LMFDB - Embedded newform 845.2.o.b.587.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			587.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.587
Dual form			845.2.o.b.488.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.36603 - 0.366025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(-1.73205 - 1.00000i) q^{7} +3.00000 q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.23205 - 0.133975i) q^{10} +(0.366025 - 1.36603i) q^{11} +(-1.00000 + 1.00000i) q^{12} -2.00000i q^{14} +(-2.09808 + 2.36603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.366025 + 1.36603i) q^{17} -1.00000i q^{18} +(-6.83013 + 1.83013i) q^{19} +(-1.23205 - 1.86603i) q^{20} +(2.00000 + 2.00000i) q^{21} +(1.36603 - 0.366025i) q^{22} +(1.09808 - 4.09808i) q^{23} +(-4.09808 - 1.09808i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +(-1.73205 + 1.00000i) q^{28} +(-3.09808 - 0.633975i) q^{30} +(-5.00000 + 5.00000i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 + 1.00000i) q^{34} +(-3.73205 + 2.46410i) 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} +(-0.732051 + 2.73205i) q^{42} +(1.36603 - 0.366025i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-1.86603 + 1.23205i) q^{45} +(4.09808 - 1.09808i) q^{46} -6.00000i q^{47} +(-0.366025 - 1.36603i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(1.96410 - 4.59808i) q^{50} -2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-1.46410 + 5.46410i) q^{54} +(-2.36603 - 2.09808i) q^{55} +(-5.19615 - 3.00000i) q^{56} +10.0000 q^{57} +(2.56218 + 9.56218i) q^{59} +(1.00000 + 3.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(-6.83013 - 1.83013i) q^{62} +(1.00000 + 1.73205i) q^{63} +7.00000 q^{64} -2.00000 q^{66} +(-2.00000 - 3.46410i) q^{67} +(1.36603 + 0.366025i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(-4.00000 - 2.00000i) q^{70} +(-0.366025 - 1.36603i) q^{71} +(-2.59808 - 1.50000i) q^{72} +10.0000 q^{73} +(2.63397 + 6.56218i) q^{75} +(-1.83013 + 6.83013i) q^{76} +(-2.00000 + 2.00000i) q^{77} -2.00000i q^{79} +(2.23205 - 0.133975i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(-2.56218 - 9.56218i) q^{82} +6.00000i q^{83} +(2.73205 - 0.732051i) q^{84} +(3.09808 + 0.633975i) q^{85} +(1.00000 + 1.00000i) q^{86} +(1.09808 - 4.09808i) q^{88} +(6.83013 + 1.83013i) q^{89} +(-2.00000 - 1.00000i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(8.66025 - 5.00000i) q^{93} +(5.19615 - 3.00000i) q^{94} +(-3.16987 + 15.4904i) q^{95} +(-5.00000 + 5.00000i) q^{96} +(1.00000 - 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 10 q^{19} + 2 q^{20} + 8 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 10 * q^19 + 2 * q^20 + 8 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 12 * q^25 + 16 * q^27 - 2 * q^30 - 20 * q^31 + 10 * q^32 - 4 * q^33 - 4 * q^34 - 8 * q^35 - 20 * q^38 + 12 * q^40 - 14 * q^41 + 4 * q^42 + 2 * q^43 - 4 * q^44 - 4 * q^45 + 6 * q^46 + 2 * q^48 - 6 * q^49 - 6 * q^50 + 20 * q^53 + 8 * q^54 - 6 * q^55 + 40 * q^57 - 14 * q^59 + 4 * q^60 + 28 * q^61 - 10 * q^62 + 4 * q^63 + 28 * q^64 - 8 * q^66 - 8 * q^67 + 2 * q^68 - 12 * q^69 - 16 * q^70 + 2 * q^71 + 40 * q^73 + 14 * q^75 + 10 * q^76 - 8 * q^77 + 2 * q^80 - 10 * q^81 + 14 * q^82 + 4 * q^84 + 2 * q^85 + 4 * q^86 - 6 * q^88 + 10 * q^89 - 8 * q^90 - 12 * q^92 - 30 * q^95 - 20 * q^96 + 4 * q^97 + 6 * q^98 - 4 * q^99

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	−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
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$5$	1.00000	−	2.00000i	0.447214	−	0.894427i
$6$	−0.366025	−	1.36603i	−0.149429	−	0.557678i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$	3.00000			1.06066
$9$	−0.866025	−	0.500000i	−0.288675	−	0.166667i
$10$	2.23205	−	0.133975i	0.705836	−	0.0423665i
$11$	0.366025	−	1.36603i	0.110361	−	0.411872i	−0.888537	−	0.458804i	$-0.848278\pi$
$11$	0.366025	−	1.36603i	0.110361	−	0.411872i	0.998898	+	0.0469323i	$0.0149445\pi$
$12$	−1.00000	+	1.00000i	−0.288675	+	0.288675i
$13$		0			0
$13$		0			0
$14$		−	2.00000i		−	0.534522i
$15$	−2.09808	+	2.36603i	−0.541721	+	0.610905i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	0.366025	+	1.36603i	0.0887742	+	0.331310i	0.996002	−	0.0893296i	$-0.0284724\pi$
$17$	0.366025	+	1.36603i	0.0887742	+	0.331310i	−0.907228	+	0.420639i	$0.861806\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−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	$0.717801\pi$
$20$	−1.23205	−	1.86603i	−0.275495	−	0.417256i
$21$	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	$-0.770820\pi$
$23$	1.09808	−	4.09808i	0.228965	−	0.854508i	0.980777	−	0.195131i	$-0.0625132\pi$
$24$	−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
$28$	−1.73205	+	1.00000i	−0.327327	+	0.188982i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	−3.09808	−	0.633975i	−0.565629	−	0.115747i
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	−0.995261	−	0.0972349i	$-0.969000\pi$
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	0.0972349	+	0.995261i	$0.469000\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	−1.00000	+	1.00000i	−0.171499	+	0.171499i
$35$	−3.73205	+	2.46410i	−0.630832	+	0.416509i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$37$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$38$	−5.00000	−	5.00000i	−0.811107	−	0.811107i
$39$		0			0
$40$	3.00000	−	6.00000i	0.474342	−	0.948683i
$41$	−9.56218	−	2.56218i	−1.49336	−	0.400145i	−0.582491	−	0.812837i	$-0.697922\pi$
$41$	−9.56218	−	2.56218i	−1.49336	−	0.400145i	−0.910870	+	0.412692i	$0.864588\pi$
$42$	−0.732051	+	2.73205i	−0.112958	+	0.421565i
$43$	1.36603	−	0.366025i	0.208317	−	0.0558184i	−0.153151	−	0.988203i	$-0.548942\pi$
$43$	1.36603	−	0.366025i	0.208317	−	0.0558184i	0.361468	+	0.932384i	$0.382276\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$	−1.86603	+	1.23205i	−0.278171	+	0.183663i
$46$	4.09808	−	1.09808i	0.604228	−	0.161903i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	−0.366025	−	1.36603i	−0.0528312	−	0.197169i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	1.96410	−	4.59808i	0.277766	−	0.650266i
$51$		−	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	$0.0885855\pi$
$54$	−1.46410	+	5.46410i	−0.199239	+	0.743570i
$55$	−2.36603	−	2.09808i	−0.319035	−	0.282905i
$56$	−5.19615	−	3.00000i	−0.694365	−	0.400892i
$57$	10.0000			1.32453
$58$		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	$0.693773\pi$
$60$	1.00000	+	3.00000i	0.129099	+	0.387298i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$	−6.83013	−	1.83013i	−0.867427	−	0.232426i
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$	7.00000			0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	1.36603	+	0.366025i	0.165655	+	0.0443871i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	−4.00000	−	2.00000i	−0.478091	−	0.239046i
