LMFDB - Embedded newform 560.2.cu.a.303.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(207,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 0, 3, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.207"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cu (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,4,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			303.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	560.303
Dual form			560.2.cu.a.207.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.67303 - 0.448288i) q^{3} +(-1.23205 - 1.86603i) q^{5} +(1.48356 + 2.19067i) q^{7} +(-2.12132 + 1.22474i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(1.22474 + 3.67423i) q^{15} +(2.73205 + 0.732051i) q^{17} +(-1.22474 + 2.12132i) q^{19} +(-1.50000 - 4.33013i) q^{21} +(1.34486 + 5.01910i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(3.67423 + 3.67423i) q^{27} +1.00000i q^{29} +(-4.24264 + 2.44949i) q^{31} +(4.09808 - 1.09808i) q^{33} +(2.26002 - 5.46739i) q^{35} +(2.92820 + 10.9282i) q^{37} +(2.44949 + 4.24264i) q^{39} -1.00000 q^{41} +(-6.12372 + 6.12372i) q^{43} +(-2.59808 + 6.50000i) q^{49} +(-4.24264 - 2.44949i) q^{51} +(-0.366025 + 1.36603i) q^{53} +(4.89898 + 2.44949i) q^{55} +(3.00000 - 3.00000i) q^{57} +(-6.12372 - 10.6066i) q^{59} +(1.50000 - 2.59808i) q^{61} +(-1.26795 + 6.19615i) q^{65} +(0.448288 - 1.67303i) q^{67} -9.00000i q^{69} -12.2474i q^{71} +(0.732051 - 2.73205i) q^{73} +(5.34727 - 6.81225i) q^{75} +(-5.83013 - 2.83013i) q^{77} +(-8.57321 + 14.8492i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(3.67423 - 3.67423i) q^{83} +(-2.00000 - 6.00000i) q^{85} +(0.448288 - 1.67303i) q^{87} +(-9.52628 - 5.50000i) q^{89} +(1.41421 - 7.34847i) q^{91} +(8.19615 - 2.19615i) q^{93} +(5.46739 - 0.328169i) q^{95} +(11.0000 - 11.0000i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 16 q^{13} + 8 q^{17} - 12 q^{21} + 12 q^{25} + 12 q^{33} - 32 q^{37} - 8 q^{41} + 4 q^{53} + 24 q^{57} + 12 q^{61} - 24 q^{65} - 8 q^{73} - 12 q^{77} - 36 q^{81} - 16 q^{85} + 24 q^{93}+ \cdots + 88 q^{97}+O(q^{100}) $ 8 * q + 4 * q^5 - 16 * q^13 + 8 * q^17 - 12 * q^21 + 12 * q^25 + 12 * q^33 - 32 * q^37 - 8 * q^41 + 4 * q^53 + 24 * q^57 + 12 * q^61 - 24 * q^65 - 8 * q^73 - 12 * q^77 - 36 * q^81 - 16 * q^85 + 24 * q^93 + 88 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i	−0.258819	−	0.965926i	$-0.583333\pi$
$3$	−1.67303	−	0.448288i	−0.965926	−	0.258819i	−0.707107	+	0.707107i	$0.750000\pi$
$4$		0			0
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$5$	−1.23205	−	1.86603i	−0.550990	−	0.834512i
$6$		0			0
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$7$	1.48356	+	2.19067i	0.560734	+	0.827996i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.12132	+	1.22474i	−0.639602	+	0.369274i	−0.784461	−	0.620178i	$-0.787060\pi$
$11$	−2.12132	+	1.22474i	−0.639602	+	0.369274i	0.144859	+	0.989452i	$0.453727\pi$
$12$		0			0
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	0.373094	−	0.927794i	$-0.378297\pi$
$13$	−2.00000	−	2.00000i	−0.554700	−	0.554700i	−0.927794	+	0.373094i	$0.878297\pi$
$14$		0			0
$15$	1.22474	+	3.67423i	0.316228	+	0.948683i
$16$		0			0
$17$	2.73205	+	0.732051i	0.662620	+	0.177548i	0.574428	−	0.818555i	$-0.305225\pi$
$17$	2.73205	+	0.732051i	0.662620	+	0.177548i	0.0881917	+	0.996104i	$0.471891\pi$
$18$		0			0
$19$	−1.22474	+	2.12132i	−0.280976	+	0.486664i	−0.971625	−	0.236525i	$-0.923991\pi$
$19$	−1.22474	+	2.12132i	−0.280976	+	0.486664i	0.690650	+	0.723190i	$0.257325\pi$
$20$		0			0
$21$	−1.50000	−	4.33013i	−0.327327	−	0.944911i
$22$		0			0
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	0.952119	+	0.305727i	$0.0988995\pi$
$23$	1.34486	+	5.01910i	0.280423	+	1.04655i	−0.671696	+	0.740827i	$0.734434\pi$
$24$		0			0
$25$	−1.96410	+	4.59808i	−0.392820	+	0.919615i
$26$		0			0
$27$	3.67423	+	3.67423i	0.707107	+	0.707107i
$28$		0			0
$29$			1.00000i			0.185695i	0.995680	+	0.0928477i	$0.0295970\pi$
$29$			1.00000i			0.185695i	−0.995680	+	0.0928477i	$0.970403\pi$
$30$		0			0
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	−0.830014	−	0.557743i	$-0.811667\pi$
$31$	−4.24264	+	2.44949i	−0.762001	+	0.439941i	0.0680129	+	0.997684i	$0.478334\pi$
$32$		0			0
$33$	4.09808	−	1.09808i	0.713384	−	0.191151i
$34$		0			0
$35$	2.26002	−	5.46739i	0.382013	−	0.924157i
$36$		0			0
$37$	2.92820	+	10.9282i	0.481394	+	1.79659i	0.595778	+	0.803149i	$0.296844\pi$
$37$	2.92820	+	10.9282i	0.481394	+	1.79659i	−0.114385	+	0.993437i	$0.536490\pi$
$38$		0			0
$39$	2.44949	+	4.24264i	0.392232	+	0.679366i
$40$		0			0
$41$	−1.00000			−0.156174			−0.0780869	−	0.996947i	$-0.524881\pi$
$41$	−1.00000			−0.156174			−0.0780869	+	0.996947i	$0.524881\pi$
$42$		0			0
$43$	−6.12372	+	6.12372i	−0.933859	+	0.933859i	−0.997944	−	0.0640852i	$-0.979587\pi$
$43$	−6.12372	+	6.12372i	−0.933859	+	0.933859i	0.0640852	+	0.997944i	$0.479587\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$47$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$48$		0			0
$49$	−2.59808	+	6.50000i	−0.371154	+	0.928571i
$50$		0			0
$51$	−4.24264	−	2.44949i	−0.594089	−	0.342997i
$52$		0			0
$53$	−0.366025	+	1.36603i	−0.0502775	+	0.187638i	−0.986498	−	0.163776i	$-0.947632\pi$
$53$	−0.366025	+	1.36603i	−0.0502775	+	0.187638i	0.936220	+	0.351414i	$0.114299\pi$
$54$		0			0
$55$	4.89898	+	2.44949i	0.660578	+	0.330289i
$56$		0			0
$57$	3.00000	−	3.00000i	0.397360	−	0.397360i
$58$		0			0
$59$	−6.12372	−	10.6066i	−0.797241	−	1.38086i	−0.921406	−	0.388600i	$-0.872959\pi$
$59$	−6.12372	−	10.6066i	−0.797241	−	1.38086i	0.124165	−	0.992262i	$-0.460375\pi$
$60$		0			0
$61$	1.50000	−	2.59808i	0.192055	−	0.332650i	−0.753876	−	0.657017i	$-0.771818\pi$
$61$	1.50000	−	2.59808i	0.192055	−	0.332650i	0.945931	+	0.324367i	$0.105151\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.26795	+	6.19615i	−0.157270	+	0.768538i
$66$		0			0
$67$	0.448288	−	1.67303i	0.0547671	−	0.204393i	−0.933121	−	0.359563i	$-0.882926\pi$
$67$	0.448288	−	1.67303i	0.0547671	−	0.204393i	0.987888	+	0.155170i	$0.0495924\pi$
$68$		0			0
$69$		−	9.00000i		−	1.08347i
$70$		0			0
$71$		−	12.2474i		−	1.45350i	−0.686900	−	0.726752i	$-0.741029\pi$
$71$		−	12.2474i		−	1.45350i	0.686900	−	0.726752i	$-0.258971\pi$
$72$		0			0
$73$	0.732051	−	2.73205i	0.0856801	−	0.319762i	−0.909762	−	0.415130i	$-0.863736\pi$
$73$	0.732051	−	2.73205i	0.0856801	−	0.319762i	0.995442	+	0.0953678i	$0.0304027\pi$
$74$		0			0
