LMFDB - Embedded newform 980.2.o.a.31.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,2,Mod(31,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,-2,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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			31.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	980.31
Dual form			980.2.o.a.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+(-1.36603 + 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(1.00000 - 1.00000i) q^{10} +(0.232051 + 0.133975i) q^{11} -3.46410i q^{12} -0.464102i q^{13} +1.73205i q^{15} +(2.00000 - 3.46410i) q^{16} +(5.59808 + 3.23205i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-1.00000 + 1.73205i) q^{20} +(-0.366025 - 0.0980762i) q^{22} +(-1.26795 + 0.732051i) q^{23} +(1.26795 + 4.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.169873 + 0.633975i) q^{26} +5.19615 q^{27} +7.92820 q^{29} +(-0.633975 - 2.36603i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(0.401924 - 0.232051i) q^{33} +(-8.83013 - 2.36603i) q^{34} +(4.73205 + 8.19615i) q^{37} +(6.00000 + 6.00000i) q^{38} +(-0.696152 - 0.401924i) q^{39} +(0.732051 - 2.73205i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +0.535898 q^{44} +(1.46410 - 1.46410i) q^{46} +(-0.866025 - 1.50000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-0.366025 + 1.36603i) q^{50} +(9.69615 - 5.59808i) q^{51} +(-0.464102 - 0.803848i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-7.09808 + 1.90192i) q^{54} -0.267949 q^{55} -10.3923 q^{57} +(-10.8301 + 2.90192i) q^{58} +(1.73205 - 3.00000i) q^{59} +(1.73205 + 3.00000i) q^{60} +(8.19615 - 4.73205i) q^{61} +(-2.19615 + 8.19615i) q^{62} -8.00000i q^{64} +(0.232051 + 0.401924i) q^{65} +(-0.464102 + 0.464102i) q^{66} +(-3.00000 - 1.73205i) q^{67} +12.9282 q^{68} +2.53590i q^{69} -7.46410i q^{71} +(-11.1962 - 6.46410i) q^{73} +(-9.46410 - 9.46410i) q^{74} +(-0.866025 - 1.50000i) q^{75} +(-10.3923 - 6.00000i) q^{76} +(1.09808 + 0.294229i) q^{78} +(-12.6962 + 7.33013i) q^{79} +4.00000i q^{80} +(4.50000 - 7.79423i) q^{81} +(1.26795 + 4.73205i) q^{82} +15.4641 q^{83} -6.46410 q^{85} +(0.732051 + 2.73205i) q^{86} +(6.86603 - 11.8923i) q^{87} +(-0.732051 + 0.196152i) q^{88} +(2.19615 - 1.26795i) q^{89} +(-1.46410 + 2.53590i) 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} -13.3923i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots + 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

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 $

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$	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			$0$
$4$	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
$6$	−0.633975	+	2.36603i	−0.258819	+	0.965926i
$7$		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
$11$	0.232051	+	0.133975i	0.0699660	+	0.0403949i	0.534575	−	0.845121i	$-0.320472\pi$
$11$	0.232051	+	0.133975i	0.0699660	+	0.0403949i	−0.464609	+	0.885516i	$0.653805\pi$
$12$		−	3.46410i		−	1.00000i
$13$		−	0.464102i		−	0.128719i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$		−	0.464102i		−	0.128719i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$		0			0
$15$			1.73205i			0.447214i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	5.59808	+	3.23205i	1.35773	+	0.783887i	0.989318	−	0.145774i	$-0.0465672\pi$
$17$	5.59808	+	3.23205i	1.35773	+	0.783887i	0.368415	+	0.929661i	$0.379901\pi$
$18$		0			0
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$		0			0
$22$	−0.366025	−	0.0980762i	−0.0780369	−	0.0209099i
$23$	−1.26795	+	0.732051i	−0.264386	+	0.152643i	−0.626334	−	0.779555i	$-0.715445\pi$
$23$	−1.26795	+	0.732051i	−0.264386	+	0.152643i	0.361948	+	0.932198i	$0.382112\pi$
$24$	1.26795	+	4.73205i	0.258819	+	0.965926i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	0.169873	+	0.633975i	0.0333148	+	0.124333i
$27$	5.19615			1.00000
$28$		0			0
$29$	7.92820			1.47223			0.736115	−	0.676856i	$-0.236658\pi$
$29$	7.92820			1.47223			0.736115	+	0.676856i	$0.236658\pi$
$30$	−0.633975	−	2.36603i	−0.115747	−	0.431975i
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$	0.401924	−	0.232051i	0.0699660	−	0.0403949i
$34$	−8.83013	−	2.36603i	−1.51435	−	0.405770i
$35$		0			0
$36$		0			0
$37$	4.73205	+	8.19615i	0.777944	+	1.34744i	0.933125	+	0.359553i	$0.117071\pi$
$37$	4.73205	+	8.19615i	0.777944	+	1.34744i	−0.155180	+	0.987886i	$0.549596\pi$
$38$	6.00000	+	6.00000i	0.973329	+	0.973329i
$39$	−0.696152	−	0.401924i	−0.111474	−	0.0643593i
$40$	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	$-0.0487319\pi$
$44$	0.535898			0.0807897
$45$		0			0
$46$	1.46410	−	1.46410i	0.215870	−	0.215870i
$47$	−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
$50$	−0.366025	+	1.36603i	−0.0517638	+	0.193185i
$51$	9.69615	−	5.59808i	1.35773	−	0.783887i
$52$	−0.464102	−	0.803848i	−0.0643593	−	0.111474i
$53$	−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	$0.210529\pi$
$54$	−7.09808	+	1.90192i	−0.965926	+	0.258819i
$55$	−0.267949			−0.0361303
$56$		0			0
$57$	−10.3923			−1.37649
$58$	−10.8301	+	2.90192i	−1.42207	+	0.381041i
$59$	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	$0.0942671\pi$
$60$	1.73205	+	3.00000i	0.223607	+	0.387298i
$61$	8.19615	−	4.73205i	1.04941	−	0.605877i	0.126926	−	0.991912i	$-0.459489\pi$
$61$	8.19615	−	4.73205i	1.04941	−	0.605877i	0.922484	+	0.386035i	$0.126156\pi$
$62$	−2.19615	+	8.19615i	−0.278912	+	1.04091i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	0.232051	+	0.401924i	0.0287824	+	0.0498525i
$66$	−0.464102	+	0.464102i	−0.0571270	+	0.0571270i
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	0.305424	−	0.952217i	$-0.401202\pi$
$67$	−3.00000	−	1.73205i	−0.366508	−	0.211604i	−0.671932	+	0.740613i	$0.734535\pi$
$68$	12.9282			1.56777
$69$			2.53590i			0.305286i
$70$		0			0
$71$		−	7.46410i		−	0.885826i	−0.896565	−	0.442913i	$-0.853945\pi$
$71$		−	7.46410i		−	0.885826i	0.896565	−	0.442913i	$-0.146055\pi$
$72$		0			0
$73$	−11.1962	−	6.46410i	−1.31041	−	0.756566i	−0.328247	−	0.944592i	$-0.606458\pi$
$73$	−11.1962	−	6.46410i	−1.31041	−	0.756566i	−0.982164	+	0.188026i	$0.939791\pi$
$74$	−9.46410	−	9.46410i	−1.10018	−	1.10018i
$75$	−0.866025	−	1.50000i	−0.100000	−	0.173205i
$76$	−10.3923	−	6.00000i	−1.19208	−	0.688247i
$77$		0			0
$78$	1.09808	+	0.294229i	0.124333	+	0.0333148i
$79$	−12.6962	+	7.33013i	−1.42843	+	0.824704i	−0.996997	−	0.0774418i	$-0.975325\pi$
$79$	−12.6962	+	7.33013i	−1.42843	+	0.824704i	−0.431432	+	0.902146i	$0.641991\pi$
$80$			4.00000i			0.447214i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	1.26795	+	4.73205i	0.140022	+	0.522568i
$83$	15.4641			1.69741			0.848703	−	0.528870i	$-0.177384\pi$
$83$	15.4641			1.69741			0.848703	+	0.528870i	$0.177384\pi$
$84$		0			0
$85$	−6.46410			−0.701130
$86$	0.732051	+	2.73205i	0.0789391	+	0.294605i
$87$	6.86603	−	11.8923i	0.736115	−	1.27499i
$88$	−0.732051	+	0.196152i	−0.0780369	+	0.0209099i
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	−0.379068	−	0.925369i	$-0.623755\pi$
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	0.611859	+	0.790967i	$0.290422\pi$
$90$		0			0
$91$		0			0
$92$	−1.46410	+	2.53590i	−0.152643	+	0.264386i
$93$	−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
$97$		−	13.3923i		−	1.35978i	−0.733313	−	0.679891i	$-0.762027\pi$
$97$		−	13.3923i		−	1.35978i	0.733313	−	0.679891i	$-0.237973\pi$
$98$		0			0
$99$		0			0
$100$		−	2.00000i		−	0.200000i
$101$	13.3923	+	7.73205i	1.33258	+	0.769368i	0.985695	−	0.168538i	$-0.0539047\pi$
