Properties

Label 441.2.f.f.295.2
Level $441$
Weight $2$
Character 441.295
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 295.2
Root \(-0.335166 + 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.f.148.2

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.959852 0.280508i \(-0.909497\pi\)
0.722853 + 0.691002i \(0.242830\pi\)
\(3\) 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 \(-0.0634454\pi\)
−0.661576 + 0.749878i \(0.730112\pi\)
\(6\) −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 −0.207623 0.978209i \(-0.566573\pi\)
0.950965 0.309297i \(-0.100094\pi\)
\(12\) −0.585065 + 2.62131i −0.168894 + 0.756708i
\(13\) 1.37730 + 2.38556i 0.381995 + 0.661635i 0.991347 0.131265i \(-0.0419038\pi\)
−0.609352 + 0.792900i \(0.708571\pi\)
\(14\) 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 \(-0.456646\pi\)
0.135781 + 0.990739i \(0.456646\pi\)
\(18\) −1.82014 0.855094i −0.429012 0.201548i
\(19\) −4.01505 −0.921115 −0.460557 0.887630i \(-0.652350\pi\)
−0.460557 + 0.887630i \(0.652350\pi\)
\(20\) −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 −0.996879 0.0789424i \(-0.974846\pi\)
0.430073 0.902794i \(-0.358488\pi\)
\(24\) −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 −0.354667 0.934993i \(-0.615406\pi\)
0.987061 0.160346i \(-0.0512611\pi\)
\(30\) −1.21817 1.11946i −0.222406 0.204384i
\(31\) 1.25292 + 2.17012i 0.225031 + 0.389765i 0.956329 0.292294i \(-0.0944184\pi\)
−0.731298 + 0.682058i \(0.761085\pi\)
\(32\) −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 \(-0.172850\pi\)
−0.875575 + 0.483083i \(0.839517\pi\)
\(42\) 0 0
\(43\) −0.498313 + 0.863104i −0.0759921 + 0.131622i −0.901517 0.432743i \(-0.857546\pi\)
0.825525 + 0.564365i \(0.190879\pi\)
\(44\) 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 0.280387 + 0.959887i \(0.409537\pi\)
−0.971480 + 0.237122i \(0.923796\pi\)
\(48\) −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 \(-0.307655\pi\)
−0.996748 + 0.0805836i \(0.974322\pi\)
\(60\) −3.65163 + 1.14561i −0.471423 + 0.147898i
\(61\) 0.0376322 0.0651809i 0.00481831 0.00834556i −0.863606 0.504167i \(-0.831800\pi\)
0.868425 + 0.495821i \(0.165133\pi\)
\(62\) −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 0.938151 + 0.346226i \(0.112537\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(68\) 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 \(-0.284836\pi\)
0.625644 + 0.780109i \(0.284836\pi\)
\(74\) 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 −0.809456 0.587180i \(-0.800238\pi\)
0.913241 + 0.407420i \(0.133571\pi\)
\(80\) −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 −0.129088 0.991633i \(-0.541205\pi\)
0.923323 0.384023i \(-0.125462\pi\)
\(84\) 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 \(-0.245575\pi\)
0.716868 + 0.697209i \(0.245575\pi\)
\(90\) −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 \(-0.921781\pi\)
0.695654 + 0.718377i \(0.255115\pi\)
\(98\) 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 \(-0.915572\pi\)
0.709534 + 0.704671i \(0.248905\pi\)
\(102\) −1.24039 + 0.389145i −0.122817 + 0.0385311i
\(103\) −7.10561 12.3073i −0.700137 1.21267i −0.968418 0.249332i \(-0.919789\pi\)
0.268282 0.963341i \(-0.413544\pi\)
\(104\) −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 0.851552 0.524270i \(-0.175662\pi\)
−0.879807 + 0.475331i \(0.842328\pi\)
\(114\) 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 −0.835660 0.549248i \(-0.814914\pi\)
−0.0578326 0.998326i \(-0.518419\pi\)
\(132\) 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 0.478028 + 0.878345i \(0.341352\pi\)
−0.999683 + 0.0251879i \(0.991982\pi\)
\(138\) 4.64772 + 4.27110i 0.395640 + 0.363580i
\(139\) 1.24092 + 2.14933i 0.105253 + 0.182304i 0.913842 0.406071i \(-0.133101\pi\)
−0.808588 + 0.588375i \(0.799768\pi\)
\(140\) 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 0.986331 0.164777i \(-0.0526903\pi\)
