Properties

Label 570.2.f.d.341.7
Level $570$
Weight $2$
Character 570.341
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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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 341.7
Root \(-1.71731 + 0.225499i\) of defining polynomial
Character \(\chi\) \(=\) 570.341
Dual form 570.2.f.d.341.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.71731 - 0.225499i) q^{3} +1.00000 q^{4} -1.00000i q^{5} +(1.71731 - 0.225499i) q^{6} -0.631989 q^{7} +1.00000 q^{8} +(2.89830 - 0.774501i) q^{9} -1.00000i q^{10} -2.00000i q^{11} +(1.71731 - 0.225499i) q^{12} -2.45100i q^{13} -0.631989 q^{14} +(-0.225499 - 1.71731i) q^{15} +1.00000 q^{16} +3.25363i q^{17} +(2.89830 - 0.774501i) q^{18} +(-2.43462 + 3.61561i) q^{19} -1.00000i q^{20} +(-1.08532 + 0.142513i) q^{21} -2.00000i q^{22} -0.812981i q^{23} +(1.71731 - 0.225499i) q^{24} -1.00000 q^{25} -2.45100i q^{26} +(4.80263 - 1.98362i) q^{27} -0.631989 q^{28} +3.43462 q^{29} +(-0.225499 - 1.71731i) q^{30} +7.16461i q^{31} +1.00000 q^{32} +(-0.450997 - 3.43462i) q^{33} +3.25363i q^{34} +0.631989i q^{35} +(2.89830 - 0.774501i) q^{36} +5.60526i q^{37} +(-2.43462 + 3.61561i) q^{38} +(-0.552696 - 4.20912i) q^{39} -1.00000i q^{40} -0.802629 q^{41} +(-1.08532 + 0.142513i) q^{42} -11.9672 q^{43} -2.00000i q^{44} +(-0.774501 - 2.89830i) q^{45} -0.812981i q^{46} -7.96724i q^{47} +(1.71731 - 0.225499i) q^{48} -6.60059 q^{49} -1.00000 q^{50} +(0.733688 + 5.58748i) q^{51} -2.45100i q^{52} +6.53262 q^{53} +(4.80263 - 1.98362i) q^{54} -2.00000 q^{55} -0.631989 q^{56} +(-3.36568 + 6.75812i) q^{57} +3.43462 q^{58} -2.09198 q^{59} +(-0.225499 - 1.71731i) q^{60} -2.70326 q^{61} +7.16461i q^{62} +(-1.83169 + 0.489476i) q^{63} +1.00000 q^{64} -2.45100 q^{65} +(-0.450997 - 3.43462i) q^{66} +14.9462i q^{67} +3.25363i q^{68} +(-0.183326 - 1.39614i) q^{69} +0.631989i q^{70} +6.16597 q^{71} +(2.89830 - 0.774501i) q^{72} -4.89461 q^{73} +5.60526i q^{74} +(-1.71731 + 0.225499i) q^{75} +(-2.43462 + 3.61561i) q^{76} +1.26398i q^{77} +(-0.552696 - 4.20912i) q^{78} -4.42859i q^{79} -1.00000i q^{80} +(7.80030 - 4.48948i) q^{81} -0.802629 q^{82} -5.86788i q^{83} +(-1.08532 + 0.142513i) q^{84} +3.25363 q^{85} -11.9672 q^{86} +(5.89830 - 0.774501i) q^{87} -2.00000i q^{88} -5.93339 q^{89} +(-0.774501 - 2.89830i) q^{90} +1.54900i q^{91} -0.812981i q^{92} +(1.61561 + 12.3039i) q^{93} -7.96724i q^{94} +(3.61561 + 2.43462i) q^{95} +(1.71731 - 0.225499i) q^{96} +3.26398i q^{97} -6.60059 q^{98} +(-1.54900 - 5.79660i) 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
\(3\) 1.71731 0.225499i 0.991489 0.130192i
\(4\) 1.00000 0.500000
\(5\) 1.00000i 0.447214i
\(6\) 1.71731 0.225499i 0.701088 0.0920594i
\(7\) −0.631989 −0.238869 −0.119435 0.992842i \(-0.538108\pi\)
−0.119435 + 0.992842i \(0.538108\pi\)
\(8\) 1.00000 0.353553
\(9\) 2.89830 0.774501i 0.966100 0.258167i
\(10\) 1.00000i 0.316228i
\(11\) 2.00000i 0.603023i −0.953463 0.301511i \(-0.902509\pi\)
0.953463 0.301511i \(-0.0974911\pi\)
\(12\) 1.71731 0.225499i 0.495744 0.0650958i
\(13\) 2.45100i 0.679784i −0.940464 0.339892i \(-0.889609\pi\)
0.940464 0.339892i \(-0.110391\pi\)
\(14\) −0.631989 −0.168906
\(15\) −0.225499 1.71731i −0.0582235 0.443407i
\(16\) 1.00000 0.250000
\(17\) 3.25363i 0.789120i 0.918870 + 0.394560i \(0.129103\pi\)
−0.918870 + 0.394560i \(0.870897\pi\)
\(18\) 2.89830 0.774501i 0.683136 0.182552i
\(19\) −2.43462 + 3.61561i −0.558540 + 0.829478i
\(20\) 1.00000i 0.223607i
\(21\) −1.08532 + 0.142513i −0.236836 + 0.0310988i
\(22\) 2.00000i 0.426401i
\(23\) 0.812981i 0.169518i −0.996401 0.0847591i \(-0.972988\pi\)
0.996401 0.0847591i \(-0.0270121\pi\)
\(24\) 1.71731 0.225499i 0.350544 0.0460297i
\(25\) −1.00000 −0.200000
\(26\) 2.45100i 0.480680i
\(27\) 4.80263 1.98362i 0.924266 0.381748i
\(28\) −0.631989 −0.119435
\(29\) 3.43462 0.637793 0.318896 0.947790i \(-0.396688\pi\)
0.318896 + 0.947790i \(0.396688\pi\)
\(30\) −0.225499 1.71731i −0.0411702 0.313536i
\(31\) 7.16461i 1.28680i 0.765529 + 0.643401i \(0.222477\pi\)
−0.765529 + 0.643401i \(0.777523\pi\)
\(32\) 1.00000 0.176777
\(33\) −0.450997 3.43462i −0.0785085 0.597890i
\(34\) 3.25363i 0.557992i
\(35\) 0.631989i 0.106826i
\(36\) 2.89830 0.774501i 0.483050 0.129084i
\(37\) 5.60526i 0.921499i 0.887530 + 0.460749i \(0.152419\pi\)
−0.887530 + 0.460749i \(0.847581\pi\)
\(38\) −2.43462 + 3.61561i −0.394947 + 0.586529i
\(39\) −0.552696 4.20912i −0.0885022 0.673999i
\(40\) 1.00000i 0.158114i
\(41\) −0.802629 −0.125350 −0.0626748 0.998034i \(-0.519963\pi\)
−0.0626748 + 0.998034i \(0.519963\pi\)
\(42\) −1.08532 + 0.142513i −0.167469 + 0.0219902i
\(43\) −11.9672 −1.82499 −0.912494 0.409091i \(-0.865846\pi\)
−0.912494 + 0.409091i \(0.865846\pi\)
\(44\) 2.00000i 0.301511i
\(45\) −0.774501 2.89830i −0.115456 0.432053i
\(46\) 0.812981i 0.119867i
\(47\) 7.96724i 1.16214i −0.813853 0.581071i \(-0.802634\pi\)
0.813853 0.581071i \(-0.197366\pi\)
\(48\) 1.71731 0.225499i 0.247872 0.0325479i
