LMFDB - Embedded newform 120.2.m.b.59.14

Newspace parameters

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.m (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
Defining polynomial:	$ x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 192x^12 + 672x^10 + 1092x^8 + 880x^6 + 352x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			59.14
Root			$-2.13875i$ of defining polynomial
Character	$\chi$	$=$	120.59
Dual form			120.2.m.b.59.15

$q$-expansion

$f(q)$	$=$	$q+(1.30656 - 0.541196i) q^{2} +(-0.541196 + 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(-1.25928 + 1.84776i) q^{5} +(0.183339 + 2.44262i) q^{6} +3.29066 q^{7} +(1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +O(q^{10})$	\(q+(1.30656 - 0.541196i) q^{2} +(-0.541196 + 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(-1.25928 + 1.84776i) q^{5} +(0.183339 + 2.44262i) q^{6} +3.29066 q^{7} +(1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +(-0.645329 + 3.09573i) q^{10} -2.51856i q^{11} +(1.56148 + 3.09221i) q^{12} -4.65369 q^{13} +(4.29945 - 1.78089i) q^{14} +(-2.35865 - 3.07193i) q^{15} -4.00000i q^{16} -3.69552 q^{17} +(-4.11813 - 1.02028i) q^{18} +0.828427 q^{19} +(0.832235 + 4.39402i) q^{20} +(-1.78089 + 5.41421i) q^{21} +(-1.36303 - 3.29066i) q^{22} +2.61313i q^{23} +(3.71366 + 3.19510i) q^{24} +(-1.82843 - 4.65369i) q^{25} +(-6.08034 + 2.51856i) q^{26} +(4.23671 - 3.00836i) q^{27} +(4.65369 - 4.65369i) q^{28} +6.08034 q^{29} +(-4.74425 - 2.73718i) q^{30} -1.17157i q^{31} +(-2.16478 - 5.22625i) q^{32} +(4.14386 + 1.36303i) q^{33} +(-4.82843 + 2.00000i) q^{34} +(-4.14386 + 6.08034i) q^{35} +(-5.93277 + 0.895653i) q^{36} -1.92762 q^{37} +(1.08239 - 0.448342i) q^{38} +(2.51856 - 7.65685i) q^{39} +(3.46539 + 5.29066i) q^{40} +8.59890i q^{41} +(0.603305 + 8.03782i) q^{42} +6.01673i q^{43} +(-3.56178 - 3.56178i) q^{44} +(6.33083 - 2.21824i) q^{45} +(1.41421 + 3.41421i) q^{46} -2.61313i q^{47} +(6.58132 + 2.16478i) q^{48} +3.82843 q^{49} +(-4.90752 - 5.09080i) q^{50} +(2.00000 - 6.08034i) q^{51} +(-6.58132 + 6.58132i) q^{52} +4.59220i q^{53} +(3.90742 - 6.22351i) q^{54} +(4.65369 + 3.17157i) q^{55} +(3.56178 - 8.59890i) q^{56} +(-0.448342 + 1.36303i) q^{57} +(7.94435 - 3.29066i) q^{58} +2.51856i q^{59} +(-7.68000 - 1.00872i) q^{60} -8.48528i q^{61} +(-0.634051 - 1.53073i) q^{62} +(-7.94435 - 5.86030i) q^{63} +(-5.65685 - 5.65685i) q^{64} +(5.86030 - 8.59890i) q^{65} +(6.15188 - 0.461750i) q^{66} -3.29066i q^{67} +(-5.22625 + 5.22625i) q^{68} +(-4.29945 - 1.41421i) q^{69} +(-2.12356 + 10.1870i) q^{70} +7.12356 q^{71} +(-7.26682 + 4.38102i) q^{72} +6.58132i q^{73} +(-2.51856 + 1.04322i) q^{74} +(8.64639 - 0.489804i) q^{75} +(1.17157 - 1.17157i) q^{76} -8.28772i q^{77} +(-0.853202 - 11.3672i) q^{78} +16.4853i q^{79} +(7.39104 + 5.03712i) q^{80} +(2.65685 + 8.59890i) q^{81} +(4.65369 + 11.2350i) q^{82} +9.37011 q^{83} +(5.13829 + 10.1754i) q^{84} +(4.65369 - 6.82843i) q^{85} +(3.25623 + 7.86123i) q^{86} +(-3.29066 + 10.0042i) q^{87} +(-6.58132 - 2.72607i) q^{88} -5.03712i q^{89} +(7.07112 - 6.32450i) q^{90} -15.3137 q^{91} +(3.69552 + 3.69552i) q^{92} +(1.92762 + 0.634051i) q^{93} +(-1.41421 - 3.41421i) q^{94} +(-1.04322 + 1.53073i) q^{95} +(9.77048 - 0.733355i) q^{96} -2.72607i q^{97} +(5.00208 - 2.07193i) q^{98} +(-4.48528 + 6.08034i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^9	$ 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) $ 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.30656	−	0.541196i	0.923880	−	0.382683i
$2$	1.30656	−	0.541196i	0.923880	−	0.382683i
$3$	−0.541196	+	1.64533i	−0.312460	+	0.949931i
$3$	−0.541196	+	1.64533i	−0.312460	+	0.949931i
$4$	1.41421	−	1.41421i	0.707107	−	0.707107i
$5$	−1.25928	+	1.84776i	−0.563167	+	0.826343i
$5$	−1.25928	+	1.84776i	−0.563167	+	0.826343i
$6$	0.183339	+	2.44262i	0.0748477	+	0.997195i
$7$	3.29066			1.24375			0.621876	−	0.783116i	$-0.286371\pi$
$7$	3.29066			1.24375			0.621876	+	0.783116i	$0.286371\pi$
$8$	1.08239	−	2.61313i	0.382683	−	0.923880i
$9$	−2.41421	−	1.78089i	−0.804738	−	0.593630i
$10$	−0.645329	+	3.09573i	−0.204071	+	0.978956i
$11$		−	2.51856i		−	0.759374i	−0.925115	−	0.379687i	$-0.876032\pi$
$11$		−	2.51856i		−	0.759374i	0.925115	−	0.379687i	$-0.123968\pi$
$12$	1.56148	+	3.09221i	0.450760	+	0.892645i
$13$	−4.65369			−1.29070			−0.645351	−	0.763886i	$-0.723289\pi$
$13$	−4.65369			−1.29070			−0.645351	+	0.763886i	$0.723289\pi$
$14$	4.29945	−	1.78089i	1.14908	−	0.475963i
$15$	−2.35865	−	3.07193i	−0.609002	−	0.793169i
$16$		−	4.00000i		−	1.00000i
$17$	−3.69552			−0.896295			−0.448147	−	0.893960i	$-0.647916\pi$
$17$	−3.69552			−0.896295			−0.448147	+	0.893960i	$0.647916\pi$
$18$	−4.11813	−	1.02028i	−0.970653	−	0.240483i
$19$	0.828427			0.190054			0.0950271	−	0.995475i	$-0.469706\pi$
$19$	0.828427			0.190054			0.0950271	+	0.995475i	$0.469706\pi$
$20$	0.832235	+	4.39402i	0.186093	+	0.982532i
$21$	−1.78089	+	5.41421i	−0.388622	+	1.18148i
$22$	−1.36303	−	3.29066i	−0.290600	−	0.701571i
$23$			2.61313i			0.544874i	0.962174	+	0.272437i	$0.0878297\pi$
$23$			2.61313i			0.544874i	−0.962174	+	0.272437i	$0.912170\pi$
$24$	3.71366	+	3.19510i	0.758049	+	0.652198i
$25$	−1.82843	−	4.65369i	−0.365685	−	0.930739i
$26$	−6.08034	+	2.51856i	−1.19245	+	0.493930i
$27$	4.23671	−	3.00836i	0.815356	−	0.578960i
$28$	4.65369	−	4.65369i	0.879465	−	0.879465i
$29$	6.08034			1.12909			0.564546	−	0.825402i	$-0.309051\pi$
$29$	6.08034			1.12909			0.564546	+	0.825402i	$0.309051\pi$
$30$	−4.74425	−	2.73718i	−0.866177	−	0.499738i
$31$		−	1.17157i		−	0.210421i	−0.994450	−	0.105210i	$-0.966448\pi$
$31$		−	1.17157i		−	0.210421i	0.994450	−	0.105210i	$-0.0335516\pi$
$32$	−2.16478	−	5.22625i	−0.382683	−	0.923880i
$33$	4.14386	+	1.36303i	0.721353	+	0.237274i
$34$	−4.82843	+	2.00000i	−0.828068	+	0.342997i
$35$	−4.14386	+	6.08034i	−0.700440	+	1.02777i
$36$	−5.93277	+	0.895653i	−0.988796	+	0.149276i
$37$	−1.92762			−0.316899			−0.158450	−	0.987367i	$-0.550650\pi$
$37$	−1.92762			−0.316899			−0.158450	+	0.987367i	$0.550650\pi$
$38$	1.08239	−	0.448342i	0.175587	−	0.0727306i
$39$	2.51856	−	7.65685i	0.403292	−	1.22608i
$40$	3.46539	+	5.29066i	0.547927	+	0.836526i
$41$			8.59890i			1.34292i	0.741039	+	0.671461i	$0.234333\pi$
$41$			8.59890i			1.34292i	−0.741039	+	0.671461i	$0.765667\pi$
$42$	0.603305	+	8.03782i	0.0930920	+	1.24026i
$43$			6.01673i			0.917542i	0.888554	+	0.458771i	$0.151710\pi$
$43$			6.01673i			0.917542i	−0.888554	+	0.458771i	$0.848290\pi$
$44$	−3.56178	−	3.56178i	−0.536959	−	0.536959i
$45$	6.33083	−	2.21824i	0.943744	−	0.330676i
$46$	1.41421	+	3.41421i	0.208514	+	0.503398i
$47$		−	2.61313i		−	0.381164i	−0.981671	−	0.190582i	$-0.938963\pi$
