LMFDB - Embedded newform 360.2.br.b.317.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			317.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.317
Dual form			360.2.br.b.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +2.00000i q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(2.86603 - 0.767949i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +2.00000i q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(2.86603 - 0.767949i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-3.09808 + 0.633975i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.73205 + 3.00000i) q^{12} +(-1.73205 + 6.46410i) q^{13} +(-3.63397 - 2.09808i) q^{14} +(0.232051 - 3.86603i) q^{15} -4.00000 q^{16} +(3.00000 - 3.00000i) q^{17} +(-4.09808 + 1.09808i) q^{18} +1.26795 q^{19} +(3.73205 + 2.46410i) q^{20} +(3.63397 - 3.63397i) q^{21} +(2.73205 - 0.732051i) q^{22} +(-0.866025 + 3.23205i) q^{23} +(1.26795 - 4.73205i) q^{24} +(-1.96410 - 4.59808i) q^{25} +(8.19615 - 4.73205i) q^{26} -5.19615i q^{27} +(1.53590 + 5.73205i) q^{28} +(-6.23205 - 3.59808i) q^{29} +(-4.09808 + 3.63397i) q^{30} +(-1.09808 - 1.90192i) q^{31} +(4.00000 + 4.00000i) q^{32} +3.46410i q^{33} -6.00000 q^{34} +(2.09808 - 6.29423i) q^{35} +(5.19615 + 3.00000i) q^{36} +(-6.46410 + 6.46410i) q^{37} +(-1.26795 - 1.26795i) q^{38} +(3.00000 + 11.1962i) q^{39} +(-1.26795 - 6.19615i) q^{40} +(-0.401924 + 0.232051i) q^{41} -7.26795 q^{42} +(-0.633975 + 0.169873i) q^{43} +(-3.46410 - 2.00000i) q^{44} +(-3.00000 - 6.00000i) q^{45} +(4.09808 - 2.36603i) q^{46} +(-1.50000 - 5.59808i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(1.56218 - 0.901924i) q^{49} +(-2.63397 + 6.56218i) q^{50} +(1.90192 - 7.09808i) q^{51} +(-12.9282 - 3.46410i) q^{52} +(-5.19615 + 5.19615i) q^{53} +(-5.19615 + 5.19615i) q^{54} +(2.00000 + 4.00000i) q^{55} +(4.19615 - 7.26795i) q^{56} +(1.90192 - 1.09808i) q^{57} +(2.63397 + 9.83013i) q^{58} +(10.5622 - 6.09808i) q^{59} +(7.73205 + 0.464102i) q^{60} +(-2.30385 - 1.33013i) q^{61} +(-0.803848 + 3.00000i) q^{62} +(2.30385 - 8.59808i) q^{63} -8.00000i q^{64} +(9.92820 + 11.1962i) q^{65} +(3.46410 - 3.46410i) q^{66} +(4.96410 + 1.33013i) q^{67} +(6.00000 + 6.00000i) q^{68} +(1.50000 + 5.59808i) q^{69} +(-8.39230 + 4.19615i) q^{70} +12.0000i q^{71} +(-2.19615 - 8.19615i) q^{72} +(0.196152 - 0.196152i) q^{73} +12.9282 q^{74} +(-6.92820 - 5.19615i) q^{75} +2.53590i q^{76} +(-1.53590 + 5.73205i) q^{77} +(8.19615 - 14.1962i) q^{78} +(7.09808 + 4.09808i) q^{79} +(-4.92820 + 7.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(0.633975 + 0.169873i) q^{82} +(2.66987 + 9.96410i) q^{83} +(7.26795 + 7.26795i) q^{84} +(-1.90192 - 9.29423i) q^{85} +(0.803848 + 0.464102i) q^{86} -12.4641 q^{87} +(1.46410 + 5.46410i) q^{88} -14.6603 q^{89} +(-3.00000 + 9.00000i) q^{90} +19.8564i q^{91} +(-6.46410 - 1.73205i) q^{92} +(-3.29423 - 1.90192i) q^{93} +(-4.09808 + 7.09808i) q^{94} +(1.56218 - 2.36603i) q^{95} +(9.46410 + 2.53590i) q^{96} +(-6.83013 + 1.83013i) q^{97} +(-2.46410 - 0.660254i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9	$ 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 6 q^{15} - 16 q^{16} + 12 q^{17} - 6 q^{18} + 12 q^{19} + 8 q^{20} + 18 q^{21} + 4 q^{22} + 12 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{28} - 18 q^{29} - 6 q^{30} + 6 q^{31} + 16 q^{32} - 24 q^{34} - 2 q^{35} - 12 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{40} - 12 q^{41} - 36 q^{42} - 6 q^{43} - 12 q^{45} + 6 q^{46} - 6 q^{47} - 24 q^{48} - 18 q^{49} - 14 q^{50} + 18 q^{51} - 24 q^{52} + 8 q^{55} - 4 q^{56} + 18 q^{57} + 14 q^{58} + 18 q^{59} + 24 q^{60} - 30 q^{61} - 24 q^{62} + 30 q^{63} + 12 q^{65} + 6 q^{67} + 24 q^{68} + 6 q^{69} + 8 q^{70} + 12 q^{72} - 20 q^{73} + 24 q^{74} - 20 q^{77} + 12 q^{78} + 18 q^{79} + 8 q^{80} - 18 q^{81} + 6 q^{82} + 28 q^{83} + 36 q^{84} - 18 q^{85} + 24 q^{86} - 36 q^{87} - 8 q^{88} - 24 q^{89} - 12 q^{90} - 12 q^{92} + 18 q^{93} - 6 q^{94} - 18 q^{95} + 24 q^{96} - 10 q^{97} + 4 q^{98} + 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 6 * q^15 - 16 * q^16 + 12 * q^17 - 6 * q^18 + 12 * q^19 + 8 * q^20 + 18 * q^21 + 4 * q^22 + 12 * q^24 + 6 * q^25 + 12 * q^26 + 20 * q^28 - 18 * q^29 - 6 * q^30 + 6 * q^31 + 16 * q^32 - 24 * q^34 - 2 * q^35 - 12 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^40 - 12 * q^41 - 36 * q^42 - 6 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 - 24 * q^48 - 18 * q^49 - 14 * q^50 + 18 * q^51 - 24 * q^52 + 8 * q^55 - 4 * q^56 + 18 * q^57 + 14 * q^58 + 18 * q^59 + 24 * q^60 - 30 * q^61 - 24 * q^62 + 30 * q^63 + 12 * q^65 + 6 * q^67 + 24 * q^68 + 6 * q^69 + 8 * q^70 + 12 * q^72 - 20 * q^73 + 24 * q^74 - 20 * q^77 + 12 * q^78 + 18 * q^79 + 8 * q^80 - 18 * q^81 + 6 * q^82 + 28 * q^83 + 36 * q^84 - 18 * q^85 + 24 * q^86 - 36 * q^87 - 8 * q^88 - 24 * q^89 - 12 * q^90 - 12 * q^92 + 18 * q^93 - 6 * q^94 - 18 * q^95 + 24 * q^96 - 10 * q^97 + 4 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$			2.00000i			1.00000i
$5$	1.23205	−	1.86603i	0.550990	−	0.834512i
$5$	1.23205	−	1.86603i	0.550990	−	0.834512i
$6$	−2.36603	−	0.633975i	−0.965926	−	0.258819i
$7$	2.86603	−	0.767949i	1.08326	−	0.290258i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	2.86603	−	0.767949i	1.08326	−	0.290258i	0.755929	+	0.654654i	$0.227186\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−3.09808	+	0.633975i	−0.979698	+	0.200480i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	1.73205	+	3.00000i	0.500000	+	0.866025i
$13$	−1.73205	+	6.46410i	−0.480384	+	1.79282i	0.119617	+	0.992820i	$0.461833\pi$
$13$	−1.73205	+	6.46410i	−0.480384	+	1.79282i	−0.600001	+	0.799999i	$0.704833\pi$
$14$	−3.63397	−	2.09808i	−0.971221	−	0.560734i
$15$	0.232051	−	3.86603i	0.0599153	−	0.998203i
$16$	−4.00000			−1.00000
$17$	3.00000	−	3.00000i	0.727607	−	0.727607i	−0.242536	−	0.970143i	$-0.577979\pi$
$17$	3.00000	−	3.00000i	0.727607	−	0.727607i	0.970143	+	0.242536i	$0.0779791\pi$
$18$	−4.09808	+	1.09808i	−0.965926	+	0.258819i
$19$	1.26795			0.290887			0.145444	−	0.989367i	$-0.453539\pi$
$19$	1.26795			0.290887			0.145444	+	0.989367i	$0.453539\pi$
$20$	3.73205	+	2.46410i	0.834512	+	0.550990i
$21$	3.63397	−	3.63397i	0.792998	−	0.792998i
$22$	2.73205	−	0.732051i	0.582475	−	0.156074i
$23$	−0.866025	+	3.23205i	−0.180579	+	0.673929i	0.814955	+	0.579524i	$0.196762\pi$
$23$	−0.866025	+	3.23205i	−0.180579	+	0.673929i	−0.995534	+	0.0944051i	$0.969905\pi$
$24$	1.26795	−	4.73205i	0.258819	−	0.965926i
$25$	−1.96410	−	4.59808i	−0.392820	−	0.919615i
$26$	8.19615	−	4.73205i	1.60740	−	0.928032i
$27$		−	5.19615i		−	1.00000i
$28$	1.53590	+	5.73205i	0.290258	+	1.08326i
$29$	−6.23205	−	3.59808i	−1.15726	−	0.668146i	−0.206616	−	0.978422i	$-0.566245\pi$
$29$	−6.23205	−	3.59808i	−1.15726	−	0.668146i	−0.950646	+	0.310276i	$0.899579\pi$
$30$	−4.09808	+	3.63397i	−0.748203	+	0.663470i
$31$	−1.09808	−	1.90192i	−0.197220	−	0.341596i	0.750406	−	0.660977i	$-0.229858\pi$
$31$	−1.09808	−	1.90192i	−0.197220	−	0.341596i	−0.947626	+	0.319382i	$0.896525\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$			3.46410i			0.603023i
$34$	−6.00000			−1.02899
$35$	2.09808	−	6.29423i	0.354640	−	1.06392i
$36$	5.19615	+	3.00000i	0.866025	+	0.500000i
$37$	−6.46410	+	6.46410i	−1.06269	+	1.06269i	−0.0647930	+	0.997899i	$0.520639\pi$
$37$	−6.46410	+	6.46410i	−1.06269	+	1.06269i	−0.997899	+	0.0647930i	$0.979361\pi$
$38$	−1.26795	−	1.26795i	−0.205689	−	0.205689i
$39$	3.00000	+	11.1962i	0.480384	+	1.79282i
$40$	−1.26795	−	6.19615i	−0.200480	−	0.979698i
$41$	−0.401924	+	0.232051i	−0.0627700	+	0.0362402i	−0.531057	−	0.847336i	$-0.678205\pi$
$41$	−0.401924	+	0.232051i	−0.0627700	+	0.0362402i	0.468287	+	0.883577i	$0.344871\pi$
$42$	−7.26795			−1.12147
$43$	−0.633975	+	0.169873i	−0.0966802	+	0.0259054i	−0.306835	−	0.951763i	$-0.599270\pi$
$43$	−0.633975	+	0.169873i	−0.0966802	+	0.0259054i	0.210155	+	0.977668i	$0.432603\pi$
$44$	−3.46410	−	2.00000i	−0.522233	−	0.301511i
$45$	−3.00000	−	6.00000i	−0.447214	−	0.894427i
$46$	4.09808	−	2.36603i	0.604228	−	0.348851i
$47$	−1.50000	−	5.59808i	−0.218797	−	0.816563i	−0.984795	−	0.173720i	$-0.944421\pi$
$47$	−1.50000	−	5.59808i	−0.218797	−	0.816563i	0.765998	−	0.642843i	$-0.222245\pi$
$48$	−6.00000	+	3.46410i	−0.866025	+	0.500000i
$49$	1.56218	−	0.901924i	0.223168	−	0.128846i
$50$	−2.63397	+	6.56218i	−0.372500	+	0.928032i
$51$	1.90192	−	7.09808i	0.266323	−	0.993929i
$52$	−12.9282	−	3.46410i	−1.79282	−	0.480384i
$53$	−5.19615	+	5.19615i	−0.713746	+	0.713746i	−0.967317	−	0.253570i	$-0.918395\pi$
$53$	−5.19615	+	5.19615i	−0.713746	+	0.713746i	0.253570	+	0.967317i	$0.418395\pi$
$54$	−5.19615	+	5.19615i	−0.707107	+	0.707107i
$55$	2.00000	+	4.00000i	0.269680	+	0.539360i
$56$	4.19615	−	7.26795i	0.560734	−	0.971221i
$57$	1.90192	−	1.09808i	0.251916	−	0.145444i
$58$	2.63397	+	9.83013i	0.345858	+	1.29076i
$59$	10.5622	−	6.09808i	1.37508	−	0.793902i	0.383516	−	0.923534i	$-0.374713\pi$
$59$	10.5622	−	6.09808i	1.37508	−	0.793902i	0.991562	+	0.129632i	$0.0413797\pi$
$60$	7.73205	+	0.464102i	0.998203	+	0.0599153i
$61$	−2.30385	−	1.33013i	−0.294977	−	0.170305i	0.345207	−	0.938527i	$-0.387809\pi$
$61$	−2.30385	−	1.33013i	−0.294977	−	0.170305i	−0.640184	+	0.768221i	$0.721142\pi$
$62$	−0.803848	+	3.00000i	−0.102089	+	0.381000i
$63$	2.30385	−	8.59808i	0.290258	−	1.08326i
