Properties

Label 84.2.b.a.55.4
Level $84$
Weight $2$
Character 84.55
Analytic conductor $0.671$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 84.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.670743376979\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: 4.0.2312.1
Defining polynomial: \(x^{4} - x^{3} - 2 x + 4\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.4
Root \(-0.780776 - 1.17915i\) of defining polynomial
Character \(\chi\) \(=\) 84.55
Dual form 84.2.b.a.55.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.780776 + 1.17915i) q^{2} -1.00000 q^{3} +(-0.780776 + 1.84130i) q^{4} +1.69614i q^{5} +(-0.780776 - 1.17915i) q^{6} +(2.56155 - 0.662153i) q^{7} +(-2.78078 + 0.516994i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(0.780776 + 1.17915i) q^{2} -1.00000 q^{3} +(-0.780776 + 1.84130i) q^{4} +1.69614i q^{5} +(-0.780776 - 1.17915i) q^{6} +(2.56155 - 0.662153i) q^{7} +(-2.78078 + 0.516994i) q^{8} +1.00000 q^{9} +(-2.00000 + 1.32431i) q^{10} -3.02045i q^{11} +(0.780776 - 1.84130i) q^{12} -6.04090i q^{13} +(2.78078 + 2.50345i) q^{14} -1.69614i q^{15} +(-2.78078 - 2.87529i) q^{16} +4.34475i q^{17} +(0.780776 + 1.17915i) q^{18} -1.12311 q^{19} +(-3.12311 - 1.32431i) q^{20} +(-2.56155 + 0.662153i) q^{21} +(3.56155 - 2.35829i) q^{22} +3.02045i q^{23} +(2.78078 - 0.516994i) q^{24} +2.12311 q^{25} +(7.12311 - 4.71659i) q^{26} -1.00000 q^{27} +(-0.780776 + 5.23358i) q^{28} -2.00000 q^{29} +(2.00000 - 1.32431i) q^{30} +(1.21922 - 5.52390i) q^{32} +3.02045i q^{33} +(-5.12311 + 3.39228i) q^{34} +(1.12311 + 4.34475i) q^{35} +(-0.780776 + 1.84130i) q^{36} -7.12311 q^{37} +(-0.876894 - 1.32431i) q^{38} +6.04090i q^{39} +(-0.876894 - 4.71659i) q^{40} -7.73704i q^{41} +(-2.78078 - 2.50345i) q^{42} +8.10887i q^{43} +(5.56155 + 2.35829i) q^{44} +1.69614i q^{45} +(-3.56155 + 2.35829i) q^{46} -10.2462 q^{47} +(2.78078 + 2.87529i) q^{48} +(6.12311 - 3.39228i) q^{49} +(1.65767 + 2.50345i) q^{50} -4.34475i q^{51} +(11.1231 + 4.71659i) q^{52} -4.24621 q^{53} +(-0.780776 - 1.17915i) q^{54} +5.12311 q^{55} +(-6.78078 + 3.16561i) q^{56} +1.12311 q^{57} +(-1.56155 - 2.35829i) q^{58} +4.00000 q^{59} +(3.12311 + 1.32431i) q^{60} +9.43318i q^{61} +(2.56155 - 0.662153i) q^{63} +(7.46543 - 2.87529i) q^{64} +10.2462 q^{65} +(-3.56155 + 2.35829i) q^{66} -2.06798i q^{67} +(-8.00000 - 3.39228i) q^{68} -3.02045i q^{69} +(-4.24621 + 4.71659i) q^{70} -12.4536i q^{71} +(-2.78078 + 0.516994i) q^{72} +3.39228i q^{73} +(-5.56155 - 8.39919i) q^{74} -2.12311 q^{75} +(0.876894 - 2.06798i) q^{76} +(-2.00000 - 7.73704i) q^{77} +(-7.12311 + 4.71659i) q^{78} -4.71659i q^{79} +(4.87689 - 4.71659i) q^{80} +1.00000 q^{81} +(9.12311 - 6.04090i) q^{82} +6.24621 q^{83} +(0.780776 - 5.23358i) q^{84} -7.36932 q^{85} +(-9.56155 + 6.33122i) q^{86} +2.00000 q^{87} +(1.56155 + 8.39919i) q^{88} +7.73704i q^{89} +(-2.00000 + 1.32431i) q^{90} +(-4.00000 - 15.4741i) q^{91} +(-5.56155 - 2.35829i) q^{92} +(-8.00000 - 12.0818i) q^{94} -1.90495i q^{95} +(-1.21922 + 5.52390i) q^{96} +8.68951i q^{97} +(8.78078 + 4.57143i) q^{98} -3.02045i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - q^{2} - 4q^{3} + q^{4} + q^{6} + 2q^{7} - 7q^{8} + 4q^{9} + O(q^{10}) \) \( 4q - q^{2} - 4q^{3} + q^{4} + q^{6} + 2q^{7} - 7q^{8} + 4q^{9} - 8q^{10} - q^{12} + 7q^{14} - 7q^{16} - q^{18} + 12q^{19} + 4q^{20} - 2q^{21} + 6q^{22} + 7q^{24} - 8q^{25} + 12q^{26} - 4q^{27} + q^{28} - 8q^{29} + 8q^{30} + 9q^{32} - 4q^{34} - 12q^{35} + q^{36} - 12q^{37} - 20q^{38} - 20q^{40} - 7q^{42} + 14q^{44} - 6q^{46} - 8q^{47} + 7q^{48} + 8q^{49} + 19q^{50} + 28q^{52} + 16q^{53} + q^{54} + 4q^{55} - 23q^{56} - 12q^{57} + 2q^{58} + 16q^{59} - 4q^{60} + 2q^{63} + q^{64} + 8q^{65} - 6q^{66} - 32q^{68} + 16q^{70} - 7q^{72} - 14q^{74} + 8q^{75} + 20q^{76} - 8q^{77} - 12q^{78} + 36q^{80} + 4q^{81} + 20q^{82} - 8q^{83} - q^{84} + 20q^{85} - 30q^{86} + 8q^{87} - 2q^{88} - 8q^{90} - 16q^{91} - 14q^{92} - 32q^{94} - 9q^{96} + 31q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.780776 + 1.17915i 0.552092 + 0.833783i
\(3\) −1.00000 −0.577350
\(4\) −0.780776 + 1.84130i −0.390388 + 0.920650i
\(5\) 1.69614i 0.758537i 0.925287 + 0.379269i \(0.123824\pi\)
−0.925287 + 0.379269i \(0.876176\pi\)
\(6\) −0.780776 1.17915i −0.318751 0.481385i
\(7\) 2.56155 0.662153i 0.968176 0.250270i
\(8\) −2.78078 + 0.516994i −0.983153 + 0.182785i
\(9\) 1.00000 0.333333
\(10\) −2.00000 + 1.32431i −0.632456 + 0.418783i
\(11\) 3.02045i 0.910699i −0.890313 0.455350i \(-0.849514\pi\)
0.890313 0.455350i \(-0.150486\pi\)
\(12\) 0.780776 1.84130i 0.225391 0.531538i
\(13\) 6.04090i 1.67544i −0.546098 0.837722i \(-0.683887\pi\)
0.546098 0.837722i \(-0.316113\pi\)
\(14\) 2.78078 + 2.50345i 0.743194 + 0.669076i
\(15\) 1.69614i 0.437942i
\(16\) −2.78078 2.87529i −0.695194 0.718822i
\(17\) 4.34475i 1.05376i 0.849940 + 0.526879i \(0.176638\pi\)
−0.849940 + 0.526879i \(0.823362\pi\)
\(18\) 0.780776 + 1.17915i 0.184031 + 0.277928i
\(19\) −1.12311 −0.257658 −0.128829 0.991667i \(-0.541122\pi\)
−0.128829 + 0.991667i \(0.541122\pi\)
\(20\) −3.12311 1.32431i −0.698348 0.296124i
\(21\) −2.56155 + 0.662153i −0.558977 + 0.144494i
\(22\) 3.56155 2.35829i 0.759326 0.502790i
\(23\) 3.02045i 0.629807i 0.949124 + 0.314903i \(0.101972\pi\)
−0.949124 + 0.314903i \(0.898028\pi\)
\(24\) 2.78078 0.516994i 0.567624 0.105531i
\(25\) 2.12311 0.424621
\(26\) 7.12311 4.71659i 1.39696 0.924999i
