LMFDB - Embedded newform 980.2.o.b.411.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(31,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("980.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.o (of order $6$, degree $2$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			411.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	980.411
Dual form			980.2.o.b.31.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-1.00000 + 1.00000i) q^{10} +(-3.23205 + 1.86603i) q^{11} -3.46410i q^{12} -6.46410i q^{13} -1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(-0.401924 + 0.232051i) q^{17} +(3.00000 - 5.19615i) q^{19} +(1.00000 + 1.73205i) q^{20} +(1.36603 + 5.09808i) q^{22} +(-4.73205 - 2.73205i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-8.83013 - 2.36603i) q^{26} +5.19615 q^{27} -5.92820 q^{29} +(-2.36603 - 0.633975i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-5.59808 - 3.23205i) q^{33} +(0.169873 + 0.633975i) q^{34} +(1.26795 - 2.19615i) q^{37} +(-6.00000 - 6.00000i) q^{38} +(9.69615 - 5.59808i) q^{39} +(2.73205 - 0.732051i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +7.46410 q^{44} +(-5.46410 + 5.46410i) q^{46} +(-0.866025 + 1.50000i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(1.36603 - 0.366025i) q^{50} +(-0.696152 - 0.401924i) q^{51} +(-6.46410 + 11.1962i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(1.90192 - 7.09808i) q^{54} +3.73205 q^{55} +10.3923 q^{57} +(-2.16987 + 8.09808i) q^{58} +(1.73205 + 3.00000i) q^{59} +(-1.73205 + 3.00000i) q^{60} +(2.19615 + 1.26795i) q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(-3.23205 + 5.59808i) q^{65} +(-6.46410 + 6.46410i) q^{66} +(-3.00000 + 1.73205i) q^{67} +0.928203 q^{68} -9.46410i q^{69} -0.535898i q^{71} +(0.803848 - 0.464102i) q^{73} +(-2.53590 - 2.53590i) q^{74} +(-0.866025 + 1.50000i) q^{75} +(-10.3923 + 6.00000i) q^{76} +(-4.09808 - 15.2942i) q^{78} +(-2.30385 - 1.33013i) q^{79} -4.00000i q^{80} +(4.50000 + 7.79423i) q^{81} +(-4.73205 - 1.26795i) q^{82} -8.53590 q^{83} +0.464102 q^{85} +(-2.73205 - 0.732051i) q^{86} +(-5.13397 - 8.89230i) q^{87} +(2.73205 - 10.1962i) q^{88} +(8.19615 + 4.73205i) q^{89} +(5.46410 + 9.46410i) q^{92} +(5.19615 - 9.00000i) q^{93} +(1.73205 + 1.73205i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(6.92820 + 6.92820i) q^{96} -7.39230i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8	$ 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8} - 4 q^{10} - 6 q^{11} + 8 q^{16} - 12 q^{17} + 12 q^{19} + 4 q^{20} + 2 q^{22} - 12 q^{23} - 12 q^{24} + 2 q^{25} - 18 q^{26} + 4 q^{29} - 6 q^{30} - 12 q^{31} + 8 q^{32} - 12 q^{33} + 18 q^{34} + 12 q^{37} - 24 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{44} - 8 q^{46} + 2 q^{50} + 18 q^{51} - 12 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 26 q^{58} - 12 q^{61} - 12 q^{62} - 6 q^{65} - 12 q^{66} - 12 q^{67} - 24 q^{68} + 24 q^{73} - 24 q^{74} - 6 q^{78} - 30 q^{79} + 18 q^{81} - 12 q^{82} - 48 q^{83} - 12 q^{85} - 4 q^{86} - 24 q^{87} + 4 q^{88} + 12 q^{89} + 8 q^{92}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8 - 4 * q^10 - 6 * q^11 + 8 * q^16 - 12 * q^17 + 12 * q^19 + 4 * q^20 + 2 * q^22 - 12 * q^23 - 12 * q^24 + 2 * q^25 - 18 * q^26 + 4 * q^29 - 6 * q^30 - 12 * q^31 + 8 * q^32 - 12 * q^33 + 18 * q^34 + 12 * q^37 - 24 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^44 - 8 * q^46 + 2 * q^50 + 18 * q^51 - 12 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 26 * q^58 - 12 * q^61 - 12 * q^62 - 6 * q^65 - 12 * q^66 - 12 * q^67 - 24 * q^68 + 24 * q^73 - 24 * q^74 - 6 * q^78 - 30 * q^79 + 18 * q^81 - 12 * q^82 - 48 * q^83 - 12 * q^85 - 4 * q^86 - 24 * q^87 + 4 * q^88 + 12 * q^89 + 8 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

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 $

$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$2$	0.366025	−	1.36603i	0.258819	−	0.965926i
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i	1.00000			$0$
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	−1.73205	−	1.00000i	−0.866025	−	0.500000i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	2.36603	−	0.633975i	0.965926	−	0.258819i
$7$		0			0
$7$		0			0
$8$	−2.00000	+	2.00000i	−0.707107	+	0.707107i
$9$		0			0
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.900605	−	0.434638i	$-0.856876\pi$
$11$	−3.23205	+	1.86603i	−0.974500	+	0.562628i	−0.0738948	+	0.997266i	$0.523543\pi$
$12$		−	3.46410i		−	1.00000i
$13$		−	6.46410i		−	1.79282i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$		−	6.46410i		−	1.79282i	0.443227	−	0.896410i	$-0.353834\pi$
$14$		0			0
$15$		−	1.73205i		−	0.447214i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−0.401924	+	0.232051i	−0.0974808	+	0.0562806i	−0.547948	−	0.836512i	$-0.684591\pi$
$17$	−0.401924	+	0.232051i	−0.0974808	+	0.0562806i	0.450467	+	0.892793i	$0.351257\pi$
$18$		0			0
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$		0			0
$22$	1.36603	+	5.09808i	0.291238	+	1.08691i
$23$	−4.73205	−	2.73205i	−0.986701	−	0.569672i	−0.0824143	−	0.996598i	$-0.526263\pi$
$23$	−4.73205	−	2.73205i	−0.986701	−	0.569672i	−0.904286	+	0.426926i	$0.859596\pi$
$24$	−4.73205	−	1.26795i	−0.965926	−	0.258819i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−8.83013	−	2.36603i	−1.73173	−	0.464016i
$27$	5.19615			1.00000
$28$		0			0
$29$	−5.92820			−1.10084			−0.550420	−	0.834888i	$-0.685532\pi$
$29$	−5.92820			−1.10084			−0.550420	+	0.834888i	$0.685532\pi$
$30$	−2.36603	−	0.633975i	−0.431975	−	0.115747i
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	5.46410	−	1.46410i	0.965926	−	0.258819i
$33$	−5.59808	−	3.23205i	−0.974500	−	0.562628i
$34$	0.169873	+	0.633975i	0.0291330	+	0.108726i
$35$		0			0
$36$		0			0
$37$	1.26795	−	2.19615i	0.208450	−	0.361045i	−0.742777	−	0.669539i	$-0.766492\pi$
$37$	1.26795	−	2.19615i	0.208450	−	0.361045i	0.951226	+	0.308494i	$0.0998250\pi$
$38$	−6.00000	−	6.00000i	−0.973329	−	0.973329i
$39$	9.69615	−	5.59808i	1.55263	−	0.896410i
$40$	2.73205	−	0.732051i	0.431975	−	0.115747i
$41$		−	3.46410i		−	0.541002i	−0.962720	−	0.270501i	$-0.912811\pi$
$41$		−	3.46410i		−	0.541002i	0.962720	−	0.270501i	$-0.0871893\pi$
$42$		0			0
$43$		−	2.00000i		−	0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$		−	2.00000i		−	0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	7.46410			1.12526
$45$		0			0
$46$	−5.46410	+	5.46410i	−0.805638	+	0.805638i
$47$	−0.866025	+	1.50000i	−0.126323	+	0.218797i	−0.922249	−	0.386596i	$-0.873651\pi$
$47$	−0.866025	+	1.50000i	−0.126323	+	0.218797i	0.795926	+	0.605393i	$0.206984\pi$
$48$	−3.46410	+	6.00000i	−0.500000	+	0.866025i
$49$		0			0
$50$	1.36603	−	0.366025i	0.193185	−	0.0517638i
$51$	−0.696152	−	0.401924i	−0.0974808	−	0.0562806i
$52$	−6.46410	+	11.1962i	−0.896410	+	1.55263i
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	0.789136	−	0.614218i	$-0.210529\pi$
$53$	−1.00000	−	1.73205i	−0.137361	−	0.237915i	−0.926497	+	0.376303i	$0.877195\pi$
$54$	1.90192	−	7.09808i	0.258819	−	0.965926i
$55$	3.73205			0.503230
$56$		0			0
$57$	10.3923			1.37649
$58$	−2.16987	+	8.09808i	−0.284918	+	1.06333i
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	0.956467	−	0.291839i	$-0.0942671\pi$
$59$	1.73205	+	3.00000i	0.225494	+	0.390567i	−0.730974	+	0.682406i	$0.760934\pi$
$60$	−1.73205	+	3.00000i	−0.223607	+	0.387298i
$61$	2.19615	+	1.26795i	0.281189	+	0.162344i	0.633961	−	0.773365i	$-0.281428\pi$
$61$	2.19615	+	1.26795i	0.281189	+	0.162344i	−0.352773	+	0.935709i	$0.614761\pi$
$62$	−8.19615	+	2.19615i	−1.04091	+	0.278912i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	−3.23205	+	5.59808i	−0.400887	+	0.694356i
$66$	−6.46410	+	6.46410i	−0.795676	+	0.795676i
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	−3.00000	+	1.73205i	−0.366508	+	0.211604i	0.305424	+	0.952217i	$0.401202\pi$
$68$	0.928203			0.112561
$69$		−	9.46410i		−	1.13934i
$70$		0			0
$71$		−	0.535898i		−	0.0635994i	−0.999494	−	0.0317997i	$-0.989876\pi$
$71$		−	0.535898i		−	0.0635994i	0.999494	−	0.0317997i	$-0.0101239\pi$
$72$		0			0
