LMFDB - Embedded newform 980.2.o.d.31.2

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			31.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	980.31
Dual form			980.2.o.d.411.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(0.866025 - 1.50000i) q^{3} +2.00000i q^{4} +(0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(0.866025 - 1.50000i) q^{3} +2.00000i q^{4} +(0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(1.36603 + 0.366025i) q^{10} +(3.23205 + 1.86603i) q^{11} +(3.00000 + 1.73205i) q^{12} -6.46410i q^{13} -1.73205i q^{15} -4.00000 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} +(1.26795 + 4.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(6.46410 - 6.46410i) q^{26} +5.19615 q^{27} -5.92820 q^{29} +(1.73205 - 1.73205i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(5.59808 - 3.23205i) q^{33} +(0.169873 + 0.633975i) q^{34} +(1.26795 + 2.19615i) q^{37} +(-2.19615 + 8.19615i) q^{38} +(-9.69615 - 5.59808i) q^{39} +(-0.732051 + 2.73205i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +(-3.73205 + 6.46410i) q^{44} +(7.46410 + 2.00000i) 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} +12.9282 q^{52} +(-1.00000 + 1.73205i) q^{53} +(5.19615 + 5.19615i) q^{54} +3.73205 q^{55} +10.3923 q^{57} +(-5.92820 - 5.92820i) q^{58} +(1.73205 - 3.00000i) q^{59} +3.46410 q^{60} +(-2.19615 + 1.26795i) q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(-3.23205 - 5.59808i) q^{65} +(8.83013 + 2.36603i) q^{66} +(3.00000 + 1.73205i) q^{67} +(-0.464102 + 0.803848i) q^{68} -9.46410i q^{69} -0.535898i q^{71} +(-0.803848 - 0.464102i) q^{73} +(-0.928203 + 3.46410i) 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} +(-3.46410 + 2.00000i) q^{80} +(4.50000 - 7.79423i) q^{81} +(3.46410 - 3.46410i) q^{82} -8.53590 q^{83} +0.464102 q^{85} +(2.00000 - 2.00000i) q^{86} +(-5.13397 + 8.89230i) q^{87} +(-10.1962 + 2.73205i) q^{88} +(-8.19615 + 4.73205i) q^{89} +(5.46410 + 9.46410i) q^{92} +(5.19615 + 9.00000i) q^{93} +(0.633975 - 2.36603i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-9.46410 + 2.53590i) q^{96} -7.39230i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 6 q^{6} - 8 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 + 6 * q^6 - 8 * q^8	$ 4 q + 4 q^{2} + 6 q^{6} - 8 q^{8} + 2 q^{10} + 6 q^{11} + 12 q^{12} - 16 q^{16} + 12 q^{17} + 12 q^{19} + 4 q^{20} + 2 q^{22} + 12 q^{23} + 12 q^{24} + 2 q^{25} + 12 q^{26} + 4 q^{29} - 12 q^{31} - 16 q^{32} + 12 q^{33} + 18 q^{34} + 12 q^{37} + 12 q^{38} - 18 q^{39} + 4 q^{40} - 8 q^{44} + 16 q^{46} + 2 q^{50} - 18 q^{51} + 24 q^{52} - 4 q^{53} + 8 q^{55} + 4 q^{58} + 12 q^{61} - 12 q^{62} - 6 q^{65} + 18 q^{66} + 12 q^{67} + 12 q^{68} - 24 q^{73} + 24 q^{74} - 6 q^{78} + 30 q^{79} + 18 q^{81} - 48 q^{83} - 12 q^{85} + 8 q^{86} - 24 q^{87} - 20 q^{88} - 12 q^{89} + 8 q^{92} + 6 q^{94} - 24 q^{96}+O(q^{100}) $ 4 * q + 4 * q^2 + 6 * q^6 - 8 * q^8 + 2 * q^10 + 6 * q^11 + 12 * q^12 - 16 * q^16 + 12 * q^17 + 12 * q^19 + 4 * q^20 + 2 * q^22 + 12 * q^23 + 12 * q^24 + 2 * q^25 + 12 * q^26 + 4 * q^29 - 12 * q^31 - 16 * q^32 + 12 * q^33 + 18 * q^34 + 12 * q^37 + 12 * q^38 - 18 * q^39 + 4 * q^40 - 8 * q^44 + 16 * q^46 + 2 * q^50 - 18 * q^51 + 24 * q^52 - 4 * q^53 + 8 * q^55 + 4 * q^58 + 12 * q^61 - 12 * q^62 - 6 * q^65 + 18 * q^66 + 12 * q^67 + 12 * q^68 - 24 * q^73 + 24 * q^74 - 6 * q^78 + 30 * q^79 + 18 * q^81 - 48 * q^83 - 12 * q^85 + 8 * q^86 - 24 * q^87 - 20 * q^88 - 12 * q^89 + 8 * q^92 + 6 * q^94 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$2$	1.00000	+	1.00000i	0.707107	+	0.707107i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i	1.00000			$0$
$4$			2.00000i			1.00000i
$5$	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
$10$	1.36603	+	0.366025i	0.431975	+	0.115747i
$11$	3.23205	+	1.86603i	0.974500	+	0.562628i	0.900605	−	0.434638i	$-0.143124\pi$
$11$	3.23205	+	1.86603i	0.974500	+	0.562628i	0.0738948	+	0.997266i	$0.476457\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$		−	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
$16$	−4.00000			−1.00000
$17$	0.401924	+	0.232051i	0.0974808	+	0.0562806i	0.547948	−	0.836512i	$-0.315409\pi$
$17$	0.401924	+	0.232051i	0.0974808	+	0.0562806i	−0.450467	+	0.892793i	$0.648743\pi$
$18$		0			0
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	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	$-0.473737\pi$
$23$	4.73205	−	2.73205i	0.986701	−	0.569672i	0.904286	+	0.426926i	$0.140404\pi$
$24$	1.26795	+	4.73205i	0.258819	+	0.965926i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	6.46410	−	6.46410i	1.26771	−	1.26771i
$27$	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	$0.685532\pi$
$30$	1.73205	−	1.73205i	0.316228	−	0.316228i
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	−4.00000	−	4.00000i	−0.707107	−	0.707107i
$33$	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	0.951226	−	0.308494i	$-0.0998250\pi$
$37$	1.26795	+	2.19615i	0.208450	+	0.361045i	−0.742777	+	0.669539i	$0.766492\pi$
$38$	−2.19615	+	8.19615i	−0.356263	+	1.32959i
$39$	−9.69615	−	5.59808i	−1.55263	−	0.896410i
$40$	−0.732051	+	2.73205i	−0.115747	+	0.431975i
$41$		−	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	$-0.0487319\pi$
$44$	−3.73205	+	6.46410i	−0.562628	+	0.974500i
$45$		0			0
$46$	7.46410	+	2.00000i	1.10052	+	0.294884i
$47$	−0.866025	−	1.50000i	−0.126323	−	0.218797i	0.795926	−	0.605393i	$-0.206984\pi$
$47$	−0.866025	−	1.50000i	−0.126323	−	0.218797i	−0.922249	+	0.386596i	$0.873651\pi$
$48$	−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
$52$	12.9282			1.79282
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	−0.926497	−	0.376303i	$-0.877195\pi$
$53$	−1.00000	+	1.73205i	−0.137361	+	0.237915i	0.789136	+	0.614218i	$0.210529\pi$
$54$	5.19615	+	5.19615i	0.707107	+	0.707107i
$55$	3.73205			0.503230
$56$		0			0
$57$	10.3923			1.37649
$58$	−5.92820	−	5.92820i	−0.778411	−	0.778411i
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	−0.730974	−	0.682406i	$-0.760934\pi$
$59$	1.73205	−	3.00000i	0.225494	−	0.390567i	0.956467	+	0.291839i	$0.0942671\pi$
$60$	3.46410			0.447214
$61$	−2.19615	+	1.26795i	−0.281189	+	0.162344i	−0.633961	−	0.773365i	$-0.718572\pi$
