LMFDB - Embedded newform 490.2.i.f.459.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(79,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("490.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.i (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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			459.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	490.459
Dual form			490.2.i.f.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +2.44949 q^{6} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +2.44949 q^{6} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.30701 - 1.81431i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(-2.12132 + 1.22474i) q^{12} -0.449490i q^{13} +(5.44949 + 0.550510i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-3.22474 - 5.58542i) q^{19} +(-0.224745 + 2.22474i) q^{20} -4.89898i q^{22} +(5.97469 - 3.44949i) q^{23} +(1.22474 - 2.12132i) q^{24} +(3.31552 - 3.74264i) q^{25} +(0.224745 + 0.389270i) q^{26} +2.89898 q^{29} +(-4.99465 + 2.24799i) q^{30} +(-0.449490 + 0.778539i) q^{31} +(0.866025 + 0.500000i) q^{32} +(10.3923 - 6.00000i) q^{33} -2.00000 q^{34} +3.00000 q^{36} +(1.73205 - 1.00000i) q^{37} +(5.58542 + 3.22474i) q^{38} +(-0.550510 + 0.953512i) q^{39} +(-0.917738 - 2.03906i) q^{40} +10.8990 q^{41} -8.89898i q^{43} +(2.44949 + 4.24264i) q^{44} +(-5.44294 - 3.92102i) q^{45} +(-3.44949 + 5.97469i) q^{46} +(0.778539 - 0.449490i) q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(-2.44949 - 4.24264i) q^{51} +(-0.389270 - 0.224745i) q^{52} +(-0.953512 - 0.550510i) q^{53} +(1.10102 - 10.8990i) q^{55} +15.7980i q^{57} +(-2.51059 + 1.44949i) q^{58} +(3.22474 - 5.58542i) q^{59} +(3.20150 - 4.44414i) q^{60} +(4.22474 + 7.31747i) q^{61} -0.898979i q^{62} -1.00000 q^{64} +(0.412514 + 0.916536i) q^{65} +(-6.00000 + 10.3923i) q^{66} +(6.92820 + 4.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -16.8990 q^{69} -10.8990 q^{71} +(-2.59808 + 1.50000i) q^{72} +(5.97469 + 3.44949i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-11.6170 + 3.87868i) q^{75} -6.44949 q^{76} -1.10102i q^{78} +(-1.44949 - 2.51059i) q^{79} +(1.81431 + 1.30701i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-9.43879 + 5.44949i) q^{82} +2.44949i q^{83} +(-4.44949 - 0.449490i) q^{85} +(4.44949 + 7.70674i) q^{86} +(-6.14966 - 3.55051i) q^{87} +(-4.24264 - 2.44949i) q^{88} +(5.00000 + 8.66025i) q^{89} +(6.67423 + 0.674235i) q^{90} -6.89898i q^{92} +(1.90702 - 1.10102i) q^{93} +(-0.449490 + 0.778539i) q^{94} +(11.7014 + 8.42953i) q^{95} +(-1.22474 - 2.12132i) q^{96} +3.79796i q^{97} -14.6969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{5} + 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 4 * q^5 + 12 * q^9	$ 8 q + 4 q^{4} + 4 q^{5} + 12 q^{9} + 4 q^{10} + 24 q^{15} - 4 q^{16} - 16 q^{19} + 8 q^{20} - 8 q^{26} - 16 q^{29} - 12 q^{30} + 16 q^{31} - 16 q^{34} + 24 q^{36} - 24 q^{39} - 4 q^{40} + 48 q^{41} - 12 q^{45} - 8 q^{46} - 8 q^{50} + 48 q^{55} + 16 q^{59} + 12 q^{60} + 24 q^{61} - 8 q^{64} + 4 q^{65} - 48 q^{66} - 96 q^{69} - 48 q^{71} - 8 q^{74} - 32 q^{76} + 8 q^{79} + 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} + 40 q^{89} + 24 q^{90} + 16 q^{94} + 4 q^{95}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^5 + 12 * q^9 + 4 * q^10 + 24 * q^15 - 4 * q^16 - 16 * q^19 + 8 * q^20 - 8 * q^26 - 16 * q^29 - 12 * q^30 + 16 * q^31 - 16 * q^34 + 24 * q^36 - 24 * q^39 - 4 * q^40 + 48 * q^41 - 12 * q^45 - 8 * q^46 - 8 * q^50 + 48 * q^55 + 16 * q^59 + 12 * q^60 + 24 * q^61 - 8 * q^64 + 4 * q^65 - 48 * q^66 - 96 * q^69 - 48 * q^71 - 8 * q^74 - 32 * q^76 + 8 * q^79 + 4 * q^80 + 36 * q^81 - 16 * q^85 + 16 * q^86 + 40 * q^89 + 24 * q^90 + 16 * q^94 + 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−2.12132	−	1.22474i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$3$	−2.12132	−	1.22474i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−2.03906	+	0.917738i	−0.911894	+	0.410425i
$5$	−2.03906	+	0.917738i	−0.911894	+	0.410425i
$6$	2.44949			1.00000
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	1.30701	−	1.81431i	0.413312	−	0.573736i
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	0.214600	+	0.976702i	$0.431155\pi$
$11$	−2.44949	+	4.24264i	−0.738549	+	1.27920i	−0.953149	+	0.302502i	$0.902178\pi$
$12$	−2.12132	+	1.22474i	−0.612372	+	0.353553i
$13$		−	0.449490i		−	0.124666i	−0.998055	−	0.0623330i	$-0.980146\pi$
$13$		−	0.449490i		−	0.124666i	0.998055	−	0.0623330i	$-0.0198541\pi$
$14$		0			0
$15$	5.44949	+	0.550510i	1.40705	+	0.142141i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	0.695113	−	0.718900i	$-0.255354\pi$
$17$	1.73205	+	1.00000i	0.420084	+	0.242536i	−0.275029	+	0.961436i	$0.588688\pi$
$18$	−2.59808	−	1.50000i	−0.612372	−	0.353553i
$19$	−3.22474	−	5.58542i	−0.739807	−	1.28138i	−0.952582	−	0.304282i	$-0.901583\pi$
$19$	−3.22474	−	5.58542i	−0.739807	−	1.28138i	0.212775	−	0.977101i	$-0.431750\pi$
$20$	−0.224745	+	2.22474i	−0.0502545	+	0.497468i
$21$		0			0
$22$		−	4.89898i		−	1.04447i
$23$	5.97469	−	3.44949i	1.24581	−	0.719268i	0.275538	−	0.961290i	$-0.411144\pi$
$23$	5.97469	−	3.44949i	1.24581	−	0.719268i	0.970271	+	0.242022i	$0.0778105\pi$
$24$	1.22474	−	2.12132i	0.250000	−	0.433013i
$25$	3.31552	−	3.74264i	0.663103	−	0.748528i
$26$	0.224745	+	0.389270i	0.0440761	+	0.0763420i
$27$		0			0
$28$		0			0
$29$	2.89898			0.538327			0.269163	−	0.963095i	$-0.413253\pi$
$29$	2.89898			0.538327			0.269163	+	0.963095i	$0.413253\pi$
$30$	−4.99465	+	2.24799i	−0.911894	+	0.410425i
$31$	−0.449490	+	0.778539i	−0.0807307	+	0.139830i	−0.903564	−	0.428453i	$-0.859059\pi$
$31$	−0.449490	+	0.778539i	−0.0807307	+	0.139830i	0.822833	+	0.568283i	$0.192392\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	10.3923	−	6.00000i	1.80907	−	1.04447i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	3.00000			0.500000
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	−0.350823	−	0.936442i	$-0.614098\pi$
$37$	1.73205	−	1.00000i	0.284747	−	0.164399i	0.635571	+	0.772043i	$0.280765\pi$
$38$	5.58542	+	3.22474i	0.906075	+	0.523123i
$39$	−0.550510	+	0.953512i	−0.0881522	+	0.152684i
$40$	−0.917738	−	2.03906i	−0.145107	−	0.322403i
$41$	10.8990			1.70213			0.851067	−	0.525057i	$-0.175956\pi$
$41$	10.8990			1.70213			0.851067	+	0.525057i	$0.175956\pi$
$42$		0			0
$43$		−	8.89898i		−	1.35708i	−0.734563	−	0.678541i	$-0.762613\pi$
$43$		−	8.89898i		−	1.35708i	0.734563	−	0.678541i	$-0.237387\pi$
$44$	2.44949	+	4.24264i	0.369274	+	0.639602i
$45$	−5.44294	−	3.92102i	−0.811386	−	0.584511i
$46$	−3.44949	+	5.97469i	−0.508600	+	0.880920i
$47$	0.778539	−	0.449490i	0.113562	−	0.0655648i	−0.442143	−	0.896944i	$-0.645782\pi$
$47$	0.778539	−	0.449490i	0.113562	−	0.0655648i	0.555705	+	0.831380i	$0.312448\pi$
$48$			2.44949i			0.353553i
$49$		0			0
$50$	−1.00000	+	4.89898i	−0.141421	+	0.692820i
$51$	−2.44949	−	4.24264i	−0.342997	−	0.594089i
$52$	−0.389270	−	0.224745i	−0.0539820	−	0.0311665i
$53$	−0.953512	−	0.550510i	−0.130975	−	0.0756184i	0.433081	−	0.901355i	$-0.357426\pi$
$53$	−0.953512	−	0.550510i	−0.130975	−	0.0756184i	−0.564056	+	0.825737i	$0.690760\pi$
$54$		0			0
$55$	1.10102	−	10.8990i	0.148462	−	1.46962i
$56$		0			0
$57$			15.7980i			2.09249i
$58$	−2.51059	+	1.44949i	−0.329657	+	0.190327i
$59$	3.22474	−	5.58542i	0.419826	−	0.727160i	−0.576096	−	0.817382i	$-0.695424\pi$
$59$	3.22474	−	5.58542i	0.419826	−	0.727160i	0.995922	+	0.0902223i	$0.0287578\pi$
$60$	3.20150	−	4.44414i	0.413312	−	0.573736i
$61$	4.22474	+	7.31747i	0.540923	+	0.936906i	0.998851	+	0.0479172i	$0.0152584\pi$
$61$	4.22474	+	7.31747i	0.540923	+	0.936906i	−0.457928	+	0.888989i	$0.651408\pi$
$62$		−	0.898979i		−	0.114171i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	0.412514	+	0.916536i	0.0511660	+	0.113682i
$66$	−6.00000	+	10.3923i	−0.738549	+	1.27920i
$67$	6.92820	+	4.00000i	0.846415	+	0.488678i	0.859440	−	0.511237i	$-0.170813\pi$
$67$	6.92820	+	4.00000i	0.846415	+	0.488678i	−0.0130248	+	0.999915i	$0.504146\pi$
$68$	1.73205	−	1.00000i	0.210042	−	0.121268i
$69$	−16.8990			−2.03440
$70$		0			0
$71$	−10.8990			−1.29347			−0.646735	−	0.762714i	$-0.723866\pi$