$71$	−0.366025	−	1.36603i	−0.0434392	−	0.162117i	0.940799	−	0.338965i	$-0.110077\pi$
$71$	−0.366025	−	1.36603i	−0.0434392	−	0.162117i	−0.984238	+	0.176847i	$0.943410\pi$
$72$	−2.59808	−	1.50000i	−0.306186	−	0.176777i
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$		0			0
$75$	2.63397	+	6.56218i	0.304145	+	0.757735i
$76$	−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	$-0.964111\pi$
$79$		−	2.00000i		−	0.225018i	0.993651	−	0.112509i	$-0.0358886\pi$
$80$	2.23205	−	0.133975i	0.249551	−	0.0149788i
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$	−2.56218	−	9.56218i	−0.282945	−	1.05597i
$83$			6.00000i			0.658586i	0.944228	+	0.329293i	$0.106810\pi$
$83$			6.00000i			0.658586i	−0.944228	+	0.329293i	$0.893190\pi$
$84$	2.73205	−	0.732051i	0.298091	−	0.0798733i
$85$	3.09808	+	0.633975i	0.336034	+	0.0687642i
$86$	1.00000	+	1.00000i	0.107833	+	0.107833i
$87$		0			0
$88$	1.09808	−	4.09808i	0.117055	−	0.436856i
$89$	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
$93$	8.66025	−	5.00000i	0.898027	−	0.518476i
$94$	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
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	1.50000	−	2.59808i	0.151523	−	0.262445i
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$	−4.96410	+	0.598076i	−0.496410	+	0.0598076i
$101$	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	$0.129684\pi$
$102$	1.73205	−	1.00000i	0.171499	−	0.0990148i
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	0.962172	−	0.272442i	$-0.0878312\pi$
$103$	7.00000	+	7.00000i	0.689730	+	0.689730i	−0.272442	+	0.962172i	$0.587831\pi$
$104$		0			0
$105$	6.00000	−	2.00000i	0.585540	−	0.195180i
$106$	6.83013	+	1.83013i	0.663401	+	0.177758i
$107$	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	0.129532	−	0.991575i	$-0.458653\pi$
$109$	−9.00000	−	9.00000i	−0.862044	−	0.862044i	−0.991575	+	0.129532i	$0.958653\pi$
$110$	0.633975	−	3.09808i	0.0604471	−	0.295390i
$111$		0			0
$112$		−	2.00000i		−	0.188982i
$113$	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
$115$	−7.09808	−	6.29423i	−0.661899	−	0.586940i
$116$		0			0
$117$		0			0
$118$	−7.00000	+	7.00000i	−0.644402	+	0.644402i
$119$	0.732051	−	2.73205i	0.0671070	−	0.250447i
$120$	−6.29423	+	7.09808i	−0.574582	+	0.647963i
$121$	7.79423	+	4.50000i	0.708566	+	0.409091i
$122$	14.0000			1.26750
$123$	12.1244	+	7.00000i	1.09322	+	0.631169i
$124$	1.83013	+	6.83013i	0.164350	+	0.613364i
$125$	−11.0000	+	2.00000i	−0.983870	+	0.178885i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−12.2942	−	3.29423i	−1.09094	−	0.292316i	−0.331868	−	0.943326i	$-0.607679\pi$
$127$	−12.2942	−	3.29423i	−1.09094	−	0.292316i	−0.759069	+	0.651010i	$0.774345\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$	−2.00000			−0.176090
$130$		0			0
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$	1.00000	+	1.73205i	0.0870388	+	0.150756i
$133$	13.6603	+	3.66025i	1.18449	+	0.317384i
$134$	2.00000	−	3.46410i	0.172774	−	0.299253i
$135$	12.0000	−	4.00000i	1.03280	−	0.344265i
$136$	1.09808	+	4.09808i	0.0941593	+	0.351407i
$137$	−13.8564	−	8.00000i	−1.18383	−	0.683486i	−0.226935	−	0.973910i	$-0.572870\pi$
$137$	−13.8564	−	8.00000i	−1.18383	−	0.683486i	−0.956898	+	0.290424i	$0.906204\pi$
$138$	−6.00000			−0.510754
$139$	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
$141$	−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
$147$	1.09808	+	4.09808i	0.0905678	+	0.338004i
$148$		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	$0.472267\pi$
$150$	−4.36603	+	5.56218i	−0.356484	+	0.454150i
$151$	−7.00000	−	7.00000i	−0.569652	−	0.569652i	0.362379	−	0.932031i	$-0.381965\pi$
$151$	−7.00000	−	7.00000i	−0.569652	−	0.569652i	−0.932031	+	0.362379i	$0.881965\pi$
$152$	−20.4904	+	5.49038i	−1.66199	+	0.445329i
$153$	0.366025	−	1.36603i	0.0295914	−	0.110437i
$154$	−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	0.999268	+	0.0382445i	$0.0121766\pi$
$157$	13.0000	+	13.0000i	1.03751	+	1.03751i	0.0382445	+	0.999268i	$0.487823\pi$
$158$	1.73205	−	1.00000i	0.137795	−	0.0795557i
$159$	−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
$162$	2.50000	−	4.33013i	0.196419	−	0.340207i
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	−7.00000	+	7.00000i	−0.546608	+	0.546608i
$165$	2.46410	+	3.73205i	0.191830	+	0.290540i
$166$	−5.19615	+	3.00000i	−0.403300	+	0.232845i
$167$	15.5885	−	9.00000i	1.20627	−	0.696441i	0.244328	−	0.969693i	$-0.421432\pi$
$167$	15.5885	−	9.00000i	1.20627	−	0.696441i	0.961943	+	0.273252i	$0.0880992\pi$
$168$	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
$172$	0.366025	−	1.36603i	0.0279092	−	0.104158i
$173$	15.0263	−	4.02628i	1.14243	−	0.306112i	0.362500	−	0.931984i	$-0.381923\pi$
$173$	15.0263	−	4.02628i	1.14243	−	0.306112i	0.779926	+	0.625871i	$0.215256\pi$
$174$		0			0
$175$	1.19615	+	9.92820i	0.0904206	+	0.750502i
$176$	1.36603	−	0.366025i	0.102968	−	0.0275902i
$177$		−	14.0000i		−	1.05230i
$178$	1.83013	+	6.83013i	0.137174	+	0.511940i
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	0.949048	+	0.315130i	$0.102048\pi$
$179$	10.0000	+	17.3205i	0.747435	+	1.29460i	−0.201613	+	0.979465i	$0.564618\pi$
$180$	0.133975	+	2.23205i	0.00998588	+	0.166367i
$181$		−	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
$187$	2.00000			0.146254
$188$	−5.19615	−	3.00000i	−0.378968	−	0.218797i
$189$	−2.92820	−	10.9282i	−0.212995	−	0.794910i
$190$	−15.0000	+	5.00000i	−1.08821	+	0.362738i
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−9.56218	−	2.56218i	−0.690091	−	0.184909i
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	−1.36603	−	0.366025i	−0.0970792	−	0.0260123i
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	−0.688705	−	0.725042i	$-0.741820\pi$
$199$	4.00000	−	6.92820i	0.283552	−	0.491127i	0.972257	+	0.233915i	$0.0751537\pi$
$200$	−9.00000	−	12.0000i	−0.636396	−	0.848528i
$201$	1.46410	+	5.46410i	0.103270	+	0.385408i
$202$	10.3923	+	6.00000i	0.731200	+	0.422159i
$203$		0			0
$204$	−1.73205	−	1.00000i	−0.121268	−	0.0700140i
$205$	−14.6865	+	16.5622i	−1.02575	+	1.15675i
$206$	−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
$210$	4.73205	+	4.19615i	0.326543	+	0.289562i
$211$	−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
$213$			2.00000i			0.137038i
$214$	9.56218	−	2.56218i	0.653657	−	0.175147i
$215$	0.633975	−	3.09808i	0.0432367	−	0.211287i
$216$	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
$219$	−13.6603	−	3.66025i	−0.923074	−	0.247337i
$220$	−3.00000	+	1.00000i	−0.202260	+	0.0674200i
$221$		0			0
$222$		0			0
$223$	1.73205	−	1.00000i	0.115987	−	0.0669650i	−0.440884	−	0.897564i	$-0.645335\pi$
$223$	1.73205	−	1.00000i	0.115987	−	0.0669650i	0.556871	+	0.830599i	$0.312002\pi$
$224$	−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
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	−0.993508	−	0.113761i	$-0.963710\pi$
