LMFDB - Embedded newform 845.2.t.b.418.1

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.366025 - 1.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(-1.00000 + 1.73205i) q^{7} +3.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.366025 - 1.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 - 1.00000i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(-1.00000 + 1.73205i) q^{7} +3.00000i q^{8} +(0.866025 + 0.500000i) q^{9} +(1.23205 - 1.86603i) q^{10} +(0.366025 - 1.36603i) q^{11} +(1.00000 + 1.00000i) q^{12} +2.00000i q^{14} +(-0.633975 - 3.09808i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.36603 - 0.366025i) q^{17} +1.00000 q^{18} +(6.83013 - 1.83013i) q^{19} +(-0.133975 + 2.23205i) q^{20} +(2.00000 + 2.00000i) q^{21} +(-0.366025 - 1.36603i) q^{22} +(4.09808 + 1.09808i) q^{23} +(4.09808 + 1.09808i) q^{24} +(3.00000 - 4.00000i) q^{25} +(4.00000 - 4.00000i) q^{27} +(-1.00000 - 1.73205i) q^{28} +(-2.09808 - 2.36603i) q^{30} +(-5.00000 + 5.00000i) q^{31} +(-4.33013 - 2.50000i) q^{32} +(-1.73205 - 1.00000i) q^{33} +(1.00000 - 1.00000i) q^{34} +(-0.267949 + 4.46410i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(5.00000 - 5.00000i) q^{38} +(3.00000 + 6.00000i) q^{40} +(-9.56218 - 2.56218i) q^{41} +(2.73205 + 0.732051i) q^{42} +(0.366025 + 1.36603i) q^{43} +(1.00000 + 1.00000i) q^{44} +(2.23205 + 0.133975i) q^{45} +(4.09808 - 1.09808i) q^{46} -6.00000 q^{47} +(1.36603 - 0.366025i) q^{48} +(1.50000 + 2.59808i) q^{49} +(0.598076 - 4.96410i) q^{50} -2.00000i q^{51} +(5.00000 + 5.00000i) q^{53} +(1.46410 - 5.46410i) q^{54} +(-0.633975 - 3.09808i) q^{55} +(-5.19615 - 3.00000i) q^{56} -10.0000i q^{57} +(-2.56218 - 9.56218i) q^{59} +(3.00000 + 1.00000i) q^{60} +(7.00000 - 12.1244i) q^{61} +(-1.83013 + 6.83013i) q^{62} +(-1.73205 + 1.00000i) q^{63} -7.00000 q^{64} -2.00000 q^{66} +(-3.46410 + 2.00000i) q^{67} +(-0.366025 + 1.36603i) q^{68} +(3.00000 - 5.19615i) q^{69} +(2.00000 + 4.00000i) q^{70} +(-0.366025 - 1.36603i) q^{71} +(-1.50000 + 2.59808i) q^{72} +10.0000i q^{73} +(-4.36603 - 5.56218i) q^{75} +(-1.83013 + 6.83013i) q^{76} +(2.00000 + 2.00000i) q^{77} +2.00000i q^{79} +(1.86603 + 1.23205i) q^{80} +(-2.50000 - 4.33013i) q^{81} +(-9.56218 + 2.56218i) q^{82} -6.00000 q^{83} +(-2.73205 + 0.732051i) q^{84} +(2.36603 - 2.09808i) q^{85} +(1.00000 + 1.00000i) q^{86} +(4.09808 + 1.09808i) q^{88} +(-6.83013 - 1.83013i) q^{89} +(2.00000 - 1.00000i) q^{90} +(-3.00000 + 3.00000i) q^{92} +(5.00000 + 8.66025i) q^{93} +(-5.19615 + 3.00000i) q^{94} +(11.8301 - 10.4904i) q^{95} +(-5.00000 + 5.00000i) q^{96} +(-1.73205 - 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} +(1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} + 8 q^{5} + 2 q^{6} - 4 q^{7}+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 $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	−0.161521	−	0.986869i	$-0.551640\pi$
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i	0.773893	+	0.633316i	$0.218307\pi$
$3$	0.366025	−	1.36603i	0.211325	−	0.788675i	−0.776103	−	0.630606i	$-0.782806\pi$
$3$	0.366025	−	1.36603i	0.211325	−	0.788675i	0.987428	−	0.158069i	$-0.0505269\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$5$	2.00000	−	1.00000i	0.894427	−	0.447214i
$6$	−0.366025	−	1.36603i	−0.149429	−	0.557678i
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	−0.990766	−	0.135583i	$-0.956709\pi$
$7$	−1.00000	+	1.73205i	−0.377964	+	0.654654i	0.612801	+	0.790237i	$0.290043\pi$
$8$			3.00000i			1.06066i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	1.23205	−	1.86603i	0.389609	−	0.590089i
$11$	0.366025	−	1.36603i	0.110361	−	0.411872i	−0.888537	−	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
$15$	−0.633975	−	3.09808i	−0.163692	−	0.799920i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.36603	−	0.366025i	0.331310	−	0.0887742i	−0.0893296	−	0.996002i	$-0.528472\pi$
$17$	1.36603	−	0.366025i	0.331310	−	0.0887742i	0.420639	+	0.907228i	$0.361806\pi$
$18$	1.00000			0.235702
$19$	6.83013	−	1.83013i	1.56694	−	0.419860i	0.632087	−	0.774898i	$-0.282199\pi$
$19$	6.83013	−	1.83013i	1.56694	−	0.419860i	0.934852	+	0.355038i	$0.115532\pi$
$20$	−0.133975	+	2.23205i	−0.0299576	+	0.499102i
$21$	2.00000	+	2.00000i	0.436436	+	0.436436i
$22$	−0.366025	−	1.36603i	−0.0780369	−	0.291238i
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.659377	−	0.751812i	$-0.270820\pi$
$23$	4.09808	+	1.09808i	0.854508	+	0.228965i	0.195131	+	0.980777i	$0.437487\pi$
$24$	4.09808	+	1.09808i	0.836516	+	0.224144i
$25$	3.00000	−	4.00000i	0.600000	−	0.800000i
$26$		0			0
$27$	4.00000	−	4.00000i	0.769800	−	0.769800i
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$	−2.09808	−	2.36603i	−0.383055	−	0.431975i
$31$	−5.00000	+	5.00000i	−0.898027	+	0.898027i	−0.995261	−	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
$35$	−0.267949	+	4.46410i	−0.0452917	+	0.754571i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$37$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$38$	5.00000	−	5.00000i	0.811107	−	0.811107i
$39$		0			0
$40$	3.00000	+	6.00000i	0.474342	+	0.948683i
$41$	−9.56218	−	2.56218i	−1.49336	−	0.400145i	−0.582491	−	0.812837i	$-0.697922\pi$
$41$	−9.56218	−	2.56218i	−1.49336	−	0.400145i	−0.910870	+	0.412692i	$0.864588\pi$
$42$	2.73205	+	0.732051i	0.421565	+	0.112958i
$43$	0.366025	+	1.36603i	0.0558184	+	0.208317i	0.988203	−	0.153151i	$-0.0489422\pi$
$43$	0.366025	+	1.36603i	0.0558184	+	0.208317i	−0.932384	+	0.361468i	$0.882276\pi$
$44$	1.00000	+	1.00000i	0.150756	+	0.150756i
$45$	2.23205	+	0.133975i	0.332734	+	0.0199718i
$46$	4.09808	−	1.09808i	0.604228	−	0.161903i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.36603	−	0.366025i	0.197169	−	0.0528312i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	0.598076	−	4.96410i	0.0845807	−	0.702030i