$71$	−10.8990			−1.29347			−0.646735	+	0.762714i	$0.723866\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$	5.97469	+	3.44949i	0.699285	+	0.403732i	0.807081	−	0.590441i	$-0.201046\pi$
$73$	5.97469	+	3.44949i	0.699285	+	0.403732i	−0.107796	+	0.994173i	$0.534379\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	−11.6170	+	3.87868i	−1.34142	+	0.447871i
$76$	−6.44949			−0.739807
$77$		0			0
$78$		−	1.10102i		−	0.124666i
$79$	−1.44949	−	2.51059i	−0.163080	−	0.282463i	0.772892	−	0.634538i	$-0.218810\pi$
$79$	−1.44949	−	2.51059i	−0.163080	−	0.282463i	−0.935972	+	0.352075i	$0.885476\pi$
$80$	1.81431	+	1.30701i	0.202846	+	0.146128i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$	−9.43879	+	5.44949i	−1.04234	+	0.601795i
$83$			2.44949i			0.268866i	0.990923	+	0.134433i	$0.0429214\pi$
$83$			2.44949i			0.268866i	−0.990923	+	0.134433i	$0.957079\pi$
$84$		0			0
$85$	−4.44949	−	0.449490i	−0.482615	−	0.0487540i
$86$	4.44949	+	7.70674i	0.479801	+	0.831039i
$87$	−6.14966	−	3.55051i	−0.659313	−	0.380655i
$88$	−4.24264	−	2.44949i	−0.452267	−	0.261116i
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	0.999388	+	0.0349934i	$0.0111410\pi$
$89$	5.00000	+	8.66025i	0.529999	+	0.917985i	−0.469389	+	0.882992i	$0.655526\pi$
$90$	6.67423	+	0.674235i	0.703526	+	0.0710706i
$91$		0			0
$92$		−	6.89898i		−	0.719268i
$93$	1.90702	−	1.10102i	0.197749	−	0.114171i
$94$	−0.449490	+	0.778539i	−0.0463613	+	0.0803002i
$95$	11.7014	+	8.42953i	1.20054	+	0.864851i
$96$	−1.22474	−	2.12132i	−0.125000	−	0.216506i
$97$			3.79796i			0.385624i	0.981236	+	0.192812i	$0.0617608\pi$
$97$			3.79796i			0.385624i	−0.981236	+	0.192812i	$0.938239\pi$
$98$		0			0
$99$	−14.6969			−1.47710
$100$	−1.58346	−	4.74264i	−0.158346	−	0.474264i
$101$	4.22474	−	7.31747i	0.420378	−	0.728116i	−0.575599	−	0.817732i	$-0.695231\pi$
$101$	4.22474	−	7.31747i	0.420378	−	0.728116i	0.995976	+	0.0896167i	$0.0285642\pi$
$102$	4.24264	+	2.44949i	0.420084	+	0.242536i
$103$	2.68556	−	1.55051i	0.264616	−	0.152776i	−0.361822	−	0.932247i	$-0.617845\pi$
$103$	2.68556	−	1.55051i	0.264616	−	0.152776i	0.626439	+	0.779471i	$0.284512\pi$
$104$	0.449490			0.0440761
$105$		0			0
$106$	1.10102			0.106941
$107$	−6.92820	+	4.00000i	−0.669775	+	0.386695i	−0.795991	−	0.605308i	$-0.793050\pi$
$107$	−6.92820	+	4.00000i	−0.669775	+	0.386695i	0.126217	+	0.992003i	$0.459717\pi$
$108$		0			0
$109$	−1.44949	+	2.51059i	−0.138836	+	0.240471i	−0.927056	−	0.374922i	$-0.877669\pi$
$109$	−1.44949	+	2.51059i	−0.138836	+	0.240471i	0.788220	+	0.615393i	$0.211003\pi$
$110$	4.49598	+	9.98930i	0.428675	+	0.952443i
$111$	−4.89898			−0.464991
$112$		0			0
$113$		−	0.202041i		−	0.0190064i	−0.999955	−	0.00950321i	$-0.996975\pi$
$113$		−	0.202041i		−	0.0190064i	0.999955	−	0.00950321i	$-0.00302501\pi$
$114$	−7.89898	−	13.6814i	−0.739807	−	1.28138i
$115$	−9.01702	+	12.5169i	−0.840841	+	1.16721i
$116$	1.44949	−	2.51059i	0.134582	−	0.233102i
$117$	1.16781	−	0.674235i	0.107964	−	0.0623330i
$118$			6.44949i			0.593724i
$119$		0			0
$120$	−0.550510	+	5.44949i	−0.0502545	+	0.497468i
$121$	−6.50000	−	11.2583i	−0.590909	−	1.02348i
$122$	−7.31747	−	4.22474i	−0.662493	−	0.382490i
$123$	−23.1202	−	13.3485i	−2.08468	−	1.20359i
$124$	0.449490	+	0.778539i	0.0403654	+	0.0699149i
$125$	−3.32577	+	10.6742i	−0.297465	+	0.954733i
$126$		0			0
$127$		−	5.10102i		−	0.452642i	−0.974053	−	0.226321i	$-0.927330\pi$
$127$		−	5.10102i		−	0.452642i	0.974053	−	0.226321i	$-0.0726699\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−10.8990	+	18.8776i	−0.959602	+	1.66208i
$130$	−0.815515	−	0.587486i	−0.0715254	−	0.0515260i
$131$	−0.775255	−	1.34278i	−0.0677344	−	0.117319i	0.830169	−	0.557511i	$-0.188244\pi$
$131$	−0.775255	−	1.34278i	−0.0677344	−	0.117319i	−0.897904	+	0.440192i	$0.854910\pi$
$132$		−	12.0000i		−	1.04447i
$133$		0			0
$134$	−8.00000			−0.691095
$135$		0			0
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	−15.4135	−	8.89898i	−1.31686	−	0.760291i	−0.333640	−	0.942700i	$-0.608277\pi$
$137$	−15.4135	−	8.89898i	−1.31686	−	0.760291i	−0.983223	+	0.182409i	$0.941610\pi$
$138$	14.6349	−	8.44949i	1.24581	−	0.719268i
$139$	6.44949			0.547039			0.273519	−	0.961867i	$-0.411812\pi$
$139$	6.44949			0.547039			0.273519	+	0.961867i	$0.411812\pi$
$140$		0			0
$141$	−2.20204			−0.185445
$142$	9.43879	−	5.44949i	0.792086	−	0.457311i
$143$	1.90702	+	1.10102i	0.159473	+	0.0920720i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	−5.91119	+	2.66050i	−0.490897	+	0.220943i
$146$	−6.89898			−0.570964
$147$		0			0
$148$		−	2.00000i		−	0.164399i
$149$	7.89898	+	13.6814i	0.647110	+	1.12083i	0.983810	+	0.179215i	$0.0573557\pi$
$149$	7.89898	+	13.6814i	0.647110	+	1.12083i	−0.336700	+	0.941612i	$0.609311\pi$
$150$	8.12132	−	9.16756i	0.663103	−	0.748528i
$151$	9.79796	−	16.9706i	0.797347	−	1.38104i	−0.123992	−	0.992283i	$-0.539570\pi$
$151$	9.79796	−	16.9706i	0.797347	−	1.38104i	0.921338	−	0.388762i	$-0.127097\pi$
$152$	5.58542	−	3.22474i	0.453038	−	0.261561i
$153$			6.00000i			0.485071i
$154$		0			0
$155$	0.202041	−	2.00000i	0.0162283	−	0.160644i
$156$	0.550510	+	0.953512i	0.0440761	+	0.0763420i
$157$	7.31747	+	4.22474i	0.583998	+	0.337171i	0.762721	−	0.646728i	$-0.223863\pi$
$157$	7.31747	+	4.22474i	0.583998	+	0.337171i	−0.178723	+	0.983899i	$0.557196\pi$
$158$	2.51059	+	1.44949i	0.199732	+	0.115315i
$159$	1.34847	+	2.33562i	0.106941	+	0.185226i
$160$	−2.22474	−	0.224745i	−0.175882	−	0.0177676i
$161$		0			0
$162$			9.00000i			0.707107i
$163$	14.6349	−	8.44949i	1.14630	−	0.661815i	0.198315	−	0.980138i	$-0.436453\pi$
$163$	14.6349	−	8.44949i	1.14630	−	0.661815i	0.947982	+	0.318323i	$0.103120\pi$
$164$	5.44949	−	9.43879i	0.425534	−	0.737046i
$165$	−15.6841	+	21.7718i	−1.22100	+	1.69493i
$166$	−1.22474	−	2.12132i	−0.0950586	−	0.164646i
$167$		−	4.89898i		−	0.379094i	−0.981872	−	0.189547i	$-0.939298\pi$
$167$		−	4.89898i		−	0.379094i	0.981872	−	0.189547i	$-0.0607020\pi$
$168$		0			0
$169$	12.7980			0.984458
$170$	4.07812	−	1.83548i	0.312777	−	0.140775i
$171$	9.67423	−	16.7563i	0.739807	−	1.28138i
$172$	−7.70674	−	4.44949i	−0.587634	−	0.339270i
$173$	15.8028	−	9.12372i	1.20146	−	0.693664i	0.240581	−	0.970629i	$-0.422662\pi$
$173$	15.8028	−	9.12372i	1.20146	−	0.693664i	0.960880	+	0.276965i	$0.0893286\pi$
$174$	7.10102			0.538327
$175$		0			0
$176$	4.89898			0.369274
$177$	−13.6814	+	7.89898i	−1.02836	+	0.593724i
$178$	−8.66025	−	5.00000i	−0.649113	−	0.374766i
$179$	−2.89898	+	5.02118i	−0.216680	+	0.375301i	−0.953791	−	0.300471i	$-0.902856\pi$
$179$	−2.89898	+	5.02118i	−0.216680	+	0.375301i	0.737111	+	0.675772i	$0.236189\pi$
$180$	−6.11717	+	2.75321i	−0.455947	+	0.205212i
$181$	−14.2474			−1.05900			−0.529502	−	0.848309i	$-0.677621\pi$
$181$	−14.2474			−1.05900			−0.529502	+	0.848309i	$0.677621\pi$
$182$		0			0
$183$		−	20.6969i		−	1.52996i
$184$	3.44949	+	5.97469i	0.254300	+	0.440460i
$185$	−2.61401	+	3.62863i	−0.192186	+	0.266782i
$186$	−1.10102	+	1.90702i	−0.0807307	+	0.139830i
$187$	−8.48528	+	4.89898i	−0.620505	+	0.358249i
$188$		−	0.898979i		−	0.0655648i
$189$		0			0
$190$	−14.3485	−	1.44949i	−1.04095	−	0.105157i
$191$	8.34847	+	14.4600i	0.604074	+	1.04629i	0.992197	+	0.124679i	$0.0397902\pi$
$191$	8.34847	+	14.4600i	0.604074	+	1.04629i	−0.388123	+	0.921608i	$0.626876\pi$
$192$	2.12132	+	1.22474i	0.153093	+	0.0883883i
$193$	15.2385	+	8.79796i	1.09689	+	0.633291i	0.935403	−	0.353584i	$-0.115037\pi$
$193$	15.2385	+	8.79796i	1.09689	+	0.633291i	0.161489	+	0.986874i	$0.448370\pi$
$194$	−1.89898	−	3.28913i	−0.136339	−	0.236146i
$195$	0.247449	−	2.44949i	0.0177202	−	0.175412i
$196$		0			0
$197$			9.10102i			0.648421i	0.945985	+	0.324210i	$0.105099\pi$
$197$			9.10102i			0.648421i	−0.945985	+	0.324210i	$0.894901\pi$
$198$	12.7279	−	7.34847i	0.904534	−	0.522233i
$199$	−3.55051	+	6.14966i	−0.251689	+	0.435938i	−0.963991	−	0.265935i	$-0.914319\pi$
$199$	−3.55051	+	6.14966i	−0.251689	+	0.435938i	0.712302	+	0.701873i	$0.247653\pi$
$200$	3.74264	+	3.31552i	0.264645	+	0.234442i
$201$	−9.79796	−	16.9706i	−0.691095	−	1.19701i
$202$			8.44949i			0.594504i
$203$		0			0
$204$	−4.89898			−0.342997
$205$	−22.2237	+	10.0024i	−1.55217	+	0.698598i
$206$	−1.55051	+	2.68556i	−0.108029	+	0.187112i
$207$	17.9241	+	10.3485i	1.24581	+	0.719268i
