Properties

Label 441.2.f.e.148.2
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 148.2
Root \(-0.335166 - 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.e.295.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.335166 - 0.580525i) q^{2} +(-1.27533 + 1.17198i) q^{3} +(0.775327 - 1.34291i) q^{4} +(-0.712469 + 1.23403i) q^{5} +(1.10781 + 0.347551i) q^{6} -2.38012 q^{8} +(0.252918 - 2.98932i) q^{9} +O(q^{10})\) \(q+(-0.335166 - 0.580525i) q^{2} +(-1.27533 + 1.17198i) q^{3} +(0.775327 - 1.34291i) q^{4} +(-0.712469 + 1.23403i) q^{5} +(1.10781 + 0.347551i) q^{6} -2.38012 q^{8} +(0.252918 - 2.98932i) q^{9} +0.955182 q^{10} +(2.46539 + 4.27018i) q^{11} +(0.585065 + 2.62131i) q^{12} +(-1.37730 + 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +(-0.752918 - 1.30409i) q^{16} -1.11968 q^{17} +(-1.82014 + 0.855094i) q^{18} +4.01505 q^{19} +(1.10479 + 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +(-2.71830 + 4.70824i) q^{23} +(3.03543 - 2.78946i) q^{24} +(1.48478 + 2.57171i) q^{25} +1.84650 q^{26} +(3.18087 + 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(-1.21817 + 1.11946i) q^{30} +(-1.25292 + 2.17012i) q^{31} +(-2.88483 + 4.99666i) q^{32} +(-8.14874 - 2.55648i) q^{33} +(0.375279 + 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} -1.41957 q^{37} +(-1.34571 - 2.33083i) q^{38} +(-1.03932 - 4.65654i) q^{39} +(1.69576 - 2.93714i) q^{40} +(0.124384 - 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +7.64592 q^{44} +(3.50872 + 2.44191i) q^{45} +3.64434 q^{46} +(4.73790 + 8.20628i) q^{47} +(2.48859 + 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(1.42796 - 1.31224i) q^{51} +(2.13572 + 3.69917i) q^{52} +0.820458 q^{53} +(1.31913 - 3.22370i) q^{54} -7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(2.28285 - 3.95401i) q^{58} +(3.29204 - 5.70197i) q^{59} +(-3.65163 - 1.14561i) q^{60} +(-0.0376322 - 0.0651809i) q^{61} +1.67974 q^{62} +0.855913 q^{64} +(-1.96257 - 3.39927i) q^{65} +(1.24708 + 5.58740i) q^{66} +(6.29385 - 10.9013i) q^{67} +(-0.868117 + 1.50362i) q^{68} +(-2.05125 - 9.19035i) q^{69} +0.0804951 q^{71} +(-0.601975 + 7.11494i) q^{72} -10.6910 q^{73} +(0.475793 + 0.824098i) q^{74} +(-4.90757 - 1.53964i) q^{75} +(3.11297 - 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} +(0.922457 + 1.59774i) q^{79} +2.14572 q^{80} +(-8.87206 - 1.51211i) q^{81} -0.166758 q^{82} +(-7.23583 - 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-0.334036 + 0.578567i) q^{86} +(-11.2562 - 3.53138i) q^{87} +(-5.86792 - 10.1635i) q^{88} -13.5258 q^{89} +(0.241583 - 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(-0.945458 - 4.23601i) q^{93} +(3.17597 - 5.50094i) q^{94} +(-2.86059 + 4.95469i) q^{95} +(-2.17690 - 9.75334i) q^{96} +(2.70160 + 4.67930i) q^{97} +(13.3885 - 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - q^{3} - 4q^{4} + 4q^{5} - 2q^{6} - 6q^{8} - 7q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - q^{3} - 4q^{4} + 4q^{5} - 2q^{6} - 6q^{8} - 7q^{9} + 14q^{10} + 4q^{11} - 2q^{12} - 8q^{13} - 19q^{15} + 2q^{16} - 24q^{17} - 2q^{18} - 2q^{19} + 5q^{20} - q^{22} + 3q^{23} - 9q^{24} - q^{25} - 22q^{26} - 7q^{27} + 7q^{29} + 10q^{30} - 3q^{31} - 2q^{32} - 13q^{33} + 3q^{34} + 34q^{36} + 20q^{38} - 22q^{39} - 3q^{40} + 5q^{41} - 7q^{43} + 20q^{44} + 17q^{45} - 6q^{46} + 27q^{47} - 5q^{48} + 19q^{50} - 15q^{51} - 10q^{52} + 42q^{53} + 52q^{54} + 4q^{55} - 4q^{57} - 10q^{58} + 30q^{59} + 31q^{60} - 14q^{61} - 12q^{62} - 50q^{64} - 11q^{65} + 22q^{66} - 2q^{67} + 27q^{68} + 15q^{69} - 6q^{71} - 12q^{72} - 30q^{73} - 36q^{74} - 17q^{75} + 5q^{76} - 20q^{78} - 4q^{79} - 40q^{80} - 31q^{81} + 10q^{82} + 9q^{83} - 6q^{85} - 8q^{86} - 34q^{87} - 18q^{88} - 56q^{89} + 28q^{90} + 27q^{92} + 18q^{93} - 3q^{94} - 14q^{95} - 58q^{96} - 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.335166 0.580525i −0.236998 0.410493i 0.722853 0.691002i \(-0.242830\pi\)
−0.959852 + 0.280508i \(0.909497\pi\)
\(3\) −1.27533 + 1.17198i −0.736310 + 0.676644i
\(4\) 0.775327 1.34291i 0.387664 0.671453i
\(5\) −0.712469 + 1.23403i −0.318626 + 0.551876i −0.980202 0.198002i \(-0.936555\pi\)
0.661576 + 0.749878i \(0.269888\pi\)
\(6\) 1.10781 + 0.347551i 0.452262 + 0.141887i
\(7\) 0 0
\(8\) −2.38012 −0.841499
\(9\) 0.252918 2.98932i 0.0843060 0.996440i
\(10\) 0.955182 0.302055
\(11\) 2.46539 + 4.27018i 0.743342 + 1.28751i 0.950965 + 0.309297i \(0.100094\pi\)
−0.207623 + 0.978209i \(0.566573\pi\)
\(12\) 0.585065 + 2.62131i 0.168894 + 0.756708i
\(13\) −1.37730 + 2.38556i −0.381995 + 0.661635i −0.991347 0.131265i \(-0.958096\pi\)
0.609352 + 0.792900i \(0.291429\pi\)
\(14\) 0 0
\(15\) −0.537632 2.40879i −0.138816 0.621948i
\(16\) −0.752918 1.30409i −0.188230 0.326023i
\(17\) −1.11968 −0.271562 −0.135781 0.990739i \(-0.543354\pi\)
−0.135781 + 0.990739i \(0.543354\pi\)
\(18\) −1.82014 + 0.855094i −0.429012 + 0.201548i
\(19\) 4.01505 0.921115 0.460557 0.887630i \(-0.347650\pi\)
0.460557 + 0.887630i \(0.347650\pi\)
\(20\) 1.10479 + 1.91356i 0.247039 + 0.427884i
\(21\) 0 0
\(22\) 1.65263 2.86244i 0.352342 0.610274i
\(23\) −2.71830 + 4.70824i −0.566806 + 0.981736i 0.430073 + 0.902794i \(0.358488\pi\)
−0.996879 + 0.0789424i \(0.974846\pi\)
\(24\) 3.03543 2.78946i 0.619605 0.569395i
\(25\) 1.48478 + 2.57171i 0.296955 + 0.514342i
\(26\) 1.84650 0.362129
\(27\) 3.18087 + 4.10878i 0.612160 + 0.790734i
\(28\) 0 0
\(29\) 3.40555 + 5.89858i 0.632394 + 1.09534i 0.987061 + 0.160346i \(0.0512611\pi\)
−0.354667 + 0.934993i \(0.615406\pi\)
\(30\) −1.21817 + 1.11946i −0.222406 + 0.204384i
