Properties

Label 570.2.f.d.341.3
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.7278137344.1
Defining polynomial: \(x^{8} - 2 x^{7} + x^{6} + 6 x^{5} - 20 x^{4} + 18 x^{3} + 9 x^{2} - 54 x + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 341.3
Root \(0.828750 + 1.52091i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.d.341.4

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.828750 - 1.52091i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.828750 - 1.52091i) q^{6} +4.83942 q^{7} +1.00000 q^{8} +(-1.62635 + 2.52091i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.828750 - 1.52091i) q^{3} +1.00000 q^{4} +1.00000i q^{5} +(-0.828750 - 1.52091i) q^{6} +4.83942 q^{7} +1.00000 q^{8} +(-1.62635 + 2.52091i) q^{9} +1.00000i q^{10} +2.00000i q^{11} +(-0.828750 - 1.52091i) q^{12} -1.04182i q^{13} +4.83942 q^{14} +(1.52091 - 0.828750i) q^{15} +1.00000 q^{16} -0.140096i q^{17} +(-1.62635 + 2.52091i) q^{18} +(2.65750 + 3.45510i) q^{19} +1.00000i q^{20} +(-4.01067 - 7.36033i) q^{21} +2.00000i q^{22} -6.63702i q^{23} +(-0.828750 - 1.52091i) q^{24} -1.00000 q^{25} -1.04182i q^{26} +(5.18192 + 0.384324i) q^{27} +4.83942 q^{28} -1.65750 q^{29} +(1.52091 - 0.828750i) q^{30} -3.58673i q^{31} +1.00000 q^{32} +(3.04182 - 1.65750i) q^{33} -0.140096i q^{34} +4.83942i q^{35} +(-1.62635 + 2.52091i) q^{36} -6.36384i q^{37} +(2.65750 + 3.45510i) q^{38} +(-1.58452 + 0.863412i) q^{39} +1.00000i q^{40} -1.18192 q^{41} +(-4.01067 - 7.36033i) q^{42} -8.76865 q^{43} +2.00000i q^{44} +(-2.52091 - 1.62635i) q^{45} -6.63702i q^{46} +4.76865i q^{47} +(-0.828750 - 1.52091i) q^{48} +16.4200 q^{49} -1.00000 q^{50} +(-0.213074 + 0.116105i) q^{51} -1.04182i q^{52} +8.42615 q^{53} +(5.18192 + 0.384324i) q^{54} -2.00000 q^{55} +4.83942 q^{56} +(3.05249 - 6.90524i) q^{57} -1.65750 q^{58} +0.350965 q^{59} +(1.52091 - 0.828750i) q^{60} -10.4475 q^{61} -3.58673i q^{62} +(-7.87057 + 12.1998i) q^{63} +1.00000 q^{64} +1.04182 q^{65} +(3.04182 - 1.65750i) q^{66} +13.6309i q^{67} -0.140096i q^{68} +(-10.0943 + 5.50043i) q^{69} +4.83942i q^{70} -11.7625 q^{71} +(-1.62635 + 2.52091i) q^{72} -2.83095 q^{73} -6.36384i q^{74} +(0.828750 + 1.52091i) q^{75} +(2.65750 + 3.45510i) q^{76} +9.67884i q^{77} +(-1.58452 + 0.863412i) q^{78} -10.0921i q^{79} +1.00000i q^{80} +(-3.70999 - 8.19975i) q^{81} -1.18192 q^{82} +10.0342i q^{83} +(-4.01067 - 7.36033i) q^{84} +0.140096 q^{85} -8.76865 q^{86} +(1.37365 + 2.52091i) q^{87} +2.00000i q^{88} -16.4969 q^{89} +(-2.52091 - 1.62635i) q^{90} -5.04182i q^{91} -6.63702i q^{92} +(-5.45510 + 2.97250i) q^{93} +4.76865i q^{94} +(-3.45510 + 2.65750i) q^{95} +(-0.828750 - 1.52091i) q^{96} +7.67884i q^{97} +16.4200 q^{98} +(-5.04182 - 3.25269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} + O(q^{10}) \) \( 8q + 8q^{2} - 2q^{3} + 8q^{4} - 2q^{6} + 4q^{7} + 8q^{8} + 2q^{9} - 2q^{12} + 4q^{14} + 8q^{16} + 2q^{18} + 12q^{19} - 2q^{21} - 2q^{24} - 8q^{25} + 16q^{27} + 4q^{28} - 4q^{29} + 8q^{32} + 2q^{36} + 12q^{38} - 22q^{39} + 16q^{41} - 2q^{42} - 40q^{43} - 8q^{45} - 2q^{48} + 4q^{49} - 8q^{50} + 18q^{51} + 28q^{53} + 16q^{54} - 16q^{55} + 4q^{56} - 30q^{57} - 4q^{58} - 4q^{59} + 16q^{61} - 34q^{63} + 8q^{64} - 16q^{65} - 2q^{69} + 24q^{71} + 2q^{72} - 4q^{73} + 2q^{75} + 12q^{76} - 22q^{78} + 34q^{81} + 16q^{82} - 2q^{84} - 40q^{86} + 26q^{87} - 88q^{89} - 8q^{90} - 24q^{93} - 8q^{95} - 2q^{96} + 4q^{98} - 16q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −0.828750 1.52091i −0.478479 0.878099i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) −0.828750 1.52091i −0.338336 0.620910i
\(7\) 4.83942 1.82913 0.914564 0.404440i \(-0.132534\pi\)
0.914564 + 0.404440i \(0.132534\pi\)
\(8\) 1.00000 0.353553
\(9\) −1.62635 + 2.52091i −0.542115 + 0.840304i
\(10\) 1.00000i 0.316228i
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) −0.828750 1.52091i −0.239240 0.439049i
\(13\) 1.04182i 0.288950i −0.989508 0.144475i \(-0.953851\pi\)
0.989508 0.144475i \(-0.0461493\pi\)
\(14\) 4.83942 1.29339
\(15\) 1.52091 0.828750i 0.392698 0.213982i
\(16\) 1.00000 0.250000
\(17\) 0.140096i 0.0339783i −0.999856 0.0169891i \(-0.994592\pi\)
0.999856 0.0169891i \(-0.00540807\pi\)
\(18\) −1.62635 + 2.52091i −0.383334 + 0.594185i
\(19\) 2.65750 + 3.45510i 0.609672 + 0.792654i
\(20\) 1.00000i 0.223607i
\(21\) −4.01067 7.36033i −0.875200 1.60616i
\(22\) 2.00000i 0.426401i
\(23\) 6.63702i 1.38391i −0.721939 0.691957i \(-0.756749\pi\)
0.721939 0.691957i \(-0.243251\pi\)
\(24\) −0.828750 1.52091i −0.169168 0.310455i
\(25\) −1.00000 −0.200000
\(26\) 1.04182i 0.204318i
\(27\) 5.18192 + 0.384324i 0.997261 + 0.0739631i
\(28\) 4.83942 0.914564
\(29\) −1.65750 −0.307790 −0.153895 0.988087i \(-0.549182\pi\)
−0.153895 + 0.988087i \(0.549182\pi\)
\(30\) 1.52091 0.828750i 0.277679 0.151308i
\(31\) 3.58673i 0.644195i −0.946706 0.322098i \(-0.895612\pi\)
0.946706 0.322098i \(-0.104388\pi\)
\(32\) 1.00000 0.176777
\(33\) 3.04182 1.65750i 0.529514 0.288534i
\(34\) 0.140096i 0.0240263i
\(35\) 4.83942i 0.818011i
\(36\) −1.62635 + 2.52091i −0.271058 + 0.420152i