\(27\) −1.00000 −0.192450
\(28\) −0.780776 + 5.23358i −0.147553 + 0.989054i
\(29\) −2.00000 −0.371391 −0.185695 0.982607i \(-0.559454\pi\)
−0.185695 + 0.982607i \(0.559454\pi\)
\(30\) 2.00000 1.32431i 0.365148 0.241784i
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) 1.21922 5.52390i 0.215530 0.976497i
\(33\) 3.02045i 0.525792i
\(34\) −5.12311 + 3.39228i −0.878605 + 0.581772i
\(35\) 1.12311 + 4.34475i 0.189839 + 0.734398i
\(36\) −0.780776 + 1.84130i −0.130129 + 0.306883i
\(37\) −7.12311 −1.17103 −0.585516 0.810661i \(-0.699108\pi\)
−0.585516 + 0.810661i \(0.699108\pi\)
\(38\) −0.876894 1.32431i −0.142251 0.214831i
\(39\) 6.04090i 0.967317i
\(40\) −0.876894 4.71659i −0.138649 0.745758i
\(41\) 7.73704i 1.20832i −0.796862 0.604161i \(-0.793508\pi\)
0.796862 0.604161i \(-0.206492\pi\)
\(42\) −2.78078 2.50345i −0.429083 0.386291i
\(43\) 8.10887i 1.23659i 0.785946 + 0.618296i \(0.212177\pi\)
−0.785946 + 0.618296i \(0.787823\pi\)
\(44\) 5.56155 + 2.35829i 0.838436 + 0.355526i
\(45\) 1.69614i 0.252846i
\(46\) −3.56155 + 2.35829i −0.525122 + 0.347712i
\(47\) −10.2462 −1.49456 −0.747282 0.664507i \(-0.768641\pi\)
−0.747282 + 0.664507i \(0.768641\pi\)
\(48\) 2.78078 + 2.87529i 0.401371 + 0.415012i
\(49\) 6.12311 3.39228i 0.874729 0.484612i
\(50\) 1.65767 + 2.50345i 0.234430 + 0.354042i
\(51\) 4.34475i 0.608387i
\(52\) 11.1231 + 4.71659i 1.54250 + 0.654073i
\(53\) −4.24621 −0.583262 −0.291631 0.956531i \(-0.594198\pi\)
−0.291631 + 0.956531i \(0.594198\pi\)
\(54\) −0.780776 1.17915i −0.106250 0.160462i
\(55\) 5.12311 0.690799
\(56\) −6.78078 + 3.16561i −0.906119 + 0.423022i
\(57\) 1.12311 0.148759
\(58\) −1.56155 2.35829i −0.205042 0.309659i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 3.12311 + 1.32431i 0.403191 + 0.170967i
\(61\) 9.43318i 1.20779i 0.797062 + 0.603897i \(0.206386\pi\)
−0.797062 + 0.603897i \(0.793614\pi\)
\(62\) 0 0
\(63\) 2.56155 0.662153i 0.322725 0.0834235i
\(64\) 7.46543 2.87529i 0.933179 0.359411i
\(65\) 10.2462 1.27089
\(66\) −3.56155 + 2.35829i −0.438397 + 0.290286i
\(67\) 2.06798i 0.252643i −0.991989 0.126322i \(-0.959683\pi\)
0.991989 0.126322i \(-0.0403172\pi\)
\(68\) −8.00000 3.39228i −0.970143 0.411375i
\(69\) 3.02045i 0.363619i
\(70\) −4.24621 + 4.71659i −0.507519 + 0.563740i
\(71\) 12.4536i 1.47797i −0.673720 0.738987i \(-0.735305\pi\)
0.673720 0.738987i \(-0.264695\pi\)
\(72\) −2.78078 + 0.516994i −0.327718 + 0.0609283i
\(73\) 3.39228i 0.397037i 0.980097 + 0.198518i \(0.0636129\pi\)
−0.980097 + 0.198518i \(0.936387\pi\)
\(74\) −5.56155 8.39919i −0.646517 0.976386i
\(75\) −2.12311 −0.245155
\(76\) 0.876894 2.06798i 0.100587 0.237213i
\(77\) −2.00000 7.73704i −0.227921 0.881717i
\(78\) −7.12311 + 4.71659i −0.806533 + 0.534049i
\(79\) 4.71659i 0.530658i −0.964158 0.265329i \(-0.914519\pi\)
0.964158 0.265329i \(-0.0854805\pi\)
\(80\) 4.87689 4.71659i 0.545253 0.527331i
\(81\) 1.00000 0.111111
\(82\) 9.12311 6.04090i 1.00748 0.667105i
\(83\) 6.24621 0.685611 0.342805 0.939406i \(-0.388623\pi\)
0.342805 + 0.939406i \(0.388623\pi\)
\(84\) 0.780776 5.23358i 0.0851897 0.571031i
\(85\) −7.36932 −0.799315
\(86\) −9.56155 + 6.33122i −1.03105 + 0.682712i
\(87\) 2.00000 0.214423
\(88\) 1.56155 + 8.39919i 0.166462 + 0.895357i
\(89\) 7.73704i 0.820124i 0.912058 + 0.410062i \(0.134493\pi\)
−0.912058 + 0.410062i \(0.865507\pi\)
\(90\) −2.00000 + 1.32431i −0.210819 + 0.139594i
\(91\) −4.00000 15.4741i −0.419314 1.62212i
\(92\) −5.56155 2.35829i −0.579832 0.245869i
\(93\) 0 0
\(94\) −8.00000 12.0818i −0.825137 1.24614i
\(95\) 1.90495i 0.195443i
\(96\) −1.21922 + 5.52390i −0.124436 + 0.563781i
\(97\) 8.68951i 0.882286i 0.897437 + 0.441143i \(0.145427\pi\)
−0.897437 + 0.441143i \(0.854573\pi\)
\(98\) 8.78078 + 4.57143i 0.886992 + 0.461784i
\(99\) 3.02045i 0.303566i
\(100\) −1.65767 + 3.90928i −0.165767 + 0.390928i
\(101\) 6.99337i 0.695866i −0.937519 0.347933i \(-0.886884\pi\)
0.937519 0.347933i \(-0.113116\pi\)
\(102\) 5.12311 3.39228i 0.507263 0.335886i
\(103\) −8.00000 −0.788263 −0.394132 0.919054i \(-0.628955\pi\)
−0.394132 + 0.919054i \(0.628955\pi\)
\(104\) 3.12311 + 16.7984i 0.306246 + 1.64722i
\(105\) −1.12311 4.34475i −0.109604 0.424005i
\(106\) −3.31534 5.00691i −0.322014 0.486314i
\(107\) 5.66906i 0.548049i 0.961723 + 0.274024i \(0.0883549\pi\)
−0.961723 + 0.274024i \(0.911645\pi\)
\(108\) 0.780776 1.84130i 0.0751302 0.177179i
\(109\) 8.24621 0.789844 0.394922 0.918715i \(-0.370772\pi\)
0.394922 + 0.918715i \(0.370772\pi\)
\(110\) 4.00000 + 6.04090i 0.381385 + 0.575977i
\(111\) 7.12311 0.676095
\(112\) −9.02699 5.52390i −0.852970 0.521960i
\(113\) 12.2462 1.15203 0.576013 0.817440i \(-0.304608\pi\)
0.576013 + 0.817440i \(0.304608\pi\)
\(114\) 0.876894 + 1.32431i 0.0821287 + 0.124033i
\(115\) −5.12311 −0.477732
\(116\) 1.56155 3.68260i 0.144987 0.341921i
\(117\) 6.04090i 0.558481i
\(118\) 3.12311 + 4.71659i 0.287505 + 0.434197i
\(119\) 2.87689 + 11.1293i 0.263724 + 1.02022i
\(120\) 0.876894 + 4.71659i 0.0800491 + 0.430564i
\(121\) 1.87689 0.170627
\(122\) −11.1231 + 7.36520i −1.00704 + 0.666814i
\(123\) 7.73704i 0.697625i
\(124\) 0 0
\(125\) 12.0818i 1.08063i
\(126\) 2.78078 + 2.50345i 0.247731 + 0.223025i
\(127\) 19.4470i 1.72564i 0.505510 + 0.862821i \(0.331304\pi\)
−0.505510 + 0.862821i \(0.668696\pi\)
\(128\) 9.21922 + 6.55789i 0.814872 + 0.579641i
\(129\) 8.10887i 0.713946i
