LMFDB - Embedded newform 570.2.m.b.493.2

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.m (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
Defining polynomial:	$x^{20} + 108 x^{16} + 1318 x^{12} + 4652 x^{8} + 5057 x^{4} + 256$
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{9} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.2
Root			$2.20512 + 2.20512i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.b.37.2

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.114611 + 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 + 1.40368i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.114611 + 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 + 1.40368i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.49802 - 1.66010i) q^{10} -5.29298 q^{11} +(0.707107 + 0.707107i) q^{12} +(-1.91968 + 1.91968i) q^{13} +1.98511 q^{14} +(1.66010 + 1.49802i) q^{15} -1.00000 q^{16} +(0.488117 - 0.488117i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-2.44789 + 3.60663i) q^{19} +(-2.23313 + 0.114611i) q^{20} +1.98511i q^{21} +(3.74270 + 3.74270i) q^{22} +(-3.88930 - 3.88930i) q^{23} -1.00000i q^{24} +(-4.97373 + 0.511883i) q^{25} +2.71483 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.40368 - 1.40368i) q^{28} -6.19060 q^{29} +(-0.114611 - 2.23313i) q^{30} -7.84986i q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.74270 + 3.74270i) q^{33} -0.690302 q^{34} +(-3.29548 - 2.97373i) q^{35} +1.00000 q^{36} +(5.60602 + 5.60602i) q^{37} +(4.28120 - 0.819353i) q^{38} +2.71483i q^{39} +(1.66010 + 1.49802i) q^{40} +1.90599i q^{41} +(1.40368 - 1.40368i) q^{42} +(7.12884 + 7.12884i) q^{43} -5.29298i q^{44} +(2.23313 - 0.114611i) q^{45} +5.50029i q^{46} +(-7.86994 + 7.86994i) q^{47} +(-0.707107 + 0.707107i) q^{48} +3.05934i q^{49} +(3.87891 + 3.15500i) q^{50} -0.690302i q^{51} +(-1.91968 - 1.91968i) q^{52} +(8.93991 - 8.93991i) q^{53} +1.00000i q^{54} +(-0.606635 - 11.8199i) q^{55} +1.98511i q^{56} +(0.819353 + 4.28120i) q^{57} +(4.37741 + 4.37741i) q^{58} -0.611185 q^{59} +(-1.49802 + 1.66010i) q^{60} +8.31021 q^{61} +(-5.55069 + 5.55069i) q^{62} +(1.40368 + 1.40368i) q^{63} -1.00000i q^{64} +(-4.50690 - 4.06687i) q^{65} +5.29298 q^{66} +(10.2011 + 10.2011i) q^{67} +(0.488117 + 0.488117i) q^{68} -5.50029 q^{69} +(0.227516 + 4.43300i) q^{70} -3.97022i q^{71} +(-0.707107 - 0.707107i) q^{72} +(7.72265 + 7.72265i) q^{73} -7.92810i q^{74} +(-3.15500 + 3.87891i) q^{75} +(-3.60663 - 2.44789i) q^{76} +(7.42967 - 7.42967i) q^{77} +(1.91968 - 1.91968i) q^{78} -17.1528 q^{79} +(-0.114611 - 2.23313i) q^{80} -1.00000 q^{81} +(1.34774 - 1.34774i) q^{82} +(5.43217 + 5.43217i) q^{83} -1.98511 q^{84} +(1.14597 + 1.03408i) q^{85} -10.0817i q^{86} +(-4.37741 + 4.37741i) q^{87} +(-3.74270 + 3.74270i) q^{88} +5.42118 q^{89} +(-1.66010 - 1.49802i) q^{90} -5.38924i q^{91} +(3.88930 - 3.88930i) q^{92} +(-5.55069 - 5.55069i) q^{93} +11.1298 q^{94} +(-8.33464 - 5.05310i) q^{95} +1.00000 q^{96} +(-3.10415 - 3.10415i) q^{97} +(2.16328 - 2.16328i) q^{98} +5.29298i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) $	$ 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$			1.00000i			0.500000i
$5$	0.114611	+	2.23313i	0.0512557	+	0.998686i
$5$	0.114611	+	2.23313i	0.0512557	+	0.998686i
$6$	−1.00000			−0.408248
$7$	−1.40368	+	1.40368i	−0.530543	+	0.530543i	−0.920734	−	0.390191i	$-0.872409\pi$
$7$	−1.40368	+	1.40368i	−0.530543	+	0.530543i	0.390191	+	0.920734i	$0.372409\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	1.49802	−	1.66010i	0.473715	−	0.524971i
$11$	−5.29298			−1.59589			−0.797947	−	0.602728i	$-0.794080\pi$
$11$	−5.29298			−1.59589			−0.797947	+	0.602728i	$0.794080\pi$
$12$	0.707107	+	0.707107i	0.204124	+	0.204124i
$13$	−1.91968	+	1.91968i	−0.532423	+	0.532423i	−0.921293	−	0.388870i	$-0.872866\pi$
$13$	−1.91968	+	1.91968i	−0.532423	+	0.532423i	0.388870	+	0.921293i	$0.372866\pi$
$14$	1.98511			0.530543
$15$	1.66010	+	1.49802i	0.428637	+	0.386787i
$16$	−1.00000			−0.250000
$17$	0.488117	−	0.488117i	0.118386	−	0.118386i	−0.645432	−	0.763818i	$-0.723323\pi$
$17$	0.488117	−	0.488117i	0.118386	−	0.118386i	0.763818	+	0.645432i	$0.223323\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−2.44789	+	3.60663i	−0.561585	+	0.827419i
$19$	−2.44789	+	3.60663i	−0.561585	+	0.827419i
$20$	−2.23313	+	0.114611i	−0.499343	+	0.0256278i
$21$			1.98511i			0.433186i
$22$	3.74270	+	3.74270i	0.797947	+	0.797947i
$23$	−3.88930	−	3.88930i	−0.810974	−	0.810974i	0.173806	−	0.984780i	$-0.444393\pi$
$23$	−3.88930	−	3.88930i	−0.810974	−	0.810974i	−0.984780	+	0.173806i	$0.944393\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−4.97373	+	0.511883i	−0.994746	+	0.102377i
$26$	2.71483			0.532423
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	−1.40368	−	1.40368i	−0.265271	−	0.265271i
$29$	−6.19060			−1.14956			−0.574782	−	0.818306i	$-0.694913\pi$
$29$	−6.19060			−1.14956			−0.574782	+	0.818306i	$0.694913\pi$
$30$	−0.114611	−	2.23313i	−0.0209250	−	0.407712i
$31$		−	7.84986i		−	1.40988i	−0.709268	−	0.704938i	$-0.750975\pi$
$31$		−	7.84986i		−	1.40988i	0.709268	−	0.704938i	$-0.249025\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−3.74270	+	3.74270i	−0.651521	+	0.651521i
$34$	−0.690302			−0.118386
$35$	−3.29548	−	2.97373i	−0.557039	−	0.502652i
$36$	1.00000			0.166667
$37$	5.60602	+	5.60602i	0.921623	+	0.921623i	0.997144	−	0.0755209i	$-0.0240620\pi$
$37$	5.60602	+	5.60602i	0.921623	+	0.921623i	−0.0755209	+	0.997144i	$0.524062\pi$
$38$	4.28120	−	0.819353i	0.694502	−	0.132917i
$39$			2.71483i			0.434721i
$40$	1.66010	+	1.49802i	0.262485	+	0.236857i
$41$			1.90599i			0.297666i	0.988862	+	0.148833i	$0.0475517\pi$
$41$			1.90599i			0.297666i	−0.988862	+	0.148833i	$0.952448\pi$
$42$	1.40368	−	1.40368i	0.216593	−	0.216593i
$43$	7.12884	+	7.12884i	1.08714	+	1.08714i	0.995822	+	0.0913152i	$0.0291071\pi$
$43$	7.12884	+	7.12884i	1.08714	+	1.08714i	0.0913152	+	0.995822i	$0.470893\pi$
$44$		−	5.29298i		−	0.797947i
$45$	2.23313	−	0.114611i	0.332895	−	0.0170852i
$46$			5.50029i			0.810974i
$47$	−7.86994	+	7.86994i	−1.14795	+	1.14795i	−0.160993	+	0.986955i	$0.551470\pi$
$47$	−7.86994	+	7.86994i	−1.14795	+	1.14795i	−0.986955	+	0.160993i	$0.948530\pi$
$48$	−0.707107	+	0.707107i	−0.102062	+	0.102062i
$49$			3.05934i			0.437049i
$50$	3.87891	+	3.15500i	0.548561	+	0.446185i
$51$		−	0.690302i		−	0.0966616i
$52$	−1.91968	−	1.91968i	−0.266211	−	0.266211i
$53$	8.93991	−	8.93991i	1.22799	−	1.22799i	0.263268	−	0.964723i	$-0.415200\pi$
$53$	8.93991	−	8.93991i	1.22799	−	1.22799i	0.964723	−	0.263268i	$-0.0848003\pi$