\(37\) 6.36384i 1.04621i −0.852269 0.523104i \(-0.824774\pi\)
0.852269 0.523104i \(-0.175226\pi\)
\(38\) 2.65750 + 3.45510i 0.431103 + 0.560491i
\(39\) −1.58452 + 0.863412i −0.253727 + 0.138257i
\(40\) 1.00000i 0.158114i
\(41\) −1.18192 −0.184585 −0.0922924 0.995732i \(-0.529419\pi\)
−0.0922924 + 0.995732i \(0.529419\pi\)
\(42\) −4.01067 7.36033i −0.618860 1.13572i
\(43\) −8.76865 −1.33721 −0.668603 0.743619i \(-0.733107\pi\)
−0.668603 + 0.743619i \(0.733107\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −2.52091 1.62635i −0.375795 0.242441i
\(46\) 6.63702i 0.978575i
\(47\) 4.76865i 0.695579i 0.937573 + 0.347789i \(0.113068\pi\)
−0.937573 + 0.347789i \(0.886932\pi\)
\(48\) −0.828750 1.52091i −0.119620 0.219525i
\(49\) 16.4200 2.34571
\(50\) −1.00000 −0.141421
\(51\) −0.213074 + 0.116105i −0.0298363 + 0.0162579i
\(52\) 1.04182i 0.144475i
\(53\) 8.42615 1.15742 0.578710 0.815533i \(-0.303556\pi\)
0.578710 + 0.815533i \(0.303556\pi\)
\(54\) 5.18192 + 0.384324i 0.705170 + 0.0522998i
\(55\) −2.00000 −0.269680
\(56\) 4.83942 0.646695
\(57\) 3.05249 6.90524i 0.404313 0.914621i
\(58\) −1.65750 −0.217640
\(59\) 0.350965 0.0456918 0.0228459 0.999739i \(-0.492727\pi\)
0.0228459 + 0.999739i \(0.492727\pi\)
\(60\) 1.52091 0.828750i 0.196349 0.106991i
\(61\) −10.4475 −1.33766 −0.668832 0.743414i \(-0.733205\pi\)
−0.668832 + 0.743414i \(0.733205\pi\)
\(62\) 3.58673i 0.455515i
\(63\) −7.87057 + 12.1998i −0.991599 + 1.53702i
\(64\) 1.00000 0.125000
\(65\) 1.04182 0.129222
\(66\) 3.04182 1.65750i 0.374423 0.204024i
\(67\) 13.6309i 1.66527i 0.553819 + 0.832637i \(0.313170\pi\)
−0.553819 + 0.832637i \(0.686830\pi\)
\(68\) 0.140096i 0.0169891i
\(69\) −10.0943 + 5.50043i −1.21521 + 0.662174i
\(70\) 4.83942i 0.578421i
\(71\) −11.7625 −1.39595 −0.697975 0.716122i \(-0.745915\pi\)
−0.697975 + 0.716122i \(0.745915\pi\)
\(72\) −1.62635 + 2.52091i −0.191667 + 0.297092i
\(73\) −2.83095 −0.331338 −0.165669 0.986181i \(-0.552978\pi\)
−0.165669 + 0.986181i \(0.552978\pi\)
\(74\) 6.36384i 0.739781i
\(75\) 0.828750 + 1.52091i 0.0956958 + 0.175620i
\(76\) 2.65750 + 3.45510i 0.304836 + 0.396327i
\(77\) 9.67884i 1.10301i
\(78\) −1.58452 + 0.863412i −0.179412 + 0.0977621i
\(79\) 10.0921i 1.13545i −0.823218 0.567726i \(-0.807823\pi\)
0.823218 0.567726i \(-0.192177\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −3.70999 8.19975i −0.412222 0.911084i
\(82\) −1.18192 −0.130521
\(83\) 10.0342i 1.10140i 0.834704 + 0.550699i \(0.185639\pi\)
−0.834704 + 0.550699i \(0.814361\pi\)
\(84\) −4.01067 7.36033i −0.437600 0.803078i
\(85\) 0.140096 0.0151956
\(86\) −8.76865 −0.945548
\(87\) 1.37365 + 2.52091i 0.147271 + 0.270270i
\(88\) 2.00000i 0.213201i
\(89\) −16.4969 −1.74867 −0.874335 0.485323i \(-0.838702\pi\)
−0.874335 + 0.485323i \(0.838702\pi\)
\(90\) −2.52091 1.62635i −0.265727 0.171432i
\(91\) 5.04182i 0.528527i
\(92\) 6.63702i 0.691957i
\(93\) −5.45510 + 2.97250i −0.565667 + 0.308234i
\(94\) 4.76865i 0.491848i
\(95\) −3.45510 + 2.65750i −0.354485 + 0.272654i
\(96\) −0.828750 1.52091i −0.0845840 0.155227i
\(97\) 7.67884i 0.779668i 0.920885 + 0.389834i \(0.127468\pi\)
−0.920885 + 0.389834i \(0.872532\pi\)
\(98\) 16.4200 1.65867
\(99\) −5.04182 3.25269i −0.506722 0.326908i
\(100\) −1.00000 −0.100000
\(101\) 10.4885i 1.04364i −0.853056 0.521820i \(-0.825253\pi\)
0.853056 0.521820i \(-0.174747\pi\)
\(102\) −0.213074 + 0.116105i −0.0210975 + 0.0114961i
\(103\) 11.5373i 1.13680i 0.822751 + 0.568402i \(0.192438\pi\)
−0.822751 + 0.568402i \(0.807562\pi\)
\(104\) 1.04182i 0.102159i
\(105\) 7.36033 4.01067i 0.718295 0.391401i
\(106\) 8.42615 0.818420
\(107\) −14.5098 −1.40271 −0.701357 0.712810i \(-0.747422\pi\)
−0.701357 + 0.712810i \(0.747422\pi\)
\(108\) 5.18192 + 0.384324i 0.498630 + 0.0369816i
\(109\) 8.62855i 0.826465i 0.910625 + 0.413233i \(0.135600\pi\)
−0.910625 + 0.413233i \(0.864400\pi\)
\(110\) −2.00000 −0.190693
\(111\) −9.67884 + 5.27403i −0.918675 + 0.500589i
\(112\) 4.83942 0.457282
\(113\) 20.2509 1.90505 0.952524 0.304463i \(-0.0984769\pi\)
0.952524 + 0.304463i \(0.0984769\pi\)
\(114\) 3.05249 6.90524i 0.285892 0.646735i
\(115\) 6.63702 0.618905
\(116\) −1.65750 −0.153895
\(117\) 2.62635 + 1.69437i 0.242806 + 0.156644i
\(118\) 0.350965 0.0323090
\(119\) 0.677984i 0.0621507i
\(120\) 1.52091 0.828750i 0.138840 0.0756542i
\(121\) 7.00000 0.636364
\(122\) −10.4475 −0.945871
\(123\) 0.979516 + 1.79760i 0.0883200 + 0.162084i
\(124\) 3.58673i 0.322098i
\(125\) 1.00000i 0.0894427i
\(126\) −7.87057 + 12.1998i −0.701166 + 1.08684i
\(127\) 5.31500i 0.471630i 0.971798 + 0.235815i \(0.0757759\pi\)
−0.971798 + 0.235815i \(0.924224\pi\)
\(128\) 1.00000 0.0883883
\(129\) 7.26702 + 13.3363i 0.639825 + 1.17420i
\(130\) 1.04182 0.0913740
\(131\) 4.22519i 0.369157i 0.982818 + 0.184578i \(0.0590920\pi\)
−0.982818 + 0.184578i \(0.940908\pi\)
\(132\) 3.04182 1.65750i 0.264757 0.144267i
\(133\) 12.8608 + 16.7207i 1.11517 + 1.44987i
\(134\) 13.6309i 1.17753i
\(135\) −0.384324 + 5.18192i −0.0330773 + 0.445989i
\(136\) 0.140096i 0.0120131i
\(137\) 22.9374i 1.95967i −0.199799 0.979837i \(-0.564029\pi\)