\(31\) −1.25292 + 2.17012i −0.225031 + 0.389765i −0.956329 0.292294i \(-0.905582\pi\)
0.731298 + 0.682058i \(0.238915\pi\)
\(32\) −2.88483 + 4.99666i −0.509970 + 0.883294i
\(33\) −8.14874 2.55648i −1.41851 0.445026i
\(34\) 0.375279 + 0.650002i 0.0643597 + 0.111474i
\(35\) 0 0
\(36\) −3.81828 2.65735i −0.636380 0.442891i
\(37\) −1.41957 −0.233376 −0.116688 0.993169i \(-0.537228\pi\)
−0.116688 + 0.993169i \(0.537228\pi\)
\(38\) −1.34571 2.33083i −0.218303 0.378111i
\(39\) −1.03932 4.65654i −0.166424 0.745643i
\(40\) 1.69576 2.93714i 0.268123 0.464403i
\(41\) 0.124384 0.215440i 0.0194256 0.0336460i −0.856149 0.516729i \(-0.827150\pi\)
0.875575 + 0.483083i \(0.160483\pi\)
\(42\) 0 0
\(43\) −0.498313 0.863104i −0.0759921 0.131622i 0.825525 0.564365i \(-0.190879\pi\)
−0.901517 + 0.432743i \(0.857546\pi\)
\(44\) 7.64592 1.15267
\(45\) 3.50872 + 2.44191i 0.523049 + 0.364018i
\(46\) 3.64434 0.537328
\(47\) 4.73790 + 8.20628i 0.691093 + 1.19701i 0.971480 + 0.237122i \(0.0762040\pi\)
−0.280387 + 0.959887i \(0.590463\pi\)
\(48\) 2.48859 + 0.780738i 0.359197 + 0.112690i
\(49\) 0 0
\(50\) 0.995294 1.72390i 0.140756 0.243796i
\(51\) 1.42796 1.31224i 0.199954 0.183751i
\(52\) 2.13572 + 3.69917i 0.296171 + 0.512983i
\(53\) 0.820458 0.112699 0.0563493 0.998411i \(-0.482054\pi\)
0.0563493 + 0.998411i \(0.482054\pi\)
\(54\) 1.31913 3.22370i 0.179510 0.438690i
\(55\) −7.02604 −0.947392
\(56\) 0 0
\(57\) −5.12050 + 4.70556i −0.678226 + 0.623267i
\(58\) 2.28285 3.95401i 0.299753 0.519187i
\(59\) 3.29204 5.70197i 0.428586 0.742334i −0.568161 0.822917i \(-0.692345\pi\)
0.996748 + 0.0805836i \(0.0256784\pi\)
\(60\) −3.65163 1.14561i −0.471423 0.147898i
\(61\) −0.0376322 0.0651809i −0.00481831 0.00834556i 0.863606 0.504167i \(-0.168200\pi\)
−0.868425 + 0.495821i \(0.834867\pi\)
\(62\) 1.67974 0.213328
\(63\) 0 0
\(64\) 0.855913 0.106989
\(65\) −1.96257 3.39927i −0.243427 0.421628i
\(66\) 1.24708 + 5.58740i 0.153505 + 0.687761i
\(67\) 6.29385 10.9013i 0.768916 1.33180i −0.169235 0.985576i \(-0.554130\pi\)
0.938151 0.346226i \(-0.112537\pi\)
\(68\) −0.868117 + 1.50362i −0.105275 + 0.182341i
\(69\) −2.05125 9.19035i −0.246941 1.10639i
\(70\) 0 0
\(71\) 0.0804951 0.00955301 0.00477651 0.999989i \(-0.498480\pi\)
0.00477651 + 0.999989i \(0.498480\pi\)
\(72\) −0.601975 + 7.11494i −0.0709435 + 0.838504i
\(73\) −10.6910 −1.25129 −0.625644 0.780109i \(-0.715164\pi\)
−0.625644 + 0.780109i \(0.715164\pi\)
\(74\) 0.475793 + 0.824098i 0.0553098 + 0.0957995i
\(75\) −4.90757 1.53964i −0.566678 0.177782i
\(76\) 3.11297 5.39183i 0.357083 0.618485i
\(77\) 0 0
\(78\) −2.35489 + 2.16407i −0.266639 + 0.245032i
\(79\) 0.922457 + 1.59774i 0.103785 + 0.179760i 0.913241 0.407420i \(-0.133571\pi\)
−0.809456 + 0.587180i \(0.800238\pi\)
\(80\) 2.14572 0.239899
\(81\) −8.87206 1.51211i −0.985785 0.168012i
\(82\) −0.166758 −0.0184153
\(83\) −7.23583 12.5328i −0.794236 1.37566i −0.923323 0.384023i \(-0.874538\pi\)
0.129088 0.991633i \(-0.458795\pi\)
\(84\) 0 0
\(85\) 0.797736 1.38172i 0.0865266 0.149868i
\(86\) −0.334036 + 0.578567i −0.0360200 + 0.0623885i
\(87\) −11.2562 3.53138i −1.20679 0.378604i
\(88\) −5.86792 10.1635i −0.625522 1.08344i
\(89\) −13.5258 −1.43374 −0.716868 0.697209i \(-0.754425\pi\)
−0.716868 + 0.697209i \(0.754425\pi\)
\(90\) 0.241583 2.85534i 0.0254651 0.300980i
\(91\) 0 0
\(92\) 4.21515 + 7.30085i 0.439460 + 0.761167i
\(93\) −0.945458 4.23601i −0.0980394 0.439253i
\(94\) 3.17597 5.50094i 0.327576 0.567378i
\(95\) −2.86059 + 4.95469i −0.293491 + 0.508341i
\(96\) −2.17690 9.75334i −0.222179 0.995446i
\(97\) 2.70160 + 4.67930i 0.274306 + 0.475111i 0.969960 0.243266i \(-0.0782187\pi\)
−0.695654 + 0.718377i \(0.744885\pi\)
\(98\) 0 0
\(99\) 13.3885 6.28982i 1.34559 0.632151i
\(100\) 4.60475 0.460475
\(101\) 2.56770 + 4.44739i 0.255496 + 0.442531i 0.965030 0.262139i \(-0.0844280\pi\)
−0.709534 + 0.704671i \(0.751095\pi\)
\(102\) −1.24039 0.389145i −0.122817 0.0385311i
\(103\) 7.10561 12.3073i 0.700137 1.21267i −0.268282 0.963341i \(-0.586456\pi\)
0.968418 0.249332i \(-0.0802109\pi\)
\(104\) 3.27814 5.67791i 0.321448 0.556765i
\(105\) 0 0
\(106\) −0.274990 0.476296i −0.0267094 0.0462620i
\(107\) −7.66030 −0.740549 −0.370274 0.928922i \(-0.620736\pi\)
−0.370274 + 0.928922i \(0.620736\pi\)
\(108\) 7.98392 1.08597i 0.768253 0.104498i
\(109\) 1.69879 0.162714 0.0813572 0.996685i \(-0.474075\pi\)
0.0813572 + 0.996685i \(0.474075\pi\)
\(110\) 2.35489 + 4.07880i 0.224530 + 0.388898i
\(111\) 1.81042 1.66371i 0.171838 0.157913i
\(112\) 0 0
\(113\) −0.300351 + 0.520224i −0.0282547 + 0.0489385i −0.879807 0.475331i \(-0.842328\pi\)
0.851552 + 0.524270i \(0.175662\pi\)
\(114\) 4.44791 + 1.39543i 0.416585 + 0.130694i
\(115\) −3.87341 6.70895i −0.361198 0.625613i
\(116\) 10.5617 0.980625
\(117\) 6.78285 + 4.72055i 0.627075 + 0.436415i
\(118\) −4.41352 −0.406297
\(119\) 0 0
\(120\) 1.27963 + 5.73322i 0.116814 + 0.523369i
\(121\) −6.65626 + 11.5290i −0.605115 + 1.04809i
\(122\) −0.0252261 + 0.0436929i −0.00228386 + 0.00395577i
\(123\) 0.0938609 + 0.420532i 0.00846316 + 0.0379181i
\(124\) 1.94284 + 3.36510i 0.174472 + 0.302195i
\(125\) −11.3561 −1.01572
\(126\) 0 0
\(127\) 7.25977 0.644200 0.322100 0.946706i \(-0.395611\pi\)
0.322100 + 0.946706i \(0.395611\pi\)
\(128\) 5.48278 + 9.49645i 0.484614 + 0.839375i
\(129\) 1.64705 + 0.516726i 0.145015 + 0.0454952i
\(130\) −1.31557 + 2.27864i −0.115384 + 0.199850i
\(131\) 10.2265 17.7128i 0.893492 1.54757i 0.0578326 0.998326i \(-0.481581\pi\)
