Properties

Label 882.4.g.bi.361.2
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{22})\)
Defining polynomial: \(x^{4} + 22 x^{2} + 484\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 98)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(2.34521 + 4.06202i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bi.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.69042 + 8.12404i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(4.69042 + 8.12404i) q^{5} -8.00000 q^{8} +(-9.38083 + 16.2481i) q^{10} +(10.0000 - 17.3205i) q^{11} +65.6658 q^{13} +(-8.00000 - 13.8564i) q^{16} +(28.1425 - 48.7442i) q^{17} +(-4.69042 - 8.12404i) q^{19} -37.5233 q^{20} +40.0000 q^{22} +(24.0000 + 41.5692i) q^{23} +(18.5000 - 32.0429i) q^{25} +(65.6658 + 113.737i) q^{26} +166.000 q^{29} +(103.189 - 178.729i) q^{31} +(16.0000 - 27.7128i) q^{32} +112.570 q^{34} +(39.0000 + 67.5500i) q^{37} +(9.38083 - 16.2481i) q^{38} +(-37.5233 - 64.9923i) q^{40} -393.995 q^{41} +436.000 q^{43} +(40.0000 + 69.2820i) q^{44} +(-48.0000 + 83.1384i) q^{46} +(103.189 + 178.729i) q^{47} +74.0000 q^{50} +(-131.332 + 227.473i) q^{52} +(31.0000 - 53.6936i) q^{53} +187.617 q^{55} +(166.000 + 287.520i) q^{58} +(-333.020 + 576.807i) q^{59} +(-136.022 - 235.597i) q^{61} +412.757 q^{62} +64.0000 q^{64} +(308.000 + 533.472i) q^{65} +(-290.000 + 502.295i) q^{67} +(112.570 + 194.977i) q^{68} +544.000 q^{71} +(300.187 - 519.938i) q^{73} +(-78.0000 + 135.100i) q^{74} +37.5233 q^{76} +(340.000 + 588.897i) q^{79} +(75.0467 - 129.985i) q^{80} +(-393.995 - 682.419i) q^{82} -196.997 q^{83} +528.000 q^{85} +(436.000 + 755.174i) q^{86} +(-80.0000 + 138.564i) q^{88} +(-750.467 - 1299.85i) q^{89} -192.000 q^{92} +(-206.378 + 357.458i) q^{94} +(44.0000 - 76.2102i) q^{95} -656.658 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} - 32q^{8} + 40q^{11} - 32q^{16} + 160q^{22} + 96q^{23} + 74q^{25} + 664q^{29} + 64q^{32} + 156q^{37} + 1744q^{43} + 160q^{44} - 192q^{46} + 296q^{50} + 124q^{53} + 664q^{58} + 256q^{64} + 1232q^{65} - 1160q^{67} + 2176q^{71} - 312q^{74} + 1360q^{79} + 2112q^{85} + 1744q^{86} - 320q^{88} - 768q^{92} + 176q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 4.69042 + 8.12404i 0.419524 + 0.726636i 0.995892 0.0905542i \(-0.0288638\pi\)
−0.576368 + 0.817190i \(0.695530\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −9.38083 + 16.2481i −0.296648 + 0.513809i
\(11\) 10.0000 17.3205i 0.274101 0.474757i −0.695807 0.718229i \(-0.744953\pi\)
0.969908 + 0.243472i \(0.0782863\pi\)
\(12\) 0 0
\(13\) 65.6658 1.40096 0.700478 0.713674i \(-0.252970\pi\)
0.700478 + 0.713674i \(0.252970\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 28.1425 48.7442i 0.401503 0.695424i −0.592404 0.805641i \(-0.701821\pi\)
0.993908 + 0.110217i \(0.0351545\pi\)
\(18\) 0 0
\(19\) −4.69042 8.12404i −0.0566345 0.0980938i 0.836318 0.548244i \(-0.184704\pi\)
−0.892953 + 0.450151i \(0.851370\pi\)
\(20\) −37.5233 −0.419524
\(21\) 0 0
\(22\) 40.0000 0.387638
\(23\) 24.0000 + 41.5692i 0.217580 + 0.376860i 0.954068 0.299591i \(-0.0968503\pi\)
−0.736487 + 0.676451i \(0.763517\pi\)
\(24\) 0 0
\(25\) 18.5000 32.0429i 0.148000 0.256344i
\(26\) 65.6658 + 113.737i 0.495313 + 0.857907i
\(27\) 0 0
\(28\) 0 0
\(29\) 166.000 1.06295 0.531473 0.847075i \(-0.321639\pi\)
0.531473 + 0.847075i \(0.321639\pi\)
\(30\) 0 0
\(31\) 103.189 178.729i 0.597849 1.03550i −0.395289 0.918557i \(-0.629356\pi\)
0.993138 0.116948i \(-0.0373111\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 112.570 0.567812
\(35\) 0 0
\(36\) 0 0
\(37\) 39.0000 + 67.5500i 0.173285 + 0.300139i 0.939567 0.342366i \(-0.111228\pi\)
−0.766281 + 0.642505i \(0.777895\pi\)
\(38\) 9.38083 16.2481i 0.0400466 0.0693628i
\(39\) 0 0
\(40\) −37.5233 64.9923i −0.148324 0.256905i
\(41\) −393.995 −1.50077 −0.750386 0.661000i \(-0.770132\pi\)
−0.750386 + 0.661000i \(0.770132\pi\)
\(42\) 0 0
\(43\) 436.000 1.54626 0.773132 0.634245i \(-0.218689\pi\)
0.773132 + 0.634245i \(0.218689\pi\)
\(44\) 40.0000 + 69.2820i 0.137051 + 0.237379i
\(45\) 0 0
\(46\) −48.0000 + 83.1384i −0.153852 + 0.266480i
\(47\) 103.189 + 178.729i 0.320249 + 0.554687i 0.980539 0.196323i \(-0.0629002\pi\)
−0.660291 + 0.751010i \(0.729567\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 74.0000 0.209304
\(51\) 0 0
\(52\) −131.332 + 227.473i −0.350239 + 0.606632i
