LMFDB - Embedded newform 490.2.i.d.459.4

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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			459.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	490.459
Dual form			490.2.i.d.79.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.19067 - 0.448288i) q^{5} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.19067 - 0.448288i) q^{5} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.67303 - 1.48356i) q^{10} +(2.00000 - 3.46410i) q^{11} +4.24264i q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.67423 - 2.12132i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(2.82843 + 4.89898i) q^{19} +(0.707107 - 2.12132i) q^{20} -4.00000i q^{22} +(4.59808 - 1.96410i) q^{25} +(2.12132 + 3.67423i) q^{26} +4.00000 q^{29} +(2.82843 - 4.89898i) q^{31} +(-0.866025 - 0.500000i) q^{32} -4.24264 q^{34} -3.00000 q^{36} +(-5.19615 + 3.00000i) q^{37} +(4.89898 + 2.82843i) q^{38} +(-0.448288 - 2.19067i) q^{40} -1.41421 q^{41} +12.0000i q^{43} +(-2.00000 - 3.46410i) q^{44} +(-4.45069 - 5.01910i) q^{45} +(3.00000 - 4.00000i) q^{50} +(3.67423 + 2.12132i) q^{52} +(-10.3923 - 6.00000i) q^{53} +(2.82843 - 8.48528i) q^{55} +(3.46410 - 2.00000i) q^{58} +(-5.65685 + 9.79796i) q^{59} +(-3.53553 - 6.12372i) q^{61} -5.65685i q^{62} -1.00000 q^{64} +(1.90192 + 9.29423i) q^{65} +(10.3923 + 6.00000i) q^{67} +(-3.67423 + 2.12132i) q^{68} +8.00000 q^{71} +(-2.59808 + 1.50000i) q^{72} +(3.67423 + 2.12132i) q^{73} +(-3.00000 + 5.19615i) q^{74} +5.65685 q^{76} +(-1.48356 - 1.67303i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-1.22474 + 0.707107i) q^{82} +16.9706i q^{83} +(-9.00000 - 3.00000i) q^{85} +(6.00000 + 10.3923i) q^{86} +(-3.46410 - 2.00000i) q^{88} +(-2.12132 - 3.67423i) q^{89} +(-6.36396 - 2.12132i) q^{90} +(8.39230 + 9.46410i) q^{95} -4.24264i q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 12 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 - 12 * q^9	$ 8 q + 4 q^{4} - 12 q^{9} + 16 q^{11} - 4 q^{16} + 16 q^{25} + 32 q^{29} - 24 q^{36} - 16 q^{44} + 24 q^{50} - 8 q^{64} + 36 q^{65} + 64 q^{71} - 24 q^{74} - 36 q^{81} - 72 q^{85} + 48 q^{86} - 16 q^{95} - 96 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 12 * q^9 + 16 * q^11 - 4 * q^16 + 16 * q^25 + 32 * q^29 - 24 * q^36 - 16 * q^44 + 24 * q^50 - 8 * q^64 + 36 * q^65 + 64 * q^71 - 24 * q^74 - 36 * q^81 - 72 * q^85 + 48 * q^86 - 16 * q^95 - 96 * q^99

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
$3$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$3$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.19067	−	0.448288i	0.979698	−	0.200480i
$5$	2.19067	−	0.448288i	0.979698	−	0.200480i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$	1.67303	−	1.48356i	0.529059	−	0.469144i
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$		0			0
$13$			4.24264i			1.17670i	0.808608	+	0.588348i	$0.200222\pi$
$13$			4.24264i			1.17670i	−0.808608	+	0.588348i	$0.799778\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.67423	−	2.12132i	−0.891133	−	0.514496i	−0.0168199	−	0.999859i	$-0.505354\pi$
$17$	−3.67423	−	2.12132i	−0.891133	−	0.514496i	−0.874313	+	0.485363i	$0.838688\pi$
$18$	−2.59808	−	1.50000i	−0.612372	−	0.353553i
$19$	2.82843	+	4.89898i	0.648886	+	1.12390i	0.983389	+	0.181509i	$0.0580980\pi$
$19$	2.82843	+	4.89898i	0.648886	+	1.12390i	−0.334504	+	0.942394i	$0.608569\pi$
$20$	0.707107	−	2.12132i	0.158114	−	0.474342i
$21$		0			0
$22$		−	4.00000i		−	0.852803i
$23$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$23$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$24$		0			0
$25$	4.59808	−	1.96410i	0.919615	−	0.392820i
$26$	2.12132	+	3.67423i	0.416025	+	0.720577i
$27$		0			0
$28$		0			0
$29$	4.00000			0.742781			0.371391	−	0.928477i	$-0.378881\pi$
$29$	4.00000			0.742781			0.371391	+	0.928477i	$0.378881\pi$
$30$		0			0
$31$	2.82843	−	4.89898i	0.508001	−	0.879883i	−0.491957	−	0.870620i	$-0.663718\pi$
$31$	2.82843	−	4.89898i	0.508001	−	0.879883i	0.999957	−	0.00926296i	$-0.00294853\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−4.24264			−0.727607
$35$		0			0
$36$	−3.00000			−0.500000
$37$	−5.19615	+	3.00000i	−0.854242	+	0.493197i	−0.862080	−	0.506772i	$-0.830838\pi$
$37$	−5.19615	+	3.00000i	−0.854242	+	0.493197i	0.00783774	+	0.999969i	$0.497505\pi$
$38$	4.89898	+	2.82843i	0.794719	+	0.458831i
$39$		0			0
$40$	−0.448288	−	2.19067i	−0.0708805	−	0.346375i
$41$	−1.41421			−0.220863			−0.110432	−	0.993884i	$-0.535223\pi$
$41$	−1.41421			−0.220863			−0.110432	+	0.993884i	$0.535223\pi$
$42$		0			0
$43$			12.0000i			1.82998i	0.403473	+	0.914991i	$0.367803\pi$
$43$			12.0000i			1.82998i	−0.403473	+	0.914991i	$0.632197\pi$
$44$	−2.00000	−	3.46410i	−0.301511	−	0.522233i
$45$	−4.45069	−	5.01910i	−0.663470	−	0.748203i
$46$		0			0
$47$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$47$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$48$		0			0
$49$		0			0
$50$	3.00000	−	4.00000i	0.424264	−	0.565685i
$51$		0			0
$52$	3.67423	+	2.12132i	0.509525	+	0.294174i
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.430570	−	0.902557i	$-0.641688\pi$
$53$	−10.3923	−	6.00000i	−1.42749	−	0.824163i	−0.996922	+	0.0783936i	$0.975021\pi$
$54$		0			0
$55$	2.82843	−	8.48528i	0.381385	−	1.14416i
$56$		0			0
$57$		0			0
$58$	3.46410	−	2.00000i	0.454859	−	0.262613i
$59$	−5.65685	+	9.79796i	−0.736460	+	1.27559i	0.217620	+	0.976034i	$0.430171\pi$
$59$	−5.65685	+	9.79796i	−0.736460	+	1.27559i	−0.954080	+	0.299552i	$0.903163\pi$
$60$		0			0
$61$	−3.53553	−	6.12372i	−0.452679	−	0.784063i	0.545873	−	0.837868i	$-0.316198\pi$
$61$	−3.53553	−	6.12372i	−0.452679	−	0.784063i	−0.998551	+	0.0538056i	$0.982865\pi$
$62$		−	5.65685i		−	0.718421i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.90192	+	9.29423i	0.235905	+	1.15281i
$66$		0			0
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.974916	−	0.222571i	$-0.0714450\pi$
$67$	10.3923	+	6.00000i	1.26962	+	0.733017i	0.294706	+	0.955588i	$0.404778\pi$
$68$	−3.67423	+	2.12132i	−0.445566	+	0.257248i
$69$		0			0
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	−2.59808	+	1.50000i	−0.306186	+	0.176777i
$73$	3.67423	+	2.12132i	0.430037	+	0.248282i	0.699362	−	0.714767i	$-0.253467\pi$
$73$	3.67423	+	2.12132i	0.430037	+	0.248282i	−0.269326	+	0.963049i	$0.586801\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$		0			0
$76$	5.65685			0.648886
$77$		0			0
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−1.48356	−	1.67303i	−0.165867	−	0.187051i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−1.22474	+	0.707107i	−0.135250	+	0.0780869i
