Properties

Label 105.4.g.b.104.2
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 104.2
Character \(\chi\) \(=\) 105.104
Dual form 105.4.g.b.104.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.11138 q^{2} +(-1.51783 + 4.96953i) q^{3} +18.1262 q^{4} +(-10.9509 - 2.25323i) q^{5} +(7.75821 - 25.4011i) q^{6} +(-11.4695 + 14.5413i) q^{7} -51.7589 q^{8} +(-22.3924 - 15.0858i) q^{9} +O(q^{10})\) \(q-5.11138 q^{2} +(-1.51783 + 4.96953i) q^{3} +18.1262 q^{4} +(-10.9509 - 2.25323i) q^{5} +(7.75821 - 25.4011i) q^{6} +(-11.4695 + 14.5413i) q^{7} -51.7589 q^{8} +(-22.3924 - 15.0858i) q^{9} +(55.9744 + 11.5171i) q^{10} +55.4308i q^{11} +(-27.5125 + 90.0786i) q^{12} -20.9550 q^{13} +(58.6250 - 74.3263i) q^{14} +(27.8192 - 51.0009i) q^{15} +119.550 q^{16} -96.8237i q^{17} +(114.456 + 77.1093i) q^{18} -33.1970i q^{19} +(-198.499 - 40.8425i) q^{20} +(-54.8548 - 79.0693i) q^{21} -283.328i q^{22} +111.288 q^{23} +(78.5612 - 257.217i) q^{24} +(114.846 + 49.3500i) q^{25} +107.109 q^{26} +(108.957 - 88.3818i) q^{27} +(-207.899 + 263.579i) q^{28} -156.784i q^{29} +(-142.194 + 260.685i) q^{30} +80.4962i q^{31} -196.992 q^{32} +(-275.465 - 84.1346i) q^{33} +494.903i q^{34} +(158.367 - 133.398i) q^{35} +(-405.889 - 273.448i) q^{36} -180.365i q^{37} +169.683i q^{38} +(31.8061 - 104.136i) q^{39} +(566.808 + 116.625i) q^{40} +36.5837 q^{41} +(280.384 + 404.153i) q^{42} +52.5826i q^{43} +1004.75i q^{44} +(211.226 + 215.659i) q^{45} -568.835 q^{46} +259.660i q^{47} +(-181.456 + 594.105i) q^{48} +(-79.9009 - 333.564i) q^{49} +(-587.021 - 252.247i) q^{50} +(481.168 + 146.962i) q^{51} -379.834 q^{52} -191.690 q^{53} +(-556.921 + 451.753i) q^{54} +(124.898 - 607.019i) q^{55} +(593.648 - 752.643i) q^{56} +(164.973 + 50.3875i) q^{57} +801.380i q^{58} -705.237 q^{59} +(504.256 - 924.453i) q^{60} -427.079i q^{61} -411.447i q^{62} +(476.197 - 152.588i) q^{63} +50.5057 q^{64} +(229.476 + 47.2164i) q^{65} +(1408.00 + 430.044i) q^{66} -306.444i q^{67} -1755.05i q^{68} +(-168.916 + 553.048i) q^{69} +(-809.473 + 681.846i) q^{70} -513.791i q^{71} +(1159.00 + 780.824i) q^{72} -360.633 q^{73} +921.916i q^{74} +(-419.563 + 495.825i) q^{75} -601.736i q^{76} +(-806.038 - 635.764i) q^{77} +(-162.573 + 532.280i) q^{78} +85.9838 q^{79} +(-1309.18 - 269.373i) q^{80} +(273.837 + 675.614i) q^{81} -186.993 q^{82} +886.893i q^{83} +(-994.309 - 1433.23i) q^{84} +(-218.166 + 1060.31i) q^{85} -268.770i q^{86} +(779.140 + 237.971i) q^{87} -2869.03i q^{88} +1417.80 q^{89} +(-1079.65 - 1102.31i) q^{90} +(240.343 - 304.713i) q^{91} +2017.23 q^{92} +(-400.028 - 122.180i) q^{93} -1327.22i q^{94} +(-74.8006 + 363.538i) q^{95} +(299.001 - 978.958i) q^{96} +1055.44 q^{97} +(408.404 + 1704.97i) q^{98} +(836.218 - 1241.23i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.11138 −1.80715 −0.903573 0.428435i \(-0.859065\pi\)
−0.903573 + 0.428435i \(0.859065\pi\)
\(3\) −1.51783 + 4.96953i −0.292107 + 0.956386i
\(4\) 18.1262 2.26578
\(5\) −10.9509 2.25323i −0.979481 0.201535i
\(6\) 7.75821 25.4011i 0.527879 1.72833i
\(7\) −11.4695 + 14.5413i −0.619295 + 0.785158i
\(8\) −51.7589 −2.28744
\(9\) −22.3924 15.0858i −0.829347 0.558733i
\(10\) 55.9744 + 11.5171i 1.77007 + 0.364204i
\(11\) 55.4308i 1.51936i 0.650294 + 0.759682i \(0.274646\pi\)
−0.650294 + 0.759682i \(0.725354\pi\)
\(12\) −27.5125 + 90.0786i −0.661848 + 2.16695i
\(13\) −20.9550 −0.447066 −0.223533 0.974696i \(-0.571759\pi\)
−0.223533 + 0.974696i \(0.571759\pi\)
\(14\) 58.6250 74.3263i 1.11916 1.41890i
\(15\) 27.8192 51.0009i 0.478859 0.877892i
\(16\) 119.550 1.86796
\(17\) 96.8237i 1.38136i −0.723158 0.690682i \(-0.757310\pi\)
0.723158 0.690682i \(-0.242690\pi\)
\(18\) 114.456 + 77.1093i 1.49875 + 1.00971i
\(19\) 33.1970i 0.400838i −0.979710 0.200419i \(-0.935770\pi\)
0.979710 0.200419i \(-0.0642303\pi\)
\(20\) −198.499 40.8425i −2.21928 0.456634i
\(21\) −54.8548 79.0693i −0.570014 0.821635i
\(22\) 283.328i 2.74571i
\(23\) 111.288 1.00892 0.504460 0.863435i \(-0.331692\pi\)
0.504460 + 0.863435i \(0.331692\pi\)
\(24\) 78.5612 257.217i 0.668177 2.18767i
\(25\) 114.846 + 49.3500i 0.918767 + 0.394800i
\(26\) 107.109 0.807914
\(27\) 108.957 88.3818i 0.776623 0.629966i
\(28\) −207.899 + 263.579i −1.40318 + 1.77899i
\(29\) 156.784i 1.00393i −0.864888 0.501965i \(-0.832611\pi\)
0.864888 0.501965i \(-0.167389\pi\)
\(30\) −142.194 + 260.685i −0.865367 + 1.58648i
\(31\) 80.4962i 0.466372i 0.972432 + 0.233186i \(0.0749152\pi\)
−0.972432 + 0.233186i \(0.925085\pi\)
\(32\) −196.992 −1.08824
\(33\) −275.465 84.1346i −1.45310 0.443817i
\(34\) 494.903i 2.49633i
\(35\) 158.367 133.398i 0.764825 0.644238i
\(36\) −405.889 273.448i −1.87911 1.26596i
\(37\) 180.365i 0.801402i −0.916209 0.400701i \(-0.868767\pi\)
0.916209 0.400701i \(-0.131233\pi\)
\(38\) 169.683i 0.724372i
\(39\) 31.8061 104.136i 0.130591 0.427568i
\(40\) 566.808 + 116.625i 2.24050 + 0.461000i
\(41\) 36.5837 0.139351 0.0696757 0.997570i \(-0.477804\pi\)
0.0696757 + 0.997570i \(0.477804\pi\)
\(42\) 280.384 + 404.153i 1.03010 + 1.48481i
\(43\) 52.5826i 0.186483i 0.995644 + 0.0932416i \(0.0297229\pi\)
−0.995644 + 0.0932416i \(0.970277\pi\)
\(44\) 1004.75i 3.44254i
\(45\) 211.226 + 215.659i 0.699726 + 0.714412i
\(46\) −568.835 −1.82326