$227$	−6.00000	+	10.3923i	−0.398234	+	0.689761i	0.595274	+	0.803523i	$0.297043\pi$
$228$	5.00000	−	8.66025i	0.331133	−	0.573539i
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	−0.601002	−	0.799248i	$-0.705232\pi$
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	0.799248	+	0.601002i	$0.205232\pi$
$230$	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	0.739104	−	0.673592i	$-0.235249\pi$
$233$	1.00000	+	1.00000i	0.0655122	+	0.0655122i	−0.673592	+	0.739104i	$0.735249\pi$
$234$		0			0
$235$	−12.0000	−	6.00000i	−0.782794	−	0.391397i
$236$	9.56218	+	2.56218i	0.622445	+	0.166784i
$237$	−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	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$	−3.09808	−	0.633975i	−0.199980	−	0.0409229i
$241$	23.2224	−	6.22243i	1.49589	−	0.400822i	0.584168	−	0.811633i	$-0.301421\pi$
$241$	23.2224	−	6.22243i	1.49589	−	0.400822i	0.911721	+	0.410811i	$0.134754\pi$
$242$			9.00000i			0.578542i
$243$	−2.56218	−	9.56218i	−0.164364	−	0.613414i
$244$	−7.00000	−	12.1244i	−0.448129	−	0.776182i
$245$	−6.69615	+	0.401924i	−0.427801	+	0.0256780i
$246$			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
$250$	−7.23205	−	8.52628i	−0.457395	−	0.539249i
$251$	−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	$0.686772\pi$
$252$	2.00000			0.125988
$253$	−5.19615	−	3.00000i	−0.326679	−	0.188608i
$254$	−3.29423	−	12.2942i	−0.206698	−	0.771409i
$255$	−4.00000	−	2.00000i	−0.250490	−	0.125245i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	15.0263	+	4.02628i	0.937314	+	0.251152i	0.694971	−	0.719038i	$-0.255417\pi$
$257$	15.0263	+	4.02628i	0.937314	+	0.251152i	0.242343	+	0.970191i	$0.422084\pi$
$258$	−1.00000	−	1.73205i	−0.0622573	−	0.107833i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−10.0000	−	17.3205i	−0.617802	−	1.07006i
$263$	−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
$265$	−5.00000	−	15.0000i	−0.307148	−	0.921443i
$266$	3.66025	+	13.6603i	0.224425	+	0.837564i
$267$	−8.66025	−	5.00000i	−0.529999	−	0.305995i
$268$	−4.00000			−0.244339
$269$	−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
$271$	3.29423	−	12.2942i	0.200110	−	0.746821i	−0.790774	−	0.612108i	$-0.790322\pi$
$271$	3.29423	−	12.2942i	0.200110	−	0.746821i	0.990885	−	0.134714i	$-0.0430114\pi$
$272$	−1.00000	+	1.00000i	−0.0606339	+	0.0606339i
$273$		0			0
$274$		−	16.0000i		−	0.966595i
$275$	−6.56218	+	2.63397i	−0.395714	+	0.158835i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−5.49038	−	20.4904i	−0.329885	−	1.23115i	−0.909309	−	0.416121i	$-0.863389\pi$
$277$	−5.49038	−	20.4904i	−0.329885	−	1.23115i	0.579424	−	0.815026i	$-0.303278\pi$
$278$			14.0000i			0.839664i
$279$	6.83013	−	1.83013i	0.408909	−	0.109567i
$280$	−11.1962	+	7.39230i	−0.669098	+	0.441775i
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	0.676650	−	0.736305i	$-0.263431\pi$
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	−0.736305	+	0.676650i	$0.763431\pi$
$282$	−8.19615	+	2.19615i	−0.488074	+	0.130779i
$283$	−3.29423	+	12.2942i	−0.195822	+	0.730816i	0.796231	+	0.604993i	$0.206824\pi$
$283$	−3.29423	+	12.2942i	−0.195822	+	0.730816i	−0.992053	+	0.125823i	$0.959843\pi$
$284$	−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
$288$	−4.33013	+	2.50000i	−0.255155	+	0.147314i
$289$	12.9904	−	7.50000i	0.764140	−	0.441176i
$290$		0			0
$291$	−2.00000	+	2.00000i	−0.117242	+	0.117242i
$292$	5.00000	−	8.66025i	0.292603	−	0.506803i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$	−3.00000	+	3.00000i	−0.174964	+	0.174964i
$295$	21.6865	+	4.43782i	1.26264	+	0.258380i
$296$		0			0
$297$	6.92820	−	4.00000i	0.402015	−	0.232104i
$298$	−3.00000	−	3.00000i	−0.173785	−	0.173785i
$299$		0			0
$300$	7.00000	+	1.00000i	0.404145	+	0.0577350i
$301$	−2.73205	−	0.732051i	−0.157473	−	0.0421947i
$302$	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
$305$	−17.2487	−	26.1244i	−0.987658	−	1.49588i
$306$	1.36603	−	0.366025i	0.0780905	−	0.0209243i
$307$		−	18.0000i		−	1.02731i	−0.857996	−	0.513657i	$-0.828290\pi$
$307$		−	18.0000i		−	1.02731i	0.857996	−	0.513657i	$-0.171710\pi$
$308$	0.732051	+	2.73205i	0.0417125	+	0.155673i
$309$	−7.00000	−	12.1244i	−0.398216	−	0.689730i
$310$	−10.4904	+	11.8301i	−0.595814	+	0.671906i
$311$			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	−0.405420	−	0.914130i	$-0.632875\pi$
$313$	9.00000	−	9.00000i	0.508710	−	0.508710i	0.914130	+	0.405420i	$0.132875\pi$
$314$	−4.75833	+	17.7583i	−0.268528	+	1.00216i
$315$	4.46410	−	0.267949i	0.251524	−	0.0150972i
$316$	−1.73205	−	1.00000i	−0.0974355	−	0.0562544i
$317$	14.0000			0.786318			0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000			0.786318			0.393159	+	0.919470i	$0.371382\pi$
$318$	−8.66025	−	5.00000i	−0.485643	−	0.280386i
$319$		0			0
$320$	7.00000	−	14.0000i	0.391312	−	0.782624i
$321$	−7.00000	+	12.1244i	−0.390702	+	0.676716i
$322$	−8.19615	−	2.19615i	−0.456754	−	0.122387i
$323$	−5.00000	−	8.66025i	−0.278207	−	0.481869i
$324$	−5.00000			−0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$	9.00000	+	15.5885i	0.497701	+	0.862044i
$328$	−28.6865	−	7.68653i	−1.58395	−	0.424418i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	−2.00000	+	4.00000i	−0.110096	+	0.220193i
$331$	1.09808	+	4.09808i	0.0603557	+	0.225251i	0.989515	−	0.144428i	$-0.0461343\pi$
$331$	1.09808	+	4.09808i	0.0603557	+	0.225251i	−0.929160	+	0.369679i	$0.879468\pi$
$332$	5.19615	+	3.00000i	0.285176	+	0.164646i
$333$		0			0
$334$	15.5885	+	9.00000i	0.852962	+	0.492458i
$335$	−8.92820	+	0.535898i	−0.487800	+	0.0292793i
$336$	−0.732051	+	2.73205i	−0.0399366	+	0.149046i
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	−0.257992	−	0.966147i	$-0.583061\pi$
$337$	13.0000	−	13.0000i	0.708155	−	0.708155i	0.966147	+	0.257992i	$0.0830608\pi$
$338$		0			0
$339$		−	10.0000i		−	0.543125i
$340$	2.09808	−	2.36603i	0.113784	−	0.128316i
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$	1.83013	+	6.83013i	0.0989619	+	0.369331i
$343$			20.0000i			1.07990i
$344$	4.09808	−	1.09808i	0.220953	−	0.0592043i
$345$	7.39230	+	11.1962i	0.397988	+	0.602781i
$346$	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
$349$	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
$353$	−10.3923	+	6.00000i	−0.553127	+	0.319348i	−0.750382	−	0.661004i	$-0.770130\pi$
$353$	−10.3923	+	6.00000i	−0.553127	+	0.319348i	0.197256	+	0.980352i	$0.436797\pi$
$354$	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
$357$	−2.00000	+	3.46410i	−0.105851	+	0.183340i
$358$	−10.0000	+	17.3205i	−0.528516	+	0.915417i
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	−0.733003	−	0.680225i	$-0.761882\pi$
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	0.680225	+	0.733003i	$0.261882\pi$
$360$	−5.59808	+	3.69615i	−0.295045	+	0.194804i
$361$	26.8468	−	15.5000i	1.41299	−	0.815789i