$54$			1.00000i			0.136083i
$55$	−0.606635	−	11.8199i	−0.0817986	−	1.59380i
$56$			1.98511i			0.265271i
$57$	0.819353	+	4.28120i	0.108526	+	0.567059i
$58$	4.37741	+	4.37741i	0.574782	+	0.574782i
$59$	−0.611185			−0.0795696			−0.0397848	−	0.999208i	$-0.512667\pi$
$59$	−0.611185			−0.0795696			−0.0397848	+	0.999208i	$0.512667\pi$
$60$	−1.49802	+	1.66010i	−0.193393	+	0.214318i
$61$	8.31021			1.06401			0.532007	−	0.846740i	$-0.321438\pi$
$61$	8.31021			1.06401			0.532007	+	0.846740i	$0.321438\pi$
$62$	−5.55069	+	5.55069i	−0.704938	+	0.704938i
$63$	1.40368	+	1.40368i	0.176848	+	0.176848i
$64$		−	1.00000i		−	0.125000i
$65$	−4.50690	−	4.06687i	−0.559013	−	0.504433i
$66$	5.29298			0.651521
$67$	10.2011	+	10.2011i	1.24626	+	1.24626i	0.957358	+	0.288905i	$0.0932913\pi$
$67$	10.2011	+	10.2011i	1.24626	+	1.24626i	0.288905	+	0.957358i	$0.406709\pi$
$68$	0.488117	+	0.488117i	0.0591929	+	0.0591929i
$69$	−5.50029			−0.662158
$70$	0.227516	+	4.43300i	0.0271933	+	0.529845i
$71$		−	3.97022i		−	0.471178i	−0.971853	−	0.235589i	$-0.924298\pi$
$71$		−	3.97022i		−	0.471178i	0.971853	−	0.235589i	$-0.0757019\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	7.72265	+	7.72265i	0.903867	+	0.903867i	0.995768	−	0.0919007i	$-0.0292942\pi$
$73$	7.72265	+	7.72265i	0.903867	+	0.903867i	−0.0919007	+	0.995768i	$0.529294\pi$
$74$		−	7.92810i		−	0.921623i
$75$	−3.15500	+	3.87891i	−0.364308	+	0.447898i
$76$	−3.60663	−	2.44789i	−0.413709	−	0.280793i
$77$	7.42967	−	7.42967i	0.846689	−	0.846689i
$78$	1.91968	−	1.91968i	0.217361	−	0.217361i
$79$	−17.1528			−1.92984			−0.964918	−	0.262550i	$-0.915437\pi$
$79$	−17.1528			−1.92984			−0.964918	+	0.262550i	$0.915437\pi$
$80$	−0.114611	−	2.23313i	−0.0128139	−	0.249671i
$81$	−1.00000			−0.111111
$82$	1.34774	−	1.34774i	0.148833	−	0.148833i
$83$	5.43217	+	5.43217i	0.596258	+	0.596258i	0.939315	−	0.343056i	$-0.111462\pi$
$83$	5.43217	+	5.43217i	0.596258	+	0.596258i	−0.343056	+	0.939315i	$0.611462\pi$
$84$	−1.98511			−0.216593
$85$	1.14597	+	1.03408i	0.124298	+	0.112162i
$86$		−	10.0817i		−	1.08714i
$87$	−4.37741	+	4.37741i	−0.469308	+	0.469308i
$88$	−3.74270	+	3.74270i	−0.398973	+	0.398973i
$89$	5.42118			0.574644			0.287322	−	0.957834i	$-0.407235\pi$
$89$	5.42118			0.574644			0.287322	+	0.957834i	$0.407235\pi$
$90$	−1.66010	−	1.49802i	−0.174990	−	0.157905i
$91$		−	5.38924i		−	0.564946i
$92$	3.88930	−	3.88930i	0.405487	−	0.405487i
$93$	−5.55069	−	5.55069i	−0.575580	−	0.575580i
$94$	11.1298			1.14795
$95$	−8.33464	−	5.05310i	−0.855116	−	0.518437i
$96$	1.00000			0.102062
$97$	−3.10415	−	3.10415i	−0.315178	−	0.315178i	0.531734	−	0.846912i	$-0.321541\pi$
$97$	−3.10415	−	3.10415i	−0.315178	−	0.315178i	−0.846912	+	0.531734i	$0.821541\pi$
$98$	2.16328	−	2.16328i	0.218525	−	0.218525i
$99$			5.29298i			0.531964i
$100$	−0.511883	−	4.97373i	−0.0511883	−	0.497373i
$101$	−2.79454			−0.278067			−0.139034	−	0.990288i	$-0.544400\pi$
$101$	−2.79454			−0.278067			−0.139034	+	0.990288i	$0.544400\pi$
$102$	−0.488117	+	0.488117i	−0.0483308	+	0.0483308i
$103$	−4.05319	+	4.05319i	−0.399372	+	0.399372i	−0.878012	−	0.478639i	$-0.841130\pi$
$103$	−4.05319	+	4.05319i	−0.399372	+	0.399372i	0.478639	+	0.878012i	$0.341130\pi$
$104$			2.71483i			0.266211i
$105$	−4.43300	+	0.227516i	−0.432617	+	0.0222033i
$106$	−12.6429			−1.22799
$107$	−7.04015	−	7.04015i	−0.680597	−	0.680597i	0.279537	−	0.960135i	$-0.409819\pi$
$107$	−7.04015	−	7.04015i	−0.680597	−	0.680597i	−0.960135	+	0.279537i	$0.909819\pi$
$108$	0.707107	−	0.707107i	0.0680414	−	0.0680414i
$109$	−8.64011			−0.827573			−0.413786	−	0.910374i	$-0.635794\pi$
$109$	−8.64011			−0.827573			−0.413786	+	0.910374i	$0.635794\pi$
$110$	−7.92898	+	8.78689i	−0.755998	+	0.837797i
$111$	7.92810			0.752502
$112$	1.40368	−	1.40368i	0.132636	−	0.132636i
$113$	−6.47280	+	6.47280i	−0.608910	+	0.608910i	−0.942661	−	0.333751i	$-0.891685\pi$
$113$	−6.47280	+	6.47280i	−0.608910	+	0.608910i	0.333751	+	0.942661i	$0.391685\pi$
$114$	2.44789	−	3.60663i	0.229266	−	0.337792i
$115$	8.23954	−	9.13105i	0.768341	−	0.851475i
$116$		−	6.19060i		−	0.574782i
$117$	1.91968	+	1.91968i	0.177474	+	0.177474i
$118$	0.432173	+	0.432173i	0.0397848	+	0.0397848i
$119$			1.37032i			0.125617i
$120$	2.23313	−	0.114611i	0.203856	−	0.0104625i
$121$	17.0156			1.54688
$122$	−5.87621	−	5.87621i	−0.532007	−	0.532007i
$123$	1.34774	+	1.34774i	0.121522	+	0.121522i
$124$	7.84986			0.704938
$125$	−1.71315	−	11.0483i	−0.153228	−	0.988191i
$126$		−	1.98511i		−	0.176848i
$127$	−1.33748	−	1.33748i	−0.118683	−	0.118683i	0.645271	−	0.763954i	$-0.276744\pi$
$127$	−1.33748	−	1.33748i	−0.118683	−	0.118683i	−0.763954	+	0.645271i	$0.776744\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	10.0817			0.887644
$130$	0.311150	+	6.06257i	0.0272897	+	0.531723i
$131$	5.33670			0.466269			0.233135	−	0.972444i	$-0.425102\pi$
$131$	5.33670			0.466269			0.233135	+	0.972444i	$0.425102\pi$
$132$	−3.74270	−	3.74270i	−0.325760	−	0.325760i
$133$	−1.62650	−	8.49864i	−0.141036	−	0.736926i
$134$		−	14.4265i		−	1.24626i
$135$	1.49802	−	1.66010i	0.128929	−	0.142879i
$136$		−	0.690302i		−	0.0591929i
$137$	−2.97373	+	2.97373i	−0.254063	+	0.254063i	−0.822634	−	0.568571i	$-0.807496\pi$
$137$	−2.97373	+	2.97373i	−0.254063	+	0.254063i	0.568571	+	0.822634i	$0.307496\pi$
$138$	3.88930	+	3.88930i	0.331079	+	0.331079i
$139$		−	13.8993i		−	1.17892i	−0.807796	−	0.589462i	$-0.799340\pi$
$139$		−	13.8993i		−	1.17892i	0.807796	−	0.589462i	$-0.200660\pi$
$140$	2.97373	−	3.29548i	0.251326	−	0.278519i
$141$			11.1298i			0.937296i
$142$	−2.80737	+	2.80737i	−0.235589	+	0.235589i
$143$	10.1608	−	10.1608i	0.849690	−	0.849690i
$144$			1.00000i			0.0833333i
$145$	−0.709511	−	13.8244i	−0.0589217	−	1.14805i
$146$		−	10.9215i		−	0.903867i
$147$	2.16328	+	2.16328i	0.178425	+	0.178425i
$148$	−5.60602	+	5.60602i	−0.460812	+	0.460812i
$149$			12.9453i			1.06052i	0.847834	+	0.530262i	$0.177906\pi$
$149$			12.9453i			1.06052i	−0.847834	+	0.530262i	$0.822094\pi$
$150$	4.97373	−	0.511883i	0.406103	−	0.0417951i
$151$		−	21.7518i		−	1.77013i	−0.465465	−	0.885066i	$-0.654113\pi$
$151$		−	21.7518i		−	1.77013i	0.465465	−	0.885066i	$-0.345887\pi$
$152$	0.819353	+	4.28120i	0.0664583	+	0.347251i
$153$	−0.488117	−	0.488117i	−0.0394619	−	0.0394619i
$154$	−10.5071			−0.846689
$155$	17.5298	−	0.899682i	1.40802	−	0.0722642i
$156$	−2.71483			−0.217361
$157$	2.34642	−	2.34642i	0.187264	−	0.187264i	−0.607248	−	0.794512i	$-0.707727\pi$
$157$	2.34642	−	2.34642i	0.187264	−	0.187264i	0.794512	+	0.607248i	$0.207727\pi$
$158$	12.1288	+	12.1288i	0.964918	+	0.964918i
$159$		−	12.6429i		−	1.00265i