$64$		−	8.00000i		−	1.00000i
$65$	9.92820	+	11.1962i	1.23144	+	1.38871i
$66$	3.46410	−	3.46410i	0.426401	−	0.426401i
$67$	4.96410	+	1.33013i	0.606462	+	0.162501i	0.548966	−	0.835845i	$-0.315022\pi$
$67$	4.96410	+	1.33013i	0.606462	+	0.162501i	0.0574958	+	0.998346i	$0.481688\pi$
$68$	6.00000	+	6.00000i	0.727607	+	0.727607i
$69$	1.50000	+	5.59808i	0.180579	+	0.673929i
$70$	−8.39230	+	4.19615i	−1.00307	+	0.501536i
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$	−2.19615	−	8.19615i	−0.258819	−	0.965926i
$73$	0.196152	−	0.196152i	0.0229579	−	0.0229579i	−0.695535	−	0.718493i	$-0.744832\pi$
$73$	0.196152	−	0.196152i	0.0229579	−	0.0229579i	0.718493	+	0.695535i	$0.244832\pi$
$74$	12.9282			1.50287
$75$	−6.92820	−	5.19615i	−0.800000	−	0.600000i
$76$			2.53590i			0.290887i
$77$	−1.53590	+	5.73205i	−0.175032	+	0.653228i
$78$	8.19615	−	14.1962i	0.928032	−	1.60740i
$79$	7.09808	+	4.09808i	0.798596	+	0.461070i	0.842980	−	0.537945i	$-0.180799\pi$
$79$	7.09808	+	4.09808i	0.798596	+	0.461070i	−0.0443840	+	0.999015i	$0.514133\pi$
$80$	−4.92820	+	7.46410i	−0.550990	+	0.834512i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	0.633975	+	0.169873i	0.0700108	+	0.0187593i
$83$	2.66987	+	9.96410i	0.293057	+	1.09370i	0.942748	+	0.333505i	$0.108231\pi$
$83$	2.66987	+	9.96410i	0.293057	+	1.09370i	−0.649692	+	0.760198i	$0.725102\pi$
$84$	7.26795	+	7.26795i	0.792998	+	0.792998i
$85$	−1.90192	−	9.29423i	−0.206293	−	1.00810i
$86$	0.803848	+	0.464102i	0.0866811	+	0.0500454i
$87$	−12.4641			−1.33629
$88$	1.46410	+	5.46410i	0.156074	+	0.582475i
$89$	−14.6603			−1.55398			−0.776992	−	0.629511i	$-0.783255\pi$
$89$	−14.6603			−1.55398			−0.776992	+	0.629511i	$0.783255\pi$
$90$	−3.00000	+	9.00000i	−0.316228	+	0.948683i
$91$			19.8564i			2.08152i
$92$	−6.46410	−	1.73205i	−0.673929	−	0.180579i
$93$	−3.29423	−	1.90192i	−0.341596	−	0.197220i
$94$	−4.09808	+	7.09808i	−0.422684	+	0.732111i
$95$	1.56218	−	2.36603i	0.160276	−	0.242749i
$96$	9.46410	+	2.53590i	0.965926	+	0.258819i
$97$	−6.83013	+	1.83013i	−0.693494	+	0.185821i	−0.588315	−	0.808632i	$-0.700208\pi$
$97$	−6.83013	+	1.83013i	−0.693494	+	0.185821i	−0.105180	+	0.994453i	$0.533542\pi$
$98$	−2.46410	−	0.660254i	−0.248912	−	0.0666957i
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$	9.19615	−	3.92820i	0.919615	−	0.392820i
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$	−9.00000	+	5.19615i	−0.891133	+	0.514496i
$103$	12.8301	+	3.43782i	1.26419	+	0.338739i	0.827802	−	0.561020i	$-0.189591\pi$
$103$	12.8301	+	3.43782i	1.26419	+	0.338739i	0.436388	+	0.899759i	$0.356258\pi$
$104$	9.46410	+	16.3923i	0.928032	+	1.60740i
$105$	−2.30385	−	11.2583i	−0.224833	−	1.09870i
$106$	10.3923			1.00939
$107$	0.901924	+	0.901924i	0.0871923	+	0.0871923i	0.749358	−	0.662165i	$-0.230362\pi$
$107$	0.901924	+	0.901924i	0.0871923	+	0.0871923i	−0.662165	+	0.749358i	$0.730362\pi$
$108$	10.3923			1.00000
$109$	8.66025			0.829502			0.414751	−	0.909935i	$-0.363869\pi$
$109$	8.66025			0.829502			0.414751	+	0.909935i	$0.363869\pi$
$110$	2.00000	−	6.00000i	0.190693	−	0.572078i
$111$	−4.09808	+	15.2942i	−0.388972	+	1.45166i
$112$	−11.4641	+	3.07180i	−1.08326	+	0.290258i
$113$	−1.73205	+	6.46410i	−0.162938	+	0.608092i	0.835357	+	0.549708i	$0.185261\pi$
$113$	−1.73205	+	6.46410i	−0.162938	+	0.608092i	−0.998294	+	0.0583831i	$0.981405\pi$
$114$	−3.00000	−	0.803848i	−0.280976	−	0.0752872i
$115$	4.96410	+	5.59808i	0.462905	+	0.522023i
$116$	7.19615	−	12.4641i	0.668146	−	1.15726i
$117$	14.1962	+	14.1962i	1.31243	+	1.31243i
$118$	−16.6603	−	4.46410i	−1.53370	−	0.410954i
$119$	6.29423	−	10.9019i	0.576991	−	0.999378i
$120$	−7.26795	−	8.19615i	−0.663470	−	0.748203i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	0.973721	+	3.63397i	0.0881565	+	0.329005i
$123$	−0.401924	+	0.696152i	−0.0362402	+	0.0627700i
$124$	3.80385	−	2.19615i	0.341596	−	0.197220i
$125$	−11.0000	−	2.00000i	−0.983870	−	0.178885i
$126$	−10.9019	+	6.29423i	−0.971221	+	0.560734i
$127$	11.0981	+	11.0981i	0.984795	+	0.984795i	0.999886	−	0.0150911i	$-0.00480383\pi$
$127$	11.0981	+	11.0981i	0.984795	+	0.984795i	−0.0150911	+	0.999886i	$0.504804\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$	−0.803848	+	0.803848i	−0.0707748	+	0.0707748i
$130$	1.26795	−	21.1244i	0.111207	−	1.85273i
$131$	−9.09808	−	15.7583i	−0.794903	−	1.37681i	−0.922901	−	0.385037i	$-0.874189\pi$
$131$	−9.09808	−	15.7583i	−0.794903	−	1.37681i	0.127998	−	0.991774i	$-0.459145\pi$
$132$	−6.92820			−0.603023
$133$	3.63397	−	0.973721i	0.315106	−	0.0844323i
$134$	−3.63397	−	6.29423i	−0.313928	−	0.543739i
$135$	−9.69615	−	6.40192i	−0.834512	−	0.550990i
$136$		−	12.0000i		−	1.02899i
$137$	−0.928203	−	3.46410i	−0.0793018	−	0.295958i	0.914873	−	0.403743i	$-0.132291\pi$
$137$	−0.928203	−	3.46410i	−0.0793018	−	0.295958i	−0.994174	+	0.107785i	$0.965624\pi$
$138$	4.09808	−	7.09808i	0.348851	−	0.604228i
$139$	−3.46410	−	6.00000i	−0.293821	−	0.508913i	0.680889	−	0.732387i	$-0.261594\pi$
$139$	−3.46410	−	6.00000i	−0.293821	−	0.508913i	−0.974710	+	0.223474i	$0.928260\pi$
$140$	12.5885	+	4.19615i	1.06392	+	0.354640i
$141$	−7.09808	−	7.09808i	−0.597766	−	0.597766i
$142$	12.0000	−	12.0000i	1.00702	−	1.00702i
$143$	−9.46410	−	9.46410i	−0.791428	−	0.791428i
$144$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$145$	−14.3923	+	7.19615i	−1.19522	+	0.597608i
$146$	−0.392305			−0.0324674
$147$	1.56218	−	2.70577i	0.128846	−	0.223168i
$148$	−12.9282	−	12.9282i	−1.06269	−	1.06269i
$149$	−6.06218	+	3.50000i	−0.496633	+	0.286731i	−0.727322	−	0.686296i	$-0.759235\pi$
$149$	−6.06218	+	3.50000i	−0.496633	+	0.286731i	0.230689	+	0.973028i	$0.425902\pi$
$150$	1.73205	+	12.1244i	0.141421	+	0.989949i
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	2.53590	−	2.53590i	0.205689	−	0.205689i
$153$	−3.29423	−	12.2942i	−0.266323	−	0.993929i
$154$	7.26795	−	4.19615i	0.585668	−	0.338136i
$155$	−4.90192	−	0.294229i	−0.393732	−	0.0236330i
$156$	−22.3923	+	6.00000i	−1.79282	+	0.480384i
$157$	12.2942	+	3.29423i	0.981186	+	0.262908i	0.713544	−	0.700610i	$-0.247089\pi$
$157$	12.2942	+	3.29423i	0.981186	+	0.262908i	0.267642	+	0.963518i	$0.413756\pi$
$158$	−3.00000	−	11.1962i	−0.238667	−	0.890718i
$159$	−3.29423	+	12.2942i	−0.261249	+	0.974996i
$160$	12.3923	−	2.53590i	0.979698	−	0.200480i
$161$			9.92820i			0.782452i
$162$	−3.29423	+	12.2942i	−0.258819	+	0.965926i
$163$	0.464102	+	0.464102i	0.0363512	+	0.0363512i	0.725049	−	0.688698i	$-0.241817\pi$
$163$	0.464102	+	0.464102i	0.0363512	+	0.0363512i	−0.688698	+	0.725049i	$0.741817\pi$
$164$	−0.464102	−	0.803848i	−0.0362402	−	0.0627700i
$165$	6.46410	+	4.26795i	0.503230	+	0.332259i
$166$	7.29423	−	12.6340i	0.566142	−	0.980587i
$167$	−10.7942	−	2.89230i	−0.835282	−	0.223813i	−0.184266	−	0.982876i	$-0.558991\pi$
$167$	−10.7942	−	2.89230i	−0.835282	−	0.223813i	−0.651017	+	0.759063i	$0.725657\pi$
$168$		−	14.5359i		−	1.12147i
$169$	−27.5263	−	15.8923i	−2.11741	−	1.22248i
$170$	−7.39230	+	11.1962i	−0.566964	+	0.858706i
$171$	1.90192	−	3.29423i	0.145444	−	0.251916i
$172$	−0.339746	−	1.26795i	−0.0259054	−	0.0966802i
$173$	0.732051	+	2.73205i	0.0556568	+	0.207714i	0.988155	−	0.153462i	$-0.0490422\pi$
$173$	0.732051	+	2.73205i	0.0556568	+	0.207714i	−0.932498	+	0.361176i	$0.882375\pi$
$174$	12.4641	+	12.4641i	0.944901	+	0.944901i
$175$	−9.16025	−	11.6699i	−0.692450	−	0.882159i
$176$	4.00000	−	6.92820i	0.301511	−	0.522233i
$177$	10.5622	−	18.2942i	0.793902	−	1.37508i
$178$	14.6603	+	14.6603i	1.09883	+	1.09883i
$179$			14.3923i			1.07573i	0.843031	+	0.537866i	$0.180769\pi$
$179$			14.3923i			1.07573i	−0.843031	+	0.537866i	$0.819231\pi$
$180$	12.0000	−	6.00000i	0.894427	−	0.447214i
$181$		−	3.00000i		−	0.222988i	−0.993765	−	0.111494i	$-0.964436\pi$
$181$		−	3.00000i		−	0.222988i	0.993765	−	0.111494i	$-0.0355636\pi$
$182$	19.8564	−	19.8564i	1.47185	−	1.47185i
$183$	−4.60770			−0.340611
$184$	4.73205	+	8.19615i	0.348851	+	0.604228i
$185$	4.09808	+	20.0263i	0.301297	+	1.47236i
$186$	1.39230	+	5.19615i	0.102089	+	0.381000i
$187$	2.19615	+	8.19615i	0.160599	+	0.599362i
$188$	11.1962	−	3.00000i	0.816563	−	0.218797i
$189$	−3.99038	−	14.8923i	−0.290258	−	1.08326i
$190$	−3.92820	+	0.803848i	−0.284982	+	0.0583172i
$191$	−10.9019	−	6.29423i	−0.788836	−	0.455434i	0.0507169	−	0.998713i	$-0.483849\pi$
$191$	−10.9019	−	6.29423i	−0.788836	−	0.455434i	−0.839552	+	0.543279i	$0.817183\pi$
$192$	−6.92820	−	12.0000i	−0.500000	−	0.866025i
$193$	13.6603	+	3.66025i	0.983287	+	0.263471i	0.714428	−	0.699709i	$-0.246687\pi$
$193$	13.6603	+	3.66025i	0.983287	+	0.263471i	0.268858	+	0.963180i	$0.413354\pi$
$194$	8.66025	+	5.00000i	0.621770	+	0.358979i
$195$	24.5885	+	8.19615i	1.76082	+	0.586939i
$196$	1.80385	+	3.12436i	0.128846	+	0.223168i
$197$	−12.0000	−	12.0000i	−0.854965	−	0.854965i	0.135775	−	0.990740i	$-0.456648\pi$
$197$	−12.0000	−	12.0000i	−0.854965	−	0.854965i	−0.990740	+	0.135775i	$0.956648\pi$
$198$	2.19615	−	8.19615i	0.156074	−	0.582475i
$199$		−	6.19615i		−	0.439234i	−0.975586	−	0.219617i	$-0.929519\pi$
$199$		−	6.19615i		−	0.439234i	0.975586	−	0.219617i	$-0.0704807\pi$
$200$	−13.1244	−	5.26795i	−0.928032	−	0.372500i
$201$	8.59808	−	2.30385i	0.606462	−	0.162501i
$202$	−2.73205	+	0.732051i	−0.192226	+	0.0515069i
$203$	−20.6244	−	5.52628i	−1.44755	−	0.387869i
$204$	14.1962	+	3.80385i	0.993929	+	0.266323i