0.835660 0.549248i \(-0.185086\pi\)
\(132\) −9.75105 + 8.96088i −0.848720 + 0.779945i
\(133\) 0 0
\(134\) −8.43794 −0.728927
\(135\) −7.33663 + 0.997927i −0.631437 + 0.0858879i
\(136\) 2.66497 0.228519
\(137\) −6.10581 10.5756i −0.521655 0.903532i −0.999683 0.0251879i \(-0.991982\pi\)
0.478028 0.878345i \(-0.341352\pi\)
\(138\) −4.64772 + 4.27110i −0.395640 + 0.363580i
\(139\) −1.24092 + 2.14933i −0.105253 + 0.182304i −0.913842 0.406071i \(-0.866899\pi\)
0.808588 + 0.588375i \(0.200232\pi\)
\(140\) 0 0
\(141\) −15.6600 4.91296i −1.31881 0.413746i
\(142\) −0.0269793 0.0467294i −0.00226405 0.00392145i
\(143\) −13.5823 −1.13581
\(144\) −4.08878 + 1.92088i −0.340731 + 0.160074i
\(145\) −9.70538 −0.805988
\(146\) 3.58327 + 6.20640i 0.296553 + 0.513645i
\(147\) 0 0
\(148\) −1.10063 + 1.90635i −0.0904715 + 0.156701i
\(149\) 4.27797 7.40966i 0.350465 0.607023i −0.635866 0.771799i \(-0.719357\pi\)
0.986331 + 0.164777i \(0.0526903\pi\)
\(150\) 0.751054 + 3.36500i 0.0613233 + 0.274751i
\(151\) 8.82962 + 15.2933i 0.718544 + 1.24455i 0.961577 + 0.274537i \(0.0885244\pi\)
−0.243033 + 0.970018i \(0.578142\pi\)
\(152\) −9.55629 −0.775117
\(153\) −0.283187 + 3.34708i −0.0228943 + 0.270595i
\(154\) 0 0
\(155\) −1.78533 3.09228i −0.143401 0.248378i
\(156\) −7.05911 2.21463i −0.565181 0.177313i
\(157\) −3.16074 + 5.47457i −0.252255 + 0.436918i −0.964146 0.265371i \(-0.914505\pi\)
0.711891 + 0.702289i \(0.247839\pi\)
\(158\) 0.618353 1.07102i 0.0491936 0.0852057i
\(159\) −1.04635 + 0.961562i −0.0829811 + 0.0762568i
\(160\) −4.11070 7.11993i −0.324979 0.562880i
\(161\) 0 0
\(162\) 2.09580 + 5.65726i 0.164662 + 0.444477i
\(163\) 8.02267 0.628384 0.314192 0.949359i \(-0.398266\pi\)
0.314192 + 0.949359i \(0.398266\pi\)
\(164\) −0.192877 0.334073i −0.0150612 0.0260867i
\(165\) 8.96050 8.23439i 0.697574 0.641047i
\(166\) −4.85041 + 8.40116i −0.376465 + 0.652057i
\(167\) 1.06038 1.83663i 0.0820545 0.142123i −0.822078 0.569375i \(-0.807185\pi\)
0.904132 + 0.427253i \(0.140518\pi\)
\(168\) 0 0
\(169\) 2.70608 + 4.68706i 0.208160 + 0.360543i
\(170\) −1.06950 −0.0820267
\(171\) 1.01548 12.0023i 0.0776555 0.917835i
\(172\) −1.54542 −0.117837
\(173\) 9.14404 + 15.8379i 0.695208 + 1.20414i 0.970110 + 0.242664i \(0.0780212\pi\)
−0.274902 + 0.961472i \(0.588646\pi\)
\(174\) 1.72265 + 7.71812i 0.130594 + 0.585109i
\(175\) 0 0
\(176\) 3.71247 6.43018i 0.279838 0.484693i
\(177\) 2.48419 + 11.1301i 0.186723 + 0.836588i
\(178\) 4.53341 + 7.85209i 0.339793 + 0.588539i
\(179\) −7.62551 −0.569958 −0.284979 0.958534i \(-0.591987\pi\)
−0.284979 + 0.958534i \(0.591987\pi\)
\(180\) 5.99965 2.81860i 0.447188 0.210086i
\(181\) 15.5305 1.15438 0.577188 0.816611i \(-0.304150\pi\)
0.577188 + 0.816611i \(0.304150\pi\)
\(182\) 0 0
\(183\) 0.124384 + 0.0390227i 0.00919475 + 0.00288464i
\(184\) 6.46989 11.2062i 0.476967 0.826130i
\(185\) 1.01140 1.75180i 0.0743597 0.128795i
\(186\) −2.14222 + 1.96863i −0.157075 + 0.144347i
\(187\) −2.76044 4.78122i −0.201863 0.349638i
\(188\) 14.6937 1.07165
\(189\) 0 0
\(190\) 3.83510 0.278227
\(191\) −7.41624 12.8453i −0.536620 0.929454i −0.999083 0.0428150i \(-0.986367\pi\)
0.462463 0.886639i \(-0.346966\pi\)
\(192\) −1.09157 + 1.00311i −0.0787772 + 0.0723935i
\(193\) −8.28387 + 14.3481i −0.596286 + 1.03280i 0.397078 + 0.917785i \(0.370024\pi\)
−0.993364 + 0.115013i \(0.963309\pi\)
\(194\) 1.81097 3.13669i 0.130020 0.225201i
\(195\) 6.48680 + 2.03509i 0.464529 + 0.145736i
\(196\) 0 0
\(197\) −4.03740 −0.287653 −0.143826 0.989603i \(-0.545941\pi\)
−0.143826 + 0.989603i \(0.545941\pi\)
\(198\) −8.13876 5.66420i −0.578397 0.402537i
\(199\) 25.2814 1.79215 0.896076 0.443901i \(-0.146406\pi\)
0.896076 + 0.443901i \(0.146406\pi\)
\(200\) −3.53395 6.12097i −0.249888 0.432818i
\(201\) 4.74937 + 21.2790i 0.334995 + 1.50090i
\(202\) 1.72121 2.98123i 0.121104 0.209758i
\(203\) 0 0
\(204\) −0.655085 2.93503i −0.0458651 0.205493i
\(205\) 0.177240 + 0.306988i 0.0123790 + 0.0214410i
\(206\) −9.52625 −0.663725
\(207\) 13.3869 + 9.31668i 0.930456 + 0.647554i
\(208\) 4.14798 0.287611
\(209\) 9.89864 + 17.1449i 0.684703 + 1.18594i
\(210\) 0 0
\(211\) −3.76246 + 6.51678i −0.259019 + 0.448634i −0.965979 0.258619i \(-0.916732\pi\)
0.706961 + 0.707253i \(0.250066\pi\)
\(212\) 0.636123 1.10180i 0.0436891 0.0756718i
\(213\) −0.102658 + 0.0943388i −0.00703398 + 0.00646399i
\(214\) 2.56747 + 4.44699i 0.175509 + 0.303990i
\(215\) 1.42013 0.0968521
\(216\) −7.57086 9.77938i −0.515132 0.665402i
\(217\) 0 0
\(218\) −0.569377 0.986190i −0.0385631 0.0667932i
\(219\) 13.6345 12.5297i 0.921337 0.846677i
\(220\) −5.44748 + 9.43531i −0.367269 + 0.636129i
\(221\) 1.54214 2.67106i 0.103735 0.179675i
\(222\) −1.57262 0.493374i −0.105547 0.0331131i
\(223\) 6.49230 + 11.2450i 0.434757 + 0.753020i 0.997276 0.0737638i \(-0.0235011\pi\)
−0.562519 + 0.826784i \(0.690168\pi\)
\(224\) 0 0
\(225\) 8.06319 3.78804i 0.537546 0.252536i
\(226\) 0.402671 0.0267852
\(227\) 14.4832 + 25.0857i 0.961286 + 1.66500i 0.719277 + 0.694723i \(0.244473\pi\)
0.242009 + 0.970274i \(0.422194\pi\)
\(228\) 2.34906 + 10.5247i 0.155571 + 0.697015i
\(229\) −7.71790 + 13.3678i −0.510013 + 0.883369i 0.489919 + 0.871768i \(0.337026\pi\)
−0.999933 + 0.0116012i \(0.996307\pi\)
\(230\) −2.59648 + 4.49723i −0.171207 + 0.296538i
\(231\) 0 0
\(232\) −8.10561 14.0393i −0.532159 0.921727i
\(233\) 4.94648 0.324055 0.162027 0.986786i \(-0.448197\pi\)
0.162027 + 0.986786i \(0.448197\pi\)
\(234\) 0.467014 5.51978i 0.0305296 0.360840i
\(235\) −13.5024 −0.880800
