LMFDB - Embedded Newform 3997.1.cz.a.13.1

Newspace parameters

Level:	$ N $	=	$ 3997 = 7 \cdot 571 $
Weight:	$ k $	=	$ 1 $
Character orbit:	$[\chi]$	=	3997.cz (of order $570$ and degree $144$)

Newform invariants

Self dual:	No
Analytic conductor:	$1.99476285549$
Analytic rank:	$0$
Dimension:	$144$
Coefficient field:	$\Q(\zeta_{570})$
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Projective image	$D_{285}$
Projective field	Galois closure of $\mathbb{Q}[x]/(x^{285} - \cdots)$

Embedding invariants

Embedding label			13.1
Root			$-0.999757 - 0.0220445i$
Character	$\chi$	=	3997.13
Dual form			3997.1.cz.a.615.1

$q$-expansion

$f(q)$	$=$	$q+(0.341150 - 1.74650i) q^{2} +(-2.00737 - 0.815325i) q^{4} +(-0.461341 + 0.887223i) q^{7} +(-1.13548 + 1.73798i) q^{8} +(-0.739446 - 0.673216i) q^{9} +O(q^{10})$	\(q+(0.341150 - 1.74650i) q^{2} +(-2.00737 - 0.815325i) q^{4} +(-0.461341 + 0.887223i) q^{7} +(-1.13548 + 1.73798i) q^{8} +(-0.739446 - 0.673216i) q^{9} +(-0.000667889 + 0.121178i) q^{11} +(1.39215 + 1.10841i) q^{14} +(1.09501 + 1.06524i) q^{16} +(-1.42803 + 1.06177i) q^{18} +(0.211410 + 0.0425064i) q^{22} +(-1.65560 + 0.448511i) q^{23} +(-0.795863 - 0.605477i) q^{25} +(1.64946 - 1.40485i) q^{28} +(-0.0415578 + 1.50764i) q^{29} +(0.527965 - 0.366083i) q^{32} +(0.935454 + 1.95429i) q^{36} +(-0.977928 - 0.0756090i) q^{37} +(0.719909 + 1.59325i) q^{43} +(0.100140 - 0.242706i) q^{44} +(0.218515 + 3.04452i) q^{46} +(-0.574329 - 0.818625i) q^{49} +(-1.32897 + 1.18341i) q^{50} +(1.39478 + 1.29826i) q^{53} +(-1.01813 - 1.80923i) q^{56} +(2.61891 + 0.586912i) q^{58} +(0.938430 - 0.345471i) q^{63} +(0.154412 + 0.352023i) q^{64} +(-0.0859078 + 0.373673i) q^{67} +(-1.46100 + 0.310546i) q^{71} +(2.00967 - 0.520720i) q^{72} +(-0.465671 + 1.68216i) q^{74} +(-0.107204 - 0.0564971i) q^{77} +(-1.77781 - 0.863058i) q^{79} +(0.0935596 + 0.995614i) q^{81} +(3.02821 - 0.713782i) q^{86} +(-0.209848 - 0.138757i) q^{88} +(3.68910 + 0.449525i) q^{92} +(-1.62566 + 0.723790i) q^{98} +(0.0820731 - 0.0891552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144q + q^{2} + 5q^{4} + 2q^{7} + 21q^{8} - q^{9} + O(q^{10}) $	$ 144q + q^{2} + 5q^{4} + 2q^{7} + 21q^{8} - q^{9} + 6q^{11} + q^{14} + 6q^{16} - 9q^{18} + 21q^{22} + 3q^{23} - q^{25} - 10q^{28} - 4q^{29} - 5q^{32} - 2q^{37} - 9q^{43} - 20q^{44} - 34q^{46} + 2q^{49} - 2q^{50} + 6q^{53} - 8q^{56} - q^{58} - q^{63} + 11q^{64} + 20q^{67} + 3q^{71} + 23q^{72} - 31q^{74} + q^{77} + 6q^{79} - q^{81} + 7q^{86} - 9q^{88} + 9q^{92} + 6q^{98} - 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character Values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3997\mathbb{Z}\right)^\times$.