$61$	−2.19615	+	1.26795i	−0.281189	+	0.162344i	0.352773	+	0.935709i	$0.385239\pi$
$62$	−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
$66$	8.83013	+	2.36603i	1.08691	+	0.291238i
$67$	3.00000	+	1.73205i	0.366508	+	0.211604i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	3.00000	+	1.73205i	0.366508	+	0.211604i	−0.305424	+	0.952217i	$0.598798\pi$
$68$	−0.464102	+	0.803848i	−0.0562806	+	0.0974808i
$69$		−	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	$-0.350632\pi$
$73$	−0.803848	−	0.464102i	−0.0940832	−	0.0543190i	−0.546303	+	0.837587i	$0.683965\pi$
$74$	−0.928203	+	3.46410i	−0.107901	+	0.402694i
$75$	−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	$-0.618852\pi$
$79$	2.30385	−	1.33013i	0.259203	−	0.149651i	0.623971	+	0.781448i	$0.285518\pi$
$80$	−3.46410	+	2.00000i	−0.387298	+	0.223607i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	3.46410	−	3.46410i	0.382546	−	0.382546i
$83$	−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
$86$	2.00000	−	2.00000i	0.215666	−	0.215666i
$87$	−5.13397	+	8.89230i	−0.550420	+	0.953355i
$88$	−10.1962	+	2.73205i	−1.08691	+	0.291238i
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.866946	−	0.498402i	$-0.833920\pi$
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.00184433	+	0.999998i	$0.500587\pi$
$90$		0			0
$91$		0			0
$92$	5.46410	+	9.46410i	0.569672	+	0.986701i
$93$	5.19615	+	9.00000i	0.538816	+	0.933257i
$94$	0.633975	−	2.36603i	0.0653895	−	0.244037i
$95$	5.19615	+	3.00000i	0.533114	+	0.307794i
$96$	−9.46410	+	2.53590i	−0.965926	+	0.258819i
$97$		−	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
$100$	1.73205	+	1.00000i	0.173205	+	0.100000i
$101$	−7.39230	−	4.26795i	−0.735562	−	0.424677i	0.0848916	−	0.996390i	$-0.472946\pi$
$101$	−7.39230	−	4.26795i	−0.735562	−	0.424677i	−0.820453	+	0.571713i	$0.806279\pi$
$102$	1.09808	+	0.294229i	0.108726	+	0.0291330i
$103$	−8.59808	−	14.8923i	−0.847194	−	1.46738i	−0.883702	−	0.468049i	$-0.844957\pi$
$103$	−8.59808	−	14.8923i	−0.847194	−	1.46738i	0.0365089	−	0.999333i	$-0.488376\pi$
$104$	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	−0.540990	+	0.841029i	$0.681950\pi$
$107$	−15.9282	+	9.19615i	−1.53984	+	0.889026i	−0.998847	+	0.0479966i	$0.984716\pi$
$108$			10.3923i			1.00000i
$109$	−7.96410	+	13.7942i	−0.762823	+	1.32125i	0.178568	+	0.983928i	$0.442854\pi$
$109$	−7.96410	+	13.7942i	−0.762823	+	1.32125i	−0.941390	+	0.337320i	$0.890480\pi$
$110$	3.73205	+	3.73205i	0.355837	+	0.355837i
$111$	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	$0.521938\pi$
$114$	10.3923	+	10.3923i	0.973329	+	0.973329i
$115$	2.73205	−	4.73205i	0.254765	−	0.441266i
$116$		−	11.8564i		−	1.10084i
$117$		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
$122$	−3.46410	−	0.928203i	−0.313625	−	0.0840356i
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$	−10.3923	−	6.00000i	−0.933257	−	0.538816i
$125$		−	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	$0.876365\pi$
$128$	8.00000	−	8.00000i	0.707107	−	0.707107i
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$	2.36603	−	8.83013i	0.207514	−	0.774453i
$131$	4.73205	+	8.19615i	0.413441	+	0.716101i	0.995263	−	0.0972148i	$-0.0309934\pi$
$131$	4.73205	+	8.19615i	0.413441	+	0.716101i	−0.581822	+	0.813316i	$0.697660\pi$
$132$	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
$136$	−1.26795	+	0.339746i	−0.108726	+	0.0291330i
$137$	0.196152	−	0.339746i	0.0167584	−	0.0290265i	−0.857525	−	0.514443i	$-0.827999\pi$
$137$	0.196152	−	0.339746i	0.0167584	−	0.0290265i	0.874283	+	0.485417i	$0.161332\pi$
$138$	9.46410	−	9.46410i	0.805638	−	0.805638i
$139$	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
$142$	0.535898	−	0.535898i	0.0449716	−	0.0449716i
$143$	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	−0.970715	−	0.240234i	$-0.922776\pi$
$149$	−8.46410	−	14.6603i	−0.693406	−	1.20101i	0.277309	−	0.960781i	$-0.410557\pi$
$150$	0.633975	−	2.36603i	0.0517638	−	0.193185i
$151$	4.16025	+	2.40192i	0.338557	+	0.195466i	0.659634	−	0.751587i	$-0.270711\pi$
$151$	4.16025	+	2.40192i	0.338557	+	0.195466i	−0.321077	+	0.947053i	$0.604045\pi$
$152$	−16.3923	−	4.39230i	−1.32959	−	0.356263i
$153$		0			0
$154$		0			0
$155$			6.00000i			0.481932i
$156$	11.1962	−	19.3923i	0.896410	−	1.55263i
$157$	−17.1962	−	9.92820i	−1.37240	−	0.792357i	−0.381172	−	0.924504i	$-0.624480\pi$
$157$	−17.1962	−	9.92820i	−1.37240	−	0.792357i	−0.991230	+	0.132147i	$0.957813\pi$
$158$	3.63397	+	0.973721i	0.289103	+	0.0774650i
$159$	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	$-0.969375\pi$
$163$	−18.0000	+	10.3923i	−1.40987	+	0.813988i	−0.414494	+	0.910052i	$0.636041\pi$
$164$	6.92820			0.541002
$165$	3.23205	−	5.59808i	0.251615	−	0.435810i
$166$	−8.53590	−	8.53590i	−0.662514	−	0.662514i
$167$	−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
$170$	0.464102	+	0.464102i	0.0355950	+	0.0355950i
$171$		0			0
$172$	4.00000			0.304997
$173$	−17.5981	+	10.1603i	−1.33796	+	0.772470i	−0.986504	−	0.163736i	$-0.947646\pi$
$173$	−17.5981	+	10.1603i	−1.33796	+	0.772470i	−0.351453	+	0.936206i	$0.614312\pi$
$174$	−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
$178$	−12.9282	−	3.46410i	−0.969010	−	0.259645i
$179$	12.4641	+	7.19615i	0.931611	+	0.537866i	0.887321	−	0.461153i	$-0.152564\pi$
$179$	12.4641	+	7.19615i	0.931611	+	0.537866i	0.0442901	+	0.999019i	$0.485897\pi$
$180$		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
$184$	−4.00000	+	14.9282i	−0.294884	+	1.10052i
$185$	2.19615	+	1.26795i	0.161464	+	0.0932215i
$186$	−3.80385	+	14.1962i	−0.278912	+	1.04091i
$187$	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	$-0.629777\pi$
$191$	2.76795	−	1.59808i	0.200282	−	0.115633i	0.596787	+	0.802400i	$0.296444\pi$
$192$	−12.0000	−	6.92820i	−0.866025	−	0.500000i
$193$	1.26795	−	2.19615i	0.0912690	−	0.158083i	−0.816776	−	0.576954i	$-0.804241\pi$
$193$	1.26795	−	2.19615i	0.0912690	−	0.158083i	0.908045	+	0.418872i	$0.137574\pi$
$194$	7.39230	−	7.39230i	0.530737	−	0.530737i
$195$	−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	−0.920864	−	0.389885i	$-0.872515\pi$
$199$	−1.73205	+	3.00000i	−0.122782	+	0.212664i	0.798082	+	0.602549i	$0.205848\pi$
$200$	0.732051	+	2.73205i	0.0517638	+	0.193185i