$83$			16.9706i			1.86276i	0.364047	+	0.931381i	$0.381395\pi$
$83$			16.9706i			1.86276i	−0.364047	+	0.931381i	$0.618605\pi$
$84$		0			0
$85$	−9.00000	−	3.00000i	−0.976187	−	0.325396i
$86$	6.00000	+	10.3923i	0.646997	+	1.12063i
$87$		0			0
$88$	−3.46410	−	2.00000i	−0.369274	−	0.213201i
$89$	−2.12132	−	3.67423i	−0.224860	−	0.389468i	0.731418	−	0.681930i	$-0.238859\pi$
$89$	−2.12132	−	3.67423i	−0.224860	−	0.389468i	−0.956277	+	0.292462i	$0.905526\pi$
$90$	−6.36396	−	2.12132i	−0.670820	−	0.223607i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.39230	+	9.46410i	0.861032	+	0.970996i
$96$		0			0
$97$		−	4.24264i		−	0.430775i	−0.976529	−	0.215387i	$-0.930899\pi$
$97$		−	4.24264i		−	0.430775i	0.976529	−	0.215387i	$-0.0691014\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$	0.598076	−	4.96410i	0.0598076	−	0.496410i
$101$	−4.94975	+	8.57321i	−0.492518	+	0.853067i	−0.999963	−	0.00861771i	$-0.997257\pi$
$101$	−4.94975	+	8.57321i	−0.492518	+	0.853067i	0.507445	+	0.861684i	$0.330590\pi$
$102$		0			0
$103$	−14.6969	+	8.48528i	−1.44813	+	0.836080i	−0.998370	−	0.0570688i	$-0.981825\pi$
$103$	−14.6969	+	8.48528i	−1.44813	+	0.836080i	−0.449762	+	0.893148i	$0.648491\pi$
$104$	4.24264			0.416025
$105$		0			0
$106$	−12.0000			−1.16554
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.0950377	−	0.995474i	$-0.469703\pi$
$107$	10.3923	−	6.00000i	1.00466	−	0.580042i	0.909624	+	0.415432i	$0.136370\pi$
$108$		0			0
$109$	−6.00000	+	10.3923i	−0.574696	+	0.995402i	0.421379	+	0.906885i	$0.361546\pi$
$109$	−6.00000	+	10.3923i	−0.574696	+	0.995402i	−0.996075	+	0.0885176i	$0.971787\pi$
$110$	−1.79315	−	8.76268i	−0.170970	−	0.835489i
$111$		0			0
$112$		0			0
$113$		0			0		1.00000			$0$
$113$		0			0		−1.00000			$\pi$
$114$		0			0
$115$		0			0
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$	11.0227	−	6.36396i	1.01905	−	0.588348i
$118$			11.3137i			1.04151i
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−6.12372	−	3.53553i	−0.554416	−	0.320092i
$123$		0			0
$124$	−2.82843	−	4.89898i	−0.254000	−	0.439941i
$125$	9.19239	−	6.36396i	0.822192	−	0.569210i
$126$		0			0
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	6.29423	+	7.09808i	0.552040	+	0.622542i
$131$	−8.48528	−	14.6969i	−0.741362	−	1.28408i	−0.951875	−	0.306486i	$-0.900847\pi$
$131$	−8.48528	−	14.6969i	−0.741362	−	1.28408i	0.210513	−	0.977591i	$-0.432487\pi$
$132$		0			0
$133$		0			0
$134$	12.0000			1.03664
$135$		0			0
$136$	−2.12132	+	3.67423i	−0.181902	+	0.315063i
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	0.261329	−	0.965250i	$-0.415839\pi$
$137$	−5.19615	−	3.00000i	−0.443937	−	0.256307i	−0.705266	+	0.708942i	$0.749173\pi$
$138$		0			0
$139$	−5.65685			−0.479808			−0.239904	−	0.970797i	$-0.577116\pi$
$139$	−5.65685			−0.479808			−0.239904	+	0.970797i	$0.577116\pi$
$140$		0			0
$141$		0			0
$142$	6.92820	−	4.00000i	0.581402	−	0.335673i
$143$	14.6969	+	8.48528i	1.22902	+	0.709575i
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$	8.76268	−	1.79315i	0.727701	−	0.148913i
$146$	4.24264			0.351123
$147$		0			0
$148$			6.00000i			0.493197i
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$		0			0
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	−0.981617	−	0.190864i	$-0.938871\pi$
$151$	−4.00000	+	6.92820i	−0.325515	+	0.563809i	0.656101	+	0.754673i	$0.272204\pi$
$152$	4.89898	−	2.82843i	0.397360	−	0.229416i
$153$			12.7279i			1.02899i
$154$		0			0
$155$	4.00000	−	12.0000i	0.321288	−	0.963863i
$156$		0			0
$157$	−3.67423	−	2.12132i	−0.293236	−	0.169300i	0.346164	−	0.938174i	$-0.387484\pi$
$157$	−3.67423	−	2.12132i	−0.293236	−	0.169300i	−0.639400	+	0.768874i	$0.720817\pi$
$158$		0			0
$159$		0			0
$160$	−2.12132	−	0.707107i	−0.167705	−	0.0559017i
$161$		0			0
$162$			9.00000i			0.707107i
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	−0.0343508	−	0.999410i	$-0.510936\pi$
$163$	10.3923	−	6.00000i	0.813988	−	0.469956i	0.848339	+	0.529454i	$0.177603\pi$
$164$	−0.707107	+	1.22474i	−0.0552158	+	0.0956365i
$165$		0			0
$166$	8.48528	+	14.6969i	0.658586	+	1.14070i
$167$		−	16.9706i		−	1.31322i	−0.754230	−	0.656611i	$-0.771989\pi$
$167$		−	16.9706i		−	1.31322i	0.754230	−	0.656611i	$-0.228011\pi$
$168$		0			0
$169$	−5.00000			−0.384615
$170$	−9.29423	+	1.90192i	−0.712835	+	0.145871i
$171$	8.48528	−	14.6969i	0.648886	−	1.12390i
$172$	10.3923	+	6.00000i	0.792406	+	0.457496i
$173$	3.67423	−	2.12132i	0.279347	−	0.161281i	−0.353781	−	0.935328i	$-0.615104\pi$
$173$	3.67423	−	2.12132i	0.279347	−	0.161281i	0.633128	+	0.774047i	$0.281771\pi$
$174$		0			0
$175$		0			0
$176$	−4.00000			−0.301511
$177$		0			0
$178$	−3.67423	−	2.12132i	−0.275396	−	0.159000i
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	−0.201613	−	0.979465i	$-0.564618\pi$
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	0.949048	−	0.315130i	$-0.102048\pi$
$180$	−6.57201	+	1.34486i	−0.489849	+	0.100240i
$181$	−15.5563			−1.15629			−0.578147	−	0.815933i	$-0.696224\pi$
$181$	−15.5563			−1.15629			−0.578147	+	0.815933i	$0.696224\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.0382	+	8.90138i	−0.738023	+	0.654443i
$186$		0			0
$187$	−14.6969	+	8.48528i	−1.07475	+	0.620505i
$188$		0			0
$189$		0			0
$190$	12.0000	+	4.00000i	0.870572	+	0.290191i
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$		0			0
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	−20.7846	−	12.0000i	−1.49611	−	0.863779i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−2.12132	−	3.67423i	−0.152302	−	0.263795i
$195$		0			0
$196$		0			0
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	−10.3923	+	6.00000i	−0.738549	+	0.426401i
$199$	5.65685	−	9.79796i	0.401004	−	0.694559i	−0.592844	−	0.805318i	$-0.701995\pi$
$199$	5.65685	−	9.79796i	0.401004	−	0.694559i	0.993847	+	0.110759i	$0.0353281\pi$
$200$	−1.96410	−	4.59808i	−0.138883	−	0.325133i
$201$		0			0
$202$			9.89949i			0.696526i
$203$		0			0
$204$		0			0
$205$	−3.09808	+	0.633975i	−0.216379	+	0.0442787i
$206$	−8.48528	+	14.6969i	−0.591198	+	1.02398i
$207$		0			0
$208$	3.67423	−	2.12132i	0.254762	−	0.147087i
$209$	22.6274			1.56517
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	−10.3923	+	6.00000i	−0.713746	+	0.412082i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	5.37945	+	26.2880i	0.366876	+	1.79283i
$216$		0			0
$217$		0			0
$218$			12.0000i			0.812743i
$219$		0			0
$220$	−5.93426	−	6.69213i	−0.400087	−	0.451183i
$221$	9.00000	−	15.5885i	0.605406	−	1.04859i
$222$		0			0
$223$		−	16.9706i		−	1.13643i	−0.822879	−	0.568216i	$-0.807634\pi$
