Properties

Label 177.4.d.c.176.6
Level $177$
Weight $4$
Character 177.176
Analytic conductor $10.443$
Analytic rank $0$
Dimension $52$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 177.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4433380710\)
Analytic rank: \(0\)
Dimension: \(52\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 176.6
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.5

$q$-expansion

\(f(q)\) \(=\) \(q-4.72011 q^{2} +(-4.94573 + 1.59367i) q^{3} +14.2794 q^{4} -15.2708i q^{5} +(23.3444 - 7.52230i) q^{6} +9.03916 q^{7} -29.6395 q^{8} +(21.9204 - 15.7637i) q^{9} +O(q^{10})\) \(q-4.72011 q^{2} +(-4.94573 + 1.59367i) q^{3} +14.2794 q^{4} -15.2708i q^{5} +(23.3444 - 7.52230i) q^{6} +9.03916 q^{7} -29.6395 q^{8} +(21.9204 - 15.7637i) q^{9} +72.0799i q^{10} -12.9980 q^{11} +(-70.6221 + 22.7567i) q^{12} +55.4535i q^{13} -42.6658 q^{14} +(24.3366 + 75.5253i) q^{15} +25.6664 q^{16} -10.8602i q^{17} +(-103.467 + 74.4065i) q^{18} +126.731 q^{19} -218.058i q^{20} +(-44.7052 + 14.4054i) q^{21} +61.3519 q^{22} +21.4430 q^{23} +(146.589 - 47.2356i) q^{24} -108.198 q^{25} -261.746i q^{26} +(-83.2902 + 112.897i) q^{27} +129.074 q^{28} -6.52115i q^{29} +(-114.872 - 356.487i) q^{30} -223.822i q^{31} +115.968 q^{32} +(64.2845 - 20.7145i) q^{33} +51.2615i q^{34} -138.035i q^{35} +(313.011 - 225.097i) q^{36} -166.344i q^{37} -598.183 q^{38} +(-88.3746 - 274.258i) q^{39} +452.619i q^{40} -152.194i q^{41} +(211.013 - 67.9952i) q^{42} -122.150i q^{43} -185.604 q^{44} +(-240.725 - 334.743i) q^{45} -101.213 q^{46} +126.500 q^{47} +(-126.939 + 40.9038i) q^{48} -261.294 q^{49} +510.705 q^{50} +(17.3076 + 53.7117i) q^{51} +791.843i q^{52} +578.820i q^{53} +(393.139 - 532.886i) q^{54} +198.490i q^{55} -267.916 q^{56} +(-626.776 + 201.967i) q^{57} +30.7805i q^{58} +(183.057 - 414.571i) q^{59} +(347.513 + 1078.46i) q^{60} -272.491i q^{61} +1056.46i q^{62} +(198.142 - 142.491i) q^{63} -752.713 q^{64} +846.820 q^{65} +(-303.430 + 97.7748i) q^{66} -957.249i q^{67} -155.078i q^{68} +(-106.051 + 34.1731i) q^{69} +651.541i q^{70} -639.771i q^{71} +(-649.711 + 467.229i) q^{72} +869.650i q^{73} +785.164i q^{74} +(535.116 - 172.431i) q^{75} +1809.64 q^{76} -117.491 q^{77} +(417.138 + 1294.53i) q^{78} +668.109 q^{79} -391.947i q^{80} +(232.010 - 691.095i) q^{81} +718.373i q^{82} -1151.69 q^{83} +(-638.364 + 205.701i) q^{84} -165.845 q^{85} +576.561i q^{86} +(10.3926 + 32.2518i) q^{87} +385.254 q^{88} -505.096 q^{89} +(1136.25 + 1580.02i) q^{90} +501.253i q^{91} +306.194 q^{92} +(356.698 + 1106.96i) q^{93} -597.093 q^{94} -1935.28i q^{95} +(-573.546 + 184.815i) q^{96} -1503.21i q^{97} +1233.33 q^{98} +(-284.921 + 204.897i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + O(q^{10}) \) \( 52q - 8q^{3} + 268q^{4} - 16q^{7} - 4q^{9} + 28q^{12} + 114q^{15} + 484q^{16} - 184q^{19} - 758q^{21} - 60q^{22} + 36q^{25} + 742q^{27} - 4q^{28} - 888q^{36} + 1402q^{45} - 660q^{46} - 488q^{48} - 924q^{49} - 1772q^{51} - 630q^{57} - 1880q^{60} - 212q^{63} + 7648q^{64} + 1316q^{66} - 1556q^{75} - 5680q^{76} + 3224q^{78} - 1504q^{79} - 276q^{81} + 1228q^{84} - 848q^{85} + 3598q^{87} + 5760q^{88} + 888q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.72011 −1.66881 −0.834405 0.551152i \(-0.814189\pi\)
−0.834405 + 0.551152i \(0.814189\pi\)
\(3\) −4.94573 + 1.59367i −0.951806 + 0.306702i
\(4\) 14.2794 1.78493
\(5\) 15.2708i 1.36586i −0.730483 0.682931i \(-0.760705\pi\)
0.730483 0.682931i \(-0.239295\pi\)
\(6\) 23.3444 7.52230i 1.58838 0.511828i
\(7\) 9.03916 0.488069 0.244034 0.969767i \(-0.421529\pi\)
0.244034 + 0.969767i \(0.421529\pi\)
\(8\) −29.6395 −1.30989
\(9\) 21.9204 15.7637i 0.811868 0.583842i
\(10\) 72.0799i 2.27937i
\(11\) −12.9980 −0.356276 −0.178138 0.984005i \(-0.557007\pi\)
−0.178138 + 0.984005i \(0.557007\pi\)
\(12\) −70.6221 + 22.7567i −1.69890 + 0.547441i
\(13\) 55.4535i 1.18308i 0.806276 + 0.591540i \(0.201480\pi\)
−0.806276 + 0.591540i \(0.798520\pi\)
\(14\) −42.6658 −0.814494
\(15\) 24.3366 + 75.5253i 0.418913 + 1.30004i
\(16\) 25.6664 0.401037
\(17\) 10.8602i 0.154941i −0.996995 0.0774704i \(-0.975316\pi\)
0.996995 0.0774704i \(-0.0246843\pi\)
\(18\) −103.467 + 74.4065i −1.35485 + 0.974321i
\(19\) 126.731 1.53021 0.765106 0.643904i \(-0.222686\pi\)
0.765106 + 0.643904i \(0.222686\pi\)
\(20\) 218.058i 2.43797i
\(21\) −44.7052 + 14.4054i −0.464546 + 0.149692i
\(22\) 61.3519 0.594558
\(23\) 21.4430 0.194399 0.0971996 0.995265i \(-0.469011\pi\)
0.0971996 + 0.995265i \(0.469011\pi\)
\(24\) 146.589 47.2356i 1.24676 0.401747i
\(25\) −108.198 −0.865581
\(26\) 261.746i 1.97433i
\(27\) −83.2902 + 112.897i −0.593675 + 0.804705i
\(28\) 129.074 0.871167
\(29\) 6.52115i 0.0417568i −0.999782 0.0208784i \(-0.993354\pi\)
0.999782 0.0208784i \(-0.00664628\pi\)
\(30\) −114.872 356.487i −0.699086 2.16951i
\(31\) 223.822i 1.29676i −0.761317 0.648380i \(-0.775447\pi\)
0.761317 0.648380i \(-0.224553\pi\)
\(32\) 115.968 0.640639