$75$	5.34727	−	6.81225i	0.617449	−	0.786611i
$76$		0			0
$77$	−5.83013	−	2.83013i	−0.664405	−	0.322523i
$78$		0			0
$79$	−8.57321	+	14.8492i	−0.964562	+	1.67067i	−0.253775	+	0.967263i	$0.581672\pi$
$79$	−8.57321	+	14.8492i	−0.964562	+	1.67067i	−0.710787	+	0.703407i	$0.751661\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	3.67423	−	3.67423i	0.403300	−	0.403300i	−0.476094	−	0.879394i	$-0.657948\pi$
$83$	3.67423	−	3.67423i	0.403300	−	0.403300i	0.879394	+	0.476094i	$0.157948\pi$
$84$		0			0
$85$	−2.00000	−	6.00000i	−0.216930	−	0.650791i
$86$		0			0
$87$	0.448288	−	1.67303i	0.0480615	−	0.179368i
$88$		0			0
$89$	−9.52628	−	5.50000i	−1.00978	−	0.582999i	−0.0986553	−	0.995122i	$-0.531454\pi$
$89$	−9.52628	−	5.50000i	−1.00978	−	0.582999i	−0.911128	+	0.412123i	$0.864787\pi$
$90$		0			0
$91$	1.41421	−	7.34847i	0.148250	−	0.770329i
$92$		0			0
$93$	8.19615	−	2.19615i	0.849901	−	0.227730i
$94$		0			0
$95$	5.46739	−	0.328169i	0.560942	−	0.0336695i
$96$		0			0
$97$	11.0000	−	11.0000i	1.11688	−	1.11688i	0.124684	−	0.992196i	$-0.460208\pi$
$97$	11.0000	−	11.0000i	1.11688	−	1.11688i	0.992196	−	0.124684i	$-0.0397918\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	0.983889	+	0.178782i	$0.0572157\pi$
$101$	6.50000	+	11.2583i	0.646774	+	1.12025i	−0.337115	+	0.941464i	$0.609451\pi$
$102$		0			0
$103$	4.03459	+	15.0573i	0.397540	+	1.48364i	0.817411	+	0.576055i	$0.195409\pi$
$103$	4.03459	+	15.0573i	0.397540	+	1.48364i	−0.419871	+	0.907584i	$0.637925\pi$
$104$		0			0
$105$	−6.23205	+	8.13397i	−0.608186	+	0.793795i
$106$		0			0
$107$	11.7112	−	3.13801i	1.13217	−	0.303363i	0.356370	−	0.934345i	$-0.384014\pi$
$107$	11.7112	−	3.13801i	1.13217	−	0.303363i	0.775798	+	0.630982i	$0.217348\pi$
$108$		0			0
$109$	−7.79423	+	4.50000i	−0.746552	+	0.431022i	−0.824447	−	0.565940i	$-0.808513\pi$
$109$	−7.79423	+	4.50000i	−0.746552	+	0.431022i	0.0778949	+	0.996962i	$0.475180\pi$
$110$		0			0
$111$		−	19.5959i		−	1.85996i
$112$		0			0
$113$	3.00000	+	3.00000i	0.282216	+	0.282216i	0.833992	−	0.551776i	$-0.186050\pi$
$113$	3.00000	+	3.00000i	0.282216	+	0.282216i	−0.551776	+	0.833992i	$0.686050\pi$
$114$		0			0
$115$	7.70882	−	8.69333i	0.718852	−	0.810657i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.44949	+	7.07107i	0.224544	+	0.648204i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$		0			0
$123$	1.67303	+	0.448288i	0.150852	+	0.0404207i
$124$		0			0
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$		0			0
$127$	−9.79796	−	9.79796i	−0.869428	−	0.869428i	0.122981	−	0.992409i	$-0.460755\pi$
$127$	−9.79796	−	9.79796i	−0.869428	−	0.869428i	−0.992409	+	0.122981i	$0.960755\pi$
$128$		0			0
$129$	12.9904	−	7.50000i	1.14374	−	0.660338i
$130$		0			0
$131$	−16.9706	−	9.79796i	−1.48272	−	0.856052i	−0.482917	−	0.875666i	$-0.660423\pi$
$131$	−16.9706	−	9.79796i	−1.48272	−	0.856052i	−0.999808	+	0.0196143i	$0.993756\pi$
$132$		0			0
$133$	−6.46410	+	0.464102i	−0.560509	+	0.0402427i
$134$		0			0
$135$	2.32937	−	11.3831i	0.200480	−	0.979698i
$136$		0			0
$137$	−16.3923	−	4.39230i	−1.40049	−	0.375260i	−0.521969	−	0.852965i	$-0.674802\pi$
$137$	−16.3923	−	4.39230i	−1.40049	−	0.375260i	−0.878520	+	0.477705i	$0.841469\pi$
$138$		0			0
$139$	−17.1464			−1.45434			−0.727171	−	0.686457i	$-0.759165\pi$
$139$	−17.1464			−1.45434			−0.727171	+	0.686457i	$0.759165\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.69213	+	1.79315i	0.559624	+	0.149951i
$144$		0			0
$145$	1.86603	−	1.23205i	0.154965	−	0.102316i
$146$		0			0
$147$	7.26054	−	9.71003i	0.598839	−	0.800869i
$148$		0			0
$149$	19.9186	+	11.5000i	1.63179	+	0.942117i	0.983540	+	0.180693i	$0.0578340\pi$
$149$	19.9186	+	11.5000i	1.63179	+	0.942117i	0.648254	+	0.761424i	$0.275499\pi$
$150$		0			0
$151$	4.24264	−	2.44949i	0.345261	−	0.199337i	−0.317335	−	0.948314i	$-0.602788\pi$
$151$	4.24264	−	2.44949i	0.345261	−	0.199337i	0.662596	+	0.748977i	$0.269455\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	9.79796	+	4.89898i	0.786991	+	0.393496i
$156$		0			0
$157$	−9.56218	−	2.56218i	−0.763145	−	0.204484i	−0.143804	−	0.989606i	$-0.545933\pi$
$157$	−9.56218	−	2.56218i	−0.763145	−	0.204484i	−0.619341	+	0.785122i	$0.712600\pi$
$158$		0			0
$159$	1.22474	−	2.12132i	0.0971286	−	0.168232i
$160$		0			0
$161$	−9.00000	+	10.3923i	−0.709299	+	0.819028i
$162$		0			0
$163$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$163$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$164$		0			0
$165$	−7.09808	−	6.29423i	−0.552584	−	0.490005i
$166$		0			0
$167$	6.12372	+	6.12372i	0.473868	+	0.473868i	0.903164	−	0.429296i	$-0.141238\pi$
$167$	6.12372	+	6.12372i	0.473868	+	0.473868i	−0.429296	+	0.903164i	$0.641238\pi$
$168$		0			0
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−16.3923	+	4.39230i	−1.24628	+	0.333941i	−0.820900	−	0.571072i	$-0.806528\pi$
$173$	−16.3923	+	4.39230i	−1.24628	+	0.333941i	−0.425384	+	0.905013i	$0.639861\pi$
$174$		0			0
$175$	−12.9867	+	2.51884i	−0.981705	+	0.190406i
$176$		0			0
$177$	5.49038	+	20.4904i	0.412682	+	1.54015i
$178$		0			0
$179$	−7.34847	−	12.7279i	−0.549250	−	0.951330i	−0.998326	−	0.0578359i	$-0.981580\pi$
$179$	−7.34847	−	12.7279i	−0.549250	−	0.951330i	0.449076	−	0.893494i	$-0.351753\pi$
$180$		0			0
$181$	15.0000			1.11494			0.557471	−	0.830197i	$-0.311772\pi$
$181$	15.0000			1.11494			0.557471	+	0.830197i	$0.311772\pi$
$182$		0			0
$183$	−3.67423	+	3.67423i	−0.271607	+	0.271607i
$184$		0			0
$185$	16.7846	−	18.9282i	1.23403	−	1.39163i
$186$		0			0
$187$	−6.69213	+	1.79315i	−0.489377	+	0.131128i
$188$		0			0
$189$	−2.59808	+	13.5000i	−0.188982	+	0.981981i
$190$		0			0
$191$	−6.36396	−	3.67423i	−0.460480	−	0.265858i	0.251766	−	0.967788i	$-0.418989\pi$
$191$	−6.36396	−	3.67423i	−0.460480	−	0.265858i	−0.712246	+	0.701930i	$0.752322\pi$
$192$		0			0
$193$	0.366025	−	1.36603i	0.0263471	−	0.0983287i	−0.951500	−	0.307648i	$-0.900458\pi$
$193$	0.366025	−	1.36603i	0.0263471	−	0.0983287i	0.977847	+	0.209319i	$0.0671248\pi$
$194$		0			0
$195$	4.89898	−	9.79796i	0.350823	−	0.701646i
$196$		0			0
$197$	−9.00000	+	9.00000i	−0.641223	+	0.641223i	−0.950856	−	0.309633i	$-0.899794\pi$
$197$	−9.00000	+	9.00000i	−0.641223	+	0.641223i	0.309633	+	0.950856i	$0.399794\pi$
$198$		0			0
$199$	4.89898	+	8.48528i	0.347279	+	0.601506i	0.985765	−	0.168128i	$-0.0537722\pi$
$199$	4.89898	+	8.48528i	0.347279	+	0.601506i	−0.638486	+	0.769634i	$0.720439\pi$
$200$		0			0
$201$	−1.50000	+	2.59808i	−0.105802	+	0.183254i
$202$		0			0
