LMFDB - Embedded newform 570.2.m.a.493.1

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:	$x^{20} + 153 x^{16} + 6416 x^{12} + 78648 x^{8} + 19120 x^{4} + 16$
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.1
Root			$-1.53190 - 1.53190i$ of defining polynomial
Character	$\chi$	$=$	570.493
Dual form			570.2.m.a.37.1

$q$-expansion

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-2.23502 - 0.0685835i) q^{5} +1.00000 q^{6} +(-2.16643 + 2.16643i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-2.23502 - 0.0685835i) q^{5} +1.00000 q^{6} +(-2.16643 + 2.16643i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.53190 + 1.62889i) q^{10} -5.68402 q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.92222 - 3.92222i) q^{13} +3.06380 q^{14} +(1.62889 - 1.53190i) q^{15} -1.00000 q^{16} +(4.99059 - 4.99059i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(4.01921 + 1.68699i) q^{19} +(0.0685835 - 2.23502i) q^{20} -3.06380i q^{21} +(4.01921 + 4.01921i) q^{22} +(4.30360 + 4.30360i) q^{23} +1.00000i q^{24} +(4.99059 + 0.306570i) q^{25} -5.54686 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.16643 - 2.16643i) q^{28} -4.04446 q^{29} +(-2.23502 - 0.0685835i) q^{30} -4.04446i q^{31} +(0.707107 + 0.707107i) q^{32} +(4.01921 - 4.01921i) q^{33} -7.05776 q^{34} +(4.99059 - 4.69343i) q^{35} +1.00000 q^{36} +(6.19934 + 6.19934i) q^{37} +(-1.64913 - 4.03490i) q^{38} +5.54686i q^{39} +(-1.62889 + 1.53190i) q^{40} -6.38884i q^{41} +(-2.16643 + 2.16643i) q^{42} +(-4.15703 - 4.15703i) q^{43} -5.68402i q^{44} +(-0.0685835 + 2.23502i) q^{45} -6.08621i q^{46} +(3.24326 - 3.24326i) q^{47} +(0.707107 - 0.707107i) q^{48} -2.38686i q^{49} +(-3.31210 - 3.74566i) q^{50} +7.05776i q^{51} +(3.92222 + 3.92222i) q^{52} +(5.40818 - 5.40818i) q^{53} -1.00000i q^{54} +(12.7039 + 0.389830i) q^{55} +3.06380i q^{56} +(-4.03490 + 1.64913i) q^{57} +(2.85986 + 2.85986i) q^{58} -2.39487 q^{59} +(1.53190 + 1.62889i) q^{60} -2.33286 q^{61} +(-2.85986 + 2.85986i) q^{62} +(2.16643 + 2.16643i) q^{63} -1.00000i q^{64} +(-9.03522 + 8.49722i) q^{65} -5.68402 q^{66} +(-6.12760 - 6.12760i) q^{67} +(4.99059 + 4.99059i) q^{68} -6.08621 q^{69} +(-6.84764 - 0.210126i) q^{70} -6.51556i q^{71} +(-0.707107 - 0.707107i) q^{72} +(-2.07682 - 2.07682i) q^{73} -8.76719i q^{74} +(-3.74566 + 3.31210i) q^{75} +(-1.68699 + 4.01921i) q^{76} +(12.3141 - 12.3141i) q^{77} +(3.92222 - 3.92222i) q^{78} +4.23844 q^{79} +(2.23502 + 0.0685835i) q^{80} -1.00000 q^{81} +(-4.51759 + 4.51759i) q^{82} +(-5.30657 - 5.30657i) q^{83} +3.06380 q^{84} +(-11.4963 + 10.8118i) q^{85} +5.87892i q^{86} +(2.85986 - 2.85986i) q^{87} +(-4.01921 + 4.01921i) q^{88} -2.50829 q^{89} +(1.62889 - 1.53190i) q^{90} +16.9944i q^{91} +(-4.30360 + 4.30360i) q^{92} +(2.85986 + 2.85986i) q^{93} -4.58666 q^{94} +(-8.86730 - 4.04611i) q^{95} -1.00000 q^{96} +(6.22010 + 6.22010i) q^{97} +(-1.68776 + 1.68776i) q^{98} +5.68402i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10}) $	$ 20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{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
$5$	−2.23502	−	0.0685835i	−0.999530	−	0.0306715i
$5$	−2.23502	−	0.0685835i	−0.999530	−	0.0306715i
$6$	1.00000			0.408248
$7$	−2.16643	+	2.16643i	−0.818835	+	0.818835i	−0.985939	−	0.167105i	$-0.946558\pi$
$7$	−2.16643	+	2.16643i	−0.818835	+	0.818835i	0.167105	+	0.985939i	$0.446558\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$		−	1.00000i		−	0.333333i
$10$	1.53190	+	1.62889i	0.484429	+	0.515100i
$11$	−5.68402			−1.71380			−0.856899	−	0.515485i	$-0.827612\pi$
$11$	−5.68402			−1.71380			−0.856899	+	0.515485i	$0.827612\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	3.92222	−	3.92222i	1.08783	−	1.08783i	0.0920758	−	0.995752i	$-0.470650\pi$
$13$	3.92222	−	3.92222i	1.08783	−	1.08783i	0.995752	−	0.0920758i	$-0.0293502\pi$
$14$	3.06380			0.818835
$15$	1.62889	−	1.53190i	0.420578	−	0.395535i
$16$	−1.00000			−0.250000
$17$	4.99059	−	4.99059i	1.21040	−	1.21040i	0.239500	−	0.970896i	$-0.423016\pi$
$17$	4.99059	−	4.99059i	1.21040	−	1.21040i	0.970896	−	0.239500i	$-0.0769836\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	4.01921	+	1.68699i	0.922070	+	0.387023i
$19$	4.01921	+	1.68699i	0.922070	+	0.387023i
$20$	0.0685835	−	2.23502i	0.0153357	−	0.499765i
$21$		−	3.06380i		−	0.668576i
$22$	4.01921	+	4.01921i	0.856899	+	0.856899i
$23$	4.30360	+	4.30360i	0.897363	+	0.897363i	0.995202	−	0.0978397i	$-0.0311932\pi$
$23$	4.30360	+	4.30360i	0.897363	+	0.897363i	−0.0978397	+	0.995202i	$0.531193\pi$
$24$			1.00000i			0.204124i
$25$	4.99059	+	0.306570i	0.998119	+	0.0613141i
$26$	−5.54686			−1.08783
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−2.16643	−	2.16643i	−0.409417	−	0.409417i
$29$	−4.04446			−0.751037			−0.375518	−	0.926815i	$-0.622535\pi$
$29$	−4.04446			−0.751037			−0.375518	+	0.926815i	$0.622535\pi$
$30$	−2.23502	−	0.0685835i	−0.408056	−	0.0125216i
$31$		−	4.04446i		−	0.726406i	−0.931710	−	0.363203i	$-0.881683\pi$
$31$		−	4.04446i		−	0.726406i	0.931710	−	0.363203i	$-0.118317\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	4.01921	−	4.01921i	0.699655	−	0.699655i
$34$	−7.05776			−1.21040
$35$	4.99059	−	4.69343i	0.843564	−	0.793334i
$36$	1.00000			0.166667
$37$	6.19934	+	6.19934i	1.01917	+	1.01917i	0.999813	+	0.0193530i	$0.00616063\pi$
$37$	6.19934	+	6.19934i	1.01917	+	1.01917i	0.0193530	+	0.999813i	$0.493839\pi$
$38$	−1.64913	−	4.03490i	−0.267524	−	0.654546i
$39$			5.54686i			0.888208i
$40$	−1.62889	+	1.53190i	−0.257550	+	0.242215i
$41$		−	6.38884i		−	0.997769i	−0.866669	−	0.498884i	$-0.833743\pi$
$41$		−	6.38884i		−	0.997769i	0.866669	−	0.498884i	$-0.166257\pi$
$42$	−2.16643	+	2.16643i	−0.334288	+	0.334288i
$43$	−4.15703	−	4.15703i	−0.633940	−	0.633940i	0.315114	−	0.949054i	$-0.397957\pi$
$43$	−4.15703	−	4.15703i	−0.633940	−	0.633940i	−0.949054	+	0.315114i	$0.897957\pi$
$44$		−	5.68402i		−	0.856899i
$45$	−0.0685835	+	2.23502i	−0.0102238	+	0.333177i
$46$		−	6.08621i		−	0.897363i
$47$	3.24326	−	3.24326i	0.473077	−	0.473077i	−0.429832	−	0.902909i	$-0.641427\pi$
$47$	3.24326	−	3.24326i	0.473077	−	0.473077i	0.902909	+	0.429832i	$0.141427\pi$
$48$	0.707107	−	0.707107i	0.102062	−	0.102062i
$49$		−	2.38686i		−	0.340980i
$50$	−3.31210	−	3.74566i	−0.468402	−	0.529716i
$51$			7.05776i			0.988285i
$52$	3.92222	+	3.92222i	0.543914	+	0.543914i
$53$	5.40818	−	5.40818i	0.742871	−	0.742871i	−0.230259	−	0.973129i	$-0.573957\pi$
$53$	5.40818	−	5.40818i	0.742871	−	0.742871i	0.973129	+	0.230259i	$0.0739573\pi$
$54$		−	1.00000i		−	0.136083i
$55$	12.7039	+	0.389830i	1.71299	+	0.0525647i
