Properties

Label 98.4.c.g.79.2
Level $98$
Weight $4$
Character 98.79
Analytic conductor $5.782$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.78218718056\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(-2.34521 + 4.06202i\) of defining polynomial
Character \(\chi\) \(=\) 98.79
Dual form 98.4.c.g.67.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(4.69042 + 8.12404i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.69042 + 8.12404i) q^{5} -18.7617 q^{6} +8.00000 q^{8} +(-30.5000 + 52.8275i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(4.69042 + 8.12404i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(-4.69042 + 8.12404i) q^{5} -18.7617 q^{6} +8.00000 q^{8} +(-30.5000 + 52.8275i) q^{9} +(-9.38083 - 16.2481i) q^{10} +(-10.0000 - 17.3205i) q^{11} +(18.7617 - 32.4962i) q^{12} +65.6658 q^{13} -88.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(-28.1425 - 48.7442i) q^{17} +(-61.0000 - 105.655i) q^{18} +(-4.69042 + 8.12404i) q^{19} +37.5233 q^{20} +40.0000 q^{22} +(-24.0000 + 41.5692i) q^{23} +(37.5233 + 64.9923i) q^{24} +(18.5000 + 32.0429i) q^{25} +(-65.6658 + 113.737i) q^{26} -318.948 q^{27} -166.000 q^{29} +(88.0000 - 152.420i) q^{30} +(103.189 + 178.729i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(93.8083 - 162.481i) q^{33} +112.570 q^{34} +244.000 q^{36} +(39.0000 - 67.5500i) q^{37} +(-9.38083 - 16.2481i) q^{38} +(308.000 + 533.472i) q^{39} +(-37.5233 + 64.9923i) q^{40} +393.995 q^{41} +436.000 q^{43} +(-40.0000 + 69.2820i) q^{44} +(-286.115 - 495.566i) q^{45} +(-48.0000 - 83.1384i) q^{46} +(-103.189 + 178.729i) q^{47} -150.093 q^{48} -74.0000 q^{50} +(264.000 - 457.261i) q^{51} +(-131.332 - 227.473i) q^{52} +(-31.0000 - 53.6936i) q^{53} +(318.948 - 552.435i) q^{54} +187.617 q^{55} -88.0000 q^{57} +(166.000 - 287.520i) q^{58} +(333.020 + 576.807i) q^{59} +(176.000 + 304.841i) q^{60} +(-136.022 + 235.597i) q^{61} -412.757 q^{62} +64.0000 q^{64} +(-308.000 + 533.472i) q^{65} +(187.617 + 324.962i) q^{66} +(-290.000 - 502.295i) q^{67} +(-112.570 + 194.977i) q^{68} -450.280 q^{69} -544.000 q^{71} +(-244.000 + 422.620i) q^{72} +(300.187 + 519.938i) q^{73} +(78.0000 + 135.100i) q^{74} +(-173.545 + 300.589i) q^{75} +37.5233 q^{76} -1232.00 q^{78} +(340.000 - 588.897i) q^{79} +(-75.0467 - 129.985i) q^{80} +(-672.500 - 1164.80i) q^{81} +(-393.995 + 682.419i) q^{82} +196.997 q^{83} +528.000 q^{85} +(-436.000 + 755.174i) q^{86} +(-778.609 - 1348.59i) q^{87} +(-80.0000 - 138.564i) q^{88} +(750.467 - 1299.85i) q^{89} +1144.46 q^{90} +192.000 q^{92} +(-968.000 + 1676.63i) q^{93} +(-206.378 - 357.458i) q^{94} +(-44.0000 - 76.2102i) q^{95} +(150.093 - 259.969i) q^{96} -656.658 q^{97} +1220.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{2} - 8q^{4} + 32q^{8} - 122q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 8q^{4} + 32q^{8} - 122q^{9} - 40q^{11} - 352q^{15} - 32q^{16} - 244q^{18} + 160q^{22} - 96q^{23} + 74q^{25} - 664q^{29} + 352q^{30} - 64q^{32} + 976q^{36} + 156q^{37} + 1232q^{39} + 1744q^{43} - 160q^{44} - 192q^{46} - 296q^{50} + 1056q^{51} - 124q^{53} - 352q^{57} + 664q^{58} + 704q^{60} + 256q^{64} - 1232q^{65} - 1160q^{67} - 2176q^{71} - 976q^{72} + 312q^{74} - 4928q^{78} + 1360q^{79} - 2690q^{81} + 2112q^{85} - 1744q^{86} - 320q^{88} + 768q^{92} - 3872q^{93} - 176q^{95} + 4880q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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
\(3\) 4.69042 + 8.12404i 0.902671 + 1.56347i 0.824013 + 0.566570i \(0.191730\pi\)
0.0786575 + 0.996902i \(0.474937\pi\)
\(4\) −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 \(0.304470\pi\)
\(6\) −18.7617 −1.27657
\(7\) 0 0
\(8\) 8.00000 0.353553
\(9\) −30.5000 + 52.8275i −1.12963 + 1.95658i
\(10\) −9.38083 16.2481i −0.296648 0.513809i
\(11\) −10.0000 17.3205i −0.274101 0.474757i 0.695807 0.718229i \(-0.255047\pi\)
−0.969908 + 0.243472i \(0.921714\pi\)
\(12\) 18.7617 32.4962i 0.451335 0.781736i
\(13\) 65.6658 1.40096 0.700478 0.713674i \(-0.252970\pi\)
0.700478 + 0.713674i \(0.252970\pi\)
\(14\) 0 0
\(15\) −88.0000 −1.51477
\(16\) −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 \(0.964846\pi\)