$205$	−0.0621778	+	1.03590i	−0.00434269	+	0.0723503i
$206$	−9.39230	−	16.2679i	−0.654393	−	1.13344i
$207$	7.09808	+	7.09808i	0.493350	+	0.493350i
$208$	6.92820	−	25.8564i	0.480384	−	1.79282i
$209$	−1.26795	+	2.19615i	−0.0877059	+	0.151911i
$210$	−8.95448	+	13.5622i	−0.617918	+	0.935879i
$211$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$211$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$212$	−10.3923	−	10.3923i	−0.713746	−	0.713746i
$213$	10.3923	+	18.0000i	0.712069	+	1.23334i
$214$		−	1.80385i		−	0.123308i
$215$	−0.464102	+	1.39230i	−0.0316515	+	0.0949544i
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$	−4.60770	−	4.60770i	−0.312791	−	0.312791i
$218$	−8.66025	−	8.66025i	−0.586546	−	0.586546i
$219$	0.124356	−	0.464102i	0.00840318	−	0.0313611i
$220$	−8.00000	+	4.00000i	−0.539360	+	0.269680i
$221$	14.1962	+	24.5885i	0.954937	+	1.65400i
$222$	19.3923	−	11.1962i	1.30153	−	0.751437i
$223$	2.52628	+	9.42820i	0.169172	+	0.631359i	0.997471	+	0.0710728i	$0.0226423\pi$
$223$	2.52628	+	9.42820i	0.169172	+	0.631359i	−0.828299	+	0.560286i	$0.810691\pi$
$224$	14.5359	+	8.39230i	0.971221	+	0.560734i
$225$	−14.8923	−	1.79423i	−0.992820	−	0.119615i
$226$	8.19615	−	4.73205i	0.545200	−	0.314771i
$227$	18.2942	−	4.90192i	1.21423	−	0.325352i	0.405810	−	0.913957i	$-0.366989\pi$
$227$	18.2942	−	4.90192i	1.21423	−	0.325352i	0.808421	+	0.588605i	$0.200323\pi$
$228$	2.19615	+	3.80385i	0.145444	+	0.251916i
$229$	−9.23205	−	15.9904i	−0.610071	−	1.05667i	−0.991228	−	0.132164i	$-0.957808\pi$
$229$	−9.23205	−	15.9904i	−0.610071	−	1.05667i	0.381157	−	0.924510i	$-0.375526\pi$
$230$	0.633975	−	10.5622i	0.0418030	−	0.696449i
$231$	2.66025	+	9.92820i	0.175032	+	0.653228i
$232$	−19.6603	+	5.26795i	−1.29076	+	0.345858i
$233$	−6.12436	−	6.12436i	−0.401220	−	0.401220i	0.477443	−	0.878663i	$-0.341564\pi$
$233$	−6.12436	−	6.12436i	−0.401220	−	0.401220i	−0.878663	+	0.477443i	$0.841564\pi$
$234$		−	28.3923i		−	1.85606i
$235$	−12.2942	−	4.09808i	−0.801987	−	0.267329i
$236$	12.1962	+	21.1244i	0.793902	+	1.37508i
$237$	14.1962			0.922139
$238$	−17.1962	+	4.60770i	−1.11466	+	0.298673i
$239$	−2.53590	−	4.39230i	−0.164034	−	0.284115i	0.772278	−	0.635285i	$-0.219117\pi$
$239$	−2.53590	−	4.39230i	−0.164034	−	0.284115i	−0.936312	+	0.351170i	$0.885784\pi$
$240$	−0.928203	+	15.4641i	−0.0599153	+	0.998203i
$241$	14.5981	−	25.2846i	0.940345	−	1.62872i	0.175531	−	0.984474i	$-0.443836\pi$
$241$	14.5981	−	25.2846i	0.940345	−	1.62872i	0.764814	−	0.644251i	$-0.222831\pi$
$242$	2.56218	−	9.56218i	0.164703	−	0.614680i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	2.66025	−	4.60770i	0.170305	−	0.294977i
$245$	0.241670	−	4.02628i	0.0154397	−	0.257230i
$246$	1.09808	−	0.294229i	0.0700108	−	0.0187593i
$247$	−2.19615	+	8.19615i	−0.139738	+	0.521509i
$248$	−6.00000	−	1.60770i	−0.381000	−	0.102089i
$249$	12.6340	+	12.6340i	0.800646	+	0.800646i
$250$	9.00000	+	13.0000i	0.569210	+	0.822192i
$251$	−4.58846			−0.289621			−0.144810	−	0.989459i	$-0.546257\pi$
$251$	−4.58846			−0.289621			−0.144810	+	0.989459i	$0.546257\pi$
$252$	17.1962	+	4.60770i	1.08326	+	0.290258i
$253$	−4.73205	−	4.73205i	−0.297501	−	0.297501i
$254$		−	22.1962i		−	1.39271i
$255$	−10.9019	−	12.2942i	−0.682705	−	0.769894i
$256$	16.0000			1.00000
$257$	25.2224	+	6.75833i	1.57333	+	0.421573i	0.936854	−	0.349721i	$-0.113724\pi$
$257$	25.2224	+	6.75833i	1.57333	+	0.421573i	0.636478	+	0.771295i	$0.280390\pi$
$258$	1.60770			0.100091
$259$	−13.5622	+	23.4904i	−0.842713	+	1.45962i
$260$	−22.3923	+	19.8564i	−1.38871	+	1.23144i
$261$	−18.6962	+	10.7942i	−1.15726	+	0.668146i
$262$	−6.66025	+	24.8564i	−0.411472	+	1.53563i
$263$	5.36603	−	1.43782i	0.330883	−	0.0886599i	−0.0895528	−	0.995982i	$-0.528544\pi$
$263$	5.36603	−	1.43782i	0.330883	−	0.0886599i	0.420436	+	0.907322i	$0.361877\pi$
$264$	6.92820	+	6.92820i	0.426401	+	0.426401i
$265$	3.29423	+	16.0981i	0.202363	+	0.988897i
$266$	−4.60770	−	2.66025i	−0.282516	−	0.163111i
$267$	−21.9904	+	12.6962i	−1.34579	+	0.776992i
$268$	−2.66025	+	9.92820i	−0.162501	+	0.606462i
$269$			1.00000i			0.0609711i	0.999535	+	0.0304855i	$0.00970535\pi$
$269$			1.00000i			0.0609711i	−0.999535	+	0.0304855i	$0.990295\pi$
$270$	3.29423	+	16.0981i	0.200480	+	0.979698i
$271$	−26.5885			−1.61513			−0.807567	−	0.589776i	$-0.799216\pi$
$271$	−26.5885			−1.61513			−0.807567	+	0.589776i	$0.799216\pi$
$272$	−12.0000	+	12.0000i	−0.727607	+	0.727607i
$273$	17.1962	+	29.7846i	1.04076	+	1.80265i
$274$	−2.53590	+	4.39230i	−0.153199	+	0.265349i
$275$	9.92820	+	1.19615i	0.598693	+	0.0721307i
$276$	−11.1962	+	3.00000i	−0.673929	+	0.180579i
$277$	−0.169873	−	0.633975i	−0.0102067	−	0.0380918i	0.960635	−	0.277815i	$-0.0896101\pi$
$277$	−0.169873	−	0.633975i	−0.0102067	−	0.0380918i	−0.970841	+	0.239723i	$0.922943\pi$
$278$	−2.53590	+	9.46410i	−0.152093	+	0.567619i
$279$	−6.58846			−0.394441
$280$	−8.39230	−	16.7846i	−0.501536	−	1.00307i
$281$	13.7942	+	7.96410i	0.822895	+	0.475098i	0.851414	−	0.524495i	$-0.175746\pi$
$281$	13.7942	+	7.96410i	0.822895	+	0.475098i	−0.0285190	+	0.999593i	$0.509079\pi$
$282$			14.1962i			0.845369i
$283$	4.50000	−	16.7942i	0.267497	−	0.998313i	−0.693207	−	0.720739i	$-0.743803\pi$
$283$	4.50000	−	16.7942i	0.267497	−	0.998313i	0.960704	−	0.277575i	$-0.0895306\pi$
$284$	−24.0000			−1.42414
$285$	0.294229	−	4.90192i	0.0174286	−	0.290365i
$286$			18.9282i			1.11925i
$287$	−0.973721	+	0.973721i	−0.0574769	+	0.0574769i
$288$	16.3923	−	4.39230i	0.965926	−	0.258819i
$289$		−	1.00000i		−	0.0588235i
$290$	21.5885	+	7.19615i	1.26772	+	0.422573i
$291$	−8.66025	+	8.66025i	−0.507673	+	0.507673i
$292$	0.392305	+	0.392305i	0.0229579	+	0.0229579i
$293$	−15.2942	−	4.09808i	−0.893498	−	0.239412i	−0.217276	−	0.976110i	$-0.569717\pi$
$293$	−15.2942	−	4.09808i	−0.893498	−	0.239412i	−0.676222	+	0.736698i	$0.736384\pi$
$294$	−4.26795	+	1.14359i	−0.248912	+	0.0666957i
$295$	1.63397	−	27.2224i	0.0951337	−	1.58495i
$296$			25.8564i			1.50287i
$297$	9.00000	+	5.19615i	0.522233	+	0.301511i
$298$	9.56218	+	2.56218i	0.553922	+	0.148423i
$299$	−19.3923	−	11.1962i	−1.12149	−	0.647490i
$300$	10.3923	−	13.8564i	0.600000	−	0.800000i
$301$	−1.68653	+	0.973721i	−0.0972102	+	0.0561243i
$302$	−21.8564	+	5.85641i	−1.25769	+	0.336998i
$303$		−	3.46410i		−	0.199007i
$304$	−5.07180			−0.290887
$305$	−5.32051	+	2.66025i	−0.304651	+	0.152326i
$306$	−9.00000	+	15.5885i	−0.514496	+	0.891133i
$307$	12.6340	−	12.6340i	0.721059	−	0.721059i	−0.247762	−	0.968821i	$-0.579695\pi$
$307$	12.6340	−	12.6340i	0.721059	−	0.721059i	0.968821	+	0.247762i	$0.0796951\pi$
$308$	−11.4641	−	3.07180i	−0.653228	−	0.175032i
$309$	22.2224	−	5.95448i	1.26419	−	0.338739i
$310$	4.60770	+	5.19615i	0.261699	+	0.295122i
$311$	−3.29423	+	1.90192i	−0.186799	+	0.107848i	−0.590483	−	0.807050i	$-0.701063\pi$
$311$	−3.29423	+	1.90192i	−0.186799	+	0.107848i	0.403684	+	0.914898i	$0.367729\pi$
$312$	28.3923	+	16.3923i	1.60740	+	0.928032i
$313$	7.53590	+	28.1244i	0.425954	+	1.58968i	0.761830	+	0.647776i	$0.224301\pi$
$313$	7.53590	+	28.1244i	0.425954	+	1.58968i	−0.335876	+	0.941906i	$0.609032\pi$
$314$	−9.00000	−	15.5885i	−0.507899	−	0.879708i
$315$	−13.2058	−	14.8923i	−0.744061	−	0.839086i
$316$	−8.19615	+	14.1962i	−0.461070	+	0.798596i
$317$	13.6603	−	3.66025i	0.767236	−	0.205580i	0.146086	−	0.989272i	$-0.453332\pi$
$317$	13.6603	−	3.66025i	0.767236	−	0.205580i	0.621150	+	0.783692i	$0.286666\pi$
$318$	15.5885	−	9.00000i	0.874157	−	0.504695i
$319$	12.4641	−	7.19615i	0.697856	−	0.402907i
$320$	−14.9282	−	9.85641i	−0.834512	−	0.550990i
$321$	2.13397	+	0.571797i	0.119107	+	0.0319146i
$322$	9.92820	−	9.92820i	0.553277	−	0.553277i
$323$	3.80385	−	3.80385i	0.211652	−	0.211652i
$324$	15.5885	−	9.00000i	0.866025	−	0.500000i
$325$	33.1244	−	4.73205i	1.83741	−	0.262487i
$326$		−	0.928203i		−	0.0514084i
$327$	12.9904	−	7.50000i	0.718370	−	0.414751i
$328$	−0.339746	+	1.26795i	−0.0187593	+	0.0700108i
$329$	−8.59808	−	14.8923i	−0.474027	−	0.821039i
$330$	−2.19615	−	10.7321i	−0.120894	−	0.590780i
$331$	−26.4904	−	15.2942i	−1.45604	−	0.840647i	−0.457230	−	0.889349i	$-0.651158\pi$
$331$	−26.4904	−	15.2942i	−1.45604	−	0.840647i	−0.998813	+	0.0487018i	$0.984492\pi$
$332$	−19.9282	+	5.33975i	−1.09370	+	0.293057i
$333$	7.09808	+	26.4904i	0.388972	+	1.45166i
$334$	7.90192	+	13.6865i	0.432374	+	0.748894i
$335$	8.59808	−	7.62436i	0.469763	−	0.416563i
$336$	−14.5359	+	14.5359i	−0.792998	+	0.792998i
$337$	−3.73205	+	13.9282i	−0.203298	+	0.758718i	0.786664	+	0.617381i	$0.211806\pi$
$337$	−3.73205	+	13.9282i	−0.203298	+	0.758718i	−0.989962	+	0.141336i	$0.954860\pi$
$338$	11.6340	+	43.4186i	0.632805	+	2.36166i
$339$	3.00000	+	11.1962i	0.162938	+	0.608092i
$340$	18.5885	−	3.80385i	1.00810	−	0.206293i
$341$	4.39230			0.237857
$342$	−5.19615	+	1.39230i	−0.280976	+	0.0752872i
$343$	−10.9019	+	10.9019i	−0.588649	+	0.588649i
$344$	−0.928203	+	1.60770i	−0.0500454	+	0.0866811i
$345$	12.2942	+	4.09808i	0.661899	+	0.220633i
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	1.90192	−	7.09808i	0.102101	−	0.381045i	−0.895899	−	0.444257i	$-0.853468\pi$
$347$	1.90192	−	7.09808i	0.102101	−	0.381045i	0.998000	+	0.0632121i	$0.0201345\pi$
$348$		−	24.9282i		−	1.33629i
$349$	14.7679	−	25.5788i	0.790510	−	1.36920i	−0.135141	−	0.990826i	$-0.543149\pi$