$223$		−	16.9706i		−	1.13643i	0.822879	−	0.568216i	$-0.192366\pi$
$224$		0			0
$225$	−12.0000	−	9.00000i	−0.800000	−	0.600000i
$226$		0			0
$227$	14.6969	+	8.48528i	0.975470	+	0.563188i	0.900899	−	0.434028i	$-0.142908\pi$
$227$	14.6969	+	8.48528i	0.975470	+	0.563188i	0.0745706	+	0.997216i	$0.476241\pi$
$228$		0			0
$229$	7.77817	+	13.4722i	0.513996	+	0.890268i	0.999868	+	0.0162376i	$0.00516881\pi$
$229$	7.77817	+	13.4722i	0.513996	+	0.890268i	−0.485872	+	0.874030i	$0.661498\pi$
$230$		0			0
$231$		0			0
$232$		−	4.00000i		−	0.262613i
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	−0.660454	−	0.750867i	$-0.729636\pi$
$233$	−5.19615	+	3.00000i	−0.340411	+	0.196537i	0.320043	+	0.947403i	$0.396303\pi$
$234$	6.36396	−	11.0227i	0.416025	−	0.720577i
$235$		0			0
$236$	5.65685	+	9.79796i	0.368230	+	0.637793i
$237$		0			0
$238$		0			0
$239$	8.00000			0.517477			0.258738	−	0.965947i	$-0.416693\pi$
$239$	8.00000			0.517477			0.258738	+	0.965947i	$0.416693\pi$
$240$		0			0
$241$	7.77817	−	13.4722i	0.501036	−	0.867820i	−0.498963	−	0.866623i	$-0.666286\pi$
$241$	7.77817	−	13.4722i	0.501036	−	0.867820i	0.999999	−	0.00119700i	$-0.000381016\pi$
$242$	−4.33013	−	2.50000i	−0.278351	−	0.160706i
$243$		0			0
$244$	−7.07107			−0.452679
$245$		0			0
$246$		0			0
$247$	−20.7846	+	12.0000i	−1.32249	+	0.763542i
$248$	−4.89898	−	2.82843i	−0.311086	−	0.179605i
$249$		0			0
$250$	4.77886	−	10.1075i	0.302242	−	0.639257i
$251$	−5.65685			−0.357057			−0.178529	−	0.983935i	$-0.557134\pi$
$251$	−5.65685			−0.357057			−0.178529	+	0.983935i	$0.557134\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.0227	−	6.36396i	0.687577	−	0.396973i	−0.115126	−	0.993351i	$-0.536727\pi$
$257$	11.0227	−	6.36396i	0.687577	−	0.396973i	0.802704	+	0.596378i	$0.203394\pi$
$258$		0			0
$259$		0			0
$260$	9.00000	+	3.00000i	0.558156	+	0.186052i
$261$	−6.00000	−	10.3923i	−0.371391	−	0.643268i
$262$	−14.6969	−	8.48528i	−0.907980	−	0.524222i
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$	−25.4558	−	8.48528i	−1.56374	−	0.521247i
$266$		0			0
$267$		0			0
$268$	10.3923	−	6.00000i	0.634811	−	0.366508i
$269$	10.6066	−	18.3712i	0.646696	−	1.12011i	−0.337211	−	0.941429i	$-0.609484\pi$
$269$	10.6066	−	18.3712i	0.646696	−	1.12011i	0.983907	−	0.178681i	$-0.0571831\pi$
$270$		0			0
$271$	5.65685	+	9.79796i	0.343629	+	0.595184i	0.985104	−	0.171961i	$-0.0550103\pi$
$271$	5.65685	+	9.79796i	0.343629	+	0.595184i	−0.641474	+	0.767144i	$0.721677\pi$
$272$			4.24264i			0.257248i
$273$		0			0
$274$	−6.00000			−0.362473
$275$	2.39230	−	19.8564i	0.144261	−	1.19739i
$276$		0			0
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	0.154172	−	0.988044i	$-0.450729\pi$
$277$	−10.3923	−	6.00000i	−0.624413	−	0.360505i	−0.778585	+	0.627539i	$0.784062\pi$
$278$	−4.89898	+	2.82843i	−0.293821	+	0.169638i
$279$	−16.9706			−1.01600
$280$		0			0
$281$	16.0000			0.954480			0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000			0.954480			0.477240	+	0.878773i	$0.341637\pi$
$282$		0			0
$283$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$283$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$		0			0
$286$	16.9706			1.00349
$287$		0			0
$288$			3.00000i			0.176777i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	6.69213	−	5.93426i	0.392975	−	0.348471i
$291$		0			0
$292$	3.67423	−	2.12132i	0.215018	−	0.124141i
$293$		−	4.24264i		−	0.247858i	−0.992291	−	0.123929i	$-0.960451\pi$
$293$		−	4.24264i		−	0.247858i	0.992291	−	0.123929i	$-0.0395495\pi$
$294$		0			0
$295$	−8.00000	+	24.0000i	−0.465778	+	1.39733i
$296$	3.00000	+	5.19615i	0.174371	+	0.302020i
$297$		0			0
$298$	8.66025	+	5.00000i	0.501675	+	0.289642i
$299$		0			0
$300$		0			0
$301$		0			0
$302$			8.00000i			0.460348i
$303$		0			0
$304$	2.82843	−	4.89898i	0.162221	−	0.280976i
$305$	−10.4904	−	11.8301i	−0.600677	−	0.677391i
$306$	6.36396	+	11.0227i	0.363803	+	0.630126i
$307$			16.9706i			0.968561i	0.874913	+	0.484281i	$0.160919\pi$
$307$			16.9706i			0.968561i	−0.874913	+	0.484281i	$0.839081\pi$
$308$		0			0
$309$		0			0
$310$	−2.53590	−	12.3923i	−0.144029	−	0.703836i
$311$	−8.48528	+	14.6969i	−0.481156	+	0.833387i	−0.999766	−	0.0216240i	$-0.993116\pi$
$311$	−8.48528	+	14.6969i	−0.481156	+	0.833387i	0.518610	+	0.855011i	$0.326450\pi$
$312$		0			0
$313$	11.0227	−	6.36396i	0.623040	−	0.359712i	−0.155012	−	0.987913i	$-0.549541\pi$
$313$	11.0227	−	6.36396i	0.623040	−	0.359712i	0.778052	+	0.628200i	$0.216208\pi$
$314$	−4.24264			−0.239426
$315$		0			0
$316$		0			0
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	−0.178908	−	0.983866i	$-0.557257\pi$
$317$	10.3923	−	6.00000i	0.583690	−	0.336994i	0.762598	+	0.646872i	$0.223923\pi$
$318$		0			0
$319$	8.00000	−	13.8564i	0.447914	−	0.775810i
$320$	−2.19067	+	0.448288i	−0.122462	+	0.0250600i
$321$		0			0
$322$		0			0
$323$		−	24.0000i		−	1.33540i
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	8.33298	+	19.5080i	0.462230	+	1.08211i
$326$	6.00000	−	10.3923i	0.332309	−	0.575577i
$327$		0			0
$328$			1.41421i			0.0780869i
$329$		0			0
$330$		0			0
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	14.6969	+	8.48528i	0.806599	+	0.465690i
$333$	15.5885	+	9.00000i	0.854242	+	0.493197i
$334$	−8.48528	−	14.6969i	−0.464294	−	0.804181i
$335$	25.4558	+	8.48528i	1.39080	+	0.463600i
$336$		0			0
$337$		−	18.0000i		−	0.980522i	−0.871576	−	0.490261i	$-0.836901\pi$
$337$		−	18.0000i		−	0.980522i	0.871576	−	0.490261i	$-0.163099\pi$
$338$	−4.33013	+	2.50000i	−0.235528	+	0.135982i
$339$		0			0
$340$	−7.09808	+	6.29423i	−0.384947	+	0.341352i
$341$	−11.3137	−	19.5959i	−0.612672	−	1.06118i
$342$		−	16.9706i		−	0.917663i
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$	2.12132	−	3.67423i	0.114043	−	0.197528i
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	0.752297	−	0.658824i	$-0.228946\pi$
$347$	10.3923	+	6.00000i	0.557888	+	0.322097i	−0.194409	+	0.980921i	$0.562279\pi$
$348$		0			0
$349$	24.0416			1.28692			0.643459	−	0.765480i	$-0.277498\pi$
$349$	24.0416			1.28692			0.643459	+	0.765480i	$0.277498\pi$
$350$		0			0
$351$		0			0
$352$	−3.46410	+	2.00000i	−0.184637	+	0.106600i
$353$	−18.3712	−	10.6066i	−0.977799	−	0.564532i	−0.0761940	−	0.997093i	$-0.524277\pi$
$353$	−18.3712	−	10.6066i	−0.977799	−	0.564532i	−0.901605	+	0.432561i	$0.857610\pi$
$354$		0			0
$355$	17.5254	−	3.58630i	0.930150	−	0.190341i
$356$	−4.24264			−0.224860
$357$		0			0
$358$		−	20.0000i		−	1.05703i
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	0.996157	−	0.0875892i	$-0.0279163\pi$
$359$	8.00000	+	13.8564i	0.422224	+	0.731313i	−0.573933	+	0.818902i	$0.694583\pi$