$47$		−	2.61313i		−	0.381164i	0.981671	−	0.190582i	$-0.0610374\pi$
$48$	6.58132	+	2.16478i	0.949931	+	0.312460i
$49$	3.82843			0.546918
$50$	−4.90752	−	5.09080i	−0.694027	−	0.719949i
$51$	2.00000	−	6.08034i	0.280056	−	0.851418i
$52$	−6.58132	+	6.58132i	−0.912664	+	0.912664i
$53$			4.59220i			0.630787i	0.948961	+	0.315394i	$0.102137\pi$
$53$			4.59220i			0.630787i	−0.948961	+	0.315394i	$0.897863\pi$
$54$	3.90742	−	6.22351i	0.531732	−	0.846912i
$55$	4.65369	+	3.17157i	0.627504	+	0.427655i
$56$	3.56178	−	8.59890i	0.475963	−	1.14908i
$57$	−0.448342	+	1.36303i	−0.0593843	+	0.180538i
$58$	7.94435	−	3.29066i	1.04314	−	0.432085i
$59$			2.51856i			0.327889i	0.986470	+	0.163944i	$0.0524217\pi$
$59$			2.51856i			0.327889i	−0.986470	+	0.163944i	$0.947578\pi$
$60$	−7.68000	−	1.00872i	−0.991484	−	0.130226i
$61$		−	8.48528i		−	1.08643i	−0.839594	−	0.543214i	$-0.817207\pi$
$61$		−	8.48528i		−	1.08643i	0.839594	−	0.543214i	$-0.182793\pi$
$62$	−0.634051	−	1.53073i	−0.0805245	−	0.194403i
$63$	−7.94435	−	5.86030i	−1.00089	−	0.738329i
$64$	−5.65685	−	5.65685i	−0.707107	−	0.707107i
$65$	5.86030	−	8.59890i	0.726881	−	1.06656i
$66$	6.15188	−	0.461750i	0.757244	−	0.0568375i
$67$		−	3.29066i		−	0.402018i	−0.979589	−	0.201009i	$-0.935578\pi$
$67$		−	3.29066i		−	0.402018i	0.979589	−	0.201009i	$-0.0644220\pi$
$68$	−5.22625	+	5.22625i	−0.633776	+	0.633776i
$69$	−4.29945	−	1.41421i	−0.517593	−	0.170251i
$70$	−2.12356	+	10.1870i	−0.253813	+	1.21758i
$71$	7.12356			0.845412			0.422706	−	0.906267i	$-0.361080\pi$
$71$	7.12356			0.845412			0.422706	+	0.906267i	$0.361080\pi$
$72$	−7.26682	+	4.38102i	−0.856403	+	0.516308i
$73$			6.58132i			0.770285i	0.922857	+	0.385142i	$0.125848\pi$
$73$			6.58132i			0.770285i	−0.922857	+	0.385142i	$0.874152\pi$
$74$	−2.51856	+	1.04322i	−0.292777	+	0.121272i
$75$	8.64639	−	0.489804i	0.998399	−	0.0565576i
$76$	1.17157	−	1.17157i	0.134389	−	0.134389i
$77$		−	8.28772i		−	0.944473i
$78$	−0.853202	−	11.3672i	−0.0966061	−	1.28708i
$79$			16.4853i			1.85474i	0.374147	+	0.927370i	$0.377936\pi$
$79$			16.4853i			1.85474i	−0.374147	+	0.927370i	$0.622064\pi$
$80$	7.39104	+	5.03712i	0.826343	+	0.563167i
$81$	2.65685	+	8.59890i	0.295206	+	0.955434i
$82$	4.65369	+	11.2350i	0.513914	+	1.24070i
$83$	9.37011			1.02850			0.514252	−	0.857639i	$-0.328070\pi$
$83$	9.37011			1.02850			0.514252	+	0.857639i	$0.328070\pi$
$84$	5.13829	+	10.1754i	0.560634	+	1.11023i
$85$	4.65369	−	6.82843i	0.504764	−	0.740647i
$86$	3.25623	+	7.86123i	0.351128	+	0.847699i
$87$	−3.29066	+	10.0042i	−0.352796	+	1.07256i
$88$	−6.58132	−	2.72607i	−0.701571	−	0.290600i
$89$		−	5.03712i		−	0.533934i	−0.963706	−	0.266967i	$-0.913979\pi$
$89$		−	5.03712i		−	0.533934i	0.963706	−	0.266967i	$-0.0860214\pi$
$90$	7.07112	−	6.32450i	0.745362	−	0.666660i
$91$	−15.3137			−1.60531
$92$	3.69552	+	3.69552i	0.385284	+	0.385284i
$93$	1.92762	+	0.634051i	0.199885	+	0.0657480i
$94$	−1.41421	−	3.41421i	−0.145865	−	0.352149i
$95$	−1.04322	+	1.53073i	−0.107032	+	0.157050i
$96$	9.77048	−	0.733355i	0.997195	−	0.0748477i
$97$		−	2.72607i		−	0.276790i	−0.990377	−	0.138395i	$-0.955806\pi$
$97$		−	2.72607i		−	0.276790i	0.990377	−	0.138395i	$-0.0441944\pi$
$98$	5.00208	−	2.07193i	0.505286	−	0.209297i
$99$	−4.48528	+	6.08034i	−0.450788	+	0.611097i
$100$	−9.16710	−	3.99553i	−0.916710	−	0.399553i
$101$	−13.2039			−1.31384			−0.656919	−	0.753961i	$-0.728141\pi$
$101$	−13.2039			−1.31384			−0.656919	+	0.753961i	$0.728141\pi$
$102$	−0.677532	−	9.02674i	−0.0670856	−	0.893781i
$103$	−6.01673			−0.592846			−0.296423	−	0.955057i	$-0.595794\pi$
$103$	−6.01673			−0.592846			−0.296423	+	0.955057i	$0.595794\pi$
$104$	−5.03712	+	12.1607i	−0.493930	+	1.19245i
$105$	−7.76152	−	10.1087i	−0.757447	−	0.986505i
$106$	2.48528	+	6.00000i	0.241392	+	0.582772i
$107$	−8.47343			−0.819157			−0.409579	−	0.912275i	$-0.634324\pi$
$107$	−8.47343			−0.819157			−0.409579	+	0.912275i	$0.634324\pi$
$108$	1.73715	−	10.2461i	0.167157	−	0.985930i
$109$			0.485281i			0.0464815i	0.999730	+	0.0232408i	$0.00739843\pi$
$109$			0.485281i			0.0464815i	−0.999730	+	0.0232408i	$0.992602\pi$
$110$	7.79679	+	1.62530i	0.743394	+	0.154966i
$111$	1.04322	−	3.17157i	0.0990182	−	0.301032i
$112$		−	13.1626i		−	1.24375i
$113$	−8.92177			−0.839290			−0.419645	−	0.907688i	$-0.637845\pi$
$113$	−8.92177			−0.839290			−0.419645	+	0.907688i	$0.637845\pi$
$114$	0.151883	+	2.02353i	0.0142251	+	0.189521i
$115$	−4.82843	−	3.29066i	−0.450253	−	0.306855i
$116$	8.59890	−	8.59890i	0.798388	−	0.798388i
$117$	11.2350	+	8.28772i	1.03868	+	0.766200i
$118$	1.36303	+	3.29066i	0.125478	+	0.302930i
$119$	−12.1607			−1.11477
$120$	−10.5803	+	2.83843i	−0.965847	+	0.259112i
$121$	4.65685			0.423350
$122$	−4.59220	−	11.0866i	−0.415758	−	1.00373i
$123$	−14.1480	−	4.65369i	−1.27568	−	0.419609i
$124$	−1.65685	−	1.65685i	−0.148790	−	0.148790i
$125$	10.9014	+	2.48181i	0.975051	+	0.221980i
$126$	−13.5514	−	3.35740i	−1.20725	−	0.299101i
$127$	−3.29066			−0.291999			−0.145999	−	0.989285i	$-0.546640\pi$
$127$	−3.29066			−0.291999			−0.145999	+	0.989285i	$0.546640\pi$
$128$	−10.4525	−	4.32957i	−0.923880	−	0.382683i
$129$	−9.89949	−	3.25623i	−0.871602	−	0.286695i
$130$	3.00316	−	14.4066i	0.263395	−	1.26354i
$131$		−	21.8028i		−	1.90492i	−0.304663	−	0.952460i	$-0.598544\pi$
$131$		−	21.8028i		−	1.90492i	0.304663	−	0.952460i	$-0.401456\pi$
$132$	7.78793	−	3.93268i	0.677852	−	0.342296i
$133$	2.72607			0.236380
$134$	−1.78089	−	4.29945i	−0.153846	−	0.371416i
$135$	0.223521	+	11.6168i	0.0192377	+	0.999815i
$136$	−4.00000	+	9.65685i	−0.342997	+	0.828068i
$137$	11.9832			1.02380			0.511899	−	0.859046i	$-0.328942\pi$
$137$	11.9832			1.02380			0.511899	+	0.859046i	$0.328942\pi$
$138$	−6.38287	+	0.479087i	−0.543346	+	0.0407826i
$139$	14.4853			1.22863			0.614313	−	0.789063i	$-0.289433\pi$
$139$	14.4853			1.22863			0.614313	+	0.789063i	$0.289433\pi$
$140$	2.73860	+	14.4592i	0.231454	+	1.22203i
$141$	4.29945	+	1.41421i	0.362079	+	0.119098i
$142$	9.30739	−	3.85525i	0.781058	−	0.323525i
$143$			11.7206i			0.980126i
$144$	−7.12356	+	9.65685i	−0.593630	+	0.804738i
$145$	−7.65685	+	11.2350i	−0.635867	+	0.933017i
$146$	3.56178	+	8.59890i	0.294775	+	0.711650i
$147$	−2.07193	+	6.29902i	−0.170890	+	0.519535i
$148$	−2.72607	+	2.72607i	−0.224082	+	0.224082i
$149$	−14.6792			−1.20257			−0.601285	−	0.799034i	$-0.705344\pi$
$149$	−14.6792			−1.20257			−0.601285	+	0.799034i	$0.705344\pi$
$150$	11.0320	−	5.31935i	0.900757	−	0.434323i
$151$			2.82843i			0.230174i	0.993355	+	0.115087i	$0.0367147\pi$
$151$			2.82843i			0.230174i	−0.993355	+	0.115087i	$0.963285\pi$
$152$	0.896683	−	2.16478i	0.0727306	−	0.175587i
$153$	8.92177	+	6.58132i	0.721282	+	0.532068i
$154$	−4.48528	−	10.8284i	−0.361434	−	0.872580i