\(130\) 8.00000 + 12.0818i 0.701646 + 1.05964i
\(131\) 22.2462 1.94366 0.971830 0.235682i \(-0.0757323\pi\)
0.971830 + 0.235682i \(0.0757323\pi\)
\(132\) −5.56155 2.35829i −0.484071 0.205263i
\(133\) −2.87689 + 0.743668i −0.249458 + 0.0644842i
\(134\) 2.43845 1.61463i 0.210650 0.139482i
\(135\) 1.69614i 0.145981i
\(136\) −2.24621 12.0818i −0.192611 1.03601i
\(137\) −16.2462 −1.38801 −0.694004 0.719971i \(-0.744155\pi\)
−0.694004 + 0.719971i \(0.744155\pi\)
\(138\) 3.56155 2.35829i 0.303180 0.200751i
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) −8.87689 1.32431i −0.750235 0.111924i
\(141\) 10.2462 0.862887
\(142\) 14.6847 9.72350i 1.23231 0.815978i
\(143\) −18.2462 −1.52582
\(144\) −2.78078 2.87529i −0.231731 0.239607i
\(145\) 3.39228i 0.281714i
\(146\) −4.00000 + 2.64861i −0.331042 + 0.219201i
\(147\) −6.12311 + 3.39228i −0.505025 + 0.279791i
\(148\) 5.56155 13.1158i 0.457157 1.07811i
\(149\) −10.0000 −0.819232 −0.409616 0.912258i \(-0.634337\pi\)
−0.409616 + 0.912258i \(0.634337\pi\)
\(150\) −1.65767 2.50345i −0.135348 0.204406i
\(151\) 8.10887i 0.659891i −0.944000 0.329945i \(-0.892970\pi\)
0.944000 0.329945i \(-0.107030\pi\)
\(152\) 3.12311 0.580639i 0.253317 0.0470960i
\(153\) 4.34475i 0.351253i
\(154\) 7.56155 8.39919i 0.609327 0.676826i
\(155\) 0 0
\(156\) −11.1231 4.71659i −0.890561 0.377629i
\(157\) 4.13595i 0.330085i −0.986286 0.165042i \(-0.947224\pi\)
0.986286 0.165042i \(-0.0527761\pi\)
\(158\) 5.56155 3.68260i 0.442453 0.292972i
\(159\) 4.24621 0.336746
\(160\) 9.36932 + 2.06798i 0.740710 + 0.163488i
\(161\) 2.00000 + 7.73704i 0.157622 + 0.609764i
\(162\) 0.780776 + 1.17915i 0.0613436 + 0.0926426i
\(163\) 11.5012i 0.900840i 0.892817 + 0.450420i \(0.148726\pi\)
−0.892817 + 0.450420i \(0.851274\pi\)
\(164\) 14.2462 + 6.04090i 1.11244 + 0.471715i
\(165\) −5.12311 −0.398833
\(166\) 4.87689 + 7.36520i 0.378520 + 0.571651i
\(167\) −2.24621 −0.173817 −0.0869085 0.996216i \(-0.527699\pi\)
−0.0869085 + 0.996216i \(0.527699\pi\)
\(168\) 6.78078 3.16561i 0.523148 0.244232i
\(169\) −23.4924 −1.80711
\(170\) −5.75379 8.68951i −0.441295 0.666455i
\(171\) −1.12311 −0.0858860
\(172\) −14.9309 6.33122i −1.13847 0.482751i
\(173\) 8.48071i 0.644776i −0.946608 0.322388i \(-0.895514\pi\)
0.946608 0.322388i \(-0.104486\pi\)
\(174\) 1.56155 + 2.35829i 0.118381 + 0.178782i
\(175\) 5.43845 1.40582i 0.411108 0.106270i
\(176\) −8.68466 + 8.39919i −0.654631 + 0.633113i
\(177\) −4.00000 −0.300658
\(178\) −9.12311 + 6.04090i −0.683806 + 0.452784i
\(179\) 2.27678i 0.170175i 0.996374 + 0.0850873i \(0.0271169\pi\)
−0.996374 + 0.0850873i \(0.972883\pi\)
\(180\) −3.12311 1.32431i −0.232783 0.0987080i
\(181\) 6.04090i 0.449016i 0.974472 + 0.224508i \(0.0720775\pi\)
−0.974472 + 0.224508i \(0.927922\pi\)
\(182\) 15.1231 16.7984i 1.12100 1.24518i
\(183\) 9.43318i 0.697321i
\(184\) −1.56155 8.39919i −0.115119 0.619197i
\(185\) 12.0818i 0.888271i
\(186\) 0 0
\(187\) 13.1231 0.959657
\(188\) 8.00000 18.8664i 0.583460 1.37597i
\(189\) −2.56155 + 0.662153i −0.186326 + 0.0481646i
\(190\) 2.24621 1.48734i 0.162957 0.107903i
\(191\) 9.06134i 0.655656i −0.944737 0.327828i \(-0.893683\pi\)
0.944737 0.327828i \(-0.106317\pi\)
\(192\) −7.46543 + 2.87529i −0.538771 + 0.207506i
\(193\) 9.36932 0.674418 0.337209 0.941430i \(-0.390517\pi\)
0.337209 + 0.941430i \(0.390517\pi\)
\(194\) −10.2462 + 6.78456i −0.735635 + 0.487103i
\(195\) −10.2462 −0.733746
\(196\) 1.46543 + 13.9231i 0.104674 + 0.994507i
\(197\) 0.246211 0.0175418 0.00877091 0.999962i \(-0.497208\pi\)
0.00877091 + 0.999962i \(0.497208\pi\)
\(198\) 3.56155 2.35829i 0.253109 0.167597i
\(199\) 5.12311 0.363167 0.181584 0.983375i \(-0.441878\pi\)
0.181584 + 0.983375i \(0.441878\pi\)
\(200\) −5.90388 + 1.09763i −0.417468 + 0.0776143i
\(201\) 2.06798i 0.145864i
\(202\) 8.24621 5.46026i 0.580201 0.384182i
\(203\) −5.12311 + 1.32431i −0.359572 + 0.0929481i
\(204\) 8.00000 + 3.39228i 0.560112 + 0.237507i
\(205\) 13.1231 0.916557
\(206\) −6.24621 9.43318i −0.435194 0.657241i
\(207\) 3.02045i 0.209936i
\(208\) −17.3693 + 16.7984i −1.20435 + 1.16476i
\(209\) 3.39228i 0.234649i
\(210\) 4.24621 4.71659i 0.293016 0.325476i
\(211\) 3.97292i 0.273507i −0.990605 0.136754i \(-0.956333\pi\)
0.990605 0.136754i \(-0.0436668\pi\)
\(212\) 3.31534 7.81855i 0.227699 0.536980i
\(213\) 12.4536i 0.853308i
\(214\) −6.68466 + 4.42627i −0.456954 + 0.302574i
\(215\) −13.7538 −0.938001
\(216\) 2.78078 0.516994i 0.189208 0.0351770i
\(217\) 0 0
\(218\) 6.43845 + 9.72350i 0.436067 + 0.658558i
\(219\) 3.39228i 0.229229i
\(220\) −4.00000 + 9.43318i −0.269680 + 0.635985i
\(221\) 26.2462 1.76551
\(222\) 5.56155 + 8.39919i 0.373267 + 0.563717i
\(223\) 18.8769 1.26409 0.632045 0.774932i \(-0.282216\pi\)
0.632045 + 0.774932i \(0.282216\pi\)
\(224\) −0.534565 14.9571i −0.0357171 0.999362i
\(225\) 2.12311 0.141540
\(226\) 9.56155 + 14.4401i 0.636025 + 0.960540i
\(227\) 16.4924 1.09464 0.547320 0.836923i \(-0.315648\pi\)
0.547320 + 0.836923i \(0.315648\pi\)
\(228\) −0.876894 + 2.06798i −0.0580737 + 0.136955i
\(229\) 18.1227i 1.19758i −0.800906 0.598790i \(-0.795648\pi\)
0.800906 0.598790i \(-0.204352\pi\)
\(230\) −4.00000 6.04090i −0.263752 0.398325i
\(231\) 2.00000 + 7.73704i 0.131590 + 0.509060i
\(232\) 5.56155 1.03399i 0.365134 0.0678846i
\(233\) −10.4924 −0.687381 −0.343691 0.939083i \(-0.611677\pi\)
−0.343691 + 0.939083i \(0.611677\pi\)
\(234\) 7.12311 4.71659i 0.465652 0.308333i