\(18\) −61.0000 105.655i −0.798769 1.38351i
\(19\) −4.69042 + 8.12404i −0.0566345 + 0.0980938i −0.892953 0.450151i \(-0.851370\pi\)
0.836318 + 0.548244i \(0.184704\pi\)
\(20\) 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 \(-0.903150\pi\)
0.736487 + 0.676451i \(0.236483\pi\)
\(24\) 37.5233 + 64.9923i 0.319142 + 0.552771i
\(25\) 18.5000 + 32.0429i 0.148000 + 0.256344i
\(26\) −65.6658 + 113.737i −0.495313 + 0.857907i
\(27\) −318.948 −2.27339
\(28\) 0 0
\(29\) −166.000 −1.06295 −0.531473 0.847075i \(-0.678361\pi\)
−0.531473 + 0.847075i \(0.678361\pi\)
\(30\) 88.0000 152.420i 0.535551 0.927601i
\(31\) 103.189 + 178.729i 0.597849 + 1.03550i 0.993138 + 0.116948i \(0.0373111\pi\)
−0.395289 + 0.918557i \(0.629356\pi\)
\(32\) −16.0000 27.7128i −0.0883883 0.153093i
\(33\) 93.8083 162.481i 0.494846 0.857099i
\(34\) 112.570 0.567812
\(35\) 0 0
\(36\) 244.000 1.12963
\(37\) 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
\(39\) 308.000 + 533.472i 1.26460 + 2.19035i
\(40\) −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
\(45\) −286.115 495.566i −0.947812 1.64166i
\(46\) −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 \(0.270433\pi\)
\(48\) −150.093 −0.451335
\(49\) 0 0
\(50\) −74.0000 −0.209304
\(51\) 264.000 457.261i 0.724851 1.25548i
\(52\) −131.332 227.473i −0.350239 0.606632i
\(53\) −31.0000 53.6936i −0.0803430 0.139158i 0.823054 0.567963i \(-0.192268\pi\)
−0.903397 + 0.428805i \(0.858935\pi\)
\(54\) 318.948 552.435i 0.803766 1.39216i
\(55\) 187.617 0.459968
\(56\) 0 0
\(57\) −88.0000 −0.204489
\(58\) 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 \(0.570591\pi\)
\(60\) 176.000 + 304.841i 0.378692 + 0.655913i
\(61\) −136.022 + 235.597i −0.285506 + 0.494510i −0.972732 0.231933i \(-0.925495\pi\)
0.687226 + 0.726444i \(0.258828\pi\)
\(62\) −412.757 −0.845486
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) −308.000 + 533.472i −0.587734 + 1.01798i
\(66\) 187.617 + 324.962i 0.349909 + 0.606061i
\(67\) −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
\(69\) −450.280 −0.785613
\(70\) 0 0
\(71\) −544.000 −0.909309 −0.454654 0.890668i \(-0.650237\pi\)
−0.454654 + 0.890668i \(0.650237\pi\)
\(72\) −244.000 + 422.620i −0.399384 + 0.691754i
\(73\) 300.187 + 519.938i 0.481290 + 0.833619i 0.999769 0.0214711i \(-0.00683499\pi\)
−0.518479 + 0.855090i \(0.673502\pi\)
\(74\) 78.0000 + 135.100i 0.122531 + 0.212230i
\(75\) −173.545 + 300.589i −0.267191 + 0.462788i
\(76\) 37.5233 0.0566345
\(77\) 0 0
\(78\) −1232.00 −1.78842
\(79\) 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
\(81\) −672.500 1164.80i −0.922497 1.59781i
\(82\) −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
\(87\) −778.609 1348.59i −0.959490 1.66189i
\(88\) −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 \(-0.185313\pi\)
\(90\) 1144.46 1.34041
\(91\) 0 0
\(92\) 192.000 0.217580
\(93\) −968.000 + 1676.63i −1.07932 + 1.86944i
\(94\) −206.378 357.458i −0.226450 0.392223i
\(95\) −44.0000 76.2102i −0.0475190 0.0823053i
\(96\) 150.093 259.969i 0.159571 0.276385i
\(97\) −656.658 −0.687356 −0.343678 0.939088i \(-0.611673\pi\)
−0.343678 + 0.939088i \(0.611673\pi\)
\(98\) 0 0
\(99\) 1220.00 1.23853
\(100\) 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 \(0.852466\pi\)
\(102\) 528.000 + 914.523i 0.512547 + 0.887757i
\(103\) 684.801 1186.11i 0.655101 1.13467i −0.326767 0.945105i \(-0.605959\pi\)
0.981868 0.189564i \(-0.0607073\pi\)
\(104\) 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 \(-0.795860\pi\)
0.918758 + 0.394821i \(0.129193\pi\)
\(108\) 637.897 + 1104.87i 0.568348 + 0.984408i
\(109\) −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
\(111\) 731.705 0.625679
\(112\) 0 0
\(113\) −1286.00 −1.07059 −0.535295 0.844665i \(-0.679800\pi\)
−0.535295 + 0.844665i \(0.679800\pi\)
\(114\) 88.0000 152.420i 0.0722979 0.125224i
\(115\) −225.140 389.954i −0.182560 0.316203i
\(116\) 332.000 + 575.041i 0.265736 + 0.460269i
\(117\) −2002.81 + 3468.96i −1.58256 + 2.74108i
\(118\) −1332.08 −1.03922
\(119\) 0 0
\(120\) −704.000 −0.535551
\(121\) 465.500 806.270i 0.349737 0.605762i