$51$		−	2.00000i		−	0.280056i
$52$		0			0
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	0.961524	−	0.274721i	$-0.0885855\pi$
$53$	5.00000	+	5.00000i	0.686803	+	0.686803i	−0.274721	+	0.961524i	$0.588586\pi$
$54$	1.46410	−	5.46410i	0.199239	−	0.743570i
$55$	−0.633975	−	3.09808i	−0.0854851	−	0.417745i
$56$	−5.19615	−	3.00000i	−0.694365	−	0.400892i
$57$		−	10.0000i		−	1.32453i
$58$		0			0
$59$	−2.56218	−	9.56218i	−0.333567	−	1.24489i	−0.905414	−	0.424529i	$-0.860440\pi$
$59$	−2.56218	−	9.56218i	−0.333567	−	1.24489i	0.571847	−	0.820360i	$-0.306227\pi$
$60$	3.00000	+	1.00000i	0.387298	+	0.129099i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$	−1.83013	+	6.83013i	−0.232426	+	0.867427i
$63$	−1.73205	+	1.00000i	−0.218218	+	0.125988i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	−0.696449	−	0.717607i	$-0.745238\pi$
$67$	−3.46410	+	2.00000i	−0.423207	+	0.244339i	0.273241	+	0.961946i	$0.411904\pi$
$68$	−0.366025	+	1.36603i	−0.0443871	+	0.165655i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$	2.00000	+	4.00000i	0.239046	+	0.478091i
$71$	−0.366025	−	1.36603i	−0.0434392	−	0.162117i	0.940799	−	0.338965i	$-0.110077\pi$
$71$	−0.366025	−	1.36603i	−0.0434392	−	0.162117i	−0.984238	+	0.176847i	$0.943410\pi$
$72$	−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
$75$	−4.36603	−	5.56218i	−0.504145	−	0.642265i
$76$	−1.83013	+	6.83013i	−0.209930	+	0.783469i
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$	1.86603	+	1.23205i	0.208628	+	0.137747i
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$	−9.56218	+	2.56218i	−1.05597	+	0.282945i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−2.73205	+	0.732051i	−0.298091	+	0.0798733i
$85$	2.36603	−	2.09808i	0.256631	−	0.227568i
$86$	1.00000	+	1.00000i	0.107833	+	0.107833i
$87$		0			0
$88$	4.09808	+	1.09808i	0.436856	+	0.117055i
$89$	−6.83013	−	1.83013i	−0.723992	−	0.193993i	−0.122040	−	0.992525i	$-0.538944\pi$
$89$	−6.83013	−	1.83013i	−0.723992	−	0.193993i	−0.601952	+	0.798532i	$0.705610\pi$
$90$	2.00000	−	1.00000i	0.210819	−	0.105409i
$91$		0			0
$92$	−3.00000	+	3.00000i	−0.312772	+	0.312772i
$93$	5.00000	+	8.66025i	0.518476	+	0.898027i
$94$	−5.19615	+	3.00000i	−0.535942	+	0.309426i
$95$	11.8301	−	10.4904i	1.21375	−	1.07629i
$96$	−5.00000	+	5.00000i	−0.510310	+	0.510310i
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$	1.00000	−	1.00000i	0.100504	−	0.100504i
$100$	1.96410	+	4.59808i	0.196410	+	0.459808i
$101$	10.3923	−	6.00000i	1.03407	−	0.597022i	0.115924	−	0.993258i	$-0.463017\pi$
$101$	10.3923	−	6.00000i	1.03407	−	0.597022i	0.918149	+	0.396236i	$0.129684\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	−0.962172	−	0.272442i	$-0.912169\pi$
$103$	−7.00000	+	7.00000i	−0.689730	+	0.689730i	0.272442	+	0.962172i	$0.412169\pi$
$104$		0			0
$105$	6.00000	+	2.00000i	0.585540	+	0.195180i
$106$	6.83013	+	1.83013i	0.663401	+	0.177758i
$107$	−9.56218	−	2.56218i	−0.924411	−	0.247695i	−0.234941	−	0.972010i	$-0.575490\pi$
$107$	−9.56218	−	2.56218i	−0.924411	−	0.247695i	−0.689470	+	0.724315i	$0.742156\pi$
$108$	1.46410	+	5.46410i	0.140883	+	0.525783i
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	0.991575	−	0.129532i	$-0.0413474\pi$
$109$	9.00000	+	9.00000i	0.862044	+	0.862044i	−0.129532	+	0.991575i	$0.541347\pi$
$110$	−2.09808	−	2.36603i	−0.200044	−	0.225592i
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−6.83013	+	1.83013i	−0.642524	+	0.172164i	−0.565347	−	0.824853i	$-0.691258\pi$
$113$	−6.83013	+	1.83013i	−0.642524	+	0.172164i	−0.0771777	+	0.997017i	$0.524591\pi$
$114$	−5.00000	−	8.66025i	−0.468293	−	0.811107i
$115$	9.29423	−	1.90192i	0.866691	−	0.177355i
$116$		0			0
$117$		0			0
$118$	−7.00000	−	7.00000i	−0.644402	−	0.644402i
$119$	−0.732051	+	2.73205i	−0.0671070	+	0.250447i
$120$	9.29423	−	1.90192i	0.848443	−	0.173621i
$121$	7.79423	+	4.50000i	0.708566	+	0.409091i
$122$		−	14.0000i		−	1.26750i
$123$	−7.00000	+	12.1244i	−0.631169	+	1.09322i
$124$	−1.83013	−	6.83013i	−0.164350	−	0.613364i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−3.29423	+	12.2942i	−0.292316	+	1.09094i	0.651010	+	0.759069i	$0.274345\pi$
$127$	−3.29423	+	12.2942i	−0.292316	+	1.09094i	−0.943326	+	0.331868i	$0.892321\pi$
$128$	2.59808	−	1.50000i	0.229640	−	0.132583i
$129$	2.00000			0.176090
$130$		0			0
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$	1.73205	−	1.00000i	0.150756	−	0.0870388i
$133$	−3.66025	+	13.6603i	−0.317384	+	1.18449i
$134$	−2.00000	+	3.46410i	−0.172774	+	0.299253i
$135$	4.00000	−	12.0000i	0.344265	−	1.03280i
$136$	1.09808	+	4.09808i	0.0941593	+	0.351407i
$137$	−8.00000	+	13.8564i	−0.683486	+	1.18383i	0.290424	+	0.956898i	$0.406204\pi$
$137$	−8.00000	+	13.8564i	−0.683486	+	1.18383i	−0.973910	+	0.226935i	$0.927130\pi$
$138$		−	6.00000i		−	0.510754i
$139$	−12.1244	−	7.00000i	−1.02837	−	0.593732i	−0.111856	−	0.993724i	$-0.535679\pi$
$139$	−12.1244	−	7.00000i	−1.02837	−	0.593732i	−0.916519	+	0.399992i	$0.869013\pi$
$140$	−3.73205	−	2.46410i	−0.315416	−	0.208255i
$141$	−2.19615	+	8.19615i	−0.184949	+	0.690241i
$142$	−1.00000	−	1.00000i	−0.0839181	−	0.0839181i
$143$		0			0
$144$			1.00000i			0.0833333i
$145$		0			0
$146$	5.00000	+	8.66025i	0.413803	+	0.716728i
$147$	4.09808	−	1.09808i	0.338004	−	0.0905678i
$148$		0			0
$149$	4.09808	−	1.09808i	0.335727	−	0.0899579i	−0.0870170	−	0.996207i	$-0.527733\pi$
$149$	4.09808	−	1.09808i	0.335727	−	0.0899579i	0.422744	+	0.906249i	$0.361067\pi$
$150$	−6.56218	−	2.63397i	−0.535800	−	0.215063i
$151$	−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	$0.881965\pi$
$152$	5.49038	+	20.4904i	0.445329	+	1.66199i
$153$	1.36603	+	0.366025i	0.110437	+	0.0295914i