0.199799 0.979837i \(-0.435971\pi\)
\(138\) −10.0943 + 5.50043i −0.859285 + 0.468228i
\(139\) −14.1673 −1.20165 −0.600827 0.799379i \(-0.705162\pi\)
−0.600827 + 0.799379i \(0.705162\pi\)
\(140\) 4.83942i 0.409006i
\(141\) 7.25269 3.95202i 0.610787 0.332820i
\(142\) −11.7625 −0.987086
\(143\) 2.08365 0.174243
\(144\) −1.62635 + 2.52091i −0.135529 + 0.210076i
\(145\) 1.65750i 0.137648i
\(146\) −2.83095 −0.234292
\(147\) −13.6081 24.9734i −1.12237 2.05977i
\(148\) 6.36384i 0.523104i
\(149\) 1.80346i 0.147745i −0.997268 0.0738724i \(-0.976464\pi\)
0.997268 0.0738724i \(-0.0235358\pi\)
\(150\) 0.828750 + 1.52091i 0.0676672 + 0.124182i
\(151\) 2.62154i 0.213338i 0.994295 + 0.106669i \(0.0340184\pi\)
−0.994295 + 0.106669i \(0.965982\pi\)
\(152\) 2.65750 + 3.45510i 0.215552 + 0.280245i
\(153\) 0.353170 + 0.227845i 0.0285521 + 0.0184202i
\(154\) 9.67884i 0.779943i
\(155\) 3.58673 0.288093
\(156\) −1.58452 + 0.863412i −0.126863 + 0.0691283i
\(157\) 0.271727 0.0216862 0.0108431 0.999941i \(-0.496548\pi\)
0.0108431 + 0.999941i \(0.496548\pi\)
\(158\) 10.0921i 0.802885i
\(159\) −6.98317 12.8154i −0.553801 1.01633i
\(160\) 1.00000i 0.0790569i
\(161\) 32.1193i 2.53136i
\(162\) −3.70999 8.19975i −0.291485 0.644233i
\(163\) −2.96519 −0.232252 −0.116126 0.993235i \(-0.537048\pi\)
−0.116126 + 0.993235i \(0.537048\pi\)
\(164\) −1.18192 −0.0922924
\(165\) 1.65750 + 3.04182i 0.129036 + 0.236806i
\(166\) 10.0342i 0.778806i
\(167\) 4.91019 0.379962 0.189981 0.981788i \(-0.439157\pi\)
0.189981 + 0.981788i \(0.439157\pi\)
\(168\) −4.01067 7.36033i −0.309430 0.567862i
\(169\) 11.9146 0.916508
\(170\) 0.140096 0.0107449
\(171\) −13.0320 + 1.08014i −0.996583 + 0.0826004i
\(172\) −8.76865 −0.668603
\(173\) −16.8692 −1.28254 −0.641272 0.767314i \(-0.721593\pi\)
−0.641272 + 0.767314i \(0.721593\pi\)
\(174\) 1.37365 + 2.52091i 0.104136 + 0.191110i
\(175\) −4.83942 −0.365826
\(176\) 2.00000i 0.150756i
\(177\) −0.290862 0.533787i −0.0218626 0.0401219i
\(178\) −16.4969 −1.23650
\(179\) 0.760182 0.0568187 0.0284093 0.999596i \(-0.490956\pi\)
0.0284093 + 0.999596i \(0.490956\pi\)
\(180\) −2.52091 1.62635i −0.187898 0.121221i
\(181\) 16.7221i 1.24294i 0.783436 + 0.621472i \(0.213465\pi\)
−0.783436 + 0.621472i \(0.786535\pi\)
\(182\) 5.04182i 0.373725i
\(183\) 8.65836 + 15.8897i 0.640044 + 1.17460i
\(184\) 6.63702i 0.489287i
\(185\) 6.36384 0.467879
\(186\) −5.45510 + 2.97250i −0.399987 + 0.217954i
\(187\) 0.280192 0.0204897
\(188\) 4.76865i 0.347789i
\(189\) 25.0775 + 1.85990i 1.82412 + 0.135288i
\(190\) −3.45510 + 2.65750i −0.250659 + 0.192795i
\(191\) 23.5062i 1.70085i −0.526095 0.850426i \(-0.676344\pi\)
0.526095 0.850426i \(-0.323656\pi\)
\(192\) −0.828750 1.52091i −0.0598099 0.109762i
\(193\) 6.10058i 0.439129i −0.975598 0.219565i \(-0.929536\pi\)
0.975598 0.219565i \(-0.0704637\pi\)
\(194\) 7.67884i 0.551309i
\(195\) −0.863412 1.58452i −0.0618302 0.113470i
\(196\) 16.4200 1.17286
\(197\) 9.07749i 0.646744i −0.946272 0.323372i \(-0.895183\pi\)
0.946272 0.323372i \(-0.104817\pi\)
\(198\) −5.04182 3.25269i −0.358307 0.231159i
\(199\) −3.87979 −0.275031 −0.137516 0.990500i \(-0.543912\pi\)
−0.137516 + 0.990500i \(0.543912\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 20.7313 11.2966i 1.46228 0.796799i
\(202\) 10.4885i 0.737965i
\(203\) −8.02134 −0.562988
\(204\) −0.213074 + 0.116105i −0.0149182 + 0.00812895i
\(205\) 1.18192i 0.0825489i
\(206\) 11.5373i 0.803841i
\(207\) 16.7313 + 10.7941i 1.16291 + 0.750241i
\(208\) 1.04182i 0.0722375i
\(209\) −6.91019 + 5.31500i −0.477988 + 0.367646i
\(210\) 7.36033 4.01067i 0.507911 0.276763i
\(211\) 18.8453i 1.29736i −0.761060 0.648681i \(-0.775321\pi\)
0.761060 0.648681i \(-0.224679\pi\)
\(212\) 8.42615 0.578710
\(213\) 9.74816 + 17.8897i 0.667933 + 1.22578i
\(214\) −14.5098 −0.991869
\(215\) 8.76865i 0.598017i
\(216\) 5.18192 + 0.384324i 0.352585 + 0.0261499i
\(217\) 17.3577i 1.17832i
\(218\) 8.62855i 0.584399i
\(219\) 2.34615 + 4.30563i 0.158538 + 0.290948i
\(220\) −2.00000 −0.134840
\(221\) −0.145955 −0.00981803
\(222\) −9.67884 + 5.27403i −0.649601 + 0.353970i
\(223\) 20.3925i 1.36558i −0.730614 0.682791i \(-0.760766\pi\)
0.730614 0.682791i \(-0.239234\pi\)
\(224\) 4.83942 0.323347
\(225\) 1.62635 2.52091i 0.108423 0.168061i
\(226\) 20.2509 1.34707
\(227\) 4.14596 0.275177 0.137588 0.990489i \(-0.456065\pi\)
0.137588 + 0.990489i \(0.456065\pi\)
\(228\) 3.05249 6.90524i 0.202156 0.457310i
\(229\) −4.50539 −0.297724 −0.148862 0.988858i \(-0.547561\pi\)
−0.148862 + 0.988858i \(0.547561\pi\)
\(230\) 6.63702 0.437632
\(231\) 14.7207 8.02134i 0.968549 0.527765i
\(232\) −1.65750 −0.108820
\(233\) 9.86982i 0.646593i −0.946298 0.323297i \(-0.895209\pi\)
0.946298 0.323297i \(-0.104791\pi\)
\(234\) 2.62635 + 1.69437i 0.171690 + 0.110764i
\(235\) −4.76865 −0.311072
\(236\) 0.350965 0.0228459
\(237\) −15.3492 + 8.36384i −0.997039 + 0.543290i
\(238\) 0.677984i 0.0439472i
\(239\) 25.8970i 1.67514i 0.546331 + 0.837569i \(0.316024\pi\)
−0.546331 + 0.837569i \(0.683976\pi\)
\(240\) 1.52091 0.828750i 0.0981744 0.0534956i