\(53\) 31.0000 53.6936i 0.0803430 0.139158i −0.823054 0.567963i \(-0.807732\pi\)
0.903397 + 0.428805i \(0.141065\pi\)
\(54\) 0 0
\(55\) 187.617 0.459968
\(56\) 0 0
\(57\) 0 0
\(58\) 166.000 + 287.520i 0.375808 + 0.650919i
\(59\) −333.020 + 576.807i −0.734838 + 1.27278i 0.219956 + 0.975510i \(0.429409\pi\)
−0.954794 + 0.297267i \(0.903925\pi\)
\(60\) 0 0
\(61\) −136.022 235.597i −0.285506 0.494510i 0.687226 0.726444i \(-0.258828\pi\)
−0.972732 + 0.231933i \(0.925495\pi\)
\(62\) 412.757 0.845486
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 308.000 + 533.472i 0.587734 + 1.01798i
\(66\) 0 0
\(67\) −290.000 + 502.295i −0.528793 + 0.915897i 0.470643 + 0.882324i \(0.344022\pi\)
−0.999436 + 0.0335729i \(0.989311\pi\)
\(68\) 112.570 + 194.977i 0.200752 + 0.347712i
\(69\) 0 0
\(70\) 0 0
\(71\) 544.000 0.909309 0.454654 0.890668i \(-0.349763\pi\)
0.454654 + 0.890668i \(0.349763\pi\)
\(72\) 0 0
\(73\) 300.187 519.938i 0.481290 0.833619i −0.518479 0.855090i \(-0.673502\pi\)
0.999769 + 0.0214711i \(0.00683499\pi\)
\(74\) −78.0000 + 135.100i −0.122531 + 0.212230i
\(75\) 0 0
\(76\) 37.5233 0.0566345
\(77\) 0 0
\(78\) 0 0
\(79\) 340.000 + 588.897i 0.484215 + 0.838685i 0.999836 0.0181320i \(-0.00577190\pi\)
−0.515621 + 0.856817i \(0.672439\pi\)
\(80\) 75.0467 129.985i 0.104881 0.181659i
\(81\) 0 0
\(82\) −393.995 682.419i −0.530603 0.919032i
\(83\) −196.997 −0.260521 −0.130261 0.991480i \(-0.541581\pi\)
−0.130261 + 0.991480i \(0.541581\pi\)
\(84\) 0 0
\(85\) 528.000 0.673760
\(86\) 436.000 + 755.174i 0.546687 + 0.946890i
\(87\) 0 0
\(88\) −80.0000 + 138.564i −0.0969094 + 0.167852i
\(89\) −750.467 1299.85i −0.893812 1.54813i −0.835268 0.549843i \(-0.814687\pi\)
−0.0585446 0.998285i \(-0.518646\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −192.000 −0.217580
\(93\) 0 0
\(94\) −206.378 + 357.458i −0.226450 + 0.392223i
\(95\) 44.0000 76.2102i 0.0475190 0.0823053i
\(96\) 0 0
\(97\) −656.658 −0.687356 −0.343678 0.939088i \(-0.611673\pi\)
−0.343678 + 0.939088i \(0.611673\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 74.0000 + 128.172i 0.0740000 + 0.128172i
\(101\) 60.9754 105.612i 0.0600721 0.104048i −0.834425 0.551121i \(-0.814200\pi\)
0.894497 + 0.447073i \(0.147534\pi\)
\(102\) 0 0
\(103\) 684.801 + 1186.11i 0.655101 + 1.13467i 0.981868 + 0.189564i \(0.0607073\pi\)
−0.326767 + 0.945105i \(0.605959\pi\)
\(104\) −525.327 −0.495313
\(105\) 0 0
\(106\) 124.000 0.113622
\(107\) −130.000 225.167i −0.117454 0.203436i 0.801304 0.598257i \(-0.204140\pi\)
−0.918758 + 0.394821i \(0.870807\pi\)
\(108\) 0 0
\(109\) −941.000 + 1629.86i −0.826894 + 1.43222i 0.0735690 + 0.997290i \(0.476561\pi\)
−0.900463 + 0.434932i \(0.856772\pi\)
\(110\) 187.617 + 324.962i 0.162623 + 0.281672i
\(111\) 0 0
\(112\) 0 0
\(113\) 1286.00 1.07059 0.535295 0.844665i \(-0.320200\pi\)
0.535295 + 0.844665i \(0.320200\pi\)
\(114\) 0 0
\(115\) −225.140 + 389.954i −0.182560 + 0.316203i
\(116\) −332.000 + 575.041i −0.265736 + 0.460269i
\(117\) 0 0
\(118\) −1332.08 −1.03922
\(119\) 0 0
\(120\) 0 0
\(121\) 465.500 + 806.270i 0.349737 + 0.605762i
\(122\) 272.044 471.194i 0.201883 0.349671i
\(123\) 0 0
\(124\) 412.757 + 714.915i 0.298924 + 0.517752i
\(125\) 1519.69 1.08741
\(126\) 0 0
\(127\) 2312.00 1.61541 0.807704 0.589588i \(-0.200710\pi\)
0.807704 + 0.589588i \(0.200710\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −616.000 + 1066.94i −0.415591 + 0.719824i
\(131\) −126.641 219.349i −0.0844633 0.146295i 0.820699 0.571361i \(-0.193584\pi\)
−0.905162 + 0.425066i \(0.860251\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −1160.00 −0.747826
\(135\) 0 0
\(136\) −225.140 + 389.954i −0.141953 + 0.245870i
\(137\) −557.000 + 964.752i −0.347356 + 0.601638i −0.985779 0.168048i \(-0.946254\pi\)
0.638423 + 0.769686i \(0.279587\pi\)
\(138\) 0 0
\(139\) 1378.98 0.841466 0.420733 0.907185i \(-0.361773\pi\)
0.420733 + 0.907185i \(0.361773\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 544.000 + 942.236i 0.321489 + 0.556836i
\(143\) 656.658 1137.37i 0.384004 0.665114i
\(144\) 0 0
\(145\) 778.609 + 1348.59i 0.445931 + 0.772375i
\(146\) 1200.75 0.680647
\(147\) 0 0
\(148\) −312.000 −0.173285
\(149\) −473.000 819.260i −0.260065 0.450446i 0.706194 0.708018i \(-0.250411\pi\)
−0.966259 + 0.257573i \(0.917077\pi\)
\(150\) 0 0
\(151\) −416.000 + 720.533i −0.224196 + 0.388319i −0.956078 0.293113i \(-0.905309\pi\)