\(47\) 259.660i 0.805858i 0.915231 + 0.402929i \(0.132008\pi\)
−0.915231 + 0.402929i \(0.867992\pi\)
\(48\) −181.456 + 594.105i −0.545644 + 1.78649i
\(49\) −79.9009 333.564i −0.232947 0.972489i
\(50\) −587.021 252.247i −1.66035 0.713461i
\(51\) 481.168 + 146.962i 1.32112 + 0.403506i
\(52\) −379.834 −1.01295
\(53\) −191.690 −0.496804 −0.248402 0.968657i \(-0.579905\pi\)
−0.248402 + 0.968657i \(0.579905\pi\)
\(54\) −556.921 + 451.753i −1.40347 + 1.13844i
\(55\) 124.898 607.019i 0.306206 1.48819i
\(56\) 593.648 752.643i 1.41660 1.79600i
\(57\) 164.973 + 50.3875i 0.383356 + 0.117087i
\(58\) 801.380i 1.81425i
\(59\) −705.237 −1.55617 −0.778085 0.628159i \(-0.783809\pi\)
−0.778085 + 0.628159i \(0.783809\pi\)
\(60\) 504.256 924.453i 1.08499 1.98911i
\(61\) 427.079i 0.896423i −0.893928 0.448212i \(-0.852061\pi\)
0.893928 0.448212i \(-0.147939\pi\)
\(62\) 411.447i 0.842803i
\(63\) 476.197 152.588i 0.952305 0.305148i
\(64\) 50.5057 0.0986440
\(65\) 229.476 + 47.2164i 0.437893 + 0.0900996i
\(66\) 1408.00 + 430.044i 2.62596 + 0.802041i
\(67\) 306.444i 0.558777i −0.960178 0.279388i \(-0.909868\pi\)
0.960178 0.279388i \(-0.0901317\pi\)
\(68\) 1755.05i 3.12986i
\(69\) −168.916 + 553.048i −0.294712 + 0.964916i
\(70\) −809.473 + 681.846i −1.38215 + 1.16423i
\(71\) 513.791i 0.858814i −0.903111 0.429407i \(-0.858723\pi\)
0.903111 0.429407i \(-0.141277\pi\)
\(72\) 1159.00 + 780.824i 1.89708 + 1.27807i
\(73\) −360.633 −0.578204 −0.289102 0.957298i \(-0.593357\pi\)
−0.289102 + 0.957298i \(0.593357\pi\)
\(74\) 921.916i 1.44825i
\(75\) −419.563 + 495.825i −0.645959 + 0.763372i
\(76\) 601.736i 0.908208i
\(77\) −806.038 635.764i −1.19294 0.940935i
\(78\) −162.573 + 532.280i −0.235997 + 0.772677i
\(79\) 85.9838 0.122455 0.0612274 0.998124i \(-0.480499\pi\)
0.0612274 + 0.998124i \(0.480499\pi\)
\(80\) −1309.18 269.373i −1.82963 0.376460i
\(81\) 273.837 + 675.614i 0.375634 + 0.926768i
\(82\) −186.993 −0.251828
\(83\) 886.893i 1.17288i 0.809992 + 0.586440i \(0.199471\pi\)
−0.809992 + 0.586440i \(0.800529\pi\)
\(84\) −994.309 1433.23i −1.29152 1.86164i
\(85\) −218.166 + 1060.31i −0.278394 + 1.35302i
\(86\) 268.770i 0.337002i
\(87\) 779.140 + 237.971i 0.960145 + 0.293255i
\(88\) 2869.03i 3.47545i
\(89\) 1417.80 1.68861 0.844305 0.535863i \(-0.180014\pi\)
0.844305 + 0.535863i \(0.180014\pi\)
\(90\) −1079.65 1102.31i −1.26451 1.29105i
\(91\) 240.343 304.713i 0.276866 0.351018i
\(92\) 2017.23 2.28598
\(93\) −400.028 122.180i −0.446032 0.136231i
\(94\) 1327.22i 1.45630i
\(95\) −74.8006 + 363.538i −0.0807830 + 0.392613i
\(96\) 299.001 978.958i 0.317882 1.04078i
\(97\) 1055.44 1.10478 0.552392 0.833584i \(-0.313715\pi\)
0.552392 + 0.833584i \(0.313715\pi\)
\(98\) 408.404 + 1704.97i 0.420970 + 1.75743i
\(99\) 836.218 1241.23i 0.848920 1.26008i
\(100\) 2081.72 + 894.528i 2.08172 + 0.894528i
\(101\) −740.746 −0.729772 −0.364886 0.931052i \(-0.618892\pi\)
−0.364886 + 0.931052i \(0.618892\pi\)
\(102\) −2459.43 751.179i −2.38745 0.729194i
\(103\) −935.584 −0.895008 −0.447504 0.894282i \(-0.647687\pi\)
−0.447504 + 0.894282i \(0.647687\pi\)
\(104\) 1084.61 1.02264
\(105\) 422.549 + 989.483i 0.392730 + 0.919654i
\(106\) 979.799 0.897797
\(107\) −794.752 −0.718052 −0.359026 0.933328i \(-0.616891\pi\)
−0.359026 + 0.933328i \(0.616891\pi\)
\(108\) 1974.98 1602.03i 1.75965 1.42736i
\(109\) −202.134 −0.177623 −0.0888117 0.996048i \(-0.528307\pi\)
−0.0888117 + 0.996048i \(0.528307\pi\)
\(110\) −638.403 + 3102.70i −0.553358 + 2.68937i
\(111\) 896.330 + 273.764i 0.766449 + 0.234095i
\(112\) −1371.17 + 1738.41i −1.15682 + 1.46665i
\(113\) −1457.83 −1.21364 −0.606818 0.794841i \(-0.707554\pi\)
−0.606818 + 0.794841i \(0.707554\pi\)
\(114\) −843.242 257.550i −0.692779 0.211594i
\(115\) −1218.71 250.758i −0.988218 0.203333i
\(116\) 2841.89i 2.27468i
\(117\) 469.232 + 316.123i 0.370773 + 0.249791i
\(118\) 3604.73 2.81223
\(119\) 1407.95 + 1110.52i 1.08459 + 0.855472i
\(120\) −1439.89 + 2639.75i −1.09536 + 2.00813i
\(121\) −1741.57 −1.30847
\(122\) 2182.96i 1.61997i
\(123\) −55.5278 + 181.803i −0.0407055 + 0.133274i
\(124\) 1459.09i 1.05669i
\(125\) −1146.47 799.203i −0.820349 0.571863i
\(126\) −2434.02 + 779.937i −1.72095 + 0.551447i
\(127\) 1189.69i 0.831242i −0.909538 0.415621i \(-0.863564\pi\)
0.909538 0.415621i \(-0.136436\pi\)
\(128\) 1317.78 0.909975
\(129\) −261.311 79.8116i −0.178350 0.0544730i
\(130\) −1172.94 241.341i −0.791337 0.162823i
\(131\) −531.346 −0.354381 −0.177190 0.984177i \(-0.556701\pi\)
−0.177190 + 0.984177i \(0.556701\pi\)
\(132\) −4993.13 1525.04i −3.29239 1.00559i
\(133\) 482.729 + 380.753i 0.314721 + 0.248237i
\(134\) 1566.35i 1.00979i
\(135\) −1392.33 + 722.357i −0.887648 + 0.460523i
\(136\) 5011.48i 3.15979i
\(137\) 1269.32 0.791572 0.395786 0.918343i \(-0.370472\pi\)
0.395786 + 0.918343i \(0.370472\pi\)
\(138\) 863.396 2826.84i 0.532588 1.74374i
\(139\) 1566.53i 0.955910i −0.878384 0.477955i \(-0.841378\pi\)
0.878384 0.477955i \(-0.158622\pi\)
\(140\) 2870.59 2417.99i 1.73292 1.45970i
\(141\) −1290.39 394.120i −0.770711 0.235397i
\(142\) 2626.18i 1.55200i
\(143\) 1161.55i 0.679257i
\(144\) −2677.00 1803.50i −1.54919 1.04369i
\(145\) −353.270 + 1716.93i −0.202327 + 0.983331i
\(146\) 1843.33 1.04490
\(147\) 1778.93 + 109.224i 0.998120 + 0.0612833i