$154$	2.73205	+	0.732051i	0.220155	+	0.0589903i
$155$	−5.00000	+	15.0000i	−0.401610	+	1.20483i
$156$		0			0
$157$	13.0000	−	13.0000i	1.03751	−	1.03751i	0.0382445	−	0.999268i	$-0.487823\pi$
$157$	13.0000	−	13.0000i	1.03751	−	1.03751i	0.999268	−	0.0382445i	$-0.0121766\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	8.66025	−	5.00000i	0.686803	−	0.396526i
$160$	−11.1603	−	0.669873i	−0.882296	−	0.0529581i
$161$	−6.00000	+	6.00000i	−0.472866	+	0.472866i
$162$	−4.33013	−	2.50000i	−0.340207	−	0.196419i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$	7.00000	−	7.00000i	0.546608	−	0.546608i
$165$	−4.46410	−	0.267949i	−0.347530	−	0.0208598i
$166$	−5.19615	+	3.00000i	−0.403300	+	0.232845i
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$	−6.00000	+	6.00000i	−0.462910	+	0.462910i
$169$		0			0
$170$	1.00000	−	3.00000i	0.0766965	−	0.230089i
$171$	6.83013	+	1.83013i	0.522313	+	0.139953i
$172$	−1.36603	−	0.366025i	−0.104158	−	0.0279092i
$173$	4.02628	+	15.0263i	0.306112	+	1.14243i	0.931984	+	0.362500i	$0.118077\pi$
$173$	4.02628	+	15.0263i	0.306112	+	1.14243i	−0.625871	+	0.779926i	$0.715256\pi$
$174$		0			0
$175$	3.92820	+	9.19615i	0.296944	+	0.695164i
$176$	1.36603	−	0.366025i	0.102968	−	0.0275902i
$177$	−14.0000			−1.05230
$178$	−6.83013	+	1.83013i	−0.511940	+	0.137174i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	−1.23205	+	1.86603i	−0.0918316	+	0.139085i
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$		0			0
$183$	−14.0000	−	14.0000i	−1.03491	−	1.03491i
$184$	−3.29423	+	12.2942i	−0.242854	+	0.906343i
$185$		0			0
$186$	8.66025	+	5.00000i	0.635001	+	0.366618i
$187$		−	2.00000i		−	0.146254i
$188$	3.00000	−	5.19615i	0.218797	−	0.378968i
$189$	2.92820	+	10.9282i	0.212995	+	0.794910i
$190$	5.00000	−	15.0000i	0.362738	−	1.08821i
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	−0.973674	−	0.227946i	$-0.926799\pi$
$191$	−4.00000	+	6.92820i	−0.289430	+	0.501307i	0.684244	+	0.729253i	$0.260132\pi$
$192$	−2.56218	+	9.56218i	−0.184909	+	0.690091i
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.941932	−	0.335805i	$-0.890992\pi$
$193$	−15.5885	+	9.00000i	−1.12208	+	0.647834i	−0.180150	+	0.983639i	$0.557658\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	−0.303340	−	0.952882i	$-0.598102\pi$
$197$	5.19615	−	3.00000i	0.370211	−	0.213741i	0.673550	+	0.739141i	$0.264768\pi$
$198$	0.366025	−	1.36603i	0.0260123	−	0.0970792i
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	12.0000	+	9.00000i	0.848528	+	0.636396i
$201$	1.46410	+	5.46410i	0.103270	+	0.385408i
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$		0			0
$204$	1.73205	+	1.00000i	0.121268	+	0.0700140i
$205$	−21.6865	+	4.43782i	−1.51465	+	0.309951i
$206$	−2.56218	+	9.56218i	−0.178515	+	0.666228i
$207$	3.00000	+	3.00000i	0.208514	+	0.208514i
$208$		0			0
$209$		−	10.0000i		−	0.691714i
$210$	6.19615	−	1.26795i	0.427575	−	0.0874968i
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	0.788935	−	0.614477i	$-0.210633\pi$
$211$	−2.00000	−	3.46410i	−0.137686	−	0.238479i	−0.926620	+	0.375999i	$0.877300\pi$
$212$	−6.83013	+	1.83013i	−0.469095	+	0.125694i
$213$	−2.00000			−0.137038
$214$	−9.56218	+	2.56218i	−0.653657	+	0.175147i
$215$	2.09808	+	2.36603i	0.143088	+	0.161362i
$216$	12.0000	+	12.0000i	0.816497	+	0.816497i
$217$	−3.66025	−	13.6603i	−0.248474	−	0.927318i
$218$	12.2942	+	3.29423i	0.832670	+	0.223113i
$219$	13.6603	+	3.66025i	0.923074	+	0.247337i
$220$	3.00000	+	1.00000i	0.202260	+	0.0674200i
$221$		0			0
$222$		0			0
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	8.66025	−	5.00000i	0.578638	−	0.334077i
$225$	4.59808	−	1.96410i	0.306538	−	0.130940i
$226$	−5.00000	+	5.00000i	−0.332595	+	0.332595i
$227$	10.3923	+	6.00000i	0.689761	+	0.398234i	0.803523	−	0.595274i	$-0.202957\pi$
$227$	10.3923	+	6.00000i	0.689761	+	0.398234i	−0.113761	+	0.993508i	$0.536290\pi$
$228$	8.66025	+	5.00000i	0.573539	+	0.331133i
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	−0.799248	−	0.601002i	$-0.794768\pi$
$229$	−3.00000	+	3.00000i	−0.198246	+	0.198246i	0.601002	+	0.799248i	$0.294768\pi$
$230$	7.09808	−	6.29423i	0.468033	−	0.415029i
$231$	3.46410	−	2.00000i	0.227921	−	0.131590i
$232$		0			0
$233$	−1.00000	+	1.00000i	−0.0655122	+	0.0655122i	−0.739104	−	0.673592i	$-0.764751\pi$
$233$	−1.00000	+	1.00000i	−0.0655122	+	0.0655122i	0.673592	+	0.739104i	$0.264751\pi$
$234$		0			0
$235$	−12.0000	+	6.00000i	−0.782794	+	0.391397i
$236$	9.56218	+	2.56218i	0.622445	+	0.166784i
$237$	2.73205	+	0.732051i	0.177466	+	0.0475518i
$238$	0.732051	+	2.73205i	0.0474518	+	0.177093i
$239$	3.00000	+	3.00000i	0.194054	+	0.194054i	0.797445	−	0.603391i	$-0.206184\pi$
$239$	3.00000	+	3.00000i	0.194054	+	0.194054i	−0.603391	+	0.797445i	$0.706184\pi$
$240$	2.36603	−	2.09808i	0.152726	−	0.135430i
$241$	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	$0.134754\pi$
$242$	9.00000			0.578542
$243$	9.56218	−	2.56218i	0.613414	−	0.164364i
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$	5.59808	+	3.69615i	0.357648	+	0.236139i
$246$			14.0000i			0.892607i
$247$		0			0
$248$	−15.0000	−	15.0000i	−0.952501	−	0.952501i
$249$	−2.19615	+	8.19615i	−0.139176	+	0.519410i
$250$	−3.76795	−	10.5263i	−0.238306	−	0.665740i
$251$	−1.73205	−	1.00000i	−0.109326	−	0.0631194i	0.444340	−	0.895858i	$-0.353438\pi$
$251$	−1.73205	−	1.00000i	−0.109326	−	0.0631194i	−0.553666	+	0.832739i	$0.686772\pi$
$252$		−	2.00000i		−	0.125988i
$253$	3.00000	−	5.19615i	0.188608	−	0.326679i
$254$	3.29423	+	12.2942i	0.206698	+	0.771409i
$255$	−2.00000	−	4.00000i	−0.125245	−	0.250490i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	4.02628	−	15.0263i	0.251152	−	0.937314i	−0.719038	−	0.694971i	$-0.755417\pi$
$257$	4.02628	−	15.0263i	0.251152	−	0.937314i	0.970191	−	0.242343i	$-0.0779159\pi$