$155$	2.16478	+	1.47534i	0.173880	+	0.118502i
$156$	−7.26665	−	14.3902i	−0.581797	−	1.15214i
$157$	5.78287			0.461523			0.230762	−	0.973010i	$-0.425878\pi$
$157$	5.78287			0.461523			0.230762	+	0.973010i	$0.425878\pi$
$158$	8.92177	+	21.5391i	0.709778	+	1.71356i
$159$	−7.55568	−	2.48528i	−0.599204	−	0.197096i
$160$	12.3829	+	2.58132i	0.978956	+	0.204071i
$161$			8.59890i			0.677688i
$162$	8.12504	+	9.79713i	0.638363	+	0.769735i
$163$		−	6.01673i		−	0.471266i	−0.971842	−	0.235633i	$-0.924284\pi$
$163$		−	6.01673i		−	0.471266i	0.971842	−	0.235633i	$-0.0757164\pi$
$164$	12.1607	+	12.1607i	0.949590	+	0.949590i
$165$	−7.73684	+	5.94041i	−0.602312	+	0.462460i
$166$	12.2426	−	5.07107i	0.950213	−	0.393591i
$167$		−	17.3952i		−	1.34608i	−0.739606	−	0.673040i	$-0.764988\pi$
$167$		−	17.3952i		−	1.34608i	0.739606	−	0.673040i	$-0.235012\pi$
$168$	12.2204	+	10.5140i	0.942824	+	0.811172i
$169$	8.65685			0.665912
$170$	2.38482	−	11.4403i	0.182908	−	0.877433i
$171$	−2.00000	−	1.47534i	−0.152944	−	0.112822i
$172$	8.50894	+	8.50894i	0.648800	+	0.648800i
$173$		−	21.5391i		−	1.63758i	−0.574090	−	0.818792i	$-0.694644\pi$
$173$		−	21.5391i		−	1.63758i	0.574090	−	0.818792i	$-0.305356\pi$
$174$	1.11476	+	14.8520i	0.0845099	+	1.12592i
$175$	−6.01673	−	15.3137i	−0.454822	−	1.15761i
$176$	−10.0742			−0.759374
$177$	−4.14386	−	1.36303i	−0.311472	−	0.102452i
$178$	−2.72607	−	6.58132i	−0.204328	−	0.493290i
$179$			9.64212i			0.720686i	0.932820	+	0.360343i	$0.117340\pi$
$179$			9.64212i			0.720686i	−0.932820	+	0.360343i	$0.882660\pi$
$180$	5.81607	−	12.0902i	0.433504	−	0.901151i
$181$			10.3431i			0.768800i	0.923167	+	0.384400i	$0.125592\pi$
$181$			10.3431i			0.768800i	−0.923167	+	0.384400i	$0.874408\pi$
$182$	−20.0083	+	8.28772i	−1.48312	+	0.614327i
$183$	13.9611	+	4.59220i	1.03203	+	0.339465i
$184$	6.82843	+	2.82843i	0.503398	+	0.208514i
$185$	2.42742	−	3.56178i	0.178467	−	0.261867i
$186$	2.86171	−	0.214795i	0.209830	−	0.0157495i
$187$			9.30739i			0.680623i
$188$	−3.69552	−	3.69552i	−0.269523	−	0.269523i
$189$	13.9416	−	9.89949i	1.01410	−	0.720082i
$190$	−0.534608	+	2.56459i	−0.0387845	+	0.186055i
$191$	5.03712			0.364473			0.182237	−	0.983255i	$-0.441666\pi$
$191$	5.03712			0.364473			0.182237	+	0.983255i	$0.441666\pi$
$192$	12.3689	−	6.24592i	0.892645	−	0.450760i
$193$		−	19.7439i		−	1.42120i	−0.703596	−	0.710600i	$-0.748424\pi$
$193$		−	19.7439i		−	1.42120i	0.703596	−	0.710600i	$-0.251576\pi$
$194$	−1.47534	−	3.56178i	−0.105923	−	0.255721i
$195$	10.9764	+	14.2958i	0.786040	+	1.02374i
$196$	5.41421	−	5.41421i	0.386730	−	0.386730i
$197$			11.9832i			0.853770i	0.904306	+	0.426885i	$0.140389\pi$
$197$			11.9832i			0.853770i	−0.904306	+	0.426885i	$0.859611\pi$
$198$	−2.56964	+	10.3718i	−0.182617	+	0.737089i
$199$		−	9.17157i		−	0.650156i	−0.945687	−	0.325078i	$-0.894610\pi$
$199$		−	9.17157i		−	0.650156i	0.945687	−	0.325078i	$-0.105390\pi$
$200$	−14.1398	−	0.259210i	−0.999832	−	0.0183289i
$201$	5.41421	+	1.78089i	0.381889	+	0.125614i
$202$	−17.2517	+	7.14590i	−1.21383	+	0.502784i
$203$	20.0083			1.40431
$204$	−5.77048	−	11.4273i	−0.404014	−	0.800073i
$205$	−15.8887	−	10.8284i	−1.10971	−	0.756290i
$206$	−7.86123	+	3.25623i	−0.547718	+	0.226872i
$207$	4.65369	−	6.30864i	0.323454	−	0.438481i
$208$			18.6148i			1.29070i
$209$		−	2.08644i		−	0.144322i
$210$	−15.6117	−	9.00711i	−1.07731	−	0.621549i
$211$	18.4853			1.27258			0.636290	−	0.771450i	$-0.280468\pi$
$211$	18.4853			1.27258			0.636290	+	0.771450i	$0.280468\pi$
$212$	6.49435	+	6.49435i	0.446034	+	0.446034i
$213$	−3.85525	+	11.7206i	−0.264157	+	0.803083i
$214$	−11.0711	+	4.58579i	−0.756803	+	0.313478i
$215$	−11.1175	−	7.57675i	−0.758205	−	0.516730i
$216$	−3.27545	−	14.3273i	−0.222866	−	0.974849i
$217$		−	3.85525i		−	0.261711i
$218$	0.262632	+	0.634051i	0.0177877	+	0.0429433i
$219$	−10.8284	−	3.56178i	−0.731717	−	0.240683i
$220$	11.0666	−	2.09603i	0.746110	−	0.141315i
$221$	17.1978			1.15685
$222$	−0.353408	−	4.70845i	−0.0237192	−	0.316010i
$223$	21.9054			1.46690			0.733448	−	0.679746i	$-0.237910\pi$
$223$	21.9054			1.46690			0.733448	+	0.679746i	$0.237910\pi$
$224$	−7.12356	−	17.1978i	−0.475963	−	1.14908i
$225$	−3.87351	+	14.4912i	−0.258234	+	0.966082i
$226$	−11.6569	+	4.82843i	−0.775402	+	0.321182i
$227$	−4.14386			−0.275038			−0.137519	−	0.990499i	$-0.543913\pi$
$227$	−4.14386			−0.275038			−0.137519	+	0.990499i	$0.543913\pi$
$228$	1.29357	+	2.56167i	0.0856689	+	0.169651i
$229$			19.3137i			1.27629i	0.769918	+	0.638143i	$0.220297\pi$
$229$			19.3137i			1.27629i	−0.769918	+	0.638143i	$0.779703\pi$
$230$	−8.08954	−	1.68633i	−0.533408	−	0.111193i
$231$	13.6360	+	4.48528i	0.897184	+	0.295110i
$232$	6.58132	−	15.8887i	0.432085	−	1.04314i
$233$	−15.9414			−1.04436			−0.522178	−	0.852837i	$-0.674880\pi$
$233$	−15.9414			−1.04436			−0.522178	+	0.852837i	$0.674880\pi$
$234$	19.1645	+	4.74808i	1.25282	+	0.310392i
$235$	4.82843	+	3.29066i	0.314972	+	0.214659i
$236$	3.56178	+	3.56178i	0.231852	+	0.231852i
$237$	−27.1237	−	8.92177i	−1.76187	−	0.579531i
$238$	−15.8887	+	6.58132i	−1.02991	+	0.426603i
$239$	22.2349			1.43826			0.719129	−	0.694877i	$-0.244541\pi$
$239$	22.2349			1.43826			0.719129	+	0.694877i	$0.244541\pi$
$240$	−12.2877	+	9.43461i	−0.793169	+	0.609002i
$241$	−6.48528			−0.417754			−0.208877	−	0.977942i	$-0.566981\pi$
$241$	−6.48528			−0.417754			−0.208877	+	0.977942i	$0.566981\pi$
$242$	6.08447	−	2.52027i	0.391125	−	0.162009i
$243$	−15.5859	−	0.282294i	−0.999836	−	0.0181092i
$244$	−12.0000	−	12.0000i	−0.768221	−	0.768221i
$245$	−4.82106	+	7.07401i	−0.308006	+	0.451942i
$246$	−21.0038	+	1.57651i	−1.33916	+	0.100515i
$247$	−3.85525			−0.245303
$248$	−3.06147	−	1.26810i	−0.194403	−	0.0805245i
$249$	−5.07107	+	15.4169i	−0.321366	+	0.977007i
$250$	15.5865	−	2.65716i	0.985778	−	0.168053i
$251$			11.7286i			0.740301i	0.928972	+	0.370150i	$0.120694\pi$
$251$			11.7286i			0.740301i	−0.928972	+	0.370150i	$0.879306\pi$
$252$	−19.5227	+	2.94729i	−1.22982	+	0.185662i
$253$	6.58132			0.413764
$254$	−4.29945	+	1.78089i	−0.269772	+	0.111743i
$255$	8.71645	+	11.3524i	0.545845	+	0.710913i
$256$	−16.0000			−1.00000
$257$	16.3128			1.01756			0.508782	−	0.860895i	$-0.330096\pi$
$257$	16.3128			1.01756			0.508782	+	0.860895i	$0.330096\pi$
$258$	−14.6966	+	1.10310i	−0.914969	+	0.0686760i
$259$	−6.34315			−0.394144
$260$	−3.87297	−	20.4484i	−0.240191	−	1.26816i
$261$	−14.6792	−	10.8284i	−0.908622	−	0.670263i
$262$	−11.7996	−	28.4867i	−0.728981	−	1.75992i
$263$		−	22.2500i		−	1.37200i	−0.727604	−	0.685998i	$-0.759366\pi$
$263$		−	22.2500i		−	1.37200i	0.727604	−	0.685998i	$-0.240634\pi$
$264$	8.04706	−	9.35309i	0.495263	−	0.575643i
$265$	−8.48528	−	5.78287i	−0.521247	−	0.355239i