$362$	6.92820	−	4.00000i	0.364138	−	0.210235i
$363$	−9.00000	−	9.00000i	−0.472377	−	0.472377i
$364$		0			0
$365$	10.0000	−	20.0000i	0.523424	−	1.04685i
$366$	−19.1244	−	5.12436i	−0.999646	−	0.267854i
$367$	−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
$371$	−13.6603	+	3.66025i	−0.709205	+	0.190031i
$372$		−	10.0000i		−	0.518476i
$373$	−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
$375$	15.7583	+	1.29423i	0.813757	+	0.0668337i
$376$		−	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	$0.0717693\pi$
$380$	11.8301	+	10.4904i	0.606873	+	0.538145i
$381$	15.5885	+	9.00000i	0.798621	+	0.461084i
$382$	−8.00000			−0.409316
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.984921	−	0.173005i	$-0.0553476\pi$
$383$	25.9808	+	15.0000i	1.32755	+	0.766464i	0.342634	+	0.939469i	$0.388681\pi$
$384$	1.09808	+	4.09808i	0.0560360	+	0.209129i
$385$	2.00000	+	6.00000i	0.101929	+	0.305788i
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$	−1.36603	−	0.366025i	−0.0694390	−	0.0186061i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$	27.3205	+	7.32051i	1.37814	+	0.369271i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−4.00000	−	2.00000i	−0.201262	−	0.100631i
$396$	0.366025	+	1.36603i	0.0183935	+	0.0686454i
$397$	13.8564	+	8.00000i	0.695433	+	0.401508i	0.805644	−	0.592400i	$-0.201819\pi$
$397$	13.8564	+	8.00000i	0.695433	+	0.401508i	−0.110211	+	0.993908i	$0.535153\pi$
$398$	8.00000			0.401004
$399$	−17.3205	−	10.0000i	−0.867110	−	0.500626i
$400$	1.96410	−	4.59808i	0.0982051	−	0.229904i
$401$	4.02628	−	15.0263i	0.201063	−	0.750377i	−0.789551	−	0.613685i	$-0.789686\pi$
$401$	4.02628	−	15.0263i	0.201063	−	0.750377i	0.990614	−	0.136691i	$-0.0436469\pi$
$402$	−4.00000	+	4.00000i	−0.199502	+	0.199502i
$403$		0			0
$404$		−	12.0000i		−	0.597022i
$405$	−11.1603	+	0.669873i	−0.554557	+	0.0332863i
$406$		0			0
$407$		0			0
$408$		−	6.00000i		−	0.297044i
$409$	−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	$0.495372\pi$
$410$	−21.6865	−	4.43782i	−1.07102	−	0.219168i
$411$	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
$414$	−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
$418$	−8.66025	+	5.00000i	−0.423587	+	0.244558i
$419$	−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	$-0.626239\pi$
$421$	11.0000	−	11.0000i	0.536107	−	0.536107i	0.922383	+	0.386276i	$0.126239\pi$
$422$	2.00000	−	3.46410i	0.0973585	−	0.168630i
$423$	−3.00000	+	5.19615i	−0.145865	+	0.252646i
$424$	15.0000	−	15.0000i	0.728464	−	0.728464i
$425$	4.36603	−	5.56218i	0.211783	−	0.269805i
$426$	−1.73205	+	1.00000i	−0.0839181	+	0.0484502i
$427$	−24.2487	+	14.0000i	−1.17348	+	0.677507i
$428$	−7.00000	−	7.00000i	−0.338358	−	0.338358i
$429$		0			0
$430$	3.00000	−	1.00000i	0.144673	−	0.0482243i
$431$	17.7583	+	4.75833i	0.855389	+	0.229201i	0.659759	−	0.751477i	$-0.270658\pi$
$431$	17.7583	+	4.75833i	0.855389	+	0.229201i	0.195630	+	0.980678i	$0.437325\pi$
$432$	−1.46410	+	5.46410i	−0.0704416	+	0.262892i
$433$	−23.2224	+	6.22243i	−1.11600	+	0.299031i	−0.769263	−	0.638932i	$-0.779377\pi$
$433$	−23.2224	+	6.22243i	−1.11600	+	0.299031i	−0.346736	+	0.937963i	$0.612710\pi$
$434$	10.0000	+	10.0000i	0.480015	+	0.480015i
$435$		0			0
$436$	−12.2942	+	3.29423i	−0.588787	+	0.157765i
$437$			30.0000i			1.43509i
$438$	−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	$0.833333\pi$
$440$	−7.09808	−	6.29423i	−0.338388	−	0.300066i
$441$			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
$447$	6.00000			0.283790
$448$	−12.1244	−	7.00000i	−0.572822	−	0.330719i
$449$	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	$0.884747\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	6.83013	+	1.83013i	0.321262	+	0.0860819i
$453$	7.00000	+	12.1244i	0.328889	+	0.569652i
$454$	−12.0000			−0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	0.888466	−	0.458942i	$-0.151771\pi$
$457$	1.00000	+	1.73205i	0.0467780	+	0.0810219i	−0.841688	+	0.539964i	$0.818438\pi$
$458$	4.09808	+	1.09808i	0.191491	+	0.0513097i
$459$	−4.00000	+	6.92820i	−0.186704	+	0.323381i
$460$	−9.00000	+	3.00000i	−0.419627	+	0.139876i
$461$	−6.22243	−	23.2224i	−0.289808	−	1.08158i	−0.945254	−	0.326335i	$-0.894186\pi$
$461$	−6.22243	−	23.2224i	−0.289808	−	1.08158i	0.655447	−	0.755241i	$-0.272480\pi$
$462$	3.46410	+	2.00000i	0.161165	+	0.0930484i
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$		0			0
$465$	−1.33975	−	22.3205i	−0.0621292	−	1.03509i
$466$	−0.366025	+	1.36603i	−0.0169558	+	0.0632799i
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	−0.467515	−	0.883985i	$-0.654851\pi$
$467$	9.00000	−	9.00000i	0.416470	−	0.416470i	0.883985	+	0.467515i	$0.154851\pi$
$468$		0			0
$469$			8.00000i			0.369406i
$470$	−0.803848	−	13.3923i	−0.0370787	−	0.617741i
$471$	−13.0000	−	22.5167i	−0.599008	−	1.03751i
$472$	7.68653	+	28.6865i	0.353801	+	1.32040i
$473$		−	2.00000i		−	0.0919601i
$474$	−2.73205	+	0.732051i	−0.125487	+	0.0336242i
$475$	27.8109	+	21.8301i	1.27605	+	1.00163i
$476$	−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
$479$	−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
$483$	10.3923	−	6.00000i	0.472866	−	0.273009i
$484$	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
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	21.0000	−	36.3731i	0.950625	−	1.64653i
$489$	−4.00000	+	4.00000i	−0.180886	+	0.180886i
$490$	−3.69615	−	5.59808i	−0.166975	−	0.252895i
$491$	−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	$0.498687\pi$
$492$	12.1244	−	7.00000i	0.546608	−	0.315584i
$493$		0			0
$494$		0			0
$495$	1.00000	+	3.00000i	0.0449467	+	0.134840i
$496$	−6.83013	−	1.83013i	−0.306682	−	0.0821751i
$497$	−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	0.636762	−	0.771060i	$-0.280273\pi$
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	−0.771060	+	0.636762i	$0.780273\pi$
$500$	−3.76795	+	10.5263i	−0.168508	+	0.470750i
$501$	−24.5885	+	6.58846i	−1.09853	+	0.294351i
$502$		−	2.00000i		−	0.0892644i
$503$	−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
$505$	−1.60770	−	26.7846i	−0.0715415	−	1.19190i
$506$		−	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	$0.949753\pi$
$510$	−0.267949	−	4.46410i	−0.0118650	−	0.197674i
$511$	−17.3205	−	10.0000i	−0.766214	−	0.442374i
$512$	11.0000			0.486136
$513$	−34.6410	−	20.0000i	−1.52944	−	0.883022i
$514$	4.02628	+	15.0263i	0.177592	+	0.662781i
$515$	21.0000	−	7.00000i	0.925371	−	0.308457i
$516$	−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
$525$	2.00000	−	14.0000i	0.0872872	−	0.611010i
$526$	−0.366025	−	1.36603i	−0.0159595	−	0.0595615i
$527$	−8.66025	−	5.00000i	−0.377247	−	0.217803i
$528$	−2.00000			−0.0870388
$529$	4.33013	+	2.50000i	0.188266	+	0.108696i
$530$	10.4904	−	11.8301i	0.455673	−	0.513868i
$531$	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