0.731882 + 0.681431i \(0.238642\pi\)
\(152\) 37.5233 + 64.9923i 0.0200233 + 0.0346814i
\(153\) 0 0
\(154\) 0 0
\(155\) 1936.00 1.00325
\(156\) 0 0
\(157\) −1439.96 + 2494.08i −0.731982 + 1.26783i 0.224053 + 0.974577i \(0.428071\pi\)
−0.956035 + 0.293253i \(0.905262\pi\)
\(158\) −680.000 + 1177.79i −0.342392 + 0.593040i
\(159\) 0 0
\(160\) 300.187 0.148324
\(161\) 0 0
\(162\) 0 0
\(163\) −318.000 550.792i −0.152808 0.264671i 0.779451 0.626463i \(-0.215498\pi\)
−0.932259 + 0.361792i \(0.882165\pi\)
\(164\) 787.990 1364.84i 0.375193 0.649854i
\(165\) 0 0
\(166\) −196.997 341.210i −0.0921082 0.159536i
\(167\) 656.658 0.304274 0.152137 0.988359i \(-0.451385\pi\)
0.152137 + 0.988359i \(0.451385\pi\)
\(168\) 0 0
\(169\) 2115.00 0.962676
\(170\) 528.000 + 914.523i 0.238210 + 0.412592i
\(171\) 0 0
\(172\) −872.000 + 1510.35i −0.386566 + 0.669552i
\(173\) 333.020 + 576.807i 0.146353 + 0.253490i 0.929877 0.367871i \(-0.119913\pi\)
−0.783524 + 0.621361i \(0.786580\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −320.000 −0.137051
\(177\) 0 0
\(178\) 1500.93 2599.69i 0.632021 1.09469i
\(179\) −1614.00 + 2795.53i −0.673944 + 1.16731i 0.302832 + 0.953044i \(0.402068\pi\)
−0.976776 + 0.214262i \(0.931265\pi\)
\(180\) 0 0
\(181\) −2823.63 −1.15955 −0.579776 0.814776i \(-0.696860\pi\)
−0.579776 + 0.814776i \(0.696860\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −192.000 332.554i −0.0769262 0.133240i
\(185\) −365.852 + 633.675i −0.145395 + 0.251831i
\(186\) 0 0
\(187\) −562.850 974.885i −0.220105 0.381233i
\(188\) −825.513 −0.320249
\(189\) 0 0
\(190\) 176.000 0.0672020
\(191\) −1068.00 1849.83i −0.404596 0.700780i 0.589679 0.807638i \(-0.299254\pi\)
−0.994274 + 0.106858i \(0.965921\pi\)
\(192\) 0 0
\(193\) −829.000 + 1435.87i −0.309185 + 0.535524i −0.978184 0.207739i \(-0.933390\pi\)
0.668999 + 0.743263i \(0.266723\pi\)
\(194\) −656.658 1137.37i −0.243017 0.420918i
\(195\) 0 0
\(196\) 0 0
\(197\) 978.000 0.353704 0.176852 0.984237i \(-0.443409\pi\)
0.176852 + 0.984237i \(0.443409\pi\)
\(198\) 0 0
\(199\) 2467.16 4273.24i 0.878855 1.52222i 0.0262574 0.999655i \(-0.491641\pi\)
0.852598 0.522567i \(-0.175026\pi\)
\(200\) −148.000 + 256.344i −0.0523259 + 0.0906311i
\(201\) 0 0
\(202\) 243.902 0.0849547
\(203\) 0 0
\(204\) 0 0
\(205\) −1848.00 3200.83i −0.629609 1.09052i
\(206\) −1369.60 + 2372.22i −0.463226 + 0.802332i
\(207\) 0 0
\(208\) −525.327 909.892i −0.175119 0.303316i
\(209\) −187.617 −0.0620943
\(210\) 0 0
\(211\) 1556.00 0.507675 0.253838 0.967247i \(-0.418307\pi\)
0.253838 + 0.967247i \(0.418307\pi\)
\(212\) 124.000 + 214.774i 0.0401715 + 0.0695791i
\(213\) 0 0
\(214\) 260.000 450.333i 0.0830525 0.143851i
\(215\) 2045.02 + 3542.08i 0.648694 + 1.12357i
\(216\) 0 0
\(217\) 0 0
\(218\) −3764.00 −1.16940
\(219\) 0 0
\(220\) −375.233 + 649.923i −0.114992 + 0.199172i
\(221\) 1848.00 3200.83i 0.562488 0.974258i
\(222\) 0 0
\(223\) 2889.30 0.867630 0.433815 0.901002i \(-0.357167\pi\)
0.433815 + 0.901002i \(0.357167\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1286.00 + 2227.42i 0.378511 + 0.655600i
\(227\) −989.678 + 1714.17i −0.289371 + 0.501205i −0.973660 0.228006i \(-0.926779\pi\)
0.684289 + 0.729211i \(0.260113\pi\)
\(228\) 0 0
\(229\) −1383.67 2396.59i −0.399282 0.691577i 0.594355 0.804203i \(-0.297407\pi\)
−0.993638 + 0.112625i \(0.964074\pi\)
\(230\) −900.560 −0.258179
\(231\) 0 0
\(232\) −1328.00 −0.375808
\(233\) −3245.00 5620.50i −0.912391 1.58031i −0.810677 0.585493i \(-0.800901\pi\)
−0.101713 0.994814i \(-0.532432\pi\)
\(234\) 0 0
\(235\) −968.000 + 1676.63i −0.268704 + 0.465408i
\(236\) −1332.08 2307.23i −0.367419 0.636388i
\(237\) 0 0
\(238\) 0 0
\(239\) 4296.00 1.16270 0.581350 0.813654i \(-0.302525\pi\)
0.581350 + 0.813654i \(0.302525\pi\)
\(240\) 0 0
\(241\) −2260.78 + 3915.79i −0.604272 + 1.04663i 0.387894 + 0.921704i \(0.373203\pi\)
−0.992166 + 0.124926i \(0.960131\pi\)
\(242\) −931.000 + 1612.54i −0.247301 + 0.428339i
\(243\) 0 0
\(244\) 1088.18 0.285506
\(245\) 0 0
\(246\) 0 0
\(247\) −308.000 533.472i −0.0793424 0.137425i
\(248\) −825.513 + 1429.83i −0.211372 + 0.366106i
\(249\) 0 0
\(250\) 1519.69 + 2632.19i 0.384456 + 0.665897i
\(251\) −5581.59 −1.40361 −0.701807 0.712367i \(-0.747623\pi\)
−0.701807 + 0.712367i \(0.747623\pi\)
\(252\) 0 0
\(253\) 960.000 0.238556