$160$	−1.49802	+	1.66010i	−0.118429	+	0.131243i
$161$	10.9187			0.860513
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−14.1411	−	14.1411i	−1.10761	−	1.10761i	−0.993464	−	0.114150i	$-0.963586\pi$
$163$	−14.1411	−	14.1411i	−1.10761	−	1.10761i	−0.114150	−	0.993464i	$-0.536414\pi$
$164$	−1.90599			−0.148833
$165$	−8.78689	−	7.92898i	−0.684058	−	0.617270i
$166$		−	7.68225i		−	0.596258i
$167$	9.19018	+	9.19018i	0.711157	+	0.711157i	0.966777	−	0.255620i	$-0.0822797\pi$
$167$	9.19018	+	9.19018i	0.711157	+	0.711157i	−0.255620	+	0.966777i	$0.582280\pi$
$168$	1.40368	+	1.40368i	0.108297	+	0.108297i
$169$			5.62968i			0.433052i
$170$	−0.0791163	−	1.54153i	−0.00606794	−	0.118230i
$171$	3.60663	+	2.44789i	0.275806	+	0.187195i
$172$	−7.12884	+	7.12884i	−0.543569	+	0.543569i
$173$	2.10806	−	2.10806i	0.160273	−	0.160273i	−0.622415	−	0.782688i	$-0.713848\pi$
$173$	2.10806	−	2.10806i	0.160273	−	0.160273i	0.782688	+	0.622415i	$0.213848\pi$
$174$	6.19060			0.469308
$175$	6.26302	−	7.70006i	0.473440	−	0.582070i
$176$	5.29298			0.398973
$177$	−0.432173	+	0.432173i	−0.0324841	+	0.0324841i
$178$	−3.83335	−	3.83335i	−0.287322	−	0.287322i
$179$	−7.93836			−0.593341			−0.296670	−	0.954980i	$-0.595876\pi$
$179$	−7.93836			−0.593341			−0.296670	+	0.954980i	$0.595876\pi$
$180$	0.114611	+	2.23313i	0.00854261	+	0.166448i
$181$			4.77157i			0.354668i	0.984151	+	0.177334i	$0.0567473\pi$
$181$			4.77157i			0.354668i	−0.984151	+	0.177334i	$0.943253\pi$
$182$	−3.81077	+	3.81077i	−0.282473	+	0.282473i
$183$	5.87621	−	5.87621i	0.434382	−	0.434382i
$184$	−5.50029			−0.405487
$185$	−11.8764	+	13.1615i	−0.873173	+	0.967650i
$186$			7.84986i			0.575580i
$187$	−2.58359	+	2.58359i	−0.188931	+	0.188931i
$188$	−7.86994	−	7.86994i	−0.573974	−	0.573974i
$189$	1.98511			0.144395
$190$	2.32039	+	9.46656i	0.168339	+	0.686776i
$191$	−13.8711			−1.00368			−0.501840	−	0.864961i	$-0.667343\pi$
$191$	−13.8711			−1.00368			−0.501840	+	0.864961i	$0.667343\pi$
$192$	−0.707107	−	0.707107i	−0.0510310	−	0.0510310i
$193$	−8.22061	+	8.22061i	−0.591733	+	0.591733i	−0.938099	−	0.346367i	$-0.887415\pi$
$193$	−8.22061	+	8.22061i	−0.591733	+	0.591733i	0.346367	+	0.938099i	$0.387415\pi$
$194$			4.38992i			0.315178i
$195$	−6.06257	+	0.311150i	−0.434150	+	0.0222819i
$196$	−3.05934			−0.218525
$197$	−0.844893	+	0.844893i	−0.0601961	+	0.0601961i	−0.736564	−	0.676368i	$-0.763553\pi$
$197$	−0.844893	+	0.844893i	−0.0601961	+	0.0601961i	0.676368	+	0.736564i	$0.263553\pi$
$198$	3.74270	−	3.74270i	0.265982	−	0.265982i
$199$			17.2265i			1.22116i	0.791956	+	0.610578i	$0.209063\pi$
$199$			17.2265i			1.22116i	−0.791956	+	0.610578i	$0.790937\pi$
$200$	−3.15500	+	3.87891i	−0.223092	+	0.274281i
$201$	14.4265			1.01757
$202$	1.97604	+	1.97604i	0.139034	+	0.139034i
$203$	8.68964	−	8.68964i	0.609893	−	0.609893i
$204$	0.690302			0.0483308
$205$	−4.25633	+	0.218448i	−0.297275	+	0.0152571i
$206$	5.73207			0.399372
$207$	−3.88930	+	3.88930i	−0.270325	+	0.270325i
$208$	1.91968	−	1.91968i	0.133106	−	0.133106i
$209$	12.9567	−	19.0898i	0.896230	−	1.32047i
$210$	3.29548	+	2.97373i	0.227410	+	0.205207i
$211$			7.30842i			0.503132i	0.967840	+	0.251566i	$0.0809456\pi$
$211$			7.30842i			0.503132i	−0.967840	+	0.251566i	$0.919054\pi$
$212$	8.93991	+	8.93991i	0.613995	+	0.613995i
$213$	−2.80737	−	2.80737i	−0.192358	−	0.192358i
$214$			9.95628i			0.680597i
$215$	−15.1026	+	16.7367i	−1.02999	+	1.14143i
$216$	−1.00000			−0.0680414
$217$	11.0187	+	11.0187i	0.748000	+	0.748000i
$218$	6.10948	+	6.10948i	0.413786	+	0.413786i
$219$	10.9215			0.738005
$220$	11.8199	−	0.606635i	0.796898	−	0.0408993i
$221$			1.87405i			0.126063i
$222$	−5.60602	−	5.60602i	−0.376251	−	0.376251i
$223$	4.27908	−	4.27908i	0.286548	−	0.286548i	−0.549165	−	0.835714i	$-0.685054\pi$
$223$	4.27908	−	4.27908i	0.286548	−	0.286548i	0.835714	+	0.549165i	$0.185054\pi$
$224$	−1.98511			−0.132636
$225$	0.511883	+	4.97373i	0.0341255	+	0.331582i
$226$	9.15392			0.608910
$227$	13.7190	+	13.7190i	0.910561	+	0.910561i	0.996316	−	0.0857552i	$-0.0273303\pi$
$227$	13.7190	+	13.7190i	0.910561	+	0.910561i	−0.0857552	+	0.996316i	$0.527330\pi$
$228$	−4.28120	+	0.819353i	−0.283529	+	0.0542630i
$229$		−	25.2634i		−	1.66945i	−0.550667	−	0.834725i	$-0.685627\pi$
$229$		−	25.2634i		−	1.66945i	0.550667	−	0.834725i	$-0.314373\pi$
$230$	−12.2829	+	0.630395i	−0.809908	+	0.0415670i
$231$		−	10.5071i		−	0.691319i
$232$	−4.37741	+	4.37741i	−0.287391	+	0.287391i
$233$	7.73738	+	7.73738i	0.506892	+	0.506892i	0.913571	−	0.406679i	$-0.133313\pi$
$233$	7.73738	+	7.73738i	0.506892	+	0.506892i	−0.406679	+	0.913571i	$0.633313\pi$
$234$		−	2.71483i		−	0.177474i
$235$	−18.4766	−	16.6726i	−1.20528	−	1.08760i
$236$		−	0.611185i		−	0.0397848i
$237$	−12.1288	+	12.1288i	−0.787853	+	0.787853i
$238$	0.968965	−	0.968965i	0.0628087	−	0.0628087i
$239$		−	11.0820i		−	0.716837i	−0.933561	−	0.358418i	$-0.883316\pi$
$239$		−	11.0820i		−	0.716837i	0.933561	−	0.358418i	$-0.116684\pi$
$240$	−1.66010	−	1.49802i	−0.107159	−	0.0966967i
$241$			14.5158i			0.935043i	0.883982	+	0.467522i	$0.154853\pi$
$241$			14.5158i			0.935043i	−0.883982	+	0.467522i	$0.845147\pi$
$242$	−12.0319	−	12.0319i	−0.773438	−	0.773438i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$			8.31021i			0.532007i
$245$	−6.83191	+	0.350635i	−0.436475	+	0.0224013i
$246$		−	1.90599i		−	0.121522i
$247$	−2.22441	−	11.6227i	−0.141536	−	0.739537i
$248$	−5.55069	−	5.55069i	−0.352469	−	0.352469i
$249$	7.68225			0.486843
$250$	−6.60096	+	9.02371i	−0.417481	+	0.570710i
$251$	6.78199			0.428075			0.214038	−	0.976825i	$-0.431338\pi$
$251$	6.78199			0.428075			0.214038	+	0.976825i	$0.431338\pi$
$252$	−1.40368	+	1.40368i	−0.0884238	+	0.0884238i
$253$	20.5860	+	20.5860i	1.29423	+	1.29423i
$254$			1.89149i			0.118683i
$255$	1.54153	−	0.0791163i	0.0965345	−	0.00495445i
$256$	1.00000			0.0625000
$257$	−13.1118	−	13.1118i	−0.817891	−	0.817891i	0.167911	−	0.985802i	$-0.446298\pi$
$257$	−13.1118	−	13.1118i	−0.817891	−	0.817891i	−0.985802	+	0.167911i	$0.946298\pi$
$258$	−7.12884	−	7.12884i	−0.443822	−	0.443822i
$259$	−15.7381			−0.977921
$260$	4.06687	−	4.50690i	0.252217	−	0.279506i
$261$			6.19060i			0.383188i
$262$	−3.77362	−	3.77362i	−0.233135	−	0.233135i
$263$	8.10698	+	8.10698i	0.499898	+	0.499898i	0.911406	−	0.411508i	$-0.134998\pi$
$263$	8.10698	+	8.10698i	0.499898	+	0.499898i	−0.411508	+	0.911406i	$0.634998\pi$
$264$			5.29298i			0.325760i
$265$	20.9886	+	18.9393i	1.28932	+	1.16343i
$266$	−4.85934	+	7.15956i	−0.297945	+	0.438981i
$267$	3.83335	−	3.83335i	0.234597	−	0.234597i
$268$	−10.2011	+	10.2011i	−0.623132	+	0.623132i
