Properties

Label 105.4.g.b.104.13
Level $105$
Weight $4$
Character 105.104
Analytic conductor $6.195$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 105.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.19520055060\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 104.13
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.14

$q$-expansion

\(f(q)\) \(=\) \(q-2.24438 q^{2} +(-1.06702 - 5.08542i) q^{3} -2.96275 q^{4} +(8.51335 - 7.24727i) q^{5} +(2.39479 + 11.4136i) q^{6} +(12.2768 - 13.8665i) q^{7} +24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +O(q^{10})\) \(q-2.24438 q^{2} +(-1.06702 - 5.08542i) q^{3} -2.96275 q^{4} +(8.51335 - 7.24727i) q^{5} +(2.39479 + 11.4136i) q^{6} +(12.2768 - 13.8665i) q^{7} +24.6046 q^{8} +(-24.7230 + 10.8524i) q^{9} +(-19.1072 + 16.2656i) q^{10} -25.7488i q^{11} +(3.16130 + 15.0668i) q^{12} -68.2910 q^{13} +(-27.5539 + 31.1217i) q^{14} +(-45.9393 - 35.5610i) q^{15} -31.5201 q^{16} -30.6502i q^{17} +(55.4878 - 24.3570i) q^{18} +109.632i q^{19} +(-25.2229 + 21.4718i) q^{20} +(-83.6165 - 47.6370i) q^{21} +57.7902i q^{22} -152.265 q^{23} +(-26.2535 - 125.125i) q^{24} +(19.9543 - 123.397i) q^{25} +153.271 q^{26} +(81.5690 + 114.147i) q^{27} +(-36.3731 + 41.0829i) q^{28} -191.763i q^{29} +(103.105 + 79.8125i) q^{30} +16.4683i q^{31} -126.094 q^{32} +(-130.944 + 27.4744i) q^{33} +68.7908i q^{34} +(4.02262 - 207.024i) q^{35} +(73.2479 - 32.1531i) q^{36} +81.9337i q^{37} -246.055i q^{38} +(72.8676 + 347.288i) q^{39} +(209.468 - 178.316i) q^{40} +372.656 q^{41} +(187.667 + 106.916i) q^{42} +192.593i q^{43} +76.2873i q^{44} +(-131.825 + 271.565i) q^{45} +341.741 q^{46} +0.366739i q^{47} +(33.6325 + 160.293i) q^{48} +(-41.5595 - 340.473i) q^{49} +(-44.7850 + 276.950i) q^{50} +(-155.869 + 32.7043i) q^{51} +202.329 q^{52} +5.95065 q^{53} +(-183.072 - 256.189i) q^{54} +(-186.609 - 219.209i) q^{55} +(302.066 - 341.180i) q^{56} +(557.523 - 116.979i) q^{57} +430.389i q^{58} -198.813 q^{59} +(136.106 + 105.358i) q^{60} +83.5752i q^{61} -36.9613i q^{62} +(-153.034 + 476.054i) q^{63} +535.163 q^{64} +(-581.385 + 494.923i) q^{65} +(293.887 - 61.6631i) q^{66} -1080.15i q^{67} +90.8089i q^{68} +(162.469 + 774.332i) q^{69} +(-9.02830 + 464.640i) q^{70} -773.288i q^{71} +(-608.298 + 267.020i) q^{72} +448.111 q^{73} -183.891i q^{74} +(-648.817 + 30.1909i) q^{75} -324.811i q^{76} +(-357.046 - 316.114i) q^{77} +(-163.543 - 779.447i) q^{78} -1270.27 q^{79} +(-268.342 + 228.435i) q^{80} +(493.449 - 536.609i) q^{81} -836.382 q^{82} -429.749i q^{83} +(247.735 + 141.136i) q^{84} +(-222.130 - 260.936i) q^{85} -432.253i q^{86} +(-975.193 + 204.614i) q^{87} -633.540i q^{88} +5.29611 q^{89} +(295.865 - 609.495i) q^{90} +(-838.395 + 946.956i) q^{91} +451.123 q^{92} +(83.7484 - 17.5720i) q^{93} -0.823102i q^{94} +(794.530 + 933.333i) q^{95} +(134.544 + 641.238i) q^{96} -435.169 q^{97} +(93.2755 + 764.151i) q^{98} +(279.438 + 636.587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q + 184q^{4} + 4q^{9} + O(q^{10}) \) \( 40q + 184q^{4} + 4q^{9} - 188q^{15} + 184q^{16} + 148q^{21} + 712q^{25} - 336q^{30} - 1520q^{36} + 644q^{39} - 1488q^{46} - 1496q^{49} - 220q^{51} + 1984q^{60} + 40q^{64} - 3000q^{70} - 1192q^{79} + 4636q^{81} - 2192q^{84} + 4808q^{85} - 4408q^{91} + 5276q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.24438 −0.793509 −0.396754 0.917925i \(-0.629864\pi\)
−0.396754 + 0.917925i \(0.629864\pi\)
\(3\) −1.06702 5.08542i −0.205347 0.978689i
\(4\) −2.96275 −0.370344
\(5\) 8.51335 7.24727i 0.761457 0.648215i
\(6\) 2.39479 + 11.4136i 0.162945 + 0.776599i
\(7\) 12.2768 13.8665i 0.662886 0.748721i
\(8\) 24.6046 1.08738
\(9\) −24.7230 + 10.8524i −0.915665 + 0.401943i
\(10\) −19.1072 + 16.2656i −0.604223 + 0.514365i
\(11\) 25.7488i 0.705779i −0.935665 0.352889i \(-0.885199\pi\)
0.935665 0.352889i \(-0.114801\pi\)
\(12\) 3.16130 + 15.0668i 0.0760491 + 0.362451i
\(13\) −68.2910 −1.45696 −0.728481 0.685066i \(-0.759773\pi\)
−0.728481 + 0.685066i \(0.759773\pi\)
\(14\) −27.5539 + 31.1217i −0.526006 + 0.594116i
\(15\) −45.9393 35.5610i −0.790764 0.612121i
\(16\) −31.5201 −0.492502
\(17\) 30.6502i 0.437281i −0.975806 0.218640i \(-0.929838\pi\)
0.975806 0.218640i \(-0.0701621\pi\)
\(18\) 55.4878 24.3570i 0.726588 0.318945i
\(19\) 109.632i 1.32375i 0.749615 + 0.661874i \(0.230239\pi\)
−0.749615 + 0.661874i \(0.769761\pi\)
\(20\) −25.2229 + 21.4718i −0.282001 + 0.240062i
\(21\) −83.6165 47.6370i −0.868887 0.495011i
\(22\) 57.7902i 0.560042i
\(23\) −152.265 −1.38041 −0.690206 0.723613i \(-0.742480\pi\)
−0.690206 + 0.723613i \(0.742480\pi\)
\(24\) −26.2535 125.125i −0.223291 1.06421i
\(25\) 19.9543 123.397i 0.159634 0.987176i
\(26\) 153.271 1.15611
\(27\) 81.5690 + 114.147i 0.581406 + 0.813613i
\(28\) −36.3731 + 41.0829i −0.245495 + 0.277284i
\(29\) 191.763i 1.22791i −0.789340 0.613956i \(-0.789577\pi\)
0.789340 0.613956i \(-0.210423\pi\)
\(30\) 103.105 + 79.8125i 0.627479 + 0.485723i
\(31\) 16.4683i 0.0954130i 0.998861 + 0.0477065i \(0.0151912\pi\)
−0.998861 + 0.0477065i \(0.984809\pi\)
\(32\) −126.094 −0.696575
\(33\) −130.944 + 27.4744i −0.690738 + 0.144930i
\(34\) 68.7908i 0.346986i
\(35\) 4.02262 207.024i 0.0194271 0.999811i
\(36\) 73.2479 32.1531i 0.339111 0.148857i
\(37\) 81.9337i 0.364049i 0.983294 + 0.182025i \(0.0582651\pi\)
−0.983294 + 0.182025i \(0.941735\pi\)
\(38\) 246.055i 1.05041i