\(148\) 3269.34i 1.81580i
\(149\) 1112.59i 0.611723i −0.952076 0.305862i \(-0.901055\pi\)
0.952076 0.305862i \(-0.0989445\pi\)
\(150\) 2144.54 2534.35i 1.16734 1.37952i
\(151\) 1252.15 0.674822 0.337411 0.941357i \(-0.390449\pi\)
0.337411 + 0.941357i \(0.390449\pi\)
\(152\) 1718.24i 0.916892i
\(153\) −1460.66 + 2168.11i −0.771815 + 1.14563i
\(154\) 4119.96 + 3249.63i 2.15582 + 1.70041i
\(155\) 181.377 881.509i 0.0939905 0.456803i
\(156\) 576.524 1887.59i 0.295890 0.968773i
\(157\) 226.625 0.115202 0.0576009 0.998340i \(-0.481655\pi\)
0.0576009 + 0.998340i \(0.481655\pi\)
\(158\) −439.496 −0.221294
\(159\) 290.953 952.607i 0.145120 0.475136i
\(160\) 2157.25 + 443.869i 1.06591 + 0.219318i
\(161\) −1276.42 + 1618.28i −0.624819 + 0.792161i
\(162\) −1399.69 3453.32i −0.678825 1.67480i
\(163\) 1843.89i 0.886042i −0.896511 0.443021i \(-0.853907\pi\)
0.896511 0.443021i \(-0.146093\pi\)
\(164\) 663.123 0.315739
\(165\) 2827.02 + 1542.04i 1.33384 + 0.727561i
\(166\) 4533.24i 2.11957i
\(167\) 2144.68i 0.993774i −0.867815 0.496887i \(-0.834476\pi\)
0.867815 0.496887i \(-0.165524\pi\)
\(168\) 2839.22 + 4092.54i 1.30387 + 1.87944i
\(169\) −1757.89 −0.800132
\(170\) 1115.13 5419.65i 0.503098 2.44511i
\(171\) −500.804 + 743.360i −0.223962 + 0.332434i
\(172\) 953.123i 0.422529i
\(173\) 3462.67i 1.52175i −0.648901 0.760873i \(-0.724771\pi\)
0.648901 0.760873i \(-0.275229\pi\)
\(174\) −3982.48 1216.36i −1.73512 0.529954i
\(175\) −2034.84 + 1103.99i −0.878968 + 0.476880i
\(176\) 6626.72i 2.83811i
\(177\) 1070.43 3504.69i 0.454568 1.48830i
\(178\) −7246.90 −3.05156
\(179\) 3089.42i 1.29002i 0.764173 + 0.645011i \(0.223147\pi\)
−0.764173 + 0.645011i \(0.776853\pi\)
\(180\) 3828.72 + 3909.08i 1.58542 + 1.61870i
\(181\) 2791.07i 1.14618i 0.819493 + 0.573090i \(0.194255\pi\)
−0.819493 + 0.573090i \(0.805745\pi\)
\(182\) −1228.48 + 1557.51i −0.500337 + 0.634340i
\(183\) 2122.38 + 648.233i 0.857326 + 0.261851i
\(184\) −5760.14 −2.30784
\(185\) −406.405 + 1975.17i −0.161511 + 0.784958i
\(186\) 2044.69 + 624.507i 0.806045 + 0.246188i
\(187\) 5367.01 2.09880
\(188\) 4706.65i 1.82589i
\(189\) 35.5048 + 2598.08i 0.0136645 + 0.999907i
\(190\) 382.334 1858.18i 0.145987 0.709509i
\(191\) 3188.41i 1.20788i −0.797029 0.603941i \(-0.793596\pi\)
0.797029 0.603941i \(-0.206404\pi\)
\(192\) −76.6591 + 250.989i −0.0288146 + 0.0943417i
\(193\) 1762.45i 0.657327i 0.944447 + 0.328664i \(0.106598\pi\)
−0.944447 + 0.328664i \(0.893402\pi\)
\(194\) −5394.77 −1.99651
\(195\) −582.950 + 1068.72i −0.214082 + 0.392476i
\(196\) −1448.30 6046.25i −0.527806 2.20344i
\(197\) −1135.69 −0.410735 −0.205367 0.978685i \(-0.565839\pi\)
−0.205367 + 0.978685i \(0.565839\pi\)
\(198\) −4274.23 + 6344.38i −1.53412 + 2.27715i
\(199\) 1200.54i 0.427658i 0.976871 + 0.213829i \(0.0685935\pi\)
−0.976871 + 0.213829i \(0.931407\pi\)
\(200\) −5944.29 2554.30i −2.10162 0.903081i
\(201\) 1522.88 + 465.130i 0.534406 + 0.163223i
\(202\) 3786.23 1.31880
\(203\) 2279.84 + 1798.23i 0.788244 + 0.621729i
\(204\) 8721.75 + 2663.86i 2.99336 + 0.914254i
\(205\) −400.625 82.4315i −0.136492 0.0280842i
\(206\) 4782.13 1.61741
\(207\) −2492.00 1678.87i −0.836744 0.563717i
\(208\) −2505.16 −0.835103
\(209\) 1840.14 0.609019
\(210\) −2159.81 5057.62i −0.709719 1.66195i
\(211\) −835.608 −0.272633 −0.136317 0.990665i \(-0.543526\pi\)
−0.136317 + 0.990665i \(0.543526\pi\)
\(212\) −3474.61 −1.12565
\(213\) 2553.30 + 779.848i 0.821357 + 0.250865i
\(214\) 4062.28 1.29762
\(215\) 118.481 575.829i 0.0375829 0.182657i
\(216\) −5639.50 + 4574.54i −1.77648 + 1.44101i
\(217\) −1170.52 923.252i −0.366176 0.288822i
\(218\) 1033.19 0.320991
\(219\) 547.380 1792.17i 0.168897 0.552986i
\(220\) 2263.93 11002.9i 0.693793 3.37190i
\(221\) 2028.94i 0.617562i
\(222\) −4581.48 1399.31i −1.38509 0.423044i
\(223\) −2734.39 −0.821115 −0.410557 0.911835i \(-0.634666\pi\)
−0.410557 + 0.911835i \(0.634666\pi\)
\(224\) 2259.40 2864.53i 0.673941 0.854440i
\(225\) −1827.19 2837.61i −0.541389 0.840772i
\(226\) 7451.50 2.19322
\(227\) 2207.95i 0.645579i −0.946471 0.322790i \(-0.895379\pi\)
0.946471 0.322790i \(-0.104621\pi\)
\(228\) 2990.34 + 913.333i 0.868597 + 0.265294i
\(229\) 1720.95i 0.496610i −0.968682 0.248305i \(-0.920126\pi\)
0.968682 0.248305i \(-0.0798735\pi\)
\(230\) 6229.27 + 1281.72i 1.78585 + 0.367452i
\(231\) 4382.87 3040.64i 1.24836 0.866059i
\(232\) 8114.94i 2.29643i
\(233\) 2915.58 0.819767 0.409884 0.912138i \(-0.365569\pi\)
0.409884 + 0.912138i \(0.365569\pi\)
\(234\) −2398.42 1615.82i −0.670041 0.451409i
\(235\) 585.075 2843.52i 0.162409 0.789323i
\(236\) −12783.3 −3.52593
\(237\) −130.509 + 427.299i −0.0357699 + 0.117114i
\(238\) −7196.55 5676.29i −1.96001 1.54596i
\(239\) 6597.22i 1.78552i −0.450536 0.892758i \(-0.648767\pi\)
0.450536 0.892758i \(-0.351233\pi\)
\(240\) 3325.77 6097.14i 0.894489 1.63987i
\(241\) 5492.27i 1.46800i 0.679149 + 0.734000i \(0.262349\pi\)
−0.679149 + 0.734000i \(0.737651\pi\)
\(242\) 8901.83 2.36459
\(243\) −3773.12 + 335.372i −0.996073 + 0.0885356i
\(244\) 7741.31i 2.03109i
\(245\) 123.392 + 3832.87i 0.0321765 + 0.999482i
\(246\) 283.824 929.266i 0.0735607 0.240845i
\(247\) 695.643i 0.179201i
\(248\) 4166.39i 1.06680i
\(249\) −4407.44 1346.15i −1.12173 0.342606i