$360$	−5.01910	+	4.45069i	−0.264530	+	0.234572i
$361$	−6.50000	+	11.2583i	−0.342105	+	0.592544i
$362$	−13.4722	+	7.77817i	−0.708083	+	0.408812i
$363$		0			0
$364$		0			0
$365$	9.00000	+	3.00000i	0.471082	+	0.157027i
$366$		0			0
$367$	−14.6969	−	8.48528i	−0.767174	−	0.442928i	0.0646916	−	0.997905i	$-0.479394\pi$
$367$	−14.6969	−	8.48528i	−0.767174	−	0.442928i	−0.831866	+	0.554977i	$0.812727\pi$
$368$		0			0
$369$	2.12132	+	3.67423i	0.110432	+	0.191273i
$370$	−4.24264	+	12.7279i	−0.220564	+	0.661693i
$371$		0			0
$372$		0			0
$373$	−10.3923	+	6.00000i	−0.538093	+	0.310668i	−0.744306	−	0.667839i	$-0.767219\pi$
$373$	−10.3923	+	6.00000i	−0.538093	+	0.310668i	0.206213	+	0.978507i	$0.433886\pi$
$374$	−8.48528	+	14.6969i	−0.438763	+	0.759961i
$375$		0			0
$376$		0			0
$377$			16.9706i			0.874028i
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	12.3923	−	2.53590i	0.635712	−	0.130089i
$381$		0			0
$382$	−6.92820	−	4.00000i	−0.354478	−	0.204658i
$383$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$383$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$384$		0			0
$385$		0			0
$386$	−24.0000			−1.22157
$387$	31.1769	−	18.0000i	1.58481	−	0.914991i
$388$	−3.67423	−	2.12132i	−0.186531	−	0.107694i
$389$	−10.0000	+	17.3205i	−0.507020	+	0.878185i	0.492947	+	0.870059i	$0.335920\pi$
$389$	−10.0000	+	17.3205i	−0.507020	+	0.878185i	−0.999967	+	0.00812520i	$0.997414\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−6.00000	−	10.3923i	−0.302276	−	0.523557i
$395$		0			0
$396$	−6.00000	+	10.3923i	−0.301511	+	0.522233i
$397$	−25.7196	+	14.8492i	−1.29083	+	0.745262i	−0.978802	−	0.204810i	$-0.934342\pi$
$397$	−25.7196	+	14.8492i	−1.29083	+	0.745262i	−0.312030	+	0.950072i	$0.601009\pi$
$398$		−	11.3137i		−	0.567105i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$	4.00000	+	6.92820i	0.199750	+	0.345978i	0.948447	−	0.316934i	$-0.102654\pi$
$401$	4.00000	+	6.92820i	0.199750	+	0.345978i	−0.748697	+	0.662912i	$0.769320\pi$
$402$		0			0
$403$	20.7846	+	12.0000i	1.03536	+	0.597763i
$404$	4.94975	+	8.57321i	0.246259	+	0.426533i
$405$	−6.36396	+	19.0919i	−0.316228	+	0.948683i
$406$		0			0
$407$			24.0000i			1.18964i
$408$		0			0
$409$	−4.94975	+	8.57321i	−0.244749	+	0.423918i	−0.962061	−	0.272834i	$-0.912039\pi$
$409$	−4.94975	+	8.57321i	−0.244749	+	0.423918i	0.717312	+	0.696752i	$0.245372\pi$
$410$	−2.36603	+	2.09808i	−0.116850	+	0.103617i
$411$		0			0
$412$			16.9706i			0.836080i
$413$		0			0
$414$		0			0
$415$	7.60770	+	37.1769i	0.373447	+	1.82494i
$416$	2.12132	−	3.67423i	0.104006	−	0.180144i
$417$		0			0
$418$	19.5959	−	11.3137i	0.958468	−	0.553372i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−6.00000			−0.292422			−0.146211	−	0.989253i	$-0.546708\pi$
$421$	−6.00000			−0.292422			−0.146211	+	0.989253i	$0.546708\pi$
$422$	10.3923	−	6.00000i	0.505889	−	0.292075i
$423$		0			0
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	−21.0609	−	2.53742i	−1.02160	−	0.123083i
$426$		0			0
$427$		0			0
$428$		−	12.0000i		−	0.580042i
$429$		0			0
$430$	17.8028	+	20.0764i	0.858526	+	0.968170i
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	−0.991817	−	0.127666i	$-0.959251\pi$
$431$	−8.00000	+	13.8564i	−0.385346	+	0.667440i	0.606471	+	0.795106i	$0.292585\pi$
$432$		0			0
$433$		−	29.6985i		−	1.42722i	−0.700544	−	0.713609i	$-0.747059\pi$
$433$		−	29.6985i		−	1.42722i	0.700544	−	0.713609i	$-0.252941\pi$
$434$		0			0
$435$		0			0
$436$	6.00000	+	10.3923i	0.287348	+	0.497701i
$437$		0			0
$438$		0			0
$439$	−19.7990	−	34.2929i	−0.944954	−	1.63671i	−0.755843	−	0.654753i	$-0.772773\pi$
$439$	−19.7990	−	34.2929i	−0.944954	−	1.63671i	−0.189111	−	0.981956i	$-0.560561\pi$
$440$	−8.48528	−	2.82843i	−0.404520	−	0.134840i
$441$		0			0
$442$		−	18.0000i		−	0.856173i
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	−0.232377	−	0.972626i	$-0.574650\pi$
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	0.726130	+	0.687557i	$0.241317\pi$
$444$		0			0
$445$	−6.29423	−	7.09808i	−0.298375	−	0.336481i
$446$	−8.48528	−	14.6969i	−0.401790	−	0.695920i
$447$		0			0
$448$		0			0
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	−14.8923	−	1.79423i	−0.702030	−	0.0845807i
$451$	−2.82843	+	4.89898i	−0.133185	+	0.230684i
$452$		0			0
$453$		0			0
$454$	16.9706			0.796468
$455$		0			0
$456$		0			0
$457$	−20.7846	+	12.0000i	−0.972263	+	0.561336i	−0.899925	−	0.436044i	$-0.856379\pi$
$457$	−20.7846	+	12.0000i	−0.972263	+	0.561336i	−0.0723376	+	0.997380i	$0.523046\pi$
$458$	13.4722	+	7.77817i	0.629514	+	0.363450i
$459$		0			0
$460$		0			0
$461$	−21.2132			−0.987997			−0.493999	−	0.869463i	$-0.664465\pi$
$461$	−21.2132			−0.987997			−0.493999	+	0.869463i	$0.664465\pi$
$462$		0			0
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$	−2.00000	−	3.46410i	−0.0928477	−	0.160817i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	14.6969	−	8.48528i	0.680093	−	0.392652i	−0.119797	−	0.992798i	$-0.538224\pi$
$467$	14.6969	−	8.48528i	0.680093	−	0.392652i	0.799890	+	0.600146i	$0.204891\pi$
$468$		−	12.7279i		−	0.588348i
$469$		0			0
$470$		0			0
$471$		0			0
$472$	9.79796	+	5.65685i	0.450988	+	0.260378i
$473$	41.5692	+	24.0000i	1.91135	+	1.10352i
$474$		0			0
$475$	22.6274	+	16.9706i	1.03822	+	0.778663i
$476$		0			0
$477$			36.0000i			1.64833i
$478$	6.92820	−	4.00000i	0.316889	−	0.182956i
$479$	−8.48528	+	14.6969i	−0.387702	+	0.671520i	−0.992140	−	0.125132i	$-0.960065\pi$
$479$	−8.48528	+	14.6969i	−0.387702	+	0.671520i	0.604438	+	0.796652i	$0.293398\pi$
$480$		0			0
$481$	−12.7279	−	22.0454i	−0.580343	−	1.00518i
$482$		−	15.5563i		−	0.708572i
$483$		0			0
$484$	−5.00000			−0.227273
$485$	−1.90192	−	9.29423i	−0.0863619	−	0.422029i
$486$		0			0
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.0513038	−	0.998683i	$-0.516338\pi$
$487$	−20.7846	−	12.0000i	−0.941841	−	0.543772i	−0.890537	+	0.454911i	$0.849671\pi$
$488$	−6.12372	+	3.53553i	−0.277208	+	0.160046i
$489$		0			0
$490$		0			0
$491$	−4.00000			−0.180517			−0.0902587	−	0.995918i	$-0.528769\pi$
$491$	−4.00000			−0.180517			−0.0902587	+	0.995918i	$0.528769\pi$
$492$		0			0
$493$	−14.6969	−	8.48528i	−0.661917	−	0.382158i
$494$	−12.0000	+	20.7846i	−0.539906	+	0.935144i
$495$	−26.2880	+	5.37945i	−1.18156	+	0.241788i
$496$	−5.65685			−0.254000
$497$		0			0
$498$		0			0
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	0.907314	−	0.420455i	$-0.138129\pi$
$499$	2.00000	+	3.46410i	0.0895323	+	0.155074i	−0.817781	+	0.575529i	$0.804796\pi$
$500$	−0.915158	−	11.1428i	−0.0409271	−	0.498322i
$501$		0			0