$349$	14.7679	−	25.5788i	0.790510	−	1.36920i	0.925651	−	0.378377i	$-0.123518\pi$
$350$	−2.50962	+	20.8301i	−0.134145	+	1.11342i
$351$	33.5885	+	9.00000i	1.79282	+	0.480384i
$352$	−10.9282	+	2.92820i	−0.582475	+	0.156074i
$353$	−3.46410	+	0.928203i	−0.184376	+	0.0494033i	−0.349825	−	0.936815i	$-0.613759\pi$
$353$	−3.46410	+	0.928203i	−0.184376	+	0.0494033i	0.165450	+	0.986218i	$0.447092\pi$
$354$	−28.8564	+	7.73205i	−1.53370	+	0.410954i
$355$	22.3923	+	14.7846i	1.18846	+	0.784686i
$356$		−	29.3205i		−	1.55398i
$357$		−	21.8038i		−	1.15398i
$358$	14.3923	−	14.3923i	0.760657	−	0.760657i
$359$	8.19615			0.432576			0.216288	−	0.976330i	$-0.430605\pi$
$359$	8.19615			0.432576			0.216288	+	0.976330i	$0.430605\pi$
$360$	−18.0000	−	6.00000i	−0.948683	−	0.316228i
$361$	−17.3923			−0.915384
$362$	−3.00000	+	3.00000i	−0.157676	+	0.157676i
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$	−39.7128			−2.08152
$365$	−0.124356	−	0.607695i	−0.00650907	−	0.0318082i
$366$	4.60770	+	4.60770i	0.240848	+	0.240848i
$367$	−9.56218	+	2.56218i	−0.499142	+	0.133745i	−0.499602	−	0.866255i	$-0.666520\pi$
$367$	−9.56218	+	2.56218i	−0.499142	+	0.133745i	0.000459976		1.00000i	$0.499854\pi$
$368$	3.46410	−	12.9282i	0.180579	−	0.673929i
$369$			1.39230i			0.0724805i
$370$	15.9282	−	24.1244i	0.828068	−	1.25417i
$371$	−10.9019	+	18.8827i	−0.566000	+	0.980340i
$372$	3.80385	−	6.58846i	0.197220	−	0.341596i
$373$	5.36603	−	20.0263i	0.277842	−	1.03692i	−0.676070	−	0.736837i	$-0.736318\pi$
$373$	5.36603	−	20.0263i	0.277842	−	1.03692i	0.953913	−	0.300084i	$-0.0970148\pi$
$374$	6.00000	−	10.3923i	0.310253	−	0.537373i
$375$	−18.2321	+	6.52628i	−0.941499	+	0.337016i
$376$	−14.1962	−	8.19615i	−0.732111	−	0.422684i
$377$	34.0526	−	34.0526i	1.75380	−	1.75380i
$378$	−10.9019	+	18.8827i	−0.560734	+	0.971221i
$379$	−8.87564			−0.455911			−0.227956	−	0.973672i	$-0.573204\pi$
$379$	−8.87564			−0.455911			−0.227956	+	0.973672i	$0.573204\pi$
$380$	4.73205	+	3.12436i	0.242749	+	0.160276i
$381$	26.2583	+	7.03590i	1.34526	+	0.360460i
$382$	4.60770	+	17.1962i	0.235750	+	0.879832i
$383$	5.24167	−	19.5622i	0.267837	−	0.999581i	−0.692654	−	0.721270i	$-0.743559\pi$
$383$	5.24167	−	19.5622i	0.267837	−	0.999581i	0.960491	−	0.278311i	$-0.0897745\pi$
$384$	−5.07180	+	18.9282i	−0.258819	+	0.965926i
$385$	8.80385	+	9.92820i	0.448686	+	0.505988i
$386$	−10.0000	−	17.3205i	−0.508987	−	0.881591i
$387$	−0.509619	+	1.90192i	−0.0259054	+	0.0966802i
$388$	−3.66025	−	13.6603i	−0.185821	−	0.693494i
$389$	2.93782	+	1.69615i	0.148953	+	0.0859983i	0.572624	−	0.819818i	$-0.305925\pi$
$389$	2.93782	+	1.69615i	0.148953	+	0.0859983i	−0.423671	+	0.905816i	$0.639259\pi$
$390$	−16.3923	−	32.7846i	−0.830057	−	1.66011i
$391$	7.09808	+	12.2942i	0.358965	+	0.621746i
$392$	1.32051	−	4.92820i	0.0666957	−	0.248912i
$393$	−27.2942	−	15.7583i	−1.37681	−	0.794903i
$394$			24.0000i			1.20910i
$395$	16.3923	−	8.19615i	0.824786	−	0.412393i
$396$	−10.3923	+	6.00000i	−0.522233	+	0.301511i
$397$	−11.1962	+	11.1962i	−0.561919	+	0.561919i	−0.929852	−	0.367933i	$-0.880065\pi$
$397$	−11.1962	+	11.1962i	−0.561919	+	0.561919i	0.367933	+	0.929852i	$0.380065\pi$
$398$	−6.19615	+	6.19615i	−0.310585	+	0.310585i
$399$	4.60770	−	4.60770i	0.230673	−	0.230673i
$400$	7.85641	+	18.3923i	0.392820	+	0.919615i
$401$	−10.6077	+	6.12436i	−0.529723	+	0.305836i	−0.740904	−	0.671611i	$-0.765603\pi$
$401$	−10.6077	+	6.12436i	−0.529723	+	0.305836i	0.211181	+	0.977447i	$0.432269\pi$
$402$	−10.9019	−	6.29423i	−0.543739	−	0.313928i
$403$	14.1962	−	3.80385i	0.707161	−	0.189483i
$404$	3.46410	+	2.00000i	0.172345	+	0.0995037i
$405$	−20.0885	−	1.20577i	−0.998203	−	0.0599153i
$406$	15.0981	+	26.1506i	0.749305	+	1.29783i
$407$	−4.73205	−	17.6603i	−0.234559	−	0.875386i
$408$	−10.3923	−	18.0000i	−0.514496	−	0.891133i
$409$	−5.19615	+	3.00000i	−0.256933	+	0.148340i	−0.622935	−	0.782274i	$-0.714060\pi$
$409$	−5.19615	+	3.00000i	−0.256933	+	0.148340i	0.366002	+	0.930614i	$0.380726\pi$
$410$	1.09808	−	0.973721i	0.0542301	−	0.0480886i
$411$	−4.39230	−	4.39230i	−0.216656	−	0.216656i
$412$	−6.87564	+	25.6603i	−0.338739	+	1.26419i
$413$	25.5885	−	25.5885i	1.25913	−	1.25913i
$414$		−	14.1962i		−	0.697703i
$415$	21.8827	+	7.29423i	1.07418	+	0.358060i
$416$	−32.7846	+	18.9282i	−1.60740	+	0.928032i
$417$	−10.3923	−	6.00000i	−0.508913	−	0.293821i
$418$	3.46410	−	0.928203i	0.169435	−	0.0453999i
$419$	−7.26795	+	4.19615i	−0.355063	+	0.204995i	−0.666913	−	0.745136i	$-0.732385\pi$
$419$	−7.26795	+	4.19615i	−0.355063	+	0.204995i	0.311850	+	0.950131i	$0.399051\pi$
$420$	22.5167	−	4.60770i	1.09870	−	0.224833i
$421$	−25.3923	−	14.6603i	−1.23755	−	0.714497i	−0.268953	−	0.963153i	$-0.586678\pi$
$421$	−25.3923	−	14.6603i	−1.23755	−	0.714497i	−0.968592	+	0.248656i	$0.920011\pi$
$422$		0			0
$423$	−16.7942	−	4.50000i	−0.816563	−	0.218797i
$424$			20.7846i			1.00939i
$425$	−19.6865	−	7.90192i	−0.954937	−	0.383300i
$426$	7.60770	−	28.3923i	0.368594	−	1.37561i
$427$	−7.62436	−	2.04294i	−0.368968	−	0.0988648i
$428$	−1.80385	+	1.80385i	−0.0871923	+	0.0871923i
$429$	−22.3923	−	6.00000i	−1.08111	−	0.289683i
$430$	1.85641	−	0.928203i	0.0895239	−	0.0447619i
$431$			16.0526i			0.773225i	0.922242	+	0.386612i	$0.126355\pi$
$431$			16.0526i			0.773225i	−0.922242	+	0.386612i	$0.873645\pi$
$432$			20.7846i			1.00000i
$433$	5.39230	−	5.39230i	0.259138	−	0.259138i	−0.565566	−	0.824703i	$-0.691342\pi$
$433$	5.39230	−	5.39230i	0.259138	−	0.259138i	0.824703	+	0.565566i	$0.191342\pi$
$434$			9.21539i			0.442353i
$435$	−15.3564	+	23.2583i	−0.736283	+	1.11515i
$436$			17.3205i			0.829502i
$437$	−1.09808	+	4.09808i	−0.0525281	+	0.196038i
$438$	−0.588457	+	0.339746i	−0.0281176	+	0.0162337i
$439$	19.7321	+	11.3923i	0.941759	+	0.543725i	0.890511	−	0.454961i	$-0.150347\pi$
$439$	19.7321	+	11.3923i	0.941759	+	0.543725i	0.0512480	+	0.998686i	$0.483680\pi$
$440$	12.0000	+	4.00000i	0.572078	+	0.190693i
$441$		−	5.41154i		−	0.257693i
$442$	10.3923	−	38.7846i	0.494312	−	1.84480i
$443$	4.28461	+	15.9904i	0.203568	+	0.759726i	0.989881	+	0.141898i	$0.0453205\pi$
$443$	4.28461	+	15.9904i	0.203568	+	0.759726i	−0.786313	+	0.617828i	$0.788013\pi$
$444$	−30.5885	−	8.19615i	−1.45166	−	0.388972i
$445$	−18.0622	+	27.3564i	−0.856229	+	1.29682i
$446$	6.90192	−	11.9545i	0.326816	−	0.566061i
$447$	−6.06218	+	10.5000i	−0.286731	+	0.496633i
$448$	−6.14359	−	22.9282i	−0.290258	−	1.08326i
$449$	8.78461			0.414571			0.207286	−	0.978280i	$-0.433537\pi$
$449$	8.78461			0.414571			0.207286	+	0.978280i	$0.433537\pi$
$450$	13.0981	+	16.6865i	0.617449	+	0.786611i
$451$		−	0.928203i		−	0.0437074i
$452$	−12.9282	−	3.46410i	−0.608092	−	0.162938i
$453$		−	27.7128i		−	1.30206i
$454$	−23.1962	−	13.3923i	−1.08865	−	0.628532i
$455$	37.0526	+	24.4641i	1.73705	+	1.14689i
$456$	1.60770	−	6.00000i	0.0752872	−	0.280976i
$457$	−4.36603	+	1.16987i	−0.204234	+	0.0547243i	−0.359486	−	0.933151i	$-0.617048\pi$
$457$	−4.36603	+	1.16987i	−0.204234	+	0.0547243i	0.155252	+	0.987875i	$0.450381\pi$
$458$	−6.75833	+	25.2224i	−0.315796	+	1.17857i
$459$	−15.5885	−	15.5885i	−0.727607	−	0.727607i
$460$	−11.1962	+	9.92820i	−0.522023	+	0.462905i
$461$	8.79423	−	15.2321i	0.409588	−	0.709427i	−0.585255	−	0.810849i	$-0.699006\pi$
$461$	8.79423	−	15.2321i	0.409588	−	0.709427i	0.994844	+	0.101422i	$0.0323391\pi$
$462$	7.26795	−	12.5885i	0.338136	−	0.585668i
$463$	20.7583	+	5.56218i	0.964721	+	0.258496i	0.706598	−	0.707616i	$-0.250229\pi$
$463$	20.7583	+	5.56218i	0.964721	+	0.258496i	0.258124	+	0.966112i	$0.416896\pi$
$464$	24.9282	+	14.3923i	1.15726	+	0.668146i
$465$	−7.60770	+	3.80385i	−0.352798	+	0.176399i
$466$			12.2487i			0.567411i
$467$	29.3923	+	29.3923i	1.36011	+	1.36011i	0.873765	+	0.486349i	$0.161672\pi$
$467$	29.3923	+	29.3923i	1.36011	+	1.36011i	0.486349	+	0.873765i	$0.338328\pi$
$468$	−28.3923	+	28.3923i	−1.31243	+	1.31243i
$469$	15.2487			0.704120
$470$	8.19615	+	16.3923i	0.378060	+	0.756121i
$471$	21.2942	−	5.70577i	0.981186	−	0.262908i
$472$	8.92820	−	33.3205i	0.410954	−	1.53370i
$473$	0.339746	−	1.26795i	0.0156215	−	0.0583004i
$474$	−14.1962	−	14.1962i	−0.652051	−	0.652051i
$475$	−2.49038	−	5.83013i	−0.114267	−	0.267505i
$476$	21.8038	+	12.5885i	0.999378	+	0.576991i
$477$	5.70577	+	21.2942i	0.261249	+	0.974996i
$478$	−1.85641	+	6.92820i	−0.0849101	+	0.316889i
$479$	−1.56218	+	2.70577i	−0.0713777	+	0.123630i	−0.899505	−	0.436910i	$-0.856073\pi$
$479$	−1.56218	+	2.70577i	−0.0713777	+	0.123630i	0.828128	+	0.560540i	$0.189406\pi$
$480$	16.3923	−	14.5359i	0.748203	−	0.663470i
$481$	−30.5885	−	52.9808i	−1.39471	−	2.41571i
$482$	−39.8827	+	10.6865i	−1.81661	+	0.486758i
$483$	8.59808	+	14.8923i	0.391226	+	0.677623i
$484$	−12.1244	+	7.00000i	−0.551107	+	0.318182i
$485$	−5.00000	+	15.0000i	−0.227038	+	0.681115i
$486$	5.70577	+	21.2942i	0.258819	+	0.965926i
$487$	−17.3923	−	17.3923i	−0.788121	−	0.788121i	0.193065	−	0.981186i	$-0.438157\pi$
$487$	−17.3923	−	17.3923i	−0.788121	−	0.788121i	−0.981186	+	0.193065i	$0.938157\pi$
$488$	−7.26795	+	1.94744i	−0.329005	+	0.0881565i
$489$	1.09808	+	0.294229i	0.0496567	+	0.0133055i
$490$	−4.26795	+	3.78461i	−0.192806	+	0.170971i
$491$	8.39230	+	14.5359i	0.378739	+	0.655996i	0.990879	−	0.134754i	$-0.0430243\pi$
$491$	8.39230	+	14.5359i	0.378739	+	0.655996i	−0.612140	+	0.790750i	$0.709691\pi$
$492$	−1.39230	−	0.803848i	−0.0627700	−	0.0362402i