$201$	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
$206$	6.29423	−	23.4904i	0.438540	−	1.63665i
$207$		0			0
$208$			25.8564i			1.79282i
$209$			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	$0.920325\pi$
$212$	−3.46410	−	2.00000i	−0.237915	−	0.137361i
$213$	−0.803848	−	0.464102i	−0.0550787	−	0.0317997i
$214$	−25.1244	−	6.73205i	−1.71747	−	0.460194i
$215$	−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
$220$			7.46410i			0.503230i
$221$	1.50000	−	2.59808i	0.100901	−	0.174766i
$222$	4.39230	+	4.39230i	0.294792	+	0.294792i
$223$	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
$226$	−1.46410	−	1.46410i	−0.0973906	−	0.0973906i
$227$	1.66987	−	2.89230i	0.110833	−	0.191969i	−0.805273	−	0.592904i	$-0.797981\pi$
$227$	1.66987	−	2.89230i	0.110833	−	0.191969i	0.916107	+	0.400935i	$0.131315\pi$
$228$			20.7846i			1.37649i
$229$	13.3923	−	7.73205i	0.884988	−	0.510948i	0.0126885	−	0.999919i	$-0.495961\pi$
$229$	13.3923	−	7.73205i	0.884988	−	0.510948i	0.872300	+	0.488971i	$0.162628\pi$
$230$	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	0.947320	+	0.320289i	$0.103780\pi$
$233$	11.4641	+	19.8564i	0.751038	+	1.30084i	−0.196282	+	0.980548i	$0.562887\pi$
$234$		0			0
$235$	−1.50000	−	0.866025i	−0.0978492	−	0.0564933i
$236$	6.00000	+	3.46410i	0.390567	+	0.225494i
$237$		−	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	$-0.360101\pi$
$240$			6.92820i			0.447214i
$241$	−3.80385	−	2.19615i	−0.245027	−	0.141467i	0.372458	−	0.928049i	$-0.378515\pi$
$241$	−3.80385	−	2.19615i	−0.245027	−	0.141467i	−0.617485	+	0.786583i	$0.711848\pi$
$242$	−1.07180	+	4.00000i	−0.0688977	+	0.257130i
$243$		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
$248$	−4.39230	−	16.3923i	−0.278912	−	1.04091i
$249$	−7.39230	+	12.8038i	−0.468468	+	0.811411i
$250$	1.00000	−	1.00000i	0.0632456	−	0.0632456i
$251$	−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
$254$	−8.53590	+	8.53590i	−0.535590	+	0.535590i
$255$	0.401924	−	0.696152i	0.0251694	−	0.0435948i
$256$	16.0000			1.00000
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	−0.653231	−	0.757159i	$-0.726587\pi$
$257$	−5.19615	+	3.00000i	−0.324127	+	0.187135i	0.329104	+	0.944294i	$0.393253\pi$
$258$	−1.26795	−	4.73205i	−0.0789391	−	0.294605i
$259$		0			0
$260$	11.1962	−	6.46410i	0.694356	−	0.400887i
$261$		0			0
$262$	−3.46410	+	12.9282i	−0.214013	+	0.798707i
$263$	−3.92820	−	2.26795i	−0.242223	−	0.139848i	0.373975	−	0.927439i	$-0.377995\pi$
$263$	−3.92820	−	2.26795i	−0.242223	−	0.139848i	−0.616198	+	0.787591i	$0.711328\pi$
$264$	−4.73205	+	17.6603i	−0.291238	+	1.08691i
$265$			2.00000i			0.122859i
$266$		0			0
$267$			16.3923i			1.00319i
$268$	−3.46410	+	6.00000i	−0.211604	+	0.366508i
$269$	−10.3923	−	6.00000i	−0.633630	−	0.365826i	0.148527	−	0.988908i	$-0.452547\pi$
$269$	−10.3923	−	6.00000i	−0.633630	−	0.365826i	−0.782157	+	0.623082i	$0.785880\pi$
$270$	7.09808	+	1.90192i	0.431975	+	0.115747i
$271$	1.26795	+	2.19615i	0.0770224	+	0.133407i	0.901964	−	0.431811i	$-0.142125\pi$
$271$	1.26795	+	2.19615i	0.0770224	+	0.133407i	−0.824942	+	0.565218i	$0.808792\pi$
$272$	−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
$276$	18.9282			1.13934
$277$	12.3923	−	21.4641i	0.744581	−	1.28965i	−0.205809	−	0.978592i	$-0.565982\pi$
$277$	12.3923	−	21.4641i	0.744581	−	1.28965i	0.950390	−	0.311061i	$-0.100684\pi$
$278$	6.92820	+	6.92820i	0.415526	+	0.415526i
$279$		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	$0.443418\pi$
$282$	−3.00000	−	3.00000i	−0.178647	−	0.178647i
$283$	−6.06218	+	10.5000i	−0.360359	+	0.624160i	−0.988020	−	0.154327i	$-0.950679\pi$
$283$	−6.06218	+	10.5000i	−0.360359	+	0.624160i	0.627661	+	0.778487i	$0.284012\pi$
$284$	1.07180			0.0635994
$285$	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
$290$	−8.09808	−	2.16987i	−0.475535	−	0.127419i
$291$	−11.0885	−	6.40192i	−0.650017	−	0.375287i
$292$	0.928203	−	1.60770i	0.0543190	−	0.0940832i
$293$			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
$296$	−6.92820	−	1.85641i	−0.402694	−	0.107901i
$297$	16.7942	+	9.69615i	0.974500	+	0.562628i
$298$	6.19615	−	23.1244i	0.358933	−	1.33956i
$299$	−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
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$	−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
$310$	−6.00000	+	6.00000i	−0.340777	+	0.340777i
$311$	−9.92820	+	17.1962i	−0.562977	+	0.975104i	0.434258	+	0.900789i	$0.357011\pi$
$311$	−9.92820	+	17.1962i	−0.562977	+	0.975104i	−0.997235	+	0.0743158i	$0.976323\pi$
$312$	30.5885	−	8.19615i	1.73173	−	0.464016i
$313$	21.1865	−	12.2321i	1.19753	−	0.691396i	0.237529	−	0.971380i	$-0.423663\pi$
$313$	21.1865	−	12.2321i	1.19753	−	0.691396i	0.960005	+	0.279984i	$0.0903292\pi$
$314$	−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	0.999603	−	0.0281863i	$-0.00897316\pi$
$317$	8.46410	+	14.6603i	0.475391	+	0.823402i	−0.524211	+	0.851588i	$0.675640\pi$
$318$	−1.26795	+	4.73205i	−0.0711031	+	0.265360i
$319$	−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
$324$	15.5885	+	9.00000i	0.866025	+	0.500000i
$325$	−5.59808	−	3.23205i	−0.310525	−	0.179282i
$326$	−28.3923	−	7.60770i	−1.57250	−	0.421351i
$327$	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	$-0.617415\pi$
$331$	4.85641	−	2.80385i	0.266932	−	0.154113i	0.627493	+	0.778622i	$0.284081\pi$
$332$		−	17.0718i		−	0.936937i
$333$		0			0
$334$	−5.19615	−	5.19615i	−0.284321	−	0.284321i
$335$	3.46410			0.189264
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−28.7846	−	28.7846i	−1.56568	−	1.56568i
$339$	−1.26795	+	2.19615i	−0.0688655	+	0.119279i
$340$			0.928203i			0.0503389i
$341$	−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
$346$	−27.7583	−	7.43782i	−1.49230	−	0.399860i
$347$	−12.3397	−	7.12436i	−0.662432	−	0.382455i	0.130771	−	0.991413i	$-0.458255\pi$
$347$	−12.3397	−	7.12436i	−0.662432	−	0.382455i	−0.793203	+	0.608957i	$0.791588\pi$
$348$	−17.7846	−	10.2679i	−0.953355	−	0.550420i
$349$		−	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
$352$	−5.46410	−	20.3923i	−0.291238	−	1.08691i
$353$	11.5981	+	6.69615i	0.617303	+	0.356400i	0.775818	−	0.630956i	$-0.217337\pi$
$353$	11.5981	+	6.69615i	0.617303	+	0.356400i	−0.158515	+	0.987357i	$0.550671\pi$