\(49\) −6.60059 −0.942941
\(50\) −1.00000 −0.141421
\(51\) 0.733688 + 5.58748i 0.102737 + 0.782404i
\(52\) 2.45100i 0.339892i
\(53\) 6.53262 0.897325 0.448662 0.893701i \(-0.351901\pi\)
0.448662 + 0.893701i \(0.351901\pi\)
\(54\) 4.80263 1.98362i 0.653555 0.269937i
\(55\) −2.00000 −0.269680
\(56\) −0.631989 −0.0844531
\(57\) −3.36568 + 6.75812i −0.445795 + 0.895135i
\(58\) 3.43462 0.450987
\(59\) −2.09198 −0.272352 −0.136176 0.990685i \(-0.543481\pi\)
−0.136176 + 0.990685i \(0.543481\pi\)
\(60\) −0.225499 1.71731i −0.0291117 0.221704i
\(61\) −2.70326 −0.346118 −0.173059 0.984912i \(-0.555365\pi\)
−0.173059 + 0.984912i \(0.555365\pi\)
\(62\) 7.16461i 0.909907i
\(63\) −1.83169 + 0.489476i −0.230772 + 0.0616682i
\(64\) 1.00000 0.125000
\(65\) −2.45100 −0.304009
\(66\) −0.450997 3.43462i −0.0555139 0.422772i
\(67\) 14.9462i 1.82597i 0.407995 + 0.912984i \(0.366228\pi\)
−0.407995 + 0.912984i \(0.633772\pi\)
\(68\) 3.25363i 0.394560i
\(69\) −0.183326 1.39614i −0.0220699 0.168075i
\(70\) 0.631989i 0.0755371i
\(71\) 6.16597 0.731766 0.365883 0.930661i \(-0.380767\pi\)
0.365883 + 0.930661i \(0.380767\pi\)
\(72\) 2.89830 0.774501i 0.341568 0.0912759i
\(73\) −4.89461 −0.572870 −0.286435 0.958100i \(-0.592470\pi\)
−0.286435 + 0.958100i \(0.592470\pi\)
\(74\) 5.60526i 0.651598i
\(75\) −1.71731 + 0.225499i −0.198298 + 0.0260383i
\(76\) −2.43462 + 3.61561i −0.279270 + 0.414739i
\(77\) 1.26398i 0.144044i
\(78\) −0.552696 4.20912i −0.0625805 0.476589i
\(79\) 4.42859i 0.498255i −0.968471 0.249128i \(-0.919856\pi\)
0.968471 0.249128i \(-0.0801439\pi\)
\(80\) 1.00000i 0.111803i
\(81\) 7.80030 4.48948i 0.866699 0.498831i
\(82\) −0.802629 −0.0886356
\(83\) 5.86788i 0.644083i −0.946726 0.322042i \(-0.895631\pi\)
0.946726 0.322042i \(-0.104369\pi\)
\(84\) −1.08532 + 0.142513i −0.118418 + 0.0155494i
\(85\) 3.25363 0.352905
\(86\) −11.9672 −1.29046
\(87\) 5.89830 0.774501i 0.632364 0.0830353i
\(88\) 2.00000i 0.213201i
\(89\) −5.93339 −0.628938 −0.314469 0.949268i \(-0.601827\pi\)
−0.314469 + 0.949268i \(0.601827\pi\)
\(90\) −0.774501 2.89830i −0.0816396 0.305508i
\(91\) 1.54900i 0.162380i
\(92\) 0.812981i 0.0847591i
\(93\) 1.61561 + 12.3039i 0.167531 + 1.27585i
\(94\) 7.96724i 0.821758i
\(95\) 3.61561 + 2.43462i 0.370954 + 0.249787i
\(96\) 1.71731 0.225499i 0.175272 0.0230149i
\(97\) 3.26398i 0.331407i 0.986176 + 0.165703i \(0.0529894\pi\)
−0.986176 + 0.165703i \(0.947011\pi\)
\(98\) −6.60059 −0.666760
\(99\) −1.54900 5.79660i −0.155681 0.582580i
\(100\) −1.00000 −0.100000
\(101\) 7.45999i 0.742297i 0.928574 + 0.371148i \(0.121036\pi\)
−0.928574 + 0.371148i \(0.878964\pi\)
\(102\) 0.733688 + 5.58748i 0.0726459 + 0.553243i
\(103\) 17.9345i 1.76714i −0.468302 0.883569i \(-0.655134\pi\)
0.468302 0.883569i \(-0.344866\pi\)
\(104\) 2.45100i 0.240340i
\(105\) 0.142513 + 1.08532i 0.0139078 + 0.105916i
\(106\) 6.53262 0.634505
\(107\) −5.63063 −0.544334 −0.272167 0.962250i \(-0.587740\pi\)
−0.272167 + 0.962250i \(0.587740\pi\)
\(108\) 4.80263 1.98362i 0.462133 0.190874i
\(109\) 8.71362i 0.834613i −0.908766 0.417307i \(-0.862974\pi\)
0.908766 0.417307i \(-0.137026\pi\)
\(110\) −2.00000 −0.190693
\(111\) 1.26398 + 9.62596i 0.119971 + 0.913656i
\(112\) −0.631989 −0.0597173
\(113\) −0.705983 −0.0664133 −0.0332066 0.999449i \(-0.510572\pi\)
−0.0332066 + 0.999449i \(0.510572\pi\)
\(114\) −3.36568 + 6.75812i −0.315225 + 0.632956i
\(115\) −0.812981 −0.0758108
\(116\) 3.43462 0.318896
\(117\) −1.89830 7.10373i −0.175498 0.656740i
\(118\) −2.09198 −0.192582
\(119\) 2.05626i 0.188497i
\(120\) −0.225499 1.71731i −0.0205851 0.156768i
\(121\) 7.00000 0.636364
\(122\) −2.70326 −0.244742
\(123\) −1.37836 + 0.180992i −0.124283 + 0.0163195i
\(124\) 7.16461i 0.643401i
\(125\) 1.00000i 0.0894427i
\(126\) −1.83169 + 0.489476i −0.163180 + 0.0436060i
\(127\) 4.86924i 0.432075i 0.976385 + 0.216037i \(0.0693133\pi\)
−0.976385 + 0.216037i \(0.930687\pi\)
\(128\) 1.00000 0.0883883
\(129\) −20.5515 + 2.69860i −1.80945 + 0.237598i
\(130\) −2.45100 −0.214967
\(131\) 20.1005i 1.75618i 0.478491 + 0.878092i \(0.341184\pi\)
−0.478491 + 0.878092i \(0.658816\pi\)
\(132\) −0.450997 3.43462i −0.0392543 0.298945i
\(133\) 1.53865 2.28503i 0.133418 0.198137i
\(134\) 14.9462i 1.29115i
\(135\) −1.98362 4.80263i −0.170723 0.413345i
\(136\) 3.25363i 0.278996i
\(137\) 8.28883i 0.708163i −0.935215 0.354081i \(-0.884794\pi\)
0.935215 0.354081i \(-0.115206\pi\)
\(138\) −0.183326 1.39614i −0.0156057 0.118847i
\(139\) −0.196012 −0.0166255 −0.00831274 0.999965i \(-0.502646\pi\)
−0.00831274 + 0.999965i \(0.502646\pi\)
\(140\) 0.631989i 0.0534128i
\(141\) −1.79660 13.6822i −0.151301 1.15225i
\(142\) 6.16597 0.517437
\(143\) −4.90199 −0.409925
\(144\) 2.89830 0.774501i 0.241525 0.0645418i
\(145\) 3.43462i 0.285230i
\(146\) −4.89461 −0.405081
\(147\) −11.3353 + 1.48842i −0.934916 + 0.122763i
\(148\) 5.60526i 0.460749i
\(149\) 11.4092i 0.934682i −0.884077 0.467341i \(-0.845212\pi\)
0.884077 0.467341i \(-0.154788\pi\)