$502$	−4.89898	+	2.82843i	−0.218652	+	0.126239i
$503$		−	33.9411i		−	1.51336i	−0.653785	−	0.756680i	$-0.726820\pi$
$503$		−	33.9411i		−	1.51336i	0.653785	−	0.756680i	$-0.273180\pi$
$504$		0			0
$505$	−7.00000	+	21.0000i	−0.311496	+	0.934488i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.36396	+	11.0227i	0.282078	+	0.488573i	0.971896	−	0.235409i	$-0.0756431\pi$
$509$	6.36396	+	11.0227i	0.282078	+	0.488573i	−0.689819	+	0.723982i	$0.742310\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	6.36396	−	11.0227i	0.280702	−	0.486191i
$515$	−28.3923	+	25.1769i	−1.25111	+	1.10943i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	9.29423	−	1.90192i	0.407579	−	0.0834049i
$521$	−6.36396	+	11.0227i	−0.278810	+	0.482913i	−0.971089	−	0.238716i	$-0.923273\pi$
$521$	−6.36396	+	11.0227i	−0.278810	+	0.482913i	0.692279	+	0.721630i	$0.256607\pi$
$522$	−10.3923	−	6.00000i	−0.454859	−	0.262613i
$523$	29.3939	−	16.9706i	1.28530	−	0.742071i	0.307492	−	0.951551i	$-0.400510\pi$
$523$	29.3939	−	16.9706i	1.28530	−	0.742071i	0.977813	+	0.209480i	$0.0671771\pi$
$524$	−16.9706			−0.741362
$525$		0			0
$526$		0			0
$527$	−20.7846	+	12.0000i	−0.905392	+	0.522728i
$528$		0			0
$529$	−11.5000	+	19.9186i	−0.500000	+	0.866025i
$530$	−26.2880	+	5.37945i	−1.14188	+	0.233668i
$531$	33.9411			1.47292
$532$		0			0
$533$		−	6.00000i		−	0.259889i
$534$		0			0
$535$	20.0764	−	17.8028i	0.867978	−	0.769681i
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$		0			0
$538$		−	21.2132i		−	0.914566i
$539$		0			0
$540$		0			0
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	0.984325	+	0.176367i	$0.0564345\pi$
$541$	15.0000	+	25.9808i	0.644900	+	1.11700i	−0.339424	+	0.940633i	$0.610232\pi$
$542$	9.79796	+	5.65685i	0.420858	+	0.242983i
$543$		0			0
$544$	2.12132	+	3.67423i	0.0909509	+	0.157532i
$545$	−8.48528	+	25.4558i	−0.363470	+	1.09041i
$546$		0			0
$547$		−	12.0000i		−	0.513083i	−0.966533	−	0.256541i	$-0.917417\pi$
$547$		−	12.0000i		−	0.513083i	0.966533	−	0.256541i	$-0.0825830\pi$
$548$	−5.19615	+	3.00000i	−0.221969	+	0.128154i
$549$	−10.6066	+	18.3712i	−0.452679	+	0.784063i
$550$	−7.85641	−	18.3923i	−0.334998	−	0.784251i
$551$	11.3137	+	19.5959i	0.481980	+	0.834814i
$552$		0			0
$553$		0			0
$554$	−12.0000			−0.509831
$555$		0			0
$556$	−2.82843	+	4.89898i	−0.119952	+	0.207763i
$557$	10.3923	+	6.00000i	0.440336	+	0.254228i	0.703740	−	0.710457i	$-0.251512\pi$
$557$	10.3923	+	6.00000i	0.440336	+	0.254228i	−0.263404	+	0.964686i	$0.584845\pi$
$558$	−14.6969	+	8.48528i	−0.622171	+	0.359211i
$559$	−50.9117			−2.15333
$560$		0			0
$561$		0			0
$562$	13.8564	−	8.00000i	0.584497	−	0.337460i
$563$	−29.3939	−	16.9706i	−1.23880	−	0.715224i	−0.269954	−	0.962873i	$-0.587009\pi$
$563$	−29.3939	−	16.9706i	−1.23880	−	0.715224i	−0.968850	+	0.247649i	$0.920342\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$		0			0
$568$		−	8.00000i		−	0.335673i
$569$	−4.00000	−	6.92820i	−0.167689	−	0.290445i	0.769918	−	0.638143i	$-0.220297\pi$
$569$	−4.00000	−	6.92820i	−0.167689	−	0.290445i	−0.937607	+	0.347697i	$0.886964\pi$
$570$		0			0
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	−0.904835	−	0.425762i	$-0.860006\pi$
$571$	−2.00000	+	3.46410i	−0.0836974	+	0.144968i	0.821138	+	0.570730i	$0.193340\pi$
$572$	14.6969	−	8.48528i	0.614510	−	0.354787i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.50000	+	2.59808i	0.0625000	+	0.108253i
$577$	18.3712	+	10.6066i	0.764802	+	0.441559i	0.831017	−	0.556247i	$-0.187759\pi$
$577$	18.3712	+	10.6066i	0.764802	+	0.441559i	−0.0662152	+	0.997805i	$0.521092\pi$
$578$	0.866025	+	0.500000i	0.0360219	+	0.0207973i
$579$		0			0
$580$	2.82843	−	8.48528i	0.117444	−	0.352332i
$581$		0			0
$582$		0			0
$583$	−41.5692	+	24.0000i	−1.72162	+	0.993978i
$584$	2.12132	−	3.67423i	0.0877809	−	0.152041i
$585$	21.2942	−	18.8827i	0.880408	−	0.780703i
$586$	−2.12132	−	3.67423i	−0.0876309	−	0.151781i
$587$			16.9706i			0.700450i	0.936666	+	0.350225i	$0.113895\pi$
$587$			16.9706i			0.700450i	−0.936666	+	0.350225i	$0.886105\pi$
$588$		0			0
$589$	32.0000			1.31854
$590$	5.07180	+	24.7846i	0.208803	+	1.02037i
$591$		0			0
$592$	5.19615	+	3.00000i	0.213561	+	0.123299i
$593$	−11.0227	+	6.36396i	−0.452648	+	0.261337i	−0.708948	−	0.705261i	$-0.750830\pi$
$593$	−11.0227	+	6.36396i	−0.452648	+	0.261337i	0.256300	+	0.966597i	$0.417497\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$		0			0
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	−0.655018	−	0.755613i	$-0.727339\pi$
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	0.981889	+	0.189456i	$0.0606724\pi$
$600$		0			0
$601$	26.8701			1.09605			0.548026	−	0.836461i	$-0.315379\pi$
$601$	26.8701			1.09605			0.548026	+	0.836461i	$0.315379\pi$
$602$		0			0
$603$		−	36.0000i		−	1.46603i
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$	−7.41782	−	8.36516i	−0.301577	−	0.340092i
$606$		0			0
$607$	−14.6969	+	8.48528i	−0.596530	+	0.344407i	−0.767675	−	0.640839i	$-0.778587\pi$
$607$	−14.6969	+	8.48528i	−0.596530	+	0.344407i	0.171145	+	0.985246i	$0.445253\pi$
$608$		−	5.65685i		−	0.229416i
$609$		0			0
$610$	−15.0000	−	5.00000i	−0.607332	−	0.202444i
$611$		0			0
$612$	11.0227	+	6.36396i	0.445566	+	0.257248i
$613$	5.19615	+	3.00000i	0.209871	+	0.121169i	0.601251	−	0.799060i	$-0.294669\pi$
$613$	5.19615	+	3.00000i	0.209871	+	0.121169i	−0.391381	+	0.920229i	$0.628002\pi$
$614$	8.48528	+	14.6969i	0.342438	+	0.593120i
$615$		0			0
$616$		0			0
$617$			42.0000i			1.69086i	0.534089	+	0.845428i	$0.320655\pi$
$617$			42.0000i			1.69086i	−0.534089	+	0.845428i	$0.679345\pi$
$618$		0			0
$619$	−22.6274	+	39.1918i	−0.909473	+	1.57525i	−0.0946744	+	0.995508i	$0.530181\pi$
$619$	−22.6274	+	39.1918i	−0.909473	+	1.57525i	−0.814798	+	0.579745i	$0.803152\pi$
$620$	−8.39230	−	9.46410i	−0.337043	−	0.380087i
$621$		0			0
$622$			16.9706i			0.680458i
$623$		0			0
$624$		0			0
$625$	17.2846	−	18.0622i	0.691384	−	0.722487i
$626$	6.36396	−	11.0227i	0.254355	−	0.440556i
$627$		0			0
$628$	−3.67423	+	2.12132i	−0.146618	+	0.0846499i
$629$	25.4558			1.01499
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$		0			0
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$		0			0
$636$		0			0
$637$		0			0
$638$		−	16.0000i		−	0.633446i
$639$	−12.0000	−	20.7846i	−0.474713	−	0.822226i
$640$	−1.67303	+	1.48356i	−0.0661324	+	0.0586430i
$641$	20.0000	−	34.6410i	0.789953	−	1.36824i	−0.136043	−	0.990703i	$-0.543438\pi$
$641$	20.0000	−	34.6410i	0.789953	−	1.36824i	0.925995	−	0.377535i	$-0.123228\pi$
$642$		0			0
$643$		0			0		1.00000			$0$
$643$		0			0		−1.00000			$\pi$
$644$		0			0
$645$		0			0
