Properties

Label 177.4.d.c.176.2
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 176.2
Character \(\chi\) \(=\) 177.176
Dual form 177.4.d.c.176.1

$q$-expansion

\(f(q)\) \(=\) \(q-5.56568 q^{2} +(-1.93387 + 4.82288i) q^{3} +22.9768 q^{4} +10.3188i q^{5} +(10.7633 - 26.8426i) q^{6} -5.13468 q^{7} -83.3558 q^{8} +(-19.5203 - 18.6536i) q^{9} +O(q^{10})\) \(q-5.56568 q^{2} +(-1.93387 + 4.82288i) q^{3} +22.9768 q^{4} +10.3188i q^{5} +(10.7633 - 26.8426i) q^{6} -5.13468 q^{7} -83.3558 q^{8} +(-19.5203 - 18.6536i) q^{9} -57.4309i q^{10} +8.23442 q^{11} +(-44.4341 + 110.814i) q^{12} +53.3544i q^{13} +28.5780 q^{14} +(-49.7661 - 19.9551i) q^{15} +280.117 q^{16} +93.0677i q^{17} +(108.644 + 103.820i) q^{18} -84.1079 q^{19} +237.092i q^{20} +(9.92981 - 24.7639i) q^{21} -45.8301 q^{22} -138.110 q^{23} +(161.199 - 402.015i) q^{24} +18.5232 q^{25} -296.953i q^{26} +(127.714 - 58.0703i) q^{27} -117.978 q^{28} -249.312i q^{29} +(276.982 + 111.064i) q^{30} +203.586i q^{31} -892.196 q^{32} +(-15.9243 + 39.7136i) q^{33} -517.985i q^{34} -52.9836i q^{35} +(-448.513 - 428.600i) q^{36} +60.4290i q^{37} +468.118 q^{38} +(-257.322 - 103.180i) q^{39} -860.128i q^{40} +36.5916i q^{41} +(-55.2661 + 137.828i) q^{42} -368.769i q^{43} +189.200 q^{44} +(192.482 - 201.425i) q^{45} +768.675 q^{46} +112.441 q^{47} +(-541.711 + 1350.97i) q^{48} -316.635 q^{49} -103.094 q^{50} +(-448.854 - 179.981i) q^{51} +1225.91i q^{52} -318.575i q^{53} +(-710.814 + 323.200i) q^{54} +84.9689i q^{55} +428.006 q^{56} +(162.654 - 405.642i) q^{57} +1387.59i q^{58} +(453.071 - 10.2958i) q^{59} +(-1143.46 - 458.504i) q^{60} -214.084i q^{61} -1133.09i q^{62} +(100.231 + 95.7805i) q^{63} +2724.74 q^{64} -550.551 q^{65} +(88.6295 - 221.033i) q^{66} -309.301i q^{67} +2138.39i q^{68} +(267.087 - 666.087i) q^{69} +294.889i q^{70} -830.490i q^{71} +(1627.13 + 1554.89i) q^{72} +110.548i q^{73} -336.328i q^{74} +(-35.8216 + 89.3354i) q^{75} -1932.53 q^{76} -42.2811 q^{77} +(1432.17 + 574.269i) q^{78} -180.521 q^{79} +2890.46i q^{80} +(33.0838 + 728.249i) q^{81} -203.657i q^{82} +339.217 q^{83} +(228.155 - 568.995i) q^{84} -960.343 q^{85} +2052.45i q^{86} +(1202.40 + 482.137i) q^{87} -686.386 q^{88} +743.168 q^{89} +(-1071.29 + 1121.07i) q^{90} -273.958i q^{91} -3173.32 q^{92} +(-981.870 - 393.709i) q^{93} -625.813 q^{94} -867.889i q^{95} +(1725.39 - 4302.95i) q^{96} -439.178i q^{97} +1762.29 q^{98} +(-160.738 - 153.602i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.56568 −1.96776 −0.983882 0.178819i \(-0.942772\pi\)
−0.983882 + 0.178819i \(0.942772\pi\)
\(3\) −1.93387 + 4.82288i −0.372173 + 0.928163i
\(4\) 22.9768 2.87209
\(5\) 10.3188i 0.922938i 0.887156 + 0.461469i \(0.152677\pi\)
−0.887156 + 0.461469i \(0.847323\pi\)
\(6\) 10.7633 26.8426i 0.732349 1.82641i
\(7\) −5.13468 −0.277247 −0.138623 0.990345i \(-0.544268\pi\)
−0.138623 + 0.990345i \(0.544268\pi\)
\(8\) −83.3558 −3.68384
\(9\) −19.5203 18.6536i −0.722974 0.690875i
\(10\) 57.4309i 1.81612i
\(11\) 8.23442 0.225706 0.112853 0.993612i \(-0.464001\pi\)
0.112853 + 0.993612i \(0.464001\pi\)
\(12\) −44.4341 + 110.814i −1.06892 + 2.66577i
\(13\) 53.3544i 1.13830i 0.822235 + 0.569148i \(0.192727\pi\)
−0.822235 + 0.569148i \(0.807273\pi\)
\(14\) 28.5780 0.545556
\(15\) −49.7661 19.9551i −0.856637 0.343493i
\(16\) 280.117 4.37683
\(17\) 93.0677i 1.32778i 0.747831 + 0.663889i \(0.231095\pi\)
−0.747831 + 0.663889i \(0.768905\pi\)
\(18\) 108.644 + 103.820i 1.42264 + 1.35948i
\(19\) −84.1079 −1.01556 −0.507781 0.861486i \(-0.669534\pi\)
−0.507781 + 0.861486i \(0.669534\pi\)
\(20\) 237.092i 2.65076i
\(21\) 9.92981 24.7639i 0.103184 0.257330i
\(22\) −45.8301 −0.444137
\(23\) −138.110 −1.25208 −0.626041 0.779790i \(-0.715326\pi\)
−0.626041 + 0.779790i \(0.715326\pi\)
\(24\) 161.199 402.015i 1.37103 3.41921i
\(25\) 18.5232 0.148186
\(26\) 296.953i 2.23990i
\(27\) 127.714 58.0703i 0.910317 0.413912i
\(28\) −117.978 −0.796279
\(29\) 249.312i 1.59642i −0.602383 0.798208i \(-0.705782\pi\)
0.602383 0.798208i \(-0.294218\pi\)
\(30\) 276.982 + 111.064i 1.68566 + 0.675913i
\(31\) 203.586i 1.17952i 0.807579 + 0.589760i \(0.200778\pi\)
−0.807579 + 0.589760i \(0.799222\pi\)
\(32\) −892.196 −4.92874
\(33\) −15.9243 + 39.7136i −0.0840019 + 0.209492i
\(34\) 517.985i 2.61275i
\(35\) 52.9836i 0.255882i
\(36\) −448.513 428.600i −2.07645 1.98426i
\(37\) 60.4290i 0.268499i 0.990948 + 0.134249i \(0.0428624\pi\)
−0.990948 + 0.134249i \(0.957138\pi\)
\(38\) 468.118 1.99839
\(39\) −257.322 103.180i −1.05652 0.423644i
\(40\) 860.128i 3.39996i
\(41\) 36.5916i 0.139382i 0.997569 + 0.0696908i \(0.0222013\pi\)
−0.997569 + 0.0696908i \(0.977799\pi\)
\(42\) −55.2661 + 137.828i −0.203042 + 0.506365i
\(43\) 368.769i 1.30783i −0.756568 0.653915i \(-0.773125\pi\)
0.756568 0.653915i \(-0.226875\pi\)
\(44\) 189.200 0.648250