\(39\) 72.8676 + 347.288i 0.299183 + 1.42591i
\(40\) 209.468 178.316i 0.827993 0.704856i
\(41\) 372.656 1.41949 0.709745 0.704459i \(-0.248810\pi\)
0.709745 + 0.704459i \(0.248810\pi\)
\(42\) 187.667 + 106.916i 0.689469 + 0.392796i
\(43\) 192.593i 0.683028i 0.939877 + 0.341514i \(0.110940\pi\)
−0.939877 + 0.341514i \(0.889060\pi\)
\(44\) 76.2873i 0.261381i
\(45\) −131.825 + 271.565i −0.436694 + 0.899610i
\(46\) 341.741 1.09537
\(47\) 0.366739i 0.00113818i 1.00000 0.000569089i \(0.000181147\pi\)
−1.00000 0.000569089i \(0.999819\pi\)
\(48\) 33.6325 + 160.293i 0.101134 + 0.482006i
\(49\) −41.5595 340.473i −0.121165 0.992632i
\(50\) −44.7850 + 276.950i −0.126671 + 0.783333i
\(51\) −155.869 + 32.7043i −0.427962 + 0.0897944i
\(52\) 202.329 0.539576
\(53\) 5.95065 0.0154223 0.00771117 0.999970i \(-0.497545\pi\)
0.00771117 + 0.999970i \(0.497545\pi\)
\(54\) −183.072 256.189i −0.461351 0.645610i
\(55\) −186.609 219.209i −0.457497 0.537420i
\(56\) 302.066 341.180i 0.720809 0.814144i
\(57\) 557.523 116.979i 1.29554 0.271828i
\(58\) 430.389i 0.974359i
\(59\) −198.813 −0.438699 −0.219349 0.975646i \(-0.570393\pi\)
−0.219349 + 0.975646i \(0.570393\pi\)
\(60\) 136.106 + 105.358i 0.292855 + 0.226695i
\(61\) 83.5752i 0.175421i 0.996146 + 0.0877107i \(0.0279551\pi\)
−0.996146 + 0.0877107i \(0.972045\pi\)
\(62\) 36.9613i 0.0757110i
\(63\) −153.034 + 476.054i −0.306039 + 0.952019i
\(64\) 535.163 1.04524
\(65\) −581.385 + 494.923i −1.10941 + 0.944425i
\(66\) 293.887 61.6631i 0.548107 0.115003i
\(67\) 1080.15i 1.96958i −0.173757 0.984789i \(-0.555591\pi\)
0.173757 0.984789i \(-0.444409\pi\)
\(68\) 90.8089i 0.161944i
\(69\) 162.469 + 774.332i 0.283464 + 1.35099i
\(70\) −9.02830 + 464.640i −0.0154156 + 0.793359i
\(71\) 773.288i 1.29257i −0.763097 0.646284i \(-0.776322\pi\)
0.763097 0.646284i \(-0.223678\pi\)
\(72\) −608.298 + 267.020i −0.995676 + 0.437064i
\(73\) 448.111 0.718459 0.359229 0.933249i \(-0.383040\pi\)
0.359229 + 0.933249i \(0.383040\pi\)
\(74\) 183.891i 0.288876i
\(75\) −648.817 + 30.1909i −0.998919 + 0.0464820i
\(76\) 324.811i 0.490242i
\(77\) −357.046 316.114i −0.528431 0.467851i
\(78\) −163.543 779.447i −0.237405 1.13147i
\(79\) −1270.27 −1.80908 −0.904538 0.426393i \(-0.859784\pi\)
−0.904538 + 0.426393i \(0.859784\pi\)
\(80\) −268.342 + 228.435i −0.375019 + 0.319247i
\(81\) 493.449 536.609i 0.676884 0.736089i
\(82\) −836.382 −1.12638
\(83\) 429.749i 0.568327i −0.958776 0.284163i \(-0.908284\pi\)
0.958776 0.284163i \(-0.0917158\pi\)
\(84\) 247.735 + 141.136i 0.321787 + 0.183324i
\(85\) −222.130 260.936i −0.283452 0.332971i
\(86\) 432.253i 0.541989i
\(87\) −975.193 + 204.614i −1.20174 + 0.252148i
\(88\) 633.540i 0.767450i
\(89\) 5.29611 0.00630772 0.00315386 0.999995i \(-0.498996\pi\)
0.00315386 + 0.999995i \(0.498996\pi\)
\(90\) 295.865 609.495i 0.346521 0.713849i
\(91\) −838.395 + 946.956i −0.965799 + 1.09086i
\(92\) 451.123 0.511227
\(93\) 83.7484 17.5720i 0.0933796 0.0195928i
\(94\) 0.823102i 0.000903154i
\(95\) 794.530 + 933.333i 0.858074 + 1.00798i
\(96\) 134.544 + 641.238i 0.143040 + 0.681730i
\(97\) −435.169 −0.455513 −0.227757 0.973718i \(-0.573139\pi\)
−0.227757 + 0.973718i \(0.573139\pi\)
\(98\) 93.2755 + 764.151i 0.0961454 + 0.787663i
\(99\) 279.438 + 636.587i 0.283682 + 0.646257i
\(100\) −59.1194 + 365.594i −0.0591194 + 0.365594i
\(101\) 1122.41 1.10578 0.552891 0.833254i \(-0.313525\pi\)
0.552891 + 0.833254i \(0.313525\pi\)
\(102\) 349.830 73.4009i 0.339592 0.0712527i
\(103\) 625.230 0.598114 0.299057 0.954235i \(-0.403328\pi\)
0.299057 + 0.954235i \(0.403328\pi\)
\(104\) −1680.27 −1.58427
\(105\) −1057.09 + 200.441i −0.982494 + 0.186296i
\(106\) −13.3555 −0.0122378
\(107\) 988.994 0.893548 0.446774 0.894647i \(-0.352573\pi\)
0.446774 + 0.894647i \(0.352573\pi\)
\(108\) −241.669 338.188i −0.215320 0.301317i
\(109\) 810.973 0.712634 0.356317 0.934365i \(-0.384032\pi\)
0.356317 + 0.934365i \(0.384032\pi\)
\(110\) 418.821 + 491.988i 0.363028 + 0.426448i
\(111\) 416.667 87.4246i 0.356291 0.0747566i
\(112\) −386.967 + 437.074i −0.326473 + 0.368746i
\(113\) −107.711 −0.0896687 −0.0448343 0.998994i \(-0.514276\pi\)
−0.0448343 + 0.998994i \(0.514276\pi\)
\(114\) −1251.29 + 262.545i −1.02802 + 0.215698i
\(115\) −1296.29 + 1103.51i −1.05112 + 0.894804i
\(116\) 568.145i 0.454749i
\(117\) 1688.35 741.124i 1.33409 0.585615i
\(118\) 446.212 0.348111
\(119\) −425.011 376.287i −0.327401 0.289867i
\(120\) −1130.32 874.964i −0.859861 0.665608i
\(121\) 667.997 0.501876
\(122\) 187.575i 0.139199i
\(123\) −397.630 1895.11i −0.291488 1.38924i
\(124\) 48.7916i 0.0353356i
\(125\) −724.414 1195.14i −0.518348 0.855170i
\(126\) 343.466 1068.45i 0.242844 0.755436i
\(127\) 33.0601i 0.0230993i −0.999933 0.0115496i \(-0.996324\pi\)
0.999933 0.0115496i \(-0.00367645\pi\)
\(128\) −192.362 −0.132833
\(129\) 979.418 205.500i 0.668472 0.140258i
\(130\) 1304.85 1110.80i 0.880330 0.749409i
\(131\) 997.301 0.665150 0.332575 0.943077i \(-0.392083\pi\)
0.332575 + 0.943077i \(0.392083\pi\)
\(132\) 387.953 81.3998i 0.255810 0.0536738i
\(133\) 1520.21 + 1345.93i 0.991118 + 0.877494i
\(134\) 2424.28i 1.56288i
\(135\) 1521.68 + 380.619i 0.970113 + 0.242655i
\(136\) 754.136i 0.475490i
\(137\) −1373.30 −0.856418 −0.428209 0.903680i \(-0.640855\pi\)
−0.428209 + 0.903680i \(0.640855\pi\)
\(138\) −364.643 1737.90i −0.224931 1.07203i