\(150\) −1.71731 + 0.225499i −0.140218 + 0.0184119i
\(151\) 10.2119i 0.831031i 0.909586 + 0.415515i \(0.136399\pi\)
−0.909586 + 0.415515i \(0.863601\pi\)
\(152\) −2.43462 + 3.61561i −0.197474 + 0.293265i
\(153\) 2.51994 + 9.42999i 0.203725 + 0.762369i
\(154\) 1.26398i 0.101854i
\(155\) 7.16461 0.575476
\(156\) −0.552696 4.20912i −0.0442511 0.336999i
\(157\) 14.0338 1.12002 0.560012 0.828485i \(-0.310797\pi\)
0.560012 + 0.828485i \(0.310797\pi\)
\(158\) 4.42859i 0.352320i
\(159\) 11.2185 1.47310i 0.889688 0.116824i
\(160\) 1.00000i 0.0790569i
\(161\) 0.513795i 0.0404927i
\(162\) 7.80030 4.48948i 0.612849 0.352727i
\(163\) −19.3765 −1.51768 −0.758842 0.651275i \(-0.774234\pi\)
−0.758842 + 0.651275i \(0.774234\pi\)
\(164\) −0.802629 −0.0626748
\(165\) −3.43462 + 0.450997i −0.267385 + 0.0351101i
\(166\) 5.86788i 0.455436i
\(167\) −9.23122 −0.714333 −0.357167 0.934041i \(-0.616257\pi\)
−0.357167 + 0.934041i \(0.616257\pi\)
\(168\) −1.08532 + 0.142513i −0.0837343 + 0.0109951i
\(169\) 6.99261 0.537893
\(170\) 3.25363 0.249542
\(171\) −4.25596 + 12.3647i −0.325461 + 0.945555i
\(172\) −11.9672 −0.912494
\(173\) 1.98794 0.151141 0.0755703 0.997140i \(-0.475922\pi\)
0.0755703 + 0.997140i \(0.475922\pi\)
\(174\) 5.89830 0.774501i 0.447149 0.0587148i
\(175\) 0.631989 0.0477739
\(176\) 2.00000i 0.150756i
\(177\) −3.59257 + 0.471738i −0.270034 + 0.0354580i
\(178\) −5.93339 −0.444727
\(179\) 11.4938 0.859090 0.429545 0.903046i \(-0.358674\pi\)
0.429545 + 0.903046i \(0.358674\pi\)
\(180\) −0.774501 2.89830i −0.0577279 0.216027i
\(181\) 18.1671i 1.35035i 0.737659 + 0.675174i \(0.235931\pi\)
−0.737659 + 0.675174i \(0.764069\pi\)
\(182\) 1.54900i 0.114820i
\(183\) −4.64234 + 0.609582i −0.343172 + 0.0450616i
\(184\) 0.812981i 0.0599337i
\(185\) 5.60526 0.412107
\(186\) 1.61561 + 12.3039i 0.118462 + 0.902162i
\(187\) 6.50725 0.475857
\(188\) 7.96724i 0.581071i
\(189\) −3.03521 + 1.25363i −0.220779 + 0.0911879i
\(190\) 3.61561 + 2.43462i 0.262304 + 0.176626i
\(191\) 2.80093i 0.202668i −0.994852 0.101334i \(-0.967689\pi\)
0.994852 0.101334i \(-0.0323110\pi\)
\(192\) 1.71731 0.225499i 0.123936 0.0162740i
\(193\) 15.9552i 1.14848i −0.818687 0.574240i \(-0.805298\pi\)
0.818687 0.574240i \(-0.194702\pi\)
\(194\) 3.26398i 0.234340i
\(195\) −4.20912 + 0.552696i −0.301421 + 0.0395794i
\(196\) −6.60059 −0.471471
\(197\) 19.0352i 1.35620i −0.734969 0.678101i \(-0.762803\pi\)
0.734969 0.678101i \(-0.237197\pi\)
\(198\) −1.54900 5.79660i −0.110083 0.411947i
\(199\) −15.3691 −1.08949 −0.544743 0.838603i \(-0.683373\pi\)
−0.544743 + 0.838603i \(0.683373\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 3.37035 + 25.6672i 0.237726 + 1.81043i
\(202\) 7.45999i 0.524883i
\(203\) −2.17064 −0.152349
\(204\) 0.733688 + 5.58748i 0.0513684 + 0.391202i
\(205\) 0.802629i 0.0560581i
\(206\) 17.9345i 1.24955i
\(207\) −0.629655 2.35626i −0.0437640 0.163772i
\(208\) 2.45100i 0.169946i
\(209\) 7.23122 + 4.86924i 0.500194 + 0.336812i
\(210\) 0.142513 + 1.08532i 0.00983430 + 0.0748942i
\(211\) 2.13976i 0.147307i 0.997284 + 0.0736534i \(0.0234659\pi\)
−0.997284 + 0.0736534i \(0.976534\pi\)
\(212\) 6.53262 0.448662
\(213\) 10.5889 1.39042i 0.725538 0.0952699i
\(214\) −5.63063 −0.384902
\(215\) 11.9672i 0.816159i
\(216\) 4.80263 1.98362i 0.326778 0.134968i
\(217\) 4.52796i 0.307378i
\(218\) 8.71362i 0.590161i
\(219\) −8.40555 + 1.10373i −0.567995 + 0.0745830i
\(220\) −2.00000 −0.134840
\(221\) 7.97463 0.536432
\(222\) 1.26398 + 9.62596i 0.0848326 + 0.646052i
\(223\) 17.9044i 1.19897i −0.800386 0.599485i \(-0.795372\pi\)
0.800386 0.599485i \(-0.204628\pi\)
\(224\) −0.631989 −0.0422265
\(225\) −2.89830 + 0.774501i −0.193220 + 0.0516334i
\(226\) −0.705983 −0.0469613
\(227\) −3.97463 −0.263805 −0.131903 0.991263i \(-0.542109\pi\)
−0.131903 + 0.991263i \(0.542109\pi\)
\(228\) −3.36568 + 6.75812i −0.222897 + 0.447568i
\(229\) 13.5932 0.898264 0.449132 0.893465i \(-0.351733\pi\)
0.449132 + 0.893465i \(0.351733\pi\)
\(230\) −0.812981 −0.0536064
\(231\) 0.285025 + 2.17064i 0.0187533 + 0.142818i
\(232\) 3.43462 0.225494
\(233\) 21.2323i 1.39097i −0.718538 0.695487i \(-0.755188\pi\)
0.718538 0.695487i \(-0.244812\pi\)
\(234\) −1.89830 7.10373i −0.124096 0.464385i
\(235\) −7.96724 −0.519726
\(236\) −2.09198 −0.136176
\(237\) −0.998641 7.60526i −0.0648687 0.494015i
\(238\) 2.05626i 0.133287i
\(239\) 22.2899i 1.44182i 0.693031 + 0.720908i \(0.256275\pi\)
−0.693031 + 0.720908i \(0.743725\pi\)
\(240\) −0.225499 1.71731i −0.0145559 0.110852i
\(241\) 4.19873i 0.270464i −0.990814 0.135232i \(-0.956822\pi\)
0.990814 0.135232i \(-0.0431780\pi\)
\(242\) 7.00000 0.449977
\(243\) 12.3831 9.46877i 0.794379 0.607422i
\(244\) −2.70326 −0.173059
\(245\) 6.60059i 0.421696i
\(246\) −1.37836 + 0.180992i −0.0878812 + 0.0115396i
\(247\) 8.86185 + 5.96724i 0.563866 + 0.379687i
\(248\) 7.16461i 0.454953i
\(249\) −1.32320 10.0770i −0.0838543 0.638601i
\(250\) 1.00000i 0.0632456i
\(251\) 18.6377i 1.17640i −0.808714 0.588202i \(-0.799836\pi\)
