	−	10.3923i	−0.273009	−	0.472866i
$484$	7.79423	−	4.50000i	0.354283	−	0.204545i
$485$	2.46410	+	3.73205i	0.111889	+	0.169464i
$486$	−7.00000	−	7.00000i	−0.317526	−	0.317526i
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	36.3731	+	21.0000i	1.64653	+	0.950625i
$489$	−4.00000	−	4.00000i	−0.180886	−	0.180886i
$490$	−3.69615	−	5.59808i	−0.166975	−	0.252895i
$491$	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	$0.167980\pi$
$492$	7.00000	+	12.1244i	0.315584	+	0.546608i
$493$		0			0
$494$		0			0
$495$	1.00000	+	3.00000i	0.0449467	+	0.134840i
$496$	−1.83013	+	6.83013i	−0.0821751	+	0.306682i
$497$	−0.732051	+	2.73205i	−0.0328370	+	0.122549i
$498$	−8.19615	+	2.19615i	−0.367278	+	0.0984119i
$499$	−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	$0.280273\pi$
$500$	10.5263	+	3.76795i	0.470750	+	0.168508i
$501$	−6.58846	−	24.5885i	−0.294351	−	1.09853i
$502$	2.00000			0.0892644
$503$	−1.09808	−	4.09808i	−0.0489608	−	0.182724i	0.937115	−	0.349021i	$-0.113486\pi$
$503$	−1.09808	−	4.09808i	−0.0489608	−	0.182724i	−0.986076	+	0.166297i	$0.946819\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	26.7846	−	1.60770i	1.19190	−	0.0715415i
$506$			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	$0.449753\pi$
$510$	−0.267949	−	4.46410i	−0.0118650	−	0.197674i
$511$	17.3205	+	10.0000i	0.766214	+	0.442374i
$512$		−	11.0000i		−	0.486136i
$513$	−20.0000	+	34.6410i	−0.883022	+	1.52944i
$514$	−15.0263	+	4.02628i	−0.662781	+	0.177592i
$515$	7.00000	+	21.0000i	0.308457	+	0.925371i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	8.19615	+	2.19615i	0.360466	+	0.0965867i
$518$		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
$523$	−12.2942	−	3.29423i	−0.537589	−	0.144047i	−0.0201986	−	0.999796i	$-0.506430\pi$
$523$	−12.2942	−	3.29423i	−0.537589	−	0.144047i	−0.517390	+	0.855749i	$0.673097\pi$
$524$	10.0000	−	17.3205i	0.436852	−	0.756650i
$525$	−14.0000	−	2.00000i	−0.611010	−	0.0872872i
$526$	−1.36603	+	0.366025i	−0.0595615	+	0.0159595i
$527$	5.00000	−	8.66025i	0.217803	−	0.377247i
$528$		−	2.00000i		−	0.0870388i
$529$	4.33013	+	2.50000i	0.188266	+	0.108696i
$530$	−10.4904	+	11.8301i	−0.455673	+	0.513868i
$531$	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
$535$	−14.6865	+	16.5622i	−0.634954	+	0.716045i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	7.32051	+	27.3205i	0.315903	+	1.17897i
$538$	−12.0000			−0.517357
$539$	1.09808	+	4.09808i	0.0472975	+	0.176517i
$540$	12.3923	+	2.53590i	0.533280	+	0.109128i
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	−0.486654	−	0.873595i	$-0.661783\pi$
$541$	9.00000	−	9.00000i	0.386940	−	0.386940i	0.873595	+	0.486654i	$0.161783\pi$
$542$	12.2942	−	3.29423i	0.528082	−	0.141499i
$543$	2.92820	−	10.9282i	0.125661	−	0.468974i
$544$	−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	0.488020	−	0.872832i	$-0.337719\pi$
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	−0.872832	+	0.488020i	$0.837719\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	−12.1244	+	7.00000i	−0.517455	+	0.298753i
$550$	5.56218	+	4.36603i	0.237172	+	0.186168i
$551$		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
$561$	−0.732051	+	2.73205i	−0.0309072	+	0.115347i
$562$	0.366025	−	1.36603i	0.0154398	−	0.0576223i
$563$	20.4904	−	5.49038i	0.863567	−	0.231392i	0.200263	−	0.979742i	$-0.435820\pi$
$563$	20.4904	−	5.49038i	0.863567	−	0.231392i	0.663304	+	0.748350i	$0.269154\pi$