$n$	$1716$	$2285$
$\chi(n)$	$e\left(\frac{176}{285}\right)$	$-1$

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 $

$2$	0.341150	−	1.74650i	0.341150	−	1.74650i	−0.277403	−	0.960754i	$-0.589474\pi$
$2$	0.341150	−	1.74650i	0.341150	−	1.74650i	0.618553	−	0.785743i	$-0.287719\pi$
$3$		0			0		0.360939	−	0.932589i	$-0.382456\pi$
$3$		0			0		−0.360939	+	0.932589i	$0.617544\pi$
$4$	−2.00737	−	0.815325i	−2.00737	−	0.815325i
$5$		0			0		0.319482	−	0.947592i	$-0.396491\pi$
$5$		0			0		−0.319482	+	0.947592i	$0.603509\pi$
$6$		0			0
$7$	−0.461341	+	0.887223i	−0.461341	+	0.887223i
$7$	−0.461341	+	0.887223i	−0.461341	+	0.887223i
$8$	−1.13548	+	1.73798i	−1.13548	+	1.73798i
$9$	−0.739446	−	0.673216i	−0.739446	−	0.673216i
$10$		0			0
$11$	−0.000667889		0.121178i	−0.000667889		0.121178i	0.997814	+	0.0660906i	$0.0210526\pi$
$11$	−0.000667889		0.121178i	−0.000667889		0.121178i	−0.998482	+	0.0550878i	$0.982456\pi$
$12$		0			0
$13$		0			0		−0.381410	−	0.924406i	$-0.624561\pi$
$13$		0			0		0.381410	+	0.924406i	$0.375439\pi$
$14$	1.39215	+	1.10841i	1.39215	+	1.10841i
$15$		0			0
$16$	1.09501	+	1.06524i	1.09501	+	1.06524i
$17$		0			0		−0.989750	−	0.142811i	$-0.954386\pi$
$17$		0			0		0.989750	+	0.142811i	$0.0456140\pi$
$18$	−1.42803	+	1.06177i	−1.42803	+	1.06177i
$19$		0			0		−0.775409	−	0.631460i	$-0.782456\pi$
$19$		0			0		0.775409	+	0.631460i	$0.217544\pi$
$20$		0			0
$21$		0			0
$22$	0.211410	+	0.0425064i	0.211410	+	0.0425064i
$23$	−1.65560	+	0.448511i	−1.65560	+	0.448511i	−0.962268	−	0.272103i	$-0.912281\pi$
$23$	−1.65560	+	0.448511i	−1.65560	+	0.448511i	−0.693336	+	0.720615i	$0.743860\pi$
$24$		0			0
$25$	−0.795863	−	0.605477i	−0.795863	−	0.605477i
$26$		0			0
$27$		0			0
$28$	1.64946	−	1.40485i	1.64946	−	1.40485i
$29$	−0.0415578	+	1.50764i	−0.0415578	+	1.50764i	0.635724	+	0.771917i	$0.280702\pi$
$29$	−0.0415578	+	1.50764i	−0.0415578	+	1.50764i	−0.677282	+	0.735724i	$0.736842\pi$
$30$		0			0
$31$		0			0		0.245485	−	0.969400i	$-0.421053\pi$
$31$		0			0		−0.245485	+	0.969400i	$0.578947\pi$
$32$	0.527965	−	0.366083i	0.527965	−	0.366083i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	0.935454	+	1.95429i	0.935454	+	1.95429i
$37$	−0.977928	−	0.0756090i	−0.977928	−	0.0756090i	−0.421786	−	0.906696i	$-0.638596\pi$
$37$	−0.977928	−	0.0756090i	−0.977928	−	0.0756090i	−0.556143	+	0.831087i	$0.687719\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		0			0		−0.298515	−	0.954405i	$-0.596491\pi$
$41$		0			0		0.298515	+	0.954405i	$0.403509\pi$
$42$		0			0
$43$	0.719909	+	1.59325i	0.719909	+	1.59325i	0.802489	+	0.596667i	$0.203509\pi$
$43$	0.719909	+	1.59325i	0.719909	+	1.59325i	−0.0825793	+	0.996584i	$0.526316\pi$
$44$	0.100140	−	0.242706i	0.100140	−	0.242706i
$45$		0			0
$46$	0.218515	+	3.04452i	0.218515	+	3.04452i
$47$		0			0		0.962268	−	0.272103i	$-0.0877193\pi$
$47$		0			0		−0.962268	+	0.272103i	$0.912281\pi$
$48$		0			0
$49$	−0.574329	−	0.818625i	−0.574329	−	0.818625i
$50$	−1.32897	+	1.18341i	−1.32897	+	1.18341i
$51$		0			0
$52$		0			0
$53$	1.39478	+	1.29826i	1.39478	+	1.29826i	0.904357	+	0.426776i	$0.140351\pi$
$53$	1.39478	+	1.29826i	1.39478	+	1.29826i	0.490424	+	0.871484i	$0.336842\pi$
$54$		0			0
$55$		0			0
$56$	−1.01813	−	1.80923i	−1.01813	−	1.80923i
$57$		0			0
$58$	2.61891	+	0.586912i	2.61891	+	0.586912i
$59$		0			0		−0.986361	−	0.164595i	$-0.947368\pi$
$59$		0			0		0.986361	+	0.164595i	$0.0526316\pi$
$60$		0			0
$61$		0			0		0.857640	−	0.514250i	$-0.171930\pi$
$61$		0			0		−0.857640	+	0.514250i	$0.828070\pi$
$62$		0			0
$63$	0.938430	−	0.345471i	0.938430	−	0.345471i
$64$	0.154412	+	0.352023i	0.154412	+	0.352023i
$65$		0			0
$66$		0			0
$67$	−0.0859078	+	0.373673i	−0.0859078	+	0.373673i	−0.999453	−	0.0330634i	$-0.989474\pi$
$67$	−0.0859078	+	0.373673i	−0.0859078	+	0.373673i	0.913545	+	0.406737i	$0.133333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.46100	+	0.310546i	−1.46100	+	0.310546i	−0.868768	−	0.495219i	$-0.835088\pi$
$71$	−1.46100	+	0.310546i	−1.46100	+	0.310546i	−0.592235	+	0.805765i	$0.701754\pi$
$72$	2.00967	−	0.520720i	2.00967	−	0.520720i
$73$		0			0		0.565270	−	0.824906i	$-0.308772\pi$
$73$		0			0		−0.565270	+	0.824906i	$0.691228\pi$
$74$	−0.465671	+	1.68216i	−0.465671	+	1.68216i
$75$		0			0
$76$		0			0
$77$	−0.107204	−	0.0564971i	−0.107204	−	0.0564971i
$78$		0			0
$79$	−1.77781	−	0.863058i	−1.77781	−	0.863058i	−0.956036	−	0.293250i	$-0.905263\pi$
$79$	−1.77781	−	0.863058i	−1.77781	−	0.863058i	−0.821778	−	0.569808i	$-0.807018\pi$
$80$		0			0
$81$	0.0935596	+	0.995614i	0.0935596	+	0.995614i
$82$		0			0
$83$		0			0		0.0385714	−	0.999256i	$-0.487719\pi$
$83$		0			0		−0.0385714	+	0.999256i	$0.512281\pi$
$84$		0			0
$85$		0			0
$86$	3.02821	−	0.713782i	3.02821	−	0.713782i
$87$		0			0
$88$	−0.209848	−	0.138757i	−0.209848	−	0.138757i
$89$		0			0		0.884667	−	0.466224i	$-0.154386\pi$
$89$		0			0		−0.884667	+	0.466224i	$0.845614\pi$
$90$		0			0
$91$		0			0
$92$	3.68910	+	0.449525i	3.68910	+	0.449525i
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$		0			0		−0.528360	−	0.849020i	$-0.677193\pi$
$97$		0			0		0.528360	+	0.849020i	$0.322807\pi$
$98$	−1.62566	+	0.723790i	−1.62566	+	0.723790i
$99$	0.0820731	−	0.0891552i	0.0820731	−	0.0891552i
$100$	1.10393	+	1.86431i	1.10393	+	1.86431i
$101$		0			0		−0.970739	−	0.240139i	$-0.922807\pi$
$101$		0			0		0.970739	+	0.240139i	$0.0771930\pi$
$102$		0			0
$103$		0			0		0.669131	−	0.743145i	$-0.266667\pi$
$103$		0			0		−0.669131	+	0.743145i	$0.733333\pi$
$104$		0			0
$105$		0			0
$106$	2.74324	−	1.99308i	2.74324	−	1.99308i
$107$	1.28265	−	1.24778i	1.28265	−	1.24778i	0.329907	−	0.944013i	$-0.392982\pi$
$107$	1.28265	−	1.24778i	1.28265	−	1.24778i	0.952745	−	0.303771i	$-0.0982456\pi$
$108$		0			0
$109$	0.0165339	+	0.0286376i	0.0165339	+	0.0286376i	0.874174	−	0.485613i	$-0.161404\pi$
$109$	0.0165339	+	0.0286376i	0.0165339	+	0.0286376i	−0.857640	+	0.514250i	$0.828070\pi$
$110$		0			0
$111$		0			0
$112$	−1.45028	+	0.480077i	−1.45028	+	0.480077i
$113$	0.464757	−	1.92417i	0.464757	−	1.92417i	0.0935596	−	0.995614i	$-0.470175\pi$
$113$	0.464757	−	1.92417i	0.464757	−	1.92417i	0.371197	−	0.928554i	$-0.378947\pi$
$114$		0			0
$115$		0			0
$116$	1.31264	−	2.99252i	1.31264	−	2.99252i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.985256	+	0.0108610i	0.985256	+	0.0108610i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		0			0
$126$	−0.283218	−	1.75682i	−0.283218	−	1.75682i
$127$	−1.36397	+	1.24180i	−1.36397	+	1.24180i	−0.421786	+	0.906696i	$0.638596\pi$
$127$	−1.36397	+	1.24180i	−1.36397	+	1.24180i	−0.942181	+	0.335105i	$0.891228\pi$
$128$	1.29440	−	0.290082i	1.29440	−	0.290082i
$129$		0			0
$130$		0			0
$131$		0			0		0.789141	−	0.614213i	$-0.210526\pi$
$131$		0			0		−0.789141	+	0.614213i	$0.789474\pi$
$132$		0			0
$133$		0			0
$134$	0.623312	+	0.277516i	0.623312	+	0.277516i
$135$		0			0
$136$		0			0