$73$	0.803848	−	0.464102i	0.0940832	−	0.0543190i	−0.452220	−	0.891906i	$-0.649368\pi$
$73$	0.803848	−	0.464102i	0.0940832	−	0.0543190i	0.546303	+	0.837587i	$0.316035\pi$
$74$	−2.53590	−	2.53590i	−0.294792	−	0.294792i
$75$	−0.866025	+	1.50000i	−0.100000	+	0.173205i
$76$	−10.3923	+	6.00000i	−1.19208	+	0.688247i
$77$		0			0
$78$	−4.09808	−	15.2942i	−0.464016	−	1.73173i
$79$	−2.30385	−	1.33013i	−0.259203	−	0.149651i	0.364768	−	0.931098i	$-0.381148\pi$
$79$	−2.30385	−	1.33013i	−0.259203	−	0.149651i	−0.623971	+	0.781448i	$0.714482\pi$
$80$		−	4.00000i		−	0.447214i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	−4.73205	−	1.26795i	−0.522568	−	0.140022i
$83$	−8.53590			−0.936937			−0.468468	−	0.883480i	$-0.655194\pi$
$83$	−8.53590			−0.936937			−0.468468	+	0.883480i	$0.655194\pi$
$84$		0			0
$85$	0.464102			0.0503389
$86$	−2.73205	−	0.732051i	−0.294605	−	0.0789391i
$87$	−5.13397	−	8.89230i	−0.550420	−	0.953355i
$88$	2.73205	−	10.1962i	0.291238	−	1.08691i
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.866946	−	0.498402i	$-0.166080\pi$
$89$	8.19615	+	4.73205i	0.868790	+	0.501596i	0.00184433	+	0.999998i	$0.499413\pi$
$90$		0			0
$91$		0			0
$92$	5.46410	+	9.46410i	0.569672	+	0.986701i
$93$	5.19615	−	9.00000i	0.538816	−	0.933257i
$94$	1.73205	+	1.73205i	0.178647	+	0.178647i
$95$	−5.19615	+	3.00000i	−0.533114	+	0.307794i
$96$	6.92820	+	6.92820i	0.707107	+	0.707107i
$97$		−	7.39230i		−	0.750575i	−0.926908	−	0.375287i	$-0.877544\pi$
$97$		−	7.39230i		−	0.750575i	0.926908	−	0.375287i	$-0.122456\pi$
$98$		0			0
$99$		0			0
$100$		−	2.00000i		−	0.200000i
$101$	7.39230	−	4.26795i	0.735562	−	0.424677i	−0.0848916	−	0.996390i	$-0.527054\pi$
$101$	7.39230	−	4.26795i	0.735562	−	0.424677i	0.820453	+	0.571713i	$0.193721\pi$
$102$	−0.803848	+	0.803848i	−0.0795928	+	0.0795928i
$103$	−8.59808	+	14.8923i	−0.847194	+	1.46738i	0.0365089	+	0.999333i	$0.488376\pi$
$103$	−8.59808	+	14.8923i	−0.847194	+	1.46738i	−0.883702	+	0.468049i	$0.844957\pi$
$104$	12.9282	+	12.9282i	1.26771	+	1.26771i
$105$		0			0
$106$	−2.73205	+	0.732051i	−0.265360	+	0.0711031i
$107$	15.9282	+	9.19615i	1.53984	+	0.889026i	0.998847	+	0.0479966i	$0.0152837\pi$
$107$	15.9282	+	9.19615i	1.53984	+	0.889026i	0.540990	+	0.841029i	$0.318050\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	−7.96410	−	13.7942i	−0.762823	−	1.32125i	−0.941390	−	0.337320i	$-0.890480\pi$
$109$	−7.96410	−	13.7942i	−0.762823	−	1.32125i	0.178568	−	0.983928i	$-0.442854\pi$
$110$	1.36603	−	5.09808i	0.130245	−	0.486082i
$111$	4.39230			0.416899
$112$		0			0
$113$	−1.46410			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$113$	−1.46410			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$114$	3.80385	−	14.1962i	0.356263	−	1.32959i
$115$	2.73205	+	4.73205i	0.254765	+	0.441266i
$116$	10.2679	+	5.92820i	0.953355	+	0.550420i
$117$		0			0
$118$	4.73205	−	1.26795i	0.435621	−	0.116724i
$119$		0			0
$120$	3.46410	+	3.46410i	0.316228	+	0.316228i
$121$	1.46410	−	2.53590i	0.133100	−	0.230536i
$122$	2.53590	−	2.53590i	0.229589	−	0.229589i
$123$	5.19615	−	3.00000i	0.468521	−	0.270501i
$124$			12.0000i			1.07763i
$125$		−	1.00000i		−	0.0894427i
$126$		0			0
$127$			8.53590i			0.757438i	0.925512	+	0.378719i	$0.123635\pi$
$127$			8.53590i			0.757438i	−0.925512	+	0.378719i	$0.876365\pi$
$128$	−10.9282	−	2.92820i	−0.965926	−	0.258819i
$129$	3.00000	−	1.73205i	0.264135	−	0.152499i
$130$	6.46410	+	6.46410i	0.566939	+	0.566939i
$131$	4.73205	−	8.19615i	0.413441	−	0.716101i	−0.581822	−	0.813316i	$-0.697660\pi$
$131$	4.73205	−	8.19615i	0.413441	−	0.716101i	0.995263	+	0.0972148i	$0.0309934\pi$
$132$	6.46410	+	11.1962i	0.562628	+	0.974500i
$133$		0			0
$134$	1.26795	+	4.73205i	0.109534	+	0.408787i
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$	0.339746	−	1.26795i	0.0291330	−	0.108726i
$137$	0.196152	+	0.339746i	0.0167584	+	0.0290265i	0.874283	−	0.485417i	$-0.161332\pi$
$137$	0.196152	+	0.339746i	0.0167584	+	0.0290265i	−0.857525	+	0.514443i	$0.827999\pi$
$138$	−12.9282	−	3.46410i	−1.10052	−	0.294884i
$139$	6.92820			0.587643			0.293821	−	0.955860i	$-0.405073\pi$
$139$	6.92820			0.587643			0.293821	+	0.955860i	$0.405073\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	−0.732051	−	0.196152i	−0.0614323	−	0.0164607i
$143$	12.0622	+	20.8923i	1.00869	+	1.74710i
$144$		0			0
$145$	5.13397	+	2.96410i	0.426353	+	0.246155i
$146$	−0.339746	−	1.26795i	−0.0281176	−	0.104936i
$147$		0			0
$148$	−4.39230	+	2.53590i	−0.361045	+	0.208450i
$149$	−8.46410	+	14.6603i	−0.693406	+	1.20101i	0.277309	+	0.960781i	$0.410557\pi$
$149$	−8.46410	+	14.6603i	−0.693406	+	1.20101i	−0.970715	+	0.240234i	$0.922776\pi$
$150$	1.73205	+	1.73205i	0.141421	+	0.141421i
$151$	−4.16025	+	2.40192i	−0.338557	+	0.195466i	−0.659634	−	0.751587i	$-0.729289\pi$
$151$	−4.16025	+	2.40192i	−0.338557	+	0.195466i	0.321077	+	0.947053i	$0.395955\pi$
$152$	4.39230	+	16.3923i	0.356263	+	1.32959i
$153$		0			0
$154$		0			0
$155$			6.00000i			0.481932i
$156$	−22.3923			−1.79282
$157$	17.1962	−	9.92820i	1.37240	−	0.792357i	0.381172	−	0.924504i	$-0.375520\pi$
$157$	17.1962	−	9.92820i	1.37240	−	0.792357i	0.991230	+	0.132147i	$0.0421871\pi$
$158$	−2.66025	+	2.66025i	−0.211638	+	0.211638i
$159$	1.73205	−	3.00000i	0.137361	−	0.237915i
$160$	−5.46410	−	1.46410i	−0.431975	−	0.115747i
$161$		0			0
$162$	12.2942	−	3.29423i	0.965926	−	0.258819i
$163$	18.0000	+	10.3923i	1.40987	+	0.813988i	0.995375	−	0.0960641i	$-0.0306254\pi$
$163$	18.0000	+	10.3923i	1.40987	+	0.813988i	0.414494	+	0.910052i	$0.363959\pi$
$164$	−3.46410	+	6.00000i	−0.270501	+	0.468521i
$165$	3.23205	+	5.59808i	0.251615	+	0.435810i
$166$	−3.12436	+	11.6603i	−0.242497	+	0.905011i
$167$	−5.19615			−0.402090			−0.201045	−	0.979582i	$-0.564434\pi$
$167$	−5.19615			−0.402090			−0.201045	+	0.979582i	$0.564434\pi$
$168$		0			0
$169$	−28.7846			−2.21420
$170$	0.169873	−	0.633975i	0.0130287	−	0.0486236i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	17.5981	+	10.1603i	1.33796	+	0.772470i	0.986504	−	0.163736i	$-0.0523545\pi$
$173$	17.5981	+	10.1603i	1.33796	+	0.772470i	0.351453	+	0.936206i	$0.385688\pi$
$174$	−14.0263	+	3.75833i	−1.06333	+	0.284918i
$175$		0			0
$176$	−12.9282	−	7.46410i	−0.974500	−	0.562628i
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	9.46410	−	9.46410i	0.709364	−	0.709364i
$179$	−12.4641	+	7.19615i	−0.931611	+	0.537866i	−0.887321	−	0.461153i	$-0.847436\pi$
$179$	−12.4641	+	7.19615i	−0.931611	+	0.537866i	−0.0442901	+	0.999019i	$0.514103\pi$
$180$		0			0
$181$		−	12.9282i		−	0.960946i	−0.877010	−	0.480473i	$-0.840465\pi$
$181$		−	12.9282i		−	0.960946i	0.877010	−	0.480473i	$-0.159535\pi$
$182$		0			0
$183$			4.39230i			0.324689i
$184$	14.9282	−	4.00000i	1.10052	−	0.294884i
$185$	−2.19615	+	1.26795i	−0.161464	+	0.0932215i
$186$	−10.3923	−	10.3923i	−0.762001	−	0.762001i
$187$	0.866025	−	1.50000i	0.0633300	−	0.109691i
$188$	3.00000	−	1.73205i	0.218797	−	0.126323i
$189$		0			0
$190$	2.19615	+	8.19615i	0.159326	+	0.594611i
$191$	−2.76795	−	1.59808i	−0.200282	−	0.115633i	0.396505	−	0.918033i	$-0.370223\pi$
$191$	−2.76795	−	1.59808i	−0.200282	−	0.115633i	−0.596787	+	0.802400i	$0.703556\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	1.26795	+	2.19615i	0.0912690	+	0.158083i	0.908045	−	0.418872i	$-0.137574\pi$
$193$	1.26795	+	2.19615i	0.0912690	+	0.158083i	−0.816776	+	0.576954i	$0.804241\pi$
$194$	−10.0981	−	2.70577i	−0.725000	−	0.194263i
$195$	−11.1962			−0.801773
$196$		0			0
$197$	21.3205			1.51902			0.759512	−	0.650494i	$-0.225438\pi$
$197$	21.3205			1.51902			0.759512	+	0.650494i	$0.225438\pi$
$198$		0			0
$199$	−1.73205	−	3.00000i	−0.122782	−	0.212664i	0.798082	−	0.602549i	$-0.205848\pi$
$199$	−1.73205	−	3.00000i	−0.122782	−	0.212664i	−0.920864	+	0.389885i	$0.872515\pi$
$200$	−2.73205	−	0.732051i	−0.193185	−	0.0517638i
$201$	−5.19615	−	3.00000i	−0.366508	−	0.211604i
$202$	−3.12436	−	11.6603i	−0.219829	−	0.820413i
$203$		0			0
$204$	0.803848	+	1.39230i	0.0562806	+	0.0974808i
$205$	−1.73205	+	3.00000i	−0.120972	+	0.209529i
$206$	17.1962	+	17.1962i	1.19811	+	1.19811i
$207$		0			0
$208$	22.3923	−	12.9282i	1.55263	−	0.896410i
$209$			22.3923i			1.54891i
$210$		0			0