$535$	−16.5622	−	14.6865i	−0.716045	−	0.634954i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	−7.32051	−	27.3205i	−0.315903	−	1.17897i
$538$		−	12.0000i		−	0.517357i
$539$	−4.09808	+	1.09808i	−0.176517	+	0.0472975i
$540$	2.53590	−	12.3923i	0.109128	−	0.533280i
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	12.2942	−	3.29423i	0.528082	−	0.141499i
$543$	−2.92820	+	10.9282i	−0.125661	+	0.468974i
$544$	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	0.488020	−	0.872832i	$-0.337719\pi$
$547$	−9.00000	−	9.00000i	−0.384812	−	0.384812i	−0.872832	+	0.488020i	$0.837719\pi$
$548$	−13.8564	+	8.00000i	−0.591916	+	0.341743i
$549$	−12.1244	+	7.00000i	−0.517455	+	0.298753i
$550$	−5.56218	−	4.36603i	−0.237172	−	0.186168i
$551$		0			0
$552$	−9.00000	+	15.5885i	−0.383065	+	0.663489i
$553$	−2.00000	+	3.46410i	−0.0850487	+	0.147309i
$554$	15.0000	−	15.0000i	0.637289	−	0.637289i
$555$		0			0
$556$	12.1244	−	7.00000i	0.514187	−	0.296866i
$557$	−20.7846	+	12.0000i	−0.880672	+	0.508456i	−0.870880	−	0.491496i	$-0.836450\pi$
$557$	−20.7846	+	12.0000i	−0.880672	+	0.508456i	−0.00979220	+	0.999952i	$0.503117\pi$
$558$	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
$562$	0.366025	−	1.36603i	0.0154398	−	0.0576223i
$563$	−20.4904	+	5.49038i	−0.863567	+	0.231392i	−0.663304	−	0.748350i	$-0.730846\pi$
$563$	−20.4904	+	5.49038i	−0.863567	+	0.231392i	−0.200263	+	0.979742i	$0.564180\pi$
$564$	6.00000	+	6.00000i	0.252646	+	0.252646i
$565$	15.4904	+	3.16987i	0.651685	+	0.133358i
$566$	−12.2942	+	3.29423i	−0.516765	+	0.138467i
$567$			10.0000i			0.419961i
$568$	−1.09808	−	4.09808i	−0.0460743	−	0.171951i
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	0.796266	−	0.604947i	$-0.206806\pi$
$569$	−3.00000	−	5.19615i	−0.125767	−	0.217834i	−0.922032	+	0.387113i	$0.873472\pi$
$570$	22.3205	−	1.33975i	0.934903	−	0.0561158i
$571$		−	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
$575$	−19.6865	+	7.90192i	−0.820985	+	0.329533i
$576$	−6.06218	−	3.50000i	−0.252591	−	0.145833i
$577$	−46.0000			−1.91501			−0.957503	−	0.288425i	$-0.906868\pi$
$577$	−46.0000			−1.91501			−0.957503	+	0.288425i	$0.906868\pi$
$578$	12.9904	+	7.50000i	0.540329	+	0.311959i
$579$	−6.58846	−	24.5885i	−0.273807	−	1.02186i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−2.73205	−	0.732051i	−0.113247	−	0.0303445i
$583$	−5.00000	−	8.66025i	−0.207079	−	0.358671i
$584$	30.0000			1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	0.821795	−	0.569783i	$-0.192973\pi$
$587$	−2.00000	−	3.46410i	−0.0825488	−	0.142979i	−0.904344	+	0.426804i	$0.859639\pi$
$588$	4.09808	+	1.09808i	0.169002	+	0.0452839i
$589$	25.0000	−	43.3013i	1.03011	−	1.78420i
$590$	7.00000	+	21.0000i	0.288185	+	0.864556i
$591$	−2.19615	−	8.19615i	−0.0903376	−	0.337145i
$592$		0			0
$593$	−10.0000			−0.410651			−0.205325	−	0.978694i	$-0.565825\pi$
$593$	−10.0000			−0.410651			−0.205325	+	0.978694i	$0.565825\pi$
$594$	6.92820	+	4.00000i	0.284268	+	0.164122i
$595$	−4.73205	−	4.19615i	−0.193995	−	0.172025i
$596$	−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	$0.209990\pi$
$599$			30.0000i			1.22577i	−0.790173	+	0.612883i	$0.790010\pi$
$600$	7.90192	+	19.6865i	0.322595	+	0.803699i
$601$	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
$603$			4.00000i			0.162893i
$604$	−9.56218	+	2.56218i	−0.389079	+	0.104254i
$605$	16.7942	−	11.0885i	0.682782	−	0.450810i
$606$	−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
$613$	−17.3205	+	10.0000i	−0.699569	+	0.403896i	−0.807187	−	0.590296i	$-0.799011\pi$
$613$	−17.3205	+	10.0000i	−0.699569	+	0.403896i	0.107618	+	0.994192i	$0.465678\pi$
$614$	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
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	−0.997899	−	0.0647859i	$-0.979364\pi$
$617$	−11.0000	+	19.0526i	−0.442843	+	0.767027i	0.555056	+	0.831813i	$0.312697\pi$
$618$	7.00000	−	12.1244i	0.281581	−	0.487713i
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.00484658	+	0.999988i	$0.501543\pi$
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.999988	+	0.00484658i	$0.998457\pi$
$620$	15.4904	+	3.16987i	0.622109	+	0.127305i
$621$	20.7846	−	12.0000i	0.834058	−	0.481543i
$622$	−5.19615	+	3.00000i	−0.208347	+	0.120289i
$623$	−10.0000	−	10.0000i	−0.400642	−	0.400642i
$624$		0			0
$625$	−7.00000	+	24.0000i	−0.280000	+	0.960000i
$626$	12.2942	+	3.29423i	0.491376	+	0.131664i
$627$	3.66025	−	13.6603i	0.146176	−	0.545538i
$628$	17.7583	−	4.75833i	0.708635	−	0.189878i
$629$		0			0
$630$	2.46410	+	3.73205i	0.0981722	+	0.148688i
$631$	15.0263	−	4.02628i	0.598187	−	0.160284i	0.0529946	−	0.998595i	$-0.483123\pi$
$631$	15.0263	−	4.02628i	0.598187	−	0.160284i	0.545192	+	0.838311i	$0.316457\pi$
$632$		−	6.00000i		−	0.238667i
$633$	1.46410	+	5.46410i	0.0581928	+	0.217179i
$634$	7.00000	+	12.1244i	0.278006	+	0.481520i
$635$	−18.8827	+	21.2942i	−0.749337	+	0.845036i
$636$			10.0000i			0.396526i
$637$		0			0
$638$		0			0
$639$	−0.366025	+	1.36603i	−0.0144797	+	0.0540391i
$640$	−6.69615	+	0.401924i	−0.264689	+	0.0158874i
$641$	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	$0.509487\pi$
$642$	−14.0000			−0.552536
$643$	29.4449	+	17.0000i	1.16119	+	0.670415i	0.951589	−	0.307372i	$-0.0994496\pi$
$643$	29.4449	+	17.0000i	1.16119	+	0.670415i	0.209603	+	0.977787i	$0.432783\pi$
$644$	2.19615	+	8.19615i	0.0865405	+	0.322974i
$645$	−2.00000	+	4.00000i	−0.0787499	+	0.157500i
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	−1.36603	−	0.366025i	−0.0537040	−	0.0143899i	0.231867	−	0.972747i	$-0.425517\pi$
$647$	−1.36603	−	0.366025i	−0.0537040	−	0.0143899i	−0.285571	+	0.958358i	$0.592183\pi$
$648$	−7.50000	−	12.9904i	−0.294628	−	0.510310i
$649$	14.0000			0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$	−2.00000	−	3.46410i	−0.0783260	−	0.135665i
$653$	−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
$655$	−20.0000	+	40.0000i	−0.781465	+	1.56293i
$656$	−2.56218	−	9.56218i	−0.100036	−	0.373340i
$657$	−8.66025	−	5.00000i	−0.337869	−	0.195069i
$658$	−12.0000			−0.467809
$659$	−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
$661$	−6.22243	+	23.2224i	−0.242025	+	0.903248i	0.732831	+	0.680411i	$0.238199\pi$
$661$	−6.22243	+	23.2224i	−0.242025	+	0.903248i	−0.974856	+	0.222837i	$0.928468\pi$
$662$	−3.00000	+	3.00000i	−0.116598	+	0.116598i
$663$		0			0
$664$			18.0000i			0.698535i
$665$	20.9808	−	23.6603i	0.813599	−	0.917505i
$666$		0			0
$667$		0			0
$668$		−	18.0000i		−	0.696441i
$669$	−2.73205	+	0.732051i	−0.105627	+	0.0283027i
$670$	−4.92820	−	7.46410i	−0.190393	−	0.288363i
$671$	−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	$0.217405\pi$
$673$	−5.49038	+	20.4904i	−0.211639	+	0.789846i	−0.987323	+	0.158725i	$0.949262\pi$
$674$	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	0.109973	−	0.993935i	$-0.464924\pi$
$677$	−23.0000	−	23.0000i	−0.883962	−	0.883962i	−0.993935	+	0.109973i	$0.964924\pi$