$266$	3.56178	−	1.47534i	0.218387	−	0.0904588i
$267$	8.28772	+	2.72607i	0.507200	+	0.166833i
$268$	−4.65369	−	4.65369i	−0.284270	−	0.284270i
$269$	9.64212			0.587891			0.293945	−	0.955822i	$-0.405032\pi$
$269$	9.64212			0.587891			0.293945	+	0.955822i	$0.405032\pi$
$270$	6.57901	+	15.0571i	0.400386	+	0.916347i
$271$		−	14.1421i		−	0.859074i	−0.903049	−	0.429537i	$-0.858677\pi$
$271$		−	14.1421i		−	0.859074i	0.903049	−	0.429537i	$-0.141323\pi$
$272$			14.7821i			0.896295i
$273$	8.28772	−	25.1961i	0.501596	−	1.52494i
$274$	15.6569	−	6.48528i	0.945865	−	0.391790i
$275$	−11.7206	+	4.60500i	−0.706779	+	0.277692i
$276$	−8.08034	+	4.08034i	−0.486379	+	0.245608i
$277$	−15.0903			−0.906685			−0.453343	−	0.891336i	$-0.649769\pi$
$277$	−15.0903			−0.906685			−0.453343	+	0.891336i	$0.649769\pi$
$278$	18.9259	−	7.83938i	1.13510	−	0.470175i
$279$	−2.08644	+	2.82843i	−0.124912	+	0.169334i
$280$	11.4034	+	17.4097i	0.681485	+	1.04043i
$281$		−	3.56178i		−	0.212478i	−0.994341	−	0.106239i	$-0.966119\pi$
$281$		−	3.56178i		−	0.212478i	0.994341	−	0.106239i	$-0.0338809\pi$
$282$	6.38287	−	0.479087i	0.380094	−	0.0285292i
$283$		−	18.0502i		−	1.07297i	−0.843909	−	0.536486i	$-0.819751\pi$
$283$		−	18.0502i		−	1.07297i	0.843909	−	0.536486i	$-0.180249\pi$
$284$	10.0742	−	10.0742i	0.597796	−	0.597796i
$285$	−1.95397	−	2.54487i	−0.115743	−	0.150745i
$286$	6.34315	+	15.3137i	0.375078	+	0.905519i
$287$			28.2960i			1.67026i
$288$	−4.08113	+	16.4725i	−0.240483	+	0.970653i
$289$	−3.34315			−0.196656
$290$	−3.92382	+	18.8231i	−0.230415	+	1.10533i
$291$	4.48528	+	1.47534i	0.262932	+	0.0864859i
$292$	9.30739	+	9.30739i	0.544674	+	0.544674i
$293$			2.42742i			0.141811i	0.997483	+	0.0709056i	$0.0225889\pi$
$293$			2.42742i			0.141811i	−0.997483	+	0.0709056i	$0.977411\pi$
$294$	0.701899	+	9.35139i	0.0409356	+	0.545384i
$295$	−4.65369	−	3.17157i	−0.270948	−	0.184656i
$296$	−2.08644	+	5.03712i	−0.121272	+	0.292777i
$297$	−7.57675	−	10.6704i	−0.439647	−	0.619161i
$298$	−19.1794	+	7.94435i	−1.11103	+	0.460204i
$299$		−	12.1607i		−	0.703271i
$300$	11.5352	−	12.9205i	0.665983	−	0.745967i
$301$			19.7990i			1.14119i
$302$	1.53073	+	3.69552i	0.0880838	+	0.212653i
$303$	7.14590	−	21.7248i	0.410521	−	1.24806i
$304$		−	3.31371i		−	0.190054i
$305$	15.6788	+	10.6853i	0.897763	+	0.611841i
$306$	15.2186	+	3.77048i	0.869992	+	0.215544i
$307$			7.14590i			0.407838i	0.978988	+	0.203919i	$0.0653680\pi$
$307$			7.14590i			0.407838i	−0.978988	+	0.203919i	$0.934632\pi$
$308$	−11.7206	−	11.7206i	−0.667843	−	0.667843i
$309$	3.25623	−	9.89949i	0.185240	−	0.563163i
$310$	3.62687	+	0.756050i	0.205993	+	0.0429407i
$311$	−34.3956			−1.95040			−0.975198	−	0.221334i	$-0.928959\pi$
$311$	−34.3956			−1.95040			−0.975198	+	0.221334i	$0.928959\pi$
$312$	−17.2823	−	14.8690i	−0.978415	−	0.841793i
$313$			17.0179i			0.961907i	0.876746	+	0.480954i	$0.159709\pi$
$313$			17.0179i			0.961907i	−0.876746	+	0.480954i	$0.840291\pi$
$314$	7.55568	−	3.12967i	0.426392	−	0.176617i
$315$	20.8326	−	7.29948i	1.17378	−	0.411279i
$316$	23.3137	+	23.3137i	1.31150	+	1.31150i
$317$			13.2513i			0.744269i	0.928179	+	0.372135i	$0.121374\pi$
$317$			13.2513i			0.744269i	−0.928179	+	0.372135i	$0.878626\pi$
$318$	−11.2170	+	0.841928i	−0.629018	+	0.0472130i
$319$		−	15.3137i		−	0.857403i
$320$	17.5761	−	3.32894i	0.982532	−	0.186093i
$321$	4.58579	−	13.9416i	0.255954	−	0.778143i
$322$	4.65369	+	11.2350i	0.259340	+	0.626102i
$323$	−3.06147			−0.170345
$324$	15.9180	+	8.40333i	0.884336	+	0.466851i
$325$	8.50894	+	21.6569i	0.471991	+	1.20131i
$326$	−3.25623	−	7.86123i	−0.180346	−	0.435393i
$327$	−0.798447	−	0.262632i	−0.0441542	−	0.0145236i
$328$	22.4700	+	9.30739i	1.24070	+	0.513914i
$329$		−	8.59890i		−	0.474073i
$330$	−6.89374	+	11.9487i	−0.379488	+	0.657753i
$331$	−18.4853			−1.01604			−0.508021	−	0.861344i	$-0.669623\pi$
$331$	−18.4853			−1.01604			−0.508021	+	0.861344i	$0.669623\pi$
$332$	13.2513	−	13.2513i	0.727262	−	0.727262i
$333$	4.65369	+	3.43289i	0.255021	+	0.188121i
$334$	−9.41421	−	22.7279i	−0.515123	−	1.24362i
$335$	6.08034	+	4.14386i	0.332205	+	0.226403i
$336$	21.6569	+	7.12356i	1.18148	+	0.388622i
$337$			27.9222i			1.52102i	0.649328	+	0.760508i	$0.275050\pi$
$337$			27.9222i			1.52102i	−0.649328	+	0.760508i	$0.724950\pi$
$338$	11.3107	−	4.68506i	0.615222	−	0.254833i
$339$	4.82843	−	14.6792i	0.262244	−	0.797267i
$340$	−3.07554	−	16.2382i	−0.166795	−	0.880638i
$341$	−2.95068			−0.159788
$342$	−3.41157	−	0.845230i	−0.184477	−	0.0457048i
$343$	−10.4366			−0.563521
$344$	15.7225	+	6.51246i	0.847699	+	0.351128i
$345$	8.02734	−	6.16346i	0.432177	−	0.331829i
$346$	−11.6569	−	28.1421i	−0.626676	−	1.51293i
$347$	0.185709			0.00996939			0.00498469	−	0.999988i	$-0.498413\pi$
$347$	0.185709			0.00996939			0.00498469	+	0.999988i	$0.498413\pi$
$348$	9.49433	+	18.8017i	0.508949	+	1.00788i
$349$			2.34315i			0.125426i	0.998032	+	0.0627129i	$0.0199752\pi$
$349$			2.34315i			0.125426i	−0.998032	+	0.0627129i	$0.980025\pi$
$350$	−16.1490	−	16.7521i	−0.863198	−	0.895437i
$351$	−19.7164	+	14.0000i	−1.05238	+	0.747265i
$352$	−13.1626	+	5.45214i	−0.701571	+	0.290600i
$353$	−32.3630			−1.72251			−0.861254	−	0.508175i	$-0.830320\pi$
$353$	−32.3630			−1.72251			−0.861254	+	0.508175i	$0.830320\pi$
$354$	−6.15188	+	0.461750i	−0.326969	+	0.0245417i
$355$	−8.97056	+	13.1626i	−0.476108	+	0.698600i
$356$	−7.12356	−	7.12356i	−0.377548	−	0.377548i
$357$	6.58132	−	20.0083i	0.348320	−	1.05895i
$358$	5.21828	+	12.5980i	0.275795	+	0.665827i
$359$	9.21001			0.486086			0.243043	−	0.970016i	$-0.421854\pi$
$359$	9.21001			0.486086			0.243043	+	0.970016i	$0.421854\pi$
$360$	1.05589	−	18.9443i	0.0556502	−	0.998450i
$361$	−18.3137			−0.963879
$362$	5.59767	+	13.5140i	0.294207	+	0.710279i
$363$	−2.52027	+	7.66206i	−0.132280	+	0.402154i
$364$	−21.6569	+	21.6569i	−1.13513	+	1.13513i
$365$	−12.1607	−	8.28772i	−0.636519	−	0.433799i
$366$	20.7263	−	1.55568i	1.08338	−	0.0813167i
$367$	−2.16148			−0.112828			−0.0564142	−	0.998407i	$-0.517967\pi$
$367$	−2.16148			−0.112828			−0.0564142	+	0.998407i	$0.517967\pi$
$368$	10.4525			0.544874
$369$	15.3137	−	20.7596i	0.797200	−	1.08070i
$370$	1.24395	−	5.96740i	0.0646699	−	0.310230i
$371$			15.1114i			0.784543i
$372$	3.62275	−	1.82939i	0.187831	−	0.0948493i
$373$	24.3976			1.26326			0.631631	−	0.775269i	$-0.282386\pi$
$373$	24.3976			1.26326			0.631631	+	0.775269i	$0.282386\pi$
$374$	5.03712	+	12.1607i	0.260463	+	0.628814i
$375$	−9.98319	+	16.5932i	−0.515530	+	0.856872i
$376$	−6.82843	−	2.82843i	−0.352149	−	0.145865i
$377$	−28.2960			−1.45732
$378$	12.8580	−	20.4794i	0.661343	−	1.05335i
$379$	20.8284			1.06988			0.534942	−	0.844889i	$-0.320333\pi$
$379$	20.8284			1.06988			0.534942	+	0.844889i	$0.320333\pi$
