LMFDB - Embedded newform 845.2.t.b.188.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			188.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.b.427.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 + 0.366025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.36603 + 0.366025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +3.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 + 8 * q^5 + 2 * q^6 - 4 * q^7	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	0.161521	−	0.986869i	$-0.448360\pi$
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	−0.773893	+	0.633316i	$0.781693\pi$
$3$	−1.36603	+	0.366025i	−0.788675	+	0.211325i	−0.630606	−	0.776103i	$-0.717194\pi$
$3$	−1.36603	+	0.366025i	−0.788675	+	0.211325i	−0.158069	+	0.987428i	$0.550527\pi$
$4$	−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	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$			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	$-0.651722\pi$
$11$	−1.36603	+	0.366025i	−0.411872	+	0.110361i	0.0469323	+	0.998898i	$0.485055\pi$
$12$	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	−0.996002	−	0.0893296i	$-0.971528\pi$
$17$	−0.366025	+	1.36603i	−0.0887742	+	0.331310i	0.907228	+	0.420639i	$0.138194\pi$
$18$	1.00000			0.235702
$19$	−1.83013	+	6.83013i	−0.419860	+	1.56694i	0.355038	+	0.934852i	$0.384468\pi$
$19$	−1.83013	+	6.83013i	−0.419860	+	1.56694i	−0.774898	+	0.632087i	$0.782199\pi$
$20$	−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	−0.980777	−	0.195131i	$-0.937487\pi$
$23$	−1.09808	−	4.09808i	−0.228965	−	0.854508i	0.751812	−	0.659377i	$-0.229180\pi$
$24$	−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	$-0.333333\pi$
$29$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$30$	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	$0.469000\pi$
$32$	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	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	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	0.812837	+	0.582491i	$0.197922\pi$
$41$	2.56218	+	9.56218i	0.400145	+	1.49336i	−0.412692	+	0.910870i	$0.635412\pi$
$42$	−0.732051	−	2.73205i	−0.112958	−	0.421565i
$43$	−1.36603	−	0.366025i	−0.208317	−	0.0558184i	0.153151	−	0.988203i	$-0.451058\pi$
$43$	−1.36603	−	0.366025i	−0.208317	−	0.0558184i	−0.361468	+	0.932384i	$0.617724\pi$
$44$	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	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−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	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$	−5.46410	+	1.46410i	−0.743570	+	0.199239i
$55$	−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	$-0.193773\pi$
$59$	9.56218	+	2.56218i	1.24489	+	0.333567i	0.424529	+	0.905414i	$0.360440\pi$
$60$	3.00000	+	1.00000i	0.387298	+	0.129099i
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	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	$-0.254762\pi$
$67$	3.46410	+	2.00000i	0.423207	+	0.244339i	−0.273241	+	0.961946i	$0.588096\pi$
$68$	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	$-0.389923\pi$
$71$	1.36603	+	0.366025i	0.162117	+	0.0434392i	−0.176847	+	0.984238i	$0.556590\pi$
$72$	−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	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$	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	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	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	0.992525	+	0.122040i	$0.0389436\pi$
$89$	1.83013	+	6.83013i	0.193993	+	0.723992i	−0.798532	+	0.601952i	$0.794390\pi$
$90$	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	$-0.634291\pi$
$97$	1.73205	−	1.00000i	0.175863	−	0.101535i	0.585348	+	0.810782i	$0.300958\pi$
$98$	−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	−0.115924	−	0.993258i	$-0.536983\pi$