\(122\) −272.044 471.194i −0.201883 0.349671i
\(123\) 1848.00 + 3200.83i 1.35470 + 2.34642i
\(124\) 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
\(129\) 2045.02 + 3542.08i 1.39577 + 2.41754i
\(130\) −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 \(0.139749\pi\)
\(132\) −750.467 −0.494846
\(133\) 0 0
\(134\) 1160.00 0.747826
\(135\) 1496.00 2591.15i 0.953742 1.65193i
\(136\) −225.140 389.954i −0.141953 0.245870i
\(137\) 557.000 + 964.752i 0.347356 + 0.601638i 0.985779 0.168048i \(-0.0537463\pi\)
−0.638423 + 0.769686i \(0.720413\pi\)
\(138\) 450.280 779.908i 0.277756 0.481088i
\(139\) 1378.98 0.841466 0.420733 0.907185i \(-0.361773\pi\)
0.420733 + 0.907185i \(0.361773\pi\)
\(140\) 0 0
\(141\) −1936.00 −1.15632
\(142\) 544.000 942.236i 0.321489 0.556836i
\(143\) −656.658 1137.37i −0.384004 0.665114i
\(144\) −488.000 845.241i −0.282407 0.489144i
\(145\) 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 \(-0.749589\pi\)
0.966259 + 0.257573i \(0.0829227\pi\)
\(150\) −347.091 601.179i −0.188932 0.327240i
\(151\) −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
\(153\) 3433.38 1.81420
\(154\) 0 0
\(155\) −1936.00 −1.00325
\(156\) 1232.00 2133.89i 0.632301 1.09518i
\(157\) −1439.96 2494.08i −0.731982 1.26783i −0.956035 0.293253i \(-0.905262\pi\)
0.224053 0.974577i \(-0.428071\pi\)
\(158\) 680.000 + 1177.79i 0.342392 + 0.593040i
\(159\) 290.806 503.690i 0.145047 0.251228i
\(160\) 300.187 0.148324
\(161\) 0 0
\(162\) 2690.00 1.30461
\(163\) −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
\(165\) 880.000 + 1524.20i 0.415199 + 0.719147i
\(166\) −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
\(171\) −286.115 495.566i −0.127952 0.221619i
\(172\) −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 \(0.213420\pi\)
\(174\) 3114.44 1.35692
\(175\) 0 0
\(176\) 320.000 0.137051
\(177\) −3124.00 + 5410.93i −1.32663 + 2.29780i
\(178\) 1500.93 + 2599.69i 0.632021 + 1.09469i
\(179\) 1614.00 + 2795.53i 0.673944 + 1.16731i 0.976776 + 0.214262i \(0.0687346\pi\)
−0.302832 + 0.953044i \(0.597932\pi\)
\(180\) −1144.46 + 1982.27i −0.473906 + 0.820830i
\(181\) −2823.63 −1.15955 −0.579776 0.814776i \(-0.696860\pi\)
−0.579776 + 0.814776i \(0.696860\pi\)
\(182\) 0 0
\(183\) −2552.00 −1.03087
\(184\) −192.000 + 332.554i −0.0769262 + 0.133240i
\(185\) 365.852 + 633.675i 0.145395 + 0.251831i
\(186\) −1936.00 3353.25i −0.763196 1.32189i
\(187\) −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 \(-0.700746\pi\)
0.994274 + 0.106858i \(0.0340789\pi\)
\(192\) 300.187 + 519.938i 0.112834 + 0.195434i
\(193\) −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
\(195\) −5778.59 −2.12212
\(196\) 0 0
\(197\) −978.000 −0.353704 −0.176852 0.984237i \(-0.556591\pi\)
−0.176852 + 0.984237i \(0.556591\pi\)
\(198\) −1220.00 + 2113.10i −0.437887 + 0.758443i
\(199\) 2467.16 + 4273.24i 0.878855 + 1.52222i 0.852598 + 0.522567i \(0.175026\pi\)
0.0262574 + 0.999655i \(0.491641\pi\)
\(200\) 148.000 + 256.344i 0.0523259 + 0.0906311i
\(201\) 2720.44 4711.94i 0.954652 1.65351i
\(202\) 243.902 0.0849547
\(203\) 0 0
\(204\) −2112.00 −0.724851
\(205\) −1848.00 + 3200.83i −0.629609 + 1.09052i
\(206\) 1369.60 + 2372.22i 0.463226 + 0.802332i
\(207\) −1464.00 2535.72i −0.491570 0.851425i
\(208\) −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
\(213\) −2551.59 4419.48i −0.820807 1.42168i
\(214\) 260.000 + 450.333i 0.0830525 + 0.143851i
\(215\) −2045.02 + 3542.08i −0.648694 + 1.12357i
\(216\) −2551.59 −0.803766
\(217\) 0 0
\(218\) 3764.00 1.16940
\(219\) −2816.00 + 4877.46i −0.868893 + 1.50497i
\(220\) −375.233 649.923i −0.114992 0.199172i
\(221\) −1848.00 3200.83i −0.562488 0.974258i
\(222\) −731.705 + 1267.35i −0.221211 + 0.383148i
\(223\) 2889.30 0.867630 0.433815 0.901002i \(-0.357167\pi\)
0.433815 + 0.901002i \(0.357167\pi\)
\(224\) 0 0
\(225\) −2257.00 −0.668741
\(226\) 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 \(0.739887\pi\)
\(228\) 176.000 + 304.841i 0.0511223 + 0.0885464i
\(229\) −1383.67 + 2396.59i −0.399282 + 0.691577i −0.993638 0.112625i \(-0.964074\pi\)
0.594355 + 0.804203i \(0.297407\pi\)