$258$	1.73205	−	1.00000i	0.107833	−	0.0622573i
$259$		0			0
$260$		0			0
$261$		0			0
$262$	−17.3205	+	10.0000i	−1.07006	+	0.617802i
$263$	0.366025	−	1.36603i	0.0225701	−	0.0842327i	−0.953722	−	0.300689i	$-0.902783\pi$
$263$	0.366025	−	1.36603i	0.0225701	−	0.0842327i	0.976292	+	0.216457i	$0.0694500\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	15.0000	+	5.00000i	0.921443	+	0.307148i
$266$	3.66025	+	13.6603i	0.224425	+	0.837564i
$267$	−5.00000	+	8.66025i	−0.305995	+	0.529999i
$268$		−	4.00000i		−	0.244339i
$269$	10.3923	+	6.00000i	0.633630	+	0.365826i	0.782157	−	0.623082i	$-0.214120\pi$
$269$	10.3923	+	6.00000i	0.633630	+	0.365826i	−0.148527	+	0.988908i	$0.547453\pi$
$270$	−2.53590	−	12.3923i	−0.154330	−	0.754172i
$271$	3.29423	−	12.2942i	0.200110	−	0.746821i	−0.790774	−	0.612108i	$-0.790322\pi$
$271$	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
$275$	−4.36603	−	5.56218i	−0.263281	−	0.335412i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−20.4904	+	5.49038i	−1.23115	+	0.329885i	−0.815026	−	0.579424i	$-0.803278\pi$
$277$	−20.4904	+	5.49038i	−1.23115	+	0.329885i	−0.416121	+	0.909309i	$0.636611\pi$
$278$	−14.0000			−0.839664
$279$	−6.83013	+	1.83013i	−0.408909	+	0.109567i
$280$	−13.3923	−	0.803848i	−0.800343	−	0.0480391i
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	0.676650	−	0.736305i	$-0.263431\pi$
$281$	−1.00000	−	1.00000i	−0.0596550	−	0.0596550i	−0.736305	+	0.676650i	$0.763431\pi$
$282$	2.19615	+	8.19615i	0.130779	+	0.488074i
$283$	−12.2942	−	3.29423i	−0.730816	−	0.195822i	−0.125823	−	0.992053i	$-0.540157\pi$
$283$	−12.2942	−	3.29423i	−0.730816	−	0.195822i	−0.604993	+	0.796231i	$0.706824\pi$
$284$	1.36603	+	0.366025i	0.0810587	+	0.0217196i
$285$	−10.0000	−	20.0000i	−0.592349	−	1.18470i
$286$		0			0
$287$	14.0000	−	14.0000i	0.826394	−	0.826394i
$288$	−2.50000	−	4.33013i	−0.147314	−	0.255155i
$289$	−12.9904	+	7.50000i	−0.764140	+	0.441176i
$290$		0			0
$291$	−2.00000	+	2.00000i	−0.117242	+	0.117242i
$292$	−8.66025	−	5.00000i	−0.506803	−	0.292603i
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	0.340480	−	0.940252i	$-0.389411\pi$
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	−0.644042	+	0.764990i	$0.722744\pi$
$294$	3.00000	−	3.00000i	0.174964	−	0.174964i
$295$	−14.6865	−	16.5622i	−0.855083	−	0.964287i
$296$		0			0
$297$	−4.00000	−	6.92820i	−0.232104	−	0.402015i
$298$	3.00000	−	3.00000i	0.173785	−	0.173785i
$299$		0			0
$300$	7.00000	−	1.00000i	0.404145	−	0.0577350i
$301$	−2.73205	−	0.732051i	−0.157473	−	0.0421947i
$302$	−9.56218	−	2.56218i	−0.550242	−	0.147437i
$303$	−4.39230	−	16.3923i	−0.252331	−	0.941713i
$304$	5.00000	+	5.00000i	0.286770	+	0.286770i
$305$	1.87564	−	31.2487i	0.107399	−	1.78930i
$306$	1.36603	−	0.366025i	0.0780905	−	0.0209243i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	−2.73205	+	0.732051i	−0.155673	+	0.0417125i
$309$	7.00000	+	12.1244i	0.398216	+	0.689730i
$310$	3.16987	+	15.4904i	0.180037	+	0.879795i
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$		0			0
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	0.914130	−	0.405420i	$-0.132875\pi$
$313$	9.00000	+	9.00000i	0.508710	+	0.508710i	−0.405420	+	0.914130i	$0.632875\pi$
$314$	4.75833	−	17.7583i	0.268528	−	1.00216i
$315$	−2.46410	+	3.73205i	−0.138836	+	0.210277i
$316$	−1.73205	−	1.00000i	−0.0974355	−	0.0562544i
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	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
$322$	−2.19615	+	8.19615i	−0.122387	+	0.456754i
$323$	8.66025	−	5.00000i	0.481869	−	0.278207i
$324$	5.00000			0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$	15.5885	−	9.00000i	0.862044	−	0.497701i
$328$	7.68653	−	28.6865i	0.424418	−	1.58395i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	−4.00000	+	2.00000i	−0.220193	+	0.110096i
$331$	1.09808	+	4.09808i	0.0603557	+	0.225251i	0.989515	−	0.144428i	$-0.0461343\pi$
$331$	1.09808	+	4.09808i	0.0603557	+	0.225251i	−0.929160	+	0.369679i	$0.879468\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$		0			0
$334$	−15.5885	−	9.00000i	−0.852962	−	0.492458i
$335$	−4.92820	+	7.46410i	−0.269257	+	0.407807i
$336$	−0.732051	+	2.73205i	−0.0399366	+	0.149046i
$337$	−13.0000	−	13.0000i	−0.708155	−	0.708155i	0.257992	−	0.966147i	$-0.416939\pi$
$337$	−13.0000	−	13.0000i	−0.708155	−	0.708155i	−0.966147	+	0.257992i	$0.916939\pi$
$338$		0			0
$339$			10.0000i			0.543125i
$340$	0.633975	+	3.09808i	0.0343821	+	0.168017i
$341$	5.00000	+	8.66025i	0.270765	+	0.468979i
$342$	6.83013	−	1.83013i	0.369331	−	0.0989619i
$343$	−20.0000			−1.07990
$344$	−4.09808	+	1.09808i	−0.220953	+	0.0592043i
$345$	0.803848	−	13.3923i	0.0432777	−	0.721017i
$346$	11.0000	+	11.0000i	0.591364	+	0.591364i
$347$	1.09808	+	4.09808i	0.0589478	+	0.219996i	0.989116	−	0.147137i	$-0.0470059\pi$
$347$	1.09808	+	4.09808i	0.0589478	+	0.219996i	−0.930168	+	0.367133i	$0.880339\pi$
$348$		0			0
$349$	−12.2942	−	3.29423i	−0.658095	−	0.176336i	−0.0857088	−	0.996320i	$-0.527315\pi$
$349$	−12.2942	−	3.29423i	−0.658095	−	0.176336i	−0.572386	+	0.819984i	$0.693982\pi$
$350$	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	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$	−12.1244	+	7.00000i	−0.644402	+	0.372046i
$355$	−2.09808	−	2.36603i	−0.111354	−	0.125576i
$356$	5.00000	−	5.00000i	0.264999	−	0.264999i
$357$	3.46410	+	2.00000i	0.183340	+	0.105851i
$358$	−17.3205	−	10.0000i	−0.915417	−	0.528516i
$359$	1.00000	−	1.00000i	0.0527780	−	0.0527780i	−0.680225	−	0.733003i	$-0.738118\pi$
$359$	1.00000	−	1.00000i	0.0527780	−	0.0527780i	0.733003	+	0.680225i	$0.238118\pi$
$360$	−0.401924	+	6.69615i	−0.0211832	+	0.352918i
$361$	26.8468	−	15.5000i	1.41299	−	0.815789i
$362$	−4.00000	−	6.92820i	−0.210235	−	0.364138i