$101$	−10.3923	−	6.00000i	−1.03407	−	0.597022i	−0.918149	+	0.396236i	$0.870316\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	−0.962172	−	0.272442i	$-0.912169\pi$
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	0.272442	+	0.962172i	$0.412169\pi$
$104$		0			0
$105$	6.00000	+	2.00000i	0.585540	+	0.195180i
$106$	−1.83013	−	6.83013i	−0.177758	−	0.663401i
$107$	2.56218	+	9.56218i	0.247695	+	0.924411i	0.972010	+	0.234941i	$0.0754897\pi$
$107$	2.56218	+	9.56218i	0.247695	+	0.924411i	−0.724315	+	0.689470i	$0.757844\pi$
$108$	−5.46410	−	1.46410i	−0.525783	−	0.140883i
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	0.991575	−	0.129532i	$-0.0413474\pi$
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	−0.129532	+	0.991575i	$0.541347\pi$
$110$	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	−0.824853	−	0.565347i	$-0.808742\pi$
$113$	1.83013	−	6.83013i	0.172164	−	0.642524i	0.997017	−	0.0771777i	$-0.0245909\pi$
$114$	−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	0.331868	−	0.943326i	$-0.392321\pi$
$127$	12.2942	−	3.29423i	1.09094	−	0.292316i	0.759069	+	0.651010i	$0.225655\pi$
$128$	−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	−0.973910	−	0.226935i	$-0.927130\pi$
$137$	−8.00000	−	13.8564i	−0.683486	−	1.18383i	0.290424	−	0.956898i	$-0.406204\pi$
$138$		−	6.00000i		−	0.510754i
$139$	12.1244	−	7.00000i	1.02837	−	0.593732i	0.111856	−	0.993724i	$-0.464321\pi$
$139$	12.1244	−	7.00000i	1.02837	−	0.593732i	0.916519	+	0.399992i	$0.130987\pi$
$140$	−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	$-0.972267\pi$
$149$	−1.09808	+	4.09808i	−0.0899579	+	0.335727i	0.906249	+	0.422744i	$0.138933\pi$
$150$	5.56218	−	4.36603i	0.454150	−	0.356484i
$151$	−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
$154$	−0.732051	−	2.73205i	−0.0589903	−	0.220155i
$155$	−5.00000	+	15.0000i	−0.401610	+	1.20483i
$156$		0			0
$157$	13.0000	−	13.0000i	1.03751	−	1.03751i	0.0382445	−	0.999268i	$-0.487823\pi$
$157$	13.0000	−	13.0000i	1.03751	−	1.03751i	0.999268	−	0.0382445i	$-0.0121766\pi$
$158$	1.00000	−	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	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$	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	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$	−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	−0.362500	−	0.931984i	$-0.618077\pi$
$173$	−15.0263	−	4.02628i	−1.14243	−	0.306112i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		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	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$	2.23205	+	0.133975i	0.166367	+	0.00998588i
$181$		−	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
$184$	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	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	9.56218	−	2.56218i	0.690091	−	0.184909i
$193$	15.5885	+	9.00000i	1.12208	+	0.647834i	0.941932	−	0.335805i	$-0.109008\pi$
$193$	15.5885	+	9.00000i	1.12208	+	0.647834i	0.180150	+	0.983639i	$0.442342\pi$
$194$	−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	$-0.401898\pi$
$197$	−5.19615	−	3.00000i	−0.370211	−	0.213741i	−0.673550	+	0.739141i	$0.735232\pi$
$198$	−1.36603	+	0.366025i	−0.0970792	+	0.0260123i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	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	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	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	$-0.812002\pi$
$223$	1.00000	−	1.73205i	0.0669650	−	0.115987i	0.897564	+	0.440884i	$0.145335\pi$
$224$	−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	$-0.797043\pi$
$227$	−10.3923	+	6.00000i	−0.689761	+	0.398234i	0.113761	+	0.993508i	$0.463710\pi$
$228$	−8.66025	+	5.00000i	−0.573539	+	0.331133i