$203$	−2.19067	+	1.48356i	−0.153755	+	0.104126i
$204$		0			0
$205$	1.23205	+	1.86603i	0.0860502	+	0.130329i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	6.00000i		−	0.415029i
$210$		0			0
$211$		−	7.34847i		−	0.505889i	−0.967481	−	0.252945i	$-0.918601\pi$
$211$		−	7.34847i		−	0.505889i	0.967481	−	0.252945i	$-0.0813991\pi$
$212$		0			0
$213$	−5.49038	+	20.4904i	−0.376195	+	1.40398i
$214$		0			0
$215$	18.9718	+	3.88229i	1.29386	+	0.264770i
$216$		0			0
$217$	−11.6603	−	5.66025i	−0.791550	−	0.384243i
$218$		0			0
$219$	−2.44949	+	4.24264i	−0.165521	+	0.286691i
$220$		0			0
$221$	−4.00000	−	6.92820i	−0.269069	−	0.466041i
$222$		0			0
$223$	−17.1464	+	17.1464i	−1.14821	+	1.14821i	−0.161305	+	0.986905i	$0.551570\pi$
$223$	−17.1464	+	17.1464i	−1.14821	+	1.14821i	−0.986905	+	0.161305i	$0.948430\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.37945	+	20.0764i	−0.357047	+	1.33252i	0.520842	+	0.853653i	$0.325618\pi$
$227$	−5.37945	+	20.0764i	−0.357047	+	1.33252i	−0.877889	+	0.478864i	$0.841049\pi$
$228$		0			0
$229$	6.92820	+	4.00000i	0.457829	+	0.264327i	0.711131	−	0.703060i	$-0.248183\pi$
$229$	6.92820	+	4.00000i	0.457829	+	0.264327i	−0.253302	+	0.967387i	$0.581517\pi$
$230$		0			0
$231$	8.48528	+	7.34847i	0.558291	+	0.483494i
$232$		0			0
$233$	2.73205	−	0.732051i	0.178983	−	0.0479582i	−0.168215	−	0.985750i	$-0.553800\pi$
$233$	2.73205	−	0.732051i	0.178983	−	0.0479582i	0.347197	+	0.937792i	$0.387133\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	21.0000	−	21.0000i	1.36410	−	1.36410i
$238$		0			0
$239$	24.4949			1.58444			0.792222	−	0.610234i	$-0.208924\pi$
$239$	24.4949			1.58444			0.792222	+	0.610234i	$0.208924\pi$
$240$		0			0
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	0.923224	−	0.384262i	$-0.125544\pi$
$241$	2.00000	+	3.46410i	0.128831	+	0.223142i	−0.794393	+	0.607404i	$0.792211\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	15.3301	−	3.16025i	0.979406	−	0.201901i
$246$		0			0
$247$	6.69213	−	1.79315i	0.425810	−	0.114095i
$248$		0			0
$249$	−7.79423	+	4.50000i	−0.493939	+	0.285176i
$250$		0			0
$251$			24.4949i			1.54610i	0.634343	+	0.773052i	$0.281271\pi$
$251$			24.4949i			1.54610i	−0.634343	+	0.773052i	$0.718729\pi$
$252$		0			0
$253$	−9.00000	−	9.00000i	−0.565825	−	0.565825i
$254$		0			0
$255$	0.656339	+	10.9348i	0.0411015	+	0.684762i
$256$		0			0
$257$	−4.39230	−	16.3923i	−0.273984	−	1.02252i	−0.956519	−	0.291670i	$-0.905789\pi$
$257$	−4.39230	−	16.3923i	−0.273984	−	1.02252i	0.682534	−	0.730853i	$-0.260878\pi$
$258$		0			0
$259$	−19.5959	+	22.6274i	−1.21763	+	1.40600i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.67303	−	0.448288i	−0.103164	−	0.0276426i	0.206868	−	0.978369i	$-0.433673\pi$
$263$	−1.67303	−	0.448288i	−0.103164	−	0.0276426i	−0.310032	+	0.950726i	$0.600340\pi$
$264$		0			0
$265$	3.00000	−	1.00000i	0.184289	−	0.0614295i
$266$		0			0
$267$	13.4722	+	13.4722i	0.824485	+	0.824485i
$268$		0			0
$269$	4.33013	−	2.50000i	0.264013	−	0.152428i	−0.362151	−	0.932119i	$-0.617958\pi$
$269$	4.33013	−	2.50000i	0.264013	−	0.152428i	0.626164	+	0.779692i	$0.284624\pi$
$270$		0			0
$271$	−6.36396	−	3.67423i	−0.386583	−	0.223194i	0.294095	−	0.955776i	$-0.404982\pi$
$271$	−6.36396	−	3.67423i	−0.386583	−	0.223194i	−0.680679	+	0.732582i	$0.738315\pi$
$272$		0			0
$273$	−5.66025	+	11.6603i	−0.342574	+	0.705711i
$274$		0			0
$275$	−1.46498	−	12.1595i	−0.0883417	−	0.733246i
$276$		0			0
$277$	2.73205	+	0.732051i	0.164153	+	0.0439847i	0.339959	−	0.940440i	$-0.389587\pi$
$277$	2.73205	+	0.732051i	0.164153	+	0.0439847i	−0.175806	+	0.984425i	$0.556253\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	28.0000			1.67034			0.835170	−	0.549992i	$-0.185369\pi$
$281$	28.0000			1.67034			0.835170	+	0.549992i	$0.185369\pi$
$282$		0			0
$283$	13.3843	+	3.58630i	0.795612	+	0.213184i	0.633656	−	0.773615i	$-0.281553\pi$
$283$	13.3843	+	3.58630i	0.795612	+	0.213184i	0.161955	+	0.986798i	$0.448220\pi$
$284$		0			0
$285$	−9.29423	−	1.90192i	−0.550543	−	0.112660i
$286$		0			0
$287$	−1.48356	−	2.19067i	−0.0875720	−	0.129311i
$288$		0			0
$289$	−7.79423	−	4.50000i	−0.458484	−	0.264706i
$290$		0			0
$291$	−23.3345	+	13.4722i	−1.36789	+	0.789754i
$292$		0			0
$293$	−12.0000	−	12.0000i	−0.701047	−	0.701047i	0.263588	−	0.964635i	$-0.415094\pi$
$293$	−12.0000	−	12.0000i	−0.701047	−	0.701047i	−0.964635	+	0.263588i	$0.915094\pi$
$294$		0			0
$295$	−12.2474	+	24.4949i	−0.713074	+	1.42615i
$296$		0			0
$297$	−12.2942	−	3.29423i	−0.713384	−	0.191151i
$298$		0			0
$299$	7.34847	−	12.7279i	0.424973	−	0.736075i
$300$		0			0
$301$	−22.5000	−	4.33013i	−1.29688	−	0.249584i
$302$		0			0
$303$	−5.82774	−	21.7494i	−0.334795	−	1.24947i
$304$		0			0
$305$	−6.69615	+	0.401924i	−0.383421	+	0.0230141i
$306$		0			0
$307$	1.22474	+	1.22474i	0.0698999	+	0.0698999i	0.741192	−	0.671293i	$-0.234261\pi$
$307$	1.22474	+	1.22474i	0.0698999	+	0.0698999i	−0.671293	+	0.741192i	$0.734261\pi$
$308$		0			0
$309$		−	27.0000i		−	1.53598i
$310$		0			0
$311$	−14.8492	+	8.57321i	−0.842023	+	0.486142i	−0.857951	−	0.513731i	$-0.828263\pi$
$311$	−14.8492	+	8.57321i	−0.842023	+	0.486142i	0.0159282	+	0.999873i	$0.494930\pi$
$312$		0			0
$313$	21.8564	−	5.85641i	1.23540	−	0.331024i	0.418718	−	0.908116i	$-0.362479\pi$
$313$	21.8564	−	5.85641i	1.23540	−	0.331024i	0.816679	+	0.577092i	$0.195813\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.12436	+	19.1244i	0.287812	+	1.07413i	0.946760	+	0.321942i	$0.104335\pi$
$317$	5.12436	+	19.1244i	0.287812	+	1.07413i	−0.658947	+	0.752189i	$0.728998\pi$
$318$		0			0
$319$	−1.22474	−	2.12132i	−0.0685725	−	0.118771i
$320$		0			0
$321$	−21.0000			−1.17211
$322$		0			0
$323$	−4.89898	+	4.89898i	−0.272587	+	0.272587i
$324$		0			0
$325$	13.1244	−	5.26795i	0.728008	−	0.292213i
$326$		0			0
$327$	15.0573	−	4.03459i	0.832670	−	0.223113i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	21.2132	+	12.2474i	1.16598	+	0.673181i	0.952731	−	0.303816i	$-0.0982610\pi$
$331$	21.2132	+	12.2474i	1.16598	+	0.673181i	0.213253	+	0.976997i	$0.431594\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.67423	+	1.22474i	−0.200745	+	0.0669150i
$336$		0			0
$337$	−5.00000	+	5.00000i	−0.272367	+	0.272367i	−0.830053	−	0.557685i	$-0.811690\pi$
$337$	−5.00000	+	5.00000i	−0.272367	+	0.272367i	0.557685	+	0.830053i	$0.311690\pi$
$338$		0			0
$339$	−3.67423	−	6.36396i	−0.199557	−	0.345643i
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	−18.0938	+	3.95164i	−0.976972	+	0.213368i
$344$		0			0