\(241\) 10.5311i 0.678370i −0.940720 0.339185i \(-0.889849\pi\)
0.940720 0.339185i \(-0.110151\pi\)
\(242\) 7.00000 0.449977
\(243\) −9.39644 + 12.4381i −0.602782 + 0.797906i
\(244\) −10.4475 −0.668832
\(245\) 16.4200i 1.04903i
\(246\) 0.979516 + 1.79760i 0.0624517 + 0.114611i
\(247\) 3.59960 2.76865i 0.229037 0.176165i
\(248\) 3.58673i 0.227757i
\(249\) 15.2612 8.31586i 0.967137 0.526996i
\(250\) 1.00000i 0.0632456i
\(251\) 19.9848i 1.26143i 0.776015 + 0.630714i \(0.217238\pi\)
−0.776015 + 0.630714i \(0.782762\pi\)
\(252\) −7.87057 + 12.1998i −0.495800 + 0.768512i
\(253\) 13.2740 0.834531
\(254\) 5.31500i 0.333493i
\(255\) −0.116105 0.213074i −0.00727076 0.0133432i
\(256\) 1.00000 0.0625000
\(257\) −9.59519 −0.598532 −0.299266 0.954170i \(-0.596742\pi\)
−0.299266 + 0.954170i \(0.596742\pi\)
\(258\) 7.26702 + 13.3363i 0.452425 + 0.830284i
\(259\) 30.7973i 1.91365i
\(260\) 1.04182 0.0646112
\(261\) 2.69567 4.17841i 0.166858 0.258637i
\(262\) 4.22519i 0.261033i
\(263\) 12.3925i 0.764154i −0.924131 0.382077i \(-0.875209\pi\)
0.924131 0.382077i \(-0.124791\pi\)
\(264\) 3.04182 1.65750i 0.187211 0.102012i
\(265\) 8.42615i 0.517614i
\(266\) 12.8608 + 16.7207i 0.788544 + 1.02521i
\(267\) 13.6718 + 25.0904i 0.836702 + 1.53551i
\(268\) 13.6309i 0.832637i
\(269\) −13.1354 −0.800879 −0.400439 0.916323i \(-0.631142\pi\)
−0.400439 + 0.916323i \(0.631142\pi\)
\(270\) −0.384324 + 5.18192i −0.0233892 + 0.315362i
\(271\) 10.2179 0.620692 0.310346 0.950624i \(-0.399555\pi\)
0.310346 + 0.950624i \(0.399555\pi\)
\(272\) 0.140096i 0.00849457i
\(273\) −7.66817 + 4.17841i −0.464099 + 0.252889i
\(274\) 22.9374i 1.38570i
\(275\) 2.00000i 0.120605i
\(276\) −10.0943 + 5.50043i −0.607607 + 0.331087i
\(277\) −10.2337 −0.614881 −0.307440 0.951567i \(-0.599472\pi\)
−0.307440 + 0.951567i \(0.599472\pi\)
\(278\) −14.1673 −0.849698
\(279\) 9.04182 + 5.83326i 0.541320 + 0.349228i
\(280\) 4.83942i 0.289211i
\(281\) −7.00231 −0.417723 −0.208861 0.977945i \(-0.566976\pi\)
−0.208861 + 0.977945i \(0.566976\pi\)
\(282\) 7.25269 3.95202i 0.431892 0.235339i
\(283\) 11.9708 0.711587 0.355794 0.934565i \(-0.384211\pi\)
0.355794 + 0.934565i \(0.384211\pi\)
\(284\) −11.7625 −0.697975
\(285\) 6.90524 + 3.05249i 0.409031 + 0.180814i
\(286\) 2.08365 0.123209
\(287\) −5.71981 −0.337630
\(288\) −1.62635 + 2.52091i −0.0958334 + 0.148546i
\(289\) 16.9804 0.998845
\(290\) 1.65750i 0.0973318i
\(291\) 11.6788 6.36384i 0.684626 0.373055i
\(292\) −2.83095 −0.165669
\(293\) 21.7581 1.27112 0.635560 0.772051i \(-0.280769\pi\)
0.635560 + 0.772051i \(0.280769\pi\)
\(294\) −13.6081 24.9734i −0.793639 1.45648i
\(295\) 0.350965i 0.0204340i
\(296\) 6.36384i 0.369891i
\(297\) −0.768647 + 10.3638i −0.0446014 + 0.601371i
\(298\) 1.80346i 0.104471i
\(299\) −6.91460 −0.399882
\(300\) 0.828750 + 1.52091i 0.0478479 + 0.0878099i
\(301\) −42.4352 −2.44592
\(302\) 2.62154i 0.150852i
\(303\) −15.9520 + 8.69231i −0.916419 + 0.499360i
\(304\) 2.65750 + 3.45510i 0.152418 + 0.198163i
\(305\) 10.4475i 0.598221i
\(306\) 0.353170 + 0.227845i 0.0201894 + 0.0130250i
\(307\) 29.4413i 1.68031i 0.542350 + 0.840153i \(0.317535\pi\)
−0.542350 + 0.840153i \(0.682465\pi\)
\(308\) 9.67884i 0.551503i
\(309\) 17.5472 9.56153i 0.998226 0.543937i
\(310\) 3.58673 0.203712
\(311\) 1.50453i 0.0853140i 0.999090 + 0.0426570i \(0.0135823\pi\)
−0.999090 + 0.0426570i \(0.986418\pi\)
\(312\) −1.58452 + 0.863412i −0.0897059 + 0.0488811i
\(313\) −26.4975 −1.49773 −0.748863 0.662725i \(-0.769400\pi\)
−0.748863 + 0.662725i \(0.769400\pi\)
\(314\) 0.271727 0.0153344
\(315\) −12.1998 7.87057i −0.687378 0.443457i
\(316\) 10.0921i 0.567726i
\(317\) 9.47499 0.532168 0.266084 0.963950i \(-0.414270\pi\)
0.266084 + 0.963950i \(0.414270\pi\)
\(318\) −6.98317 12.8154i −0.391597 0.718654i
\(319\) 3.31500i 0.185604i
\(320\) 1.00000i 0.0559017i
\(321\) 12.0250 + 22.0681i 0.671170 + 1.23172i
\(322\) 32.1193i 1.78994i
\(323\) 0.484046 0.372305i 0.0269330 0.0207156i
\(324\) −3.70999 8.19975i −0.206111 0.455542i
\(325\) 1.04182i 0.0577900i
\(326\) −2.96519 −0.164227
\(327\) 13.1233 7.15091i 0.725718 0.395446i
\(328\) −1.18192 −0.0652606
\(329\) 23.0775i 1.27230i
\(330\) 1.65750 + 3.04182i 0.0912424 + 0.167447i
\(331\) 1.48931i 0.0818600i 0.999162 + 0.0409300i \(0.0130321\pi\)
−0.999162 + 0.0409300i \(0.986968\pi\)
\(332\) 10.0342i 0.550699i
\(333\) 16.0427 + 10.3498i 0.879133 + 0.567166i
\(334\) 4.91019 0.268674
\(335\) −13.6309 −0.744733
\(336\) −4.01067 7.36033i −0.218800 0.401539i
\(337\) 22.2392i 1.21145i 0.795675 + 0.605724i \(0.207116\pi\)
−0.795675 + 0.605724i \(0.792884\pi\)
\(338\) 11.9146 0.648069
\(339\) −16.7830 30.7999i −0.911526 1.67282i
\(340\) 0.140096 0.00759778
\(341\) 7.17345 0.388464
\(342\) −13.0320 + 1.08014i −0.704690 + 0.0584073i
\(343\) 45.5873 2.46148
\(344\) −8.76865 −0.472774
\(345\) −5.50043 10.0943i −0.296133 0.543460i
\(346\) −16.8692 −0.906895
\(347\) 1.04327i 0.0560059i −0.999608 0.0280029i \(-0.991085\pi\)
0.999608 0.0280029i \(-0.00891478\pi\)
\(348\) 1.37365 + 2.52091i 0.0736356 + 0.135135i