−0.635866 + 0.771799i \(0.719357\pi\)
\(150\) −0.751054 + 3.36500i −0.0613233 + 0.274751i
\(151\) 8.82962 15.2933i 0.718544 1.24455i −0.243033 0.970018i \(-0.578142\pi\)
0.961577 0.274537i \(-0.0885244\pi\)
\(152\) 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 \(-0.0854946\pi\)
−0.711891 + 0.702289i \(0.752161\pi\)
\(158\) 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 \(-0.192815\pi\)
−0.904132 + 0.427253i \(0.859482\pi\)
\(168\) 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 0.274902 + 0.961472i \(0.411354\pi\)
−0.970110 + 0.242664i \(0.921979\pi\)
\(174\) −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 \(-0.695850\pi\)
−0.577188 + 0.816611i \(0.695850\pi\)
\(182\) 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 0.462463 + 0.886639i \(0.346966\pi\)
−0.999083 + 0.0428150i \(0.986367\pi\)
\(192\) 1.09157 + 1.00311i 0.0787772 + 0.0723935i
\(193\) −8.28387 14.3481i −0.596286 1.03280i −0.993364 0.115013i \(-0.963309\pi\)
0.397078 0.917785i \(-0.370024\pi\)
\(194\) −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 \(-0.853594\pi\)
−0.896076 + 0.443901i \(0.853594\pi\)
\(200\) −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 0.706961 0.707253i \(-0.250066\pi\)
−0.965979 + 0.258619i \(0.916732\pi\)
\(212\) 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 \(-0.976499\pi\)
0.562519 + 0.826784i \(0.309832\pi\)
\(224\) 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 −0.242009 + 0.970274i \(0.577806\pi\)
−0.719277 + 0.694723i \(0.755527\pi\)
\(228\) 2.34906 10.5247i 0.155571 0.697015i
\(229\) 7.71790 + 13.3678i 0.510013 + 0.883369i 0.999933 + 0.0116012i \(0.00369285\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(230\) 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 0.996093 0.0883069i \(-0.0281456\pi\)
−0.574523 + 0.818489i \(0.694812\pi\)
\(240\) −2.73650 2.51475i −0.176640 0.162326i
\(241\) 7.29123 12.6288i 0.469670 0.813492i −0.529729 0.848167i \(-0.677706\pi\)
0.999399 + 0.0346754i \(0.0110397\pi\)
\(242\) 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 \(-0.353526\pi\)
0.444094 + 0.895980i \(0.353526\pi\)
\(252\) 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 \(-0.250656\pi\)
−0.966457 + 0.256829i \(0.917322\pi\)
\(258\) 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 −0.912030 0.410122i \(-0.865486\pi\)
0.811192 + 0.584780i \(0.198819\pi\)
\(264\) −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 \(-0.655415\pi\)
−0.469081 + 0.883155i \(0.655415\pi\)
\(270\) 3.03831 3.92463i 0.184906 0.238845i
\(271\) 8.12617 0.493630 0.246815 0.969063i \(-0.420616\pi\)
0.246815 + 0.969063i \(0.420616\pi\)
\(272\) −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 −0.991895 0.127057i \(-0.959447\pi\)
0.605982 + 0.795478i \(0.292780\pi\)
\(278\) −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 −0.886815 0.462125i \(-0.847087\pi\)
0.843620 + 0.536941i \(0.180420\pi\)
\(282\) 2.39660 10.7377i 0.142715 0.639419i
\(283\) −8.71926 15.1022i −0.518306 0.897732i −0.999774 0.0212686i \(-0.993229\pi\)
0.481468 0.876464i \(-0.340104\pi\)
\(284\) 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 \(-0.149922\pi\)
−0.838537 + 0.544845i \(0.816588\pi\)
\(294\) 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 \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(308\) 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 \(-0.326025\pi\)
−0.999736 + 0.0229591i \(0.992691\pi\)
\(312\) 2.47370 11.0831i 0.140046 0.627458i
\(313\) −4.13928 + 7.16944i −0.233966 + 0.405241i −0.958972 0.283502i \(-0.908504\pi\)
0.725006 + 0.688743i \(0.241837\pi\)
\(314\) −4.23750 −0.239136
\(315\) 0 0
\(316\) 2.86082 0.160934
\(317\) −3.27371 + 5.67023i −0.183870 + 0.318472i −0.943195 0.332239i \(-0.892196\pi\)
0.759325 + 0.650711i \(0.225529\pi\)
\(318\) −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 −0.220453 0.975398i \(-0.570754\pi\)