$564$	6.00000	−	6.00000i	0.252646	−	0.252646i
$565$	3.16987	−	15.4904i	0.133358	−	0.651685i
$566$	−3.29423	−	12.2942i	−0.138467	−	0.516765i
$567$	−10.0000			−0.419961
$568$	−1.09808	−	4.09808i	−0.0460743	−	0.171951i
$569$	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	$0.793194\pi$
$570$	1.33975	+	22.3205i	0.0561158	+	0.934903i
$571$			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
$575$	−19.6865	+	7.90192i	−0.820985	+	0.329533i
$576$	6.06218	+	3.50000i	0.252591	+	0.145833i
$577$			46.0000i			1.91501i	0.288425	+	0.957503i	$0.406868\pi$
$577$			46.0000i			1.91501i	−0.288425	+	0.957503i	$0.593132\pi$
$578$	7.50000	−	12.9904i	0.311959	−	0.540329i
$579$	24.5885	−	6.58846i	1.02186	−	0.273807i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	2.73205	+	0.732051i	0.113247	+	0.0303445i
$583$	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	−0.569783	−	0.821795i	$-0.692973\pi$
$587$	−3.46410	+	2.00000i	−0.142979	+	0.0825488i	0.426804	+	0.904344i	$0.359639\pi$
$588$	4.09808	+	1.09808i	0.169002	+	0.0452839i
$589$	−25.0000	+	43.3013i	−1.03011	+	1.78420i
$590$	21.0000	−	7.00000i	0.864556	−	0.288185i
$591$	−8.19615	+	2.19615i	−0.337145	+	0.0903376i
$592$		0			0
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$	6.92820	+	4.00000i	0.284268	+	0.164122i
$595$	4.73205	+	4.19615i	0.193995	+	0.172025i
$596$	−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	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	19.6865	−	7.90192i	0.803699	−	0.322595i
$601$	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	$0.551070\pi$
$602$	0.732051	+	2.73205i	0.0298362	+	0.111350i
$603$	4.00000			0.162893
$604$	2.56218	+	9.56218i	0.104254	+	0.389079i
$605$	11.0885	+	16.7942i	0.450810	+	0.682782i
$606$	12.0000	−	12.0000i	0.487467	−	0.487467i
$607$	17.7583	−	4.75833i	0.720788	−	0.193135i	0.120265	−	0.992742i	$-0.461626\pi$
$607$	17.7583	−	4.75833i	0.720788	−	0.193135i	0.600523	+	0.799607i	$0.294959\pi$
$608$	9.15064	−	34.1506i	0.371107	−	1.38499i
$609$		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
$615$	−26.1244	+	17.2487i	−1.05344	+	0.695535i
$616$	6.00000	+	6.00000i	0.241747	+	0.241747i
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	0.831813	−	0.555056i	$-0.187303\pi$
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	−0.0647859	+	0.997899i	$0.520636\pi$
$618$	12.1244	+	7.00000i	0.487713	+	0.281581i
$619$	−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	$-0.501543\pi$
$620$	15.4904	+	3.16987i	0.622109	+	0.127305i
$621$	−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
$626$	3.29423	−	12.2942i	0.131664	−	0.491376i
$627$	3.66025	−	13.6603i	0.146176	−	0.545538i
$628$	−17.7583	+	4.75833i	−0.708635	+	0.189878i
$629$		0			0
$630$	3.73205	−	2.46410i	0.148688	−	0.0981722i
$631$	4.02628	+	15.0263i	0.160284	+	0.598187i	0.998595	+	0.0529946i	$0.0168766\pi$
$631$	4.02628	+	15.0263i	0.160284	+	0.598187i	−0.838311	+	0.545192i	$0.816457\pi$
$632$	6.00000			0.238667
$633$	1.46410	+	5.46410i	0.0581928	+	0.217179i
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$	−21.2942	−	18.8827i	−0.845036	−	0.749337i
$636$		−	10.0000i		−	0.396526i
$637$		0			0
$638$		0			0
$639$	1.36603	+	0.366025i	0.0540391	+	0.0144797i
$640$	−6.69615	+	0.401924i	−0.264689	+	0.0158874i
$641$	−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	$0.823847\pi$