$137$	1.24524	−	0.947356i	1.24524	−	0.947356i	0.245485	−	0.969400i	$-0.421053\pi$
$137$	1.24524	−	0.947356i	1.24524	−	0.947356i	0.999757	+	0.0220445i	$0.00701754\pi$
$138$		0			0
$139$		0			0		−0.952745	−	0.303771i	$-0.901754\pi$
$139$		0			0		0.952745	+	0.303771i	$0.0982456\pi$
$140$		0			0
$141$		0			0
$142$	0.0439463	+	2.65758i	0.0439463	+	2.65758i
$143$		0			0
$144$	−0.0925618	−	1.52486i	−0.0925618	−	1.52486i
$145$		0			0
$146$		0			0
$147$		0			0
$148$	1.90142	+	0.949105i	1.90142	+	0.949105i
$149$	−1.85758	−	0.503228i	−1.85758	−	0.503228i	−0.857640	−	0.514250i	$-0.828070\pi$
$149$	−1.85758	−	0.503228i	−1.85758	−	0.503228i	−0.999939	+	0.0110229i	$0.996491\pi$
$150$		0			0
$151$	−1.82698	+	0.0201399i	−1.82698	+	0.0201399i	−0.917973	−	0.396642i	$-0.870175\pi$
$151$	−1.82698	+	0.0201399i	−1.82698	+	0.0201399i	−0.909007	+	0.416782i	$0.863158\pi$
$152$		0			0
$153$		0			0
$154$	−0.135245	+	0.167958i	−0.135245	+	0.167958i
$155$		0			0
$156$		0			0
$157$		0			0		0.618553	−	0.785743i	$-0.287719\pi$
$157$		0			0		−0.618553	+	0.785743i	$0.712281\pi$
$158$	−2.11383	+	2.81051i	−2.11383	+	2.81051i
$159$		0			0
$160$		0			0
$161$	0.365869	−	1.67581i	0.365869	−	1.67581i
$162$	1.77075	+	0.176252i	1.77075	+	0.176252i
$163$	0.918145	+	1.76572i	0.918145	+	1.76572i	0.546948	+	0.837166i	$0.315789\pi$
$163$	0.918145	+	1.76572i	0.918145	+	1.76572i	0.371197	+	0.928554i	$0.378947\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$167$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$168$		0			0
$169$	−0.709053	+	0.705155i	−0.709053	+	0.705155i
$170$		0			0
$171$		0			0
$172$	−0.146110	−	3.78521i	−0.146110	−	3.78521i
$173$		0			0		0.930586	−	0.366074i	$-0.119298\pi$
$173$		0			0		−0.930586	+	0.366074i	$0.880702\pi$
$174$		0			0
$175$	0.904357	−	0.426776i	0.904357	−	0.426776i
$176$	−0.129815	+	0.131980i	−0.129815	+	0.131980i
$177$		0			0
$178$		0			0
$179$	−1.91737	+	0.0634294i	−1.91737	+	0.0634294i	−0.968033	−	0.250825i	$-0.919298\pi$
$179$	−1.91737	+	0.0634294i	−1.91737	+	0.0634294i	−0.949339	+	0.314254i	$0.898246\pi$
$180$		0			0
$181$		0			0		−0.879474	−	0.475947i	$-0.842105\pi$
$181$		0			0		0.879474	+	0.475947i	$0.157895\pi$
$182$		0			0
$183$		0			0
$184$	1.10040	−	3.38669i	1.10040	−	3.38669i
$185$		0			0
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.248931	+	0.0443650i	−0.248931	+	0.0443650i	−0.298515	−	0.954405i	$-0.596491\pi$
$191$	−0.248931	+	0.0443650i	−0.248931	+	0.0443650i	0.0495838	+	0.998770i	$0.484211\pi$
$192$		0			0
$193$	−1.73067	−	0.367865i	−1.73067	−	0.367865i	−0.768401	−	0.639969i	$-0.778947\pi$
$193$	−1.73067	−	0.367865i	−1.73067	−	0.367865i	−0.962268	+	0.272103i	$0.912281\pi$
$194$		0			0
$195$		0			0
$196$	0.485447	+	2.11155i	0.485447	+	2.11155i
$197$	−0.422202	−	0.150165i	−0.422202	−	0.150165i	0.115485	−	0.993309i	$-0.463158\pi$
$197$	−0.422202	−	0.150165i	−0.422202	−	0.150165i	−0.537687	+	0.843145i	$0.680702\pi$
$198$	−0.127710	−	0.173756i	−0.127710	−	0.173756i
$199$		0			0		−0.537687	−	0.843145i	$-0.680702\pi$
$199$		0			0		0.537687	+	0.843145i	$0.319298\pi$
$200$	1.95600	−	0.695689i	1.95600	−	0.695689i
$201$		0			0
$202$		0			0
$203$	−1.31844	−	0.732408i	−1.31844	−	0.732408i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	1.52617	+	0.782930i	1.52617	+	0.782930i
$208$		0			0
$209$		0			0
$210$		0			0
$211$	−0.0992705	+	1.38311i	−0.0992705	+	1.38311i	0.669131	+	0.743145i	$0.266667\pi$
$211$	−0.0992705	+	1.38311i	−0.0992705	+	1.38311i	−0.768401	+	0.639969i	$0.778947\pi$
$212$	−1.74134	−	3.74329i	−1.74134	−	3.74329i
$213$		0			0
$214$	−1.74167	−	2.66583i	−1.74167	−	2.66583i
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.0556561	−	0.0191068i	0.0556561	−	0.0191068i
$219$		0			0
$220$		0			0
$221$		0			0
$222$		0			0
$223$		0			0		−0.709053	−	0.705155i	$-0.750877\pi$
$223$		0			0		0.709053	+	0.705155i	$0.249123\pi$
$224$	0.0812250	+	0.637311i	0.0812250	+	0.637311i
$225$	0.180881	+	0.983505i	0.180881	+	0.983505i
$226$	−3.20200	−	1.46813i	−3.20200	−	1.46813i
$227$		0			0		−0.988116	−	0.153712i	$-0.950877\pi$
$227$		0			0		0.988116	+	0.153712i	$0.0491228\pi$
$228$		0			0
$229$		0			0		−0.999028	−	0.0440782i	$-0.985965\pi$
$229$		0			0		0.999028	+	0.0440782i	$0.0140351\pi$
$230$		0			0
$231$		0			0
$232$	−2.57307	−	1.78412i	−2.57307	−	1.78412i
$233$	−0.725862	−	1.08471i	−0.725862	−	1.08471i	−0.992658	−	0.120958i	$-0.961404\pi$
$233$	−0.725862	−	1.08471i	−0.725862	−	1.08471i	0.266796	−	0.963753i	$-0.414035\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.701582	−	1.55269i	0.701582	−	1.55269i	−0.126427	−	0.991976i	$-0.540351\pi$
$239$	0.701582	−	1.55269i	0.701582	−	1.55269i	0.828009	−	0.560715i	$-0.189474\pi$
$240$		0			0
$241$		0			0		−0.627176	−	0.778877i	$-0.715789\pi$
$241$		0			0		0.627176	+	0.778877i	$0.284211\pi$
$242$	0.355089	−	1.71704i	0.355089	−	1.71704i
$243$		0			0
$244$		0			0
$245$		0			0
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$		0			0
$251$		0			0		0.996114	−	0.0880708i	$-0.0280702\pi$
$251$		0			0		−0.996114	+	0.0880708i	$0.971930\pi$
$252$	−2.16545	−	0.0716362i	−2.16545	−	0.0716362i
$253$	−0.0532441	−	0.200923i	−0.0532441	−	0.200923i
$254$	1.70348	+	2.80580i	1.70348	+	2.80580i
$255$		0			0
$256$	−0.0544509	−	1.97538i	−0.0544509	−	1.97538i
$257$		0			0		−0.652586	−	0.757715i	$-0.726316\pi$
$257$		0			0		0.652586	+	0.757715i	$0.273684\pi$
$258$		0			0
$259$	0.518241	−	0.832759i	0.518241	−	0.832759i
$260$		0			0
$261$	1.04570	−	1.08684i	1.04570	−	1.08684i
$262$		0			0
$263$	0.933341	+	1.10817i	0.933341	+	1.10817i	0.993931	+	0.110008i	$0.0350877\pi$
$263$	0.933341	+	1.10817i	0.933341	+	1.10817i	−0.0605901	+	0.998163i	$0.519298\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	0.477114	−	0.680059i	0.477114	−	0.680059i
$269$		0			0		0.180881	−	0.983505i	$-0.442105\pi$
$269$		0			0		−0.180881	+	0.983505i	$0.557895\pi$
$270$		0			0
$271$		0			0		0.986361	−	0.164595i	$-0.0526316\pi$
$271$		0			0		−0.986361	+	0.164595i	$0.947368\pi$
$272$		0			0
$273$		0			0
$274$	−1.22974	−	2.49800i	−1.22974	−	2.49800i
$275$	0.0739022	−	0.0960370i	0.0739022	−	0.0960370i
$276$		0			0
$277$	−0.0621955	−	1.25281i	−0.0621955	−	1.25281i	−0.809017	−	0.587785i	$-0.800000\pi$
$277$	−0.0621955	−	1.25281i	−0.0621955	−	1.25281i	0.746821	−	0.665025i	$-0.231579\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.0743051	+	0.122388i	−0.0743051	+	0.122388i	−0.889752	−	0.456444i	$-0.849123\pi$
$281$	−0.0743051	+	0.122388i	−0.0743051	+	0.122388i	0.815447	+	0.578832i	$0.196491\pi$
$282$		0			0
$283$		0			0		−0.991264	−	0.131892i	$-0.957895\pi$
$283$		0			0		0.991264	+	0.131892i	$0.0421053\pi$
$284$	3.18598	+	0.567811i	3.18598	+	0.567811i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.636854	−	0.0847363i	−0.636854	−	0.0847363i
$289$	0.959210	+	0.282694i	0.959210	+	0.282694i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		0			0		0.480787	−	0.876837i	$-0.340351\pi$