$363$	9.00000	−	9.00000i	0.472377	−	0.472377i
$364$		0			0
$365$	10.0000	+	20.0000i	0.523424	+	1.04685i
$366$	−19.1244	−	5.12436i	−0.999646	−	0.267854i
$367$	1.36603	+	0.366025i	0.0713059	+	0.0191064i	0.294296	−	0.955714i	$-0.404915\pi$
$367$	1.36603	+	0.366025i	0.0713059	+	0.0191064i	−0.222990	+	0.974821i	$0.571582\pi$
$368$	1.09808	+	4.09808i	0.0572412	+	0.213627i
$369$	−7.00000	−	7.00000i	−0.364405	−	0.364405i
$370$		0			0
$371$	−13.6603	+	3.66025i	−0.709205	+	0.190031i
$372$	−10.0000			−0.518476
$373$	20.4904	−	5.49038i	1.06095	−	0.284281i	0.314181	−	0.949363i	$-0.398270\pi$
$373$	20.4904	−	5.49038i	1.06095	−	0.284281i	0.746770	+	0.665082i	$0.231603\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$	−14.2942	−	6.75833i	−0.738151	−	0.348999i
$376$		−	18.0000i		−	0.928279i
$377$		0			0
$378$	8.00000	+	8.00000i	0.411476	+	0.411476i
$379$	−0.366025	+	1.36603i	−0.0188015	+	0.0701680i	−0.974689	−	0.223564i	$-0.928231\pi$
$379$	−0.366025	+	1.36603i	−0.0188015	+	0.0701680i	0.955888	+	0.293732i	$0.0948974\pi$
$380$	3.16987	+	15.4904i	0.162611	+	0.794640i
$381$	15.5885	+	9.00000i	0.798621	+	0.461084i
$382$			8.00000i			0.409316i
$383$	−15.0000	+	25.9808i	−0.766464	+	1.32755i	0.173005	+	0.984921i	$0.444652\pi$
$383$	−15.0000	+	25.9808i	−0.766464	+	1.32755i	−0.939469	+	0.342634i	$0.888681\pi$
$384$	−1.09808	−	4.09808i	−0.0560360	−	0.209129i
$385$	6.00000	+	2.00000i	0.305788	+	0.101929i
$386$	−9.00000	+	15.5885i	−0.458088	+	0.793432i
$387$	−0.366025	+	1.36603i	−0.0186061	+	0.0694390i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$	−7.79423	+	4.50000i	−0.393668	+	0.227284i
$393$	−7.32051	+	27.3205i	−0.369271	+	1.37814i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$	2.00000	+	4.00000i	0.100631	+	0.201262i
$396$	0.366025	+	1.36603i	0.0183935	+	0.0686454i
$397$	8.00000	−	13.8564i	0.401508	−	0.695433i	−0.592400	−	0.805644i	$-0.701819\pi$
$397$	8.00000	−	13.8564i	0.401508	−	0.695433i	0.993908	+	0.110211i	$0.0351527\pi$
$398$			8.00000i			0.401004i
$399$	17.3205	+	10.0000i	0.867110	+	0.500626i
$400$	4.96410	+	0.598076i	0.248205	+	0.0299038i
$401$	4.02628	−	15.0263i	0.201063	−	0.750377i	−0.789551	−	0.613685i	$-0.789686\pi$
$401$	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
$405$	−9.33013	−	6.16025i	−0.463618	−	0.306105i
$406$		0			0
$407$		0			0
$408$	6.00000			0.297044
$409$	9.56218	−	2.56218i	0.472819	−	0.126692i	−0.0145378	−	0.999894i	$-0.504628\pi$
$409$	9.56218	−	2.56218i	0.472819	−	0.126692i	0.487357	+	0.873203i	$0.337961\pi$
$410$	−16.5622	+	14.6865i	−0.817948	+	0.725316i
$411$	16.0000	+	16.0000i	0.789222	+	0.789222i
$412$	−2.56218	−	9.56218i	−0.126229	−	0.471095i
$413$	19.1244	+	5.12436i	0.941048	+	0.252153i
$414$	4.09808	+	1.09808i	0.201409	+	0.0539675i
$415$	−12.0000	+	6.00000i	−0.589057	+	0.294528i
$416$		0			0
$417$	−14.0000	+	14.0000i	−0.685583	+	0.685583i
$418$	−5.00000	−	8.66025i	−0.244558	−	0.423587i
$419$	32.9090	−	19.0000i	1.60771	−	0.928211i	0.617827	−	0.786314i	$-0.288013\pi$
$419$	32.9090	−	19.0000i	1.60771	−	0.928211i	0.989882	−	0.141896i	$-0.0453200\pi$
$420$	−4.73205	+	4.19615i	−0.230900	+	0.204751i
$421$	11.0000	−	11.0000i	0.536107	−	0.536107i	−0.386276	−	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
$425$	2.63397	−	6.56218i	0.127767	−	0.318312i
$426$	−1.73205	+	1.00000i	−0.0839181	+	0.0484502i
$427$	14.0000	+	24.2487i	0.677507	+	1.17348i
$428$	7.00000	−	7.00000i	0.338358	−	0.338358i
$429$		0			0
$430$	3.00000	+	1.00000i	0.144673	+	0.0482243i
$431$	17.7583	+	4.75833i	0.855389	+	0.229201i	0.659759	−	0.751477i	$-0.270658\pi$
$431$	17.7583	+	4.75833i	0.855389	+	0.229201i	0.195630	+	0.980678i	$0.437325\pi$
$432$	5.46410	+	1.46410i	0.262892	+	0.0704416i
$433$	−6.22243	−	23.2224i	−0.299031	−	1.11600i	−0.937963	−	0.346736i	$-0.887290\pi$
$433$	−6.22243	−	23.2224i	−0.299031	−	1.11600i	0.638932	−	0.769263i	$-0.279377\pi$
$434$	−10.0000	−	10.0000i	−0.480015	−	0.480015i
$435$		0			0
$436$	−12.2942	+	3.29423i	−0.588787	+	0.157765i
$437$	30.0000			1.43509
$438$	13.6603	−	3.66025i	0.652712	−	0.174894i
$439$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	9.29423	−	1.90192i	0.443085	−	0.0906707i
$441$			3.00000i			0.142857i
$442$		0			0
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.977678	+	0.210108i	$0.0673814\pi$
$443$	25.0000	+	25.0000i	1.18779	+	1.18779i	0.210108	+	0.977678i	$0.432619\pi$
$444$		0			0
$445$	−15.4904	+	3.16987i	−0.734314	+	0.150266i
$446$	1.73205	+	1.00000i	0.0820150	+	0.0473514i
$447$		−	6.00000i		−	0.283790i
$448$	7.00000	−	12.1244i	0.330719	−	0.572822i
$449$	−1.09808	−	4.09808i	−0.0518214	−	0.193400i	0.935163	−	0.354219i	$-0.115253\pi$
$449$	−1.09808	−	4.09808i	−0.0518214	−	0.193400i	−0.986984	+	0.160819i	$0.948587\pi$
$450$	3.00000	−	4.00000i	0.141421	−	0.188562i
$451$	−7.00000	+	12.1244i	−0.329617	+	0.570914i
$452$	1.83013	−	6.83013i	0.0860819	−	0.321262i
$453$	−12.1244	+	7.00000i	−0.569652	+	0.328889i
$454$	12.0000			0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$	1.73205	−	1.00000i	0.0810219	−	0.0467780i	−0.458942	−	0.888466i	$-0.651771\pi$
$457$	1.73205	−	1.00000i	0.0810219	−	0.0467780i	0.539964	+	0.841688i	$0.318438\pi$
$458$	−1.09808	+	4.09808i	−0.0513097	+	0.191491i
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$	−3.00000	+	9.00000i	−0.139876	+	0.419627i
$461$	−6.22243	−	23.2224i	−0.289808	−	1.08158i	−0.945254	−	0.326335i	$-0.894186\pi$
$461$	−6.22243	−	23.2224i	−0.289808	−	1.08158i	0.655447	−	0.755241i	$-0.272480\pi$
$462$	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
$465$	18.6603	+	12.3205i	0.865349	+	0.571350i
$466$	−0.366025	+	1.36603i	−0.0169558	+	0.0632799i
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	0.467515	−	0.883985i	$-0.345149\pi$