\(33\) 64.2845 20.7145i 0.339106 0.109271i
\(34\) 51.2615i 0.258567i
\(35\) 138.035i 0.666635i
\(36\) 313.011 225.097i 1.44912 1.04211i
\(37\) 166.344i 0.739104i −0.929210 0.369552i \(-0.879511\pi\)
0.929210 0.369552i \(-0.120489\pi\)
\(38\) −598.183 −2.55363
\(39\) −88.3746 274.258i −0.362853 1.12606i
\(40\) 452.619i 1.78914i
\(41\) 152.194i 0.579725i −0.957068 0.289863i \(-0.906390\pi\)
0.957068 0.289863i \(-0.0936096\pi\)
\(42\) 211.013 67.9952i 0.775240 0.249807i
\(43\) 122.150i 0.433202i −0.976260 0.216601i \(-0.930503\pi\)
0.976260 0.216601i \(-0.0694971\pi\)
\(44\) −185.604 −0.635928
\(45\) −240.725 334.743i −0.797447 1.10890i
\(46\) −101.213 −0.324415
\(47\) 126.500 0.392594 0.196297 0.980545i \(-0.437108\pi\)
0.196297 + 0.980545i \(0.437108\pi\)
\(48\) −126.939 + 40.9038i −0.381710 + 0.122999i
\(49\) −261.294 −0.761789
\(50\) 510.705 1.44449
\(51\) 17.3076 + 53.7117i 0.0475207 + 0.147473i
\(52\) 791.843i 2.11171i
\(53\) 578.820i 1.50013i 0.661363 + 0.750066i \(0.269978\pi\)
−0.661363 + 0.750066i \(0.730022\pi\)
\(54\) 393.139 532.886i 0.990730 1.34290i
\(55\) 198.490i 0.486625i
\(56\) −267.916 −0.639318
\(57\) −626.776 + 201.967i −1.45647 + 0.469320i
\(58\) 30.7805i 0.0696842i
\(59\) 183.057 414.571i 0.403932 0.914789i
\(60\) 347.513 + 1078.46i 0.747729 + 2.32047i
\(61\) 272.491i 0.571949i −0.958237 0.285975i \(-0.907683\pi\)
0.958237 0.285975i \(-0.0923173\pi\)
\(62\) 1056.46i 2.16404i
\(63\) 198.142 142.491i 0.396247 0.284955i
\(64\) −752.713 −1.47014
\(65\) 846.820 1.61592
\(66\) −303.430 + 97.7748i −0.565903 + 0.182352i
\(67\) 957.249i 1.74547i −0.488193 0.872736i \(-0.662344\pi\)
0.488193 0.872736i \(-0.337656\pi\)
\(68\) 155.078i 0.276558i
\(69\) −106.051 + 34.1731i −0.185030 + 0.0596226i
\(70\) 651.541i 1.11249i
\(71\) 639.771i 1.06939i −0.845044 0.534696i \(-0.820426\pi\)
0.845044 0.534696i \(-0.179574\pi\)
\(72\) −649.711 + 467.229i −1.06346 + 0.764771i
\(73\) 869.650i 1.39431i 0.716919 + 0.697156i \(0.245552\pi\)
−0.716919 + 0.697156i \(0.754448\pi\)
\(74\) 785.164i 1.23342i
\(75\) 535.116 172.431i 0.823865 0.265476i
\(76\) 1809.64 2.73132
\(77\) −117.491 −0.173887
\(78\) 417.138 + 1294.53i 0.605532 + 1.87918i
\(79\) 668.109 0.951496 0.475748 0.879582i \(-0.342177\pi\)
0.475748 + 0.879582i \(0.342177\pi\)
\(80\) 391.947i 0.547762i
\(81\) 232.010 691.095i 0.318258 0.948004i
\(82\) 718.373i 0.967452i
\(83\) −1151.69 −1.52307 −0.761533 0.648126i \(-0.775553\pi\)
−0.761533 + 0.648126i \(0.775553\pi\)
\(84\) −638.364 + 205.701i −0.829182 + 0.267189i
\(85\) −165.845 −0.211628
\(86\) 576.561i 0.722932i
\(87\) 10.3926 + 32.2518i 0.0128069 + 0.0397443i
\(88\) 385.254 0.466684
\(89\) −505.096 −0.601573 −0.300787 0.953691i \(-0.597249\pi\)
−0.300787 + 0.953691i \(0.597249\pi\)
\(90\) 1136.25 + 1580.02i 1.33079 + 1.85054i
\(91\) 501.253i 0.577424i
\(92\) 306.194 0.346988
\(93\) 356.698 + 1106.96i 0.397719 + 1.23426i
\(94\) −597.093 −0.655164
\(95\) 1935.28i 2.09006i
\(96\) −573.546 + 184.815i −0.609764 + 0.196485i
\(97\) 1503.21i 1.57348i −0.617282 0.786742i \(-0.711766\pi\)
0.617282 0.786742i \(-0.288234\pi\)
\(98\) 1233.33 1.27128
\(99\) −284.921 + 204.897i −0.289249 + 0.208009i
\(100\) −1545.00 −1.54500
\(101\) −1835.63 −1.80843 −0.904217 0.427074i \(-0.859544\pi\)
−0.904217 + 0.427074i \(0.859544\pi\)
\(102\) −81.6939 253.525i −0.0793030 0.246105i
\(103\) 348.680i 0.333558i −0.985994 0.166779i \(-0.946663\pi\)
0.985994 0.166779i \(-0.0533367\pi\)
\(104\) 1643.61i 1.54971i
\(105\) 219.983 + 682.685i 0.204458 + 0.634507i
\(106\) 2732.09i 2.50344i
\(107\) 519.223i 0.469114i 0.972102 + 0.234557i \(0.0753640\pi\)
−0.972102 + 0.234557i \(0.924636\pi\)
\(108\) −1189.34 + 1612.10i −1.05967 + 1.43634i
\(109\) 1817.46i 1.59708i −0.601944 0.798538i \(-0.705607\pi\)
0.601944 0.798538i \(-0.294393\pi\)
\(110\) 936.893i 0.812084i
\(111\) 265.098 + 822.694i 0.226685 + 0.703484i
\(112\) 232.003 0.195734
\(113\) −1249.57 −1.04027 −0.520133 0.854085i \(-0.674118\pi\)
−0.520133 + 0.854085i \(0.674118\pi\)
\(114\) 2958.45 953.307i 2.43056 0.783205i
\(115\) 327.452i 0.265523i
\(116\) 93.1182i 0.0745328i
\(117\) 874.153 + 1215.56i 0.690731 + 0.960504i
\(118\) −864.049 + 1956.82i −0.674086 + 1.52661i
\(119\) 98.1674i 0.0756217i
\(120\) −721.327 2238.53i −0.548732 1.70291i
\(121\) −1162.05 −0.873067
\(122\) 1286.19i 0.954475i
\(123\) 242.547 + 752.711i 0.177803 + 0.551786i
\(124\) 3196.04i 2.31462i
\(125\) 256.585i 0.183598i
\(126\) −935.252 + 672.572i −0.661261 + 0.475535i
\(127\) 1254.17 0.876294 0.438147 0.898903i \(-0.355635\pi\)
0.438147 + 0.898903i \(0.355635\pi\)
\(128\) 2625.14 1.81275
\(129\) 194.667 + 604.120i 0.132864 + 0.412324i
\(130\) −3997.08 −2.69667
\(131\) 1262.94 0.842315 0.421157 0.906988i \(-0.361624\pi\)
0.421157 + 0.906988i \(0.361624\pi\)
\(132\) 917.945 295.791i 0.605279 0.195040i
\(133\) 1145.54 0.746849
\(134\) 4518.32i 2.91286i
\(135\) 1724.03 + 1271.91i 1.09912 + 0.810878i