\(139\) 1361.65i 0.830891i −0.909618 0.415446i \(-0.863626\pi\)
0.909618 0.415446i \(-0.136374\pi\)
\(140\) −11.9180 + 613.359i −0.00719469 + 0.370274i
\(141\) 1.86502 0.391316i 0.00111392 0.000233722i
\(142\) 1735.55i 1.02567i
\(143\) 1758.41i 1.02829i
\(144\) 779.271 342.071i 0.450967 0.197958i
\(145\) −1389.76 1632.54i −0.795951 0.935002i
\(146\) −1005.73 −0.570103
\(147\) −1687.10 + 574.638i −0.946598 + 0.322417i
\(148\) 242.749i 0.134823i
\(149\) 2971.73i 1.63392i −0.576697 0.816958i \(-0.695659\pi\)
0.576697 0.816958i \(-0.304341\pi\)
\(150\) 1456.19 67.7600i 0.792651 0.0368839i
\(151\) 1456.31 0.784851 0.392425 0.919784i \(-0.371636\pi\)
0.392425 + 0.919784i \(0.371636\pi\)
\(152\) 2697.44i 1.43942i
\(153\) 332.630 + 757.764i 0.175762 + 0.400403i
\(154\) 801.348 + 709.480i 0.419315 + 0.371244i
\(155\) 119.350 + 140.201i 0.0618481 + 0.0726529i
\(156\) −215.888 1028.93i −0.110801 0.528078i
\(157\) 2903.14 1.47577 0.737885 0.674927i \(-0.235825\pi\)
0.737885 + 0.674927i \(0.235825\pi\)
\(158\) 2850.98 1.43552
\(159\) −6.34944 30.2615i −0.00316694 0.0150937i
\(160\) −1073.48 + 913.834i −0.530412 + 0.451531i
\(161\) −1869.33 + 2111.38i −0.915056 + 1.03354i
\(162\) −1107.49 + 1204.36i −0.537114 + 0.584093i
\(163\) 1666.60i 0.800850i 0.916330 + 0.400425i \(0.131137\pi\)
−0.916330 + 0.400425i \(0.868863\pi\)
\(164\) −1104.09 −0.525699
\(165\) −915.654 + 1182.88i −0.432022 + 0.558105i
\(166\) 964.522i 0.450972i
\(167\) 1688.52i 0.782403i 0.920305 + 0.391201i \(0.127940\pi\)
−0.920305 + 0.391201i \(0.872060\pi\)
\(168\) −2057.35 1172.09i −0.944810 0.538265i
\(169\) 2466.65 1.12274
\(170\) 498.545 + 585.640i 0.224922 + 0.264215i
\(171\) −1189.77 2710.42i −0.532071 1.21211i
\(172\) 570.606i 0.252955i
\(173\) 719.668i 0.316274i −0.987417 0.158137i \(-0.949451\pi\)
0.987417 0.158137i \(-0.0505487\pi\)
\(174\) 2188.71 459.232i 0.953594 0.200082i
\(175\) −1466.11 1791.62i −0.633300 0.773906i
\(176\) 811.607i 0.347598i
\(177\) 212.136 + 1011.05i 0.0900856 + 0.429350i
\(178\) −11.8865 −0.00500523
\(179\) 1130.92i 0.472231i −0.971725 0.236115i \(-0.924126\pi\)
0.971725 0.236115i \(-0.0758743\pi\)
\(180\) 390.563 804.577i 0.161727 0.333165i
\(181\) 1072.04i 0.440243i −0.975472 0.220121i \(-0.929355\pi\)
0.975472 0.220121i \(-0.0706453\pi\)
\(182\) 1881.68 2125.33i 0.766370 0.865605i
\(183\) 425.015 89.1761i 0.171683 0.0360223i
\(184\) −3746.42 −1.50103
\(185\) 593.796 + 697.530i 0.235982 + 0.277208i
\(186\) −187.963 + 39.4383i −0.0740976 + 0.0155471i
\(187\) −789.208 −0.308623
\(188\) 1.08655i 0.000421517i
\(189\) 2584.22 + 270.283i 0.994575 + 0.104022i
\(190\) −1783.23 2094.75i −0.680889 0.799839i
\(191\) 1611.22i 0.610386i 0.952291 + 0.305193i \(0.0987209\pi\)
−0.952291 + 0.305193i \(0.901279\pi\)
\(192\) −571.028 2721.53i −0.214637 1.02297i
\(193\) 1961.99i 0.731747i 0.930665 + 0.365874i \(0.119230\pi\)
−0.930665 + 0.365874i \(0.880770\pi\)
\(194\) 976.687 0.361454
\(195\) 3137.24 + 2428.49i 1.15211 + 0.891836i
\(196\) 123.130 + 1008.74i 0.0448726 + 0.367615i
\(197\) −658.980 −0.238327 −0.119163 0.992875i \(-0.538021\pi\)
−0.119163 + 0.992875i \(0.538021\pi\)
\(198\) −627.165 1428.75i −0.225105 0.512811i
\(199\) 5062.64i 1.80342i 0.432338 + 0.901712i \(0.357689\pi\)
−0.432338 + 0.901712i \(0.642311\pi\)
\(200\) 490.966 3036.13i 0.173583 1.07344i
\(201\) −5493.03 + 1152.54i −1.92760 + 0.404447i
\(202\) −2519.12 −0.877447
\(203\) −2659.08 2354.23i −0.919362 0.813965i
\(204\) 461.801 96.8946i 0.158493 0.0332548i
\(205\) 3172.55 2700.74i 1.08088 0.920135i
\(206\) −1403.26 −0.474609
\(207\) 3764.44 1652.45i 1.26399 0.554846i
\(208\) 2152.54 0.717557
\(209\) 2822.89 0.934274
\(210\) 2372.52 449.866i 0.779618 0.147827i
\(211\) −3467.27 −1.13126 −0.565631 0.824658i \(-0.691368\pi\)
−0.565631 + 0.824658i \(0.691368\pi\)
\(212\) −17.6303 −0.00571157
\(213\) −3932.49 + 825.111i −1.26502 + 0.265426i
\(214\) −2219.68 −0.709038
\(215\) 1395.78 + 1639.61i 0.442749 + 0.520097i
\(216\) 2006.97 + 2808.54i 0.632209 + 0.884707i
\(217\) 228.358 + 202.179i 0.0714376 + 0.0632479i
\(218\) −1820.13 −0.565481
\(219\) −478.142 2278.83i −0.147534 0.703148i
\(220\) 552.875 + 649.461i 0.169431 + 0.199030i
\(221\) 2093.13i 0.637101i
\(222\) −935.161 + 196.214i −0.282720 + 0.0593200i
\(223\) −2047.08 −0.614720 −0.307360 0.951593i \(-0.599445\pi\)
−0.307360 + 0.951593i \(0.599445\pi\)
\(224\) −1548.03 + 1748.48i −0.461750 + 0.521540i
\(225\) 845.832 + 3267.29i 0.250617 + 0.968086i
\(226\) 241.744 0.0711529
\(227\) 3998.46i 1.16911i −0.811355 0.584553i \(-0.801270\pi\)
0.811355 0.584553i \(-0.198730\pi\)
\(228\) −1651.80 + 346.579i −0.479794 + 0.100670i
\(229\) 3325.60i 0.959659i −0.877362 0.479829i \(-0.840699\pi\)
0.877362 0.479829i \(-0.159301\pi\)
\(230\) 2909.36 2476.69i 0.834077 0.710035i
\(231\) −1226.60 + 2153.03i −0.349368 + 0.613242i
\(232\) 4718.24i 1.33521i
\(233\) 3464.53 0.974116 0.487058 0.873370i \(-0.338070\pi\)
0.487058 + 0.873370i \(0.338070\pi\)
\(234\) −3789.31 + 1663.37i −1.05861 + 0.464691i
\(235\) 2.65785 + 3.12217i 0.000737784 + 0.000866673i
\(236\) 589.032 0.162469
\(237\) 1355.40 + 6459.88i 0.371489 + 1.77052i
\(238\) 953.888 + 844.532i 0.259796 + 0.230012i
\(239\) 4519.56i 1.22321i −0.791165 0.611603i \(-0.790525\pi\)
0.791165 0.611603i \(-0.209475\pi\)
\(240\) 1448.01 + 1120.89i 0.389453 + 0.301471i
\(241\) 7087.15i 1.89429i −0.320810 0.947143i \(-0.603955\pi\)
