Properties

Label 98.4.c.g.67.1
Level $98$
Weight $4$
Character 98.67
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 67.1
Root \(2.34521 + 4.06202i\) of defining polynomial
Character \(\chi\) \(=\) 98.67
Dual form 98.4.c.g.79.1

$q$-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 \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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 −0.0786575 + 0.996902i \(0.525063\pi\)
−0.824013 + 0.566570i \(0.808270\pi\)
\(4\) −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 \(0.695530\pi\)
\(6\) 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 −0.969908 0.243472i \(-0.921714\pi\)
0.695807 + 0.718229i \(0.255047\pi\)
\(12\) −18.7617 32.4962i −0.451335 0.781736i
\(13\) −65.6658 −1.40096 −0.700478 0.713674i \(-0.747030\pi\)
−0.700478 + 0.713674i \(0.747030\pi\)
\(14\) 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 \(-0.701821\pi\)
0.993908 + 0.110217i \(0.0351545\pi\)
\(18\) −61.0000 + 105.655i −0.798769 + 1.38351i
\(19\) 4.69042 + 8.12404i 0.0566345 + 0.0980938i 0.892953 0.450151i \(-0.148630\pi\)
−0.836318 + 0.548244i \(0.815296\pi\)
\(20\) −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 \(-0.236483\pi\)
−0.954068 + 0.299591i \(0.903150\pi\)
\(24\) −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 0.395289 + 0.918557i \(0.370644\pi\)
−0.993138 + 0.116948i \(0.962689\pi\)
\(32\) −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 0.939567 0.342366i \(-0.111228\pi\)
−0.766281 + 0.642505i \(0.777895\pi\)
\(38\) 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 \(-0.770132\pi\)
−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
\(45\) 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 \(-0.0629002\pi\)
−0.660291 + 0.751010i \(0.729567\pi\)
\(48\) 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 −0.903397 0.428805i \(-0.858935\pi\)
0.823054 + 0.567963i \(0.192268\pi\)
\(54\) −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 0.219956 + 0.975510i \(0.429409\pi\)
−0.954794 + 0.297267i \(0.903925\pi\)
\(60\) 176.000 304.841i 0.378692 0.655913i
\(61\) 136.022 + 235.597i 0.285506 + 0.494510i 0.972732 0.231933i \(-0.0745052\pi\)
−0.687226 + 0.726444i \(0.741172\pi\)
\(62\) 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 0.470643 + 0.882324i \(0.344022\pi\)
−0.999436 + 0.0335729i \(0.989311\pi\)
\(68\) 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 \(-0.993165\pi\)
0.518479 + 0.855090i \(0.326498\pi\)
\(74\) 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 0.999836 0.0181320i \(-0.00577190\pi\)
−0.515621 + 0.856817i \(0.672439\pi\)
\(80\) 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 \(-0.541581\pi\)
−0.130261 + 0.991480i \(0.541581\pi\)
\(84\) 0 0
\(85\) 528.000 0.673760
\(86\) −436.000 755.174i −0.546687 0.946890i
\(87\) 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 −0.835268 0.549843i \(-0.814687\pi\)
−0.0585446 0.998285i \(-0.518646\pi\)
\(90\) −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 \(-0.388327\pi\)
0.343678 + 0.939088i \(0.388327\pi\)
\(98\) 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 \(-0.814200\pi\)
0.894497 + 0.447073i \(0.147534\pi\)
\(102\) 528.000 914.523i 0.512547 0.887757i
\(103\) −684.801 1186.11i −0.655101 1.13467i −0.981868 0.189564i \(-0.939293\pi\)
0.326767 0.945105i \(-0.394041\pi\)
\(104\) −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 \(-0.129193\pi\)
−0.801304 + 0.598257i \(0.795860\pi\)
\(108\) −637.897 + 1104.87i −0.568348 + 0.984408i
\(109\) −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
\(111\) −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 \(-0.193584\pi\)
−0.905162 + 0.425066i \(0.860251\pi\)
\(132\) 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 −0.638423 0.769686i \(-0.720413\pi\)
0.985779 + 0.168048i \(0.0537463\pi\)
\(138\) −450.280 779.908i −0.277756 0.481088i
\(139\) −1378.98 −0.841466 −0.420733 0.907185i \(-0.638227\pi\)
