Properties

Label 882.4.g.bi.667.1
Level $882$
Weight $4$
Character 882.667
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 667.1
Root \(-2.34521 + 4.06202i\) of defining polynomial
Character \(\chi\) \(=\) 882.667
Dual form 882.4.g.bi.361.1

$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

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

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 \(-0.971136\pi\)
0.576368 + 0.817190i \(0.304470\pi\)
\(6\) 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 0.969908 0.243472i \(-0.0782863\pi\)
−0.695807 + 0.718229i \(0.744953\pi\)
\(12\) 0 0
\(13\) −65.6658 −1.40096 −0.700478 0.713674i \(-0.747030\pi\)
−0.700478 + 0.713674i \(0.747030\pi\)
\(14\) 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 \(-0.298179\pi\)
−0.993908 + 0.110217i \(0.964846\pi\)
\(18\) 0 0
\(19\) 4.69042 8.12404i 0.0566345 0.0980938i −0.836318 0.548244i \(-0.815296\pi\)
0.892953 + 0.450151i \(0.148630\pi\)
\(20\) 37.5233 0.419524
\(21\) 0 0
\(22\) 40.0000 0.387638
\(23\) 24.0000 41.5692i 0.217580 0.376860i −0.736487 0.676451i \(-0.763517\pi\)
0.954068 + 0.299591i \(0.0968503\pi\)
\(24\) 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 −0.993138 0.116948i \(-0.962689\pi\)
0.395289 0.918557i \(-0.370644\pi\)
\(32\) 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 −0.766281 0.642505i \(-0.777895\pi\)
0.939567 + 0.342366i \(0.111228\pi\)
\(38\) −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 \(-0.229868\pi\)
0.750386 + 0.661000i \(0.229868\pi\)
\(42\) 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 \(-0.937100\pi\)
0.660291 + 0.751010i \(0.270433\pi\)
\(48\) 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 0.903397 0.428805i \(-0.141065\pi\)
−0.823054 + 0.567963i \(0.807732\pi\)
\(54\) 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 0.954794 + 0.297267i \(0.0960752\pi\)
−0.219956 + 0.975510i \(0.570591\pi\)
\(60\) 0 0
\(61\) 136.022 235.597i 0.285506 0.494510i −0.687226 0.726444i \(-0.741172\pi\)
0.972732 + 0.231933i \(0.0745052\pi\)
\(62\) −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 −0.999436 0.0335729i \(-0.989311\pi\)
0.470643 0.882324i \(-0.344022\pi\)
\(68\) −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 \(-0.326498\pi\)
−0.999769 + 0.0214711i \(0.993165\pi\)
\(74\) −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 −0.515621 0.856817i \(-0.672439\pi\)
0.999836 + 0.0181320i \(0.00577190\pi\)
\(80\) −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 \(-0.458419\pi\)
0.130261 + 0.991480i \(0.458419\pi\)
\(84\) 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 0.0585446 0.998285i \(-0.481354\pi\)
0.835268 0.549843i \(-0.185313\pi\)
\(90\) 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 \(-0.388327\pi\)
0.343678 + 0.939088i \(0.388327\pi\)
\(98\) 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 \(-0.185800\pi\)
−0.894497 + 0.447073i \(0.852466\pi\)
\(102\) 0 0
\(103\) −684.801 + 1186.11i −0.655101 + 1.13467i 0.326767 + 0.945105i \(0.394041\pi\)
−0.981868 + 0.189564i \(0.939293\pi\)
\(104\) 525.327 0.495313
\(105\) 0 0
\(106\) 124.000 0.113622
\(107\) −130.000 + 225.167i −0.117454 + 0.203436i −0.918758 0.394821i \(-0.870807\pi\)
0.801304 + 0.598257i \(0.204140\pi\)
\(108\) 0 0
\(109\) −941.000 1629.86i −0.826894 1.43222i −0.900463 0.434932i \(-0.856772\pi\)
0.0735690 0.997290i \(-0.476561\pi\)
\(110\) −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 \(-0.806416\pi\)
0.905162 + 0.425066i \(0.139749\pi\)
\(132\) 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 0.638423 0.769686i \(-0.279587\pi\)
−0.985779 + 0.168048i \(0.946254\pi\)
\(138\) 0 0
\(139\) −1378.98 −0.841466 −0.420733 0.907185i \(-0.638227\pi\)
−0.420733 + 0.907185i \(0.638227\pi\)
\(140\) 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 −0.966259 0.257573i \(-0.917077\pi\)