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	14.6969	+	8.48528i	0.577796	+	0.333591i	0.760257	−	0.649622i	$-0.225073\pi$
$647$	14.6969	+	8.48528i	0.577796	+	0.333591i	−0.182461	+	0.983213i	$0.558406\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	22.6274	+	39.1918i	0.888204	+	1.53841i
$650$	16.9706	+	12.7279i	0.665640	+	0.499230i
$651$		0			0
$652$		−	12.0000i		−	0.469956i
$653$	15.5885	−	9.00000i	0.610023	−	0.352197i	−0.162951	−	0.986634i	$-0.552101\pi$
$653$	15.5885	−	9.00000i	0.610023	−	0.352197i	0.772975	+	0.634437i	$0.218768\pi$
$654$		0			0
$655$	−25.1769	−	28.3923i	−0.983743	−	1.10938i
$656$	0.707107	+	1.22474i	0.0276079	+	0.0478183i
$657$		−	12.7279i		−	0.496564i
$658$		0			0
$659$	−20.0000			−0.779089			−0.389545	−	0.921008i	$-0.627368\pi$
$659$	−20.0000			−0.779089			−0.389545	+	0.921008i	$0.627368\pi$
$660$		0			0
$661$	12.0208	−	20.8207i	0.467556	−	0.809830i	−0.531757	−	0.846897i	$-0.678468\pi$
$661$	12.0208	−	20.8207i	0.467556	−	0.809830i	0.999313	+	0.0370669i	$0.0118015\pi$
$662$	−10.3923	−	6.00000i	−0.403908	−	0.233197i
$663$		0			0
$664$	16.9706			0.658586
$665$		0			0
$666$	18.0000			0.697486
$667$		0			0
$668$	−14.6969	−	8.48528i	−0.568642	−	0.328305i
$669$		0			0
$670$	26.2880	−	5.37945i	1.01560	−	0.207826i
$671$	−28.2843			−1.09190
$672$		0			0
$673$		−	18.0000i		−	0.693849i	−0.937893	−	0.346925i	$-0.887226\pi$
$673$		−	18.0000i		−	0.693849i	0.937893	−	0.346925i	$-0.112774\pi$
$674$	−9.00000	−	15.5885i	−0.346667	−	0.600445i
$675$		0			0
$676$	−2.50000	+	4.33013i	−0.0961538	+	0.166543i
$677$	18.3712	−	10.6066i	0.706062	−	0.407645i	−0.103540	−	0.994625i	$-0.533017\pi$
$677$	18.3712	−	10.6066i	0.706062	−	0.407645i	0.809601	+	0.586981i	$0.199683\pi$
$678$		0			0
$679$		0			0
$680$	−3.00000	+	9.00000i	−0.115045	+	0.345134i
$681$		0			0
$682$	−19.5959	−	11.3137i	−0.750366	−	0.433224i
$683$	10.3923	+	6.00000i	0.397650	+	0.229584i	0.685470	−	0.728101i	$-0.259597\pi$
$683$	10.3923	+	6.00000i	0.397650	+	0.229584i	−0.287819	+	0.957685i	$0.592930\pi$
$684$	−8.48528	−	14.6969i	−0.324443	−	0.561951i
$685$	−12.7279	−	4.24264i	−0.486309	−	0.162103i
$686$		0			0
$687$		0			0
$688$	10.3923	−	6.00000i	0.396203	−	0.228748i
$689$	25.4558	−	44.0908i	0.969790	−	1.67973i
$690$		0			0
$691$	2.82843	+	4.89898i	0.107598	+	0.186366i	0.914797	−	0.403914i	$-0.132351\pi$
$691$	2.82843	+	4.89898i	0.107598	+	0.186366i	−0.807198	+	0.590280i	$0.799017\pi$
$692$		−	4.24264i		−	0.161281i
$693$		0			0
$694$	12.0000			0.455514
$695$	−12.3923	+	2.53590i	−0.470067	+	0.0961921i
$696$		0			0
$697$	5.19615	+	3.00000i	0.196818	+	0.113633i
$698$	20.8207	−	12.0208i	0.788074	−	0.454995i
$699$		0			0
$700$		0			0
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$		0			0
$703$	−29.3939	−	16.9706i	−1.10861	−	0.640057i
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	−21.2132			−0.798369
$707$		0			0
$708$		0			0
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	−0.900978	−	0.433865i	$-0.857149\pi$
$709$	−22.0000	−	38.1051i	−0.826227	−	1.43107i	0.0747503	−	0.997202i	$-0.476184\pi$
$710$	13.3843	−	11.8685i	0.502302	−	0.445417i
$711$		0			0
$712$	−3.67423	+	2.12132i	−0.137698	+	0.0794998i
$713$		0			0
$714$		0			0
$715$	36.0000	+	12.0000i	1.34632	+	0.448775i
$716$	−10.0000	−	17.3205i	−0.373718	−	0.647298i
$717$		0			0
$718$	13.8564	+	8.00000i	0.517116	+	0.298557i
$719$	−2.82843	−	4.89898i	−0.105483	−	0.182701i	0.808453	−	0.588561i	$-0.200305\pi$
$719$	−2.82843	−	4.89898i	−0.105483	−	0.182701i	−0.913935	+	0.405860i	$0.866972\pi$
$720$	−2.12132	+	6.36396i	−0.0790569	+	0.237171i
$721$		0			0
$722$			13.0000i			0.483810i
$723$		0			0
$724$	−7.77817	+	13.4722i	−0.289074	+	0.500690i
$725$	18.3923	−	7.85641i	0.683073	−	0.291780i
$726$		0			0
$727$			16.9706i			0.629403i	0.949191	+	0.314702i	$0.101904\pi$
$727$			16.9706i			0.629403i	−0.949191	+	0.314702i	$0.898096\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$	9.29423	−	1.90192i	0.343995	−	0.0703934i
$731$	25.4558	−	44.0908i	0.941518	−	1.63076i
$732$		0			0
$733$	11.0227	−	6.36396i	0.407133	−	0.235058i	−0.282424	−	0.959290i	$-0.591139\pi$
$733$	11.0227	−	6.36396i	0.407133	−	0.235058i	0.689557	+	0.724231i	$0.257805\pi$
$734$	−16.9706			−0.626395
$735$		0			0
$736$		0			0
$737$	41.5692	−	24.0000i	1.53122	−	0.884051i
$738$	3.67423	+	2.12132i	0.135250	+	0.0780869i
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	−0.621374	−	0.783514i	$-0.713425\pi$
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	0.989230	+	0.146369i	$0.0467586\pi$
$740$	2.68973	+	13.1440i	0.0988763	+	0.483184i
$741$		0			0
$742$		0			0
$743$		0			0		1.00000			$0$
$743$		0			0		−1.00000			$\pi$
$744$		0			0
$745$	14.8356	+	16.7303i	0.543536	+	0.612952i
$746$	−6.00000	+	10.3923i	−0.219676	+	0.380489i
$747$	44.0908	−	25.4558i	1.61320	−	0.931381i
$748$			16.9706i			0.620505i
$749$		0			0
$750$		0			0
$751$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$751$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$752$		0			0
$753$		0			0
$754$	8.48528	+	14.6969i	0.309016	+	0.535231i
$755$	−5.65685	+	16.9706i	−0.205874	+	0.617622i
$756$		0			0
$757$		−	42.0000i		−	1.52652i	−0.646094	−	0.763258i	$-0.723599\pi$
$757$		−	42.0000i		−	1.52652i	0.646094	−	0.763258i	$-0.276401\pi$
$758$	−17.3205	+	10.0000i	−0.629109	+	0.363216i
$759$		0			0
$760$	9.46410	−	8.39230i	0.343299	−	0.304421i
$761$	23.3345	+	40.4166i	0.845876	+	1.46510i	0.884858	+	0.465860i	$0.154255\pi$
$761$	23.3345	+	40.4166i	0.845876	+	1.46510i	−0.0389826	+	0.999240i	$0.512412\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$	5.70577	+	27.8827i	0.206293	+	1.00810i
$766$		0			0
$767$	−41.5692	−	24.0000i	−1.50098	−	0.866590i
$768$		0			0
$769$	−7.07107			−0.254989			−0.127495	−	0.991839i	$-0.540694\pi$
$769$	−7.07107			−0.254989			−0.127495	+	0.991839i	$0.540694\pi$
$770$		0			0
$771$		0			0
$772$	−20.7846	+	12.0000i	−0.748054	+	0.431889i
$773$	33.0681	+	19.0919i	1.18938	+	0.686687i	0.958165	−	0.286216i	$-0.0923975\pi$
$773$	33.0681	+	19.0919i	1.18938	+	0.686687i	0.231212	+	0.972903i	$0.425731\pi$
$774$	18.0000	−	31.1769i	0.646997	−	1.12063i
$775$	3.38323	−	28.0812i	0.121529	−	1.00871i
$776$	−4.24264			−0.152302
$777$		0			0
$778$			20.0000i			0.717035i
$779$	−4.00000	−	6.92820i	−0.143315	−	0.248229i
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.00000	−	3.00000i	−0.321224	−	0.107075i
$786$		0			0
$787$	−44.0908	−	25.4558i	−1.57167	−	0.907403i	−0.995965	−	0.0897439i	$-0.971395\pi$
$787$	−44.0908	−	25.4558i	−1.57167	−	0.907403i	−0.575703	−	0.817659i	$-0.695272\pi$