$101$	13.3923	+	7.73205i	1.33258	+	0.769368i	0.346889	+	0.937906i	$0.387238\pi$
$102$	−11.1962	+	11.1962i	−1.10858	+	1.10858i
$103$	3.40192	+	5.89230i	0.335202	+	0.580586i	0.983524	−	0.180780i	$-0.0578623\pi$
$103$	3.40192	+	5.89230i	0.335202	+	0.580586i	−0.648322	+	0.761366i	$0.724529\pi$
$104$	0.928203	+	0.928203i	0.0910178	+	0.0910178i
$105$		0			0
$106$	0.732051	−	2.73205i	0.0711031	−	0.265360i
$107$	2.07180	−	1.19615i	0.200288	−	0.115636i	−0.396502	−	0.918034i	$-0.629776\pi$
$107$	2.07180	−	1.19615i	0.200288	−	0.115636i	0.596790	+	0.802398i	$0.296443\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	−1.03590	+	1.79423i	−0.0992211	+	0.171856i	−0.911362	−	0.411605i	$-0.864968\pi$
$109$	−1.03590	+	1.79423i	−0.0992211	+	0.171856i	0.812141	+	0.583461i	$0.198302\pi$
$110$	0.366025	−	0.0980762i	0.0348992	−	0.00935120i
$111$	16.3923			1.55589
$112$		0			0
$113$	5.46410			0.514019			0.257010	−	0.966409i	$-0.417263\pi$
$113$	5.46410			0.514019			0.257010	+	0.966409i	$0.417263\pi$
$114$	14.1962	−	3.80385i	1.32959	−	0.356263i
$115$	0.732051	−	1.26795i	0.0682641	−	0.118237i
$116$	13.7321	−	7.92820i	1.27499	−	0.736115i
$117$		0			0
$118$	−1.26795	+	4.73205i	−0.116724	+	0.435621i
$119$		0			0
$120$	−3.46410	−	3.46410i	−0.316228	−	0.316228i
$121$	−5.46410	−	9.46410i	−0.496737	−	0.860373i
$122$	−9.46410	+	9.46410i	−0.856840	+	0.856840i
$123$	−5.19615	−	3.00000i	−0.468521	−	0.270501i
$124$		−	12.0000i		−	1.07763i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$			15.4641i			1.37222i	0.727499	+	0.686109i	$0.240683\pi$
$127$			15.4641i			1.37222i	−0.727499	+	0.686109i	$0.759317\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$	−3.00000	−	1.73205i	−0.264135	−	0.152499i
$130$	−0.464102	−	0.464102i	−0.0407044	−	0.0407044i
$131$	−1.26795	−	2.19615i	−0.110781	−	0.191879i	0.805304	−	0.592862i	$-0.202002\pi$
$131$	−1.26795	−	2.19615i	−0.110781	−	0.191879i	−0.916085	+	0.400983i	$0.868669\pi$
$132$	0.464102	−	0.803848i	0.0403949	−	0.0699660i
$133$		0			0
$134$	4.73205	+	1.26795i	0.408787	+	0.109534i
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$	−17.6603	+	4.73205i	−1.51435	+	0.405770i
$137$	−10.1962	+	17.6603i	−0.871116	+	1.50882i	−0.0102728	+	0.999947i	$0.503270\pi$
$137$	−10.1962	+	17.6603i	−0.871116	+	1.50882i	−0.860843	+	0.508870i	$0.830063\pi$
$138$	−0.928203	−	3.46410i	−0.0790139	−	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
$142$	2.73205	+	10.1962i	0.229269	+	0.855642i
$143$	0.0621778	−	0.107695i	0.00519957	−	0.00900592i
$144$		0			0
$145$	−6.86603	+	3.96410i	−0.570192	+	0.329201i
$146$	17.6603	+	4.73205i	1.46157	+	0.391627i
$147$		0			0
$148$	16.3923	+	9.46410i	1.34744	+	0.777944i
$149$	−1.53590	−	2.66025i	−0.125826	−	0.217937i	0.796230	−	0.604994i	$-0.206825\pi$
$149$	−1.53590	−	2.66025i	−0.125826	−	0.217937i	−0.922055	+	0.387058i	$0.873491\pi$
$150$	1.73205	+	1.73205i	0.141421	+	0.141421i
$151$	13.1603	+	7.59808i	1.07097	+	0.618323i	0.928445	−	0.371469i	$-0.121146\pi$
$151$	13.1603	+	7.59808i	1.07097	+	0.618323i	0.142521	+	0.989792i	$0.454479\pi$
$152$	16.3923	+	4.39230i	1.32959	+	0.356263i
$153$		0			0
$154$		0			0
$155$			6.00000i			0.481932i
$156$	−1.60770			−0.128719
$157$	−6.80385	−	3.92820i	−0.543006	−	0.313505i	0.203290	−	0.979119i	$-0.434837\pi$
$157$	−6.80385	−	3.92820i	−0.543006	−	0.313505i	−0.746296	+	0.665614i	$0.768170\pi$
$158$	14.6603	−	14.6603i	1.16631	−	1.16631i
$159$	1.73205	+	3.00000i	0.137361	+	0.237915i
$160$	−1.46410	−	5.46410i	−0.115747	−	0.431975i
$161$		0			0
$162$	−3.29423	+	12.2942i	−0.258819	+	0.965926i
$163$	18.0000	−	10.3923i	1.40987	−	0.813988i	0.414494	−	0.910052i	$-0.363959\pi$
$163$	18.0000	−	10.3923i	1.40987	−	0.813988i	0.995375	+	0.0960641i	$0.0306254\pi$
$164$	−3.46410	−	6.00000i	−0.270501	−	0.468521i
$165$	−0.232051	+	0.401924i	−0.0180651	+	0.0312897i
$166$	−21.1244	+	5.66025i	−1.63957	+	0.439321i
$167$	−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
$169$	12.7846			0.983432
$170$	8.83013	−	2.36603i	0.677240	−	0.181466i
$171$		0			0
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−12.4019	+	7.16025i	−0.942901	+	0.544384i	−0.890868	−	0.454261i	$-0.849903\pi$
$173$	−12.4019	+	7.16025i	−0.942901	+	0.544384i	−0.0520323	+	0.998645i	$0.516570\pi$
$174$	−5.02628	+	18.7583i	−0.381041	+	1.42207i
$175$		0			0
$176$	0.928203	−	0.535898i	0.0699660	−	0.0403949i
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	−2.53590	+	2.53590i	−0.190074	+	0.190074i
$179$	−5.53590	−	3.19615i	−0.413772	−	0.238892i	0.278637	−	0.960397i	$-0.410117\pi$
$179$	−5.53590	−	3.19615i	−0.413772	−	0.238892i	−0.692409	+	0.721505i	$0.743451\pi$
$180$		0			0
$181$		−	0.928203i		−	0.0689928i	−0.999405	−	0.0344964i	$-0.989017\pi$
$181$		−	0.928203i		−	0.0689928i	0.999405	−	0.0344964i	$-0.0109827\pi$
$182$		0			0
$183$		−	16.3923i		−	1.21175i
$184$	1.07180	−	4.00000i	0.0790139	−	0.294884i
$185$	−8.19615	−	4.73205i	−0.602593	−	0.347907i
$186$	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
$190$	−8.19615	−	2.19615i	−0.594611	−	0.159326i
$191$	−6.23205	+	3.59808i	−0.450935	+	0.260348i	−0.708225	−	0.705987i	$-0.750504\pi$
$191$	−6.23205	+	3.59808i	−0.450935	+	0.260348i	0.257290	+	0.966334i	$0.417171\pi$
$192$	−12.0000	−	6.92820i	−0.866025	−	0.500000i
$193$	4.73205	−	8.19615i	0.340620	−	0.589972i	−0.643928	−	0.765086i	$-0.722696\pi$
$193$	4.73205	−	8.19615i	0.340620	−	0.589972i	0.984548	+	0.175114i	$0.0560296\pi$
$194$	4.90192	+	18.2942i	0.351938	+	1.31345i
$195$	0.803848			0.0575647
$196$		0			0
$197$	−13.3205			−0.949047			−0.474523	−	0.880243i	$-0.657380\pi$
$197$	−13.3205			−0.949047			−0.474523	+	0.880243i	$0.657380\pi$
$198$		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
$202$	−21.1244	−	5.66025i	−1.48630	−	0.398254i
$203$		0			0
$204$	11.1962	−	19.3923i	0.783887	−	1.35773i
$205$	1.73205	+	3.00000i	0.120972	+	0.209529i
$206$	−6.80385	−	6.80385i	−0.474047	−	0.474047i
$207$		0			0
$208$	−1.60770	−	0.928203i	−0.111474	−	0.0643593i
$209$		−	1.60770i		−	0.111207i
$210$		0			0
$211$		−	3.19615i		−	0.220032i	−0.993930	−	0.110016i	$-0.964910\pi$
$211$		−	3.19615i		−	0.220032i	0.993930	−	0.110016i	$-0.0350902\pi$
$212$			4.00000i			0.274721i
$213$	−11.1962	−	6.46410i	−0.767148	−	0.442913i
$214$	−2.39230	+	2.39230i	−0.163535	+	0.163535i
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$	−10.3923	+	10.3923i	−0.707107	+	0.707107i
$217$		0			0
$218$	0.758330	−	2.83013i	0.0513606	−	0.191680i
$219$	−19.3923	+	11.1962i	−1.31041	+	0.756566i
$220$	−0.464102	+	0.267949i	−0.0312897	+	0.0180651i
$221$	1.50000	−	2.59808i	0.100901	−	0.174766i
$222$	−22.3923	+	6.00000i	−1.50287	+	0.402694i
$223$	−13.7321			−0.919566			−0.459783	−	0.888031i	$-0.652073\pi$
$223$	−13.7321			−0.919566			−0.459783	+	0.888031i	$0.652073\pi$
$224$		0			0
$225$		0			0
$226$	−7.46410	+	2.00000i	−0.496505	+	0.133038i
$227$	−10.3301	+	17.8923i	−0.685635	+	1.18755i	0.287602	+	0.957750i	$0.407142\pi$
$227$	−10.3301	+	17.8923i	−0.685635	+	1.18755i	−0.973237	+	0.229804i	$0.926191\pi$
$228$	−18.0000	+	10.3923i	−1.19208	+	0.688247i
$229$	−7.39230	+	4.26795i	−0.488497	+	0.282034i	−0.723951	−	0.689852i	$-0.757676\pi$
$229$	−7.39230	+	4.26795i	−0.488497	+	0.282034i	0.235454	+	0.971886i	$0.424342\pi$
$230$	−0.535898	+	2.00000i	−0.0353361	+	0.131876i
$231$		0			0
$232$	−15.8564	+	15.8564i	−1.04102	+	1.04102i
$233$	4.53590	+	7.85641i	0.297157	+	0.514690i	0.975484	−	0.220069i	$-0.0706283\pi$
$233$	4.53590	+	7.85641i	0.297157	+	0.514690i	−0.678328	+	0.734760i	$0.737295\pi$
$234$		0			0