\(254\) 2312.00 + 4004.50i 0.571133 + 0.989231i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −750.467 1299.85i −0.182151 0.315495i 0.760462 0.649383i \(-0.224973\pi\)
−0.942613 + 0.333888i \(0.891639\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −2464.00 −0.587734
\(261\) 0 0
\(262\) 253.282 438.698i 0.0597246 0.103446i
\(263\) −200.000 + 346.410i −0.0468917 + 0.0812189i −0.888519 0.458841i \(-0.848265\pi\)
0.841627 + 0.540059i \(0.181598\pi\)
\(264\) 0 0
\(265\) 581.612 0.134823
\(266\) 0 0
\(267\) 0 0
\(268\) −1160.00 2009.18i −0.264397 0.457948i
\(269\) −136.022 + 235.597i −0.0308305 + 0.0534000i −0.881029 0.473062i \(-0.843149\pi\)
0.850198 + 0.526462i \(0.176482\pi\)
\(270\) 0 0
\(271\) −3452.15 5979.29i −0.773812 1.34028i −0.935460 0.353433i \(-0.885014\pi\)
0.161648 0.986848i \(-0.448319\pi\)
\(272\) −900.560 −0.200752
\(273\) 0 0
\(274\) −2228.00 −0.491235
\(275\) −370.000 640.859i −0.0811340 0.140528i
\(276\) 0 0
\(277\) 3385.00 5862.99i 0.734242 1.27174i −0.220814 0.975316i \(-0.570871\pi\)
0.955055 0.296428i \(-0.0957954\pi\)
\(278\) 1378.98 + 2388.47i 0.297503 + 0.515290i
\(279\) 0 0
\(280\) 0 0
\(281\) −1878.00 −0.398691 −0.199345 0.979929i \(-0.563882\pi\)
−0.199345 + 0.979929i \(0.563882\pi\)
\(282\) 0 0
\(283\) −192.307 + 333.086i −0.0403939 + 0.0699642i −0.885516 0.464610i \(-0.846195\pi\)
0.845122 + 0.534574i \(0.179528\pi\)
\(284\) −1088.00 + 1884.47i −0.227327 + 0.393742i
\(285\) 0 0
\(286\) 2626.63 0.543063
\(287\) 0 0
\(288\) 0 0
\(289\) 872.500 + 1511.21i 0.177590 + 0.307595i
\(290\) −1557.22 + 2697.18i −0.315321 + 0.546151i
\(291\) 0 0
\(292\) 1200.75 + 2079.75i 0.240645 + 0.416810i
\(293\) 3742.95 0.746299 0.373149 0.927771i \(-0.378278\pi\)
0.373149 + 0.927771i \(0.378278\pi\)
\(294\) 0 0
\(295\) −6248.00 −1.23313
\(296\) −312.000 540.400i −0.0612656 0.106115i
\(297\) 0 0
\(298\) 946.000 1638.52i 0.183894 0.318513i
\(299\) 1575.98 + 2729.68i 0.304820 + 0.527964i
\(300\) 0 0
\(301\) 0 0
\(302\) −1664.00 −0.317061
\(303\) 0 0
\(304\) −75.0467 + 129.985i −0.0141586 + 0.0245235i
\(305\) 1276.00 2210.10i 0.239553 0.414917i
\(306\) 0 0
\(307\) 722.324 0.134284 0.0671420 0.997743i \(-0.478612\pi\)
0.0671420 + 0.997743i \(0.478612\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1936.00 + 3353.25i 0.354701 + 0.614361i
\(311\) 3639.76 6304.25i 0.663640 1.14946i −0.316012 0.948755i \(-0.602344\pi\)
0.979652 0.200703i \(-0.0643226\pi\)
\(312\) 0 0
\(313\) −759.847 1316.09i −0.137218 0.237668i 0.789225 0.614104i \(-0.210483\pi\)
−0.926442 + 0.376437i \(0.877149\pi\)
\(314\) −5759.83 −1.03518
\(315\) 0 0
\(316\) −2720.00 −0.484215
\(317\) 1179.00 + 2042.09i 0.208893 + 0.361814i 0.951366 0.308062i \(-0.0996805\pi\)
−0.742473 + 0.669876i \(0.766347\pi\)
\(318\) 0 0
\(319\) 1660.00 2875.20i 0.291355 0.504641i
\(320\) 300.187 + 519.938i 0.0524404 + 0.0908295i
\(321\) 0 0
\(322\) 0 0
\(323\) −528.000 −0.0909557
\(324\) 0 0
\(325\) 1214.82 2104.13i 0.207341 0.359126i
\(326\) 636.000 1101.58i 0.108051 0.187151i
\(327\) 0 0
\(328\) 3151.96 0.530603
\(329\) 0 0
\(330\) 0 0
\(331\) −1186.00 2054.21i −0.196944 0.341117i 0.750592 0.660766i \(-0.229768\pi\)
−0.947536 + 0.319649i \(0.896435\pi\)
\(332\) 393.995 682.419i 0.0651304 0.112809i
\(333\) 0 0
\(334\) 656.658 + 1137.37i 0.107577 + 0.186329i
\(335\) −5440.88 −0.887365
\(336\) 0 0
\(337\) −250.000 −0.0404106 −0.0202053 0.999796i \(-0.506432\pi\)
−0.0202053 + 0.999796i \(0.506432\pi\)
\(338\) 2115.00 + 3663.29i 0.340357 + 0.589516i
\(339\) 0 0
\(340\) −1056.00 + 1829.05i −0.168440 + 0.291747i
\(341\) −2063.78 3574.58i −0.327742 0.567666i
\(342\) 0 0
\(343\) 0 0
\(344\) −3488.00 −0.546687
\(345\) 0 0
\(346\) −666.039 + 1153.61i −0.103487 + 0.179245i
\(347\) 4770.00 8261.88i 0.737945 1.27816i −0.215474 0.976510i \(-0.569130\pi\)
0.953419 0.301649i \(-0.0975371\pi\)
\(348\) 0 0
\(349\) −5712.93 −0.876235 −0.438117 0.898918i \(-0.644355\pi\)
−0.438117 + 0.898918i \(0.644355\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −320.000 554.256i −0.0484547 0.0839260i
\(353\) 2195.11 3802.05i 0.330975 0.573265i −0.651728 0.758452i \(-0.725956\pi\)
0.982703 + 0.185187i \(0.0592891\pi\)
\(354\) 0 0
\(355\) 2551.59 + 4419.48i 0.381476 + 0.660737i
\(356\) 6003.73 0.893812
\(357\) 0 0
\(358\) −6456.00 −0.953101
\(359\) 920.000 + 1593.49i 0.135253 + 0.234265i 0.925694 0.378273i \(-0.123482\pi\)