\(349\) −6.14155 −0.328749 −0.164375 0.986398i \(-0.552561\pi\)
−0.164375 + 0.986398i \(0.552561\pi\)
\(350\) −4.83942 −0.258678
\(351\) 0.400398 5.39865i 0.0213716 0.288159i
\(352\) 2.00000i 0.106600i
\(353\) 2.22374i 0.118358i −0.998247 0.0591790i \(-0.981152\pi\)
0.998247 0.0591790i \(-0.0188483\pi\)
\(354\) −0.290862 0.533787i −0.0154592 0.0283705i
\(355\) 11.7625i 0.624288i
\(356\) −16.4969 −0.874335
\(357\) −1.03115 + 0.561879i −0.0545744 + 0.0297378i
\(358\) 0.760182 0.0401769
\(359\) 2.83646i 0.149703i 0.997195 + 0.0748513i \(0.0238482\pi\)
−0.997195 + 0.0748513i \(0.976152\pi\)
\(360\) −2.52091 1.62635i −0.132864 0.0857160i
\(361\) −4.87538 + 18.3638i −0.256599 + 0.966518i
\(362\) 16.7221i 0.878895i
\(363\) −5.80125 10.6464i −0.304487 0.558790i
\(364\) 5.04182i 0.264263i
\(365\) 2.83095i 0.148179i
\(366\) 8.65836 + 15.8897i 0.452580 + 0.830568i
\(367\) 7.87864 0.411262 0.205631 0.978630i \(-0.434075\pi\)
0.205631 + 0.978630i \(0.434075\pi\)
\(368\) 6.63702i 0.345978i
\(369\) 1.92221 2.97952i 0.100066 0.155107i
\(370\) 6.36384 0.330840
\(371\) 40.7777 2.11707
\(372\) −5.45510 + 2.97250i −0.282834 + 0.154117i
\(373\) 13.8684i 0.718077i −0.933323 0.359038i \(-0.883105\pi\)
0.933323 0.359038i \(-0.116895\pi\)
\(374\) 0.280192 0.0144884
\(375\) −1.52091 + 0.828750i −0.0785396 + 0.0427965i
\(376\) 4.76865i 0.245924i
\(377\) 1.72682i 0.0889359i
\(378\) 25.0775 + 1.85990i 1.28985 + 0.0956631i
\(379\) 20.9430i 1.07577i −0.843019 0.537884i \(-0.819224\pi\)
0.843019 0.537884i \(-0.180776\pi\)
\(380\) −3.45510 + 2.65750i −0.177243 + 0.136327i
\(381\) 8.08365 4.40481i 0.414138 0.225665i
\(382\) 23.5062i 1.20268i
\(383\) 22.2848 1.13870 0.569350 0.822095i \(-0.307195\pi\)
0.569350 + 0.822095i \(0.307195\pi\)
\(384\) −0.828750 1.52091i −0.0422920 0.0776137i
\(385\) −9.67884 −0.493279
\(386\) 6.10058i 0.310511i
\(387\) 14.2609 22.1050i 0.724920 1.12366i
\(388\) 7.67884i 0.389834i
\(389\) 1.92807i 0.0977571i −0.998805 0.0488785i \(-0.984435\pi\)
0.998805 0.0488785i \(-0.0155647\pi\)
\(390\) −0.863412 1.58452i −0.0437206 0.0802354i
\(391\) −0.929820 −0.0470230
\(392\) 16.4200 0.829335
\(393\) 6.42615 3.50163i 0.324156 0.176634i
\(394\) 9.07749i 0.457317i
\(395\) 10.0921 0.507789
\(396\) −5.04182 3.25269i −0.253361 0.163454i
\(397\) 28.4986 1.43031 0.715153 0.698968i \(-0.246357\pi\)
0.715153 + 0.698968i \(0.246357\pi\)
\(398\) −3.87979 −0.194477
\(399\) 14.7723 33.4173i 0.739540 1.67296i
\(400\) −1.00000 −0.0500000
\(401\) 2.25770 0.112744 0.0563720 0.998410i \(-0.482047\pi\)
0.0563720 + 0.998410i \(0.482047\pi\)
\(402\) 20.7313 11.2966i 1.03398 0.563422i
\(403\) −3.73674 −0.186140
\(404\) 10.4885i 0.521820i
\(405\) 8.19975 3.70999i 0.407449 0.184351i
\(406\) −8.02134 −0.398092
\(407\) 12.7277 0.630888
\(408\) −0.213074 + 0.116105i −0.0105487 + 0.00574804i
\(409\) 15.8754i 0.784987i −0.919755 0.392494i \(-0.871613\pi\)
0.919755 0.392494i \(-0.128387\pi\)
\(410\) 1.18192i 0.0583709i
\(411\) −34.8858 + 19.0094i −1.72079 + 0.937663i
\(412\) 11.5373i 0.568402i
\(413\) 1.69847 0.0835761
\(414\) 16.7313 + 10.7941i 0.822300 + 0.530501i
\(415\) −10.0342 −0.492560
\(416\) 1.04182i 0.0510796i
\(417\) 11.7411 + 21.5472i 0.574966 + 1.05517i
\(418\) −6.91019 + 5.31500i −0.337989 + 0.259965i
\(419\) 2.56038i 0.125083i −0.998042 0.0625415i \(-0.980079\pi\)
0.998042 0.0625415i \(-0.0199206\pi\)
\(420\) 7.36033 4.01067i 0.359147 0.195701i
\(421\) 9.06201i 0.441655i −0.975313 0.220828i \(-0.929124\pi\)
0.975313 0.220828i \(-0.0708758\pi\)
\(422\) 18.8453i 0.917374i
\(423\) −12.0213 7.75547i −0.584498 0.377084i
\(424\) 8.42615 0.409210
\(425\) 0.140096i 0.00679566i
\(426\) 9.74816 + 17.8897i 0.472300 + 0.866759i
\(427\) −50.5598 −2.44676
\(428\) −14.5098 −0.701357
\(429\) −1.72682 3.16905i −0.0833718 0.153003i
\(430\) 8.76865i 0.422862i
\(431\) 30.8259 1.48483 0.742417 0.669938i \(-0.233679\pi\)
0.742417 + 0.669938i \(0.233679\pi\)
\(432\) 5.18192 + 0.384324i 0.249315 + 0.0184908i
\(433\) 36.8692i 1.77182i −0.463855 0.885911i \(-0.653534\pi\)
0.463855 0.885911i \(-0.346466\pi\)
\(434\) 17.3577i 0.833195i
\(435\) −2.52091 + 1.37365i −0.120868 + 0.0658616i
\(436\) 8.62855i 0.413233i
\(437\) 22.9315 17.6379i 1.09696 0.843734i
\(438\) 2.34615 + 4.30563i 0.112104 + 0.205731i
\(439\) 25.5715i 1.22046i 0.792224 + 0.610231i \(0.208923\pi\)
−0.792224 + 0.610231i \(0.791077\pi\)
\(440\) −2.00000 −0.0953463
\(441\) −26.7046 + 41.3933i −1.27165 + 1.97111i
\(442\) −0.145955 −0.00694239
\(443\) 32.4267i 1.54064i 0.637658 + 0.770320i \(0.279903\pi\)
−0.637658 + 0.770320i \(0.720097\pi\)
\(444\) −9.67884 + 5.27403i −0.459337 + 0.250295i
\(445\) 16.4969i 0.782029i
\(446\) 20.3925i 0.965612i
\(447\) −2.74290 + 1.49461i −0.129735 + 0.0706928i
\(448\) 4.83942 0.228641
\(449\) −21.3521 −1.00767 −0.503834 0.863800i \(-0.668078\pi\)
−0.503834 + 0.863800i \(0.668078\pi\)
\(450\) 1.62635 2.52091i 0.0766667 0.118837i
\(451\) 2.36384i 0.111309i
\(452\) 20.2509 0.952524
\(453\) 3.98712 2.17260i 0.187331 0.102078i
\(454\) 4.14596 0.194579
\(455\) 5.04182 0.236364