\(236\) −5.10481 8.84179i −0.332295 0.575551i
\(237\) −3.04896 0.956542i −0.198051 0.0621341i
\(238\) 0 0
\(239\) 6.51732 11.2883i 0.421571 0.730182i −0.574523 0.818489i \(-0.694812\pi\)
0.996093 + 0.0883069i \(0.0281456\pi\)
\(240\) −2.73650 + 2.51475i −0.176640 + 0.162326i
\(241\) −7.29123 12.6288i −0.469670 0.813492i 0.529729 0.848167i \(-0.322294\pi\)
−0.999399 + 0.0346754i \(0.988960\pi\)
\(242\) 8.92382 0.573645
\(243\) 13.0869 8.46947i 0.839528 0.543317i
\(244\) −0.116709 −0.00747154
\(245\) 0 0
\(246\) 0.212671 0.195437i 0.0135594 0.0124606i
\(247\) −5.52993 + 9.57812i −0.351861 + 0.609441i
\(248\) 2.98209 5.16514i 0.189363 0.327987i
\(249\) 23.9163 + 7.50319i 1.51563 + 0.475495i
\(250\) 3.80619 + 6.59251i 0.240724 + 0.416947i
\(251\) −14.0715 −0.888187 −0.444094 0.895980i \(-0.646474\pi\)
−0.444094 + 0.895980i \(0.646474\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) −2.43323 4.21448i −0.152674 0.264440i
\(255\) 0.601975 + 2.69708i 0.0376972 + 0.168897i
\(256\) 4.53120 7.84826i 0.283200 0.490517i
\(257\) 4.18108 7.24184i 0.260808 0.451733i −0.705649 0.708562i \(-0.749344\pi\)
0.966457 + 0.256829i \(0.0826776\pi\)
\(258\) −0.252065 1.12935i −0.0156929 0.0703100i
\(259\) 0 0
\(260\) −6.08653 −0.377471
\(261\) 18.4941 8.68841i 1.14475 0.537799i
\(262\) −13.7103 −0.847025
\(263\) −1.63533 2.83247i −0.100839 0.174658i 0.811192 0.584780i \(-0.198819\pi\)
−0.912030 + 0.410122i \(0.865486\pi\)
\(264\) 19.3950 + 6.08473i 1.19368 + 0.374489i
\(265\) −0.584551 + 1.01247i −0.0359087 + 0.0621956i
\(266\) 0 0
\(267\) 17.2499 15.8520i 1.05568 0.970129i
\(268\) −9.75958 16.9041i −0.596161 1.03258i
\(269\) 15.3870 0.938161 0.469081 0.883155i \(-0.344585\pi\)
0.469081 + 0.883155i \(0.344585\pi\)
\(270\) 3.03831 + 3.92463i 0.184906 + 0.238845i
\(271\) −8.12617 −0.493630 −0.246815 0.969063i \(-0.579384\pi\)
−0.246815 + 0.969063i \(0.579384\pi\)
\(272\) 0.843026 + 1.46016i 0.0511160 + 0.0885355i
\(273\) 0 0
\(274\) −4.09293 + 7.08915i −0.247263 + 0.428271i
\(275\) −7.32110 + 12.6805i −0.441479 + 0.764664i
\(276\) −13.9322 4.37090i −0.838618 0.263097i
\(277\) −6.42287 11.1247i −0.385913 0.668421i 0.605982 0.795478i \(-0.292780\pi\)
−0.991895 + 0.127057i \(0.959447\pi\)
\(278\) 1.66365 0.0997793
\(279\) 6.17029 + 4.29423i 0.369406 + 0.257089i
\(280\) 0 0
\(281\) −0.724081 1.25415i −0.0431951 0.0748161i 0.843620 0.536941i \(-0.180420\pi\)
−0.886815 + 0.462125i \(0.847087\pi\)
\(282\) 2.39660 + 10.7377i 0.142715 + 0.639419i
\(283\) 8.71926 15.1022i 0.518306 0.897732i −0.481468 0.876464i \(-0.659896\pi\)
0.999774 0.0212686i \(-0.00677053\pi\)
\(284\) 0.0624100 0.108097i 0.00370335 0.00641440i
\(285\) −2.15862 9.67142i −0.127865 0.572885i
\(286\) 4.55234 + 7.88489i 0.269186 + 0.466243i
\(287\) 0 0
\(288\) 14.2070 + 9.88741i 0.837156 + 0.582621i
\(289\) −15.7463 −0.926254
\(290\) 3.25292 + 5.63422i 0.191018 + 0.330853i
\(291\) −8.92948 2.80142i −0.523455 0.164222i
\(292\) −8.28903 + 14.3570i −0.485079 + 0.840181i
\(293\) −0.900048 + 1.55893i −0.0525814 + 0.0910736i −0.891118 0.453772i \(-0.850078\pi\)
0.838537 + 0.544845i \(0.183412\pi\)
\(294\) 0 0
\(295\) 4.69094 + 8.12495i 0.273117 + 0.473053i
\(296\) 3.37875 0.196386
\(297\) −9.70311 + 23.7126i −0.563031 + 1.37595i
\(298\) −5.73532 −0.332238
\(299\) −7.48786 12.9693i −0.433034 0.750037i
\(300\) −5.87256 + 5.39668i −0.339053 + 0.311578i
\(301\) 0 0
\(302\) 5.91878 10.2516i 0.340588 0.589915i
\(303\) −8.48691 2.66257i −0.487560 0.152961i
\(304\) −3.02300 5.23599i −0.173381 0.300305i
\(305\) 0.107247 0.00614095
\(306\) 2.03798 0.957431i 0.116503 0.0547327i
\(307\) 1.06478 0.0607699 0.0303850 0.999538i \(-0.490327\pi\)
0.0303850 + 0.999538i \(0.490327\pi\)
\(308\) 0 0
\(309\) 5.36193 + 24.0234i 0.305029 + 1.36665i
\(310\) −1.19676 + 2.07286i −0.0679717 + 0.117730i
\(311\) 8.46463 14.6612i 0.479985 0.831359i −0.519751 0.854318i \(-0.673975\pi\)
0.999736 + 0.0229591i \(0.00730874\pi\)
\(312\) 2.47370 + 11.0831i 0.140046 + 0.627458i
\(313\) 4.13928 + 7.16944i 0.233966 + 0.405241i 0.958972 0.283502i \(-0.0914963\pi\)
−0.725006 + 0.688743i \(0.758163\pi\)
\(314\) 4.23750 0.239136
\(315\) 0 0
\(316\) 2.86082 0.160934
\(317\) −3.27371 5.67023i −0.183870 0.318472i 0.759325 0.650711i \(-0.225529\pi\)
−0.943195 + 0.332239i \(0.892196\pi\)
\(318\) 0.908913 + 0.285151i 0.0509693 + 0.0159905i
\(319\) −16.7920 + 29.0846i −0.940171 + 1.62842i
\(320\) −0.609811 + 1.05622i −0.0340895 + 0.0590447i
\(321\) 9.76938 8.97773i 0.545274 0.501088i
\(322\) 0 0
\(323\) −4.49556 −0.250140
\(324\) −8.90937 + 10.7420i −0.494965 + 0.596776i
\(325\) −8.17995 −0.453742
\(326\) −2.68893 4.65736i −0.148926 0.257947i
\(327\) −2.16651 + 1.99095i −0.119808 + 0.110100i
\(328\) −0.296049 + 0.512773i −0.0163466 + 0.0283131i
\(329\) 0 0
\(330\) −7.78353 2.44191i −0.428469 0.134422i
\(331\) 13.3629 + 23.1453i 0.734493 + 1.27218i 0.954946 + 0.296781i \(0.0959131\pi\)
−0.220453 + 0.975398i \(0.570754\pi\)
\(332\) −22.4405 −1.23158
\(333\) −0.359036 + 4.24356i −0.0196750 + 0.232546i
\(334\) −1.42161 −0.0777872
\(335\) 8.96834 + 15.5336i 0.489993 + 0.848692i
\(336\) 0 0
\(337\) −4.76164 + 8.24740i −0.259383 + 0.449264i −0.966077 0.258255i \(-0.916853\pi\)
0.706694 + 0.707520i \(0.250186\pi\)
\(338\) 1.81397 3.14189i 0.0986670 0.170896i
\(339\) −0.226647 1.01546i −0.0123097 0.0551523i
\(340\) −1.23701 2.14257i −0.0670864 0.116197i
\(341\) −12.3557 −0.669099
\(342\) −7.30796 + 3.43324i −0.395169 + 0.185648i
\(343\) 0 0
\(344\) 1.18605 + 2.05429i 0.0639473 + 0.110760i