$467$	−9.00000	−	9.00000i	−0.416470	−	0.416470i	−0.883985	+	0.467515i	$0.845149\pi$
$468$		0			0
$469$		−	8.00000i		−	0.369406i
$470$	−7.39230	+	11.1962i	−0.340982	+	0.516440i
$471$	−13.0000	−	22.5167i	−0.599008	−	1.03751i
$472$	28.6865	−	7.68653i	1.32040	−	0.353801i
$473$	2.00000			0.0919601
$474$	2.73205	−	0.732051i	0.125487	−	0.0336242i
$475$	13.1699	−	32.8109i	0.604275	−	1.50547i
$476$	−2.00000	−	2.00000i	−0.0916698	−	0.0916698i
$477$	1.83013	+	6.83013i	0.0837958	+	0.312730i
$478$	4.09808	+	1.09808i	0.187442	+	0.0502248i
$479$	9.56218	+	2.56218i	0.436907	+	0.117069i	0.470567	−	0.882364i	$-0.344050\pi$
$479$	9.56218	+	2.56218i	0.436907	+	0.117069i	−0.0336596	+	0.999433i	$0.510716\pi$
$480$	−5.00000	+	15.0000i	−0.228218	+	0.684653i
$481$		0			0
$482$	17.0000	−	17.0000i	0.774329	−	0.774329i
$483$	6.00000	+	10.3923i	0.273009	+	0.472866i
$484$	−7.79423	+	4.50000i	−0.354283	+	0.204545i
$485$	−4.46410	−	0.267949i	−0.202704	−	0.0121669i
$486$	7.00000	−	7.00000i	0.317526	−	0.317526i
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	36.3731	+	21.0000i	1.64653	+	0.950625i
$489$	4.00000	−	4.00000i	0.180886	−	0.180886i
$490$	6.69615	+	0.401924i	0.302501	+	0.0181571i
$491$	−19.0526	+	11.0000i	−0.859830	+	0.496423i	−0.863955	−	0.503568i	$-0.832020\pi$
$491$	−19.0526	+	11.0000i	−0.859830	+	0.496423i	0.00412539	+	0.999991i	$0.498687\pi$
$492$	−7.00000	−	12.1244i	−0.315584	−	0.546608i
$493$		0			0
$494$		0			0
$495$	1.00000	−	3.00000i	0.0449467	−	0.134840i
$496$	−6.83013	−	1.83013i	−0.306682	−	0.0821751i
$497$	2.73205	+	0.732051i	0.122549	+	0.0328370i
$498$	2.19615	+	8.19615i	0.0984119	+	0.367278i
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	0.771060	−	0.636762i	$-0.219727\pi$
$499$	3.00000	+	3.00000i	0.134298	+	0.134298i	−0.636762	+	0.771060i	$0.719727\pi$
$500$	8.52628	+	7.23205i	0.381307	+	0.323427i
$501$	−24.5885	+	6.58846i	−1.09853	+	0.294351i
$502$	−2.00000			−0.0892644
$503$	4.09808	−	1.09808i	0.182724	−	0.0489608i	−0.166297	−	0.986076i	$-0.553181\pi$
$503$	4.09808	−	1.09808i	0.182724	−	0.0489608i	0.349021	+	0.937115i	$0.386514\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	14.7846	−	22.3923i	0.657906	−	0.996444i
$506$		−	6.00000i		−	0.266733i
$507$		0			0
$508$	−9.00000	−	9.00000i	−0.399310	−	0.399310i
$509$	4.75833	−	17.7583i	0.210909	−	0.787124i	−0.776657	−	0.629923i	$-0.783086\pi$
$509$	4.75833	−	17.7583i	0.210909	−	0.787124i	0.987567	−	0.157201i	$-0.0502470\pi$
$510$	−3.73205	−	2.46410i	−0.165258	−	0.109112i
$511$	−17.3205	−	10.0000i	−0.766214	−	0.442374i
$512$		−	11.0000i		−	0.486136i
$513$	20.0000	−	34.6410i	0.883022	−	1.52944i
$514$	−4.02628	−	15.0263i	−0.177592	−	0.662781i
$515$	−7.00000	+	21.0000i	−0.308457	+	0.925371i
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$	−2.19615	+	8.19615i	−0.0965867	+	0.360466i
$518$		0			0
$519$	22.0000			0.965693
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	3.29423	−	12.2942i	0.144047	−	0.537589i	−0.855749	−	0.517390i	$-0.826903\pi$
$523$	3.29423	−	12.2942i	0.144047	−	0.537589i	0.999796	−	0.0201986i	$-0.00642985\pi$
$524$	10.0000	−	17.3205i	0.436852	−	0.756650i
$525$	14.0000	−	2.00000i	0.611010	−	0.0872872i
$526$	−0.366025	−	1.36603i	−0.0159595	−	0.0595615i
$527$	−5.00000	+	8.66025i	−0.217803	+	0.377247i
$528$		−	2.00000i		−	0.0870388i
$529$	−4.33013	−	2.50000i	−0.188266	−	0.108696i
$530$	15.4904	−	3.16987i	0.672859	−	0.137690i
$531$	2.56218	−	9.56218i	0.111189	−	0.414963i
$532$	−10.0000	−	10.0000i	−0.433555	−	0.433555i
$533$		0			0
$534$			10.0000i			0.432742i
$535$	−21.6865	+	4.43782i	−0.937591	+	0.191864i
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	−27.3205	+	7.32051i	−1.17897	+	0.315903i
$538$	12.0000			0.517357
$539$	4.09808	−	1.09808i	0.176517	−	0.0472975i
$540$	8.39230	+	9.46410i	0.361147	+	0.407270i
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$	−3.29423	−	12.2942i	−0.141499	−	0.528082i
$543$	−10.9282	−	2.92820i	−0.468974	−	0.125661i
$544$	−6.83013	−	1.83013i	−0.292839	−	0.0784660i
$545$	27.0000	+	9.00000i	1.15655	+	0.385518i
$546$		0			0
$547$	−9.00000	+	9.00000i	−0.384812	+	0.384812i	−0.872832	−	0.488020i	$-0.837719\pi$
$547$	−9.00000	+	9.00000i	−0.384812	+	0.384812i	0.488020	+	0.872832i	$0.337719\pi$
$548$	−8.00000	−	13.8564i	−0.341743	−	0.591916i
$549$	12.1244	−	7.00000i	0.517455	−	0.298753i
$550$	−6.56218	−	2.63397i	−0.279812	−	0.112313i
$551$		0			0
$552$	15.5885	+	9.00000i	0.663489	+	0.383065i
$553$	−3.46410	−	2.00000i	−0.147309	−	0.0850487i
$554$	−15.0000	+	15.0000i	−0.637289	+	0.637289i
$555$		0			0
$556$	12.1244	−	7.00000i	0.514187	−	0.296866i
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	0.999952	+	0.00979220i	$0.00311700\pi$
$557$	12.0000	+	20.7846i	0.508456	+	0.880672i	−0.491496	+	0.870880i	$0.663550\pi$
$558$	−5.00000	+	5.00000i	−0.211667	+	0.211667i
$559$		0			0
$560$	−4.00000	+	2.00000i	−0.169031	+	0.0845154i
$561$	−2.73205	−	0.732051i	−0.115347	−	0.0309072i
$562$	−1.36603	−	0.366025i	−0.0576223	−	0.0154398i
$563$	−5.49038	−	20.4904i	−0.231392	−	0.863567i	−0.979742	−	0.200263i	$-0.935820\pi$
$563$	−5.49038	−	20.4904i	−0.231392	−	0.863567i	0.748350	−	0.663304i	$-0.230846\pi$
$564$	−6.00000	−	6.00000i	−0.252646	−	0.252646i
$565$	−11.8301	+	10.4904i	−0.497697	+	0.441334i
$566$	−12.2942	+	3.29423i	−0.516765	+	0.138467i
$567$	10.0000			0.419961
$568$	4.09808	−	1.09808i	0.171951	−	0.0460743i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	−18.6603	−	12.3205i	−0.781592	−	0.516049i
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$		0			0
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$	5.12436	−	19.1244i	0.213886	−	0.798235i
$575$	16.6865	−	13.0981i	0.695877	−	0.546228i
$576$	−6.06218	−	3.50000i	−0.252591	−	0.145833i