$235$	1.50000	+	0.866025i	0.0978492	+	0.0564933i
$236$		−	6.92820i		−	0.450988i
$237$			25.3923i			1.64941i
$238$		0			0
$239$			23.9808i			1.55119i	0.631233	+	0.775593i	$0.282549\pi$
$239$			23.9808i			1.55119i	−0.631233	+	0.775593i	$0.717451\pi$
$240$	6.00000	+	3.46410i	0.387298	+	0.223607i
$241$	−14.1962	−	8.19615i	−0.914455	−	0.527961i	−0.0325928	−	0.999469i	$-0.510376\pi$
$241$	−14.1962	−	8.19615i	−0.914455	−	0.527961i	−0.881862	+	0.471508i	$0.843710\pi$
$242$	10.9282	+	10.9282i	0.702492	+	0.702492i
$243$		0			0
$244$	9.46410	−	16.3923i	0.605877	−	1.04941i
$245$		0			0
$246$	8.19615	+	2.19615i	0.522568	+	0.140022i
$247$	−2.41154	+	1.39230i	−0.153443	+	0.0885902i
$248$	4.39230	+	16.3923i	0.278912	+	1.04091i
$249$	13.3923	−	23.1962i	0.848703	−	1.47000i
$250$	−0.366025	−	1.36603i	−0.0231495	−	0.0863950i
$251$	−25.8564			−1.63204			−0.816021	−	0.578022i	$-0.803825\pi$
$251$	−25.8564			−1.63204			−0.816021	+	0.578022i	$0.803825\pi$
$252$		0			0
$253$	−0.392305			−0.0246640
$254$	−5.66025	−	21.1244i	−0.355156	−	1.32546i
$255$	−5.59808	+	9.69615i	−0.350565	+	0.607197i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	−0.329104	−	0.944294i	$-0.606747\pi$
$257$	5.19615	−	3.00000i	0.324127	−	0.187135i	0.653231	+	0.757159i	$0.273413\pi$
$258$	4.73205	+	1.26795i	0.294605	+	0.0789391i
$259$		0			0
$260$	0.803848	+	0.464102i	0.0498525	+	0.0287824i
$261$		0			0
$262$	2.53590	+	2.53590i	0.156668	+	0.156668i
$263$	−9.92820	−	5.73205i	−0.612199	−	0.353453i	0.161626	−	0.986852i	$-0.448326\pi$
$263$	−9.92820	−	5.73205i	−0.612199	−	0.353453i	−0.773826	+	0.633399i	$0.781659\pi$
$264$	−0.339746	+	1.26795i	−0.0209099	+	0.0780369i
$265$		−	2.00000i		−	0.122859i
$266$		0			0
$267$		−	4.39230i		−	0.268805i
$268$	−6.92820			−0.423207
$269$	10.3923	+	6.00000i	0.633630	+	0.365826i	0.782157	−	0.623082i	$-0.214120\pi$
$269$	10.3923	+	6.00000i	0.633630	+	0.365826i	−0.148527	+	0.988908i	$0.547453\pi$
$270$	5.19615	−	5.19615i	0.316228	−	0.316228i
$271$	−4.73205	−	8.19615i	−0.287452	−	0.497881i	0.685749	−	0.727838i	$-0.259475\pi$
$271$	−4.73205	−	8.19615i	−0.287452	−	0.497881i	−0.973201	+	0.229957i	$0.926141\pi$
$272$	22.3923	−	12.9282i	1.35773	−	0.783887i
$273$		0			0
$274$	7.46410	−	27.8564i	0.450923	−	1.68287i
$275$	0.232051	−	0.133975i	0.0139932	−	0.00807897i
$276$	2.53590	+	4.39230i	0.152643	+	0.264386i
$277$	−8.39230	+	14.5359i	−0.504245	+	0.873377i	0.495743	+	0.868469i	$0.334896\pi$
$277$	−8.39230	+	14.5359i	−0.504245	+	0.873377i	−0.999988	+	0.00490834i	$0.998438\pi$
$278$	−9.46410	+	2.53590i	−0.567619	+	0.152093i
$279$		0			0
$280$		0			0
$281$	−7.92820			−0.472957			−0.236478	−	0.971637i	$-0.575993\pi$
$281$	−7.92820			−0.472957			−0.236478	+	0.971637i	$0.575993\pi$
$282$	4.09808	−	1.09808i	0.244037	−	0.0653895i
$283$	−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	$0.284012\pi$
$284$	−7.46410	−	12.9282i	−0.442913	−	0.767148i
$285$	9.00000	−	5.19615i	0.533114	−	0.307794i
$286$	−0.0455173	+	0.169873i	−0.00269150	+	0.0100448i
$287$		0			0
$288$		0			0
$289$	12.3923	+	21.4641i	0.728959	+	1.26259i
$290$	7.92820	−	7.92820i	0.465560	−	0.465560i
$291$	−20.0885	−	11.5981i	−1.17761	−	0.679891i
$292$	−25.8564			−1.51313
$293$			20.3205i			1.18714i	0.804784	+	0.593568i	$0.202281\pi$
$293$			20.3205i			1.18714i	−0.804784	+	0.593568i	$0.797719\pi$
$294$		0			0
$295$			3.46410i			0.201688i
$296$	−25.8564	−	6.92820i	−1.50287	−	0.402694i
$297$	1.20577	+	0.696152i	0.0699660	+	0.0403949i
$298$	3.07180	+	3.07180i	0.177944	+	0.177944i
$299$	0.339746	+	0.588457i	0.0196480	+	0.0340314i
$300$	−3.00000	−	1.73205i	−0.173205	−	0.100000i
$301$		0			0
$302$	−20.7583	−	5.56218i	−1.19451	−	0.320067i
$303$	23.1962	−	13.3923i	1.33258	−	0.769368i
$304$	−24.0000			−1.37649
$305$	−4.73205	+	8.19615i	−0.270956	+	0.469310i
$306$		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
$309$	11.7846			0.670403
$310$	−2.19615	−	8.19615i	−0.124733	−	0.465510i
$311$	−3.92820	+	6.80385i	−0.222748	+	0.385811i	−0.955641	−	0.294533i	$-0.904836\pi$
$311$	−3.92820	+	6.80385i	−0.222748	+	0.385811i	0.732893	+	0.680343i	$0.238169\pi$
$312$	2.19615	−	0.588457i	0.124333	−	0.0333148i
$313$	−15.1865	+	8.76795i	−0.858394	+	0.495594i	−0.863474	−	0.504393i	$-0.831716\pi$
$313$	−15.1865	+	8.76795i	−0.858394	+	0.495594i	0.00508040	+	0.999987i	$0.498383\pi$
$314$	10.7321	+	2.87564i	0.605645	+	0.162282i
$315$		0			0
$316$	−14.6603	+	25.3923i	−0.824704	+	1.42843i
$317$	1.53590	+	2.66025i	0.0862646	+	0.149415i	0.905929	−	0.423429i	$-0.139174\pi$
$317$	1.53590	+	2.66025i	0.0862646	+	0.149415i	−0.819665	+	0.572844i	$0.805840\pi$
$318$	−3.46410	−	3.46410i	−0.194257	−	0.194257i
$319$	1.83975	+	1.06218i	0.103006	+	0.0594705i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$		−	4.14359i		−	0.231273i
$322$		0			0
$323$		−	38.7846i		−	2.15803i
$324$		−	18.0000i		−	1.00000i
$325$	−0.401924	−	0.232051i	−0.0222947	−	0.0128719i
$326$	−20.7846	+	20.7846i	−1.15115	+	1.15115i
$327$	1.79423	+	3.10770i	0.0992211	+	0.171856i
$328$	6.92820	+	6.92820i	0.382546	+	0.382546i
$329$		0			0
$330$	0.169873	−	0.633975i	0.00935120	−	0.0348992i
$331$	22.8564	−	13.1962i	1.25630	−	0.725326i	0.283948	−	0.958840i	$-0.408356\pi$
$331$	22.8564	−	13.1962i	1.25630	−	0.725326i	0.972354	+	0.233513i	$0.0750223\pi$
$332$	26.7846	−	15.4641i	1.47000	−	0.848703i
$333$		0			0
$334$	7.09808	−	1.90192i	0.388389	−	0.104069i
$335$	3.46410			0.189264
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	−17.4641	+	4.67949i	−0.949922	+	0.254531i
$339$	4.73205	−	8.19615i	0.257010	−	0.445154i
$340$	−11.1962	+	6.46410i	−0.607197	+	0.350565i
$341$	1.39230	−	0.803848i	0.0753975	−	0.0435308i
$342$		0			0
$343$		0			0
$344$	4.00000	+	4.00000i	0.215666	+	0.215666i
$345$	−1.26795	−	2.19615i	−0.0682641	−	0.118237i
$346$	14.3205	−	14.3205i	0.769875	−	0.769875i
$347$	29.6603	+	17.1244i	1.59225	+	0.919284i	0.992921	+	0.118778i	$0.0378976\pi$
$347$	29.6603	+	17.1244i	1.59225	+	0.919284i	0.599325	+	0.800506i	$0.295436\pi$
$348$		−	27.4641i		−	1.47223i
$349$		−	5.32051i		−	0.284800i	−0.989809	−	0.142400i	$-0.954518\pi$
$349$		−	5.32051i		−	0.284800i	0.989809	−	0.142400i	$-0.0454820\pi$
$350$		0			0
$351$		−	2.41154i		−	0.128719i
$352$	−1.07180	+	1.07180i	−0.0571270	+	0.0571270i
$353$	6.40192	+	3.69615i	0.340740	+	0.196726i	0.660599	−	0.750739i	$-0.270302\pi$
$353$	6.40192	+	3.69615i	0.340740	+	0.196726i	−0.319859	+	0.947465i	$0.603636\pi$
$354$	6.00000	+	6.00000i	0.318896	+	0.318896i
$355$	3.73205	+	6.46410i	0.198077	+	0.343079i
$356$	2.53590	−	4.39230i	0.134402	−	0.232792i
$357$		0			0
$358$	8.73205	+	2.33975i	0.461503	+	0.123659i
$359$	−21.9282	+	12.6603i	−1.15733	+	0.668183i	−0.950662	−	0.310229i	$-0.899594\pi$
$359$	−21.9282	+	12.6603i	−1.15733	+	0.668183i	−0.206665	+	0.978412i	$0.566261\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	0.339746	+	1.26795i	0.0178567	+	0.0666419i
$363$	−18.9282			−0.993473
$364$		0			0
$365$	12.9282			0.676693
$366$	6.00000	+	22.3923i	0.313625	+	1.17046i
$367$	−5.93782	+	10.2846i	−0.309952	+	0.536852i	−0.978352	−	0.206950i	$-0.933646\pi$
$367$	−5.93782	+	10.2846i	−0.309952	+	0.536852i	0.668400	+	0.743802i	$0.266980\pi$
$368$			5.85641i			0.305286i
$369$		0			0
$370$	12.9282	+	3.46410i	0.672105	+	0.180090i
$371$		0			0
$372$	−18.0000	−	10.3923i	−0.933257	−	0.538816i
$373$	1.80385	+	3.12436i	0.0933997	+	0.161773i	0.908940	−	0.416928i	$-0.136893\pi$
$373$	1.80385	+	3.12436i	0.0933997	+	0.161773i	−0.815540	+	0.578701i	$0.803560\pi$
$374$	−1.73205	−	1.73205i	−0.0895622	−	0.0895622i