0.706194 + 0.708018i \(0.250411\pi\)
\(150\) 0 0
\(151\) −416.000 720.533i −0.224196 0.388319i 0.731882 0.681431i \(-0.238642\pi\)
−0.956078 + 0.293113i \(0.905309\pi\)
\(152\) −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 0.956035 + 0.293253i \(0.0947377\pi\)
−0.224053 + 0.974577i \(0.571929\pi\)
\(158\) −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 −0.932259 0.361792i \(-0.882165\pi\)
0.779451 + 0.626463i \(0.215498\pi\)
\(164\) −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 \(-0.548615\pi\)
−0.152137 + 0.988359i \(0.548615\pi\)
\(168\) 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 \(-0.880087\pi\)
0.783524 + 0.621361i \(0.213420\pi\)
\(174\) 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 −0.976776 0.214262i \(-0.931265\pi\)
0.302832 0.953044i \(-0.402068\pi\)
\(180\) 0 0
\(181\) 2823.63 1.15955 0.579776 0.814776i \(-0.303140\pi\)
0.579776 + 0.814776i \(0.303140\pi\)
\(182\) 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 −0.994274 0.106858i \(-0.965921\pi\)
0.589679 + 0.807638i \(0.299254\pi\)
\(192\) 0 0
\(193\) −829.000 1435.87i −0.309185 0.535524i 0.668999 0.743263i \(-0.266723\pi\)
−0.978184 + 0.207739i \(0.933390\pi\)
\(194\) 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 −0.852598 0.522567i \(-0.824974\pi\)
−0.0262574 0.999655i \(-0.508359\pi\)
\(200\) −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 \(-0.642833\pi\)
−0.433815 + 0.901002i \(0.642833\pi\)
\(224\) 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 \(-0.0732205\pi\)
−0.684289 + 0.729211i \(0.739887\pi\)
\(228\) 0 0
\(229\) 1383.67 2396.59i 0.399282 0.691577i −0.594355 0.804203i \(-0.702593\pi\)
0.993638 + 0.112625i \(0.0359260\pi\)
\(230\) 900.560 0.258179
\(231\) 0 0
\(232\) −1328.00 −0.375808
\(233\) −3245.00 + 5620.50i −0.912391 + 1.58031i −0.101713 + 0.994814i \(0.532432\pi\)
−0.810677 + 0.585493i \(0.800901\pi\)
\(234\) 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 0.992166 + 0.124926i \(0.0398695\pi\)
−0.387894 + 0.921704i \(0.626797\pi\)
\(242\) −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 \(-0.252377\pi\)
0.701807 + 0.712367i \(0.252377\pi\)
\(252\) 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 \(-0.775027\pi\)
0.942613 + 0.333888i \(0.108361\pi\)
\(258\) 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 0.841627 0.540059i \(-0.181598\pi\)
−0.888519 + 0.458841i \(0.848265\pi\)
\(264\) 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 \(-0.156851\pi\)
−0.850198 + 0.526462i \(0.823518\pi\)
\(270\) 0 0
\(271\) 3452.15 5979.29i 0.773812 1.34028i −0.161648 0.986848i \(-0.551681\pi\)
0.935460 0.353433i \(-0.114986\pi\)
\(272\) 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 0.955055 + 0.296428i \(0.0957954\pi\)
−0.220814 + 0.975316i \(0.570871\pi\)
\(278\) −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 \(-0.153805\pi\)
−0.845122 + 0.534574i \(0.820472\pi\)
\(284\) −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 \(-0.621722\pi\)
−0.373149 + 0.927771i \(0.621722\pi\)
\(294\) 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 \(-0.521388\pi\)
−0.0671420 + 0.997743i \(0.521388\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 1936.00 3353.25i 0.354701 0.614361i
\(311\) −3639.76 6304.25i −0.663640 1.14946i −0.979652 0.200703i \(-0.935677\pi\)
0.316012 0.948755i \(-0.397656\pi\)
\(312\) 0 0
\(313\) 759.847 1316.09i 0.137218 0.237668i −0.789225 0.614104i \(-0.789517\pi\)
0.926442 + 0.376437i \(0.122851\pi\)
\(314\) 5759.83 1.03518
\(315\) 0 0
\(316\) −2720.00 −0.484215
\(317\) 1179.00 2042.09i 0.208893 0.361814i −0.742473 0.669876i \(-0.766347\pi\)
0.951366 + 0.308062i \(0.0996805\pi\)
\(318\) 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 −0.947536 0.319649i \(-0.896435\pi\)