$269$	−16.5207			−1.00729			−0.503644	−	0.863911i	$-0.668008\pi$
$269$	−16.5207			−1.00729			−0.503644	+	0.863911i	$0.668008\pi$
$270$	−2.23313	+	0.114611i	−0.135904	+	0.00697501i
$271$	−1.20001			−0.0728953			−0.0364477	−	0.999336i	$-0.511604\pi$
$271$	−1.20001			−0.0728953			−0.0364477	+	0.999336i	$0.511604\pi$
$272$	−0.488117	+	0.488117i	−0.0295964	+	0.0295964i
$273$	−3.81077	−	3.81077i	−0.230638	−	0.230638i
$274$	4.20549			0.254063
$275$	26.3258	−	2.70939i	1.58751	−	0.163382i
$276$		−	5.50029i		−	0.331079i
$277$	−5.15378	+	5.15378i	−0.309661	+	0.309661i	−0.844778	−	0.535117i	$-0.820268\pi$
$277$	−5.15378	+	5.15378i	−0.309661	+	0.309661i	0.535117	+	0.844778i	$0.320268\pi$
$278$	−9.82829	+	9.82829i	−0.589462	+	0.589462i
$279$	−7.84986			−0.469959
$280$	−4.43300	+	0.227516i	−0.264923	+	0.0135967i
$281$			21.1406i			1.26114i	0.776132	+	0.630570i	$0.217179\pi$
$281$			21.1406i			1.26114i	−0.776132	+	0.630570i	$0.782821\pi$
$282$	7.86994	−	7.86994i	0.468648	−	0.468648i
$283$	−15.7352	−	15.7352i	−0.935358	−	0.935358i	0.0626758	−	0.998034i	$-0.480037\pi$
$283$	−15.7352	−	15.7352i	−0.935358	−	0.935358i	−0.998034	+	0.0626758i	$0.980037\pi$
$284$	3.97022			0.235589
$285$	−9.46656	+	2.32039i	−0.560751	+	0.137448i
$286$	−14.3696			−0.849690
$287$	−2.67541	−	2.67541i	−0.157924	−	0.157924i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$			16.5235i			0.971970i
$290$	−9.27362	+	10.2770i	−0.544566	+	0.603488i
$291$	−4.38992			−0.257342
$292$	−7.72265	+	7.72265i	−0.451934	+	0.451934i
$293$	−11.6988	+	11.6988i	−0.683451	+	0.683451i	−0.960776	−	0.277325i	$-0.910552\pi$
$293$	−11.6988	+	11.6988i	−0.683451	+	0.683451i	0.277325	+	0.960776i	$0.410552\pi$
$294$		−	3.05934i		−	0.178425i
$295$	−0.0700487	−	1.36486i	−0.00407839	−	0.0794650i
$296$	7.92810			0.460812
$297$	3.74270	+	3.74270i	0.217174	+	0.217174i
$298$	9.15374	−	9.15374i	0.530262	−	0.530262i
$299$	14.9324			0.863562
$300$	−3.87891	−	3.15500i	−0.223949	−	0.182154i
$301$	−20.0133			−1.15355
$302$	−15.3808	+	15.3808i	−0.885066	+	0.885066i
$303$	−1.97604	+	1.97604i	−0.113521	+	0.113521i
$304$	2.44789	−	3.60663i	0.140396	−	0.206855i
$305$	0.952444	+	18.5578i	0.0545368	+	1.06262i
$306$			0.690302i			0.0394619i
$307$	13.8361	+	13.8361i	0.789668	+	0.789668i	0.981440	−	0.191772i	$-0.0614233\pi$
$307$	13.8361	+	13.8361i	0.789668	+	0.789668i	−0.191772	+	0.981440i	$0.561423\pi$
$308$	7.42967	+	7.42967i	0.423345	+	0.423345i
$309$			5.73207i			0.326086i
$310$	−13.0316	−	11.7592i	−0.740144	−	0.667880i
$311$	−0.990577			−0.0561705			−0.0280852	−	0.999606i	$-0.508941\pi$
$311$	−0.990577			−0.0561705			−0.0280852	+	0.999606i	$0.508941\pi$
$312$	1.91968	+	1.91968i	0.108680	+	0.108680i
$313$	5.68394	+	5.68394i	0.321275	+	0.321275i	0.849256	−	0.527981i	$-0.177051\pi$
$313$	5.68394	+	5.68394i	0.321275	+	0.321275i	−0.527981	+	0.849256i	$0.677051\pi$
$314$	−3.31834			−0.187264
$315$	−2.97373	+	3.29548i	−0.167551	+	0.185680i
$316$		−	17.1528i		−	0.964918i
$317$	9.63331	+	9.63331i	0.541061	+	0.541061i	0.923840	−	0.382779i	$-0.125033\pi$
$317$	9.63331	+	9.63331i	0.541061	+	0.541061i	−0.382779	+	0.923840i	$0.625033\pi$
$318$	−8.93991	+	8.93991i	−0.501325	+	0.501325i
$319$	32.7667			1.83458
$320$	2.23313	−	0.114611i	0.124836	−	0.00640696i
$321$	−9.95628			−0.555705
$322$	−7.72067	−	7.72067i	−0.430256	−	0.430256i
$323$	0.565601	+	2.95532i	0.0314709	+	0.164438i
$324$		−	1.00000i		−	0.0555556i
$325$	8.56530	−	10.5306i	0.475118	−	0.584133i
$326$			19.9985i			1.10761i
$327$	−6.10948	+	6.10948i	−0.337855	+	0.337855i
$328$	1.34774	+	1.34774i	0.0744165	+	0.0744165i
$329$		−	22.0938i		−	1.21807i
$330$	0.606635	+	11.8199i	0.0333941	+	0.650664i
$331$		−	19.9864i		−	1.09855i	−0.835641	−	0.549276i	$-0.814904\pi$
$331$		−	19.9864i		−	1.09855i	0.835641	−	0.549276i	$-0.185096\pi$
$332$	−5.43217	+	5.43217i	−0.298129	+	0.298129i
$333$	5.60602	−	5.60602i	0.307208	−	0.307208i
$334$		−	12.9969i		−	0.711157i
$335$	−21.6112	+	23.9495i	−1.18075	+	1.30850i
$336$		−	1.98511i		−	0.108297i
$337$	−4.18460	−	4.18460i	−0.227950	−	0.227950i	0.583886	−	0.811836i	$-0.301532\pi$
$337$	−4.18460	−	4.18460i	−0.227950	−	0.227950i	−0.811836	+	0.583886i	$0.801532\pi$
$338$	3.98078	−	3.98078i	0.216526	−	0.216526i
$339$			9.15392i			0.497173i
$340$	−1.03408	+	1.14597i	−0.0560811	+	0.0621490i
$341$			41.5492i			2.25001i
$342$	−0.819353	−	4.28120i	−0.0443055	−	0.231501i
$343$	−14.1201	−	14.1201i	−0.762416	−	0.762416i
$344$	10.0817			0.543569
$345$	−0.630395	−	12.2829i	−0.0339393	−	0.661287i
$346$	−2.98124			−0.160273
$347$	2.65197	−	2.65197i	0.142365	−	0.142365i	−0.632332	−	0.774697i	$-0.717902\pi$
$347$	2.65197	−	2.65197i	0.142365	−	0.142365i	0.774697	+	0.632332i	$0.217902\pi$
$348$	−4.37741	−	4.37741i	−0.234654	−	0.234654i
$349$			17.8125i			0.953481i	0.879044	+	0.476740i	$0.158182\pi$
$349$			17.8125i			0.953481i	−0.879044	+	0.476740i	$0.841818\pi$
$350$	−9.87339	+	1.01614i	−0.527755	+	0.0543151i
$351$	2.71483			0.144907
$352$	−3.74270	−	3.74270i	−0.199487	−	0.199487i
$353$	−11.6167	−	11.6167i	−0.618293	−	0.618293i	0.326801	−	0.945093i	$-0.394029\pi$
$353$	−11.6167	−	11.6167i	−0.618293	−	0.618293i	−0.945093	+	0.326801i	$0.894029\pi$
$354$	0.611185			0.0324841
$355$	8.86601	−	0.455031i	0.470559	−	0.0241506i
$356$			5.42118i			0.287322i
$357$	0.968965	+	0.968965i	0.0512831	+	0.0512831i
$358$	5.61326	+	5.61326i	0.296670	+	0.296670i
$359$			4.76092i			0.251272i	0.992076	+	0.125636i	$0.0400971\pi$
$359$			4.76092i			0.251272i	−0.992076	+	0.125636i	$0.959903\pi$
$360$	1.49802	−	1.66010i	0.0789525	−	0.0874951i
$361$	−7.01563	−	17.6573i	−0.369243	−	0.929333i
$362$	3.37401	−	3.37401i	0.177334	−	0.177334i
$363$	12.0319	−	12.0319i	0.631509	−	0.631509i
$364$	5.38924			0.282473
$365$	−16.3606	+	18.1308i	−0.856351	+	0.949008i
$366$	−8.31021			−0.434382
$367$	12.6008	−	12.6008i	0.657754	−	0.657754i	−0.297094	−	0.954848i	$-0.596018\pi$
$367$	12.6008	−	12.6008i	0.657754	−	0.657754i	0.954848	+	0.297094i	$0.0960176\pi$
$368$	3.88930	+	3.88930i	0.202744	+	0.202744i
$369$	1.90599			0.0992220
$370$	17.7045	−	0.908649i	0.920412	−	0.0472384i
$371$			25.0976i			1.30300i
$372$	5.55069	−	5.55069i	0.287790	−	0.287790i
$373$	6.72967	−	6.72967i	0.348449	−	0.348449i	−0.511083	−	0.859532i	$-0.670755\pi$
$373$	6.72967	−	6.72967i	0.348449	−	0.348449i	0.859532	+	0.511083i	$0.170755\pi$
$374$	3.65375			0.188931
$375$	−9.02371	−	6.60096i	−0.465982	−	0.340872i
$376$			11.1298i			0.573974i
$377$	11.8839	−	11.8839i	0.612054	−	0.612054i
$378$	−1.40368	−	1.40368i	−0.0721977	−	0.0721977i
$379$	−10.5434			−0.541578			−0.270789	−	0.962639i	$-0.587285\pi$