0.320810 0.947143i \(-0.396045\pi\)
\(242\) −1499.24 −0.398243
\(243\) −3255.40 1936.82i −0.859399 0.511305i
\(244\) 247.612i 0.0649662i
\(245\) −2821.31 2597.37i −0.735701 0.677306i
\(246\) 892.433 + 4253.35i 0.231299 + 1.10237i
\(247\) 7486.85i 1.92865i
\(248\) 405.197i 0.103750i
\(249\) −2185.46 + 458.550i −0.556215 + 0.116704i
\(250\) 1625.86 + 2682.34i 0.411314 + 0.678585i
\(251\) −4749.21 −1.19429 −0.597146 0.802132i \(-0.703699\pi\)
−0.597146 + 0.802132i \(0.703699\pi\)
\(252\) 453.400 1410.43i 0.113339 0.352574i
\(253\) 3920.65i 0.974266i
\(254\) 74.1995i 0.0183295i
\(255\) −1089.95 + 1408.05i −0.267669 + 0.345786i
\(256\) −3849.57 −0.939837
\(257\) 1571.33i 0.381389i 0.981649 + 0.190695i \(0.0610740\pi\)
−0.981649 + 0.190695i \(0.938926\pi\)
\(258\) −2198.19 + 461.221i −0.530439 + 0.111296i
\(259\) 1136.13 + 1005.89i 0.272571 + 0.241323i
\(260\) 1722.50 1466.33i 0.410864 0.349762i
\(261\) 2081.09 + 4740.94i 0.493550 + 1.12436i
\(262\) −2238.33 −0.527802
\(263\) −5430.48 −1.27322 −0.636612 0.771184i \(-0.719665\pi\)
−0.636612 + 0.771184i \(0.719665\pi\)
\(264\) −3221.81 + 675.997i −0.751095 + 0.157594i
\(265\) 50.6599 43.1259i 0.0117435 0.00999700i
\(266\) −3411.93 3020.78i −0.786461 0.696299i
\(267\) −5.65104 26.9330i −0.00129527 0.00617330i
\(268\) 3200.22i 0.729420i
\(269\) 5118.42 1.16013 0.580066 0.814570i \(-0.303027\pi\)
0.580066 + 0.814570i \(0.303027\pi\)
\(270\) −3415.23 854.255i −0.769793 0.192549i
\(271\) 6280.28i 1.40775i 0.710324 + 0.703875i \(0.248548\pi\)
−0.710324 + 0.703875i \(0.751452\pi\)
\(272\) 966.099i 0.215362i
\(273\) 5710.25 + 3253.17i 1.26593 + 0.721213i
\(274\) 3082.22 0.679575
\(275\) −3177.33 513.799i −0.696728 0.112666i
\(276\) −481.356 2294.15i −0.104979 0.500332i
\(277\) 5807.51i 1.25971i 0.776713 + 0.629854i \(0.216885\pi\)
−0.776713 + 0.629854i \(0.783115\pi\)
\(278\) 3056.07i 0.659320i
\(279\) −178.722 407.146i −0.0383505 0.0873663i
\(280\) 98.9750 5093.74i 0.0211246 1.08717i
\(281\) 201.056i 0.0426833i 0.999772 + 0.0213416i \(0.00679377\pi\)
−0.999772 + 0.0213416i \(0.993206\pi\)
\(282\) −4.18582 + 0.878263i −0.000883907 + 0.000185460i
\(283\) 4808.75 1.01007 0.505036 0.863098i \(-0.331479\pi\)
0.505036 + 0.863098i \(0.331479\pi\)
\(284\) 2291.06i 0.478695i
\(285\) 3898.61 5036.40i 0.810294 1.04677i
\(286\) 3946.55i 0.815959i
\(287\) 4575.03 5167.43i 0.940959 1.06280i
\(288\) 3117.40 1368.42i 0.637829 0.279983i
\(289\) 3973.56 0.808786
\(290\) 3119.14 + 3664.05i 0.631594 + 0.741932i
\(291\) 464.333 + 2213.02i 0.0935384 + 0.445806i
\(292\) −1327.64 −0.266076
\(293\) 6701.42i 1.33618i −0.744080 0.668091i \(-0.767112\pi\)
0.744080 0.668091i \(-0.232888\pi\)
\(294\) 3786.50 1289.71i 0.751134 0.255841i
\(295\) −1692.56 + 1440.85i −0.334050 + 0.284371i
\(296\) 2015.95i 0.395860i
\(297\) 2939.15 2100.31i 0.574231 0.410344i
\(298\) 6669.69i 1.29653i
\(299\) 10398.3 2.01121
\(300\) 1922.28 89.4482i 0.369943 0.0172143i
\(301\) 2670.60 + 2364.43i 0.511397 + 0.452770i
\(302\) −3268.51 −0.622786
\(303\) −1197.63 5707.92i −0.227069 1.08222i
\(304\) 3455.60i 0.651949i
\(305\) 605.692 + 711.505i 0.113711 + 0.133576i
\(306\) −746.549 1700.71i −0.139468 0.317723i
\(307\) −1476.12 −0.274419 −0.137209 0.990542i \(-0.543813\pi\)
−0.137209 + 0.990542i \(0.543813\pi\)
\(308\) 1057.84 + 936.566i 0.195701 + 0.173266i
\(309\) −667.131 3179.56i −0.122821 0.585368i
\(310\) −267.868 314.664i −0.0490771 0.0576507i
\(311\) 2162.00 0.394199 0.197100 0.980383i \(-0.436848\pi\)
0.197100 + 0.980383i \(0.436848\pi\)
\(312\) 1792.88 + 8544.88i 0.325326 + 1.55051i
\(313\) 1187.83 0.214505 0.107253 0.994232i \(-0.465795\pi\)
0.107253 + 0.994232i \(0.465795\pi\)
\(314\) −6515.75 −1.17104
\(315\) 2147.26 + 5161.89i 0.384078 + 0.923301i
\(316\) 3763.50 0.669980
\(317\) −4280.71 −0.758450 −0.379225 0.925305i \(-0.623809\pi\)
−0.379225 + 0.925305i \(0.623809\pi\)
\(318\) 14.2506 + 67.9184i 0.00251299 + 0.0119770i
\(319\) −4937.67 −0.866634
\(320\) 4556.03 3878.47i 0.795906 0.677541i
\(321\) −1055.27 5029.45i −0.183488 0.874506i
\(322\) 4195.49 4738.75i 0.726105 0.820125i
\(323\) 3360.23 0.578850
\(324\) −1461.96 + 1589.84i −0.250680 + 0.272606i
\(325\) −1362.69 + 8426.90i −0.232581 + 1.43828i
\(326\) 3740.50i 0.635481i
\(327\) −865.321 4124.13i −0.146337 0.697447i
\(328\) 9169.05 1.54352
\(329\) 5.08538 + 4.50238i 0.000852177 + 0.000754481i
\(330\) 2055.08 2654.84i 0.342813 0.442861i
\(331\) 4975.22 0.826172 0.413086 0.910692i \(-0.364451\pi\)
0.413086 + 0.910692i \(0.364451\pi\)
\(332\) 1273.24i 0.210476i
\(333\) −889.181 2025.64i −0.146327 0.333347i
\(334\) 3789.67i 0.620843i
\(335\) −7828.16 9195.72i −1.27671 1.49975i
\(336\) 2635.60 + 1501.52i 0.427928 + 0.243794i
\(337\) 8230.66i 1.33042i 0.746655 + 0.665212i \(0.231659\pi\)
−0.746655 + 0.665212i \(0.768341\pi\)
\(338\) −5536.11 −0.890902
\(339\) 114.929 + 547.754i 0.0184132 + 0.0877578i
\(340\) 658.116 + 773.088i 0.104975 + 0.123313i
\(341\) 424.041 0.0673404
\(342\) 2670.30 + 6083.21i 0.422203 + 0.961820i
\(343\) −5231.39 3603.64i −0.823523 0.567283i
\(344\) 4738.68i 0.742711i
\(345\) 6994.95 + 5414.70i 1.09158 + 0.844979i
\(346\) 1615.21i 0.250966i
\(347\) −864.297 −0.133712 −0.0668558 0.997763i \(-0.521297\pi\)
−0.0668558 + 0.997763i \(0.521297\pi\)
\(348\) 2889.25 606.219i 0.445058 0.0933815i
\(349\) 4811.80i 0.738022i 0.929425 + 0.369011i \(0.120304\pi\)