$380$	0.689446	+	3.64012i	0.0353678	+	0.186734i
$381$	1.78089	−	5.41421i	0.0912378	−	0.277379i
$382$	6.58132	−	2.72607i	0.336729	−	0.139478i
$383$			29.1158i			1.48775i	0.668320	+	0.743874i	$0.267014\pi$
$383$			29.1158i			1.48775i	−0.668320	+	0.743874i	$0.732986\pi$
$384$	12.7804	−	14.8547i	0.652198	−	0.758049i
$385$	15.3137	+	10.4366i	0.780459	+	0.531896i
$386$	−10.6853	−	25.7967i	−0.543870	−	1.31302i
$387$	10.7151	−	14.5257i	0.544681	−	0.738381i
$388$	−3.85525	−	3.85525i	−0.195720	−	0.195720i
$389$	7.55568			0.383088			0.191544	−	0.981484i	$-0.438650\pi$
$389$	7.55568			0.383088			0.191544	+	0.981484i	$0.438650\pi$
$390$	22.0783	+	12.7380i	1.11798	+	0.645012i
$391$		−	9.65685i		−	0.488368i
$392$	4.14386	−	10.0042i	0.209297	−	0.505286i
$393$	35.8728	+	11.7996i	1.80954	+	0.595211i
$394$	6.48528	+	15.6569i	0.326724	+	0.788781i
$395$	−30.4608	−	20.7596i	−1.53265	−	1.04453i
$396$	2.25576	+	14.9420i	0.113356	+	0.750866i
$397$	27.1237			1.36130			0.680650	−	0.732609i	$-0.261697\pi$
$397$	27.1237			1.36130			0.680650	+	0.732609i	$0.261697\pi$
$398$	−4.96362	−	11.9832i	−0.248804	−	0.600665i
$399$	−1.47534	+	4.48528i	−0.0738593	+	0.224545i
$400$	−18.6148	+	7.31371i	−0.930739	+	0.365685i
$401$		−	15.1114i		−	0.754625i	−0.926086	−	0.377313i	$-0.876848\pi$
$401$		−	15.1114i		−	0.754625i	0.926086	−	0.377313i	$-0.123152\pi$
$402$	8.03782	−	0.603305i	0.400890	−	0.0300901i
$403$			5.45214i			0.271590i
$404$	−18.6731	+	18.6731i	−0.929024	+	0.929024i
$405$	−19.2344	−	5.91920i	−0.955766	−	0.294127i
$406$	26.1421	−	10.8284i	1.29741	−	0.537406i
$407$			4.85483i			0.240645i
$408$	−13.7239	−	11.8076i	−0.679435	−	0.584562i
$409$	−12.8284			−0.634325			−0.317162	−	0.948371i	$-0.602730\pi$
$409$	−12.8284			−0.634325			−0.317162	+	0.948371i	$0.602730\pi$
$410$	−26.6199	−	5.54912i	−1.31466	−	0.274051i
$411$	−6.48528	+	19.7164i	−0.319895	+	0.972537i
$412$	−8.50894	+	8.50894i	−0.419205	+	0.419205i
$413$			8.28772i			0.407812i
$414$	2.66613	−	10.7612i	0.131033	−	0.528884i
$415$	−11.7996	+	17.3137i	−0.579219	+	0.849897i
$416$	10.0742	+	24.3214i	0.493930	+	1.19245i
$417$	−7.83938	+	23.8331i	−0.383896	+	1.16711i
$418$	−1.12918	−	2.72607i	−0.0552298	−	0.133336i
$419$		−	2.51856i		−	0.123040i	−0.998106	−	0.0615199i	$-0.980405\pi$
$419$		−	2.51856i		−	0.123040i	0.998106	−	0.0615199i	$-0.0195948\pi$
$420$	−25.2723	−	3.31937i	−1.23316	−	0.161969i
$421$		−	34.8284i		−	1.69743i	−0.528848	−	0.848717i	$-0.677376\pi$
$421$		−	34.8284i		−	1.69743i	0.528848	−	0.848717i	$-0.322624\pi$
$422$	24.1522	−	10.0042i	1.17571	−	0.486995i
$423$	−4.65369	+	6.30864i	−0.226270	+	0.306737i
$424$	12.0000	+	4.97056i	0.582772	+	0.241392i
$425$	6.75699	+	17.1978i	0.327762	+	0.834216i
$426$	1.30603	+	17.4002i	0.0632771	+	0.843040i
$427$		−	27.9222i		−	1.35125i
$428$	−11.9832	+	11.9832i	−0.579232	+	0.579232i
$429$	−19.2842	−	6.34315i	−0.931052	−	0.306250i
$430$	−18.6262	−	3.88277i	−0.898234	−	0.187244i
$431$	27.2720			1.31365			0.656824	−	0.754044i	$-0.271899\pi$
$431$	27.2720			1.31365			0.656824	+	0.754044i	$0.271899\pi$
$432$	−12.0335	−	16.9469i	−0.578960	−	0.815356i
$433$		−	23.5992i		−	1.13410i	−0.823682	−	0.567052i	$-0.808084\pi$
$433$		−	23.5992i		−	1.13410i	0.823682	−	0.567052i	$-0.191916\pi$
$434$	−2.08644	−	5.03712i	−0.100152	−	0.241790i
$435$	−14.3414	−	18.6784i	−0.687619	−	0.895560i
$436$	0.686292	+	0.686292i	0.0328674	+	0.0328674i
$437$			2.16478i			0.103556i
$438$	−16.0756	+	1.20661i	−0.768124	+	0.0576541i
$439$			28.4853i			1.35953i	0.733431	+	0.679764i	$0.237918\pi$
$439$			28.4853i			1.35953i	−0.733431	+	0.679764i	$0.762082\pi$
$440$	13.3248	−	8.72780i	0.635237	−	0.416081i
$441$	−9.24264	−	6.81801i	−0.440126	−	0.324667i
$442$	22.4700	−	9.30739i	1.06879	−	0.442707i
$443$	1.60766			0.0763821			0.0381910	−	0.999270i	$-0.487840\pi$
$443$	1.60766			0.0763821			0.0381910	+	0.999270i	$0.487840\pi$
$444$	−3.00994	−	5.96062i	−0.142846	−	0.282878i
$445$	9.30739	+	6.34315i	0.441212	+	0.300694i
$446$	28.6208	−	11.8551i	1.35524	−	0.561357i
$447$	7.94435	−	24.1522i	0.375755	−	1.14236i
$448$	−18.6148	−	18.6148i	−0.879465	−	0.879465i
$449$			35.0067i			1.65207i	0.563620	+	0.826035i	$0.309408\pi$
$449$			35.0067i			1.65207i	−0.563620	+	0.826035i	$0.690592\pi$
$450$	2.78162	+	21.0300i	0.131127	+	0.991366i
$451$	21.6569			1.01978
$452$	−12.6173	+	12.6173i	−0.593467	+	0.593467i
$453$	−4.65369	−	1.53073i	−0.218650	−	0.0719201i
$454$	−5.41421	+	2.24264i	−0.254102	+	0.105252i
$455$	19.2842	−	28.2960i	0.904060	−	1.32654i
$456$	3.07650	+	2.64691i	0.144070	+	0.123953i
$457$		−	18.6148i		−	0.870762i	−0.900246	−	0.435381i	$-0.856614\pi$
$457$		−	18.6148i		−	0.870762i	0.900246	−	0.435381i	$-0.143386\pi$
$458$	10.4525	+	25.2346i	0.488413	+	1.17913i
$459$	−15.6569	+	11.1175i	−0.730799	+	0.518919i
$460$	−11.4821	+	2.17473i	−0.535357	+	0.101398i
$461$	−3.99390			−0.186014			−0.0930072	−	0.995665i	$-0.529648\pi$
$461$	−3.99390			−0.186014			−0.0930072	+	0.995665i	$0.529648\pi$
$462$	20.2437	−	1.51946i	0.941824	−	0.0706917i
$463$	−25.7607			−1.19720			−0.598600	−	0.801048i	$-0.704276\pi$
$463$	−25.7607			−1.19720			−0.598600	+	0.801048i	$0.704276\pi$
$464$		−	24.3214i		−	1.12909i
$465$	−3.59899	+	2.76333i	−0.166899	+	0.128147i
$466$	−20.8284	+	8.62742i	−0.964858	+	0.399657i
$467$	15.8645			0.734120			0.367060	−	0.930197i	$-0.380364\pi$
$467$	15.8645			0.734120			0.367060	+	0.930197i	$0.380364\pi$
$468$	27.6093	−	4.16810i	1.27624	−	0.192670i
$469$		−	10.8284i		−	0.500010i
$470$	8.08954	+	1.68633i	0.373142	+	0.0777844i
$471$	−3.12967	+	9.51472i	−0.144207	+	0.438415i
$472$	6.58132	+	2.72607i	0.302930	+	0.125478i
$473$	15.1535			0.696758
$474$	−40.2673	+	3.02239i	−1.84954	+	0.138823i
$475$	−1.51472	−	3.85525i	−0.0695001	−	0.176891i
$476$	−17.1978	+	17.1978i	−0.788260	+	0.788260i
$477$	8.17821	−	11.0866i	0.374455	−	0.507618i
$478$	29.0513	−	12.0335i	1.32878	−	0.550397i
$479$	−19.2842			−0.881120			−0.440560	−	0.897723i	$-0.645220\pi$
$479$	−19.2842			−0.881120			−0.440560	+	0.897723i	$0.645220\pi$
$480$	−10.9487	+	18.9770i	−0.499738	+	0.866177i
$481$	8.97056			0.409022
$482$	−8.47343	+	3.50981i	−0.385954	+	0.159867i
$483$	−14.1480	−	4.65369i	−0.643757	−	0.211750i
$484$	6.58579	−	6.58579i	0.299354	−	0.299354i
$485$	5.03712	+	3.43289i	0.228724	+	0.155879i
$486$	−20.5167	+	8.06619i	−0.930658	+	0.365890i
$487$	−8.74280			−0.396174			−0.198087	−	0.980184i	$-0.563473\pi$
$487$	−8.74280			−0.396174			−0.198087	+	0.980184i	$0.563473\pi$
$488$	−22.1731	−	9.18440i	−1.00373	−	0.415758i
$489$	9.89949	+	3.25623i	0.447671	+	0.147252i
$490$	−2.47059	+	11.8518i	−0.111610	+	0.535409i
$491$			36.9142i			1.66591i	0.553338	+	0.832957i	$0.313354\pi$
$491$			36.9142i			1.66591i	−0.553338	+	0.832957i	$0.686646\pi$