\(45\) 192.482 201.425i 0.637635 0.667260i
\(46\) 768.675 2.46380
\(47\) 112.441 0.348963 0.174482 0.984660i \(-0.444175\pi\)
0.174482 + 0.984660i \(0.444175\pi\)
\(48\) −541.711 + 1350.97i −1.62894 + 4.06242i
\(49\) −316.635 −0.923134
\(50\) −103.094 −0.291595
\(51\) −448.854 179.981i −1.23240 0.494164i
\(52\) 1225.91i 3.26929i
\(53\) 318.575i 0.825655i −0.910809 0.412827i \(-0.864541\pi\)
0.910809 0.412827i \(-0.135459\pi\)
\(54\) −710.814 + 323.200i −1.79129 + 0.814482i
\(55\) 84.9689i 0.208313i
\(56\) 428.006 1.02133
\(57\) 162.654 405.642i 0.377965 0.942608i
\(58\) 1387.59i 3.14137i
\(59\) 453.071 10.2958i 0.999742 0.0227186i
\(60\) −1143.46 458.504i −2.46034 0.986544i
\(61\) 214.084i 0.449355i −0.974433 0.224678i \(-0.927867\pi\)
0.974433 0.224678i \(-0.0721329\pi\)
\(62\) 1133.09i 2.32102i
\(63\) 100.231 + 95.7805i 0.200442 + 0.191543i
\(64\) 2724.74 5.32175
\(65\) −550.551 −1.05058
\(66\) 88.6295 221.033i 0.165296 0.412231i
\(67\) 309.301i 0.563987i −0.959416 0.281993i \(-0.909004\pi\)
0.959416 0.281993i \(-0.0909956\pi\)
\(68\) 2138.39i 3.81351i
\(69\) 267.087 666.087i 0.465992 1.16214i
\(70\) 294.889i 0.503515i
\(71\) 830.490i 1.38818i −0.719886 0.694092i \(-0.755806\pi\)
0.719886 0.694092i \(-0.244194\pi\)
\(72\) 1627.13 + 1554.89i 2.66332 + 2.54507i
\(73\) 110.548i 0.177243i 0.996065 + 0.0886214i \(0.0282461\pi\)
−0.996065 + 0.0886214i \(0.971754\pi\)
\(74\) 336.328i 0.528343i
\(75\) −35.8216 + 89.3354i −0.0551509 + 0.137541i
\(76\) −1932.53 −2.91679
\(77\) −42.2811 −0.0625764
\(78\) 1432.17 + 574.269i 2.07899 + 0.833631i
\(79\) −180.521 −0.257091 −0.128546 0.991704i \(-0.541031\pi\)
−0.128546 + 0.991704i \(0.541031\pi\)
\(80\) 2890.46i 4.03955i
\(81\) 33.0838 + 728.249i 0.0453824 + 0.998970i
\(82\) 203.657i 0.274270i
\(83\) 339.217 0.448602 0.224301 0.974520i \(-0.427990\pi\)
0.224301 + 0.974520i \(0.427990\pi\)
\(84\) 228.155 568.995i 0.296354 0.739077i
\(85\) −960.343 −1.22546
\(86\) 2052.45i 2.57350i
\(87\) 1202.40 + 482.137i 1.48173 + 0.594143i
\(88\) −686.386 −0.831466
\(89\) 743.168 0.885120 0.442560 0.896739i \(-0.354070\pi\)
0.442560 + 0.896739i \(0.354070\pi\)
\(90\) −1071.29 + 1121.07i −1.25472 + 1.31301i
\(91\) 273.958i 0.315589i
\(92\) −3173.32 −3.59610
\(93\) −981.870 393.709i −1.09479 0.438986i
\(94\) −625.813 −0.686677
\(95\) 867.889i 0.937301i
\(96\) 1725.39 4302.95i 1.83434 4.57467i
\(97\) 439.178i 0.459709i −0.973225 0.229854i \(-0.926175\pi\)
0.973225 0.229854i \(-0.0738250\pi\)
\(98\) 1762.29 1.81651
\(99\) −160.738 153.602i −0.163180 0.155935i
\(100\) 425.604 0.425604
\(101\) −1299.12 −1.27988 −0.639939 0.768426i \(-0.721040\pi\)
−0.639939 + 0.768426i \(0.721040\pi\)
\(102\) 2498.18 + 1001.72i 2.42506 + 0.972398i
\(103\) 1553.76i 1.48638i −0.669083 0.743188i \(-0.733313\pi\)
0.669083 0.743188i \(-0.266687\pi\)
\(104\) 4447.40i 4.19330i
\(105\) 255.533 + 102.463i 0.237500 + 0.0952323i
\(106\) 1773.09i 1.62469i
\(107\) 1293.66i 1.16881i 0.811462 + 0.584406i \(0.198672\pi\)
−0.811462 + 0.584406i \(0.801328\pi\)
\(108\) 2934.45 1334.27i 2.61452 1.18880i
\(109\) 1671.05i 1.46841i 0.678926 + 0.734207i \(0.262446\pi\)
−0.678926 + 0.734207i \(0.737554\pi\)
\(110\) 472.910i 0.409911i
\(111\) −291.442 116.862i −0.249211 0.0999282i
\(112\) −1438.31 −1.21346
\(113\) −121.231 −0.100924 −0.0504621 0.998726i \(-0.516069\pi\)
−0.0504621 + 0.998726i \(0.516069\pi\)
\(114\) −905.279 + 2257.67i −0.743747 + 1.85483i
\(115\) 1425.12i 1.15559i
\(116\) 5728.38i 4.58506i
\(117\) 995.254 1041.49i 0.786421 0.822958i
\(118\) −2521.64 + 57.3030i −1.96726 + 0.0447048i
\(119\) 477.873i 0.368122i
\(120\) 4148.29 + 1663.38i 3.15571 + 1.26537i
\(121\) −1263.19 −0.949057
\(122\) 1191.52i 0.884225i
\(123\) −176.477 70.7634i −0.129369 0.0518741i
\(124\) 4677.74i 3.38769i
\(125\) 1480.98i 1.05970i
\(126\) −557.851 533.083i −0.394423 0.376911i
\(127\) −1216.64 −0.850071 −0.425035 0.905177i \(-0.639738\pi\)
−0.425035 + 0.905177i \(0.639738\pi\)
\(128\) −8027.44 −5.54322
\(129\) 1778.53 + 713.151i 1.21388 + 0.486740i
\(130\) 3064.19 2.06729
\(131\) −1764.68 −1.17695 −0.588477 0.808514i \(-0.700272\pi\)
−0.588477 + 0.808514i \(0.700272\pi\)
\(132\) −365.889 + 912.489i −0.241261 + 0.601682i
\(133\) 431.868 0.281561
\(134\) 1721.47i 1.10979i
\(135\) 599.213 + 1317.85i 0.382015 + 0.840166i
\(136\) 7757.73i 4.89132i
\(137\) 1726.01i 1.07637i 0.842826 + 0.538186i \(0.180890\pi\)
−0.842826 + 0.538186i \(0.819110\pi\)
\(138\) −1486.52 + 3707.23i −0.916962 + 2.28681i
\(139\) −720.662 −0.439754 −0.219877 0.975528i \(-0.570566\pi\)
−0.219877 + 0.975528i \(0.570566\pi\)
\(140\) 1217.39i 0.734916i
\(141\) −217.447 + 542.291i −0.129875 + 0.323895i
\(142\) 4622.24i 2.73162i
\(143\) 439.342i 0.256921i
\(144\) −5467.97 5225.21i −3.16434 3.02385i
\(145\) 2572.59 1.47339
\(146\) 615.277i 0.348772i
\(147\) 612.331 1527.09i 0.343566 0.856819i