$56$			3.06380i			0.409417i
$57$	−4.03490	+	1.64913i	−0.534435	+	0.218432i
$58$	2.85986	+	2.85986i	0.375518	+	0.375518i
$59$	−2.39487			−0.311786			−0.155893	−	0.987774i	$-0.549825\pi$
$59$	−2.39487			−0.311786			−0.155893	+	0.987774i	$0.549825\pi$
$60$	1.53190	+	1.62889i	0.197767	+	0.210289i
$61$	−2.33286			−0.298693			−0.149346	−	0.988785i	$-0.547717\pi$
$61$	−2.33286			−0.298693			−0.149346	+	0.988785i	$0.547717\pi$
$62$	−2.85986	+	2.85986i	−0.363203	+	0.363203i
$63$	2.16643	+	2.16643i	0.272945	+	0.272945i
$64$		−	1.00000i		−	0.125000i
$65$	−9.03522	+	8.49722i	−1.12068	+	1.05395i
$66$	−5.68402			−0.699655
$67$	−6.12760	−	6.12760i	−0.748605	−	0.748605i	0.225612	−	0.974217i	$-0.427562\pi$
$67$	−6.12760	−	6.12760i	−0.748605	−	0.748605i	−0.974217	+	0.225612i	$0.927562\pi$
$68$	4.99059	+	4.99059i	0.605198	+	0.605198i
$69$	−6.08621			−0.732693
$70$	−6.84764	−	0.210126i	−0.818449	−	0.0251149i
$71$		−	6.51556i		−	0.773255i	−0.922236	−	0.386628i	$-0.873640\pi$
$71$		−	6.51556i		−	0.773255i	0.922236	−	0.386628i	$-0.126360\pi$
$72$	−0.707107	−	0.707107i	−0.0833333	−	0.0833333i
$73$	−2.07682	−	2.07682i	−0.243074	−	0.243074i	0.575047	−	0.818121i	$-0.304984\pi$
$73$	−2.07682	−	2.07682i	−0.243074	−	0.243074i	−0.818121	+	0.575047i	$0.804984\pi$
$74$		−	8.76719i		−	1.01917i
$75$	−3.74566	+	3.31210i	−0.432512	+	0.382449i
$76$	−1.68699	+	4.01921i	−0.193511	+	0.461035i
$77$	12.3141	−	12.3141i	1.40332	−	1.40332i
$78$	3.92222	−	3.92222i	0.444104	−	0.444104i
$79$	4.23844			0.476862			0.238431	−	0.971159i	$-0.423367\pi$
$79$	4.23844			0.476862			0.238431	+	0.971159i	$0.423367\pi$
$80$	2.23502	+	0.0685835i	0.249882	+	0.00766787i
$81$	−1.00000			−0.111111
$82$	−4.51759	+	4.51759i	−0.498884	+	0.498884i
$83$	−5.30657	−	5.30657i	−0.582472	−	0.582472i	0.353110	−	0.935582i	$-0.385124\pi$
$83$	−5.30657	−	5.30657i	−0.582472	−	0.582472i	−0.935582	+	0.353110i	$0.885124\pi$
$84$	3.06380			0.334288
$85$	−11.4963	+	10.8118i	−1.24695	+	1.17270i
$86$			5.87892i			0.633940i
$87$	2.85986	−	2.85986i	0.306609	−	0.306609i
$88$	−4.01921	+	4.01921i	−0.428449	+	0.428449i
$89$	−2.50829			−0.265879			−0.132939	−	0.991124i	$-0.542442\pi$
$89$	−2.50829			−0.265879			−0.132939	+	0.991124i	$0.542442\pi$
$90$	1.62889	−	1.53190i	0.171700	−	0.161476i
$91$			16.9944i			1.78150i
$92$	−4.30360	+	4.30360i	−0.448681	+	0.448681i
$93$	2.85986	+	2.85986i	0.296554	+	0.296554i
$94$	−4.58666			−0.473077
$95$	−8.86730	−	4.04611i	−0.909766	−	0.415122i
$96$	−1.00000			−0.102062
$97$	6.22010	+	6.22010i	0.631555	+	0.631555i	0.948458	−	0.316903i	$-0.102643\pi$
$97$	6.22010	+	6.22010i	0.631555	+	0.631555i	−0.316903	+	0.948458i	$0.602643\pi$
$98$	−1.68776	+	1.68776i	−0.170490	+	0.170490i
$99$			5.68402i			0.571266i
$100$	−0.306570	+	4.99059i	−0.0306570	+	0.499059i
$101$	3.42891			0.341189			0.170595	−	0.985341i	$-0.445431\pi$
$101$	3.42891			0.341189			0.170595	+	0.985341i	$0.445431\pi$
$102$	4.99059	−	4.99059i	0.494142	−	0.494142i
$103$	13.0842	−	13.0842i	1.28922	−	1.28922i	0.353961	−	0.935260i	$-0.384835\pi$
$103$	13.0842	−	13.0842i	1.28922	−	1.28922i	0.935260	−	0.353961i	$-0.115165\pi$
$104$		−	5.54686i		−	0.543914i
$105$	−0.210126	+	6.84764i	−0.0205062	+	0.668261i
$106$	−7.64832			−0.742871
$107$	5.02931	+	5.02931i	0.486202	+	0.486202i	0.907106	−	0.420903i	$-0.138287\pi$
$107$	5.02931	+	5.02931i	0.486202	+	0.486202i	−0.420903	+	0.907106i	$0.638287\pi$
$108$	−0.707107	+	0.707107i	−0.0680414	+	0.0680414i
$109$	−5.95528			−0.570412			−0.285206	−	0.958466i	$-0.592062\pi$
$109$	−5.95528			−0.570412			−0.285206	+	0.958466i	$0.592062\pi$
$110$	−8.70735	−	9.25865i	−0.830213	−	0.882778i
$111$	−8.76719			−0.832145
$112$	2.16643	−	2.16643i	0.204709	−	0.204709i
$113$	−0.0413876	+	0.0413876i	−0.00389342	+	0.00389342i	−0.709051	−	0.705157i	$-0.750876\pi$
$113$	−0.0413876	+	0.0413876i	−0.00389342	+	0.00389342i	0.705157	+	0.709051i	$0.250876\pi$
$114$	4.01921	+	1.68699i	0.376434	+	0.158001i
$115$	−9.32346	−	9.91377i	−0.869417	−	0.924464i
$116$		−	4.04446i		−	0.375518i
$117$	−3.92222	−	3.92222i	−0.362609	−	0.362609i
$118$	1.69343	+	1.69343i	0.155893	+	0.155893i
$119$			21.6236i			1.98223i
$120$	0.0685835	−	2.23502i	0.00626079	−	0.204028i
$121$	21.3081			1.93710
$122$	1.64958	+	1.64958i	0.149346	+	0.149346i
$123$	4.51759	+	4.51759i	0.407337	+	0.407337i
$124$	4.04446			0.363203
$125$	−11.1330	−	1.02746i	−0.995768	−	0.0918990i
$126$		−	3.06380i		−	0.272945i
$127$	−10.0379	−	10.0379i	−0.890717	−	0.890717i	0.103873	−	0.994591i	$-0.466876\pi$
$127$	−10.0379	−	10.0379i	−0.890717	−	0.890717i	−0.994591	+	0.103873i	$0.966876\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	5.87892			0.517610
$130$	12.3973	+	0.380423i	1.08732	+	0.0333653i
$131$	4.64290			0.405652			0.202826	−	0.979215i	$-0.434987\pi$
$131$	4.64290			0.405652			0.202826	+	0.979215i	$0.434987\pi$
$132$	4.01921	+	4.01921i	0.349827	+	0.349827i
$133$	−12.3621	+	5.05259i	−1.07193	+	0.438115i
$134$			8.66573i			0.748605i
$135$	−1.53190	−	1.62889i	−0.131845	−	0.140193i
$136$		−	7.05776i		−	0.605198i
$137$	−2.26545	+	2.26545i	−0.193550	+	0.193550i	−0.797228	−	0.603678i	$-0.793701\pi$
$137$	−2.26545	+	2.26545i	−0.193550	+	0.193550i	0.603678	+	0.797228i	$0.293701\pi$
$138$	4.30360	+	4.30360i	0.366347	+	0.366347i
$139$			17.4266i			1.47810i	0.673649	+	0.739051i	$0.264726\pi$
$139$			17.4266i			1.47810i	−0.673649	+	0.739051i	$0.735274\pi$
$140$	4.69343	+	4.99059i	0.396667	+	0.421782i
$141$			4.58666i			0.386266i
$142$	−4.60720	+	4.60720i	−0.386628	+	0.386628i
$143$	−22.2940	+	22.2940i	−1.86432	+	1.86432i
$144$			1.00000i			0.0833333i
$145$	9.03942	+	0.277383i	0.750683	+	0.0230354i
$146$			2.93707i			0.243074i
$147$	1.68776	+	1.68776i	0.139204	+	0.139204i
$148$	−6.19934	+	6.19934i	−0.509583	+	0.509583i
$149$			1.79836i			0.147327i	0.997283	+	0.0736637i	$0.0234691\pi$
$149$			1.79836i			0.147327i	−0.997283	+	0.0736637i	$0.976531\pi$
$150$	4.99059	+	0.306570i	0.407480	+	0.0250314i
$151$		−	8.62201i		−	0.701649i	−0.936441	−	0.350825i	$-0.885901\pi$
$151$		−	8.62201i		−	0.701649i	0.936441	−	0.350825i	$-0.114099\pi$
$152$	4.03490	−	1.64913i	0.327273	−	0.133762i
$153$	−4.99059	−	4.99059i	−0.403465	−	0.403465i
$154$	−17.4147			−1.40332
$155$	−0.277383	+	9.03942i	−0.0222799	+	0.726064i
$156$	−5.54686			−0.444104
$157$	7.79308	−	7.79308i	0.621956	−	0.621956i	−0.324076	−	0.946031i	$-0.605053\pi$
$157$	7.79308	−	7.79308i	0.621956	−	0.621956i	0.946031	+	0.324076i	$0.105053\pi$
$158$	−2.99703	−	2.99703i	−0.238431	−	0.238431i
$159$			7.64832i			0.606551i
$160$	−1.53190	−	1.62889i	−0.121107	−	0.128775i
$161$	−18.6469			−1.46958