0.954946 0.296781i \(-0.0959131\pi\)
\(332\) 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 0.706694 0.707520i \(-0.250186\pi\)
−0.966077 + 0.258255i \(0.916853\pi\)
\(338\) 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 0.999997 + 0.00233189i \(0.000742265\pi\)
−0.497979 + 0.867189i \(0.665924\pi\)
\(348\) 13.4696 + 12.3781i 0.722044 + 0.663534i
\(349\) 15.0542 26.0747i 0.805834 1.39574i −0.109893 0.993943i \(-0.535051\pi\)
0.915727 0.401801i \(-0.131616\pi\)
\(350\) 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 \(-0.780062\pi\)
0.937214 + 0.348756i \(0.113396\pi\)
\(354\) 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 0.200918 + 0.979608i \(0.435608\pi\)
−0.948824 + 0.315804i \(0.897726\pi\)
\(368\) 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 0.995546 0.0942796i \(-0.0300548\pi\)
−0.579421 + 0.815028i \(0.696721\pi\)
\(374\) 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 \(-0.262327\pi\)
−0.975222 + 0.221228i \(0.928994\pi\)
\(384\) 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 −0.998485 0.0550239i \(-0.982476\pi\)
0.546895 + 0.837201i \(0.315810\pi\)
\(390\) 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 \(-0.606492\pi\)
−0.328348 + 0.944557i \(0.606492\pi\)
\(398\) 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 0.634482 0.772938i \(-0.281213\pi\)
−0.986625 + 0.163009i \(0.947880\pi\)
\(402\) −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 \(-0.187505\pi\)
−0.896879 + 0.442275i \(0.854171\pi\)
\(410\) 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 −0.906700 0.421776i \(-0.861407\pi\)
0.0880816 0.996113i \(-0.471926\pi\)
\(420\) 0 0
\(421\) −2.41950 + 4.19071i −0.117919 + 0.204242i −0.918943 0.394390i \(-0.870956\pi\)
0.801024 + 0.598633i \(0.204289\pi\)
\(422\) 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 \(-0.541990\pi\)
−0.131533 + 0.991312i \(0.541990\pi\)
\(434\) 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 \(-0.784542\pi\)
0.932213 + 0.361911i \(0.117875\pi\)
\(440\) −16.7228 −0.797229
\(441\) 0 0
\(442\) −2.06749 −0.0983404
\(443\) 3.19341 5.53115i 0.151723 0.262793i −0.780138 0.625608i \(-0.784851\pi\)
0.931861 + 0.362815i \(0.118184\pi\)
\(444\) 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 −0.962443 0.271485i \(-0.912485\pi\)
0.716334 + 0.697757i \(0.245819\pi\)
\(458\) −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 \(-0.780570\pi\)
0.936657 + 0.350249i \(0.113903\pi\)
\(462\) 0 0
\(463\) 16.3760 + 28.3641i 0.761059 + 1.31819i 0.942305 + 0.334755i \(0.108654\pi\)
−0.181246 + 0.983438i \(0.558013\pi\)
\(464\) 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 \(-0.471058\pi\)
0.0907978 + 0.995869i \(0.471058\pi\)
\(468\) −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 \(-0.713545\pi\)
0.989175 + 0.146742i \(0.0468787\pi\)
\(480\) 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 −0.787296 0.616575i \(-0.788520\pi\)
−0.140321 0.990106i \(-0.544814\pi\)
\(492\) 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 0.702722 0.711465i \(-0.251968\pi\)
−0.967507 + 0.252843i \(0.918634\pi\)
\(500\) 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 \(-0.662030\pi\)
−0.487332 + 0.873217i \(0.662030\pi\)
\(504\) 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 \(-0.0444931\pi\)
−0.615782 + 0.787917i \(0.711160\pi\)
\(510\) −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 \(-0.772648\pi\)
−0.755587 + 0.655048i \(0.772648\pi\)
\(522\) −11.2424 + 7.82421i −0.492068 + 0.342456i
\(523\) 1.99123 0.0870704 0.0435352 0.999052i \(-0.486138\pi\)
0.0435352 + 0.999052i \(0.486138\pi\)
\(524\) 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 −0.653792 0.756674i \(-0.726823\pi\)
0.982195 + 0.187864i \(0.0601563\pi\)
\(548\) −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 \(-0.136041\pi\)
−0.813987 + 0.580883i \(0.802707\pi\)