$678$	8.66025	−	5.00000i	0.332595	−	0.192024i
$679$	−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
$682$	−5.00000	+	8.66025i	−0.191460	+	0.331618i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	5.00000	−	5.00000i	0.191180	−	0.191180i
$685$	−29.8564	+	19.7128i	−1.14075	+	0.753188i
$686$	−17.3205	+	10.0000i	−0.661300	+	0.381802i
$687$	−5.19615	+	3.00000i	−0.198246	+	0.114457i
$688$	1.00000	+	1.00000i	0.0381246	+	0.0381246i
$689$		0			0
$690$	−6.00000	+	12.0000i	−0.228416	+	0.456832i
$691$	−4.09808	−	1.09808i	−0.155898	−	0.0417728i	0.180026	−	0.983662i	$-0.442382\pi$
$691$	−4.09808	−	1.09808i	−0.155898	−	0.0417728i	−0.335924	+	0.941889i	$0.609049\pi$
$692$	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
$695$	26.1244	−	17.2487i	0.990953	−	0.654281i
$696$		0			0
$697$		−	14.0000i		−	0.530288i
$698$	3.29423	+	12.2942i	0.124688	+	0.465343i
$699$	−1.00000	−	1.73205i	−0.0378235	−	0.0655122i
$700$	9.19615	+	3.92820i	0.347582	+	0.148472i
$701$			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
$705$	14.1962	+	12.5885i	0.534658	+	0.474109i
$706$	−10.3923	−	6.00000i	−0.391120	−	0.225813i
$707$	−24.0000			−0.902613
$708$	−12.1244	−	7.00000i	−0.455661	−	0.263076i
$709$	−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	$-0.363138\pi$
$710$	−1.00000	−	3.00000i	−0.0375293	−	0.112588i
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$	20.4904	+	5.49038i	0.767909	+	0.205761i
$713$	15.0000	+	25.9808i	0.561754	+	0.972987i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	−1.36603	−	0.366025i	−0.0509796	−	0.0136599i
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	−0.781748	−	0.623595i	$-0.785672\pi$
$719$	4.00000	−	6.92820i	0.149175	−	0.258378i	0.930923	+	0.365216i	$0.119005\pi$
$720$	−2.00000	−	1.00000i	−0.0745356	−	0.0372678i
$721$	−5.12436	−	19.1244i	−0.190841	−	0.712228i
$722$	26.8468	+	15.5000i	0.999134	+	0.576850i
$723$	−34.0000			−1.26447
$724$	−6.92820	−	4.00000i	−0.257485	−	0.148659i
$725$		0			0
$726$	3.29423	−	12.2942i	0.122260	−	0.456282i
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.368418	+	0.929660i	$0.620100\pi$
$727$	−35.0000	+	35.0000i	−1.29808	+	1.29808i	−0.929660	+	0.368418i	$0.879900\pi$
$728$		0			0
$729$			29.0000i			1.07407i
$730$	22.3205	−	1.33975i	0.826119	−	0.0495862i
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$	5.12436	+	19.1244i	0.189402	+	0.706857i
$733$		−	4.00000i		−	0.147743i	−0.997268	−	0.0738717i	$-0.976464\pi$
$733$		−	4.00000i		−	0.147743i	0.997268	−	0.0738717i	$-0.0235355\pi$
$734$	−1.36603	+	0.366025i	−0.0504209	+	0.0135102i
$735$	9.29423	+	1.90192i	0.342823	+	0.0701535i
$736$	−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
$739$	−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
$743$	29.4449	−	17.0000i	1.08023	−	0.623670i	0.149270	−	0.988797i	$-0.452308\pi$
$743$	29.4449	−	17.0000i	1.08023	−	0.623670i	0.930958	+	0.365127i	$0.118974\pi$
$744$	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
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	1.00000	−	1.73205i	0.0365636	−	0.0633300i
$749$	−14.0000	+	14.0000i	−0.511549	+	0.511549i
$750$	6.75833	+	14.2942i	0.246779	+	0.521951i
$751$	−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	$0.967667\pi$
$752$	5.19615	−	3.00000i	0.189484	−	0.109399i
$753$	2.00000	+	2.00000i	0.0728841	+	0.0728841i
$754$		0			0
$755$	−21.0000	+	7.00000i	−0.764268	+	0.254756i
$756$	−10.9282	−	2.92820i	−0.397455	−	0.106498i
$757$	−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
$760$	−9.50962	+	46.4711i	−0.344950	+	1.68569i
$761$	−9.56218	+	2.56218i	−0.346629	+	0.0928789i	−0.427933	−	0.903810i	$-0.640758\pi$
$761$	−9.56218	+	2.56218i	−0.346629	+	0.0928789i	0.0813044	+	0.996689i	$0.474091\pi$
$762$			18.0000i			0.652071i
$763$	6.58846	+	24.5885i	0.238518	+	0.890162i
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$	−2.36603	−	2.09808i	−0.0855438	−	0.0758561i
$766$			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	$-0.0415979\pi$
$770$	−4.19615	+	4.73205i	−0.151219	+	0.170531i
$771$	−19.0526	−	11.0000i	−0.686161	−	0.396155i
$772$	18.0000			0.647834
$773$	27.7128	+	16.0000i	0.996761	+	0.575480i	0.907288	−	0.420509i	$-0.138149\pi$
$773$	27.7128	+	16.0000i	0.996761	+	0.575480i	0.0894724	+	0.995989i	$0.471482\pi$
$774$	−0.366025	−	1.36603i	−0.0131565	−	0.0491008i
$775$	35.0000	+	5.00000i	1.25724	+	0.179605i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$		0			0
$778$	−9.00000	−	15.5885i	−0.322666	−	0.558873i
$779$	70.0000			2.50801
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	3.00000	+	5.19615i	0.107280	+	0.185814i
$783$		0			0
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$	39.0000	−	13.0000i	1.39197	−	0.463990i
$786$	7.32051	+	27.3205i	0.261114	+	0.974490i
$787$	−19.0526	−	11.0000i	−0.679150	−	0.392108i	0.120384	−	0.992727i	$-0.461587\pi$
$787$	−19.0526	−	11.0000i	−0.679150	−	0.392108i	−0.799535	+	0.600620i	$0.794921\pi$
$788$	6.00000			0.213741
$789$	1.73205	+	1.00000i	0.0616626	+	0.0356009i
$790$	−0.267949	−	4.46410i	−0.00953320	−	0.158826i
$791$	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
$795$	1.33975	+	22.3205i	0.0475159	+	0.791627i
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	6.22243	+	23.2224i	0.220410	+	0.822581i	0.984192	+	0.177106i	$0.0566736\pi$
$797$	6.22243	+	23.2224i	0.220410	+	0.822581i	−0.763782	+	0.645474i	$0.776660\pi$
$798$		−	20.0000i		−	0.707992i
$799$	8.19615	−	2.19615i	0.289959	−	0.0776943i
$800$	−24.8205	+	2.99038i	−0.877537	+	0.105726i
$801$	−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
$804$	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
$808$	31.1769	−	18.0000i	1.09680	−	0.633238i
$809$	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	$-0.516120\pi$
$811$	27.0000	−	27.0000i	0.948098	−	0.948098i	0.998718	+	0.0506198i	$0.0161197\pi$
$812$		0			0
$813$	−9.00000	+	15.5885i	−0.315644	+	0.546711i
$814$		0			0
$815$	−4.92820	−	7.46410i	−0.172627	−	0.261456i
$816$	1.73205	−	1.00000i	0.0606339	−	0.0350070i
$817$	−8.66025	+	5.00000i	−0.302984	+	0.174928i
$818$	−7.00000	−	7.00000i	−0.244749	−	0.244749i
$819$		0			0
$820$	7.00000	+	21.0000i	0.244451	+	0.733352i
$821$	12.2942	+	3.29423i	0.429072	+	0.114969i	0.466890	−	0.884315i	$-0.345374\pi$
$821$	12.2942	+	3.29423i	0.429072	+	0.114969i	−0.0378188	+	0.999285i	$0.512041\pi$
$822$	−5.85641	+	21.8564i	−0.204266	+	0.762330i
$823$	12.2942	−	3.29423i	0.428550	−	0.114830i	−0.0380955	−	0.999274i	$-0.512129\pi$
$823$	12.2942	−	3.29423i	0.428550	−	0.114830i	0.466645	+	0.884445i	$0.345462\pi$
$824$	21.0000	+	21.0000i	0.731570	+	0.731570i
$825$	9.92820	−	1.19615i	0.345656	−	0.0416447i
$826$	19.1244	−	5.12436i	0.665421	−	0.178299i
$827$			46.0000i			1.59958i	0.600282	+	0.799788i	$0.295055\pi$
$827$			46.0000i			1.59958i	−0.600282	+	0.799788i	$0.704945\pi$