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	7.85986	+	7.85986i	0.615632	+	0.615632i	0.944408	−	0.328776i	$-0.106636\pi$
$163$	7.85986	+	7.85986i	0.615632	+	0.615632i	−0.328776	+	0.944408i	$0.606636\pi$
$164$	6.38884			0.498884
$165$	−9.25865	+	8.70735i	−0.720785	+	0.677866i
$166$			7.50462i			0.582472i
$167$	17.5764	+	17.5764i	1.36010	+	1.36010i	0.873779	+	0.486323i	$0.161662\pi$
$167$	17.5764	+	17.5764i	1.36010	+	1.36010i	0.486323	+	0.873779i	$0.338338\pi$
$168$	−2.16643	−	2.16643i	−0.167144	−	0.167144i
$169$		−	17.7676i		−	1.36674i
$170$	15.7742	+	0.484046i	1.20983	+	0.0371246i
$171$	1.68699	−	4.01921i	0.129008	−	0.307357i
$172$	4.15703	−	4.15703i	0.316970	−	0.316970i
$173$	−0.108645	+	0.108645i	−0.00826009	+	0.00826009i	−0.711225	−	0.702965i	$-0.751859\pi$
$173$	−0.108645	+	0.108645i	−0.00826009	+	0.00826009i	0.702965	+	0.711225i	$0.251859\pi$
$174$	−4.04446			−0.306609
$175$	−11.4759	+	10.1476i	−0.867500	+	0.767088i
$176$	5.68402			0.428449
$177$	1.69343	−	1.69343i	0.127286	−	0.127286i
$178$	1.77363	+	1.77363i	0.132939	+	0.132939i
$179$	9.54798			0.713649			0.356825	−	0.934171i	$-0.383859\pi$
$179$	9.54798			0.713649			0.356825	+	0.934171i	$0.383859\pi$
$180$	−2.23502	−	0.0685835i	−0.166588	−	0.00511191i
$181$		−	19.4384i		−	1.44484i	−0.691453	−	0.722421i	$-0.743029\pi$
$181$		−	19.4384i		−	1.44484i	0.691453	−	0.722421i	$-0.256971\pi$
$182$	12.0169	−	12.0169i	0.890751	−	0.890751i
$183$	1.64958	−	1.64958i	0.121941	−	0.121941i
$184$	6.08621			0.448681
$185$	−13.4305	−	14.2808i	−0.987427	−	1.04995i
$186$		−	4.04446i		−	0.296554i
$187$	−28.3666	+	28.3666i	−2.07437	+	2.07437i
$188$	3.24326	+	3.24326i	0.236539	+	0.236539i
$189$	−3.06380			−0.222859
$190$	3.40910	+	9.13116i	0.247322	+	0.662444i
$191$	25.1526			1.81998			0.909991	−	0.414628i	$-0.136088\pi$
$191$	25.1526			1.81998			0.909991	+	0.414628i	$0.136088\pi$
$192$	0.707107	+	0.707107i	0.0510310	+	0.0510310i
$193$	−1.23637	+	1.23637i	−0.0889961	+	0.0889961i	−0.750203	−	0.661207i	$-0.770044\pi$
$193$	−1.23637	+	1.23637i	−0.0889961	+	0.0889961i	0.661207	+	0.750203i	$0.270044\pi$
$194$		−	8.79655i		−	0.631555i
$195$	0.380423	−	12.3973i	0.0272426	−	0.887790i
$196$	2.38686			0.170490
$197$	5.67759	−	5.67759i	0.404511	−	0.404511i	−0.475308	−	0.879819i	$-0.657663\pi$
$197$	5.67759	−	5.67759i	0.404511	−	0.404511i	0.879819	+	0.475308i	$0.157663\pi$
$198$	4.01921	−	4.01921i	0.285633	−	0.285633i
$199$			3.89894i			0.276389i	0.990405	+	0.138194i	$0.0441299\pi$
$199$			3.89894i			0.276389i	−0.990405	+	0.138194i	$0.955870\pi$
$200$	3.74566	−	3.31210i	0.264858	−	0.234201i
$201$	8.66573			0.611233
$202$	−2.42461	−	2.42461i	−0.170595	−	0.170595i
$203$	8.76204	−	8.76204i	0.614975	−	0.614975i
$204$	−7.05776			−0.494142
$205$	−0.438169	+	14.2792i	−0.0306030	+	0.997299i
$206$	−18.5038			−1.28922
$207$	4.30360	−	4.30360i	0.299121	−	0.299121i
$208$	−3.92222	+	3.92222i	−0.271957	+	0.271957i
$209$	−22.8453	−	9.58891i	−1.58024	−	0.663279i
$210$	4.99059	−	4.69343i	0.344384	−	0.323877i
$211$		−	18.9376i		−	1.30372i	−0.758341	−	0.651858i	$-0.773990\pi$
$211$		−	18.9376i		−	1.30372i	0.758341	−	0.651858i	$-0.226010\pi$
$212$	5.40818	+	5.40818i	0.371435	+	0.371435i
$213$	4.60720	+	4.60720i	0.315680	+	0.315680i
$214$		−	7.11253i		−	0.486202i
$215$	9.00591	+	9.57612i	0.614198	+	0.653086i
$216$	1.00000			0.0680414
$217$	8.76204	+	8.76204i	0.594806	+	0.594806i
$218$	4.21102	+	4.21102i	0.285206	+	0.285206i
$219$	2.93707			0.198469
$220$	−0.389830	+	12.7039i	−0.0262823	+	0.856495i
$221$		−	39.1484i		−	2.63341i
$222$	6.19934	+	6.19934i	0.416073	+	0.416073i
$223$	9.26030	−	9.26030i	0.620116	−	0.620116i	−0.325445	−	0.945561i	$-0.605514\pi$
$223$	9.26030	−	9.26030i	0.620116	−	0.620116i	0.945561	+	0.325445i	$0.105514\pi$
$224$	−3.06380			−0.204709
$225$	0.306570	−	4.99059i	0.0204380	−	0.332706i
$226$	0.0585309			0.00389342
$227$	2.63934	+	2.63934i	0.175179	+	0.175179i	0.789251	−	0.614071i	$-0.210469\pi$
$227$	2.63934	+	2.63934i	0.175179	+	0.175179i	−0.614071	+	0.789251i	$0.710469\pi$
$228$	−1.64913	−	4.03490i	−0.109216	−	0.267217i
$229$			4.94601i			0.326841i	0.986556	+	0.163421i	$0.0522528\pi$
$229$			4.94601i			0.326841i	−0.986556	+	0.163421i	$0.947747\pi$
$230$	−0.417413	+	13.6028i	−0.0275234	+	0.896940i
$231$			17.4147i			1.14580i
$232$	−2.85986	+	2.85986i	−0.187759	+	0.187759i
$233$	−18.1200	−	18.1200i	−1.18708	−	1.18708i	−0.977871	−	0.209210i	$-0.932911\pi$
$233$	−18.1200	−	18.1200i	−1.18708	−	1.18708i	−0.209210	−	0.977871i	$-0.567089\pi$
$234$			5.54686i			0.362609i
$235$	−7.47116	+	7.02629i	−0.487365	+	0.458345i
$236$		−	2.39487i		−	0.155893i
$237$	−2.99703	+	2.99703i	−0.194678	+	0.194678i
$238$	15.2902	−	15.2902i	0.991114	−	0.991114i
$239$		−	6.98300i		−	0.451693i	−0.974163	−	0.225846i	$-0.927485\pi$
$239$		−	6.98300i		−	0.451693i	0.974163	−	0.225846i	$-0.0725147\pi$
$240$	−1.62889	+	1.53190i	−0.105144	+	0.0988837i
$241$		−	7.54947i		−	0.486304i	−0.969988	−	0.243152i	$-0.921819\pi$
$241$		−	7.54947i		−	0.486304i	0.969988	−	0.243152i	$-0.0781814\pi$
$242$	−15.0671	−	15.0671i	−0.968550	−	0.968550i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$		−	2.33286i		−	0.149346i
$245$	−0.163699	+	5.33467i	−0.0104584	+	0.340819i
$246$		−	6.38884i		−	0.407337i
$247$	22.3810	−	9.14747i	1.42407	−	0.582039i
$248$	−2.85986	−	2.85986i	−0.181601	−	0.181601i
$249$	7.50462			0.475586
$250$	7.14571	+	8.59877i	0.451935	+	0.543834i
$251$	−20.0566			−1.26596			−0.632981	−	0.774168i	$-0.718169\pi$
$251$	−20.0566			−1.26596			−0.632981	+	0.774168i	$0.718169\pi$
$252$	−2.16643	+	2.16643i	−0.136472	+	0.136472i
$253$	−24.4618	−	24.4618i	−1.53790	−	1.53790i
$254$			14.1957i			0.890717i
$255$	0.484046	−	15.7742i	0.0303121	−	0.987820i
$256$	1.00000			0.0625000
$257$	8.66176	+	8.66176i	0.540306	+	0.540306i	0.923619	−	0.383313i	$-0.125217\pi$
$257$	8.66176	+	8.66176i	0.540306	+	0.540306i	−0.383313	+	0.923619i	$0.625217\pi$
$258$	−4.15703	−	4.15703i	−0.258805	−	0.258805i
$259$	−26.8609			−1.66906
$260$	−8.49722	−	9.03522i	−0.526975	−	0.560341i
$261$			4.04446i			0.250346i
$262$	−3.28303	−	3.28303i	−0.202826	−	0.202826i
$263$	7.51759	+	7.51759i	0.463554	+	0.463554i	0.899819	−	0.436264i	$-0.143699\pi$
$263$	7.51759	+	7.51759i	0.463554	+	0.463554i	−0.436264	+	0.899819i	$0.643699\pi$
$264$		−	5.68402i		−	0.349827i
$265$	−12.4583	+	11.7165i	−0.765306	+	0.719736i
$266$	12.3141	+	5.16861i	0.755023	+	0.316908i
$267$	1.77363	−	1.77363i	0.108544	−	0.108544i
$268$	6.12760	−	6.12760i	0.374303	−	0.374303i
$269$	20.3832			1.24278			0.621391	−	0.783500i	$-0.286568\pi$