0.808714 0.588202i \(-0.200164\pi\)
\(252\) −1.83169 + 0.489476i −0.115386 + 0.0308341i
\(253\) −1.62596 −0.102223
\(254\) 4.86924i 0.305523i
\(255\) 5.58748 0.733688i 0.349902 0.0459453i
\(256\) 1.00000 0.0625000
\(257\) −5.63802 −0.351690 −0.175845 0.984418i \(-0.556266\pi\)
−0.175845 + 0.984418i \(0.556266\pi\)
\(258\) −20.5515 + 2.69860i −1.27948 + 0.168007i
\(259\) 3.54246i 0.220118i
\(260\) −2.45100 −0.152004
\(261\) 9.95456 2.66012i 0.616172 0.164657i
\(262\) 20.1005i 1.24181i
\(263\) 25.9044i 1.59734i −0.601772 0.798668i \(-0.705538\pi\)
0.601772 0.798668i \(-0.294462\pi\)
\(264\) −0.450997 3.43462i −0.0277570 0.211386i
\(265\) 6.53262i 0.401296i
\(266\) 1.53865 2.28503i 0.0943408 0.140104i
\(267\) −10.1895 + 1.33797i −0.623585 + 0.0818825i
\(268\) 14.9462i 0.912984i
\(269\) 25.3317 1.54450 0.772250 0.635319i \(-0.219131\pi\)
0.772250 + 0.635319i \(0.219131\pi\)
\(270\) −1.98362 4.80263i −0.120719 0.292279i
\(271\) 17.5799 1.06790 0.533951 0.845515i \(-0.320707\pi\)
0.533951 + 0.845515i \(0.320707\pi\)
\(272\) 3.25363i 0.197280i
\(273\) 0.349298 + 2.66012i 0.0211405 + 0.160998i
\(274\) 8.28883i 0.500747i
\(275\) 2.00000i 0.120605i
\(276\) −0.183326 1.39614i −0.0110349 0.0840377i
\(277\) 21.6271 1.29944 0.649722 0.760172i \(-0.274885\pi\)
0.649722 + 0.760172i \(0.274885\pi\)
\(278\) −0.196012 −0.0117560
\(279\) 5.54900 + 20.7652i 0.332210 + 1.24318i
\(280\) 0.631989i 0.0377686i
\(281\) 21.6598 1.29212 0.646058 0.763288i \(-0.276416\pi\)
0.646058 + 0.763288i \(0.276416\pi\)
\(282\) −1.79660 13.6822i −0.106986 0.814764i
\(283\) −15.2132 −0.904333 −0.452166 0.891934i \(-0.649349\pi\)
−0.452166 + 0.891934i \(0.649349\pi\)
\(284\) 6.16597 0.365883
\(285\) 6.75812 + 3.36568i 0.400317 + 0.199365i
\(286\) −4.90199 −0.289861
\(287\) 0.507253 0.0299422
\(288\) 2.89830 0.774501i 0.170784 0.0456379i
\(289\) 6.41392 0.377289
\(290\) 3.43462i 0.201688i
\(291\) 0.736022 + 5.60526i 0.0431464 + 0.328586i
\(292\) −4.89461 −0.286435
\(293\) −5.38980 −0.314876 −0.157438 0.987529i \(-0.550323\pi\)
−0.157438 + 0.987529i \(0.550323\pi\)
\(294\) −11.3353 + 1.48842i −0.661085 + 0.0868066i
\(295\) 2.09198i 0.121800i
\(296\) 5.60526i 0.325799i
\(297\) −3.96724 9.60526i −0.230203 0.557354i
\(298\) 11.4092i 0.660920i
\(299\) −1.99261 −0.115236
\(300\) −1.71731 + 0.225499i −0.0991489 + 0.0130192i
\(301\) 7.56316 0.435934
\(302\) 10.2119i 0.587627i
\(303\) 1.68222 + 12.8111i 0.0966408 + 0.735979i
\(304\) −2.43462 + 3.61561i −0.139635 + 0.207369i
\(305\) 2.70326i 0.154788i
\(306\) 2.51994 + 9.42999i 0.144055 + 0.539077i
\(307\) 0.570050i 0.0325345i −0.999868 0.0162672i \(-0.994822\pi\)
0.999868 0.0162672i \(-0.00517825\pi\)
\(308\) 1.26398i 0.0720218i
\(309\) −4.04420 30.7991i −0.230067 1.75210i
\(310\) 7.16461 0.406923
\(311\) 8.38548i 0.475497i 0.971327 + 0.237749i \(0.0764094\pi\)
−0.971327 + 0.237749i \(0.923591\pi\)
\(312\) −0.552696 4.20912i −0.0312903 0.238294i
\(313\) 24.6358 1.39250 0.696249 0.717801i \(-0.254851\pi\)
0.696249 + 0.717801i \(0.254851\pi\)
\(314\) 14.0338 0.791976
\(315\) 0.489476 + 1.83169i 0.0275789 + 0.103204i
\(316\) 4.42859i 0.249128i
\(317\) 17.0071 0.955215 0.477607 0.878573i \(-0.341504\pi\)
0.477607 + 0.878573i \(0.341504\pi\)
\(318\) 11.2185 1.47310i 0.629104 0.0826072i
\(319\) 6.86924i 0.384603i
\(320\) 1.00000i 0.0559017i
\(321\) −9.66953 + 1.26970i −0.539701 + 0.0708677i
\(322\) 0.513795i 0.0286327i
\(323\) −11.7638 7.92134i −0.654558 0.440755i
\(324\) 7.80030 4.48948i 0.433350 0.249415i
\(325\) 2.45100i 0.135957i
\(326\) −19.3765 −1.07316
\(327\) −1.96491 14.9640i −0.108660 0.827509i
\(328\) −0.802629 −0.0443178
\(329\) 5.03521i 0.277600i
\(330\) −3.43462 + 0.450997i −0.189070 + 0.0248266i
\(331\) 9.74773i 0.535784i 0.963449 + 0.267892i \(0.0863270\pi\)
−0.963449 + 0.267892i \(0.913673\pi\)
\(332\) 5.86788i 0.322042i
\(333\) 4.34128 + 16.2457i 0.237901 + 0.890260i
\(334\) −9.23122 −0.505110
\(335\) 14.9462 0.816598
\(336\) −1.08532 + 0.142513i −0.0592091 + 0.00777470i
\(337\) 23.7505i 1.29377i −0.762586 0.646887i \(-0.776071\pi\)
0.762586 0.646887i \(-0.223929\pi\)
\(338\) 6.99261 0.380348
\(339\) −1.21239 + 0.159198i −0.0658480 + 0.00864645i
\(340\) 3.25363 0.176453
\(341\) 14.3292 0.775971
\(342\) −4.25596 + 12.3647i −0.230136 + 0.668609i
\(343\) 8.59542 0.464109
\(344\) −11.9672 −0.645230
\(345\) −1.39614 + 0.183326i −0.0751656 + 0.00986994i
\(346\) 1.98794 0.106873
\(347\) 22.9031i 1.22950i −0.788721 0.614751i \(-0.789256\pi\)
0.788721 0.614751i \(-0.210744\pi\)
\(348\) 5.89830 0.774501i 0.316182 0.0415176i
\(349\) 11.1985 0.599440 0.299720 0.954027i \(-0.403107\pi\)
0.299720 + 0.954027i \(0.403107\pi\)
\(350\) 0.631989 0.0337812
\(351\) −4.86185 11.7712i −0.259506 0.628302i
\(352\) 2.00000i 0.106600i
\(353\) 1.64837i 0.0877338i −0.999037 0.0438669i \(-0.986032\pi\)
0.999037 0.0438669i \(-0.0139677\pi\)
\(354\) −3.59257 + 0.471738i −0.190943 + 0.0250726i
\(355\) 6.16597i 0.327256i
\(356\) −5.93339 −0.314469