$345$	−16.7942	+	11.0885i	−0.904171	+	0.596982i
$346$		0			0
$347$	−4.93117	+	18.4034i	−0.264719	+	0.987944i	0.697703	+	0.716387i	$0.254205\pi$
$347$	−4.93117	+	18.4034i	−0.264719	+	0.987944i	−0.962422	+	0.271557i	$0.912461\pi$
$348$		0			0
$349$			15.0000i			0.802932i	0.915874	+	0.401466i	$0.131499\pi$
$349$			15.0000i			0.802932i	−0.915874	+	0.401466i	$0.868501\pi$
$350$		0			0
$351$		−	14.6969i		−	0.784465i
$352$		0			0
$353$	−1.83013	+	6.83013i	−0.0974078	+	0.363531i	−0.997374	−	0.0724298i	$-0.976925\pi$
$353$	−1.83013	+	6.83013i	−0.0974078	+	0.363531i	0.899966	+	0.435961i	$0.143591\pi$
$354$		0			0
$355$	−22.8541	+	15.0895i	−1.21297	+	0.800866i
$356$		0			0
$357$	−0.928203	−	12.9282i	−0.0491257	−	0.684233i
$358$		0			0
$359$	7.34847	−	12.7279i	0.387837	−	0.671754i	−0.604321	−	0.796741i	$-0.706556\pi$
$359$	7.34847	−	12.7279i	0.387837	−	0.671754i	0.992158	+	0.124987i	$0.0398889\pi$
$360$		0			0
$361$	6.50000	+	11.2583i	0.342105	+	0.592544i
$362$		0			0
$363$	6.12372	−	6.12372i	0.321412	−	0.321412i
$364$		0			0
$365$	−6.00000	+	2.00000i	−0.314054	+	0.104685i
$366$		0			0
$367$	−2.24144	+	8.36516i	−0.117002	+	0.436658i	−0.999429	−	0.0337919i	$-0.989242\pi$
$367$	−2.24144	+	8.36516i	−0.117002	+	0.436658i	0.882427	+	0.470450i	$0.155908\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.53553	+	1.22474i	−0.183556	+	0.0635856i
$372$		0			0
$373$	27.3205	−	7.32051i	1.41460	−	0.379042i	0.531037	−	0.847349i	$-0.321803\pi$
$373$	27.3205	−	7.32051i	1.41460	−	0.379042i	0.883566	+	0.468307i	$0.155136\pi$
$374$		0			0
$375$	−19.2999	−	1.58510i	−0.996644	−	0.0818542i
$376$		0			0
$377$	2.00000	−	2.00000i	0.103005	−	0.103005i
$378$		0			0
$379$	7.34847			0.377466			0.188733	−	0.982028i	$-0.439562\pi$
$379$	7.34847			0.377466			0.188733	+	0.982028i	$0.439562\pi$
$380$		0			0
$381$	12.0000	+	20.7846i	0.614779	+	1.06483i
$382$		0			0
$383$	−4.03459	−	15.0573i	−0.206158	−	0.769392i	−0.989094	−	0.147289i	$-0.952945\pi$
$383$	−4.03459	−	15.0573i	−0.206158	−	0.769392i	0.782936	−	0.622103i	$-0.213721\pi$
$384$		0			0
$385$	1.90192	+	14.3660i	0.0969310	+	0.732160i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−13.8564	+	8.00000i	−0.702548	+	0.405616i	−0.808296	−	0.588777i	$-0.799610\pi$
$389$	−13.8564	+	8.00000i	−0.702548	+	0.405616i	0.105748	+	0.994393i	$0.466276\pi$
$390$		0			0
$391$			14.6969i			0.743256i
$392$		0			0
$393$	24.0000	+	24.0000i	1.21064	+	1.21064i
$394$		0			0
$395$	38.2717	−	2.29719i	1.92566	−	0.115584i
$396$		0			0
$397$	2.56218	+	9.56218i	0.128592	+	0.479912i	0.999942	−	0.0107497i	$-0.00342179\pi$
$397$	2.56218	+	9.56218i	0.128592	+	0.479912i	−0.871350	+	0.490662i	$0.836755\pi$
$398$		0			0
$399$	11.0227	+	2.12132i	0.551825	+	0.106199i
$400$		0			0
$401$	3.50000	−	6.06218i	0.174782	−	0.302731i	−0.765304	−	0.643669i	$-0.777411\pi$
$401$	3.50000	−	6.06218i	0.174782	−	0.302731i	0.940086	+	0.340938i	$0.110745\pi$
$402$		0			0
$403$	13.3843	+	3.58630i	0.666718	+	0.178646i
$404$		0			0
$405$	−9.00000	+	18.0000i	−0.447214	+	0.894427i
$406$		0			0
$407$	−19.5959	−	19.5959i	−0.971334	−	0.971334i
$408$		0			0
$409$	12.9904	−	7.50000i	0.642333	−	0.370851i	−0.143180	−	0.989697i	$-0.545733\pi$
$409$	12.9904	−	7.50000i	0.642333	−	0.370851i	0.785513	+	0.618846i	$0.212399\pi$
$410$		0			0
$411$	25.4558	+	14.6969i	1.25564	+	0.724947i
$412$		0			0
$413$	14.1506	−	29.1506i	0.696307	−	1.43441i
$414$		0			0
$415$	−11.3831	−	2.32937i	−0.558772	−	0.114344i
$416$		0			0
$417$	28.6865	+	7.68653i	1.40479	+	0.376411i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−23.0000			−1.12095			−0.560476	−	0.828171i	$-0.689382\pi$
$421$	−23.0000			−1.12095			−0.560476	+	0.828171i	$0.689382\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−8.73205	+	11.1244i	−0.423567	+	0.539611i
$426$		0			0
$427$	7.91688	−	0.568406i	0.383124	−	0.0275071i
$428$		0			0
$429$	−10.3923	−	6.00000i	−0.501745	−	0.289683i
$430$		0			0
$431$	27.5772	−	15.9217i	1.32835	−	0.766921i	0.343302	−	0.939225i	$-0.388455\pi$
$431$	27.5772	−	15.9217i	1.32835	−	0.766921i	0.985044	+	0.172305i	$0.0551214\pi$
$432$		0			0
$433$	−13.0000	−	13.0000i	−0.624740	−	0.624740i	0.322000	−	0.946740i	$-0.395645\pi$
$433$	−13.0000	−	13.0000i	−0.624740	−	0.624740i	−0.946740	+	0.322000i	$0.895645\pi$
$434$		0			0
$435$	−3.67423	+	1.22474i	−0.176166	+	0.0587220i
$436$		0			0
$437$	−12.2942	−	3.29423i	−0.588113	−	0.157584i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.34486	+	5.01910i	0.0638964	+	0.238465i	0.990487	−	0.137607i	$-0.0439412\pi$
$443$	1.34486	+	5.01910i	0.0638964	+	0.238465i	−0.926590	+	0.376072i	$0.877275\pi$
$444$		0			0
$445$	1.47372	+	24.5526i	0.0698611	+	1.16390i
$446$		0			0
$447$	−28.1691	−	28.1691i	−1.33235	−	1.33235i
$448$		0			0
$449$			25.0000i			1.17982i	0.807468	+	0.589911i	$0.200837\pi$
$449$			25.0000i			1.17982i	−0.807468	+	0.589911i	$0.799163\pi$
$450$		0			0
$451$	2.12132	−	1.22474i	0.0998891	−	0.0576710i
$452$		0			0
$453$	−8.19615	+	2.19615i	−0.385089	+	0.103184i
$454$		0			0
$455$	−15.4548	+	6.41473i	−0.724533	+	0.300727i
$456$		0			0
$457$	7.32051	+	27.3205i	0.342439	+	1.27800i	0.895576	+	0.444909i	$0.146764\pi$
$457$	7.32051	+	27.3205i	0.342439	+	1.27800i	−0.553137	+	0.833090i	$0.686569\pi$
$458$		0			0
$459$	7.34847	+	12.7279i	0.342997	+	0.594089i
$460$		0			0
$461$	−20.0000			−0.931493			−0.465746	−	0.884918i	$-0.654214\pi$
$461$	−20.0000			−0.931493			−0.465746	+	0.884918i	$0.654214\pi$
$462$		0			0
$463$	13.4722	−	13.4722i	0.626106	−	0.626106i	−0.320980	−	0.947086i	$-0.604012\pi$
$463$	13.4722	−	13.4722i	0.626106	−	0.626106i	0.947086	+	0.320980i	$0.104012\pi$
$464$		0			0
$465$	−14.1962	−	12.5885i	−0.658331	−	0.583776i
$466$		0			0
$467$	−21.7494	+	5.82774i	−1.00644	+	0.269676i	−0.724143	−	0.689650i	$-0.757764\pi$
$467$	−21.7494	+	5.82774i	−1.00644	+	0.269676i	−0.282301	+	0.959326i	$0.591098\pi$
$468$		0			0
$469$	4.33013	−	1.50000i	0.199947	−	0.0692636i
$470$		0			0
$471$	14.8492	+	8.57321i	0.684217	+	0.395033i
$472$		0			0
$473$	5.49038	−	20.4904i	0.252448	−	0.942149i
$474$		0			0
$475$	−7.34847	−	9.79796i	−0.337171	−	0.449561i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−17.1464	−	29.6985i	−0.783440	−	1.35696i	−0.929926	−	0.367746i	$-0.880130\pi$
$479$	−17.1464	−	29.6985i	−0.783440	−	1.35696i	0.146486	−	0.989213i	$-0.453204\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$		0			0
$483$	19.7160	−	13.3521i	0.897111	−	0.607540i
$484$		0			0
$485$	−34.0788	−	6.97372i	−1.54744	−	0.316660i