$208$	−0.389270	+	0.224745i	−0.0269910	+	0.0155833i
$209$	31.5959			2.18554
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−0.953512	+	0.550510i	−0.0654875	+	0.0378092i
$213$	23.1202	+	13.3485i	1.58417	+	0.914622i
$214$	4.00000	−	6.92820i	0.273434	−	0.473602i
$215$	8.16693	+	18.1455i	0.556980	+	1.23752i
$216$		0			0
$217$		0			0
$218$		−	2.89898i		−	0.196344i
$219$	−8.44949	−	14.6349i	−0.570964	−	0.988938i
$220$	−8.88828	−	6.40300i	−0.599248	−	0.431690i
$221$	0.449490	−	0.778539i	0.0302360	−	0.0523702i
$222$	4.24264	−	2.44949i	0.284747	−	0.164399i
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$		0			0
$225$	14.6969	+	3.00000i	0.979796	+	0.200000i
$226$	0.101021	+	0.174973i	0.00671978	+	0.0116390i
$227$	−6.36396	−	3.67423i	−0.422391	−	0.243868i	0.273709	−	0.961813i	$-0.411750\pi$
$227$	−6.36396	−	3.67423i	−0.422391	−	0.243868i	−0.696100	+	0.717945i	$0.745083\pi$
$228$	13.6814	+	7.89898i	0.906075	+	0.523123i
$229$	−7.57321	−	13.1172i	−0.500452	−	0.866808i	−1.00000		0.000522089i	$-0.999834\pi$
$229$	−7.57321	−	13.1172i	−0.500452	−	0.866808i	0.499548	−	0.866286i	$-0.333500\pi$
$230$	1.55051	−	15.3485i	0.102238	−	1.01205i
$231$		0			0
$232$			2.89898i			0.190327i
$233$	−8.83523	+	5.10102i	−0.578815	+	0.334179i	−0.760662	−	0.649148i	$-0.775126\pi$
$233$	−8.83523	+	5.10102i	−0.578815	+	0.334179i	0.181847	+	0.983327i	$0.441792\pi$
$234$	−0.674235	+	1.16781i	−0.0440761	+	0.0763420i
$235$	−1.17497	+	1.63103i	−0.0766468	+	0.106397i
$236$	−3.22474	−	5.58542i	−0.209913	−	0.363580i
$237$			7.10102i			0.461261i
$238$		0			0
$239$	25.7980			1.66873			0.834366	−	0.551211i	$-0.185834\pi$
$239$	25.7980			1.66873			0.834366	+	0.551211i	$0.185834\pi$
$240$	−2.24799	−	4.99465i	−0.145107	−	0.322403i
$241$	10.3485	−	17.9241i	0.666604	−	1.15459i	−0.312244	−	0.950002i	$-0.601081\pi$
$241$	10.3485	−	17.9241i	0.666604	−	1.15459i	0.978848	−	0.204589i	$-0.0655859\pi$
$242$	11.2583	+	6.50000i	0.723713	+	0.417836i
$243$	−19.0919	+	11.0227i	−1.22474	+	0.707107i
$244$	8.44949			0.540923
$245$		0			0
$246$	26.6969			1.70213
$247$	−2.51059	+	1.44949i	−0.159745	+	0.0922288i
$248$	−0.778539	−	0.449490i	−0.0494373	−	0.0285426i
$249$	3.00000	−	5.19615i	0.190117	−	0.329293i
$250$	−2.45692	−	10.9070i	−0.155389	−	0.689822i
$251$	1.55051			0.0978673			0.0489337	−	0.998802i	$-0.484418\pi$
$251$	1.55051			0.0978673			0.0489337	+	0.998802i	$0.484418\pi$
$252$		0			0
$253$			33.7980i			2.12486i
$254$	2.55051	+	4.41761i	0.160033	+	0.277186i
$255$	8.88828	+	6.40300i	0.556606	+	0.400972i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−17.9241	+	10.3485i	−1.11807	+	0.645520i	−0.940908	−	0.338661i	$-0.890026\pi$
$257$	−17.9241	+	10.3485i	−1.11807	+	0.645520i	−0.177165	+	0.984181i	$0.556693\pi$
$258$		−	21.7980i		−	1.35708i
$259$		0			0
$260$	1.00000	+	0.101021i	0.0620174	+	0.00626503i
$261$	4.34847	+	7.53177i	0.269163	+	0.466205i
$262$	1.34278	+	0.775255i	0.0829573	+	0.0478954i
$263$	−8.48528	−	4.89898i	−0.523225	−	0.302084i	0.215028	−	0.976608i	$-0.431016\pi$
$263$	−8.48528	−	4.89898i	−0.523225	−	0.302084i	−0.738253	+	0.674524i	$0.764349\pi$
$264$	6.00000	+	10.3923i	0.369274	+	0.639602i
$265$	2.44949	+	0.247449i	0.150471	+	0.0152007i
$266$		0			0
$267$		−	24.4949i		−	1.49906i
$268$	6.92820	−	4.00000i	0.423207	−	0.244339i
$269$	7.57321	−	13.1172i	0.461747	−	0.799769i	−0.537301	−	0.843390i	$-0.680556\pi$
$269$	7.57321	−	13.1172i	0.461747	−	0.799769i	0.999048	+	0.0436212i	$0.0138895\pi$
$270$		0			0
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	0.988692	−	0.149963i	$-0.0479155\pi$
$271$	6.00000	+	10.3923i	0.364474	+	0.631288i	−0.624218	+	0.781251i	$0.714582\pi$
$272$		−	2.00000i		−	0.121268i
$273$		0			0
$274$	17.7980			1.07521
$275$	7.75736	+	23.2341i	0.467786	+	1.40107i
$276$	−8.44949	+	14.6349i	−0.508600	+	0.880920i
$277$	4.41761	+	2.55051i	0.265429	+	0.153245i	0.626808	−	0.779173i	$-0.284361\pi$
$277$	4.41761	+	2.55051i	0.265429	+	0.153245i	−0.361380	+	0.932419i	$0.617694\pi$
$278$	−5.58542	+	3.22474i	−0.334991	+	0.193407i
$279$	−2.69694			−0.161461
$280$		0			0
$281$	−18.0000			−1.07379			−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000			−1.07379			−0.536895	+	0.843649i	$0.680403\pi$
$282$	1.90702	−	1.10102i	0.113562	−	0.0655648i
$283$	−24.4630	−	14.1237i	−1.45417	−	0.839568i	−0.455460	−	0.890256i	$-0.650525\pi$
$283$	−24.4630	−	14.1237i	−1.45417	−	0.839568i	−0.998715	+	0.0506878i	$0.983859\pi$
$284$	−5.44949	+	9.43879i	−0.323368	+	0.560089i
$285$	−14.4984	−	32.2130i	−0.858810	−	1.90813i
$286$	−2.20204			−0.130209
$287$		0			0
$288$			3.00000i			0.176777i
$289$	−6.50000	−	11.2583i	−0.382353	−	0.662255i
$290$	3.78899	−	5.25966i	0.222497	−	0.308858i
$291$	4.65153	−	8.05669i	0.272678	−	0.472291i
$292$	5.97469	−	3.44949i	0.349642	−	0.201866i
$293$		−	6.24745i		−	0.364980i	−0.983208	−	0.182490i	$-0.941584\pi$
$293$		−	6.24745i		−	0.364980i	0.983208	−	0.182490i	$-0.0584157\pi$
$294$		0			0
$295$	−1.44949	+	14.3485i	−0.0843926	+	0.835400i
$296$	1.00000	+	1.73205i	0.0581238	+	0.100673i
$297$		0			0
$298$	−13.6814	−	7.89898i	−0.792544	−	0.457576i
$299$	−1.55051	−	2.68556i	−0.0896683	−	0.155310i
$300$	−2.44949	+	12.0000i	−0.141421	+	0.692820i
$301$		0			0
$302$			19.5959i			1.12762i
$303$	−17.9241	+	10.3485i	−1.02971	+	0.594504i
$304$	−3.22474	+	5.58542i	−0.184952	+	0.320346i
$305$	−15.3300	−	11.0435i	−0.877794	−	0.632351i
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$		−	4.24745i		−	0.242415i	−0.992627	−	0.121207i	$-0.961323\pi$
$307$		−	4.24745i		−	0.242415i	0.992627	−	0.121207i	$-0.0386766\pi$
$308$		0			0
$309$	−7.59592			−0.432117
$310$	0.825027	+	1.83307i	0.0468584	+	0.104111i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$	−0.953512	−	0.550510i	−0.0539820	−	0.0311665i
$313$	15.2385	−	8.79796i	0.861332	−	0.497290i	−0.00312637	−	0.999995i	$-0.500995\pi$
$313$	15.2385	−	8.79796i	0.861332	−	0.497290i	0.864458	+	0.502705i	$0.167662\pi$
$314$	−8.44949			−0.476832
$315$		0			0
$316$	−2.89898			−0.163080
$317$	22.9453	−	13.2474i	1.28873	−	0.744051i	0.310305	−	0.950637i	$-0.399569\pi$
$317$	22.9453	−	13.2474i	1.28873	−	0.744051i	0.978428	+	0.206586i	$0.0662353\pi$
$318$	−2.33562	−	1.34847i	−0.130975	−	0.0756184i
$319$	−7.10102	+	12.2993i	−0.397581	+	0.688630i
$320$	2.03906	−	0.917738i	0.113987	−	0.0513031i
$321$	19.5959			1.09374
$322$		0			0
$323$		−	12.8990i		−	0.717718i
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−1.68228	−	1.49029i	−0.0933160	−	0.0826664i
$326$	−8.44949	+	14.6349i	−0.467974	+	0.810555i
$327$	6.14966	−	3.55051i	0.340077	−	0.196344i
$328$			10.8990i			0.601795i
$329$		0			0
$330$	2.69694	−	26.6969i	0.148462	−	1.46962i
$331$	−5.34847	−	9.26382i	−0.293978	−	0.509186i	0.680768	−	0.732499i	$-0.261646\pi$
$331$	−5.34847	−	9.26382i	−0.293978	−	0.509186i	−0.974747	+	0.223313i	$0.928313\pi$
$332$	2.12132	+	1.22474i	0.116423	+	0.0672166i
$333$	5.19615	+	3.00000i	0.284747	+	0.164399i
$334$	2.44949	+	4.24264i	0.134030	+	0.232147i
$335$	−17.7980	−	1.79796i	−0.972406	−	0.0982330i
$336$		0			0
$337$		−	29.5959i		−	1.61219i	−0.591785	−	0.806096i	$-0.701576\pi$
$337$		−	29.5959i		−	1.61219i	0.591785	−	0.806096i	$-0.298424\pi$
$338$	−11.0834	+	6.39898i	−0.602855	+	0.348059i
$339$	−0.247449	+	0.428594i	−0.0134396	+	0.0232780i
$340$	−2.61401	+	3.62863i	−0.141765	+	0.196790i
$341$	−2.20204	−	3.81405i	−0.119247	−	0.206542i
$342$			19.3485i			1.04625i
$343$		0			0
$344$	8.89898			0.479801
$345$	34.4580	−	15.5088i	1.85516	−	0.834967i
$346$	−9.12372	+	15.8028i	−0.490494	+	0.849561i
$347$	−16.5420	−	9.55051i	−0.888019	−	0.512698i	−0.0147253	−	0.999892i	$-0.504687\pi$
$347$	−16.5420	−	9.55051i	−0.888019	−	0.512698i	−0.873294	+	0.487193i	$0.838021\pi$
$348$	−6.14966	+	3.55051i	−0.329657	+	0.190327i
$349$	−3.55051			−0.190054			−0.0950272	−	0.995475i	$-0.530294\pi$
$349$	−3.55051			−0.190054			−0.0950272	+	0.995475i	$0.530294\pi$
$350$		0			0
$351$		0			0
$352$	−4.24264	+	2.44949i	−0.226134	+	0.130558i
$353$	−11.3458	−	6.55051i	−0.603877	−	0.348648i	0.166688	−	0.986010i	$-0.446693\pi$
$353$	−11.3458	−	6.55051i	−0.603877	−	0.348648i	−0.770565	+	0.637361i	$0.780026\pi$
$354$	7.89898	−	13.6814i	0.419826	−	0.727160i
$355$	22.2237	−	10.0024i	1.17951	−	0.530872i