\(148\) 1388.46i 0.771155i
\(149\) 1960.40 1.07787 0.538933 0.842348i \(-0.318827\pi\)
0.538933 + 0.842348i \(0.318827\pi\)
\(150\) 199.371 497.212i 0.108524 0.270648i
\(151\) 2940.00i 1.58446i −0.610221 0.792231i \(-0.708920\pi\)
0.610221 0.792231i \(-0.291080\pi\)
\(152\) 7010.89 3.74117
\(153\) 1736.05 1816.71i 0.917329 0.959949i
\(154\) 235.323 0.123136
\(155\) −2100.75 −1.08862
\(156\) −5912.42 2370.75i −3.03444 1.21674i
\(157\) 2907.11i 1.47779i 0.673821 + 0.738895i \(0.264652\pi\)
−0.673821 + 0.738895i \(0.735348\pi\)
\(158\) 1004.72 0.505895
\(159\) 1536.45 + 616.083i 0.766342 + 0.307287i
\(160\) 9206.36i 4.54892i
\(161\) 709.151 0.347136
\(162\) −184.134 4053.20i −0.0893019 1.96574i
\(163\) −1619.97 −0.778442 −0.389221 0.921144i \(-0.627256\pi\)
−0.389221 + 0.921144i \(0.627256\pi\)
\(164\) 840.756i 0.400317i
\(165\) −409.795 164.319i −0.193348 0.0775285i
\(166\) −1887.97 −0.882742
\(167\) 1514.57i 0.701804i 0.936412 + 0.350902i \(0.114125\pi\)
−0.936412 + 0.350902i \(0.885875\pi\)
\(168\) −827.707 + 2064.22i −0.380113 + 0.947964i
\(169\) −649.693 −0.295718
\(170\) 5344.96 2.41141
\(171\) 1641.81 + 1568.92i 0.734225 + 0.701627i
\(172\) 8473.11i 3.75621i
\(173\) −1756.60 −0.771977 −0.385989 0.922503i \(-0.626140\pi\)
−0.385989 + 0.922503i \(0.626140\pi\)
\(174\) −6692.17 2683.42i −2.91570 1.16913i
\(175\) −95.1110 −0.0410841
\(176\) 2306.60 0.987879
\(177\) −826.524 + 2205.01i −0.350991 + 0.936379i
\(178\) −4136.23 −1.74171
\(179\) −2833.03 −1.18296 −0.591481 0.806319i \(-0.701457\pi\)
−0.591481 + 0.806319i \(0.701457\pi\)
\(180\) 4422.62 4628.10i 1.83135 1.91643i
\(181\) 344.955 0.141659 0.0708295 0.997488i \(-0.477435\pi\)
0.0708295 + 0.997488i \(0.477435\pi\)
\(182\) 1524.76i 0.621005i
\(183\) 1032.50 + 414.011i 0.417075 + 0.167238i
\(184\) 11512.3 4.61247
\(185\) −623.552 −0.247808
\(186\) 5464.77 + 2191.26i 2.15428 + 0.863821i
\(187\) 766.358i 0.299688i
\(188\) 2583.54 1.00226
\(189\) −655.770 + 298.173i −0.252382 + 0.114756i
\(190\) 4830.39i 1.84439i
\(191\) 4289.37 1.62496 0.812482 0.582986i \(-0.198116\pi\)
0.812482 + 0.582986i \(0.198116\pi\)
\(192\) −5269.29 + 13141.1i −1.98062 + 4.93946i
\(193\) −1977.19 −0.737415 −0.368708 0.929545i \(-0.620200\pi\)
−0.368708 + 0.929545i \(0.620200\pi\)
\(194\) 2444.32i 0.904598i
\(195\) 1064.69 2655.24i 0.390997 0.975107i
\(196\) −7275.25 −2.65133
\(197\) 13.2281i 0.00478408i −0.999997 0.00239204i \(-0.999239\pi\)
0.999997 0.00239204i \(-0.000761410\pi\)
\(198\) 894.617 + 854.898i 0.321099 + 0.306843i
\(199\) 4236.79 1.50924 0.754618 0.656164i \(-0.227822\pi\)
0.754618 + 0.656164i \(0.227822\pi\)
\(200\) −1544.02 −0.545894
\(201\) 1491.72 + 598.148i 0.523472 + 0.209901i
\(202\) 7230.50 2.51850
\(203\) 1280.14i 0.442601i
\(204\) −10313.2 4135.38i −3.53956 1.41929i
\(205\) −377.580 −0.128641
\(206\) 8647.74i 2.92484i
\(207\) 2695.95 + 2576.25i 0.905223 + 0.865033i
\(208\) 14945.5i 4.98213i
\(209\) −692.580 −0.229219
\(210\) −1422.22 570.278i −0.467344 0.187395i
\(211\) 2664.87i 0.869466i −0.900559 0.434733i \(-0.856843\pi\)
0.900559 0.434733i \(-0.143157\pi\)
\(212\) 7319.83i 2.37136i
\(213\) 4005.35 + 1606.06i 1.28846 + 0.516645i
\(214\) 7200.09i 2.29995i
\(215\) 3805.24 1.20705
\(216\) −10645.7 + 4840.50i −3.35346 + 1.52479i
\(217\) 1045.35i 0.327018i
\(218\) 9300.50i 2.88949i
\(219\) −533.162 213.786i −0.164510 0.0659650i
\(220\) 1952.31i 0.598294i
\(221\) −4965.57 −1.51141
\(222\) 1622.07 + 650.415i 0.490388 + 0.196635i
\(223\) −4836.11 −1.45224 −0.726120 0.687567i \(-0.758679\pi\)
−0.726120 + 0.687567i \(0.758679\pi\)
\(224\) 4581.15 1.36648
\(225\) −361.579 345.526i −0.107135 0.102378i
\(226\) 674.731 0.198595
\(227\) −2329.04 −0.680986 −0.340493 0.940247i \(-0.610594\pi\)
−0.340493 + 0.940247i \(0.610594\pi\)
\(228\) 3737.26 9320.35i 1.08555 2.70726i
\(229\) 4734.44i 1.36620i 0.730323 + 0.683102i \(0.239370\pi\)
−0.730323 + 0.683102i \(0.760630\pi\)
\(230\) 7931.77i 2.27394i
\(231\) 81.7662 203.917i 0.0232893 0.0580811i
\(232\) 20781.6i 5.88094i
\(233\) −2827.38 −0.794971 −0.397485 0.917609i \(-0.630117\pi\)
−0.397485 + 0.917609i \(0.630117\pi\)
\(234\) −5539.26 + 5796.62i −1.54749 + 1.61939i
\(235\) 1160.26i 0.322071i
\(236\) 10410.1 236.564i 2.87135 0.0652500i
\(237\) 349.105 870.632i 0.0956826 0.238623i
\(238\) 2659.69i 0.724378i
\(239\) 640.800i 0.173431i −0.996233 0.0867153i \(-0.972363\pi\)
0.996233 0.0867153i \(-0.0276371\pi\)
\(240\) −13940.4 5589.78i −3.74936 1.50341i
\(241\) −1123.12 −0.300194 −0.150097 0.988671i \(-0.547959\pi\)
−0.150097 + 0.988671i \(0.547959\pi\)
\(242\) 7030.53 1.86752
\(243\) −3576.23 1248.78i −0.944097 0.329668i
\(244\) 4918.96i 1.29059i
\(245\) 3267.28i 0.851995i
\(246\) 982.213 + 393.846i 0.254567 + 0.102076i
\(247\) 4487.53i 1.15601i
\(248\) 16970.1i 4.34516i
\(249\) −656.002 + 1636.00i −0.166958 + 0.416376i