\(235\) 17.3790i 1.13368i
\(236\) −3.12311 + 7.36520i −0.203297 + 0.479434i
\(237\) 4.71659i 0.306375i
\(238\) −10.8769 + 12.0818i −0.705044 + 0.783146i
\(239\) 2.27678i 0.147273i −0.997285 0.0736363i \(-0.976540\pi\)
0.997285 0.0736363i \(-0.0234604\pi\)
\(240\) −4.87689 + 4.71659i −0.314802 + 0.304455i
\(241\) 1.90495i 0.122708i −0.998116 0.0613542i \(-0.980458\pi\)
0.998116 0.0613542i \(-0.0195419\pi\)
\(242\) 1.46543 + 2.21313i 0.0942017 + 0.142266i
\(243\) −1.00000 −0.0641500
\(244\) −17.3693 7.36520i −1.11196 0.471509i
\(245\) 5.75379 + 10.3857i 0.367596 + 0.663515i
\(246\) −9.12311 + 6.04090i −0.581668 + 0.385153i
\(247\) 6.78456i 0.431691i
\(248\) 0 0
\(249\) −6.24621 −0.395838
\(250\) −14.2462 + 9.43318i −0.901010 + 0.596607i
\(251\) −22.2462 −1.40417 −0.702084 0.712094i \(-0.747747\pi\)
−0.702084 + 0.712094i \(0.747747\pi\)
\(252\) −0.780776 + 5.23358i −0.0491843 + 0.329685i
\(253\) 9.12311 0.573565
\(254\) −22.9309 + 15.1838i −1.43881 + 0.952713i
\(255\) 7.36932 0.461485
\(256\) −0.534565 + 15.9911i −0.0334103 + 0.999442i
\(257\) 19.8188i 1.23626i −0.786074 0.618132i \(-0.787890\pi\)
0.786074 0.618132i \(-0.212110\pi\)
\(258\) 9.56155 6.33122i 0.595276 0.394164i
\(259\) −18.2462 + 4.71659i −1.13376 + 0.293075i
\(260\) −8.00000 + 18.8664i −0.496139 + 1.17004i
\(261\) −2.00000 −0.123797
\(262\) 17.3693 + 26.2316i 1.07308 + 1.62059i
\(263\) 4.92539i 0.303713i 0.988403 + 0.151856i \(0.0485251\pi\)
−0.988403 + 0.151856i \(0.951475\pi\)
\(264\) −1.56155 8.39919i −0.0961069 0.516934i
\(265\) 7.20217i 0.442426i
\(266\) −3.12311 2.81164i −0.191490 0.172393i
\(267\) 7.73704i 0.473499i
\(268\) 3.80776 + 1.61463i 0.232596 + 0.0986290i
\(269\) 22.4674i 1.36986i 0.728607 + 0.684932i \(0.240168\pi\)
−0.728607 + 0.684932i \(0.759832\pi\)
\(270\) 2.00000 1.32431i 0.121716 0.0805948i
\(271\) 4.49242 0.272895 0.136448 0.990647i \(-0.456431\pi\)
0.136448 + 0.990647i \(0.456431\pi\)
\(272\) 12.4924 12.0818i 0.757464 0.732566i
\(273\) 4.00000 + 15.4741i 0.242091 + 0.936534i
\(274\) −12.6847 19.1567i −0.766308 1.15730i
\(275\) 6.41273i 0.386702i
\(276\) 5.56155 + 2.35829i 0.334766 + 0.141953i
\(277\) 3.12311 0.187649 0.0938246 0.995589i \(-0.470091\pi\)
0.0938246 + 0.995589i \(0.470091\pi\)
\(278\) −9.36932 14.1498i −0.561934 0.848647i
\(279\) 0 0
\(280\) −5.36932 11.5012i −0.320878 0.687325i
\(281\) −0.246211 −0.0146877 −0.00734387 0.999973i \(-0.502338\pi\)
−0.00734387 + 0.999973i \(0.502338\pi\)
\(282\) 8.00000 + 12.0818i 0.476393 + 0.719460i
\(283\) 17.1231 1.01786 0.508931 0.860807i \(-0.330041\pi\)
0.508931 + 0.860807i \(0.330041\pi\)
\(284\) 22.9309 + 9.72350i 1.36070 + 0.576983i
\(285\) 1.90495i 0.112839i
\(286\) −14.2462 21.5150i −0.842396 1.27221i
\(287\) −5.12311 19.8188i −0.302407 1.16987i
\(288\) 1.21922 5.52390i 0.0718434 0.325499i
\(289\) −1.87689 −0.110406
\(290\) 4.00000 2.64861i 0.234888 0.155532i
\(291\) 8.68951i 0.509388i
\(292\) −6.24621 2.64861i −0.365532 0.154998i
\(293\) 6.99337i 0.408557i −0.978913 0.204278i \(-0.934515\pi\)
0.978913 0.204278i \(-0.0654848\pi\)
\(294\) −8.78078 4.57143i −0.512105 0.266611i
\(295\) 6.78456i 0.395013i
\(296\) 19.8078 3.68260i 1.15130 0.214047i
\(297\) 3.02045i 0.175264i
\(298\) −7.80776 11.7915i −0.452292 0.683062i
\(299\) 18.2462 1.05521
\(300\) 1.65767 3.90928i 0.0957057 0.225702i
\(301\) 5.36932 + 20.7713i 0.309482 + 1.19724i
\(302\) 9.56155 6.33122i 0.550206 0.364320i
\(303\) 6.99337i 0.401759i
\(304\) 3.12311 + 3.22925i 0.179122 + 0.185210i
\(305\) −16.0000 −0.916157
\(306\) −5.12311 + 3.39228i −0.292868 + 0.193924i
\(307\) −21.6155 −1.23366 −0.616832 0.787095i \(-0.711584\pi\)
−0.616832 + 0.787095i \(0.711584\pi\)
\(308\) 15.8078 + 2.35829i 0.900731 + 0.134376i
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 8.00000 0.453638 0.226819 0.973937i \(-0.427167\pi\)
0.226819 + 0.973937i \(0.427167\pi\)
\(312\) −3.12311 16.7984i −0.176811 0.951021i
\(313\) 25.6509i 1.44988i −0.688814 0.724938i \(-0.741868\pi\)
0.688814 0.724938i \(-0.258132\pi\)
\(314\) 4.87689 3.22925i 0.275219 0.182237i
\(315\) 1.12311 + 4.34475i 0.0632798 + 0.244799i
\(316\) 8.68466 + 3.68260i 0.488550 + 0.207163i
\(317\) 18.4924 1.03864 0.519319 0.854580i \(-0.326186\pi\)
0.519319 + 0.854580i \(0.326186\pi\)
\(318\) 3.31534 + 5.00691i 0.185915 + 0.280773i
\(319\) 6.04090i 0.338225i
\(320\) 4.87689 + 12.6624i 0.272627 + 0.707851i
\(321\) 5.66906i 0.316416i
\(322\) −7.56155 + 8.39919i −0.421389 + 0.468069i
\(323\) 4.87962i 0.271509i
\(324\) −0.780776 + 1.84130i −0.0433765 + 0.102294i
\(325\) 12.8255i 0.711429i
\(326\) −13.5616 + 8.97983i −0.751105 + 0.497347i
\(327\) −8.24621 −0.456017
\(328\) 4.00000 + 21.5150i 0.220863 + 1.18797i
\(329\) −26.2462 + 6.78456i −1.44700 + 0.374045i
\(330\) −4.00000 6.04090i −0.220193 0.332540i
\(331\) 5.46026i 0.300123i −0.988677 0.150061i \(-0.952053\pi\)
0.988677 0.150061i \(-0.0479472\pi\)
\(332\) −4.87689 + 11.5012i −0.267654 + 0.631208i
\(333\) −7.12311 −0.390344
\(334\) −1.75379 2.64861i −0.0959631 0.144926i
\(335\) 3.50758 0.191639
\(336\) 9.02699 + 5.52390i 0.492463 + 0.301354i
\(337\) −8.24621 −0.449200 −0.224600 0.974451i \(-0.572108\pi\)
−0.224600 + 0.974451i \(0.572108\pi\)
\(338\) −18.3423 27.7010i −0.997691 1.50674i
\(339\) −12.2462 −0.665123
\(340\) 5.75379 13.5691i 0.312043 0.735889i
\(341\) 0 0
\(342\) −0.876894 1.32431i −0.0474170 0.0716103i