\(136\) 321.892i 0.202956i
\(137\) 1067.52i 0.665724i −0.942975 0.332862i \(-0.891986\pi\)
0.942975 0.332862i \(-0.108014\pi\)
\(138\) 500.574 161.301i 0.308780 0.0994988i
\(139\) 1083.44 0.661126 0.330563 0.943784i \(-0.392761\pi\)
0.330563 + 0.943784i \(0.392761\pi\)
\(140\) 1971.06i 1.18989i
\(141\) −625.634 + 201.599i −0.373673 + 0.120409i
\(142\) 3019.79i 1.78461i
\(143\) 720.784i 0.421503i
\(144\) 562.618 404.598i 0.325589 0.234142i
\(145\) −99.5832 −0.0570341
\(146\) 4104.84i 2.32684i
\(147\) 1292.29 416.416i 0.725075 0.233642i
\(148\) 2375.30i 1.31925i
\(149\) 2330.79 1.28152 0.640758 0.767743i \(-0.278620\pi\)
0.640758 + 0.767743i \(0.278620\pi\)
\(150\) −2525.81 + 813.895i −1.37487 + 0.443028i
\(151\) 760.811i 0.410026i −0.978759 0.205013i \(-0.934276\pi\)
0.978759 0.205013i \(-0.0657236\pi\)
\(152\) −3756.24 −2.00442
\(153\) −171.198 238.061i −0.0904609 0.125791i
\(154\) 554.570 0.290185
\(155\) −3417.94 −1.77120
\(156\) −1261.94 3916.24i −0.647666 2.00994i
\(157\) 3112.47i 1.58218i 0.611701 + 0.791089i \(0.290485\pi\)
−0.611701 + 0.791089i \(0.709515\pi\)
\(158\) −3153.55 −1.58787
\(159\) −922.448 2862.68i −0.460094 1.42783i
\(160\) 1770.93i 0.875025i
\(161\) 193.827 0.0948801
\(162\) −1095.11 + 3262.04i −0.531112 + 1.58204i
\(163\) −3254.31 −1.56379 −0.781893 0.623413i \(-0.785746\pi\)
−0.781893 + 0.623413i \(0.785746\pi\)
\(164\) 2173.24i 1.03477i
\(165\) −316.327 981.676i −0.149249 0.463172i
\(166\) 5436.11 2.54171
\(167\) 1503.32i 0.696587i −0.937385 0.348294i \(-0.886761\pi\)
0.937385 0.348294i \(-0.113239\pi\)
\(168\) 1325.04 426.970i 0.608507 0.196080i
\(169\) −878.088 −0.399676
\(170\) 782.804 0.353167
\(171\) 2777.99 1997.75i 1.24233 0.893402i
\(172\) 1744.23i 0.773234i
\(173\) 4365.91 1.91870 0.959348 0.282227i \(-0.0910730\pi\)
0.959348 + 0.282227i \(0.0910730\pi\)
\(174\) −49.0540 152.232i −0.0213723 0.0663258i
\(175\) −978.016 −0.422463
\(176\) −333.612 −0.142880
\(177\) −244.661 + 2342.09i −0.103897 + 0.994588i
\(178\) 2384.11 1.00391
\(179\) 2897.20 1.20976 0.604880 0.796317i \(-0.293221\pi\)
0.604880 + 0.796317i \(0.293221\pi\)
\(180\) −3437.41 4779.93i −1.42339 1.97931i
\(181\) 1411.26 0.579549 0.289774 0.957095i \(-0.406420\pi\)
0.289774 + 0.957095i \(0.406420\pi\)
\(182\) 2365.97i 0.963611i
\(183\) 434.261 + 1347.67i 0.175418 + 0.544385i
\(184\) −635.561 −0.254642
\(185\) −2540.21 −1.00952
\(186\) −1683.65 5224.97i −0.663717 2.05975i
\(187\) 141.161i 0.0552018i
\(188\) 1806.34 0.700751
\(189\) −752.874 + 1020.49i −0.289754 + 0.392751i
\(190\) 9134.74i 3.48791i
\(191\) −3909.32 −1.48099 −0.740493 0.672064i \(-0.765408\pi\)
−0.740493 + 0.672064i \(0.765408\pi\)
\(192\) 3722.71 1199.58i 1.39929 0.450896i
\(193\) −318.770 −0.118889 −0.0594445 0.998232i \(-0.518933\pi\)
−0.0594445 + 0.998232i \(0.518933\pi\)
\(194\) 7095.32i 2.62585i
\(195\) −4188.14 + 1349.55i −1.53805 + 0.495607i
\(196\) −3731.12 −1.35974
\(197\) 5007.83i 1.81113i 0.424206 + 0.905566i \(0.360553\pi\)
−0.424206 + 0.905566i \(0.639447\pi\)
\(198\) 1344.86 967.134i 0.482702 0.347128i
\(199\) −904.934 −0.322357 −0.161178 0.986925i \(-0.551529\pi\)
−0.161178 + 0.986925i \(0.551529\pi\)
\(200\) 3206.93 1.13382
\(201\) 1525.54 + 4734.29i 0.535340 + 1.66135i
\(202\) 8664.36 3.01793
\(203\) 58.9457i 0.0203802i
\(204\) 247.143 + 766.972i 0.0848209 + 0.263229i
\(205\) −2324.13 −0.791825
\(206\) 1645.81i 0.556645i
\(207\) 470.040 338.022i 0.157826 0.113498i
\(208\) 1423.29i 0.474459i
\(209\) −1647.25 −0.545179
\(210\) −1038.34 3222.35i −0.341202 1.05887i
\(211\) 2400.18i 0.783106i 0.920156 + 0.391553i \(0.128062\pi\)
−0.920156 + 0.391553i \(0.871938\pi\)
\(212\) 8265.21i 2.67763i
\(213\) 1019.58 + 3164.13i 0.327985 + 1.01785i
\(214\) 2450.79i 0.782862i
\(215\) −1865.33 −0.591695
\(216\) 2468.68 3346.21i 0.777651 1.05408i
\(217\) 2023.16i 0.632908i
\(218\) 8578.62i 2.66522i
\(219\) −1385.94 4301.05i −0.427639 1.32711i
\(220\) 2834.32i 0.868590i
\(221\) 602.238 0.183307
\(222\) −1251.29 3883.21i −0.378294 1.17398i
\(223\) −1236.31 −0.371252 −0.185626 0.982620i \(-0.559431\pi\)
−0.185626 + 0.982620i \(0.559431\pi\)
\(224\) 1048.25 0.312676
\(225\) −2371.74 + 1705.60i −0.702737 + 0.505362i
\(226\) 5898.12 1.73601
\(227\) 1595.09 0.466388 0.233194 0.972430i \(-0.425082\pi\)
0.233194 + 0.972430i \(0.425082\pi\)
\(228\) −8950.00 + 2883.97i −2.59968 + 0.837701i
\(229\) 895.868i 0.258518i 0.991611 + 0.129259i \(0.0412599\pi\)
−0.991611 + 0.129259i \(0.958740\pi\)
\(230\) 1545.61i 0.443107i
\(231\) 581.078 187.242i 0.165507 0.0533316i
\(232\) 193.284i 0.0546970i
\(233\) 4173.18 1.17336 0.586682 0.809817i \(-0.300434\pi\)
0.586682 + 0.809817i \(0.300434\pi\)
\(234\) −4126.10 5737.59i −1.15270 1.60290i
\(235\) 1931.75i 0.536229i
\(236\) 2613.95 5919.83i 0.720990 1.63283i
\(237\) −3304.29 + 1064.75i −0.905639 + 0.291826i
\(238\) 463.361i 0.126198i
\(239\) 4715.74i 1.27630i −0.769911 0.638151i \(-0.779700\pi\)
0.769911 0.638151i \(-0.220300\pi\)