$356$	10.0000			0.529999
$357$		0			0
$358$		−	5.79796i		−	0.306432i
$359$	5.79796	+	10.0424i	0.306005	+	0.530015i	0.977484	−	0.211007i	$-0.0676744\pi$
$359$	5.79796	+	10.0424i	0.306005	+	0.530015i	−0.671480	+	0.741023i	$0.734341\pi$
$360$	3.92102	−	5.44294i	0.206656	−	0.286868i
$361$	−11.2980	+	19.5686i	−0.594629	+	1.02993i
$362$	12.3387	−	7.12372i	0.648505	−	0.374415i
$363$			31.8434i			1.67134i
$364$		0			0
$365$	−15.3485	−	1.55051i	−0.803376	−	0.0811574i
$366$	10.3485	+	17.9241i	0.540923	+	0.936906i
$367$	27.7128	+	16.0000i	1.44660	+	0.835193i	0.998277	−	0.0586798i	$-0.0186891\pi$
$367$	27.7128	+	16.0000i	1.44660	+	0.835193i	0.448320	+	0.893873i	$0.352022\pi$
$368$	−5.97469	−	3.44949i	−0.311452	−	0.179817i
$369$	16.3485	+	28.3164i	0.851067	+	1.47409i
$370$	0.449490	−	4.44949i	0.0233679	−	0.231318i
$371$		0			0
$372$		−	2.20204i		−	0.114171i
$373$	−21.3882	+	12.3485i	−1.10744	+	0.639380i	−0.938165	−	0.346190i	$-0.887475\pi$
$373$	−21.3882	+	12.3485i	−1.10744	+	0.639380i	−0.169273	+	0.985569i	$0.554142\pi$
$374$	4.89898	−	8.48528i	0.253320	−	0.438763i
$375$	20.1282	−	18.5703i	1.03942	−	0.958964i
$376$	0.449490	+	0.778539i	0.0231807	+	0.0401501i
$377$		−	1.30306i		−	0.0671111i
$378$		0			0
$379$	−1.30306			−0.0669338			−0.0334669	−	0.999440i	$-0.510655\pi$
$379$	−1.30306			−0.0669338			−0.0334669	+	0.999440i	$0.510655\pi$
$380$	13.1509	−	5.91894i	0.674626	−	0.303635i
$381$	−6.24745	+	10.8209i	−0.320066	+	0.554371i
$382$	−14.4600	−	8.34847i	−0.739837	−	0.427145i
$383$	−14.6349	+	8.44949i	−0.747811	+	0.431749i	−0.824902	−	0.565275i	$-0.808770\pi$
$383$	−14.6349	+	8.44949i	−0.747811	+	0.431749i	0.0770916	+	0.997024i	$0.475437\pi$
$384$	−2.44949			−0.125000
$385$		0			0
$386$	−17.5959			−0.895609
$387$	23.1202	−	13.3485i	1.17527	−	0.678541i
$388$	3.28913	+	1.89898i	0.166980	+	0.0964061i
$389$	11.4495	−	19.8311i	0.580512	−	1.00548i	−0.414906	−	0.909864i	$-0.636186\pi$
$389$	11.4495	−	19.8311i	0.580512	−	1.00548i	0.995419	−	0.0956125i	$-0.0304810\pi$
$390$	1.01045	+	2.24504i	0.0511660	+	0.113682i
$391$	13.7980			0.697793
$392$		0			0
$393$			3.79796i			0.191582i
$394$	−4.55051	−	7.88171i	−0.229251	−	0.397075i
$395$	5.25966	+	3.78899i	0.264642	+	0.190645i
$396$	−7.34847	+	12.7279i	−0.369274	+	0.639602i
$397$	15.0242	−	8.67423i	0.754044	−	0.435347i	−0.0731094	−	0.997324i	$-0.523292\pi$
$397$	15.0242	−	8.67423i	0.754044	−	0.435347i	0.827153	+	0.561977i	$0.189959\pi$
$398$		−	7.10102i		−	0.355942i
$399$		0			0
$400$	−4.89898	−	1.00000i	−0.244949	−	0.0500000i
$401$	−14.6969	−	25.4558i	−0.733930	−	1.27120i	−0.955191	−	0.295990i	$-0.904351\pi$
$401$	−14.6969	−	25.4558i	−0.733930	−	1.27120i	0.221261	−	0.975215i	$-0.428983\pi$
$402$	16.9706	+	9.79796i	0.846415	+	0.488678i
$403$	0.349945	+	0.202041i	0.0174320	+	0.0100644i
$404$	−4.22474	−	7.31747i	−0.210189	−	0.364058i
$405$	−2.02270	+	20.0227i	−0.100509	+	0.994936i
$406$		0			0
$407$			9.79796i			0.485667i
$408$	4.24264	−	2.44949i	0.210042	−	0.121268i
$409$	7.24745	−	12.5529i	0.358363	−	0.620703i	−0.629324	−	0.777143i	$-0.716668\pi$
$409$	7.24745	−	12.5529i	0.358363	−	0.620703i	0.987688	+	0.156439i	$0.0500016\pi$
$410$	14.2450	−	19.7742i	0.703513	−	0.976576i
$411$	21.7980	+	37.7552i	1.07521	+	1.86233i
$412$		−	3.10102i		−	0.152776i
$413$		0			0
$414$	−20.6969			−1.01720
$415$	−2.24799	−	4.99465i	−0.110349	−	0.245178i
$416$	0.224745	−	0.389270i	0.0110190	−	0.0190855i
$417$	−13.6814	−	7.89898i	−0.669983	−	0.386815i
$418$	−27.3629	+	15.7980i	−1.33836	+	0.772703i
$419$	−6.44949			−0.315078			−0.157539	−	0.987513i	$-0.550356\pi$
$419$	−6.44949			−0.315078			−0.157539	+	0.987513i	$0.550356\pi$
$420$		0			0
$421$	−23.7980			−1.15984			−0.579921	−	0.814673i	$-0.696917\pi$
$421$	−23.7980			−1.15984			−0.579921	+	0.814673i	$0.696917\pi$
$422$	−10.3923	+	6.00000i	−0.505889	+	0.292075i
$423$	2.33562	+	1.34847i	0.113562	+	0.0655648i
$424$	0.550510	−	0.953512i	0.0267351	−	0.0463066i
$425$	9.48528	−	3.16693i	0.460104	−	0.153619i
$426$	−26.6969			−1.29347
$427$		0			0
$428$			8.00000i			0.386695i
$429$	−2.69694	−	4.67123i	−0.130209	−	0.225529i
$430$	−16.1455	−	11.6310i	−0.778607	−	0.560898i
$431$	−8.89898	+	15.4135i	−0.428649	+	0.742441i	−0.996753	−	0.0805149i	$-0.974344\pi$
$431$	−8.89898	+	15.4135i	−0.428649	+	0.742441i	0.568105	+	0.822956i	$0.307677\pi$
$432$		0			0
$433$		−	19.7980i		−	0.951429i	−0.879600	−	0.475715i	$-0.842190\pi$
$433$		−	19.7980i		−	0.951429i	0.879600	−	0.475715i	$-0.157810\pi$
$434$		0			0
$435$	15.7980	+	1.59592i	0.757454	+	0.0765184i
$436$	1.44949	+	2.51059i	0.0694180	+	0.120235i
$437$	−38.5337	−	22.2474i	−1.84332	−	1.06424i
$438$	14.6349	+	8.44949i	0.699285	+	0.403732i
$439$	−18.6969	−	32.3840i	−0.892356	−	1.54561i	−0.837043	−	0.547137i	$-0.815718\pi$
$439$	−18.6969	−	32.3840i	−0.892356	−	1.54561i	−0.0553132	−	0.998469i	$-0.517616\pi$
$440$	10.8990	+	1.10102i	0.519588	+	0.0524891i
$441$		0			0
$442$			0.898979i			0.0427601i
$443$	8.48528	−	4.89898i	0.403148	−	0.232758i	−0.284693	−	0.958619i	$-0.591892\pi$
$443$	8.48528	−	4.89898i	0.403148	−	0.232758i	0.687841	+	0.725861i	$0.258558\pi$
$444$	−2.44949	+	4.24264i	−0.116248	+	0.201347i
$445$	−18.1431	−	13.0701i	−0.860067	−	0.619581i
$446$	2.00000	+	3.46410i	0.0947027	+	0.164030i
$447$		−	38.6969i		−	1.83030i
$448$		0			0
$449$	10.0000			0.471929			0.235965	−	0.971762i	$-0.424175\pi$
$449$	10.0000			0.471929			0.235965	+	0.971762i	$0.424175\pi$
$450$	−14.2279	+	4.75039i	−0.670711	+	0.223936i
$451$	−26.6969	+	46.2405i	−1.25711	+	2.17738i
$452$	−0.174973	−	0.101021i	−0.00823002	−	0.00475161i
$453$	−41.5692	+	24.0000i	−1.95309	+	1.12762i
$454$	7.34847			0.344881
$455$		0			0
$456$	−15.7980			−0.739807
$457$	−8.31031	+	4.79796i	−0.388740	+	0.224439i	−0.681614	−	0.731712i	$-0.738722\pi$
$457$	−8.31031	+	4.79796i	−0.388740	+	0.224439i	0.292874	+	0.956151i	$0.405388\pi$
$458$	13.1172	+	7.57321i	0.612926	+	0.353873i
$459$		0			0
$460$	6.33145	+	14.0674i	0.295206	+	0.655897i
$461$	−2.65153			−0.123494			−0.0617470	−	0.998092i	$-0.519667\pi$
$461$	−2.65153			−0.123494			−0.0617470	+	0.998092i	$0.519667\pi$
$462$		0			0
$463$			35.5959i			1.65428i	0.561994	+	0.827141i	$0.310034\pi$
$463$			35.5959i			1.65428i	−0.561994	+	0.827141i	$0.689966\pi$
$464$	−1.44949	−	2.51059i	−0.0672909	−	0.116551i
$465$	−2.87808	+	3.99519i	−0.133468	+	0.185273i
$466$	5.10102	−	8.83523i	0.236300	−	0.409284i
$467$	−4.80688	+	2.77526i	−0.222436	+	0.128423i	−0.607078	−	0.794642i	$-0.707658\pi$
$467$	−4.80688	+	2.77526i	−0.222436	+	0.128423i	0.384642	+	0.923066i	$0.374325\pi$
$468$		−	1.34847i		−	0.0623330i
$469$		0			0
$470$	0.202041	−	2.00000i	0.00931946	−	0.0922531i
$471$	−10.3485	−	17.9241i	−0.476832	−	0.825898i
$472$	5.58542	+	3.22474i	0.257090	+	0.148431i
$473$	37.7552	+	21.7980i	1.73598	+	1.00227i
$474$	−3.55051	−	6.14966i	−0.163080	−	0.282463i
$475$	−31.5959	−	6.44949i	−1.44972	−	0.295923i
$476$		0			0
$477$		−	3.30306i		−	0.151237i
$478$	−22.3417	+	12.8990i	−1.02189	+	0.589986i
$479$	−19.3485	+	33.5125i	−0.884054	+	1.53123i	−0.0372602	+	0.999306i	$0.511863\pi$
$479$	−19.3485	+	33.5125i	−0.884054	+	1.53123i	−0.846794	+	0.531921i	$0.821470\pi$
$480$	4.44414	+	3.20150i	0.202846	+	0.146128i
$481$	−0.449490	−	0.778539i	−0.0204950	−	0.0354983i
$482$			20.6969i			0.942720i
$483$		0			0
$484$	−13.0000			−0.590909
$485$	−3.48553	−	7.74426i	−0.158270	−	0.351649i
$486$	11.0227	−	19.0919i	0.500000	−	0.866025i
$487$	31.7805	+	18.3485i	1.44011	+	0.831449i	0.997856	−	0.0654410i	$-0.0208454\pi$
$487$	31.7805	+	18.3485i	1.44011	+	0.831449i	0.442255	+	0.896890i	$0.354179\pi$
$488$	−7.31747	+	4.22474i	−0.331246	+	0.191245i
$489$	−41.3939			−1.87190
$490$		0			0
$491$	−19.5959			−0.884351			−0.442176	−	0.896928i	$-0.645793\pi$
$491$	−19.5959			−0.884351			−0.442176	+	0.896928i	$0.645793\pi$
$492$	−23.1202	+	13.3485i	−1.04234	+	0.601795i
$493$	5.02118	+	2.89898i	0.226143	+	0.130563i
$494$	1.44949	−	2.51059i	0.0652156	−	0.112957i
$495$	29.9679	−	13.4879i	1.34696	−	0.606238i
$496$	0.898979			0.0403654
$497$		0			0
$498$			6.00000i			0.268866i
$499$	12.8990	+	22.3417i	0.577438	+	1.00015i	0.995772	+	0.0918583i	$0.0292807\pi$
$499$	12.8990	+	22.3417i	0.577438	+	1.00015i	−0.418334	+	0.908293i	$0.637386\pi$