\(357\) −0.463683 3.53123i −0.0245407 0.186892i
\(358\) 11.4938 0.607468
\(359\) 32.3079i 1.70515i 0.522608 + 0.852573i \(0.324959\pi\)
−0.522608 + 0.852573i \(0.675041\pi\)
\(360\) −0.774501 2.89830i −0.0408198 0.152754i
\(361\) −7.14527 17.6053i −0.376067 0.926593i
\(362\) 18.1671i 0.954840i
\(363\) 12.0212 1.57849i 0.630947 0.0828492i
\(364\) 1.54900i 0.0811898i
\(365\) 4.89461i 0.256195i
\(366\) −4.64234 + 0.609582i −0.242659 + 0.0318634i
\(367\) −4.78465 −0.249756 −0.124878 0.992172i \(-0.539854\pi\)
−0.124878 + 0.992172i \(0.539854\pi\)
\(368\) 0.812981i 0.0423795i
\(369\) −2.32626 + 0.621638i −0.121100 + 0.0323612i
\(370\) 5.60526 0.291404
\(371\) −4.12855 −0.214343
\(372\) 1.61561 + 12.3039i 0.0837655 + 0.637925i
\(373\) 3.21978i 0.166714i 0.996520 + 0.0833569i \(0.0265641\pi\)
−0.996520 + 0.0833569i \(0.973436\pi\)
\(374\) 6.50725 0.336482
\(375\) 0.225499 + 1.71731i 0.0116447 + 0.0886815i
\(376\) 7.96724i 0.410879i
\(377\) 8.41824i 0.433561i
\(378\) −3.03521 + 1.25363i −0.156114 + 0.0644796i
\(379\) 23.0887i 1.18599i 0.805206 + 0.592995i \(0.202054\pi\)
−0.805206 + 0.592995i \(0.797946\pi\)
\(380\) 3.61561 + 2.43462i 0.185477 + 0.124893i
\(381\) 1.09801 + 8.36198i 0.0562525 + 0.428397i
\(382\) 2.80093i 0.143308i
\(383\) −28.8124 −1.47224 −0.736122 0.676849i \(-0.763345\pi\)
−0.736122 + 0.676849i \(0.763345\pi\)
\(384\) 1.71731 0.225499i 0.0876361 0.0115074i
\(385\) 1.26398 0.0644183
\(386\) 15.9552i 0.812098i
\(387\) −34.6847 + 9.26865i −1.76312 + 0.471152i
\(388\) 3.26398i 0.165703i
\(389\) 13.5545i 0.687241i −0.939109 0.343621i \(-0.888347\pi\)
0.939109 0.343621i \(-0.111653\pi\)
\(390\) −4.20912 + 0.552696i −0.213137 + 0.0279869i
\(391\) 2.64514 0.133770
\(392\) −6.60059 −0.333380
\(393\) 4.53262 + 34.5187i 0.228641 + 1.74124i
\(394\) 19.0352i 0.958980i
\(395\) −4.42859 −0.222827
\(396\) −1.54900 5.79660i −0.0778403 0.291290i
\(397\) 1.51795 0.0761837 0.0380918 0.999274i \(-0.487872\pi\)
0.0380918 + 0.999274i \(0.487872\pi\)
\(398\) −15.3691 −0.770383
\(399\) 2.12707 4.27106i 0.106487 0.213820i
\(400\) −1.00000 −0.0500000
\(401\) −9.81713 −0.490244 −0.245122 0.969492i \(-0.578828\pi\)
−0.245122 + 0.969492i \(0.578828\pi\)
\(402\) 3.37035 + 25.6672i 0.168098 + 1.28017i
\(403\) 17.5604 0.874748
\(404\) 7.45999i 0.371148i
\(405\) −4.48948 7.80030i −0.223084 0.387600i
\(406\) −2.17064 −0.107727
\(407\) 11.2105 0.555685
\(408\) 0.733688 + 5.58748i 0.0363230 + 0.276622i
\(409\) 18.1453i 0.897226i 0.893726 + 0.448613i \(0.148082\pi\)
−0.893726 + 0.448613i \(0.851918\pi\)
\(410\) 0.802629i 0.0396390i
\(411\) −1.86912 14.2345i −0.0921969 0.702136i
\(412\) 17.9345i 0.883569i
\(413\) 1.32211 0.0650566
\(414\) −0.629655 2.35626i −0.0309458 0.115804i
\(415\) −5.86788 −0.288043
\(416\) 2.45100i 0.120170i
\(417\) −0.336612 + 0.0442003i −0.0164840 + 0.00216450i
\(418\) 7.23122 + 4.86924i 0.353691 + 0.238162i
\(419\) 15.0145i 0.733507i 0.930318 + 0.366753i \(0.119531\pi\)
−0.930318 + 0.366753i \(0.880469\pi\)
\(420\) 0.142513 + 1.08532i 0.00695390 + 0.0529582i
\(421\) 24.4341i 1.19085i −0.803413 0.595423i \(-0.796985\pi\)
0.803413 0.595423i \(-0.203015\pi\)
\(422\) 2.13976i 0.104162i
\(423\) −6.17064 23.0915i −0.300027 1.12275i
\(424\) 6.53262 0.317252
\(425\) 3.25363i 0.157824i
\(426\) 10.5889 1.39042i 0.513033 0.0673660i
\(427\) 1.70843 0.0826769
\(428\) −5.63063 −0.272167
\(429\) −8.41824 + 1.10539i −0.406436 + 0.0533689i
\(430\) 11.9672i 0.577112i
\(431\) −41.0522 −1.97741 −0.988707 0.149864i \(-0.952116\pi\)
−0.988707 + 0.149864i \(0.952116\pi\)
\(432\) 4.80263 1.98362i 0.231067 0.0954370i
\(433\) 18.0121i 0.865604i 0.901489 + 0.432802i \(0.142475\pi\)
−0.901489 + 0.432802i \(0.857525\pi\)
\(434\) 4.52796i 0.217349i
\(435\) −0.774501 5.89830i −0.0371345 0.282802i
\(436\) 8.71362i 0.417307i
\(437\) 2.93942 + 1.97930i 0.140612 + 0.0946826i
\(438\) −8.40555 + 1.10373i −0.401633 + 0.0527381i
\(439\) 27.8024i 1.32693i −0.748205 0.663467i \(-0.769084\pi\)
0.748205 0.663467i \(-0.230916\pi\)
\(440\) −2.00000 −0.0953463
\(441\) −19.1305 + 5.11217i −0.910976 + 0.243437i
\(442\) 7.97463 0.379314
\(443\) 10.0366i 0.476852i 0.971161 + 0.238426i \(0.0766314\pi\)
−0.971161 + 0.238426i \(0.923369\pi\)
\(444\) 1.26398 + 9.62596i 0.0599857 + 0.456828i
\(445\) 5.93339i 0.281270i
\(446\) 17.9044i 0.847800i
\(447\) −2.57277 19.5932i −0.121688 0.926727i
\(448\) −0.631989 −0.0298587
\(449\) 33.9055 1.60010 0.800051 0.599933i \(-0.204806\pi\)
0.800051 + 0.599933i \(0.204806\pi\)
\(450\) −2.89830 + 0.774501i −0.136627 + 0.0365103i
\(451\) 1.60526i 0.0755887i
\(452\) −0.705983 −0.0332066
\(453\) 2.30276 + 17.5369i 0.108193 + 0.823958i
\(454\) −3.97463 −0.186539
\(455\) 1.54900 0.0726184
\(456\) −3.36568 + 6.75812i −0.157612 + 0.316478i
\(457\) −31.7131 −1.48348 −0.741738 0.670690i \(-0.765998\pi\)
−0.741738 + 0.670690i \(0.765998\pi\)
\(458\) 13.5932 0.635169
\(459\) 6.45396 + 15.6260i 0.301245 + 0.729357i
\(460\) −0.812981 −0.0379054
\(461\) 23.1029i 1.07601i −0.842942 0.538005i \(-0.819178\pi\)