\(250\) 5860.06 + 4085.03i 1.48249 + 1.03344i
\(251\) −3852.51 −0.968798 −0.484399 0.874847i \(-0.660962\pi\)
−0.484399 + 0.874847i \(0.660962\pi\)
\(252\) 8631.65 2765.85i 2.15771 0.691397i
\(253\) 6168.78i 1.53292i
\(254\) 6080.95i 1.50218i
\(255\) −4938.10 2693.56i −1.21269 0.661478i
\(256\) −7139.74 −1.74310
\(257\) 445.140i 0.108043i 0.998540 + 0.0540215i \(0.0172040\pi\)
−0.998540 + 0.0540215i \(0.982796\pi\)
\(258\) 1335.66 + 407.947i 0.322304 + 0.0984406i
\(259\) 2622.75 + 2068.70i 0.629227 + 0.496304i
\(260\) 4159.54 + 855.854i 0.992167 + 0.204146i
\(261\) −2365.21 + 3510.76i −0.560929 + 0.832607i
\(262\) 2715.91 0.640418
\(263\) −5539.14 −1.29870 −0.649350 0.760490i \(-0.724959\pi\)
−0.649350 + 0.760490i \(0.724959\pi\)
\(264\) 14257.7 + 4354.71i 3.32388 + 1.01520i
\(265\) 2099.18 + 431.922i 0.486610 + 0.100124i
\(266\) −2467.41 1946.18i −0.568747 0.448600i
\(267\) −2151.98 + 7045.78i −0.493254 + 1.61496i
\(268\) 5554.66i 1.26606i
\(269\) 6822.25 1.54632 0.773160 0.634211i \(-0.218675\pi\)
0.773160 + 0.634211i \(0.218675\pi\)
\(270\) 7116.71 3692.24i 1.60411 0.832232i
\(271\) 3566.70i 0.799490i −0.916626 0.399745i \(-0.869099\pi\)
0.916626 0.399745i \(-0.130901\pi\)
\(272\) 11575.2i 2.58034i
\(273\) 1149.48 + 1656.89i 0.254834 + 0.367325i
\(274\) −6487.98 −1.43049
\(275\) −2735.51 + 6366.00i −0.599845 + 1.39594i
\(276\) −3061.81 + 10024.7i −0.667751 + 2.18628i
\(277\) 4554.17i 0.987847i −0.869505 0.493923i \(-0.835562\pi\)
0.869505 0.493923i \(-0.164438\pi\)
\(278\) 8007.14i 1.72747i
\(279\) 1214.35 1802.50i 0.260578 0.386785i
\(280\) −8196.88 + 6904.51i −1.74949 + 1.47366i
\(281\) 4934.61i 1.04759i −0.851843 0.523797i \(-0.824515\pi\)
0.851843 0.523797i \(-0.175485\pi\)
\(282\) 6595.67 + 2014.50i 1.39279 + 0.425396i
\(283\) 456.724 0.0959344 0.0479672 0.998849i \(-0.484726\pi\)
0.0479672 + 0.998849i \(0.484726\pi\)
\(284\) 9313.08i 1.94588i
\(285\) −1693.08 923.513i −0.351892 0.191945i
\(286\) 5937.12i 1.22752i
\(287\) −419.596 + 531.975i −0.0862996 + 0.109413i
\(288\) 4411.12 + 2971.79i 0.902528 + 0.608035i
\(289\) −4461.83 −0.908168
\(290\) 1805.70 8775.86i 0.365635 1.77702i
\(291\) −1601.99 + 5245.05i −0.322715 + 1.05660i
\(292\) −6536.90 −1.31008
\(293\) 2102.29i 0.419171i −0.977790 0.209585i \(-0.932789\pi\)
0.977790 0.209585i \(-0.0672114\pi\)
\(294\) −9092.79 558.286i −1.80375 0.110748i
\(295\) 7723.00 + 1589.06i 1.52424 + 0.313623i
\(296\) 9335.50i 1.83316i
\(297\) 4899.07 + 6039.58i 0.957148 + 1.17997i
\(298\) 5686.86i 1.10547i
\(299\) −2332.04 −0.451054
\(300\) −7605.08 + 8987.42i −1.46360 + 1.72963i
\(301\) −764.622 603.097i −0.146419 0.115488i
\(302\) −6400.19 −1.21950
\(303\) 1124.33 3681.16i 0.213171 0.697944i
\(304\) 3968.69i 0.748750i
\(305\) −962.308 + 4676.91i −0.180661 + 0.878030i
\(306\) 7466.01 11082.0i 1.39478 2.07032i
\(307\) −2780.68 −0.516944 −0.258472 0.966019i \(-0.583219\pi\)
−0.258472 + 0.966019i \(0.583219\pi\)
\(308\) −14610.4 11524.0i −2.70294 2.13195i
\(309\) 1420.06 4649.41i 0.261438 0.855973i
\(310\) −927.085 + 4505.72i −0.169854 + 0.825510i
\(311\) 440.562 0.0803280 0.0401640 0.999193i \(-0.487212\pi\)
0.0401640 + 0.999193i \(0.487212\pi\)
\(312\) −1646.25 + 5389.97i −0.298719 + 0.978036i
\(313\) 6998.87 1.26390 0.631948 0.775010i \(-0.282255\pi\)
0.631948 + 0.775010i \(0.282255\pi\)
\(314\) −1158.37 −0.208186
\(315\) −5558.62 + 598.002i −0.994263 + 0.106964i
\(316\) 1558.56 0.277455
\(317\) −10112.3 −1.79168 −0.895839 0.444379i \(-0.853424\pi\)
−0.895839 + 0.444379i \(0.853424\pi\)
\(318\) −1487.17 + 4869.14i −0.262253 + 0.858640i
\(319\) 8690.64 1.52534
\(320\) −553.085 113.801i −0.0966199 0.0198802i
\(321\) 1206.30 3949.54i 0.209748 0.686735i
\(322\) 6524.26 8271.62i 1.12914 1.43155i
\(323\) −3214.26 −0.553703
\(324\) 4963.63 + 12246.3i 0.851102 + 2.09985i
\(325\) −2406.59 1034.13i −0.410750 0.176502i
\(326\) 9424.84i 1.60121i
\(327\) 306.806 1004.51i 0.0518850 0.169877i
\(328\) −1893.53 −0.318758
\(329\) −3775.81 2978.17i −0.632726 0.499064i
\(330\) −14450.0 7881.94i −2.41044 1.31481i
\(331\) 5030.87 0.835413 0.417706 0.908582i \(-0.362834\pi\)
0.417706 + 0.908582i \(0.362834\pi\)
\(332\) 16076.0i 2.65748i
\(333\) −2720.96 + 4038.81i −0.447770 + 0.664641i
\(334\) 10962.3i 1.79589i
\(335\) −690.489 + 3355.84i −0.112613 + 0.547311i
\(336\) −6557.86 9452.70i −1.06476 1.53478i
\(337\) 3231.43i 0.522335i −0.965293 0.261168i \(-0.915892\pi\)
0.965293 0.261168i \(-0.0841075\pi\)
\(338\) 8985.24 1.44595
\(339\) 2212.73 7244.71i 0.354511 1.16070i
\(340\) −3954.53 + 19219.4i −0.630778 + 3.06564i
\(341\) −4461.97 −0.708590
\(342\) 2559.80 3799.60i 0.404731 0.600756i
\(343\) 5766.89 + 2663.95i 0.907821 + 0.419357i
\(344\) 2721.62i 0.426569i
\(345\) 3095.94 5675.79i 0.483130 0.885722i
\(346\) 17699.0i 2.75002i
\(347\) 8184.28 1.26615 0.633077 0.774089i \(-0.281792\pi\)
0.633077 + 0.774089i \(0.281792\pi\)
\(348\) 14122.8 + 4313.51i 2.17547 + 0.664449i
\(349\) 11214.5i 1.72005i 0.510248 + 0.860027i \(0.329554\pi\)
−0.510248 + 0.860027i \(0.670446\pi\)
\(350\) 10400.8 5642.92i 1.58842 0.861791i
\(351\) −2283.19 + 1852.04i −0.347202 + 0.281637i
\(352\) 10919.4i 1.65343i
\(353\) 804.207i 0.121257i 0.998160 + 0.0606284i \(0.0193105\pi\)