$500$	7.58128	+	8.21731i	0.339045	+	0.367489i
$501$	−6.00000	+	10.3923i	−0.268060	+	0.464294i
$502$	−1.34278	+	0.775255i	−0.0599313	+	0.0346013i
$503$		−	4.00000i		−	0.178351i	−0.996016	−	0.0891756i	$-0.971577\pi$
$503$		−	4.00000i		−	0.178351i	0.996016	−	0.0891756i	$-0.0284232\pi$
$504$		0			0
$505$	−1.89898	+	18.7980i	−0.0845035	+	0.836498i
$506$	−16.8990	−	29.2699i	−0.751251	−	1.30121i
$507$	−27.1486	−	15.6742i	−1.20571	−	0.696117i
$508$	−4.41761	−	2.55051i	−0.196000	−	0.113161i
$509$	18.2247	+	31.5662i	0.807798	+	1.39915i	0.914386	+	0.404843i	$0.132674\pi$
$509$	18.2247	+	31.5662i	0.807798	+	1.39915i	−0.106588	+	0.994303i	$0.533993\pi$
$510$	−10.8990	−	1.10102i	−0.482615	−	0.0487540i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	10.3485	−	17.9241i	0.456451	−	0.790597i
$515$	−4.05306	+	5.62622i	−0.178599	+	0.247921i
$516$	10.8990	+	18.8776i	0.479801	+	0.831039i
$517$			4.40408i			0.193691i
$518$		0			0
$519$	−44.6969			−1.96198
$520$	−0.916536	+	0.412514i	−0.0401927	+	0.0180899i
$521$	1.65153	−	2.86054i	0.0723549	−	0.125322i	−0.827578	−	0.561351i	$-0.810282\pi$
$521$	1.65153	−	2.86054i	0.0723549	−	0.125322i	0.899933	+	0.436028i	$0.143615\pi$
$522$	−7.53177	−	4.34847i	−0.329657	−	0.190327i
$523$	0.992836	−	0.573214i	0.0434137	−	0.0250649i	−0.478136	−	0.878286i	$-0.658687\pi$
$523$	0.992836	−	0.573214i	0.0434137	−	0.0250649i	0.521550	+	0.853221i	$0.325354\pi$
$524$	−1.55051			−0.0677344
$525$		0			0
$526$	9.79796			0.427211
$527$	−1.55708	+	0.898979i	−0.0678274	+	0.0391602i
$528$	−10.3923	−	6.00000i	−0.452267	−	0.261116i
$529$	12.2980	−	21.3007i	0.534694	−	0.926117i
$530$	−2.24504	+	1.01045i	−0.0975185	+	0.0438911i
$531$	19.3485			0.839652
$532$		0			0
$533$		−	4.89898i		−	0.212198i
$534$	12.2474	+	21.2132i	0.529999	+	0.917985i
$535$	10.4561	−	14.5145i	0.452055	−	0.627517i
$536$	−4.00000	+	6.92820i	−0.172774	+	0.299253i
$537$	12.2993	−	7.10102i	0.530755	−	0.306432i
$538$			15.1464i			0.653009i
$539$		0			0
$540$		0			0
$541$	14.7980	+	25.6308i	0.636214	+	1.10195i	0.986257	+	0.165221i	$0.0528338\pi$
$541$	14.7980	+	25.6308i	0.636214	+	1.10195i	−0.350043	+	0.936734i	$0.613833\pi$
$542$	−10.3923	−	6.00000i	−0.446388	−	0.257722i
$543$	30.2234	+	17.4495i	1.29701	+	0.748829i
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	0.651531	−	6.44949i	0.0279085	−	0.276266i
$546$		0			0
$547$			10.6969i			0.457368i	0.973501	+	0.228684i	$0.0734423\pi$
$547$			10.6969i			0.457368i	−0.973501	+	0.228684i	$0.926558\pi$
$548$	−15.4135	+	8.89898i	−0.658431	+	0.380146i
$549$	−12.6742	+	21.9524i	−0.540923	+	0.936906i
$550$	−18.3351	−	16.2426i	−0.781812	−	0.692589i
$551$	−9.34847	−	16.1920i	−0.398258	−	0.689803i
$552$		−	16.8990i		−	0.719268i
$553$		0			0
$554$	−5.10102			−0.216722
$555$	9.98930	−	4.49598i	0.424022	−	0.190844i
$556$	3.22474	−	5.58542i	0.136760	−	0.236875i
$557$	14.4600	+	8.34847i	0.612689	+	0.353736i	0.774017	−	0.633165i	$-0.218244\pi$
$557$	14.4600	+	8.34847i	0.612689	+	0.353736i	−0.161328	+	0.986901i	$0.551578\pi$
$558$	2.33562	−	1.34847i	0.0988746	−	0.0570853i
$559$	−4.00000			−0.169182
$560$		0			0
$561$	24.0000			1.01328
$562$	15.5885	−	9.00000i	0.657559	−	0.379642i
$563$	−12.1637	−	7.02270i	−0.512638	−	0.295972i	0.221279	−	0.975210i	$-0.428977\pi$
$563$	−12.1637	−	7.02270i	−0.512638	−	0.295972i	−0.733917	+	0.679239i	$0.762310\pi$
$564$	−1.10102	+	1.90702i	−0.0463613	+	0.0803002i
$565$	0.185421	+	0.411973i	0.00780071	+	0.0173319i
$566$	28.2474			1.18733
$567$		0			0
$568$		−	10.8990i		−	0.457311i
$569$	7.10102	+	12.2993i	0.297690	+	0.515615i	0.975607	−	0.219524i	$-0.0704504\pi$
$569$	7.10102	+	12.2993i	0.297690	+	0.515615i	−0.677917	+	0.735139i	$0.737117\pi$
$570$	28.6624	+	20.6480i	1.20054	+	0.864851i
$571$	10.4495	−	18.0990i	0.437298	−	0.757422i	−0.560183	−	0.828369i	$-0.689269\pi$
$571$	10.4495	−	18.0990i	0.437298	−	0.757422i	0.997480	+	0.0709477i	$0.0226023\pi$
$572$	1.90702	−	1.10102i	0.0797367	−	0.0460360i
$573$		−	40.8990i		−	1.70858i
$574$		0			0
$575$	6.89898	−	33.7980i	0.287707	−	1.40947i
$576$	−1.50000	−	2.59808i	−0.0625000	−	0.108253i
$577$	40.2658	+	23.2474i	1.67629	+	0.967804i	0.963995	+	0.265919i	$0.0856753\pi$
$577$	40.2658	+	23.2474i	1.67629	+	0.967804i	0.712290	+	0.701885i	$0.247658\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$	−21.5505	−	37.3266i	−0.895609	−	1.55124i
$580$	−0.651531	+	6.44949i	−0.0270533	+	0.267800i
$581$		0			0
$582$			9.30306i			0.385624i
$583$	4.67123	−	2.69694i	0.193463	−	0.111696i
$584$	−3.44949	+	5.97469i	−0.142741	+	0.247234i
$585$	−1.76246	+	2.44655i	−0.0728687	+	0.101152i
$586$	3.12372	+	5.41045i	0.129040	+	0.223504i
$587$			33.1464i			1.36810i	0.729435	+	0.684050i	$0.239783\pi$
$587$			33.1464i			1.36810i	−0.729435	+	0.684050i	$0.760217\pi$
$588$		0			0
$589$	5.79796			0.238901
$590$	−5.91894	−	13.1509i	−0.243679	−	0.541413i
$591$	11.1464	−	19.3062i	0.458503	−	0.794150i
$592$	−1.73205	−	1.00000i	−0.0711868	−	0.0410997i
$593$	−0.953512	+	0.550510i	−0.0391560	+	0.0226067i	−0.519450	−	0.854501i	$-0.673863\pi$
$593$	−0.953512	+	0.550510i	−0.0391560	+	0.0226067i	0.480294	+	0.877107i	$0.340530\pi$
$594$		0			0
$595$		0			0
$596$	15.7980			0.647110
$597$	15.0635	−	8.69694i	0.616510	−	0.355942i
$598$	2.68556	+	1.55051i	0.109821	+	0.0634051i
$599$	−11.4495	+	19.8311i	−0.467813	+	0.810277i	−0.999324	−	0.0367753i	$-0.988291\pi$
$599$	−11.4495	+	19.8311i	−0.467813	+	0.810277i	0.531510	+	0.847052i	$0.321625\pi$
$600$	−3.87868	−	11.6170i	−0.158346	−	0.474264i
$601$	−19.3939			−0.791093			−0.395546	−	0.918446i	$-0.629445\pi$
$601$	−19.3939			−0.791093			−0.395546	+	0.918446i	$0.629445\pi$
$602$		0			0
$603$			24.0000i			0.977356i
$604$	−9.79796	−	16.9706i	−0.398673	−	0.690522i
$605$	23.5861	+	16.9911i	0.958910	+	0.690786i
$606$	10.3485	−	17.9241i	0.420378	−	0.728116i
$607$	21.9917	−	12.6969i	0.892617	−	0.515353i	0.0178196	−	0.999841i	$-0.494328\pi$
$607$	21.9917	−	12.6969i	0.892617	−	0.515353i	0.874798	+	0.484488i	$0.160994\pi$
$608$		−	6.44949i		−	0.261561i
$609$		0			0
$610$	18.7980	+	1.89898i	0.761107	+	0.0768874i
$611$	−0.202041	−	0.349945i	−0.00817371	−	0.0141573i
$612$	5.19615	+	3.00000i	0.210042	+	0.121268i
$613$	−7.10318	−	4.10102i	−0.286895	−	0.165639i	0.349646	−	0.936882i	$-0.386302\pi$
$613$	−7.10318	−	4.10102i	−0.286895	−	0.165639i	−0.636541	+	0.771243i	$0.719635\pi$
$614$	2.12372	+	3.67840i	0.0857065	+	0.148448i
$615$	59.3939	+	6.00000i	2.39499	+	0.241943i
$616$		0			0
$617$		−	9.59592i		−	0.386317i	−0.981168	−	0.193159i	$-0.938127\pi$
$617$		−	9.59592i		−	0.386317i	0.981168	−	0.193159i	$-0.0618732\pi$
$618$	6.57826	−	3.79796i	0.264616	−	0.152776i
$619$	23.2247	−	40.2264i	0.933481	−	1.61684i	0.156161	−	0.987732i	$-0.450088\pi$
$619$	23.2247	−	40.2264i	0.933481	−	1.61684i	0.777320	−	0.629106i	$-0.216579\pi$
$620$	−1.63103	−	1.17497i	−0.0655038	−	0.0471880i
$621$		0			0
$622$			12.0000i			0.481156i
$623$		0			0
$624$	1.10102			0.0440761
$625$	−3.01472	−	24.8176i	−0.120589	−	0.992703i
$626$	−8.79796	+	15.2385i	−0.351637	+	0.609053i
$627$	−67.0251	−	38.6969i	−2.67672	−	1.54541i
$628$	7.31747	−	4.22474i	0.291999	−	0.168586i
$629$	4.00000			0.159490
$630$		0			0
$631$	6.49490			0.258558			0.129279	−	0.991608i	$-0.458734\pi$
$631$	6.49490			0.258558			0.129279	+	0.991608i	$0.458734\pi$
$632$	2.51059	−	1.44949i	0.0998659	−	0.0576576i
$633$	−25.4558	−	14.6969i	−1.01178	−	0.584151i
$634$	−13.2474	+	22.9453i	−0.526123	+	0.911272i
$635$	4.68140	+	10.4013i	0.185776	+	0.412762i
$636$	2.69694			0.106941
$637$		0			0
$638$		−	14.2020i		−	0.562264i
$639$	−16.3485	−	28.3164i	−0.646735	−	1.12018i
$640$	−1.30701	+	1.81431i	−0.0516640	+	0.0717170i
$641$	−3.10102	+	5.37113i	−0.122483	+	0.212147i	−0.920746	−	0.390162i	$-0.872419\pi$
$641$	−3.10102	+	5.37113i	−0.122483	+	0.212147i	0.798263	+	0.602309i	$0.205752\pi$
$642$	−16.9706	+	9.79796i	−0.669775	+	0.386695i
$643$		−	9.14643i		−	0.360700i	−0.983603	−	0.180350i	$-0.942277\pi$
$643$		−	9.14643i		−	0.360700i	0.983603	−	0.180350i	$-0.0577230\pi$
$644$		0			0
$645$	4.89898	−	48.4949i	0.192897	−	1.90948i
$646$	6.44949	+	11.1708i	0.253752	+	0.439511i
$647$	19.3062	+	11.1464i	0.759004	+	0.438211i	0.828938	−	0.559340i	$-0.188945\pi$