−0.790441 + 0.612538i \(0.790149\pi\)
\(360\) 0 0
\(361\) 3385.50 5863.86i 0.493585 0.854914i
\(362\) −2823.63 4890.67i −0.409963 0.710077i
\(363\) 0 0
\(364\) 0 0
\(365\) 5632.00 0.807650
\(366\) 0 0
\(367\) 1482.17 2567.20i 0.210814 0.365140i −0.741156 0.671333i \(-0.765722\pi\)
0.951969 + 0.306193i \(0.0990552\pi\)
\(368\) 384.000 665.108i 0.0543951 0.0942150i
\(369\) 0 0
\(370\) −1463.41 −0.205619
\(371\) 0 0
\(372\) 0 0
\(373\) −1991.00 3448.51i −0.276381 0.478706i 0.694102 0.719877i \(-0.255802\pi\)
−0.970483 + 0.241171i \(0.922468\pi\)
\(374\) 1125.70 1949.77i 0.155638 0.269573i
\(375\) 0 0
\(376\) −825.513 1429.83i −0.113225 0.196111i
\(377\) 10900.5 1.48914
\(378\) 0 0
\(379\) 2676.00 0.362683 0.181342 0.983420i \(-0.441956\pi\)
0.181342 + 0.983420i \(0.441956\pi\)
\(380\) 176.000 + 304.841i 0.0237595 + 0.0411527i
\(381\) 0 0
\(382\) 2136.00 3699.66i 0.286092 0.495526i
\(383\) 3517.81 + 6093.03i 0.469326 + 0.812896i 0.999385 0.0350645i \(-0.0111637\pi\)
−0.530059 + 0.847961i \(0.677830\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −3316.00 −0.437254
\(387\) 0 0
\(388\) 1313.32 2274.73i 0.171839 0.297634i
\(389\) 4329.00 7498.05i 0.564239 0.977291i −0.432881 0.901451i \(-0.642503\pi\)
0.997120 0.0758397i \(-0.0241637\pi\)
\(390\) 0 0
\(391\) 2701.68 0.349437
\(392\) 0 0
\(393\) 0 0
\(394\) 978.000 + 1693.95i 0.125053 + 0.216598i
\(395\) −3189.48 + 5524.35i −0.406279 + 0.703696i
\(396\) 0 0
\(397\) 4526.25 + 7839.70i 0.572207 + 0.991091i 0.996339 + 0.0854907i \(0.0272458\pi\)
−0.424132 + 0.905600i \(0.639421\pi\)
\(398\) 9868.63 1.24289
\(399\) 0 0
\(400\) −592.000 −0.0740000
\(401\) −2853.00 4941.54i −0.355292 0.615383i 0.631876 0.775069i \(-0.282285\pi\)
−0.987168 + 0.159686i \(0.948952\pi\)
\(402\) 0 0
\(403\) 6776.00 11736.4i 0.837560 1.45070i
\(404\) 243.902 + 422.450i 0.0300360 + 0.0520239i
\(405\) 0 0
\(406\) 0 0
\(407\) 1560.00 0.189991
\(408\) 0 0
\(409\) −1210.13 + 2096.00i −0.146301 + 0.253400i −0.929857 0.367920i \(-0.880070\pi\)
0.783557 + 0.621320i \(0.213403\pi\)
\(410\) 3696.00 6401.66i 0.445201 0.771111i
\(411\) 0 0
\(412\) −5478.41 −0.655101
\(413\) 0 0
\(414\) 0 0
\(415\) −924.000 1600.41i −0.109295 0.189304i
\(416\) 1050.65 1819.78i 0.123828 0.214477i
\(417\) 0 0
\(418\) −187.617 324.962i −0.0219537 0.0380249i
\(419\) 1510.31 0.176095 0.0880473 0.996116i \(-0.471937\pi\)
0.0880473 + 0.996116i \(0.471937\pi\)
\(420\) 0 0
\(421\) −16770.0 −1.94138 −0.970689 0.240341i \(-0.922741\pi\)
−0.970689 + 0.240341i \(0.922741\pi\)
\(422\) 1556.00 + 2695.07i 0.179490 + 0.310886i
\(423\) 0 0
\(424\) −248.000 + 429.549i −0.0284055 + 0.0491998i
\(425\) −1041.27 1803.54i −0.118845 0.205846i
\(426\) 0 0
\(427\) 0 0
\(428\) 1040.00 0.117454
\(429\) 0 0
\(430\) −4090.04 + 7084.16i −0.458696 + 0.794485i
\(431\) 668.000 1157.01i 0.0746553 0.129307i −0.826281 0.563258i \(-0.809548\pi\)
0.900936 + 0.433951i \(0.142881\pi\)
\(432\) 0 0
\(433\) −11163.2 −1.23896 −0.619479 0.785013i \(-0.712656\pi\)
−0.619479 + 0.785013i \(0.712656\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −3764.00 6519.44i −0.413447 0.716111i
\(437\) 225.140 389.954i 0.0246451 0.0426865i
\(438\) 0 0
\(439\) 1801.12 + 3119.63i 0.195815 + 0.339161i 0.947167 0.320740i \(-0.103931\pi\)
−0.751352 + 0.659901i \(0.770598\pi\)
\(440\) −1500.93 −0.162623
\(441\) 0 0
\(442\) 7392.00 0.795479
\(443\) 3174.00 + 5497.53i 0.340409 + 0.589606i 0.984509 0.175336i \(-0.0561011\pi\)
−0.644099 + 0.764942i \(0.722768\pi\)
\(444\) 0 0
\(445\) 7040.00 12193.6i 0.749951 1.29895i
\(446\) 2889.30 + 5004.41i 0.306754 + 0.531313i
\(447\) 0 0
\(448\) 0 0
\(449\) −7170.00 −0.753615 −0.376808 0.926292i \(-0.622978\pi\)
−0.376808 + 0.926292i \(0.622978\pi\)
\(450\) 0 0
\(451\) −3939.95 + 6824.19i −0.411364 + 0.712503i
\(452\) −2572.00 + 4454.83i −0.267648 + 0.463579i
\(453\) 0 0
\(454\) −3958.71 −0.409232
\(455\) 0 0
\(456\) 0 0
\(457\) −3433.00 5946.13i −0.351398 0.608639i 0.635097 0.772433i \(-0.280960\pi\)
−0.986495 + 0.163793i \(0.947627\pi\)
\(458\) 2767.35 4793.18i 0.282335 0.489019i
\(459\) 0 0
\(460\) −900.560 1559.82i −0.0912800 0.158102i
\(461\) −1378.98 −0.139318 −0.0696590 0.997571i \(-0.522191\pi\)
−0.0696590 + 0.997571i \(0.522191\pi\)
\(462\) 0 0
\(463\) 2648.00 0.265795 0.132897 0.991130i \(-0.457572\pi\)