$293$		0			0		−0.480787	+	0.876837i	$0.659649\pi$
$294$		0			0
$295$		0			0
$296$	1.24183	−	1.61377i	1.24183	−	1.61377i
$297$		0			0
$298$	−1.51260	+	3.07258i	−1.51260	+	3.07258i
$299$		0			0
$300$		0			0
$301$	−1.74569	−	0.0963126i	−1.74569	−	0.0963126i
$302$	−0.588100	+	3.19769i	−0.588100	+	3.19769i
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$		0			0		0.815447	−	0.578832i	$-0.196491\pi$
$307$		0			0		−0.815447	+	0.578832i	$0.803509\pi$
$308$	0.169135	+	0.200817i	0.169135	+	0.200817i
$309$		0			0
$310$		0			0
$311$		0			0		−0.949339	−	0.314254i	$-0.898246\pi$
$311$		0			0		0.949339	+	0.314254i	$0.101754\pi$
$312$		0			0
$313$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$313$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$314$		0			0
$315$		0			0
$316$	2.86506	+	3.18198i	2.86506	+	3.18198i
$317$	−0.406433	−	0.669434i	−0.406433	−	0.669434i	0.583317	−	0.812244i	$-0.301754\pi$
$317$	−0.406433	−	0.669434i	−0.406433	−	0.669434i	−0.989750	+	0.142811i	$0.954386\pi$
$318$		0			0
$319$	−0.182666	−	0.00604285i	−0.182666	−	0.00604285i
$320$		0			0
$321$		0			0
$322$	−2.80197	−	1.21069i	−2.80197	−	1.21069i
$323$		0			0
$324$	0.623940	−	2.07485i	0.623940	−	2.07485i
$325$		0			0
$326$	3.39705	−	1.00116i	3.39705	−	1.00116i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	0.195377	+	1.85889i	0.195377	+	1.85889i	0.451533	+	0.892254i	$0.350877\pi$
$331$	0.195377	+	1.85889i	0.195377	+	1.85889i	−0.256156	+	0.966635i	$0.582456\pi$
$332$		0			0
$333$	0.672224	+	0.714266i	0.672224	+	0.714266i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.60967	−	0.965176i	−1.60967	−	0.965176i	−0.982493	−	0.186298i	$-0.940351\pi$
$337$	−1.60967	−	0.965176i	−1.60967	−	0.965176i	−0.627176	−	0.778877i	$-0.715789\pi$
$338$	0.989659	+	1.47892i	0.989659	+	1.47892i
$339$		0			0
$340$		0			0
$341$		0			0
$342$		0			0
$343$	0.991264	−	0.131892i	0.991264	−	0.131892i
$344$	−3.58649	−	0.557917i	−3.58649	−	0.557917i
$345$		0			0
$346$		0			0
$347$	−0.138298	−	1.08512i	−0.138298	−	1.08512i	−0.899598	−	0.436719i	$-0.856140\pi$
$347$	−0.138298	−	1.08512i	−0.138298	−	1.08512i	0.761300	−	0.648400i	$-0.224561\pi$
$348$		0			0
$349$		0			0		−0.802489	−	0.596667i	$-0.796491\pi$
$349$		0			0		0.802489	+	0.596667i	$0.203509\pi$
$350$	−0.436842	−	1.72505i	−0.436842	−	1.72505i
$351$		0			0
$352$	0.0440087	+	0.0642224i	0.0440087	+	0.0642224i
$353$		0			0		0.945817	−	0.324699i	$-0.105263\pi$
$353$		0			0		−0.945817	+	0.324699i	$0.894737\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$	−0.543332	+	3.37032i	−0.543332	+	3.37032i
$359$	−0.507055	−	1.09000i	−0.507055	−	1.09000i	−0.978148	−	0.207912i	$-0.933333\pi$
$359$	−0.507055	−	1.09000i	−0.507055	−	1.09000i	0.471093	−	0.882084i	$-0.343860\pi$
$360$		0			0
$361$	0.202517	+	0.979279i	0.202517	+	0.979279i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$		0			0		0.782322	−	0.622874i	$-0.214035\pi$
$367$		0			0		−0.782322	+	0.622874i	$0.785965\pi$
$368$	−2.29067	−	1.27249i	−2.29067	−	1.27249i
$369$		0			0
$370$		0			0
$371$	−1.79532	+	0.638540i	−1.79532	+	0.638540i
$372$		0			0
$373$	−0.0587305	−	0.0799057i	−0.0587305	−	0.0799057i	0.775409	−	0.631460i	$-0.217544\pi$
$373$	−0.0587305	−	0.0799057i	−0.0587305	−	0.0799057i	−0.834139	+	0.551554i	$0.814035\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	1.85936	−	0.0820372i	1.85936	−	0.0820372i	0.913545	−	0.406737i	$-0.133333\pi$
$379$	1.85936	−	0.0820372i	1.85936	−	0.0820372i	0.945817	+	0.324699i	$0.105263\pi$
$380$		0			0
$381$		0			0
$382$	−0.00743951	+	0.449892i	−0.00743951	+	0.449892i
$383$		0			0		−0.993931	−	0.110008i	$-0.964912\pi$
$383$		0			0		0.993931	+	0.110008i	$0.0350877\pi$
$384$		0			0
$385$		0			0
$386$	−1.23289	+	2.89711i	−1.23289	+	2.89711i
$387$	0.540269	−	1.66278i	0.540269	−	1.66278i
$388$		0			0
$389$	0.266744	−	0.923837i	0.266744	−	0.923837i	−0.709053	−	0.705155i	$-0.750877\pi$
$389$	0.266744	−	0.923837i	0.266744	−	0.923837i	0.975796	−	0.218681i	$-0.0701754\pi$
$390$		0			0
$391$		0			0
$392$	2.07490	−	0.0686406i	2.07490	−	0.0686406i
$393$		0			0
$394$	−0.406296	+	0.686146i	−0.406296	+	0.686146i
$395$		0			0
$396$	−0.237442	+	0.112052i	−0.237442	+	0.112052i
$397$		0			0		0.556143	−	0.831087i	$-0.312281\pi$
$397$		0			0		−0.556143	+	0.831087i	$0.687719\pi$
$398$		0			0
$399$		0			0
$400$	−0.226498	−	1.51079i	−0.226498	−	1.51079i
$401$	0.216783	+	0.168729i	0.216783	+	0.168729i	0.716783	−	0.697297i	$-0.245614\pi$
$401$	0.216783	+	0.168729i	0.216783	+	0.168729i	−0.500000	+	0.866025i	$0.666667\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$		0			0
$406$	−1.72893	+	2.05279i	−1.72893	+	2.05279i
$407$	0.00981532	−	0.118453i	0.00981532	−	0.118453i
$408$		0			0
$409$		0			0		−0.995083	−	0.0990455i	$-0.968421\pi$
$409$		0			0		0.995083	+	0.0990455i	$0.0315789\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$	1.88804	−	2.39836i	1.88804	−	2.39836i
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		0			0		0.952745	−	0.303771i	$-0.0982456\pi$
$419$		0			0		−0.952745	+	0.303771i	$0.901754\pi$
$420$		0			0
$421$	−0.660728	−	1.76473i	−0.660728	−	1.76473i	−0.644194	−	0.764862i	$-0.722807\pi$
$421$	−0.660728	−	1.76473i	−0.660728	−	1.76473i	−0.0165339	−	0.999863i	$-0.505263\pi$
$422$	2.38174	+	0.645225i	2.38174	+	0.645225i
$423$		0			0
$424$	−3.84010	+	0.949955i	−3.84010	+	0.949955i
$425$		0			0
$426$		0			0
$427$		0			0
$428$	−3.59211	+	1.45899i	−3.59211	+	1.45899i
$429$		0			0
$430$		0			0
$431$	−0.190169	−	0.475710i	−0.190169	−	0.475710i	0.802489	−	0.596667i	$-0.203509\pi$
$431$	−0.190169	−	0.475710i	−0.190169	−	0.475710i	−0.992658	+	0.120958i	$0.961404\pi$
$432$		0			0
$433$		0			0		−0.956036	−	0.293250i	$-0.905263\pi$
$433$		0			0		0.956036	+	0.293250i	$0.0947368\pi$
$434$		0			0
$435$		0			0
$436$	−0.00984084	−	0.0709670i	−0.00984084	−	0.0709670i
$437$		0			0
$438$		0			0
$439$		0			0		−0.724425	−	0.689353i	$-0.757895\pi$
$439$		0			0		0.724425	+	0.689353i	$0.242105\pi$
$440$		0			0
$441$	−0.126427	+	0.991976i	−0.126427	+	0.991976i
$442$		0			0
$443$	1.24067	−	0.278042i	1.24067	−	0.278042i	0.451533	−	0.892254i	$-0.350877\pi$
$443$	1.24067	−	0.278042i	1.24067	−	0.278042i	0.789141	+	0.614213i	$0.210526\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$		0			0
$448$	−0.383560	−	0.0254052i	−0.383560	−	0.0254052i
$449$	0.115719	+	0.319762i	0.115719	+	0.319762i	0.984487	−	0.175457i	$-0.0561404\pi$
$449$	0.115719	+	0.319762i	0.115719	+	0.319762i	−0.868768	+	0.495219i	$0.835088\pi$
$450$	1.77940	+	0.0196153i	1.77940	+	0.0196153i
$451$		0			0
$452$	−2.50176	+	3.48360i	−2.50176	+	3.48360i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	0.580822	+	1.72274i	0.580822	+	1.72274i	0.685350	+	0.728214i	$0.259649\pi$
$457$	0.580822	+	1.72274i	0.580822	+	1.72274i	−0.104528	+	0.994522i	$0.533333\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$461$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$462$		0			0