$493$	−29.4904	+	7.90192i	−1.32818	+	0.355885i
$494$	10.3923	−	6.00000i	0.467572	−	0.269953i
$495$	13.3923	+	0.803848i	0.601939	+	0.0361303i
$496$	4.39230	+	7.60770i	0.197220	+	0.341596i
$497$	9.21539	+	34.3923i	0.413367	+	1.54271i
$498$		−	25.2679i		−	1.13228i
$499$	−7.39230	−	12.8038i	−0.330925	−	0.573179i	0.651768	−	0.758418i	$-0.274027\pi$
$499$	−7.39230	−	12.8038i	−0.330925	−	0.573179i	−0.982693	+	0.185239i	$0.940694\pi$
$500$	4.00000	−	22.0000i	0.178885	−	0.983870i
$501$	−18.6962	+	5.00962i	−0.835282	+	0.223813i
$502$	4.58846	+	4.58846i	0.204793	+	0.204793i
$503$	−23.0263	−	23.0263i	−1.02669	−	1.02669i	−0.999634	−	0.0270572i	$-0.991386\pi$
$503$	−23.0263	−	23.0263i	−1.02669	−	1.02669i	−0.0270572	−	0.999634i	$-0.508614\pi$
$504$	−12.5885	−	21.8038i	−0.560734	−	0.971221i
$505$	−2.00000	−	4.00000i	−0.0889988	−	0.177998i
$506$			9.46410i			0.420731i
$507$	−55.0526			−2.44497
$508$	−22.1962	+	22.1962i	−0.984795	+	0.984795i
$509$	20.4282	−	11.7942i	0.905464	−	0.522770i	0.0264952	−	0.999649i	$-0.491565\pi$
$509$	20.4282	−	11.7942i	0.905464	−	0.522770i	0.878969	+	0.476879i	$0.158232\pi$
$510$	−1.39230	+	23.1962i	−0.0616523	+	1.02714i
$511$	0.411543	−	0.712813i	0.0182056	−	0.0315330i
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		−	6.58846i		−	0.290887i
$514$	−18.4641	−	31.9808i	−0.814417	−	1.41061i
$515$	22.2224	−	19.7058i	0.979237	−	0.868340i
$516$	−1.60770	−	1.60770i	−0.0707748	−	0.0707748i
$517$	11.1962	+	3.00000i	0.492406	+	0.131940i
$518$	37.0526	−	9.92820i	1.62800	−	0.436220i
$519$	3.46410	+	3.46410i	0.152057	+	0.152057i
$520$	42.2487	+	2.53590i	1.85273	+	0.111207i
$521$		−	2.66025i		−	0.116548i	−0.998301	−	0.0582739i	$-0.981440\pi$
$521$		−	2.66025i		−	0.116548i	0.998301	−	0.0582739i	$-0.0185597\pi$
$522$	29.4904	+	7.90192i	1.29076	+	0.345858i
$523$	10.5622	+	10.5622i	0.461852	+	0.461852i	0.899262	−	0.437410i	$-0.144104\pi$
$523$	10.5622	+	10.5622i	0.461852	+	0.461852i	−0.437410	+	0.899262i	$0.644104\pi$
$524$	31.5167	−	18.1962i	1.37681	−	0.794903i
$525$	−23.8468	−	9.57180i	−1.04076	−	0.417747i
$526$	−6.80385	−	3.92820i	−0.296662	−	0.171278i
$527$	−9.00000	−	2.41154i	−0.392046	−	0.105048i
$528$		−	13.8564i		−	0.603023i
$529$	10.2224	+	5.90192i	0.444454	+	0.256605i
$530$	12.8038	−	19.3923i	0.556164	−	0.842348i
$531$		−	36.5885i		−	1.58780i
$532$	1.94744	+	7.26795i	0.0844323	+	0.315106i
$533$	−0.803848	−	3.00000i	−0.0348185	−	0.129944i
$534$	34.6865	+	9.29423i	1.50103	+	0.402201i
$535$	2.79423	−	0.571797i	0.120805	−	0.0247209i
$536$	12.5885	−	7.26795i	0.543739	−	0.313928i
$537$	12.4641	+	21.5885i	0.537866	+	0.931611i
$538$	1.00000	−	1.00000i	0.0431131	−	0.0431131i
$539$			3.60770i			0.155394i
$540$	12.8038	−	19.3923i	0.550990	−	0.834512i
$541$			5.53590i			0.238007i	0.992894	+	0.119003i	$0.0379700\pi$
$541$			5.53590i			0.238007i	−0.992894	+	0.119003i	$0.962030\pi$
$542$	26.5885	+	26.5885i	1.14207	+	1.14207i
$543$	−2.59808	−	4.50000i	−0.111494	−	0.193113i
$544$	24.0000			1.02899
$545$	10.6699	−	16.1603i	0.457047	−	0.692229i
$546$	12.5885	−	46.9808i	0.538736	−	2.01059i
$547$	−11.5526	−	43.1147i	−0.493952	−	1.84345i	−0.535823	−	0.844330i	$-0.679999\pi$
$547$	−11.5526	−	43.1147i	−0.493952	−	1.84345i	0.0418717	−	0.999123i	$-0.486668\pi$
$548$	6.92820	−	1.85641i	0.295958	−	0.0793018i
$549$	−6.91154	+	3.99038i	−0.294977	+	0.170305i
$550$	−8.73205	−	11.1244i	−0.372336	−	0.474344i
$551$	−7.90192	−	4.56218i	−0.336633	−	0.194355i
$552$	14.1962	+	8.19615i	0.604228	+	0.348851i
$553$	23.4904	+	6.29423i	0.998913	+	0.267658i
$554$	−0.464102	+	0.803848i	−0.0197178	+	0.0341522i
$555$	23.4904	+	26.4904i	0.997111	+	1.12445i
$556$	12.0000	−	6.92820i	0.508913	−	0.293821i
$557$	−11.1962	−	11.1962i	−0.474396	−	0.474396i	0.428938	−	0.903334i	$-0.358888\pi$
$557$	−11.1962	−	11.1962i	−0.474396	−	0.474396i	−0.903334	+	0.428938i	$0.858888\pi$
$558$	6.58846	+	6.58846i	0.278912	+	0.278912i
$559$		−	4.39230i		−	0.185775i
$560$	−8.39230	+	25.1769i	−0.354640	+	1.06392i
$561$	10.3923	+	10.3923i	0.438763	+	0.438763i
$562$	−5.83013	−	21.7583i	−0.245929	−	0.917820i
$563$	3.40192	+	0.911543i	0.143374	+	0.0384169i	0.329792	−	0.944054i	$-0.393021\pi$
$563$	3.40192	+	0.911543i	0.143374	+	0.0384169i	−0.186418	+	0.982470i	$0.559688\pi$
$564$	14.1962	−	14.1962i	0.597766	−	0.597766i
$565$	9.92820	+	11.1962i	0.417683	+	0.471026i
$566$	−21.2942	+	12.2942i	−0.895063	+	0.516765i
$567$	−18.8827	−	18.8827i	−0.792998	−	0.792998i
$568$	24.0000	+	24.0000i	1.00702	+	1.00702i
$569$	−4.73205	+	8.19615i	−0.198378	+	0.343601i	−0.948003	−	0.318263i	$-0.896901\pi$
$569$	−4.73205	+	8.19615i	−0.198378	+	0.343601i	0.749625	+	0.661863i	$0.230234\pi$
$570$	−5.19615	+	4.60770i	−0.217643	+	0.192995i
$571$	−3.00000	+	1.73205i	−0.125546	+	0.0724841i	−0.561458	−	0.827505i	$-0.689759\pi$
$571$	−3.00000	+	1.73205i	−0.125546	+	0.0724841i	0.435912	+	0.899989i	$0.356426\pi$
$572$	18.9282	−	18.9282i	0.791428	−	0.791428i
$573$	−21.8038			−0.910869
$574$	1.94744			0.0812846
$575$	16.5622	−	2.36603i	0.690691	−	0.0986701i
$576$	−20.7846	−	12.0000i	−0.866025	−	0.500000i
$577$	−15.3923	−	15.3923i	−0.640790	−	0.640790i	0.309960	−	0.950750i	$-0.399684\pi$
$577$	−15.3923	−	15.3923i	−0.640790	−	0.640790i	−0.950750	+	0.309960i	$0.899684\pi$
$578$	−1.00000	+	1.00000i	−0.0415945	+	0.0415945i
$579$	23.6603	−	6.33975i	0.983287	−	0.263471i
$580$	−14.3923	−	28.7846i	−0.597608	−	1.19522i
$581$	15.3038	+	26.5070i	0.634911	+	1.09970i
$582$	17.3205			0.717958
$583$	−3.80385	−	14.1962i	−0.157539	−	0.587945i
$584$		−	0.784610i		−	0.0324674i
$585$	43.9808	−	9.00000i	1.81838	−	0.372104i
$586$	11.1962	+	19.3923i	0.462509	+	0.801089i
$587$	−39.7487	+	10.6506i	−1.64060	+	0.439599i	−0.956961	−	0.290217i	$-0.906273\pi$
$587$	−39.7487	+	10.6506i	−1.64060	+	0.439599i	−0.683644	+	0.729816i	$0.739606\pi$
$588$	5.41154	+	3.12436i	0.223168	+	0.128846i
$589$	−1.39230	−	2.41154i	−0.0573689	−	0.0993659i
$590$	−28.8564	+	25.5885i	−1.18800	+	1.05346i
$591$	−28.3923	−	7.60770i	−1.16790	−	0.312939i
$592$	25.8564	−	25.8564i	1.06269	−	1.06269i
$593$	2.66025	+	2.66025i	0.109244	+	0.109244i	0.759616	−	0.650372i	$-0.225387\pi$
$593$	2.66025	+	2.66025i	0.109244	+	0.109244i	−0.650372	+	0.759616i	$0.725387\pi$
$594$	−3.80385	−	14.1962i	−0.156074	−	0.582475i
$595$	−12.5885	−	25.1769i	−0.516076	−	1.03215i
$596$	−7.00000	−	12.1244i	−0.286731	−	0.496633i
$597$	−5.36603	−	9.29423i	−0.219617	−	0.380387i
$598$	8.19615	+	30.5885i	0.335166	+	1.25086i
$599$	−0.294229	−	0.509619i	−0.0120219	−	0.0208225i	0.859952	−	0.510375i	$-0.170493\pi$
$599$	−0.294229	−	0.509619i	−0.0120219	−	0.0208225i	−0.871974	+	0.489553i	$0.837160\pi$
$600$	−24.2487	+	3.46410i	−0.989949	+	0.141421i
$601$	−10.8038	+	18.7128i	−0.440698	+	0.763312i	−0.997741	−	0.0671719i	$-0.978602\pi$
$601$	−10.8038	+	18.7128i	−0.440698	+	0.763312i	0.557043	+	0.830483i	$0.311936\pi$
$602$	2.66025	+	0.712813i	0.108424	+	0.0290521i
$603$	10.9019	−	10.9019i	0.443961	−	0.443961i
$604$	27.7128	+	16.0000i	1.12762	+	0.651031i
$605$	15.6244	+	0.937822i	0.635220	+	0.0381279i
$606$	−3.46410	+	3.46410i	−0.140720	+	0.140720i
$607$	−5.74167	+	21.4282i	−0.233047	+	0.869744i	0.745972	+	0.665977i	$0.231985\pi$
$607$	−5.74167	+	21.4282i	−0.233047	+	0.869744i	−0.979019	+	0.203767i	$0.934682\pi$
$608$	5.07180	+	5.07180i	0.205689	+	0.205689i
$609$	−35.7224	+	9.57180i	−1.44755	+	0.387869i
$610$	7.98076	+	2.66025i	0.323132	+	0.107711i
$611$	38.7846			1.56906
$612$	24.5885	−	6.58846i	0.993929	−	0.266323i
$613$	−17.7846	−	17.7846i	−0.718314	−	0.718314i	0.249946	−	0.968260i	$-0.419587\pi$
$613$	−17.7846	−	17.7846i	−0.718314	−	0.718314i	−0.968260	+	0.249946i	$0.919587\pi$
$614$	−25.2679			−1.01973
$615$	0.803848	+	1.60770i	0.0324143	+	0.0648285i
$616$	8.39230	+	14.5359i	0.338136	+	0.585668i
$617$	−37.5167	−	10.0526i	−1.51036	−	0.404701i	−0.593808	−	0.804607i	$-0.702376\pi$
$617$	−37.5167	−	10.0526i	−1.51036	−	0.404701i	−0.916556	+	0.399906i	$0.869043\pi$
$618$	−28.1769	−	16.2679i	−1.13344	−	0.654393i
$619$	−7.09808	+	12.2942i	−0.285296	+	0.494147i	−0.972681	−	0.232146i	$-0.925425\pi$
$619$	−7.09808	+	12.2942i	−0.285296	+	0.494147i	0.687385	+	0.726293i	$0.258758\pi$
$620$	0.588457	−	9.80385i	0.0236330	−	0.393732i
$621$	16.7942	+	4.50000i	0.673929	+	0.180579i
$622$	5.19615	+	1.39230i	0.208347	+	0.0558263i
$623$	−42.0167	+	11.2583i	−1.68336	+	0.451055i
$624$	−12.0000	−	44.7846i	−0.480384	−	1.79282i
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	20.5885	−	35.6603i	0.822880	−	1.42527i
$627$			4.39230i			0.175412i
$628$	−6.58846	+	24.5885i	−0.262908	+	0.981186i
$629$			38.7846i			1.54644i
$630$	−1.68653	+	28.0981i	−0.0671931	+	1.11945i
$631$	−18.0000			−0.716569			−0.358284	−	0.933613i	$-0.616638\pi$
$631$	−18.0000			−0.716569			−0.358284	+	0.933613i	$0.616638\pi$
$632$	22.3923	−	6.00000i	0.890718	−	0.238667i
$633$		0			0
$634$	−17.3205	−	10.0000i	−0.687885	−	0.397151i
$635$	34.3827	−	7.03590i	1.36444	−	0.279211i
$636$	−24.5885	−	6.58846i	−0.974996	−	0.261249i
$637$	3.12436	+	11.6603i	0.123791	+	0.461996i
$638$	−19.6603	−	5.26795i	−0.778357	−	0.208560i
$639$	31.1769	+	18.0000i	1.23334	+	0.712069i
$640$	5.07180	+	24.7846i	0.200480	+	0.979698i
$641$	0.186533	+	0.107695i	0.00736763	+	0.00425370i	0.503679	−	0.863891i	$-0.331979\pi$
$641$	0.186533	+	0.107695i	0.00736763	+	0.00425370i	−0.496312	+	0.868144i	$0.665313\pi$