$269$	20.3832			1.24278			0.621391	+	0.783500i	$0.286568\pi$
$270$	−0.0685835	+	2.23502i	−0.00417386	+	0.136019i
$271$	−20.5647			−1.24921			−0.624607	−	0.780939i	$-0.714741\pi$
$271$	−20.5647			−1.24921			−0.624607	+	0.780939i	$0.714741\pi$
$272$	−4.99059	+	4.99059i	−0.302599	+	0.302599i
$273$	−12.0169	−	12.0169i	−0.727295	−	0.727295i
$274$	3.20383			0.193550
$275$	−28.3666	−	1.74255i	−1.71057	−	0.105080i
$276$		−	6.08621i		−	0.366347i
$277$	16.5022	−	16.5022i	0.991518	−	0.991518i	−0.00844603	−	0.999964i	$-0.502688\pi$
$277$	16.5022	−	16.5022i	0.991518	−	0.991518i	0.999964	+	0.00844603i	$0.00268849\pi$
$278$	12.3224	−	12.3224i	0.739051	−	0.739051i
$279$	−4.04446			−0.242135
$280$	0.210126	−	6.84764i	0.0125574	−	0.409225i
$281$			16.7009i			0.996293i	0.867093	+	0.498147i	$0.165986\pi$
$281$			16.7009i			0.996293i	−0.867093	+	0.498147i	$0.834014\pi$
$282$	3.24326	−	3.24326i	0.193133	−	0.193133i
$283$	−9.16938	−	9.16938i	−0.545063	−	0.545063i	0.379946	−	0.925009i	$-0.375943\pi$
$283$	−9.16938	−	9.16938i	−0.545063	−	0.545063i	−0.925009	+	0.379946i	$0.875943\pi$
$284$	6.51556			0.386628
$285$	9.13116	−	3.40910i	0.540883	−	0.201938i
$286$	31.5284			1.86432
$287$	13.8410	+	13.8410i	0.817007	+	0.817007i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$		−	32.8120i		−	1.93012i
$290$	−6.19570	−	6.58798i	−0.363824	−	0.386859i
$291$	−8.79655			−0.515663
$292$	2.07682	−	2.07682i	0.121537	−	0.121537i
$293$	−11.7298	+	11.7298i	−0.685260	+	0.685260i	−0.961180	−	0.275921i	$-0.911017\pi$
$293$	−11.7298	+	11.7298i	−0.685260	+	0.685260i	0.275921	+	0.961180i	$0.411017\pi$
$294$		−	2.38686i		−	0.139204i
$295$	5.35258	+	0.164249i	0.311639	+	0.00956293i
$296$	8.76719			0.509583
$297$	−4.01921	−	4.01921i	−0.233218	−	0.233218i
$298$	1.27163	−	1.27163i	0.0736637	−	0.0736637i
$299$	33.7593			1.95235
$300$	−3.31210	−	3.74566i	−0.191224	−	0.216256i
$301$	18.0118			1.03818
$302$	−6.09668	+	6.09668i	−0.350825	+	0.350825i
$303$	−2.42461	+	2.42461i	−0.139290	+	0.139290i
$304$	−4.01921	−	1.68699i	−0.230518	−	0.0967557i
$305$	5.21399	+	0.159996i	0.298552	+	0.00916135i
$306$			7.05776i			0.403465i
$307$	−7.51719	−	7.51719i	−0.429029	−	0.429029i	0.459269	−	0.888297i	$-0.348111\pi$
$307$	−7.51719	−	7.51719i	−0.429029	−	0.429029i	−0.888297	+	0.459269i	$0.848111\pi$
$308$	12.3141	+	12.3141i	0.701658	+	0.701658i
$309$			18.5038i			1.05264i
$310$	6.58798	−	6.19570i	0.374172	−	0.351892i
$311$	−17.0941			−0.969318			−0.484659	−	0.874703i	$-0.661056\pi$
$311$	−17.0941			−0.969318			−0.484659	+	0.874703i	$0.661056\pi$
$312$	3.92222	+	3.92222i	0.222052	+	0.222052i
$313$	−4.46822	−	4.46822i	−0.252559	−	0.252559i	0.569460	−	0.822019i	$-0.307152\pi$
$313$	−4.46822	−	4.46822i	−0.252559	−	0.252559i	−0.822019	+	0.569460i	$0.807152\pi$
$314$	−11.0211			−0.621956
$315$	−4.69343	−	4.99059i	−0.264445	−	0.281188i
$316$			4.23844i			0.238431i
$317$	−20.3285	−	20.3285i	−1.14176	−	1.14176i	−0.988128	−	0.153632i	$-0.950903\pi$
$317$	−20.3285	−	20.3285i	−1.14176	−	1.14176i	−0.153632	−	0.988128i	$-0.549097\pi$
$318$	5.40818	−	5.40818i	0.303276	−	0.303276i
$319$	22.9888			1.28712
$320$	−0.0685835	+	2.23502i	−0.00383393	+	0.124941i
$321$	−7.11253			−0.396982
$322$	13.1854	+	13.1854i	0.734791	+	0.734791i
$323$	28.4773	−	11.6391i	1.58452	−	0.647619i
$324$		−	1.00000i		−	0.0555556i
$325$	20.7766	−	18.3718i	1.15248	−	1.01908i
$326$		−	11.1155i		−	0.615632i
$327$	4.21102	−	4.21102i	0.232870	−	0.232870i
$328$	−4.51759	−	4.51759i	−0.249442	−	0.249442i
$329$			14.0526i			0.774744i
$330$	12.7039	+	0.389830i	0.699326	+	0.0214594i
$331$		−	21.9956i		−	1.20898i	−0.796611	−	0.604492i	$-0.793376\pi$
$331$		−	21.9956i		−	1.20898i	0.796611	−	0.604492i	$-0.206624\pi$
$332$	5.30657	−	5.30657i	0.291236	−	0.291236i
$333$	6.19934	−	6.19934i	0.339722	−	0.339722i
$334$		−	24.8568i		−	1.36010i
$335$	13.2750	+	14.1155i	0.725292	+	0.771214i
$336$			3.06380i			0.167144i
$337$	4.20829	+	4.20829i	0.229240	+	0.229240i	0.812375	−	0.583135i	$-0.198174\pi$
$337$	4.20829	+	4.20829i	0.229240	+	0.229240i	−0.583135	+	0.812375i	$0.698174\pi$
$338$	−12.5636	+	12.5636i	−0.683369	+	0.683369i
$339$		−	0.0585309i		−	0.00317896i
$340$	−10.8118	−	11.4963i	−0.586351	−	0.623476i
$341$			22.9888i			1.24491i
$342$	−4.03490	+	1.64913i	−0.218182	+	0.0891746i
$343$	−9.99406	−	9.99406i	−0.539628	−	0.539628i
$344$	−5.87892			−0.316970
$345$	13.6028	+	0.417413i	0.732349	+	0.0224728i
$346$	0.153647			0.00826009
$347$	−18.8707	+	18.8707i	−1.01303	+	1.01303i	−0.0131194	+	0.999914i	$0.504176\pi$
$347$	−18.8707	+	18.8707i	−1.01303	+	1.01303i	−0.999914	+	0.0131194i	$0.995824\pi$
$348$	2.85986	+	2.85986i	0.153305	+	0.153305i
$349$		−	3.34923i		−	0.179280i	−0.995974	−	0.0896401i	$-0.971428\pi$
$349$		−	3.34923i		−	0.179280i	0.995974	−	0.0896401i	$-0.0285717\pi$
$350$	15.2902	+	0.939270i	0.817294	+	0.0502061i
$351$	5.54686			0.296069
$352$	−4.01921	−	4.01921i	−0.214225	−	0.214225i
$353$	21.8457	+	21.8457i	1.16273	+	1.16273i	0.983876	+	0.178852i	$0.0572382\pi$
$353$	21.8457	+	21.8457i	1.16273	+	1.16273i	0.178852	+	0.983876i	$0.442762\pi$
$354$	−2.39487			−0.127286
$355$	−0.446860	+	14.5624i	−0.0237169	+	0.772891i
$356$		−	2.50829i		−	0.132939i
$357$	−15.2902	−	15.2902i	−0.809242	−	0.809242i
$358$	−6.75144	−	6.75144i	−0.356825	−	0.356825i
$359$		−	5.22092i		−	0.275550i	−0.990464	−	0.137775i	$-0.956005\pi$
$359$		−	5.22092i		−	0.275550i	0.990464	−	0.137775i	$-0.0439950\pi$
$360$	1.53190	+	1.62889i	0.0807382	+	0.0858501i
$361$	13.3081	+	13.5608i	0.700427	+	0.713724i
$362$	−13.7450	+	13.7450i	−0.722421	+	0.722421i
$363$	−15.0671	+	15.0671i	−0.790818	+	0.790818i
$364$	−16.9944			−0.890751
$365$	4.49930	+	4.78417i	0.235504	+	0.250415i
$366$	−2.33286			−0.121941
$367$	3.73845	−	3.73845i	0.195146	−	0.195146i	−0.602770	−	0.797915i	$-0.705936\pi$
$367$	3.73845	−	3.73845i	0.195146	−	0.195146i	0.797915	+	0.602770i	$0.205936\pi$
$368$	−4.30360	−	4.30360i	−0.224341	−	0.224341i
$369$	−6.38884			−0.332590
$370$	−0.601285	+	19.5948i	−0.0312593	+	1.01869i
$371$			23.4329i			1.21658i
$372$	−2.85986	+	2.85986i	−0.148277	+	0.148277i
$373$	−16.6782	+	16.6782i	−0.863566	+	0.863566i	−0.991750	−	0.128185i	$-0.959085\pi$
$373$	−16.6782	+	16.6782i	−0.863566	+	0.863566i	0.128185	+	0.991750i	$0.459085\pi$
$374$	40.1165			2.07437
$375$	8.59877	−	7.14571i	0.444038	−	0.369003i
$376$		−	4.58666i		−	0.236539i
$377$	−15.8632	+	15.8632i	−0.816998	+	0.816998i
$378$	2.16643	+	2.16643i	0.111429	+	0.111429i
$379$	−20.7405			−1.06537			−0.532683	−	0.846315i	$-0.678816\pi$
$379$	−20.7405			−1.06537			−0.532683	+	0.846315i	$0.678816\pi$