$642$			14.0000i			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	$-0.0672170\pi$
$644$	−8.19615	+	2.19615i	−0.322974	+	0.0865405i
$645$	−4.00000	−	2.00000i	−0.157500	−	0.0787499i
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	1.36603	+	0.366025i	0.0537040	+	0.0143899i	0.285571	−	0.958358i	$-0.407817\pi$
$647$	1.36603	+	0.366025i	0.0537040	+	0.0143899i	−0.231867	+	0.972747i	$0.574483\pi$
$648$	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
$653$	−17.7583	−	4.75833i	−0.694937	−	0.186208i	−0.105975	−	0.994369i	$-0.533796\pi$
$653$	−17.7583	−	4.75833i	−0.694937	−	0.186208i	−0.588962	+	0.808161i	$0.700463\pi$
$654$	9.00000	−	15.5885i	0.351928	−	0.609557i
$655$	40.0000	+	20.0000i	1.56293	+	0.781465i
$656$	−9.56218	+	2.56218i	−0.373340	+	0.100036i
$657$	5.00000	−	8.66025i	0.195069	−	0.337869i
$658$		−	12.0000i		−	0.467809i
$659$	−22.5167	−	13.0000i	−0.877125	−	0.506408i	−0.00741531	−	0.999973i	$-0.502360\pi$
$659$	−22.5167	−	13.0000i	−0.877125	−	0.506408i	−0.869709	+	0.493564i	$0.835694\pi$
$660$	−4.46410	+	0.267949i	−0.173765	+	0.0104299i
$661$	−23.2224	−	6.22243i	−0.903248	−	0.242025i	−0.222837	−	0.974856i	$-0.571532\pi$
$661$	−23.2224	−	6.22243i	−0.903248	−	0.242025i	−0.680411	+	0.732831i	$0.738199\pi$
$662$	3.00000	−	3.00000i	0.116598	−	0.116598i
$663$		0			0
$664$			18.0000i			0.698535i
$665$	−23.6603	−	20.9808i	−0.917505	−	0.813599i
$666$		0			0
$667$		0			0
$668$	−18.0000			−0.696441
$669$	0.732051	+	2.73205i	0.0283027	+	0.105627i
$670$	7.46410	−	4.92820i	0.288363	−	0.190393i
$671$	14.0000	−	14.0000i	0.540464	−	0.540464i
$672$	13.6603	−	3.66025i	0.526956	−	0.141197i
$673$	5.49038	−	20.4904i	0.211639	−	0.789846i	−0.775684	−	0.631121i	$-0.782595\pi$
$673$	5.49038	−	20.4904i	0.211639	−	0.789846i	0.987323	−	0.158725i	$-0.0507383\pi$
$674$	−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	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$	−5.00000	−	8.66025i	−0.192024	−	0.332595i
$679$	−3.46410	+	2.00000i	−0.132940	+	0.0767530i
$680$	−9.29423	−	1.90192i	−0.356417	−	0.0729354i
$681$	−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	0.287819	−	0.957685i	$-0.407070\pi$
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$684$	5.00000	+	5.00000i	0.191180	+	0.191180i
$685$	−29.8564	+	19.7128i	−1.14075	+	0.753188i
$686$	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
$691$	−1.09808	+	4.09808i	−0.0417728	+	0.155898i	−0.983662	−	0.180026i	$-0.942382\pi$
$691$	−1.09808	+	4.09808i	−0.0417728	+	0.155898i	0.941889	+	0.335924i	$0.109049\pi$
$692$	4.02628	−	15.0263i	0.153056	−	0.571213i
$693$	−2.73205	+	0.732051i	−0.103782	+	0.0278083i
$694$	−3.00000	+	3.00000i	−0.113878	+	0.113878i
$695$	−17.2487	−	26.1244i	−0.654281	−	0.990953i
$696$		0			0
$697$	14.0000			0.530288
$698$	3.29423	+	12.2942i	0.124688	+	0.465343i
$699$	1.00000	+	1.73205i	0.0378235	+	0.0655122i
$700$	−3.92820	+	9.19615i	−0.148472	+	0.347582i
$701$		−	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
$705$	14.1962	+	12.5885i	0.534658	+	0.474109i
$706$	10.3923	+	6.00000i	0.391120	+	0.225813i
$707$			24.0000i			0.902613i
$708$	−7.00000	+	12.1244i	−0.263076	+	0.455661i
$709$	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	$0.136862\pi$
$710$	3.00000	−	1.00000i	0.112588	−	0.0375293i
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$	−20.4904	−	5.49038i	−0.767909	−	0.205761i