\(250\) 8242.66i 2.08525i
\(251\) 4798.42i 1.20667i 0.797489 + 0.603333i \(0.206161\pi\)
−0.797489 + 0.603333i \(0.793839\pi\)
\(252\) 2302.97 + 2200.73i 0.575689 + 0.550130i
\(253\) −1137.25 −0.282603
\(254\) 6771.40 1.67274
\(255\) 1857.18 4631.62i 0.456082 1.13742i
\(256\) 22880.2 5.58599
\(257\) 719.646i 0.174670i −0.996179 0.0873351i \(-0.972165\pi\)
0.996179 0.0873351i \(-0.0278351\pi\)
\(258\) −9898.71 3969.17i −2.38863 0.957789i
\(259\) 310.284i 0.0744405i
\(260\) −12649.9 −3.01736
\(261\) −4650.57 + 4866.64i −1.10292 + 1.15417i
\(262\) 9821.64 2.31597
\(263\) 1763.93i 0.413569i −0.978386 0.206785i \(-0.933700\pi\)
0.978386 0.206785i \(-0.0663000\pi\)
\(264\) 1327.38 3310.36i 0.309450 0.771736i
\(265\) 3287.30 0.762028
\(266\) −2403.64 −0.554047
\(267\) −1437.19 + 3584.21i −0.329418 + 0.821536i
\(268\) 7106.73i 1.61982i
\(269\) −4111.19 −0.931834 −0.465917 0.884828i \(-0.654276\pi\)
−0.465917 + 0.884828i \(0.654276\pi\)
\(270\) −3335.03 7334.72i −0.751716 1.65325i
\(271\) −4331.06 −0.970824 −0.485412 0.874286i \(-0.661330\pi\)
−0.485412 + 0.874286i \(0.661330\pi\)
\(272\) 26069.9i 5.81147i
\(273\) 1321.27 + 529.799i 0.292918 + 0.117454i
\(274\) 9606.41i 2.11805i
\(275\) 152.528 0.0334465
\(276\) 6136.78 15304.5i 1.33837 3.33777i
\(277\) −2518.92 −0.546381 −0.273190 0.961960i \(-0.588079\pi\)
−0.273190 + 0.961960i \(0.588079\pi\)
\(278\) 4010.97 0.865332
\(279\) 3797.62 3974.06i 0.814901 0.852762i
\(280\) 4416.49i 0.942627i
\(281\) 506.498i 0.107527i −0.998554 0.0537636i \(-0.982878\pi\)
0.998554 0.0537636i \(-0.0171218\pi\)
\(282\) 1210.24 3018.22i 0.255563 0.637348i
\(283\) 599.808i 0.125989i 0.998014 + 0.0629945i \(0.0200651\pi\)
−0.998014 + 0.0629945i \(0.979935\pi\)
\(284\) 19082.0i 3.98700i
\(285\) 4185.72 + 1678.39i 0.869968 + 0.348838i
\(286\) 2445.24i 0.505559i
\(287\) 187.886i 0.0386431i
\(288\) 17415.9 + 16642.7i 3.56335 + 3.40514i
\(289\) −3748.60 −0.762995
\(290\) −14318.2 −2.89929
\(291\) 2118.10 + 849.313i 0.426685 + 0.171091i
\(292\) 2540.05i 0.509058i
\(293\) 2503.29i 0.499126i −0.968359 0.249563i \(-0.919713\pi\)
0.968359 0.249563i \(-0.0802870\pi\)
\(294\) −3408.04 + 8499.30i −0.676057 + 1.68602i
\(295\) 106.240 + 4675.13i 0.0209679 + 0.922699i
\(296\) 5037.11i 0.989108i
\(297\) 1051.65 478.175i 0.205464 0.0934226i
\(298\) −10910.9 −2.12099
\(299\) 7368.77i 1.42524i
\(300\) −823.063 + 2052.64i −0.158399 + 0.395030i
\(301\) 1893.51i 0.362592i
\(302\) 16363.1i 3.11785i
\(303\) 2512.34 6265.52i 0.476337 1.18794i
\(304\) −23560.1 −4.44495
\(305\) 2209.08 0.414727
\(306\) −9662.30 + 10111.2i −1.80509 + 1.88895i
\(307\) 760.651 0.141409 0.0707046 0.997497i \(-0.477475\pi\)
0.0707046 + 0.997497i \(0.477475\pi\)
\(308\) −971.483 −0.179725
\(309\) 7493.60 + 3004.77i 1.37960 + 0.553190i
\(310\) 11692.1 2.14215
\(311\) 1585.14i 0.289020i 0.989503 + 0.144510i \(0.0461606\pi\)
−0.989503 + 0.144510i \(0.953839\pi\)
\(312\) 21449.3 + 8600.69i 3.89207 + 1.56064i
\(313\) 9851.30i 1.77901i 0.456930 + 0.889503i \(0.348949\pi\)
−0.456930 + 0.889503i \(0.651051\pi\)
\(314\) 16180.1i 2.90794i
\(315\) −988.336 + 1034.25i −0.176782 + 0.184996i
\(316\) −4147.79 −0.738391
\(317\) 8857.22i 1.56931i −0.619933 0.784655i \(-0.712840\pi\)
0.619933 0.784655i \(-0.287160\pi\)
\(318\) −8551.38 3428.92i −1.50798 0.604668i
\(319\) 2052.94i 0.360321i
\(320\) 28115.9i 4.91165i
\(321\) −6239.16 2501.77i −1.08485 0.435001i
\(322\) −3946.90 −0.683082
\(323\) 7827.73i 1.34844i
\(324\) 760.159 + 16732.8i 0.130343 + 2.86914i
\(325\) 988.297i 0.168680i
\(326\) 9016.25 1.53179
\(327\) −8059.25 3231.58i −1.36293 0.546505i
\(328\) 3050.12i 0.513460i
\(329\) −577.351 −0.0967489
\(330\) 2280.79 + 914.546i 0.380464 + 0.152558i
\(331\) 6102.28 1.01333 0.506664 0.862144i \(-0.330879\pi\)
0.506664 + 0.862144i \(0.330879\pi\)
\(332\) 7794.11 1.28843
\(333\) 1127.22 1179.59i 0.185499 0.194118i
\(334\) 8429.62i 1.38098i
\(335\) 3191.60 0.520525
\(336\) 2781.51 6936.81i 0.451619 1.12629i
\(337\) 461.351i 0.0745738i 0.999305 + 0.0372869i \(0.0118715\pi\)
−0.999305 + 0.0372869i \(0.988128\pi\)
\(338\) 3615.98 0.581904
\(339\) 234.445 584.681i 0.0375613 0.0936741i
\(340\) −22065.6 −3.51963
\(341\) 1676.41i 0.266225i
\(342\) −9137.79 8732.10i −1.44478 1.38064i
\(343\) 3387.02 0.533183
\(344\) 30739.0i 4.81784i
\(345\) 6873.19 + 2756.00i 1.07258 + 0.430081i
\(346\) 9776.69 1.51907
\(347\) −11976.1 −1.85277 −0.926383 0.376583i \(-0.877099\pi\)
−0.926383 + 0.376583i \(0.877099\pi\)
\(348\) 27627.3 + 11077.9i 4.25568 + 1.70644i
\(349\) 4647.83i 0.712873i 0.934320 + 0.356437i \(0.116008\pi\)
−0.934320 + 0.356437i \(0.883992\pi\)
\(350\) 529.357 0.0808438
\(351\) 3098.31 + 6814.10i 0.471155 + 1.03621i
\(352\) −7346.72 −1.11245
\(353\) 3004.19 0.452966 0.226483 0.974015i \(-0.427277\pi\)
0.226483 + 0.974015i \(0.427277\pi\)