$788$	−10.3923	−	6.00000i	−0.370211	−	0.213741i
$789$		0			0
$790$		0			0
$791$		0			0
$792$			12.0000i			0.426401i
$793$	25.9808	−	15.0000i	0.922604	−	0.532666i
$794$	−14.8492	+	25.7196i	−0.526980	+	0.912756i
$795$		0			0
$796$	−5.65685	−	9.79796i	−0.200502	−	0.347279i
$797$			4.24264i			0.150282i	0.997173	+	0.0751410i	$0.0239407\pi$
$797$			4.24264i			0.150282i	−0.997173	+	0.0751410i	$0.976059\pi$
$798$		0			0
$799$		0			0
$800$	−4.96410	−	0.598076i	−0.175507	−	0.0211452i
$801$	−6.36396	+	11.0227i	−0.224860	+	0.389468i
$802$	6.92820	+	4.00000i	0.244643	+	0.141245i
$803$	14.6969	−	8.48528i	0.518644	−	0.299439i
$804$		0			0
$805$		0			0
$806$	24.0000			0.845364
$807$		0			0
$808$	8.57321	+	4.94975i	0.301605	+	0.174132i
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	−0.998804	−	0.0488972i	$-0.984429\pi$
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	0.541748	+	0.840541i	$0.317763\pi$
$810$	4.03459	+	19.7160i	0.141761	+	0.692751i
$811$	45.2548			1.58911			0.794556	−	0.607191i	$-0.207704\pi$
$811$	45.2548			1.58911			0.794556	+	0.607191i	$0.207704\pi$
$812$		0			0
$813$		0			0
$814$	12.0000	+	20.7846i	0.420600	+	0.728500i
$815$	20.0764	−	17.8028i	0.703245	−	0.623604i
$816$		0			0
$817$	−58.7878	+	33.9411i	−2.05672	+	1.18745i
$818$			9.89949i			0.346128i
$819$		0			0
$820$	−1.00000	+	3.00000i	−0.0349215	+	0.104765i
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	0.765487	−	0.643451i	$-0.222498\pi$
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	−0.939989	+	0.341206i	$0.889165\pi$
$822$		0			0
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	0.0919029	−	0.995768i	$-0.470705\pi$
$823$	−20.7846	−	12.0000i	−0.724506	−	0.418294i	−0.816409	+	0.577474i	$0.804038\pi$
$824$	8.48528	+	14.6969i	0.295599	+	0.511992i
$825$		0			0
$826$		0			0
$827$		−	36.0000i		−	1.25184i	−0.779886	−	0.625921i	$-0.784723\pi$
$827$		−	36.0000i		−	1.25184i	0.779886	−	0.625921i	$-0.215277\pi$
$828$		0			0
$829$	7.77817	−	13.4722i	0.270147	−	0.467909i	−0.698752	−	0.715364i	$-0.746261\pi$
$829$	7.77817	−	13.4722i	0.270147	−	0.467909i	0.968899	+	0.247455i	$0.0795943\pi$
$830$	25.1769	+	28.3923i	0.873903	+	0.985511i
$831$		0			0
$832$		−	4.24264i		−	0.147087i
$833$		0			0
$834$		0			0
$835$	−7.60770	−	37.1769i	−0.263275	−	1.28656i
$836$	11.3137	−	19.5959i	0.391293	−	0.677739i
$837$		0			0
$838$		0			0
$839$	−22.6274			−0.781185			−0.390593	−	0.920564i	$-0.627730\pi$
$839$	−22.6274			−0.781185			−0.390593	+	0.920564i	$0.627730\pi$
$840$		0			0
$841$	−13.0000			−0.448276
$842$	−5.19615	+	3.00000i	−0.179071	+	0.103387i
$843$		0			0
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	−10.9534	+	2.24144i	−0.376807	+	0.0771078i
$846$		0			0
$847$		0			0
$848$			12.0000i			0.412082i
$849$		0			0
$850$	−19.5080	+	8.33298i	−0.669118	+	0.285819i
$851$		0			0
$852$		0			0
$853$		−	46.6690i		−	1.59792i	−0.601386	−	0.798959i	$-0.705384\pi$
$853$		−	46.6690i		−	1.59792i	0.601386	−	0.798959i	$-0.294616\pi$
$854$		0			0
$855$	12.0000	−	36.0000i	0.410391	−	1.23117i
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−11.0227	−	6.36396i	−0.376528	−	0.217389i	0.299778	−	0.954009i	$-0.403087\pi$
$857$	−11.0227	−	6.36396i	−0.376528	−	0.217389i	−0.676307	+	0.736620i	$0.736421\pi$
$858$		0			0
$859$	2.82843	+	4.89898i	0.0965047	+	0.167151i	0.910236	−	0.414091i	$-0.135900\pi$
$859$	2.82843	+	4.89898i	0.0965047	+	0.167151i	−0.813731	+	0.581242i	$0.802567\pi$
$860$	25.4558	+	8.48528i	0.868037	+	0.289346i
$861$		0			0
$862$			16.0000i			0.544962i
$863$	−20.7846	+	12.0000i	−0.707516	+	0.408485i	−0.810141	−	0.586235i	$-0.800609\pi$
$863$	−20.7846	+	12.0000i	−0.707516	+	0.408485i	0.102624	+	0.994720i	$0.467276\pi$
$864$		0			0
$865$	7.09808	−	6.29423i	0.241342	−	0.214010i
$866$	−14.8492	−	25.7196i	−0.504598	−	0.873989i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−25.4558	+	44.0908i	−0.862538	+	1.49396i
$872$	10.3923	+	6.00000i	0.351928	+	0.203186i
$873$	−11.0227	+	6.36396i	−0.373062	+	0.215387i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	−0.739543	−	0.673109i	$-0.764958\pi$
$877$	−15.5885	+	9.00000i	−0.526385	+	0.303908i	0.213158	+	0.977018i	$0.431625\pi$
$878$	−34.2929	−	19.7990i	−1.15733	−	0.668184i
$879$		0			0
$880$	−8.76268	+	1.79315i	−0.295390	+	0.0604471i
$881$	−32.5269			−1.09586			−0.547930	−	0.836524i	$-0.684584\pi$
$881$	−32.5269			−1.09586			−0.547930	+	0.836524i	$0.684584\pi$
$882$		0			0
$883$			12.0000i			0.403832i	0.979403	+	0.201916i	$0.0647168\pi$
$883$			12.0000i			0.403832i	−0.979403	+	0.201916i	$0.935283\pi$
$884$	−9.00000	−	15.5885i	−0.302703	−	0.524297i
$885$		0			0
$886$	6.00000	−	10.3923i	0.201574	−	0.349136i
$887$	−14.6969	+	8.48528i	−0.493475	+	0.284908i	−0.726015	−	0.687679i	$-0.758630\pi$
$887$	−14.6969	+	8.48528i	−0.493475	+	0.284908i	0.232540	+	0.972587i	$0.425296\pi$
$888$		0			0
$889$		0			0
$890$	−9.00000	−	3.00000i	−0.301681	−	0.100560i
$891$	18.0000	+	31.1769i	0.603023	+	1.04447i
$892$	−14.6969	−	8.48528i	−0.492090	−	0.284108i
$893$		0			0
$894$		0			0
$895$	14.1421	−	42.4264i	0.472719	−	1.41816i
$896$		0			0
$897$		0			0
$898$	1.73205	−	1.00000i	0.0577993	−	0.0333704i
$899$	11.3137	−	19.5959i	0.377333	−	0.653560i
$900$	−13.7942	+	5.89230i	−0.459808	+	0.196410i
$901$	25.4558	+	44.0908i	0.848057	+	1.46888i
$902$			5.65685i			0.188353i
$903$		0			0
$904$		0			0
$905$	−34.0788	+	6.97372i	−1.13282	+	0.231814i
$906$		0			0
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	0.662512	−	0.749051i	$-0.269490\pi$
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	−0.317441	+	0.948278i	$0.602824\pi$
$908$	14.6969	−	8.48528i	0.487735	−	0.281594i
$909$	29.6985			0.985037
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$		0			0
$913$	58.7878	+	33.9411i	1.94559	+	1.12329i
$914$	−12.0000	+	20.7846i	−0.396925	+	0.687494i
$915$		0			0
$916$	15.5563			0.513996
$917$		0			0
$918$		0			0
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	0.924922	+	0.380158i	$0.124130\pi$
$919$	24.0000	+	41.5692i	0.791687	+	1.37124i	−0.133235	+	0.991084i	$0.542536\pi$
$920$		0			0
$921$		0			0
$922$	−18.3712	+	10.6066i	−0.605022	+	0.349310i
$923$			33.9411i			1.11719i
$924$		0			0
$925$	−18.0000	+	24.0000i	−0.591836	+	0.789115i
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	44.0908	+	25.4558i	1.44813	+	0.836080i
$928$	−3.46410	−	2.00000i	−0.113715	−	0.0656532i
$929$	−14.8492	−	25.7196i	−0.487188	−	0.843834i	0.512704	−	0.858566i	$-0.328644\pi$
$929$	−14.8492	−	25.7196i	−0.487188	−	0.843834i	−0.999891	+	0.0147316i	$0.995311\pi$
$930$		0			0
$931$		0			0
$932$			6.00000i			0.196537i