\(345\) 12.8026 + 4.01654i 0.689271 + 0.216243i
\(346\) 6.12955 10.6167i 0.329526 0.570757i
\(347\) 9.35156 16.1974i 0.502018 0.869521i −0.497979 0.867189i \(-0.665924\pi\)
0.999997 0.00233189i \(-0.000742265\pi\)
\(348\) −13.4696 + 12.3781i −0.722044 + 0.663534i
\(349\) −15.0542 26.0747i −0.805834 1.39574i −0.915727 0.401801i \(-0.868384\pi\)
0.109893 0.993943i \(-0.464949\pi\)
\(350\) 0 0
\(351\) −14.1827 + 1.92913i −0.757019 + 0.102970i
\(352\) −28.4488 −1.51633
\(353\) −3.12966 5.42074i −0.166575 0.288517i 0.770638 0.637273i \(-0.219938\pi\)
−0.937214 + 0.348756i \(0.886604\pi\)
\(354\) 5.62868 5.17256i 0.299161 0.274919i
\(355\) −0.0573502 + 0.0993335i −0.00304383 + 0.00527208i
\(356\) −10.4870 + 18.1639i −0.555807 + 0.962686i
\(357\) 0 0
\(358\) 2.55582 + 4.42680i 0.135079 + 0.233964i
\(359\) 10.1951 0.538077 0.269038 0.963129i \(-0.413294\pi\)
0.269038 + 0.963129i \(0.413294\pi\)
\(360\) −8.35117 5.81203i −0.440145 0.306321i
\(361\) −2.87941 −0.151548
\(362\) −5.20532 9.01587i −0.273585 0.473864i
\(363\) −5.02285 22.5042i −0.263631 1.18117i
\(364\) 0 0
\(365\) 7.61701 13.1931i 0.398693 0.690556i
\(366\) −0.0190357 0.0852873i −0.000995014 0.00445804i
\(367\) 14.3278 + 24.8165i 0.747906 + 1.29541i 0.948824 + 0.315804i \(0.102274\pi\)
−0.200918 + 0.979608i \(0.564392\pi\)
\(368\) 8.18664 0.426758
\(369\) −0.612560 0.426313i −0.0318886 0.0221930i
\(370\) −1.35595 −0.0704926
\(371\) 0 0
\(372\) −6.42160 2.01463i −0.332944 0.104454i
\(373\) 8.03670 13.9200i 0.416124 0.720749i −0.579421 0.815028i \(-0.696721\pi\)
0.995546 + 0.0942796i \(0.0300548\pi\)
\(374\) −1.85041 + 3.20501i −0.0956826 + 0.165727i
\(375\) 14.4828 13.3092i 0.747887 0.687282i
\(376\) −11.2768 19.5319i −0.581555 1.00728i
\(377\) −18.7619 −0.966286
\(378\) 0 0
\(379\) −1.01893 −0.0523388 −0.0261694 0.999658i \(-0.508331\pi\)
−0.0261694 + 0.999658i \(0.508331\pi\)
\(380\) 4.43579 + 7.68302i 0.227551 + 0.394130i
\(381\) −9.25858 + 8.50831i −0.474331 + 0.435894i
\(382\) −4.97135 + 8.61063i −0.254356 + 0.440558i
\(383\) 5.79327 10.0342i 0.296022 0.512725i −0.679200 0.733953i \(-0.737673\pi\)
0.975222 + 0.221228i \(0.0710065\pi\)
\(384\) −18.1220 5.68536i −0.924784 0.290130i
\(385\) 0 0
\(386\) 11.1059 0.565275
\(387\) −2.70613 + 1.27132i −0.137560 + 0.0646250i
\(388\) 8.37848 0.425353
\(389\) −8.90675 15.4270i −0.451590 0.782178i 0.546895 0.837201i \(-0.315810\pi\)
−0.998485 + 0.0550239i \(0.982476\pi\)
\(390\) −0.992739 4.44784i −0.0502693 0.225225i
\(391\) 3.04363 5.27172i 0.153923 0.266602i
\(392\) 0 0
\(393\) 7.71695 + 34.5749i 0.389269 + 1.74407i
\(394\) 1.35320 + 2.34381i 0.0681732 + 0.118079i
\(395\) −2.62889 −0.132274
\(396\) 1.93379 22.8561i 0.0971767 1.14856i
\(397\) 13.0846 0.656696 0.328348 0.944557i \(-0.393508\pi\)
0.328348 + 0.944557i \(0.393508\pi\)
\(398\) −8.47348 14.6765i −0.424737 0.735666i
\(399\) 0 0
\(400\) 2.23583 3.87257i 0.111792 0.193629i
\(401\) −7.05165 + 12.2138i −0.352143 + 0.609929i −0.986625 0.163009i \(-0.947880\pi\)
0.634482 + 0.772938i \(0.281213\pi\)
\(402\) 10.7611 9.88912i 0.536717 0.493224i
\(403\) −3.45129 5.97782i −0.171921 0.297776i
\(404\) 7.96323 0.396185
\(405\) 8.18706 9.87108i 0.406818 0.490498i
\(406\) 0 0
\(407\) −3.49980 6.06183i −0.173479 0.300474i
\(408\) −3.39871 + 3.12329i −0.168261 + 0.154626i
\(409\) 1.32300 2.29150i 0.0654179 0.113307i −0.831461 0.555583i \(-0.812495\pi\)
0.896879 + 0.442275i \(0.145829\pi\)
\(410\) 0.118810 0.205784i 0.00586759 0.0101630i
\(411\) 20.1813 + 6.33142i 0.995470 + 0.312306i
\(412\) −11.0183 19.0843i −0.542835 0.940217i
\(413\) 0 0
\(414\) 0.921719 10.8941i 0.0453000 0.535415i
\(415\) 20.6212 1.01226
\(416\) −7.94655 13.7638i −0.389612 0.674827i
\(417\) −0.936401 4.19543i −0.0458557 0.205451i
\(418\) 6.63538 11.4928i 0.324547 0.562132i
\(419\) 16.7567 29.0235i 0.818619 1.41789i −0.0880816 0.996113i \(-0.528074\pi\)
0.906700 0.421776i \(-0.138593\pi\)
\(420\) 0 0
\(421\) −2.41950 4.19071i −0.117919 0.204242i 0.801024 0.598633i \(-0.204289\pi\)
−0.918943 + 0.394390i \(0.870956\pi\)
\(422\) 5.04421 0.245548
\(423\) 25.7295 12.0876i 1.25101 0.587718i
\(424\) −1.95279 −0.0948358
\(425\) −1.66247 2.87949i −0.0806418 0.139676i
\(426\) 0.0891734 + 0.0279761i 0.00432047 + 0.00135545i
\(427\) 0 0
\(428\) −5.93923 + 10.2871i −0.287084 + 0.497244i
\(429\) 17.3219 15.9182i 0.836310 0.768540i
\(430\) −0.475980 0.824422i −0.0229538 0.0397571i
\(431\) −35.3285 −1.70172 −0.850858 0.525396i \(-0.823917\pi\)
−0.850858 + 0.525396i \(0.823917\pi\)
\(432\) 2.96329 7.24173i 0.142571 0.348418i
\(433\) 5.47404 0.263066 0.131533 0.991312i \(-0.458010\pi\)
0.131533 + 0.991312i \(0.458010\pi\)
\(434\) 0 0
\(435\) 12.3775 11.3745i 0.593458 0.545367i
\(436\) 1.31712 2.28131i 0.0630785 0.109255i
\(437\) −10.9141 + 18.9038i −0.522093 + 0.904292i
\(438\) −11.8436 3.71567i −0.565910 0.177541i
\(439\) −3.19906 5.54093i −0.152683 0.264454i 0.779530 0.626365i \(-0.215458\pi\)
−0.932213 + 0.361911i \(0.882125\pi\)
\(440\) 16.7228 0.797229
\(441\) 0 0
\(442\) −2.06749 −0.0983404
\(443\) 3.19341 + 5.53115i 0.151723 + 0.262793i 0.931861 0.362815i \(-0.118184\pi\)
−0.780138 + 0.625608i \(0.784851\pi\)
\(444\) −0.830543 3.72115i −0.0394158 0.176598i
\(445\) 9.63674 16.6913i 0.456825 0.791245i
\(446\) 4.35200 7.53789i 0.206073 0.356929i
\(447\) 3.22817 + 14.4634i 0.152687 + 0.684097i
\(448\) 0 0
\(449\) −11.7460 −0.554327 −0.277163 0.960823i \(-0.589394\pi\)
−0.277163 + 0.960823i \(0.589394\pi\)
\(450\) −4.90156 3.41126i −0.231062 0.160808i
\(451\) 1.22662 0.0577593