\(240\) 624.634 + 1938.46i 0.168000 + 0.521363i
\(241\) 111.516 0.0298066 0.0149033 0.999889i \(-0.495256\pi\)
0.0149033 + 0.999889i \(0.495256\pi\)
\(242\) 5485.01 1.45698
\(243\) −46.0806 + 3787.71i −0.0121649 + 0.999926i
\(244\) 3891.01i 1.02089i
\(245\) 3990.17i 1.04050i
\(246\) −1144.85 3552.88i −0.296719 0.920826i
\(247\) 7027.66i 1.81036i
\(248\) 6633.96i 1.69862i
\(249\) 5695.95 1835.42i 1.44966 0.467128i
\(250\) 1211.11i 0.306390i
\(251\) 504.008i 0.126744i 0.997990 + 0.0633719i \(0.0201854\pi\)
−0.997990 + 0.0633719i \(0.979815\pi\)
\(252\) 2829.35 2034.69i 0.707272 0.508623i
\(253\) −278.716 −0.0692598
\(254\) −5919.80 −1.46237
\(255\) 820.222 264.302i 0.201429 0.0649067i
\(256\) −6369.25 −1.55499
\(257\) 1386.31i 0.336480i −0.985746 0.168240i \(-0.946192\pi\)
0.985746 0.168240i \(-0.0538084\pi\)
\(258\) −918.848 2851.51i −0.221725 0.688091i
\(259\) 1503.61i 0.360734i
\(260\) 12092.1 2.88431
\(261\) −102.798 142.946i −0.0243794 0.0339010i
\(262\) −5961.19 −1.40566
\(263\) 7832.10i 1.83630i −0.396228 0.918152i \(-0.629681\pi\)
0.396228 0.918152i \(-0.370319\pi\)
\(264\) −1905.36 + 613.968i −0.444193 + 0.143133i
\(265\) 8839.05 2.04897
\(266\) −5407.07 −1.24635
\(267\) 2498.06 804.956i 0.572581 0.184504i
\(268\) 13669.0i 3.11554i
\(269\) −711.848 −0.161346 −0.0806731 0.996741i \(-0.525707\pi\)
−0.0806731 + 0.996741i \(0.525707\pi\)
\(270\) −8137.60 6003.55i −1.83422 1.35320i
\(271\) −2607.47 −0.584474 −0.292237 0.956346i \(-0.594400\pi\)
−0.292237 + 0.956346i \(0.594400\pi\)
\(272\) 278.743i 0.0621371i
\(273\) −798.832 2479.06i −0.177097 0.549595i
\(274\) 5038.80i 1.11097i
\(275\) 1406.35 0.308386
\(276\) −1514.35 + 487.972i −0.330265 + 0.106422i
\(277\) −5056.77 −1.09687 −0.548433 0.836195i \(-0.684775\pi\)
−0.548433 + 0.836195i \(0.684775\pi\)
\(278\) −5113.98 −1.10329
\(279\) −3528.26 4906.26i −0.757102 1.05280i
\(280\) 4091.30i 0.873221i
\(281\) 559.120i 0.118699i −0.998237 0.0593493i \(-0.981097\pi\)
0.998237 0.0593493i \(-0.0189026\pi\)
\(282\) 2953.06 951.569i 0.623589 0.200940i
\(283\) 4024.72i 0.845387i −0.906273 0.422693i \(-0.861085\pi\)
0.906273 0.422693i \(-0.138915\pi\)
\(284\) 9135.56i 1.90879i
\(285\) 3084.20 + 9571.38i 0.641026 + 1.98933i
\(286\) 3402.18i 0.703409i
\(287\) 1375.71i 0.282946i
\(288\) 2542.07 1828.09i 0.520114 0.374032i
\(289\) 4795.06 0.975993
\(290\) 470.044 0.0951790
\(291\) 2395.62 + 7434.47i 0.482591 + 1.49765i
\(292\) 12418.1i 2.48875i
\(293\) 736.817i 0.146912i −0.997298 0.0734562i \(-0.976597\pi\)
0.997298 0.0734562i \(-0.0234029\pi\)
\(294\) −6099.73 + 1965.53i −1.21001 + 0.389905i
\(295\) −6330.83 2795.43i −1.24948 0.551716i
\(296\) 4930.37i 0.968148i
\(297\) 1082.61 1467.43i 0.211512 0.286698i
\(298\) −11001.6 −2.13861
\(299\) 1189.09i 0.229990i
\(300\) 7641.14 2462.22i 1.47054 0.473855i
\(301\) 1104.13i 0.211432i
\(302\) 3591.11i 0.684255i
\(303\) 9078.51 2925.39i 1.72128 0.554650i
\(304\) 3252.72 0.613673
\(305\) −4161.16 −0.781204
\(306\) 808.072 + 1123.67i 0.150962 + 0.209922i
\(307\) −452.628 −0.0841461 −0.0420730 0.999115i \(-0.513396\pi\)
−0.0420730 + 0.999115i \(0.513396\pi\)
\(308\) −1677.70 −0.310376
\(309\) 555.682 + 1724.48i 0.102303 + 0.317483i
\(310\) 16133.0 2.95579
\(311\) 3689.41i 0.672692i 0.941738 + 0.336346i \(0.109191\pi\)
−0.941738 + 0.336346i \(0.890809\pi\)
\(312\) 2619.38 + 8128.87i 0.475299 + 1.47502i
\(313\) 10707.6i 1.93364i −0.255450 0.966822i \(-0.582224\pi\)
0.255450 0.966822i \(-0.417776\pi\)
\(314\) 14691.2i 2.64035i
\(315\) −2175.95 3025.79i −0.389209 0.541219i
\(316\) 9540.21 1.69835
\(317\) 4660.59i 0.825756i 0.910786 + 0.412878i \(0.135476\pi\)
−0.910786 + 0.412878i \(0.864524\pi\)
\(318\) 4354.05 + 13512.2i 0.767809 + 2.38278i
\(319\) 84.7618i 0.0148770i
\(320\) 11494.5i 2.00801i
\(321\) −827.471 2567.94i −0.143878 0.446505i
\(322\) −914.884 −0.158337
\(323\) 1376.33i 0.237092i
\(324\) 3312.97 9868.43i 0.568067 1.69212i
\(325\) 5999.94i 1.02405i
\(326\) 15360.7 2.60966
\(327\) 2896.44 + 8988.67i 0.489827 + 1.52011i
\(328\) 4510.96i 0.759379i
\(329\) 1143.45 0.191613
\(330\) 1493.10 + 4633.62i 0.249068 + 0.772946i
\(331\) 8908.61 1.47934 0.739670 0.672969i \(-0.234981\pi\)
0.739670 + 0.672969i \(0.234981\pi\)
\(332\) −16445.5 −2.71856
\(333\) −2622.21 3646.34i −0.431520 0.600055i
\(334\) 7095.81i 1.16247i
\(335\) −14618.0 −2.38407
\(336\) −1147.42 + 369.736i −0.186301 + 0.0600320i
\(337\) 3654.41i 0.590707i 0.955388 + 0.295354i \(0.0954375\pi\)
−0.955388 + 0.295354i \(0.904563\pi\)
\(338\) 4144.67 0.666983
\(339\) 6180.05 1991.41i 0.990131 0.319052i
\(340\) −2368.16 −0.377740
\(341\) 2909.23i 0.462005i
\(342\) −13112.4 + 9429.59i −2.07321 + 1.49092i
\(343\) −5462.31 −0.859874
\(344\) 3620.46i 0.567449i
\(345\) 521.851 + 1619.49i 0.0814363 + 0.252726i
\(346\) −20607.6 −3.20194
\(347\) 3873.17 0.599200 0.299600 0.954065i \(-0.403147\pi\)
0.299600 + 0.954065i \(0.403147\pi\)
\(348\) 148.400 + 460.537i 0.0228594 + 0.0709408i