\(564\) −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 −0.991274 0.131815i \(-0.957919\pi\)
0.609793 + 0.792561i \(0.291253\pi\)
\(570\) 4.89101 + 4.49467i 0.204862 + 0.188261i
\(571\) 8.52275 + 14.7618i 0.356666 + 0.617763i 0.987402 0.158234i \(-0.0505801\pi\)
−0.630736 + 0.775998i \(0.717247\pi\)
\(572\) 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 \(-0.576325\pi\)
−0.237491 + 0.971390i \(0.576325\pi\)
\(578\) 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 \(-0.866573\pi\)
0.809190 + 0.587548i \(0.199906\pi\)
\(588\) 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 \(-0.634540\pi\)
−0.410196 + 0.911998i \(0.634540\pi\)
\(594\) −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 0.817655 0.575709i \(-0.195274\pi\)
−0.907406 + 0.420256i \(0.861940\pi\)
\(600\) −11.6806 + 3.66452i −0.476859 + 0.149604i
\(601\) −12.1778 + 21.0926i −0.496743 + 0.860385i −0.999993 0.00375637i \(-0.998804\pi\)
0.503250 + 0.864141i \(0.332138\pi\)
\(602\) 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 \(-0.0808403\pi\)
−0.701547 + 0.712623i \(0.747507\pi\)
\(608\) 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 0.996416 + 0.0845873i \(0.0269572\pi\)
−0.424953 + 0.905215i \(0.639709\pi\)
\(618\) 12.1491 + 11.1646i 0.488708 + 0.449105i
\(619\) 15.9606 27.6446i 0.641511 1.11113i −0.343585 0.939122i \(-0.611641\pi\)
0.985096 0.172008i \(-0.0550254\pi\)
\(620\) −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 −0.123157 0.992387i \(-0.539302\pi\)
0.921011 0.389537i \(-0.127365\pi\)
\(642\) 8.48616 2.66234i 0.334922 0.105074i
\(643\) −6.27355 10.8661i −0.247405 0.428517i 0.715400 0.698715i \(-0.246244\pi\)
−0.962805 + 0.270198i \(0.912911\pi\)
\(644\) 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 \(-0.262308\pi\)
0.679245 + 0.733912i \(0.262308\pi\)
\(648\) 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 0.997395 0.0721392i \(-0.0229826\pi\)
−0.561172 + 0.827699i \(0.689649\pi\)
\(654\) −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 −0.787957 0.615730i \(-0.788861\pi\)
0.927217 + 0.374526i \(0.122194\pi\)
\(660\) −4.11070 + 18.4175i −0.160009 + 0.716899i
\(661\) 21.4530 + 37.1577i 0.834425 + 1.44527i 0.894498 + 0.447072i \(0.147533\pi\)
−0.0600736 + 0.998194i \(0.519134\pi\)
\(662\) 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 0.232944 + 0.972490i \(0.425164\pi\)
−0.958673 + 0.284510i \(0.908169\pi\)
\(674\) 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 0.493391 + 0.869808i \(0.335757\pi\)
−0.999971 + 0.00761453i \(0.997576\pi\)
\(678\) 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 \(-0.709761\pi\)
0.990849 + 0.134972i \(0.0430944\pi\)
\(692\) −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 0.0533097 + 0.998578i \(0.483023\pi\)
−0.891449 + 0.453121i \(0.850310\pi\)
\(710\) −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 \(-0.759358\pi\)
−0.727586 + 0.686016i \(0.759358\pi\)
\(720\) −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 \(-0.696261\pi\)
0.995681 + 0.0928402i \(0.0295946\pi\)
\(728\) 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 \(-0.171940\pi\)
−0.874190 + 0.485584i \(0.838607\pi\)
\(734\) −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 −0.814493 0.580173i \(-0.802985\pi\)
−0.0951977 0.995458i \(-0.530348\pi\)
\(744\) 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 0.930319 + 0.366752i \(0.119530\pi\)
−0.147543 + 0.989056i \(0.547136\pi\)
\(752\) −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 0.953375 + 0.301789i \(0.0975839\pi\)
−0.215330 + 0.976541i \(0.569083\pi\)
\(762\) −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 \(-0.231085\pi\)
−0.948850 + 0.315728i \(0.897751\pi\)
\(770\) 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 \(-0.505299\pi\)
−0.0166469 + 0.999861i \(0.505299\pi\)
\(774\) 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 0.343728i 0.