\(343\) 13.4384 12.7439i 0.725608 0.688108i
\(344\) −4.19224 22.5490i −0.226030 1.21576i
\(345\) 5.12311 0.275819
\(346\) 10.0000 6.62153i 0.537603 0.355976i
\(347\) 34.7123i 1.86345i 0.363162 + 0.931726i \(0.381697\pi\)
−0.363162 + 0.931726i \(0.618303\pi\)
\(348\) −1.56155 + 3.68260i −0.0837080 + 0.197408i
\(349\) 4.13595i 0.221392i −0.993854 0.110696i \(-0.964692\pi\)
0.993854 0.110696i \(-0.0353080\pi\)
\(350\) 5.90388 + 5.31510i 0.315576 + 0.284104i
\(351\) 6.04090i 0.322439i
\(352\) −16.6847 3.68260i −0.889295 0.196283i
\(353\) 6.24970i 0.332638i 0.986072 + 0.166319i \(0.0531881\pi\)
−0.986072 + 0.166319i \(0.946812\pi\)
\(354\) −3.12311 4.71659i −0.165991 0.250684i
\(355\) 21.1231 1.12110
\(356\) −14.2462 6.04090i −0.755048 0.320167i
\(357\) −2.87689 11.1293i −0.152261 0.589026i
\(358\) −2.68466 + 1.77766i −0.141889 + 0.0939520i
\(359\) 1.11550i 0.0588740i 0.999567 + 0.0294370i \(0.00937144\pi\)
−0.999567 + 0.0294370i \(0.990629\pi\)
\(360\) −0.876894 4.71659i −0.0462164 0.248586i
\(361\) −17.7386 −0.933612
\(362\) −7.12311 + 4.71659i −0.374382 + 0.247898i
\(363\) −1.87689 −0.0985114
\(364\) 31.6155 + 4.71659i 1.65710 + 0.247216i
\(365\) −5.75379 −0.301167
\(366\) 11.1231 7.36520i 0.581414 0.384985i
\(367\) −8.63068 −0.450518 −0.225259 0.974299i \(-0.572323\pi\)
−0.225259 + 0.974299i \(0.572323\pi\)
\(368\) 8.68466 8.39919i 0.452719 0.437838i
\(369\) 7.73704i 0.402774i
\(370\) 14.2462 9.43318i 0.740625 0.490408i
\(371\) −10.8769 + 2.81164i −0.564700 + 0.145973i
\(372\) 0 0
\(373\) −10.0000 −0.517780 −0.258890 0.965907i \(-0.583357\pi\)
−0.258890 + 0.965907i \(0.583357\pi\)
\(374\) 10.2462 + 15.4741i 0.529819 + 0.800145i
\(375\) 12.0818i 0.623901i
\(376\) 28.4924 5.29723i 1.46938 0.273184i
\(377\) 12.0818i 0.622244i
\(378\) −2.78078 2.50345i −0.143028 0.128764i
\(379\) 18.7033i 0.960725i 0.877070 + 0.480363i \(0.159495\pi\)
−0.877070 + 0.480363i \(0.840505\pi\)
\(380\) 3.50758 + 1.48734i 0.179935 + 0.0762988i
\(381\) 19.4470i 0.996300i
\(382\) 10.6847 7.07488i 0.546675 0.361983i
\(383\) −26.2462 −1.34112 −0.670559 0.741856i \(-0.733946\pi\)
−0.670559 + 0.741856i \(0.733946\pi\)
\(384\) −9.21922 6.55789i −0.470467 0.334656i
\(385\) 13.1231 3.39228i 0.668815 0.172887i
\(386\) 7.31534 + 11.0478i 0.372341 + 0.562318i
\(387\) 8.10887i 0.412197i
\(388\) −16.0000 6.78456i −0.812277 0.344434i
\(389\) 0.246211 0.0124834 0.00624170 0.999981i \(-0.498013\pi\)
0.00624170 + 0.999981i \(0.498013\pi\)
\(390\) −8.00000 12.0818i −0.405096 0.611785i
\(391\) −13.1231 −0.663664
\(392\) −15.2732 + 12.5988i −0.771413 + 0.636335i
\(393\) −22.2462 −1.12217
\(394\) 0.192236 + 0.290319i 0.00968471 + 0.0146261i
\(395\) 8.00000 0.402524
\(396\) 5.56155 + 2.35829i 0.279479 + 0.118509i
\(397\) 16.2177i 0.813945i 0.913440 + 0.406973i \(0.133416\pi\)
−0.913440 + 0.406973i \(0.866584\pi\)
\(398\) 4.00000 + 6.04090i 0.200502 + 0.302803i
\(399\) 2.87689 0.743668i 0.144025 0.0372300i
\(400\) −5.90388 6.10454i −0.295194 0.305227i
\(401\) −8.24621 −0.411796 −0.205898 0.978573i \(-0.566012\pi\)
−0.205898 + 0.978573i \(0.566012\pi\)
\(402\) −2.43845 + 1.61463i −0.121619 + 0.0805302i
\(403\) 0 0
\(404\) 12.8769 + 5.46026i 0.640649 + 0.271658i
\(405\) 1.69614i 0.0842819i
\(406\) −5.56155 5.00691i −0.276015 0.248489i
\(407\) 21.5150i 1.06646i
\(408\) 2.24621 + 12.0818i 0.111204 + 0.598138i
\(409\) 27.5559i 1.36255i 0.732028 + 0.681275i \(0.238574\pi\)
−0.732028 + 0.681275i \(0.761426\pi\)
\(410\) 10.2462 + 15.4741i 0.506024 + 0.764210i
\(411\) 16.2462 0.801367
\(412\) 6.24621 14.7304i 0.307729 0.725715i
\(413\) 10.2462 2.64861i 0.504183 0.130330i
\(414\) −3.56155 + 2.35829i −0.175041 + 0.115904i
\(415\) 10.5945i 0.520061i
\(416\) −33.3693 7.36520i −1.63607 0.361109i
\(417\) 12.0000 0.587643
\(418\) −4.00000 + 2.64861i −0.195646 + 0.129548i
\(419\) 16.4924 0.805708 0.402854 0.915264i \(-0.368018\pi\)
0.402854 + 0.915264i \(0.368018\pi\)
\(420\) 8.87689 + 1.32431i 0.433148 + 0.0646196i
\(421\) 19.1231 0.932003 0.466002 0.884784i \(-0.345694\pi\)
0.466002 + 0.884784i \(0.345694\pi\)
\(422\) 4.68466 3.10196i 0.228046 0.151001i
\(423\) −10.2462 −0.498188
\(424\) 11.8078 2.19526i 0.573436 0.106611i
\(425\) 9.22437i 0.447448i
\(426\) −14.6847 + 9.72350i −0.711474 + 0.471105i
\(427\) 6.24621 + 24.1636i 0.302275 + 1.16936i
\(428\) −10.4384 4.42627i −0.504561 0.213952i
\(429\) 18.2462 0.880935
\(430\) −10.7386 16.2177i −0.517863 0.782089i
\(431\) 15.1022i 0.727449i 0.931507 + 0.363725i \(0.118495\pi\)
−0.931507 + 0.363725i \(0.881505\pi\)
\(432\) 2.78078 + 2.87529i 0.133790 + 0.138337i
\(433\) 6.78456i 0.326045i −0.986622 0.163023i \(-0.947876\pi\)
0.986622 0.163023i \(-0.0521244\pi\)
\(434\) 0 0
\(435\) 3.39228i 0.162647i
\(436\) −6.43845 + 15.1838i −0.308346 + 0.727170i
\(437\) 3.39228i 0.162275i
\(438\) 4.00000 2.64861i 0.191127 0.126556i
\(439\) −31.3693 −1.49718 −0.748588 0.663036i \(-0.769268\pi\)
−0.748588 + 0.663036i \(0.769268\pi\)
\(440\) −14.2462 + 2.64861i −0.679161 + 0.126268i
\(441\) 6.12311 3.39228i 0.291576 0.161537i
\(442\) 20.4924 + 30.9481i 0.974725 + 1.47205i
\(443\) 35.8735i 1.70440i −0.523213 0.852202i \(-0.675267\pi\)
0.523213 0.852202i \(-0.324733\pi\)
\(444\) −5.56155 + 13.1158i −0.263940 + 0.622447i
\(445\) −13.1231 −0.622095
\(446\) 14.7386 + 22.2586i 0.697895 + 1.05398i
\(447\) 10.0000 0.472984
\(448\) 17.2192 12.3085i 0.813532 0.581520i