\(349\) 1703.25i 0.261241i 0.991432 + 0.130620i \(0.0416969\pi\)
−0.991432 + 0.130620i \(0.958303\pi\)
\(350\) 4616.34 0.705011
\(351\) −6260.53 4618.73i −0.952030 0.702364i
\(352\) −1507.35 −0.228245
\(353\) −853.113 −0.128631 −0.0643153 0.997930i \(-0.520486\pi\)
−0.0643153 + 0.997930i \(0.520486\pi\)
\(354\) 1154.82 11054.9i 0.173385 1.65978i
\(355\) −9769.82 −1.46064
\(356\) −7212.47 −1.07376
\(357\) 156.446 + 485.509i 0.0231933 + 0.0719772i
\(358\) −13675.1 −2.01886
\(359\) 6930.62i 1.01890i 0.860501 + 0.509448i \(0.170151\pi\)
−0.860501 + 0.509448i \(0.829849\pi\)
\(360\) 7134.97 + 9921.61i 1.04457 + 1.45254i
\(361\) 9201.70 1.34155
\(362\) −6661.31 −0.967157
\(363\) 5747.19 1851.93i 0.830990 0.267772i
\(364\) 7157.60i 1.03066i
\(365\) 13280.3 1.90444
\(366\) −2049.76 6361.13i −0.292739 0.908474i
\(367\) 9975.19i 1.41880i −0.704804 0.709402i \(-0.748965\pi\)
0.704804 0.709402i \(-0.251035\pi\)
\(368\) 550.365 0.0779613
\(369\) −2399.15 3336.16i −0.338468 0.470660i
\(370\) 11990.1 1.68469
\(371\) 5232.04i 0.732167i
\(372\) 5093.44 + 15806.7i 0.709899 + 2.20307i
\(373\) −12889.7 −1.78928 −0.894642 0.446784i \(-0.852569\pi\)
−0.894642 + 0.446784i \(0.852569\pi\)
\(374\) 666.296i 0.0921212i
\(375\) 408.913 + 1269.00i 0.0563098 + 0.174749i
\(376\) −3749.39 −0.514256
\(377\) 361.620 0.0494016
\(378\) 3553.65 4816.84i 0.483544 0.655427i
\(379\) 9726.01 1.31818 0.659092 0.752062i \(-0.270941\pi\)
0.659092 + 0.752062i \(0.270941\pi\)
\(380\) 27634.7i 3.73061i
\(381\) −6202.77 + 1998.73i −0.834061 + 0.268761i
\(382\) 18452.4 2.47148
\(383\) 6768.75i 0.903047i −0.892259 0.451524i \(-0.850881\pi\)
0.892259 0.451524i \(-0.149119\pi\)
\(384\) −12983.2 + 4183.61i −1.72538 + 0.555974i
\(385\) 1794.18i 0.237506i
\(386\) 1504.63 0.198403
\(387\) −1925.54 2677.58i −0.252921 0.351703i
\(388\) 21465.0i 2.80855i
\(389\) 6858.16i 0.893888i −0.894562 0.446944i \(-0.852512\pi\)
0.894562 0.446944i \(-0.147488\pi\)
\(390\) 19768.5 6370.03i 2.56671 0.827074i
\(391\) 232.876i 0.0301204i
\(392\) 7744.62 0.997863
\(393\) −6246.14 + 2012.70i −0.801720 + 0.258340i
\(394\) 23637.5i 3.02243i
\(395\) 10202.6i 1.29961i
\(396\) −4068.51 + 2925.81i −0.516289 + 0.371281i
\(397\) 7447.83i 0.941552i 0.882253 + 0.470776i \(0.156026\pi\)
−0.882253 + 0.470776i \(0.843974\pi\)
\(398\) 4271.38 0.537953
\(399\) −5665.53 + 1825.61i −0.710855 + 0.229060i
\(400\) −2777.04 −0.347130
\(401\) −4411.38 −0.549362 −0.274681 0.961535i \(-0.588572\pi\)
−0.274681 + 0.961535i \(0.588572\pi\)
\(402\) −7200.71 22346.4i −0.893380 2.77248i
\(403\) 12411.7 1.53417
\(404\) −26211.7 −3.22792
\(405\) −10553.6 3542.98i −1.29484 0.434697i
\(406\) 278.230i 0.0340107i
\(407\) 2162.14i 0.263325i
\(408\) −512.990 1591.99i −0.0622470 0.193175i
\(409\) 669.354i 0.0809228i 0.999181 + 0.0404614i \(0.0128828\pi\)
−0.999181 + 0.0404614i \(0.987117\pi\)
\(410\) 10970.1 1.32141
\(411\) 1701.27 + 5279.65i 0.204179 + 0.633640i
\(412\) 4978.95i 0.595377i
\(413\) 1654.68 3747.37i 0.197147 0.446480i
\(414\) −2218.64 + 1595.50i −0.263382 + 0.189407i
\(415\) 17587.3i 2.08030i
\(416\) 6430.83i 0.757926i
\(417\) −5358.42 + 1726.65i −0.629264 + 0.202769i
\(418\) 7775.18 0.909800
\(419\) 616.743 0.0719090 0.0359545 0.999353i \(-0.488553\pi\)
0.0359545 + 0.999353i \(0.488553\pi\)
\(420\) 3141.23 + 9748.34i 0.364943 + 1.13255i
\(421\) 7169.53i 0.829979i 0.909826 + 0.414990i \(0.136215\pi\)
−0.909826 + 0.414990i \(0.863785\pi\)
\(422\) 11329.1i 1.30685i
\(423\) 2772.93 1994.11i 0.318734 0.229212i
\(424\) 17155.9i 1.96501i
\(425\) 1175.05i 0.134114i
\(426\) −4812.55 14935.0i −0.547344 1.69860i
\(427\) 2463.09i 0.279151i
\(428\) 7414.21i 0.837334i
\(429\) 1148.69 + 3564.80i 0.129276 + 0.401189i
\(430\) 8804.55 0.987426
\(431\) 13322.7 1.48894 0.744468 0.667659i \(-0.232703\pi\)
0.744468 + 0.667659i \(0.232703\pi\)
\(432\) −2137.76 + 2897.66i −0.238086 + 0.322717i
\(433\) 5914.82 0.656462 0.328231 0.944598i \(-0.393548\pi\)
0.328231 + 0.944598i \(0.393548\pi\)
\(434\) 9549.52i 1.05620i
\(435\) 492.511 158.703i 0.0542853 0.0174925i
\(436\) 25952.3i 2.85067i
\(437\) 2717.49 0.297472
\(438\) 6541.77 + 20301.4i 0.713648 + 2.21470i
\(439\) −9240.25 −1.00459 −0.502293 0.864698i \(-0.667510\pi\)
−0.502293 + 0.864698i \(0.667510\pi\)
\(440\) 5883.14i 0.637427i
\(441\) −5727.67 + 4118.96i −0.618472 + 0.444764i
\(442\) −2842.63 −0.305905
\(443\) −8689.46 −0.931938 −0.465969 0.884801i \(-0.654294\pi\)
−0.465969 + 0.884801i \(0.654294\pi\)
\(444\) 3785.45 + 11747.6i 0.404616 + 1.25567i
\(445\) 7713.22i 0.821667i
\(446\) 5835.50 0.619550
\(447\) −11527.5 + 3714.52i −1.21975 + 0.393044i
\(448\) −6803.89 −0.717530
\(449\) 952.486i 0.100113i −0.998746 0.0500563i \(-0.984060\pi\)
0.998746 0.0500563i \(-0.0159401\pi\)
\(450\) 11194.9 8050.61i 1.17274 0.843354i
\(451\) 1978.22i 0.206543i
\(452\) −17843.2 −1.85680
\(453\) 1212.48 + 3762.76i 0.125756 + 0.390265i
\(454\) −7529.01 −0.778313
\(455\) 7654.54 0.788682