\(456\) 3.05249 6.90524i 0.142946 0.323367i
\(457\) −3.22404 −0.150814 −0.0754072 0.997153i \(-0.524026\pi\)
−0.0754072 + 0.997153i \(0.524026\pi\)
\(458\) −4.50539 −0.210523
\(459\) 0.0538422 0.725967i 0.00251314 0.0338852i
\(460\) 6.63702 0.309452
\(461\) 32.5340i 1.51526i −0.652684 0.757631i \(-0.726357\pi\)
0.652684 0.757631i \(-0.273643\pi\)
\(462\) 14.7207 8.02134i 0.684867 0.373187i
\(463\) −24.0798 −1.11908 −0.559541 0.828802i \(-0.689023\pi\)
−0.559541 + 0.828802i \(0.689023\pi\)
\(464\) −1.65750 −0.0769475
\(465\) −2.97250 5.45510i −0.137846 0.252974i
\(466\) 9.86982i 0.457211i
\(467\) 33.7996i 1.56406i 0.623241 + 0.782030i \(0.285815\pi\)
−0.623241 + 0.782030i \(0.714185\pi\)
\(468\) 2.62635 + 1.69437i 0.121403 + 0.0783221i
\(469\) 65.9654i 3.04600i
\(470\) −4.76865 −0.219961
\(471\) −0.225194 0.413273i −0.0103764 0.0190426i
\(472\) 0.350965 0.0161545
\(473\) 17.5373i 0.806366i
\(474\) −15.3492 + 8.36384i −0.705013 + 0.384164i
\(475\) −2.65750 3.45510i −0.121934 0.158531i
\(476\) 0.677984i 0.0310753i
\(477\) −13.7038 + 21.2416i −0.627456 + 0.972585i
\(478\) 25.8970i 1.18450i
\(479\) 0.601352i 0.0274765i −0.999906 0.0137382i \(-0.995627\pi\)
0.999906 0.0137382i \(-0.00437315\pi\)
\(480\) 1.52091 0.828750i 0.0694198 0.0378271i
\(481\) −6.63000 −0.302302
\(482\) 10.5311i 0.479680i
\(483\) −48.8506 + 26.6189i −2.22278 + 1.21120i
\(484\) 7.00000 0.318182
\(485\) −7.67884 −0.348678
\(486\) −9.39644 + 12.4381i −0.426231 + 0.564205i
\(487\) 6.40481i 0.290230i 0.989415 + 0.145115i \(0.0463551\pi\)
−0.989415 + 0.145115i \(0.953645\pi\)
\(488\) −10.4475 −0.472936
\(489\) 2.45740 + 4.50980i 0.111128 + 0.203940i
\(490\) 16.4200i 0.741779i
\(491\) 38.6148i 1.74266i 0.490697 + 0.871330i \(0.336742\pi\)
−0.490697 + 0.871330i \(0.663258\pi\)
\(492\) 0.979516 + 1.79760i 0.0441600 + 0.0810419i
\(493\) 0.232209i 0.0104582i
\(494\) 3.59960 2.76865i 0.161954 0.124567i
\(495\) 3.25269 5.04182i 0.146198 0.226613i
\(496\) 3.58673i 0.161049i
\(497\) −56.9236 −2.55337
\(498\) 15.2612 8.31586i 0.683869 0.372642i
\(499\) −32.2936 −1.44566 −0.722831 0.691025i \(-0.757159\pi\)
−0.722831 + 0.691025i \(0.757159\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −4.06932 7.46797i −0.181804 0.333644i
\(502\) 19.9848i 0.891965i
\(503\) 32.0643i 1.42968i −0.699290 0.714839i \(-0.746500\pi\)
0.699290 0.714839i \(-0.253500\pi\)
\(504\) −7.87057 + 12.1998i −0.350583 + 0.543420i
\(505\) 10.4885 0.466730
\(506\) 13.2740 0.590103
\(507\) −9.87423 18.1211i −0.438530 0.804785i
\(508\) 5.31500i 0.235815i
\(509\) 9.15232 0.405669 0.202835 0.979213i \(-0.434985\pi\)
0.202835 + 0.979213i \(0.434985\pi\)
\(510\) −0.116105 0.213074i −0.00514120 0.00943507i
\(511\) −13.7002 −0.606060
\(512\) 1.00000 0.0441942
\(513\) 12.4431 + 18.9254i 0.549375 + 0.835576i
\(514\) −9.59519 −0.423226
\(515\) −11.5373 −0.508394
\(516\) 7.26702 + 13.3363i 0.319913 + 0.587100i
\(517\) −9.53729 −0.419450
\(518\) 30.7973i 1.35316i
\(519\) 13.9804 + 25.6566i 0.613670 + 1.12620i
\(520\) 1.04182 0.0456870
\(521\) −37.6721 −1.65044 −0.825222 0.564808i \(-0.808950\pi\)
−0.825222 + 0.564808i \(0.808950\pi\)
\(522\) 2.69567 4.17841i 0.117986 0.182884i
\(523\) 6.44047i 0.281622i 0.990036 + 0.140811i \(0.0449710\pi\)
−0.990036 + 0.140811i \(0.955029\pi\)
\(524\) 4.22519i 0.184578i
\(525\) 4.01067 + 7.36033i 0.175040 + 0.321231i
\(526\) 12.3925i 0.540338i
\(527\) −0.502486 −0.0218887
\(528\) 3.04182 1.65750i 0.132378 0.0721334i
\(529\) −21.0500 −0.915217
\(530\) 8.42615i 0.366008i
\(531\) −0.570791 + 0.884752i −0.0247702 + 0.0383950i
\(532\) 12.8608 + 16.7207i 0.557585 + 0.724933i
\(533\) 1.23135i 0.0533358i
\(534\) 13.6718 + 25.0904i 0.591638 + 1.08577i
\(535\) 14.5098i 0.627313i
\(536\) 13.6309i 0.588763i
\(537\) −0.630001 1.15617i −0.0271865 0.0498924i
\(538\) −13.1354 −0.566307
\(539\) 32.8400i 1.41452i
\(540\) −0.384324 + 5.18192i −0.0165387 + 0.222994i
\(541\) −32.9190 −1.41530 −0.707649 0.706564i \(-0.750244\pi\)
−0.707649 + 0.706564i \(0.750244\pi\)
\(542\) 10.2179 0.438896
\(543\) 25.4329 13.8585i 1.09143 0.594723i
\(544\) 0.140096i 0.00600657i
\(545\) −8.62855 −0.369607
\(546\) −7.66817 + 4.17841i −0.328167 + 0.178820i
\(547\) 31.3436i 1.34016i −0.742290 0.670079i \(-0.766260\pi\)
0.742290 0.670079i \(-0.233740\pi\)
\(548\) 22.9374i 0.979837i
\(549\) 16.9912 26.3372i 0.725168 1.12404i
\(550\) 2.00000i 0.0852803i
\(551\) −4.40481 5.72682i −0.187651 0.243971i
\(552\) −10.0943 + 5.50043i −0.429643 + 0.234114i
\(553\) 48.8400i 2.07689i
\(554\) −10.2337 −0.434787
\(555\) −5.27403 9.67884i −0.223870 0.410844i
\(556\) −14.1673 −0.600827
\(557\) 4.58442i 0.194248i −0.995272 0.0971241i \(-0.969036\pi\)
0.995272 0.0971241i \(-0.0309644\pi\)
\(558\) 9.04182 + 5.83326i 0.382771 + 0.246942i
\(559\) 9.13539i 0.386386i
\(560\) 4.83942i 0.204503i
\(561\) −0.232209 0.426148i −0.00980388 0.0179920i
\(562\) −7.00231 −0.295374
\(563\) −6.08075 −0.256273 −0.128136 0.991757i \(-0.540900\pi\)
−0.128136 + 0.991757i \(0.540900\pi\)
\(564\) 7.25269 3.95202i 0.305393 0.166410i
\(565\) 20.2509i 0.851964i
\(566\) 11.9708 0.503168