\(354\) 4600.17 12272.4i 0.690667 1.84257i
\(355\) 8569.63 1.28121
\(356\) 17075.6 2.54215
\(357\) 2304.72 + 924.145i 0.341678 + 0.137005i
\(358\) 15767.7 2.32779
\(359\) 3839.91i 0.564520i 0.959338 + 0.282260i \(0.0910841\pi\)
−0.959338 + 0.282260i \(0.908916\pi\)
\(360\) −16044.5 + 16790.0i −2.34895 + 2.45808i
\(361\) 215.146 0.0313670
\(362\) −1919.91 −0.278752
\(363\) 2442.85 6092.23i 0.353214 0.880879i
\(364\) 6294.67i 0.906402i
\(365\) −1140.72 −0.163584
\(366\) −5746.57 2304.25i −0.820705 0.329085i
\(367\) 3094.76i 0.440178i −0.975480 0.220089i \(-0.929365\pi\)
0.975480 0.220089i \(-0.0706348\pi\)
\(368\) −38687.0 −5.48016
\(369\) 682.566 714.279i 0.0962953 0.100769i
\(370\) 3470.49 0.487627
\(371\) 1635.78i 0.228910i
\(372\) −22560.2 9046.15i −3.14433 1.26081i
\(373\) −4.21229 −0.000584729 −0.000292365 1.00000i \(-0.500093\pi\)
−0.000292365 1.00000i \(0.500093\pi\)
\(374\) 4265.30i 0.589715i
\(375\) −7142.59 2864.03i −0.983578 0.394394i
\(376\) −9372.64 −1.28552
\(377\) 13301.9 1.81719
\(378\) 3649.81 1659.53i 0.496629 0.225812i
\(379\) 6414.25 0.869335 0.434667 0.900591i \(-0.356866\pi\)
0.434667 + 0.900591i \(0.356866\pi\)
\(380\) 19941.3i 2.69202i
\(381\) 2352.82 5867.69i 0.316374 0.789005i
\(382\) −23873.3 −3.19755
\(383\) 5181.02i 0.691221i 0.938378 + 0.345611i \(0.112328\pi\)
−0.938378 + 0.345611i \(0.887672\pi\)
\(384\) 15524.0 38715.4i 2.06304 5.14501i
\(385\) 436.289i 0.0577541i
\(386\) 11004.4 1.45106
\(387\) −6878.88 + 7198.48i −0.903548 + 0.945527i
\(388\) 10090.9i 1.32033i
\(389\) 459.528i 0.0598946i −0.999551 0.0299473i \(-0.990466\pi\)
0.999551 0.0299473i \(-0.00953395\pi\)
\(390\) −5925.75 + 14778.2i −0.769389 + 1.91878i
\(391\) 12853.6i 1.66249i
\(392\) 26393.4 3.40068
\(393\) 3412.66 8510.84i 0.438031 1.09240i
\(394\) 73.6233i 0.00941393i
\(395\) 1862.75i 0.237279i
\(396\) −3693.24 3529.27i −0.468668 0.447860i
\(397\) 107.728i 0.0136189i −0.999977 0.00680946i \(-0.997832\pi\)
0.999977 0.00680946i \(-0.00216754\pi\)
\(398\) −23580.6 −2.96982
\(399\) −835.176 + 2082.84i −0.104790 + 0.261335i
\(400\) 5188.68 0.648586
\(401\) 588.735 0.0733168 0.0366584 0.999328i \(-0.488329\pi\)
0.0366584 + 0.999328i \(0.488329\pi\)
\(402\) −8302.43 3329.10i −1.03007 0.413035i
\(403\) −10862.2 −1.34264
\(404\) −29849.7 −3.67593
\(405\) −7514.62 + 341.384i −0.921987 + 0.0418852i
\(406\) 7124.83i 0.870934i
\(407\) 497.597i 0.0606019i
\(408\) 37414.6 + 15002.4i 4.53995 + 1.82042i
\(409\) 2665.79i 0.322286i 0.986931 + 0.161143i \(0.0515181\pi\)
−0.986931 + 0.161143i \(0.948482\pi\)
\(410\) 2101.49 0.253134
\(411\) −8324.33 3337.88i −0.999049 0.400597i
\(412\) 35700.4i 4.26901i
\(413\) −2326.37 + 52.8656i −0.277175 + 0.00629866i
\(414\) −15004.8 14338.6i −1.78127 1.70218i
\(415\) 3500.30i 0.414031i
\(416\) 47602.6i 5.61036i
\(417\) 1393.67 3475.67i 0.163665 0.408163i
\(418\) 3854.68 0.451049
\(419\) 8979.23 1.04693 0.523466 0.852047i \(-0.324639\pi\)
0.523466 + 0.852047i \(0.324639\pi\)
\(420\) 5871.32 + 2354.27i 0.682122 + 0.273516i
\(421\) 10132.1i 1.17294i 0.809972 + 0.586468i \(0.199482\pi\)
−0.809972 + 0.586468i \(0.800518\pi\)
\(422\) 14831.8i 1.71090i
\(423\) −2194.89 2097.44i −0.252291 0.241090i
\(424\) 26555.1i 3.04158i
\(425\) 1723.92i 0.196758i
\(426\) −22292.5 8938.81i −2.53539 1.01664i
\(427\) 1099.25i 0.124582i
\(428\) 29724.1i 3.35694i
\(429\) −2118.89 849.631i −0.238464 0.0956191i
\(430\) −21178.7 −2.37518
\(431\) −8993.68 −1.00513 −0.502564 0.864540i \(-0.667610\pi\)
−0.502564 + 0.864540i \(0.667610\pi\)
\(432\) 35774.9 16266.5i 3.98431 1.81163i
\(433\) 8835.09 0.980571 0.490286 0.871562i \(-0.336892\pi\)
0.490286 + 0.871562i \(0.336892\pi\)
\(434\) 5818.08i 0.643494i
\(435\) −4975.05 + 12407.3i −0.548357 + 1.36755i
\(436\) 38395.2i 4.21742i
\(437\) 11616.1 1.27157
\(438\) 2967.41 + 1189.87i 0.323717 + 0.129804i
\(439\) −8504.84 −0.924633 −0.462317 0.886715i \(-0.652982\pi\)
−0.462317 + 0.886715i \(0.652982\pi\)
\(440\) 7082.65i 0.767392i
\(441\) 6180.81 + 5906.39i 0.667402 + 0.637771i
\(442\) 27636.8 2.97409
\(443\) −10992.3 −1.17892 −0.589460 0.807798i \(-0.700659\pi\)
−0.589460 + 0.807798i \(0.700659\pi\)
\(444\) −6696.38 2685.11i −0.715757 0.287003i
\(445\) 7668.57i 0.816911i
\(446\) 26916.2 2.85767
\(447\) −3791.16 + 9454.76i −0.401153 + 1.00044i
\(448\) −13990.7 −1.47544
\(449\) 14359.3i 1.50926i 0.656150 + 0.754630i \(0.272184\pi\)
−0.656150 + 0.754630i \(0.727816\pi\)
\(450\) 2012.43 + 1923.09i 0.210816 + 0.201456i
\(451\) 301.310i 0.0314593i
\(452\) −2785.49 −0.289864
\(453\) 14179.3 + 5685.58i 1.47064 + 0.589695i
\(454\) 12962.7 1.34002
\(455\) 2826.91 0.291269
\(456\) −13558.1 + 33812.6i −1.39236 + 3.47242i
\(457\) 4257.86i 0.435830i 0.975968 + 0.217915i \(0.0699255\pi\)
−0.975968 + 0.217915i \(0.930075\pi\)
\(458\) 26350.4i 2.68837i
\(459\) 5404.47 + 11886.0i 0.549584 + 1.20870i