$577$			46.0000i			1.91501i	0.288425	+	0.957503i	$0.406868\pi$
$577$			46.0000i			1.91501i	−0.288425	+	0.957503i	$0.593132\pi$
$578$	−7.50000	+	12.9904i	−0.311959	+	0.540329i
$579$	6.58846	+	24.5885i	0.273807	+	1.02186i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−0.732051	+	2.73205i	−0.0303445	+	0.113247i
$583$	8.66025	−	5.00000i	0.358671	−	0.207079i
$584$	−30.0000			−1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−3.46410	+	2.00000i	−0.142979	+	0.0825488i	−0.569783	−	0.821795i	$-0.692973\pi$
$587$	−3.46410	+	2.00000i	−0.142979	+	0.0825488i	0.426804	+	0.904344i	$0.359639\pi$
$588$	−1.09808	+	4.09808i	−0.0452839	+	0.169002i
$589$	−25.0000	+	43.3013i	−1.03011	+	1.78420i
$590$	−21.0000	−	7.00000i	−0.864556	−	0.288185i
$591$	−2.19615	−	8.19615i	−0.0903376	−	0.337145i
$592$		0			0
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$	−6.92820	−	4.00000i	−0.284268	−	0.164122i
$595$	1.26795	+	6.19615i	0.0519808	+	0.254017i
$596$	−1.09808	+	4.09808i	−0.0449790	+	0.167864i
$597$	8.00000	+	8.00000i	0.327418	+	0.327418i
$598$		0			0
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$	16.6865	−	13.0981i	0.681225	−	0.534727i
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	0.934780	+	0.355228i	$0.115597\pi$
$601$	19.0000	+	32.9090i	0.775026	+	1.34238i	−0.159754	+	0.987157i	$0.551070\pi$
$602$	−2.73205	+	0.732051i	−0.111350	+	0.0298362i
$603$	−4.00000			−0.162893
$604$	9.56218	−	2.56218i	0.389079	−	0.104254i
$605$	20.0885	+	1.20577i	0.816712	+	0.0490216i
$606$	−12.0000	−	12.0000i	−0.487467	−	0.487467i
$607$	−4.75833	−	17.7583i	−0.193135	−	0.720788i	−0.992742	−	0.120265i	$-0.961626\pi$
$607$	−4.75833	−	17.7583i	−0.193135	−	0.720788i	0.799607	−	0.600523i	$-0.205041\pi$
$608$	−34.1506	−	9.15064i	−1.38499	−	0.371107i
$609$		0			0
$610$	−14.0000	−	28.0000i	−0.566843	−	1.13369i
$611$		0			0
$612$	−1.00000	+	1.00000i	−0.0404226	+	0.0404226i
$613$	−10.0000	−	17.3205i	−0.403896	−	0.699569i	0.590296	−	0.807187i	$-0.299011\pi$
$613$	−10.0000	−	17.3205i	−0.403896	−	0.699569i	−0.994192	+	0.107618i	$0.965678\pi$
$614$	−15.5885	+	9.00000i	−0.629099	+	0.363210i
$615$	−1.87564	+	31.2487i	−0.0756333	+	1.26007i
$616$	−6.00000	+	6.00000i	−0.241747	+	0.241747i
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	0.831813	−	0.555056i	$-0.187303\pi$
$617$	19.0526	+	11.0000i	0.767027	+	0.442843i	−0.0647859	+	0.997899i	$0.520636\pi$
$618$	12.1244	+	7.00000i	0.487713	+	0.281581i
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.00484658	−	0.999988i	$-0.498457\pi$
$619$	25.0000	−	25.0000i	1.00483	−	1.00483i	0.999988	−	0.00484658i	$-0.00154272\pi$
$620$	−10.4904	−	11.8301i	−0.421304	−	0.475109i
$621$	20.7846	−	12.0000i	0.834058	−	0.481543i
$622$	3.00000	+	5.19615i	0.120289	+	0.208347i
$623$	10.0000	−	10.0000i	0.400642	−	0.400642i
$624$		0			0
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	12.2942	+	3.29423i	0.491376	+	0.131664i
$627$	−13.6603	−	3.66025i	−0.545538	−	0.146176i
$628$	4.75833	+	17.7583i	0.189878	+	0.708635i
$629$		0			0
$630$	−0.267949	+	4.46410i	−0.0106754	+	0.177854i
$631$	15.0263	−	4.02628i	0.598187	−	0.160284i	0.0529946	−	0.998595i	$-0.483123\pi$
$631$	15.0263	−	4.02628i	0.598187	−	0.160284i	0.545192	+	0.838311i	$0.316457\pi$
$632$	−6.00000			−0.238667
$633$	−5.46410	+	1.46410i	−0.217179	+	0.0581928i
$634$	−7.00000	−	12.1244i	−0.278006	−	0.481520i
$635$	5.70577	+	27.8827i	0.226427	+	1.10649i
$636$			10.0000i			0.396526i
$637$		0			0
$638$		0			0
$639$	0.366025	−	1.36603i	0.0144797	−	0.0540391i
$640$	3.69615	−	5.59808i	0.146103	−	0.221283i
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	0.850741	−	0.525584i	$-0.176153\pi$
$641$	20.7846	+	12.0000i	0.820943	+	0.473972i	−0.0297987	+	0.999556i	$0.509487\pi$
$642$			14.0000i			0.552536i
$643$	−17.0000	+	29.4449i	−0.670415	+	1.16119i	0.307372	+	0.951589i	$0.400550\pi$
$643$	−17.0000	+	29.4449i	−0.670415	+	1.16119i	−0.977787	+	0.209603i	$0.932783\pi$
$644$	−2.19615	−	8.19615i	−0.0865405	−	0.322974i
$645$	4.00000	−	2.00000i	0.157500	−	0.0787499i
$646$	5.00000	−	8.66025i	0.196722	−	0.340733i
$647$	−0.366025	+	1.36603i	−0.0143899	+	0.0537040i	−0.972747	−	0.231867i	$-0.925517\pi$
$647$	−0.366025	+	1.36603i	−0.0143899	+	0.0537040i	0.958358	+	0.285571i	$0.0921832\pi$
$648$	12.9904	−	7.50000i	0.510310	−	0.294628i
$649$	−14.0000			−0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$	−3.46410	+	2.00000i	−0.135665	+	0.0783260i
$653$	4.75833	−	17.7583i	0.186208	−	0.694937i	−0.808161	−	0.588962i	$-0.799537\pi$
$653$	4.75833	−	17.7583i	0.186208	−	0.694937i	0.994369	−	0.105975i	$-0.0337965\pi$
$654$	9.00000	−	15.5885i	0.351928	−	0.609557i
$655$	−40.0000	+	20.0000i	−1.56293	+	0.781465i
$656$	−2.56218	−	9.56218i	−0.100036	−	0.373340i
$657$	−5.00000	+	8.66025i	−0.195069	+	0.337869i
$658$		−	12.0000i		−	0.467809i
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.869709	−	0.493564i	$-0.164306\pi$
$659$	22.5167	+	13.0000i	0.877125	+	0.506408i	0.00741531	+	0.999973i	$0.497640\pi$
$660$	2.46410	−	3.73205i	0.0959150	−	0.145270i
$661$	−6.22243	+	23.2224i	−0.242025	+	0.903248i	0.732831	+	0.680411i	$0.238199\pi$
$661$	−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
$665$	6.33975	+	30.9808i	0.245845	+	1.20138i
$666$		0			0
$667$		0			0
$668$	18.0000			0.696441
$669$	2.73205	−	0.732051i	0.105627	−	0.0283027i
$670$	−0.535898	+	8.92820i	−0.0207036	+	0.344927i
$671$	−14.0000	−	14.0000i	−0.540464	−	0.540464i
$672$	−3.66025	−	13.6603i	−0.141197	−	0.526956i
$673$	−20.4904	−	5.49038i	−0.789846	−	0.211639i	−0.158725	−	0.987323i	$-0.550738\pi$
$673$	−20.4904	−	5.49038i	−0.789846	−	0.211639i	−0.631121	+	0.775684i	$0.717405\pi$
$674$	−17.7583	−	4.75833i	−0.684025	−	0.183284i
$675$	−4.00000	−	28.0000i	−0.153960	−	1.07772i
$676$		0			0