\(449\) 28.2462 1.33302 0.666511 0.745496i \(-0.267787\pi\)
0.666511 + 0.745496i \(0.267787\pi\)
\(450\) 1.65767 + 2.50345i 0.0781434 + 0.118014i
\(451\) −23.3693 −1.10042
\(452\) −9.56155 + 22.5490i −0.449738 + 1.06061i
\(453\) 8.10887i 0.380988i
\(454\) 12.8769 + 19.4470i 0.604343 + 0.912693i
\(455\) 26.2462 6.78456i 1.23044 0.318065i
\(456\) −3.12311 + 0.580639i −0.146253 + 0.0271909i
\(457\) −16.2462 −0.759966 −0.379983 0.924994i \(-0.624070\pi\)
−0.379983 + 0.924994i \(0.624070\pi\)
\(458\) 21.3693 14.1498i 0.998523 0.661175i
\(459\) 4.34475i 0.202796i
\(460\) 4.00000 9.43318i 0.186501 0.439824i
\(461\) 17.1702i 0.799697i −0.916581 0.399848i \(-0.869063\pi\)
0.916581 0.399848i \(-0.130937\pi\)
\(462\) −7.56155 + 8.39919i −0.351795 + 0.390766i
\(463\) 39.4746i 1.83454i −0.398264 0.917271i \(-0.630387\pi\)
0.398264 0.917271i \(-0.369613\pi\)
\(464\) 5.56155 + 5.75058i 0.258189 + 0.266964i
\(465\) 0 0
\(466\) −8.19224 12.3721i −0.379498 0.573127i
\(467\) 17.7538 0.821547 0.410774 0.911737i \(-0.365259\pi\)
0.410774 + 0.911737i \(0.365259\pi\)
\(468\) 11.1231 + 4.71659i 0.514166 + 0.218024i
\(469\) −1.36932 5.29723i −0.0632292 0.244603i
\(470\) 20.4924 13.5691i 0.945245 0.625897i
\(471\) 4.13595i 0.190575i
\(472\) −11.1231 + 2.06798i −0.511982 + 0.0951863i
\(473\) 24.4924 1.12616
\(474\) −5.56155 + 3.68260i −0.255451 + 0.169147i
\(475\) −2.38447 −0.109407
\(476\) −22.7386 3.39228i −1.04222 0.155485i
\(477\) −4.24621 −0.194421
\(478\) 2.68466 1.77766i 0.122793 0.0813081i
\(479\) −20.4924 −0.936323 −0.468161 0.883643i \(-0.655083\pi\)
−0.468161 + 0.883643i \(0.655083\pi\)
\(480\) −9.36932 2.06798i −0.427649 0.0943897i
\(481\) 43.0299i 1.96200i
\(482\) 2.24621 1.48734i 0.102312 0.0677463i
\(483\) −2.00000 7.73704i −0.0910032 0.352047i
\(484\) −1.46543 + 3.45593i −0.0666107 + 0.157088i
\(485\) −14.7386 −0.669247
\(486\) −0.780776 1.17915i −0.0354167 0.0534872i
\(487\) 32.2725i 1.46240i −0.682161 0.731202i \(-0.738960\pi\)
0.682161 0.731202i \(-0.261040\pi\)
\(488\) −4.87689 26.2316i −0.220767 1.18745i
\(489\) 11.5012i 0.520100i
\(490\) −7.75379 + 14.8934i −0.350280 + 0.672817i
\(491\) 11.7100i 0.528463i −0.964459 0.264231i \(-0.914882\pi\)
0.964459 0.264231i \(-0.0851183\pi\)
\(492\) −14.2462 6.04090i −0.642269 0.272345i
\(493\) 8.68951i 0.391356i
\(494\) −8.00000 + 5.29723i −0.359937 + 0.238334i
\(495\) 5.12311 0.230266
\(496\) 0 0
\(497\) −8.24621 31.9006i −0.369893 1.43094i
\(498\) −4.87689 7.36520i −0.218539 0.330043i
\(499\) 17.5420i 0.785290i −0.919690 0.392645i \(-0.871560\pi\)
0.919690 0.392645i \(-0.128440\pi\)
\(500\) −22.2462 9.43318i −0.994881 0.421865i
\(501\) 2.24621 0.100353
\(502\) −17.3693 26.2316i −0.775231 1.17077i
\(503\) 22.7386 1.01387 0.506933 0.861986i \(-0.330779\pi\)
0.506933 + 0.861986i \(0.330779\pi\)
\(504\) −6.78078 + 3.16561i −0.302040 + 0.141007i
\(505\) 11.8617 0.527840
\(506\) 7.12311 + 10.7575i 0.316661 + 0.478229i
\(507\) 23.4924 1.04334
\(508\) −35.8078 15.1838i −1.58871 0.673670i
\(509\) 1.69614i 0.0751801i −0.999293 0.0375901i \(-0.988032\pi\)
0.999293 0.0375901i \(-0.0119681\pi\)
\(510\) 5.75379 + 8.68951i 0.254782 + 0.384778i
\(511\) 2.24621 + 8.68951i 0.0993665 + 0.384401i
\(512\) −19.2732 + 11.8551i −0.851763 + 0.523927i
\(513\) 1.12311 0.0495863
\(514\) 23.3693 15.4741i 1.03078 0.682532i
\(515\) 13.5691i 0.597927i
\(516\) 14.9309 + 6.33122i 0.657295 + 0.278716i
\(517\) 30.9481i 1.36110i
\(518\) −19.8078 17.8324i −0.870303 0.783509i
\(519\) 8.48071i 0.372262i
\(520\) −28.4924 + 5.29723i −1.24948 + 0.232299i
\(521\) 33.8056i 1.48105i −0.672030 0.740524i \(-0.734577\pi\)
0.672030 0.740524i \(-0.265423\pi\)
\(522\) −1.56155 2.35829i −0.0683473 0.103220i
\(523\) −0.492423 −0.0215321 −0.0107661 0.999942i \(-0.503427\pi\)
−0.0107661 + 0.999942i \(0.503427\pi\)
\(524\) −17.3693 + 40.9620i −0.758782 + 1.78943i
\(525\) −5.43845 + 1.40582i −0.237353 + 0.0613551i
\(526\) −5.80776 + 3.84563i −0.253231 + 0.167677i
\(527\) 0 0
\(528\) 8.68466 8.39919i 0.377951 0.365528i
\(529\) 13.8769 0.603343
\(530\) 8.49242 5.62329i 0.368887 0.244260i
\(531\) 4.00000 0.173585
\(532\) 0.876894 5.87787i 0.0380182 0.254838i
\(533\) −46.7386 −2.02447
\(534\) 9.12311 6.04090i 0.394795 0.261415i
\(535\) −9.61553 −0.415716
\(536\) 1.06913 + 5.75058i 0.0461794 + 0.248387i
\(537\) 2.27678i 0.0982503i
\(538\) −26.4924 + 17.5420i −1.14217 + 0.756291i
\(539\) −10.2462 18.4945i −0.441336 0.796615i
\(540\) 3.12311 + 1.32431i 0.134397 + 0.0569891i
\(541\) 11.1231 0.478220 0.239110 0.970993i \(-0.423144\pi\)
0.239110 + 0.970993i \(0.423144\pi\)
\(542\) 3.50758 + 5.29723i 0.150663 + 0.227535i
\(543\) 6.04090i 0.259240i
\(544\) 24.0000 + 5.29723i 1.02899 + 0.227117i
\(545\) 13.9867i 0.599126i
\(546\) −15.1231 + 16.7984i −0.647209 + 0.718904i
\(547\) 33.0161i 1.41167i −0.708378 0.705834i \(-0.750573\pi\)
0.708378 0.705834i \(-0.249427\pi\)
\(548\) 12.6847 29.9142i 0.541862 1.27787i
\(549\) 9.43318i 0.402598i
\(550\) 7.56155 5.00691i 0.322426 0.213495i
\(551\) 2.24621 0.0956918
\(552\) 1.56155 + 8.39919i 0.0664641 + 0.357493i
\(553\) −3.12311 12.0818i −0.132808 0.513770i
\(554\) 2.43845 + 3.68260i 0.103600 + 0.156459i
\(555\) 12.0818i 0.512843i
\(556\) 9.36932 22.0956i 0.397348 0.937063i
\(557\) 14.0000 0.593199 0.296600 0.955002i \(-0.404147\pi\)
0.296600 + 0.955002i \(0.404147\pi\)
\(558\) 0 0
\(559\) 48.9848 2.07184
\(560\) 9.36932 15.3110i 0.395926 0.647010i