\(452\) 0.465741 + 0.806687i 0.0219066 + 0.0379434i
\(453\) −29.1842 9.15587i −1.37119 0.430180i
\(454\) 9.70859 16.8158i 0.455647 0.789203i
\(455\) 0 0
\(456\) 12.1874 11.1998i 0.570727 0.524478i
\(457\) −5.26120 9.11266i −0.246108 0.426272i 0.716334 0.697757i \(-0.245819\pi\)
−0.962443 + 0.271485i \(0.912485\pi\)
\(458\) 10.3471 0.483489
\(459\) −3.56156 4.60051i −0.166239 0.214733i
\(460\) −12.0127 −0.560093
\(461\) −3.54278 6.13627i −0.165004 0.285794i 0.771653 0.636044i \(-0.219430\pi\)
−0.936657 + 0.350249i \(0.886097\pi\)
\(462\) 0 0
\(463\) 16.3760 28.3641i 0.761059 1.31819i −0.181246 0.983438i \(-0.558013\pi\)
0.942305 0.334755i \(-0.108654\pi\)
\(464\) 5.12820 8.88230i 0.238071 0.412350i
\(465\) 5.90098 + 1.85130i 0.273651 + 0.0858518i
\(466\) −1.65789 2.87156i −0.0768004 0.133022i
\(467\) −3.92431 −0.181596 −0.0907978 0.995869i \(-0.528942\pi\)
−0.0907978 + 0.995869i \(0.528942\pi\)
\(468\) 11.5982 5.44876i 0.536126 0.251869i
\(469\) 0 0
\(470\) 4.52555 + 7.83849i 0.208748 + 0.361563i
\(471\) −2.38511 10.6862i −0.109900 0.492394i
\(472\) −7.83544 + 13.5714i −0.360655 + 0.624673i
\(473\) 2.45707 4.25577i 0.112976 0.195681i
\(474\) 0.466612 + 2.09060i 0.0214322 + 0.0960244i
\(475\) 5.96145 + 10.3255i 0.273530 + 0.473768i
\(476\) 0 0
\(477\) 0.207509 2.45261i 0.00950117 0.112297i
\(478\) −8.73755 −0.399646
\(479\) −8.04324 13.9313i −0.367505 0.636537i 0.621670 0.783279i \(-0.286455\pi\)
−0.989175 + 0.146742i \(0.953121\pi\)
\(480\) 13.5869 + 4.26258i 0.620155 + 0.194559i
\(481\) 1.95518 3.38647i 0.0891486 0.154410i
\(482\) −4.88755 + 8.46549i −0.222622 + 0.385592i
\(483\) 0 0
\(484\) 10.3216 + 17.8775i 0.469162 + 0.812612i
\(485\) −7.69921 −0.349603
\(486\) −9.30304 4.75862i −0.421995 0.215855i
\(487\) 3.50344 0.158756 0.0793781 0.996845i \(-0.474707\pi\)
0.0793781 + 0.996845i \(0.474707\pi\)
\(488\) 0.0895692 + 0.155138i 0.00405461 + 0.00702279i
\(489\) −10.2315 + 9.40242i −0.462686 + 0.425192i
\(490\) 0 0
\(491\) −20.5546 + 35.6017i −0.927618 + 1.60668i −0.140321 + 0.990106i \(0.544814\pi\)
−0.787296 + 0.616575i \(0.788520\pi\)
\(492\) 0.637508 + 0.200004i 0.0287411 + 0.00901686i
\(493\) −3.81312 6.60452i −0.171734 0.297452i
\(494\) 7.41379 0.333562
\(495\) −1.77701 + 21.0031i −0.0798708 + 0.944019i
\(496\) 3.77338 0.169430
\(497\) 0 0
\(498\) −3.66015 16.3988i −0.164015 0.734849i
\(499\) −5.91486 + 10.2448i −0.264785 + 0.458622i −0.967507 0.252843i \(-0.918634\pi\)
0.702722 + 0.711465i \(0.251968\pi\)
\(500\) −8.80470 + 15.2502i −0.393758 + 0.682009i
\(501\) 0.800166 + 3.58505i 0.0357488 + 0.160168i
\(502\) 4.71631 + 8.16888i 0.210499 + 0.364595i
\(503\) 21.8595 0.974665 0.487332 0.873217i \(-0.337970\pi\)
0.487332 + 0.873217i \(0.337970\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) 8.98470 + 15.5620i 0.399419 + 0.691813i
\(507\) −8.94428 2.80606i −0.397230 0.124622i
\(508\) 5.62869 9.74918i 0.249733 0.432550i
\(509\) −8.44831 + 14.6329i −0.374465 + 0.648592i −0.990247 0.139324i \(-0.955507\pi\)
0.615782 + 0.787917i \(0.288840\pi\)
\(510\) 1.36396 1.25343i 0.0603971 0.0555029i
\(511\) 0 0
\(512\) 15.8563 0.700756
\(513\) 12.7714 + 16.4969i 0.563869 + 0.728357i
\(514\) −5.60542 −0.247245
\(515\) 10.1250 + 17.5371i 0.446163 + 0.772777i
\(516\) 1.97092 1.81121i 0.0867649 0.0797340i
\(517\) −23.3615 + 40.4633i −1.02744 + 1.77957i
\(518\) 0 0
\(519\) −30.2234 9.48190i −1.32666 0.416209i
\(520\) 4.67115 + 8.09067i 0.204843 + 0.354799i
\(521\) 34.4932 1.51117 0.755587 0.655048i \(-0.227352\pi\)
0.755587 + 0.655048i \(0.227352\pi\)
\(522\) −11.2424 7.82421i −0.492068 0.342456i
\(523\) −1.99123 −0.0870704 −0.0435352 0.999052i \(-0.513862\pi\)
−0.0435352 + 0.999052i \(0.513862\pi\)
\(524\) −15.8577 27.4664i −0.692749 1.19988i
\(525\) 0 0
\(526\) −1.09622 + 1.89870i −0.0477972 + 0.0827873i
\(527\) 1.40287 2.42983i 0.0611098 0.105845i
\(528\) 2.80145 + 12.5515i 0.121917 + 0.546235i
\(529\) −3.27836 5.67829i −0.142538 0.246882i
\(530\) 0.783687 0.0340412
\(531\) −16.2124 11.2831i −0.703558 0.489644i
\(532\) 0 0
\(533\) 0.342629 + 0.593452i 0.0148409 + 0.0257052i
\(534\) −14.9841 4.70091i −0.648425 0.203428i
\(535\) 5.45772 9.45305i 0.235958 0.408691i
\(536\) −14.9801 + 25.9463i −0.647042 + 1.12071i
\(537\) 9.72503 8.93696i 0.419666 0.385658i
\(538\) −5.15720 8.93253i −0.222343 0.385109i
\(539\) 0 0
\(540\) −4.34817 + 10.6261i −0.187115 + 0.457276i
\(541\) 30.1363 1.29566 0.647830 0.761785i \(-0.275677\pi\)
0.647830 + 0.761785i \(0.275677\pi\)
\(542\) 2.72362 + 4.71745i 0.116989 + 0.202632i
\(543\) −19.8065 + 18.2015i −0.849979 + 0.781102i
\(544\) 3.23008 5.59466i 0.138488 0.239869i
\(545\) −1.21033 + 2.09636i −0.0518450 + 0.0897982i
\(546\) 0 0
\(547\) 7.68070 + 13.3034i 0.328403 + 0.568810i 0.982195 0.187864i \(-0.0601563\pi\)
−0.653792 + 0.756674i \(0.726823\pi\)
\(548\) −18.9360 −0.808906
\(549\) −0.204365 + 0.0960093i −0.00872206 + 0.00409758i
\(550\) 9.81514 0.418519
\(551\) 13.6734 + 23.6831i 0.582508 + 1.00893i
\(552\) 4.88221 + 21.8741i 0.207801 + 0.931025i
\(553\) 0 0
\(554\) −4.30546 + 7.45728i −0.182921 + 0.316829i
\(555\) 0.763209 + 3.41946i 0.0323964 + 0.145148i
\(556\) 1.92423 + 3.33287i 0.0816056 + 0.141345i
\(557\) 23.2823 0.986504 0.493252 0.869886i \(-0.335808\pi\)
0.493252 + 0.869886i \(0.335808\pi\)
\(558\) 0.424838 5.02129i 0.0179848 0.212568i
\(559\) 2.74531 0.116114
\(560\) 0 0
\(561\) 9.12397 + 2.86244i 0.385214 + 0.120852i
\(562\) −0.485375 + 0.840695i −0.0204743 + 0.0354626i