$933$		0			0
$934$	8.48528	−	14.6969i	0.277647	−	0.480899i
$935$	−28.3923	+	25.1769i	−0.928528	+	0.823373i
$936$	−6.36396	−	11.0227i	−0.208013	−	0.360288i
$937$		−	4.24264i		−	0.138601i	−0.997596	−	0.0693005i	$-0.977923\pi$
$937$		−	4.24264i		−	0.138601i	0.997596	−	0.0693005i	$-0.0220767\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−24.7487	+	42.8661i	−0.806786	+	1.39739i	0.108293	+	0.994119i	$0.465462\pi$
$941$	−24.7487	+	42.8661i	−0.806786	+	1.39739i	−0.915079	+	0.403275i	$0.867872\pi$
$942$		0			0
$943$		0			0
$944$	11.3137			0.368230
$945$		0			0
$946$	48.0000			1.56061
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	−0.659256	−	0.751918i	$-0.729129\pi$
$947$	−10.3923	+	6.00000i	−0.337705	+	0.194974i	0.321552	+	0.946892i	$0.395796\pi$
$948$		0			0
$949$	−9.00000	+	15.5885i	−0.292152	+	0.506023i
$950$	28.0812	+	3.38323i	0.911074	+	0.109766i
$951$		0			0
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$	18.0000	+	31.1769i	0.582772	+	1.00939i
$955$	−11.8685	−	13.3843i	−0.384056	−	0.433105i
$956$	4.00000	−	6.92820i	0.129369	−	0.224074i
$957$		0			0
$958$			16.9706i			0.548294i
$959$		0			0
$960$		0			0
$961$	−0.500000	−	0.866025i	−0.0161290	−	0.0279363i
$962$	−22.0454	−	12.7279i	−0.710772	−	0.410365i
$963$	−31.1769	−	18.0000i	−1.00466	−	0.580042i
$964$	−7.77817	−	13.4722i	−0.250518	−	0.433910i
$965$	−50.9117	−	16.9706i	−1.63891	−	0.546302i
$966$		0			0
$967$		−	24.0000i		−	0.771788i	−0.922543	−	0.385894i	$-0.873893\pi$
$967$		−	24.0000i		−	0.771788i	0.922543	−	0.385894i	$-0.126107\pi$
$968$	−4.33013	+	2.50000i	−0.139176	+	0.0803530i
$969$		0			0
$970$	−6.29423	−	7.09808i	−0.202096	−	0.227905i
$971$	−22.6274	−	39.1918i	−0.726148	−	1.25773i	−0.958500	−	0.285094i	$-0.907975\pi$
$971$	−22.6274	−	39.1918i	−0.726148	−	1.25773i	0.232351	−	0.972632i	$-0.425358\pi$
$972$		0			0
$973$		0			0
$974$	−24.0000			−0.769010
$975$		0			0
$976$	−3.53553	+	6.12372i	−0.113170	+	0.196016i
$977$	25.9808	+	15.0000i	0.831198	+	0.479893i	0.854263	−	0.519841i	$-0.174009\pi$
$977$	25.9808	+	15.0000i	0.831198	+	0.479893i	−0.0230645	+	0.999734i	$0.507342\pi$
$978$		0			0
$979$	−16.9706			−0.542382
$980$		0			0
$981$	36.0000			1.14939
$982$	−3.46410	+	2.00000i	−0.110544	+	0.0638226i
$983$	14.6969	+	8.48528i	0.468760	+	0.270638i	0.715720	−	0.698387i	$-0.246099\pi$
$983$	14.6969	+	8.48528i	0.468760	+	0.270638i	−0.246961	+	0.969025i	$0.579432\pi$
$984$		0			0
$985$	−5.37945	−	26.2880i	−0.171404	−	0.837607i
$986$	−16.9706			−0.540453
$987$		0			0
$988$			24.0000i			0.763542i
$989$		0			0
$990$	−20.0764	+	17.8028i	−0.638070	+	0.565809i
$991$	−24.0000	+	41.5692i	−0.762385	+	1.32049i	0.179233	+	0.983807i	$0.442638\pi$
$991$	−24.0000	+	41.5692i	−0.762385	+	1.32049i	−0.941618	+	0.336683i	$0.890695\pi$
$992$	−4.89898	+	2.82843i	−0.155543	+	0.0898027i
$993$		0			0
$994$		0			0
$995$	8.00000	−	24.0000i	0.253617	−	0.760851i
$996$		0			0
$997$	33.0681	+	19.0919i	1.04728	+	0.604646i	0.921886	−	0.387461i	$-0.126648\pi$
$997$	33.0681	+	19.0919i	1.04728	+	0.604646i	0.125392	+	0.992107i	$0.459981\pi$
$998$	3.46410	+	2.00000i	0.109654	+	0.0633089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.i.d.459.4		8
5.4	even	2	inner	490.2.i.d.459.1		8
7.2	even	3	inner	490.2.i.d.79.1		8
7.3	odd	6		490.2.c.g.99.4	yes	4
7.4	even	3		490.2.c.g.99.3	yes	4
7.5	odd	6	inner	490.2.i.d.79.2		8
7.6	odd	2	inner	490.2.i.d.459.3		8
35.3	even	12		2450.2.a.bo.1.2		2
35.4	even	6		490.2.c.g.99.1	✓	4
35.9	even	6	inner	490.2.i.d.79.4		8
35.17	even	12		2450.2.a.bi.1.1		2
35.18	odd	12		2450.2.a.bo.1.1		2
35.19	odd	6	inner	490.2.i.d.79.3		8
35.24	odd	6		490.2.c.g.99.2	yes	4
35.32	odd	12		2450.2.a.bi.1.2		2
35.34	odd	2	inner	490.2.i.d.459.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
490.2.c.g.99.1	✓	4	35.4	even	6
490.2.c.g.99.2	yes	4	35.24	odd	6
490.2.c.g.99.3	yes	4	7.4	even	3
490.2.c.g.99.4	yes	4	7.3	odd	6
490.2.i.d.79.1		8	7.2	even	3	inner
490.2.i.d.79.2		8	7.5	odd	6	inner
490.2.i.d.79.3		8	35.19	odd	6	inner
490.2.i.d.79.4		8	35.9	even	6	inner
490.2.i.d.459.1		8	5.4	even	2	inner
490.2.i.d.459.2		8	35.34	odd	2	inner
490.2.i.d.459.3		8	7.6	odd	2	inner
490.2.i.d.459.4		8	1.1	even	1	trivial
2450.2.a.bi.1.1		2	35.17	even	12
2450.2.a.bi.1.2		2	35.32	odd	12
2450.2.a.bo.1.1		2	35.18	odd	12
2450.2.a.bo.1.2		2	35.3	even	12

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.19067 - 0.448288i) q^{5} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.19067 - 0.448288i) q^{5} -1.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(1.67303 - 1.48356i) q^{10} +(2.00000 - 3.46410i) q^{11} +4.24264i q^{13} +(-0.500000 - 0.866025i) q^{16} +(-3.67423 - 2.12132i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(2.82843 + 4.89898i) q^{19} +(0.707107 - 2.12132i) q^{20} -4.00000i q^{22} +(4.59808 - 1.96410i) q^{25} +(2.12132 + 3.67423i) q^{26} +4.00000 q^{29} +(2.82843 - 4.89898i) q^{31} +(-0.866025 - 0.500000i) q^{32} -4.24264 q^{34} -3.00000 q^{36} +(-5.19615 + 3.00000i) q^{37} +(4.89898 + 2.82843i) q^{38} +(-0.448288 - 2.19067i) q^{40} -1.41421 q^{41} +12.0000i q^{43} +(-2.00000 - 3.46410i) q^{44} +(-4.45069 - 5.01910i) q^{45} +(3.00000 - 4.00000i) q^{50} +(3.67423 + 2.12132i) q^{52} +(-10.3923 - 6.00000i) q^{53} +(2.82843 - 8.48528i) q^{55} +(3.46410 - 2.00000i) q^{58} +(-5.65685 + 9.79796i) q^{59} +(-3.53553 - 6.12372i) q^{61} -5.65685i q^{62} -1.00000 q^{64} +(1.90192 + 9.29423i) q^{65} +(10.3923 + 6.00000i) q^{67} +(-3.67423 + 2.12132i) q^{68} +8.00000 q^{71} +(-2.59808 + 1.50000i) q^{72} +(3.67423 + 2.12132i) q^{73} +(-3.00000 + 5.19615i) q^{74} +5.65685 q^{76} +(-1.48356 - 1.67303i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-1.22474 + 0.707107i) q^{82} +16.9706i q^{83} +(-9.00000 - 3.00000i) q^{85} +(6.00000 + 10.3923i) q^{86} +(-3.46410 - 2.00000i) q^{88} +(-2.12132 - 3.67423i) q^{89} +(-6.36396 - 2.12132i) q^{90} +(8.39230 + 9.46410i) q^{95} -4.24264i q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 12 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 - 12 * q^9	\( 8 q + 4 q^{4} - 12 q^{9} + 16 q^{11} - 4 q^{16} + 16 q^{25} + 32 q^{29} - 24 q^{36} - 16 q^{44} + 24 q^{50} - 8 q^{64} + 36 q^{65} + 64 q^{71} - 24 q^{74} - 36 q^{81} - 72 q^{85} + 48 q^{86} - 16 q^{95} - 96 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 12 * q^9 + 16 * q^11 - 4 * q^16 + 16 * q^25 + 32 * q^29 - 24 * q^36 - 16 * q^44 + 24 * q^50 - 8 * q^64 + 36 * q^65 + 64 * q^71 - 24 * q^74 - 36 * q^81 - 72 * q^85 + 48 * q^86 - 16 * q^95 - 96 * q^99

Introduction

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