0.842942 0.538005i \(-0.180822\pi\)
\(462\) 0.285025 + 2.17064i 0.0132606 + 0.100987i
\(463\) 32.6950 1.51947 0.759733 0.650235i \(-0.225330\pi\)
0.759733 + 0.650235i \(0.225330\pi\)
\(464\) 3.43462 0.159448
\(465\) 12.3039 1.61561i 0.570578 0.0749221i
\(466\) 21.2323i 0.983568i
\(467\) 29.2023i 1.35132i 0.737213 + 0.675660i \(0.236141\pi\)
−0.737213 + 0.675660i \(0.763859\pi\)
\(468\) −1.89830 7.10373i −0.0877490 0.328370i
\(469\) 9.44583i 0.436168i
\(470\) −7.96724 −0.367501
\(471\) 24.1005 3.16461i 1.11049 0.145818i
\(472\) −2.09198 −0.0962911
\(473\) 23.9345i 1.10051i
\(474\) −0.998641 7.60526i −0.0458691 0.349321i
\(475\) 2.43462 3.61561i 0.111708 0.165896i
\(476\) 2.05626i 0.0942483i
\(477\) 18.9335 5.05953i 0.866906 0.231660i
\(478\) 22.2899i 1.01952i
\(479\) 17.7712i 0.811988i 0.913876 + 0.405994i \(0.133075\pi\)
−0.913876 + 0.405994i \(0.866925\pi\)
\(480\) −0.225499 1.71731i −0.0102926 0.0783841i
\(481\) 13.7385 0.626420
\(482\) 4.19873i 0.191247i
\(483\) 0.115860 + 0.882344i 0.00527181 + 0.0401481i
\(484\) 7.00000 0.318182
\(485\) 3.26398 0.148210
\(486\) 12.3831 9.46877i 0.561711 0.429512i
\(487\) 10.3620i 0.469546i −0.972050 0.234773i \(-0.924565\pi\)
0.972050 0.234773i \(-0.0754347\pi\)
\(488\) −2.70326 −0.122371
\(489\) −33.2754 + 4.36937i −1.50477 + 0.197590i
\(490\) 6.60059i 0.298184i
\(491\) 16.8993i 0.762654i −0.924440 0.381327i \(-0.875467\pi\)
0.924440 0.381327i \(-0.124533\pi\)
\(492\) −1.37836 + 0.180992i −0.0621414 + 0.00815974i
\(493\) 11.1750i 0.503295i
\(494\) 8.86185 + 5.96724i 0.398713 + 0.268479i
\(495\) −5.79660 + 1.54900i −0.260538 + 0.0696225i
\(496\) 7.16461i 0.321701i
\(497\) −3.89683 −0.174797
\(498\) −1.32320 10.0770i −0.0592939 0.451559i
\(499\) 0.364702 0.0163263 0.00816315 0.999967i \(-0.497402\pi\)
0.00816315 + 0.999967i \(0.497402\pi\)
\(500\) 1.00000i 0.0447214i
\(501\) −15.8529 + 2.08163i −0.708253 + 0.0930002i
\(502\) 18.6377i 0.831843i
\(503\) 30.0939i 1.34182i −0.741538 0.670911i \(-0.765903\pi\)
0.741538 0.670911i \(-0.234097\pi\)
\(504\) −1.83169 + 0.489476i −0.0815901 + 0.0218030i
\(505\) 7.45999 0.331965
\(506\) −1.62596 −0.0722828
\(507\) 12.0085 1.57682i 0.533315 0.0700292i
\(508\) 4.86924i 0.216037i
\(509\) −44.3849 −1.96732 −0.983662 0.180023i \(-0.942383\pi\)
−0.983662 + 0.180023i \(0.942383\pi\)
\(510\) 5.58748 0.733688i 0.247418 0.0324883i
\(511\) 3.09334 0.136841
\(512\) 1.00000 0.0441942
\(513\) −4.52057 + 22.1938i −0.199588 + 0.979880i
\(514\) −5.63802 −0.248682
\(515\) −17.9345 −0.790288
\(516\) −20.5515 + 2.69860i −0.904727 + 0.118799i
\(517\) −15.9345 −0.700798
\(518\) 3.54246i 0.155647i
\(519\) 3.41392 0.448279i 0.149854 0.0196772i
\(520\) −2.45100 −0.107483
\(521\) −17.8472 −0.781899 −0.390949 0.920412i \(-0.627853\pi\)
−0.390949 + 0.920412i \(0.627853\pi\)
\(522\) 9.95456 2.66012i 0.435699 0.116430i
\(523\) 14.2222i 0.621895i 0.950427 + 0.310947i \(0.100646\pi\)
−0.950427 + 0.310947i \(0.899354\pi\)
\(524\) 20.1005i 0.878092i
\(525\) 1.08532 0.142513i 0.0473673 0.00621976i
\(526\) 25.9044i 1.12949i
\(527\) −23.3110 −1.01544
\(528\) −0.450997 3.43462i −0.0196271 0.149473i
\(529\) 22.3391 0.971264
\(530\) 6.53262i 0.283759i
\(531\) −6.06318 + 1.62024i −0.263120 + 0.0703124i
\(532\) 1.53865 2.28503i 0.0667090 0.0990684i
\(533\) 1.96724i 0.0852107i
\(534\) −10.1895 + 1.33797i −0.440941 + 0.0578997i
\(535\) 5.63063i 0.243433i
\(536\) 14.9462i 0.645577i
\(537\) 19.7385 2.59184i 0.851778 0.111846i
\(538\) 25.3317 1.09213
\(539\) 13.2012i 0.568615i
\(540\) −1.98362 4.80263i −0.0853615 0.206672i
\(541\) −37.2164 −1.60006 −0.800030 0.599960i \(-0.795183\pi\)
−0.800030 + 0.599960i \(0.795183\pi\)
\(542\) 17.5799 0.755121
\(543\) 4.09665 + 31.1985i 0.175804 + 1.33885i
\(544\) 3.25363i 0.139498i
\(545\) −8.71362 −0.373250
\(546\) 0.349298 + 2.66012i 0.0149486 + 0.113842i
\(547\) 16.3789i 0.700313i −0.936691 0.350156i \(-0.886128\pi\)
0.936691 0.350156i \(-0.113872\pi\)
\(548\) 8.28883i 0.354081i
\(549\) −7.83487 + 2.09368i −0.334384 + 0.0893562i
\(550\) 2.00000i 0.0852803i
\(551\) −8.36198 + 12.4182i −0.356232 + 0.529035i
\(552\) −0.183326 1.39614i −0.00780287 0.0594236i
\(553\) 2.79882i 0.119018i
\(554\) 21.6271 0.918845
\(555\) 9.62596 1.26398i 0.408599 0.0536529i
\(556\) −0.196012 −0.00831274
\(557\) 36.8244i 1.56030i 0.625592 + 0.780150i \(0.284858\pi\)
−0.625592 + 0.780150i \(0.715142\pi\)
\(558\) 5.54900 + 20.7652i 0.234908 + 0.879061i
\(559\) 29.3317i 1.24060i
\(560\) 0.631989i 0.0267064i
\(561\) 11.1750 1.46738i 0.471807 0.0619527i
\(562\) 21.6598 0.913664
\(563\) −40.0022 −1.68589 −0.842945 0.537999i \(-0.819180\pi\)
−0.842945 + 0.537999i \(0.819180\pi\)
\(564\) −1.79660 13.6822i −0.0756506 0.576125i
\(565\) 0.705983i 0.0297009i
\(566\) −15.2132 −0.639460
\(567\) −4.92970 + 2.83730i −0.207028 + 0.119155i
\(568\) 6.16597 0.258718
\(569\) −21.6953 −0.909514 −0.454757 0.890616i \(-0.650274\pi\)
−0.454757 + 0.890616i \(0.650274\pi\)
\(570\) 6.75812 + 3.36568i 0.283067 + 0.140973i