−0.998160 + 0.0606284i \(0.980690\pi\)
\(354\) −5471.38 + 17913.8i −0.821470 + 2.68957i
\(355\) −1157.69 + 5626.49i −0.173081 + 0.841192i
\(356\) 25699.3 3.82601
\(357\) −7655.78 + 5311.24i −1.13498 + 0.787397i
\(358\) 15791.2i 2.33126i
\(359\) 4210.90i 0.619060i −0.950890 0.309530i \(-0.899828\pi\)
0.950890 0.309530i \(-0.100172\pi\)
\(360\) −10932.8 11162.3i −1.60058 1.63417i
\(361\) 5756.96 0.839329
\(362\) 14266.2i 2.07131i
\(363\) 2643.41 8654.79i 0.382213 1.25140i
\(364\) 4356.51 5523.29i 0.627316 0.795328i
\(365\) 3949.27 + 812.590i 0.566340 + 0.116528i
\(366\) −10848.3 3313.37i −1.54931 0.473203i
\(367\) −12710.6 −1.80787 −0.903935 0.427670i \(-0.859334\pi\)
−0.903935 + 0.427670i \(0.859334\pi\)
\(368\) 13304.4 1.88462
\(369\) −819.195 551.894i −0.115571 0.0778603i
\(370\) 2077.29 10095.8i 0.291873 1.41853i
\(371\) 2198.59 2787.43i 0.307668 0.390070i
\(372\) −7250.99 2214.65i −1.01061 0.308668i
\(373\) 10529.6i 1.46167i −0.682555 0.730835i \(-0.739131\pi\)
0.682555 0.730835i \(-0.260869\pi\)
\(374\) −27432.8 −3.79283
\(375\) 5711.81 4484.37i 0.786551 0.617525i
\(376\) 13439.7i 1.84335i
\(377\) 3285.39i 0.448823i
\(378\) −181.478 13279.8i −0.0246938 1.80698i
\(379\) −7340.38 −0.994855 −0.497428 0.867505i \(-0.665722\pi\)
−0.497428 + 0.867505i \(0.665722\pi\)
\(380\) −1355.85 + 6589.57i −0.183036 + 0.889573i
\(381\) 5912.19 + 1805.75i 0.794988 + 0.242811i
\(382\) 16297.2i 2.18282i
\(383\) 12222.6i 1.63067i 0.578991 + 0.815334i \(0.303447\pi\)
−0.578991 + 0.815334i \(0.696553\pi\)
\(384\) −2000.17 + 6548.76i −0.265810 + 0.870287i
\(385\) 7394.34 + 8778.40i 0.978832 + 1.16205i
\(386\) 9008.57i 1.18789i
\(387\) 793.251 1177.45i 0.104194 0.154659i
\(388\) 19131.2 2.50319
\(389\) 1069.72i 0.139426i 0.997567 + 0.0697131i \(0.0222084\pi\)
−0.997567 + 0.0697131i \(0.977792\pi\)
\(390\) 2979.68 5462.65i 0.386877 0.709261i
\(391\) 10775.3i 1.39369i
\(392\) 4135.58 + 17264.9i 0.532853 + 2.22451i
\(393\) 806.493 2640.54i 0.103517 0.338925i
\(394\) 5804.95 0.742257
\(395\) −941.603 193.742i −0.119942 0.0246790i
\(396\) 15157.5 22498.7i 1.92346 2.85506i
\(397\) −11929.8 −1.50816 −0.754082 0.656780i \(-0.771918\pi\)
−0.754082 + 0.656780i \(0.771918\pi\)
\(398\) 6136.40i 0.772839i
\(399\) −2624.87 + 1821.01i −0.329342 + 0.228483i
\(400\) 13729.8 + 5899.77i 1.71622 + 0.737471i
\(401\) 5198.65i 0.647402i 0.946159 + 0.323701i \(0.104927\pi\)
−0.946159 + 0.323701i \(0.895073\pi\)
\(402\) −7784.02 2377.45i −0.965750 0.294967i
\(403\) 1686.80i 0.208499i
\(404\) −13426.9 −1.65350
\(405\) −1476.46 8015.62i −0.181150 0.983456i
\(406\) −11653.1 9191.44i −1.42447 1.12355i
\(407\) 9997.79 1.21762
\(408\) −24904.7 7606.59i −3.02198 0.922996i
\(409\) 16413.0i 1.98428i −0.125136 0.992140i \(-0.539937\pi\)
0.125136 0.992140i \(-0.460063\pi\)
\(410\) 2047.75 + 421.339i 0.246661 + 0.0507523i
\(411\) −1926.61 + 6307.92i −0.231223 + 0.757048i
\(412\) −16958.6 −2.02789
\(413\) 8088.72 10255.1i 0.963729 1.22184i
\(414\) 12737.6 + 8581.33i 1.51212 + 1.01872i
\(415\) 1998.38 9712.30i 0.236377 1.14881i
\(416\) 4127.97 0.486515
\(417\) 7784.92 + 2377.73i 0.914219 + 0.279228i
\(418\) −9405.64 −1.10059
\(419\) 8997.49 1.04906 0.524530 0.851392i \(-0.324241\pi\)
0.524530 + 0.851392i \(0.324241\pi\)
\(420\) 7659.22 + 17935.6i 0.889837 + 2.08373i
\(421\) 2279.63 0.263901 0.131950 0.991256i \(-0.457876\pi\)
0.131950 + 0.991256i \(0.457876\pi\)
\(422\) 4271.11 0.492688
\(423\) 3917.18 5814.41i 0.450260 0.668336i
\(424\) 9921.64 1.13641
\(425\) 4778.25 11119.8i 0.545363 1.26915i
\(426\) −13050.9 3986.10i −1.48431 0.453350i
\(427\) 6210.29 + 4898.38i 0.703834 + 0.555150i
\(428\) −14405.8 −1.62694
\(429\) 5772.35 + 1763.04i 0.649631 + 0.198416i
\(430\) −605.601 + 2943.28i −0.0679178 + 0.330087i
\(431\) 14695.9i 1.64240i −0.570638 0.821202i \(-0.693304\pi\)
0.570638 0.821202i \(-0.306696\pi\)
\(432\) 13025.8 10566.0i 1.45070 1.17675i
\(433\) 3577.42 0.397043 0.198522 0.980097i \(-0.436386\pi\)
0.198522 + 0.980097i \(0.436386\pi\)
\(434\) 5982.98 + 4719.09i 0.661734 + 0.521944i
\(435\) −7996.11 4361.59i −0.881342 0.480741i
\(436\) −3663.93 −0.402455
\(437\) 3694.43i 0.404413i
\(438\) −2797.87 + 9160.48i −0.305222 + 0.999326i
\(439\) 7413.92i 0.806030i −0.915193 0.403015i \(-0.867962\pi\)
0.915193 0.403015i \(-0.132038\pi\)
\(440\) −6464.60 + 31418.6i −0.700427 + 3.40414i
\(441\) −3242.91 + 8674.66i −0.350168 + 0.936687i
\(442\) 10370.7i 1.11602i
\(443\) 5151.58 0.552503 0.276252 0.961085i \(-0.410908\pi\)
0.276252 + 0.961085i \(0.410908\pi\)
\(444\) 16247.1 + 4962.30i 1.73660 + 0.530406i
\(445\) −15526.2 3194.63i −1.65396 0.340314i
\(446\) 13976.5 1.48387
\(447\) 5529.04 + 1688.72i 0.585043 + 0.178689i
\(448\) −579.276 + 734.421i −0.0610897 + 0.0774511i
\(449\) 5031.60i 0.528855i 0.964406 + 0.264427i \(0.0851830\pi\)
−0.964406 + 0.264427i \(0.914817\pi\)
\(450\) 9339.45 + 14504.1i 0.978369 + 1.51940i
\(451\) 2027.86i 0.211726i
\(452\) −26424.9 −2.74982
\(453\) −1900.55 + 6222.57i −0.197120 + 0.645391i
\(454\) 11285.7i 1.16666i
\(455\) −3318.57 + 2795.35i −0.341928 + 0.288017i
\(456\) −8538.84 2608.00i −0.876903 0.267830i
\(457\) 1781.33i 0.182335i −0.995836 0.0911673i \(-0.970940\pi\)
0.995836 0.0911673i \(-0.0290598\pi\)
\(458\) 8796.44i 0.897447i