$486$		0			0
$487$	5.37945	−	20.0764i	0.243766	−	0.909748i	−0.730233	−	0.683198i	$-0.760589\pi$
$487$	5.37945	−	20.0764i	0.243766	−	0.909748i	0.973999	−	0.226550i	$-0.0727447\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			4.89898i			0.221088i	0.993871	+	0.110544i	$0.0352593\pi$
$491$			4.89898i			0.221088i	−0.993871	+	0.110544i	$0.964741\pi$
$492$		0			0
$493$	−0.732051	+	2.73205i	−0.0329699	+	0.123045i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	26.8301	−	18.1699i	1.20350	−	0.815030i
$498$		0			0
$499$	−3.67423	+	6.36396i	−0.164481	+	0.284890i	−0.936471	−	0.350745i	$-0.885928\pi$
$499$	−3.67423	+	6.36396i	−0.164481	+	0.284890i	0.771990	+	0.635635i	$0.219262\pi$
$500$		0			0
$501$	−7.50000	−	12.9904i	−0.335075	−	0.580367i
$502$		0			0
$503$	15.9217	−	15.9217i	0.709913	−	0.709913i	−0.256604	−	0.966517i	$-0.582604\pi$
$503$	15.9217	−	15.9217i	0.709913	−	0.709913i	0.966517	+	0.256604i	$0.0826036\pi$
$504$		0			0
$505$	13.0000	−	26.0000i	0.578492	−	1.15698i
$506$		0			0
$507$	−2.24144	+	8.36516i	−0.0995458	+	0.371510i
$508$		0			0
$509$	−19.9186	−	11.5000i	−0.882876	−	0.509729i	−0.0112702	−	0.999936i	$-0.503587\pi$
$509$	−19.9186	−	11.5000i	−0.882876	−	0.509729i	−0.871606	+	0.490208i	$0.836921\pi$
$510$		0			0
$511$	7.07107	−	2.44949i	0.312806	−	0.108359i
$512$		0			0
$513$	−12.2942	+	3.29423i	−0.542803	+	0.145444i
$514$		0			0
$515$	23.1265	−	26.0800i	1.01907	−	1.14922i
$516$		0			0
$517$		0			0
$518$		0			0
$519$	29.3939			1.29025
$520$		0			0
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	0.818884	−	0.573959i	$-0.194593\pi$
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	−0.906505	+	0.422194i	$0.861260\pi$
$522$		0			0
$523$	−5.37945	−	20.0764i	−0.235227	−	0.877879i	−0.978046	−	0.208387i	$-0.933179\pi$
$523$	−5.37945	−	20.0764i	−0.235227	−	0.877879i	0.742819	−	0.669492i	$-0.233488\pi$
$524$		0			0
$525$	22.8564	+	1.60770i	0.997535	+	0.0701656i
$526$		0			0
$527$	−13.3843	+	3.58630i	−0.583028	+	0.156222i
$528$		0			0
$529$	−3.46410	+	2.00000i	−0.150613	+	0.0869565i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.00000	+	2.00000i	0.0866296	+	0.0866296i
$534$		0			0
$535$	−20.2844	−	17.9873i	−0.876973	−	0.777657i
$536$		0			0
$537$	6.58846	+	24.5885i	0.284313	+	1.06107i
$538$		0			0
$539$	−2.44949	−	16.9706i	−0.105507	−	0.730974i
$540$		0			0
$541$	22.5000	−	38.9711i	0.967351	−	1.67550i	0.264188	−	0.964471i	$-0.414896\pi$
$541$	22.5000	−	38.9711i	0.967351	−	1.67550i	0.703163	−	0.711029i	$-0.251771\pi$
$542$		0			0
$543$	−25.0955	−	6.72432i	−1.07695	−	0.288568i
$544$		0			0
$545$	18.0000	+	9.00000i	0.771035	+	0.385518i
$546$		0			0
$547$	−18.3712	−	18.3712i	−0.785495	−	0.785495i	0.195257	−	0.980752i	$-0.437446\pi$
$547$	−18.3712	−	18.3712i	−0.785495	−	0.785495i	−0.980752	+	0.195257i	$0.937446\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.12132	−	1.22474i	−0.0903713	−	0.0521759i
$552$		0			0
$553$	−45.2487	+	3.24871i	−1.92417	+	0.138149i
$554$		0			0
$555$	−36.5665	+	24.1432i	−1.55216	+	1.02482i
$556$		0			0
$557$	34.1506	+	9.15064i	1.44701	+	0.387725i	0.894982	−	0.446102i	$-0.147188\pi$
$557$	34.1506	+	9.15064i	1.44701	+	0.387725i	0.552027	+	0.833827i	$0.313855\pi$
$558$		0			0
$559$	24.4949			1.03602
$560$		0			0
$561$	12.0000			0.506640
$562$		0			0
$563$	8.36516	+	2.24144i	0.352550	+	0.0944654i	0.430748	−	0.902472i	$-0.358250\pi$
$563$	8.36516	+	2.24144i	0.352550	+	0.0944654i	−0.0781979	+	0.996938i	$0.524917\pi$
$564$		0			0
$565$	1.90192	−	9.29423i	0.0800145	−	0.391011i
$566$		0			0
$567$	10.3986	−	21.4213i	0.436698	−	0.899608i
$568$		0			0
$569$	−17.3205	−	10.0000i	−0.726113	−	0.419222i	0.0908852	−	0.995861i	$-0.471030\pi$
$569$	−17.3205	−	10.0000i	−0.726113	−	0.419222i	−0.816999	+	0.576640i	$0.804364\pi$
$570$		0			0
$571$	10.6066	−	6.12372i	0.443872	−	0.256270i	−0.261366	−	0.965240i	$-0.584173\pi$
$571$	10.6066	−	6.12372i	0.443872	−	0.256270i	0.705239	+	0.708970i	$0.250840\pi$
$572$		0			0
$573$	9.00000	+	9.00000i	0.375980	+	0.375980i
$574$		0			0
$575$	−25.7196	−	3.67423i	−1.07258	−	0.153226i
$576$		0			0
$577$	−39.6147	−	10.6147i	−1.64918	−	0.441897i	−0.689799	−	0.724001i	$-0.742301\pi$
$577$	−39.6147	−	10.6147i	−1.64918	−	0.441897i	−0.959384	+	0.282104i	$0.908968\pi$
$578$		0			0
$579$	−1.22474	+	2.12132i	−0.0508987	+	0.0881591i
$580$		0			0
$581$	13.5000	+	2.59808i	0.560074	+	0.107786i
$582$		0			0
$583$	−0.896575	−	3.34607i	−0.0371324	−	0.138580i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	4.89898	+	4.89898i	0.202203	+	0.202203i	0.800943	−	0.598741i	$-0.204332\pi$
$587$	4.89898	+	4.89898i	0.202203	+	0.202203i	−0.598741	+	0.800943i	$0.704332\pi$
$588$		0			0
$589$		−	12.0000i		−	0.494451i
$590$		0			0
$591$	19.0919	−	11.0227i	0.785335	−	0.453413i
$592$		0			0
$593$	12.2942	−	3.29423i	0.504863	−	0.135278i	0.00260723	−	0.999997i	$-0.499170\pi$
$593$	12.2942	−	3.29423i	0.504863	−	0.135278i	0.502256	+	0.864719i	$0.332503\pi$
$594$		0			0
$595$	10.1769	−	13.2827i	0.417212	−	0.544539i
$596$		0			0
$597$	−4.39230	−	16.3923i	−0.179765	−	0.670892i
$598$		0			0
$599$	−9.79796	−	16.9706i	−0.400334	−	0.693398i	0.593432	−	0.804884i	$-0.297772\pi$
$599$	−9.79796	−	16.9706i	−0.400334	−	0.693398i	−0.993766	+	0.111486i	$0.964439\pi$
$600$		0			0
$601$	−12.0000			−0.489490			−0.244745	−	0.969587i	$-0.578704\pi$
$601$	−12.0000			−0.489490			−0.244745	+	0.969587i	$0.578704\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	11.1603	−	0.669873i	0.453729	−	0.0272342i
$606$		0			0
$607$	−5.01910	+	1.34486i	−0.203719	+	0.0545863i	−0.359235	−	0.933247i	$-0.616962\pi$
$607$	−5.01910	+	1.34486i	−0.203719	+	0.0545863i	0.155517	+	0.987833i	$0.450296\pi$
$608$		0			0
$609$	4.33013	−	1.50000i	0.175466	−	0.0607831i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−3.66025	+	13.6603i	−0.147836	+	0.551732i	0.851776	+	0.523905i	$0.175525\pi$
$613$	−3.66025	+	13.6603i	−0.147836	+	0.551732i	−0.999613	+	0.0278271i	$0.991141\pi$
$614$		0			0
$615$	−1.22474	−	3.67423i	−0.0493865	−	0.148159i
$616$		0			0
$617$	−16.0000	+	16.0000i	−0.644136	+	0.644136i	−0.951569	−	0.307434i	$-0.900530\pi$
$617$	−16.0000	+	16.0000i	−0.644136	+	0.644136i	0.307434	+	0.951569i	$0.400530\pi$
$618$		0			0
$619$	−6.12372	−	10.6066i	−0.246133	−	0.426315i	0.716316	−	0.697776i	$-0.245827\pi$
$619$	−6.12372	−	10.6066i	−0.246133	−	0.426315i	−0.962450	+	0.271460i	$0.912493\pi$
$620$		0			0
$621$	−13.5000	+	23.3827i	−0.541736	+	0.938315i