\(571\) 3.37377 0.141188 0.0705940 0.997505i \(-0.477511\pi\)
0.0705940 + 0.997505i \(0.477511\pi\)
\(572\) −4.90199 −0.204963
\(573\) −0.631605 4.81005i −0.0263857 0.200943i
\(574\) 0.507253 0.0211723
\(575\) 0.812981i 0.0339036i
\(576\) 2.89830 0.774501i 0.120763 0.0322709i
\(577\) −31.3740 −1.30612 −0.653058 0.757308i \(-0.726514\pi\)
−0.653058 + 0.757308i \(0.726514\pi\)
\(578\) 6.41392 0.266784
\(579\) −3.59787 27.4000i −0.149522 1.13870i
\(580\) 3.43462i 0.142615i
\(581\) 3.70843i 0.153852i
\(582\) 0.736022 + 5.60526i 0.0305091 + 0.232345i
\(583\) 13.0652i 0.541107i
\(584\) −4.89461 −0.202540
\(585\) −7.10373 + 1.89830i −0.293703 + 0.0784851i
\(586\) −5.38980 −0.222651
\(587\) 39.0718i 1.61266i 0.591463 + 0.806332i \(0.298551\pi\)
−0.591463 + 0.806332i \(0.701449\pi\)
\(588\) −11.3353 + 1.48842i −0.467458 + 0.0613816i
\(589\) −25.9044 17.4431i −1.06737 0.718730i
\(590\) 2.09198i 0.0861254i
\(591\) −4.29241 32.6893i −0.176566 1.34466i
\(592\) 5.60526i 0.230375i
\(593\) 26.6367i 1.09384i 0.837186 + 0.546918i \(0.184199\pi\)
−0.837186 + 0.546918i \(0.815801\pi\)
\(594\) −3.96724 9.60526i −0.162778 0.394109i
\(595\) −2.05626 −0.0842983
\(596\) 11.4092i 0.467341i
\(597\) −26.3935 + 3.46571i −1.08021 + 0.141842i
\(598\) −1.99261 −0.0814840
\(599\) 0.952736 0.0389278 0.0194639 0.999811i \(-0.493804\pi\)
0.0194639 + 0.999811i \(0.493804\pi\)
\(600\) −1.71731 + 0.225499i −0.0701088 + 0.00920594i
\(601\) 14.6050i 0.595750i −0.954605 0.297875i \(-0.903722\pi\)
0.954605 0.297875i \(-0.0962779\pi\)
\(602\) 7.56316 0.308252
\(603\) 11.5758 + 43.3186i 0.471405 + 1.76407i
\(604\) 10.2119i 0.415515i
\(605\) 7.00000i 0.284590i
\(606\) 1.68222 + 12.8111i 0.0683354 + 0.520416i
\(607\) 11.5304i 0.468005i 0.972236 + 0.234002i \(0.0751823\pi\)
−0.972236 + 0.234002i \(0.924818\pi\)
\(608\) −2.43462 + 3.61561i −0.0987368 + 0.146632i
\(609\) −3.72766 + 0.489476i −0.151052 + 0.0198346i
\(610\) 2.70326i 0.109452i
\(611\) −19.5277 −0.790006
\(612\) 2.51994 + 9.42999i 0.101862 + 0.381185i
\(613\) −25.1996 −1.01780 −0.508900 0.860826i \(-0.669948\pi\)
−0.508900 + 0.860826i \(0.669948\pi\)
\(614\) 0.570050i 0.0230054i
\(615\) 0.180992 + 1.37836i 0.00729829 + 0.0555809i
\(616\) 1.26398i 0.0509271i
\(617\) 18.3724i 0.739645i −0.929102 0.369823i \(-0.879418\pi\)
0.929102 0.369823i \(-0.120582\pi\)
\(618\) −4.04420 30.7991i −0.162682 1.23892i
\(619\) −16.4952 −0.662998 −0.331499 0.943456i \(-0.607554\pi\)
−0.331499 + 0.943456i \(0.607554\pi\)
\(620\) 7.16461 0.287738
\(621\) −1.61265 3.90444i −0.0647132 0.156680i
\(622\) 8.38548i 0.336227i
\(623\) 3.74984 0.150234
\(624\) −0.552696 4.20912i −0.0221256 0.168500i
\(625\) 1.00000 0.0400000
\(626\) 24.6358 0.984645
\(627\) 13.5162 + 6.73135i 0.539787 + 0.268824i
\(628\) 14.0338 0.560012
\(629\) −18.2374 −0.727173
\(630\) 0.489476 + 1.83169i 0.0195012 + 0.0729764i
\(631\) −11.0532 −0.440021 −0.220010 0.975498i \(-0.570609\pi\)
−0.220010 + 0.975498i \(0.570609\pi\)
\(632\) 4.42859i 0.176160i
\(633\) 0.482512 + 3.67462i 0.0191781 + 0.146053i
\(634\) 17.0071 0.675439
\(635\) 4.86924 0.193230
\(636\) 11.2185 1.47310i 0.444844 0.0584121i
\(637\) 16.1780i 0.640997i
\(638\) 6.86924i 0.271956i
\(639\) 17.8708 4.77555i 0.706960 0.188918i
\(640\) 1.00000i 0.0395285i
\(641\) 33.7368 1.33253 0.666263 0.745717i \(-0.267893\pi\)
0.666263 + 0.745717i \(0.267893\pi\)
\(642\) −9.66953 + 1.26970i −0.381626 + 0.0501110i
\(643\) −28.9369 −1.14116 −0.570581 0.821242i \(-0.693282\pi\)
−0.570581 + 0.821242i \(0.693282\pi\)
\(644\) 0.513795i 0.0202463i
\(645\) 2.69860 + 20.5515i 0.106257 + 0.809213i
\(646\) −11.7638 7.92134i −0.462842 0.311661i
\(647\) 35.3409i 1.38940i −0.719302 0.694698i \(-0.755538\pi\)
0.719302 0.694698i \(-0.244462\pi\)
\(648\) 7.80030 4.48948i 0.306425 0.176363i
\(649\) 4.18396i 0.164235i
\(650\) 2.45100i 0.0961360i
\(651\) −1.02105 7.77590i −0.0400180 0.304762i
\(652\) −19.3765 −0.758842
\(653\) 5.41518i 0.211912i −0.994371 0.105956i \(-0.966210\pi\)
0.994371 0.105956i \(-0.0337903\pi\)
\(654\) −1.96491 14.9640i −0.0768340 0.585138i
\(655\) 20.1005 0.785390
\(656\) −0.802629 −0.0313374
\(657\) −14.1860 + 3.79088i −0.553450 + 0.147896i
\(658\) 5.03521i 0.196293i
\(659\) 23.8546 0.929242 0.464621 0.885510i \(-0.346191\pi\)
0.464621 + 0.885510i \(0.346191\pi\)
\(660\) −3.43462 + 0.450997i −0.133692 + 0.0175550i
\(661\) 14.3396i 0.557745i 0.960328 + 0.278872i \(0.0899607\pi\)
−0.960328 + 0.278872i \(0.910039\pi\)
\(662\) 9.74773i 0.378856i
\(663\) 13.6949 1.79827i 0.531866 0.0698389i
\(664\) 5.86788i 0.227718i
\(665\) −2.28503 1.53865i −0.0886095 0.0596663i
\(666\) 4.34128 + 16.2457i 0.168221 + 0.629509i
\(667\) 2.79228i 0.108117i
\(668\) −9.23122 −0.357167
\(669\) −4.03743 30.7475i −0.156096 1.18877i
\(670\) 14.9462 0.577422
\(671\) 5.40653i 0.208717i
\(672\) −1.08532 + 0.142513i −0.0418671 + 0.00549754i
\(673\) 49.3290i 1.90149i 0.309972 + 0.950746i \(0.399680\pi\)
−0.309972 + 0.950746i \(0.600320\pi\)
\(674\) 23.7505i 0.914836i