$354$	2.19615	−	8.19615i	0.116724	−	0.435621i
$355$	−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	$-0.587564\pi$
$359$	8.07180	−	4.66025i	0.426013	−	0.245959i	0.697647	+	0.716442i	$0.254231\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	12.9282	−	12.9282i	0.679491	−	0.679491i
$363$	5.07180			0.266200
$364$		0			0
$365$	−0.928203			−0.0485844
$366$	−4.39230	+	4.39230i	−0.229589	+	0.229589i
$367$	18.0622	−	31.2846i	0.942838	−	1.63304i	0.182815	−	0.983147i	$-0.441479\pi$
$367$	18.0622	−	31.2846i	0.942838	−	1.63304i	0.760023	−	0.649896i	$-0.225188\pi$
$368$	−18.9282	+	10.9282i	−0.986701	+	0.569672i
$369$		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	0.987247	+	0.159198i	$0.0508908\pi$
$373$	12.1962	+	21.1244i	0.631493	+	1.09378i	−0.355754	+	0.934580i	$0.615776\pi$
$374$	−0.633975	+	2.36603i	−0.0327820	+	0.122344i
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$	4.73205	+	1.26795i	0.244037	+	0.0653895i
$377$			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	$-0.237084\pi$
$380$	−6.00000	+	10.3923i	−0.307794	+	0.533114i
$381$	12.8038	+	7.39230i	0.655961	+	0.378719i
$382$	4.36603	+	1.16987i	0.223385	+	0.0598559i
$383$	10.2679	+	17.7846i	0.524668	+	0.908751i	0.999587	+	0.0287220i	$0.00914375\pi$
$383$	10.2679	+	17.7846i	0.524668	+	0.908751i	−0.474920	+	0.880029i	$0.657523\pi$
$384$	−5.07180	−	18.9282i	−0.258819	−	0.965926i
$385$		0			0
$386$	3.46410	−	0.928203i	0.176318	−	0.0472443i
$387$		0			0
$388$	14.7846			0.750575
$389$	−3.42820	+	5.93782i	−0.173817	+	0.301060i	−0.939751	−	0.341859i	$-0.888943\pi$
$389$	−3.42820	+	5.93782i	−0.173817	+	0.301060i	0.765934	+	0.642919i	$0.222277\pi$
$390$	−11.1962	−	11.1962i	−0.566939	−	0.566939i
$391$	2.53590			0.128246
$392$		0			0
$393$	16.3923			0.826882
$394$	21.3205	+	21.3205i	1.07411	+	1.07411i
$395$	1.33013	−	2.30385i	0.0669260	−	0.115919i
$396$		0			0
$397$	−4.79423	+	2.76795i	−0.240615	+	0.138919i	−0.615460	−	0.788168i	$-0.711030\pi$
$397$	−4.79423	+	2.76795i	−0.240615	+	0.138919i	0.374844	+	0.927088i	$0.377696\pi$
$398$	−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	0.993195	+	0.116465i	$0.0371562\pi$
$401$	11.9641	+	20.7224i	0.597459	+	1.03483i	−0.395736	+	0.918364i	$0.629511\pi$
$402$	8.19615	+	2.19615i	0.408787	+	0.109534i
$403$	33.5885	+	19.3923i	1.67316	+	0.966000i
$404$	8.53590	−	14.7846i	0.424677	−	0.735562i
$405$		−	9.00000i		−	0.447214i
$406$		0			0
$407$			9.46410i			0.469118i
$408$	−0.588457	+	2.19615i	−0.0291330	+	0.108726i
$409$	27.5885	+	15.9282i	1.36416	+	0.787599i	0.990175	−	0.139835i	$-0.0446573\pi$
$409$	27.5885	+	15.9282i	1.36416	+	0.787599i	0.373987	+	0.927434i	$0.377991\pi$
$410$	1.26795	−	4.73205i	0.0626195	−	0.233699i
$411$	−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
$416$	−25.8564	+	25.8564i	−1.26771	+	1.26771i
$417$	6.00000	−	10.3923i	0.293821	−	0.508913i
$418$	−22.3923	+	22.3923i	−1.09524	+	1.09524i
$419$	−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	$0.346772\pi$
$422$	−7.19615	+	7.19615i	−0.350303	+	0.350303i
$423$		0			0
$424$	−1.46410	−	5.46410i	−0.0711031	−	0.265360i
$425$	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
$430$	0.732051	−	2.73205i	0.0353026	−	0.131751i
$431$	15.2321	+	8.79423i	0.733702	+	0.423603i	0.819775	−	0.572686i	$-0.194098\pi$
$431$	15.2321	+	8.79423i	0.733702	+	0.423603i	−0.0860729	+	0.996289i	$0.527432\pi$
$432$	−20.7846			−1.00000
$433$			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
$436$	−27.5885	−	15.9282i	−1.32125	−	0.762823i
$437$	28.3923	+	16.3923i	1.35819	+	0.784150i
$438$	−2.19615	−	0.588457i	−0.104936	−	0.0281176i
$439$	7.85641	+	13.6077i	0.374966	+	0.649460i	0.990322	−	0.138789i	$-0.0443211\pi$
$439$	7.85641	+	13.6077i	0.374966	+	0.649460i	−0.615356	+	0.788249i	$0.710988\pi$
$440$	−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	$-0.454752\pi$
$443$	22.5167	−	13.0000i	1.06980	−	0.617649i	0.928126	+	0.372265i	$0.121419\pi$
$444$			8.78461i			0.416899i
$445$	−4.73205	+	8.19615i	−0.224321	+	0.388535i
$446$	10.2679	+	10.2679i	0.486201	+	0.486201i
$447$	−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
$452$		−	2.92820i		−	0.137731i
$453$	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	−0.984905	−	0.173096i	$-0.944623\pi$
$457$	−13.7321	−	23.7846i	−0.642358	−	1.11260i	0.342547	−	0.939501i	$-0.388711\pi$
$458$	21.1244	+	5.66025i	0.987076	+	0.264486i
$459$	2.08846	+	1.20577i	0.0974808	+	0.0562806i
$460$	9.46410	+	5.46410i	0.441266	+	0.254765i
$461$			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	$-0.0325446\pi$
$464$	23.7128			1.10084
$465$	9.00000	+	5.19615i	0.417365	+	0.240966i
$466$	−8.39230	+	31.3205i	−0.388766	+	1.45089i
$467$	−11.2583	−	19.5000i	−0.520973	−	0.902352i	−0.999703	−	0.0243897i	$-0.992236\pi$
$467$	−11.2583	−	19.5000i	−0.520973	−	0.902352i	0.478729	−	0.877963i	$-0.341098\pi$
$468$		0			0
$469$		0			0
$470$	−0.633975	−	2.36603i	−0.0292431	−	0.109137i
$471$	−29.7846	+	17.1962i	−1.37240	+	0.792357i
$472$	2.53590	+	9.46410i	0.116724	+	0.435621i
$473$	3.73205	−	6.46410i	0.171600	−	0.297220i
$474$	4.60770	−	4.60770i	0.211638	−	0.211638i
$475$	6.00000			0.275299
$476$		0			0
$477$		0			0
$478$	27.9808	−	27.9808i	1.27981	−	1.27981i
$479$	−18.5885	+	32.1962i	−0.849328	+	1.47108i	0.0324804	+	0.999472i	$0.489659\pi$
$479$	−18.5885	+	32.1962i	−0.849328	+	1.47108i	−0.881809	+	0.471607i	$0.843674\pi$
$480$	−6.92820	+	6.92820i	−0.316228	+	0.316228i
$481$	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	$-0.107189\pi$
$487$	24.9282	+	14.3923i	1.12960	+	0.652178i	0.185769	+	0.982593i	$0.440522\pi$
$488$	1.85641	−	6.92820i	0.0840356	−	0.313625i
$489$			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	$0.720254\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	−2.38269	−	1.37564i	−0.107311	−	0.0619559i
$494$	52.9808	+	14.1962i	2.38372	+	0.638715i
$495$		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	$-0.626746\pi$
$499$	4.83975	−	2.79423i	0.216657	−	0.125087i	0.604401	+	0.796680i	$0.293412\pi$
$500$	2.00000			0.0894427
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$	−1.85641	−	1.85641i	−0.0828555	−	0.0828555i
$503$	−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
$506$	20.3923	+	20.3923i	0.906549	+	0.906549i