−0.420733 + 0.907185i \(0.638227\pi\)
\(140\) 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 0.966259 0.257573i \(-0.0829227\pi\)
−0.706194 + 0.708018i \(0.749589\pi\)
\(150\) 347.091 601.179i 0.188932 0.327240i
\(151\) −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
\(153\) −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 −0.224053 0.974577i \(-0.571929\pi\)
0.956035 0.293253i \(-0.0947377\pi\)
\(158\) 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 0.779451 0.626463i \(-0.215498\pi\)
−0.932259 + 0.361792i \(0.882165\pi\)
\(164\) 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 \(-0.451385\pi\)
0.152137 + 0.988359i \(0.451385\pi\)
\(168\) 0 0
\(169\) 2115.00 0.962676
\(170\) −528.000 914.523i −0.238210 0.412592i
\(171\) 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 \(-0.119913\pi\)
−0.783524 + 0.621361i \(0.786580\pi\)
\(174\) −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 −0.302832 0.953044i \(-0.597932\pi\)
0.976776 0.214262i \(-0.0687346\pi\)
\(180\) 1144.46 + 1982.27i 0.473906 + 0.820830i
\(181\) 2823.63 1.15955 0.579776 0.814776i \(-0.303140\pi\)
0.579776 + 0.814776i \(0.303140\pi\)
\(182\) 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 0.994274 0.106858i \(-0.0340789\pi\)
−0.589679 + 0.807638i \(0.700746\pi\)
\(192\) −300.187 + 519.938i −0.112834 + 0.195434i
\(193\) −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
\(195\) 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 −0.0262574 + 0.999655i \(0.508359\pi\)
−0.852598 + 0.522567i \(0.824974\pi\)
\(200\) 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 \(-0.642833\pi\)
−0.433815 + 0.901002i \(0.642833\pi\)
\(224\) 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 \(-0.926779\pi\)
0.684289 + 0.729211i \(0.260113\pi\)
\(228\) 176.000 304.841i 0.0511223 0.0885464i
\(229\) 1383.67 + 2396.59i 0.399282 + 0.691577i 0.993638 0.112625i \(-0.0359260\pi\)
−0.594355 + 0.804203i \(0.702593\pi\)
\(230\) −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 \(0.199099\pi\)
0.101713 + 0.994814i \(0.467568\pi\)
\(234\) 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 −0.387894 0.921704i \(-0.626797\pi\)
0.992166 0.124926i \(-0.0398695\pi\)
\(242\) 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 \(-0.747623\pi\)
−0.701807 + 0.712367i \(0.747623\pi\)
\(252\) 0 0
\(253\) 960.000 0.238556
\(254\) −2312.00 4004.50i −0.571133 0.989231i
\(255\) −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 \(-0.224973\pi\)
−0.942613 + 0.333888i \(0.891639\pi\)
\(258\) 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 −0.841627 0.540059i \(-0.818402\pi\)
0.888519 + 0.458841i \(0.151735\pi\)
\(264\) −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 \(-0.843149\pi\)
0.850198 + 0.526462i \(0.176482\pi\)
\(270\) 2992.00 5182.30i 0.674397 1.16809i
\(271\) 3452.15 + 5979.29i 0.773812 + 1.34028i 0.935460 + 0.353433i \(0.114986\pi\)
−0.161648 + 0.986848i \(0.551681\pi\)
\(272\) −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 −0.220814 0.975316i \(-0.570871\pi\)
0.955055 0.296428i \(-0.0957954\pi\)
\(278\) 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 \(-0.820472\pi\)
0.885516 + 0.464610i \(0.153805\pi\)
\(284\) 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 \(-0.378278\pi\)
0.373149 + 0.927771i \(0.378278\pi\)
\(294\) 0 0
\(295\) −6248.00 −1.23313
\(296\) 312.000 + 540.400i 0.0612656 + 0.106115i
\(297\) −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 \(-0.521388\pi\)
−0.0671420 + 0.997743i \(0.521388\pi\)
\(308\) 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 −0.316012 0.948755i \(-0.602344\pi\)
0.979652 0.200703i \(-0.0643226\pi\)
\(312\) 2464.00 4267.77i 0.447104 0.774407i
\(313\) 759.847 + 1316.09i 0.137218 + 0.237668i 0.926442 0.376437i \(-0.122851\pi\)
−0.789225 + 0.614104i \(0.789517\pi\)
\(314\) −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 \(-0.233653\pi\)