$379$	−10.5434			−0.541578			−0.270789	+	0.962639i	$0.587285\pi$
$380$	5.05310	−	8.33464i	0.259219	−	0.427558i
$381$	−1.89149			−0.0969039
$382$	9.80837	+	9.80837i	0.501840	+	0.501840i
$383$	8.53662	−	8.53662i	0.436201	−	0.436201i	−0.454530	−	0.890731i	$-0.650193\pi$
$383$	8.53662	−	8.53662i	0.436201	−	0.436201i	0.890731	+	0.454530i	$0.150193\pi$
$384$			1.00000i			0.0510310i
$385$	17.4429	+	15.7399i	0.888974	+	0.802179i
$386$	11.6257			0.591733
$387$	7.12884	−	7.12884i	0.362379	−	0.362379i
$388$	3.10415	−	3.10415i	0.157589	−	0.157589i
$389$			25.1180i			1.27353i	0.771056	+	0.636767i	$0.219729\pi$
$389$			25.1180i			1.27353i	−0.771056	+	0.636767i	$0.780271\pi$
$390$	4.50690	+	4.06687i	0.228216	+	0.205934i
$391$	−3.79686			−0.192016
$392$	2.16328	+	2.16328i	0.109262	+	0.109262i
$393$	3.77362	−	3.77362i	0.190354	−	0.190354i
$394$	1.19486			0.0601961
$395$	−1.96590	−	38.3043i	−0.0989151	−	1.92730i
$396$	−5.29298			−0.265982
$397$	10.0839	−	10.0839i	0.506098	−	0.506098i	−0.407228	−	0.913326i	$-0.633505\pi$
$397$	10.0839	−	10.0839i	0.506098	−	0.506098i	0.913326	+	0.407228i	$0.133505\pi$
$398$	12.1810	−	12.1810i	0.610578	−	0.610578i
$399$	−7.15956	−	4.85934i	−0.358426	−	0.243271i
$400$	4.97373	−	0.511883i	0.248686	−	0.0255942i
$401$			1.57077i			0.0784407i	0.999231	+	0.0392203i	$0.0124874\pi$
$401$			1.57077i			0.0784407i	−0.999231	+	0.0392203i	$0.987513\pi$
$402$	−10.2011	−	10.2011i	−0.508785	−	0.508785i
$403$	15.0692	+	15.0692i	0.750651	+	0.750651i
$404$		−	2.79454i		−	0.139034i
$405$	−0.114611	−	2.23313i	−0.00569508	−	0.110965i
$406$	−12.2890			−0.609893
$407$	−29.6725	−	29.6725i	−1.47081	−	1.47081i
$408$	−0.488117	−	0.488117i	−0.0241654	−	0.0241654i
$409$	10.9037			0.539153			0.269576	−	0.962979i	$-0.413116\pi$
$409$	10.9037			0.539153			0.269576	+	0.962979i	$0.413116\pi$
$410$	3.16414	+	2.85521i	0.156266	+	0.141009i
$411$			4.20549i			0.207441i
$412$	−4.05319	−	4.05319i	−0.199686	−	0.199686i
$413$	0.857911	−	0.857911i	0.0422150	−	0.0422150i
$414$	5.50029			0.270325
$415$	−11.5082	+	12.7533i	−0.564913	+	0.626036i
$416$	−2.71483			−0.133106
$417$	−9.82829	−	9.82829i	−0.481293	−	0.481293i
$418$	−22.6603	+	4.33682i	−1.10835	+	0.212121i
$419$			6.93967i			0.339025i	0.985528	+	0.169512i	$0.0542193\pi$
$419$			6.93967i			0.339025i	−0.985528	+	0.169512i	$0.945781\pi$
$420$	−0.227516	−	4.43300i	−0.0111016	−	0.216308i
$421$		−	17.7896i		−	0.867010i	−0.901151	−	0.433505i	$-0.857277\pi$
$421$		−	17.7896i		−	0.867010i	0.901151	−	0.433505i	$-0.142723\pi$
$422$	5.16783	−	5.16783i	0.251566	−	0.251566i
$423$	7.86994	+	7.86994i	0.382650	+	0.382650i
$424$		−	12.6429i		−	0.613995i
$425$	−2.17790	+	2.67762i	−0.105644	+	0.129884i
$426$			3.97022i			0.192358i
$427$	−11.6649	+	11.6649i	−0.564505	+	0.564505i
$428$	7.04015	−	7.04015i	0.340299	−	0.340299i
$429$		−	14.3696i		−	0.693769i
$430$	22.5137	−	1.15548i	1.08571	−	0.0557220i
$431$			35.0344i			1.68755i	0.536697	+	0.843775i	$0.319672\pi$
$431$			35.0344i			1.68755i	−0.536697	+	0.843775i	$0.680328\pi$
$432$	0.707107	+	0.707107i	0.0340207	+	0.0340207i
$433$	14.6222	−	14.6222i	0.702699	−	0.702699i	−0.262290	−	0.964989i	$-0.584478\pi$
$433$	14.6222	−	14.6222i	0.702699	−	0.702699i	0.964989	+	0.262290i	$0.0844778\pi$
$434$		−	15.5828i		−	0.748000i
$435$	−10.2770	−	9.27362i	−0.492746	−	0.444636i
$436$		−	8.64011i		−	0.413786i
$437$	23.5479	−	4.50668i	1.12645	−	0.215584i
$438$	−7.72265	−	7.72265i	−0.369002	−	0.369002i
$439$	−25.2333			−1.20432			−0.602160	−	0.798376i	$-0.705693\pi$
$439$	−25.2333			−1.20432			−0.602160	+	0.798376i	$0.705693\pi$
$440$	−8.78689	−	7.92898i	−0.418899	−	0.377999i
$441$	3.05934			0.145683
$442$	1.32516	−	1.32516i	0.0630313	−	0.0630313i
$443$	−17.3294	−	17.3294i	−0.823344	−	0.823344i	0.163242	−	0.986586i	$-0.447805\pi$
$443$	−17.3294	−	17.3294i	−0.823344	−	0.823344i	−0.986586	+	0.163242i	$0.947805\pi$
$444$			7.92810i			0.376251i
$445$	0.621328	+	12.1062i	0.0294538	+	0.573888i
$446$	−6.05153			−0.286548
$447$	9.15374	+	9.15374i	0.432957	+	0.432957i
$448$	1.40368	+	1.40368i	0.0663178	+	0.0663178i
$449$	20.6855			0.976211			0.488105	−	0.872785i	$-0.337688\pi$
$449$	20.6855			0.976211			0.488105	+	0.872785i	$0.337688\pi$
$450$	3.15500	−	3.87891i	0.148728	−	0.182854i
$451$		−	10.0884i		−	0.475043i
$452$	−6.47280	−	6.47280i	−0.304455	−	0.304455i
$453$	−15.3808	−	15.3808i	−0.722654	−	0.722654i
$454$		−	19.4016i		−	0.910561i
$455$	12.0349	−	0.617667i	0.564203	−	0.0289567i
$456$	3.60663	+	2.44789i	0.168896	+	0.114633i
$457$	−7.86170	+	7.86170i	−0.367755	+	0.367755i	−0.866658	−	0.498903i	$-0.833736\pi$
$457$	−7.86170	+	7.86170i	−0.367755	+	0.367755i	0.498903	+	0.866658i	$0.333736\pi$
$458$	−17.8639	+	17.8639i	−0.834725	+	0.834725i
$459$	−0.690302			−0.0322205
$460$	9.13105	+	8.23954i	0.425738	+	0.384171i
$461$	23.8664			1.11157			0.555784	−	0.831327i	$-0.312418\pi$
$461$	23.8664			1.11157			0.555784	+	0.831327i	$0.312418\pi$
$462$	−7.42967	+	7.42967i	−0.345659	+	0.345659i
$463$	22.3224	+	22.3224i	1.03741	+	1.03741i	0.999273	+	0.0381357i	$0.0121419\pi$
$463$	22.3224	+	22.3224i	1.03741	+	1.03741i	0.0381357	+	0.999273i	$0.487858\pi$
$464$	6.19060			0.287391
$465$	11.7592	−	13.0316i	0.545322	−	0.604325i
$466$		−	10.9423i		−	0.506892i
$467$	20.6661	−	20.6661i	0.956312	−	0.956312i	−0.0427727	−	0.999085i	$-0.513619\pi$
$467$	20.6661	−	20.6661i	0.956312	−	0.956312i	0.999085	+	0.0427727i	$0.0136191\pi$
$468$	−1.91968	+	1.91968i	−0.0887371	+	0.0887371i
$469$	−28.6382			−1.32239
$470$	1.27560	+	24.8542i	0.0588389	+	1.14644i
$471$		−	3.31834i		−	0.152901i
$472$	−0.432173	+	0.432173i	−0.0198924	+	0.0198924i
$473$	−37.7328	−	37.7328i	−1.73495	−	1.73495i
$474$	17.1528			0.787853
$475$	10.3290	−	19.1915i	0.473926	−	0.880564i
$476$	−1.37032			−0.0628087
$477$	−8.93991	−	8.93991i	−0.409330	−	0.409330i
$478$	−7.83618	+	7.83618i	−0.358418	+	0.358418i
$479$			15.9212i			0.727459i	0.931505	+	0.363730i	$0.118497\pi$
$479$			15.9212i			0.727459i	−0.931505	+	0.363730i	$0.881503\pi$
$480$	0.114611	+	2.23313i	0.00523126	+	0.101928i
$481$	−21.5235			−0.981386
$482$	10.2642	−	10.2642i	0.467522	−	0.467522i
$483$	7.72067	−	7.72067i	0.351303	−	0.351303i
$484$			17.0156i			0.773438i
$485$	6.57619	−	7.28773i	0.298609	−	0.330919i
$486$	1.00000			0.0453609
$487$	−10.4874	−	10.4874i	−0.475228	−	0.475228i	0.428374	−	0.903602i	$-0.359087\pi$
$487$	−10.4874	−	10.4874i	−0.475228	−	0.475228i	−0.903602	+	0.428374i	$0.859087\pi$
$488$	5.87621	−	5.87621i	0.266003	−	0.266003i
$489$	−19.9985			−0.904363
$490$	5.07883	+	4.58295i	0.229438	+	0.207037i
$491$	15.8352			0.714633			0.357317	−	0.933983i	$-0.383692\pi$