\(456\) 18577.3 5986.21i 1.90781 0.614759i
\(457\) 10514.9i 1.07629i −0.842852 0.538146i \(-0.819125\pi\)
0.842852 0.538146i \(-0.180875\pi\)
\(458\) 4228.60i 0.431418i
\(459\) 1226.09 + 904.551i 0.124682 + 0.0919844i
\(460\) 4675.83i 0.473938i
\(461\) 2406.90i 0.243168i −0.992581 0.121584i \(-0.961203\pi\)
0.992581 0.121584i \(-0.0387974\pi\)
\(462\) −2742.75 + 883.801i −0.276200 + 0.0890004i
\(463\) 9106.31i 0.914052i 0.889453 + 0.457026i \(0.151085\pi\)
−0.889453 + 0.457026i \(0.848915\pi\)
\(464\) 167.374i 0.0167460i
\(465\) 16904.2 5447.07i 1.68583 0.543229i
\(466\) −19697.8 −1.95812
\(467\) −2006.05 −0.198777 −0.0993883 0.995049i \(-0.531689\pi\)
−0.0993883 + 0.995049i \(0.531689\pi\)
\(468\) 12482.4 + 17357.5i 1.23290 + 1.71443i
\(469\) 8652.72i 0.851910i
\(470\) 9118.09i 0.894864i
\(471\) −4960.25 15393.4i −0.485257 1.50593i
\(472\) −5425.72 + 12287.7i −0.529108 + 1.19828i
\(473\) 1587.70i 0.154340i
\(474\) 15596.6 5025.72i 1.51134 0.487002i
\(475\) −13712.0 −1.32452
\(476\) 1401.77i 0.134979i
\(477\) 9124.35 + 12688.0i 0.875839 + 1.21791i
\(478\) 22258.8i 2.12991i
\(479\) 5805.96i 0.553822i −0.960896 0.276911i \(-0.910689\pi\)
0.960896 0.276911i \(-0.0893108\pi\)
\(480\) 2822.27 + 8758.51i 0.268372 + 0.832853i
\(481\) 9224.38 0.874419
\(482\) −526.369 −0.0497416
\(483\) −958.615 + 308.896i −0.0903074 + 0.0290999i
\(484\) −16593.4 −1.55836
\(485\) −22955.2 −2.14916
\(486\) 217.506 17878.4i 0.0203009 1.66869i
\(487\) 12433.3 1.15689 0.578444 0.815722i \(-0.303660\pi\)
0.578444 + 0.815722i \(0.303660\pi\)
\(488\) 8076.51i 0.749193i
\(489\) 16094.9 5186.30i 1.48842 0.479616i
\(490\) 18834.0i 1.73640i
\(491\) 15237.2i 1.40050i 0.713897 + 0.700251i \(0.246928\pi\)
−0.713897 + 0.700251i \(0.753072\pi\)
\(492\) 3463.44 + 10748.3i 0.317365 + 0.984897i
\(493\) −70.8212 −0.00646983
\(494\) 33171.3i 3.02115i
\(495\) 3128.94 + 4350.98i 0.284112 + 0.395075i
\(496\) 5744.69i 0.520049i
\(497\) 5782.99i 0.521937i
\(498\) −26885.5 + 8663.36i −2.41921 + 0.779547i
\(499\) 341.264 0.0306154 0.0153077 0.999883i \(-0.495127\pi\)
0.0153077 + 0.999883i \(0.495127\pi\)
\(500\) 3663.89i 0.327708i
\(501\) 2395.79 + 7434.99i 0.213645 + 0.663016i
\(502\) 2378.97i 0.211511i
\(503\) −1834.71 −0.162636 −0.0813179 0.996688i \(-0.525913\pi\)
−0.0813179 + 0.996688i \(0.525913\pi\)
\(504\) −5872.84 + 4223.36i −0.519042 + 0.373261i
\(505\) 28031.5i 2.47007i
\(506\) 1315.57 0.115582
\(507\) 4342.78 1399.38i 0.380414 0.122581i
\(508\) 17908.8 1.56412
\(509\) 12183.2 1.06093 0.530465 0.847707i \(-0.322018\pi\)
0.530465 + 0.847707i \(0.322018\pi\)
\(510\) −3871.54 + 1247.53i −0.336146 + 0.108317i
\(511\) 7860.90i 0.680520i
\(512\) 9062.40 0.782237
\(513\) −10555.4 + 14307.5i −0.908449 + 1.23137i
\(514\) 6543.52i 0.561522i
\(515\) −5324.63 −0.455595
\(516\) 2779.73 + 8626.48i 0.237153 + 0.735968i
\(517\) −1644.24 −0.139872
\(518\) 7097.22i 0.601996i
\(519\) −21592.6 + 6957.83i −1.82623 + 0.588468i
\(520\) −25099.3 −2.11669
\(521\) 2837.05i 0.238567i 0.992860 + 0.119284i \(0.0380598\pi\)
−0.992860 + 0.119284i \(0.961940\pi\)
\(522\) 485.216 + 674.722i 0.0406845 + 0.0565743i
\(523\) 6034.65 0.504545 0.252272 0.967656i \(-0.418822\pi\)
0.252272 + 0.967656i \(0.418822\pi\)
\(524\) 18034.0 1.50347
\(525\) 4837.00 1558.64i 0.402103 0.129570i
\(526\) 36968.4i 3.06444i
\(527\) −2430.75 −0.200921
\(528\) 1649.95 531.667i 0.135994 0.0438217i
\(529\) −11707.2 −0.962209
\(530\) −41721.2 −3.41935
\(531\) −2522.49 11973.2i −0.206152 0.978520i
\(532\) 16357.6 1.33307
\(533\) 8439.70 0.685861
\(534\) −11791.1 + 3799.48i −0.955528 + 0.307902i
\(535\) 7928.96 0.640746
\(536\) 28372.4i 2.28638i
\(537\) −14328.8 + 4617.18i −1.15146 + 0.371036i
\(538\) 3360.00 0.269256
\(539\) 3396.29 0.271407
\(540\) 24618.1 + 18162.1i 1.96184 + 1.44736i
\(541\) 16326.5i 1.29747i 0.761013 + 0.648736i \(0.224702\pi\)
−0.761013 + 0.648736i \(0.775298\pi\)
\(542\) 12307.5 0.975375
\(543\) −6979.72 + 2249.09i −0.551618 + 0.177749i
\(544\) 1259.44i 0.0992611i
\(545\) −27754.1 −2.18139
\(546\) 3770.57 + 11701.4i 0.295541 + 0.917170i
\(547\) 16651.3 1.30157 0.650784 0.759263i \(-0.274440\pi\)
0.650784 + 0.759263i \(0.274440\pi\)
\(548\) 15243.5i 1.18827i
\(549\) −4295.47 5973.12i −0.333928 0.464347i
\(550\) −6638.13 −0.514638
\(551\) 826.431i 0.0638968i
\(552\) 3143.31 1012.88i 0.242370 0.0780993i
\(553\) 6039.15 0.464395
\(554\) 23868.5 1.83046
\(555\) 12563.2 4048.27i 0.960862 0.309620i
\(556\) 15471.0 1.18006
\(557\) 16078.8i 1.22312i −0.791197 0.611561i \(-0.790542\pi\)
0.791197 0.611561i \(-0.209458\pi\)
\(558\) 16653.8 + 23158.1i 1.26346 + 1.75692i
\(559\) 6773.64 0.512512
\(560\) 3542.87i 0.267346i
\(561\) −224.964 698.145i −0.0169305 0.0525413i
\(562\) 2639.11i 0.198086i
\(563\) −8735.26 −0.653903 −0.326951 0.945041i \(-0.606021\pi\)
−0.326951 + 0.945041i \(0.606021\pi\)
\(564\) −8933.68 + 2878.72i −0.666979 + 0.214922i
\(565\) 19082.0i 1.42086i
\(566\) 18997.1i 1.41079i