\(459\) −8557.45 10549.6i −0.870213 1.07280i
\(460\) −22090.5 4545.28i −2.23908 0.460706i
\(461\) −17966.1 −1.81511 −0.907556 0.419931i \(-0.862054\pi\)
−0.907556 + 0.419931i \(0.862054\pi\)
\(462\) −22402.5 + 15541.9i −2.25597 + 1.56509i
\(463\) 7730.37i 0.775941i 0.921672 + 0.387971i \(0.126824\pi\)
−0.921672 + 0.387971i \(0.873176\pi\)
\(464\) 18743.4i 1.87530i
\(465\) 4105.38 + 2239.34i 0.409425 + 0.223326i
\(466\) −14902.6 −1.48144
\(467\) 7613.81i 0.754443i 0.926123 + 0.377222i \(0.123121\pi\)
−0.926123 + 0.377222i \(0.876879\pi\)
\(468\) 8505.39 + 5730.10i 0.840089 + 0.565970i
\(469\) 4456.10 + 3514.76i 0.438728 + 0.346048i
\(470\) −2990.54 + 14534.3i −0.293497 + 1.42642i
\(471\) −343.979 + 1126.22i −0.0336512 + 0.110177i
\(472\) 36502.3 3.55965
\(473\) −2914.70 −0.283336
\(474\) 667.081 2184.09i 0.0646414 0.211642i
\(475\) 1638.27 3812.54i 0.158251 0.368277i
\(476\) 25520.7 + 20129.5i 2.45744 + 1.93831i
\(477\) 4292.39 + 2891.79i 0.412023 + 0.277581i
\(478\) 33720.9i 3.22669i
\(479\) −1660.45 −0.158388 −0.0791939 0.996859i \(-0.525235\pi\)
−0.0791939 + 0.996859i \(0.525235\pi\)
\(480\) −5480.16 + 10046.8i −0.521112 + 0.955356i
\(481\) 3779.55i 0.358280i
\(482\) 28073.1i 2.65289i
\(483\) −6104.68 8799.46i −0.575098 0.828963i
\(484\) −31568.1 −2.96470
\(485\) −11558.1 2378.16i −1.08212 0.222653i
\(486\) 19285.8 1714.21i 1.80005 0.159997i
\(487\) 1783.16i 0.165920i 0.996553 + 0.0829599i \(0.0264373\pi\)
−0.996553 + 0.0829599i \(0.973563\pi\)
\(488\) 22105.1i 2.05051i
\(489\) 9163.28 + 2798.72i 0.847398 + 0.258819i
\(490\) −630.705 19591.3i −0.0581477 1.80621i
\(491\) 4975.18i 0.457284i 0.973511 + 0.228642i \(0.0734286\pi\)
−0.973511 + 0.228642i \(0.926571\pi\)
\(492\) −1006.51 + 3295.41i −0.0922295 + 0.301968i
\(493\) −15180.4 −1.38679
\(494\) 3555.69i 0.323842i
\(495\) −11954.1 + 11708.4i −1.08545 + 1.06314i
\(496\) 9623.28i 0.871166i
\(497\) 7471.21 + 5892.93i 0.674305 + 0.531859i
\(498\) 22528.1 + 6880.70i 2.02712 + 0.619140i
\(499\) −7878.69 −0.706811 −0.353406 0.935470i \(-0.614976\pi\)
−0.353406 + 0.935470i \(0.614976\pi\)
\(500\) −20781.2 14486.5i −1.85873 1.29571i
\(501\) 10658.0 + 3255.26i 0.950431 + 0.290288i
\(502\) 19691.6 1.75076
\(503\) 3798.11i 0.336678i −0.985729 0.168339i \(-0.946160\pi\)
0.985729 0.168339i \(-0.0538404\pi\)
\(504\) −24647.4 + 7897.80i −2.17834 + 0.698008i
\(505\) 8111.86 + 1669.07i 0.714798 + 0.147075i
\(506\) 31531.0i 2.77020i
\(507\) 2668.18 8735.88i 0.233724 0.765234i
\(508\) 21564.5i 1.88341i
\(509\) 12066.4 1.05075 0.525377 0.850870i \(-0.323924\pi\)
0.525377 + 0.850870i \(0.323924\pi\)
\(510\) 25240.5 + 13767.8i 2.19151 + 1.19539i
\(511\) 4136.28 5244.08i 0.358079 0.453982i
\(512\) 25951.6 2.24006
\(513\) −2934.01 3617.05i −0.252514 0.311300i
\(514\) 2275.28i 0.195249i
\(515\) 10245.5 + 2108.09i 0.876644 + 0.180376i
\(516\) −4736.57 1446.68i −0.404101 0.123424i
\(517\) −14393.2 −1.22439
\(518\) −13405.9 10573.9i −1.13711 0.896894i
\(519\) 17207.8 + 5255.75i 1.45538 + 0.444512i
\(520\) −11877.4 2443.87i −1.00165 0.206098i
\(521\) −671.033 −0.0564270 −0.0282135 0.999602i \(-0.508982\pi\)
−0.0282135 + 0.999602i \(0.508982\pi\)
\(522\) 12089.5 17944.8i 1.01368 1.50464i
\(523\) 8833.34 0.738538 0.369269 0.929323i \(-0.379608\pi\)
0.369269 + 0.929323i \(0.379608\pi\)
\(524\) −9631.28 −0.802947
\(525\) −2397.77 11787.9i −0.199328 0.979933i
\(526\) 28312.6 2.34694
\(527\) 7793.94 0.644230
\(528\) −32931.7 10058.2i −2.71433 0.829032i
\(529\) 218.010 0.0179181
\(530\) −10729.7 2207.72i −0.879376 0.180938i
\(531\) 15791.9 + 10639.1i 1.29061 + 0.869484i
\(532\) 8750.04 + 6901.61i 0.713087 + 0.562449i
\(533\) −766.609 −0.0622993
\(534\) 10999.6 36013.7i 0.891382 2.91847i
\(535\) 8703.27 + 1790.76i 0.703318 + 0.144713i
\(536\) 15861.2i 1.27817i
\(537\) −15352.9 4689.22i −1.23376 0.376824i
\(538\) −34871.1 −2.79443
\(539\) 18489.7 4428.97i 1.47757 0.353932i
\(540\) −25237.6 + 13093.6i −2.01121 + 1.04344i
\(541\) −16688.3 −1.32623 −0.663113 0.748519i \(-0.730765\pi\)
−0.663113 + 0.748519i \(0.730765\pi\)
\(542\) 18230.8i 1.44480i
\(543\) −13870.3 4236.37i −1.09619 0.334807i
\(544\) 19073.5i 1.50325i
\(545\) 2213.56 + 455.456i 0.173979 + 0.0357974i
\(546\) −5875.43 8469.02i −0.460522 0.663810i
\(547\) 19572.5i 1.52991i 0.644086 + 0.764953i \(0.277238\pi\)
−0.644086 + 0.764953i \(0.722762\pi\)
\(548\) 23008.0 1.79352
\(549\) −6442.82 + 9563.30i −0.500862 + 0.743446i
\(550\) 13982.2 32539.0i 1.08401 2.52267i
\(551\) −5204.75 −0.402413
\(552\) 8742.92 28625.2i 0.674136 2.20719i
\(553\) −986.192 + 1250.32i −0.0758357 + 0.0961464i
\(554\) 23278.1i 1.78518i
\(555\) −9198.80 5017.61i −0.703544 0.383758i
\(556\) 28395.3i 2.16588i
\(557\) −23150.1 −1.76104 −0.880521 0.474008i \(-0.842807\pi\)
−0.880521 + 0.474008i \(0.842807\pi\)
\(558\) −6207.00 + 9213.27i −0.470902 + 0.698976i
\(559\) 1101.87i 0.0833704i
\(560\) 18932.7 15947.6i 1.42866 1.20341i
\(561\) −8146.22 + 26671.5i −0.613073 + 2.00726i
\(562\) 25222.7i 1.89316i
\(563\) 5111.84i 0.382661i 0.981526 + 0.191331i \(0.0612803\pi\)
−0.981526 + 0.191331i \(0.938720\pi\)
\(564\) −23389.8 7143.91i −1.74626 0.533356i
\(565\) 15964.6 + 3284.82i 1.18873 + 0.244590i
\(566\) −2334.49 −0.173367
\(567\) −12965.1 3767.00i −0.960288 0.279011i