\(460\) 32744.7i 3.31898i
\(461\) 18982.3i 1.91778i 0.283785 + 0.958888i \(0.408410\pi\)
−0.283785 + 0.958888i \(0.591590\pi\)
\(462\) −455.084 + 1134.93i −0.0458278 + 0.114290i
\(463\) 10943.5i 1.09846i −0.835670 0.549232i \(-0.814920\pi\)
0.835670 0.549232i \(-0.185080\pi\)
\(464\) 69836.6i 6.98724i
\(465\) 4062.58 10131.7i 0.405157 1.01042i
\(466\) 15736.3 1.56431
\(467\) −8060.59 −0.798714 −0.399357 0.916795i \(-0.630767\pi\)
−0.399357 + 0.916795i \(0.630767\pi\)
\(468\) 22867.7 23930.2i 2.25868 2.36361i
\(469\) 1588.16i 0.156364i
\(470\) 6457.61i 0.633760i
\(471\) −14020.7 5621.98i −1.37163 0.549994i
\(472\) −37766.1 + 858.214i −3.68289 + 0.0836917i
\(473\) 3036.60i 0.295186i
\(474\) −1943.00 + 4845.66i −0.188281 + 0.469553i
\(475\) −1557.95 −0.150492
\(476\) 10980.0i 1.05728i
\(477\) −5942.59 + 6218.69i −0.570424 + 0.596927i
\(478\) 3566.49i 0.341271i
\(479\) 7956.38i 0.758948i −0.925202 0.379474i \(-0.876105\pi\)
0.925202 0.379474i \(-0.123895\pi\)
\(480\) 44401.1 + 17803.9i 4.22214 + 1.69299i
\(481\) −3224.15 −0.305631
\(482\) 6250.94 0.590710
\(483\) −1371.40 + 3420.15i −0.129195 + 0.322199i
\(484\) −29024.1 −2.72578
\(485\) 4531.77 0.424283
\(486\) 19904.2 + 6950.30i 1.85776 + 0.648708i
\(487\) 5472.03 0.509161 0.254580 0.967052i \(-0.418063\pi\)
0.254580 + 0.967052i \(0.418063\pi\)
\(488\) 17845.2i 1.65535i
\(489\) 3132.82 7812.93i 0.289716 0.722522i
\(490\) 18184.6i 1.67653i
\(491\) 7832.96i 0.719952i 0.932962 + 0.359976i \(0.117215\pi\)
−0.932962 + 0.359976i \(0.882785\pi\)
\(492\) −4054.86 1625.91i −0.371560 0.148987i
\(493\) 23202.9 2.11969
\(494\) 24976.1i 2.27476i
\(495\) 1584.98 1658.62i 0.143918 0.150605i
\(496\) 57028.0i 5.16256i
\(497\) 4264.30i 0.384870i
\(498\) 3651.10 9105.47i 0.328533 0.819329i
\(499\) 7091.23 0.636166 0.318083 0.948063i \(-0.396961\pi\)
0.318083 + 0.948063i \(0.396961\pi\)
\(500\) 34028.2i 3.04357i
\(501\) −7304.60 2928.99i −0.651388 0.261193i
\(502\) 26706.4i 2.37443i
\(503\) −10710.6 −0.949427 −0.474714 0.880140i \(-0.657448\pi\)
−0.474714 + 0.880140i \(0.657448\pi\)
\(504\) −8354.80 7983.86i −0.738397 0.705614i
\(505\) 13405.3i 1.18125i
\(506\) 6329.59 0.556096
\(507\) 1256.42 3133.39i 0.110059 0.274475i
\(508\) −27954.4 −2.44148
\(509\) −15860.7 −1.38116 −0.690581 0.723255i \(-0.742645\pi\)
−0.690581 + 0.723255i \(0.742645\pi\)
\(510\) −10336.5 + 25778.1i −0.897463 + 2.23818i
\(511\) 567.631i 0.0491400i
\(512\) −63124.5 −5.44870
\(513\) −10741.8 + 4884.17i −0.924483 + 0.420354i
\(514\) 4005.31i 0.343710i
\(515\) 16032.9 1.37183
\(516\) 40864.8 + 16385.9i 3.48638 + 1.39796i
\(517\) 925.889 0.0787632
\(518\) 1726.94i 0.146481i
\(519\) 3397.04 8471.88i 0.287310 0.716521i
\(520\) 45891.6 3.87016
\(521\) 4684.28i 0.393901i −0.980413 0.196950i \(-0.936896\pi\)
0.980413 0.196950i \(-0.0631038\pi\)
\(522\) 25883.6 27086.1i 2.17029 2.27113i
\(523\) 1065.36 0.0890727 0.0445363 0.999008i \(-0.485819\pi\)
0.0445363 + 0.999008i \(0.485819\pi\)
\(524\) −40546.6 −3.38032
\(525\) 183.932 458.709i 0.0152904 0.0381328i
\(526\) 9817.48i 0.813807i
\(527\) −18947.3 −1.56614
\(528\) −4460.67 + 11124.5i −0.367662 + 0.916913i
\(529\) 6907.34 0.567711
\(530\) −18296.1 −1.49949
\(531\) −9036.13 8250.44i −0.738483 0.674272i
\(532\) 9922.92 0.808671
\(533\) −1952.32 −0.158658
\(534\) 7998.94 19948.6i 0.648217 1.61659i
\(535\) −13349.0 −1.07874
\(536\) 25782.0i 2.07764i
\(537\) 5478.70 13663.3i 0.440267 1.09798i
\(538\) 22881.5 1.83363
\(539\) −2607.30 −0.208357
\(540\) 13768.0 + 30279.9i 1.09718 + 2.41304i
\(541\) 11849.6i 0.941688i 0.882216 + 0.470844i \(0.156051\pi\)
−0.882216 + 0.470844i \(0.843949\pi\)
\(542\) 24105.3 1.91035
\(543\) −667.098 + 1663.67i −0.0527217 + 0.131483i
\(544\) 83034.7i 6.54427i
\(545\) −17243.1 −1.35525
\(546\) −7353.74 2948.69i −0.576394 0.231121i
\(547\) 15106.1 1.18079 0.590395 0.807114i \(-0.298972\pi\)
0.590395 + 0.807114i \(0.298972\pi\)
\(548\) 39658.1i 3.09144i
\(549\) −3993.45 + 4178.99i −0.310448 + 0.324872i
\(550\) −848.922 −0.0658149
\(551\) 20969.1i 1.62126i
\(552\) −22263.2 + 55522.2i −1.71664 + 4.28113i
\(553\) 926.919 0.0712778
\(554\) 14019.5 1.07515
\(555\) 1205.87 3007.31i 0.0922275 0.230006i
\(556\) −16558.5 −1.26301
\(557\) 15577.1i 1.18496i −0.805585 0.592480i \(-0.798149\pi\)
0.805585 0.592480i \(-0.201851\pi\)
\(558\) −21136.3 + 22118.3i −1.60353 + 1.67803i
\(559\) 19675.4 1.48870
\(560\) 14841.6i 1.11995i
\(561\) −3696.05 1482.04i −0.278159 0.111536i
\(562\) 2819.01i 0.211588i
\(563\) −184.983 −0.0138474 −0.00692370 0.999976i \(-0.502204\pi\)
−0.00692370 + 0.999976i \(0.502204\pi\)
\(564\) −4996.23 + 12460.1i −0.373013 + 0.930256i
\(565\) 1250.95i 0.0931467i
\(566\) 3338.34i 0.247917i
\(567\) −169.875 3739.33i −0.0125821 0.276961i
\(568\) 69226.2i 5.11385i
\(569\) 22124.0 1.63003 0.815014 0.579441i \(-0.196729\pi\)
0.815014 + 0.579441i \(0.196729\pi\)