−0.929425 + 0.369011i \(0.879696\pi\)
\(350\) 3290.51 + 4021.08i 0.502529 + 0.614102i
\(351\) −5570.43 7795.19i −0.847086 1.18540i
\(352\) 3246.76i 0.491628i
\(353\) 1206.50i 0.181913i 0.995855 + 0.0909565i \(0.0289924\pi\)
−0.995855 + 0.0909565i \(0.971008\pi\)
\(354\) −476.115 2269.17i −0.0714837 0.340693i
\(355\) −5604.22 6583.27i −0.837863 0.984236i
\(356\) −15.6911 −0.00233602
\(357\) −1460.08 + 2562.86i −0.216459 + 0.379947i
\(358\) 2538.23i 0.374719i
\(359\) 7589.54i 1.11577i 0.829919 + 0.557884i \(0.188387\pi\)
−0.829919 + 0.557884i \(0.811613\pi\)
\(360\) −3243.49 + 6681.74i −0.474853 + 0.978218i
\(361\) −5160.10 −0.752310
\(362\) 2406.06i 0.349337i
\(363\) −712.764 3397.05i −0.103059 0.491181i
\(364\) 2483.95 2805.59i 0.357678 0.403992i
\(365\) 3814.93 3247.58i 0.547075 0.465716i
\(366\) −953.896 + 200.145i −0.136232 + 0.0285840i
\(367\) −6905.34 −0.982168 −0.491084 0.871112i \(-0.663399\pi\)
−0.491084 + 0.871112i \(0.663399\pi\)
\(368\) 4799.42 0.679856
\(369\) −9213.15 + 4044.23i −1.29978 + 0.570553i
\(370\) −1332.70 1565.52i −0.187254 0.219967i
\(371\) 73.0550 82.5146i 0.0102233 0.0115470i
\(372\) −248.126 + 52.0614i −0.0345825 + 0.00725607i
\(373\) 11871.0i 1.64788i −0.566678 0.823939i \(-0.691772\pi\)
0.566678 0.823939i \(-0.308228\pi\)
\(374\) 1771.28 0.244895
\(375\) −5304.80 + 4959.18i −0.730504 + 0.682909i
\(376\) 9.02346i 0.00123763i
\(377\) 13095.7i 1.78902i
\(378\) −5799.99 606.618i −0.789204 0.0825425i
\(379\) −4071.94 −0.551877 −0.275938 0.961175i \(-0.588989\pi\)
−0.275938 + 0.961175i \(0.588989\pi\)
\(380\) −2353.99 2765.23i −0.317782 0.373298i
\(381\) −168.124 + 35.2757i −0.0226070 + 0.00474338i
\(382\) 3616.19i 0.484346i
\(383\) 9559.09i 1.27532i 0.770319 + 0.637659i \(0.220097\pi\)
−0.770319 + 0.637659i \(0.779903\pi\)
\(384\) 205.254 + 978.243i 0.0272768 + 0.130002i
\(385\) −5330.62 103.578i −0.705646 0.0137112i
\(386\) 4403.46i 0.580648i
\(387\) −2090.11 4761.48i −0.274538 0.625425i
\(388\) 1289.30 0.168696
\(389\) 6559.03i 0.854899i −0.904039 0.427450i \(-0.859412\pi\)
0.904039 0.427450i \(-0.140588\pi\)
\(390\) −7041.16 5450.47i −0.914212 0.707680i
\(391\) 4666.96i 0.603628i
\(392\) −1022.56 8377.20i −0.131752 1.07937i
\(393\) −1064.14 5071.69i −0.136587 0.650975i
\(394\) 1479.00 0.189115
\(395\) −10814.3 + 9206.02i −1.37753 + 1.17267i
\(396\) −827.904 1886.05i −0.105060 0.239337i
\(397\) 3903.80 0.493516 0.246758 0.969077i \(-0.420635\pi\)
0.246758 + 0.969077i \(0.420635\pi\)
\(398\) 11362.5i 1.43103i
\(399\) 5222.52 9167.01i 0.655271 1.15019i
\(400\) −628.961 + 3889.49i −0.0786201 + 0.486186i
\(401\) 3085.45i 0.384239i −0.981372 0.192120i \(-0.938464\pi\)
0.981372 0.192120i \(-0.0615362\pi\)
\(402\) 12328.5 2586.74i 1.52957 0.320933i
\(403\) 1124.64i 0.139013i
\(404\) −3325.42 −0.409519
\(405\) 311.953 8144.50i 0.0382742 0.999267i
\(406\) 5967.98 + 5283.80i 0.729522 + 0.645889i
\(407\) 2109.70 0.256938
\(408\) −3835.10 + 804.676i −0.465357 + 0.0976407i
\(409\) 254.304i 0.0307446i 0.999882 + 0.0153723i \(0.00489335\pi\)
−0.999882 + 0.0153723i \(0.995107\pi\)
\(410\) −7120.41 + 6061.48i −0.857688 + 0.730135i
\(411\) 1465.34 + 6983.82i 0.175863 + 0.838167i
\(412\) −1852.40 −0.221508
\(413\) −2440.79 + 2756.84i −0.290807 + 0.328463i
\(414\) −8448.85 + 3708.73i −1.00299 + 0.440275i
\(415\) −3114.51 3658.61i −0.368398 0.432756i
\(416\) 8611.05 1.01488
\(417\) −6924.57 + 1452.91i −0.813184 + 0.170621i
\(418\) −6335.64 −0.741355
\(419\) −1777.00 −0.207189 −0.103594 0.994620i \(-0.533034\pi\)
−0.103594 + 0.994620i \(0.533034\pi\)
\(420\) 3131.90 593.856i 0.363860 0.0689934i
\(421\) −6856.09 −0.793695 −0.396847 0.917885i \(-0.629896\pi\)
−0.396847 + 0.917885i \(0.629896\pi\)
\(422\) 7781.87 0.897667
\(423\) −3.98001 9.06686i −0.000457482 0.00104219i
\(424\) 146.413 0.0167699
\(425\) −3782.15 611.602i −0.431673 0.0698049i
\(426\) 8826.02 1851.86i 1.00381 0.210618i
\(427\) 1158.90 + 1026.04i 0.131342 + 0.116284i
\(428\) −2930.14 −0.330920
\(429\) 8942.26 1876.25i 1.00638 0.211157i
\(430\) −3132.65 3679.92i −0.351325 0.412701i
\(431\) 1425.61i 0.159325i 0.996822 + 0.0796625i \(0.0253842\pi\)
−0.996822 + 0.0796625i \(0.974616\pi\)
\(432\) −2571.07 3597.92i −0.286344 0.400706i
\(433\) 5863.42 0.650757 0.325379 0.945584i \(-0.394508\pi\)
0.325379 + 0.945584i \(0.394508\pi\)
\(434\) −512.523 453.767i −0.0566864 0.0501878i
\(435\) −6819.27 + 8809.44i −0.751630 + 0.970989i
\(436\) −2402.71 −0.263919
\(437\) 16693.1i 1.82732i
\(438\) 1073.13 + 5114.57i 0.117069 + 0.557954i
\(439\) 9688.48i 1.05332i 0.850077 + 0.526658i \(0.176555\pi\)
−0.850077 + 0.526658i \(0.823445\pi\)
\(440\) −4591.43 5393.55i −0.497473 0.584380i
\(441\) 4722.44 + 7966.47i 0.509928 + 0.860217i
\(442\) 4697.79i 0.505546i
\(443\) 17681.9 1.89637 0.948185 0.317719i \(-0.102917\pi\)
0.948185 + 0.317719i \(0.102917\pi\)
\(444\) −1234.48 + 259.017i −0.131950 + 0.0276856i
\(445\) 45.0877 38.3824i 0.00480306 0.00408876i
\(446\) 4594.42 0.487785
\(447\) −15112.5 + 3170.88i −1.59910 + 0.335520i
\(448\) 6570.10 7420.84i 0.692875 0.782593i
\(449\) 5275.90i 0.554533i 0.960793 + 0.277266i \(0.0894285\pi\)
−0.960793 + 0.277266i \(0.910572\pi\)
\(450\) −1898.37 7333.05i −0.198867 0.768185i
\(451\) 9595.45i 1.00185i
\(452\) 319.119 0.0332082
\(453\) −1553.90 7405.92i −0.161167 0.768125i
\(454\) 8974.08i 0.927697i