\(230\) 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 \(-0.467568\pi\)
0.810677 0.585493i \(-0.199099\pi\)
\(234\) −4005.62 6937.93i −1.11904 1.93823i
\(235\) −968.000 1676.63i −0.268704 0.465408i
\(236\) 1332.08 2307.23i 0.367419 0.636388i
\(237\) 6378.97 1.74835
\(238\) 0 0
\(239\) −4296.00 −1.16270 −0.581350 0.813654i \(-0.697475\pi\)
−0.581350 + 0.813654i \(0.697475\pi\)
\(240\) 704.000 1219.36i 0.189346 0.327957i
\(241\) −2260.78 3915.79i −0.604272 1.04663i −0.992166 0.124926i \(-0.960131\pi\)
0.387894 0.921704i \(-0.373203\pi\)
\(242\) 931.000 + 1612.54i 0.247301 + 0.428339i
\(243\) 2002.81 3468.96i 0.528725 0.915778i
\(244\) 1088.18 0.285506
\(245\) 0 0
\(246\) −7392.00 −1.91584
\(247\) −308.000 + 533.472i −0.0793424 + 0.137425i
\(248\) 825.513 + 1429.83i 0.211372 + 0.366106i
\(249\) 924.000 + 1600.41i 0.235165 + 0.407318i
\(250\) 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
\(255\) 2476.54 + 4289.49i 0.608184 + 1.05341i
\(256\) −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 \(0.108361\pi\)
\(258\) −8180.09 −1.97391
\(259\) 0 0
\(260\) 2464.00 0.587734
\(261\) 5063.00 8769.37i 1.20073 2.07973i
\(262\) 253.282 + 438.698i 0.0597246 + 0.103446i
\(263\) 200.000 + 346.410i 0.0468917 + 0.0812189i 0.888519 0.458841i \(-0.151735\pi\)
−0.841627 + 0.540059i \(0.818402\pi\)
\(264\) 750.467 1299.85i 0.174955 0.303030i
\(265\) 581.612 0.134823
\(266\) 0 0
\(267\) 14080.0 3.22727
\(268\) −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 \(0.823518\pi\)
\(270\) 2992.00 + 5182.30i 0.674397 + 1.16809i
\(271\) −3452.15 + 5979.29i −0.773812 + 1.34028i 0.161648 + 0.986848i \(0.448319\pi\)
−0.935460 + 0.353433i \(0.885014\pi\)
\(272\) 900.560 0.200752
\(273\) 0 0
\(274\) −2228.00 −0.491235
\(275\) 370.000 640.859i 0.0811340 0.140528i
\(276\) 900.560 + 1559.82i 0.196403 + 0.340181i
\(277\) 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
\(279\) −12589.1 −2.70139
\(280\) 0 0
\(281\) 1878.00 0.398691 0.199345 0.979929i \(-0.436118\pi\)
0.199345 + 0.979929i \(0.436118\pi\)
\(282\) 1936.00 3353.25i 0.408820 0.708096i
\(283\) −192.307 333.086i −0.0403939 0.0699642i 0.845122 0.534574i \(-0.179528\pi\)
−0.885516 + 0.464610i \(0.846195\pi\)
\(284\) 1088.00 + 1884.47i 0.227327 + 0.393742i
\(285\) 412.757 714.915i 0.0857880 0.148589i
\(286\) 2626.63 0.543063
\(287\) 0 0
\(288\) 1952.00 0.399384
\(289\) 872.500 1511.21i 0.177590 0.307595i
\(290\) 1557.22 + 2697.18i 0.315321 + 0.546151i
\(291\) −3080.00 5334.72i −0.620456 1.07466i
\(292\) 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
\(297\) 3189.48 + 5524.35i 0.623140 + 1.07931i
\(298\) 946.000 + 1638.52i 0.183894 + 0.318513i
\(299\) −1575.98 + 2729.68i −0.304820 + 0.527964i
\(300\) 1388.36 0.267191
\(301\) 0 0
\(302\) 1664.00 0.317061
\(303\) 572.000 990.733i 0.108451 0.187842i
\(304\) −75.0467 129.985i −0.0141586 0.0245235i
\(305\) −1276.00 2210.10i −0.239553 0.414917i
\(306\) −3433.38 + 5946.80i −0.641417 + 1.11097i
\(307\) 722.324 0.134284 0.0671420 0.997743i \(-0.478612\pi\)
0.0671420 + 0.997743i \(0.478612\pi\)
\(308\) 0 0
\(309\) 12848.0 2.36536
\(310\) 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 \(-0.397656\pi\)
\(312\) 2464.00 + 4267.77i 0.447104 + 0.774407i
\(313\) −759.847 + 1316.09i −0.137218 + 0.237668i −0.926442 0.376437i \(-0.877149\pi\)
0.789225 + 0.614104i \(0.210483\pi\)
\(314\) 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 \(-0.900320\pi\)
0.742473 + 0.669876i \(0.233653\pi\)
\(318\) 581.612 + 1007.38i 0.102563 + 0.177645i
\(319\) 1660.00 + 2875.20i 0.291355 + 0.504641i
\(320\) −300.187 + 519.938i −0.0524404 + 0.0908295i
\(321\) 2439.02 0.424089
\(322\) 0 0
\(323\) 528.000 0.0909557
\(324\) −2690.00 + 4659.22i −0.461248 + 0.798905i
\(325\) 1214.82 + 2104.13i 0.207341 + 0.359126i
\(326\) −636.000 1101.58i −0.108051 0.187151i
\(327\) 8827.36 15289.4i 1.49283 2.58565i
\(328\) 3151.96 0.530603
\(329\) 0 0
\(330\) −3520.00 −0.587181
\(331\) −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
\(333\) 2379.00 + 4120.55i 0.391497 + 0.678092i
\(334\) 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