\(567\) −17.9542 39.6820i −0.754006 1.66649i
\(568\) −11.7625 −0.493543
\(569\) 32.4694 1.36119 0.680594 0.732661i \(-0.261722\pi\)
0.680594 + 0.732661i \(0.261722\pi\)
\(570\) 6.90524 + 3.05249i 0.289228 + 0.127855i
\(571\) 15.6636 0.655502 0.327751 0.944764i \(-0.393709\pi\)
0.327751 + 0.944764i \(0.393709\pi\)
\(572\) 2.08365 0.0871217
\(573\) −35.7509 + 19.4808i −1.49352 + 0.813822i
\(574\) −5.71981 −0.238740
\(575\) 6.63702i 0.276783i
\(576\) −1.62635 + 2.52091i −0.0677644 + 0.105038i
\(577\) 42.7379 1.77920 0.889601 0.456739i \(-0.150983\pi\)
0.889601 + 0.456739i \(0.150983\pi\)
\(578\) 16.9804 0.706290
\(579\) −9.27844 + 5.05586i −0.385599 + 0.210114i
\(580\) 1.65750i 0.0688240i
\(581\) 48.5598i 2.01460i
\(582\) 11.6788 6.36384i 0.484104 0.263790i
\(583\) 16.8523i 0.697951i
\(584\) −2.83095 −0.117146
\(585\) −1.69437 + 2.62635i −0.0700534 + 0.108586i
\(586\) 21.7581 0.898818
\(587\) 31.5042i 1.30032i 0.759799 + 0.650159i \(0.225298\pi\)
−0.759799 + 0.650159i \(0.774702\pi\)
\(588\) −13.6081 24.9734i −0.561187 1.02988i
\(589\) 12.3925 9.53173i 0.510624 0.392748i
\(590\) 0.350965i 0.0144490i
\(591\) −13.8061 + 7.52297i −0.567905 + 0.309454i
\(592\) 6.36384i 0.261552i
\(593\) 44.9444i 1.84565i −0.385225 0.922823i \(-0.625876\pi\)
0.385225 0.922823i \(-0.374124\pi\)
\(594\) −0.768647 + 10.3638i −0.0315380 + 0.425234i
\(595\) 0.677984 0.0277946
\(596\) 1.80346i 0.0738724i
\(597\) 3.21538 + 5.90083i 0.131597 + 0.241505i
\(598\) −6.91460 −0.282759
\(599\) 10.2083 0.417098 0.208549 0.978012i \(-0.433126\pi\)
0.208549 + 0.978012i \(0.433126\pi\)
\(600\) 0.828750 + 1.52091i 0.0338336 + 0.0620910i
\(601\) 12.7534i 0.520223i 0.965579 + 0.260112i \(0.0837594\pi\)
−0.965579 + 0.260112i \(0.916241\pi\)
\(602\) −42.4352 −1.72953
\(603\) −34.3622 22.1685i −1.39934 0.902771i
\(604\) 2.62154i 0.106669i
\(605\) 7.00000i 0.284590i
\(606\) −15.9520 + 8.69231i −0.648006 + 0.353101i
\(607\) 41.6665i 1.69119i 0.533823 + 0.845596i \(0.320755\pi\)
−0.533823 + 0.845596i \(0.679245\pi\)
\(608\) 2.65750 + 3.45510i 0.107776 + 0.140123i
\(609\) 6.64769 + 12.1998i 0.269378 + 0.494359i
\(610\) 10.4475i 0.423006i
\(611\) 4.96809 0.200987
\(612\) 0.353170 + 0.227845i 0.0142760 + 0.00921008i
\(613\) 9.10117 0.367593 0.183796 0.982964i \(-0.441161\pi\)
0.183796 + 0.982964i \(0.441161\pi\)
\(614\) 29.4413i 1.18816i
\(615\) −1.79760 + 0.979516i −0.0724861 + 0.0394979i
\(616\) 9.67884i 0.389972i
\(617\) 45.0128i 1.81215i 0.423119 + 0.906074i \(0.360935\pi\)
−0.423119 + 0.906074i \(0.639065\pi\)
\(618\) 17.5472 9.56153i 0.705852 0.384621i
\(619\) 8.58903 0.345222 0.172611 0.984990i \(-0.444780\pi\)
0.172611 + 0.984990i \(0.444780\pi\)
\(620\) 3.58673 0.144046
\(621\) 2.55076 34.3925i 0.102359 1.38012i
\(622\) 1.50453i 0.0603261i
\(623\) −79.8355 −3.19854
\(624\) −1.58452 + 0.863412i −0.0634317 + 0.0345641i
\(625\) 1.00000 0.0400000
\(626\) −26.4975 −1.05905
\(627\) 13.8105 + 6.10499i 0.551537 + 0.243810i
\(628\) 0.271727 0.0108431
\(629\) −0.891549 −0.0355484
\(630\) −12.1998 7.87057i −0.486050 0.313571i
\(631\) 4.01693 0.159911 0.0799557 0.996798i \(-0.474522\pi\)
0.0799557 + 0.996798i \(0.474522\pi\)
\(632\) 10.0921i 0.401443i
\(633\) −28.6620 + 15.6180i −1.13921 + 0.620761i
\(634\) 9.47499 0.376300
\(635\) −5.31500 −0.210919
\(636\) −6.98317 12.8154i −0.276901 0.508165i
\(637\) 17.1067i 0.677794i
\(638\) 3.31500i 0.131242i
\(639\) 19.1299 29.6522i 0.756766 1.17302i
\(640\) 1.00000i 0.0395285i
\(641\) 25.1088 0.991738 0.495869 0.868397i \(-0.334850\pi\)
0.495869 + 0.868397i \(0.334850\pi\)
\(642\) 12.0250 + 22.0681i 0.474589 + 0.870959i
\(643\) 8.77155 0.345916 0.172958 0.984929i \(-0.444668\pi\)
0.172958 + 0.984929i \(0.444668\pi\)
\(644\) 32.1193i 1.26568i
\(645\) −13.3363 + 7.26702i −0.525118 + 0.286139i
\(646\) 0.484046 0.372305i 0.0190445 0.0146482i
\(647\) 6.00530i 0.236093i 0.993008 + 0.118046i \(0.0376632\pi\)
−0.993008 + 0.118046i \(0.962337\pi\)
\(648\) −3.70999 8.19975i −0.145742 0.322117i
\(649\) 0.701930i 0.0275532i
\(650\) 1.04182i 0.0408637i
\(651\) −26.3995 + 14.3852i −1.03468 + 0.563800i
\(652\) −2.96519 −0.116126
\(653\) 13.6121i 0.532684i −0.963879 0.266342i \(-0.914185\pi\)
0.963879 0.266342i \(-0.0858150\pi\)
\(654\) 13.1233 7.15091i 0.513160 0.279623i
\(655\) −4.22519 −0.165092
\(656\) −1.18192 −0.0461462
\(657\) 4.60411 7.13659i 0.179624 0.278425i
\(658\) 23.0775i 0.899654i
\(659\) 38.7575 1.50978 0.754889 0.655853i \(-0.227691\pi\)
0.754889 + 0.655853i \(0.227691\pi\)
\(660\) 1.65750 + 3.04182i 0.0645181 + 0.118403i
\(661\) 0.645482i 0.0251063i 0.999921 + 0.0125532i \(0.00399590\pi\)
−0.999921 + 0.0125532i \(0.996004\pi\)
\(662\) 1.48931i 0.0578838i
\(663\) 0.120961 + 0.221985i 0.00469772 + 0.00862120i
\(664\) 10.0342i 0.389403i
\(665\) −16.7207 + 12.8608i −0.648400 + 0.498719i
\(666\) 16.0427 + 10.3498i 0.621641 + 0.401047i
\(667\) 11.0009i 0.425955i
\(668\) 4.91019 0.189981
\(669\) −31.0152 + 16.9003i −1.19912 + 0.653403i
\(670\) −13.6309 −0.526606
\(671\) 20.8950i 0.806642i
\(672\) −4.01067 7.36033i −0.154715 0.283931i