$491$	15.8352			0.714633			0.357317	+	0.933983i	$0.383692\pi$
$492$	−1.34774	+	1.34774i	−0.0607608	+	0.0607608i
$493$	−3.02173	+	3.02173i	−0.136092	+	0.136092i
$494$	−6.64563	+	9.79141i	−0.299001	+	0.440537i
$495$	−11.8199	+	0.606635i	−0.531265	+	0.0272662i
$496$			7.84986i			0.352469i
$497$	5.57293	+	5.57293i	0.249980	+	0.249980i
$498$	−5.43217	−	5.43217i	−0.243422	−	0.243422i
$499$			21.1108i			0.945050i	0.881317	+	0.472525i	$0.156657\pi$
$499$			21.1108i			0.945050i	−0.881317	+	0.472525i	$0.843343\pi$
$500$	11.0483	−	1.71315i	0.494095	−	0.0766142i
$501$	12.9969			0.580657
$502$	−4.79559	−	4.79559i	−0.214038	−	0.214038i
$503$	11.3484	+	11.3484i	0.506001	+	0.506001i	0.913297	−	0.407295i	$-0.133528\pi$
$503$	11.3484	+	11.3484i	0.506001	+	0.506001i	−0.407295	+	0.913297i	$0.633528\pi$
$504$	1.98511			0.0884238
$505$	−0.320286	−	6.24058i	−0.0142525	−	0.277702i
$506$		−	29.1129i		−	1.29423i
$507$	3.98078	+	3.98078i	0.176793	+	0.176793i
$508$	1.33748	−	1.33748i	0.0593413	−	0.0593413i
$509$	−36.8026			−1.63125			−0.815624	−	0.578582i	$-0.803606\pi$
$509$	−36.8026			−1.63125			−0.815624	+	0.578582i	$0.803606\pi$
$510$	−1.14597	−	1.03408i	−0.0507445	−	0.0457900i
$511$	−21.6803			−0.959080
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.28120	−	0.819353i	0.189020	−	0.0361753i
$514$			18.5429i			0.817891i
$515$	−9.51583	−	8.58674i	−0.419317	−	0.378377i
$516$			10.0817i			0.443822i
$517$	41.6554	−	41.6554i	1.83200	−	1.83200i
$518$	11.1285	+	11.1285i	0.488960	+	0.488960i
$519$		−	2.98124i		−	0.130862i
$520$	−6.06257	+	0.311150i	−0.265861	+	0.0136448i
$521$		−	6.00142i		−	0.262927i	−0.991321	−	0.131463i	$-0.958032\pi$
$521$		−	6.00142i		−	0.262927i	0.991321	−	0.131463i	$-0.0419676\pi$
$522$	4.37741	−	4.37741i	0.191594	−	0.191594i
$523$	−19.4311	+	19.4311i	−0.849664	+	0.849664i	−0.990091	−	0.140427i	$-0.955152\pi$
$523$	−19.4311	+	19.4311i	−0.849664	+	0.849664i	0.140427	+	0.990091i	$0.455152\pi$
$524$			5.33670i			0.233135i
$525$	−1.01614	−	9.87339i	−0.0443481	−	0.430910i
$526$		−	11.4650i		−	0.499898i
$527$	−3.83165	−	3.83165i	−0.166909	−	0.166909i
$528$	3.74270	−	3.74270i	0.162880	−	0.162880i
$529$			7.25324i			0.315358i
$530$	−1.44902	−	28.2333i	−0.0629415	−	1.22638i
$531$			0.611185i			0.0265232i
$532$	8.49864	−	1.62650i	0.368463	−	0.0705179i
$533$	−3.65889	−	3.65889i	−0.158484	−	0.158484i
$534$	−5.42118			−0.234597
$535$	14.9147	−	16.5285i	0.644818	−	0.714587i
$536$	14.4265			0.623132
$537$	−5.61326	+	5.61326i	−0.242230	+	0.242230i
$538$	11.6819	+	11.6819i	0.503644	+	0.503644i
$539$		−	16.1930i		−	0.697484i
$540$	1.66010	+	1.49802i	0.0714395	+	0.0644644i
$541$	19.3859			0.833467			0.416734	−	0.909029i	$-0.363175\pi$
$541$	19.3859			0.833467			0.416734	+	0.909029i	$0.363175\pi$
$542$	0.848534	+	0.848534i	0.0364477	+	0.0364477i
$543$	3.37401	+	3.37401i	0.144793	+	0.144793i
$544$	0.690302			0.0295964
$545$	−0.990253	−	19.2945i	−0.0424178	−	0.826485i
$546$			5.38924i			0.230638i
$547$	6.28887	+	6.28887i	0.268893	+	0.268893i	0.828654	−	0.559761i	$-0.189107\pi$
$547$	6.28887	+	6.28887i	0.268893	+	0.268893i	−0.559761	+	0.828654i	$0.689107\pi$
$548$	−2.97373	−	2.97373i	−0.127031	−	0.127031i
$549$		−	8.31021i		−	0.354671i
$550$	−20.5310	−	16.6994i	−0.875445	−	0.712063i
$551$	15.1539	−	22.3272i	0.645579	−	0.951171i
$552$	−3.88930	+	3.88930i	−0.165539	+	0.165539i
$553$	24.0771	−	24.0771i	1.02386	−	1.02386i
$554$	7.28855			0.309661
$555$	0.908649	+	17.7045i	0.0385700	+	0.751513i
$556$	13.8993			0.589462
$557$	9.88148	−	9.88148i	0.418692	−	0.418692i	−0.466061	−	0.884753i	$-0.654327\pi$
$557$	9.88148	−	9.88148i	0.418692	−	0.418692i	0.884753	+	0.466061i	$0.154327\pi$
$558$	5.55069	+	5.55069i	0.234979	+	0.234979i
$559$	−27.3701			−1.15763
$560$	3.29548	+	2.97373i	0.139260	+	0.125663i
$561$			3.65375i			0.154262i
$562$	14.9486	−	14.9486i	0.630570	−	0.630570i
$563$	−16.7009	+	16.7009i	−0.703858	+	0.703858i	−0.965236	−	0.261379i	$-0.915823\pi$
$563$	−16.7009	+	16.7009i	−0.703858	+	0.703858i	0.261379	+	0.965236i	$0.415823\pi$
$564$	−11.1298			−0.468648
$565$	−15.1965	−	13.7127i	−0.639320	−	0.576900i
$566$			22.2529i			0.935358i
$567$	1.40368	−	1.40368i	0.0589492	−	0.0589492i
$568$	−2.80737	−	2.80737i	−0.117795	−	0.117795i
$569$	1.12910			0.0473344			0.0236672	−	0.999720i	$-0.492466\pi$
$569$	1.12910			0.0473344			0.0236672	+	0.999720i	$0.492466\pi$
$570$	8.33464	+	5.05310i	0.349099	+	0.211651i
$571$	−7.89992			−0.330602			−0.165301	−	0.986243i	$-0.552859\pi$
$571$	−7.89992			−0.330602			−0.165301	+	0.986243i	$0.552859\pi$
$572$	10.1608	+	10.1608i	0.424845	+	0.424845i
$573$	−9.80837	+	9.80837i	−0.409750	+	0.409750i
$574$			3.78360i			0.157924i
$575$	21.3352	+	17.3534i	0.889738	+	0.723688i
$576$	−1.00000			−0.0416667
$577$	−31.1021	+	31.1021i	−1.29480	+	1.29480i	−0.363011	+	0.931785i	$0.618251\pi$
$577$	−31.1021	+	31.1021i	−1.29480	+	1.29480i	−0.931785	+	0.363011i	$0.881749\pi$
$578$	11.6839	−	11.6839i	0.485985	−	0.485985i
$579$			11.6257i			0.483148i
$580$	13.8244	−	0.709511i	0.574027	−	0.0294609i
$581$	−15.2501			−0.632681
$582$	3.10415	+	3.10415i	0.128671	+	0.128671i
$583$	−47.3187	+	47.3187i	−1.95974	+	1.95974i
$584$	10.9215			0.451934
$585$	−4.06687	+	4.50690i	−0.168144	+	0.186338i
$586$	16.5446			0.683451
$587$	−6.49465	+	6.49465i	−0.268063	+	0.268063i	−0.828319	−	0.560256i	$-0.810703\pi$
$587$	−6.49465	+	6.49465i	−0.268063	+	0.268063i	0.560256	+	0.828319i	$0.310703\pi$
$588$	−2.16328	+	2.16328i	−0.0892123	+	0.0892123i
$589$	28.3116	+	19.2156i	1.16656	+	0.791766i
$590$	−0.915567	+	1.01463i	−0.0376933	+	0.0417717i
$591$			1.19486i			0.0491499i
$592$	−5.60602	−	5.60602i	−0.230406	−	0.230406i
$593$	16.2871	+	16.2871i	0.668830	+	0.668830i	0.957445	−	0.288615i	$-0.0931948\pi$
$593$	16.2871	+	16.2871i	0.668830	+	0.668830i	−0.288615	+	0.957445i	$0.593195\pi$
$594$		−	5.29298i		−	0.217174i
$595$	−3.06011	+	0.157054i	−0.125452	+	0.00643860i
$596$	−12.9453			−0.530262
$597$	12.1810	+	12.1810i	0.498535	+	0.498535i
$598$	−10.5588	−	10.5588i	−0.431781	−	0.431781i
$599$	−45.2347			−1.84824			−0.924119	−	0.382104i	$-0.875200\pi$
$599$	−45.2347			−1.84824			−0.924119	+	0.382104i	$0.875200\pi$
$600$	0.511883	+	4.97373i	0.0208975	+	0.203052i
$601$			18.3122i			0.746972i	0.927636	+	0.373486i	$0.121838\pi$
$601$			18.3122i			0.746972i	−0.927636	+	0.373486i	$0.878162\pi$
$602$	14.1515	+	14.1515i	0.576773	+	0.576773i
$603$	10.2011	−	10.2011i	0.415421	−	0.415421i
$604$	21.7518			0.885066
$605$	1.95018	+	37.9981i	0.0792861	+	1.54484i
$606$	2.79454			0.113521
$607$	−17.5130	−	17.5130i	−0.710829	−	0.710829i	0.255879	−	0.966709i	$-0.417635\pi$