\(455\) −274.709 + 14137.8i −0.0283045 + 1.45669i
\(456\) 13717.6 2878.22i 1.40874 0.295581i
\(457\) 696.329i 0.0712755i −0.999365 0.0356378i \(-0.988654\pi\)
0.999365 0.0356378i \(-0.0113463\pi\)
\(458\) 7463.92i 0.761498i
\(459\) 3498.63 2500.11i 0.355777 0.254238i
\(460\) 3840.57 3269.41i 0.389277 0.331385i
\(461\) 7690.68 0.776986 0.388493 0.921452i \(-0.372996\pi\)
0.388493 + 0.921452i \(0.372996\pi\)
\(462\) 2752.95 4832.22i 0.277227 0.486613i
\(463\) 4517.49i 0.453446i 0.973959 + 0.226723i \(0.0728012\pi\)
−0.973959 + 0.226723i \(0.927199\pi\)
\(464\) 6044.38i 0.604749i
\(465\) 585.631 756.544i 0.0584042 0.0754492i
\(466\) −7775.73 −0.772970
\(467\) 17707.4i 1.75461i 0.479934 + 0.877304i \(0.340661\pi\)
−0.479934 + 0.877304i \(0.659339\pi\)
\(468\) −5002.17 + 2195.76i −0.494071 + 0.216879i
\(469\) −14977.9 13260.8i −1.47466 1.30560i
\(470\) −5.96524 7.00735i −0.000585438 0.000687713i
\(471\) −3097.70 14763.7i −0.303045 1.44432i
\(472\) −4891.71 −0.477032
\(473\) 4959.05 0.482067
\(474\) −3042.04 14498.4i −0.294780 1.40493i
\(475\) 13528.2 + 2187.62i 1.30677 + 0.211315i
\(476\) 1259.20 + 1114.84i 0.121251 + 0.107350i
\(477\) −147.118 + 64.5791i −0.0141217 + 0.00619890i
\(478\) 10143.6i 0.970624i
\(479\) −12707.4 −1.21214 −0.606072 0.795410i \(-0.707256\pi\)
−0.606072 + 0.795410i \(0.707256\pi\)
\(480\) 5792.65 + 4484.01i 0.550827 + 0.426388i
\(481\) 5595.33i 0.530406i
\(482\) 15906.3i 1.50313i
\(483\) 12731.9 + 7253.45i 1.19942 + 0.683320i
\(484\) −1979.11 −0.185867
\(485\) −3704.75 + 3153.79i −0.346854 + 0.295271i
\(486\) 7306.36 + 4346.97i 0.681941 + 0.405725i
\(487\) 224.275i 0.0208684i −0.999946 0.0104342i \(-0.996679\pi\)
0.999946 0.0104342i \(-0.00332136\pi\)
\(488\) 2056.33i 0.190750i
\(489\) 8475.38 1778.29i 0.783783 0.164452i
\(490\) 6332.10 + 5829.50i 0.583786 + 0.537448i
\(491\) 6605.29i 0.607113i 0.952813 + 0.303557i \(0.0981742\pi\)
−0.952813 + 0.303557i \(0.901826\pi\)
\(492\) 1178.08 + 5614.74i 0.107951 + 0.514496i
\(493\) −5877.57 −0.536942
\(494\) 16803.4i 1.53040i
\(495\) 6992.47 + 3394.33i 0.634926 + 0.308210i
\(496\) 519.084i 0.0469911i
\(497\) −10722.8 9493.51i −0.967773 0.856826i
\(498\) 4905.00 1029.16i 0.441362 0.0926060i
\(499\) 14083.4 1.26344 0.631722 0.775195i \(-0.282349\pi\)
0.631722 + 0.775195i \(0.282349\pi\)
\(500\) 2146.26 + 3540.89i 0.191967 + 0.316707i
\(501\) 8586.81 1801.67i 0.765729 0.160664i
\(502\) 10659.0 0.947682
\(503\) 23.1056i 0.00204816i −0.999999 0.00102408i \(-0.999674\pi\)
0.999999 0.00102408i \(-0.000325975\pi\)
\(504\) −3765.33 + 11713.1i −0.332780 + 1.03521i
\(505\) 9555.46 8134.40i 0.842005 0.716784i
\(506\) 8799.44i 0.773088i
\(507\) −2631.96 12544.0i −0.230551 1.09881i
\(508\) 97.9487i 0.00855467i
\(509\) 3934.85 0.342650 0.171325 0.985215i \(-0.445195\pi\)
0.171325 + 0.985215i \(0.445195\pi\)
\(510\) 2446.27 3160.20i 0.212397 0.274384i
\(511\) 5501.38 6213.74i 0.476256 0.537925i
\(512\) 10178.8 0.878602
\(513\) −12514.1 + 8942.55i −1.07702 + 0.769636i
\(514\) 3526.67i 0.302636i
\(515\) 5322.81 4531.21i 0.455438 0.387707i
\(516\) −2901.77 + 608.845i −0.247564 + 0.0519437i
\(517\) 9.44309 0.000803301
\(518\) −2549.92 2257.59i −0.216288 0.191492i
\(519\) −3659.81 + 767.897i −0.309533 + 0.0649459i
\(520\) −14304.7 + 12177.4i −1.20635 + 1.02695i
\(521\) −8113.65 −0.682275 −0.341138 0.940013i \(-0.610812\pi\)
−0.341138 + 0.940013i \(0.610812\pi\)
\(522\) −4670.77 10640.5i −0.391636 0.892186i
\(523\) 5518.74 0.461410 0.230705 0.973024i \(-0.425897\pi\)
0.230705 + 0.973024i \(0.425897\pi\)
\(524\) −2954.75 −0.246334
\(525\) −7546.76 + 9367.47i −0.627367 + 0.778724i
\(526\) 12188.1 1.01031
\(527\) 504.759 0.0417223
\(528\) 4127.36 865.998i 0.340190 0.0713782i
\(529\) 11017.7 0.905537
\(530\) −113.700 + 96.7911i −0.00931854 + 0.00793271i
\(531\) 4915.24 2157.61i 0.401701 0.176332i
\(532\) −4503.99 3987.64i −0.367054 0.324974i
\(533\) −25449.0 −2.06814
\(534\) 12.6831 + 60.4478i 0.00102781 + 0.00489857i
\(535\) 8419.65 7167.50i 0.680398 0.579211i
\(536\) 26576.7i 2.14168i
\(537\) −5751.22 + 1206.72i −0.462167 + 0.0969713i
\(538\) −11487.7 −0.920575
\(539\) −8766.78 + 1070.11i −0.700579 + 0.0855156i
\(540\) −4508.35 1127.68i −0.359275 0.0898659i
\(541\) 3915.43 0.311160 0.155580 0.987823i \(-0.450275\pi\)
0.155580 + 0.987823i \(0.450275\pi\)
\(542\) 14095.4i 1.11706i
\(543\) −5451.76 + 1143.88i −0.430861 + 0.0904027i
\(544\) 3864.80i 0.304599i
\(545\) 6904.09 5877.33i 0.542640 0.461940i
\(546\) −12816.0 7301.36i −1.00453 0.572289i
\(547\) 5022.18i 0.392564i 0.980547 + 0.196282i \(0.0628869\pi\)
−0.980547 + 0.196282i \(0.937113\pi\)
\(548\) 4068.75 0.317169
\(549\) −906.996 2066.23i −0.0705093 0.160627i
\(550\) 7131.14 + 1153.16i 0.552860 + 0.0894017i
\(551\) 21023.3 1.62545
\(552\) 3997.49 + 19052.1i 0.308233 + 1.46904i
\(553\) −15594.9 + 17614.3i −1.19921 + 1.35449i
\(554\) 13034.3i 0.999590i
\(555\) 2913.64 3763.97i 0.222842 0.287877i
\(556\) 4034.23i 0.307715i
\(557\) 13585.5 1.03346 0.516729 0.856149i \(-0.327149\pi\)
0.516729 + 0.856149i \(0.327149\pi\)
\(558\) 401.120 + 913.791i 0.0304315 + 0.0693259i
\(559\) 13152.4i 0.995146i
\(560\) −126.794 + 6525.42i −0.00956787 + 0.492409i
\(561\) 842.097 + 4013.45i 0.0633750 + 0.302046i
\(562\) 451.247i 0.0338696i
\(563\) 12293.5i 0.920267i 0.887850 + 0.460133i \(0.152198\pi\)
−0.887850 + 0.460133i \(0.847802\pi\)