$375$	1.50000	+	0.866025i	0.0774597	+	0.0447214i
$376$	4.73205	+	1.26795i	0.244037	+	0.0653895i
$377$		−	3.67949i		−	0.189503i
$378$		0			0
$379$		−	5.60770i		−	0.288048i	−0.989574	−	0.144024i	$-0.953996\pi$
$379$		−	5.60770i		−	0.288048i	0.989574	−	0.144024i	$-0.0460042\pi$
$380$	12.0000			0.615587
$381$	23.1962	+	13.3923i	1.18837	+	0.686109i
$382$	7.19615	−	7.19615i	0.368187	−	0.368187i
$383$	−13.7321	−	23.7846i	−0.701675	−	1.21534i	−0.967878	−	0.251420i	$-0.919103\pi$
$383$	−13.7321	−	23.7846i	−0.701675	−	1.21534i	0.266203	−	0.963917i	$-0.414231\pi$
$384$	18.9282	+	5.07180i	0.965926	+	0.258819i
$385$		0			0
$386$	−3.46410	+	12.9282i	−0.176318	+	0.658028i
$387$		0			0
$388$	−13.3923	−	23.1962i	−0.679891	−	1.17761i
$389$	10.4282	−	18.0622i	0.528731	−	0.915789i	−0.470708	−	0.882289i	$-0.656001\pi$
$389$	10.4282	−	18.0622i	0.528731	−	0.915789i	0.999439	−	0.0334996i	$-0.0106653\pi$
$390$	−1.09808	+	0.294229i	−0.0556033	+	0.0148988i
$391$	−9.46410			−0.478620
$392$		0			0
$393$	−4.39230			−0.221562
$394$	18.1962	−	4.87564i	0.916709	−	0.245631i
$395$	7.33013	−	12.6962i	0.368819	−	0.638813i
$396$		0			0
$397$	10.7942	−	6.23205i	0.541747	−	0.312778i	−0.204040	−	0.978963i	$-0.565407\pi$
$397$	10.7942	−	6.23205i	0.541747	−	0.312778i	0.745787	+	0.666185i	$0.232074\pi$
$398$	1.26795	−	4.73205i	0.0635566	−	0.237196i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	5.03590	+	8.72243i	0.251481	+	0.435577i	0.963934	−	0.266142i	$-0.0857491\pi$
$401$	5.03590	+	8.72243i	0.251481	+	0.435577i	−0.712453	+	0.701720i	$0.752416\pi$
$402$	6.00000	−	6.00000i	0.299253	−	0.299253i
$403$	−2.41154	−	1.39230i	−0.120127	−	0.0693556i
$404$	30.9282			1.53874
$405$			9.00000i			0.447214i
$406$		0			0
$407$			2.53590i			0.125700i
$408$	−8.19615	+	30.5885i	−0.405770	+	1.51435i
$409$	−3.58846	−	2.07180i	−0.177438	−	0.102444i	0.408651	−	0.912691i	$-0.366000\pi$
$409$	−3.58846	−	2.07180i	−0.177438	−	0.102444i	−0.586088	+	0.810247i	$0.699333\pi$
$410$	−3.46410	−	3.46410i	−0.171080	−	0.171080i
$411$	17.6603	+	30.5885i	0.871116	+	1.50882i
$412$	11.7846	+	6.80385i	0.580586	+	0.335202i
$413$		0			0
$414$		0			0
$415$	−13.3923	+	7.73205i	−0.657402	+	0.379551i
$416$	2.53590	+	0.679492i	0.124333	+	0.0333148i
$417$	6.00000	−	10.3923i	0.293821	−	0.508913i
$418$	0.588457	+	2.19615i	0.0287824	+	0.107417i
$419$	−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	$0.346772\pi$
$422$	1.16987	+	4.36603i	0.0569485	+	0.212535i
$423$		0			0
$424$	−1.46410	−	5.46410i	−0.0711031	−	0.265360i
$425$	5.59808	−	3.23205i	0.271547	−	0.156777i
$426$	17.6603	+	4.73205i	0.855642	+	0.229269i
$427$		0			0
$428$	2.39230	−	4.14359i	0.115636	−	0.200288i
$429$	−0.107695	−	0.186533i	−0.00519957	−	0.00900592i
$430$	−2.00000	−	2.00000i	−0.0964486	−	0.0964486i
$431$	−11.7679	−	6.79423i	−0.566842	−	0.327266i	0.189045	−	0.981968i	$-0.439461\pi$
$431$	−11.7679	−	6.79423i	−0.566842	−	0.327266i	−0.755887	+	0.654702i	$0.772794\pi$
$432$	10.3923	−	18.0000i	0.500000	−	0.866025i
$433$		−	31.8564i		−	1.53092i	−0.643483	−	0.765461i	$-0.722511\pi$
$433$		−	31.8564i		−	1.53092i	0.643483	−	0.765461i	$-0.277489\pi$
$434$		0			0
$435$			13.7321i			0.658401i
$436$			4.14359i			0.198442i
$437$	7.60770	+	4.39230i	0.363925	+	0.210112i
$438$	22.3923	−	22.3923i	1.06995	−	1.06995i
$439$	19.8564	+	34.3923i	0.947695	+	1.64146i	0.750264	+	0.661138i	$0.229926\pi$
$439$	19.8564	+	34.3923i	0.947695	+	1.64146i	0.197430	+	0.980317i	$0.436740\pi$
$440$	0.535898	−	0.535898i	0.0255480	−	0.0255480i
$441$		0			0
$442$	−1.09808	+	4.09808i	−0.0522302	+	0.194926i
$443$	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	$0.121419\pi$
$444$	28.3923	−	16.3923i	1.34744	−	0.777944i
$445$	−1.26795	+	2.19615i	−0.0601066	+	0.104108i
$446$	18.7583	−	5.02628i	0.888233	−	0.238001i
$447$	−5.32051			−0.251651
$448$		0			0
$449$	11.9282			0.562927			0.281463	−	0.959572i	$-0.409180\pi$
$449$	11.9282			0.562927			0.281463	+	0.959572i	$0.409180\pi$
$450$		0			0
$451$	0.464102	−	0.803848i	0.0218537	−	0.0378517i
$452$	9.46410	−	5.46410i	0.445154	−	0.257010i
$453$	22.7942	−	13.1603i	1.07097	−	0.618323i
$454$	7.56218	−	28.2224i	0.354911	−	1.32454i
$455$		0			0
$456$	20.7846	−	20.7846i	0.973329	−	0.973329i
$457$	−10.2679	−	17.7846i	−0.480314	−	0.831929i	0.519431	−	0.854513i	$-0.326144\pi$
$457$	−10.2679	−	17.7846i	−0.480314	−	0.831929i	−0.999745	+	0.0225837i	$0.992811\pi$
$458$	8.53590	−	8.53590i	0.398856	−	0.398856i
$459$	29.0885	+	16.7942i	1.35773	+	0.783887i
$460$		−	2.92820i		−	0.136528i
$461$			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
$463$			16.3923i			0.761815i	0.924613	+	0.380908i	$0.124388\pi$
$463$			16.3923i			0.761815i	−0.924613	+	0.380908i	$0.875612\pi$
$464$	15.8564	−	27.4641i	0.736115	−	1.27499i
$465$	9.00000	+	5.19615i	0.417365	+	0.240966i
$466$	−9.07180	−	9.07180i	−0.420243	−	0.420243i
$467$	−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
$470$	−2.36603	−	0.633975i	−0.109137	−	0.0292431i
$471$	−11.7846	+	6.80385i	−0.543006	+	0.313505i
$472$	2.53590	+	9.46410i	0.116724	+	0.435621i
$473$	0.267949	−	0.464102i	0.0123203	−	0.0213394i
$474$	−9.29423	−	34.6865i	−0.426898	−	1.59321i
$475$	−6.00000			−0.275299
$476$		0			0
$477$		0			0
$478$	−8.77757	−	32.7583i	−0.401477	−	1.49833i
$479$	−12.5885	+	21.8038i	−0.575181	+	0.996243i	0.420841	+	0.907135i	$0.361735\pi$
$479$	−12.5885	+	21.8038i	−0.575181	+	0.996243i	−0.996022	+	0.0891086i	$0.971598\pi$
$480$	−9.46410	−	2.53590i	−0.431975	−	0.115747i
$481$	3.80385	−	2.19615i	0.173441	−	0.100136i
$482$	22.3923	+	6.00000i	1.01994	+	0.273293i
$483$		0			0
$484$	−18.9282	−	10.9282i	−0.860373	−	0.496737i
$485$	6.69615	+	11.5981i	0.304057	+	0.526642i
$486$		0			0
$487$	−11.0718	−	6.39230i	−0.501711	−	0.289663i	0.227709	−	0.973729i	$-0.426877\pi$
$487$	−11.0718	−	6.39230i	−0.501711	−	0.289663i	−0.729420	+	0.684066i	$0.760210\pi$
$488$	−6.92820	+	25.8564i	−0.313625	+	1.17046i
$489$		−	36.0000i		−	1.62798i
$490$		0			0
$491$			9.87564i			0.445682i	0.974855	+	0.222841i	$0.0715330\pi$
$491$			9.87564i			0.445682i	−0.974855	+	0.222841i	$0.928467\pi$
$492$	−12.0000			−0.541002
$493$	44.3827	+	25.6244i	1.99890	+	1.15406i
$494$	2.78461	−	2.78461i	0.125286	−	0.125286i
$495$		0			0
$496$	−12.0000	−	20.7846i	−0.538816	−	0.933257i
$497$		0			0
$498$	−9.80385	+	36.5885i	−0.439321	+	1.63957i
$499$	−22.1603	+	12.7942i	−0.992029	+	0.572748i	−0.905880	−	0.423534i	$-0.860789\pi$
$499$	−22.1603	+	12.7942i	−0.992029	+	0.572748i	−0.0861490	+	0.996282i	$0.527456\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$	−4.50000	+	7.79423i	−0.201045	+	0.348220i
$502$	35.3205	−	9.46410i	1.57643	−	0.422404i
$503$	−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
$505$	−15.4641			−0.688143
$506$	0.535898	−	0.143594i	0.0238236	−	0.00638351i
$507$	11.0718	−	19.1769i	0.491716	−	0.851677i
$508$	15.4641	+	26.7846i	0.686109	+	1.18837i
$509$	22.3923	−	12.9282i	0.992521	−	0.573033i	0.0864944	−	0.996252i	$-0.472434\pi$
$509$	22.3923	−	12.9282i	0.992521	−	0.573033i	0.906027	+	0.423220i	$0.139100\pi$
$510$	4.09808	−	15.2942i	0.181466	−	0.677240i
$511$		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
$515$	−5.89230	−	3.40192i	−0.259646	−	0.149907i
$516$	−6.92820			−0.304997
$517$		−	0.464102i		−	0.0204112i
$518$		0			0
$519$			24.8038i			1.08877i
$520$	−1.26795	−	0.339746i	−0.0556033	−	0.0148988i
$521$	−11.7846	−	6.80385i	−0.516293	−	0.298082i	0.219124	−	0.975697i	$-0.429680\pi$
$521$	−11.7846	−	6.80385i	−0.516293	−	0.298082i	−0.735417	+	0.677615i	$0.763014\pi$