0.132897 + 0.991130i \(0.457572\pi\)
\(464\) −1328.00 2300.16i −0.132868 0.230135i
\(465\) 0 0
\(466\) 6490.00 11241.0i 0.645158 1.11745i
\(467\) −6167.90 10683.1i −0.611170 1.05858i −0.991044 0.133539i \(-0.957366\pi\)
0.379874 0.925038i \(-0.375967\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −3872.00 −0.380004
\(471\) 0 0
\(472\) 2664.16 4614.45i 0.259805 0.449995i
\(473\) 4360.00 7551.74i 0.423833 0.734100i
\(474\) 0 0
\(475\) −347.091 −0.0335276
\(476\) 0 0
\(477\) 0 0
\(478\) 4296.00 + 7440.89i 0.411076 + 0.712005i
\(479\) −6669.77 + 11552.4i −0.636221 + 1.10197i 0.350035 + 0.936737i \(0.386170\pi\)
−0.986255 + 0.165229i \(0.947164\pi\)
\(480\) 0 0
\(481\) 2560.97 + 4435.72i 0.242765 + 0.420482i
\(482\) −9043.12 −0.854570
\(483\) 0 0
\(484\) −3724.00 −0.349737
\(485\) −3080.00 5334.72i −0.288362 0.499458i
\(486\) 0 0
\(487\) −6968.00 + 12068.9i −0.648358 + 1.12299i 0.335157 + 0.942162i \(0.391211\pi\)
−0.983515 + 0.180826i \(0.942123\pi\)
\(488\) 1088.18 + 1884.78i 0.100941 + 0.174836i
\(489\) 0 0
\(490\) 0 0
\(491\) 12276.0 1.12833 0.564163 0.825663i \(-0.309199\pi\)
0.564163 + 0.825663i \(0.309199\pi\)
\(492\) 0 0
\(493\) 4671.65 8091.54i 0.426776 0.739198i
\(494\) 616.000 1066.94i 0.0561035 0.0971742i
\(495\) 0 0
\(496\) −3302.05 −0.298924
\(497\) 0 0
\(498\) 0 0
\(499\) 1110.00 + 1922.58i 0.0995800 + 0.172478i 0.911511 0.411276i \(-0.134917\pi\)
−0.811931 + 0.583754i \(0.801583\pi\)
\(500\) −3039.39 + 5264.38i −0.271851 + 0.470860i
\(501\) 0 0
\(502\) −5581.59 9667.61i −0.496253 0.859535i
\(503\) 11294.5 1.00119 0.500594 0.865682i \(-0.333115\pi\)
0.500594 + 0.865682i \(0.333115\pi\)
\(504\) 0 0
\(505\) 1144.00 0.100807
\(506\) 960.000 + 1662.77i 0.0843423 + 0.146085i
\(507\) 0 0
\(508\) −4624.00 + 8009.00i −0.403852 + 0.699492i
\(509\) −7940.87 13754.0i −0.691499 1.19771i −0.971347 0.237667i \(-0.923617\pi\)
0.279848 0.960044i \(-0.409716\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 1500.93 2599.69i 0.128800 0.223089i
\(515\) −6424.00 + 11126.7i −0.549661 + 0.952040i
\(516\) 0 0
\(517\) 4127.57 0.351122
\(518\) 0 0
\(519\) 0 0
\(520\) −2464.00 4267.77i −0.207795 0.359912i
\(521\) 5806.73 10057.6i 0.488287 0.845738i −0.511622 0.859211i \(-0.670955\pi\)
0.999909 + 0.0134723i \(0.00428850\pi\)
\(522\) 0 0
\(523\) −6308.61 10926.8i −0.527450 0.913570i −0.999488 0.0319918i \(-0.989815\pi\)
0.472038 0.881578i \(-0.343518\pi\)
\(524\) 1013.13 0.0844633
\(525\) 0 0
\(526\) −800.000 −0.0663149
\(527\) −5808.00 10059.8i −0.480077 0.831517i
\(528\) 0 0
\(529\) 4931.50 8541.61i 0.405318 0.702031i
\(530\) 581.612 + 1007.38i 0.0476672 + 0.0825619i
\(531\) 0 0
\(532\) 0 0
\(533\) −25872.0 −2.10252
\(534\) 0 0
\(535\) 1219.51 2112.25i 0.0985494 0.170693i
\(536\) 2320.00 4018.36i 0.186957 0.323818i
\(537\) 0 0
\(538\) −544.088 −0.0436009
\(539\) 0 0
\(540\) 0 0
\(541\) −899.000 1557.11i −0.0714437 0.123744i 0.828091 0.560594i \(-0.189427\pi\)
−0.899534 + 0.436850i \(0.856094\pi\)
\(542\) 6904.29 11958.6i 0.547167 0.947722i
\(543\) 0 0
\(544\) −900.560 1559.82i −0.0709764 0.122935i
\(545\) −17654.7 −1.38761
\(546\) 0 0
\(547\) 1276.00 0.0997401 0.0498700 0.998756i \(-0.484119\pi\)
0.0498700 + 0.998756i \(0.484119\pi\)
\(548\) −2228.00 3859.01i −0.173678 0.300819i
\(549\) 0 0
\(550\) 740.000 1281.72i 0.0573704 0.0993684i
\(551\) −778.609 1348.59i −0.0601994 0.104268i
\(552\) 0 0
\(553\) 0 0
\(554\) 13540.0 1.03837
\(555\) 0 0
\(556\) −2757.96 + 4776.93i −0.210366 + 0.364365i
\(557\) 1347.00 2333.07i 0.102467 0.177478i −0.810233 0.586107i \(-0.800660\pi\)
0.912701 + 0.408629i \(0.133993\pi\)
\(558\) 0 0
\(559\) 28630.3 2.16625
\(560\) 0 0
\(561\) 0 0
\(562\) −1878.00 3252.79i −0.140958 0.244147i
\(563\) −7884.59 + 13656.5i −0.590223 + 1.02230i 0.403979 + 0.914768i \(0.367627\pi\)
−0.994202 + 0.107529i \(0.965706\pi\)
\(564\) 0 0
\(565\) 6031.87 + 10447.5i 0.449138 + 0.777930i
\(566\) −769.228 −0.0571256
\(567\) 0 0
\(568\) −4352.00 −0.321489
\(569\) 6303.00 + 10917.1i 0.464386 + 0.804340i 0.999174 0.0406466i \(-0.0129418\pi\)
−0.534788 + 0.844986i \(0.679608\pi\)
\(570\) 0 0
\(571\) −3426.00 + 5934.01i −0.251092 + 0.434904i −0.963827 0.266529i \(-0.914123\pi\)
0.712735 + 0.701434i \(0.247456\pi\)
\(572\) 2626.63 + 4549.46i 0.192002 + 0.332557i
\(573\) 0 0
\(574\) 0 0
\(575\) 1776.00 0.128808
\(576\) 0 0