\(564\) −5.52558 + 1.15937i −0.000412534 + 8.65573e-5i
\(565\) −916.978 + 780.608i −0.0682789 + 0.0581246i
\(566\) −10792.7 −0.801502
\(567\) −1382.91 13430.3i −0.102428 0.994740i
\(568\) 19026.4i 1.40551i
\(569\) 10764.9i 0.793123i −0.918008 0.396562i \(-0.870203\pi\)
0.918008 0.396562i \(-0.129797\pi\)
\(570\) −8749.97 + 11303.6i −0.642975 + 0.830624i
\(571\) 14290.9 1.04738 0.523690 0.851909i \(-0.324555\pi\)
0.523690 + 0.851909i \(0.324555\pi\)
\(572\) 5209.73i 0.380822i
\(573\) 8193.72 1719.20i 0.597378 0.125341i
\(574\) −10268.1 + 11597.7i −0.746660 + 0.843342i
\(575\) −3038.34 + 18789.1i −0.220361 + 1.36271i
\(576\) −13230.8 + 5807.83i −0.957090 + 0.420127i
\(577\) 25946.6 1.87205 0.936024 0.351937i \(-0.114477\pi\)
0.936024 + 0.351937i \(0.114477\pi\)
\(578\) −8918.20 −0.641779
\(579\) 9977.55 2093.48i 0.716153 0.150262i
\(580\) 4117.49 + 4836.81i 0.294775 + 0.346272i
\(581\) −5959.12 5275.95i −0.425518 0.376736i
\(582\) −1042.14 4966.86i −0.0742236 0.353751i
\(583\) 153.222i 0.0108848i
\(584\) 11025.6 0.781237
\(585\) 9002.42 18545.4i 0.636247 1.31070i
\(586\) 15040.6i 1.06027i
\(587\) 18044.2i 1.26876i 0.773020 + 0.634382i \(0.218745\pi\)
−0.773020 + 0.634382i \(0.781255\pi\)
\(588\) 4998.46 1702.51i 0.350566 0.119405i
\(589\) −1805.45 −0.126303
\(590\) 3798.76 3233.82i 0.265072 0.225651i
\(591\) 703.143 + 3351.19i 0.0489398 + 0.233248i
\(592\) 2582.56i 0.179295i
\(593\) 14485.3i 1.00310i −0.865129 0.501550i \(-0.832763\pi\)
0.865129 0.501550i \(-0.167237\pi\)
\(594\) −6596.57 + 4713.89i −0.455658 + 0.325612i
\(595\) −6345.32 123.294i −0.437198 0.00849508i
\(596\) 8804.48i 0.605110i
\(597\) 25745.7 5401.92i 1.76499 0.370328i
\(598\) −23337.8 −1.59591
\(599\) 2982.21i 0.203422i 0.994814 + 0.101711i \(0.0324317\pi\)
−0.994814 + 0.101711i \(0.967568\pi\)
\(600\) −15963.9 + 742.836i −1.08620 + 0.0505436i
\(601\) 15274.2i 1.03668i 0.855174 + 0.518341i \(0.173450\pi\)
−0.855174 + 0.518341i \(0.826550\pi\)
\(602\) −5993.84 5306.69i −0.405798 0.359277i
\(603\) 11722.3 + 26704.6i 0.791657 + 1.80347i
\(604\) −4314.67 −0.290664
\(605\) 5686.90 4841.16i 0.382157 0.325324i
\(606\) 2687.94 + 12810.8i 0.180182 + 0.858748i
\(607\) −14554.3 −0.973214 −0.486607 0.873621i \(-0.661766\pi\)
−0.486607 + 0.873621i \(0.661766\pi\)
\(608\) 13823.8i 0.922090i
\(609\) −9134.99 + 16034.5i −0.607830 + 1.06692i
\(610\) −1359.40 1596.89i −0.0902306 0.105994i
\(611\) 25.0449i 0.00165828i
\(612\) −985.499 2245.06i −0.0650922 0.148287i
\(613\) 18176.4i 1.19761i −0.800893 0.598807i \(-0.795642\pi\)
0.800893 0.598807i \(-0.204358\pi\)
\(614\) 3312.98 0.217754
\(615\) −17119.5 13252.0i −1.12248 0.868899i
\(616\) −8784.98 7777.85i −0.574605 0.508731i
\(617\) 7001.54 0.456842 0.228421 0.973562i \(-0.426644\pi\)
0.228421 + 0.973562i \(0.426644\pi\)
\(618\) 1497.30 + 7136.14i 0.0974597 + 0.464495i
\(619\) 382.714i 0.0248507i −0.999923 0.0124253i \(-0.996045\pi\)
0.999923 0.0124253i \(-0.00395521\pi\)
\(620\) −353.605 415.380i −0.0229051 0.0269065i
\(621\) −12420.1 17380.6i −0.802580 1.12312i
\(622\) −4852.36 −0.312801
\(623\) 65.0194 73.4386i 0.00418130 0.00472272i
\(624\) −2296.80 10946.6i −0.147348 0.702265i
\(625\) −14828.7 4924.59i −0.949034 0.315174i
\(626\) −2665.95 −0.170212
\(627\) −3012.07 14355.6i −0.191851 0.914364i
\(628\) −8601.27 −0.546542
\(629\) 2511.29 0.159192
\(630\) −4819.28 11585.3i −0.304769 0.732647i
\(631\) −20481.5 −1.29217 −0.646083 0.763267i \(-0.723594\pi\)
−0.646083 + 0.763267i \(0.723594\pi\)
\(632\) −31254.6 −1.96715
\(633\) 3699.63 + 17632.5i 0.232302 + 1.10715i
\(634\) 9607.55 0.601837
\(635\) −239.595 281.452i −0.0149733 0.0175891i
\(636\) 18.8118 + 89.6573i 0.00117286 + 0.00558985i
\(637\) 2838.14 + 23251.2i 0.176533 + 1.44623i
\(638\) 11082.0 0.687682
\(639\) 8392.07 + 19118.0i 0.519538 + 1.18356i
\(640\) −1637.65 + 1394.10i −0.101146 + 0.0861042i
\(641\) 28510.2i 1.75676i 0.477962 + 0.878380i \(0.341376\pi\)
−0.477962 + 0.878380i \(0.658624\pi\)
\(642\) 2368.43 + 11288.0i 0.145599 + 0.693928i
\(643\) 1013.84 0.0621802 0.0310901 0.999517i \(-0.490102\pi\)
0.0310901 + 0.999517i \(0.490102\pi\)
\(644\) 5538.36 6255.50i 0.338885 0.382766i
\(645\) 6848.81 8847.60i 0.418096 0.540114i
\(646\) −7541.65 −0.459322
\(647\) 9793.59i 0.595094i −0.954707 0.297547i \(-0.903832\pi\)
0.954707 0.297547i \(-0.0961685\pi\)
\(648\) 12141.1 13203.1i 0.736031 0.800409i
\(649\) 5119.20i 0.309624i
\(650\) 3058.41 18913.2i 0.184555 1.14129i
\(651\) 784.502 1377.03i 0.0472305 0.0829030i
\(652\) 4937.73i 0.296590i
\(653\) 9713.50 0.582111 0.291056 0.956706i \(-0.405994\pi\)
0.291056 + 0.956706i \(0.405994\pi\)
\(654\) 1942.11 + 9256.13i 0.116120 + 0.553430i
\(655\) 8490.38 7227.71i 0.506483 0.431160i
\(656\) −11746.2 −0.699101
\(657\) −11078.6 + 4863.11i −0.657867 + 0.288779i
\(658\) −11.4135 10.1051i −0.000676210 0.000598688i
\(659\) 14730.6i 0.870745i −0.900250 0.435373i \(-0.856617\pi\)
0.900250 0.435373i \(-0.143383\pi\)
\(660\) 2712.85 3504.58i 0.159996 0.206691i
\(661\) 23656.2i 1.39201i 0.718036 + 0.696006i \(0.245041\pi\)
−0.718036 + 0.696006i \(0.754959\pi\)
\(662\) −11166.3 −0.655575
\(663\) 10644.5 2233.41i 0.623524 0.130827i
\(664\) 10573.8i 0.617987i
\(665\) 22696.4 + 441.007i 1.32350 + 0.0257166i
\(666\) 1995.66 + 4546.32i 0.116112 + 0.264514i
\(667\) 29198.8i 1.69502i
\(668\) 5002.65i 0.289758i
\(669\) 2184.27 + 10410.2i 0.126231 + 0.601619i