$211$			7.19615i			0.495404i	0.968836	+	0.247702i	$0.0796753\pi$
$211$			7.19615i			0.495404i	−0.968836	+	0.247702i	$0.920325\pi$
$212$			4.00000i			0.274721i
$213$	0.803848	−	0.464102i	0.0550787	−	0.0317997i
$214$	18.3923	−	18.3923i	1.25727	−	1.25727i
$215$	−1.00000	+	1.73205i	−0.0681994	+	0.118125i
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$		0			0
$218$	−21.7583	+	5.83013i	−1.47366	+	0.394866i
$219$	1.39230	+	0.803848i	0.0940832	+	0.0543190i
$220$	−6.46410	−	3.73205i	−0.435810	−	0.251615i
$221$	1.50000	+	2.59808i	0.100901	+	0.174766i
$222$	1.60770	−	6.00000i	0.107901	−	0.402694i
$223$	10.2679			0.687593			0.343796	−	0.939044i	$-0.388287\pi$
$223$	10.2679			0.687593			0.343796	+	0.939044i	$0.388287\pi$
$224$		0			0
$225$		0			0
$226$	−0.535898	+	2.00000i	−0.0356474	+	0.133038i
$227$	1.66987	+	2.89230i	0.110833	+	0.191969i	0.916107	−	0.400935i	$-0.131315\pi$
$227$	1.66987	+	2.89230i	0.110833	+	0.191969i	−0.805273	+	0.592904i	$0.797981\pi$
$228$	−18.0000	−	10.3923i	−1.19208	−	0.688247i
$229$	−13.3923	−	7.73205i	−0.884988	−	0.510948i	−0.0126885	−	0.999919i	$-0.504039\pi$
$229$	−13.3923	−	7.73205i	−0.884988	−	0.510948i	−0.872300	+	0.488971i	$0.837372\pi$
$230$	7.46410	−	2.00000i	0.492168	−	0.131876i
$231$		0			0
$232$	11.8564	−	11.8564i	0.778411	−	0.778411i
$233$	11.4641	−	19.8564i	0.751038	−	1.30084i	−0.196282	−	0.980548i	$-0.562887\pi$
$233$	11.4641	−	19.8564i	0.751038	−	1.30084i	0.947320	−	0.320289i	$-0.103780\pi$
$234$		0			0
$235$	1.50000	−	0.866025i	0.0978492	−	0.0564933i
$236$		−	6.92820i		−	0.450988i
$237$		−	4.60770i		−	0.299302i
$238$		0			0
$239$		−	27.9808i		−	1.80993i	−0.425491	−	0.904963i	$-0.639899\pi$
$239$		−	27.9808i		−	1.80993i	0.425491	−	0.904963i	$-0.360101\pi$
$240$	6.00000	−	3.46410i	0.387298	−	0.223607i
$241$	3.80385	−	2.19615i	0.245027	−	0.141467i	−0.372458	−	0.928049i	$-0.621485\pi$
$241$	3.80385	−	2.19615i	0.245027	−	0.141467i	0.617485	+	0.786583i	$0.288152\pi$
$242$	−2.92820	−	2.92820i	−0.188232	−	0.188232i
$243$		0			0
$244$	−2.53590	−	4.39230i	−0.162344	−	0.281189i
$245$		0			0
$246$	−2.19615	−	8.19615i	−0.140022	−	0.522568i
$247$	−33.5885	−	19.3923i	−2.13718	−	1.23390i
$248$	16.3923	+	4.39230i	1.04091	+	0.278912i
$249$	−7.39230	−	12.8038i	−0.468468	−	0.811411i
$250$	−1.36603	−	0.366025i	−0.0863950	−	0.0231495i
$251$	−1.85641			−0.117175			−0.0585877	−	0.998282i	$-0.518660\pi$
$251$	−1.85641			−0.117175			−0.0585877	+	0.998282i	$0.518660\pi$
$252$		0			0
$253$	20.3923			1.28205
$254$	11.6603	+	3.12436i	0.731629	+	0.196040i
$255$	0.401924	+	0.696152i	0.0251694	+	0.0435948i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	5.19615	+	3.00000i	0.324127	+	0.187135i	0.653231	−	0.757159i	$-0.273413\pi$
$257$	5.19615	+	3.00000i	0.324127	+	0.187135i	−0.329104	+	0.944294i	$0.606747\pi$
$258$	−1.26795	−	4.73205i	−0.0789391	−	0.294605i
$259$		0			0
$260$	11.1962	−	6.46410i	0.694356	−	0.400887i
$261$		0			0
$262$	−9.46410	−	9.46410i	−0.584694	−	0.584694i
$263$	3.92820	−	2.26795i	0.242223	−	0.139848i	−0.373975	−	0.927439i	$-0.622005\pi$
$263$	3.92820	−	2.26795i	0.242223	−	0.139848i	0.616198	+	0.787591i	$0.288672\pi$
$264$	17.6603	−	4.73205i	1.08691	−	0.291238i
$265$			2.00000i			0.122859i
$266$		0			0
$267$			16.3923i			1.00319i
$268$	6.92820			0.423207
$269$	10.3923	−	6.00000i	0.633630	−	0.365826i	−0.148527	−	0.988908i	$-0.547453\pi$
$269$	10.3923	−	6.00000i	0.633630	−	0.365826i	0.782157	+	0.623082i	$0.214120\pi$
$270$	−5.19615	+	5.19615i	−0.316228	+	0.316228i
$271$	1.26795	−	2.19615i	0.0770224	−	0.133407i	−0.824942	−	0.565218i	$-0.808792\pi$
$271$	1.26795	−	2.19615i	0.0770224	−	0.133407i	0.901964	+	0.431811i	$0.142125\pi$
$272$	−1.60770	−	0.928203i	−0.0974808	−	0.0562806i
$273$		0			0
$274$	0.535898	−	0.143594i	0.0323748	−	0.00867480i
$275$	−3.23205	−	1.86603i	−0.194900	−	0.112526i
$276$	−9.46410	+	16.3923i	−0.569672	+	0.986701i
$277$	12.3923	+	21.4641i	0.744581	+	1.28965i	0.950390	+	0.311061i	$0.100684\pi$
$277$	12.3923	+	21.4641i	0.744581	+	1.28965i	−0.205809	+	0.978592i	$0.565982\pi$
$278$	2.53590	−	9.46410i	0.152093	−	0.567619i
$279$		0			0
$280$		0			0
$281$	5.92820			0.353647			0.176823	−	0.984243i	$-0.443418\pi$
$281$	5.92820			0.353647			0.176823	+	0.984243i	$0.443418\pi$
$282$	−1.09808	+	4.09808i	−0.0653895	+	0.244037i
$283$	−6.06218	−	10.5000i	−0.360359	−	0.624160i	0.627661	−	0.778487i	$-0.284012\pi$
$283$	−6.06218	−	10.5000i	−0.360359	−	0.624160i	−0.988020	+	0.154327i	$0.950679\pi$
$284$	−0.535898	+	0.928203i	−0.0317997	+	0.0550787i
$285$	−9.00000	−	5.19615i	−0.533114	−	0.307794i
$286$	32.9545	−	8.83013i	1.94864	−	0.522136i
$287$		0			0
$288$		0			0
$289$	−8.39230	+	14.5359i	−0.493665	+	0.855053i
$290$	5.92820	−	5.92820i	0.348116	−	0.348116i
$291$	11.0885	−	6.40192i	0.650017	−	0.375287i
$292$	−1.85641			−0.108638
$293$			14.3205i			0.836613i	0.908306	+	0.418307i	$0.137376\pi$
$293$			14.3205i			0.836613i	−0.908306	+	0.418307i	$0.862624\pi$
$294$		0			0
$295$		−	3.46410i		−	0.201688i
$296$	1.85641	+	6.92820i	0.107901	+	0.402694i
$297$	−16.7942	+	9.69615i	−0.974500	+	0.562628i
$298$	16.9282	+	16.9282i	0.980624	+	0.980624i
$299$	−17.6603	+	30.5885i	−1.02132	+	1.76898i
$300$	3.00000	−	1.73205i	0.173205	−	0.100000i
$301$		0			0
$302$	1.75833	+	6.56218i	0.101181	+	0.377611i
$303$	12.8038	+	7.39230i	0.735562	+	0.424677i
$304$	24.0000			1.37649
$305$	−1.26795	−	2.19615i	−0.0726026	−	0.125751i
$306$		0			0
$307$	1.73205			0.0988534			0.0494267	−	0.998778i	$-0.484261\pi$
$307$	1.73205			0.0988534			0.0494267	+	0.998778i	$0.484261\pi$
$308$		0			0
$309$	−29.7846			−1.69439
$310$	8.19615	+	2.19615i	0.465510	+	0.124733i
$311$	−9.92820	−	17.1962i	−0.562977	−	0.975104i	−0.997235	−	0.0743158i	$-0.976323\pi$
$311$	−9.92820	−	17.1962i	−0.562977	−	0.975104i	0.434258	−	0.900789i	$-0.357011\pi$
$312$	−8.19615	+	30.5885i	−0.464016	+	1.73173i
$313$	−21.1865	−	12.2321i	−1.19753	−	0.691396i	−0.237529	−	0.971380i	$-0.576337\pi$
$313$	−21.1865	−	12.2321i	−1.19753	−	0.691396i	−0.960005	+	0.279984i	$0.909671\pi$
$314$	−7.26795	−	27.1244i	−0.410154	−	1.53072i
$315$		0			0
$316$	2.66025	+	4.60770i	0.149651	+	0.259203i
$317$	8.46410	−	14.6603i	0.475391	−	0.823402i	−0.524211	−	0.851588i	$-0.675640\pi$
$317$	8.46410	−	14.6603i	0.475391	−	0.823402i	0.999603	+	0.0281863i	$0.00897316\pi$
$318$	−3.46410	−	3.46410i	−0.194257	−	0.194257i
$319$	19.1603	−	11.0622i	1.07277	−	0.619363i
$320$	−4.00000	+	6.92820i	−0.223607	+	0.387298i
$321$			31.8564i			1.77805i
$322$		0			0
$323$			2.78461i			0.154940i
$324$		−	18.0000i		−	1.00000i
$325$	5.59808	−	3.23205i	0.310525	−	0.179282i
$326$	20.7846	−	20.7846i	1.15115	−	1.15115i
$327$	13.7942	−	23.8923i	0.762823	−	1.32125i
$328$	6.92820	+	6.92820i	0.382546	+	0.382546i
$329$		0			0
$330$	8.83013	−	2.36603i	0.486082	−	0.130245i
$331$	−4.85641	−	2.80385i	−0.266932	−	0.154113i	0.360560	−	0.932736i	$-0.382585\pi$
$331$	−4.85641	−	2.80385i	−0.266932	−	0.154113i	−0.627493	+	0.778622i	$0.715919\pi$
$332$	14.7846	+	8.53590i	0.811411	+	0.468468i
$333$		0			0
$334$	−1.90192	+	7.09808i	−0.104069	+	0.388389i
$335$	3.46410			0.189264
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−10.5359	+	39.3205i	−0.573077	+	2.13875i
$339$	−1.26795	−	2.19615i	−0.0688655	−	0.119279i
$340$	−0.803848	−	0.464102i	−0.0435948	−	0.0251694i
$341$	19.3923	+	11.1962i	1.05015	+	0.606306i
$342$		0			0
$343$		0			0
$344$	4.00000	+	4.00000i	0.215666	+	0.215666i
$345$	−4.73205	+	8.19615i	−0.254765	+	0.441266i
$346$	20.3205	−	20.3205i	1.09244	−	1.09244i
$347$	12.3397	−	7.12436i	0.662432	−	0.382455i	−0.130771	−	0.991413i	$-0.541745\pi$
$347$	12.3397	−	7.12436i	0.662432	−	0.382455i	0.793203	+	0.608957i	$0.208412\pi$
$348$			20.5359i			1.10084i
$349$		−	29.3205i		−	1.56949i	−0.619818	−	0.784745i	$-0.712794\pi$
$349$		−	29.3205i		−	1.56949i	0.619818	−	0.784745i	$-0.287206\pi$
$350$		0			0
$351$		−	33.5885i		−	1.79282i
$352$	−14.9282	+	14.9282i	−0.795676	+	0.795676i
$353$	−11.5981	+	6.69615i	−0.617303	+	0.356400i	−0.775818	−	0.630956i	$-0.782663\pi$
$353$	−11.5981	+	6.69615i	−0.617303	+	0.356400i	0.158515	+	0.987357i	$0.449329\pi$
$354$	6.00000	+	6.00000i	0.318896	+	0.318896i