\(563\) −2.27942 + 3.94808i −0.0960663 + 0.166392i −0.910053 0.414492i \(-0.863959\pi\)
0.813987 + 0.580883i \(0.197293\pi\)
\(564\) −18.7392 + 17.2207i −0.789065 + 0.725123i
\(565\) −0.427982 0.741286i −0.0180053 0.0311861i
\(566\) −11.6896 −0.491351
\(567\) 0 0
\(568\) −0.191588 −0.00803885
\(569\) −9.09976 15.7612i −0.381482 0.660746i 0.609793 0.792561i \(-0.291253\pi\)
−0.991274 + 0.131815i \(0.957919\pi\)
\(570\) −4.89101 + 4.49467i −0.204862 + 0.188261i
\(571\) 8.52275 14.7618i 0.356666 0.617763i −0.630736 0.775998i \(-0.717247\pi\)
0.987402 + 0.158234i \(0.0505801\pi\)
\(572\) −10.5307 + 18.2398i −0.440313 + 0.762644i
\(573\) 24.5126 + 7.69027i 1.02403 + 0.321266i
\(574\) 0 0
\(575\) −16.1443 −0.673264
\(576\) 0.216476 2.55860i 0.00901983 0.106608i
\(577\) 11.4095 0.474982 0.237491 0.971390i \(-0.423675\pi\)
0.237491 + 0.971390i \(0.423675\pi\)
\(578\) 5.27764 + 9.14113i 0.219521 + 0.380221i
\(579\) −6.25105 28.0070i −0.259785 1.16393i
\(580\) −7.52485 + 13.0334i −0.312452 + 0.541183i
\(581\) 0 0
\(582\) 1.36657 + 6.12273i 0.0566460 + 0.253795i
\(583\) 2.02275 + 3.50350i 0.0837736 + 0.145100i
\(584\) 25.4459 1.05296
\(585\) −10.6579 + 5.00701i −0.440649 + 0.207014i
\(586\) 1.20666 0.0498468
\(587\) 2.52544 + 4.37420i 0.104236 + 0.180543i 0.913426 0.407005i \(-0.133427\pi\)
−0.809190 + 0.587548i \(0.800094\pi\)
\(588\) 0 0
\(589\) −5.03052 + 8.71312i −0.207279 + 0.359018i
\(590\) 3.14449 5.44642i 0.129457 0.224226i
\(591\) 5.14900 4.73176i 0.211802 0.194638i
\(592\) 1.06882 + 1.85126i 0.0439283 + 0.0760861i
\(593\) 19.9778 0.820391 0.410196 0.911998i \(-0.365460\pi\)
0.410196 + 0.911998i \(0.365460\pi\)
\(594\) 17.0179 2.31477i 0.698254 0.0949763i
\(595\) 0 0
\(596\) −6.63365 11.4898i −0.271725 0.470641i
\(597\) −32.2421 + 29.6293i −1.31958 + 1.21265i
\(598\) −5.01935 + 8.69378i −0.205257 + 0.355515i
\(599\) −2.19660 + 3.80463i −0.0897508 + 0.155453i −0.907406 0.420256i \(-0.861940\pi\)
0.817655 + 0.575709i \(0.195274\pi\)
\(600\) 11.6806 + 3.66452i 0.476859 + 0.149604i
\(601\) 12.1778 + 21.0926i 0.496743 + 0.860385i 0.999993 0.00375637i \(-0.00119569\pi\)
−0.503250 + 0.864141i \(0.667862\pi\)
\(602\) 0 0
\(603\) −30.9955 21.5715i −1.26224 0.878457i
\(604\) 27.3834 1.11421
\(605\) −9.48476 16.4281i −0.385610 0.667897i
\(606\) 1.29884 + 5.81927i 0.0527616 + 0.236392i
\(607\) −6.56281 + 11.3671i −0.266376 + 0.461377i −0.967923 0.251246i \(-0.919160\pi\)
0.701547 + 0.712623i \(0.252493\pi\)
\(608\) −11.5827 + 20.0618i −0.469741 + 0.813615i
\(609\) 0 0
\(610\) −0.0359456 0.0622597i −0.00145540 0.00252082i
\(611\) −26.1021 −1.05598
\(612\) 4.27525 + 2.97537i 0.172817 + 0.120272i
\(613\) 46.4806 1.87733 0.938667 0.344825i \(-0.112062\pi\)
0.938667 + 0.344825i \(0.112062\pi\)
\(614\) −0.356877 0.618129i −0.0144024 0.0249456i
\(615\) −0.585823 0.183789i −0.0236227 0.00741108i
\(616\) 0 0
\(617\) 14.1948 24.5862i 0.571463 0.989803i −0.424953 0.905215i \(-0.639709\pi\)
0.996416 0.0845873i \(-0.0269572\pi\)
\(618\) 12.1491 11.1646i 0.488708 0.449105i
\(619\) −15.9606 27.6446i −0.641511 1.11113i −0.985096 0.172008i \(-0.944975\pi\)
0.343585 0.939122i \(-0.388359\pi\)
\(620\) −5.53686 −0.222366
\(621\) −27.9917 + 3.80742i −1.12327 + 0.152787i
\(622\) −11.3482 −0.455023
\(623\) 0 0
\(624\) −5.29004 + 4.86136i −0.211771 + 0.194610i
\(625\) 0.666993 1.15527i 0.0266797 0.0462106i
\(626\) 2.77469 4.80591i 0.110899 0.192083i
\(627\) −32.7176 10.2644i −1.30661 0.409920i
\(628\) 4.90122 + 8.48916i 0.195580 + 0.338754i
\(629\) 1.58947 0.0633762
\(630\) 0 0
\(631\) 38.7184 1.54135 0.770677 0.637226i \(-0.219918\pi\)
0.770677 + 0.637226i \(0.219918\pi\)
\(632\) −2.19556 3.80282i −0.0873346 0.151268i
\(633\) −2.83917 12.7206i −0.112847 0.505597i
\(634\) −2.19447 + 3.80094i −0.0871537 + 0.150955i
\(635\) −5.17236 + 8.95878i −0.205259 + 0.355519i
\(636\) 0.480022 + 2.15068i 0.0190341 + 0.0852799i
\(637\) 0 0
\(638\) 22.5124 0.891276
\(639\) 0.0203587 0.240626i 0.000805377 0.00951900i
\(640\) −15.6252 −0.617641
\(641\) 20.2001 + 34.9875i 0.797854 + 1.38192i 0.921011 + 0.389537i \(0.127365\pi\)
−0.123157 + 0.992387i \(0.539302\pi\)
\(642\) −8.48616 2.66234i −0.334922 0.105074i
\(643\) 6.27355 10.8661i 0.247405 0.428517i −0.715400 0.698715i \(-0.753756\pi\)
0.962805 + 0.270198i \(0.0870890\pi\)
\(644\) 0 0
\(645\) −1.81113 + 1.66437i −0.0713132 + 0.0655344i
\(646\) 1.50676 + 2.60979i 0.0592827 + 0.102681i
\(647\) −34.5548 −1.35849 −0.679245 0.733912i \(-0.737692\pi\)
−0.679245 + 0.733912i \(0.737692\pi\)
\(648\) 21.1166 + 3.59899i 0.829537 + 0.141382i
\(649\) 32.4646 1.27435
\(650\) 2.74164 + 4.74866i 0.107536 + 0.186258i
\(651\) 0 0
\(652\) 6.22019 10.7737i 0.243602 0.421930i
\(653\) 11.1472 19.3075i 0.436223 0.755560i −0.561172 0.827699i \(-0.689649\pi\)
0.997395 + 0.0721392i \(0.0229826\pi\)
\(654\) 1.88194 + 0.590415i 0.0735896 + 0.0230871i
\(655\) 14.5721 + 25.2396i 0.569379 + 0.986194i
\(656\) −0.374605 −0.0146259
\(657\) −2.70395 + 31.9589i −0.105491 + 1.24683i
\(658\) 0 0
\(659\) 3.57493 + 6.19196i 0.139259 + 0.241204i 0.927217 0.374526i \(-0.122194\pi\)
−0.787957 + 0.615730i \(0.788861\pi\)
\(660\) −4.11070 18.4175i −0.160009 0.716899i
\(661\) −21.4530 + 37.1577i −0.834425 + 1.44527i 0.0600736 + 0.998194i \(0.480866\pi\)
−0.894498 + 0.447072i \(0.852467\pi\)
\(662\) 8.95760 15.5150i 0.348147 0.603008i
\(663\) 1.16370 + 5.21383i 0.0451945 + 0.202488i
\(664\) 17.2221 + 29.8296i 0.668349 + 1.15761i
\(665\) 0 0
\(666\) 2.58383 1.21387i 0.100121 0.0470365i
\(667\) −37.0293 −1.43378
\(668\) −1.64428 2.84798i −0.0636191 0.110192i