$522$		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	$0.655465\pi$
$524$	−4.39230	−	2.53590i	−0.191879	−	0.110781i
$525$		0			0
$526$	15.6603	+	4.19615i	0.682820	+	0.182961i
$527$	33.5885	−	19.3923i	1.46314	−	0.844742i
$528$		−	1.85641i		−	0.0807897i
$529$	−10.4282	+	18.0622i	−0.453400	+	0.785312i
$530$	0.732051	+	2.73205i	0.0317983	+	0.118673i
$531$		0			0
$532$		0			0
$533$	−1.60770			−0.0696370
$534$	1.60770	+	6.00000i	0.0695718	+	0.259645i
$535$	−1.19615	+	2.07180i	−0.0517142	+	0.0895716i
$536$	9.46410	−	2.53590i	0.408787	−	0.109534i
$537$	−9.58846	+	5.53590i	−0.413772	+	0.238892i
$538$	−16.3923	−	4.39230i	−0.706722	−	0.189366i
$539$		0			0
$540$	−5.19615	+	9.00000i	−0.223607	+	0.387298i
$541$	−3.89230	−	6.74167i	−0.167343	−	0.289847i	0.770142	−	0.637873i	$-0.220185\pi$
$541$	−3.89230	−	6.74167i	−0.167343	−	0.289847i	−0.937485	+	0.348026i	$0.886852\pi$
$542$	9.46410	+	9.46410i	0.406518	+	0.406518i
$543$	−1.39230	−	0.803848i	−0.0597495	−	0.0344964i
$544$	−25.8564	+	25.8564i	−1.10858	+	1.10858i
$545$		−	2.07180i		−	0.0887460i
$546$		0			0
$547$		−	21.4641i		−	0.917739i	−0.888504	−	0.458869i	$-0.848255\pi$
$547$		−	21.4641i		−	0.917739i	0.888504	−	0.458869i	$-0.151745\pi$
$548$			40.7846i			1.74223i
$549$		0			0
$550$	−0.267949	+	0.267949i	−0.0114254	+	0.0114254i
$551$	−23.7846	−	41.1962i	−1.01326	−	1.75502i
$552$	−5.07180	−	5.07180i	−0.215870	−	0.215870i
$553$		0			0
$554$	6.14359	−	22.9282i	0.261016	−	0.974126i
$555$	−14.1962	+	8.19615i	−0.602593	+	0.347907i
$556$	12.0000	−	6.92820i	0.508913	−	0.293821i
$557$	10.9282	−	18.9282i	0.463043	−	0.802014i	−0.536068	−	0.844175i	$-0.680091\pi$
$557$	10.9282	−	18.9282i	0.463043	−	0.802014i	0.999111	+	0.0421611i	$0.0134243\pi$
$558$		0			0
$559$	−0.928203			−0.0392588
$560$		0			0
$561$	3.00000			0.126660
$562$	10.8301	−	2.90192i	0.456841	−	0.122410i
$563$	−9.58846	+	16.6077i	−0.404105	+	0.699931i	−0.994217	−	0.107391i	$-0.965750\pi$
$563$	−9.58846	+	16.6077i	−0.404105	+	0.699931i	0.590112	+	0.807322i	$0.299084\pi$
$564$	−5.19615	+	3.00000i	−0.218797	+	0.126323i
$565$	−4.73205	+	2.73205i	−0.199079	+	0.114938i
$566$	4.43782	−	16.5622i	0.186536	−	0.696160i
$567$		0			0
$568$	14.9282	+	14.9282i	0.626373	+	0.626373i
$569$	−3.53590	−	6.12436i	−0.148233	−	0.256746i	0.782342	−	0.622849i	$-0.214025\pi$
$569$	−3.53590	−	6.12436i	−0.148233	−	0.256746i	−0.930574	+	0.366103i	$0.880692\pi$
$570$	−10.3923	+	10.3923i	−0.435286	+	0.435286i
$571$	−5.78461	−	3.33975i	−0.242078	−	0.139764i	0.374053	−	0.927407i	$-0.377968\pi$
$571$	−5.78461	−	3.33975i	−0.242078	−	0.139764i	−0.616132	+	0.787643i	$0.711301\pi$
$572$		−	0.248711i		−	0.0103991i
$573$			12.4641i			0.520695i
$574$		0			0
$575$			1.46410i			0.0610573i
$576$		0			0
$577$	−16.7942	−	9.69615i	−0.699153	−	0.403656i	0.107879	−	0.994164i	$-0.465594\pi$
$577$	−16.7942	−	9.69615i	−0.699153	−	0.403656i	−0.807032	+	0.590508i	$0.798927\pi$
$578$	−24.7846	−	24.7846i	−1.03090	−	1.03090i
$579$	−8.19615	−	14.1962i	−0.340620	−	0.589972i
$580$	−7.92820	+	13.7321i	−0.329201	+	0.570192i
$581$		0			0
$582$	31.6865	+	8.49038i	1.31345	+	0.351938i
$583$	−0.464102	+	0.267949i	−0.0192211	+	0.0110973i
$584$	35.3205	−	9.46410i	1.46157	−	0.391627i
$585$		0			0
$586$	−7.43782	−	27.7583i	−0.307254	−	1.14669i
$587$	−20.5359			−0.847607			−0.423804	−	0.905754i	$-0.639305\pi$
$587$	−20.5359			−0.847607			−0.423804	+	0.905754i	$0.639305\pi$
$588$		0			0
$589$	−36.0000			−1.48335
$590$	−1.26795	−	4.73205i	−0.0522006	−	0.194815i
$591$	−11.5359	+	19.9808i	−0.474523	+	0.821899i
$592$	37.8564			1.55589
$593$	26.3827	−	15.2321i	1.08341	−	0.625505i	0.151594	−	0.988443i	$-0.451560\pi$
$593$	26.3827	−	15.2321i	1.08341	−	0.625505i	0.931813	+	0.362938i	$0.118226\pi$
$594$	−1.90192	−	0.509619i	−0.0780369	−	0.0209099i
$595$		0			0
$596$	−5.32051	−	3.07180i	−0.217937	−	0.125826i
$597$	3.00000	+	5.19615i	0.122782	+	0.212664i
$598$	−0.679492	−	0.679492i	−0.0277865	−	0.0277865i
$599$	−8.76795	−	5.06218i	−0.358249	−	0.206835i	0.310064	−	0.950716i	$-0.399650\pi$
$599$	−8.76795	−	5.06218i	−0.358249	−	0.206835i	−0.668312	+	0.743881i	$0.732983\pi$
$600$	4.73205	+	1.26795i	0.193185	+	0.0517638i
$601$		−	14.7846i		−	0.603077i	−0.953454	−	0.301538i	$-0.902500\pi$
$601$		−	14.7846i		−	0.603077i	0.953454	−	0.301538i	$-0.0975001\pi$
$602$		0			0
$603$		0			0
$604$	30.3923			1.23665
$605$	9.46410	+	5.46410i	0.384770	+	0.222147i
$606$	−26.7846	+	26.7846i	−1.08805	+	1.08805i
$607$	14.5981	+	25.2846i	0.592518	+	1.02627i	0.993892	+	0.110357i	$0.0351993\pi$
$607$	14.5981	+	25.2846i	0.592518	+	1.02627i	−0.401374	+	0.915914i	$0.631467\pi$
$608$	32.7846	−	8.78461i	1.32959	−	0.356263i
$609$		0			0
$610$	3.46410	−	12.9282i	0.140257	−	0.523448i
$611$	−0.696152	+	0.401924i	−0.0281633	+	0.0162601i
$612$		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	$0.101939\pi$
$614$	−2.36603	+	0.633975i	−0.0954850	+	0.0255851i
$615$	6.00000			0.241943
$616$		0			0
$617$	−22.9282			−0.923055			−0.461527	−	0.887126i	$-0.652698\pi$
$617$	−22.9282			−0.923055			−0.461527	+	0.887126i	$0.652698\pi$
$618$	−16.0981	+	4.31347i	−0.647560	+	0.173513i
$619$	−0.339746	+	0.588457i	−0.0136555	+	0.0236521i	−0.872772	−	0.488127i	$-0.837680\pi$
$619$	−0.339746	+	0.588457i	−0.0136555	+	0.0236521i	0.859117	+	0.511779i	$0.171013\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$	−6.58846	+	3.80385i	−0.264386	+	0.152643i
$622$	2.87564	−	10.7321i	0.115303	−	0.430316i
$623$		0			0
$624$	−2.78461	+	1.60770i	−0.111474	+	0.0643593i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	17.5359	−	17.5359i	0.700875	−	0.700875i
$627$	−2.41154	−	1.39230i	−0.0963077	−	0.0556033i
$628$	−15.7128			−0.627009
$629$			61.1769i			2.43928i
$630$		0			0
$631$		−	38.9090i		−	1.54894i	−0.632610	−	0.774471i	$-0.718016\pi$
$631$		−	38.9090i		−	1.54894i	0.632610	−	0.774471i	$-0.281984\pi$
$632$	10.7321	−	40.0526i	0.426898	−	1.59321i
$633$	−4.79423	−	2.76795i	−0.190553	−	0.110016i
$634$	−3.07180	−	3.07180i	−0.121997	−	0.121997i
$635$	−7.73205	−	13.3923i	−0.306837	−	0.531457i
$636$	6.00000	+	3.46410i	0.237915	+	0.137361i
$637$		0			0
$638$	−2.90192	−	0.777568i	−0.114888	−	0.0307842i
$639$		0			0
$640$	−8.00000	−	8.00000i	−0.316228	−	0.316228i
$641$	−4.46410	+	7.73205i	−0.176321	+	0.305398i	−0.940618	−	0.339468i	$-0.889753\pi$
$641$	−4.46410	+	7.73205i	−0.176321	+	0.305398i	0.764296	+	0.644865i	$0.223086\pi$
$642$	1.51666	+	5.66025i	0.0598578	+	0.223392i
$643$	7.05256			0.278126			0.139063	−	0.990284i	$-0.455591\pi$
$643$	7.05256			0.278126			0.139063	+	0.990284i	$0.455591\pi$
$644$		0			0
$645$	3.46410			0.136399
$646$	14.1962	+	52.9808i	0.558540	+	2.08450i
$647$	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
$649$	0.803848	−	0.464102i	0.0315538	−	0.0182176i
$650$	0.633975	+	0.169873i	0.0248665	+	0.00666297i
$651$		0			0
$652$	20.7846	−	36.0000i	0.813988	−	1.40987i
$653$	−8.80385	−	15.2487i	−0.344521	−	0.596728i	0.640745	−	0.767753i	$-0.278625\pi$
$653$	−8.80385	−	15.2487i	−0.344521	−	0.596728i	−0.985267	+	0.171025i	$0.945292\pi$
$654$	−3.58846	−	3.58846i	−0.140320	−	0.140320i
$655$	2.19615	+	1.26795i	0.0858108	+	0.0495429i
$656$	−12.0000	−	6.92820i	−0.468521	−	0.270501i
$657$		0			0
$658$		0			0
$659$			31.1962i			1.21523i	0.794232	+	0.607615i	$0.207874\pi$
$659$			31.1962i			1.21523i	−0.794232	+	0.607615i	$0.792126\pi$
$660$			0.928203i			0.0361303i
$661$	−34.3923	−	19.8564i	−1.33771	−	0.772325i	−0.351239	−	0.936286i	$-0.614239\pi$
$661$	−34.3923	−	19.8564i	−1.33771	−	0.772325i	−0.986467	+	0.163961i	$0.947573\pi$