−0.951366 + 0.308062i \(0.900320\pi\)
\(318\) −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 0.750592 0.660766i \(-0.229768\pi\)
−0.947536 + 0.319649i \(0.896435\pi\)
\(332\) 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 0.215474 + 0.976510i \(0.430870\pi\)
−0.953419 + 0.301649i \(0.902463\pi\)
\(348\) 3114.44 + 5394.36i 0.479745 + 0.830943i
\(349\) 5712.93 0.876235 0.438117 0.898918i \(-0.355645\pi\)
0.438117 + 0.898918i \(0.355645\pi\)
\(350\) 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 \(-0.725956\pi\)
0.982703 + 0.185187i \(0.0592891\pi\)
\(354\) −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 0.790441 0.612538i \(-0.209851\pi\)
−0.925694 + 0.378273i \(0.876518\pi\)
\(360\) 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 \(-0.900945\pi\)
0.741156 + 0.671333i \(0.234278\pi\)
\(368\) −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 0.694102 0.719877i \(-0.255802\pi\)
−0.970483 + 0.241171i \(0.922468\pi\)
\(374\) 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 \(-0.0111637\pi\)
−0.530059 + 0.847961i \(0.677830\pi\)
\(384\) 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 0.432881 + 0.901451i \(0.357497\pi\)
−0.997120 + 0.0758397i \(0.975836\pi\)
\(390\) −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 −0.996339 0.0854907i \(-0.972754\pi\)
0.424132 0.905600i \(-0.360579\pi\)
\(398\) 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 \(-0.0510482\pi\)
−0.631876 + 0.775069i \(0.717715\pi\)
\(402\) −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 \(-0.786597\pi\)
0.929857 + 0.367920i \(0.119930\pi\)
\(410\) −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 \(-0.471937\pi\)
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
\(423\) 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 −0.900936 0.433951i \(-0.857119\pi\)
0.826281 + 0.563258i \(0.190452\pi\)
\(432\) −2551.59 4419.48i −0.284174 0.492204i
\(433\) 11163.2 1.23896 0.619479 0.785013i \(-0.287344\pi\)
0.619479 + 0.785013i \(0.287344\pi\)
\(434\) 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 \(-0.229402\pi\)
−0.947167 + 0.320740i \(0.896069\pi\)
\(440\) −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 \(-0.277232\pi\)
−0.984509 + 0.175336i \(0.943899\pi\)
\(444\) 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 0.635097 0.772433i \(-0.280960\pi\)
−0.986495 + 0.163793i \(0.947627\pi\)
\(458\) 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 \(-0.522191\pi\)
−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
\(465\) 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 −0.991044 0.133539i \(-0.957366\pi\)
0.379874 0.925038i \(-0.375967\pi\)
\(468\) −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 0.350035 + 0.936737i \(0.386170\pi\)
−0.986255 + 0.165229i \(0.947164\pi\)
\(480\) 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 0.335157 + 0.942162i \(0.391211\pi\)
−0.983515 + 0.180826i \(0.942123\pi\)
\(488\) 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 0.911511 0.411276i \(-0.134917\pi\)
−0.811931 + 0.583754i \(0.801583\pi\)
\(500\) −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 \(-0.333115\pi\)
0.500594 + 0.865682i \(0.333115\pi\)
\(504\) 0 0
\(505\) 1144.00 0.100807
\(506\) −960.000 1662.77i −0.0843423 0.146085i
\(507\) −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 −0.971347 0.237667i \(-0.923617\pi\)
0.279848 0.960044i \(-0.409716\pi\)
\(510\) 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 \(-0.670955\pi\)
0.999909 + 0.0134723i \(0.00428850\pi\)
\(522\) 10126.0 17538.7i 0.849048 1.47059i
\(523\) 6308.61 + 10926.8i 0.527450 + 0.913570i 0.999488 + 0.0319918i \(0.0101850\pi\)
−0.472038 + 0.881578i \(0.656482\pi\)
\(524\) 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 0.828091 0.560594i \(-0.189427\pi\)
−0.899534 + 0.436850i \(0.856094\pi\)
\(542\) 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 −0.912701 0.408629i \(-0.866007\pi\)