$492$	−26.5896	+	13.4270i	−1.19875	+	0.605336i
$493$	−22.4700			−1.01200
$494$	−5.03712	+	2.08644i	−0.226631	+	0.0938735i
$495$	−5.58678	−	15.9446i	−0.251107	−	0.716655i
$496$	−4.68629			−0.210421
$497$	23.4412			1.05148
$498$	1.71790	+	22.8876i	0.0769811	+	1.02562i
$499$	−37.1127			−1.66139			−0.830696	−	0.556726i	$-0.812057\pi$
$499$	−37.1127			−1.66139			−0.830696	+	0.556726i	$0.812057\pi$
$500$	18.9267	−	11.9071i	0.846429	−	0.532502i
$501$	28.6208	+	9.41421i	1.27868	+	0.420596i
$502$	6.34746	+	15.3241i	0.283301	+	0.683949i
$503$			9.63274i			0.429503i	0.976669	+	0.214751i	$0.0688941\pi$
$503$			9.63274i			0.429503i	−0.976669	+	0.214751i	$0.931106\pi$
$504$	−23.9126	+	14.4164i	−1.06515	+	0.642159i
$505$	16.6274	−	24.3976i	0.739910	−	1.08568i
$506$	8.59890	−	3.56178i	0.382268	−	0.158341i
$507$	−4.68506	+	14.2434i	−0.208071	+	0.632570i
$508$	−4.65369	+	4.65369i	−0.206474	+	0.206474i
$509$	−13.2039			−0.585253			−0.292626	−	0.956227i	$-0.594529\pi$
$509$	−13.2039			−0.585253			−0.292626	+	0.956227i	$0.594529\pi$
$510$	17.5324	+	10.1153i	0.776350	+	0.447912i
$511$			21.6569i			0.958043i
$512$	−20.9050	+	8.65914i	−0.923880	+	0.382683i
$513$	3.50981	−	2.49221i	0.154962	−	0.110034i
$514$	21.3137	−	8.82843i	0.940107	−	0.389405i
$515$	7.57675	−	11.1175i	0.333871	−	0.489894i
$516$	−18.6050	+	9.39500i	−0.819040	+	0.413592i
$517$	−6.58132			−0.289446
$518$	−8.28772	+	3.43289i	−0.364141	+	0.150832i
$519$	35.4388	+	11.6569i	1.55559	+	0.511679i
$520$	−16.1269	−	24.6211i	−0.707210	−	1.07971i
$521$		−	34.3956i		−	1.50690i	−0.657506	−	0.753450i	$-0.728388\pi$
$521$		−	34.3956i		−	1.50690i	0.657506	−	0.753450i	$-0.271612\pi$
$522$	−25.0397	−	6.20367i	−1.09596	−	0.271527i
$523$			12.5980i			0.550874i	0.961319	+	0.275437i	$0.0888225\pi$
$523$			12.5980i			0.550874i	−0.961319	+	0.275437i	$0.911177\pi$
$524$	−30.8338	−	30.8338i	−1.34698	−	1.34698i
$525$	28.4523	−	1.61178i	1.24176	−	0.0703437i
$526$	−12.0416	−	29.0711i	−0.525040	−	1.26756i
$527$			4.32957i			0.188599i
$528$	5.45214	−	16.5754i	0.237274	−	0.721353i
$529$	16.1716			0.703112
$530$	−14.2162	−	2.96348i	−0.617513	−	0.128725i
$531$	4.48528	−	6.08034i	0.194645	−	0.263864i
$532$	3.85525	−	3.85525i	0.167146	−	0.167146i
$533$		−	40.0166i		−	1.73331i
$534$	12.3038	−	0.923499i	0.532436	−	0.0399637i
$535$	10.6704	−	15.6569i	0.461322	−	0.676905i
$536$	−8.59890	−	3.56178i	−0.371416	−	0.153846i
$537$	−15.8645	−	5.21828i	−0.684602	−	0.225185i
$538$	12.5980	−	5.21828i	0.543140	−	0.224976i
$539$		−	9.64212i		−	0.415316i
$540$	16.7447	+	16.1125i	0.720579	+	0.693373i
$541$		−	16.0000i		−	0.687894i	−0.938989	−	0.343947i	$-0.888236\pi$
$541$		−	16.0000i		−	0.687894i	0.938989	−	0.343947i	$-0.111764\pi$
$542$	−7.65367	−	18.4776i	−0.328753	−	0.793680i
$543$	−17.0179	−	5.59767i	−0.730307	−	0.240219i
$544$	8.00000	+	19.3137i	0.342997	+	0.828068i
$545$	−0.896683	−	0.611105i	−0.0384097	−	0.0261769i
$546$	−2.80760	−	37.4056i	−0.120154	−	1.60081i
$547$		−	11.0011i		−	0.470375i	−0.971950	−	0.235188i	$-0.924430\pi$
$547$		−	11.0011i		−	0.470375i	0.971950	−	0.235188i	$-0.0755704\pi$
$548$	16.9469	−	16.9469i	0.723934	−	0.723934i
$549$	−15.1114	+	20.4853i	−0.644937	+	0.874291i
$550$	−12.8215	+	12.3599i	−0.546711	+	0.527027i
$551$	5.03712			0.214589
$552$	−8.34921	+	9.70427i	−0.355366	+	0.413041i
$553$			54.2474i			2.30683i
$554$	−19.7164	+	8.16679i	−0.837668	+	0.346973i
$555$	4.54659	+	5.92152i	0.192992	+	0.251355i
$556$	20.4853	−	20.4853i	0.868769	−	0.868769i
$557$		−	4.96362i		−	0.210315i	−0.994456	−	0.105158i	$-0.966465\pi$
$557$		−	4.96362i		−	0.210315i	0.994456	−	0.105158i	$-0.0335347\pi$
$558$	−1.19534	+	4.82469i	−0.0506026	+	0.204246i
$559$		−	28.0000i		−	1.18427i
$560$	24.3214	+	16.5754i	1.02777	+	0.700440i
$561$	−15.3137	−	5.03712i	−0.646545	−	0.212667i
$562$	−1.92762	−	4.65369i	−0.0813119	−	0.196304i
$563$	21.9874			0.926658			0.463329	−	0.886186i	$-0.346655\pi$
$563$	21.9874			0.926658			0.463329	+	0.886186i	$0.346655\pi$
$564$	8.08034	−	4.08034i	0.340244	−	0.171813i
$565$	11.2350	−	16.4853i	0.472660	−	0.693541i
$566$	−9.76869	−	23.5837i	−0.410609	−	0.991297i
$567$	8.74280	+	28.2960i	0.367163	+	1.18832i
$568$	7.71049	−	18.6148i	0.323525	−	0.781058i
$569$			15.7225i			0.659120i	0.944135	+	0.329560i	$0.106900\pi$
$569$			15.7225i			0.659120i	−0.944135	+	0.329560i	$0.893100\pi$
$570$	−3.93026	−	2.26755i	−0.164621	−	0.0949772i
$571$	21.1127			0.883539			0.441769	−	0.897129i	$-0.354351\pi$
$571$	21.1127			0.883539			0.441769	+	0.897129i	$0.354351\pi$
$572$	16.5754	+	16.5754i	0.693054	+	0.693054i
$573$	−2.72607	+	8.28772i	−0.113883	+	0.346224i
$574$	15.3137	+	36.9706i	0.639182	+	1.54312i
$575$	12.1607	−	4.77791i	0.507136	−	0.199253i
$576$	3.58261	+	23.7311i	0.149276	+	0.988796i
$577$			3.85525i			0.160496i	0.996775	+	0.0802480i	$0.0255712\pi$
$577$			3.85525i			0.160496i	−0.996775	+	0.0802480i	$0.974429\pi$
$578$	−4.36803	+	1.80930i	−0.181686	+	0.0752569i
$579$	32.4853	+	10.6853i	1.35004	+	0.444068i
$580$	5.06027	+	26.7171i	0.210116	+	1.10937i
$581$	30.8338			1.27920
$582$	6.65875	−	0.499794i	0.276014	−	0.0207171i
$583$	11.5657			0.479004
$584$	17.1978	+	7.12356i	0.711650	+	0.294775i
$585$	−29.4617	+	10.3230i	−1.21809	+	0.426805i
$586$	1.31371	+	3.17157i	0.0542688	+	0.131016i
$587$	−7.20533			−0.297396			−0.148698	−	0.988883i	$-0.547508\pi$
$587$	−7.20533			−0.297396			−0.148698	+	0.988883i	$0.547508\pi$
$588$	5.97801	+	11.8383i	0.246529	+	0.488204i
$589$		−	0.970563i		−	0.0399913i
$590$	−7.79679	−	1.62530i	−0.320989	−	0.0669125i
$591$	−19.7164	−	6.48528i	−0.811023	−	0.266769i
$592$			7.71049i			0.316899i
$593$	−1.00547			−0.0412897			−0.0206448	−	0.999787i	$-0.506572\pi$
$593$	−1.00547			−0.0412897			−0.0206448	+	0.999787i	$0.506572\pi$
$594$	−15.6743	−	9.84107i	−0.643124	−	0.403784i
$595$	15.3137	−	22.4700i	0.627801	−	0.921181i
$596$	−20.7596	+	20.7596i	−0.850346	+	0.850346i
$597$	15.0903	+	4.96362i	0.617603	+	0.203147i
$598$	−6.58132	−	15.8887i	−0.269130	−	0.649737i
$599$	−32.3092			−1.32012			−0.660058	−	0.751214i	$-0.729468\pi$
$599$	−32.3092			−1.32012			−0.660058	+	0.751214i	$0.729468\pi$
$600$	8.07887	−	23.1243i	0.329818	−	0.944044i
$601$	13.5147			0.551277			0.275638	−	0.961261i	$-0.411111\pi$
$601$	13.5147			0.551277			0.275638	+	0.961261i	$0.411111\pi$
$602$	10.7151	+	25.8686i	0.436716	+	1.05433i
$603$	−5.86030	+	7.94435i	−0.238650	+	0.323519i
$604$	4.00000	+	4.00000i	0.162758	+	0.162758i
$605$	−5.86428	+	8.60474i	−0.238417	+	0.349833i
$606$	−2.42079	−	32.2521i	−0.0983378	−	1.31015i
$607$	4.88755			0.198380			0.0991898	−	0.995069i	$-0.468375\pi$
$607$	4.88755			0.198380			0.0991898	+	0.995069i	$0.468375\pi$
$608$	−1.79337	−	4.32957i	−0.0727306	−	0.175587i