$662$	−26.3923	+	26.3923i	−1.02577	+	1.02577i
$663$	−2.59808	−	4.50000i	−0.100901	−	0.174766i
$664$	−30.9282	+	30.9282i	−1.20025	+	1.20025i
$665$		0			0
$666$		0			0
$667$	−10.0526	+	5.80385i	−0.389237	+	0.224726i
$668$	−9.00000	+	5.19615i	−0.348220	+	0.201045i
$669$	−11.8923	+	20.5981i	−0.459783	+	0.796368i
$670$	−4.73205	+	1.26795i	−0.182815	+	0.0489852i
$671$	2.53590			0.0978973
$672$		0			0
$673$	−13.1769			−0.507933			−0.253966	−	0.967213i	$-0.581735\pi$
$673$	−13.1769			−0.507933			−0.253966	+	0.967213i	$0.581735\pi$
$674$		0			0
$675$	2.59808	−	4.50000i	0.100000	−	0.173205i
$676$	22.1436	−	12.7846i	0.851677	−	0.491716i
$677$	−21.9904	+	12.6962i	−0.845159	+	0.487953i	−0.859015	−	0.511951i	$-0.828923\pi$
$677$	−21.9904	+	12.6962i	−0.845159	+	0.487953i	0.0138555	+	0.999904i	$0.495590\pi$
$678$	−3.46410	+	12.9282i	−0.133038	+	0.496505i
$679$		0			0
$680$	12.9282	−	12.9282i	0.495774	−	0.495774i
$681$	17.8923	+	30.9904i	0.685635	+	1.18755i
$682$	−1.60770	+	1.60770i	−0.0615618	+	0.0615618i
$683$	6.33975	+	3.66025i	0.242584	+	0.140056i	0.616364	−	0.787462i	$-0.288605\pi$
$683$	6.33975	+	3.66025i	0.242584	+	0.140056i	−0.373780	+	0.927517i	$0.621938\pi$
$684$		0			0
$685$		−	20.3923i		−	0.779150i
$686$		0			0
$687$			14.7846i			0.564068i
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$	0.803848	+	0.464102i	0.0306242	+	0.0176809i
$690$	2.53590	+	2.53590i	0.0965400	+	0.0965400i
$691$	11.3205	+	19.6077i	0.430652	+	0.745912i	0.996930	−	0.0783030i	$-0.0249502\pi$
$691$	11.3205	+	19.6077i	0.430652	+	0.745912i	−0.566277	+	0.824215i	$0.691617\pi$
$692$	−14.3205	+	24.8038i	−0.544384	+	0.942901i
$693$		0			0
$694$	−46.7846	−	12.5359i	−1.77592	−	0.475856i
$695$	−6.00000	+	3.46410i	−0.227593	+	0.131401i
$696$	10.0526	+	37.5167i	0.381041	+	1.42207i
$697$	11.1962	−	19.3923i	0.424085	−	0.734536i
$698$	1.94744	+	7.26795i	0.0737117	+	0.275096i
$699$	15.7128			0.594313
$700$		0			0
$701$	−37.7846			−1.42711			−0.713553	−	0.700602i	$-0.752915\pi$
$701$	−37.7846			−1.42711			−0.713553	+	0.700602i	$0.752915\pi$
$702$	0.882686	+	3.29423i	0.0333148	+	0.124333i
$703$	28.3923	−	49.1769i	1.07084	−	1.85474i
$704$	1.07180	−	1.85641i	0.0403949	−	0.0699660i
$705$	2.59808	−	1.50000i	0.0978492	−	0.0564933i
$706$	−10.0981	−	2.70577i	−0.380046	−	0.101833i
$707$		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	$0.962359\pi$
$710$	−7.46410	−	7.46410i	−0.280123	−	0.280123i
$711$		0			0
$712$	−1.85641	+	6.92820i	−0.0695718	+	0.259645i
$713$			8.78461i			0.328986i
$714$		0			0
$715$			0.124356i			0.00465064i
$716$	−12.7846			−0.477783
$717$	35.9711	+	20.7679i	1.34337	+	0.775593i
$718$	25.3205	−	25.3205i	0.944953	−	0.944953i
$719$	−19.2679	−	33.3731i	−0.718573	−	1.24461i	−0.961565	−	0.274577i	$-0.911462\pi$
$719$	−19.2679	−	33.3731i	−0.718573	−	1.24461i	0.242992	−	0.970028i	$-0.421871\pi$
$720$		0			0
$721$		0			0
$722$	6.22243	−	23.2224i	0.231575	−	0.864249i
$723$	−24.5885	+	14.1962i	−0.914455	+	0.527961i
$724$	−0.928203	−	1.60770i	−0.0344964	−	0.0597495i
$725$	3.96410	−	6.86603i	0.147223	−	0.254998i
$726$	25.8564	−	6.92820i	0.959621	−	0.257130i
$727$	−13.6077			−0.504681			−0.252341	−	0.967638i	$-0.581200\pi$
$727$	−13.6077			−0.504681			−0.252341	+	0.967638i	$0.581200\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	−17.6603	+	4.73205i	−0.653635	+	0.175141i
$731$	6.46410	−	11.1962i	0.239083	−	0.414105i
$732$	−16.3923	−	28.3923i	−0.605877	−	1.04941i
$733$	9.99038	−	5.76795i	0.369003	−	0.213044i	−0.304020	−	0.952666i	$-0.598329\pi$
$733$	9.99038	−	5.76795i	0.369003	−	0.213044i	0.673023	+	0.739622i	$0.264996\pi$
$734$	4.34679	−	16.2224i	0.160443	−	0.598781i
$735$		0			0
$736$	−2.14359	−	8.00000i	−0.0790139	−	0.294884i
$737$	−0.464102	−	0.803848i	−0.0170954	−	0.0296101i
$738$		0			0
$739$	−3.69615	−	2.13397i	−0.135965	−	0.0784995i	0.430474	−	0.902603i	$-0.358346\pi$
$739$	−3.69615	−	2.13397i	−0.135965	−	0.0784995i	−0.566440	+	0.824103i	$0.691680\pi$
$740$	−18.9282			−0.695815
$741$			4.82309i			0.177180i
$742$		0			0
$743$		−	30.3923i		−	1.11499i	−0.830182	−	0.557493i	$-0.811763\pi$
$743$		−	30.3923i		−	1.11499i	0.830182	−	0.557493i	$-0.188237\pi$
$744$	28.3923	+	7.60770i	1.04091	+	0.278912i
$745$	2.66025	+	1.53590i	0.0974642	+	0.0562710i
$746$	−3.60770	−	3.60770i	−0.132087	−	0.132087i
$747$		0			0
$748$	3.00000	+	1.73205i	0.109691	+	0.0633300i
$749$		0			0
$750$	−2.36603	−	0.633975i	−0.0863950	−	0.0231495i
$751$	22.1603	−	12.7942i	0.808639	−	0.466868i	−0.0378439	−	0.999284i	$-0.512049\pi$
$751$	22.1603	−	12.7942i	0.808639	−	0.466868i	0.846483	+	0.532416i	$0.178716\pi$
$752$	−6.92820			−0.252646
$753$	−22.3923	+	38.7846i	−0.816021	+	1.41339i
$754$	1.34679	+	5.02628i	0.0490471	+	0.183046i
$755$	−15.1962			−0.553045
$756$		0			0
$757$	37.8564			1.37591			0.687957	−	0.725751i	$-0.258508\pi$
$757$	37.8564			1.37591			0.687957	+	0.725751i	$0.258508\pi$
$758$	2.05256	+	7.66025i	0.0745523	+	0.278233i
$759$	−0.339746	+	0.588457i	−0.0123320	+	0.0213596i
$760$	−16.3923	+	4.39230i	−0.594611	+	0.159326i
$761$	−36.5885	+	21.1244i	−1.32633	+	0.765757i	−0.984730	−	0.174088i	$-0.944302\pi$
$761$	−36.5885	+	21.1244i	−1.32633	+	0.765757i	−0.341600	+	0.939845i	$0.610969\pi$
$762$	−36.5885	−	9.80385i	−1.32546	−	0.355156i
$763$		0			0
$764$	−7.19615	+	12.4641i	−0.260348	+	0.450935i
$765$		0			0
$766$	27.4641	+	27.4641i	0.992318	+	0.992318i
$767$	−1.39230	−	0.803848i	−0.0502732	−	0.0290253i
$768$	−27.7128			−1.00000
$769$			18.0000i			0.649097i	0.945869	+	0.324548i	$0.105212\pi$
$769$			18.0000i			0.649097i	−0.945869	+	0.324548i	$0.894788\pi$
$770$		0			0
$771$		−	10.3923i		−	0.374270i
$772$		−	18.9282i		−	0.681241i
$773$	4.79423	+	2.76795i	0.172436	+	0.0995562i	0.583734	−	0.811945i	$-0.301591\pi$
$773$	4.79423	+	2.76795i	0.172436	+	0.0995562i	−0.411298	+	0.911501i	$0.634924\pi$
$774$		0			0
$775$	−3.00000	−	5.19615i	−0.107763	−	0.186651i
$776$	26.7846	+	26.7846i	0.961511	+	0.961511i
$777$		0			0
$778$	−7.63397	+	28.4904i	−0.273691	+	1.02143i
$779$	−18.0000	+	10.3923i	−0.644917	+	0.372343i
$780$	1.39230	−	0.803848i	0.0498525	−	0.0287824i
$781$	1.00000	−	1.73205i	0.0357828	−	0.0619777i
$782$	12.9282	−	3.46410i	0.462312	−	0.123876i
$783$	41.1962			1.47223
$784$		0			0
$785$	7.85641			0.280407
$786$	6.00000	−	1.60770i	0.214013	−	0.0573446i
$787$	−16.3301	+	28.2846i	−0.582106	+	1.00824i	0.413123	+	0.910675i	$0.364438\pi$
$787$	−16.3301	+	28.2846i	−0.582106	+	1.00824i	−0.995229	+	0.0975623i	$0.968895\pi$
$788$	−23.0718	+	13.3205i	−0.821899	+	0.474523i
$789$	−17.1962	+	9.92820i	−0.612199	+	0.353453i
$790$	−5.36603	+	20.0263i	−0.190915	+	0.712503i
$791$		0			0
$792$		0			0
$793$	−2.19615	−	3.80385i	−0.0779877	−	0.135079i
$794$	−12.4641	+	12.4641i	−0.442334	+	0.442334i
$795$	−3.00000	−	1.73205i	−0.106399	−	0.0614295i
$796$			6.92820i			0.245564i
$797$		−	22.1769i		−	0.785547i	−0.919635	−	0.392773i	$-0.871516\pi$
$797$		−	22.1769i		−	0.785547i	0.919635	−	0.392773i	$-0.128484\pi$
$798$		0			0
$799$		−	11.1962i		−	0.396091i
$800$	4.00000	+	4.00000i	0.141421	+	0.141421i
$801$		0			0
$802$	−10.0718	−	10.0718i	−0.355648	−	0.355648i
$803$	−1.73205	−	3.00000i	−0.0611227	−	0.105868i
$804$	−6.00000	+	10.3923i	−0.211604	+	0.366508i
$805$		0			0
$806$	3.80385	+	1.01924i	0.133985	+	0.0359011i
$807$	18.0000	−	10.3923i	0.633630	−	0.365826i
$808$	−42.2487	+	11.3205i	−1.48630	+	0.398254i
$809$	−3.96410	+	6.86603i	−0.139370	+	0.241397i	−0.927258	−	0.374422i	$-0.877841\pi$
$809$	−3.96410	+	6.86603i	−0.139370	+	0.241397i	0.787888	+	0.615818i	$0.211175\pi$