$647$	19.3062	+	11.1464i	0.759004	+	0.438211i	−0.0699339	+	0.997552i	$0.522279\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	15.7980	+	27.3629i	0.620124	+	1.07409i
$650$	2.20204	+	0.449490i	0.0863712	+	0.0176304i
$651$		0			0
$652$		−	16.8990i		−	0.661815i
$653$	34.4660	−	19.8990i	1.34876	−	0.778707i	0.360687	−	0.932687i	$-0.382542\pi$
$653$	34.4660	−	19.8990i	1.34876	−	0.778707i	0.988074	+	0.153980i	$0.0492091\pi$
$654$	−3.55051	+	6.14966i	−0.138836	+	0.240471i
$655$	2.81311	+	2.02653i	0.109917	+	0.0791830i
$656$	−5.44949	−	9.43879i	−0.212767	−	0.368523i
$657$			20.6969i			0.807464i
$658$		0			0
$659$	−7.10102			−0.276616			−0.138308	−	0.990389i	$-0.544166\pi$
$659$	−7.10102			−0.276616			−0.138308	+	0.990389i	$0.544166\pi$
$660$	11.0129	+	24.4687i	0.428675	+	0.952443i
$661$	6.47219	−	11.2102i	0.251739	−	0.436025i	−0.712266	−	0.701910i	$-0.752331\pi$
$661$	6.47219	−	11.2102i	0.251739	−	0.436025i	0.964005	+	0.265885i	$0.0856642\pi$
$662$	9.26382	+	5.34847i	0.360049	+	0.207874i
$663$	−1.90702	+	1.10102i	−0.0740627	+	0.0427601i
$664$	−2.44949			−0.0950586
$665$		0			0
$666$	−6.00000			−0.232495
$667$	17.3205	−	10.0000i	0.670653	−	0.387202i
$668$	−4.24264	−	2.44949i	−0.164153	−	0.0947736i
$669$	−4.89898	+	8.48528i	−0.189405	+	0.328060i
$670$	16.3125	−	7.34190i	0.630205	−	0.283642i
$671$	−41.3939			−1.59799
$672$		0			0
$673$		−	1.79796i		−	0.0693062i	−0.999399	−	0.0346531i	$-0.988967\pi$
$673$		−	1.79796i		−	0.0693062i	0.999399	−	0.0346531i	$-0.0110326\pi$
$674$	14.7980	+	25.6308i	0.569996	+	0.987262i
$675$		0			0
$676$	6.39898	−	11.0834i	0.246115	−	0.426283i
$677$	27.3235	−	15.7753i	1.05013	−	0.606292i	0.127444	−	0.991846i	$-0.459323\pi$
$677$	27.3235	−	15.7753i	1.05013	−	0.606292i	0.922685	+	0.385554i	$0.125989\pi$
$678$		−	0.494897i		−	0.0190064i
$679$		0			0
$680$	0.449490	−	4.44949i	0.0172371	−	0.170630i
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$	3.81405	+	2.20204i	0.146047	+	0.0843205i
$683$	−30.8270	−	17.7980i	−1.17956	−	0.681020i	−0.223648	−	0.974670i	$-0.571797\pi$
$683$	−30.8270	−	17.7980i	−1.17956	−	0.681020i	−0.955913	+	0.293650i	$0.905130\pi$
$684$	−9.67423	−	16.7563i	−0.369904	−	0.640692i
$685$	39.5959	+	4.00000i	1.51288	+	0.152832i
$686$		0			0
$687$			37.1010i			1.41549i
$688$	−7.70674	+	4.44949i	−0.293817	+	0.169635i
$689$	−0.247449	+	0.428594i	−0.00942705	+	0.0163281i
$690$	−22.0871	+	30.6600i	−0.840841	+	1.16721i
$691$	−6.57321	−	11.3851i	−0.250057	−	0.433111i	0.713484	−	0.700671i	$-0.247116\pi$
$691$	−6.57321	−	11.3851i	−0.250057	−	0.433111i	−0.963541	+	0.267560i	$0.913783\pi$
$692$		−	18.2474i		−	0.693664i
$693$		0			0
$694$	19.1010			0.725065
$695$	−13.1509	+	5.91894i	−0.498841	+	0.224518i
$696$	3.55051	−	6.14966i	0.134582	−	0.233102i
$697$	18.8776	+	10.8990i	0.715040	+	0.412828i
$698$	3.07483	−	1.77526i	0.116384	−	0.0671944i
$699$	24.9898			0.945201
$700$		0			0
$701$	40.6969			1.53710			0.768551	−	0.639788i	$-0.220978\pi$
$701$	40.6969			1.53710			0.768551	+	0.639788i	$0.220978\pi$
$702$		0			0
$703$	−11.1708	−	6.44949i	−0.421316	−	0.243247i
$704$	2.44949	−	4.24264i	0.0923186	−	0.159901i
$705$	4.49009	−	2.02090i	0.169107	−	0.0761113i
$706$	13.1010			0.493063
$707$		0			0
$708$			15.7980i			0.593724i
$709$	20.1464	+	34.8946i	0.756615	+	1.31050i	0.944567	+	0.328317i	$0.106482\pi$
$709$	20.1464	+	34.8946i	0.756615	+	1.31050i	−0.187952	+	0.982178i	$0.560185\pi$
$710$	−14.2450	+	19.7742i	−0.534607	+	0.742111i
$711$	4.34847	−	7.53177i	0.163080	−	0.282463i
$712$	−8.66025	+	5.00000i	−0.324557	+	0.187383i
$713$			6.20204i			0.232268i
$714$		0			0
$715$	−4.89898	−	0.494897i	−0.183211	−	0.0185081i
$716$	2.89898	+	5.02118i	0.108340	+	0.187650i
$717$	−54.7257	−	31.5959i	−2.04377	−	1.17997i
$718$	−10.0424	−	5.79796i	−0.374778	−	0.216378i
$719$	−22.2474	−	38.5337i	−0.829690	−	1.43706i	−0.898282	−	0.439420i	$-0.855184\pi$
$719$	−22.2474	−	38.5337i	−0.829690	−	1.43706i	0.0685918	−	0.997645i	$-0.478149\pi$
$720$	−0.674235	+	6.67423i	−0.0251272	+	0.248734i
$721$		0			0
$722$		−	22.5959i		−	0.840933i
$723$	−43.9048	+	25.3485i	−1.63284	+	0.942720i
$724$	−7.12372	+	12.3387i	−0.264751	+	0.458562i
$725$	9.61161	−	10.8498i	0.356966	−	0.402953i
$726$	−15.9217	−	27.5772i	−0.590909	−	1.02348i
$727$			6.69694i			0.248376i	0.992259	+	0.124188i	$0.0396325\pi$
$727$			6.69694i			0.248376i	−0.992259	+	0.124188i	$0.960367\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	14.0674	−	6.33145i	0.520659	−	0.234338i
$731$	8.89898	−	15.4135i	0.329141	−	0.570088i
$732$	−17.9241	−	10.3485i	−0.662493	−	0.382490i
$733$	−37.7945	+	21.8207i	−1.39597	+	0.805965i	−0.993968	−	0.109673i	$-0.965020\pi$
$733$	−37.7945	+	21.8207i	−1.39597	+	0.805965i	−0.402004	+	0.915638i	$0.631686\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	6.89898			0.254300
$737$	−33.9411	+	19.5959i	−1.25024	+	0.721825i
$738$	−28.3164	−	16.3485i	−1.04234	−	0.601795i
$739$	−22.2474	+	38.5337i	−0.818386	+	1.41749i	0.0884855	+	0.996077i	$0.471797\pi$
$739$	−22.2474	+	38.5337i	−0.818386	+	1.41749i	−0.906871	+	0.421408i	$0.861536\pi$
$740$	1.83548	+	4.07812i	0.0674734	+	0.149915i
$741$	7.10102			0.260863
$742$		0			0
$743$			15.3031i			0.561415i	0.959793	+	0.280707i	$0.0905691\pi$
$743$			15.3031i			0.561415i	−0.959793	+	0.280707i	$0.909431\pi$
$744$	1.10102	+	1.90702i	0.0403654	+	0.0699149i
$745$	−28.6624	−	20.6480i	−1.05011	−	0.756486i
$746$	12.3485	−	21.3882i	0.452110	−	0.783077i
$747$	−6.36396	+	3.67423i	−0.232845	+	0.134433i
$748$			9.79796i			0.358249i
$749$		0			0
$750$	−8.14643	+	26.1464i	−0.297465	+	0.954733i
$751$	11.1010	+	19.2275i	0.405082	+	0.701623i	0.994331	−	0.106329i	$-0.0339096\pi$
$751$	11.1010	+	19.2275i	0.405082	+	0.701623i	−0.589249	+	0.807951i	$0.700576\pi$
$752$	−0.778539	−	0.449490i	−0.0283904	−	0.0163912i
$753$	−3.28913	−	1.89898i	−0.119863	−	0.0692027i
$754$	0.651531	+	1.12848i	0.0237274	+	0.0410970i
$755$	−4.40408	+	43.5959i	−0.160281	+	1.58662i
$756$		0			0
$757$		−	32.2020i		−	1.17040i	−0.810888	−	0.585202i	$-0.801015\pi$
$757$		−	32.2020i		−	1.17040i	0.810888	−	0.585202i	$-0.198985\pi$
$758$	1.12848	−	0.651531i	0.0409884	−	0.0236647i
$759$	41.3939	−	71.6963i	1.50250	−	2.60241i
$760$	−8.42953	+	11.7014i	−0.305771	+	0.424454i
$761$	−15.4495	−	26.7593i	−0.560044	−	0.970024i	−0.997492	−	0.0707804i	$-0.977451\pi$
$761$	−15.4495	−	26.7593i	−0.560044	−	0.970024i	0.437448	−	0.899244i	$-0.355882\pi$
$762$		−	12.4949i		−	0.452642i
$763$		0			0
$764$	16.6969			0.604074
$765$	−5.50643	−	12.2343i	−0.199085	−	0.442334i
$766$	8.44949	−	14.6349i	0.305292	−	0.528782i
$767$	−2.51059	−	1.44949i	−0.0906521	−	0.0523380i
$768$	2.12132	−	1.22474i	0.0765466	−	0.0441942i
$769$	−11.3031			−0.407599			−0.203799	−	0.979013i	$-0.565329\pi$
$769$	−11.3031			−0.407599			−0.203799	+	0.979013i	$0.565329\pi$
$770$		0			0
$771$	50.6969			1.82581
$772$	15.2385	−	8.79796i	0.548446	−	0.316645i
$773$	11.5601	+	6.67423i	0.415788	+	0.240056i	0.693274	−	0.720674i	$-0.256168\pi$
$773$	11.5601	+	6.67423i	0.415788	+	0.240056i	−0.277485	+	0.960730i	$0.589501\pi$
$774$	−13.3485	+	23.1202i	−0.479801	+	0.831039i
$775$	1.42350	+	4.26354i	0.0511337	+	0.153151i
$776$	−3.79796			−0.136339
$777$		0			0
$778$			22.8990i			0.820968i
$779$	−35.1464	−	60.8754i	−1.25925	−	2.18109i
$780$	−1.99760	−	1.43904i	−0.0715254	−	0.0515260i
$781$	26.6969	−	46.2405i	0.955292	−	1.65461i
$782$	−11.9494	+	6.89898i	−0.427309	+	0.246707i
$783$		0			0
$784$		0			0
$785$	−18.7980	−	1.89898i	−0.670928	−	0.0677775i
$786$	−1.89898	−	3.28913i	−0.0677344	−	0.117319i
$787$	39.4479	+	22.7753i	1.40617	+	0.811850i	0.995016	−	0.0997176i	$-0.0317939\pi$
$787$	39.4479	+	22.7753i	1.40617	+	0.811850i	0.411150	+	0.911568i	$0.365127\pi$
$788$	7.88171	+	4.55051i	0.280774	+	0.162105i
$789$	12.0000	+	20.7846i	0.427211	+	0.739952i
$790$	−6.44949	−	0.651531i	−0.229463	−	0.0231804i
$791$		0			0
$792$		−	14.6969i		−	0.522233i
$793$	3.28913	−	1.89898i	0.116800	−	0.0674347i
$794$	−8.67423	+	15.0242i	−0.307837	+	0.533189i
$795$	−4.89309	−	3.52492i	−0.173540	−	0.125016i
$796$	3.55051	+	6.14966i	0.125844	+	0.217969i
$797$		−	52.9444i		−	1.87539i	−0.347464	−	0.937693i	$-0.612957\pi$