$355$	−0.267949	+	0.464102i	−0.0142213	+	0.0246320i
$356$	−9.46410	−	16.3923i	−0.501596	−	0.868790i
$357$		0			0
$358$	5.26795	+	19.6603i	0.278420	+	1.03908i
$359$	−8.07180	−	4.66025i	−0.426013	−	0.245959i	0.271634	−	0.962401i	$-0.412436\pi$
$359$	−8.07180	−	4.66025i	−0.426013	−	0.245959i	−0.697647	+	0.716442i	$0.745769\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−17.6603	−	4.73205i	−0.928202	−	0.248711i
$363$	5.07180			0.266200
$364$		0			0
$365$	−0.928203			−0.0485844
$366$	6.00000	+	1.60770i	0.313625	+	0.0840356i
$367$	18.0622	+	31.2846i	0.942838	+	1.63304i	0.760023	+	0.649896i	$0.225188\pi$
$367$	18.0622	+	31.2846i	0.942838	+	1.63304i	0.182815	+	0.983147i	$0.441479\pi$
$368$		−	21.8564i		−	1.13934i
$369$		0			0
$370$	0.928203	+	3.46410i	0.0482550	+	0.180090i
$371$		0			0
$372$	−18.0000	+	10.3923i	−0.933257	+	0.538816i
$373$	12.1962	−	21.1244i	0.631493	−	1.09378i	−0.355754	−	0.934580i	$-0.615776\pi$
$373$	12.1962	−	21.1244i	0.631493	−	1.09378i	0.987247	−	0.159198i	$-0.0508908\pi$
$374$	−1.73205	−	1.73205i	−0.0895622	−	0.0895622i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	−1.26795	−	4.73205i	−0.0653895	−	0.244037i
$377$			38.3205i			1.97361i
$378$		0			0
$379$		−	26.3923i		−	1.35568i	−0.735209	−	0.677841i	$-0.762916\pi$
$379$		−	26.3923i		−	1.35568i	0.735209	−	0.677841i	$-0.237084\pi$
$380$	12.0000			0.615587
$381$	−12.8038	+	7.39230i	−0.655961	+	0.378719i
$382$	−3.19615	+	3.19615i	−0.163529	+	0.163529i
$383$	10.2679	−	17.7846i	0.524668	−	0.908751i	−0.474920	−	0.880029i	$-0.657523\pi$
$383$	10.2679	−	17.7846i	0.524668	−	0.908751i	0.999587	−	0.0287220i	$-0.00914375\pi$
$384$	−5.07180	−	18.9282i	−0.258819	−	0.965926i
$385$		0			0
$386$	3.46410	−	0.928203i	0.176318	−	0.0472443i
$387$		0			0
$388$	−7.39230	+	12.8038i	−0.375287	+	0.650017i
$389$	−3.42820	−	5.93782i	−0.173817	−	0.301060i	0.765934	−	0.642919i	$-0.222277\pi$
$389$	−3.42820	−	5.93782i	−0.173817	−	0.301060i	−0.939751	+	0.341859i	$0.888943\pi$
$390$	−4.09808	+	15.2942i	−0.207514	+	0.774453i
$391$	2.53590			0.128246
$392$		0			0
$393$	16.3923			0.826882
$394$	7.80385	−	29.1244i	0.393152	−	1.46726i
$395$	1.33013	+	2.30385i	0.0669260	+	0.115919i
$396$		0			0
$397$	4.79423	+	2.76795i	0.240615	+	0.138919i	0.615460	−	0.788168i	$-0.288970\pi$
$397$	4.79423	+	2.76795i	0.240615	+	0.138919i	−0.374844	+	0.927088i	$0.622304\pi$
$398$	−4.73205	+	1.26795i	−0.237196	+	0.0635566i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	11.9641	−	20.7224i	0.597459	−	1.03483i	−0.395736	−	0.918364i	$-0.629511\pi$
$401$	11.9641	−	20.7224i	0.597459	−	1.03483i	0.993195	−	0.116465i	$-0.0371562\pi$
$402$	−6.00000	+	6.00000i	−0.299253	+	0.299253i
$403$	−33.5885	+	19.3923i	−1.67316	+	0.966000i
$404$	−17.0718			−0.849354
$405$		−	9.00000i		−	0.447214i
$406$		0			0
$407$			9.46410i			0.469118i
$408$	2.19615	−	0.588457i	0.108726	−	0.0291330i
$409$	−27.5885	+	15.9282i	−1.36416	+	0.787599i	−0.990175	−	0.139835i	$-0.955343\pi$
$409$	−27.5885	+	15.9282i	−1.36416	+	0.787599i	−0.373987	+	0.927434i	$0.622009\pi$
$410$	3.46410	+	3.46410i	0.171080	+	0.171080i
$411$	−0.339746	+	0.588457i	−0.0167584	+	0.0290265i
$412$	29.7846	−	17.1962i	1.46738	−	0.847194i
$413$		0			0
$414$		0			0
$415$	7.39230	+	4.26795i	0.362874	+	0.209505i
$416$	−9.46410	−	35.3205i	−0.464016	−	1.73173i
$417$	6.00000	+	10.3923i	0.293821	+	0.508913i
$418$	30.5885	+	8.19615i	1.49613	+	0.400887i
$419$	−24.2487			−1.18463			−0.592314	−	0.805708i	$-0.701785\pi$
$419$	−24.2487			−1.18463			−0.592314	+	0.805708i	$0.701785\pi$
$420$		0			0
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	9.83013	+	2.63397i	0.478523	+	0.128220i
$423$		0			0
$424$	5.46410	+	1.46410i	0.265360	+	0.0711031i
$425$	−0.401924	−	0.232051i	−0.0194962	−	0.0112561i
$426$	−0.339746	−	1.26795i	−0.0164607	−	0.0614323i
$427$		0			0
$428$	−18.3923	−	31.8564i	−0.889026	−	1.53984i
$429$	−20.8923	+	36.1865i	−1.00869	+	1.74710i
$430$	2.00000	+	2.00000i	0.0964486	+	0.0964486i
$431$	−15.2321	+	8.79423i	−0.733702	+	0.423603i	−0.819775	−	0.572686i	$-0.805902\pi$
$431$	−15.2321	+	8.79423i	−0.733702	+	0.423603i	0.0860729	+	0.996289i	$0.472568\pi$
$432$	10.3923	+	18.0000i	0.500000	+	0.866025i
$433$			4.14359i			0.199128i	0.995031	+	0.0995642i	$0.0317449\pi$
$433$			4.14359i			0.199128i	−0.995031	+	0.0995642i	$0.968255\pi$
$434$		0			0
$435$			10.2679i			0.492310i
$436$			31.8564i			1.52565i
$437$	−28.3923	+	16.3923i	−1.35819	+	0.784150i
$438$	1.60770	−	1.60770i	0.0768186	−	0.0768186i
$439$	7.85641	−	13.6077i	0.374966	−	0.649460i	−0.615356	−	0.788249i	$-0.710988\pi$
$439$	7.85641	−	13.6077i	0.374966	−	0.649460i	0.990322	+	0.138789i	$0.0443211\pi$
$440$	−7.46410	+	7.46410i	−0.355837	+	0.355837i
$441$		0			0
$442$	4.09808	−	1.09808i	0.194926	−	0.0522302i
$443$	−22.5167	−	13.0000i	−1.06980	−	0.617649i	−0.141672	−	0.989914i	$-0.545248\pi$
$443$	−22.5167	−	13.0000i	−1.06980	−	0.617649i	−0.928126	+	0.372265i	$0.878581\pi$
$444$	−7.60770	−	4.39230i	−0.361045	−	0.208450i
$445$	−4.73205	−	8.19615i	−0.224321	−	0.388535i
$446$	3.75833	−	14.0263i	0.177962	−	0.664164i
$447$	−29.3205			−1.38681
$448$		0			0
$449$	−1.92820			−0.0909975			−0.0454988	−	0.998964i	$-0.514488\pi$
$449$	−1.92820			−0.0909975			−0.0454988	+	0.998964i	$0.514488\pi$
$450$		0			0
$451$	6.46410	+	11.1962i	0.304383	+	0.527206i
$452$	2.53590	+	1.46410i	0.119279	+	0.0688655i
$453$	−7.20577	−	4.16025i	−0.338557	−	0.195466i
$454$	4.56218	−	1.22243i	0.214114	−	0.0573716i
$455$		0			0
$456$	−20.7846	+	20.7846i	−0.973329	+	0.973329i
$457$	−13.7321	+	23.7846i	−0.642358	+	1.11260i	0.342547	+	0.939501i	$0.388711\pi$
$457$	−13.7321	+	23.7846i	−0.642358	+	1.11260i	−0.984905	+	0.173096i	$0.944623\pi$
$458$	−15.4641	+	15.4641i	−0.722590	+	0.722590i
$459$	−2.08846	+	1.20577i	−0.0974808	+	0.0562806i
$460$		−	10.9282i		−	0.509530i
$461$			27.7128i			1.29071i	0.763881	+	0.645357i	$0.223291\pi$
$461$			27.7128i			1.29071i	−0.763881	+	0.645357i	$0.776709\pi$
$462$		0			0
$463$		−	4.39230i		−	0.204128i	−0.994778	−	0.102064i	$-0.967455\pi$
$463$		−	4.39230i		−	0.204128i	0.994778	−	0.102064i	$-0.0325446\pi$
$464$	−11.8564	−	20.5359i	−0.550420	−	0.953355i
$465$	−9.00000	+	5.19615i	−0.417365	+	0.240966i
$466$	−22.9282	−	22.9282i	−1.06213	−	1.06213i
$467$	−11.2583	+	19.5000i	−0.520973	+	0.902352i	0.478729	+	0.877963i	$0.341098\pi$
$467$	−11.2583	+	19.5000i	−0.520973	+	0.902352i	−0.999703	+	0.0243897i	$0.992236\pi$
$468$		0			0
$469$		0			0
$470$	−0.633975	−	2.36603i	−0.0292431	−	0.109137i
$471$	29.7846	+	17.1962i	1.37240	+	0.792357i
$472$	−9.46410	−	2.53590i	−0.435621	−	0.116724i
$473$	3.73205	+	6.46410i	0.171600	+	0.297220i
$474$	−6.29423	−	1.68653i	−0.289103	−	0.0774650i
$475$	6.00000			0.275299
$476$		0			0
$477$		0			0
$478$	−38.2224	−	10.2417i	−1.74825	−	0.468443i
$479$	−18.5885	−	32.1962i	−0.849328	−	1.47108i	−0.881809	−	0.471607i	$-0.843674\pi$
$479$	−18.5885	−	32.1962i	−0.849328	−	1.47108i	0.0324804	−	0.999472i	$-0.489659\pi$
$480$	−2.53590	−	9.46410i	−0.115747	−	0.431975i
$481$	−14.1962	−	8.19615i	−0.647289	−	0.373712i
$482$	−1.60770	−	6.00000i	−0.0732285	−	0.273293i
$483$		0			0
$484$	−5.07180	+	2.92820i	−0.230536	+	0.133100i
$485$	−3.69615	+	6.40192i	−0.167834	+	0.290696i
$486$		0			0
$487$	−24.9282	+	14.3923i	−1.12960	+	0.652178i	−0.943835	−	0.330416i	$-0.892811\pi$
$487$	−24.9282	+	14.3923i	−1.12960	+	0.652178i	−0.185769	+	0.982593i	$0.559478\pi$
$488$	−6.92820	+	1.85641i	−0.313625	+	0.0840356i
$489$			36.0000i			1.62798i
$490$		0			0
$491$			34.1244i			1.54001i	0.638037	+	0.770005i	$0.279746\pi$
$491$			34.1244i			1.54001i	−0.638037	+	0.770005i	$0.720254\pi$
$492$	−12.0000			−0.541002
$493$	2.38269	−	1.37564i	0.107311	−	0.0619559i
$494$	−38.7846	+	38.7846i	−1.74500	+	1.74500i
$495$		0			0
$496$	12.0000	−	20.7846i	0.538816	−	0.933257i
$497$		0			0
$498$	−20.1962	+	5.41154i	−0.905011	+	0.242497i
$499$	−4.83975	−	2.79423i	−0.216657	−	0.125087i	0.387745	−	0.921767i	$-0.373254\pi$
$499$	−4.83975	−	2.79423i	−0.216657	−	0.125087i	−0.604401	+	0.796680i	$0.706588\pi$
$500$	−1.00000	+	1.73205i	−0.0447214	+	0.0774597i