$622$		0			0
$623$	−2.08416	−	29.0285i	−0.0834999	−	1.16300i
$624$		0			0
$625$	−17.2846	−	18.0622i	−0.691384	−	0.722487i
$626$		0			0
$627$	−2.68973	+	10.0382i	−0.107417	+	0.400887i
$628$		0			0
$629$			32.0000i			1.27592i
$630$		0			0
$631$			26.9444i			1.07264i	0.844015	+	0.536320i	$0.180186\pi$
$631$			26.9444i			1.07264i	−0.844015	+	0.536320i	$0.819814\pi$
$632$		0			0
$633$	−3.29423	+	12.2942i	−0.130934	+	0.488652i
$634$		0			0
$635$	−6.21166	+	30.3548i	−0.246502	+	1.20459i
$636$		0			0
$637$	18.1962	−	7.80385i	0.720958	−	0.309200i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−11.5000	−	19.9186i	−0.454223	−	0.786737i	0.544420	−	0.838812i	$-0.316750\pi$
$641$	−11.5000	−	19.9186i	−0.454223	−	0.786737i	−0.998643	+	0.0520757i	$0.983416\pi$
$642$		0			0
$643$	24.4949	−	24.4949i	0.965984	−	0.965984i	−0.0334557	−	0.999440i	$-0.510651\pi$
$643$	24.4949	−	24.4949i	0.965984	−	0.965984i	0.999440	+	0.0334557i	$0.0106513\pi$
$644$		0			0
$645$	−30.0000	−	15.0000i	−1.18125	−	0.590624i
$646$		0			0
$647$	6.72432	−	25.0955i	0.264360	−	0.986605i	−0.698281	−	0.715824i	$-0.746051\pi$
$647$	6.72432	−	25.0955i	0.264360	−	0.986605i	0.962641	−	0.270781i	$-0.0872821\pi$
$648$		0			0
$649$	25.9808	+	15.0000i	1.01983	+	0.588802i
$650$		0			0
$651$	16.9706	+	14.6969i	0.665129	+	0.576018i
$652$		0			0
$653$	19.1244	−	5.12436i	0.748394	−	0.200532i	0.135588	−	0.990765i	$-0.456708\pi$
$653$	19.1244	−	5.12436i	0.748394	−	0.200532i	0.612806	+	0.790234i	$0.290041\pi$
$654$		0			0
$655$	2.62536	+	43.7391i	0.102581	+	1.70903i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−17.1464			−0.667930			−0.333965	−	0.942585i	$-0.608387\pi$
$659$	−17.1464			−0.667930			−0.333965	+	0.942585i	$0.608387\pi$
$660$		0			0
$661$	19.5000	+	33.7750i	0.758462	+	1.31369i	0.943635	+	0.330989i	$0.107382\pi$
$661$	19.5000	+	33.7750i	0.758462	+	1.31369i	−0.185173	+	0.982706i	$0.559284\pi$
$662$		0			0
$663$	3.58630	+	13.3843i	0.139280	+	0.519802i
$664$		0			0
$665$	8.83013	+	11.4904i	0.342418	+	0.445578i
$666$		0			0
$667$	−5.01910	+	1.34486i	−0.194340	+	0.0520733i
$668$		0			0
$669$	36.3731	−	21.0000i	1.40626	−	0.811907i
$670$		0			0
$671$			7.34847i			0.283685i
$672$		0			0
$673$	−8.00000	−	8.00000i	−0.308377	−	0.308377i	0.535903	−	0.844280i	$-0.319971\pi$
$673$	−8.00000	−	8.00000i	−0.308377	−	0.308377i	−0.844280	+	0.535903i	$0.819971\pi$
$674$		0			0
$675$	−24.1110	+	9.67784i	−0.928032	+	0.372500i
$676$		0			0
$677$	8.05256	+	30.0526i	0.309485	+	1.15501i	0.929015	+	0.370041i	$0.120656\pi$
$677$	8.05256	+	30.0526i	0.309485	+	1.15501i	−0.619530	+	0.784973i	$0.712677\pi$
$678$		0			0
$679$	40.4166	+	7.77817i	1.55105	+	0.298499i
$680$		0			0
$681$	18.0000	−	31.1769i	0.689761	−	1.19470i
$682$		0			0
$683$	35.1337	+	9.41404i	1.34435	+	0.360218i	0.858047	−	0.513570i	$-0.171677\pi$
$683$	35.1337	+	9.41404i	1.34435	+	0.360218i	0.486306	+	0.873789i	$0.338344\pi$
$684$		0			0
$685$	12.0000	+	36.0000i	0.458496	+	1.37549i
$686$		0			0
$687$	−9.79796	−	9.79796i	−0.373815	−	0.373815i
$688$		0			0
$689$	3.46410	−	2.00000i	0.131972	−	0.0761939i
$690$		0			0
$691$	19.0919	+	11.0227i	0.726289	+	0.419323i	0.817063	−	0.576548i	$-0.195601\pi$
$691$	19.0919	+	11.0227i	0.726289	+	0.419323i	−0.0907737	+	0.995872i	$0.528934\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.1253	+	31.9957i	0.801327	+	1.21366i
$696$		0			0
$697$	−2.73205	−	0.732051i	−0.103484	−	0.0277284i
$698$		0			0
$699$	−4.89898			−0.185296
$700$		0			0
$701$	−1.00000			−0.0377695			−0.0188847	−	0.999822i	$-0.506012\pi$
$701$	−1.00000			−0.0377695			−0.0188847	+	0.999822i	$0.506012\pi$
$702$		0			0
$703$	−26.7685	−	7.17260i	−1.00959	−	0.270520i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−15.0201	+	30.9418i	−0.564890	+	1.16369i
$708$		0			0
$709$	−40.7032	−	23.5000i	−1.52864	−	0.882561i	−0.999419	−	0.0340772i	$-0.989151\pi$
$709$	−40.7032	−	23.5000i	−1.52864	−	0.882561i	−0.529221	−	0.848484i	$-0.677516\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−18.0000	−	18.0000i	−0.674105	−	0.674105i
$714$		0			0
$715$	−4.89898	−	14.6969i	−0.183211	−	0.549634i
$716$		0			0
$717$	−40.9808	−	10.9808i	−1.53045	−	0.410084i
$718$		0			0
$719$	11.0227	−	19.0919i	0.411077	−	0.712007i	−0.583930	−	0.811804i	$-0.698486\pi$
$719$	11.0227	−	19.0919i	0.411077	−	0.712007i	0.995008	+	0.0997967i	$0.0318192\pi$
$720$		0			0
$721$	−27.0000	+	31.1769i	−1.00553	+	1.16109i
$722$		0			0
$723$	−1.79315	−	6.69213i	−0.0666880	−	0.248883i
$724$		0			0
$725$	−4.59808	−	1.96410i	−0.170768	−	0.0729449i
$726$		0			0
$727$	23.2702	+	23.2702i	0.863042	+	0.863042i	0.991690	−	0.128648i	$-0.0410638\pi$
$727$	23.2702	+	23.2702i	0.863042	+	0.863042i	−0.128648	+	0.991690i	$0.541064\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	−21.2132	+	12.2474i	−0.784599	+	0.452988i
$732$		0			0
$733$	6.83013	−	1.83013i	0.252276	−	0.0675973i	−0.130464	−	0.991453i	$-0.541647\pi$
$733$	6.83013	−	1.83013i	0.252276	−	0.0675973i	0.382741	+	0.923856i	$0.374980\pi$
$734$		0			0
$735$	−27.0645	−	1.58510i	−0.998289	−	0.0584673i
$736$		0			0
$737$	1.09808	+	4.09808i	0.0404482	+	0.150955i
$738$		0			0
$739$	1.22474	+	2.12132i	0.0450530	+	0.0780340i	0.887673	−	0.460475i	$-0.152321\pi$
$739$	1.22474	+	2.12132i	0.0450530	+	0.0780340i	−0.842620	+	0.538509i	$0.818988\pi$
$740$		0			0
$741$	−12.0000			−0.440831
$742$		0			0
$743$	−8.57321	+	8.57321i	−0.314521	+	0.314521i	−0.846658	−	0.532137i	$-0.821389\pi$
$743$	−8.57321	+	8.57321i	−0.314521	+	0.314521i	0.532137	+	0.846658i	$0.321389\pi$
$744$		0			0
$745$	−3.08142	−	51.3372i	−0.112894	−	1.88085i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	24.2487	+	21.0000i	0.886029	+	0.767323i
$750$		0			0
$751$	16.9706	+	9.79796i	0.619265	+	0.357533i	0.776583	−	0.630015i	$-0.216951\pi$
$751$	16.9706	+	9.79796i	0.619265	+	0.357533i	−0.157318	+	0.987548i	$0.550285\pi$
$752$		0			0
$753$	10.9808	−	40.9808i	0.400161	−	1.49342i
$754$		0			0
$755$	−9.79796	−	4.89898i	−0.356584	−	0.178292i
$756$		0			0
$757$	−10.0000	+	10.0000i	−0.363456	+	0.363456i	−0.865084	−	0.501628i	$-0.832735\pi$
$757$	−10.0000	+	10.0000i	−0.363456	+	0.363456i	0.501628	+	0.865084i	$0.332735\pi$
$758$		0			0
$759$	11.0227	+	19.0919i	0.400099	+	0.692991i
$760$		0			0
$761$	−23.0000	+	39.8372i	−0.833749	+	1.44410i	0.0612953	+	0.998120i	$0.480477\pi$
$761$	−23.0000	+	39.8372i	−0.833749	+	1.44410i	−0.895045	+	0.445977i	$0.852856\pi$
$762$		0			0