\(669\) −21.4587 6.73219i −0.829642 0.260281i
\(670\) 6.01177 10.4127i 0.232255 0.402277i
\(671\) 0.185556 0.321392i 0.00716331 0.0124072i
\(672\) 0 0
\(673\) −18.8270 32.6094i −0.725729 1.25700i −0.958673 0.284510i \(-0.908169\pi\)
0.232944 0.972490i \(-0.425164\pi\)
\(674\) 6.38376 0.245893
\(675\) −5.84369 + 14.2809i −0.224924 + 0.549672i
\(676\) 8.39238 0.322784
\(677\) 13.1808 + 22.8298i 0.506580 + 0.877422i 0.999971 + 0.00761453i \(0.00242380\pi\)
−0.493391 + 0.869808i \(0.664243\pi\)
\(678\) −0.513537 + 0.471923i −0.0197223 + 0.0181241i
\(679\) 0 0
\(680\) −1.89871 + 3.28866i −0.0728121 + 0.126114i
\(681\) −47.8709 15.0184i −1.83442 0.575506i
\(682\) 4.14122 + 7.17280i 0.158575 + 0.274661i
\(683\) −3.93175 −0.150444 −0.0752222 0.997167i \(-0.523967\pi\)
−0.0752222 + 0.997167i \(0.523967\pi\)
\(684\) −15.3306 10.6694i −0.586179 0.407953i
\(685\) 17.4008 0.664850
\(686\) 0 0
\(687\) −5.82396 26.0936i −0.222198 0.995531i
\(688\) −0.750378 + 1.29969i −0.0286079 + 0.0495503i
\(689\) −1.13002 + 1.95725i −0.0430503 + 0.0745653i
\(690\) −1.95931 8.77846i −0.0745898 0.334190i
\(691\) −9.95052 17.2348i −0.378536 0.655643i 0.612314 0.790615i \(-0.290239\pi\)
−0.990849 + 0.134972i \(0.956906\pi\)
\(692\) 28.3585 1.07803
\(693\) 0 0
\(694\) −12.5373 −0.475910
\(695\) −1.76823 3.06266i −0.0670727 0.116173i
\(696\) 26.7911 + 8.40511i 1.01552 + 0.318595i
\(697\) −0.139270 + 0.241223i −0.00527524 + 0.00913699i
\(698\) −10.0913 + 17.4787i −0.381963 + 0.661579i
\(699\) −6.30838 + 5.79718i −0.238605 + 0.219270i
\(700\) 0 0
\(701\) 43.7908 1.65396 0.826979 0.562234i \(-0.190058\pi\)
0.826979 + 0.562234i \(0.190058\pi\)
\(702\) 5.87349 + 7.58686i 0.221681 + 0.286348i
\(703\) −5.69965 −0.214966
\(704\) 2.11016 + 3.65490i 0.0795295 + 0.137749i
\(705\) 17.2200 15.8246i 0.648542 0.595988i
\(706\) −2.09792 + 3.63370i −0.0789561 + 0.136756i
\(707\) 0 0
\(708\) 16.8727 + 5.29343i 0.634115 + 0.198939i
\(709\) −22.3172 38.6545i −0.838139 1.45170i −0.891449 0.453121i \(-0.850310\pi\)
0.0533097 0.998578i \(-0.483023\pi\)
\(710\) 0.0768875 0.00288554
\(711\) 5.00947 2.35342i 0.187870 0.0882602i
\(712\) 32.1931 1.20649
\(713\) −6.81163 11.7981i −0.255097 0.441842i
\(714\) 0 0
\(715\) 9.67699 16.7610i 0.361899 0.626827i
\(716\) −5.91227 + 10.2403i −0.220952 + 0.382700i
\(717\) 4.91800 + 22.0345i 0.183666 + 0.822894i
\(718\) −3.41705 5.91851i −0.127523 0.220877i
\(719\) 39.0192 1.45517 0.727586 0.686016i \(-0.240642\pi\)
0.727586 + 0.686016i \(0.240642\pi\)
\(720\) 0.542692 6.41425i 0.0202249 0.239045i
\(721\) 0 0
\(722\) 0.965081 + 1.67157i 0.0359166 + 0.0622094i
\(723\) 24.0994 + 7.56064i 0.896267 + 0.281183i
\(724\) 12.0413 20.8561i 0.447510 0.775109i
\(725\) −10.1130 + 17.5162i −0.375586 + 0.650534i
\(726\) −11.3808 + 10.4586i −0.422381 + 0.388153i
\(727\) −11.2554 19.4949i −0.417439 0.723025i 0.578242 0.815865i \(-0.303739\pi\)
−0.995681 + 0.0928402i \(0.970405\pi\)
\(728\) 0 0
\(729\) −6.76407 + 26.1390i −0.250521 + 0.968111i
\(730\) −10.2119 −0.377958
\(731\) 0.557951 + 0.966399i 0.0206366 + 0.0357436i
\(732\) 0.148842 0.136781i 0.00550137 0.00505557i
\(733\) 0.448519 0.776858i 0.0165664 0.0286939i −0.857623 0.514278i \(-0.828060\pi\)
0.874190 + 0.485584i \(0.161393\pi\)
\(734\) 9.60441 16.6353i 0.354505 0.614021i
\(735\) 0 0
\(736\) −15.6837 27.1649i −0.578108 1.00131i
\(737\) 62.0671 2.28627
\(738\) −0.0421760 + 0.498492i −0.00155252 + 0.0183497i
\(739\) −3.58063 −0.131716 −0.0658578 0.997829i \(-0.520978\pi\)
−0.0658578 + 0.997829i \(0.520978\pi\)
\(740\) −1.56833 2.71643i −0.0576531 0.0998581i
\(741\) −4.17291 18.6962i −0.153296 0.686823i
\(742\) 0 0
\(743\) −24.7964 + 42.9486i −0.909691 + 1.57563i −0.0951977 + 0.995458i \(0.530348\pi\)
−0.814493 + 0.580173i \(0.802985\pi\)
\(744\) 2.25030 + 10.0822i 0.0825001 + 0.369631i
\(745\) 6.09583 + 10.5583i 0.223334 + 0.386826i
\(746\) −10.7745 −0.394483
\(747\) −39.2947 + 18.4604i −1.43772 + 0.675432i
\(748\) −8.56098 −0.313020
\(749\) 0 0
\(750\) −12.5804 3.94682i −0.459373 0.144118i
\(751\) 21.4515 37.1551i 0.782776 1.35581i −0.147543 0.989056i \(-0.547136\pi\)
0.930319 0.366752i \(-0.119530\pi\)
\(752\) 7.13450 12.3573i 0.260168 0.450625i
\(753\) 17.9458 16.4916i 0.653982 0.600987i
\(754\) 6.28835 + 10.8917i 0.229008 + 0.396654i
\(755\) −25.1633 −0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) 0.341510 + 0.591513i 0.0124042 + 0.0214847i
\(759\) 34.1873 31.4170i 1.24092 1.14036i
\(760\) 6.80856 11.7928i 0.246972 0.427769i
\(761\) −20.3599 + 35.2643i −0.738044 + 1.27833i 0.215330 + 0.976541i \(0.430917\pi\)
−0.953375 + 0.301789i \(0.902416\pi\)
\(762\) 8.04245 + 2.52314i 0.291347 + 0.0914036i
\(763\) 0 0
\(764\) −23.0001 −0.832113
\(765\) −3.92864 2.73415i −0.142040 0.0988534i
\(766\) −7.76683 −0.280627
\(767\) 9.06826 + 15.7067i 0.327436 + 0.567135i
\(768\) 3.41926 + 15.3196i 0.123382 + 0.552798i
\(769\) 5.57381 9.65413i 0.200997 0.348137i −0.747853 0.663864i \(-0.768915\pi\)
0.948850 + 0.315728i \(0.102249\pi\)
\(770\) 0 0
\(771\) 3.15506 + 14.1359i 0.113627 + 0.509090i
\(772\) 12.8454 + 22.2489i 0.462317 + 0.800756i
\(773\) 0.925662 0.0332937 0.0166469 0.999861i \(-0.494701\pi\)
0.0166469 + 0.999861i \(0.494701\pi\)
\(774\) 1.64504 + 1.14487i 0.0591297 + 0.0411515i
\(775\) −7.44121 −0.267296
\(776\) −6.43012 11.1373i −0.230828 0.399806i
\(777\) 0 0
\(778\) −5.97049 + 10.3412i −0.214052 + 0.370750i
\(779\) 0.499408 0.865001i 0.0178932 0.0309919i
\(780\) 7.76232 7.13331i 0.277936 0.255413i
\(781\) 0.198452 +