\(561\) −13.1231 −0.554058
\(562\) −0.192236 0.290319i −0.00810898 0.0122464i
\(563\) −14.2462 −0.600406 −0.300203 0.953875i \(-0.597054\pi\)
−0.300203 + 0.953875i \(0.597054\pi\)
\(564\) −8.00000 + 18.8664i −0.336861 + 0.794417i
\(565\) 20.7713i 0.873855i
\(566\) 13.3693 + 20.1907i 0.561954 + 0.848677i
\(567\) 2.56155 0.662153i 0.107575 0.0278078i
\(568\) 6.43845 + 34.6307i 0.270151 + 1.45307i
\(569\) 34.9848 1.46664 0.733320 0.679883i \(-0.237969\pi\)
0.733320 + 0.679883i \(0.237969\pi\)
\(570\) −2.24621 + 1.48734i −0.0940834 + 0.0622977i
\(571\) 40.9620i 1.71420i 0.515146 + 0.857102i \(0.327738\pi\)
−0.515146 + 0.857102i \(0.672262\pi\)
\(572\) 14.2462 33.5968i 0.595664 1.40475i
\(573\) 9.06134i 0.378543i
\(574\) 19.3693 21.5150i 0.808460 0.898017i
\(575\) 6.41273i 0.267429i
\(576\) 7.46543 2.87529i 0.311060 0.119804i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −1.46543 2.21313i −0.0609541 0.0920543i
\(579\) −9.36932 −0.389376
\(580\) 6.24621 + 2.64861i 0.259360 + 0.109978i
\(581\) 16.0000 4.13595i 0.663792 0.171588i
\(582\) 10.2462 6.78456i 0.424719 0.281229i
\(583\) 12.8255i 0.531176i
\(584\) −1.75379 9.43318i −0.0725723 0.390348i
\(585\) 10.2462 0.423629
\(586\) 8.24621 5.46026i 0.340648 0.225561i
\(587\) −38.2462 −1.57859 −0.789295 0.614014i \(-0.789554\pi\)
−0.789295 + 0.614014i \(0.789554\pi\)
\(588\) −1.46543 13.9231i −0.0604335 0.574179i
\(589\) 0 0
\(590\) −8.00000 + 5.29723i −0.329355 + 0.218083i
\(591\) −0.246211 −0.0101278
\(592\) 19.8078 + 20.4810i 0.814094 + 0.841763i
\(593\) 21.7238i 0.892088i 0.895011 + 0.446044i \(0.147168\pi\)
−0.895011 + 0.446044i \(0.852832\pi\)
\(594\) −3.56155 + 2.35829i −0.146132 + 0.0967620i
\(595\) −18.8769 + 4.87962i −0.773877 + 0.200045i
\(596\) 7.80776 18.4130i 0.319818 0.754226i
\(597\) −5.12311 −0.209675
\(598\) 14.2462 + 21.5150i 0.582571 + 0.879813i
\(599\) 19.2382i 0.786051i −0.919528 0.393026i \(-0.871428\pi\)
0.919528 0.393026i \(-0.128572\pi\)
\(600\) 5.90388 1.09763i 0.241025 0.0448107i
\(601\) 5.29723i 0.216078i 0.994147 + 0.108039i \(0.0344572\pi\)
−0.994147 + 0.108039i \(0.965543\pi\)
\(602\) −20.3002 + 22.5490i −0.827374 + 0.919027i
\(603\) 2.06798i 0.0842145i
\(604\) 14.9309 + 6.33122i 0.607528 + 0.257613i
\(605\) 3.18348i 0.129427i
\(606\) −8.24621 + 5.46026i −0.334979 + 0.221808i
\(607\) −33.6155 −1.36441 −0.682206 0.731160i \(-0.738979\pi\)
−0.682206 + 0.731160i \(0.738979\pi\)
\(608\) −1.36932 + 6.20393i −0.0555331 + 0.251602i
\(609\) 5.12311 1.32431i 0.207599 0.0536636i
\(610\) −12.4924 18.8664i −0.505803 0.763876i
\(611\) 61.8963i 2.50406i
\(612\) −8.00000 3.39228i −0.323381 0.137125i
\(613\) −40.7386 −1.64542 −0.822709 0.568463i \(-0.807538\pi\)
−0.822709 + 0.568463i \(0.807538\pi\)
\(614\) −16.8769 25.4879i −0.681096 1.02861i
\(615\) −13.1231 −0.529175
\(616\) 9.56155 + 20.4810i 0.385246 + 0.825202i
\(617\) 15.7538 0.634224 0.317112 0.948388i \(-0.397287\pi\)
0.317112 + 0.948388i \(0.397287\pi\)
\(618\) 6.24621 + 9.43318i 0.251259 + 0.379458i
\(619\) 20.0000 0.803868 0.401934 0.915669i \(-0.368338\pi\)
0.401934 + 0.915669i \(0.368338\pi\)
\(620\) 0 0
\(621\) 3.02045i 0.121206i
\(622\) 6.24621 + 9.43318i 0.250450 + 0.378236i
\(623\) 5.12311 + 19.8188i 0.205253 + 0.794025i
\(624\) 17.3693 16.7984i 0.695329 0.672473i
\(625\) −9.87689 −0.395076
\(626\) 30.2462 20.0276i 1.20888 0.800465i
\(627\) 3.39228i 0.135475i
\(628\) 7.61553 + 3.22925i 0.303893 + 0.128861i
\(629\) 30.9481i 1.23398i
\(630\) −4.24621 + 4.71659i −0.169173 + 0.187913i
\(631\) 17.9597i 0.714963i 0.933920 + 0.357481i \(0.116364\pi\)
−0.933920 + 0.357481i \(0.883636\pi\)
\(632\) 2.43845 + 13.1158i 0.0969962 + 0.521718i
\(633\) 3.97292i 0.157909i
\(634\) 14.4384 + 21.8053i 0.573424 + 0.865999i
\(635\) −32.9848 −1.30896
\(636\) −3.31534 + 7.81855i −0.131462 + 0.310026i
\(637\) −20.4924 36.9890i −0.811939 1.46556i
\(638\) −7.12311 + 4.71659i −0.282006 + 0.186732i
\(639\) 12.4536i 0.492658i
\(640\) −11.1231 + 15.6371i −0.439679 + 0.618111i
\(641\) −9.50758 −0.375527 −0.187763 0.982214i \(-0.560124\pi\)
−0.187763 + 0.982214i \(0.560124\pi\)
\(642\) 6.68466 4.42627i 0.263822 0.174691i
\(643\) 29.6155 1.16792 0.583961 0.811782i \(-0.301502\pi\)
0.583961 + 0.811782i \(0.301502\pi\)
\(644\) −15.8078 2.35829i −0.622913 0.0929298i
\(645\) 13.7538 0.541555
\(646\) 5.75379 3.80989i 0.226380 0.149898i
\(647\) 32.9848 1.29677 0.648384 0.761313i \(-0.275445\pi\)
0.648384 + 0.761313i \(0.275445\pi\)
\(648\) −2.78078 + 0.516994i −0.109239 + 0.0203094i
\(649\) 12.0818i 0.474252i
\(650\) 15.1231 10.0138i 0.593177 0.392774i
\(651\) 0 0
\(652\) −21.1771 8.97983i −0.829358 0.351677i
\(653\) −32.7386 −1.28116 −0.640581 0.767891i \(-0.721306\pi\)
−0.640581 + 0.767891i \(0.721306\pi\)
\(654\) −6.43845 9.72350i −0.251763 0.380219i
\(655\) 37.7327i 1.47434i
\(656\) −22.2462 + 21.5150i −0.868569 + 0.840018i
\(657\) 3.39228i 0.132346i
\(658\) −28.4924 25.6509i −1.11075 0.999977i
\(659\) 38.1045i 1.48434i 0.670210 + 0.742171i \(0.266204\pi\)
−0.670210 + 0.742171i \(0.733796\pi\)
\(660\) 4.00000 9.43318i 0.155700 0.367186i
\(661\) 2.64861i 0.103019i −0.998673 0.0515096i \(-0.983597\pi\)
0.998673 0.0515096i \(-0.0164033\pi\)
\(662\) 6.43845 4.26324i 0.250237 0.165696i
\(663\) −26.2462 −1.01932
\(664\) −17.3693 + 3.22925i −0.674060 + 0.125319i
\(665\) −1.26137 4.87962i −0.0489137 0.189223i
\(666\) −5.56155 8.39919i −0.215506 0.325462i