$380$	4.04611	−	8.86730i	0.207561	−	0.454883i
$381$	14.1957			0.727268
$382$	−17.7856	−	17.7856i	−0.909991	−	0.909991i
$383$	0.963152	−	0.963152i	0.0492148	−	0.0492148i	−0.682071	−	0.731286i	$-0.738921\pi$
$383$	0.963152	−	0.963152i	0.0492148	−	0.0492148i	0.731286	+	0.682071i	$0.238921\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	−28.3666	+	26.6776i	−1.44570	+	1.35961i
$386$	1.74850			0.0889961
$387$	−4.15703	+	4.15703i	−0.211313	+	0.211313i
$388$	−6.22010	+	6.22010i	−0.315778	+	0.315778i
$389$			37.2714i			1.88974i	0.327452	+	0.944868i	$0.393810\pi$
$389$			37.2714i			1.88974i	−0.327452	+	0.944868i	$0.606190\pi$
$390$	−9.03522	+	8.49722i	−0.457516	+	0.430274i
$391$	42.9550			2.17233
$392$	−1.68776	−	1.68776i	−0.0852450	−	0.0852450i
$393$	−3.28303	+	3.28303i	−0.165607	+	0.165607i
$394$	−8.02932			−0.404511
$395$	−9.47298	−	0.290687i	−0.476637	−	0.0146260i
$396$	−5.68402			−0.285633
$397$	10.2595	−	10.2595i	0.514910	−	0.514910i	−0.401117	−	0.916027i	$-0.631378\pi$
$397$	10.2595	−	10.2595i	0.514910	−	0.514910i	0.916027	+	0.401117i	$0.131378\pi$
$398$	2.75697	−	2.75697i	0.138194	−	0.138194i
$399$	5.16861	−	12.3141i	0.258754	−	0.616474i
$400$	−4.99059	−	0.306570i	−0.249530	−	0.0153285i
$401$		−	7.24755i		−	0.361925i	−0.983490	−	0.180963i	$-0.942079\pi$
$401$		−	7.24755i		−	0.361925i	0.983490	−	0.180963i	$-0.0579213\pi$
$402$	−6.12760	−	6.12760i	−0.305617	−	0.305617i
$403$	−15.8632	−	15.8632i	−0.790204	−	0.790204i
$404$			3.42891i			0.170595i
$405$	2.23502	+	0.0685835i	0.111059	+	0.00340794i
$406$	−12.3914			−0.614975
$407$	−35.2372	−	35.2372i	−1.74664	−	1.74664i
$408$	4.99059	+	4.99059i	0.247071	+	0.247071i
$409$	−4.10739			−0.203097			−0.101549	−	0.994831i	$-0.532380\pi$
$409$	−4.10739			−0.203097			−0.101549	+	0.994831i	$0.532380\pi$
$410$	10.4067	−	9.78705i	0.513951	−	0.483348i
$411$		−	3.20383i		−	0.158033i
$412$	13.0842	+	13.0842i	0.644611	+	0.644611i
$413$	5.18833	−	5.18833i	0.255301	−	0.255301i
$414$	−6.08621			−0.299121
$415$	11.4963	+	12.2242i	0.564332	+	0.600063i
$416$	5.54686			0.271957
$417$	−12.3224	−	12.3224i	−0.603433	−	0.603433i
$418$	9.37367	+	22.9344i	0.458481	+	1.12176i
$419$			11.2890i			0.551504i	0.961229	+	0.275752i	$0.0889268\pi$
$419$			11.2890i			0.551504i	−0.961229	+	0.275752i	$0.911073\pi$
$420$	−6.84764	−	0.210126i	−0.334131	−	0.0102531i
$421$			4.87088i			0.237392i	0.992931	+	0.118696i	$0.0378714\pi$
$421$			4.87088i			0.237392i	−0.992931	+	0.118696i	$0.962129\pi$
$422$	−13.3909	+	13.3909i	−0.651858	+	0.651858i
$423$	−3.24326	−	3.24326i	−0.157692	−	0.157692i
$424$		−	7.64832i		−	0.371435i
$425$	26.4360	−	23.3760i	1.28233	−	1.13390i
$426$		−	6.51556i		−	0.315680i
$427$	5.05399	−	5.05399i	0.244580	−	0.244580i
$428$	−5.02931	+	5.02931i	−0.243101	+	0.243101i
$429$		−	31.5284i		−	1.52221i
$430$	0.403197	−	13.1395i	0.0194439	−	0.633642i
$431$		−	7.08729i		−	0.341383i	−0.985325	−	0.170691i	$-0.945400\pi$
$431$		−	7.08729i		−	0.341383i	0.985325	−	0.170691i	$-0.0546001\pi$
$432$	−0.707107	−	0.707107i	−0.0340207	−	0.0340207i
$433$	21.2804	−	21.2804i	1.02267	−	1.02267i	0.0229344	−	0.999737i	$-0.492699\pi$
$433$	21.2804	−	21.2804i	1.02267	−	1.02267i	0.999737	−	0.0229344i	$-0.00730088\pi$
$434$		−	12.3914i		−	0.594806i
$435$	−6.58798	+	6.19570i	−0.315869	+	0.297061i
$436$		−	5.95528i		−	0.285206i
$437$	10.0369	+	24.5572i	0.480131	+	1.17473i
$438$	−2.07682	−	2.07682i	−0.0992345	−	0.0992345i
$439$	27.9747			1.33516			0.667580	−	0.744538i	$-0.267330\pi$
$439$	27.9747			1.33516			0.667580	+	0.744538i	$0.267330\pi$
$440$	9.25865	−	8.70735i	0.441389	−	0.415107i
$441$	−2.38686			−0.113660
$442$	−27.6821	+	27.6821i	−1.31670	+	1.31670i
$443$	−11.9554	−	11.9554i	−0.568019	−	0.568019i	0.363554	−	0.931573i	$-0.381563\pi$
$443$	−11.9554	−	11.9554i	−0.568019	−	0.568019i	−0.931573	+	0.363554i	$0.881563\pi$
$444$		−	8.76719i		−	0.416073i
$445$	5.60608	+	0.172028i	0.265753	+	0.00815489i
$446$	−13.0960			−0.620116
$447$	−1.27163	−	1.27163i	−0.0601462	−	0.0601462i
$448$	2.16643	+	2.16643i	0.102354	+	0.102354i
$449$	−0.799279			−0.0377203			−0.0188602	−	0.999822i	$-0.506004\pi$
$449$	−0.799279			−0.0377203			−0.0188602	+	0.999822i	$0.506004\pi$
$450$	−3.74566	+	3.31210i	−0.176572	+	0.156134i
$451$			36.3143i			1.70997i
$452$	−0.0413876	−	0.0413876i	−0.00194671	−	0.00194671i
$453$	6.09668	+	6.09668i	0.286447	+	0.286447i
$454$		−	3.73260i		−	0.175179i
$455$	1.16554	−	37.9829i	0.0546413	−	1.78066i
$456$	−1.68699	+	4.01921i	−0.0790007	+	0.188217i
$457$	−19.9638	+	19.9638i	−0.933866	+	0.933866i	−0.997945	−	0.0640788i	$-0.979589\pi$
$457$	−19.9638	+	19.9638i	−0.933866	+	0.933866i	0.0640788	+	0.997945i	$0.479589\pi$
$458$	3.49735	−	3.49735i	0.163421	−	0.163421i
$459$	7.05776			0.329428
$460$	9.91377	−	9.32346i	0.462232	−	0.434708i
$461$	−16.7900			−0.781989			−0.390995	−	0.920393i	$-0.627869\pi$
$461$	−16.7900			−0.781989			−0.390995	+	0.920393i	$0.627869\pi$
$462$	12.3141	−	12.3141i	0.572901	−	0.572901i
$463$	13.2413	+	13.2413i	0.615377	+	0.615377i	0.944342	−	0.328965i	$-0.106700\pi$
$463$	13.2413	+	13.2413i	0.615377	+	0.615377i	−0.328965	+	0.944342i	$0.606700\pi$
$464$	4.04446			0.187759
$465$	−6.19570	−	6.58798i	−0.287319	−	0.305510i
$466$			25.6256i			1.18708i
$467$	18.9064	−	18.9064i	0.874885	−	0.874885i	−0.118115	−	0.993000i	$-0.537685\pi$
$467$	18.9064	−	18.9064i	0.874885	−	0.874885i	0.993000	+	0.118115i	$0.0376852\pi$
$468$	3.92222	−	3.92222i	0.181305	−	0.181305i
$469$	26.5500			1.22597
$470$	10.2512	+	0.314569i	0.472855	+	0.0145100i
$471$			11.0211i			0.507825i
$472$	−1.69343	+	1.69343i	−0.0779464	+	0.0779464i
$473$	23.6286	+	23.6286i	1.08645	+	1.08645i
$474$	4.23844			0.194678
$475$	19.5411	+	9.65127i	0.896605	+	0.442830i
$476$	−21.6236			−0.991114
$477$	−5.40818	−	5.40818i	−0.247624	−	0.247624i
$478$	−4.93773	+	4.93773i	−0.225846	+	0.225846i
$479$			6.59491i			0.301329i	0.988585	+	0.150665i	$0.0481413\pi$
$479$			6.59491i			0.301329i	−0.988585	+	0.150665i	$0.951859\pi$
$480$	2.23502	+	0.0685835i	0.102014	+	0.00313039i
$481$	48.6304			2.21735
$482$	−5.33828	+	5.33828i	−0.243152	+	0.243152i
$483$	13.1854	−	13.1854i	0.599955	−	0.599955i
$484$			21.3081i			0.968550i
$485$	−13.4754	−	14.3286i	−0.611887	−	0.650629i
$486$	−1.00000			−0.0453609
$487$	−3.62733	−	3.62733i	−0.164370	−	0.164370i	0.620129	−	0.784499i	$-0.287080\pi$
$487$	−3.62733	−	3.62733i	−0.164370	−	0.164370i	−0.784499	+	0.620129i	$0.787080\pi$
$488$	−1.64958	+	1.64958i	−0.0746732	+	0.0746732i
$489$	−11.1155			−0.502661
$490$	3.88793	−	3.65643i	0.175639	−	0.165181i
$491$	3.35710			0.151504			0.0757519	−	0.997127i	$-0.475864\pi$