$463$	−1.94579	+	0.150439i	−1.94579	+	0.150439i	−0.989750	−	0.142811i	$-0.954386\pi$
$463$	−1.94579	+	0.150439i	−1.94579	+	0.150439i	−0.956036	+	0.293250i	$0.905263\pi$
$464$	−1.65151	+	1.60661i	−1.65151	+	1.60661i
$465$		0			0
$466$	−2.14207	+	0.897667i	−2.14207	+	0.897667i
$467$		0			0		−0.982493	−	0.186298i	$-0.940351\pi$
$467$		0			0		0.982493	+	0.186298i	$0.0596491\pi$
$468$		0			0
$469$	−0.291899	−	0.248610i	−0.291899	−	0.248610i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.193548	+	0.0861733i	−0.193548	+	0.0861733i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−0.157354	−	1.89898i	−0.157354	−	1.89898i
$478$	−2.47243	−	1.75501i	−2.47243	−	1.75501i
$479$		0			0		−0.992658	−	0.120958i	$-0.961404\pi$
$479$		0			0		0.992658	+	0.120958i	$0.0385965\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$		0			0
$484$	−1.96892	−	0.825106i	−1.96892	−	0.825106i
$485$		0			0
$486$		0			0
$487$	0.636859	+	1.82234i	0.636859	+	1.82234i	0.565270	+	0.824906i	$0.308772\pi$
$487$	0.636859	+	1.82234i	0.636859	+	1.82234i	0.0715891	+	0.997434i	$0.477193\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−0.205505	+	0.105425i	−0.205505	+	0.105425i	−0.556143	−	0.831087i	$-0.687719\pi$
$491$	−0.205505	+	0.105425i	−0.205505	+	0.105425i	0.350638	+	0.936511i	$0.385965\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.398498	−	1.43950i	0.398498	−	1.43950i
$498$		0			0
$499$	−0.516534	+	0.133838i	−0.516534	+	0.133838i	−0.500000	−	0.866025i	$-0.666667\pi$
$499$	−0.516534	+	0.133838i	−0.516534	+	0.133838i	−0.0165339	+	0.999863i	$0.505263\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		0			0		−0.863256	−	0.504766i	$-0.831579\pi$
$503$		0			0		0.863256	+	0.504766i	$0.168421\pi$
$504$	−0.465147	+	2.02325i	−0.465147	+	2.02325i
$505$		0			0
$506$	−0.369075	+	0.0244459i	−0.369075	+	0.0244459i
$507$		0			0
$508$	3.75046	−	1.38068i	3.75046	−	1.38068i
$509$		0			0		−0.904357	−	0.426776i	$-0.859649\pi$
$509$		0			0		0.904357	+	0.426776i	$0.140351\pi$
$510$		0			0
$511$		0			0
$512$	−2.16015	−	0.360465i	−2.16015	−	0.360465i
$513$		0			0
$514$		0			0
$515$		0			0
$516$		0			0
$517$		0			0
$518$	−1.27761	−	1.18920i	−1.27761	−	1.18920i
$519$		0			0
$520$		0			0
$521$		0			0		0.746821	−	0.665025i	$-0.231579\pi$
$521$		0			0		−0.746821	+	0.665025i	$0.768421\pi$
$522$	−1.54142	−	2.19708i	−1.54142	−	2.19708i
$523$		0			0		0.909007	−	0.416782i	$-0.136842\pi$
$523$		0			0		−0.909007	+	0.416782i	$0.863158\pi$
$524$		0			0
$525$		0			0
$526$	2.25383	−	1.25202i	2.25383	−	1.25202i
$527$		0			0
$528$		0			0
$529$	1.67660	−	0.980348i	1.67660	−	0.980348i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$		0			0
$536$	−0.551891	−	0.573605i	−0.551891	−	0.573605i
$537$		0			0
$538$		0			0
$539$	0.0995832	−	0.0690494i	0.0995832	−	0.0690494i
$540$		0			0
$541$	−1.27443	+	1.03784i	−1.27443	+	1.03784i	−0.277403	+	0.960754i	$0.589474\pi$
$541$	−1.27443	+	1.03784i	−1.27443	+	1.03784i	−0.997024	+	0.0770854i	$0.975439\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−0.943827	−	1.31424i	−0.943827	−	1.31424i	−0.949339	−	0.314254i	$-0.898246\pi$
$547$	−0.943827	−	1.31424i	−0.943827	−	1.31424i	0.00551154	−	0.999985i	$-0.498246\pi$
$548$	−3.27207	+	0.886420i	−3.27207	+	0.886420i
$549$		0			0
$550$	−0.142517	−	0.161833i	−0.142517	−	0.161833i
$551$		0			0
$552$		0			0
$553$	1.58590	−	1.17915i	1.58590	−	1.17915i
$554$	−2.20925	−	0.318772i	−2.20925	−	0.318772i
$555$		0			0
$556$		0			0
$557$	0.659944	+	0.525439i	0.659944	+	0.525439i	0.894729	−	0.446609i	$-0.147368\pi$
$557$	0.659944	+	0.525439i	0.659944	+	0.525439i	−0.234785	+	0.972047i	$0.575439\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.188400	+	0.171526i	0.188400	+	0.171526i
$563$		0			0		0.546948	−	0.837166i	$-0.315789\pi$
$563$		0			0		−0.546948	+	0.837166i	$0.684211\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−0.926494	−	0.376309i	−0.926494	−	0.376309i
$568$	1.11922	−	2.89182i	1.11922	−	2.89182i
$569$	−0.383328	+	1.96243i	−0.383328	+	1.96243i	−0.170028	+	0.985439i	$0.554386\pi$
$569$	−0.383328	+	1.96243i	−0.383328	+	1.96243i	−0.213300	+	0.976987i	$0.568421\pi$
$570$		0			0
$571$	0.716783	+	0.697297i	0.716783	+	0.697297i
$571$	0.716783	+	0.697297i	0.716783	+	0.697297i
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.58920	+	0.645476i	1.58920	+	0.645476i
$576$	0.122809	−	0.364255i	0.122809	−	0.364255i
$577$		0			0		−0.846095	−	0.533032i	$-0.821053\pi$
$577$		0			0		0.846095	+	0.533032i	$0.178947\pi$
$578$	0.820958	−	1.57882i	0.820958	−	1.57882i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.158253	+	0.168150i	−0.158253	+	0.168150i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		0			0		−0.716783	−	0.697297i	$-0.754386\pi$
$587$		0			0		0.716783	+	0.697297i	$0.245614\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−0.990298	−	1.12452i	−0.990298	−	1.12452i
$593$		0			0		−0.980380	−	0.197117i	$-0.936842\pi$
$593$		0			0		0.980380	+	0.197117i	$0.0631579\pi$
$594$		0			0
$595$		0			0
$596$	3.31856	+	2.52470i	3.31856	+	2.52470i
$597$		0			0
$598$		0			0
$599$	−1.32279	+	1.12662i	−1.32279	+	1.12662i	−0.340293	+	0.940319i	$0.610526\pi$
$599$	−1.32279	+	1.12662i	−1.32279	+	1.12662i	−0.982493	+	0.186298i	$0.940351\pi$
$600$		0			0
$601$		0			0		0.775409	−	0.631460i	$-0.217544\pi$
$601$		0			0		−0.775409	+	0.631460i	$0.782456\pi$
$602$	−0.763753	+	3.01599i	−0.763753	+	3.01599i
$603$	0.315087	−	0.218477i	0.315087	−	0.218477i
$604$	3.68385	+	1.44915i	3.68385	+	1.44915i
$605$		0			0
$606$		0			0
$607$		0			0		−0.431754	−	0.901991i	$-0.642105\pi$
$607$		0			0		0.431754	+	0.901991i	$0.357895\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−0.478940	+	0.280047i	−0.478940	+	0.280047i	−0.724425	−	0.689353i	$-0.757895\pi$
$613$	−0.478940	+	0.280047i	−0.478940	+	0.280047i	0.245485	+	0.969400i	$0.421053\pi$
$614$		0			0
$615$		0			0
$616$	0.219919	−	0.122167i	0.219919	−	0.122167i
$617$	−0.113950	−	1.58764i	−0.113950	−	1.58764i	−0.660898	−	0.750475i	$-0.729825\pi$
$617$	−0.113950	−	1.58764i	−0.113950	−	1.58764i	0.546948	−	0.837166i	$-0.315789\pi$
$618$		0			0
$619$		0			0		0.909007	−	0.416782i	$-0.136842\pi$
$619$		0			0		−0.909007	+	0.416782i	$0.863158\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	0.266796	+	0.963753i	0.266796	+	0.963753i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		0			0
$630$		0			0
$631$	0.941270	+	1.76245i	0.941270	+	1.76245i	0.509516	+	0.860461i	$0.329825\pi$
$631$	0.941270	+	1.76245i	0.941270	+	1.76245i	0.431754	+	0.901991i	$0.357895\pi$
$632$	3.51866	−	2.10982i	3.51866	−	2.10982i
$633$		0			0
$634$	−1.30782	+	0.481456i	−1.30782	+	0.481456i
$635$		0			0
$636$		0			0
$637$		0			0
$638$	−0.0728702	+	0.316963i	−0.0728702	+	0.316963i
$639$	1.28940	+	0.753939i	1.28940	+	0.753939i
$640$		0			0