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$	−0.679492	+	2.53590i	−0.0303272	+	0.113183i
$503$	−15.5885			−0.695055			−0.347527	−	0.937670i	$-0.612979\pi$
$503$	−15.5885			−0.695055			−0.347527	+	0.937670i	$0.612979\pi$
$504$		0			0
$505$	−8.53590			−0.379842
$506$	7.46410	−	27.8564i	0.331820	−	1.23837i
$507$	−24.9282	−	43.1769i	−1.10710	−	1.91755i
$508$	8.53590	−	14.7846i	0.378719	−	0.655961i
$509$	−1.60770	−	0.928203i	−0.0712598	−	0.0411419i	0.463947	−	0.885863i	$-0.346433\pi$
$509$	−1.60770	−	0.928203i	−0.0712598	−	0.0411419i	−0.535207	+	0.844721i	$0.679766\pi$
$510$	1.09808	−	0.294229i	0.0486236	−	0.0130287i
$511$		0			0
$512$	16.0000	+	16.0000i	0.707107	+	0.707107i
$513$	15.5885	−	27.0000i	0.688247	−	1.19208i
$514$	6.00000	−	6.00000i	0.264649	−	0.264649i
$515$	14.8923	−	8.59808i	0.656233	−	0.378877i
$516$	−6.92820			−0.304997
$517$		−	6.46410i		−	0.284291i
$518$		0			0
$519$			35.1962i			1.54494i
$520$	−4.73205	−	17.6603i	−0.207514	−	0.774453i
$521$	−29.7846	+	17.1962i	−1.30489	+	0.753377i	−0.981238	−	0.192800i	$-0.938243\pi$
$521$	−29.7846	+	17.1962i	−1.30489	+	0.753377i	−0.323649	+	0.946177i	$0.604910\pi$
$522$		0			0
$523$	12.1244	−	21.0000i	0.530161	−	0.918266i	−0.469220	−	0.883081i	$-0.655465\pi$
$523$	12.1244	−	21.0000i	0.530161	−	0.918266i	0.999381	−	0.0351845i	$-0.0112019\pi$
$524$	−16.3923	+	9.46410i	−0.716101	+	0.413441i
$525$		0			0
$526$	−1.66025	−	6.19615i	−0.0723905	−	0.270165i
$527$	2.41154	+	1.39230i	0.105048	+	0.0606498i
$528$		−	25.8564i		−	1.12526i
$529$	3.42820	+	5.93782i	0.149052	+	0.258166i
$530$	2.73205	+	0.732051i	0.118673	+	0.0317983i
$531$		0			0
$532$		0			0
$533$	−22.3923			−0.969918
$534$	22.3923	+	6.00000i	0.969010	+	0.259645i
$535$	−9.19615	−	15.9282i	−0.397584	−	0.688636i
$536$	2.53590	−	9.46410i	0.109534	−	0.408787i
$537$	−21.5885	−	12.4641i	−0.931611	−	0.537866i
$538$	−4.39230	−	16.3923i	−0.189366	−	0.706722i
$539$		0			0
$540$	5.19615	+	9.00000i	0.223607	+	0.387298i
$541$	16.8923	−	29.2583i	0.726257	−	1.25791i	−0.232198	−	0.972669i	$-0.574592\pi$
$541$	16.8923	−	29.2583i	0.726257	−	1.25791i	0.958455	−	0.285245i	$-0.0920750\pi$
$542$	−2.53590	−	2.53590i	−0.108926	−	0.108926i
$543$	19.3923	−	11.1962i	0.832203	−	0.480473i
$544$	−1.85641	+	1.85641i	−0.0795928	+	0.0795928i
$545$			15.9282i			0.682289i
$546$		0			0
$547$		−	14.5359i		−	0.621510i	−0.950490	−	0.310755i	$-0.899418\pi$
$547$		−	14.5359i		−	0.621510i	0.950490	−	0.310755i	$-0.100582\pi$
$548$		−	0.784610i		−	0.0335169i
$549$		0			0
$550$	−3.73205	+	3.73205i	−0.159135	+	0.159135i
$551$	−17.7846	+	30.8038i	−0.757650	+	1.31229i
$552$	18.9282	+	18.9282i	0.805638	+	0.805638i
$553$		0			0
$554$	33.8564	−	9.07180i	1.43842	−	0.385424i
$555$	−3.80385	−	2.19615i	−0.161464	−	0.0932215i
$556$	−12.0000	−	6.92820i	−0.508913	−	0.293821i
$557$	−2.92820	−	5.07180i	−0.124072	−	0.214899i	0.797298	−	0.603586i	$-0.206262\pi$
$557$	−2.92820	−	5.07180i	−0.124072	−	0.214899i	−0.921370	+	0.388687i	$0.872929\pi$
$558$		0			0
$559$	−12.9282			−0.546805
$560$		0			0
$561$	3.00000			0.126660
$562$	2.16987	−	8.09808i	0.0915306	−	0.341597i
$563$	−21.5885	−	37.3923i	−0.909845	−	1.57590i	−0.814278	−	0.580475i	$-0.802867\pi$
$563$	−21.5885	−	37.3923i	−0.909845	−	1.57590i	−0.0955667	−	0.995423i	$-0.530466\pi$
$564$	5.19615	+	3.00000i	0.218797	+	0.126323i
$565$	1.26795	+	0.732051i	0.0533430	+	0.0307976i
$566$	−16.5622	+	4.43782i	−0.696160	+	0.186536i
$567$		0			0
$568$	1.07180	+	1.07180i	0.0449716	+	0.0449716i
$569$	−10.4641	+	18.1244i	−0.438678	+	0.759813i	−0.997588	−	0.0694159i	$-0.977886\pi$
$569$	−10.4641	+	18.1244i	−0.438678	+	0.759813i	0.558910	+	0.829228i	$0.311220\pi$
$570$	−10.3923	+	10.3923i	−0.435286	+	0.435286i
$571$	35.7846	−	20.6603i	1.49754	−	0.864605i	0.497543	−	0.867439i	$-0.334236\pi$
$571$	35.7846	−	20.6603i	1.49754	−	0.864605i	0.999996	+	0.00283441i	$0.000902221\pi$
$572$		−	48.2487i		−	2.01738i
$573$		−	5.53590i		−	0.231265i
$574$		0			0
$575$		−	5.46410i		−	0.227869i
$576$		0			0
$577$	1.20577	−	0.696152i	0.0501969	−	0.0289812i	−0.474692	−	0.880152i	$-0.657440\pi$
$577$	1.20577	−	0.696152i	0.0501969	−	0.0289812i	0.524888	+	0.851171i	$0.324107\pi$
$578$	16.7846	+	16.7846i	0.698148	+	0.698148i
$579$	−2.19615	+	3.80385i	−0.0912690	+	0.158083i
$580$	−5.92820	−	10.2679i	−0.246155	−	0.426353i
$581$		0			0
$582$	−4.68653	−	17.4904i	−0.194263	−	0.725000i
$583$	6.46410	+	3.73205i	0.267716	+	0.154566i
$584$	−0.679492	+	2.53590i	−0.0281176	+	0.104936i
$585$		0			0
$586$	19.5622	+	5.24167i	0.808106	+	0.216531i
$587$	27.4641			1.13356			0.566782	−	0.823868i	$-0.308188\pi$
$587$	27.4641			1.13356			0.566782	+	0.823868i	$0.308188\pi$
$588$		0			0
$589$	−36.0000			−1.48335
$590$	−4.73205	−	1.26795i	−0.194815	−	0.0522006i
$591$	18.4641	+	31.9808i	0.759512	+	1.31551i
$592$	10.1436			0.416899
$593$	20.3827	+	11.7679i	0.837017	+	0.483252i	0.856249	−	0.516563i	$-0.172789\pi$
$593$	20.3827	+	11.7679i	0.837017	+	0.483252i	−0.0192324	+	0.999815i	$0.506122\pi$
$594$	7.09808	+	26.4904i	0.291238	+	1.08691i
$595$		0			0
$596$	29.3205	−	16.9282i	1.20101	−	0.693406i
$597$	3.00000	−	5.19615i	0.122782	−	0.212664i
$598$	35.3205	+	35.3205i	1.44436	+	1.44436i
$599$	−12.2321	+	7.06218i	−0.499788	+	0.288553i	−0.728626	−	0.684912i	$-0.759841\pi$
$599$	−12.2321	+	7.06218i	−0.499788	+	0.288553i	0.228838	+	0.973465i	$0.426507\pi$
$600$	−1.26795	−	4.73205i	−0.0517638	−	0.193185i
$601$		−	26.7846i		−	1.09257i	−0.837600	−	0.546284i	$-0.816042\pi$
$601$		−	26.7846i		−	1.09257i	0.837600	−	0.546284i	$-0.183958\pi$
$602$		0			0
$603$		0			0
$604$	9.60770			0.390932
$605$	−2.53590	+	1.46410i	−0.103099	+	0.0595242i
$606$	14.7846	−	14.7846i	0.600584	−	0.600584i
$607$	−9.40192	+	16.2846i	−0.381612	+	0.660972i	−0.991293	−	0.131675i	$-0.957964\pi$
$607$	−9.40192	+	16.2846i	−0.381612	+	0.660972i	0.609681	+	0.792647i	$0.291298\pi$
$608$	8.78461	−	32.7846i	0.356263	−	1.32959i
$609$		0			0
$610$	−3.46410	+	0.928203i	−0.140257	+	0.0375819i
$611$	9.69615	+	5.59808i	0.392264	+	0.226474i
$612$		0			0
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	0.949156	−	0.314806i	$-0.101939\pi$
$613$	5.00000	+	8.66025i	0.201948	+	0.349784i	−0.747208	+	0.664590i	$0.768606\pi$
$614$	0.633975	−	2.36603i	0.0255851	−	0.0954850i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−9.07180			−0.365217			−0.182608	−	0.983186i	$-0.558454\pi$
$617$	−9.07180			−0.365217			−0.182608	+	0.983186i	$0.558454\pi$
$618$	−10.9019	+	40.6865i	−0.438540	+	1.63665i
$619$	17.6603	+	30.5885i	0.709826	+	1.22945i	0.964922	+	0.262538i	$0.0845596\pi$
$619$	17.6603	+	30.5885i	0.709826	+	1.22945i	−0.255096	+	0.966916i	$0.582107\pi$
$620$	6.00000	−	10.3923i	0.240966	−	0.417365i
$621$	−24.5885	−	14.1962i	−0.986701	−	0.569672i
$622$	−27.1244	+	7.26795i	−1.08759	+	0.291418i
$623$		0			0
$624$	38.7846	+	22.3923i	1.55263	+	0.896410i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−24.4641	+	24.4641i	−0.977782	+	0.977782i
$627$	−33.5885	+	19.3923i	−1.34139	+	0.774454i
$628$	−39.7128			−1.58471
$629$			1.17691i			0.0469267i
$630$		0			0
$631$			26.9090i			1.07123i	0.844463	+	0.535614i	$0.179920\pi$
$631$			26.9090i			1.07123i	−0.844463	+	0.535614i	$0.820080\pi$
$632$	7.26795	−	1.94744i	0.289103	−	0.0774650i
$633$	−10.7942	+	6.23205i	−0.429032	+	0.247702i
$634$	−16.9282	−	16.9282i	−0.672305	−	0.672305i
$635$	4.26795	−	7.39230i	0.169368	−	0.293355i
$636$	−6.00000	+	3.46410i	−0.237915	+	0.137361i
$637$		0			0
$638$	−8.09808	−	30.2224i	−0.320606	−	1.19652i
$639$		0			0
$640$	8.00000	+	8.00000i	0.316228	+	0.316228i
$641$	2.46410	+	4.26795i	0.0973262	+	0.168574i	0.910577	−	0.413339i	$-0.135638\pi$
$641$	2.46410	+	4.26795i	0.0973262	+	0.168574i	−0.813251	+	0.581913i	$0.802304\pi$
$642$	43.5167	+	11.6603i	1.71747	+	0.460194i
$643$	31.0526			1.22459			0.612297	−	0.790628i	$-0.290246\pi$
$643$	31.0526			1.22459			0.612297	+	0.790628i	$0.290246\pi$
$644$		0			0
$645$	−3.46410			−0.136399
$646$	3.80385	+	1.01924i	0.149660	+	0.0401014i
$647$	5.19615	+	9.00000i	0.204282	+	0.353827i	0.949904	−	0.312543i	$-0.101181\pi$
$647$	5.19615	+	9.00000i	0.204282	+	0.353827i	−0.745622	+	0.666369i	$0.767847\pi$
$648$	−24.5885	−	6.58846i	−0.965926	−	0.258819i