$491$	3.35710			0.151504			0.0757519	+	0.997127i	$0.475864\pi$
$492$	−4.51759	+	4.51759i	−0.203669	+	0.203669i
$493$	−20.1842	+	20.1842i	−0.909052	+	0.909052i
$494$	−22.2940	−	9.35751i	−1.00305	−	0.421014i
$495$	0.389830	−	12.7039i	0.0175216	−	0.570997i
$496$			4.04446i			0.181601i
$497$	14.1155	+	14.1155i	0.633168	+	0.633168i
$498$	−5.30657	−	5.30657i	−0.237793	−	0.237793i
$499$		−	13.9250i		−	0.623367i	−0.950186	−	0.311684i	$-0.899107\pi$
$499$		−	13.9250i		−	0.623367i	0.950186	−	0.311684i	$-0.100893\pi$
$500$	1.02746	−	11.1330i	0.0459495	−	0.497884i
$501$	−24.8568			−1.11052
$502$	14.1822	+	14.1822i	0.632981	+	0.632981i
$503$	18.2263	+	18.2263i	0.812668	+	0.812668i	0.985033	−	0.172365i	$-0.0551408\pi$
$503$	18.2263	+	18.2263i	0.812668	+	0.812668i	−0.172365	+	0.985033i	$0.555141\pi$
$504$	3.06380			0.136472
$505$	−7.66367	−	0.235167i	−0.341029	−	0.0104648i
$506$			34.5941i			1.53790i
$507$	12.5636	+	12.5636i	0.557969	+	0.557969i
$508$	10.0379	−	10.0379i	0.445359	−	0.445359i
$509$	−31.4996			−1.39619			−0.698097	−	0.716003i	$-0.745970\pi$
$509$	−31.4996			−1.39619			−0.698097	+	0.716003i	$0.745970\pi$
$510$	−11.4963	+	10.8118i	−0.509066	+	0.478754i
$511$	8.99859			0.398074
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.64913	+	4.03490i	0.0728107	+	0.178145i
$514$		−	12.2496i		−	0.540306i
$515$	−30.1407	+	28.3460i	−1.32816	+	1.24907i
$516$			5.87892i			0.258805i
$517$	−18.4347	+	18.4347i	−0.810759	+	0.810759i
$518$	18.9935	+	18.9935i	0.834528	+	0.834528i
$519$		−	0.153647i		−	0.00674434i
$520$	−0.380423	+	12.3973i	−0.0166826	+	0.543658i
$521$			32.9541i			1.44375i	0.692026	+	0.721873i	$0.256719\pi$
$521$			32.9541i			1.44375i	−0.692026	+	0.721873i	$0.743281\pi$
$522$	2.85986	−	2.85986i	0.125173	−	0.125173i
$523$	−30.6631	+	30.6631i	−1.34080	+	1.34080i	−0.445544	+	0.895260i	$0.646990\pi$
$523$	−30.6631	+	30.6631i	−1.34080	+	1.34080i	−0.895260	+	0.445544i	$0.853010\pi$
$524$			4.64290i			0.202826i
$525$	0.939270	−	15.2902i	0.0409931	−	0.667318i
$526$		−	10.6315i		−	0.463554i
$527$	−20.1842	−	20.1842i	−0.879239	−	0.879239i
$528$	−4.01921	+	4.01921i	−0.174914	+	0.174914i
$529$			14.0419i			0.610519i
$530$	17.0941	+	0.524549i	0.742521	+	0.0227849i
$531$			2.39487i			0.103929i
$532$	−5.05259	−	12.3621i	−0.219058	−	0.535965i
$533$	−25.0584	−	25.0584i	−1.08540	−	1.08540i
$534$	−2.50829			−0.108544
$535$	−10.8957	−	11.5855i	−0.471061	−	0.500886i
$536$	−8.66573			−0.374303
$537$	−6.75144	+	6.75144i	−0.291346	+	0.291346i
$538$	−14.4131	−	14.4131i	−0.621391	−	0.621391i
$539$			13.5670i			0.584370i
$540$	1.62889	−	1.53190i	0.0700963	−	0.0659224i
$541$	−5.86517			−0.252163			−0.126082	−	0.992020i	$-0.540240\pi$
$541$	−5.86517			−0.252163			−0.126082	+	0.992020i	$0.540240\pi$
$542$	14.5414	+	14.5414i	0.624607	+	0.624607i
$543$	13.7450	+	13.7450i	0.589854	+	0.589854i
$544$	7.05776			0.302599
$545$	13.3101	+	0.408434i	0.570144	+	0.0174954i
$546$			16.9944i			0.727295i
$547$	−27.3401	−	27.3401i	−1.16898	−	1.16898i	−0.982450	−	0.186527i	$-0.940277\pi$
$547$	−27.3401	−	27.3401i	−1.16898	−	1.16898i	−0.186527	−	0.982450i	$-0.559723\pi$
$548$	−2.26545	−	2.26545i	−0.0967752	−	0.0967752i
$549$			2.33286i			0.0995642i
$550$	18.8261	+	21.2904i	0.802746	+	0.907826i
$551$	−16.2555	−	6.82297i	−0.692508	−	0.290668i
$552$	−4.30360	+	4.30360i	−0.183173	+	0.183173i
$553$	−9.18229	+	9.18229i	−0.390471	+	0.390471i
$554$	−23.3376			−0.991518
$555$	19.5948	+	0.601285i	0.831754	+	0.0255231i
$556$	−17.4266			−0.739051
$557$	30.4617	−	30.4617i	1.29070	−	1.29070i	0.356350	−	0.934353i	$-0.384021\pi$
$557$	30.4617	−	30.4617i	1.29070	−	1.29070i	0.934353	−	0.356350i	$-0.115979\pi$
$558$	2.85986	+	2.85986i	0.121068	+	0.121068i
$559$	−32.6095			−1.37924
$560$	−4.99059	+	4.69343i	−0.210891	+	0.198334i
$561$		−	40.1165i		−	1.69372i
$562$	11.8093	−	11.8093i	0.498147	−	0.498147i
$563$	−9.62507	+	9.62507i	−0.405648	+	0.405648i	−0.880218	−	0.474570i	$-0.842604\pi$
$563$	−9.62507	+	9.62507i	−0.405648	+	0.405648i	0.474570	+	0.880218i	$0.342604\pi$
$564$	−4.58666			−0.193133
$565$	0.0953405	−	0.0896635i	0.00401100	−	0.00377217i
$566$			12.9675i			0.545063i
$567$	2.16643	−	2.16643i	0.0909816	−	0.0909816i
$568$	−4.60720	−	4.60720i	−0.193314	−	0.193314i
$569$	−12.8721			−0.539627			−0.269814	−	0.962913i	$-0.586962\pi$
$569$	−12.8721			−0.539627			−0.269814	+	0.962913i	$0.586962\pi$
$570$	−8.86730	−	4.04611i	−0.371410	−	0.169473i
$571$	6.13588			0.256778			0.128389	−	0.991724i	$-0.459019\pi$
$571$	6.13588			0.256778			0.128389	+	0.991724i	$0.459019\pi$
$572$	−22.2940	−	22.2940i	−0.932158	−	0.932158i
$573$	−17.7856	+	17.7856i	−0.743004	+	0.743004i
$574$		−	19.5741i		−	0.817007i
$575$	20.1582	+	22.7969i	0.840653	+	0.950695i
$576$	−1.00000			−0.0416667
$577$	−18.5088	+	18.5088i	−0.770532	+	0.770532i	−0.978200	−	0.207667i	$-0.933413\pi$
$577$	−18.5088	+	18.5088i	−0.770532	+	0.770532i	0.207667	+	0.978200i	$0.433413\pi$
$578$	−23.2016	+	23.2016i	−0.965060	+	0.965060i
$579$		−	1.74850i		−	0.0726650i
$580$	−0.277383	+	9.03942i	−0.0115177	+	0.375342i
$581$	22.9927			0.953896
$582$	6.22010	+	6.22010i	0.257831	+	0.257831i
$583$	−30.7402	+	30.7402i	−1.27313	+	1.27313i
$584$	−2.93707			−0.121537
$585$	8.49722	+	9.03522i	0.351317	+	0.373560i
$586$	16.5884			0.685260
$587$	25.9416	−	25.9416i	1.07072	−	1.07072i	0.0734236	−	0.997301i	$-0.476607\pi$
$587$	25.9416	−	25.9416i	1.07072	−	1.07072i	0.997301	−	0.0734236i	$-0.0233925\pi$
$588$	−1.68776	+	1.68776i	−0.0696022	+	0.0696022i
$589$	6.82297	−	16.2555i	0.281136	−	0.669797i
$590$	−3.66870	−	3.90098i	−0.151038	−	0.160601i
$591$			8.02932i			0.330282i
$592$	−6.19934	−	6.19934i	−0.254791	−	0.254791i
$593$	5.30063	+	5.30063i	0.217671	+	0.217671i	0.807516	−	0.589845i	$-0.200811\pi$
$593$	5.30063	+	5.30063i	0.217671	+	0.217671i	−0.589845	+	0.807516i	$0.700811\pi$
$594$			5.68402i			0.233218i
$595$	1.48302	−	48.3290i	0.0607979	−	1.98130i
$596$	−1.79836			−0.0736637
$597$	−2.75697	−	2.75697i	−0.112835	−	0.112835i
$598$	−23.8714	−	23.8714i	−0.976176	−	0.976176i
$599$	8.38430			0.342573			0.171287	−	0.985221i	$-0.445208\pi$
$599$	8.38430			0.342573			0.171287	+	0.985221i	$0.445208\pi$
$600$	−0.306570	+	4.99059i	−0.0125157	+	0.203740i
$601$			11.8588i			0.483731i	0.970310	+	0.241866i	$0.0777594\pi$
$601$			11.8588i			0.483731i	−0.970310	+	0.241866i	$0.922241\pi$
$602$	−12.7363	−	12.7363i	−0.519092	−	0.519092i
$603$	−6.12760	+	6.12760i	−0.249535	+	0.249535i
$604$	8.62201			0.350825
$605$	−47.6240	−	1.46138i	−1.93619	−	0.0594137i
$606$	3.42891			0.139290
$607$	11.1795	+	11.1795i	0.453763	+	0.453763i	0.896601	−	0.442838i	$-0.146028\pi$