\(567\) 2097.18 6246.92i 0.155332 0.462691i
\(568\) 18962.5i 1.40079i
\(569\) 14260.2 1.05064 0.525322 0.850903i \(-0.323945\pi\)
0.525322 + 0.850903i \(0.323945\pi\)
\(570\) −14557.8 45177.9i −1.06975 3.31982i
\(571\) 9210.71i 0.675055i 0.941316 + 0.337527i \(0.109591\pi\)
−0.941316 + 0.337527i \(0.890409\pi\)
\(572\) 10292.4i 0.752353i
\(573\) 19334.4 6230.17i 1.40961 0.454222i
\(574\) 6493.49i 0.472183i
\(575\) −2320.09 −0.168268
\(576\) −16499.8 + 11865.6i −1.19356 + 0.858330i
\(577\) −7145.53 −0.515550 −0.257775 0.966205i \(-0.582989\pi\)
−0.257775 + 0.966205i \(0.582989\pi\)
\(578\) −22633.2 −1.62875
\(579\) 1576.55 508.015i 0.113159 0.0364635i
\(580\) −1421.99 −0.101802
\(581\) −10410.3 −0.743361
\(582\) −11307.6 35091.5i −0.805352 2.49929i
\(583\) 7523.49i 0.534462i
\(584\) 25776.0i 1.82640i
\(585\) 18562.6 13349.0i 1.31192 0.943443i
\(586\) 3477.86i 0.245169i
\(587\) 23849.3 1.67695 0.838473 0.544943i \(-0.183449\pi\)
0.838473 + 0.544943i \(0.183449\pi\)
\(588\) 18453.1 5946.18i 1.29421 0.417034i
\(589\) 28365.1i 1.98432i
\(590\) 29882.2 + 13194.7i 2.08514 + 0.920709i
\(591\) −7980.83 24767.3i −0.555478 1.72385i
\(592\) 4269.46i 0.296409i
\(593\) 22393.0i 1.55071i −0.631526 0.775355i \(-0.717571\pi\)
0.631526 0.775355i \(-0.282429\pi\)
\(594\) −5110.02 + 6926.45i −0.352974 + 0.478444i
\(595\) −1499.10 −0.103289
\(596\) 33282.3 2.28741
\(597\) 4475.55 1442.17i 0.306821 0.0988676i
\(598\) 5612.63i 0.383809i
\(599\) 1908.02i 0.130150i 0.997880 + 0.0650749i \(0.0207286\pi\)
−0.997880 + 0.0650749i \(0.979271\pi\)
\(600\) −15860.6 + 5110.79i −1.07918 + 0.347745i
\(601\) 3985.09i 0.270475i 0.990813 + 0.135237i \(0.0431797\pi\)
−0.990813 + 0.135237i \(0.956820\pi\)
\(602\) 5211.62i 0.352840i
\(603\) −15089.8 20983.3i −1.01908 1.41709i
\(604\) 10863.9i 0.731866i
\(605\) 17745.5i 1.19249i
\(606\) −42851.6 + 13808.1i −2.87248 + 0.925606i
\(607\) −18670.7 −1.24847 −0.624235 0.781237i \(-0.714589\pi\)
−0.624235 + 0.781237i \(0.714589\pi\)
\(608\) 14696.7 0.980314
\(609\) 93.9400 + 291.529i 0.00625064 + 0.0193980i
\(610\) 19641.1 1.30368
\(611\) 7014.86i 0.464469i
\(612\) −2444.60 3399.37i −0.161466 0.224528i
\(613\) 9951.11i 0.655663i 0.944736 + 0.327832i \(0.106318\pi\)
−0.944736 + 0.327832i \(0.893682\pi\)
\(614\) 2136.45 0.140424
\(615\) 11494.5 3703.90i 0.753664 0.242855i
\(616\) 3482.37 0.227774
\(617\) 15527.0i 1.01311i 0.862206 + 0.506557i \(0.169082\pi\)
−0.862206 + 0.506557i \(0.830918\pi\)
\(618\) −2622.88 8139.72i −0.170724 0.529818i
\(619\) 9610.37 0.624028 0.312014 0.950077i \(-0.398996\pi\)
0.312014 + 0.950077i \(0.398996\pi\)
\(620\) −48806.1 −3.16145
\(621\) −1786.00 + 2420.85i −0.115410 + 0.156434i
\(622\) 17414.4i 1.12260i
\(623\) −4565.64 −0.293609
\(624\) −2268.26 7039.21i −0.145518 0.451593i
\(625\) −17443.0 −1.11635
\(626\) 50541.1i 3.22689i
\(627\) 8146.83 2625.17i 0.518904 0.167208i
\(628\) 44444.2i 2.82407i
\(629\) −1806.54 −0.114517
\(630\) 10270.7 + 14282.1i 0.649516 + 0.903192i
\(631\) 22899.0 1.44468 0.722342 0.691536i \(-0.243066\pi\)
0.722342 + 0.691536i \(0.243066\pi\)
\(632\) −19802.4 −1.24636
\(633\) −3825.10 11870.6i −0.240180 0.745364i
\(634\) 21998.5i 1.37803i
\(635\) 19152.1i 1.19690i
\(636\) −13172.0 40877.5i −0.821234 2.54858i
\(637\) 14489.6i 0.901257i
\(638\) 400.085i 0.0248268i
\(639\) −10085.2 14024.1i −0.624356 0.868205i
\(640\) 40088.0i 2.47597i
\(641\) 15494.1i 0.954728i 0.878706 + 0.477364i \(0.158408\pi\)
−0.878706 + 0.477364i \(0.841592\pi\)
\(642\) 3905.75 + 12120.9i 0.240106 + 0.745133i
\(643\) 5728.58 0.351342 0.175671 0.984449i \(-0.443790\pi\)
0.175671 + 0.984449i \(0.443790\pi\)
\(644\) 2767.74 0.169354
\(645\) 9225.40 2972.72i 0.563178 0.181474i
\(646\) 6496.41i 0.395662i
\(647\) 25348.3i 1.54026i −0.637889 0.770128i \(-0.720192\pi\)
0.637889 0.770128i \(-0.279808\pi\)
\(648\) −6876.67 + 20483.7i −0.416884 + 1.24178i
\(649\) −2379.37 + 5388.59i −0.143912 + 0.325918i
\(650\) 28320.3i 1.70895i
\(651\) 3224.25 + 10006.0i 0.194114 + 0.602405i
\(652\) −46469.6 −2.79124
\(653\) 5226.26i 0.313199i 0.987662 + 0.156600i \(0.0500533\pi\)
−0.987662 + 0.156600i \(0.949947\pi\)
\(654\) −13671.5 42427.5i −0.817428 2.53677i
\(655\) 19286.1i 1.15049i
\(656\) 3906.28i 0.232492i
\(657\) 13708.9 + 19063.1i 0.814058 + 1.13200i
\(658\) −5397.22 −0.319765
\(659\) −11053.9 −0.653411 −0.326706 0.945126i \(-0.605939\pi\)
−0.326706 + 0.945126i \(0.605939\pi\)
\(660\) −4516.97 14017.8i −0.266398 0.826729i
\(661\) −20881.3 −1.22873 −0.614365 0.789022i \(-0.710588\pi\)
−0.614365 + 0.789022i \(0.710588\pi\)
\(662\) −42049.6 −2.46874
\(663\) −2978.50 + 959.769i −0.174473 + 0.0562207i
\(664\) 34135.6 1.99506
\(665\) 17493.3i 1.02009i
\(666\) 12377.1 + 17211.1i 0.720125 + 1.00138i
\(667\) 139.833i 0.00811748i
\(668\) 21466.5i 1.24336i
\(669\) 6114.44 1970.27i 0.353360 0.113864i
\(670\) 68998.4 3.97857
\(671\) 3541.84i 0.203772i
\(672\) −5184.37 + 1670.57i −0.297606 + 0.0958983i