0.750592 + 0.660766i \(0.229768\pi\)
\(332\) −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 0.953419 + 0.301649i \(0.0975371\pi\)
−0.215474 + 0.976510i \(0.569130\pi\)
\(348\) 0 0
\(349\) 5712.93 0.876235 0.438117 0.898918i \(-0.355645\pi\)
0.438117 + 0.898918i \(0.355645\pi\)
\(350\) 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 \(-0.274044\pi\)
−0.982703 + 0.185187i \(0.940711\pi\)
\(354\) 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 −0.790441 0.612538i \(-0.790149\pi\)
0.925694 + 0.378273i \(0.123482\pi\)
\(360\) 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 \(-0.234278\pi\)
−0.951969 + 0.306193i \(0.900945\pi\)
\(368\) 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 −0.970483 0.241171i \(-0.922468\pi\)
0.694102 + 0.719877i \(0.255802\pi\)
\(374\) −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 \(-0.988836\pi\)
0.530059 + 0.847961i \(0.322170\pi\)
\(384\) 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 0.997120 + 0.0758397i \(0.0241637\pi\)
−0.432881 + 0.901451i \(0.642503\pi\)
\(390\) 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 0.424132 + 0.905600i \(0.360579\pi\)
−0.996339 + 0.0854907i \(0.972754\pi\)
\(398\) −9868.63 −1.24289
\(399\) 0 0
\(400\) −592.000 −0.0740000
\(401\) −2853.00 + 4941.54i −0.355292 + 0.615383i −0.987168 0.159686i \(-0.948952\pi\)
0.631876 + 0.775069i \(0.282285\pi\)
\(402\) 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 \(-0.119930\pi\)
−0.783557 + 0.621320i \(0.786597\pi\)
\(410\) 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 \(-0.528063\pi\)
−0.0880473 + 0.996116i \(0.528063\pi\)
\(420\) 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 0.900936 0.433951i \(-0.142881\pi\)
−0.826281 + 0.563258i \(0.809548\pi\)
\(432\) 0 0
\(433\) 11163.2 1.23896 0.619479 0.785013i \(-0.287344\pi\)
0.619479 + 0.785013i \(0.287344\pi\)
\(434\) 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 \(-0.896069\pi\)
0.751352 + 0.659901i \(0.229402\pi\)
\(440\) 1500.93 0.162623
\(441\) 0 0
\(442\) 7392.00 0.795479
\(443\) 3174.00 5497.53i 0.340409 0.589606i −0.644099 0.764942i \(-0.722768\pi\)
0.984509 + 0.175336i \(0.0561011\pi\)
\(444\) 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 −0.986495 0.163793i \(-0.947627\pi\)
0.635097 + 0.772433i \(0.280960\pi\)
\(458\) −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 \(-0.477809\pi\)
0.0696590 + 0.997571i \(0.477809\pi\)
\(462\) 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 −0.379874 0.925038i \(-0.624033\pi\)
0.991044 0.133539i \(-0.0426340\pi\)
\(468\) 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 0.986255 + 0.165229i \(0.0528365\pi\)
−0.350035 + 0.936737i \(0.613830\pi\)
\(480\) 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 −0.983515 0.180826i \(-0.942123\pi\)
0.335157 0.942162i \(-0.391211\pi\)
\(488\) −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 −0.811931 0.583754i \(-0.801583\pi\)
0.911511 + 0.411276i \(0.134917\pi\)
\(500\) 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 \(-0.666885\pi\)
−0.500594 + 0.865682i \(0.666885\pi\)
\(504\) 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 −0.279848 0.960044i \(-0.590284\pi\)
0.971347 0.237667i \(-0.0763827\pi\)
\(510\) 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 \(-0.329045\pi\)
−0.999909 + 0.0134723i \(0.995712\pi\)
\(522\) 0 0
\(523\) 6308.61 10926.8i 0.527450 0.913570i −0.472038 0.881578i \(-0.656482\pi\)
0.999488 0.0319918i \(-0.0101850\pi\)
\(524\) −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 −0.899534 0.436850i \(-0.856094\pi\)
0.828091 + 0.560594i \(0.189427\pi\)
\(542\) −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 0.912701 0.408629i \(-0.133993\pi\)
−0.810233 + 0.586107i \(0.800660\pi\)
\(558\) 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 0.994202 + 0.107529i \(0.0342937\pi\)