\(339\) −6031.87 10447.5i −0.966391 1.67384i
\(340\) −1056.00 1829.05i −0.168440 0.291747i
\(341\) 2063.78 3574.58i 0.327742 0.567666i
\(342\) 1144.46 0.180951
\(343\) 0 0
\(344\) 3488.00 0.546687
\(345\) 2112.00 3658.09i 0.329583 0.570855i
\(346\) −666.039 1153.61i −0.103487 0.179245i
\(347\) −4770.00 8261.88i −0.737945 1.27816i −0.953419 0.301649i \(-0.902463\pi\)
0.215474 0.976510i \(-0.430870\pi\)
\(348\) −3114.44 + 5394.36i −0.479745 + 0.830943i
\(349\) −5712.93 −0.876235 −0.438117 0.898918i \(-0.644355\pi\)
−0.438117 + 0.898918i \(0.644355\pi\)
\(350\) 0 0
\(351\) −20944.0 −3.18492
\(352\) −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 \(0.940711\pi\)
\(354\) −6248.00 10821.9i −0.938072 1.62479i
\(355\) 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 \(-0.876518\pi\)
0.790441 + 0.612538i \(0.209851\pi\)
\(360\) −2288.92 3964.53i −0.335102 0.580414i
\(361\) 3385.50 + 5863.86i 0.493585 + 0.854914i
\(362\) 2823.63 4890.67i 0.409963 0.710077i
\(363\) 8733.55 1.26279
\(364\) 0 0
\(365\) −5632.00 −0.807650
\(366\) 2552.00 4420.19i 0.364468 0.631277i
\(367\) 1482.17 + 2567.20i 0.210814 + 0.365140i 0.951969 0.306193i \(-0.0990552\pi\)
−0.741156 + 0.671333i \(0.765722\pi\)
\(368\) −384.000 665.108i −0.0543951 0.0942150i
\(369\) −12016.8 + 20813.8i −1.69532 + 2.93638i
\(370\) −1463.41 −0.205619
\(371\) 0 0
\(372\) 7744.00 1.07932
\(373\) −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
\(375\) −7128.00 12346.1i −0.981569 1.70013i
\(376\) −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
\(381\) 10844.2 + 18782.8i 1.45818 + 2.52565i
\(382\) 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 \(0.322170\pi\)
\(384\) −1200.75 −0.159571
\(385\) 0 0
\(386\) 3316.00 0.437254
\(387\) −13298.0 + 23032.8i −1.74671 + 3.02538i
\(388\) 1313.32 + 2274.73i 0.171839 + 0.297634i
\(389\) −4329.00 7498.05i −0.564239 0.977291i −0.997120 0.0758397i \(-0.975836\pi\)
0.432881 0.901451i \(-0.357497\pi\)
\(390\) 5778.59 10008.8i 0.750283 1.29953i
\(391\) 2701.68 0.349437
\(392\) 0 0
\(393\) 2376.00 0.304970
\(394\) 978.000 1693.95i 0.125053 0.216598i
\(395\) 3189.48 + 5524.35i 0.406279 + 0.703696i
\(396\) −2440.00 4226.20i −0.309633 0.536300i
\(397\) 4526.25 7839.70i 0.572207 0.991091i −0.424132 0.905600i \(-0.639421\pi\)
0.996339 0.0854907i \(-0.0272458\pi\)
\(398\) −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 \(-0.717715\pi\)
0.987168 + 0.159686i \(0.0510482\pi\)
\(402\) 5440.88 + 9423.88i 0.675041 + 1.16921i
\(403\) 6776.00 + 11736.4i 0.837560 + 1.45070i
\(404\) −243.902 + 422.450i −0.0300360 + 0.0520239i
\(405\) 12617.2 1.54804
\(406\) 0 0
\(407\) −1560.00 −0.189991
\(408\) 2112.00 3658.09i 0.256273 0.443879i
\(409\) −1210.13 2096.00i −0.146301 0.253400i 0.783557 0.621320i \(-0.213403\pi\)
−0.929857 + 0.367920i \(0.880070\pi\)
\(410\) −3696.00 6401.66i −0.445201 0.771111i
\(411\) −5225.12 + 9050.18i −0.627096 + 1.08616i
\(412\) −5478.41 −0.655101
\(413\) 0 0
\(414\) 5856.00 0.695185
\(415\) −924.000 + 1600.41i −0.109295 + 0.189304i
\(416\) −1050.65 1819.78i −0.123828 0.214477i
\(417\) 6468.00 + 11202.9i 0.759567 + 1.31561i
\(418\) −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
\(423\) −6294.54 10902.5i −0.723525 1.25318i
\(424\) −248.000 429.549i −0.0284055 0.0491998i
\(425\) 1041.27 1803.54i 0.118845 0.205846i
\(426\) 10206.3 1.16080
\(427\) 0 0
\(428\) −1040.00 −0.117454
\(429\) 6160.00 10669.4i 0.693258 1.20076i
\(430\) −4090.04 7084.16i −0.458696 0.794485i
\(431\) −668.000 1157.01i −0.0746553 0.129307i 0.826281 0.563258i \(-0.190452\pi\)
−0.900936 + 0.433951i \(0.857119\pi\)
\(432\) 2551.59 4419.48i 0.284174 0.492204i
\(433\) −11163.2 −1.23896 −0.619479 0.785013i \(-0.712656\pi\)
−0.619479 + 0.785013i \(0.712656\pi\)
\(434\) 0 0
\(435\) 14608.0 1.61011
\(436\) −3764.00 + 6519.44i −0.413447 + 0.716111i
\(437\) −225.140 389.954i −0.0246451 0.0426865i
\(438\) −5632.00 9754.91i −0.614400 1.06417i
\(439\) 1801.12 3119.63i 0.195815 0.339161i −0.751352 0.659901i \(-0.770598\pi\)
0.947167 + 0.320740i \(0.103931\pi\)
\(440\) 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 \(-0.943899\pi\)