\(673\) 5558.12i 0.318350i −0.987250 0.159175i \(-0.949117\pi\)
0.987250 0.159175i \(-0.0508834\pi\)
\(674\) 17249.2i 0.985778i
\(675\) 9011.81 12215.2i 0.513874 0.696538i
\(676\) −12538.6 −0.713393
\(677\) 442.874i 0.0251419i −0.999921 0.0125709i \(-0.995998\pi\)
0.999921 0.0125709i \(-0.00400156\pi\)
\(678\) −29170.5 + 9399.67i −1.65234 + 0.532437i
\(679\) 13587.8i 0.767968i
\(680\) 4915.55 0.277210
\(681\) −7888.90 + 2542.05i −0.443911 + 0.143042i
\(682\) 13731.9i 0.770998i
\(683\) 13997.4 0.784180 0.392090 0.919927i \(-0.371752\pi\)
0.392090 + 0.919927i \(0.371752\pi\)
\(684\) 39668.1 28526.7i 2.21747 1.59466i
\(685\) −16301.9 −0.909288
\(686\) 25782.7 1.43497
\(687\) −1427.72 4430.72i −0.0792881 0.246059i
\(688\) 3135.15i 0.173730i
\(689\) −32097.6 −1.77477
\(690\) −2463.19 7644.17i −0.135902 0.421751i
\(691\) 14932.8i 0.822100i 0.911613 + 0.411050i \(0.134838\pi\)
−0.911613 + 0.411050i \(0.865162\pi\)
\(692\) 62342.7 3.42473
\(693\) −2575.45 + 1852.09i −0.141174 + 0.101523i
\(694\) −18281.8 −0.999951
\(695\) 16545.1i 0.903008i
\(696\) −308.031 955.929i −0.0167757 0.0520609i
\(697\) −1652.86 −0.0898231
\(698\) 8039.54i 0.435962i
\(699\) −20639.4 + 6650.67i −1.11681 + 0.359873i
\(700\) −13965.5 −0.754066
\(701\) −18225.0 −0.981952 −0.490976 0.871173i \(-0.663360\pi\)
−0.490976 + 0.871173i \(0.663360\pi\)
\(702\) 29550.4 + 21800.9i 1.58876 + 1.17211i
\(703\) 21081.0i 1.13099i
\(704\) 9783.75 0.523777
\(705\) 3078.58 + 9553.93i 0.164463 + 0.510386i
\(706\) 4026.78 0.214660
\(707\) −16592.5 −0.882640
\(708\) −3493.61 + 33443.6i −0.185449 + 1.77527i
\(709\) 29479.6 1.56153 0.780767 0.624822i \(-0.214828\pi\)
0.780767 + 0.624822i \(0.214828\pi\)
\(710\) 46114.6 2.43754
\(711\) 14645.2 10531.9i 0.772489 0.555523i
\(712\) 14970.8 0.787997
\(713\) 4799.41i 0.252089i
\(714\) −738.444 2291.65i −0.0387053 0.120116i
\(715\) −11007.0 −0.575716
\(716\) 41370.3 2.15933
\(717\) 7515.35 + 23322.8i 0.391445 + 1.21479i
\(718\) 32713.3i 1.70035i
\(719\) 17184.2 0.891325 0.445663 0.895201i \(-0.352968\pi\)
0.445663 + 0.895201i \(0.352968\pi\)
\(720\) −6178.54 8591.64i −0.319806 0.444710i
\(721\) 3151.78i 0.162799i
\(722\) −43433.0 −2.23879
\(723\) −551.529 + 177.720i −0.0283701 + 0.00914175i
\(724\) 20152.0 1.03445
\(725\) 705.573i 0.0361439i
\(726\) −27127.4 + 8741.30i −1.38676 + 0.446860i
\(727\) 7341.84 0.374544 0.187272 0.982308i \(-0.440035\pi\)
0.187272 + 0.982308i \(0.440035\pi\)
\(728\) 14856.9i 0.756364i
\(729\) −5808.47 18806.4i −0.295101 0.955466i
\(730\) −62684.3 −3.17815
\(731\) −1326.58 −0.0671207
\(732\) 6201.00 + 19243.9i 0.313108 + 0.971687i
\(733\) −24371.5 −1.22808 −0.614040 0.789275i \(-0.710457\pi\)
−0.614040 + 0.789275i \(0.710457\pi\)
\(734\) 47084.0i 2.36771i
\(735\) −6359.01 19734.3i −0.319123 0.990353i
\(736\) 2486.71 0.124540
\(737\) 12442.3i 0.621870i
\(738\) 11324.2 + 15747.0i 0.564838 + 0.785443i
\(739\) 24359.0i 1.21253i −0.795262 0.606265i \(-0.792667\pi\)
0.795262 0.606265i \(-0.207333\pi\)
\(740\) −36272.8 −1.80191
\(741\) −11199.8 34756.9i −0.555242 1.72311i
\(742\) 24695.8i 1.22185i
\(743\) 13871.0i 0.684895i 0.939537 + 0.342447i \(0.111256\pi\)
−0.939537 + 0.342447i \(0.888744\pi\)
\(744\) −10572.4 32809.8i −0.520969 1.61675i
\(745\) 35593.1i 1.75038i
\(746\) 60840.7 2.98597
\(747\) −25245.6 + 18154.9i −1.23653 + 0.889229i
\(748\) 2015.70i 0.0985311i
\(749\) 4693.34i 0.228960i
\(750\) −1930.11 5989.82i −0.0939703 0.291623i
\(751\) 36319.4i 1.76473i 0.470563 + 0.882366i \(0.344051\pi\)
−0.470563 + 0.882366i \(0.655949\pi\)
\(752\) 3246.79 0.157445
\(753\) −803.223 2492.69i −0.0388726 0.120635i
\(754\) −1706.89 −0.0824419
\(755\) −11618.2 −0.560039
\(756\) −10750.6 + 14572.1i −0.517190 + 0.701033i
\(757\) −2905.61 −0.139506 −0.0697530 0.997564i \(-0.522221\pi\)
−0.0697530 + 0.997564i \(0.522221\pi\)
\(758\) −45907.8 −2.19980
\(759\) 1378.45 444.182i 0.0659219 0.0212421i
\(760\) 57360.8i 2.73776i
\(761\) 30835.4i 1.46883i −0.678699 0.734416i \(-0.737456\pi\)
0.678699 0.734416i \(-0.262544\pi\)
\(762\) 29277.7 9434.22i 1.39189 0.448511i
\(763\) 16428.3i 0.779483i
\(764\) −55822.8 −2.64345
\(765\) −3635.38 + 2614.33i −0.171814 + 0.123557i
\(766\) 31949.2i 1.50701i
\(767\) 22989.4 + 10151.2i 1.08227 + 0.477884i
\(768\) 31500.5 10150.5i 1.48005 0.476919i
\(769\) 25096.4i 1.17685i 0.808551 + 0.588426i \(0.200252\pi\)
−0.808551 + 0.588426i \(0.799748\pi\)
\(770\) 8468.73i 0.396353i
\(771\) 2209.32 + 6856.30i 0.103199 + 0.320264i
\(772\) −4551.86 −0.212208
\(773\) 33445.3 1.55620 0.778100 0.628140i \(-0.216183\pi\)
0.778100 + 0.628140i \(0.216183\pi\)
\(774\) 9088.74 + 12638.5i 0.422078 + 0.586925i
\(775\) 24217.0i 1.12245i
\(776\) 44554.4i 2.06110i
\(777\) 2396.27 + 7436.46i 0.110638 + 0.343348i
\(778\) 32371.3i 1.49173i
\(779\) 19287.7i 0.887103i
\(780\) −59804.2 + 19270.8i −2.74530 + 0.884623i
\(781\) 8315.74i 0.380999i
\(782\) 1099.20i 0.0502652i
\(783\) 736.218 + 543.148i 0.0336019 + 0.0247899i
\(784\) −6706.47