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$	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	$-0.764751\pi$
$233$	−1.00000	+	1.00000i	−0.0655122	+	0.0655122i	0.673592	+	0.739104i	$0.264751\pi$
$234$		0			0
$235$	−12.0000	+	6.00000i	−0.782794	+	0.391397i
$236$	−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	$-0.206184\pi$
$239$	3.00000	+	3.00000i	0.194054	+	0.194054i	−0.603391	+	0.797445i	$0.706184\pi$
$240$	0.633975	+	3.09808i	0.0409229	+	0.199980i
$241$	−6.22243	+	23.2224i	−0.400822	+	1.49589i	0.410811	+	0.911721i	$0.365246\pi$
$241$	−6.22243	+	23.2224i	−0.400822	+	1.49589i	−0.811633	+	0.584168i	$0.801421\pi$
$242$	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	−0.444340	−	0.895858i	$-0.646562\pi$
$251$	1.73205	−	1.00000i	0.109326	−	0.0631194i	0.553666	+	0.832739i	$0.313228\pi$
$252$		−	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	−0.694971	−	0.719038i	$-0.744583\pi$
$257$	−15.0263	+	4.02628i	−0.937314	+	0.251152i	−0.242343	+	0.970191i	$0.577916\pi$
$258$	−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	−0.300689	−	0.953722i	$-0.597217\pi$
$263$	−1.36603	+	0.366025i	−0.0842327	+	0.0225701i	0.216457	+	0.976292i	$0.430550\pi$
$264$	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	−0.782157	−	0.623082i	$-0.785880\pi$
$269$	−10.3923	+	6.00000i	−0.633630	+	0.365826i	0.148527	+	0.988908i	$0.452547\pi$
$270$	−9.46410	+	8.39230i	−0.575967	+	0.510739i
$271$	−12.2942	+	3.29423i	−0.746821	+	0.200110i	−0.612108	−	0.790774i	$-0.709678\pi$
$271$	−12.2942	+	3.29423i	−0.746821	+	0.200110i	−0.134714	+	0.990885i	$0.543011\pi$
$272$	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	−0.579424	−	0.815026i	$-0.696722\pi$
$277$	5.49038	−	20.4904i	0.329885	−	1.23115i	0.909309	−	0.416121i	$-0.136611\pi$
$278$	−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	$-0.263431\pi$
$281$	−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	0.992053	+	0.125823i	$0.0401573\pi$
$283$	3.29423	+	12.2942i	0.195822	+	0.730816i	−0.796231	+	0.604993i	$0.793176\pi$
$284$	−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	$-0.610589\pi$
$293$	5.19615	−	3.00000i	0.303562	−	0.175262i	0.644042	+	0.764990i	$0.277256\pi$
$294$	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	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	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	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$	−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	$-0.453866\pi$
$331$	−4.09808	−	1.09808i	−0.225251	−	0.0603557i	−0.369679	+	0.929160i	$0.620532\pi$
$332$	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	0.257992	−	0.966147i	$-0.416939\pi$
$337$	−13.0000	−	13.0000i	−0.708155	−	0.708155i	−0.966147	+	0.257992i	$0.916939\pi$
$338$		0			0
$339$			10.0000i			0.543125i
$340$	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	0.147137	−	0.989116i	$-0.452994\pi$
$347$	−4.09808	−	1.09808i	−0.219996	−	0.0589478i	−0.367133	+	0.930168i	$0.619661\pi$
$348$		0			0
$349$	3.29423	+	12.2942i	0.176336	+	0.658095i	0.996320	+	0.0857088i	$0.0273155\pi$
$349$	3.29423	+	12.2942i	0.176336	+	0.658095i	−0.819984	+	0.572386i	$0.806018\pi$
$350$	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	$-0.936797\pi$
$353$	−6.00000	+	10.3923i	−0.319348	+	0.553127i	0.661004	+	0.750382i	$0.270130\pi$
$354$	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	$-0.738118\pi$
$359$	1.00000	−	1.00000i	0.0527780	−	0.0527780i	0.733003	+	0.680225i	$0.238118\pi$
$360$	−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	0.955714	−	0.294296i	$-0.0950850\pi$
$367$	−0.366025	−	1.36603i	−0.0191064	−	0.0713059i	−0.974821	+	0.222990i	$0.928418\pi$
$368$	−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	0.665082	+	0.746770i	$0.268397\pi$
$373$	−5.49038	+	20.4904i	−0.284281	+	1.06095i	−0.949363	+	0.314181i	$0.898270\pi$