0.644099 + 0.764942i \(0.277232\pi\)
\(444\) −1463.41 2534.70i −0.156420 0.270927i
\(445\) 7040.00 + 12193.6i 0.749951 + 1.29895i
\(446\) −2889.30 + 5004.41i −0.306754 + 0.531313i
\(447\) 8874.27 0.939012
\(448\) 0 0
\(449\) 7170.00 0.753615 0.376808 0.926292i \(-0.377022\pi\)
0.376808 + 0.926292i \(0.377022\pi\)
\(450\) 2257.00 3909.24i 0.236436 0.409518i
\(451\) −3939.95 6824.19i −0.411364 0.712503i
\(452\) 2572.00 + 4454.83i 0.267648 + 0.463579i
\(453\) 3902.43 6759.20i 0.404750 0.701048i
\(454\) −3958.71 −0.409232
\(455\) 0 0
\(456\) −704.000 −0.0722979
\(457\) −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
\(459\) 8976.00 + 15546.9i 0.912775 + 1.58097i
\(460\) −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
\(465\) −9080.64 15728.1i −0.905602 1.56855i
\(466\) 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 \(-0.0426340\pi\)
\(468\) 16022.5 1.58256
\(469\) 0 0
\(470\) 3872.00 0.380004
\(471\) 13508.0 23396.5i 1.32148 2.28887i
\(472\) 2664.16 + 4614.45i 0.259805 + 0.449995i
\(473\) −4360.00 7551.74i −0.423833 0.734100i
\(474\) −6378.97 + 11048.7i −0.618134 + 1.07064i
\(475\) −347.091 −0.0335276
\(476\) 0 0
\(477\) 3782.00 0.363031
\(478\) 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 \(0.613830\pi\)
\(480\) 1408.00 + 2438.73i 0.133888 + 0.231900i
\(481\) 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
\(486\) 4005.62 + 6937.93i 0.373865 + 0.647553i
\(487\) −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
\(489\) −5966.21 −0.551741
\(490\) 0 0
\(491\) −12276.0 −1.12833 −0.564163 0.825663i \(-0.690801\pi\)
−0.564163 + 0.825663i \(0.690801\pi\)
\(492\) 7392.00 12803.3i 0.677352 1.17321i
\(493\) 4671.65 + 8091.54i 0.426776 + 0.739198i
\(494\) −616.000 1066.94i −0.0561035 0.0971742i
\(495\) −5722.31 + 9911.33i −0.519593 + 0.899962i
\(496\) −3302.05 −0.298924
\(497\) 0 0
\(498\) −3696.00 −0.332574
\(499\) 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
\(501\) −3080.00 5334.72i −0.274659 0.475724i
\(502\) −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
\(507\) 9920.23 + 17182.3i 0.868980 + 1.50512i
\(508\) −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 \(-0.0763827\pi\)
\(510\) −9906.16 −0.860102
\(511\) 0 0
\(512\) 512.000 0.0441942
\(513\) 1496.00 2591.15i 0.128752 0.223006i
\(514\) 1500.93 + 2599.69i 0.128800 + 0.223089i
\(515\) 6424.00 + 11126.7i 0.549661 + 0.952040i
\(516\) 8180.09 14168.3i 0.697884 1.20877i
\(517\) 4127.57 0.351122
\(518\) 0 0
\(519\) −6248.00 −0.528433
\(520\) −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 \(0.995712\pi\)
\(522\) 10126.0 + 17538.7i 0.849048 + 1.47059i
\(523\) −6308.61 + 10926.8i −0.527450 + 0.913570i 0.472038 + 0.881578i \(0.343518\pi\)
−0.999488 + 0.0319918i \(0.989815\pi\)
\(524\) −1013.13 −0.0844633
\(525\) 0 0
\(526\) −800.000 −0.0663149
\(527\) 5808.00 10059.8i 0.480077 0.831517i
\(528\) 1500.93 + 2599.69i 0.123712 + 0.214275i
\(529\) 4931.50 + 8541.61i 0.405318 + 0.702031i
\(530\) −581.612 + 1007.38i −0.0476672 + 0.0825619i
\(531\) −40628.4 −3.32038
\(532\) 0 0
\(533\) 25872.0 2.10252
\(534\) −14080.0 + 24387.3i −1.14101 + 1.97629i
\(535\) 1219.51 + 2112.25i 0.0985494 + 0.170693i
\(536\) −2320.00 4018.36i −0.186957 0.323818i
\(537\) −15140.7 + 26224.4i −1.21670 + 2.10739i
\(538\) −544.088 −0.0436009
\(539\) 0 0
\(540\) −11968.0 −0.953742
\(541\) −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
\(543\) −13244.0 22939.3i −1.04669 1.81293i
\(544\) −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
\(549\) −8297.35 14371.4i −0.645031 1.11723i
\(550\) 740.000 + 1281.72i 0.0573704 + 0.0993684i
\(551\) 778.609 1348.59i 0.0601994 0.104268i
\(552\) −3602.24 −0.277756
\(553\) 0 0
\(554\) −13540.0 −1.03837
\(555\) −3432.00 + 5944.40i −0.262487 + 0.454641i
\(556\) −2757.96 4776.93i −0.210366 0.364365i
\(557\) −1347.00 2333.07i −0.102467 0.177478i 0.810233 0.586107i \(-0.199340\pi\)
−0.912701 + 0.408629i \(0.866007\pi\)
\(558\) 12589.1 21804.9i 0.955086 1.65426i
\(559\) 28630.3 2.16625
\(560\) 0 0
\(561\) −10560.0 −0.794730
\(562\) −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 \(0.632373\pi\)