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	−0.993935	−	0.109973i	$-0.964924\pi$
$677$	−23.0000	+	23.0000i	−0.883962	+	0.883962i	0.109973	+	0.993935i	$0.464924\pi$
$678$	5.00000	+	8.66025i	0.192024	+	0.332595i
$679$	3.46410	−	2.00000i	0.132940	−	0.0767530i
$680$	6.29423	+	7.09808i	0.241373	+	0.272199i
$681$	12.0000	−	12.0000i	0.459841	−	0.459841i
$682$	8.66025	+	5.00000i	0.331618	+	0.191460i
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	0.287819	−	0.957685i	$-0.407070\pi$
$683$	−10.3923	−	6.00000i	−0.397650	−	0.229584i	−0.685470	+	0.728101i	$0.740403\pi$
$684$	−5.00000	+	5.00000i	−0.191180	+	0.191180i
$685$	−2.14359	+	35.7128i	−0.0819025	+	1.36452i
$686$	−17.3205	+	10.0000i	−0.661300	+	0.381802i
$687$	3.00000	+	5.19615i	0.114457	+	0.198246i
$688$	−1.00000	+	1.00000i	−0.0381246	+	0.0381246i
$689$		0			0
$690$	−6.00000	−	12.0000i	−0.228416	−	0.456832i
$691$	−4.09808	−	1.09808i	−0.155898	−	0.0417728i	0.180026	−	0.983662i	$-0.442382\pi$
$691$	−4.09808	−	1.09808i	−0.155898	−	0.0417728i	−0.335924	+	0.941889i	$0.609049\pi$
$692$	−15.0263	−	4.02628i	−0.571213	−	0.153056i
$693$	0.732051	+	2.73205i	0.0278083	+	0.103782i
$694$	3.00000	+	3.00000i	0.113878	+	0.113878i
$695$	−31.2487	−	1.87564i	−1.18533	−	0.0711472i
$696$		0			0
$697$	−14.0000			−0.530288
$698$	−12.2942	+	3.29423i	−0.465343	+	0.124688i
$699$	1.00000	+	1.73205i	0.0378235	+	0.0655122i
$700$	−9.92820	−	1.19615i	−0.375251	−	0.0452103i
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$		0			0
$703$		0			0
$704$	−2.56218	+	9.56218i	−0.0965657	+	0.360388i
$705$	3.80385	+	18.5885i	0.143261	+	0.700082i
$706$	−10.3923	−	6.00000i	−0.391120	−	0.225813i
$707$			24.0000i			0.902613i
$708$	7.00000	−	12.1244i	0.263076	−	0.455661i
$709$	10.6147	+	39.6147i	0.398645	+	1.48776i	0.815482	+	0.578782i	$0.196472\pi$
$709$	10.6147	+	39.6147i	0.398645	+	1.48776i	−0.416838	+	0.908981i	$0.636862\pi$
$710$	−3.00000	−	1.00000i	−0.112588	−	0.0375293i
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$	5.49038	−	20.4904i	0.205761	−	0.767909i
$713$	−25.9808	+	15.0000i	−0.972987	+	0.561754i
$714$	4.00000			0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$	5.19615	−	3.00000i	0.194054	−	0.112037i
$718$	0.366025	−	1.36603i	0.0136599	−	0.0509796i
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	−0.930923	−	0.365216i	$-0.880995\pi$
$719$	−4.00000	+	6.92820i	−0.149175	+	0.258378i	0.781748	+	0.623595i	$0.214328\pi$
$720$	1.00000	+	2.00000i	0.0372678	+	0.0745356i
$721$	−5.12436	−	19.1244i	−0.190841	−	0.712228i
$722$	15.5000	−	26.8468i	0.576850	−	0.999134i
$723$		−	34.0000i		−	1.26447i
$724$	6.92820	+	4.00000i	0.257485	+	0.148659i
$725$		0			0
$726$	3.29423	−	12.2942i	0.122260	−	0.456282i
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.929660	+	0.368418i	$0.120100\pi$
$727$	35.0000	+	35.0000i	1.29808	+	1.29808i	0.368418	+	0.929660i	$0.379900\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$	18.6603	+	12.3205i	0.690647	+	0.456002i
$731$	1.00000	+	1.73205i	0.0369863	+	0.0640622i
$732$	19.1244	−	5.12436i	0.706857	−	0.189402i
$733$	4.00000			0.147743			0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000			0.147743			0.0738717	+	0.997268i	$0.476464\pi$
$734$	1.36603	−	0.366025i	0.0504209	−	0.0135102i
$735$	7.09808	−	6.29423i	0.261816	−	0.232166i
$736$	−15.0000	−	15.0000i	−0.552907	−	0.552907i
$737$	1.46410	+	5.46410i	0.0539309	+	0.201273i
$738$	−9.56218	−	2.56218i	−0.351989	−	0.0943151i
$739$	4.09808	+	1.09808i	0.150750	+	0.0403934i	0.333405	−	0.942784i	$-0.391802\pi$
$739$	4.09808	+	1.09808i	0.150750	+	0.0403934i	−0.182655	+	0.983177i	$0.558469\pi$
$740$		0			0
$741$		0			0
$742$	−10.0000	+	10.0000i	−0.367112	+	0.367112i
$743$	17.0000	+	29.4449i	0.623670	+	1.08023i	0.988797	+	0.149270i	$0.0476922\pi$
$743$	17.0000	+	29.4449i	0.623670	+	1.08023i	−0.365127	+	0.930958i	$0.618974\pi$
$744$	−25.9808	+	15.0000i	−0.952501	+	0.549927i
$745$	7.09808	−	6.29423i	0.260053	−	0.230603i
$746$	15.0000	−	15.0000i	0.549189	−	0.549189i
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$	1.73205	+	1.00000i	0.0633300	+	0.0365636i
$749$	14.0000	−	14.0000i	0.511549	−	0.511549i
$750$	−15.7583	+	1.29423i	−0.575413	+	0.0472585i
$751$	−43.3013	+	25.0000i	−1.58009	+	0.912263i	−0.585240	+	0.810860i	$0.699000\pi$
$751$	−43.3013	+	25.0000i	−1.58009	+	0.912263i	−0.994845	+	0.101403i	$0.967667\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	−2.00000	+	2.00000i	−0.0728841	+	0.0728841i
$754$		0			0
$755$	−21.0000	−	7.00000i	−0.764268	−	0.254756i
$756$	−10.9282	−	2.92820i	−0.397455	−	0.106498i
$757$	47.8109	+	12.8109i	1.73772	+	0.465620i	0.981937	−	0.189207i	$-0.0605917\pi$
$757$	47.8109	+	12.8109i	1.73772	+	0.465620i	0.755779	+	0.654827i	$0.227258\pi$
$758$	0.366025	+	1.36603i	0.0132946	+	0.0496163i
$759$	−6.00000	−	6.00000i	−0.217786	−	0.217786i
$760$	31.4711	+	35.4904i	1.14158	+	1.28737i
$761$	−9.56218	+	2.56218i	−0.346629	+	0.0928789i	−0.427933	−	0.903810i	$-0.640758\pi$
$761$	−9.56218	+	2.56218i	−0.346629	+	0.0928789i	0.0813044	+	0.996689i	$0.474091\pi$
$762$	18.0000			0.652071
$763$	−24.5885	+	6.58846i	−0.890162	+	0.238518i
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$	3.09808	−	0.633975i	0.112011	−	0.0229214i
$766$			30.0000i			1.08394i
$767$		0			0
$768$	−17.0000	−	17.0000i	−0.613435	−	0.613435i
$769$	−5.49038	+	20.4904i	−0.197988	+	0.738902i	0.793485	+	0.608590i	$0.208265\pi$
$769$	−5.49038	+	20.4904i	−0.197988	+	0.738902i	−0.991473	+	0.130312i	$0.958402\pi$
$770$	6.19615	−	1.26795i	0.223294	−

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)

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

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Groups

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