$641$	0.758728	−	0.489756i	0.758728	−	0.489756i	−0.104528	−	0.994522i	$-0.533333\pi$
$641$	0.758728	−	0.489756i	0.758728	−	0.489756i	0.863256	+	0.504766i	$0.168421\pi$
$642$		0			0
$643$		0			0		0.968033	−	0.250825i	$-0.0807018\pi$
$643$		0			0		−0.968033	+	0.250825i	$0.919298\pi$
$644$	−2.10076	+	3.06567i	−2.10076	+	3.06567i
$645$		0			0
$646$		0			0
$647$		0			0		−0.480787	−	0.876837i	$-0.659649\pi$
$647$		0			0		0.480787	+	0.876837i	$0.340351\pi$
$648$	−1.83660	−	0.967896i	−1.83660	−	0.967896i
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−0.403425	−	4.29305i	−0.403425	−	4.29305i
$653$	0.572457	−	0.0633595i	0.572457	−	0.0633595i	0.180881	−	0.983505i	$-0.442105\pi$
$653$	0.572457	−	0.0633595i	0.572457	−	0.0633595i	0.391577	+	0.920146i	$0.371930\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.445090	−	0.294304i	−0.445090	−	0.294304i	0.309017	−	0.951057i	$-0.400000\pi$
$659$	−0.445090	−	0.294304i	−0.445090	−	0.294304i	−0.754107	+	0.656752i	$0.771930\pi$
$660$		0			0
$661$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$661$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$662$	3.31320	+	0.292934i	3.31320	+	0.292934i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.47679	−	0.930365i	1.47679	−	0.930365i
$667$	−0.607391	−	2.51469i	−0.607391	−	2.51469i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.901738	−	0.768010i	−0.901738	−	0.768010i	0.0715891	−	0.997434i	$-0.477193\pi$
$673$	−0.901738	−	0.768010i	−0.901738	−	0.768010i	−0.973327	+	0.229424i	$0.926316\pi$
$674$	−2.23481	+	2.48201i	−2.23481	+	2.48201i
$675$		0			0
$676$	1.99827	−	0.837403i	1.99827	−	0.837403i
$677$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$677$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.89579	−	0.627554i	1.89579	−	0.627554i	0.930586	−	0.366074i	$-0.119298\pi$
$683$	1.89579	−	0.627554i	1.89579	−	0.627554i	0.965209	−	0.261480i	$-0.0842105\pi$
$684$		0			0
$685$		0			0
$686$	0.107820	−	1.77623i	0.107820	−	1.77623i
$687$		0			0
$688$	−0.908890	+	2.51150i	−0.908890	+	2.51150i
$689$		0			0
$690$		0			0
$691$		0			0		0.956036	−	0.293250i	$-0.0947368\pi$
$691$		0			0		−0.956036	+	0.293250i	$0.905263\pi$
$692$		0			0
$693$	0.0412368	+	0.113948i	0.0412368	+	0.113948i
$694$	−1.94234	−	0.128651i	−1.94234	−	0.128651i
$695$		0			0
$696$		0			0
$697$		0			0
$698$		0			0
$699$		0			0
$700$	−2.16334	+	0.119355i	−2.16334	+	0.119355i
$701$	−0.252792	+	1.98347i	−0.252792	+	1.98347i	−0.104528	+	0.994522i	$0.533333\pi$
$701$	−0.252792	+	1.98347i	−0.252792	+	1.98347i	−0.148264	+	0.988948i	$0.547368\pi$
$702$		0			0
$703$		0			0
$704$	−0.0427607	+	0.0184762i	−0.0427607	+	0.0184762i
$705$		0			0
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.31044	−	0.401958i	−1.31044	−	0.401958i	−0.441671	−	0.897177i	$-0.645614\pi$
$709$	−1.31044	−	0.401958i	−1.31044	−	0.401958i	−0.868768	+	0.495219i	$0.835088\pi$
$710$		0			0
$711$	0.733572	+	1.83504i	0.733572	+	1.83504i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	3.90060	+	1.43595i	3.90060	+	1.43595i
$717$		0			0
$718$	−2.07666	+	0.513718i	−2.07666	+	0.513718i
$719$		0			0		−0.894729	−	0.446609i	$-0.852632\pi$
$719$		0			0		0.894729	+	0.446609i	$0.147368\pi$
$720$		0			0
$721$		0			0
$722$	1.77940	−	0.0196153i	1.77940	−	0.0196153i
$723$		0			0
$724$		0			0
$725$	0.945916	−	1.17471i	0.945916	−	1.17471i
$726$		0			0
$727$		0			0		−0.934564	−	0.355794i	$-0.884211\pi$
$727$		0			0		0.934564	+	0.355794i	$0.115789\pi$
$728$		0			0
$729$	0.601081	−	0.799188i	0.601081	−	0.799188i
$730$		0			0
$731$		0			0
$732$		0			0
$733$		0			0		−0.995083	−	0.0990455i	$-0.968421\pi$
$733$		0			0		0.995083	+	0.0990455i	$0.0315789\pi$
$734$		0			0
$735$		0			0
$736$	−0.709908	+	0.842886i	−0.709908	+	0.842886i
$737$	−0.0452237	−	0.0106597i	−0.0452237	−	0.0106597i
$738$		0			0
$739$	−0.0545438	+	0.00787011i	−0.0545438	+	0.00787011i	−0.170028	−	0.985439i	$-0.554386\pi$
$739$	−0.0545438	+	0.00787011i	−0.0545438	+	0.00787011i	0.115485	+	0.993309i	$0.463158\pi$
$740$		0			0
$741$		0			0
$742$	0.502737	+	3.35335i	0.502737	+	3.35335i
$743$	−0.0638749	−	1.65479i	−0.0638749	−	1.65479i	−0.592235	−	0.805765i	$-0.701754\pi$
$743$	−0.0638749	−	1.65479i	−0.0638749	−	1.65479i	0.528360	−	0.849020i	$-0.322807\pi$
$744$		0			0
$745$		0			0
$746$	−0.159591	+	0.0753128i	−0.159591	+	0.0753128i
$747$		0			0
$748$		0			0
$749$	0.515322	+	1.71365i	0.515322	+	1.71365i
$750$		0			0
$751$	1.74603	−	0.212758i	1.74603	−	0.212758i	0.815447	−	0.578832i	$-0.196491\pi$
$751$	1.74603	−	0.212758i	1.74603	−	0.212758i	0.930586	+	0.366074i	$0.119298\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−1.43619	+	1.36666i	−1.43619	+	1.36666i	−0.627176	+	0.778877i	$0.715789\pi$
$757$	−1.43619	+	1.36666i	−1.43619	+	1.36666i	−0.809017	+	0.587785i	$0.800000\pi$
$758$	0.491044	−	3.27536i	0.491044	−	3.27536i
$759$		0			0
$760$		0			0
$761$		0			0		−0.360939	−	0.932589i	$-0.617544\pi$
$761$		0			0		0.360939	+	0.932589i	$0.382456\pi$
$762$		0			0
$763$	−0.0330358	+	0.00145757i	−0.0330358	+	0.00145757i
$764$	0.535870	+	0.113903i	0.535870	+	0.113903i
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$		0			0		−0.592235	−	0.805765i	$-0.701754\pi$
$769$		0			0		0.592235	+	0.805765i	$0.298246\pi$
$770$		0			0
$771$		0			0
$772$	3.17417	+	2.14950i	3.17417	+	2.14950i
$773$		0			0		0.421786	−	0.906696i	$-0.361404\pi$
$773$		0			0		−0.421786	+	0.906696i	$0.638596\pi$
$774$	−2.71972	−	1.51083i	−2.71972	−	1.51083i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	−1.52248	−	0.781034i	−1.52248	−	0.781034i
$779$		0			0
$780$		0			0
$781$	−0.0366556	−	0.177249i	−0.0366556	−	0.177249i
$782$		0			0
$783$		0			0
$784$	0.243138	−	1.50820i	0.243138	−	1.50820i
$785$		0			0
$786$		0			0
$787$		0			0		0.115485	−	0.993309i	$-0.463158\pi$
$787$		0			0		−0.115485	+	0.993309i	$0.536842\pi$
$788$	0.725085	+	0.645669i	0.725085	+	0.645669i
$789$		0			0
$790$		0			0
$791$	1.49275	+	1.30004i	1.49275	+	1.30004i
$792$	0.0617577	+	0.243876i	0.0617577	+	0.243876i
$793$		0			0
$794$		0			0
$795$		0			0
$796$		0			0
$797$		0			0		−0.909007	−	0.416782i	$-0.863158\pi$
$797$		0			0		0.909007	+	0.416782i	$0.136842\pi$
$798$		0			0
$799$		0			0
$800$	−0.641842	−	0.0283188i	−0.641842	−	0.0283188i
$801$		0			0
$802$	0.368639	−	0.321048i	0.368639	−	0.321048i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.564407	+	0.599706i	0.564407	+	0.599706i	0.945817	−	0.324699i	$-0.105263\pi$
$809$	0.564407	+	0.599706i	0.564407	+	0.599706i	−0.381410	+	0.924406i	$0.624561\pi$
$810$		0			0
$811$		0			0		−0.104528	−	0.994522i	$-0.533333\pi$
$811$		0			0		0.104528	+	0.994522i	$0.466667\pi$
$812$	2.04945	+	2.54517i	2.04945	+	2.54517i
$813$		0			0
$814$	−0.203530	−	0.0575527i	−0.203530	−	0.0575527i
$815$		0			0
$816$		0			0
$817$		0			0
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.133158	−	0.312902i	−0.133158	−	0.312902i	0.840168	−	0.542326i	$-0.182456\pi$