\(568\) 26593.2i 1.96448i
\(569\) 1896.42i 0.139723i 0.997557 + 0.0698613i \(0.0222557\pi\)
−0.997557 + 0.0698613i \(0.977744\pi\)
\(570\) 8653.97 + 4720.43i 0.635921 + 0.346872i
\(571\) −17070.6 −1.25111 −0.625554 0.780181i \(-0.715127\pi\)
−0.625554 + 0.780181i \(0.715127\pi\)
\(572\) 21054.5i 1.53904i
\(573\) 15844.9 + 4839.47i 1.15520 + 0.352831i
\(574\) 2144.72 2719.13i 0.155956 0.197725i
\(575\) 12781.0 + 5492.06i 0.926962 + 0.398321i
\(576\) −1130.94 761.919i −0.0818101 0.0551157i
\(577\) −4537.92 −0.327411 −0.163705 0.986509i \(-0.552345\pi\)
−0.163705 + 0.986509i \(0.552345\pi\)
\(578\) 22806.1 1.64119
\(579\) −8758.56 2675.11i −0.628658 0.192010i
\(580\) −6403.44 + 31121.4i −0.458428 + 2.22801i
\(581\) −12896.6 10172.2i −0.920897 0.726359i
\(582\) 8188.35 26809.5i 0.583193 1.90943i
\(583\) 10625.5i 0.754826i
\(584\) 18665.9 1.32261
\(585\) −4426.23 4519.13i −0.312824 0.319389i
\(586\) 10745.6i 0.757503i
\(587\) 15763.7i 1.10841i 0.832380 + 0.554205i \(0.186978\pi\)
−0.832380 + 0.554205i \(0.813022\pi\)
\(588\) 32245.2 + 1979.82i 2.26152 + 0.138854i
\(589\) 2672.23 0.186940
\(590\) −39475.2 8122.31i −2.75452 0.566763i
\(591\) 1723.79 5643.85i 0.119978 0.392821i
\(592\) 21562.6i 1.49699i
\(593\) 2405.31i 0.166567i −0.996526 0.0832834i \(-0.973459\pi\)
0.996526 0.0832834i \(-0.0265407\pi\)
\(594\) −25041.0 30870.6i −1.72971 2.13238i
\(595\) −12916.1 15333.7i −0.889928 1.05650i
\(596\) 20167.0i 1.38603i
\(597\) −5966.10 1822.21i −0.409006 0.124922i
\(598\) 11919.9 0.815120
\(599\) 8892.20i 0.606553i 0.952903 + 0.303277i \(0.0980806\pi\)
−0.952903 + 0.303277i \(0.901919\pi\)
\(600\) 21716.1 25663.3i 1.47759 1.74617i
\(601\) 2916.97i 0.197980i 0.995088 + 0.0989898i \(0.0315611\pi\)
−0.995088 + 0.0989898i \(0.968439\pi\)
\(602\) 3908.27 + 3082.66i 0.264600 + 0.208704i
\(603\) −4622.95 + 6862.00i −0.312207 + 0.463420i
\(604\) 22696.6 1.52900
\(605\) 19071.8 + 3924.17i 1.28162 + 0.263703i
\(606\) −5746.86 + 18815.8i −0.385232 + 1.26129i
\(607\) 12105.3 0.809458 0.404729 0.914437i \(-0.367366\pi\)
0.404729 + 0.914437i \(0.367366\pi\)
\(608\) 6539.55i 0.436207i
\(609\) −12396.8 + 8600.33i −0.824864 + 0.572254i
\(610\) 4918.72 23905.5i 0.326481 1.58673i
\(611\) 5441.17i 0.360272i
\(612\) −26476.3 + 39299.7i −1.74876 + 2.59574i
\(613\) 11262.7i 0.742083i 0.928616 + 0.371041i \(0.120999\pi\)
−0.928616 + 0.371041i \(0.879001\pi\)
\(614\) 14213.1 0.934194
\(615\) 1017.73 1865.80i 0.0667296 0.122335i
\(616\) 41719.6 + 32906.4i 2.72878 + 2.15233i
\(617\) −5183.80 −0.338236 −0.169118 0.985596i \(-0.554092\pi\)
−0.169118 + 0.985596i \(0.554092\pi\)
\(618\) −7258.46 + 23764.9i −0.472456 + 1.54687i
\(619\) 26124.4i 1.69633i 0.529734 + 0.848164i \(0.322292\pi\)
−0.529734 + 0.848164i \(0.677708\pi\)
\(620\) 3287.67 15978.4i 0.212961 1.03501i
\(621\) 12125.6 9835.83i 0.783550 0.635585i
\(622\) −2251.88 −0.145164
\(623\) −16261.4 + 20616.7i −1.04575 + 1.32583i
\(624\) 3802.41 12449.4i 0.243939 0.798680i
\(625\) 10754.2 + 11335.3i 0.688266 + 0.725459i
\(626\) −35773.9 −2.28405
\(627\) −2793.02 + 9144.61i −0.177899 + 0.582457i
\(628\) 4107.86 0.261021
\(629\) −17463.6 −1.10703
\(630\) 28412.2 3056.61i 1.79678 0.193299i
\(631\) −10304.6 −0.650110 −0.325055 0.945695i \(-0.605383\pi\)
−0.325055 + 0.945695i \(0.605383\pi\)
\(632\) −4450.42 −0.280108
\(633\) 1268.31 4152.58i 0.0796380 0.260743i
\(634\) 51687.7 3.23782
\(635\) −2680.64 + 13028.2i −0.167525 + 0.814186i
\(636\) 5273.87 17267.2i 0.328809 1.07655i
\(637\) 1674.32 + 6989.82i 0.104143 + 0.434767i
\(638\) −44421.1 −2.75650
\(639\) −7750.95 + 11505.0i −0.479848 + 0.712255i
\(640\) −14431.0 2969.27i −0.891303 0.183392i
\(641\) 23841.8i 1.46910i −0.678552 0.734552i \(-0.737392\pi\)
0.678552 0.734552i \(-0.262608\pi\)
\(642\) −6165.85 + 20187.6i −0.379045 + 1.24103i
\(643\) −8773.65 −0.538101 −0.269050 0.963126i \(-0.586710\pi\)
−0.269050 + 0.963126i \(0.586710\pi\)
\(644\) −23136.6 + 29333.2i −1.41570 + 1.79486i
\(645\) 2681.76 + 1462.81i 0.163712 + 0.0892991i
\(646\) 16429.3 1.00062
\(647\) 8008.70i 0.486638i 0.969946 + 0.243319i \(0.0782362\pi\)
−0.969946 + 0.243319i \(0.921764\pi\)
\(648\) −14173.5 34969.0i −0.859240 2.11993i
\(649\) 39091.8i 2.36439i
\(650\) 12301.0 + 5285.82i 0.742285 + 0.318964i
\(651\) 6364.78 4415.60i 0.383188 0.265839i
\(652\) 33422.8i 2.00757i
\(653\) 4305.61 0.258027 0.129014 0.991643i \(-0.458819\pi\)
0.129014 + 0.991643i \(0.458819\pi\)
\(654\) −1568.20 + 5134.44i −0.0937638 + 0.306992i
\(655\) 5818.73 + 1197.25i 0.347109 + 0.0714202i
\(656\) 4373.56 0.260303
\(657\) 8075.43 + 5440.44i 0.479532 + 0.323062i
\(658\) 19299.6 + 15222.6i 1.14343 + 0.901882i
\(659\) 24759.2i 1.46355i 0.681545 + 0.731777i \(0.261309\pi\)
−0.681545 + 0.731777i \(0.738691\pi\)
\(660\) 51243.1 + 27951.3i 3.02218 + 1.64849i
\(661\) 10995.7i 0.647022i −0.946224 0.323511i \(-0.895137\pi\)
0.946224 0.323511i \(-0.104863\pi\)
\(662\) −25714.7 −1.50971
\(663\) −10082.9 3079.59i −0.590627 0.180394i
\(664\) 45904.5i 2.68289i
\(665\) −4428.41 5257.31i −0.258235 0.306571i
\(666\) 13907.8 20643.9i 0.809186 1.20110i
\(667\) 17448.1i 1.01288i
\(668\) 38874.9i 2.25167i
\(669\) 4150.35 13588.6i 0.239853 0.785302i
\(670\) 3529.35 17153.0i 0.203509 0.989071i