$607$	−17.5130	−	17.5130i	−0.710829	−	0.710829i	−0.966709	+	0.255879i	$0.917635\pi$
$608$	−4.28120	+	0.819353i	−0.173626	+	0.0332292i
$609$		−	12.2890i		−	0.497976i
$610$	12.4489	−	13.7958i	0.504039	−	0.558576i
$611$		−	30.2155i		−	1.22239i
$612$	0.488117	−	0.488117i	0.0197310	−	0.0197310i
$613$	2.65427	+	2.65427i	0.107205	+	0.107205i	0.758675	−	0.651470i	$-0.225847\pi$
$613$	2.65427	+	2.65427i	0.107205	+	0.107205i	−0.651470	+	0.758675i	$0.725847\pi$
$614$		−	19.5672i		−	0.789668i
$615$	−2.85521	+	3.16414i	−0.115133	+	0.127591i
$616$		−	10.5071i		−	0.423345i
$617$	6.67261	−	6.67261i	0.268629	−	0.268629i	−0.559919	−	0.828548i	$-0.689168\pi$
$617$	6.67261	−	6.67261i	0.268629	−	0.268629i	0.828548	+	0.559919i	$0.189168\pi$
$618$	4.05319	−	4.05319i	0.163043	−	0.163043i
$619$		−	21.6368i		−	0.869657i	−0.900513	−	0.434829i	$-0.856809\pi$
$619$		−	21.6368i		−	0.869657i	0.900513	−	0.434829i	$-0.143191\pi$
$620$	0.899682	+	17.5298i	0.0361321	+	0.704012i
$621$			5.50029i			0.220719i
$622$	0.700444	+	0.700444i	0.0280852	+	0.0280852i
$623$	−7.60962	+	7.60962i	−0.304873	+	0.304873i
$624$		−	2.71483i		−	0.108680i
$625$	24.4760	−	5.09193i	0.979038	−	0.203677i
$626$		−	8.03830i		−	0.321275i
$627$	−4.33682	−	22.6603i	−0.173196	−	0.904965i
$628$	2.34642	+	2.34642i	0.0936322	+	0.0936322i
$629$	5.47278			0.218214
$630$	4.43300	−	0.227516i	0.176615	−	0.00906444i
$631$	−0.652184			−0.0259631			−0.0129815	−	0.999916i	$-0.504132\pi$
$631$	−0.652184			−0.0259631			−0.0129815	+	0.999916i	$0.504132\pi$
$632$	−12.1288	+	12.1288i	−0.482459	+	0.482459i
$633$	5.16783	+	5.16783i	0.205403	+	0.205403i
$634$		−	13.6236i		−	0.541061i
$635$	2.83349	−	3.14007i	0.112443	−	0.124610i
$636$	12.6429			0.501325
$637$	−5.87295	−	5.87295i	−0.232695	−	0.232695i
$638$	−23.1696	−	23.1696i	−0.917291	−	0.917291i
$639$	−3.97022			−0.157059
$640$	−1.66010	−	1.49802i	−0.0656213	−	0.0592144i
$641$			6.00938i			0.237356i	0.992933	+	0.118678i	$0.0378657\pi$
$641$			6.00938i			0.237356i	−0.992933	+	0.118678i	$0.962134\pi$
$642$	7.04015	+	7.04015i	0.277853	+	0.277853i
$643$	−7.37061	−	7.37061i	−0.290669	−	0.290669i	0.546676	−	0.837344i	$-0.315893\pi$
$643$	−7.37061	−	7.37061i	−0.290669	−	0.290669i	−0.837344	+	0.546676i	$0.815893\pi$
$644$			10.9187i			0.430256i
$645$	1.15548	+	22.5137i	0.0454968	+	0.886477i
$646$	1.68979	−	2.48967i	0.0664837	−	0.0979546i
$647$	6.73802	−	6.73802i	0.264899	−	0.264899i	−0.562142	−	0.827041i	$-0.690023\pi$
$647$	6.73802	−	6.73802i	0.264899	−	0.264899i	0.827041	+	0.562142i	$0.190023\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	3.23499			0.126985
$650$	−13.5028	+	1.38968i	−0.529625	+	0.0545076i
$651$	15.5828			0.610739
$652$	14.1411	−	14.1411i	0.553807	−	0.553807i
$653$	−4.47188	−	4.47188i	−0.174998	−	0.174998i	0.614173	−	0.789171i	$-0.289490\pi$
$653$	−4.47188	−	4.47188i	−0.174998	−	0.174998i	−0.789171	+	0.614173i	$0.789490\pi$
$654$	8.64011			0.337855
$655$	0.611645	+	11.9175i	0.0238990	+	0.465657i
$656$		−	1.90599i		−	0.0744165i
$657$	7.72265	−	7.72265i	0.301289	−	0.301289i
$658$	−15.6227	+	15.6227i	−0.609036	+	0.609036i
$659$	29.4239			1.14619			0.573096	−	0.819489i	$-0.305742\pi$
$659$	29.4239			1.14619			0.573096	+	0.819489i	$0.305742\pi$
$660$	7.92898	−	8.78689i	0.308635	−	0.342029i
$661$		−	18.0453i		−	0.701881i	−0.936398	−	0.350941i	$-0.885862\pi$
$661$		−	18.0453i		−	0.701881i	0.936398	−	0.350941i	$-0.114138\pi$
$662$	−14.1325	+	14.1325i	−0.549276	+	0.549276i
$663$	1.32516	+	1.32516i	0.0514648	+	0.0514648i
$664$	7.68225			0.298129
$665$	18.7921	−	4.60623i	0.728728	−	0.178622i
$666$	−7.92810			−0.307208
$667$	24.0771	+	24.0771i	0.932267	+	0.932267i
$668$	−9.19018	+	9.19018i	−0.355579	+	0.355579i
$669$		−	6.05153i		−	0.233966i
$670$	32.2163	−	1.65344i	1.24462	−	0.0638781i
$671$	−43.9858			−1.69805
$672$	−1.40368	+	1.40368i	−0.0541483	+	0.0541483i
$673$	−8.20956	+	8.20956i	−0.316455	+	0.316455i	−0.847404	−	0.530949i	$-0.821836\pi$
$673$	−8.20956	+	8.20956i	−0.316455	+	0.316455i	0.530949	+	0.847404i	$0.321836\pi$
$674$			5.91793i			0.227950i
$675$	3.87891	+	3.15500i	0.149299	+	0.121436i
$676$	−5.62968			−0.216526
$677$	−24.0239	−	24.0239i	−0.923313	−	0.923313i	0.0739493	−	0.997262i	$-0.476440\pi$
$677$	−24.0239	−	24.0239i	−0.923313	−	0.923313i	−0.997262	+	0.0739493i	$0.976440\pi$
$678$	6.47280	−	6.47280i	0.248586	−	0.248586i
$679$	8.71448			0.334431
$680$	1.54153	−	0.0791163i	0.0591151	−	0.00303397i
$681$	19.4016			0.743470
$682$	29.3797	−	29.3797i	1.12501	−	1.12501i
$683$	−14.5663	+	14.5663i	−0.557363	+	0.557363i	−0.928556	−	0.371192i	$-0.878949\pi$
$683$	−14.5663	+	14.5663i	−0.557363	+	0.557363i	0.371192	+	0.928556i	$0.378949\pi$
$684$	−2.44789	+	3.60663i	−0.0935976	+	0.137903i
$685$	−6.98154	−	6.29990i	−0.266751	−	0.240707i
$686$			19.9689i			0.762416i
$687$	−17.8639	−	17.8639i	−0.681550	−	0.681550i
$688$	−7.12884	−	7.12884i	−0.271784	−	0.271784i
$689$			34.3235i			1.30762i
$690$	−8.23954	+	9.13105i	−0.313674	+	0.347613i
$691$	−39.3797			−1.49807			−0.749037	−	0.662528i	$-0.769483\pi$
$691$	−39.3797			−1.49807			−0.749037	+	0.662528i	$0.769483\pi$
$692$	2.10806	+	2.10806i	0.0801363	+	0.0801363i
$693$	−7.42967	−	7.42967i	−0.282230	−	0.282230i
$694$	−3.75046			−0.142365
$695$	31.0389	−	1.59302i	1.17737	−	0.0604265i
$696$			6.19060i			0.234654i
$697$	0.930347	+	0.930347i	0.0352394	+	0.0352394i
$698$	12.5953	−	12.5953i	0.476740	−	0.476740i
$699$	10.9423			0.413876
$700$	7.70006	+	6.26302i	0.291035	+	0.236720i
$701$	5.40623			0.204190			0.102095	−	0.994775i	$-0.467445\pi$
$701$	5.40623			0.204190			0.102095	+	0.994775i	$0.467445\pi$
$702$	−1.91968	−	1.91968i	−0.0724536	−	0.0724536i
$703$	−33.9418	+	6.49592i	−1.28014	+	0.244998i
$704$			5.29298i			0.199487i
$705$	−24.8542	+	1.27560i	−0.936064	+	0.0480418i
$706$			16.4284i			0.618293i
$707$	3.92266	−	3.92266i	0.147527	−	0.147527i
$708$	−0.432173	−	0.432173i	−0.0162421	−	0.0162421i
$709$		−	10.1007i		−	0.379340i	−0.981848	−	0.189670i	$-0.939258\pi$
$709$		−	10.1007i		−	0.379340i	0.981848	−	0.189670i	$-0.0607418\pi$
$710$	−6.59097	−	5.94746i	−0.247355	−	0.223204i
$711$			17.1528i			0.643279i
$712$	3.83335	−	3.83335i	0.143661	−	0.143661i
$713$	−30.5304	+	30.5304i	−1.14337	+	1.14337i
$714$		−	1.37032i		−	0.0512831i
$715$	23.8549	+	21.5259i	0.892124	+	0.805022i
$716$		−	7.93836i		−	0.296670i
$717$	−7.83618	−	7.83618i	−0.292647	−	0.292647i
$718$	3.36648	−	3.36648i	0.125636	−	0.125636i
$719$			41.4079i			1.54425i	0.635469	+	0.772126i	$0.280807\pi$
$719$			41.4079i			1.54425i	−0.635469	+	0.772126i	$0.719193\pi$
$720$	−2.23313	+	0.114611i	−0.0832238	+	0.00427131i