\(570\) −23296.4 9341.35i −1.71189 0.686432i
\(571\) 9518.89i 0.697641i −0.937190 0.348820i \(-0.886582\pi\)
0.937190 0.348820i \(-0.113418\pi\)
\(572\) 10094.7i 0.737901i
\(573\) −8295.09 + 20687.1i −0.604768 + 1.50823i
\(574\) 1045.71i 0.0760405i
\(575\) −2558.24 −0.185541
\(576\) −53187.7 50826.3i −3.84749 3.67667i
\(577\) 7109.80 0.512972 0.256486 0.966548i \(-0.417435\pi\)
0.256486 + 0.966548i \(0.417435\pi\)
\(578\) 20863.5 1.50139
\(579\) 3823.63 9535.74i 0.274446 0.684442i
\(580\) 59109.7 4.23172
\(581\) −1741.77 −0.124373
\(582\) −11788.7 4727.00i −0.839615 0.336668i
\(583\) 2623.28i 0.186355i
\(584\) 9214.86i 0.652934i
\(585\) 10746.9 + 10269.8i 0.759539 + 0.725817i
\(586\) 13932.5i 0.982162i
\(587\) 15101.6 1.06185 0.530927 0.847418i \(-0.321844\pi\)
0.530927 + 0.847418i \(0.321844\pi\)
\(588\) 14069.4 35087.6i 0.986754 2.46087i
\(589\) 17123.2i 1.19788i
\(590\) −591.296 26020.2i −0.0412598 1.81565i
\(591\) 63.7975 + 25.5814i 0.00444040 + 0.00178051i
\(592\) 16927.2i 1.17518i
\(593\) 6719.14i 0.465299i −0.972561 0.232649i \(-0.925261\pi\)
0.972561 0.232649i \(-0.0747395\pi\)
\(594\) −5853.14 + 2661.37i −0.404305 + 0.183834i
\(595\) 4931.06 0.339754
\(596\) 45043.6 3.09574
\(597\) −8193.40 + 20433.5i −0.561698 + 1.40082i
\(598\) 41012.2i 2.80454i
\(599\) 1436.88i 0.0980125i −0.998798 0.0490063i \(-0.984395\pi\)
0.998798 0.0490063i \(-0.0156054\pi\)
\(600\) 2985.93 7446.62i 0.203167 0.506678i
\(601\) 6652.88i 0.451542i −0.974180 0.225771i \(-0.927510\pi\)
0.974180 0.225771i \(-0.0724901\pi\)
\(602\) 10538.7i 0.713495i
\(603\) −5769.58 + 6037.64i −0.389645 + 0.407748i
\(604\) 67551.7i 4.55072i
\(605\) 13034.6i 0.875920i
\(606\) −13982.9 + 34871.8i −0.937318 + 2.33758i
\(607\) 25508.3 1.70568 0.852842 0.522170i \(-0.174877\pi\)
0.852842 + 0.522170i \(0.174877\pi\)
\(608\) 75040.8 5.00544
\(609\) −6173.94 2475.62i −0.410806 0.164724i
\(610\) −12295.0 −0.816085
\(611\) 5999.24i 0.397223i
\(612\) 39888.8 41742.1i 2.63466 2.75706i
\(613\) 12332.0i 0.812539i −0.913753 0.406270i \(-0.866829\pi\)
0.913753 0.406270i \(-0.133171\pi\)
\(614\) −4233.54 −0.278260
\(615\) 730.190 1821.02i 0.0478766 0.119399i
\(616\) 3524.38 0.230521
\(617\) 1837.26i 0.119879i 0.998202 + 0.0599394i \(0.0190908\pi\)
−0.998202 + 0.0599394i \(0.980909\pi\)
\(618\) −41707.0 16723.6i −2.71473 1.08855i
\(619\) −23555.3 −1.52951 −0.764754 0.644322i \(-0.777140\pi\)
−0.764754 + 0.644322i \(0.777140\pi\)
\(620\) −48268.5 −3.12663
\(621\) −17638.6 + 8020.08i −1.13979 + 0.518252i
\(622\) 8822.39i 0.568723i
\(623\) −3815.93 −0.245397
\(624\) −72080.3 28902.7i −4.62423 1.85422i
\(625\) −12966.5 −0.829855
\(626\) 54829.2i 3.50066i
\(627\) 1339.36 3340.23i 0.0853092 0.212753i
\(628\) 66796.1i 4.24435i
\(629\) −5623.99 −0.356507
\(630\) 5500.76 5756.33i 0.347866 0.364028i
\(631\) 1509.61 0.0952405 0.0476203 0.998866i \(-0.484836\pi\)
0.0476203 + 0.998866i \(0.484836\pi\)
\(632\) 15047.5 0.947084
\(633\) 12852.4 + 5153.52i 0.807007 + 0.323592i
\(634\) 49296.4i 3.08803i
\(635\) 12554.2i 0.784563i
\(636\) 35302.6 + 14155.6i 2.20101 + 0.882557i
\(637\) 16893.9i 1.05080i
\(638\) 11426.0i 0.709027i
\(639\) −15491.7 + 16211.4i −0.959062 + 1.00362i
\(640\) 82833.2i 5.11605i
\(641\) 8463.28i 0.521497i 0.965407 + 0.260748i \(0.0839693\pi\)
−0.965407 + 0.260748i \(0.916031\pi\)
\(642\) 34725.2 + 13924.0i 2.13472 + 0.855979i
\(643\) −18771.3 −1.15127 −0.575637 0.817706i \(-0.695246\pi\)
−0.575637 + 0.817706i \(0.695246\pi\)
\(644\) 16294.0 0.997007
\(645\) −7358.83 + 18352.2i −0.449231 + 1.12034i
\(646\) 43566.6i 2.65342i
\(647\) 21564.6i 1.31034i −0.755481 0.655171i \(-0.772597\pi\)
0.755481 0.655171i \(-0.227403\pi\)
\(648\) −2757.73 60703.8i −0.167182 3.68005i
\(649\) 3730.77 84.7798i 0.225648 0.00512773i
\(650\) 5500.54i 0.331922i
\(651\) 5041.59 + 2021.57i 0.303526 + 0.121707i
\(652\) −37221.7 −2.23576
\(653\) 26279.9i 1.57490i 0.616376 + 0.787452i \(0.288600\pi\)
−0.616376 + 0.787452i \(0.711400\pi\)
\(654\) 44855.2 + 17986.0i 2.68192 + 1.07539i
\(655\) 18209.3i 1.08625i
\(656\) 10249.9i 0.610050i
\(657\) 2062.13 2157.94i 0.122453 0.128142i
\(658\) 3213.35 0.190379
\(659\) 3824.67 0.226082 0.113041 0.993590i \(-0.463941\pi\)
0.113041 + 0.993590i \(0.463941\pi\)
\(660\) −9415.76 3775.52i −0.555315 0.222669i
\(661\) 7544.32 0.443934 0.221967 0.975054i \(-0.428752\pi\)
0.221967 + 0.975054i \(0.428752\pi\)
\(662\) −33963.3 −1.99399
\(663\) 9602.77 23948.3i 0.562505 1.40283i
\(664\) −28275.7 −1.65258
\(665\) 4456.34i 0.259864i
\(666\) −6273.74 + 6565.23i −0.365019 + 0.381978i
\(667\) 34432.4i 1.99884i
\(668\) 34800.0i 2.01565i
\(669\) 9352.40 23324.0i 0.540486 1.34792i
\(670\) −17763.4 −1.02427
\(671\) 1762.86i 0.101422i
\(672\) −8859.34 + 22094.3i −0.508566 + 1.26831i
\(673\) 27395.9i 1.56914i −0.620037 0.784572i \(-0.712883\pi\)