\(667\) 6.04090i 0.233904i
\(668\) 1.75379 4.13595i 0.0678561 0.160025i
\(669\) −18.8769 −0.729823
\(670\) 2.73863 + 4.13595i 0.105803 + 0.159786i
\(671\) 28.4924 1.09994
\(672\) 0.534565 + 14.9571i 0.0206213 + 0.576982i
\(673\) 29.8617 1.15109 0.575543 0.817772i \(-0.304791\pi\)
0.575543 + 0.817772i \(0.304791\pi\)
\(674\) −6.43845 9.72350i −0.248000 0.374535i
\(675\) −2.12311 −0.0817184
\(676\) 18.3423 43.2566i 0.705474 1.66372i
\(677\) 32.6443i 1.25462i 0.778769 + 0.627311i \(0.215844\pi\)
−0.778769 + 0.627311i \(0.784156\pi\)
\(678\) −9.56155 14.4401i −0.367209 0.554568i
\(679\) 5.75379 + 22.2586i 0.220810 + 0.854208i
\(680\) 20.4924 3.80989i 0.785849 0.146103i
\(681\) −16.4924 −0.631991
\(682\) 0 0
\(683\) 29.0890i 1.11306i −0.830828 0.556529i \(-0.812133\pi\)
0.830828 0.556529i \(-0.187867\pi\)
\(684\) 0.876894 2.06798i 0.0335289 0.0790710i
\(685\) 27.5559i 1.05286i
\(686\) 25.5194 + 5.89574i 0.974336 + 0.225100i
\(687\) 18.1227i 0.691424i
\(688\) 23.3153 22.5490i 0.888889 0.859671i
\(689\) 25.6509i 0.977222i
\(690\) 4.00000 + 6.04090i 0.152277 + 0.229973i
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) 15.6155 + 6.62153i 0.593613 + 0.251713i
\(693\) −2.00000 7.73704i −0.0759737 0.293906i
\(694\) −40.9309 + 27.1025i −1.55371 + 1.02880i
\(695\) 20.3537i 0.772060i
\(696\) −5.56155 + 1.03399i −0.210810 + 0.0391932i
\(697\) 33.6155 1.27328
\(698\) 4.87689 3.22925i 0.184593 0.122229i
\(699\) 10.4924 0.396860
\(700\) −1.65767 + 11.1114i −0.0626541 + 0.419973i
\(701\) −34.0000 −1.28416 −0.642081 0.766637i \(-0.721929\pi\)
−0.642081 + 0.766637i \(0.721929\pi\)
\(702\) −7.12311 + 4.71659i −0.268844 + 0.178016i
\(703\) 8.00000 0.301726
\(704\) −8.68466 22.5490i −0.327315 0.849846i
\(705\) 17.3790i 0.654532i
\(706\) −7.36932 + 4.87962i −0.277348 + 0.183647i
\(707\) −4.63068 17.9139i −0.174155 0.673721i
\(708\) 3.12311 7.36520i 0.117373 0.276801i
\(709\) 6.00000 0.225335 0.112667 0.993633i \(-0.464061\pi\)
0.112667 + 0.993633i \(0.464061\pi\)
\(710\) 16.4924 + 24.9073i 0.618950 + 0.934752i
\(711\) 4.71659i 0.176886i
\(712\) −4.00000 21.5150i −0.149906 0.806308i
\(713\) 0 0
\(714\) 10.8769 12.0818i 0.407058 0.452150i
\(715\) 30.9481i 1.15740i
\(716\) −4.19224 1.77766i −0.156671 0.0664341i
\(717\) 2.27678i 0.0850279i
\(718\) −1.31534 + 0.870958i −0.0490881 + 0.0325039i
\(719\) −4.49242 −0.167539 −0.0837695 0.996485i \(-0.526696\pi\)
−0.0837695 + 0.996485i \(0.526696\pi\)
\(720\) 4.87689 4.71659i 0.181751 0.175777i
\(721\) −20.4924 + 5.29723i −0.763178 + 0.197279i
\(722\) −13.8499 20.9165i −0.515440 0.778430i
\(723\) 1.90495i 0.0708457i
\(724\) −11.1231 4.71659i −0.413387 0.175291i
\(725\) −4.24621 −0.157700
\(726\) −1.46543 2.21313i −0.0543874 0.0821371i
\(727\) −32.9848 −1.22334 −0.611670 0.791113i \(-0.709502\pi\)
−0.611670 + 0.791113i \(0.709502\pi\)
\(728\) 19.1231 + 40.9620i 0.708749 + 1.51815i
\(729\) 1.00000 0.0370370
\(730\) −4.49242 6.78456i −0.166272 0.251108i
\(731\) −35.2311 −1.30307
\(732\) 17.3693 + 7.36520i 0.641988 + 0.272226i
\(733\) 16.6354i 0.614441i −0.951638 0.307220i \(-0.900601\pi\)
0.951638 0.307220i \(-0.0993989\pi\)
\(734\) −6.73863 10.1768i −0.248728 0.375634i
\(735\) −5.75379 10.3857i −0.212232 0.383080i
\(736\) 16.6847 + 3.68260i 0.615005 + 0.135742i
\(737\) −6.24621 −0.230082
\(738\) 9.12311 6.04090i 0.335826 0.222368i
\(739\) 5.87787i 0.216221i −0.994139 0.108110i \(-0.965520\pi\)
0.994139 0.108110i \(-0.0344800\pi\)
\(740\) 22.2462 + 9.43318i 0.817787 + 0.346771i
\(741\) 6.78456i 0.249237i
\(742\) −11.8078 10.6302i −0.433477 0.390247i
\(743\) 13.6149i 0.499482i 0.968313 + 0.249741i \(0.0803455\pi\)
−0.968313 + 0.249741i \(0.919654\pi\)
\(744\) 0 0
\(745\) 16.9614i 0.621418i
\(746\) −7.80776 11.7915i −0.285863 0.431716i
\(747\) 6.24621 0.228537
\(748\) −10.2462 + 24.1636i −0.374639 + 0.883508i
\(749\) 3.75379 + 14.5216i 0.137160 + 0.530608i
\(750\) 14.2462 9.43318i 0.520198 0.344451i
\(751\) 30.7851i 1.12336i −0.827353 0.561682i \(-0.810154\pi\)
0.827353 0.561682i \(-0.189846\pi\)
\(752\) 28.4924 + 29.4608i 1.03901 + 1.07433i
\(753\) 22.2462 0.810697
\(754\) −14.2462 + 9.43318i −0.518816 + 0.343536i
\(755\) 13.7538 0.500552
\(756\) 0.780776 5.23358i 0.0283966 0.190344i
\(757\) 30.9848 1.12616 0.563082 0.826401i \(-0.309616\pi\)
0.563082 + 0.826401i \(0.309616\pi\)
\(758\) −22.0540 + 14.6031i −0.801036 + 0.530409i
\(759\) −9.12311 −0.331148
\(760\) 0.984845 + 5.29723i 0.0357241 + 0.192151i
\(761\) 33.8056i 1.22545i 0.790296 + 0.612725i \(0.209927\pi\)
−0.790296 + 0.612725i \(0.790073\pi\)
\(762\) 22.9309 15.1838i 0.830698 0.550049i
\(763\) 21.1231 5.46026i 0.764708 0.197675i
\(764\) 16.6847 + 7.07488i 0.603630 + 0.255960i
\(765\) −7.36932 −0.266438
\(766\) −20.4924 30.9481i −0.740421 1.11820i
\(767\) 24.1636i 0.872496i
\(768\) 0.534565 15.9911i 0.0192895 0.577028i
\(769\) 44.5173i 1.60533i −0.596427 0.802667i \(-0.703414\pi\)
0.596427 0.802667i \(-0.296586\pi\)
\(770\) 14.2462 + 12.8255i 0.513398 + 0.462197i
\(771\) 19.8188i 0.713758i
\(772\) −7.31534 + 17.2517i −0.263285 + 0.620903i
\(773\) 1.69614i 0.0610060i 0.999535 + 0.0305030i \(0.00971091\pi\)
−0.999535 + 0.0305030i \(0.990289\pi\)
\(774\) −9.56155 + 6.33122i −0.343683 + 0.227571i
\(775\) 0 0
\(776\) −4.49242 24.1636i −0.161269 0.867422i
\(777\) 18.2462 4.71659i 0.654579 0.169207i
\(778\) 0.192236 + 0.290319i 0.00689199 + 0.0104085i
\(779\) 8.68951i 0.311334i