$713$	−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
$718$	−1.36603	−	0.366025i	−0.0509796	−	0.0136599i
$719$	−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
$721$	−19.1244	+	5.12436i	−0.712228	+	0.190841i
$722$	−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
$726$	12.2942	+	3.29423i	0.456282	+	0.122260i
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.368418	−	0.929660i	$-0.379900\pi$
$727$	35.0000	−	35.0000i	1.29808	−	1.29808i	0.929660	−	0.368418i	$-0.120100\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$	−1.33975	−	22.3205i	−0.0495862	−	0.826119i
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$	−5.12436	−	19.1244i	−0.189402	−	0.706857i
$733$	−4.00000			−0.147743			−0.0738717	−	0.997268i	$-0.523536\pi$
$733$	−4.00000			−0.147743			−0.0738717	+	0.997268i	$0.523536\pi$
$734$	0.366025	+	1.36603i	0.0135102	+	0.0504209i
$735$	−1.90192	+	9.29423i	−0.0701535	+	0.342823i
$736$	15.0000	−	15.0000i	0.552907	−	0.552907i
$737$	−5.46410	+	1.46410i	−0.201273	+	0.0539309i
$738$	2.56218	−	9.56218i	0.0943151	−	0.351989i
$739$	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
$743$	−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
$745$	1.90192	−	9.29423i	0.0696811	−	0.340514i
$746$	−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
$750$	6.75833	+	14.2942i	0.246779	+	0.521951i
$751$	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	$-0.0323332\pi$
$752$	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
$756$	−2.92820	+	10.9282i	−0.106498	+	0.397455i
$757$	−12.8109	+	47.8109i	−0.465620	+	1.73772i	0.189207	+	0.981937i	$0.439408\pi$
$757$	−12.8109	+	47.8109i	−0.465620	+	1.73772i	−0.654827	+	0.755779i	$0.727258\pi$
$758$	−1.36603	+	0.366025i	−0.0496163	+	0.0132946i
$759$	6.00000	−	6.00000i	0.217786	−	0.217786i
$760$	46.4711	+	9.50962i	1.68569	+	0.344950i
$761$	−2.56218	−	9.56218i	−0.0928789	−	0.346629i	0.903810	−	0.427933i	$-0.140758\pi$
$761$	−2.56218	−	9.56218i	−0.0928789	−	0.346629i	−0.996689	+	0.0813044i	$0.974091\pi$
$762$	−18.0000			−0.652071
$763$	6.58846	+	24.5885i	0.238518	+	0.890162i
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$	2.09808	−	2.36603i	0.0758561	−	0.0855438i
$766$		−	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	$0.708265\pi$
$770$	−4.19615	+	4.73205i	−0.151219	+	0.170531i
$771$	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	$-0.0285181\pi$
$774$	1.36603	−	0.366025i	0.0491008	−	0.0131565i
$775$	−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
$786$	27.3205	−	7.32051i	0.974490	−	0.261114i
$787$	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
$790$	0.267949	+	4.46410i	0.00953320	+	0.158826i
$791$	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
$795$	22.3205	−	1.33975i	0.791627	−	0.0475159i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	−6.22243	−	23.2224i	−0.220410	−	0.822581i	−0.984192	−	0.177106i	$-0.943326\pi$
$797$	−6.22243	−	23.2224i	−0.220410	−	0.822581i	0.763782	−	0.645474i	$-0.223340\pi$
$798$	−20.0000			−0.707992
$799$	−2.19615	−	8.19615i	−0.0776943	−	0.289959i
$800$	−2.99038	−	24.8205i	−0.105726	−	0.877537i
$801$	5.00000	−	5.00000i	0.176666	−	0.176666i
$802$	15.0263	−	4.02628i	0.530596	−	0.142173i
$803$	−3.66025	+	13.6603i	−0.129168	+	0.482060i
$804$	−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
$808$	−18.0000	−	31.1769i	−0.633238	−	1.09680i
$809$	24.2487	−	14.0000i	0.852539	−	0.492214i	−0.00896753	−	0.999960i	$-0.502854\pi$