$810$	−3.29423	−	12.2942i	−0.115747	−	0.431975i
$811$	29.0718			1.02085			0.510424	−	0.859923i	$-0.329488\pi$
$811$	29.0718			1.02085			0.510424	+	0.859923i	$0.329488\pi$
$812$		0			0
$813$	−16.3923			−0.574903
$814$	−0.928203	−	3.46410i	−0.0325335	−	0.121417i
$815$	−10.3923	+	18.0000i	−0.364027	+	0.630512i
$816$		−	44.7846i		−	1.56777i
$817$	−10.3923	+	6.00000i	−0.363581	+	0.209913i
$818$	5.66025	+	1.51666i	0.197906	+	0.0530288i
$819$		0			0
$820$	6.00000	+	3.46410i	0.209529	+	0.120972i
$821$	−13.8923	−	24.0622i	−0.484845	−	0.839776i	0.515004	−	0.857188i	$-0.327791\pi$
$821$	−13.8923	−	24.0622i	−0.484845	−	0.839776i	−0.999848	+	0.0174122i	$0.994457\pi$
$822$	−35.3205	−	35.3205i	−1.23194	−	1.23194i
$823$	9.58846	+	5.53590i	0.334233	+	0.192969i	0.657719	−	0.753264i	$-0.271522\pi$
$823$	9.58846	+	5.53590i	0.334233	+	0.192969i	−0.323486	+	0.946233i	$0.604855\pi$
$824$	−18.5885	−	4.98076i	−0.647560	−	0.173513i
$825$		−	0.464102i		−	0.0161579i
$826$		0			0
$827$		−	14.1436i		−	0.491821i	−0.969293	−	0.245910i	$-0.920913\pi$
$827$		−	14.1436i		−	0.491821i	0.969293	−	0.245910i	$-0.0790869\pi$
$828$		0			0
$829$	−0.215390	−	0.124356i	−0.00748081	−	0.00431905i	0.496255	−	0.868177i	$-0.334708\pi$
$829$	−0.215390	−	0.124356i	−0.00748081	−	0.00431905i	−0.503736	+	0.863858i	$0.668041\pi$
$830$	15.4641	−	15.4641i	0.536767	−	0.536767i
$831$	14.5359	+	25.1769i	0.504245	+	0.873377i
$832$	−3.71281			−0.128719
$833$		0			0
$834$	−4.39230	+	16.3923i	−0.152093	+	0.567619i
$835$	4.50000	−	2.59808i	0.155729	−	0.0899101i
$836$	−1.60770	−	2.78461i	−0.0556033	−	0.0963077i
$837$	15.5885	−	27.0000i	0.538816	−	0.933257i
$838$	33.1244	−	8.87564i	1.14426	−	0.306604i
$839$	4.39230			0.151639			0.0758196	−	0.997122i	$-0.475843\pi$
$839$	4.39230			0.151639			0.0758196	+	0.997122i	$0.475843\pi$
$840$		0			0
$841$	33.8564			1.16746
$842$	−25.9545	+	6.95448i	−0.894451	+	0.239667i
$843$	−6.86603	+	11.8923i	−0.236478	+	0.409593i
$844$	−3.19615	−	5.53590i	−0.110016	−	0.190553i
$845$	−11.0718	+	6.39230i	−0.380881	+	0.219902i
$846$		0			0
$847$		0			0
$848$	4.00000	+	6.92820i	0.137361	+	0.237915i
$849$	10.5000	+	18.1865i	0.360359	+	0.624160i
$850$	−6.46410	+	6.46410i	−0.221717	+	0.221717i
$851$	−12.0000	−	6.92820i	−0.411355	−	0.237496i
$852$	−25.8564			−0.885826
$853$		−	2.78461i		−	0.0953432i	−0.998863	−	0.0476716i	$-0.984820\pi$
$853$		−	2.78461i		−	0.0953432i	0.998863	−	0.0476716i	$-0.0151801\pi$
$854$		0			0
$855$		0			0
$856$	−1.75129	+	6.53590i	−0.0598578	+	0.223392i
$857$	−49.9808	−	28.8564i	−1.70731	−	0.985716i	−0.937863	−	0.347006i	$-0.887198\pi$
$857$	−49.9808	−	28.8564i	−1.70731	−	0.985716i	−0.769447	−	0.638710i	$-0.779468\pi$
$858$	0.215390	+	0.215390i	0.00735330	+	0.00735330i
$859$	−19.8564	−	34.3923i	−0.677492	−	1.17345i	−0.975734	−	0.218960i	$-0.929734\pi$
$859$	−19.8564	−	34.3923i	−0.677492	−	1.17345i	0.298242	−	0.954490i	$-0.403600\pi$
$860$	3.46410	+	2.00000i	0.118125	+	0.0681994i
$861$		0			0
$862$	18.5622	+	4.97372i	0.632230	+	0.169406i
$863$	34.5167	−	19.9282i	1.17496	−	0.678364i	0.220117	−	0.975473i	$-0.429356\pi$
$863$	34.5167	−	19.9282i	1.17496	−	0.678364i	0.954843	+	0.297109i	$0.0960226\pi$
$864$	−7.60770	+	28.3923i	−0.258819	+	0.965926i
$865$	7.16025	−	12.4019i	0.243456	−	0.421678i
$866$	11.6603	+	43.5167i	0.396232	+	1.47876i
$867$	42.9282			1.45792
$868$		0			0
$869$	−3.92820			−0.133255
$870$	−5.02628	−	18.7583i	−0.170407	−	0.635967i
$871$	−0.803848	+	1.39230i	−0.0272373	+	0.0471764i
$872$	−1.51666	−	5.66025i	−0.0513606	−	0.191680i
$873$		0			0
$874$	−12.0000	−	3.21539i	−0.405906	−	0.108762i
$875$		0			0
$876$	−22.3923	+	38.7846i	−0.756566	+	1.31041i
$877$	9.19615	+	15.9282i	0.310532	+	0.537857i	0.978478	−	0.206353i	$-0.0661595\pi$
$877$	9.19615	+	15.9282i	0.310532	+	0.537857i	−0.667946	+	0.744210i	$0.732826\pi$
$878$	−39.7128	−	39.7128i	−1.34024	−	1.34024i
$879$	30.4808	+	17.5981i	1.02809	+	0.593568i
$880$	−0.535898	+	0.928203i	−0.0180651	+	0.0312897i
$881$		−	29.0718i		−	0.979454i	−0.871876	−	0.489727i	$-0.837096\pi$
$881$		−	29.0718i		−	0.979454i	0.871876	−	0.489727i	$-0.162904\pi$
$882$		0			0
$883$			23.6077i			0.794462i	0.917719	+	0.397231i	$0.130029\pi$
$883$			23.6077i			0.794462i	−0.917719	+	0.397231i	$0.869971\pi$
$884$		−	6.00000i		−	0.201802i
$885$	5.19615	+	3.00000i	0.174667	+	0.100844i
$886$	−26.0000	+	26.0000i	−0.873487	+	0.873487i
$887$	4.26795	+	7.39230i	0.143304	+	0.248209i	0.928739	−	0.370735i	$-0.120894\pi$
$887$	4.26795	+	7.39230i	0.143304	+	0.248209i	−0.785435	+	0.618944i	$0.787561\pi$
$888$	−32.7846	+	32.7846i	−1.10018	+	1.10018i
$889$		0			0
$890$	0.928203	−	3.46410i	0.0311134	−	0.116117i
$891$	2.08846	−	1.20577i	0.0699660	−	0.0403949i
$892$	−23.7846	+	13.7321i	−0.796368	+	0.459783i
$893$	−5.19615	+	9.00000i	−0.173883	+	0.301174i
$894$	7.26795	−	1.94744i	0.243077	−	0.0651322i
$895$	6.39230			0.213671
$896$		0			0
$897$	1.17691			0.0392960
$898$	−16.2942	+	4.36603i	−0.543745	+	0.145696i
$899$	23.7846	−	41.1962i	0.793261	−	1.37397i
$900$		0			0
$901$	−11.1962	+	6.46410i	−0.372998	+	0.215350i
$902$	−0.339746	+	1.26795i	−0.0113123	+	0.0422181i
$903$		0			0
$904$	−10.9282	+	10.9282i	−0.363467	+	0.363467i
$905$	0.464102	+	0.803848i	0.0154273	+	0.0267208i
$906$	−26.3205	+	26.3205i	−0.874440	+	0.874440i
$907$	−28.0526	−	16.1962i	−0.931470	−	0.537784i	−0.0441938	−	0.999023i	$-0.514072\pi$
$907$	−28.0526	−	16.1962i	−0.931470	−	0.537784i	−0.887276	+	0.461239i	$0.847405\pi$
$908$			41.3205i			1.37127i
$909$		0			0
$910$		0			0
$911$			20.2487i			0.670870i	0.942063	+	0.335435i	$0.108883\pi$
$911$			20.2487i			0.670870i	−0.942063	+	0.335435i	$0.891117\pi$
$912$	−20.7846	+	36.0000i	−0.688247	+	1.19208i
$913$	3.58846	+	2.07180i	0.118761	+	0.0685665i
$914$	20.5359	+	20.5359i	0.679267	+	0.679267i
$915$	8.19615	+	14.1962i	0.270956	+	0.469310i
$916$	−8.53590	+	14.7846i	−0.282034	+	0.488497i
$917$		0			0
$918$	−45.8827	−	12.2942i	−1.51435	−	0.405770i
$919$	5.55256	−	3.20577i	0.183162	−	0.105749i	−0.405615	−	0.914044i	$-0.632943\pi$
$919$	5.55256	−	3.20577i	0.183162	−	0.105749i	0.588777	+	0.808295i	$0.299609\pi$
$920$	1.07180	+	4.00000i	0.0353361	+	0.131876i
$921$	1.50000	−	2.59808i	0.0494267	−	0.0856095i
$922$	−10.1436	−	37.8564i	−0.334061	−	1.24673i
$923$	−3.46410			−0.114022
$924$		0			0
$925$	9.46410			0.311178
$926$	−6.00000	−	22.3923i	−0.197172	−	0.735857i
$927$		0			0
$928$	−11.6077	+	43.3205i	−0.381041	+	1.42207i
$929$	−47.1962	+	27.2487i	−1.54846	+	0.894001i	−0.550196	+	0.835036i	$0.685447\pi$
$929$	−47.1962	+	27.2487i	−1.54846	+	0.894001i	−0.998260	+	0.0589653i	$0.981220\pi$
$930$	−14.1962	−	3.80385i	−0.465510	−	0.124733i
$931$		0			0
$932$	15.7128	+	9.07180i	0.514690	+	0.297157i
$933$	6.80385	+	11.7846i	0.222748	+	0.385811i
$934$	22.5167	+	22.5167i	0.736768	+	0.736768i
$935$	−1.50000	−	0.866025i	−0.0490552	−	0.0283221i
$936$		0			0
$937$		−	25.3923i		−	0.829530i	−0.909928	−	0.414765i	$-0.863864\pi$
$937$		−	25.3923i		−	0.829530i	0.909928	−	0.414765i	$-0.136136\pi$
$938$		0			0
$939$			30.3731i			0.991188i
$940$	3.46410			0.112987
$941$	−33.8038	−	19.5167i	−1.10197	−	0.636225i	−0.165235	−	0.986254i	$-0.552838\pi$
$941$	−33.8038	−	19.5167i	−1.10197	−	0.636225i	−0.936739	+	0.350029i	$0.886172\pi$
$942$	13.6077	−	13.6077i	0.443363	−	0.443363i
$943$	2.53590	+	4.39230i	0.0825802	+	0.143033i
$944$	−6.92820	−	12.0000i	−0.225494	−	0.390567i
$945$		0			0
$946$	−0.196152	+	0.732051i	−0.00637747	+	0.0238010i
$947$	−19.7321	+	11.3923i	−0.641205	+	0.370200i	−0.785079	−	0.619396i	$-0.787378\pi$