$607$	11.1795	+	11.1795i	0.453763	+	0.453763i	−0.442838	+	0.896601i	$0.646028\pi$
$608$	1.64913	+	4.03490i	0.0668809	+	0.163637i
$609$			12.3914i			0.502125i
$610$	−3.57371	−	3.79998i	−0.144695	−	0.153857i
$611$		−	25.4415i		−	1.02925i
$612$	4.99059	−	4.99059i	0.201733	−	0.201733i
$613$	27.8634	+	27.8634i	1.12539	+	1.12539i	0.990917	+	0.134477i	$0.0429355\pi$
$613$	27.8634	+	27.8634i	1.12539	+	1.12539i	0.134477	+	0.990917i	$0.457065\pi$
$614$			10.6309i			0.429029i
$615$	−9.78705	−	10.4067i	−0.394652	−	0.419639i
$616$		−	17.4147i		−	0.701658i
$617$	−9.90590	+	9.90590i	−0.398797	+	0.398797i	−0.877808	−	0.479012i	$-0.840995\pi$
$617$	−9.90590	+	9.90590i	−0.398797	+	0.398797i	0.479012	+	0.877808i	$0.340995\pi$
$618$	13.0842	−	13.0842i	0.526322	−	0.526322i
$619$			13.1404i			0.528156i	0.964501	+	0.264078i	$0.0850676\pi$
$619$			13.1404i			0.528156i	−0.964501	+	0.264078i	$0.914932\pi$
$620$	−9.03942	−	0.277383i	−0.363032	−	0.0111400i
$621$			6.08621i			0.244231i
$622$	12.0874	+	12.0874i	0.484659	+	0.484659i
$623$	5.43405	−	5.43405i	0.217711	−	0.217711i
$624$		−	5.54686i		−	0.222052i
$625$	24.8120	+	3.05994i	0.992481	+	0.122397i
$626$			6.31902i			0.252559i
$627$	22.9344	−	9.37367i	0.915913	−	0.374348i
$628$	7.79308	+	7.79308i	0.310978	+	0.310978i
$629$	61.8768			2.46719
$630$	−0.210126	+	6.84764i	−0.00837162	+	0.272816i
$631$	−1.22727			−0.0488569			−0.0244284	−	0.999702i	$-0.507777\pi$
$631$	−1.22727			−0.0488569			−0.0244284	+	0.999702i	$0.507777\pi$
$632$	2.99703	−	2.99703i	0.119215	−	0.119215i
$633$	13.3909	+	13.3909i	0.532239	+	0.532239i
$634$			28.7488i			1.14176i
$635$	21.7464	+	23.1232i	0.862979	+	0.917618i
$636$	−7.64832			−0.303276
$637$	−9.36178	−	9.36178i	−0.370927	−	0.370927i
$638$	−16.2555	−	16.2555i	−0.643562	−	0.643562i
$639$	−6.51556			−0.257752
$640$	1.62889	−	1.53190i	0.0643876	−	0.0605536i
$641$		−	36.0180i		−	1.42263i	−0.702875	−	0.711313i	$-0.748101\pi$
$641$		−	36.0180i		−	1.42263i	0.702875	−	0.711313i	$-0.251899\pi$
$642$	5.02931	+	5.02931i	0.198491	+	0.198491i
$643$	−2.37113	−	2.37113i	−0.0935082	−	0.0935082i	0.658805	−	0.752314i	$-0.271062\pi$
$643$	−2.37113	−	2.37113i	−0.0935082	−	0.0935082i	−0.752314	+	0.658805i	$0.771062\pi$
$644$		−	18.6469i		−	0.734791i
$645$	−13.1395	−	0.403197i	−0.517367	−	0.0158759i
$646$	−28.3666	−	11.9064i	−1.11607	−	0.468451i
$647$	−1.07039	+	1.07039i	−0.0420812	+	0.0420812i	−0.727834	−	0.685753i	$-0.759473\pi$
$647$	−1.07039	+	1.07039i	−0.0420812	+	0.0420812i	0.685753	+	0.727834i	$0.259473\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	13.6125			0.534337
$650$	−27.6821	−	1.70050i	−1.08578	−	0.0666992i
$651$	−12.3914			−0.485657
$652$	−7.85986	+	7.85986i	−0.307816	+	0.307816i
$653$	−17.2204	−	17.2204i	−0.673887	−	0.673887i	0.284723	−	0.958610i	$-0.408099\pi$
$653$	−17.2204	−	17.2204i	−0.673887	−	0.673887i	−0.958610	+	0.284723i	$0.908099\pi$
$654$	−5.95528			−0.232870
$655$	−10.3770	−	0.318426i	−0.405461	−	0.0124419i
$656$			6.38884i			0.249442i
$657$	−2.07682	+	2.07682i	−0.0810246	+	0.0810246i
$658$	9.93668	−	9.93668i	0.387372	−	0.387372i
$659$	−33.5146			−1.30555			−0.652773	−	0.757554i	$-0.726394\pi$
$659$	−33.5146			−1.30555			−0.652773	+	0.757554i	$0.726394\pi$
$660$	−8.70735	−	9.25865i	−0.338933	−	0.360393i
$661$		−	38.1923i		−	1.48551i	−0.669564	−	0.742754i	$-0.733519\pi$
$661$		−	38.1923i		−	1.48551i	0.669564	−	0.742754i	$-0.266481\pi$
$662$	−15.5532	+	15.5532i	−0.604492	+	0.604492i
$663$	27.6821	+	27.6821i	1.07508	+	1.07508i
$664$	−7.50462			−0.291236
$665$	27.9760	−	10.4448i	1.08486	−	0.405031i
$666$	−8.76719			−0.339722
$667$	−17.4057	−	17.4057i	−0.673952	−	0.673952i
$668$	−17.5764	+	17.5764i	−0.680051	+	0.680051i
$669$			13.0960i			0.506322i
$670$	0.594326	−	19.3680i	0.0229608	−	0.748253i
$671$	13.2601			0.511899
$672$	2.16643	−	2.16643i	0.0835719	−	0.0835719i
$673$	−12.1639	+	12.1639i	−0.468885	+	0.468885i	−0.901553	−	0.432668i	$-0.857572\pi$
$673$	−12.1639	+	12.1639i	−0.468885	+	0.468885i	0.432668	+	0.901553i	$0.357572\pi$
$674$		−	5.95143i		−	0.229240i
$675$	3.31210	+	3.74566i	0.127483	+	0.144171i
$676$	17.7676			0.683369
$677$	27.8121	+	27.8121i	1.06891	+	1.06891i	0.997443	+	0.0714633i	$0.0227669\pi$
$677$	27.8121	+	27.8121i	1.06891	+	1.06891i	0.0714633	+	0.997443i	$0.477233\pi$
$678$	−0.0413876	+	0.0413876i	−0.00158948	+	0.00158948i
$679$	−26.9508			−1.03428
$680$	−0.484046	+	15.7742i	−0.0185623	+	0.604914i
$681$	−3.73260			−0.143033
$682$	16.2555	−	16.2555i	0.622456	−	0.622456i
$683$	17.1745	−	17.1745i	0.657166	−	0.657166i	−0.297543	−	0.954709i	$-0.596167\pi$
$683$	17.1745	−	17.1745i	0.657166	−	0.657166i	0.954709	+	0.297543i	$0.0961671\pi$
$684$	4.01921	+	1.68699i	0.153678	+	0.0645038i
$685$	5.21869	−	4.90794i	0.199396	−	0.187523i
$686$			14.1337i			0.539628i
$687$	−3.49735	−	3.49735i	−0.133432	−	0.133432i
$688$	4.15703	+	4.15703i	0.158485	+	0.158485i
$689$		−	42.4241i		−	1.61623i
$690$	−9.32346	−	9.91377i	−0.354938	−	0.377411i
$691$	−9.98119			−0.379702			−0.189851	−	0.981813i	$-0.560801\pi$
$691$	−9.98119			−0.379702			−0.189851	+	0.981813i	$0.560801\pi$
$692$	−0.108645	−	0.108645i	−0.00413005	−	0.00413005i
$693$	−12.3141	−	12.3141i	−0.467772	−	0.467772i
$694$	26.6872			1.01303
$695$	1.19518	−	38.9487i	0.0453356	−	1.47741i
$696$		−	4.04446i		−	0.153305i
$697$	−31.8841	−	31.8841i	−1.20770	−	1.20770i
$698$	−2.36826	+	2.36826i	−0.0896401	+	0.0896401i
$699$	25.6256			0.969248
$700$	−10.1476	−	11.4759i	−0.383544	−	0.433750i
$701$	8.14987			0.307816			0.153908	−	0.988085i	$-0.450814\pi$
$701$	8.14987			0.307816			0.153908	+	0.988085i	$0.450814\pi$
$702$	−3.92222	−	3.92222i	−0.148035	−	0.148035i
$703$	14.4582	+	35.3747i	0.545302	+	1.33418i
$704$			5.68402i			0.214225i
$705$	0.314569	−	10.2512i	0.0118474	−	0.386084i
$706$		−	30.8944i		−	1.16273i
$707$	−7.42850	+	7.42850i	−0.279378	+	0.279378i
$708$	1.69343	+	1.69343i	0.0636430	+	0.0636430i
$709$			24.1408i			0.906626i	0.891351	+	0.453313i	$0.149758\pi$
$709$			24.1408i			0.906626i	−0.891351	+	0.453313i	$0.850242\pi$
$710$	10.6131	−	9.98119i	0.398304	−	0.374587i
$711$		−	4.23844i		−	0.158954i
$712$	−1.77363	+	1.77363i	−0.0664696	+	0.0664696i
$713$	17.4057	−	17.4057i	0.651849	−	0.651849i
$714$			21.6236i			0.809242i
$715$	51.3564	−	48.2984i	1.92062	−	1.80626i
$716$			9.54798i			0.356825i
$717$	4.93773	+	4.93773i	0.184403	+	0.184403i
$718$	−3.69175	+	3.69175i	−0.137775	+	0.137775i
$719$		−	12.6723i		−	0.472595i	−0.971681	−	0.236298i	$-0.924066\pi$
$719$		−	12.6723i		−	0.472595i	0.971681	−	0.236298i	$-0.0759340\pi$
$720$	0.0685835	−	2.23502i	0.00255596	−	0.0832941i