$809$	24.2487	−	14.0000i	0.852539	−	0.492214i	0.861507	+	0.507746i	$0.169521\pi$
$810$	6.16025	+	9.33013i	0.216449	+	0.327827i
$811$	−27.0000	−	27.0000i	−0.948098	−	0.948098i	0.0506198	−	0.998718i	$-0.483880\pi$
$811$	−27.0000	−	27.0000i	−0.948098	−	0.948098i	−0.998718	+	0.0506198i	$0.983880\pi$
$812$		0			0
$813$	−15.5885	−	9.00000i	−0.546711	−	0.315644i
$814$		0			0
$815$	−4.92820	−	7.46410i	−0.172627	−	0.261456i
$816$	−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
$821$	3.29423	−	12.2942i	0.114969	−	0.429072i	−0.884315	−	0.466890i	$-0.845374\pi$
$821$	3.29423	−	12.2942i	0.114969	−	0.429072i	0.999285	+	0.0378188i	$0.0120410\pi$
$822$	−5.85641	+	21.8564i	−0.204266	+	0.762330i
$823$	−12.2942	+	3.29423i	−0.428550	+	0.114830i	−0.466645	−	0.884445i	$-0.654538\pi$
$823$	−12.2942	+	3.29423i	−0.428550	+	0.114830i	0.0380955	+	0.999274i	$0.487871\pi$
$824$	21.0000	−	21.0000i	0.731570	−	0.731570i
$825$	−1.19615	−	9.92820i	−0.0416447	−	0.345656i
$826$	5.12436	+	19.1244i	0.178299	+	0.665421i
$827$	−46.0000			−1.59958			−0.799788	−	0.600282i	$-0.795055\pi$
$827$	−46.0000			−1.59958			−0.799788	+	0.600282i	$0.795055\pi$
$828$	1.09808	+	4.09808i	0.0381608	+	0.142418i
$829$	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	$0.632290\pi$
$830$	−13.3923	+	0.803848i	−0.464854	+	0.0279020i
$831$		−	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
$835$	−2.41154	−	40.1769i	−0.0834549	−	1.39038i
$836$	−8.66025	−	5.00000i	−0.299521	−	0.172929i
$837$			40.0000i			1.38260i
$838$	−19.0000	+	32.9090i	−0.656344	+	1.13682i
$839$	−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	$0.742755\pi$
$840$	6.00000	+	18.0000i	0.207020	+	0.621059i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$	−15.0263	−	4.02628i	−0.517840	−	0.138755i
$843$	−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
$848$	6.83013	+	1.83013i	0.234548	+	0.0628468i
$849$	−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	$-0.853164\pi$
$853$		−	26.0000i		−	0.890223i	0.895475	−	0.445112i	$-0.146836\pi$
$854$	−24.2487	−	14.0000i	−0.829774	−	0.479070i
$855$	−10.4904	+	11.8301i	−0.358763	+	0.404582i
$856$	28.6865	+	7.68653i	0.980486	+	0.262720i
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	−0.654009	−	0.756487i	$-0.726914\pi$
$857$	3.00000	−	3.00000i	0.102478	−	0.102478i	0.756487	+	0.654009i	$0.226914\pi$
$858$		0			0
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	−2.09808	+	2.36603i	−0.0715438	+	0.0806808i
$861$	−14.0000	−	24.2487i	−0.477119	−	0.826394i
$862$	−4.75833	−	17.7583i	−0.162069	−	0.604851i
$863$	−30.0000			−1.02121			−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000			−1.02121			−0.510606	+	0.859815i	$0.670579\pi$
$864$	−7.32051	−	27.3205i	−0.249049	−	0.929463i
$865$	34.0788	+	6.97372i	1.15872	+	0.237114i
$866$	17.0000	−	17.0000i	0.577684	−	0.577684i
$867$	−20.4904	+	5.49038i	−0.695890	+	0.186463i
$868$	−3.66025	+	13.6603i	−0.124237	+	0.463659i
$869$	0.732051	−	2.73205i	0.0248331	−	0.0926785i
$870$		0			0
$871$		0			0
$872$	−27.0000	−	27.0000i	−0.914335	−	0.914335i
$873$	1.00000	+	1.73205i	0.0338449	+	0.0586210i
$874$	−25.9808	+	15.0000i	−0.878812	+	0.507383i
$875$	−21.0526	−	7.53590i	−0.711706	−	0.254760i
$876$	10.0000	+	10.0000i	0.337869	+	0.337869i
$877$	−32.9090	−	19.0000i	−1.11126	−	0.641584i	−0.172102	−	0.985079i	$-0.555056\pi$