$507$	−24.9282	+	43.1769i	−1.10710	+	1.91755i
$508$	−17.0718			−0.757438
$509$	1.60770	−	0.928203i	0.0712598	−	0.0411419i	−0.463947	−	0.885863i	$-0.653567\pi$
$509$	1.60770	−	0.928203i	0.0712598	−	0.0411419i	0.535207	+	0.844721i	$0.320234\pi$
$510$	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
$514$	−8.19615	−	2.19615i	−0.361517	−	0.0968681i
$515$	−14.8923	−	8.59808i	−0.656233	−	0.378877i
$516$	3.46410	−	6.00000i	0.152499	−	0.264135i
$517$		−	6.46410i		−	0.284291i
$518$		0			0
$519$			35.1962i			1.54494i
$520$	17.6603	+	4.73205i	0.774453	+	0.207514i
$521$	29.7846	+	17.1962i	1.30489	+	0.753377i	0.981238	−	0.192800i	$-0.0617568\pi$
$521$	29.7846	+	17.1962i	1.30489	+	0.753377i	0.323649	+	0.946177i	$0.395090\pi$
$522$		0			0
$523$	12.1244	+	21.0000i	0.530161	+	0.918266i	0.999381	+	0.0351845i	$0.0112019\pi$
$523$	12.1244	+	21.0000i	0.530161	+	0.918266i	−0.469220	+	0.883081i	$0.655465\pi$
$524$	−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
$528$	−22.3923	+	12.9282i	−0.974500	+	0.562628i
$529$	3.42820	−	5.93782i	0.149052	−	0.258166i
$530$	−2.00000	+	2.00000i	−0.0868744	+	0.0868744i
$531$		0			0
$532$		0			0
$533$	−22.3923			−0.969918
$534$	−16.3923	+	16.3923i	−0.709364	+	0.709364i
$535$	−9.19615	+	15.9282i	−0.397584	+	0.688636i
$536$	−9.46410	+	2.53590i	−0.408787	+	0.109534i
$537$	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	0.958455	+	0.285245i	$0.0920750\pi$
$541$	16.8923	+	29.2583i	0.726257	+	1.25791i	−0.232198	+	0.972669i	$0.574592\pi$
$542$	−0.928203	+	3.46410i	−0.0398697	+	0.148796i
$543$	−19.3923	−	11.1962i	−0.832203	−	0.480473i
$544$	−0.679492	−	2.53590i	−0.0291330	−	0.108726i
$545$			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	$-0.100582\pi$
$548$	0.679492	+	0.392305i	0.0290265	+	0.0167584i
$549$		0			0
$550$	5.09808	+	1.36603i	0.217383	+	0.0582475i
$551$	−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
$556$			13.8564i			0.587643i
$557$	−2.92820	+	5.07180i	−0.124072	+	0.214899i	−0.921370	−	0.388687i	$-0.872929\pi$
$557$	−2.92820	+	5.07180i	−0.124072	+	0.214899i	0.797298	+	0.603586i	$0.206262\pi$
$558$		0			0
$559$	−12.9282			−0.546805
$560$		0			0
$561$	3.00000			0.126660
$562$	5.92820	+	5.92820i	0.250066	+	0.250066i
$563$	−21.5885	+	37.3923i	−0.909845	+	1.57590i	−0.0955667	+	0.995423i	$0.530466\pi$
$563$	−21.5885	+	37.3923i	−0.909845	+	1.57590i	−0.814278	+	0.580475i	$0.802867\pi$
$564$		−	6.00000i		−	0.252646i
$565$	−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	0.558910	−	0.829228i	$-0.311220\pi$
$569$	−10.4641	−	18.1244i	−0.438678	−	0.759813i	−0.997588	+	0.0694159i	$0.977886\pi$
$570$	14.1962	+	3.80385i	0.594611	+	0.159326i
$571$	−35.7846	−	20.6603i	−1.49754	−	0.864605i	−0.497543	−	0.867439i	$-0.665764\pi$
$571$	−35.7846	−	20.6603i	−1.49754	−	0.864605i	−0.999996	+	0.00283441i	$0.999098\pi$
$572$	41.7846	+	24.1244i	1.74710	+	1.00869i
$573$		−	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	$-0.342560\pi$
$577$	−1.20577	−	0.696152i	−0.0501969	−	0.0289812i	−0.524888	+	0.851171i	$0.675893\pi$
$578$	6.14359	−	22.9282i	0.255540	−	0.953688i
$579$	−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
$584$	2.53590	−	0.679492i	0.104936	−	0.0281176i
$585$		0			0
$586$	−14.3205	+	14.3205i	−0.591575	+	0.591575i
$587$	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
$590$	3.46410	−	3.46410i	0.142615	−	0.142615i
$591$	18.4641	−	31.9808i	0.759512	−	1.31551i
$592$	−5.07180	−	8.78461i	−0.208450	−	0.361045i
$593$	−20.3827	+	11.7679i	−0.837017	+	0.483252i	−0.856249	−	0.516563i	$-0.827211\pi$
$593$	−20.3827	+	11.7679i	−0.837017	+	0.483252i	0.0192324	+	0.999815i	$0.493878\pi$
$594$	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
$598$	12.9282	−	48.2487i	0.528674	−	1.97304i
$599$	12.2321	+	7.06218i	0.499788	+	0.288553i	0.728626	−	0.684912i	$-0.240159\pi$
$599$	12.2321	+	7.06218i	0.499788	+	0.288553i	−0.228838	+	0.973465i	$0.573493\pi$
$600$	4.73205	+	1.26795i	0.193185	+	0.0517638i
$601$		−	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
$604$	−4.80385	+	8.32051i	−0.195466	+	0.338557i
$605$	2.53590	+	1.46410i	0.103099	+	0.0595242i
$606$	−20.1962	−	5.41154i	−0.820413	−	0.219829i
$607$	−9.40192	−	16.2846i	−0.381612	−	0.660972i	0.609681	−	0.792647i	$-0.291298\pi$
$607$	−9.40192	−	16.2846i	−0.381612	−	0.660972i	−0.991293	+	0.131675i	$0.957964\pi$
$608$	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	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	1.73205	+	1.73205i	0.0698999	+	0.0698999i
$615$	−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	$0.558454\pi$
$618$	−29.7846	−	29.7846i	−1.19811	−	1.19811i
$619$	17.6603	−	30.5885i	0.709826	−	1.22945i	−0.255096	−	0.966916i	$-0.582107\pi$
$619$	17.6603	−	30.5885i	0.709826	−	1.22945i	0.964922	−	0.262538i	$-0.0845596\pi$
$620$	−12.0000			−0.481932
$621$	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
$626$	33.4186	+	8.95448i	1.33568	+	0.357893i
$627$	33.5885	+	19.3923i	1.34139	+	0.774454i
$628$	19.8564	−	34.3923i	0.792357	−	1.37240i
$629$			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	$0.820080\pi$
$632$	−1.94744	+	7.26795i	−0.0774650	+	0.289103i
$633$	10.7942	+	6.23205i	0.429032	+	0.247702i
$634$	−6.19615	+	23.1244i	−0.246081	+	0.918385i
$635$	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
$640$	2.92820	−	10.9282i	0.115747	−	0.431975i
$641$	2.46410	−	4.26795i	0.0973262	−	0.168574i	−0.813251	−	0.581913i	$-0.802304\pi$
$641$	2.46410	−	4.26795i	0.0973262	−	0.168574i	0.910577	+	0.413339i	$0.135638\pi$
$642$	−31.8564	+	31.8564i	−1.25727	+	1.25727i
$643$	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
$646$	−2.78461	+	2.78461i	−0.109559	+	0.109559i
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	−0.745622	−	0.666369i	$-0.767847\pi$
$647$	5.19615	−	9.00000i	0.204282	−	0.353827i	0.949904	+	0.312543i	$0.101181\pi$
$648$	6.58846	+	24.5885i	0.258819	+	0.965926i
$649$	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	−0.947240	−	0.320526i	$-0.896140\pi$
$653$	−19.1962	−	33.2487i	−0.751203	−	1.30112i	0.196036	−	0.980597i	$-0.437193\pi$
$654$	−10.0981	+	37.6865i	−0.394866	+	1.47366i
$655$	8.19615	+	4.73205i	0.320250	+	0.184897i
$656$			13.8564i			0.541002i
$657$		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	$0.867201\pi$