$642$	−1.56218	−	2.70577i	−0.0616542	−	0.106788i
$643$	−10.2058	+	38.0885i	−0.402476	+	1.50206i	0.406187	+	0.913790i	$0.366858\pi$
$643$	−10.2058	+	38.0885i	−0.402476	+	1.50206i	−0.808663	+	0.588272i	$0.799808\pi$
$644$	−19.8564			−0.782452
$645$	0.509619	+	2.49038i	0.0200662	+	0.0980587i
$646$	−7.60770			−0.299321
$647$	−16.6865	+	16.6865i	−0.656015	+	0.656015i	−0.954435	−	0.298419i	$-0.903541\pi$
$647$	−16.6865	+	16.6865i	−0.656015	+	0.656015i	0.298419	+	0.954435i	$0.403541\pi$
$648$	−24.5885	−	6.58846i	−0.965926	−	0.258819i
$649$			24.3923i			0.957482i
$650$	−37.8564	−	28.3923i	−1.48485	−	1.11364i
$651$	−10.9019	−	2.92116i	−0.427280	−	0.114489i
$652$	−0.928203	+	0.928203i	−0.0363512	+	0.0363512i
$653$	0.830127	+	0.222432i	0.0324854	+	0.00870443i	0.275025	−	0.961437i	$-0.411314\pi$
$653$	0.830127	+	0.222432i	0.0324854	+	0.00870443i	−0.242540	+	0.970141i	$0.577980\pi$
$654$	−20.4904	−	5.49038i	−0.801237	−	0.214691i
$655$	−40.6147	−	2.43782i	−1.58695	−	0.0952536i
$656$	1.60770	−	0.928203i	0.0627700	−	0.0362402i
$657$	−0.215390	−	0.803848i	−0.00840318	−	0.0313611i
$658$	−6.29423	+	23.4904i	−0.245375	+	0.915750i
$659$	7.26795	+	4.19615i	0.283119	+	0.163459i	0.634835	−	0.772648i	$-0.281068\pi$
$659$	7.26795	+	4.19615i	0.283119	+	0.163459i	−0.351716	+	0.936107i	$0.614402\pi$
$660$	−8.53590	+	12.9282i	−0.332259	+	0.503230i
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	−0.378754	−	0.925497i	$-0.623647\pi$
$661$	6.00000	−	3.46410i	0.233373	−	0.134738i	0.612127	+	0.790759i	$0.290314\pi$
$662$	11.1962	+	41.7846i	0.435151	+	1.62400i
$663$	42.5885	+	24.5885i	1.65400	+	0.954937i
$664$	25.2679	+	14.5885i	0.980587	+	0.566142i
$665$	2.66025	−	7.98076i	0.103160	−	0.309481i
$666$	19.3923	−	33.5885i	0.751437	−	1.30153i
$667$	17.0263	−	17.0263i	0.659260	−	0.659260i
$668$	5.78461	−	21.5885i	0.223813	−	0.835282i
$669$	11.9545	+	11.9545i	0.462187	+	0.462187i
$670$	−16.2224	−	0.973721i	−0.626727	−	0.0376181i
$671$	4.60770	−	2.66025i	0.177878	−	0.102698i
$672$	29.0718			1.12147
$673$	−12.6603	−	47.2487i	−0.488017	−	1.82130i	−0.566073	−	0.824355i	$-0.691538\pi$
$673$	−12.6603	−	47.2487i	−0.488017	−	1.82130i	0.0780562	−	0.996949i	$-0.475129\pi$
$674$	17.6603	−	10.1962i	0.680248	−	0.392741i
$675$	−23.8923	+	10.2058i	−0.919615	+	0.392820i
$676$	31.7846	−	55.0526i	1.22248	−	2.11741i
$677$	−17.4641	+	4.67949i	−0.671200	+	0.179847i	−0.578295	−	0.815828i	$-0.696282\pi$
$677$	−17.4641	+	4.67949i	−0.671200	+	0.179847i	−0.0929047	+	0.995675i	$0.529615\pi$
$678$	8.19615	−	14.1962i	0.314771	−	0.545200i
$679$	−18.1699	+	10.4904i	−0.697296	+	0.402584i
$680$	−22.3923	−	14.7846i	−0.858706	−	0.566964i
$681$	23.1962	−	23.1962i	0.888878	−	0.888878i
$682$	−4.39230	−	4.39230i	−0.168190	−	0.168190i
$683$	7.00000	−	7.00000i	0.267848	−	0.267848i	−0.560385	−	0.828232i	$-0.689347\pi$
$683$	7.00000	−	7.00000i	0.267848	−	0.267848i	0.828232	+	0.560385i	$0.189347\pi$
$684$	6.58846	+	3.80385i	0.251916	+	0.145444i
$685$	−7.60770	−	2.53590i	−0.290675	−	0.0968917i
$686$	21.8038			0.832475
$687$	−27.6962	−	15.9904i	−1.05667	−	0.610071i
$688$	2.53590	−	0.679492i	0.0966802	−	0.0259054i
$689$	−24.5885	−	42.5885i	−0.936746	−	1.62249i
$690$	−8.19615	−	16.3923i	−0.312022	−	0.624044i
$691$	37.4711	+	21.6340i	1.42547	+	0.822995i	0.996759	−	0.0804467i	$-0.0256347\pi$
$691$	37.4711	+	21.6340i	1.42547	+	0.822995i	0.428711	+	0.903442i	$0.358968\pi$
$692$	−5.46410	+	1.46410i	−0.207714	+	0.0556568i
$693$	12.5885	+	12.5885i	0.478196	+	0.478196i
$694$	−9.00000	+	5.19615i	−0.341635	+	0.197243i
$695$	−15.4641	−	0.928203i	−0.586587	−	0.0352088i
$696$	−24.9282	+	24.9282i	−0.944901	+	0.944901i
$697$	−0.509619	+	1.90192i	−0.0193032	+	0.0720405i
$698$	−40.3468	+	10.8109i	−1.52715	+	0.409198i
$699$	−14.4904	−	3.88269i	−0.548077	−	0.146857i
$700$	23.3397	−	18.3205i	0.882159	−	0.692450i
$701$	12.1769			0.459916			0.229958	−	0.973201i	$-0.426141\pi$
$701$	12.1769			0.459916			0.229958	+	0.973201i	$0.426141\pi$
$702$	−24.5885	−	42.5885i	−0.928032	−	1.60740i
$703$	−8.19615	+	8.19615i	−0.309124	+	0.309124i
$704$	13.8564	+	8.00000i	0.522233	+	0.301511i
$705$	−21.9904	+	4.50000i	−0.828206	+	0.169480i
$706$	4.39230	+	2.53590i	0.165307	+	0.0954398i
$707$	1.53590	−	5.73205i	0.0577634	−	0.215576i
$708$	36.5885	+	21.1244i	1.37508	+	0.793902i
$709$	−23.4282	+	40.5788i	−0.879865	+	1.52397i	−0.0283759	+	0.999597i	$0.509034\pi$
$709$	−23.4282	+	40.5788i	−0.879865	+	1.52397i	−0.851489	+	0.524373i	$0.824300\pi$
$710$	−7.60770	−	37.1769i	−0.285512	−	1.39522i
$711$	21.2942	−	12.2942i	0.798596	−	0.461070i
$712$	−29.3205	+	29.3205i	−1.09883	+	1.09883i
$713$	7.09808	−	1.90192i	0.265825	−	0.0712276i
$714$	−21.8038	+	21.8038i	−0.815988	+	0.815988i
$715$	−29.3205	+	6.00000i	−1.09652	+	0.224387i
$716$	−28.7846			−1.07573
$717$	−7.60770	−	4.39230i	−0.284115	−	0.164034i
$718$	−8.19615	−	8.19615i	−0.305878	−	0.305878i
$719$	43.5167			1.62290			0.811449	−	0.584424i	$-0.198679\pi$
$719$	43.5167			1.62290			0.811449	+	0.584424i	$0.198679\pi$
$720$	12.0000	+	24.0000i	0.447214	+	0.894427i
$721$	39.4115			1.46776
$722$	17.3923	+	17.3923i	0.647275	+	0.647275i
$723$		−	50.5692i		−	1.88069i
$724$	6.00000			0.222988
$725$	−4.30385	+	35.7224i	−0.159841	+	1.32670i
$726$	−4.43782	−	16.5622i	−0.164703	−	0.614680i
$727$	−4.23205	+	1.13397i	−0.156958	+	0.0420568i	−0.336442	−	0.941704i	$-0.609224\pi$
$727$	−4.23205	+	1.13397i	−0.156958	+	0.0420568i	0.179484	+	0.983761i	$0.442557\pi$
$728$	39.7128	+	39.7128i	1.47185	+	1.47185i
$729$	−27.0000			−1.00000
$730$	−0.483340	+	0.732051i	−0.0178892	+	0.0270944i
$731$	−1.39230	+	2.41154i	−0.0514963	+	0.0891941i
$732$		−	9.21539i		−	0.340611i
$733$	1.56218	−	5.83013i	0.0577004	−	0.215341i	−0.931056	−	0.364876i	$-0.881111\pi$
$733$	1.56218	−	5.83013i	0.0577004	−	0.215341i	0.988756	+	0.149536i	$0.0477779\pi$
$734$	12.1244	+	7.00000i	0.447518	+	0.258375i
$735$	−3.12436	−	6.24871i	−0.115244	−	0.230487i
$736$	−16.3923	+	9.46410i	−0.604228	+	0.348851i
$737$	−7.26795	+	7.26795i	−0.267718	+	0.267718i
$738$	1.39230	−	1.39230i	0.0512514	−	0.0512514i
$739$	19.2679			0.708783			0.354391	−	0.935097i	$-0.384688\pi$
$739$	19.2679			0.708783			0.354391	+	0.935097i	$0.384688\pi$
$740$	−40.0526	+	8.19615i	−1.47236	+	0.301297i
$741$	3.80385	+	14.1962i	0.139738	+	0.521509i
$742$	29.7846	−	7.98076i	1.09343	−	0.292983i
$743$	7.45448	−	27.8205i	0.273478	−	1.02064i	−0.683376	−	0.730067i	$-0.739489\pi$
$743$	7.45448	−	27.8205i	0.273478	−	1.02064i	0.956854	−	0.290569i	$-0.0938444\pi$
$744$	−10.3923	+	2.78461i	−0.381000	+	0.102089i
$745$	−0.937822	+	15.6244i	−0.0343591	+	0.572432i
$746$	−25.3923	+	14.6603i	−0.929678	+	0.536750i
$747$	29.8923	+	8.00962i	1.09370	+	0.293057i
$748$	−16.3923	+	4.39230i	−0.599362	+	0.160599i
$749$	3.27757	+	1.89230i	0.119760	+	0.0691433i
$750$	24.7583	+	11.7058i	0.904046	+	0.427434i
$751$	−17.1962	−	29.7846i	−0.627497	−	1.08686i	−0.988052	−	0.154118i	$-0.950746\pi$
$751$	−17.1962	−	29.7846i	−0.627497	−	1.08686i	0.360556	−	0.932738i	$-0.382587\pi$
$752$	6.00000	+	22.3923i	0.218797	+	0.816563i
$753$	−6.88269	+	3.97372i	−0.250819	+	0.144810i
$754$	−68.1051			−2.48024
$755$	−16.0000	−	32.0000i	−0.582300	−	1.16460i
$756$	29.7846	−	7.98076i	1.08326	−	0.290258i
$757$	−4.05256	+	4.05256i	−0.147293	+	0.147293i	−0.776908	−	0.629615i	$-0.783213\pi$
$757$	−4.05256	+	4.05256i	−0.147293	+	0.147293i	0.629615	+	0.776908i	$0.283213\pi$
$758$	8.87564	+	8.87564i	0.322378	+	0.322378i
$759$	−11.1962	−	3.00000i	−0.406395	−	0.108893i
$760$	−1.60770	−	7.85641i	−0.0583172	−	0.284982i
$761$	−30.4808	+	17.5981i	−1.10493	+	0.637930i	−0.937511	−	0.347957i	$-0.886876\pi$
$761$	−30.4808	+	17.5981i	−1.10493	+	0.637930i	−0.167416	+	0.985886i	$0.553542\pi$
$762$	−19.2224	−	33.2942i	−0.696355	−	1.20612i
$763$	24.8205	−	6.65064i	0.898563	−	0.240769i
$764$	12.5885	−	21.8038i	0.455434	−	0.788836i
$765$	−27.0000	−	9.00000i	−0.976187	−	0.325396i
$766$	−24.8038	+	14.3205i	−0.896199	+	0.517421i
$767$	21.1244	+	78.8372i	0.762756	+	2.84665i
$768$	24.0000	−	13.8564i	0.866025	−	0.500000i
$769$	42.0622	−	24.2846i	1.51680	−	0.875725i	0.516996	−	0.855988i	$-0.327050\pi$
$769$	42.0622	−	24.2846i	1.51680	−	0.875725i	0.999805	−	0.0197374i	$-0.00628303\pi$
$770$	1.12436	−	18.7321i	0.0405190	−	0.675056i
$771$	43.6865	−	11.7058i	1.57333	−	0.421573i
$772$	−7.32051	+	27.3205i	−0.263471	+	0.983287i
$773$	5.80385	−	5.80385i	0.208750	−	0.208750i	−0.594986	−	0.803736i	$-0.702842\pi$
$773$	5.80385	−	5.80385i	0.208750	−	0.208750i	0.803736	+	0.594986i	$0.202842\pi$
$774$	2.41154	−	1.39230i	0.0866811	−	0.0500454i
$775$	−6.58846	+	8.78461i	−0.236664	+	0.315552i
$776$	−10.0000	+	17.3205i	−0.358979	+	0.621770i
$777$			46.9808i			1.68543i
$778$	−1.24167	−	4.63397i	−0.0445160	−	0.166136i
$779$	−0.509619	+	0.294229i	−0.0182590	+	0.0105418i
$780$	−16.3923	+	49.1769i	−0.586939	+	1.76082i
$781$	−20.7846	−	12.0000i	−0.743732	−	0.429394i
$782$	5.19615	−	19.3923i	0.185814	−	0.693467i
$783$	−18.6962	+	32.3827i	−0.668146	+	1.15726i
$784$	−6.24871	+	3.60770i	−0.223168	+	0.128846i
$785$	21.2942	−	18.8827i	0.760024	−	0.673952i
$786$	11.5359	+	43.0526i	0.411472	+	1.53563i
$787$	22.5622	+	6.04552i	0.804255	+	0.215499i	0.637451	−	0.770491i	$-0.279989\pi$
$787$	22.5622	+	6.04552i	0.804255	+	0.215499i	0.166804	+	0.985990i	$0.446655\pi$
$788$	24.0000	−	24.0000i	0.854965	−	0.854965i