0.810233 + 0.586107i \(0.199340\pi\)
\(558\) −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 0.403979 + 0.914768i \(0.367627\pi\)
−0.994202 + 0.107529i \(0.965706\pi\)
\(564\) 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 0.534788 0.844986i \(-0.320392\pi\)
−0.999174 + 0.0406466i \(0.987058\pi\)
\(570\) −825.513 + 1429.83i −0.0606613 + 0.105068i
\(571\) −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
\(573\) −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 −0.481321 0.876545i \(-0.659843\pi\)
0.999770 0.0214362i \(-0.00682388\pi\)
\(578\) 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 \(-0.732503\pi\)
−0.667191 + 0.744887i \(0.732503\pi\)
\(588\) 0 0
\(589\) −1936.00 −0.135435
\(590\) 6248.00 + 10821.9i 0.435976 + 0.755133i
\(591\) 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 \(-0.0748280\pi\)
−0.687962 + 0.725746i \(0.741495\pi\)
\(594\) 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 −0.331185 0.943566i \(-0.607448\pi\)
0.982744 0.184968i \(-0.0592182\pi\)
\(600\) 1388.36 + 2404.72i 0.0944661 + 0.163620i
\(601\) −21538.4 −1.46185 −0.730923 0.682460i \(-0.760910\pi\)
−0.730923 + 0.682460i \(0.760910\pi\)
\(602\) 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 \(-0.0148151\pi\)
−0.539751 + 0.841824i \(0.681482\pi\)
\(608\) −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 −0.129695 + 0.991554i \(0.541400\pi\)
−0.793863 + 0.608096i \(0.791934\pi\)
\(614\) 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 \(-0.886611\pi\)
0.770625 + 0.637288i \(0.219944\pi\)
\(620\) 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 −0.851990 0.523559i \(-0.824604\pi\)
0.879410 + 0.476065i \(0.157937\pi\)
\(642\) 2439.02 + 4224.50i 0.149938 + 0.259700i
\(643\) 29352.6 1.80024 0.900120 0.435642i \(-0.143479\pi\)
0.900120 + 0.435642i \(0.143479\pi\)
\(644\) 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 \(-0.715831\pi\)
0.988096 + 0.153840i \(0.0491641\pi\)
\(648\) −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 0.984300 + 0.176502i \(0.0564784\pi\)
−0.339294 + 0.940680i \(0.610188\pi\)
\(654\) −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 0.144529 + 0.989501i \(0.453833\pi\)
−0.929197 + 0.369584i \(0.879500\pi\)
\(662\) −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 0.797808 + 0.602912i \(0.205993\pi\)
0.123233 + 0.992378i \(0.460674\pi\)
\(678\) −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 −0.153423 0.988161i \(-0.549030\pi\)
0.932484 0.361212i \(-0.117637\pi\)
\(684\) 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 \(-0.178094\pi\)
−0.883414 + 0.468594i \(0.844761\pi\)
\(692\) −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 0.993671 0.112332i \(-0.0358319\pi\)
−0.594117 + 0.804378i \(0.702499\pi\)
\(710\) −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 −0.999266 0.0382947i \(-0.987807\pi\)
0.466469 0.884538i \(-0.345526\pi\)
\(720\) −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 \(-0.441015\pi\)
0.184247 + 0.982880i \(0.441015\pi\)
\(728\) 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 0.951844 + 0.306581i \(0.0991852\pi\)
−0.210415 + 0.977612i \(0.567481\pi\)
\(734\) 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 0.0976420 + 0.995222i \(0.468870\pi\)
−0.910708 + 0.413050i \(0.864463\pi\)
\(740\) −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 0.999633 0.0270752i \(-0.00861935\pi\)
−0.523265 + 0.852170i \(0.675286\pi\)
\(752\) 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 \(-0.274696\pi\)
−0.983080 + 0.183176i \(0.941362\pi\)
\(762\) 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 \(-0.564144\pi\)
−0.200154 + 0.979765i \(0.564144\pi\)
\(770\) 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 0.292924 + 0.956136i \(0.405372\pi\)
−0.974500 + 0.224388i \(0.927962\pi\)
\(774\) −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