$374$	−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	$-0.571769\pi$
$379$	1.36603	−	0.366025i	0.0701680	−	0.0188015i	0.293732	+	0.955888i	$0.405103\pi$
$380$	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	−0.939469	−	0.342634i	$-0.888681\pi$
$383$	−15.0000	−	25.9808i	−0.766464	−	1.32755i	0.173005	−	0.984921i	$-0.444652\pi$
$384$	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	$-0.0351527\pi$
$397$	8.00000	+	13.8564i	0.401508	+	0.695433i	−0.592400	+	0.805644i	$0.701819\pi$
$398$			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	$-0.710314\pi$
$401$	−15.0263	+	4.02628i	−0.750377	+	0.201063i	−0.136691	+	0.990614i	$0.543647\pi$
$402$	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	$-0.995372\pi$
$409$	−2.56218	+	9.56218i	−0.126692	+	0.472819i	0.873203	+	0.487357i	$0.162039\pi$
$410$	−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	−0.989882	−	0.141896i	$-0.954680\pi$
$419$	−32.9090	−	19.0000i	−1.60771	−	0.928211i	−0.617827	−	0.786314i	$-0.711987\pi$
$420$	−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	$0.126239\pi$
$422$	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	−0.980678	−	0.195630i	$-0.937325\pi$
$431$	−4.75833	−	17.7583i	−0.229201	−	0.855389i	0.751477	−	0.659759i	$-0.229342\pi$
$432$	−1.46410	−	5.46410i	−0.0704416	−	0.262892i
$433$	23.2224	+	6.22243i	1.11600	+	0.299031i	0.769263	−	0.638932i	$-0.220623\pi$
$433$	23.2224	+	6.22243i	1.11600	+	0.299031i	0.346736	+	0.937963i	$0.387290\pi$
$434$	−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	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	−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	0.977678	+	0.210108i	$0.0673814\pi$
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.210108	+	0.977678i	$0.432619\pi$
$444$		0			0
$445$	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	$-0.384747\pi$
$449$	4.09808	+	1.09808i	0.193400	+	0.0518214i	−0.160819	+	0.986984i	$0.551413\pi$
$450$	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	$-0.348229\pi$
$457$	−1.73205	−	1.00000i	−0.0810219	−	0.0467780i	−0.539964	+	0.841688i	$0.681562\pi$
$458$	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	$-0.227520\pi$
$461$	23.2224	+	6.22243i	1.08158	+	0.289808i	0.326335	+	0.945254i	$0.394186\pi$
$462$	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	0.467515	−	0.883985i	$-0.345149\pi$
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	−0.883985	+	0.467515i	$0.845149\pi$
$468$		0			0
$469$		−	8.00000i		−	0.369406i
$470$	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	$-0.155950\pi$
$479$	−2.56218	−	9.56218i	−0.117069	−	0.436907i	−0.999433	+	0.0336596i	$0.989284\pi$
$480$	−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	$-0.548585\pi$
$487$	13.8564	−	8.00000i	0.627894	−	0.362515i	0.779936	+	0.625859i	$0.215252\pi$
$488$	−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	0.863955	−	0.503568i	$-0.167980\pi$
$491$	19.0526	+	11.0000i	0.859830	+	0.496423i	−0.00412539	+	0.999991i	$0.501313\pi$
$492$	−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	$-0.219727\pi$
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	−0.636762	+	0.771060i	$0.719727\pi$
$500$	−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	−0.986076	−	0.166297i	$-0.946819\pi$
$503$	−1.09808	+	4.09808i	−0.0489608	+	0.182724i	0.937115	+	0.349021i	$0.113486\pi$
$504$	−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	$-0.716914\pi$
$509$	−17.7583	+	4.75833i	−0.787124	+	0.210909i	−0.157201	+	0.987567i	$0.550247\pi$
$510$	−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	−0.517390	−	0.855749i	$-0.673097\pi$
$523$	−12.2942	+	3.29423i	−0.537589	+	0.144047i	−0.0201986	+	0.999796i	$0.506430\pi$
$524$	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	$-0.338217\pi$