$609$	−10.8284	+	32.9203i	−0.438790	+	1.33400i
$610$	26.2681	+	5.47580i	1.06357	+	0.221709i
$611$			12.1607i			0.491969i
$612$	21.9247	−	3.30990i	0.886252	−	0.133795i
$613$	−23.2685			−0.939804			−0.469902	−	0.882718i	$-0.655711\pi$
$613$	−23.2685			−0.939804			−0.469902	+	0.882718i	$0.655711\pi$
$614$	3.86733	+	9.33657i	0.156073	+	0.376793i
$615$	26.4152	−	20.2818i	1.06516	−	0.817842i
$616$	−21.6569	−	8.97056i	−0.872580	−	0.361434i
$617$	8.55035			0.344224			0.172112	−	0.985077i	$-0.444941\pi$
$617$	8.55035			0.344224			0.172112	+	0.985077i	$0.444941\pi$
$618$	−1.10310	−	14.6966i	−0.0443732	−	0.591183i
$619$	−2.48528			−0.0998919			−0.0499459	−	0.998752i	$-0.515905\pi$
$619$	−2.48528			−0.0998919			−0.0499459	+	0.998752i	$0.515905\pi$
$620$	5.14791	−	0.975024i	0.206745	−	0.0391579i
$621$	7.86123	+	11.0711i	0.315460	+	0.444267i
$622$	−44.9400	+	18.6148i	−1.80193	+	0.746384i
$623$		−	16.5754i		−	0.664081i
$624$	−30.6274	−	10.0742i	−1.22608	−	0.403292i
$625$	−18.3137	+	17.0179i	−0.732548	+	0.680715i
$626$	9.21001	+	22.2349i	0.368106	+	0.888686i
$627$	3.43289	+	1.12918i	0.137096	+	0.0450949i
$628$	8.17821	−	8.17821i	0.326346	−	0.326346i
$629$	7.12356			0.284035
$630$	23.2686	−	20.8117i	0.927045	−	0.829160i
$631$		−	2.14214i		−	0.0852771i	−0.999091	−	0.0426385i	$-0.986424\pi$
$631$		−	2.14214i		−	0.0852771i	0.999091	−	0.0426385i	$-0.0135764\pi$
$632$	43.0781	+	17.8435i	1.71356	+	0.709778i
$633$	−10.0042	+	30.4144i	−0.397630	+	1.20886i
$634$	7.17157	+	17.3137i	0.284820	+	0.687615i
$635$	4.14386	−	6.08034i	0.164444	−	0.241291i
$636$	−14.2001	+	7.17063i	−0.563069	+	0.284334i
$637$	−17.8163			−0.705908
$638$	−8.28772	−	20.0083i	−0.328114	−	0.792137i
$639$	−17.1978	−	12.6863i	−0.680335	−	0.501862i
$640$	21.1626	−	13.8616i	0.836526	−	0.547927i
$641$		−	35.0067i		−	1.38268i	−0.722529	−	0.691341i	$-0.757020\pi$
$641$		−	35.0067i		−	1.38268i	0.722529	−	0.691341i	$-0.242980\pi$
$642$	−1.55351	−	20.6974i	−0.0613121	−	0.816859i
$643$			35.0681i			1.38295i	0.722401	+	0.691475i	$0.243039\pi$
$643$			35.0681i			1.38295i	−0.722401	+	0.691475i	$0.756961\pi$
$644$	12.1607	+	12.1607i	0.479198	+	0.479198i
$645$	18.4830	−	14.1914i	0.727766	−	0.558785i
$646$	−4.00000	+	1.65685i	−0.157378	+	0.0651881i
$647$		−	28.3730i		−	1.11546i	−0.830024	−	0.557728i	$-0.811673\pi$
$647$		−	28.3730i		−	1.11546i	0.830024	−	0.557728i	$-0.188327\pi$
$648$	25.3458	+	2.36469i	0.995676	+	0.0928938i
$649$	6.34315			0.248990
$650$	22.8381	+	23.6910i	0.895783	+	0.929239i
$651$	6.34315	+	2.08644i	0.248607	+	0.0817742i
$652$	−8.50894	−	8.50894i	−0.333236	−	0.333236i
$653$			24.2291i			0.948158i	0.880482	+	0.474079i	$0.157219\pi$
$653$			24.2291i			0.948158i	−0.880482	+	0.474079i	$0.842781\pi$
$654$	−1.18536	+	0.0889709i	−0.0463511	+	0.00347904i
$655$	40.2863	+	27.4558i	1.57412	+	1.07279i
$656$	34.3956			1.34292
$657$	11.7206	−	15.8887i	0.457264	−	0.619877i
$658$	−4.65369	−	11.2350i	−0.181420	−	0.437986i
$659$		−	14.6792i		−	0.571822i	−0.958256	−	0.285911i	$-0.907704\pi$
$659$		−	14.6792i		−	0.571822i	0.958256	−	0.285911i	$-0.0922962\pi$
$660$	−2.54053	+	19.3426i	−0.0988902	+	0.752908i
$661$			44.7696i			1.74133i	0.491873	+	0.870667i	$0.336312\pi$
$661$			44.7696i			1.74133i	−0.491873	+	0.870667i	$0.663688\pi$
$662$	−24.1522	+	10.0042i	−0.938701	+	0.388823i
$663$	−9.30739	+	28.2960i	−0.361469	+	1.09893i
$664$	10.1421	−	24.4853i	0.393591	−	0.950213i
$665$	−3.43289	+	5.03712i	−0.133122	+	0.195331i
$666$	7.93821	+	1.96672i	0.307599	+	0.0762089i
$667$			15.8887i			0.615213i
$668$	−24.6005	−	24.6005i	−0.951823	−	0.951823i
$669$	−11.8551	+	36.0416i	−0.458346	+	1.39345i
$670$	10.1870	+	2.12356i	0.393558	+	0.0820401i
$671$	−21.3707			−0.825006
$672$	32.1513	−	2.41322i	1.24026	−	0.0930920i
$673$		−	47.6661i		−	1.83739i	−0.394964	−	0.918697i	$-0.629243\pi$
$673$		−	47.6661i		−	1.83739i	0.394964	−	0.918697i	$-0.370757\pi$
$674$	15.1114	+	36.4821i	0.582068	+	1.40524i
$675$	−21.7465	−	14.2158i	−0.837024	−	0.547166i
$676$	12.2426	−	12.2426i	0.470871	−	0.470871i
$677$			1.00547i			0.0386433i	0.999813	+	0.0193217i	$0.00615066\pi$
$677$			1.00547i			0.0386433i	−0.999813	+	0.0193217i	$0.993849\pi$
$678$	−1.63571	−	21.7925i	−0.0628189	−	0.836935i
$679$		−	8.97056i		−	0.344259i
$680$	−12.8064	−	19.5517i	−0.491104	−	0.749774i
$681$	2.24264	−	6.81801i	0.0859382	−	0.261267i
$682$	−3.85525	+	1.59689i	−0.147625	+	0.0611483i
$683$	14.9678			0.572726			0.286363	−	0.958121i	$-0.407554\pi$
$683$	14.9678			0.572726			0.286363	+	0.958121i	$0.407554\pi$
$684$	−4.91487	+	0.741983i	−0.187925	+	0.0283704i
$685$	−15.0903	+	22.1421i	−0.576569	+	0.846008i
$686$	−13.6360	+	5.64823i	−0.520626	+	0.215650i
$687$	−31.7774	−	10.4525i	−1.21238	−	0.398788i
$688$	24.0669			0.917542
$689$		−	21.3707i		−	0.814159i
$690$	7.15258	−	12.3973i	0.272294	−	0.471958i
$691$	−7.17157			−0.272819			−0.136410	−	0.990653i	$-0.543556\pi$
$691$	−7.17157			−0.272819			−0.136410	+	0.990653i	$0.543556\pi$
$692$	−30.4608	−	30.4608i	−1.15795	−	1.15795i
$693$	−14.7595	+	20.0083i	−0.560668	+	0.760053i
$694$	0.242641	−	0.100505i	0.00921051	−	0.00381512i
$695$	−18.2410	+	26.7653i	−0.691922	+	1.01527i
$696$	22.5804	+	19.4273i	0.855906	+	0.736391i
$697$		−	31.7774i		−	1.20365i
$698$	1.26810	+	3.06147i	0.0479983	+	0.115878i
$699$	8.62742	−	26.2288i	0.326319	−	0.992065i
$700$	−30.1658	−	13.1479i	−1.14016	−	0.496945i
$701$	−26.8399			−1.01373			−0.506865	−	0.862025i	$-0.669196\pi$
$701$	−26.8399			−1.01373			−0.506865	+	0.862025i	$0.669196\pi$
$702$	−18.1839	+	28.9623i	−0.686308	+	1.09311i
$703$	−1.59689			−0.0602280
$704$	−14.2471	+	14.2471i	−0.536959	+	0.536959i
$705$	−8.02734	+	6.16346i	−0.302327	+	0.232129i
$706$	−42.2843	+	17.5147i	−1.59139	+	0.659175i
$707$	−43.4495			−1.63409
$708$	−7.78793	+	3.93268i	−0.292688	+	0.147799i
$709$		−	36.2843i		−	1.36268i	−0.731965	−	0.681342i	$-0.761397\pi$
$709$		−	36.2843i		−	1.36268i	0.731965	−	0.681342i	$-0.238603\pi$
$710$	−4.59704	+	22.0526i	−0.172524	+	0.827621i
$711$	29.3585	−	39.7990i	1.10103	−	1.49258i
$712$	−13.1626	−	5.45214i	−0.493290	−	0.204328i
$713$	3.06147			0.114653
$714$	−2.22952	−	29.7039i	−0.0834379	−	1.11164i
$715$	−21.6569	−	14.7595i	−0.809920	−	0.551975i
$716$	13.6360	+	13.6360i	0.509602	+	0.509602i
$717$	−12.0335	+	36.5838i	−0.449398	+	1.36625i
$718$	12.0335	−	4.98442i	0.449085	−	0.186017i
$719$	2.95068			0.110042			0.0550208	−	0.998485i	$-0.482477\pi$
$719$	2.95068			0.110042			0.0550208	+	0.998485i	$0.482477\pi$
$720$	−8.87298	−	25.3233i	−0.330676	−	0.943744i
$721$	−19.7990			−0.737353
$722$	−23.9280	+	9.91131i	−0.890508	+	0.368861i
$723$	3.50981	−	10.6704i	0.130531	−	0.396837i
$724$	14.6274	+	14.6274i	0.543624	+	0.543624i