$721$		−	11.3788i		−	0.423768i
$722$	−7.52482	+	17.4464i	−0.280045	+	0.649288i
$723$	10.2642	+	10.2642i	0.381730	+	0.381730i
$724$	−4.77157			−0.177334
$725$	30.7903	−	3.16886i	1.14352	−	0.117689i
$726$	−17.0156			−0.631509
$727$	16.2887	−	16.2887i	0.604113	−	0.604113i	−0.337288	−	0.941401i	$-0.609510\pi$
$727$	16.2887	−	16.2887i	0.604113	−	0.604113i	0.941401	+	0.337288i	$0.109510\pi$
$728$	−3.81077	−	3.81077i	−0.141236	−	0.141236i
$729$			1.00000i			0.0370370i
$730$	24.3891	−	1.25172i	0.902679	−	0.0463283i
$731$	6.95941			0.257403
$732$	5.87621	+	5.87621i	0.217191	+	0.217191i
$733$	−8.03197	−	8.03197i	−0.296667	−	0.296667i	0.543040	−	0.839707i	$-0.317273\pi$
$733$	−8.03197	−	8.03197i	−0.296667	−	0.296667i	−0.839707	+	0.543040i	$0.817273\pi$
$734$	−17.8202			−0.657754
$735$	−4.58295	+	5.07883i	−0.169045	+	0.187335i
$736$		−	5.50029i		−	0.202744i
$737$	−53.9942	−	53.9942i	−1.98890	−	1.98890i
$738$	−1.34774	−	1.34774i	−0.0496110	−	0.0496110i
$739$		−	2.95079i		−	0.108546i	−0.998526	−	0.0542732i	$-0.982716\pi$
$739$		−	2.95079i		−	0.108546i	0.998526	−	0.0542732i	$-0.0172842\pi$
$740$	−13.1615	−	11.8764i	−0.483825	−	0.436587i
$741$	−9.79141	−	6.64563i	−0.359697	−	0.244133i
$742$	17.7467	−	17.7467i	0.651501	−	0.651501i
$743$	15.8575	−	15.8575i	0.581756	−	0.581756i	−0.353630	−	0.935386i	$-0.615053\pi$
$743$	15.8575	−	15.8575i	0.581756	−	0.581756i	0.935386	+	0.353630i	$0.115053\pi$
$744$	−7.84986			−0.287790
$745$	−28.9086	+	1.48368i	−1.05913	+	0.0543579i
$746$	−9.51719			−0.348449
$747$	5.43217	−	5.43217i	0.198753	−	0.198753i
$748$	−2.58359	−	2.58359i	−0.0944655	−	0.0944655i
$749$	19.7643			0.722172
$750$	1.71315	+	11.0483i	0.0625552	+	0.403427i
$751$			42.3190i			1.54424i	0.635475	+	0.772121i	$0.280804\pi$
$751$			42.3190i			1.54424i	−0.635475	+	0.772121i	$0.719196\pi$
$752$	7.86994	−	7.86994i	0.286987	−	0.286987i
$753$	4.79559	−	4.79559i	0.174761	−	0.174761i
$754$	−16.8064			−0.612054
$755$	48.5745	−	2.49299i	1.76781	−	0.0907294i
$756$			1.98511i			0.0721977i
$757$	6.14572	−	6.14572i	0.223370	−	0.223370i	−0.586546	−	0.809916i	$-0.699513\pi$
$757$	6.14572	−	6.14572i	0.223370	−	0.223370i	0.809916	+	0.586546i	$0.199513\pi$
$758$	7.45532	+	7.45532i	0.270789	+	0.270789i
$759$	29.1129			1.05673
$760$	−9.46656	+	2.32039i	−0.343388	+	0.0841695i
$761$	−32.5422			−1.17966			−0.589828	−	0.807529i	$-0.700804\pi$
$761$	−32.5422			−1.17966			−0.589828	+	0.807529i	$0.700804\pi$
$762$	1.33748	+	1.33748i	0.0484520	+	0.0484520i
$763$	12.1280	−	12.1280i	0.439063	−	0.439063i
$764$		−	13.8711i		−	0.501840i
$765$	1.03408	−	1.14597i	0.0373874	−	0.0414327i
$766$	−12.0726			−0.436201
$767$	1.17328	−	1.17328i	0.0423646	−	0.0423646i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$			7.15156i			0.257892i	0.991652	+	0.128946i	$0.0411594\pi$
$769$			7.15156i			0.257892i	−0.991652	+	0.128946i	$0.958841\pi$
$770$	−1.20424	−	23.4638i	−0.0433976	−	0.845576i
$771$	−18.5429			−0.667805
$772$	−8.22061	−	8.22061i	−0.295866	−	0.295866i
$773$	28.5163	−	28.5163i	1.02566	−	1.02566i	0.0259998	−	0.999662i	$-0.491723\pi$
$773$	28.5163	−	28.5163i	1.02566	−	1.02566i	0.999662	−	0.0259998i	$-0.00827692\pi$
$774$	−10.0817			−0.362379
$775$	4.01821	+	39.0431i	0.144338	+	1.40247i
$776$	−4.38992			−0.157589
$777$	−11.1285	+	11.1285i	−0.399234	+	0.399234i
$778$	17.7611	−	17.7611i	0.636767	−	0.636767i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.114611 + 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 + 1.40368i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(0.707107 - 0.707107i) q^{3} +1.00000i q^{4} +(0.114611 + 2.23313i) q^{5} -1.00000 q^{6} +(-1.40368 + 1.40368i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.49802 - 1.66010i) q^{10} -5.29298 q^{11} +(0.707107 + 0.707107i) q^{12} +(-1.91968 + 1.91968i) q^{13} +1.98511 q^{14} +(1.66010 + 1.49802i) q^{15} -1.00000 q^{16} +(0.488117 - 0.488117i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-2.44789 + 3.60663i) q^{19} +(-2.23313 + 0.114611i) q^{20} +1.98511i q^{21} +(3.74270 + 3.74270i) q^{22} +(-3.88930 - 3.88930i) q^{23} -1.00000i q^{24} +(-4.97373 + 0.511883i) q^{25} +2.71483 q^{26} +(-0.707107 - 0.707107i) q^{27} +(-1.40368 - 1.40368i) q^{28} -6.19060 q^{29} +(-0.114611 - 2.23313i) q^{30} -7.84986i q^{31} +(0.707107 + 0.707107i) q^{32} +(-3.74270 + 3.74270i) q^{33} -0.690302 q^{34} +(-3.29548 - 2.97373i) q^{35} +1.00000 q^{36} +(5.60602 + 5.60602i) q^{37} +(4.28120 - 0.819353i) q^{38} +2.71483i q^{39} +(1.66010 + 1.49802i) q^{40} +1.90599i q^{41} +(1.40368 - 1.40368i) q^{42} +(7.12884 + 7.12884i) q^{43} -5.29298i q^{44} +(2.23313 - 0.114611i) q^{45} +5.50029i q^{46} +(-7.86994 + 7.86994i) q^{47} +(-0.707107 + 0.707107i) q^{48} +3.05934i q^{49} +(3.87891 + 3.15500i) q^{50} -0.690302i q^{51} +(-1.91968 - 1.91968i) q^{52} +(8.93991 - 8.93991i) q^{53} +1.00000i q^{54} +(-0.606635 - 11.8199i) q^{55} +1.98511i q^{56} +(0.819353 + 4.28120i) q^{57} +(4.37741 + 4.37741i) q^{58} -0.611185 q^{59} +(-1.49802 + 1.66010i) q^{60} +8.31021 q^{61} +(-5.55069 + 5.55069i) q^{62} +(1.40368 + 1.40368i) q^{63} -1.00000i q^{64} +(-4.50690 - 4.06687i) q^{65} +5.29298 q^{66} +(10.2011 + 10.2011i) q^{67} +(0.488117 + 0.488117i) q^{68} -5.50029 q^{69} +(0.227516 + 4.43300i) q^{70} -3.97022i q^{71} +(-0.707107 - 0.707107i) q^{72} +(7.72265 + 7.72265i) q^{73} -7.92810i q^{74} +(-3.15500 + 3.87891i) q^{75} +(-3.60663 - 2.44789i) q^{76} +(7.42967 - 7.42967i) q^{77} +(1.91968 - 1.91968i) q^{78} -17.1528 q^{79} +(-0.114611 - 2.23313i) q^{80} -1.00000 q^{81} +(1.34774 - 1.34774i) q^{82} +(5.43217 + 5.43217i) q^{83} -1.98511 q^{84} +(1.14597 + 1.03408i) q^{85} -10.0817i q^{86} +(-4.37741 + 4.37741i) q^{87} +(-3.74270 + 3.74270i) q^{88} +5.42118 q^{89} +(-1.66010 - 1.49802i) q^{90} -5.38924i q^{91} +(3.88930 - 3.88930i) q^{92} +(-5.55069 - 5.55069i) q^{93} +11.1298 q^{94} +(-8.33464 - 5.05310i) q^{95} +1.00000 q^{96} +(-3.10415 - 3.10415i) q^{97} +(2.16328 - 2.16328i) q^{98} +5.29298i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20q + 12q^{5} - 20q^{6} - 4q^{7} + O(q^{10}) \)	\( 20q + 12q^{5} - 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} - 12q^{17} - 4q^{23} - 28q^{25} + 24q^{26} - 4q^{28} - 12q^{30} + 4q^{35} + 20q^{36} - 12q^{38} + 4q^{42} - 12q^{43} - 44q^{47} + 64q^{55} + 12q^{57} - 8q^{58} - 24q^{62} + 4q^{63} + 8q^{66} - 12q^{68} - 4q^{73} + 4q^{76} + 88q^{77} - 12q^{80} - 20q^{81} - 8q^{82} + 76q^{83} - 12q^{85} + 8q^{87} + 4q^{92} - 24q^{93} - 24q^{95} + 20q^{96} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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