−0.403979 + 0.914768i \(0.632373\pi\)
\(564\) 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 −0.534788 0.844986i \(-0.679608\pi\)
0.999174 + 0.0406466i \(0.0129418\pi\)
\(570\) 0 0
\(571\) −3426.00 5934.01i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) −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 0.999770 + 0.0214362i \(0.00682388\pi\)
−0.481321 + 0.876545i \(0.659843\pi\)
\(578\) −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 \(-0.267497\pi\)
0.667191 + 0.744887i \(0.267497\pi\)
\(588\) 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 \(-0.925172\pi\)
0.687962 + 0.725746i \(0.258505\pi\)
\(594\) 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 −0.982744 0.184968i \(-0.940782\pi\)
0.331185 0.943566i \(-0.392552\pi\)
\(600\) 0 0
\(601\) −21538.4 −1.46185 −0.730923 0.682460i \(-0.760910\pi\)
−0.730923 + 0.682460i \(0.760910\pi\)
\(602\) 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 \(-0.681482\pi\)
0.998917 + 0.0465262i \(0.0148151\pi\)
\(608\) 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 −0.793863 0.608096i \(-0.791934\pi\)
−0.129695 0.991554i \(-0.541400\pi\)
\(614\) −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 \(-0.219944\pi\)
−0.937221 + 0.348737i \(0.886611\pi\)
\(620\) −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 0.851990 0.523559i \(-0.175396\pi\)
−0.879410 + 0.476065i \(0.842063\pi\)
\(642\) 0 0
\(643\) 29352.6 1.80024 0.900120 0.435642i \(-0.143479\pi\)
0.900120 + 0.435642i \(0.143479\pi\)
\(644\) 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 \(-0.284169\pi\)
−0.988096 + 0.153840i \(0.950836\pi\)
\(648\) 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 0.339294 + 0.940680i \(0.389812\pi\)
−0.984300 + 0.176502i \(0.943522\pi\)
\(654\) 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 −0.929197 0.369584i \(-0.879500\pi\)
0.144529 0.989501i \(-0.453833\pi\)
\(662\) 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 −0.123233 + 0.992378i \(0.539326\pi\)
−0.797808 + 0.602912i \(0.794007\pi\)
\(678\) 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 −0.932484 0.361212i \(-0.882363\pi\)
0.153423 0.988161i \(-0.450970\pi\)
\(684\) 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 \(-0.844761\pi\)
0.847521 + 0.530762i \(0.178094\pi\)
\(692\) 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 −0.594117 0.804378i \(-0.702499\pi\)
0.993671 + 0.112332i \(0.0358319\pi\)
\(710\) 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 −0.466469 0.884538i \(-0.654474\pi\)
0.999266 0.0382947i \(-0.0121926\pi\)
\(720\) 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 \(-0.441015\pi\)
0.184247 + 0.982880i \(0.441015\pi\)
\(728\) 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 −0.210415 0.977612i \(-0.567481\pi\)
0.951844 0.306581i \(-0.0991852\pi\)
\(734\) −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 −0.910708 0.413050i \(-0.864463\pi\)
0.0976420 0.995222i \(-0.468870\pi\)
\(740\) 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 −0.523265 0.852170i \(-0.675286\pi\)
0.999633 + 0.0270752i \(0.00861935\pi\)
\(752\) −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 \(-0.725304\pi\)
0.983080 + 0.183176i \(0.0586377\pi\)
\(762\) 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 \(-0.564144\pi\)
−0.200154 + 0.979765i \(0.564144\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −3316.00 + 5743.48i −0.154593 + 0.267762i
\(773\) 14648.2 + 25371.4i 0.681576 + 1.18052i 0.974500 + 0.224388i \(0.0720383\pi\)
−0.292924 + 0.956136i \(0.594628\pi\)
\(774\) 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 \(-0.0656397\pi\)
−0.666730 + 0.745300i \(0.732306\pi\)
\(788\) −1956.00 3387.89i −0.0884259 0.153158i
\(789\) 0 0
\(790\) 12757.9 0.574566
\(791\) 0 0