$877$	−32.9090	−	19.0000i	−1.11126	−	0.641584i	−0.939155	+	0.343495i	$0.888389\pi$
$878$		0			0
$879$	6.00000	+	6.00000i	0.202375	+	0.202375i
$880$	0.633975	−	3.09808i	0.0213713	−	0.104436i
$881$	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	$-0.00643924\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	−39.0000	−	39.0000i	−1.31245	−	1.31245i	−0.919601	−	0.392853i	$-0.871488\pi$
$883$	−39.0000	−	39.0000i	−1.31245	−	1.31245i	−0.392853	−	0.919601i	$-0.628512\pi$
$884$		0			0
$885$	−28.0000	−	14.0000i	−0.941210	−	0.470605i
$886$	9.15064	−	34.1506i	0.307422	−	1.14731i
$887$	−0.366025	+	1.36603i	−0.0122899	+	0.0458666i	−0.971799	−	0.235813i	$-0.924225\pi$
$887$	−0.366025	+	1.36603i	−0.0122899	+	0.0458666i	0.959509	+	0.281679i	$0.0908915\pi$
$888$		0			0
$889$	18.0000	−	18.0000i	0.603701	−	0.603701i
$890$	3.16987	−	15.4904i	0.106254	−	0.519239i
$891$	−1.83013	−	6.83013i	−0.0613116	−	0.228818i
$892$	2.00000			0.0669650
$893$	10.9808	+	40.9808i	0.367457	+	1.37137i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$	2.67949	+	44.6410i	0.0895655	+	1.49218i
$896$		−	6.00000i		−	0.200446i
$897$		0			0
$898$	−3.00000	+	3.00000i	−0.100111	+	0.100111i
$899$		0			0
$900$	4.59808	+	1.96410i	0.153269	+	0.0654701i
$901$	−8.66025	−	5.00000i	−0.288515	−	0.166574i
$902$			14.0000i			0.466149i
$903$	2.00000	−	3.46410i	0.0665558	−	0.115278i
$904$	−20.4904	+	5.49038i	−0.681500	+	0.182607i
$905$	8.00000	−	16.0000i	0.265929	−	0.531858i
$906$	−7.00000	+	12.1244i	−0.232559	+	0.402805i
$907$	−53.2750	−	14.2750i	−1.76897	−	0.473993i	−0.780465	−	0.625200i	$-0.785018\pi$
$907$	−53.2750	−	14.2750i	−1.76897	−	0.473993i	−0.988502	+	0.151206i	$0.951684\pi$
$908$	−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
$913$	8.19615	+	2.19615i	0.271253	+	0.0726820i
$914$	1.00000	−	1.73205i	0.0330771	−	0.0572911i
$915$	42.0000	−	14.0000i	1.38848	−	0.462826i
$916$	−4.09808	+	1.09808i	−0.135404	+	0.0362815i
$917$	−20.0000	+	34.6410i	−0.660458	+	1.14395i
$918$		−	8.00000i		−	0.264039i
$919$	8.66025	+	5.00000i	0.285675	+	0.164935i	0.635990	−	0.771697i	$-0.280592\pi$
$919$	8.66025	+	5.00000i	0.285675	+	0.164935i	−0.350315	+	0.936632i	$0.613925\pi$
$920$	21.2942	+	18.8827i	0.702050	+	0.622544i
$921$	−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
$927$	2.56218	+	9.56218i	0.0841530	+	0.314063i
$928$		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	$0.771365\pi$
$930$	12.3205	+	18.6603i	0.404005	+	0.611894i
$931$	−15.0000	+	15.0000i	−0.491605	+	0.491605i
$932$	1.36603	−	0.366025i	0.0447456	−	0.0119896i
$933$	−2.19615	+	8.19615i	−0.0718988	+	0.268330i
$934$	−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	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$	4.00000	+	6.92820i	0.130605	+	0.226214i
$939$	−15.5885	+	9.00000i	−0.508710	+	0.293704i
$940$	11.1962	−	7.39230i	0.365178	−	0.241110i
$941$	21.0000	+	21.0000i	0.684580	+	0.684580i	0.961029	−	0.276448i	$-0.0891575\pi$
$941$	21.0000	+	21.0000i	0.684580	+	0.684580i	−0.276448	+	0.961029i	$0.589157\pi$
$942$	−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
$945$	−24.7846	−	5.07180i	−0.806243	−	0.164986i
$946$	−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
$951$	−5.12436	+	19.1244i	−0.166169	+	0.620150i
$952$	2.19615	−	8.19615i	0.0711777	−	0.265639i
$953$	17.7583	−	4.75833i	0.575249	−	0.154137i	0.0405460	−	0.999178i	$-0.487090\pi$