0.620037 0.784572i \(-0.287117\pi\)
\(674\) 2567.73i 0.146744i
\(675\) 2365.68 1075.65i 0.134896 0.0613360i
\(676\) −14927.8 −0.849331
\(677\) 5385.78i 0.305749i −0.988246 0.152875i \(-0.951147\pi\)
0.988246 0.152875i \(-0.0488531\pi\)
\(678\) −1304.84 + 3254.15i −0.0739118 + 0.184329i
\(679\) 2255.04i 0.127453i
\(680\) 80050.2 4.51439
\(681\) 4504.06 11232.7i 0.253445 0.632066i
\(682\) 9330.36i 0.523868i
\(683\) 1944.56 0.108941 0.0544703 0.998515i \(-0.482653\pi\)
0.0544703 + 0.998515i \(0.482653\pi\)
\(684\) 37723.5 + 36048.7i 2.10876 + 2.01514i
\(685\) −17810.3 −0.993424
\(686\) −18851.0 −1.04918
\(687\) −22833.6 9155.80i −1.26806 0.508465i
\(688\) 103299.i 5.72416i
\(689\) 16997.4 0.939840
\(690\) −38254.0 15339.0i −2.11058 0.846299i
\(691\) 8078.30i 0.444737i 0.974963 + 0.222368i \(0.0713787\pi\)
−0.974963 + 0.222368i \(0.928621\pi\)
\(692\) −40361.1 −2.21719
\(693\) 825.340 + 788.697i 0.0452411 + 0.0432325i
\(694\) 66655.0 3.64580
\(695\) 7436.34i 0.405865i
\(696\) −100227. 40188.9i −5.45847 2.18873i
\(697\) −3405.50 −0.185068
\(698\) 25868.3i 1.40277i
\(699\) 5467.79 13636.1i 0.295867 0.737862i
\(700\) −2185.34 −0.117997
\(701\) 3543.67 0.190931 0.0954655 0.995433i \(-0.469566\pi\)
0.0954655 + 0.995433i \(0.469566\pi\)
\(702\) −17244.2 37925.1i −0.927121 2.03902i
\(703\) 5082.56i 0.272677i
\(704\) 22436.6 1.20115
\(705\) −5595.77 2243.78i −0.298935 0.119866i
\(706\) −16720.4 −0.891330
\(707\) 6670.59 0.354842
\(708\) −18990.9 + 50664.1i −1.00808 + 2.68937i
\(709\) −35599.1 −1.88569 −0.942844 0.333234i \(-0.891860\pi\)
−0.942844 + 0.333234i \(0.891860\pi\)
\(710\) −47695.8 −2.52111
\(711\) 3523.83 + 3367.38i 0.185870 + 0.177618i
\(712\) −61947.4 −3.26064
\(713\) 28117.2i 1.47686i
\(714\) −12827.3 5143.49i −0.672341 0.269594i
\(715\) −4533.47 −0.237122
\(716\) −65093.7 −3.39758
\(717\) 3090.50 + 1239.22i 0.160972 + 0.0645463i
\(718\) 21371.7i 1.11084i
\(719\) 10953.5 0.568145 0.284072 0.958803i \(-0.408314\pi\)
0.284072 + 0.958803i \(0.408314\pi\)
\(720\) 53917.6 56422.7i 2.79082 2.92049i
\(721\) 7978.08i 0.412093i
\(722\) −1197.43 −0.0617229
\(723\) 2171.97 5416.68i 0.111724 0.278629i
\(724\) 7925.94 0.406858
\(725\) 4618.06i 0.236566i
\(726\) −13596.1 + 33907.4i −0.695041 + 1.73336i
\(727\) −18093.5 −0.923040 −0.461520 0.887130i \(-0.652696\pi\)
−0.461520 + 0.887130i \(0.652696\pi\)
\(728\) 22836.0i 1.16258i
\(729\) 12938.7 14832.8i 0.657353 0.753583i
\(730\) 6348.90 0.321895
\(731\) 34320.5 1.73651
\(732\) 23723.5 + 9512.63i 1.19788 + 0.480324i
\(733\) −7730.58 −0.389543 −0.194772 0.980849i \(-0.562397\pi\)
−0.194772 + 0.980849i \(0.562397\pi\)
\(734\) 17224.4i 0.866166i
\(735\) 15757.7 + 6318.49i 0.790791 + 0.317090i
\(736\) 123221. 6.17118
\(737\) 2546.91i 0.127295i
\(738\) −3798.94 + 3975.44i −0.189486 + 0.198290i
\(739\) 1695.25i 0.0843853i −0.999109 0.0421926i \(-0.986566\pi\)
0.999109 0.0421926i \(-0.0134343\pi\)
\(740\) −14327.2 −0.711728
\(741\) 21642.8 + 8678.30i 1.07297 + 0.430237i
\(742\) 9104.24i 0.450441i
\(743\) 29123.9i 1.43803i −0.694997 0.719013i \(-0.744594\pi\)
0.694997 0.719013i \(-0.255406\pi\)
\(744\) 81844.6 + 32817.9i 4.03302 + 1.61715i
\(745\) 20228.9i 0.994804i
\(746\) 23.4442 0.00115061
\(747\) −6621.62 6327.64i −0.324327 0.309928i
\(748\) 17608.4i 0.860732i
\(749\) 6642.54i 0.324049i
\(750\) 39753.4 + 15940.2i 1.93545 + 0.776074i
\(751\) 28450.7i 1.38240i −0.722663 0.691200i \(-0.757082\pi\)
0.722663 0.691200i \(-0.242918\pi\)
\(752\) 31496.8 1.52735
\(753\) −23142.2 9279.51i −1.11998 0.449089i
\(754\) −74034.0 −3.57581
\(755\) 30337.1 1.46236
\(756\) −15067.5 + 6851.04i −0.724866 + 0.329590i
\(757\) 32205.6 1.54628 0.773138 0.634238i \(-0.218686\pi\)
0.773138 + 0.634238i \(0.218686\pi\)
\(758\) −35699.6 −1.71065
\(759\) 2199.30 5484.84i 0.105177 0.262302i
\(760\) 72343.6i 3.45287i
\(761\) 34842.8i 1.65972i 0.557969 + 0.829861i \(0.311581\pi\)
−0.557969 + 0.829861i \(0.688419\pi\)
\(762\) −13095.0 + 32657.7i −0.622549 + 1.55257i
\(763\) 8580.29i 0.407113i
\(764\) 98555.9 4.66705
\(765\) 18746.2 + 17913.9i 0.885973 + 0.846638i
\(766\) 28835.9i 1.36016i
\(767\) 549.326 + 24173.3i 0.0258605 + 1.13800i
\(768\) −44247.4 + 110349.i −2.07896 + 5.18471i
\(769\) 27342.3i 1.28217i 0.767470 + 0.641085i \(0.221515\pi\)
−0.767470 + 0.641085i \(0.778485\pi\)
\(770\) 2428.24i 0.113646i
\(771\) 3470.76 + 1391.70i 0.162123 + 0.0650076i
\(772\) −45429.4 −2.11793
\(773\) −23177.9 −1.07846 −0.539231 0.842158i \(-0.681285\pi\)
−0.539231 + 0.842158i \(0.681285\pi\)
\(774\) 38285.6 40064.4i 1.77797 1.86057i
\(775\) 3771.07i 0.174788i
\(776\) 36608.0i 1.69349i
\(777\) 1496.46 + 600.048i 0.0690929 + 0.0277048i
\(778\) 2557.59i 0.117858i
\(779\) 3077.64i 0.141551i
\(780\) 24463.2 61008.8i 1.12298 2.80060i
\(781\) 6838.60i 0.313322i
\(782\) 71538.8i 3.27138i
\(783\) −14477.6 31840.6i −0.660776 1.45324i