\(673\) 39.5630i 1.52504i −0.646963 0.762522i \(-0.723961\pi\)
0.646963 0.762522i \(-0.276039\pi\)
\(674\) 22.2392i 0.856623i
\(675\) −5.18192 0.384324i −0.199452 0.0147926i
\(676\) 11.9146 0.458254
\(677\) 34.2173 1.31508 0.657539 0.753421i \(-0.271598\pi\)
0.657539 + 0.753421i \(0.271598\pi\)
\(678\) −16.7830 30.7999i −0.644546 1.18286i
\(679\) 37.1611i 1.42611i
\(680\) 0.140096 0.00537244
\(681\) −3.43596 6.30563i −0.131666 0.241632i
\(682\) 7.17345 0.274686
\(683\) 15.7508 0.602686 0.301343 0.953516i \(-0.402565\pi\)
0.301343 + 0.953516i \(0.402565\pi\)
\(684\) −13.0320 + 1.08014i −0.498291 + 0.0413002i
\(685\) 22.9374 0.876393
\(686\) 45.5873 1.74053
\(687\) 3.73384 + 6.85230i 0.142455 + 0.261431i
\(688\) −8.76865 −0.334302
\(689\) 8.77856i 0.334437i
\(690\) −5.50043 10.0943i −0.209398 0.384284i
\(691\) 3.35768 0.127732 0.0638661 0.997958i \(-0.479657\pi\)
0.0638661 + 0.997958i \(0.479657\pi\)
\(692\) −16.8692 −0.641272
\(693\) −24.3995 15.7411i −0.926861 0.597957i
\(694\) 1.04327i 0.0396021i
\(695\) 14.1673i 0.537396i
\(696\) 1.37365 + 2.52091i 0.0520682 + 0.0955549i
\(697\) 0.165582i 0.00627188i
\(698\) −6.14155 −0.232461
\(699\) −15.0111 + 8.17961i −0.567773 + 0.309381i
\(700\) −4.83942 −0.182913
\(701\) 9.06577i 0.342409i −0.985235 0.171205i \(-0.945234\pi\)
0.985235 0.171205i \(-0.0547659\pi\)
\(702\) 0.400398 5.39865i 0.0151120 0.203759i
\(703\) 21.9877 16.9119i 0.829281 0.637845i
\(704\) 2.00000i 0.0753778i
\(705\) 3.95202 + 7.25269i 0.148842 + 0.273152i
\(706\) 2.22374i 0.0836917i
\(707\) 50.7580i 1.90895i
\(708\) −0.290862 0.533787i −0.0109313 0.0200609i
\(709\) −8.60425 −0.323139 −0.161570 0.986861i \(-0.551656\pi\)
−0.161570 + 0.986861i \(0.551656\pi\)
\(710\) 11.7625i 0.441438i
\(711\) 25.4413 + 16.4133i 0.954124 + 0.615546i
\(712\) −16.4969 −0.618248
\(713\) −23.8052 −0.891511
\(714\) −1.03115 + 0.561879i −0.0385900 + 0.0210278i
\(715\) 2.08365i 0.0779240i
\(716\) 0.760182 0.0284093
\(717\) 39.3871 21.4622i 1.47094 0.801519i
\(718\) 2.83646i 0.105856i
\(719\) 24.3738i 0.908988i 0.890750 + 0.454494i \(0.150180\pi\)
−0.890750 + 0.454494i \(0.849820\pi\)
\(720\) −2.52091 1.62635i −0.0939488 0.0606104i
\(721\) 55.8338i 2.07936i
\(722\) −4.87538 + 18.3638i −0.181443 + 0.683431i
\(723\) −16.0169 + 8.72768i −0.595676 + 0.324586i
\(724\) 16.7221i 0.621472i
\(725\) 1.65750 0.0615580
\(726\) −5.80125 10.6464i −0.215305 0.395124i
\(727\) −51.2863 −1.90210 −0.951052 0.309031i \(-0.899995\pi\)
−0.951052 + 0.309031i \(0.899995\pi\)
\(728\) 5.04182i 0.186862i
\(729\) 26.7046 + 3.98307i 0.989059 + 0.147521i
\(730\) 2.83095i 0.104778i
\(731\) 1.22845i 0.0454360i
\(732\) 8.65836 + 15.8897i 0.320022 + 0.587301i
\(733\) 23.0263 0.850497 0.425249 0.905077i \(-0.360187\pi\)
0.425249 + 0.905077i \(0.360187\pi\)
\(734\) 7.87864 0.290806
\(735\) 24.9734 13.6081i 0.921156 0.501941i
\(736\) 6.63702i 0.244644i
\(737\) −27.2617 −1.00420
\(738\) 1.92221 2.97952i 0.0707576 0.109678i
\(739\) 17.8490 0.656587 0.328294 0.944576i \(-0.393526\pi\)
0.328294 + 0.944576i \(0.393526\pi\)
\(740\) 6.36384 0.233939
\(741\) −7.19404 3.18016i −0.264280 0.116826i
\(742\) 40.7777 1.49700
\(743\) 26.9652 0.989257 0.494628 0.869105i \(-0.335304\pi\)
0.494628 + 0.869105i \(0.335304\pi\)
\(744\) −5.45510 + 2.97250i −0.199994 + 0.108977i
\(745\) 1.80346 0.0660735
\(746\) 13.8684i 0.507757i
\(747\) −25.2954 16.3191i −0.925509 0.597085i
\(748\) 0.280192 0.0102448
\(749\) −70.2190 −2.56575
\(750\) −1.52091 + 0.828750i −0.0555359 + 0.0302617i
\(751\) 45.1134i 1.64621i −0.567888 0.823106i \(-0.692239\pi\)
0.567888 0.823106i \(-0.307761\pi\)
\(752\) 4.76865i 0.173895i
\(753\) 30.3951 16.5624i 1.10766 0.603567i
\(754\) 1.72682i 0.0628872i
\(755\) −2.62154 −0.0954075
\(756\) 25.0775 + 1.85990i 0.912059 + 0.0676441i
\(757\) 19.0860 0.693691 0.346845 0.937922i \(-0.387253\pi\)
0.346845 + 0.937922i \(0.387253\pi\)
\(758\) 20.9430i 0.760683i
\(759\) −11.0009 20.1886i −0.399306 0.732801i
\(760\) −3.45510 + 2.65750i −0.125330 + 0.0963977i
\(761\) 33.1301i 1.20096i 0.799638 + 0.600482i \(0.205025\pi\)
−0.799638 + 0.600482i \(0.794975\pi\)
\(762\) 8.08365 4.40481i 0.292840 0.159569i
\(763\) 41.7572i 1.51171i
\(764\) 23.5062i 0.850426i
\(765\) −0.227845 + 0.353170i −0.00823775 + 0.0127689i
\(766\) 22.2848 0.805183
\(767\) 0.365644i 0.0132026i
\(768\) −0.828750 1.52091i −0.0299049 0.0548812i
\(769\) 12.7350 0.459235 0.229618 0.973281i \(-0.426252\pi\)
0.229618 + 0.973281i \(0.426252\pi\)
\(770\) −9.67884 −0.348801
\(771\) 7.95202 + 14.5934i 0.286385 + 0.525570i
\(772\) 6.10058i 0.219565i
\(773\) −4.46001 −0.160415 −0.0802077 0.996778i \(-0.525558\pi\)
−0.0802077 + 0.996778i \(0.525558\pi\)
\(774\) 14.2609 22.1050i 0.512596 0.794547i
\(775\) 3.58673i 0.128839i
\(776\) 7.67884i 0.275654i
\(777\) −46.8400 + 25.5233i −1.68037 + 0.915642i
\(778\) 1.92807i 0.0691247i
\(779\) −3.14095 4.08365i −0.112536 0.146312i
\(780\) −0.863412 1.58452i −0.0309151 0.0567350i
\(781\) 23.5250i 0.841790i
\(782\) −0.929820 −0.0332503
\(783\) −8.58903 0.637017i −0.306947 0.0227651i
\(784\) 16.4200 0.586428