$953$	17.7583	−	4.75833i	0.575249	−	0.154137i	0.534703	+	0.845040i	$0.320424\pi$
$954$	−5.00000	+	5.00000i	−0.161881	+	0.161881i
$955$	14.9282	−	9.85641i	0.483065	−	0.318946i
$956$	−1.09808	−	4.09808i	−0.0355143	−	0.132541i
$957$		0			0
$958$	−2.56218	−	9.56218i	−0.0827802	−	0.308940i
$959$	−16.0000	−	27.7128i	−0.516667	−	0.894893i
$960$	−16.5622	−	14.6865i	−0.534542	−	0.474006i
$961$			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
$965$	40.1769	−	2.41154i	1.29334	−	0.0776303i
$966$	−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
$969$	−13.6603	+	3.66025i	−0.438831	+	0.117584i
$970$	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	$-0.246175\pi$
$972$	9.56218	+	2.56218i	0.306707	+	0.0821819i
$973$	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	$-0.207513\pi$
$977$	53.6936	−	31.0000i	1.71781	−	0.991778i	0.922890	−	0.385063i	$-0.125820\pi$
$978$	−5.46410	−	1.46410i	−0.174723	−	0.0468168i
$979$	−5.00000	+	8.66025i	−0.159801	+	0.276783i
$980$	6.00000	+	3.00000i	0.191663	+	0.0958315i
$981$	12.2942	−	3.29423i	0.392525	−	0.105177i
$982$	11.0000	−	19.0526i	0.351024	−	0.607992i
$983$			24.0000i			0.765481i	0.923856	+	0.382741i	$0.125020\pi$
$983$			24.0000i			0.765481i	−0.923856	+	0.382741i	$0.874980\pi$
$984$	36.3731	+	21.0000i	1.15953	+	0.669456i
$985$	−13.3923	+	0.803848i	−0.426714	+	0.0256127i
$986$		0			0
$987$	−12.0000	+	12.0000i	−0.381964	+	0.381964i
$988$		0			0
$989$		−	6.00000i		−	0.190789i
$990$	2.36603	+	2.09808i	0.0751972	+	0.0666812i
$991$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$991$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$992$	−9.15064	−	34.1506i	−0.290533	−	1.08428i
$993$	−6.00000			−0.190404
$994$	0.732051	+	2.73205i	0.0232192	+	0.0866554i
$995$	14.9282	−	9.85641i	0.473256	−	0.312469i
$996$	6.00000	−	6.00000i	0.190117	−	0.190117i
$997$	−12.2942	+	3.29423i	−0.389362	+	0.104329i	−0.448189	−	0.893939i	$-0.647931\pi$
$997$	−12.2942	+	3.29423i	−0.389362	+	0.104329i	0.0588266	+	0.998268i	$0.481264\pi$
$998$	−1.09808	+	4.09808i	−0.0347590	+	0.129722i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.a.427.1		4
5.3	odd	4		845.2.o.a.258.1		4
13.2	odd	12		65.2.k.a.57.1	yes	2
13.3	even	3		65.2.f.a.47.1	yes	2
13.4	even	6		845.2.t.b.657.1		4
13.5	odd	4		845.2.o.a.587.1		4
13.6	odd	12		845.2.o.a.357.1		4
13.7	odd	12		845.2.o.b.357.1		4
13.8	odd	4		845.2.o.b.587.1		4
13.9	even	3	inner	845.2.t.a.657.1		4
13.10	even	6		845.2.f.a.437.1		2
13.11	odd	12		845.2.k.a.577.1		2
13.12	even	2		845.2.t.b.427.1		4
39.2	even	12		585.2.w.b.577.1		2
39.29	odd	6		585.2.n.c.307.1		2
52.3	odd	6		1040.2.cd.b.177.1		2
52.15	even	12		1040.2.bg.a.577.1		2
65.2	even	12		325.2.f.a.18.1		2
65.3	odd	12		65.2.k.a.8.1	yes	2
65.8	even	4		845.2.t.b.418.1		4
65.18	even	4	inner	845.2.t.a.418.1		4
65.23	odd	12		845.2.k.a.268.1		2
65.28	even	12		65.2.f.a.18.1	✓	2
65.29	even	6		325.2.f.a.307.1		2
65.33	even	12		845.2.t.b.188.1		4
65.38	odd	4		845.2.o.b.258.1		4
65.42	odd	12		325.2.k.a.268.1		2
65.43	odd	12		845.2.o.b.488.1		4
65.48	odd	12		845.2.o.a.488.1		4
65.54	odd	12		325.2.k.a.57.1		2
65.58	even	12	inner	845.2.t.a.188.1		4
65.63	even	12		845.2.f.a.408.1		2
195.68	even	12		585.2.w.b.73.1		2
195.158	odd	12		585.2.n.c.343.1		2
260.3	even	12		1040.2.bg.a.593.1		2
260.223	odd	12		1040.2.cd.b.993.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	65.28	even	12
65.2.f.a.47.1	yes	2	13.3	even	3