$725$	−11.1175	−	28.2960i	−0.412892	−	1.05089i
$726$	0.853782	+	11.3749i	0.0316868	+	0.422163i
$727$	47.1015			1.74690			0.873449	−	0.486915i	$-0.161878\pi$
$727$	47.1015			1.74690			0.873449	+	0.486915i	$0.161878\pi$
$728$	−16.5754	+	40.0166i	−0.614327	+	1.48312i
$729$	8.89949	−	25.4912i	0.329611	−	0.944117i
$730$	−20.3740	−	4.24711i	−0.754075	−	0.157193i
$731$		−	22.2349i		−	0.822388i
$732$	26.2383	−	13.2496i	0.969795	−	0.489719i
$733$	−9.63811			−0.355992			−0.177996	−	0.984031i	$-0.556961\pi$
$733$	−9.63811			−0.355992			−0.177996	+	0.984031i	$0.556961\pi$
$734$	−2.82411	+	1.16979i	−0.104240	+	0.0431776i
$735$	−9.02993	−	11.7607i	−0.333074	−	0.433798i
$736$	13.6569	−	5.65685i	0.503398	−	0.208514i
$737$	−8.28772			−0.305282
$738$	8.77332	−	35.4114i	0.322950	−	1.30351i
$739$	−27.1716			−0.999522			−0.499761	−	0.866163i	$-0.666579\pi$
$739$	−27.1716			−0.999522			−0.499761	+	0.866163i	$0.666579\pi$
$740$	−1.60423	−	8.47001i	−0.0589728	−	0.311364i
$741$	2.08644	−	6.34315i	0.0766474	−	0.233021i
$742$	8.17821	+	19.7439i	0.300232	+	0.724823i
$743$		−	15.2304i		−	0.558750i	−0.960182	−	0.279375i	$-0.909873\pi$
$743$		−	15.2304i		−	0.558750i	0.960182	−	0.279375i	$-0.0901272\pi$
$744$	3.74330	−	4.35083i	0.137236	−	0.159509i
$745$	18.4853	−	27.1237i	0.677248	−	0.993736i
$746$	31.8771	−	13.2039i	1.16710	−	0.483429i
$747$	−22.6215	−	16.6871i	−0.827676	−	0.610551i
$748$	13.1626	+	13.1626i	0.481273	+	0.481273i
$749$	−27.8832			−1.01883
$750$	−4.06347	+	27.0830i	−0.148377	+	0.988931i
$751$			35.1127i			1.28128i	0.767841	+	0.640640i	$0.221331\pi$
$751$			35.1127i			1.28128i	−0.767841	+	0.640640i	$0.778669\pi$
$752$	−10.4525			−0.381164
$753$	−19.2974	−	6.34746i	−0.703235	−	0.231314i
$754$	−36.9706	+	15.3137i	−1.34639	+	0.557692i
$755$	−5.22625	−	3.56178i	−0.190203	−	0.129627i
$756$	5.71637	−	33.7164i	0.207902	−	1.22625i
$757$	−12.8319			−0.466383			−0.233192	−	0.972431i	$-0.574917\pi$
$757$	−12.8319			−0.466383			−0.233192	+	0.972431i	$0.574917\pi$
$758$	27.2137	−	11.2723i	0.988444	−	0.409427i
$759$	−3.56178	+	10.8284i	−0.129284	+	0.393047i
$760$	2.87082	+	4.38292i	0.104136	+	0.158985i
$761$			17.1978i			0.623420i	0.950177	+	0.311710i	$0.100902\pi$
$761$			17.1978i			0.623420i	−0.950177	+	0.311710i	$0.899098\pi$
$762$	−0.603305	−	8.03782i	−0.0218554	−	0.291180i
$763$			1.59689i			0.0578115i
$764$	7.12356	−	7.12356i	0.257722	−	0.257722i
$765$	−23.3957	+	8.19756i	−0.845873	+	0.296383i
$766$	15.7574	+	38.0416i	0.569337	+	1.37450i
$767$		−	11.7206i		−	0.423207i
$768$	8.65914	−	26.3253i	0.312460	−	0.949931i
$769$	−49.5980			−1.78855			−0.894274	−	0.447519i	$-0.852308\pi$
$769$	−49.5980			−1.78855			−0.894274	+	0.447519i	$0.852308\pi$
$770$	25.6566	+	5.34830i	0.924598	+	0.192739i
$771$	−8.82843	+	26.8399i	−0.317948	+	0.966616i
$772$	−27.9222	−	27.9222i	−1.00494	−	1.00494i
$773$			18.8490i			0.677952i	0.940795	+	0.338976i	$0.110081\pi$
$773$			18.8490i			0.677952i	−0.940795	+	0.338976i	$0.889919\pi$
$774$	6.13877	−	24.7777i	0.220653	−

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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.m (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30656 - 0.541196i) q^{2} +(-0.541196 + 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(-1.25928 + 1.84776i) q^{5} +(0.183339 + 2.44262i) q^{6} +3.29066 q^{7} +(1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +O(q^{10})\)	\(q+(1.30656 - 0.541196i) q^{2} +(-0.541196 + 1.64533i) q^{3} +(1.41421 - 1.41421i) q^{4} +(-1.25928 + 1.84776i) q^{5} +(0.183339 + 2.44262i) q^{6} +3.29066 q^{7} +(1.08239 - 2.61313i) q^{8} +(-2.41421 - 1.78089i) q^{9} +(-0.645329 + 3.09573i) q^{10} -2.51856i q^{11} +(1.56148 + 3.09221i) q^{12} -4.65369 q^{13} +(4.29945 - 1.78089i) q^{14} +(-2.35865 - 3.07193i) q^{15} -4.00000i q^{16} -3.69552 q^{17} +(-4.11813 - 1.02028i) q^{18} +0.828427 q^{19} +(0.832235 + 4.39402i) q^{20} +(-1.78089 + 5.41421i) q^{21} +(-1.36303 - 3.29066i) q^{22} +2.61313i q^{23} +(3.71366 + 3.19510i) q^{24} +(-1.82843 - 4.65369i) q^{25} +(-6.08034 + 2.51856i) q^{26} +(4.23671 - 3.00836i) q^{27} +(4.65369 - 4.65369i) q^{28} +6.08034 q^{29} +(-4.74425 - 2.73718i) q^{30} -1.17157i q^{31} +(-2.16478 - 5.22625i) q^{32} +(4.14386 + 1.36303i) q^{33} +(-4.82843 + 2.00000i) q^{34} +(-4.14386 + 6.08034i) q^{35} +(-5.93277 + 0.895653i) q^{36} -1.92762 q^{37} +(1.08239 - 0.448342i) q^{38} +(2.51856 - 7.65685i) q^{39} +(3.46539 + 5.29066i) q^{40} +8.59890i q^{41} +(0.603305 + 8.03782i) q^{42} +6.01673i q^{43} +(-3.56178 - 3.56178i) q^{44} +(6.33083 - 2.21824i) q^{45} +(1.41421 + 3.41421i) q^{46} -2.61313i q^{47} +(6.58132 + 2.16478i) q^{48} +3.82843 q^{49} +(-4.90752 - 5.09080i) q^{50} +(2.00000 - 6.08034i) q^{51} +(-6.58132 + 6.58132i) q^{52} +4.59220i q^{53} +(3.90742 - 6.22351i) q^{54} +(4.65369 + 3.17157i) q^{55} +(3.56178 - 8.59890i) q^{56} +(-0.448342 + 1.36303i) q^{57} +(7.94435 - 3.29066i) q^{58} +2.51856i q^{59} +(-7.68000 - 1.00872i) q^{60} -8.48528i q^{61} +(-0.634051 - 1.53073i) q^{62} +(-7.94435 - 5.86030i) q^{63} +(-5.65685 - 5.65685i) q^{64} +(5.86030 - 8.59890i) q^{65} +(6.15188 - 0.461750i) q^{66} -3.29066i q^{67} +(-5.22625 + 5.22625i) q^{68} +(-4.29945 - 1.41421i) q^{69} +(-2.12356 + 10.1870i) q^{70} +7.12356 q^{71} +(-7.26682 + 4.38102i) q^{72} +6.58132i q^{73} +(-2.51856 + 1.04322i) q^{74} +(8.64639 - 0.489804i) q^{75} +(1.17157 - 1.17157i) q^{76} -8.28772i q^{77} +(-0.853202 - 11.3672i) q^{78} +16.4853i q^{79} +(7.39104 + 5.03712i) q^{80} +(2.65685 + 8.59890i) q^{81} +(4.65369 + 11.2350i) q^{82} +9.37011 q^{83} +(5.13829 + 10.1754i) q^{84} +(4.65369 - 6.82843i) q^{85} +(3.25623 + 7.86123i) q^{86} +(-3.29066 + 10.0042i) q^{87} +(-6.58132 - 2.72607i) q^{88} -5.03712i q^{89} +(7.07112 - 6.32450i) q^{90} -15.3137 q^{91} +(3.69552 + 3.69552i) q^{92} +(1.92762 + 0.634051i) q^{93} +(-1.41421 - 3.41421i) q^{94} +(-1.04322 + 1.53073i) q^{95} +(9.77048 - 0.733355i) q^{96} -2.72607i q^{97} +(5.00208 - 2.07193i) q^{98} +(-4.48528 + 6.08034i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^9	\( 16 q - 16 q^{9} + 16 q^{10} - 32 q^{19} - 32 q^{24} + 16 q^{25} + 16 q^{30} - 32 q^{34} - 32 q^{36} + 32 q^{40} + 16 q^{49} + 32 q^{51} + 32 q^{54} + 64 q^{66} - 64 q^{70} + 32 q^{75} + 64 q^{76} - 48 q^{81} + 32 q^{84} - 16 q^{90} - 64 q^{91} + 64 q^{96} + 64 q^{99}+O(q^{100}) \) 16 * q - 16 * q^9 + 16 * q^10 - 32 * q^19 - 32 * q^24 + 16 * q^25 + 16 * q^30 - 32 * q^34 - 32 * q^36 + 32 * q^40 + 16 * q^49 + 32 * q^51 + 32 * q^54 + 64 * q^66 - 64 * q^70 + 32 * q^75 + 64 * q^76 - 48 * q^81 + 32 * q^84 - 16 * q^90 - 64 * q^91 + 64 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

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