\(670\) 17569.4 + 20638.7i 1.01308 + 1.19006i
\(671\) 2151.96 0.123809
\(672\) 10543.5 + 6006.71i 0.605245 + 0.344813i
\(673\) 23206.9i 1.32921i −0.747194 0.664606i \(-0.768600\pi\)
0.747194 0.664606i \(-0.231400\pi\)
\(674\) 18472.7i 1.05570i
\(675\) 15713.0 7787.66i 0.895992 0.444070i
\(676\) −7308.08 −0.415799
\(677\) 2008.10i 0.113999i 0.998374 + 0.0569997i \(0.0181534\pi\)
−0.998374 + 0.0569997i \(0.981847\pi\)
\(678\) −257.945 1229.37i −0.0146111 0.0696366i
\(679\) −5342.50 + 6034.28i −0.301953 + 0.341052i
\(680\) −5465.43 6420.23i −0.308220 0.362065i
\(681\) −20333.8 + 4266.42i −1.14419 + 0.240073i
\(682\) −951.709 −0.0534352
\(683\) 9344.15 0.523491 0.261745 0.965137i \(-0.415702\pi\)
0.261745 + 0.965137i \(0.415702\pi\)
\(684\) 3524.99 + 8030.29i 0.197049 + 0.448897i
\(685\) −11691.4 + 9952.70i −0.652125 + 0.555143i
\(686\) 11741.2 + 8087.94i 0.653473 + 0.450144i
\(687\) −16912.1 + 3548.47i −0.939208 + 0.197063i
\(688\) 6070.57i 0.336393i
\(689\) −406.375 −0.0224698
\(690\) −15699.3 12152.7i −0.866179 0.670498i
\(691\) 28869.6i 1.58937i −0.607025 0.794683i \(-0.707637\pi\)
0.607025 0.794683i \(-0.292363\pi\)
\(692\) 2132.19i 0.117130i
\(693\) 12257.8 + 3940.44i 0.671915 + 0.215996i
\(694\) 1939.81 0.106101
\(695\) −9868.26 11592.2i −0.538596 0.632688i
\(696\) −23994.2 + 5034.44i −1.30675 + 0.274181i
\(697\) 11422.0i 0.620715i
\(698\) 10799.5i 0.585627i
\(699\) −3696.71 17618.6i −0.200032 0.953357i
\(700\) 4343.72 + 5308.11i 0.234539 + 0.286611i
\(701\) 3198.20i 0.172317i −0.996281 0.0861585i \(-0.972541\pi\)
0.996281 0.0861585i \(-0.0274592\pi\)
\(702\) 12502.2 + 17495.4i 0.672171 + 0.940628i
\(703\) −8982.53 −0.481910
\(704\) 13779.8i 0.737709i
\(705\) 13.0416 16.8477i 0.000696702 0.000900030i
\(706\) 2707.84i 0.144350i
\(707\) 13779.6 15563.9i 0.733007 0.827921i
\(708\) −628.507 2995.48i −0.0333626 0.159007i
\(709\) −5643.25 −0.298923 −0.149462 0.988768i \(-0.547754\pi\)
−0.149462 + 0.988768i \(0.547754\pi\)
\(710\) 12578.0 + 14775.4i 0.664852 + 0.781000i
\(711\) 31404.9 13785.6i 1.65651 0.727145i
\(712\) 130.309 0.00685889
\(713\) 2507.55i 0.131709i
\(714\) 3276.99 5752.05i 0.171762 0.301492i
\(715\) 12743.7 + 14970.0i 0.666555 + 0.783001i
\(716\) 3350.65i 0.174888i
\(717\) −22983.9 + 4822.44i −1.19714 + 0.251182i
\(718\) 17033.8i 0.885372i
\(719\) −31212.4 −1.61895 −0.809475 0.587154i \(-0.800248\pi\)
−0.809475 + 0.587154i \(0.800248\pi\)
\(720\) 4155.13 8559.75i 0.215073 0.443060i
\(721\) 7675.84 8669.76i 0.396482 0.447821i
\(722\) 11581.2 0.596965
\(723\) −36041.1 + 7562.10i −1.85392 + 0.388987i
\(724\) 3176.18i 0.163041i
\(725\) −23662.9 3826.48i −1.21217 0.196016i
\(726\) 1599.71 + 7624.27i 0.0817782 + 0.389756i
\(727\) 34019.5 1.73551 0.867753 0.496995i \(-0.165563\pi\)
0.867753 + 0.496995i \(0.165563\pi\)
\(728\) −20628.4 + 23299.5i −1.05019 + 1.18618i
\(729\) −6375.99 + 18621.7i −0.323934 + 0.946080i
\(730\) −8562.16 + 7288.82i −0.434109 + 0.369550i
\(731\) 5903.03 0.298675
\(732\) −1259.21 + 264.206i −0.0635817 + 0.0133406i
\(733\) 7823.52 0.394227 0.197113 0.980381i \(-0.436843\pi\)
0.197113 + 0.980381i \(0.436843\pi\)
\(734\) 15498.2 0.779359
\(735\) −10198.3 + 17119.0i −0.511798 + 0.859106i
\(736\) 19199.7 0.961561
\(737\) −27812.7 −1.39009
\(738\) 20677.8 9076.79i 1.03138 0.452739i
\(739\) 14767.9 0.735107 0.367554 0.930002i \(-0.380195\pi\)
0.367554 + 0.930002i \(0.380195\pi\)
\(740\) −1759.27 2066.61i −0.0873945 0.102662i
\(741\) −38073.8 + 7988.59i −1.88755 + 0.396043i
\(742\) −163.963 + 185.194i −0.00811224 + 0.00916267i
\(743\) −13145.6 −0.649077 −0.324539 0.945872i \(-0.605209\pi\)
−0.324539 + 0.945872i \(0.605209\pi\)
\(744\) 2060.60 432.352i 0.101539 0.0213048i
\(745\) −21536.9 25299.4i −1.05913 1.24416i
\(746\) 26643.1i 1.30761i
\(747\) 4663.83 + 10624.7i 0.228435 + 0.520397i
\(748\) 2338.22 0.114297
\(749\) 12141.7 13713.9i 0.592320 0.669018i
\(750\) 11906.0 11130.3i 0.579661 0.541894i
\(751\) 326.336 0.0158564 0.00792821 0.999969i \(-0.497476\pi\)
0.00792821 + 0.999969i \(0.497476\pi\)
\(752\) 11.5596i 0.000560555i
\(753\) 5067.48 + 24151.7i 0.245245 + 1.16884i
\(754\) 29391.7i 1.41960i
\(755\) 12398.0 10554.2i 0.597630 0.508752i
\(756\) −7656.41 800.780i −0.368334 0.0385239i
\(757\) 361.891i 0.0173754i 0.999962 + 0.00868769i \(0.00276541\pi\)
−0.999962 + 0.00868769i \(0.997235\pi\)
\(758\) 9138.98 0.437919
\(759\) 19938.1 4183.40i 0.953503 0.200063i
\(760\) 19549.1 + 22964.3i 0.933052 + 1.09605i
\(761\) −31708.0 −1.51040 −0.755199 0.655495i \(-0.772460\pi\)
−0.755199 + 0.655495i \(0.772460\pi\)
\(762\) 377.335 79.1721i 0.0179389 0.00376391i
\(763\) 9956.16 11245.4i 0.472395 0.533564i
\(764\) 4773.63i 0.226052i
\(765\) 8323.51 + 4040.45i 0.393382 + 0.190958i
\(766\) 21454.3i 1.01198i
\(767\) 13577.1 0.639167
\(768\) 4107.55 + 19576.7i 0.192993 + 0.919808i
\(769\) 4392.75i 0.205990i −0.994682 0.102995i \(-0.967157\pi\)
0.994682 0.102995i \(-0.0328426\pi\)
\(770\) 11963.9 + 232.468i 0.559936 + 0.0108800i
\(771\) 7990.89 1676.64i 0.373262 0.0783173i
\(772\) 5812.89i 0.270998i
\(773\) 11252.2i 0.523563i 0.965127 + 0.261782i \(0.0843100\pi\)
−0.965127 + 0.261782i \(0.915690\pi\)
\(774\) 4691.00 + 10686.6i 0.217848 + 0.496280i
\(775\) 2032.14 + 328.613i 0.0941894 + 0.0152312i
\(776\) −10707.2 −0.495316
\(777\) 3903.07 6851.01i 0.180208 0.316317i
\(778\) 14721.0i 0.678370i
\(779\) 40854.9i