$828$	1.09808	+	4.09808i	0.0381608	+	0.142418i
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	−0.994174	−	0.107788i	$-0.965623\pi$
$829$	−17.0000	−	29.4449i	−0.590434	−	1.02266i	0.403739	−	0.914874i	$-0.367710\pi$
$830$	0.803848	+	13.3923i	0.0279020	+	0.464854i
$831$			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
$835$	−2.41154	−	40.1769i	−0.0834549	−	1.39038i
$836$	8.66025	+	5.00000i	0.299521	+	0.172929i
$837$	−40.0000			−1.38260
$838$	−32.9090	−	19.0000i	−1.13682	−	0.656344i
$839$	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	$0.590579\pi$
$840$	18.0000	−	6.00000i	0.621059	−	0.207020i
$841$	−14.5000	+	25.1147i	−0.500000	+	0.866025i
$842$	15.0263	+	4.02628i	0.517840	+	0.138755i
$843$	1.00000	+	1.73205i	0.0344418	+	0.0596550i
$844$	−4.00000			−0.137686
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−9.00000	−	15.5885i	−0.309244	−	0.535626i
$848$	6.83013	+	1.83013i	0.234548	+	0.0628468i
$849$	9.00000	−	15.5885i	0.308879	−	0.534994i
$850$	7.00000	+	1.00000i	0.240098	+	0.0342997i
$851$		0			0
$852$	1.73205	+	1.00000i	0.0593391	+	0.0342594i
$853$	−26.0000			−0.890223			−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000			−0.890223			−0.445112	+	0.895475i	$0.646836\pi$
$854$	−24.2487	−	14.0000i	−0.829774	−	0.479070i
$855$	10.4904	−	11.8301i	0.358763	−	0.404582i
$856$	7.68653	−	28.6865i	0.262720	−	0.980486i
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	−0.756487	−	0.654009i	$-0.773086\pi$
$857$	−3.00000	+	3.00000i	−0.102478	+	0.102478i	0.654009	+	0.756487i	$0.273086\pi$
$858$		0			0
$859$		−	30.0000i		−	1.02359i	−0.859109	−	0.511793i	$-0.828981\pi$
$859$		−	30.0000i		−	1.02359i	0.859109	−	0.511793i	$-0.171019\pi$
$860$	−2.36603	−	2.09808i	−0.0806808	−	0.0715438i
$861$	−14.0000	−	24.2487i	−0.477119	−	0.826394i
$862$	4.75833	+	17.7583i	0.162069	+	0.604851i
$863$		−	30.0000i		−	1.02121i	−0.859815	−	0.510606i	$-0.829421\pi$
$863$		−	30.0000i		−	1.02121i	0.859815	−	0.510606i	$-0.170579\pi$
$864$	27.3205	−	7.32051i	0.929463	−	0.249049i
$865$	6.97372	−	34.0788i	0.237114	−	1.15872i
$866$	−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
$869$	−2.73205	−	0.732051i	−0.0926785	−	0.0248331i
$870$		0			0
$871$		0			0
$872$	−27.0000	−	27.0000i	−0.914335	−	0.914335i
$873$	−1.73205	+	1.00000i	−0.0586210	+	0.0338449i
$874$	−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
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	−0.343495	−	0.939155i	$-0.611611\pi$
$877$	19.0000	−	32.9090i	0.641584	−	1.11126i	0.985079	−	0.172102i	$-0.0550559\pi$
$878$		0			0
$879$	6.00000	−	6.00000i	0.202375	−	0.202375i
$880$	0.633975	−	3.09808i	0.0213713	−	0.104436i
$881$	−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	$0.993561\pi$
$882$	−2.59808	+	1.50000i	−0.0874818	+	0.0505076i
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.919601	+	0.392853i	$0.128512\pi$
$883$	39.0000	+	39.0000i	1.31245	+	1.31245i	0.392853	+	0.919601i	$0.371488\pi$
$884$		0			0
$885$	−28.0000	−	14.0000i	−0.941210	−	0.470605i
$886$	34.1506	+	9.15064i	1.14731	+	0.307422i
$887$	−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
$890$	15.4904	+	3.16987i	0.519239	+	0.106254i
$891$	−6.83013	+	1.83013i	−0.228818	+	0.0613116i
$892$		−	2.00000i		−	0.0669650i
$893$	10.9808	+	40.9808i	0.367457	+	1.37137i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$	44.6410	−	2.67949i	1.49218	−	0.0895655i
$896$			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
$902$	−14.0000			−0.466149
$903$	3.46410	+	2.00000i	0.115278	+	0.0665558i
$904$	5.49038	+	20.4904i	0.182607	+	0.681500i
$905$	−16.0000	−	8.00000i	−0.531858	−	0.265929i
$906$	−7.00000	+	12.1244i	−0.232559	+	0.402805i
$907$	53.2750	+	14.2750i	1.76897	+	0.473993i	0.988502	−	0.151206i	$-0.0483158\pi$
$907$	53.2750	+	14.2750i	1.76897	+	0.473993i	0.780465	+	0.625200i	$0.214982\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	24.0000			0.795155			0.397578	−	0.917568i	$-0.369851\pi$
$911$	24.0000			0.795155			0.397578	+	0.917568i	$0.369851\pi$
$912$	5.00000	+	8.66025i	0.165567	+	0.286770i
$913$	8.19615	+	2.19615i	0.271253	+	0.0726820i
$914$	−1.00000	+	1.73205i	−0.0330771	+	0.0572911i
$915$	14.0000	+	42.0000i	0.462826	+	1.38848i
$916$	−1.09808	−	4.09808i	−0.0362815	−	0.135404i
$917$	34.6410	+	20.0000i	1.14395	+	0.660458i
$918$	−8.00000			−0.264039
$919$	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
$921$	−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
$927$	−2.56218	−	9.56218i	−0.0841530	−	0.314063i
$928$		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	$0.561968\pi$
$930$	18.6603	−	12.3205i	0.611894	−	0.404005i
$931$	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
$934$	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	0.583461	−	0.812141i	$-0.301698\pi$
$937$	−7.00000	−	7.00000i	−0.228680	−	0.228680i	−0.812141	+	0.583461i	$0.801698\pi$
$938$	−6.92820	+	4.00000i	−0.226214	+	0.130605i
$939$	−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	$-0.910843\pi$
$941$	−21.0000	+	21.0000i	−0.684580	+	0.684580i	0.276448	+	0.961029i	$0.410843\pi$
$942$	13.0000	−	22.5167i	0.423563	−	0.733632i
$943$	−21.0000	+	36.3731i	−0.683854	+	1.18447i
$944$	−7.00000	+	7.00000i	−0.227831	+	0.227831i
$945$	−24.7846	−	5.07180i	−0.806243	−	0.164986i
$946$	1.73205	−	1.00000i	0.0563138	−	0.0325128i
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	−0.731417	−	0.681930i	$-0.761141\pi$
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	0.224860	+	0.974391i	$0.427807\pi$
$948$	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
$952$	2.19615	−	8.19615i	0.0711777	−	0.265639i
$953$	−17.7583	+	4.75833i	−0.575249	+	0.154137i	−0.534703	−	0.845040i	$-0.679576\pi$
$953$	−17.7583	+	4.75833i	−0.575249	+	0.154137i	−0.0405460	+	0.999178i	$0.512910\pi$
$954$	−5.00000	−	5.00000i	−0.161881	−	0.161881i
$955$	9.85641	+	14.9282i	0.318946	+	0.483065i
$956$	−4.09808	+	1.09808i	−0.132541	+	0.0355143i
$957$		0			0
$958$	−2.56218	−	9.56218i	−0.0827802	−	0.308940i
$959$	16.0000	+	27.7128i	0.516667	+	0.894893i
$960$	−14.6865	+	16.5622i	−0.474006	+	0.534542i
$961$		−	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
$965$	40.1769	−	2.41154i	1.29334	−	0.0776303i
$966$	10.3923	+	6.00000i	0.334367	+	0.193047i
$967$		0			0			−	1.00000i	$-0.5\pi$
$967$		0			0				1.00000i	$0.5\pi$
$968$	23.3827	+	13.5000i	0.751548	+	0.433906i
$969$	3.66025	+	13.6603i	0.117584	+	0.438831i
$970$	2.00000	−	4.00000i	0.0642161	−	0.128432i
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.247193	−	0.968966i	$-0.420492\pi$
$971$	30.0000	−	51.9615i	0.962746	−	1.66752i	0.715553	−	0.698558i	$-0.246175\pi$
$972$	−9.56218	−	2.56218i	−0.306707	−	0.0821819i
$973$	−14.0000	−	24.2487i	−0.448819	−	0.777378i
$974$	16.0000			0.512673
$975$		0			0
$976$	14.0000			0.448129
$977$	31.0000	+	53.6936i	0.991778	+	1.71781i	0.606715	+	0.794919i	$0.292487\pi$