\(564\) 3872.00 + 6706.50i 0.289079 + 0.500700i
\(565\) 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 \(-0.987058\pi\)
0.534788 + 0.844986i \(0.320392\pi\)
\(570\) 825.513 + 1429.83i 0.0606613 + 0.105068i
\(571\) −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
\(573\) 20037.5 1.46087
\(574\) 0 0
\(575\) −1776.00 −0.128808
\(576\) −1952.00 + 3380.96i −0.141204 + 0.244572i
\(577\) −7185.72 12446.0i −0.518449 0.897981i −0.999770 0.0214362i \(-0.993176\pi\)
0.481321 0.876545i \(-0.340157\pi\)
\(578\) 1745.00 + 3022.43i 0.125575 + 0.217503i
\(579\) 7776.71 13469.7i 0.558185 0.966804i
\(580\) −6228.87 −0.445931
\(581\) 0 0
\(582\) 12320.0 0.877458
\(583\) −620.000 + 1073.87i −0.0440442 + 0.0762868i
\(584\) 2401.49 + 4159.51i 0.170162 + 0.294729i
\(585\) −18788.0 32541.8i −1.32784 2.29989i
\(586\) 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
\(591\) −4587.23 7945.31i −0.319278 0.553006i
\(592\) 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 \(0.258505\pi\)
\(594\) −12757.9 −0.881253
\(595\) 0 0
\(596\) −3784.00 −0.260065
\(597\) −23144.0 + 40086.6i −1.58663 + 2.74813i
\(598\) −3151.96 5459.35i −0.215540 0.373327i
\(599\) 9552.00 + 16544.5i 0.651559 + 1.12853i 0.982744 + 0.184968i \(0.0592182\pi\)
−0.331185 + 0.943566i \(0.607448\pi\)
\(600\) −1388.36 + 2404.72i −0.0944661 + 0.163620i
\(601\) 21538.4 1.46185 0.730923 0.682460i \(-0.239090\pi\)
0.730923 + 0.682460i \(0.239090\pi\)
\(602\) 0 0
\(603\) 35380.0 2.38936
\(604\) −1664.00 + 2882.13i −0.112098 + 0.194159i
\(605\) 4366.78 + 7563.48i 0.293446 + 0.508263i
\(606\) 1144.00 + 1981.47i 0.0766862 + 0.132824i
\(607\) −6866.77 + 11893.6i −0.459166 + 0.795298i −0.998917 0.0465262i \(-0.985185\pi\)
0.539751 + 0.841824i \(0.318518\pi\)
\(608\) 300.187 0.0200233
\(609\) 0 0
\(610\) 5104.00 0.338779
\(611\) −6776.00 + 11736.4i −0.448654 + 0.777092i
\(612\) −6866.77 11893.6i −0.453550 0.785572i
\(613\) −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
\(615\) −34671.6 −2.27332
\(616\) 0 0
\(617\) −8258.00 −0.538824 −0.269412 0.963025i \(-0.586829\pi\)
−0.269412 + 0.963025i \(0.586829\pi\)
\(618\) −12848.0 + 22253.4i −0.836282 + 1.44848i
\(619\) 2565.66 + 4443.85i 0.166595 + 0.288551i 0.937221 0.348737i \(-0.113389\pi\)
−0.770625 + 0.637288i \(0.780056\pi\)
\(620\) 3872.00 + 6706.50i 0.250812 + 0.434419i
\(621\) 7654.76 13258.4i 0.494646 0.856751i
\(622\) 14559.1 0.938529
\(623\) 0 0
\(624\) −9856.00 −0.632301
\(625\) 4815.50 8340.69i 0.308192 0.533804i
\(626\) −1519.69 2632.19i −0.0970275 0.168057i
\(627\) 880.000 + 1524.20i 0.0560507 + 0.0970827i
\(628\) −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
\(633\) 7298.29 + 12641.0i 0.458264 + 0.793736i
\(634\) −2358.00 4084.18i −0.147710 0.255841i
\(635\) −10844.2 + 18782.8i −0.677702 + 1.17381i
\(636\) −2326.45 −0.145047
\(637\) 0 0
\(638\) −6640.00 −0.412038
\(639\) 16592.0 28738.2i 1.02718 1.77913i
\(640\) −600.373 1039.88i −0.0370810 0.0642262i
\(641\) 445.000 + 770.763i 0.0274203 + 0.0474934i 0.879410 0.476065i \(-0.157937\pi\)
−0.851990 + 0.523559i \(0.824604\pi\)
\(642\) −2439.02 + 4224.50i −0.149938 + 0.259700i
\(643\) −29352.6 −1.80024 −0.900120 0.435642i \(-0.856521\pi\)
−0.900120 + 0.435642i \(0.856521\pi\)
\(644\) 0 0
\(645\) −38368.0 −2.34223
\(646\) −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 \(0.950836\pi\)
\(648\) −5380.00 9318.43i −0.326152 0.564911i
\(649\) 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 \(-0.610188\pi\)
0.984300 0.176502i \(-0.0564784\pi\)
\(654\) 17654.7 + 30578.9i 1.05559 + 1.82833i
\(655\) 1188.00 + 2057.68i 0.0708687 + 0.122748i
\(656\) −3151.96 + 5459.35i −0.187597 + 0.324927i
\(657\) −36622.8 −2.17472
\(658\) 0 0
\(659\) 23452.0 1.38628 0.693141 0.720802i \(-0.256226\pi\)
0.693141 + 0.720802i \(0.256226\pi\)
\(660\) 3520.00 6096.82i 0.207600 0.359573i
\(661\) 13334.9 + 23096.6i 0.784668 + 1.35909i 0.929197 + 0.369584i \(0.120500\pi\)
−0.144529 + 0.989501i \(0.546167\pi\)
\(662\) −2372.00 4108.42i −0.139260 0.241206i
\(663\) 17335.8 30026.4i 1.01548 1.75887i
\(664\) 1575.98 0.0921082
\(665\) 0 0
\(666\) −9516.00 −0.553660