$797$		−	52.9444i		−	1.87539i	0.347464	−	0.937693i	$-0.387043\pi$
$798$		0			0
$799$	1.79796			0.0636072
$800$	4.74264	−	1.58346i	0.167678	−	0.0559839i
$801$	−15.0000	+	25.9808i	−0.529999	+	0.917985i
$802$	25.4558	+	14.6969i	0.898877	+	0.518967i
$803$	−29.2699	+	16.8990i	−1.03291	+	0.596352i
$804$	−19.5959			−0.691095
$805$		0			0
$806$	−0.404082			−0.0142332
$807$	−32.1304	+	18.5505i	−1.13104	+	0.653009i
$808$	7.31747	+	4.22474i	0.257428	+	0.148626i
$809$	4.20204	−	7.27815i	0.147736	−	0.255886i	−0.782654	−	0.622456i	$-0.786135\pi$
$809$	4.20204	−	7.27815i	0.147736	−	0.255886i	0.930390	+	0.366570i	$0.119468\pi$
$810$	−8.25964	−	18.3515i	−0.290214	−	0.644807i
$811$	38.9444			1.36752			0.683761	−	0.729706i	$-0.260343\pi$
$811$	38.9444			1.36752			0.683761	+	0.729706i	$0.260343\pi$
$812$		0			0
$813$		−	29.3939i		−	1.03089i
$814$	−4.89898	−	8.48528i	−0.171709	−	0.297409i
$815$	−22.0871	+	30.6600i	−0.773677	+	1.07397i
$816$	−2.44949	+	4.24264i	−0.0857493	+	0.148522i
$817$	−49.7046	+	28.6969i	−1.73894	+	1.00398i
$818$			14.4949i			0.506802i
$819$		0			0
$820$	−2.44949	+	24.2474i	−0.0855399	+	0.846758i
$821$	−13.8990	−	24.0737i	−0.485078	−	0.840179i	0.514775	−	0.857325i	$-0.327875\pi$
$821$	−13.8990	−	24.0737i	−0.485078	−	0.840179i	−0.999853	+	0.0171459i	$0.994542\pi$
$822$	−37.7552	−	21.7980i	−1.31686	−	0.760291i
$823$	33.9411	+	19.5959i	1.18311	+	0.683071i	0.956733	−	0.290968i	$-0.0939774\pi$
$823$	33.9411	+	19.5959i	1.18311	+	0.683071i	0.226381	+	0.974039i	$0.427311\pi$
$824$	1.55051	+	2.68556i	0.0540146	+	0.0935560i
$825$	12.0000	−	58.7878i	0.417786	−	2.04673i
$826$		0			0
$827$			23.5959i			0.820510i	0.911971	+	0.410255i	$0.134560\pi$
$827$			23.5959i			0.820510i	−0.911971	+	0.410255i	$0.865440\pi$
$828$	17.9241	−	10.3485i	0.622905	−	0.359634i
$829$	−19.8207	+	34.3304i	−0.688400	+	1.19234i	0.283955	+	0.958838i	$0.408353\pi$
$829$	−19.8207	+	34.3304i	−0.688400	+	1.19234i	−0.972355	+	0.233506i	$0.924980\pi$
$830$	4.44414	+	3.20150i	0.154258	+	0.111126i
$831$	−6.24745	−	10.8209i	−0.216722	−	0.375373i
$832$			0.449490i			0.0155833i
$833$		0			0
$834$	15.7980			0.547039
$835$	4.49598	+	9.98930i	0.155590	+	0.345694i
$836$	15.7980	−	27.3629i	0.546384	−	0.946365i
$837$		0			0
$838$	5.58542	−	3.22474i	0.192945	−	0.111397i
$839$	27.1010			0.935631			0.467816	−	0.883826i	$-0.345041\pi$
$839$	27.1010			0.935631			0.467816	+	0.883826i	$0.345041\pi$
$840$		0			0
$841$	−20.5959			−0.710204
$842$	20.6096	−	11.8990i	0.710255	−	0.410066i
$843$	38.1838	+	22.0454i	1.31512	+	0.759284i
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	−26.0958	+	11.7452i	−0.897722	+	0.404046i
$846$	−2.69694			−0.0927227
$847$		0			0
$848$			1.10102i			0.0378092i
$849$	34.5959	+	59.9219i	1.18733	+	2.05651i
$850$	−6.63103	+	7.48528i	−0.227442	+	0.256743i
$851$	6.89898	−	11.9494i	0.236494	−	0.409620i
$852$	23.1202	−	13.3485i	0.792086	−	0.457311i
$853$			29.8434i			1.02182i	0.859635	+	0.510909i	$0.170691\pi$
$853$			29.8434i			1.02182i	−0.859635	+	0.510909i	$0.829309\pi$
$854$		0			0
$855$	−4.34847	+	43.0454i	−0.148715	+	1.47212i
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	21.8168	+	12.5959i	0.745247	+	0.430268i	0.823974	−	0.566628i	$-0.191752\pi$
$857$	21.8168	+	12.5959i	0.745247	+	0.430268i	−0.0787272	+	0.996896i	$0.525086\pi$
$858$	4.67123	+	2.69694i	0.159473	+	0.0920720i
$859$	14.8207	+	25.6701i	0.505674	+	0.875854i	0.999978	+	0.00656478i	$0.00208965\pi$
$859$	14.8207	+	25.6701i	0.505674	+	0.875854i	−0.494304	+	0.869289i	$0.664577\pi$
$860$	19.7980	+	2.00000i	0.675105	+	0.0681994i
$861$		0			0
$862$		−	17.7980i		−	0.606201i
$863$	−11.5994	+	6.69694i	−0.394849	+	0.227966i	−0.684259	−	0.729239i	$-0.739874\pi$
$863$	−11.5994	+	6.69694i	−0.394849	+	0.227966i	0.289410	+	0.957205i	$0.406541\pi$
$864$		0			0
$865$	−23.8495	+	33.1066i	−0.810909	+	1.12566i
$866$	9.89898	+	17.1455i	0.336381	+	0.582629i
$867$			31.8434i			1.08146i
$868$		0			0
$869$	14.2020			0.481771
$870$	−14.4794	+	6.51687i	−0.490897	+	0.220943i
$871$	1.79796	−	3.11416i	0.0609215	−	0.105519i
$872$	−2.51059	−	1.44949i	−0.0850193	−	0.0490859i
$873$	−9.86739	+	5.69694i	−0.333960	+	0.192812i
$874$	44.4949			1.50506
$875$		0			0
$876$	−16.8990			−0.570964
$877$	16.7956	−	9.69694i	0.567147	−	0.327442i	−0.188862	−	0.982004i	$-0.560480\pi$
$877$	16.7956	−	9.69694i	0.567147	−	0.327442i	0.756009	+	0.654561i	$0.227147\pi$
$878$	32.3840	+	18.6969i	1.09291	+	0.630991i
$879$	−7.65153	+	13.2528i	−0.258080	+	0.447007i
$880$	−9.98930	+	4.49598i	−0.336739	+	0.151559i
$881$	−27.7980			−0.936537			−0.468269	−	0.883586i	$-0.655122\pi$
$881$	−27.7980			−0.936537			−0.468269	+	0.883586i	$0.655122\pi$
$882$		0			0
$883$		−	41.7980i		−	1.40661i	−0.710887	−	0.703307i	$-0.751706\pi$
$883$		−	41.7980i		−	1.40661i	0.710887	−	0.703307i	$-0.248294\pi$
$884$	−0.449490	−	0.778539i	−0.0151180	−	0.0261851i
$885$	20.6480	−	28.6624i	0.694076	−	0.963478i
$886$	−4.89898	+	8.48528i	−0.164584	+	0.285069i
$887$	23.1202	−	13.3485i	0.776301	−	0.448198i	−0.0588166	−	0.998269i	$-0.518733\pi$
$887$	23.1202	−	13.3485i	0.776301	−	0.448198i	0.835118	+	0.550071i	$0.185399\pi$
$888$		−	4.89898i		−	0.164399i
$889$		0			0
$890$	22.2474	+	2.24745i	0.745736	+	0.0753347i
$891$	22.0454	+	38.1838i	0.738549	+	1.27920i
$892$	−3.46410	−	2.00000i	−0.115987	−	0.0669650i
$893$	−5.02118	−	2.89898i	−0.168027	−	0.0970106i
$894$	19.3485	+	33.5125i	0.647110	+	1.12083i
$895$	1.30306	−	12.8990i	0.0435565	−	0.431165i
$896$		0			0
$897$			7.59592i			0.253620i
$898$	−8.66025	+	5.00000i	−0.288996	+	0.166852i
$899$	−1.30306	+	2.25697i	−0.0434595	+	0.0752741i
$900$	9.94655	−	11.2279i	0.331552	−	0.374264i
$901$	−1.10102	−	1.90702i	−0.0366803	−	0.0635322i
$902$		−	53.3939i		−	1.77782i
$903$		0			0
$904$	0.202041			0.00671978
$905$	29.0514	−	13.0754i	0.965700	−	0.434642i
$906$	24.0000	−	41.5692i	0.797347	−	1.38104i
$907$	19.2275	+	11.1010i	0.638440	+	0.368603i	0.784013	−	0.620744i	$-0.213169\pi$
$907$	19.2275	+	11.1010i	0.638440	+	0.368603i	−0.145574	+	0.989347i	$0.546503\pi$
$908$	−6.36396	+	3.67423i	−0.211195	+	0.121934i
$909$	25.3485			0.840756
$910$		0			0
$911$	3.59592			0.119138			0.0595690	−	0.998224i	$-0.481027\pi$
$911$	3.59592			0.119138			0.0595690	+	0.998224i	$0.481027\pi$
$912$	13.6814	−	7.89898i	0.453038	−	0.261561i
$913$	−10.3923	−	6.00000i	−0.343935	−	0.198571i
$914$	4.79796	−	8.31031i	0.158702	−	0.274881i
$915$	18.9944	+	42.2023i	0.627934	+	1.39516i
$916$	−15.1464			−0.500452
$917$		0			0
$918$		0			0
$919$	−8.55051	−	14.8099i	−0.282055	−	0.488534i	0.689836	−	0.723966i	$-0.257683\pi$
$919$	−8.55051	−	14.8099i	−0.282055	−	0.488534i	−0.971891	+	0.235432i	$0.924350\pi$
$920$	−12.5169	−	9.01702i	−0.412670	−	0.297282i
$921$	−5.20204	+	9.01020i	−0.171413	+	0.296896i
$922$	2.29629	−	1.32577i	0.0756244	−	0.0436618i
$923$			4.89898i			0.161252i
$924$		0			0
$925$	2.00000	−	9.79796i	0.0657596	−	0.322155i
$926$	−17.7980	−	30.8270i	−0.584877	−	1.01304i
$927$	8.05669	+	4.65153i	0.264616	+	0.152776i
$928$	2.51059	+	1.44949i	0.0824142	+	0.0475818i
$929$	−20.1464	−	34.8946i	−0.660983	−	1.14486i	−0.980358	−	0.197227i	$-0.936806\pi$
$929$	−20.1464	−	34.8946i	−0.660983	−	1.14486i	0.319375	−	0.947628i	$-0.396527\pi$
$930$	0.494897	−	4.89898i	0.0162283	−	0.160644i
$931$		0			0
$932$			10.2020i			0.334179i
$933$	−25.4558	+	14.6969i	−0.833387	+	0.481156i
$934$	2.77526	−	4.80688i	0.0908091	−	0.157286i
$935$	12.8060	−	17.7766i	0.418801	−	0.581356i
$936$	0.674235	+	1.16781i	0.0220380	+	0.0381710i
$937$			50.8990i			1.66280i	0.555677	+	0.831399i	$0.312459\pi$
$937$			50.8990i			1.66280i	−0.555677	+	0.831399i	$0.687541\pi$
$938$		0			0
$939$	−43.1010			−1.40655
$940$	0.825027	+	1.83307i	0.0269094	+	0.0597882i
$941$	−12.2247	+	21.1739i	−0.398515	+	0.690249i	−0.993543	−	0.113456i	$-0.963808\pi$
$941$	−12.2247	+	21.1739i	−0.398515	+	0.690249i	0.595028	+	0.803705i	$0.297141\pi$
$942$	17.9241	+	10.3485i	0.583998	+	0.337171i
$943$	65.1180	−	37.5959i	2.12054	−	1.22429i
$944$	−6.44949			−0.209913
$945$		0			0
$946$	−43.5959			−1.41743
$947$	−38.1838	+	22.0454i	−1.24081	+	0.716379i	−0.969258	−	0.246046i	$-0.920869\pi$
$947$	−38.1838	+	22.0454i	−1.24081	+	0.716379i	−0.271547	+	0.962425i	$0.587535\pi$