$660$	11.1962	+	6.46410i	0.435810	+	0.251615i
$661$	−13.6077	−	7.85641i	−0.529278	−	0.305579i	0.211444	−	0.977390i	$-0.432183\pi$
$661$	−13.6077	−	7.85641i	−0.529278	−	0.305579i	−0.740722	+	0.671811i	$0.765517\pi$
$662$	7.66025	+	2.05256i	0.297724	+	0.0797750i
$663$	−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
$668$		−	10.3923i		−	0.402090i
$669$	8.89230	−	15.4019i	0.343796	−	0.595473i
$670$	3.46410	+	3.46410i	0.133830	+	0.133830i
$671$	−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
$676$		−	57.5692i		−	2.21420i
$677$	3.99038	−	2.30385i	0.153363	−	0.0885441i	−0.421355	−	0.906896i	$-0.638445\pi$
$677$	3.99038	−	2.30385i	0.153363	−	0.0885441i	0.574718	+	0.818352i	$0.305112\pi$
$678$	−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
$682$	−30.5885	−	8.19615i	−1.17129	−	0.313847i
$683$	−23.6603	−	13.6603i	−0.905334	−	0.522695i	−0.0264074	−	0.999651i	$-0.508407\pi$
$683$	−23.6603	−	13.6603i	−0.905334	−	0.522695i	−0.878927	+	0.476956i	$0.841740\pi$
$684$		0			0
$685$		−	0.392305i		−	0.0149892i
$686$		0			0
$687$		−	26.7846i		−	1.02190i
$688$			8.00000i			0.304997i
$689$	11.1962	+	6.46410i	0.426539	+	0.246263i
$690$	3.46410	−	12.9282i	0.131876	−	0.492168i
$691$	23.3205	+	40.3923i	0.887154	+	1.53660i	0.843225	+	0.537561i	$0.180654\pi$
$691$	23.3205	+	40.3923i	0.887154	+	1.53660i	0.0439291	+	0.999035i	$0.486012\pi$
$692$	−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
$696$	−7.51666	−	28.0526i	−0.284918	−	1.06333i
$697$	0.803848	−	1.39230i	0.0304479	−	0.0527373i
$698$	29.3205	−	29.3205i	1.10980	−	1.10980i
$699$	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	$0.477231\pi$
$702$	33.5885	−	33.5885i	1.26771	−	1.26771i
$703$	−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	0.598680	−	0.800988i	$-0.295692\pi$
$709$	−10.5000	−	18.1865i	−0.394336	−	0.683010i	−0.993016	+	0.117978i	$0.962359\pi$
$710$	0.196152	−	0.732051i	0.00736147	−	0.0274734i
$711$		0			0
$712$	6.92820	−	25.8564i	0.259645	−	0.969010i
$713$			32.7846i			1.22779i
$714$		0			0
$715$		−	24.1244i		−	0.902200i
$716$	−14.3923	+	24.9282i	−0.537866	+	0.931611i
$717$	−41.9711	−	24.2321i	−1.56744	−	0.904963i
$718$	12.7321	+	3.41154i	0.475156	+	0.127318i
$719$	22.7321	+	39.3731i	0.847762	+	1.46837i	0.883200	+	0.468996i	$0.155384\pi$
$719$	22.7321	+	39.3731i	0.847762	+	1.46837i	−0.0354380	+	0.999372i	$0.511283\pi$
$720$		0			0
$721$		0			0
$722$	−23.2224	+	6.22243i	−0.864249	+	0.231575i
$723$	−6.58846	+	3.80385i	−0.245027	+	0.141467i
$724$	25.8564			0.960946
$725$	−2.96410	+	5.13397i	−0.110084	+	0.190671i
$726$	5.07180	+	5.07180i	0.188232	+	0.188232i
$727$	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
$730$	−0.928203	−	0.928203i	−0.0343543	−	0.0343543i
$731$	0.464102	−	0.803848i	0.0171654	−	0.0297314i
$732$	−8.78461			−0.324689
$733$	−15.9904	+	9.23205i	−0.590618	+	0.340994i	−0.765342	−	0.643624i	$-0.777430\pi$
$733$	−15.9904	+	9.23205i	−0.590618	+	0.340994i	0.174724	+	0.984618i	$0.444097\pi$
$734$	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	$-0.378755\pi$
$739$	−6.69615	−	3.86603i	−0.246322	−	0.142214i	−0.618079	+	0.786116i	$0.712089\pi$
$740$	−2.53590	+	4.39230i	−0.0932215	+	0.161464i
$741$		−	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	$-0.0563922\pi$
$744$	−28.3923	−	7.60770i	−1.04091	−	0.278912i
$745$	−14.6603	−	8.46410i	−0.537110	−	0.310101i
$746$	−8.92820	+	33.3205i	−0.326885	+	1.21995i
$747$		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	$-0.699179\pi$
$751$	−4.83975	+	2.79423i	−0.176605	+	0.101963i	0.409092	+	0.912493i	$0.365846\pi$
$752$	3.46410	+	6.00000i	0.126323	+	0.218797i
$753$	−1.60770	+	2.78461i	−0.0585877	+	0.101477i
$754$	−38.3205	+	38.3205i	−1.39555	+	1.39555i
$755$	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	$0.440986\pi$
$758$	26.3923	−	26.3923i	0.958612	−	0.958612i
$759$	17.6603	−	30.5885i	0.641027	−	1.11029i
$760$	−16.3923	+	4.39230i	−0.594611	+	0.159326i
$761$	−5.41154	+	3.12436i	−0.196168	+	0.113258i	−0.594867	−	0.803824i	$-0.702795\pi$
$761$	−5.41154	+	3.12436i	−0.196168	+	0.113258i	0.398699	+	0.917082i	$0.369462\pi$
$762$	5.41154	+	20.1962i	0.196040	+	0.731629i
$763$		0			0
$764$	3.19615	+	5.53590i	0.115633	+	0.200282i
$765$		0			0
$766$	−7.51666	+	28.0526i	−0.271588	+	1.01358i
$767$	−19.3923	−	11.1962i	−0.700216	−	0.404270i
$768$	13.8564	−	24.0000i	0.500000	−	0.866025i
$769$		−	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
$772$	4.39230	+	2.53590i	0.158083	+	0.0912690i
$773$	−10.7942	−	6.23205i	−0.388241	−	0.224151i	0.293156	−	0.956064i	$-0.405294\pi$
$773$	−10.7942	−	6.23205i	−0.388241	−	0.224151i	−0.681398	+	0.731913i	$0.738628\pi$
$774$		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
$780$		−	22.3923i		−	0.801773i
$781$	1.00000	−	1.73205i	0.0357828	−	0.0619777i
$782$	2.53590	+	2.53590i	0.0906835	+	0.0906835i
$783$	−30.8038			−1.10084
$784$		0			0
$785$	−19.8564			−0.708706
$786$	16.3923	+	16.3923i	0.584694	+	0.584694i
$787$	7.66987	−	13.2846i	0.273401	−	0.473545i	−0.696329	−	0.717723i	$-0.745185\pi$
$787$	7.66987	−	13.2846i	0.273401	−	0.473545i	0.969731	+	0.244177i	$0.0785179\pi$
$788$			42.6410i			1.51902i
$789$	−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
$794$	−7.56218	−	2.02628i	−0.268372	−	0.0719100i
$795$	3.00000	+	1.73205i	0.106399	+	0.0614295i
$796$	−6.00000	−	3.46410i	−0.212664	−	0.122782i
$797$		−	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
$800$	−5.46410	+	1.46410i	−0.193185	+	0.0517638i
$801$		0			0
$802$	−8.75833	+	32.6865i	−0.309267	+	1.15420i
$803$	−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
$808$	23.3205	−	6.24871i	0.820413	−	0.219829i
$809$	2.96410	−	5.13397i	0.104212	−	0.180501i	−0.809204	−	0.587528i	$-0.800101\pi$
$809$	2.96410	−	5.13397i	0.104212	−	0.180501i	0.913416	+	0.407027i	$0.133435\pi$
$810$	9.00000	−	9.00000i	0.316228	−	0.316228i
$811$	−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
$814$	−9.46410	+	9.46410i	−0.331717	+	0.331717i
$815$	−10.3923	+	18.0000i	−0.364027	+	0.630512i
$816$	−2.78461	+	1.60770i	−0.0974808	+	0.0562806i
$817$	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	0.960869	−	0.277003i	$-0.0893411\pi$
$821$	6.89230	+	11.9378i	0.240543	+	0.416633i	−0.720326	+	0.693636i	$0.756008\pi$