$649$	−11.1962	−	6.46410i	−0.439487	−	0.253738i
$650$	−2.36603	−	8.83013i	−0.0928032	−	0.346346i
$651$		0			0
$652$	−20.7846	−	36.0000i	−0.813988	−	1.40987i
$653$	−19.1962	+	33.2487i	−0.751203	+	1.30112i	0.196036	+	0.980597i	$0.437193\pi$
$653$	−19.1962	+	33.2487i	−0.751203	+	1.30112i	−0.947240	+	0.320526i	$0.896140\pi$
$654$	−27.5885	−	27.5885i	−1.07879	−	1.07879i
$655$	−8.19615	+	4.73205i	−0.320250	+	0.184897i
$656$	12.0000	−	6.92820i	0.468521	−	0.270501i
$657$		0			0
$658$		0			0
$659$			20.8038i			0.810403i	0.914227	+	0.405201i	$0.132799\pi$
$659$			20.8038i			0.810403i	−0.914227	+	0.405201i	$0.867201\pi$
$660$		−	12.9282i		−	0.503230i
$661$	13.6077	−	7.85641i	0.529278	−	0.305579i	−0.211444	−	0.977390i	$-0.567817\pi$
$661$	13.6077	−	7.85641i	0.529278	−	0.305579i	0.740722	+	0.671811i	$0.234483\pi$
$662$	−5.60770	+	5.60770i	−0.217949	+	0.217949i
$663$	−2.59808	+	4.50000i	−0.100901	+	0.174766i
$664$	17.0718	−	17.0718i	0.662514	−	0.662514i
$665$		0			0
$666$		0			0
$667$	28.0526	+	16.1962i	1.08620	+	0.627118i
$668$	9.00000	+	5.19615i	0.348220	+	0.201045i
$669$	8.89230	+	15.4019i	0.343796	+	0.595473i
$670$	1.26795	−	4.73205i	0.0489852	−	0.182815i
$671$	−9.46410			−0.365358
$672$		0			0
$673$	49.1769			1.89563			0.947815	−	0.318820i	$-0.103286\pi$
$673$	49.1769			1.89563			0.947815	+	0.318820i	$0.103286\pi$
$674$		0			0
$675$	2.59808	+	4.50000i	0.100000	+	0.173205i
$676$	49.8564	+	28.7846i	1.91755	+	1.10710i
$677$	−3.99038	−	2.30385i	−0.153363	−	0.0885441i	0.421355	−	0.906896i	$-0.361555\pi$
$677$	−3.99038	−	2.30385i	−0.153363	−	0.0885441i	−0.574718	+	0.818352i	$0.694888\pi$
$678$	−3.46410	+	0.928203i	−0.133038	+	0.0356474i
$679$		0			0
$680$	−0.928203	+	0.928203i	−0.0355950	+	0.0355950i
$681$	−2.89230	+	5.00962i	−0.110833	+	0.191969i
$682$	22.3923	−	22.3923i	0.857446	−	0.857446i
$683$	23.6603	−	13.6603i	0.905334	−	0.522695i	0.0264074	−	0.999651i	$-0.491593\pi$
$683$	23.6603	−	13.6603i	0.905334	−	0.522695i	0.878927	+	0.476956i	$0.158260\pi$
$684$		0			0
$685$		−	0.392305i		−	0.0149892i
$686$		0			0
$687$		−	26.7846i		−	1.02190i
$688$	6.92820	−	4.00000i	0.264135	−	0.152499i
$689$	−11.1962	+	6.46410i	−0.426539	+	0.246263i
$690$	9.46410	+	9.46410i	0.360292	+	0.360292i
$691$	23.3205	−	40.3923i	0.887154	−	1.53660i	0.0439291	−	0.999035i	$-0.486012\pi$
$691$	23.3205	−	40.3923i	0.887154	−	1.53660i	0.843225	−	0.537561i	$-0.180654\pi$
$692$	−20.3205	−	35.1962i	−0.772470	−	1.33796i
$693$		0			0
$694$	−5.21539	−	19.4641i	−0.197974	−	0.738847i
$695$	−6.00000	−	3.46410i	−0.227593	−	0.131401i
$696$	28.0526	+	7.51666i	1.06333	+	0.284918i
$697$	0.803848	+	1.39230i	0.0304479	+	0.0527373i
$698$	−40.0526	−	10.7321i	−1.51601	−	0.406214i
$699$	39.7128			1.50208
$700$		0			0
$701$	3.78461			0.142943			0.0714714	−	0.997443i	$-0.477231\pi$
$701$	3.78461			0.142943			0.0714714	+	0.997443i	$0.477231\pi$
$702$	−45.8827	−	12.2942i	−1.73173	−	0.464016i
$703$	−7.60770	−	13.1769i	−0.286930	−	0.496977i
$704$	14.9282	+	25.8564i	0.562628	+	0.974500i
$705$	2.59808	+	1.50000i	0.0978492	+	0.0564933i
$706$	4.90192	+	18.2942i	0.184486	+	0.688512i
$707$		0			0
$708$	10.3923	−	6.00000i	0.390567	−	0.225494i
$709$	−10.5000	+	18.1865i	−0.394336	+	0.683010i	−0.993016	−	0.117978i	$-0.962359\pi$
$709$	−10.5000	+	18.1865i	−0.394336	+	0.683010i	0.598680	+	0.800988i	$0.295692\pi$
$710$	0.535898	+	0.535898i	0.0201119	+	0.0201119i
$711$		0			0
$712$	−25.8564	+	6.92820i	−0.969010	+	0.259645i
$713$			32.7846i			1.22779i
$714$		0			0
$715$		−	24.1244i		−	0.902200i
$716$	28.7846			1.07573
$717$	41.9711	−	24.2321i	1.56744	−	0.904963i
$718$	−9.32051	+	9.32051i	−0.347838	+	0.347838i
$719$	22.7321	−	39.3731i	0.847762	−	1.46837i	−0.0354380	−	0.999372i	$-0.511283\pi$
$719$	22.7321	−	39.3731i	0.847762	−	1.46837i	0.883200	−	0.468996i	$-0.155384\pi$
$720$		0			0
$721$		0			0
$722$	−23.2224	+	6.22243i	−0.864249	+	0.231575i
$723$	6.58846	+	3.80385i	0.245027	+	0.141467i
$724$	−12.9282	+	22.3923i	−0.480473	+	0.832203i
$725$	−2.96410	−	5.13397i	−0.110084	−	0.190671i
$726$	1.85641	−	6.92820i	0.0688977	−	0.257130i
$727$	34.3923			1.27554			0.637770	−	0.770227i	$-0.279857\pi$
$727$	34.3923			1.27554			0.637770	+	0.770227i	$0.279857\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−0.339746	+	1.26795i	−0.0125746	+	0.0469289i
$731$	0.464102	+	0.803848i	0.0171654	+	0.0297314i
$732$	4.39230	−	7.60770i	0.162344	−	0.281189i
$733$	15.9904	+	9.23205i	0.590618	+	0.340994i	0.765342	−	0.643624i	$-0.222570\pi$
$733$	15.9904	+	9.23205i	0.590618	+	0.340994i	−0.174724	+	0.984618i	$0.555903\pi$
$734$	49.3468	−	13.2224i	1.82142	−	0.488049i
$735$		0			0
$736$	−29.8564	−	8.00000i	−1.10052	−	0.294884i
$737$	6.46410	−	11.1962i	0.238108	−	0.412416i
$738$		0			0
$739$	6.69615	−	3.86603i	0.246322	−	0.142214i	−0.371757	−	0.928330i	$-0.621245\pi$
$739$	6.69615	−	3.86603i	0.246322	−	0.142214i	0.618079	+	0.786116i	$0.287911\pi$
$740$	5.07180			0.186443
$741$		−	67.1769i		−	2.46781i
$742$		0			0
$743$		−	9.60770i		−	0.352472i	−0.984348	−	0.176236i	$-0.943608\pi$
$743$		−	9.60770i		−	0.352472i	0.984348	−	0.176236i	$-0.0563922\pi$
$744$	7.60770	+	28.3923i	0.278912	+	1.04091i
$745$	14.6603	−	8.46410i	0.537110	−	0.310101i
$746$	−24.3923	−	24.3923i	−0.893066	−	0.893066i
$747$		0			0
$748$	−3.00000	+	1.73205i	−0.109691	+	0.0633300i
$749$		0			0
$750$	−0.633975	−	2.36603i	−0.0231495	−	0.0863950i
$751$	4.83975	+	2.79423i	0.176605	+	0.101963i	0.585697	−	0.810530i	$-0.300821\pi$
$751$	4.83975	+	2.79423i	0.176605	+	0.101963i	−0.409092	+	0.912493i	$0.634154\pi$
$752$	−6.92820			−0.252646
$753$	−1.60770	−	2.78461i	−0.0585877	−	0.101477i
$754$	52.3468	+	14.0263i	1.90636	+	0.510807i
$755$	4.80385			0.174830
$756$		0			0
$757$	10.1436			0.368675			0.184338	−	0.982863i	$-0.440986\pi$
$757$	10.1436			0.368675			0.184338	+	0.982863i	$0.440986\pi$
$758$	−36.0526	−	9.66025i	−1.30949	−	0.350876i
$759$	17.6603	+	30.5885i	0.641027	+	1.11029i
$760$	4.39230	−	16.3923i	0.159326	−	0.594611i
$761$	5.41154	+	3.12436i	0.196168	+	0.113258i	0.594867	−	0.803824i	$-0.297205\pi$
$761$	5.41154	+	3.12436i	0.196168	+	0.113258i	−0.398699	+	0.917082i	$0.630538\pi$
$762$	5.41154	+	20.1962i	0.196040	+	0.731629i
$763$		0			0
$764$	3.19615	+	5.53590i	0.115633	+	0.200282i
$765$		0			0
$766$	−20.5359	−	20.5359i	−0.741992	−	0.741992i
$767$	19.3923	−	11.1962i	0.700216	−	0.404270i
$768$	−27.7128			−1.00000
$769$		−	18.0000i		−	0.649097i	−0.945869	−	0.324548i	$-0.894788\pi$
$769$		−	18.0000i		−	0.649097i	0.945869	−	0.324548i	$-0.105212\pi$
$770$		0			0
$771$			10.3923i			0.374270i
$772$		−	5.07180i		−	0.182538i
$773$	10.7942	−	6.23205i	0.388241	−	0.224151i	−0.293156	−	0.956064i	$-0.594706\pi$
$773$	10.7942	−	6.23205i	0.388241	−	0.224151i	0.681398	+	0.731913i	$0.261372\pi$
$774$		0			0
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$	14.7846	+	14.7846i	0.530737	+	0.530737i
$777$		0			0
$778$	−9.36603	+	2.50962i	−0.335788	+	0.0899742i
$779$	−18.0000	−	10.3923i	−0.644917	−	0.372343i
$780$	19.3923	+	11.1962i	0.694356	+	0.400887i
$781$	1.00000	+	1.73205i	0.0357828	+	0.0619777i
$782$	0.928203	−	3.46410i	0.0331925	−	0.123876i
$783$	−30.8038			−1.10084
$784$		0			0
$785$	−19.8564			−0.708706
$786$	6.00000	−	22.3923i	0.214013	−	0.798707i
$787$	7.66987	+	13.2846i	0.273401	+	0.473545i	0.969731	−	0.244177i	$-0.0785179\pi$
$787$	7.66987	+	13.2846i	0.273401	+	0.473545i	−0.696329	+	0.717723i	$0.745185\pi$
$788$	−36.9282	−	21.3205i	−1.31551	−	0.759512i
$789$	6.80385	+	3.92820i	0.242223	+	0.139848i
$790$	3.63397	−	0.973721i	0.129291	−	0.0346434i
$791$		0			0
$792$		0			0
$793$	8.19615	−	14.1962i	0.291054	−	0.504120i
$794$	5.53590	−	5.53590i	0.196462	−	0.196462i
$795$	−3.00000	+	1.73205i	−0.106399	+	0.0614295i
$796$			6.92820i			0.245564i
$797$		−	40.1769i		−	1.42314i	−0.702616	−	0.711570i	$-0.747985\pi$
$797$		−	40.1769i		−	1.42314i	0.702616	−	0.711570i	$-0.252015\pi$
$798$		0			0
$799$		−	0.803848i		−	0.0284381i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$		0			0
$802$	−23.9282	−	23.9282i	−0.844934	−	0.844934i
$803$	−1.73205	+	3.00000i	−0.0611227	+	0.105868i
$804$	6.00000	+	10.3923i	0.211604	+	0.366508i