$789$	6.80385	−	6.80385i	0.242223	−	0.242223i
$790$	−24.5885	−	8.19615i	−0.874818	−	0.291606i
$791$			19.8564i			0.706013i
$792$	16.3923	+	4.39230i	0.582475	+	0.156074i
$793$	12.5885	−	12.5885i	0.447029	−	0.447029i
$794$	22.3923			0.794673
$795$	18.8827	+	21.2942i	0.669700	+	0.755228i
$796$	12.3923			0.439234
$797$	2.12436	−	7.92820i	0.0752485	−	0.280831i	−0.918041	−	0.396485i	$-0.870230\pi$
$797$	2.12436	−	7.92820i	0.0752485	−	0.280831i	0.993290	+	0.115654i	$0.0368964\pi$
$798$	−9.21539			−0.326221
$799$	−21.2942	−	12.2942i	−0.753336	−	0.434939i
$800$	10.5359	−	26.2487i	0.372500	−	0.928032i
$801$	−21.9904	+	38.0885i	−0.776992	+	1.34579i
$802$	16.7321	+	4.48334i	0.590829	+	0.158312i
$803$	0.143594	+	0.535898i	0.00506731	+	0.0189114i
$804$	4.60770	+	17.1962i	0.162501	+	0.606462i
$805$	18.5263	+	12.2321i	0.652966	+	0.431123i
$806$	−18.0000	−	10.3923i	−0.634023	−	0.366053i
$807$	0.866025	+	1.50000i	0.0304855	+	0.0528025i
$808$	−1.46410	−	5.46410i	−0.0515069	−	0.192226i
$809$	9.71281			0.341484			0.170742	−	0.985316i	$-0.445383\pi$
$809$	9.71281			0.341484			0.170742	+	0.985316i	$0.445383\pi$
$810$	18.8827	+	21.2942i	0.663470	+	0.748203i
$811$			13.2679i			0.465901i	0.972489	+	0.232950i	$0.0748380\pi$
$811$			13.2679i			0.465901i	−0.972489	+	0.232950i	$0.925162\pi$
$812$	11.0526	−	41.2487i	0.387869	−	1.44755i
$813$	−39.8827	+	23.0263i	−1.39875	+	0.807567i
$814$	−12.9282	+	22.3923i	−0.453133	+	0.784850i
$815$	1.43782	−	0.294229i	0.0503647	−	0.0103064i
$816$	−7.60770	+	28.3923i	−0.266323	+	0.993929i
$817$	−0.803848	+	0.215390i	−0.0281231	+	0.00753555i
$818$	8.19615	+	2.19615i	0.286572	+	0.0767867i
$819$	51.5885	+	29.7846i	1.80265	+	1.04076i
$820$	−2.07180	−	0.124356i	−0.0723503	−	0.00434269i
$821$	27.2846	−	47.2583i	0.952239	−	1.64933i	0.211677	−	0.977340i	$-0.432108\pi$
$821$	27.2846	−	47.2583i	0.952239	−	1.64933i	0.740563	−	0.671987i	$-0.234559\pi$
$822$			8.78461i			0.306398i
$823$	−3.96410	−	1.06218i	−0.138180	−	0.0370252i	0.189066	−	0.981964i	$-0.439454\pi$
$823$	−3.96410	−	1.06218i	−0.138180	−	0.0370252i	−0.327246	+	0.944939i	$0.606121\pi$
$824$	32.5359	−	18.7846i	1.13344	−	0.654393i
$825$	15.9282	−	6.80385i	0.554549	−	0.236880i
$826$	−51.1769			−1.78067
$827$	−6.29423	−	6.29423i	−0.218872	−	0.218872i	0.589151	−	0.808023i	$-0.299462\pi$
$827$	−6.29423	−	6.29423i	−0.218872	−	0.218872i	−0.808023	+	0.589151i	$0.799462\pi$
$828$	−14.1962	+	14.1962i	−0.493350	+	0.493350i
$829$	−13.0526			−0.453334			−0.226667	−	0.973972i	$-0.572783\pi$
$829$	−13.0526			−0.453334			−0.226667	+	0.973972i	$0.572783\pi$
$830$	−14.5885	−	29.1769i	−0.506373	−	1.01275i
$831$	−0.803848	−	0.803848i	−0.0278852	−	0.0278852i
$832$	51.7128	+	13.8564i	1.79282	+	0.480384i
$833$	1.98076	−	7.39230i	0.0686293	−	0.256128i
$834$	4.39230	+	16.3923i	0.152093	+	0.567619i
$835$	−18.6962	+	16.5788i	−0.647007	+	0.573734i
$836$	−4.39230	−	2.53590i	−0.151911	−	0.0877059i
$837$	−9.88269	+	5.70577i	−0.341596	+	0.197220i
$838$	11.4641	+	3.07180i	0.396021	+	0.106113i
$839$	−5.02628	+	8.70577i	−0.173526	+	0.300557i	−0.939650	−	0.342136i	$-0.888850\pi$
$839$	−5.02628	+	8.70577i	−0.173526	+	0.300557i	0.766124	+	0.642693i	$0.222183\pi$
$840$	−27.1244	−	17.9090i	−0.935879	−	0.617918i
$841$	11.3923	+	19.7321i	0.392838	+	0.680416i
$842$	10.7321	+	40.0526i	0.369851	+	1.38030i
$843$	27.5885			0.950197
$844$		0			0
$845$	−63.5692	+	31.7846i	−2.18685	+	1.09342i
$846$	12.2942	+	21.2942i	0.422684	+	0.732111i
$847$	14.6865	+	14.6865i	0.504635	+	0.504635i
$848$	20.7846	−	20.7846i	0.713746	−	0.713746i
$849$	−7.79423	−	29.0885i	−0.267497	−	0.998313i
$850$	11.7846	+	27.5885i	0.404209	+	0.946276i
$851$	−15.2942	−	26.4904i	−0.524279	−	0.908079i
$852$	−36.0000	+	20.7846i	−1.23334	+	0.712069i
$853$	12.0000	−	3.21539i	0.410872	−	0.110093i	−0.0474615	−	0.998873i	$-0.515113\pi$
$853$	12.0000	−	3.21539i	0.410872	−	0.110093i	0.458334	+	0.888780i	$0.348446\pi$
$854$	5.58142	+	9.66730i	0.190992	+	0.330808i
$855$	−3.80385	−	7.60770i	−0.130089	−	0.260178i
$856$	3.60770			0.123308
$857$	−14.0718	−	52.5167i	−0.480683	−	1.79393i	−0.598758	−	0.800930i	$-0.704339\pi$
$857$	−14.0718	−	52.5167i	−0.480683	−	1.79393i	0.118074	−	0.993005i	$-0.462328\pi$
$858$	16.3923	+	28.3923i	0.559624	+	0.969297i
$859$	−8.66025	−	15.0000i	−0.295484	−	0.511793i	0.679613	−	0.733571i	$-0.262148\pi$
$859$	−8.66025	−	15.0000i	−0.295484	−	0.511793i	−0.975097	+	0.221777i	$0.928814\pi$
$860$	−2.78461	−	0.928203i	−0.0949544	−	0.0316515i
$861$	−0.617314	+	2.30385i	−0.0210380	+	0.0785149i
$862$	16.0526	−	16.0526i	0.546752	−	0.546752i
$863$	27.4186	+	27.4186i	0.933339	+	0.933339i	0.997913	−	0.0645735i	$-0.0205687\pi$
$863$	27.4186	+	27.4186i	0.933339	+	0.933339i	−0.0645735	+	0.997913i	$0.520569\pi$
$864$	20.7846	−	20.7846i	0.707107	−	0.707107i
$865$	6.00000	+	2.00000i	0.204006	+	0.0680020i
$866$	−10.7846			−0.366476
$867$	−0.866025	−	1.50000i	−0.0294118	−	0.0509427i
$868$	9.21539	−	9.21539i	0.312791	−	0.312791i
$869$	−14.1962	+	8.19615i	−0.481571	+	0.278035i
$870$	38.6147	−	7.90192i	1.30916	−	0.267900i
$871$	−17.1962	+	29.7846i	−0.582669	+	1.00921i
$872$	17.3205	−	17.3205i	0.586546	−	0.586546i
$873$	−5.49038	+	20.4904i	−0.185821	+	0.693494i
$874$	5.19615	−	3.00000i	0.175762	−	0.101477i
$875$	−33.0622	+	2.71539i	−1.11771	+	0.0917969i
$876$	0.928203	+	0.248711i	0.0313611	+	0.00840318i
$877$	0.464102	+	0.124356i	0.0156716	+	0.00419919i	0.266646	−	0.963794i	$-0.414084\pi$
$877$	0.464102	+	0.124356i	0.0156716	+	0.00419919i	−0.250975	+	0.967994i	$0.580751\pi$
$878$	−8.33975	−	31.1244i	−0.281453	−	1.05040i
$879$	−26.4904	+	7.09808i	−0.893498	+	0.239412i
$880$	−8.00000	−	16.0000i	−0.269680	−	0.539360i
$881$			15.9282i			0.536635i	0.963331	+	0.268317i	$0.0864676\pi$
$881$			15.9282i			0.536635i	−0.963331	+	0.268317i	$0.913532\pi$
$882$	−5.41154	+	5.41154i	−0.182216	+	0.182216i
$883$	12.4186	+	12.4186i	0.417919	+	0.417919i	0.884486	−	0.466567i	$-0.154509\pi$
$883$	12.4186	+	12.4186i	0.417919	+	0.417919i	−0.466567	+	0.884486i	$0.654509\pi$
$884$	−49.1769	+	28.3923i	−1.65400	+	0.954937i
$885$	−21.1244	−	42.2487i	−0.710087	−	1.42017i
$886$	11.7058	−	20.2750i	0.393263	−	0.681152i
$887$	39.4186	+	10.5622i	1.32355	+	0.354643i	0.850305	−	0.526290i	$-0.176417\pi$
$887$	39.4186	+	10.5622i	1.32355	+	0.354643i	0.473241	+	0.880933i	$0.343084\pi$
$888$	22.3923	+	38.7846i	0.751437	+	1.30153i
$889$	40.3301	+	23.2846i	1.35263	+	0.780941i
$890$	45.4186	−	9.29423i	1.52243	−	0.311543i
$891$	18.0000			0.603023
$892$	−18.8564	+	5.05256i	−0.631359	+	0.169172i
$893$	−1.90192	−	7.09808i	−0.0636455	−	0.237528i
$894$	16.5622	−	4.43782i	0.553922	−	0.148423i
$895$	26.8564	+	17.7321i	0.897711	+	0.592717i
$896$	−16.7846	+	29.0718i	−0.560734	+	0.971221i
$897$	−38.7846			−1.29498
$898$	−8.78461	−	8.78461i	−0.293146	−	0.293146i
$899$			15.8038i			0.527088i
$900$	3.58846	−	29.7846i	0.119615	−	0.992820i
$901$			31.1769i			1.03865i
$902$	−0.928203	+	0.928203i	−0.0309058	+	0.0309058i
$903$	−1.68653	+	2.92116i	−0.0561243	+	0.0972102i
$904$	9.46410	+	16.3923i	0.314771	+	0.545200i
$905$	−5.59808	−	3.69615i	−0.186086	−	0.122864i
$906$	−27.7128	+	27.7128i	−0.920697	+	0.920697i
$907$	−15.5263	−	57.9449i	−0.515542	−	1.92403i	−0.344616	−	0.938744i	$-0.611991\pi$
$907$	−15.5263	−	57.9449i	−0.515542	−	1.92403i	−0.170925	−	0.985284i	$-0.554676\pi$
$908$	9.80385	+	36.5885i	0.325352	+	1.21423i
$909$	−3.00000	−	5.19615i	−0.0995037	−	0.172345i
$910$	−12.5885	−	61.5167i	−0.417303	−	2.03926i
$911$	−2.49038	−	1.43782i	−0.0825100	−	0.0476372i	0.458177	−	0.888861i	$-0.348502\pi$
$911$	−2.49038	−	1.43782i	−0.0825100	−	0.0476372i	−0.540687	+	0.841224i	$0.681836\pi$
$912$	−7.60770	+	4.39230i	−0.251916	+	0.145444i
$913$	−19.9282	−	5.33975i	−0.659527	−	0.176720i
$914$	5.53590	+	3.19615i	0.183111	+	0.105719i
$915$	−5.67691	+	8.59808i	−0.187673	+	0.284244i
$916$	31.9808	−	18.4641i	1.05667	−	0.610071i
$917$	−38.1769	−	38.1769i	−1.26071	−	1.26071i
$918$			31.1769i			1.02899i
$919$		−	9.80385i		−	0.323399i	−0.986840	−	0.161700i	$-0.948302\pi$
$919$		−	9.80385i		−	0.323399i	0.986840	−	0.161700i	$-0.0516975\pi$
$920$	21.1244	+	1.26795i	0.696449	+	0.0418030i
$921$	8.00962	−	29.8923i	0.263926	−	0.984985i
$922$	−24.0263	+	6.43782i	−0.791263	+	0.212018i
$923$	−77.5692	−	20.7846i	−2.55322	−	0.684134i
$924$	−19.8564	+	5.32051i	−0.653228	+	0.175032i
$925$	42.4186	+	17.0263i	1.39471	+	0.559821i
$926$	−15.1962	−	26.3205i	−0.499377	−	0.864946i
$927$	28.1769	−	28.1769i	0.925451	−	0.925451i
$928$	−10.5359	−	39.3205i	−0.345858	−	1.29076i
$929$	−8.19615	+	14.1962i	−0.268907	+	0.465761i	−0.968580	−	0.248703i	$-0.919996\pi$
$929$	−8.19615	+	14.1962i	−0.268907	+	0.465761i	0.699673	+	0.714463i	$0.253329\pi$
$930$	11.4115	+	3.80385i	0.374199	+	0.124733i
$931$	1.98076	−	1.14359i	0.0649169	−	0.0374798i
$932$	12.2487	−	12.2487i	0.401220	−	0.401220i
$933$	−3.29423	+	5.70577i	−0.107848	+	0.186799i
$934$		−	58.7846i		−	1.92349i
$935$	18.0000	+	6.00000i	0.588663	+	0.196221i
$936$	56.7846			1.85606
$937$	26.5885	+	26.5885i	0.868607	+	0.868607i	0.992318	−	0.123711i	$-0.0394796\pi$
$937$	26.5885	+	26.5885i	0.868607	+	0.868607i	−0.123711	+	0.992318i	$0.539480\pi$
$938$	−15.2487	−	15.2487i	−0.497888	−	0.497888i
$939$	35.6603	+	35.6603i	1.16373	+	1.16373i
$940$	8.19615	−	24.5885i	0.267329	−	0.801987i
$941$	−9.59808	−	16.6244i	−0.312888	−	0.541939i	0.666098	−	0.745864i	$-0.267963\pi$