\(577\) −7185.72 + 12446.0i −0.518449 + 0.897981i 0.481321 + 0.876545i \(0.340157\pi\)
−0.999770 + 0.0214362i \(0.993176\pi\)
\(578\) −1745.00 + 3022.43i −0.125575 + 0.217503i
\(579\) 0 0
\(580\) −6228.87 −0.445931
\(581\) 0 0
\(582\) 0 0
\(583\) −620.000 1073.87i −0.0440442 0.0762868i
\(584\) −2401.49 + 4159.51i −0.170162 + 0.294729i
\(585\) 0 0
\(586\) 3742.95 + 6482.98i 0.263857 + 0.457013i
\(587\) −18977.4 −1.33438 −0.667191 0.744887i \(-0.732503\pi\)
−0.667191 + 0.744887i \(0.732503\pi\)
\(588\) 0 0
\(589\) −1936.00 −0.135435
\(590\) −6248.00 10821.9i −0.435976 0.755133i
\(591\) 0 0
\(592\) 624.000 1080.80i 0.0433214 0.0750348i
\(593\) 4108.80 + 7116.66i 0.284534 + 0.492826i 0.972496 0.232920i \(-0.0748280\pi\)
−0.687962 + 0.725746i \(0.741495\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 3784.00 0.260065
\(597\) 0 0
\(598\) −3151.96 + 5459.35i −0.215540 + 0.373327i
\(599\) −9552.00 + 16544.5i −0.651559 + 1.12853i 0.331185 + 0.943566i \(0.392552\pi\)
−0.982744 + 0.184968i \(0.940782\pi\)
\(600\) 0 0
\(601\) 21538.4 1.46185 0.730923 0.682460i \(-0.239090\pi\)
0.730923 + 0.682460i \(0.239090\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −1664.00 2882.13i −0.112098 0.194159i
\(605\) −4366.78 + 7563.48i −0.293446 + 0.508263i
\(606\) 0 0
\(607\) −6866.77 11893.6i −0.459166 0.795298i 0.539751 0.841824i \(-0.318518\pi\)
−0.998917 + 0.0465262i \(0.985185\pi\)
\(608\) −300.187 −0.0200233
\(609\) 0 0
\(610\) 5104.00 0.338779
\(611\) 6776.00 + 11736.4i 0.448654 + 0.777092i
\(612\) 0 0
\(613\) −14017.0 + 24278.2i −0.923558 + 1.59965i −0.129695 + 0.991554i \(0.541400\pi\)
−0.793863 + 0.608096i \(0.791934\pi\)
\(614\) 722.324 + 1251.10i 0.0474766 + 0.0822319i
\(615\) 0 0
\(616\) 0 0
\(617\) 8258.00 0.538824 0.269412 0.963025i \(-0.413171\pi\)
0.269412 + 0.963025i \(0.413171\pi\)
\(618\) 0 0
\(619\) 2565.66 4443.85i 0.166595 0.288551i −0.770625 0.637288i \(-0.780056\pi\)
0.937221 + 0.348737i \(0.113389\pi\)
\(620\) −3872.00 + 6706.50i −0.250812 + 0.434419i
\(621\) 0 0
\(622\) 14559.1 0.938529
\(623\) 0 0
\(624\) 0 0
\(625\) 4815.50 + 8340.69i 0.308192 + 0.533804i
\(626\) 1519.69 2632.19i 0.0970275 0.168057i
\(627\) 0 0
\(628\) −5759.83 9976.32i −0.365991 0.633915i
\(629\) 4390.23 0.278299
\(630\) 0 0
\(631\) 912.000 0.0575375 0.0287687 0.999586i \(-0.490841\pi\)
0.0287687 + 0.999586i \(0.490841\pi\)
\(632\) −2720.00 4711.18i −0.171196 0.296520i
\(633\) 0 0
\(634\) −2358.00 + 4084.18i −0.147710 + 0.255841i
\(635\) 10844.2 + 18782.8i 0.677702 + 1.17381i
\(636\) 0 0
\(637\) 0 0
\(638\) 6640.00 0.412038
\(639\) 0 0
\(640\) −600.373 + 1039.88i −0.0370810 + 0.0642262i
\(641\) −445.000 + 770.763i −0.0274203 + 0.0474934i −0.879410 0.476065i \(-0.842063\pi\)
0.851990 + 0.523559i \(0.175396\pi\)
\(642\) 0 0
\(643\) −29352.6 −1.80024 −0.900120 0.435642i \(-0.856521\pi\)
−0.900120 + 0.435642i \(0.856521\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −528.000 914.523i −0.0321577 0.0556988i
\(647\) 5938.07 10285.0i 0.360818 0.624956i −0.627277 0.778796i \(-0.715831\pi\)
0.988096 + 0.153840i \(0.0491641\pi\)
\(648\) 0 0
\(649\) 6660.39 + 11536.1i 0.402840 + 0.697739i
\(650\) 4859.27 0.293225
\(651\) 0 0
\(652\) 2544.00 0.152808
\(653\) −10763.0 18642.1i −0.645006 1.11718i −0.984300 0.176502i \(-0.943522\pi\)
0.339294 0.940680i \(-0.389812\pi\)
\(654\) 0 0
\(655\) 1188.00 2057.68i 0.0708687 0.122748i
\(656\) 3151.96 + 5459.35i 0.187597 + 0.324927i
\(657\) 0 0
\(658\) 0 0
\(659\) −23452.0 −1.38628 −0.693141 0.720802i \(-0.743774\pi\)
−0.693141 + 0.720802i \(0.743774\pi\)
\(660\) 0 0
\(661\) 13334.9 23096.6i 0.784668 1.35909i −0.144529 0.989501i \(-0.546167\pi\)
0.929197 0.369584i \(-0.120500\pi\)
\(662\) 2372.00 4108.42i 0.139260 0.241206i
\(663\) 0 0
\(664\) 1575.98 0.0921082
\(665\) 0 0
\(666\) 0 0
\(667\) 3984.00 + 6900.49i 0.231276 + 0.400582i
\(668\) −1313.32 + 2274.73i −0.0760685 + 0.131754i
\(669\) 0 0
\(670\) −5440.88 9423.88i −0.313731 0.543398i
\(671\) −5440.88 −0.313030
\(672\) 0 0
\(673\) −13858.0 −0.793739 −0.396870 0.917875i \(-0.629904\pi\)
−0.396870 + 0.917875i \(0.629904\pi\)
\(674\) −250.000 433.013i −0.0142873 0.0247463i
\(675\) 0 0
\(676\) −4230.00 + 7326.57i −0.240669 + 0.416851i
\(677\) 16224.1 + 28101.0i 0.921041 + 1.59529i 0.797808 + 0.602912i \(0.205993\pi\)
0.123233 + 0.992378i \(0.460674\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4224.00 −0.238210