\(671\) 23673.3 1.36199
\(672\) 10806.0 + 15576.0i 0.620311 + 0.894135i
\(673\) 18477.5i 1.05833i −0.848520 0.529163i \(-0.822506\pi\)
0.848520 0.529163i \(-0.177494\pi\)
\(674\) 16517.0i 0.943936i
\(675\) 16874.9 4773.25i 0.962246 0.272181i
\(676\) −31863.9 −1.81292
\(677\) 6639.83i 0.376942i −0.982079 0.188471i \(-0.939647\pi\)
0.982079 0.188471i \(-0.0603531\pi\)
\(678\) −11310.1 + 37030.4i −0.640653 + 2.09756i
\(679\) −12105.4 + 15347.6i −0.684187 + 0.867430i
\(680\) 11292.0 54880.4i 0.636809 3.09495i
\(681\) 10972.4 + 3351.29i 0.617423 + 0.188578i
\(682\) 22806.8 1.28052
\(683\) 6422.87 0.359830 0.179915 0.983682i \(-0.442418\pi\)
0.179915 + 0.983682i \(0.442418\pi\)
\(684\) −9077.67 + 13474.3i −0.507446 + 0.753220i
\(685\) −13900.2 2860.07i −0.775330 0.159530i
\(686\) −29476.8 13616.4i −1.64057 0.757840i
\(687\) 8552.32 + 2612.11i 0.474951 + 0.145063i
\(688\) 6286.23i 0.348343i
\(689\) 4016.85 0.222104
\(690\) −15824.5 + 29011.1i −0.873086 + 1.60063i
\(691\) 33292.1i 1.83284i 0.400221 + 0.916419i \(0.368933\pi\)
−0.400221 + 0.916419i \(0.631067\pi\)
\(692\) 62765.1i 3.44793i
\(693\) 8458.09 + 26396.0i 0.463631 + 1.44690i
\(694\) −41833.0 −2.28812
\(695\) −3529.76 + 17155.0i −0.192650 + 0.936296i
\(696\) −40327.4 12317.1i −2.19627 0.670803i
\(697\) 3542.17i 0.192495i
\(698\) 57321.6i 3.10839i
\(699\) −4425.35 + 14489.0i −0.239460 + 0.784014i
\(700\) −36883.9 + 20011.2i −1.99154 + 1.08050i
\(701\) 21719.6i 1.17024i 0.810946 + 0.585121i \(0.198953\pi\)
−0.810946 + 0.585121i \(0.801047\pi\)
\(702\) 11670.3 9466.47i 0.627444 0.508958i
\(703\) −5987.59 −0.321232
\(704\) 2799.57i 0.149876i
\(705\) 13242.9 + 7223.53i 0.707457 + 0.385892i
\(706\) 4110.61i 0.219129i
\(707\) 8495.99 10771.4i 0.451944 0.572987i
\(708\) 19402.8 63526.8i 1.02995 3.37215i
\(709\) 9450.02 0.500568 0.250284 0.968172i \(-0.419476\pi\)
0.250284 + 0.968172i \(0.419476\pi\)
\(710\) 5917.40 28759.1i 0.312783 1.52016i
\(711\) −1925.38 1297.13i −0.101558 0.0684196i
\(712\) −73383.6 −3.86259
\(713\) 8958.26i 0.470532i
\(714\) 39131.6 27147.8i 2.05107 1.42294i
\(715\) −2617.24 + 12720.1i −0.136894 + 0.665319i
\(716\) 55999.4i 2.92290i
\(717\) 32785.0 + 10013.5i 1.70764 + 0.521562i
\(718\) 21523.5i 1.11873i
\(719\) −29056.2 −1.50711 −0.753555 0.657385i \(-0.771662\pi\)
−0.753555 + 0.657385i \(0.771662\pi\)
\(720\) 25251.9 + 25781.9i 1.30706 + 1.33449i
\(721\) 10730.7 13604.6i 0.554274 0.702723i
\(722\) −29426.0 −1.51679
\(723\) −27294.0 8336.34i −1.40398 0.428813i
\(724\) 50591.4i 2.59698i
\(725\) 7737.27 18005.9i 0.396352 0.922378i
\(726\) −13511.5 + 44237.9i −0.690714 + 2.26146i
\(727\) −3457.74 −0.176397 −0.0881983 0.996103i \(-0.528111\pi\)
−0.0881983 + 0.996103i \(0.528111\pi\)
\(728\) −12439.9 + 15771.6i −0.633314 + 0.802932i
\(729\) 4060.32 19259.7i 0.206286 0.978492i
\(730\) −20186.2 4153.45i −1.02346 0.210584i
\(731\) 5091.25 0.257601
\(732\) 38470.7 + 11750.0i 1.94251 + 0.593296i
\(733\) 22212.1 1.11927 0.559634 0.828740i \(-0.310942\pi\)
0.559634 + 0.828740i \(0.310942\pi\)
\(734\) 64968.7 3.26708
\(735\) −19234.8 5204.45i −0.965289 0.261182i
\(736\) −21922.9 −1.09794
\(737\) 16986.4 0.848986
\(738\) 4187.22 + 2820.94i 0.208853 + 0.140705i
\(739\) −35565.7 −1.77037 −0.885186 0.465237i \(-0.845969\pi\)
−0.885186 + 0.465237i \(0.845969\pi\)
\(740\) −7366.58 + 35802.3i −0.365947 + 1.77854i
\(741\) −3457.01 1055.87i −0.171385 0.0523459i
\(742\) −11237.8 + 14247.6i −0.556001 + 0.704913i
\(743\) 20992.4 1.03652 0.518262 0.855222i \(-0.326579\pi\)
0.518262 + 0.855222i \(0.326579\pi\)
\(744\) 20705.0 + 6323.88i 1.02027 + 0.311619i
\(745\) −2506.92 + 12183.9i −0.123284 + 0.599172i
\(746\) 53820.8i 2.64145i
\(747\) 13379.5 19859.6i 0.655328 0.972725i
\(748\) 97283.6 4.75540
\(749\) 9115.41 11556.8i 0.444686 0.563785i
\(750\) −29195.2 + 22921.3i −1.42141 + 1.11596i
\(751\) 5971.01 0.290127 0.145063 0.989422i \(-0.453661\pi\)
0.145063 + 0.989422i \(0.453661\pi\)
\(752\) 31042.3i 1.50531i
\(753\) 5847.46 19145.1i 0.282992 0.926545i
\(754\) 16792.9i 0.811089i
\(755\) −13712.2 2821.38i −0.660976 0.136001i
\(756\) 643.567 + 47093.3i 0.0309607 + 2.26556i
\(757\) 23358.2i 1.12149i −0.827988 0.560745i \(-0.810515\pi\)
0.827988 0.560745i \(-0.189485\pi\)
\(758\) 37519.5 1.79785
\(759\) −30655.9 9363.17i −1.46606 0.447775i
\(760\) 3871.59 18816.3i 0.184786 0.898079i
\(761\) 428.292 0.0204015 0.0102008 0.999948i \(-0.496753\pi\)
0.0102008 + 0.999948i \(0.496753\pi\)
\(762\) −30219.4 9229.85i −1.43666 0.438796i
\(763\) 2318.38 2939.30i 0.110001 0.139463i
\(764\) 57793.8i 2.73679i
\(765\) 20880.9 20451.6i 0.986863 0.966576i
\(766\) 62474.4i 2.94686i
\(767\) 14778.2 0.695711
\(768\) 10836.9 35481.1i 0.509171 1.66708i
\(769\) 16393.0i 0.768720i 0.923183 + 0.384360i \(0.125578\pi\)
−0.923183 + 0.384360i \(0.874422\pi\)
\(770\) −37795.3 44869.7i −1.76889 2.09999i
\(771\) −2212.13 675.647i −0.103331 0.0315601i
\(772\) 31946.6i 1.48936i
\(773\) 22894.4i 1.06527i −0.846344 0.532636i \(-0.821201\pi\)
0.846344 0.532636i \(-0.178799\pi\)
\(774\) −4054.61 + 6018.39i −0.188294 + 0.279492i
\(775\) −3972.49 + 9244.66i −0.184124 + 0.428488i
\(776\) −54628.5 −2.52713
\(777\) −14261.4 + 9893.90i −0.658460 + 0.456810i
\(778\) 5467.73i 0.251963i
\(779\) 1214.47i