\(667\) 3984.00 6900.49i 0.231276 0.400582i
\(668\) 1313.32 + 2274.73i 0.0760685 + 0.131754i
\(669\) 13552.0 + 23472.8i 0.783185 + 1.35652i
\(670\) −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
\(675\) −5900.54 10220.0i −0.336462 0.582770i
\(676\) −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 \(0.794007\pi\)
\(678\) 24127.5 1.36668
\(679\) 0 0
\(680\) 4224.00 0.238210
\(681\) −9284.00 + 16080.4i −0.522414 + 0.904847i
\(682\) 4127.57 + 7149.15i 0.231749 + 0.401401i
\(683\) 13906.0 + 24085.9i 0.779060 + 1.34937i 0.932484 + 0.361212i \(0.117637\pi\)
−0.153423 + 0.988161i \(0.549030\pi\)
\(684\) −1144.46 + 1982.27i −0.0639760 + 0.110810i
\(685\) −10450.2 −0.582895
\(686\) 0 0
\(687\) −25960.0 −1.44168
\(688\) −3488.00 + 6041.39i −0.193283 + 0.334776i
\(689\) −2035.64 3525.83i −0.112557 0.194954i
\(690\) 4224.00 + 7316.18i 0.233051 + 0.403656i
\(691\) 651.968 1129.24i 0.0358929 0.0621684i −0.847521 0.530762i \(-0.821906\pi\)
0.883414 + 0.468594i \(0.155239\pi\)
\(692\) 2664.16 0.146353
\(693\) 0 0
\(694\) 19080.0 1.04361
\(695\) −6468.00 + 11202.9i −0.353015 + 0.611439i
\(696\) −6228.87 10788.7i −0.339231 0.587565i
\(697\) −11088.0 19205.0i −0.602565 1.04367i
\(698\) 5712.93 9895.08i 0.309796 0.536582i
\(699\) 60881.6 3.29435
\(700\) 0 0
\(701\) 22906.0 1.23416 0.617081 0.786900i \(-0.288315\pi\)
0.617081 + 0.786900i \(0.288315\pi\)
\(702\) 20944.0 36276.1i 1.12604 1.95036i
\(703\) 365.852 + 633.675i 0.0196279 + 0.0339965i
\(704\) −640.000 1108.51i −0.0342627 0.0593447i
\(705\) 9080.64 15728.1i 0.485102 0.840221i
\(706\) 8780.46 0.468069
\(707\) 0 0
\(708\) 24992.0 1.32663
\(709\) 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
\(711\) 20740.0 + 35922.7i 1.09397 + 1.89481i
\(712\) 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
\(717\) −20150.0 34900.9i −1.04953 1.81785i
\(718\) −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 \(-0.0121926\pi\)
\(720\) 9155.69 0.473906
\(721\) 0 0
\(722\) −13542.0 −0.698035
\(723\) 21208.0 36733.3i 1.09092 1.88953i
\(724\) 5647.26 + 9781.34i 0.289888 + 0.502100i
\(725\) −3071.00 5319.13i −0.157316 0.272479i
\(726\) −8733.55 + 15127.0i −0.446464 + 0.773298i
\(727\) −7223.24 −0.368494 −0.184247 0.982880i \(-0.558985\pi\)
−0.184247 + 0.982880i \(0.558985\pi\)
\(728\) 0 0
\(729\) 1261.00 0.0640654
\(730\) 5632.00 9754.91i 0.285547 0.494583i
\(731\) −12270.1 21252.5i −0.620830 1.07531i
\(732\) 5104.00 + 8840.39i 0.257718 + 0.446380i
\(733\) −14713.8 + 25485.1i −0.741430 + 1.28419i 0.210415 + 0.977612i \(0.432519\pi\)
−0.951844 + 0.306581i \(0.900815\pi\)
\(734\) −5928.69 −0.298136
\(735\) 0 0
\(736\) 1536.00 0.0769262
\(737\) −5800.00 + 10045.9i −0.289886 + 0.502097i
\(738\) −24033.7 41627.6i −1.19877 2.07633i
\(739\) −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
\(741\) −5778.59 −0.286480
\(742\) 0 0
\(743\) −37056.0 −1.82968 −0.914840 0.403816i \(-0.867684\pi\)
−0.914840 + 0.403816i \(0.867684\pi\)
\(744\) −7744.00 + 13413.0i −0.381598 + 0.660947i
\(745\) 4437.13 + 7685.34i 0.218207 + 0.377945i
\(746\) −3982.00 6897.03i −0.195431 0.338496i
\(747\) −6008.42 + 10406.9i −0.294293 + 0.509730i
\(748\) 4502.80 0.220105
\(749\) 0 0
\(750\) 28512.0 1.38815
\(751\) 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
\(753\) 26180.0 + 45345.1i 1.26700 + 2.19451i
\(754\) 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
\(759\) 4502.80 + 7799.08i 0.215338 + 0.372976i
\(760\) −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 \(0.0586377\pi\)
\(762\) −43377.0 −2.06218
\(763\) 0 0
\(764\) −8544.00 −0.404596
\(765\) −16104.0 + 27892.9i −0.761100 + 1.31826i
\(766\) −7035.62 12186.1i −0.331863 0.574804i
\(767\) 21868.0 + 37876.5i 1.02948 + 1.78310i
\(768\) 1200.75 2079.75i 0.0564169 0.0977170i
\(769\) 8536.56 0.400307 0.200154 0.979765i \(-0.435856\pi\)
0.200154 + 0.979765i \(0.435856\pi\)
\(770\) 0 0
\(771\) 14080.0 0.657690
\(772\) −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 \(0.594628\pi\)
\(774\) −26596.0 46065.6i −1.23511 2.13927i
\(775\) −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
\(780\) 11557.2 + 20017.6i 0.530530 + 0.918905i