$941$	−9.59808	−	16.6244i	−0.312888	−	0.541939i	−0.978986	+	0.203926i	$0.934630\pi$
$942$	−27.0000	−	15.5885i	−0.879708	−	0.507899i
$943$	−0.401924	−	1.50000i	−0.0130884	−	0.0488467i
$944$	−42.2487	+	24.3923i	−1.37508	+	0.793902i
$945$	−32.7058	−	10.9019i	−1.06392	−	0.354640i
$946$	−1.60770	+	0.928203i	−0.0522707	+	0.0301785i
$947$	−30.1865	+	8.08846i	−0.980931	+	0.262840i	−0.713436	−	0.700720i	$-0.752862\pi$
$947$	−30.1865	+	8.08846i	−0.980931	+	0.262840i	−0.267494	+	0.963559i	$0.586196\pi$
$948$			28.3923i			0.922139i
$949$	0.928203	+	1.60770i	0.0301308	+	0.0521880i
$950$	−3.33975	+	8.32051i	−0.108356	+	0.269953i
$951$	17.3205	−	17.3205i	0.561656	−	0.561656i
$952$	−9.21539	−	34.3923i	−0.298673	−	1.11466i
$953$	−11.0718	−	11.0718i	−0.358651	−	0.358651i	0.504665	−	0.863315i	$-0.331616\pi$
$953$	−11.0718	−	11.0718i	−0.358651	−	0.358651i	−0.863315	+	0.504665i	$0.831616\pi$
$954$	15.5885	−	27.0000i	0.504695	−	0.874157i
$955$	−25.1769	+	12.5885i	−0.814706	+	0.407353i
$956$	8.78461	−	5.07180i	0.284115	−	0.164034i
$957$	12.4641	−	21.5885i	0.402907	−	0.697856i
$958$	4.26795	−	1.14359i	0.137891	−	0.0369478i
$959$	−5.32051	−	9.21539i	−0.171808	−	0.297580i
$960$	−30.9282	−	1.85641i	−0.998203	−	0.0599153i
$961$	13.0885	−	22.6699i	0.422208	−	0.731286i
$962$	−22.3923	+	83.5692i	−0.721957	+	2.69438i
$963$	3.69615	−	0.990381i	0.119107	−	0.0319146i
$964$	50.5692	+	29.1962i	1.62872	+	0.940345i
$965$	23.6603	−	20.9808i	0.761651	−	0.675395i
$966$	6.29423	−	23.4904i	0.202513	−	0.755791i
$967$	9.03590	−	33.7224i	0.290575	−	1.08444i	−0.654094	−	0.756414i	$-0.726950\pi$
$967$	9.03590	−	33.7224i	0.290575	−	1.08444i	0.944668	−	0.328027i	$-0.106384\pi$
$968$	19.1244	+	5.12436i	0.614680	+	0.164703i
$969$	2.41154	−	9.00000i	0.0774699	−	0.289122i
$970$	20.0000	−	10.0000i	0.642161	−	0.321081i
$971$	−40.1962			−1.28996			−0.644978	−	0.764201i	$-0.723133\pi$
$971$	−40.1962			−1.28996			−0.644978	+	0.764201i	$0.723133\pi$
$972$	15.5885	−	27.0000i	0.500000	−	0.866025i
$973$	−14.5359	−	14.5359i	−0.466000	−	0.466000i
$974$			34.7846i			1.11457i
$975$	45.5885	−	35.7846i	1.46000	−	1.14602i
$976$	9.21539	+	5.32051i	0.294977	+	0.170305i
$977$	−7.26795	−	1.94744i	−0.232522	−	0.0623042i	0.140676	−	0.990056i	$-0.455072\pi$
$977$	−7.26795	−	1.94744i	−0.232522	−	0.0623042i	−0.373199	+	0.927751i	$0.621739\pi$
$978$	−0.803848	−	1.39230i	−0.0257042	−	0.0445210i
$979$	14.6603	−	25.3923i	0.468544	−	0.811542i
$980$	8.05256	+	0.483340i	0.257230	+	0.0154397i
$981$	12.9904	−	22.5000i	0.414751	−	0.718370i
$982$	6.14359	−	22.9282i	0.196050	−	0.731668i
$983$	17.4282	−	4.66987i	0.555873	−	0.148946i	0.0300636	−	0.999548i	$-0.490429\pi$
$983$	17.4282	−	4.66987i	0.555873	−	0.148946i	0.525810	+	0.850602i	$0.323762\pi$
$984$	0.588457	+	2.19615i	0.0187593	+	0.0700108i
$985$	−37.1769	+	7.60770i	−1.18455	+	0.242401i
$986$	37.3923	+	21.5885i	1.19081	+	0.687517i
$987$	−25.7942	−	14.8923i	−0.821039	−	0.474027i
$988$	−16.3923	−	4.39230i	−0.521509	−	0.139738i
$989$		−	2.19615i		−	0.0698336i
$990$	−12.5885	−	14.1962i	−0.400087	−	0.451183i
$991$	−0.196152			−0.00623099			−0.00311549	−	0.999995i	$-0.500992\pi$
$991$	−0.196152			−0.00623099			−0.00311549	+	0.999995i	$0.500992\pi$
$992$	3.21539	−	12.0000i	0.102089	−	0.381000i
$993$	−52.9808			−1.68129
$994$	25.1769	−	43.6077i	0.798563	−	1.38315i
$995$	−11.5622	−	7.63397i	−0.366546	−	0.242013i
$996$	−25.2679	+	25.2679i	−0.800646	+	0.800646i
$997$	8.36603	+	31.2224i	0.264955	+	0.988824i	0.962278	+	0.272068i	$0.0877075\pi$
$997$	8.36603	+	31.2224i	0.264955	+	0.988824i	−0.697323	+	0.716757i	$0.745626\pi$
$998$	−5.41154	+	20.1962i	−0.171299	+	0.639298i
$999$	33.5885	+	33.5885i	1.06269	+	1.06269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.b.317.1	yes	4
5.3	odd	4		360.2.br.a.173.1	yes	4
8.5	even	2		360.2.br.c.317.1	yes	4
9.5	odd	6		360.2.br.d.77.1	yes	4
40.13	odd	4		360.2.br.d.173.1	yes	4
45.23	even	12		360.2.br.c.293.1	yes	4
72.5	odd	6		360.2.br.a.77.1	✓	4
360.293	even	12	inner	360.2.br.b.293.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.a.77.1	✓	4	72.5	odd	6
360.2.br.a.173.1	yes	4	5.3	odd	4
360.2.br.b.293.1	yes	4	360.293	even	12	inner
360.2.br.b.317.1	yes	4	1.1	even	1	trivial
360.2.br.c.293.1	yes	4	45.23	even	12
360.2.br.c.317.1	yes	4	8.5	even	2
360.2.br.d.77.1	yes	4	9.5	odd	6
360.2.br.d.173.1	yes	4	40.13	odd	4

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +2.00000i q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(2.86603 - 0.767949i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(1.50000 - 0.866025i) q^{3} +2.00000i q^{4} +(1.23205 - 1.86603i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(2.86603 - 0.767949i) q^{7} +(2.00000 - 2.00000i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-3.09808 + 0.633975i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.73205 + 3.00000i) q^{12} +(-1.73205 + 6.46410i) q^{13} +(-3.63397 - 2.09808i) q^{14} +(0.232051 - 3.86603i) q^{15} -4.00000 q^{16} +(3.00000 - 3.00000i) q^{17} +(-4.09808 + 1.09808i) q^{18} +1.26795 q^{19} +(3.73205 + 2.46410i) q^{20} +(3.63397 - 3.63397i) q^{21} +(2.73205 - 0.732051i) q^{22} +(-0.866025 + 3.23205i) q^{23} +(1.26795 - 4.73205i) q^{24} +(-1.96410 - 4.59808i) q^{25} +(8.19615 - 4.73205i) q^{26} -5.19615i q^{27} +(1.53590 + 5.73205i) q^{28} +(-6.23205 - 3.59808i) q^{29} +(-4.09808 + 3.63397i) q^{30} +(-1.09808 - 1.90192i) q^{31} +(4.00000 + 4.00000i) q^{32} +3.46410i q^{33} -6.00000 q^{34} +(2.09808 - 6.29423i) q^{35} +(5.19615 + 3.00000i) q^{36} +(-6.46410 + 6.46410i) q^{37} +(-1.26795 - 1.26795i) q^{38} +(3.00000 + 11.1962i) q^{39} +(-1.26795 - 6.19615i) q^{40} +(-0.401924 + 0.232051i) q^{41} -7.26795 q^{42} +(-0.633975 + 0.169873i) q^{43} +(-3.46410 - 2.00000i) q^{44} +(-3.00000 - 6.00000i) q^{45} +(4.09808 - 2.36603i) q^{46} +(-1.50000 - 5.59808i) q^{47} +(-6.00000 + 3.46410i) q^{48} +(1.56218 - 0.901924i) q^{49} +(-2.63397 + 6.56218i) q^{50} +(1.90192 - 7.09808i) q^{51} +(-12.9282 - 3.46410i) q^{52} +(-5.19615 + 5.19615i) q^{53} +(-5.19615 + 5.19615i) q^{54} +(2.00000 + 4.00000i) q^{55} +(4.19615 - 7.26795i) q^{56} +(1.90192 - 1.09808i) q^{57} +(2.63397 + 9.83013i) q^{58} +(10.5622 - 6.09808i) q^{59} +(7.73205 + 0.464102i) q^{60} +(-2.30385 - 1.33013i) q^{61} +(-0.803848 + 3.00000i) q^{62} +(2.30385 - 8.59808i) q^{63} -8.00000i q^{64} +(9.92820 + 11.1962i) q^{65} +(3.46410 - 3.46410i) q^{66} +(4.96410 + 1.33013i) q^{67} +(6.00000 + 6.00000i) q^{68} +(1.50000 + 5.59808i) q^{69} +(-8.39230 + 4.19615i) q^{70} +12.0000i q^{71} +(-2.19615 - 8.19615i) q^{72} +(0.196152 - 0.196152i) q^{73} +12.9282 q^{74} +(-6.92820 - 5.19615i) q^{75} +2.53590i q^{76} +(-1.53590 + 5.73205i) q^{77} +(8.19615 - 14.1962i) q^{78} +(7.09808 + 4.09808i) q^{79} +(-4.92820 + 7.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(0.633975 + 0.169873i) q^{82} +(2.66987 + 9.96410i) q^{83} +(7.26795 + 7.26795i) q^{84} +(-1.90192 - 9.29423i) q^{85} +(0.803848 + 0.464102i) q^{86} -12.4641 q^{87} +(1.46410 + 5.46410i) q^{88} -14.6603 q^{89} +(-3.00000 + 9.00000i) q^{90} +19.8564i q^{91} +(-6.46410 - 1.73205i) q^{92} +(-3.29423 - 1.90192i) q^{93} +(-4.09808 + 7.09808i) q^{94} +(1.56218 - 2.36603i) q^{95} +(9.46410 + 2.53590i) q^{96} +(-6.83013 + 1.83013i) q^{97} +(-2.46410 - 0.660254i) q^{98} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 2 q^{5} - 6 q^{6} + 8 q^{7} + 8 q^{8} + 6 q^{9} - 2 q^{10} - 4 q^{11} - 18 q^{14} - 6 q^{15} - 16 q^{16} + 12 q^{17} - 6 q^{18} + 12 q^{19} + 8 q^{20} + 18 q^{21} + 4 q^{22} + 12 q^{24} + 6 q^{25} + 12 q^{26} + 20 q^{28} - 18 q^{29} - 6 q^{30} + 6 q^{31} + 16 q^{32} - 24 q^{34} - 2 q^{35} - 12 q^{37} - 12 q^{38} + 12 q^{39} - 12 q^{40} - 12 q^{41} - 36 q^{42} - 6 q^{43} - 12 q^{45} + 6 q^{46} - 6 q^{47} - 24 q^{48} - 18 q^{49} - 14 q^{50} + 18 q^{51} - 24 q^{52} + 8 q^{55} - 4 q^{56} + 18 q^{57} + 14 q^{58} + 18 q^{59} + 24 q^{60} - 30 q^{61} - 24 q^{62} + 30 q^{63} + 12 q^{65} + 6 q^{67} + 24 q^{68} + 6 q^{69} + 8 q^{70} + 12 q^{72} - 20 q^{73} + 24 q^{74} - 20 q^{77} + 12 q^{78} + 18 q^{79} + 8 q^{80} - 18 q^{81} + 6 q^{82} + 28 q^{83} + 36 q^{84} - 18 q^{85} + 24 q^{86} - 36 q^{87} - 8 q^{88} - 24 q^{89} - 12 q^{90} - 12 q^{92} + 18 q^{93} - 6 q^{94} - 18 q^{95} + 24 q^{96} - 10 q^{97} + 4 q^{98} + 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 2 * q^5 - 6 * q^6 + 8 * q^7 + 8 * q^8 + 6 * q^9 - 2 * q^10 - 4 * q^11 - 18 * q^14 - 6 * q^15 - 16 * q^16 + 12 * q^17 - 6 * q^18 + 12 * q^19 + 8 * q^20 + 18 * q^21 + 4 * q^22 + 12 * q^24 + 6 * q^25 + 12 * q^26 + 20 * q^28 - 18 * q^29 - 6 * q^30 + 6 * q^31 + 16 * q^32 - 24 * q^34 - 2 * q^35 - 12 * q^37 - 12 * q^38 + 12 * q^39 - 12 * q^40 - 12 * q^41 - 36 * q^42 - 6 * q^43 - 12 * q^45 + 6 * q^46 - 6 * q^47 - 24 * q^48 - 18 * q^49 - 14 * q^50 + 18 * q^51 - 24 * q^52 + 8 * q^55 - 4 * q^56 + 18 * q^57 + 14 * q^58 + 18 * q^59 + 24 * q^60 - 30 * q^61 - 24 * q^62 + 30 * q^63 + 12 * q^65 + 6 * q^67 + 24 * q^68 + 6 * q^69 + 8 * q^70 + 12 * q^72 - 20 * q^73 + 24 * q^74 - 20 * q^77 + 12 * q^78 + 18 * q^79 + 8 * q^80 - 18 * q^81 + 6 * q^82 + 28 * q^83 + 36 * q^84 - 18 * q^85 + 24 * q^86 - 36 * q^87 - 8 * q^88 - 24 * q^89 - 12 * q^90 - 12 * q^92 + 18 * q^93 - 6 * q^94 - 18 * q^95 + 24 * q^96 - 10 * q^97 + 4 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more