$541$	−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
$544$	1.83013	+	6.83013i	0.0784660	+	0.292839i
$545$	27.0000	+	9.00000i	1.15655	+	0.385518i
$546$		0			0
$547$	−9.00000	+	9.00000i	−0.384812	+	0.384812i	−0.872832	−	0.488020i	$-0.837719\pi$
$547$	−9.00000	+	9.00000i	−0.384812	+	0.384812i	0.488020	+	0.872832i	$0.337719\pi$
$548$	−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	−0.491496	−	0.870880i	$-0.663550\pi$
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	0.999952	−	0.00979220i	$-0.00311700\pi$
$558$	−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	0.663304	−	0.748350i	$-0.269154\pi$
$563$	20.4904	+	5.49038i	0.863567	+	0.231392i	0.200263	+	0.979742i	$0.435820\pi$
$564$	−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	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	−1.33975	+	22.3205i	−0.0561158	+	0.934903i
$571$		−	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
$574$	−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	$-0.307027\pi$
$587$	3.46410	+	2.00000i	0.142979	+	0.0825488i	−0.426804	+	0.904344i	$0.640361\pi$
$588$	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	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$	−19.6865	−	7.90192i	−0.803699	−	0.322595i
$601$	19.0000	−	32.9090i	0.775026	−	1.34238i	−0.159754	−	0.987157i	$-0.551070\pi$
$601$	19.0000	−	32.9090i	0.775026	−	1.34238i	0.934780	−	0.355228i	$-0.115597\pi$
$602$	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	0.600523	−	0.799607i	$-0.294959\pi$
$607$	17.7583	+	4.75833i	0.720788	+	0.193135i	0.120265	+	0.992742i	$0.461626\pi$
$608$	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	$-0.965678\pi$
$613$	−10.0000	+	17.3205i	−0.403896	+	0.699569i	0.590296	+	0.807187i	$0.299011\pi$
$614$	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	$-0.812697\pi$
$617$	−19.0526	+	11.0000i	−0.767027	+	0.442843i	0.0647859	+	0.997899i	$0.479364\pi$
$618$	−12.1244	+	7.00000i	−0.487713	+	0.281581i
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.00484658	−	0.999988i	$-0.498457\pi$
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.999988	−	0.00484658i	$-0.00154272\pi$
$620$	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	0.838311	+	0.545192i	$0.183543\pi$
$631$	−4.02628	+	15.0263i	−0.160284	+	0.598187i	−0.998595	+	0.0529946i	$0.983123\pi$
$632$	−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	−0.850741	−	0.525584i	$-0.823847\pi$
$641$	−20.7846	+	12.0000i	−0.820943	+	0.473972i	0.0297987	+	0.999556i	$0.490513\pi$
$642$			14.0000i			0.552536i
$643$	−17.0000	−	29.4449i	−0.670415	−	1.16119i	−0.977787	−	0.209603i	$-0.932783\pi$
$643$	−17.0000	−	29.4449i	−0.670415	−	1.16119i	0.307372	−	0.951589i	$-0.400550\pi$
$644$	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	−0.231867	−	0.972747i	$-0.574483\pi$
$647$	1.36603	−	0.366025i	0.0537040	−	0.0143899i	0.285571	+	0.958358i	$0.407817\pi$
$648$	−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	−0.588962	−	0.808161i	$-0.700463\pi$
$653$	−17.7583	+	4.75833i	−0.694937	+	0.186208i	−0.105975	+	0.994369i	$0.533796\pi$
$654$	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	−0.869709	−	0.493564i	$-0.835694\pi$
$659$	−22.5167	+	13.0000i	−0.877125	+	0.506408i	−0.00741531	+	0.999973i	$0.502360\pi$
$660$	−4.46410	−	0.267949i	−0.173765	−	0.0104299i
$661$	23.2224	−	6.22243i	0.903248	−	0.242025i	0.222837	−	0.974856i	$-0.428468\pi$
$661$	23.2224	−	6.22243i	0.903248	−	0.242025i	0.680411	+	0.732831i	$0.261801\pi$
$662$	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	0.987323	+	0.158725i	$0.0507383\pi$
$673$	5.49038	+	20.4904i	0.211639	+	0.789846i	−0.775684	+	0.631121i	$0.782595\pi$
$674$	4.75833	+	17.7583i	0.183284	+	0.684025i
$675$	−4.00000	−	28.0000i	−0.153960	−	1.07772i
$676$		0			0
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	−0.993935	−	0.109973i	$-0.964924\pi$