\(681\) 0 0
\(682\) 4127.57 7149.15i 0.231749 0.401401i
\(683\) −13906.0 + 24085.9i −0.779060 + 1.34937i 0.153423 + 0.988161i \(0.450970\pi\)
−0.932484 + 0.361212i \(0.882363\pi\)
\(684\) 0 0
\(685\) −10450.2 −0.582895
\(686\) 0 0
\(687\) 0 0
\(688\) −3488.00 6041.39i −0.193283 0.334776i
\(689\) 2035.64 3525.83i 0.112557 0.194954i
\(690\) 0 0
\(691\) 651.968 + 1129.24i 0.0358929 + 0.0621684i 0.883414 0.468594i \(-0.155239\pi\)
−0.847521 + 0.530762i \(0.821906\pi\)
\(692\) −2664.16 −0.146353
\(693\) 0 0
\(694\) 19080.0 1.04361
\(695\) 6468.00 + 11202.9i 0.353015 + 0.611439i
\(696\) 0 0
\(697\) −11088.0 + 19205.0i −0.602565 + 1.04367i
\(698\) −5712.93 9895.08i −0.309796 0.536582i
\(699\) 0 0
\(700\) 0 0
\(701\) −22906.0 −1.23416 −0.617081 0.786900i \(-0.711685\pi\)
−0.617081 + 0.786900i \(0.711685\pi\)
\(702\) 0 0
\(703\) 365.852 633.675i 0.0196279 0.0339965i
\(704\) 640.000 1108.51i 0.0342627 0.0593447i
\(705\) 0 0
\(706\) 8780.46 0.468069
\(707\) 0 0
\(708\) 0 0
\(709\) 7543.00 + 13064.9i 0.399553 + 0.692047i 0.993671 0.112332i \(-0.0358319\pi\)
−0.594117 + 0.804378i \(0.702499\pi\)
\(710\) −5103.17 + 8838.95i −0.269745 + 0.467211i
\(711\) 0 0
\(712\) 6003.73 + 10398.8i 0.316010 + 0.547346i
\(713\) 9906.16 0.520321
\(714\) 0 0
\(715\) 12320.0 0.644394
\(716\) −6456.00 11182.1i −0.336972 0.583653i
\(717\) 0 0
\(718\) −1840.00 + 3186.97i −0.0956381 + 0.165650i
\(719\) −10272.0 17791.6i −0.532797 0.922832i −0.999266 0.0382947i \(-0.987807\pi\)
0.466469 0.884538i \(-0.345526\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 13542.0 0.698035
\(723\) 0 0
\(724\) 5647.26 9781.34i 0.289888 0.502100i
\(725\) 3071.00 5319.13i 0.157316 0.272479i
\(726\) 0 0
\(727\) −7223.24 −0.368494 −0.184247 0.982880i \(-0.558985\pi\)
−0.184247 + 0.982880i \(0.558985\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 5632.00 + 9754.91i 0.285547 + 0.494583i
\(731\) 12270.1 21252.5i 0.620830 1.07531i
\(732\) 0 0
\(733\) −14713.8 25485.1i −0.741430 1.28419i −0.951844 0.306581i \(-0.900815\pi\)
0.210415 0.977612i \(-0.432519\pi\)
\(734\) 5928.69 0.298136
\(735\) 0 0
\(736\) 1536.00 0.0769262
\(737\) 5800.00 + 10045.9i 0.289886 + 0.502097i
\(738\) 0 0
\(739\) −16334.0 + 28291.3i −0.813066 + 1.40827i 0.0976420 + 0.995222i \(0.468870\pi\)
−0.910708 + 0.413050i \(0.864463\pi\)
\(740\) −1463.41 2534.70i −0.0726973 0.125915i
\(741\) 0 0
\(742\) 0 0
\(743\) 37056.0 1.82968 0.914840 0.403816i \(-0.132316\pi\)
0.914840 + 0.403816i \(0.132316\pi\)
\(744\) 0 0
\(745\) 4437.13 7685.34i 0.218207 0.377945i
\(746\) 3982.00 6897.03i 0.195431 0.338496i
\(747\) 0 0
\(748\) 4502.80 0.220105
\(749\) 0 0
\(750\) 0 0
\(751\) 9804.00 + 16981.0i 0.476369 + 0.825095i 0.999633 0.0270752i \(-0.00861935\pi\)
−0.523265 + 0.852170i \(0.675286\pi\)
\(752\) 1651.03 2859.66i 0.0800621 0.138672i
\(753\) 0 0
\(754\) 10900.5 + 18880.3i 0.526490 + 0.911908i
\(755\) −7804.85 −0.376222
\(756\) 0 0
\(757\) 19378.0 0.930390 0.465195 0.885208i \(-0.345984\pi\)
0.465195 + 0.885208i \(0.345984\pi\)
\(758\) 2676.00 + 4634.97i 0.128228 + 0.222097i
\(759\) 0 0
\(760\) −352.000 + 609.682i −0.0168005 + 0.0290993i
\(761\) −6988.72 12104.8i −0.332905 0.576609i 0.650175 0.759785i \(-0.274696\pi\)
−0.983080 + 0.183176i \(0.941362\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 8544.00 0.404596
\(765\) 0 0
\(766\) −7035.62 + 12186.1i −0.331863 + 0.574804i
\(767\) −21868.0 + 37876.5i −1.02948 + 1.78310i
\(768\) 0 0
\(769\) 8536.56 0.400307 0.200154 0.979765i \(-0.435856\pi\)
0.200154 + 0.979765i \(0.435856\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3316.00 5743.48i −0.154593 0.267762i
\(773\) −14648.2 + 25371.4i −0.681576 + 1.18052i 0.292924 + 0.956136i \(0.405372\pi\)
−0.974500 + 0.224388i \(0.927962\pi\)
\(774\) 0 0
\(775\) −3818.00 6612.97i −0.176963 0.306509i
\(776\) 5253.27 0.243017
\(777\) 0 0
\(778\) 17316.0 0.797955
\(779\) 1848.00 + 3200.83i 0.0849955 + 0.147216i
\(780\) 0 0
\(781\) 5440.00 9422.36i 0.249243 0.431701i
\(782\) 2701.68 + 4679.45i 0.123545 + 0.213985i
\(783\) 0 0
\(784\) 0 0
\(785\) −27016.0 −1.22833
\(786\) 0 0
\(787\) −6890.22 + 11934.2i −0.312084 + 0.540545i −0.978813 0.204755i \(-0.934360\pi\)
0.666730 + 0.745300i \(0.267694\pi\)
\(788\) −1956.00 + 3387.89i −0.0884259 + 0.153158i
\(789\) 0 0
\(790\) −12757.9 −0.574566
\(791\) 0 0