$721$			56.6919i			2.11132i
$722$	0.178653	−	18.9992i	0.00664878	−	0.707076i
$723$	5.33828	+	5.33828i	0.198533	+	0.198533i
$724$	19.4384			0.722421
$725$	−20.1842	−	1.23991i	−0.749624	−	0.0460491i
$726$	21.3081			0.790818
$727$	12.3201	−	12.3201i	0.456926	−	0.456926i	−0.440719	−	0.897645i	$-0.645276\pi$
$727$	12.3201	−	12.3201i	0.456926	−	0.456926i	0.897645	+	0.440719i	$0.145276\pi$
$728$	12.0169	+	12.0169i	0.445375	+	0.445375i
$729$			1.00000i			0.0370370i
$730$	0.201435	−	6.56440i	0.00745543	−	0.242959i
$731$	−41.4920			−1.53464
$732$	1.64958	+	1.64958i	0.0609704	+	0.0609704i
$733$	−1.44833	−	1.44833i	−0.0534954	−	0.0534954i	0.679853	−	0.733348i	$-0.262044\pi$
$733$	−1.44833	−	1.44833i	−0.0534954	−	0.0534954i	−0.733348	+	0.679853i	$0.762044\pi$
$734$	−5.28697			−0.195146
$735$	−3.65643	−	3.88793i	−0.134869	−	0.143409i
$736$			6.08621i			0.224341i
$737$	34.8294	+	34.8294i	1.28296	+	1.28296i
$738$	4.51759	+	4.51759i	0.166295	+	0.166295i
$739$			8.64709i			0.318088i	0.987271	+	0.159044i	$0.0508412\pi$
$739$			8.64709i			0.318088i	−0.987271	+	0.159044i	$0.949159\pi$
$740$	14.2808	−	13.4305i	0.524973	−	0.493713i
$741$	−9.35751	+	22.2940i	−0.343757	+	0.818990i
$742$	16.5696	−	16.5696i	0.608288	−	0.608288i
$743$	18.4885	−	18.4885i	0.678277	−	0.678277i	−0.281333	−	0.959610i	$-0.590777\pi$
$743$	18.4885	−	18.4885i	0.678277	−	0.678277i	0.959610	+	0.281333i	$0.0907767\pi$
$744$	4.04446			0.148277
$745$	0.123338	−	4.01936i	0.00451875	−	0.147258i
$746$	23.5866			0.863566
$747$	−5.30657	+	5.30657i	−0.194157	+	0.194157i
$748$	−28.3666	−	28.3666i	−1.03719	−	1.03719i
$749$	−21.7913			−0.796238
$750$	−11.1330	−	1.02746i	−0.406521	−	0.0375176i
$751$		−	7.72319i		−	0.281823i	−0.990022	−	0.140912i	$-0.954997\pi$
$751$		−	7.72319i		−	0.281823i	0.990022	−	0.140912i	$-0.0450033\pi$
$752$	−3.24326	+	3.24326i	−0.118269	+	0.118269i
$753$	14.1822	−	14.1822i	0.516827	−	0.516827i
$754$	22.4340			0.816998
$755$	−0.591328	+	19.2703i	−0.0215206	+	0.701319i
$756$		−	3.06380i		−	0.111429i
$757$	−16.2864	+	16.2864i	−0.591937	+	0.591937i	−0.938154	−	0.346217i	$-0.887466\pi$
$757$	−16.2864	+	16.2864i	−0.591937	+	0.591937i	0.346217	+	0.938154i	$0.387466\pi$
$758$	14.6657	+	14.6657i	0.532683	+	0.532683i
$759$	34.5941			1.25569
$760$	−9.13116	+	3.40910i	−0.331222	+	0.123661i
$761$	0.887475			0.0321709			0.0160855	−	0.999871i	$-0.494880\pi$
$761$	0.887475			0.0321709			0.0160855	+	0.999871i	$0.494880\pi$
$762$	−10.0379	−	10.0379i	−0.363634	−	0.363634i
$763$	12.9017	−	12.9017i	0.467073	−	0.467073i
$764$			25.1526i			0.909991i
$765$	10.8118	+	11.4963i	0.390901	+	0.415651i
$766$	−1.36210			−0.0492148
$767$	−9.39321	+	9.39321i	−0.339169	+	0.339169i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$		−	1.13134i		−	0.0407972i	−0.999792	−	0.0203986i	$-0.993506\pi$
$769$		−	1.13134i		−	0.0407972i	0.999792	−	0.0203986i	$-0.00649352\pi$
$770$	38.9221	+	1.19436i	1.40266	+	0.0430418i
$771$	−12.2496			−0.441158
$772$	−1.23637	−	1.23637i	−0.0444980	−	0.0444980i
$773$	6.34620	−	6.34620i	0.228257	−	0.228257i	−0.583707	−	0.811964i	$-0.698398\pi$
$773$	6.34620	−	6.34620i	0.228257	−	0.228257i	0.811964	+	0.583707i	$0.198398\pi$
$774$	5.87892			0.211313
$775$	1.23991	−	20.1842i	0.0445389	−	0.725039i
$776$	8.79655			0.315778
$777$	18.9935	−	18.9935i	0.681389	−	0.681389i
$778$	26.3549	−	26.3549i	0.944868	−	0.944868i

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-2.23502 - 0.0685835i) q^{5} +1.00000 q^{6} +(-2.16643 + 2.16643i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000i q^{4} +(-2.23502 - 0.0685835i) q^{5} +1.00000 q^{6} +(-2.16643 + 2.16643i) q^{7} +(0.707107 - 0.707107i) q^{8} -1.00000i q^{9} +(1.53190 + 1.62889i) q^{10} -5.68402 q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.92222 - 3.92222i) q^{13} +3.06380 q^{14} +(1.62889 - 1.53190i) q^{15} -1.00000 q^{16} +(4.99059 - 4.99059i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(4.01921 + 1.68699i) q^{19} +(0.0685835 - 2.23502i) q^{20} -3.06380i q^{21} +(4.01921 + 4.01921i) q^{22} +(4.30360 + 4.30360i) q^{23} +1.00000i q^{24} +(4.99059 + 0.306570i) q^{25} -5.54686 q^{26} +(0.707107 + 0.707107i) q^{27} +(-2.16643 - 2.16643i) q^{28} -4.04446 q^{29} +(-2.23502 - 0.0685835i) q^{30} -4.04446i q^{31} +(0.707107 + 0.707107i) q^{32} +(4.01921 - 4.01921i) q^{33} -7.05776 q^{34} +(4.99059 - 4.69343i) q^{35} +1.00000 q^{36} +(6.19934 + 6.19934i) q^{37} +(-1.64913 - 4.03490i) q^{38} +5.54686i q^{39} +(-1.62889 + 1.53190i) q^{40} -6.38884i q^{41} +(-2.16643 + 2.16643i) q^{42} +(-4.15703 - 4.15703i) q^{43} -5.68402i q^{44} +(-0.0685835 + 2.23502i) q^{45} -6.08621i q^{46} +(3.24326 - 3.24326i) q^{47} +(0.707107 - 0.707107i) q^{48} -2.38686i q^{49} +(-3.31210 - 3.74566i) q^{50} +7.05776i q^{51} +(3.92222 + 3.92222i) q^{52} +(5.40818 - 5.40818i) q^{53} -1.00000i q^{54} +(12.7039 + 0.389830i) q^{55} +3.06380i q^{56} +(-4.03490 + 1.64913i) q^{57} +(2.85986 + 2.85986i) q^{58} -2.39487 q^{59} +(1.53190 + 1.62889i) q^{60} -2.33286 q^{61} +(-2.85986 + 2.85986i) q^{62} +(2.16643 + 2.16643i) q^{63} -1.00000i q^{64} +(-9.03522 + 8.49722i) q^{65} -5.68402 q^{66} +(-6.12760 - 6.12760i) q^{67} +(4.99059 + 4.99059i) q^{68} -6.08621 q^{69} +(-6.84764 - 0.210126i) q^{70} -6.51556i q^{71} +(-0.707107 - 0.707107i) q^{72} +(-2.07682 - 2.07682i) q^{73} -8.76719i q^{74} +(-3.74566 + 3.31210i) q^{75} +(-1.68699 + 4.01921i) q^{76} +(12.3141 - 12.3141i) q^{77} +(3.92222 - 3.92222i) q^{78} +4.23844 q^{79} +(2.23502 + 0.0685835i) q^{80} -1.00000 q^{81} +(-4.51759 + 4.51759i) q^{82} +(-5.30657 - 5.30657i) q^{83} +3.06380 q^{84} +(-11.4963 + 10.8118i) q^{85} +5.87892i q^{86} +(2.85986 - 2.85986i) q^{87} +(-4.01921 + 4.01921i) q^{88} -2.50829 q^{89} +(1.62889 - 1.53190i) q^{90} +16.9944i q^{91} +(-4.30360 + 4.30360i) q^{92} +(2.85986 + 2.85986i) q^{93} -4.58666 q^{94} +(-8.86730 - 4.04611i) q^{95} -1.00000 q^{96} +(6.22010 + 6.22010i) q^{97} +(-1.68776 + 1.68776i) q^{98} +5.68402i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20q - 4q^{5} + 20q^{6} - 4q^{7} + O(q^{10}) \)	\( 20q - 4q^{5} + 20q^{6} - 4q^{7} - 8q^{11} - 20q^{16} + 4q^{17} + 44q^{23} + 4q^{25} - 8q^{26} - 4q^{28} - 4q^{30} + 4q^{35} + 20q^{36} - 4q^{38} - 4q^{42} + 52q^{43} + 4q^{47} + 16q^{55} - 4q^{57} + 8q^{58} + 32q^{61} - 8q^{62} + 4q^{63} - 8q^{66} + 4q^{68} - 20q^{73} + 20q^{76} - 24q^{77} + 4q^{80} - 20q^{81} - 24q^{82} - 116q^{83} - 60q^{85} + 8q^{87} - 44q^{92} + 8q^{93} - 32q^{95} - 20q^{96} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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