$948$	6.14966	+	3.55051i	0.199732	+	0.115315i
$949$	1.55051	−	2.68556i	0.0503317	−	0.0871770i
$950$	30.5876	−	10.2125i	0.992393	−	0.331338i
$951$	−64.8990			−2.10449
$952$		0			0
$953$		−	21.7980i		−	0.706105i	−0.935603	−	0.353053i	$-0.885144\pi$
$953$		−	21.7980i		−	0.706105i	0.935603	−	0.353053i	$-0.114856\pi$
$954$	1.65153	+	2.86054i	0.0534703	+	0.0926132i
$955$	−30.2935	−	21.8230i	−0.980274	−	0.706176i
$956$	12.8990	−	22.3417i	0.417183	−	0.722582i
$957$	30.1271	−	17.3939i	0.973870	−	0.562264i
$958$		−	38.6969i		−	1.25024i
$959$		0			0
$960$	−5.44949	−	0.550510i	−0.175882	−	0.0177676i
$961$	15.0959	+	26.1469i	0.486965	+	0.843448i
$962$	0.778539	+	0.449490i	0.0251011	+	0.0144921i
$963$	−20.7846	−	12.0000i	−0.669775	−	0.386695i
$964$	−10.3485	−	17.9241i	−0.333302	−	0.577296i
$965$	−39.1464	−	3.95459i	−1.26017	−	0.127303i
$966$		0			0
$967$			32.2929i			1.03847i	0.854632	+	0.519234i	$0.173783\pi$
$967$			32.2929i			1.03847i	−0.854632	+	0.519234i	$0.826217\pi$
$968$	11.2583	−	6.50000i	0.361856	−	0.208918i
$969$	−15.7980	+	27.3629i	−0.507504	+	0.879022i
$970$	6.89069	+	4.96396i	0.221247	+	0.159383i
$971$	−7.22474	−	12.5136i	−0.231853	−	0.401581i	0.726500	−	0.687166i	$-0.241146\pi$
$971$	−7.22474	−	12.5136i	−0.231853	−	0.401581i	−0.958353	+	0.285585i	$0.907812\pi$
$972$			22.0454i			0.707107i
$973$		0			0
$974$	−36.6969			−1.17585
$975$	1.74343	+	5.22174i	0.0558343	+	0.167230i
$976$	4.22474	−	7.31747i	0.135231	−	0.234227i
$977$	−25.4558	−	14.6969i	−0.814405	−	0.470197i	0.0340785	−	0.999419i	$-0.489150\pi$
$977$	−25.4558	−	14.6969i	−0.814405	−	0.470197i	−0.848483	+	0.529222i	$0.822484\pi$
$978$	35.8481	−	20.6969i	1.14630	−	0.661815i
$979$	−48.9898			−1.56572
$980$		0			0
$981$	−8.69694			−0.277672
$982$	16.9706	−	9.79796i	0.541552	−	0.312665i
$983$	36.9766	+	21.3485i	1.17937	+	0.680910i	0.955869	−	0.293793i	$-0.0949176\pi$
$983$	36.9766	+	21.3485i	1.17937	+	0.680910i	0.223502	+	0.974703i	$0.428251\pi$
$984$	13.3485	−	23.1202i	0.425534	−	0.737046i
$985$	−8.35235	−	18.5575i	−0.266128	−	0.591291i
$986$	−5.79796			−0.184645
$987$		0			0
$988$			2.89898i			0.0922288i
$989$	−30.6969	−	53.1687i	−0.976106	−	1.69066i
$990$	−19.2090	+	26.6648i	−0.610502	+	0.847465i
$991$	−30.3485	+	52.5651i	−0.964051	+	1.66979i	−0.251907	+	0.967751i	$0.581058\pi$
$991$	−30.3485	+	52.5651i	−0.964051	+	1.66979i	−0.712144	+	0.702034i	$0.752276\pi$
$992$	−0.778539	+	0.449490i	−0.0247186	+	0.0142713i
$993$			26.2020i			0.831497i
$994$		0			0
$995$	1.59592	−	15.7980i	0.0505940	−	0.500829i
$996$	−3.00000	−	5.19615i	−0.0950586	−	0.164646i
$997$	36.9373	+	21.3258i	1.16982	+	0.675394i	0.953637	−	0.300960i	$-0.0973070\pi$
$997$	36.9373	+	21.3258i	1.16982	+	0.675394i	0.216180	+	0.976354i	$0.430640\pi$
$998$	−22.3417	−	12.8990i	−0.707214	−	0.408310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.i.f.459.1		8
5.4	even	2	inner	490.2.i.f.459.4		8
7.2	even	3	inner	490.2.i.f.79.4		8
7.3	odd	6		70.2.c.a.29.1	✓	4
7.4	even	3		490.2.c.e.99.2		4
7.5	odd	6		490.2.i.c.79.3		8
7.6	odd	2		490.2.i.c.459.2		8
21.17	even	6		630.2.g.g.379.4		4
28.3	even	6		560.2.g.e.449.3		4
35.3	even	12		350.2.a.g.1.2		2
35.4	even	6		490.2.c.e.99.3		4
35.9	even	6	inner	490.2.i.f.79.1		8
35.17	even	12		350.2.a.h.1.1		2
35.18	odd	12		2450.2.a.bl.1.1		2
35.19	odd	6		490.2.i.c.79.2		8
35.24	odd	6		70.2.c.a.29.4	yes	4
35.32	odd	12		2450.2.a.bq.1.2		2
35.34	odd	2		490.2.i.c.459.3		8
56.3	even	6		2240.2.g.i.449.2		4
56.45	odd	6		2240.2.g.j.449.4		4
84.59	odd	6		5040.2.t.t.1009.3		4
105.17	odd	12		3150.2.a.bs.1.1		2
105.38	odd	12		3150.2.a.bt.1.1		2
105.59	even	6		630.2.g.g.379.2		4
140.3	odd	12		2800.2.a.bm.1.1		2
140.59	even	6		560.2.g.e.449.1		4
140.87	odd	12		2800.2.a.bl.1.2		2
280.59	even	6		2240.2.g.i.449.4		4
280.269	odd	6		2240.2.g.j.449.2		4
420.59	odd	6		5040.2.t.t.1009.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.c.a.29.1	✓	4	7.3	odd	6
70.2.c.a.29.4	yes	4	35.24	odd	6
350.2.a.g.1.2		2	35.3	even	12
350.2.a.h.1.1		2	35.17	even	12
490.2.c.e.99.2		4	7.4	even	3
490.2.c.e.99.3		4	35.4	even	6
490.2.i.c.79.2		8	35.19	odd	6
490.2.i.c.79.3		8	7.5	odd	6
490.2.i.c.459.2		8	7.6	odd	2
490.2.i.c.459.3		8	35.34	odd	2
490.2.i.f.79.1		8	35.9	even	6	inner
490.2.i.f.79.4		8	7.2	even	3	inner
490.2.i.f.459.1		8	1.1	even	1	trivial
490.2.i.f.459.4		8	5.4	even	2	inner
560.2.g.e.449.1		4	140.59	even	6
560.2.g.e.449.3		4	28.3	even	6
630.2.g.g.379.2		4	105.59	even	6
630.2.g.g.379.4		4	21.17	even	6
2240.2.g.i.449.2		4	56.3	even	6
2240.2.g.i.449.4		4	280.59	even	6
2240.2.g.j.449.2		4	280.269	odd	6
2240.2.g.j.449.4		4	56.45	odd	6
2450.2.a.bl.1.1		2	35.18	odd	12
2450.2.a.bq.1.2		2	35.32	odd	12
2800.2.a.bl.1.2		2	140.87	odd	12
2800.2.a.bm.1.1		2	140.3	odd	12
3150.2.a.bs.1.1		2	105.17	odd	12
3150.2.a.bt.1.1		2	105.38	odd	12
5040.2.t.t.1009.3		4	84.59	odd	6
5040.2.t.t.1009.4		4	420.59	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +2.44949 q^{6} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +2.44949 q^{6} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.30701 - 1.81431i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(-2.12132 + 1.22474i) q^{12} -0.449490i q^{13} +(5.44949 + 0.550510i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-3.22474 - 5.58542i) q^{19} +(-0.224745 + 2.22474i) q^{20} -4.89898i q^{22} +(5.97469 - 3.44949i) q^{23} +(1.22474 - 2.12132i) q^{24} +(3.31552 - 3.74264i) q^{25} +(0.224745 + 0.389270i) q^{26} +2.89898 q^{29} +(-4.99465 + 2.24799i) q^{30} +(-0.449490 + 0.778539i) q^{31} +(0.866025 + 0.500000i) q^{32} +(10.3923 - 6.00000i) q^{33} -2.00000 q^{34} +3.00000 q^{36} +(1.73205 - 1.00000i) q^{37} +(5.58542 + 3.22474i) q^{38} +(-0.550510 + 0.953512i) q^{39} +(-0.917738 - 2.03906i) q^{40} +10.8990 q^{41} -8.89898i q^{43} +(2.44949 + 4.24264i) q^{44} +(-5.44294 - 3.92102i) q^{45} +(-3.44949 + 5.97469i) q^{46} +(0.778539 - 0.449490i) q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(-2.44949 - 4.24264i) q^{51} +(-0.389270 - 0.224745i) q^{52} +(-0.953512 - 0.550510i) q^{53} +(1.10102 - 10.8990i) q^{55} +15.7980i q^{57} +(-2.51059 + 1.44949i) q^{58} +(3.22474 - 5.58542i) q^{59} +(3.20150 - 4.44414i) q^{60} +(4.22474 + 7.31747i) q^{61} -0.898979i q^{62} -1.00000 q^{64} +(0.412514 + 0.916536i) q^{65} +(-6.00000 + 10.3923i) q^{66} +(6.92820 + 4.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -16.8990 q^{69} -10.8990 q^{71} +(-2.59808 + 1.50000i) q^{72} +(5.97469 + 3.44949i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-11.6170 + 3.87868i) q^{75} -6.44949 q^{76} -1.10102i q^{78} +(-1.44949 - 2.51059i) q^{79} +(1.81431 + 1.30701i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-9.43879 + 5.44949i) q^{82} +2.44949i q^{83} +(-4.44949 - 0.449490i) q^{85} +(4.44949 + 7.70674i) q^{86} +(-6.14966 - 3.55051i) q^{87} +(-4.24264 - 2.44949i) q^{88} +(5.00000 + 8.66025i) q^{89} +(6.67423 + 0.674235i) q^{90} -6.89898i q^{92} +(1.90702 - 1.10102i) q^{93} +(-0.449490 + 0.778539i) q^{94} +(11.7014 + 8.42953i) q^{95} +(-1.22474 - 2.12132i) q^{96} +3.79796i q^{97} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{5} + 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 4 * q^5 + 12 * q^9	\( 8 q + 4 q^{4} + 4 q^{5} + 12 q^{9} + 4 q^{10} + 24 q^{15} - 4 q^{16} - 16 q^{19} + 8 q^{20} - 8 q^{26} - 16 q^{29} - 12 q^{30} + 16 q^{31} - 16 q^{34} + 24 q^{36} - 24 q^{39} - 4 q^{40} + 48 q^{41} - 12 q^{45} - 8 q^{46} - 8 q^{50} + 48 q^{55} + 16 q^{59} + 12 q^{60} + 24 q^{61} - 8 q^{64} + 4 q^{65} - 48 q^{66} - 96 q^{69} - 48 q^{71} - 8 q^{74} - 32 q^{76} + 8 q^{79} + 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} + 40 q^{89} + 24 q^{90} + 16 q^{94} + 4 q^{95}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^5 + 12 * q^9 + 4 * q^10 + 24 * q^15 - 4 * q^16 - 16 * q^19 + 8 * q^20 - 8 * q^26 - 16 * q^29 - 12 * q^30 + 16 * q^31 - 16 * q^34 + 24 * q^36 - 24 * q^39 - 4 * q^40 + 48 * q^41 - 12 * q^45 - 8 * q^46 - 8 * q^50 + 48 * q^55 + 16 * q^59 + 12 * q^60 + 24 * q^61 - 8 * q^64 + 4 * q^65 - 48 * q^66 - 96 * q^69 - 48 * q^71 - 8 * q^74 - 32 * q^76 + 8 * q^79 + 4 * q^80 + 36 * q^81 - 16 * q^85 + 16 * q^86 + 40 * q^89 + 24 * q^90 + 16 * q^94 + 4 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more