$763$	−21.4213	−	10.3986i	−0.775501	−	0.376453i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.96575	+	33.4607i	−0.323735	+	1.20819i
$768$		0			0
$769$			24.0000i			0.865462i	0.901523	+	0.432731i	$0.142450\pi$
$769$			24.0000i			0.865462i	−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$			29.3939i			1.05859i
$772$		0			0
$773$	−9.51666	+	35.5167i	−0.342290	+	1.27745i	0.553455	+	0.832879i	$0.313309\pi$
$773$	−9.51666	+	35.5167i	−0.342290	+	1.27745i	−0.895746	+	0.444567i	$0.853358\pi$
$774$		0			0
$775$	−2.92996	−	24.3190i	−0.105247	−	0.873565i
$776$		0			0
$777$	42.9282	−	29.0718i	1.54004	−	1.04294i
$778$		0			0
$779$	1.22474	−	2.12132i	0.0438810	−	0.0760042i
$780$		0			0
$781$	15.0000	+	25.9808i	0.536742	+	0.929665i
$782$		0			0
$783$	−3.67423	+	3.67423i	−0.131306	+	0.131306i
$784$		0			0
$785$	7.00000	+	21.0000i	0.249841	+	0.749522i
$786$		0			0
$787$	4.93117	−	18.4034i	0.175777	−	0.656009i	−0.820641	−	0.571444i	$-0.806383\pi$
$787$	4.93117	−	18.4034i	0.175777	−	0.656009i	0.996418	−	0.0845647i	$-0.0269500\pi$
$788$		0			0
$789$	2.59808	+	1.50000i	0.0924940	+	0.0534014i
$790$		0			0
$791$	−2.12132	+	11.0227i	−0.0754255	+	0.391922i
$792$		0			0
$793$	−8.19615	+	2.19615i	−0.291054	+	0.0779877i
$794$		0			0
$795$	−5.46739	+	0.328169i	−0.193908	+	0.0116390i
$796$		0			0
$797$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$797$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.79315	+	6.69213i	0.0632789	+	0.236160i
$804$		0			0
$805$	30.4808	+	3.99038i	1.07431	+	0.140642i
$806$		0			0
$807$	−8.36516	+	2.24144i	−0.294468	+	0.0789024i
$808$		0			0
$809$	26.8468	−	15.5000i	0.943883	−	0.544951i	0.0527074	−	0.998610i	$-0.483215\pi$
$809$	26.8468	−	15.5000i	0.943883	−	0.544951i	0.891175	+	0.453659i	$0.149882\pi$
$810$		0			0
$811$			24.4949i			0.860132i	0.902797	+	0.430066i	$0.141510\pi$
$811$			24.4949i			0.860132i	−0.902797	+	0.430066i	$0.858490\pi$
$812$		0			0
$813$	9.00000	+	9.00000i	0.315644	+	0.315644i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.49038	−	20.4904i	−0.192084	−	0.716868i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	10.0000	−	17.3205i	0.349002	−	0.604490i	−0.637070	−	0.770806i	$-0.719854\pi$
$821$	10.0000	−	17.3205i	0.349002	−	0.604490i	0.986073	+	0.166316i	$0.0531872\pi$
$822$		0			0
$823$	−31.7876	−	8.51747i	−1.10805	−	0.296900i	−0.342010	−	0.939696i	$-0.611108\pi$
$823$	−31.7876	−	8.51747i	−1.10805	−	0.296900i	−0.766037	+	0.642796i	$0.777774\pi$
$824$		0			0
$825$	−3.00000	+	21.0000i	−0.104447	+	0.731126i
$826$		0			0
$827$	25.7196	+	25.7196i	0.894360	+	0.894360i	0.994930	−	0.100570i	$-0.0320668\pi$
$827$	25.7196	+	25.7196i	0.894360	+	0.894360i	−0.100570	+	0.994930i	$0.532067\pi$
$828$		0			0
$829$	−10.3923	+	6.00000i	−0.360940	+	0.208389i	−0.669493	−	0.742818i	$-0.733489\pi$
$829$	−10.3923	+	6.00000i	−0.360940	+	0.208389i	0.308553	+	0.951207i	$0.400155\pi$
$830$		0			0
$831$	−4.24264	−	2.44949i	−0.147176	−	0.0849719i
$832$		0			0
$833$	−11.8564	+	15.8564i	−0.410800	+	0.549392i
$834$		0			0
$835$	3.88229	−	18.9718i	0.134352	−	0.656545i
$836$		0			0
$837$	−24.5885	−	6.58846i	−0.849901	−	0.227730i
$838$		0			0
$839$	17.1464			0.591960			0.295980	−	0.955194i	$-0.404354\pi$
$839$	17.1464			0.591960			0.295980	+	0.955194i	$0.404354\pi$
$840$		0			0
$841$	28.0000			0.965517
$842$		0			0
$843$	−46.8449	−	12.5521i	−1.61342	−	0.432316i
$844$		0			0
$845$	−9.33013	+	6.16025i	−0.320966	+	0.211919i
$846$		0			0
$847$	−13.1948	+	0.947343i	−0.453378	+	0.0325511i
$848$		0			0
$849$	−20.7846	−	12.0000i	−0.713326	−	0.411839i
$850$		0			0
$851$	−50.9117	+	29.3939i	−1.74523	+	1.00761i
$852$		0			0
$853$	37.0000	+	37.0000i	1.26686	+	1.26686i	0.947703	+	0.319152i	$0.103398\pi$
$853$	37.0000	+	37.0000i	1.26686	+	1.26686i	0.319152	+	0.947703i	$0.396602\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−42.3468	−	11.3468i	−1.44654	−	0.387599i	−0.551720	−	0.834029i	$-0.686028\pi$
$857$	−42.3468	−	11.3468i	−1.44654	−	0.387599i	−0.894818	+	0.446430i	$0.852695\pi$
$858$		0			0
$859$	14.6969	−	25.4558i	0.501453	−	0.868542i	−0.498546	−	0.866864i	$-0.666132\pi$
$859$	14.6969	−	25.4558i	0.501453	−	0.868542i	0.999999	−	0.00167867i	$-0.000534338\pi$
$860$		0			0
$861$	1.50000	+	4.33013i	0.0511199	+	0.147570i
$862$		0			0
$863$	5.82774	+	21.7494i	0.198379	+	0.740359i	0.991366	+	0.131121i	$0.0418578\pi$
$863$	5.82774	+	21.7494i	0.198379	+	0.740359i	−0.792988	+	0.609238i	$0.791476\pi$
$864$		0			0
$865$	28.3923	+	25.1769i	0.965367	+	0.856041i
$866$		0			0
$867$	11.0227	+	11.0227i	0.374351	+	0.374351i
$868$		0			0
$869$		−	42.0000i		−	1.42475i
$870$		0			0
$871$	−4.24264	+	2.44949i	−0.143756	+	0.0829978i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20.7005	+	21.1302i	0.699806	+	0.714333i
$876$		0			0
$877$	−9.15064	−	34.1506i	−0.308995	−	1.15319i	−0.929452	−	0.368944i	$-0.879719\pi$
$877$	−9.15064	−	34.1506i	−0.308995	−	1.15319i	0.620457	−	0.784241i	$-0.286947\pi$
$878$		0			0
$879$	14.6969	+	25.4558i	0.495715	+	0.858604i
$880$		0			0
$881$	−11.0000			−0.370599			−0.185300	−	0.982682i	$-0.559326\pi$
$881$	−11.0000			−0.370599			−0.185300	+	0.982682i	$0.559326\pi$
$882$		0			0
$883$	24.4949	−	24.4949i	0.824319	−	0.824319i	−0.162405	−	0.986724i	$-0.551925\pi$
$883$	24.4949	−	24.4949i	0.824319	−	0.824319i	0.986724	+	0.162405i	$0.0519252\pi$
$884$		0			0
$885$	31.4711	−	35.4904i	1.05789	−	1.19300i
$886$		0			0
$887$	−41.8258	+	11.2072i	−1.40437	+	0.376301i	−0.879913	−	0.475134i	$-0.842399\pi$
$887$	−41.8258	+	11.2072i	−1.40437	+	0.376301i	−0.524460	+	0.851435i	$0.675733\pi$
$888$		0			0
$889$	6.92820	−	36.0000i	0.232364	−	1.20740i
$890$		0			0
$891$	19.0919	+	11.0227i	0.639602	+	0.369274i
$892$		0			0
$893$		0			0
$894$		0			0
$895$	−14.6969	+	29.3939i	−0.491264	+	0.982529i
$896$		0			0
$897$	−18.0000	+	18.0000i	−0.601003	+	0.601003i
$898$		0			0
$899$	−2.44949	−	4.24264i	−0.0816951	−	0.141500i
$900$		0			0
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$		0			0
$903$	35.7021	+	17.3309i	1.18809	+	0.576737i
$904$		0			0
$905$	−18.4808	−	27.9904i	−0.614321	−	0.930432i
$906$		0			0
$907$	8.51747	−	31.7876i	0.282818	−	1.05549i	−0.667601	−	0.744519i	$-0.732679\pi$
$907$	8.51747	−	31.7876i	0.282818	−	1.05549i	0.950419	−	0.310972i	$-0.100654\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			36.7423i			1.21733i	0.793428	+	0.608664i	$0.208294\pi$
$911$			36.7423i			1.21733i	−0.793428	+	0.608664i	$0.791706\pi$
$912$		0			0
$913$	−3.29423	+	12.2942i	−0.109023	+	0.406880i
$914$		0			0