$822$	0.248711	−	0.928203i	0.00867480	−	0.0323748i
$823$	21.5885	+	12.4641i	0.752526	+	0.434471i	0.826606	−	0.562781i	$-0.190269\pi$
$823$	21.5885	+	12.4641i	0.752526	+	0.434471i	−0.0740797	+	0.997252i	$0.523602\pi$
$824$	46.9808	+	12.5885i	1.63665	+	0.438540i
$825$		−	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	$-0.649535\pi$
$829$	−41.7846	−	24.1244i	−1.45124	−	0.837874i	−0.998552	+	0.0537957i	$0.982868\pi$
$830$	−11.6603	−	3.12436i	−0.404733	−	0.108448i
$831$	−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
$836$	−44.7846			−1.54891
$837$	−15.5885	+	27.0000i	−0.538816	+	0.933257i
$838$	−24.2487	−	24.2487i	−0.837658	−	0.837658i
$839$	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
$842$	19.0000	+	19.0000i	0.654783	+	0.654783i
$843$	5.13397	−	8.89230i	0.176823	−	0.306267i
$844$	−14.3923			−0.495404
$845$	−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
$850$	0.633975	+	0.169873i	0.0217451	+	0.00582660i
$851$	12.0000	+	6.92820i	0.411355	+	0.237496i
$852$	0.928203	−	1.60770i	0.0317997	−	0.0550787i
$853$		−	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
$856$	13.4641	−	50.2487i	0.460194	−	1.71747i
$857$	1.98076	+	1.14359i	0.0676615	+	0.0390644i	0.533449	−	0.845832i	$-0.320896\pi$
$857$	1.98076	+	1.14359i	0.0676615	+	0.0390644i	−0.465788	+	0.884897i	$0.654229\pi$
$858$	15.2942	−	57.0788i	0.522136	−	1.94864i
$859$	−7.85641	−	13.6077i	−0.268057	−	0.464289i	0.700303	−	0.713846i	$-0.253048\pi$
$859$	−7.85641	−	13.6077i	−0.268057	−	0.464289i	−0.968360	+	0.249557i	$0.919715\pi$
$860$	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	$-0.600399\pi$
$863$	10.5167	−	6.07180i	0.357991	−	0.206686i	0.668199	+	0.743982i	$0.267065\pi$
$864$	−20.7846	−	20.7846i	−0.707107	−	0.707107i
$865$	−10.1603	+	17.5981i	−0.345459	+	0.598353i
$866$	−4.14359	+	4.14359i	−0.140805	+	0.140805i
$867$	−29.0718			−0.987330
$868$		0			0
$869$	9.92820			0.336791
$870$	−10.2679	+	10.2679i	−0.348116	+	0.348116i
$871$	11.1962	−	19.3923i	0.379367	−	0.657083i
$872$	−11.6603	−	43.5167i	−0.394866	−	1.47366i
$873$		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	0.845123	−	0.534572i	$-0.179527\pi$
$877$	−1.19615	−	2.07180i	−0.0403912	−	0.0699596i	−0.885514	+	0.464612i	$0.846194\pi$
$878$	−5.75129	+	21.4641i	−0.194097	+	0.724378i
$879$	21.4808	+	12.4019i	0.724528	+	0.418307i
$880$	−14.9282			−0.503230
$881$			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	$0.731513\pi$
$884$	5.19615	+	3.00000i	0.174766	+	0.100901i
$885$	−5.19615	−	3.00000i	−0.174667	−	0.100844i
$886$	35.5167	+	9.51666i	1.19321	+	0.319718i
$887$	−7.73205	−	13.3923i	−0.259617	−	0.449670i	0.706522	−	0.707691i	$-0.250263\pi$
$887$	−7.73205	−	13.3923i	−0.259617	−	0.449670i	−0.966139	+	0.258021i	$0.916930\pi$
$888$	−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
$892$			20.5359i			0.687593i
$893$	5.19615	−	9.00000i	0.173883	−	0.301174i
$894$	−29.3205	−	29.3205i	−0.980624	−	0.980624i
$895$	14.3923			0.481082
$896$		0			0
$897$	−61.1769			−2.04264
$898$	−1.92820	−	1.92820i	−0.0643450	−	0.0643450i
$899$	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
$906$	11.3660	+	3.04552i	0.377611	+	0.101181i
$907$	−10.0526	−	5.80385i	−0.333790	−	0.192714i	0.323733	−	0.946149i	$-0.395062\pi$
$907$	−10.0526	−	5.80385i	−0.333790	−	0.192714i	−0.657522	+	0.753435i	$0.728395\pi$
$908$	5.78461	+	3.33975i	0.191969	+	0.110833i
$909$		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	$-0.155011\pi$
$912$	−41.5692			−1.37649
$913$	−27.5885	−	15.9282i	−0.913045	−	0.527147i
$914$	10.0526	−	37.5167i	0.332509	−	1.24094i
$915$	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	$-0.453814\pi$
$919$	32.5526	−	18.7942i	1.07381	−	0.619964i	0.929220	+	0.369527i	$0.120480\pi$
$920$	4.00000	+	14.9282i	0.131876	+	0.492168i
$921$	1.50000	−	2.59808i	0.0494267	−	0.0856095i
$922$	−27.7128	+	27.7128i	−0.912673	+	0.912673i
$923$	−3.46410			−0.114022
$924$		0			0
$925$	2.53590			0.0833798
$926$	4.39230	−	4.39230i	0.144340	−	0.144340i
$927$		0			0
$928$	23.7128	+	23.7128i	0.778411	+	0.778411i
$929$	−36.8038	+	21.2487i	−1.20750	+	0.697148i	−0.962211	−	0.272304i	$-0.912214\pi$
$929$	−36.8038	+	21.2487i	−1.20750	+	0.697148i	−0.245284	+	0.969451i	$0.578881\pi$
$930$	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
$934$	8.24167	−	30.7583i	0.269676	−	1.00644i
$935$	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
$940$	1.73205	−	3.00000i	0.0564933	−	0.0978492i
$941$	−44.1962	−	25.5167i	−1.44075	−	0.831819i	−0.442853	−	0.896594i	$-0.646034\pi$
$941$	−44.1962	−	25.5167i	−1.44075	−	0.831819i	−0.997900	+	0.0647746i	$0.979367\pi$
$942$	−46.9808	−	12.5885i	−1.53072	−	0.410154i
$943$	−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	$-0.567940\pi$
$947$	16.2679	−	9.39230i	0.528637	−	0.305209i	0.740461	+	0.672099i	$0.234607\pi$
$948$	9.21539			0.299302
$949$	−3.00000	+	5.19615i	−0.0973841	+	0.168674i
$950$	6.00000	+	6.00000i	0.194666	+	0.194666i
$951$	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
$956$	55.9615			1.80993
$957$	−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
$962$	22.3923	+	6.00000i	0.721957	+	0.193448i
$963$		0			0
$964$	4.39230	−	7.60770i	0.141467	−	0.245027i
$965$		−	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	$0.832859\pi$
$968$	−8.00000	−	2.14359i	−0.257130	−	0.0688977i
$969$	4.17691	+	2.41154i	0.134182	+	0.0774699i
$970$	2.70577	−	10.0981i	0.0868771	−	0.324230i
$971$	−13.3923	−	23.1962i	−0.429780	−	0.744400i	0.567074	−	0.823667i	$-0.308075\pi$
$971$	−13.3923	−	23.1962i	−0.429780	−	0.744400i	−0.996853	+	0.0792670i	$0.974742\pi$
$972$		0			0
$973$		0			0
$974$	10.5359	+	39.3205i	0.337592	+	1.25991i
$975$	−9.69615	+	5.59808i	−0.310525	+	0.179282i
$976$	8.78461	−	5.07180i	0.281189	−	0.162344i
$977$	−22.1244	+	38.3205i	−0.707821	+	1.22598i	0.257843	+	0.966187i	$0.416988\pi$
$977$	−22.1244	+	38.3205i	−0.707821	+	1.22598i	−0.965664	+	0.259795i	$0.916345\pi$
$978$	−36.0000	+	36.0000i	−1.15115	+	1.15115i
$979$	−35.3205			−1.12885
$980$		0			0
$981$		0			0
$982$	−34.1244	+	34.1244i	−1.08895	+	1.08895i
$983$	1.79423	−	3.10770i	0.0572270	−	0.0991201i	−0.835993	−	0.548741i	$-0.815107\pi$
$983$	1.79423	−	3.10770i	0.0572270	−	0.0991201i	0.893220	+	0.449621i	$0.148441\pi$