$821$	−0.133158	−	0.312902i	−0.133158	−	0.312902i	−0.973327	+	0.229424i	$0.926316\pi$
$822$		0			0
$823$	0.512032	+	0.0169388i	0.512032	+	0.0169388i	0.287976	−	0.957638i	$-0.407018\pi$
$823$	0.512032	+	0.0169388i	0.512032	+	0.0169388i	0.224056	+	0.974576i	$0.428070\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	0.0403384	+	1.46340i	0.0403384	+	1.46340i	0.701237	+	0.712928i	$0.252632\pi$
$827$	0.0403384	+	1.46340i	0.0403384	+	1.46340i	−0.660898	+	0.750475i	$0.729825\pi$
$828$	−2.42526	−	2.81596i	−2.42526	−	2.81596i
$829$		0			0		0.137354	−	0.990522i	$-0.456140\pi$
$829$		0			0		−0.137354	+	0.990522i	$0.543860\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.574329	−	0.818625i	$-0.305263\pi$
$839$		0			0		−0.574329	+	0.818625i	$0.694737\pi$
$840$		0			0
$841$	−1.27277	−	0.0702208i	−1.27277	−	0.0702208i
$842$	−3.30749	+	0.551923i	−3.30749	+	0.551923i
$843$		0			0
$844$	1.32696	−	2.69549i	1.32696	−	2.69549i
$845$		0			0
$846$		0			0
$847$	−0.464175	+	0.869131i	−0.464175	+	0.869131i
$848$	0.144337	+	2.90738i	0.144337	+	2.90738i
$849$		0			0
$850$		0			0
$851$	1.65297	−	0.313434i	1.65297	−	0.313434i
$852$		0			0
$853$		0			0		−0.959210	−	0.282694i	$-0.908772\pi$
$853$		0			0		0.959210	+	0.282694i	$0.0912281\pi$
$854$		0			0
$855$		0			0
$856$	0.712200	+	3.64607i	0.712200	+	3.64607i
$857$		0			0		−0.191711	−	0.981451i	$-0.561404\pi$
$857$		0			0		0.191711	+	0.981451i	$0.438596\pi$
$858$		0			0
$859$		0			0		−0.991264	−	0.131892i	$-0.957895\pi$
$859$		0			0		0.991264	+	0.131892i	$0.0421053\pi$
$860$		0			0
$861$		0			0
$862$	−0.895702	+	0.169841i	−0.895702	+	0.169841i
$863$	1.50078	−	0.992354i	1.50078	−	0.992354i	0.509516	−	0.860461i	$-0.329825\pi$
$863$	1.50078	−	0.992354i	1.50078	−	0.992354i	0.991264	−	0.131892i	$-0.0421053\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.105771	−	0.214856i	0.105771	−	0.214856i
$870$		0			0
$871$		0			0
$872$	−0.0685457	−	0.00378177i	−0.0685457	−	0.00378177i
$873$		0			0
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1.38806	+	0.751179i	−1.38806	+	0.751179i	−0.986361	−	0.164595i	$-0.947368\pi$
$877$	−1.38806	+	0.751179i	−1.38806	+	0.751179i	−0.401695	+	0.915773i	$0.631579\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		0			0		0.693336	−	0.720615i	$-0.256140\pi$
$881$		0			0		−0.693336	+	0.720615i	$0.743860\pi$
$882$	1.68935	+	0.559216i	1.68935	+	0.559216i
$883$	−0.110457	+	0.177494i	−0.110457	+	0.177494i	−0.899598	−	0.436719i	$-0.856140\pi$
$883$	−0.110457	+	0.177494i	−0.110457	+	0.177494i	0.789141	+	0.614213i	$0.210526\pi$
$884$		0			0
$885$		0			0
$886$	−0.0623430	−	2.26169i	−0.0623430	−	2.26169i
$887$		0			0		−0.669131	−	0.743145i	$-0.733333\pi$
$887$		0			0		0.669131	+	0.743145i	$0.266667\pi$
$888$		0			0
$889$	−0.472500	−	1.78304i	−0.472500	−	1.78304i
$890$		0			0
$891$	−0.120709	+	0.0106724i	−0.120709	+	0.0106724i
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$	−0.339793	+	1.28225i	−0.339793	+	1.28225i
$897$		0			0
$898$	0.597941	−	0.0930162i	0.597941	−	0.0930162i
$899$		0			0
$900$	0.438781	−	2.12174i	0.438781	−	2.12174i
$901$		0			0
$902$		0			0
$903$		0			0
$904$	2.81645	+	2.99260i	2.81645	+	2.99260i
$905$		0			0
$906$		0			0
$907$	−0.0296030	+	0.596295i	−0.0296030	+	0.596295i	0.938430	+	0.345471i	$0.112281\pi$
$907$	−0.0296030	+	0.596295i	−0.0296030	+	0.596295i	−0.968033	+	0.250825i	$0.919298\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.906559	+	0.789523i	−0.906559	+	0.789523i	−0.978148	−	0.207912i	$-0.933333\pi$
$911$	−0.906559	+	0.789523i	−0.906559	+	0.789523i	0.0715891	+	0.997434i	$0.477193\pi$
$912$		0			0
$913$		0			0
$914$	3.20690	−	0.426692i	3.20690	−	0.426692i
$915$		0			0
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−0.256508	−	0.255098i	−0.256508	−	0.255098i	0.565270	−	0.824906i	$-0.308772\pi$
$919$	−0.256508	−	0.255098i	−0.256508	−	0.255098i	−0.821778	+	0.569808i	$0.807018\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	0.732518	+	0.652287i	0.732518	+	0.652287i
$926$	−0.401063	+	3.44963i	−0.401063	+	3.44963i
$927$		0			0
$928$	0.529980	+	0.811194i	0.529980	+	0.811194i
$929$		0			0		0.159156	−	0.987253i	$-0.449123\pi$
$929$		0			0		−0.159156	+	0.987253i	$0.550877\pi$
$930$		0			0
$931$		0			0
$932$	0.572685	+	2.76923i	0.572685	+	2.76923i
$933$		0			0
$934$		0			0
$935$		0			0
$936$		0			0
$937$		0			0		−0.999757	−	0.0220445i	$-0.992982\pi$
$937$		0			0		0.999757	+	0.0220445i	$0.00701754\pi$
$938$	−0.533778	+	0.424987i	−0.533778	+	0.424987i
$939$		0			0
$940$		0			0
$941$		0			0		−0.828009	−	0.560715i	$-0.810526\pi$
$941$		0			0		0.828009	+	0.560715i	$0.189474\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	0.0844724	+	0.367430i	0.0844724	+	0.367430i
$947$	0.394576	−	1.26153i	0.394576	−	1.26153i	−0.518970	−	0.854793i	$-0.673684\pi$
$947$	0.394576	−	1.26153i	0.394576	−	1.26153i	0.913545	−	0.406737i	$-0.133333\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−0.0299052	+	1.80847i	−0.0299052	+	1.80847i	0.411766	+	0.911290i	$0.364912\pi$
$953$	−0.0299052	+	1.80847i	−0.0299052	+	1.80847i	−0.441671	+	0.897177i	$0.645614\pi$
$954$	−3.37025	−	0.373019i	−3.37025	−	0.373019i
$955$		0			0
$956$	−2.67429	+	2.54481i	−2.67429	+	2.54481i
$957$		0			0
$958$		0			0
$959$	0.266034	+	1.54186i	0.266034	+	1.54186i
$960$		0			0
$961$	−0.879474	−	0.475947i	−0.879474	−	0.475947i
$962$		0			0
$963$	−1.78848	+	0.0591655i	−1.78848	+	0.0591655i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	1.21027	−	0.571138i	1.21027	−	0.571138i	0.287976	−	0.957638i	$-0.407018\pi$
$967$	1.21027	−	0.571138i	1.21027	−	0.571138i	0.922290	+	0.386499i	$0.126316\pi$
$968$	−1.13762	+	1.70003i	−1.13762	+	1.70003i
$969$		0			0
$970$		0			0
$971$		0			0		−0.148264	−	0.988948i	$-0.547368\pi$
$971$		0			0		0.148264	+	0.988948i	$0.452632\pi$
$972$		0			0
$973$		0			0
$974$	3.39998	−	0.490582i	3.39998	−	0.490582i
$975$		0			0
$976$		0			0
$977$	0.739958	−	0.878565i	0.739958	−	0.878565i	−0.256156	−	0.966635i	$-0.582456\pi$
$977$	0.739958	−	0.878565i	0.739958	−	0.878565i	0.996114	+	0.0880708i	$0.0280702\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	0.00705337	−	0.0323069i	0.00705337	−	0.0323069i
$982$	0.114016	+	0.394880i	0.114016	+	0.394880i
$983$		0			0		0.899598	−	0.436719i	$-0.143860\pi$
$983$		0			0		−0.899598	+	0.436719i	$0.856140\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.90648	−	2.31491i	−1.90648	−	2.31491i
$990$		0			0
$991$	−0.701233	+	0.00773009i	−0.701233	+	0.00773009i	−0.360939	−	0.932589i	$-0.617544\pi$
$991$	−0.701233	+	0.00773009i	−0.701233	+	0.00773009i	−0.340293	+	0.940319i	$0.610526\pi$
$992$		0			0
$993$		0			0
$994$	−2.37814	−	1.18706i	−2.37814	−	1.18706i
$995$		0			0
$996$		0			0
$997$		0			0		−0.938430	−	0.345471i	$-0.887719\pi$
$997$		0			0		0.938430	+	0.345471i	$0.112281\pi$
$998$	0.0575320	+	0.947784i	0.0575320	+	0.947784i
$999$		0			0