65.2.k.a.8.1	yes	2	65.3	odd	12
65.2.k.a.57.1	yes	2	13.2	odd	12
325.2.f.a.18.1		2	65.2	even	12
325.2.f.a.307.1		2	65.29	even	6
325.2.k.a.57.1		2	65.54	odd	12
325.2.k.a.268.1		2	65.42	odd	12
585.2.n.c.307.1		2	39.29	odd	6
585.2.n.c.343.1		2	195.158	odd	12
585.2.w.b.73.1		2	195.68	even	12
585.2.w.b.577.1		2	39.2	even	12
845.2.f.a.408.1		2	65.63	even	12
845.2.f.a.437.1		2	13.10	even	6
845.2.k.a.268.1		2	65.23	odd	12
845.2.k.a.577.1		2	13.11	odd	12
845.2.o.a.258.1		4	5.3	odd	4
845.2.o.a.357.1		4	13.6	odd	12
845.2.o.a.488.1		4	65.48	odd	12
845.2.o.a.587.1		4	13.5	odd	4
845.2.o.b.258.1		4	65.38	odd	4
845.2.o.b.357.1		4	13.7	odd	12
845.2.o.b.488.1		4	65.43	odd	12
845.2.o.b.587.1		4	13.8	odd	4
845.2.t.a.188.1		4	65.58	even	12	inner
845.2.t.a.418.1		4	65.18	even	4	inner
845.2.t.a.427.1		4	1.1	even	1	trivial
845.2.t.a.657.1		4	13.9	even	3	inner
845.2.t.b.188.1		4	65.33	even	12
845.2.t.b.418.1		4	65.8	even	4
845.2.t.b.427.1		4	13.12	even	2
845.2.t.b.657.1		4	13.4	even	6
1040.2.bg.a.577.1		2	52.15	even	12
1040.2.bg.a.593.1		2	260.3	even	12
1040.2.cd.b.177.1		2	52.3	odd	6
1040.2.cd.b.993.1		2	260.223	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-1.36603 - 0.366025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 1.00000i) q^{5} +(-1.36603 + 0.366025i) q^{6} +(1.00000 - 1.73205i) q^{7} +3.00000i q^{8} +(-0.866025 - 0.500000i) q^{9} +(-2.23205 + 0.133975i) q^{10} +(1.36603 + 0.366025i) q^{11} +(1.00000 - 1.00000i) q^{12} -2.00000i q^{14} +(2.36603 + 2.09808i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.366025 - 1.36603i) q^{17} -1.00000 q^{18} +(1.83013 + 6.83013i) q^{19} +(1.86603 - 1.23205i) q^{20} +(-2.00000 + 2.00000i) q^{21} +(1.36603 - 0.366025i) q^{22} +(-1.09808 + 4.09808i) q^{23} +(1.09808 - 4.09808i) q^{24} +(3.00000 + 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +(1.00000 + 1.73205i) q^{28} +(3.09808 + 0.633975i) 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} +(-3.73205 + 2.46410i) 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} +(-0.732051 + 2.73205i) q^{42} +(-1.36603 + 0.366025i) q^{43} +(-1.00000 + 1.00000i) q^{44} +(1.23205 + 1.86603i) q^{45} +(1.09808 + 4.09808i) q^{46} +6.00000 q^{47} +(-0.366025 - 1.36603i) q^{48} +(1.50000 + 2.59808i) q^{49} +(4.59808 + 1.96410i) q^{50} +2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(5.46410 + 1.46410i) q^{54} +(-2.36603 - 2.09808i) q^{55} +(5.19615 + 3.00000i) q^{56} -10.0000i q^{57} +(-9.56218 + 2.56218i) q^{59} +(-3.00000 + 1.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(6.83013 + 1.83013i) q^{62} +(-1.73205 + 1.00000i) q^{63} -7.00000 q^{64} -2.00000 q^{66} +(-3.46410 + 2.00000i) q^{67} +(1.36603 + 0.366025i) q^{68} +(3.00000 - 5.19615i) q^{69} +(-2.00000 + 4.00000i) q^{70} +(-1.36603 + 0.366025i) q^{71} +(1.50000 - 2.59808i) q^{72} +10.0000i q^{73} +(-2.63397 - 6.56218i) q^{75} +(-6.83013 - 1.83013i) q^{76} +(2.00000 - 2.00000i) q^{77} -2.00000i q^{79} +(-0.133975 - 2.23205i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(2.56218 + 9.56218i) q^{82} +6.00000 q^{83} +(-0.732051 - 2.73205i) q^{84} +(-0.633975 + 3.09808i) q^{85} +(-1.00000 + 1.00000i) q^{86} +(-1.09808 + 4.09808i) q^{88} +(-1.83013 + 6.83013i) 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} +(3.16987 - 15.4904i) 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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