$984$	16.3923	−	4.39230i	0.522568	−	0.140022i
$985$	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	$-0.410827\pi$
$991$	−13.1436	−	7.58846i	−0.417520	−	0.241055i	−0.694016	+	0.719960i	$0.744160\pi$
$992$	32.7846	−	8.78461i	1.04091	−	0.278912i
$993$		−	9.71281i		−	0.308227i
$994$		0			0
$995$			3.46410i			0.109819i
$996$	−25.6077	−	14.7846i	−0.811411	−	0.468468i
$997$	10.7942	+	6.23205i	0.341857	+	0.197371i	0.661093	−	0.750304i	$-0.270093\pi$
$997$	10.7942	+	6.23205i	0.341857	+	0.197371i	−0.319236	+	0.947675i	$0.603426\pi$
$998$	7.63397	+	2.04552i	0.241649	+	0.0647497i
$999$	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.d.31.2		4
4.3	odd	2		980.2.o.a.31.2		4
7.2	even	3		980.2.o.b.411.2		4
7.3	odd	6		140.2.g.a.111.2	yes	4
7.4	even	3		140.2.g.b.111.2	yes	4
7.5	odd	6		980.2.o.a.411.2		4
7.6	odd	2		980.2.o.c.31.2		4
21.11	odd	6		1260.2.c.b.811.3		4
21.17	even	6		1260.2.c.a.811.3		4
28.3	even	6		140.2.g.b.111.1	yes	4
28.11	odd	6		140.2.g.a.111.1	✓	4
28.19	even	6	inner	980.2.o.d.411.1		4
28.23	odd	6		980.2.o.c.411.1		4
28.27	even	2		980.2.o.b.31.2		4
35.3	even	12		700.2.c.b.699.4		4
35.4	even	6		700.2.g.g.251.3		4
35.17	even	12		700.2.c.e.699.1		4
35.18	odd	12		700.2.c.c.699.4		4
35.24	odd	6		700.2.g.f.251.3		4
35.32	odd	12		700.2.c.f.699.1		4
56.3	even	6		2240.2.k.b.1791.4		4
56.11	odd	6		2240.2.k.a.1791.1		4
56.45	odd	6		2240.2.k.a.1791.2		4
56.53	even	6		2240.2.k.b.1791.3		4
84.11	even	6		1260.2.c.a.811.4		4
84.59	odd	6		1260.2.c.b.811.4		4
140.3	odd	12		700.2.c.f.699.2		4
140.39	odd	6		700.2.g.f.251.4		4
140.59	even	6		700.2.g.g.251.4		4
140.67	even	12		700.2.c.b.699.3		4
140.87	odd	12		700.2.c.c.699.3		4
140.123	even	12		700.2.c.e.699.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.1	✓	4	28.11	odd	6
140.2.g.a.111.2	yes	4	7.3	odd	6
140.2.g.b.111.1	yes	4	28.3	even	6
140.2.g.b.111.2	yes	4	7.4	even	3
700.2.c.b.699.3		4	140.67	even	12
700.2.c.b.699.4		4	35.3	even	12
700.2.c.c.699.3		4	140.87	odd	12
700.2.c.c.699.4		4	35.18	odd	12
700.2.c.e.699.1		4	35.17	even	12
700.2.c.e.699.2		4	140.123	even	12
700.2.c.f.699.1		4	35.32	odd	12
700.2.c.f.699.2		4	140.3	odd	12
700.2.g.f.251.3		4	35.24	odd	6
700.2.g.f.251.4		4	140.39	odd	6
700.2.g.g.251.3		4	35.4	even	6
700.2.g.g.251.4		4	140.59	even	6
980.2.o.a.31.2		4	4.3	odd	2
980.2.o.a.411.2		4	7.5	odd	6
980.2.o.b.31.2		4	28.27	even	2
980.2.o.b.411.2		4	7.2	even	3
980.2.o.c.31.2		4	7.6	odd	2
980.2.o.c.411.1		4	28.23	odd	6
980.2.o.d.31.2		4	1.1	even	1	trivial
980.2.o.d.411.1		4	28.19	even	6	inner
1260.2.c.a.811.3		4	21.17	even	6
1260.2.c.a.811.4		4	84.11	even	6
1260.2.c.b.811.3		4	21.11	odd	6
1260.2.c.b.811.4		4	84.59	odd	6
2240.2.k.a.1791.1		4	56.11	odd	6
2240.2.k.a.1791.2		4	56.45	odd	6
2240.2.k.b.1791.3		4	56.53	even	6
2240.2.k.b.1791.4		4	56.3	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(0.866025 - 1.50000i) q^{3} +2.00000i q^{4} +(0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(0.866025 - 1.50000i) q^{3} +2.00000i q^{4} +(0.866025 - 0.500000i) q^{5} +(2.36603 - 0.633975i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(1.36603 + 0.366025i) q^{10} +(3.23205 + 1.86603i) q^{11} +(3.00000 + 1.73205i) q^{12} -6.46410i q^{13} -1.73205i q^{15} -4.00000 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} +(1.26795 + 4.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(6.46410 - 6.46410i) q^{26} +5.19615 q^{27} -5.92820 q^{29} +(1.73205 - 1.73205i) q^{30} +(-3.00000 + 5.19615i) q^{31} +(-4.00000 - 4.00000i) q^{32} +(5.59808 - 3.23205i) q^{33} +(0.169873 + 0.633975i) q^{34} +(1.26795 + 2.19615i) q^{37} +(-2.19615 + 8.19615i) q^{38} +(-9.69615 - 5.59808i) q^{39} +(-0.732051 + 2.73205i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +(-3.73205 + 6.46410i) q^{44} +(7.46410 + 2.00000i) 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} +12.9282 q^{52} +(-1.00000 + 1.73205i) q^{53} +(5.19615 + 5.19615i) q^{54} +3.73205 q^{55} +10.3923 q^{57} +(-5.92820 - 5.92820i) q^{58} +(1.73205 - 3.00000i) q^{59} +3.46410 q^{60} +(-2.19615 + 1.26795i) q^{61} +(-8.19615 + 2.19615i) q^{62} -8.00000i q^{64} +(-3.23205 - 5.59808i) q^{65} +(8.83013 + 2.36603i) q^{66} +(3.00000 + 1.73205i) q^{67} +(-0.464102 + 0.803848i) q^{68} -9.46410i q^{69} -0.535898i q^{71} +(-0.803848 - 0.464102i) q^{73} +(-0.928203 + 3.46410i) 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} +(-3.46410 + 2.00000i) q^{80} +(4.50000 - 7.79423i) q^{81} +(3.46410 - 3.46410i) q^{82} -8.53590 q^{83} +0.464102 q^{85} +(2.00000 - 2.00000i) q^{86} +(-5.13397 + 8.89230i) q^{87} +(-10.1962 + 2.73205i) q^{88} +(-8.19615 + 4.73205i) q^{89} +(5.46410 + 9.46410i) q^{92} +(5.19615 + 9.00000i) q^{93} +(0.633975 - 2.36603i) q^{94} +(5.19615 + 3.00000i) q^{95} +(-9.46410 + 2.53590i) q^{96} -7.39230i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 6 q^{6} - 8 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 + 6 * q^6 - 8 * q^8	\( 4 q + 4 q^{2} + 6 q^{6} - 8 q^{8} + 2 q^{10} + 6 q^{11} + 12 q^{12} - 16 q^{16} + 12 q^{17} + 12 q^{19} + 4 q^{20} + 2 q^{22} + 12 q^{23} + 12 q^{24} + 2 q^{25} + 12 q^{26} + 4 q^{29} - 12 q^{31} - 16 q^{32} + 12 q^{33} + 18 q^{34} + 12 q^{37} + 12 q^{38} - 18 q^{39} + 4 q^{40} - 8 q^{44} + 16 q^{46} + 2 q^{50} - 18 q^{51} + 24 q^{52} - 4 q^{53} + 8 q^{55} + 4 q^{58} + 12 q^{61} - 12 q^{62} - 6 q^{65} + 18 q^{66} + 12 q^{67} + 12 q^{68} - 24 q^{73} + 24 q^{74} - 6 q^{78} + 30 q^{79} + 18 q^{81} - 48 q^{83} - 12 q^{85} + 8 q^{86} - 24 q^{87} - 20 q^{88} - 12 q^{89} + 8 q^{92} + 6 q^{94} - 24 q^{96}+O(q^{100}) \) 4 * q + 4 * q^2 + 6 * q^6 - 8 * q^8 + 2 * q^10 + 6 * q^11 + 12 * q^12 - 16 * q^16 + 12 * q^17 + 12 * q^19 + 4 * q^20 + 2 * q^22 + 12 * q^23 + 12 * q^24 + 2 * q^25 + 12 * q^26 + 4 * q^29 - 12 * q^31 - 16 * q^32 + 12 * q^33 + 18 * q^34 + 12 * q^37 + 12 * q^38 - 18 * q^39 + 4 * q^40 - 8 * q^44 + 16 * q^46 + 2 * q^50 - 18 * q^51 + 24 * q^52 - 4 * q^53 + 8 * q^55 + 4 * q^58 + 12 * q^61 - 12 * q^62 - 6 * q^65 + 18 * q^66 + 12 * q^67 + 12 * q^68 - 24 * q^73 + 24 * q^74 - 6 * q^78 + 30 * q^79 + 18 * q^81 - 48 * q^83 - 12 * q^85 + 8 * q^86 - 24 * q^87 - 20 * q^88 - 12 * q^89 + 8 * q^92 + 6 * q^94 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more