$805$		0			0
$806$	14.1962	+	52.9808i	0.500038	+	1.86617i
$807$	18.0000	+	10.3923i	0.633630	+	0.365826i
$808$	−6.24871	+	23.3205i	−0.219829	+	0.820413i
$809$	2.96410	+	5.13397i	0.104212	+	0.180501i	0.913416	−	0.407027i	$-0.133435\pi$
$809$	2.96410	+	5.13397i	0.104212	+	0.180501i	−0.809204	+	0.587528i	$0.800101\pi$
$810$	−12.2942	−	3.29423i	−0.431975	−	0.115747i
$811$	−42.9282			−1.50741			−0.753707	−	0.657211i	$-0.771736\pi$
$811$	−42.9282			−1.50741			−0.753707	+	0.657211i	$0.771736\pi$
$812$		0			0
$813$	4.39230			0.154045
$814$	12.9282	+	3.46410i	0.453133	+	0.121417i
$815$	−10.3923	−	18.0000i	−0.364027	−	0.630512i
$816$		−	3.21539i		−	0.112561i
$817$	−10.3923	−	6.00000i	−0.363581	−	0.209913i
$818$	11.6603	+	43.5167i	0.407691	+	1.52152i
$819$		0			0
$820$	6.00000	−	3.46410i	0.209529	−	0.120972i
$821$	6.89230	−	11.9378i	0.240543	−	0.416633i	−0.720326	−	0.693636i	$-0.756008\pi$
$821$	6.89230	−	11.9378i	0.240543	−	0.416633i	0.960869	+	0.277003i	$0.0893411\pi$
$822$	0.679492	+	0.679492i	0.0237000	+	0.0237000i
$823$	−21.5885	+	12.4641i	−0.752526	+	0.434471i	−0.826606	−	0.562781i	$-0.809731\pi$
$823$	−21.5885	+	12.4641i	−0.752526	+	0.434471i	0.0740797	+	0.997252i	$0.476398\pi$
$824$	−12.5885	−	46.9808i	−0.438540	−	1.63665i
$825$		−	6.46410i		−	0.225051i
$826$		0			0
$827$		−	41.8564i		−	1.45549i	−0.685848	−	0.727745i	$-0.740568\pi$
$827$		−	41.8564i		−	1.45549i	0.685848	−	0.727745i	$-0.259432\pi$
$828$		0			0
$829$	41.7846	−	24.1244i	1.45124	−	0.837874i	0.452688	−	0.891669i	$-0.350465\pi$
$829$	41.7846	−	24.1244i	1.45124	−	0.837874i	0.998552	+	0.0537957i	$0.0171320\pi$
$830$	8.53590	−	8.53590i	0.296285	−	0.296285i
$831$	−21.4641	+	37.1769i	−0.744581	+	1.28965i
$832$	−51.7128			−1.79282
$833$		0			0
$834$	16.3923	−	4.39230i	0.567619	−	0.152093i
$835$	4.50000	+	2.59808i	0.155729	+	0.0899101i
$836$	22.3923	−	38.7846i	0.774454	−	1.34139i
$837$	−15.5885	−	27.0000i	−0.538816	−	0.933257i
$838$	−8.87564	+	33.1244i	−0.306604	+	1.14426i
$839$	16.3923			0.565925			0.282963	−	0.959131i	$-0.408683\pi$
$839$	16.3923			0.565925			0.282963	+	0.959131i	$0.408683\pi$
$840$		0			0
$841$	6.14359			0.211848
$842$	6.95448	−	25.9545i	0.239667	−	0.894451i
$843$	5.13397	+	8.89230i	0.176823	+	0.306267i
$844$	7.19615	−	12.4641i	0.247702	−	0.429032i
$845$	24.9282	+	14.3923i	0.857556	+	0.495110i
$846$		0			0
$847$		0			0
$848$	4.00000	−	6.92820i	0.137361	−	0.237915i
$849$	10.5000	−	18.1865i	0.360359	−	0.624160i
$850$	−0.464102	+	0.464102i	−0.0159186	+	0.0159186i
$851$	−12.0000	+	6.92820i	−0.411355	+	0.237496i
$852$	−1.85641			−0.0635994
$853$		−	38.7846i		−	1.32796i	−0.747750	−	0.663980i	$-0.768866\pi$
$853$		−	38.7846i		−	1.32796i	0.747750	−	0.663980i	$-0.231134\pi$
$854$		0			0
$855$		0			0
$856$	−50.2487	+	13.4641i	−1.71747	+	0.460194i
$857$	−1.98076	+	1.14359i	−0.0676615	+	0.0390644i	−0.533449	−	0.845832i	$-0.679104\pi$
$857$	−1.98076	+	1.14359i	−0.0676615	+	0.0390644i	0.465788	+	0.884897i	$0.345771\pi$
$858$	41.7846	+	41.7846i	1.42650	+	1.42650i
$859$	−7.85641	+	13.6077i	−0.268057	+	0.464289i	−0.968360	−	0.249557i	$-0.919715\pi$
$859$	−7.85641	+	13.6077i	−0.268057	+	0.464289i	0.700303	+	0.713846i	$0.253048\pi$
$860$	3.46410	−	2.00000i	0.118125	−	0.0681994i
$861$		0			0
$862$	6.43782	+	24.0263i	0.219273	+	0.818338i
$863$	−10.5167	−	6.07180i	−0.357991	−	0.206686i	0.310208	−	0.950669i	$-0.399601\pi$
$863$	−10.5167	−	6.07180i	−0.357991	−	0.206686i	−0.668199	+	0.743982i	$0.732935\pi$
$864$	28.3923	−	7.60770i	0.965926	−	0.258819i
$865$	−10.1603	−	17.5981i	−0.345459	−	0.598353i
$866$	5.66025	+	1.51666i	0.192343	+	0.0515382i
$867$	−29.0718			−0.987330
$868$		0			0
$869$	9.92820			0.336791
$870$	14.0263	+	3.75833i	0.475535	+	0.127419i
$871$	11.1962	+	19.3923i	0.379367	+	0.657083i
$872$	43.5167	+	11.6603i	1.47366	+	0.394866i
$873$		0			0
$874$	12.0000	+	44.7846i	0.405906	+	1.51486i
$875$		0			0
$876$	−1.60770	−	2.78461i	−0.0543190	−	0.0940832i
$877$	−1.19615	+	2.07180i	−0.0403912	+	0.0699596i	−0.885514	−	0.464612i	$-0.846194\pi$
$877$	−1.19615	+	2.07180i	−0.0403912	+	0.0699596i	0.845123	+	0.534572i	$0.179527\pi$
$878$	−15.7128	−	15.7128i	−0.530282	−	0.530282i
$879$	−21.4808	+	12.4019i	−0.724528	+	0.418307i
$880$	7.46410	+	12.9282i	0.251615	+	0.435810i
$881$			42.9282i			1.44629i	0.690697	+	0.723144i	$0.257304\pi$
$881$			42.9282i			1.44629i	−0.690697	+	0.723144i	$0.742696\pi$
$882$		0			0
$883$			44.3923i			1.49392i	0.664869	+	0.746960i	$0.268487\pi$
$883$			44.3923i			1.49392i	−0.664869	+	0.746960i	$0.731513\pi$
$884$		−	6.00000i		−	0.201802i
$885$	5.19615	−	3.00000i	0.174667	−	0.100844i
$886$	−26.0000	+	26.0000i	−0.873487	+	0.873487i
$887$	−7.73205	+	13.3923i	−0.259617	+	0.449670i	−0.966139	−	0.258021i	$-0.916930\pi$
$887$	−7.73205	+	13.3923i	−0.259617	+	0.449670i	0.706522	+	0.707691i	$0.250263\pi$
$888$	−8.78461	+	8.78461i	−0.294792	+	0.294792i
$889$		0			0
$890$	−12.9282	+	3.46410i	−0.433354	+	0.116117i
$891$	−29.0885	−	16.7942i	−0.974500	−	0.562628i
$892$	−17.7846	−	10.2679i	−0.595473	−	0.343796i
$893$	5.19615	+	9.00000i	0.173883	+	0.301174i
$894$	−10.7321	+	40.0526i	−0.358933	+	1.33956i
$895$	14.3923			0.481082
$896$		0			0
$897$	−61.1769			−2.04264
$898$	−0.705771	+	2.63397i	−0.0235519	+	0.0878969i
$899$	17.7846	+	30.8038i	0.593150	+	1.02737i
$900$		0			0
$901$	0.803848	+	0.464102i	0.0267800	+	0.0154615i
$902$	17.6603	−	4.73205i	0.588022	−	0.157560i
$903$		0			0
$904$	2.92820	−	2.92820i	0.0973906	−	0.0973906i
$905$	−6.46410	+	11.1962i	−0.214874	+	0.372173i
$906$	−8.32051	+	8.32051i	−0.276430	+	0.276430i
$907$	10.0526	−	5.80385i	0.333790	−	0.192714i	−0.323733	−	0.946149i	$-0.604938\pi$
$907$	10.0526	−	5.80385i	0.333790	−	0.192714i	0.657522	+	0.753435i	$0.271605\pi$
$908$		−	6.67949i		−	0.221667i
$909$		0			0
$910$		0			0
$911$		−	28.2487i		−	0.935922i	−0.883749	−	0.467961i	$-0.844989\pi$
$911$		−	28.2487i		−	0.935922i	0.883749	−	0.467961i	$-0.155011\pi$
$912$	20.7846	+	36.0000i	0.688247	+	1.19208i
$913$	27.5885	−	15.9282i	0.913045	−	0.527147i
$914$	27.4641	+	27.4641i	0.908432	+	0.908432i
$915$	2.19615	−	3.80385i	0.0726026	−	0.125751i
$916$	15.4641	+	26.7846i	0.510948	+	0.884988i
$917$		0			0
$918$	0.882686	+	3.29423i	0.0291330	+	0.108726i
$919$	−32.5526	−	18.7942i	−1.07381	−	0.619964i	−0.144590	−	0.989492i	$-0.546186\pi$
$919$	−32.5526	−	18.7942i	−1.07381	−	0.619964i	−0.929220	+	0.369527i	$0.879520\pi$
$920$	−14.9282	−	4.00000i	−0.492168	−	0.131876i
$921$	1.50000	+	2.59808i	0.0494267	+	0.0856095i
$922$	37.8564	+	10.1436i	1.24673	+	0.334061i
$923$	−3.46410			−0.114022
$924$		0			0
$925$	2.53590			0.0833798
$926$	−6.00000	−	1.60770i	−0.197172	−	0.0528321i
$927$		0			0
$928$	−32.3923	+	8.67949i	−1.06333	+	0.284918i
$929$	36.8038	+	21.2487i	1.20750	+	0.697148i	0.962211	−	0.272304i	$-0.0877855\pi$
$929$	36.8038	+	21.2487i	1.20750	+	0.697148i	0.245284	+	0.969451i	$0.421119\pi$
$930$	3.80385	+	14.1962i	0.124733	+	0.465510i
$931$		0			0
$932$	−39.7128	+	22.9282i	−1.30084	+	0.751038i
$933$	17.1962	−	29.7846i	0.562977	−	0.975104i
$934$	22.5167	+	22.5167i	0.736768	+	0.736768i
$935$	−1.50000	+	0.866025i	−0.0490552	+	0.0283221i
$936$		0			0
$937$			4.60770i			0.150527i	0.997164	+	0.0752634i	$0.0239798\pi$
$937$			4.60770i			0.150527i	−0.997164	+	0.0752634i	$0.976020\pi$
$938$		0			0
$939$		−	42.3731i		−	1.38279i
$940$	−3.46410			−0.112987
$941$	44.1962	−	25.5167i	1.44075	−	0.831819i	0.442853	−	0.896594i	$-0.353966\pi$
$941$	44.1962	−	25.5167i	1.44075	−	0.831819i	0.997900	+	0.0647746i	$0.0206329\pi$
$942$	34.3923	−	34.3923i	1.12056	−	1.12056i
$943$	−9.46410	+	16.3923i	−0.308194	+	0.533807i
$944$	−6.92820	+	12.0000i	−0.225494	+	0.390567i
$945$		0			0
$946$	10.1962	−	2.73205i	0.331506	−	0.0888266i
$947$	−16.2679	−	9.39230i	−0.528637	−	0.305209i	0.211824	−	0.977308i	$-0.432060\pi$
$947$	−16.2679	−	9.39230i	−0.528637	−	0.305209i	−0.740461	+	0.672099i	$0.765393\pi$
$948$	−4.60770	+	7.98076i	−0.149651	+	0.259203i
$949$	−3.00000	−	5.19615i	−0.0973841	−	0.168674i
$950$	2.19615	−	8.19615i	0.0712526	−	0.265918i
$951$	29.3205			0.950783
$952$		0			0
$953$	−13.3205			−0.431494			−0.215747	−	0.976449i	$-0.569219\pi$