$947$	−19.7321	+	11.3923i	−0.641205	+	0.370200i	0.143873	+	0.989596i	$0.454044\pi$
$948$	25.3923	+	43.9808i	0.824704	+	1.42843i
$949$	−3.00000	+	5.19615i	−0.0973841	+	0.168674i
$950$	8.19615	−	2.19615i	0.265918	−	0.0712526i
$951$	5.32051			0.172529
$952$		0			0
$953$	21.3205			0.690639			0.345320	−	0.938485i	$-0.387771\pi$
$953$	21.3205			0.690639			0.345320	+	0.938485i	$0.387771\pi$
$954$		0			0
$955$	3.59808	−	6.23205i	0.116431	−	0.201664i
$956$	23.9808	+	41.5359i	0.775593	+	1.34337i
$957$	3.18653	−	1.83975i	0.103006	−	0.0594705i
$958$	9.21539	−	34.3923i	0.297736	−	1.11116i
$959$		0			0
$960$	13.8564			0.447214
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	−4.39230	+	4.39230i	−0.141614	+	0.141614i
$963$		0			0
$964$	−32.7846			−1.05592
$965$			9.46410i			0.304660i
$966$		0			0
$967$		−	31.1769i		−	1.00258i	−0.865279	−	0.501291i	$-0.832859\pi$
$967$		−	31.1769i		−	1.00258i	0.865279	−	0.501291i	$-0.167141\pi$
$968$	29.8564	+	8.00000i	0.959621	+	0.257130i
$969$	−58.1769	−	33.5885i	−1.86891	−	1.07902i
$970$	−13.3923	−	13.3923i	−0.430001	−	0.430001i
$971$	−7.39230	−	12.8038i	−0.237230	−	0.410895i	0.722688	−	0.691174i	$-0.242906\pi$
$971$	−7.39230	−	12.8038i	−0.237230	−	0.410895i	−0.959919	+	0.280279i	$0.909573\pi$
$972$		0			0
$973$		0			0
$974$	17.4641	+	4.67949i	0.559586	+	0.149941i
$975$	−0.696152	+	0.401924i	−0.0222947	+	0.0128719i
$976$		−	37.8564i		−	1.21175i
$977$	2.12436	−	3.67949i	0.0679642	−	0.117717i	−0.830041	−	0.557703i	$-0.811683\pi$
$977$	2.12436	−	3.67949i	0.0679642	−	0.117717i	0.898005	+	0.439985i	$0.145016\pi$
$978$	13.1769	+	49.1769i	0.421351	+	1.57250i
$979$	0.679492			0.0217167
$980$		0			0
$981$		0			0
$982$	−3.61474	−	13.4904i	−0.115351	−	0.430495i
$983$	13.7942	−	23.8923i	0.439968	−	0.762046i	−0.557719	−	0.830030i	$-0.688323\pi$
$983$	13.7942	−	23.8923i	0.439968	−	0.762046i	0.997686	+	0.0679837i	$0.0216566\pi$
$984$	16.3923	−	4.39230i	0.522568	−	0.140022i
$985$	11.5359	−	6.66025i	0.367564	−	0.212213i
$986$	−70.0070	−	18.7583i	−2.22948	−	0.597387i
$987$		0			0
$988$	−2.78461	+	4.82309i	−0.0885902	+	0.153443i
$989$	1.46410	+	2.53590i	0.0465557	+	0.0806369i
$990$		0			0
$991$	40.8564	+	23.5885i	1.29785	+	0.749312i	0.980032	−	0.198841i	$-0.0637177\pi$
$991$	40.8564	+	23.5885i	1.29785	+	0.749312i	0.317815	+	0.948153i	$0.397051\pi$
$992$	24.0000	+	24.0000i	0.762001	+	0.762001i
$993$		−	45.7128i		−	1.45065i
$994$		0			0
$995$		−	3.46410i		−	0.109819i
$996$		−	53.5692i		−	1.69741i
$997$	−4.79423	−	2.76795i	−0.151835	−	0.0876618i	0.422158	−	0.906522i	$-0.361273\pi$
$997$	−4.79423	−	2.76795i	−0.151835	−	0.0876618i	−0.573993	+	0.818861i	$0.694606\pi$
$998$	25.5885	−	25.5885i	0.809988	−	0.809988i
$999$	24.5885	+	42.5885i	0.777944	+	1.34744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.o.a.31.1		4
4.3	odd	2		980.2.o.d.31.1		4
7.2	even	3		980.2.o.c.411.2		4
7.3	odd	6		140.2.g.b.111.3	yes	4
7.4	even	3		140.2.g.a.111.3	✓	4
7.5	odd	6		980.2.o.d.411.2		4
7.6	odd	2		980.2.o.b.31.1		4
21.11	odd	6		1260.2.c.a.811.2		4
21.17	even	6		1260.2.c.b.811.2		4
28.3	even	6		140.2.g.a.111.4	yes	4
28.11	odd	6		140.2.g.b.111.4	yes	4
28.19	even	6	inner	980.2.o.a.411.1		4
28.23	odd	6		980.2.o.b.411.1		4
28.27	even	2		980.2.o.c.31.1		4
35.3	even	12		700.2.c.c.699.1		4
35.4	even	6		700.2.g.f.251.2		4
35.17	even	12		700.2.c.f.699.4		4
35.18	odd	12		700.2.c.b.699.1		4
35.24	odd	6		700.2.g.g.251.2		4
35.32	odd	12		700.2.c.e.699.4		4
56.3	even	6		2240.2.k.a.1791.3		4
56.11	odd	6		2240.2.k.b.1791.2		4
56.45	odd	6		2240.2.k.b.1791.1		4
56.53	even	6		2240.2.k.a.1791.4		4
84.11	even	6		1260.2.c.b.811.1		4
84.59	odd	6		1260.2.c.a.811.1		4
140.3	odd	12		700.2.c.e.699.3		4
140.39	odd	6		700.2.g.g.251.1		4
140.59	even	6		700.2.g.f.251.1		4
140.67	even	12		700.2.c.c.699.2		4
140.87	odd	12		700.2.c.b.699.2		4
140.123	even	12		700.2.c.f.699.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.g.a.111.3	✓	4	7.4	even	3
140.2.g.a.111.4	yes	4	28.3	even	6
140.2.g.b.111.3	yes	4	7.3	odd	6
140.2.g.b.111.4	yes	4	28.11	odd	6
700.2.c.b.699.1		4	35.18	odd	12
700.2.c.b.699.2		4	140.87	odd	12
700.2.c.c.699.1		4	35.3	even	12
700.2.c.c.699.2		4	140.67	even	12
700.2.c.e.699.3		4	140.3	odd	12
700.2.c.e.699.4		4	35.32	odd	12
700.2.c.f.699.3		4	140.123	even	12
700.2.c.f.699.4		4	35.17	even	12
700.2.g.f.251.1		4	140.59	even	6
700.2.g.f.251.2		4	35.4	even	6
700.2.g.g.251.1		4	140.39	odd	6
700.2.g.g.251.2		4	35.24	odd	6
980.2.o.a.31.1		4	1.1	even	1	trivial
980.2.o.a.411.1		4	28.19	even	6	inner
980.2.o.b.31.1		4	7.6	odd	2
980.2.o.b.411.1		4	28.23	odd	6
980.2.o.c.31.1		4	28.27	even	2
980.2.o.c.411.2		4	7.2	even	3
980.2.o.d.31.1		4	4.3	odd	2
980.2.o.d.411.2		4	7.5	odd	6
1260.2.c.a.811.1		4	84.59	odd	6
1260.2.c.a.811.2		4	21.11	odd	6
1260.2.c.b.811.1		4	84.11	even	6
1260.2.c.b.811.2		4	21.17	even	6
2240.2.k.a.1791.3		4	56.3	even	6
2240.2.k.a.1791.4		4	56.53	even	6
2240.2.k.b.1791.1		4	56.45	odd	6
2240.2.k.b.1791.2		4	56.11	odd	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 $\F_{q}$
Belyi maps

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+(-1.36603 + 0.366025i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-0.866025 + 0.500000i) q^{5} +(-0.633975 + 2.36603i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(1.00000 - 1.00000i) q^{10} +(0.232051 + 0.133975i) q^{11} -3.46410i q^{12} -0.464102i q^{13} +1.73205i q^{15} +(2.00000 - 3.46410i) q^{16} +(5.59808 + 3.23205i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-1.00000 + 1.73205i) q^{20} +(-0.366025 - 0.0980762i) q^{22} +(-1.26795 + 0.732051i) q^{23} +(1.26795 + 4.73205i) q^{24} +(0.500000 - 0.866025i) q^{25} +(0.169873 + 0.633975i) q^{26} +5.19615 q^{27} +7.92820 q^{29} +(-0.633975 - 2.36603i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(0.401924 - 0.232051i) q^{33} +(-8.83013 - 2.36603i) q^{34} +(4.73205 + 8.19615i) q^{37} +(6.00000 + 6.00000i) q^{38} +(-0.696152 - 0.401924i) q^{39} +(0.732051 - 2.73205i) q^{40} -3.46410i q^{41} -2.00000i q^{43} +0.535898 q^{44} +(1.46410 - 1.46410i) q^{46} +(-0.866025 - 1.50000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-0.366025 + 1.36603i) q^{50} +(9.69615 - 5.59808i) q^{51} +(-0.464102 - 0.803848i) q^{52} +(-1.00000 + 1.73205i) q^{53} +(-7.09808 + 1.90192i) q^{54} -0.267949 q^{55} -10.3923 q^{57} +(-10.8301 + 2.90192i) q^{58} +(1.73205 - 3.00000i) q^{59} +(1.73205 + 3.00000i) q^{60} +(8.19615 - 4.73205i) q^{61} +(-2.19615 + 8.19615i) q^{62} -8.00000i q^{64} +(0.232051 + 0.401924i) q^{65} +(-0.464102 + 0.464102i) q^{66} +(-3.00000 - 1.73205i) q^{67} +12.9282 q^{68} +2.53590i q^{69} -7.46410i q^{71} +(-11.1962 - 6.46410i) q^{73} +(-9.46410 - 9.46410i) q^{74} +(-0.866025 - 1.50000i) q^{75} +(-10.3923 - 6.00000i) q^{76} +(1.09808 + 0.294229i) q^{78} +(-12.6962 + 7.33013i) q^{79} +4.00000i q^{80} +(4.50000 - 7.79423i) q^{81} +(1.26795 + 4.73205i) q^{82} +15.4641 q^{83} -6.46410 q^{85} +(0.732051 + 2.73205i) q^{86} +(6.86603 - 11.8923i) q^{87} +(-0.732051 + 0.196152i) q^{88} +(2.19615 - 1.26795i) q^{89} +(-1.46410 + 2.53590i) 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} -13.3923i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 6 q^{6} - 8 q^{8} + 4 q^{10} - 6 q^{11} + 8 q^{16} + 12 q^{17} - 12 q^{19} - 4 q^{20} + 2 q^{22} - 12 q^{23} + 12 q^{24} + 2 q^{25} + 18 q^{26} + 4 q^{29} - 6 q^{30} + 12 q^{31} + 8 q^{32}+ \cdots + 8 q^{92}+O(q^{100}) \) 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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