$977$	31.0000	+	53.6936i	0.991778	+	1.71781i	0.385063	+	0.922890i	$0.374180\pi$
$978$	−5.46410	−	1.46410i	−0.174723	−	0.0468168i
$979$	5.00000	−	8.66025i	0.159801	−	0.276783i
$980$	−3.00000	+	6.00000i	−0.0958315	+	0.191663i
$981$	3.29423	+	12.2942i	0.105177	+	0.392525i
$982$	−19.0526	−	11.0000i	−0.607992	−	0.351024i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$	36.3731	+	21.0000i	1.15953	+	0.669456i
$985$	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
$990$	−2.09808	+	2.36603i	−0.0666812	+	0.0751972i
$991$		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
$993$		−	6.00000i		−	0.190404i
$994$	−2.73205	+	0.732051i	−0.0866554	+	0.0232192i
$995$	−9.85641	−	14.9282i	−0.312469	−	0.473256i
$996$	−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.o.b.587.1		4
5.3	odd	4		845.2.t.b.418.1		4
13.2	odd	12		65.2.f.a.47.1	yes	2
13.3	even	3		845.2.k.a.577.1		2
13.4	even	6		845.2.o.a.357.1		4
13.5	odd	4		845.2.t.a.427.1		4
13.6	odd	12		845.2.t.a.657.1		4
13.7	odd	12		845.2.t.b.657.1		4
13.8	odd	4		845.2.t.b.427.1		4
13.9	even	3	inner	845.2.o.b.357.1		4
13.10	even	6		65.2.k.a.57.1	yes	2
13.11	odd	12		845.2.f.a.437.1		2
13.12	even	2		845.2.o.a.587.1		4
39.2	even	12		585.2.n.c.307.1		2
39.23	odd	6		585.2.w.b.577.1		2
52.15	even	12		1040.2.cd.b.177.1		2
52.23	odd	6		1040.2.bg.a.577.1		2
65.2	even	12		325.2.k.a.268.1		2
65.3	odd	12		845.2.f.a.408.1		2
65.8	even	4	inner	845.2.o.b.258.1		4
65.18	even	4		845.2.o.a.258.1		4
65.23	odd	12		65.2.f.a.18.1	✓	2
65.28	even	12		65.2.k.a.8.1	yes	2
65.33	even	12	inner	845.2.o.b.488.1		4
65.38	odd	4		845.2.t.a.418.1		4
65.43	odd	12		845.2.t.a.188.1		4
65.48	odd	12		845.2.t.b.188.1		4
65.49	even	6		325.2.k.a.57.1		2
65.54	odd	12		325.2.f.a.307.1		2
65.58	even	12		845.2.o.a.488.1		4
65.62	odd	12		325.2.f.a.18.1		2
65.63	even	12		845.2.k.a.268.1		2
195.23	even	12		585.2.n.c.343.1		2
195.158	odd	12		585.2.w.b.73.1		2
260.23	even	12		1040.2.cd.b.993.1		2
260.223	odd	12		1040.2.bg.a.593.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.a.18.1	✓	2	65.23	odd	12
65.2.f.a.47.1	yes	2	13.2	odd	12
65.2.k.a.8.1	yes	2	65.28	even	12
65.2.k.a.57.1	yes	2	13.10	even	6
325.2.f.a.18.1		2	65.62	odd	12
325.2.f.a.307.1		2	65.54	odd	12
325.2.k.a.57.1		2	65.49	even	6
325.2.k.a.268.1		2	65.2	even	12
585.2.n.c.307.1		2	39.2	even	12
585.2.n.c.343.1		2	195.23	even	12
585.2.w.b.73.1		2	195.158	odd	12
585.2.w.b.577.1		2	39.23	odd	6
845.2.f.a.408.1		2	65.3	odd	12
845.2.f.a.437.1		2	13.11	odd	12
845.2.k.a.268.1		2	65.63	even	12
845.2.k.a.577.1		2	13.3	even	3
845.2.o.a.258.1		4	65.18	even	4
845.2.o.a.357.1		4	13.4	even	6
845.2.o.a.488.1		4	65.58	even	12
845.2.o.a.587.1		4	13.12	even	2
845.2.o.b.258.1		4	65.8	even	4	inner
845.2.o.b.357.1		4	13.9	even	3	inner
845.2.o.b.488.1		4	65.33	even	12	inner
845.2.o.b.587.1		4	1.1	even	1	trivial
845.2.t.a.188.1		4	65.43	odd	12
845.2.t.a.418.1		4	65.38	odd	4
845.2.t.a.427.1		4	13.5	odd	4
845.2.t.a.657.1		4	13.6	odd	12
845.2.t.b.188.1		4	65.48	odd	12
845.2.t.b.418.1		4	5.3	odd	4
845.2.t.b.427.1		4	13.8	odd	4
845.2.t.b.657.1		4	13.7	odd	12
1040.2.bg.a.577.1		2	52.23	odd	6
1040.2.bg.a.593.1		2	260.223	odd	12
1040.2.cd.b.177.1		2	52.15	even	12
1040.2.cd.b.993.1		2	260.23	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.36603 - 0.366025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.00000 - 2.00000i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(-1.73205 - 1.00000i) q^{7} +3.00000 q^{8} +(-0.866025 - 0.500000i) q^{9} +(2.23205 - 0.133975i) q^{10} +(0.366025 - 1.36603i) q^{11} +(-1.00000 + 1.00000i) q^{12} -2.00000i q^{14} +(-2.09808 + 2.36603i) q^{15} +(0.500000 + 0.866025i) q^{16} +(0.366025 + 1.36603i) q^{17} -1.00000i q^{18} +(-6.83013 + 1.83013i) q^{19} +(-1.23205 - 1.86603i) q^{20} +(2.00000 + 2.00000i) q^{21} +(1.36603 - 0.366025i) q^{22} +(1.09808 - 4.09808i) q^{23} +(-4.09808 - 1.09808i) q^{24} +(-3.00000 - 4.00000i) q^{25} +(4.00000 + 4.00000i) q^{27} +(-1.73205 + 1.00000i) q^{28} +(-3.09808 - 0.633975i) q^{30} +(-5.00000 + 5.00000i) q^{31} +(2.50000 - 4.33013i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-1.00000 + 1.00000i) q^{34} +(-3.73205 + 2.46410i) 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} +(-0.732051 + 2.73205i) q^{42} +(1.36603 - 0.366025i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(-1.86603 + 1.23205i) q^{45} +(4.09808 - 1.09808i) q^{46} -6.00000i q^{47} +(-0.366025 - 1.36603i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(1.96410 - 4.59808i) q^{50} -2.00000i q^{51} +(5.00000 - 5.00000i) q^{53} +(-1.46410 + 5.46410i) q^{54} +(-2.36603 - 2.09808i) q^{55} +(-5.19615 - 3.00000i) q^{56} +10.0000 q^{57} +(2.56218 + 9.56218i) q^{59} +(1.00000 + 3.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(-6.83013 - 1.83013i) q^{62} +(1.00000 + 1.73205i) q^{63} +7.00000 q^{64} -2.00000 q^{66} +(-2.00000 - 3.46410i) q^{67} +(1.36603 + 0.366025i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(-4.00000 - 2.00000i) q^{70} +(-0.366025 - 1.36603i) q^{71} +(-2.59808 - 1.50000i) q^{72} +10.0000 q^{73} +(2.63397 + 6.56218i) q^{75} +(-1.83013 + 6.83013i) q^{76} +(-2.00000 + 2.00000i) q^{77} -2.00000i q^{79} +(2.23205 - 0.133975i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(-2.56218 - 9.56218i) q^{82} +6.00000i q^{83} +(2.73205 - 0.732051i) q^{84} +(3.09808 + 0.633975i) q^{85} +(1.00000 + 1.00000i) q^{86} +(1.09808 - 4.09808i) q^{88} +(6.83013 + 1.83013i) q^{89} +(-2.00000 - 1.00000i) q^{90} +(-3.00000 - 3.00000i) q^{92} +(8.66025 - 5.00000i) q^{93} +(5.19615 - 3.00000i) q^{94} +(-3.16987 + 15.4904i) q^{95} +(-5.00000 + 5.00000i) q^{96} +(1.00000 - 1.73205i) q^{97} +(1.50000 - 2.59808i) q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 4 q^{5} + 2 q^{6} + 12 q^{8} + 2 q^{10} - 2 q^{11} - 4 q^{12} + 2 q^{15} + 2 q^{16} - 2 q^{17} - 10 q^{19} + 2 q^{20} + 8 q^{21} + 2 q^{22} - 6 q^{23} - 6 q^{24} - 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 4 * q^5 + 2 * q^6 + 12 * q^8 + 2 * q^10 - 2 * q^11 - 4 * q^12 + 2 * q^15 + 2 * q^16 - 2 * q^17 - 10 * q^19 + 2 * q^20 + 8 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 - 12 * q^25 + 16 * q^27 - 2 * q^30 - 20 * q^31 + 10 * q^32 - 4 * q^33 - 4 * q^34 - 8 * q^35 - 20 * q^38 + 12 * q^40 - 14 * q^41 + 4 * q^42 + 2 * q^43 - 4 * q^44 - 4 * q^45 + 6 * q^46 + 2 * q^48 - 6 * q^49 - 6 * q^50 + 20 * q^53 + 8 * q^54 - 6 * q^55 + 40 * q^57 - 14 * q^59 + 4 * q^60 + 28 * q^61 - 10 * q^62 + 4 * q^63 + 28 * q^64 - 8 * q^66 - 8 * q^67 + 2 * q^68 - 12 * q^69 - 16 * q^70 + 2 * q^71 + 40 * q^73 + 14 * q^75 + 10 * q^76 - 8 * q^77 + 2 * q^80 - 10 * q^81 + 14 * q^82 + 4 * q^84 + 2 * q^85 + 4 * q^86 - 6 * q^88 + 10 * q^89 - 8 * q^90 - 12 * q^92 - 30 * q^95 - 20 * q^96 + 4 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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