\(675\) −4.80263 + 1.98362i −0.184853 + 0.0763496i
\(676\) 6.99261 0.268947
\(677\) −23.1431 −0.889460 −0.444730 0.895665i \(-0.646700\pi\)
−0.444730 + 0.895665i \(0.646700\pi\)
\(678\) −1.21239 + 0.159198i −0.0465616 + 0.00611397i
\(679\) 2.06280i 0.0791629i
\(680\) 3.25363 0.124771
\(681\) −6.82567 + 0.896273i −0.261560 + 0.0343453i
\(682\) 14.3292 0.548694
\(683\) 20.2905 0.776396 0.388198 0.921576i \(-0.373098\pi\)
0.388198 + 0.921576i \(0.373098\pi\)
\(684\) −4.25596 + 12.3647i −0.162731 + 0.472778i
\(685\) −8.28883 −0.316700
\(686\) 8.59542 0.328175
\(687\) 23.3437 3.06525i 0.890619 0.116946i
\(688\) −11.9672 −0.456247
\(689\) 16.0114i 0.609987i
\(690\) −1.39614 + 0.183326i −0.0531501 + 0.00697910i
\(691\) −18.5280 −0.704837 −0.352418 0.935843i \(-0.614641\pi\)
−0.352418 + 0.935843i \(0.614641\pi\)
\(692\) 1.98794 0.0755703
\(693\) 0.978953 + 3.66339i 0.0371873 + 0.139161i
\(694\) 22.9031i 0.869389i
\(695\) 0.196012i 0.00743514i
\(696\) 5.89830 0.774501i 0.223575 0.0293574i
\(697\) 2.61146i 0.0989159i
\(698\) 11.1985 0.423868
\(699\) −4.78786 36.4624i −0.181093 1.37914i
\(700\) 0.631989 0.0238869
\(701\) 3.42130i 0.129221i 0.997911 + 0.0646104i \(0.0205805\pi\)
−0.997911 + 0.0646104i \(0.979420\pi\)
\(702\) −4.86185 11.7712i −0.183499 0.444276i
\(703\) −20.2664 13.6467i −0.764363 0.514694i
\(704\) 2.00000i 0.0753778i
\(705\) −13.6822 + 1.79660i −0.515302 + 0.0676639i
\(706\) 1.64837i 0.0620371i
\(707\) 4.71463i 0.177312i
\(708\) −3.59257 + 0.471738i −0.135017 + 0.0177290i
\(709\) 15.1329 0.568330 0.284165 0.958775i \(-0.408284\pi\)
0.284165 + 0.958775i \(0.408284\pi\)
\(710\) 6.16597i 0.231405i
\(711\) −3.42995 12.8354i −0.128633 0.481365i
\(712\) −5.93339 −0.222363
\(713\) 5.82469 0.218136
\(714\) −0.463683 3.53123i −0.0173529 0.132153i
\(715\) 4.90199i 0.183324i
\(716\) 11.4938 0.429545
\(717\) 5.02635 + 38.2787i 0.187712 + 1.42954i
\(718\) 32.3079i 1.20572i
\(719\) 4.37343i 0.163101i 0.996669 + 0.0815506i \(0.0259872\pi\)
−0.996669 + 0.0815506i \(0.974013\pi\)
\(720\) −0.774501 2.89830i −0.0288640 0.108013i
\(721\) 11.3344i 0.422115i
\(722\) −7.14527 17.6053i −0.265919 0.655200i
\(723\) −0.946808 7.21052i −0.0352122 0.268162i
\(724\) 18.1671i 0.675174i
\(725\) −3.43462 −0.127559
\(726\) 12.0212 1.57849i 0.446147 0.0585833i
\(727\) 26.6517 0.988455 0.494228 0.869332i \(-0.335451\pi\)
0.494228 + 0.869332i \(0.335451\pi\)
\(728\) 1.54900i 0.0574099i
\(729\) 19.1305 19.0532i 0.708537 0.705674i
\(730\) 4.89461i 0.181158i
\(731\) 38.9369i 1.44013i
\(732\) −4.64234 + 0.609582i −0.171586 + 0.0225308i
\(733\) 14.1501 0.522646 0.261323 0.965251i \(-0.415841\pi\)
0.261323 + 0.965251i \(0.415841\pi\)
\(734\) −4.78465 −0.176604
\(735\) 1.48842 + 11.3353i 0.0549013 + 0.418107i
\(736\) 0.812981i 0.0299669i
\(737\) 29.8924 1.10110
\(738\) −2.32626 + 0.621638i −0.0856309 + 0.0228828i
\(739\) −47.9721 −1.76468 −0.882342 0.470609i \(-0.844034\pi\)
−0.882342 + 0.470609i \(0.844034\pi\)
\(740\) 5.60526 0.206053
\(741\) 16.5641 + 8.24926i 0.608499 + 0.303044i
\(742\) −4.12855 −0.151564
\(743\) 43.3765 1.59133 0.795665 0.605738i \(-0.207122\pi\)
0.795665 + 0.605738i \(0.207122\pi\)
\(744\) 1.61561 + 12.3039i 0.0592311 + 0.451081i
\(745\) −11.4092 −0.418002
\(746\) 3.21978i 0.117884i
\(747\) −4.54468 17.0069i −0.166281 0.622249i
\(748\) 6.50725 0.237929
\(749\) 3.55850 0.130025
\(750\) 0.225499 + 1.71731i 0.00823404 + 0.0627073i
\(751\) 3.58278i 0.130737i −0.997861 0.0653687i \(-0.979178\pi\)
0.997861 0.0653687i \(-0.0208223\pi\)
\(752\) 7.96724i 0.290535i
\(753\) −4.20279 32.0068i −0.153158 1.16639i
\(754\) 8.41824i 0.306574i
\(755\) 10.2119 0.371648
\(756\) −3.03521 + 1.25363i −0.110389 + 0.0455940i
\(757\) −16.5618 −0.601949 −0.300975 0.953632i \(-0.597312\pi\)
−0.300975 + 0.953632i \(0.597312\pi\)
\(758\) 23.0887i 0.838621i
\(759\) −2.79228 + 0.366652i −0.101353 + 0.0133086i
\(760\) 3.61561 + 2.43462i 0.131152 + 0.0883129i
\(761\) 34.6726i 1.25688i 0.777858 + 0.628441i \(0.216306\pi\)
−0.777858 + 0.628441i \(0.783694\pi\)
\(762\) 1.09801 + 8.36198i 0.0397766 + 0.302923i
\(763\) 5.50691i 0.199363i
\(764\) 2.80093i 0.101334i
\(765\) 9.42999 2.51994i 0.340942 0.0911086i
\(766\) −28.8124 −1.04103
\(767\) 5.12743i 0.185141i
\(768\) 1.71731 0.225499i 0.0619681 0.00813698i
\(769\) −20.4698 −0.738161 −0.369080 0.929397i \(-0.620327\pi\)
−0.369080 + 0.929397i \(0.620327\pi\)
\(770\) 1.26398 0.0455506
\(771\) −9.68222 + 1.27136i −0.348697 + 0.0457871i
\(772\) 15.9552i 0.574240i
\(773\) 27.5738 0.991759 0.495880 0.868391i \(-0.334846\pi\)
0.495880 + 0.868391i \(0.334846\pi\)
\(774\) −34.6847 + 9.26865i −1.24671 + 0.333155i
\(775\) 7.16461i 0.257360i
\(776\) 3.26398i 0.117170i
\(777\) −0.798820 6.08350i −0.0286575 0.218244i
\(778\) 13.5545i 0.485953i
\(779\) 1.95410 2.90199i 0.0700127 0.103975i
\(780\) −4.20912 + 0.552696i −0.150711 + 0.0197897i
\(781\) 12.3319i 0.441272i
\(782\) 2.64514 0.0945898
\(783\) 16.4952 6.81298i 0.589490 0.243476i
\(784\) −6.60059