Introduction	Features
Universe	News

Level:	\( N \)	=	\( 3997 = 7 \cdot 571 \)
Weight:	\( k \)	=	\( 1 \)
Character orbit:	\([\chi]\)	=	3997.cz (of order \(570\) and degree \(144\))

\(f(q)\)	\(=\)	\(q+(0.341150 - 1.74650i) q^{2} +(-2.00737 - 0.815325i) q^{4} +(-0.461341 + 0.887223i) q^{7} +(-1.13548 + 1.73798i) q^{8} +(-0.739446 - 0.673216i) q^{9} +O(q^{10})\)	\(q+(0.341150 - 1.74650i) q^{2} +(-2.00737 - 0.815325i) q^{4} +(-0.461341 + 0.887223i) q^{7} +(-1.13548 + 1.73798i) q^{8} +(-0.739446 - 0.673216i) q^{9} +(-0.000667889 + 0.121178i) q^{11} +(1.39215 + 1.10841i) q^{14} +(1.09501 + 1.06524i) q^{16} +(-1.42803 + 1.06177i) q^{18} +(0.211410 + 0.0425064i) q^{22} +(-1.65560 + 0.448511i) q^{23} +(-0.795863 - 0.605477i) q^{25} +(1.64946 - 1.40485i) q^{28} +(-0.0415578 + 1.50764i) q^{29} +(0.527965 - 0.366083i) q^{32} +(0.935454 + 1.95429i) q^{36} +(-0.977928 - 0.0756090i) q^{37} +(0.719909 + 1.59325i) q^{43} +(0.100140 - 0.242706i) q^{44} +(0.218515 + 3.04452i) q^{46} +(-0.574329 - 0.818625i) q^{49} +(-1.32897 + 1.18341i) q^{50} +(1.39478 + 1.29826i) q^{53} +(-1.01813 - 1.80923i) q^{56} +(2.61891 + 0.586912i) q^{58} +(0.938430 - 0.345471i) q^{63} +(0.154412 + 0.352023i) q^{64} +(-0.0859078 + 0.373673i) q^{67} +(-1.46100 + 0.310546i) q^{71} +(2.00967 - 0.520720i) q^{72} +(-0.465671 + 1.68216i) q^{74} +(-0.107204 - 0.0564971i) q^{77} +(-1.77781 - 0.863058i) q^{79} +(0.0935596 + 0.995614i) q^{81} +(3.02821 - 0.713782i) q^{86} +(-0.209848 - 0.138757i) q^{88} +(3.68910 + 0.449525i) q^{92} +(-1.62566 + 0.723790i) q^{98} +(0.0820731 - 0.0891552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144q + q^{2} + 5q^{4} + 2q^{7} + 21q^{8} - q^{9} + O(q^{10}) \)	\( 144q + q^{2} + 5q^{4} + 2q^{7} + 21q^{8} - q^{9} + 6q^{11} + q^{14} + 6q^{16} - 9q^{18} + 21q^{22} + 3q^{23} - q^{25} - 10q^{28} - 4q^{29} - 5q^{32} - 2q^{37} - 9q^{43} - 20q^{44} - 34q^{46} + 2q^{49} - 2q^{50} + 6q^{53} - 8q^{56} - q^{58} - q^{63} + 11q^{64} + 20q^{67} + 3q^{71} + 23q^{72} - 31q^{74} + q^{77} + 6q^{79} - q^{81} + 7q^{86} - 9q^{88} + 9q^{92} + 6q^{98} - 2q^{99} + O(q^{100}) \)

\(n\)	\(1716\)	\(2285\)
\(\chi(n)\)	\(e\left(\frac{176}{285}\right)\)	\(-1\)

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