$953$	−13.3205			−0.431494			−0.215747	+	0.976449i	$0.569219\pi$
$954$		0			0
$955$	1.59808	+	2.76795i	0.0517125	+	0.0895687i
$956$	−27.9808	+	48.4641i	−0.904963	+	1.56744i
$957$	33.1865	+	19.1603i	1.07277	+	0.619363i
$958$	−50.7846	+	13.6077i	−1.64078	+	0.439645i
$959$		0			0
$960$	−13.8564			−0.447214
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−16.3923	+	16.3923i	−0.528509	+	0.528509i
$963$		0			0
$964$	−8.78461			−0.282933
$965$		−	2.53590i		−	0.0816335i
$966$		0			0
$967$			31.1769i			1.00258i	0.865279	+	0.501291i	$0.167141\pi$
$967$			31.1769i			1.00258i	−0.865279	+	0.501291i	$0.832859\pi$
$968$	2.14359	+	8.00000i	0.0688977	+	0.257130i
$969$	−4.17691	+	2.41154i	−0.134182	+	0.0774699i
$970$	7.39230	+	7.39230i	0.237353	+	0.237353i
$971$	−13.3923	+	23.1962i	−0.429780	+	0.744400i	−0.996853	−	0.0792670i	$-0.974742\pi$
$971$	−13.3923	+	23.1962i	−0.429780	+	0.744400i	0.567074	+	0.823667i	$0.308075\pi$
$972$		0			0
$973$		0			0
$974$	10.5359	+	39.3205i	0.337592	+	1.25991i
$975$	9.69615	+	5.59808i	0.310525	+	0.179282i
$976$			10.1436i			0.324689i
$977$	−22.1244	−	38.3205i	−0.707821	−	1.22598i	−0.965664	−	0.259795i	$-0.916345\pi$
$977$	−22.1244	−	38.3205i	−0.707821	−	1.22598i	0.257843	−	0.966187i	$-0.416988\pi$
$978$	49.1769	+	13.1769i	1.57250	+	0.421351i
$979$	−35.3205			−1.12885
$980$		0			0
$981$		0			0
$982$	46.6147	+	12.4904i	1.48754	+	0.398584i
$983$	1.79423	+	3.10770i	0.0572270	+	0.0991201i	0.893220	−	0.449621i	$-0.148441\pi$
$983$	1.79423	+	3.10770i	0.0572270	+	0.0991201i	−0.835993	+	0.548741i	$0.815107\pi$
$984$	−4.39230	+	16.3923i	−0.140022	+	0.522568i
$985$	−18.4641	−	10.6603i	−0.588315	−	0.339664i
$986$	−1.00704	−	3.75833i	−0.0320707	−	0.119690i
$987$		0			0
$988$	38.7846	+	67.1769i	1.23390	+	2.13718i
$989$	−5.46410	+	9.46410i	−0.173748	+	0.300941i
$990$		0			0
$991$	13.1436	−	7.58846i	0.417520	−	0.241055i	−0.276496	−	0.961015i	$-0.589173\pi$
$991$	13.1436	−	7.58846i	0.417520	−	0.241055i	0.694016	+	0.719960i	$0.255840\pi$
$992$	−24.0000	−	24.0000i	−0.762001	−	0.762001i
$993$		−	9.71281i		−	0.308227i
$994$		0			0
$995$			3.46410i			0.109819i
$996$			29.5692i			0.936937i
$997$	−10.7942	+	6.23205i	−0.341857	+	0.197371i	−0.661093	−	0.750304i	$-0.729907\pi$
$997$	−10.7942	+	6.23205i	−0.341857	+	0.197371i	0.319236	+	0.947675i	$0.396574\pi$
$998$	−5.58846	+	5.58846i	−0.176900	+	0.176900i
$999$	6.58846	−	11.4115i	0.208450	−	0.361045i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.b.411.2		4
4.3	odd	2		980.2.o.c.411.1		4
7.2	even	3		140.2.g.b.111.2	yes	4
7.3	odd	6		980.2.o.c.31.2		4
7.4	even	3		980.2.o.d.31.2		4
7.5	odd	6		140.2.g.a.111.2	yes	4
7.6	odd	2		980.2.o.a.411.2		4
21.2	odd	6		1260.2.c.b.811.3		4
21.5	even	6		1260.2.c.a.811.3		4
28.3	even	6	inner	980.2.o.b.31.2		4
28.11	odd	6		980.2.o.a.31.2		4
28.19	even	6		140.2.g.b.111.1	yes	4
28.23	odd	6		140.2.g.a.111.1	✓	4
28.27	even	2		980.2.o.d.411.1		4
35.2	odd	12		700.2.c.f.699.1		4
35.9	even	6		700.2.g.g.251.3		4
35.12	even	12		700.2.c.e.699.1		4
35.19	odd	6		700.2.g.f.251.3		4
35.23	odd	12		700.2.c.c.699.4		4
35.33	even	12		700.2.c.b.699.4		4
56.5	odd	6		2240.2.k.a.1791.2		4
56.19	even	6		2240.2.k.b.1791.4		4
56.37	even	6		2240.2.k.b.1791.3		4
56.51	odd	6		2240.2.k.a.1791.1		4
84.23	even	6		1260.2.c.a.811.4		4
84.47	odd	6		1260.2.c.b.811.4		4
140.19	even	6		700.2.g.g.251.4		4
140.23	even	12		700.2.c.e.699.2		4
140.47	odd	12		700.2.c.c.699.3		4
140.79	odd	6		700.2.g.f.251.4		4
140.103	odd	12		700.2.c.f.699.2		4
140.107	even	12		700.2.c.b.699.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.1	✓	4	28.23	odd	6
140.2.g.a.111.2	yes	4	7.5	odd	6
140.2.g.b.111.1	yes	4	28.19	even	6
140.2.g.b.111.2	yes	4	7.2	even	3
700.2.c.b.699.3		4	140.107	even	12
700.2.c.b.699.4		4	35.33	even	12
700.2.c.c.699.3		4	140.47	odd	12
700.2.c.c.699.4		4	35.23	odd	12
700.2.c.e.699.1		4	35.12	even	12
700.2.c.e.699.2		4	140.23	even	12
700.2.c.f.699.1		4	35.2	odd	12
700.2.c.f.699.2		4	140.103	odd	12
700.2.g.f.251.3		4	35.19	odd	6
700.2.g.f.251.4		4	140.79	odd	6
700.2.g.g.251.3		4	35.9	even	6
700.2.g.g.251.4		4	140.19	even	6
980.2.o.a.31.2		4	28.11	odd	6
980.2.o.a.411.2		4	7.6	odd	2
980.2.o.b.31.2		4	28.3	even	6	inner
980.2.o.b.411.2		4	1.1	even	1	trivial
980.2.o.c.31.2		4	7.3	odd	6
980.2.o.c.411.1		4	4.3	odd	2
980.2.o.d.31.2		4	7.4	even	3
980.2.o.d.411.1		4	28.27	even	2
1260.2.c.a.811.3		4	21.5	even	6
1260.2.c.a.811.4		4	84.23	even	6
1260.2.c.b.811.3		4	21.2	odd	6
1260.2.c.b.811.4		4	84.47	odd	6
2240.2.k.a.1791.1		4	56.51	odd	6
2240.2.k.a.1791.2		4	56.5	odd	6
2240.2.k.b.1791.3		4	56.37	even	6
2240.2.k.b.1791.4		4	56.19	even	6

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:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 - 1.36603i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-1.00000 + 1.00000i) q^{10} +(-3.23205 + 1.86603i) q^{11} -3.46410i q^{12} -6.46410i q^{13} -1.73205i q^{15} +(2.00000 + 3.46410i) q^{16} +(-0.401924 + 0.232051i) q^{17} +(3.00000 - 5.19615i) q^{19} +(1.00000 + 1.73205i) q^{20} +(1.36603 + 5.09808i) q^{22} +(-4.73205 - 2.73205i) q^{23} +(-4.73205 - 1.26795i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-8.83013 - 2.36603i) q^{26} +5.19615 q^{27} -5.92820 q^{29} +(-2.36603 - 0.633975i) q^{30} +(-3.00000 - 5.19615i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-5.59808 - 3.23205i) q^{33} +(0.169873 + 0.633975i) q^{34} +(1.26795 - 2.19615i) q^{37} +(-6.00000 - 6.00000i) q^{38} +(9.69615 - 5.59808i) q^{39} +(2.73205 - 0.732051i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +7.46410 q^{44} +(-5.46410 + 5.46410i) q^{46} +(-0.866025 + 1.50000i) q^{47} +(-3.46410 + 6.00000i) q^{48} +(1.36603 - 0.366025i) q^{50} +(-0.696152 - 0.401924i) q^{51} +(-6.46410 + 11.1962i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(1.90192 - 7.09808i) q^{54} +3.73205 q^{55} +10.3923 q^{57} +(-2.16987 + 8.09808i) q^{58} +(1.73205 + 3.00000i) q^{59} +(-1.73205 + 3.00000i) q^{60} +(2.19615 + 1.26795i) q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(-3.23205 + 5.59808i) q^{65} +(-6.46410 + 6.46410i) q^{66} +(-3.00000 + 1.73205i) q^{67} +0.928203 q^{68} -9.46410i q^{69} -0.535898i q^{71} +(0.803848 - 0.464102i) q^{73} +(-2.53590 - 2.53590i) q^{74} +(-0.866025 + 1.50000i) q^{75} +(-10.3923 + 6.00000i) q^{76} +(-4.09808 - 15.2942i) q^{78} +(-2.30385 - 1.33013i) q^{79} -4.00000i q^{80} +(4.50000 + 7.79423i) q^{81} +(-4.73205 - 1.26795i) q^{82} -8.53590 q^{83} +0.464102 q^{85} +(-2.73205 - 0.732051i) q^{86} +(-5.13397 - 8.89230i) q^{87} +(2.73205 - 10.1962i) q^{88} +(8.19615 + 4.73205i) q^{89} +(5.46410 + 9.46410i) q^{92} +(5.19615 - 9.00000i) q^{93} +(1.73205 + 1.73205i) q^{94} +(-5.19615 + 3.00000i) q^{95} +(6.92820 + 6.92820i) q^{96} -7.39230i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8	\( 4 q - 2 q^{2} + 6 q^{6} - 8 q^{8} - 4 q^{10} - 6 q^{11} + 8 q^{16} - 12 q^{17} + 12 q^{19} + 4 q^{20} + 2 q^{22} - 12 q^{23} - 12 q^{24} + 2 q^{25} - 18 q^{26} + 4 q^{29} - 6 q^{30} - 12 q^{31} + 8 q^{32} - 12 q^{33} + 18 q^{34} + 12 q^{37} - 24 q^{38} + 18 q^{39} + 4 q^{40} + 16 q^{44} - 8 q^{46} + 2 q^{50} + 18 q^{51} - 12 q^{52} - 4 q^{53} + 18 q^{54} + 8 q^{55} - 26 q^{58} - 12 q^{61} - 12 q^{62} - 6 q^{65} - 12 q^{66} - 12 q^{67} - 24 q^{68} + 24 q^{73} - 24 q^{74} - 6 q^{78} - 30 q^{79} + 18 q^{81} - 12 q^{82} - 48 q^{83} - 12 q^{85} - 4 q^{86} - 24 q^{87} + 4 q^{88} + 12 q^{89} + 8 q^{92}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^6 - 8 * q^8 - 4 * q^10 - 6 * q^11 + 8 * q^16 - 12 * q^17 + 12 * q^19 + 4 * q^20 + 2 * q^22 - 12 * q^23 - 12 * q^24 + 2 * q^25 - 18 * q^26 + 4 * q^29 - 6 * q^30 - 12 * q^31 + 8 * q^32 - 12 * q^33 + 18 * q^34 + 12 * q^37 - 24 * q^38 + 18 * q^39 + 4 * q^40 + 16 * q^44 - 8 * q^46 + 2 * q^50 + 18 * q^51 - 12 * q^52 - 4 * q^53 + 18 * q^54 + 8 * q^55 - 26 * q^58 - 12 * q^61 - 12 * q^62 - 6 * q^65 - 12 * q^66 - 12 * q^67 - 24 * q^68 + 24 * q^73 - 24 * q^74 - 6 * q^78 - 30 * q^79 + 18 * q^81 - 12 * q^82 - 48 * q^83 - 12 * q^85 - 4 * q^86 - 24 * q^87 + 4 * q^88 + 12 * q^89 + 8 * q^92

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