$915$	11.3831	+	2.32937i	0.376312	+	0.0770066i
$916$		0			0
$917$	−3.71281	−	51.7128i	−0.122608	−	1.70771i
$918$		0			0
$919$	−1.22474	+	2.12132i	−0.0404006	+	0.0699759i	−0.885519	−	0.464604i	$-0.846197\pi$
$919$	−1.22474	+	2.12132i	−0.0404006	+	0.0699759i	0.845118	+	0.534580i	$0.179530\pi$
$920$		0			0
$921$	−1.50000	−	2.59808i	−0.0494267	−	0.0856095i
$922$		0			0
$923$	−24.4949	+	24.4949i	−0.806259	+	0.806259i
$924$		0			0
$925$	−56.0000	−	8.00000i	−1.84127	−	0.263038i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.4545	−	9.50000i	−0.539854	−	0.311685i	0.205166	−	0.978727i	$-0.434227\pi$
$929$	−16.4545	−	9.50000i	−0.539854	−	0.311685i	−0.745020	+	0.667042i	$0.767560\pi$
$930$		0			0
$931$	−10.6066	−	13.4722i	−0.347617	−	0.441533i
$932$		0			0
$933$	28.6865	−	7.68653i	0.939155	−	0.251646i
$934$		0			0
$935$	11.5911	+	10.2784i	0.379070	+	0.336141i
$936$		0			0
$937$	4.00000	−	4.00000i	0.130674	−	0.130674i	−0.638745	−	0.769419i	$-0.720546\pi$
$937$	4.00000	−	4.00000i	0.130674	−	0.130674i	0.769419	+	0.638745i	$0.220546\pi$
$938$		0			0
$939$	−39.1918			−1.27898
$940$		0			0
$941$	8.00000	+	13.8564i	0.260793	+	0.451706i	0.966453	−	0.256844i	$-0.0826828\pi$
$941$	8.00000	+	13.8564i	0.260793	+	0.451706i	−0.705660	+	0.708550i	$0.749349\pi$
$942$		0			0
$943$	−1.34486	−	5.01910i	−0.0437948	−	0.163444i
$944$		0			0
$945$	28.3923	−	11.7846i	0.923602	−	0.383353i
$946$		0			0
$947$	−8.36516	+	2.24144i	−0.271831	+	0.0728370i	−0.392160	−	0.919897i	$-0.628272\pi$
$947$	−8.36516	+	2.24144i	−0.271831	+	0.0728370i	0.120328	+	0.992734i	$0.461605\pi$
$948$		0			0
$949$	−6.92820	+	4.00000i	−0.224899	+	0.129845i
$950$		0			0
$951$		−	34.2929i		−	1.11202i
$952$		0			0
$953$	12.0000	+	12.0000i	0.388718	+	0.388718i	0.874230	−	0.485512i	$-0.161367\pi$
$953$	12.0000	+	12.0000i	0.388718	+	0.388718i	−0.485512	+	0.874230i	$0.661367\pi$
$954$		0			0
$955$	0.984508	+	16.4022i	0.0318579	+	0.530761i
$956$		0			0
$957$	1.09808	+	4.09808i	0.0354958	+	0.132472i
$958$		0			0
$959$	−14.6969	−	42.4264i	−0.474589	−	1.37002i
$960$		0			0
$961$	−3.50000	+	6.06218i	−0.112903	+	0.195554i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−3.00000	+	1.00000i	−0.0965734	+	0.0321911i
$966$		0			0
$967$	30.6186	+	30.6186i	0.984628	+	0.984628i	0.999884	−	0.0152551i	$-0.00485605\pi$
$967$	30.6186	+	30.6186i	0.984628	+	0.984628i	−0.0152551	+	0.999884i	$0.504856\pi$
$968$		0			0
$969$	10.3923	−	6.00000i	0.333849	−	0.192748i
$970$		0			0
$971$	25.4558	+	14.6969i	0.816917	+	0.471647i	0.849352	−	0.527827i	$-0.176993\pi$
$971$	25.4558	+	14.6969i	0.816917	+	0.471647i	−0.0324352	+	0.999474i	$0.510326\pi$
$972$		0			0
$973$	−25.4378	−	37.5622i	−0.815499	−	1.20419i
$974$		0			0
$975$	−24.3190	+	2.92996i	−0.778832	+	0.0938339i
$976$		0			0
$977$	39.6147	+	10.6147i	1.26739	+	0.339596i	0.829030	−	0.559205i	$-0.188893\pi$
$977$	39.6147	+	10.6147i	1.26739	+	0.339596i	0.438358	+	0.898800i	$0.355560\pi$
$978$		0			0
$979$	26.9444			0.861146
$980$		0			0
$981$		0			0
$982$		0			0
$983$	35.1337	+	9.41404i	1.12059	+	0.300261i	0.771122	−	0.636687i	$-0.219696\pi$
$983$	35.1337	+	9.41404i	1.12059	+	0.300261i	0.349468	+	0.936948i	$0.386362\pi$
$984$		0			0
$985$	27.8827	+	5.70577i	0.888416	+	0.181801i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−38.9711	−	22.5000i	−1.23921	−	0.715458i
$990$		0			0
$991$	29.6985	−	17.1464i	0.943403	−	0.544674i	0.0523779	−	0.998627i	$-0.483320\pi$
$991$	29.6985	−	17.1464i	0.943403	−	0.544674i	0.891026	+	0.453953i	$0.149987\pi$
$992$		0			0
$993$	−30.0000	−	30.0000i	−0.952021	−	0.952021i
$994$		0			0
$995$	9.79796	−	19.5959i	0.310616	−	0.621232i
$996$		0			0
$997$	−31.4186	−	8.41858i	−0.995037	−	0.266619i	−0.275672	−	0.961252i	$-0.588900\pi$
$997$	−31.4186	−	8.41858i	−0.995037	−	0.266619i	−0.719365	+	0.694633i	$0.755567\pi$
$998$		0			0
$999$	−29.3939	+	50.9117i	−0.929981	+	1.61077i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cu.a.303.1	yes	8
4.3	odd	2	inner	560.2.cu.a.303.2	yes	8
5.2	odd	4	inner	560.2.cu.a.527.1	yes	8
7.4	even	3	inner	560.2.cu.a.543.2	yes	8
20.7	even	4	inner	560.2.cu.a.527.2	yes	8
28.11	odd	6	inner	560.2.cu.a.543.1	yes	8
35.32	odd	12	inner	560.2.cu.a.207.2	yes	8
140.67	even	12	inner	560.2.cu.a.207.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cu.a.207.1	✓	8	140.67	even	12	inner
560.2.cu.a.207.2	yes	8	35.32	odd	12	inner
560.2.cu.a.303.1	yes	8	1.1	even	1	trivial
560.2.cu.a.303.2	yes	8	4.3	odd	2	inner
560.2.cu.a.527.1	yes	8	5.2	odd	4	inner
560.2.cu.a.527.2	yes	8	20.7	even	4	inner
560.2.cu.a.543.1	yes	8	28.11	odd	6	inner
560.2.cu.a.543.2	yes	8	7.4	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.67303 - 0.448288i) q^{3} +(-1.23205 - 1.86603i) q^{5} +(1.48356 + 2.19067i) q^{7} +(-2.12132 + 1.22474i) q^{11} +(-2.00000 - 2.00000i) q^{13} +(1.22474 + 3.67423i) q^{15} +(2.73205 + 0.732051i) q^{17} +(-1.22474 + 2.12132i) q^{19} +(-1.50000 - 4.33013i) q^{21} +(1.34486 + 5.01910i) q^{23} +(-1.96410 + 4.59808i) q^{25} +(3.67423 + 3.67423i) q^{27} +1.00000i q^{29} +(-4.24264 + 2.44949i) q^{31} +(4.09808 - 1.09808i) q^{33} +(2.26002 - 5.46739i) q^{35} +(2.92820 + 10.9282i) q^{37} +(2.44949 + 4.24264i) q^{39} -1.00000 q^{41} +(-6.12372 + 6.12372i) q^{43} +(-2.59808 + 6.50000i) q^{49} +(-4.24264 - 2.44949i) q^{51} +(-0.366025 + 1.36603i) q^{53} +(4.89898 + 2.44949i) q^{55} +(3.00000 - 3.00000i) q^{57} +(-6.12372 - 10.6066i) q^{59} +(1.50000 - 2.59808i) q^{61} +(-1.26795 + 6.19615i) q^{65} +(0.448288 - 1.67303i) q^{67} -9.00000i q^{69} -12.2474i q^{71} +(0.732051 - 2.73205i) q^{73} +(5.34727 - 6.81225i) q^{75} +(-5.83013 - 2.83013i) q^{77} +(-8.57321 + 14.8492i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(3.67423 - 3.67423i) q^{83} +(-2.00000 - 6.00000i) q^{85} +(0.448288 - 1.67303i) q^{87} +(-9.52628 - 5.50000i) q^{89} +(1.41421 - 7.34847i) q^{91} +(8.19615 - 2.19615i) q^{93} +(5.46739 - 0.328169i) q^{95} +(11.0000 - 11.0000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 16 q^{13} + 8 q^{17} - 12 q^{21} + 12 q^{25} + 12 q^{33} - 32 q^{37} - 8 q^{41} + 4 q^{53} + 24 q^{57} + 12 q^{61} - 24 q^{65} - 8 q^{73} - 12 q^{77} - 36 q^{81} - 16 q^{85} + 24 q^{93}+ \cdots + 88 q^{97}+O(q^{100}) \) 8 * q + 4 * q^5 - 16 * q^13 + 8 * q^17 - 12 * q^21 + 12 * q^25 + 12 * q^33 - 32 * q^37 - 8 * q^41 + 4 * q^53 + 24 * q^57 + 12 * q^61 - 24 * q^65 - 8 * q^73 - 12 * q^77 - 36 * q^81 - 16 * q^85 + 24 * q^93 + 88 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more