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	0.109973	+	0.993935i	$0.464924\pi$
$678$	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	$-0.592930\pi$
$683$	10.3923	−	6.00000i	0.397650	−	0.229584i	0.685470	+	0.728101i	$0.259597\pi$
$684$	−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	$-0.0576181\pi$
$691$	1.09808	+	4.09808i	0.0417728	+	0.155898i	−0.941889	+	0.335924i	$0.890951\pi$
$692$	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	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$		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	$-0.696472\pi$
$709$	−39.6147	−	10.6147i	−1.48776	−	0.398645i	−0.908981	+	0.416838i	$0.863138\pi$
$710$	−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	0.781748	−	0.623595i	$-0.214328\pi$
$719$	−4.00000	−	6.92820i	−0.149175	−	0.258378i	−0.930923	+	0.365216i	$0.880995\pi$
$720$	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	0.929660	+	0.368418i	$0.120100\pi$
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.368418	+	0.929660i	$0.379900\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$	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	$-0.476464\pi$
$733$	4.00000			0.147743			0.0738717	+	0.997268i	$0.476464\pi$
$734$	−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	$-0.108198\pi$
$739$	−1.09808	−	4.09808i	−0.0403934	−	0.150750i	−0.983177	+	0.182655i	$0.941531\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	+	10.0000i	−0.367112	+	0.367112i
$743$	17.0000	−	29.4449i	0.623670	−	1.08023i	−0.365127	−	0.930958i	$-0.618974\pi$
$743$	17.0000	−	29.4449i	0.623670	−	1.08023i	0.988797	−	0.149270i	$-0.0476922\pi$
$744$	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	0.994845	+	0.101403i	$0.0323332\pi$
$751$	43.3013	+	25.0000i	1.58009	+	0.912263i	0.585240	+	0.810860i	$0.301000\pi$
$752$	−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	−0.654827	−	0.755779i	$-0.727258\pi$
$757$	−12.8109	−	47.8109i	−0.465620	−	1.73772i	0.189207	−	0.981937i	$-0.439408\pi$
$758$	−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	$-0.859242\pi$
$761$	2.56218	−	9.56218i	0.0928789	−	0.346629i	0.996689	+	0.0813044i	$0.0259086\pi$
$762$	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	$-0.458402\pi$
$769$	20.4904	−	5.49038i	0.738902	−	0.197988i	0.608590	+	0.793485i	$0.291735\pi$
$770$	−4.19615	−	4.73205i	−0.151219

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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.36603 + 0.366025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.00000 - 1.00000i) q^{5} +(1.36603 + 0.366025i) q^{6} +(-1.00000 - 1.73205i) q^{7} +3.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} + 8 q^{5} + 2 q^{6} - 4 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 + 8 * q^5 + 2 * q^6 - 4 * q^7	\( 4 q - 2 q^{3} - 2 q^{4} + 8 q^{5} + 2 q^{6} - 4 q^{7} - 2 q^{10} - 2 q^{11} + 4 q^{12} - 6 q^{15} + 2 q^{16} + 2 q^{17} + 4 q^{18} + 10 q^{19} - 4 q^{20} + 8 q^{21} + 2 q^{22} + 6 q^{23} + 6 q^{24} + 12 q^{25} + 16 q^{27} - 4 q^{28} + 2 q^{30} - 20 q^{31} + 4 q^{34} - 8 q^{35} + 20 q^{38} + 12 q^{40} - 14 q^{41} + 4 q^{42} - 2 q^{43} + 4 q^{44} + 2 q^{45} + 6 q^{46} - 24 q^{47} + 2 q^{48} + 6 q^{49} - 8 q^{50} + 20 q^{53} - 8 q^{54} - 6 q^{55} + 14 q^{59} + 12 q^{60} + 28 q^{61} + 10 q^{62} - 28 q^{64} - 8 q^{66} + 2 q^{68} + 12 q^{69} + 8 q^{70} + 2 q^{71} - 6 q^{72} - 14 q^{75} + 10 q^{76} + 8 q^{77} + 4 q^{80} - 10 q^{81} - 14 q^{82} - 24 q^{83} - 4 q^{84} + 6 q^{85} + 4 q^{86} + 6 q^{88} - 10 q^{89} + 8 q^{90} - 12 q^{92} + 20 q^{93} + 30 q^{95} - 20 q^{96} + 4 q^{99}+O(q^{100}) \) 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

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Groups

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